Salusbury, Thomas Mathematical collections and translations 1667 London en salus_mathe_040_en_1667.xml 040.xml

MATHEMATICAL Collections and Tran&longs;lations: In twoTOMES.

MATHEMATICAL COLLECTIONS AND TRANSLATIONS: THE FIRST TOME. IN TWO PARTS.

THE FIRST PART;

Containing,

I. GALILEUS GALILEUS His SYSTEM of the WORLD.

II. GALILEUS His EPISTLE to the GRAND DUTCHESSE MOTHER, concerning the Au­thority of Holy SCRIPTURE in Philo&longs;ophical Controver&longs;ies.

III. JOHANNES KEPLERUS His Reconcilings of SCRI­PTURE Texts, &c.

IV. DIDACUS à STUNICA His Reconcilings of SCRI­PTURE Texts, &c.

V. P. A. FOSCARINUS His Epi&longs;tle to Father FANTONUS, reconciling the Authority of SCRIPTURE, and Judg­ments of Divines alledged again&longs;t this SYSTEM.

By THOMAS SALUSBURY, E&longs;que

LONDON, Printed by WILLIAM LEYBOURN, MDCLXI.

To the Noble and mo&longs;t perfectly Accompli&longs;hed S^{t.} JOHN DENHAM Knight of the Noble Order of the BATH, And Surveyor General of his Ma^{ties} Works, &c.

SIR,

I humbly begge your Pardon for bringing this Book under your Pro­tection. Were it a Work of my own, or I any thing but the Tran&longs;la­tour, I should ma&longs;ter my Thoughts to a meaner Dedication; But being a Collection of &longs;ome of the greate&longs;t Ma&longs;ters in the World, and never made English till now, I conceived I might &longs;ooner procure their Welcome to a per&longs;on &longs;o eminent for Noble Candor, as well as for all tho&longs;e Intellectual Excellencies wherewith Your Rich Soulis known to be furnished. I re&longs;olv'd to be as kind to this Book as I could, and &longs;eriou&longs;ly con&longs;idering which way to effect it, I at la&longs;t concluded to prefix Your Name, whom His Maje&longs;ty and all his Subjects, (who have a higher Sen&longs;e and Judgement of Excel­lent Parts) know be&longs;t able to defend my Im­perfections. And yet I confe&longs;s there's one thing makes again&longs;t me, which is your eminent Integrity and great Affection to Truth, where­by my Lap&longs;esin a Work of this Nature might ju&longs;tly de&longs;pair of Shelter, but that the Excel­lency of Your Native Candor &longs;trives for Pre­dominancy over all Your great Abilities. For 'tis all-mo&longs;t impo&longs;&longs;ible to think what Your Matchle&longs;s Wit is not able to Conquer, would Your known Mode&longs;ty but give leave: there­fore Galileus, Kepler, and tho&longs;e other worthies in Learning are now brought before You in English Habit, having chang'd their Latine, Italian and French, whereby they were almo&longs;t Strangers to our Nation, unle&longs;s to &longs;uch as You, who &longs;o perfectly ma&longs;ter the Originals. I know you have &longs;o much and great imployment for His Maje&longs;ty, and his good Subjects that I shall not robb you of another Minutes lo&longs;s; be&longs;ides the liberty of &longs;ub&longs;cribing my Self;

SIR,

Your Honours

Mo&longs;t Humble and Mo&longs;t obedient Servant

THOMAS SALUSBURY.

READER,

Mathematical Learning (to &longs;peak nothing touching the nece&longs;sity & delight thereof) hath bin &longs;o &longs;paring­ly imparted to our Countrymen in their native Engli&longs;h, e&longs;pecially the nobler and &longs;ublimer part, that in Compliance with the Solicitations of &longs;everal of my noble and learned Friends, and the Incli­nations of &longs;uch as are Mathematically di&longs;po&longs;ed, more e&longs;pecially tho&longs;e, who either want Time or Patience to look into the vulgar and un&longs;tudied Languages, I did adventure upon this Work of Collecting & Tran&longs;­lating from among&longs;t the excellent Pieces that are &longs;o abounding in the Italian and French Tongues, &longs;ome of tho&longs;e that my own ob&longs;ervation and the intimation of Friends were mo&longs;t u&longs;efull and de&longs;ired, and with all mo&longs;t wanting in their Own.

I was, indeed, at fir&longs;t &longs;eriou&longs;ly Con&longs;cious, and am now, by experience, fully convinced how di&longs;proportionate the weight of the Enterprize is to the weakne&longs;s of the Vndertaker, but yet the Pa&longs;sion I ever had to be &longs;ub&longs;ervient to my Friends and Compatriots in their Inqui&longs;ition after the&longs;e Sublime Studies, and a Patience which I owe to the Flegme that is predominant in my Con&longs;titution, joyned with a nine-years conver&longs;ence in the&longs;e Languages, as al&longs;o an unhappy and long Vacation that the per&longs;ecutions of the late Tyrants gave me from more advantagious employ­ments &longs;o prevailed with me, that I re&longs;olved to improve even my very Confinement to &longs;erve tho&longs;e Friends, whom, as the Times then &longs;tood, I could not &longs;ee.

The Book being for Subject and De&longs;ign intended chiefly for Gentlemen, I have hin as carele&longs;s of u&longs;ing a &longs;tudied Pedantry in my Style; as careful in contriving a plea&longs;ant and beautiful Impre&longs;&longs;ion. And when I had con&longs;idered the hazard, and computed the charge of the undertaking, I found it to exceed the ability of a private Pur&longs;e, e&longs;pe­cially of mine, that had bin &longs;o lately emptied by the hand of violent enemies, and perfidious friends; not to make mention here of the Sums that a Loyal Reflexion upon my Princes Affairs had at the &longs;ame time drawn from me; and judg'd that the most &longs;afe, ea&longs;y, and rea&longs;onable way was to invite tho&longs;e Per&longs;ons who had appeared de&longs;irous of the Book, to be contributary to their own Contentment, by &longs;ub&longs;cribing towards the charge of this Pu­blication.

And for the better management of the Work, I joyned to my &longs;elf a Printer, who&longs;e Genius having rendered him Mathematical, and my overtures of profit having intere&longs;&longs;ed his diligence, I was induced to promi&longs;e my &longs;elf a more than common A&longs;&longs;i&longs;tance from him: and at his door I with rea&longs;on lay all mi&longs;carriages that concerns his Profe&longs;&longs;ion in the Bu&longs;ine&longs;s.

In this Work I found more than ordinary Encouragement from that publick &longs;pirited Per&longs;on the Reverend and Learned Dr. Thomas Barlow, Provo&longs;t of Queens Colledge Oxford, and Margaret Profe&longs;&longs;or in that Vniver­&longs;ity, as al&longs;o from tho&longs;e two able Mathematicians and my Reall Friends Major Miles Symner, and Mr. Robert Wood of Trinity Colledge Dublin, and &longs;ome few others who&longs;e Mode&longs;ty hath expre&longs;ly enjoin'd me a concealment of their Names.

Well, at length I have got to the end of my fir&longs;t Stage; and if I have not rid Po&longs;t, let my excu&longs;e be that my long &longs;tay for my Warrant cau&longs;ed me to &longs;et out late; and being ill mounted, and in a road full of rubbs, I could not with any &longs;afety go fa&longs;ter; but hope to get it up in the next Stage, for in that I intend to &longs;hift my Hor&longs;es.

The names of tho&longs;e Authors and Treatices which I judged would mo&longs;t grace our Language, and gratify Stu­dents, are particularly expre&longs;t in the General Title of the two Tomes. Di&longs;tinct Tomes they are as con&longs;i&longs;ting of &longs;everat Pieces: Collections I call them, becau&longs;e they have bin &longs;o publi&longs;hed, di&longs;per&longs;t, and worn out of Print, that they very rarely meet in one hand: and Tran&longs;lations I own them to be, as not pretending to any thing more than the di&longs;po&longs;ure and conver&longs;ion of them: tho&longs;e Tracts only excepted which compo&longs;e the &longs;econd Part of the &longs;econd Tome.

The fir&longs;t Book which offers it &longs;elf to your view in this Tome is that &longs;ingular and unimitable Piece of Rea&longs;on and Demon&longs;tration the Sy&longs;teme of Galilco. The &longs;ubject of it is a new and Noble port of A&longs;tronomy, to wit the Doctrine and Hypothe&longs;is of the Mobility of the carth and the Stability of the Sun; the Hi&longs;tory whereof I &longs;hall hereafter give you at large in the Life of that famous Man. Only this by the by; that the Reader may not wonder why the&longs;e Dialogues found &longs;o various entertainment in Italy (for he cannot but have heard that though they have been with all veneration valued, read & applauded by the Iudicious yet they were with much dete&longs;tation per&longs;ecuted, &longs;uppre&longs;&longs;ed & exploded by the Super&longs;titious) I am to tell him that our Author having a&longs;&longs;igned his intimate FriendsSalviati and Sagredo the more &longs;ucceßfull Parts of the Challenger, and Moderater, he made the famous Commen­tator Simplicius to per&longs;onate the Peripatetick. The Book coming out, and Pope Urban the VIII. taking his Ho­nour to be concern'd as having in his private Capacity bin very po&longs;itive in declaiming against the Samian Philo­&longs;ophy, and now (as he &longs;uppo&longs;ed) being ill delt with by Galilco who had &longs;ummed up all his Arguments, and pur them into the mouth of Simplicius; his Holine&longs;s thereupon conceived an implacable Di&longs;plea&longs;ure against our Au­thor, and thinking no other revenge &longs;ufficient, he employed his Apo&longs;tolical Authority, and deals with the Con&longs;i&longs;tory to condemn him and pro&longs;cribe his Book as Heretical; pro&longs;tituting the Cen&longs;ure of the Church to his private revenge. This was Galilco's fortune in Italy: but had I not rea&longs;on to hope that the Engli&longs;h will be more ho&longs;pitable, on the account of that Principle which induceth them to be civil to (I &longs;ay not to dote on) Strangers, I &longs;hould fear to be charged with imprudence for appearing an Interpreter to that great Philo&longs;opher. And in this confidence I &longs;hall forbear to make any large Exordium concerning him or his Book: & the rather in regard that &longs;uch kind of Gau­deries become not the Gravity of the Subject; as al&longs;o knowing how much (coming from me) they must fall &longs;hort of the Merits of it, or him: but principally becau&longs;e I court only per&longs;ons of Judgement & Candor, that can di&longs;tingui&longs;h between a Native Beauty, and &longs;purious Verni&longs;h. This only let me premi&longs;e, though more to excu&longs;e my weakne&longs;s in the menaging, than to in&longs;inuate my ability in accompli&longs;hing this &longs;o arduous a Task, that the&longs;e profound Dialogues have bin found &longs;o unea&longs;y to Tran&longs;late, that neither affectation of Novelty could induce the French, nor the Tran&longs;lating humour per&longs;wade the Germans to undertake them. This difficulty, as I conceived, was charged either upon the Intricacy of this manner of Writing, or upon the &longs;ingular Elegance in the &longs;tile of Galilco, or el&longs;e upon themi&longs;carriage of the unfortunate Mathias Berneggeius who fir&longs;t attempted to turn them into Latine for the benefit of the Learned World.

I &longs;hall not pre&longs;ume to Cen&longs;ure the Cen&longs;ure which the Church of Rome pa&longs;t upon this Doctrine and its A&longs;&longs;ectors. But, on the contrary, my Author having bin indefinite in his di&longs;cour&longs;e, I &longs;hall forbear to exa&longs;perate, and attempt to reconcile &longs;uch per&longs;ons to this Hypothe&longs;is as devout e&longs;teem for Holy Scripture, and dutifull Re&longs;pect to Canonical Injunctions hath made to &longs;tand off from this Opinion: and therefore for their &longs;akes I have at the end of the Dia­logues by way of &longs;upplement added an Epi&longs;tle of Galilco to Her Most Serene Highne&longs;s Chri&longs;tina Lotharinga the Grand Dutche&longs;&longs;e Mother of Tu&longs;cany; as al&longs;o certain Ab&longs;tracts of John Kepler, Mathematician to two Empe­rours, and Didacus à Stunica a famous Divine of Salamanca, with an Epi&longs;tle of Paulo Antonio Fo&longs;carini a learn­ed Carmelite of Naples, that &longs;hew the Authority of Sacred Scripture in determining of Philo&longs;ophical and Natu­ral Controver&longs;ies: hoping that the ingenious & impartial Reader will meet with full &longs;atisfaction in the &longs;ame. And lea&longs;t what I have &longs;poken of the prohibiting of the&longs;e Pieces by the Inqui&longs;ition may deterre any &longs;crupulous per&longs;on from reading of them, I have purpo&longs;ely in&longs;erted the Imprimatur by which that Office licenced them. And for a larger account of the Book or Author, I refer you to the Relation of his Life, which &longs;hall bring up the Reare in the Second Tome.

What remains of this, is that Excellent Di&longs;cour&longs;e of D. Benedetto Ca&longs;telli Abbate di San Benedetto Aloy&longs;io, concerning the Men&longs;uration of Running waters, with other Treati&longs;es of that Learned Prelate, & of the Superin­tendent Cor&longs;ini. Some may alledge, and I doe confe&longs;s that I promi&longs;ed to publi&longs;h the Life of Galilco in this place: But the great mi&longs;carriages of Letters from &longs;ome Friends in Italy and el&longs;e where, to whom I am a Debtor for &longs;e­veral Remarques, & from whom I daily expect yet greater Helps concerning the Hi&longs;tory of that famous Per&longs;onage: the&longs;e di&longs;appointments, I &longs;ay, joyned with the undeniable Reque&longs;t of &longs;ome Friends, who were impatient to &longs;ee Ca&longs;telli in Engli&longs;h, together with a con&longs;ideration of the di&longs;proportionate Bulk that would otherwi&longs;e have bin betwixt the two Volumes, per&longs;waded me to this exchange. This deviation from my Promi&longs;e I hope is Venial, and for the ex­plating of it I plead Supererrogation: having in each Tome made &longs;o large Aditions (though to my great ex­pen&longs;e) that they make neer a third part more than I &longs;tood by promi&longs;e bound to Publi&longs;h. That this is &longs;o will appearby comparing the Contents I here prefix with the Adverti&longs;ment I formerly Printed. For not to mention tho&longs;e Epitomes of Kepler and à Stunica, the whole &longs;econd and following Books of Ca&longs;tclli, were not come to my hands at the time of my penning that Paper; yet knowing how imperfect the Volume would be without them, they being partly a &longs;up­plement to the Theoremes and Problemes which the Abbot had formerly Printed, and partly experiments that had procured him and his Doctrine a very great Reputation, knowing this I &longs;ay, I apprehended a nece&longs;&longs;ity of pu­bli&longs;hing them with the re&longs;t: and hope that if you think not the &longs;ervice I have done therein worth your acknowledge­ment, you will yet at lea&longs;t account the encrea&longs;e of my expence a &longs;ufficient extenuation of the Tre&longs;pa&longs;s that tho&longs;e Additions have forced me to commit upon your Patience in point of Time.

As for the &longs;econd Tome, I have only this to a&longs;&longs;ure the Generous Readers; 1 that I am very confident I &longs;hall be much more punctual in publi&longs;hing that, than (for the rea&longs;ons above related.) I was able to be in &longs;etting forth this: 2 that they &longs;hall not be abu&longs;ed in advancing of their moneys, (as hath bin u&longs;ed in the like ca&longs;e) by &longs;elling the remaining Copyes at an under rate; and 2 that I have a very great care that no di&longs;e&longs;teem may by my means a­ri&longs;e unto this way of publi&longs;hing Books, for that it is of excellent u&longs;e in u&longs;hering Great and Co&longs;tly Volumes into the World.

To &longs;ay nothing of the di&longs;advantages of Tran&longs;lations in general, this of mine doubtle&longs;s is not without it's Er­rours, and over&longs;ights: but tho&longs;e of the Printer di&longs;counted, I hope the re&longs;t may be allowed me upon the &longs;core of Hu­man Imbecilitic. The truth is, I have a&longs;&longs;umed the Liberty to note the Mi&longs;takes in the Florid Ver&longs;ion of Bernegge­rus in the Margent, not &longs;o much to reproach him, as to convince tho&longs;e who told me that they accounted my pains needle&longs;s, having his Latine Tran&longs;lation by them. The like they &longs;aid of the whole two Tomes: but they thereby cau&longs;ed me to question their Under&longs;tanding or Veracity. For &longs;ome of the Books were yet never extant: As for in&longs;tance; the Mcchanicks of Mon&longs;ieur Des Cartes, a Manu&longs;cript which I found among&longs;t the many other Rarities that en­rich the well-cho&longs;en Library of my Learned and Worthy Friend Dr. Charles Scarburgh; the Experiments of Gra­vity, and the Life of Galileo, both my own: Others were included in Volumes of great price, or &longs;o di&longs;per&longs;ed that they were not to be purcha&longs;ed for any money; as tho&longs;e of Kepler, à Stunica, Archimedes, Tartaglia, and the Mecha­nicks of Galileo: And the remainder, though ea&longs;yer to procure, were harder to be under&longs;tood; as Tartaglia his notes on Archimedes, Torricellio his Doctrine of Projects, Galileo his Epi&longs;tle to the Dutche&longs;&longs;e of Tu&longs;cany, and above all his Dialogues de Motu; (never till now done into any Language) which were &longs;o intermixt of Latine and Italian, that the difficulty of the Stile, joyned with the intricatne&longs;&longs;e of the Subject rendered them Unplea&longs;ant, if not wholly Vnintelligible, to &longs;uch as were not ab&longs;olute Ma&longs;ters of both the Tongues.

To conclude; according to the entertainment that you plea&longs;e to afford the&longs;e Collections, I &longs;hall be encouraged to proceed with the Publication of a large Body of Hydrography; declaring the Hi&longs;tory, Art, Lawes, and Apendages of that Princely Study of Navigation, wherein I have omitted nothing of note that can be found either in Dud­ley, Fournier, Aurigarius, Nonius, Snellus, Mar&longs;ennus, Bay&longs;ius, Mori&longs;etus, Blondus, Wagoner, abroad, or learnt amongst our Mariners at home, touching the Office of an Admiral, Commander, Pilot, Modelli&longs;t, Shipwright, Gunner, &c.

But order requiring that I &longs;hould di&longs;charge my fir&longs;t Obligation before I contract a &longs;econd; I &longs;hall detein you no longer in the Portall, but put you into po&longs;&longs;e&longs;&longs;ion of the Premi&longs;es,

Novemb. 20, 1661.

T. S.

The CONTENTS of the FIRST TOME.

PART THE FIRST.

Treati&longs;e

I. GALILEUS GALILEUS, his SYSIEME of the WORLD: in Four DIALOGUES.

II. HIS EPISTLE to her SERENE HIGHNESSE CHRISTIANA LOTHERINGA GRAND DUTCHESSE of TUSCANY, touching the Ancient and Modern DOCTRINE of HOLY FATHERS, and JUDICIOUS DIVINES, concerning the AUTHORITY of SACRED SCRIPTURE in PHYLOSOPHICAL CONTROVERSIES.

III. JOHANNES KEPLERUS, his RECONCILINGS of TEXTS of SACRED SCRIPTURE that &longs;eem to oppo&longs;e the DOCTRINE of the EARTHS MOBILI­TY: ab&longs;tracted from his INTRODUCTION unto his LEARNED COMMEN­TARIES upon the PLANET MARS.

IV. DIDACUS A STUNICA, a learned SPANISH DIVINE, his RECONCILINGS of the &longs;aid DOCTRINE with the TEXTS of SACRED SCRIPTURE; ab&longs;tracted from his COMMENTARIE upon JOB.

V. PAULUS ANTONIUS FOSCARINUS, a CARMELITE, his EPISTLE to SEBASTIANUS FANTONUS, the GENERAL of his ORDER, concerning the PYTHAGOREAN and COPERNICAN OPINION of the MOBILITY OF THE EARTH, and STABILITY OF THE SUN; and of the NEW SYSTEME or CONSTITUTION of the WORLD: in which he reconcileth the TEXTS OF SACRED SCRIPTURE, and ASSERTIONS of DIVINES, commonly alledged against this OPINION.

A Table of the most ob&longs;ervable Per&longs;ons and Matters mentioned in the Fir&longs;t Part.

PART THE SECOND.

I. D. BENEDICTUS CASTELLUS, ABBOT OF S. BENEDICTUS ALOYSIUS, his DISCOURSE of the MENSURATION OF RUNNING WATERS: The Fir&longs;t BOOK.

II. HIS LETTER to GALILEUS, repre&longs;enting the &longs;tate of the Lake of PERUGIA in TUSCANY.

III. HIS GEOMETRICAL DEMONSTRATIONS of the MEASURE of RUNNING WATERS.

IV. HIS DISCOURSE of the MENSURATION OF RUNNING WATERS: The Second BOOK.

V. HIS CONSIDERATIONS concerning the LAKE OF VENICE. In two DISCOURSES.

VI. HIS RULE for computing the quantity of MUD and SAND that LAND-FLOODS bring down to, and leave in the LAKE of VENICE.

VII. HIS LETTER to Father FRANCESCO DI S. GIVSEPPE, wherein, at the in&longs;tance of PRINCE LEOPALDO, he delivereth his judgment concerning the turning FIUME MORTO (a River near PISA in TUSCANY) into the SEA, and into the River SERCHIO.

VIII. HIS &longs;econd LETTER in anfwer to certain OBJECTIONS propo&longs;ed, and DIFFICUL­TIES ob&longs;erved by SIGNORE BARTOLOTTI, in that affair of the DIVERSION of FIUME MORTO.

IX. HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALA­BRIA.

X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOG­NA, FERRARA, and ROMAGNA.

XI. HIS LETTER to D. FERRANTE CESARINI, applying his DOCTRINE to the MENSURATION of the LENGTH, and DISTRIBUTION of the QUANTITY of the WATERS of RIVERS, SPRINGS, AQUEDUCTS, &c.

XII. D. CORSINUS, SUPERINTENDENT of the GENERAL DRAINS and PRESIDENT of ROMAGNA, his RELATION of the &longs;tate of the WATERS in the TERRITORIES of BOLOGNA and FERRARA.

A Table of the mo&longs;t ob&longs;ervable Per&longs;ons and Matters mentioned in the Second Part.

The CONTENTS of the SECOND TOME,

PART THE FIRST.

Treati&longs;e

I. GALILEUS GALILEUS, his MATHEMATICAL DISCOURSES and DEMON­STRATIOMS touching two NEVV SCIENCES, pertaining to the MECHA­NICKS, and LOCAL MOTION: with an APPENDIX of the CENTRE of GRAVITY of &longs;ome SOLIDS in Four DIALOGUES.

II. HIS MECHANICKS; a New PEICE.

III. RHENATUS DES CARTES, his MECHANICKS; tran&longs;lated from his FRENCM MANUSCRIPT; a New PEICE.

IV. ARCHIMEDES, his Tract DE INSIDENTIBUS HUMIDO; with the NOTES and DEMONSTRASIONS of NICOLAUS TARTALEUS, in Two BOOKS.

V. GALILEUS his DISCOURSE of the things that move in or upon the WATER.

VI. NICOLAUS TARTALEUS his INVENTIONS for DIVING UNDER WATER, RAISING OF SHIPS SUNK, &c. in Two BOOKS.

PART THE SECOND.

I. EVANGELISTA TORRICELLIUS, his DOCTRINE OF PROJECTS, and TABLES of the RANGES of GREAT GUNNS of all &longs;orts; wherein he detects &longs;undry ERRORS in GUNNERY: An EPITOME.

II T. S. his EXPERIMENTS of the COMPARATIVE GRAVITY OF BODIES in the AIRE and WATER.

III. GALILEUS GALILEUS, his LIFE: in Five BOOKS,

BOOK I. Containing Five Chapters.

Chap. 1. His Country.

2. His Parents and Extraction.

3. His time of Birth.

4. His fir&longs;t Education.

5. His Ma&longs;ters.

II. Containing Three Chapters.

Chap. 1. His judgment in &longs;everal Learnings.

2. His Opinions and Doctrine.

3. His Auditors and Scholars.

III. Containing Four Chapters.

Chap. 1. His behaviour in Civil Affairs.

2. His manner of Living.

3. His morall Virtues.

4. His misfortunes and troubles.

IV. Containing Four Chapters.

Chap. 1. His per&longs;on de&longs;cribed.

2. His Will and Death.

3. His Inventions.

4. His Writings.

5. His Dialogues of the Sy&longs;teme in particular, containing Nine Sections.

Section 1. Of A&longs;tronomy in General; its Definition, Prai&longs;e, Original.

2. Of A&longs;tronomers: a Chronological Catalogue of the mo&longs;t famous of them.

3. Of the Doctrine of the Earths Mobility, &c. its Antiquity, and Progre&longs;&longs;e from Pythagoras to the time of Copernicus.

4. Of the Followers of Copernicus, unto the time of Galileus.

5. Of the &longs;everall Sy&longs;temes among&longs;t A&longs;tronomers.

6. Of the Allegations again&longs;t the Copern. Sy&longs;teme, in 77 Arguments taken out of Ricciolo, with An&longs;wers to them.

7. Of the Allegations for the Copern. Sy&longs;teme in so Arguments.

8. Of the Scriptures Authorities produced again&longs;t and for the Earths mobility.

9. The Conclu&longs;ion of the whole Chapter.

V. Containing Four Chapters.

Chap. 1. His Patrons, Friends, and Emulators.

2. Authors judgments of him.

3. Authors that have writ for, or again&longs;t him.

4. A Conclu&longs;ion in certain Reflections upon his whole Life.

A Table of the whole Second TOME.

THE SYSTEME OF THE WORLD: IN FOUR DIALOGUES. Wherein the Two GRAND SYSTEMES

Of PTOLOMY and COPERNICUS are largely di&longs;cour&longs;ed of:

And the REASONS, both Phylo&longs;ophical and Phy&longs;ical, as well on the one &longs;ide as the other, impartially and indefinitely propounded:

By GALILEUS GALILEUS LINCEUS, A Gentleman of FLORENCE: Extraordinary Profe&longs;&longs;or of the Mathematicks in the UNIVERSITY of PISA; and Chief Mathematician to the GRAND DUKE of TVSCANY.

Ingli&longs;hed from the Original Italián Copy, by THOMAS SALUSBURY.

ALCINOUS, *dei_ d) e)leuge/rion ei)_nai th_| gnwmh_| r\n me/llonta filosofei_n.

SENECA, Inter nullos magis quam inter PHILOSOPHOS e&longs;&longs;e debet aqua LIBERTAS.

LONDON, Printed by WILLIAM LEYBOURNE. MDCLXI.

To the mo&longs;t Serene Grand DUKE OF TUSCANY.

Though the difference between Men and other living Creatures be very great, yet happly he that &longs;hould &longs;ay that he could &longs;hew little le&longs;s between Man and Man would not &longs;peak more than he might prove. What proportion doth one bear to athou&longs;and? and yet it is a common Proverb, One Man is worth athou&longs;and, when as a thou&longs;and are not worth one. This difference hath dependence upon the different abilities of their Intelle­ ctuals; which I reduce to the being, or not being a Philo&longs;o­ pher; in regard that Philo&longs;ophy as being the proper food of &longs;uch as live by it, di&longs;tingui&longs;heth a Man from the common E&longs;­ &longs;ence of the Vulgar in a more or le&longs;s honourable degree accord­ ing to the variety of that diet. In this &longs;ence he that hath the highe&longs;t looks, is of highe&longs;t quality; and the turning over of the great Volume of Nature, which is the proper Object of Philo&longs;ophy is the way to make one look high: in which Book, although what&longs;oever we read, as being the Work of Al­ mighty God, is therefore mo&longs;t proportionate; yet notwith­ &longs;tanding that is more ab&longs;olute and noble wherein we more plainly de&longs;erne his art and skill. The Con&longs;titution of the Vnivers, among all Phy&longs;ical points that fall within Humane Compre­ hen&longs;ion, may, in my opinion, be preferred to the Precedency: for if that in regard of univer&longs;al extent it excell all others, it ought as the Rule and Standard of the re&longs;t to goe before them in Nobility. Now if ever any per&longs;ons might challenge to be &longs;ignally di&longs;tingui&longs;hed for Intellectuals from other men; Ptolomey and Copernicus were they that have had the honour to &longs;ee farthe&longs;t into, and di&longs;cour&longs;e mo&longs;t profoundly of the Worlds Sy&longs;teme. About the Works of which famous Men the&longs;e Dia­ lous being chiefly conver&longs;ant, I conceived it my duty to De­ dicate them only to Your Highne&longs;s. For laying all the weight upon the&longs;e two, whom I hold to be the Able&longs;t Wits that have left us their Works upon the&longs;e Subjects; to avoid a Sole­ ci&longs;mein Manners, I was obliged to addre&longs;s them to Him, who with me, is the Greate&longs;t of all Men, from whom they can re­ ceive either Glory or Patrociny. And if the&longs;e two per&longs;ons have &longs;o farre illuminated my Under&longs;tanding as that this my Book may in a great part be confe&longs;&longs;ed to belong to them, well may it al&longs;o be acknowledged to belong to Your Highne&longs;s, unto who&longs;e Bounteous Magnificence I owe the time and lea&longs;ure I had to write it, as al&longs;o unto Your Powerful A&longs;&longs;i&longs;tance, (never weary of honouring me) the means that at length I have had to publi&longs;h it. May Your Highne&longs;s therefore be plea&longs;ed to accept of it according to Your accu&longs;tomed Goodne&longs;s; and if any thing &longs;hall be found therein, that may be &longs;ub&longs;ervient towards the information or &longs;atisfaction of tho&longs;e that are Lovers of Truth; let them acknowledge it to be due to Your Self, who are &longs;o expert in doing good, that Your Happy Dominion cannot &longs;hew the man that is concerned in any of tho&longs;e general Cala­ mities that di&longs;turb the World; &longs;o that Praying for Your Pro&longs;pe­ rity, and continuance in this Your Pious and Laudable Cu­ &longs;tome, I humbly ki&longs;s Your Hands;

Your Mo&longs;t Serene Highne&longs;&longs;es

Mo&longs;t Humble and mo&longs;t devoted

Servant and Subject

GALILEO GALILEI.

THE AUTHOR'S INTRODUCTION.

Judicious Reader,

There was publi&longs;hed &longs;ome years &longs;ince in Rome a &longs;alutiferous Edict, that, for the obviating of the dangerous Scandals of the pre&longs;ent Age, impo&longs;ed a &longs;ea­ &longs;onable Silence upon the Pythagorean Opinion of the Mobility of the Earth. There want not &longs;uch as unadvi&longs;edly affirm, that that Decree was not the produ­ ction of a &longs;ober Scrutiny, but of an ill informed Pa&longs;sion; & one may hear &longs;ome mut­ ter that Con&longs;ultors altogether ignorant of A&longs;tronomical Ob&longs;ervations ought not to clipp the Wings of Speculative Wits with ra&longs;h Prohibitions. My zeale can­ not keep &longs;ilence when I hear the&longs;e incon&longs;iderate complaints. I thought fit, as being thoroughly ac­ quainted with that prudent Determination, to appear openly upon the Theatre of the World as a Wit­ ne&longs;s of the naked Truth. I was at that time in Rome; and had not only the audiences, but applauds of the mo&longs;t Eminent Prelates of that Court; nor was that Decree Publi&longs;hed without Previous Notice given me thereof. Therefore it is my re&longs;olution in the pre&longs;ent ca&longs;e to give Foraign Nations to &longs;ee that this point is as well under stood in Italy, and particularly in Rome, as Tran&longs;alpine Diligence can imagine it to be: and collecting together all the proper Speculations that concern the Copernican Sy&longs;teme, to let them know, that the notice of all preceded the Cen&longs;ure of the Roman Court; and that there proceed from this Climate not only Doctrines for the health of the Soul, but al&longs;o ingenious Di&longs;coveries for the recreating of the Mind.

To this end I have per&longs;onated the Copernican in this Di&longs;cour&longs;e; proceeding upon an Hypothe&longs;is purely Mathematical; &longs;triving by all artificial wayes to repre&longs;ent it Superiour, not to that of the Im­ mobility of the Earth ab&longs;olutely, but according as it is mentioned by &longs;ome, that retein no more, but the name of Peripateticks, and are content, without going farther, to adore Shadows, not philo&longs;ophizing with requi&longs;it caution, but with the &longs;ole remembrance of four Principles, but badly under &longs;tood.

We &longs;hall treat of three principall heads. Fir&longs;t I will endeavour to &longs;hew that all Experiments that can be made upon the Earth are in&longs;ufficient means to conclude it's Mobility, but are indifferently applicable to the Earth moveable or immoveable: and I hope that on this occa&longs;ion we &longs;hall di&longs;cover many ob&longs;er­ vable pa&longs;&longs;ages unknown to the Ancients. Secondly we will examine the Cœle&longs;tiall Phœnomena that make for the Copernican Hypothe&longs;is, as if it were to prove ab&longs;olutely victorious; adding by the way certain new Ob&longs;ervations, which yet &longs;erve only for the A&longs;tronomical Facility, not for Natural Neceßity. In the third place I will propo&longs;e an ingenuous Fancy. I remember that I have &longs;aid many years &longs;ince, that the unknown Probleme of the Tide might receive &longs;ome light, admitting the Earths Motion. This Po&longs;ition of mine pa&longs;sing from one to another had found charitable Fathers that adopted it for the I&longs;&longs;ue of their own wit. Now, becau&longs;e no &longs;tranger may ever appear that defending him­ &longs;elf with our armes &longs;hall charge us with want of caution in &longs;o principal an Accident, I have thought good to lay down tho&longs;e probabilities that would render it credible, admitting that the Earth did move. I hope, that by the&longs;e Con&longs;ider ations the World will come to know, that if other Nations have Navigated more than we, we have not &longs;tudied le&longs;s than they; & that our returning to a&longs;&longs;ert the Earths Stability, and to take the contrary only for a Mathematical Capriccio, proceeds not from inadvertency of what others have thought thereof, but (had we no other inducements) from tho&longs;e Rea&longs;ons that Pic­ ty, Religion, the Knowledge of the Divine Omnipotency, and a con&longs;ciou&longs;ne&longs;s of the incapacity of mans Vnder&longs;tanding dictate unto us.

With all I conceived it very proper to expre&longs;s the&longs;e conceits by way of Dialogue, which, as not being bound up to the riggid ob&longs;ervance of Mathematical Laws, gives place al&longs;o to Digre&longs;sions that are &longs;ometimes no le&longs;s curious than the principal Argument.

I chanced to be &longs;everal years &longs;ince, at &longs;everal times, in the Stupendious Citty of Venice, where I conver&longs;ed with Signore Giovan France&longs;co Sagredo of a Noble Extraction, and piercing wit. There came thither from Florence at the &longs;ame time Signore Filippo Salviati, who&longs;e lea&longs;t glory was the Emi­ nence of his Blood, and Magnificence of his E&longs;tate: a &longs;ublime Wit that fed not more hungerly upon any plea&longs;ure than on elevated Speculations. In the company of the&longs;e two I often di&longs;cour&longs;ed of the&longs;e matters before a certain Peripatetick Philo&longs;opher who &longs;eemed to have no geater ob&longs;tacle in under&longs;tand­ ing of the Truth, than the Fame he had acquired by Ari&longs;totelical Interpretations.

Now, &longs;eeing that inexorable Death hath deprived Venice and Florence of tho&longs;e two great Lights in the very Meridian of their years, I did re&longs;olve, as far as my poor ability would permit, to perpetuate their lives to their honour in the&longs;e leaves, bringing them in as Interlocutors in the pre&longs;ent Controver&longs;y. Nor &longs;hall the Honest Peripatetick want his place, to whom for his exce&longs;sive affection to wards the Com­ mentaries of Simplicius, I thought fit, without mentioning his own Name, to leave that of the Author he &longs;o much re&longs;pected. Let tho&longs;e two great Souls, ever venerable to my heart, plea&longs;e to accept this pu­ blick Monument of my never dying Love; and let the remembr ance of their Eloquence a&longs;si&longs;t me in delivering to Po&longs;terity the Con&longs;ider ations that I have promi&longs;ed.

There ca&longs;ually happened (as was u&longs;uall) &longs;everal di&longs;cour&longs;es at times between the&longs;e Gentlemen, the which had rather inflamed than &longs;atisfied in their wits the thir&longs;t they had to be learning; whereupon they took a di&longs;creet re&longs;olution to meet together for certain dayes, in which all other bu&longs;ine&longs;s &longs;et a&longs;ide, they might betake them&longs;elves more methodically to contemplate the Wonders of God in Heaven, and in the Earth: the place appointed for their meeting being in the Palace of the Noble Sagredo, after the due, but very &longs;hort complements; Signore Salviati began in this manner.

GALILÆUS Galilæus Lyncæus, HIS SYSTEME OF THE WORLD.

The Fir&longs;t Dialogue.

INTERLOCVTORS.

SALVIATUS, SAGREDUS, and SIMPLICIUS.

SALVIATUS.

It was our ye&longs;terdayes re&longs;olution, and a­ greement, that we &longs;hould to day di&longs;cour&longs;e the mo&longs;t di&longs;tinctly, and particularly we could po&longs;&longs;ible, of the natural rea&longs;ons, and their efficacy that have been hitherto al­ ledged on the one or other part, by the maintainers of the Po&longs;itions, Aristotelian, and Ptolomaique; and by the followers

of the Copernican Sy&longs;teme: And becau&longs;e Copernicus placing the Earth among the moveable Bodies of Hea­ ven, comes to con&longs;titute a Globe for the &longs;ame like to a Planet; it would be good that we began our di&longs;putation with the examina­ tion of what, and how great the energy of the Peripateticks ar­ guments is, when they demon&longs;trate, that this Hypothe&longs;is is impo&longs;­ &longs;ible: Since that it is nece&longs;&longs;ary to introduce in Nature, &longs;ub&longs;tances different betwixt them&longs;elves, that is, the Cœle&longs;tial, and Elementa­ ry; that impa&longs;&longs;ible and immortal, this alterable and corruptible. Which argument Ari&longs;totle handleth in his book De Cœlo, in&longs;inu­ ating it fir&longs;t, by &longs;ome di&longs;cour&longs;es dependent on certain general a&longs;­ &longs;umptions, and afterwards confirming it with experiments and per­ ticular demon&longs;trations: following the &longs;ame method, I will pro­ pound, and freely &longs;peak my judgement, &longs;ubmitting my &longs;elf to your cen&longs;ure, and particularly to Simplicius, a Stout Champion and contender for the Ari&longs;totelian Doctrine.

Copernicus repu­ teth the earth œ Globe like to a Pla­ net.

Cœle&longs;tial &longs;ub&longs;tan­ ces that are inalte­ rable, and Elemen­ tary that be alte­ rable, are nece&longs;&longs;ary in the opinion of Ari&longs;totle.

Ari&longs;totle maketh the World perfect, becau&longs;e it hath the threefold demen&longs;i­ on.

And the fir&longs;t Step of the Peripatetick arguments is that, where ri&longs;totle proveth the integrity and perfection of the World, telling us, that it is not a &longs;imple line, nor a bare &longs;uperficies, but a body adorned with Longitude, Latitude, and Profundity; and becau&longs;e there are no more dimen&longs;ions but the&longs;e three; The World having them, hath all, and having all, is to be concluded perfect. And again, that by &longs;imple length, that magnitude is con&longs;tituted, which is called a Line, to which adding breadth, there is framed the Su­ perficies, and yet further adding the altitude or profoundity, there re&longs;ults the Body, and after the&longs;e three dimen&longs;ions there is no pa&longs;&longs;ing farther, &longs;o that in the&longs;e three the integrity, and to &longs;o &longs;peak, totality is terminated, which I might but with ju&longs;tice have requi­ red Ari&longs;totle to have proved to me by nece&longs;&longs;ary con&longs;equences, the rather in regard he was able to do it very plainly, and &longs;peedily.

SIMPL. What &longs;ay you to the excellent demon&longs;trations in the

2. 3. and 4. Texts, after the definition of Continual? have you it not fir&longs;t there proved, that there is no more but three dimen&longs;ions, for that tho&longs;e three are all things, and that they are every where? And is not this confirmed by the Doctrine and Authority of the Pythagorians, who &longs;ay that all things are determined by three, be­ ginning, middle, and end, which is the number of All? And where leave you that rea&longs;on, namely, that as it were by the law of Na­ ture, this number is u&longs;ed in the &longs;acrifices of the Gods? And why being &longs;o dictated by nature, do we atribute to tho&longs;e things that are three, and not to le&longs;&longs;e, the title of all? why of two is it &longs;aid both, and not all, unle&longs;s they be three? And all this Doctrine you have in the &longs;econd Text. Afterwards in the third, Ad pleniorem &longs;cientiam, we read that All, the Whole, and Perfect, are formally one and the &longs;ame; and that therefore onely the Body, among&longs;t magnitudes is perfect: becau&longs;e it is determined by three, which is All, and being divi&longs;ible three manner of waies, it is every way di­ vi&longs;ible; but of the others, &longs;ome are dividible in one manner, and &longs;ome in two, becau&longs;e according to the number a&longs;&longs;ixed, they have their divi&longs;ion and continuity, and thus one magnitude is continu­ ate one way, another two, a third, namely the Body, every way. Moreover in the fourth Text; doth he not after &longs;ome other Do­ ctrines, prove it by another demon&longs;tration? Scilicet, That no tran­ &longs;ition is made but according to &longs;ome defect (and &longs;o there is a tran­ &longs;ition or pa&longs;&longs;ing from the line to the &longs;uperficies, becau&longs;e the line is defective in breadth) and that it is impo&longs;&longs;ible for the perfect to want any thing, it being every way &longs;o; therefore there is no tran­ &longs;ition from the Solid or Body to any other magnitude. Now think you not that by all the&longs;e places he hath &longs;ufficiently proved, how that there's no going beyond the three dimen&longs;ions, Length, Breadth, and Thickne&longs;s, and that therefore the body or &longs;olid, which hath them all, is perfect?

Ari&longs;totles demon­ &longs;trations to prove the dimen&longs;ions to be three and no more.

The number three celebrated among &longs;t the Pythagorians

Omne, Totum & Perfectum.

Or Solid.

SALV. To tell you true, I think not my &longs;elf bound by all the&longs;e rea&longs;ons to grant any more but onely this, That that which hath beginning, middle, and end, may, and ought to be called perfect: But that then, becau&longs;e beginning, middle, and end, are Three, the num­ ber Three is a perfect number, and hath a faculty of conferring Perfection on tho&longs;e things that have the &longs;ame, I find no inducement to grant; neither do I under&longs;tand, nor believe that, for example, of feet, the number three is more perfect then four or two, nor do I conceive the number four to be any imperfection to the Ele­ ments: and that they would be more perfect if they were three. Better therefore it had been to have left the&longs;e &longs;ubtleties to the Rhetoricians, and to have proved his intent, by nece&longs;&longs;ary demon&longs;tra­ tion; for &longs;o it behoves to do in demon&longs;trative &longs;ciences.

SIMPL. You &longs;eem to &longs;corn the&longs;e rea&longs;ons, and yet it is all the Doctrine of the Pythagorians, who attribute &longs;o much to numbers; and you that be a Mathematician, and believe many opinions in the Pythagorick Philo&longs;ophy, &longs;eem now to contemn their My­ &longs;teries.

SALV. That the Pythagorians had the &longs;cience of numbers in high e&longs;teem, and that Plato him&longs;elf admired humane under&longs;tand­ ing, and thought that it pertook of Divinity, for that it under­ &longs;tood the nature of numbers, I know very well, nor &longs;hould I be far from being of the &longs;ame opinion: But that the My&longs;teries for which Pythagoras and his &longs;ect, had the Science of numbers in &longs;uch veneration, are the follies that abound in the mouths and writings of the vulgar, I no waies credit: but rather becau&longs;e I know that they, to the end admirable things might not be expo&longs;ed to the con­ tempt, and &longs;corne of the vulgar, cen&longs;ured as &longs;acrilegious, the pub­ li&longs;hing of the ab&longs;truce properties of Numbers, and incommen­ &longs;urable and irrational quantities, by them inve&longs;tigated; and di­ vulged, that he who di&longs;covered them, was tormented in the other World: I believe that &longs;ome one of them to deter the common &longs;ort, and free him&longs;elf from their inqui&longs;itivene&longs;s, told them that the my&longs;teries of numbers were tho&longs;e trifles, which afterwards did &longs;o &longs;pread among&longs;t the vulgar; and this with a di&longs;cretion and &longs;ubtlety re&longs;embling that of the prudent young man, that to be freed from the importunity of his inqui&longs;itive Mother or Wife, I know not whether, who pre&longs;&longs;ed him to impart the &longs;ecrets of the Senate, contrived that &longs;tory, which afterwards brought her and many o­ ther women to be derided and laught at by the &longs;ame Senate.

Plato held that humane under­ &longs;tanding partook of divinity, becau&longs;e it understood num­ bers.

The My&longs;tery of Pythagorick num­ bers fabulous.

De Papyrio præ­ textato, Gellius I: 2. 3.

SIMPL. I will not be of the number of tho&longs;e who are over curi­ ous about the Pythagorick my&longs;teries; but adhering to the point in hand; I reply, that the rea&longs;ons produced by Ari&longs;totle to prove the dimen&longs;ions to be no more than three, &longs;eem to me conclu­ dent, and I believe, That had there been any more evident demon­ &longs;trations thereof, Ari&longs;totle would not have omitted them.

SAGR. Put in at lea&longs;t, if he had known, or remembred any more. But you Salviatus would do me a great plea&longs;ure to alledge unto me &longs;ome arguments that may be evident, and clear enough for me to comprehend.

SALV. I will; and they &longs;hall be &longs;uch as are not onely to be ap­ prehended by you, but even by Simplicius him&longs;elf: nor onely to be comprehended, but are al&longs;o already known, although hap­ ly unob&longs;erved; and for the more ea&longs;ie under&longs;tanding thereof, we will take this Pen and Ink, which I &longs;ee already prepared for &longs;uch occa&longs;ions, and de&longs;cribe a few figures. And fir&longs;t we will note [Fig. 1. at the end of this Dialog.] the&longs;e two points AB, and draw from the one to the other the curved lines, ACB, and ADB, and the right line A B, I demand of you which of them, in your mind, is that which determines the di&longs;tance between the terms AB, & why?

A Geometrical de­ mon&longs;tration of the triple dimen&longs;ion.

SAGR. I &longs;hould &longs;ay the right line, and not the crooked, as well becau&longs;e the right is &longs;horter, as becau&longs;e it is one, &longs;ole, and deter­ minate, whereas the others are infinit, unequal, and longer; and my determination is grounded upon that, That it is one, and certain.

SALV. We have then the right line to determine the length be­ tween the two terms; let us add another right line and parallel to AB, which let be CD, [Fig. 2.] &longs;o that there is put between them a &longs;uperficies, of which I de&longs;ire you to a&longs;&longs;ign me the breadth, therefore departing from the point A, tell me how, and which way you will go, to end in the line C D, and &longs;o to point me out the breadth com­ prehended between tho&longs;e lines; let me know whether you will terminate it according to the quantity of the curved line A E, or the right line A F, or any other.

SIMPL. According to the right A F, and not according to the crooked, that being already excluded from &longs;uch an u&longs;e.

SAGR. But I would take neither of them, &longs;eeing the right line A F runs obliquely; But would draw a line, perpendicular to C D, for this &longs;hould &longs;eem to me the &longs;horte&longs;t, and the propere&longs;t of infinite that are greater, and unequal to one another, which may be produced from the term A to any other part of the oppo&longs;ite line C D.

SALV. Your choice, and the rea&longs;on you bring for it in my judg­ ment is mo&longs;t excellent; &longs;o that by this time we have proved that the fir&longs;t dimen&longs;ion is determined by a right line, the &longs;econd name­ ly the breadth with another line right al&longs;o, and not onely right, but withall, at right-angles to the other that determineth the length, and thus we have the two dimen&longs;ions of length and breadth, definite and certain. But were you to bound or termi­ nate a height, as for example, how high this Roof is from the pave­ ment, that we tread on, being that from any point in the Roof, we may draw infinite lines, both curved, and right, and all of di­ ver&longs;e lengths to infinite points of the pavement, which of all the&longs;e lines would you make u&longs;e of?

SAGR. I would fa&longs;ten a line to the Seeling, and with a plummet that &longs;hould hang at it, would let it freely di&longs;tend it &longs;elf till it &longs;hould reach well near to the pavement, and the length of &longs;uch a thread being the &longs;treighte&longs;t and &longs;horte&longs;t of all the lines, that could po&longs;sibly be drawn from the &longs;ame point to the pavement, I would &longs;ay was the true height of this Room.

SALV. Very well, And when from the point noted in the pave­ ment by this pendent thread (taking the pavement to be levell and not declining) you &longs;hould produce two other right lines, one for the length, and the other for the breadth of the &longs;uperficies of the&longs;aid pavement, what angles &longs;hould they make with the &longs;aid thread?

SAGR. They would doubtle&longs;s meet at right angles, the &longs;aid lines falling perpendicular, and the pavement being very plain and levell.

SALV. Therefore if you a&longs;&longs;ign any point, for the term from whence to begin your mea&longs;ure; and from thence do draw a right line, as the terminator of the fir&longs;t mea&longs;ure, namely of the length, it will follow of nece&longs;&longs;ity, that that which is to de&longs;ign out the largene&longs;s or breadth, toucheth the fir&longs;t at right-angles, and that that which is to denote the altitude, which is the third dimen&longs;ion, going from the &longs;ame point formeth al&longs;o with the other two, not oblique but right angles, and thus by the three perpendiculars, as by three lines, one, certain, and as &longs;hort as is po&longs;&longs;ible, you have the three dimen&longs;ions A B length, A C breadth, and A D height; and becau&longs;e, clear it is, that there cannot concurre any more lines in the &longs;aid point, &longs;o as to make therewith right-angles, and the dimen&longs;ions ought to be determined by the &longs;ole right lines, which make between them­ &longs;elves right-angles; therefore the dimen&longs;ions are no more but three, and that which hath three hath all, and that which hath all, is divi&longs;ible on all &longs;ides, and that which is &longs;o, is perfect, &c.

SIMPL. And who &longs;aith that I cannot draw other lines? why may not I protract another line underneath, unto the point A, that may be perpendicular to the re&longs;t?

SALV. You can doubtle&longs;s, at one and the &longs;ame point, make no more than three right lines concurre, that con&longs;titute right angles between them&longs;elves.

SAGR. I &longs;ee what Simplicius means, namely, that &longs;hould the &longs;aid D A be prolonged downward, then by that means there might be drawn two others, but they would be the &longs;ame with the fir&longs;t three, differing onely in this, that whereas now they onely touch, then they would inter&longs;ect, but not produce new dimen&longs;ions.

In phyfical proofs geometrical exact­ ne&longs;s is not nece&longs;&longs;a­ ry.

SIMPL. I will not &longs;ay that this your argument may not be con­ cludent; but yet this I &longs;ay with Ari&longs;totle, that in things natural it is not alwaies nece&longs;&longs;ary, to bring Mathematical demon&longs;trations.

SAGR. Grant that it were &longs;o where &longs;uch proofs cannot be had, yet if this ca&longs;e admit of them, why do not you u&longs;e them? But it would be good we &longs;pent no more words on this particular, for I think that Salviatus will yield, both to Ari&longs;totle, and you, with­ out farther demon&longs;tration, that the World is a body, and perfect, yea mo&longs;t perfect, as being the greate&longs;t work of God.

SALV. So really it is, therefore leaving the general contempla­

tion of the whole, let us de&longs;cend to the con&longs;ideration of its parts, which Ari&longs;totle, in his fir&longs;t divi&longs;ion, makes two, and they very diffe­ rent and almo&longs;t contrary to one another; namely the Cœle&longs;tial, and Elementary: that ingenerable, incorruptible, unalterable, un­ pa&longs;&longs;ible, &c. and this expo&longs;ed to a continual alteration, mutati­ on, &c. Which difference, as from its original principle, he de­ rives from the diver&longs;ity of local motions, and in this method he proceeds.

Parts of the world are two, according to Ari&longs;totle, Cœle­ &longs;tial and Elemen­ tary contrary to one another.

Leaving the &longs;en&longs;ible, if I may &longs;o &longs;peak, and retiring into the Ideal world, he begins Architectonically to con&longs;ider that nature being the principle of motion, it followeth that natural bodies be indued with local motion. Next he declares local motion to be of three kinds, namely, circular, right, and mixt of right and cir­ cular: and the two fir&longs;t he calleth &longs;imple, for that of all lines the circular, and right are onely &longs;imple; and here &longs;omewhat re­ &longs;training him&longs;elf, he defineth anew, of &longs;imple motions, one to be circular, namely that which is made about the medium, and the other namely the right, upwards, and downwards; upwards, that which moveth from the medium; downwards, that which goeth to­ wards the medium. And from hence he infers, as he may by and ne­ ce&longs;&longs;ary con&longs;equence, that all &longs;imple motions are confined to the&longs;e three kinds, namely, to the medium, from the medium, and about the medium; the which corre&longs;ponds &longs;aith he, with what hath been &longs;aid before of a body, that it al&longs;o is perfected by three things, and &longs;o is its motion. Having confirmed the&longs;e motions, he proceeds &longs;aying, that of natural bodies &longs;ome being &longs;imple, and &longs;ome compo&longs;ed of them (and he calleth &longs;imple bodies tho&longs;e, that have a principle of motion from nature, as the Fire and Earth) it follows that &longs;imple motions belong to &longs;imple bodies, and mixt to the com­ pound; yet in &longs;uch &longs;ort, that the compounded incline to the part predominant in the compo&longs;ition.

Local motion of three kinds, right, circular, & mixt.

Circular, and &longs;treight motions are &longs;imple, as pro­ ceeding by &longs;imple lines.

Ad medium, à me­ dio, & circa medi­ um.

SAGR. Pray you hold a little Salviatus, for I find &longs;o many doubts to &longs;pring up on all &longs;ides in this di&longs;cour&longs;e, that I &longs;hall be con&longs;trained, either to communicate them if I would attentively hearken to what you &longs;hall add, or to take off my attention from the things &longs;poken, if I would remember objections.

SALV. I will very willingly &longs;tay, for that I al&longs;o run the &longs;ame hazard, and am ready at every &longs;tep to lo&longs;e my &longs;elf whil&longs;t I &longs;ail be­ tween Rocks, and boi&longs;terous Waves, that make me, as they &longs;ay, to lo&longs;e my Compa&longs;s; therefore before I make them more, propound your difficulties.

The definition of Nature, either im­ perfect, or un&longs;ea&longs;o­ nable, produced by Ari&longs;totle.

SAGR. You and Ari&longs;totle together would at fir&longs;t take me a little out of the &longs;en&longs;ible World, to tell me of the Architecture, wherewith it ought to be fabricated; and very appo&longs;itly begin to tell me, that a natural body is by nature moveable, nature being (as el&longs;ewhere it is defined) the principle of motion. But here I am &longs;omewhat doubtfull why Ari&longs;totle &longs;aid not that of natural bo­ dies, &longs;ome are moveable by nature, and others immoveable, for that in the definition, nature is &longs;aid to be the principle of Motion, and Re&longs;t; for if natural bodies have all a principle of motion, either he might have omitted the mention of Re&longs;t, in the definiti­ on of nature: or not have introduced &longs;uch a definition in this place. Next, as to the declaration of what Ari&longs;totle intends by &longs;imple motions, and how by Spaces he determines them, calling tho&longs;e &longs;im­ ple, that are made by &longs;imple lines, which are onely the right, and

circular, I entertain it willingly; nor do I de&longs;ire to tenter the in&longs;tance of the Helix, about the Cylinder; which in that it is in e­ very part like to it &longs;elf, might &longs;eemingly be numbred among &longs;im­ ple lines. But herein I cannot concurre, that he &longs;hould &longs;o re­ &longs;train &longs;imple motions (whil&longs;t he &longs;eems to go about to repeat the &longs;ame definition in other words) as to call one of them the motion about the medium, the others Sur&longs;um & Deor&longs;um, namely up­ wards and downward; which terms are not to be u&longs;ed, out of the World fabricated, but imply it not onely made, but already in­ habited by us; for if the right motion be &longs;imple, by the &longs;implicity of the right line, and if the &longs;imple motion be natural, it is made on every &longs;ide, to wit, upwards, downwards, backwards, forwards, to the right, to the left, and if any other way can be imagined, pro­ vided it be &longs;traight, it &longs;hall agree to any &longs;imple natural body; or if not &longs;o, then the &longs;uppo&longs;ion of Ari&longs;totle is defective. It appears moreover that Ari&longs;totle hinteth but one circular motion alone to be in the World, and con&longs;equently but one onely Center, to which alone the motions of upwards and downwards, refer. All which are apparent proofs, that Ari&longs;totles aim is, to make white black, and to accommodate Architectur to the building, and not to modle the building according to the precepts of Arthitecture: for if I &longs;hould &longs;ay that Nature in Univer&longs;al may have a thou­ &longs;and Circular Motions, and by con&longs;equence a thou&longs;and Cen­ ters, there would be al&longs;o a thou&longs;and motions upwards, and downwards. Again he makes as hath been &longs;aid, a &longs;imple motion, and a mixt motion, calling &longs;imple, the circular and right; and mixt, the compound of them two: of natural bodies he calls &longs;ome &longs;imple (namely tho&longs;e that have a natural principle to &longs;imple mo­ tion) and others compound: and &longs;imple motions he attributes to &longs;imple bodies, and the compounded to the compound; but by compound motion he doth no longer under&longs;tand the mixt of right and circular, which may be in the World; but introduceth a mixt motion as impo&longs;&longs;ible, as it is impo&longs;&longs;ible to mixe oppo&longs;ite motions made in the &longs;ame right line, &longs;o as to produce from them a motion partly upwards, partly downwards; and, to moderate &longs;uch an ab­ &longs;urdity, and impo&longs;&longs;ibility, he a&longs;&longs;erts that &longs;uch mixt bodies move according to the &longs;imple part predominant: which nece&longs;&longs;itates others to &longs;ay, that even the motion made by the &longs;ame right line is &longs;ometimes &longs;imple, and &longs;ometimes al&longs;o compound: &longs;o that the &longs;im­ plicity of the motion, is no longer dependent onely on the &longs;im­ plicity of the line.

The Helix about the Cylinder may be &longs;aid to be a &longs;im­ ple line.

Ari&longs;totle accom­ modates the rules of Architecture to the frame of the World, and not the frame to the rules.

Right motion, &longs;ome­ times &longs;imple, ard &longs;ometimes mixt ac­ cording to Ari&longs;t.

SIMPL. How? Is it not difference &longs;ufficient, that the &longs;imple and ab&longs;olute are more &longs;wift than that which proceeds from predomi­ nion? and how much fa&longs;ter doth a piece of pure Earth de&longs;cend, than a piece of Wood?

SAGR. Well, Simplicius; But put ca&longs;e the &longs;implicity for this cau&longs;e was changed, be&longs;ides that there would be a hundred thou­ &longs;and mixt motions, you would not be able to determine the &longs;im­ ple; nay farther, if the greater or le&longs;&longs;e velocity be able to alter the &longs;implicity of the motion, no &longs;imple body &longs;hould move with a &longs;imple motion; &longs;ince that in all natural right motions, the veloci­ ty is ever encrea&longs;ing, and by con&longs;equence &longs;till changing the &longs;impli­ city, which as it is &longs;implicity, ought of con&longs;equence to be immu­ table, and that which more importeth, you charge Ari&longs;totle with another thing, that in the definition of motions compounded, he hath not made mention of tardity nor velocity, which you now in&longs;ert for a nece&longs;&longs;ary and e&longs;&longs;ential point. Again you can draw no advantage from this rule, for that there will be among&longs;t the mixt bodies &longs;ome, (and that not a few) that will move &longs;wiftly, and others more &longs;lowly than the &longs;imple; as for example, Lead, and Wood, in compari&longs;on of earth; and therefore among&longs;t the&longs;e mo­ tions, which call you the &longs;imple, and which the mixt?

SIMPL. I would call that &longs;imple motion, which is made by a &longs;imple body, and mixt, that of a compound body.

SAGR. Very well, and yet Simplicius a little before you &longs;aid, that the &longs;imple, and compound motions, di&longs;covered which were mixt, and which were &longs;imple bodies; now you will have me by &longs;imple and mixt bodies, come to know which is the &longs;imple, and which is the compound motion: an excellent way to keep us igno­ rant, both of motions and bodies. Moreover you have al&longs;o a little above declared, how that a greater velocity did not &longs;uffice, but you &longs;eek a third condition for the definement of &longs;imple motion, for which Ari&longs;totle contented him&longs;elf with one alone, namely, of the &longs;implicity of the Space, or Medium: But now according to you, the &longs;imple motion, &longs;hall be that which is made upon a &longs;imple line, with a certain determinate velocity, by a body &longs;imply moveable. Now be it as you plea&longs;e, and let us return to Ari&longs;totle, who defi­ neth the mixt motion to be that compounded of the right, and cir­ cular, but produceth not any body, which naturally moveth with &longs;uch a motion.

SALV. I come again to Ari&longs;totle, who having very well, and Methodically begun his di&longs;cour&longs;e, but having a greater aim to re&longs;t at, and hit a marke, predefigned in his minde, then that to which his method lead him, digre&longs;&longs;ing from the purpo&longs;e, he comes to a&longs;&longs;ert, as a thing known and manife&longs;t, that as to the motions directly upwards or downwards, they naturally agree to Fire, and Earth; and that therefore it is nece&longs;&longs;ary, that be&longs;ides the&longs;e bodies, which are neer unto us, there mu&longs;t be in nature another, to which the circular motion may agree: which &longs;hall be &longs;o much the more excellent by how much the circular motion is more perfect, then the &longs;treight, but how much more perfect that is than this, he deter­ mines from the greatne&longs;s of the circular lines perfection above the right line; calling that perfect, and this imperfect; imperfect, be­ cau&longs;e if infinite it wanteth a termination, and end: and if it be fi­ nite, there is yet &longs;omething beyond which it may be prolonged. This is the ba&longs;is, ground work, and ma&longs;ter-&longs;tone of all the Fabrick of the Aristotelian World, upon which they &longs;uper&longs;truct all their other properties, of neither heavy nor light, of ingenerable incor­ ruptible, exemption from all motions, &longs;ome onely the local, &c. And all the&longs;e pa&longs;&longs;ions he affirmeth to be proper to a &longs;imple body that is moved circularly; and the contrary qualities of gravity, levity, corruptibility, &c. he a&longs;&longs;igns to bodies naturally moveable in a &longs;treight line, for that if we have already di&longs;covered defects in the foundation, we may rationally que&longs;tion what &longs;oever may far­ ther built thereon. I deny not, that this which Ari&longs;totle hitherto hath introduced, with a general di&longs;cour&longs;e dependent upon univer­ &longs;al primary principles, hathbeen &longs;ince in proce&longs;s of time, re-inforced with particular rea&longs;ons, and experiments; all which it would be nece&longs;&longs;ary di&longs;tinctly to con&longs;ider and weigh; but becau&longs;e what hath been &longs;aid hitherto pre&longs;ents to &longs;uch as con&longs;ider the &longs;ame many and no &longs;mall difficulties, (and yet it would be nece&longs;&longs;ary, that the pri­ mary principles and fundamentals, were certain, firm, and e&longs;tabli&longs;h­ ed, that &longs;o they might with more confidence be built upon) it would not be ami&longs;s, before we farther multiply doubts, to &longs;ee if haply (as I conjecture) betaking our &longs;elves to other waies, we may not light upon a more direct and &longs;ecure method; and with better con&longs;idered principles of Architecture lay our primary fundamen­ tals. Therefore &longs;u&longs;pending for the pre&longs;ent the method of Ari&longs;to­ tle, (which we will re-a&longs;&longs;ume again in its proper place, and parti­ cularly examine;) I &longs;ay, that in the things hitherto affirmed by him, I agree with him, and admit that the World is a body enjoy­ ing all dimen&longs;ions, and therefore mo&longs;t perfect; and I add, that as &longs;uch, it is nece&longs;&longs;arily mo&longs;t ordinate, that is, having parts between them&longs;elves, with exqui&longs;ite and mo&longs;t perfect order di&longs;po&longs;ed; which a&longs;&longs;umption I think is not to be denied, neither by you or any other.

The circular line perfect, according to Ari&longs;totle, and but the right im­ perfect, and why.

The world is &longs;up­ po&longs;ed by the Au­ thor to be perfectly ordinate.

SIMPL. Who can deny it? the fir&longs;t particular (of the worlds dimen&longs;ions) is taken from Ari&longs;totle him&longs;elf, and its denominati­ on of ordinate &longs;eems onely to be a&longs;&longs;umed from the order which it mo&longs;t exactly keeps.

Streight motion impo&longs;&longs;ible in the world exactly or­ dinate.

SALV. This principle then e&longs;tabli&longs;hed, one may immediately conclude, that if the entire parts of the World &longs;hould be by their nature moveable, it is impo&longs;&longs;ible that their motions &longs;hould be right, or other than circular; and the rea&longs;on is &longs;ufficiently ea&longs;ie, and manife&longs;t; for that what&longs;oever moveth with a right motion, changeth place; and continuing to move, doth by degrees more and more remove from the term from whence it departed, and from all the places thorow which it &longs;ucce&longs;&longs;ively pa&longs;&longs;ed; and if &longs;uch motion naturally &longs;uited with it, then it was not at the be­ ginning in its proper place; and &longs;o the parts of the World were not di&longs;po&longs;ed with perfect order. But we &longs;uppo&longs;e them to be per­ fectly ordinate, therefore as &longs;uch, it is impo&longs;&longs;ible that they &longs;hould by nature change place, and con&longs;equently move in a right moti­

on. Again, the right motion being by nature infinite, for that the right line is infinite and indeterminate, it is impo&longs;&longs;ible that any moveable can have a natural principle of moving in a right line; namely toward the place whither it is impo&longs;&longs;ible to arrive, there being no præ-&longs;inite term; and nature, as Ari&longs;totle him&longs;elf &longs;aith well, never attempts to do that which can never be done, nor e&longs;&longs;aies to move whither it is impo&longs;&longs;ible to arrive. And if any one &longs;hould yet object, that albeit the right line, and con&longs;equent­ ly the motion by it is producible in infinitum, that is to &longs;ay, is in­ terminate; yet neverthele&longs;s Nature, as one may &longs;ay, arbitrarily hath a&longs;&longs;igned them &longs;ome terms, and given natural in&longs;tincts to its natural bodies to move unto the &longs;ame; I will reply, that this might perhaps be fabled to have come to pa&longs;s in the fir&longs;t Chaos, where indi&longs;tinct matters confu&longs;edly and inordinately wandered; to regulate which, Nature very appo&longs;itely made u&longs;e of right mo­ tions, by which, like as the well-con&longs;tituted, moving, di&longs;dorder them&longs;elves, &longs;o were they which were before depravedly di&longs;po&longs;ed by this motion ranged in order: but after their exqui&longs;ite di&longs;tribu­ tion and collocation, it is impo&longs;&longs;ible that there &longs;hould remain na­ tural inclinations in them of longer moving in a right motion, from which now would en&longs;ue their removal from their proper and natural place, that is to &longs;ay, their di&longs;ordination; we may there­ fore &longs;ay that the right motion &longs;erves to conduct the matter to erect the work; but once erected, that it is to re&longs;t immoveable, or if moveable, to move it &longs;elf onely circularly. Unle&longs;s we will &longs;ay with Plato, that the&longs;e mundane bodies, after they had been made and fini&longs;hed, were for a certain time moved by their Maker, in a right motion, but that after their attainment to certain and de­ terminate places, they were revolved one by one in Spheres, pa&longs;­ &longs;ing from the right to the circular motion, wherein they have been ever &longs;ince kept and maintained. A &longs;ublime conceipt, and worthy indeed of Plato: upon which, I remember to have heard our common friend the ^{*}Lyncean Academick di&longs;cour&longs;e in this man­ ner, if I have not forgot it. Every body for any rea&longs;on con&longs;titu­ ted in a &longs;tate of re&longs;t, but which is by nature moveable, being &longs;et at liberty doth move; provided withal, that it have an inclina­ tion to &longs;ome particular place; for &longs;hould it &longs;tand indifferently af­ fected to all, it would remain in its re&longs;t, not having greater in­ ducement to move one way than another. From the having of this inclination nece&longs;&longs;arily proceeds, that it in its moving &longs;hall con­ tinually increa&longs;e its acceleration, and beginning with a mo&longs;t &longs;low motion, it &longs;hall not acquire any degree of velocity, before it &longs;hall have pa&longs;&longs;ed thorow all the degrees of le&longs;s velocity, or grea­ ter tardity: for pa&longs;&longs;ing from the &longs;tate of quiet (which is the in­ finite degree of tardity of motion) there is no rea&longs;on by which it &longs;hould enter into &longs;uch a determinate degree of velocity, before it &longs;hall have entred into a le&longs;s, and into yet a le&longs;s, before it entred into that: but rather it &longs;tands with rea&longs;on, to pa&longs;s fir&longs;t by tho&longs;e degrees neare&longs;t to that from which it departed, and from tho&longs;e to the more remote; but the degree from whence the moveable began to move, is that of extreme tardity, namely of re&longs;t. Now this acceleration of motion is never made, but when the moveable in moving acquireth it; nor is its acqui&longs;t other than an approaching to the place de&longs;ired, to wit, whither its natural in­ clination attracts it, and thither it tendeth by the &longs;horte&longs;t way; namely, by a right line. We may upon good grounds therefore &longs;ay, That Nature, to confer upon a moveable fir&longs;t con&longs;tituted in re&longs;t a determinate velocity, u&longs;eth to make it move according to a certain time and &longs;pace with a right motion. This pre&longs;uppo&longs;ed, let us imagine God to have created the Orb v. g. of Jupiter, on which he had determined to confer &longs;uch a certain velocity, which it ought afterwards to retain perpetually uniform; we may with Plato &longs;ay, that he gave it at the beginning a right and accelerate motion, and that it afterwards being arrived to that intended de­ gree of velocity, he converted its right, into a circular motion, the velocity of which came afterwards naturally to be uniform.

Right motion by nature infinite.

Motion by a right line naturally im­ po&longs;&longs;ible.

Nature attempts not things impo&longs;&longs;i­ ble to be effected.

Right motion might perhaps be in the fir&longs;t Chaos.

Right motion is commodious to range in order, things ous of or­ der.

Mundane bodies moved in the be­ ginning in a right line, and after­ wards circularly? according to Plato.

* Thus doth he co­ vertly and mode&longs;t­ ly &longs;tile him&longs;elfe throughout this work.

A moveable be­ ing in a &longs;tate of re&longs;t, &longs;hall not move unle&longs;s it have an inclination to &longs;ome particular place.

The moveable ac­ celerates its moti­ on, going towards the place whither it hath an inclina­ tion.

The moveable pa&longs;­ &longs;ing from re&longs;t, go­ eth thorow all the degrees of tardity.

Re&longs;t the in&longs;inioe degree of tardity.

The moveable doth not accelerate, &longs;ave only as it approach­ eth nearer to its term.

Nature, to intro­ duce in the move­ able a certain de­ gree of velocity, made it move in a right line.

Vniform velocity convenient to the circular motion.

SAGR. I hearken to this Di&longs;cour&longs;e with great delight; and I believe the content I take therein will be greater, when you have &longs;atisfied me in a doubt: that is, (which I do not very well com­ prehend) how it of nece&longs;&longs;ity en&longs;ues, that a moveable departing from its re&longs;t, and entring into a motion to which it had a natural inclination, it pa&longs;&longs;eth thorow all the precedent degrees o&longs; tardity, comprehended between any a&longs;&longs;igned degree of velocity, and the &longs;tate of re&longs;t, which degrees are infinite? &longs;o that Nature was not able to confer them upon the body of Jupiter, his circular moti­ on being in&longs;tantly created with &longs;uch and &longs;uch velocity.

Betwixt re&longs;t, and any a&longs;&longs;igned degree of velocity, infinite degrees of le&longs;s ve­ locity interpo&longs;e.

Nature doth not immediately con­ fer a determinate degree of velocity, howbeit &longs;he could.

SALV. I neither did, nor dare &longs;ay, that it was impo&longs;&longs;ible for God or Nature to confer that velocity which you &longs;peak of, imme­ diately; but this I &longs;ay, that de facto &longs;he did not doit; &longs;o that the doing it would be a work extra-natural, and by confequence mi­ raculous.

SAGR. Then you believe, that a &longs;tone leaving its re&longs;t, and en­ tring into its natural motion towards the centre of the Earth, pa&longs;­ &longs;eth thorow all the degrees of tardity inferiour to any degree of velocity?

SALV. I do believe it, nay am certain of it; and &longs;o certain, that I am able to make you al&longs;o very well &longs;atisfied with the truth thereof.

SAGR. Though by all this daies di&longs;cour&longs;e I &longs;hould gain no more but &longs;uch a knowledge, I &longs;hould think my time very well be&longs;towed.

SALV. By what I collect from our di&longs;cour&longs;e, a great part of your &longs;cruple lieth in that it &longs;hould in a time, and that very &longs;hort, pa&longs;s thorow tho&longs;e infinite degrees of tardity precedent to any ve­ locity, acquired by the moveable in that time: and therefore be­ fore we go any farther, I will &longs;eek to remove this difficulty, which &longs;hall be an ea&longs;ie task; for I reply, that the moveable pa&longs;&longs;eth by the afore&longs;aid degrees, but the pa&longs;&longs;age is made without &longs;taying in

any of them; &longs;o that the pa&longs;&longs;age requiring but one &longs;ole in&longs;tant of time, and every &longs;mall time containing infinite in&longs;tants, we &longs;hall not want enough of them to a&longs;&longs;ign its own to each of the infinite degrees of tardity; although the time were never &longs;o &longs;hort.

The moveable de­ parting from re&longs;v pa&longs;&longs;eth thorow all degrees of velocity without &longs;taying in any.

SAGR. Hitherto I apprehend you; neverthele&longs;s it is very much that that Ball &longs;hot from a Cannon (for &longs;uch I conceive the ca­ dent moveable) which yet we &longs;ee to fall with &longs;uch a precipice, that in le&longs;s than ten pul&longs;es it will pa&longs;s two hundred yards of al­ titude; &longs;hould in its motion be found conjoyned with &longs;o &longs;mall a degree of velocity, that, &longs;hould it have continued to have moved at that rate without farther acceleration, it would not have pa&longs;t the &longs;ame in a day.

SALV. You may &longs;ay, nor yet in a year, nor in ten, no nor in a thou&longs;and; as I will endeavour to &longs;hew you, and al&longs;o happily with­ out your contradiction, to &longs;ome &longs;ufficiently &longs;imple que&longs;tions that I will propound to you. Therefore tell me if you make any que­ &longs;tion of granting that, that that ball in de&longs;cending goeth increa­ &longs;ing its impetus and velocity.

SAGR. I am mo&longs;t certain it doth.

SALV. And if I &longs;hould &longs;ay that the impetus acquired in any place of its motion, is &longs;o much, that it would &longs;uffice to re-carry it to that place from which it came, would you grant it?

SAGR. I &longs;hould con&longs;ent to it without contradiction, provided al­ waies, that it might imploy without impediment its whole impetus in that &longs;ole work of re-conducting it &longs;elf, or another equal toit, to that &longs;elf-&longs;ame height as it would do, in ca&longs;e the Earth were bored thorow the centre, and the Bullet fell a thou&longs;and yards from the &longs;aid centre, for I verily believe it would pa&longs;s beyond the centre, a&longs;cending as much as it had de&longs;cended; and this I &longs;ee plainly in the experiment of a plummet hanging at a line, which removed from the perpendicular, which is its &longs;tate of re&longs;t, and afterwards let go, falleth towards the &longs;aid perpendicular, and goes as far be­ yond it; or onely &longs;o much le&longs;s, as the oppo&longs;ition of the air, and line, or other accidents have hindred it. The like I &longs;ee in the wa­ ter, which de&longs;cending thorow a pipe, re-mounts as much as it had de&longs;cended.

The ponderous mo­ ver de&longs;cending ac­ quireth impetus &longs;ufficient to re­ carry it to the like height.

SALV. You argue very well. And for that I know you will not &longs;cruple to grant that the acqui&longs;t of the impetus is by means of the receding from the term whence the moveable departed, and its ap­ proach to the centre, whither its motion tendeth; will you &longs;tick to yeeld, that two equal moveables, though de&longs;cending by divers lines, without any impediment, acquire equal impetus, provided that the approaches to the centre be equal?

SAGR. I do not very well under&longs;tand the que&longs;tion.

SALV. I will expre&longs;s it better by drawing a Figure: therefore I will &longs;uppo&longs;e the line A B [in Fig. 3.] parallel to the Horizon, and upon the point B, I will erect a perpendicular B C; and after that I adde this &longs;launt line C A. Under&longs;tanding now the line C A to be an inclining plain exqui&longs;itely poli&longs;hed, and hard, upon which de&longs;cendeth a ball perfectly round and of very hard matter, and &longs;uch another I &longs;uppo&longs;e freely to de&longs;cend by the perpendicular C B: will you now confe&longs;s that the impetus of that which de­ &longs;cends by the plain C A, being arrived to the point A, may be equal to the impetus acquired by the other in the point B, after the de&longs;cent by the perpendicular C B?

The impetuo&longs;ity of moveables equally approaching to the centre, are equal.

SAGR. I re&longs;olutely believe &longs;o: for in effect they have both the &longs;ame proximity to the centre, and by that, which I have already granted, their impetuo&longs;ities would be equally &longs;ufficient to re-carry them to the &longs;ame height.

SALV. Tell me now what you believe the &longs;ame ball would do put upon the Horizontal plane A B?

Vpon an horizon­ tall plane the move­ able lieth &longs;till.

SAGR. It would lie &longs;till, the &longs;aid plane having no declination.

SALV. But on the inclining plane C A it would de&longs;cend, but with a gentler motion than by the perpendicular C B?

SAGR. I may confidently an&longs;wer in the affirmative, it &longs;eem­ ing to me nece&longs;&longs;ary that the motion by the perpendicular C B &longs;hould be more &longs;wift, than by the inclining plane C A; yet ne­ verthele&longs;s, i&longs; this be, how can the Cadent by the inclination ar­ rived to the point A, have as much impetus, that is, the &longs;ame de­ gree of velocity, that the Cadent by the perpendicular &longs;hall have in the point B? the&longs;e two Propo&longs;itions &longs;eem contradictory.

The veloeity by the inclining plane e­ qual to the veloci­ ty by the perpendi­ oular, and the mo­ tion by the perpen­ dicular &longs;wifter than by the incli­ nation.

SALV. Then you would think it much more fal&longs;e, &longs;hould I &longs;ay, that the velocity of the Cadents by the perpendicular, and inclination, are ab&longs;olutely equal: and yet this is a Propo&longs;ition mo&longs;t true, as is al&longs;o this that the Cadent moveth more &longs;wiftly by the perpendicular, than by the inclination.

SAGR. The&longs;e Propo&longs;itions to my ears &longs;ound very har&longs;h: and I believe to yours Simplicius?

SIMPL. I have the &longs;ame &longs;en&longs;e of them.

SALV. I conceit you je&longs;t with me, pretending not to compre­ hend what you know better than my &longs;elf: therefore tell me Sim­ plicius, when you imagine a moveable more &longs;wift than ano­ ther, what conceit do you fancy in your mind?

SIMPL. I fancie one to pa&longs;s in the &longs;ame time a greater &longs;pace than the other, or to move equal &longs;paces, but in le&longs;&longs;er time.

SALV. Very well: and for moveables equally &longs;wift, what's your conceit of them?

SIMPL. I fancie that they pa&longs;s equal &longs;paces in equal times.

SALV. And have you no other conceit thereof than this?

SIMPL. This I think to be the proper definition of equal mo­ tions.

Velocities are &longs;aid to be equal, when the &longs;paces pa&longs;&longs;ed are proportionate to their time.

SAGR. We will add moreover this other: and call that equal velocity, when the &longs;paces pa&longs;&longs;ed have the &longs;ame proportion, as the times wherein they are pa&longs;t, and it is a more univer&longs;al definition.

SALV. It is &longs;o: for it comprehendeth the equal &longs;paces pa&longs;t in equal times, and al&longs;o the unequal pa&longs;t in times unequal, but pro­ portionate to tho&longs;e &longs;paces. Take now the &longs;ame Figure, and apply­ ing the conceipt that you had of the more ha&longs;tie motion, tell me why you think the velocity of the Cadent by C B, is greater than the velocity of the De&longs;cendent by C A?

SIMPL. I think &longs;o; becau&longs;e in the &longs;ame time that the Cadent &longs;hall pa&longs;s all C B, the De&longs;cendent &longs;hall pa&longs;s in C A, a part le&longs;s than C B.

SALV. True; and thus it is proved, that the moveable moves more &longs;wiftly by the perpendicular, than by the inclination. Now con&longs;ider, if in this &longs;ame Figure one may any way evince the o­ ther conceipt, and finde that the moveables were equally &longs;wift by both the lines C A and C B.

SIMPL. I &longs;ee no &longs;uch thing; nay rather it &longs;eems to contradict what was &longs;aid before.

SALV. And what &longs;ay you, Sagredus? I would not teach you what you knew before, and that of which but ju&longs;t now you pro­ duced me the definition.

SAGR. The definition I gave you, was, that moveables may be called equally &longs;wift, when the &longs;paces pa&longs;&longs;ed are proportional to the times in which they pa&longs;&longs;ed; therefore to apply the defini­ tion to the pre&longs;ent ca&longs;e, it will be requi&longs;ite, that the time of de­ &longs;cent by C A, to the time of falling by C B, &longs;hould have the &longs;ame proportion that the line C A hath to the line C B; but I under&longs;tand not how that can be, for that the motion by C B is &longs;wifter than by C A.

SALV. And yet you mu&longs;t of nece&longs;&longs;ity know it. Tell me a little, do not the&longs;e motions go continually accelerating?

SAGR. They do; but more in the perpendicular than in the inclination.

SALV. But this acceleration in the perpendicular, is it yet not­ with&longs;tanding &longs;uch in compari&longs;on of that of the inclined, that two equal parts being taken in any place of the &longs;aid perpendicu­ lar and inclining lines, the motion in the parts of the perpendicu­ lar is alwaies more &longs;wift, than in the part of the inclination?

SAGR. I &longs;ay not &longs;o: but I could take a &longs;pace in the inclinati­ on, in which the velocity &longs;hall be far greater than in the like &longs;pace taken in the perpendicular; and this &longs;hall be, if the &longs;pace in the perpendicular &longs;hould be taken near to the end C, and in the in­ clination, far from it.

SALV. You &longs;ee then, that the Propo&longs;ition which &longs;aith, that the motion by the perpendicular is more &longs;wift than by the incli­ nation, holds not true univer&longs;ally, but onely of the motions, which begin from the extremity, namely from the point of re&longs;t: without which re&longs;triction, the Propo&longs;ition would be &longs;o deficient, that its very direct contrary might be true; namely, that the mo­ tion in the inclining plane is &longs;wifter than in the perpendicular: for it is certain, that in the &longs;aid inclination, we may take a &longs;pace pa&longs;t by the moveable in le&longs;s time, than the like &longs;pace pa&longs;t in the perpendicular. Now becau&longs;e the motion in the inclination is in &longs;ome places more, in &longs;ome le&longs;s, than in the perpendicular; there­ fore in &longs;ome places of the inclination, the time of motion of the moveable, &longs;hall have a greater proportion to the time of the motion of the moveable, by &longs;ome places of the perpendicular, than the &longs;pace pa&longs;&longs;ed, to the &longs;pace pa&longs;&longs;ed: and in other places, the pro­ portion of the time to the time, &longs;hall be le&longs;s than that of the &longs;pace to the &longs;pace. As for example: two moveables departing from their quie&longs;cence, namely, from the point C, one by the per­ pendicular C B, [in Fig. 4.] and the other by the inclination C A, in the time that, in the perpendicular, the moveable &longs;hall have pa&longs;t all C B, the other &longs;hall have pa&longs;t C T le&longs;&longs;er. And therefore the time by C T, to the time by C B (which is equal) &longs;hall have a greater proportion than the line C T to C B, being that the &longs;ame to the le&longs;s, hath a greater proportion than to the greater. And on the contrary, if in C A, prolonged as much as is requi­ &longs;ite, one &longs;hould take a part equal to C B, but pa&longs;t in a &longs;horter time; the time in the inclination &longs;hall have a le&longs;s proportion to the time in the perpendicular, than the &longs;pace to the &longs;pace. If therefore in the inclination and perpendicular, we may &longs;uppo&longs;e &longs;uch &longs;paces and velocities, that the proportion between the &longs;aid &longs;paces be greater and le&longs;s than the proportion of the times; we may ea&longs;ily grant, that there are al&longs;o &longs;paces, by which the times of the motions retain the &longs;ame proportion as the &longs;paces.

SAGR. I am already freed from my greate&longs;t doubt, and con­ ceive that to be not onely po&longs;&longs;ible, but nece&longs;&longs;ary, which I but now thought a contradiction: but neverthele&longs;s I under&longs;tand not as yet, that this whereof we now are &longs;peaking, is one of the&longs;e po&longs;&longs;ible or nece&longs;&longs;ary ca&longs;es; &longs;o as that it &longs;hould be true, that the time of de&longs;cent by C A, to the time of the fall by C B, hath the &longs;ame proportion that the line C A hath to C B; whence it may without contradiction be affirmed, that the velocity by the incli­ nation C A, and by the perpendicular C B, are equal.

SALV. Content your &longs;elf for this time, that I have removed your incredulity; but for the knowledge of this, expect it at &longs;ome other time, namely, when you &longs;hall &longs;ee the matters concer­ ning local motion demon&longs;trated by our Academick; at which time you &longs;hall find it proved, that in the time that the one movea­ ble falls all the &longs;pace C B, the other de&longs;cendeth by C A as far as the point T, in which falls the perpendicular drawn from the point B: and to find where the &longs;ame Cadent by the perpendi­ cular would be when the other arriveth at the point A, draw from A the perpendicular unto C A, continuing it, and C B unto the interfection, and that &longs;hall be the point &longs;ought. Whereby you &longs;ee how it is true, that the motion by C B is &longs;wifter than by the inclination C A (&longs;uppo&longs;ing the term C for the beginning of the motions compared) becau&longs;e the line C B is greater than C T, and the other from C unto the inter&longs;ection of the perpendicular drawn from A, unto the line C A, is greater than C A, and therefore the motion by it is &longs;wifter than by C A But when we compare the motion made by all C A, not with all the motion made in the &longs;ame time by the perpendicular continued, but with that made in part of the time, by the &longs;ole part C B, it hinders not, that the motion by C A, continuing to de&longs;cend beyond, may arrive to A in &longs;uch a time as is in proportion to the other time, as the line C A is to the line C B. Now returning to our fir&longs;t purpo&longs;e; which was to &longs;hew, that the grave moveable leaving its quie&longs;cence, pa&longs;&longs;eth defcending by all the degrees of tardity, precedent to any what&longs;oever degree of velocity that it aequireth, re-a&longs;&longs;uming the &longs;ame Figure which we u&longs;ed before, let us remem­ ber that we did agree, that the De&longs;cendent by the inclination C A, and the Cadent by the perpendicular C B, were found to have acquired equal degrees of velocity in the terms B and A: now to proceed, I &longs;uppo&longs;e you will not &longs;cruple to grant, that upon ano­ ther plane le&longs;s &longs;teep than A C; as for example, A D [in Fig. 5.] the motion of the de&longs;cendent would be yet more &longs;low than in the plane A C. So that it is not any whit dubitable, but that there may be planes &longs;o little elevated above the Horizon A B, that the moveable, namely the &longs;ame ball, in any the longe&longs;t time may reach the point A, which being to move by the plane A B, an infi­ nite time would not &longs;uffice: and the motion is made always more &longs;lowly, by how much the declination is le&longs;s. It mu&longs;t be therefore confe&longs;t, that there may be a point taken upon the term B, &longs;o near to the &longs;aid B, that drawing from thence to the point A a plane, the ball would not pa&longs;s it in a whole year. It is requi&longs;ite next for you to know, that the impetus, namely the degree of velo­ city the ball is found to have acquired when it arriveth at the point A, is &longs;uch, that &longs;hould it continue to move with this &longs;elf-&longs;ame degree uniformly, that is to &longs;ay, without accelerating or retarding; in as much more time as it was in coming by the inclining plane, it would pa&longs;s double the &longs;pace of the plane inclined: namely (for example) if the ball had pa&longs;t the plane D A in an hour, con­ tinuing to move uniformly with that degree of velocity which it is found to have in its arriving at the term A, it &longs;hall pa&longs;s in an hour a &longs;pace double the length D A; and becau&longs;e (as we have &longs;aid) the degrees of velocity acquired in the points B and A, by the moveables that depart from any point taken in the perpendicu­ lar C B, and that de&longs;cend, the one by the inclined plane, the o­ ther by the &longs;aid perpendicular, are always equal: therefore the cadent by the perpendicular may depart from a term &longs;o near to B, that the degree of velocity acquired in B, would not &longs;uffice (&longs;till maintaining the &longs;ame) to conduct the moveable by a &longs;pace dou­ ble the length of the plane inclined in a year, nor in ten, no nor in a hundred. We may therefore conclude, that if it be true, that according to the ordinary cour&longs;e of nature a moveable, all external and accidental impediments removed, moves upon an in­ clining plane with greater and greater tardity, according as the inclination &longs;hall be le&longs;s; &longs;o that in the end the tardity comes to be infinite, which is, when the inclination concludeth in, and joyneth to the horizontal plane; and if it be true likewi&longs;e, that the de­ gree of velocity acquired in &longs;ome point of the inclined plane, is equal to that degree of velocity which is found to be in the move­ able that de&longs;cends by the perpendicular, in the point cut by a parallel to the Horizon, which pa&longs;&longs;eth by that point of the incli­ ning plane; it mu&longs;t of nece&longs;&longs;ity be granted, that the cadent de­ parting from re&longs;t, pa&longs;&longs;eth thorow all the infinite degrees of tar­ dity, and that con&longs;equently, to acquire a determinate degree of velocity, it is nece&longs;&longs;ary that it move fir&longs;t by right lines, de&longs;cend­ ing by a &longs;hort or long &longs;pace, according as the velocity to be acqui­ red, ought to be either le&longs;s or greater, and according as the plane on which it de&longs;cendeth is more or le&longs;s inclined; &longs;o that a plane may be given with &longs;o &longs;mall inclination, that to acquire in it the a&longs;&longs;igned degree of velocity, it mu&longs;t fir&longs;t move in a very great &longs;pace, and take a very long time; whereupon in the horizontal plane, any how little &longs;oever velocity, would never be naturally acquired, &longs;ince that the moveable in this ca&longs;e will never move: but the

motion by the horizontal line, which is neither declined or incli­ ned, is a circular motion about the centre: therefore the circu­ lar motion is never acquired naturally, without the right motion precede it; but being once acquired, it will continue perpetually with uniform velocity. I could with other di&longs;cour&longs;es evince and demon&longs;trate the &longs;ame truth, but I will not by &longs;o great a digre&longs;­ fion interrupt our principal argument: but rather will return to it upon &longs;ome other occa&longs;ion; e&longs;pecially &longs;ince we now a&longs;&longs;umed the &longs;ame, not to &longs;erve for a nece&longs;&longs;ary demon&longs;tration, but to adorn a Platonick Conceit; to which I will add another particular ob&longs;er­ vation of our Academick, which hath in it &longs;omething of admira­ ble. Let us &longs;uppo&longs;e among&longs;t the decrees of the divine Architect, a purpo&longs;e of creating in the World the&longs;e Globes, which we be­ hold continually moving round, and of a&longs;&longs;igning the centre of their conver&longs;ions; and that in it he had placed the Sun immoveable, and had afterwards made all the &longs;aid Globes in the &longs;ame place, and with the intended inclinations of moving towards the Centre, till they had acquired tho&longs;e degrees of velocity, which at fir&longs;t &longs;ee­ med good to the &longs;ame Divine Minde; the which being acquired, we la&longs;tly &longs;uppo&longs;e that they were turned round, each in his Sphere retaining the &longs;aid acquired velocity: it is now demanded, in what altitude and di&longs;tance from the Sun the place was where the &longs;aid Orbs were primarily created; and whether it be po&longs;&longs;ible that they might all be created in the &longs;ame place? To make this inve­ &longs;tigation, we mu&longs;t take from the mo&longs;t skilfull A&longs;tronomers the magnitude of the Spheres in which the Planets revolve, and like­ wi&longs;e the time of their revolutions: from which two cognitions is gathered how much (for example) Jupiter is &longs;wifter than Sa­ turne; and being found (as indeed it is) that Jupiter moves more &longs;wiftly, it is requi&longs;ite, that departing from the &longs;ame altitude, Ju­ piter be de&longs;cended more than Saturne, as we really know it is, its Orbe being inferiour to that of Saturne. But by proceeding for­ wards, from the proportions of the two velocities of Jupiter and Saturne, and from the di&longs;tance between their Orbs, and from the proportion of acceleration of natural motion, one may finde in what altitude and di&longs;tance from the centre of their revolutions, was the place from whence they fir&longs;t departed. This found out, and agreed upon, it is to be &longs;ought, whether Mars de&longs;cending from thence to his Orb, the magnitude of the Orb, and the ve­ locity of the motion, agree with that which is found by calcula­ tion; and let the like be done of the Eartb, of Venus, and of Mercury; the greatne&longs;s of which Spheres, and the velocity of their motions, agree &longs;o nearly to what computation gives, that it is very admirable.

