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<?xml version="1.0"?>

<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >

<author>Casati, Paolo</author>

<info>

<title>Terra machinis mota</title>

<author>Cardano, Girolamo</author>

<title>Opus novum de proportionibus</title>

<place>Basel</place>

<cvs_file>casat_terra_018_la_1658.xml</cvs_file>

<cvs_file>carda_propo_015_la_1570.xml</cvs_file>

<cvs_version/>

</info> <text> <front> </front> <body> <chap> <pb xlink:href="018/01/001.jpg"/>

</info>

<text>

<s><emph type="center"/>TERRA <lb/>MACHINIS MOTA <lb/>DISSERTATIONES<emph.end type="center"/></s>

<front>

<s><emph type="center"/>GEOMETRICAE, MECHANICAE <lb/>PHYSICAE, HYDROSTATICAE<emph.end type="center"/></s>

<s><emph type="center"/>In quibus<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Machinarum Coniugatarum vires inter &longs;e comparantur: <lb/>Multiplici Noua Methodo Terræ magnitudo & <lb/>Grauitas inue&longs;tigatur: ARCHIMEDES <lb/>terræ motionem &longs;pondens ab arrogantiæ <lb/>&longs;u&longs;picione vindicatur.<emph.end type="italics"/><emph.end type="center"/></s>

<s id="id000001">HIERONYMI <lb/>CARDANI MEDIO<lb/>LANENSIS, CIVISQVE BONO<lb/>NIENSIS, PHILOSOPHI, MEDICI ET <lb/>Mathematici clari&longs;simi,</s>

<s><emph type="center"/>AVTHORE <lb/>PAVLO CASATO <lb/>E SOCIETATE IESV <lb/><figure id="id.018.01.001.1.jpg" xlink:href="018/01/001/1.jpg"/><lb/>ROMÆ.<emph.end type="center"/></s>

<s><emph type="center"/>Ex Typographia Ignatij de Lazaris. </s>

<s id="id000002">OPVS NOVVM DE <lb/>PROPORTIONIBVS NVMERORVM, MO<lb/>TVVM, PONDERVM, SONORVM, ALIARVMQVE RERVM <lb/>men&longs;urandarum, non &longs;olùm Geometrico more &longs;tabilitum, &longs;ed etiam <lb/>uarijs experimentis & ob&longs;eruationibus rerum in natura, &longs;olerti <lb/>demon&longs;tratione illu&longs;tratum, ad multiplices u&longs;us ac<lb/>commodatum, & in V libros dige&longs;tum.</s>

<s>M.DC.LVIII. <lb/><emph type="italics"/>SVPERIORVM PERMISSV.<emph.end type="italics"/><emph.end type="center"/></s><pb xlink:href="018/01/002.jpg"/>

<s id="id000003">PRAETEREA.</s>

<s><emph type="center"/>ILLVSTRISS. AC REVERENDISS. DOMINO <lb/>D. IOANNI GEORGIO <lb/>PATRITIO VENETO<emph.end type="center"/></s>

<s id="id000004">ARTIS MAGNÆ, SIVE DE REGVLIS <lb/>ALGEBRAICIS, LIBER VNVS, ABSTRVSISSIMVS <lb/>& inexhau&longs;tus plane totius Arithmeticæ the&longs;aurus, ab <lb/>authore recens multis in locis recogni<lb/>tus & auctus.</s>

<s><emph type="center"/><expan abbr="VTRIVSq;">VTRIVSque</expan> SIGNATVRÆ REFERENDARIO <lb/><emph type="italics"/>PAVLVS CASATVS E SOCIET AT E IESV<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Felicitatem.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>APVD multos arrogantiæ opinione la<lb/>borat Archimedes, quòd dato, vbi ip<lb/>&longs;e con&longs;i&longs;teret, loco tellurem &longs;uis à fun<lb/>damentis conuellere &longs;e po&longs;&longs;e affirma<lb/>ret: id &longs;cilicet per &longs;ummam confiden<lb/>tiam dictum putant, quod cum reap<lb/>&longs;e ne tentari quidem, ne dum perfici, <lb/>queat, experimento refelli non pote&longs;t. </s>

<s id="id000006">DE ALIZA REGVLA LIBER, HOC EST, ALGEBRAICAE <lb/>logi&longs;ticæ &longs;uæ, numeros recondita numerandi &longs;ubtilitate, &longs;ecundum Geo<lb/>metricas quantitates inquirentis, nece&longs;&longs;aria Coronis, <lb/>nunc demum in lucem edita.</s>

<s>Di&longs;cutienda fuit <lb/>conflata in bonum Senem inuidia criminis, quo &longs;oli erudi<lb/>tuli afflantur, qui &longs;cientijs leuiter a&longs;per&longs;i &longs;ibi &longs;apientes vi<lb/>dentur. </s>

<s id="id000007">O<emph type="italics"/>pus<emph.end type="italics"/> P<emph type="italics"/>hy&longs;icis &<emph.end type="italics"/> M<emph type="italics"/>athematicis imprimis <lb/>utile & nece&longs;&longs;arium.<emph.end type="italics"/></s>

<s>Et quanquam me vindice non eget Archimedes, <lb/>&longs;ua &longs;apientia aduersùs calumniantium tela &longs;atis protectus; <lb/>illud forta&longs;&longs;e non inutile accidat, &longs;i vel minùs eruditi in<lb/>telligant nihil e&longs;&longs;e tam arduum, quod &longs;uperari non po&longs;&longs;it &longs;a<lb/>pientis indu&longs;tria. </s>

<s>Tibi certè, Illu&longs;tri&longs;&longs;ime Domine, non <lb/>iniucundam fore hanc elucubratiunculam præ&longs;agit animus <lb/>pro ea humanitatis abundantia, qua literarios omnes cona<emph.end type="italics"/><pb xlink:href="018/01/004.jpg"/><emph type="italics"/>tus complecti &longs;oles: Illa enim, vbi in lucem prodire datum <lb/>e&longs;t, continuò ge&longs;tijt tuum conuolare in &longs;inum, in quo &longs;e be<lb/>nignè fouendam &longs;peraret. </s>

<s id="id000008">Cum Cæ&longs;. </s>

<s id="id000009">Maie&longs;t. </s>

<s>Alliciebat ingenita clari&longs;&longs;imi <lb/>&longs;anguinis nobilitas auorum nominibus con&longs;picua, innutrita <lb/>virtutibus indoles, morum facilitas &longs;uaui&longs;&longs;ima, grauitas<lb/>que comitate condita, ingenij acies per&longs;picua, eruditio varia <lb/>atque præclara. </s>

<s id="id000010">Gratia & Priuilegio.</s>

<s>Illud vnum ab&longs;terrere poterat properan<lb/>tem, quod de mouenda tellure di&longs;putans vix &longs;e &longs;u&longs;picari <lb/>debui&longs;&longs;et a&longs;piciendam ab homine, qui inter eos delectus, <lb/>quos aut ad proponendas dirimendasque partium cau&longs;as, aut <lb/>ad Bonum Regimen aduigilare Sapienti&longs;&longs;imus Princeps iu&longs;<lb/>&longs;it, intentis in Reipublicæ quietem, componendosque ciuium <lb/>motus oculis hæret. </s>

<s id="id000011">BASILEÆ.</s>

<s>Sed cum nulla tibi pereant temporis <lb/>momenta, qui enim potui&longs;&longs;es hunc iuuentutis florem matu<lb/>ris tot &longs;cientiarum fructibus coronare, naturæ rece&longs;&longs;us phi<lb/>lo&longs;ophando rimari, in infinitas Iuris ambages excurrere, <lb/>Theologicæ facultatis adyta penetrare, monumenta Eccle<lb/>&longs;ia&longs;ticæ vetu&longs;tatis euoluere, ni&longs;i velocis ingenij vigorem a&longs;<lb/>&longs;iduo &longs;tudio foui&longs;&longs;es? </s>

</section>

<s>Cum, inquam, nulla tibi pereant <lb/>temporis momenta, de&longs;peran dum non fuit hi&longs;ce Di&longs;&longs;ertatio<lb/>nibus impetrari po&longs;&longs;e ea horarum re&longs;egmina, quæ aut amæ<lb/>nioribus Mu&longs;is, aut Mathematicæ contemplationi tribuere <lb/>&longs;oles, vt &longs;euerioris negotij laborem literato otio interrum<lb/>pas. </s>

<s>Nihil hìc tua dignum eruditione, quæ e&longs;t Authoris <lb/>tenuitas, inuenies: meæ tamen ob&longs;eruantiæ ve&longs;tigia non ob<lb/>&longs;cura deprehendas, maximè velim. </s>

<s>Multo autem notior <lb/>atquè illu&longs;trior meus erga te animus erit, vbi per tua iu&longs;&longs;a <lb/>licuerit mea in re &longs;tudia officijs vberioribus te&longs;tari. </s>

<s id="id000012">IN LIBRVM DE <lb/>PROPORTIONIBVS HIERONYMI <lb/>CARDANI MEDIOLANENSIS, CIVISQVE <lb/>Bononien&longs;is, Medici, Præfatio ad M. A. </s>

<s id="id000013">Amulium <lb/>Venetum Card. </s>

<s>Tuæ <lb/>erit magnanimitatis exilem hanc ob&longs;equij mei te&longs;&longs;eram non <lb/>contemnere. </s>

<s id="id000014">Illu&longs;tri&longs;simum.</s>

<s id="id000015">Bene Dictum e&longs;t meo iudicio à Platone M. <lb/>A. </s>

<s><emph type="center"/>Amice Lector.<emph.end type="center"/></s>

<s id="id000016">Amuli optime, beatas fore Re&longs;pub. </s>

<s id="id000017">&longs;i uel <lb/>illarum domini &longs;apientiæ amatores e&longs;&longs;ent, <lb/>aut qui &longs;apientiæ e&longs;&longs;ent amatores domina<lb/>rentur, hoc ip&longs;um clarè intelligens, &longs;tudio &longs;a<lb/>pientiæ nihil e&longs;&longs;e utilius humano generi: <lb/>quo &longs;imul & pietas, & iu&longs;titia, & mutuus <lb/>amor hominum inter &longs;e & eorum commo<lb/>da continerentur. </s>

<s>MACHINALIS & Hydro&longs;taticæ Philo&longs;ophiæ, <lb/>quam premo, &longs;pecimen aliquod exhibi<lb/>turus, ac Prodromum tanti&longs;per emi&longs;&longs;u<lb/>rus dum extrema manus operi accedat, <lb/>Archimedæum Problema &longs;elegi, quo tel<lb/>lurem moueri po&longs;&longs;e pro&longs;itebatur, ni&longs;i locus, vbi machi<lb/>na con&longs;i&longs;teret, defui&longs;&longs;et. </s>

<s id="id000018">Nempe hi&longs;ce quatuor tota no&longs;tra felicitas com<lb/>prehenditur. </s>

<s id="id000019">Si quidem pietate in Deos nihil ni&longs;i &longs;anctum, & pu<lb/>rum, & illu&longs;tre &longs;apimus: hoc ip&longs;o primum quod &longs;upra nos e&longs;t, intel<lb/>ligimus, Deos ueneramur, gratias agimus, timor cum ueneratione <lb/>no&longs;tros animos &longs;ubit, & de futura uita cogitamus, hæc ip&longs;a morta<lb/>lia &longs;i non negligentes &longs;altem paruifacientes. </s>

<s>Qua ille machinatione id per<lb/>ficere moliretur, Hi&longs;toricis di&longs;putandum relinquo. </s>

<s id="id000020">Iu&longs;titiam autem adeò <lb/>nece&longs;&longs;ariam humano generi e&longs;&longs;e &longs;cimus, ut &longs;ine illa neque e&longs;&longs;e, nedum <lb/>benè e&longs;&longs;e po&longs;símus, ut neque latronum c&oelig;tus ab&longs;que ea diu &longs;tare po&longs;<lb/>&longs;int. </s>

<s id="id000021">Porrò quid dicam de concordia, & mutua hominum beneuo<lb/>lentia, in quibus omnis uit&etail; human&etail; dulcedo repo&longs;ita e&longs;t: nec quis <lb/>&longs;u&longs;tineat uiuere, qui &longs;e omnibus odio&longs;um e&longs;&longs;e &longs;entiat. </s>

<s>Mul<lb/>tiplex &longs;uppetebat methodus; &longs;atis &longs;cio. </s>

<s id="id000022">His ip&longs;is fi<lb/>lios in &longs;pem alimus, parentes fouemus, fratres tuemur, & adiuua<lb/>mus, amicis opitulamur, cum hominibus hilarem & iucundam ui<lb/>tam ducimus. </s>

<s id="id000023">Si quis &longs;erpentem in lecto haberet, nunquam &longs;om<lb/>num caperet: ita nihil mole&longs;tius e&longs;t in hac uita, quam e&longs;&longs;e cum quo <lb/>nolis, & priuari con&longs;uetudine eorum cum quibus maximè uiuere <lb/>cupias. </s>

<s>Placuit tamen <lb/>poti&longs;&longs;imùm o&longs;tendere, quantum in hoc negotio machi<lb/>narum Compo&longs;itio præ&longs;tet earundem Augmento: id<lb/>que intrà eiu&longs;dem Facultatis genus; vt vel &longs;olos Vectes <lb/>adhibendo, vel &longs;olas Trochleas &c. </s>

<s id="id000024">Quid enim habent Principes præcipuum cum tota illa po<lb/>tentia quam habent, ni&longs;i hoc unum, quod &longs;uis quos amant bene fa<lb/>cere po&longs;sint: nam reliqua omnia exerceri, uenari, edere, bibere, dor<lb/>mire, iter agere, loca amæna inui&longs;ere multis alijs conce&longs;&longs;um e&longs;t, ma<lb/>ioreque commodo qui in uita priuata degunt. </s>

<s id="id000025">Si ergo principatum <lb/>cum tot laboribus, curis, periculis, & meritò omnes appetunt: nec <lb/>e&longs;t in eo quicquam præcipuum præter hoc, cui dubium e&longs;t quin <lb/>hoc non &longs;it &longs;ummum huius uitæ hominibus bonum? </s>

<s>quod verò in vno <lb/>genere explicatur, de cæteris dictum facilè intelligitur. </s>

<s id="id000026">propter cu<lb/>ius uel dubiam &longs;pem eorum, quæ habent obliti mortales pericli<lb/>tantur. </s>

<s id="id000027">Succedunt inde tot commoda, non &longs;olum utilia, &longs;ed pleraque<pb xlink:href="015/01/007.jpg"/>etiam nece&longs;&longs;aria, quæ nos &longs;apientia docet: huiu&longs;modi ergo omnia <lb/>cùm libris contineantur, meritò optimus qui&longs;que librorum bono<lb/>rum perpetuitati atque in columitati fauere debet. </s>

<s><lb/>Ne quis autem in motu i&longs;to perficiendo aut immen&longs;as, <lb/>aut innumeras requiri machinas exi&longs;timaret, tentaui to<lb/>tius globi terraquei grauitatem, quantum coniiciendo <lb/>a&longs;&longs;equi fas e&longs;t, explorare: vnde apertâ con&longs;ecutione con<lb/>&longs;icitur non adeò multis membris di&longs;tingui oportere ma<lb/>chinam hoc in opere nece&longs;&longs;ariam: vtinam de materi&etail; <lb/>ipsâ non &longs;atis firmâ dubitari non po&longs;&longs;et. </s>

<s id="id000029">Caligulam exe<lb/>cramur &longs;olum ob id quod Vergilij, & T. </s>

<s>Quoniam ve<lb/>rò grauitatis notitia pendet ex mole præcognitâ; vt ab<lb/>&longs;olutum e&longs;&longs;et Problema, methodos indicaui, quibus <lb/>terræ magnitudinem indagare po&longs;simus: vt videlicet ex <lb/>notâ mole pondus innote&longs;cat, & hinc definiri po&longs;&longs;it ma<lb/>china quæ datæ grauitati mouendæ proportione re&longs;pon<lb/>deat. </s>

<s id="id000030">Liuij &longs;cripta delere cogi<lb/>tauerit. </s>

<s id="id000031">Quid facturi e&longs;&longs;emus, &longs;i feci&longs;&longs;et quod cogitauerat? </s>

<s>Sed quia in motu ip&longs;o aqua in partem &longs;ecederet, <lb/>motumque faciliorem efficeret; examinandum fuit, <pb xlink:href="018/01/006.jpg"/>quantum illa afferre po&longs;&longs;et momenti; id quod fieri non <lb/>potuit &longs;inè Hydro&longs;taticâ exercitatione, qua ignis terræ <lb/>vi&longs;ceribus inclu&longs;i, aëris, & aquæ grauitates inuice&mtail; <lb/>conferrentur. </s>

<s id="id000032">E&longs;t in &longs;a<lb/>pientum monumentis bonum &longs;ine malo, mens &longs;ine corporea labe: <lb/>Virtutes ab&longs;que uitijs, gratiæ & iucunditas &longs;ine &longs;orde, & immundi<lb/>tia, uoluptas &longs;ine dolore, conuer&longs;atio ab&longs;que tædio, delitiæ ab&longs;que mi&longs;e<lb/>ria nuda, omnia bona præ&longs;tant, atque laudabilia ab omnibus morta<lb/>litatis exuuijs libera, tantum commodi afferunt libri. </s>

<s id="id000033">Sed & in eo<lb/>rum electione ac &longs;tudijs modus, ac medio critas quædam &longs;eruanda <lb/>e&longs;t, quæ &longs;i quis neglexerit non leui incommodo afficietur: eam an<lb/>tiqui rationem alij proportionem appellarunt, non equidem etiam <lb/>in pertritis tam <expan abbr="facillimã">facillimam</expan>, ut rentur homines: nam in alijs rebus per<lb/>ob&longs;curam e&longs;&longs;e fatentur, ego difficillimam puto undique, & magis for<lb/>&longs;an ubi non exi&longs;timamus. </s>

<s>Duas in di&longs;&longs;ertationes tribueram hoc opu&longs;culum, <lb/>cum primùm problema hoc in Collegio Romano <lb/>&longs;ub au&longs;picijs Eminenti&longs;&longs;imi Principis Cardinalis Ha&longs;<lb/>&longs;iæ Lantgrauij explicatum e&longs;t ab Illu&longs;tri&longs;&longs;imo Co<lb/>mite Antonio de Mont&longs;ort. </s>

<s id="id000034">Vnde plures decidere uidemus magnis <lb/>cum auxilijs, & euidenti &longs;pe: quid aliud e&longs;t in cau&longs;a quàm ignota <lb/>men&longs;ura rerum? </s>

<s id="id000035">quam tamen plerique tenere &longs;e putant. </s>

<s>Sed quoniam di&longs;&longs;ertatio<lb/>nes illæ longiores erant, quàm vt facilè hominem ad <lb/>legendum allicerent, & per tempus non licuerat ad <lb/>marginem notas, qua&longs;i eorum, quæ dicuntur, indices, <lb/>apponere, placuit rem totam in quinque di&longs;&longs;ertationes <lb/>di&longs;pertiri, vt legentium commodo &longs;eruirem, additis ad <lb/>marginem notis. </s>

<s id="id000036">Ergo, cùm <lb/>&longs;ummum bonum in hac men&longs;ura &longs;itum e&longs;&longs;e cernerem, ut clarè o&longs;ten<lb/>dunt mu&longs;icæ uoces, quæ non ni&longs;i indiuiduo (ut ita dicam) &longs;patio <lb/>&longs;eu loco &longs;tare po&longs;&longs;unt, ita & in figuris picturarum & &longs;tatuarum, & <lb/>diebus decretorijs, & negotijs ciuilibus oper&etail; pretium me factu<lb/>rum exi&longs;timaui, &longs;i omnia hæc quæ latè patebant breuiter in unum <lb/>redegi&longs;&longs;em, <expan abbr="nõ">non</expan> tantum ne lectorem tædio afficerem, quàm ut quòd <lb/>aliàs do cui, breuibus tractationibus, & plura continerentur, & faci<lb/>lius docerentur. </s>

<s id="id000037">Cum uerò bona fortuna quædam effeci&longs;&longs;et, ut tibi <lb/>libellum dedica&longs;&longs;em de Prouidentia ex con&longs;titutione temporum, <lb/>longe meliore occa&longs;ione nominis tui typographi obliti &longs;int, indi<lb/>gnum fore putaui, ut non ærea (quemadmodum cum Glauco Dio<lb/>medes) cum aureis commutarem. </s>

<s>Ne verò pauculis ijs, ad quorum ma<lb/>nus olim veni<gap/>hæc elucubratiuncula, videar malè co<lb/>ctam cramben recoxi&longs;&longs;e, non prodeunt &longs;inè auctario hæ <lb/>di&longs;&longs;ertationes, quas plurium eruditorum virorum iudi<lb/>cia &longs;ubire de&longs;idero, vt doctior fiam. </s>

<s id="id000038">Itaque infinitis licet circumuentus <lb/>negotijs totus huic operæ in cubui, atque adeò ut præter &longs;pem unius <lb/>anni penè &longs;patio liber ab&longs;olueretur. </s>

<s id="id000039">Qui cum tibi (ut dixi) iam iurè <lb/>deberetur, eò tamen magis dedicandum putaui, quod non ego &longs;o<lb/>lum quanquam id maximè, &longs;ed communis con&longs;en&longs;us ho<lb/>minum exi&longs;timet, te &longs;ingulari uirtute omnibus <lb/>&longs;tudio&longs;is plurimum fauere, <lb/>Vale.</s>

<s>Fru&longs;tra quæras ex me, vt ea quæ di&longs;&longs;ertatione comple<lb/>xus &longs;um, aliorum authoritate firmentur: hæc enim &longs;i <lb/>legi&longs;&longs;em, nolui&longs;&longs;em ex&longs;cribere: ideo plura omi&longs;i, quæ <lb/>ab alijs dicta deprehendi. </s>

</section>

<s>Non adeò tamen de&longs;ipui, vt <lb/>mihi vni Solem illuxi&longs;&longs;e cen&longs;eam: fieri potuit vt hæc ea<lb/>dem alijs occurrerent; &longs;ed quæcunque tandem illa &longs;int, <lb/>mihi primùm, nemine prælucente, in mentem vene<lb/>runt. </s>

<s>Hæc autem eo tantùm con&longs;ilio dicta &longs;unt, n&etail; <lb/>plura, quæ in hanc &longs;ententiam afferri potui&longs;&longs;ent, omi&longs;&longs;a <lb/>calumnieris: neque enim omnia per&longs;equi otium &longs;uit. </s>

<s id="id000040">TABVLA PRO<lb/>POSITIONVM DE <lb/>PROPORTIONIBVS.<lb/><arrow.to.target n="table1"/></s>

<s>Quod &longs;pectat ad &longs;criptionis methodum dialogicam; <pb xlink:href="018/01/007.jpg"/>illam Platonis exemplum ab omni calumniâ vindicat: <lb/>Breuitatem cum per&longs;picuitate con&longs;ectanti methodus hec <lb/>magis arridebat. </s>

<table>

<s>At quid opus erat calculorum progre&longs;<lb/>&longs;us, quibus numeri illi indagantur, quos in colloquio <lb/>di&longs;&longs;ertatores afferunt, ad fa&longs;tidium inculcare? </s>

<table.target id="table1"/>

<row>

<s>Id enim <lb/>communiter periti Arithmetici non faciunt; &longs;ed calamo <lb/>in &longs;chedulâ taciti inue&longs;tigant: id quod ab huius dialogi <lb/>interlocutoribus factum ponimus. </s>

<cell>Proportionem <emph type="italics"/>in proportionem duci, e&longs;t &longs;uperiores numeros atque inferiores inuicem ducere.<emph.end type="italics"/></cell>

<s>Quod &longs;i quis id mihi <lb/>culpæ vertat, &longs;ciat me peccare malui&longs;&longs;e omittendo, <lb/>quam tantâ numerorum vi lectorem onerando. </s>

<cell><emph type="italics"/>pagina<emph.end type="italics"/> 6</cell>

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<s>Placuit <lb/>verò tres viros de Mathematicis di&longs;ciplinis optimè me<lb/>ritos (qui diem no&longs;tro æuo obierunt) Galilæum, Mer<lb/>&longs;ennum, Guldinum di&longs;&longs;ertatores exhibere; vt ex Italicâ <lb/>pariter, Gallicâ, atque Germanicâ Mathe&longs;i commen<lb/>tatiuncula hæc lucem mutuaretur, quam non potuit ab <lb/>authore recipere. </s>

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<s>Nec te pluribus volo. </s>

<cell>P<emph type="italics"/>roportio extremorum producitur ex intermedijs.<emph.end type="italics"/></cell>

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<s><emph type="center"/>SYNOPSIS TOTIVS OPERIS: <lb/><emph type="italics"/>DISSERTATIO PRIMA <lb/>Machinarum vires inter &longs;e comparat. </s>

<cell>S<emph type="italics"/>i proportio ex duabus proportionibus in quatuor terminis producatur, ip&longs;a uerò proportio inter duas alias quantitates fuerit con&longs;tituta: con&longs;urgent trecenti &longs;exaginta modi productionis proportionis.<emph.end type="italics"/></cell>

<s><lb/>DISSERTATIO SECVNDA <lb/>Terræ grauitatem inue&longs;tigat. </s>

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<s><lb/>DISSERTATIO TERTIA <lb/>Methodos varias inueniendi terræ quantitatem proponit. </s>

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<s><lb/>DISSERTATIO QVARTA <lb/>Ex aquæ &longs;eparatione à terræ motus facilitatem infert. </s>

<cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportionibus tertij ad quartum, & quinti ad &longs;extum, producetur etiam ex proportione tertij ad &longs;extum, & quinti ad quartum.<emph.end type="italics"/></cell>

<s><lb/>DISSERTATIO QVINTA <lb/>Minorem telluris grauitatem in aqua explicat.<emph.end type="italics"/><emph.end type="center"/></s><pb xlink:href="018/01/008.jpg"/>

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<s><emph type="center"/>Ioannes Rhò Præpo&longs;itus Prouincialis Societatis Ie&longs;u. </s>

<cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportione tertij ad quartum, & quinti ad &longs;extum: erit proportio tertij ad &longs;extum, producta ex proportionibus primi ad &longs;ecundum, & quarti ad quintum.<emph.end type="italics"/></cell>

<s><lb/>In Prouincia Romana.<emph.end type="center"/></s>

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<s>O<emph type="italics"/>Pu&longs;culum, cui titulus e&longs;t Terra Machinis mota à <lb/>P. Paulo Ca&longs;ato Societ. </s>

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<cell>E<emph type="italics"/>x trecentis &longs;exaginta modis producendarum proportionum triginta &longs;ex tantum e&longs;&longs;e nece&longs;&longs;arios.<emph.end type="italics"/></cell>

<s>No&longs;træ compo&longs;itum, tres viri <lb/>graues, ac docti Eiu&longs;dem No&longs;træ Societ. </s>

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<s>perlegerunt, & <lb/>in lucem edi po&longs;&longs;e iudicarunt: quarè facultate mihi conce&longs;&longs;a <lb/>ab Adm. Reu. Padre No&longs;tro Go&longs;vvino Ni<emph.end type="italics"/>K<emph type="italics"/>el Præpo&longs;ito Ge<lb/>nerali, pote&longs;tatem facio vt imprimatur, &longs;i alijs, ad quos <lb/>&longs;pectat, ità vi&longs;um fuerit. </s>

<cell>I<emph type="italics"/>n modis qui nece&longs;&longs;ariò producuntur ex duabus proportionibus, cum duæ quantitates ex illis quæ modos conficiunt, æquales fuerint: proportio producta ad quatuor quantitates omiologas reducetur.<emph.end type="italics"/></cell>

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<cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicentur atque coniungantur, erit proportio aggregati ad productum ex inferioribus inuicem proportio, ex primis proportionibus compo&longs;ita.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Ioannes Rhò<emph.end type="italics"/></s><figure id="id.018.01.008.1.jpg" xlink:href="018/01/008/1.jpg"/>

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<s><emph type="italics"/>Imprimatur, <lb/>Si videbitur Reuerendi&longs;s. Patri Sacri Palatij Apoct. Mag. <lb/>M. </s>

<cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicentur, minusque productum ex maiore detrahatur, erit re&longs;idui ad productum ex in&longs;erioribus proportio uelut illa, quæ relinquitur detracta minore proportione ex maiore.<emph.end type="italics"/></cell>

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<cell>S<emph type="italics"/>i fuerit alicuius quantitatis ad unam partem proportio, uelut alterius partis ad &longs;ecundam quantitatem, erit proportio cuiu&longs;uis quantitatis eiu&longs;dem generis ad &longs;ecundam compo&longs;ita proportio, ex proportionibus eiu&longs;dem quantitatis, a&longs;&longs;umptæ ad utranque partem primæ quantitatis &longs;eor&longs;um.<emph.end type="italics"/></cell>

<s>Oddus Vice&longs;g.<emph.end type="italics"/></s><figure id="id.018.01.008.2.jpg" xlink:href="018/01/008/2.jpg"/>

</row>

<row>

<s><emph type="italics"/>Imprimatur <lb/>Fr. Vinoentius Maria Guini&longs;ius Magi&longs;ter, & Reuerendi&longs;simi <lb/>P. Fr. Raymundi Capi&longs;uechi Sac. Apo&longs;t. Pal. Magistri Socius Ord. <lb/>Præd.<emph.end type="italics"/></s>

<cell>P<emph type="italics"/>roportio aggregati quarumlibet duarum quantitatum ad aggregatum duarum æqualium <expan abbr="quantitat&utilde;">quantitatum</expan> e&longs;t, compo&longs;ita ex proportionibus primis, & diui&longs;a per duplam.<emph.end type="italics"/></cell>

</row>

<row>

<cell>P<emph type="italics"/>ropo&longs;itis duabus proportionibus unam alteri iungere ab&longs;que multiplicatione.<emph.end type="italics"/></cell>

</row>

<row>

<cell>P<emph type="italics"/>roportio confu&longs;a aggregata primæ & tertiæ quatuor quantitatum omiologarum ad aggregatum &longs;ecundæ & quartæ, e&longs;t uelut compo&longs;ita ex ei&longs;dem diui&longs;a per duplam.<emph.end type="italics"/></cell>

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<s><emph type="center"/>DISSERTATIO <lb/>PRIMA<emph.end type="center"/></s>

<row>

<cell>XIIII.</cell>

<s><emph type="center"/>Machinarum vires inter &longs;e <lb/>comparat.<emph.end type="center"/></s>

<cell>P<emph type="italics"/>roportiones confu&longs;æ & coniunctæ in tribus quantitatibus inuicem commutantur.<emph.end type="italics"/></cell>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

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<row>

<s>NVNQVAM minùs alieno tempo<lb/>re acce&longs;&longs;i&longs;tis, Amici, vt me <lb/>ve&longs;tro a&longs;pectu pariter ac fa<lb/>miliari&longs;&longs;imâ collocutione re<lb/>crearetis longo &longs;anè fa&longs;tidio <lb/>grauem. </s>

<cell>S<emph type="italics"/>i fuerint quatuor quantitates proportio confu&longs;a, aggregati primæ & tertiæ, ad aggregatum &longs;ecundæ & quartæ, erit ut monadis addito prouentu, qui fit diui&longs;a differentia, differentiarum primæ & &longs;ecundæ, atque quartæ & tertiæ, per aggregatum tertiæ & quartæ ad ip&longs;am monadem.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Mer.<emph.end type="italics"/></s><s> Satis in tempore accedo, &longs;i ob&longs;eruan<lb/>tiam, qua te plurimos no&longs;tri æui Mathema<lb/>ticos &longs;apientiâ facilè antecedentem colo, <lb/>certis documentis liceat declarate. </s><pb xlink:href="018/01/010.jpg" pagenum="2"/>

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<s><emph type="italics"/>Gul.<emph.end type="italics"/></s><s> Id nobis quoquè lucro futurum e&longs;t, <lb/>quod dolueris; quos nimirùm &longs;uaui&longs;&longs;im&atail; <lb/>illa tua dicendi facundia po&longs;t mole&longs;tas animi <lb/>curas luculentiùs beabit: nemo &longs;iquide&mtail; <lb/>pleniùs ex fonte bibit, quàm qui &longs;ubducto <lb/>recens fi&longs;tulæ epi&longs;tomio aquam in libertatem <lb/>vindicat. </s>

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<s>Sed quæ demùm nebula &longs;ere na&mtail; <lb/>tranquillæ mentis diem valuit infu&longs;care? </s>

<cell>O<emph type="italics"/>mnium quatuor quantitatum propo&longs;ita prima, quæ non minorem habet proportionem ad &longs;uam corre&longs;pondentem quàm alia ad aliam, erit proportio confu&longs;a illarum,<emph.end type="italics"/></cell>

<cell/>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Haud procul ab hi&longs;ce ædibus obuias <lb/>habui&longs;tis lappas, quæ nec à &longs;e inuicem, nec à <lb/>me, quamuis lite compo&longs;itâ, diuelli poterant. </s>

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<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Itane Verò, Galilæe? </s>

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<cell/>

<s>auocatum à <lb/>mathematicis contemplationibus animum <lb/>(quod &longs;uperi omen obruant) ad fori conten<lb/>tiones tran&longs;tuli&longs;ti? </s>

<cell><emph type="italics"/>ut producti ex aggregato primæ & tertiæ, in tertiam ad productum ex aggregato tertiæ & omiotatæ ad &longs;ecundam in ip&longs;am quartam.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> No&longs;tri &longs;ub&longs;ellij erat, quam detule<lb/>runt litem dirimendam. </s>

</row>

<row>

<s>Hæc autem illos <lb/>controuer&longs;ia torquebat contentionis forta&longs;sè <lb/>cupidiores quàm veritatis: Qua videlicet <lb/>machinatione tellurem loco mouere decreui&longs;<lb/>&longs;et Archimedes, ni&longs;i locus, vbi po&longs;&longs;et <expan abbr="cõ&longs;i&longs;tere">con&longs;i&longs;tere</expan>, <lb/>defui&longs;&longs;et. </s>

<cell>O<emph type="italics"/>mnes duæ proportiones conuer&longs;æ producunt æqualem proportionem.<emph.end type="italics"/></cell>

<s>Hic quidem aptâ quinque <expan abbr="facultat&utilde;">facultatum</expan> <lb/>coagmentatione rem totam fui&longs;&longs;e perficien<lb/>dam a&longs;&longs;erebat: Cont<emph type="italics"/>r<emph.end type="italics"/>à verò ille eximias hu<lb/>iu&longs;modi vires vni Glo&longs;&longs;ocomo <expan abbr="tribu&etilde;das">tribuendas</expan> con<lb/>tendebat. </s>

</row>

<s>Nec planè nullius operæ fuit homi<lb/>nes Mathematicis leui&longs;simè a&longs;per&longs;os ad con<lb/>cordiam reuocare; cum alter <expan abbr="diuer&longs;ar&utilde;">diuer&longs;arum</expan> facul<pb xlink:href="018/01/011.jpg" pagenum="3"/>tatum compo&longs;itioni plus ine&longs;&longs;e ad mouen<lb/>dum momenti &longs;atis frigidè cen&longs;eret, alter Ar<lb/>chimedem in multiplici tympanorum denta<lb/>torum acce&longs;sione facilitatis compendia quæ<lb/>&longs;i&longs;&longs;e affirmaret<gap/></s>

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<cell>XVIII.</cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Illud crediderim potiùs vocari <lb/>po&longs;&longs;e in controuer&longs;iam, vtrùm &longs;olâ tympano<lb/>rum dentatorum collabellatione, an verò <lb/>multiplicatâ helice infinitâ mechanicu&mtail; <lb/>hoc miraculum fui&longs;&longs;et patraturus. </s>

<cell>S<emph type="italics"/>i fuerint quotlibet quantitates in continua proportione multiplici præter, <expan abbr="ultimã">ultimam</expan> proportio uerò penultimæ ad ultimam, qualis re&longs;idui primæ ad &longs;ecundam, erit primæ ad aggregatum reliquarum, uelut penultimæ ad ultimam.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita lanè: modò inter nos conue<lb/>niat fieri po&longs;&longs;e, vt &longs;tatuamus, quibus mem<lb/>bris di&longs;tingueretur celeberrimum illud Ar<lb/>chimedis Inuentum Quadrage&longs;imum, quo <lb/>datâ potentiâ datum pondus moueri po&longs;&longs;e <lb/>iactabat; cui idcircò nonnulli nomen fecere <lb/>Pancratio: nullus &longs;iquidem dubitandi locus <lb/>relinquitur, quin hac machinâ telluri motum <lb/>conciliare moliretur. </s>

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<s>Cæterùm cum nihil <lb/>nobis ni&longs;i coniectura &longs;uppetat, & quide&mtail; <lb/>quæ varias duci pote&longs;t in partes, qua nihil <lb/>incertius (neque enim me Heronis Alexan<lb/>drini in Barulco Glo&longs;&longs;ocomum quicqua&mtail; <lb/>moratur) nihil facilè de Archimedis mente <lb/>au&longs;im affirmare, cùm dentatis rotis æquè at<lb/>que multiplici cochleâ infinitâ idem a&longs;&longs;equi <lb/>potuerit, quod perficere meditabatur. </s>

<cell>S<emph type="italics"/>i fuerint aliquot quantitates arithmeticæ omiologæ, quarum exce&longs;&longs;us &longs;it æqualis minimè, omnibus autem deficientibus &longs;upplementa ad æqualitatem maximè adiungantur, erunt quadrata omnium quantitatum æqualium, adiecto rur&longs;us quadrato primæ cum eo quod fit ex minima primi ordinis in aggregatum omnium quantitatum eiu&longs;dem, tripla aggregato quadratorum omnium quantitatum primi ordinis pariter acceptis.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Athelicis vires inuentorem &longs;uum <pb xlink:href="018/01/012.jpg" pagenum="4"/>atque architectum latuerint? </s>

</row>

<s>latui&longs;&longs;e aute&mtail; <lb/>oporteat, &longs;i eam Glo&longs;&longs;ocomo, quod mera tym<lb/>pana dentata con&longs;tituant, po&longs;thabuerit; ne mo <lb/>enim &longs;apiens longioribus ambagibus id per&longs;e<lb/>quitur, quod po&longs;&longs;it breuiore <expan abbr="comp&etilde;dio">compendio</expan> a&longs;&longs;equi. </s>

<row>

<cell>C<emph type="italics"/>um fuerint quatuor quantitates, fueritque <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> æqualis tertiæ, aut prima æqualis quartæ, erit proportio primæ ad quartam, aut tertiæ ad &longs;ecundam, producta ex proportionibus primæ ad &longs;ecundam & tertiæ ad quartam.<emph.end type="italics"/></cell>

<s><margin.target id="note1"/><emph type="italics"/><lb/>I <lb/>Glo&longs;&longs;ocomi <lb/>&longs;eu Pan<gap/>ra <lb/>tij constru<lb/>ctio. <lb/><emph.end type="italics"/></s>

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<row>

<s>Sint tympana dentata quinque maior&atail; <lb/>A, B, C, D, E, totidemque minora F, G, H, <lb/>I, K; maximum A circa eundem axem cum <lb/>cylindro S, cui ductarius funis circumducitur, <lb/>con uertatur: quatuor minor a F, G, H, I, com<lb/>munem cum maioribus B, C, D, E, quibus <lb/>&longs;ingula in axe eodem cohærent, habeant con<lb/>uer&longs;ionem: minimum verò K, addito manu<lb/>brio LM, circùm &longs;e torqueatur, & ex illo <lb/>totius machinæ motus initium &longs;umat. </s>

<cell>C<emph type="italics"/>um decu&longs;&longs;atim ducta fuerit prima in quartam, & &longs;ecunda in tertiam, productumque primæ in quartam, diui&longs;um fuerit per productum &longs;ecundæ in tertiam, erit proportio primæ ad &longs;ecundam, diui&longs;a per proportíonem tertiæ ad quartam.<emph.end type="italics"/> E<emph type="italics"/>t &longs;imiliter interpo&longs;ita omiologa.<emph.end type="italics"/></cell>

<s>Ma<lb/>nubrii autem flexus LM, ad tympani K &longs;emi<lb/>diametrum Rationem habeat quintupla&mtail;; <lb/>&longs;ibique pariter reliqua tympana, maiora vi<lb/>delicet cum minoribus &longs;ibi cohærentibus <lb/>comparata, pro portione re&longs;pondeant: nec <lb/>maximi tympani A Radius, atque cylindri <lb/>S illi infixi &longs;emidiameter, à Ratione hac quin<lb/>tuplâ di&longs;sideant. </s>

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<s><margin.target id="note2"/><emph type="italics"/><lb/>II <lb/>Glo&longs;&longs;ocomi <lb/>vires e<gap/>pli<lb/><gap/>tur. <lb/><emph.end type="italics"/></s>

<cell>C<emph type="italics"/>um fuerit proportio primæ ad &longs;ecundam maior quàm tertiæ ad quartam, erit confu&longs;a ex his maior quàm tertiæ ad quartam, minor autem quàm primæ ad &longs;ecundam.<emph.end type="italics"/></cell>

<s>His ita con&longs;titutis &longs;atis liquet potentiam <lb/>in M applicatam quintuplo velociorem e&longs;&longs;e <lb/>peripheriâ E, quæ ex mutuâ &longs;uorum denti<lb/>culorum ac tympani K collabellatione con<lb/>uertitur. </s>

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<row>

<s>At peripheria E quintuplo pariter <pb xlink:href="018/01/013.jpg"/><figure id="id.018.01.013.1.jpg" xlink:href="018/01/013/1.jpg"/><pb xlink:href="018/01/014.jpg" pagenum="6"/>velociùs mouetur quàm D, & D quàm C, & C <lb/>quàm B, & B quàm A, & A quàm S, hoc e&longs;t <lb/>pondus P illi adne xum. </s>

<cell>XXIII.</cell>

<cell>O<emph type="italics"/>mnis motus naturalis ad locum &longs;uum e&longs;t: ideò per rectam lineam fit.<emph.end type="italics"/></cell>

<s>Igitur motus poten<lb/>tiæ in M (liceat in pagellâ rem ad calculos <lb/>reuocare) ad <expan abbr="mot&utilde;">motum</expan> ponderis P e&longs;t vt 15625 <lb/>ad 1. &longs;unt nimirum &longs;ex Rationes quintuplæ, <lb/>ex quibus Ratio motûs potentiæ ad motum <lb/>ponderis componitur. </s>

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<s>Quare potentia, quæ <lb/>ab&longs;que machinæ &longs;ub&longs;idio centum pondo mo<lb/>uere valeret, hac adhibitâ machinâ pondus <lb/>P librarum 1562500. attollet. </s>

<row>

<cell>XXIIII.</cell>

<cell>O<emph type="italics"/>mnis motus circularis uoluntarius e&longs;t.<emph.end type="italics"/></cell>

<s><margin.target id="note3"/><emph type="italics"/><lb/>III <lb/>Cochleæ in<lb/>finitæ Com<lb/>po&longs;itæ uires <lb/>cum Glo&longs;&longs;o<lb/>como com<lb/>parantur. <lb/><emph.end type="italics"/></s>

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<row>

<s>Iam verò in minorum tympanorum FG <lb/>HIK locum reponantur helices maioru&mtail; <lb/>tympanorum ABCDE denticulis (quos 25 in <lb/>toto ambitu fui&longs;&longs;e exempli gratia &longs;tatuamus) <lb/>congruentes: ip&longs;aque tympana cum &longs;uis <lb/>axibus in &longs;piram deformatis in quadrato lo<lb/>culamento, vt helicis in&longs;initæ natura fert, <lb/>aptè di&longs;ponantur. </s>

<cell>T<emph type="italics"/>res &longs;unt motus omnino &longs;implices naturalis, uoluntarius, & uiolentus.<emph.end type="italics"/></cell>

<s>Con&longs;tat tympani A pe<lb/>ripheriam quintuplo tantùm velociorem e&longs;&longs;e <lb/>pondere P; at peripheriam B vigequintuplo <lb/>velociorem quàm A: vnicus enim tympani A <lb/>denticulus promouetur ab integrâ ip&longs;ius B <lb/>conuer&longs;ione; ideoque vt &longs;emel A gyrum ab<lb/>&longs;oluat, vicies & quinquies tympanum B con<lb/>uertatur oportet. </s>

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<s>Eademque ratione tympani <lb/>C motus cum tympani B motu comparatur, <lb/>cuiuse&longs;t vigequintuplus: quemadmodum & <pb xlink:href="018/01/015.jpg" pagenum="7"/>D ip&longs;ius C, & E ip&longs;ius D, & M ip&longs;ius E. </s>

<row>

<s>Quare <lb/>Ratio motûs potentiæ M ad motum ponderis <lb/>P, ex vnicâ Ratione quintuplâ, & quinque <lb/>vigequintuplis componitur: E&longs;t igitur motus <lb/>potentiæ ad motum ponderis vt 48828125 <lb/>ad 1: & potentia, quæ pondo centum valeat <lb/>attollere, pondus librarum 4882812500 <lb/>mouebit. </s>

<cell>M<emph type="italics"/>otus ergo compo&longs;iti quatuor nece&longs;&longs;ariò &longs;unt &longs;pecies.<emph.end type="italics"/></cell>

<s>Cum itaque tam immane pondus moueri <lb/>po&longs;&longs;it quinque tantum cochleis in&longs;initis, <lb/>quæ totidem dentatis tympanis congruant; <lb/>contra verò, reiectâ helice, decem maiora <lb/>totidemque minora tympana componi opus <lb/>&longs;it, vt pondus idem attollatur; liquidò con&longs;tat <lb/>longè <expan abbr="facilior&etilde;">faciliorem</expan> e&longs;&longs;e multiplicis cochleæ, quàm <lb/>Glo&longs;&longs;ocomi v&longs;um; ac proinde quadrage&longs;i<lb/>mum Archimedis inuentum helicem fui&longs;&longs;e, <lb/>procliuius e&longs;t opinari. </s>

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<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Nec ego inficior, nec diffitetur Gul<lb/>dinus helicis infinitæ vires cæteris machi<lb/>nationibus longè præ&longs;tare: &longs;ed quæ nos cogit <lb/>nece&longs;&longs;itas affirmandi Archimedem quadra<lb/>ge&longs;imo loco in inuentum planè facillimum <lb/>incidi&longs;&longs;e? </s>

<cell>XXVII.</cell>

<cell>M<emph type="italics"/>otus uoluntarius e&longs;t in loco: naturalis ad locum: uiolentus ex loco.<emph.end type="italics"/></cell>

<s>Quis fuerit Archimedææ contem<lb/>plationis &longs;copus, in quo conquie&longs;ceret, me, <lb/>fateor, later Quid verò, &longs;i quis machinæ faci<lb/>litatem non in eo &longs;tatuendam cen&longs;eat, quod <lb/>illa paucioribus membris contineatur; &longs;ed in <pb xlink:href="018/01/016.jpg" pagenum="8"/>hoc potiùs, quod minore operâ parari queat? </s>

</row>

<s><arrow.to.target n="note4"/><lb/>Atqui tympanorum ambitum in denticulos <lb/><figure id="id.018.01.016.1.jpg" xlink:href="018/01/016/1.jpg"/><lb/>æquales di&longs;tribue<lb/>re, eosque &longs;atis &longs;it<lb/>mos, ne facilè vi <lb/>ponderis commi<lb/>nuantur, & i&ntail; <lb/>cylindro ver&longs;atili <lb/>helicem tympani <lb/>denticulis ritè <expan abbr="cõ-gruentem">con<lb/>gruentem</expan> incide<lb/>re, haud &longs;anè o<lb/>&longs;citantem exigunt <lb/>arti&longs;icem. </s>

<row>

<cell>XXVIII.</cell>

<s>Porrò <lb/>a&longs;&longs;iduus ille toe <lb/>partium &longs;e inui<lb/>cem atterentium <lb/>affrictus mora&mtail; <lb/>infert non leuem. </s>

<cell>M<emph type="italics"/>otus quilibet uoluntarius aut uiolentus in aliquo medio fit.<emph.end type="italics"/></cell>

<s><lb/>Quare nec teme<lb/>re dixerit qui&longs;<lb/>piam, denticula<lb/>tis tympanis va<lb/>lere iu&longs;&longs;is, re&mtail; <lb/>totam faciliùs per<lb/></s>

</row>

<row>

<s>fici po&longs;&longs;e multiplici axe in peritrochio, qui <lb/>& leui negotio paratur, & moram recipit nul<lb/>lam ex mutuâ membrorum affrictione. </s><pb xlink:href="018/01/017.jpg" pagenum="9"/>

<cell>O<emph type="italics"/>mnis motus uoluntarius æqualis e&longs;t &longs;emper: &longs;impliciter etiam quilibet alius motus.<emph.end type="italics"/></cell>

<s><margin.target id="note4"/><emph type="italics"/><lb/>IV <lb/>Difficulta<lb/>tes in heli<lb/>cis constru<lb/>ctione & <lb/><gap/>&longs;<gap/>. <lb/><emph.end type="italics"/></s>

</row>

<s>A&longs;&longs;umantur quinque cylindri ABCDE <lb/><arrow.to.target n="note5"/><lb/>cra&longs;&longs;itudine inæquali (quo enim magis à <lb/>pondere di&longs;tant, graciliores e&longs;&longs;e po&longs;&longs;unt) <lb/>&longs;ingulisque rota canaliculum in ambitu ex<lb/>cauatum habens adijciatur, cuius d<emph type="italics"/>i<emph.end type="italics"/>ameter <lb/>diametri cylindri &longs;ibi cohærentis quintupla <lb/>&longs;it. </s>

<row>

<s>Demùm cylindro F addatur manubrium <lb/>OP eandem Rationem quintuplam habens <lb/>ad illius &longs;emidiametrum. </s>

<cell>I<emph type="italics"/>n omni corpore mobili in medio partes medij re&longs;i&longs;tunt obuiæ, aliæ impellunt.<emph.end type="italics"/></cell>

<s>Hi verò cylindri <lb/>paralleli in &longs;uo conceptaculo facilè ver&longs;atiles <lb/>ita di&longs;ponantur, vt funis &longs;ingulas rotas am<lb/>biens ad &longs;uperiorem cylindrum ductus (&longs;i <lb/>fieri id commode po&longs;&longs;it) congruat lineæ, <lb/>quæ horizonti ad perpendiculum in&longs;i&longs;tit. </s>

</row>

<row>

<s><lb/>Hìc pariter con&longs;tat Rationem motûs poten<lb/>tiæ P ad motum ponderis M ex rationibus <lb/>intermedijs, nimirum &longs;ex quintuplis, com<lb/>poni. </s>

<cell>O<emph type="italics"/>mnis motus naturalis in æquali medio ualidior e&longs;t in fine quàm in principio.<emph.end type="italics"/>V<emph type="italics"/>iolentus contrà.<emph.end type="italics"/></cell>

<s>Quarè & hìc motus potentiæ ad pon<lb/>deris motum e&longs;t vt 15625 ad 1, vt &longs;uperiùs, <lb/>Mer&longs;enne, ratiocinabaris. </s>

</row>

<s>Maiore tame&ntail; <lb/>forta&longs;sè compendio, quod hìc rotæ cylindros <lb/>non atterant, nec vllum immineat pericu<lb/>lum, ne ex mutuâ illâ collabellatione den<lb/>tes aliquando excutiantur: quàm ægrè au<lb/>tem excu&longs;&longs;i dentis detrimento occurras, pa<lb/>làm e&longs;t; cum tamen di&longs;ruptum funem ite<lb/>rum facilè connectas. </s>

<row>

<cell>XXXII.</cell>

<s><margin.target id="note5"/><emph type="italics"/><lb/>V <lb/>Axes in Pe<lb/>ritrochio <expan abbr="Cõ">Com</expan><lb/>po&longs;iti faci<lb/>liùs con&longs;tru<lb/>untur, & <lb/>idem præ&longs;ta <lb/>re po&longs;sunt. <lb/><emph.end type="italics"/></s>

<cell>O<emph type="italics"/>mne mobile naturaliter motum &longs;eu uiolenter uelocius mouetur in medio rariore quàm den&longs;iore.<emph.end type="italics"/> M<emph type="italics"/>aior quoque e&longs;t proportio finis motus in corpore rariore ad finem motus in corpore den&longs;iore quàm principij.<emph.end type="italics"/> I<emph type="italics"/>n uiolento autem celerius perueniret ad finem motus in corpore den&longs;iore.<emph.end type="italics"/></cell>

<s>Vbi licet obiter animum aduertere ad <pb xlink:href="018/01/018.jpg" pagenum="10"/><arrow.to.target n="note6"/><lb/>multorum artificum imperitiam, qui ex ma<lb/>chinarum tantùm augmento vires ad mo<lb/>uenda pondera augeri autumantes, multo la<lb/>bore, nec modicâ argenti iacturâ immanes <lb/>aliquando machinas con&longs;truunt, quæ vel mo<lb/>le &longs;uâ prægrauatæ fati&longs;cunt, vel motam mo<lb/>tui inferunt non mediocrem, adeò vt &longs;olius <lb/>machinæ motio, etiam &longs;eclu&longs;o pondere, cui <lb/>mouendo de&longs;tinatur machina, validioris po<lb/>tentiæ vires ab&longs;umat: cum tamen rem to<lb/>tam minore negotio, nec &longs;pernendo pecu<lb/>niæ atquè laboris compendio, perficere po&longs;<lb/>&longs;ent, &longs;i rectè intelligerent, quantum machi<lb/>narum compo&longs;itio præ&longs;tet earum augmento. </s>

</row>

<row>

<s><lb/>Id quod ex quinque his axibus in Peritrochio <lb/>inter &longs;e compo&longs;itis luculenti&longs;&longs;imè demon<lb/>&longs;tratur; &longs;i enim axi, cuius diameter palma<lb/>ris, rotam velis infigere, qua po&longs;&longs;is ide&mtail; <lb/>mouere pondus, quod tribus tantùm ex pro<lb/>po&longs;itis rotis A, B, C, mouetur, quàm imma<lb/>nis illa erit? </s>

<cell>XXXIII.</cell>

<cell>O<emph type="italics"/>mnia duo mobilia æqualis undique magnitudinis quæ æquali in tempore æqualia &longs;pacia pertran&longs;eunt in diuer&longs;is &longs;ub&longs;tantia medijs nece&longs;&longs;e e&longs;t, ut &longs;it ponderis ad pondus, quem ad modum medij ad medium proportio duplicata.<emph.end type="italics"/></cell>

<s>Quippe quæ 125 palmos &longs;e<lb/>cundùm diametrum obtineat: quàm diffi<lb/>cilis ad conuer&longs;ionem? </s>

</row>

<s>ob ingentem grauita<lb/>tis cardines prementis re&longs;i&longs;tentiam: quàm <lb/>multo argento parabilis? </s>

<row>

<cell>XXXIIII.</cell>

<s>cum ea &longs;ola ad tres <lb/>A, B, C, &longs;imul &longs;umptas e&longs;&longs;et vt minimùm in <lb/>Ratione Quadrati &longs;uæ diametri 125 ad tri<lb/>plum Quadratum diametri rotæ A, hoc e&longs;t <pb xlink:href="018/01/019.jpg" pagenum="11"/>vt 15625 ad 75; materiem autem tantæ mo<lb/>li nece&longs;&longs;ariam nec modicâ pecuniâ nec &longs;inò <lb/>multis operis comparari po&longs;&longs;e & elaborari <lb/>palàm e&longs;t. </s>

<cell>P<emph type="italics"/>roportio corporis cubi ad &longs;uam &longs;uperficiem quadratam, e&longs;t uelut eiu&longs;dem &longs;uperficiei, ad latus eiu&longs;dem uerò ad monadem.<emph.end type="italics"/></cell>

<s>Adde quòd illam ex alio in a<lb/>lium locum transferendi pro multiplici ne<lb/>ce&longs;&longs;itate, vix &longs;pes aliqua &longs;upere&longs;&longs;et. </s>

</row>

<row>

<s><margin.target id="note6"/><emph type="italics"/>VI <lb/>Machina<lb/>rum Com<lb/>po&longs;itio me<lb/>lior e&longs;t, <expan abbr="quã">quam</expan> <lb/>earum Aug<lb/>mentum, &longs;e<lb/>cundùm ma <lb/>gnitudinem<emph.end type="italics"/></s>

<cell>V<emph type="italics"/>ocum magnitudines excre&longs;cunt in acumine, non in grauitate, finis autem e&longs;t in utroque extremo.<emph.end type="italics"/> P<emph type="italics"/>ropter hoc minima facta uariatione in hypate acutæ uix ferunt.<emph.end type="italics"/></cell>

<s>Quamuis verò quinque alios in&longs;uper cy<lb/>lindros cum &longs;uis rotis adijcere opus e&longs;&longs;et, vt <lb/>æquale pondus attolleretur, atque tuâ illâ <lb/>quinque helicum coagmentatione; in diffi<lb/>cultates tamen longè maiores incurrat arti<lb/>fex, nece&longs;&longs;e e&longs;t, qui cochleas quinque cum <lb/>tympanis examu&longs;&longs;im congruentes formare <lb/>iubeatur, ac ille qui decem aut plures axes <lb/>in peritrochio effingere velit; in quibus fi<lb/>guram exqui&longs;itè rotundam &longs;i de&longs;ideret, &longs;u<lb/>peruacuo &longs;e labore conficiat: neque enim <lb/>anguli, &longs;i qui &longs;int, obe&longs;&longs;e quicquam po&longs;&longs;unt, <lb/>modò poli, &longs;eu cardines, circa quos ver&longs;an<lb/>tur, læues &longs;int ac politi. </s>

