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<?xml version="1.0"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Schott, Gaspar</author> <title>Mechanica Hydraulico-pneumatica. Pars I. Mechanicæ Hydraulico-pnevmaticæ Theoriam continet.</title> <date>1657</date> <place/> <translator/> <lang>la</lang> <cvs_file>schot_mecha_051_la_1657.xml</cvs_file> <locator>051.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="051/01/001.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>A. R.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>P. GASPARIS <lb/>SCHOTTI<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>SOCIETATIS JESU<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>MECHANICA <lb/>HIDRAULICO -PNEVMATICA<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Cum<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FIGURIS ÆNÊIS, ET PRIVILEGIO SACRÆ<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Ce&longs;aræ Maje&longs;tatis.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>ANNO M DC LVIII.<emph.end type="italics"/><emph.end type="center"/> <pb xlink:href="051/01/002.jpg"/> <arrow.to.target n="fig1"/></s></p> <figure id="id.051.01.002.1.jpg" xlink:href="051/01/002/1.jpg"/> <p type="caption"> <s>MECHANICA <lb/>HYDRAVLICOPNEVMATICA</s></p> <p type="caption"> <s>Ad Eminenti&longs;s: S.R.I. Principem <lb/>Ioannem Philippum <lb/>Electorem Mogunt: <lb/>Auctore.</s></p> <p type="caption"> <s>P. GASPARE SCHOTTO.</s></p> <p type="caption"> <s>Soci Iesu</s></p> <pb xlink:href="051/01/003.jpg"/><pb xlink:href="051/01/004.jpg"/> <p type="main"> <s><emph type="center"/>P. GASPARIS SCHOTTI<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>REGISCURIANI, E SOCIE­<lb/>TATE JESU,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Olim in Panormitana Siciliæ, nunc in Herbipo­<lb/>litana Franconiæ eju&longs;dem SOCIETATIS Academia <lb/>Mathe&longs;eos Profe&longs;&longs;oris,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>MECHANICA <lb/>HYDRAULICO-PNEV­<lb/>MATICA,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Qua <lb/><emph type="italics"/>Præterquàm quòd Aquei elementi natura, proprietas, vis <lb/>motrix, atque occultus cum aëre conflictus, à primis fundamentis de­<lb/>mon&longs;tratur; omnis quoque generis Experimenta Hydraulico-pnevmatica <lb/>recluduntur; & ab&longs;oluta Machinarum aquâ & aere animandarum ratio <lb/>ac methodus præ&longs;cribitur.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>OPUS BIPARTITUM,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>Cujus<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s>Pars I. Mechanicæ Hydraulico-pnevmaticæ Theoriam continet. </s></p> <p type="main"> <s>Pars II. Eju&longs;dem Praxin exhibet, Machinasque Aquarias innumeras, uti & Organa, ali­<lb/>aque In&longs;trumenta, in motum ac &longs;onum concitat; nec non varia techna&longs;inata, <lb/>quæ motum perpetuum vi aquæ &longs;pondent, exponit. </s></p> <p type="main"> <s><emph type="center"/>ACCESSIT<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>Experimentum novum Magdeburgicum, quo vacuum alij &longs;ta­<lb/>bilire, alij evertere conantur.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Sumptu Heredum JOANNIS GODEFRIDI Schôn wetteri,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Bibliopol: Francofurten&longs;.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>Excudebat<emph.end type="italics"/> HENRICUS PIGRIN <emph type="italics"/>Typographus Herbipoli,<emph.end type="italics"/><lb/>ANNO M. DC. LVII.<emph.end type="center"/></s></p> <pb xlink:href="051/01/005.jpg"/> <figure id="id.051.01.005.1.jpg" xlink:href="051/01/005/1.jpg"/> <pb xlink:href="051/01/006.jpg"/> <p type="main"> <s><emph type="center"/>DEDICATIO.<emph.end type="center"/></s></p> <figure id="id.051.01.006.1.jpg" xlink:href="051/01/006/1.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>Eminenti&longs;&longs;imo, & Reverendi&longs;&longs;imo Principi <lb/>ac Domino,<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>D. JOANNI <lb/>PHILIPPO,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>SACRÆ SEDIS MOGUNTINÆ<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Archiepi&longs;copo, S. Rom. Imp. per Germani­<lb/>am Archi-Cancellario, & Principi Electori; Epi&longs;copo <lb/>Herbipolen&longs;i, Franciæ Orientalis Duci, <lb/>Domino meo clementi&longs;&longs;imo.