The circular mo­ tion is never ac­ quired naturally, without right mo­ tion precede it. Circular motion perpetually uni­ form.

The magnitude of the Orbs, and the velocity of the mo­ tion of the Planets, an&longs;wer proportion­ ably, as if de&longs;cend­ ed from the &longs;ame place.

SAGR. I have hearkened to this conceit with extreme delight; and, but that I believe the making of the&longs;e calculations truly would be a long and painfull task, and perhaps too hard for me to comprehend, I would make a trial of them.

SALV. The operation indeed is long and difficult; nor could I be certain to finde it &longs;o readily; therefore we &longs;hall refer it to an­ other time, and for the pre&longs;ent we will return to our fir&longs;t propo­ &longs;al, going on there where we made digre&longs;&longs;ion; which, if I well remember, was about the proving the motion by a right line of no u&longs;e, in the ordinate parts of the World; and we did proceed to &longs;ay, that it was not &longs;o in circular motions, of which that which is made by the moveable in it &longs;elf, &longs;till retains it in the &longs;ame place, and that which carrieth the moveable by the circumference of a circle about its fixed centre, neither puts it &longs;elf, nor tho&longs;e about it in di&longs;order; for that &longs;uch a motion primarily is finite and terminate (though not yet fini&longs;hed and determined) but there is no point in the circumference, that is not the fir&longs;t and la&longs;t term in the cir­ culation; and continuing it in the circumference a&longs;&longs;igned it, it leaveth all the re&longs;t, within and without that, free for the u&longs;e of others, without ever impeding or di&longs;ordering them. This being a motion that makes the moveable continually leave, and con­ tinually arrive at the end; it alone therefore can primarily be u­ niform; for that acceleration of motion is made in the moveable, when it goeth towards the term, to which it hath inclination; and the retardation happens by the repugnance that it hath to leave and part from the &longs;ame term; and becau&longs;e in circular mo­ tion, the moveable continually leaves the natural term, and con­ tinually moveth towards the &longs;ame, therefore, in it, the repug­ nance and inclination are always of equal force: from which e­ quality re&longs;ults a velocity, neither retarded nor accelerated, i. e. an uniformity in motion. From this conformity, and from the being terminate, may follow the perpetual continuation by &longs;ucce&longs;&longs;ively reiterating the circulations; which in an undeterminated line, and in a motion continually retarded or accelerated, cannot na­ turally be. I &longs;ay, naturally; becau&longs;e the right motion which is retarded, is the violent, which cannot be perpetual; and the ac­ celerate arriveth nece&longs;&longs;arily at the term, if one there be; and if there be none, it cannot be moved to it, becau&longs;e nature moves not whether it is impo&longs;&longs;ible to attain. I conclude therefore, that the circular motion can onely naturally con&longs;i&longs;t with natural bo­ dies, parts of the univer&longs;e, and con&longs;tituted in an excellent di&longs;po­ &longs;ure; and that the right, at the mo&longs;t that can be &longs;aid for it, is a&longs;&longs;igned by nature to its bodies, and their parts, at &longs;uch time as they &longs;hall be out of their proper places, con&longs;tituted in a depraved di&longs;po&longs;ition, and for that cau&longs;e needing to be redured by the &longs;hort­ e&longs;t way to their natural &longs;tate. Hence, me thinks, it may ratio­ nally be concluded, that for maintenance of perfect order among &longs;t the parts of the World, it is nece&longs;&longs;ary to &longs;ay, that moveables are moveable onely circularly; and if there be any that move not circularly, the&longs;e of nece&longs;&longs;ity are immoveable: there being no­ thing but re&longs;t and circular motion apt to the con&longs;ervation of or­ der. And I do not a little wonder with my &longs;elf, that Ari&longs;totle, who held that the Terre&longs;trial globe was placed in the centre of the World, and there remained immoveable, &longs;hould not &longs;ay, that of natural bodies &longs;ome are moveable by nature, and others immo­ veable; e&longs;pecially having before defined Nature, to be the prin­ ciple of Motion and Re&longs;t.

Finite and termi­ nate circular mo­ tions di&longs;order not the parts of the World.

In the circular mo­ tion, every point in the circumference is the begining and end.

Circular motion onely is uniform.

Circular motion may be continued perpetually.

Right motion can­ not naturally be perpetual.

Right motion a&longs;­ &longs;igned to natural bodies, to reduce them to perfect or­ der, when removed from their places.

Re&longs;t onely, and circular motion are apt to con&longs;erve or­ der.

SIMPL. Ari&longs;totle, though of a very per&longs;picacious wit, would not &longs;train it further than needed: holding in all his argumen­ tations, that &longs;en&longs;ible experiments were to be preferred before any rea&longs;ons founded upon &longs;trength of wit, and &longs;aid tho&longs;e which &longs;hould deny the te&longs;timony of &longs;en&longs;e de&longs;erved to be puni&longs;hed with the lo&longs;s of that &longs;en&longs;e; now who is &longs;o blind, that &longs;ees not the parts of the Earth and Water to move, as being grave, natural­ ly downwards, namely, towards the centre of the Univer&longs;e, a&longs;­ &longs;igned by nature her &longs;elf for the end and term of right motion deor&longs;ùm; and doth not likewi&longs;e &longs;ee the Fire and Air to move right upwards towards the Concave of the Lunar Orb, as to the natural end of motion &longs;ur&longs;ùm? And this being &longs;o manife&longs;tly &longs;een, and we being certain, that eadem est ratio totius & partium, why may we not a&longs;&longs;ert it for a true and manife&longs;t propo&longs;ition, that the natural motion of the Earth is the right motion ad medium, and that of the Fire, the right à medio?

Sen&longs;ible experi­ ments are to be pre­ ferred before hu­ mane argument a­ tions.

He who denies &longs;en&longs;e, de&longs;erves to be deprived of it. Sen&longs;e &longs;heweth that things grave move to the medium, and the light to the concave.

SALV. The mo&longs;t that you can pretend from this your Di&longs;­ cour&longs;e, were it granted to be true, is that, like as the parts of the Earth removed from the whole, namely, from the place where they naturally re&longs;t, that is in &longs;hort reduced to a depraved and di&longs;­ ordered di&longs;po&longs;ure, return to their place &longs;pontaneou&longs;ly, and there­ fore naturally in a right motion, (it being granted, that eadem &longs;it ratio totius & partium) &longs;o it may be inferred, that the Terre&longs;trial Globe removed violently from the place a&longs;&longs;igned it by nature, it would return by a right line. This, as I have &longs;aid, is the mo&longs;t that can be granted you, and that onely for want of examination; but he that &longs;hall with exactne&longs;s revi&longs;e the&longs;e things, will fir&longs;t deny, that the parts of the Earth, in returning to its whole, move in a right line, and not by a circular or mixt; and really you would have enough to do to demon&longs;trate the contra­ ry, as you &longs;hall plainly &longs;ee in the an&longs;wers to the particular rea&longs;ons and experiments alledged by Ptolomey and Ari&longs;totle. Secondly, If another &longs;hould &longs;ay that the parts of the Earth, go not in their motion towards the Centre of the World, but to unite with its Whole, and that for that rea&longs;on they naturally incline towards the centre of the Terre&longs;trial Globe, by which inclination they con­ &longs;pire to form and pre&longs;erve it, what other All, or what other Centre would you find for the World, to which the whole Terrene Globe, being thence removed, would &longs;eek to return, that &longs;o the rea&longs;on of the Whole might be like to that of its parts? It may be added, That neither Ari&longs;totle, nor you can ever prove, that the Earth de facto is in the centre of the Univer&longs;e; but if any Centre may be a&longs;ligned to the Univer&longs;e, we &longs;hall rather find the Sun placed in it, as by the &longs;equel you &longs;hall under&longs;tand.

It is que&longs;tionable whether de&longs;cending weights move in a right line.

The Earth speri­ cal by the con&longs;pi­ ration of its parts to its Centre.

The Sun more pro­ bably in the centre of the Vniver&longs;e, than the Earth.

Now, like as from the con&longs;entaneous con&longs;piration of all the parts of the Earth to form its whole, doth follow, that they with equal inclination concurr thither from all parts; and to unite them&longs;elves as much as is po&longs;&longs;ible together, they there &longs;phelically adapt them&longs;elves; why may we not believe that the Sun, Moon, and other mundane Bodies, be al&longs;o of a round figure, not by o­ ther than a concordant in&longs;tinct, and natural concour&longs;e of all the parts compo&longs;ing them? Of which, if any, at any time, by any violence were &longs;eparated from the whole, is it not rea&longs;onable to think, that they would &longs;pontaneou&longs;ly and by natural in&longs;tinct re­ turn? and in this manner to infer, that the right motion agreeth with all mundane bodies alike.

Natural inclina­ tion of the parts of all the globes of the World to go to their centre.

SIMPL. Certainly, if you in this manner deny not onely the Principles of Sciences, but manife&longs;t Experience, and the Sen&longs;es them&longs;elves, you can never be convinced or removed from any o­ pinion which you once conceit, therefore I will choo&longs;e rather to be &longs;ilent (for, contra negantes principia non e&longs;t di&longs;putandum) than contend with you. And in&longs;i&longs;ting on the things alledged by you even now (&longs;ince you que&longs;tion &longs;o much as whether grave move­ ables have a right motion or no) how can you ever rationally de­ ny, that the parts of the Earth; or, if you will, that ponderous matters de&longs;cend towards the Centre, with a right motion; when­ as, if from a very high Tower, who&longs;e walls are vcry upright and perpendicular, you let them fall, they &longs;hall de&longs;cend gliding and &longs;liding by the Tower to the Earth, exactly in that very place where a plummet would fall, being hanged by a line fa&longs;tned above, ju&longs;t there, whence the &longs;aid weights were let fall? is not this a more than evident argument of the motions being right, and to­ wards the Centre? In the &longs;econd place you call in doubt, whe­ ther the parts of the Earth are moved, as Ari&longs;totle affirms, to­ wards the Centre of the World; as if he had not rationally de­ mon&longs;trated it by contrary motions, whil&longs;t he thus argueth; The motion of heavie bodies is contrary to that of the light: but the motion of the light is manife&longs;t to be directly upwards, namely, towards the circumference of the World, therefore the motion of the heavie is directly towards the Centre of the World: and it happens per accidens, that it be towards the centre of the Earth, for that this &longs;triveth to be united to that. The &longs;eeking in the next place, what a part of the Globe of the Sun or Moon would do, were it &longs;eparated from its whole, is vanity; becau&longs;e that there­ by that is &longs;ought, which would be the con&longs;equence of an impo&longs;&longs;i­ bility; in regard that, as Ari&longs;totle al&longs;o demon&longs;trates, the cœle&longs;tial bodies are impa&longs;&longs;ible, impenetrable, and infrangible; &longs;o that &longs;uch a ca&longs;e can never happen: and though it &longs;hould, and that the &longs;e­ parated part &longs;hould return to its whole, it would not return as grave or light, for that the &longs;ame Ari&longs;totle proveth, that the Cœ­ le&longs;tial Bodies are neither heavie nor light.

The right motion of grave bodies manife&longs;t to &longs;en&longs;e.

Arguments ofri&longs;totle, to prove that grave bodies move with an in­ clination to arrive at the centre of the Vniver&longs;e.

Heavie bodies move towards the centre of the Earth per accidens.

To &longs;eek what would follow upon an impo&longs;&longs;ibility, is folly.

Cœle&longs;tial bodies neither heavie nor light, according to Ari&longs;totle.

SALV. With what rea&longs;on I doubt, whether grave bodies move by a right and perpendicular line, you &longs;hall hear, as I &longs;aid be­ fore, when I &longs;hall examine this particular argument. Touching the &longs;econd point, I wonder that you &longs;hould need to di&longs;cover the Paralogi&longs;m of Ari&longs;totle, being of it &longs;elf &longs;o manife&longs;t; and that you perceive not, that Ari&longs;totle &longs;uppo&longs;eth that which is in que&longs;ti­ on: therefore take notice.

SIMPL. Pray Salviatus &longs;peak with more re&longs;pect of Ari&longs;totle: for who can you ever per&longs;wade, that he who was the fir&longs;t, only, and admirable explainer of the Syllogi&longs;tick forms of demon&longs;tration, of Elenchs, of the manner of di&longs;covering Sophi&longs;ms, Paralogi&longs;ms, and in &longs;hort, of all the parts of Logick, &longs;hould afterwards &longs;o notoriou&longs;ly equivocate in impo&longs;ing that for known, which is in que&longs;tion? It would be better, my Ma&longs;ters, fir&longs;t perfectly to under&longs;tand him, and then to try, if you have a minde, to oppo&longs;e him.

Ari&longs;totle cannot e­ quivocate, being the inventer of Lo­ gick.

SALV. Simplicius, we are here familiarly di&longs;cour&longs;ing among our &longs;elves, to inve&longs;tigate &longs;ome truth; I &longs;hall not be di&longs;plea&longs;ed that you di&longs;cover my errors; and if I do not follow the mind of Ari&longs;totle, freely reprehend me, and I &longs;hall take it in good part. Onely give me leave to expound my doubts, and to reply &longs;ome­ thing to your la&longs;t words, telling you, that Logick, as it is well under&longs;tood, is the Organe with which we philo&longs;ophate; but as it may be po&longs;&longs;ible, that an Arti&longs;t may be excellent in making Or­ gans, but unlearned in playing on them, thus he might be a great Logician, but unexpert in making u&longs;e of Logick; like as we have many that theorically under&longs;tand the whole Art of Poetry, and yet are unfortunate in compo&longs;ing but meer four Ver&longs;es; others enjoy all the precepts of Vinci^{*}, and yet know not how to paint a Stoole. The playing on the Organs is not taught by them who know how to make Organs, but by him that knows how to play on them: Poetry is learnt by continual reading of Poets: Limn­ ing is learnt by continual painting and de&longs;igning: Demon&longs;tration from the reading of Books full of demon&longs;trations, which are the Mathematical onely, and not the Logical. Now returning to our purpo&longs;e, I &longs;ay, that that which Ari&longs;totle &longs;eeth of the motion of light bodies, is the departing of the Fire from any part of the Superficies of the Terre&longs;trial Globe, and directly retreating from it, mounting upwards; and this indeed is to move towards a circumference greater than that of the Earth; yea, the &longs;ame ri&longs;totle makes it to move to the concave of the Moon, but that this circumference is that of the World, or concentrick to it, &longs;o that to move towards this, is a moving towards that of the World, that he cannot affirm, unle&longs;s he &longs;uppo&longs;eth, That the Centre of the Earth, from which we &longs;ee the&longs;e light a&longs;cendent bodies to depart, be the &longs;ame with the Centre of the World; which is as much as to &longs;ay, that the terre&longs;trial Globe is con&longs;tituted in the mid&longs;t of the World: which is yet that of which we were in doubt, and which Aristotle intended to prove. And do you &longs;ay that this is not a manife&longs;t Paralogi&longs;m?

* A famous Italian Painter.

Paralogi&longs;m ofri&longs;totle, in proving the Earth to be in the Centre of the World.

The Paralogi&longs;me of Ari&longs;totle another way di&longs;covered.

SAGR. This Argument of Ari&longs;totle appeared to me deficient al&longs;o, and non-concludent for another re&longs;pect; though it were granted, that that Circumference, to which the Fire directly mo­ veth, be that which includeth the World: for that in a circle, not onely the centre, but any other point being taken, every move­ able which departing thence, &longs;hall move in a right line, and to­ wards any what&longs;oever part, &longs;hall without any doubt go towards the circumference, and continuing the motion, &longs;hall al&longs;o arrive thither; &longs;o that we may truly &longs;ay, that it moveth towards the circumference: but yet it doth not follow, that that which mo­ veth by the &longs;ame line with a contrary motion, would go towards the centre, unle&longs;s when the point taken were the centre it &longs;elf, or that the motion were made by that onely line, which produced from the point a&longs;&longs;igned, pa&longs;&longs;eth thorow the centre. So that to &longs;ay, that Fire moving in a right line, goeth towards the circumfe­ rence of the World, therefore the parts of the Earth which by the &longs;ame lines move with a contrary motion, go towards the cen­ tre of the World, concludeth not, unle&longs;s then when it is pre­ &longs;uppo&longs;ed, that the lines of the Fire prolonged pa&longs;s by the centre of the World; and becau&longs;e we know certainly of them, that they pa&longs;s by the centre of the Terre&longs;trial Globe (being perpendicu­ lar to its &longs;uperficies, and not inclined) therefore to conclude, it mu&longs;t be &longs;uppo&longs;ed, that the centre of the Earth is the &longs;ame with the centre of the World; or at lea&longs;t, that the parts of the Fire and Earth de&longs;cend not, &longs;ave onely by one &longs;ole line which pa&longs;&longs;eth by the centre of the World. Which neverthele&longs;s is fal&longs;e, and re­ pugnant to experience, which &longs;heweth us, that the parts of Fire, not by one line onely, but by infinite, produced from the centre of the Earth towards all the parts of the World, a&longs;cend always by lines perpendicular to the Superficies of the Terre&longs;tri­ al Globe.

SALV. You do very ingeniou&longs;ly lead Ari&longs;totle to the &longs;ame in­ convenience, Sagredus, &longs;hewing his manife&longs;t equivoke; but withal you add another incon&longs;i&longs;tency. We &longs;ee the Earth to be &longs;pherical, and therefore are certain that it hath its centre, to which we &longs;ee all its parts are moved; for &longs;o we mu&longs;t &longs;ay, whil&longs;t their motions are all perpendicular to the Superficies of the Earth; we mean, that as they move to the centre of the Earth, they move to their Whole, and to their Univer&longs;al Mother: and we are &longs;till far­ ther &longs;o free, that we will &longs;uffer our &longs;elves to be per&longs;waded, that their natural in&longs;tinct is, not to go towards the centre of the Earth, but towards that of the Univer&longs;e; which we know not where to find, or whether it be or no; and were it granted to be, it is but an imaginary point, and a nothing without any quality. As to what Simplicius &longs;aid la&longs;t, that the contending whether the parts of the Sun, Moon, or other cœle&longs;tial Body, &longs;eparated from their Whole, &longs;hould naturally return to it, is a vanity, for that the ca&longs;e is impo&longs;&longs;ible; it being clear by the Demon&longs;trations of Ari&longs;totle, that the cœle&longs;tial Bodies are impa&longs;&longs;ible, impenetrable, unparta­ ble, &c. I an&longs;wer, that none of the conditions, whereby Aristo­ tle di&longs;tingui&longs;heth the Cœle&longs;tial Bodies from Elementary, hath o­ ther foundation than what he deduceth from the diver&longs;ity of the natural motion of tho&longs;e and the&longs;e; in&longs;omuch that it being deni­ ed, that the circular motion is peculiar to Cœle&longs;tial Bodies, and affirmed, that it is agreeable to all Bodies naturally moveable, it is behoofull upon nece&longs;&longs;ary con&longs;equence to &longs;ay, either that the attributes of generable, or ingenerable, alterable, or unalterable, partable, or unpartable, &c. equally and commonly agree with all worldly bodies, namely, as well to the Cœle&longs;tial as to the E­ lementary; or that Ari&longs;totle hath badly and erroneou&longs;ly dedu­ ced tho&longs;e from the circular motion, which he hath a&longs;&longs;igned to Cœ­ le&longs;tial Bodies.

Grave bodies may more rationally be affirmed to tend to the Centre of the Earth, than of the Vniver&longs;e.

The conditions and attributes which differ the cœle&longs;tial bodies from Ele­ mentary, depend on the motions a&longs;&longs;ign­ ed them by Ari&longs;t.

SIMPL. This manner of argumentation tends to the &longs;ubver&longs;i­ on of all Natural Philo&longs;ophy, and to the di&longs;order and &longs;ubver&longs;ion of Heaven and Earth, and the whole Univer&longs;e; but I believe the Fundamentals of the Peripateticks are &longs;uch, that we need not fear that new Sciences can be erected upon their ruines.

SALV. Take no thought in this place for Heaven or the Earth, neither fear their &longs;ubver&longs;ion, or the ruine of Philo&longs;ophy. As to Heaven, your fears are vain for that which you your &longs;elf hold unalterable and impa&longs;&longs;ible; as for the Earth, we &longs;trive to enoble and perfect it, whil&longs;t we make it like to the Cœle&longs;tial Bodies, and as it were place it in Heaven, whence your Philo&longs;ophers have exiled it. Philo&longs;ophy it &longs;elf cannot but receive benefit from our Di&longs;putes, for if our conceptions prove true, new Di&longs;coveries will be made; if fal&longs;e, the fir&longs;t Doctrine will be more confirmed. Rather be&longs;tow your care upon &longs;ome Philo&longs;ophers, and help and defend them; for as to the Science it &longs;elf, it cannot but improve. And that we may return to our purpo&longs;e, be plea&longs;ed freely to pro­ duce what pre&longs;ents it &longs;elf to you in confirmation of that great dif­ ference which Ari&longs;totle puts between the Cœle&longs;tial Bodies, and the Elementary parts of the World, in making tho&longs;e ingenerable, incorruptible, unalterable, &c. and this corruptible, alterable, &c.

The di&longs;putes and contradictions of Philo&longs;ophers may conduce to the benefit of Philo&longs;o­ phy.

SIMPL. I &longs;ee not yet any need that Ari&longs;totle hath of help, &longs;tanding as he doth &longs;toutly and &longs;trongly on his feet; yea not be­ ing yet a&longs;&longs;aulted, much le&longs;s foiled by you. And what ward will you choo&longs;e in this combate for this fir&longs;t blow? Aristotle writeth, that whatever is generated, is made out of a contrary in &longs;ome &longs;ubject, and likewi&longs;e is corrupted in &longs;ome certain &longs;ubject from a contrary into a contrary; &longs;o that (ob&longs;erve) corruption and ge­ neration is never but onely in contraries; If therefore to a Cœ­ le&longs;tial Body no contrary can be a&longs;&longs;igned, for that to the circular motion no other motion is contrary, then Nature hath done very well to make that exempt from contraries, which was to be in­ generable and incorruptible, This fundamental fir&longs;t confirmed, it immediately followeth of con&longs;equence, that it is inaugmenta­ ble, inalterable, impa&longs;&longs;ible, and finally eternal, and a propor­ tionate habitation to the immortal Deities, conformable to the opinion even of all men that have any conceit of the Gods. He afterwards confirmeth the &longs;ame by &longs;en&longs;e; in regard, that in all times pa&longs;t, according to memory or tradition, we &longs;ee nothing re­ moved, according to the whole outward Heaven, nor any of its proper parts. Next, as to the circular motion, that no other is contrary to it, Aristotle proveth many ways; but without reci­ ting them all, it is &longs;ufficiently demon&longs;trated, &longs;ince fimple motions are but three, to the medium, from the medium, and about the medium, of which the two right, &longs;ur&longs;um and deor&longs;um, are mani­ fe&longs;tly contrary; and becau&longs;e one onely hath onely one for con­ trary, therefore there re&longs;ts no other motion which may be contra­ ry to the circular. You &longs;ee the &longs;ubtle and mo&longs;t concluding di&longs;­ cour&longs;e of Ari&longs;totle, whereby he proveth the incorruptibility of Heaven.

Ari&longs;totles di&longs;cour&longs;e to prove the incor­ ruptibility of Hea­ ven.

Generation & cor­ ruption is onely a­ mong&longs;t contraries, according to Ari&longs;t.

To the circular motion no other motion is contrary.

Heaven an habi­ tation for the imm­ ortal Gods.

Immutability of Heaven evident to &longs;ex&longs;e.

He proveth that the circular motion hath no contrary.

SALV. This is nothing more, &longs;ave the pure progre&longs;s of Ari&longs;to­ tle, by me hinted before; wherein, be&longs;ides that I affirm, that the motion which you attribute to the Cœle&longs;tial Bodies agreeth al&longs;o to the Earth, its illation proves nothing. I tell you therefore, that that circular motion which you a&longs;&longs;ign to Cœle&longs;tial Bodies, &longs;uiteth al&longs;o to the Earth, from which, &longs;uppo&longs;ing that the re&longs;t of your di&longs;cour&longs;e were concludent, will follow one of the&longs;e three things, as I told you a little before, and &longs;hall repeat; namely, either that the Earth it &longs;elf is al&longs;o ingenerable, and incorruptible, as the Cœle&longs;tial bodies; or that the Cœle&longs;tial bodies are, like as the Elementary generable, alterable &c. or that this difference of motion hath nothing to do with Generation and Corruption. The di&longs;cour&longs;e of Ari&longs;totle, and yours al&longs;o contain many Propo&longs;i­ tions not to be lightly admitted, and the better to examine them, it will be convenient to reduce them to the mo&longs;t ab&longs;tracted and di&longs;tinct that can be po&longs;&longs;ible; and excu&longs;e me Sagredus, if haply with &longs;ome tediou&longs;ne&longs;s you hear me oft repeat the &longs;ame things, and fancie that you &longs;ee me rea&longs;&longs;ume my argument in the pub­ lick circle of Di&longs;putations. You &longs;ay Generation and Corrupti­ on are onely made where there are contraries; contraries are onely among&longs;t &longs;imple natural bodies, moveable with contrary motions; contrary motions are onely tho&longs;e which are made by a right line between contrary terms; and the&longs;e are onely two, that is to &longs;ay, from the medium, and towards the medium; and &longs;uch motions belong to no other natural bodies, but to the Earth, the Fire, and the other two Elements: therefore Generation and Corruption is onely among&longs;t the Elements. And becau&longs;e the third &longs;imple motion, namely, the circular about the medium, hath no contrary, (for that the other two are contraries, and one onely, hath but onely one contrary) therefore that natural body with which &longs;uch motion agreeth, wants a contrary; and having no contrary is ingenerable and incorruptible, &c. Becau&longs;e where there is no contrariety, there is no generation or corruption, &c. But &longs;uch motion agreeth onely with the Cœle&longs;tial bodies; there­ fore onely the&longs;e are ingenerable, incorruptible, &c. And to begin, I think it a more ea&longs;ie thing, and &longs;ooner done to re&longs;olve, whether the Earth (a mo&longs;t va&longs;t Body, and for its vicinity to us, mo&longs;t tractable) moveth with a &longs;peedy motion, &longs;uch as its revo­ lution about its own axis in twenty four hours would be, than it is to under&longs;tand and re&longs;olve, whether Generation and Corruption ari&longs;eth from contrariety, or el&longs;e whether there be &longs;uch things as generation, corruption and contrariety in nature. And if you, Simplicius, can tell me what method Nature ob&longs;erves in working, when &longs;he in a very &longs;hort time begets an infinite number of flies from a little vapour of the Mu&longs;t of wine, and can &longs;hew me which are there the contraries you &longs;peak of, what it is that corrupteth, and how; I &longs;hould think you would do more than I can; for I profe&longs;s I cannot comprehend the&longs;e things. Be&longs;ides, I would ve­ ry gladly under&longs;tand how, and why the&longs;e corruptive contraries are &longs;o favourable to Daws, and &longs;o cruel to Doves; &longs;o indulgent to Stags, and &longs;o ha&longs;ty to Hor&longs;es, that they do grant to them many more years of life, that is, of incorruptibility, than weeks to the&longs;e. Peaches and Olives are planted in the &longs;ame &longs;oil, expo&longs;ed to the &longs;ame heat and cold, to the &longs;ame wind and rains, and, in a word, to the &longs;ame contrarieties; and yet tho&longs;e decay in a &longs;hort time, and the&longs;e live many hundred years. Furthermore, I never was thorowly &longs;atisfied about this &longs;ub&longs;tantial tran&longs;mutation (&longs;till keep­ ing within pure natural bounds) whereby a matter becometh &longs;o transform'd, that it &longs;hould be nece&longs;&longs;arily &longs;aid to be de&longs;troy'd, &longs;o that nothing remaineth of its fir&longs;t being, and that another body quite differing there-from &longs;hould be thence produced; and if I fancy to my &longs;elf a body under one a&longs;pect, and by and by under another very different, I cannot think it impo&longs;&longs;ible but that it may happen by a &longs;imple tran&longs;po&longs;ition of parts, without corrupting or ingendring any thing a-new; for we &longs;ee &longs;uch kinds of Metamor­ pho&longs;es dayly: &longs;o that to return to my purpo&longs;e, I an&longs;wer you, that ina&longs;much as you go about to per&longs;wade me that the Earth can not move circularly by way of corruptibility and generability, you have undertook a much harder task than I, that with argu­ ments more difficult indeed, but no le&longs;s concluding, will prove the contrary.

Its ea&longs;ier to prove the Earth to move, than that corrupti­ on is made by con­ traries.

Bare tran&longs;po&longs;ition of parts may repre­ &longs;ent bodies under diver&longs;e asp cts.

SAGR. Pardon me, Salviatus, if I interrupt your di&longs;cour&longs;e, which, as it delights me much, for that I al&longs;o am gravel'd with the &longs;ame doubts; &longs;o I fear that you can never conclude the &longs;ame, without altogether digre&longs;&longs;ing from your chief de&longs;ign: therefore if it be permitted to proceed in our fir&longs;t argument, I &longs;hould think that it were convenient to remit this que&longs;tion of generation and corruption to another di&longs;tinct and &longs;ingle conference; as al&longs;o, if it &longs;hall plea&longs;e you and Simplicius, we may do by other particular que&longs;tions which may fall in the way of our di&longs;cour&longs;e; which I will keep in my mind to propo&longs;e, and exactly di&longs;cu&longs;s them &longs;ome other time. Now as for the pre&longs;ent, &longs;ince you &longs;ay, that if Ari­ &longs;totle deny circular motion to the Earth in common with other bodies Cœle&longs;tial, it chence will follow, that the &longs;ame which be­ falleth the Earth, as to its being generable, alterable, &c. will hold al&longs;o of Heaven, let us enquire no further if there be &longs;uch things in nature, as generation and corruption, or not; but let us return to enquire what the Globe of the Earth doth.

SIMPL. I cannot &longs;uffer my ears to hear it que&longs;tion'd, whether generation and corruption be in rerum naturà, it being a thing which we have continually before our eyes, and whereof Ari&longs;totle hath written two whole Books. But if you go about to deny the Principles of Sciences, and que&longs;tion things mo&longs;t manife&longs;t, who knows not, but that you may prove what you will, and maintain any Paradox? And if you do not dayly &longs;ee herbs, plants, ani­ mals to generate and corrupt, what is it that you do &longs;ee? Al&longs;o, do you not continually behold contrarieties contend together, and the Earth change into Water, the Water turn to Air, the Air into Fire, and again the Air to conden&longs;e into Clouds, Rains, Hails and Storms?

By denying Prin­ ciples in the Scien­ ces, any Paradox may be maintain­ ed.

SAGR. Yes, we &longs;ee the&longs;e things indeed, and therefore will grant you the di&longs;cour&longs;e of Ari&longs;totle, as to this part of generation and corruption made by contraries; but if I &longs;hall conclude by virtue of the &longs;ame propo&longs;itions which are granted to Ari&longs;totle, that the Cœle&longs;tial bodies them&longs;elves are al&longs;o generable and cor­ ruptible, a&longs;well as the Elementary, what will you &longs;ay then?

SIMPL. I will &longs;ay you have done that which is impo&longs;&longs;ible to be done.

SAGR. Go to; tell me, Simplicius, are not the&longs;e affections contrary to one another?

SIMPL. Which?

SAGR. Why the&longs;e; Alterable, unalterable; pa&longs;&longs;ible, ^{*} impa&longs;­ &longs;ible; generable, ingenerable; corruptible, incorruptible?

* Or, Impatible.

SIMPL. They are mo&longs;t contrary.

SAGR. Well then, if this be true, and it be al&longs;o granted, that Cœle&longs;tial Bodies are ingenerable and incorruptible; I prove that of nece&longs;&longs;ity Cœle&longs;tial Bodies mu&longs;t be generable and corru­ ptible.

SIMPL. This mu&longs;t needs be a Sophi&longs;m.

SAGR. Hear my Argument, and then cen&longs;ure and re&longs;olve it. Cœle&longs;tial Bodies, for that they are ingenerable and incorruptible, have in Nature their contraries, which are tho&longs;e Bodies that be generable and corruptible; but where there is contrariety, there is al&longs;o generation and corruption; therefore Cœle&longs;tial Bodies are generable and corruptible.

Cœlestial Bodies are generable and corruptible, be­ cau&longs;e they are in­ generable and in­ corruptible.

SIMPL. Did I not &longs;ay it could be no other than a Sophi&longs;m? This is one of tho&longs;e forked Arguments called Soritæ: like that of the Cretan, who &longs;aid that all Cretans were lyars; but he as being a Cretan, had told a lye, in &longs;aying that the Cretans were ly­ ars; it followed therefore, that the Cretans were no lyars, and con&longs;equently that he, as being a Cretan, had &longs;poke truth: And yet in &longs;aying the Cretans were lyars, he had &longs;aid true, and com­ prehending him&longs;elf as a Cretan, he mu&longs;t con&longs;equently be a lyar. And thus in the&longs;e kinds of Sophi&longs;ms a man may dwell to eternity, and never come to any conclu&longs;ion.

The forked Syllo­ gi&longs;m cal'd *cwri/ths.

SAGR. You have hitherto cen&longs;ured it, it remaineth now that you an&longs;wer it, &longs;hewing the fallacie.

SIMPL. As to the re&longs;olving of it, and finding out its fallacie, do you not in the fir&longs;t place &longs;ee a manife&longs;t contradiction in it? Cœle&longs;tial Bodies are ingenerable and incorruptible; Ergo, Cœle­ &longs;tial Bodies are generable and corruptible. And again, the con­ trariety is not betwixt the Cœle&longs;tial Bodies, but betwixt the E­ lements, which have the contrariety of the Motions, &longs;ur&longs;ùm and deor&longs;ùm, and of levity and gravity; But the Heavens which move circularly, to which motion no other motion is contrary, want contrariety, and therefore they are incorruptible.

Among&longs;t Cœle&longs;tial Bodies there is no contrariety.

SAGR. Fair and &longs;oftly, Simplicius; this contrariety whereby you &longs;ay &longs;ome &longs;imple Bodies become corruptible, re&longs;ides it in the &longs;ame Body which is corrupted, or el&longs;e hath it relation to &longs;ome o­ other? I &longs;ay, for example, the humidity by which a piece of Earth is corrupted, re&longs;ides it in the &longs;ame Earth or in &longs;ome other bodie, which mu&longs;t either be the Air or Water? I believe you will grant, that like as the Motions upwards and downwards, and gravity and levity, which you make the fir&longs;t contraries, cannot be in the &longs;ame Subject, &longs;o neither can moi&longs;t and dry, hot and cold: you mu&longs;t therefore con&longs;equently acknowledg that when a bodie cor­ rupteth, it is occa&longs;ioned by &longs;ome quality re&longs;iding in another con­ trary to its own: therefore to make the Cœle&longs;tial Body become corruptible, it &longs;ufficeth that there are in Nature, bodies that have a contrariety to that Cœle&longs;tial body; and &longs;uch are the Elements, if it be true that corruptibility be contrary to incorruptibility.

Contraries which are the cau&longs;es of corruption, re&longs;ide not in the &longs;ame bo­ dy that corrupteth.

SIMPL. This &longs;ufficeth not, Sir; The Elements alter and cor­ rupt, becau&longs;e they are intermixed, and are joyn'd to one another, and &longs;o may exerci&longs;e their contrariety; but Cœle&longs;tial bodies are &longs;eparated from the Elements, by which they are not &longs;o much as toucht, though indeed they have an influence upon the Elements. It is requi&longs;ite, if you will prove generation and corruption in Cœ­ le&longs;tial bodies, that you &longs;hew, that there re&longs;ides contrarieties be­ tween them.

Cœle&longs;tial Bodies touch, but are not touched by the E­ lements.

SAGR. See how I will find tho&longs;e contrarieties between them. The fir&longs;t fountain from whence you derive the contrariety of the Elements, is the contrariety of their motions upwards and down­ wards: it therefore is nece&longs;&longs;ary that tho&longs;e Principles be in like manner contraries to each other, upon which tho&longs;e motions de­ pend. and becau&longs;e that is moveable upwards by lightne&longs;s, and this downwards by gravitv, it is nece&longs;&longs;ary that lightne&longs;s and gravity are contrary to each other: no le&longs;s are we to believe tho&longs;e other Principles to be contraries, which are the cau&longs;es that this is heavy, and that light: but by your own confe&longs;&longs;ion, levity and gravity follow as con&longs;equents of rarity and den&longs;ity; therefore rarity and den&longs;ity &longs;hall be contraries: the which conditions or affections are &longs;o amply found in Cœle&longs;tial bodies, that you e­ &longs;teem the &longs;tars to be onely more den&longs;e parts of their Heaven: and if this be &longs;o, it followeth that the den&longs;ity of the &longs;tars exceeds that of the re&longs;t of Heaven, by almo&longs;t infinite degrees: which is manife&longs;t, in that Heaven is infinitely tran&longs;parent, and the &longs;tars extremely opacous; and for that there are there above no other qualities, but more and le&longs;s den&longs;ity and rarity, which may be cau&longs;es of the greater or le&longs;s tran&longs;parency. There being then &longs;uch contrariety between the Cœleftial bodies, it is nece&longs;&longs;ary that they al&longs;o be generable and corruptible, in the &longs;ame manner as the Elementary bodies are; or el&longs;e that contrariety is not the cau&longs;e of corruptibility, &c.

Gravity & levity, varity and den&longs;ity, are contrary qua­ lities.

The &longs;tars infinitely &longs;urpa&longs;s the &longs;ub­ &longs;tance of the re&longs;t of Heaven in den&longs;ity.

Rarity & den&longs;ity in Cœle&longs;tial bodies, is different from the rarity & den­ &longs;ity of the elements.

SIMPL. There is no nece&longs;&longs;ity either of one or the other, for that den&longs;ity and rarity in Cœle&longs;tial bodies, are not contraries to each other, as in Elementary bodies; for that they depend not on the primary qualities, cold and heat, which are contraries; but on the more or le&longs;s matter in proportion to quantity: now much and little, &longs;peak onely a relative oppo&longs;ition, that is, the lea&longs;t of oppo&longs;itions, and which hath nothing to do with generation and corruption.

SAGR. Therefore affirming, that den&longs;ity and rarity, which a­ mong&longs;t the Elements &longs;hould be the cau&longs;e of gravity and levity, which may be the cau&longs;es of contrary motions &longs;ur&longs;ùm and deor­ &longs;ùm, on which, again, dependeth the contrarieties for generation and corruption; it &longs;ufficeth not that they be tho&longs;e den&longs;ne&longs;&longs;es and rarene&longs;&longs;es which under the &longs;ame quantity, or (if you will) ma&longs;s contain much or little matter, but it is nece&longs;&longs;ary that they be den&longs;­ ne&longs;&longs;es and rarene&longs;&longs;es cau&longs;ed by the primary qualities, hot and cold, otherwi&longs;e they would operate nothing at all: but if this be &longs;o, Ari&longs;totle hath deceived us, for that he &longs;hould have told it us at fir&longs;t, and &longs;o have left written that tho&longs;e &longs;imple bodies are gene­ rable and corruptible, that are moveable with &longs;imple motions upwards and downwards, dependent on levity and gravity, cau­ &longs;ed by rarity and den&longs;ity, made by much or little matter, by rea&longs;on of heat and cold; and not to have &longs;taid at the &longs;imple mo­ tion &longs;ur&longs;ùm and deor&longs;ùm: for I a&longs;&longs;ure you that to the making of bodies heavy or light, whereby they come to be moved with contrary motions, any kind of den&longs;ity and rarity &longs;ufficeth, whe­ ther it proceed from heat and cold, or what el&longs;e you plea&longs;e; for heat and cold have nothing to do in this affair: and you &longs;hall upon experiment find, that a red hot iron, which you mu&longs;t grant to have heat, weigheth as much, and moves in the &longs;ame manner as when it is cold. But to overpa&longs;s this al&longs;o, how know you but that Cœle&longs;tial rarity and den&longs;ity depend on heat and cold?

Ari&longs;totle defective in a&longs;&longs;igning the cau&longs;es why the ele­ ments are genera­ ble & corruptible.

SIMPL. I know it, becau&longs;e tho&longs;e qualities are not among&longs;t Cœle&longs;tial bodies, which are neither hot nor cold.

SALV. I &longs;ee we are again going about to engulph our &longs;elves in a bottomle&longs;s ocean, where there is no getting to &longs;hore; for this is a Navigation without Compa&longs;s, Stars, Oars or Rudder: &longs;o that it will follow either that we be forced to pa&longs;s from Shelf to Shelf, or run on ground, or to &longs;ail continually in danger of being lo&longs;t. Therefore, if according to your advice we &longs;hall proceed in our main de&longs;ign, we mu&longs;t of nece&longs;&longs;ity for the pre&longs;ent overpa&longs;s this general con&longs;ideration, whether direct motion be nece&longs;&longs;ary in Na­ ture, and agree with &longs;ome bodies; and come to the particular demon&longs;trations, ob&longs;ervations and experiments; propounding in the fir&longs;t place all tho&longs;e that have been hitherto alledged by Ari­ &longs;totle, Ptolomey, and others, to prove the &longs;tability of the Earth, en­ deavouring in the next place to an&longs;wer them: and producing in the la&longs;t place, tho&longs;e, by which others may be per&longs;waded, that the Earth is no le&longs;s than the Moon, or any other Planet to be num­ bered among&longs;t natural bodies that move circularly.

SAGR. I &longs;hall the more willingly incline to this, in that I am better &longs;atisfied with your Architectonical and general di&longs;cour&longs;e, than with that of Ari&longs;totle, for yours convinceth me without the lea&longs;t &longs;cruple, and the other at every &longs;tep cro&longs;&longs;eth my way with &longs;ome block. And I &longs;ee no rea&longs;on why Simplicius &longs;hould not be pre&longs;ently &longs;atisfied with the Argument you alledg, to prove that there can be no &longs;uch thing in nature as a motion by a right line, if we do but pre&longs;uppo&longs;e that the parts of the Univer&longs;e are di&longs;po­ &longs;ed in an excellent con&longs;titution and perfect order.

SALV. Stay a little, good Sagredus, for ju&longs;t now a way comes into my mind, how I may give Simplicius &longs;atisfaction, provided that he will not be &longs;o &longs;trictly wedded to every expre&longs;&longs;ion of ri&longs;totle, as to hold it here&longs;ie to recede in any thing from him. Nor is there any que&longs;tion to be made, but that if we grant the excel­ lent di&longs;po&longs;ition and perfect order of the parts of the Univer&longs;e, as to local &longs;cituation, that then there is no other but the circular motion, and re&longs;t; for as to the motion by a right line, I &longs;ee not how it can be of u&longs;e for any thing, but to reduce to their natural con&longs;titution, &longs;ome integral bodies, that by &longs;ome accident were re­ mov'd and &longs;eparated from their whole, as we &longs;aid above.

Let us now con&longs;ider the whole Terre&longs;trial Globe, and enquire the be&longs;t we can, whether it, and the other Mundane bodies are to con&longs;erve them&longs;elves in their perfect and natural di&longs;po&longs;ition. It is nece&longs;&longs;ary to &longs;ay, either that it re&longs;ts and keeps perpetually im­ moveable in its place; or el&longs;e that continuing always in its place, it revolves in its &longs;elf; or that it turneth about a Centre, moving by the circumference of a circle. Of which accidents, both Ari­ &longs;totle and Ptolomey, and all their followers &longs;ay, that it hath ever ob&longs;erved, and &longs;hall continually keep the fir&longs;t, that is, a perpetual re&longs;t in the &longs;ame place. Now, why, I pray you, ought they not to have &longs;aid, that its natural affection is to re&longs;t immoveable, ra­ ther than to make natural unto it the motion ^{*} downwards, with which motion it never did or &longs;hall move? And as to the motion by a right line, they mu&longs;t grant us that Nature maketh u&longs;e of it to reduce the &longs;mall parts of the Earth, Water, Air, Fire, and every other integral Mundane body to their Whole, when any of them by chance are &longs;eparated, and &longs;o tran&longs;ported out of their proper place; if al&longs;o haply, &longs;ome circular motion might not be found to be more convenient to make this re&longs;titution. In my judg­ ment, this primary po&longs;ition an&longs;wers much better, even according to Ari&longs;totles own method, to all the other con&longs;equences, than to attribute the &longs;traight motion to be an intrin&longs;ick and natural principle of the Elements. Which is manife&longs;t, for that if I aske the Peripatetick, if, being of opinion that Cœle&longs;tial bodies are incorruptibe and eternal, he believeth that the Terre&longs;tial Globe is not &longs;o, but corruptible and mortal, &longs;o that there &longs;hall come a time, when the Sun and Moon and other Stars, continuing their beings and operations, the Earth &longs;hall not be found in the World, but &longs;hall with the re&longs;t of the Elements be de&longs;troyed and annihilated, I am certain that he would an&longs;wer me, no: therefore generation and corruption is in the parts and not in the whole; and in the parts very &longs;mall and &longs;uperficial, which are, as it were, incen&longs;ible in compari&longs;on of the whole ma&longs;&longs;e. And becau&longs;e Ari&longs;totle deduceth generation and corruption from the contrariety of &longs;treight motions, let us remit &longs;uch motions to the parts, which onely change and decay, and to the whole Globe and Sphere of the Elements, let us a&longs;cribe either the circular mo­ tion, or a perpetual con&longs;i&longs;tance in its proper place: the only affections apt for perpetuation, and maintaining of perfect order. This which is &longs;poken of the Earth, may be &longs;aid with the &longs;ame rea&longs;on of Fire, and of the greate&longs;t part of the Air; to which Elements, the Peripateticks are forced to a&longs;cribe for intrin&longs;ical and natural, a motion wherewith they were never yet moved, nor never &longs;hall be; and to call that motion preternatural to them, wherewith, if they move at all, they do and ever &longs;hall move. This I &longs;ay, becau&longs;e they a&longs;&longs;ign to the Air aud Fire the motion upwards, wherewith tho&longs;e Elements were never moved, but only &longs;ome parts of them, and tho&longs;e were &longs;o moved onely in or­ der to the recovery of their perfect con&longs;titution, when they were out of their natural places; and on the contrary they call the circular motion preternatural to them, though they are thereby ince&longs;&longs;antly moved: forgeting, as it &longs;eemeth, what Ari&longs;totle oft in­ culcateth, that nothing violent can be permanent.

Ari&longs;t. & Ptolomey make the Terre­ strial Globe immo­ veable.

It is better to &longs;ay, that the Terre&longs;tri­ al Globe naturally resteth, than that it moveth directly downwards.

*The word is, all' ingiù, which the Latine ver&longs;ion ren­ dreth &longs;ur&longs;ùm, which is quite con­ trary to the Au­ thors &longs;en&longs;e.

Right Motion with more rea&longs;on attributed to the parts, than to the whole Elements.

The Peripateticks improperly a&longs;&longs;ign tho&longs;e motious to the Elements for Natural, with which they never were moved, and tho&longs;e for Preter­ natural with which they alwayes are moved.

SIMPL. To all the&longs;e we have very pertinent an&longs;wers, which I for this time omit, that we may come to the more particular rea&longs;ons, and &longs;en&longs;ible experiments, which ought in conclu&longs;ion to be oppo&longs;ed, as Ari&longs;totle &longs;aitn well, to whatever humane rea&longs;on can pre&longs;ent us with.

Sen&longs;ible experi­ ments to be prefer­ red to humane Arguments.

SAGR. What hath been &longs;poken hitherto, &longs;erves to clear up unto us which of the two general di&longs;cour&longs;es carrieth with it mo&longs;t of probability, I mean that of Ari&longs;totle, which would per&longs;wade us, that the &longs;ublunary bodies are by nature generable, and corru­ ptible, &c. and therefore mo&longs;t different from the e&longs;&longs;ence of Cœ­ leftial bodies, which are impa&longs;&longs;ible, ingenerable, incorruptible, &c. drawn from the diver&longs;ity of &longs;imple motions; or el&longs;e this of Salviatus, who &longs;uppo&longs;ing the integral parts of the World to be di&longs;po&longs;ed in a perfect con&longs;titution, excludes by nece&longs;&longs;ary confe­ quence the right or &longs;traight motion of &longs;imple natural bodies, as being of no u&longs;e in nature, and e&longs;teems the Earth it &longs;elf al&longs;o to be one of the Cœle&longs;tial bodies adorn'd with all the prerogatives that agree with them; which la&longs;t di&longs;cour&longs;e is hitherto much more likely, in my judgment, than that other. Therefore re­ &longs;olve, Simplicius, to produce all the particular rea&longs;ons, experi­ ments and ob&longs;ervations, as well Natural as A&longs;tronomical, that may &longs;erve to per&longs;wade us that the Earth differeth from the Cœ­ le&longs;tial bodies, is immoveable, and &longs;ituated in the Centre of the World, and what ever el&longs;e excludes its moving like to the Planets, as Jupiter or the Moon, &c. And Salviatus will be plea&longs;ed to be &longs;o civil as to an&longs;wer to them one by one.

SIMPL. See here for a beginning, two mo&longs;t convincing Argu­ ments to demon&longs;trate the Earth to be mo&longs;t different from the Cœle&longs;tial bodies. Fir&longs;t, the bodies that are generable, corru­ ptible, alterable, &c. are quite different from tho&longs;e that are in­ generable, incorruptible, unalterable, &c. But the Earth is ge­ nerable, corruptible, alterable, &c. and the Cœle&longs;tial bodies in­ generable, incorruptible, unalterable, &c. Therefore the Earth is quite different from the Cœle&longs;tial bodies.

SAGR. By your fir&longs;t Argument you &longs;pread the Table with the &longs;ame Viands, which but ju&longs;t now with much adoe were voided.

SIMPL. Hold a little, Sir, and take the re&longs;t along with you, and then tell me if this be not different from what you had be­ fore. In the former, the Minor was proved à priori, & now you &longs;ee it proved à po&longs;teriori: Judg then if it be the &longs;ame. I prove the Minor, therefore (the Major being mo&longs;t manife&longs;t) by &longs;en&longs;ible ex­ perience, which &longs;hews us that in the Earth there are made conti­ nual generations, corruptions, alterations, &c. which neither our &longs;en&longs;es, nor the traditions or memories of our Ance&longs;tors, ever &longs;aw an in&longs;tance of in Heaven; therefore Heaven is unalterable, &c. and the Earth alterable, &c. and therefore different from Hea­ ven. I take my &longs;econd Argument from a principal and e&longs;&longs;ential accident, and it is this. That body which is by its nature ob­ &longs;cure and deprived of light, is divers from the luminous and &longs;hi­ ning bodies; but the Earth is ob&longs;cure and void of light, and the Cœle&longs;tial bodies &longs;plendid, and full of light; Ergo, &c. An&longs;wer to the&longs;e Arguments fir&longs;t, that we may not heap up too many, and then I will alledge others.

Heaven immuta­ ble, becau&longs;e there never was any mu­ tation &longs;een in it.

Bodies naturally lucid, are different from tho&longs;e which are by nature ob­ &longs;cure.

SALV. As to the fir&longs;t, the &longs;tre&longs;&longs;e whereof you lay upon ex­ perience, I de&longs;ire that you would a little more di&longs;tinctly produce me the alteration which you &longs;ee made in the Earth, and not in Heaven; upon which you call the Earth alterable, and the Hea­ vens not &longs;o.

SIMPL. I &longs;ee in the Earth, plants and animals continually ge­ nerating and decaying; winds, rains, tempe&longs;ts, &longs;torms ari&longs;ing; and in a word, the a&longs;pect of the Earth to be perpetually metamorpho­ &longs;ing; none of which mutations are to be di&longs;cern'd in the Cœle&longs;tial bodies; the con&longs;titution and figuration of which is mo&longs;t punctu­ ally conformable to that they ever were time out of mind; without the generation of any thing that is new, or corruption of any thing that was old.

SALV. But if you content your &longs;elf with the&longs;e vi&longs;ible, or to &longs;ay better, &longs;een experiments, you mu&longs;t con&longs;equently account China and America Cœle&longs;tial bodies, for doubtle&longs;&longs;e you never beheld in them the&longs;e alterations which you &longs;ee here in Italy, and that therefore according to your apprehen&longs;ion they are inal­ terable.

SIMPL. Though I never did &longs;ee the&longs;e alterations &longs;enfibly in tho&longs;e places, the relations of them are not to be que&longs;tioned; be&longs;ides that, cum eadem &longs;it ratio totius, & partium, tho&longs;e Countreys being a part of the Earth, as well as ours, they mu&longs;t of nece&longs;&longs;ity be alterable as the&longs;e are.

SALV. And why have you not, without being put to believe other mens relations, examined and ob&longs;erved tho&longs;e alterations with your own eyes?

SIMPL. Becau&longs;e tho&longs;e places, be&longs;ides that they are not ex­ po&longs;ed to our eyes, are &longs;o remote, that our &longs;ight cannot reach to comprehend therein &longs;uch like mutations.

SALV. See now, how you have unawares di&longs;covered the falla­ cy of your Argument; for, if you &longs;ay that the alterations that are &longs;een on the Earth neer at hand, cannot, by rea&longs;on of the too great di&longs;tance, be &longs;een in America, much le&longs;&longs;e can you &longs;ee them in the Moon, which is &longs;o many hundred times more remote: And if you believe the alterations in Mexico upon the report of tho&longs;e that come from thence, what intelligence have you from the Moon, to a&longs;&longs;ure you that there is no &longs;uch alterations in it? Therefore, from your not &longs;eeing any alterations in Heaven, whereas, if there were any &longs;uch, you could not &longs;ee them by rea­ &longs;on of their too great di&longs;tance, and from your not having intel­ ligence thereof, in regard that it cannot be had, you ought not to argue, that there are no &longs;uch alterations; howbeit, from the &longs;eeing and ob&longs;erving of them on Earth, you well argue that therein &longs;uch there are.

SIMPL. I will &longs;hew &longs;o great mutations that have befaln on the Earth; that if any &longs;uch had happened in the Moon, they might very well have been ob&longs;erved here below. We find in very antient records, that heretofore at the Streights of Gibraltar, the two great Mountains Abila, and Calpen, were continued to­ gether by certain other le&longs;&longs;e Mountains which there gave check to the Ocean: but tho&longs;e Hills, being by &longs;ome cau&longs;e or other &longs;e­ parated, and a way being opened to the Sea to break in, it made &longs;uch an inundation, that it gave occa&longs;ion to the calling of it &longs;ince the Mid-land Sea: the greatne&longs;s whereof con&longs;idered, and the di­ vers a&longs;pect the &longs;urface of the Water and Earth then made, had it been beheld afar off, there is no doubt but &longs;o great a change might have been di&longs;cerned by one that was then in the Moon; as al&longs;o to us inhabitants of the Earth, the like alterations would be perceived in the Moon; but we find not in antiquity, that e­ ver there was &longs;uch a thing &longs;een; therefore we have no cau&longs;e to &longs;ay, that any of the Cœle&longs;tial bodies are alterable, &c.

The Mediterr ani­ an Sea made by the &longs;eparation of Abi­ la and Calpen.

SALV. That &longs;o great alterations have hapned in the Moon, I dare not &longs;ay, but for all that, I am not yet certain but that &longs;uch changes might occur; and becau&longs;e &longs;uch a mutation could onely repre&longs;ent unto us &longs;ome kind of variation between the more clear, and more ob&longs;cure parts of the Moon, I know not whether we have had on Earth ob&longs;ervant Selenographers, who have for any con&longs;iderable number of years, in&longs;tructed us with &longs;o exact Seleno­ graphy, as that we &longs;hould confidently conclude, that there hath no &longs;uch change hapned in the face of the Moon; of the figura­ tion of which I find no more particular de&longs;cription, than the &longs;ay­ ing of &longs;ome, that it repre&longs;ents an humane face; of others, that it is like the muzzle of a lyon; and of others, that it is Cain with a bundle of thorns on his back: therefore, to &longs;ay Heaven is un­ alterable, becau&longs;e that in the Moon, or other Cœle&longs;tial bodies, no &longs;uch alterations are &longs;een, as di&longs;cover them&longs;elves on Earth, is a bad illation, and concludeth nothing.

SAGR. And there is another odd kind of &longs;cruple in this Argu­ ment of Simplicius, running in my mind, which I would gladly have an&longs;wered; therefore I demand of him, whether the Earth before the Mediterranian inundation was generable and corrupti­ ble, or el&longs;e began then &longs;o to be?

SIMPL. It was doubtle&longs;s generable and corruptible al&longs;o be­ fore that time; but that was &longs;o va&longs;t a mutation, that it might have been ob&longs;erved as far as the Moon.

SAGR. Go to; if the Earth was generable and corruptible before that Inundation, why may not the Moon be &longs;o like­ wi&longs;e without &longs;uch a change? Or why &longs;hould that be nece&longs;&longs;ary in the Moon, which importeth nothing on Earth?

SALV. It is a &longs;hrewd que&longs;tion: But I am doubtfull that Sim­ plicius a little altereth the Text of Ari&longs;totle, and the other Peri­ patelicks, who &longs;ay, they hold the Heavens unalterable, for that they &longs;ee therein no one &longs;tar generate or corrupt, which is proba­ bly a le&longs;s part of Heaven, than a City is of the Earth, and yet innumerable of the&longs;e have been de&longs;troyed, &longs;o as that no mark of them hath remain'd.

SAGR. I verily believed otherwi&longs;e, and conceited that Sim­ plicius di&longs;&longs;embled this expo&longs;ition of the Text, that he might not charge his Ma&longs;ter and Con&longs;ectators, with a notion more ab&longs;urd than the former. And what a folly it is to &longs;ay the Cœle&longs;tial part is unalterable, becau&longs;e no &longs;tars do generate or corrupt there­ in? What then? hath any &longs;een a Terre&longs;trial Globe corrupt, and another regenerate in its place? And yet is it not on all hands granted by Philo&longs;ophers, that there are very few &longs;tars in Heaven le&longs;s than the Earth, but very many that are much bigger? So that for a &longs;tar in Heaven to corrupt, would be no le&longs;s than if the whole Terre&longs;trial Globe &longs;hould be de&longs;troy'd. Therefore, if for the true proof of generation and corruption in the Univer&longs;e, it be nece&longs;&longs;ary that &longs;o va&longs;t bodies as a &longs;tar, mu&longs;t corrupt and regene­ rate, you may &longs;atisfie your &longs;elf and cea&longs;e your opinion; for I a&longs;&longs;ure you, that you &longs;hall never &longs;ee the Terre&longs;trial Globe or any other integral body of the World, to corrupt or decay &longs;o, that having been beheld by us for &longs;o many years pa&longs;t, they &longs;hould &longs;o di&longs;&longs;olve, as not to leave any foot&longs;teps of them.

Its no le&longs;s impo&longs;&longs;i­ ble for a &longs;tar to corrupt, than for the whole Terre­ &longs;trial Globe.

SALV. But to give Simplicius yet fuller &longs;atisfaction, and to reclaim him, if po&longs;&longs;ible, from his error; I affirm, that we have in our age new accidents and ob&longs;ervations, and &longs;uch, that I que&longs;tion not in the lea&longs;t, but if Ari&longs;totle were now alive, they would make him change his opinion; which may be ea&longs;ily collected from the very manner of his di&longs;cour&longs;ing: For when he writeth that he e­ &longs;teemeth the Heavens inalterable, &c. becau&longs;e no new thing was &longs;een to be begot therein, or any old to be di&longs;&longs;olved, he &longs;eems im­ plicitely to hint unto us, that when he &longs;hould &longs;ee any &longs;uch acci­ dent, he would hold the contrary; and confront, as indeed it is meet, &longs;en&longs;ible experiments to natural rea&longs;on: for had he not made any reckoning of the &longs;en&longs;es, he would not then from the not &longs;eeing of any &longs;en&longs;ible mutation, have argued immutability.

Ari&longs;totle would change his opinion, did he &longs;ee the no­ velties of our age.

SIMPL. Ari&longs;totle deduceth his principal Argument à priori, &longs;hewing the nece&longs;&longs;ity of the inalterability of Heaven by natural, manife&longs;t and clear principles; and then &longs;tabli&longs;heth the &longs;ame à po­ &longs;teriori, by &longs;en&longs;e, and the traditions of the antients.

SALV. This you &longs;peak of is the Method he hath ob&longs;erved in delivering his Doctrine, but I do not bethink it yet to be that wherewith he invented it; for I do believe for certain, that he fir&longs;t procured by help of the &longs;en&longs;es, &longs;uch experiments and ob&longs;er­ vations as he could, to a&longs;&longs;ure him as much as it was po&longs;&longs;ible, of the conclu&longs;ion, and that he afterwards &longs;ought out the means how to demon&longs;trate it: For this, the u&longs;ual cour&longs;e in demon&longs;trative Scien­ ces, and the rea&longs;on thereof is, becau&longs;e when the conclu&longs;ion is true, by help of re&longs;olutive Method, one may hit upon &longs;ome pro­ po&longs;ition before demon&longs;trated, or come to &longs;ome principle known per &longs;e; but if the conclu&longs;ion be fal&longs;e, a man may proceed in in­ finitum, and never meet with any truth already known; but ve­ ry oft he &longs;hall meet with &longs;ome impo&longs;&longs;ibility or manife&longs;t ab&longs;urdi­ ty. Nor need you que&longs;tion but that Pythagoras along time be­ fore he found the demon&longs;tration for which he offered the Heca­ tomb, had been certain, that the &longs;quare of the &longs;ide &longs;ubtending the right angle in a rectangle triangle, was equal to the &longs;quare of the other two &longs;ides: and the certainty of the conclu&longs;ion condu­ ced not a little to the inve&longs;tigating of the demon&longs;tration, un­ der&longs;tanding me alwayes to mean in demon&longs;trative Sciences. But what ever was the method of Ari&longs;totle, and whether his arguing à priori preceded &longs;en&longs;e à po&longs;teriori, or the contrary; it &longs;ufficeth that the &longs;ame Ari&longs;totle preferreth (as hath been oft &longs;aid) &longs;en&longs;ible ex­ periments before all di&longs;cour&longs;es; be&longs;ides, as to the Arugments à priori their force hath been already examined. Now returning to my purpo&longs;ed matter, I &longs;ay, that the things in our times di&longs;­ covered in the Heavens, are, and have been &longs;uch, that they may give ab&longs;olute &longs;atisfaction to all Philo&longs;ophers; fora&longs;much as in the particular bodies, and in the univer&longs;al expan&longs;ion of Heaven, there have been, and are continually, &longs;een ju&longs;t &longs;uch accidents as we call generations and corruptions, being that excellent A­ &longs;tronomers have ob&longs;erved many Comets generated and di&longs;&longs;olved in parts higher than the Lunar Orb, be&longs;ides the two new Stars, Anuo 1572, and Anno 1604, without contradiction much higher than all the Planets; and in the face of the Sun it &longs;elf, by help of the Tele&longs;cope, certain den&longs;e and ob&longs;cure &longs;ub&longs;tances, in &longs;em­ blance very like to the foggs about the Earth, are &longs;een to be produced and di&longs;&longs;olved; and many of the&longs;e are &longs;o va&longs;t, that they far exceed not only the Mediterranian Streight, but all Affrica and A&longs;ia al&longs;o. Now if Ari&longs;totle had &longs;een the&longs;e things, what think you he would have &longs;aid, and done Simplicius?

The certaixty of the conclu&longs;ion hel­ peth by are&longs;olutive method to &longs;ind the demonstration.

Pythagoras offered an Hecatomb for a Geometrical de­ mon&longs;tration which he found.

New &longs;tars di&longs;co­ vered in Heaven.

Spots generate and di&longs;&longs;olve in the face of the Sun.

Solar spots are bigger than all&longs;ia and Affrick.

SIMPL. I know not what Ari&longs;totle would have done or &longs;aid, that was the great Ma&longs;ter of all the Sciences, but yet I know in part, what his Sectators do and &longs;ay, and ought to do and &longs;ay, unle&longs;&longs;e they would deprive them&longs;elves of their guide, leader, and Prince in Philo&longs;ophy. As to the Comets, are not tho&longs;e Modern A&longs;tronomers, who would make them Cœle&longs;tial, convinced by the ^{*}Anti-Tycho, yea, and overcome with their own weapons, I mean by way of Paralaxes and Calculations, every way tryed, concluding at the la&longs;t in favour of Aristotle, that they are all Elementary? And this being overthrown, which was as it were their foundation, have the&longs;e Novelli&longs;ts any thing more where­ with to maintain their a&longs;&longs;ertion?

* A&longs;tronomers con­ futed by Anti-Ty­ cho.

SALV. Hold a little, good Simplicius, this modern Author, what &longs;aith he to the new Stars, Anno 1572, and 1604, and to the Solar &longs;pots? for as to the Comets, I for my own particular little care to make them generated under or above the Moon; nor did I ever put much &longs;tre&longs;&longs;e on the loquacity of Tycho; nor am I hard to believe that their matter is Elementary, and that they may elevate (&longs;ublimate) them&longs;elves at their plea&longs;ure, with­ out meeting with any ob&longs;tacle from the impenetrability of the Peripatetick Heaven, which I hold to be far more thin, yielding, and &longs;ubtil than our Air; and as to the calculations of the Pa­ rallaxes, fir&longs;t, the uncertainty whether Comets are &longs;ubject to &longs;uch accidents, and next, the incon&longs;tancy of the ob&longs;ervations, upon which the computations are made, make me equally &longs;u&longs;­ pect both tho&longs;e opinions: and the rather, for that I &longs;ee him you call Anti-Tycho, &longs;ometimes &longs;tretch to his purpo&longs;e, or el&longs;e reject tho&longs;e ob&longs;ervations which interfere with his de&longs;ign.

Anti-Tycho wre­ &longs;teth A&longs;tronomical ob&longs;ervations to his own parpo&longs;e.

SIMPL. As to the new Stars, Anti-Tycho extricates him&longs;elf finely in three or four words; &longs;aying, That tho&longs;e mo­ dern new Stars are no certain parts of the Cœle&longs;tial bodies, and that the adver&longs;aries, if they will prove alteration and genera­ tion in tho&longs;e &longs;uperior bodies, mu&longs;t &longs;hew &longs;ome mutations that have been made in the Stars de&longs;cribed &longs;o many ages pa&longs;t, of which there is no doubt but that they be Cœle&longs;tial bodies, which they can never be able to do: Next, as to tho&longs;e mat­ ters which &longs;ome affirm, to generate and di&longs;&longs;ipate in the face of the Sun, he makes no mention thereof; wherefore I conclude, that he believed them fictious, or the illu&longs;ions of the Tube, or at mo&longs;t, &longs;ome petty effecs cau&longs;ed by the Air, and in brief, any thing rather than matters Cœle&longs;tial.

SALV. But you, Simplicius, what an&longs;wer could you give to the oppo&longs;ition of the&longs;e importunate &longs;pots which are &longs;tarted up to di&longs;turb the Heavens, and more than that, the Peripatetick Philo&longs;ophy? It cannot be but that you, who are &longs;o re&longs;olute a Champion of it, have found &longs;ome reply or &longs;olution for the &longs;ame, of which you ought not to deprive us.

SIMPL. I have heard &longs;undry opinions about this particular. One &longs;aith: “They are Stars which in their proper Orbs, like as Venus and Mervury, revolve about the Sun, and in pa&longs;&longs;ing un­ der it, repre&longs;ent them&longs;elves to us ob&longs;cure; and for that they are many, they oft happen to aggregate their parts together, and afterwards &longs;eperate again. Others believe them to be aerial impre&longs;&longs;ions; others, the illu&longs;ions of the chry&longs;tals; and o­ thers, other things: But I incline to think, yea am verily per­ &longs;waded, That they are an aggregate of many &longs;everal opacous bodies, as it were ca&longs;ually concurrent among them&longs;elves. And therefore we often &longs;ee, that in one of tho&longs;e &longs;pots one may number ten or more &longs;uch &longs;mall bodies, which are of irregu­ lar figures, and &longs;eem to us like flakes of &longs;now, or flocks of wooll, or moaths flying: they vary &longs;ite among&longs;t them&longs;elves, and one while &longs;ever, another while meet, and mo&longs;t of all be­ neath the Sun, about which, as about their Centre, they con­ tinually move. But yet, mu&longs;t we not therefore grant, that they are generated or di&longs;&longs;olved, but that at &longs;ometimes they are hid behind the body of the Sun, and at other times, though remote from it, yet are they not &longs;een for the vicinity of the immea&longs;urable light of the Sun; in regard that in the eccentrick Orb of the Sun, there is con&longs;tituted, as it were, an Onion, com­ po&longs;ed of many folds one within another, each of which, being ^{*}&longs;tudded with certain &longs;mall &longs;pots, doth move; and albeit their motion at fir&longs;t &longs;eemeth incon&longs;tant and irregular, yet neverthe­ le&longs;&longs;e, it is &longs;aid at la&longs;t, to be ob&longs;erved that the very &longs;ame &longs;pots, as before,” do within a determinate time return again. This &longs;eemeth to me the fitte&longs;t an&longs;wer that hath been found to a&longs;&longs;igne a rea&longs;on of that &longs;ame appearance, and withal to maintain the incorruptability and ingenerability of the Heavens; and if this doth not &longs;uffice; there wants not more elevated wits, which will give you other, more convincing.

Sundry opinions touching the Solar &longs;pots.

* The Original &longs;aith [tempe&longs;tata &longs;i muove] which the Latine Tran&longs;lati­ on, (Mi&longs;taking Tempectata, aword in Heraldry, for Tempe&longs;tato,) ren­ dereth [incitata movetur] which &longs;ignifieth a violent tran&longs;portmeut, as in a &longs;torm, that of a Ship.

SALV. If this of which we di&longs;pute, were &longs;ome point of Law, or other part of the Studies called Humanity, wherein there is neither truth nor fal&longs;hood, if we will give &longs;ufficient credit to the acutene&longs;&longs;e of the wit, readine&longs;&longs;e of an&longs;wers, and the gene­ ral practice of Writers, then he who mo&longs;t aboundeth in the&longs;e, makes his rea&longs;on more probable and plau&longs;ible; but in Natural Sciences, the conclu&longs;ions of which are true and nece&longs;&longs;ary, and wherewith the judgment of men hath nothing to do, one is to be more cautious how he goeth about to maintain any thing that is fal&longs;e; for a man but of an ordinary wit, if it be his good for­ tune to be of the right &longs;ide, may lay a thou&longs;and Demo&longs;thenes and a thou&longs;and Ari&longs;totles at his feet. Therefore reject tho&longs;e hopes and conceits, wherewith you flatter your &longs;elf, that there can be any men &longs;o much more learned, read, and ver&longs;ed in Authors, than we, that in de&longs;pite of nature, they &longs;hould be able to make that become true, which is fal&longs;e. And &longs;eeing that of all the opinions that have been hitherto alledged touching the e&longs;­ &longs;ence of the&longs;e Solar &longs;pots, this in&longs;tanced in by you, is in your judgment the true&longs;t, it followeth (if this be &longs;o) that all the re&longs;t are fal&longs;e; and to deliver you from this al&longs;o, which doubtle&longs;&longs;e is a mo&longs;t fal&longs;e Chimœra, over-pa&longs;&longs;ing infinite other improbabilities that are therein, I &longs;hall propo&longs;e again&longs;t it onely two experiments; one is, that many of tho&longs;e &longs;pots are &longs;een to ari&longs;e in the mid&longs;t of the Solar ring, and many likewi&longs;e to di&longs;&longs;olve and vani&longs;h at a great di&longs;tance from the circumference of the Sun; a nece&longs;&longs;ary Argu­ ment that they generate and di&longs;&longs;olve; for if without generating or corrrupting, they &longs;hould appear there by onely local motion, they would all be &longs;een to enter, and pa&longs;s out by the extreme cir­ cumference. The other ob&longs;ervation to &longs;uch as are not &longs;ituate in the lowe&longs;t degree of ignorance in Per&longs;pective, by the mutation of the appearing figures, and by the apparent mutations of the velocity of motion is nece&longs;&longs;arily concluding, that the &longs;pots are contiguous to the body of the Sun, and that touching its &longs;uperfi­ cies, they move either with it or upon it, and that they in no wi&longs;e move in circles remote from the &longs;ame. The motion proves it, which towards the circumference of the Solar Circle, appeareth very &longs;low, and towards the mid&longs;t, more &longs;wift; the fi­ gures of the &longs;pots confirmeth it, which towards the circumference appear exceeding narrow in compari&longs;on of that which they &longs;eem to be in the parts nearer the middle; and this becau&longs;e in the mid&longs;t they are &longs;een in their full lu&longs;ter, and as they truly be; and towards the circumference by rea&longs;on of the convexity of the glo­ bous &longs;uperficies, they &longs;eem more compre&longs;&longs;'d: And both the&longs;e diminutions of figure and motion, to &longs;uch as know how to ob&longs;erve and calculate them exactly, preci&longs;ely an&longs;wer to that which &longs;hould appear, the &longs;pots being contiguous to the Sun, and differ irrecon­ cileably from a motion in circles remote, though but for &longs;mal intervalls from the body of the Sun; as hath been diffu&longs;ely de­ mon&longs;trated by our ^{*} Friend, in his Letters about the Solar &longs;pots, to Marcus Vel&longs;erus. It may be gathered from the &longs;ame muta­ tion of figure, that none of them are &longs;tars, or other bodies of &longs;pherical figure; for that among&longs;t all figures the &longs;phere never appeareth compre&longs;&longs;ed, nor can ever be repre&longs;ented but onely per­ fectly round; and thus in ca&longs;e any particular &longs;pot were a round body, as all the &longs;tars are held to be, the &longs;aid roundne&longs;s would as well appear in the mid&longs;t of the Solar ring, as when the &longs;pot is near the extreme: whereas, its &longs;o great compre&longs;&longs;ion, and &longs;hewing its &longs;elf &longs;o &longs;mall towards the extreme, and contrariwi&longs;e, &longs;patious and large towards the middle, a&longs;&longs;ureth us, that the&longs;e &longs;pots are flat plates of &longs;mall thickne&longs;s or depth, in compari&longs;on of their length and breadth. La&longs;tly, whereas you &longs;ay that the &longs;pots after their determinate periods are ob&longs;erved to return to their former a&longs;pect, believe it not, Simplicius, for he that told you &longs;o, will deceive you; and that I &longs;peak the truth, you may ob&longs;erve them to be hid in the face of the Sun far from the circumference; nor hath your Ob&longs;ervator told you a word of that compre&longs;&longs;ion, which nece&longs;&longs;a­ rily argueth them to be contiguous to the Sun. That which he tells you of the return of the &longs;aid &longs;pots, is nothing el&longs;e but what is read in the forementioned Letters, namely, that &longs;ome of them may &longs;ometimes &longs;o happen that are of &longs;o long a duration, that they cannot be di&longs;&longs;ipated by one &longs;ole conver&longs;ion about the Sun, which is accompli&longs;hed in le&longs;s than a moneth.

In natural Sci­ ences, the art of Oratory is of no force.

An Argument that nece&longs;&longs;arily proveth the Solar &longs;pots to generate and di&longs;&longs;olwe.

A conclu&longs;ive de­ mon&longs;tration, that the &longs;pots are conti­ guous to the body of the Sun.

The motion of the spots towards the circumference of the Sun appears &longs;low.

The figure of the spots appears nar­ row towards the circumference of the Suns di&longs;cus, & why.

* Under this word Friend, as al&longs;o that of Academick, & Common Friend, Galilœus mode&longs;tly conceals him&longs;elf throughout the&longs;e Dialogues.

The Solar spots are not &longs;pherical, but flat like thin plates.

SIMPL. I, for my part, have not made either &longs;o long, or &longs;o exact ob&longs;ervations, as to enable me to boa&longs;t my &longs;elf Ma&longs;ter of the Quod ect of this matter: but I will more accurately con&longs;ider the &longs;ame, and make tryal my &longs;elf for my own &longs;atisfaction, whether I can reconcile that which experience &longs;hews us, with that which Ari&longs;totle teacheth us; for it's a certain Maxim, that two Truths cannot be contrary to one another.

SALV. If you would reconcile that which &longs;en&longs;e &longs;heweth you, with the &longs;olider Doctrines of Ari&longs;totle, you will find no great dif­ ficulty in the undertaking; and that &longs;o it is, doth not Ari&longs;totle &longs;ay, that one cannot treat confidently of the things of Heaven, by rea&longs;on of their great remotene&longs;s?

One cannot (&longs;aith Ari&longs;totle) &longs;peak confidently of Hea­ ven, by rea&longs;on of its great di&longs;tance.

SIMPL. He expre&longs;ly &longs;aith &longs;o.

Ari&longs;totle prefers &longs;en&longs;e before ratio­ cination.

SALV. And doth he not likewi&longs;e affirm, that we ought to pre­ fer that which &longs;en&longs;e demon&longs;trates, before all Arguments, though in appearance never &longs;o well grounded? and &longs;aith he not this without the lea&longs;t doubt or hæ&longs;itation?

SIMPL. He doth &longs;o.

SALV. Why then, the &longs;econd of the&longs;e propo&longs;itions, which are both the doctrine of Ari&longs;totle, that &longs;aith, that &longs;en&longs;e is to take

place of Logick, is a doctrine much more &longs;olid and undoubted, than that other which holdeth the Heavens to be unalterable; and therefore you &longs;hall argue more Ari&longs;totelically, &longs;aying, the Hea­ vens are alterable, for that &longs;o my &longs;en&longs;e telleth me, than if you &longs;hould &longs;ay, the Heavens are u alterable, for that Logick &longs;o per&longs;wa­ ded Aristotle. Furthermore, we may di&longs;cour&longs;e of Cœle&longs;tial mat­ ters much better than Ari&longs;totle; becau&longs;e, he confe&longs;&longs;ing the know­ ledg thereof to be difficult to him, by rea&longs;on of their remotene&longs;s from the &longs;en&longs;es, he thereby acknowledgeth, that one to whom the &longs;en&longs;es can better repre&longs;ent the &longs;ame, may philo&longs;ophate upon them with more certainty. Now we by help of the Tele&longs;cope, are brought thirty or forty times nearer to the Heavens, than ever Ari&longs;totle came; &longs;o that we may di&longs;cover in them an hundred things, which he could not &longs;ee, and among&longs;t the re&longs;t, the&longs;e &longs;pots in the Sun, which were to him ab&longs;olutely invi&longs;ible; therefore we may di&longs;cour&longs;e of the Heavens and Sun, with more certainty than Ari&longs;tolte.

Its a doctrine more agreeing withri&longs;totle, to &longs;ay the Heavens are alter­ able, than that which affirms them inalterable.

We may by help of the Tele&longs;cope di&longs;­ cour&longs;e better of cœ­ le&longs;tial matters, than Ari&longs;tot. him­ &longs;elf.

SAGR. I &longs;ee into the heart of Simplicius, and know that he is much moved at the &longs;trength of the&longs;e &longs;o convincing Arguments; but on the other &longs;ide, when he con&longs;idereth the great authority which Ari&longs;totle hath won with all men, and remembreth the great number of famous Interpreters, which have made it their bu&longs;ine&longs;s to explain his &longs;en&longs;e; and &longs;eeth other Sciences, &longs;o nece&longs;&longs;ary and profitable to the publick, to build a great part of their e&longs;teem and reputation on the credit of Ari&longs;totle he is much puzzled and perplexed: and methinks I hear him &longs;ay, To whom then &longs;hould we repair for the deci&longs;ion of our controver&longs;ies, if Ari&longs;totle were removed from the chair? What other Author &longs;hould we follow in the Schools, Academies and Studies? What Philo&longs;opher hath writ all the parts of Natural Philo&longs;ophy, and that &longs;o methodically without omitting &longs;o much as one &longs;ingle conclu&longs;ion? Shall we then overthrow that Fabrick under which &longs;o many pa&longs;&longs;engers find &longs;helter? Shall we de&longs;troy that A&longs;ylum, that Prytaneum, where­ in &longs;o many Students meet with commodious harbour, where without expo&longs;ing them&longs;elves to the injuries of the air, with the onely turning over of a few leaves, one may learn all the &longs;e­ crets of Nature? Shall we di&longs;mantle that fort in which we are &longs;afe from all ho&longs;tile a&longs;&longs;aults? But I pitie him no more than I do that Gentleman who with great expence of time and trea&longs;ure, and the help of many hundred arti&longs;ts, erects a very &longs;umptu­ ous Pallace, and afterwards beholds it ready to fall, by rea&longs;on of the bad foundation; but being extremely unwilling to &longs;ee the Walls &longs;tript which are adorned with &longs;o many beautifull Pictures; or to &longs;uffer the columns to fall, that uphold the &longs;tate­ ly Galleries; or the gilded roofs, chimney-pieces, the freizes, the corni&longs;hes of marble, with &longs;o much co&longs;t erected, to be rui­ ned; goeth about with girders, props, &longs;hoars, buttera&longs;&longs;es, to pre­ vent their &longs;ubver&longs;ion.

The Declamation of Simplicius.

SALV. But ala&longs;s, Simplicius as yet fears no &longs;uch fall, and I would undertake to &longs;ecure him from that mi&longs;chief at a far le&longs;s charge. There is no danger that &longs;o great a multitude of &longs;ubtle and wi&longs;e Philo&longs;ophers, &longs;hould &longs;uffer them&longs;elves to be Hector'd by one or two, who make a little blu&longs;tering; nay, they will rather, without ever turning the points of their pens again&longs;t them, by their &longs;ilence onely render them the object of univer&longs;al &longs;corn and contempt. It is a fond conceit for any one to think to introduce new Philo&longs;ophy, by reproving this or that Author: it will be fir&longs;t nece&longs;&longs;ary to new-mold the brains of men, and make them apt to di&longs;tingui&longs;h truth from fal&longs;hood. A thing which onely God can do. But from one di&longs;cour&longs;e to another whither are we &longs;tray'd? your memory mu&longs;t help to guide me into the way again.

Peripatetick Phi­ lo&longs;ophy unchange­ able.

SIMPL. I remember very well where we left. We were upon the an&longs;wer of Anti-Tycho, to the objections again&longs;t the immutability of the Heavens, among which you in&longs;erted this of the Solar fpots, not &longs;poke of by him; and I believe you intended to examine his an&longs;wer to the in&longs;tance of the New Stars.

SALV. Now I remember the re&longs;t, and to proceed, Methinks there are &longs;ome things in the an&longs;wer of Anti-Tycho, worthy of reprehen&longs;ion. And fir&longs;t, if the two New Stars, which he can do no le&longs;s than place in the uppermo&longs;t parts of the Heavens, and which were of a long duration, but finally vani&longs;hed, give him no ob&longs;truction in maintaining the inalterability of Heaven, in that they were not certain parts thereof, nor mutations made in the antient Stars, why doth he &longs;et him&longs;elf &longs;o vigorou&longs;ly and earne&longs;tly again&longs;t the Comets, to bani&longs;h them by all ways from the Cœle­ &longs;tial Regions? Was it not enough that he could &longs;ay of them the &longs;ame which he &longs;poke of the New &longs;tars? to wit, that in re­ gard they were no certain parts of Heaven, nor mutations made in any of the Stars, they could no wi&longs;e prejudice either Heaven, or the Doctrine of Ari&longs;totle? Secondly, I am not very well &longs;atis­ fied of his meaning; when he &longs;aith that the alterations that &longs;hould be granted to be made in the Stars, would be de&longs;tructive to the prerogative of Heaven; namely, its incorruptibility, &c. and this, becau&longs;e the Stars are Cœle&longs;tial &longs;ub&longs;tances, as is manife&longs;t by the con&longs;ent of every one; and yet is nothing troubled that the &longs;ame alterations &longs;hould be made ^{*} without the Stars in the re&longs;t of the Cœle&longs;tial expan&longs;ion. Doth he think that Heaven is no Cœle&longs;tial &longs;ub&longs;tance? I, for my part, did believe that the Stars were called Cœle&longs;tial bodies, by rea&longs;on that they were in Hea­ ven, or for that they were made of the &longs;ub&longs;tance of Heaven; and yet I thought that Heaven was more Cœle&longs;tial than they; in like &longs;ort, as nothing can be &longs;aid to be more Terre&longs;trial, or more fiery than the Earth or Fire them&longs;elves. And again, in that he ne­ ver made any mention of the Solar &longs;pots, which have been evi­ dently demon&longs;trated to be produced, and di&longs;&longs;olved, and to be neer the Sun, and to turn either with, or about the &longs;ame, I have rea&longs;on to think that this Author probably did write more for others plea&longs;ure, than for his own &longs;atisfaction; and this I affirm, fora&longs;­ much as he having &longs;hewn him&longs;elf to be skilful in the Mathema­ ticks, it is impo&longs;&longs;ible but that he &longs;hould have been convinced by Demon&longs;trations, that tho&longs;e &longs;ub&longs;tances are of nece&longs;&longs;ity contigu­ ous with the body of the Sun, and are &longs;o great generations and corruptions, that none comparable to them, ever happen in the Earth: And if &longs;uch, &longs;o many, and &longs;o frequent be made in the very Globe of the Sun, which may with rea&longs;on be held one of the noble&longs;t parts of Heaven, what &longs;hould make us think that others may not happen in the other Orbs?

* Ex tra Stellas.

Generability and alteration is a greater perfection in the Worlds bo­ dies than the con­ trary qualities.

SAGR. I cannot without great admiration, nay more, deni­ al of my under&longs;tanding, hear it to be attributed to natural bodies, for a great honour and perfection that they are ^{*} impa&longs;&longs;ible, im­ mutable, inalterable, &c. And on the contrary, to hear it to

be e&longs;teemed a great imperfection to be alterable, generable, mu­ table, &c. It is my opinion that the Earth is very noble and ad­ mirable, by rea&longs;on of &longs;o many and &longs;o different alterations, mu­ tations, generations, &c. which are ince&longs;&longs;antly made therein; and if without being &longs;ubject to any alteration, it had been all one va&longs;t heap of &longs;and, or a ma&longs;&longs;e of Ja&longs;per, or that in the time of the Deluge, the waters freezing which covered it, it had continued an immen&longs;e Globe of Chri&longs;tal, wherein nothing had ever grown, altered, or changed, I &longs;hould have e&longs;teemed it a lump of no benefit to the World, full of idlene&longs;&longs;e, and in a word &longs;uperfluous, and as if it had never been in nature; and &longs;hould make the &longs;ame difference in it, as between a living and dead creature: The like I &longs;ay of the Moon, Jupiter, and all the other Globes of the World. But the more I dive into the con­ &longs;ideration of the vanity of popular di&longs;cour&longs;es, the more empty and &longs;imple I find them. And what greater folly can there be imagined, than to call Jems, Silver and Gold pretious; and Earth and dirt vile? For do not the&longs;e per&longs;ons con&longs;ider, that if there &longs;hould be as great a &longs;carcity of Earth, as there is of Jewels and pretious metals, there would be no Prince, but would gladly give a heap of Diamonds and Rubies, and many Wedges of Gold, to purcha&longs;e onely &longs;o much Earth as &longs;hould &longs;uffice to plant a Ge&longs;&longs;e­ mine in a little pot, or to &longs;et therein a China Orange, that he might &longs;ee it &longs;prout, grow up, and bring forth &longs;o goodly leaves, &longs;o odi­ riferous flowers, and &longs;o delicate fruit? It is therefore &longs;carcity and plenty that make things e&longs;teemed and contemned by the vulgar; who will &longs;ay that &longs;ame is a mo&longs;t beautiful Diamond, for that it re&longs;embleth a cleer water, and yet will not part with it for ten Tun of water: The&longs;e men that &longs;o extol incorruptibility, inalte­ rability, &c. &longs;peak thus I believe out of the great de&longs;ire they have to live long, and for fear of death; not confidering, that if men had been immortal, they &longs;hould have had nothing to do in the World. The&longs;e de&longs;erve to meet with a Medu&longs;a's head, that would transform them into Statues of Dimond and Ja&longs;per, that &longs;o they might become more perfect than they are.

* Impatible.

The Earth very noble, by rea&longs;on of the many mutati­ ons made therein.

The carth unpro­ &longs;itable and full of idlene&longs;&longs;e, its alte­ rations taken away

The Earth more noble than Gold and Jewels.

Scarcity and plen­ ty enhan&longs;e and de­ ba&longs;e the price of things.

Incorruptibility e­ &longs;teemed by the vul­ gar out of their fear of death.

The di&longs;paragers of corraptibility de­ &longs;erve to be turned into Statua's.

SALV. And it may be &longs;uch a Metamorpho&longs;is would not be al­ together unprofitable to them; for I am of opinion that it is bet­ ter not to di&longs;cour&longs;e at all, than to argue erroniou&longs;ly.

SIMPL. There is not the lea&longs;t que&longs;tion to be made, but that the Earth is much more perfect, being as it is alterable, mutable, &c. than if it had been a ma&longs;&longs;e of &longs;tone; yea although it were one entire Diamond, mo&longs;t hard and impa&longs;&longs;ile. But look how mueh the&longs;e qualifications enoble the Earth, they render the Heavenly bodies again on the other &longs;ide &longs;o much the more imperfect, in which, &longs;uch conditions would be &longs;uperfluous; in regard that the Cœle&longs;tial bodies, namely, the Sun, Moon, and the other Stars, which are ordained for no other u&longs;e but to &longs;erve the Earth, need no other qualities for attaining of that end, &longs;ave onely tho&longs;e of light and motion.

The Cœle&longs;tial bo­ dies de&longs;igned to &longs;erve the Earth, need no more but motion and light.