</row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Sed quanto impendio &longs;taret tan<lb/><arrow.to.target n="note7"/><lb/>tam funium vim comparare, quæ &longs;atis e&longs;&longs;et; <lb/>vt pondus ad vnius decempedæ altitudinem <lb/>&longs;ubleuaretur? </s>

<row>

<cell>XXXVI.</cell>

<s>Primùm enim funis, cui pon<lb/>dus adnecteretur, decem pedes in longitudi<lb/>ne haberet; igitur qui rotam primam A am<lb/>biret, e&longs;&longs;et vt minimùm pedum 50. At rotæ <lb/>&longs;ecundæ motus e&longs;&longs;et prioris quintuplus, igi<pb xlink:href="018/01/020.jpg" pagenum="12"/>tur rotæ B circumduceretur funis pedum <lb/>250, nec di&longs;pari argumentatione conficitur <lb/>rotam tertiam C exigere funem pedum <lb/>1250, quartam D 6250, quintam demùm <lb/>E 31250: ex quibus conflatur &longs;umma pe<lb/>dum 39060, quæ e&longs;&longs;et totius funis longitu<lb/>do. </s>

<cell>S<emph type="italics"/>i proportio per proportionem minorem æquali ducatur, proportio minor pro<emph.end type="italics"/></cell>

<cell/>

<s>Liceat autem hìc di&longs;&longs;imulanter præte<lb/>rire immodicam rotarum E, D, & C cra&longs;&longs;i<lb/>tudinem, vt tàm longus funis earum am<lb/>bitûs terminis contineri po&longs;&longs;et. </s>

</row>

<s>Nam &longs;i mul<lb/>tiplici &longs;pirarum &longs;erie ita duceretur funis, vt <lb/>ip&longs;e &longs;e circumplecteretur, motuum Ratio<lb/>nes, &, quod inde con&longs;equitur, potentiæ mo<lb/>menta, ipsâ euolutione mutarentur, auctis <lb/>&longs;cilicet aut diminutis ex &longs;ubiectâ &longs;pirarum &longs;e<lb/>rie rotarum ac cylindorum diametris. </s>

<row>

<cell/>

<s><margin.target id="note7"/><emph type="italics"/>VII <lb/>Difficultati <lb/>ex funis lon<lb/>gitudine.<emph.end type="italics"/></s>

<cell><emph type="italics"/>ducetur.<emph.end type="italics"/> V<emph type="italics"/>nde manife&longs;tum e&longs;t duas proportiones minores æqualitate <expan abbr="inuic&etilde;">inuicem</expan> ductas proportionem minorem unaquaque illarum producere.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Hæc eadem, quæ nunc obijcis, mi<lb/><arrow.to.target n="note8"/><lb/>hi pariter aliquandò non nihil fecere negotij. </s>

</row>

<row>

<s><lb/>Et primùm quidem earum rotularum, qua<lb/>rum velocior e&longs;t motus, funes quoquè gra<lb/>ciliores e&longs;&longs;e debere ob&longs;eruabam, quippe qui<lb/>bus ponderis grauitas minùs reluctetur. </s>

<cell>XXXVII.</cell>

<cell>S<emph type="italics"/>i plures homines, quorum per &longs;e nauim mouere poßint, aut pondus ferre &longs;imul iuncti eam moueant, aut pondus ferant, erunt illæ proportiones coniunctæ non productæ.<emph.end type="italics"/></cell>

<s>Hinc <lb/>verò &longs;atis commodâ con&longs;ecutione conficie<lb/>bam fieri po&longs;&longs;e, vt exiguis &longs;patijs tanta funi<lb/>culi longitudo citrà incommodum compre<lb/>henderetur. </s>

</row>

<s>Deinde quamuis non adeò lon<lb/>gus &longs;uppeteret funiculus, operæ pretium vi<lb/>debatur futurum, &longs;i illo euoluto rotas &longs;i<pb xlink:href="018/01/021.jpg" pagenum="13"/>&longs;teremus (annulum videlicet auer&longs;æ rotæ A <lb/>infixum arctè cum &longs;uperiore cylindro, n&etail; <lb/>pondus relaberetur, connectentes) explica<lb/>tum que funiculum, qui in conuer&longs;ione fui&longs;<lb/>&longs;et cylindrum &longs;uperiorem circumplexus, ite<lb/>rum rotæ ap&longs;idi circumduceremus. </s>

<row>

<cell>XXXVIII.</cell>

<s><margin.target id="note8"/><emph type="italics"/>Occurritur.<emph.end type="italics"/></s>

<cell>O<emph type="italics"/>mne corpus tantum re&longs;i&longs;tit motui contrario &longs;uo natúrali, quantum mouetur occulto motu quie&longs;cendo.<emph.end type="italics"/></cell>

<s>Verùm cum vrbem obambulans oculos <lb/>fortè in officinam quandam conijcerem, vbi <lb/>obtu&longs;arum nouacularum acies re&longs;tituuntur, <lb/>En, inquam, funiculus in &longs;e&longs;e rediens maio<lb/>ri ac minori rotulæ ità circumplicatus, vt al<lb/>tera ex alterius conuer&longs;ione rotetur, nullos <lb/>motui terminos præ&longs;cribit: quidni igitur con<lb/>&longs;imili ratione funiculus vnâ aut alterâ &longs;pirâ <lb/>cylindrum &longs;uperiorem complectens &longs;ubie<lb/>ctum peritrochium ita apprehendere valeat, <lb/>vt pariter moueantur, nec conuer&longs;ionis fi<lb/>nem inueniant, cum tantundem &longs;uccedere <lb/>po&longs;&longs;it funiculi, quantum dece&longs;&longs;erit? </s>

</row>

<row>

<s>Id au<lb/>tem &longs;i fieri po&longs;&longs;e concedas, in &longs;uperioribus <lb/>&longs;altem FEDC (nam in inferioribus forta&longs;sè <lb/>ob ponderis nimiam grauitatem &longs;atius e&longs;&longs;et <lb/>funis extremum religare, ne excurreret) <lb/>difficultas omnis propo&longs;ita euane&longs;cit. </s>

<cell>XXXIX.</cell>

<cell>A<emph type="italics"/>b æquali aut minore ui quàm &longs;it impedimentum non fit motus.<emph.end type="italics"/></cell>

<s>Vti<lb/>nam & in trochleis &longs;imile funis compen<lb/>dium liceret inuenire. </s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> An & trochleis tellurem ab Archi<lb/>mede fui&longs;&longs;e loco dimouendam exi&longs;timas? <pb xlink:href="018/01/022.jpg" pagenum="14"/>Non funium tantùm longitudo aut cra&longs;&longs;itu<lb/>do, operi non &longs;atis congrua negotium face&longs;<lb/>&longs;eret, &longs;ed & aptæ trochleæ con&longs;trui omninò <lb/>non po&longs;&longs;ent. </s>

<row>

<s>Quis enim Chilio&longs;pa&longs;tum com<lb/>ponat? </s>

<cell>O<emph type="italics"/>mne corpus &longs;phæricum tangens planum in puncto mouetur ad latus per quamcunque uim, quæ medium diuidere pote&longs;t.<emph.end type="italics"/></cell>

<s>&longs;ed quantulum demùm e&longs;t Chilio&longs;pa<lb/>&longs;ti momentum? </s>

</row>

<row>

<s>Neque &longs;i trochleas decem <lb/>orbiculorum millibus in&longs;trueres, quicquam <lb/>po&longs;&longs;es efficere. </s>

<cell>S<emph type="italics"/>i fuerint duæ quantitates &longs;umaturque toties <expan abbr="aggregat&utilde;">aggregatum</expan> maioris & minoris, quoties aggregatum minoris & maioris, erit proportio confu&longs;a maioris aggregati ad minus, minor quam multiplicis maioris ad multiplex minoris.<emph.end type="italics"/></cell>

<s>Nam &longs;i duas huiu&longs;modi tro<lb/>chleas ità componeres, vt altera ponderi ad<lb/>necteretur, altera in &longs;uperiore loco firmare<lb/>tur, eumque adhiberes conatum, quo libras <lb/>centum ab&longs;que machinâ attolleres, conatu <lb/>eodem librarum vicies centena millia moue<lb/>re po&longs;&longs;es: &longs;ed quid hoc ad immen&longs;um terre<lb/>ni globi pondus? </s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quæ fuerit Archimedi mens, planè <lb/><arrow.to.target n="note9"/><lb/>ignoro: potui&longs;&longs;e tamen fieri, vt ille propo&longs;i<lb/>tum trochleis adhibitis a&longs;&longs;equeretur, con<lb/>&longs;tanter a&longs;&longs;ero. </s>

<row>

<s>Et quidem, quod ad trochleas <lb/>ip&longs;as attinet, ludum puto, modò funes, & <lb/>locus vbi con&longs;i&longs;terem, non dee&longs;&longs;ent. </s>

<cell>T<emph type="italics"/>rahentium nauim, aut ferentium pondera proportiones in &longs;e inuicem, quomodo ducere oporteat con&longs;iderare.<emph.end type="italics"/></cell>

<s>Cedo <lb/>mihi orbiculos quatuor aut &longs;ex &longs;upra cen<lb/>tum; &longs;atis habeo trochlearum, vt vnicâ ma<lb/>nu terram à fundamentis, quibus in&longs;i&longs;tit, <lb/>conuellam. </s>

</row>

<row>

<s>Id quod vt minimè dubia de<lb/>mon&longs;tratione conficiam; illud primum, in <lb/>trochleatum v&longs;u extra controuer&longs;iam po&longs;i<lb/>tum accipio, quod, funis extremo trochleæ, <pb xlink:href="018/01/023.jpg" pagenum="15"/>cui pondus adnectitur, alligato, potentia re<lb/>liquum extremum arreptum trahens plus <lb/>obtinet ad mouendum momenti, quàm &longs;i <lb/>funis alteri trochleæ à pondere remotæ ad<lb/>necteretur; in primo enim ca&longs;u motus po<lb/>tentiæ ad motum ponderis maiorem habet <lb/>Rationem, quàm in &longs;ecundo. </s>

<cell>XLIII.</cell>

<cell>P<emph type="italics"/>roductionem ad additionem retrahere.<emph.end type="italics"/></cell>

<s><margin.target id="note9"/><emph type="italics"/>VIII <lb/>Orbiculi <lb/>pauci in plu<lb/>res minores <lb/>trochleas di <lb/>stributi plus <lb/>po&longs;&longs;unt, <lb/>quàm duæ <lb/>trochleæ ex <lb/>multis mil<lb/>libus orbi<lb/>culorum.<emph.end type="italics"/></s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Id ego tibi lubens permitto. </s>

<row>

<cell>XLIIII.</cell>

<s>Nam <lb/><figure id="id.018.01.023.1.jpg" xlink:href="018/01/023/1.jpg"/><lb/>&longs;i trochleas duas R & <emph type="italics"/>S<emph.end type="italics"/> pona<lb/><arrow.to.target n="note10"/><lb/>mus binis orbiculis in&longs;tructas, <lb/>funis autem extremum A tro<lb/>chleæ S annulo alligetur, & <lb/>ducatur funis per ABCDEF <lb/>GHIK, con&longs;tat totius funis <lb/>longitudinem quadruplam e&longs;<lb/>&longs;e interualli, quo trochleæ à <lb/>&longs;e inuicem &longs;eiunguntur. </s>

<cell>S<emph type="italics"/>i fuerit proportio motoris ad id quod e&longs;t maximum non mouens, & &longs;patium & tempus, nota erit etiam reliquorum nota.<emph.end type="italics"/></cell>

<s>Iam <lb/>verò plurimum intere&longs;t, vtri <lb/>trochlearum pondus adiunxe<lb/>ris: &longs;i enim pondus in R ad<lb/>nectatur, potentia K tamdiu <lb/>mouetur, ac ab <emph type="italics"/>S<emph.end type="italics"/> recedit, do<lb/>nec funis totus explicetur: per<lb/>currit igitur &longs;patium funis <lb/>longitudini æquale, videlicet <lb/>quadruplum interualli inter <lb/>R & S. </s>

</row>

<row>

<s>At verò &longs;i pondus in <lb/>S alligetur, eadem potenti&atail; <pb xlink:href="018/01/024.jpg" pagenum="16"/>K ad trochleam R fixam accedit, illamqu&etail; <lb/>tanto &longs;patio tran&longs;greditur, quanta e&longs;t funis <lb/>longitudo: igitur in toto motu percurrit &longs;pa<lb/>tium quintuplum eius, quod à pondere ver<lb/>sùs trochleam R moto perficitur. </s>

<cell>R<emph type="italics"/>ationem &longs;tateræ o&longs;tendere.<emph.end type="italics"/></cell>

<s>Quoniam <lb/>autem quò tardior e&longs;t ponderis motus cum <lb/>motu potentiæ comparatus, eò minùs pon<lb/>deris grauitas virtuti potentiæ trahentis ob<lb/>&longs;i&longs;tit; apertum e&longs;t ac manife&longs;tum faciliùs <lb/>trahi pondus, &longs;i trochleæ S (cui funis in A <lb/>adnectitur) quàm &longs;i trochleæ R alligetur: in <lb/>S nimirum motum obtinet motûs potentiæ <lb/>&longs;ubquintuplum, in R autem &longs;ubquadru<lb/>plum. </s>

</row>

<s><margin.target id="note10"/><emph type="italics"/>IX <lb/>Non æqua<lb/>li facilitate <lb/>moueri pon<lb/>dus. </s>

<row>

<s>vtrili<lb/>bet trochleæ <lb/>adnexu&mtail;, <lb/>demonstra<lb/>tur.<emph.end type="italics"/></s>

<cell>A<emph type="italics"/>n &longs;it aliqua proportio & qualis inter animam & uitas, & &longs;ua corpora con&longs;iderare.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quod præterea Ratione aliquâ mi<gap/><lb/>noris Inæqualitatis propo&longs;itâ, Antecedens <lb/><arrow.to.target n="note11"/><lb/>terminus ad Con&longs;equentem duplum maio<lb/>rem habeat Rationem, quàm ad alium Con<lb/>&longs;equentem, ad quem habeat Rationem pro<lb/>po&longs;itæ rationis duplicatam (&longs;i tamen &longs;ubdu<lb/>plam excipias, cùm eadem &longs;umma fiat ex <lb/>duplicis binarij additione, ac ex mutuâ illo<lb/>rum multiplicatione) nihil habet dubitatio<lb/>nis. </s>

</row>

<row>

<s>Datâ &longs;iquidem Ratione &longs;ubtriplâ 3 ad <lb/>9, &longs;i Con&longs;equens 9 geminetur, & fiat 18, <lb/>Ratio autem duplicetur inuento tertio con<lb/>tinuè proportionali 27, maior e&longs;t Ratio 3 ad <lb/>18, quàm 3 ad 27. Similiter maior erit <pb xlink:href="018/01/025.jpg" pagenum="17"/>Ratio ad Con&longs;equentem triplum aut qua<lb/>druplum, quàm ad alium Con&longs;equente&mtail; <lb/>terminum Rationis triplicatæ aut quadru<lb/>plicatæ, etiam &longs;i propo&longs;ita Ratio &longs;ubdupl&atail; <lb/>e&longs;&longs;et: &longs;ic &longs;i fuerit Ratio 2 ad 4, triplus Con<lb/>&longs;equens e&longs;t 12. Con&longs;equens verò Rationis tri<lb/>plicatæ e&longs;t 16: e&longs;t autem maior Ratio 2 ad <lb/>12, quàm 2 ad 16. </s>

<cell>XLVII.</cell>

<cell>S<emph type="italics"/>i duo mobilia æqualister in eodem circulo iuxta proprios motus moueantur, productum temporis circuituum inuicem, erit æquale producto differentiæ temporum circuitus ductæ in tempus coniunctionis primæ.<emph.end type="italics"/></cell>

<s><margin.target id="note11"/><emph type="italics"/>X <lb/>Maior est <lb/>Ratio ad ter<lb/>minu&mtail; <lb/>Multipli<lb/>cem, quàm <lb/>ad termi<lb/>num Ratio<lb/>nis &longs;imiliter <lb/>Multiplica<lb/>tæ.<emph.end type="italics"/></s>

</row>

<s>Hinc infero maximum e&longs;&longs;e di&longs;crimen i&ntail; <lb/>augendo potentiæ momento, vtrùm trochleæ <lb/>augeantur orbiculis, an verò trochleæ mul<lb/>tiplices ex ii&longs;dem orbiculis con&longs;tituantur. </s>

<row>

<cell>XLVIII.</cell>

<s>Si <lb/>enim trochleæ duæ S & R, quas nuperrimè <lb/>de&longs;crip&longs;i&longs;ti, binis prætereà orbiculis augean<lb/>tur, ita vt &longs;ingulæ quaternos habeant, mani<lb/>fe&longs;tum e&longs;t potentiam in K, quæ priùs mo<lb/>tum habebat quadruplum motûs ponderis in <lb/>R con&longs;tituti, factâ huiu&longs;modi orbiculorum <lb/>acce&longs;sione, motum habere octuplum, vel <lb/>quæ priùs quintuplò velocior erat pondere in <lb/>S adnexo, factam e&longs;&longs;e noncuplò velociorem. </s>

<cell>S<emph type="italics"/>i tria mobilia ex eodem puncto di&longs;cedant, fuerintque duorum ac duorum coniunctiones in temporibus commen&longs;is, illa tria mobilia denuo coniungentur in tem pore producto ex denominatore diui&longs;ionis temporis maioris per minus in minus aut numeratore in maius.<emph.end type="italics"/></cell>

<s><lb/>At &longs;i quatuor ho&longs;ce orbiculos non adijcias <lb/>prioribus, &longs;ed duas alias trochleas ex illis com<lb/>ponas, iam multò maior e&longs;t potentiæ motus <lb/>cum ponderis motu comparatus. </s>

</row>

<row>

<s>Sint duæ trochleæ binos orbiculos haben<lb/>tes A & B: huic autem tum pondus P, tum <lb/>funis extremum adnectatur. </s>

<cell>P<emph type="italics"/>ropofitio mobilis in circulo circuitus tempore dataque ratione di&longs;tantiæ ab illo mo bilis circuitum inuenire, quod ex <expan abbr="eod&etilde;">eodem</expan> puncto di&longs;cedens <expan abbr="c&utilde;alio">cunalio</expan> mobili in dato puncto <expan abbr="cõueniat">conueniat</expan> &longs;ub <expan abbr="quoc&utilde;que">quocunque</expan> numero <expan abbr="circuitu&utilde;">circuituum</expan> <expan abbr="t&etilde;pus">tempus</expan> quoque <expan abbr="cõiunctionis">coniunctionis</expan>.<emph.end type="italics"/></cell>

<s>Vtique poten<pb xlink:href="018/01/026.jpg" pagenum="18"/><arrow.to.target n="note12"/><lb/><figure id="id.018.01.026.1.jpg" xlink:href="018/01/026/1.jpg"/><lb/>tia in F motum ha<lb/>beret quintuplò velo<lb/>ciorem motu ponde<lb/>ris P. </s>

</row>

<s>Ex quatuor a<lb/>lijs orbiculis duæ pa<lb/>riter trochleæ D & C <lb/>con&longs;tituantur: & tro<lb/>chleæ C adnectatur <lb/>prioris funis <expan abbr="extrem&utilde;">extremum</expan>. </s>

<row>

<s><lb/>Potentia E quintuplò <lb/>&longs;anè velociùs moue<lb/>tur quàm F, at F quin<lb/>tuplò velociùs quàm <lb/>P; igitur motus po<lb/>tentiæ E ad motum <lb/>ponderis P e&longs;t vt 25 <lb/>ad 1. Quare potentia <lb/>vires habens decem <lb/>pondo trahendi &longs;inè <lb/>machinâ, in F trahe<lb/>ret libras 50, at in E <lb/>libras 250. Quod &longs;i <lb/>tam A quàm B qua<lb/>ternos haberent or<lb/>biculos, potentia i&ntail; <lb/>F tantum 90 libras <lb/>mouere po&longs;&longs;et. </s>

<cell>O<emph type="italics"/>mnes circuituum portiones in ei&longs;dem temporibus repetuntur.<emph.end type="italics"/></cell>

<s><margin.target id="note12"/><emph type="italics"/>XI <lb/>Trochlea<lb/>rum coniu<lb/>gatoru&mtail; <lb/>Compo&longs;itio, <lb/>quàm ma<lb/>gnas vires. </s>

</row>

<row>

<s><lb/>habeat.<emph.end type="italics"/></s>

<cell>O<emph type="italics"/>perationes dictas exemplo declarare.<emph.end type="italics"/></cell>

<s>Con&longs;tat itaque du<pb xlink:href="018/01/027.jpg" pagenum="19"/>plicatis trochleis æquali orbiculorum nume<lb/>ro in&longs;tructis, motum potentiæ in E haber&etail; <lb/>Rationem duplicatam Rationis, quam habet <lb/>motus potentiæ in F ad motum ponderis in <lb/>P: multiplicatis autem pari numero in ea<lb/>dem trochleâ orbiculis, ne duplicari quidem <lb/>motum ip&longs;ius potentiæ F. </s>

</row>

<s>Quod &longs;i in E pa<lb/>riter duæ aliæ trochleæ &longs;imiles adiicerentur, <lb/>iam triplicaretur Ratio motûs in F ad mo<lb/>tum in P, & &longs;ic deinceps. </s>

<row>

<s>Vno verbo di<lb/>cam: quot &longs;unt paria &longs;imilium trochlearum, <lb/>progre&longs;&longs;io fit tot Rationum &longs;imilium Ratio<lb/>ni, quam habet motus ponderis ad motum <lb/>potentiæ primis trochleis applicatæ. </s>

<cell>T<emph type="italics"/>ria mobilia coniuncta in <expan abbr="eod&etilde;">eodem</expan> puncto, quorum duo & duo conueniant in partib. incommen&longs;is inter &longs;e, in perpetuum in nullo unquam puncto conuenient.<emph.end type="italics"/></cell>

<s>Sic &longs;i <lb/>e&longs;&longs;ent talium, quales exhibui, trochlearu&mtail; <lb/>paria decem, a&longs;&longs;umendæ e&longs;&longs;ent decem Ra<lb/>tiones quintuplæ; & motus potentiæ ad mo<lb/>tum ponderis Rationem haberet ex his com<lb/>po&longs;itam, quam &longs;cilicet habet vndecimus ter<lb/>minus in progre&longs;sione Rationis quintuplæ <lb/>ad vnitatem, hoc e&longs;t 9765625 ad 1. </s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si igitur trochleæ omnes ABCD <lb/><arrow.to.target n="note13"/><lb/>tri&longs;pa&longs;ti e&longs;&longs;ent, vnicus equus in E idem pon<lb/>dus trahere po&longs;&longs;et, quod equi 49; cum ta<lb/>men in F, &longs;i A & B tripa&longs;ti fuerint, idem <lb/>valeat trahere quod equi &longs;eptem: &longs;i vero A <lb/>& B &longs;enis in&longs;truerentur orbiculis, æquiuale<lb/>ret equis tredecim. </s>

<cell>C<emph type="italics"/>irculorum &longs;e in aduer&longs;um mouentium proportionem declarare.<emph.end type="italics"/></cell>

<s>Quis ergo adeò debilis <pb xlink:href="018/01/028.jpg" pagenum="20"/>cantherius, qui nequear &longs;olus trochlearum <lb/>multiplicium ope, maius tormentum belli<lb/>cum trahere? </s>

</row>

<s><margin.target id="note13"/><emph type="italics"/>XII <lb/>Vnicus e<lb/>quus facilè <lb/>pote&longs;t mo<lb/>uere ingens <lb/><expan abbr="põdus">pondus</expan>, quod <lb/>vix po&longs;&longs;ent <lb/>plures equi.<emph.end type="italics"/></s>

<row>

<cell>LIIII.</cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Ita planè: &longs;ed ob&longs;eruandum in fu<lb/>nibus. <lb/><arrow.to.target n="note14"/></s>

<cell>P<emph type="italics"/>roportio circuli ad &longs;uum diametrum per &longs;imilitudinem e&longs;t quarta pars peripheriæ.<emph.end type="italics"/> R<emph type="italics"/>ur&longs;usque eiu&longs;dem circuli ad peripheriam diametri quarta pars.<emph.end type="italics"/></cell>

<s><margin.target id="note14"/><emph type="italics"/>XIII <lb/>Quantum <lb/>funium in <lb/>hac machi<lb/>natione re<lb/>quiratur.<emph.end type="italics"/></s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Ne plura: &longs;atis animum ad hoc <lb/>aduerti. </s>

<cell>P<emph type="italics"/>roportionem medicamentorum per ordines &longs;up po&longs;ita æquali proportione in ordinibus per quantitates & proportiones demon&longs;trare.<emph.end type="italics"/></cell>

<s>Monere volebas tantam requiri <lb/>longitudinem funis, qui &longs;ecundas trochleas <lb/>D & C circumplectitur, vt vnicus ex D in <lb/>C ductus æqualis &longs;it longitudini &longs;patij, quod <lb/>potentia in F totum explicans funem, & pon<lb/>dus P ad trochleam A v&longs;que deducens, per<lb/>curreret. </s>

</row>

<s>Quarè &longs;i interuallum trochlearum <lb/>AB &longs;it pa&longs;&longs;uum decem, potentia ex F per<lb/>curreret pa&longs;&longs;us 50: funis itaque trochleas D <lb/>& C ambiens longitudinem habeat nece&longs;&longs;&etail; <lb/>e&longs;t pa&longs;&longs;uum vt minimum 200; trochle&atail; <lb/>enim D ibi firmanda e&longs;t, quò funis ABF <lb/>explicatus pertingere po&longs;&longs;it. </s>

<row>

<s>Eademque d&etail; <lb/>cæteris, &longs;i plures fuerint trochleæ, ratio e&longs;to. </s>

<cell>P<emph type="italics"/>roportio cuiu&longs;uis binomij ad &longs;uum reci&longs;um, uel ei commen&longs;um e&longs;t duplicata ei quæ ad numeri latus.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Non falsâ coniecturâ animum meum <lb/>pro&longs;pexi&longs;ti. </s>

</row>

<row>

<s>Sed vt ad rem ip&longs;am propiùs <lb/>accedamus ob&longs;eruandum e&longs;t, propo&longs;ito quo<lb/>cunque orbiculorum numero, qui tame&ntail; <lb/>per 2, vel 4, vel 6, vel alium quemcunque <lb/>numerum parem diuidi po&longs;sit, longè maius <lb/>e&longs;&longs;e potentiæ momentum, &longs;i plures trochleæ <lb/>pauciorum orbiculorum, quàm &longs;i pauciores <pb xlink:href="018/01/029.jpg" pagenum="21"/>trochleæ plurium orbiculorum con&longs;tituan</s><s><arrow.to.target n="note15"/><lb/>tur. </s>

<cell>M<emph type="italics"/>otus rationem ad pondus inuenire.<emph.end type="italics"/></cell>

<s>Exhibeantur enim, exempli gratiâ, orbi<lb/>culi 60, ex quibus &longs;i fiant 20 trochleæ trium <lb/>orbiculorum, iam &longs;unt decem trochlearum <lb/>paria, ac proinde decem Rationes vt &longs;um<lb/>mum &longs;eptuplæ; igitur momentum potentiæ, <lb/>hoc e&longs;t vndecimus ab vnitate terminus, e&longs;t <lb/>vt 282475249. Si verò fiant binos haben<lb/>tes orbiculos, erunt 15 trochlearum pari&atail; <gap/><lb/>ideoq quindecim Rationes quintuplæ, ex qui<lb/>bus Ratio motûs potentiæ ad motum ponde<lb/>ris componitur; erit igitur vt 30517578125 <lb/>ad 1. Con&longs;tat autem ne additis quidem ad<lb/>huc duobus tri&longs;pa&longs;torum paribus, vt &longs;int in <lb/>vniuer&longs;um orbiculi 72, po&longs;&longs;e adeò augeri po<lb/>tentiæ momentum: po&longs;itis &longs;iquidem 12 tri<lb/>&longs;pa&longs;torum paribus momentum potentiæ e&longs;t <lb/>&longs;olùm vt 13841287201. Hinc colligitur <lb/>plus ad mouendum momenti obtinere pau<lb/>ciores orbiculos in &longs;implicioribus trochleis, <lb/>quàm in trochleis maioribus plures orbicu<lb/>los: id quod alicui forta&longs;sè paradoxum ac<lb/>cidat. </s>

</row>

<s><margin.target id="note15"/><emph type="italics"/>XIV <lb/>Pauciores <lb/>orbiculos in <lb/>&longs;implicibus <lb/>trochleis <lb/>plus po&longs;&longs;&etail;, <lb/>quàm plu<lb/>res in maio<lb/>ribus o&longs;ten<lb/>ditur.<emph.end type="italics"/></s>

<row>

<cell>LVIII.</cell>

<s>Nunc igitur &longs;i mihi orbiculos centum ex<lb/>hibeas, &longs;implices trochleas ex &longs;ingulis orbi<lb/>culis &longs;tatuo, fiuntquè 50 trochlearum &longs;im<lb/>plicium paria: adnexo autem pondere eidem <lb/>trochleæ, cui funis extremum alligatur, mo<pb xlink:href="018/01/030.jpg" pagenum="22"/>mentum potentiæ erit triplum: &longs;unt igitur <lb/>50 Rationes triplæ, ex quibus componitur <lb/>Ratio motûs potentiæ ad motum ponderis. </s>

<cell>Q<emph type="italics"/>uæ ex alto de&longs;cendunt, cur non eandem pro di&longs;tantia motus rationem in libero aëre &longs;eruent con&longs;iderare.<emph.end type="italics"/></cell>

<s><lb/>Quærendus iraque e&longs;t terminus in progre&longs;<lb/>&longs;ione datæ Rationis triplæ ab vnitate quin<lb/>quage&longs;imus primus. </s>

</row>

<row>

<s>Ratio autem tripla quintuplicata e&longs;t 243 <lb/>ad 1. Ducatur 243 per &longs;e ip&longs;um, & e&longs;t Ra<lb/>tio decuplicata 59049 ad 1. Hic iterum ter<lb/>minus 59049 per &longs;e ip&longs;um ducatur, & Ratio <lb/>3486.784401 ad 1 e&longs;t ex viginti Rationi<lb/>bus triplis compo&longs;ita. </s>

<cell>O<emph type="italics"/>mne mobile motum duobus motibus non ad idem tendentibus utroque &longs;eor&longs;um tardius mouetur &longs;imili motu.<emph.end type="italics"/></cell>

<s>Ducatur pariter 3486. <lb/>784401 per &longs;e ip&longs;um, & e&longs;t Ratio ex qua<lb/>draginta Rationibus triplis compo&longs;ita 12. <lb/>157665.459056.928801. ad 1. Hæc de<lb/>mùm Ratio ducatur per Rationem triplam <lb/>decuplicatam nimirum per 59049, & pro<lb/>ducitur Ratio, quæ ex 50 Rationibus tri<lb/>plis componitur 717897.987691.852588. <lb/>770249. ad 1. </s>

</row>

<s>Quod &longs;i placeat duas adhuc trochleas ter<lb/>nis orbiculis in&longs;tructas adijcere ip&longs;ique pon<lb/>deri immediatè adnectere, vt funium &longs;eptu<lb/>plici ductu faciliùs &longs;u&longs;tineri valeat, adhuc <lb/>Ratio &longs;eptupla addenda, vt ex hac & 50 tri<lb/>plis tota Ratio componatur: & quinquage&longs;i<lb/>mus primus terminus progre&longs;sionis Rationis <lb/>triplæ ducendus e&longs;t per 7, vt habeatur totum <pb xlink:href="018/01/031.jpg" pagenum="23"/><arrow.to.target n="note16"/><lb/>potentiæ momentum 5025285.913842. <lb/>968121.391743. Quarè adhibito conatu, <lb/>quo libras decem ab&longs;què machinâ traheres, <lb/>mouere po&longs;&longs;es libras 50.252859.138429. <lb/>681213.917430. Quod pondus totius ter<lb/>reni globi grauitatem &longs;uperat. </s>

<row>

<s>Orbiculis ita<lb/>que &longs;ex &longs;upra centum Archimedæum pro<gap/><lb/>blema de terræ motione ab&longs;olui po&longs;&longs;e o&longs;ten<lb/>di. </s>

<cell>O<emph type="italics"/>mne mobile motu naturali de&longs;cendentis parte, de&longs;cendit grauiore &longs;ecundum gra<emph.end type="italics"/></cell>

<cell/>

<s><margin.target id="note16"/><emph type="italics"/>XV <lb/>Orbiculis <lb/>106 po&longs;&longs;&etail; <lb/>tellure&mtail; <lb/>moueri <expan abbr="de-mõ">de<lb/>mon</expan>&longs;tratur.<emph.end type="italics"/></s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Quid verò, &longs;i quis maiorem ad<lb/>huc grauitatem telluri tribuat? </s>

<row>

<cell/>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Parum mihi face&longs;&longs;at hic negotij. </s>

<cell><emph type="italics"/>uitatis centrum.<emph.end type="italics"/></cell>

<s><lb/>Addat duas præterea trochleas aut quatuor, <lb/>aut plures; & fortè non adeò multas adijcere <lb/>oportebit: Mihi &longs;atis e&longs;t chiliadas illas orbi<lb/>culorum atque myriadas, quas multi ad<lb/>&longs;truunt, tanquam minimè nece&longs;&longs;arias refu<lb/>ta&longs;&longs;e. </s>

</row>

<row>

<s>Nunc quidem &longs;olâ coniecturâ terreni <lb/>globi grauitatem venari po&longs;&longs;umus: dato au<lb/>tem extra terram loco, in quo con&longs;i&longs;teremus, <lb/>facile e&longs;&longs;et trochlearum numerum definire: <lb/>examinato nimirum &longs;taterâ telluris pondere; <lb/>quo demum cognito trochlearum, quibus <lb/>opus e&longs;&longs;et, numerus innote&longs;ceret. </s>

<cell>P<emph type="italics"/>roportionum ictus ad pondus rei & di&longs;tantiam generaliter con&longs;iderare.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> At &longs;taterâ, cuius iugum aliquot <lb/>pa&longs;&longs;uum millia occuparet, &longs;acomatis autem <lb/>munere rupes non exigua fungeretur. </s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Mittamus i&longs;thæc; quæ à te reru&mtail; <pb xlink:href="018/01/032.jpg" pagenum="24"/>huiu&longs;modi apprimè gnaro, animi tantùm <lb/>causâ, in medium proferri &longs;atis video. </s>

<row>

<s>La<lb/>nius vel cætarius opportunam &longs;tateram &longs;up<lb/>peditare po&longs;&longs;et; modò &longs;ingulæ libræ in &longs;uas <lb/>vncias ritè di&longs;tributæ iugum di&longs;tinguerent. </s><figure id="id.018.01.032.1.jpg" xlink:href="018/01/032/1.jpg"/>

<cell>P<emph type="italics"/>roportionem motoris in plano ad motorem, qui eleuat pondus iuxta id quod mouet, inuenire.<emph.end type="italics"/></cell>

<s>Erige enim ad perpendiculum trabes <gap/>uas <lb/>æquali interuallo à &longs;e inuicem di&longs;tinctas: A&longs;<lb/>&longs;umaturque vectis AB, cuius pars decim&atail; <pb xlink:href="018/01/033.jpg" pagenum="25"/>&longs;it AC, (quanquam id &longs;culptor non expre&longs;<lb/><arrow.to.target n="note17"/><lb/>&longs;it) & extremum A &longs;it circa axem trabi AO <lb/>infixum ver&longs;atile, extremum verò B ita à <lb/>trabe ER di&longs;ter, vt a&longs;&longs;umpto &longs;imili vect&etail; <lb/>DE circùm E ver&longs;atili, & vtroque DE, AB <lb/>parallelo horizonti, perpendicularis BF &longs;e<lb/>cet pariter FE partem decimam totius DE. </s>

</row>

<row>

<s><lb/>Idquè in con&longs;equentibus vectibus factum in<lb/>telligatur. </s>

<cell>LXIII.</cell>

<cell>O<emph type="italics"/>mne graue quanto proximius alligatum plano, tantò facilius trabitur.<emph.end type="italics"/></cell>

<s>Porrò BF, DI &c. </s>

</row>

<s>&longs;int ex ma<lb/>teriâ &longs;olidâ, & circa clauiculos extrema B, F, <lb/>D &c. </s>

<row>

<cell>LXIIII.</cell>

<s>moueri po&longs;&longs;int; ac po&longs;tremus vectis <lb/>MR habeat propè V lingulam &longs;eu momen<lb/>tum, vt quandò trabi ER congruit, &longs;ignifi<lb/>cet vectes omnes con&longs;titutos e&longs;&longs;e horizonti <lb/>parallelos. </s>

<cell>O<emph type="italics"/>mne mobile quantò latius tanto tardius mouitur in plano.<emph.end type="italics"/></cell>

<s><margin.target id="note17"/><emph type="italics"/>XVI <lb/>Statera <expan abbr="cõ-muni">con<lb/>muni</expan> pote&longs;t <lb/>ingens pon<lb/>dus exami<lb/>nari.<emph.end type="italics"/></s>

</row>

<row>

<s>Tum applicatâ in M &longs;taterâ examinetur <lb/>omnium vectium &longs;imul momentum graui<lb/>tatis. </s>

<cell>P<emph type="italics"/>roportionem duorum mobilium inter &longs;e cum auxilio medij inuenire.<emph.end type="italics"/></cell>

<s>Non grauitatem dico, &longs;ed momen<lb/>tum grauitatis; quia vectis AB in F &longs;u&longs;pen<lb/>&longs;us non &longs;ecundùm totam &longs;uam grauitate&mtail; <lb/>deor&longs;um nititur, quia & in A &longs;u&longs;tinetur, &longs;ed <lb/>tantùm &longs;emi&longs;&longs;em totius &longs;uæ grauitatis exer<lb/>cet. </s>

</row>

<s>Quia verò DE e&longs;t longitudo decupla <lb/>ip&longs;ius FE, ideò grauitas totius AB non per<lb/>cipitur in D ni&longs;i &longs;ecundùm partem &longs;ui vige<lb/>&longs;imam, in H verò &longs;ecundùm partem ducen<lb/>te&longs;imam, & &longs;ic deinceps; ita vt &longs;i fuerint in <lb/>vniuer&longs;um octo vectes, percipiatur in M &longs;o<pb xlink:href="018/01/034.jpg" pagenum="26"/>lùm pars vicies millies mille&longs;ima grauitatis <lb/>totius AB. <emph type="italics"/>S<emph.end type="italics"/>ecundi autem vectis DF gra<lb/>uitas percipitur in M &longs;ecundùm partem &longs;ui <lb/>bis millies mille&longs;imam. </s>

<row>

<s>Tertius &longs;ecundùm <lb/>partem ducenties mille&longs;imam; & &longs;ic dein<lb/>ceps, donec vltimus MR grauitet in M &longs;e<lb/>cundùm &longs;uæ grauitatis &longs;emi&longs;&longs;em. </s>

<cell>P<emph type="italics"/>roportionem laterum eptagoni, & &longs;ubten&longs;arum con&longs;iderare, & quæ à reflexa proportione pendent.<emph.end type="italics"/></cell>

<s>Hinc e&longs;t <lb/>quod quamuis primus vectis AB valdè cra&longs;<lb/>&longs;us e&longs;&longs;e deberet, atque adeò grauis, vt pon<lb/>dus valeret &longs;u&longs;tinere, con&longs;equentes tame&ntail; <lb/>vectes minores, ac minores, quod ad cra&longs;&longs;i<lb/>tudinem &longs;pectat, requirerentur: ac proinde <lb/>eorum momenta in M &longs;imul &longs;umpta no&ntail; <lb/>e&longs;&longs;ent adeò multa. </s>

</row>

<row>

<s>Ponamus itaque facoma<lb/>te in N exi&longs;tente fieri æquilibrium cum ve<lb/>ctibus horizonti parallelis. </s>

<cell>LXVII.</cell>

<cell>S<emph type="italics"/>i fuerint aliquot quantitates ab una quantitate aliæque totidem ab eadem analogæ, erit proportio tertiæ unius ordinis ad tertiam alterius, ut &longs;ecundæ ad &longs;ecundum duplicata, & quartæ ad quartam triplicata, quintæ ad quintam quadruplicata, atque &longs;ic de alijs.<emph.end type="italics"/></cell>

<s>His ita con&longs;titutis dimittantur vectes, vt <lb/>ferè quantùm po&longs;&longs;unt de&longs;cendant: & in Gad<lb/>nectatur pondus. </s>

</row>

<s>Vel forta&longs;&longs;e opportunius <lb/>erit, &longs;i BF habeat in B annulum, cui in&longs;eri <lb/>po&longs;sit extremum vectis AB; vectis enim ex <lb/>annulo extractus &longs;olus deprimitur, quantum <lb/>pote&longs;t, & pondere in C adnexo, aliâ machi<lb/>nâ tractoriâ tanti&longs;per eleuatur, dum po&longs;sit <lb/>iterum annulo B in&longs;eri. </s>

<row>

<cell>LXVIII.</cell>

<s>Ni&longs;i fortè commo<lb/>dius alicui accidat ita machinam con&longs;truere, <lb/>vt iacens pondus illi adnectatur, deinde ma<lb/>china ip&longs;a æqualiter eleuetur, vnde fiat vt <pb xlink:href="018/01/035.jpg" pagenum="27"/>vectium capita deprimantur. </s>

<cell>P<emph type="italics"/>ropo&longs;itio collectorum ab<emph.end type="italics"/> E<emph type="italics"/>uclide &<emph.end type="italics"/> A<emph type="italics"/>rchimede.<emph.end type="italics"/></cell>

<s>Tum &longs;acoma <lb/>in &longs;tateræ iugo ab aginâ remoueatur adeò, <lb/>vt vectis MR (atque adeò reliqui omnes) <lb/>horizonti parallelus con&longs;tituatur, & &longs;tatera <lb/>indicet æquilibrium ex. </s>

</row>

<row>

<cell>P<emph type="italics"/>ropo&longs;itio collectorum ex quatuor libris<emph.end type="italics"/> A<emph type="italics"/>pollonij<emph.end type="italics"/> P<emph type="italics"/>ergei &<emph.end type="italics"/> <expan abbr="q.">que</expan> S<emph type="italics"/>ereni.<emph.end type="italics"/></cell>

<s> Sumatur <lb/>igitur differentia SN, quot nimirum libras <lb/>aut vncias contineat: hæc autem multipli<lb/>cetur per momentum, quod habet potentia <lb/>in M applicata; id quod fit tot additis ci<lb/>phris, quot &longs;unt vectes, quos &longs;tatuamus e&longs;&longs;e <lb/>octo, SN verò indicare libras 3 vnc. </s>

</row>

<s>6. Sa<lb/>coma igitur in S o&longs;tendit pondus P e&longs;&longs;e libr. </s>

<row>

<s><lb/>300.000000. vnc. 600.000000, hoc e&longs;t in <lb/>vniuer&longs;um libr.350.000000. Quare con&longs;tat <lb/>di&longs;po&longs;itis hac ratione 25. vectibus, po&longs;&longs;&etail; <lb/>vulgari &longs;taterâ examinari pondus libr. </s>

<cell>S<emph type="italics"/>i fuerint tres quantitates in continua proportione, aliæque totidem in continua proportione poterunt con&longs;tituere tres quantitates in æquali differentia peruer&longs;im copulatæ.<emph.end type="italics"/></cell>

<s>250. <lb/>000000.000000.000000.000000. Vectium <lb/>autem huiu&longs;modi apta di&longs;po&longs;itio non ijs &longs;ca<lb/>teret difficultatibus, quæ &longs;uperari non po&longs;<lb/>&longs;ent. </s>

</row>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Mihi quidem &longs;atis per&longs;ua&longs;um e&longs;t, <lb/>cas, de quibus hactenus di&longs;&longs;eruimus, machi<lb/>nationes ad tellurem loco dimouenda&mtail;, <lb/>eiusque pondus examinandum aptas e&longs;&longs;&etail;, <lb/>atquè ad potentiæ momenta ferè in immen<lb/>&longs;um augenda longè præ&longs;tare machinæ eiu&longs;<lb/>dem multiplicis quàm maioris v&longs;um; in ma<lb/>iori etenim augetur &longs;olùm Ratio, quæ i&ntail; <pb xlink:href="018/01/036.jpg" pagenum="28"/>multiplici componitur. </s>

<cell>P<emph type="italics"/>roportionem leuitatis ponderis per uirgam torcularem attracti ad rectam &longs;u&longs;pen&longs;ionem inuenire.<emph.end type="italics"/></cell>

<s>Sic peritrochiu&mtail; <lb/>diametrum habens decuplam &longs;ui axis facit <lb/>potentiæ momentum decuplum: at duo pe<lb/>ritrochia Rationem quintuplam ad &longs;uos axes <lb/>habentia &longs;i componantur &longs;imul, potentiæ <lb/>momentum con&longs;tituunt vigequintuplu&mtail;. </s>

</row>

<s><lb/>Id quod & in cochlearum compo&longs;itione ma<lb/>nife&longs;tum e&longs;t, cum &longs;atius &longs;it duas cochleas cum <lb/>duobus tympanis componere, quam heli<lb/>cem vnam &longs;trictiorem vni tympano maiori <lb/>congruentem adhibere. </s>

<row>

<cell>LXXII.</cell>

<s>Hoc in vectibus, <lb/>hoc in trochleis abundè e&longs;t demon&longs;tratum. </s>

<cell>P<emph type="italics"/>roportionem ponderis &longs;phæræ pendentis ad a&longs;cendentem per accliue planum inuenire.<emph.end type="italics"/></cell>

<s>Sed adhuc rudioribus quibu&longs;dam eximen<lb/>da e&longs;t dubitatio, quæ ancipitem animu&mtail; <lb/>torquet, an videlicet ea &longs;it totius globi huius, <lb/>quem terram dicimus, grauitas, quæ ad <lb/>librarum numerum reuocata paucioribus <lb/>quàm triginta ciphris explicari queat. </s>

</row>

<row>

<s>Quam<lb/>uis enim illam certis finibus circum&longs;cri<lb/>ptam, ac numero definitam exi&longs;timent, &longs;ibi <lb/>tamen facilè per&longs;uadent <foreign lang="greek">mhdi/va talixou_ton xatw<lb/>nomasme/non u/pa/rxein</foreign>, vt quidam apud Archi<lb/>medem arenæ multitudinem con&longs;iderantes <lb/>opinabantur: qua&longs;i Arithmeticæ facultatis <lb/>labor vltimus omnem po&longs;t &longs;e relinqueret no<lb/>menclaturam. </s>

<cell>LXXIII.</cell>

<cell>P<emph type="italics"/>roportionem ponderum attractorum penes figuram in plano inuenire.<emph.end type="italics"/></cell>

<s>Quantam igitur grauitatem <lb/>globo huic, qui terras ac maria complecti<lb/>tur, tribuemus? </s><pb xlink:href="018/01/037.jpg" pagenum="29"/>

</row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Vereor ne vobis grauis fiam, &longs;i ea <lb/>exponere voluero, quæ aliquando placuit in <lb/>hanc &longs;ententiam commentari. </s>

<row>

<cell>LXXIIII.</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Immò verò aures meæ ad iucun<lb/>dam hanc di&longs;putationem patent: ni&longs;i fortè <lb/>negotia habeas, Galilæe, quibus te nunc o<lb/>porteat intere&longs;&longs;e. </s>

<cell>P<emph type="italics"/>roportionem concutientis ad concu&longs;&longs;um in&longs;tabili inuenire.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Sum planè vacuus: nec facilè patiar <lb/>tam citò abire amicos, quorum eruditâ con<lb/>&longs;uetudine tantoperè recreor. </s>

</row>

<row>

<s>An a&longs;ymbo<lb/>lum te rece&longs;&longs;urum putas, Guldine; Vnum <lb/>habeo, de quo te pariter interrogem, qui a<lb/>lios ad dicendum excitas: vbi tamen Mer<lb/>&longs;ennus &longs;uas de terræ grauitate commentatio<lb/>nes in medium protulerit. </s>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> immoti in aqua, ad <expan abbr="immot&utilde;">immotum</expan> in terra in excipiendo <expan abbr="ict&utilde;">ictum</expan> inuenire.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si me audieritis, di&longs;putatione&mtail; <lb/>hanc in &longs;equentem diem transferemus; cum <lb/>enim numeris aliquot maioribus<emph type="sup"/><emph.end type="sup"/> opus ha<lb/>beam, longè commodius accidet eos in &longs;che<lb/>dulâ domi priuatim adnotatos in promptu <lb/>habere, quàm illos inter colloquendum in<lb/>ue&longs;tigare non &longs;ine mole&longs;tâ &longs;ermonis interru<lb/>ptione, temporis iacturâ, & capitis defati<lb/>gatione: nam &longs;atis nos hodiè tor&longs;imus tot <lb/>Rationum compo&longs;itarum inuentione. </s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Fiat, vt Mer&longs;enno placet. </s><pb xlink:href="018/01/038.jpg" pagenum="30"/><figure id="id.018.01.038.1.jpg" xlink:href="018/01/038/1.jpg"/>

<row>

<cell>LXXVI.</cell>

<s><emph type="center"/>DISSERTATIO <lb/>SECVNDA<emph.end type="center"/></s>

<cell>P<emph type="italics"/>roportionem <expan abbr="duor&utilde;">duorum</expan> mobilium &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> <expan abbr="concurrenti&utilde;">concurrentium</expan> per <expan abbr="rectã">rectam</expan> inuenire.<emph.end type="italics"/></cell>

<s><emph type="center"/>Terræ grauitatem inue<lb/>&longs;tigat.<emph.end type="center"/></s>

</row>

<row>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

<cell>LXXVII.</cell>

<cell>P<emph type="italics"/>roportionem motus obliqui ad motum rectum in nauibus inuenire.<emph.end type="italics"/></cell>

<s>CVM ad ingentia onera loco <lb/>mouenda machinam mem<lb/>bris non adeò multis di&longs;tin<lb/>ctam, neque paratu valdè <lb/>difficilem con&longs;trui po&longs;&longs;e, &longs;atis <lb/>he&longs;ternâ di&longs;&longs;ertatione o&longs;tenderimus; illud <lb/>nunc ex te, Mer&longs;enne, audire expectamus, <lb/>quanta &longs;it terreni orbis grauitas, vt quà&mtail; <lb/>magnâ pariter ad eam &longs;uperandam machi<pb xlink:href="018/01/039.jpg" pagenum="31"/>natione opus habui&longs;&longs;et Archimedes, intelli<lb/>gamus. </s>

</row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Principio, quoniam id ex me pla<lb/>cet audire, grauitatem ex mole inue&longs;tigan<lb/>dam intelligens, quotquot apud authores <lb/>extabant de terræ magnitudine opiniones, <lb/>c&oelig;pi ad examen reuocare, vt eas, quæ pro<lb/>babili alicui coniecturæ & rationi niterentur, <lb/>à temerè con&longs;titutis, &longs;ecernerem. </s>

<row>

<cell>LXXVIII.</cell>

<s>Cum ve<lb/>rò in omnibus <foreign lang="greek">geometrik/n a)xri/beian</foreign> de&longs;idera<lb/>rem, & in &longs;ingulis labem aliquam mihi vi<lb/>derer deprehendere, vulgati&longs;&longs;imæ demù&mtail; <lb/>opinioni acquie&longs;cendum cen&longs;ui, quæ 60 mil<lb/>liaria Italica mediocria &longs;ingulis gradibus tri<lb/>buit; vt à veritate minimùm recederem, vel <lb/>&longs;altem eos &longs;olùm haberem aduer&longs;arios, qui <lb/>nimio in antiquitatem &longs;tudio feruntur. <emph type="italics"/>S<emph.end type="italics"/>cru<lb/>pulus tamen, fateor, animum quantumuis <lb/>di&longs;&longs;imulantem &longs;timulabat, quoties milliaria <lb/>huiu&longs;modi minoribus men&longs;uris di&longs;tinguere <lb/>atque ad pedes reuocare opus erat; que&mtail; <lb/>enim poti&longs;simùm pedem v&longs;urparem, incer<lb/>tus hærebam; cùm pro diuer&longs;a a&longs;&longs;umpti pe<lb/>dis longitudine moles tota terreni globi alia <lb/>atquè alia deprehenderetur, di&longs;crimine non <lb/>contemnendo. </s>

<cell>P<emph type="italics"/>roportionem nauis ad triremes quotuis concurrentes demon&longs;trare.<emph.end type="italics"/></cell>

<s>Perpendens itaque corporum vmbras ideo <lb/>&longs;emper in oppo&longs;itam Soli plagam proijci, <pb xlink:href="018/01/040.jpg" pagenum="32"/><arrow.to.target n="note18"/><lb/>quia nulla Solis particula ad perpendiculum <lb/>imminet corpori, quod luce afficitur, i&ntail; <lb/>&longs;pem erigebar aliquid deprehendendi ex &longs;pa<lb/>tio circa Syenen ab antiquis apud Cleome<lb/>dem ob&longs;eruato, in quo gnomones nullam <lb/>proijciunt vmbram meridianam Sole Tro<lb/>picum Cancri percurrente. </s>

</row>

<row>

<s>Si enim in pla<lb/>no AB erigatur &longs;tylus TI perpendicularis, <lb/>cui immineat Solis extremus limbus O, nul<lb/>la fit vmbra, quia quamuis ab alio extremo S <lb/>veniat radius SN vltimus, & intrà &longs;patium <lb/><figure id="id.018.01.040.1.jpg" xlink:href="018/01/040/1.jpg"/><lb/>TN nullus alius ve<lb/>niat radius ab eodem <lb/>puncto S radios in or<lb/>bem diffundente, in<lb/>trà illud tamen &longs;pa<lb/>tium TN veniunt <lb/>radij à cæteris om<lb/>nibus punctis inter <lb/>S & O intermediis: <lb/>quare nec vmbra vl<lb/>la aut penumbra ob&longs;eruari pote&longs;t. </s>

<cell>LXXIX.</cell>

<cell>P<emph type="italics"/>roportionem medicamentorum purgantium inuicem declarare<emph.end type="italics"/></cell>

<s>At &longs;i &longs;ty<lb/>lus in LM fuerit, proiicit vmbram LP, in<lb/>trà quod &longs;patium nullus cadit radius dire<lb/>ctus á punctis O & S aut intermediis; penum<lb/>bra verò ex P ad B procedit, donec in B me<lb/>ra lux incipiat. </s>

</row>

<s>Cum itaque &longs;patio 300 &longs;ta<lb/>diorum gnomones vmbram non proiicerent, <pb xlink:href="018/01/041.jpg" pagenum="33"/>totum hoc &longs;pa<lb/><figure id="id.018.01.041.1.jpg" xlink:href="018/01/041/1.jpg"/><lb/>tium illud e&longs;t, <lb/>cui Sol ad per<lb/>pendiculum im<lb/>minet. </s>

<row>

<s><margin.target id="note18"/><emph type="italics"/>XVII <lb/>Terræ ma<lb/>gnitudinem <lb/>eiu&longs;que ad <lb/>Solem pro<lb/>portione&mtail; <lb/>inue&longs;tigare <lb/>ex &longs;patio, <lb/>quod umbris <lb/>caret.<emph.end type="italics"/></s>

<cell>P<emph type="italics"/>roportionem motus &longs;ecundum obliquum ad rectum in &longs;pacio declarare.<emph.end type="italics"/></cell>

<s>Sed <expan abbr="quærend&utilde;">quærendum</expan> <lb/>&longs;upererat, quo<lb/>ta totius circuli <lb/>maximi pars e&longs;<lb/>&longs;ent &longs;tadia 300. <lb/>Con&longs;tituto ita<lb/>que terræ centro <lb/>in C, & oculo <lb/>ob&longs;eruatoris i&ntail; <lb/>O, ductum <expan abbr="in-telligebã">in<lb/>telligebam</expan> ex cen<lb/>tro S radium S <lb/>OC, qui cu&mtail; <lb/>radio OT Solem <lb/>contingente da<lb/>bat angulum S <lb/>OT &longs;emidiametrum apparentem Solis Apo<lb/>gæi gr.o.m.15., vt placet Tychoni, Longo<lb/>montano, Magino, Keplero. </s>

</row>

<row>

<s>Item ex C du<lb/>ctus intelligatur radius Solem tangens, qui <lb/>terræ circulum maximum &longs;ecat in K; & e&longs;t <lb/>OK &longs;emi&longs;sis &longs;patij, quod caret vmbris meri<lb/>dianis die &longs;ol&longs;titij æ&longs;tiui; continet autem &longs;ta<pb xlink:href="018/01/042.jpg" pagenum="34"/>dia 150. Certum e&longs;t angulum OCK mino<lb/>rem e&longs;&longs;e angulo <emph type="italics"/>S<emph.end type="italics"/>OT: &longs;i enim linea CK pro<lb/>ducta terminaretur in T, tunc angulus SOT <lb/>externus maior e&longs;&longs;et interno oppo&longs;ito OCT: <lb/>quia verò, quod veritati magis e&longs;t con&longs;enta<lb/>neum, radius ex C Solem tangens e&longs;t CI vl<lb/>tra T, angulus ISC maior e&longs;t angulo T<emph type="italics"/>S<emph.end type="italics"/>O; <lb/>ac proinde, cum anguli ad T & I &longs;int recti, <lb/>reliquus SCI e&longs;t reliquo SOT minor. </s>