<emph.end type="center"/></s></p> <p type="main"> <s>EMINENTISSIME PRIN­<lb/>CEPS. Fontes quos Natura <lb/>producit ad hominum utilitatem, <lb/><emph type="italics"/>Mare<emph.end type="italics"/> petunt, ut fluant. </s><s><emph type="italics"/>Omnia quippe <lb/>flumina,<emph.end type="italics"/> ac proinde & fontes flumi- <pb xlink:href="051/01/007.jpg"/>num origines, <emph type="italics"/>intrant in Mare, & Mare non <lb/>redundat; ad locum, unde exeunt flumina, revertun­<lb/>tur, vt iterum fluant.<emph.end type="italics"/> </s><s>Fontes quos hoc <lb/>in Opere produco ex Hydrotech­<lb/>nica Arte ad Principum delecta­<lb/>tionem, ut &longs;aliant, FONTEM petunt <lb/>PULCHRUM, Te inquam, EMI­<lb/>NENTISSIME DOMINE, <expan abbr="Tuumq;">Tuumque</expan> <lb/>favorem ac benevolentiam. </s><s>Ni&longs;i <lb/>enim ope Tua, qui FONS es PUL­<lb/>CHERRIMUS, foveantur, & <lb/>Tua augeantur ditenturque co­<lb/>pia; exare&longs;cant nece&longs;&longs;e e&longs;t, ma­<lb/>gno licet labore, nec minori <lb/>Arte, in fluxum ac &longs;altum àme <lb/>animati. </s><s> Pateat igitur Fontibus <pb xlink:href="051/01/008.jpg"/>meis FONS PULCHER; <expan abbr="deriv&etilde;tur">deriventur</expan> <lb/>in eos Humanitatis Tuæ aquæ, ut <lb/>gloriari liceat, ac dicere: FONS <lb/>PULCHER SUFFICIT UNDAS. </s><s><lb/>Dixi quod volebain, & hîc finio, <lb/>nè peccare cogar peccatum quo <lb/>Scriptorum plerique reos &longs;e con­<lb/>&longs;tituunt, dum in Mecænatum <lb/>&longs;uorum laudes ip&longs;o in Librorum <lb/>ve&longs;tibulo quàm pro loci oppor­<lb/>tunitate longiùs excurrunt. </s><s>Ma­<lb/>jor e&longs;t virtutum Tuarum &longs;plen­<lb/>dor, majora in Eccle&longs;iam & Im­<lb/>perium Romanum merita, quàm <lb/>ut exili calamo meo, præ&longs;ertim <lb/>hoc loco, exarentur. </s></p> <pb xlink:href="051/01/009.jpg"/> <p type="main"> <s>Vale PRINCEPS EMINEN­<lb/>TISSIME, Imperii columen, <lb/>& Eccle&longs;iæ decus; ae bono utrius­<lb/>que quàm diutis&longs;imè vive. </s><s> Ita <lb/>optat Herbipoli Die VIII. Julij, <lb/>Anno MDCL VII. </s></p> <p type="main"> <s>EMINENTISSIMÆ <lb/>TUÆ </s></p> <p type="main"> <s>CELSITUDINIS </s></p> <p type="main"> <s><emph type="italics"/>Humillimus Cliens<emph.end type="italics"/></s></p> <p type="main"> <s>Ca&longs;parus Schottè So­<lb/>cietate JESU. </s></p> <pb xlink:href="051/01/010.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>IN FRONTEM LIBRI<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>ACROAMA EXEGETICUM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>FONS PULCHER SUFFICIT UNDAS.<emph.end type="italics"/><emph.end type="center"/></s></p> <figure id="id.051.01.010.1.jpg" xlink:href="051/01/010/1.jpg"/> <p type="main"> <s><emph type="center"/>Obmute&longs;ce Antiquitas; <lb/>Jam dudum exaruit lympha, <lb/>Quam propinavit Pincerna vatum<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PEGASUS.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Riget in&longs;tar pumicis, qui Parna&longs;&longs;um irrigavit: <lb/>Qui infantium etiam linguas fecerat di&longs;ertas, <lb/>Dudum, prô pudor, e&longs;t de&longs;ertus. </s><s><lb/>Pone cri&longs;tas Heliconis Nympha;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>HIPPOCRENE FUIT!<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Unde, aut ubi fluxerit olim, quis &longs;ciat? <lb/>Ca&longs;talides ip&longs;æ nefciunt, <lb/>Ex quo toties potæ cecinerunt.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Et quid mirum Helicona nu&longs;quam apparere, <lb/>Si ip&longs;a Græcia di&longs;paruit, & migravit <lb/>In EUKOPAM reliquam;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>In quâ non unas numeres Athenas, <lb/>Quando pæne innumera vides Athenæa, <lb/>Suo quodque formo&longs;um Apolline, <lb/>Suo quodque irriguum fonte, <lb/>E quo bibunt &longs;apientes Europæi, <lb/>Et entheantur.<emph.end type="center"/></s></p> <pb xlink:href="051/01/011.jpg"/> <p type="main"> <s><emph type="center"/>De Europa univer&longs;a periculum facin &longs;ola<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>GERMANIA:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De Germania verò pronuncia, <lb/>Si, quæ Rhenus, Mœnusve alluit, invi&longs;as<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>ATHENÆA, <lb/>MOGANUM ET ARTAUNIUM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quæ, qualésve ea incolant Mu&longs;æ, <lb/>Di&longs;ce ex latice, qui eas reficit.