SAGR. How? Will you affirm that nature hath produced and de&longs;igned &longs;o many va&longs;t perfect and noble Cœle&longs;tial bodies, impa&longs;­ &longs;ible, immortal, and divine, to no other u&longs;e but to &longs;erve the pa&longs;­ &longs;ible, frail, and mortal Earth? to &longs;erve that which you call the dro&longs;&longs;e of the World, and &longs;ink of all uncleanne&longs;&longs;e? To what purpo&longs;e were the Cœle&longs;tial bodies made immortal, &c. to &longs;erve a frail, &c. Take away this &longs;ub&longs;erviency to the Earth, and the in­ numerable multitude of Cœle&longs;tial bodies become wholly unu&longs;e­ ful, and &longs;uperfluous, &longs;ince they neither have nor can have any mutual operation betwixt them&longs;elves; becau&longs;e they are all unal­ terable, immutable, impa&longs;&longs;ible: For if, for Example, the Moon be impa&longs;&longs;ible, what influence can the Sun or any other Star have upon her? it would doubtle&longs;&longs;e have far le&longs;&longs;e effect upon her, than that of one who would with his looks or imagination, lignifie a piece of Gold. Moreover, it &longs;eemeth to me, that whil&longs;t the Cœ­ le&longs;tial bodies concurre to the generation and alteration of the Earth, they them&longs;elves are al&longs;o of nece&longs;&longs;ity alterable; for other­ wi&longs;e I cannot under&longs;tand how the application of the Sun or Moon to the Earth, to effect production, &longs;hould be any other than to lay a marble Statue by a Womans &longs;ide, and from that conjunction to expect children.

Celestial bodies want an inter­ changeable opera­ tion upon each o­ ther.

Alterability, &c. are not in the whole Terre&longs;trial Globe, but in &longs;ome of its parts.

SIMPL. Corruptibility, alteration, mutation, &c. are not in the whole Terre&longs;trial Globe, which as to its whole, is no le&longs;&longs;e eter­ nal than the Sun or Moon, but it is generable and corruptible as to its external parts; but yet it is al&longs;o true that likewi&longs;e in them ge­ neration and corruption are perpetual, and as &longs;uch require the heavenly eternal operations; and therefore it is nece&longs;&longs;ary that the Cœle&longs;tial bodies be eternal.

SAGR. All this is right; but if the corruptibility of the &longs;uper­ ficial parts of the Earth be nowi&longs;e prejudicial to the eternity of its whole Globe, yea, if their being generable, corruptible, alter­ able, &c. gain them great ornament and perfection; why can­

not, and ought not you to admit alteration, generation, &c. like­ wi&longs;e in the external parts of the Cœle&longs;tial Globes, adding to them ornament, without taking from them perfection, or berea­ ving them of action; yea rather encrea&longs;ing their effects, by grant­ ing not onely that they all operate on the Earth, but that they mu­ tually operate upon each other, and the Earth al&longs;o upon them all?

Cœle&longs;tial bodies alterable in their outward parts.

SIMPL. This cannot be, becau&longs;e the generations, mutations, &c. which we &longs;hould &longs;uppo&longs;e v. g. in the Moon; would be vain and u&longs;ele&longs;&longs;e, & natura nihil fru&longs;tra facit.

SAGR. And why &longs;hould they be vain and u&longs;ele&longs;&longs;e?

SIMPL. Becau&longs;e we cleerly &longs;ee, and feel with our hands, that all generations, corruptions, &c. made in the Earth, are all ei­ ther mediately or immediately directed to the u&longs;e, convenience, and benefit of man; for the u&longs;e of man are hor&longs;es brought forth, for the feeding of hor&longs;es, the Earth produceth gra&longs;&longs;e, and the Clouds water it; for the u&longs;e and nouri&longs;hment of man, herbs, corn, fruits, bea&longs;ts, birds, fi&longs;hes, are brought forth; and in &longs;um, if we &longs;hould one by one dilligently examine and re&longs;olve all the&longs;e things, we &longs;hould find the end to which they are all directed, to be the nece&longs;&longs;ity, u&longs;e, convenience, and delight of man. Now of what u&longs;e could the generations which we &longs;uppo&longs;e to be made in the Moon or other Planets, ever be to mankind? unle&longs;&longs;e you &longs;hould &longs;ay that there were al&longs;o men in the Moon, that might enjoy the benefit thereof; a conceit either fabulous or impious.

The generations & mutations happen­ ing in the Earth, are all for the good of Man.

SAGR. That in the Moon or other Planets, there are genera­ ted either herbs, or plants, or animals, like to ours, or that there are rains, winds, or thunders there, as about the Earth, I nei­ ther know, nor believe, and much le&longs;&longs;e, that it is inhabited by men: but yet I under&longs;tand not, becau&longs;e there are not genera­ ted things like to ours, that therefore it nece&longs;&longs;arily followeth, that no alteration is wrought therein, or that there may not be other things that change, generate, and di&longs;&longs;olve, which are not onely different from ours, but exceedingly beyond our imagina­ tion, and in a word, not to be thought of by us. And if, as I am certain, that one born and brought up in a &longs;patious Forre&longs;t, among&longs;t bea&longs;ts and birds, and that hath no knowledg at all of the Element of Water, could never come to imagine another World to be in Nature, different from the Eatth, full of living crea­ tures, which without legs or wings &longs;wiftly move, and not upon the &longs;urface onely, as bea&longs;ts do upon the Earth, but in the very bowels thereof; and not onely move, but al&longs;o &longs;tay them&longs;elves and cea&longs;e to move at their plea&longs;ure, which birds cannot do in the air; and that moreover men live therein, and build Palaces and Cities, and have &longs;o great convenience in travailing, that without the lea&longs;t trouble, they can go with their Family, Hou&longs;e, and whole Cities, to places far remote, like as I &longs;ay, I am certain, &longs;uch a per&longs;on, though of never &longs;o piercing an imagination, could never fancy to him&longs;elf Fi&longs;hes, the Ocean, Ships, Fleets, Arma­ do's at Sea; thus, and much more ea&longs;ily, may it happn, that in the Moon, remote from us by &longs;o great a &longs;pace, and of a &longs;ub­ &longs;tance perchance very different from the Earth, there may be mat­ ters, and operations, not only wide off, but altogether beyond all our imaginations, as being &longs;uch as have no re&longs;emblance to ours, and therefore wholly inexcogitable, in regard, that what we imagine to our &longs;elves, mu&longs;t nece&longs;&longs;arily be either a thing already &longs;een, or a compo&longs;ition of things, or parts of things &longs;een at ano­ ther time; for &longs;uch are the Sphinxes, Sirenes, Chimœra's, Cen­ taurs, &c.

The Moon hath no generatings of things, like as we have, nor is it in­ habited by men.

In the Moon may be a generation of things different from ours.

He that had not heard of the Ele­ ment of Water, could never fancy to him&longs;elf Ships and Fi&longs;hes.

SALV. I have very often let my fancy ruminate upon the&longs;e &longs;pe­ culations, and in the end, have thought that I had found &longs;ome things that neither are nor can be in the Moon; but yet I have not found therein any of tho&longs;e which I believe are, and may be there, &longs;ave onely in a very general acceptation, namely, things that adorn it by operating, moving and living; and perhaps in a way very different from ours; beholding and admiring the greatne&longs;s and beauty of the World, and of its Maker and Ruler, and with continual Encomiums &longs;inging his pray&longs;es; and in &longs;umme (which is that which I intend) doing what &longs;acred Writers &longs;o frequently af­ firm, to wit, all the creatures making it their perpetual imploy­ ment to laud God.

There may be &longs;ub­ &longs;tances in the Moon very diffe­ rent from ours.

SAGR. The&longs;e are the things, which &longs;peaking in general terms, may be there; but I would gladly hear you in&longs;tance in &longs;uch as you believe neither are nor can be there; which perchance may be more particularly named.

SALV. Take notice Sagredus that this will be the third time that we have unawares by running from one thing to another, lo&longs;t our principal &longs;ubject; and if we continue the&longs;e digre&longs;&longs;ions, it will be longere we come to a conclu&longs;ion of our di&longs;cour&longs;e; there­ fore I &longs;hould judg it better to remit this, as al&longs;o &longs;uch other points, to be decided on a particular occa&longs;ion.

SAGR. Since we are now got into the Moon, if you plea&longs;e, let us di&longs;patch &longs;uch things as concern her, that &longs;o we be not forced to &longs;uch another tedious journey.

SALV. It &longs;hall be as you would have it. And to begin with things more general, I believe that the Lunar Globe is far diffe­ rent from the Terre&longs;trial, though in &longs;ome things they agree. I will recount fir&longs;t their re&longs;emblances, and next their differences. The Moon is manife&longs;tly like to the Earth in figure, which undoubtedly is &longs;pherical, as may be nece&longs;&longs;arily concluded from the a&longs;pect of its &longs;urface, which is perfectly Orbicular, and the manner of its re­ ceiving the light of the Sun, from which, if its &longs;urface were flat, it would come to be all in one and the &longs;ame time illuminated, and likewi&longs;e again in another in&longs;tant of time ob&longs;cured, and not tho&longs;e parts fir&longs;t, which are &longs;ituate towards the Sun, and the re&longs;t &longs;ucce&longs;­ &longs;ively, &longs;o that in its oppo&longs;ition, and not till then, its whole apparent circumference is enlightned; which would happen quite contrary, if the vi&longs;ible &longs;urface were concave; namely, the illu­ mination would begin from the parts oppo&longs;ite or aver&longs;e to the Sun. Secondly &longs;he is as the Earth, in her &longs;elf ob&longs;cure and opacous, by which opacity it is enabled to receive, and reflect the light of the Sun; which were it not &longs;o, it could not do. Thirdly, I hold its matter to be mo&longs;t den&longs;e and &longs;olid as the Earth is, which I clearly argue from the unevenne&longs;s of its &longs;uperficies in mo&longs;t places, by means of the many eminencies and cavities di&longs;covered therein by help of the &longs;ele&longs;cope: of which eminencies there are many all over it, di­ rectly re&longs;embling our mo&longs;t &longs;harp and craggy mountains, of which you &longs;hall there perceive &longs;ome extend and run in ledges of an hun­ dred miles long; others are contracted into rounder forms; and there are al&longs;o many craggy, &longs;olitary, &longs;teep and cliffy rocks. But that of which there are frequente&longs;t appearances, are certain Banks (I u&longs;e this word, becau&longs;e I cannot thing of another that better ex­ pre&longs;&longs;eth them) pretty high rai&longs;ed, which environ and inclo&longs;e fields of &longs;everal bigne&longs;&longs;es, and form &longs;undry figures, but for the mo&longs;t part circular; many of which have in the mid&longs;t a mount rai&longs;ed pretty high, and &longs;ome few are repleni&longs;hed with a matter &longs;omewhat ob­ &longs;cure, to wit, like to the great &longs;pots di&longs;cerned by the bare eye, and the&longs;e are of the greate&longs;t magnitude; the number moreover of tho&longs;e that are le&longs;&longs;er and le&longs;&longs;er is very great, and yet almo&longs;t all circular. Fourthly, like as the &longs;urface of our Globe is di&longs;tingui&longs;hed into two principal parts, namely, into the Terre&longs;trial and Aquatick: &longs;o in the Lunar &longs;urface we di&longs;cern a great di&longs;tinction of &longs;ome great fields more re&longs;plendant, and &longs;ome le&longs;s: who&longs;e a&longs;pect makes me believe, that that of the Earth would &longs;eem very like it, beheld by any one from the Moon, or any other the like di&longs;tance, to be illuminated by the Sun: and the &longs;urface of the &longs;ea would appear more ob­ &longs;cure, and that of the Earth more bright. Fifthly, like as we from the Earth behold the Moon, one while all illuminated, another while half; &longs;ometimes more, &longs;ometimes le&longs;s; &longs;ometimes horned, &longs;ometimes wholly invi&longs;ibly; namely, when its ju&longs;t under the Sun beams; &longs;o that the parts which look towards the Earth are dark: Thus in every re&longs;pect, one &longs;tanding in the Moon would &longs;ee the illumination of the Earths &longs;urface by the Sun, with the &longs;ame periods to an hair, and under the &longs;ame changes of figures. Sixtly, -----

The Fir&longs;t re&longs;em­ blance between the Moon and Earth; which is that of figure; is proved by the manner of be­ ing illuminated by the Sun.

The Second con­ formity is the Moons being opa­ cous as the Earth.

Thirdly, The mat­ ter of the Moon is den&longs;e and mo ita­ nous as the Earth.

Fourthly, The Moon is di&longs;tin­ gui&longs;hed into two different parts for clarity and ob&longs;cu­ rity, as the Terre­ strial Globe into Sea and Land.

The &longs;urface of the Sea would &longs;hew at a di&longs;tance more ob­ &longs;oure than that of the Earth.

Fiftly, Muta­ tion of &longs;igures in the Earth, like to tho&longs;e of the Moon, and made with the &longs;ame periods.

SAGR. Stay a little, Salviatus; That the illumination of the Earth, as to the &longs;everal figures, would repre&longs;ent it &longs;elf to a per&longs;on placed in the Moon, like in all things to that which we di&longs;cover in the Moon, I under&longs;tand very well, but yet I cannot conceive how it &longs;hall appear to be done in the &longs;ame period; &longs;eeing that that which the Suns illumination doth in the Lunar &longs;uperficies in a month, it doth in the Terre&longs;trial in twenty four hours.

SALV. Its true, the effect of the Sun about the illuminating the&longs;e two bodies, and repleni&longs;hing with its &longs;plendor their whole &longs;urfaces, is di&longs;patch'd in the Earth in a Natural day, and in the Moon in a Month; but the variation of the figures in which the illuminated parts of the Terre&longs;trial &longs;uperficies appear beheld from the Moon, depends not on this alone, but on the divers a&longs;pects which the Moon is &longs;till changing with the Sun; &longs;o that, if for in­ &longs;tance, the Moon punctually followed the motion of the Sun, and &longs;tood, for example, always in a direct line between it and the Earth, in that a&longs;pect which we call Conjunction, it looking always to the &longs;ame Hemi&longs;phere of the Earth which the Sun looks unto, &longs;he would behold the &longs;ame all light: as on the contrary, if it &longs;hould always &longs;tay in Oppo&longs;ition to the Sun, it would never behold the Earth, of which the dark part would be continually turn'd towards the Moon, and therefore invi&longs;ible. But when the Moon is in Quadrature of the Sun, that half of the Terre&longs;trial Hemi&longs;phere ex­ po&longs;ed to the &longs;ight of the Moon which is towards the Sun, is lumi­ nous; and the other towards the contrary is ob&longs;cure: and there­ fore the illuminated part of the Earth would repre&longs;ent it &longs;elf to the Moon in a &longs;emi-circular figure.

SAGR. I clearly perceive all this, and under&longs;tand very well, that the Moon departing from its Oppo&longs;ition to the Sun, where it &longs;aw no part of the illumination of the Terre&longs;trial &longs;uperficies, and approaching day by day nearer the Sun, &longs;he begins by little and little to di&longs;cover &longs;ome part of the face of the illuminated Earth; and that which appeareth of it &longs;hall re&longs;emble a thin &longs;ickle, in regard the figure of the Earth is round: and the Moon thus acquiring by its motion day by day greater proximity to the Sun, &longs;ucce&longs;&longs;ively di&longs;covers more and more of the Terre&longs;trial Hemi&longs;phere enlightned, &longs;o that at the Quadrature there is ju&longs;t half of it vi&longs;ible, in&longs;omuch that we may &longs;ee the other part of her: continuing next to proceed towards the Conjunction, it &longs;ucce&longs;&longs;ively di&longs;covers more and more of its &longs;urface to be illuminated, and in fine, at the time of Conjun­ ction &longs;eeth the whole Hemi&longs;phere enlightned. And in &longs;hort, I very well conceive, that what befalls the Inhabitants of the Earth, in beholding the changes of the Moon, would happen to him that from the Moon &longs;hould ob&longs;erve the Earth; but in a contrary order, namely, that when the Moon is to us at her full, and in Oppo&longs;ition to the Sun, then the Earth would be in Conjunction with the Sun, and wholly ob&longs;cure and invi&longs;ible; on the contrary, that po&longs;ition which is to us a Conjunction of the Moon with the Sun, and for that cau&longs;e a Moon &longs;ilent and un&longs;een, would be there an Oppo&longs;ition of the Earth to the Sun, and, to &longs;o &longs;peak, Full Earth, to wit, all enlightned. And la&longs;tly, look what part of the Lunar &longs;urface ap­ pears to us from time to time illuminated, &longs;o much of the Earth in the &longs;ame time &longs;hall you behold from the Moon to be ob&longs;cured: and look how much of the Moon is to us deprived of light, &longs;o much of the Earth is to the Moon illuminated. In one thing yet the&longs;e mutual operations in my judgment &longs;eem to differ, and it is, that it being &longs;uppo&longs;ed, and not granted, that &longs;ome one being placed in the Moon to ob&longs;erve the Earth, he would every day &longs;ee the whole Terre&longs;trial &longs;uperficies, by means of the Moons going about the Earth in twenty four or twenty five hours; but we never &longs;ee but half of the Moon, &longs;ince it revolves not in it &longs;elf, as it mu&longs;t do to be &longs;een in every part of it.

SALV. So that this, befals not contrarily, namely, that her re­ volving in her &longs;elf, is the cau&longs;e that we &longs;ee not the other half of her, for &longs;o it would be nece&longs;&longs;ary it &longs;hould be, if &longs;he had the Epicy­ cle. But what other difference have you behind, to exchange for this which you have named?

SAGR. Let me &longs;ee; Well for the pre&longs;ent I cannot think of any other.

SALV. And what if the Earth (as you have well noted) &longs;eeth no more than half the Moon, whereas from the Moon one may &longs;ee all the Earth; and on the contrary, all the Earth &longs;eeth the Moon, and but onely half of it &longs;eeth the Earth? For the inhabitants, to &longs;o &longs;peak, of the &longs;uperior Hemi&longs;phere of the Moon, which is to us invi&longs;ible, are deprived of the &longs;ight of the Earth: and the&longs;e haply are the Anticthones. But here I remember a particular accident, newly ob&longs;erved by our Academian, in the Moon, from whch are gathered two nece&longs;&longs;ary con&longs;equences; one is, that we &longs;ee &longs;omewhat more than half of the Moon; and the other is, that the motion of the Moon hath exact concentricity with the Earth: and thus he finds the Phœnomenon and ob&longs;ervation. When the Moon hath a cor­ re&longs;pondence and natural &longs;ympathy with the Earth, towards which it hath its a&longs;pect in &longs;uch a determinate part, it is nece&longs;&longs;ary that the right line which conjoyns their centers, do pa&longs;&longs;e ever by the &longs;ame point of the Moons &longs;uperficies; &longs;o that, who &longs;o &longs;hall from the cen­ ter of the Earth behold the &longs;ame, &longs;hall alwayes &longs;ee the &longs;ame Di&longs;cus or Face of the Moon punctually determined by one and the &longs;ame circumference; But if a man be placed upon the Terre­ &longs;trial &longs;urface, the ray which from his eye pa&longs;&longs;eth to the centre of the Lunar Globe, will not pa&longs;s by the &longs;ame point of its &longs;uperficies, by which the line pa&longs;&longs;eth that is drawn from the centre of the Earth to that of the Moon, &longs;ave onely when it is vertical to him: but the Moon being placed in the Ea&longs;t, or in the We&longs;t, the point of incidence of the vi&longs;ual ray, is higher than that of the line which conjoyns the centres; and therefore the ob&longs;erver may di&longs;cern &longs;ome part of the Lunar Hemi&longs;phere towards the upper circumfe­ rence, and alike part of the other is invi&longs;ible: they are di&longs;cerna­ ble and undi&longs;cernable, in re&longs;pect of the Hemi&longs;phere beheld from the true centre of the Earth: and becau&longs;e the part of the Moons circumference, which is &longs;uperiour in its ri&longs;ing, is nethermo&longs;t in its &longs;etting; therefore the difference of the &longs;aid &longs;uperiour and inferi­ our parts mu&longs;t needs be very ob&longs;ervable; certain &longs;pots and other notable things in tho&longs;e parts, being one while di&longs;cernable, and another while not. A like variation may al&longs;o be ob&longs;erved towards the North and South extremities of the &longs;ame Di&longs;cus (or Surface) according as the Moons po&longs;ition is in one or the other Section of its Dragon; For, if it be North, &longs;ome of its parts towards the North are hid, and &longs;ome of tho&longs;e parts towards the South are di&longs;covered, and &longs;o on the contrary. Now that the&longs;e con&longs;equen­ ces are really true, is verified by the Tele&longs;cope, for there be in the Moon two remarkable &longs;pots, one of which, when the Moon is in the meridian, is &longs;ituate to the Northwe&longs;t, and the other is almo&longs;t diametrically oppo&longs;ite unto it; and the fir&longs;t of the&longs;e is vi­ &longs;ible even without the Tele&longs;cope; but the other is not. That to­ wards the Northwe&longs;t is a rea&longs;onable great &longs;pot of oval figure, &longs;e­ parated from the other great ones; the oppo&longs;ite one is le&longs;&longs;e, and al&longs;o &longs;evered from the bigge&longs;t, and &longs;ituate in a very cleer field; in both the&longs;e we may manife&longs;tly di&longs;cern the fore&longs;aid variations, and &longs;ee them one after another; now neer the edge or limb of the Lunar Di&longs;cus, and anon remote, with &longs;o great difference that the di&longs;tance betwixt the Northwe&longs;t and the circumference of the Di&longs;cus is more than twice as great at one time, as at the other; and as to the &longs;econd &longs;pot (becau&longs;e it is neerer to the circumfe­ rence) &longs;uch mutation importeth more, than twice &longs;o much in the former. Hence its manife&longs;t, that the Moon, as if it were drawn by a magnetick vertue, con&longs;tantly beholds the Terre&longs;trial Globe with one and the &longs;ame a&longs;pect, never deviating from the &longs;ame.

All the Earth &longs;eeth half onely of the Moon, & the half onely of the Moon &longs;eeth all the Earth.

From the Earth we &longs;ee more than half the Lunar Globe.

Two &longs;pots in the Moon, by which it is perceived that &longs;he hath respect to the centre of the Earth in her mo­ tion.

SAGR. Oh! when will there be an end put to the new ob­ &longs;ervations aud di&longs;coveries of this admirable In&longs;trument?

SALV. If this &longs;ucceed according to the progre&longs;&longs;e of other great inventions, it is to be hoped, that in proce&longs;&longs;e of time, one may arrive to the &longs;ight of things, to us at pre&longs;ent not to be imagined. But returning to our fir&longs;t di&longs;cour&longs;e, I &longs;ay for the &longs;ixth re&longs;emblance betwixt the Moon and Earth, that as the Moon for a great part of time, &longs;upplies the want of the Suns light, and makes the nights, by the reflection of its own, rea&longs;onable clear; &longs;o the Earth, in recompence, affordeth it when it &longs;tands in mo&longs;t need, by reflecting the Solar rayes, a very cleer illumination, and &longs;o much, in my opinion, greater than that which cometh from her to us, by how much the &longs;uperficies of the Earth is greater than that of the Moon.

Sixthly, The Earth and Moon interchangeably do illuminate.

SAGR. Hold there, Salviatus hold there, and permit me the plea&longs;ure of relating to you, how at this fir&longs;t hint I have penetrated the cau&longs;e of an accident, which I have a thou&longs;and times thought upon, but could never find out. You would &longs;ay, that the imper­ fect light which is &longs;een in the Moon, e&longs;pecially when it is horned, comes from the reflection of the light of the Sun on the Superfi­ cies of the Earth and Sea; and that light is more clear, by how much the horns are le&longs;&longs;e, for then the luminous part of the Earth, beheld by the Moon, is greater, according to that which was a little before proved; to wit, that the luminous part of the Earth, expo&longs;ed to the Moon, is alway as great as the ob&longs;cure part of the Moon, that is vi&longs;ible to the Earth; whereupon, at &longs;uch time as the Moon is &longs;harp-forked, and con&longs;equently its tenebrous part great, great al&longs;o is the illuminated part of the Earth beheld from the Moon, and its reflection of light &longs;o much the more potent.

Light reflected from the Earth in­ to the Moon.

SALV. This is exactly the &longs;ame with what I was about to &longs;ay. In a word, it is a great plea&longs;ure to &longs;peak with per&longs;ons judicious and apprehen&longs;ive, and the rather to me, for that while&longs;t others conver&longs;e and di&longs;cour&longs;e touching Axiomatical truths, I have ma­ ny times creeping into my brain &longs;uch arduous Paradoxes, that though I have a thou&longs;and times rehear&longs;ed this which you at the ve­ ry fir&longs;t, have of your &longs;elf apprehended, yet could I never beat it into mens brains.

SIMPL. If you mean by your not being able to per&longs;wade them to it, that you could not make them under&longs;tand the &longs;ame, I much wonder thereat, and am very confident that if they did not under&longs;tand it by your demon&longs;tration (your way of expre&longs;&longs;ion, being, in my judgment, very plain) they would very hardly have apprehended it upon the explication of any other man; but if you mean you have not per&longs;waded them, &longs;o as to make them be­ lieve it, I wonder not, in the lea&longs;t, at this; for I confe&longs;&longs;e my &longs;elf to be one of tho&longs;e who under&longs;tand your di&longs;cour&longs;es, but am not &longs;atisfied therewith; for there are in this, and &longs;ome of the other &longs;ix congruities, or re&longs;emblances, many difficulties, which I &longs;hall in&longs;tance in, when you have gone through them all.

SALV. The de&longs;ire I have to find out any truth, in the acqui&longs;t whereof the objections of intelligent per&longs;ons (&longs;uch as your &longs;elf) may much a&longs;&longs;i&longs;t me, will cau&longs;e me to be very brief in di&longs;patching that which remains. For a &longs;eventh conformity, take their reci­ procal re&longs;pon&longs;ion as well to injuries, as favours; whereby the Moon, which very often in the height of its illumination, by the interpo&longs;ure of the Earth betwixt it and the Sun, is deprived of light, and eclip&longs;ed, doth by way of revenge; in like manner, in­ terpo&longs;e it &longs;elf between the Earth and the Sun, and with its &longs;hadow ob&longs;cureth the Earth; and although the revenge be not an&longs;wer­ able to the injury, for that the Moon often continueth, and that for a rea&longs;onable long time, wholly immer&longs;ed in the Earths &longs;hadow, but never was the Earth wholly, nor for any long time, eclip&longs;ed by the Moon; yet, neverthele&longs;&longs;e, having re&longs;pect to the &longs;malne&longs;&longs;e of the body of this, in compari&longs;on to the magnitude of the other, it cannot be denied but that the will and as it were valour of this, is very great. Thus much for their con­ gruities or re&longs;emblances. It &longs;hould next follow that we di&longs;cour&longs;e touching their di&longs;parity; but becau&longs;e Simplicius will favour us with his objections again&longs;t the former, its nece&longs;&longs;ary that we hear and examine them, before we proceed any farther.

Seventhly, The Earth and Moon do mutually eclip&longs;e.

SAGR. And the rather, becau&longs;e it is to be &longs;uppo&longs;ed that Simplicius will not any wayes oppo&longs;e the di&longs;parities, and incon­ gruities betwixt the Earth and Moon, &longs;ince that he accounts their &longs;ub&longs;tances extremely different.

SIMPL. Among&longs;t the re&longs;emblances by you recited, in the pa­ rallel you make betwixt the Earth and Moon, I find that I can admit none confidently &longs;ave onely the fir&longs;t, and two others; I grant the fir&longs;t, namely, the &longs;pherical figure; howbeit, even in this there is &longs;ome kind of difference, for that I hold that of the Moon to be very &longs;mooth and even, as a looking-gla&longs;&longs;e, where­ as, we find and feel this of the Earth to be extraordinary montu­ ous and rugged; but this belonging to the inequality of &longs;uperfi­ cies, it &longs;hall be anon con&longs;idered, in another of tho&longs;e Re&longs;emblan­ ces by you alledged; I &longs;hall therefore re&longs;erve what I have to &longs;ay thereof, till I come to the con&longs;ideration of that. Of what you affirm next, that the Moon &longs;eemeth, as you &longs;ay in your &longs;econd Re&longs;emblance, opacous and ob&longs;cure in its &longs;elf, like the Earth; I admit not any more than the fir&longs;t attribute of opacity, of which the Eclip&longs;es of the Sun a&longs;&longs;ure me. For were the Moon tran&longs;pa­ rent, the air in the total ob&longs;curation of the Sun, would not be­ come &longs;o duski&longs;h, as at &longs;uch a time it is, but by means of the tran&longs;parency of the body of the Moon, a refracted light would pa&longs;&longs;e through it, as we &longs;ee it doth through the thicke&longs;t clouds. But as to the ob&longs;curity, I believe not that the Moon is wholly depri­ ved of light, as the Earth; nay, that clarity which is &longs;een in the remainder of its Di&longs;cus, over and above the &longs;mall cre&longs;cent en­ lightened by the Sun, I repute to be its proper and natural light, and not a reflection of the Earth, which I e&longs;teem unable, by rea&longs;on of its a&longs;perity (craggine&longs;&longs;e) and ob&longs;curity, to reflect the raies of the Sun. In the third Parallel I a&longs;&longs;ent unto you in one part, and di&longs;&longs;ent in another: I agree in judging the body of the Moon to be mo&longs;t &longs;olid and hard, like the Earth, yea much more; for if from Ari&longs;totle we receive that the Heavens are impenetrable, and the Stars the mo&longs;t den&longs;e parts of Heaven, it mu&longs;t nece&longs;&longs;arily follow, that they are mo&longs;t &longs;olid and mo&longs;t impenetrable.

The &longs;econd clarity of the Moon e­ &longs;teemed to be its native light.

The Earth unable to reflect the Suns raies.

The &longs;ub&longs;tance of the Heavens impe­ netrable, accord­ ing to Ari&longs;totle.

SAGR. What excellent matter would the Heavens afford us for to make Pallaces of, if we could procure a &longs;ub&longs;tance &longs;o hard and &longs;o tran&longs;parent?

SALV. Rather how improper, for being by its tran&longs;parence, wholly invi&longs;ible, a man would not be able without &longs;tumbling at the thre&longs;holds, and breaking his head again&longs;t the Walls, to pa&longs;s from room to room.

SAGR. This danger would not befall him, if it be true, as &longs;ome Peripateticks &longs;ay, that it is intangible: and if one cannot touch it, much le&longs;s can it hurt him.

The &longs;ubstance of Heaven intangi­ ble.

SALV. This would not &longs;erve the turn, for though the matter of the Heavens cannot be toucht, as wanting tangible qualities: yet may it ea&longs;ily touch the elementary bodies; and to offend us it is as &longs;ufficient that it &longs;trike us, nay wor&longs;e, than if we &longs;hould &longs;trike it. But let us leave the&longs;e Pallaces, or, to &longs;ay better, the&longs;e Ca&longs;tles in the air, and not interrupt Simplicius.

SIMPL. The que&longs;tion which you have &longs;o ca&longs;ually &longs;tarted, is one of the mo&longs;t difficulty that is di&longs;puted in Philo&longs;ophy; and I have on that &longs;ubject mo&longs;t excellent conceits of a very learned Doctor of Padoua, but it is not now time to enter upon them. Therefore returning to our purpo&longs;e, I &longs;ay that the Moon, in my opinion, is much more &longs;olid than the Earth, but do not infer the &longs;ame, as you do, from the craggine&longs;s and montuo&longs;ity of its &longs;uperficies; but rather from the contrary, namely, from its aptitude to receive (as we &longs;ee it experimented in the harde&longs;t &longs;tones) a poli&longs;h and lu&longs;tre exceeding that of the &longs;moothe&longs;t gla&longs;s, for &longs;uch nece&longs;&longs;arily mu&longs;t its &longs;uperficies be, to render it apt to make &longs;o lively reflection of the Suns rays. And for tho&longs;e appearances which you mention, of Mountains, Cliffs, Hills, Valleys, &c. they are all illu&longs;ions: and I have been pre&longs;ent at certain publick di&longs;putes, where I have heard it &longs;trongly maintained again&longs;t the&longs;e introducers of novelties, that &longs;uch appearances proceed from nothing el&longs;e, but from the un­ equal di&longs;tribution of the opacous and per&longs;picuous parts, of which the Moon is inwardly and outwardly compo&longs;ed: as we &longs;ee it often fall out in chry&longs;tal, amber, and many other precious &longs;tones of perfect lu&longs;tre; in which by rea&longs;on of the opacity of &longs;ome parts, and the tran&longs;parency of others, there doth appear &longs;everal conca­ vities and prominencies. In the fourth re&longs;emblance, I grant, that the &longs;uperficies of Terre&longs;trial Globe beheld from afar, would make two different appearances, namely, one more clear, the other more dark; but I believe that &longs;uch diver&longs;ity would &longs;ucceed quite con­ trary to what you &longs;ay; that is, I hold that the &longs;urface of the wa­ ter would appear lucid, becau&longs;e that it is &longs;mooth and tran&longs;parent; and that of the Earth would appear ob&longs;cure, by rea&longs;on of its o­ pacity and &longs;cabro&longs;ity, ill accommodated for reflecting the light of the Sun. Concernïng the fifth compari&longs;on, I grant it wholly, and am able, in ca&longs;e the Earth did &longs;hine as the Moon, to &longs;how the &longs;ame to any one that &longs;hould from thence above behold it, repre­ &longs;ented by figures an&longs;werable to tho&longs;e which we &longs;ee in the Moon: I comprehend al&longs;o, how the period of its illumination and varia­ tion of figure, would be monthly, albeit the Sun revolves round about it in twenty four hours: and la&longs;tly, I do not &longs;cruple to admit, that the half onely of the Moon &longs;eeth all the Earth, and that all the Earth &longs;eeth but onely half of the Moon. For what remains, I repute it mo&longs;t fal&longs;e, that the Moon can receive light from the Earth, which is mo&longs;t ob&longs;cure, opacous, and utterly un­ apt to reflect the Suns light, as the Moon doth reflect it to us: and as I have &longs;aid, I hold that that light which we &longs;ee in the remain­ der of the Moons face (the &longs;plendid cre&longs;cents &longs;ubducted) by the illumination, is the proper and natural light of the Moon, and no ea&longs;ie matter would induce me to believe otherwi&longs;e. The &longs;eventh, touching the mutual Eclip&longs;es, may be al&longs;o admitted; howbeit that is wont to be called the eclip&longs;e of the Sun, which you are plea&longs;ed to phra&longs;e the eclip&longs;e of the Earth. And this is what I have at this time to &longs;ay in oppo&longs;ition to your &longs;even congruities or re&longs;emblances, to which objections, if you are minded to make any reply, I &longs;hall willingly hear you.

The &longs;uperficies of the Moon more &longs;leek than any Looking-glaß.

The eminencies and cavities in the Moon are illu&longs;ions of its opacous and perspicuous parts.

SALV. If I have well apprehended what you have an&longs;wered, it &longs;eems to me, that there &longs;till remains in controver&longs;ie between us, cer­ tain conditions, which I made common betwixt the Moon & Earth, and they are the&longs;e; You e&longs;teem the Moon to be &longs;mooth and poli&longs;ht, as a Looking-gla&longs;s, and as &longs;uch, able to reflect the Suns light; and contrarily, the Earth, by rea&longs;on of its montuo&longs;ity, unable to make &longs;uch reflection: You yield the Moon to be &longs;olid and hard, and that you argue from its being &longs;mooth and polite, and not from its being montuous; and for its appearing montuous, you a&longs;&longs;ign as the cau&longs;e, that it con&longs;i&longs;ts of parts more and le&longs;s opacous and per&longs;pi­ cuous. And la&longs;tly, you e&longs;teem that &longs;econdary light, to be proper to the Moon, and not reflected from the Earth; howbeit you &longs;eem not to deny the &longs;ea, as being of a &longs;mooth &longs;urface, &longs;ome kind of reflection. As to the convincing you of that error, that the reflection of the Moon is made, as it were, like that of a Looking-gla&longs;s, I have &longs;mall hope, whil&longs;t I &longs;ee, that what hath been read in the ^{*} Saggiator and in the Solar Letters of our Com­ mon Friend, hath profited nothing in your judgment, if haply you have attentively read what he hath there written on this &longs;ub­ ject.

* Il Saggiatore, & Lettere Solari, two Treati&longs;es of Galilæus.

SIMPL. I have peru&longs;ed the &longs;ame &longs;o &longs;uperficially, according to the &longs;mall time of lea&longs;ure allowed me from more &longs;olid &longs;tudies; therefore, if you think you can, either by repeating &longs;ome of tho&longs;e rea&longs;ons, or by alledging others, re&longs;olve me the&longs;e doubts, I will hearken to them attentively.

SALV. I will tell you what comes into my mind upon the in&longs;tant, and its po&longs;&longs;ible it may be a commixtion of my own con­ ceipts; and tho&longs;e which I have &longs;ometime read in the fore-&longs;aid Books, by which I well remember, that I was then perfectly &longs;atisfied, although the conclu&longs;ions, at fir&longs;t &longs;ight &longs;eem'd unto me &longs;trange Paradoxes. We enquire Simplicius, whether to the ma­ king a reflection of light, like that which we receive from the Moon, it be nece&longs;&longs;ary that the &longs;uperficies from whence the refle­ ction commeth, be &longs;o &longs;mooth and polite, as the face of a Looking­ Gla&longs;&longs;e, or whether a &longs;uperficies not &longs;mooth or poli&longs;ht, but rough and uneven, be more apt for &longs;uch a purpo&longs;e. Now &longs;uppo&longs;ing two reflections &longs;hould come unto us, one more bright, the other le&longs;&longs;e, from two &longs;uperficies oppo&longs;ite unto us, I demand of you, which of the two &longs;uperficies you think would repre&longs;ent it &longs;elf to our &longs;ight, to be the cleare&longs;t, and which the ob&longs;cure&longs;t.

SIMPL. I am very confident, that that &longs;ame, which mo&longs;t for­ cibly reflected the light upon me, would &longs;hew its &longs;elf in its a&longs;pect the clearer, and the other darker.

SALV. Be plea&longs;ed to take that Gla&longs;&longs;e which hangs on yonder Wall, and let us go out into the Court-yard. Come Sagredus. Now hang the gla&longs;&longs;e yonder, again&longs;t that &longs;ame Wall, on which the Sun &longs;hines, and now let us with-draw our &longs;elves into the &longs;hade. See yonder two &longs;uperficies beaten by the Sun, namely, the Wall and the Gla&longs;&longs;e. Tell me now which appears cleare&longs;t unto you, that of the Wall or that of the Gla&longs;&longs;e? Why do you not an&longs;wer me?

It is proved at large that the Moons &longs;urface is &longs;harp.

SAGR. I leave the reply to Simplicius, who made the que&longs;ti­ on; but I, for my own part, am per&longs;waded upon this &longs;mall be­ ginning of the experiment, that the Moon mu&longs;t be of a very un­ poli&longs;ht &longs;urface.

SALV. What &longs;ay you Simplicius, if you were to depaint that Wall, and that Gla&longs;&longs;e fa&longs;tened unto it, where would you u&longs;e your darke&longs;t colours, in de&longs;igning the Wall, or el&longs;e in painting the Looking-Gla&longs;&longs;e.

SIMPL. Much the darker in depainting the Gla&longs;&longs;e.

SALV. Now if from the &longs;uperficies, which repre&longs;ents it &longs;elf more clear, there proceedeth a more powerful reflection of light, the Wall will more forcibly reflect the raies of the Sun, than the Gla&longs;&longs;e.

SIMPL. Very well, Sir, have you ever a better experiment than this? you have placed us where the Gla&longs;&longs;e doth not rever­ berate upon us; but come along with me a little this way; how, will you not &longs;tir?

SAGR. You perhaps &longs;eek the place of the reflection, which the Gla&longs;&longs;e makth.

SIMPL. I do &longs;o.

SAGR. Why look you, there it is upon the oppo&longs;ite Wall, ju&longs;t as big as the Gla&longs;&longs;e, and little le&longs;&longs;e bright than if the Sun had directly &longs;hined upon it.

SIMPL. Come hither therefore, and &longs;ee from hence the &longs;ur­ face of the Gla&longs;&longs;e, and tell me whether you think it more ob­ &longs;cure than that of the Wall.

SAGR. Look on it your &longs;elf, for I have no mind at this time, to dazle my eyes; and I know very well, without &longs;eeing it, that it there appears as &longs;plendid and bright as the Sun it &longs;elf, or little le&longs;&longs;e.

SIMPL. What &longs;ay you therefore, is the reflection of a Gla&longs;&longs;e le&longs;&longs;e powerful than that of a Wall? I &longs;ee, that in this oppo&longs;ite Wall, where the reflection of the other illuminated Wall comes, together with that of the Gla&longs;&longs;e, this of the Gla&longs;&longs;e is much clearer; and I &longs;ee likewi&longs;e, that, from this place where I &longs;tand, the gla&longs;&longs;e it &longs;elf appears with much more lu&longs;tre than the Wall.

SALV. You have prevented me with your &longs;ubtlety; for I &longs;tood in need of this very ob&longs;ervation to demon&longs;trate what remains. You &longs;ee then the difference which happens betwixt the two refle­ ctions made by the two &longs;uperficies of the Wall and Gla&longs;&longs;e, per­ cu'&longs;t in the &longs;elf-&longs;ame manner, by the rayes of the Sun; and you &longs;ee, how the reflection which comes from the Wall, diffu&longs;eth it &longs;elf towards all the parts oppo&longs;ite to it, but that of the Gla&longs;&longs;e goeth towards one part onely, not at all bigger than the Gla&longs;&longs;e it &longs;elf: you &longs;ee likewi&longs;e, how the &longs;uperficies of the Wall, beheld from what part &longs;oever, alwayes &longs;hews it &longs;elf of one and the &longs;ame cleerne&longs;&longs;e, and every way, much clearer than that of the Gla&longs;&longs;e, excepting only in that little place, on which the Gla&longs;&longs;es reflection reverberates, for from thence indeed the Gla&longs;&longs;e appears much more lucid than the Wall. By the&longs;e &longs;o &longs;en&longs;ible, and palpable experi­ ments, my thinks one may &longs;oon come to know, whether the reflection which the Moon &longs;ends upon us, proceed as from a Gla&longs;&longs;e, or el&longs;e, as from a Wall, that is, from a &longs;mooth &longs;uperfi­ cies, or a rugged.

SAGR. If I were in the Moon it &longs;elf, I think I could not with my hands more plainly feel the unevenne&longs;&longs;e of its &longs;uperficies, than I do now perceive it, by apprehending your di&longs;cour&longs;e. The Moon beheld in any po&longs;ture, in re&longs;pect of the Sun and us, &longs;heweth us its &longs;uperficies, touch't by the Suns rayes, alwayes equally clear; an effect, which an&longs;wers to an hair that of the Wall, which be­ held from what place &longs;oever, appeareth equally bright, and dif­ fereth from the Gla&longs;&longs;e, which from one place onely appeareth lu­ cid, and from all others ob&longs;cure. Moreover, the light which cometh to me from the reflection of the Wall, is tollerable, and weak, in compari&longs;on of that of the Gla&longs;&longs;e, which is little le&longs;&longs;e forcible and offen&longs;ive to the &longs;ight, than that primary and direct light of the Sun. And thus without trouble do we behold the face of the Moon; which were it as a Gla&longs;&longs;e, it appearing to us by rea&longs;on of its vicinity, as big as the Sun it &longs;elf, its &longs;plendor would be ab&longs;olutely intollerable, and would &longs;eem as if we beheld another Sun.

SALV. A&longs;cribe not, I be&longs;eech you Sagredus, more to my de­ mon&longs;tration, than it produceth. I will oppo&longs;e you with an in&longs;tance, which I &longs;ee not well how you can ea&longs;ily re&longs;olve. You in&longs;i&longs;t upon it as a grand difference between the Moon and Gla&longs;&longs;e, that it emits its reflection towards all parts equally, as doth the Wall; where­ as the Gla&longs;&longs;e ca&longs;ts it upon one onely determinate place; and from hence you conclude the Moon to be like to the Wall, and not to the Gla&longs;&longs;e: But I mu&longs;t tell you, that that &longs;ame Gla&longs;&longs;e ca&longs;ts its reflection on one place onely, becau&longs;e its &longs;urface is flat, and the reflex rayes being to depart at angles equal to tho&longs;e of the rayes of incidence, it mu&longs;t follow that from a plane or flat &longs;uperficies, they do depart unitedly towards the &longs;ame place; but in regard that the &longs;uperficies of the Moon is not plain, but &longs;pherical, and the incident rayes upon &longs;uch a &longs;uperficies, being to reflect them­ &longs;elves at angles equal to tho&longs;e of the incidence towards all parts, by means of the infinity of the inclinations which compo&longs;e the &longs;pherical &longs;uperficies, therefore the Moon may &longs;end forth its reflecti­ on every way; and there is no nece&longs;&longs;ity for its repercu&longs;&longs;ion upon one place onely, as that Gla&longs;&longs;e which is flat.

Flat Looking­ gla&longs;&longs;es ca&longs;t forth the reflection to­ wards but one place, but the &longs;pherical every way.

SIMPL. This is one of the very &longs;ame objections, which I in­ tended to have made again&longs;t him.

SAGR. If this be one, you had need have more of them; yet I tell you, that as to this fir&longs;t, it &longs;eems to me to make more a­ gain&longs;t you, than for you.

SIMPL. You have pronounced as a thing manife&longs;t, that the refle­ ction made by that Wall, is as cleer and lucid as that which the Moon &longs;ends forth, and I e&longs;teem it nothing in compari&longs;on thereto. “For, in this bu&longs;ine&longs;&longs;e of the illumination, its requi&longs;ite to re&longs;pect, and to di&longs;tingui&longs;h the Sphere of Activity; and who que&longs;tions but the Cœle&longs;tial bodies have greater Spheres of activity, than the&longs;e our elementary, frail, and mortal ones? and that Wall, finally, what el&longs;e is it but a little ob&longs;cure Earth, unapt to &longs;hine?”

The &longs;phere of Activity greater in the Cœle&longs;tial bodies than in Ele­ mentary.

SAGR. And here al&longs;o I believe, that you very much deceive your felf. But I come to the fir&longs;t objection moved by Salviatus; and I con&longs;ider, that to make a body appear unto us luminous, it &longs;uf­ ficeth not that the rayes of the illuminating body fall upon it, but it is moreover requi&longs;ite that the reflex rayes arrive to our eye; as is manife&longs;tly &longs;een in the example of that Gla&longs;&longs;e, upon which, without que&longs;tion, the illuminating rayes of the Sun do come; yet neverthele&longs;&longs;e, it appears not to us bright and &longs;hining, unle&longs;&longs;e we &longs;et our eye in that particular place, where the refle­ ction arriveth. Now let us con&longs;ider what would &longs;ucceed, were the gla&longs;&longs;e of a &longs;pherical figure; for without doubt, we &longs;hould find, that of the reflection made by the whole &longs;urface illumina­ ted, that to be but a very &longs;mall part, which arriveth to the eye of a particular beholder; by rea&longs;on that that is but an incon&longs;ide­ rable particle of the whole &longs;pherical &longs;uperficies, the inclination of which ca&longs;ts the ray to the particular place of the eye; whence the part of the &longs;pherical &longs;uperficies, which &longs;hews it &longs;elf &longs;hining to the eye, mu&longs;t needs be very &longs;mall; all the re&longs;t being repre­ &longs;ented ob&longs;cure. So that were the Moon &longs;mooth, as a Looking­ gla&longs;&longs;e, a very &longs;mall part would be &longs;een by any particular eye to be illu&longs;trated by the Sun, although its whole Hemi&longs;phere were ex­ po&longs;ed to the Suns rayes; and the re&longs;t would appear to the eye of the beholder as not illuminated, and therefore invi&longs;ible; and finally, the whole Moon would be likewi&longs;e invi&longs;ible, for &longs;o much as that particle, whence the reflection &longs;hould come, by rea&longs;on of its &longs;malne&longs;&longs;e and remotene&longs;&longs;e, would be lo&longs;t. And as it would be invi&longs;ible to the eye, &longs;o would it not afford any light; for it is al­ together impo&longs;&longs;ible, that a bright body &longs;hould take away our darkne&longs;&longs;e by its &longs;plendor, and we not to &longs;ee it.

The Moon if it were &longs;mooth, like a &longs;pherical gla&longs;&longs;e, would be invi&longs;ible.

SALV. Stay good Sagredus, for I &longs;ee &longs;ome emotions in the face and eyes of Simplicius, which are to me as indices that he is not either very apprehen&longs;ive of, or &longs;atisfied with this which you, with admirable proof, and ab&longs;olute truth have &longs;poken. And yet I now call to mind, that I can by another experiment remove all &longs;cruple. I have &longs;een above in a Chamber, a great &longs;pherical Looking-gla&longs;&longs;e; let us &longs;end for it hither, and while&longs;t it is in bringing, let Simplicius return to con&longs;ider, how great the clarity is which cometh to the Wall here, under the penthou&longs;e, from the reflection of the flat gla&longs;&longs;e.

SIMPL. I &longs;ee it is little le&longs;&longs;e &longs;hining, than if the Sun had di­ rectly beat upon it.

SALV. So indeed it is. Now tell me, if taking away that &longs;mall flat gla&longs;&longs;e, we &longs;hould put that great &longs;pherical one in the &longs;ame place, what effect (think you) would its reflection have upon the &longs;ame Wall?

SIMPL. I believe that it would eject upon it a far greater and more diffu&longs;ed light.

SALV. But if the illumination &longs;hould be nothing, or &longs;o &longs;mall, that you would &longs;car&longs;e di&longs;cern it, what would you &longs;ay then?

SIMPL. When I have &longs;een the effect, I will bethink my &longs;elf of an an&longs;wer.

SALV. See here is the gla&longs;&longs;e, which I would have to be placed clo&longs;e to the other. But fir&longs;t let us go yonder towards the reflection of that flat one, and attentively ob&longs;erve its clarity; &longs;ee how bright it is here where it &longs;hines, and how di&longs;tinctly one may di&longs;cern the&longs;e &longs;mall unevenne&longs;&longs;es in the Wall.

SIMPL. I have &longs;een and very well ob&longs;erved the &longs;ame, now place the other gla&longs;&longs;e by the &longs;ide of the fir&longs;t.

SALV. See where it is. It was placed there a&longs;&longs;oon as you be­ gan to look upon the Walls &longs;mall unevenne&longs;&longs;es, and you percei­ ved it not, &longs;o great was the encrea&longs;e of the light all over the re&longs;t of the Wall. Now take away the flat gla&longs;&longs;e. Behold now all refle­ ction removed, though the great convex gla&longs;&longs;e &longs;till remaineth. Remove this al&longs;o, and place it there again if you plea&longs;e, and you &longs;hall &longs;ee no alteration of light in all the Wall. See here then de­ mon&longs;trated to &longs;en&longs;e, that the reflection of the Sun, made upon a &longs;pherical convex gla&longs;&longs;e, doth not &longs;en&longs;ibly illuminate the places neer unto it. Now what &longs;ay you to this experiment?

SIMPL. I am afraid that there may be &longs;ome Leigerdemain, u&longs;ed in this affair; yet in beholding that gla&longs;&longs;e I &longs;ee it dart forth a great &longs;plendor, which dazleth my eyes; and that which im­ ports mo&longs;t of all, I &longs;ee it from what place &longs;oever I look upon it; and I &longs;ee it go changing &longs;ituation upon the &longs;uperficies of the gla&longs;&longs;e, which way &longs;oever I place my &longs;elf to look upon it; a nece&longs;&longs;ary ar­ gument, that the light is livelily reflected towards every &longs;ide, and con&longs;equently, as &longs;trongly upon all that Wall, as upon my eye.

SALV. Now you &longs;ee how cautiou&longs;ly and re&longs;ervedly you ought to proceed in lending your a&longs;&longs;ent to that, which di&longs;cour&longs;e alone re­ pre&longs;enteth to you. There is no doubt but that this which you &longs;ay, carrieth with it probability enough, yet you may &longs;ee, how &longs;en&longs;i­ ble experience proves the contrary.

SIMPL. How then doth this come to pa&longs;s?

SALV. I will deliver you my thoughts thereof, but I cannot tell how you may be plea&longs;'d therewith. And fir&longs;t, that lively &longs;plendor which you &longs;ee upon the gla&longs;s, and which you think occu­ pieth a good part thereof, is nothing near &longs;o great, nay is very ex­ ceeding &longs;mall; but its liveline&longs;s occa&longs;ioneth in your eye, (by means of the reflection made on the humidity of the extream parts of the eye-brows, which di&longs;tendeth upon the pupil) an adventitious irradi­ ation, like to that blaze which we think we &longs;ee about the flame of a candle placed at &longs;ome di&longs;tance; or if you will, you may re&longs;emble it to the adventitious &longs;plendor of a &longs;tar; for if you &longs;hould compare the &longs;mall body v. g. of the Canicula, &longs;een in the day time with the Tele&longs;cope, when it is &longs;een without &longs;uch irradiation, with the &longs;ame &longs;een by night by the eye it &longs;elf, you will doubtle&longs;s com­ prehend that being irradiated, it appeareth above a thou&longs;and times bigger than the naked and real body: and a like or greater augmentation doth the image of the Sun make, which you &longs;ee in that gla&longs;s. I &longs;ay greater, for that it is more lively than the &longs;tar, as is manife&longs;t from our being able to behold the &longs;tar with much le&longs;s offence, than this reflection of the gla&longs;s. The reverberation therefore which is to di&longs;pere it &longs;elf all over this wall, cometh from a &longs;mall part of that gla&longs;s, and that which even now came from the whole flat gla&longs;s di&longs;per&longs;ed and re&longs;train'd it &longs;elf to a very &longs;mall part of the &longs;aid wall. What wonder is it then, that the fir&longs;t re­ flection very lively illuminates, and that this other is almo&longs;t im­ perceptible?

The &longs;mall body of the &longs;tars fringed round about with rays, appeareth ve­ ry much biggerthan plain and naked, and in its native clarity.

SIMPL. I find my &longs;elf more perplexed than ever, and there pre&longs;ents it &longs;elf unto me the other difficulty, how it can be that that wall, being of a matter &longs;o ob&longs;cure, and of a &longs;uperficies &longs;o un­ poli&longs;h'd, &longs;hould be able to dart from it greater light, than a gla&longs;s very &longs;mooth and polite.

SALV. Greater light it is not, but more univer&longs;al; for as to the degree of brightne&longs;s, you &longs;ee that the reflection of that &longs;mall flat gla&longs;s, where it beamed forth yonder under the &longs;hadow of the penthou&longs;e, illuminateth very much; and the re&longs;t of the wall which receiveth the reflection of the wall on which the gla&longs;s is placed, is not in any great mea&longs;ure illuminated, as was the &longs;mall part on which the reflection of the gla&longs;s fell. And if you would under­ &longs;tand the whole of this bu&longs;ine&longs;s, you mu&longs;t con&longs;ider that the &longs;uper­ ficies of that wall's being rough, is the &longs;ame as if it were compo­ &longs;ed of innumerable &longs;mall &longs;uperficies, di&longs;po&longs;ed according to in­ numerable diver&longs;ities of inclinations: among&longs;t which it nece&longs;&longs;a­ rily happens, that there are many di&longs;po&longs;ed to &longs;end forth their reflex rays from them into &longs;uch a place, many others into another: and in &longs;um, there is not any place to which there comes not very many rays, reflected from very many &longs;mall &longs;uperficies, di&longs;per&longs;ed throughout the whole &longs;uperficies of the rugged body, upon which the rays of the Sun fall. From which it nece&longs;&longs;arily follow­ eth, That upon any, what&longs;oever, part of any &longs;uperficies, oppo&longs;ed to that which receiveth the primary incident rays, there is produced reflex rays, and con&longs;equently illumi­ nation. There doth al&longs;o follow thereupon, That the &longs;ame body upon which the illuminating rays fall, beheld from what&longs;oever place, appeareth all illuminated and &longs;hining: and therefore the Moon, as being of a &longs;uperficies rugged and not &longs;mooth, beameth forth the light of the Sun on every &longs;ide, and to all beholders appeareth equally lucid. But if the &longs;urface of it, being &longs;pherical, were al&longs;o &longs;mooth as a gla&longs;s, it would become wholly invi&longs;ible; fora&longs;much as that &longs;mall part, from which the image of the Sun &longs;hould be reflected unto the eye of a particular per&longs;on, by rea&longs;on of its great di&longs;tance would be in­ vi&longs;ible, as I have &longs;aid before.

The reflex light of uneven bodies, is more univer&longs;al than that of the &longs;mooth, & why.

The Moon, if it were &longs;mooth and &longs;leek, would be in­ vi&longs;ible.

SIMPL. I am very apprehen&longs;ive of your di&longs;cour&longs;e; yet me­ thinks I am able to re&longs;olve the &longs;ame with very little trouble; and ea&longs;ily to maintain, that the Moon is rotund and polite, and that it reflects the Suns light unto us in manner of a gla&longs;s; nor there­ fore ought the image of the Sun to be &longs;een in the middle of it, “for­ a&longs;much as the &longs;pecies of the Sun it &longs;elf admits not its &longs;mall figure to be &longs;een at &longs;o great a di&longs;tance, but the light produced by the Sun may help us to conceive that it illuminateth the whole Lu­ nar Body: a like effect we may &longs;ee in a plate gilded and well polli&longs;h'd, which touch't by a luminous body, appeareth to him that beholds it at &longs;ome di&longs;tance to be all &longs;hining; and onely near at hand one may di&longs;cover in the middle of it the &longs;mall image of the luminous body.”

SALV. Ingenuou&longs;ly confe&longs;&longs;ing my dullne&longs;s of apprehen&longs;ion, I mu&longs;t tell you, that I under&longs;tand not any thing of this your di&longs;­ cour&longs;e, &longs;ave onely what concerns the gilt plate: and if you permit me to &longs;peak freely, I have a great conceit that you al&longs;o under&longs;tand not the &longs;ame, but have learnt by heart tho&longs;e words written by &longs;ome one out of a de&longs;ire of contradiction, and to &longs;hew him&longs;elf more intel­ ligent than his adver&longs;ary; but it mu&longs;t be to tho&longs;e, which to appear al&longs;o more wi&longs;e, applaud that which they do not under&longs;tand, and entertain a greater conceit of per&longs;ons, the le&longs;s they are by them under&longs;tood: and the writer him&longs;elf may be one of tho&longs;e (of which there are many) who write what they do not under&longs;tand, and con&longs;equently under&longs;tand not what they write. Therefore, o­ mitting the re&longs;t, I reply, as to the gilt plate, that if it be flat and not very big, it may appear at a di&longs;tance very bright, whil&longs;t a great light beameth upon it, but yet it mu&longs;t be when the eye is in a de­ terminate line, namely in that of the reflex rays: and it will ap­ pear the more &longs;hining, if it were v. g. of &longs;ilver, by means of its being burni&longs;hed, and apt through the great den&longs;ity of the metal, to receive a perfect poli&longs;h. And though its &longs;uperficies, being very well brightned, were not exactly plain, but &longs;hould have various in­ clinations, yet then al&longs;o would its &longs;plendor be &longs;een many ways; namely, from as many places as the various reflections, made by the &longs;everal &longs;uperficies, do reach: for therefore are Diamonds ground to many &longs;ides, that &longs;o their plea&longs;ing lu&longs;tre might be beheld from many places. But if the Plate were very big, though it &longs;hould be all plain, yet would it not at a di&longs;tance appear all over &longs;hining: and the better to expre&longs;s my &longs;elf, Let us &longs;uppo&longs;e a very large gilt plate expo&longs;ed to the Sun, it will &longs;hew to an eye far di&longs;tant, the image of the Sun, to occupy no more but a certain part of the &longs;aid plate; to wit, that from whence the reflection of the incident &longs;olar rays come: but it is true that by the vivacity of the light, the &longs;aid image will appear fringed about with many rays, and &longs;o will &longs;eem to occupie a far greater part of the plate, than really it doth. And to &longs;hew that this is true, when you have noted the particular place of the plate from whence the reflection cometh, and concei­ ved likewi&longs;e how great the &longs;hining place appeared to you, cover the greater part of that &longs;ame &longs;pace, leaving it only vi&longs;ible about the mid&longs;t; and all this &longs;hall not any whit dimini&longs;h the apparent &longs;plen­ dor to one that beholds it from afar; but you &longs;hall &longs;ee it largely di&longs;pers'd upon the cloth or other matter, wherewith you covered it. If therefore any one, by &longs;eeing from a good di&longs;tance a &longs;mall gilt plate to be all over &longs;hining, &longs;hould imagine that the &longs;ame would al&longs;o even in a plate as broad as the Moon, he is no le&longs;s de­ ceived, than if he &longs;hould believe the Moon to be no bigger than the bottom of a tub. If again the plate were turn'd into a &longs;phe­ rical &longs;uperficies, the reflection would be &longs;een &longs;trong in but one &longs;ole particle of it; but yet by rea&longs;on of its liveline&longs;s, it will appear fringed about with many glittering rays: the re&longs;t of the Ball would appear according as it was burni&longs;hed; and this al&longs;o onely then when it was not very much poli&longs;hed, for &longs;hould it be perfectly brightned, it would appear ob&longs;cure. An example of this we have dayly before our eyes in &longs;ilver ve&longs;&longs;els, which whil&longs;t they are only boyl'd in the Argol and Salt, they are all as white as &longs;now, and do not reflect any image; but if they be in any part burni&longs;h'd, they become in that place pre&longs;ently ob&longs;cure: and in them one may &longs;ee the repre&longs;entation of any thing as in Looking-gla&longs;&longs;es. And that chan­ to ob&longs;curity, proceeds from nothing el&longs;e but the &longs;moothing and plaining of a fine grain, which made the &longs;uperficies of the &longs;ilver rough, and yet &longs;uch, as that it reflected the light into all parts, whereby it &longs;eemed from all parts equally illuminated: which &longs;mall unevenne&longs;&longs;es, when they come to be exqui&longs;itely plained by the burni&longs;h, &longs;o that the reflection of the rays of incidence are all directed unto one determinate place; then, from that &longs;ame place, the burni&longs;h'd part &longs;hall &longs;hew much more bright and &longs;hining than the re&longs;t which is onely whitened by boyling; but from all other places it looks very ob&longs;cure. And note, that the diver&longs;ity of &longs;ights of looking upon burni&longs;h'd &longs;uperficies, occa&longs;ioneth &longs;uch difference in appearances, that to imitate and repre&longs;ent in picture, v. g. a poli&longs;h'd Cuirace, one mu&longs;t couple black plains with white, one &longs;ideways to the other, in tho&longs;e parts of the arms where the light falleth equally.

Some write what they under&longs;tand not, and therefore under&longs;tand not what they write.

Diamonds ground to divers &longs;ides, & why.

Silver burni&longs;hed appears more ob­ &longs;cuee, than the not burni&longs;hed, & why.

Burni&longs;h'd Steel beheld from one place appears very bright, and from another, very ob­ &longs;cure.

SAGR. If therefore the&longs;e great Philo&longs;ophers would acquie&longs;e in granting, that the Moon, Venus and the other Planets, were not of &longs;o bright and &longs;mooth a &longs;urface as a Looking-gla&longs;s, but wanted &longs;ome &longs;mall matter of it, namely, were as a &longs;ilver plate, onely boyled white, but not burni&longs;hed; would this yet &longs;uffice to the making of it vi&longs;ible, and apt for darting forth the light of the Sun?

SALV. It would &longs;uffice in part; but would not give a light &longs;o &longs;trong, as it doth being mountainous, and in &longs;um, full of eminencies and great cavities. But the&longs;e Philo&longs;ophers will never yield it to be le&longs;&longs;e polite than a gla&longs;&longs;e; but far more, if more it can be imagined; for they e&longs;teeming that to perfect bodies perfect figures are mo&longs;t &longs;utable; it is nece&longs;&longs;ary, that the &longs;phericity of tho&longs;e Cœle&longs;tial Globes be mo&longs;t exact; be&longs;ides, that if they &longs;hould grant me &longs;ome inequality, though never &longs;o &longs;mall, I would not &longs;cruple to take any other greater; for that &longs;uch perfection con&longs;i&longs;t­ ing in indivi&longs;ibles, an hair doth as much detract from its perfection as a mountain.

SAGR. Here I meet with two difficulties, one is to know the rea&longs;on why the greater inequality of &longs;uperficies maketh the &longs;tron­ ger reflection of light; the other is, why the&longs;e Peripatetick Gen­ tlemen are for this exact figure.

SALV. I will an&longs;wer to the fir&longs;t; and leave to Simplieius the care of making reply to the &longs;econd. You mu&longs;t know therefore, that the &longs;ame &longs;uperficies happen to be by the &longs;ame light more or le&longs;s illuminated, according as the rayes of illumination fall upon them more or le&longs;&longs;e obliquely; &longs;o that the greate&longs;t illumination is where the rayes are perpendicular. And &longs;ee, how I will prove it to your &longs;en&longs;e. I bend this paper, &longs;o, that one part of it makes an angle upon the other: and expo&longs;ing both the&longs;e parts to the reflection of the light of that oppo&longs;ite Wall, you &longs;ee how this &longs;ide which re­ ceiveth the rayes obliquely, is le&longs;&longs;e &longs;hining than this other, where the reflection fals at right angles; and ob&longs;erve, that as I by degrees receive the illumination more obliquely, it groweth weaker.

The more rough &longs;uperficies make greater reflection of light, than the le&longs;s rough.

Perpendicular rays illuminate more than the ob­ lique, and why.

SAGR. I &longs;ee the effect, but comprehend not the cau&longs;e.

SALV. If you thought upon it but a minute of an hour, you would find it; but that I may not wa&longs;te the time, &longs;ee a kind of demon&longs;tration thereof in Fig. 7.

SAGR. The bare &longs;ight of this Figure hath fully &longs;atisfied me, therefore proceed.

SIMPL. Pray you let me hear you out, for I am not of &longs;o quick an apprehen&longs;ion.

SALV. Fancie to your &longs;elf, that all the paralel lines, which you &longs;ee to depart from the terms A. B. are the rays which fall upon the line C. D. at right angles: then incline the &longs;aid C. D. till it hang as D. O. now do not you &longs;ee that a great part of tho&longs;e rays which peirce C. D. pa&longs;s by without touching D. O? If therefore D. O. be illuminated by fewer rays, it is very rea&longs;onable, that the light received by it be more weak. Let us return now to the Moon, which being of a &longs;pherical figure, if its &longs;uperficies were &longs;mooth, as this paper, the parts of its hemi&longs;phere illuminated by the Sun, which are towards its extremity, would receive much le&longs;s light, than the middle parts; the rays falling upon them mo&longs;t obliquely, and upon the&longs;e at right angles; whereupon at the time of full Moon, when we &longs;ee almo&longs;t its whole Hemi&longs;phere illuminated, the parts towards the mid&longs;t, would &longs;hew them&longs;elves to us with more &longs;plendor, than tho&longs;e others towards the circumference: which is not &longs;o in effect. Now the face of the Moon being repre&longs;ented to me full of indifferent high mountains, do not you &longs;ee how their tops and continuate ridges, being elevated above the convexity of the perfect &longs;pherical &longs;uperficies, come to be expo&longs;ed to the view of the Sun, and accommodated to receive its rays much le&longs;s ob­ liquely, and con&longs;equently to appear as luminous as the re&longs;t?

The more oblique Rayes illuminate leß, and why.

SAGR. All this I well perceive: and if there are &longs;uch moun­ tains, its true, the Sun will dart upon them much more directly than it would do upon the inclination of a polite &longs;uperficies: but it is al&longs;o true, that betwixt tho&longs;e mountains all the valleys would become ob&longs;cure, by rea&longs;on of the va&longs;t &longs;hadows, which in that time would be ca&longs;t from the mountains, whereas the parts towards the middle, though full of valleys and hills, by rea&longs;on they have the Sun elevated, would appear without &longs;hadow, and therefore more lucid by far than the extreme parts, which are no le&longs;s diffu­ &longs;ed with &longs;hadow than light, and yet we can perceive no &longs;uch diffe­ rence.

SIMPL. I was ruminating upon the like difficulty.

SALV. How much readier is Simplicius to apprehend the ob­ jections which favour the opinions of Ari&longs;totle, than their &longs;oluti­ ons? I have a kind of &longs;u&longs;pition, that he &longs;trives al&longs;o &longs;ometimes to di&longs;&longs;emble them; and in the pre&longs;ent ca&longs;e, he being of him&longs;elf able to hit upon the doubt, which yet is very ingenious, I cannot be­ lieve but that he al&longs;o was advi&longs;'d of the an&longs;wer; wherefore I will attempt to wre&longs;t the &longs;ame (as they &longs;ay) out of his mouth. There­ fore tell me, Simplicius, do you think there can be any &longs;hadow, where the rays of the Sun do &longs;hine?

SIMPL. I believe, nay I am certain that there cannot; for that it being the grand luminary, which with its rays driveth away dark­ ne&longs;s, it is impo&longs;&longs;ible any tenebro&longs;ity &longs;hould remain where it com­ eth; moreover, we have the definition, that Tenebræ &longs;unt priva­ tio luminis.

SALV. Therefore the Sun, beholding the Earth, Moon or o­ ther opacous body, never &longs;eeth any of its &longs;hady parts, it not ha­ ving any other eyes to &longs;ee with, &longs;ave its rays, the conveyers of light: and con&longs;equently, one &longs;tanding in the Sun would never &longs;ee any thing of umbrage, fora&longs;much as his vi&longs;ive rays would ever go accompanied with tho&longs;e illuminating beams of the Sun.

SIMPL. This is true, without any contradiction.

SALV. But when the Moon is oppo&longs;ite to the Sun, what dif­ ference is there between the tract of the rayes of your &longs;ight, and that motion which the Suns rayes make?

SIMPL. Now I under&longs;tand you; for you would &longs;ay, that the rayes of the &longs;ight and tho&longs;e of the Sun, moving by the &longs;ame lines, we cannot perceive any of the ob&longs;cure valleys of the Moon. Be plea&longs;ed to change this your opinion, that I have either &longs;imulation or di&longs;&longs;imulation in me; for I prote&longs;t unto you, as I am a Gentle­ man, that I did not gue&longs;&longs;e at this &longs;olution, nor &longs;hould I have thought upon it, without your help, or without long &longs;tudy.

SAGR. The re&longs;olutions, which between you two have been alledged touching this la&longs;t doubt, hath, to &longs;peak the truth, &longs;atisfi­ ed me al&longs;o. But at the &longs;ame time this con&longs;ideration of the vi­ fible rayes accompanying the rayes of the Sun, hath begotten in me another &longs;cruple, about the other part, but I know not whether I can expre&longs;&longs;e it right, or no: for it but ju&longs;t now comming into my mind, I have not yet methodized it to my mind: but let us &longs;ee if we can, all together, make it intelligible. There is no que&longs;tion, but that the parts towards the circumference of that poli&longs;h't, but not burni&longs;h't Hemi&longs;phere, which is illuminated by the Sun, receiving the rayes obliquely, receive much fewer thereof, than the middle­ mo&longs;t parts, which receive them directly. And its po&longs;&longs;ible, that a tract or &longs;pace of v. g. twenty degrees in breadth, and which is to­ wards the extremity of the Hemi&longs;phere, may not receive more rays than another towards the middle parts, of but four degree broad: &longs;o that that doubtle&longs;s will be much more ob&longs;cure than this; and &longs;uch it will appear to whoever &longs;hall behold them both in the face, or (as I may &longs;ay) in their full magnitude. But if the eye of the beholder were con&longs;tituted in &longs;uch a place, that the breadth of the twenty degrees of the ob&longs;cure &longs;pace, appeared not to it longer than one of four degrees, placed in the mid&longs;t of the Hemi&longs;phere, I hold it not impo&longs;&longs;ible for it to appear to the &longs;aid beholder e­ qually clear and lucid with the other; becau&longs;e, finally, between two equal angles, to wit, of four degrees apiece, there come to the eye the reflections of two equal numbers of rayes: namely, tho&longs;e which are reflected from the middlemo&longs;t &longs;pace, four degrees in breadth, and tho&longs;e reflected from the other of twenty degrees, but &longs;een by compre&longs;&longs;ion, under the quantity of four degrees: and &longs;uch a &longs;ituation &longs;hall the eye obtain, when it is placed between the &longs;aid Hemi&longs;phere, and the body which illuminates it; for then the &longs;ight and rayes move in the &longs;ame lines. It &longs;eemeth not impo&longs;&longs;ible therefore, but that the Moon may be of a very equal &longs;uperficies; and that neverthele&longs;&longs;e, it may appear when it is at the full, no le&longs;s light in the extremities, than in the middle parts.

SALV. The doubt is ingenious and worthy of con&longs;ideration; and as it but ju&longs;t now came into your mind unawares, &longs;o I will like wi&longs;e an&longs;wer with what fir&longs;t comes into my thoughts, and it may happily fall out, that by thinking more upon it, I may &longs;tumble upon a better reply. But before, that I labyrinth my &longs;elf any far­ ther, it would be nece&longs;&longs;ary, that we a&longs;&longs;ure our &longs;elves by &longs;ome ex­ periment, whether your objection prove in effect, what it &longs;eemeth to conclude in appearance; and therefore taking once more the &longs;ame paper, and making it to incline, by bending a little part thereof upon the remainder, let us try whether expo&longs;ing it to the Sun, &longs;o that the rayes of light fall upon the le&longs;&longs;er part directly, and upon the other obliquely; this which receiveth the rayes direct­ ly appeareth more lucid; and &longs;ee here by manife&longs;t experience, that it is notably more clear. Now if your objection be conclu&longs;ive, it will follow, that &longs;tooping with our eye &longs;o, that in beholding the other greater part, le&longs;s illuminated, in compre&longs;&longs;ion or fore­ &longs;hortning, it appear unto us no bigger than the other, more &longs;hining; and that con&longs;equently, it be not beheld at a greater angle than that; it will nece&longs;&longs;arily en&longs;ue, I &longs;ay, that its light be encrea&longs;ed, &longs;o that it do &longs;eem to us as bright as the other. See how I behold, and look upon it &longs;o obliquely, that it appeareth to me narrower than the other; but yet, notwith&longs;tanding its ob&longs;curity, doth not to my perceiving, at all grow clearer. Try now if the &longs;ame &longs;ucceed to you.

SAGR. I have look't upon it, and though I have &longs;tooped with my eye, yet cannot I &longs;ee the &longs;aid &longs;uperficies encrea&longs;e in light or clarity; nay me thinks it rather grows more dusky.

SALV. We are hitherto confident of the invalidity of the ob­ jection; In the next place, as to the &longs;olution, I believe, that, by rea&longs;on the Superficies of this paper is little le&longs;&longs;e than &longs;mooth, the rayes are very few, which be reflected towards the point of inci­ dence, in compari&longs;on of the multitude, which are reflected to­ wards the oppo&longs;ite parts; and that of tho&longs;e few more and more are lo&longs;t, the nearer the vi&longs;ive rayes approach to tho&longs;e lucid rayes of incidence; and becau&longs;e it is not the incident rayes, but tho&longs;e which are reflected to the eye, that make the object appear lu­ minous; therefore, in &longs;tooping the eye, there is more lo&longs;t than got, as you your &longs;elf confe&longs;&longs;e to have &longs;een in looking upon the ob&longs;cu­ rer part of the paper.

SAGR. I re&longs;t &longs;atisfied with this experiment and rea&longs;on: It re­ mains now, that Simplicius an&longs;wer to my other que&longs;tion, and tell me what moves the Peripateticks to require this &longs;o exact rotundity in the Cœle&longs;tial bodies.

SIMPL. The Cœle&longs;tial bodies being ingenerable, inalterable, im­ pa&longs;&longs;ible, immortal, &c. they mu&longs;t needs be ab&longs;olutely perfect; and their being ab&longs;olute perfect, nece&longs;&longs;arily implies that there is in them all kinds of perfection; and con&longs;equently, that their figure be al&longs;o perfect, that is to &longs;ay, &longs;pherical; and ab&longs;olutely and perfectly &longs;pherical, and not rough and irregular.

Perfect &longs;phericity why a&longs;cribed to Cœlestial bodies, by the Peripate­ ticks.

SALV. And this incorruptibility, from whence do you prove it?

SIMPL. Immediately by its freedom from contraries, and me­ diately, by its &longs;imple circular motion.

SALV. So that; by what I gather from your di&longs;cour&longs;e, in ma­ king the e&longs;&longs;ence of the Cœle&longs;tial bodies to be incorruptible, inal­ terable, &c, there is no need of rotundity as a cau&longs;e, or requi­ &longs;ite; for if this &longs;hould cau&longs;e inalterability, we might at our plea­ &longs;ure make wood, wax, and other Elementary matters, incorrup­ tible, by reducing them to a &longs;pherical figure.

The Figure is not the cau&longs;e of incor­ ruptibility, but of longer duration.

SIMPL. And is it not manife&longs;t that a ball of Wood will better and longer be preferved, than an oblong, or other angular fi­ gure, made of a like quantity of the &longs;ame wood.

SALV. This is mo&longs;t certain, but yet it doth not of corruptible become incorruptible, but &longs;till remains corruptible, though of a much longer duration. Therefore you mu&longs;t note, that a thing cor­ ruptible, is capable of being more or le&longs;&longs;e &longs;uch, and we may properly &longs;ay this is le&longs;&longs;e corruptible than that; as for example, the Ja&longs;per, than the Pietra Sirena; but incorruptibility admits not of more, or le&longs;&longs;e, &longs;o as that it may be &longs;aid this is more incorrupti­ ble than that, if both be incorruptible and eternal. The diver­ &longs;ity of figure therefore cannot operate: &longs;ave onely in matters ca­ pable of more or le&longs;&longs;e duration; but in the eternal, which can­ not be other than equally eternal, the operation of figure cea&longs;eth. And therefore, &longs;ince the Cœle&longs;tial matter is not incorruptible by figure, but otherwayes no man needs to be &longs;o &longs;olicitous for this perfect &longs;phericity; for if the matter be incorruptible, let it have what figure it will, it &longs;hall be alwayes &longs;uch.

Corruptibility ad­ mits of more or le&longs;&longs;e; &longs;o doth noe incorruptibiliiy.

The perfection of figure, operateth in corruptible bo­ dies, but not in the eternal.

SAGR. But I am con&longs;idering another thing, and &longs;ay, that if we &longs;hould grant the &longs;pherical figure a faculty of conferring incor­ ruptibility, all bodies of what&longs;oever figure, would be incorrupti­ ble; fora&longs;much as if the rotund body be incorruptible, corrupti­ bility would then &longs;ub&longs;i&longs;t in tho&longs;e parts which alter the perfect ro­ tundity; as for in&longs;tance, there is in a Die a body perfectly round, and, as &longs;uch, incorruptible; therefore it remaineth that tho&longs;e an­ gles be corruptible which cover and hide the rotundity; &longs;o that the mo&longs;t that could happen, would be, that tho&longs;e angles, and (to &longs;o &longs;peak) excre&longs;cencies, would corrupt. But if we proceed to a more inward con&longs;ideration, that in tho&longs;e parts al&longs;o towards the angles, there are compri&longs;ed other le&longs;&longs;er bals of the &longs;ame matter; and therefore they al&longs;o, as being round, mu&longs;t be al&longs;o incorrup­ tible; and likewife in the remainders, which environ the&longs;e eight le&longs;&longs;er Spheres, a man may under&longs;tand that there are others: &longs;o that in the end, re&longs;olving the whole Die into innumerable balls, it mu&longs;t nece&longs;&longs;arily be granted incorruptible. And the &longs;ame di&longs;­ cour&longs;e and re&longs;olution may be made in all other figures.

If the &longs;pherical fi­ gure conferreth e­ ternity, all bodies would be eternal.

SALV. Your method in making the conclu&longs;ion, for if v. g. a round Chry&longs;tal were, by rea&longs;on of its figure, incorruptible; namely, received from thence a faculy of re&longs;i&longs;ting all internal and external alterations, we &longs;hould not find, that the joyning to it other Chry­ &longs;tal, and reducing it v. g. into a Cube, would any whit alter it within, or without; &longs;o as that it would thereupon become le&longs;&longs;e apt to re&longs;i&longs;t the new ambient, made of the &longs;ame matter, than it was to re&longs;i&longs;t the other, of a matter different; and e&longs;pecially, if it be true, that corruption is generated by contraries, as Ari­ &longs;totle &longs;aith; and with what can you enclo&longs;e that ball of Cry&longs;tal, that is le&longs;&longs;e contrary to it, than Cry&longs;tal it &longs;elf? But we are not a­ ware how time flies away; and it will be too late before we come to an end of our di&longs;pute, if we &longs;hould make &longs;o long di&longs;cour&longs;es, upon every particular; be&longs;ides our memories are &longs;o confounded in the multiplicity of notions, that I can very hardly recal to mind the Propot&longs;iions, which I propo&longs;ed in order to Simplicius, for our con&longs;ideration.

SIMPL. I very well remember them: And as to this particular que&longs;tion of the montuo&longs;ity of the Moon, there yet remains un­ an&longs;wered that which I have alledged, as the cau&longs;e, (and which may very well &longs;erve for a &longs;olution) of that Phænomenon, &longs;aying, that it is an illu&longs;ion proceeding from the parts of the Moon, be­ ing unequally opacous, and per&longs;picuous.

SAGR. Even now, when Simplicius a&longs;cribed the apparent Pro­ tnberancies or unevenne&longs;&longs;es of the Moon (according to the opinion of a certain Peripatetick his friend) to the diver&longs;ly opacous, and per&longs;picuous parts of the &longs;aid Moon, conformable to which the like illu&longs;ions are &longs;een in Cry&longs;tal, and Jems of divers kinds, I bethought my &longs;elf of a matter much more commodious for the repre&longs;enting &longs;uch effects; which is &longs;uch, that I verily believe, that that Philo&longs;o­ pher would give any price for it; and it is the mother of Pearl, which is wrought into divers figures, and though it be brought to an ex­ treme evenne&longs;&longs;e, yet it &longs;eemeth to the eye in &longs;everal parts, &longs;o vari­ ou&longs;ly hollow and knotty, that we can &longs;carce credit our feeling of their evenne&longs;&longs;e.

Mother of Pearl accommodated to imitate the appa­ rent unevenne&longs;&longs;es of the Moons &longs;ur­ face.

SALV. This invention is truly ingenious; and that which hath not been done already, may be done in time to come; and if there have been produced other Jems, and Cry&longs;tals, which have nothing to do with the illu&longs;ions of the mother of Pearl, the&longs;e may be produced al&longs;o; in the mean time, that I may not prevent any one, I will &longs;uppre&longs;&longs;e the an&longs;wer which might be given, and onely for this time betake my &longs;elf to &longs;atisfie the objections brought by Simplicius. I &longs;ay therefore, that this rea&longs;on of yours is too ge­ neral, and as you apply it not to all the appearances one by one; which are &longs;een in the Moon, and for which my &longs;elf and others are induced to hold it mountainous, I believe you will not find any one that will be &longs;atisfied with &longs;uch a doctrine; nor can I think, that either you, or the Author him&longs;elf, find in it any greater quietude, than in any other thing wide from the purpo&longs;e. Of the very many &longs;everal appearances which are &longs;een night by night in the cour&longs;e of Moon, you cannot imitate &longs;o much as one, by making a Ball at your choice, more or le&longs;s opacous and per&longs;picuous, and that is of a polite &longs;uperficies; whereas on the contrary, one may make Balls of any &longs;olid matter what&longs;oever, that is not tran&longs;parent, which onely with eminencies and cavities, and by receiving the il­ lumination &longs;everal ways, &longs;hall repre&longs;ent the &longs;ame appearances and mutations to an hair, which from hour to hour are di&longs;covered in the Moon. In them you &longs;hall &longs;ee the ledges of Hills expo&longs;ed to the Suns light, to be very &longs;hining, and after them the projections of their &longs;hadows very ob&longs;cure; you &longs;hall &longs;ee them greater and le&longs;s, according as the &longs;aid eminencies &longs;hall be more or le&longs;s di&longs;tant from the confines which di&longs;tingui&longs;h the parts of the Moon illuminated, from the ob&longs;cure: you &longs;hall &longs;ee the &longs;ame term and confine, not equally diftended, as it would be if the Ball were poli&longs;h'd, but craggie and rugged. You &longs;hall &longs;ee beyond the &longs;ame term, in the dark parts of the Moon many bright prominencies, and di&longs;tinct from the re&longs;t of the illuminations: you &longs;hall &longs;ee the &longs;hadows a­ fore&longs;aid, according as the illumination gradually ri&longs;eth, to demi­ ni&longs;h by degrees, till they wholly di&longs;appear; nor are there any of them to be &longs;een when the whole Hemi&longs;phere is enlightned. gain on the contrary, in the lights pa&longs;&longs;age towards the other He­ mi&longs;phere of the Moon, you &longs;hall again ob&longs;erve the &longs;ame eminen­ cies that were marked, and you &longs;hall &longs;ee the projections of their &longs;hadows to be made a contrary way, and to decrea&longs;e by degrees: of which things, once more I &longs;ay, you cannot &longs;hew me &longs;o much as one in yours that are opacous and per&longs;picuous.

The apparent un­ evenne&longs;&longs;es of the Moon cannot be i­ mitated by way of more and le&longs;s opa­ city & per&longs;picuity.

The various a­ &longs;pects of the Moon, imitable with any opacous matter.

Various appear an­ ces from which the Moons montuo&longs;ity is argued.

SAGR. One of them certainly he may imitate, namely, that of the Full-Moon, when by rea&longs;on of its being all illuminated, there is not to be &longs;een either &longs;hadow, or other thing, which receiveth any alteration from its eminencies and cavities. But I be&longs;eech you, Salviatus, let us &longs;pend no more time on this Argument, for a per&longs;on that hath had but the patience to make ob&longs;ervation of but one or two Lunations, and is not &longs;atisfied with this mo&longs;t &longs;en&longs;ible truth, may well be adjudged void of all judgment; and upon &longs;uch why &longs;hould we throw away our time and breath in vain?

SIMPI. I mu&longs;t confe&longs;s I have not made the ob&longs;ervations, for that I never had &longs;o much curio&longs;ity, or the In&longs;truments proper for the bu&longs;ine&longs;s; but I will not fail to do it. In the mean time, we may leave this que&longs;tion in &longs;u&longs;pen&longs;e, and pa&longs;s to that point which follows, producing the motives inducing you to think that the Earth may reflect the light of the Sun no le&longs;s forceably than the Moon, for it &longs;eems to me &longs;o ob&longs;cure and opacous, that I judg &longs;uch an effect altogether impo&longs;&longs;ible.

SALV. The cau&longs;e for which you repute the Earth unapt for illumination, may rather evince the contrary: And would it not be &longs;trange, Simplicius, if I &longs;hould apprehend your di&longs;cour&longs;es bet­ ter than you your &longs;elf?

SIMPL. Whether I argue well or ill, it may be, that you may better under&longs;tand the &longs;ame than I; but be it ill or well that I di&longs;cour&longs;e, I &longs;hall never believe that you can penetrate what I mean better than I my &longs;elf.

SALV. Well, I will make you believe the &longs;ame pre&longs;ently. Tell me a little, when the Moon is near the Full, &longs;o that it may be &longs;een by day, and al&longs;o at midnight, at what do you think it more &longs;plen­ did, by day or by night?

SIMPL. By night, without all compari&longs;on. And methinks the Moon re&longs;embleth that pillar of Clouds and pillar of Fire, which guided the I&longs;raelites; which at the pre&longs;ence of the Sun, appeared like a Cloud, but in the night was very glorious. Thus I have by day ob&longs;erved the Moon amid&longs;t certain &longs;mall Clouds, ju&longs;t as if one of them had been coloured white, but by night it &longs;hines with much &longs;plendor.

The Moon ap­ pears brighter by night than by day.

The Moon be­ held in the day time, is like to a little cloud.

SALV. So that if you had never happened to &longs;ee the Moon, &longs;ave onely in the day time, you would not have thought it more &longs;hining than one of tho&longs;e Clouds.

SIMPL. I verily believe I &longs;hould not.

SALV. Tell me now; do you believe that the Moon is really more &longs;hining in the night than day, or that by &longs;ome accident it &longs;eemeth &longs;o?

SIMPL. I am of opinion, that it re&longs;plends in it &longs;elf as much in the day as night, but that its light appears greater by night, be­ cau&longs;e we behold it in the dark mantle of Heaven; and in the day time, the whole Atmo&longs;phere being very clear, &longs;o that &longs;he little exceedeth it in lu&longs;tre, &longs;he &longs;eems to us much le&longs;s bright.

SALV. Now tell me; have you ever at midnight &longs;een the Ter­ re&longs;trial Globe illuminated by the Sun?

SIMPL. This &longs;eemeth to me a que&longs;tion not to be ask'd, unle&longs;s in je&longs;t, or of &longs;ome per&longs;on known to be altogether void of &longs;en&longs;e.

SALV. No, no; I e&longs;teem you to be a very rational man, and do ask the que&longs;tion &longs;eriou&longs;ly; and therefore an&longs;wer me: and if afterwards you &longs;hall think that I &longs;peak impertinently, I will be content to be the &longs;en&longs;ele&longs;s man: for he is much more a fool who interrogates &longs;imply, than he to whom the que&longs;tion is put.

SIMPL. If then you do not think me altogether &longs;imple, take it for granted that I have an&longs;wered you already, and &longs;aid, that it is impo&longs;&longs;ible, that one that is upon the Earth, as we are, &longs;hould &longs;ee by night that part of the Earth where it is day, namely, that is il­ luminated by the Sun.

SALV. Therefore you have never &longs;een the Earth enlightned, &longs;ave onely by day; but you &longs;ee the Moon to &longs;hine al&longs;o in the dead of night. And this is the cau&longs;e, Simplicius, which makes you believe that the Earth doth not &longs;hine like the Moon; but if you could &longs;ee the Earth illuminated, whil&longs;t you were in &longs;ome dark place, like our night, you would &longs;ee it &longs;hine brighter than the Moon. Now if you de&longs;ire that the compari&longs;on may proceed well, you mu&longs;t compare the light of the Earth, with that of the Moon &longs;een in the day time, and not with the &longs;ame by night: for it is not in our power to &longs;ee the Earth illuminated, &longs;ave onely in the day. Is it not &longs;o?

SIMPL. So it ought to be.

SALV. And fora&longs;much as you your &longs;elf have already confe&longs;&longs;ed to have &longs;een the Moon by day among &longs;ome little white Clouds, and very nearly, as to its a&longs;pect, re&longs;embling one of them; you did thereby grant, that tho&longs;e Clouds, which yet are Elementary matters, are as apt to receive illumination, as the Moon, yea more, if you will but call to mind that you have &longs;ometimes &longs;een &longs;ome Clouds of va&longs;t greatne&longs;s, and as perfect white as the Snow; and there is no que&longs;tion, but that if &longs;uch a Cloud could be con­ tinued &longs;o luminous in the deep of night, it would illuminate the places near about it, more than an hundred Moons. If therefore we were a&longs;&longs;ured that the Earth is illuminated by the Sun, like one of tho&longs;e Clouds, it would be undubitable, but that it would be no le&longs;s &longs;hining than the Moon. But of this there is no que&longs;tion to be made, in regard we &longs;ee tho&longs;e very Clouds in the ab&longs;ence of the Sun, to remain by night, as ob&longs;cure as the Earth: and that which is more, there is not any one of us, but hath &longs;een many times &longs;ome &longs;uch Clouds low, and far off, and que&longs;tioned whether they were Clouds or Mountains: an evident &longs;ign that the Moun­ tains are no le&longs;s luminous than tho&longs;e Clouds.

Clouds are no le&longs;s apt than the Moon to be illuminated by the Sun.

A wall illumina­ ted by the Sun, compared to the Moon &longs;hineth no le&longs;s than it.