<cell>LXXXI.</cell>

<cell>Q<emph type="italics"/>ualis &longs;it angulus, per quem pote&longs;t moueri nauis ad rectum explorare.<emph.end type="italics"/></cell>

<s>E&longs;t igi<lb/>tur &longs;patium OK minus quàm min.15. Qua<lb/>re vnus gradus complectitur plura quàm <lb/>600 &longs;tadia, ideoquè totus telluris ambitus <lb/>maior e&longs;t &longs;tadijs 216000. <lb/><arrow.to.target n="note19"/></s>

</row>

<s><margin.target id="note19"/><emph type="italics"/>XVIII <lb/>Stadij Græ<lb/>si quanti<lb/>tas.<emph.end type="italics"/></s>

<row>

<cell>LXXXII.</cell>

<s>Hìc. autem hærebam in &longs;tadio, ne cum <lb/>Suida errarem; hic enim primùm Milio &longs;ta<lb/>dia 7 1/2 tribuit; &longs;ed po&longs;tmodum Milijs de<lb/>cem, æqualia facit &longs;tadia 80: Cùm verò &longs;ta<lb/>dium pedibus 600 definierit, Milium dein<lb/>de in pedes 4200 di&longs;tribuit: Vnde conficitur <lb/>Milium & 7, & 7 1/2, & 8 &longs;tadia comprehen<lb/>dere. </s>

<cell>P<emph type="italics"/>roportionem uelorum indagare.<emph.end type="italics"/></cell>

</row>

<row>

<s>Quarè acquie&longs;cendum potius duxian<lb/>tiquo Scholia&longs;ti Græco in propo&longs;. </s>

<cell>LXXXIII.</cell>

<cell>P<emph type="italics"/>roportionem rece&longs;&longs;us à recta uia ad obliquitatem inue&longs;tigare.<emph.end type="italics"/></cell>

<s>5. lib d&etail; <lb/>Gæod. Heronis Mechanici, qui &longs;tadium fui&longs;<lb/>&longs;e pa&longs;&longs;uum 100, pa&longs;&longs;um cubitorum 4, cu<lb/>bitum verò digitorum 24 &longs;cribit. </s>

</row>

<row>

<cell>LXXXIIII.</cell>

<s>Cum ita<lb/>que pa&longs;&longs;us Romanus pedibus quinque con<lb/>&longs;taret, &longs;inguli verò pedes palmis 4, hoc e&longs;t <lb/>digitis 16, pa&longs;&longs;us <emph type="italics"/>R<emph.end type="italics"/>omanus digitos 80 com<pb xlink:href="018/01/043.jpg" pagenum="35"/>plectebatur, quorum pa&longs;&longs;us Græcus habebat <lb/>96, &longs;c.4.cubitos, &longs;eu, quod idem e&longs;t, pedes <lb/>&longs;ex Romanos. </s>

<cell>D<emph type="italics"/><expan abbr="i&longs;tantiã">i&longs;tantiam</expan> centri terræ à centro mundi per motum lapidis<emph.end type="italics"/> H<emph type="italics"/>erculei declarare.<emph.end type="italics"/></cell>

<s>Stadia igitur &longs;ingula pedes <lb/>Rom. antiquos 600 continebant, hoc e&longs;t pa&longs;<lb/>&longs;us 120. Hinc fit<gap/> terræ ambitum maiorem <lb/>&longs;tadijs 216000, maiorem quoquè e&longs;&longs;e pa&longs;si<lb/>bus <emph type="italics"/>R<emph.end type="italics"/>om. <expan abbr="antiq.">antique</expan> 25920000, hoc e&longs;t mill. <lb/>Rom. 25920. Quarè etiam gradibus &longs;in<lb/>gulis milliaria Rom. antiqua plura quàm 72 <lb/>re&longs;pondent. </s>

</row>

<row>

<cell>LXXXV.</cell>

<cell>P<emph type="italics"/>roportio ponderis unius grauis ad aliud &longs;ub eadem men&longs;ura e&longs;t ueluti eiu&longs;dem ad differentiam ponderis ua&longs;is repleti ex altero graui, & ex ambobus detracto priore.<emph.end type="italics"/></cell>

</row>

<row>

<cell>LXXXVI.</cell>

<cell>S<emph type="italics"/>i circuli in æ quales &longs;eu in &longs;phæra &longs;eu in plano &longs;e &longs;ecuerint, nunquàm oppo&longs;itos angulos æquales habent.<emph.end type="italics"/></cell>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> At anguli OCK quantitatem quot <lb/>&longs;crupulis definiebas minorem angulo <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>min. 15? </s>

<cell>LXXXVII.</cell>

<cell>P<emph type="italics"/>roportiones craßitiei aquæ ad <expan abbr="a&etilde;r&etilde;">aerem</expan> in <expan abbr="cõparatione">comparatione</expan> ad radios demon&longs;trare.<emph.end type="italics"/></cell>

</row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Quæ&longs;iui primùm quoties Solis &longs;e<lb/>midiameter ST contineretur à lineâ SO: dato <lb/>autem SOT gr.o.m.15. reliquus e&longs;t TSO gr. <lb/>89.m.45.cuius Secans SO <expan abbr="parti&utilde;">partium</expan> 22918384. <lb/>52745, quarum Radius ST e&longs;t 100000. <lb/>00000. Deinde po&longs;itâ terræ &longs;emidiametro <lb/>CO Algebricè 1 &rx;, e&longs;t tota CS 1 &rx; &dagger; 22918384 <lb/>52745, cui ex Tychone æquantur &longs;emidia<lb/>metri terre&longs;tres, 1182, hoc e&longs;t 1182 &rx;. </s>

<row>

<cell>LXXXVIII.</cell>

<cell>I<emph type="italics"/><expan abbr="n&longs;trument&utilde;">n&longs;trumentum</expan><emph.end type="italics"/> A<emph type="italics"/>colingen, quo momenta temporum <expan abbr="deprehendãtur">deprehendantur</expan> fabricare.<emph.end type="italics"/></cell>

<s>Qua<lb/>re <expan abbr="vtrinq;">vtrinque</expan> &longs;ublatâ 1 &rx;, manet æquatio 1181 &rx; <lb/>& 22918384.52745: & in&longs;titutâ diui&longs;ion&etail; <lb/>prouenit pretium vnius Radic<gap/>s 19405. <lb/>91407. &longs;emidiameter terræ CO, quarum So<lb/>lis &longs;emidiameter e&longs;t 100000.00000. E&longs;t igi<lb/>tur tota SC, &longs;i CO inuenta addatur ip&longs;i SO, <pb xlink:href="018/01/044.jpg" pagenum="36"/>partium 22937790.44152, quæ e&longs;t Secans <lb/>gr.89.m.45.&longs;ec.o.Ter.43. Quar. 53. &c. </s>

</row>

<row>

<cell>LXXXIX.</cell>

<cell>P<emph type="italics"/>roportionem den&longs;itatis aquæ ad aërem per pondera inuenire.<emph.end type="italics"/></cell>

<s><lb/>hoc e&longs;t anguli ISC: atque adeò eius comple<lb/>mentum SCI erit gr.o.m.14.&longs;ec.59. Ter. <lb/>16. Quar. 7. quem metitur arcus OK &longs;tad. </s>

</row>

<row>

<cell>R<emph type="italics"/>ationem impetus uiolenti extra mißi ponderis ad æqualitatem reducere.<emph.end type="italics"/></cell>

<s><lb/>150. Fiat demùm vt arcus OK inuentus <lb/>&longs;crupulorum Quart. 3237367 ad &longs;tadia 150, <lb/>ita totius circuli ambitus &longs;crupulorum Quart. <lb/>4665600000. ad &longs;tadia 216175 (67/100), hoc e&longs;t, <lb/>neglectâ fractione, milliaria Rom. antiqu&atail; <lb/>25941. Quapropter &longs;ingulis gradibus mill. <lb/>Rom. 72. pa&longs;&longs;.58 re&longs;pondent. </s>

</row>

<row>

<cell>P<emph type="italics"/>roportionem grauis cubi, & &longs;phærici æqualium in accliui, & de&longs;cen&longs;us eorum demon&longs;trare.<emph.end type="italics"/></cell>

</row>

<row>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> ponderis æqualis iuxta longitudinis <expan abbr="cõparation&etilde;">comparationem</expan> demon&longs;trare.<emph.end type="italics"/></cell>

</row>

<row>

<s>Porrò inuentâ peripheriâ, &longs;i fiat vt 22 ad 7 </s>

<cell>XCIII.</cell>

<cell>P<emph type="italics"/>ropter qd in <expan abbr="cõcußione">concußione</expan> <expan abbr="etiã">etiam</expan> leui nauis loco moueatar <expan abbr="o&longs;t&etilde;dere">o&longs;tendere</expan>.<emph.end type="italics"/> V<emph type="italics"/>nde manife<expan abbr="&longs;i&utilde;">&longs;tum</expan> e&longs;t duas naues &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> occur&longs;antes retrocedere, & <expan abbr="quãt&utilde;">quantum</expan> <expan abbr="retrocedãt">retrocedant</expan> ambæ.<emph.end type="italics"/></cell>

<s><arrow.to.target n="note20"/><lb/>ita mill. 25941. ad mill. 8253 (21/22), habetur <lb/>diameter proximè minor verâ; & &longs;i fiat vt <lb/>223 ad 71 ita mill. 25941. ad mill. 8259 (54/223), <lb/>diametrum verâ proximè maiorem reperi<lb/>mus: & electo medio Arithmetico rectè &longs;ta<lb/>tuitur terræ diameter mill. Rom. ant. </s>

</row>

<row>

<cell>XCIIII.</cell>

<cell>S<emph type="italics"/>i <expan abbr="quãtitas">quantitas</expan> aliqua nota atque proportio erit producta, <expan abbr="quãtitas">quantitas</expan> nota &longs;imiliter.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i duæ proportiones notæ fuerint, erit producta ex his atque diui&longs;a coniunctaque atque detracta nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit totius ad partem proportio nota, erit et ad aliam partem nota: & alterius partis ad <expan abbr="alterã">alteram</expan> uno minor.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit partis ad partem, erit ad totum monade minor atque nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit unius <expan abbr="quãtitatis">quantitatis</expan> ad duas <expan abbr="quãtitates">quantitates</expan> proportio nota, erit & <expan abbr="cõfu&longs;a">confu&longs;a</expan> ex eis nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerint trium quantitatum omiologarum, aut quatuor analogarum omnes præter unam cognitæ, erunt & illa alia cognita.<emph.end type="italics"/></cell>

</row>

<row>

<cell>C<emph type="italics"/>uiu&longs;uis trigoni rectanguli, aut cuius duo anguli &longs;int in dupla proportione, aut qui circulo in&longs;criptus &longs;it cognita quantitate unius lateris in comparatione ad dimetien<expan abbr="t&etilde;">tem</expan>, &longs;i proportio duorum laterum cognita fuerit, <expan abbr="er&utilde;t">erunt</expan> omnia eius latera cognita.<emph.end type="italics"/></cell>

</row>

<row>

<s>8255. <lb/>pa&longs;&longs; 644, ideòque &longs;emidiameter mill. 4127. <lb/>pa&longs;&longs;. </s>

<cell>C<emph type="italics"/>um in <expan abbr="per&longs;picu&utilde;">per&longs;picuum</expan> den&longs;um radij lumino&longs;i inciderint, quatuor fiunt luminis genera.<emph.end type="italics"/></cell>

</row>

<s>822. Quod &longs;i libeat exactiùs operari, <lb/>quoniam circuli diametro po&longs;itâ 1, perime<lb/>ter polygoni laterum 2560 circulo circum<lb/>&longs;cripti minor e&longs;t quàm 3 (14160/100000), perimeter ve<lb/>rò in&longs;cripti maior e&longs;t quàm 3 (14159/100000); fiat pri<lb/>mò vt 3. 14160. ad 1, ita mill. 25941 ad <lb/>mill.8257.pa&longs;&longs;.257, quæ e&longs;t diameter mi-

<row>

<cell>XCVII.</cell>

<cell>M<emph type="italics"/><expan abbr="ot&utilde;">otum</expan> inuer&longs;ionis in figuris in <expan abbr="cõparatione">comparatione</expan> ad <expan abbr="mot&utilde;">motum</expan> &longs;phæræ in plano inue&longs;tigare.<emph.end type="italics"/></cell>

nor verâ deinde vt 3.14159 ad 1, ita mill. <lb/>

</row>

25941 ad mill. 8257 pa&longs;&longs;. 283 diametrum<lb/>

<row>

maiorem verâ. </s><s>Quare cum differentia &longs;it <lb/>

<cell>XCVIII.</cell>

pa&longs;&longs; 26, electo medio Arithmetico po<lb/>

<cell>P<emph type="italics"/>roportionem ponderum æqualium per differentiam angulorum inuenire.<emph.end type="italics"/></cell>

terit a&longs;&longs;umi pro terræ diametro <expan abbr="quãtitas">quantitas</expan> mill. <lb/>

Rom. antiq. 8257 pas&longs;&longs;. 270. Sed certas <lb/>

</row>

ob causas placuit a&longs;&longs;umere ambitum mill. <lb/>

<row>

25941, atque &longs;emidiametrum mill. 4127. <lb/>

pa&longs;&longs; 822.</s>

<cell>P<emph type="italics"/>roportionem grauitatum per multitudinem &longs;uppo&longs;itorum orbium o&longs;tendere.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Guld.<emph.end/> Methodum hanc, qua & Solaris &longs;e<lb/>midiametri cum terrenâ comparatæ Ratio<lb/>

nem venatus es, & telluris ip&longs;ius magnitu<lb/>

</row>

dinem indaga&longs;ti, omnino improbare non <lb/>

<row>

au&longs;im; quippe qui apparentem Solis &longs;emi<lb/>diametrum ob&longs;eruari po&longs;&longs;e &longs;atis &longs;cio, & Solis <lb/>

à terrâ di&longs;tantiam poti&longs;&longs;imùm ex lunari di<lb/>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> grauitatis <expan abbr="ponder&utilde;">ponderum</expan> attractorum per <expan abbr="trochlear&utilde;">trochlearum</expan> <expan abbr="numer&utilde;">numerum</expan> inue&longs;tigare.<emph.end type="italics"/></cell>

chotomiâ haberi ex Ari&longs;tarcho didici: quan<lb/>

tum verò interuallum à nobis Lunam &longs;eiun<lb/>gat, eiu&longs;dem parallaxes palà faciunt. </s><s> Quæ <lb/>

</row>

omnia &longs;i retè fuerint con&longs;tituta, non infir<lb/>mis nititur fundamentis inuenta terræ ma<lb/>

<row>

gnitudo: Sed, vt vera fatear, quamuis Sol <lb/>

quotidie terrma circumiens lu&longs;tret, illum <lb/>

<cell>P<emph type="italics"/>roportionem pretij gemmarum ex tribus in eodem genere cognitis inuenire.<emph.end type="italics"/></cell>

tamen de terrâ, terræ incola inuitus interro<lb/>go; quotus enim qui&longs;que e&longs;t, qui ignoret, <lb/>

quàm oculatum exigat Astronomum appa<lb/>rentium Solis ac Lunæ &longs;emidiametrorum <lb/>

</row>

con&longs;titutio? &longs;ivè illæ organis deprehendantur, <lb/>

<row>

<cell>P<emph type="italics"/>roportionem motuum inuer&longs;ionis, & attractionis in plano inuenire.<emph.end type="italics"/></cell>

<pb xlink:href="018/01/046.jpg" pagenum="38"/>tur, &longs;iue ex lucidâ &longs;pecie (quam ab omni pe<lb/>numbrâ ægrè &longs;ecernas) &longs;iuè ex eclip&longs;ibus in<lb/>ferantur. </s>

</row>

<row>

<cell>P<emph type="italics"/>roportionem eorundem in accliui demon&longs;trare.<emph.end type="italics"/></cell>

<s>Quod &longs;i a&longs;&longs;umpta Lunæ parallaxis <lb/>à vero aliquantulum ab&longs;it, vel quia à radio<lb/>rum refractione turbetur, vel quia motuum <lb/>periodi non &longs;atis accuratè ad calculos reuo<lb/>centur, interuallorum pariter, quæ inde col<lb/>liguntur, veritas nutat. </s>

</row>

<s>Ad hæc fides adhi<lb/>benda e&longs;t antiquis &longs;patium, quod meridianis <lb/>vmbris caret, dimetientibus, atque &longs;tadijs <lb/>300 definientibus; quæ tamen ad notas no<lb/>bis men&longs;uras vt reuocemus, certioribus ad<lb/>huc argumentis indigemus. </s>

<row>

<cell>CIIII.</cell>

<s>Illud tame&ntail; <lb/>hìc minimè di&longs;simulandum videtur, quod <lb/>eruditis non paucis placere video: non eam <lb/>&longs;cilicet &longs;tadij men&longs;uram, quam ex Græco <lb/>Heronis &longs;cholia&longs;te a&longs;&longs;ump&longs;i&longs;ti, adhibendam <lb/><arrow.to.target n="note21"/><lb/>e&longs;&longs;e, &longs;ed eam potiùs, quæ ex ip&longs;ius Heronis <lb/>Mechanici I&longs;agoge colligitur dicentis, <emph type="italics"/>Diau<emph.end type="italics"/><lb/>l<emph type="italics"/>on habet Stadia duo, Plethra duodecim, Ace<lb/>nas centum viginti, Cubitos octingentos, Pe<lb/>des Alexandrinos Philetæreos mille ducentos, <lb/>Italicos autem pedes mille quadringentos qua<lb/>draginta.<emph.end type="italics"/></s><s> Quare Stadium non Romanis pe<lb/>dibus 600 con&longs;tat, &longs;ed Alexandrinis 600, hoc <lb/>e&longs;t Italicis, pedibus 720, &longs;eu pa&longs;&longs;ibus 144. <lb/>Neque enim coniecturâ &longs;atis probabili caret <lb/>Erato&longs;thenem Alexandrinæ Bibliothecæ præ<pb xlink:href="018/01/047.jpg" pagenum="39"/>&longs;ectum à Ptolemæis Euergete, Philopatore, <lb/>& Epiphane, v&longs;um fui&longs;&longs;e men&longs;urâ Ægyptijs <lb/>tunc familiari, pede nimirum Alexandrino, <lb/>atquè adeò etiam &longs;tadio, quod ille metieba<lb/>tur. </s>

<cell>P<emph type="italics"/>roportionem motus attractionis in decliui ad motum in plano determinare.<emph.end type="italics"/></cell>

<s>Hinc fit &longs;tadia illa 300 re&longs;pondere pa&longs;<lb/>&longs;ibus Romanis 43200: arcum verò OK e&longs;&longs;e <lb/>pa&longs;&longs; Rom. 21600. Igitur &longs;i fiat vt arcus OK <lb/>à te nuper inuentus &longs;crupulorum Quart. <lb/>3237367 ad pa&longs;&longs;. </s>

</row>

<row>

<cell>P<emph type="italics"/>roportionem ferentium pondus in pertica inuenire.<emph.end type="italics"/></cell>

</row>

<s>Rom. 21600, ita tota pe<lb/>ripheria &longs;crup. </s>

<row>

<cell>Q<emph type="italics"/>uales proportiones angulorum doceant laterum proportiones.<emph.end type="italics"/> A<emph type="italics"/>tque uicißim determinare.<emph.end type="italics"/></cell>

<s>Quart. 4665600000. ad pa&longs;&longs;. </s>

</row>

<row>

<cell>S<emph type="italics"/>i in circulo duæ diametri ad rectum angulum &longs;e &longs;ecauerint: aliæ uerò ad perpendiculum ex diametro exierint ad circum ferentiam, &longs;ingulæ &longs;upra diametrum erunt maiores portionibus reliquis diametri &longs;uperioribus, infra autem minores.<emph.end type="italics"/> D<emph type="italics"/>imidium autem portionis &longs;uperioris re&longs;iduum ad centrum maius &longs;agitta habebit.<emph.end type="italics"/> I<emph type="italics"/>n aliqua præterea portionis &longs;uperioris parte, quæ uer&longs;us diametrum tran&longs;uer&longs;um po&longs;ita e&longs;t, maior e&longs;t differentia partis diametri ei <expan abbr="corre&longs;põdentis">corre&longs;pondentis</expan>, <expan abbr="&qtilde;">quae</expan> line æ tran&longs;uer&longs;æ.<emph.end type="italics"/></cell>

<s><lb/>Rom. 31.129297, erit multo maior terræ <lb/>ambitus, quàm à te fuerit deprehen&longs;us. </s>

</row>

<row>

<cell>CVIII.</cell>

<s><margin.target id="note20"/><emph type="italics"/>XIX <lb/>Terræ am<lb/>bitus, & dia<lb/>meter.<emph.end type="italics"/></s>

<cell>P<emph type="italics"/>unctum æqualitatis differentiæ de&longs;cen&longs;us & remotionis à centro inuenire.<emph.end type="italics"/></cell>

<s><margin.target id="note21"/><emph type="italics"/>XXI <lb/>Stadium A<lb/>lexandri<lb/>num.<emph.end type="italics"/></s>

</row>

<row>

<s>Sed & con&longs;titutam à Tychone Solis di<lb/>&longs;tantiam, nimis breuibus terminis defini<lb/>tam exi&longs;timant Recentiores A&longs;tronomi, So<lb/>lemque altiùs promouendum cen&longs;ent, vt &longs;i<lb/>bi inuicem ph&oelig;nomena omnia ritè re&longs;pon<lb/>deant. </s>

<cell>R<emph type="italics"/>ationem libræ expendere.<emph.end type="italics"/></cell>

<s>Certè P. Io. Bapti&longs;ta Ricciolius no<lb/>&longs;træ Societatis, qui iam annos plures in A<lb/>&longs;tronomiæ in&longs;tauratione feliciter de&longs;udat, <lb/>Solem Apogæum à telluris centro remouet <lb/>&longs;emidiam. </s>

</row>

<row>

<cell>S<emph type="italics"/>i duæ &longs;phæræ ex eadem materia de&longs;cendant in aëre, eodem temporis momento ad planum ueniunt.<emph.end type="italics"/></cell>

<s>7580., & Solis Apogæi dia<lb/>metrum apparentem &longs;tatuit Tychonicâ ma<lb/><arrow.to.target n="note22"/><lb/>iorem, nimirùm gr.o.m.30.&longs;ec.30. Qua<lb/>rè &longs;i angulus SOT &longs;it gr.o.m.15.&longs;ec.15., <lb/>complementum TSO e&longs;t gr.89.min.44. <lb/>&longs;ec.45., cuius Secans, SO 22551105.10158, <lb/>quarum partium Radius ST e&longs;t 100000. <pb xlink:href="018/01/048.jpg" pagenum="40"/>00000. Sit iam SC &longs;emid. </s>

</row>

<row>

<s>terre&longs;t. </s>

<cell>C<emph type="italics"/>ur ex medio tela ualidiorem ictum, & naues in &longs;calmo à remo ac malo recipiant inde ex puppi explorare.<emph.end type="italics"/></cell>

<s>7580, & <lb/>SO &longs;emid.terr. </s>

</row>

<s>7579: & Secans SO diuida<lb/>tur per 7579, vt Quotiens 2975.47237, <lb/>prodat quantitatem &longs;emidiametri OC i&ntail; <lb/>partibus Radij ST. </s>

<row>

<s>Additâ igitur CO ip&longs;i <lb/>OS, erit tota SC 22554080.57395, quæ <lb/>e&longs;t Secans anguli ISC gr.89.m.44.&longs;ec.45. <lb/>Ter. 7. Quar. 17. Quint. 28 1/2, atquè adeo <lb/>complementum SCI gr.o.m.15.&longs;ec.14. <lb/>Ter. 52. Quar. 42. Quint. 31 1/2. Duplicetur <lb/>itaque angulus SCI, & in Scrupula Quinta <lb/>reducatur, & &longs;crupula Quinta 395227503 <lb/>re&longs;pondent &longs;tadijs Alexandrinis 300, hoc e&longs;t <lb/>pa&longs;sibus Rom. 43200. Si igitur arcus OK <lb/>duplicatus e&longs;t pa&longs;&longs;. </s>

<cell>C<emph type="italics"/>ur ex imo leuia longiùs ferantur declarare,<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXIII.</cell>

<cell>C<emph type="italics"/>ur uirga longius mittatur à puero quam à uiro inuestigare.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXIIII.</cell>

<cell>C<emph type="italics"/>ircularis motus differentias quatuor e&longs;&longs;e, earumque rationem contemplari.<emph.end type="italics"/></cell>

</row>

<row>

<cell>P<emph type="italics"/>roportionem motuum impul&longs;ionis, & attractionis inter &longs;e, ab eadem ui declarare.<emph.end type="italics"/></cell>

<s>43200, totus circuli am<lb/>bitus &longs;crup. </s>

</row>

<s>Quint. 279936.000000.erit pa&longs;&longs;. <lb/><arrow.to.target n="note23"/><lb/>Rom. 30598162. </s>

<row>

<cell>C<emph type="italics"/>ur machinæ oblongæ igneæ longius emittant &longs;phæram explorare.<emph.end type="italics"/></cell>

</row>

<row>

<s><margin.target id="note22"/><emph type="italics"/>XXII <lb/>Probabilior <lb/>terræ ma<lb/>gnitudo ex <lb/>eadem me <lb/>tbodo inue<lb/>stigatur.<emph.end type="italics"/></s>

<cell>CXVII.</cell>

<cell>I<emph type="italics"/>n curriculis maior e&longs;t uis pulueris copio&longs;ioris ampliore in &longs;pacio, quàm paucioris in minore iuxta proportionem eandem.<emph.end type="italics"/></cell>

<s><margin.target id="note23"/><emph type="italics"/>XXIII <lb/>Solis distan <lb/>tiam à ter<lb/>ra, & pro<lb/>portione&mtail; <lb/>cum ill&atail; <lb/>inue&longs;tiga<lb/>re ex da<lb/>ta terræ ma<lb/>gnitudine, <lb/>Solis Apog. <lb/>diametro ap. </s>

</row>

<row>

<cell>CXVIII.</cell>

<s><lb/>parenti, & <lb/>&longs;patio, quod <lb/>vmbris ca<lb/>ret.<emph.end type="italics"/></s>

<cell>Q<emph type="italics"/>uanta proportione decedat ictus in obliquum parietem ab eo qui e&longs;t ad perpendiculum declarare.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Plurimam, opinor, inires gratiam <lb/>ab Eruditi&longs;&longs;. Domino 10. Bapt. Baliano Pa<lb/>tritio Genuen&longs;i, &longs;i ille no&longs;tro huic colloquio <lb/>intere&longs;&longs;et; ab eo enim accepi &longs;e certi&longs;simo <lb/>experimento didici&longs;&longs;e, telluris ambitum non <lb/>minorem e&longs;&longs;e triginta millibus milliarium. </s>

</row>

<row>

<cell>Q<emph type="italics"/>uantum ictus machinæ procliuis ad angulum minuatur explorare.<emph.end type="italics"/></cell>

</row>

<s><lb/>Tunc verò non poteram illi acquie&longs;cer&etail;, <lb/>cum viderem indè colligi Solem terræ it&atail; <lb/>vicinum, vt ab illâ non abe&longs;&longs;et &longs;emidiam. </s>

<row>

<s><lb/>terr.25; id quod e&longs;t manife&longs;tè fal&longs;um. </s>

<cell>P<emph type="italics"/>roportionem partium nauis ad eundem obliquum uentum explorare.<emph.end type="italics"/></cell>

<s>Tri<lb/>buebam autem &longs;ingulis &longs;tadiis pa&longs;&longs;us Rom. <pb xlink:href="018/01/049.jpg" pagenum="41"/>120, vt 300 &longs;tadia e&longs;&longs;ent totius circuli gr. <lb/>o.m.28.&longs;ec. 35. Ter. 12., dato ambitu <lb/>mill. 30000: & arcus OK cum e&longs;&longs;et gr.o. <lb/>m. </s>

</row>

<row>

<cell>F<emph type="italics"/>labelli uires atque naturam declarare.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXII.</cell>

<cell>C<emph type="italics"/>ontemptus circa<emph.end type="italics"/> S<emph type="italics"/>olis rationem in umbris declarare.<emph.end type="italics"/></cell>

</row>

<s>14.&longs;ec.17. Ter. 36., angulus ISC gr.89. <lb/>m. </s>

<row>

<cell>CXXIII.</cell>

<cell>C<emph type="italics"/>ognita ratione umbræ ad gnomonem &longs;inum, & arcum altitudinis ab horizonte, quouis tempore digno&longs;cere.<emph.end type="italics"/></cell>

<s>45. &longs;ec. 42. Ter. 24. dabat Secantem SC <lb/>24052069.35. in partibus Radij SI 100000. <lb/>00. Po&longs;itâ verò Tychonicâ &longs;emidiametro <lb/>apparente Solis SOT gr.o.m.15., Secans <lb/>SO erat 22918384. 52. Quare &longs;i per Se<lb/>cantium SO, SC, differentiam OC 1133684. <lb/>83. diuidatur Secans SC, Quotiens 21 dabit <lb/>di&longs;tantiam Solis à terræ centro in &longs;emidia<lb/>metris terre&longs;tribus; id quod aperti&longs;simè fal<lb/>&longs;um e&longs;&longs;e omnibus con&longs;tat. </s>

</row>

<row>

<cell>CXXIIII.</cell>

<cell>P<emph type="italics"/>roportionem umbræ uer&longs;æ e&longs;&longs;e ad gnomonem, uelut gnomonis ad umbram uer&longs;am.<emph.end type="italics"/></cell>

<s>At quoniam vis, Guldine, &longs;tadia illa 300 <lb/>e&longs;&longs;e pa&longs;&longs;us Romanos 43200, tentemus a&ntail; <lb/>illa terræ magnitudo milliaribus 30000 de<lb/>finita &longs;ub&longs;i&longs;tat. </s>

</row>

<s>Si ergo circuli totius peri<lb/>pheria ritè &longs;uas in partes tribuatur, con&longs;tat <lb/>pa&longs;&longs;. </s>

<row>

<s>43200 re&longs;pondere gr. o.m. </s>

<cell>P<emph type="italics"/>roportionem dimetientis, & peripheriæ cuiuslibet circuli paralleli æquinoctiali per cognitam partem magni circuli demon&longs;trare.<emph.end type="italics"/></cell>

</row>

<row>

<s>31. &longs;ec. 6. <lb/>Ter. 14. Quar. 24. præcisè: & angulus SCI <lb/>gr. o. </s>

<cell>CXXVI.</cell>

<cell>C<emph type="italics"/>irculi horarij naturam declarare.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXVII.</cell>

<cell>D<emph type="italics"/>ata poli altitudine ortus amplitudinem demonstrare.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXVIII.</cell>

<cell>N<emph type="italics"/>ota amplitudine ortus, cuiu&longs;que puncti arcum &longs;emidiurnum inuenire.<emph.end type="italics"/></cell>

<s>15. &longs;ec. 33. Ter.7. Quar. 12. habet <lb/><expan abbr="cõplementum">complementum</expan> ISC gr. 89. m. 44. &longs;ec. 26. Ter. <lb/>52. Quar. 48., cuius Secans SC 22110369. <lb/>79050, quarum Radius SI e&longs;t 100000.00000. <lb/>Porrò angu'us SOT &longs;emidiameter apparens <lb/>Solis Apogæi nece&longs;&longs;ariò maior &longs;tatui debet <lb/>angulo SCI con&longs;tituto, cum &longs;ub maiore an-<pb xlink:href="018/01/050.jpg" pagenum="42"/>gulo appareat <emph type="italics"/>S<emph.end type="italics"/>ol ex puncto O vicinior&etail;, <lb/>quàm ex puncto C remotiore. </s>

</row>

<row>

<cell>CXXIX.</cell>

<cell>D<emph type="italics"/>ata altitudine<emph.end type="italics"/> S<emph type="italics"/>olis in quacunque regione, quacunque die di&longs;tantiam<emph.end type="italics"/> S<emph type="italics"/>olis à meridiano cogno&longs;cere.<emph.end type="italics"/></cell>

</row>

<row>

<s>Quare a&longs;&longs;u<lb/>mi non pote&longs;t Solis Apogæi &longs;emidiameter <lb/>apparens, quam ex Ricciolio a&longs;&longs;umebas, gr. <lb/>o m. </s>

<cell>D<emph type="italics"/>ata regionis altitudine, & loco<emph.end type="italics"/> S<emph type="italics"/>olis proportionem gnomonis, tam ad umbram rectam quàm uer&longs;am, uel etiam in cylindro determinare.<emph.end type="italics"/></cell>

</row>

<s>15. &longs;ec. 15., neque Tychonica gr.o. <lb/>m.15. multò minùs Vendelinica gr.o.m.14. <lb/>&longs;ec.45: Eam igitur ex no&longs;tro Bullialdo de<lb/>&longs;umamus gr.o.m.16.&longs;ec.9., & complemen<lb/>ti Secans SO e&longs;t 21288752.30947. Ablata <lb/>itaque SO ex SC relinquit terræ &longs;emidiame<lb/>trum OC 821617.48103. in partibus Radij <lb/>SI 100000.00000: id quod fieri omnino non <lb/>pote&longs;t, ni&longs;i tellus multò maior &longs;it Sole, & hic <lb/>ab illâ remoueatur tantùm &longs;emidiametros <lb/>terre&longs;tres ferè 27: quæ omnia à vero longi&longs;<lb/>&longs;imè ab&longs;unt. </s>

<row>

<cell>CXXXI.</cell>

<cell>S<emph type="italics"/>i lineæ alicui duplum alterius adiungatur, erit proportio duarum ad primam maior quàm dupli cum prima ad primam cum una adiecta.<emph.end type="italics"/></cell>

</row>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> At fortè Balianus non ita telluris <lb/>ambitum tricies millenis milliaribus circum<lb/>&longs;cribit, vt nihil in&longs;uper additum velit, ne<lb/>què facilè cum Bullialdo tam magnam &longs;ta<lb/>tuet apparentem &longs;olis Apogæi &longs;emidiame<lb/>trum, hæc enim &longs;ibi inuicem cohærere non <lb/>po&longs;&longs;unt. </s>

<cell>CXXXII.</cell>

<cell>S<emph type="italics"/>i ad duas lineas quarum una alteri dupla &longs;it eadem linea addatur, erit aggregati ex minore, & adiecta ad ip&longs;am minorem, minor proportio quàm aggregati ex maiore, & adiecta ad ip&longs;am maiorem duplicata.<emph.end type="italics"/></cell>

<s>Et (quoniam hìc ex amicoru&mtail; <lb/>placitis aliquid vterque depromimus) quod <lb/>&longs;pectat ad apparentem Solis Apogæi diame<lb/>trum P. Ricciolius, qui eam labore improbo <lb/>plu&longs;quam trig inta diuer&longs;is methodis quadrin<lb/>genties, & eo amplius, ob&longs;eruando venatus <pb xlink:href="018/01/051.jpg" pagenum="43"/>e&longs;t, certi&longs;simè &longs;e demum deprehendi&longs;&longs;e mi<lb/>hi aliquando affirmabat, illam nec mino<lb/>rem minutis 30. nec maiorem min. 31. <lb/>Fac igitur à Baliano mediam inter hæc ex<lb/>trema Solis Apogæi diametrum apparen<lb/>tem gr. o. m. 30. &longs;ec. 30. a&longs;&longs;umi, & telluris <lb/>ambitum ita augeri, vt ad illum pa&longs;&longs;us 43200 <lb/>minorem habeant Rationem: & &longs;ibi omnia <lb/>re&longs;pondebunt. </s>

</row>

<row>

<cell>CXXXIII.</cell>

<s>Statuatur itaque terræ peri<lb/>pheria pa&longs;&longs;. 30598162; & pa&longs;&longs;us Rom. 43200 <lb/>&longs;unt gr. o. m. 30. &longs;ec. 29. Ter.45 Quar. 25. <lb/>Quint.4., adeoquè angulus SCI gr.o.min. <lb/>15.&longs;ec. 14. Ter. 52: Quar. 42. Quint. 32. <lb/>cuius Complementi Secans SC 22554080. <lb/>57395 in partibus Radij <emph type="italics"/>S<emph.end type="italics"/>I. </s>

<cell>S<emph type="italics"/>i fuerint duæ quantitates, <expan abbr="quar&utilde;">quarum</expan> una alteri dupla &longs;it: minuatur à minore quædam quantitas, <expan abbr="ead&etilde;que">eadenque</expan> maiori addatur, erit minoris ad re&longs;iduum maior proportio, quàm aggregati ad maiorem duplicata.<emph.end type="italics"/> S<emph type="italics"/>i uerò minori addatur, & à maiore detrabatur, erit aggregati ad minorem minor proportio quàm maioris ad re&longs;iduum duplicata.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXXIIII.</cell>

<cell>S<emph type="italics"/>i rectangula &longs;uperficies &longs;it, cuius pars tertia quadrata &longs;it corpus, quod ex latere quadratæ in re&longs;iduum &longs;uperficiei con&longs;tat, maius e&longs;t quouis corpore ex eadem &longs;uperficies, aliter diui&longs;a con&longs;tituto.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXXV.</cell>

<cell>S<emph type="italics"/>i linea in duas partes, quarum una fit alteri dupla diuidatur, erit quod fit ex tertia parte in quadratum re&longs;idui parallelipedum maius omni pararallelipedo, quod ex diui&longs;ione eiu&longs;dem lineæ creari poßit.<emph.end type="italics"/></cell>

</row>

<row>

<s>Iam anguli SOT <lb/>gr. o. m. 15. &longs;ec. 15. Secans Complem. SO <lb/>22551105.10158. auferatur ex SC; & per <lb/>earum differentiam OC 2975.47237 diui<lb/>sâ totâ SC, prodibit di&longs;tantia SC &longs;emid. </s>

<cell>CXXXVI.</cell>

<cell>D<emph type="italics"/>enominationes in infinitum extendere.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CXXXVII.</cell>

<cell>R<emph type="italics"/>ationem numerorum ex progreßione declarare.<emph.end type="italics"/></cell>

<s><lb/>7580, vt P. Ricciolio placet. </s>

</row>

<row>

<cell>CXXXVIII.</cell>

<cell>M<emph type="italics"/>odos u&longs;us horum numerorum declarare.<emph.end type="italics"/></cell>

<s>Quarè ex iis, quæ hactenus di&longs;putauimus, <lb/>illud infero, quod auctâ Solis Apogæi diame<lb/>tro apparente, minui debet terræ ambitus, <lb/>vt ad eum pa&longs;&longs;us 43200 maiorem habeant <lb/>Rationem, ne videlicet tam magno inter &longs;e <lb/>di&longs;crimine differant anguli S O T & <emph type="italics"/>S<emph.end type="italics"/>CI, vt <lb/>per Secantium SO & SC, differentiam OC <lb/>diuisâ di&longs;tantiâ SC <emph type="italics"/>S<emph.end type="italics"/>ol terræ vicinior &longs;tatua<pb xlink:href="018/01/052.jpg" pagenum="44"/>tur, quàm par &longs;it ad ph&oelig;nomena omni&atail; <lb/>explicanda. </s>

</row>

<s>Hinc fit retentâ eadem terræ <lb/>magnitudine non ita augeri &longs;emidiametrum <lb/>apparentem <emph type="italics"/>S<emph.end type="italics"/>olis Apogæi, vt angulus <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>&longs;it gr. o. m. 15. &longs;ec. 25.; Secans enim <emph type="italics"/>S<emph.end type="italics"/>O e&longs;&longs;et <lb/>22306254.81750; quæ ablata ex inuentâ <lb/>&longs;uperiùs <emph type="italics"/>S<emph.end type="italics"/>C 22554080.57395. relinqueret <lb/>differentiam OC 247825.75645.atque adeò <lb/><emph type="italics"/>S<emph.end type="italics"/>ol Apogæus &longs;emid. </s>

<row>

<cell>CXXXIX.</cell>

<cell>R<emph type="italics"/>adices omnes à propo&longs;itis numeris extrahere.<emph.end type="italics"/></cell>

<s>91. à terrâ remoue<lb/>retur. </s>

</row>

<row>

<s>Minuenda itaque e&longs;t vel Solis appa<lb/>rens diameter, vel terræ magnitudo; ego ve<lb/>rò illam potiùs paucioribus &longs;crupulis &longs;ecun<lb/>dis definiendam cen&longs;erem, quàm terræ am<lb/>bitum ad pauciora milliaria reuocandum. </s>

<cell>R<emph type="italics"/>adices per numeros fractos determinare.<emph.end type="italics"/></cell>

</row>

<s>S<emph.end type="italics"/>ed quid his longiùs immoramur? </s>

<row>

<s><lb/>quorum &longs;ubtilior inue&longs;tigatio à no&longs;tro in<lb/>&longs;tituto aliena deprehenditur. </s>

<cell>N<emph type="italics"/>umeros fractos ad minores in ea <expan abbr="i&etilde;">iem</expan> proportione ualde propinqud deducere<emph.end type="italics"/></cell>

<s>Nemo t&etail;, <lb/>Mer&longs;enne, reprehendat cæle&longs;tes hypothe&longs;es <lb/>ex magno illo Atlante Tychone a&longs;&longs;umen<lb/>tem; & quamuis ego pariter in eâ &longs;im &longs;en<lb/>tentiâ, vt exi&longs;timem ab Eratho&longs;tene homi<lb/>ne Cyrenen&longs;i adhibitum &longs;tadium Alexandri<lb/>num, non autem Græcum, quod a&longs;&longs;umebas, <lb/>hanc tamen litem hìc agitare non e&longs;t operæ <lb/>pretium. </s>

</row>

<row>

<s>Quapropter perge, &longs;i placet, qua <lb/>cæpi&longs;ti viâ, terreni globi grauitatem exp<gap/>o. </s>

<cell>CXLII.</cell>

<cell>D<emph type="italics"/><expan abbr="enomination&utilde;">enominationum</expan> in <expan abbr="crem&etilde;ta">crementa</expan> ex extrema cognita inuenire.<emph.end type="italics"/> E<emph type="italics"/>t <expan abbr="cõuer&longs;o">conuer&longs;o</expan> modo.<emph.end type="italics"/></cell>

</row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Inuentam terræ &longs;emidiametrum <pb xlink:href="018/01/053.jpg" pagenum="45"/>mill. Rom. 4127 pa&longs;&longs;.822. ad pedes reuoco, <lb/><arrow.to.target n="note24"/><lb/>pedes quinque Romanos antiquos pa&longs;&longs;ibus <lb/>&longs;ingulis tribuens, & &longs;unt pedes 20639110. <lb/>Quia verò &longs;phæræ &longs;unt in triplicatâ Ratione <lb/>&longs;emidiametrorum, comparo terrenam &longs;e<lb/>midiametrum cum &longs;emidiametro pedali al<lb/>terius globi, & <emph type="italics"/>R<emph.end type="italics"/>ationem 1. ad 20.639110 <lb/>v&longs;que, ad quartum terminum continuo, vt <lb/>&longs;it tertius terminus 425.972861.592100. <lb/>quartus autem 8791.700747.414127. <lb/>031000. <emph type="italics"/>S<emph.end type="italics"/>phæra igitur &longs;emidiametri pedalis <lb/>ad terrenam &longs;phæram <emph type="italics"/>R<emph.end type="italics"/>ationem habet ean<lb/>dem, quam vnitas ad quartum hunc termi<lb/>num. </s>

<row>

<cell>CXLIII.</cell>

<cell>S<emph type="italics"/>i linea in duas partes diuidatur, corpora quæ fiunt ex una parte in alterius quadratum mutuo æqualia &longs;unt corpori, quod fit ex tota linea in &longs;uperficiem unius partis in alteram.<emph.end type="italics"/></cell>

</row>

<row>

<s>Vt autem &longs;phæræ argillaceæ, cuius <lb/>&longs;emidiameter pedalis &longs;it, grauitatem per<lb/>&longs;pectam haberem, argillam cum aquâ con<lb/>tuli, & experimento didici argillæ grauita<lb/>tem ad aquæ pondus e&longs;&longs;e vt 27 ad 16. At <lb/>&longs;tanni grauitas ad aquæ grauitatem apud <lb/>Ghetaldum in Archimede Promoto e&longs;t vt <lb/>100 ad (13 19/37), hoc e&longs;t, vt 37 ad 5. <emph type="italics"/>S<emph.end type="italics"/>i igitur <lb/>Ratio &longs;tanni ad aquam, & aquæ ad argillam, <lb/>&longs;cilicet 37 ad 5. & 16 ad 27 in tribus termi<lb/>nis continuetur, ita vt &longs;int 592,80. 135, <lb/>Ratio grauitatis &longs;tanni ad argillæ pondus, da<lb/>tâ molis æqualitate, e&longs;t vt 592 ad 135. </s>

<cell>CXLIIII.</cell>

<cell>D<emph type="italics"/>uplum cubi medietatis maius e&longs;t aggregato corporum mutuorum, cuiuslibet diui&longs;ionis quantum e&longs;t, quod fit ex tota in quadratum differentiæ.<emph.end type="italics"/></cell>

<s><margin.target id="note24"/><emph type="italics"/>XXIV <lb/>Terreni glo<lb/>bi &longs;oliditas <lb/>inue&longs;tiga<lb/>tur.<emph.end type="italics"/></s>

</row>

<s>Quoniam verò apud eundem Ghetaldum <lb/>&longs;tanneæ &longs;phæræ, cuius diameter &longs;it vnius pe<pb xlink:href="018/01/054.jpg" pagenum="46"/>dis Rom. antiqui, grauitas e&longs;t exactè lib.

<row>

304 <lb/>& &longs;phæræ &longs;unt in triplicatâ Ratione diame<lb/>trorum, &longs;phæra &longs;tannea &longs;emidiametrum ha<lb/>bens pedalem, ac proinde diametrum bipe<lb/>dalem, e&longs;t octuplo grauior illâ, atque adeò <lb/>lib, 2432. Atqui &longs;tannum ad argillam, e&longs;t <lb/>vt 592 2d 135, igitur & eandem Rationem <lb/>habent æquales &longs;phæræ; ideoque &longs;i &longs;tannea <lb/>&longs;phæra &longs;emidiametrum pedalem habens nu<lb/>merat in grauitate libras 2432, argillace&atail; <lb/>æqualis erit lib. (554 22/37). Hæc autem ad terræ <lb/>globum e&longs;t vt vnitas ad quartum illum ter<lb/>minum continuè proportionalem in Ratione <lb/>&longs;emidiametrorum. </s>

<cell>S<emph type="italics"/>i linea in duas partes diuidatur quadrata ambarum partium detracto eo, quod fit ex una parte in alteram, æqualia &longs;unt producto unius in alteram cum quadrato differentiæ.<emph.end type="italics"/></cell>

</row>

<row>

<s>Multiplicetur igitur quar<lb/><arrow.to.target n="note25"/><lb/>tus ille terminus 8791.700747.414127. <lb/>031000. per libras (554 22/37), & prodibit totius <lb/>terræ grauitas, &longs;i ex merâ argillâ con&longs;taret, <lb/>librarum 4.875829.711809.132072. <lb/>(327567 21/37). </s>

<cell>CXLVI.</cell>

<cell>C<emph type="italics"/>orpus quod fit ex linea diui&longs;a in &longs;uperficiem æqualem quadratis ambarum partium detracta &longs;uperficie unius partis in alteram, e&longs;t æquale aggregato cuborum ambarum partium.<emph.end type="italics"/></cell>

<s><margin.target id="note25"/><emph type="italics"/>XXV <lb/>Terreni glo <lb/>bi grauitas.<emph.end type="italics"/></s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Immen&longs;um places, Mer&longs;enne: lu<lb/>culenti&longs;simè enim demon&longs;tra&longs;ti quatuor illis <lb/>aut &longs;ex &longs;upra centum orbiculis, de quibus <lb/>heri nobis &longs;ermo erat, tellurem totam facil<lb/>limè moueri po&longs;&longs;e, etiam &longs;i eius grauitati <lb/>quingenties millies millena librarum mil<lb/>lia adiiceres. </s>

<row>

<cell>CXLVII.</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita planè, &longs;i mera e&longs;&longs;et argilla: &longs;ed <lb/>tot marmora ac lapides, ingentesque metal<pb xlink:href="018/01/055.jpg" pagenum="47"/>lorum fodinæ, quæ argillæ grauitatem lon<lb/>go &longs;uperant interuallo, non eam vim ad<lb/>dunt ponderis, quæ non facilè æ&longs;timari <lb/>queat? </s>

<cell>P<emph type="italics"/>ropo&longs;ita linea diui&longs;a duas ei lineas adijcere, ut proportio <expan abbr="additar&utilde;">additarum</expan> &longs;ingularium<emph.end type="italics"/></cell>

<cell/>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Immò verò, ni&longs;i hæc pariter ad<lb/>mi&longs;cerentur, vererer plurimùm, ne mihi <lb/>tanquam prodigo &longs;uccen&longs;eretis, qui tantam <lb/>telluri grauitatem concederem. </s>

</row>

<s>Metall&atail;, <lb/><arrow.to.target n="note26"/><lb/>fateor, ac marmora æqualem argillæ molem <lb/>pondere &longs;uperant: &longs;ed quota demum &longs;phæ<lb/>ræ huius pars illa &longs;unt? </s>

<row>

<cell/>

<s>Quod &longs;i quis ill&atail; <lb/>grauiora e&longs;&longs;e inculcet, longè leuiorem a<lb/>quam cogitet, ex qua vici&longs;sim globus hic <lb/>terraqueus con&longs;tat. </s>

<cell><emph type="italics"/>& partium &longs;imul iunctarum ad additas &longs;it mutua.<emph.end type="italics"/></cell>

<s>Qui&longs;quis enim &longs;e æquum <lb/>rerum æ&longs;timatorem præbuerit, non plus re<lb/>periri <expan abbr="metallor&utilde;">metallorum</expan> quàm aquæ autumet: qui&ntail;<lb/>immo illorum grauitatem ab huius leuitate <lb/>&longs;i non æquari, aut &longs;uperari, magnâ &longs;altem <lb/>ex parte compen&longs;ari facilè concedat. </s>

</row>

<row>

<s>Iam <lb/>verò &longs;i ad aëris vim non modicam terræ ca<lb/>uernis atque cuniculis inclu&longs;am, &longs;eque intrà <lb/>&longs;iccorum corporum particulas non &longs;ibi om<lb/>ninò cohærentes in&longs;inuantem, animum ad<lb/>uertamus, apparebit illicò exuperantiam il<lb/>lam grauitatis hoc defectu vberrimè com<lb/>pen&longs;ari. </s>

<cell>CXLVIII.</cell>

<cell>P<emph type="italics"/>ropo&longs;itis tribus lineis primam &longs;ic diuidere, ut adiectis duabus alijs lineis, &longs;ecundum <expan abbr="ration&etilde;">rationem</expan> mutuam &longs;ingularum &longs;ingulis, <expan abbr="aggregat&utilde;">aggregatum</expan> ex una <expan abbr="adiectar&utilde;">adiectarum</expan>, & par te ad <expan abbr="aggregat&utilde;">aggregatum</expan> ex alia parte, & adiecta &longs;e habeat, ut &longs;ecunda ad <expan abbr="tertiã">tertiam</expan>.<emph.end type="italics"/></cell>

<s><margin.target id="note26"/><emph type="italics"/>XXVI <lb/>Terræ gra<lb/>uitatem pe<lb/>rinde &longs;e ba<lb/>bere proba<lb/>tur, ac &longs;i e&longs;<lb/>&longs;et mera ar<lb/>gilla.<emph.end type="italics"/></s>

</row>

<s>Sed quoniam motus, cui tellus &longs;uo pon<lb/>dere ob&longs;i&longs;teret, in circumfu&longs;o hoc aëre per<pb xlink:href="018/01/056.jpg" pagenum="48"/>ficiendus e&longs;&longs;et; minuitur adhuc momen<lb/>tum ab halituum aëre leuiorum copiâ penè <lb/>infinitâ, quæ totam hanc molem peruadit. </s>

<row>

<cell>CXLIX.</cell>

<s><lb/>Quemadmodum enim nauis aërem aquâ <lb/>leuiorem includens in aquâ non mergitur, &longs;i <lb/>tota moles compo&longs;ita æqualis aquæ grauita<lb/>tem non vincat; vel &longs;altem minore mo<lb/>mento de&longs;cendit pro inclu&longs;i aëris portione; <lb/>haud ab&longs;imili ratione fieri pote&longs;t, vt grauiori <lb/>corpori tot &longs;piritus aëre leuiores permi&longs;cean<lb/>tur, vt totius compo&longs;itæ molis grauitas non <lb/>mediocriter minuatur. </s>

<cell>D<emph type="italics"/>atam lineam &longs;ic diuidere, ut proportio quadratorum ad duplum unius partis in alteram &longs;it, ut lineæ datæ ad lineam datam.<emph.end type="italics"/></cell>

<s>Quantum verò hu<lb/>iu&longs;modi halituum metallicis lapidibus im<lb/>mi&longs;ceatur, &longs;atis &longs;ciunt, quotquot &longs;odinarum <lb/>latebras penetrârunt. </s>

</row>

<row>

<s>Et vt cæteras mi&longs;&longs;as <lb/>faciam, Hungaricæ aurifodinæ, mihi ma<lb/>gis notæ, omnem præcidunt dubitandi an<lb/>&longs;am. </s>

<cell>P<emph type="italics"/>ropo&longs;itis duabus lineis, lineam communem utrique adiungere, ut &longs;it maioris ad additam proportio, uelut quadratorum minoris, & adiectæ ad duplum unius in alteram.<emph.end type="italics"/></cell>

<s>Cum enim duæ pateant ad de&longs;cen<lb/>dendum viæ, altera breui&longs;sima, vtpote re<lb/>cta, putei in modum (caminum rectiùs <lb/>forta&longs;&longs;e dixeris) cuius latera muniunt arctè <lb/>compacti arborum trunci: altera obliqu&atail;, <lb/>& longior per cuniculos: per hanc perpetuò <lb/>&longs;e frigidus aër magno impetu in ima fodinæ <lb/>vi&longs;cera in&longs;inuat, dum ex illâ calida pariter <lb/>atque graueolens expiratio erumpit. </s>

</row>

<s>Ne<lb/>que indigent metallarii A&longs;trologorum næ<lb/>nijs, qui imminentem cæli mutationem <pb xlink:href="018/01/057.jpg" pagenum="49"/>prædicant; cum ip&longs;i ex immodicâ halituum <lb/>infernè a&longs;cendentium copiâ, quibus vix non <lb/>præfocantur, c&oelig;lum nubibus proximè ob<lb/>ducendum nec dubiè pronuncient. </s>

<row>

<cell>P<emph type="italics"/>roportio differentiæ quadratorum partium cuiu&longs;uis lineæ, ad quadratum differentiæ illarum e&longs;t, uelut totius lineæ ad differentiam.<emph.end type="italics"/></cell>

<s><lb/>quod aqua ip&longs;a (licet aëre grauior, &longs;i &longs;ibi ip&longs;a <lb/>relinquatur) leui&longs;simi vaporis &longs;peciem induit <lb/>calore &longs;ollicitata, quo interior terræ plag&atail; <lb/>abundat: Vbi enim octoginta circiter hexa<lb/>podas, quibus extima hæc terræ regio frigi<lb/>di&longs;sima definitur, de&longs;cenderis, tepor primùm <lb/>grati&longs;simus ex frigidâ regione venientem ex<lb/>cipit ac recreat, paulatimque adeò augetur <lb/>calor, vt demùm metalli fo&longs;&longs;ores ve&longs;tem nul<lb/>lam ferant. </s>

</row>

<row>

<s>Quantum autem momenti ad pondus mi<lb/>nuendum obtineat grauium hæc atque le<lb/>uium mi&longs;cella, ille facilè intelliget, qui ob<lb/>&longs;eruauerit aliquando &longs;tibium ad v&longs;us medi<lb/>cos excoctum æquè graue reperiri, ac de<lb/>prehen&longs;um fui&longs;&longs;et, antequam igni commit<lb/>teretur; quamuis inde vi flammæ ingens va<lb/>porum ac fumi copia eruperit; &longs;piritus enim, <lb/>qui auolârunt, cum aërem leuitate vince<lb/>rent, cæteris partibus admi&longs;ti molem con<lb/>&longs;tituebant maiorem quidem, &longs;ed non grauio<lb/>rem, ac &longs;it deinde reliqua moles minor, fa<lb/>ctâ hac halituum &longs;ece&longs;sione. </s>