SAGR. But what needs more di&longs;cour&longs;e? See yonder the Moon is ri&longs;en, and more than half of it illuminated; &longs;ee there that wall, on which the Sun &longs;hineth; retire a little this way, &longs;o that you &longs;ee the Moon &longs;ideways with the wall: look now; which of them &longs;hews more lucid? Do not you &longs;ee, that if there is any advantage, the wall hath it? The Sun &longs;hineth on that wall; from thence it

is reverberated upon the wall of the Hall, from thence it's refle­ cted upon that chamber, &longs;o that it falls on it at the third reflection: and I am very certain, that there is in that place more light, than if the Moons light had directly faln upon it.

The third re&longs;le­ ction of a Wall illu­ minates more than the fir&longs;t of the Moon.

SIMPL. But this I cannot believe; for the illumination of the Moon, e&longs;pecially when it is at the full, is very great.

SAGR. It &longs;eemeth great by rea&longs;on of the circumjacent dark places; but ab&longs;olutely it is not much, and is le&longs;s than that of the twilight half an hour after the Sun is &longs;et; which is manife&longs;t, be­ cau&longs;e you &longs;ee not the &longs;hadows of the bodies illuminated by the Moon till then, to begin to be di&longs;tingui&longs;hed on the Earth. Whe­ ther, again, that third reflection upon that chamber, illuminates more than the fir&longs;t of the Moon, may be known by going thether, and reading a Book, and afterwards &longs;tanding there in the night by the Moons light, which will &longs;hew by which of them lights one may read more or le&longs;s plainly, but I believe without further tryal, that one &longs;hould &longs;ee le&longs;s di&longs;tinctly by this later.

The light of the Moon weaker than that of the twi­ light.

SALV. Now, Simplicius, (if haply you be &longs;atisfied) you may conceive, as you your &longs;elf know very well, that the Earth doth &longs;hine no le&longs;s than the Moon; and the only remembring you of &longs;ome things, which you knew of your &longs;elf, and learn'd not of me, hath a&longs;&longs;ured you thereof: for I taught you not that the Moon &longs;hews lighter by night than by day, but you under&longs;tood it of your &longs;elf; as al&longs;o you could tell me that a little Cloud appeareth as lucid as the Moon: you knew al&longs;o, that the illumination of the Earth can­ not be &longs;een by night; and in a word, you knew all this, without knowing that you knew it. So that you have no rea&longs;on to be &longs;cru­ pulous of granting, that the dark part of the Earth may illuminate the dark part of the Moon, with no le&longs;s a light than that where­ with the Moon illuminates the ob&longs;curities of the night, yea rather &longs;o much the greater, ina&longs;much as the Earth is forty times bigger than the Moon.

SIMPL. I mu&longs;t confe&longs;s that I did believe, that that &longs;econdary light had been the natural light of the Moon.

SALV. And this al&longs;o you know of your &longs;elf, and perceive not that you know it. Tell me, do not you know without teaching, that the Moon &longs;hews it &longs;elf more bright by night than by day, in re&longs;pect of the ob&longs;curity of the &longs;pace of the ambient? and con&longs;e­ quently, do you not know in genere, that every bright body &longs;hews the clearer, by how much the ambient is ob&longs;curer?

Luminous bodies appear the brighter in an ob&longs;curer am­ bient.

SIMPL. This I know very well.

SALV. When the Moon is horned, and that &longs;econdary light &longs;eemeth to you very bright, is it not ever nigh the Sun, and con­ &longs;equently, in the light of the crepu&longs;culum, (twilight?)

SIMPL. It is &longs;o; and I have oftentimes wi&longs;h'd that the Air would grow thicker, that I might be able to &longs;ee that &longs;ame light more plainly; but it ever di&longs;appeared before dark night.

SALV. You know then very certainly, that in the depth of night, that light would be more con&longs;picuous.

SIMPL. I do &longs;o; and al&longs;o more than that, if one could but take away the great light of the cre&longs;cent illuminated by the Sun, the pre&longs;ence of which much ob&longs;cureth the other le&longs;&longs;er.

SALV. Why, doth it not &longs;ometimes come to pa&longs;s, that one may in a very dark night &longs;ee the whole face of the Moon, without be­ ing at all illuminated by the Sun?

SIMPL. I know not whether this ever happeneth, &longs;ave onely in the total Ecclip&longs;es of the Moon.

SALV. Why, at that time this its light would appear very clear, being in a mo&longs;t ob&longs;cure medium, and not darkned by the clarity of the luminous cre&longs;cents: but in that po&longs;ition, how light did it appear to you?

SIMPL. I have &longs;ometimes &longs;een it of the colour of bra&longs;s, and a little whiti&longs;h; but at other times it hath been &longs;o ob&longs;cure, that I have wholly lo&longs;t the &longs;ight of it.

SALV. How then can that light be &longs;o natural, which you &longs;ee &longs;o cleer in the clo&longs;e of the twilight, notwith&longs;tanding the impediment of the great and contiguous &longs;plendor of the cre&longs;cents; and which again, in the more ob&longs;cure time of night, all other light removed, appears not at all?

SIMPL. I have heard of &longs;ome that believed that &longs;ame light to be participated to the&longs;e cre&longs;cents from the other Stars, and in par­ ticular from Venus, the Moons neighbour.

SALV. And this likewi&longs;e is a vanity; becau&longs;e in the time of its total ob&longs;curation, it ought to appear more &longs;hining than ever; for you cannot &longs;ay, that the &longs;hadow of the Earth intercepts the &longs;ight of Venus, or the other Stars. But to &longs;ay true, it is not at that in&longs;tant wholly deprived thereof, for that the Terre&longs;trial He­ mi&longs;phere, which in that time looketh towards the Moon, is that where it is night, that is, an intire privation of the light of the Sun. And if you but diligently ob&longs;erve, you will very &longs;en&longs;ibly perceive, that like as the Moon, when it is &longs;harp-horned, doth give very little light to the Earth; and according as in her the parts illumi­ nated by the Suns light do encrea&longs;e: &longs;o likewi&longs;e the &longs;plendor to our &longs;eeming encrea&longs;eth, which from her is reflected towards us; thus the Moon, whil&longs;t it is &longs;harp-forked, and that by being between the Sun and the Earth, it di&longs;covereth a very great part of the Ter­ re&longs;trial Hemi&longs;phere illuminated, appeareth very clear: and depart­ ing from the Sun, and pa&longs;&longs;ing towards the ^{*}Quadrature, you may &longs;ee the &longs;aid light by degrees to grow dim; and after the Quadrature, the &longs;ame appears very weak, becau&longs;e it continually lo&longs;eth more and more of the view of the luminous part of the Earth: and yet it &longs;hould &longs;ucceed quite contrary, if that light were its own, or communicated to it from the Stars; for then we &longs;hould &longs;ee it in the depth of night, and in &longs;o very dark an ambient.

*By the Moons two Quadratures you are to under&longs;tand its fir&longs;t and last quarters, as A­ &longs;trologers call them

SIMPL. Stay a little; for I ju&longs;t now remember, that I have read in a little modern tract, full of many novelties; “That this &longs;econdary light is not derived from the Stars, nor innate in the Moon, and lea&longs;t of all communicated by the Earth, but that it is received from the &longs;ame illumination of the Sun, which, the &longs;ub­ &longs;tance of the Lunar Globe being &longs;omewhat tran&longs;parent, pene­ trateth thorow all its body; but more livelily illuminateth the &longs;uperficies of the Hemi&longs;phere expo&longs;ed to the rays of the Sun: and its pro&longs;undity imbuing, and (as I may &longs;ay) &longs;wallowing that light, after the manner of a cloud or chry&longs;tal, tran&longs;mits it, and renders it vi&longs;ibly lucid. And this (if I remember aright) he proveth by Authority, Experience and Rea&longs;on; citing Cleomedes, Vitellion, Macrobius, and a certain other modern Author: and adding, That it is &longs;een by experience to &longs;hine mo&longs;t in the days neare&longs;t the Conjunction, that is, when it is horned, and is chiefly bright about its limb. And he farther writes, That in the Solar Ecclip&longs;es, when it is under the Di&longs;cus of the Sun, it may be &longs;een tran&longs;lucid, and more e&longs;pecially towards its utmo&longs;t Circle. And in the next place, for Arguments, as I think, he &longs;aith, That it not being able to derive that light either from the Earth, or from the Stars, or from it &longs;elf, it nece&longs;&longs;arily follows, that it cometh from the Sun. Be&longs;ides that, if you do but grant this &longs;uppo&longs;ition, one may ea&longs;ily give convenient rea&longs;ons for all the particulars that occur. For the rea&longs;on why that &longs;ecundary light &longs;hews more lively towards the outmo&longs;t limb, is, the &longs;hortne&longs;s of the &longs;pace that the Suns rays hath to penetrate, in regard that of the lines which pa&longs;s through a circle, the greate&longs;t is that which pa&longs;&longs;eth through the centre, and of the re&longs;t, tho&longs;e which are farthe&longs;t from it, are always le&longs;s than tho&longs;e that are nearer. From the &longs;ame principle, he &longs;aith, may be &longs;hewn why the &longs;aid light doth not much dimini&longs;h. And la&longs;tly, by this way the cau&longs;e is a&longs;&longs;igned whence it comes, that that &longs;ame more &longs;hining circle about the utmo&longs;t edge of the Moon, is &longs;een at the time of the Solar Ec­ clip&longs;e, in that part which lyeth ju&longs;t under the Di&longs;cus of the Sun, but not in that which is be&longs;ide the Di&longs;cus: which happeneth becau&longs;e the rays of the Sun pa&longs;s directly to our eye, through the parts of the Moon underneath: but as for the parts which are be&longs;ides it, they fall be&longs;ides the eye.”

The &longs;econdary light of the Moon cau&longs;ed by the Sun, according to &longs;ome.

SALV. If this Philo&longs;opher had been the fir&longs;t Author of this o­ pinion, I would not wonder that he &longs;hould be &longs;o affectionate to it, as to have received it for truth; but borrowing it from others, I cannot find any rea&longs;on &longs;ufficient to excu&longs;e him for not perceiving its fallacies; and e&longs;pecially after he had heard the true cau&longs;e of that effect, and had it in his power to &longs;atisfie him&longs;elf by a thou&longs;and experiments, and manife&longs;t circum&longs;tances, that the &longs;ame proceeded from the reflection of the Earth, and from nothing el&longs;e: and the more this &longs;peculation makes &longs;omething to be de&longs;ired, in the judgment of this Author, and of all tho&longs;e who give no credit to it: &longs;o much the more doth their not having under&longs;tood and remembred it, excu&longs;e tho&longs;e more rece&longs;s Antients, who, I am very certain, did they now under&longs;tand it, would without the lea&longs;t repugnance admit thereof. And if I may freely tell you what I think, I cannot believe but that this Modern doth in his heart believe it; but I rather think, that the conceit he &longs;hould not be the fir&longs;t Author thereof, did a little move him to endeavour to &longs;uppre&longs;&longs;e it, or to di&longs;parage it at lea&longs;t among&longs;t the &longs;imple, who&longs;e number we know to be very great; and many there are, who much more affect the nume­ rous applauds of the people, than the approbation of a few not vulgar judgments.

SAGR. Hold good Salviatus, for me thinks, I &longs;ee that you go not the way to hit the true mark in this your di&longs;cour&longs;e, for the&longs;e that ^{*} confound all propriety, know al&longs;o how to make them&longs;elves Authors of others inventions, provided they be not &longs;o &longs;tale, and publick in the Schools and Market-places, as that they are more then notorious to every one.

* Tendono le pare­ te al commune.

SALV. Ha! well aimed, you blame me for roving from the point in hand; but what have you to do with Schools and Mar­ kets? Is it not all one whether opinions and inventions be new to men, or the men new to them? If you ^{*} contend about the e­ &longs;teem of the Founders of Sciences, which in all times do &longs;tart up, you may make your &longs;elf their inventor, even to the Alphabet it &longs;elf, and &longs;o gain admiration among&longs;t that illiterate rabble; and though in proce&longs;&longs;e of time your craft &longs;hould be perceived, that would but little prejudice your de&longs;igne; for that others would &longs;ucceed them in maintaining the number of your fautors; but let us return to prove to Simplicius the invalidity of the rea&longs;ons of his modern Author, in which there are &longs;everal fal&longs;ities, incon&longs;equen­ cies, and incredible Paradoxes. And fir&longs;t, it is fal&longs;e that this &longs;e­ condary light is clearer about the utmo&longs;t limb than in the middle parts, &longs;o as to form, as it were, a ring or circle more bright than the re&longs;t of its &longs;pace or contence. True it is, indeed, that looking on the Moon at the time of twilight, at fir&longs;t &longs;ight there is the re­ &longs;emblance of &longs;uch a circle, but by an illu&longs;ion ari&longs;ing from the di­ ver&longs;ity of confines that bound the Moons Di&longs;cus, which are con­ fu&longs;ed by means of this &longs;econdary light; fora&longs;much as on the part towards the Sun it is bounded by the lucid horns of the Moon, and on the other part, its confining term is the ob&longs;cure tract of the twilight; who&longs;e relation makes us think the candor of the Moons Di&longs;cus to be &longs;o much the clearer; the which happens to be ob­ fu&longs;cated in the oppo&longs;ite part, by the greater clarity of the cre&longs;­ cents; but if this modern Author had e&longs;&longs;aied to make an inter­ po&longs;ition between the eye and the primary &longs;plendor, by the ridg of &longs;ome hou&longs;e, or &longs;ome other &longs;creen, &longs;o as to have left vi&longs;ible only the gro&longs;e of the Moon, the horns excluded, he might have &longs;een it all alike luminous.

Its all one whe­ ther opinions be new to men, or men new to opinions.

* Conte&longs;tare fal&longs;ly rendered in the Latine Tran&longs;lation content are.

The &longs;econdary light of the Moon appears in form of a Ring, that is to &longs;ay, bright in the extreme circumfe­ rence, and not in the mid&longs;t, and why.

The may to ob­ &longs;erve the &longs;econda­ ry light of the Moon.

SIMPL, I think, now I remember, that he writes of his making u&longs;e of &longs;uch another Artifice, to hide from us the fal&longs;e Incidum.

SALV. Oh! how is this (as I believed) inadvertency of his, changed into a lie, bordering on ra&longs;hne&longs;&longs;e; for that every one may frequently make proof of the contrary. That in the next place, at the Suns Eclip&longs;e, the Moons Di&longs;cus is &longs;een otherwayes than by privation, I much doubt, and &longs;pecially when the E­ clip&longs;e is not total, as tho&longs;e mu&longs;t nece&longs;&longs;arily have been, which were ob&longs;erved by the Author; but if al&longs;o he &longs;hould have di&longs;cove­ red &longs;omewhat of light, this contradicts not, rather favoureth our opinion; for that at &longs;uch a time, the whole Terre&longs;trial Hemi­ &longs;phere illuminated by the Sun, is oppo&longs;ite to the Moon, &longs;o that although the Moons &longs;hadow doth ob&longs;cure a part thereof, yet this is very &longs;mall in compari&longs;on of that which remains illuminated. That which he farther adds, that in this ca&longs;e, the part of the limb, lying under the Sun, doth appear very lucid, but that which lyeth be&longs;ides it, not &longs;o; and that to proceed from the co­ ming of the &longs;olar rayes directly through that part to the eye, but not through this, is really one of tho&longs;e fopperies, which di&longs;co ver the other fictions, of him which relates them: For if it be requi&longs;ite to the making a &longs;econdary light vi&longs;ible in the lunar Di&longs;­ cus, that the rayes of the Sun came directly through it to our eyes, doth not this pitiful Philo&longs;opher perceive, that we &longs;hould ne­ ver &longs;ee this &longs;ame &longs;econdary light, &longs;ave onely at the Eclip&longs;e of the Sun? And if a part onely of the Moon, far le&longs;&longs;e than half a de­ gree, by being remote from the Suns Di&longs;cus, can deflect or de­ viate the rayes of the Sun, &longs;o that they arrive not at our eye; what &longs;hall it do when it is di&longs;tant twenty or thirty degrees, as it is at its fir&longs;t apparition? and what cour&longs;e &longs;hall the rayes of the Sun keep, which are to pa&longs;&longs;e thorow the body of the Moon, that they may find out our eye? This man doth go &longs;ucce&longs;&longs;ively con&longs;i­ dering what things ought to be, that they may &longs;erve his purpo&longs;e, but doth not gradually proceed, accommodating his conceits to the things, as really they are. As for in&longs;tance, to make the light of the Sun capable to penetrate the &longs;ub&longs;tance of the Moon, he makes her in part diaphanous, as is v. g. the tran&longs;parence of a cloud, or cry&longs;tal: but I know not what he would think of &longs;uch a tran­ &longs;parency, in ca&longs;e the &longs;olar rayes were to pa&longs;&longs;e a depth of clouds of above two thou&longs;and miles; but let it be &longs;uppo&longs;ed that he &longs;hould boldly an&longs;wer, that might well be in the Cœle&longs;tial, which are quite other things from the&longs;e our Elementary, impure, and feculent bodies; and let us convict his error by &longs;uch wayes, as admit him no reply, or (to &longs;ay better) &longs;ubter-fuge. If he will maintain, that the &longs;ub&longs;tance of the Moon is diaphanous, he mu&longs;t &longs;ay that it is &longs;o, while&longs;t that the rayes of the Sun are to pe­ netrate its whole profundity, that is, more than two thou&longs;and miles; but that if you oppo&longs;e unto them onely one mile, or le&longs;&longs;e, they &longs;hould no more penetrate that, than they penetrate one of our mountains.

The Moons Dif­ cus in a &longs;olar E­ clip&longs;e can be &longs;een onely by privation.

The Author of the Book of conclu&longs;i­ ons, accommodates the things to his purpo&longs;es, and not his purpo&longs;es to the things.

SAGR. You put me in mind of a man, who would have &longs;old me a &longs;ecret how to corre&longs;pond, by means of a certain &longs;ympathy of magnetick needles, with one, that &longs;hould be two or three thou­ &longs;and miles di&longs;tant; and I telling him, that I would willingly buy the &longs;ame, but that I de&longs;ired fir&longs;t to &longs;ee the experiment thereof, and that it did &longs;uffice me to make it, I being in one Chamber, and he in the next, he an&longs;wered me, that in &longs;o &longs;mall a di&longs;tance one could not &longs;o well perceive the operation; whereupon I turn'd him going, telling him, that I had no mind, at that time, to take a journey unto Grand Cairo, or to Mu&longs;covy, to make the experi­ ment; but that, if he would go him&longs;elf, I would perform the other part, &longs;taying in Venice. But let us hear whither the dedu­ ction of our Author tendeth, and what nece&longs;&longs;ity there is, that he mu&longs;t grant the matter of the Moon to be mo&longs;t perforable by the rayes of the Sun, in a depth of two thou&longs;and miles, but more opacous than one of our mountains, in a thickne&longs;&longs;e of one mile onely.

A je&longs;t put upon one that would &longs;ell a certain &longs;ecret for holding corre&longs;pon­ dency with a per&longs;on a thou&longs;and miles off

SALV. The very mountains of the Moon them&longs;elves are a proof thereof, which percu&longs;&longs;ed on one &longs;ide of the Sun, do ca&longs;t on the contrary &longs;ide very dark &longs;hadows, terminate, and more di­ &longs;tinct by much, than the &longs;hadows of ours; but had the&longs;e moun­ tains been diaphanous, we could never have come to the know­ ledg of any unevenne&longs;&longs;e in the &longs;uperficies of the Moon, nor have &longs;een tho&longs;e luminous montuo&longs;ities di&longs;tingui&longs;hed by the terms which &longs;eparate the lucid parts from the dark: much le&longs;&longs;e, &longs;hould we &longs;ee this &longs;ame term &longs;o di&longs;tinct, if it were true, that the Suns light did penetrate the whole thickne&longs;&longs;e of the Moon; yea rather, accord­ ing to the Authors own words, we &longs;hould of nece&longs;&longs;ity di&longs;cern the pa&longs;&longs;age, and confine, between the part of the Sun &longs;een, and the part not &longs;een, to be very confu&longs;ed, and mixt with light and darkne&longs;&longs;e; for that that matter which admits the pa&longs;&longs;age of the Suns rayes thorow a &longs;pace of two thou&longs;and miles, mu&longs;t needs be &longs;o tran&longs;parent, that it would very weakly re&longs;i&longs;t them in a hun­ dredth, or le&longs;&longs;er part of that thickne&longs;&longs;e; neverthele&longs;&longs;e, the term which &longs;eparateth the part illuminated from the ob&longs;cure, is inci­ dent, and as di&longs;tinct, as white is di&longs;tinct from black; and e­ &longs;pecially where the Section pa&longs;&longs;eth through the part of the Moon, that is naturally more clear and montanous; but where the old &longs;pots do part, which are certain plains, that by means of their &longs;pherical inclination, receive the rayes of the Sun obliquely, there the term is not &longs;o di&longs;tinct, by rea&longs;on of the more dimme il­ lumination. That, la&longs;tly, which he &longs;aith, how that the &longs;econdary light doth not dimini&longs;h and langui&longs;h, according as the Moon en­ crea&longs;eth, but con&longs;erveth it &longs;elf continually in the &longs;ame efficacy; is mo&longs;t fal&longs;e; nay it is hardly &longs;een in the quadrature, when, on the contrary, it &longs;hould appear more &longs;plendid, and be vi&longs;ible after the crepu&longs;culum in the dark of night. Let us conclude therefore, that the Earths reflection is very &longs;trong upon the Moon; and that, which you ought more to e&longs;teem, we may deduce from thence an­ other admirable congruity between the Moon and Earth; name­ ly, that if it be true, the Planets operate upon the Earth by their motion and light, the Earth may probably be no le&longs;&longs;e potent in operating reciprocally upon them with the &longs;ame light, and perad­ venture, motion al&longs;o. And though it &longs;hould not move, yet may it retain the &longs;ame operation; becau&longs;e, as it hath been proved al­ ready, the action of the light is the &longs;elf &longs;ame, I mean of the light of the Sun reflected; and motion doth nothing, &longs;ave only vary the a&longs;pects, which fall out in the &longs;ame manner, whether we make the Earth move, and the Sun &longs;tand &longs;till, or the contrary.

The Earth may re­ ciprocally operate upon Cœle&longs;tial bo­ dies, with its light.

SIMPL. None of the Philo&longs;ophers are found to have &longs;aid, that the&longs;e inferiour bodies operate on the Cœle&longs;tial, nay, Ari&longs;totle af­ firmes the direct contrary.

SALV. Aristotle and the re&longs;t, who knew not that the Earth and Moon mutually illuminated each other, are to be excu&longs;ed; but they would ju&longs;tly de&longs;erve our cen&longs;ure, if while&longs;t they de&longs;ire that we &longs;hould grant and believe with them, that the Moon operateth upon the Earth with light, they &longs;hould deny to us, who have taught them that the Earth illuminates the Moon, the operation the Earth hath on the Moon.

SIMPL. In &longs;hort, I find in my &longs;elf a great unwillingne&longs;&longs;e to admit this commerce, which you would per&longs;wade me to be be­ twixt the Earth and Moon, placing it, as we &longs;ay, among&longs;t the number of the Stars; for if there were nothing el&longs;e, the great &longs;eparation and di&longs;tance between it and the Cœle&longs;tial bodies, doth in my opinion nece&longs;&longs;arily conclude a va&longs;t di&longs;parity between them.

SALV. See Simplicius what an inveterate affection and radica­ ted opinion can do, &longs;ince it is &longs;o powerful, that it makes you think that tho&longs;e very things favour you, which you produce again&longs;t your &longs;elf. For if &longs;eparation and di&longs;tance are accidents &longs;ufficient to per&longs;wade with you a great diver&longs;ity of natures, it mn&longs;t follow that proximity and contiguity import &longs;imilitude. Now how much more neerer is the Moon to the Earth, than to any other of the Cœle&longs;tial Orbs? You mu&longs;t acknowledg therefore, according to your own con­ ce&longs;&longs;ion (and you &longs;hall have other Philo&longs;ophers bear you company) that there is a very great affinity betwixt the Earth and Moon. Now let us proceed, and &longs;ee whether any thing remains to be con­ &longs;idered, touching tho&longs;e objections which you made again&longs;t the re­ &longs;emblances that are between the&longs;e two bodies.

Affinity between he Earth & Moon in re&longs;pect of their vicinity.

SIMPL. It re&longs;ts, that we &longs;ay &longs;omething touching the &longs;olidity of the Moon, which I argued from its being exqui&longs;ite &longs;mooth and polite, and you from its montuo&longs;ity. There is another &longs;cruple al­ &longs;o comes into my mind, from an opinion which I have, that the Seas reflection ought by the equality of its &longs;urface, to be rendered &longs;tronger than that of the Earth, who&longs;e &longs;uperficies is &longs;o rough and opacous.

SALV. As to the fir&longs;t objection; I &longs;ay, that like as among the parts of the Earth, which all by their gravity &longs;trive to approach the neare&longs;t they can po&longs;&longs;ible to the center, &longs;ome of them alwayes are more remote from it than the re&longs;t, as the mountains more than the valleys, and that by rea&longs;on of their &longs;olidity and firmne&longs;&longs;e (for if they were of fluid, they would be even) &longs;o the &longs;eeing &longs;ome parts of the Moon to be elevated above the &longs;phericity of the low­ er parts, argueth their hardne&longs;&longs;e; for it is probable that the mat­ ter of the Moon is reduced into a &longs;pherical form by the harmoni­ ous con&longs;piration of all its parts to the &longs;ame &longs;enten&longs;e. Touching the &longs;econd doubt, my thinks that the particulars already ob&longs;erved to happen in the Looking-gla&longs;&longs;es, may very well a&longs;&longs;ure us, that the reflection of light comming from the Sea, is far weaker than that which cometh from Land; under&longs;tanding it alwayes of the univer&longs;al reflection; for as to that particular, on which the wa­ ter being calm, ca&longs;teth upon a determinate place, there is no doubt, but that he who &longs;hall &longs;tand in that place, &longs;hall &longs;ee a very great reflection in the water, but every way el&longs;e he &longs;hall &longs;ee the &longs;urface of the Water more ob&longs;cure than that of the Land; and to prove it to your &longs;en&longs;es, let us go into yonder Hall, and power forth a little water upon the Pavement. Tell me now, doth not this wet brick &longs;hew more dull than the other dry ones? Doubt­ le&longs;&longs;e it doth, and will &longs;o appear, from what place &longs;oever you be­ hold it, except one onely, and this is that way which the light cometh, that entereth in at yonder window; go backwards therefore by a little and a little.

Solidity of the Lunar Globe argu­ ed from its being montainous.

The Seas refle­ ction of light much weaker than that of the Earth.

An experiment to prove the refle­ ction of the Water le&longs;&longs;e clear than that of the Land.

SIMPL. Here I &longs;ee the we&longs;t part &longs;hine more than all the re&longs;t of the pavement, and I &longs;ee that it &longs;o hapneth, becau&longs;e the refle­ ction of the light which entereth in at the window, cometh to­ wards me.

SALV. That moi&longs;ture hath done no more but filled tho&longs;e little cavities which are in the brick with water, and reduced its &longs;uper­ ficies to an exact evene&longs;&longs;e; whereupon the reflex rayes i&longs;&longs;ue unitedly towards one and the &longs;ame place; but the re&longs;t of the pavement which is dry, hath its protuberances, that is, an innu­ merable variety of inclinations in its &longs;malle&longs;t particles; whereup­ on the reflections of the light &longs;catter towards all parts, but more weakly than if they had gone all united together; and therefore, the &longs;ame &longs;heweth almo&longs;t all alike, beheld &longs;everal wayes, but far le&longs;&longs;e clear than the moi&longs;tned brick. I conclude therefore, that the &longs;urface of the Sea, beheld from the Moon, in like manner, as it would appear mo&longs;t equal, (the I&longs;lands and Rocks deducted) &longs;o it would &longs;hew le&longs;&longs;e clear than that of the Earth, which is montanous and uneven. And but that I would not &longs;eem, as the &longs;aying is, to harp too much on one &longs;tring, I could tell you that I have ob­ &longs;erved in the Moon that &longs;econdary light which I told you came to her from the reflection of the Terre&longs;trial Globe, to be notably more clear two or three dayes before the conjunction, than after, that is, when we &longs;ee it before break of day in the Ea&longs;t, than when it is &longs;een at night after Sun-&longs;et in the We&longs;t; of which dif­ ference the cau&longs;e is, that the Terre&longs;trial Hemi&longs;phere, which looks towards the Ea&longs;tern Moon, hath little Sea, and much Land, to wit, all A&longs;ia, whereas, when it is in the We&longs;t, it beholds very great Seas, that is, the whole Atlantick Ocean as far as America: An Argument &longs;ufficiently probable that the &longs;urface of the water appears le&longs;&longs;e &longs;plendid than that of the Earth.

The &longs;econdary light of the Moon clearer before the conjunction, than after.

SIMPL. So that perhaps you believe, tho&longs;e great &longs;pots di&longs;co­ vered in the face of the Moon, to be Seas, and the other clearer parts to be Land, or &longs;ome &longs;uch thing?

SALV. This which you ask me, is the beginning of tho&longs;e in­ congruities which I e&longs;teem to be between the Moon and the Earth, out of which it is time to di&longs;-ingage our &longs;elves, for we have &longs;tayed too long in the Moon. I &longs;ay therefore, that if there were in nature but one way onely, to make two &longs;uperficies illu&longs;tra­ ted by the Sun, to appear one more clear than the other, and that this were by the being of the one Earth, and the other Wa­ ter; it would be nece&longs;&longs;ary to &longs;ay that the &longs;urface of the Moon were part earthy and part aquatick; but becau&longs;e we know many wayes to produce the &longs;ame effect (and others there may be which we know not of;) therefore I dare not affirm the Moon to con­ &longs;i&longs;t of one thing more than another: It hath been &longs;een already that a &longs;ilver plate boiled, being toucht with the Burni&longs;her, be­ cometh of white ob&longs;cure; that the moi&longs;t part of the Earth &longs;hews more ob&longs;cure than the dry; that in the tops of Hills, the woody parts appear more gloomy than the naked and barren; which hapneth becau&longs;e there falleth very much &longs;hadow among the Trees, but the open places are illuminated all over by the Sun. And this mixtion of &longs;hadow hath &longs;uch operation, that in tu&longs;ted velvet, the &longs;ilk which is cut, is of a far darker colour than that which is not cut, by means of the &longs;hadows diffu&longs;ed betwixt thred and thred, and a plain velvet &longs;hews much blacker than a Taffata, made of the &longs;ame &longs;ilk. So that if there were in the Moon things which &longs;hould look like great Woods, their a&longs;pect might repre&longs;ent unto us the &longs;pots which we di&longs;cover; alike difference would be occa&longs;ioned, if there were Seas in her: and la&longs;tly, nothing hindreth, but that tho&longs;e &longs;pots may really be of an ob&longs;curer colour than the re&longs;t; for thus the &longs;now makes the mountains &longs;hew brighter. That which is plain­ ly ob&longs;erved in the Moon is, that its mo&longs;t ob&longs;cure parts are all plains, with few ri&longs;es and bancks in them; though &longs;ome there be; the re&longs;t which is of a brighter colour, is all full of rocks, moun­ tains, hillocks of &longs;pherical and other figures; and in particular, round about the &longs;pots are very great ledges of mountains. That the &longs;pots be plain &longs;uperficies, we have a&longs;&longs;uredproof, in that we &longs;ee, how that the term which di&longs;tingui&longs;heth the part illuminated from the ob&longs;cure, in cro&longs;&longs;ing the &longs;pots makes the inter&longs;ection even, but in the clear parts it &longs;hews all craggy and &longs;hagged. But I know not as yet whether this evenne&longs;&longs;e of &longs;uperficies may be &longs;ufficient of it &longs;elf alone, to make the ob&longs;curity appear, and I rather think not. Be&longs;ides, I account the Moon exceeding different from the Earth; for although I imagine to my &longs;elf that tho&longs;e are not idle and dead Regions, yet I affirm not, that there are in them motion and life, much le&longs;s that there are bred plants, animals or other things like to ours; but, if &longs;uch there be, they &longs;hould neverthele&longs;s be very different, and remote from our imagination. And I am induced &longs;o to think, becau&longs;e in the fir&longs;t place, I e&longs;teem that the matter of the Lunar Globe con&longs;i&longs;ts not of Earth and Water; and this alone &longs;ufficeth to take away the generations and alterations re&longs;embling ours: but now &longs;uppo&longs;ing that there were in the Moon, Water and Earth, yet would they not produce plants and animals like to ours; and this for two principal rea&longs;ons: The fir&longs;t is, that unto our productions there are required &longs;o many variable a&longs;pects of the Sun, that without them they would all mi&longs;carry: now the habitudes of the Sun towards the Earth are far different from tho&longs;e towards the Moon. We as to the diurnal illumination, have, in the greater part of the Earth, every twenty four hours part day, and part night, which effect in the Moon is monethly: and that annual decli­ nation and elevation of the Sun in the Zodiack, by which it pro­ duceth diver&longs;ity of Sea&longs;ons, and inequality of dayes and nights, are fini&longs;hed in the Moon in a moneth; and whereas the Sun to us ri&longs;eth and declineth &longs;o much, that from the greate&longs;t to the lea&longs;t al­ titude, there is a difference of almo&longs;t 47 degrees, for &longs;o much is the di&longs;tance from one to the other Tropick; this is in the Moon but ten degrees only, or little more; namely, as much as the grea­ te&longs;t Latitudes of the Dragon on each &longs;ide the Ecliptick. Now con&longs;ider what effect the Sun would have in the torrid Zone, &longs;hould it continually for fifteen dayes together beam forth its Rayes upon it; which without all que&longs;tion would de&longs;troy plants, herbs, and living creatures: and if it &longs;hould chance that there were any production, it would be of herbs, plants, and creatures very diffe­ rent from tho&longs;e which are now there. Secondly, I verily believe that in the Moon there are no rains, for if Clouds &longs;hould gather in any part thereof, as they do about the Earth, they would there­ upon hide from our &longs;ight &longs;ome of tho&longs;e things, which we with the Tele&longs;cope behold in the Moon, and in a word, would &longs;ome way or other change its Phœnomenon, an effect which I could never by long and diligent ob&longs;ervations di&longs;cover; but alwayes beheld it in a even and pure &longs;erenity.

The ob&longs;curer parts of the Moon are plains, and the more bright moun­ tainous.

Long ledges of mountaixs about the &longs;pots of the Moon.

There are not generated in the Moon things like to ours, but if there be any pro­ ductions, they are very different.

The Moon not compo&longs;ed of Water and Earth.

Tho&longs;e a&longs;pects of the Sun nece&longs;&longs;ary for our generati­ ons, are not &longs;o in the Moon.

Natural dayas in the Moon are of a Moneth long.

To the Moon the Sun a&longs;eondeth and declineth with a difference of ten degrees, and to the Earth of forty &longs;e­ ven degrees.

There are no rains in the Moon.

SAGR. To this may be an&longs;wered, either that there might be great mi&longs;ts, or that it might rain in the time of their night, that is, when the Sun doth not illuminate it.

SALV. If other pa&longs;&longs;ages did but a&longs;&longs;ure us, that there were ge­ nerations in it like to ours, and that there was onely wanting the concour&longs;e of rains, we might find out this, or &longs;ome other tempe­ rament to &longs;erve in&longs;tead thereof, as it happens in Egypt by the in­ undation of Nile: but not meeting with any accident, which cor­ re&longs;ponds with ours, of many that have been &longs;ought out for the pro­ duction of the like effects, we need not trouble our &longs;elves to intro­ duce one alone; and that al&longs;o, not becau&longs;e we have certain ob&longs;er­ vation of it, but for a bare non-repugnance that we find therein. Moreover, if I was demanded what my fir&longs;t apprehen&longs;ion, and pure natural rea&longs;on dictated to me concerning the production of things like or unlike there above, I would alwayes reply, that they are mo&longs;t different, and to us altogether unimaginable, for &longs;o me thinks the riches of Nature, and the omnipotence of our Creator and Governour, do require.

SAGR. I ever accounted extraordinary madne&longs;&longs;e that of tho&longs;e, who would make humane comprehen&longs;ion the mea&longs;ure of what na­ ture hath a power or knowledge to effect; whereas on the con­ trary there is not any the lea&longs;t effect in Nature, which can be fully under&longs;tood by the mo&longs;t &longs;peculative wits in the world. This their &longs;o vain pre&longs;umption of knowing all, can take beginning from no­ thing, unle&longs;&longs;e from their never having known any thing; for if one hath but once onely experienced the perfect knowledg of one onely thing, and but truly ta&longs;ted what it is to know, he &longs;hall per­ ceive that of infinite other conclu&longs;ions, he under&longs;tands not &longs;o much as one.

The having a perfect knowledg of nothing, maketh &longs;ome believe they under&longs;tand all things.

SALV. Your di&longs;cour&longs;e is very concluding; in confirmation of which we have the example of tho&longs;e who under&longs;tand, or have known &longs;ome thing, which the more knowing they are, the more they know, and freely confe&longs;&longs;e that they know little; nay, the wi&longs;e&longs;t man in all Greece, and for &longs;uch pronounced by the Oracle, openly profe&longs;&longs;ed to know that he knew nothing.

SIMPL. It mu&longs;t be granted therefore, either that Socrates or that the Oracle it &longs;elf was a lyar, that declaring him to be mo&longs;t wi&longs;e, and he confe&longs;&longs;ing that he knew him&longs;elf to be mo&longs;t ig­ norant.

SALV. Neither one nor the other doth follow, for that both the a&longs;&longs;ertions may be true. The Oracle adjudged Socrates the wi­ &longs;e&longs;t of all men, who&longs;e knowledg is limited; Socrates acknow­ ledgeth that he knew nothing in relation to ab&longs;olute wi&longs;dome, which is infinite; and becau&longs;e of infinite, much is the &longs;ame part, as is little, and as is nothing (for to arrive v. g. to the infinite number, it is all one to accumulate thou&longs;ands, tens, or ciphers,) therefore Socrates well perceived his wi&longs;dom to be nothing, in compari&longs;on of the infinite knowledg which he wanted. But yet, becau&longs;e there is &longs;ome knowledg found among&longs;t men, and this not equally &longs;hared to all, Socrates might have a greater &longs;hare thereof than others, and therefore verified the an&longs;wer of the Oracle.

The an&longs;wer of the Oracle true in judging Socrates the wi&longs;eft of his time.

SAGR. I think I very well under&longs;tand this particular among&longs;t men, Simplicius there is a power of operating, but not equally di&longs;pen&longs;ed to all; and it is without que&longs;tion, that the power of an Emperor is far greater than that of a private per&longs;on; but, both this and that are nothing in compari&longs;on of the Divine Omnipo­ tence. Among&longs;t men, there are &longs;ome that better under&longs;tand Agriculture than many others; but the knowledg of planting a Vine in a trench, what hath it to do with the knowledg of ma­ king it to &longs;prout forth, to attract nouri&longs;hment, to &longs;elect this good part from that other, for to make thereof leaves, another to make &longs;prouts, another to make grapes, another to make rai&longs;ins, ano­ ther to make the huskes of them, which are the works of mo&longs;t wi&longs;e Nature? This is one only particular act of the innumerable, which Nature doth, and in it alone is di&longs;covered an infinite wi&longs;­ dom, &longs;o that Divine Wi&longs;dom may be concluded to be infinitely infinite.

Divine Wi&longs;dom infinitely infinise.

SALV. Take hereof another example. Do we not &longs;ay that the judicious di&longs;covering of a mo&longs;t lovely Statua in a piece of Marble, hath &longs;ublimated the wit of Buonarruotti far above the vulgar wits of other men? And yet this work is onely the imitation of a meer aptitude and di&longs;po&longs;ition of exteriour and &longs;uperficial mem­ bers of an immoveable man; but what is it in compari&longs;on of a man made by nature, compo&longs;ed of as many exteriour and inte­ riour members, of &longs;o many mu&longs;cles, tendons, nerves, bones, which &longs;erve to &longs;o many and &longs;undry motions? but what &longs;hall we &longs;ay of the &longs;en&longs;es, and of the powers of the &longs;oul, and la&longs;tly, of the under&longs;tanding? May we not &longs;ay, and that with rea&longs;on, that the &longs;tructure of a Statue fals far &longs;hort of the formation of a living man, yea more of a contemptible worm?

Buonarruotti, a &longs;tatuary of admi­ rable ingenuity.

SAGR. And what difference think you, was there betwixt the Dove of Architas, and one made by Nature?

SIMPL. Either I am none of the&longs;e knowing men, or el&longs;e there is a manife&longs;t contradiction in this your di&longs;cour&longs;e. You ac­ count under&longs;tanding among&longs;t the greate&longs;t (if you make it not the chief of the) Encomiums a&longs;cribed to man made by Nature, and a little before you &longs;aid with Socrates, that he had no knowledg at all; therefore you mu&longs;t &longs;ay, that neither did Nature under&longs;tand how to make an under&longs;tanding that under&longs;tandeth.

SALV. You argue very cunningly, but to reply to your obje­ ction I mu&longs;t have recour&longs;e to a Philo&longs;ophical di&longs;tinction, and &longs;ay that the under&longs;tanding is to be taken too ways, that is inten&longs;ivè, or exten&longs;ivè; and that exten&longs;ive, that is, as to the multitude of intel­ ligibles, which are infinite, the under&longs;tanding of man is as no­ thing, though he &longs;hould under&longs;tand a thou&longs;and propo&longs;itions; for that a thou&longs;and, in re&longs;pect of infinity is but as a cypher: but taking the under&longs;tanding inten&longs;ive, (in as much as that term imports) in­ ten&longs;ively, that is, perfectly &longs;ome propo&longs;itions, I &longs;ay, that humane wi&longs;­ dom under&longs;tandeth &longs;ome propo&longs;itions &longs;o perfectly, and is as ab&longs;o­ lutely certain thereof, as Nature her &longs;elf; and &longs;uch are the pure Mathematical &longs;ciences, to wit, Geometry and Arithmetick: in which Divine Wi&longs;dom knows infinite more propo&longs;itions, becau&longs;e it knows them all; but I believe that the knowledge of tho&longs;e few compre­ hended by humane under&longs;tanding, equalleth the divine, as to the certainty objectivè, for that it arriveth to comprehend the nece&longs;­ &longs;ity thereof, than which there can be no greater certainty.

Man under&longs;tand­ eth very well in­ ten&longs;ivè, but little exten&longs;ivè.

SIMPL. This &longs;eemeth to me a very bold and ra&longs;h expre&longs;&longs;ion.

SALV. The&longs;e are common notions, and far from all umbrage of temerity, or boldne&longs;s, and detract not in the lea&longs;t from the Ma­ je&longs;ty of divine wi&longs;dom; as it nothing dimini&longs;heth the omnipotence thereof to &longs;ay, that God cannot make what is once done, to be un­ done: but I doubt, Simplicius, that your &longs;cruple ari&longs;eth from an o­ pinion you have, that my words are &longs;omewhat equivocal; there­ fore the better to expre&longs;s my &longs;elf I &longs;ay, that as to the truth, of which Mathematical demon&longs;trations give us the knowledge, it is the &longs;ame, which the divine wi&longs;dom knoweth; but this I mu&longs;t grant you, that the manner whereby God knoweth the infinite propo­ &longs;itions, of which we under&longs;tand &longs;ome few, is highly more excellent than ours, which proceedeth by ratiocination, and pa&longs;&longs;eth from con­ clu&longs;ion to conclu&longs;ion, whereas his is done at one &longs;ingle thought or intuition; and whereas we, for example, to attain the knowledg of &longs;ome pa&longs;&longs;ion of the Circle, which hath infinite, beginning from one of the mo&longs;t &longs;imple, and taking that for its definition, do proceed with argumentation to another, and from that to a third, and then to a fourth, &c. the Divine Wi&longs;dom, by the apprehen&longs;ion of its e&longs;&longs;ence comprehends, without temporary raci­ ocination, all the&longs;e infinite pa&longs;&longs;ions; which notwith&longs;tanding, are in effect virtually compri&longs;ed in the definitions of all things; and, to conclude, as being infinite, perhaps are but one alone in their nature, and in the Divine Mind; the which neither is wholly unknown to humane under&longs;tanding, but onely be-clouded with thick and gro&longs;&longs;e mi&longs;ts; which come in part to be di&longs;&longs;ipated and clarified, when we are made Ma&longs;ters of any conclu&longs;ions, firmly demon­ &longs;trated, and &longs;o perfectly made ours, as that we can &longs;peedily run through them; for in &longs;um, what other, is that propo&longs;ition, that the &longs;quare of the &longs;ide &longs;ubtending the right angle in any triangle, is equal to the &longs;quares of the other two, which include it, but onely the Paralellograms being upon common ba&longs;es, and between parallels equal among&longs;t them&longs;elves? and this, la&longs;tly, is it not the &longs;ame, as to &longs;ay that tho&longs;e two &longs;uperficies are equal, of which equal parts applyed to equal parts, po&longs;&longs;e&longs;&longs;e equal place? Now the&longs;e inferences, which our intellect apprehendeth with time and a gradual motion, the Divine Wi&longs;dom, like light, penetrateth in an in&longs;tant, which is the &longs;ame as to &longs;ay, hath them alwayes pre­ &longs;ent: I conclude therefore, that our under&longs;tanding, both as to the manner and the multitude of the things comprehended by us, is infinitely &longs;urpa&longs;t by the Divine Wi&longs;dom; but yet I do not &longs;o vilifie it, as to repute it ab&longs;olutely nothing; yea rather, when I con&longs;ider how many and how great mi&longs;teries men have under&longs;tood, di&longs;covered, and contrived, I very plainly know and under&longs;tand the mind of man to be one of the works, yea one of the mo&longs;t ex­ cellent works of God.

Gods manner of knowing different from that of men.

Humane under­ &longs;tanding done by raciocination.

Definitions con­ tein virtually all the pa&longs;&longs;ions of the things defined.

Infinite Pa&longs;&longs;ions are perhaps but one onely.

The di&longs;cour&longs;es which humane rea&longs;on makes in a certain time, the Divine Wi&longs;dom re­ &longs;olveth in a mo­ ment; that is, hath them alwayes pre­ &longs;ent.

SAGR. I have oft times con&longs;idered with my &longs;elf, in pur&longs;uance of that which you &longs;peak of, how great the wit of man is; and whil'&longs;t I run thorow &longs;uch and &longs;o many admirable inventions found out by him, as well in the Arts, as Sciences; and again reflecting upon my own wit, &longs;o far from promi&longs;ing me the di&longs;covery of any thing new, that I de&longs;pair of comprehending what is already di&longs;­ covered, confounded with wonder, and &longs;urpri&longs;ed with de&longs;pera­ tion, I account my &longs;elf little le&longs;&longs;e than mi&longs;erable. If I behold a Statue of &longs;ome excellent Ma&longs;ter, I &longs;ay with my &longs;elf; When wilt thou know how to chizzle away the refu&longs;e of a piece of Marble, and di&longs;cover &longs;o lovely a figure, as lyeth hid therein? When wilt thou mix and &longs;pread &longs;o many different colours upon a Cloth, or Wall, and repre&longs;ent therewith all vi&longs;ible objects, like a Michael Angelo, a Raphaello, or a Tizvano? If I behold what inventions men have in comparting Mu&longs;ical intervals, in e&longs;tabli&longs;hing Pre­ cepts and Rules for the management thereof with admirable de­ light to the ear: When &longs;hall I cea&longs;e my a&longs;toni&longs;hment? What &longs;hall I &longs;ay of &longs;uch and &longs;o various In&longs;truments of that Art? The reading of excellent Poets, with what admiration doth it &longs;well any one that attentively con&longs;idereth the invention of conceits, and their explanation? What &longs;hall we &longs;ay of Architecture? What of Navigation? But, above all other &longs;tupendious inventi­ ons, what &longs;ublimity of mind was that in him, that imagined to him&longs;elf to find out a way to communicate his mo&longs;t &longs;ecret thoughts to any other per&longs;on, though very far di&longs;tant from him either in time, or place, &longs;peaking with tho&longs;e that are in the India's; &longs;peak­ ing to tho&longs;e that are not yet born, nor &longs;hall be this thou&longs;and, or ten thou&longs;and years? and with how much facility? but by the va­ rious collocation of ^{*} twenty little letters upon a paper? Let this be the Seal of all the admirable inventions of man, and the clo&longs;e of our Di&longs;cour&longs;e for this day: For the warmer hours being pa&longs;t, I &longs;uppo&longs;e that Salviatus hath a de&longs;ire to go and take the air in his Gondelo; but too morrow we will both wait upon you, to con­ tinue the Di&longs;cour&longs;es we have begun, &c.

The wit of man admirably acute.

The invention of writing &longs;tupendious above all others.

* For of &longs;o many only the Italian Alphabet con&longs;i&longs;ts.

Place this Plate at the end of the firstDialogue

GALILÆUS Galilæus Lyncæus, HIS SYSTEME OF THE WORLD.

The Second Dialogue.

INTERLOCVTORS.

SALVIATUS, SAGREDUS, and SIMPLICIUS.

SALV. The ye&longs;ter-dayes diver&longs;ions which led us out of the path of our principal di&longs;cour&longs;e, were &longs;uch and &longs;o many, that I know not how I can without your a&longs;&longs;i&longs;tance reco­ ver the track in which I am to proceed.

SAGR. I wonder not, that you, who have your fancy charged and laden with both what hath been, and is to be &longs;po­ ken, do find your &longs;elf in &longs;ome confu&longs;i­ on; but I, who as being onely an Auditor, have nothing to bur­ then my memory withal, but &longs;uch things as I have heard, may happily by a &longs;uccinct rehear&longs;al of them, recover the fir&longs;t thred of our Di&longs;cour&longs;e. As far therefore as my memory &longs;erves me, the &longs;um of ye&longs;terdayes conferences were an examination of the Prin­ ciples of Ptolomy and Copernicus, and which of their opinions is the more probable and rational; that, which affirmeth the &longs;ub­ &longs;tance of the Cœle&longs;tial bodies to be ingenerable, incorruptible, un­ alterable, impa&longs;&longs;ible, and in a word, exempt from all kind of change, &longs;ave that of local, and therefore to be a fifth e&longs;&longs;ence, quite different from this of our Elementary bodies, which are generable, corrup­ tible, alterable, &c. or el&longs;e the other, which taking away &longs;uch deformity from the parts of the World, holdeth the Earth to en­ joy the &longs;ame perfections as the other integral bodies of the uni­ ver&longs;e; and e&longs;teemeth it a moveable and erratick Globe, no le&longs;&longs;e than the Moon, Jupiter, Venus, or any other Planet: And la&longs;tly, maketh many particular parallels betwixt the Earth and Moon; and more with the Moon, than with any other Planet; hap­ ly by rea&longs;on we have greater and more certain notice of it, as being le&longs;&longs;e di&longs;tant from us. And having, la&longs;tly, concluded this &longs;econd opinion to have more of probability with it than the fir&longs;t, I &longs;hould think it be&longs;t in the &longs;ub&longs;equent di&longs;cour&longs;es to begin to exa­ mine whether the Earth be e&longs;teemed immoveable, as it hath been till now believed by mo&longs;t men, or el&longs;e moveable, as &longs;ome ancient Philo&longs;ophers held, and others of not very rece&longs;&longs;e times, were of opinion; and if it be moveable, to enquire of what kind its motion may be?

SALV. I &longs;ee already what way I am to take; but before we offer to proceed any farther, I am to &longs;ay &longs;omething to you touch­ ing tho&longs;e la&longs;t words which you &longs;pake, how that the opinion which holds the Earth to be endued with the &longs;ame conditions that the Cœle&longs;tial bodies enjoy, &longs;eems to be more true than the contra­ ry; for that I affirmed no &longs;uch thing, nor would I have any of the Propo&longs;itions in controver&longs;ie, be made to &longs;peak to any definitive &longs;en&longs;e: but I onely intended to produce on either part, tho&longs;e rea­ &longs;ons and an&longs;wers, arguments and &longs;olutions, which have been hi­ therto thought upon by others, together with certain others, which I have &longs;tumbled upon in my long &longs;earching thereinto, al­ wayes remitting the deci&longs;ion thereof to the judgment of others.

SAGR. I was unawares tran&longs;ported by my own &longs;en&longs;e of the thing; and believing that others ought to judg as I did, I made that conclu&longs;ion univer&longs;al, which &longs;hould have been particular; and therefore confe&longs;&longs;e I have erred, and the rather, in that I know not what Simplicius his judgment is in this particular.

SIMPL. I mu&longs;t confe&longs;&longs;e, that I have been ruminating all this night of what pa&longs;t ye&longs;terday, and to &longs;ay the truth, I meet there­ in with many acute, new, aud plau&longs;ible notions; yet neverthele&longs;s, I find my &longs;elf over-per&longs;waded by the authority of &longs;o many great Writers, and in particular -------&c. I &longs;ee you &longs;hake your head Sagredus, and &longs;mile to your &longs;elf, as if I had uttered &longs;ome great ab&longs;urdity.

SAGR. I not onely &longs;mile, but to tell you true, am ready to bur&longs;t with holding in my &longs;elf from laughing outright, for you have put me in mind of a very pretty pa&longs;&longs;age, that I was a wit­ ne&longs;&longs;e of, not many years &longs;ince, together with &longs;ome others of my worthy friends, which I could yet name unto you.

SALV. It would be well that you told us what it was, that &longs;o Simplicius may not &longs;till think that he gave you the occa&longs;ion of laughter.

SAGR. I am content. I found one day, at home in his hou&longs;e, at Venice, a famous Phi&longs;ician, to whom &longs;ome flockt for their &longs;tudies, and others out of curio&longs;ity, &longs;ometimes came thither to &longs;ee certain A­ natomies di&longs;&longs;ected by the hand of a no le&longs;&longs;e learned, than careful and experienced Anatomi&longs;t. It chanced upon that day, when I was there, that he was in &longs;earch of the original and ri&longs;e of the Nerves, about which there is a famous controver&longs;ie between the Galeni&longs;ts and Peripateticks; and the Anatomi&longs;t &longs;hewing, how that the great number of Nerves departing from the Brain, as their root, and pa&longs;&longs;ing by the nape of the Neck, di&longs;tend them&longs;elves afterwards along by the Back-bone, and branch them&longs;elves thorow all the Body; and that a very &longs;mall filament, as fine as a thred went to the Heart; he turned to a Gentleman whom he knew to be a Pe­ ripatetick Philo&longs;opher, and for who&longs;e &longs;ake he had with extraor­ dinary exactne&longs;&longs;e, di&longs;covered and proved every thing, and demand­ ed of him, if he was at length &longs;atisfied and per&longs;waded that the origi­ nal of the Nerves proceeded from the Brain, and not from the Heart? To which the Philo&longs;opher, after he had &longs;tood mu&longs;ing a while, an&longs;wered; you have made me to &longs;ee this bu&longs;ine&longs;&longs;e &longs;o plainly and &longs;en&longs;ibly, that did not the Text of Ari&longs;totle a&longs;&longs;ert the contrary, which po&longs;itively affirmeth the Nerves to proceed from the Heart, I &longs;hould be con&longs;trained to confe&longs;&longs;e your opinion to be true.

The original of the Nerv s. ac­ cording to Ari&longs;to­ tle, and according to Phi&longs;icians.

The ridiculus an&longs;wer of a Philo­ &longs;opher, determi­ ning the original of the Nerves.

SIMPL. I would have you know my Ma&longs;ters, that this contro­ ver&longs;ie about the original of the Nerves is not yet &longs;o proved and decided, as &longs;ome may perhaps per&longs;wade them&longs;elves.

SAGR. Nor que&longs;tionle&longs;&longs;e ever &longs;hall it be, if it find &longs;uch like contradictors; but that which you &longs;ay, doth not at all le&longs;&longs;en the extravagance of the an&longs;wer of that Peripatetick, who again&longs;t &longs;uch &longs;en&longs;ible experience produced not other experiments, or rea­ &longs;ons of Ari&longs;totle, but his bare authority and pure ip&longs;e dixit.

SIMPL. Ari&longs;totle had not gained &longs;o great authority, but for the force of his Demon&longs;trations, and the profoundne&longs;&longs;e of his arguments; but it is requi&longs;ite that we under&longs;tand him, and not onely under&longs;tand him, but have &longs;o great familiarity with his Books, that we form a perfect Idea thereof in our minds, &longs;o as that every &longs;aying of his may be alwayes as it were, pre&longs;ent in our memory for he did not write to the vulgar, nor is he obliged to &longs;pin out his Sillogi&longs;mes with the trivial method of di&longs;putes; nay rather, u&longs;ing a freedome, he hath &longs;ometimes placed the proof of one Propo&longs;ition among&longs;t Texts, which &longs;eem to treat of quite another point; and therefore it is requi&longs;ite to be ma&longs;ter of all that va&longs;t Idea, and to learn how to connect this pa&longs;&longs;age with that, and to combine this Text with another far remote from it; for it is not to be que&longs;tioned but that he who hath thus &longs;tudied him, knows how to gather from his Books the demon&longs;trations of every knowable deduction, for that they contein all things.

Requi&longs;ites to fit a man to philo&longs;o­ phate well after the manner ofri&longs;totle.

SAGR. But good Simplicius, like as the things &longs;cattered here and there in Ari&longs;totle, give you no trouble in collecting them, but that you per&longs;wade your &longs;elf to be able by comparing and connecting &longs;everal &longs;mall &longs;entences to extract thence the juice of &longs;ome de&longs;ired conclu&longs;ion, &longs;o this, which you and other egregi­ ous Philo&longs;ophers do with the Text of Ari&longs;totle, I could do by the ver&longs;es of Virgil, or of Ovid, compo&longs;ing thereof ^{*} Centones, and therewith explaining all the affairs of men, and &longs;ecrets of Na­ ture. But what talk I of Virgil, or any other Poet? I have a lit­ tle Book much &longs;horter than Ari&longs;totle and Ovid, in which are con­ teined all the Sciences, and with very little &longs;tudy, one may gather out of it a mo&longs;t perfect Idea, and this is the Alphabet; and there is no doubt but that he who knows how to couple and di&longs;po&longs;e aright this and that vowel, with tho&longs;e, or tho&longs;e other con&longs;onants, may gather thence the infallible an&longs;wers to all doubts, and de­ duce from them the principles of all Sciences and Arts, ju&longs;t in the &longs;ame manner as the Painter from divers &longs;imple colours, laid &longs;eve­ rally upon his Pallate, proceedeth by mixing a little of this and a little of that, with a little of a third, to repre&longs;ent to the life men, plants, buildings, birds, fi&longs;hes, and in a word, counterfeit­ ing what ever object is vi&longs;ible, though there be not on the Pallate all the while, either eyes, or feathers, or fins, or leaves, or &longs;tones. Nay, farther, it is nece&longs;&longs;ary, that none of the things to be imita­ ted, or any part of them, be actually among colours, if you would be able therewith to repre&longs;ent all things; for &longs;hould there be among&longs;t them v. gr. feathers, the&longs;e would &longs;erve to repre&longs;ent nothing &longs;ave birds, and plumed creatures.

A cunning way to gather Philo&longs;o­ phy out of any book what&longs;oever.

* A word &longs;ignify­ ing works compo­ &longs;ed of many frag­ ments of ver&longs;es collected out of the Poets.

SALV. And there are certain Gentlemen yet living, and in health, who were pre&longs;ent, when a Doctor, that was Profe&longs;&longs;or in a fa­ mous Academy, hearing the de&longs;cription of the Tele&longs;cope, by him not &longs;een as then, &longs;aid, that the invention was taken from Ari­ &longs;totle, and cau&longs;ing his works to be fetch't, he turned to a place where the Philo&longs;opher gives the rea&longs;on, whence it commeth, that from the bottom of a very deep Well, one may &longs;ee the &longs;tars in Heaven, at noon day; and, addre&longs;&longs;ing him&longs;elf to the company, &longs;ee here, &longs;aith he, the Well, which repre&longs;enteth the Tube, &longs;ee here the gro&longs;s vapours, from whence is taken the invention of the Cry&longs;tals, and &longs;ee here la&longs;tly the &longs;ight fortified by the pa&longs;&longs;age of the rays through a diaphanous, but more den&longs;e and ob&longs;cure medium.

Invention of the Tele&longs;cope taken from Ari&longs;totle.

SAGR. This is a way to comprehend all things knowable, much like to that wherewith a piece of marble conteineth in it one, yea, a thou&longs;and very beautiful Statua's, but the difficulty lieth in be­ ing able to di&longs;cover them; or we may &longs;ay, that it is like to the prophe&longs;ies of Abbot Joachim, or the an&longs;wers of the Heathen Oracles, which are not to be under&longs;tood, till after the things fore-told are come to pa&longs;&longs;e.

SALV. And why do you not adde the predictions of the Ge­ nethliacks, which are with like cleerne&longs;&longs;e &longs;een after the event, in their Horo&longs;copes, or, if you will, Configurations of the Heavens.

SAGR. In this manner the Chymi&longs;ts find, being led by their melancholly humour, that all the &longs;ublime&longs;t wits of the World have writ of nothing el&longs;e in reality, than of the way to make Gold; but, that they might tran&longs;mit the &longs;ecret to po&longs;terity with­ out di&longs;covering it to the vulgar, they contrived &longs;ome one way, and &longs;ome another how to conceal the &longs;ame under &longs;everal maskes; and it would make one merry to hear their comments upon the ancient Poets, finding out the important mi&longs;teries, which lie hid under their Fables; and the &longs;ignification of the Loves of the Moon, and her de&longs;cending to the Earth for Endimion; her di&longs;plea&longs;ure again&longs;t Acteon, and what was meant by Jupiters turning him&longs;elf into a &longs;howre of Gold; and into flames of fire; and what great &longs;ecrets of Art are conteined in that Mercury the Interpreter; in tho&longs;e thefts of Pluto; and in tho&longs;e Branches of Gold.

Chymi&longs;ts inter­ pret the Eables of the Poets to be &longs;e­ crets for making of Gold.

SIMPL. I believe, and in part know, that there want not in the World very extravagant heads, the vanities of whom ought not to redound to the prejudice of Ari&longs;totle, of whom my thinks you &longs;peak &longs;ometimes with too little re&longs;pect, and the onely antiquity and bare name that he hath acquired in the opinions of &longs;o many famous men, &longs;hould &longs;uffice to render him honourable with all that profe&longs;&longs;e them&longs;elves learned.

SALV. You &longs;tate not the matter rightly, Simplicius; There are &longs;ome of his followers that fear before they are in danger, who give us occa&longs;ion, or, to &longs;ay better, would give us cau&longs;e to e&longs;teem him le&longs;&longs;e, &longs;hould we con&longs;ent to applaud their Capricio's. And you, pray you tell me, are you for your part &longs;o &longs;imple, as not to know that had Arictotle been pre&longs;ent, to have heard the Doctor that would have made him Author of the Tele&longs;cope, he would have been much more di&longs;plea&longs;ed with him, than with tho&longs;e, who laught at the Doctor and his Comments? Do you que&longs;tion whether Ari&longs;totle, had he but &longs;een the novelties di&longs;covered in Hea­ ven, would not have changed his opinion, amended his Books, and embraced the more &longs;en&longs;ible Doctrine; rejecting tho&longs;e &longs;illy Gulls, which too &longs;crupulou&longs;ly, go about to defend what ever he hath &longs;aid; not con&longs;idering, that if Ari&longs;totle were &longs;uch a one as they fancy him to them&longs;elves, he would be a man of an untracta­ ble wit, an ob&longs;tinate mind, a barbarous &longs;oul, a &longs;tubborn will, that accounting all men el&longs;e but as &longs;illy &longs;heep, would have his Oracles preferred before the Sen&longs;es, Experience, and Nature her &longs;elf? They are the Sectators of Aristotle that have given him this Authority, and not he that hath u&longs;urped or taken it upon him; and becau&longs;e it is more ea&longs;ie for a man to &longs;culk under anothers &longs;hield than to &longs;hew him&longs;elf openly, they tremble, and are affraid to &longs;tir one &longs;tep from him; and rather than they will admit &longs;ome alterations in the Heaven of Ari&longs;totle, they will impertinently de­ ny tho&longs;e they behold in the Heaven of Nature.

Some of Ari&longs;to­ tles Sectators im­ pare the reputation of their Ma&longs;ter, in going about to en­ han&longs;e it.

SAGR. The&longs;e kind of Drolleries put me in mind of that Statu­ ary which having reduced a great piece of Marble to the Image of an Hercules, or a thundring Jupiter, I know not whether, and given it with admirable Art &longs;uch a vivacity and threatning fury, that it moved terror in as many as beheld it; he him&longs;elf began al&longs;o to be affraid thereof, though all its &longs;prightfulne&longs;&longs;e, and life was his own workman&longs;hip; and his affrightment was &longs;uch, that he had no longer the courage to affront it with his Chizzels and Mallet.

A ridiculous pa&longs;&longs;age of a certain Statuary.

SALV. I have many times wondered how the&longs;e nice maintain­ ers of what ever fell from Ari&longs;totle, are not aware how great a pre­ judice they are to his reputation and credit; and how that the more they go about to encrea&longs;e his Authority, the more they dimini&longs;h it; for while&longs;t I &longs;ee them ob&longs;tinate in their attempts to maintain tho&longs;e Propo&longs;itions which I palpably di&longs;cover to be manife&longs;tly fal&longs;e; and in their de&longs;ires to per&longs;wade me that &longs;o to do, is the part of a Philo&longs;opher; and that Ari&longs;totle him&longs;elf would do the &longs;ame, it much abates in me of the opinion that he hath rightly philo&longs;ophated about other conclu&longs;ions, to me more ab&longs;tru&longs;e: for if I could &longs;ee them concede and change opinion in a manife&longs;t truth, I would believe, that in tho&longs;e in which they &longs;hould per&longs;i&longs;t, they may have &longs;ome &longs;olid demon&longs;trations to me un­ known, and unheard of.

SAGR. Or when they &longs;hould be made to &longs;ee that they have ha­ zarded too much of their own and Ari&longs;totle's repuatation in con­ fe&longs;&longs;ing, that they had not under&longs;tood this or that conclu&longs;ion found out by &longs;ome other man; would it not be a le&longs;s evil for them to &longs;eek for it among&longs;t his Texts, by laying many of them together, according to the art intimated to us by Simplicius? for if his works contain all things knowable, it mu&longs;t follow al&longs;o that they may be therein di&longs;covered.

SALV. Good Sagredus, make no je&longs;t of this advice, which me thinks you rehear&longs;e in too Ironical a way; for it is not long &longs;ince that a very eminent Philo&longs;opher having compo&longs;ed a Book de animà, wherein, citing the opinion of Ari&longs;totle, about its being or not be­ ing immortal, he alledged many Texts, (not any of tho&longs;e hereto­ fore quoted by Alexander ab Alexandro: for in tho&longs;e he &longs;aid, that Ari&longs;totle had not &longs;o much as treated of that matter, much le&longs;s de­ termined any thing pertaining to the &longs;ame, but others) by him&longs;elf found out in other more ab&longs;tru&longs;e places, which tended to an er­ roneous &longs;en&longs;e: and being advi&longs;ed, that he would find it an hard matter to get a Licence from the Inqui&longs;itors, he writ back unto his friend, that he would notwith&longs;tanding, with all expedition procure the &longs;ame, for that if no other ob&longs;tacle &longs;hould interpo&longs;e, he would not much &longs;cruple to change the Doctrine of Ari&longs;totle, and with other expo&longs;itions, and other Texts to maintain the con­ trary opinion, which yet &longs;hould be al&longs;o agreeable to the &longs;en&longs;e of Ari&longs;totle.

A brave re&longs;olu­ tion of a certain Peripatetick Phi­ lo&longs;opher.

SAGR. Oh mo&longs;t profound Doctor, this! that can command me that I &longs;tir not a &longs;tep from Ari&longs;totle, but will him&longs;elf lead him by the no&longs;e, and make him &longs;peak as he plea&longs;eth. See how much it importeth to learn to take Time by the Fore-top. Nor is it &longs;ea&longs;onable to have to do with Hercules, whil'&longs;t he is en­ raged, and among&longs;t the Furies, but when he is telling merry tales among&longs;t the Meonion Damo&longs;els. Ah, unheard of &longs;ordidne&longs;&longs;e of &longs;ervile &longs;ouls! to make them&longs;elves willing &longs;laves to other mens opi­ nions; to receive them for inviolable Decrees, to engage them­ &longs;elves to &longs;eem &longs;atisfied and convinced by arguments, of &longs;uch effi­ cacy, and &longs;o manife&longs;tly concludent, that they them&longs;elves can­ not certainly re&longs;olve whether they were really writ to that pur­ po&longs;e, or &longs;erve to prove that a&longs;&longs;umption in hand, or the contrary. But, which is a greater madne&longs;&longs;e, they are at variance among&longs;t them&longs;elves, whether the Author him&longs;elf hath held the affirmative part, or the negative. What is this, but to make an Oracle of a Log, and to run to that for an&longs;wers, to fear that, to reverence and adore that?

The &longs;ervile &longs;pi­ rit of &longs;ome of Ari­ &longs;totles followers.

SIMPL. But in ca&longs;e we &longs;hould recede from Aristotle, who have we to be our Guid in Philo&longs;ophy? Name you &longs;ome Author.

SALV. We need a Guid in unknown and uncouth wayes, but in champion places, and open plains, the blind only &longs;tand in need of a Leader; and for &longs;uch, it is better that they &longs;tay at home. But he that hath eyes in his head, and in his mind, him &longs;hould a man choo&longs;e for his Guid. Yet mi&longs;take me not, thinking that I &longs;peak this, for that I am again&longs;t hearing of Ari&longs;totle; for on the contrary, I commend the reading, and diligently &longs;tudying of him; and onely blame the &longs;ervile giving ones &longs;elf up a &longs;lave unto him, &longs;o, as blindly to &longs;ub&longs;cribe to what ever he delivers, and without &longs;earch of any farther rea&longs;on thereof, to receive the &longs;ame for an in­ violable decree. Which is an abu&longs;e, that carrieth with it ano­ ther great inconvenience, to wit, that others will no longer take pains to under&longs;tand the validity of his Demon&longs;trations. And what is more &longs;hameful, than in the midde&longs;t of publique di&longs;putes, while&longs;t one per&longs;on is treating of demon&longs;trable conclu&longs;ions, to hear aother interpo&longs;e with a pa&longs;&longs;age of Ari&longs;totle, and not &longs;el­ dome writ to quite another purpo&longs;e, and with that to &longs;top the mouth of his opponent? But if you will continue to &longs;tudy in this manner, I would have you lay a&longs;ide the name of Philo&longs;ophers; and call your &longs;elves either Hi&longs;torians or Doctors of Memory, for it is not &longs;it, that tho&longs;e who never philo&longs;ophate, &longs;hould u&longs;urp the honourable title of Philo&longs;ophers. But it is be&longs;t for us to re­ turn to &longs;hore, and not lanch farther into a boundle&longs;&longs;e Gulph, out of which we &longs;hall not be able to get before night. Therefore Simplicius, come either with arguments and demon&longs;trations of your own, or of Ari&longs;totle, and bring us no more Texts and na­ ked authorities, for our di&longs;putes are about the Sen&longs;ible World, and not one of Paper. And fora&longs;much as in our di&longs;cour&longs;es ye&longs;ter­ day, we retrein'd the Earth from darkne&longs;&longs;e, and expo&longs;ed it to the open skie, &longs;hewing, that the attempt to enumerate it among&longs;t tho&longs;e which we call Cœle&longs;tial bodies, was not a po&longs;ition &longs;o foil'd, and vanqui&longs;h't, as that it had no life left in it; it followeth next, that we proceed to examine what probability there is for holding of it fixt, and wholly immoveable, &longs;cilicet as to its entire Globe, what likelyhood there is for making it moveable with &longs;ome motion, and of what kind that may be. And fora&longs;much as in this &longs;ame que&longs;tion I am ambiguous, and Simplicius is re&longs;olute, as likewi&longs;e Ari&longs;totle for the opinion of its immobility, he &longs;hall one by one produce the arguments in favour of their opinion, and I will al­ ledge the an&longs;wers and rea&longs;ons on the contrary part; and next Sa­ gredus &longs;hall tell us his thoughts, and to which &longs;ide he finds him­ &longs;elf inclined.

Too clo&longs;e adhe­ ring to Ari&longs;totle is blameable.

It is not ju&longs;t, that tho&longs;e who never philo&longs;ophate, &longs;hould u&longs;urp the title of Philo&longs;ophers.

The Sen&longs;ible World.

SAGR. Content; provided alwayes that I may re&longs;erve the li­ berty to my &longs;elf of alledging what pure natural rea&longs;on &longs;hall &longs;ome­ times dictate to me.

SALV. Nay more, it is that which I particularly beg of you; for, among&longs;t the more ea&longs;ie, and, to &longs;o &longs;peak, material con&longs;idera­ tions, I believe there are but few of them that have been omit­ ted by Writers, &longs;o that onely &longs;ome of the more &longs;ubtle, and re­ mote can be de&longs;ired, or wanting; and to inve&longs;tigate the&longs;e, what other ingenuity can be more &longs;it than that of the mo&longs;t acute and piercing wit of Sagredus?

SAGR. I am what ever plea&longs;eth Salviatus, but I pray you, let us not &longs;ally out into another kind of digre&longs;&longs;ion complemental; for at this time I am a Philo&longs;opher, and in the Schools, not in the Court.

SALV. Let our contemplation begin therefore with this con&longs;i­ deration, that what&longs;oever motion may be a&longs;cribed to the Earth, it is nece&longs;&longs;ary that it be to us, (as inhabitants upon it, and con&longs;e­ quently partakers of the &longs;ame) altogether imperceptible, and as if it were not at all, &longs;o long as we have regard onely to terre&longs;trial things; but yet it is on the contrary, as nece&longs;&longs;ary that the &longs;ame motion do &longs;eem common to all other bodies, and vi&longs;ible ob­ jects, that being &longs;eparated from the Earth, participate not of the &longs;ame. So that the true method to find whether any kind of motion may be a&longs;cribed to the Earth, and that found, to know what it is, is to con&longs;ider and ob&longs;erve if in bodies &longs;eparated from the Earth, one may di&longs;cover any appearance of motion, which e­ qually &longs;uiteth to all the re&longs;t; for a motion that is onely &longs;een, v. gr. in the Moon, and that hath nothing to do with Venus or Jupiter, or any other Stars, cannot any way belong to the Earth, or to any other &longs;ave the Moon alone. Now there is a mo&longs;t general and grand motion above all others, and it is that by which the Sun, the Moon, the other Planets, and the Fixed Stars, and in a word, the whole Univer&longs;e, the Earth onely excepted, appeareth in our thinking to move from the Ea&longs;t towards the We&longs;t, in the &longs;pace of twenty four hours; and this, as to this fir&longs;t appearance, hath no ob&longs;tacle to hinder it, that it may not belong to the Earth alone, as well as to all the World be&longs;ides, the Earth excepted; for the &longs;ame a&longs;pects will appear in the one po&longs;ition, as in the other. Hence it is that Ari&longs;totle and Ptolomy, as having hit upon this con­ &longs;ideration, in going about to prove the Earth to be immoveable, argue not again&longs;t any other than this Diurnal Motion; &longs;ave onely that Ari&longs;totle hinteth &longs;omething in ob&longs;cure terms again&longs;t another Motion a&longs;cribed to it by an Ancient, of which we &longs;hall &longs;peak in its place.

The motions of the Earth are im­ perceptible to its inhabitants.

The Earth can have no other mo­ tions, than tho&longs;e which to us appear commune to all the rest of the Vni­ ver&longs;e, the Earth excepted.

The Diurnal Mo­ tion, &longs;eemeth com­ mune to all the V­ niver&longs;e, &longs;ave onely the Earth excepted.

Ari&longs;totle and Ptolomy argue a­ gain&longs;t the Diur­ nal Motion attri­ buted to the Earth.

SAGR. I very well perceive the nece&longs;&longs;ity of your illation: but I meet with a doubt which I know not how to free my &longs;elf from, and this it is, That Copernicus a&longs;&longs;igning to the Earth another mo­ tion be&longs;ide the Diurnal, which, according to the rule even now laid down, ought to be to us, as to appearance, imperceptible in the Earth, but vi&longs;ible in all the re&longs;t of the World; me thinks I may nece&longs;&longs;arily infer, either that he hath manife&longs;tly erred in a&longs;&longs;igning the Earth a motion, to which there appears not a general corre­ &longs;pondence in Heaven; or el&longs;e that if there be &longs;uch a congruity therein, Ptolomy on the other hand hath been deficient in not con­ futing this, as he hath done the other.

SALV. You have good cau&longs;e for your doubt: and when we come to treat of the other Motion, you &longs;hall &longs;ee how far Coper­ nicus excelled Ptolomey in clearne&longs;s and &longs;ublimity of wit, in that he &longs;aw what the other did not, I mean the admirable harmony wherein that Motion agreed with all the other Cœle&longs;tial Bodies. But for the pre&longs;ent we will &longs;u&longs;pend this particular, and return to our fir&longs;t con&longs;ideration; touching which I will proceed to propo&longs;e (begining with things more general) tho&longs;e rea&longs;ons which &longs;eem to favour the mobility of the Earth, and then wait the an&longs;wers which Simplicius &longs;hall make thereto. And fir&longs;t, if we con&longs;ider onely the immen&longs;e magnitude of the Starry Sphere, compared to the &longs;malne&longs;s of the Terre&longs;trial Globe, contained therein &longs;o many mil­ lions of times; and moreover weigh the velocity of the motion which mu&longs;t in a day and night make an entire revolution thereof, I cannot per&longs;wade my &longs;elf, that there is any man who believes it more rea&longs;onable and credible, that the Cœle&longs;tial Sphere turneth round, and the Terre&longs;trial Globe &longs;tands &longs;till.

Why the diurnal motion more pro­ bably &longs;hould belong to the Earth, than to the re&longs;t of the Vniver&longs;e.

SAGR. If from the univer&longs;ality of effects, which may in nature have dependence upon &longs;uch like motions, there &longs;hould indifferent­ ly follow all the &longs;ame con&longs;equences to an hair, a&longs;well in one Hypo­ the&longs;is as in the other; yet I for my part, as to my fir&longs;t and general apprehen&longs;ion, would e&longs;teem, that he which &longs;hould hold it more ra­ tional to make the whole Univer&longs;e move, and thereby to &longs;alve the Earths mobility, is more unrea&longs;onable than he that being got to the top of your Turret, &longs;hould de&longs;ire, to the end onely that he might behold the City, and the Fields about it, that the whole Country might turn round, that &longs;o he might not be put to the trouble to &longs;tir his head. And yet doubtle&longs;s the advantages would be many and great which the Copernican Hypothe&longs;is is attended with, above tho&longs;e of the Ptolomaique, which in my opinion re­ &longs;embleth, nay &longs;urpa&longs;&longs;eth that other folly; &longs;o that all this makes me think that far more probable than this. But haply Ari&longs;totle, Ptolomey, and Simplicius may find the advantages of their Sy­ &longs;teme, which they would do well to communicate to us al&longs;o, if any &longs;uch there be; or el&longs;e declare to me, that there neither are or can be any &longs;uch things.

SALV. For my part, as I have not been able, as much as I have thought upon it, to find any diver&longs;ity therein; &longs;o I think I have found, that no &longs;uch diver&longs;ity can be in them: in &longs;o much that I e&longs;teem it to no purpo&longs;e to &longs;eek farther after it. Therefore ob­ &longs;erve: Motion is &longs;o far Motion, and as Motion operateth, by how far it hath relation to things which want Motion: but in tho&longs;e things which all equally partake thereof it hath nothing to do, and is as if it never were. And thus the Merchandi&longs;es with which a &longs;hip is laden, &longs;o far move, by how far leaving London, they pa&longs;s by France, Spain, Italy, and &longs;ail to Aleppo, which London, France, Spain &c. &longs;tand &longs;till, not moving with the &longs;hip: but as to the Che&longs;ts, Bales and other Parcels, wherewith the &longs;hip is &longs;tow'd and and laden, and in re&longs;pect of the &longs;hip it &longs;elf, the Motion from Lon­ don to Syria is as much as nothing; and nothing-altereth the re­ lation which is between them: and this, becau&longs;e it is common to all, and is participated by all alike: and of the Cargo which is in the &longs;hip, if a Bale were romag'd from a Che&longs;t but one inch onely, this alone would be in that Cargo, a greater Motion in re&longs;pect of the Che&longs;t, than the whole Voyage of above three thou&longs;and miles, made by them as they were &longs;tived together.

Motion, as to the things that equally move thereby, is as of it never were, & &longs;o far operates as it hath relation to things deprived of motion.

SIMPL. This Doctrine is good, &longs;ound, and altogether Peri­ patetick.

SALV. I hold it to be much more antient: and &longs;u&longs;pect that A- ri&longs;totle in receiving it from &longs;ome good School, did not fully under­ &longs;tand it, and that therefore, having delivered it with &longs;ome altera­ tion, it hath been an occa&longs;ion of confu&longs;ion among&longs;t tho&longs;e, who would defend whatever he &longs;aith. And when he writ, that what­ &longs;oever moveth, doth move upon &longs;omething immoveable, I &longs;uppo&longs;e that he equivocated, and meant, that whatever moveth, moveth in re&longs;pect to &longs;omething immoveable; which propo&longs;ition admitteth no doubt, and the other many.

A propo&longs;ition ta­ ken by Ari&longs;totle from the Antients, but &longs;omewhat al­ tered by him.

SAGR. Pray you make no digre&longs;&longs;ion, but proceed in the di&longs;­ &longs;ertation you began.

SALV. It being therefore manife&longs;t, that the motion which is common to many moveables, is idle, and as it were, null as to the relation of tho&longs;e moveables between them&longs;elves, becau&longs;e that a­ mong them&longs;elves they have made no change: and that it is ope­ rative onely in the relation that tho&longs;e moveables have to other things, which want that motion, among which the habitude is changed: and we having divided the Univer&longs;e into two parts, one of which is nece&longs;&longs;arily moveable, and the other immoveable; for the obtaining of what&longs;oever may depend upon, or be required from &longs;uch a motion, it may as well be done by making the Earth alone, as by making all the re&longs;t of the World to move: for that the operation of &longs;uch a motion con&longs;i&longs;ts in nothing el&longs;e, &longs;ave in the relation or habitude which is between the Cœle&longs;tial Bodies, and the Earth, the which relation is all that is changed. Now if for the obtaining of the &longs;ame effect ad unguem, it be all one whe­ ther the Earth alone moveth, the re&longs;t of the Univer&longs;e &longs;tanding &longs;till; or that, the Earth onely &longs;tanding &longs;till, the whole Univer&longs;e moveth with one and the &longs;ame motion; who would believe, that Nature (which by common con&longs;ent, doth not that by many things, which may be done by few) hath cho&longs;en to make an innumerable number of mo&longs;t va&longs;t bodies move, and that with an unconceivable velocity, to perform that, which might be done by the moderate motion of one alone about its own Centre?

The fir&longs;t di&longs;cour&longs;e to prove that the diurnal motion be­ longs to the Earth.

Nature never doth that by many things, which may be done by a few.

SIMPL. I do not well under&longs;tand, how this grand motion &longs;ig­ ni&longs;ieth nothing as to the Sun, as to the Moon, as to the other Pla­ nets, and as to the innumerable multitude of fixed &longs;tars: or why you &longs;hould &longs;ay that it is to no purpo&longs;e for the Sun to pa&longs;s from one Meridian to another; to ri&longs;e above this Horizon, to &longs;et beneath that other; to make it one while day, another while night: the like variations are made by the Moon, the other Planets, and the fixed &longs;tars them&longs;elves.

SALV. All the&longs;e alterations in&longs;tanced by you, are nothing, &longs;ave onely in relation to the Earth: and that this is true, do but i­ magine the Earth to move, and there will be no &longs;uch thing in the World as the ri&longs;ing or &longs;etting of the Sun or Moon, nor Horizons, nor Meridians, nor days, nor nights; nor, in a word, will &longs;uch a motion cau&longs;e any mutation between the Moon and Sun, or any other &longs;tar what&longs;oever, whether fixed or erratick; but all the&longs;e changes have relation to the Earth: which all do yet in &longs;um import no other than as if the Sun &longs;hould &longs;hew it &longs;elf now to China, anon to Per&longs;ia, then to Egypt, Greece, France, Spain, A­ merica, &c. and the like holdeth in the Moon, and the re&longs;t of the Cœle&longs;tial Bodies: which &longs;elf &longs;ame effect falls out exactly in the &longs;ame manner, if, without troubling &longs;o great a part of the Univer&longs;e, the Terre&longs;trial Globe be made to revolve in it &longs;elf. But we will augment the difficulty by the addition of this other, which is a very great one, namely, that if you will a&longs;cribe this Great Motion to Heaven, you mu&longs;t of nece&longs;&longs;ity make it contrary to the particular motion of all the Orbs of the Planets, each of which without controver&longs;ie hath its peculiar motion from the We&longs;t towards the Ea&longs;t, and this but very ea&longs;ie and moderate: and then you make them to be hurried to the contrary part, i. e. from Ea&longs;t to We&longs;t, by this mo&longs;t furious diurnal motion: whereas, on the contrary, making the Earth to move in it &longs;elf, the contrariety of motions is taken away, and the onely motion from We&longs;t to Ea&longs;t is accom­ modated to all appearances, and exactly &longs;atisfieth every Phœno­ menon.

The diurnal mo­ tion cau&longs;eth no mutation among&longs;t the Cœle&longs;tial Bo­ dies, but all chan­ ges have relation to the Earth.

A &longs;ccond con­ firmation that the diurnal motion be­ longs to the Earth.

SIMPL. As to the contrariety of Motions it would import lit­ tle, for Ari&longs;totle demon&longs;trateth, that circular motions, are not con­ trary to one another; and that theirs cannot be truly called con­ trariety.

Circular moti­ ons are not contra­ ry, according to Ari&longs;totle.

SALV. Doth Ari&longs;totle demon&longs;trate this, or doth he not rather barely affirm it, as &longs;erving to &longs;ome certain de&longs;ign of his? If con­ traries be tho&longs;e things, that de&longs;troy one another, as he him&longs;elf affirmeth, I do not &longs;ee how two moveables that encounter each other in a circular line, &longs;hould le&longs;&longs;e prejudice one another, than if they interfered in a right line.

SAGR. Hold a little, I pray you. Tell me Simplicius, when two Knights encounter each other, tilting in open field, or when two whole Squadrons, or two Fleets at Sea, make up to grapple, and are broken and &longs;unk, do you call the&longs;e encounters contrary to one another?

SIMPL. Yes, we &longs;ay they are contrary.

SAGR. How then, is there no contrariety in circular motions. The&longs;e motions, being made upon the &longs;uper&longs;icies of the Earth or Water, which are, as you know, &longs;pherical, come to be circular. Can you tell, Simplicius, which tho&longs;e circular motions be, that are not contrary to each other? They are (if I mi&longs;take not) tho&longs;e of two circles, which touching one another without, one thereof being turn'd round, naturally maketh the other move the contra­ ry ^{*} way; but if one of them &longs;hall be within the other, it is im­ po&longs;&longs;ible that their motion being made towards different points, they &longs;hould not ju&longs;tle one another.

As you &longs;ee in a Mill, wherein the implicated cogs &longs;et the wheels on mo­ ving.

SALV. But be they contrary, or not contrary, the&longs;e are but alterations of words; and I know, that upon the matter, it would be far more proper and agreeable with Nature, if we could &longs;alve all with one motion onely, than to introduce two that are (if you will not call them contrary) oppo&longs;ite; yet do I not cen&longs;ure this introduction (of contrary motions) as impo&longs;&longs;ible; nor pretend I from the denial thereof, to inferre a nece&longs;&longs;ary Demon&longs;tration, but onely a greater probability, of the other. A third rea&longs;on which maketh the Ptolomaique Hypothe&longs;is le&longs;&longs;e probable is, that it mo&longs;t unrea&longs;onably confoundeth the order, which we a&longs;&longs;uredly &longs;ee to be among&longs;t tho&longs;e Cœle&longs;tial Bodies, the circumgyration of which is not que&longs;tionable, but mo&longs;t certain. And that Order is, that according as an Orb is greater, it fini&longs;heth its revolution in a longer time, and the le&longs;&longs;er, in &longs;horter. And thus Saturn de&longs;cri­ bing a greater Circle than all the other Planets, compleateth the &longs;ame in thirty yeares: Jupiter fini&longs;heth his; that is le&longs;&longs;e, in twelve years: Mars in two: The Moon runneth thorow hers, &longs;o much le&longs;&longs;e than the re&longs;t, in a Moneth onely. Nor do we le&longs;&longs;e &longs;en&longs;ibly &longs;ee that of the Medicean Stars, which is neare&longs;t to Ju- piter, to make its revolution in a very &longs;hort time, that is, in four and forty hours, or thereabouts, the next to that in three dayes and an half, the third in &longs;even dayes, and the mo&longs;t remote in &longs;ixteen. And this rate holdeth well enough, nor will it at all alter, while&longs;t we a&longs;&longs;ign the motion of 24 hours to the Terre&longs;trial Globe, for it to move round its own center in that time; but if you would have the Earth immoveable, it is nece&longs;&longs;ary, that when you have pa&longs;t from the &longs;hort period of the Moon, to the others &longs;ucce&longs;&longs;ively bigger, until you come to that of Mars in two years, and from thence to that of the bigger Sphere of Jupiter in twelve years, and from this to the other yet bigger of Saturn, who&longs;e period is of thirty years, it is nece&longs;&longs;ary, I &longs;ay, that you pa&longs;&longs;e to another Sphere incomparably greater &longs;till than that, and make this to ac­ compli&longs;h an entire revolution in twenty four hours. And this yet is the lea&longs;t di&longs;order that can follow. For if any one &longs;hould pa&longs;&longs;e from the Sphere of Saturn to the Starry Orb, and make it &longs;o much bigger than that of Saturn, as proportion would require, in re&longs;pect of its very &longs;low motion, of many thou&longs;ands of years, then it mu&longs;t needs be a Salt much more ab&longs;urd, to skip from this to another bigger, and to make it convertible in twenty four hours. But the motion of the Earth being granted, the order of the pe­ riods will be exactly ob&longs;erved, and from the very &longs;low Sphere of Saturn, we come to the fixed Stars, which are wholly immovea­ ble, and &longs;o avoid a fourth difficulty, which we mu&longs;t of nece&longs;&longs;ity ad­ mit, if the Starry Sphere be &longs;uppo&longs;ed moveable, and that is the immen&longs;e di&longs;parity between the motions of tho&longs;e &longs;tars them&longs;elves; of which &longs;ome would come to move mo&longs;t &longs;wiftly in mo&longs;t va&longs;t cir­ cles, others mo&longs;t &longs;lowly in circles very &longs;mall, according as tho&longs;e or the&longs;e &longs;hould be found nearer, or more remote from the Poles; which &longs;till is accompanied with an inconvenience, as well becau&longs;e we &longs;ee tho&longs;e, of who&longs;e motion there is no que&longs;tion to be made, to move all in very immen&longs;e circles; as al&longs;o, becau&longs;e it &longs;eems to be an act done with no good con&longs;ideration, to con&longs;titute bodies, that are de&longs;igned to move circularly, at immen&longs;e di&longs;tances from the centre, and afterwards to make them move in very &longs;mall cir­ cles. And not onely the magnitudes of the circles, and con&longs;e­ quently the velocity of the motions of the&longs;e Stars, &longs;hall be mo&longs;t different from the circles and motions of tho&longs;e others, but (which &longs;hall be the fifth inconvenience) the &longs;elf-&longs;ame Stars &longs;hall &longs;ucce&longs;&longs;ively vary its circles and velocities: For that tho&longs;e, which two thou&longs;and years &longs;ince were in the Equinoctial, and con&longs;equently did with their motion de&longs;cribe very va&longs;t cir­ cles, being in our dayes many degrees di&longs;tant from thence, mu&longs;t of nece&longs;&longs;ity become more &longs;low of motion, and be reduced to move in le&longs;&longs;er circles, and it is not altogether impo&longs;&longs;ible but that a time may come, in which &longs;ome of them which in aforetime had continually moved, &longs;hall be reduced by uniting with the Pole, to a &longs;tate of re&longs;t, and then after &longs;ome time of ce&longs;&longs;ation, &longs;hall return to their motion again; whereas the other Stars, touching who&longs;e motion none &longs;tand in doubt, do all de&longs;cribe, as hath been &longs;aid, the great circle of their Orb, and in that maintain them&longs;elves without any variation. The ab&longs;urdity is farther enlarged (which let be the &longs;ixth inconvenience) to him that more &longs;eriou&longs;ly exami­ neth the thing, in that no thought can comprehend what ought to be the &longs;olidity of that immen&longs;e Sphere, who&longs;e depth &longs;o &longs;tedfa&longs;tly holdeth fa&longs;t &longs;uch a multitude of Stars, which without ever chang­ ing fite among them&longs;elves, are with &longs;o much concord carried a­ bout, with &longs;o great di&longs;parity of motions. Or el&longs;e, &longs;uppo&longs;ing the Heavens to be fluid, as we are with more rea&longs;on to believe, &longs;o as that every Star wandereth to and fro in it, by wayes of its own, what rules &longs;hall regulate their motions, and to what pur­ po&longs;e, &longs;o, as that being beheld from the Earth, they appear as if they were made by one onely Sphere? It is my opinion, that they might &longs;o much more ea&longs;ily do that, and in a more commodious manner, by being con&longs;tituted immoveable, than by being made errant, by how much more facile it is to number the quarries in the Pavement of a Piazza, than the rout of boyes which run up and down upon them. And la&longs;tly, which is the &longs;eventh in&longs;tance, if we atribute the Diurnal Motion to the highe&longs;t Heaven, it mu&longs;t be con&longs;tituted of &longs;uch a force and efficacy, as to carry along with it the innumerable multitude of fixed Stars, Bodies all of va&longs;t magnitude, and far bigger than the Earth; and moreover all the Spheres of the Planets; notwith&longs;tanding that both the&longs;e and tho&longs;e of their own nature move the contrary way. And be&longs;ides all this, it mu&longs;t be granted, that al&longs;o the Element of Fire, and the great­ er part of the Air, are likewi&longs;e forcibly hurried along with the re&longs;t, and that the &longs;ole little Globe of the Earth pertinaciou&longs;ly &longs;tands &longs;till, and unmoved again&longs;t &longs;uch an impul&longs;e; a thing, which in my thinking, is very difficult; nor can I &longs;ee how the Earth, a pendent body, and equilibrated upon its centre, expo&longs;ed indif­ ferently to either motion or re&longs;t, and environed with a liquid am­ bient, &longs;hould not yield al&longs;o as the re&longs;t, and be carried about. But we find none of the&longs;e ob&longs;tacles in making the Earth to move; a &longs;mall body, and in&longs;en&longs;ible, compared to the Univer&longs;e, and therefore unable to offer it any violence.

A third confir­ mation of the &longs;ame Doctrine.

The greater Orbs make their conver­ &longs;ions in greater times.

The times of the Medicean Planets conver&longs;ions.

The motion of 24 hours a&longs;cribed to the highe&longs;t Sphere di&longs;orders the period of the inferiour.

The fourth Con­ firmation.

Great di&longs;parity among&longs;t the moti­ ons of the particu­ lar fixed &longs;tars, if their Sphere be moveable.

The fifth Con­ firmation.

The motions of the fixed &longs;tars would accelerate and grow &longs;low in divers times, if the &longs;tarry Sphere were moueable.

The &longs;ixth Con­ firmatiox.

The Seventh Con­ firmation.

The Earth a pendent Body, and equilibrated in a fluid Medium &longs;eems unable to re&longs;i&longs;t the rapture of the Diurnal Motion.

SAGR. I find my fancy di&longs;turbed with certain conjectures &longs;o con­ fu&longs;edly &longs;prung from your later di&longs;cour&longs;es; that, if I would be ena­ bled to apply my &longs;elf with atention to what followeth, I mu&longs;t of ne­ ce&longs;&longs;ity attempt whether I can better methodize them, and gather thence their true con&longs;truction, if haply any can be made of them; and peradventure, the proceeding by interrogations may help me the more ea&longs;ily to expre&longs;&longs;e my &longs;elf. Therefore I demand fir&longs;t of Sim­ plicius, whether he believeth, that divers motions may natural­ ly agree to one and the &longs;ame moveable body, or el&longs;e that it be requi&longs;ite its natural and proper motion be onely one.

SIMPL. To one &longs;ingle moveable, there can naturally agree but one &longs;ole motion, and no more; the re&longs;t all happen acciden­ tally and by participation; like as to him that walketh upon the Deck of a Ship, his proper motion is that of his walk, his motion by participation that which carrieth him to his Port, whither he would never with his walking have arrived, if the Ship with its motion had not wafted him thither.

A &longs;ingle move­ able hath but onely one natural moti­ on, and all the re&longs;t are by partici­ pation.

SAGR. Tell me &longs;econdly. That motion, which is communi­ cated to any moveable by participation, while&longs;t it moveth by it &longs;elf, with another motion different from the participated, is it nece&longs;&longs;ary, that it do re&longs;ide in &longs;ome certain &longs;ubject by it &longs;elf, or el&longs;e can it &longs;ub&longs;i&longs;t in nature alone, without other &longs;upport.

SIMPL. Ari&longs;totle giveth you an an&longs;wer to all the&longs;e que&longs;tions, and tels you, that as of one &longs;ole moveable the motion is but one; &longs;o of one &longs;ole motion the moveable is but one; and con&longs;equent­ ly, that without the inherence in its &longs;ubject, no motion can ei­ ther &longs;ub&longs;i&longs;t, or be imagined.

Motion cannot be made without its moveable &longs;ub­ ject.

SAGR. I would have you tell me in the third place, whether you beblieve that the Moon and the other Planets and Cœle&longs;tial bodies, have their proper motions, and what they are.

SIMPL. They have &longs;o, and they be tho&longs;e according to which they run through the Zodiack, the Moon in a Moneth, the Sun in a Year, Mars in two, the Starry Sphere in tho&longs;e &longs;o many thou­ &longs;and. And the&longs;e are their proper, or natural motions.

SAGR. But that motion wherewith I &longs;ee the fixed Stars, and with them all the Planets go unitedly from Ea&longs;t to We&longs;t, and re­ turn round to the Ea&longs;t again in twenty four hours, how doth it agree with them?

SIMPL. It &longs;uiteth with them by participation.

SAGR. This then re&longs;ides not in them, and not re&longs;iding in them, nor being able to &longs;ub&longs;i&longs;t without &longs;ome &longs;ubject in which it is re&longs;ident, it mu&longs;t of force be the proper and natural motion of &longs;ome other Sphere.

SIMPL. For this purpo&longs;e A&longs;tronomers, and Philo&longs;ophers have found another high Sphere, above all the re&longs;t, without Stars, to which Natural agreeth the Diurnal Motion; and this they call the Primum mobile; the which carrieth along with it all the in­ feriour Spheres, contributing and imparting its motion to them.

SAGR. But when, without introducing other Spheres unknown and hugely va&longs;t, without other motions or communicated raptures, with leaving to each Sphere its &longs;ole and &longs;imple motion, without intermixing contrary motions, but making all turn one way, as it is nece&longs;&longs;ary that they do, depending all upon one &longs;ole principle, all things proceed orderly, and corre&longs;pond with mo&longs;t perfect har­ mony, why do we reject this Phœnomenon, and give our a&longs;&longs;ent to tho&longs;e prodigious and laborious conditions?

SIMPL. The difficulty lyeth in finding out this &longs;o natural and expeditious way.

SAGR. In my judgment this is found. Make the Earth the Primum mobile, that is, make it turn round its own axis in twenty four hours, and towards the &longs;ame point with all the other Spheres; and without participating this &longs;ame motion to any other Planet or Star, all &longs;hall have their ri&longs;ings, &longs;ettings, and in a word, all their other appearances.

SIMPL. The bu&longs;ine&longs;s is, to be able to make the Earth move without athou&longs;and inconveniences.

SALV. All the inconveniences &longs;hall be removed as fa&longs;t as you propound them: and the things &longs;poken hitherto are onely the primary and more general inducements which give us to believe that the diurnal conver&longs;ion may not altogether without probabi­ lity be applyed to the Earth, rather than to all the re&longs;t of the U­ niver&longs;e: the which inducements I impo&longs;e not upon you as invio­ lable Axioms, but as hints, which carry with them &longs;omewhat of likelihood. And in regard I know very well, that one &longs;ole ex­ periment, or concludent demon&longs;tration, produced on the contrary part, &longs;ufficeth to batter to the ground the&longs;e and a thou&longs;and other probable Arguments; therefore it is not fit to &longs;tay here, but proceed forwards and hear what Simplicius an&longs;wereth, and what greater probabilities, or &longs;tronger arguments he alledgeth on the contrary.

One &longs;ingle ex­ periment, or &longs;ound demon&longs;tration bat­ tereth down all ar­ guments meerly probable.

SIMPL. I will fir&longs;t &longs;ay &longs;omething in general upon all the&longs;e con­ &longs;iderations together, and then I will de&longs;cend to &longs;ome particulars. It &longs;eems that you univer&longs;ally bottom all you &longs;ay upon the greater &longs;implicity and facility of producing the &longs;ame effects, whil&longs;t you hold, that as to the cau&longs;ing of them, the motion of the Earth a­ lone, &longs;erveth as well as that of all the re&longs;t of the World, the Earth deducted: but as to the operations, you e&longs;teem that much ea&longs;ier than this. To which I reply, that I am al&longs;o of the &longs;ame opinion, &longs;o long as I regard my own not onely finite, but feeble power; but having a re&longs;pect to the &longs;trength of the Mover, which is in­ finite, its no le&longs;&longs;e ea&longs;ie to move the Univer&longs;e, than the Earth, yea than a &longs;traw. And if his power be infinite, why &longs;hould he not rather exerci&longs;e a greater part thereof than a le&longs;&longs;e? Therefore, I hold that your di&longs;cour&longs;e in general is not convincing.

Of an infinite power one would think a greater part &longs;hould rather be imploy'd than a le&longs;&longs;e.

SALV. If I had at any time &longs;aid, that the Univer&longs;e moved not for want of power in the Mover, I &longs;hould have erred, and your reproof would have been &longs;ea&longs;onable; and I grant you, that to an infinite power, it is as ea&longs;ie to move an hundred thou&longs;and, as one. But that which I did &longs;ay, concerns not the Mover, but one­ ly hath re&longs;pect to the Moveables; and in them, not onely to their re&longs;i&longs;tance, which doubtle&longs;&longs;e is le&longs;&longs;er in the Earth, than in the Univer&longs;e; but to the many other particulars, but even now con&longs;idered. As to what you &longs;ay in the next place, that of an in­ finite power it is better to exerci&longs;e a great part than a &longs;mall: I an­ &longs;wer, that of infinite one part is not greater than another, &longs;ince both are infinite; nor can it be &longs;aid, that of the infinite number, an hundred thou&longs;and is a greater part than two, though that be fifty thou&longs;and times greater than this; and if to the moving of the Univer&longs;e there be required a finite power, though very great in compari&longs;on of that which &longs;ufficeth to move the Earth onely; yet is there not implied therein a greater part of the infinite power, nor is that part le&longs;&longs;e infinite which remaineth unimploy'd. So that to apply unto a particular effect, a little more, or a little le&longs;&longs;e power, importeth nothing; be&longs;ides that the operation of &longs;uch vertue, hath not for its bound or end the Diurnal Motion onely; but there are &longs;everal other motions in the World, which we know of, and many others there may be, that are to us unknown. Therefore if we re&longs;pect the Moveables, and granting it as out of que&longs;tion, that it is a &longs;horter and ea&longs;ier way to move the Earth, than the Univer&longs;e; and moreover, having an eye to the &longs;o many other abreviations, and facilities that onely this way are to be ob­ tained, an infallible Maxime of Ari&longs;totle, which he teacheth us, that, fru&longs;tra fit per plura, quod pote&longs;t fieri per pauciora, ren­ dereth it more probable that the Diurnal Motion belongs to the Earth alone, than to the Univer&longs;e, the Earth &longs;ubducted.

Of infinity one part is no bigger than auother, al­ though they are comparatively un­ equal.

SIMPL. In reciting that Axiom, you have omitted a &longs;mall clau&longs;e, which importeth as much as all the re&longs;t, e&longs;pecially in our ca&longs;e, that is to &longs;ay, the words æquè bene. It is requi&longs;ite therefore to examine whether this Hypothe&longs;is doth equally well &longs;atisfie in all particulars, as the other.

SALV. The knowledg whether both the&longs;e po&longs;itions do æquè bene, &longs;atisfie, may be comprehended from the particular exami­ nation of the appearances which they are to &longs;atisfie; for hitherto we have di&longs;cour&longs;ed, and will continue to argue ex hypothe&longs;i, namely, &longs;uppo&longs;ing, that as to the &longs;atisfaction of the appearances, both the a&longs;&longs;umptions are equally accomodated. As to the clau&longs;e which you &longs;ay was omitted by me, I have more rea&longs;on to &longs;u&longs;pect that it was &longs;uperfluou&longs;ly in&longs;erted by you. For the expre&longs;&longs;ion æquè bene, is a relative that nece&longs;&longs;arily requireth two terms at lea&longs;t, for a thing cannot have relation to its &longs;elf, nor do we &longs;ay, v. gr. re&longs;t to be equally good, as re&longs;t. And becau&longs;e, when we &longs;ay, that is done in vain by many means, which may be done with fewer, we mean, that that which is to be done, ought to be the &longs;ame thing, not two different ones; and becau&longs;e the &longs;ame thing can­ not be &longs;aid to be done as well as its &longs;elf; therefore, the addition of the Phra&longs;e æquè bene is &longs;uperfluous, and a relation, that hath but one term onely.

In the Axiome Fru&longs;tra fit per plu­ ra, &c. the addi­ tion of æque benè, is &longs;uperfluous.

SAGR. Unle&longs;&longs;e you will have the &longs;ame befal us, as did ye&longs;ter­ day, let us return to our matter in hand; and let Simplicius be­ gin to produce tho&longs;e difficulties that &longs;eem in his opinion, to thwart this new di&longs;po&longs;ition of the World.

SIMPL. That di&longs;po&longs;ition is not new, but very old, and that you may &longs;ee it is &longs;o, Ari&longs;totle confuteth it; and his confutations are the&longs;e: “Fir&longs;t if the Earth moveth either in it felf about its own Centre, or in an Excentrick Circle, it is nece&longs;&longs;ary that that &longs;ame motion be violent; for it is not its natural motion, for if it were, each of its parts would partake thereof; but each of them moveth in a right line towards its Centre. It being therefore violent and pteternatural, it could never be perpetu­ al: But the order of the World is perpetual. Therefore, &c. Secondly, all the other moveables that move circularly, &longs;eem to ^{*} &longs;tay behind, and to move with more than one motion, the Primum Mobile excepted: Whence it would be nece&longs;&longs;ary that the Earth al&longs;o do move with two motions; and if that &longs;hould be &longs;o, it would inevitably follow, that mutations &longs;hould be made in the Fixed Stars, the which none do perceive; nay without any variation, the &longs;ame Stars alwayes ri&longs;e from towards the &longs;ame places, and in the &longs;ame places do &longs;et. Thirdly, the mo­ tion of the parts is the &longs;ame with that of the whole, and natural­ ly tendeth towards the Centre of the Univer&longs;e; and for the &longs;ame cau&longs;e re&longs;t, being arrived thither. He thereupon moves the que­ &longs;tion whether the motion of the parts hath a tendency to the centre of the Univer&longs;e, or to the centre of the Earth; and conclu­ deth that it goeth by proper in&longs;tinct to the centre of the Univer&longs;e, and per accidence to that of the Earth; of which point we largely di&longs;cour&longs;ed ye&longs;terday. He la&longs;tly confirmeth the &longs;ame with a fourth argument taken from the experiment of grave bodies, which fal­ ing from on high, de&longs;cend perpendicularly unto the Earths&longs;urface; and in the &longs;ame manner Projections &longs;hot perpendicularly upwards, do by the &longs;ame lines return perpendicularly down again, though they were &longs;hot to a very great height. All which arguments nece&longs;­ &longs;arily prove their motion to be towards the Centre of the Earth, which without moving at all waits for, and receiveth them. He intimateth in the la&longs;t place that the A&longs;tronomers alledg other rea&longs;ons in confirmation of the &longs;ame conclu&longs;ions, I mean of the Earths being in the Centre of the Univer&longs;e, and immoveable; and in&longs;tanceth onely in one of them, to wit, that all the Phæ­ nomena or appearances that are &longs;een in the motions of the Stars, perfectly agree with the po&longs;ition of the Earth in the Centre; which would not be &longs;o, were the Earth &longs;eated otherwi&longs;e. The re&longs;t produced by Ptolomy and the other A&longs;tronomers, I can give you now if you plea&longs;e, or after you have &longs;poken what you have to &longs;ay in an&longs;wer to the&longs;e of Ari&longs;totle.”

Ari&longs;totles Ar­ guments for the Earths quie&longs;&longs;ence.

* Re&longs;tino indietzo, which is meant here of that moti­ on which a bowl makes when its born by its by as to one &longs;ide or other, and &longs;o hindered in its direct motion.

SALV. The arguments which are brought upon this occa&longs;ion are of two kinds: &longs;ome have re&longs;pect to the accidents Terre&longs;trial, without any relation to the Stars, and others are taken from the Phænomena and ob&longs;ervations of things Cœle&longs;tial. The arguments of Ari&longs;totle are for the mo&longs;t part taken from things neer at hand, and he leaveth the others to A&longs;tronomers; and therefore it is the be&longs;t way, if you like of it, to examine the&longs;e taken from experi­ ments touching the Earth, and then proceed to tho&longs;e of the other kind. And becau&longs;e Ptolomy, Tycho, and the other A&longs;tronomers and Philo&longs;ophers, be&longs;ides the arguments of Ari&longs;totle by them a&longs;&longs;u­ med, confirmed, and made good, do produce certain others; we will put them all together, that &longs;o we may not an&longs;wer twice to the &longs;ame, or the like objections. Therefore Simplicius, choo&longs;e whether you will recite them your &longs;elf, or cau&longs;e me to ea&longs;e you of this task, for I am ready to &longs;erve you.

Two kindes of Arguments tou­ ching the Earths motion or rest.

Arguments of Ptolomy and Ty­ cho, and other per­ &longs;ons, over and a­ bove tho&longs;e of Ari­ &longs;totle.

SIMPL. It is better that you quote them, becau&longs;e, as having taken more pains in the &longs;tudy of them, you can produce them with more readine&longs;&longs;e, and in greater number.

The fir&longs;t argu­ ment taken from grave bodies fal­ ling from on high to the ground.

SALV. All, for the &longs;tronge&longs;t rea&longs;on, alledge that of grave bo­ dies, which falling downwards from on high, move by a right line, that is perpendicular to the &longs;urface of the Earth, an argument which is held undeniably to prove that the Earth is immoveable: for in ca&longs;e it &longs;hould have the diurnal motion, a Tower, from the top of which a &longs;tone is let fall, being carried along by the conver­ &longs;ion of the Earth, in the time that the &longs;tone &longs;pends in falling, would be tran&longs;ported many hundred yards Ea&longs;tward, and &longs;o far di&longs;tant from the Towers foot would the &longs;tone come to ground. The which effect they back with another experiment; to wit, by let­

ting a bullet of lead fall from the round top of a Ship, that lieth at anchor, and ob&longs;erving the mark it makes where it lights, which they find to be neer the ^{*} partners of the Ma&longs;t; but if the &longs;ame bullet be let fall from the &longs;ame place when the &longs;hip is under &longs;ail, it &longs;hall light as far from the former place, as the &longs;hip hath run in the time of the leads de&longs;cent; and this for no other rea&longs;on, than becau&longs;e the natural motion of the ball being at liberty is by a right line to­ wards the centre of the Earth. They forti&longs;ie this argument with the experiment of a projection &longs;hot on high at a very great di­ &longs;tance; as for example, a ball &longs;ent out of a Cannon, erected per­ pendicular to the horizon, the which &longs;pendeth &longs;o much time in a&longs;­ cending and falling, that in our parallel the Cannon and we both &longs;hould be carried by the Earth many miles towards the Ea&longs;t, &longs;o that the ball in its return could never come neer the Peece, but would fall as far We&longs;t, as the Earth had run Ea&longs;t. They againe adde a third, and very evident experiment, &longs;cilicet, that &longs;hooting a bullet point blank (or as Gunners &longs;ay, neither above nor under me­ tal) out of a Culverin towards the Ea&longs;t, and afterwards another, with the &longs;ame charge, and at the &longs;ame elevation or di&longs;port towards the We&longs;t, the range towards the We&longs;t &longs;hould be very much grea­ ter then the other towards the Ea&longs;t: for that whil'&longs;t the ball goeth We&longs;tward, and the Peece is carried along by the Earth Ea&longs;tward, the ball will fall from the Peece as far di&longs;tant as is the aggregate of the two motions, one made by it &longs;elf towards the We&longs;t, and the other by the Peece carried about by the Earth towards the Ea&longs;t; and on the contrary, from the range of the ball &longs;hot Ea&longs;tward you are to &longs;ub&longs;tract the &longs;pace the Peece moved, being carried after it. Now &longs;uppo&longs;e, for example, that the range of the ball &longs;hot We&longs;t were five miles, and that the Earth in the &longs;ame parallel and in the time of the Bals ranging &longs;hould remove three miles, the Ball in this ca&longs;e would fall eight miles di&longs;tant from the Culverin, namely, its own five We&longs;tward, and the Culverins three miles Ea&longs;tward: but the range of the &longs;hot towards the Ea&longs;t would be but two miles long, for &longs;o much is the remainder, after you have &longs;ub&longs;tracted from the five miles of the range, the three miles which the Peece had moved towards the &longs;ame part. But experience &longs;heweth the Ranges to be equal, therefore the Culverin, and con&longs;equently the Earth are immoveable. And the &longs;tability of the Earth is no le&longs;fe confirmed by two other &longs;hots made North and South; for they would never hit the mark, but the Ranges would be alwayes wide, or towards the We&longs;t, by meanes of the remove the mark would make, being carried along with the Earth towards the Ea&longs;t, whil'&longs;t the ball is flying. And not onely &longs;hots made by the Meridians, but al&longs;o tho&longs;e aimed Ea&longs;t or We&longs;t would prove uncertain; for tho&longs;e aim'd Ea&longs;t would be too high, and tho&longs;e directed We&longs;t too low, although they were &longs;hot point blank, as I &longs;aid. For the Range of the Ball in both the &longs;hots being made by the Tangent, that is, by a line parallel to the Horizon, and being that in the di­ urnal motion, if it be of the Earth, the Horizon goeth continually de&longs;cending towards the Ea&longs;t, and ri&longs;ing from the We&longs;t (therefore the Oriental Stars &longs;eem to ri&longs;e, and the Occidental to decline) &longs;o that the Oriental mark would de&longs;cend below the aime, and there­ upon the &longs;hot would fly too high, and the a&longs;cending of the We&longs;t­ ern mark would make the &longs;hot aimed that way range too low; &longs;o that the Peece would never carry true towards any point; and for that experience telleth us the contrary, it is requi&longs;ite to &longs;ay, that the Earth is immoveable.

Which is confir­ med by the experi­ ment of a body let fall from the round top of a Ship.

* That is, at the foot of the Ma&longs;t, upon the upper deck.

The &longs;econd ar­ gument taken from a Projection &longs;hot very high.

The third argu­ ment taken from the &longs;hots of a Can­ non, towards the Ea&longs;t, and towards the West.

This argument is confirmed by two &longs;hots towards the South and towards the North.

And it is like­ wi&longs;e confirmed by two &longs;hots towards the Ea&longs;t, and to­ wards the We&longs;t.

SIMPL. The&longs;e are &longs;olid rea&longs;ons, and &longs;uch as I believe no man can an&longs;wer.

SALV. Perhaps they are new to you?

SIMPL. Really they are; and now I &longs;ee with how many ad­ mirable experiments Nature is plea&longs;ed to favour us, wherewith to a&longs;&longs;i&longs;t us in the knowledge of the Truth. Oh! how exactly one truth agreeth with another, and all con&longs;pire to render each other inexpugnable!

SAGR. What pity it is that Guns were not u&longs;ed in Ari&longs;totles age, he would with help of them have ea&longs;ily battered down ig­ norance, and &longs;poke without hæ&longs;itation of the&longs;e mundane points.

SALV. I am very glad that the&longs;e rea&longs;ons are new unto you, that &longs;o you may not re&longs;t in the opinion of the major part of Peripate­ ticks, who believe, that if any one for&longs;akes the Doctrine of Ari­ &longs;totle, it is becau&longs;e they did not under&longs;tand or rightly apprehend his demon&longs;trations. But you may expect to hear of other Novel­ ties, and you &longs;hall &longs;ee the followers of this new Sy&longs;teme produce a­ gain&longs;t them&longs;elves ob&longs;ervations, experiences, and rea&longs;ons of farre greater force than tho&longs;e alledged by Aristotle, Ptolomy, and other oppo&longs;ers of the &longs;ame conclu&longs;ions, and by this means you &longs;hall come to a&longs;certain your &longs;elf that they were not induced through want of knowledge or experience to follow that opinion.

Copernicus his followers are not moved through ig­ nor ance of the ar­ guments on the o­ ther part.

SAGR. It is requi&longs;ite that upon this occa&longs;ion I relate unto you &longs;ome accidents that befell me, &longs;o &longs;oon as I fir&longs;t began to hear &longs;peak of this new doctrine. Being very young, and having &longs;carcely fi­ ni&longs;hed my cour&longs;e of Philo&longs;ophy, which I left off, as being &longs;et upon other employments, there chanced to come into the&longs;e parts a cer­ tain Foreigner of Ro&longs;tock, who&longs;e name, as I remember, was Chri- &longs;tianus Vur&longs;titius, a follower of Copernicus, who in an Academy made two or three Lectures upon this point, to whom many flock't as Auditors; but I thinking they went more for the novelty of the &longs;ubject than otherwi&longs;e, did not go to hear him: for I had conclu­ ded with my &longs;elf that that opinion could be no other than a &longs;olemn madne&longs;&longs;e. And que&longs;tioning &longs;ome of tho&longs;e who had been there, I perceived they all made a je&longs;t thereof, execpt one, who told me that the bu&longs;ine&longs;&longs;e was not altogether to be laugh't at, and becau&longs;e this man was reputed by me to be very intelligent and wary, I re­ pented that I was not there, and began from that time forward as oft as I met with any one of the Copernican per&longs;wa&longs;ion, to demand of them, if they had been alwayes of the &longs;ame judgment; and of as many as I examined, I found not &longs;o much as one, who told me not that he had been a long time of the contrary opinion, but to have changed it for this, as convinced by the &longs;trength of the rea&longs;ons pro­ ving the &longs;ame: and afterwards que&longs;tioning them, one by one; to &longs;ee whether they were well po&longs;&longs;e&longs;t of the rea&longs;ons of the other &longs;ide; I found them all to be very ready and perfect in them; &longs;o that I could not truly &longs;ay, that they had took up this opinion out of ig­ norance, vanity, or to &longs;hew the acutene&longs;&longs;e of their wits. On the contrary, of as many of the Peripateticks and Ptolomeans as I have asked (and out of curio&longs;ity I have talked with many) what pains they had taken in the Book of Copernicus, I found very few that had &longs;o much as &longs;uperficially peru&longs;ed it; but of tho&longs;e whom, I thought, had under&longs;tood the &longs;ame, not one; and more­ over, I have enquired among&longs;t the followers of the Peripatetick Doctrine, if ever any of them had held the contrary opinion, and likewi&longs;e found none that had. Whereupon con&longs;idering that there was no man who followed the opinion of Copernicus, that had not been fir&longs;t on the contrary &longs;ide, and that was not very well ac­ quainted with the rea&longs;ons of Ari&longs;totle and Ptolomy; and, on the contrary, that there is not one of the followers of Ptolomy that had ever been of the judgment of Copernicus, and had left that, to imbrace this of Ari&longs;totle, con&longs;idering, I &longs;ay, the&longs;e things, I began to think, that one, who leaveth an opinion imbued with his milk, and followed by very many, to take up another owned by very few, and denied by all the Schools, and that really &longs;eems a very great Paradox, mu&longs;t needs have been moved, not to &longs;ay forced, by more powerful rea&longs;ons. For this cau&longs;e, I am become very curious to dive, as they &longs;ay, into the bottom of this bu&longs;ine&longs;&longs;e, and account it my great good fortune that I have met you two, from whom I may without any trouble, hear all that hath been, and, haply, can be &longs;aid on this argument, a&longs;&longs;uring my &longs;elf that the &longs;trength of your rea&longs;ons will re&longs;olve all &longs;cruples, and bring me to a certainty in this &longs;ubject.

Chri&longs;tianus Vur­ &longs;titius read certain Lectures touching the opinion of Co­ pernicus, & what en&longs;ued thereupon.

The followers of Copernicus were all fir&longs;t again&longs;t that opinion, but the Sectators of Ari&longs;totle & Pto­ lomy, were never of the other &longs;ide.

SIMPL. But its po&longs;&longs;ible your opinion and hopes may be di&longs;ap­ pointed, and that you may find your &longs;elves more at a lo&longs;&longs;e in the end than you was at fir&longs;t.

SAGR. I am very confident that this can in no wi&longs;e befal me.

SIMPL. And why not? I have a manife&longs;t example in my &longs;elf, that the farther I go, the more I am confounded.

SAGR. This is a &longs;ign that tho&longs;e rea&longs;ons that hitherto &longs;eemed concluding unto you, and a&longs;&longs;ured you in the truth of your opi­ nion, begin to change countenance in your mind, and to let you by degrees, if not imbrace, at lea&longs;t look towards the contrary te­ nent; but I, that have been hitherto indifferent, do greatly hope to acquire re&longs;t and &longs;atisfaction by our future di&longs;cour&longs;es, and you will not deny but I may, if you plea&longs;e but to hear what per&longs;wa­ deth me to this expectation.

SIMPL. I will gladly hearken to the &longs;ame, and &longs;hould be no le&longs;&longs;e glad that the like effect might be wrought in me.

SAGR. Favour me therefore with an&longs;wering to what I &longs;hall ask you. And fir&longs;t, tell me, Simplicius, is not the conclu&longs;ion, which we &longs;eek the truth of, Whether we ought to hold with Ari&longs;totle and Ptolomy, that the Earth onely abiding without motion in the Centre of the Univer&longs;e, the Cœle&longs;tial bodies all move, or el&longs;e, Whether the Starry Sphere and the Sun &longs;tanding &longs;till in the Centre, the Earth is without the &longs;ame, and owner of all tho&longs;e motions that in our &longs;eeming belong to the Sun and fixed Stars?

SIMPL. The&longs;e are the conclu&longs;ions which are in di&longs;pute.

SAGR. And the&longs;e two conclu&longs;ions, are they not of &longs;uch a na­ ture, that one of them mu&longs;t nece&longs;&longs;arily be true, and the other fal&longs;e?

SIMPL. They are &longs;o. We are in a Dilemma, one part of which mu&longs;t of nece&longs;&longs;ity be true, and the other untrue; for between Mo­ tion and Re&longs;t, which are contradictories, there cannot be in&longs;tanced a third, &longs;o as that one cannot &longs;ay the Earth moves not, nor &longs;tands &longs;till; the Sun and Stars do not move, and yet &longs;tand not &longs;till.

SAGR. The Earth, the Sun, and Stars, what things are they in nature? are they petite things not worth our notice, or grand and worthy of con&longs;ideration?

SIMPL They are principal, noble, integral bodies of the Uni­ ver&longs;e, mo&longs;t va&longs;t and con&longs;iderable.

SAGR. And Motion, and Re&longs;t, what accidents are they in Nature?

Motion and re&longs;t principal accidents in nature.

SIMPL. So great and principal, that Nature her &longs;elf is defined by them.

SAGR. So that moving eternally, and the being wholly immo­ veable are two conditions very con&longs;iderable in Nature, and indi­ cate very great diver&longs;ity; and e&longs;pecially when a&longs;cribed to the principal bodies of the Univer&longs;e, from which can en&longs;ue none but very different events.

SIMPL. Yea doubtle&longs;&longs;e.

SAGR. Now an&longs;wer me to another point. Do you believe that in Logick, Rhethorick, the Phy&longs;icks, Metaphy&longs;icks, Mathematicks, and finally, in the univer&longs;ality of Di&longs;putations there are arguments &longs;ufficient to per&longs;wade and demon&longs;trate to a per&longs;on the fallacious, no le&longs;&longs;e then the true conclu&longs;ions?

Vntruths cannot be demonstrated, as Truths are.

SIMPL. No Sir; rather I am very confident and certain, that for the proving of a true and nece&longs;&longs;ary conclu&longs;ion, there are in

nature not onely one, but many very powerfull demon&longs;trations: and that one may di&longs;cu&longs;&longs;e and handle the &longs;ame divers and &longs;undry wayes, without ever falling into any ab&longs;urdity; and that the more any Sophi&longs;t would di&longs;turb and muddy it, the more clear would its certainty appear: And that on the contrary to make a fal&longs;e po&longs;i­ tion pa&longs;&longs;e for true, and to per&longs;wade the belief thereof, there can­ not be any thing produced but fallacies, Sophi&longs;ms, Paralogi&longs;mes, Equivocations, and Di&longs;cour&longs;es vain, incon&longs;i&longs;tant, and full of re­ pugnances and contradictions.

For proof of true conclu&longs;ions, many &longs;olid arguments may be produced, but to prove a fal­ &longs;ity, none.

SAGR. Now if eternal motion, and eternal re&longs;t be &longs;o princi­ pal accidents of Nature, and &longs;o different, that there can depend on them only mo&longs;t different con&longs;equences, and e&longs;pecially when applyed to the Sun, and to the Earth, &longs;o va&longs;t and famous bodies of the Univer&longs;e; and it being, moreover, impo&longs;&longs;ible, that one of two contradictory Propo&longs;itions, &longs;hould not be true, and the other fal&longs;e; and that for proof of the fal&longs;e one, any thing can be pro­ duced but fallacies; but the true one being per&longs;wadeable by all kind of concluding and demon&longs;trative arguments, why &longs;hould you think that he, of you two, who &longs;hall be &longs;o fortunate as to maintain the true Propo&longs;ition ought not to per&longs;wade me? You mu&longs;t &longs;uppo&longs;e me to be of a &longs;tupid wit, perver&longs;e judgment, dull mind and intellect, and of a blind rea&longs;on, that I &longs;hould not be able to di&longs;tingui&longs;h light from darkne&longs;&longs;e, jewels from coals, or truth from fal&longs;hood.

SIMPL. I tell you now, and have told you upon other occa&longs;ions, that the be&longs;t Ma&longs;ter to teach us how to di&longs;cern So­ phi&longs;mes, Paralogi&longs;mes, and other fallacies, was Ari&longs;totle, who in this particular can never be deceived.

SAGR. You in&longs;i&longs;t upon Aristotle, who cannot &longs;peak. Yet I tell you, that if Ari&longs;totle were here, he would either yield him­ &longs;elf to be per&longs;waded by us, or refuting our arguments, convince us by better of his own. And you your &longs;elf, when you heard the experiments of the Suns related, did you not acknowledg and admire them, and confe&longs;&longs;e them more concludent than tho&longs;e of Ari&longs;totle? Yet neverthele&longs;&longs;e I cannot perceive that Salviatus, who hath produced them, examined them, and with exqui&longs;ite care &longs;can'd them, doth confe&longs;&longs;e him&longs;elf per&longs;waded by them; no nor by others of greater force, which he intimated that he was about to give us an account of. And I know not on what grounds you &longs;hould cen&longs;ure Nature, as one that for many Ages hath been lazie, and forgetful to produce &longs;peculative wits; and that knoweth not how to make more &longs;uch, unle&longs;&longs;e they be &longs;uch kind of men as &longs;lavi&longs;hly giving up their judgments to Ari&longs;totle, do under&longs;tand with his brain, and re&longs;ent with his &longs;en&longs;es. But let us hear the re&longs;idue of tho&longs;e rea&longs;ons which favour his opinion, that we may thereupon proceed to &longs;peak to them; comparing and weighing them in the ballance of impartiality.

Ari&longs;totle would either refute his adver&longs;aries argu­ ments, or would alter his opinion.

SALV. Before I proceed any farther, I mu&longs;t tell Sagredus, that in the&longs;e our Di&longs;putations, I per&longs;onate the Copernican,, and imi­ tate him, as if I were his Zany; but what hath been effected in my private thoughts by the&longs;e arguments which I &longs;eem to alledg in his favour, I would not have you to judg by what I &longs;ay, whil'&longs;t I am in the heat of acting my part in the Fable; but after I have laid by my di&longs;gui&longs;e, for you may chance to find me different from what you &longs;ee me upon the Stage. Now let us go on.

Ptolomy and his followers produce another experiment like to that of the Projections, and it is of things that being &longs;eparated from the Earth, continue a good &longs;pace of time in the Air, &longs;uch as are the Clouds, Birds of flight; and as of them it cannot be &longs;aid that they are rapt or tran&longs;parted by the Earth, having no ad­ he&longs;ion thereto, it &longs;eems not po&longs;&longs;ible, that they &longs;hould be able to keep pace with the velocity thereof; nay it &longs;hould rather &longs;eem to us, that they all &longs;wiftly move towards the We&longs;t: And if being carried about by the Earth, pa&longs;&longs;e our parallel in twenty four hours, which yet is at lea&longs;t &longs;ixteen thou&longs;and miles, how can Birds follow &longs;uch a cour&longs;e or revolution? Whereas on the con­ trary, we &longs;ee them fly as well towards the Ea&longs;t, as towards the We&longs;t, or any other part, without any &longs;en&longs;ible difference. More­ over, if when we run a Hor&longs;e at his &longs;peed, we feel the air beat vehemently again&longs;t our face, what an impetuous bla&longs;t ought we perpetually to feel from the Ea&longs;t, being carried with &longs;o rapid a cour&longs;e again&longs;t the wind? and yet no &longs;uch effect is perceived. Take another very ingenious argument inferred from the following ex­ periment. The circular motion hath a faculty to extrude and di&longs;­ &longs;ipate from its Centre the parts of the moving body, when&longs;oever either the motion is not very &longs;low, or tho&longs;e parts are not very well fa&longs;tened together; and therefore, if v. g. we &longs;hould turn one of tho&longs;e great wheels very fa&longs;t about, wherein one or more men walking, crane up very great weights, as the huge ma&longs;&longs;ie &longs;tone, u&longs;ed by the Callander for pre&longs;&longs;ing of Cloaths; or the fraighted Barks which being haled on &longs;hore, are hoi&longs;ted out of one river into another; in ca&longs;e the parts of that &longs;ame Wheel &longs;o &longs;wiftly turn'd round, be not very well joyn'd and pin'd together, they would all be &longs;hattered to pieces; and though many &longs;tones or other ponderous &longs;ub&longs;tances, &longs;hould be very fa&longs;t bound to its outward Rimme, yet could they not re&longs;i&longs;t the impetuo&longs;ity, which with great violence would hurl them every way far from the Wheel, and con&longs;equently from its Centre. So that if the Earth did move with &longs;uch and &longs;o much greater velocity, what gravity, what tena­ city of lime or plai&longs;ter would keep together Stones, Buildings, and whole Cities, that they &longs;hould not be to&longs;t into the Air by &longs;o pre­ cipitous a motion? And both men and bea&longs;ts, which are not fa­ &longs;tened to the Earth, how could they re&longs;i&longs;t &longs;o great an impetus? Whereas, on the other &longs;ide, we &longs;ee both the&longs;e, and far le&longs;&longs;e re­ &longs;i&longs;tances of pebles, &longs;ands, leaves re&longs;t quietly on the Earth, and to return to it in falling, though with a very &longs;low motion. See here, Simplicius, the mo&longs;t potent arguments, taken, to &longs;o &longs;peak, from things Terre&longs;trial; there remain tho&longs;e of the other kind, namely, &longs;uch as have relation to the appearances of Heaven, which rea&longs;ons, to confe&longs;&longs;e the truth, tend more to prove the Earth to be in the centre of the Univer&longs;e, and con&longs;equently, to deprive it of the annual motion about the &longs;ame, a&longs;cribed unto it by Copernicus. Which arguments, as being of &longs;omewhat a di&longs;te­ rent nature, may be produced, after we have examined the &longs;trength of the&longs;e already propounded.

An argument taken from the Clouds, and from Birds.

An argument taken from the air which we feel to beat upon us when we run a Hor&longs;e at full &longs;peed.

An argument taken from the whirling of circu­ lar motion, which hath a faculty to extrude and di&longs;&longs;i­ pate.

SAGR. What &longs;ay you Simplicius? do you think that Salviatus is Ma&longs;ter of, and knoweth how to unfold the Ptolomean and Ari­ &longs;totelian arguments? Or do you think that any Peripatetick is e­ qually ver&longs;t in the Copernican demon&longs;trations?

SIMPL. Were it not for the high e&longs;teem, that the pa&longs;t di&longs;cour­ &longs;es have begot in me of the learning of Salviatus, and of the a­ cutene&longs;&longs;e of Sagredus, I would by their good leave have gone my way without &longs;taying for their an&longs;wers; it &longs;eeming to me a thing impo&longs;&longs;ible, that &longs;o palpable experiments &longs;hould be contradicted; and would, without hearing them farther, con&longs;irm my &longs;elf in my old per&longs;wa&longs;ion; for though I &longs;hould be made to &longs;ee that it was er­ roneous, its being upheld by &longs;o many probable rea&longs;ons, would ren­ der it excu&longs;eable. And if the&longs;e are fallacies, what true demon&longs;tra­ tions were ever &longs;o fair?

SAGR. Yet its good that we hear the re&longs;pon&longs;ions of Salviatus; which if they be true, mu&longs;t of nece&longs;&longs;ity be more fair, and that by in&longs;inite degrees; and tho&longs;e mu&longs;t be deformed, yea mo&longs;t deformed, if the Metaphy &longs;ical Axiome hold, That true and fair are one and the &longs;ame thing; as al&longs;o fal&longs;e and deformed. Therefore Salviatus let's no longer lo&longs;e time.

True and fair are one and the &longs;ame, as al&longs;o fal&longs;e and deformed.

SALV. The fir&longs;t Argument alledged by Simplicius, if I well re­ member it, was this. The Earth cannot move circularly, becau&longs;e &longs;uch motion would be violent to the &longs;ame, and therefore not per­ petual: that it is violent, the rea&longs;on was: Becau&longs;e, that had it been natural, its parts would likewi&longs;e naturally move round, which is impo&longs;&longs;ible, for that it is natural for the parts thereof to move with a right motion downwards. To this my reply is, that I could glad­ ly wi&longs;h, that Ari&longs;totle had more cleerly expre&longs;t him&longs;elf, where he &longs;aid; That its parts would likewi&longs;e move circularly; for this mo­ ving circularly is to be under&longs;tood two wayes, one is, that every particle or atome &longs;eparated from its Whole would move circularly about its particular centre, de&longs;cribing its &longs;mall Circulets; the other is, that the whole Globe moving about its centre in twenty four hours, the parts al&longs;o would turn about the &longs;ame centre in four and twenty hours. The fir&longs;t would be no le&longs;&longs;e an impertinency, than if one &longs;hould &longs;ay, that every part of the circumference of a Circle ought to be a Circle; or becau&longs;e that the Earth is Spherical, that therefore every part thereof be a Globe, for &longs;o doth the Axiome require: Eadem e&longs;t ratio totius, & partium. But if he took it in the other &longs;en&longs;e, to wit, that the parts in imitation of the Whole &longs;hould move naturally round the Centre of the whole Globe in twenty four hours, I &longs;ay, that they do &longs;o; and it concerns you, in&longs;tead of Ari&longs;totle, to prove that they do not.

The an&longs;wer to Ari&longs;totles fir&longs;t ar­ gument.

SIMPL. This is proved by Ari&longs;totle in the &longs;ame place, when he &longs;aith, that the natural motion of the parts is the right motion downwards to the centre of the Univer&longs;e; &longs;o that the circular motion cannot naturally agree therewith.

SALV. But do not you &longs;ee, that tho&longs;e very words carry in them a confutation of this &longs;olution?

SIMPL. How? and where?

SALV. Doth not he &longs;ay that the circular motion of the Earth would be violent? and therefore not eternal? and that this is ab­ &longs;urd, for that the order of the World is eternal?

SIMPL. He &longs;aith &longs;o.

SALV. But if that which is violent cannot be eternal, then by conver&longs;ion, that which cannot be eternal, cannot be natural: but the motion of the Earth downwards cannot be otherwi&longs;e eternal; therefore much le&longs;&longs;e can it be natural: nor can any other motion be natural to it, &longs;ave onely that which is eternal. But if we make the Earth move with a circular motion, this may be eternal to it, and to its parts, and therefore natural.

That which is violent, cannot be eternal, and that which cannot be e­ ternal, cannot be natural.

SIMPL. The right motion is mo&longs;t natural to the parts of the Earth, and is to them eternal; nor &longs;hall it ever happen that they move not with a right motion; alwayes provided that the impe­ diments be removed.

SALV. You equivocate Simplicius; and I will try to free you from the equivoke. Tell me, therefore, do you think that a Ship which &longs;hould &longs;ail from the Strait of Gibralter towards Pale­ &longs;tina can eternally move towards that Coa&longs;t? keeping alwayes an equal cour&longs;e?

SIMPL. No doubtle&longs;&longs;e.

SALV. And why not?

SIMPL. Becau&longs;e that Voyage is bounded and terminated be­ tween the Herculean Pillars, and the &longs;hore of the Holy-land; and the di&longs;tance being limited, it is pa&longs;t in a finite time, unle&longs;&longs;e one by returning back &longs;hould with a contrary motion begin the &longs;ame Voy­ age anew; but this would be an interrupted and no continued motion.

SALV. Very true. But the Navigation from the Strait of Ma­ galanes by the Pacifick Ocean, the Moluccha's, the Cape di buona Speranza, and from thence by the &longs;ame Strait, and then again by the Pacifick Ocean, &c. do you believe that it may be perpe­ tuated?

SIMPL. It may; for this being a circumgyration, which re­ turneth about its &longs;elf, with infinite replications, it may be perpetu­ ated without any interruption.

SALV. A Ship then may in this Voyage continue &longs;ailing eter­ nally.

SIMPL. It may, in ca&longs;e the Ship were incorruptible, but the Ship decaying, the Navigation mu&longs;t of nece&longs;&longs;ity come to an end.

SALV. But in the Mediterrane, though the Ve&longs;&longs;el were incor­ ruptible, yet could &longs;he not &longs;ail perpetually towards Pale&longs;tina, that Voyage being determined. Two things then are required, to the end a moveable may without intermi&longs;&longs;ion move perpetually; the one is, that the motion may of its own nature be indeterminate and infinite; the other, that the moveable be likewi&longs;e incorruptible and eternal.

Two things re­ qui&longs;ite to the end a motion may per­ petuate it &longs;elf; an unlimited &longs;pace, and an incorrupti­ ble moveable.

SIMPL. All this is nece&longs;&longs;ary.

SALV. Therefore you may &longs;ee how of your own accord you have confe&longs;&longs;ed it impo&longs;&longs;ible that any moveable &longs;hould move eter­ nally in a right line, in regard that right motion, whether it be up­ wards, or downwards, is by you your &longs;elf bounded by the circum­ ference and centre; &longs;o that if a Moveable, as &longs;uppo&longs;e the Earth be eternal, yet fora&longs;much as the right motion is not of its own na­ ture eternall, but mo&longs;t ^{*}terminate, it cannot naturally &longs;uit with the Earth. Nay, as was &longs;aid ^{*} ye&longs;terday, Ari&longs;totle him&longs;elf is con&longs;trained to make the Terre&longs;trial Globe eternally immoveable. When again you &longs;ay, that the parts of the Earth evermore move downwards, all impediments being removed, you egregiou&longs;ly equi­ vocate; for then, on the other &longs;ide they mu&longs;t be impeded, contra­ ried, and forced, if you would have them move; for, when they are once fallen to the ground, they mu&longs;t be violently thrown up­ wards, that they may a &longs;econd time fall; and as to the impedi­ ments, the&longs;e only hinder its arrival at the centre; but if there were a Well, that did pa&longs;&longs;e thorow and beyond the centre, yet would not a clod of Earth pa&longs;&longs;e beyond it, unle&longs;&longs;e ina&longs;much as being tran&longs;­ ported by its impetus, it &longs;hould pa&longs;&longs;e the &longs;ame to return thither a­ gain, and in the end there to re&longs;t. As therefore to the defending, that the motion by a right line doth or can agree naturally neither to the Earth, nor to any other moveable, whil'&longs;t the Univer&longs;e re­ taineth its perfect order, I would have you take no further paines a­ bout it, but (unle&longs;&longs;e you will grant them the circular motion) your be&longs;t way will be to defend and maintain their immobility.

Right motion cannot be eternal, and con&longs;equently cannot be natural to the Earth.

* Terminati&longs;&longs;imo.

* By this expre&longs;&longs;i­ on he every where means the prece­ ding Dialogue, or Giornata.

SIMPL. As to their immoveablene&longs;&longs;e, the arguments of Ari­ &longs;totle, and moreover tho&longs;e alledged by your &longs;elf &longs;eem in my opini­ on nece&longs;&longs;arily to conclude the &longs;ame, as yet; and I conceive it will be a hard matter to refute them.

SALV. Come we therefore to the &longs;econd Argument, which was, That tho&longs;e bodies, which we are a&longs;&longs;ured do move circularly, have more than one motion, unle&longs;&longs;e it be the Primum Mobile; and therefore, if the Earth did move circularly, it ought to have two motions; from which alterations would follow in the ri&longs;ing and &longs;etting of the Fixed Stars: Which effect is not perceived to en&longs;ue. Therefore, &c. The mo&longs;t proper and genuine an&longs;wer to this Alle­ gation is contained in the Argument it &longs;elf; and even Aristotle puts it in our mouths, which it is impo&longs;&longs;ible, Simplicius, that you &longs;hould not have &longs;een.

The an&longs;wer to the &longs;econd argu­ ment.

SIMPL. I neither have &longs;een it, nor do I yet apprehend it.

SALV. This cannot be, &longs;ure, the thing is &longs;o very plain.

SIMPL. I will with your leave, ca&longs;t an eye upon the Text.

SAGR. We will command the Text to be brought forthwith.

SIMPL. I alwayes carry it about with me: See here it is, and I know the place perfectly well, which is in lib. 2. De Cælo, cap. 16. Here it is, Text 97. Preterea omnia, quæ feruntur latione circulari &longs;ubdeficere videntur, ac moveri pluribus una latione, præter primam Sphæram; quare & Terram nece&longs;&longs;ariam e&longs;t, &longs;ive circa medium, &longs;ive in medio po&longs;ita feratur, duabus moveri lationibus. Si autem hoc acciderit, nece&longs;&longs;ariam e&longs;t fieri muta­ tiones, ac conver&longs;iones fixorum a&longs;trorum. Hoc autem non vide­ tur ficri, &longs;ed &longs;emper eadem, apud eadem loca ip&longs;ius, & oriun­ tur, & occidunt. [In Engli&longs;h thus:] Furthermore all that are carried with circular motion, &longs;eem to ^{*} fore&longs;low, and to move with more than one motion, except the fir&longs;t Sphere; wherefore it is nece&longs;&longs;ary that the Earth move with two motions, whether it be carried about the ^{*} middle, or placed in the middle. But if it be &longs;o, there would of nece&longs;&longs;ity be alterations and conver&longs;i­ ons made among&longs;t the fixed Stars. But no &longs;uch thing is &longs;een to be done, but the &longs;ame Star doth alwayes ri&longs;e and &longs;et in the &longs;ame place. In all this I find not any falacy, and my thinks the argu­ ment is very forcible.

* Subde&longs;icere.

* Or Centre.

SALV. And this new reading of the place hath confirmed me in the fallacy of the Sillogi&longs;me, and moreover, di&longs;covered ano­ ther fal&longs;ity. Therefore ob&longs;erve. The Po&longs;itions, or if you will, Conclu&longs;ions, which Ari&longs;totle endeavours to oppo&longs;e, are two; one is that of tho&longs;e, who placing the Earth in the mid&longs;t of the World, do make it move in it &longs;elf about its own centre. The other is of tho&longs;e, who con&longs;tituting it far from the middle, do make it re­ volve with a circular motion about the middle of the Univer&longs;e. And both the&longs;e Po&longs;itions he conjointly impugneth with one and the &longs;ame argument. Now I affirm that he is out in both the one and the other impugnation; and that his error again&longs;t the fir&longs;t Po&longs;ition is an Equivoke or Paralogi&longs;me; and his mi&longs;take touch­ ing the &longs;econd is a fal&longs;e con&longs;equence. Let us begin with the fir&longs;t A&longs;&longs;ertion, which con&longs;tituteth the Earth in the mid&longs;t of the World, and maketh it move in it &longs;elf about its own centre; and let us confront it with the objection of Ari&longs;totle; &longs;aying, All moveables, that move circularly, &longs;eem to ^{*} fore&longs;low, and move with more than one Byas, except the fir&longs;t Sphere (that is the pri- mum mobile) therefore the Earth moving about its own centre, being placed in the middle, mu&longs;t of nece&longs;&longs;ity have two bya&longs;&longs;es, and fore&longs;low. But if this were &longs;o, it would follow, that there &longs;hould be a variation in the ri&longs;ing and &longs;etting of the fixed Stars, which we do not perceive to be done: Therefore the Earth doth not move, &c. Here is the Paralogi&longs;me, and to di&longs;cover it, I will argue with Ari&longs;totle in this manner. Thou &longs;ai&longs;t, oh Ari&longs;totle, that the Earth placed in the middle of the World, cannot move in it &longs;elf (i. e. upon its own axis) for then it would be requi&longs;ite to allow it two bya&longs;&longs;es; &longs;o that, if it &longs;hould not be nece&longs;&longs;ary to allow it more than one Byas onely, thou woulde&longs;t not then hold it impo&longs;&longs;ible for it to move onely with that one; for thou would'&longs;t unnece&longs;&longs;arily have con&longs;ined the impo&longs;&longs;ibility to the plurality of bya&longs;&longs;es, if in ca&longs;e it had no more but one, yet it could not move with that. And becau&longs;e that of all the moveables in the World, thou make&longs;t but one alone to move with one &longs;ole byas; and all the re&longs;t with more than one; and this &longs;ame moveable thou af­ firme&longs;t to be the fir&longs;t Sphere, namely, that by which all the fix­ ed and erratick Stars &longs;eem harmoniou&longs;ly to move from Ea&longs;t to We&longs;t, if in ca&longs;e the Earth may be that fir&longs;t Sphere, that by mo­ ving with one by as onely, may make the Stars appear to move from Ea&longs;t to We&longs;t, thou wilt not deny them it: But he that af­ firmeth, that the Earth being placed in the mid&longs;t of the World, moveth about its own Axis, a&longs;cribes unto it no other motion, &longs;ave that by which all the Stars appear to move from Ea&longs;t to We&longs;t; and &longs;o it cometh to be that fir&longs;t Sphere, which thou thy &longs;elf ac­ knowledge&longs;t to move with but one by as onely. It is therefore ne­ ce&longs;&longs;ary, oh Ari&longs;totle, if thou wilt conclude any thing, that thou demon&longs;trate, that the Earth being placed in the mid&longs;t of the World, cannot move with &longs;o much as one by as onely; or el&longs;e, that much le&longs;&longs;e can the fir&longs;t Sphere have one &longs;ole motion; for o­ therwi&longs;e thou doe&longs;t in thy very Sillogi&longs;me both commit the falacy, and detect it, denying, and at that very time proving the &longs;ame thing. I come now to the &longs;econd Po&longs;ition, namely, of tho&longs;e who placing the Earth far from the mid&longs;t of the Univer&longs;e, make it moveable about the &longs;ame; that is, make it a Planet and erra­ tick Star; again&longs;t which the argument is directed, and as to form is concludent, but faileth in matter. For it being granted, that the Earth doth in that manner move, and that with two by­ a&longs;&longs;es, yet doth it not nece&longs;&longs;arily follow that though it were &longs;o, it &longs;hould make alterations in the ri&longs;ings and &longs;ettings of the fixed Stars, as I &longs;hall in its proper place declare. And here I could gladly excu&longs;e Ari&longs;totle; rather I could highly applaud him for ha­ ving light upon the mo&longs;t &longs;ubtil argument that could be produced again&longs;t the Copernican Hypothe&longs;is; and if the objection be inge­ nious, and to outward appearance mo&longs;t powerful, you may &longs;ee how much more acute and ingenious the &longs;olution mu&longs;t be, and not to be found by a wit le&longs;&longs;e piercing than that of Copernicus; and again from the difficulty in under&longs;tanding it, you may argue the &longs;o much greater difficulty in finding it. But let us for the pre­ &longs;ent &longs;u&longs;pend our an&longs;wer, which you &longs;hall under&longs;tand in due time and place, after we have repeated the objection of Ari&longs;totle, and that in his favour, much &longs;trengthened. Now pa&longs;&longs;e we to Ari- &longs;totles third Argument, touching which we need give no farther reply, it having been &longs;ufficiently an&longs;wered betwixt the di&longs;cour&longs;es of ye&longs;terday and to day: In as much as he urgeth, that the mo­ tion of grave bodies is naturally by a right line to the centre; and then enquireth, whether to the centre of the Earth, or to that of the Univer&longs;e, and concludeth that they tend naturally to the centre of the Univer&longs;e, but accidentally to that of the Earth. Therefore we may proceed to the fourth, upon which its requi&longs;ite that we &longs;tay &longs;ome time, by rea&longs;on it is founded upon that expe­ riment, from whence the greater part of the remaining argu­ ments derive all their &longs;trength. Ari&longs;totle &longs;aith therefore, that it is a mo&longs;t convincing argument of the Earths immobility, to &longs;ee that projections thrown or &longs;hot upright, return perpendicularly by the &longs;ame line unto the &longs;ame place from whence they were &longs;hot or thrown. And this holdeth true, although the motion be of a very great height; which could never come to pa&longs;&longs;e, did the Earth move: for in the time that the projected body is moving upwards and downwards in a &longs;tate of &longs;eparation from the Earth, the place from whence the motion of the projection began, would be pa&longs;t, by means of the Earths revolution, a great way to­ wards the Ea&longs;t, and look how great that &longs;pace was, &longs;o far from that place would the projected body in its de&longs;cent come to the ground. So that hither may be referred the argument taken from a bullet &longs;hot from a Canon directly upwards; as al&longs;o that other u&longs;ed by Ari&longs;totle and Ptolomy, of the grave bodies that falling from on high, are ob&longs;erved to de&longs;cend by a direct and perpendicu­ lar line to the &longs;urface of the Earth. Now that I may begin to untie the&longs;e knots, I demand of Simplicius that in ca&longs;e one &longs;hould deny to Ptolomy and Ari&longs;totle that weights in falling freely from on high, de&longs;cend by a right and perpendicular line, that is, directly to the centre, what means he would u&longs;e to prove it?

Ari&longs;totles argu­ ment again&longs;t the Earths motion, is defective in two things

* The &longs;ame word which a little above I tendred &longs;tay be­ hind, as a bowle when it meets with ruls.

The an&longs;wer to the third argu­ ment.

The an&longs;wer to the fourth argu­ ment.

SIMPL. The means of the &longs;en&longs;es; the which a&longs;&longs;ureth us, that that Tower or other altitude, is upright and perpendicular, and &longs;heweth us that that &longs;tone, or other grave body, doth &longs;lide along the Wall, without inclining a hairs breadth to one &longs;ide or ano­ ther, and light at the foot thereof ju&longs;t under the place from whence it was let fall.

SALV. But if it &longs;hould happen that the Terre&longs;trial Globe did move round, and con&longs;equently carry the Tower al&longs;o along with it, and that the &longs;tone did then al&longs;o grate and &longs;lide along the &longs;ide of the Tower, what mu&longs;t its motion be then?

SIMPL. In this ca&longs;e we may rather &longs;ay its motions: for it would have one wherewith to de&longs;cend from the top of the Tower to the bottom, and &longs;hould nece&longs;&longs;arily have another to follow the cour&longs;e of the &longs;aid Tower.

SALV. So that its motion &longs;hould be compounded of two, to wit, of that wherewith it mea&longs;ureth the Tower, and of that o­ ther wherewith it followeth the &longs;ame: From which compo&longs;ition would follow, that the &longs;tone would no longer de&longs;cribe that &longs;imple right and perpendicular line, but one tran&longs;ver&longs;e, and perhaps not &longs;treight.

SIMPL. I can &longs;ay nothing of its non-rectitude, but this I know very well, that it would of nece&longs;&longs;ity be tran&longs;ver&longs;e, and different from the other directly perpendicular, which it doth de&longs;cribe, the Earth &longs;tanding &longs;till.

SALV. You &longs;ee then, that upon the meer ob&longs;erving the falling &longs;tone to glide along the Tower, you cannot certainly affirm that it de&longs;cribeth a line which is &longs;treight and perpendicular, unle&longs;s you fir&longs;t &longs;uppo&longs;e that the Earth &longs;tandeth &longs;till.

SIMPL. True; for if the Earth &longs;hould move, the &longs;tones mo­ tion would be tran&longs;ver&longs;e, and not perpendicular.

SALV. Behold then the Paralogi&longs;m of Ari&longs;totle and Ptolomey to be evident and manife&longs;t, and di&longs;covered by you your &longs;elf, wherein that is &longs;uppo&longs;ed for known, which is intended to be de­ mon&longs;trated.

The Paralogi&longs;m of Ari&longs;totle and Ptolomey in &longs;up­ po&longs;ing that for known, which is in que&longs;tion.

SIMPL. How can that be? To me it appeareth that the Syllogi&longs;m is rightly demon&longs;trated without petitionem principii.

SALV. You &longs;hall &longs;ee how it is; an&longs;wer me a little. Doth he not lay down the conclu&longs;ion as unknown?

SIMPL. Unknown; why otherwi&longs;e the demon&longs;trating it would be &longs;uperfluous.

SALV. But the middle term, ought not that to be known?

SIMPL. Its nece&longs;&longs;ary that it &longs;hould; for otherwi&longs;e it would be a proving ignotum per æquè ignotum.

SALV. Our conclu&longs;ion which is to be proved, and which is un­ known, is it not the &longs;tability of the Earth?

SIMPL. It is the &longs;ame.

SALV. The middle term, which ought to be known, is it not the &longs;treight and perpendicular de&longs;cent of the &longs;tone?

SIMPL. It is &longs;o.

SALV. But was it not ju&longs;t now concluded, that we can have no certain knowledg whether that &longs;ame &longs;hall be direct and perpen­ dicular, unle&longs;s we fir&longs;t know that the Earth &longs;tands &longs;till? Therefore in your Syllogi&longs;m the certainty of the middle term is a&longs;&longs;umed from the uncertainty of the conclu&longs;ion. You may &longs;ee then, what and how great the Paralogi&longs;m is.

SAGR. I would, in favour of Simplicius, defend Ari&longs;totle if it were po&longs;&longs;ible, or at lea&longs;t better &longs;atisfie my &longs;elf concerning the &longs;trength of your illation. You &longs;ay, that the &longs;eeing the &longs;tone rake along the Tower, is not &longs;ufficient to a&longs;&longs;ure us, that its motion is perpendicular (which is the middle term of the Syllogi&longs;m) unle&longs;s it be pre&longs;uppo&longs;ed, that the Earth &longs;tandeth &longs;till, which is the con­ clu&longs;ion to be proved: For that if the Tower did move together with the Earth, and the &longs;tone did &longs;lide along the &longs;ame, the motion of the &longs;tone would be tran&longs;ver&longs;e, and not perpendicular. But I &longs;hall an&longs;wer, that &longs;hould the Tower move, it would be impo&longs;&longs;ible that the &longs;tone &longs;hould fall gliding along the &longs;ide of it; and there­ fore from its falling in that manner the &longs;tability of the Earth is in­ ferred.

SIMPL. It is &longs;o; for if you would have the &longs;tone in de&longs;cend­ ing to grate upon the Tower, though it were carried round by the Earth, you mu&longs;t allow the &longs;tone two natural motions, to wit, the &longs;traight motion towards the Centre, and the circular about the Centre, the which is impo&longs;&longs;ible.

SALV. Ari&longs;totles defen&longs;e then con&longs;i&longs;teth in the impo&longs;&longs;ibilitie, or at lea&longs;t in his e&longs;teeming it an impo&longs;&longs;ibility, that the &longs;tone &longs;hould move with a motion mixt of right and circular: for if he did not hold it impo&longs;&longs;ible that the &longs;tone could move to the Centre, and about the Centre at once, he mu&longs;t have under&longs;tood, that it might come to pa&longs;s that the cadent &longs;tone might in its de&longs;cent, race the Tower as well when it moved as when it &longs;tood &longs;till; and con­ &longs;equently he mu&longs;t have perceived, that from this grating nothing could be inferred touching the mobility or immobility of the Earth. But this doth not any way excu&longs;e Aristotle; a&longs;well be­ cau&longs;e he ought to have expre&longs;t it, if he had had &longs;uch a conceit, it being &longs;o material a part of his Argument; as al&longs;o becau&longs;e it can neither be &longs;aid that &longs;uch an effect is impo&longs;&longs;ible, nor that Ari&longs;totle did e&longs;teem it &longs;o. The fir&longs;t cannot be affirmed, for that by and by I &longs;hall &longs;hew that it is not onely po&longs;&longs;ible, but nece&longs;&longs;ary: nor much le&longs;s can the &longs;econd be averred, for that Ari&longs;totle him&longs;elf granteth fire to move naturally upwards in a right line, and to move about with the diurnal motion, imparted by Heaven to the whole Element of Fire, and the greater part of the Air: If there­ fore he held it not impo&longs;&longs;ible to mix the right motion upwards, with the circular communicated to the Fire and Air from the con­ cave of the Moon, much le&longs;s ought he to account impo&longs;&longs;ible the mixture of the right motion downwards of the &longs;tone, with the circular which we pre&longs;uppo&longs;e natural to the whole Terre&longs;trial Globe, of which the &longs;tone is a part.

Ari&longs;totle admit­ teth that the Fire moveth directly upwards by na­ ture, and round a­ bout by participa­ tion.

SIMPL. I &longs;ee no &longs;uch thing: for if the element of Fire re­ volve round together with the Air, it is a very ea&longs;ie, yea a nece&longs;&longs;ary thing, that a &longs;park of fire which from the Earth mounts upwards, in pa&longs;&longs;ing thorow the moving air, &longs;hould receive the &longs;ame motion, being a body &longs;o thin, light, and ea&longs;ie to be moved: but that a very heavy &longs;tone, or a Canon bullet, that de&longs;cendeth from on high, and that is at liberty to move whither it will, &longs;hould &longs;uffer it &longs;elf to be tran&longs;ported either by the air or any other thing, is altogether incredible. Be&longs;ides that, we have the Experiment, which is &longs;o proper to our purpo&longs;e, of the &longs;tone let fall from the round top of the Ma&longs;t of a &longs;hip, which when the &longs;hip lyeth &longs;till, falleth at the Partners of the Ma&longs;t; but when the &longs;hip &longs;aileth, falls &longs;o far di&longs;tant from that place, by how far the &longs;hip in the time of the &longs;tones falling had run forward; which will not be a few fa­ thoms, when the &longs;hips cour&longs;e is &longs;wift.

SALV. There is a great di&longs;parity between the ca&longs;e of the Ship and that of the Earth, if the Terre&longs;trial Globe be &longs;uppo&longs;ed to have a diurnal motion. For it is a thing very manife&longs;t, that the mo­ tion of the Ship, as it is not natural to it, &longs;o the motion of all tho&longs;e things that are in it is accidental, whence it is no wonder that the &longs;tone which was retained in the round top, being left at liberty, de&longs;cendeth downwards without any obligation to follow the mo­ tion of the Ship. But the diurnal conver&longs;ion is a&longs;cribed to the Terre&longs;trial Globe for its proper and natural motion, and con&longs;e­ quently, it is &longs;o to all the parts of the &longs;aid Globe; and, as being impre&longs;s'd by nature, is indelible in them; and therefore that &longs;tone that is on the top of the Tower hath an intrin&longs;ick inclination of revolving about the Centre of its Whole in twenty four hours, and this &longs;ame natural in&longs;tinct it exerci&longs;eth eternally, be it placed in any &longs;tate what&longs;oever. And to be a&longs;&longs;ured of the truth of this, you have no more to do but to alter an antiquated impre&longs;&longs;ion made in your mind; and to &longs;ay, Like as in that I hitherto holding it to be the property of the Terre&longs;trial Globe to re&longs;t immoveable about its Centre, did never doubt or que&longs;tion but that all what&longs;oever particles thereof do al&longs;o naturally remain in the &longs;ame &longs;tate of re&longs;t: So it is rea&longs;on, in ca&longs;e the Terre&longs;trial Globe did move round by natural in&longs;tinct in twenty four hours, that the intrin&longs;ick and natu­ ral inclination of all its parts &longs;hould al&longs;o be, not to &longs;tand &longs;till, but to follow the &longs;ame revolution. And thus without running into any inconvenience, one may conclude, that in regard the motion conferred by the force of ^{*}Oars on the Ship, and by it on all the things that are contained within her, is not natural but forreign, it is very rea&longs;onable that that &longs;tone, it being &longs;eparated from the &longs;hip, do reduce its &longs;elf to its natural di&longs;po&longs;ure, and return to exerci&longs;e its pure &longs;imple in&longs;tinct given it by nature. To this I add, that it's nece&longs;&longs;ary, that at lea&longs;t that part of the Air which is beneath the greater heights of mountains, &longs;hould be tran&longs;ported and carried round by the roughne&longs;s of the Earths &longs;urface; or that, as being mixt with many Vapours, and terrene Exhalations, it do na­ turally follow the diurnal motion, which occurreth not in the Air about the &longs;hip rowed by Oars: So that your arguing from the &longs;hip to the Tower hath not the force of an illation; becau&longs;e that &longs;tone which falls from the round top of the Ma&longs;t, entereth into a medium, which is unconcern'd in the motion of the &longs;hip: but that which departeth from the top of the Tower, finds a medium that hath a motion in common with the whole Ter­ re&longs;trial Globe; &longs;o that without being hindred, rather being a&longs;&longs;i&longs;ted by the motion of the air, it may follow the univer&longs;al cour&longs;e of the Earth.

The di&longs;parity be­ tween the fall of a &longs;tone from the round top of a &longs;hip, and from the top of a tower.

*That you may not &longs;u&longs;pect my tran&longs;la­ tion, or wonder what Oars have to do with a &longs;hip, you are to know that the Author intends the Gallies u&longs;ed in the Mediterrane.

The part of the Air inferiour to the higher moun­ tains doth follow the motion of the Earth.

SIMPL. I cannot conceive that the air can imprint in a very great &longs;tone, or in a gro&longs;s Globe of Wood or Ball of Lead, as &longs;uppo&longs;e of two hundred weight, the motion wherewith its &longs;elf is moved, and which it doth perhaps communicate to feathers, &longs;now, and other very light things: nay, I &longs;ee that a weight of that na­ ture, being expo&longs;ed to any the mo&longs;t impetuous wind, is not there­ by removed an inch from its place; now con&longs;ider with your &longs;elf whether the air will carry it along therewith.

The motion of the Air apt to carry with it light things but not heavy.

SALV. There is great difference between your experiment and our ca&longs;e. You introduce the wind blowing again&longs;t that &longs;tone, &longs;uppo&longs;ed in a &longs;tate of re&longs;t, and we expo&longs;e to the air, which already moveth, the &longs;tone which doth al&longs;o move with the &longs;ame velocity; &longs;o that the air is not to conferr a new motion upon it, but onely to maintain, or to &longs;peak better, not to hinder the motion already acquired: you would drive the &longs;tone with a &longs;trange and preter­ natural motion, and we de&longs;ire to con&longs;erve it in its natural. If you would produce a more pertinent experiment, you &longs;hould &longs;ay, that it is ob&longs;erved, if not with the eye of the forehead, yet with that of the mind, what would evene, if an eagle that is carried by the cour&longs;e of the wind, &longs;hould let a &longs;tone fall from its talons; which, in regard that at its being let go, it went along with the wind, and after it was let fall it entered into a medium that mo­ ved with equal velocity, I am very confident that it would not be &longs;een to de&longs;cend in its fall perpendicularly, but that following the cour&longs;e of the wind, and adding thereto that of its particular gra­ vity, it would move with a tran&longs;ver&longs;e motion.

SIMPI. But it would fir&longs;t be known how &longs;uch an experiment may be made; and then one might judg according to the event. In the mean time the effect of the &longs;hip doth hitherto incline to fa­ vour our opinion.

SALV. Well &longs;aid you hitherto, for perhaps it may anon change countenance. And that I may no longer hold you in &longs;u&longs;pen&longs;e, tell me, Simplicius, do you really believe, that the Experiment of the &longs;hip &longs;quares &longs;o very well with our purpo&longs;e, as that it ought to be believed, that that which we &longs;ee happen in it, ought al&longs;o to evene in the Terre&longs;trial Globe?

SIMPL. As yet I am of that opinion; and though you have alledged &longs;ome &longs;mall di&longs;parities, I do not think them of &longs;o great moment, as that they &longs;hould make me change my judgment.

SALV. I rather de&longs;ire that you would continue therein, and hold for certain, that the effect of the Earth would exactly an&longs;wer that of the &longs;hip: provided, that when it &longs;hall appear prejudicial to your cau&longs;e, you would not be humorous and alter your thoughts. You may haply &longs;ay, Fora&longs;much as when the &longs;hip &longs;tands &longs;till, the &longs;tone falls at the foot of the Ma&longs;t, and when &longs;he is under &longs;ail, it lights far from thence, that therefore by conver&longs;ion, from the &longs;tones falling at the foot is argued the &longs;hips &longs;tanding &longs;till, and from its falling far from thence is argued her moving; and becau&longs;e that which occurreth to the &longs;hip, ought likewi&longs;e to befall the Earth: that therefore from the falling of the &longs;tone at the foot of the Tow­ er is nece&longs;&longs;arily inferred the immobility of the Terre&longs;trial Globe. Is not this your argumentation?

SIMPL. It is; and reduced into that conci&longs;ene&longs;s, as that it is become mo&longs;t ea&longs;ie to be apprehended.

SALV. Now tell me; if the &longs;tone let fall from the Round­ top, when the &longs;hip is in a &longs;wift cour&longs;e, &longs;hould fall exactly in the &longs;ame place of the &longs;hip, in which it falleth when the &longs;hip is at anchor, what &longs;ervice would the&longs;e experiments do you, in order to the a&longs;certaining whether the ve&longs;&longs;el doth &longs;tand &longs;till or move?

SIMPL. Ju&longs;t none: Like as, for exemple, from the beating of the pul&longs;e one cannot know whether a per&longs;on be a&longs;leep or awake, &longs;eeing that the pul&longs;e beateth after the &longs;ame manner in &longs;leeping as in waking.

SALV. Very well. Have you ever tryed the experiment of the Ship?

SIMPL. I have not; but yet I believe that tho&longs;e Authors which alledg the &longs;ame, have accurately ob&longs;erved it; be&longs;ides that the cau&longs;e of the di&longs;parity is &longs;o manife&longs;tly known, that it admits of no que&longs;tion.

SALV. That it is po&longs;&longs;ible that tho&longs;e Authors in&longs;tance in it, without having made tryal of it, you your &longs;elf are a good te&longs;ti­ mony, that without having examined it, alledg it as certain, and in a credulous way remit it to their authority; as it is now not onely po&longs;&longs;ible, but very probable that they likewi&longs;e did; I mean, did remit the &longs;ame to their Predece&longs;&longs;ors, without ever arriving at one that had made the experiment: for whoever &longs;hall examine the &longs;ame, &longs;hall find the event &longs;ucceed quite contrary to what hath been written of it: that is, he &longs;hall &longs;ee the &longs;tone fall at all times in the &longs;ame place of the Ship, whether it &longs;tand &longs;till, or move with any what&longs;oever velocity. So that the &longs;ame holding true in the Earth, as in the Ship, one cannot from the &longs;tones falling perpen­ dicularly at the foot of the Tower, conclude any thing touching the motion or re&longs;t of the Earth.

The stone falling from the Mast of a &longs;hip lights in the &longs;ame place, whe­ ther the &longs;hip doth move or ly still.

SIMPL. If you &longs;hould refer me to any other means than to experience, I verily believe our Di&longs;putations would not come to an end in ha&longs;te; for this &longs;eemeth to me a thing &longs;o remote from all humane rea&longs;on, as that it leaveth not the lea&longs;t place for credulity or probability.

SALV. And yet it hath left place in me for both.

SIMPL. How is this? You have not made an hundred, no nor one proof thereof, and do you &longs;o confidently affirm it for true? I for my part will return to my incredulity, and to the confidence I had that the Experiment hath been tried by the principal Au­ thors who made u&longs;e thereof, and that the event &longs;ucceeded as they affirm.

SALV. I am a&longs;&longs;ured that the effect will en&longs;ue as I tell you; for &longs;o it is nece&longs;&longs;ary that it &longs;hould: and I farther add, that you know your &longs;elf that it cannot fall out otherwi&longs;e, however you feign or &longs;eem to feign that you know it not. Yet I am &longs;o good at taming of wits, that I will make you confe&longs;s the &longs;ame whether you will or no. But Sagredus &longs;tands very mute, and yet, if I mi&longs;take not, I &longs;aw him make an offer to &longs;peak &longs;omewhat.

SAGR. I had an intent to &longs;ay &longs;omething, but to tell you true, I know not what it was; for the curio&longs;ity that you have moved in me, by promi&longs;ing that you would force Simplicius to di&longs;cover the knowledg which he would conceal from us, hath made me to de­ po&longs;e all other thoughts: therefore I pray you to make good your vaunt.

SALV. Provided that Simplicius do con&longs;ent to reply to what I &longs;hall ask him, I will not fail to do it.

SIMPL. I will an&longs;wer what I know, a&longs;&longs;ured that I &longs;hall not be much put to it, for that of tho&longs;e things which I hold to be fal&longs;e, I think nothing can be known, in regard that Science re&longs;pecteth truths and not fal&longs;hoods.

SALV. I de&longs;ire not that you &longs;hould &longs;ay or reply, that you know any thing, &longs;ave that which you mo&longs;t a&longs;&longs;uredly know. Therefore tell me; If you had here a flat &longs;uperficies as polite as a Looking­ gla&longs;s, and of a &longs;ub&longs;tance as hard as &longs;teel, and that it were not pa­ ralel to the Horizon, but &longs;omewhat inclining, and that upon it you did put a Ball perfectly &longs;pherical, and of a &longs;ub&longs;tance grave and hard, as &longs;uppo&longs;e of bra&longs;s; what think you it would do being let go? do not you believe (as for my part I do) that it would lie &longs;till?

SIMPL. If that &longs;uperficies were inclining?

SALV. Yes; for &longs;o I have already &longs;uppo&longs;ed.

SIMPL. I cannot conceive how it &longs;hould lie &longs;till: nay, I am confident that it would move towards the declivity with much pro­ pen&longs;ne&longs;s.

SALV. Take good heed what you &longs;ay, Simplicius, for I am confident that it would lie &longs;till in what ever place you &longs;hould lay it.

SIMPL. So long as you make u&longs;e of &longs;uch &longs;uppo&longs;itions, Sal­ viatus, I &longs;hall cea&longs;e to wonder if you inferr mo&longs;t ab&longs;urd con­ clu&longs;ions.

SALV. Are you a&longs;&longs;ured, then, that it would freely move to­ wards the declivity?

SIMPL. Who doubts it?

SALV. And this you verily believe, not becau&longs;e I told you &longs;o, (for I endeavoured to per&longs;wade you to think the contrary) but of your &longs;elf, and upon your natural judgment.

SIMPL. Now I &longs;ee what you would be at; you &longs;poke not this as really believing the &longs;ame; but to try me, and to wre&longs;t matter out of my own mouth wherewith to condemn me.

SALV. You are in the right. And how long would that Ball move, and with what velocity? But take notice that I in&longs;tanced in a Ball exactly round, and a plain exqui&longs;itely poli&longs;hed, that all external and accidental impediments might be taken away. And &longs;o would I have you remove all ob&longs;tructions cau&longs;ed by the Airs re­ &longs;i&longs;tance to divi&longs;ion, and all other ca&longs;ual ob&longs;tacles, if any other there can be.

SIMPL. I very well under&longs;tand your meaning, and as to your demand, I an&longs;wer, that the Ball would continue to move in in­ finitum, if the inclination of the plain &longs;hould &longs;o long la&longs;t, and con­ tinually with an accelerating motion; for &longs;uch is the nature of ponderous moveables, that vires acquirant eundo: and the great­ er the declivity was, the greater the velocity would be.

SALV. But if one &longs;hould require that that Ball &longs;hould move upwards on that &longs;ame &longs;uperficies, do you believe that it would &longs;o do?

SIMPL. Not &longs;pontaneou&longs;ly; but being drawn, or violently thrown, it may.

SALV. And in ca&longs;e it were thru&longs;t forward by the impre&longs;&longs;ion of &longs;ome violent impetus from without, what and how great would its motion be?

SIMPL. The motion would go continually decrea&longs;ing and re­ tarding, as being contrary to nature; and would be longer or &longs;horter, according to the greater or le&longs;s impul&longs;e, and according to the greater or le&longs;s acclivity.

SALV. It &longs;eems, then, that hitherto you have explained to me the accidents of a moveable upon two different Planes; and that in the inclining plane, the grave moveable doth &longs;pontaneou&longs;ly de­ &longs;cend, and goeth continually accelerating, and that to retain it in re&longs;t, force mu&longs;t be u&longs;ed therein: but that on the a&longs;cending plane, there is required a force to thru&longs;t it forward, and al&longs;o to &longs;tay it in re&longs;t, and that the motion impre&longs;&longs;ed goeth continually dimini&longs;hing, till that in the end it cometh to nothing. You &longs;ay yet farther, that in both the one and the other ca&longs;e, there do ari&longs;e differences from the planes having a greater or le&longs;s declivity or acclivity; &longs;o that the greater inclination is attended with the greater velocity; and contrariwi&longs;e, upon the a&longs;cending plane, the &longs;ame moveable thrown with the &longs;ame force, moveth a greater di&longs;tance, by how much the elevation is le&longs;s. Now tell me, what would befall the &longs;ame moveable upon a &longs;uperficies that had neither acclivity nor declivity?

SIMPL. Here you mu&longs;t give me a little time to con&longs;ider of an an&longs;wer. There being no declivity, there can be no natural incli­ nation to motion: and there being no acclivity, there can be no re&longs;i&longs;tance to being moved; &longs;o that there would ari&longs;e an indiffe­ rence between propen&longs;ion and re&longs;i&longs;tance of motion; therefore, methinks it ought naturally to &longs;tand &longs;till. But I had forgot my &longs;elf: it was but even now that Sagredus gave me to under&longs;tand that it would &longs;o do.

SALV. So I think, provided one did lay it down gently: but if it had an impetus given it towards any part, what would fol­ low?

SIMP. There would follow, that it &longs;hould move towards that part.

SALV. But with what kind of motion? with the continually accelerated, as in declining planes; or with the &longs;ucce&longs;&longs;ively re­ tarded, as in tho&longs;e a&longs;cending.

SIMP. I cannot tell how to di&longs;cover any cau&longs;e of acceleration, or retardation, there being no declivity or acclivity.

SALV. Well: but if there be no cau&longs;e of retardation, much le&longs;s ought there to be any cau&longs;e of re&longs;t. How long therefore would you have the moveable to move?

SIMP. As long as that &longs;uperficies, neither inclined nor decli­ ned &longs;hall la&longs;t.

SALV. Therefore if &longs;uch a &longs;pace were interminate, the motion upon the &longs;ame would likewi&longs;e have no termination, that is, would be perpetual.

SIMP. I think &longs;o, if &longs;o be the moveable be of a matter durable.

SALV. That hath been already &longs;uppo&longs;ed, when it was &longs;aid, that all external and accidental impediments were removed, and the brittlene&longs;&longs;e of the moveable in this our ca&longs;e, is one of tho&longs;e impediments accidental. Tell me now, what do you think is the cau&longs;e that that &longs;ame Ball moveth &longs;pontaneou&longs;ly upon the inclining plane, and not without violence upon the erected?

SIMP. Becau&longs;e the inclination of grave bodies is to move to­ wards the centre of the Earth, and onely by violence upwards to­ wards the circumference; and the inclining &longs;uperficies is that which acquireth vicinity to the centre, and the a&longs;cending one, remotene&longs;&longs;e.

SALV. Therefore a &longs;uperficies, which &longs;hould be neither de­ clining nor a&longs;cending, ought in all its parts to be equally di­ &longs;tant from the centre. But is there any &longs;uch &longs;uperficies in the World?

SIMP. There is no want thereof: Such is our Terre&longs;trial Globe, if it were more even, and not as it is rough and montai­ nous; but you have that of the Water, at &longs;uch time as it is calm and &longs;till.

SALV. Then a &longs;hip which moveth in a calm at Sea, is one of tho&longs;e moveables, which run along one of tho&longs;e &longs;uperficies that are neither declining nor a&longs;cending, and therefore di&longs;po&longs;ed, in ca&longs;e all ob&longs;tacles external and accidental were removed, to move with the impul&longs;e once imparted ince&longs;&longs;antly and uniformly.

SIMPL. It &longs;hould &longs;eem to be &longs;o.

SALV. And that &longs;tone which is on the round top, doth not it move, as being together with the &longs;hip carried about by the cir­ cumference of a Circle about the Centre; and therefore con&longs;e­ quently by a motion in it indelible, if all extern ob&longs;tacles be removed? And is not this motion as &longs;wift as that of the &longs;hip.

SIMPL. Hitherto all is well. But what followeth?

SALV. Then in good time recant, I pray you, that your la&longs;t conclu&longs;ion, if you are &longs;atisfied with the truth of all the pre­ mi&longs;es.

SIMPL. By my la&longs;t conclu&longs;ion, you mean, That that &longs;ame &longs;tone moving with a motion indelibly impre&longs;&longs;ed upon it, is not to leave, nay rather is to follow the &longs;hip, and in the end to light in the &longs;elf &longs;ame place, where it falleth when the &longs;hip lyeth &longs;till; and &longs;o I al&longs;o grant it would do, in ca&longs;e there were no outward impe­ diments that might di&longs;turb the &longs;tones motion, after its being let go, the which impediments are two, the one is the moveables inability to break through the air with its meer impetus onely, it being deprived of that of the &longs;trength of Oars, of which it had been partaker, as part of the &longs;hip, at the time that it was upon the Ma&longs;t; the other is the new motion of de&longs;cent, which al&longs;o mu&longs;t needs be an hinderance of that other progre&longs;&longs;ive motion.

SALV. As to the impediment of the Air, I do not deny it you; and if the thing falling were a light matter, as a feather, or a lock of wool, the retardation would be very great, but in an heavy &longs;tone is very exceeding &longs;mall. And you your &longs;elf but even now did &longs;ay, that the force of the mo&longs;t impetuous wind &longs;ufficeth not to &longs;tir a great &longs;tone from its place; now do but con­ &longs;ider what the calmer air is able to do, being encountred by a &longs;tone no more &longs;wift than the whole &longs;hip. Neverthele&longs;&longs;e, as I &longs;aid before, I do allow you this &longs;mall effect, that may depend upon &longs;uch an impediment; like as I know, that you will grant to me, that if the air &longs;hould move with the &longs;ame velocity that the &longs;hip and &longs;tone hath, then the impediment would be nothing at all. As to the other of the additional motion downwards; in the fir&longs;t place it is manife&longs;t, that the&longs;e two, I mean the circular, about the centre, and the &longs;treight, towards the centre, are not contra­ ries, or de&longs;tructive to one another, or incompatible. Becau&longs;e that as to the moveable, it hath no repugnance at all to &longs;uch motions, for you your &longs;elf have already confe&longs;t the repugnance to be a­ gain&longs;t the motion which removeth from the centre, and the incli­ nation to be towards the motion which approacheth to the centre. Whence it doth of nece&longs;&longs;ity follow, that the moveable hath nei­ ther repugnance, nor propen&longs;ion to the motion which neither ap­ proacheth, nor goeth from the centre, nor con&longs;equently is there any cau&longs;e for the dimini&longs;hing in it the faculty impre&longs;&longs;ed. And for­ a&longs;much as the moving cau&longs;e is not one alone, which it hath at­ tained by the new operation of retardation; but that they are two, di&longs;tinct from each other, of which, the gravity attends on­ ly to the drawing of the moveable towards the centre, and the vertue impre&longs;s't to the conducting it about the centre, there re­ maineth no occa&longs;ion of impediment.

SIMPL. Your argumentation, to give you your due, is very probable; but in reality it is invelloped with certain intricacies, that are not ea&longs;ie to be extricated. You have all along built upon a &longs;uppo&longs;ition, which the Peripatetick Schools will not ea&longs;ily grant you, as being directly contrary to Aristotle, and it is to take for known and manife&longs;t, That the project &longs;eparated from the proji­ cient, continueth the motion by vertue impre&longs;&longs;ed on it by the &longs;aid projicient, which vertue impre&longs;&longs;ed is a thing as much dete­ &longs;ted in Peripatetick Philo&longs;ophy, as the pa&longs;&longs;age of any accident from one &longs;ubject into another. Which doctrine doth hold, as I believe it is well known unto you, that the project is carried by the medium, which in our ca&longs;e happeneth to be the Air. And therefore if that &longs;tone let fall from the round top, ought to fol­ low the motion of the &longs;hip, that effect &longs;hould be a&longs;cribed to the Air, and not to the vertue impre&longs;&longs;ed. But you pre&longs;uppo&longs;e that the Air doth not follow the motion of the &longs;hip, but is tranquil. Moreover, he that letteth it fall, is not to throw it, or to give it impetus with his arm, but ought barely to open his hand and let it go; and by this means, the &longs;tone, neither through the vertue impre&longs;&longs;ed by the projicient, nor through the help of the Air, &longs;hall be able to follow the &longs;hips motion, and therefore &longs;hall be left behind.

The project ac­ cording to Ari&longs;to­ tle, is not moved by vertue impre&longs;&longs;ed, but by the medium.

SALV. I think then that you would &longs;ay, that if the &longs;tone be not thrown by the arm of that per&longs;on, it is no longer a pro­ jection.

SIMPL. It cannot be properly called a motion of projection.

SALV. So then that which Ari&longs;totle &longs;peaks of the motion, the moveable, and the mover of the projects, hath nothing to do with the bu&longs;ine&longs;&longs;e in hand; and if it concern not our purpo&longs;e, why do you alledg the &longs;ame?

SIMP. I produce it on the ocea&longs;ion of that impre&longs;&longs;ed vertue, named and introduced by you, which having no being in the World, can be of no force; for non-entium nullæ &longs;unt operatio­ nes; and therefore not onely of projected, but of all other pre­ ternatural motions, the moving cau&longs;e ought to be a&longs;cribed to the medium, of which there hath been no due con&longs;ideration had; and therefore all that hath been &longs;aid hitherto is to no purpo&longs;e.