<cell>S<emph type="italics"/>i linea in duas partes æquales, duasque inæquales diuidatur, fueritque proportio aggregati ex maiore, & dimidio ad ip&longs;am maiorem, uelut ex minore, & aliqua linea ad ip&longs;am minorem, & rur&longs;us aggregati ex minore, & dimidio ad ip&longs;am minorem, uelut aggregati ex maiore, & alia addita ad ip&longs;am maiorem, erit proportio dimidij ad partem unam inæqualem, uelut alterius partis inæqualis ad &longs;uam additam mutuò, & etiam proportio additarum inuicem, uelut proportio <expan abbr="parti&utilde;">partium</expan> <expan abbr="inæquali&utilde;">inæqualium</expan> duplicata, & rur&longs;us ip&longs;um <expan abbr="dimidi&utilde;">dimidium</expan> lineæ a&longs;&longs;umptæ <expan abbr="medi&utilde;">medium</expan>, erit proportione inter additas.<emph.end type="italics"/> D<emph type="italics"/><expan abbr="em&utilde;">emum</expan> proportio dimidij <expan abbr="c&utilde;">cum</expan> addita maiore ad <expan abbr="dimidi&utilde;">dimidium</expan>, cum addita minore, uelut maioris partis ad <expan abbr="minor&etilde;">minorem</expan>.<emph.end type="italics"/></cell>

<s>Perinde atque <lb/>&longs;i vas æreum aquâ iuxta ac aëre plenum in<pb xlink:href="018/01/058.jpg" pagenum="50"/>trà aquam ponderetur, deinde ita eius late<lb/>ra comprimantur, vt aquam omnem ac <expan abbr="a&etilde;-rem">ae<lb/>rem</expan> excludant, etiam &longs;i modicum aliquid æ<lb/>ris deteratur, adhuc æqualibus momentis in <lb/>aquâ grauitare deprehenditur, &longs;i ad libræ <lb/>examen reuocetur; aeris nimirùm leuitas <lb/>æris momenta minuebat. </s>

</row>

<s>Ne quis verò ductam ex va&longs;e &longs;imilitudi<lb/>nem calumnietur; Liberum patrem coga<lb/>mus pauli&longs;per philo&longs;ophari. </s>

<row>

<cell>CLIII.</cell>

<s>Dabitis, opinor <lb/>vini grauitatem ferè aquæ &longs;ub&longs;e&longs;qui-&longs;exage<lb/>cuplam, vel certè aquæ pondere non maio<lb/>rem; ita vt quodcunque aquæ grauitate præ<lb/>&longs;titerit, haud immeritò vino pariter grauius <lb/>cen&longs;eatur. </s>

<cell>V<emph type="italics"/>im quamcunque manus multiplicare.<emph.end type="italics"/></cell>

<s>Atqui Tartarum ex vino &longs;ub&longs;ide<lb/>re nemo ne&longs;cit; & quod inde elicitur oleum <lb/>Tartari, e&longs;t proximè ad aquam vt 3 ad 2: &longs;pi<lb/>ritus autem vini ad aquam communem, Ra<lb/>tionem habet proximè, quam 3 ad 4. Qua<lb/>re &longs;i vinum eiu&longs;dem cum aquâ grauitatis <lb/>con&longs;tituatur, Oleum Tartari ad vinum e&longs;t <lb/>vt 6 ad 4, vinum autem ad &longs;piritum vini vt <lb/><arrow.to.target n="note27"/><lb/>4 ad 3. </s>

</row>

<row>

<s><margin.target id="note27"/><emph type="italics"/>XXVII <lb/>Vini graui<lb/>tas medi&atail; <lb/>Harmonicè <lb/>inter Oleum <lb/>Tartari, & <lb/>Spiritu&mtail; <lb/>vini.<emph.end type="italics"/></s>

<cell>CLIIII.</cell>

<cell>S<emph type="italics"/>i lineæ datæ alia linea adiungatur, ab extremitatibus autem prioris lineæ duæ rectæ in unum punctum concurrant proportionem habentes, quam mediam inter tota m & adiectam, & adiectam erit punctus, concur&longs;us à puncto extremo lineæ adiectæ di&longs;tans per lineam mediam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i ab extremo alicuius lineæ æqualis mediæ, &longs;eu peripheria circuli, cuius &longs;emidiameter &longs;it media linea duæ lineæ ad prædicta puncta producantur, ip&longs;æ erunt in proportione mediæ ad adiectam.<emph.end type="italics"/></cell>

<s>Quod &longs;i vini Tartarum &longs;imul ac &longs;piritum <lb/>complectentis grauitas medio loco &longs;e habet <lb/>(& quidem medietate Harmonicâ) inter id <lb/>quod grauius, & id quod leuius e&longs;t, quamuis <lb/>extrema illa non ita multo di&longs;criminentur in<pb xlink:href="018/01/059.jpg" pagenum="51"/>teruallo: quidni terrena hæc moles ex gra<lb/>ui&longs;simis quidem metallis atque lapidibus, <lb/>&longs;ed & ex corporibus alijs argillâ leuioribus, <lb/>ex aquâ, <expan abbr="a&etilde;re">aere</expan>, &longs;ubtili&longs;simisque expirationi<lb/>bus coagmentata mediocrem argillæ graui<lb/>tatem (quantum fas e&longs;t coniecturâ a&longs;&longs;equi) <lb/>obtinere dicatur? </s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Fallor, &longs;i Tartarus ip&longs;e ad exte<lb/>nuandam terræ grauitatem tibi &longs;uppetias <lb/>non tulerit. </s>

<row>

<s>Ob oculos pones immen&longs;a &longs;pe<lb/>læa æternis flammarum globis redundantia, <lb/>& exaggeratâ longè latèque patentis impio<lb/>rum carceris magnitudine (quam penetra<lb/>bilis ignis implet, non modò nihil habens <lb/>proni, &longs;ed & &longs;ur&longs;um rectis lineis in c&oelig;le&longs;tem <lb/>locum &longs;ubuolare contendens) tantum ex tel<lb/>lure detrahes ponderis, quantum metall&atail; <lb/>omnia atque marmora re&longs;tituere non va<lb/>leant. </s>

<cell>Q<emph type="italics"/>uadratorum numerum proportionem & inuentionem con&longs;iderare.<emph.end type="italics"/></cell>

<s>Nec deerit docti&longs;simorum virorum <lb/>&longs;uffragium, qui cauernam hanc totius ter<lb/>reni globi partem quartam præci&longs;i&longs;&longs;imè &longs;ta<lb/>tuunt, cum qua pariter admirabilem illam <lb/>Lunaris motûs librationem con&longs;entire inge<lb/>niosè opinantur. </s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Et verò talia afferentem ca&longs;tigare <lb/>quis audeat? </s>

<cell>H<emph type="italics"/>orologiorum tempus multiplicare.<emph.end type="italics"/></cell>

<s>Ab&longs;tineo tamen, ne fortè ex <lb/>vobis audire cogerer iterum, quæ haud ita <lb/>pridem ne&longs;cio quis di&longs;&longs;erebat. </s>

</row>

<s>Nihil e&longs;t, <pb xlink:href="018/01/060.jpg" pagenum="52"/><arrow.to.target n="note28"/><lb/>aiebat ille, quod vim pati perpetuam cen<lb/>&longs;endum &longs;it. </s>

<row>

<cell>CLVII.</cell>

<s>At &longs;i elementis omnibus terra <lb/>grauitare, ignis leuitate præ&longs;tet; an non. </s>

<cell>H<emph type="italics"/>orologiorum molarium rationem o&longs;tendere.<emph.end type="italics"/></cell>

<s>æ<lb/>ternum aberunt loco, quem &longs;ingulis naturâ <lb/>tributum e&longs;t vt velint con&longs;equi? </s>

</row>

<row>

<s>Terra ete<lb/>nim, ni&longs;i columnis ba&longs;im in centro haben<lb/>tibus nixa fingatur, tota procul à centro con<lb/>quie&longs;cit; ignis verò infimum locum tenet. </s>

<cell>CLVIII.</cell>

<cell>R<emph type="italics"/>ationem indicis mobilis cum rota, qua horarum numerus per ictus indicatur explicare.<emph.end type="italics"/></cell>

<s><lb/>Qui&longs;quis autem ibi ignem à Deo perpetuis <lb/>vinculis eo tantùm con&longs;ilio coerceri exi&longs;ti<lb/>mat, vt &longs;celeratorum carnificinam exerceat; <lb/>diligenter per&longs;piciat velim, an non magis <lb/>pro Diuinæ &longs;apientiæ atque omnipotentiæ <lb/>dignitate locuturus ille &longs;it, qui, quemadmo<lb/>dum Iridem licèt naturæ penicillo in nubi<lb/>bus de&longs;criptam, in &longs;empiterni tamen f&oelig;de<lb/>ris te&longs;&longs;eram à Deo a&longs;&longs;umptam nouit, &longs;ic re<lb/>rum naturæ con&longs;entaneum ad&longs;truat hunc or<lb/>dinem, quo vniuer&longs;itatis rerum &longs;ubluna<lb/>rium elementa pro &longs;ui ponderis ratione ita <lb/>di&longs;ponantur, vt centrum omnium graui&longs;si<lb/>mus ignis impiorum carcer atque carnifex <lb/>con&longs;titutus obtineat, illumque minùs gra<lb/>uia elementa terra & aqua deinceps con&longs;e<lb/>quantur, v&longs;que eò dum leui&longs;simus aër cir<lb/>cumfu&longs;us reliqua complectatur. </s>

</row>

<s><margin.target id="note28"/><emph type="italics"/>XXVIII <lb/>Coniecturæ <lb/>pro adstru<lb/>enda ignis <lb/>inferni gra<lb/>uitate.<emph.end type="italics"/></s>

<row>

<s>Fru&longs;tra a&longs;cendentem flammam aperti&longs;si<lb/>mum igneæ leuitatis argumentum obiicie<pb xlink:href="018/01/061.jpg" pagenum="53"/>bant. </s>

<cell>N<emph type="italics"/>ullus angulus rectilineus æqualis e&longs;&longs;e pote&longs;t alicui angulo contento recta, & circuli portione.<emph.end type="italics"/></cell>

<s>Nàm ille &longs;upremo ætheri terrenis ex<lb/>pirationibus immuni, ac lunari orbitæ fini<lb/>timo, quem Ari&longs;totele te&longs;te propter con&longs;ue<lb/>tudinem ignem dicimus, vix aliquid ignis <lb/>præter &longs;plendidum nomen reliquum facie<lb/>bat. </s>

</row>

<row>

<s>A&longs;cendit in flammâ (&longs;ic ille) humido <lb/>vapori, quem calor eximius rarum fecit, <lb/>permi&longs;ta fuligo, aére &longs;anè non leuior: quidni <lb/>pariter à flammâ in c&oelig;lum &longs;ubuolante par<lb/>ticulæ igneæ abripiantur? </s>

<cell>P<emph type="italics"/>ropo&longs;ita linea tribusque in ea &longs;ignis punctum inuenire, ex quo ductæ tres lineæ ad &longs;igna &longs;int in proportionibus datis.<emph.end type="italics"/></cell>

<s>quibus vel pru<lb/>narum vel candentis ferri incolis, nullum e&longs;t <lb/>cum æthereâ regione commercium. </s>

</row>

<s>A&ntail; <lb/>fumeus vapor igniculorum coloniam in c&oelig;<lb/>lum deduxi&longs;&longs;e cen&longs;endus e&longs;t, quia illi nobis <lb/>non videntibus in terram relabuntur? </s>

<row>

<s>Sed <lb/>quis neget, incendio &longs;yluam depopulante, <lb/>immodicam fuliginum copiam in &longs;uperiora <lb/>rapi? </s>

<cell>S<emph type="italics"/>i fuerint duo trianguli, quorum ba&longs;es in eadem linea &longs;int con&longs;tituti, & æquales ad unum punctum terminati, & latus unum commune inter reliqua quantitate medium nece&longs;&longs;e e&longs;t angulum à maioribus lineis <expan abbr="content&utilde;">contentum</expan> minorem e&longs;&longs;e.<emph.end type="italics"/></cell>

<s>quibus tamen ætheream &longs;edem ineptè <lb/>ad&longs;criberemus, quia illas iterum de&longs;cenden<lb/>tes ob&longs;eruando notare non po&longs;&longs;umus. </s>

</row>

<row>

<s>Quod <lb/>&longs;i ignibus &longs;ub dio &longs;emper excitatis, fuligo <lb/>nulla camino vnquam adhæ&longs;i&longs;&longs;et; nonnè &longs;a<lb/>tis habui&longs;&longs;emus argumenti, ex quo illius gra<lb/>uitas innotui&longs;&longs;et, &longs;i quando ingentem fuligi<lb/>nis ma&longs;&longs;am ex aëre decidentem licui&longs;&longs;et in<lb/><gap/>ueri? </s>

<cell>CLXII.</cell>

<cell>P<emph type="italics"/>roportionem duorum orbium, quorum diametrorum conuexæ partis, & concauæ proportiones datæ &longs;int inue&longs;tigare.<emph.end type="italics"/></cell>

<s>Neque enim ideò grauitate &longs;poliamus <lb/>terre&longs;tres pului&longs;culi atomos, quia in aëre va<lb/>gantes ita &longs;en&longs;um di&longs;sipatæ fugiunt, vt eas <pb xlink:href="018/01/062.jpg" pagenum="54"/>de&longs;cendentes animaduertere nequeamus: &longs;ed <lb/>ad earum grauitatem ad&longs;truendam &longs;atis e&longs;&longs;e <lb/>putamus, quod particulæ illæ vinculum na<lb/>ctæ, quo lapidem con&longs;tituant, de&longs;cendentes <lb/>&longs;ub a&longs;pectum cadant. </s>

</row>

<s>Cur igitur tanta&mtail; <lb/>ignium vim in fulmine delap&longs;am, &longs;eque in <lb/>ima terræ vi&longs;cera in&longs;inuantem cernentes, <lb/>perinde atque &longs;axum in aquam decidens <lb/>mergitur, igneæ grauitatis &longs;u&longs;picioni locum <lb/>non damus? </s>

<row>

<cell>CLXIII.</cell>

<s>Nemo &longs;iquidem facilè credat <lb/>accen&longs;um fulmen á &longs;uperioribus nubis parti<lb/>bus, quæ inferioribus tenuiores &longs;unt ac leuio<lb/>res, minùsque ad aqueam naturam vergen<lb/>tes, deor&longs;um reflecti: cùm nec ignis ex Auro, <lb/>quod ob impetûs ac efficaciæ &longs;imilitudinem <lb/>nomen à fulmine obtinuit, à quoquam re<lb/>flectatur, &longs;ed in&longs;itâ naturæ vi præceps deor<lb/>&longs;um feratur: </s>

<cell>P<emph type="italics"/>roportionem uirium &longs;tellarum per motus &longs;uos indagare.<emph.end type="italics"/></cell>

<s>Ad hæc ignis genus vniuer&longs;um in &longs;pecies <lb/>certas, quibus iterum partes aliæ atquè aliæ <lb/>&longs;ube&longs;&longs;ent, partiebatur & di&longs;tinguebat: Alti <lb/>enim reperiuntur Ignes luce iuxta atque ca<lb/>lore con&longs;picui, quorum frequenti&longs;simus e&longs;t <lb/>& communis v&longs;us, atque vulgati&longs;sima noti<lb/>tia: Alii &longs;unt, qui, quoniam plus fulgoris <lb/>habentes, quàm caloris, o<gap/>lis tantùm blan<lb/>diuntur, cum Fatuis Ignibus numerantur: <lb/>Alios demùm qua&longs;i latentes &longs;inu natura fo<pb xlink:href="018/01/063.jpg" pagenum="55"/>uet, quos luce carentes quamuis Mortuos <lb/>vulgus appellet, nimis tamen viuaci virtute <lb/>præditos vis cau&longs;tica &longs;atis prodit. </s>

</row>

<row>

<s>Ad ter<lb/>tium hoc ignium genus, qui calidi cum &longs;int, <lb/>non tamen &longs;unt lucidi, reuocabat igniculos, <lb/>qui aquis acribus (Aquas Fortes vulgus ap<lb/>pellat) permi&longs;ti ac oleo Tartari &longs;eu Vitrioli <lb/>metalla &longs;oluunt, & in Chymicam calce&mtail; <lb/>redigunt breui temporis morâ, cum tamen <lb/>plurium dierum interuallo indigeat, qui&longs;<lb/>quis ea voluerit ardenti&longs;simæ fornacis igne in <lb/>calcem excoquere. </s>

<cell>CLXIIII.</cell>

<cell>S<emph type="italics"/>yderum proportionem in magnitudine o&longs;tendere.<emph.end type="italics"/></cell>

<s>Porrò aquas huiu&longs;modi <lb/>acres ex &longs;alibus extillari, &longs;ales autem graui<lb/>tate præditos non mediocri ob&longs;eruans illud <lb/>demum inferebat, quod ignes omnium ve<lb/>hementi<gap/>simi, quantum quidem experimen<lb/>to a&longs;&longs;equi po&longs;&longs;umus, cum grauitate &longs;unt con<lb/>iuncti, vt in Aquis Fortibus, Oleo Tartari, <lb/>&. </s>

</row>

<s>Vitrioli, in Auro pulueris pyrii &longs;peciem <lb/>nacto, & in Fulmine licet pa&longs;sim experiri. </s>

<row>

<s>Hæc ferè &longs;unt, &longs;ed paulò pre&longs;siùs atqu&etail; <lb/>&longs;ummatim expo&longs;ita, ex quibus ille conficie<lb/>bat ignium generi lati&longs;simè patenti &longs;ube&longs;&longs;&etail; <lb/>&longs;pecies qua&longs;dam graui&longs;simorum corporum <lb/>eximiâ vrendi facultate præditorum, quæ <lb/>mundanæ &longs;phæræ centrum meritò teneant, <lb/>ibique perpetuam efficiant noctem, ni&longs;i for<lb/>tè &longs;ublu&longs;trem, quantum &longs;atis &longs;it ad impia<pb xlink:href="018/01/064.jpg" pagenum="56"/>rum cruciatus &longs;uarum alienarumque cala<lb/>mitatum a&longs;pectu augendos. </s>

<cell>P<emph type="italics"/>roportionem motuum omnium &longs;tellarum ad<emph.end type="italics"/> S<emph type="italics"/>olem con&longs;iderare.<emph.end type="italics"/></cell>

<s>Quare Tarta<lb/>rum ille concipiebat qua&longs;i immen&longs;as Ther<lb/>mas ac balneas efficaci&longs;&longs;imis omnium cau<lb/>&longs;ticorum particulis plenas; quæ proptere&atail; <lb/>lacus & &longs;tagnum ignis, ob quietem &longs;cilicet, <lb/>à Diuinis literis dicuntur. </s>

</row>

<row>

<s>Cumque plur&atail; <lb/>ijs quidem, quæ à Diuinis literis docemur, <lb/>con&longs;ona, &longs;ed præter eorum, qui aderant, opi<lb/>nionem, de ignis i&longs;tiu&longs;modi naturâ di&longs;pu<lb/>ta&longs;&longs;et; ne quid temerè prolatum videretur, <lb/>&longs;ermonem claudens Lactantij l. 7. diu. </s>

<cell>CLXVI.</cell>

<cell>P<emph type="italics"/>roportiones mu&longs;icas &longs;uperpartientes in eas, quæ particulá una tantum abundant reducere.<emph.end type="italics"/></cell>

</row>

<s>in&longs;t. </s>

<row>

<s><lb/>cap.

<cell>CLXVII.</cell>

<cell>P<emph type="italics"/>roportionem mu&longs;icam ad &longs;apores & odores coaptare.<emph.end type="italics"/></cell>

21. authoritate firmauit, vbi de igne <lb/>illo &longs;empiterno impiorum corpora crucian<lb/>te loquitur, <emph type="italics"/>Cuius natura,<emph.end type="italics"/> inquit, <emph type="italics"/>diuer&longs;a <lb/>e&longs;t ab hoc no&longs;tro, quo ad vitæ nece&longs;&longs;aria vti<lb/>mur, qui ni&longs;i alicuius materiæ fomite alatur, <lb/>extinguitur. </s>

</row>

<s>At ille Diuinus per &longs;e ip&longs;um <lb/>&longs;emper viuit ac viget &longs;ine vllis alimentis, nec <lb/>admi&longs;tum habet fumum, &longs;ed e&longs;t purus ac li<lb/>quidus, & in aquæ modum fluidus: non enim <lb/>vi aliqua &longs;ur&longs;um ver&longs;us vrgetur, &longs;icut no&longs;ter, <lb/>quem labes terreni corporis, quo tenetur, & fu<lb/>mus intermi&longs;tus exilire cogit &c.<emph.end type="italics"/></s><s> Cum ita<lb/>que &longs;u&longs;picarer, ne quis ve&longs;trum hæc eadem <lb/>obiiceret, &longs;i fortè ad extenuandum telluris <lb/>pondus ex inferorum ignibus argument&atail; <lb/>de&longs;ump&longs;i&longs;&longs;em, &longs;atius duxi ab&longs;tinere, ne co<pb xlink:href="018/01/065.jpg" pagenum="57"/>gerer hanc inire di&longs;putatione&mtail;. </s>

<row>

<cell>CLXVIII.</cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Haud ego &longs;anè ineptam dixeri&mtail; <lb/>philo&longs;ophiam illam, quæ rerum naturam <lb/>per experimenta ve&longs;tigat: &longs;ed nec aliquid te<lb/>merè pronunciandum, quo vetus opinio <lb/>tot &longs;apientum authoritate firmata de po&longs;&longs;e&longs;<lb/>&longs;ione deiiciatur. </s>

<cell>P<emph type="italics"/>icturarum proportiones explicare.<emph.end type="italics"/></cell>

<s>Quamuis autem &longs;ententia <lb/>hæc videatur adhuc enucleariùs explicanda, <lb/>vt igni &longs;ummam grauitatem ad&longs;truat; non <lb/>is tamen ego &longs;um, cui &longs;tomachum moueant <lb/>quæcunque præter opinionem audire con<lb/>tigerit. </s>

</row>

<row>

<s>Nec dubito quin, &longs;i rem penitiùs <lb/>intro&longs;picere vellemus, plura occurrerent à <lb/>no&longs;træ di&longs;putationis in&longs;tituto non alien&atail;. </s>

<cell>CLXIX.</cell>

<cell>P<emph type="italics"/>roportionem mu&longs;icam in in&longs;trumentis declarare iuxta compo&longs;itionis rationem.<emph.end type="italics"/></cell>

<s><lb/>Sed quoniam non placet his diutiùs immo<lb/>rari, ea commodiorem in locum reiiciamus. </s>

</row>

<s><lb/>Tibi interim datur, Mer&longs;enne, terreni glo<lb/>bi grauitatem, perpen&longs;is omnibus, haud <lb/>multum abe&longs;&longs;e ab eâ grauitate, quam æqua<lb/>lis moles argillacea obtineret. </s>

<row>

<s>Cum verò <lb/>res tota ex telluris magnitudine pendere vi<lb/>deatur, ne quis &longs;upere&longs;&longs;et dubitandi locus, <lb/>opus e&longs;&longs;et Geometricè per&longs;pectam haber&etail; <lb/>telluris magnitudinem. </s>

<cell>C<emph type="italics"/>oniugationes cuiu&longs;uis numeri breuiter inuenire.<emph.end type="italics"/></cell>

<s>Quare &longs;i quid ha<lb/>bes, Guldine, quo nos po&longs;sis, methodo non <lb/>adeò operosâ, in huius problematis cogni<lb/>tionem deducere, in medium proferre n&etail; <lb/>graueris. </s><pb xlink:href="018/01/066.jpg" pagenum="58"/>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Vnum præterea, quod non parùm <lb/><arrow.to.target n="note29"/><lb/>in rem tuam facit, Galilæe, audire placeat. </s>

<cell>CLXXI.</cell>

<cell>P<emph type="italics"/>ropo&longs;itis duobus quibuslibet numeris, quotuis alios &longs;eu in continuum &longs;eu medios in continua proportione arithmetica, geometrica & mu&longs;ica inuenire.<emph.end type="italics"/></cell>

<s><lb/>Illud autem e&longs;t, quod quamuis terram decu<lb/>plò grauiorem quis con&longs;titueret, ac ego de<lb/>prehenderim, nihilo tamen minùs tuis illis <lb/>orbiculis moueri facilè po&longs;&longs;et: non tantum <lb/>quia decuplex i&longs;ta grauitas non pertingeret <lb/>ad libras illas 50.000000.000000.000000. <lb/>000000. & eo amplius, verùm etiam qui&atail; <lb/>non totum illud pondus &longs;imul motui repu<lb/><figure id="id.018.01.066.1.jpg" xlink:href="018/01/066/1.jpg"/><lb/>gnaret. </s>

</row>

<s>Sit eni&mtail; <lb/>totus terræ globus <lb/>HIKL, cuius cen<lb/>trum C congruat v<lb/>niuer&longs;i centro, i&ntail; <lb/>quo nullum habet <lb/>momentum ad de<lb/>&longs;cen&longs;um, &longs;ed in eo <lb/>quie&longs;cit. </s>

<row>

<cell>CLXXII.</cell>

<s>An non &longs;a<lb/>tis Archimedi fui&longs;<lb/>&longs;et, &longs;i terram vnum <lb/>aut alterum milliare aliò tran&longs;tuli&longs;&longs;et? </s>

<cell>P<emph type="italics"/>roportiones<emph.end type="italics"/> S<emph type="italics"/>tiphelij de&longs;cribere.<emph.end type="italics"/></cell>

<s>Mo<lb/>ueri igitur intelligatur centrum ex C in T, <lb/>& &longs;it terra translata SORV. </s>

</row>

<row>

<s>Huic motui <lb/>primùm, præter hemi&longs;phærium &longs;uperius <lb/>HLK, non repugnat totum hemi&longs;phærium <lb/>inferius HIK, cuius videlicet partes plurimæ <lb/>fiunt centro C propiores, in quod &longs;uis nuti<pb xlink:href="018/01/067.jpg" pagenum="59"/>bus feruntur. </s>

<cell>CLXXIII.</cell>

<cell>C<emph type="italics"/>irculum &longs;uper centro &longs;uo mouere æqualiter, ita quod omnia illius puncta per rectam lineam moueantur ultro citroque.<emph.end type="italics"/></cell>

<s>Ponatur enim CT &longs;emidia<lb/>metri pars mille&longs;ima, hoc e&longs;t mill. 4. & eo <lb/>amplius; &longs;egmentorum MON & MVN Ra<lb/>tio inuenietur, ex ijs quæ Archimedes docet <lb/>l. 2. de &longs;ph. </s>

</row>

<row>

<cell>CLXXIIII.</cell>

<cell>P<emph type="italics"/>rogre&longs;&longs;us & regre&longs;&longs;us, tam &longs;ine latitudine quàm cum latitudine in planetis per &longs;olos concentricos circulos æqualiter motos demon&longs;trare.<emph.end type="italics"/></cell>

</row>

<row>

<s>prop.

<cell>CLXXV.</cell>

<cell>C<emph type="italics"/>au&longs;am uarietatis diametrorum ex &longs;uppo&longs;itis concentricis demon&longs;trare.<emph.end type="italics"/></cell>

2. &longs;unt enim &longs;eg<lb/>menta illa æqualia conis eandem ba&longs;im MN <lb/>habentibus, hi autem ex Eucl. l. 12. prop. </s>

</row>

<row>

<cell>CLXXVI.</cell>

<cell>R<emph type="italics"/>ationem centri grauitatis declarare.<emph.end type="italics"/></cell>

<s><lb/>14 inter &longs;e &longs;unt vt altitudines: Quapropter <lb/>inuentis conorum altitudinibus, quas Ar<lb/>chimedes docet, innote&longs;cit Ratio &longs;egmen<lb/>torum &longs;phæricorum conis illis æqualiu&mtail;. </s>

</row>

<row>

<s><lb/>Cum itaque CT &longs;it Radij (1/1000), &longs;egmenti <lb/>MVN altitudo e&longs;t 999, &longs;egmenti verò <lb/>MON altitudo e&longs;t 1001. Fiat igitur vt alti<lb/>tudo &longs;egmenti maioris 1001 ad &longs;ummam <lb/>ex eadem altitudine & Radio 2001, ita al<lb/>titudo &longs;egmenti &longs;phærici minoris 999, ad <lb/>coni æqualis altitudinem 1997. Similiter vt <lb/>altitudo minoris &longs;egmenti 999 ad &longs;ummam <lb/>ex eadem & Radio 1999, ita altitudo &longs;eg<lb/>menti &longs;phærici maioris 1001 ad coni æqua<lb/>lis altitudinem 2003. E&longs;t igitur MON ad <lb/>MVN vt 2003 ad 1997: atque adeò &longs;eg<lb/>mentum maius addit vltra hemi&longs;phærium <lb/>&longs;olùm totius globi (6/4000). Quare vt tellus ve<lb/>niret in T, &longs;olum &longs;egmentum &longs;phæricu&mtail; <lb/>MSORN vt &longs;ummum deor&longs;um versùs C <lb/>vrgeret; cui tamen, ne po&longs;tea de&longs;cende<gap/>, <pb xlink:href="018/01/068.jpg" pagenum="60"/>reliquum &longs;egmentum MVN ob&longs;i&longs;teret, cum <lb/>deberet à centro remoueri illo de&longs;cendente: <lb/>ac proinde quamuis in motu &longs;emper auge<lb/>retur difficultas mouendi, nunquam tamen <lb/>tota grauitas, perciperetur, ni&longs;i quando I ve<lb/>ni&longs;&longs;et in C; tunc enim tota &longs;phæra deor&longs;um <lb/>niteretur. </s>

<cell>CLXXVII.</cell>

<cell>S<emph type="italics"/>i proportio aliqua ex duabus proportionibus eiu&longs;dem quantitatis ad alias duas componatur, erit proportio illarum duarum eadem proportioni producti ex proportione in primam duarum quantitatum, detracta priore illa quantitate, quæ ad duas comparatur, ad eandem priorem quantitatem.<emph.end type="italics"/></cell>

<s>Præterea &longs;egmentum illud MON <lb/>non eadem obtineret ad de&longs;cendendum mo<lb/>menta in tantâ centri vicinitate, ac valdè <lb/>procul à centro: neque enim ex hoc, quòd <lb/>experimentis euincere non po&longs;&longs;imus grauia <lb/>centro propiora minùs vrgere deor&longs;u&mtail; <lb/>quàm remotiora (cum illa, quæ in experi<lb/>mentum a&longs;&longs;umuntur, non ea e&longs;&longs;e queant, <lb/>quæ di&longs;crimen inferant &longs;en&longs;u perceptibil&etail;) <lb/>repugnandum e&longs;t rationi manife&longs;tæ id &longs;ua<lb/>denti, vbi & ponderis amplitudo & inter<lb/>ualli differentia in&longs;ignis e&longs;t atque con&longs;pi<lb/>cu&atail;. </s>

</row>

<s><margin.target id="note29"/><emph type="italics"/>XXIX <lb/>Telluris <lb/>grauitas <expan abbr="nõ">non</expan> <lb/>tota re&longs;i&longs;te<lb/>ret Archi<lb/>medi traben<lb/>ti.<emph.end type="italics"/></s>

<row>

<cell>CLXXVIII.</cell>

<s>Hinc fit 24 axibus in peritrochio aut tym<lb/><arrow.to.target n="note30"/><lb/>panis dentatis, quorum partes e&longs;&longs;ent in Ra<lb/>tione decuplâ, fieri po&longs;&longs;e, vt virtute tres li<lb/>bras mouere valente terra per aliquod &longs;pa<lb/>tium moueretur; illa enim mouere po&longs;&longs;et <lb/>lib 3000000.000000.000000.000000; qui <lb/>numerus excedit &longs;emi&longs;&longs;em ponderis totius <lb/>terræ; ac proinde eou&longs;que moueret, du&mtail; <lb/>&longs;egmentum MON æquale e&longs;&longs;et toti ponderi, <pb xlink:href="018/01/069.jpg" pagenum="61"/>quod ab eadem potentiâ po&longs;&longs;et &longs;u&longs;tineri ad<lb/>hibitâ eadem machinâ, habitâ tamen ratio<lb/>ne &longs;egmenti MVN ex parte &longs;u&longs;tentantis &longs;eg<lb/>mentum &longs;uperius, ne tanto impetu deor&longs;um <lb/>vrgeat, quanto vrgeret, &longs;i &longs;egmentum MVN <lb/>non ade&longs;&longs;et. </s>

<cell>P<emph type="italics"/>roportionem mi&longs;tionis metallorum, maximè auri & argenti declarare.<emph.end type="italics"/></cell>

<s>At verò compo&longs;itis tantùm 17 <lb/>helicibus cum tympanis denticulos 25 ha<lb/>bentibus, & vltimo tympano ad axem, cui <lb/>funis ductarius circumuoluitur, Rationem <lb/>quintuplam habente, potentia vnius libræ <lb/>&longs;u&longs;tentatiua applicata manubrio æqualis lon<lb/>gitudinis cum tympanorum &longs;emidiametro, <lb/>po&longs;&longs;et mouere terram ex C in T v&longs;que eò <lb/>dum &longs;egmentum MON e&longs;&longs;et lib 2.910383. <lb/>045673.370361.328125. qui pariter libra<lb/>rum numerus excedit totius terrenæ graui<lb/>tatis &longs;emi&longs;&longs;em: at potentia decem libras lo<lb/>co transferre valens, decuplum pondus mo<lb/>uere po&longs;&longs;et, atque adeò totum globum ele<lb/>uare. </s>

</row>

<row>

<s>Sed iam Guldinum audiamus, vt cer<lb/>tam telluris magnitudinem &longs;tatuamus. </s>

<cell>CLXXIX.</cell>

<cell>S<emph type="italics"/>i duobus totis duæ portiones &longs;imiles ab&longs;cindantur ab ei&longs;dem denuò, & ab&longs;cißis portionibus partes eædem auferantur, denuoque ac denuò quoties libuerit à portionibus, & ù re&longs;iduis ip&longs;arum quantitatum partes eædem auferantur, erit re&longs;iduí ad re&longs;iduum, ueluti totius ad totum.<emph.end type="italics"/></cell>

<s><margin.target id="note30"/><emph type="italics"/>XXX <lb/>Definitur <lb/>machin&atail;, <lb/>qua potui&longs;<lb/>&longs;et tellus mo<lb/>ueri ab Ar<lb/>chimede.<emph.end type="italics"/></s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Fieri non pote&longs;t, vt paucis me ex<lb/>pediam, quia non vna tantùm, aut alter&atail; <lb/>&longs;uppetit methodus, &longs;ed plures aliquando ex<lb/>cogitaui, cum hac &longs;uper re animum diligen<lb/>tiùs aduerterem vehementer admirans ab <lb/>antiquis nihil ad nos veni&longs;&longs;e, in quo animus <lb/>Gemetricus po&longs;&longs;et conquie&longs;cere. </s>

<row>

<cell>CLXXX.</cell>

<s>Neque fa<pb xlink:href="018/01/070.jpg" pagenum="62"/>cilè dixerim, quænam præ cæteris metho<lb/>dus arrideat, cum pro diuersâ locorum op<lb/>portunitate aliâ atque aliâ methodo vti opor<lb/>teat. </s>

<cell>S<emph type="italics"/>i aliqua quantitas in duas partes diuidatur, fueritque alicuius quantitatis ad partes illas compo&longs;ita proportio, non poterit eiu&longs;dem quantitatis ad partes alias quantitatis diui&longs;a, aliter proportio eadem componi.<emph.end type="italics"/></cell>

<s>Quarè con&longs;ultius forta&longs;&longs;e fuerit, vel <lb/>omnes pariter &longs;ilentio obuoluere, vel in aliam <lb/>di&longs;&longs;ertationem reijcere. </s>

</row>

<row>

<s>Quod &longs;i, quam he<lb/>ri Mer&longs;ennus temporis dilationem ad am<lb/>pliores numeros in pagellâ priuatim de&longs;cri<lb/>bendos impetrauit, mihi non denegetis, tæ<lb/>dio ve&longs;tro parcetur, & meo labori. </s>

<cell>CLXXXI.</cell>

<cell>C<emph type="italics"/>um fuerit aliqua proportio, compo&longs;ita ex proportionibus primæ ad &longs;ecundam & tertiam, & rur&longs;us quartæ ad quintam & &longs;extam: ita &longs;e habebit proportio &longs;ecundæ ad tertiam, ad proportionem quintæ ad &longs;extam, uelut producti ex proportione in &longs;ecundam detracta prima ad primam ad productum ex proportione in quintam, detracta quarta ad quartam.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Rationi con&longs;entanea &longs;unt, quæ po<lb/>&longs;tulas; neque æquum e&longs;t præproperæ curio<lb/>&longs;itati ob&longs;ecundantes multiplicis methodi co<lb/>gnitione fraudari. <lb/><figure id="id.018.01.070.1.jpg" xlink:href="018/01/070/1.jpg"/></s><pb xlink:href="018/01/071.jpg" pagenum="63"/><figure id="id.018.01.071.1.jpg" xlink:href="018/01/071/1.jpg"/>

</row>

<s><emph type="center"/>DISSERTATIO <lb/>TERTIA<emph.end type="center"/></s>

<row>

<cell>CLXXXII.</cell>

<s><emph type="center"/>Methodos varias inueniendi <lb/>terræ quantitatem <lb/>proponit.<emph.end type="center"/></s>

<cell>P<emph type="italics"/>ropo&longs;ita differentia proportionum partium &longs;imilium ad partes a&longs;&longs;umptas, propo&longs;itaque proportione totius ad re&longs;idua eadem, differentiam proportionum totius ad reliquum re&longs;idui inuenire.<emph.end type="italics"/></cell>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

</row>

<row>

<s>HAVD &longs;atis &longs;cio, an po&longs;<lb/>&longs;im aliquid proferr&etail;, <lb/>quod ve&longs;træ exspectatio<lb/>ni faciat &longs;atis in eâ, quam <lb/>nobis hodiè examinan<lb/>dam &longs;tatuimus quæ&longs;tio<lb/>nem de terraquei huius <lb/>globi magnitudine inue&longs;tigandâ: vos idcircò <pb xlink:href="018/01/072.jpg" pagenum="64"/>pro ve&longs;trâ humanitate tenuitati meæ ve<lb/>niam dabitis, &longs;i quid afferre contigerit ita <lb/>planum ac facilè, vt ve&longs;trorum ingeniorum <lb/>&longs;ublimitati non re&longs;pondeat. </s>

<cell>CLXXXIII.</cell>

<cell>S<emph type="italics"/>patium uitæ naturalis per &longs;pacium uitæ fortuitum declarare.<emph.end type="italics"/></cell>

<s>Nihil habe<gap/><lb/>certi quod &longs;tatuam de terræ quantitate, ne<lb/>que enim hactenus otium fuit, quæ conce<lb/>peram, in praxim deducere. </s>

</row>

<s>Fieri autem <lb/>po&longs;&longs;e exi&longs;timo, vt operâ non longâ propo<lb/>&longs;itum &longs;copum a&longs;&longs;equamur: duo nimiru&mtail; <lb/>præcogno&longs;ci oportet, quibus notis ac certis <lb/>terrenam diametrum po&longs;&longs;umus inue&longs;tigar&etail;. </s>

<row>

<cell>CLXXXIIII.</cell>

<s><lb/>Primum e&longs;t altitudo oculi &longs;upra maris i&ntail; <lb/>immen&longs;um patentis &longs;uperficiem, quæ non <lb/>æquabili planitie explicatur, &longs;ed &longs;phæra&mtail; <lb/>æmulatur: hanc verò altitudinem certi&longs;&longs;i<lb/>mè nobis innote&longs;cere po&longs;&longs;e quis neget? </s>

<cell>Q<emph type="italics"/>uæcunque grauia in uorticibus aquarum, merguntur, in medio uorticis, primum uer&longs;a mergantur.<emph.end type="italics"/></cell>

<s>cum <lb/>eam funiculo vel phy&longs;icâ aliâ men&longs;urâ &longs;æ<lb/>piùs dimetiri liceat. </s>

</row>

<row>

<s>Alterum, quod in hoc <lb/>negotio requiritur, e&longs;t angulus, quem cum <lb/>lineâ perpendiculi ad terræ centrum ductâ <lb/>con&longs;tituit opticus radius extremum hori<lb/>zontem allambens: hunc &longs;i organo ad id <lb/>affabrè elaborato ob&longs;eruaueris, &longs;ereno c<gap/>lo, <lb/>tranquillo mari, cum minima refractionis <lb/>&longs;u&longs;picio &longs;ube&longs;&longs;e pote&longs;t, quid certius requi<lb/>ras? </s>

<cell>CLXXXV.</cell>

<cell>C<emph type="italics"/>ur homo &longs;edens quanto altius &longs;edet, & quanto magis crura ad f&oelig;mora, & f&oelig;mora ad pectus reclinata habet, facilius con&longs;urgat, cum tamen hæc oppo&longs;ito modo inuicem &longs;e habeant, declarare.<emph.end type="italics"/></cell>

<s>cum organo eidem in dimetiendis &longs;y<lb/>derum altitudinibus aut di&longs;tantijs acquie<lb/>&longs;cas. </s>

</row>

<s>His autem duobus cognitis terræ quo<pb xlink:href="018/01/073.jpg" pagenum="65"/>que &longs;emidiametrum latere non po&longs;&longs;e de<lb/>mon&longs;tro. </s>

<row>

<cell>CLXXXVI.</cell>

<s>Sit enim, exempli gratiâ, nota altitudo <lb/>BA Phari Genuen&longs;is (laternam vocant) cum <lb/><arrow.to.target n="note31"/><lb/>&longs;copulo palmorum Genuen&longs;ium 440, hoc <lb/>e&longs;t pedum Rom. ant. </s>

<cell>S<emph type="italics"/>i fuerit proportio primæ & &longs;ecundæ quantitatis ad tertiam, ut primæ & quartæ ad quintam, fueritque quarta &longs;ecunda maior, erit proportio quartæ ad quintam maior quàm &longs;ecundæ ad tertiam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i fuerit maior<emph.end type="italics"/></cell>

<cell/>

</row>

<s>480, ob&longs;eruatusque <lb/>angulus BAD &longs;it gr. 89. m. 36. &longs;ec. 33. Quo<lb/>niam ergo linea AD circulum tangit in D, <lb/>angulus CDA e&longs;t rectus. </s>

<row>

<cell/>

<s>Ex B ducta intel<lb/>ligatur BE parallela ip&longs;i CD; e&longs;tque triangu<lb/>lum ABE rectangulum ad E, cuius hypo<lb/>thenu&longs;a AB, & angulus adiacens innotue<lb/>runt. </s>

<cell><emph type="italics"/>quartæ ad quintam quàm &longs;ecundæ ad tertiam, nece&longs;&longs;e e&longs;t quartam &longs;ecunda e&longs;&longs;e maiorem.<emph.end type="italics"/></cell>

<s>Quare fiat vt Radius 100000. 00000. <lb/>ad &longs;inum gr. 89. m. 36. &longs;ec. 33. hoc e&longs;t 99997. <lb/>67348, ita AB ped. 480. ad BE ped. (479 <lb/>98883.27040/100000.00000). Porrò triangula ABE, ACD æqui<lb/>angula &longs;unt propter linearum BE, CD pa<lb/>ralleli&longs;mum, adeoque & &longs;imilia, ac vt AB <lb/>ad BE, ita AC ad CD. </s>

</row>

<row>

<cell>CLXXXVII.</cell>

<cell>S<emph type="italics"/>i ei&longs;dem uiribus & ‘eadem’ proportione cum auxilio ponderis tertij quartum pondus moueatur quibus &longs;ecundum, auxilio primi nece&longs;&longs;e e&longs;t <expan abbr="quart&utilde;">quartum</expan> pondus tardius & maiore cum difficultate moueri quàm &longs;ecundum.<emph.end type="italics"/></cell>

<s>Ponatur autem BC <lb/>vna Radix Algebricè. </s>

</row>

<s>Igitur vt AB ped. 480 <lb/>ad BE ped. (479 98883.27040/10000000000), ita AC ped. 1 &rx; + <lb/>480 ad CD ped. (47998883.27040/48000000.00000) &rx; + (479 47463969.79200/48000000.00000). <lb/>E&longs;t autem CD æqualis ip&longs;i CB 1 &rx;. </s>

<row>

<cell>CLXXXVIII.</cell>

<cell>S<emph type="italics"/>i uires aliquæ moueant cum ponderibus aliqua pondera, ut compo&longs;ita proportio &longs;it eadem proportioni uirium & duorum ponderum mouentium aggregatum æquale duorum ponderum, ubi maior fuerit partium in æqualitas, ibi erit maior difficultas.<emph.end type="italics"/></cell>

<s>Quare <lb/>factâ Antithe&longs;i iuxta Algebræ regulas, ma<lb/>net æquatio inter hos terminos (111672960/48000000.00000) &rx; & <lb/>pedes (479 47463969.79200/48000000.00000). In&longs;titutâ denique di<lb/>ui&longs;ione prodit quotiens ped. 20631193., <pb xlink:href="018/01/074.jpg" pagenum="66"/>pretium 1 &rx; CB vel <lb/><figure id="id.018.01.074.1.jpg" xlink:href="018/01/074/1.jpg"/><lb/>CD. </s>

</row>

<row>

<cell>CLXXXIX.</cell>

<cell>S<emph type="italics"/>i pondus minus ad longitudinem minorem &longs;ub æquali proportione coaptetur, facilius deor&longs;um trahetur quàm quod maius e&longs;t & propius.<emph.end type="italics"/></cell>

<s>E&longs;t ergo inuen<lb/>ta terræ &longs;emidiameter <lb/>mill. Rom. ant. </s>

</row>

<row>

<cell>S<emph type="italics"/>i fuerit primum graue minus &longs;ecundo, & &longs;ecundum minus tertio, proportio autem primi ad &longs;ecundum multo maior quàm &longs;ecundi ad tertium, pos&longs;ibile erit propo&longs;itis uiribus ei&longs;dem addere pondus <expan abbr="&longs;ec&utilde;do">&longs;ecundo</expan>, ut ip&longs;um & tertium moueatur faciliùs ab ei&longs;dem uiribus, & primo uel &longs;ecundo quàm antea.<emph.end type="italics"/></cell>

<s>4126, <lb/>pa&longs;&longs;. </s>

</row>

<row>

<s>238. po&longs;ito angu<lb/>lo ad A gr.89.m.36. <lb/>&longs;ec 33. præcisè. </s>

<cell>C<emph type="italics"/>um fuerint duo pondera & uires, duxerisque aggregatum ex uiribus & minore pondere in maius, addiderisque in&longs;uper quantum e&longs;t productum dimidij uirium in &longs;e latus aggregati detracto dimidio uirium, dicetur pondus auxiliare æqualis proportionis.<emph.end type="italics"/></cell>

<s><margin.target id="note31"/><emph type="italics"/>XXXI <lb/>Prima me<lb/>thodus in<lb/>ueniendi tel<lb/>luris &longs;emi<lb/>diametrum, <lb/>per Trigo<lb/>nometriam <lb/>& Alge<lb/>bram.<emph.end type="italics"/></s>

</row>

<s>Quod &longs;i rem breuiùs <lb/>a&longs;&longs;equi velis, dato an<lb/><arrow.to.target n="note32"/><lb/>gulo ob&longs;eruato in A gr. <lb/>89. m. 36. &longs;ec. 33, &longs;umatur AC vt Radius, & <lb/>CD, vt &longs;inus dati anguli. </s>

<row>

<cell>CXCII.</cell>

<cell>S<emph type="italics"/>i ex medio diametri linea ad perpendiculum erigatur ad circuli peripheriam, ex eo puncto autem quotlibet lineæ ducantur &longs;eu intus ad circun ferentiam u&longs;que, &longs;eu extra ad diametrum, erit proportio totius lineæ ad totam uelut mutuo partis ad partem.<emph.end type="italics"/></cell>

<s>Et a&longs;&longs;umptâ BC <lb/>1 &rx; fiat vt Radius 100000.00000. ad dati an<lb/>guli &longs;inum 99997.67348, ita AC ped. 1 &rx; <lb/>+ 480 ad CD ped. (99997.67348&rx;+4799888327040/100000.00000). E&longs;t <lb/>CD ip&longs;i CB 1 &rx; æqualis, atque adeò vtrinque <lb/>demptâ fractione (99997.67348/100000.00000) &rx;, remanet æqua<lb/>tio inter (232652/100000.00000) &rx; & ped. (4799888327040/100000.00000). Qua<lb/>rè factâ diui&longs;ione habetur pretium 1 &rx; ped. <lb/>20631193 vt priùs. </s>

</row>

<row>

<cell>CXCIII.</cell>

<cell>R<emph type="italics"/>ationem ponderis triplicem explicare.<emph.end type="italics"/></cell>

</row>

<s><margin.target id="note32"/><emph type="italics"/>XXXII <lb/>Idem aliter, <lb/>& breuiùs.<emph.end type="italics"/></s>

<row>

<cell>CXCIIII.</cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Methodus hæc plana e&longs;t atque fa<lb/>cilis cuiuis vel leuiter Analyticâ &longs;cientiâ a&longs;<lb/>per&longs;o: &longs;ed aliquos forta&longs;&longs;e deterreret, qui vel <lb/>ip&longs;um. </s>

<cell>P<emph type="italics"/>roportionem ponderis longioris in medio &longs;u&longs;pen&longs;i, ad breuius illi æquale & in medio &longs;u&longs;pen&longs;um declarare.<emph.end type="italics"/></cell>

<s>Algebræ nomen horrent, quamuis <lb/>Mathematici audire velint. </s>

</row>

<row>

<s>Alios angulo<lb/>rum ob&longs;eruatio, & linearum circulo ad&longs;cri<lb/>ptarum vel in&longs;criptarum inue&longs;tigatio ex Ca<pb xlink:href="018/01/075.jpg" pagenum="67"/>noné defatigat, &longs;i maximè res ad minimas <lb/>A&longs;tronomicas fractiones deducta exigat par<lb/>tis proportionalis inqui&longs;itionem. </s>

<cell>S<emph type="italics"/>i lectus fiat dupla longitudine ad latitudinem, melius &longs;uffulcietur re&longs;tibus ex medio ad angulos & eius æquidi&longs;tantibus quàm &longs;ecundum longitudinem & latitudinem.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Satis e&longs;t, &longs;i peritis Geometris hac <lb/>in re fiat &longs;atis. </s>

</row>

<s>Verùm adhuc ab&longs;que Cano<lb/><arrow.to.target n="note33"/><lb/>ne Trigonometrico res tota perfici po&longs;&longs;et, <lb/>&longs;ed non &longs;ine Algebrâ. </s>

<row>

<cell>CXCVI.</cell>

<s>Habeatur enim qua<lb/>dratum Geometricum <emph type="italics"/>S<emph.end type="italics"/>H; <lb/>vel etiam &longs;it rectangulum, <lb/><figure id="id.018.01.075.1.jpg" xlink:href="018/01/075/1.jpg"/><lb/>cuius latus AS maius &longs;it late<lb/>re AH, id quod aliquando <lb/>commodius accidet. </s>

<cell>S<emph type="italics"/>i duo circuli &longs;uper eodem centro eodem motu trans feruntur, æquale &longs;pacium &longs;uperant.<emph.end type="italics"/></cell>

<s>Obuer<lb/>tatur latus AH ita, vt con<lb/>gruat radio optico terra&mtail; <lb/>tangenti AD, in &longs;uperior&etail; <lb/>figurâ: eritque triangulum <lb/>ABE &longs;imile triangulo OAS: Nam anguli <lb/>SAH & BEA &longs;unt recti, ac proinde lineæ <lb/>SA, BE parallelæ, intrà quas anguli alterni <lb/>SAO, EBA &longs;unt æquales; &longs;icut & alterni <lb/>EAB, SOA, intra parallelas SO, AE. </s>

</row>

<row>

<s>Igi<lb/>tur vt OA ad AS, ita AB ad BE: &longs;ed vt AB <lb/>ad BE, ita in &longs;uperiore figurâ AC ad CD; <lb/>ergo vt OA ad AS, ita AC ad CD. </s>

<cell>CXCVII.</cell>

<cell>C<emph type="italics"/>ur lances ad locum &longs;uum &longs;u&longs;pen&longs;i redeant, impendentes <expan abbr="nõ">non</expan>, <expan abbr="demõ&longs;trare">demon&longs;trare</expan>.<emph.end type="italics"/></cell>

<s>Quare <lb/>&longs;i latus AS Quadrati vel rectanguli notum &longs;it <lb/>in particulis quibuslibet, facilè innote&longs;cet, <lb/>quot huiu&longs;modi particulas contineat AO. </s>

</row>

<s><lb/>Cum verò altitudo AB nota &longs;it ex. gr. ped. <pb xlink:href="018/01/076.jpg" pagenum="68"/>480, a&longs;&longs;umatur BC 1 &rx;: tum fiat vt particu<lb/>læ OA ad particulas AS, ita ped. 1 &rx; + 480 <lb/>ad aliud, & proueniet quartus terminus CD <lb/>æqualis ip&longs;i CB 1 &rx;: atque adeò factâ Anti<lb/>the&longs;i, & in&longs;titutâ diui&longs;ione habetur quanti<lb/>tas ip&longs;ius CD. </s>

<row>

<cell>CXCVIII.</cell>

<cell>C<emph type="italics"/>ur &longs;olidum quod cubus uocatur<emph.end type="italics"/> P<emph type="italics"/>yramide &longs;tabilius &longs;it o&longs;tendere.<emph.end type="italics"/></cell>

<s><margin.target id="note33"/><emph type="italics"/>XXXIII <lb/>Idem aliter <lb/>&longs;ine Trigo<lb/>nometria.<emph.end type="italics"/></s>

</row>

<row>

<cell>CXCIX.</cell>

<cell>R<emph type="italics"/>ationem remorum nauim impellentium inuenire.<emph.end type="italics"/></cell>

<s>quod &longs;inè Algebrâ res tam facilis <lb/><arrow.to.target n="note34"/><lb/>e&longs;t, vt penè non audeam dicere, ne vulgata <lb/>vilecat. </s>

</row>

<s>Fiat vt OI, differentia inter OA & <lb/>AS, ad ip&longs;am AS, ita nota altitudo AB ad <lb/>aliud, & proueniet CD quæ&longs;ita terræ &longs;emi<lb/>diameter. </s>

<row>

<s>E&longs;t nimirum AB differentia inter <lb/>AC & CD, & vt tota AC ad totam AO, ita <lb/>ablata CB ad ablatam AI; igitur & reliqua <lb/>AB ad reliquam IO vt tota AC ad totam <lb/>AO: ergo permutando, & diuidendo, vt <lb/>AB ad BC, hoc e&longs;t CD, ita OI ad IA, hoc <lb/>e&longs;t AS. </s>

<cell>C<emph type="italics"/>ur temo cum paruus &longs;it, magnam nauim agere pote&longs;t, & cur cùm uarietas &longs;it in prora, ip&longs;e con&longs;tituatur in puppi.<emph.end type="italics"/> E<emph type="italics"/>t cum transuer&longs;im ab aqua prematur rectà nauim dirigat.<emph.end type="italics"/></cell>

<s><margin.target id="note34"/><emph type="italics"/>XXXIV <lb/>Idem &longs;ine <lb/>Trigonome<lb/>tria & &longs;ine <lb/>Algebra.<emph.end type="italics"/></s>

</row>

<row>

<s>Et hæc quidem dicta &longs;int, &longs;i fortè angu<lb/><arrow.to.target n="note35"/><lb/>lum CAD præcogno&longs;cere non libeat. </s>

<cell>S<emph type="italics"/>i duæ lineæ non &longs;ecantes circuli peripheriam in unum punctum ex ea coeant exterius, nece&longs;&longs;e e&longs;t illas peripheria contenta e&longs;&longs;e maiores.<emph.end type="italics"/></cell>

<s>Cæ<lb/>terùm illo cognito rem aggredi licet &longs;ine <lb/>Algebrâ ope &longs;oliûs Trigonometriæ, quæ <lb/>multiplicem &longs;ubmini&longs;trare poterit metho<lb/>dum. </s>

</row>

<s>Et primò datâ altitudine AB, & an<lb/>gulo ad A ob&longs;eruato ex. </s>

<row>

<s>gr.gr.89.m.36.&longs;ec. <lb/>33., notus e&longs;t angulus ad centrum C gr.o. <lb/>m. 23. &longs;ec. 27, ac proinde eius &longs;ubten&longs;a i&ntail; <lb/>partibus Radij innote&longs;cit. </s>

<cell>R<emph type="italics"/>ationem &longs;trepitus o&longs;tendere.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CCIII.</cell>

<cell>C<emph type="italics"/>ur &longs;cytalis onera portentur faciliùs, explorare.<emph.end type="italics"/></cell>

<s>Igitur ductâ BD, <pb xlink:href="018/01/077.jpg" pagenum="69"/>duo anguli ad ba&longs;im BD &longs;imul &longs;umpti &longs;unt <lb/>æquales recto CDA vnâ cum angulo ob&longs;er<lb/>uato A. </s>

</row>

<s>Cum verò triangulum CBD &longs;it <gap/>&longs;o<lb/>&longs;celes, vnu&longs;qui&longs;que an<lb/><figure id="id.018.01.077.1.jpg" xlink:href="018/01/077/1.jpg"/><lb/>gulorum ad ba&longs;im BD <lb/>e&longs;t æqualis &longs;emirecto & <lb/>&longs;emiangulo ob&longs;eruato. </s>

<row>

<cell>CCIIII.</cell>

<s><lb/>Deme ergo &longs;emiangu<lb/>lum ob&longs;eruatum gr.44. <lb/>48. 16 1/2, ex angulo &longs;e<lb/>mirecto, hoc e&longs;t grad. <lb/>45, remanet gr. o. m. 11. <lb/>fec. </s>

<cell>C<emph type="italics"/>ur pluribus trochleis, pondera facilius eleuentur o&longs;tendere.<emph.end type="italics"/></cell>

</row>

<row>

<s>43 1/2 quantitas angu<lb/>li ADB: Hic autem angulus ADB &longs;emper <lb/>e&longs;t &longs;emi&longs;&longs;is complementi anguli ad A ob&longs;er<lb/>uati; angulo enim ADB facto ad punctum <lb/>contactûs e&longs;t æqualis angulus in &longs;egmento <lb/>alterno, anguli verò ad peripheriam duplex <lb/>e&longs;t angulus ad centrum C. </s>

<cell>S<emph type="italics"/>uper uerbis<emph.end type="italics"/> P<emph type="italics"/>latonis de fine<emph.end type="italics"/> R<emph type="italics"/>eipublicæ.<emph.end type="italics"/></cell>

<s>In triangulo ita<lb/>que ADB noti &longs;unt duo anguli ad A & ad D; <lb/>& latus BD notum e&longs;t in partibus 682. <lb/>13152.quarum Radius 100000.00000; ideo<lb/>que in ij&longs;dem Radij partibus inuenitur AB <lb/>partium 232657. Iam fiat vt AB partium <lb/>232657 ad Radium 100000.00000, ita AB <lb/>ped. 480 ad aliud, & prodibit quantitas BC <lb/>terrenæ &longs;emidiametri ped. 20631229, hoc <lb/>e&longs;t mill. 4126. pa&longs;&longs;. </s>

</row>

<row>

<cell>R<emph type="italics"/>hombi paßiones qua&longs;dam declarare.<emph.end type="italics"/></cell>

</row>

<row>

<s>246. Quod verò ali<pb xlink:href="018/01/078.jpg" pagenum="70"/>quod intercedat di&longs;crimen inter hanc & dia<lb/>trum &longs;uperiùs inuentam, nil mirum, qui&atail; <lb/>vbi multiplex diui&longs;io intercedit, fractiones <lb/>aliquæ neglegun<lb/><figure id="id.018.01.078.1.jpg" xlink:href="018/01/078/1.jpg"/><lb/>tur, vnde demum <lb/>aliqua oritur dif<lb/>ferentia. </s>

<cell>CCVII.</cell>

<cell>P<emph type="italics"/>roportionem agentium naturalium in tran&longs;mutatione con&longs;iderare.<emph.end type="italics"/></cell>

<s><margin.target id="note35"/><emph type="italics"/>XXXV <lb/>Idem aliter <lb/>per Trigo<lb/><gap/>ometriam.<emph.end type="italics"/></s>

</row>

<s>Sed placeat hìc <lb/><arrow.to.target n="note36"/><lb/>vnum prætere&atail; <lb/>ob&longs;eruare, quo mi<lb/>rificè &longs;um delecta<lb/>tus, cum primùm <lb/>animaduerti: <expan abbr="Do-ctrinã">Do<lb/>ctrinam</expan> &longs;cilicet Tri<lb/>gonometricam illud idem exhibere po&longs;&longs;&etail;, <lb/>quod ab Algebrâ, in &longs;ecundâ methodo indi<lb/>catâ, po&longs;t omnes æquationes &longs;ubmini&longs;tra<lb/>tur. </s>

<row>

<cell>CCVIII.</cell>

<s>Fiat enim vt Sinus Ver&longs;us comple<lb/>menti anguli ob&longs;eruati, ad eiu&longs;dem anguli <lb/>ob&longs;eruati Sinum Rectum, ita nota altitudo <lb/>ad aliud, & habebitur quæ&longs;ita terræ &longs;emi<lb/>diameter. </s>

<cell>M<emph type="italics"/>ota res à centro grauitatis per <expan abbr="prior&etilde;">priorem</expan> motum, in reditu uelocius mouetur quam &longs;i quieuerit.<emph.end type="italics"/></cell>

<s>Sit enim CB terræ &longs;emidiame<lb/>ter, BA nota altitudo, AD linea optica tan<lb/>gens in D, per quod ex centro C ducatur re<lb/>cta CD, quæ producta in E occurrat peri<lb/>pheriæ circuli, interuallo CA, ex eodem <lb/>centro de&longs;cripti. </s>

</row>

<s>Eadem ergo e&longs;t Ratio AB <lb/>ad BC, quæ e&longs;t ED ad DC. </s>

<row>

<s>E&longs;t autem AD <pb xlink:href="018/01/079.jpg" pagenum="71"/>Sinus anguli ACE, eiusque Sinus Ver&longs;us e&longs;t <lb/>DE. </s>

<cell>S<emph type="italics"/>i &longs;uperficies rectangula in duas partes æquales diui&longs;a intelligatur, quæ ambæ quadratæ &longs;int, itemque in duas inæquales, erit parallelipedum ex latere mediæ partis in totam &longs;uperficiem maius aggregato parallelipedorum ex partibus inæqualibus in latera alterius partis mutuo, in eo, quod fit ex differentia lateris minoris partis à mediæ latere in differentiam maioris partis &longs;uperficiei à media &longs;uperficie bis, & ex differentia amborum laterum inæqualium iunctorum ad ambo latera, æqualia iuncta in minorem partem &longs;uperficiei.<emph.end type="italics"/></cell>

<s>At CD e&longs;t æqualis Sinui Recto anguli <lb/>CAD ob&longs;eruati; e&longs;t &longs;iquidem CD æqualis <lb/>&longs;inui complementi anguli C. </s>

</row>

<row>

<s>Igitur quæ <lb/>Ratio e&longs;t ip&longs;ius DE Sinus Ver&longs;i complemen<lb/>ti anguli ob&longs;eruati, ad DC Sinum anguli A <lb/>ob&longs;eruati, ea e&longs;t ip&longs;ius altitudinis notæ BA, <lb/>ad| quæ&longs;itam terræ &longs;emidiametrum BC. </s>

<cell>S<emph type="italics"/>i duæ lineæ ad æquales angulos ab eodem puncto peripheriæ circuli reflectantur, nece&longs;&longs;e e&longs;t angulos cum dimetiente factos æquales e&longs;&longs;e.<emph.end type="italics"/> V<emph type="italics"/>nde manife&longs;tum e&longs;t, protractam diametrum angulum &longs;uppo&longs;itum per æqualia diuidere.<emph.end type="italics"/></cell>

<s><lb/>Quarè &longs;inum anguli ob&longs;eruati 99997.67348 <lb/>deme ex Radio, & remanet 232652. Sinus <lb/>Ver&longs;us complementi.Iam &longs;i fiat vt 232652. <lb/>ad 99997.67348, ita nota altitudo ped. <lb/>480. ad ped. 20631193, eadem inuenitur <lb/>&longs;emidiameter, quæ &longs;uperiùs per Algebram <lb/>innotuit. </s>

</row>

<row>

<cell>S<emph type="italics"/>i duæ lineæ ex duobus punctis peripheriam contingentes, in eandem partem protrahantur, &longs;emper magis di&longs;tabunt inuicem ea ex parte, & nunquam concurrent.<emph.end type="italics"/></cell>

<s><margin.target id="note36"/><emph type="italics"/>XXXVI <lb/>Idem aliter <lb/>et breui&longs;&longs;i<lb/>mè.<emph.end type="italics"/></s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si perfici res commodè po&longs;&longs;it &longs;inè <lb/><arrow.to.target n="note37"/><lb/>inue&longs;tigatione anguli, quem cum perpendi<lb/>culo facit opticus radius &longs;phæricam terræ &longs;u<lb/>perficiem tangens, angulum illum libens <lb/>prætermitterem: vix enim &longs;cio, quàm exa<lb/>ctè deprehendi queat, quamuis organis di<lb/>ligenti&longs;&longs;imè elaboratis non caream. </s>

<cell>CCXII.</cell>

<cell>S<emph type="italics"/>i ab eodem puncto ad circuli peripheriam lineæ quotuis ducantur, tres inuenire lineas, quæ non in alium punctum reflectentur.<emph.end type="italics"/></cell>

<s><margin.target id="note37"/><emph type="italics"/>XXXVII <lb/>Quam exa<lb/>ctè ob&longs;erua. </s>

</row>

<s><lb/>ri po&longs;sint <lb/>anguli.<emph.end type="italics"/></s>

<row>

<cell>CCXIII.</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Omnem mihi eximo &longs;crupulum, <lb/>&longs;i quando contingat in Quadrante lineas, in <lb/>quibus minuta di&longs;tinguuntur, ita obliquè &longs;e<lb/>cari â perpendiculo, vt anceps hæream, in <lb/>quam minuti partem cadat, cum tame&ntail; <lb/>etiam ip&longs;as minutorum minutias per&longs;equi <pb xlink:href="018/01/080.jpg" pagenum="72"/>operæ pretium &longs;it. </s>

<cell>P<emph type="italics"/>ropo&longs;ito circulo, atque in eius peripheria puncto &longs;ignato, lineas contingentes ultra cítraque, & eam ab ip&longs;omet deducere.<emph.end type="italics"/></cell>

<s>Latus vnum Quadran<lb/>tis ita duplico, vt iam perpendiculum non <lb/>ex circuli centro, &longs;ed ab extremâ diametro <lb/>pendeat, & ob&longs;eruationem in&longs;tituo: hinc <lb/>enim &longs;æpiùs fit, vt &longs;ilum &longs;ericum crudum, <lb/>ex quo pilula plumbea &longs;u&longs;penditur, minùs <lb/>obliquè lineam minutorum &longs;ecet, quàm &longs;i <lb/>ex centro penderet: Et quoniam angulus ad <lb/>peripheriam &longs;ubduplus e&longs;t anguli ad cen<lb/>trum, notæ verò graduum & minutoru&mtail; <lb/>Quadrantis limbo appo&longs;itæ indicant angulos <lb/>ad centrum, angulus à perpendiculo nota<lb/>tus, ex. gr. 1. 45 1/2, bifariam diuiditur, & <lb/>quæ&longs;itus angulus e&longs;t, gr. o. m. 52. &longs;ec. 45. <lb/>Quare &longs;i qua labes ob&longs;eruationi adhæreat, <lb/>pauculis &longs;crupulis &longs;ecundis definitur. </s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Dari id quidem facilè pote&longs;t &longs;y<lb/>derum ob&longs;eruatori; in tantâ nimirum di&longs;tan<lb/>tiâ ip&longs;ius organi magnitudo, quantacunque <lb/>demùm illa &longs;it, planè euane&longs;cit; ac proinde <lb/>i&longs;ta, vt ita dicam, virtualis duplicatio Qua<lb/>drantis nihil officit. </s>

<cell>CCXIIII.</cell>

<cell>S<emph type="italics"/>i extra circulum duo puncta æqualiter à centro di&longs;tantia &longs;ignentur, erit punctum reflexionis æqualis in medio arcus intercepti inter lineas, quæ à centro ducuntur ad illa puncta.<emph.end type="italics"/> S<emph type="italics"/>i uerò unum centro proximius fuerit altero, punctum æqualitatis in peripheria tantò longius, uer&longs;us breuiorem lineam, quantò punctum aliud à centro magis di&longs;teterit.<emph.end type="italics"/></cell>

<s>At verò telluris ma<lb/>gnitudinem indaganti ex radio optico, res <lb/>non ita in plano e&longs;t: &longs;i enim oculum centro <lb/>Quadrantis admoueas ita, vt latus alterum <lb/>in&longs;trumenti congruat lineæ visûs, reliquum <lb/>verò latus fuerit, vt dicebas, duplicatum; <lb/>angulus à perpendiculo & lineâ visûs ex cen<pb xlink:href="018/01/081.jpg" pagenum="73"/>tro, non e&longs;t æqualis angulo à perpendiculo, <lb/>& lineâ visûs ex extremâ diametro, quia pa<lb/>rallelæ e&longs;&longs;e non po&longs;&longs;unt duæ lineæ eunde&mtail; <lb/>circuli quadrantem tangentes. </s>

</row>

<s>Oculus au<lb/>tem in extremâ diametro po&longs;itus, vtpotè <lb/>magis à tellure remotus, plus terræ videt &longs;ub <lb/>minore angulo: neque omninò contemnen<lb/>da e&longs;t altitudinum differentia, &longs;i Quadrantis <lb/>Radius pedes quinque &longs;ecundùm longitudi<lb/>nem habere ponatur; cum circuli in terrâ <lb/>maximi quantitas, quæ patet oculo decem <lb/>pedes alto, &longs;it ferè &longs;e&longs;quialtera eius, quæ pro<lb/>&longs;picitur ab oculo quinque tantùm pedes à <lb/>terrâ remoto. </s>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Non eadem e&longs;t ratio; &longs;i in arenâ <lb/>litoreâ, ac in editâ turri, aut in colle ob&longs;er<lb/>uationem, vt hìc &longs;upponimus, in&longs;tituas; cum <lb/>enim terræ &longs;emidiameter aucta oculi altitu<lb/>dine &longs;it Secans Complementi anguli ob&longs;er<lb/>uati, &longs;ecantes autem angulorum æqualiter <lb/>cre&longs;centium addant &longs;emper maiorem, & <lb/>maiorem differentiam, patet quàm modi<lb/>cum anguli di&longs;crimen intercederet, &longs;i non <lb/>ad centrum Quadrantis, &longs;ed ad extremam <lb/>circuli diametrum applicaretur oculus i&ntail; <lb/>vltimum Horizontem directus &longs;ecundùm <lb/>regulam lateri Quadrantis parallelam. </s>

<cell>P<emph type="italics"/>unctum reflexionis punctorum inæqualiter di&longs;tantium à centro, æqualiter di&longs;tat à lineis, ductis à centro ad puncta æqualiter di&longs;tantia alterutrinque.<emph.end type="italics"/></cell>

<s>Sed <lb/>quicquid de hoc e&longs;&longs;e contingat, certum e&longs;t <pb xlink:href="018/01/082.jpg" pagenum="74"/>oculo ad centrum applicato perpendiculum <lb/>indè &longs;u&longs;pen&longs;um cadere parallelum perpendi<lb/>culo, quod ex extremâ diametro pendet, & <lb/>con&longs;tituere angulum cum diametro æqua<lb/>lem illi, quem cum eâdem diametro facit <lb/>perpendiculum ex eius extremitate &longs;u&longs;pen<lb/>&longs;um. </s>

</row>

<row>

<s>Quare &longs;ola centri altitudo &longs;upra terræ <lb/>&longs;uperficiem, a&longs;&longs;umenda e&longs;t tanquam oculi <lb/>ob&longs;eruatoris altitudo. </s>

<cell>CCXVI.</cell>

<cell>S<emph type="italics"/>i fuerint circuli duo inæquales, & extra utrunqúe punctum ad illud ex minore reflexè per magnam partem minoris à maiore perueuire poterunt.<emph.end type="italics"/></cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vel &longs;i minùs placeat perpendiculo <lb/>vti, Quadrantis latus horizontaliter iacens <lb/>duplicetur, & in extremâ diametro fiat cen<lb/>trum, circa quod conuer&longs;a dioptra tanti&longs;per <lb/>eleuetur, dum linea fiduciæ congruat radio <lb/>optico terram tangenti; nam &longs;emi&longs;sis anguli <lb/>ad centrum facti cum latere horizontaliter <lb/>iacente in&longs;i&longs;tentis eidem arcui, e&longs;t angulus <lb/>depre&longs;sionis infra horizontem, æqualis an<lb/>gulo ACD facto in centro terræ; cuius com<lb/>plementum e&longs;t quæ&longs;itus angulus CAD. </s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> An non operæ pretium facturus e&longs;<lb/>&longs;et, qui illud demum in praxim deduceret, <lb/>quod ego olim aliud ne&longs;cio quid meditans <lb/>perficiendum iu&longs;si, &longs;ed aliis curis di&longs;tractus <lb/>ad exitum non perduxi? </s>

<row>

<cell>CCXVII.</cell>

<s>Duxeram in plano <lb/>verticali lineam horizontalem longam pe<lb/>des Rom. ferè quinquaginta, & in eius ex<lb/>tremo puncto, quod eam cæli plagam re-<pb xlink:href="018/01/083.jpg" pagenum="75"/>&longs;peciebat, in qua aliquid occurrebat ob&longs;er<lb/>uandum, axiculum ritè infigi curaui, circa <lb/>quem po&longs;&longs;et dioptra conuerti. </s>

<cell>O<emph type="italics"/>culus uidet partem &longs;uperficiei<emph.end type="italics"/> L<emph type="italics"/>unæ illuminatam à<emph.end type="italics"/> S<emph type="italics"/>ole per radios reflexos à<emph.end type="italics"/> S<emph type="italics"/>olis corpore: nec tamen pote&longs;t uidere imaginem ip&longs;ius in<emph.end type="italics"/> L<emph type="italics"/>una tanquam in &longs;peculo.<emph.end type="italics"/></cell>

</row>

<row>

<s>Erat autem <lb/>animus parare regulam longam pedes 42, <lb/>cuius latitudo 4. digitos, cra&longs;&longs;ities aute&mtail; <lb/>duos digitos obtineret; &longs;ic enim fieri po&longs;&longs;e <lb/>&longs;perabam, vt latitudine in altitudinem con<lb/>uersâ, regula non adeò grauis horizontali<lb/>ter con&longs;tituta, & &longs;ecundum alteram extremi<lb/>tatem axiculo in&longs;erta, non &longs;inuaretur, nec <lb/>à &longs;uâ rectitudine deflecteret: cùm maximè <lb/>decreui&longs;&longs;em ita illi aliam regulam breuiorem <lb/>&longs;ubiicere, in modum vectis primi generis, vt <lb/>inferiorem regulam premens eleuarem &longs;u<lb/>periorem, quæ circiter duas tertias &longs;uæ lon<lb/>gitudinis partes (hoc e&longs;t circiter pedem ab <lb/>axiculo, circa quem volueretur, trige&longs;imum) <lb/>&longs;u&longs;tentata à &longs;uppo&longs;ito vecte non e&longs;&longs;et adeò <lb/>obnoxia inflexioni. </s>

<cell>CCXVIII.</cell>

<cell>R<emph type="italics"/>ationem maculæ<emph.end type="italics"/> L<emph type="italics"/>unæ indagare.<emph.end type="italics"/></cell>

<s>Tum regulæ longitudi<lb/>ne in pedes di&longs;tinctâ; accipiendi erant pedes <lb/>41 2/3, vt e&longs;&longs;ent in vniuer&longs;um vnciæ 500; cum <lb/>enim pedis vncia ita &longs;en&longs;ibiliter in laminâ <lb/>metallicâ diuidi queat in particulas 50 vt ha<lb/>beantur vnciæ particulæ cente&longs;imæ, erat Ra<lb/>dius circuli de&longs;cribendi partium 50000, &longs;ub<lb/>duplus numeri, qui habetur in Canone Tri<lb/>gonometrico communi. </s>

</row>

<s>Quare &longs;i hoc Ra<lb/>dio in plano verticali de&longs;cribatur arcus, & <pb xlink:href="018/01/084.jpg" pagenum="76"/>ad lineam horizontalem excitetur perpendi<lb/>cularis æqualis Tangenti gr. 1. (accepto &longs;e. <lb/></s>

<row>

<cell>CCXIX.</cell>

<cell>R<emph type="italics"/>ationem eorum quæ apparent circa<emph.end type="italics"/> S<emph type="italics"/>olem &longs;peculo in aqua po&longs;ito declarare.<emph.end type="italics"/></cell>

<s>&longs;emi&longs;&longs;e numeri Canonis in partibus vnciæ <lb/>cente&longs;imis) ab&longs;cindi poterit ex arcu gradus <lb/>vnus, cuius &longs;inus parum di&longs;tabit à palmo <lb/>Romano architectonico. </s>

</row>

<row>

<s>Quare facilè pote<lb/>rit arcus in 60 minuta diuidi, & ex eodem <lb/>centro interuallo maiore de&longs;cripto alio arcu, <lb/>poterunt duci lineæ tran&longs;uer&longs;æ, in quibus <lb/>minutorum partes &longs;exage&longs;imæ di&longs;tingui po<lb/>terunt, prout moris e&longs;t. </s>

<cell>C<emph type="italics"/>au&longs;am cur<emph.end type="italics"/> S<emph type="italics"/>ol æ&longs;tiuis diebus exoriens umbram ad meridiem, cum in meridie ad boream mittat, explorare.<emph.end type="italics"/></cell>

<s>Hoc in&longs;trumento pa<lb/>rato angulum depre&longs;sionis in&longs;ra horizontem, <lb/>&longs;eu potiùs infra lineam horizonti parallelam, <lb/>tam clarè po&longs;&longs;umus deprehendere, vt nihil <lb/>reliquum <gap/>quod de&longs;ideremus. </s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Nec omnibus nec vbique locorum <lb/>commodum erit tuum hoc in&longs;trumentum <lb/>fabricari, quod vel vni loco affixum &longs;it opor<lb/>tet, vel ægerrimè transferri po&longs;&longs;it. </s>

<row>

<cell>CCXXI.</cell>

<s>Ne&longs;cio <lb/><arrow.to.target n="note38"/><lb/>quo fato adhuc penès me in &longs;emilacerâfffff pa<lb/>gellâ durat &longs;chedia&longs;ma hoc, quo ante men<lb/>&longs;es aliquot cuidam, qui &longs;e in Geometriæ pra<lb/>xi exercens dolebat nullum hactenus à &longs;e ad<lb/>hibitum in&longs;trumentum, cui citrà in&longs;ignis <lb/>erroris &longs;u&longs;picionem po&longs;&longs;et fidere, organum <lb/>propo&longs;ui, quod & facilè con&longs;truitur, & vix <lb/>vllum relinquit errandi periculum, prout ip&longs;a <lb/>docuit experientia. </s>

<cell>M<emph type="italics"/>agnitudo<emph.end type="italics"/> L<emph type="italics"/>unæ & cæterorum a&longs;trorum digno&longs;citur ex proportione aliorum ad eam iuxta di&longs;tantiam: ip&longs;ius uerò iuxta rationem pupillæ ad<emph.end type="italics"/> L<emph type="italics"/>unam di&longs;tantiæ ratione.<emph.end type="italics"/></cell>

<s>In triangulum còag<!--<pb xlink:href="018/01/085.jpg"/><pb xlink:href="018/01/086.jpg"/>

</row>

NOTE: fig15 and fig16 extend over 2 pages

<row>

<figure id="id.018.01.086.1.jpg" xlink:href="018/01/086/1.jpg"/><pb xlink:href="018/01/087.jpg"/><pb xlink:href="018/01/088.jpg"/><figure id="id.018.01.088.1.jpg" xlink:href="018/01/088/1.jpg"/><pb xlink:href="018/01/089.jpg"/><figure id="id.018.01.089.1.jpg" xlink:href="018/01/089/1.jpg"/>--><pb xlink:href="018/01/090.jpg" pagenum="77"/>mentatis tribus tigillis, ducatur recta AB <lb/>vnciarum 10. ex. </s>

<cell>CCXXII.</cell>

<cell>Q<emph type="italics"/>uantitates quæ æquales e&longs;&longs;e non po&longs;&longs;unt in eodem genere, maius tamen & minus recipiunt, &longs;unt in proportione pote&longs;tatis.<emph.end type="italics"/></cell>

<s>gr. & &longs;uper eâ fiat triangu<lb/>lum æquilaterum AEB. </s>

</row>

<row>

<cell>CCXXIII.</cell>

<s>Quod &longs;i tigilli ni<lb/>mis longi e&longs;&longs;ent, interuallo A<emph type="italics"/>e<emph.end type="italics"/> de&longs;cribantur <lb/>duo arcus &longs;e inuicem &longs;ecantes in <emph type="italics"/>i<emph.end type="italics"/>, & inter<lb/>uallo A<emph type="italics"/>u<emph.end type="italics"/> arcus &longs;e &longs;ecantes in <emph type="italics"/>o<emph.end type="italics"/>: per hæc enim <lb/>puncta ductâ lineâ ex A, accipi poterit AE <lb/>æqualis ip&longs;i AB, & erit angulus BAE gr. 60. <lb/>Relinquitur autem tigillus EF longior, vt in <lb/>FA &longs;ecundùm rectam EA productam in F <lb/>con&longs;tituatur tubulus H infundibuli in mo<lb/>rem excauatus, per quem vi&longs;us rectâ traii<lb/>ciatur in de&longs;tinatum &longs;copum per aciculam <lb/>in E perpendiculariter erectam, ex qua de<lb/>pendet perpendiculum; hoc enim facit cum <lb/>lineâ EA angulum di&longs;tantiæ obiecti à verti<lb/>ce ob&longs;eruatoris. </s>

<cell>Q<emph type="italics"/>uantitates quæ actu æquales e&longs;&longs;e non po&longs;&longs;unt, in nulla proportione actu e&longs;&longs;e po&longs;&longs;unt.<emph.end type="italics"/></cell>

</row>

<row>

<s>Quantitas verò huius an<lb/>guli per Trigonometriam reperitur ex datis <lb/>lateribus AE, & A<emph type="italics"/>u<emph.end type="italics"/> & angulo <emph type="italics"/>u<emph.end type="italics"/> AE compre<lb/>hen&longs;o gr. 60. ex con&longs;tructione. </s>

<cell>CCXXIIII.</cell>

<cell>N<emph type="italics"/>eque temporis totius, ut imaginamur, ip&longs;um e&longs;&longs;e infinitum, neque æui uitarum proportio ulla e&longs;t ad tempus, quod pote&longs;tate e&longs;t, utpotè diem<emph.end type="italics"/></cell>

<cell/>

</row>

<s>Vel &longs;i fortè <lb/>breuiùs operari placeat, fingatur ex E puncto <lb/>in &longs;emi&longs;&longs;em lateris AB cadere linea perpen<lb/>dicularis, cuius quantitas facilè innote&longs;cit: <lb/>deinde illâ a&longs;&longs;umptâ vt Radio, vt Tangent&etail; <lb/>verò di&longs;tantiâ perpendiculi à medio lineæ <lb/>AB, angulus quæratur, quem facit perpen<lb/>diculum cum fictâ illâ perpendiculari; hic <lb/>enim angulus additus gradibus 30. &longs;i perpen<pb xlink:href="018/01/091.jpg"/><figure id="id.018.01.091.1.jpg" xlink:href="018/01/091/1.jpg"/><pb xlink:href="018/01/092.jpg" pagenum="78"/>diculum cadat vltra &longs;emi&longs;&longs;em lineæ AB; <lb/>demptus autem ex gr. 30. &longs;i cadat citrà &longs;e<lb/>mi&longs;&longs;em, dabit angulum di&longs;tantiæ à vertice <lb/>quæ&longs;itum. </s>

<row>

<cell/>

<cell><emph type="italics"/>uel men&longs;em.<emph.end type="italics"/></cell>

<s>Quod &longs;i di&longs;tantia à vertice exce&longs;<lb/>&longs;erit gr. 60 perpendiculum cadet extrà latus <lb/>BE; idcirco &longs;u&longs;pendendum èrit ex I puncto, <lb/>quod bifariam diuidit rectam AE; & &longs;iqui<lb/>dem obiectum in Horizonte fuerit, perpen<lb/>diculum ex I cadet in B, &longs;i verò &longs;upra Hori<lb/>zontem, cadet in latus AB, &longs;i demum infra <lb/>lineam Horizonti parallelam depre&longs;&longs;um fue<lb/>rit, cadet perpendiculum in latus BE: &longs;em<lb/>per autem in note&longs;cet angulus factus à perpen<lb/>diculo & lineâ FI visûs, dantur enim vel la<lb/>tera IA & AB, vel IE & EB cum angulo <lb/>comprehen&longs;o: vel &longs;altem in vtroque latere <lb/>de&longs;ignari poterit punctum, in quod ad rectos <lb/>angulos cadit linea ex I. </s>

</row>

<row>

<cell>CCXXV.</cell>

<s><margin.target id="note38"/><emph type="italics"/>XXXVIII <lb/>V&longs;us Tri<lb/>goni æqui<lb/>lateri ad <lb/>ob&longs;eruandos <lb/>angulos, in <lb/>quo vix er<lb/>rari po&longs;sit à <lb/>Geometra.<emph.end type="italics"/></s>

<cell>P<emph type="italics"/>roportio media non e&longs;t ex ratione agentis, &longs;ed patientis.<emph.end type="italics"/></cell>

<s>Vt verò in quàm minimas particulas di<lb/>ui&longs;am haberet rectam AB, iubebam duci <lb/>AC æqualem vni ex ijs partibus, in quas pri<lb/>mò di&longs;tinctam eam po&longs;uimus, nempe i&ntail; <lb/>vncias pedis, & perfici parallelogrammum <lb/>ABDC. </s>

</row>

<row>

<s>Tum diuisâ AC, & BD in quinque <lb/>æquales partes, & ductis parallelis ip&longs;i AB, <lb/>inter po&longs;tremas <emph type="italics"/>a d<emph.end type="italics"/> & CD ducatur diagona<lb/>li; C <emph type="italics"/>d<emph.end type="italics"/>; & diui&longs;is pariter &longs;ingulis vncijs i&ntail; <lb/>quinque partes, vt factum hìc e&longs;t in vnciâ <pb xlink:href="018/01/093.jpg" pagenum="79"/>quintâ, ducantur lineolæ parallelæ ip&longs;i CA, <lb/>donec diagonalem attingant: & his paratis <lb/>habetur vncia AC diui&longs;a in partes 500, vel <lb/>&longs;altem in 250, &longs;i differentia inter duas pro<lb/>ximas lineolas &longs;en&longs;ibilis non &longs;it. </s>

<cell>CCXXVI.</cell>

<cell>P<emph type="italics"/>roportio &longs;ublimis non con&longs;i&longs;tit in magnitudine, &longs;ed ordine, iuxta quem differentia e&longs;t eius quod e&longs;t ante & po&longs;t.<emph.end type="italics"/></cell>

<s>Quamuis autem tam exiguum triangu<lb/>lum AEB non &longs;it aptum ad acutiores angu<lb/>los inueniendos, con&longs;tat tamen po&longs;&longs;e illud <lb/>&longs;inè magno incommodo con&longs;trui ita, vt pe<lb/>des aliquot &longs;ingula latera obtineant; & tunc <lb/>etiam minores angulorum particulæ innote<lb/>&longs;cent. </s>

</row>

<s>Quod &longs;i quando res &longs;it quàm exa<lb/>cti&longs;simè perficienda, poterit lateri FE addi <lb/>regula, ex cuius extremo &longs;ecundùm rectam <lb/>AE productam &longs;u&longs;pendatur perpendiculum, <lb/>perinde enim erit ac &longs;i totum triangulum <lb/>augeretur. </s>

<row>

<cell>CCXXVII.</cell>

<s>At &longs;i ex editiore loco deor&longs;um <lb/>&longs;pectandum &longs;it, & perpendiculum ex I &longs;u<lb/>&longs;pen&longs;um cadat in latus EB tam propè ip&longs;um <lb/>B, vt non facilè po&longs;sint particulæ numera<lb/>ri, erigatur ad latus AE regula perpendicu<lb/>laris, in qua recta ex B per I ducta faciat an<lb/>gulum EIG rectum, & &longs;umatur IG æqualis <lb/>ip&longs;i IE, & ex G &longs;u&longs;pendatur perpendiculum, <lb/>quod intelligatur cadere ex. </s>

<cell>V<emph type="italics"/>itæ iuxta numerum perfectionum in comparatione ad cogitationem no&longs;tram proportionem quandam habent.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CCXXVIII.</cell>

<cell>P<emph type="italics"/>roportionem &longs;cientiæ futurorum & cæterorum occultorum con&longs;iderare.<emph.end type="italics"/></cell>

<s>Si <lb/>enim concipiatur ex I aliud perpendiculum <lb/>IS, vtique linea IG incidens in duas paralle<lb/>las IS, & GR facit angulum SIB externum <pb xlink:href="018/01/094.jpg" pagenum="80"/>æqualem interno RGI: inuento igitur RGI, <lb/>innote&longs;cit angulus, quem cum perpendicu<lb/>lo facit linea vi&longs;ualis AE. </s>

</row>

<s>Cum itaque IE & <lb/>IG æquales &longs;int & ad angulum rectum, con<lb/>ceptâ rectâ EG angulus EGI e&longs;t gr. 45, cui <lb/>æqualis reliquus GEI additus angulo BEA gr. <lb/>60. fit totus angulus GER gr. 105; latus au<lb/>tem EG &longs;ubtendens angulum rectum, no<lb/>tum e&longs;t, cum nota &longs;int latera IG, & IE; de<lb/>mum notum e&longs;t latus ER. </s>

<row>

<cell>CCXXIX.</cell>

<cell>I<emph type="italics"/>ncorporea omnia unum &longs;unt, neque numerus e&longs;t eorum.<emph.end type="italics"/></cell>

</row>

<row>

<cell>CCXXX.</cell>

<cell>P<emph type="italics"/>roportio incorporeorum a&longs;cendentium &longs;emper maior e&longs;t.<emph.end type="italics"/></cell>

<s>Quare ex notis <lb/>lateribus EG & ER vnâ cum angulo com<lb/>prehen&longs;o inuenitur angulus EGR, qui dem<lb/>ptus ex EGI gr. 45. relinquit notum RGI <lb/>æqualem angulo SIB; & &longs;ic innote&longs;cit angu<lb/>lus SIE æqualis angulo, quem facit linea vi<lb/>&longs;ualis EA <expan abbr="c&utilde;">cum</expan> lineâ AT iungente oculum ob<lb/>&longs;eruatoris cum centro terræ. </s>

</row>

<row>

<cell>CCXXXI.</cell>

<s>Cum igitur &longs;atis <lb/>amplum huiu&longs;modi triangulum facilè po&longs;si<lb/>mus con&longs;truere, etiam additâ regulâ IG, & <lb/>alibi diui&longs;am vnciam habere po&longs;simus i&ntail; <lb/>partes &longs;altem cente&longs;imas eâ methodo, quam <lb/>indicat Adrianus Metius in &longs;uâ Geometriâ, <lb/>patet fieri po&longs;&longs;e, vt quàm euidenti&longs;simè in<lb/>note&longs;cat angulus ille, quem ob&longs;eruatum &longs;up<lb/>ponebam ad inue&longs;tigandam terræ magnitu<lb/>dinem. </s>

<cell>T<emph type="italics"/>res e&longs;&longs;e mundos atque inter ip&longs;os nullam e&longs;&longs;e proportionem: nec numero eos definiri.<emph.end type="italics"/></cell>

<s>Sed mi&longs;sis organis ad in&longs;titutum <lb/>redeamus. </s>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Audiui haud ita pridem hominem, <pb xlink:href="018/01/095.jpg" pagenum="81"/>qui ex maximâ visûs di&longs;tantiâ, &longs;eu Hori<lb/><arrow.to.target n="note39"/><lb/>zontis Phy&longs;ici &longs;emidiametro, totius telluris <lb/>&longs;emidiametrum colligere &longs;e po&longs;&longs;e cen&longs;eban. </s>

<cell>CCXXXII.</cell>

<cell>O<emph type="italics"/>mnis motus naturalis quanto uelocior e&longs;t tanto propior e&longs;t & magis &longs;imilflimus quieti.<emph.end type="italics"/></cell>

<s><lb/>Primùm verò &longs;tatuebat, quod certum e&longs;t, ab <lb/>iis qui de maximâ visûs di&longs;tantiâ di&longs;putant, <lb/>non eam inquiri, quæ vel ab oculis variè af<lb/>fectis, vel à diuersâ corporum videndorum <lb/>magnitudine, vel ab inæquali &longs;pecierum, <lb/>quas vocant, intentionalium, quibus obie<lb/>ctum repræ&longs;entandi vis ine&longs;t, diffu&longs;ione ea<lb/>rumue inten&longs;ione petenda e&longs;t. </s>

</row>

<s>Nemo enim <lb/>ignorat, &longs;i i&longs;ta &longs;pectentur, fieri non po&longs;&longs;&etail;, <lb/>vt certa visûs di&longs;tantia vniuer&longs;im præ&longs;criba<lb/>tur. </s>

<row>

<cell>CCXXXIII.</cell>

<s>Acribus &longs;iquidem & acutis oculis longè <lb/>remotiora patere con&longs;tat, quàm hebetiori<lb/>bus, quos languidiores radii procul immi&longs;si <lb/>ad vi&longs;um non excitant. </s>

<cell>Q<emph type="italics"/>uod e&longs;t in mundo incorporeo æternum e&longs;t, beatum, &longs;ecurum, immutabile &longs;ecundum locum, &longs;olum iuxta e&longs;&longs;entiam fit: iuxta quod uelut à leui &longs;u&longs;urro aquæ & aura æ&longs;tiua demulcetur.<emph.end type="italics"/></cell>

<s>Vbi verò obiectum <lb/>corpus non oculorum vitio latet, &longs;æpè &longs;uâ <lb/>&longs;e paruitate ita protegit, vt admi&longs;si à pupillâ <lb/>radii in tenui&longs;simum angulum coale&longs;centes <lb/>eam demùm afficiant Retinæ particulam, <lb/>quæ eum &longs;en&longs;um omnem effugiat, &longs;entiendi <lb/>quoquè munere &longs;olitaria fungi non pote&longs;t: <lb/>vt proinde Dioptrica &longs;ub&longs;idiarias lentes vi<lb/>treas in tubo&longs;picillo ritè di&longs;po&longs;itas mortali<lb/>bus tran&longs;mi&longs;erit, quarum ope inflexi Radii <lb/>ampliorem angulum con&longs;tituant, ideòqu&etail; <lb/>maiorem Retinæ particulam ad videndum <pb xlink:href="018/01/096.jpg" pagenum="82"/>proritent. </s>

</row>

</table>

<s>Sed & illud maximè ambiguam <lb/>facit visûs di&longs;tantiam, quod pro di&longs;pari luce, <lb/>qua corpora imbuuntur, di&longs;par quoque exi<lb/>gunt interuallum, vt &longs;ub a&longs;pectum cadant: <lb/>&longs;ic aliquando Perigæam Lunam, quæ ant&etail; <lb/>pauculas horas ferè pleno orbe immen&longs;&atail; <lb/>collucebat, &longs;ereno c&oelig;lo ami&longs;&longs;am quærimus, <lb/>&longs;i fortè eius centrum in terre&longs;tris vmbræ a<lb/>xem inciderit; cum tamen eadem tenebra<lb/>rum immunis, quamuis Apogæa Soli pa<lb/>riter Apogæo oppo&longs;ita, &longs;ponte in oculos <lb/>incurrat. </s>

<s id="id000041">FINIS.</s>

<s>Ea nimirum quamuis remotior&atail; <lb/>con&longs;piciuntur, quæ vberiori lumine &longs;iuè in<lb/>nato, & in&longs;ito, &longs;iuè extrin&longs;ecùs mutuato per<lb/>funduntur. </s>

<s><margin.target id="note39"/><emph type="italics"/>XXXIX <lb/>Maxima vi<lb/>&longs;us di&longs;tan<lb/>tia ex qui<lb/>bus debeat <lb/>definiri.<emph.end type="italics"/></s>

</section>

</front>

<s>Semotis igitur omnibus hi&longs;ce impedi<lb/>mentis, per quæ fieret, quominùs certi ali<lb/>quid de visûs di&longs;tantiâ &longs;tatui po&longs;&longs;et; phy&longs;ici <lb/>horizontis &longs;emidiameter ex ipsâ terreni glo<lb/>bi configuratione petenda e&longs;t. </s>

<body>

<chap>

<s>Cum enim <lb/>vetus ille error opinantium terræ faciem æ<lb/>quabili planitie diffu&longs;am iam dudum exta<lb/>buerit, & nemo &longs;it, qui pilæ in &longs;peciem ter<lb/>ras ac maria vndique in &longs;e&longs;e nutibus &longs;uis con<lb/>globata non intelligat; nemo pariter ambi<lb/>gat, quin ob conuexam huiu&longs;ce globi &longs;uper<lb/>ficiem, inclinatis nimirùm partibus, &longs;eque <lb/>oculo &longs;ubducentibus, a&longs;pectus omnis quan<pb xlink:href="018/01/097.jpg" pagenum="83"/>tumuis acerrimus certis terminis circum<lb/>&longs;cribatur. </s>

<s>Hinc circulus partem hanc a&longs;pe<lb/>ctabilem à latente di&longs;pe&longs;cens, Horizontis <lb/>Phy&longs;ici nomine donatus e&longs;t, vt ab eo &longs;ecer<lb/>natur Horizonte, qui tellurem in duo hemi<lb/>&longs;phæria &longs;egregans, quia non oculo, &longs;ed <expan abbr="&longs;olã">&longs;olam</expan> <lb/>ratione comprehendi pote&longs;t, Rationalis di<lb/>citur. </s>

<s id="id000042">HIERONYMI CAR<lb/>DANI MEDIOLANENSIS, CI<lb/>VISQVE BONONIENSIS, MEDICI <lb/>de Proportionibus, &longs;eu Ope<lb/>ris Perfecti <lb/>LIBER QVINTVS.</s>

<s>Quamuis autem Phy&longs;ici Horizontis dia<lb/>meter tota intrà terræ cra&longs;situdinem deliteat, <lb/>quippe quæ recta e&longs;t linea arcui illi &longs;ubten&longs;a, <lb/>qui extremis terminis oculi Ortum Occa<lb/>&longs;umque circum&longs;picientis intercluditur: quia <lb/>tamen arcus huiu&longs;modi exiguo di&longs;crimin&etail; <lb/>quod vix &longs;ub &longs;en&longs;um ca<lb/><figure id="id.018.01.097.1.jpg" xlink:href="018/01/097/1.jpg"/><lb/>dat, &longs;ubten&longs;æ rectæ li<lb/>neæ longitudinem &longs;upe<lb/>rat; ideò non abs re ar<lb/>cus ip&longs;e pro phy&longs;ici hori<lb/>zontis &longs;emidiametro in<lb/>di&longs;criminatim v&longs;urpatur; <lb/>huiu&longs;ce &longs;emi&longs;sis maxi<lb/>mam obiecti a&longs;pectabilis <lb/>di&longs;tantiam metitur. </s>

<s id="id000043">Prima diffinitio.</s>

<s>Ex his &longs;ic ille argumentabatur. </s>

<s>Sit arcus <lb/><arrow.to.target n="note40"/><lb/>AB men&longs;ura di&longs;tantiæ vi&longs;us, qui non à rectâ <lb/>lineâ &longs;en&longs;ibiliter deflectat<gap/>e&longs;t igitur AB recta <lb/>perpendiculariter in&longs;i&longs;tens rectæ DC: radius <pb xlink:href="018/01/098.jpg" pagenum="84"/>autem opticus DB terram tangens facit cum <lb/>&longs;emidiametro angulum DBC rectum. </s>

<s id="id000044">Proportio ab Euclide &longs;ic de&longs;cribitur, Quòd <lb/>&longs;it duarum quantitatum eiu&longs;dem generis, <lb/>quod ad magnitudinem attinet, compara<lb/>tio certa.</s>

<s>Igi<lb/>tur recta AB ab angulo recto ad B cadens i&ntail; <lb/>ba&longs;im perpendicularis, e&longs;t medio loco pro<lb/>portionalis inter &longs;egmenta DA & AC. </s>

<s id="id000045">Secunda diffinitio.</s>

<s>Qua<lb/>rè diui&longs;o quadrato maximæ visûs di&longs;tantiæ <lb/>AB per altitudinem AD, prouenit quæ&longs;it&atail; <lb/>terræ &longs;emidiameter AC. </s>

<s>Verùm arcum <lb/>pro rectâ lineâ a&longs;&longs;umere parùm Geometri<lb/>cum e&longs;t. </s>

<s id="id000046">Proportiones per &longs;imilitudinem <expan abbr="dic&utilde;tur">dicuntur</expan>, <lb/>cùm quantitas quantitati <expan abbr="compara&ttilde;">comparatur</expan> alterius <lb/>generis, cui fingitur æqualis e&longs;&longs;e pote&longs;tate.</s>

<s><margin.target id="note40"/><emph type="italics"/>XXXX <lb/>Abu&longs;us li<lb/>neæ curuæ <lb/>pro rect&atail;, <lb/>inutilis.<emph.end type="italics"/></s>

<s id="id000047">Velut &longs;i a b fingatur monas in comparatione <lb/>ad b c erit rectangulum a c æquale lineæ b c.</s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Ideò paruipendendendam cen&longs;ui <lb/>methodum, quæ mihi aliquando occurrit <lb/><arrow.to.target n="note41"/><lb/>per circulos Azimuthales; &longs;i nimirùm duo<lb/>rum locorum, quorum alteruter ex alterius <lb/>editâ turri con&longs;pici queat, nota fuerit di&longs;tan<lb/>tia, & poli altitudo. </s>

<s>In &longs;ummâ enim turri <lb/>planum horizontale con&longs;tituatur, in eoque <lb/>meridiana linea de&longs;cribatur: tum ob&longs;eruetur <lb/>&longs;ub quo Azimutho locus alter con&longs;picuus <lb/>appareat: & ex his datis quæ&longs;ita eruantur. </s>

<s id="id000048">Tertia diffinitio.</s>

<s><lb/>Sit PAC loci Meridianus, vbi ob&longs;eruatio in<lb/>&longs;tituitur<gap/>; Verticalis per vtrumque locum <lb/>tran&longs;iens AB, cum Meridiano faciat angu<lb/>lum CAB ob&longs;eruatum; P verò &longs;it Polus, & <lb/>AP, BP &longs;int complementa nota datarum <lb/>poli eleuationum. </s>

<s>Cum itaque in triangu<lb/>lo &longs;phærico BAP nota &longs;int duo latera AP, <lb/>BP, & angulus BAP complementum angu<pb xlink:href="018/01/099.jpg" pagenum="85"/>li ob&longs;eruati CAB ad duos rectos, inueniatur <lb/>AB in gradibus &longs;eu <lb/>graduum particulis. <lb/><figure id="id.018.01.099.1.jpg" xlink:href="018/01/099/1.jpg"/><lb/>Tum fiat vt AB pars, <lb/>inuenta ad totum cir<lb/>culum, hoc e&longs;t gr. <lb/>360, ita data duorum <lb/>locorum di&longs;tantia ad <lb/>aliud, & prodibunt <lb/>milliaria toti circulo <lb/>in terrâ maximo re&longs;pondentia. </s>

<s id="id000049">Proportio æqualis proportioni e&longs;t, cùm eodem modo termini <lb/>&longs;e habent inuicem in utraque</s>

<s id="id000050">Quarta diffinitio.</s>

<s>Notâ autem <lb/>circularis peripheriæ quantitate neminem <lb/>Geometram diameter quæ&longs;ita latere poterit. </s>

<s><lb/>Sed quoniam di&longs;tantia illa non adeò exigua <lb/>e&longs;&longs;e pote&longs;t, quæ careat omni &longs;u&longs;picione abu<lb/>sûs rectæ lineæ pro curuâ, ideò methodum <lb/>hanc inter qui&longs;quilias, à quibus parùm di<lb/>&longs;tat, reieci. </s>

<s id="id000051">Proportiones &longs;ecundum genus notæ dicuntur, cùm nouimus, <lb/>quòd &longs;int maiores, aut minores. </s>

<s id="id000052">Nam cùm æquales &longs;unt, &longs;imul ne<lb/>cesse e&longs;t, ut cogno&longs;camus genus, & &longs;peciem.</s>

<s><margin.target id="note41"/><emph type="italics"/>XXXXI <lb/>Secunda me <lb/>thodus in<lb/>uestigandi <lb/>telluris am<lb/>bitum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Id tamen per &longs;ummam iniuriam <lb/><arrow.to.target n="note42"/><lb/>factum: neque enim magnum intercedere <lb/>pote&longs;t di&longs;crimen, quod propo&longs;ito officiat: e&longs;t <lb/>&longs;cilicet di&longs;crimen minus datâ altitudine. </s>

<s id="id000053">Quinta diffinitio.</s>

<s>Ex <lb/>altitudine enim BA pro&longs;piciénti pateat ar<lb/>cus BD, quem &longs;ubtendit recta BD, Tan<lb/>gens autem e&longs;t AD. </s>

<s id="id000054">Datum po&longs;itione e&longs;t: quod nece&longs;&longs;ariò ex po&longs;itis certam habet <lb/>quantitatem.</s>

<s>Con&longs;tat ex Archimede <lb/>lib.

1. de &longs;phær. & cyl. </s>

<s id="id000055">Sexta diffinitio.</s>

<s>Tangentem AD ma<lb/>iorem e&longs;&longs;e arcu BD, arcum autem BD maio<lb/>rem rectâ BD &longs;ubtensâ: At duæ rectæ BD, <pb xlink:href="018/01/100.jpg" pagenum="86"/>BA &longs;imul &longs;umptæ maiores &longs;unt quàm AD, <lb/>igitur exce&longs;&longs;us ip&longs;ius <lb/><figure id="id.018.01.100.1.jpg" xlink:href="018/01/100/1.jpg"/><lb/>AD &longs;upra rectam BD <lb/>minor e&longs;t, quàm &longs;it <lb/>data altitudo BA; er<lb/>go multò minor e&longs;t <lb/>exce&longs;&longs;us rectæ AD <lb/>tangentis &longs;upra ar<lb/>cum BD, vel arcûs <lb/>BD &longs;upra rectam BD <lb/>&longs;ubten&longs;am. </s>

<s id="id000056">Datum &longs;impliciter dicitur, quod ex propo&longs;itis cogno&longs;ci pote&longs;t, <lb/>quantum &longs;it.</s>

<s>Ne verò <lb/>po&longs;itâ altitudine BA notabili, cen&longs;eret quis <lb/>in&longs;ignem quoque e&longs;&longs;e differentiam inter cur<lb/>uam & rectam lineam, quæ locorum inter<lb/>ualla metiatur, animaduertere oportet ar<lb/>cum BD maiorem e&longs;&longs;e latere BD polygoni <lb/>in&longs;cripti, minorem autem latere EF polygo<lb/>ni circum&longs;cripti: at exce&longs;&longs;us lateris EF ad la<lb/>tus BD habet Rationem, quam EB ad BC. </s>

<s><lb/>Vnde liquet manife&longs;tè, quàm modico di<lb/>&longs;crimine differat arcus à rectâ vel &longs;ubtensâ <lb/>BD, vel tangente EF. </s>

<s id="id000057">Septima diffinitio.</s>

<s><margin.target id="note42"/><emph type="italics"/>XXXXII. </s>

<s id="id000058">Proportiones pote&longs;tate <expan abbr="dicun&ttilde;">dicuntur</expan>, quæ &longs;ub comparatione aliarum <lb/><expan abbr="quantitat&utilde;">quantitatum</expan> nece&longs;&longs;ariam habentium <expan abbr="cõnexionem">connexionem</expan> <expan abbr="&longs;ol&utilde;">&longs;olum</expan> <expan abbr="cogno&longs;cun&ttilde;">cogno&longs;cuntur</expan>.</s>

<s><lb/>Differentia <lb/>longitudinis <lb/>inter arcum <lb/>et eius Tan<lb/>gentem vel <lb/>&longs;ubten&longs;am.<emph.end type="italics"/></s>

<s>Memini me aliquando calculos &longs;ubducen<lb/>tem, quàm longè pateat vi&longs;us Romæ è &longs;um<lb/>mo crucis apice, quæ ædis Apo&longs;tolorum <lb/>Principi &longs;acræ tholo incumbit. </s>

<s id="id000059">Hæ autem &longs;unt aliquando eiu&longs;dem generis, cum primis ut nu<lb/>meri: aliquandò alterius, ut linearum & &longs;uperficierum, angulorum, <lb/>& arcuum: aliquando eiu&longs;dem generis, & diuer&longs;arum &longs;pecierum, <lb/>ut arcuum per &longs;inus, qua utuntur A&longs;tronomi.</s>

<s>deprehendi&longs;<lb/>&longs;e arcum DB gr. o. </s>

<s id="id000060">Octaua diffinitio.</s>

<s id="id000061">Proportio homonyma dicitur duarum quantitatum diuer&longs;i ge</s>

<s>23. &longs;tatuebam autem <lb/>in &longs;ingulos gradus milliaria Italica 60, vt <pb xlink:href="018/01/101.jpg" pagenum="87"/>nunc vulgaris fert opinio, crucis verò altitu<lb/>dinem &longs;upra maris Mediterranci &longs;uperfi<lb/>ciem ponebam palmorum, quorum v&longs;us ho<lb/>diè e&longs;t apud Romanos architectos, circiter <lb/>700. Quare arcus BD erat mill. 23. & Tan<lb/>gens AD mill. (23 441/100000), di&longs;crimine vix pa&longs;<lb/>&longs;uum 4 1/2. Quid igitur officiat, &longs;i quis pro <lb/>arcu BD a&longs;&longs;umat, aut &longs;ubten&longs;am BD, aut <lb/>tangentem EF, aut aliquam ex intermediis? </s>

<s id="id000062"><arrow.to.target n="marg1"/><lb/>neris, &longs;ed alterius a b altero dependentium, uelut motus ad tem

<s><lb/>nullus &longs;iquidem oriri pote&longs;t error, qui &longs;ub <lb/>&longs;en&longs;um cadat. </s>

<s>Quod &longs;i, vt &longs;æpè fieri pote&longs;t, <lb/>di&longs;tantiam BD decempedâ dimetiamur, ni<lb/>hil erit quod de tuâ illâ methodo dubites, <lb/>Mer&longs;enne, non enim arcu pro rectâ abu<lb/>teris. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Su&longs;picor Mer&longs;enne (detur hoc Ger<lb/>mano candori) non tibi rectam pro arcûs <lb/>men&longs;urâ a&longs;&longs;umptam di&longs;plicui&longs;&longs;e; &longs;ed metho<lb/>dum illam, quæ tibi nihil de Ptolemæo co<lb/>gitanti occurrerat, demùm di&longs;plicui&longs;&longs;e faci<lb/>lè crediderim, vbi eam veteribus quoquè <lb/>innotui&longs;&longs;e deprehendi&longs;ti: ideo illam inter <lb/>&longs;cruta reieci&longs;ti. </s>

<s id="id000063">Dicimus enim motum tardum, uel uelocem in comparatione <lb/>ad tempus.</s>

<s>Ego quoque, vt vera nar<lb/>rem, &longs;æpiùs doleo, quod veritatem tan<lb/>quam peregrinam exceperim, qua&longs;i ad m&etail; <lb/>primum diuerti&longs;&longs;et; quam po&longs;tea alienum <lb/>limen triui&longs;&longs;e comperio: nec &longs;anè me pro<lb/>bro&longs;is &longs;uis &longs;timulis vrget inuidentia, qua cæ<pb xlink:href="018/01/102.jpg" pagenum="88"/>teris veritatis lumen inuideam; &longs;ed terret <lb/>calumnia, qua &longs;æpè apud iniquos iudices fur<lb/>ti reus laboras, ni&longs;i id aliundè acceptum <lb/>&longs;ponte profitens mentiaris: perinde atque &longs;i <lb/>nemo &longs;olem po&longs;&longs;et intueri, qui alios de eius <lb/><arrow.to.target n="note43"/><lb/>luce narrantes non audierit. </s>

<s>Simile quid in <lb/>hoc eodem Problemate mihi contigit expe<lb/>riri. </s>

<s>Cum enim locorum duorum AB di<lb/>&longs;tantiam notam ponerem, ac complemen<lb/>ta eleuationum poli; ob&longs;eruabam Solis di<lb/>&longs;tantiam à vertice SA, quam per Tabulas <lb/>Anacla&longs;ticas, & Parallacticas corrigebam; <lb/>Tum ex complemento declinationis Solis <lb/>SP, complemento altitudinis Poli AP: & di<lb/>&longs;tantia Solis à vertice SA, inquirebam angu<lb/>lum ASP; ex quo inuento, vnâ cum latere <lb/>SP, & complemento altitudinis poli BP, <lb/>inueniebam SB, quod demptum ex SA re<lb/>linquebat arcum BA quæ&longs;itum. </s>

<s id="id000065">Nona diffinitio.</s>

<s>Hæc ta<lb/>men methodus po&longs;t dies aliquos di&longs;plicuit, <lb/>cum animaduerterem ingenio&longs;um A&longs;trono<lb/>mum eâdem viâ ince&longs;si&longs;&longs;e, & quidem fe<lb/>liciùs non Solem &longs;ed &longs;ydera fixa vertici pro<lb/>xima ob&longs;eruando, quæ nec parallaxi nec re, <lb/>fractioni &longs;unt obnoxia. </s>

<s id="id000066">Proportionum aliæ dicuntur rhete, aliæ alogæ, rhetæ quæ &longs;unt <lb/>ut numeri ad numerum, alogæ quæ non &longs;unt numeri ad numerum.</s>

<s><margin.target id="note43"/><emph type="italics"/>XXXXIII. </s>

<s><lb/>Tertia me<lb/>thodus in<lb/>uestigandi <lb/>ambitu&mtail; <lb/>terræ.<emph.end type="italics"/></s>

<s id="id000067">Decima diffinitio</s>

<s>Cæterùm ne ab in&longs;titutâ quæ&longs;tione de<lb/>flectamus, illud e&longs;t ob&longs;eruandum, quod &longs;i <lb/>cognitâ altitudine BA, & dato angulo ad A, <pb xlink:href="018/01/103.jpg" pagenum="89"/>vellet a&longs;&longs;umere triangulum rectangulum ad <lb/>B, vt notam faceret <lb/><figure id="id.018.01.103.1.jpg" xlink:href="018/01/103/1.jpg"/><lb/>di&longs;tantiam inter B & <lb/>D, &longs;ibique per&longs;uaderet <lb/>aut à ba&longs;i aut ab hy<lb/>pothenusâ illius <expan abbr="triã-guli">trian<lb/>guli</expan> exhiberi di&longs;tan<lb/>tiam BD, longè di<lb/>&longs;taret à veritate. </s>

<s id="id000068">Proportio rhete alia æqualis, alia multiplex, uel &longs;ubmultiplex: <lb/>alia unius partis exce&longs;&longs;us, aut defectus, alia plurium, quam &longs;uper<lb/>partientem, aut &longs;upartientem uocant.</s>

<s>Du<lb/>cta &longs;iquidem perpen<lb/>dicularis BH longè <lb/>minor e&longs;t arcu BD, cum &longs;it Tangens &longs;e<lb/>mi&longs;sis illius arcûs: hypothenu&longs;a verò AH <lb/>minor e&longs;t quàm tota Tangens AD, de<lb/>fectu æquali ip&longs;i ba&longs;i BH; &longs;unt enim HB, <lb/>HD æquales, cùm vtraque &longs;it circulum <lb/>tangens ab eodem puncto H ducta. </s>

<s>Qua<lb/>propter deberet aggregatum ex ba&longs;i BH <lb/>& hypothenusâ AH accipere, vt totam <lb/>AD haberet, quæ non multùm differt ab ar<lb/>cu BD, ni&longs;i altitudo BA fuerit mons aut &longs;co<lb/>pulus. </s>

<s id="id000069">Vndecima diffinitio.</s>

<s>Quod &longs;i tuus ille terrenæ magnitudinis <lb/><arrow.to.target n="note44"/><lb/>inue&longs;tigator lineam BD pro maximâ vi<lb/>sûs di&longs;tantiâ a&longs;&longs;ump&longs;i&longs;&longs;et, illa vtique media <lb/>e&longs;t proportionalis, ex cuius quadrato per no<lb/>tam altitudinem DA diui&longs;o prouenit tertius <pb xlink:href="018/01/104.jpg" pagenum="90"/>terminus, vnde terrena <lb/><figure id="id.018.01.104.1.jpg" xlink:href="018/01/104/1.jpg"/><lb/>&longs;emidiameter cogno&longs;ci<lb/>tur, non tamen ip&longs;a &longs;e<lb/>midiameter AG e&longs;t ter<lb/>tius analogiæ terminus, <lb/>&longs;ed potius conflatum ex <lb/>DC, CB: latus enim v<lb/>num trianguli rectan<lb/>guli e&longs;t medium propor<lb/>tionale inter differentiam <lb/>hypothenu&longs;æ ac reliqui lateris, & eorum ag<lb/>gregatum: ac proinde vt AD ad DB, it&atail; <lb/>DB ad DCB. </s>

<s id="id000070">Cum diui&longs;o denominatore per numeratorem exit quantitas alo<lb/>ga, proportio dicitur aloga: &longs;i autem numerus integer, aut pars nu<lb/>meri nota dicitur rhete.</s>

<s>Quare ex inuento tertio ter<lb/>mino debui&longs;&longs;et datam altitudinem DA de<lb/>mere, & re&longs;iduum bifariam diui&longs;um dedi&longs;<lb/>&longs;et quæ&longs;itam &longs;emidiametrum AC. </s>

<s>Hinc <lb/>rectè dicebas arcum illum pro rectâ lineâ <lb/>parùm Geometricè a&longs;&longs;umptum. </s>

<s id="id000071">Duodecima diffinitio.</s>

<s><margin.target id="note44"/><emph type="italics"/>XXXXIV <lb/>Quarta me<lb/>thodus in<lb/>neniendi ter<lb/>ra &longs;emidia<lb/>metrum.<emph.end type="italics"/></s>

<s id="id000072">Proportionem in proportionem duci e&longs;t, quoties recto ordine <lb/>tres quantitates in ei&longs;dem collo<expan abbr="can&ttilde;">cantur</expan>: ut &longs;int tres quan<lb/><figure id="id.015.01.021.1.jpg" xlink:href="015/01/021/1.jpg"/><lb/>titates a b c dicetur proportio a ad c producta ex pro <lb/>portione a ad b & b ad c, & &longs;imiliter proportio c ad <lb/>a producitur ex proportione b ad a, & c ad b.</s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Nunquam hominem potui à con<lb/>ceptâ &longs;ententiâ reuocare, ni&longs;i vbi eum iu&longs;&longs;i <lb/>rem rotam in praxim deducere. </s>

<s>Statuimus <lb/>primùm extra omnem controuer&longs;iam po&longs;i<lb/>tum videri, in decernendâ Phy&longs;ici horizon<lb/>tis amplitudine non incertam ædium aut <lb/>montium altitudinem e&longs;&longs;e &longs;pectandam, &longs;ed <lb/>eam ex communi vulgarique hominum ma<lb/>gnitudine definiendam. </s>

<s id="id000073">Tertia decima diffinitio.</s>

<s>Quandoquidem <pb xlink:href="018/01/105.jpg" pagenum="91"/>cum ex &longs;ublimiori loco longiùs vi&longs;us eat, ex <lb/>humiliori autem breuioribus terminis coer<lb/>ceatur, quis non videt certam &longs;tatui non po&longs;<lb/>&longs;e visûs di&longs;tantiam, quin certa pariter alti<lb/>tudo, ex qua oculus circum&longs;picere valeat, <lb/>con&longs;tituta intelligatur? </s>

<s id="id000074">Proportionem per proportionem diuidi e&longs;t, quoties ad eandem <lb/>quantitatem duæ quantitates comparantur, tunc illarum propor<lb/>tio e&longs;t, quæ prodit una per alteram diui&longs;a.</s>

<s>præter eam verò, <lb/>quam humano corpori natura plerunqu&etail; <lb/>conce&longs;&longs;it, cur hanc præ aliâ eligas altitudi<lb/>nem, nulla &longs;uppetit ratio. </s>

<s>Nec ambigi vllo <lb/>pacto pote&longs;t, an Veteres horizontis phy&longs;ici <lb/>amplitudinem indagantes, altitudinem vl<lb/>lam humanâ maiorem a&longs;&longs;ump&longs;erint; eam <lb/>&longs;iquidem horizonti tribuendam cen&longs;uer&etail; <lb/>magnitudinem, quæ cum &longs;phæricæ &longs;uperfi<lb/>ciei pars &longs;it, à planâ tamen minimùm differ<lb/>re po&longs;&longs;it. </s>

<s id="id000075">Sint proportiones a & b ad c & interponatur b inter a & c, dico <lb/>proportionem a ad c diui&longs;am per proportionem a ad b, & prodire <lb/>proportionem b ad c, con&longs;tat ex conuer&longs;a præcedentis.</s>

<s>Hinc Macrobius Saturnal. lib.