SALV. Go to now, in good time. But tell me, &longs;eeing that your in&longs;tance is wholly grounded upon the nullity of the vertue impre&longs;&longs;ed, if I &longs;hall demon&longs;trate to you, that the medium hath nothing to do in the continuation of projects, after they are &longs;e­ patated from the projicient, will you admit of the impre&longs;&longs;ed ver­ tue, or will you make another attempt to overthrow it?

SIMP. The operation of the medium being removed, I &longs;ee not how one can have recour&longs;e to any thing el&longs;e &longs;ave the faculty im­ pre&longs;&longs;ed by the mover.

SALV. It would be well, for the removing, as much as is po&longs;&longs;ible, the occa&longs;ions of multiplying contentions, that you would explain with as much di&longs;tinctne&longs;&longs;e as may be, what is that operation of the medium in continuing the motion of the project.

Operation of the medium in continu­ ing the motion of the project.

SIMP. The projicient hath the &longs;tone in his hand, and with force and violence throws his arm, with which jactation the &longs;tone doth not move &longs;o much as the circumambient Air; &longs;o that when the &longs;tone at its being for&longs;aken by the hand, findeth it &longs;elf in the Air, which at the &longs;ame time moveth with impetou&longs;ity, it is thereby born away; for, if the air did not operate, the &longs;tone would fall at the foot of the projicient or thrower.

Many experi­ ments, and rea­ &longs;ons again&longs;t the cau&longs;e of the moti­ on of projects, a&longs;­ &longs;igned by Ari&longs;totle.

SALV. And was you &longs;o credulous, as to &longs;uffer your &longs;elf to be per&longs;waded to believe the&longs;e fopperies, &longs;o long as you had your &longs;en&longs;es about you to confute them, and to under&longs;tand the truth thereof? Therefore tell me, that great &longs;tone, and that Canon bullet, which but onely laid upon a table, did continue immoveable again&longs;t the mo&longs;t impetuous winds, according as you a little before did affirm, if it had been a ball of cork or other light &longs;tuffe, think you that the wind would have removed it from its place?

SIMP. Yes, and I am a&longs;&longs;ured that it would have blown it quite away, and with &longs;o much more velocity, by how much the matter was lighter, for upon this rea&longs;on we &longs;ee the clouds to be tran&longs;ported with a velocity equal to that of the wind that drives them.

SALV. And what is the Wind?

SIMP. The Wind is defined to be nothing el&longs;e but air moved.

SALV. Then the moved air doth carry light things more &longs;wiftly, and to a greater di&longs;tance, then it doth heavy.

SIMP. Yes certainly.

SALV. But if you were to throw with your arm a &longs;tone, and a lock of cotton wool, which would move &longs;wi&longs;te&longs;t and farthe&longs;t?

SIMP. The &longs;tone by much; nay the wool would fall at my feet.

SALV. But, if that which moveth the projected &longs;ub&longs;tance, af­ ter it is delivered from the hand, be no other than the air moved by the arm, and the moved air do more ea&longs;ily bear away light than grave matters, how cometh it that the project of wool flieth not farther, and &longs;wifter than that of &longs;tone? Certainly it argu­ eth that the &longs;tone hath &longs;ome other impul&longs;e be&longs;ides the motion of the air. Furthermore, if two &longs;trings of equal length did hang at yonder beam, and at the end of one there was fa&longs;tened a bul­ let of lead, and a ball of cotton wool at the other, and both were carried to an equal di&longs;tance from the perpendicular, and then let go; it is not to be doubted, but that both the one and the other would move towards the perpendicular, and that being carried by their own impetus, they would go a certain &longs;pace be­ yond it, and afterwards return thither again. But which of the&longs;e two pendent Globes do you think, would continue longe&longs;t in mo­ tion, before that it would come to re&longs;t in its perpendicularity?

SIMP. The ball of lead would &longs;wing to and again many times, and that of wool but two or three at the mo&longs;t.

SALV. So that that impetus and that mobility what&longs;oever is the cau&longs;e thereof, would con&longs;erve its &longs;elf longer in grave &longs;ub­ &longs;tances, than light; I proceed now to another particular, and de­ mand of you, why the air doth not carry away that Lemon which is upon that &longs;ame Table?

SIMP. Becau&longs;e that the air it &longs;elf is not moved

SALV. It is requi&longs;ite then, that the projicient do confer mo­ tion on the Air, with which it afterward moveth the project. But if &longs;uch a motion cannot be impre&longs;&longs;ed [i. e. imparted] it being im­ po&longs;&longs;ible to make an accident pa&longs;&longs;e out of one &longs;ubject into another, how can it pa&longs;&longs;e from the arm into the Air? Will you &longs;ay that the Air is not a &longs;ubject different from the arm?

SIMP. To this it is an&longs;wered that the Air, in regard it is nei­ ther heavy nor light in its own Region, is di&longs;po&longs;ed with facility to receive every impul&longs;e, and al&longs;o to retain the &longs;ame.

SALV. But if tho&longs;e penduli even now named, did prove unto us, that the moveable, the le&longs;&longs;e it had of gravity, the le&longs;&longs;e apt it was to con&longs;erve its motion, how can it be that the Air which in the Air hath no gravity at all, doth of it &longs;elf alone re­ tain the motion acquired? I believe, and know that you by this time are of the &longs;ame opinion, that the arm doth not &longs;ooner re­ turn to re&longs;t, than doth the circumambient Air. Let's go into the Chamber, and with a towel let us agitate the Air as much as we can, and then holding the cloth &longs;till, let a little candle be brought, that was lighted in the next room, or in the &longs;ame place let a leaf of beaten Gold be left at liberty to flie any wav, and you &longs;hall by the calm vagation of them be a&longs;&longs;ured that the Air is imme­ diately reduced to tranquilty. I could alledg many other experi­ ments to the &longs;ame purpo&longs;e, but if one of the&longs;e &longs;hould not &longs;uf­ fice, I &longs;hould think your folly altogether incurable.

SAGR. When an arrow is &longs;hot again&longs;t the Wind, how incredi­ ble a thing is it, that that &longs;ame &longs;mall filament of air, impelled by the bow-&longs;tring, &longs;hould in de&longs;pite of fate go along with the arrow? But I would willingly know another particular of Ari&longs;totle, to which I intreat Simplicius would vouch&longs;afe me an an&longs;wer. Sup­ po&longs;ing that with the &longs;ame Bow there were &longs;hot two arrows, one ju&longs;t after the u&longs;ual manner, and the other &longs;ide-wayes, placing it long-wayes upon the Bow-&longs;tring, and then letting it flie, I would know which of them would go farthe&longs;t. Favour me, I pray you with an an&longs;wer, though the que&longs;tion may &longs;eem to you rather ridiculous than otherwi&longs;e; and excu&longs;e me, for that I, who am, as you &longs;ee, rather blocki&longs;h, than not, can reach no higher with my &longs;peculative faculty.

SIMPL. I have never &longs;een an arrow &longs;hot in that manner, yet neverthele&longs;&longs;e I believe, that it would not flie &longs;ide-long, the twentieth part of the &longs;pace that it goeth end-wayes.

SAGR. And for that I am of the &longs;ame opinion, hence it is, that I have a doubt ri&longs;en in me, whether Aristotle doth not contradict experience. For as to experience, if I lay two arrows upon this Table, in a time when a &longs;trong Wind bloweth, one towards the cour&longs;e of the wind, and the other &longs;idelong, the wind will quickly carry away this later, and leave the other where it was; and the &longs;ame to my &longs;eeming, ought to happen, if the Doctrine of Ari&longs;totle were true, of tho&longs;e two &longs;hot out of a Bow: fora&longs;much as the arrow &longs;hot &longs;ideways is driven by a great quantity of Air, moved by the bow&longs;tring, to wit by as much as the &longs;aid &longs;tring is long, whereas the other arrow receiveth no greater a quantity of air, than the &longs;mall circle of the &longs;trings thickne&longs;s. And I cannot imagine what may be the rea&longs;on of &longs;uch a difference, but would fain know the &longs;ame.

SIMP. The cau&longs;e &longs;eemeth to me &longs;ufficiently manife&longs;t; and it is, becau&longs;e the arrow &longs;hot endways, hath but a little quantity of air to penetrate, and the other is to make its way through a quan­ tity as great as its whole length.

SALV. Then it &longs;eems the arrows &longs;hot, are to penetrate the air? but if the air goeth along with them, yea, is that which carrieth them, what penetration can they make therein? Do you not &longs;ee that, in this ca&longs;e, the arrow would of nece&longs;&longs;ity move with greater velocity than the air? and this greater velocity, what doth confer it on the arrow? Will you &longs;ay the air giveth them a velocity greater than its own? Know then, Simplicius, that the bu&longs;ine&longs;s proceeds quite contrary to that which Ari&longs;totle &longs;aith, and that the

medium conferreth the motion on the project, is as fal&longs;e, as it is true, that it is the onely thing which procureth its ob&longs;truction; and having known this, you &longs;hall under&longs;tand without finding any thing whereof to make que&longs;tion, that if the air be really moved, it doth much better carry the dart along with it longways, than endways, for that the air which impelleth it in that po&longs;ture, is much, and in this very little. But &longs;hooting with the Bow, fora&longs;much as the air &longs;tands &longs;till, the tran&longs;ver&longs;e arrow, being to force its pa&longs;&longs;age through much air, comes to be much impeded, and the other that was nock't ea&longs;ily overcometh the ob&longs;truction of the &longs;mall quantity of air, which oppo&longs;eth it &longs;elf thereto.

The medium doth impede and not cor­ fer the motion of projects.

SALV. How many Propo&longs;itions have I ob&longs;erved in Ari&longs;totle, (meaning &longs;till in Natural Philo&longs;ophy) that are not onely fal&longs;e, but fal&longs;e in &longs;uch &longs;ort, that its diametrical contrary is true, as it happens in this ca&longs;e. But pur&longs;uing the point in hand, I think that Simplicius is per&longs;waded, that, from &longs;eeing the &longs;tone always to fall in the &longs;ame place, he cannot conjecture either the motion or &longs;ta­ bility of the Ship: and if what hath been hitherto &longs;poken, &longs;hould not &longs;uffice, there is the Experiment of the medium which may thorowly a&longs;&longs;ure us thereof; in which experiment, the mo&longs;t that could be &longs;een would be, that the cadent moveable might be left behind, if it were light, and that the air did not follow the motion of the &longs;hip: but in ca&longs;e the air &longs;hould move with equal velocity, no imaginable diver&longs;ity could be found either in this, or any other experiment what&longs;oever, as I am anon to tell you. Now if in this ca&longs;e there appeareth no difference at all, what can be pretended to be &longs;een in the &longs;tone falling from the top of the Tower, where the motion in gyration is not adventitious, and ac­ cidental, but natural and eternal; and where the air exactly fol­ loweth the motion of the Tower, and the Tower that of the Ter­ re&longs;trial Globe? have you any thing el&longs;e to &longs;ay, Simplicius, upon this particular?

SIMP. No more but this, that I &longs;ee not the mobility of the Earth as yet proved.

SALV. Nor have I any intention at this time, but onely to &longs;hew, that nothing can be concluded from the experiments alledg­ ed by our adver&longs;aries for convincing Arguments: as I think I &longs;hall prove the others to be.

SAGR. I be&longs;eech you, Salviatus, before you proceed any far­ ther, to permit me to &longs;tart certain que&longs;tions, which have been rouling in my fancy all the while that you with &longs;o much patience and equanimity, was minutely explaining to Simplicius the expe­ riment of the Ship.

SALV. We are here met with a purpo&longs;e to di&longs;pute, and it's fit that every one &longs;hould move the difficulties that he meets withall, for this is the way to come to the knowledg of the truth. Therefore &longs;peak freely.

SAGR. If it be true, that the impetus wherewith the &longs;hip moves, doth remain indelibly impre&longs;&longs;'d in the &longs;tone, after it is let fall from the Ma&longs;t; and if it be farther true, that this motion brings no im­ pediment or retardment to the motion directly downwards, na­ tural to the &longs;tone: it's nece&longs;&longs;ary, that there do an effect en&longs;ue of a very wonderful nature. Let a Ship be &longs;uppo&longs;ed to &longs;tand &longs;till, and let the time of the falling of a &longs;tone from the Ma&longs;ts Round-top to the ground, be two beats of the pul&longs;e; let the Ship afterwards be under &longs;ail, and let the &longs;ame &longs;tone depart from the &longs;ame place, and it, according to what hath been premi&longs;ed, &longs;hall &longs;till take up the time of two pul&longs;es in its fall, in which time the &longs;hip will have run, &longs;uppo&longs;e, twenty yards; To that the true motion of the &longs;tone will be a tran&longs;ver&longs;e line, con&longs;iderably longer than the fir&longs;t &longs;traight and perpendicular line, which is the length of the ^{*} Ma&longs;t, and yet neverthele&longs;s the ^{*} &longs;tone will have pa&longs;t it in the &longs;ame time. Let it be farther &longs;uppo&longs;ed, that the Ships motion is much more accele­ rated, &longs;o that the &longs;tone in falling &longs;hall be to pa&longs;s a tran&longs;ver&longs;e line much longer than the other; and in &longs;um, increa&longs;ing the Ships ve­ locity as much as you will, the falling &longs;tone &longs;hall de&longs;cribe its tran&longs;­ ver&longs;e lines &longs;till longer and longer, and yet &longs;hall pa&longs;s them all in tho&longs;e &longs;elf &longs;ame two pul&longs;es. And in this fa&longs;hion, if a Canon were level'd on the top of a Tower, and &longs;hots were made therewith point blank, that is, paralel to the Horizon, let the Piece have a greater or le&longs;s charge, &longs;o as that the ball may fall &longs;ometimes a thou&longs;and yards di&longs;tant, &longs;ometimes four thou&longs;and, &longs;ometimes &longs;ix, &longs;ometimes ten, &c. and all the&longs;e &longs;hots &longs;hall curry or fini&longs;h their ranges in times equal to each other, and every one equal to the time which the ball would take to pa&longs;s from the mouth of the Piece to the ground, being left, without other impul&longs;e, to fall &longs;imply downwards in a perpendicular line. Now it &longs;eems a very admirable thing, that in the &longs;ame &longs;hort time of its falling perpen­ dicularly down to the ground, from the height of, &longs;uppo&longs;e, an hundred yards, the &longs;ame ball, being thru&longs;t violently out of the Piece by the Fire, &longs;hould be able to pa&longs;s one while four hundred, another while a thou&longs;and, another while four, another while ten thou&longs;and yards, &longs;o as that the &longs;aid ball in all &longs;hots made point blank, always continueth an equal time in the air.

An admirable accident in the mo­ tion of projects.

*By the length of the ma&longs;t he means the di&longs;tance be­ tween the upper­ deck and Round­ top.

* La palla.

SALV. The con&longs;ideration for its novelty is very pretty, and if the effect be true, very admirable: and of the truth thereof, I make no que&longs;tion: and were it not for the accidental impediment of the air, I verily believe, that, if at the time of the balls going out of the Piece, another were let fall from the &longs;ame height di­ rectly downwards, they would both come to the ground at the &longs;ame in&longs;tant, though that &longs;hould have curried ten thou&longs;and miles in its range, and this but an hundred onely: pre&longs;uppo&longs;ing the &longs;urface of the Earth to be equal, which to be a&longs;&longs;ured of, the experiment may be made upon &longs;ome lake. As for the impediment which might come from the air, it would con&longs;i&longs;t in retarding the extreme &longs;wift motion of the &longs;hot. Now, if you think fit, we will proceed to the &longs;olution of the other Objections, &longs;eeing that Sim­ plicius (as far as I can &longs;ee) is convinc'd of the nullity of this fir&longs;t, taken from things falling from on high downwards.

SIMP. I find not all my &longs;cruples removed, but it may be the fault is my own, as not being of &longs;o ea&longs;ie and quick an apprehen&longs;ion as Sagredus. And it &longs;eems to me, that if this motion, of which the &longs;tone did partake whil&longs;t it was on the Round-top of the Ships Ma&longs;t, be, as you &longs;ay, to con&longs;erve it &longs;elf indelibly in the &longs;aid &longs;tone, even after it is &longs;eparated from the Ship, it would follow, that like­ wi&longs;e in ca&longs;e any one, riding a hor&longs;e that was upon his &longs;peed, &longs;hould let a bowl drop out of his hand, that bowl being fallen to the ground would continue its motion and follow the hor&longs;es &longs;teps, without tarrying behind him: the which effect, I believe, is not to be &longs;een, unle&longs;s when he that is upon the hor&longs;e &longs;hould throw it with violence that way towards which he runneth; but otherwi&longs;e, I believe it will &longs;tay on the ground in the &longs;ame place where it fell.

SALV. I believe that you very much deceive your &longs;elf, and am certain, that experience will &longs;hew you the contrary, and that the ball being once arrived at the ground, will run together with the hor&longs;e, not &longs;taying behind him, unle&longs;s &longs;o far as the a&longs;perity and uneven­ ne&longs;s of the Earth &longs;hall hinder it. And the rea&longs;on &longs;eems to me very manife&longs;t: for if you, &longs;tanding &longs;till, throw the &longs;aid ball a­ long the ground, do you think it would not continue its motion even after you had delivered it out of your hand? and that for &longs;o much a greater &longs;pace, by how much the &longs;uperficies were more &longs;mooth, &longs;o that v. g. upon ice it would run a great way?

SIMP. There is no doubt of it, if I give it impetus with my arm; but in the other ca&longs;e it is &longs;uppo&longs;ed, that he who is upon the hor&longs;e, onely drops it out of his hand:

SALV. So I de&longs;ire that it &longs;hould be: but when you throw it with your arm, what other remaineth to the ball being once gone out of your hand, than the motion received from your arm, which motion being con&longs;erved in the boul, it doth continue to carry it forward? Now, what doth it import, that that impetus be con­ ferred on the ball rather from the arm than from the hor&longs;e? Whil&longs;t you were on hor&longs;eback, did not your hand, and con&longs;equently the ball run as fa&longs;t as the hor&longs;e it &longs;elf? Doubtle&longs;s it did: therefore in onely opening of the hand, the ball departs with the motion al­ ready conceived, not from your arm, by your particular motion, but from the motion dependant on the &longs;aid hor&longs;e, which cometh to be communicated to you, to your arm, to your hand, and la&longs;tly to the ball. Nay, I will tell you farther, that if the rider upon his &longs;peed fling the ball with his arm to the part contrary to the cour&longs;e, it &longs;hall, after it is fallen to the ground, &longs;ometimes (albeit thrown to the contrary part) follow the cour&longs;e of the hor&longs;e, and &longs;ometimes lie &longs;till on the ground; and &longs;hall onely move contrary to the &longs;aid cour&longs;e, when the motion received from the arm, &longs;hall exceed that of the carrier in velocity. And it is a vanity, that of &longs;ome, who &longs;ay that a hor&longs;eman is able to ca&longs;t a javelin thorow the air, that way which the hor&longs;e runs, and with the hor&longs;e to follow and over­ take the &longs;ame; and la&longs;tly, to catch it again. It is, I &longs;ay, a vanity, for that to make the project return into the hand, it is requi&longs;ite to ca&longs;t it upwards, in the &longs;ame manner as if you &longs;tood &longs;till. For, let the carrier be never &longs;o &longs;wift, provided it be uniform, and the pro­ ject not over-light, it &longs;hall always fall back again into the hand of the projicient, though never &longs;o high thrown.

SAGR. By this Doctrine I come to know &longs;ome Problems very curious upon this &longs;ubject of projections; the fir&longs;t of which mu&longs;t &longs;eem very &longs;trange to Simplicius. And the Problem is this; I af­ firm it to be po&longs;&longs;ible, that the ball being barely dropt or let fall, by one that any way runneth very &longs;wiftly, being arrived at the Earth, doth not onely follow the cour&longs;e of that per&longs;on, but doth much out go him. Which Problem is connexed with this, that the moveable being thrown by the projicient above the plane of the Horizon, may acquire new velocity, greater by far than that confer'd upon it by the projicient. The which effect I have with admiration ob&longs;erved, in looking upon tho&longs;e who u&longs;e the &longs;port of tops, which, &longs;o &longs;oon as they are &longs;et out of the hand, are &longs;een to move in the air with a certain velocity, the which they afterwards much encrea&longs;e at their coming to the ground; and if whipping them, they rub at any uneven place that makes them skip on high, they are &longs;een to move very &longs;lowly through the air, and falling a­ gain to the Earth, they &longs;till come to move with a greater velocity: But that which is yet more &longs;trange, I have farther ob&longs;erved, that they not onely turn always more &longs;wiftly on the ground, than in the air, but of two &longs;paces both upon the Earth, &longs;ometimes a mo­ tion in the &longs;econd &longs;pace is more &longs;wift than in the fir&longs;t. Now what would Simplicius &longs;ay to this?

Sundry curious Problems, touch­ ing the motions of projects.

SIMP. He would &longs;ay in the fir&longs;t place, that he had never made &longs;uch an ob&longs;ervation. Secondly, he would &longs;ay, that he did not be­ lieve the &longs;ame. He would &longs;ay again, in the third place, that if you could a&longs;&longs;ure him thereof, and demon&longs;tratively convince him of the &longs;ame, he would account you a great Dæmon.

SAGR. I hope then that it is one of the Socratick, not infernal ones. But that I may make you under&longs;tand this particular, you mu&longs;t know, that if a per&longs;on apprehend not a truth of him&longs;elf, it is impo&longs;&longs;ible that others &longs;hould make him under&longs;tand it: I may in­ deed in&longs;truct you in tho&longs;e things which are neither true nor fal&longs;e; but the true, that is, the nece&longs;&longs;ary, namely, &longs;uch as it is impo&longs;&longs;ible &longs;hould be otherwi&longs;e, every common capacity either comprehendeth them of him&longs;elf, or el&longs;e it is impo&longs;&longs;ible he &longs;hould ever know them. And of this opinion I am confident is Salviatus al&longs;o: and there­ fore I tell you, that the rea&longs;ons of the pre&longs;ent Problems are known by you, but it may be, not apprehended.

SIMP. Let us, for the pre&longs;ent, pa&longs;s by that controver&longs;ie, and permit me to plead ignorance of the&longs;e things you &longs;peak of, and try whether you can make me capable of under&longs;tanding the&longs;e Pro­ blems.

SAGR. This fir&longs;t dependeth upon another, which is, Whence cometh it, that &longs;etting a top with the la&longs;h, it runneth farther, and con&longs;equently with greater force, than when its &longs;et with the fin­ gers?

SIMP. Ari&longs;totle al&longs;o makes certain Problems about the&longs;e kinds of projects.

SALV. He doth &longs;o; and very ingenious they are: particular­ ly, That, Whence it cometh to pa&longs;s that round tops run better than the &longs;quare?

SAGR. And cannot you, Simplicius, give a rea&longs;on for this, without others prompting you?

SIMP. Very good, I can &longs;o; but leave your jeering.

SAGR. In like manner you do know the rea&longs;on of this other al&longs;o. Tell me therefore; know you that a thing which moveth, being impeded &longs;tands &longs;till?

SIMP. I know it doth, if the impediment be &longs;o great as to &longs;uffice.

SAGR. Do you know, that moving upon the Earth is a greater impediment to the moveable, than moving in the air, the Earth be­ ing rough and hard, and the air &longs;oft and yielding?

SIMP. And knowing this, I know that the top will turn fa&longs;ter in the air, than on the ground, &longs;o that my knowledg is quite con­ trary to what you think it.

SAGR. Fair and &longs;oftly, Simplicius. You know that in the parts of a moveable, that turneth about its centre, there are found motions towards all &longs;ides; &longs;o that &longs;ome a&longs;cend, others de&longs;cend; &longs;ome go forwards, others backwards?

SIMP. I know it, and Aristotle taught me the &longs;ame.

SAGR. And with what demon&longs;tration, I pray you?

SIMP. With that of &longs;en&longs;e.

SAGR. Ari&longs;totle, then, hath made you &longs;ee that which without him you would not have &longs;een? Did he ever lend you his eyes? You would &longs;ay, that Ari&longs;totle hath told, adverti&longs;ed, remembered you of the &longs;ame; and not taught you it. When then a top, with­ out changing place, turns round, (or in the childrens phra&longs;e, &longs;leep­ eth) not paralel, but erect to the Horizon, &longs;ome of its parts a&longs;cend, and the oppo&longs;ite de&longs;cend; the &longs;uperiour go one way, the infe­ riour another. Fancie now to your &longs;elf, a top, that without chan­ ging place, &longs;wiftly turns round in that manner, and &longs;tands &longs;u&longs;pen­ ded in the air, and that in that manner turning, it be let fall to the Earth perpendicularly, do you believe, that when it is arrived at the ground, it will continue to turn round in the &longs;ame manner, without changing place, as before?

SIMP. No, Sir.

SAGR. What will it do then?

SIMP. It will run along the ground very fa&longs;t.

SAGR. And towards what part?

SIMP. Towards that, whither its ^{*}reeling carrieth it.

* Vertigine.

SAGR. In its reeling there are parts, that is the uppermo&longs;t, which do move contrary to the inferiour; therefore you mu&longs;t in&longs;tance which it &longs;hall obey: for as to the parts a&longs;cending and de&longs;cending, the one kind will not yield to the other; nor will they all go downwards, being hindered by the Earth, nor upwards as being heavy.

SIMP. The top will run reeling along the floor towards that part whither its upper parts encline it.

SAGR. And why not whither the contrary parts tend, namely, tho&longs;e which touch the ground?

SIMP. Becau&longs;e tho&longs;e upon the ground happen to be impeded by the roughne&longs;s of the touch, that is, by the floors unevenne&longs;s; but the &longs;uperiour, which are in the tenuous and flexible air, are hindred very little, if at all; and therefore the top will obey their inclination.

SAGR. So that that taction, if I may &longs;o &longs;ay, of the neither parts on the floor, is the cau&longs;e that they &longs;tay, and onely the upper parts &longs;pring the top forward.

SALV. And therefore, if the top &longs;hould fall upon the ice, or other very &longs;mooth &longs;uperficies, it would not &longs;o well run forward, but might peradventure continue to revolve in it &longs;elf, (or &longs;leep) with­ out acquiring any progre&longs;&longs;ive motion.

SAGR. It is an ea&longs;ie thing for it &longs;o to do; but yet neverthe­ le&longs;s, it would not &longs;o &longs;peedily come to &longs;leep, as when it falleth on a &longs;uperficies &longs;omewhat rugged. But tell me, Simplicius, when the top turning round about it &longs;elf, in that manner, is let fall, why doth it not move forwards in the air, as it doth afterwards when it is upon the ground?

SIMP. Becau&longs;e having air above it, and beneath, neither tho&longs;e parts, nor the&longs;e have any where to touch, and not having more oc­ ca&longs;ion to go forward than backward, it falls perpendicularly.

SAGR. So then the onely reeling about its &longs;elf, without other impetus, can drive the top forward, being arrived at the ground, very nimbly. Now proceed we to what remains. That la&longs;h, which the driver tyeth to his Top-&longs;tick, and with which, winding it about the top, he &longs;ets it (i. e. makes it go) what effect hath it on the &longs;aid top?

SIMP. It con&longs;trains it to turn round upon its toe, that &longs;o it may free it &longs;elf from the Top-la&longs;h.

SAGR. So then, when the top arriveth at the ground, it cometh all the way turning about its &longs;elf, by means of the la&longs;h. Hath it not rea&longs;on then to move in it &longs;elf more &longs;wiftly upon the ground, than it did whil&longs;t it was in the air?

SIMP. Yes doubtle&longs;s; for in the air it had no other impul&longs;e than that of the arm of the projicient; and if it had al&longs;o the reel­ ing, this (as hath been &longs;aid) in the air drives it not forward at all: but arriving at the floor, to the motion of the arm is added the progre&longs;&longs;ion of the reeling, whereby the velocity is redoubled. And I know already very well, that the top skipping from the ground, its velocity will demini&longs;h, becau&longs;e the help of its circulation is wanting; and returning to the Earth will get it again, and by that means move again fa&longs;ter, than in the air. It onely re&longs;ts for me to under&longs;tand, whether in this &longs;econd motion on the Earth it move more &longs;wiftly, than in the fir&longs;t; for then it would move in infini­ tum, alwayes accelerating.

SAGR. I did not ab&longs;olutely affirm, that this &longs;econd motion is more &longs;wift than the fir&longs;t; but that it may happen &longs;o to be &longs;ome­ times.

SIMP. This is that, which I apprehend not, and which I de&longs;ire to know.

SAGR. And this al&longs;o you know of your &longs;elf. Therefore tell me: When you let the top fall out of your hand, without ma­ king it turn round (i. e. &longs;etting it) what will it do at its coming to the ground?

SIMP. Nothing, but there lie &longs;till.

SAGR. May it not chance, that in its fall to the ground it may acquire a motion? Think better on it.

SIMP. Unle&longs;&longs;e we let it fall upon &longs;ome inclining &longs;tone, as children do playing at ^{*} Chio&longs;a, and that falling &longs;ide-wayes upon

the &longs;ame, it do acquire the motion of turning round upon its toe, wherewith it afterwards continueth to move progre&longs;&longs;ively on the floor, I know not in what other manner it can do any thing but lie &longs;till where it falleth.

* A Game in Italy, which is, to glide bullets down an inclining &longs;tone, &c.

SAGR. You &longs;ee then that in &longs;ome ca&longs;e it may acquire a new revolution. When then the top jerked up from the ground, falleth down again, why may it not ca&longs;ually hit upon the declivity of &longs;ome &longs;tone fixed in the floor, and that hath an inclination that way towards which it moveth, and acquiring by that &longs;lip a new whirle over and above that conferred by the la&longs;h, why may it not redouble its motion, and make it &longs;wifter than it was at its fir&longs;t lighting upon the ground?

SIMP. Now I &longs;ee that the &longs;ame may ea&longs;ily happen. And I am thinking that if the top &longs;hould turn the contrary way, in ar­ riving at the ground, it would work a contrary effect, that is, the motion of the accidental whirl would retard that of the pro­ jicient.

SAGR. And it would &longs;ometimes wholly retard and &longs;top it, in ca&longs;e the revolution of the top were very &longs;wift. And from hence a­ ri&longs;eth the re&longs;olution of that &longs;light, which the more skilful Tennis Players u&longs;e to their advantage; that is, to gull their adver&longs;ary by cutting (for &longs;o is their Phra&longs;e) the Ball; which is, to return it with a &longs;ide Rachet, in &longs;uch a manner, that it doth thereby ac­ quire a motion by it &longs;elf contrary to the projected motion, and &longs;o by that means, at its coming to the ground, the rebound, which if the ball did not turn in that manner, would be towards the adver&longs;ary, giving him the u&longs;ual time to to&longs;&longs;e it back again, doth fail, and the ball runs tripping along the ground, or rebounds le&longs;&longs;e than u&longs;ual, and breaketh the time of the return. Hence it is that you &longs;ee, tho&longs;e who play at ^{*} Stool-ball, when they play in a &longs;tony way, or a place full of. holes and rubs that make the ball trip an hundred &longs;everal wayes, never &longs;uffering it to come neer the mark, to avoid them all, they do not trundle the ball upon the ground, but throw it, as if they were to pitch a quait. But be­ cau&longs;e in throwing the ball, it i&longs;&longs;ueth out of the hand with &longs;ome roling conferred by the fingers, when ever the hand is under the ball, as it is mo&longs;t commonly held; whereupon the ball in its lighting on the ground neer to the mark, between the motion of the pro­ jicient and that of the roling, would run a great way from the &longs;ame: To make the ball &longs;tay, they hold it artificially, with their hand uppermo&longs;t, and it undermo&longs;t, which in its delivery hath a contrary twirl or roling conferred upon it by the fingers, by means whereof in its coming to the ground neer the mark it &longs;tays there, or runs very very little forwards. But to return to our principal problem which gave occa&longs;ion for &longs;tarting the&longs;e others; I &longs;ay it is po&longs;&longs;ible that a per&longs;on carried very &longs;wiftly, may let a ball drop out of his hand, that being come to the Earth, &longs;hall not onely follow his motion, but al&longs;o out-go it, moving with a great­ er velocity. And to &longs;ee &longs;uch an effect, I de&longs;ire that the cour&longs;e may be that of a Chariot, to which on the out-&longs;ide let a decli­ ning board be fa&longs;tened; &longs;o as that the neither part may be towards the hor&longs;es, and the upper towards the hind Wheel. Now, if in the Chariots full career, a man within it, let a ball fall gliding a­ long the declivity of that board, it &longs;hall in roling downward ac­ quire a particular vertigo or turning, the which added to the motion impre&longs;&longs;ed by the Chariot, will carrie the ball along the ground much fa&longs;ter than the Chariot. And if one accommodate another declining board over again&longs;t it, the motion of the Cha­ riot may be qualified &longs;o, that the ball, gliding downwards along the board, in its coming to the ground &longs;hall re&longs;t immoveable, and al&longs;o &longs;hall &longs;ometimes run the contrary way to the Chariot. But we are &longs;trayed too far from the purpo&longs;e, therefore if Simplicius be &longs;atisfied with the re&longs;olution of the fir&longs;t argnment again&longs;t the Earths mobility, taken from things falling perpendicularly, we may pa&longs;&longs;e to the re&longs;t

*A Game in Italy, wherein they &longs;trive who &longs;hall trundle or throw a wooden bowle neere&longs;t to an a&longs;&longs;igned mark.

SALV. The digre&longs;&longs;ions made hitherto, are not &longs;o alienated from the matter in hand, as that one can &longs;ay they are wholly &longs;trangers to it. Be&longs;ides the&longs;e argumentations depend on tho&longs;e things that &longs;tart up in the fancy not of one per&longs;on, but of three, that we are: And moreover we di&longs;cour&longs;e for our plea&longs;ure, nor are we obliged to that &longs;trictne&longs;&longs;e of one who ex profe&longs;&longs;o treateth methodically of an argument, with an intent to publi&longs;h the &longs;ame. I will not con&longs;ent that our Poem &longs;hould be &longs;o confined to that unity, as not to leave us fields open for Ep&longs;ody's, which every &longs;mall connection &longs;hould &longs;uffice to introduce; but with almo&longs;t as much liberry as if we were met to tell &longs;tories, it &longs;hall be lawful for me to &longs;peak, what ever your di&longs;cour&longs;e brings into my mind.

SAGR. I like this motion very well; and &longs;ince we are at this liberty, let me take leave, before we pa&longs;&longs;e any farther to ask of you Salviatus, whether you did ever con&longs;ider what that line may be that is de&longs;cribed by the grave moveable naturally falling down from the top of a Tower; and if you have reflected on it, be plea&longs;ed to tell me what you think thereof.

SALV. I have &longs;ometimes con&longs;idered of it, and make no que­ &longs;tion, that if one could be certain of the nature of that motion wherewith the grave body de&longs;cendeth to approach the centre of the Terre&longs;trial Globe, mixing it &longs;elf afterwards with the common circular motion of the diurnal conver&longs;ion; it might be exactly found what kind of line that is, that the centre of gravity of the moveable de&longs;cribeth in tho&longs;e two motions.

SAGR. Touching the &longs;imple motion towards the centre de­ pendent on the gravity, I think that one may confidently, with­ out error, believe that it is by a right line, as it would be, were the Earth immoveable.

SALV. As to this particular, we may not onely believe it, but experience rendereth us certain of the &longs;ame.

SAGR. But how doth experience a&longs;&longs;ure us thereof, if we ne­ ver &longs;ee any motions but &longs;uch as are compo&longs;ed of the two, circular and de&longs;cending.

SALV. Nay rather Sagredus we onely &longs;ee the &longs;imple motion of de&longs;cent; &longs;ince that other circular one common to the Earth, the Tower and our &longs;elves remains imperceptible, and as if it never were, and there remaineth perceptible to us that of the &longs;tone, one­ ly not participated by us, and for this, &longs;en&longs;e demon&longs;trateth that it is by a right line, ever parallel to the &longs;aid Tower, which is built upright and perpendicular upon the Terre&longs;trial &longs;urface.

SAGR. You are in the right; and this was but too plainly de­ mon&longs;trated to me even now, &longs;eeing that I could not remember &longs;o ea&longs;ie a thing; but this being &longs;o manife&longs;t, what more is it that you &longs;ay you de&longs;ire, for under&longs;tanding the nature of this motion downwards?

SALV. It &longs;ufficeth not to know that it is &longs;treight, but its requi­ &longs;ite to know whether it be uniform, or irregular; that is, whe­ ther it maintain alwayes one and the &longs;ame velocity, or el&longs;e goeth retarding or accelerating.

SAGR. It is already clear, that it goeth continually accelle­ rating.

SALV. Neither doth this &longs;uffice, but its requi&longs;ite to know ac­ cording to what proportion &longs;uch accelleration is made; a Pro­ blem, that I believe was never hitherto under&longs;tood by any Phi­ lo&longs;opher or Mathematician; although Philo&longs;ophers, and particu­ larly the Peripateticks, have writ great and entire Volumes, touching motion.

SIMP. Philo&longs;ophers principally bu&longs;ie them&longs;elves about univer­ &longs;als; they find the definitions and more common &longs;ymptomes, o­ mitting certain &longs;ubtilties and niceties, which are rather curio­ &longs;ities to the Mathematicians. And Aristotle did content him&longs;elf to de&longs;ine excellently what motion was in general; and of the lo­ cal, to &longs;hew the principal qualities, to wit, that one is natural, another violent; one is &longs;imple, another compound; one is equal, another accellerate; and concerning the accelerate, con­ tents him&longs;elf to give the rea&longs;on of acceleration, remitting the finding out of the proportion of &longs;uch acceleration, and other particular accidents to the Mechanitian, or other inferiour Arti&longs;t.

SAGR. Very well Simplicius. But you Salviatus, when you de&longs;cend &longs;ometimes from the Throne of Peripatetick Maje&longs;ty, have you ever thrown away any of your hours in &longs;tudying to find this proportion of the acceleration of the motion of de&longs;cending grave bodies?

SALV. There was no need that I &longs;hould &longs;tudy for it, in regard that the Academick our common friend, heretofore &longs;hewed me a Treati&longs;e of his ^{*} De Motu, where this, and many other acci­ dents were demon&longs;trated. But it would be too great a digre&longs;&longs;ion, if for this particular, we &longs;hould interrupt our pre&longs;ent di&longs;cour&longs;e, (which yet it &longs;elf is al&longs;o no better than a digre&longs;&longs;ion) and make as the Saying is, a Comedy within a Comedy.

This is that ex­ cellent tract which we give the fir&longs;t place in our &longs;econd Volume.

SAGR. I am content to excu&longs;e you from this narration for the pre&longs;ent, provided that this may be one of the Propo&longs;itions re&longs;er­ ved to be examined among&longs;t the re&longs;t in another particular meeting, for that the knowledg thereof is by me very much de&longs;ired; and in the mean time let us return to the line de&longs;cribed by the grave body in its fall from the top of the Tower to its ba&longs;e.

SALV. If the right motion towards the centre of the Earth was uniforme, the circular towards the Ea&longs;t being al&longs;o uniforme, you would &longs;ee compo&longs;ed of them both a motion by a &longs;piral line, of that kind with tho&longs;e defined by Archimedes in his Book Dc Spira­ libus; which are, when a point moveth uniformly upon a right line, while&longs;t that line in the mean time turneth uniformly about one of its extreme points fixed, as the centre of his gyration. But becau&longs;e the right motion of grave bodies falling, is continu­ ally accelerated, it is nece&longs;&longs;ary, that the line re&longs;ulting of the compo&longs;ition of the two motions do go alwayes receding with greater and greater proportion from the circumference of that cir­ cle, which the centre of the &longs;tones gravity would have de&longs;igned, if it had alwayes &longs;taid upon the Tower; it followeth of nece&longs;&longs;ity that this rece&longs;&longs;ion at the fir&longs;t be but little, yea very &longs;inall, yea, more, as &longs;mall as can be imagined, &longs;eeing that the de&longs;cending grave body departing from re&longs;t, that is, from the privation of motion, towards the bottom and entring into the right motion downwards, it mu&longs;t needs pa&longs;&longs;e through all the degrees of tardi­ ty, that are betwixt re&longs;t, and any a&longs;&longs;igned velocity; the which degrees are infinite; as already hath been at large di&longs;cour&longs;ed and proved.

It being &longs;uppo&longs;ed therefore, that the progre&longs;&longs;e of the accele­ ration being after this manner, and it being moreover true, that the de&longs;cending grave body goeth to terminate in the centre of the Earth, it is nece&longs;&longs;ary that the line of its mixt motion be &longs;uch, that it go continually receding with greater and greater proportion from the top of the Tower, or to &longs;peak more properly, from the circumference of the circle de&longs;cribed by the top of the Tower, by means of the Earths conver&longs;ion; but that &longs;uch rece&longs;&longs;ions be le&longs;&longs;er and le&longs;&longs;er in infinitum; by how much the moveable finds it &longs;elf to be le&longs;&longs;e and le&longs;&longs;e removed from the fir&longs;t term where it re&longs;ted. Moreover it is nece&longs;&longs;ary, that this line of the compound­ ed motion do go to terminate in the centre of the Earth. Now having pre&longs;uppo&longs;ed the&longs;e two things, I come to de&longs;cribe about the centre A [in Fig. 1. of this &longs;econd Dialogue;] with the &longs;emi­ diameter A B, the circle B I, repre&longs;enting to me the Terre&longs;trial Globe, and prolonging the &longs;emidiameter A B to C, I have de­ &longs;cribed the height of the Tower B C; the which being carried about by the Earth along the circumference B I, de&longs;cribeth with its top the arch C D: Dividing, in the next place, the line C A in the middle at E; upon the centre E, at the di&longs;tance E C, I de­ &longs;cribe the &longs;emicircle C I A: In which, I now affirm, that it is very probable that a &longs;tone falling from the top of the Tower C, doth move, with a motion mixt of the circular, which is in common, and of its peculiar right motion. If therefore in the circumference C D, certain equal parts C F, F G, G H, H L, be marked, and from the points F, G, H, L, right lines be drawn towards the centre A, the parts of them intercepted between the two cir­ cumferences C D and B I, &longs;hall repre&longs;ent unto us the &longs;ame Tower C B, tran&longs;ported by the Terre&longs;trial Globe towards D I; in which lines the points where they come to be inter&longs;ected by the arch of the &longs;emicircle C I, are the places by whichfrom time to time the falling &longs;tone doth pa&longs;&longs;e; which points go continually with greater and greater proportion receding from the top of the Tower. And this is the cau&longs;e why the right motion made along the &longs;ide of the Tower appeareth to us more and more accelerate. It appeareth al&longs;o, how by rea&longs;on of the infinite acutene&longs;&longs;e of the contact of tho&longs;e two circles D C, C I, the rece&longs;&longs;ion of the cadent moveable from the circumference C F D; namely, from the top of the Tower, is towards the beginning extream &longs;mall, which is as much as if one &longs;aid its motion downwards is very &longs;low, and more and more &longs;low in infinitum, according to its vicinity to the term C, that is to the &longs;tate of re&longs;t. And la&longs;tly it is &longs;een how in the end this &longs;ame motion goeth to terminate in the centre of the Earth A.

The line de&longs;cri­ bed by a moveable in its natural de­ &longs;cent, the motion of the Earth a­ bout its own centre being pre&longs;uppo&longs;ed, would probably be the circumference of a circle.

SAGR. I under&longs;tand all this very well, nor can I per&longs;wade my &longs;elf that the falling moveable doth de&longs;cribe with the centre of its gravity any other line, but &longs;uch an one as this.

SALV. But &longs;tay a little Sagredus, for I am to acquaint you al&longs;o with three Ob&longs;ervations of mine, that its po&longs;&longs;ible will not di&longs;­ plea&longs;e you. The fir&longs;t of which is, that if we do well con&longs;ider, the moveable moveth not really with any more than onely one motion &longs;imply circular, as when being placed upon the Tower, it moved with one &longs;ingle and circular motion. The &longs;econd is yet more plea­ &longs;ant; for, it moveth neither more nor le&longs;&longs;e then if it had &longs;taid con­ tinually upon the Tower, being that to the arches C F, F G, G H, &c. that it would have pa&longs;&longs;ed continuing alwayes upon the Tower, the arches of the circumference C I are exactly equal, an&longs;wering under the &longs;ame C F, F G, G H, &c. Whence followeth the third wonder, That the true and real motion of the &longs;tone is never acce­ lerated, but alwayes even and uniforme, &longs;ince that all the equal ar­ ches noted in the circumference C D, and their re&longs;pondent ones marked in the circumference C I, are pa&longs;t in equal times; &longs;o that we are left at liberty to &longs;eek new cau&longs;es of acceleration, or of o­ ther motions, &longs;eeing that the moveable, as well &longs;tanding upon the Tower, as de&longs;cending thence, alwayes moveth in the &longs;ame fa&longs;hion, that is, circularly, with the &longs;ame velocity, and with the &longs;ame uni­ formity. Now tell me what you think of this my fanta&longs;tical con­ jecture.

A moveable fal­ ting from the top of the Tower, moveth in the circumfe­ rence of a circle.

It moveth neither more nor le&longs;&longs;e, than if it had &longs;taid al­ wayes there.

It moveth with an uniform, not an accelerate mo­ tion.

SAGR. I mu&longs;t tell you, that I cannot with words &longs;ufficiently expre&longs;&longs;e how admirable it &longs;eemeth to me; and for what at pre­ &longs;ent offereth it &longs;elf to my under&longs;tanding, I cannot think that the bu&longs;ine&longs;s happeneth otherwi&longs;e; and would to God that all the demon&longs;trations of Philo&longs;ophers were but half &longs;o probable as this. However for my perfect &longs;atisfaction I would gladly hear how you prove tho&longs;e arches to be equal.

SALV. The demon&longs;tration is mo&longs;t ea&longs;ie. Suppo&longs;e to your &longs;elf a line drawn from I to E. And the Semidiameter of the circle CD, that is, the line C A, being double the Semidiameter C E of the circle C I, the circumference &longs;hall be double to the circumference, and every arch of the greater circle double to every like arch of the le&longs;&longs;er; and con&longs;equently, the half of the arch of the greater circle, equal to the whole arch of the le&longs;&longs;e. And becau&longs;e the an­ gle C E I made in the centre E of the le&longs;&longs;er circle, and which in&longs;i­ &longs;teth upon the arch C I, is double the angle C A D, made in the centre A of the greater circle, to which the arch C D &longs;ubtendeth; therefore the arch C D is half of the arch of the greater circle like to the arch C I, and therefore the two arches C D and C I are e­ qual; and in the &longs;ame manner we may demon&longs;trate of all their parts. But that the bu&longs;ine&longs;s, as to the motion of de&longs;cending grave bodies, proceedeth exactly thus, I will not at this time affirm; but this I will &longs;ay, that if the line de&longs;cribed by the cadent moveable be not exactly the &longs;ame with this, it doth extream neerly re&longs;emble the &longs;ame.

SAGR. But I, Salviatus, am ju&longs;t now con&longs;idering another par­ ticular very admirable; and this it is; That admitting the&longs;e con­ &longs;iderations, the right motion doth go wholly ^{*} mounting, and that Nature never makes u&longs;e thereof, &longs;ince that, even that that u&longs;e, which was from the beginning granted to it, which was of redu­ cing the parts of integral bodies to their place, when they were &longs;eparated from their whole, and therefore con&longs;tituted in a depra­ ved di&longs;po&longs;ition, is taken from it, and a&longs;&longs;igned to the circular motion.

Right motion &longs;eemeth wholly ex­ cluded in nature.

* Vadia del tutto a monte, rendered in the Latixe omni­ no pe&longs;&longs;um eat.

SALV. This would nece&longs;&longs;arily follow, if it were concluded that the Terre&longs;trial Globe moveth circularly; a thing, which I pretend not to be done, but have onely hitherto attempted, as I &longs;hall &longs;till, to examine the &longs;trength of tho&longs;e rea&longs;ons, which have been alledged by Philo&longs;ophers to prove the immobility of the Earth, of which this fir&longs;t taken from things falling perpendicu­ larly, hath begat the doubts, that have been mentioned; which I know not of what force they may have &longs;eemed to Simplicius; and therefore before I pa&longs;&longs;e to the examination of the remaining arguments, it would be convenient that he produce what he hath to reply to the contrary.

SIMP. As to this fir&longs;t, I confe&longs;&longs;e indeed that I have heard &longs;undry pretty notions, which I never thought upon before, and in regard they are new unto me, I cannot have an&longs;wers &longs;o ready for them, but this argument taken from things falling perpendi­ cularly, I e&longs;teem it not one of the &longs;tronge&longs;t proofs of the mobi­ lity of the Earth; and I know not what may happen touching the &longs;hots of great Guns, e&longs;pecially tho&longs;e aimed contrary to the diur­ nal motion.

SAGR. The flying of the birds as much puzzleth me as the objection of the Gun-&longs;hot, and all the other experiments above alledged. For the&longs;e birds which at their plea&longs;ure flie for­ wards and backwards, and wind to and again in a thou&longs;and fa&longs;hions, and, which more importeth, lie whole hours upon the wing, the&longs;e I &longs;ay do not a little po&longs;e me, nor do I &longs;ee, how a­ mong&longs;t &longs;o many circumgyrations, they &longs;hould not lo&longs;e the motion of the Earth, and how they &longs;hould be able to keep pace with &longs;o great a velocity as that which they &longs;o far exceed with their flight.

SALV. To &longs;peak the truth, your &longs;cruple is not without rea&longs;on, and its po&longs;&longs;ible Copernicus him&longs;elf could not find an an&longs;wer for it, that was to him&longs;elf entirely &longs;atisfactory; and therefore haply pa&longs;t it over in &longs;ilence albeit he was, indeed, very brief in examining the other allegations of his adver&longs;aries, I believe through his height of wit, placed on greater aud &longs;ublimer contemplations, like as Lions are not much moved at the barking of little Dogs. We will therefore re&longs;erve the in&longs;tance of birds to the la&longs;t place, and for the pre&longs;ent, &longs;ee if we can give Simplicius &longs;atisfaction in the others, by &longs;hewing him in our wonted manner, that he him­ &longs;elf hath their an&longs;wers at hand, though upon fir&longs;t thoughts he doth not di&longs;cover them. And to begin with the &longs;hots made at randome, with the &longs;elf &longs;ame piece, powder, and ball, the one towards the Ea&longs;t, the other towards the We&longs;t, let him tell me what it is that per&longs;wades him to think that the Range towards the We&longs;t (if the diurnal con­ ver&longs;ion belonged to the Earth) ought to be much longer than that towards the Ea&longs;t.

The rea&longs;on why a Gun &longs;hould &longs;iem to carry farther to­ wards the We&longs;t than towards the Ea&longs;t.

SIMP. I am moved &longs;o to think; becau&longs;e in the &longs;hot made to­ wards the Ea&longs;t, the ball whil'&longs;t it is out of the piece, is follow­ ed by the &longs;aid piece, the which being carried round by the Earth, runneth al&longs;o with much velocity towards the &longs;ame part, where­ upon the fall of the ball to the ground, cometh to be but little di&longs;tant from the piece. On the contrary in the &longs;hot towards the We&longs;t, before that the ball falleth to the ground, the piece is re­ tired very far towards the Ea&longs;t, by which means the &longs;pace be­ tween the ball and the piece, that is Range, will appear longer than the other, by how much the piece, that is the Earth, had run in the time that both the bals were in the air.

SALV. I could wi&longs;h, that we did know &longs;ome way to make an experiment corre&longs;ponding to the motion of the&longs;e projects, as that of the &longs;hip doth to the motion of things perpendicularly falling from on high; and I am thinking how it may be done.

The experiment of a running cha­ riot to find out the difference of Ran­ ges.

SAGR. I believe, that it would be a very oppo&longs;ite proof, to take an open Chariot, and to accomodate therein a ^{*}Stock-bow at half elevation, to the end the flight may prove the greate&longs;t

that my be, and whil'&longs;t the hor&longs;es &longs;hall run, to &longs;hoot fir&longs;t towards the part whither you drive, and then another backwards towards the contrary part, cau&longs;ing &longs;ome one to mark diligently where the Chariot was in that moment f time when the &longs;haft came to the ground, as well in the one &longs;hot as in the other: for thus you may &longs;ee exactly how much one &longs;haft flew farther than the other.

* Bale&longs;trone da bol­ zoni.

SIMP. In my thoughts this experiment is very proper: and I do not doubt but that the flight, that is, the &longs;pace between the &longs;haft and the place where the chariot was at the &longs;hafts fall, will be le&longs;s by much when one &longs;hooteth towards the chariots cour&longs;e, than when one &longs;hooteth the contrary way. For an example, let the flight of it &longs;elf be three hundred yards, and the cour&longs;e of the cha­ riot in the time whil&longs;t the &longs;haft &longs;tayeth in the air, an hundred yards, therefore &longs;hooting towards the cour&longs;e, of the three hundred yards of the flight, the chariot will have gone one hundred; &longs;o then at the &longs;hafts coming to the ground, the &longs;pace between it and the chariot, &longs;hall be but two hundred yards onely; but on the contrary, in the other &longs;hoot, the chariot running contrary to the &longs;haft, when the &longs;haft &longs;hall have pa&longs;&longs;ed its three hundred yards, and the chariot its other hundred the contrary way, the di&longs;tance inter­ po&longs;ing &longs;hall be found to be four hundred yards.

SALV. Is there any way to &longs;hoot &longs;o that the&longs;e flights may be equal?

SIMP. I know no other way, unle&longs;s by making the chariot to &longs;tand &longs;till.

SALV. This we know; but I mean when the chariot runneth in full carreer.

SIMP. In that ca&longs;e you are to draw the Bow higher in &longs;hoot­ ing forwards, and to &longs;lack it in &longs;hooting the contrary way.

SALV. Then you &longs;ee that there is one way more. But how much is the bow to be drawn, and how much &longs;lackened?

SIMP. In our ca&longs;e, where we have &longs;uppo&longs;ed that the bow car­ ried three hundred yards, it would be requi&longs;ite to draw it &longs;o, as that it might carry four hundred, and in the other to &longs;lacken it &longs;o, as that it might carry no more than two hundred. For &longs;o each of the flights would be but three hundred in relation to the chariot, the which, with its cour&longs;e of an hundred yards which it &longs;ub&longs;tracts from the &longs;hoot of four hundred, and addeth to that of two hun­ dred, would reduce them both to three hundred.

SALV. But what effect hath the greater or le&longs;s inten&longs;ne&longs;s of the bow upon the &longs;haft?

SIMP. The &longs;tiffer bow carrieth it with greater velocity, and the weaker with le&longs;s; and the &longs;ame &longs;haft flieth &longs;o much farther at one time than another, with how much greater velocity it goeth out of the tiller at one time, than another.

SALV. So that to make the &longs;haft &longs;hot either way, to flie at e­ qual di&longs;tance from the running chariot, it is requi&longs;ite, that if in the fir&longs;t &longs;hoot of the precedent example, it goeth out of the tiller with v. g. four degrees of velocity, that then in the other &longs;hoot it de­ part but with two onely: but if the &longs;ame bow be u&longs;ed, it always receiveth thence three degrees.

SIMP. It doth &longs;o; and for this rea&longs;on, &longs;hooting with the &longs;ame bow in the chariots cour&longs;e, the &longs;hoots cannot be equal.

SALV. I had forgot to ask, with what velocity it is &longs;uppo&longs;ed in this particular experiment, that the chariot runneth.

SIMP. The velocity of the chariot mu&longs;t be &longs;uppo&longs;ed to be one degree in compari&longs;on to that of the bow, which is three,

SALV. Very right, for &longs;o computation gives it. But tell me, when the chariot moveth, doth not all things in the &longs;ame move with the &longs;ame velocity?

SIMP. Yes doubtle&longs;s.

SALV. Then &longs;o doth the &longs;haft al&longs;o, and the bow, and the &longs;tring, upon which the &longs;haft is nock't.

SIMP. They do &longs;o.

SALV. Why then, in di&longs;charging the &longs;haft towards the cour&longs;e of the chariot, the bow impre&longs;&longs;eth its three degrees of velocity on a &longs;haft that had one degree of velocity before, by means of the chariot which tran&longs;ported it &longs;o fa&longs;t towards that part; &longs;o that in its going off it hath four degrees of velocity. On the contrary, in the other &longs;hoot, the &longs;ame bow conferreth its &longs;ame three degrees of velocity on a &longs;haft that moveth the contrary way, with one de­ gree; &longs;o that in its departing from the bow-&longs;tring, it hath no more left but onely two degrees of velocity. But you your &longs;elf have already &longs;aid, that the way to make the &longs;hoots equal, is to cau&longs;e that the &longs;haft be let flie the fir&longs;t time with four degrees of velocity, and the &longs;econd time with two. Therefore without changing the bow, the very cour&longs;e of the chariot is that which adju&longs;teth the flights, and the experiment doth &longs;o repre&longs;ent them to any one who is not either wilfully or naturally incapable of rea&longs;on. Now apply this di&longs;cour&longs;e to Gunnery, and you &longs;hall find, that whether the Earth move or &longs;tand &longs;till, the &longs;hots made with the &longs;ame force, will always curry equal ranges, to what part &longs;oever aimed. The error of Ari&longs;totle, Ptolomey, Iycho, your &longs;elf, and all the re&longs;t, is ground­ ed upon that fixed and &longs;trong per&longs;ua&longs;ion, that the Earth &longs;tandeth &longs;till, which you have not judgment nor power to depo&longs;e, no not when you have a de&longs;ire to argue of that which would en&longs;ue, pre­ &longs;uppo&longs;ing the Earth to move. And thus, in the other argument, not con&longs;idering that whil'&longs;t the &longs;tone is upon the Tower, it doth, as to moving or not moving, the &longs;ame that the Terre&longs;trial Globe doth, becau&longs;e you have concluded with your &longs;elf, that the Earth &longs;tands &longs;till, you always di&longs;cour&longs;e touching the fall of the &longs;tone, as if it were to depart from re&longs;t: whereas it behooveth to &longs;ay, that if the Earth &longs;tandeth &longs;till, the &longs;tone departeth from re&longs;t, and de­ &longs;cendeth perpendicularly; but if the Earth do move, the &longs;tone likewi&longs;e moveth with like velocity, nor doth it depart from re&longs;t, but from a motion equal to that of the Earth, wherewith it inter­ mixeth the &longs;upervenient motion of de&longs;cent, and of tho&longs;e two com­ po&longs;eth a third which is tran&longs;ver&longs;al or &longs;ide-ways.

The &longs;olution of the argument ta­ ken from great­ Guns &longs;hot towards the East & We&longs;t.

SIMP. But for Gods &longs;ake, if it move tran&longs;ver&longs;ly, how is it that I behold it to move directly and perpendicularly? This is no bet­ ter than the denial of manife&longs;t &longs;en&longs;e; and if we may not believe &longs;en&longs;e, at what other door &longs;hall we enter into di&longs;qui&longs;itions of Philo­ &longs;ophy?

SALV. In re&longs;pect to the Earth, to the Tower, and to our &longs;elves, which all as one piece move with the diurnal motion together with the &longs;tone, the diurnal motion is as if it never had been, and becom­ eth in&longs;en&longs;ible, imperceptible, and without any action at all; and the onely motion which we can perceive, is that of which we par­ take not, that is the de&longs;cent gliding along the &longs;ide of the Tower: You are not the fir&longs;t that hath felt great repugnance in apprehen­ ding this non-operating of motion upon things to which it is com­ mon.

SAGR. Now I do remember a certain conceipt, that came one day into my fancy, whil&longs;t I &longs;ailed in my voyage to Aleppo, whither I went Con&longs;ul for our Countrey, and po&longs;&longs;ibly it may be of &longs;ome u&longs;e, for explaining this nullity of operation of common motion, and being as if it never were to all the partakers thereof. And if it &longs;tand with the good liking of Simplicius, I will rea&longs;on with him upon that which then I thought of by my &longs;elf alone.

A notable ca&longs;e of Sagredus, to &longs;hew the non-operating of common motion.

SIMP. The novelty of the things which I hear, makes me not &longs;o much a patient, as a greedy and curious auditor: therefore go on.

SAGR. If the neb of a writing pen, that I carried along with me in the &longs;hip, through all my navigation from Venice to ^{*} Scan- deron, had had a facultie of leaving vi&longs;ible marks of its whole voy­ age, what &longs;igns, what marks, what lines would it have left?

* Ale&longs;&longs;andretta.

SIMP. It would have left a line di&longs;tended from Venice thither, not perfectly &longs;treight, or to &longs;ay better, di&longs;tended in a perfect arch of a circle, but in &longs;ome places more, in &longs;ome le&longs;s curved, according as the ve&longs;&longs;el had gone more or le&longs;s fluctuating; but this its infle­ cting in &longs;ome places a fathom or two to the right hand or to the left, upwards or downwards, in a length of many hundred miles, would have brought but little alteration to the intire tract of the line, &longs;o that it would have been hardly &longs;en&longs;ible; and without any con&longs;iderable error, might have been called the part of a perfect arch.

SAGR. So that the true and mo&longs;t exact motion of the neb of my pen would have al&longs;o been an arch of a perfect circle, if the ve&longs;&longs;els motion, the fluctuation of the billows cea&longs;ing, had been calm and tranquill. And if I had continually held that pen in my hand, and had onely moved it &longs;ometimes an inch or two this way or that way, what alteration &longs;hould I have made in that its principal, and very long tract or &longs;troke?

SIMP. Le&longs;s than that which the declining in &longs;everal places from ab&longs;olute rectitude, but the quantity of a flea's eye makes in a right line of a thou&longs;and yards long.

SAGR. If a Painter, then, at our launching from the Port, had began to de&longs;ign upon a paper with that pen, and continued his work till he came to Scanderon, he would have been able to have taken by its motion a perfect draught of all tho&longs;e figures perfectly interwoven and &longs;hadowed on &longs;everal &longs;ides with countreys, build­ ings, living creatures, and other things; albeit all the true, real, and e&longs;&longs;ential motion traced out by the neb of that pen, would have been no other than a very long, but &longs;imple line: and as to the proper operation of the Painter, he would have delineated the &longs;ame to an hair, if the &longs;hip had &longs;tood &longs;till. That therefore of the huge long motion of the pen there doth remain no other marks, than tho&longs;e tracks drawn upon the paper, the rea&longs;on thereof is be­ cau&longs;e the grand motion from Venice to Scanderon, was common to the paper, the pen, and all that which was in the &longs;hip: but the petty motions forwards and backwards, to the right, to the left, com­ municated by the fingers of the Painter unto the pen, and not to the paper, as being peculiar thereunto, might leave marks of it &longs;elf upon the paper, which did not move with that motion. Thus it is likewi&longs;e true, that the Earth moving, the motion of the &longs;tone in de&longs;cending downwards, was really a long tract of many hundreds and thou&longs;ands of yards, and if it could have been able to have de­ lineated in a calm air, or other &longs;uperficies, the track of its cour&longs;e, it would have left behind an huge long tran&longs;ver&longs;e line. But that part of all this motion which is common to the &longs;tone, the Tower, and our &longs;elves, is imperceptible to us, and as if it had never been, and that part onely remaineth ob&longs;ervable, of which neither the Tower nor we are partakers, which is in fine, that wherewith the &longs;tone falling mea&longs;ureth the Tower.

SALV. A mo&longs;t witty conceipt to clear up this point, which was not a little difficult to many capacities. Now if Simplicius will make no farther reply, we may pa&longs;s to the other experiments, the unfolding of which will receive no &longs;mall facility from the things already declared.

SIMP. I have nothing more to &longs;ay: and I was well-nigh tran&longs;­ ported with that delineation, and with thinking how tho&longs;e &longs;trokes drawn &longs;o many ways, hither, thither, upwards, downwards, for­ wards, backwards, and interwoven with thou&longs;ands of turnings, are not e&longs;&longs;entially or really other, than &longs;mall pieces of one &longs;ole line drawn all one way, and the &longs;ame without any other alteration &longs;ave the declining the direct rectitude, &longs;ometimes a very in&longs;en&longs;ible mat­ ter towards one &longs;ide or another, and the pens moving its neb one while &longs;ofter, another while &longs;lower, but with very &longs;mall inequality. And I think that it would in the &longs;ame manner write a letter, and that tho&longs;e frollike penmen, who to &longs;hew their command of hand, without taking their pen from the paper in one &longs;ole &longs;troke, with infinite turnings draw a plea&longs;ant knot, if they were in a boat that did tide it along &longs;wiftly they would convert the whole motion of the pen, which in reality is but one &longs;ole line, drawn all towards one and the &longs;ame part, and very little curved, or declining from perfect rectitude, into a knot or flouri&longs;h. And I am much plea&longs;ed that S agredus hath helped me to this conceit: therefore let us go on, for the hope of meeting with more of them, will make me the &longs;tricter in my attention.

SAGR. If you have a curio&longs;ity to hear &longs;uch like &longs;ubtilties, which occurr not thus to every one, you will find no want of them, e&longs;pe­ cially in this particular of Navigation; and do you not think that a witty conceit which I met with likewi&longs;e in the &longs;ame voyage, when I ob&longs;erved that the ma&longs;t of the &longs;hip, without either breaking or bend­ ing, had made a greater voyage with its round-top, that is with its top-gallant, than with its foot; for the round top being more di&longs;tant from the centre of the Earth than the foot is, it had de&longs;cribed the arch of a circle bigger than the circle by which the foot had pa&longs;&longs;ed.

Subtilties &longs;uffici­ ently in&longs;ipid, ironi­ cally, &longs;poken and taken from a cer­ tain Encyclopædia.

SIMP. And thus when a man walketh he goeth farther with his head than with his feet.

SAGR. You have found out the matter your &longs;elf by help of your own mother-wit: But let us not interrupt Salviatus.

SALV. It plea&longs;eth me to &longs;ee Simplicius how he &longs;ootheth up him&longs;elf in this conceit, if happly it be his own, and that he hath not borrowed it from a certain little pamphlet of conclu&longs;ions, where there are a great many more &longs;uch fancies no le&longs;s plea&longs;ant & witty. It followeth that we &longs;peak of the peice of Ordinance mounted per­ pendicular to the Horizon, that is, of a &longs;hot towards our vertical point, and to conclude, of the return of the ball by the &longs;ame line unto the &longs;ame peice, though that in the long time which it is &longs;e­ parated from the peice, the earth hath tran&longs;ported it many miles towards the Ea&longs;t; now it &longs;eemeth, that the ball ought to fall a like di&longs;tance from the peice towards the We&longs;t; the which doth not happen: therefore the peice without having been moved did &longs;tay expecting the &longs;ame. The an&longs;wer is the &longs;ame with that of the &longs;tone falling from the Tower; and all the fallacy, and equivocati­ on con&longs;i&longs;teth in &longs;uppo&longs;ing &longs;till for true, that which is in que&longs;tion; for the Opponent hath it &longs;till fixed in his conceit that the ball departs from its re&longs;t, being di&longs;charged by the fire from the piece; and the departing from the &longs;tate of re&longs;t, cannot be, unle&longs;&longs;e the immobility of the Terre&longs;trial Globe be pre&longs;uppo­ &longs;ed, which is the conclu&longs;ion of that was in di&longs;pute; Therefore, I reply, that tho&longs;e who make the Earth moveable, an&longs;wer, that the piece, and the ball that is in it, partake of the &longs;ame motion with the Earth; nay that they have this together with her from nature; and that therefore the ball departs in no other manner from its quie&longs;cence, but conjoyned with its motion about the cen­ tre, the which by its projection upwards, is neither taken away, nor hindered; and in this manner following, the univer&longs;al motion of the Earth towards the Ea&longs;t, it alwayes keepeth perpendicular over the &longs;aid piece, as well in its ri&longs;e as in its return. And the &longs;ame you &longs;ee to en&longs;ue, in making the experiment in a &longs;hip with a bullet &longs;hot upwards perpendicularly with a Cro&longs;&longs;e-bow, which returneth to the &longs;ame place whether the &longs;hip doth move, or &longs;tand &longs;till.

An in&longs;tance a­ gainst the diurnal motion of the earth, taken from the &longs;hot of a Peece of Ordi­ nance perpendicu­ larly.

The an&longs;wer to the objection, &longs;hewing the equivoke.

Another an&longs;wer to the &longs;ame objecti­ on.

SAGR. This &longs;atisfieth very well to all; but becau&longs;e that I have &longs;een that Simplicius taketh plea&longs;ure with certain &longs;ubtilties to puzzle his companions, I will demand of him whether, &longs;uppo­ &longs;ing for this time that the Earth &longs;tandeth &longs;till, and the piece ere­ cted upon it perpendicularly, directed to our Zenith, he do at all que&longs;tion that to be the true perpendicular &longs;hot, and that the ball in departing, and in its return is to go by the &longs;ame right line, &longs;till &longs;uppo&longs;ing all external and accidental impediments to be re­ moved?

SIMP. I under&longs;tand that the matter ought to &longs;ucceed exactly in that manner.

SAGR. But if the piece were placed, not perpendicularly, but inclining towards &longs;ome place, what would the motion of the ball be? Would it go haply, as in the other &longs;hot, by the perpendi­ cular line, and return again by the &longs;ame?

SIMP. It would not &longs;o do; but i&longs;&longs;uing out of the piece, it would pur&longs;ue its motion by a right line which prolongeth the e­ rect perpendicularity of the concave cylinder of the piece, unle&longs;&longs;e &longs;o far as its own weight would make it decline from that erection towards the Earth.

SAGR. So that the mounture of the cylinder is the regulator of the motion of the ball, nor doth it, or would it move out of that line, if its own gravity did not make it decline downwards. And

therefore placing the cylinder perpendicularly, and &longs;hooting the ball upwards, it returneth by the &longs;ame right line downwards; be­ cau&longs;e the motion of the ball dependent on its gravity is down­ ward, by the &longs;ame perpendicular. The journey therefore of the ball out of the piece, continueth or prolongeth the rectitude or perpendicularity of that &longs;mall part of the &longs;aid journey, which it made within the &longs;aid piece; is it not &longs;o?

Projects conti­ nue their motion by the right line that followeth the direction of the motion, made to­ gether with the projicient, whil'&longs;t they were conjoin'd therewith.

SIMP. So it is, in my opinion.

SAGR. Now imagine the cylinder to be erected, and that the Earth doth revolve about with a diurnal motion, carrying the piece along with it, tell me what &longs;hall be the motion of the ball within the cylinder, having given fire?

SIMP. It &longs;hall be a &longs;treight and perpendicular motion, the cylin­ der being erected perpendicularly.

SAGR. Con&longs;ider well what you &longs;ay: for I believe that it will not be perpendicular. It would indeed be perpendicular, if the Earth &longs;tood &longs;till, for &longs;o the ball would have no other motion but that proceeding from the fire. But in ca&longs;e the Earth turns round, the ball that is in the piece, hath likewi&longs;e a diurnal motion, &longs;o that there being added to the &longs;ame the impul&longs;e of the fire, it mo­ veth from the breech of the piece to the muzzle with two motions, from the compo&longs;ition whereof it cometh to pa&longs;&longs;e that the motion made by the centre of the balls gravity is an inclining line. And for your clearer under&longs;tanding the &longs;ame, let the piece A C [in Fig. 2.] be erected, and in it the ball B; it is manife&longs;t, that the piece &longs;tanding immoveable, and fire being given to it, the ball will make its way out by the mouth A, and with its centre, pa&longs;­ &longs;ing thorow the the piece, &longs;hall have de&longs;cribed the perpendicular line B A, and it &longs;hall pur&longs;ue that rectitude when it is out of the piece, moving toward the Zenith. But in ca&longs;e the Earth &longs;hould move round, and con&longs;equently carry the piece along with it, in the time that the ball driven out of the piece &longs;hall move along the cylinder, the piece being carried by the Earth, &longs;hall pa&longs;&longs;e in­ to the &longs;ituation D E, and the ball B, in going off, would be at the corni&longs;h D, and the motion of the bals centre, would have been according to the line B D, no longer perpendicular, but in­ clining towards the Ea&longs;t; and the ball (as hath been concluded) being to continue its motion through the air, according to the direction of the motion made in the piece, the &longs;aid motion &longs;hall continue on according to the inclination of the line B D, and &longs;o &longs;hall no longer be perpendicular, but inclined towards the Ea&longs;t, to which part the piece doth al&longs;o move; whereupon the ball may follow the motion of the Eerth, and of the piece. Now Simplicius, you &longs;ee it demon&longs;trated, that the Range which you took to be perpendicular, is not &longs;o.

The revolution of the Earth &longs;up­ po&longs;ed, the ball in the piece erected perpendicularly, doth not move by a perpendicular, but an inclined line.

SIMP. I do not very well under&longs;tand this bu&longs;ine&longs;s; do you, Salviatus?

SALV. I apprehend it in part; but I have a certain kind of &longs;cruple, which I wi&longs;h I knew how to expre&longs;s. It &longs;eems to me, that according to what hath been &longs;aid, if the Piece be erected perpen­ dicular, and the Earth do move, the ball would not be to fall, as Ari&longs;totle and Tycho will have it, far from the Piece towards the We&longs;t, nor as you would have it, upon the Piece, but rather far di&longs;tant towards the Ea&longs;t. For according to your explanation, it would have two motions, the which would with one con&longs;ent carry it thitherward, to wit, the common motion of the Earth, which carrieth the Piece and the ball from C A towards E D; and the fire which carrieth it by the inclined line B D, both motions to­ wards the Ea&longs;t, and therefore they are &longs;uperiour to the motion of the Earth.

SAGR. Not &longs;o, Sir. The motion which carrieth the ball to­ wards the Ea&longs;t, cometh all from the Earth, and the fire hath no part at all therein: the motion which mounteth the ball upwards, is wholly of fire, wherewith the Earth hath nothing to do. And that it is &longs;o, if you give not fire, the ball will never go out of the Piece, nor yet ri&longs;e upwards a hairs breadth; as al&longs;o if you make the Earth immoveable, and give fire, the ball without any incli­ nation &longs;hall go perpendicularly upwards. The ball therefore ha­ ving two motions, one upwards, and the other in gyration, of both which the tran&longs;ver&longs;e line B D is compounded, the impul&longs;e upward is wholly of fire, the circular cometh wholly from the Earth, and is equal to the Earths motion: and being equal to it, the ball maintaineth it &longs;elf all the way directly over the mouth of the Piece, and at la&longs;t falleth back into the &longs;ame: and becau&longs;e it al­ ways ob&longs;erveth the erection of the Piece, it appeareth al&longs;o conti­ nually over the head of him that is near the Piece, and therefore it appeareth to mount exactly perpendicular towards our Zenith, or vertical point.

SIMP. I have yet one doubt more remaining, and it is, that in regard the motion of the ball is very &longs;wift in the Piece, it &longs;eems not po&longs;&longs;ible, that in that moment of time the tran&longs;po&longs;ition of the Piece from C A to A D &longs;hould confer &longs;uch an inclination upon the tran&longs;ver&longs;e line C D, that by means thereof, the ball when it cometh afterwards into the air &longs;hould be able to follow the cour&longs;e of the Earth.

SAGR. You err upon many accounts; and fir&longs;t, the inclination of the tran&longs;ver&longs;e line C D, I believe it is much greater than you take it to be, for I verily think that the velocity of the Earths mo­ tion, not onely under the Equinoctial, but in our paralel al&longs;o, is greater than that of the ball whil&longs;t it moveth in the Piece; &longs;o that the interval C E would be ab&longs;olutely much bigger than the whole length of the Piece, and the inclination of the tran&longs;ver&longs;e line con­ &longs;equently bigger than half a right angle: but be the velocity of the Earth more, or be it le&longs;s, in compari&longs;on of the velocity of the fire, this imports nothing; for if the velocity of the Earth be &longs;mall, and con&longs;equently the inclination of the tran&longs;ver&longs;e line be little al&longs;o; there is then al&longs;o need but of little inclination to make the ball &longs;u&longs;pend it &longs;elf in its range directly over the Piece. And in a word, if you do but attentively con&longs;ider, you will comprehend, that the motion of the Earth in transferring the Piece along with it from C A to E D, conferreth upon the tran&longs;ver&longs;e line C D, &longs;o much of little or great inclination, as is required to adju&longs;t the range to its perpendicularity. But you err, &longs;econdly, in that you referr the faculty of carrying the ball along with the Earth to the impul&longs;e of the fire, and you run into the &longs;ame error, into which Salviatus, but even now &longs;eemed to have fallen; for the faculty of following the motion of the Earth, is the primary and perpetual motion, indelibly and in&longs;eparably imparted to the &longs;aid ball, as to a thing terre&longs;trial, and that of its own nature doth and ever &longs;hall po&longs;&longs;e&longs;s the &longs;ame.

SALV. Let us yield, Simplicius, for the bu&longs;ine&longs;s is ju&longs;t as he &longs;aith. And now from this di&longs;cour&longs;e let us come to under&longs;tand the rea&longs;on of a Venatorian Problem, of tho&longs;e Fowlers who with their guns &longs;hoot a bird flying; and becau&longs;e I did imagine, that in regard the bird flieth a great pace, therefore they &longs;hould aim their &longs;hot far from the bird, anticipating its flight for a certain &longs;pace, and more or le&longs;s according to its velocity and the di&longs;tance of the bird, that &longs;o the bullet ha&longs;ting directly to the mark aimed at, it might come to arrive at the &longs;elf &longs;ame time in the &longs;ame point with its motion, and the bird with its flight, and by that means one to encounter the other: and asking one of them, if their practi&longs;e was not &longs;o to do; He told me, no; but that the &longs;light was very ea&longs;ie and certain, and that they took aim ju&longs;t in the &longs;ame manner as if they had &longs;hot at a bird that did &longs;it &longs;till; that is, they made the flying bird their mark, and by moving their fowling-piece they followed her, keeping their aim &longs;till full upon her, till &longs;uch time as they let fly, and in this manner &longs;hot her as they did others &longs;itting &longs;till. It is nece&longs;&longs;ary therefore that that motion, though &longs;low, which the fowl­ ing-piece maketh in turning and following after the flight of the bird do communicate it &longs;elf to the bullet al&longs;o, and that it be joyned with that of the fire; &longs;o that the ball hath from the fire the mo­ tion directly upwards, and from the concave Cylinder of the barrel the declination according to the flight of the Bird, ju&longs;t as was &longs;aid before of the &longs;hot of a Canon; where the ball receiveth from the fire a virtue of mounting upwards towards the Zenith, and from the motion of the Earth its winding towards the Ea&longs;t, and of both maketh a compound motion that followeth the cour&longs;e of the Earth, and that to the beholder &longs;eemeth onely to go directly up­ wards, and return again downwards by the &longs;ame line. The hold­ ing therefore of the gun continually directed towards the mark, maketh the &longs;hoot hit right, and that you may keep your gun di­ rected to the mark, in ca&longs;e the mark &longs;tands &longs;till, you mu&longs;t al&longs;o hold your gun &longs;till; and if the mark &longs;hall move, the gun mu&longs;t be kept upon the mark by moving. And upon this dependeth the proper an&longs;wer to the other argument taken from the &longs;hot of a Canon, at the mark placed towards the South or North: wherein is alledged, that if the Earth &longs;hould move, the &longs;hots would all range We&longs;t­ ward of the mark, becau&longs;e that in the time whil&longs;t the ball, being forc'd out of the Piece, goeth through the air to the mark, the &longs;aid mark being carried toward the Ea&longs;t, would leave the ball to the We&longs;tward. I an&longs;wer therefore, demanding whether if the Ca­ non be aimed true at the mark, and permitted &longs;o to continue, it will con&longs;tantly hit the &longs;aid mark, whether the Earth move or &longs;tand &longs;till? It mu&longs;t be replied, that the aim altereth not at all, for if the mark doth &longs;tand &longs;till, the Piece al&longs;o doth &longs;tand &longs;till, and if it, being tran&longs;ported by the Earths motion, doth move, the Piece doth al&longs;o move at the &longs;ame rate, and, the aim maintained, the &longs;hot proveth always true, as by what hath been &longs;aid above, is mani­ fe&longs;t.

The manner how Fowlers &longs;hoot birds flying.

The an&longs;wer to the objection tak n from the &longs;hots of great Guns made towards the North and South.

SAGR. Stay a little, I entreat you, Salviatus, till I have pro­ pounded a certain conceit touching the&longs;e &longs;hooters of birds flying, who&longs;e proceeding I believe to be the &longs;ame which you relate, and believe the effect of hitting the bird doth likewi&longs;e follow: but yet I cannot think that act altogether conformable to this of &longs;hooting in great Guns, which ought to hit as well when the piece and mark moveth, as when they both &longs;tand &longs;till; and the&longs;e, in my opinion, are the particulars in which they di&longs;agree. In &longs;hooting with a great Gun both it and the mark move with equal velocity, being both tran&longs;ported by the motion of the Terre&longs;trial Globe: and al­ beit &longs;ometimes the piece being planted more towards the Pole, than the mark, and con&longs;equently its motion being &longs;omewhat flow­ er than the motion of the mark, as being made in a le&longs;&longs;er circle, &longs;uch a difference is in&longs;en&longs;ible, at that little di&longs;tance of the piece from the mark: but in the &longs;hot of the Fowler the motion of the Fowling-piece wherewith it goeth following the bird, is very &longs;low in compari&longs;on of the flight of the &longs;aid bird; whence me thinks it &longs;hould follow, that that &longs;mall motion which the turning of the Birding-piece conferreth on the bullet that is within it, cannot, when it is once gone forth of it, multiply it &longs;elf in the air, untill it come to equal the velocity of the birds flight, &longs;o as that the &longs;aid bullet &longs;hould always keep direct upon it: nay, me thinketh the bird would anticipate it and leave it behind. Let me add, that in this act, the air through which the bullet is to pa&longs;s, partaketh not of the motion of the bird: whereas in the ca&longs;e of the Canon, both it, the mark, and the intermediate air, do equally partake of the com­ mon diurnal motion. So that the true cau&longs;e of the Marks-man his hitting the mark, as it &longs;hould &longs;eem, moreover and be&longs;ides the following the birds flight with the piece, is his &longs;omewhat anticipa­ ting it, taking his aim before it; as al&longs;o his &longs;hooting (as I believe) not with one bullet, but with many &longs;mall balls (called &longs;hot) the which &longs;cattering in the air po&longs;&longs;e&longs;s a great &longs;pace; and al&longs;o the ex­ treme velocity wherewith the&longs;e &longs;hot, being di&longs;charged from the Gun, go towards the bird.

SALV. See how far the winged wit of Sagredus anticipateth, and out-goeth the dulne&longs;s of mine; which perhaps would have light upon the&longs;e di&longs;parities, but not without long &longs;tudie. Now turning to the matter in hand, there do remain to be con&longs;idered by us the &longs;hots at point blank, towards the Ea&longs;t and towards the We&longs;t; the fir&longs;t of which, if the Earth did move, would always happen to be too high above the mark, and the &longs;econd too low; fora&longs;much as the parts of the Earth Ea&longs;tward, by rea&longs;on of the di­ urnal motion, do continually de&longs;cend beneath the tangent paralel to the Horizon, whereupon the Ea&longs;tern &longs;tars to us appear to a&longs;cend; and on the contrary, the parts We&longs;tward do more and more a&longs;­ cend, whereupon the We&longs;tern &longs;tars do in our &longs;eeming de&longs;cend: and therefore the ranges which are leveled according to the &longs;aid tangent at the Oriental mark, (which whil&longs;t the ball pa&longs;&longs;eth along by the tangent de&longs;cendeth) &longs;hould prove too high, and the Occidental too low by means of the elevation of the mark, whil&longs;t the ball pa&longs;&longs;eth along the tangent. The an&longs;wer is like to the re&longs;t: for as the Ea&longs;tern mark goeth continually de&longs;cending, by rea&longs;on of the Earths motion, under a tangent that continueth immove­ able; &longs;o likewi&longs;e the piece for the &longs;ame rea&longs;on goeth continually inclining, and with its mounture pur&longs;uing the &longs;aid mark: by which means the &longs;hot proveth true.

The an&longs;wer to the Argument taken from the &longs;hots at point blanck to­ wards the Ea&longs;t & We&longs;t.

But here I think it a convenient opportunity to give notice of certain conce&longs;&longs;ions, which are granted perhaps over liberally by the followers of Copernicus unto their Adver&longs;aries: I mean of yielding to them certain experiments for &longs;ure and certain, which yet the Adver&longs;aries them&longs;elves had never made tryal of: as for example, that of things falling from the round-top of a &longs;hip whil&longs;t it is in motion, and many others; among&longs;t which I verily believe, that this of experimenting whether the &longs;hot made by a Canon to­ wards the Ea&longs;t proveth too high, and the We&longs;tern &longs;hot too low, is one: and becau&longs;e I believe that they have never made tryal thereof, I de&longs;ire that they would tell me what difference they think ought to happen between the &longs;aid &longs;hots, &longs;uppo&longs;ing the Earth moveable, or &longs;uppo&longs;ing it moveable; and let Simplieius for this time an&longs;wer for them.

The followers of Copernicus too freely admit cer­ tain propo&longs;itions for true, which are very doubtfull.

SIMP. I will not undertake to an&longs;wer &longs;o confidently as another more intelligent perhaps might do; but &longs;hall &longs;peak what thus upon the &longs;udden I think they would reply; which is in effect the &longs;ame with that which hath been &longs;aid already, namely, that in ca&longs;e the Earth &longs;hould move, the &longs;hots made Ea&longs;tward would prove too high, &c. the ball, as it is probable, being to move along the tan­ gent.

SALV. But if I &longs;hould &longs;ay, that &longs;o it falleth out upon triall, how would you cen&longs;ure me?

SIMP. It is nece&longs;&longs;ary to proceed to experiments for the pro­ ving of it.

SALV. But do you think, that there is to be found a Gunner &longs;o skilful, as to hit the mark at every &longs;hoot, in a di&longs;tance of v.g. five hundred paces?

SIMP. No Sir; nay I believe that there is no one, how good a marks-man &longs;oever that would promi&longs;e to come within a pace of the mark,

SALV. How can we then, with &longs;hots &longs;o uncertain, a&longs;&longs;ure our &longs;elves of that which is in di&longs;pute?

SIMP. We may be a&longs;&longs;ured thereof two wayes; one, by ma­ king many &longs;hots; the other, becau&longs;e in re&longs;pect of the great velo­ city of the Earths motion, the deviation from the mark would in my opinion be very great.

SALV. Very great, that is more than one pace; in regard that the varying &longs;o much, yea and more, is granted to happen ordinarily even in the Earths mobility.

SIMP. I verily believe the variation from the mark would be more than &longs;o.

A Computation how much the ran­ ges of great &longs;hot ought to vary from the marke, the Earths motion be­ ing granted.

SALV. Now I de&longs;ire that for our &longs;atisfaction we do make thus in gro&longs;&longs;e a &longs;light calculation, if you con&longs;ent thereto, which will &longs;tand us in &longs;tead likewi&longs;e (if the computation &longs;ucceed as I expect) for a warning how we do in other occurrences &longs;uffer our &longs;elves, as the &longs;aying is, to be taken with the enemies &longs;houts, and &longs;urrender up our belief to what ever fir&longs;t pre&longs;ents it &longs;elf to our fancy. And now to give all advantages to the Peripateticks and Tychonicks, let us &longs;uppo&longs;e our &longs;elves to be under the Equinoctial, there to &longs;hoot a piece of Ordinance point blank Ea&longs;twards at a mark five hun­ dred paces off. Fir&longs;t, let us &longs;ee thus (as I &longs;aid) in a level, what time the &longs;hot after it is gone out of the Piece taketh to arrive at the mark; which we know to be very little, and is certainly no more than that wherein a travailer walketh two &longs;teps, which al&longs;o is le&longs;s than the &longs;econd of a minute of an hour; for &longs;uppo&longs;ing that the travailer walketh three miles in an hour, which are nine thou&longs;and paces, being that an hour containes three thou&longs;and, &longs;ix hundred &longs;econd minutes, the travailer walketh two &longs;teps and an half in a &longs;econd, a &longs;econd therefore is more than the time of the balls motion. And for that the diurnal revolution is twenty four hours, the We&longs;tern horizon ri&longs;eth fifteen degrees in an hour, that is, fifteen fir&longs;t minutes of a degree, in one fir&longs;t minute of an hour; that is, fifteen &longs;econds of a degree, in one &longs;econd of an hour; and becau&longs;e one &longs;econd is the time of the &longs;hot, therefore in this time the We&longs;tern horizon ri&longs;eth fifteen &longs;econds of a degree, and &longs;o much likewi&longs;e the mark; and therefore fifteen &longs;econds of that cir­ cle, who&longs;e &longs;emidiameter is five hundred paces (for &longs;o much the di­ &longs;tance of the mark from the Piece was &longs;uppo&longs;ed.) Now let us look in the table of Arches and Chords (&longs;ee here is Copernicus his book) what part is the chord of fifteen &longs;econds of the &longs;emidiame­ ter, that is, five hundred paces. Here you &longs;ee the chord (or &longs;ub­ ten&longs;e) of a fir&longs;t minute to be le&longs;s than thirty of tho&longs;e parts, of which the &longs;emidiameter is an hundred thou&longs;and. Therefore the chord of a &longs;econd minute &longs;hall be le&longs;s then half of one of tho&longs;e parts, that is le&longs;s than one of tho&longs;e parts, of whichthe &longs;emidiame­ ter is two hundred thou&longs;and; and therefore the chord of fifteen conds &longs;hall be le&longs;s than fifteen of tho&longs;e &longs;ame two hundred thou&longs;and parts; but that which is le&longs;s than (a) fifteen parts of two hun­

dred thou&longs;and, is al&longs;o more than that which is four cente&longs;mes of five hundred; therefore the a&longs;cent of the mark in the time of the balls motion is le&longs;&longs;e than four cente&longs;mes, that is, than one twenty fifth part of a pace; it &longs;hall be therefore (b) about two inches: And &longs;o much con&longs;equently &longs;hall be the variation of each We&longs;tern &longs;hot, the Earth being &longs;uppo&longs;ed to have a diurnal motion. Now if I &longs;hall tell you, that this variation (I mean of falling two inches &longs;hort of what they would do in ca&longs;e the Earth did not move) upon tri­ all doth happen in all &longs;hots, how will you convince me Simplicius, &longs;hewing me by an experiment that it is not &longs;o? Do you not &longs;ee that it is impo&longs;&longs;ible to confute me, unle&longs;s you fir&longs;t find out a way to &longs;hoot at a mark with &longs;o much exactne&longs;&longs;e, as never to mi&longs;&longs;e an hairs bredth? For whil&longs;t the ranges of great &longs;hot con&longs;i&longs;t of diffe­ rent numbers of paces, as de facto they do, I will affirm that in each of tho&longs;e variations there is contained that of two inches cau­ &longs;ed by the motion of the Earth.

(a) That is, in plainer termes the fraction 15/200000, is more than the fra­ ction 4/50000, for di­ viding the denomi­ nators by their no­ minators, and the fir&longs;t produceth 13333 1/3 the other but 12500.

(b) It &longs;hall be neer 2 2/5 inches, ac­ counting the pace to be Geometrical, containing 5 foot.

SAGR. Pardon me, Salviatus, you are too liberal. For I would tell the Peripateticks, that though every &longs;hot &longs;hould hit the very centre of the mark, that &longs;hould not in the lea&longs;t di&longs;prove the motion of the Earth. For the Gunners are &longs;o con&longs;tantly imployed in le­ velling the &longs;ight and gun to the mark, as that they can hit the &longs;ame, notwith&longs;tanding the motion of the Earth. And I &longs;ay, that if the Earth &longs;hould &longs;tand &longs;till, the &longs;hots would not prove true; but the Occidental would be too low, and the Oriental too high: now let Simplicius di&longs;prove me if he can.

It is demon&longs;tra­ ted with great &longs;ub­ tilty, that the Earths motion &longs;up­ po&longs;ed, Canon &longs;hot ought not to vary more than in re&longs;t.