<s id="id000076">Quarta decima diffinitio.</s>

7. <lb/>cap.

14. <emph type="italics"/>Vbicunque terrarum &longs;teteris<emph.end type="italics"/>, inquit, <lb/><emph type="italics"/>videris tibi quandam c&oelig;li conclu&longs;ionem vide<lb/>re; & hoc e&longs;t quod Horizontem veteres voca<lb/>uerunt: quorum indago fideliter deprehendit, <lb/>directam ab oculis aciem per planum contrà <lb/>a&longs;picientibus non pergere vltra CLXXX &longs;ta<lb/>dia, & inde in orbem iam recuruari. </s>

<s id="id000077">Additio proportionum intelligitur quotiens duarum quanti<lb/>tatum ad unam tertiam, proportiones per aggregatum ip&longs;arum <lb/>quantitatum ad eandem coniunguntur.</s>

<s id="id000078">Velut &longs;i comparentur a b & b c ad d, inde tota <lb/><figure id="id.015.01.021.2.jpg" xlink:href="015/01/021/2.jpg"/><lb/>a c ad d dicemus proportionem, ac ad d e&longs;&longs;e con<lb/><expan abbr="iunctã">iunctam</expan> ex duabus proportionibus a b ad d & b c <lb/>ad <expan abbr="eand&etilde;">eandem</expan> d. </s>

<s>Per pla<lb/>num, ideò adieci, quia altitudines longi&longs;&longs;imè <lb/>a&longs;picimus; quippe qui & cælum videmus. </s>

<s id="id000079">Hoc & duo &longs;equentes &longs;icut & du&etail; <expan abbr="anteced&etilde;tes">antecedentes</expan> demon<lb/>&longs;trabitur e&longs;&longs;e. </s>

<s id="id000080">nunc &longs;olum quomodo <expan abbr="intelligend&utilde;">intelligendum</expan> &longs;it proponimus.</s>

<s><lb/>Ergo in omni horizontis orbe ip&longs;e qui intuetur, <lb/>centron e&longs;t. </s>

<s>Et quia diximus quantum à cen<emph.end type="italics"/><pb xlink:href="018/01/106.jpg" pagenum="92"/><emph type="italics"/>tro acies v&longs;que ad partem orbis extenditur, &longs;i<lb/>nè dubio in horizonte diametros orbis CCCLX <lb/>&longs;tadiorum e&longs;t: & &longs;i vlteriùs qui intuetur ac<lb/>ce&longs;&longs;erit, &longs;eu retror&longs;um rece&longs;&longs;erit, &longs;imilem cir<lb/>ca &longs;e orbem videbit.<emph.end type="italics"/></s>

<s id="id000081">Quinta decima diffinitio.</s>

<s>Rogaui deinde vtrùm Macrobio potiùs <lb/><arrow.to.target n="note45"/><lb/>&longs;tadijs 180 Phy&longs;ici Horizontis &longs;emidiame<lb/>trum definienti acquie&longs;ceret, an verò &longs;ibi <lb/>cum Recentioribus quibu&longs;dam conueniret, <lb/>qui cum Clauio (cui facilè adhæ&longs;it Blanca<lb/>nus) in cap.2. &longs;phær. </s>

<s id="id000082">Detractionem proportionis à proportione intelligimus fieri <lb/>per <expan abbr="detraction&etilde;">detractionem</expan> minoris quantitatis à maiore, comparatam ad ean<lb/>dem quantitatem.</s>

<s>tanquam veritati ma<lb/>ximè con&longs;entaneam ad mittunt eorum &longs;en<lb/>tentiam, qui a&longs;pectum ad milliaria 62 1/2 pro<lb/>trahi opinantur. </s>

<s>Neque enim illum aut cum <lb/>Alberto Magno aut cum Proclo &longs;entire cen<lb/>&longs;ebam, quorum prior &longs;tadia mille, po&longs;te<lb/>rior bis mille horizontis phy&longs;ici &longs;emidiame<lb/>tro dedit. </s>

<s id="id000083">Velut in exemplo &longs;uperiore detracta proportione b c ad d ex

<s><margin.target id="note45"/><emph type="italics"/>XXXXV <lb/>Ostenditur <lb/>error ex ab<lb/>u&longs;u lineæ <lb/>curuæ pro <lb/>recta.<emph.end type="italics"/></s>

<pb pagenum="3" xlink:href="015/01/022.jpg"/>proportione a c ad d, relinquetur proportio a b ad d. </s>

<s>Ille quidem confe&longs;tim Neotericoru&mtail;<lb/>&longs;ententiam arripuit: &longs;ed vbi iu&longs;&longs;us e&longs;t AB <lb/>mill. 62 1/2 ad pedes 312500 reuocare, & <lb/>huius numeri quadratum 97656.250000. <lb/>diuidere per DA ped. 6, quanta e&longs;t hominis <lb/>mediocris altitudo, videns AC prouenir&etail; <lb/>maiorem milliarijs 3.000000, ad Macro<lb/>bium con&longs;ugit, & longitudinem AB &longs;tadiis <lb/>180 circum&longs;crip&longs;it: nec &longs;tadia Romana ped. <pb xlink:href="018/01/107.jpg" pagenum="93"/>625, &longs;ed Græca ped. 600 fui&longs;&longs;e contende<lb/>bat, cum ex Erato&longs;thene men&longs;ura illa de<lb/>&longs;umpta fui&longs;&longs;et. </s>

<s id="id000084">& probatur <lb/>ex conuer&longs;ione præcedentis.</s>

<s id="id000085">Sexta decima diffinitio.</s>

<s id="id000086">Extractio radicum alicuius proportionis fit per extractionem <lb/>radicum quantitatum illius iuxta unam, & eandem rationem.</s>

<s>Sed hìc pariter Syrtes inue<lb/>nit, cum reuocato &longs;tadiorum 180 numero <lb/>ad pedes 108000, eius quadratum 11664. <lb/>000000. diuidere tentans per pedes 6, quo<lb/>tientem pariter ampli&longs;&longs;imum deprehendit. </s>

<s id="id000087">Velut quadratæ, uel cubæ, uel pronicæ, uel uniner&longs;alis, uel alte<lb/>rius modi.</s>

<s><lb/>Quid &longs;i volui&longs;&longs;em contentio&longs;iùs agene, affir<lb/>mando Erato&longs;thenem nec Romanis, nec <lb/>Græcis, &longs;ed Alexandrinis &longs;tadijs longioribus <lb/>v&longs;um fui&longs;&longs;e? </s>

<s>Quantò longiùs aberrâ&longs;&longs;et? </s>

<s id="id000088">Decima &longs;eptima diffinitio.</s>

<s>Sed <lb/>placuit miti&longs;&longs;imè agere. </s>

<s id="id000089">Cùm fuerint duæ proportiones &longs;imiles in tribus terminis con<lb/>tinuatæ, dicetur proportio primæ quantitatis ad tertiam ueluti <lb/>primæ ad &longs;ecundam duplicata. </s>

<s>Quapropter eum <lb/>rogaui, vt &longs;altem AB milliarium trium, hoc <lb/>e&longs;t ped. 15000 con&longs;tituens tentaret, an ex <lb/>a&longs;&longs;umptâ priùs iu&longs;to maiore &longs;emidiametro <lb/>horizontis phy&longs;ici, an verò etiam ex metho<lb/>di ageometriâ enormis illa magnitudo ori<lb/>retur: Quadratum itaque ped. 225.000000 <lb/>diuidens per DA ped.6, inueniebat AC ped. <lb/>37.500000, hoc e&longs;t mill. 7500; vnde oritur <lb/>terræ ambitus mill. 47 142 6/7 duplo maior, <lb/>quàm communiter concedatur. </s>

<s id="id000090">Et &longs;i &longs;int tres proportiones &longs;imiles <lb/>in quatuor terminis, dicetur proportio primæ quantitatis ad quar<lb/>tam triplicatà ei, quæ e&longs;t primæ ad &longs;ecundam,</s>

<s id="id000091">Decima octaua diffinitio.</s>

<s id="id000092">Confu&longs;a proportio dicitur &longs;implicis, aut compo&longs;itæ quantitatis <lb/>ad compo&longs;itam in comparatione ad proportiones ad partes.</s>

<s id="id000093">Decima nona diffinitio.</s>

<s>Mirabatur ille vehementer, quòd præter <lb/>&longs;pem tam procul à vero rece&longs;&longs;i&longs;&longs;et: &longs;ed nec <lb/>conceptam de maiore, iuxta communem <lb/>errorem, horizontis phy&longs;ici &longs;emidiametro <lb/>opinionem deponere audebat: hærebant &longs;ci<lb/>licet animo altè impre&longs;&longs;a plurium authorum <pb xlink:href="018/01/108.jpg" pagenum="94"/>effata, quibus 30 milliaria Italica videntur <lb/>mediocris visûs di&longs;tantia: quare multò pro<lb/>babilior ei apparebat Macrobrii atque Era<lb/>to&longs;thenis &longs;ententia di&longs;tantiam huiu&longs;modi &longs;ta, <lb/>&longs;tijs 180 definientium. </s>

<s id="id000094">Quantitates qu&etail; in continua &longs;unt proportione Analogæ <expan abbr="uocan&ttilde;">uocantur</expan>.</s>

<s>Nos igitur ad exa<lb/>minandum contulimus telluris ambitum ab <lb/>Erato&longs;thene con&longs;titutum, an cum illa &longs;emi<lb/>diametto &longs;tadiorum 180 cohæreret: <emph type="italics"/>Eui<emph.end type="italics"/><lb/><arrow.to.target n="note46"/><lb/><emph type="italics"/>denti&longs;&longs;imis<emph.end type="italics"/> enim, vt Macrobius loquitur lib. <lb/>1. in &longs;omn. </s>

<s id="id000095">Dictum e&longs;t hoc ad fugiendum nomen barbarum, etiam ut bre<lb/>uiter tamen po&longs;&longs;emus &longs;ententiam explicare.</s>

<s>Scip. cap.

<s id="id000096">Vige&longs;ima diffinitio.</s>

20. <emph type="italics"/>& indubitabilibus <lb/>dimen&longs;ionibus con&longs;tat vniuer&longs;æ terræ ambitum, <lb/>quæ vbicunque vel incolitur, vel inhabitabilis <lb/>iacet, habere &longs;tadiorum millia ducenta quin<lb/>quaginta duo.<emph.end type="italics"/></s>

<s id="id000097">Reflexa proportio dicitur cum trium quantitatum aggregatum <lb/>primæ, & tertiæ &longs;e habet ad &longs;ecundam uelut &longs;ecunda ad tertiam,</s>

<s> Cum verò huius peripheriæ <lb/>pars mille&longs;ima quadringente&longs;ima &longs;int &longs;tadia <lb/>180, per quæ directa ab oculis acies pergit, <lb/>arcus BA gr.o.m.15.&longs;ec.25. Ter. 42. &c. </s>

<s id="id000098">Vige&longs;ima prima diffinitio.</s>

<s><lb/>metitur angulum BCD in centro factum. </s>

<s id="id000099">Trium quantitatum analogarum aliæ quidem Geometricæ, <lb/>cùm proportio &longs;imilis e&longs;t: Aliæ Arithmeticæ, cum fuerit æqualis <lb/>exce&longs;&longs;us huc indè: Aliæ mu&longs;icæ cum fuerit proportio primæ ad ter<lb/>tiam multiplex, aut &longs;implex, aut compo&longs;ita exce&longs;&longs;us quæ &longs;implici <lb/>iuncta &longs;it ad multiplicis perfectionem: eadem autem &longs;it proportio <lb/>exce&longs;&longs;us primæ, & &longs;ecundæ ad exce&longs;&longs;um &longs;ecundæ &longs;upra tertiam.</s>

<s><lb/>At quoniam peripheria ponitur &longs;tad 252000 <lb/>e&longs;t diameter minor verâ &longs;tad. (80181 9/11), maior <lb/>autem verâ (80233 41/223): quarè &longs;umpto medio <lb/>Arithmetico e<gap/> diameter AC &longs;tad. </s>

<s>80207 1/2, <lb/>& &longs;emidiameter CA &longs;tad. </s>

<s id="id000100">Velut proportio 6. 4. 3. dupla e&longs;t utrinque, & 6. 3. 2 tripla. </s>

<s id="id000101">& 28. 24. <lb/>21. & 45. 40. 36. Geometrica uerò & arithmetica facilius continuan<lb/>tur in quotquot quantitatibus, &longs;ed & mu&longs;ica uelut 12. 8. 6. 4. 3. & <lb/>proportio 8 ad 5 mu&longs;ica e&longs;t: quia proportio 5 ad 4 mu&longs;ica e&longs;t, & <lb/>bene &longs;onans, igitur con&longs;titutis 8. 5. 4. cum 8 ad 4 benè &longs;onet, & 5 <lb/>ad 4, & 4 &longs;it extrema non media inde 8. & 5 benè <expan abbr="&longs;onãt">&longs;onant</expan>. </s>

<s>40103 3/4. Fiat igitur <lb/>vt CB 99998.99293. &longs;inus complementi <lb/>gr.o.m.15.&longs;ec. 25. Ter.42. ad CD Radium <lb/>100000.00000, ita CB &longs;tad.40103 3/4 ad CD <lb/>&longs;tad, 40104, & ped.92. Demptâ autem CA <pb xlink:href="018/01/109.jpg" pagenum="95"/>&longs;emidiametro, remanet AD ped. 242, alti<lb/>tudo, ex qua pro&longs;pici pote&longs;t in B ita, vt a&longs;pe<lb/>ctui pateant &longs;tadia 180. Quî autem fieri po&longs;<lb/>&longs;it ab intuente &longs;imilem &longs;emper orbem vide<lb/>ri, &longs;iuè vlteriùs acce&longs;&longs;erit, &longs;iue retror&longs;um re<lb/>ce&longs;&longs;erit, Macrobius ip&longs;e viderit: an &longs;emper <lb/>eam inueniat altitudinem, cui in&longs;i&longs;tat, vt <lb/>oculus ab extimâ telluris facie pedibus 242 <lb/>&longs;emoueatur? </s>

<s id="id000102">nam in me<lb/>dijs <expan abbr="nõ">non</expan> e&longs;t <expan abbr="uer&utilde;">uerum</expan>, ut in 9. 6. 4 bis diapente, & 16. 12. 9 bis diate&longs;&longs;aron.</s>

<s id="id000103">Vige&longs;ima &longs;ecunda diffinitio.</s>

<s>Horizontis igitur &longs;emidiame<lb/>trum aut &longs;tadijs 180 minorem e&longs;&longs;e, aut non <lb/>ex humani corporis altitudine definiri ne<lb/>ce&longs;&longs;e e&longs;t. </s>

<s id="id000104">Quantitates quæ &longs;imilem habent proportionem non continua<lb/>tam, omiologæ appellantur.</s>

<s><margin.target id="note46"/><emph type="italics"/>XXXXVI <lb/>Authorum <lb/>aliquorum <lb/>lap&longs;us i&ntail; <lb/>statuend&atail; <lb/>nimia vi&longs;us <lb/>distantia.<emph.end type="italics"/></s>

<s id="id000105">Vige&longs;ima tertia diffinitio.</s>

<s>Cum verò ille labantem Macrobij &longs;en<lb/>tentiam &longs;uffulcire aliquatenus &longs;e po&longs;&longs;e con<lb/>&longs;ideret, &longs;tadia 180 tribuendo non arcui AB, <lb/>&longs;ed rectæ DB terram tangenti, quæ & radij <lb/>optici ex oculo D prodeuntis men&longs;ura e&longs;t, & <lb/>arcu AB longior; operam demum &longs;e ludere <lb/>&longs;en&longs;it, cum re ad Geometricam normam <lb/>reuocatâ tantam opticæ lineæ longitudinem <lb/>terrenæ magnitudini minimè congruere ma<lb/>nife&longs;tè deprehendit, etiam &longs;i oculus à terrâ <lb/>pedum 50. interuallo AD &longs;eiunctus intelliga<lb/>tur. </s>

<s>Quoniam enim quadratum Tangentis <lb/>BD, quæ &longs;tad. </s>

<s id="id000106">Prima operatione con&longs;i&longs;tere dicuntur proportiones, cùm inter <lb/>primo conflatas quantitates con&longs;titerint.</s>

<s>180 ponitur, æquale e&longs;t re<lb/>ctangulo ADE, diuidatur quadratum ped. <lb/>11664.000000 per 50, & erit DE ped. 233 <lb/>280000, hoc e&longs;t &longs;tadiorum Græcorum (quæ <pb xlink:href="018/01/110.jpg" pagenum="96"/>hìc v&longs;urpantur) 388800. Quare diameter <lb/>AE, demptis pedibus 50, erit &longs;tad. </s>

<s id="id000107">PRIMA Animi communis &longs;ententia.</s>

<s id="id000108">Omnis Proportio e&longs;t, aut æqualitatis, aut maior inæqualis, <lb/>aut minor.</s>

<s>388799 <lb/>ped. 550. Ex qua diametro colligitur am<lb/>bitus longè maior eo, quem Macrobius cum <lb/>Erato&longs;thene con&longs;tituit. </s>

<s id="id000109">Secunda animi communis &longs;ententia.</s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Sed lap&longs;is in ageometriam Erato<lb/>&longs;thene ac Macrobio, quod &longs;tadia 180 tribue<lb/>rint horizontis phy&longs;ici &longs;emidiametro, cum <lb/>totum telluris ambitum &longs;tadijs 252000 de<lb/>&longs;inierint; quid de ijs dicendum, qui terram <lb/>paucioribus &longs;tadijs circum&longs;cribentes (mil<lb/>liarijs nimirum 21600, quæ ad &longs;tadia Græca <lb/>180000 reuocantur, quot Ptolemæus toti <lb/>terrenæ peripheriæ conce&longs;sit) oculum tamen <lb/>ad maiora &longs;patia longo limite ducunt? </s>

<s id="id000110">Quilibet numerus tantus dicitur, quanta e&longs;t illius proportio ad <lb/>monadem.</s>

<s>Hi <lb/>&longs;anè longi&longs;simè ab&longs;unt à veritate, cum lineæ <lb/>opticæ tribuunt longitudinem &longs;tadiorum <lb/>vt minimum 500. Nam quadratum lineæ <lb/>opticæ e&longs;t æquale rectangulo &longs;ub altitudin&etail; <lb/>oculi, & terræ diametro auctâ eâdem altitu<lb/>dine. </s>

<s>Sit ergo D linea optica, & B &longs;it terræ <lb/>diameter, & A &longs;it altitudo: igitur DQ æqua<lb/>tur AQ+A in B. </s>

<s id="id000111">Dicimus enim quatuor, quod monadem quater contineat. </s>

<s id="id000112">Et <lb/>duo cum dimidio cùm monadem bis & &longs;emis contineat.</s>

<s>Quare ad inueniendam A <lb/>fiat expurgatio per vncias conditionarias qua<lb/>drati, &longs;c. </s>

<s>per &longs;emi&longs;&longs;em coëfficientis B. </s>

<s id="id000113">Tertia animi communis &longs;ententia.</s>

<s>Sit er<lb/>go E æqualis A+B 1/2: igitur E——B 1/2 e&longs;t æqua<lb/>lis ip&longs;i A. </s>

<s id="id000114">Proportionem defectus, &longs;eu detractæ quantitatis ad defectum <lb/>e&longs;&longs;e po&longs;&longs;e, ut quantitatis ad quantitatem dicuntur communes ani<lb/>mi &longs;ententiæ, quæ ex intellectu &longs;olo terminorum, quod ueræ &longs;int, <lb/>cogno&longs;cuntur. </s>

<s>Factâ itaque prioris æquationis in<lb/>terpretatione erit æquatio inter EQ——BQ 1/4 <pb xlink:href="018/01/111.jpg" pagenum="97"/>& DQ: & per Antithe&longs;im EQ æquatur <lb/>DQ+BQ 1/4 </s>

<s id="id000115">Si ergo defectus e&longs;t quantitas, & quantitas eiu&longs;dem <lb/>&longs;peciei, quia detrahitur, & defectus non e&longs;t &longs;implicitur, &longs;ed detra<lb/>cto ergo per quartam petitionem: uel primam diffinitionem erit <lb/>proportio inter illas. </s>

<s id="id000116">Sunt enim ambæ detractæ.</s>

<s>Cum igitur data &longs;it peripheria &longs;tad. </s>

<s>180000, <lb/>erit diameter B &longs;tad. </s>

<s id="id000117">Quarta animi communis &longs;ententia.</s>

<s>57291 2/3 proximè: atquè <lb/>adeò BQ 1/4 e&longs;t 820583766 2/3; ip&longs;ius verò D <lb/>&longs;tad. </s>

<s id="id000118">Inter quantitatem, & defectum minorem quantitate, cuius e&longs;t de<lb/>fectus, e&longs;t proportio, quatenus e&longs;t quantitas. </s>

<s>500, quadratum 250000. ex quotum <lb/>&longs;ummâ 820833766 2/3, quæ æqualis e&longs;t EQ, <lb/>&longs;i eruatur radix, erit E, hoc e&longs;t A+B 1/2 &longs;tad. <lb/>(28650 196/1000), ablatâ autem B 1/2, quæ e&longs;t &longs;tad. </s>

<s id="id000119">Sit a b linea, & detra<lb/>cta quantitas b c, non maior a b & d &longs;it alia quæuis quantitas eiu&longs;<lb/><figure id="id.015.01.023.1.jpg" xlink:href="015/01/023/1.jpg"/><lb/><expan abbr="d&etilde;">dem</expan> generis, dico quòd inter d & b c e&longs;t propor<lb/>tio quatenus b c e&longs;t quantitas, quia &longs;unt eiu&longs;<lb/>dem generis ideo &longs;unt in aliqua proportione <lb/>per primam diffinitionem. </s>

<s id="id000120">Sed ut b c e&longs;t defectus, nulla e&longs;t propor<lb/>tio: quia quanto b c augetur, tanto augetur proportio d ad b c, & <lb/>hoc e&longs;t contra demon&longs;trata ab Euclide.</s>

<s><lb/>28645 5/6, remanet A &longs;tad. (<gap/>4 36/100) proximè alti<lb/>tudo oculi: ex qua altitudine con&longs;tat no&ntail; <lb/>e&longs;&longs;e definiendam horizontis phy&longs;ici amplitu<lb/>dinem. </s>

<s>Quod &longs;<gap/> altitudinem oculi &longs;tatuere<lb/>mus vnius &longs;tadij, retentâ eâdem opticæ li<lb/>neæ longitudine, proueniret terræ diameter <lb/>&longs;tad. </s>

<s id="id000121">Quinta animi communis &longs;ententia.</s>

<s>249999, quæ maior e&longs;t totâ periphe<lb/>riâ ab ip&longs;is con&longs;titutâ. </s>

<s id="id000122">Cum proportio producitur ex proportionibus quælibet illa<lb/>rum dicetur producta diui&longs;a per alteram.</s>

<s>Hinc pariter Blancano fucum factu&mtail; <lb/>comperiemus (nam & quandoque bonus <lb/>dormitat Homerus) qui maximam mon<lb/>tium altitudinem &longs;e&longs;quimilliari aut duobus <lb/>vt &longs;ummum milliaribus definiens, Ætnæ in <lb/>Siciliâ duo tantùm milliaria conce&longs;sit, ad<lb/>mi&longs;it tamen ex Maurolyco dial. </s>

<s>3. Co&longs;mogr. <lb/>pag. 75.indè pro&longs;pici in mare vltra ducenta <lb/>pa&longs;&longs;uum millia. </s>

<s id="id000123">Sexta animi communis &longs;ententia.</s>

<s id="id000124">Æqualium quantitatum &longs;eu proportionum ad tertiam compa<lb/>rabilium eadem e&longs;t proportio atque uici&longs;sim. </s>

<s>Namque a&longs;&longs;umptâ lineæ <lb/>opticæ terrenum globum tangentis longitu<pb xlink:href="018/01/112.jpg" pagenum="98"/>dine mill. 200, huiusque quadrato 40000 <lb/>per Ætnæ altitudinem con&longs;titutam mill. 2 <lb/>diui&longs;o, & ex Quotiente 20000 demptâ mon<lb/>tis altitudine, ne&longs;cio qua ratione re&longs;iduum <lb/>mill. 19998 terrenæ diametro tribuendum, <lb/>idem Blancanus Sphæræ part. </s>

<s id="id000125">Hæc et&longs;i demon&longs;tre<lb/>tur ab Euclide, e&longs;t tamen hic generalior: & &longs;atis per &longs;e nota. </s>

<s id="id000126">Vt &longs;it <lb/>propior animi communi &longs;ententiæ, quàm rei demon&longs;trandæ.</s>

<s id="id000127">Septima animi communis &longs;ententia.</s>

<s id="id000128">Ad quod quantitas proportionem habet infinitam, id in genere <lb/>illius quantitatis non comprehenditur.</s>

<s>3.c.5.pag.93. <lb/>&longs;ibi gratulatur proximè conuenire cum am<lb/>bitu mill. 21600 ab aliis po&longs;ito, & à &longs;e ad<lb/>mi&longs;&longs;o. </s>

<s id="id000129">Nam proportio e&longs;t duarum quantitatum eiu&longs;dem generis com<lb/>paratio certa: at hæc comparatio certa non e&longs;t: non igitur quantita<lb/>tes ambæ &longs;unt, aut non eiu&longs;dem generis.</s>

<s>Cum tamen hinc debui&longs;&longs;et potiùs <lb/>&longs;u&longs;picari montium altitudinem à &longs;e breuiori<lb/>bus, quàm par &longs;it, terminis definitam, ex <lb/>qua tanta ferè colligitur diameter, quant&atail; <lb/>e&longs;&longs;e deberet peripheria. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> An igitur eos quoque mendacii <lb/>manife&longs;tos redarguas, qui Alexandrina&mtail; <lb/>&longs;peculam ab in&longs;ulâ, in qua extructa fuit, Pha<lb/>ron dictam ad eam prouehunt altitudinem, <lb/>vt indè naues &longs;excentorum milliarium in<lb/>teruallo di&longs;sitas videri potui&longs;&longs;e per &longs;ummam <lb/>con&longs;identiam âffirment? </s>

<s id="id000130">PRIMA Petitio.</s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vnde fabulam i&longs;tam Io.Bapt. Por<lb/>ta lib.17. Mag. nat.in proëm. </s>

<s id="id000131">Si fuerit primi ad &longs;ecundum, ut tertij ad quartum, & ex primo in <lb/>&longs;ecundum producatur æquale, aut maius, aut minus primo, uel <lb/>&longs;ecundo, producetur eodem modo ex tertio in quartum &etail;quale aut <lb/>maius, aut minus tertio, uel quarto eadem ratione & ordine.</s>

<s>hau&longs;erit, pror<lb/><arrow.to.target n="note47"/><lb/>&longs;us ignoro. </s>

<s id="id000132">Secunda petitio.</s>

<s>Neque enim Diodorus Siculus, <lb/>aut Strabo, aut Cæ&longs;ar, aut A. Hirtius, aut <lb/>Plinius, aut Lucianus, aut Solinus, aut Am<lb/>mianus Marcellinus, aut alius ex ijs, quos le<lb/>gerim, cum turris illius Alexandrinæ me<lb/>minerint, adeò in&longs;anam altitudinem nobis <pb xlink:href="018/01/113.jpg" pagenum="99"/>obtrudunt. </s>

<s id="id000133">Proportiones po&longs;&longs;unt duci, diuidi, iungi, & auferri, & &longs;umi radix <lb/>in eis cuiu&longs;cunque generis, atque earum quantitatis, ut libet, po&longs;&longs;e <lb/>tran&longs;ponere.</s>

<s>Quod autem Porta a&longs;&longs;erit in eâ <lb/>turri à Ptolemæo con&longs;titutum &longs;peculu&mtail;, <lb/>quod deinde cap.

11. ip&longs;e &longs;pecillum potiùs <lb/>quàm &longs;peculum vocat, vt ad 600 pa&longs;&longs;uum <lb/>millia ho&longs;tium naues, quæ eius regiones in<lb/>uaderent, con&longs;piceret, occa&longs;io fuit aliquan<lb/>do non nemini opinandi ad ea v&longs;que tempo<lb/>ra referendum v&longs;um Tubi optici. </s>

<s id="id000134">Tertia petitio.</s>

<s>Huiu&longs;ce <lb/>tamen &longs;peculi, &longs;iue &longs;pecilli, ve&longs;tigium nul<lb/>lum apud antiquos &longs;criptores deprehender&etail; <lb/>potui; quamuis eorum libros multâ diligen<lb/>tiâ per&longs;crutatus. </s>

<s id="id000135">Proportionis cuiu&longs;uis nomen à denominatore &longs;uprà &longs;cripto, & <lb/>numeratore infrà &longs;cripto &longs;umitur.</s>

<s>Quapropter ea mihi mens <lb/>incidit, vt exi&longs;timarem Portæ, viro cætero<lb/>qui erudito, fucum factum ab inepto quo<lb/>piam Typographo, vel ignaro &longs;criptore, qui <lb/>pro &longs;peculâ in Pharo (in&longs;ulâ) extructâ, &longs;pe<lb/>culum in Pharo (turri) con&longs;titutum &longs;uppo<lb/>&longs;uerit. </s>

<s><margin.target id="note47"/><emph type="italics"/>XLVII <lb/>Fabula de <lb/>altitudin&etail; <lb/>Phari Ale<lb/>xandrinæ <lb/>reijcitur.<emph.end type="italics"/></s>

<s id="id000136">Quarta petitio.</s>

<s>Cæterùm cum tubus opticus vitreis lenti<lb/>bus ritè in&longs;tructus ea &longs;olum corpora di&longs;tinctè <lb/>articulatimque videnda proponar, ad quæ <lb/>recta oculorum acies pergit, tota hæc fabu<lb/>la euane&longs;cet, vbi tantam altitudinem, quæ <lb/>vi&longs;um ad milliaria 600 producat, probabili<lb/>tate omni carere con&longs;titerit. </s>

<s id="id000137">Diui&longs;a quauis quantitate per aliam eiu&longs;dem generis, quod exit <lb/>proportio dicitur.</s>

<s>Neque opus <lb/>erat altitudine illâ immani, cum ideò turris <lb/>illa à Ptolemæo Philadelpho (quamuis Amm. <lb/>Marcell. lib.

22. à Cleopatrâ, quæ &longs;oror, & <pb xlink:href="018/01/114.jpg" pagenum="100"/>vxor fuit vltimi Ptolemæi cognomento Dio<lb/>ny&longs;ij turrim illam excel&longs;am excogitatam &longs;cri<lb/>bat) So&longs;trati Cnidij architecti operâ extructa <lb/>&longs;uerit, vt noctu accen&longs;æ faces indè præluce<lb/>rent nauigantibus, quò breuia & &longs;yrtes de<lb/>clinarent, quibus ora illa fallacibus & in&longs;i<lb/>dio&longs;is acce&longs;sibus importuo&longs;a &longs;catebat, & di<lb/>&longs;criminibus plurimis incautos nautas affli<lb/>gebat. </s>

<s id="id000138">Quinta petitio.</s>

<s id="id000139">Qu&etail;libet proportio e&longs;t uel inter duas quantitates, uel per unam <lb/>&longs;ignificatur.</s>

<s>Sed iam examinemus quantâ altitudine è <lb/>mari eminuerit Pharos illa Alexandrina, &longs;i <lb/>inde ad milliaria 600 vi&longs;us excurrere potuit. </s>

<s id="id000140">Nam per tertiam petitionem &longs;i &longs;int duæ quantitates, quæ non ha<lb/>beant unius rationem, nomen &longs;umit proportio à duobus numeris, <lb/>&longs;in autem &longs;it altera monas, erit per &longs;ecundam animi communem &longs;en<lb/>tentiam, proportio numerus ip&longs;e Ideò patet, quod dicitur.</s>

<s><lb/>Po&longs;ito terræ ambitu mill. 21600, arcus BA, <lb/>in &longs;uperiori figurâ mill.600 complectitur gra<lb/>dus 10. Fiat igitur vt CB Radius 100000. <lb/>00000. ad CD 101542.66119 &longs;ecante&mtail; <lb/>grad. 10, ita &longs;emidia<lb/><figure id="id.018.01.114.1.jpg" xlink:href="018/01/114/1.jpg"/><lb/>metet CB mill. 3437 1/2 <lb/>proximè ad CD mill. <lb/>3490 1/2. Ablatâ autem <lb/>femidiametro CA, re<lb/>manet AD mill. 53. al<lb/>titudo turris Alexandri<lb/>næ: quanta videlicet <lb/>communiter tribui &longs;olet <lb/>halitibus illis, quibus <lb/>tum prima illuce&longs;centis diei, tum po&longs;trema <lb/>aduentantis noctis crepu&longs;cula debemus. </s>

<s id="id000141">Sexta petitio.</s>

<s id="id000142">Propo&longs;ita proportione quacunque, & monade quantitatem inue<lb/>nire, quæ &longs;e habeat ad monadem in proportione propo&longs;ita.</s>

<s id="id000143">Nam cùm per quartam petitionem diui&longs;a quantitate per quan<lb/>titatem exeat proportio, & numerus ad <expan abbr="monad&etilde;">monadem</expan> &longs;e habeat, ut pro<lb/>portio, ideo &longs;umpta monade &longs;ecundum illum numerum, ille nume <lb/>rus e&longs;t quantitas quæ&longs;ita.</s>

<s id="id000144">Septima petitio.</s>

<s>Id <pb xlink:href="018/01/115.jpg" pagenum="101"/>verò quàm longè à veritate recedat, quid <lb/>pluribus opus e&longs;t explicare? </s>

<s id="id000145">Quamlibet quantitatem per aliam eiu&longs;dem generis diuidere <lb/>po&longs;&longs;e.</s>

<s>quotus enim <lb/>qui&longs;que e&longs;t, qui turri octingentis talentis ex<lb/>citatæ duûm triumue milliarium altitudi<lb/>nem concedat? </s>

<s>Pharos igitur In&longs;ula imma<lb/>nis &longs;copulus fuit 50 &longs;erè milliaria iuxta per<lb/>pendiculum numerans; qua de re mirum <lb/>apud &longs;criptores omnes &longs;ilentium: ac proin<lb/>de tantæ altitudini parùm vtilis accidi&longs;&longs;et &longs;pe<lb/>culæ acce&longs;sio. </s>

<s id="id000146">Octaua petitio.</s>

<s>At &longs;tatuamus cum Erato&longs;the<lb/>ne telluris ambitum &longs;tadiorum 252000, & <lb/>&longs;tadia &longs;ingula &longs;int Alexandrina |ped. Rom. <lb/>720., totus ambitus e&longs;&longs;et mill.Rom. 36288; <lb/>igitur milliaria 600 e&longs;&longs;ent gr. 5. m. </s>

<s id="id000147">Proportionem in proportionem ducere po&longs;&longs;e: quamuis &longs;int in<lb/>ter quantitates diuer&longs;i generis.</s>

<s id="id000148">Quod dicitur de multiplicatione intelligendum e&longs;t de alijs ope<lb/>rationibus &longs;uprà enumeratis.</s>

<s id="id000149">Nona petitio.</s>

<s>57. Qua<lb/>re vt Radius 100000.00000. ad 100541. <lb/>64449. &longs;ecantem gr.5.m. 57., ita &longs;emidia<lb/>meter CB mill. 5775. pa&longs;&longs;. </s>

<s id="id000150">Monadem &longs;emper &longs;umere in quo cunque genere po&longs;&longs;e propo&longs;i<lb/>ta proportione.</s>

<s id="id000151">Nam licet diuidere per &longs;eptimam petitionem quantitatem per <lb/>quantitatem proportionis: & quod exit, e&longs;t proportio per quar<lb/>tam petitionem, & per &longs;ecundam animi communem &longs;ententiam <lb/>illa proportio e&longs;t numero æqualis: ergo diui&longs;a proportione, per &longs;i<lb/>milem numerum &longs;tatuetur monas.</s>

<s>419. ad CD <lb/>mill. 5806. pa&longs;&longs;. </s>

<s id="id000152">Decima petitio.</s>

<s>701: ex qua &longs;i auferatur &longs;e<lb/>midiameter CA, remaneret altitudo AD <lb/>mill. 31 & pa&longs;&longs;. </s>

<s id="id000153">In quouis genere quantitatum &longs;umere po&longs;&longs;e quantitatem, quæ <lb/><arrow.to.target n="marg2"/><lb/>&longs;e habeat ad monadem in proportione data. </s>

<s id="id000154">Similem huic propo<lb/>nit Euclides in lineis generaliter: nos autem contrà generaliter in <lb/>omnibus quantitatibus, &longs;ed de monade tantum.</s>

<s>282; quæ altitudo adhuc e&longs;t <lb/>immanis: & maior hac e&longs;&longs;et, &longs;i &longs;tadia ill&atail; <lb/>252000. non. </s>

<s id="id000155"><margin.target id="marg2"/>D<emph type="italics"/>uodecima <lb/>&longs;exti<emph.end type="italics"/> E<emph type="italics"/>lem.<emph.end type="italics"/>Vndecima petitio.</s>

<s>Alexandrina &longs;ed Græca a&longs;&longs;um<lb/>pta fui&longs;&longs;ent; e&longs;&longs;et enim CD &longs;ecans anguli <lb/>DCB gr.7.m.8.&longs;ec.38. Non itaque fieri po<lb/>tuit, vt ex Alexandrinâ turri ad &longs;excenta pa&longs;<lb/>&longs;uum millia pro&longs;pectus pateret. </s>

<s id="id000156">Monadem in quancunque quantitatem ductam æquale ip&longs;i pro<lb/>ducere. </s>

<s>Longè minor e&longs;t Phy&longs;ici Horizontis &longs;e<lb/>midiameter, quàm vulgus cen&longs;eat, &longs;i res Geo<pb xlink:href="018/01/116.jpg" pagenum="102"/>metricè perpendatur: cre&longs;cit autem eius am<lb/>plitudo pro maiori &longs;pectatoris altitudin&etail;. </s>

<s id="id000157">Similiter & proportionem æqualem.</s>

<s><lb/>Hinc quamuis nauclerorum plurimos Geo. <lb/>metriâ non &longs;atis in&longs;tructos &longs;æpè fugiat ratio, <lb/>eorum tamen varia in determinandâ visûs <lb/>di&longs;tantiâ &longs;ententias facilè po&longs;&longs;umus concilia<lb/>re; alijs &longs;iquidem ex altiori, alijs ex humilio<lb/>ri &longs;peculâ pro&longs; picientibus obiectum idem, <lb/>illis quidem longiùs, his verò propiùs &longs;e ob<lb/>tulit contemplandum. </s>

<s id="id000158">Nam cum aliqua quantitas augeat ducta aliqua minuat, nece&longs;&longs;e <lb/>e&longs;t aliquam e&longs;&longs;e, quæ nec augeat, nec minuat, & hæc e&longs;t monas. <lb/></s>

<s id="id000159">Idem dico de diui&longs;ione. </s>

<s id="id000160">Aequalitas etiam ducta, uel diuidens non <lb/><arrow.to.target n="marg3"/><lb/>mutat proportionem: nec quantitatem ip&longs;am, igitur monas æqua<lb/>litatem refert. </s>

<s>Quocirca ex huiu&longs;<lb/>modi hominum effatis nihil timendum, <lb/>quod datâ telluris magnitudine con&longs;titutam <lb/>Geometricisque rationibus &longs;olidatam de vi<lb/>sûs di&longs;tantiâ &longs;ententiam labefactare po&longs;sit: <lb/>duo enim hæc inuicem perpetuo vinculo <lb/>colligantur. </s>

<s id="id000161">Quod etiam e&longs;t per&longs;picuum ex &longs;upradictis.</s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> At qui&longs;quis ex eorum numero &longs;ue<lb/>rit, quos pudet aliquando &longs;apere, & antiquos <lb/>errores dedi&longs;cere, vbi visûs di&longs;tantiam eius <lb/>opinione minorem demon&longs;traueris, illicò <lb/>terræ magnitudinem non ritè con&longs;titutam <lb/>calumniabitur, & ad Ari&longs;totelem prouoca<lb/>bit, qui lib.

<s id="id000162"><margin.target id="marg3"/>S<emph type="italics"/>ecunda ani<lb/>mi <expan abbr="cõmunis">communis</expan> <lb/>&longs;ententia.<emph.end type="italics"/></s>

2. de C&oelig;lo text. </s>

<s id="id000163">Duodecima petitio.</s>

<s>&longs;cribit terræ <lb/>circuitum patere quadraginta &longs;tadioru&mtail; <lb/>myriadibus, hoc e&longs;t &longs;tadiis 400000. aut ad <lb/>Archimedem, qui in Arenario telluris am<lb/>bitum ter mille &longs;tadiorum millia & eo am<lb/>pliùs complecti con&longs;tituit. </s><pb xlink:href="018/01/117.jpg" pagenum="103"/>

<s id="id000164">Cum fuerint quatuor quantitates & ad primam, & tertiam æquè <lb/>multiplicibus a&longs;&longs;umptis, item que ad &longs;ecundam & quartam, & &longs;i mul<lb/>tiplex primæ maius e&longs;t multiplici &longs;ecundæ, multiplex tertiæ &longs;it ma<lb/>ius multiplici quartæ, & &longs;i minus minus, & &longs;i æquale æquale, idque<lb/> &longs;emper quouis modo a&longs;&longs;umptis his proportionibus ad primam & <lb/>tertiam, & ad &longs;ecundam & quartam erit proportio primæ ad &longs;ecun<lb/>dam, ut tertiæ ad quartam. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Prouocet: per me licet. </s>

<s id="id000165">Hæc etiam a&longs;&longs;umitur ab Euclide. </s>

<s id="id000166">Et per <lb/><arrow.to.target n="marg4"/><lb/>hanc intelligimus etiam conuer&longs;am.</s>

<s>Eum ta<lb/>men monitum velim parum ex Archimede <lb/>&longs;perandum, cum eam <lb/>ille magnitudinem da<lb/><figure id="id.018.01.117.1.jpg" xlink:href="018/01/117/1.jpg"/><lb/>tâ operâ ponere volue<lb/>rit, quam nemo eo<lb/>rum, quibu&longs;cum di<lb/>&longs;putabat, iu&longs;to mino<lb/>rem calumniari po&longs;&longs;et. </s>

<s><lb/>Quodverò ad Ari&longs;tote<lb/>lem &longs;pectat, non mul<lb/>tum habet momen<lb/>ti Peripatetica autho<lb/>ritas, cui apodictica ratio aduer&longs;atur. </s>

<s id="id000167"><margin.target id="marg4"/>Q<emph type="italics"/>uinto<emph.end type="italics"/> E<emph type="italics"/>le. <lb/>diff.<emph.end type="italics"/> 6.</s>

<s>Porrò <lb/>longè melius e&longs;t opticæ lineæ longitudinem <lb/>præcogno&longs;cere, & ex illâ terræ magnitudi<lb/><arrow.to.target n="note48"/><lb/>nem inue&longs;tigare, quàm incertis coniecturis <lb/>telluris ambitum &longs;tatuere; & infirmo huic <lb/>fundamento æquè nutantem de a&longs;pectûs lon<lb/>gitudine &longs;ententiam &longs;uper&longs;truere. </s>

<s id="id000168">Tertia decima petitio.</s>

<s>Sit enim <lb/>nota altitudo BA, & ob&longs;eruatus fuerit angu<lb/>lus BAD; notus e&longs;t angulus complementi, <lb/>qui e&longs;t ad C: ducta autem recta BD facit <lb/>angulum BDA, qui e&longs;t &longs;emi&longs;&longs;is noti anguli <lb/>ad C, vt paulò antè dicebam. </s>

<s>Cum itaque <lb/>in triangulo BAD datum &longs;it latus AB, & duo <lb/>anguli ad A & ad D innotuerint, inueniri <lb/>poterit quantitas lineæ opticæ AD. </s>

<s id="id000169">Quantitates æquales, atque proportiones in qua&longs;uis quanti<lb/>tates ductæ eandem &longs;eruant rationem. </s>

<s id="id000170">Euclides hanc demon&longs;trat, <lb/>nos autem ad uitandum tædium petimus concedi, &longs;ub qua in<lb/><arrow.to.target n="marg5"/><lb/>cluduntur diui&longs;io etiam additio, detractio, laterum omnium in<lb/>uentio.</s>

<s>Tum <pb xlink:href="018/01/118.jpg" pagenum="104"/>ex B intelligatur educta perpendiculatis BE, <lb/>& in triangulo rectangulo ABE, datis angu<lb/>lo A & latere AB, inueniatur latus BE. </s>

<s>De<lb/>mum quia triangula ABE, ADC rectangula <lb/>habentia communem angulum ad A &longs;unt &longs;i<gap/><lb/>milia, fiat vt AB data ad BE inuentam, ita <lb/>AD lineæ opticæ longitudo inuenta ad DC <lb/>quæ&longs;itam terræ &longs;emidiametrum. </s>

<s id="id000171"><margin.target id="marg5"/>Q<emph type="italics"/>uarta quin<lb/>ti<emph.end type="italics"/> E<emph type="italics"/>lem.<emph.end type="italics"/></s>

<s><margin.target id="note48"/><emph type="italics"/>XLVIII <lb/>Inuenir&etail; <lb/><expan abbr="longitudin&etilde;">longitudinem</expan> <lb/>vi&longs;us: & ex <lb/>ea Quint&atail; <lb/>methodus <lb/>vestigandi <lb/>terræ &longs;emi<lb/>diametrum,<emph.end type="italics"/></s>

<s id="id000172">Quarta decima petitio.</s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> In ijs, quæ hactenus attuli&longs;ti ad <lb/>terræ &longs;emidiametrum inueniendam, illud <lb/>accidit incommodum, quod totam altitu<lb/>dinem &longs;upra maris &longs;uperficiem innote&longs;cere <lb/>oportet: id quod haberi non pote&longs;t, ni&longs;i aut <lb/>prærupta rupes mari immineat, aut turris in <lb/>litore &longs;it con&longs;tituta. </s>

<s>Quin methodum ali<lb/>quam excogitas, qua etiam ex turri procul ab <lb/>æquore in colle po&longs;itâ explorare po&longs;&longs;imus, <lb/>quanta &longs;it terræ magnitudo? </s>

<s id="id000173">Cùm termini alicuius quantitatis eandem &longs;eruant rationem in <lb/>omnibus, & firmi &longs;unt ac &longs;tabiles eiu&longs;dem rationis comparatione <lb/>contentæ partes æqualem &longs;eruant exce&longs;&longs;um, &longs;eu proportionem.</s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Tentemus pariter, quid po&longs;&longs;imus: <lb/>tertius ade&longs;t Galilæus; ni&longs;i aliquid inueneri<lb/><arrow.to.target n="note49"/><lb/>mus, dicam nos iratis Mu&longs;is conueni&longs;&longs;e. </s>

<s id="id000174">PROPOSITIO prima.</s>

<s>Sit <lb/>igitur in perpendiculari AC, nota in&longs;ignis <lb/>aliqua altitudo BA, at non talis, vt eius hu<lb/>millimum punctum B &longs;phæricæ &longs;uperficiei <lb/>adhæreat, cum potiùs ex illâ emineat i&ntail; <lb/>colle DB, cuius altitudo ignota e&longs;t: fieri au<lb/>tem po&longs;&longs;it, vt liber pro&longs;pectus in Horizon<lb/>tem pateat, &longs;iue in &longs;ummo A, &longs;iue in imo B <pb xlink:href="018/01/119.jpg" pagenum="105"/>con&longs;i&longs;tas angulos CAE, CBF ob&longs;eruaturus. <lb/><figure id="id.018.01.119.1.jpg" xlink:href="018/01/119/1.jpg"/><lb/>Quibus angulis ob&longs;er<lb/>uatis intellige rectam <lb/>BF occurrere Tangen<lb/>ti AE in G. </s>

<s>In triangu<lb/>lo itaque ABG angu<lb/>lus AGB e&longs;t notus, vt<lb/>pote differentia duo<lb/>rum ob&longs;eruatorum C <lb/>BG, CAG: angulus A <lb/>e&longs;t ob&longs;eruatus, & data <lb/>e&longs;t altitudo BA: ergo <lb/>inueniri pote&longs;t quantitas rectæ BG. </s>

<s id="id000175">Proportionem in proportionem duci e&longs;t &longs;uperiores nume<lb/>ros atque inferiores inuicem ducere.</s>

<s>Iam du<lb/>cantur rectæ CF, CE, & &longs;unt duo triangula <lb/>AEC, BFC rectangula, in quibus duo an<lb/>guli EAC, ECA &longs;imul &longs;unt æquales duo<lb/>bus FBC, FCB: Atqui angulus ECA e&longs;t æ<lb/>qualis duobus ECF, FCB; ergo tres ECF, <lb/>FCB, CAE &longs;unt æquales duobus FBC, FCB; <lb/>& dempto communi FCB, remanet FBC <lb/>æqualis duobus ECF, EAC. </s>

<s>E&longs;t igitur ECF <lb/>differentia nota duorum ob&longs;eruatorum CAE, <lb/>CBF. </s>

<s id="id000176">Sit proportio lineæ a ad lineam b, ut anguli c ad angulum d, &longs;ta<lb/><arrow.to.target n="marg6"/><lb/>tuatur e monas in genere a <lb/><figure id="id.015.01.026.1.jpg" xlink:href="015/01/026/1.jpg"/><lb/>b, & fiat f ad e, ut c ad d, & du<lb/><arrow.to.target n="marg7"/><lb/>catur a in f & b in e, & pro<lb/>ducantur g & h. </s>

<s id="id000177">Quia ergo <lb/><arrow.to.target n="marg8"/><lb/>f e&longs;t proportio ip&longs;a, erit g ad <lb/><arrow.to.target n="marg9"/><lb/>a ut c ad d, &longs;ed h e&longs;t æqualis <lb/>b, igitur a ad h ut ad b. </s>

<s>Ducatur demùm recta CG. </s>

<s id="id000178">Du<lb/>cta ergo dicetur proportio a <lb/><arrow.to.target n="marg10"/><lb/>ad b in proportionem c ad d <lb/>ducendo terminos proportionis, &longs;eu quantitatis recta &longs;cilicet &longs;u<lb/>periores cum &longs;uperioribus, & inferiores cum inferioribus. </s>