SALV. This is a &longs;ubtilty worthy of Sagredus: But whether this variation be to be ob&longs;erved in the motion, or in the re&longs;t of the Earth, it mu&longs;t needs be very &longs;mall, it mu&longs;t needs be &longs;wallowed up in tho&longs;e very great ones which &longs;undry accidents continually pro­ duce. And all this hath been &longs;poken and granted on good grounds to Simplicius, and only with an intent to adverti&longs;e him how much it importeth to be cautious in granting many experiments for true to tho&longs;e who never had tried them, but only eagerly alledged them ju&longs;t as they ought to be for the &longs;erving their purpo&longs;e: This is &longs;po­ ken, I &longs;ay, by way of &longs;urplu&longs;&longs;age and Corollary to Simplicius, for the real truth is, that as concerning the&longs;e &longs;hots, the &longs;ame ought ex­ actly to befall a&longs;well in the motion as in the re&longs;t of the Terre&longs;trial Globe; as likewi&longs;e it will happen in all the other experiments that either have been or can be produced, which have at fir&longs;t blu&longs;h &longs;o mnch &longs;emblance of truth, as the antiquated opinion of the Earths motion hath of equivocation.

It is requi&longs;ite to be very cautious in admitting experi­ ments for true, to tho&longs;e who never tried them.

Experiments and arguments again&longs;t the Earths motion &longs;eem &longs;o far con­ cluding, as they lie hid under equi­ vokes.

SAGR. As for my part I am fully &longs;atisfied, and very well un­ der&longs;tand that who &longs;o &longs;hall imprint in his fancy this general com­ munity of the diurnal conver&longs;ion among&longs;t all things Terre&longs;trial, to all which it naturally agreeth, a&longs;well as in the old conceit of its re&longs;t about the centre, &longs;hall doubtle&longs;&longs;e di&longs;cern the fallacy and equi­ voke which made the arguments produced &longs;eem eoncluding. There yet remains in me &longs;ome hæ&longs;itancy (as I have hinted be­ fore) touching the flight of birds; the which having as it were an animate faculty of moving at their plea&longs;ure with a thou&longs;and mo­ tions, and to &longs;tay long in the Air &longs;eparated from the Earth, and therein with mo&longs;t irregular windings to go fluttering to and again, I cannot conceive how among&longs;t &longs;o great a confu&longs;ion of motions, they &longs;hould be able to retain the fir&longs;t commune motion; and in what manner, having once made any &longs;tay behind, they can get it up again, and overtake the &longs;ame with flying, and kcep pace with the Towers and trees which hurry with &longs;o precipitant a cour&longs;e towards the Ea&longs;t; I &longs;ay &longs;o precipitant, for in the great circle of the Globe it is little le&longs;&longs;e than a thou&longs;and miles an hour, whereof the flight of the &longs;wallow I believe makes not fifty.

SALV. If the birds were to keep pace with the cour&longs;e of the trees by help of their wings, they would o&longs; nece&longs;&longs;ity flie very fa&longs;t; and if they were deprived of the univer&longs;al conver&longs;ion, they would lag as far behind; and their flight would &longs;eem as furious towards the We&longs;t, and to him that could di&longs;cern the &longs;ame, it would much exceed the flight of an arrow; but I think we could not be able to perceive it, no more than we &longs;ee a Canon bullet, whil'&longs;t driven by the fury of the fire, it flieth through the Air: But the truth is that the proper motion of birds, I mean of their flight, hath nothing to do with the univer&longs;al motion, to which it is nei­ ther an help, nor an hinderance; and that which maintaineth the &longs;aid motion unaltered in the birds, is the Air it &longs;elf, thorough which they flie, which naturally following the Vertigo of the Earth, like as it carrieth the clouds along with it, &longs;o it tran&longs;porteth birds and every thing el&longs;e which is pendent in the &longs;ame; in &longs;o much that as to the bu&longs;ine&longs;&longs;e of keeping pace with the Earth, the birds need take no care thereof, but for that work might &longs;leep perpe­ tually.

SAGR. That the Air can carry the clouds along with it, as being matters ea&longs;ie for their lightne&longs;&longs;e to be moved and deprived of all other contrary inclination, yea more, as being matters that partake al&longs;o of the conditions and properties of the Earth; I com­ prehend without any difficulty; but that birds, which as having life, may move with a motion quite contrary to the diurnal, once having &longs;urcea&longs;ed the &longs;aid motion, the Air &longs;hould re&longs;tore them to it, &longs;eems to me a little &longs;trange, and the rather for that they are &longs;olid and weighty bodies; and withal, we &longs;ee; as hath been &longs;aid, &longs;tones and other grave bodies to lie unmoved again&longs;t the impetus of the air; and when they &longs;uffer them&longs;elves to be overcome thereby, they never acquire &longs;o much velocity as the wind which carrieth them.

SALV. We a&longs;cribe not &longs;o little force, Sagredus, to the moved Air, which is able to move and bear before it &longs;hips full fraught, to tear up trees by the roots, and overthrow Towers when it moveth &longs;wiftly; and yet we cannot &longs;ay that the motion of the Air in the&longs;e violent operations is neer &longs;o violent, as that of the diurnal revolution.

SIMP. You &longs;ee then that the moved Air may al&longs;o cotinue the motion of projects, according to the Doctrine of Ari&longs;totle; and it &longs;eemed to me very &longs;trange that he &longs;hould have erred in this particular.

SALV. It may without doubt, in ca&longs;e it could continue it &longs;elf, but lik as when the wind cea&longs;ing neither &longs;hips go on, nor trees are blown down, &longs;o the motion in the Air not continuing after the &longs;tone is gone out of the hand, and the Air cea&longs;ing to move, it followeth that it mu&longs;t be &longs;omething el&longs;e be&longs;ides the Air that ma­ keth the projects to move.

SIMP. But how upon the winds being laid, doth the &longs;hip cea&longs;e to move? Nay you may &longs;ee that when the wind is down, and the &longs;ails furl'd, the ve&longs;&longs;el continueth to run whole miles.

SALV. But this maketh again&longs;t your &longs;elf Simplicius, for that the wind being laid that filling the &longs;ails drove on the &longs;hip, yet ne­ verthele&longs;&longs;e doth it without help of the medium continue its cour&longs;e.

SIMP. It might be &longs;aid that the water was the medium which carried forward the &longs;hip, and maintain'd it in motion.

SALV. It might indeed be &longs;o affirmed, if you would &longs;peak quite contrary to truth; for the truth is, that the water, by rea­ &longs;on of its great re&longs;i&longs;tance to the divi&longs;ion made by the hull of the &longs;hip, doth with great noi&longs;e re&longs;i&longs;t the &longs;ame; nor doth it permit it of a great while to acquire that velocity which the wind would confer upon it, were the ob&longs;tacle of the water removed. Per­ haps Simplicius you have never con&longs;idered with what fury the water be&longs;ets a bark, whil'&longs;t it forceth its way through a &longs;tanding water by help of Oars or Sails: for if you had ever minded that effect, you would not now have produced &longs;uch an ab&longs;urdity. And I am thinking that you have hitherto been one of tho&longs;e who to find out how &longs;uch things &longs;ucceed, and to come to the know­ ledg of natural effects, do not betake them&longs;elves to a Ship, a Cro&longs;&longs;e-bow, or a piece of Ordinance, but retire into their &longs;tu­ dies, and turn over Indexes and Tables to &longs;ee whether Aristotle hath &longs;poken any thing thereof, and being a&longs;&longs;ured of the true &longs;en&longs;e of the Text, neither de&longs;ire nor care for knowing any more.

The great feli­ city for which they are much to be en­ vied who per&longs;wade them&longs;elves that they know every thing.

SAGR. This is a great felicity, and they are to be much en­ vied for it. For if knowledg be de&longs;ired by all, and if to be wi&longs;e, be to think ones &longs;elf &longs;o, they enjoy a very great happine&longs;&longs;e, for that they may per&longs;wade them&longs;elves that they know and under&longs;tand all things, in &longs;corn of tho&longs;e who knowing, that they under&longs;tand not what the&longs;e think they under&longs;tand, and con&longs;equently &longs;eeking that they know not the very lea&longs;t particle of what is knowable, kill them&longs;elves with waking and &longs;tudying, and con&longs;ume their days in experiments and ob&longs;ervations. But pray you let us return to our birds; touching which you have &longs;aid, that the Air being mo­ ved with great velocity, might re&longs;tore unto them that part of the diurnal motion which among&longs;t the windings of their flight they might have lo&longs;t; to which I reply, that the agitated Air &longs;eemeth unable to confer on a &longs;olid and grave body, &longs;o great a velocity as its own: And becau&longs;e that of the Air is as great as that of the Earth, I cannot think that the Air is able to make good the lo&longs;&longs;e of the birds retardation in flight.

SALV. Your di&longs;cour&longs;e hath in it much of probability, and to &longs;tick at trivial doubts is not for an acute wit; yet neverthele&longs;&longs;e the probability being removed, I believed that it hath not a jot more force than the others already con&longs;idered and re&longs;olved.

SAGR. It is mo&longs;t certain that if it be not nece&longs;&longs;atily conclu­ dent, its efficacy mu&longs;t needs be ju&longs;t nothing at all, for it is onely when the conclu&longs;ion is nece&longs;&longs;ary that the opponent hath no­ thing to alledg on the contrary.

SALV. Your making a greater &longs;cruple of this than of the other in&longs;tances dependeth, if I mi&longs;take not, upon the birds being ani­ mated, and thereby enabled to u&longs;e their &longs;trength at plea&longs;ure a­ gain&longs;t the primary motion in-bred in terrene bodies: like as for example, we &longs;ee them whil'&longs;t they are alive to fly upwards, a thing altogether impo&longs;&longs;ible for them to do as they are grave bodies; whereas being dead they can onely fall downwards; and there­ fore you hold that the rea&longs;ons that are of force in all the kinds of projects above named, cannot take place in birds: Now this is very true; and becau&longs;e it is &longs;o, Sagredus, that doth not appear to be done in tho&longs;e projects, which we &longs;ee the birds to do. For if

from the top of a Tower you let fall a dead bird and a live one, the dead bird &longs;hall do the &longs;ame that a &longs;tone doth, that is, it &longs;hall fir&longs;t follow the general motion diurnal, and then the motion of de&longs;cent, as grave; but if the bird let fall, be a live, what &longs;hall hinder it, (there ever remaining in it the diurnal motion) from &longs;oaring by help of its wings to what place of the Horizon it &longs;hall plea&longs;e? and this new motion, as being peculiar to the bird, and not participated by us, mu&longs;t of nece&longs;&longs;ity be vi&longs;ible to us; and if it be moved by help of its wings towards the We&longs;t, what &longs;hall hinder it from returning with a like help of its wings unto the Tower. And, becau&longs;e, in the la&longs;t place, the birds wending its flight towards the We&longs;t was no other than a withdrawing from the diurnal motion, (which hath, &longs;upppo&longs;e ten degrees of velocity) one degree onely, there did thereupon remain to the bird whil'&longs;t it was in its flight nine degrees of velocity, and &longs;o &longs;oon as it did alight upon the the Earth, the ten common degrees returned to it, to which, by flying towards the Ea&longs;t it might adde one, and with tho&longs;e eleven overtake the Tower. And in &longs;hort, if we well con­ &longs;ider, and more narrowly examine the effects of the flight of birds, they differ from the projects &longs;hot or thrown to any part of the World in nothing, &longs;ave onely that the projects are moved by an external projicient, and the birds by an internal principle. And here for a final proof of the nullity of all the experiments before alledged, I conceive it now a time and place convenient to demon&longs;trate a way how to make an exact trial of them all. Shut your &longs;elf up with &longs;ome friend in the grand Cabbin between the decks of &longs;ome large Ship, and there procure gnats, flies, and &longs;uch other &longs;mall winged creatures: get al&longs;o a great tub (or other ve&longs;&longs;el) full of water, and within it put certain fi&longs;hes; let al&longs;o a certain bottle be hung up, which drop by drop letteth forth its water into another bottle placed underneath, having a narrow neck: and, the Ship lying &longs;till, ob&longs;erve diligently how tho&longs;e &longs;mall winged animals fly with like velocity towards all parts of the Ca­ bin; how the fi&longs;hes &longs;wim indifferently towards all &longs;ides; and how the di&longs;tilling drops all fall into the bottle placed underneath. And ca&longs;ting any thing towards your friend, you need not throw it with more force one way then another, provided the di&longs;tances be equal: and leaping, as the &longs;aying is, with your feet clo&longs;ed, you will reach as far one way as another. Having ob&longs;erved all the&longs;e particulars, though no man doubteth that &longs;o long as the ve&longs;&longs;el &longs;tands &longs;till, they ought to &longs;ucceed in this manner; make the Ship to move with what velocity you plea&longs;e; for (&longs;o long as the motion is uniforme, and not fluctuating this way and that way) you &longs;hall not di&longs;cern any the lea&longs;t alteration in all the forenamed effects; nor can you gather by any of them whether the Ship doth move or &longs;tand &longs;till. In leaping you &longs;hall reach as far upon the floor, as before; nor for that the Ship moveth &longs;hall you make a greater leap towards the poop than towards the prow; howbeit in the time that you &longs;taid in the Air, the floor under your feet &longs;hall have run the contrary way to that of your jump; and throwing any thing to your companion you &longs;hall not need to ca&longs;t it with more &longs;trength that it may reach him, if he &longs;hall be towards the prow, and you towards the poop, then if you &longs;tood in a contrary &longs;ituation; the drops &longs;hall all di&longs;till as before into the inferiour bottle and not &longs;o much as one &longs;hall fall towards the poop, albeit whil'&longs;t the drop is in the Air, the Ship &longs;hall have run many feet; the Fi&longs;hes in their water &longs;hall not &longs;wim with more trouble towards the fore-part, than towards the hinder part of the tub; but &longs;hall with equal velocity make to the bait placed on any &longs;ide of the tub; and la&longs;tly, the flies and gnats &longs;hall continue their flight indifferently towards all parts; nor &longs;hall they ever happen to be driven together towards the &longs;ide of the Cabbin next the prow, as if they were wearied with fol­ lowing the &longs;wift cour&longs;e of the Ship, from which through their &longs;u&longs;pen&longs;ion in the Air, they had been long &longs;eparated; and if burning a few graines of incen&longs;e you make a little &longs;moke, you &longs;hall &longs;ee it a&longs;cend on high, and there in manner of a cloud &longs;u&longs;pend it &longs;elf, and move indifferently, not inclining more to one &longs;ide than another: and of this corre&longs;pondence of effects the cau&longs;e is for that the Ships motion is common to all the things contained in it, and to the Air al&longs;o; I mean if tho&longs;e things be &longs;hut up in the Cabbin: but in ca&longs;e tho&longs;e things were above deck in the open Air, and not obliged to follow the cour&longs;e of the Ship, differences more or le&longs;&longs;e notable would be ob&longs;erved in &longs;ome of the fore-named ef­ fects, and there is no doubt but that the &longs;moke would &longs;tay behind as much as the Air it &longs;elf; the flies al&longs;o, and the gnats being hin­ dered by the Air would not be able to follow the motion of the Ship, if they were &longs;eparated at any di&longs;tance from it. But keeping neer thereto, becau&longs;e the Ship it &longs;elf as being an unfractuous Fa­ brick, carrieth along with it part of its neere&longs;t Air, they would follow the &longs;aid Ship without any pains or difficulty. And for the like rea&longs;on we &longs;ee &longs;ometimes in riding po&longs;t, that the trouble&longs;ome flies and ^{*} hornets do follow the hor&longs;es flying &longs;ometimes to one, &longs;ometimes to another part of the body, but in the falling drops the difference would be very &longs;mall; and in the &longs;alts, and projecti­ ons of grave bodies altogether imperceptible.

The an&longs;wer to the argument ta­ ken from the flight of birds contrary to the motion of the Earth.

An experiment with which alone is &longs;hewn the nullity of all the objecti­ ons produced a­ gainst the motion of the Earth.

* Tafaris, bor&longs;e­ flyes.

SAGR. Though it came not into my thoughts to make triall of the&longs;e ob&longs;ervations, when I was at Sea, yet am I confident that they will &longs;ucceed in the &longs;ame manner, as you have related; in confirma­ tion of which I remember that being in my Cabbin I have asked an hundred times whether the Ship moved or &longs;tood &longs;till; and &longs;ometimes I have imagined that it moved one way, when it &longs;teered quite another way. I am therefore as hitherto &longs;atisfied and con­ vinced of the nullity of all tho&longs;e experiments that have been pro­ duced in proof of the negative part. There now remains the ob­ jection founded upon that which experience &longs;hews us, namely, that a &longs;wift Vertigo or whirling about hath a faculty to extrude and di&longs;per&longs;e the matters adherent to the machine that turns round; whereupon many were of opinion, and Ptolomy among&longs;t the re&longs;t, that if the Earth &longs;hould turn round with &longs;o great velocity, the &longs;tones and creatures upon it &longs;hould be to&longs;t into the Skie, and that there could not be a morter &longs;trong enough to fa&longs;ten buildings &longs;o to their foundations, but that they would likewi&longs;e &longs;uffer a like extru&longs;ion.

SALV. Before I come to an&longs;wer this objection, I cannot but take notice of that which I have an hundred times ob&longs;erved, and not without laughter, to come into the minds of mo&longs;t men &longs;o &longs;oon as ever they hear mention made of this motion of the Earth, which is believed by them &longs;o fixt and immoveable, that they not only ne­ ver doubted of that re&longs;t, but have ever &longs;trongly believed that all other men a&longs;well as they, have held it to be created immoveable, and &longs;o to have continued through all &longs;ucceeding ages: and being &longs;etled in this per&longs;wa&longs;ion, they &longs;tand amazed to hear that any one &longs;hould grant it motion, as if, after that he had held it to be immo­ veable, he had fondly thought it to commence its motion then (and not till then) when Pythagoras (or whoever el&longs;e was the fir&longs;t hinter of its mobility) &longs;aid that it did move. Now that &longs;uch a foo­ li&longs;h conceit (I mean of thinking that tho&longs;e who admit the motion of the Earth, have fir&longs;t thought it to &longs;tand &longs;till from its creation, untill the time of Pythagoras, and have onely made it moveable after that Pythagor as e&longs;teemed it &longs;o) findeth a place in the mindes of the vulgar, and men of &longs;hallow capacities, I do not much won­ der; but that &longs;uch per&longs;ons as Ari&longs;totle and Ptolomy &longs;hould al&longs;o run into this childi&longs;h mi&longs;take, is to my thinking a more admirable and unpardonable folly.

The &longs;tupidity of &longs;ome that think the Earth to have be­ gun to move, when Pythagoras began to affirme that it did &longs;o.

SAGR. You believe then, Salviatus, that Ptolomy thought, that in his Di&longs;putation he was to maintain the &longs;tability of the Earth again&longs;t &longs;uch per&longs;ons, as granting it to have been immoveable, un­ till the time of Pythagoras, did affirm it to have been but then made moveable, when the &longs;aid Pythagoras a&longs;cribed unto it mo­ tion.

SALV. We can think no other, if we do but con&longs;ider the way he taketh to confute their a&longs;&longs;ertion; the confutation of which con&longs;i&longs;ts in the demolition of buildings, and the to&longs;&longs;ing of &longs;tones, living creatures and men them&longs;elves up into the Air. And be­ cau&longs;e &longs;uch overthrows and extru&longs;ions cannot be made upon buil­ dings and men, which were not before on the Earth, nor can men be placed, nor buildings erected upon the Earth, unle&longs;&longs;e when it &longs;tandeth &longs;till; hence therefore it is cleer, that Ptolomy argueth a­ gain&longs;t tho&longs;e, who having granted the &longs;tability of the Earth for &longs;ome time, that is, &longs;o long as living creatures, &longs;tones, and Ma&longs;ons were able to abide there, and to build Palaces and Cities, make it afterwards precipitately moveable to the overthrow and de&longs;tructi­ of Edifices, and living creatures, &c. For if he had undertook to di&longs;pute again&longs;t &longs;uch as had a&longs;cribed that revolution to the Earth from its fir&longs;t creation, he would have confuted them by &longs;aying, that if the Earth had alwayes moved, there could never have been placed upon it either men or &longs;tones; much le&longs;s could buildings have been erected, or Cities founded, &c.

Ari&longs;totle and Ptolomy &longs;eem to confute the mobili­ ty of the Earth a­ gain&longs;t tho&longs;e who thought that it ha­ ving a long time &longs;tood still, did be­ gin to move in the time of Pythagoras

SIMP. I do not well conceive the&longs;e Ari&longs;totelick and Ptolo­ maick inconveniences.

SALV. Ptolomey either argueth again&longs;t tho&longs;e who have e&longs;teem­ ed the Earth always moveable; or again&longs;t &longs;uch as have held that it &longs;tood for &longs;ome time &longs;till, and hath &longs;ince been &longs;et on moving. If again&longs;t the fir&longs;t, he ought to &longs;ay, that the Earth did not always move, for that then there would never have been men, animals, or edifices on the Earth, its vertigo not permitting them to &longs;tay thereon. But in that he arguing, &longs;aith that the Earth doth not move, becau&longs;e that bea&longs;ts, men, and hou&longs;es before plac'd on the Earth would precipitate, he &longs;uppo&longs;eth the Earth to have been once in &longs;uch a &longs;tate, as that it did admit men and bea&longs;ts to &longs;tay, and build thereon; the which draweth on the con&longs;equence, that it did for &longs;ome time &longs;tand &longs;till, to wit, was apt for the abode of a­ nimals and erection of buildings. Do you now conceive what I would &longs;ay?

SIMP. I do, and I do not: but this little importeth to the merit of the cau&longs;e; nor can a &longs;mall mi&longs;take of Ptolomey, com­ mitted through inadvertencie be &longs;ufficient to move the Earth, when it is immoveable. But omitting cavils, let us come to the &longs;ub&longs;tance of the argument, which to me &longs;eems unan&longs;werable.

SALV. And I, Simplicius, will drive it home, and re-inforce it, by &longs;hewing yet more &longs;en&longs;ibly, that it is true that grave bodies turn'd with velocity about a &longs;ettled centre, do acquire an impetus of moving, and receding to a di&longs;tance from that centre, even then when they are in a &longs;tate of having a propen&longs;ion of moving naturally to the &longs;ame. Tie a bottle that hath water in it, to the end of a cord, and holding the other end fa&longs;t in your hand, and making the cord and your arm the &longs;emi-diameter, and the knitting of the &longs;houlder the centre, &longs;wing the bottle very fa&longs;t a­ bout, &longs;o as that it may de&longs;cribe the circumference of a circle, which, whether it be parallel to the Horizon, or perpendicular to it, or any way inclined, it &longs;hall in all ca&longs;es follow, that the wa­ ter will not fall out of the bottle: nay, he that &longs;hall &longs;wing it, &longs;hall find the cord always draw, and &longs;trive to go farther from the &longs;houlder. And if you bore a hole in the bottom of the bottle, you &longs;hall &longs;ee the water &longs;pout forth no le&longs;s upwards into the skie, than laterally, and downwards to the Earth; and if in&longs;tead of wa­ ter, you &longs;hall put little pebble &longs;tones into the bottle, and &longs;wing it in the &longs;ame manner, you &longs;hall find that they will &longs;trive in the like manner again&longs;t the cord. And la&longs;tly, we &longs;ee boys throw &longs;tones a great way, by &longs;winging round a piece of a &longs;tick, at the end of which the &longs;tone is let into a &longs;lit (which &longs;tick is called by them a &longs;ling;) all which are arguments of the truth of the conclu&longs;ion, to wit, that the vertigo or &longs;wing conferreth upon the moveable, a motion towards the circumference, in ca&longs;e the motion be &longs;wift: and therefore if the Earth revolve about its own centre, the mo­ tion of the &longs;uperficies, and e&longs;pecially towards the great circle, as being incomparably more &longs;wift than tho&longs;e before named, ought to extrude all things up into the air.

SIMP. The Argument &longs;eemeth to me very well proved and inforced; and I believe it would be an hard matter to an&longs;wer and overthrow it.

SALV. Its &longs;olution dependeth upon certain notions no le&longs;s known and believed by you, than by my &longs;elf: but becau&longs;e they come not into your mind, therefore it is that you perceive not the an&longs;wer; wherefore, without telling you it (for that you know the &longs;ame already) I &longs;hall with onely a&longs;&longs;i&longs;ting your memory, make you to refute this argument.

SIMP. I have often thought of your way of arguing, which hath made me almo&longs;t think that you lean to that opinion of Pla- to, Quòd no&longs;trum &longs;cire &longs;it quoddam remini&longs;ci; therefore I intreat you to free me from this doubt, by letting me know your judg­ ment.

Our krowledg is a kind of remini&longs;­ cence according to Plato.

SALV. What I think of the opinion of Plato, you may gather from my words and actions. I have already in the precedent con­ ferences expre&longs;ly declared my &longs;elf more than once; I will pur&longs;ue the &longs;ame &longs;tyle in the pre&longs;ent ca&longs;e, which may hereafter &longs;erve you for an example, thereby the more ea&longs;ily to gather what my opi­ nion is touching the attainment of knowledg, when a time &longs;hall offer upon &longs;ome other day: but I would not have Sagredus of­ fended at this digre&longs;&longs;ion.

SAGR. I am rather very much plea&longs;ed with it, for that I re­ member that when I &longs;tudied Logick, I could never comprehend that &longs;o much cry'd up and mo&longs;t potent demon&longs;tration of Ari&longs;totle.

SALV. Let us go on therefore; and let Simplicius, tell me what that motion is which the &longs;tone maketh that is held fa&longs;t in the &longs;lit of the &longs;ling, when the boy &longs;wings it about to throw it a great way?

SIMP. The motion of the &longs;tone, &longs;o long as it is in the &longs;lit, is circular, that is, moveth by the arch of a circle, who&longs;e &longs;tedfa&longs;t centre is the knitting of the &longs;houlder, and its &longs;emi-diameter the arm and &longs;tick.

SALV. And when the &longs;tone leaveth the &longs;ling, what is its mo­ tion? Doth it continue to follow its former circle, or doth it go by another line?

SIMP. It will continue no longer to &longs;wing round, for then it would not go farther from the arm of the projicient, whereas we &longs;ee it go a great way off.

SALV. With what motion doth it move then?

SIMP. Give me a little time to think thereof; For I have ne­ ver con&longs;idered it before.

SALV. Hark hither, Sagredus; this is the Quoddam remini&longs;ci in a &longs;ubject well under&longs;tood. You have pau&longs;ed a great while, Simplicius.

SIMP. As far as I can &longs;ee, the motion received in going out of the &longs;ling, can be no other than by a right line; nay, it mu&longs;t ne­ ce&longs;&longs;arily be &longs;o, if we &longs;peak of the pure adventitious impetus. I was a little puzled to &longs;ee it make an arch, but becau&longs;e that arch bended all the way upwards, and no other way, I conceive that that incurvation cometh from the gravity of the &longs;tone, which na­ turally draweth it downwards. The impre&longs;&longs;ed impetus, I &longs;ay, without re&longs;pecting the natural, is by a right line.

The motion im­ pre&longs;&longs;ed by the pro­ jicient is onely by a right line.

SALV. But by what right line? Becau&longs;e infinite, and towards every &longs;ide may be produced from the &longs;lit of the &longs;ling, and from the point of the &longs;tones &longs;eparation from the &longs;ling.

SIMP. It moveth by that line which goeth directly from the motion which the &longs;tone made in the &longs;ling.

SALV. The motion of the &longs;tone whil&longs;t it was in the &longs;lit, you have affirmed already to be circular; now circularity oppo&longs;eth directne&longs;s, there not being in the circular line any part that is di­ rect or &longs;treight.

SIMP I mean not that the projected motion is direct in re­ &longs;pect of the whole circle, but in reference to that ultimate point, where the circular motion determineth. I know what I would &longs;ay, but do not well know how to expre&longs;s my &longs;elf.

SALV. And I al&longs;o perceive that you under&longs;tand the bu&longs;ine&longs;s, but that you have not the proper terms, wherewith to expre&longs;s the &longs;ame. Now the&longs;e I can ea&longs;ily teach you; teach you, that is, as to the words, but not as to the truths, which are things. And that you may plainly &longs;ee that you know the thing I ask you, and onely want language to expre&longs;s it, tell me, when you &longs;hoot a bullet out of a gun, towards what part is it, that its acquired impetus carri­ eth it?

SIMP. Its acquired impetus carrieth it in a right line, which continueth the rectitude of the barrel, that is, which inclineth nei­ ther to the right hand nor to the left, nor upwards not down­ wards.

SALV. Which in &longs;hort is a&longs;much as to &longs;ay, it maketh no angle with the line of &longs;treight motion made by the &longs;ling.

SIMP. So I would have &longs;aid.

SALV. If then the line of the projects motion be to continue without making an angle upon the circular line de&longs;cribed by it, whil&longs;t it was with the projicient; and if from this circular motion it ought to pa&longs;s to the right motion, what ought this right line to be?

SIMP. It mu&longs;t needs be that which toucheth the circle in the point of &longs;eparation, for that all others, in my opinion, being pro­ longed would inter&longs;ect the circumference, and by that means make &longs;ome angle therewith.

SALV. You have argued very well, and &longs;hewn your &longs;elf half a Geometrician. Keep in mind therefore, that your true opinion is expre&longs;t in the&longs;e words, namely, That the project acquireth an impetus of moving by the Tangent, the arch de&longs;cribed by the motion of the projicient, in the point of the &longs;aid projects &longs;epara­ tion from the projicient.

SIMP. I under&longs;tand you very well, and this is that which I would &longs;ay.

SALV. Of a right line which toucheth a circle, which of its points is the neare&longs;t to the centre of that circle?

SIMP. That of the contact without doubt: for that is in the circumference of a circle, and the re&longs;t without: and the points of the circumference are all equidi&longs;tant from the centre.

SALV. Therefore a moveable departing from the contact, and moving by the &longs;treight Tangent, goeth continually farther and farther from the contact, and al&longs;o from the centre of the circle.

SIMP. It doth &longs;o doubtle&longs;s.

SALV. Now if you have kept in mind the propo&longs;itions, which you have told me, lay them together, and tell me what you gather from them.

SIMP. I think I am not &longs;o forgetful, but that I do remember them. From the things premi&longs;ed I gather that the project &longs;wiftly &longs;winged round by the projicient, in its &longs;eparating from it, doth re­ tain an impetus of continuing its motion by the right line, which toucheth the circle de&longs;cribed by the motion of the projicient in the point of &longs;eparation, by which motion the project goeth con­ tinually receding from the centre of the circle de&longs;cribed by the motion of the projicient.

The project mo­ veth by the Tan­ gent of the circle of the motion prece­ dent in the point of &longs;eparation.

SALV. You know then by this time the rea&longs;on why grave bo­ dies &longs;ticking to the rim of a wheele, &longs;wiftly moved, are extruded and thrown beyond the circumference to yet a farther di&longs;tance from the centre.

SIMP. I think I under&longs;tand this very well; but this new know­ ledg rather increa&longs;eth than le&longs;&longs;eneth my incredulity that the Earth can turn round with &longs;o great velocity, without extruding up into the sky, &longs;tones, animals, &c.

SALV. In the &longs;ame manner that you have under&longs;tood all this, you &longs;hall, nay you do under&longs;tand the re&longs;t: and with recollecting your &longs;elf, you may remember the &longs;ame without the help of o­ thers: but that we may lo&longs;e no time, I will help your memory therein. You do already know of your &longs;elf, that the circular mo­ tion of the projicient impre&longs;&longs;eth on the project an impetus of mo­ ving (when they come to &longs;eparate) by the right Tangent, the circle of the motion in the point of &longs;eparation, and continuing a­ long by the &longs;ame the motion ever goeth receding farther and far­ ther from the projicient: and you have &longs;aid, that the project would continue to move along by that right line, if there were not by its proper weight an inclination of de&longs;cent added unto it; from which the incurvation of the line of motion is derived. It &longs;eems moreover that you knew of your &longs;elf, that this incurvation al­ ways bended towards the centre of the Earth, for thither do all grave bodies tend. Now I proceed a little farther, and ask you, whe­ ther the moveable after its &longs;eparation, in continuing the right mo­ tion goeth always equally receding from the centre, or if you will, from the circumference of that circle, of which the precedent mo­ tion was a part; which is as much as to &longs;ay, Whether a moveable, that for&longs;aking the point of a Tangent, and moving along by the &longs;aid Tangent, doth equally recede from the point of contact, and from the circumference of the circle?

SIMP. No, Sir: for the Tangent near to the point of contact, recedeth very little from the circumference, wherewith it keepeth a very narrow angle, but in its going farther and farther off, the di&longs;tance always encrea&longs;eth with a greater proportion; &longs;o that in a circle that &longs;hould have v. g. ten yards of diameter, a point of the Tangent that was di&longs;tant from the contact but two palms, would be three or four times as far di&longs;tant from the circumference of the circle, as a point that was di&longs;tant from the contaction one palm, and the point that was di&longs;tant half a palm, I likewi&longs;e believe would &longs;car&longs;e recede the fourth part of the di&longs;tance of the &longs;econd: fo that within an inch or two of the contact, the &longs;eparation of the Tangent from the circumference is &longs;car&longs;e di&longs;cernable.

SALV. So that the rece&longs;&longs;ion of the project from the circumfe­ rence of the precedent circular motion is very &longs;mall in the begin­ ing?

SIMP. Almo&longs;t in&longs;en&longs;ible.

SALV. Now tell me a little; the project, which from the mo­ tion of the projicient receiveth an impetus of moving along the Tangent in a right line, and that would keep unto the &longs;ame, did not its own weight depre&longs;s it downwards, how long is it after the &longs;eparation, ere it begin to decline downwards.

SIMP. I believe that it beginneth pre&longs;ently; for it not ha­ ving any thing to uphold it, its proper gravity cannot but ope­ rate.

A grave project, as &longs;oon as it is &longs;e­ parated from the projicient begineth to decline.

SALV. So that, if that &longs;ame &longs;tone, which being extruded from that wheel turn'd about very fa&longs;t, had as great a natural propen­ &longs;ion of moving towards the centre of the &longs;aid wheel, as it hath to move towards the centre of the Earth, it would be an ea&longs;ie mat­ ter for it to return unto the wheel, or rather not to depart from it; in regard that upon the begining of the &longs;eparation, the rece&longs;&longs;ion be­ ing &longs;o &longs;inall, by rea&longs;on of the infinite acutene&longs;s of the angle of contact, every very little of inclination that draweth it back to­ wards the centie of the wheel, would be &longs;ufficient to retain it up­ on the rim or circumference.

SIMP. I que&longs;tion not, but that if one &longs;uppo&longs;e that which nei­ ther is, nor can be, to wit, that the inclination of tho&longs;e grave bo­ dies was to go towards the centre of the wheel, they would never come to be extruded or &longs;haken off.

SALV. But I neither do, nor need to &longs;uppo&longs;e that which is not; for I will not deny but that the &longs;tones are extruded. Yet I &longs;peak this by way of &longs;uppo&longs;ition, to the end that you might grant me the re&longs;t. Now fancy to your &longs;elf, that the Earth is that great wheel, which moved with &longs;o great velocity is to extrude the &longs;tones. You could tell me very well even now, that the motion of proje­ ction ought to be by that right line which toucheth the Earth in the point of &longs;eparation: and this Tangent, how doth it notably recede from the &longs;uperficies of the Terre&longs;trial Globe?

SIMP. I believe, that in a thou&longs;and yards, it will not recede from the Earth an inch.

SALV. And did you not &longs;ay, that the project being drawn by its own weight, declineth from the Tangent towards the centre of the Earth?

SIMP. I &longs;aid &longs;o, and al&longs;o confe&longs;&longs;e the re&longs;t: and do now plainly under&longs;tand that the &longs;tone will not &longs;eparate from the Earth, for that its rece&longs;&longs;ion in the beginning would be &longs;uch, and &longs;o &longs;mall, that it is a thou&longs;and times exceeded by the inclination which the &longs;tone hath to move towards the centre of the Earth, which cen­ tre in this ca&longs;e is al&longs;o the centre of the wheel. And indeed it mu&longs;t be confe&longs;&longs;ed that the &longs;tones, the living creatures, and the other grave bodies cannot be extruded; but here again the lighter things beget in me a new doubt, they having but a very weak propen&longs;ion of de&longs;cent towards the centre; &longs;o that there being wanting in them that faculty of withdrawing from the &longs;uperficies, I &longs;ee not, but that they may be extruded; and you know the rule, that ad de&longs;truendum &longs;ufficit unum.

SAVL. We will al&longs;o give you &longs;atisfaction in this. Tell me therefore in the fir&longs;t place, what you under&longs;tand by light matters, that is, whether you thereby mean things really &longs;o light, as that they go upwards, or el&longs;e not ab&longs;olutely light, but of &longs;o &longs;mall gra­ vity, that though they de&longs;cend downwards, it is but very &longs;lowly; for if you mean the ab&longs;olutely light, I will be readier than your &longs;elf to admit their extru&longs;ion.

SIMP. I &longs;peak of the other &longs;ort, &longs;uch as are feathers, wool, cot­ ton, and the like; to lift up which every &longs;mall force &longs;ufficeth: yet neverthele&longs;&longs;e we &longs;ee they re&longs;t on the Earth very quietly.

SALV. This pen, as it hath a natural propen&longs;ion to de&longs;cend to­ wards the &longs;uperficies of the Earth, though it be very &longs;mall, yet I mu&longs;t tell you that it &longs;ufficeth to keep it from mounting upwards: and this again is not unknown to you your &longs;elf; therefore tell me if the pen were extruded by the Vertigo of the Earth, by what line would it move?

SIMP. By the tangent in the point of &longs;eparation.

SALV. And when it &longs;hould be to return, and re-unite it &longs;elf to the Earth, by what line would it then move?

SIMP. By that which goeth from it to the centre of the Earth.

SALV. So then here falls under our con&longs;ideration two moti­ ons; one the motion of projection, which beginneth from the point of contact, and proceedeth along the tangent; and the o­ ther the motion of inclination downwards, which beginneth from the project it &longs;elf, and goeth by the &longs;ecant towards the centre; and if you de&longs;ire that the projection follow, it is nece&longs;&longs;ary that the im­ petus by the tangent overcome the inclination by the &longs;ecant: is it not &longs;o?

SIMP. So it &longs;eemeth to me.

SALV. But what is it that you think nece&longs;&longs;ary in the motion of the projicient, to make that it may prevail over that inclina­ tion, from which en&longs;ueth the &longs;eparation and elongation of the pen from the Earth?

SIMP. I cannot tell.

SALV. How, do you not know that? The moveable is here the &longs;ame, that is, the &longs;ame pen; now how can the &longs;ame moveable &longs;uperate and exceed it &longs;elf in motion?

SIMP. I do not &longs;ee how it can overcome or yield to it &longs;elf in motion, unle&longs;&longs;e by moving one while fa&longs;ter, and another while &longs;lower.

SALV. You &longs;ee then, that you do know it. If therefore the projection of the pen ought to follow, and its motion by the tan­ gent be to overcome its motion by the &longs;ecant, what is it requi&longs;ite that their velocities &longs;hould be?

SIMP. It is requi&longs;ite that the motion by the tangent be greater than that other by the &longs;ecant. But wretch that I am! Is it not only many thou&longs;and times greater than the de&longs;cending motion of the pen, but than that of the &longs;tone? And yet like a &longs;imple fellow I had &longs;uffered my &longs;elf to be per&longs;waded, that &longs;tones could not be extruded by the revolution of the Earth. I do therefore revoke my former &longs;entence, and &longs;ay, that if the Earth &longs;hould move, &longs;tones, Elephants, Towers, and whole Cities would of nece&longs;&longs;ity be to&longs;t up into the Air; and becau&longs;e that that doth not evene, I con­ clude that the Earth doth not move.

SALV. Softly Simplicius, you go on &longs;o fa&longs;t, that I begin to be more afraid for you, than for the pen. Re&longs;t a little, and ob&longs;erve what I am going to &longs;peap. If for the reteining of the &longs;tone or pen an­ nexed to the Earths &longs;urface it were nece&longs;&longs;ary that its motion of de&longs;cent were greater, or as much as the motion made by the tan­ gent; you would have had rea&longs;on to &longs;ay, that it ought of nece&longs;&longs;ity to move as fa&longs;t, or fa&longs;ter by the &longs;ecant downwards, than by the tangent Ea&longs;twards: But did not you tell me even now, that a thou&longs;and yards of di&longs;tance by the tangent from the contact, do remove hardly an inch from the circumference? It is not &longs;uffici­ ent therefore that the motion by the tangent, which is the &longs;ame with that of the diurnall Vertigo, (or ha&longs;ty revolution) be fimply more &longs;wift than the motion by the &longs;ecant, which is the &longs;ame with that of the pen in de&longs;cending; but it is requi&longs;ite that the &longs;ame be &longs;o much more &longs;wift as that the time which &longs;ufficeth for the pen to move v.g. a thou&longs;and yards by the tangent, be in&longs;ufficient for it to move one &longs;ole inch by the &longs;ecant. The which I tell you &longs;hall never be, though you &longs;hould make that motion never &longs;o &longs;wift, and this never &longs;o &longs;low.

SIMP. And why might not that by the tangent be &longs;o &longs;wift, as not to give the pen time to return to the &longs;urface of the Earth?

SALV. Try whether you can &longs;tate the ca&longs;e in proper termes, and I will give you an an&longs;wer. Tell me therefore, how much do you think &longs;ufficeth to make that motion &longs;wifter than this?

SIMP. I will &longs;ay for example, that if that motion by the tan­ gent were a million of times &longs;wifter than this by the &longs;ecant, the pen, yea, and the &longs;tone al&longs;o would come to be extruded.

SALV. You &longs;ay &longs;o, and &longs;ay that which is fal&longs;e, onely for want, not of Logick, Phy&longs;icks, or Metaphy&longs;icks, but of Geome­ try; for if you did but under&longs;tand its fir&longs;t elements, you would know, that from the centre of a circle a right line may be drawn to meet the tangent, which inter&longs;ecteth it in &longs;uch a manner, that the part of the tangent between the contact and the &longs;ecant, may be one, two, or three millions of times greater than that part of the &longs;ecant which lieth between the tangent and the circumference, and that the neerer and neerer the &longs;ecant &longs;hall be to the contact, this proportion &longs;hall grow greater and greater in infinitum; &longs;o that it need not be feared, though the vertigo be &longs;wift, and the motion downwards &longs;low, that the pen or other lighter matter can begin to ri&longs;e upwards, for that the inclination downwards always exceedeth the velocity of the projection.

SAGR. I do not perfectly apprehend this bu&longs;ine&longs;&longs;e.

SALV. I will give you a mo&longs;t univer&longs;al yet very ea&longs;ie demon­

&longs;tration thereof. Let a proportion be given between B A [in Fig. 3.] and C: And let B A be greater than C at plea&longs;ure. And let there be de&longs;cribed a circle, who&longs;e centre is D. From which it is required to draw a &longs;ecant, in &longs;uch manner, that the tangent may be in proportion to the &longs;aid &longs;ecant, as B A to C. Let A I be &longs;uppo&longs;ed a third proportional to B A and C. And as B I is to I A, &longs;o let the diameter F E be to E G; and from the point G, let there be drawn the tangent G H. I &longs;ay that all this is done as was required; and as B A is to C, &longs;o is H G to G E. And in re­ gard that as B I is to I A, &longs;o is F E to E G; therefore by compo­ &longs;ition, as B A is to A I; &longs;o &longs;hall F G be to G E. And becau&longs;e C is the middle proportion between B A and A I; and G H is a middle term between F G and G E; therefore, as B A is to C, &longs;o &longs;hall F G be to G H; that is H G to G E, which was to be demon&longs;trated.

A geometrical demon&longs;tration to prove the impo&longs;&longs;i­ bility of extru&longs;ion by means of the terre&longs;trial vertigo.

SAGR. I apprehend this demon&longs;tration; yet neverthele&longs;&longs;e, I am not left wholly without hæ&longs;itation; for I find certain confu­ &longs;ed &longs;cruples role to and again in my mind, which like thick and dark clouds, permit me not to di&longs;cern the cleerne&longs;&longs;e and nece&longs;&longs;ity of the conclu&longs;ion with that per&longs;picuity, which is u&longs;ual in Mathe­ matical Demon&longs;trations. And that which I &longs;tick at is this. It is true that the &longs;paces between the tangent and the circumference do gradually dimini&longs;h in infinitum towards the contact; but it is al&longs;o true on the contrary, that the propen&longs;ion of the moveable to de&longs;cending groweth le&longs;s & le&longs;s in it, the nearer it is to the fir&longs;t term of its de&longs;cent; that is, to the &longs;tate of re&longs;t; as is manife&longs;t from that which you declare unto us, demon&longs;trating that the de&longs;cending grave body departing from re&longs;t, ought to pa&longs;&longs;e thorow all the degrees of tardity comprehended between the &longs;aid re&longs;t, & any a&longs;&longs;igned degree of velocity, the which grow le&longs;s and le&longs;s in infinitum. To which may be added, that the &longs;aid velocity and propen&longs;ion to motion, doth for another rea&longs;on dimini&longs;h to infinity; and it is becau&longs;e the gravity of the &longs;aid moveable may infinitely dimini&longs;h. So that the cau&longs;es which dimini&longs;h the propen&longs;ion of a&longs;cending, and con&longs;equently favour the projection, are two; that is, the levity of the moveable, and its vicinity to the &longs;tate of re&longs;t; both which are augmentable in infinit. and the&longs;e two on the contrary being to contract but with one &longs;ole cau&longs;e of making the projection, I cannot conceive how it alone, al­ though it al&longs;o do admit of infinite augmentation, &longs;hould be able to remain invincible again&longs;t the union & confederacy of the others, w^{ch} are two, and are in like manner capable of infinite augmentation.

SALV. This is a doubt worthy of Sagredus; and to explain it &longs;o as that we may more cleerly apprehend it, for that you &longs;ay that you your &longs;elf have but a confu&longs;ed Idea of it, we will di&longs;tingui&longs;h of the &longs;ame by reducing it into figure; which may al&longs;o perhaps afford us &longs;ome ca&longs;e in re&longs;olving the &longs;ame. Let us therefore [in Fig. 4.] draw a perpendicular line towards the centre, and let it be AC, and to it at right angles let there be drawn the Horizontal line A B, upon which the motion of the projection ought to be made; now the pro­ ject would continue to move along the &longs;ame with an even motion, if &longs;o be its gravity did not incline it downwards. Let us &longs;uppo&longs;e from the point A a right line to be drawn, that may make any angle at plea&longs;ure with the line A B; which let be A E, and upon AB let us mark &longs;ome equal &longs;paces AF, FH, HK, and from them let us let fall the perpendiculars FG, HI, K L, as far as AE. And becau&longs;e, as al ready hath been &longs;aid, the de&longs;cending grave body departing from re&longs;t, goeth from time to time acquiring a greater degree of velocity, according as the &longs;aid time doth &longs;ucce&longs;&longs;ively encrea&longs;e; we may con­ ceive the &longs;paces AF, FH, HK, to repre&longs;ent unto us equal times; and the perpendiculars FG, HI, KL, degrees of velocity acquired in the &longs;aid times; &longs;o that the degree of velocity acquired in the whole time A K, is as the line K L, in re&longs;pect to the degree H I, acquired in the time AH, and the degree FG in the time AF; the which degrees KL, HI, FG, are (as is manife&longs;t) the &longs;ame in proportion, as the times K A, HA, F A, and if other perpendiculars were drawn from the points marked at plea&longs;ure in the line F A, one might &longs;ucce&longs;&longs;ively find de­ grees le&longs;&longs;e and le&longs;&longs;e in infinitum, proceeding towards the point A, repre&longs;enting the fir&longs;t in&longs;tant of time, and the fir&longs;t &longs;tate of re&longs;t. And this retreat towards A, repre&longs;enteth the fir&longs;t propen&longs;ion to the motion of de&longs;cent, dimini&longs;hed in infinitum by the approach of the moveable to the fir&longs;t &longs;tate of re&longs;t, which approximation is augmentable in infinitum. Now let us find the other diminution of velocity, which likewi&longs;e may proceed to infinity, by the di­ minution of the gravity of the moveable, and this &longs;hall be repre­ &longs;ented by drawing other lines from the point A, which contein angles le&longs;&longs;e than the angle B A E, which would be this line A D, the which inter&longs;ecting the parallels K L, H I, F G, in the points M, N, and O, repre&longs;ent unto us the degrees F O, H N, K M, acquired in the times A F, A H, A K, le&longs;&longs;e than the other de­ grees F G, H I, K L, acquired in the &longs;ame times; but the&longs;e latter by a moveable more ponderous, and tho&longs;e other by a moveable more light. And it is manife&longs;t, that by the retreat of the line E A towards A B, contracting the angle E A B (the which may be done in infinitum, like as the gravity may in infi­ nitum be dimini&longs;hed) the velocity of the cadent moveable may in like manner be dimini&longs;hed in infinitum, and &longs;o con&longs;equently the cau&longs;e that impeded the projection; and therefore my thinks that the union of the&longs;e two rea&longs;ons again&longs;t the projection, dimi­ ni&longs;hed to infinity, cannot be any impediment to the &longs;aid proje­ ction. And couching the whole argument in its &longs;horte&longs;t terms, we will &longs;ay, that by contracting the angle E A B, the degrees of ve­ locity L K, I H, G F, are dimini&longs;hed; and moreover by the re­ treat of the parallels K L, H I, F G, towards the angle A, the fame degrees are again dimini&longs;hed; and both the&longs;e diminutions extend to infinity: Therefore the velocity of the motion of de­ &longs;cent may very well dimini&longs;h &longs;o much, (it admitting of a two&longs;old diminution in infinitum) as that it may not &longs;uffice to re&longs;tore the moveable to the circumference of the wheel, and thereupon may occa&longs;ion the projection to be hindered and wholly obviated.

Again on the contrary, to impede the projection, it is nece&longs;­ &longs;ary that the &longs;paces by which the project is to de&longs;cend for the reuniting it &longs;elf to the Wheel, be made &longs;o &longs;hort and clo&longs;e toge­ ther, that though the de&longs;cent of the moveable be retarded, yea more, dimini&longs;hed in infinitum, yet it &longs;ufficeth to reconduct it thither: and therefore it would be requi&longs;ite, that you find out a diminuti­ on of the &longs;aid &longs;paces, not only produced to infinity, but to &longs;uch an infinity, as that it may &longs;uperate the double infinity that is made in the diminution of the velocity of the de&longs;cending moveable. But how can a magnitude be dimini&longs;hed more than another, which hath a twofold diminution in infinitum? Now let Simplicius ob­ &longs;erve how hard it is to philo&longs;ophate well in nature, without Geo­ metry. The degrees of velocity dimini&longs;hed in infinitum, as well by the diminution of the gravity of the moveable, as by the ap­ proxination to the fir&longs;t term of the motion, that is, to the &longs;tate of re&longs;t, are alwayes determinate, and an&longs;wer in proportion to the parallels comprehended between two right lines that concur in an angle, like to the angle B A E, or B A D, or any other infinitely more acute, alwayes provided it be rectilineall­ But the diminution of the &longs;paces thorow which the moveable is to be conducted along the circumference of the wheel, is propor­ tionate to another kind of diminution, comprehended between lines that contain an angle infinitely more narrow and acute, than any rectilineal angle, how acute &longs;oever, which is that in our pre­ &longs;ent ca&longs;e. Let any point be taken in the perpendicular A C, and making it the centre, de&longs;cribe at the di&longs;tance C A, an arch A M P, the which &longs;hall inter&longs;ect the parallels that determine the degrees of velocity, though they be very minute, and comprehended within a mo&longs;t acute rectilineal angle; of which parallels the parts that lie between the arch and the tangent A B, are the quantities of the &longs;paces, and of the returns upon the wheel, alwayes le&longs;&longs;er (and with greater proportion le&longs;&longs;er, by how much neerer they approach to the contact) than the &longs;aid parallels of which they are parts. The parallels comprehended between the right lines in retiring to­ wards the angle dimini&longs;h alwayes at the &longs;ame rate, as v.g. A H be­ ing divided in two equal parts in F, the parallel H I &longs;hall be dou­ ble to F G, and &longs;ub-dividing F A, in two equal parts, the paral­ lel produced from the point of the divi&longs;ion &longs;hall be the half of F G; and continuing the &longs;ub-divi&longs;ion in infinitum, the &longs;ub&longs;equent parallels &longs;hall be alwayes half of the next preceding; but it doth not &longs;o fall out in the lines intercepted between the tangent and the circumference of the circle: For if the &longs;ame &longs;ub-divi&longs;ion be made in F A; and &longs;uppo&longs;ing for example, that the parallel which cometh from the point H, were double unto that which commeth from F, this &longs;hall be more then double to the next following, and continually the neerer we come towards the contact A, we &longs;hall find the precedent lines contein the next following three, four, ten, an hundred, a thou&longs;and, an hundred thou&longs;and, an hundred millions of times, and more in infinitum. The brevity therefore of &longs;uch lines is &longs;o reduced, that it far exceeds what is requi&longs;ite to make the project, though never &longs;o light, return, nay more, continue unremoveable upon the circumference.

SAGR. I very well comprehend the whole di&longs;cour&longs;e, and upon what it layeth all its &longs;tre&longs;&longs;e, yet neverthele&longs;&longs;e methinks that he that would take pains to pur&longs;ue it, might yet &longs;tart &longs;ome further que&longs;tions, by &longs;aying, that of tho&longs;e two cau&longs;es which render the de&longs;cent of the moveable &longs;lower and &longs;lower in infinitum, it is mani­ fe&longs;t, that that which dependeth on the vicinity to the fir&longs;t term of the de&longs;cent, increa&longs;eth alwayes in the &longs;ame proportion, like as the parallels alwayes retain the &longs;ame proportion to each other, &c. but that the diminution of the &longs;ame velocity, dependent on the diminution of the gravity of the moveable (which vvas the &longs;econd cau&longs;e) doth al&longs;o ob&longs;erve the &longs;ame proportion, doth not &longs;o plainly appear, And vvho &longs;hall a&longs;&longs;ure us that it doth not proceed accor­ ding to the proportion of the lines intercepted between the &longs;ecant, and the circumference; or vvhether vvith a greater proportion?

SALV. I have a&longs;&longs;umed for a truth, that the velocities of movea­ bles de&longs;cending naturally, vvill follovv the proportion of their gra­ vities, with the favour of Simplicius, and of Ari&longs;totle, who doth in many places affirm the &longs;ame, as a propo&longs;ition manife&longs;t: You, in favour of my adver&longs;ary, bring the &longs;ame into que&longs;tion, and &longs;ay that its po&longs;&longs;ible that the velocity increa&longs;eth with greater propor­ tion, yea and greater in infinitum than that of the gravity; &longs;o that all that hath been &longs;aid falleth to the ground: For maintaining whereof, I &longs;ay, that the proportion of the velocities is much le&longs;&longs;e than that of the gravities; and thereby I do not onely &longs;upport but confirme the premi&longs;es. And for proof of this I appeal unto experience, which will &longs;hew us, that a grave body, howbeit thirty or fourty times bigger then another; as for example, a ball of lead, and another of &longs;ugar, will not move much more than twice as fa&longs;t. Now if the projection would not be made, albeit the ve­ locity of the cadent body &longs;hould dimini&longs;h according to the pro­ portion of the gravity, much le&longs;&longs;e would it be made &longs;o long as the velocity is but little dimini&longs;hed, by abating much from the gravi­ ty. But yet &longs;uppo&longs;ing that the velocity dimini&longs;heth with a propor­ tion much greater than that wherewith the gravity decrea&longs;eth, nay though it were the &longs;elf-&longs;ame wherewith tho&longs;e parallels conteined between the tangent and circumference do decrea&longs;e, yet cannot I &longs;ee any nece&longs;&longs;ity why I &longs;hould grant the projection of matters of never &longs;o great levity; yea I farther averre, that there could no &longs;uch projection follow, meaning alwayes of matters not properly and ab&longs;olutely light, that is, void of all gravity, and that of their own natures move upwards, but that de&longs;cend very &longs;lowly, and have very &longs;mall gravity. And that which moveth me &longs;o to think is, that the diminution of gravity, made according to the propor­ tion of the parallels between the tangent and the circumference, hath for its ultimate and highe&longs;t term the nullity of weight, as tho&longs;e parallels have for their la&longs;t term of their diminution the contact it &longs;elf, which is an indivi&longs;ible point: Now gravity never dimini&longs;heth &longs;o far as to its la&longs;t term, for then the moveable would cea&longs;e to be grave; but yet the &longs;pace of the rever&longs;ion of the project to the circumference is reduced to the ultimate minuity, which is when the moveable re&longs;teth upon the circumference in the very point of contact; &longs;o as that to return thither it hath no need of &longs;pace: and therefore let the propen&longs;ion to the motion of de&longs;cent be ne­ ver &longs;o &longs;mall, yet is it alwayes more than &longs;ufficient to reconduct the moveable to the circumference, from which it is di&longs;tant but its lea&longs;t &longs;pace, that is, nothing at all.

SAGR. Your di&longs;cour&longs;e, I mu&longs;t confe&longs;s, is very accurate; and yet no le&longs;s concluding than it is ingenuous; and it mu&longs;t be gran­ ted that to go about to handle natural que&longs;tions, without Geome­ try, is to attempt an impo&longs;&longs;ibility.

SALV. But Simplicius will not &longs;ay &longs;o; and yet I do not think that he is one of tho&longs;e Peripateticks that di&longs;&longs;wade their Di&longs;ciples from &longs;tudying the Mathematicks, as Sciences that vitiate the rea­ &longs;on, and render it le&longs;&longs;e apt for contemplation.

SIMP. I would not do &longs;o much wrong to Plato, but yet I may truly &longs;ay with Aristotle, that he too much lo&longs;t him&longs;elf in, and too much doted upon that his Geometry: for that in conclu&longs;ion the&longs;e Mathematical &longs;ubtilties Salviatus are true in ab&longs;tract, but applied to &longs;en&longs;ible and Phy&longs;ical matter, they hold not good. For the Mathematicians will very well demon&longs;trate for example, that Sphæratangit planum in puncto; a po&longs;ition like to that in di&longs;pute, but when one cometh to the matter, things &longs;ucceed quite another way. And &longs;o I may &longs;ay of the&longs;e angles of contact, and the&longs;e proportions; which all evaporate into Air, when they are applied to things material and &longs;en&longs;ible.

SALV. You do not think then, that the tangent toucheth the &longs;uperficies of the terre&longs;trial Globe in one point only?

SIMP. No, not in one &longs;ole point; but I believe that a right line goeth many tens and hundreds of yards touching the &longs;urface not onely of the Earth, but of the water, before it &longs;eparate from the &longs;ame.

SALV. But if I grant you this, do not you perceive that it ma­ keth &longs;o much the more again&longs;t your cau&longs;e? For if it be &longs;uppo&longs;ed that the tangent was &longs;eparated from the terre&longs;trial &longs;uperficies, yet it hath been however demon&longs;trated that by rea&longs;on of the great a­ cuity of the angle of contingence (if happily it may be call'd an angle) the project would not &longs;eparate from the &longs;ame; how much le&longs;&longs;e cau&longs;e of &longs;eparation would it have, if that angle &longs;hould be wholly clo&longs;ed, and the &longs;uperficies and the tangent become all one? Perceive you not that the Projection would do the &longs;ame thing up­ on the &longs;urface of the Earth, which is a&longs;much as to &longs;ay, it would do ju&longs;t nothing at all? You &longs;ee then the power of truth, which while you &longs;trive to oppo&longs;e it, your own a&longs;&longs;aults them&longs;elves uphold and defend it. But in regard that you have retracted this errour, I would be loth to leave you in that other which you hold, namely, that a material Sphere doth not touch a plain in one &longs;ole point: and I could wi&longs;h &longs;ome few hours conver&longs;ation with &longs;ome per&longs;ons conver&longs;ant in Geometry, might make you a little more intelligent among&longs;t tho&longs;e who know nothing thereof. Now to &longs;hew you how great their errour is who &longs;ay, that a Sphere v.g. of bra&longs;&longs;e, doth not touch a plain v.g. of &longs;teel in one &longs;ole point, Tell me what con­ ceipt you would entertain of one that &longs;hould con&longs;tantly aver, that the Sphere is not truly a Sphere.

The truth &longs;ometimes gaines &longs;trength by con­ tradiction.

SIMP. I would e&longs;teem him wholly devoid of rea&longs;on.

SALV. He is in the &longs;ame ca&longs;e who &longs;aith that the material Sphere doth not touch a plain, al&longs;o material, in one onely point; for to &longs;ay this is the &longs;ame, as to affirm that the Sphere is not a Sphere. And that this is true, tell me in what it is that you con&longs;titute the Sphere to con&longs;i&longs;t, that is, what it is that maketh the Sphere differ from all other &longs;olid bodies.

The sphere al­ though material, toucheth the mate­ rial plane but in one point onely.

SIMP. I believe that the e&longs;&longs;ence of a Sphere con&longs;i&longs;teth in ha­ ving all the right lines produced from its centre to the circumfe­ rence, equal.

The definition of the &longs;phere.

SALV. So that, if tho&longs;e lines &longs;hould not be equal, there &longs;ame &longs;olidity would be no longer a &longs;phere?

SIMP. True.

SALV. Go to; tell me whether you believe that among&longs;t the many lines that may be drawn between two points, that may be more than one right line onely.

SIMP. There can be but one.

SALV. But yet you under&longs;tand that this onely right line &longs;hall again of nece&longs;&longs;ity be the &longs;horte&longs;t of them all?

SIMP. I know it, and al&longs;o have a demon&longs;tration thereof, pro­ duced by a great Peripatetick Philo&longs;opher, and as I take it, if my memory do not deceive me, he alledgeth it by way of reprehending Archimedes, that &longs;uppo&longs;eth it as known, when it may be demon­ &longs;trated.

SALV. This mu&longs;t needs be a great Mathematician, that knew how to demon&longs;trate that which Archimedes neither did, nor could demon&longs;trate. And if you remember his demon&longs;tration, I would gladly hear it: for I remember very well, that Archimedes in his Books, de Sphærà & Cylindro, placeth this Propo&longs;ition among&longs;t the Po&longs;tulata; and I verily believe that he thought it demon&longs;trated.

SIMP. I think I &longs;hall remember it, for it is very ea&longs;ie and &longs;hort.

SALV. The di&longs;grace of Archimedes, and the honour of this Phi­ lo&longs;opher &longs;hall be &longs;o much the greater.

SIMP. I will de&longs;cribe the Figure of it. Between the points A and B, [in Fig. 5.] draw the right line A B, and the curve line A C B, of which we will prove the right to be the &longs;horter: and the proof is this; take a point in the curve-line, which let be C, and draw two other lines, A C and C B, which two lines together; are longer than the &longs;ole line A B, for &longs;o demon&longs;trateth Euelid. But the curve-line A C B, is greater than the two right-lines A C, and C B; therefore, à fortiori, the curve-line A C B, is much greater than the right line A B, which was to be demon&longs;trated.

The demon&longs;tra­ tion of a Peripate­ tick, to prove the right line to be the &longs;horte&longs;t of all lines.

The Paralogi&longs;m of the &longs;ame Peripa­ tetick, which pro­ veth ignotum per ignotius.

SALV. I do not think that if one &longs;hould ran&longs;ack all the Para­ logi&longs;ms of the world, there could be found one more commodious than this, to give an example of the mo&longs;t &longs;olemn fallacy of all fallacies, namely, than that which proveth ignotum per ignotius.

SIMP. How &longs;o?

SALV. Do you ask me how &longs;o? The unknown conclu&longs;ion which you de&longs;ire to prove, is it not, that the curved line A C B, is longer than the right line A B; the middle term which is taken for known, is that the curve-line A C B, is greater than the two lines A C and C B, the which are known to be greater than A B; And if it be unknown whether the curve-line be greater than the &longs;ingle right-line A B, &longs;hall it not be much more unknown whether it be greater than the two right lines A C & C B, which are known to be greater than the &longs;ole line A B, & yet you a&longs;&longs;ume it as known?

SIMP. I do not yet very well perceive wherein lyeth the fal­ lacy.

SALV. As the two right lines are greater than A B, (as may be known by Euclid) and in as much as the curve line is longer than the two right lines A C and B C, &longs;hall it not not be much greater than the &longs;ole right line A B?

SIMP. It &longs;hall &longs;o.

SALV. That the curve-line A C B, is greater than the right line A B, is the conclu&longs;ion more known than the middle term, which is, that the &longs;ame curve-line is greater than the two right­ lines A C and C B. Now when the middle term is le&longs;s known than the conclu&longs;ion, it is called a proving ignotum per ignotius. But to return to our purpo&longs;e, it is &longs;ufficient that you know the right line to be the &longs;horte&longs;t of all the lines that can be drawn be­ tween two points. And as to the principal conclu&longs;ion, you &longs;ay, that the material &longs;phere doth not touch the &longs;phere in one &longs;ole point. What then is its contact?

SIMP. It &longs;hall be a part of its &longs;uperficies.

SALV. And the contact likewi&longs;e of another &longs;phere equal to the fir&longs;t, &longs;hall be al&longs;o a like particle of its &longs;uperficies?

SIMP. There is no rea&longs;on vvhy it &longs;hould be othervvi&longs;e.

SALV. Then the tvvo &longs;pheres vvhich touch each other, &longs;hall touch vvith the tvvo &longs;ame particles of a &longs;uperficies, for each of them agreeing to one and the &longs;ame plane, they mu&longs;t of nece&longs;&longs;ity agree in like manner to each other. Imagine now that the two &longs;pheres

[in Fig. 6.] who&longs;e centres are A and B, do touch one another: and let their centres be conjoyned by the right line A B, which pa&longs;&longs;eth through the contact. It pa&longs;&longs;eth thorow the point C, and another point in the contact being taken as D, conjoyn the two right lines A D and B D, &longs;o as that they make the triangle A D B; of which the two &longs;ides A D and D B &longs;hall be equal to the other one A C B, both tho&longs;e and this containing two &longs;emidiameters, which by the definition of the &longs;phere are all equal: and thus the right line A B, drawn between the two centres A and B, &longs;hall not be the &longs;horte&longs;t of all, the two lines A D and D B being equal to it: which by your own conce&longs;&longs;ion is ab&longs;urd.

A demon &longs;tration that the &longs;phere tou­ cheth the plane but in one point.

SIMP. This demon&longs;tration holdeth in the ab&longs;tracted, but not in the material &longs;pheres.

SALV. In&longs;tance then wherein the fallacy of my argument con­ &longs;i&longs;teth, if as you &longs;ay it is not concluding in the material &longs;pheres, but holdeth good in the immaterial and ab&longs;tracted.

Why the &longs;phere in ab&longs;tract, toucheth the plane onely in one point, and not the material in conerete.

SIMP. The material &longs;pheres are &longs;ubject to many accidents, which the immaterial are free from. And becau&longs;e it cannot be, that a &longs;phere of metal pa&longs;&longs;ing along a plane, its own weight &longs;hould not &longs;o depre&longs;s it, as that the plain &longs;hould yield &longs;omewhat, or that the &longs;phere it &longs;elf &longs;hould not in the contact admit of &longs;ome impre&longs;&longs;i­ on. Moreover, it is very hard for that plane to be perfect, if for nothing el&longs;e, yet at lea&longs;t for that its matter is porous: and per­ haps it will be no le&longs;s difficult to find a &longs;phere &longs;o perfect, as that it hath all the lines from the centre to the &longs;uperficies, exactly equal.

SALV. I very readily grant you all this that you have &longs;aid; but it is very much be&longs;ide our purpo&longs;e: for whil&longs;t you go about to &longs;hew me that a material &longs;phere toucheth not a material plane in one point alone, you make u&longs;e of a &longs;phere that is not a &longs;phere, and of a plane that is not a plane; for that, according to what you &longs;ay, either the&longs;e things cannot be found in the world, or if they may be found, they are &longs;poiled in applying them to work the effect. It had been therefore a le&longs;s evil, for you to have granted the con­ clu&longs;ion, but conditionally, to wit, that if there could be made of matter a &longs;phere and a plane that were and could continue perfect, they would touch in one &longs;ole point, and then to have denied that any &longs;uch could be made.

SIMP. I believe that the propo&longs;ition of Philo&longs;ophers is to be under&longs;tood in this &longs;en&longs;e; for it is not to be doubted, but that the imperfection of the matter, maketh the matters taken in con­ crete, to di&longs;agree with tho&longs;e taken in ab&longs;tract.

SALV. What, do they not agree? Why, that which you your &longs;elf &longs;ay at this in&longs;tant, proveth that they punctually agree.

SIMP. How can that be?

SALV. Do you not &longs;ay, that through the imperfection of the matter, that body which ought to be perfectly &longs;pherical, and that plane which ought to be perfectly level, do not prove to be the &longs;ame in concrete, as they are imagined to be in ab&longs;tract?

SIMP. This I do affirm.

SALV. Then when ever in concrete you do apply a material Sphere

to a material plane, youapply an imperfect Sphere to an imperfect plane, & the&longs;e you &longs;ay do not touch only in one point. But I mu&longs;t tell you, that even in ab&longs;tract an immaterial Sphere, that is, not a perfect Sphere, may touch an immaterial plane, that is, not a per­ fect plane, not in one point, but with part of its &longs;uperficies, &longs;o that hitherto that which falleth out in concrete, doth in like manner hold true in ab&longs;tract. And it would be a new thing that the com­ putations and rates made in ab&longs;tract numbers, &longs;hould not after­ wards an&longs;wer to the Coines of Gold and Silver, and to the mer­ chandizes in concrete. But do you know Simplicius, how this commeth to pa&longs;&longs;e? Like as to make that the computations agree with the Sugars, the Silks, the Wools, it is nece&longs;&longs;ary that the accomptant reckon his tares of che&longs;ts, bags, and &longs;uch other things: So when the Geometricall Philo&longs;opher would ob&longs;erve in concrete the effects demon&longs;trated in ab&longs;tract, he mu&longs;t defalke the impedi­ ments of the matter, and if he know how to do that, I do a&longs;&longs;ure you, the things &longs;hall jump no le&longs;&longs;e exactly, than Arithmstical computations. The errours therefore lyeth neither in ab&longs;tract, nor in concrete, nor in Geometry, nor in Phy&longs;icks, but in the Calcula­ tor, that knoweth not how to adju&longs;t his accompts. Therefore if you had a perfect Sphere and plane, though they were material, you need not doubt but that they would touch onely in one point. And if &longs;uch a Sphere was and is impo&longs;&longs;ible to be procured, it was much be&longs;ides the purpo&longs;e to &longs;ay, Quod Sphæra ænea non tangit in puncto. Furthermore, if I grant you Simplicius, that in matter a figure cannot be procured that is perfectly &longs;pherical, or perfectly level: Do you think there may be had two materiall bodies, who&longs;e &longs;uperficies in &longs;ome part, and in &longs;ome &longs;ort are incurvated as irregularly as can be de&longs;ired?

Things are ex­ actly the &longs;ame in ab&longs;tract as in con­ crete.

SIMP. Of the&longs;e I believe that there is no want.

SALV. If &longs;uch there be, then they al&longs;o will touch in one &longs;ole point; for this contact in but one point alone is not the &longs;ole and peculiar priviledge of the perfect Sphere and perfect plane. Nay, he that &longs;hould pro&longs;ecute this point with more &longs;ubtil contemplations would finde that it is much harder to procure two bodies that touch with part of their &longs;nper&longs;icies, than with one point onely. For if two &longs;uperficies be required to combine well together, it is nece&longs;&longs;ary either, that they be both exactly plane, or that if one be convex, the other be concave; but in &longs;uch a manner concave, that the concavity do exactly an&longs;wer to the convexity of the other: the which conditions are much harder to be found, in regard of their too narrow determination, than tho&longs;e others, which in their ca&longs;uall latitude are infinite.

Contact in a &longs;in­ gle point is not pe­ culiar to the per­ fect Spheres onely? but belongeth to all curved figures.

It is more diffi­ cult to find Figures that touch with a part of their &longs;ur­ face, than in one &longs;ole point.

SIMP. You believe then, that two &longs;tones, or two pieces of I­ ron taken at chance, and put together, do for the mo&longs;t part touch in one &longs;ole point?

SALV. In ca&longs;ual encounters, I do not think they do; as well becau&longs;e for the mo&longs;t part there will be &longs;ome &longs;mall yielding filth upon them, as becau&longs;e that no diligence is u&longs;ed in applying them without &longs;triking one another; and every &longs;mall matter &longs;ufficeth to make the one &longs;uperficies yield &longs;omewhat to the other; &longs;o that they interchangeably, at lea&longs;t in &longs;ome &longs;mall particle, receive &longs;igure from the impre&longs;&longs;ion of each other. But in ca&longs;e their &longs;uperficies were very ter&longs;e and polite, and that they were both laid upon a table, that &longs;o one might not pre&longs;&longs;e upon the other, and gently put towards one another, I que&longs;tion not, but that they might be brought to the &longs;imple contact in one onely point.

SAGR. It is requi&longs;ite, with your permi&longs;&longs;ion, that I propound a certain &longs;cruple of mine, which came into my minde, whil'&longs;t I heard propo&longs;ed by Simplicius, the impo&longs;&longs;ibility of finding a materiall and &longs;olid body, that is, perfectly of a Spherical figure, and whil'&longs;t J law Salviatus in a certain manner, not gain&longs;aying, to give his con&longs;ent thereto; therefore I would know, whether there would be the &longs;ame difficulty in forming a &longs;olid of &longs;ome other figure, that is, to expre&longs;&longs;e my &longs;elf better, whether there is more difficulty in reducing a piece of Marble into the figure of a perfect Sphere, than into a perfect Pyramid, or into a perfect Hor&longs;e, or into a perfect Gra&longs;&longs;e-hopper?

SALV. To this I will make you the fir&longs;t an&longs;wer: and in the fir&longs;t place, I will acquit my &longs;elf of the a&longs;&longs;ent which you think I gave to Simplicius, which was only for a time; for I had it al&longs;o in my thoughts, betore I intended to enter upon any other matter, to &longs;peak that, which, it may be, is the &longs;ame, or very like to that which you are about to &longs;ay, And an&longs;wering to your fir&longs;t que&longs;tion, I &longs;ay, that if any figure can be given to a Solid, the Spherical is the ea&longs;i­ e&longs;t of all others, as it is likewi&longs;e the mo&longs;t &longs;imple, and holdeth the &longs;ame place among&longs;t &longs;olid figures, as the Circle holdeth among&longs;t the &longs;uperficial. The de&longs;cription of which Circle, as being more ea­ &longs;ie than all the re&longs;t, hath alone been judged by Mathematicians worthy to be put among&longs;t the ^{*} po&longs;tulata belonging to the de&longs;cri­ ption of all other figures. And the formation of the Sphere is &longs;o very ea&longs;ie, that if in a plain plate of hard metal you take an empty or hollow circle, within which any Solid goeth ca&longs;ually re­ volving that was before but gro&longs;ly rounded, it &longs;hall, without any other artifice be reduced to a Spherical figure, as perfect as is po&longs;­ &longs;ible for it to be; provided, that that &longs;ame Solid be not le&longs;&longs;e than the Sphere that would pa&longs;&longs;e thorow that Circle. And that which is yet more worthy of our con&longs;ideration is, that within the &longs;elf-&longs;ame incavity one may form Spheres of &longs;everal magnitudes. But what is required to the making of an Hor&longs;e, or (as you &longs;ay) of a Gra&longs;s­ hopper, I leave to you to judge, who know that there are but few &longs;tatuaries in the world able to undertake &longs;uch a piece of work. And I think that herein Simplicius will not di&longs;&longs;ent from me.

The Sphericall Figure is ea&longs;ier to be made than any other.

The circular Fi­ gure only is placed amongst the po&longs;tu­ lata of Mathema­ ticians.

* Demands or Petitions.

Sphericall Fi­ gures of &longs;undry magnitudes may be made with one onely in&longs;trument.

SIMP. I know not whether I do at all diffent from you; my opinion is this, that none of the afore-named figures can be per­ fectly obteined; but for the approaching as neer as is po&longs;&longs;ible to the mo&longs;t perfect degree, I believe that it is incomparably more ea­ &longs;ie to reduce the Solid into a Spherical figure, than into the &longs;hape of an Hor&longs;e, or Gra&longs;&longs;e-hopper?

SAGR. And this greater difficulty, wherein think you doth it depend?

SIMP. Like as the great facility in forming the Sphere ari&longs;eth from its ab&longs;olute &longs;implicity and uniformity &longs;o the great irregu­ larity rendereth the con&longs;truction of all other figures difficult.

Irregular forms difficult to be in­ troduced.

SAGR. Therefore the irregularity being the cau&longs;e of the diffi­ culty, than the figure of a &longs;tone broken with an hammer by chance, &longs;hall be one of the figures that are difficult to be introdu­ ced, it being perhaps more irregular than that of the hor&longs;e?

SIMP. So it &longs;hould be.

SAGR. But tell me; that figure what ever it is which the &longs;tone hath, hath it the &longs;ame in perfection, or no?

SIMP. What it hath, it hath &longs;o perfectly, that nothing can be more exact.

SAGR. Then, if of figures that are irregular, and con&longs;equent­ ly hard to be procured, there are yet infinite which are mo&longs;t per­ fectly obteined, with what rea&longs;on can it be &longs;aid, that the mo&longs;t &longs;imple, and con&longs;equently the mo&longs;t ea&longs;ie of all, is impo&longs;&longs;ible to be procured?

SALV. Gentlemen, with your favour, I may &longs;ay that we have &longs;allied out into a di&longs;pute not much more worth than the wool of a goat; and whereas our argumentations &longs;hould continually be con­ ver&longs;ant about &longs;erious and weighty points, we con&longs;ume our time in frivolous and impertinent wranglings. Let us call to minde, I pray you, that the &longs;earch of the worlds con&longs;titution, is one of the grea­ te&longs;t and noble&longs;t Problems that are in nature; and &longs;o much the greater, ina&longs;much as it is directed to the re&longs;olving of that other; to wit, of the cau&longs;e of the Seas ebbing and flowing, enquired in­ to by all the famous men, that have hitherto been in the world, and po&longs;&longs;ibly found out by none of them. Therefore if we have nothing more remaining for the full confutation of the argument taken from the Earths vertigo, which was the la&longs;t, alledged to prove its immobility upon its own centre, let us pa&longs;&longs;e to the ex­ amination of tho&longs;e things that are alledged for, and again&longs;t the Annual Motion.

The con&longs;titution of the Univer&longs;e is one of the mo&longs;t no­ ble Problems.

SAGR. I would not have you, Salviatus, mea&longs;ure our wits by the &longs;cale of yours: you, who u&longs;e to be continually bu&longs;ied about the &longs;ublime&longs;t contemplations, e&longs;teem tho&longs;e notions frivolous and below you, which we think matters worthy of our profounde&longs;t thoughts: yet &longs;ometimes for our &longs;atisfaction do not di&longs;dain to &longs;toop &longs;o low as to give way a little to our curio&longs;ity. As to the refutation of the la&longs;t argument, taken from the extru&longs;ions of the diurnal vertigo, far le&longs;s than what hath been &longs;aid, would have given me &longs;atisfaction: and yet the things &longs;uperfluou&longs;ly &longs;poken, &longs;eemed to me &longs;o ingenious, that they have been &longs;o far from wea­ rying my fancy, as that they have, by rea&longs;on of their novelty, en­ tertained me all along with &longs;o great delight, that I know not how to de&longs;ire greater: Therefore, if you have any other &longs;peculation to add, produce it, for I, as to my own particular, &longs;hall gladly hearken to it.

SALV. I have always taken great delight in tho&longs;e things which I have had the fortune to di&longs;cover, and next to that, which is my chief content, I find great plea&longs;ure in imparting them to &longs;ome friends, that apprehendeth and &longs;eemeth to like them: Now, in re­ gard you are one of the&longs;e, &longs;lacking a little the reins of my ambi­ tion, which is much plea&longs;ed when I &longs;hew my &longs;elf more per&longs;pi­ cacious, than &longs;ome other that hath the reputation of a &longs;harp &longs;ight, I will for a full and true mea&longs;ure of the pa&longs;t di&longs;pute, pro­ duce another fallacy of the Sectators of Ptolomey and Ari&longs;totle, which I take from the argument alledged.

SAGR. See how greedily I wait to hear it.

SALV. We have hitherto over-pa&longs;&longs;ed, and granted to Ptolomey, as an effect indubitable, that the extru&longs;ion of the &longs;tone proceed­ ing from the velocity of the wheel turn'd round upon its centre, the cau&longs;e of the &longs;aid extru&longs;ion encrea&longs;eth in proportion, as the ve­ locity of the vertigo (or whirling) is augmented: from whence it was inferred, that the velocity of the Earth's vertigo being very much greater than that of any machin what&longs;oever, that we can make to turn round artificially; the extru&longs;ion of &longs;tones, of animals, &c. would con&longs;equently be far more violent. Now, I ob&longs;erve that there is a great fallacy in this di&longs;cour&longs;e, in that we do compare the&longs;e velocities indifferently and ab&longs;olutely to one ano­ ther. It's true, that if I compare the velocities of the &longs;ame wheel, or of two wheels equal to each other, that which &longs;hall be more &longs;wiftly turn'd round, &longs;hall extrude the &longs;tone with greater vio­ lence; and the velocity encrea&longs;ing, the cau&longs;e of the projection &longs;hall likewi&longs;e encrea&longs;e: but when the velocity is augmented, not by encrea&longs;ing the velocity in the &longs;ame wheel, which would be by cau&longs;ing it to make a greater number of revolutions in equal times; but by encrea&longs;ing the diameter, and making the wheel greater, &longs;o as that the conver&longs;ion taking up the &longs;ame time in the le&longs;&longs;er wheel, as in the greater, the velocity is greater onely in the bigger wheel, for that its circumference is bigger; there is no man that thinketh that the cau&longs;e of the extru&longs;ion in the great wheel will encrea&longs;e ac­ cording to the proportion of the velocity of its circumference, to the velocity of the circumference of the other le&longs;&longs;er wheel; for that this is mo&longs;t fal&longs;e, as by a mo&longs;t expeditious experiment I &longs;hall thus gro&longs;ly declare: We may &longs;ling a &longs;tone with a &longs;tick of a yard long, farther than we can do with a &longs;tick &longs;ix yards long, though the motion of the end of the long &longs;tick, that is of the &longs;tone placed in the &longs;lit thereof, were more than double as &longs;wift as the mo­ tion of the end of the other &longs;horter &longs;tick, as it would be if the velocities were &longs;uch that the le&longs;&longs;er &longs;tick &longs;hould turn thrice round in the time whil&longs;t the greater is making one onely con­ ver&longs;ion.

The cau&longs;e of the projection increa&longs;­ eth not according to the proportion of the velocity, in­ crea&longs;ed by making the wheel bigger.

SAGR. This which you tell me, Salviatus, mu&longs;t, I &longs;ee, needs &longs;ucceed in this very manner; but I do not &longs;o readily apprehend the cau&longs;e why equal velocities &longs;hould not operate equally in extruding projects, but that of the le&longs;&longs;er wheel much more than the other of the greater wheel; therefore I intreat you to tell me how this cometh to pa&longs;s.

SIMP. Herein, Sagredus, you &longs;eem to differ much from your &longs;elf, for that you were wont to penetrate all things in an in&longs;tant, and now you have overlook'd a fallacy couched in the experiment of the &longs;tick, which I my &longs;elf have been able to di&longs;cover: and this is the different manner of operating, in making the projection one while with the &longs;hort &longs;ling and another while with the long one, for if you will have the &longs;tone fly out of the &longs;lit, you need not con­ tinue its motion uniformly, but at &longs;uch time as it is at the &longs;wifte&longs;t, you are to &longs;tay your arm, and &longs;top the velocity of the &longs;tick; where­ upon the &longs;tone which was in its &longs;wifte&longs;t motion, flyeth out, and moveth with impetuo&longs;ity: but now that &longs;top cannot be made in the great &longs;tick, which by rea&longs;on of its length and flexibility, doth not entirely obey the check of the arm, but continueth to accom­ pany the &longs;tone for &longs;ome &longs;pace, and holdeth it in with &longs;o much le&longs;s force, and not as if you had with a &longs;tiff &longs;ling &longs;ent it going with a jerk: for if both the &longs;ticks or &longs;lings &longs;hould be check'd by one and the &longs;ame ob&longs;tacle, I do believe they would fly a&longs;well out of the one, as out of the other, howbeit their motions were equally &longs;wift.

SAGR. With the permi&longs;&longs;ion of Salviatus, I will an&longs;wer &longs;ome­ thing to Simplicius, in regard he hath addre&longs;&longs;ed him&longs;elf to me; and I &longs;ay, that in his di&longs;cour&longs;e there is &longs;omewhat good and &longs;omewhat bad: good, becau&longs;e it is almo&longs;t all true; bad, becau&longs;e it doth not agree with our ca&longs;e: Truth is, that when that which carrieth the &longs;tones with velocity, &longs;hall meet with a check that is immoveable, they &longs;hall fly out with great impetuo­ &longs;ity: the &longs;ame effect following in that ca&longs;e, which we &longs;ee dayly to fall out in a boat that running a &longs;wift cour&longs;e, runs a-ground, or meets with &longs;ome &longs;udden &longs;top, for all tho&longs;e in the boat, being &longs;ur­ prized, &longs;tumble forwards, and fall towards the part whither the boat &longs;teered. And in ca&longs;e the Earth &longs;hould meet with &longs;uch a check, as &longs;hould be able to re&longs;i&longs;t and arre&longs;t its vertigo, then indeed I do believe that not onely bea&longs;ts, buildings and cities, but moun­ tains, lakes and &longs;eas would overturn, and the globe it &longs;elf would go near to &longs;hake in pieces; but nothing of all this concerns our pre&longs;ent purpo&longs;e, for we &longs;peak of what may follow to the motion of the Earth, it being turn'd round uniformly, and quietly about its own centre, howbeit with a great velocity. That likewi&longs;e which you &longs;ay of the &longs;lings, is true in part; but was not alledged by Salviatus, as a thing that punctually agreed with the matter whereof we treat, but onely, as an example, for &longs;o in gro&longs;s it may prompt us in the more accurate con&longs;ideration of that point, whe­ ther, the velocity increa&longs;ing at any rate, the cau&longs;e of the proje­ ction doth increa&longs;e at the &longs;ame rate: &longs;o that v. g. if a wheel of ten yards diameter, moving in &longs;uch a manner that a point of its circumference will pa&longs;s an hundred yards in a minute of an hour, and &longs;o hath an impetus able to extrude a &longs;tone, that &longs;ame impetus &longs;hall be increa&longs;ed an hundred thou&longs;and times in a wheel of a million of yards diameter; the which Salviatus denieth, and I incline to his opinion; but not knowing the rea&longs;on thereof, I have reque&longs;ted it of him, and &longs;tand impatiently expecting it.

Graming the di­ urnal vertigo of the Earth, & that by &longs;ome &longs;udden &longs;top or ob&longs;tacle it were arre&longs;ted, hou&longs;es, mountains them­ &longs;elves, and perhaps the whole Globe would be &longs;haken n pieces.

SALV. I am ready to give you the be&longs;t &longs;atisfaction, that my abilities will give leave: And though in my fir&longs;t di&longs;cour&longs;e you thought that I had enquired into things e&longs;tranged from our pur­ po&longs;e, yet neverthele&longs;&longs;e I believe that in the &longs;equel of the di&longs;pute, you will find that they do not prove &longs;o. Therefore let Sagredus tell me wherein he hath ob&longs;erved that the re&longs;i&longs;tance of any move­ able to motion doth con&longs;i&longs;t.

SAGR. I &longs;ee not for the pre&longs;ent that the moveable hath any internal re&longs;i&longs;tance to motion, unle&longs;&longs;e it be its natural inclination and propen&longs;ion to the contrary motion, as in grave bodies, that have a propen&longs;ion to the motion downwards, the re&longs;i&longs;tance is to the motion upwards; and I &longs;aid an internal re&longs;i&longs;tance, becau&longs;e of this, I think, it is you intend to &longs;peak, and not of the external re&longs;i&longs;tances, which are many and accidental.

SALV. It is that indeed I mean, and your nimblene&longs;&longs;e of wit hath been too hard for my craftine&longs;&longs;e, but if I have been too &longs;hort in asking the que&longs;tion, I doubt whether Sagredus hath been full enough in his an&longs;wer to &longs;atis&longs;ie the demand; and whether there be not in the moveable, be&longs;ides the natural inclination to the contrary term, another intrin&longs;ick and natural quality, which ma­ keth it aver&longs;e to motion. Therefore tell me again; do you not think that the inclination v. g. of grave bodies to move down­ wards, is equal to the re&longs;i&longs;tance of the &longs;ame to the motion of pro­ jection upwards?

The inclination of grave bodies to the motion downwards, is equal to their re&longs;i&longs;tance to the motion upwards.

SAGR. I believe that it is exactly the &longs;ame. And for this rea&longs;on I &longs;ee that two equal weights being put into a ballance, they do &longs;tand &longs;till in equilibrium, the gravity of the one re&longs;i&longs;ting its be­ ing rai&longs;ed by the gravity wherewith the other pre&longs;&longs;ing down­ wards would rai&longs;e it.

SALV. Very well; &longs;o that if you would have one rai&longs;e up the other, you mu&longs;t encrea&longs;e the weight of that which depre&longs;&longs;eth, or le&longs;&longs;en the weight of the other. But if the re&longs;i&longs;tance to a&longs;cend­ ing motion cun&longs;i&longs;t onely in gravity, how cometh it to pa&longs;&longs;e, that in ballances of unequal arms, to wit in the ^{*} Stiliard, a weight &longs;ometimes of an hundred pounds, with its pre&longs;&longs;ion downwards, doth not &longs;uffice to rai&longs;e up on of four pounds; that &longs;hall counter­ poi&longs;e with it, nay this of four, de&longs;cending &longs;hall rai&longs;e up that of an hundred; for &longs;uch is the effect of the pendant weight upon the weight which we would weigh? If the re&longs;i&longs;tance to motion re&longs;ideth onely in the gravity, how can the arm with its weight of four pounds onely, re&longs;i&longs;t the weight of a &longs;ack of wool, or bale of &longs;ilk, which &longs;hall be eight hundred, or a thou&longs;and weight; yea more, how can it overcome the &longs;ack with its moment, and rai&longs;e it up? It mu&longs;t therefore be confe&longs;t Sagredus, that here it maketh u&longs;e of &longs;ome other re&longs;i&longs;tance, and other force, be&longs;ides that of &longs;imple gravity.

* A portable bal­ lance wherewith market-people weigh their com­ modities, giving it gravity by remo­ ving the weight farther from the cock: call'd by the Latines, Campana trutina.

SAGR. It mu&longs;t needs be &longs;o; therefore tell me what this &longs;e­ cond virtue &longs;hould be.

SALV. It is that which was not in the ballance of equal arms; you &longs;ee then what variety there is in the Stiliard; and up­ on this doubtle&longs;&longs;e dependeth the cau&longs;e of the new effect.

SAGR. I think that your putting me to it a &longs;econd time, hath made me remember &longs;omething that may be to the purpo&longs;e. In both the&longs;e beams the bu&longs;ine&longs;s is done by the weight, and by the motion; in the ballance, the motions are equal, and therefore the one weight mu&longs;t exceed it in gravity before it can move it; in the &longs;tiliard, the le&longs;&longs;er weight will not move the greater, unle&longs;s when this latter moveth little, as being &longs;lung at a le&longs;&longs;er di&longs;tance, and the other much, as hanging at a greater di&longs;tance from the lacquet or cock. It is nece&longs;&longs;ary therefore to conclude, that the le&longs;&longs;er weight overcometh the re&longs;i&longs;tance of the greater, by moving much, whil&longs;t the other is moved but little.