<s id="id000179">Nam &longs;i <lb/><arrow.to.target n="marg11"/><lb/>rur&longs;um con&longs;tituantur f ad e ut a ad b cùm f &longs;it proportio, & k ad f ut <lb/><arrow.to.target n="marg12"/><lb/>c ad d, erit k ad e, ut g ad h, k autem fit ex ductu proportionis a ad b, <lb/>quæ e&longs;t fin proportionem c ad d, liquet igitur propo&longs;itum.</s>

<s>Et quo<lb/>niam GF, GE &longs;unt tangentes circulum ab <lb/>eodem puncto exeuntes, inter &longs;e æquales <lb/>&longs;unt, &longs;icut & CF, CE ex centro ductæ; CG <lb/>verò e&longs;t vtrique triangulo FCG, ECG com<lb/>munis; ergo angulus ECF notus diuiditur à <pb xlink:href="018/01/120.jpg" pagenum="106"/>rectâ CG bifariam. </s>

<s>Quare &longs;i angulorum ob<lb/>&longs;eruatorum &longs;emidifferentiam GCF addas an<lb/>gulo FCB complemento noto anguli ob&longs;er<lb/>uati in B, notus e&longs;t etiam angulus BCG; ex <lb/>quo, vnâ cum angulo CBG ob&longs;eruato, & la<lb/>tere BG inuento, inuenitur latus CB: Cui &longs;i <lb/>addatur data altitudo BA, notum erit latus <lb/>CA vnâ cum angulo ad A ob&longs;eruato in trian<lb/>gulo AEC rectangulo: quare & inuenitur CE <lb/>&longs;emidiameter quæ&longs;ita, quæ e&longs;t ip&longs;i CD æqua<lb/>lis, vnde innote&longs;cit altitudo collis BD, & <lb/>lineæ opticæ AE longitudo cogno&longs;ci pote&longs;t. </s>

<s><margin.target id="note49"/><emph type="italics"/>XLIX <lb/>Sexta me<lb/>thodus ter<lb/>ræ &longs;emidia<lb/>metrum in<lb/>quirendi, & <lb/>montis alti<lb/>tudinem co<lb/>gno&longs;cendi.<emph.end type="italics"/></s>

<s>At contingat ex edito quidem monte pro<lb/>&longs;pici po&longs;&longs;e in <expan abbr="extrem&utilde;">extremum</expan> <lb/><arrow.to.target n="note50"/><lb/><figure id="id.018.01.120.1.jpg" xlink:href="018/01/120/1.jpg"/><lb/>horizontem, &longs;ed planè <lb/>ignotam e&longs;&longs;e montis al<lb/>titudinem. </s>

<s>Eligatur lo<lb/>cus aliquis con&longs;picuus, <lb/>qui ita di&longs;tare cen&longs;ea<lb/>tur, vt perpendicula<lb/>res ex vtroque loco ad <lb/>centrum ductæ à pa<lb/>ralleli&longs;mo deflectentes <lb/>&longs;en&longs;u digno&longs;ci queant. </s>

<s><lb/>Hinc enim terræ &longs;emidiametrum eruer&etail; <lb/>po&longs;&longs;umus. </s>

<s>Ex A igitur &longs;it linea AD terram <lb/>tangens: ob&longs;eruetur angulus CAD. </s>

<s>Tum <lb/>ad ea&longs;dem vel alias partes eligatur locus B <pb xlink:href="018/01/121.jpg" pagenum="107"/>valde di&longs;tans, & ob&longs;eruetur pariter angulus <lb/>CAB. </s>

<s id="id000184"><margin.target id="marg10"/>P<emph type="italics"/>er<emph.end type="italics"/> 2. A<emph type="italics"/>ni<lb/>mi &longs;entent.<emph.end type="italics"/></s>

<s>Di&longs;tantia autem BA vel &longs;it præcogni<lb/>ta, vel ex tertio loco ob&longs;eruetur, vt fieri com<lb/>muniter &longs;olet. </s>

<s>Demum ex B ob&longs;eruetur an<lb/>gulus ABC; cognitâ &longs;cilicet di&longs;tantiâ ip&longs;ius <lb/>A puncti à vertice ob&longs;eruatoris in B, com<lb/>plementum ad duos rectos dat angulum <lb/>ABC: erit autem indicium di&longs;tantiæ AB <lb/>&longs;ufficientis, &longs;i anguli CAB, CBA &longs;imul &longs;um<lb/>pti minores fuerint duobus rectis. </s>

<s>Quare in <lb/>triangulo ABC dato latere BA & angulis <lb/>adiacentibus inuenitur latus AC. </s>

<s>Inuento <lb/>autem latere AC & ob&longs;eruato angulo CAD <lb/>in triangulo CDA rectangulo, inuenitur CD <lb/>quæ&longs;ita terræ &longs;emidiameter, nec latebit <lb/>montis altitudo. </s>

<s id="id000187">Propo&longs;itio <expan abbr="&longs;ec&utilde;nda">&longs;ecunda</expan>.</s>

<s><lb/>Septima me<lb/>thodus in<lb/>uestigandi <lb/>&longs;emidiame<lb/>trum terræ, <lb/>& montis <lb/>altitudine.<emph.end type="italics"/></s>

<s id="id000188">Proportio extremorum producitur ex intermedijs.<lb/><arrow.to.target n="marg13"/></s>

<s>Quod &longs;i locorum opportunitas ferat, vt <lb/>detur altitudo FE nota, ex qua ob&longs;eruari <lb/><arrow.to.target n="note51"/><lb/>queat angulus CED, & in monte procul po&longs;i<lb/>to liber &longs;it a&longs;cen&longs;us, donec ex A puncto per <lb/>E in extremum horizontem D productus ra<lb/>dius efficiat angulum CAD, qui ob&longs;eruatio<lb/>ne cogno&longs;catur; ea habemus, quæ ad inue<lb/>niendam terræ &longs;emidiametrum, vel ad exa<lb/>minandamiam inuentam &longs;ufficiant. </s>

<s>Intel<lb/>ligatur enim ex F exire recta FG parallela ip&longs;i <lb/>CA (perpendiculares &longs;iquidem EC, AG á <lb/>paralleli&longs;mo deflectere ponimus) efformatur <pb xlink:href="018/01/122.jpg" pagenum="108"/>triangulum FEG, cuius latus FE datur, an<lb/>gulus EGF æqualis angulo EAC ob&longs;eruato <lb/>innote&longs;cit propter linearum CA, FG paral<lb/>leli&longs;mum, & GEF e&longs;t complementum ad <lb/>duos rectos anguli FED ob&longs;eruati. </s>

<s>Inuenia<lb/>tur itaque latus EG; quod ablatum ex EA <lb/>di&longs;tantiâ iam notâ duorum locorum, i&ntail; <lb/>quibus in&longs;titutæ &longs;unt ob&longs;eruationes, relin<lb/>quit GA. </s>

<s id="id000190">Sint a b c quantitates dico proportio<lb/><figure id="id.015.01.026.2.jpg" xlink:href="015/01/026/2.jpg"/><lb/>nem a ad c, produci ex proportione a ad b </s>

<s>At in triangulo EAC, lateri AC <lb/>parallela e&longs;t GF, ergo vt EG ad GA, ita EF <lb/>data altitudo ad FC quæ&longs;itam &longs;emidiame<lb/>trum. </s>

<s id="id000191"><arrow.to.target n="marg14"/><lb/>& b ad c, &longs;tatuantur totidem à monade d e <lb/>f, erúntque ex demon&longs;trantis ab Euclide in <lb/>quinto <expan abbr="Elem&etilde;torum">Elementorum</expan> in eadem proportio<lb/>ne, &longs;tatuatur ergo d prima quantitas e &longs;e<lb/>cunda & tertia f quarta. </s>

<s>Vel etiam ij&longs;dem po&longs;itis, & ob&longs;erua<lb/>tis angulis CED, GAE, atque di&longs;tantiâ AE, <lb/><arrow.to.target n="note52"/><lb/>in triangulo CAE noti &longs;unt duo anguli, (an<lb/>gulus &longs;iquidem CEA e&longs;t complementum ad <lb/>duos rectos anguli CED ob&longs;eruati) & latus <lb/>adiacens AE: inueniatur igitur latus EC, ex <lb/>quo dempta nota altitudo FE relinquit quæ<lb/>&longs;itam terræ &longs;emidiametrum. </s>

<s id="id000192">eritqúe per præce<lb/><arrow.to.target n="marg15"/><lb/>dentem proportio productorum ex d in e <lb/>& &longs;it g, & in f & &longs;it h, producta ex propor<lb/>tionibus d ad e & e ad f, quare ex propor<lb/>tionibus a ad b & b ad e, &longs;ed ex dictis cum <lb/>e &longs;it eadem, erit proportio d ad f, ut g ad h & proportio, d ad f per <lb/>æquam proportionem ab Euclide demon&longs;tratam, ut a ad c, igitur <lb/><arrow.to.target n="marg16"/><lb/>proportio a ad c producitur ex proportionibus a ad b & b ad c, & <lb/>e&longs;t proportio ip&longs;a a ad c d numerus, ut o&longs;ten&longs;um e&longs;t.</s>

<s>Erit autem <lb/>indicium &longs;ufficientis di&longs;tantiæ inter A & E, &longs;i <lb/>angulus CED ob&longs;eruatus fuerit maior angu<lb/>lo CAE. </s>

<s><lb/>Octaua me<lb/>thodus in<lb/>ueniendi ter<lb/>ræ &longs;emidia<lb/>metrum.<emph.end type="italics"/></s>

<s><lb/>Idem aliter.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Ea profectò &longs;unt, quæ hactenus di<lb/>&longs;putata &longs;unt, vt vix cen&longs;eam fieri po&longs;&longs;e, vt <lb/>alicui nulla ex his methodis arrideat. </s>

<s id="id000196">Ex hoc &longs;equitur, quòd cùm fuerit quantitas tertia monas ex pro<lb/><arrow.to.target n="marg17"/><lb/>portionibus inuicem ductis producetur prima quantitas.<lb/><arrow.to.target n="marg18"/></s>

<s>Ve<lb/>rùm &longs;crupulus e&longs;t, quem forta&longs;&longs;e ex multo<lb/>rum animis non facilè eximas: exi&longs;tima<lb/>bunt &longs;iquidem angulum, quem cum per<pb xlink:href="018/01/123.jpg" pagenum="109"/>pendiculo opticus radius con&longs;tituit, nun<lb/>quam minimè dubiâ ob&longs;eruatione inue&longs;tiga<lb/>ri po&longs;&longs;e. </s>

<s>Nam vltimum visûs terminum &longs;i <lb/>in terrâ &longs;pectes, quamuis plani&longs;&longs;ima facies <lb/>videatur, quî fiat, vt nullus pateat dubita<lb/>tioni locus, an molli inclinatione indè per <lb/>longa terrarum &longs;patia in mare de&longs;cendatur? </s>

<s><lb/>ac proinde linea illa ab oculo exiens non cir<lb/>culum in &longs;phæricâ &longs;uperficie contingeret, vt <lb/>exigitur. </s>

<s>Si verò in immen&longs;um æquor vi<lb/>&longs;us excurrat, et&longs;i &longs;opitis fructibus otia agat, <lb/>nulloque æ&longs;tu intume&longs;cat, quis ne&longs;ciat At<lb/>mo&longs;phæram vaporibus non adeò paucis te<lb/>nuibu&longs;ue &longs;catere, vt nulla refractionis, qua <lb/>Oceani partes infra horizontem depre&longs;&longs;æ <lb/><expan abbr="&etilde;mergant">emmergant</expan>, &longs;u&longs;picio &longs;uboriri po&longs;&longs;it? </s>

<s id="id000199">Ex hoc &longs;equitur, quòd conuer&longs;a proportio producitur ex con<lb/>uer&longs;is proportionibus.</s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Hæc quidem non ea e&longs;&longs;e videntur, <lb/>quæ telluris &longs;emidiametro his methodis in<lb/>uentæ officere po&longs;&longs;int: Si enim aliâ atque <lb/>aliâ methodo inue&longs;tigetur, nec valdè in&longs;i<lb/>gni di&longs;crimine differant, quæ inueniuntur, <lb/>medium Arithmeticum inter extrema in<lb/>uenta dabit quantitatem quæ&longs;itam &longs;emidia<lb/>metro terræ tribuendam. </s>

<s>Tellus quipp&etail; <lb/>toreuma non e&longs;t vndequaque expolitum; &longs;ed <lb/>cum eius partes à centro di&longs;paribus interual<lb/>lis ab&longs;int, ita tamen vt proximè &longs;phæra&mtail; <lb/>æmuletur, facis e&longs;t &longs;i mediocris à centro di-<pb xlink:href="018/01/124.jpg" pagenum="110"/>&longs;tantia innote&longs;cat. </s>

<s id="id000200">Propo&longs;itio tertia.</s>

<s>Nihilominus tamen aliam <lb/>placet tentare viam nullâ habitâ ratione radii <lb/>optici terram tangentis, modò ea &longs;it duo<lb/>rum locorum di&longs;tantia, vt perpendiculares <lb/>ad centrum notabiliter deflectant à paralle<lb/>li&longs;mo. <lb/><arrow.to.target n="note53"/></s>

<s id="id000201">Si proportio ex duabus proportionibus in quatuor terminis <lb/>producatur, ip&longs;a uerò proportio inter duas alias quantitates fue

<s><margin.target id="note53"/><emph type="italics"/>LIII: <lb/>Nona me<lb/>thodus tel<lb/>luris &longs;emi<lb/>diametrum <lb/>inquirendi.<emph.end type="italics"/></s><figure id="id.018.01.124.1.jpg" xlink:href="018/01/124/1.jpg"/>

<s>Eligatur itaque alti<lb/>tudo quæpiam in&longs;ignis <lb/>& nota AB, ex cuius <lb/>vtroque extremo vi<lb/>deatur in monte ad <lb/>plura milliaria procul <lb/>po&longs;ito locus D: loca ve<lb/>rò huiu&longs;modi di&longs;tantia <lb/>po&longs;&longs;unt ob&longs;eruari poti&longs;<lb/>&longs;imùm noctu accen&longs;o <lb/>ibi igné ab amico, ni&longs;i <lb/>ad&longs;it nota aliqua peculiaris, vt ædificium, <lb/>turris &c. </s>

<pb pagenum="8" xlink:href="015/01/027.jpg"/>rit con&longs;tituta: con&longs;urgent trecenti &longs;exaginta modi productionis <lb/>proportionis.</s>

<s>Tum ex A ob&longs;eruetur angulus <lb/>BAD, & ex B angulus ABD, notus enim fiet <lb/>reliquus angulus BDA. </s>

<s>Ex puncto autem <lb/>D ob&longs;eruetur angulus BDC, vnde ablato an<lb/>gulo BDA noto, reliquus ADC innote&longs;cit. </s>

<s><lb/>His paratis in triangulo ABD dantur duo an<lb/>guli A & B cum latere adiacente BA, inue<lb/>niatur igitur latus AD. </s>

<s>Ex hoc autem late<lb/>re AD inuento vnâ cum angulo ADC, qu <lb/>ex ob&longs;eruatione innotuit, & angulo DAC <pb xlink:href="018/01/125.jpg" pagenum="111"/>qui e&longs;t complementum anguli ob&longs;eruati <lb/>DAB ad duos rectos, inueniri pote&longs;t latus <lb/>AC quæ&longs;ita terræ &longs;emidiameter. </s>

<s id="id000204">H&etail;c propo&longs;itio ut præcedens & <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> tres ab Alchindo &longs;um<lb/>ptæ &longs;unt, & ab eo demon&longs;trantur. </s>

<s>At non vacat montem con&longs;cendere? </s>

<s id="id000205">Sit ergo proportio a ad b, pro<lb/><arrow.to.target n="table2"/><lb/><figure id="id.015.01.027.1.jpg" xlink:href="015/01/027/1.jpg"/>ducta ex proportione c ad d & e ad f, con&longs;tat <lb/>quòd cum &longs;int &longs;ex quantitates, quòd fieri pote<lb/>runt quindecim coniugationes, quas po&longs;ui à la<lb/>tere facilitatis gratia, quibus re&longs;pondent totidem <lb/><arrow.to.target n="table3"/><lb/>conuer&longs;æ: erunt ergo triginta. </s>

<s id="id000206">Singulæ autem ha<lb/>rum produci po&longs;&longs;unt duodecim modis: ductis <lb/><figure id="id.015.01.027.2.jpg" xlink:href="015/01/027/2.jpg"/>duodecim in triginta, fiunt trecenti &longs;exaginta mo <lb/>di. </s>

<s>alia <lb/><arrow.to.target n="note54"/><lb/>&longs;uppetit via, qua leuiori labore propo&longs;itum <lb/>a&longs;&longs;equamur. </s>

<s id="id000207">Et hoc e&longs;t clarum per&longs;e, modo <expan abbr="demõ&longs;tremus">demon&longs;tremus</expan>, <lb/>quod &longs;inguli horum modorum po&longs;sint produ<lb/>ci duodecim modis, & capiamus ab primam qu&etail; <lb/>pote&longs;t produci ex c d & e f: Item ambabus con<lb/>uer&longs;is d c & fe: & rur&longs;us altera recta altera con<lb/>uer&longs;a: & hoc bifariam c d & f e, & d c & e f, &longs;unt er<lb/>go iam quatuor modi. </s>

<s id="id000208">Totidem ex c e & d f, toti<lb/>demque ex c f & d e, igitur erunt duodecim mo<lb/>di, quibus produci po&longs;&longs;e intelligitur propor<lb/>tio a ad b.</s>

<s>Sit nota altitudo IG, vnde vi<lb/>deatur locus aliquis in &longs;uperficie terræ F: ob<lb/>&longs;erueturque angulus IGF. </s>

<table>

<s>Quod &longs;i di&longs;tantia <lb/><figure id="id.018.01.125.1.jpg" xlink:href="018/01/125/1.jpg"/><lb/>GF iam nota non <lb/>fuerit, ex tertio <lb/>quopiam loco e&atail; <lb/>ob&longs;eruetur, <expan abbr="inue-niaturq.">inue<lb/>niaturque</expan> iuxta Tri<lb/>gonometriæ præ<lb/>cepta. </s>

<table.target id="table2"/>

<row>

<s>His com<lb/>paratis producatur <lb/>GI per terræ cen<lb/>trum T v&longs;qu&etail; <lb/>in O, vt IO &longs;it <lb/>terræ diameter: ex <lb/>F cadat in dia<lb/>metrum perpendicularis FC. </s>

<s>Quonia&mtail; <lb/>igitur in triangulo GCF rectangulo datur hy<lb/>pothenu&longs;a GF, & angulus CGF, inueniantur <lb/>reliqua latera FC, CG. </s>

</row>

<row>

<s>Auferatur autem <lb/>IG data altitudo ex GC, & remanet IC. </s>

<s><lb/>Quia verò FC à puncto peripheriæ F cadit <lb/>perpendicularis in diametrum IO, e&longs;t me<pb xlink:href="018/01/126.jpg" pagenum="112"/>dio loco proportionalis inter diametri &longs;eg<lb/>menta IC, CO; ac proinde quadratum me<lb/>diæ CF æquale e&longs;t rectangulo &longs;ub extremis. </s>

</row>

<row>

<s><lb/>Itaque quadrato ip&longs;ius CF diui&longs;o per IC &longs;eg<lb/>mentum notum, Quotiens dabit CO, cui <lb/>addatur CI, & habetur tota diameter IO <lb/><arrow.to.target n="note55"/><lb/>quæ&longs;ita. </s>

</row>

<row>

<s><lb/>Decima me<lb/>thodus, qua <lb/>terræ dia<lb/>meter inue<lb/>nitur.<emph.end type="italics"/></s>

</row>

<row>

<s><lb/>Idem aliter.<emph.end type="italics"/></s>

<s>Hæc mihi methodus magis arridet vtpo<lb/>te breuior, qua quadratum CF diuido per <lb/>IC: cæterùm &longs;i rem merè Trigonome<lb/>tricè perficere quis malit, inuentis CF <lb/>& IC, quærat angulum IFC; quem du<lb/>plicet, & dupli &longs;inum ex Tabulis inue<lb/>niat: tum fiat vt &longs;inus inuentus ad Ra<lb/>dium ita inuenta CF ad quæ&longs;itam &longs;emidia<lb/>metrum FT. </s>

</row>

<row>

<s>Huius operationis ratio pa<lb/>tet, quia cum angulus IFO in &longs;emicircu<lb/>lo &longs;it rectus, triângulum ICF e&longs;t &longs;imile trian<lb/>gulo IFO, igitur angulus inuentus IFC æqua<lb/>lis e&longs;t angulo FOC; huius autem duplex e&longs;t <lb/>angulus ITF ad centrum, qui proinde inno<lb/>te&longs;cit, vnâ cum &longs;inu FC in partibus Radii <lb/>hæc verò linea cum nota &longs;it etiam in men<lb/>&longs;urâ homogeneâ altitudini datæ IG, manife<lb/>&longs;tabit pariter in eâdem men&longs;urâ Radium TF. </s>

<s>Placetne aliam adhuc inire viam? </s>

</row>

</table>

<s>nec <lb/>Diony&longs;iodori Geometræ protritam ve&longs;tigiis; <lb/>cuius in &longs;epulchro inuenta e&longs;t epi&longs;tola ad <pb xlink:href="018/01/127.jpg" pagenum="113"/>&longs;uperos mi&longs;&longs;a, qua &longs;e à &longs;epulchro ad intimam <lb/>terram de&longs;cendi&longs;&longs;e &longs;ignificabat, illudque &longs;pa<lb/>tium &longs;tadia 42000. complecti. </s>

<table>

<table.target id="table3"/>

<s>Sint datæ al<lb/>titudo eadem IG, ac di&longs;tantia GF, & angu<lb/>lus IGF ob&longs;eruetur. </s>

<row>

<s>Ducatur ex I tangens <lb/><arrow.to.target n="note56"/><lb/>IH; quæ &longs;ecet GF in H. </s>

</row>

<s>Quæratur ergo i&ntail; <lb/>triangulo GIH rectangulo, ex dato latere GI <lb/>& angulo G, latus GH, quod ex GF ablatum <lb/>relinquit HF, & quæratur latus IH. </s>

<row>

<s>Deinde du<lb/>ctâ rectâ IF, in triangulo IHF nota &longs;unt la<lb/>tera IH & HF, angulus autem compræhen<lb/>&longs;us IHF æqualis e&longs;t duobus internis notis, &longs;ci<lb/>licet recto GIH, & IGH ob&longs;eruato: quar&etail; <lb/>inueniri pote&longs;t tum latus IF, tum angulus <lb/>HIF: cui æqualis e&longs;t angulus IOF in alterno <lb/>&longs;egmento: huius autem duplus e&longs;t angulus <lb/>ITF ad centrum. </s>

</row>

<s>Fiat igitur vt &longs;inus &longs;emian<lb/>guli inuenti ITF, hoc e&longs;t &longs;inus anguli HIF, <lb/>ad Radium, ita &longs;emi&longs;sis inuenti lateris IF <lb/>ad quæ&longs;itam &longs;emidiametrum TF. </s>

<row>

</row>

<s><lb/>Vndecim&atail; <lb/>methodus <lb/>inueniendi <lb/>terræ &longs;emi<lb/>diametrum:<emph.end type="italics"/></s>

<row>

<s>Compendio&longs;iùs forta&longs;&longs;e operabimur, &longs;i da<lb/>tis IG & GF cum angulo G compræhen&longs;o, <lb/><arrow.to.target n="note57"/><lb/>inueniatur ba&longs;is IF & angulus GIF, qui e&longs;t <lb/>nece&longs;&longs;ariò obtu&longs;us. </s>

</row>

<s>Fiat ergo vt &longs;inus exce&longs;<lb/>sûs anguli GIF &longs;upra rectum ad Radium, <lb/>ita &longs;emi&longs;sis inuentæ ba&longs;is IF ad quæ&longs;itam <lb/>terræ &longs;emidiametrum. </s>

<row>

<s><margin.target id="note57"/><emph type="italics"/>LVII. <lb/>Id<gap/> breuiùs.<emph.end type="italics"/></s>

</row>

<s>Verùm omi&longs;&longs;o tot linearum apparatu res <pb xlink:href="018/01/128.jpg" pagenum="114"/><arrow.to.target n="note58"/><lb/><figure id="id.018.01.128.1.jpg" xlink:href="018/01/128/1.jpg"/><lb/>facillimè conficitur, e<lb/>tiam&longs;i nulla &longs;it data al<lb/>titudo nota. </s>

<row>

<s>Ob&longs;erue<lb/>tur di&longs;tantia AD: tum <lb/>in A accipiatur angulus <lb/>CAD, & in D ob&longs;erue<lb/>tur angulus, quem cum <lb/>verticali lineâ ex D ad <lb/>Zenith productâ facit <lb/>radius opticus DA; hu<lb/>ius enim complementum ad duos rectos <lb/>e&longs;t angulus ADC: dato autem latere AD <lb/>cum angulis adiacentibus, latere non po&longs;<lb/>&longs;unt reliqua latera CD quæ&longs;ita terræ &longs;emidia<lb/>meter, & CA &longs;emidiameter aucta montis <lb/>AB altitudine. </s>

</row>

<s><margin.target id="note58"/><emph type="italics"/>LVIII. </s>

<row>

<s><lb/>Duodecima <lb/>methodus <lb/>&longs;emidiame<lb/>trum terræ <lb/>inuestigan<lb/>di, & montis <lb/>altitudini.<emph.end type="italics"/></s>

</row>

<s>Sed iam, Mer&longs;enne, cadunt altis d&etail; <lb/>montibus vmbræ; nec Galilæum diutur<lb/>niore colloquio di&longs;tinere fas e&longs;t. </s>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Rectè mones: præceps in noctem <lb/>ruit dies: &longs;ed huiu&longs;modi colloquia cum in<lb/>&longs;tituuntur, omnis hora momentum e&longs;t. </s>

</row>

<s>Va<lb/>le Galilæe. </s>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Valete amici; & quas debeo gratias <lb/>pro humani&longs;simâ con&longs;uetudine, nunc planè <lb/>non reddo, &longs;ed apud me &longs;eruo, vt iterum <lb/>redire cogamini depo&longs;itum repetituri. </s><pb xlink:href="018/01/129.jpg" pagenum="115"/><figure id="id.018.01.129.1.jpg" xlink:href="018/01/129/1.jpg"/>

</row>

<s><emph type="center"/>DISSERTATIO <lb/>QVARTA<emph.end type="center"/></s>

<row>

<s><emph type="center"/>Ex aquæ &longs;eparatione à ter<lb/>ra, motus facilitatem <lb/>infert.<emph.end type="center"/></s>

</row>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

<row>

<s>PVRGARE ne tibi m&etail; <lb/>debeo, Galilæe, quòd con<lb/>dictam Mer&longs;enno horam te <lb/>adeundi importunus præ<lb/>uenerim? </s>

</row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Si putas Batauis in nouâ Zem<lb/>blâ po&longs;t longas dierum 84 tenebras lu<pb xlink:href="018/01/130.jpg" pagenum="116"/>cem præ&longs;to lancibus, Solem dies 14 antici<lb/>pantem accidi&longs;&longs;e importunum, ac purgatio<lb/>ne opus habui&longs;&longs;e, quòd legitimum exoriendi <lb/>tempus anteuerterit; præ&longs;tò &longs;um, vt intelli<lb/>gam, qua te demum excu&longs;atione ab imma<lb/>ni hac culpâ eximas. </s>

<row>

<s>Sed cum expectatus <lb/>adueneris, quam tuorum in me meritorum <lb/>partem referendâ gratiâ con&longs;equi potero? </s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Culpam hanc omnem, quantæ<lb/>cunque e&longs;t, in te transfero: id &longs;cilicet profu<lb/>sâ tuæ humanitatis &longs;ignificatione effeci&longs;ti, vt <lb/>mihi liceat e&longs;&longs;e temerario; nec ab&longs;urdu&mtail; <lb/>duxerim &longs;tatim, ac me tui de&longs;iderium ce<lb/>pit, aduolare, & immaturum f&oelig;tum, ve<lb/>riùs dixerim víx dum conceptum, ante t&etail; <lb/>ponere, vt vitæ igniculos illi tuâ luce imper<lb/>tias. </s>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Siccine iuuat fe&longs;tiuis inanium offi<lb/>ciorum argutijs iocari? </s>

</row>

<s>Mittamus i&longs;thæc: & <lb/>quam primum edi&longs;&longs;ere, quæ te benigna ege<lb/>rit Minerua, vt frigidos no&longs;tros cineres fodi<lb/>catum venires, ignem ætheriâ vtique domo <lb/>&longs;ubductum depo&longs;iturus. </s>

<row>

<s><emph type="italics"/>Guld:<emph.end type="italics"/> Ari&longs;totelem fortè præ manibus ha<lb/>bebam; cumque aliud meditans pagellas te<lb/>merè oculo percurrerem, incidi in textum <lb/>78. lib.

</row>

2. de C&oelig;lo, vbi Thaletis Mile&longs;ii d&etail; <lb/>causâ terræ quie&longs;centis &longs;ententiam exponit, <pb xlink:href="018/01/131.jpg" pagenum="117"/><emph type="italics"/>an quam ex eo, quia innatans &longs;it, tellus ma<lb/>neat, quemadmodum lignum vel aliquid tale <lb/>aliud; etenim horum &longs;uper aerem quidem ni<lb/>hil natura aptum e&longs;t manere, &longs;ed &longs;uper aquam.<emph.end type="italics"/><lb/>Id quod mihi in mentem reuocauit eadem <lb/>pror&longs;us apud Senecam à me iam pridem le<lb/>cta lib.

<row>

6. Nat. quæ&longs;t. </s>

</row>

<row>

<cell>direc.</cell>

<s>cap.

<cell>conuer.</cell>

</row>

6. terram videli<lb/>cet totam, Thaletis opinione, &longs;ubiecto hu<lb/>more portari, & innatare, ita vt vndâ &longs;u&longs;ti<lb/>neatur orbis velut aliquod grande nauigium. </s>

</table>

<s><lb/>Ex quo ille ab eodem Senecâ lib.

<s id="id000209">Propo&longs;itio quarta.</s>

3. cap.

<s id="id000210">Si fuerit proportio primi ad &longs;ecundum produ<lb/>cta ex proportionibus tertij ad quartum, & quin <lb/>ti ad &longs;extum, producetur etiam ex proportione <lb/>tertij ad &longs;extum, & quinti ad quartum.</s>

13. <lb/>reiectus non &longs;atis aptè terræ motuum cau&longs;am <lb/>inferebat, perindè atque &longs;i nauigium hoc in<lb/>natans concuteretur. </s>

<s>Tum, quæ e&longs;t phan<lb/>ta&longs;matum atque formarum menti inhæren<lb/>tium mira connexio, vix cæperam tacitus <lb/>ridere commenticium ingentis huius nauigii <lb/>nullos in &longs;copulos impacti tremorem, cum <lb/>in eius grauitatis con&longs;iderationem delap&longs;us <lb/>&longs;um: tenuique hac vellicatione excitatæ he<lb/>&longs;terni no&longs;tri congre&longs;&longs;us reliquiæ animo in&longs;i<lb/>dentes me protinus abripuerunt, & &longs;en&longs;im <lb/>nec aduertentem deduxerunt ad eam cogi<lb/>tationem, vt &longs;u&longs;picarer ex aquarum naturâ, <lb/>ad tellurem Archimedæis machinationibus <lb/>mouendam, &longs;ub&longs;idium aliquod comparari <lb/>po&longs;&longs;e. </s>

<s id="id000211">Sit proportio a b producta ex proportioni<lb/><arrow.to.target n="table4"/><lb/><figure id="id.015.01.027.3.jpg" xlink:href="015/01/027/3.jpg"/>bus c ad d, & e ad f, dico quod etiam erit produ</s>

<s>Plura illicò huic cogitato affinia i&ntail; <lb/>mentem confusè & permixtè irruperunt, <pb xlink:href="018/01/132.jpg" pagenum="118"/>quæ &longs;ubitam approbationem temerè extor<lb/>quere viderentur; &longs;ed quoniam, vbi multa <lb/>&longs;unt, quæ &longs;ibi aptis nexibus cohærere de<lb/>beant, ne veritatis compages luxata pereat, <lb/>periculo&longs;um & lubricum e&longs;t facilè a&longs;&longs;entiri, <lb/>nolui me in præcipitem locum committere; <lb/>&longs;u&longs;tinendam potiùs tanti&longs;per omnem a&longs;&longs;en<lb/>&longs;ionem duxi, dum rem totam di&longs;cretè & <lb/>electè &longs;uas in partes, te pro tuâ &longs;apientiâ <lb/>opem ferente, digererem. </s>

<table>

<table.target id="table4"/>

<s>En habes, qui<lb/>bus &longs;timulis actus mihi imperare non potue<lb/>rim, vt à te diutiùs abe&longs;&longs;em. </s>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Gratias tibi habeo, mi Guldine, im<lb/>mortales; quod &longs;pem iniicias audiendi ex te <lb/>hodie, quid de iis &longs;entias, quæ iam tum ab <lb/>anno huius &longs;æculi duodecimo con&longs;crip&longs;i de <lb/>Innatantibus. </s>

<cell/>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Librum legi tuo dignum ingenio; <lb/>nec potuit feliciùs enodari, quam con&longs;titue<lb/>ras examinandam quæ&longs;tionem de &longs;olidis in<lb/>natantibus, quamuis humido &longs;ecundùm &longs;pe<lb/>ciem grauioribus, &longs;i quidem &longs;olitaria &longs;uman<lb/>tur, componentibus tamen vnâ cum aër&etail; <lb/>&longs;ibi adhære&longs;cente molem aquâ non grauio<lb/>rem. </s>

</row>

<row>

<s>Illud maximè dolui, quod nactus &longs;im <lb/>exemplar &longs;iue Bibliopolæ &longs;ine Bibliopegi in<lb/>curiâ mutilarum integro folio, & quidem il<lb/>lo ip&longs;o, in quo totius futuræ di&longs;putationis <pb xlink:href="018/01/133.jpg" pagenum="119"/>fundamenta &longs;ternis: ac, quæ mihi aduer&longs;&atail; <lb/>e&longs;t fortuna, nu&longs;quam licuit integrum librum <lb/>reperire, ex quo no&longs;tri exemplaris hiatum <lb/>&longs;upplerem, Id quod te præmonui&longs;&longs;e oppor<lb/>tunum fuit, ne, &longs;i fortè nobis non conuene<lb/>rit, me contradicendi &longs;tudio actum putes: <lb/>ni&longs;i me tamen mea fallit opinio, in minimis <lb/>di&longs;&longs;entiemus. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Libens audio, qui contra &longs;en&longs;erint. </s>

</row>

<s><lb/>Sed ne te longiùs ab in&longs;tituto tuo, veriùs di<lb/>cam, no&longs;tro, abducam; quidnam ex aquâ <lb/>emolumenti &longs;peras ad facilem terræ motio<lb/>nem, de qua nobis fuit di&longs;putatio? </s>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Futurum puto, vt plurimum pon<lb/>deris de terreno hoc orbe, qui aquam pariter <lb/>ac terram complectitur, deduceretur. </s>

<s>Illud <lb/>enim extra omnem controuer&longs;iam po&longs;itum <lb/><arrow.to.target n="note59"/><lb/>accipio, quod aqua aëre grauior e&longs;t; & fluida <lb/>cùm &longs;it, &longs;emper ad inferiora delabitur, vt <lb/>infra aërem vniuer&longs;i centro vicinior con&longs;i&longs;tat. </s>

</row>

<row>

<s><lb/>Ex quo fit, vt nu&longs;quam quie&longs;cat, ni&longs;i vbi <lb/>nullus patet locus, in quem de&longs;cendat. </s>

<s>Qua<lb/>rè cum &longs;ola &longs;uperficies &longs;phærica paribus ra<lb/>diis à centro remoueatur, aquæ quie&longs;centis <lb/>&longs;uperficiem &longs;phæricam e&longs;&longs;e nece&longs;&longs;e e&longs;t: quan<lb/>doquidem &longs;iquæ &longs;uperficiei partes à centro <lb/>longiùs abe&longs;&longs;ent, vtpote altiores ad motum <lb/>procliues non &longs;ub&longs;i&longs;terent, &longs;ed humiliorem <pb xlink:href="018/01/134.jpg" pagenum="120"/>in locum defluerent: neque enim ex eo a<lb/>quam &longs;ponte a&longs;cendere dixerim, quòd ea in <lb/>vitreis fi&longs;tulis immer&longs;is aliquantulum a&longs;cen<lb/>dat. </s>

</row>

<s><margin.target id="note59"/><emph type="italics"/>LIX <lb/>Aquæ &longs;u<lb/>perficies est <lb/>&longs;phærica.<emph.end type="italics"/></s>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Nemo id facilè inficietur: immo, &longs;i <lb/>id quidem in rem tuam faciat, vltro dabo <lb/>maria omnia, quæ aquarum communion&etail; <lb/>iunguntur (&longs;i æ&longs;tum omnem &longs;ublatum, ven<lb/>tosque &longs;ilentes animo fingamus) non e&longs;&longs;&etail; <lb/>alia alijs &longs;ecundùm &longs;uperficiem altiora: qui<lb/>bus enim frænis cohiberentur Sinûs Arabici <lb/>aquæ, &longs;i altiores e&longs;&longs;ent, ne in Erytræum ma<lb/>re influerent? </s>

<s>aut quibus aggeribus ob&longs;true<lb/>retur fretum Herculeum, ne Oceanus Atlan<lb/>ticus ac Mediterraneum mare in vnâ &longs;u<lb/>perficie aquarum libramentum &longs;u&longs;ciperent? </s>

</row>

<row>

<s>Quod verò de aquâ in immer&longs;is fi&longs;tulis <lb/>vtrinque hiantibus a&longs;cendente addis, nihil <lb/>planè officit naturæ aquarum &longs;e in &longs;phæram <lb/>circa terræ centrum conglobantium; neque <lb/>illicò po&longs;&longs;e aquam ad digiti altitudine&mtail; <lb/>&longs;ponte a&longs;cendere affirmandum e&longs;t, quòd il<lb/>lam in tenui&longs;&longs;imis fi&longs;tulis eò pertingere ali<lb/>quando videamus; quò enim ampliores &longs;unt <lb/>fi&longs;tulæ, eò minùs in iis aquam a&longs;&longs;urger&etail; <lb/>con&longs;tat, nec fortè &longs;ine &longs;u&longs;picione minoris, <lb/>quàm appareat, altitudinis, propter &longs;pecie<lb/>rum vi&longs;ibilium ex vitro refractionem, i&ntail; <pb xlink:href="018/01/135.jpg" pagenum="121"/>ampli&longs;simis igitur lacuum marium que alueis <lb/>quantùm illa a&longs;cendat, quod &longs;phæricam &longs;u<lb/>perficiem corrumpat? </s>

<s>Sed nec aquam om<lb/>ninò &longs;ponte dixerim in fi&longs;tulâ a&longs;cender&etail; <lb/>Quando enim fi&longs;tula deprimitur, vt aquæ <lb/>immergatur, vtique &longs;ubiectus aër premitur, <lb/><arrow.to.target n="note60"/><lb/>& locum &longs;ubeunti fi&longs;tulæ concedens, quâ <lb/>patet via, recedit, vt locum &longs;uppleat à fi&longs;tu<lb/>lâ deor&longs;um motâ relictum. </s>

</row>

<s>Sicut autem <lb/>aër, cui corpus in motu occurrit, comprimi<lb/>tur, ita is, qui ponè e&longs;t, paululum di&longs;trahi<lb/>tur ac rare&longs;cit; hic verò ad ingenium rediens <lb/>proximum aërem attrahit ad &longs;upplendum <lb/>locum à fi&longs;tulâ relictum; cumque nullus <lb/>&longs;ubiectus aër tam in promptu &longs;it, quàm is <lb/>qui fi&longs;tulæ cauitatem implet, hic exfugitur; <lb/>atque adeò cum aér fi&longs;tulæ &longs;ur&longs;um mouea<lb/>tur, &longs;ubiectus aër compre&longs;&longs;us in fi&longs;tulæ caui<lb/>tatem &longs;uccedit, per quam faciliùs elabitur, <lb/>ac per impul&longs;ionem, aut compre&longs;&longs;ionem <lb/>contigui aëris, qui lateribus adiacet. </s>

</table>

<s>Por<lb/>rò ea e&longs;t fluidorum corporum natura, vt <lb/>conceptum ex motu impetum, etiam intrà <lb/>homogeneum corpus, non ita facilè remit<lb/>tant; quemadmodum in aquâ colore aliquo <lb/>infectâ intrà aliam aquam leui&longs;&longs;imè effusâ <lb/>videre e&longs;t. </s>

<s id="id000212"><arrow.to.target n="marg20"/><lb/>cta ex proportionibus c ad f, & e ad d, di&longs;ponan<lb/>tur ut in figura & fiat ex c in e g, & ex d in fh, ergo <lb/><arrow.to.target n="marg21"/><lb/>per primam harum g ad h ut a ad b, &longs;ed per præ<lb/>&longs;uppo&longs;ita in &longs;ecunda productione etiam prode<lb/>unt g & h, igitur per primam propo&longs;itionem ha<lb/>rum a ad b proportio producitur ex proportionibus c ad f tertiæ <lb/>&longs;cilicet ad &longs;extam, & e ad d quint&etail; ad quartam, quod fuit <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan>.</s>

<s>Hinc e&longs;t aërem &longs;ur&longs;um in fi&longs;tulâ <lb/>incitatum ex concepto impetu tanti&longs;per per<pb xlink:href="018/01/136.jpg" pagenum="122"/>gere in motu, & ita pellere &longs;uperiorem aë<lb/>rem, vt hic eum qui fi&longs;tulæ latera extrin&longs;e<lb/>cùs ob&longs;idet, propellat, fiatque per inferius <lb/>hiantis fi&longs;tulæ o&longs;culum illa circumpul&longs;io, de <lb/>qua Pla<emph type="italics"/>t<emph.end type="italics"/>o in Timæo, vel &longs;altem, vt cum ve<lb/><gap/>tris Philo&longs;ophis loquar, ab a&longs;cendente aëre <lb/>per fi&longs;tulam liberrimè ab&longs;que vllo alterius <lb/>aëris intercurrentis obice, attrahitur aër in<lb/>ferior. </s>

<s id="id000213"><margin.target id="marg20"/>P<emph type="italics"/>er<emph.end type="italics"/> 8. <emph type="italics"/>petit.<emph.end type="italics"/></s>

<s><lb/>Cur aqu&atail; <lb/>in tubo v<lb/>trinque bi<lb/>ante a&longs;een<lb/>dat aliquan <lb/>tulum.<emph.end type="italics"/></s>

<s id="id000214"><margin.target id="marg21"/>I<emph type="italics"/>n<emph.end type="italics"/> 13. <emph type="italics"/>petit.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Veriùs forta&longs;&longs;e dixeris & attrahi <lb/>pariter & circumpelli: </s>

<s id="id000215">Propo&longs;itio quinta.</s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Vbi igitur inferioris o&longs; o&longs;culi labra &longs;u<lb/>biectam aquam ita attigerint, vt aer &longs;ucce<lb/>dere nequeat, illud nece&longs;&longs;ariò fit, vt a&longs;cen<lb/>dentem aerem aqua &longs;ubiecta con&longs;equatur <lb/>&longs;iue attracta, &longs;iue ex circumpul&longs;ione propul<lb/>&longs;a. </s>

<s>Cum autem hoc à naturâ liquoribus <lb/>comparatum &longs;it, quod &longs;olidis corporibus ad<lb/>hære&longs;cant; vbi aliquid aquæ &longs;ur&longs;um ab aere <lb/>a&longs;cendente eleuatæ, internis fi&longs;tulæ lateribus <lb/>adhæ&longs;erit, iam non deor&longs;um vrget contr&atail; <lb/>vim aéris a&longs;cendentis, qui propterea in reli<lb/>quam aquam non adhære&longs;centem vires &longs;uas <lb/>omnes exercet. </s>

<s id="id000216">Si fuerit proportio primi ad &longs;ecundum producta ex proportio<lb/>ne tertij ad quartum, & quinta ad &longs;extum: erit proportio tertij ad <lb/>&longs;extum producta ex proportionibus primi ad &longs;ecundum, & quar<lb/>ti ad quintum.</s>

<s>At quia in tenui&longs;simâ fi&longs;tu<lb/>lâ cylindrulus aquæ primùm eleuatus ita ferè <lb/>totu<gap/> adhæret fi&longs;tulæ, vt vix in medio relin<lb/>quat capillarem medullam ab aëre &longs;u&longs;tenta<lb/>tam, multò faciliùs pergit in a&longs;cen&longs;u, & alias <pb xlink:href="018/01/137.jpg" pagenum="123"/>aquæ particulas &longs;ecum rapit &longs;ur&longs;um; donec <lb/>demum præter aquam &longs;ponte adhærentem <lb/>lateribus, tantum aquæ ab aere &longs;u&longs;tineatur, <lb/>vt eam dimittere non po&longs;&longs;it, quin ip&longs;e magis <lb/>di&longs;trahatur & rare&longs;cat: id quod natura potiùs <lb/>refugit, quàm permittere tantillæ aquæ <lb/>&longs;u&longs;pen&longs;ionem. </s>

<s>Ni&longs;i fortè malles dicere, a<lb/>quam illam medullarem con&longs;titutam intrà <lb/>aquam lateribus adhærentem iam non conari <lb/>deor&longs;um. </s>

<s id="id000217">Sit proportio a ad b producta ex proportio<lb/><arrow.to.target n="marg22"/><lb/><arrow.to.target n="table5"/><lb/>nibus c ad d, & e ad f, dico quod proportio c ad <lb/>f producitur ex proportione a ad b & d ad e. </s>

<s>Quando verò amplior e&longs;t fi&longs;tulæ <lb/>capacitas, con&longs;tat <expan abbr="a&etilde;rem">aerrem</expan> non tantâ velocita<lb/>te per eam ferri &longs;ur&longs;um cæteris paribus, ac per <lb/>fi&longs;tulam tenuiorem, & præterea cylindrulus <lb/>aquæ &longs;ur&longs;um attractus ampliorem habet ba<lb/>&longs;im, & in minori altitudine habetur tota ea <lb/>quantitas aquæ, quæ valet ab aere &longs;u&longs;tentari: <lb/>hinc fit eò minùs aquam attolli, quò am<lb/>plior e&longs;t fi&longs;tula. </s>

<s id="id000218">In<lb/>terponam d e inter c & f, eritque ex &longs;ecunda pro<lb/>po&longs;itione repetita proportio c ad f producta ex <lb/>tribus proportionibus c ad d, d ad e, e ad f, &longs;ed <lb/>proportiones c ad d, & e ad f producunt pro<lb/><figure id="id.015.01.028.2.jpg" xlink:href="015/01/028/2.jpg"/>portionem a ad b, igitur proportio c ad f produ<lb/>citur ex proportionibus a ad b, & e ad f.<lb/><arrow.to.target n="table6"/></s>

<s>Mitto hìc di&longs;putare an in<lb/>&longs;en&longs;ibilis aquæ expiratio adhærens fi&longs;tulæ, <lb/>vel in eam incurrens, excitet electricam <lb/>vitri expirationem; an verò ea fi&longs;tulam le<lb/>ui&longs;&longs;imè humectans, dum attactu illo &longs;tatim <lb/>concre&longs;cit, &longs;tatim &longs;ubiectam aquam attrahat <lb/>vt &longs;ibi veniat, quemadmodum in calamo <lb/>&longs;criptorio &longs;æpe ob&longs;eruare e&longs;t, quando atra<lb/>mento valdè diluto vtimur; vix enim hu<lb/>mens calamus &longs;ubiectum atramentum con<lb/>tingit, cum eo confe&longs;tim imbuitur. </s>

<s>Hæc <pb xlink:href="018/01/138.jpg" pagenum="124"/>&longs;cilicet nos longiùs, quàm par &longs;it, abdu<lb/>cerent. </s>

<table>

<s>Illud certum e&longs;t, quod aqua &longs;ponte <lb/>fluens ita &longs;emper ad humiliora loca delabi<lb/>tur, vt à &longs;phæricâ &longs;uperficie non recedat, &longs;i <lb/>res Phy&longs;icè &longs;altem con&longs;ideretur. </s>

<table.target id="table5"/>

<row>

<s>Atque adeò <lb/>id tibi vltrò concedens audire expecto, quid <lb/>indè conficias. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Non eandem e&longs;&longs;e &longs;emper aquæ &longs;u<lb/>perficiem; quò enim maioribus à centro in<lb/>teruallis &longs;emouetur, eò propiùs æquata&mtail; <lb/>planitiem æmulatur; at centro vicinior ma<lb/>iori conuexitate inflectitur; hìc &longs;cilicet mi<lb/>noris, ibi maioris &longs;phæræ portio e&longs;t. </s>

</row>

<row>

<s>Iam <lb/>verò vt pla<lb/>niùs & aper<lb/>tiùs verbis <lb/><figure id="id.018.01.138.1.jpg" xlink:href="018/01/138/1.jpg"/><lb/><arrow.to.target n="note61"/><lb/>complectar, <lb/>quod volo, <lb/>ex Graphi<lb/>de <expan abbr="&longs;ub&longs;idi&utilde;">&longs;ub&longs;idium</expan> <lb/><expan abbr="petã">petam</expan>. </s>

<s>Sit pro <lb/>globo terra<lb/>queo circu<lb/>lus ABCD, <lb/>cuius cen<lb/>trum T <expan abbr="cõ-gruat">con<lb/>gruat</expan> vniuer&longs;i centro, & BAE mare Hyper<lb/><gap/>oreum, FCD Oceanus Indicus aut Æthio<pb xlink:href="018/01/139.jpg" pagenum="125"/>picus, vel alius, quamcunque demum &longs;or<lb/>tiatur appellationem. </s>

</row>

<row>

<s>Ambigi non pote&longs;t, <lb/>quin maria hæc in eadem &longs;phæricâ &longs;uperficie <lb/>exi&longs;tant, quandoquidem ab vniuer&longs;i centro <lb/>T paribus interuallis di&longs;iunguntur. </s>

<s>At &longs;i <lb/>tellurem ab vniuer&longs;i centro (quod, ne i&ntail; <lb/>vocabulis laboremus, centrum grauiu&mtail; <lb/>liceat appellare, cum eius rationem habue<lb/>rit natura &longs;uum cuique corpori locum tri<lb/>buens) remotam intelligamus, ita vt illius <lb/>quidem centrum &longs;it T, centrum verò gra<lb/>uium &longs;it V; non eadem manere pote&longs;t v<lb/>triu&longs;que maris &longs;uperficies; &longs;ed Hyperboreum <lb/>&longs;ub&longs;idere magis & explicari debet, Indicum <lb/>verò a&longs;&longs;urgere, Cum enim aqua A remo<lb/>tior &longs;it quàm B & E à centro V, pote&longs;t de<lb/>&longs;cendere, nec con&longs;i&longs;tet, ni&longs;i vbi fuerit &longs;u<lb/>perficies BIE. </s>

</row>

<row>

<s>Contra autem aqua F & D <lb/>remotior e&longs;t quàm C à centro V; pote&longs;t <lb/>igitur ver&longs;us C de&longs;cendere; & relicto loco <lb/>ad F & ad D, a&longs;&longs;urget<gap/> in H, & erit &longs;uper<lb/>ficies FHD maiorem habens conuexita<lb/>te&mtail;. </s>

<s><margin.target id="note61"/><emph type="italics"/>LXI <lb/>Si tellus a<lb/>liò trahere<lb/>tur, aqu&atail; <lb/>mutaret fi<lb/>guram.<emph.end type="italics"/></s>

</row>

<row>

<s>Quod &longs;i ad latus iaceat aqua, vt MNO, <lb/>factâ translatione centri ex Vin T, vtique <lb/>ex M versùs O de&longs;cendet; &longs;ed &longs;i mons OS <lb/>prohibeat, demùm con&longs;i&longs;tet aqua circa vni<lb/>uer&longs;i centrum V in &longs;uperficie &longs;phæricâ RNS. <pb xlink:href="018/01/140.jpg" pagenum="126"/>Idemque d&etail; <lb/><figure id="id.018.01.140.1.jpg" xlink:href="018/01/140/1.jpg"/><lb/>cæteris e&longs;to iu<lb/>dicium; nulla <lb/>&longs;iquidem repe<lb/>riri po&longs;&longs;et a<lb/>quarum con<lb/>gregatio, quæ <lb/>tellure transla<lb/>tâ, &longs;e aliam in <lb/><expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> non <lb/>conglobaret, <lb/>altioribus par<lb/>tibus in inferiorem locum delap&longs;is. <lb/><arrow.to.target n="note62"/></s>

<s><margin.target id="note62"/><emph type="italics"/>LXII <lb/>Noua hypo<lb/>the&longs;is mari<lb/>ni æstus in<lb/>dicatur, &longs;ed <lb/>non proba<lb/>tur.<emph.end type="italics"/></s>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Igno&longs;ce, quæ&longs;o, interpellanti. </s>

<s>Ne<lb/>&longs;cio quam mihi inijcis &longs;u&longs;picionem nouæ <lb/>hypothe&longs;is, qua citra omnem telluris verti<lb/>ginem &longs;iuè in orbe annuo, &longs;iuè circa &longs;uum <lb/>axem, marinus æ&longs;tus explicari po&longs;&longs;et: &longs;i ni<lb/>mirum terræ centrum lento ac tenui motu <lb/>vltro citroque commeans centro grauium<lb/>congrueret &longs;olùm in medio fluxu aut reflu<lb/>xu. </s>

</row>

</table>

<s>Si enim T accedat ad V, aqua incipit <lb/>ex S refluere ver&longs;us M, vbi aqua &longs;emper au<lb/>getur, quò magis centrum T recedit ab V <lb/>in X: iterumque fluit ex M in O, cum cen<lb/>trum ab X recedens in V & in T &longs;ua per <lb/>ve&longs;tigia eò remeat, vnde di&longs;ce&longs;&longs;it, &longs;eruatâ<lb/>que in motu reciprocando con&longs;tantiâ, al<pb xlink:href="018/01/141.jpg" pagenum="127"/>ternas fluxûs, & refluxûs vices efficit in ad<lb/>uer&longs;is litoribus. </s>

<table>

<table.target id="table6"/>

<s>Quod &longs;i in oppo&longs;itis eiu&longs;<lb/>dem aluei ripis eodem tempore fluxus con<lb/>tingat aut refluxus, vt in B & E, aut in F & <lb/>D; tunc opinari quis po&longs;&longs;et mare illud eam <lb/>habere po&longs;itionem, vt in illud incidat linea <lb/>motûs, quæ ex centro grauium per terræ <lb/>centrum ducitur: dum enim aqua deprimitur <lb/>ex A in I, augetur in B & E, &longs;i litus fluxui <lb/>ob&longs;tet, aut vlteriora &longs;patia occupat in P & K: <lb/>dum verò a&longs;&longs;urgit ex C in H, minuitur in F & <lb/>D. </s>

<row>

<s>Porrò alternâ hac nutantis terræ mo<lb/>tione non magis eius &longs;tabilitas vacillaret, <lb/>quàm illiùs firmitati ob&longs;it trepidationis mo<lb/>tus à pleri&longs;que admi&longs;&longs;us ob variam centri <lb/>grauitatis po&longs;itionem: &longs;tare &longs;iquidem terra <lb/>dicitur, quæ &longs;uo ex loco non decedit, quam<lb/>quam in eo &longs;uæ diametri particulam (1/4000000) <lb/>percurrat. </s>

</row>

<row>

<s>Finge enim motûs extremos <lb/>terminos T & X non ampliùs pa&longs;&longs;um vnum <lb/>di&longs;tare à grauium centro V: tanta e&longs;t aqua<lb/>rum in immen&longs;um patentium copia, vt èxi<lb/>guâ inclinatione, quam motu illo acquire<lb/>rent, dilabentes æ&longs;tum non exiguum effi<lb/>cerent: qui tamen in lacubus, angu&longs;tiori<lb/>busque alueis ob minorem aquarum copiam <lb/>non perciperetur. </s>

</row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Blandiuntur i&longs;thæc facilè mentis <pb xlink:href="018/01/142.jpg" pagenum="128"/>oculis: &longs;ed &longs;i rem penitiùs intro&longs;picere per <lb/>otium liceret, haud &longs;atis &longs;cio, quàm aptè <lb/>commentum hoc cum marini æ&longs;tûs phæno<lb/>menis cohæreret. </s>

<row>

<s>Nec pauca in hanc &longs;en<lb/>tentiam afferri po&longs;&longs;ent: &longs;ed non vacat his im<lb/>morari, ne longiùs ab in&longs;tituto digrediar, <lb/>aut &longs;ortè, quæ e&longs;t fugacis memoriæ incon<lb/>&longs;tantia, excidant, quæ nunc animo obuer<lb/>&longs;antur. </s>

</row>

<row>

<s>De mari certè, quod Kiùn, in In<lb/>&longs;ulâ Hainan, alluit, illud notatu dignum <lb/>&longs;cribunt Sinæ Geographi, quod maris æ&longs;tum <lb/>Diurnum non &longs;entiat, &longs;ed per dimidiam <lb/>men&longs;is partem versùs Ortum, per reliquam <lb/>dimidiam versùs Occa&longs;um fluat. </s>