SALV. Which is as much as to &longs;ay, that the velocity of the moveable le&longs;s grave, compen&longs;ateth the gravity of the moveable more grave and le&longs;s &longs;wift.

The greater velo­ city exactly com­ pen&longs;ates thegreater gravity.

SAGR. But do you think that the velocity doth fully make good the gravity? that is, that the moment and force of a move­ able of v. g. four pounds weight, is as great as that of one of an hundred weight, when&longs;oever that the fir&longs;t hath an hundred degrees of velocity, and the later but four onely?

SALV. Yes doubtle&longs;s, as I am able by many experiments to demon&longs;trate: but for the pre&longs;ent, let this onely of the &longs;tiliard &longs;uffice: in which you &longs;ee that the light end of the beam is then able to &longs;u&longs;tain and equilibrate the great Wool &longs;ack, when its di­ &longs;tance from the centre, upon which the &longs;tiliard re&longs;teth and turn­ eth, &longs;hall &longs;o much exceed the le&longs;&longs;er di&longs;tance, by how much the ab­ &longs;olute gravity of the Wool-&longs;ack exceedeth that of the pendent weight. And we &longs;ee nothing that can cau&longs;e this in&longs;ufficiencie in the great &longs;ack of Wool, to rai&longs;e with its weight the pendent weight &longs;o much le&longs;s grave, &longs;ave the di&longs;parity of the motions which the one and the other &longs;hould make, whil&longs;t that the Wool &longs;ack by de&longs;cending but one inch onely, will rai&longs;e the pendent weight an hundred inclies: (&longs;uppo&longs;ing that the &longs;ack did weigh an hundred times as much, and that the di&longs;tance of the &longs;mall weight from the centre of the beam were an hundred times greater, than the di­ &longs;tance between the &longs;aid centre and the point of the &longs;acks &longs;u&longs;pen&longs;i­ on.) And again, the pendent weight its moving the &longs;pace of an hundred inches, in the time that the &longs;ack moveth but one inch onely, is the &longs;ame as to &longs;ay, that the velocity of the motion of the little pendent weight, is an hundred times greater than the velo­ city of the motion of the &longs;ack. Now fix it in your belief, as a true and manife&longs;t axiom, that the re&longs;i&longs;tance which proceedeth from the velocity of motion, compen&longs;ateth that which dependeth on the gravity of another moveable: So that con&longs;equently, a move­ able of one pound, that moveth with an hundred degrees of ve­ locity, doth as much re&longs;i&longs;t all ob&longs;truction, as another moveable of an hundred weight, who&longs;e velocity is but one degree onely. And two equal moveables will equally re&longs;i&longs;t their being moved, if that they &longs;hall be moved with equal velocity: but if one be to be moved more &longs;wiftly than the other, it &longs;hall make greater re­ &longs;i&longs;tance, according to the greater velocity that &longs;hall be conferred on it. The&longs;e things being premi&longs;ed, let us proceed to the expla­ nation of our Problem; and for the better under&longs;tanding of things, let us make a &longs;hort Scheme thereof. Let two unequal wheels be de&longs;cribed about this centre A, [in Fig. 7.] and let the circumference of the le&longs;&longs;er be B G, and of the greater C E H, and let the &longs;emidiameter A B C, be perpendicular to the Horizon; and by the points B and C, let us draw the right lined Tangents B F and C D; and in the arches B G and C E, take two equal parts B G and C E: and let the two wheels be &longs;uppo&longs;ed to be turn'd round upon their centres with equal velocities, &longs;o as that two mo­ veables, which &longs;uppo&longs;e for example to be two &longs;tones placed in the points B and C, come to be carried along the circumferences B G and C E, with equal velocities; &longs;o that in the &longs;ame time that the &longs;tone B &longs;hall have run the arch B G, the &longs;tone C will have pa&longs;t the arch C E. I &longs;ay now, that the whirl or vertigo of the le&longs;&longs;er wheel is much more potent to make the projection of the &longs;tone B, than the vertigo of the bigger wheel to make that of the &longs;tone C. Therefore the projection, as we have already declared, being to be made along the tangent, when the &longs;tones B and C are to &longs;eparate from their wheels, and to begin the motion of projection from the points B and C, then &longs;hall they be extruded by the impetus con­ ceived from the vertigo by (or along) the tangents B F and C D. The two &longs;tones therefore have equal impetuo&longs;ities of running a­ long the tangents B F and C D, and would run along the &longs;ame, if they were not turn'd a&longs;ide by &longs;ome other force: is it not &longs;o Sa­ gredus?

SAGR. In my opinion the bu&longs;ine&longs;&longs;e is as you &longs;ay.

SALV. But what force, think you, &longs;hould that be which averts the &longs;tones from moving by the tangents, along which they are cer­ tainly driven by the impetus of the vertigo.

SAGR. It is either their own gravity, or el&longs;e &longs;ome glutinous matter that holdeth them fa&longs;t and clo&longs;e to the wheels.

SALV. But for the diverting of a moveable from the motion to which nature inciteth it, is there not required greater or le&longs;&longs;er force, according as the deviation is intended to be greater or le&longs;­ &longs;er? that is, according as the &longs;aid moveable in its deviation hath a greater or le&longs;&longs;er &longs;pace to move in the &longs;ame time?

SAGR. Yes certainly: for it was concluded even now, that to make a moveable to move; the movent vertue mu&longs;t be increa&longs;ed in proportion to the velocity wherewith it is to move.

SALV. Now con&longs;ider, that for the deviating the &longs;tone upon the le&longs;&longs;e wheel from the motion of projection, which it would make by the tangent B F, and for the holding of it fa&longs;t to the wheel, it is required, that its own gravity draw it back the whole length of the &longs;ecant F G, or of the perpendicular rai&longs;ed from the point G, to the line B F, whereas in the greater wheel the retracti­ on needs to be no more than the &longs;ecant D E, or the perpendicu­ lar let fall from the tangent D G to the point E, le&longs;&longs;e by much than F G, and alwayes le&longs;&longs;er and le&longs;&longs;er according as the wheel is made bigger. And fora&longs;much as the&longs;e retractions (as I may call them) are required to be made in equal times, that is, whil'&longs;t the wheels pa&longs;&longs;e the two equal arches B G and C E, that of the &longs;tone B, that is, the retraction F G ought to be more &longs;wift than the o­ ther D E; and therefore much greater force will be required for holding fa&longs;t the &longs;tone B to its little wheel, than for the holding the &longs;tone C to its great one, which is as much as to &longs;ay, that &longs;uch a &longs;mall thing will impede the extru&longs;ion in the great wheel, as will not at all hinder it in the little one. It is manife&longs;t therefore that the more the wheel augmenteth, the more the cau&longs;e of the pro­ jection dimini&longs;heth.

SAGR. From this which I now under&longs;tand, by help of your mi­ nute di&longs;&longs;ertation, I am induced to think, that I am able to &longs;atisfie my judgment in a very few words. For equal impetus being im­ pre&longs;&longs;ed on both the &longs;tones that move along the tangents, by the equal velocity of the two wheels, we &longs;ee the great circumference, by means of its &longs;mall deviation from the tangent, to go &longs;econding, as it were, and in a fair way refraining in the &longs;tone the appetite, if I may &longs;o &longs;ay, of &longs;eparating from the circumference; &longs;o that any &longs;mall retention, either of its own inclination, or of &longs;ome glutina­ tion &longs;ufficeth to hold it fa&longs;t to the wheel. Which, again, is not a­ ble to work the like effect in the little wheel, which but little pro­ &longs;ecuting the direction of the tangent, &longs;eeketh with too much ea­ gerne&longs;&longs;e to hold fa&longs;t the &longs;tone; and the re&longs;triction and glutination not being &longs;tronger than that which holdeth the other &longs;tone fa&longs;t to

the greater wheel, it ^{*} breaks loo&longs;e, and runneth along the tan­ gent. Therefore I do not only finde that all tho&longs;e have erred, who have believed the cau&longs;e of the projection to increa&longs;e accor­ ding to the augmentation of the vertigo's velocity; but I am further thinking, that the projection dimini&longs;hing in the inlarging of the wheel, &longs;o long as the &longs;ame velocity is reteined in tho&longs;e wheels; it may po&longs;&longs;ibly be true, that he that would make the great wheel extrude things like the little one, would be forced to increa&longs;e them as much in velocity, as they increa&longs;e in diameter, which he might do, by making them to fini&longs;h their conver&longs;ions in equal times; and thus we may conclude, that the Earths revolution or vertigo would be no more able to extrude &longs;tones, than any little wheel that goeth &longs;o &longs;lowly, as that it maketh but one turn in twen­ ty four hours.

* Strappar la ca­ vezza, is to break the bridle.

SALV. We will enquire no further into this point for the pre­ &longs;ent: let it &longs;uffice that we have abundantly (if I deceive not my &longs;elf) demon&longs;trated the invalidity of the argument, which at fir&longs;t &longs;ight &longs;eemed very concluding, and was &longs;o held by very famous men: and I &longs;hall think my time and words well be&longs;towed, if I have but gained &longs;ome belief in the opinion of Simplicius, I will not &longs;ay or the Earths mobility, but only that the opinion of tho&longs;e that believe it, is not &longs;o ridiculous and fond, as the rout of vulgar Philo&longs;ophers e&longs;teem it.

SIMP. The an&longs;wers hitherto produced again&longs;t the arguments brought again&longs;t this Diurnal Revolution of the Earth taken from grave bodies falling from the top of a Tower, and from proje­ ctions made perpendicularly upwards, or according to any inclina­ tion &longs;idewayes towards the Ea&longs;t, We&longs;t, North, South, &c. have &longs;omewhat abated in me the antiquated incredulity I had conceived again&longs;t that opinion: but other greater doubts run in my mind at this very in&longs;tant, which I know not in the lea&longs;t how to free my &longs;elf of, and haply you your &longs;elf will not be able to re&longs;olve them; nay, its po&longs;&longs;ible you may not have heard them, for they are very modern. And the&longs;e are the objections of two Authours, that ex profe&longs;&longs;o write again&longs;t Copernicus. Some of which are read in a little Tract of natural conclu&longs;ions; The re&longs;t are by a great both Philo&longs;opher and Mathematician, in&longs;erted in a Treati&longs;e which he hath written in favour of Aristotle, and his opinion touching the inalterability of the Heavens, where he proveth, that not onely the Comets, but al&longs;o the new &longs;tars, namely, that anno 1572. in Ca&longs;&longs;iopeia, and that anno 1604. in Sagittarius were not above the Spheres of the Planets, but ab&longs;olutely beneath the concave of the Moon in the Elementary Sphere, and this he demon&longs;trateth a­ gain&longs;t Tycho, Kepler, and many other Aftronomical Ob&longs;ervators, and beateth them at their own weapon; to wit, the Doctrine of Parallaxes. If you like thereof, I will give you the rea&longs;ons of both the&longs;e Authours, for I have read them more than once, with attention; and you may examine their &longs;trength, and give your opinion thereon.

Other objections of two modern Au­ thors against Co­ pernicus.

SALV. In regard that our principal end is to bring upon the &longs;tage, and to con&longs;ider what ever hath been &longs;aid for, or again&longs;t the two Sy&longs;temes, Ptolomaick, and Copernican, it is not good to omit any thing that hath been written on this &longs;ubject.

SIMP. I will begin therefore with the objections which I finde in the Treati&longs;e of Conclu&longs;ions, and afterwards proceed to the re&longs;t. In the fir&longs;t place then, he be&longs;toweth much paines in calcu­ lating exactly how many miles an hour a point of the terre&longs;trial Globe &longs;ituate under the Equinoctial, goeth, and how many miles are pa&longs;t by other points &longs;ituate in other parallels: and not being content with finding out &longs;uch motions in horary times, he findeth them al&longs;o in a minute of an hour; and not contenting him&longs;elf with a minute, he findes them al&longs;o in a &longs;econd minute; yea more, he goeth on to &longs;hew plainly, how many miles a Cannon bullet would go in the &longs;ame time, being placed in the concave of the Lu­ nar Orb, &longs;uppo&longs;ing it al&longs;o as big as Copernicus him&longs;elf repre&longs;enteth it, to take away all &longs;ubterfuges from his adver&longs;ary. And having made this mo&longs;t ingenious and exqui&longs;ite &longs;upputation, he &longs;heweth, that a grave body falling from thence above would con&longs;ume more than &longs;ix dayes in attaining to the centre of the Earth, to which all grave bodies naturally move. Now if by the ab&longs;olute Divine Power, or by &longs;ome Angel, a very great Cannon bullet were carri­ ed up thither, and placed in our Zenith or vertical point, and from thence let go at liberty, it is in his, and al&longs;o in my opinion, a mo&longs;t incredible thing that it, in de&longs;cending downwards, &longs;hould all the way maintain it &longs;elf in our vertical line, continuing to turn round with the Earth, about its centre, for &longs;o many dayes, de&longs;cribing under the Equinoctial a Spiral line in the plain of the great circle it &longs;elf: and under other Parallels, Spiral lines about Cones, and under the Poles falling by a &longs;imple right line. He, in the next place, &longs;tabli&longs;heth and confirmeth this great improbability by pro­ ving, in the way of interrogations, many difficulties impo&longs;&longs;ible to be removed by the followers of Copernicus; and they are, if I do well remember-----.

The fir&longs;t obje­ ction of the mo­ dern Author of the little tract of Conclu&longs;ions.

A Cannon bul­ let would &longs;pend more than &longs;ix days in falling from the Concave of the Moon to the cen­ tre of the Earth, according to the o­ pinion of that mo­ dern Author of the Conclu&longs;ions.

SALV. Take up a little, good Simplicius, and do not load me with &longs;o many novelties at once: I have but a bad memory, and therefore I mu&longs;t not go too fa&longs;t. And in regard it cometh into my minde, that I once undertook to calculate how long time &longs;uch a grave body falling from the concave of the Moon, would be in pa&longs;&longs;ing to the centre of the Earth, and that I think I remember that the time would not be &longs;o long; it would be fit that you &longs;hew us by what rule this Author made his calculation.

SIMP. He hath done it by proving his intent à fortiori, a &longs;uffi­ cient advantage for his adver&longs;aries, &longs;uppo&longs;ing that the velocity of the body falling along the vertical line, towards the centre of the Earth, were equal to the velocity of its circular motion, which it made in the grand circle of the concave of the Lunar Orb. Which by equation would come to pa&longs;&longs;e in an hour, twelve thou­ &longs;and &longs;ix hundred German miles, a thing which indeed &longs;avours of impo&longs;&longs;ibility: Yet neverthele&longs;&longs;e, to &longs;hew his abundant caution, and to give all advantages to his adver&longs;aries, he &longs;uppo&longs;eth it for true, and concludeth, that the time o&longs; the fall ought however to be more than &longs;ix dayes.

SALV. And is this the &longs;um of his method? And doth he by this demon&longs;tration prove the time of the fall to be above &longs;ix dayes?

SAGR. Me thinks that he hath behaved him&longs;elf too mode&longs;tly, for that having it in the power of his will to give what velocity he plea&longs;ed to &longs;uch a de&longs;cending body, and might a&longs;well have made it &longs;ix moneths, nay, &longs;ix years in falling to the Earth, he is content with &longs;ix dayes. But, good Salviatus, &longs;harpen my appetite a lit­ tle, by telling me in what manner you made your computation, in regard you &longs;ay, that you have heretofore ca&longs;t it up: for I am con­ fident that if the que&longs;tion had not required &longs;ome ingenuity in working it, you would never have applied your minde unto it.

SALV. It is not enough, Sagredus, that the &longs;ubjects be noble and great, but the bu&longs;ine&longs;&longs;e con&longs;i&longs;ts in handling it nobly. And who knoweth not, that in the di&longs;&longs;ection of the members of a bea&longs;t, there may be di&longs;covered infinite wonders of provident and prudent Nature; and yet for one, that the Anatomi&longs;t di&longs;­ &longs;ects, the butcher cuts up a thou&longs;and. Thus I, who am now &longs;eeking how to &longs;atisfie your demand, cannot tell with which of the two &longs;hapes I had be&longs;t to appear on the Stage; but yet, taking heart from the example of Simplicius, his Authour, I will, with­ out more delays, give you an account (if I have not forgot) how I proceeded. But before I go any further, I mu&longs;t not omit to tell you, that I much fear that Simplicius hath not faithfully related the manner how this his Authour found, that the Cannon bul­ let in coming from the concave of the Moon to the centre of the Earth, would &longs;pend more than fix dayes: for if he had &longs;uppo­ &longs;ed that its velocity in de&longs;cending was equal to that of the concave (as Simplicius &longs;aith he doth &longs;uppo&longs;e) he would have &longs;hewn him&longs;elf ignorant of the fir&longs;t, and more &longs;imple principles of Geometry; yea, I admire that Simplicius, in admitting the &longs;uppo&longs;ition which he &longs;peaketh of, doth not &longs;ee the mon&longs;trous ab­ &longs;urdity that is couched in it.

SIMP. Its po&longs;&longs;ible that I may have erred in relating it; but that I &longs;ee any fallacy in it, I am &longs;ure is not true.

SALV. Perhaps I did not rightly apprehend that which you &longs;aid, Do you not &longs;ay, that this Authour maketh the velocity of the bullet in de&longs;cending equall to that which it had in tur­ ning round, being in the concave of the Moon, and that com­ ming down with the &longs;ame velocity, it would reach to the centre in &longs;ix dayes?

SIMP. So, as I think, he writeth.

SALV. And do not you perceive a &longs;hamefull errour therein? But que&longs;tionle&longs;&longs;e you di&longs;&longs;emble it: For it cannot be, but that you &longs;hould know that the &longs;emidiameter of the Circle is le&longs;&longs;e than the &longs;ixth part of the circumference; and that con&longs;equently, the time in which the moveable &longs;hall pa&longs;&longs;e the &longs;emidiameter, &longs;hall be le&longs;&longs;e than the &longs;ixth part of the time; in which, being moved with the &longs;ame velocity, it would pa&longs;&longs;e the circumference; and that therefore the bullet de&longs;cending with the velocity, where­ with it moved in the concave, will arrive in le&longs;&longs;e than four hours at the centre, &longs;uppo&longs;ing that in the concave one revolution &longs;hould be con&longs;ummate in twenty four hours, as he mu&longs;t of ne­ ce&longs;&longs;ity have &longs;uppo&longs;ed it, for to keep it all the way in the &longs;ame vertical line.

A &longs;hamefull errour in the Ar­ gument taken from the bullets falling out of the Moons concave.

SIMP. Now I thorowly perceive the mi&longs;take: but yet I would not lay it upon him unde&longs;ervedly, for it's po&longs;&longs;ible that I may have erred in rehear&longs;ing his Argument, and to avoid running into the &longs;ame mi&longs;takes for the future, I could wi&longs;h I had his Book; and if you had any body to &longs;end for it, I would take it for a great favour.

SAGR. You &longs;hall not want a Lacquey that will runne for it with all &longs;peed: and he &longs;hall do it pre&longs;ently, without lo&longs;ing any time; in the mean time Salviatus may plea&longs;e to oblige us with his computation.

SIMP. If he go, he &longs;hall finde it lie open upon my Desk, together with that of the other Author, who al&longs;o argueth a­ gain&longs;t Copernicus.

SAGR. We will make him bring that al&longs;o for the more cer­ tainty: and in the interim Salviatus &longs;hall make his calculation: I have di&longs;patch't away a me&longs;&longs;enger.

SALV. Above all things it mu&longs;t be con&longs;idered, that the motion of de&longs;cending grave bodies is not uniform, but departing from re&longs;t they go continually accelerating: An effect known and ob­ &longs;erved by all men, unle&longs;&longs;e it be by the forementioned modern Au­ thour, who not &longs;peaking of acceleration, maketh it even and u­ niforme. But this general notion is of no avail, if it be not known according to what proportion this increa&longs;e of velocity is made; a conclu&longs;ion that hath been until our times unknown to all Philo&longs;o­ phers; and was fir&longs;t found out & demon&longs;trated by the ^{*} Academick, our common friend, who in &longs;ome of his ^{*} writings not yet publi&longs;h­ ed, but in familiarity &longs;hewn to me, and &longs;ome others of his ac­ quaintance he proveth, how that the acceleration of the right mo­ tion of grave bodies, is made according to the numbers uneven beginning ab unitate, that is, any number of equal times being a&longs;­ &longs;igned, if in the fir&longs;t time the moveable departing from re&longs;t &longs;hall have pa&longs;&longs;ed &longs;uch a certain &longs;pace, as for example, an ell, in the &longs;e­ cond time it &longs;hall have pa&longs;&longs;ed three ells, in the third five, in the fourth &longs;even, and &longs;o progre&longs;&longs;ively, according to the following odd numbers; which in &longs;hort is the &longs;ame, as if I &longs;hould &longs;ay, that the &longs;paces pa&longs;&longs;ed by the moveable departing from its re&longs;t, are unto each other in proportion double to the proportion of the times, in which tho&longs;e &longs;paces are mea&longs;ured; or we will &longs;ay, that the &longs;paces pa&longs;&longs;ed are to each other, as the &longs;quares of their times.

An exact com­ pute of the time of the fall of the Ca­ non bullet from the Moons concave to the Earths centre.

* The Author.

* By the&longs;e Wri­ tings, he every where meanes his Dialogues, De mo­ tu, which I promi&longs;e to give you in my &longs;econd Volume.

Acceleration of the natural motion of grave bodies is made according to the odde numbers beginning at unity.

The &longs;paces pa&longs;t by the falling grave body are as the &longs;quares of their times.

SAGR. This is truly admirable: and do you &longs;ay that there is a Mathematical demon&longs;tration for it?

SALV. Yes, purely Mathematical; and not onely for this, but for many other very admirable pa&longs;&longs;ions, pertaining to natural mo­ tions, and to projects al&longs;o, all invented, and demon&longs;trated by Our Friend, and I have &longs;een and con&longs;idered them all to my very great content and admiration, &longs;eeing a new compleat Doctrine to &longs;pring up touching a &longs;ubject, upon which have been written hundreds of Volumes; and yet not &longs;o much as one of the infinite admirable conclu&longs;ions that tho&longs;e his writings contain, hath ever been ob­ &longs;erved, or under&longs;tood by any one, before Our Friend made them out.

An intire and new Science of the Academick concer­ ning local motion.

SAGR. You make me lo&longs;e the de&longs;ire I had to under&longs;tand more in our di&longs;putes in hand, onely that I may hear &longs;ome of tho&longs;e demon&longs;trations which you &longs;peak of; therefore either give them me pre&longs;ently, or at lea&longs;t promi&longs;e me upon your word, to appoint a particular conference concerning them, at which Sim­ plicius al&longs;o may be pre&longs;ent, if he &longs;hall have a mind to hear the pa&longs;&longs;ions and accidents of the primary effect in Nature.

SIMP. I &longs;hall undoubtedly be much plea&longs;ed therewith, though indeed, as to what concerneth Natural Philo&longs;ophy, I do not think that it is nece&longs;&longs;ary to de&longs;cend unto minute particularities, a gene­ ral knowledg of the definition of motion, and of the di&longs;tin­ ction of natural and violent, even and accelerate, and the like, &longs;ufficing: For if this were not &longs;ufficient, I do not think that Ari­ &longs;totle would have omitted to have taught us what ever more was nece&longs;&longs;ary.

SALV. It may be &longs;o. But let us not lo&longs;e more time about this, which I promi&longs;e to &longs;pend half a day apart in, for your &longs;atis­ faction; nay, now I remember, I did promi&longs;e you once before to &longs;atisfie you herein. Returning therefore to our begun calcula­ tion of the time, wherein the grave cadent body would pa&longs;s from the concave of the Moon to the centre of the Earth, that we may not proceed arbitrarily and at randon, but with a Logical method, we will fir&longs;t attempt to a&longs;certain our &longs;elves by experiments often repeated, in how long time a ball v. g. of Iron de&longs;cendeth to the Earth from an altitude of an hundred yards.

SAGR. Let us therefore take a ball of &longs;uch a determinate weight, and let it be the &longs;ame wherewith we intend to make the computation of the time of de&longs;cent from the Moon.

SALV. This is not material, for that a ball of one, of ten, of an hundred, of a thou&longs;and pounds, will all mea&longs;ure the &longs;ame hundred yards in the &longs;ame time.

SIMP. But this I cannot believe, nor much le&longs;s doth Ari&longs;totle think &longs;o, who writeth, that the velocities of de&longs;cending grave bodies, are in the &longs;ame proportion to one another, as their gra­ vities.

SALV. If you will admit this for true, Simplicius, you mu&longs;t be­ lieve al&longs;o, that two balls of the &longs;ame matter, being let fall in the &longs;ame moment, one of an hundred pounds, and another of one, from an altitude of an hundred yards, the great one arriveth at the ground, before the other is de&longs;cended but one yard onely: Now bring your fancy, if you can, to imagine, that you &longs;ee the great ball got to the ground, when the little one is &longs;till within le&longs;s than a yard of the top of the Tower.

The error of Ari­ &longs;totle in affirming, falling grave bo­ dies to move accor­ ding to the propor­ tion of their gravi­ ties.

SAGR. That this propo&longs;ition is mo&longs;t fal&longs;e, I make no doubt in the world; but yet that yours is ab&longs;olutely true, I cannot well a&longs;&longs;ure my &longs;elf: neverthele&longs;s, I believe it, &longs;eeing that you &longs;o re­ &longs;olutely affirm it; which I am &longs;ure you would not do, if you had not certain experience, or &longs;ome clear demon&longs;tration thereof.

SALV. I have both: and when we &longs;hall handle the bu&longs;ine&longs;s of motions apart, I will communicate them: in the interim, that we may have no more occa&longs;ions of interrupting our di&longs;cour&longs;e, we will &longs;uppo&longs;e, that we are to make our computation upon a ball of Iron of an hundred (a) pounds, the which by reiterated experi­ ments de&longs;cendeth from the altitude of an hundred (b) yards, in five &longs;econd-minutes of an hour. And becau&longs;e, as we have &longs;aid, the &longs;paces that are mea&longs;ured by the cadent moveable, increa&longs;e in double proportion; that is, according to the &longs;quares of the times, being that the time of one fir&longs;t-minute is duodecuple to the time of five &longs;econds, if we multiply the hundred yards by the &longs;quare of 12, that is by 144, we &longs;hall have 14400, which &longs;hall be the num­ ber of yards that the &longs;ame moveable &longs;hall pa&longs;s in one fir&longs;t-minute of an hour: and following the &longs;ame rule becau&longs;e one hour is 60 minutes, multiplying 14400, the number of yards pa&longs;t in one mi­ nute, by the &longs;quare of 60, that is, by 3600, there &longs;hall come forth 51840000, the number of yards to be pa&longs;&longs;ed in an hour, which make 17280 miles. And de&longs;iring to know the &longs;pace that the &longs;aid ball would pa&longs;s in 4 hours, let us multiply 17280 by 16, (which is the &longs;quare of 4) and the product will be 276480 miles: which number is much greater than the di&longs;tance from the Lunar concave to the centre of the Earth, which is but 196000 miles, making the di&longs;tance of the concave 56 &longs;emidiameters of the Earth, as that mo­ dern Author doth; and the &longs;emidiameter of the Earth 3500 miles, of 3000 ^{*}Braces to a †mile, which are our Italian miles.

(a) (b) Note that the&longs;e Calculations are made in Itali­ an weights and mea&longs;ures. And 100 pounds Haverdu­ poi&longs;e make 131 l. Florentine. And 100 Engli&longs;h yards makes 150 2/5 Braces Florent. &longs;o that the brace or yard of our Author is 3/4 of cur yard.

* The Italian mea­ &longs;ure which I com­ monly tran&longs;l te yards.

Therefore, Simplicius, that &longs;pace from the concave of the Moon to the centre of the Earth, which your Accomptant &longs;aid could not be pa&longs;&longs;ed under more than &longs;ix days, you &longs;ee that (computing by experience, and not upon the fingers ends) that it &longs;hall be pa&longs;­ &longs;ed in much le&longs;s than four hours; and making the computation exact, it &longs;hall be pa&longs;&longs;ed by the moveable in 3 hours, 22 min. prim. and 4 &longs;econds.

† The Italian mile is 1000/1056 of our mile.

SAGR. I be&longs;eech you, dear Sir, do not defraud me of this ex­ act calculation, for it mu&longs;t needs be very excellent.

SALV. So indeed it is: therefore having (as I have &longs;aid) by diligent tryal ob&longs;erved, that &longs;uch a moveable pa&longs;&longs;eth in its de&longs;cent, the height of 100 yards in 5 &longs;econds of an hour, we will &longs;ay, if 100 yards are pa&longs;&longs;ed in 5 &longs;econds; in how many &longs;econds &longs;hall 588000000 yards (for &longs;o many are in 56 diameters of the Earth) be pa&longs;&longs;ed? The rule for this work is, that the third number mu&longs;t be multiplied by the &longs;quare of the &longs;econd, of which doth come 14700000000, which ought to be divided by the fir&longs;t, that is, by 100, and the root &longs;quare of the quotient, that is, 12124 is the number &longs;ought, namely 12124 min. &longs;ecun. of an hour, which are 3 hours, 22 min. prim. and 4 &longs;econds.

SAGR. I have &longs;een the working, but I know nothing of the rea&longs;on for &longs;o working, nor do I now think it a time to ask it.

SALV. Yet I will give it, though you do not ask it, becau&longs;e it is very ea&longs;ie. Let us mark the&longs;e three numbers with the Letters A fir&longs;t, B &longs;econd, C

third. A and C are the numbers of the &longs;paces, B is the number of the time; the fourth number is &longs;ought, of the time al&longs;o. And becau&longs;e we know, that look what proportion the &longs;pace A, hath to the &longs;puace C, the &longs;ame proportion &longs;hall the &longs;quare of the time B have to the &longs;qare of the time, which is &longs;ought. Therefore by the Golden Rule, let the number C be multi­ plied by the &longs;quare of the number B, and let the product be di­ vided by the number A, and the quotient &longs;hall be the &longs;quare of the number &longs;ought, and its &longs;quare root &longs;hall be the number it &longs;elf that is &longs;ought. Now you &longs;ee how ea&longs;ie it is to be under&longs;tood.

SAGR. So are all truths, when once they are found out, but the difficulty lyeth in finding them. I very well apprehend it, and kindly thank you. And if there remain any other curio&longs;ity touching this point, I pray you let us hear it; for if I may &longs;peak my mind, I will with the favour of Simplicius, that from your di&longs;cour&longs;es I al­ wayes learn &longs;ome new motion, but from tho&longs;e of his Philo&longs;o­ phers, I do not remember that I have learn't any thing of mo­ ment.

SALV. There might be much more &longs;aid touching the&longs;e local motions; but according to agreement, we will re&longs;erve it to a par­ ticular conference, and for the pre&longs;ent I will &longs;peak &longs;omething touching the Author named by Simplicius, who thinketh he hath given a great advantage to the adver&longs;e party in granting that, that Canon bullet in falling from the concave of the Moon may de­ &longs;cend with a velocity equal to the velocity wherewith it would turn round, &longs;taying there above, and moving along with the di­ urnal conver&longs;ion. Now I tell him, that that &longs;ame ball falling from the concave unto the centre, will acquire a degree of velocity much more than double the velocity of the diurnal motion of the Lunar concave; and this I will make out by &longs;olid and not imper­ tinent &longs;uppo&longs;itions. You mu&longs;t know therefore that the grave body falling and acquiring all the way new velocity according to the proportion already mentioned, hath in any what&longs;oever place of the line of its motion &longs;uch a degree of velocity, that if it &longs;hould continue to move therewith, uniformly without farther encrea&longs;ing it; in another time like to that of its de&longs;cent, it would pa&longs;&longs;e a &longs;pace double to that pa&longs;&longs;ed in the line of the precedent motion of de&longs;cent. And thus for example, if that ball in coming from the concave of the Moon to its centre hath &longs;pent three hours, 22 min. prim. and 4 &longs;econds, I &longs;ay, that being arrived at the cen­ tre, it &longs;hall find it &longs;elf con&longs;tituted in &longs;uch a degree of velocity, that if with that, without farther encrea&longs;ing it, it &longs;hould continue to move uniformly, it would in other 3 hours, 22 min. prim. and 4 &longs;econds, pa&longs;&longs;e double that &longs;pace, namely as much as the whole diameter of the Lunar Orb; and becau&longs;e from the Moons con­ cave to the centre are 196000 miles, which the ball pa&longs;&longs;eth in 3 hours 22 prim. min. and 4 &longs;econds, therefore (according to what hath been &longs;aid) the ball continuing to move with the velocity which it is found to have in its arrival at the centre, it would pa&longs;&longs;e in other 3 hours 22 min. prim. and 4 &longs;econds, a &longs;pace dou­ ble to that, namely 392000 miles; but the &longs;ame continuing in the concave of the Moon, which is in circuit 1232000 miles, and moving therewith in a diurnal motion, it would make in the &longs;ame time, that is in 3 hours 22 min. prim. and 4 &longs;econds, 172880 miles, which are fewer by many than the half of the 392000 miles. You &longs;ee then that the motion in the concave is not as the modern Author &longs;aith, that is, of a velocity impo&longs;&longs;ible for the fall­ ing ball to partake of, &c.

The falling move­ able if it move with a degree of veloci­ ty acquired in a like time with an uniform motion, it &longs;hall paß a &longs;pace double to that pa&longs;­ &longs;ed with the acce­ leratedmotion.

SAGR. The di&longs;cour&longs;e would pa&longs;s for current, and would give me full &longs;atisfaction, if that particular was but &longs;alved, of the mo­ ving of the moveable by a double &longs;pace to that pa&longs;&longs;ed in falling in another time equal to that of the de&longs;cent, in ca&longs;e it doth continue to move uniformly with the greate&longs;t degree of velocity acquired in de&longs;cending. A propo&longs;ition which you al&longs;o once before &longs;uppo­ &longs;ed as true, but never demon&longs;trated.

SALV. This is one of the demon&longs;trations of Our Friend, and you &longs;hall &longs;ee it in due time; but for the pre&longs;ent, I will with &longs;ome conjectures (not teach you any thing that is new, but) remember you of a certain contrary opinion, and &longs;hew you, that it may haply &longs;o be. A bullet of lead hanging in a long and fine thread fa&longs;tened to the roof, if we remove it far from perpendicularity, and then let it go, have you not ob&longs;erved that, it declining, will pa&longs;s freely, and well near as far to the other &longs;ide of the perpendicular?

SAGR. I have ob&longs;erved it very well, and find (e&longs;pecially if the plummet be of any con&longs;iderable weight) that it ri&longs;eth &longs;o little le&longs;s than it de&longs;cended, &longs;o that I have &longs;ometimes thought, that the a­ &longs;cending arch is equal to that de&longs;cending, and thereupon made it a que&longs;tion whether the vibrations might not perpetuate them&longs;elves; and I believe that they might, if that it were po&longs;&longs;ible to remove the impediment of the Air, which re&longs;i&longs;ting penetration, doth &longs;ome &longs;mall matter retard and impede the motion of the pendulum, though indeed that impediment is but &longs;mall: in favour of which opinion the great number of vibrations that are made before the moveable wholly cea&longs;eth to move, &longs;eems to plead.

The motion of grave penduli might be perpetua­ ted, impediments being removed.

SALV. The motion would not be perpetual, Sagredus, al­ though the impediment of the Air were totally removed, becau&longs;e there is another much more ab&longs;tru&longs;e.

SAGR. And what is that? as for my part I can think of no other?

SALV. You will be plea&longs;ed when you hear it, but I &longs;hall not tell it you till anon: in the mean time, let us proceed. I have propo&longs;ed the ob&longs;ervation of this Pendulum, to the intent, that you &longs;hould under&longs;tand, that the impetus acquired in the de&longs;cending arch, where the motion is natural, is of it &longs;elf able to drive the &longs;aid ball with a violent motion, as far on the other &longs;ide in the like a&longs;cending arch; if &longs;o, I &longs;ay, of it &longs;elf, all external impediments being removed: I believe al&longs;o that every one takes it for granted, that as in the de&longs;cending arch the velocity all the way increa&longs;eth, till it come to the lowe&longs;t point, or its perpendicularity; &longs;o from this point, by the other a&longs;cending arch, it all the wav dimini&longs;heth, untill it come to its extreme and highe&longs;t point: and dimini&longs;hing with the &longs;ame proportions, where with it did before increa&longs;e, &longs;o that the dgrees of the velocities in the points equidi&longs;tant from the point of perpendicularity, are equal to each other. Hence it &longs;eemeth to me (arguing with all due mode&longs;ty) that I might ea&longs;ily be induced to believe, that if the Terre&longs;trial Globe were bored thorow the centre, a Canon bullet de&longs;cending through that Well, would ac­ quire by that time it came to the centre, &longs;uch an impul&longs;e of velo­ city, that, it having pa&longs;&longs;ed beyond the centre, would &longs;pring it up­ wards the other way, as great a &longs;pace, as that was wherewith it had de&longs;cended, all the way beyond the centre dimini&longs;hing the velocity with decrea&longs;ements like to the increa&longs;ements acquired in the de­ &longs;cent: and the time &longs;pent in this &longs;econd motion of a&longs;cent, I be­ lieve, would be equal to the time of de&longs;cent. Now if the move­ able by dimini&longs;hing that its greate&longs;t degree of velocity which it had in the centre, &longs;ucce&longs;&longs;ively until it come to total extinction, do carry the moveable in &longs;uch a time &longs;uch a certain &longs;pace, as it had gone in &longs;uch a like quantity of time, by the acqui&longs;t of velocity from the total privation of it until it came to that its greate&longs;t degree; it &longs;eemeth very rea&longs;onable, that if it &longs;hould move always with the &longs;aid greate&longs;t degree of velocity it would pa&longs;s, in &longs;uch another quantity of time, both tho&longs;e &longs;paces: For if we do but in our mind &longs;ucce&longs;&longs;ively divide tho&longs;e velocities into ri&longs;ing and falling degrees, as v. g. the&longs;e numbers in the margine; &longs;o that the fir&longs;t &longs;ort unto 10 be &longs;uppo&longs;ed the increa&longs;ing velocities, and the others unto 1, be the decrea&longs;ing; and let tho&longs;e of the time of the de&longs;cent, and the others of the time of the a&longs;cent being added all together, make as many, as if one of the two &longs;ums of them had been all of the greate&longs;t degrees, and therefore the whole &longs;pace pa&longs;&longs;ed by all the degrees of the increa&longs;ing veloci­ ties, and decrea&longs;ing, (which put together is the whole diame­ ter) ought to be equal to the &longs;pace pa&longs;&longs;ed by the greate&longs;t velo­ cities, that are in number half the aggregate of the increa&longs;ing and decrea&longs;ing velocities. I know that I have but ob&longs;curely expre&longs;&longs;ed my &longs;elf, and I wi&longs;h I may be under&longs;tood.

If the Terre&longs;trial Globe were perfo­ rated, a grave bo­ dy de&longs;cending by that bore, would paß and a&longs;cend as far beyond the cen­ tre, as it did de­ &longs;cend.

SAGR. I think I under&longs;tand you very well; and al&longs;o that I can in a few words &longs;hew, that I do under&longs;tand you. You had a mind to &longs;ay, that the motion begining from re&longs;t, and all the way increa&longs;ing the velocity with equal augmentations, &longs;uch as are tho&longs;e of continuate numbers begining at 1, rather at 0, which repre&longs;enteth the &longs;tate of re&longs;t, di&longs;po&longs;ed as in the margine: and continued at plea&longs;ure, &longs;o as that the lea&longs;t degree may be 0, and the greate&longs;t v. g. 5, all the&longs;e degrees of velocity wherewith the moveable is moved, make the &longs;um of 15; but if the moveable &longs;hould move with as many degrees in number as the&longs;e are, and each of them equal to the bigge&longs;t, which is 5, the aggregate of all the&longs;e la&longs;t velocities would be double to the others, namely 30. And therefore the moveable moving with a like time, but with uniform velocity, which is that of the highe&longs;t degree 5, ought to pa&longs;s a &longs;pace double to that which it pa&longs;&longs;eth in the accelerate time, which beginneth at the &longs;tate of re&longs;t.

SALV. According to your quick and piercing way of appre­ hending things, you have explained the whole bu&longs;ine&longs;s with more plainne&longs;s than I my &longs;elf; and put me al&longs;o in mind of adding &longs;ome­ thing more: for in the accelerate motion, the augmentation be­ ing continual, you cannot divide the degrees of velocity, which continually increa&longs;e, into any determinate number, becau&longs;e chan­ ging every moment, they are evermore infinite. Therefore we &longs;hall be the better able to exemplifie our intentions by de&longs;cribing a Triangle, which let be this A B C, [in Fig. 8.] taking in the &longs;ide A C, as many equal parts as we plea&longs;e, A D, D E, E F, F G, and drawing by the points D, E, F, G, right lines parallel to the ba&longs;e B C. Now let us imagine the parts marked in the line A C, to be equal times, and let the parallels drawn by the points D, E, F, G, repre&longs;ent unto us the degrees of velocity accelerated, and increa&longs;­ ing equally in equal times; and let the point A be the &longs;tate of re&longs;t, from which the moveable departing, hath v. g. in the time A D, acquired the degree of velocity D H, in the &longs;econd time we will &longs;uppo&longs;e, that it hath increa&longs;ed the velocity from D H, as far as to E I, and &longs;o &longs;uppo&longs;ing it to have grown greater in the &longs;ucceeding times, according to the increa&longs;e of the lines F K, G L, &c. but becau&longs;e the acceleration is made continually from moment to mo­ ment, and not disjunctly from one certain part of time to another; the point A being put for the lowe&longs;t moment of velocity, that is, for the &longs;tate of re&longs;t, and A D for the fir&longs;t in&longs;tant of time follow­ ing; it is manife&longs;t, that before the acqui&longs;t of the degree of velocity D H, made in the time A D, the moveable mu&longs;t have pa&longs;t by infinite other le&longs;&longs;er and le&longs;&longs;er degrees gained in the infinite in&longs;tants that are in the time D A, an&longs;wering the infinite points that are in the line D A; therefore to repre&longs;ent unto us the infinite degrees of velocity that precede the degree D H, it is nece&longs;&longs;ary to imagine infinite lines &longs;ucce&longs;&longs;ively le&longs;&longs;er and le&longs;&longs;er, which are &longs;uppo&longs;ed to be drawn by the infinite points of the line D A, and parallels to D H, the which infinite lines repre&longs;ent unto us the &longs;uperficies of the Triangle A H D, and thus we may imagine any &longs;pace pa&longs;&longs;ed by the moveable, with a motion which begining at re&longs;t, goeth uni­ formly accelerating, to have &longs;pent and made u&longs;e of infinite degrees of velocity, increa&longs;ing according to the infinite lines that begin­ ing from the point A, are &longs;uppo&longs;ed to be drawn parallel to the line H D, and to the re&longs;t I E, K F, L G, the motion continuing as far as one will.

The acceleration of grave bodies na­ turally de&longs;cendent, increa&longs;eth from moment to moment.

Now let us compleat the whole Parallelogram A M B C, and let us prolong as far as to the &longs;ide thereof B M, not onely the Parallels marked in the Triangle, but tho&longs;e infinite others imagined to be drawn from all the points of the &longs;ide A C; and like as B C, was the greate&longs;t of tho&longs;e infinite parallels of the Triangle, repre&longs;ent­ ing unto us the greate&longs;t degree of velocity acquired by the move­ able in the accelerate motion, and the whole &longs;uperficies of the &longs;aid Triangle, was the ma&longs;s and &longs;um of the whole velocity, wherewith in the time A C it pa&longs;&longs;ed &longs;uch a certain &longs;pace, &longs;o the parallelogram is now a ma&longs;s and aggregate of a like number of degrees of ve­ locity, but each equal to the greate&longs;t B C, the which ma&longs;s of ve­ locities will be double to the ma&longs;s of the increa&longs;ing velocities in the Triangle, like as the &longs;aid Parallelogram is double to the Tri­ angle: and therefore if the moveable, that falling did make u&longs;e of the accelerated degrees of velocity, an&longs;wering to the triangle A B C, hath pa&longs;&longs;ed in &longs;uch a time &longs;uch a &longs;pace, it is very rea&longs;onable and probable, that making u&longs;e of the uniform velocities an&longs;wering to the parallelogram, it &longs;hall pa&longs;&longs;e with an even motion in the &longs;ame time a &longs;pace double to that pa&longs;&longs;ed by the accelerate mo­ tion.

SAGR. I am entirely &longs;atisfied. And if you call this a probable Di&longs;cour&longs;e, what &longs;hall the nece&longs;&longs;ary demon&longs;trations be? I wi&longs;h that in the whole body of common Philo&longs;ophy, I could find one that was but thus concludent.

In natural Sci­ ences it is not ne­ ce&longs;&longs;ary to &longs;eek Ma­ thematicall evi­ dence.

SIMP. It is not nece&longs;&longs;ary in natural Philo&longs;ophy to &longs;eek exqui­ &longs;ite Mathematical evidence.

SAGR. But this point of motion, is it not a natural que&longs;tion? and yet I cannot find that Ari&longs;totle hath demon&longs;trated any the lea&longs;t accident of it. But let us no longer divert our intended Theme, nor do you fail, I pray you Salviatus, to tell me that which you hinted to me to be the cau&longs;e of the Pendulum's qui­ e&longs;cence, be&longs;ides the re&longs;i&longs;tance of the Medium ro penetration.

SALV. Tell me; of two penduli hanging at unequal di&longs;tan­ ces, doth not that which is fa&longs;tned to the longer threed make its vibrations more &longs;eldome?

The pendulum hanging at a long­ er threed, maketh its vibrations more &longs;eldome than the pendulum hanging at a &longs;horter threed.

SAGR. Yes, if they be moved to equall di&longs;tances from their perpendicularity.

SALV. This greater or le&longs;&longs;e elongation importeth nothing at all, for the &longs;ame pendulum alwayes maketh its reciprocations in e­ quall times, be they longer or &longs;horter, that is, though the pendulum

be little or much removed from its perpendicularity, and if they are not ab&longs;olutely equal, they are in&longs;en&longs;ibly different, as expe­ rience may &longs;hew you: and though they were very unequal, yet would they not di&longs;countenance, but favour our cau&longs;e. There­ fore let us draw the perpendicular A B [in Fig. 9.] and hang from the point A, upon the threed A C, a plummet C, and another up­ on the &longs;ame threed al&longs;o, which let be E, and the threed A C, being removed from its perpendicularity, and then letting go the plum­ mets C and E, they &longs;hall move by the arches C B D, E G F, and the plummet E, as hanging at a le&longs;&longs;er di&longs;tance, and withall, as (by what you &longs;aid) le&longs;&longs;e removed, will return back again fa&longs;ter, and make its vibrations more frequent than the plummet C, and therefore &longs;hall hinder the &longs;aid plummet C, from running &longs;o much farther towards the term D, as it would do, if it were free: and thus the plummet E bringing unto it in every vibration continuall impediment, it &longs;hall finally reduce it to quie&longs;cence. Now the &longs;ame threed, (taking away the middle plummet) is a compo&longs;ition of many grave penduli, that is, each of its parts is &longs;uch a pendu­ lum fa&longs;tned neerer and neerer to the point A, and therefore di&longs;po­ &longs;ed to make its vibrations &longs;ucce&longs;&longs;ively more and more frequent; and con&longs;equently is able to bring a continual impediment to the plummet C; and for a proof that this is &longs;o, if we do but ob&longs;erve the thread A C, we &longs;hall &longs;ee it di&longs;tended not directly, but in an arch; and if in&longs;tead of the thread we take a chain, we &longs;hall di&longs;­ cern the effect more per&longs;ectly; and e&longs;pecially removing the gra­ vity C, to a con&longs;iderable di&longs;tance from the perpendicular A B, for that the chain being compo&longs;ed of many loo&longs;e particles, and each of them of &longs;ome weight, the arches A E C, and A F D, will appear notably incurvated. By rea&longs;on therefore, that the parts of the chain, according as they are neerer to the point A, de&longs;ire to make their vibrations more frequent, they permit not the lower parts of the &longs;aid chain to &longs;wing &longs;o far as naturally they would: and by continual detracting from the vibrations of the plummet C, they finally make it cea&longs;e to move, although the impediment of the air might be removed.

The vibrations of the &longs;ame pen­ dulum are made with the &longs;ame fre­ quency, whether they be &longs;mall or great.

The cau&longs;e which impedeth the pen­ dulum, and redu­ ceth it to re&longs;t.

The thread or chain to which a pendulum is fa&longs;t­ ned, maketh an arch, and doth not &longs;tretch it &longs;elfe &longs;treight out in its vibrations.

SAGR. The books are now come; here take them Simplicius, and find the place you are in doubt of.

SIMP. See, here it is where he beginneth to argue again&longs;t the diurnal motion of the Earth, he having fir&longs;t confuted the annual. Motus terræ annuus a&longs;&longs;errere Copernicanos cogit conver&longs;ionem e­ ju&longs;dem quotidianam; alias idem terræ Hemi&longs;phærium continenter ad Solem e&longs;&longs;et conver&longs;um obumbrato &longs;emper aver&longs;o. [In Engli&longs;h thus:] The annual motion of the Earth doth compell the Co­ pernicans to a&longs;&longs;ert the daily conver&longs;ion thereof; otherwi&longs;e the &longs;ame Hemi&longs;phere of the Earth would be continually turned to­ wards the Sun, the &longs;hady &longs;ide being always aver&longs;e. And &longs;o one half of the Earth would never come to &longs;ee the Sun.

SALV. I find at the very &longs;ir&longs;t &longs;ight, that this man hath not rightly apprehended the Copernican Hypothe&longs;is, for if he had but taken notice how he alwayes makes the Axis of the terre&longs;trial Globe perpetually parallel to it &longs;elf, he would not have &longs;aid, that one half of the Earth would never &longs;ee the Sun, but that the year would be one entire natural day, that is, that thorow all parts of the Earth there would be &longs;ix moneths day, and &longs;ix moneths night, as it now befalleth to the inhabitants under the Pole, but let this mi&longs;take be forgiven him, and let us come to what remai­ neth.

SIMP. It followeth, Hanc autem gyrationem Terræ im­ po&longs;&longs;ibilem e&longs;&longs;e &longs;ic demon&longs;tramus. Which &longs;peaks in Engli&longs;h thus: That this gyration of the Earth is impo&longs;&longs;ible we thus demon&longs;trate. That which en&longs;ueth is the declaration of the following figure, wherein is delineated many de&longs;cending grave bodies, and a&longs;cend­ ing light bodies, and birds that fly too and again in the air, &c.

SAGR. Let us &longs;ee them, I pray you. Oh! what fine figures, what birds, what balls, and what other pretty things are here?

SIMP. The&longs;e are balls which come from the concave of the Moon.

SAGR. And what is this?

SIMP. This is a kind of Shell-fi&longs;h, which here at Venice they call buovoli; and this al&longs;o came from the Moons concave.

SAGR. Indeed, it &longs;eems then, that the Moon hath a great pow­ er over the&longs;e Oy&longs;ter-fi&longs;hes, which we call ^{*} armed &longs;i&longs;bes.

* Pe&longs;ci armai, or armati.

SIMP. And this is that calculation, which I mentioned, of this Journey in a natural day, in an hour, in a fir&longs;t minute, and in a &longs;econd, which a point of the Earth would make placed under the Equinoctial, and al&longs;o in the parallel of 48 gr. And then followeth this, which I doubted I had committed &longs;ome mi&longs;take in reciting, therefore let us read it. His po&longs;itis, nece&longs;&longs;e est, terra circulariter mota, omnia ex aëre eidem, &c. Quod &longs;i ha&longs;ce pilas æquales po­ nemus pondere, magnitudine, gravitate, & in concavo Sphæræ Lu­ naris po&longs;itas libero de&longs;cen&longs;ui permittamus, &longs;i motum deor&longs;um æque­ mus celeritate motui circum, (quod tamen &longs;ecus e&longs;t, cum pila A, &c.) elabentur minimum (ut multum cedamus adver&longs;ariis) dies &longs;ex: quo tempore &longs;exies circa terram, &c. [In Engli&longs;b thus.] The&longs;e things being &longs;uppo&longs;ed, it is nece&longs;&longs;ary, the Earth being cir­ cularly moved, that all things from the air to the &longs;ame, &c. So that if we &longs;uppo&longs;e the&longs;e balls to be equal in magnitude and gra­ vity, and being placed in the concave of the Lunar Sphere, we permit them a free de&longs;cent, and if we make the motion down­ wards equal in velocity to the motion about, (which neverthele&longs;s is otherwi&longs;e, if the ball A, &c.) they &longs;hall be falling at lea&longs;t (that we may grant much to our adver&longs;aries) &longs;ix dayes; in which time they &longs;hall be turned &longs;ix times about the Earth, &c.

SALV. You have but too faithfully cited the argument of this per&longs;on. From hence you may collect Simplicius, with what cau­ tion they ought to proceed, who would give them&longs;elves up to be­ lieve others in tho&longs;e things, which perhaps they do not believe them&longs;elves. For me thinks it a thing impo&longs;&longs;ible, but that this Au­ thor was advi&longs;ed, that he did de&longs;ign to him&longs;elf a circle, who&longs;e dia­ meter (which among&longs;t Mathematicians, is le&longs;&longs;e than one third part of the circumference) is above 72 times bigger than it &longs;elf: an errour that affirmeth that to be con&longs;iderably more than 200, which is le&longs;&longs;e than one.

SAGR. It may be, that the&longs;e Mathematical proportions, which are true in ab&longs;tract, being once applied in concrete to Phy&longs;ical and Elementary circles, do not &longs;o exactly agree: And yet, I think, that the Cooper, to find the &longs;emidiameter of the bottom, which he is to fit to the Cask, doth make u&longs;e of the rule of Mathematicians in ab&longs;tract, although &longs;uch bottomes be things meerly material, and concrete: therefore let Simplicius plead in excu&longs;e of this Author; and whether he chinks that the Phy&longs;icks can differ &longs;o very much from the Mathematicks.

SIMP. The &longs;ub&longs;tractions are in my opinion in&longs;ufficient to &longs;alve this difference, which is &longs;o extreamly too great to be reconciled: and in this ca&longs;e I have no more to &longs;ay but that, Quandoque bonus dormitet Homerus. But &longs;uppo&longs;ing the calculation of ^{*} Salviatus to be more exact, and that the time of the de&longs;cent of the ball were no more than three hours; yet me thinks, that coming from the concave of the Moon, which is &longs;o great a di&longs;tance off, it would be an admirable thing, that it &longs;hould have an in&longs;tinct of maintain­ ing it &longs;elf all the way over the &longs;elf-&longs;ame point of the Earth, over which it did hang in its departure thence and not rather be left a very great way behind.

* Not Sagre­ dus, as the Latine ha hit.

SALV. The effect may be admirable, and not admirable, but natural and ordinary, according as the things precedent may fall out. For if the ball (according to the Authors &longs;uppo&longs;itions) whil&longs;t it &longs;taid in the concave of the Moon, had the circular motion of twenty four hours together with the Earth, and with the re&longs;t of the things contained within the &longs;aid Concave; that very vertue which made it turn round before its de&longs;cent, will continue it in the &longs;ame motion in its de&longs;cending. And &longs;o far it is from not keep­ ing pace with the motion of the Earth, and from &longs;taying behind, that it is more likely to out-go it; being that in its approaches to the Earth, the motion of gyration is to be made with circles con­ tinually le&longs;&longs;er and le&longs;&longs;er; &longs;o that the ball retaining in it &longs;elf that &longs;elf-&longs;ame velocity which it had in the concave, it ought to antici­ pate, as I have &longs;aid, the vertigo or conver&longs;ion of the Earth. But if the ball in the concave did want that circulation, it is not obli­ ged in de&longs;cending to maintain it &longs;elf perpendicularly over that point of the Earth, which was ju&longs;t under it when the de&longs;cent be­ gan. Nor will Copernicus, or any of his followers affirm the &longs;ame.

SIMP. But the Author maketh an objection, as you &longs;ee, de­ manding on what principle this circular motion of grave and light bodies, doth depend: that is, whether upon an internal or an ex­ ternal principle.

SALV. Keeping to the Probleme of which we &longs;peak, I &longs;ay, that that very principle which made the ball turn round, whil'&longs;t it was in the Lunar concave, is the &longs;ame that maintaineth al&longs;o the circulation in the de&longs;cent: yet I leave the Author at liberty to make it internal or external at his plea&longs;ure.

SIMP. The Author proveth, that it can neither be inward nor outward.

SALV. And I will &longs;ay then, that the ball in the concave did not move, and &longs;o he &longs;hall not be bound to &longs;hew how that in de&longs;­ cending it continueth all the way vertically over one point, for that it will not do any &longs;uch thing.

SIMP. Very well; But if grave bodies, and light can have no principle, either internal or external of moving circularly, than neither can the terre&longs;trial Globe move with a circular motion: and thus you have the intent of the Author.

SALV. I did not &longs;ay, that the Earth had no principle, either interne, or externe to the motion of gyration, but I &longs;ay, that I do not know which of the two it hath; and yet my not knowing it hath not a power to deprive it of the &longs;ame; but if this Author can tell by what principle other mundane bodies are moved round, of who&longs;e motion there is no doubt; I &longs;ay, that that which ma­ keth the Earth to move, is a vertue, like to that, by which Mars and Jupiter are moved, and wherewith he believes that the &longs;tarry Sphere it &longs;elf al&longs;o doth move; and if he will but a&longs;&longs;ure me, who is the mover of one of the&longs;e moveables, I will undertake to be able to tell him who maketh the Earth to move. Nay more; I will undertake to do the &longs;ame, if he can but tell me, who moveth the parts of the Earth downwards.

SIMP. The cau&longs;e of this is mo&longs;t manife&longs;t, and every one knows that it is gravity.

SALV. You are out, Simplicius, you &longs;hould &longs;ay, that every one knowes, that it is called Gravity: but I do not que&longs;tion you about the name, but the e&longs;&longs;ence of the thing, of which e&longs;&longs;ence you know not a tittle more than you know the e&longs;&longs;ence of the mover of the &longs;tars in gyration; unle&longs;&longs;e it be the name that hath been put to this, and made familiar, and dome&longs;tical, by the many experiences which we &longs;ee thereof every hour in the day,: but not as if we really under&longs;tand any more, what principle or vertue that is which moveth a &longs;tone downwards, than we know who moveth it upwards, when it is &longs;eparated from the projicient, or who mo­ veth the Moon round, except (as I have &longs;aid) onely the name, which more particularly and properly we have a&longs;&longs;igned to the mo­ tion of de&longs;cent, namely, Gravity; whereas for the cau&longs;e of cir­ cular motion, in more general termes, we a&longs;&longs;ign the Vertue impre&longs;­ &longs;ed, and call the &longs;ame an Intelligence, either a&longs;&longs;i&longs;ting, or informing; and to infinite other motions we a&longs;cribe Nature for their cau&longs;e.

We know no more who moveth grave bodies downwards; than who moveth the Stars round, nor know we any thing of the&longs;e cau­ &longs;es, more than the names impo&longs;ed on them by us.

SIMP. It is my opinion, that this Author asketh far le&longs;&longs;e than that, to which you deny to make an&longs;wer; for he doth not ask what is nominally and particularly the principle that moveth grave and light bodies circularly, but what&longs;oever it be, he de&longs;i­ reth to know, whether you think it intrin&longs;ecal, or extrin&longs;ecal: For howbeit, v. gr. I do not know, what kind of thing that gravity is, by which the Earth de&longs;cendeth; yet I know that it is an intern principle, &longs;eeing that if it be not hindered, it moveth &longs;pontane­ ou&longs;ly: and on the contrary, I know that the principle which mo­ veth it upwards, is external, although that I do not know, what thing that vertue is, impre&longs;&longs;ed on it by the projicient.

SALV. Into how many que&longs;tions mu&longs;t we excurre, if we would decide all the difficulties, which &longs;ucce&longs;&longs;ively have dependance one upon another! You call that an external (and you al&longs;o call it a preternatural and violent) principle, which moveth the grave pro­ ject upwards; but its po&longs;&longs;ible that it may be no le&longs;&longs;e interne and natural, than that which moveth it downwards; it may peradven­ ture be called external and violent, &longs;o long as the moveable is joy­ ned to the projicient; but being &longs;eparated, what external thing remaineth for a mover of the arrow, or ball? In &longs;umme, it mu&longs;t nece&longs;&longs;arliy be granted, that that vertue which carrieth &longs;uch a move­ able upwards, is no le&longs;&longs;e interne, than that which moveth it down­ wards; and I think the motion of grave bodies a&longs;cending by the impetus conceived, to be altogether as natural, as the motion of de&longs;cent depending on gravity.

The vertue which carrieth grave pro­ jects upwards, is no le&longs;&longs;e natural to them, than the gravity which mo­ veth them down­ wards.

SIMP. I will never grant this; for the motion of de&longs;cent hath its principle internal, natural, and perpetual, and the motion of a&longs;cent hath its principle externe, violent, and finite.

SALV. If you refu&longs;e to grant me, that the principles of the motions of grave bodies downwards and upwards, are equally in­ ternal and natural; what would you do, if I &longs;hould &longs;ay, that they may al&longs;o be the &longs;ame in number?

Contrary prin­ ciples cannot natu­ rally re&longs;ide in the &longs;ame &longs;ubject.

SIMP. I leave it to you to judge.

SALV. But I de&longs;ire you your &longs;elf to be the Judge: Therefore tell me, Do you believe that in the &longs;ame natural body, there may re&longs;ide interne principles, that are contrary to one another?

SIMP. I do verily believe there cannot.

SALV. What do you think to be the natural inclination of Earth, of Lead, of Gold, and in &longs;um, of the mo&longs;t ponderous mat­ ters; that is, to what motion do you believe that their interne principle draweth them?

SIMP. To that towards the centre of things grave, that is, to the centre of the Univer&longs;e, and of the Earth, whither, if they be not hindered, it will carry them.

SALV. So that, if the Terre&longs;trial Globe were bored thorow, and a Well made that &longs;hould pa&longs;&longs;e through the centre of it, a Cannon bullet being let fall into the &longs;ame, as being moved by a natural and intrin&longs;ick principle, would pa&longs;&longs;e to the centre; and it would make all this motion &longs;pontaneou&longs;ly, and by intrin&longs;ick prin­ ciple, is it not &longs;o?

SIMP. So I verily believe.

SALV. But when it is arrived at the centre, do you think that it will pa&longs;&longs;e any further, or el&longs;e that there it would immediately &longs;tand &longs;till, and move no further?

SIMP. I believe that it would continue to move a great way further.

SALV. But this motion beyond the centre, would it not be up­ wards, and according to your a&longs;&longs;ertion preternatural, and violent? And yet on what other principle do you make it to depend, but only upon the &longs;elf &longs;ame, which did carry the ball to the centre, and which you called intrin&longs;ecal, and natural? Finde, if you can, another external projicient, that overtaketh it again to drive it upwards. And this that hath been &longs;aid of the motion thorow the centre, is al&longs;o &longs;een by us here above; for the interne impetus of a grave body falling along a declining &longs;uperficies, if the &longs;aid &longs;uperficies be reflected the other way, it &longs;hall carry it, without a jot interrupting the motion, al&longs;o upwards. A ball of lead that hangeth by a thread, being removed from its perpendicularity, de­ &longs;cendeth &longs;pontaneou&longs;ly, as being drawn by its internal inclination, and without any interpo&longs;ure of re&longs;t, pa&longs;&longs;eth beyond the lowe&longs;t point of perpendicularity: and without any additional mover, moveth upwards. I know that you will not deny, but that the principle of grave bodies that moveth them downwards, is no le&longs;s natural, and intrin&longs;ecal, than that principle of light bodies, which moveth them upwards: &longs;o that I propo&longs;e to your con&longs;ideration a ball of lead, which de&longs;cending through the Air from a great al­ titude, and &longs;o moving by an intern principle, and comming to a depth of water, continueth its de&longs;cent, and without any other ex­ terne mover, &longs;ubmergeth a great way; and yet the motion of de&longs;cent in the water is preternatural unto it; but yet neverthele&longs;s dependeth on a principle that is internal, and not external to the ball. You &longs;ee it demon&longs;trated then, that a moveable may be moved by one and the &longs;ame internal principle, with contrary mo­ tions.

The natural mo­ tion changeth it &longs;elfe into that which is called pre­ ternatural and vi­ olent.

SIMP. I believe there are &longs;olutions to all the&longs;e objections, though for the pre&longs;ent I do not remember them; but however it be, the Author continueth to demand, on what principle this cir­ cular motion of grave and light bodies dependeth; that is, whe­ ther on a principle internal, or external; and proceeding for­ wards, &longs;heweth, that it can be neither on the one, nor on the other, &longs;aying; Si ab externo; Deu&longs;ne illum excitat per continuum mira­ culum? an verò Angelus, an aër? Et hunc quidem multi a&longs;&longs;ig­ nant. Sed contra----[In Engli&longs;h thus] If from an externe prin­ ciple; Whether God doth not excite it by a continued Miracle? or an Angel, or the Air? And indeed many do a&longs;&longs;ign this. But on the contrary-----.

SALV. Trouble not your &longs;elf to read his argument; for I am none of tho&longs;e who a&longs;cribe that principle to the ambient air. As to the Miracle, or an Angel, I &longs;hould rather incline to this &longs;ide; for that which taketh beginning from a Divine Miracle, or from an Angelical operation; as for in&longs;tance, the tran&longs;portation of a Can­ non ball or bullet into the concave of the Moon, doth in all pro­ bability depend on the vertue of the &longs;ame principle for perform­ ing the re&longs;t. But, as to the Air, it &longs;erveth my turn, that it doth not hinder the circular motion of the moveables, which we did &longs;uppo&longs;e to move thorow it. And to prove that, it &longs;ufficeth (nor is more required) that it moveth with the &longs;ame motion, and fini&longs;h­ eth its circulations with the &longs;ame velocity, that the Terre&longs;trial Globe doth.

SIMP. And he likewi&longs;e makes his oppo&longs;ition to this al&longs;o; demanding who carrieth the air about, Nature, or Violence? And proveth, that it cannot be Nature, alledging that that is con­ trary to truth, experience, and to Copernicus him&longs;elf.

SALV. It is not contrary to Copernicus in the lea&longs;t, who writeth no &longs;uch thing; and this Author a&longs;cribes the&longs;e things to him with two exce&longs;&longs;ive courte&longs;ie. It's true, he &longs;aith, and for my part I think he &longs;aith well, that the part of the air neer to the Earth, be­ ing rather a terre&longs;trial evaporation, may have the &longs;ame nature, and naturally follow its motion; or, as being contiguous to it, may follow it in the &longs;ame manner, as the Peripateticks &longs;ay, that the &longs;uperiour part of it, and the Element of fire, follow the mo­ tion of the Lunar Concave, &longs;o that it lyeth upon them to declare, whether that motion be natural, or violent.

SIMP. The Author will reply, that if Copernicus maketh only the inferiour part of the Air to move, and &longs;uppo&longs;eth the upper part thereof to want the &longs;aid motion, he cannot give a rea&longs;on, how that quiet air can be able to carry tho&longs;e grave bodies along with it, and make them keep pace with the motion of the Earth.

SALV. Copernicus will &longs;ay, that this natural propen&longs;ion of the elementary bodies to &longs;ollow the motion of the Earth, hath a li­ mited Sphere, out of which &longs;uch a natural inclination would cea&longs;e; be&longs;ides that, as I have &longs;aid, the Air is not that which carrieth the moveables along with it; which being &longs;eparated from the Earth, do follow its motion; &longs;o that all the objections come to nothing, which this Author produceth to prove, that the Air cannot cau&longs;e &longs;uch effects.

The propen&longs;ion of elementary bo­ dies to follow the Earth, hath a li­ mited Sphere of activity.

SIMP. To &longs;hew therefore, that that cannot be, it will be nece&longs;­ &longs;ary to &longs;ay, that &longs;uch like effects depend on an interne principle, again&longs;t which po&longs;ition, oboriuntur difficillimæ, immò inextricabiles quæ&longs;tiones &longs;ecundæ, of which &longs;ort are the&longs;e that follow. Princi­ pium illud internum vel e&longs;t accidens, vel &longs;ub&longs;tantia. Si primum; quale nam illud? nam qualitas locomotiva circum, hactenus nulla videtur agnita. (In Engli&longs;h thus:) Contrary to which po&longs;ition there do ari&longs;e mo&longs;t difficult, yea inextricable &longs;econd que&longs;tions, &longs;uch as the&longs;e; That intern principle is either an accident, or a &longs;ub&longs;tance. If the fir&longs;t; what manner of accident is it? For a locomotive quality about the centre, &longs;eemeth to be hitherto ac­ knowledged by none.

SALV. How, is there no &longs;uch thing acknowledged? Is it not known to us, that all the&longs;e elementary matters move round, to­ gether with the Earth? You &longs;ee how this Author &longs;uppo&longs;eth for true, that which is in que&longs;tion.

SIMP. He &longs;aith, that we do not &longs;ee the &longs;ame; and me thinks, he hath therein rea&longs;on on his &longs;ide.

SALV. We &longs;ee it not, becau&longs;e we turn round together with them.

SIMP. Hear his other Argument. Quæ etiam &longs;i e&longs;&longs;et, quo­ modo tamen inveniretur in rebus tam contrariis? in igne, ut in a­ quâ; in aëre, ut in terra; in viventibus, ut in anima carentibus? [in Engli&longs;h thus:] Which although it were, yet how could it be found in things &longs;o contrary? in the fire, as in the water? in the air, as in the earth? in living creatures, as in things wanting life?

SALV. Suppo&longs;ing for this time, that water and fire are contra­ ries; as al&longs;o the air and earth; (of which yet much may be &longs;aid) the mo&longs;t that could follow from thence would be, that tho&longs;e mo­ tions cannot be common to them, that are contrary to one ano­ ther: &longs;o that v. g. the motion upwards, which naturally agreeth to fire, cannot agree to water; but that, like as it is by nature con­ trary to fire: &longs;o to it that motion &longs;uiteth, which is contrary to the motion of fire, which &longs;hall be the motion deor&longs;ùm; but the cir­ cular motion, which is not contrary either to the motion &longs;ur&longs;ùm, or to the motion deor&longs;ùm, but may mix with both, as Aristotle him&longs;elf affirmeth, why may it not equally &longs;uit with grave bodies and with light? The motions in the next place, which cannot be common to things alive, and dead, are tho&longs;e which depend on the &longs;oul: but tho&longs;e which belong to the body, in as much as it is ele­ mentary, and con&longs;equently participateth of the qualities of the e­ lements, why may not they be common as well to the dead corps, as to the living body? And therefore, if the circular motion be proper to the elements, it ought to be common to the mixt bodies al&longs;o.

SAGR. It mu&longs;t needs be, that this Author holdeth, that a dead cat, falling from a window, it is not po&longs;&longs;ible that a live cat al&longs;o could fall; it not being a thing convenient, that a carca&longs;e &longs;hould partake of the qualities which &longs;uit with things alive.

SALV. Therefore the di&longs;cour&longs;e of this Author concludeth nothing again&longs;t one that &longs;hould affirm, that the principle of the cir­ cular motions of grave and light bodies is an intern accident: I know not how he may prove, that it cannot be a &longs;ub&longs;tance.

SIMP. He brings many Arguments again&longs;t this. The fir&longs;t of which is in the&longs;e words: Si &longs;ecundum (nempè, &longs;i dieas tale princi­ pium e&longs;&longs;e &longs;ub&longs;tantiam) illud e&longs;t aut materia, aut forma, aut compo­ &longs;itum. Sed repugnant iterum tot diver&longs;æ rerum naturæ, quales &longs;unt aves, limaces, &longs;axa, &longs;agittæ, nives, fumi, grandines, pi&longs;ces, &c. quæ tamen omnia &longs;pecie & genere differentia, moverentur à naturâ &longs;uâ circulariter, ip&longs;a naturis diver&longs;i&longs;&longs;ima, &c. [In Engli&longs;h thus] If the &longs;econd, (that is, if you &longs;hall &longs;ay that this principle is a &longs;ub&longs;tance) it is either matter, or form, or a compound of both. But &longs;uch diver&longs;e natures of things are again repugnant, &longs;uch as are birds, &longs;nails, &longs;tones, darts, &longs;nows, &longs;moaks, hails, fi&longs;hes, &c. all which notwith&longs;tanding their differences in &longs;pecies and kind, are moved of their own nature circularly, they being of their natures mo&longs;t different, &c.

SALV. If the&longs;e things before named are of diver&longs;e natures, and things of diver&longs;e natures cannot have a motion in common, it mu&longs;t follow, if you would give &longs;atisfaction to all, that you are to think of, more than two motions onely of upwards and downwards: and if there mu&longs;t be one for the arrows, another for the &longs;nails, another for the &longs;tones, and another for fi&longs;hes; then are you to bethink your &longs;elf of worms, topazes and mu&longs;hrums, which are not le&longs;s different in nature from one another, than &longs;now and hail.

SIMP. It &longs;eems that you make a je&longs;t of the&longs;e Arguments.

SALV. No indeed, Simplicius, but it hath been already an­ &longs;wered above, to wit, that if one motion, whether downwards or upwards, can agree with all tho&longs;e things afore named, a circular motion may no le&longs;s agree with them: and as you are a Peripate­ tick, do not you put a greater difference between an elementary comet and a celeftial &longs;tar, than between a fi&longs;h and a bird? and yet both tho&longs;e move circularly. Now propo&longs;e your &longs;econd Ar­ gument.

SIMP. Si terra &longs;taret per voluntatem Dei, rotaréntne cætera, an non? &longs;i hoc, fal&longs;um e&longs;t à naturâ gyrare; &longs;i illud, redeunt priores quæ&longs;tiones. Et &longs;anè mirum e&longs;&longs;et, quòd Gavia pi&longs;ciculo, Alauda nidulo &longs;uo, & corvus limaci, petraque, etiam volans, imminere non po&longs;&longs;et. [Which I thus render:] If the Earth be &longs;uppo&longs;ed to &longs;tand &longs;till by the will of God, &longs;hould the re&longs;t of bodies turn round or no? If not, then it's fal&longs;e that they are revolved by nature; if the other, the former que&longs;tions will return upon us. And truly it would be &longs;trange that the Sea-pie &longs;hould not be able to hover over the &longs;mall fi&longs;h, the Lark over her ne&longs;t, and the Crow o­ ver the &longs;nail and rock, though flying.

SALV. I would an&longs;wer for my &longs;elf in general terms, that if it were appointed by the will of God, that the Earth &longs;hould cea&longs;e from its diurnal revolution, tho&longs;e birds would do what ever &longs;hould plea&longs;e the &longs;ame Divine will. But if this Author de&longs;ire a more particular an&longs;wer, I &longs;hould tell him, that they would do quite con­ trary to what they do now, if whil&longs;t they, being &longs;eparated from the Earth, do bear them&longs;elves up in the air, the Terre&longs;trial Globe by the will of God, &longs;hould all on a &longs;udden be put upon a precipi­ tate motion; it concerneth this Author now to a&longs;certain us what would in this ca&longs;e &longs;ucceed.

SAGR. I pray you, Salviatus, at my reque&longs;t to grant to this Author, that the Earth &longs;tanding &longs;till by the will of God, the other things, &longs;eparated from it, would continue to turn round of their own natural motion, and let us hear what impo&longs;&longs;ibilities or incon­ veniences would follow: for I, as to my own particular, do not &longs;ee how there can be greater di&longs;orders, than the&longs;e produced by the Author him&longs;elf, that is, that Larks, though they &longs;hould flie, could not be able to hover over their ne&longs;ts, nor Crows over &longs;nails, or rocks: from whence would follow, that Crows mu&longs;t &longs;uffer for want of &longs;nails, and young Larks mu&longs;t die of hunger, and cold, not being able to be fed or &longs;heltered by the wings of the old ones. This is all the ruine that I can conceive would follow, &longs;uppo&longs;ing the Authors &longs;peech to be true. Do you &longs;ee, Simplicius, if grea­ ter inconveniences would happen?

SIMP. I know not how to di&longs;cover greater; but it is very cre­ dible, that the Author be&longs;ides the&longs;e, di&longs;covered other di&longs;orders in Nature, which perhaps in reverend re&longs;pect of her, he was not will­ ing to in&longs;tance in. Therefore let us proceed to the third Obje­ ction. In&longs;uper quî fit, ut istæ res tam variæ tantùm moveantur ab Occa&longs;u in Ortum, parallelæ ad Æquatorem? ut &longs;emper movean­ tur, nunquam quie&longs;cant? [which &longs;peaks to this &longs;en&longs;e:] Moreover, how comes it to pa&longs;s that the&longs;e things, &longs;o diver&longs;e, are onely moved from the We&longs;t towards the Ea&longs;t, parallel to the Æquinoctial? that they always move, and never re&longs;t?

SALV. They move from We&longs;t to Ea&longs;t parallel to the Æqui­ noctial without cea&longs;ing, in the &longs;ame manner as you believe the fixed &longs;tars to move from Ea&longs;t to We&longs;t, parallel to the Æquinocti­ al, without ever re&longs;ting.

SIMP. Quarè, quò &longs;unt altiores, celeriùs; quò humiliores, tar­ diùs? (i. e.) Why are the higher the &longs;wifter, and the lower the &longs;lower?

SALV. Becau&longs;e that in a Sphere or circle, that turns about up­ on its own centre, the remoter parts de&longs;cribe greater circuits, and the parts nearer at hand de&longs;cribe le&longs;&longs;er in the &longs;ame time.

SIMP. Quare, quæ Æquinoctiali propriores, in majori; quæ remotiores, in minori circulo feruntur? [&longs;cilicet:] Why are tho&longs;e near the Æquinoctial carried about in a greater circle, and tho&longs;e which are remote in a le&longs;&longs;er?

SALV. To imitate the &longs;tarry Sphere, in which tho&longs;e neare&longs;t to the Æquinoctial, move in greater circles, than the more re­ mote.

SIMP. Quarè Pila eadem &longs;ub Æquinoctiali tota circa centrum terr æ, ambitu maximo, celeritate incredibili; &longs;ub Polo verò circa centrum proprium, gyro nullo, tarditate &longs;upremâ volveretur? [That is:] Why is the &longs;ame ball under the Æquinoctial wholly turned round the centre of the Earth in the greate&longs;t circumfe­ rence, with an incredible celerity; but under the Pole about its own centre, in no circuite, but with the ultimate degree of tar­ dity?

SALV. To imitate the &longs;tars of the Firmament, that would do the like if they had the diurnal motion.

SIMP. Quare eadem res, pila v. g. plumbea, &longs;i &longs;emel terram circuivit, de&longs;cripto circulo maximo, eandem ubique non circum­ migret &longs;ecundùm circulum maximum, &longs;ed tran&longs;lata extra Æquino­ ctialem in circulis minoribus agetur? [Which &longs;peaketh thus:] Why doth not the &longs;ame thing, as for example, a ball of lead turn round every where according to the &longs;ame great circle, if once de&longs;cribing a great circle, it hath incompa&longs;&longs;ed the Earth, but being removed from the Æquinoctial, doth move in le&longs;&longs;er circles?

SALV. Becau&longs;e &longs;o would, nay, according to the doctrine of Ptolomey, &longs;o have &longs;ome fixed &longs;tars done, which once were very near the Æquinoctial, and de&longs;cribed very va&longs;t circles, and now that they are farther off, de&longs;cribe le&longs;&longs;er.

SAGR. If I could now but keep in mind all the&longs;e fine no­ tions, I &longs;hould think that I had made a great purcha&longs;e; I mu&longs;t needs intreat you, Simplicius, to lend me this Book, for there can­ not chu&longs;e but be a &longs;ea of rare and ingenious matters contained in it.

SIMP. I will pre&longs;ent you with it.

SAGR. Not &longs;o, Sir; I would not deprive you of it: but are the Queries yet at an end?

SIMP. No Sir; hearken therefore. Si latio circularis gra­ vibus & levibus e&longs;t naturalis, qualis e&longs;t ea quæ fit &longs;ecundùm line­ am rectam? Nam &longs;i naturalis, quomodo & is motus qui circum est, naturalis e&longs;t, cùm &longs;pecie differat à recto? Si violentus, quî fit, ut mi&longs;&longs;ile ignitum &longs;ur&longs;ùm evolans &longs;cintillo&longs;um caput &longs;ur&longs;ùm à terrâ, non autem circum volvatur, &c. [Which take in our idiom:] If a circular lation is natural to heavy and light things, what is that which is made according to a right line? For if it be natural, how then is that motion which is about the centre natural, &longs;eeing it differs in &longs;pecies from a right motion? If it be violent, how is it that a fiery dart flying upwards, &longs;parkling over our heads at a di­ &longs;tance from the Earth, but not turning about, &c.

Of the mixt mo­ tion we &longs;ee not the part that is circu­ lar, becau&longs;e we partake thereof.

SALV. It hath been &longs;aid already very often, that the circular motion is natural to the whole, and to its parts, whil&longs;t they are in perfect di&longs;po&longs;ure, and the right is to reduce to order the parts di&longs;ordered; though indeed it is better to &longs;ay, that neither the parts ordered or di&longs;ordered ever move with a right motion, but with one mixed, which might as well be averred meerly circular: but to us but one part onely of this motion is vi&longs;ible and ob&longs;er­ vable, that is, the part of the right, the other part of the circular being imperceptible to us, becau&longs;e we partake thereof. And this an&longs;wers to the rays which move upwards, and round about, but we cannot di&longs;tingui&longs;h their circular motion, for that, with that we our &longs;elves move al&longs;o. But I believe that this Author never thought of this mixture; for you may &longs;ee that he re&longs;olutely &longs;aith, that the rays go directly upwards, and not at all in gyration.

SIMP. Quare centrum &longs;phære delap&longs;æ &longs;ub Æquatore &longs;piram de­ &longs;cribit in ejus plano: &longs;ub aliis parallelis &longs;piram de&longs;cribit in cono? &longs;ub Polo de&longs;cendit in axe lineam gyralem, decurrens in &longs;uperficie cylindricâ con&longs;ignatam? (In Engli&longs;h to this purpo&longs;e:) Why doth the centre of a falling Globe under the Æquinoctial de&longs;cribe a &longs;piral line in the plane of the Æquator; and in other parallels a &longs;piral about a Cone; and under the Pole de&longs;cend in the axis de&longs;cribing a gyral line, running in a Cylindrical Super&longs;i­ cies?

SALV. Becau&longs;e of the lines drawn from the Centre to the cir­ cumference of the &longs;phere, which are tho&longs;e by which graves de­ fcend, that which terminates in the Æquinoctial de&longs;igneth a cir­ cle, and tho&longs;e that terminate in other parallels de&longs;cribe conical &longs;uperficies; now the axis de&longs;cribeth nothing at all, but continueth in its own being. And if I may give you my judgment freely, I will &longs;ay, that I cannot draw from all the&longs;e Queries, any &longs;en&longs;e that interfereth with the motion of the Earth; for if I demand of this Author, (granting him that the Earth doth not move) what would follow in all the&longs;e particulars, &longs;uppo&longs;ing that it do move, as Co­ pernicus will have it; I am very confident, that he would &longs;ay that all the&longs;e effects would happen, that he hath objected, as inconve­ niences to di&longs;prove its mobility: &longs;o that in this mans opinion ne­ ce&longs;&longs;ary con&longs;equences are accounted ab&longs;urdities: but I be&longs;eech you, if there be any more, di&longs;patch them, and free us &longs;peedily from this weari&longs;om task.

SIMP. In this which follows he oppo&longs;es Copernicus & his Sectators, who affirm, that the motion of the parts &longs;eparated from their whole, is onely to unite them&longs;elves to their whole; but that the moving circularly along with the vertigenous diurnal revolution is ab&longs;o­ lutely natural: again&longs;t which he objecteth, &longs;aying, that according to the&longs;e mens opinion; Si tota terra, unà cum aquâ in nihilum redigeretur, nulla grando aut pluvia è nube decideret, &longs;ed natu­ raliter tantùm circumferetur, neque ignis ullus, aut igneum a&longs;cen­ deret, cùm illorum non improbabili &longs;ententià ignis nullus &longs;it &longs;uprà. [Which I tran&longs;late to this &longs;en&longs;e:] If the whole Earth, together with the Water were reduced into nothing, no hail or rain would fall from the clouds, but would be onely naturally carried round; neither any fire or fiery thing would a&longs;cend, &longs;eeing to the&longs;e that men it is no improbable opinion that there is no fire above.

SALV. The providence of this Philo&longs;opher is admirable, and worthy of great applau&longs;e, for he is not content to provide for things that might happen, the cour&longs;e of Nature continuing, but will &longs;hew hic care in what may follow from tho&longs;e things that he very well knows &longs;hall never come to pa&longs;s. I will grant him there­ fore, (that I may get &longs;om pretty pa&longs;&longs;ages out of him) that if the Earth and Water &longs;hould be reduced to nothing, there would be no more hails or rains, nor would igneal matters a&longs;cend any longer upwards, but would continually turn round: what will follow? what will the Philo&longs;opher &longs;ay then?

SIMP. The objection is in the words which immediately fol­ low; here they are: Quibus tamen experientia & ratio adver­ &longs;atur. Which neverthele&longs;s (&longs;aith he) is contrary to experience and rea&longs;on.

SALV. Now I mu&longs;t yield, &longs;eeing he hath &longs;o great an advan­ tage of me as experience, of which I am unprovided. For as yet I never had the fortune to &longs;ee the Terre&longs;trial Globe and the ele­ ment of Water turn'd to nothing, &longs;o as to have been able to ob­ &longs;erve what the hail and water did in that little Chaos. But he perhaps tells us for our in&longs;truction what they did.

SIMP. No, he doth not.

SALV. I would give any thing to change a word or two with this per&longs;on, to ask him, whether when this Globe vani&longs;hed, it car­ ried away with it the common centre of gravity, as I believe it did; in which ca&longs;e, I think that the hail and water would remain in&longs;en­ &longs;ate and &longs;tupid among&longs;t the clouds, without knowing what to do with them&longs;elves. It might be al&longs;o, that attracted by that great void Vacuum, left by the Earths ab&longs;enting, all the ambients would be rarified, and particularly, the air, which is extreme ea&longs;ily drawn, and would run thither with very great ha&longs;te to fill it up. And perhaps the more &longs;olid and material bodies, as birds, (for there would in all probability be many of them &longs;cattered up and down in the air) would retire more towards the centre of the great va­ cant &longs;phere; (for it &longs;eemeth very rea&longs;onable, that &longs;ub&longs;tances that under &longs;mall bulk contain much matter, &longs;hould have narrower pla­ ces a&longs;&longs;igned them, leaving the more &longs;pacious to the more rarified) and there being dead of hunger, and re&longs;olved into Earth, would form a new little Globe, with that little water, which at that time was among the clouds. It might be al&longs;o, that tho&longs;e matters as not beholding the light, would not perceive the Earths departure, but like blind things, would de&longs;cend according to their u&longs;ual cu&longs;tom to the centre, whither they would now go, if that globe did not hinder them. And la&longs;tly, that I may give this Philo&longs;opher a le&longs;s irre&longs;olute an&longs;wer, I do tell him, that I know as much of what would follow upon the annihilation of the Terre&longs;trial Globe, as he would have done that was to have followed in and about the &longs;ame, before it was created. And becau&longs;e I am certain he will &longs;ay, that he would never have been able to have known any of all tho&longs;e things which experience alone hath made him knowing in, he ought not to deny me pardon, and to excu&longs;e me if I know not that which he knows, touching what would en&longs;ue upon the annihilation of the &longs;aid Globe: for that I want that experience which he hath. Let us hear if he have any thing el&longs;e to &longs;ay.

SIMP. There remains this figure, which repre&longs;ents the Terre­ &longs;trial Globe with a great cavity about its centre, full of air; and to &longs;hew that Graves move not downwards to unite with the Ter­ re&longs;trial Globe, as Copernicus &longs;aith, he con&longs;tituteth this &longs;tone in the centre; and demandeth, it being left at liberty, what it would do; and he placeth another in the &longs;pace of this great vacuum, and asketh the &longs;ame que&longs;tion. Saying, as to the fir&longs;t: Lapis in centro con&longs;titutus, aut a&longs;cendet ad terram in punctum aliquod, aut non. Si &longs;ecundum; fal&longs;um est, partes ob &longs;olam &longs;ejunctionem à toto, ad il­ lud moveri. Si primum; omnis ratio & experientia renititur, neque gravia in &longs;uœ gravitatis centro conquie&longs;cent. Item &longs;i &longs;u­ &longs;pen&longs;us lapis, liberatus decidat in centrum, &longs;eparabit &longs;e à toto, con­ tra Copernicum: &longs;i pendeat, refragatur omnis experientia, cùm videamus integros fornices corruere. (Wherein he &longs;aith:) The &longs;tone placed in the centre, either a&longs;cendeth to the Earth in &longs;ome point, or no. If the &longs;econd, it is fal&longs;e that the parts &longs;eparated from the whole, move unto it. If the fir&longs;t; it contradicteth all rea&longs;on and experience, nor doth the grave body re&longs;t in the centre of its gravity. And if the &longs;tone being &longs;u&longs;pended in the air, be let go, do de&longs;cend to the centre, it will &longs;eparate from its whole, con­ trary to Copernicus: if it do hang in the air, it contradicteth all experience: &longs;ince we &longs;ee whole Vaults to fall down.

SALV. I will an&longs;wer, though with great di&longs;advantage to my &longs;elf, &longs;eeing I have to do with one who hath &longs;een by experience, what the&longs;e &longs;tones do in this great Cave: a thing, which for my part I have not &longs;een; and will &longs;ay, that things grave have an exi­ &longs;tence before the common centre of gravity: &longs;o that it is not one

centre alone, which is no other than indivi&longs;ible point, and therefore of no efficacie, that can attract unto it grave matters; but that tho&longs;e matters con&longs;piring naturally to unite, form to them&longs;elves a com­ mon centre, which is that about which parts of equal moment con&longs;i&longs;t: &longs;o that I hold, that if the great aggregate of grave bo­ dies were gathered all into any one place, the &longs;mall parts that were &longs;eparated from their whole, would follow the &longs;ame, and if they were not hindered, would penetrate wherever they &longs;hould find parts le&longs;s grave than them&longs;elves: but coming where they &longs;hould meet with matters more grave, they would de&longs;cend no farther. And therefore I hold, that in the Cave full of air, the whole Vault would pre&longs;s, and violently re&longs;t it &longs;elf onely upon that air, in ca&longs;e its hardne&longs;s could not be overcome and broken by its gravity; but loo&longs;e &longs;tones, I believe, would de&longs;cend to the centre, and not &longs;wim above in the air: nor may it be &longs;aid, that they move not to their whole, though they move whither all the parts of the whole would transfer them&longs;elves, if all impediments were removed.

Things grave are before the centre of gravity.

The great ma&longs;s of grave bodies be­ ing transferred out of their place, the &longs;eparated parts would follow that maß.

SIMP. That which remaineth, is a certain Errour which he ob­ &longs;erveth in a Di&longs;ciple of Copernicus, who making the Earth to move with an annual motion, and a diurnal, in the &longs;ame manner as the Cart-wheel moveth upon the circle of the Earth, and in it &longs;elf, did con&longs;titute the Terre&longs;trial Globe too great, or the great Orb too little; for that 365 revolutions of the Æquinoctial, are le&longs;s by far than the circumference of the great Orb.

SALV. Take notice that you mi&longs;take, and tell us the direct contrary to what mu&longs;t needs be written in that Book; for you &longs;hould &longs;ay, that that &longs;ame Copernican Author did con&longs;titute the Terre&longs;tri