</row>

<row>

<s><lb/>Quod in vertice montis Hucùng in Fokien <lb/>Prouinciâ puteus e&longs;t (Hiai nomen e&longs;t) cuius <lb/>aqua æ&longs;tum marinum &longs;uo acce&longs;&longs;u & rece&longs;&longs;u <lb/>refert. </s>

</row>

<row>

<s>Adde huic fontem prope Nuikiang <lb/>in Suchuen Prouinciâ, quem modò a&longs;cen<lb/>dentem modò de&longs;cendentem æ&longs;tûs marini <lb/>horas adeò procul à mari &longs;equi ob&longs;eruatum <lb/>e&longs;t. </s>

</row>

<s>Hos autem æ&longs;tus ex motu illo orbis, <lb/>quem innuebas, non oriri palàm e&longs;t. </s>

<row>

<s>Quòd <lb/>&longs;i ex tam remotâ Sinatum regione petitum <lb/>argumentum reijcis, mihi &longs;anè con&longs;tat non <lb/>hanc e&longs;&longs;e æ&longs;tûs effectricem cau&longs;am; nam <lb/>ip&longs;a quoque flumina, terræ centro accedente <lb/>ad centrum grauitatis aut recedente, diebus <pb xlink:href="018/01/143.jpg" pagenum="129"/>&longs;ingulis cursûs velocitatem incitarent re<lb/>mitterentque, aut etiam &longs;uum in caput re<lb/>laberentur; id quod nondum licuit ob&longs;erua<lb/>re. </s>

</row>

<row>

<s>Præterquam quod vix dixeris, quo mo<lb/>uente tellus vici&longs;&longs;im commearet, citrà fabu<lb/>larum figmenta. </s>

</row>

<s>At &longs;i contingere po&longs;&longs;et, vt machinarum </s>

</table>

<s><arrow.to.target n="note63"/><lb/>ope telluris centrum ex V in T transferretur, <lb/>fluminis GL aqua ex G reflueret in L, & in <lb/>eundem alueum &longs;e in&longs;inuaret mare v&longs;qu&etail; <lb/>dum tota aquæ &longs;uperficies continua in &longs;phæ<lb/>ram inflexa con&longs;i&longs;teret, cum non haberet, <lb/>quò de&longs;cenderet. </s>

<s id="id000220">Propo&longs;itio &longs;exta.</s>

<s>Hinc illud fit, quod cum <lb/>maria omnia (ni&longs;i fortè Ca&longs;pium velis exci<lb/>pere, cui tamen per &longs;ubterraneos cuniculos <lb/>cum Ponto Euxino communio e&longs;t) &longs;ibi in<lb/>uicem continuata iunctaque &longs;int, terrâ in <lb/>partem vnam translatâ, aquæ ferè omnes in <lb/>oppo&longs;itam recederent, vel per patentem al<lb/>ueum dilabentes, vel etiam exundantes: <lb/>idem quippe tunc aquarum conceptaculis <lb/>contingeret, ac &longs;i nunc vas liquore qua&longs;i <lb/>plenum magis & magis inclinaretur, totus <lb/>enim demùm liquor effunderetur. </s>

<s id="id000221">Ex trecentis &longs;exaginta modis producenda<lb/>rum proportionum triginta &longs;ex tantum e&longs;&longs;e ne<lb/>ce&longs;&longs;arios.<lb/><arrow.to.target n="table7"/></s>

<s>Quarè <lb/>vniuer&longs;a ferè aqua &longs;uperiorem locum relin<lb/>quens in H conflueret eò velociùs, quò lon<lb/>giùs telluris centrum T recederet ab V cen<lb/>tro grauium &longs;eu vniuer&longs;i. </s><pb xlink:href="018/01/144.jpg" pagenum="130"/>

<table>

<s><margin.target id="note63"/><emph type="italics"/>LXIII <lb/>Tellur&etail; <lb/>translata fe<lb/>rè tota aqua <lb/>ab ea &longs;eiun<lb/>geretur.<emph.end type="italics"/></s>

<table.target id="table7"/>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> In eo igitur, &longs;i quid video, machi<lb/>nalis motionis, qua terra transferretur, faci<lb/>litatem con&longs;tituis, quod eo ip&longs;o tempore, <lb/>quo terra &longs;upra FVD planum (quod ho<lb/>rizontale vocetur) attolleretur, aqua de<lb/>&longs;cenderet; ac proinde &longs;uperioris partis pon<lb/>dus minueretur, donec demum terra pro<lb/>cul à centro translata totius ferè aquæ ponde<lb/>re leuaretur, quæ circa vniuer&longs;i centrum V <lb/>aqueum in globum &longs;uis &longs;e nutibus confor<lb/>maret. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita planè: nec illud quidem con<lb/>temnendum e&longs;&longs;et compendium, &longs;i ponderis <lb/>aquæ rationes ineamus. </s>

</row>

<row>

<s>Quotam enim ter<lb/>raquei huius globi partem con&longs;tituendam <lb/>e&longs;&longs;e aquam cen&longs;es? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Res e&longs;t, in qua Geometriæ apices <lb/>per&longs;equi non po&longs;&longs;umus, cum exactâ ma<lb/>rium omnium notitiâ careamus, & planè <lb/>varia &longs;it aquarum profunditas: qua propter <lb/>coniecturis contentos nos e&longs;&longs;e oportet. </s>

</row>

<row>

<s>Et <lb/>quidem quod ad aquarum &longs;uperficiem per<lb/>tinet, eas arbitror æquis cum terrâ portioni<lb/>bus globi conuexitatem di&longs;pertire: altitudi<lb/>nem verò adeò incon&longs;tantem reperio, vt &longs;i <lb/>profunditates maiores cum minoribus com<lb/>pen&longs;emus, vix vltra milliaris dodrantem aut <lb/>integrum milliare altitudini in vniuer&longs;um <pb xlink:href="018/01/145.jpg" pagenum="131"/>tribuendum exi&longs;time&mtail;. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Qúæ &longs;entis, approbo; immen&longs;æ <lb/><arrow.to.target n="note64"/><lb/>&longs;iquidem illæ altitudines & aby&longs;&longs;i aquarum <lb/>rari&longs;&longs;imæ &longs;unt, quæ bolide nullâ explorari <lb/>po&longs;&longs;int. </s>

</row>

<row>

<s>Idcircò libentiùs vniuersè altitu<lb/>dinem &longs;olùm dodrantalem aquis tribuo, mil<lb/>liari a&longs;&longs;umpto pro a&longs;&longs;e. </s>

<s>Iam, &longs;i placet, <lb/>aquæ grauitatem ad calculos reuocemus, & <lb/>globi perimetrum accipiamus, quam olim <lb/>Mer&longs;ennus, nobis non repugnantibus, con<lb/>&longs;tituebat mill. Rom. ant. </s>

</row>

<row>

</row>

<row>

<s>25941. Perime<lb/>tro con&longs;titutâ, diametrum &longs;ic inquiro ex ra<lb/>tionibus Vietæ: Vt 31415.926536 ad <lb/>10000.000000, ita maximi circuli periphe<lb/>ria mill. 25941 ad diametrum mill. 8257<lb/>pa&longs;&longs;. </s>

</row>

</table>

<s>276. Igitur &longs;i diameter in peripheriam <lb/>ducatur, producetur &longs;phærica &longs;uperficies <lb/>mill. quadrat. </s>

<s id="id000222">Per quartam enim proportio a ad b produ<lb/><arrow.to.target n="marg23"/><lb/>citur bifariam, & ex c ad d, & e ad f, & ex c ad f, & <lb/>e ad d. </s>

<s id="id000223">& per præcedentem c ad f producitur ex <lb/>a ad b, & d ad e, & per quartam rur&longs;us ex a ad e, <lb/>& d ad b. </s>

<s id="id000224">Et per præcedentem rur&longs;us a ad e ex c <lb/>ad f & b ad d, igitur per quartam eadem produ<lb/>cetur ex c ad d & b ad f. </s>

<s id="id000225">Quare per præceden<lb/>tem c ad f ex a ad e, & d ad b, & ita di&longs;ponemus <lb/>hos modos in tabula. </s>

<s>214.201996. pa&longs;&longs;. </s>

<s id="id000226">Vides etiam <lb/><arrow.to.target n="table8"/><lb/><figure id="id.015.01.028.4.jpg" xlink:href="015/01/028/4.jpg"/>aliquos modos non produci, ut pri<lb/>mi ad quartum nec ad &longs;extum, & li<lb/>quet, quòd cùm &longs;int quindecim o<lb/>mnes modi qui produci po&longs;&longs;e intelli<lb/>guntur, & nouem tantum producan<lb/>tur &longs;ex e&longs;&longs;e, qui non producuntur, quos <lb/>&longs;eor&longs;um in tabula coniunxi. </s>

<s id="id000227">Et con<lb/>&longs;tat etiam, quod totidem conuer&longs;i &longs;ci<lb/>licet decem octo <expan abbr="produc&utilde;tur">producuntur</expan>, de qui<lb/>bus diximus, ut &longs;int omnes triginta <lb/>&longs;ex, qui con&longs;tat ex duabus propo&longs;i<lb/>tionibus præmi&longs;sis, & hac tertia, <expan abbr="quã">quam</expan> <lb/>adiungemus &longs;cilicet, quòd propor<lb/>tio primi ad tertium producatur ex <lb/>proportionibus <expan abbr="&longs;ec&utilde;di">&longs;ecundi</expan> ad quartum, <lb/>& quinti ad <expan abbr="&longs;ext&utilde;">&longs;extum</expan>. </s>

<s id="id000228">Hoc enim ex præ<lb/>cedentibus non liquet: benè liquet <lb/>permutatis ordinibus, quod &longs;i pro<lb/>portio primi ad tertium producitur,

<s><lb/>716000: Huius autem &longs;emi&longs;sis mill. 107. <lb/>100998. pa&longs;&longs;. </s>

<pb pagenum="9 [=10]" xlink:href="015/01/029.jpg"/>quod etiam propor<lb/><figure id="id.015.01.029.1.jpg" xlink:href="015/01/029/1.jpg"/><arrow.to.target n="marg24"/><lb/>tio primi ad <expan abbr="quint&utilde;">quintum</expan>. <lb/></s>

<s id="id000229">Nam tertium, & quin <lb/>tum, item que quartum, <lb/>& &longs;extum non <expan abbr="differ&utilde;t">diffe<lb/>runt</expan> ni&longs;i ordine uolun<lb/>tario. </s>

<s id="id000230">Ergo interpo&longs;i<lb/>to e inter a, & c per &longs;e<lb/>cundam propo&longs;itio<lb/>nem proportio a ad c <lb/>producitur ex proportionibus a ad <lb/>e, & e ad c, ut ex demon&longs;tratis in præ<lb/>&longs;enti proportio a ad c producitur ex <lb/>c ad f & b ad d. </s>

<s>358000. erit &longs;uperficies a<lb/>quæ. </s>

<s id="id000231">Proportio ergo a ad <lb/>c producitur ex proportionibus e <lb/>ad c & c ad f & b ad d, at e ad c & c ad <lb/>f producunt eam, quæ e&longs;t e ad f per <lb/><expan abbr="&longs;ec&utilde;dam">&longs;ecundam</expan> propo&longs;itionem. </s>

<s id="id000232">Igitur pro<lb/>portio a ad c producitur ex propor<lb/>tionibus b ad d &longs;ecundi ad quartum, <lb/>& e ad f quinti ad &longs;extum. </s>

<s><margin.target id="note64"/><emph type="italics"/>LXIV <lb/>Totius a<lb/>quæ quanti<lb/>tas, & gra<lb/>uitas inqui<lb/>ritur.<emph.end type="italics"/></s>

<s id="id000233">Hæc Al<lb/>chindus in &longs;uo libello: &longs;ed licet inge<lb/>nio &longs;a ualde: parum <expan abbr="tam&etilde;">tamen</expan> utilia olim <lb/><expan abbr="erãt">erant</expan> nece&longs;&longs;aria ad intelligendum ma<lb/>gnam <expan abbr="cõpo&longs;itionem">compo&longs;itionem</expan> Ptolem&etail;i, nunc <lb/>po&longs;tquam Heber has &longs;ex quantita<lb/>tes traduxit ad quatuor, pror&longs;us hæc <lb/>&longs;cientia ulli u&longs;ui e&longs;&longs;e de&longs;ijt.<lb/><arrow.to.target n="table9"/></s>

<s>Et vt breuitati &longs;eruiam, duco inuentam <lb/>aquæ &longs;uperficiem in altitudinem con&longs;titutam <lb/>mill.3/4: ne &longs;cilicet longioribus ambagibus in <lb/>quiram totius globi &longs;oliditatem. </s>

<s>Deinde in<lb/>&longs;titutâ analogiâ, <emph type="italics"/>vt cubus diametri inuentæ <lb/>ad cubum eiu&longs;dem diametri mulctatæ dodran<lb/>te milliaris, ita &longs;oliditas &longs;phæræ ex inuenta dia<emph.end type="italics"/><pb xlink:href="018/01/146.jpg" pagenum="132"/><emph type="italics"/>metro ad &longs;oliditatem alterius &longs;phæræ,<emph.end type="italics"/> inue<lb/>niam harum &longs;phærarum differentiam, cuius <lb/>differentiæ &longs;emi&longs;&longs;is aquarum &longs;oliditati tri<lb/>buatur. </s>

<s>Neque enim e&longs;t operæ pretium <lb/>nos ip&longs;os hoc labore conficere; quandoqui<lb/>dem vix di&longs;creparet inuentus numerus ab eo, <lb/>qui ex ductu &longs;uperficiei in altitudinem pro<lb/>dibit. </s>

<s id="id000235"><margin.target id="marg24"/>Modi qui <expan abbr="nõ">non</expan> <lb/>producuntur <lb/>pri. ad quartu <lb/>pri. ad &longs;extum <lb/>&longs;ec. ad <expan abbr="terti&utilde;">tertium</expan> <lb/>&longs;ec. ad <expan abbr="quint&utilde;">quintum</expan> <lb/>tert. </s>

<s id="id000236">ad quint. <lb/></s>

<s>Duco igitur aquæ &longs;uperficiem mill. <lb/>107.100998 pa&longs;&longs;. </s>

<s id="id000237">quart. </s>

<s id="id000238">ad &longs;ext.</s>

<table>

<s>358000 in altitudinem <lb/>mill. 3/4, & prodit &longs;oliditas milliarium cubi<lb/>corum 80.325748, & pa&longs;&longs;. </s>

<table.target id="table8"/>

<row>

<cell/>

<cell>Primi ad &longs;ecundum.</cell>

<s>cubic. </s>

</row>

<row>

<cell>tertij ad <expan abbr="quart&utilde;">quartum</expan>, & quin</cell>

<s>Inuentâ &longs;oliditate grauitatem inue&longs;tigo: <lb/>& quamuis &longs;ciam marinam aquam ob ad<lb/>mixtam &longs;alis copiam grauiorem e&longs;&longs;e aquâ <lb/>communi; vt tamen compen&longs;etur, &longs;i quid <lb/>plus æquo tributum e&longs;t &longs;uperficiei, aut pro<lb/>funditati, communem aquæ grauitatem ac<lb/>cipio; Et quoniam milliaribus Romanis an<lb/>tiquis vtimur, pondus pedis cubici antiqui, <lb/>hoc e&longs;t amphoræ aquâ plenæ, e&longs;t lib.

</row>

<row>

80. <lb/>Igitur quia milliare cubicum con&longs;tat pedi<lb/>bus &longs;olidis 125000.000000, hic numerus per <lb/>lib.

<cell/>

<cell>ti ad &longs;extum.</cell>

80 ductus dabit libras 10.000000.000000 <lb/>grauitatem &longs;ingularium milliarium cubico<lb/>rum aquæ. </s>

</row>

<row>

<s>Iam &longs;i &longs;oliditas mill. 80.325748 <lb/>pa&longs;&longs;. </s>

<cell>tertij ad &longs;extum, & quin</cell>

</row>

<row>

<s>768.500000. ducatur per libras 10. <lb/>000000.000000. erit totius aquæ pondus lib. <pb xlink:href="018/01/147.jpg" pagenum="133"/>803.257487.685000.000000. <lb/><arrow.to.target n="note65"/></s>

<cell/>

<cell>ti ad quartum.</cell>

<s><margin.target id="note65"/><emph type="italics"/>LXV <lb/>Pondus ter<lb/>reni globi <lb/>quàm nota<lb/>biliter mi<lb/>nueretur ex <lb/>aquæ &longs;ece&longs;<lb/>&longs;ione.<emph.end type="italics"/></s>

</row>

<row>

<s>Hoc autem pondus ex totius globi graui<lb/>tate demptum faciliorem efficeret terræ <lb/>motionem, vbi iam tota terra aliquo u&longs;que <lb/>ab vniuer&longs;i centro rece&longs;&longs;i&longs;&longs;et, ibique aquam <lb/>ferè totam, quæ nunc in globi &longs;uperfici&etail; <lb/>fluit, reliqui&longs;&longs;et. </s>

<cell/>

<cell>Primi ad tertium.</cell>

<s>Sed quid &longs;i in maris fundo <lb/>amplæ pateant voragines, per quas in tellu<lb/>ris cuniculos aqua &longs;e in&longs;inuer, ingentesque <lb/>aby&longs;&longs;os creet? </s>

</row>

<row>

<s>An non per hiatus eo&longs;dem <lb/>aqua &longs;e exoneraret tellure in altum &longs;ublatâ ? <lb/>Ex quo & illud con&longs;equeretur, quod in im<lb/>men&longs;a illa hydrophylacia aër tenuisque va<lb/>por defluenti aquæ &longs;uccederet, fieretque to<lb/>tius compo&longs;itæ molis grauitas &longs;ecundùm <lb/>&longs;peciem minor. </s>

<cell>&longs;ecundi ad quartum, &</cell>

<s>Verùm terræ vi&longs;cera n&etail; <lb/>&longs;crutemur; aquasque illas hypogæas &longs;uis in <lb/>conceptaculis &longs;tagnantes relinquamus. </s>

</row>

<row>

<s>A<lb/>qua certè, quæ terræ faciem nunc alluit, <lb/>tanta e&longs;t, vt &longs;i eam di&longs;ce&longs;&longs;i&longs;&longs;e in locum alium <lb/>à tellure animo concipiamus, continuo non <lb/>exigua &longs;anè momenta ex globo terraqueo <lb/>dempta intelligamus. </s>

<cell/>

<cell>quinti ad &longs;extum.</cell>

<s>Et &longs;i ad manum e&longs;&longs;et <lb/>&longs;chedula, in qua Mer&longs;ennus rationes dige&longs;&longs;it, <lb/>quibus telluris grauitatem nudius tertius in<lb/>ue&longs;tigabat, numerum hunc librarum ex illo <lb/>&longs;ubducentibus con&longs;taret non planè contem<lb/>nendum e&longs;&longs;e hoc laboris compendium. </s><pb xlink:href="018/01/148.jpg" pagenum="134"/>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Secum illam tulit Mer&longs;ennus: &longs;ed <lb/>non e&longs;t opus grauitatem hanc aquæ cum to<lb/>tius globi pondere comparare, &longs;atis enim per <lb/>&longs;e patet, quàm in&longs;ignis foret i&longs;ta ponderis <lb/>dece&longs;&longs;io. </s>

<cell>&longs;ecundi ad &longs;extum, &</cell>

<s>Vnum autem hìc ob&longs;eruo, quod </s>

</row>

<row>

<s><arrow.to.target n="note66"/><lb/>nimirum, quamuis ingens hæc ponderis di<lb/>minutio tunc &longs;olùm contingeret, quando <lb/>terra e&longs;&longs;et ab aquis diuul&longs;a, & ab vniuer&longs;i <lb/>centro V tota abe&longs;&longs;et, emolumentum tamen <lb/>non paruum faceret in motione a&longs;&longs;iduus a<lb/>quarum fluxus in partem oppo&longs;itam. </s>

<cell/>

<cell>quinti ad quartum.</cell>

<s>Si enim <lb/>globus plano FD &longs;ectus eò transferatur, vt <lb/>vniuer&longs;i <expan abbr="c&etilde;-trum">cen<lb/>trum</expan> V i&ntail; <lb/><figure id="id.018.01.148.1.jpg" xlink:href="018/01/148/1.jpg"/><lb/><expan abbr="eod&etilde;">eodem</expan> &longs;it pla<lb/>no, non &longs;o<lb/>lùm <expan abbr="nõ">non</expan> per<lb/>cipitur toti<lb/>us globi, &longs;ed <lb/>ne totius qui<lb/>dem <expan abbr="fegm&etilde;-ti">fegmen<lb/>ti</expan> FAD gra<lb/>uitas: <expan abbr="quan-doquid&etilde;">quan<lb/>doquidem</expan> &longs;eg<lb/>mentum FA <lb/>D de or&longs;um non conatur contra vim &longs;ur&longs;um <lb/>mouentem aut &longs;u&longs;tinentem, ni&longs;i iuxta mo<lb/>menta ponderis, quibus &longs;uperat moment&atail; <pb xlink:href="018/01/149.jpg" pagenum="135"/>&longs;egmenti FCD oppo&longs;ito conatu in idem cen<lb/>trum V nitentis, ne indè remoueatur. </s>

</row>

<row>

<s>At<lb/>qui aquæ pars aliqua &longs;upra planum FD exi<lb/>&longs;tens infra illud de&longs;cendit; igitur in &longs;egmen<lb/>to FAE minuitur pondus, & fit ponderis ac<lb/>ce&longs;&longs;io &longs;egmento FCD; quarè multò minor <lb/>e&longs;t differentia grauitatum inter &longs;egmenta, ac <lb/>proinde minor in mouendo labor, aut in &longs;u<lb/>&longs;tinendo. </s>

<cell/>

<cell>Primi ad quintum.</cell>

<s>Quemad modum enim &longs;i in libræ <lb/>lancibus po&longs;ita fuerint pondera inæqualia, & <lb/>exlance grauiore pars ponderis transferatur <lb/>in alteram lancem, propiùs accedunt ad <lb/>æquilibrium, & faciliùs &longs;u&longs;tinetur lanx gra<lb/>uior; Sic etiam pondus aliquod aquæ ex <lb/>&longs;egmento maiore FAD tran&longs;latum in &longs;eg<lb/>mentum minus FCD, efficit minorem <lb/>ponderum inæqualitatem, ac proinde minor <lb/>grauitas percipitur à mouente globum, vel <lb/>&longs;u&longs;tinente. </s>

</row>

<row>

<s><margin.target id="note66"/><emph type="italics"/>LXVI <lb/>Facilitas <lb/>mouendi ter<lb/>ram ex de<lb/>fluxu aqua<lb/>rum.<emph.end type="italics"/></s>

<cell>&longs;ecundi ad <expan abbr="&longs;ext&utilde;">&longs;extum</expan>, & ter</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Opportunè &longs;ugge&longs;&longs;i&longs;ti, quæ m&etail; <lb/>aliò ab&longs;tractum pror&longs;us effugerant. </s>

</row>

<row>

<s>Thales <lb/>Mile&longs;ius &longs;uo illo ingenti nauigio me longiùs <lb/>abduxerat. </s>

<cell/>

<cell>tij ad quartum.</cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quid illud e&longs;t? </s>

</row>

<row>

<s>an putas terra&mtail; <lb/>aquis innatare, aut po&longs;&longs;e pari facilitate atque <lb/>nauigium trahi &longs;eu impelli? </s>

<cell>&longs;ecundi ad quartum, &</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Minimè omnium: &longs;ed ne&longs;cio quæ <lb/>mens mihi incidit, vt inciperem &longs;u&longs;picari, <pb xlink:href="018/01/150.jpg" pagenum="136"/>an telluris centro ex V<gap/>in T machinationi<lb/>bus translato, & aquâ in oppo&longs;itam partem <lb/>confluente, fieri po&longs;&longs;et, vt aquæ terra inna<lb/>taret, aut &longs;altem aliquid de grauitare remit<lb/>teret. </s>

</row>

<row>

<s>Id quod opportuniore &longs;chemate ex<lb/>hibeo. </s>

<cell/>

<cell>tertij ad &longs;extum.</cell>

<s>Sit idem terræ globus ABCE, cu<lb/>ius centrum T non congruat ampliùs cum <lb/>centro V. </s>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> At ecce Mer&longs;ennum in ip&longs;o tem<lb/>pore. </s>

<cell/>

<cell>Secundi ad quartum.</cell>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> In facinore manife&longs;to deprehen&longs;i <lb/>p&oelig;nas dabitis, boni viri. </s>

</row>

<row>

<s>Nullus e&longs;t infi<lb/>ciandi locus. </s>

<cell>primi ad tertium, & &longs;ex</cell>

<s>Graphium adhuc tenet Gul<lb/>dinus; Galilæus cubito incumbens attentus <lb/>operam dabat. </s>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Salue amicum caput. </s>

<cell/>

<cell>ti ad quintum.</cell>

<s>Quicquid in <lb/>nobis e&longs;t criminis, animaduertatur; &longs;ed te <lb/>iudice. </s>

</row>

<row>

<s>Dabimus, quas volueris p&oelig;nas. </s>

<cell>primi ad quintum, et &longs;ex</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vtique leues, &longs;i fuerint peccato <lb/>pares. </s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Vos nunquam &longs;atis de hoc apud <lb/>me purgabitis, quod ante condictam mihi <lb/>horam conueneritis, amæna &longs;cientiarum <lb/>&longs;patia, me prætermi&longs;&longs;o, percurrentes. </s>

<cell/>

<cell>ti ad tertium.</cell>

<s>Ve<lb/>niam non impetrabitis, ni&longs;i me illicò in &longs;ua<lb/>ui&longs;&longs;imi docti&longs;&longs;imique ve&longs;tri &longs;ermonis con<lb/>&longs;ortium admittentes probaueritis vos mihi <lb/>ve&longs;tra cogitata non inuidi&longs;&longs;e, </s><pb xlink:href="018/01/151.jpg" pagenum="137"/>

</row>

<row>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Præclarè nobi&longs;cum agitur, te iudicè. </s>

<cell/>

<cell>Secundi ad &longs;extum.</cell>

<s><lb/>Culpâ vacamus: nam præmium nobis, non <lb/>p&oelig;na decernitur. </s>

</row>

<row>

<s>Quarè rumpe moras, Gul<lb/>dine, & quæ nobis e&longs;&longs;et di&longs;putatio, edi&longs;<lb/>&longs;ere. </s>

<cell>primi ad <expan abbr="quint&utilde;">quintum</expan>, & quar</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ex ingenitâ aquarum propen&longs;io<lb/>ne, qua &longs;emper ad ima delabuntur, animad<lb/>uertebamus oriri po&longs;&longs;e, vt &longs;i telluris globus <lb/>Archimedæis machinationibus extra vniuer&longs;i <lb/>centrum transferretur, aquæ in oppo&longs;itam <lb/>motui partem delabentes, vt fierent centro <lb/>viciniores, minùs grauem relinquerent &longs;u<lb/>periorem terræ portionem. </s>

</row>

<row>

<s>Si enim e&longs;&longs;et <lb/>ABCE terræ globus, cuius centrum T non <lb/>congrueret centro V, quod vniuer&longs;i, aut &longs;al<lb/><figure id="id.018.01.151.1.jpg" xlink:href="018/01/151/1.jpg"/><lb/>tem <expan abbr="graui&utilde;">grauium</expan> <lb/><expan abbr="elementari&utilde;">elementarium</expan> <lb/>centrum &longs;ta</s>

<cell/>

<cell>ti ad tertium.</cell>

<s><lb/>tuitur, aquæ <lb/>omnes, qui<lb/>bus liber&atail; <lb/>pateret ad <lb/><expan abbr="fluend&utilde;">fluendum</expan> via, <lb/><expan abbr="de&longs;cender&etilde;t">de&longs;cenderent</expan> <lb/>ver&longs;us C, vt <lb/>ad centrum <lb/>V propiùs <lb/>accederent, <pb xlink:href="018/01/152.jpg" pagenum="138"/>& in &longs;phæricâ demum &longs;uperficie FHD pari<lb/>bus radijs à centro V remota con&longs;i&longs;terent. </s>

</row>

<row>

<s><lb/>Cum itaque &longs;uperiori &longs;egmento fieret pon<lb/>deris aquæ dece&longs;&longs;io, inferiori autem acce&longs;<lb/>&longs;io, aliquod haberetur in perficiendâ mo<lb/>tione compendium: Hæc verò di&longs;&longs;erenti<lb/>bus nobis incidit &longs;u&longs;picio, an fortè continge<lb/>re po&longs;&longs;et, aquis in partem vnam delap&longs;is <lb/>terram innatare. </s>

<cell>primi ad <expan abbr="terti&utilde;">tertium</expan>, & quar</cell>

<s>Sit enim globus terraqueus ABCE, cu<lb/>ius centrum T ad illud interuallum à centro <lb/>V venerit machinarum vi, vt aqua deor&longs;um <lb/><arrow.to.target n="note67"/><lb/><figure id="id.018.01.152.1.jpg" xlink:href="018/01/152/1.jpg"/><lb/>delap&longs;a &longs;it B <lb/>HECB, & <lb/>portionem B <lb/>CE circum<lb/>plectatur. </s>

</row>

<row>

<s><expan abbr="Iã">Iam</expan> <lb/>verò dimit<lb/>tatur tellus à <lb/>&longs;u&longs;pendente: <lb/><expan abbr="nõ">non</expan> facilè de. </s>

<cell/>

<cell>ti ad quintum.</cell>

<s><lb/>finirem, v<lb/>trùm terr&atail; <lb/>con&longs;i&longs;teret, <lb/>an potius de<lb/>&longs;cenderet ex T in V, an verò etiam &longs;ponte <lb/>a&longs;cenderet longiùs recedens ab V. </s>

</row>

<row>

<s>Verùm <lb/>&longs;i &longs;ponte &longs;uâ aliquo u&longs;que a&longs;cenderet, ia&mtail; <pb xlink:href="018/01/153.jpg" pagenum="139"/>nihil &longs;upere&longs;&longs;et laboris Archimedi, vt eò il<lb/>lam deduceret: &longs;i con&longs;i&longs;teret, iam innataret <lb/>aquis, ac proinde non multo labore fui&longs;&longs;et <lb/>opus, vt ex V in T transferretur: &longs;i demùm <lb/>de&longs;cenderet, illud &longs;altem haberetur emolu<lb/>menti, quod intrà aquam exi&longs;tenti multum <lb/>ponderis decederet, & motio faciliùs perfi<lb/>ceretur. </s>

<cell/>

<cell>Tertij ad quartum.</cell>

<s><margin.target id="note67"/><emph type="italics"/>LXVII <lb/>Facilitas <lb/>motus terræ, <lb/>antequa&mtail; <lb/>ab aqua &longs;e<lb/>iungeretur.<emph.end type="italics"/></s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Lepidum &longs;anè inuentum ad vin<lb/>dicandum à calumniâ Archimedem, &longs;i cui <lb/>fortè audaciùs locutus videatur: neque enim <lb/>ex machinis &longs;olùm, de quibus abundè Gali<lb/>læus di&longs;putabat, verùm etiam ex ipsâ aquâ <lb/>&longs;ub&longs;idium non leue peti po&longs;&longs;et ad tellure&mtail; <lb/>loco dimouendam. </s>

<cell>primi ad &longs;ecundum, &</cell>

<s>Sed quid potiùs dicen<lb/>dum exi&longs;timas? </s>

</row>

<row>

<s>innataret-ne? </s>

<cell/>

<cell>&longs;exti ad quintum.</cell>

<s>an verò de<lb/>&longs;cenderet? </s>

</row>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ex his fluctibus enauigare &longs;olus <lb/>non po&longs;&longs;um: vobis pariter adremigandum <lb/>e&longs;t. </s>

<cell>primi ad quintum, & &longs;ex</cell>

<s>Illud primum &longs;tatuere oportet, vtrùm <lb/>terrenus globus &longs;it aquâ leuior &longs;ecundùm <lb/>&longs;peciem; deinde quota pars ex aquis &longs;ponte <lb/>emergeret: vt hinc innote&longs;cat, quantu&mtail; <lb/>fui&longs;&longs;et Archimedi laborandum. </s>

</row>

<row>

<s>Et quod <lb/>ad primum &longs;pectat, certum e&longs;t aërem vni<lb/>uer&longs;um in terræ cauernis delite&longs;cente&mtail;, <lb/>omnesque halitus, & corpora aquis leuiora <lb/>plurimum po&longs;&longs;e demere de grauitate: aër <pb xlink:href="018/01/154.jpg" pagenum="140"/>enim, dum corpus in aëre &longs;u&longs;penditur, nec <lb/>grauitatem addit, nec leuitatem: at &longs;i cor<lb/>pus aquæ in&longs;i&longs;tat, ex aëre recipit leuita<lb/>tem. <lb/><arrow.to.target n="note68"/></s>

<cell/>

<cell>ti ad &longs;ecundum.</cell>

<s><margin.target id="note68"/><emph type="italics"/>LXVIII <lb/>Pondus tel<lb/>luris in a<lb/>qua minue<lb/>retur, ob in<lb/>clu&longs;os bali<lb/>tus.<emph.end type="italics"/></s><figure id="id.018.01.154.1.jpg" xlink:href="018/01/154/1.jpg"/>

</row>

<row>

<s>Sit enim vas AR æreum <lb/>parallelepipedum <expan abbr="vacu&utilde;">vacuum</expan>, <lb/>cuius moles &longs;olida, hoc e&longs;t <lb/>vnâ cum aëre inclu&longs;o, &longs;it <lb/>pedalis: expendatur i&ntail; <lb/>aëre, & &longs;it lib.

<cell/>

<cell>Tertij ad &longs;extum.</cell>

12. Vtique <lb/>&longs;i aquæ imponatur, nata<lb/>bit, cum pes cubicus a<lb/>quæ &longs;it lib. Rom. 80; e&longs;t <lb/>enim grauitas molis compo&longs;itæ ex va&longs;is ma<lb/>tèriâ & aëre ad grauitatem aquæ, vt;. </s>

</row>

<row>

<cell>primi ad &longs;ecundum, &</cell>

</row>

<row>

<s>3. ad 20. <lb/>At &longs;i &longs;eruata eadem materia, & æris den&longs;i<lb/>tate eâdem manente, confletur in ma&longs;&longs;am, <lb/>aut ex eâ fiat vas minoris capacitatis, erit <lb/>quidem in aëre idem pondus, at non item <lb/>in aquâ. </s>

<cell/>

<cell>quarti ad quintum.</cell>

<s>Haud di&longs;pari ratione aër terræ vi<lb/>&longs;ceribus inclu&longs;us, qui ad extenuandum orbis <lb/>pondus in aëre nihil iuuat, ni&longs;i quatenus lo<lb/>cum occupat cæteroqui grauioribus corpo<lb/>ribus replendum, intrà aquam conferret in<lb/>&longs;uper leuitatem, & de grauiorum corporum <lb/>pondere aliquid demeret. </s>

</row>

<row>

<s>Quod &longs;i ignem <lb/>aëre multò leuiorem addamus, qui plurima <lb/>globi huius &longs;patia implet, incrementum ac<pb xlink:href="018/01/155.jpg" pagenum="141"/>cipiet leuitas non contemnendum; cum po<lb/>ti&longs;&longs;imùm ex globi totius grauitate demen<lb/>dum &longs;it huius aquæ terram circumplectentis <lb/>pondus: iam enim non pars e&longs;&longs;et oneris mo<lb/>uendi, &longs;ed e&longs;&longs;et medium, in quo motus per<lb/>ficeretur. </s>

<cell>primi ad quintum, &</cell>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Aëris, & ignis copiam in terrâ de<lb/><arrow.to.target n="note69"/><lb/>lite&longs;centem certis men&longs;uris definire non po&longs;<lb/>&longs;umus, &longs;ed coniecturas tantùm per&longs;equi ne<lb/>ce&longs;&longs;e e&longs;t: illud potius à Philo&longs;opho exigi po&longs;<lb/>&longs;e videtur, vt aëris grauitatem cum aquâ <lb/>comparatam determinet. </s>

</row>

<row>

<s>Quamuis autem <lb/>con&longs;tipato intrà vas aëre aliquando depre<lb/>henderim aërem quadringenties aquâ leuio<lb/>rem, mihi tamen omninò non &longs;atis facio: ex <lb/>illo enim experimento hoc certè euincitur, <lb/>quod aër con&longs;tipatus in aere communi non <lb/>con&longs;tipato grauitat: &longs;ed cum varia &longs;it aëris <lb/>con&longs;tipatio, incon&longs;tans pariter e&longs;t grauitatis <lb/>men&longs;ura, quæ ex illâ colligitur. </s>

<cell/>

<cell>quarti ad &longs;ecundum.</cell>

<s>Quare aëris <lb/>grauitatem explorare oporteret in medio le<lb/>uiore, quemadmodum aqua non intrà aquam <lb/>&longs;ed in aëre expenditur. </s>

</row>

<row>

<s>Et quidem &longs;ubiit ani<lb/>mum aliquando hæc cogitatio, vt &longs;ubiectis <lb/>pruni aërem vehementer calefacerem, in <lb/>quo aërem <expan abbr="cõmunem">communem</expan> phialæ inclu&longs;um ex<lb/>penderem; vt exploratâ deinde eiu&longs;dem <pb xlink:href="018/01/156.jpg" pagenum="142"/>phialæ grauitate in aëre communi minùs ta<lb/>ro, innote&longs;ceret aëris pondus: &longs;ed cum per<lb/>&longs;pectum haberem ex prunis vaporem cali<lb/>dum a&longs;cendere, timui, ne motus a&longs;cenden<lb/>tis vaporis ac medii commoti mihi fucum <lb/>faceret, vt detractum de grauitate cen&longs;erem, <lb/>quicquid virium ad de&longs;cendendum occur<lb/>rentis vaporis motus impediret. </s>

<cell/>

<cell>Quarti ad quintum.</cell>

<s>Præter<lb/>quam quod ex variâ aeris calefacti raritat&etail;, <lb/>varia pariter deprehenderetur aëris commu<lb/>nis grauitas. </s>

</row>

<row>

<s><margin.target id="note69"/><emph type="italics"/>LXIX <lb/>Aquæ & aë<lb/>ris grauita<lb/>tes compa<lb/>rantur, & <lb/>inquirun<lb/>tur.<emph.end type="italics"/></s>

<cell>&longs;ecundi ad primum, &</cell>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> De aëris con&longs;tipati grauitate nullus <lb/>dubito, nequè de eiu&longs;dem dilatati leuitate; Id <lb/>quod ex hac poti&longs;&longs;imùm occa&longs;ione depre<lb/>hendi. </s>

</row>

<row>

<s>Mirabar maris æ&longs;tum Lunæ moti<lb/>bus adeò con&longs;tanter ob&longs;equentem, cau&longs;am<lb/>que curio&longs;iùs inue&longs;tigans animus nunquam <lb/>quieuit, ni&longs;i vbi &longs;u&longs;picari c&oelig;pit latere in ma<lb/>ris fundo corpora, quæ a&longs;cendente ad Me<lb/>ridianum Lunâ intume&longs;cerent, aquasque <lb/>attollerent, Lunâ verò ad Occa&longs;um de&longs;cen<lb/>dente &longs;ub&longs;iderent cum aquis. </s>

<cell/>

<cell>tertij ad &longs;extum.</cell>

<s>Hinc pro <lb/>maiore huiu&longs;modi corporum copiâ, aut mi<lb/>nore, aut pro inæquali eorum contumaciâ, <lb/>aut facilitate ad intume&longs;cendum, æ&longs;tuum <lb/>inæqualitas &longs;atis explicata videbatur. </s>

</row>

<row>

<s>Vt au<lb/>tem aliquod marini æ&longs;tûs, ex corpore ad Lu<pb xlink:href="018/01/157.jpg" pagenum="143"/>næ nutum intume&longs;cente, ve&longs;tigium ob&longs;er<lb/>uarem, Bi&longs;emuti glebam nullum ignem pa&longs;<lb/>&longs;am mihi comparaui (Bi&longs;emutum no&longs;tri ho<lb/>mines vocant plumbum cinereum, quod in<lb/>ter plumbi albi & nigri &longs;peciem medium <lb/>e&longs;t) congruæ retortæ impo&longs;ui, ignem &longs;e<lb/>cundùm gradus admini&longs;traui horas duode<lb/>cim, & qui extillauit humor candidus ac dul<lb/>cis, amplo capacique Recipiente excepi: <lb/>hunc iterum ac tertiò, vt artifices loquuntur, <lb/>rectificaui, vt purior euaderet ac dulcior. </s>

<cell>&longs;ecundi ad &longs;extum, & ter</cell>

<s><lb/>Huius liquoris libram vnam conieci in vi<lb/>treum va&longs;culum tantæ capacitatis, vt liquor <lb/>phialæ be&longs;&longs;em impleret, reliquum trientem <lb/>aër occuparet. </s>

</row>

<row>

<s>Vitrum optimè clau&longs;um, ne <lb/>quid expirare po&longs;&longs;et, in loco, vbi quie&longs;ceret, <lb/>&longs;tatui; nec &longs;inè animi voluptate licebat in <lb/>Plenilunijs manife&longs;ta inclu&longs;i liquoris incre<lb/>menta ob&longs;eruare, in Nouilunijs verò decre<lb/>menta, neque ea tantùm, quæ prioribus in<lb/>crementis re&longs;ponderent, &longs;ed vt aliquid de<lb/>ce&longs;&longs;i&longs;&longs;e videretur ex eâ liquoris quantitate, <lb/>quam primùm infuderam. </s>

<cell/>

<cell>tij ad primum.</cell>

<s>Contigit au<lb/>tem, vt, curio&longs;itate animum vellicant&etail;, <lb/>phialam tùm in Pleniluniis, tum in Noui<lb/>luniis expenderem, &longs;emperque paria depre<lb/>hendi grauitatis momenta, perinde atque &longs;i <lb/>tunc primùm in phialam liquorem inieci&longs;&longs;<pb xlink:href="018/01/158.jpg" pagenum="144"/>&longs;em. </s>

</row>

<row>

<s>Ex quibus intellexi, quantum grauita<lb/>tis &longs;ecundùm &longs;peciem decederet liquori in<lb/>tume&longs;centi, tantum accedere aëri intrà phia<lb/>lam apprimè occlu&longs;am con&longs;tipato: contrà <lb/>verò liquore ad minora &longs;patia coangu&longs;tato <lb/>aërem quidem inclu&longs;um dilatari<gap/>&longs;ed huius <lb/>rare&longs;centis leuitate auctâ, maiorem illius <lb/>conden&longs;ati grauitatem compen&longs;ari. </s>

<cell/>

<cell>Quinti ad &longs;extum.</cell>

<s>Nec di&longs;similem grauitatis con&longs;tantiam <lb/>ob&longs;eruabimus, &longs;i vitreum globum, cui lon<lb/>giu&longs;culum collum & gracile adhæreat, vini <lb/>&longs;piritu ex multiplici di&longs;tillatione tenui&longs;&longs;imo <lb/>repleamus, aëre collum occupante; o&longs;cu<lb/>lum autem Hermetis &longs;igillo claudatur. </s>

</row>

<row>

<s>Ex <lb/>calore enim rare&longs;cet vini &longs;piritus, aëremque <lb/>con&longs;tipabit, & frigore &longs;ub&longs;equente &longs;ub&longs;idet, <lb/>aëri locum relinquens: neque tamen Ther<lb/>mo&longs;copii huius grauitas variabitur, cu&mtail; <lb/>vnius corporis con&longs;tipati grauitas alterius rari <lb/>leuitate compen&longs;etur. </s>

<cell>primi ad &longs;ecundum, &</cell>

<s>Hinc tamen cert&atail; <lb/>definiri non po&longs;&longs;e momenta, quibus aër <lb/>compre&longs;&longs;us deor&longs;um nitatur, palam e&longs;t. </s>

</row>

<row>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Rem ego quantâ potui diligentiâ <lb/>aliter inue&longs;tigaui, & aërem non quadrin<lb/>genties tantùm, &longs;ed etiam adhuc triplo le<lb/>uiorem inueni, ita vt grauitas aquæ ad gra<lb/>uitatem aëris non &longs;it in minori Ratione quàm <lb/>1200 ad 1, &longs;ed potiùs in maiori Ration&etail;. <pb xlink:href="018/01/159.jpg" pagenum="145"/>Ita verò &longs;e habuit ob&longs;eruatio. </s>

<cell/>

<cell>quarti ad tertium.</cell>

<s>Æream Æo<lb/>lipilam propemodùm candentem omnique <lb/>humore de&longs;titutam expendi primùm bilan<lb/>ce iu&longs;ti&longs;simâ; deinde eiu&longs;dem refrigeratæ & <lb/>ad naturalem temperiem re&longs;titutæ pondus <lb/>examinaui, & animaduerti illam facta&mtail; <lb/>fui&longs;&longs;e quatuor vt minimum grauis grauio<lb/>rem: Hinc intuli aërem, qui rarefaction&etail; <lb/>exierat, & naturali conden&longs;atione fuerat ite<lb/>rùm in Æolipilam admi&longs;&longs;us, habere in gra<lb/>uitate quatuor grana. </s>

</row>

<row>

<s>Iterum Æolipilam, <lb/>vt priùs, calefeci, quæ eiu&longs;dem quoquè pon<lb/>deris, vt priùs, inuenta e&longs;t: & illicò eius ro<lb/>&longs;trum in aquam immer&longs;i, vt aquam &longs;ugeret: <lb/>&longs;uxit autem aquæ vncias 9, drachmas 3, gra<lb/>na 25; quæ &longs;unt in vniuer&longs;um (&longs;i &longs;ingulis <lb/>drachmis grana 72 tribuantur, & vnciis gra<lb/>na 576) grana 5425; quod e&longs;t pondus aquæ <lb/>occupantis idem &longs;patium, quod occupabat <lb/>aër vi rarefactionis exclu&longs;us. </s>

<cell>primi ad <expan abbr="terti&utilde;">tertium</expan>, & quar</cell>

<s>E&longs;t igitur gra<lb/>uitas aquæ granorum 5425 ad grauitate&mtail; <lb/>aëris &longs;ecundùm molem æqualis gran 4, hoc <lb/>e&longs;t vt 1356 ad 1. Quarè &longs;atis liberaliter age<lb/>re mihi videor, &longs;i dixero aërem ad aquam in <lb/>leuitate e&longs;&longs;e vt 1200 ad 1. </s>

</row>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Quàm vellem hæc omninò veri<lb/>tati congruere! Sed veniam dabis non qui<lb/>dem improbanti conatum, &longs;ed pen&longs;icula<pb xlink:href="018/01/160.jpg" pagenum="146"/><arrow.to.target n="note70"/><lb/>tiùs examinanti, vtrùm omni pror&longs;us labe <lb/>careat tua hæc argumentatio. </s>

<cell/>

<cell>ti ad &longs;ecundum.</cell>

<s>Sit vas cu<lb/>preum AR molis vnâ cum inclu&longs;o aëre pe<lb/>dalis, & va&longs;is pondus lib.

</row>

</table>

80, quod e&longs;t pon<lb/>dus pedis cubici aquæ. </s>

<table>

<table.target id="table9"/>

<s>E&longs;t igitur vas eiu&longs;<lb/>dem &longs;pecificæ grauitatis cum aquâ; atque <lb/>adeò cum grauitas cupri ad grauitatem aquæ <lb/>&longs;it vt 71. ad 8, moles cupri ad molem aëris <lb/>inclu&longs;i e&longs;t vt 8 ad 63. Quarè vas aëre plenum <lb/>nihil in aquâ grauitat, aut leuitat; &longs;ed &longs;i mer<lb/>gatur intrà aquam, quæ aëre exclu&longs;o impleat <lb/>va&longs;is capacitatem, iam vas intrà aquam pon<lb/>dus habebit lib.

<row>

80. minùs pondere, quod <lb/>habet aqua &longs;ecundùm molem cupro æqualis. </s>

<s><lb/>Quia igitur moles cupri e&longs;t (8/71) pedis cubici, <lb/>fiat vt 71 ad 8, ita lib.

</row>

80 pondus pedis cu<lb/>bici aquæ, ad lib.

<row>

<cell/>

9. (1/71) pondus aquæ æqualis <lb/>cupro va&longs;is. </s>

<cell/>

<s>Erit itaque va&longs;is pleni aquâ in<lb/>trà aquam grauitas lib. (70 70/71): quod quidem <lb/>pondus tribuendum e&longs;t cupro, non autem <lb/>aquæ vas implenti, quæ intrà aquam non <lb/>grauitat: cum maximè idem e&longs;&longs;et in aquâ <lb/>eiu&longs;dem cupri pondus, etiam&longs;i in ma&longs;&longs;am <lb/>conflatum nihil aquæ contineret. </s>

</row>

<s>Quan<lb/>quam non nego grauitatem illam cupri i&ntail; <lb/>aquâ e&longs;&longs;e æqualem grauitati molis aqueæ vas <lb/>implentis, &longs;i illa extra aquam in aere<gap/><lb/>transferatur; e&longs;t enim moles aquæ vas im<pb xlink:href="018/01/161.jpg" pagenum="147"/>plentis (63/71) pedis cubici. </s>

<row>

<cell/>

<s><margin.target id="note70"/><emph type="italics"/>LXX <lb/>Si vas in li<lb/>quore <expan abbr="põde-retur">ponde<lb/>retur</expan> nunc <lb/>plenum aë<lb/>re, nunc ple<lb/>num liquo<lb/>re illo, diffe<lb/>rentia pon<lb/>derum est <lb/>pondus li<lb/>quoris im<lb/>plentis capa<lb/>citatem va<lb/>&longs;is.<emph.end type="italics"/></s>

<cell/>

<s>At manente eâdem va&longs;is mole intelliga<lb/>tur aucta materia; & diminuta capacitas, ita <lb/>vt &longs;it va&longs;is pondus in aëre lib.

</row>

100 &longs;e&longs;qui<lb/>quartum prioris: erit moles cupri (10/71) pedis <lb/>cubici, & capacitas (61/71). Quarè aqua æqualis <lb/>cupro habet pondus lib. (11 19/71): igitur vas intrà <lb/>aquam plenum aquâ habet pondus lib. (88 52/71) <lb/>at plenum aëre intrà aquam amittet pondus <lb/>integri pedis cubici, & &longs;olùm erit lib.

<row>

<cell/>

20. <lb/>Horum igitur ponderum differentia (68 52/71) æ<lb/>qualis e&longs;t ponderi aquæ implentis capacita<lb/>tem va&longs;is, quæ ex con&longs;titutâ hypothe&longs;i e&longs;t (61/71) <lb/>pedis cubici. </s>

<cell/>

<s>Similiter &longs;i intrà idem vas admittantur <lb/>aquæ (10/71), reliquam capacitatem (51/71) impleat <lb/>aër: moles cupri & aëris occupat in aquâ (61/71) <lb/>pedis cubici: igitur ex lib.

</row>

100 auferuntur <lb/>lib. (68 52/71), & pondus va&longs;is in aquâ e&longs;t lib. (31 19/71). <lb/>At quando totum replebatur aquâ, pondus <lb/>erat lib. (88 52/71), igitur differentia lib. (57 33/71) e&longs;t <lb/>grauitas æqualis grauitati (51/71) pedis cubici aquæ, <lb/>quæ impleret va&longs;is &longs;patium ab aëre occupa<lb/>tum, &longs;i aqua illa in aëre extra aquam ex<lb/>penderetur. </s>

</table>

<s>Quemadmodum igitur ex eiu&longs;dem va&longs;is <pb xlink:href="018/01/162.jpg" pagenum="148"/><arrow.to.target n="note71"/><lb/>ponderibus intrà <expan abbr="aquã">aquam</expan>, <expan abbr="quãdo">quando</expan> e&longs;t <expan abbr="plen&utilde;">plenum</expan> aquâ, <lb/>ac quando e&longs;t plenum aëre, rectè infertur ho. <lb/></s>

<s id="id000239">Propo&longs;itio &longs;eptima.</s>

<s><expan abbr="r&utilde;">rum</expan> ponderum <expan abbr="differentiã">differentiam</expan> e&longs;&longs;e æqualem pon<lb/>deri aquæ implentis locum <expan abbr="a&etilde;ris">aeris</expan>, &longs;i illa pon<lb/>deretur in aëre: &longs;ic ex differentiâ ponderum <lb/>Æolipilæ intrà aërem communem con&longs;titu<lb/>tæ, quando plena e&longs;t aëre communi, ac <lb/>quando plena e&longs;t aëre ignito, ex hac, inquam, <lb/>differentiâ rectè illata videtur grauitas aëris <lb/>communis Æolipilam implentis, &longs;i aër i&longs;te <lb/>ponderaretur in aëre ignito tanquam in me<gap/><lb/>dio. </s>

<s>Cum autem differentia huiu&longs;modi &longs;it <lb/>granorum quatuor, pondus aëris communis <lb/>æolipilam implentis e&longs;t gran. 4. non quidem <lb/>ab&longs;olutè, &longs;ed tantùm in medio leuitatis eiu&longs;<lb/>dem ac raritatis, quam habebat aër Æolipi<lb/><emph type="italics"/>l<emph.end type="italics"/>æ candentis: &longs;icuti etiam aqua vas A R im<lb/>plens, de quo dicebam, non habet graui<lb/>tatem lib. (68 52/71) in quocunque medio, &longs;ed tan<lb/>tùm in aëre leuitatis ac raritatis eiu&longs;dem cum <lb/>aëre, qui va&longs;is capacitatem implebat. </s>

<s id="id000240">In modis qui nece&longs;&longs;ariò produ<lb/>cuntur ex duabus proportionibus, <lb/>cum du&etail; quantitates ex illis, qu&etail; mo <lb/><figure id="id.015.01.029.3.jpg" xlink:href="015/01/029/3.jpg"/>dos conficiunt, æquales fuerint: pro<lb/><arrow.to.target n="table10"/><lb/>portio producta ad quatuor quanti<lb/>tates omiologas reducetur.<lb/><arrow.to.target n="marg25"/></s>

<s>Qua<lb/>re non ego facilè dixerim quatuor illa grana <lb/>fui&longs;&longs;e pondus aëris primùm eiecti, qui iterùm <lb/>receptus fuit; ille enim aër nullum habebat <lb/>pondus in aëre communi; & &longs;i pondus ha<lb/>beat in aëre ignito, tota illa grauitas non <lb/>pertinet ad &longs;olum aërem, qui recipitur, &longs;ed <lb/>ad illum, qui totam Æolipilam implet. </s>

<table>

<s>Si<pb xlink:href="018/01/163.jpg" pagenum="149"/>cut &longs;i aqua implens vas A R attenuaretur &longs;e<lb/>cundùm aliquam partem in aërem, & reli<lb/>qua eiiceretur, iterum autem ad naturalem <lb/>den&longs;itatem rediens eiectam aquam ex&longs;uge<lb/>ret, differentia ponderis va&longs;is non &longs;oli aquæ <lb/>eiectæ tribuenda e&longs;&longs;et, &longs;ed toti aquæ vas im<lb/>plenti. </s>

<table.target id="table10"/>

<row>

<s>Hinc e&longs;t quod, cum aqua in Æoli<lb/>pilam admi&longs;&longs;a non &longs;it &longs;ecundùm mole&mtail; <lb/>æqualis toti aëri, qui eam implebat, ac pro<lb/>inde non &longs;it æqualis moli, quæ habet pon<lb/>dus gran. 4, non habetur præcisè Ratio gra<lb/>uitatum &longs;ecundùm &longs;peciem. </s>

</row>

<row>

<s><margin.target id="note71"/><emph type="italics"/>LXXI <lb/>Experimen<lb/>tum Aeoli<lb/>pilæ ad &longs;um<lb/>mum osten<lb/>dit grauita<lb/>tem aëris <expan abbr="cõ-munis">con<lb/>munis</expan> i&ntail; <lb/>aëre ignito, <lb/>non autem <lb/>ab&longs;olutè: nec <lb/>ex eo habe<lb/>tur quæ&longs;ita <lb/>proportio <lb/>grauitatum <lb/>aquæ & aë<lb/>ris.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Id meæ &longs;ententiæ vlteriùs fauet: &longs;i <lb/>enim aquæ moles, quam &longs;uxit Æolipila, <lb/>minor e&longs;t mole aëris, qui numerat in pon<lb/>dere grana 4, plus aliquid aquæ addendum <lb/>erit, vt moles æquales &longs;int; atque adeò mul<lb/>tò maior erit Ratio grauitatis aquæ ad gra<lb/>uitatem aëris, quam &longs;it deprehen&longs;a Ratio <lb/>1356 ad 1. </s>

</row>

<row>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Non hæc eo con&longs;ilio afferebam, vt <lb/>irem contrà; &longs;ed tantùm vt rem paulò ob<lb/>&longs;curiorem mihi ip&longs;e enucleatiùs explicarem, <lb/>& te audirem, &longs;i quid &longs;ortè à veritate aut à <lb/>tuâ mente alienum intelligerem. </s>

<s>Cæterùm <lb/>non nego maiorem e&longs;&longs;e Rationem grauitatis <lb/>aquæ æolipilam implentis ad grauitatem aë<lb/>ris eam pariter implentis, ac &longs;it Ratio gra<pb xlink:href="018/01/164.jpg" pagenum="150"/>uitatis aqu&ae