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Medio bullit è Nobilitatis Rhenanæ jugo, <lb/>Non &longs;onipedis Pega&longs;i extu&longs;us ungulâ; <lb/>Sed jubati LEONIS effo&longs;&longs;us ungue,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>CALLOCRENE.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc uno ambæ libant & vivunt de fonte, <lb/>Cælo divi&longs;æ, non zelo,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>MOGANIDES MUSÆ ET FRANCONIDES.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>His <lb/>Seu &longs;itim arentis gutturis levent, <lb/>Seu barbita pulvere glorio&longs;o &longs;ordida lavent, <lb/>Seu in carmina animent Vates, <lb/>Seu fugientes Vatibus venas revocent, <lb/>Seu in pr&ecedil;mia lauros & palmas rigent, <lb/>Seu fe&longs;tivè cum Nymphis ludant <lb/>Apollinis honori,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PULCHER SUFFICIT UNDAS.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Verùm quid Mu&longs;as, Nymphásque memoro? <lb/>Ip&longs;a adeò Natura hoc fonte haurit, <lb/>Ut parturientem juvet Artem:<emph.end type="center"/></s></p> <pb xlink:href="051/01/012.jpg"/> <p type="main"> <s><emph type="center"/>Hinc Ars bibit, ut languentem fulciat Naturam, <lb/>Experti di&longs;cimus: <lb/>Quod non &longs;ola Natura audet. </s><s><lb/>Nec Ars &longs;ola pote&longs;t, <lb/>Et pote&longs;t cum Arte Natura & audet. </s><s><lb/>Verùm deficerent, ni&longs;i &longs;ufficeret,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PULCHER<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Undas, Animos, Vires. </s><s><lb/>Hoc manante animatur emortuus Æolus, <lb/>Et &longs;pirat:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc &longs;tillante lique&longs;cunt, licet ære fu&longs;æ, Phaëtontiades, <lb/>Et lacrymantur:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc illabente alterni folles inflantur & efflantur, <lb/>Et organa re&longs;onant:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc &longs;aliente Deorum &longs;imulacra irrorantur, <lb/>Et tripudiant.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Verbo, <lb/>Paucis multa dicam:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>CRESCIT QUODCUNQUE RIGAT, <lb/>VIGET QUODCUNQUE LAVAT,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PULCHER.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hinc e&longs;t quod &longs;tupent ob&longs;tipi; <lb/>Et ægrè vident Invidi,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>HOC FONTE,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Virere lauros, Musásque vigere.<emph.end type="center"/></s></p> <pb xlink:href="051/01/013.jpg"/> <p type="main"> <s><emph type="center"/>FONS PULCHER.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Feras cicurat, mon&longs;tra domat: <lb/>Hercule felicior!<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quæ is exanimabat, hic animat;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quæ i&longs;te clavâ fregit, ille regit <lb/>Suaviter influendo.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc &longs;tratagemate, <lb/><emph type="italics"/>Rotas Moganas<emph.end type="italics"/> firmavit, <lb/>Ut bene verterentur, <lb/>Quæ à procellis, quia rapiebantur, <lb/>Pæne evertebantur.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Pluris &longs;cilicet &longs;æpe e&longs;t e&longs;&longs;e humanum quàm fortem, <lb/>Ubi gloria e&longs;t major, <lb/>Vincere amoribus quàm viribus. </s><s><lb/>In fontibus reliquis eximium hoc habet<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PULCHER,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quòd non aquam &longs;olùm fundat, <lb/>Quâ &longs;uam effæta reparet Juventam<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>AQUILA;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Sed & oleum &longs;tillet, <lb/>Quo repullulantes pennas ad robur <lb/><emph type="italics"/>Ungat.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Nec <emph type="italics"/>Aquilæ<emph.end type="italics"/> modò hoc <emph type="italics"/>Fonte<emph.end type="italics"/> lotæ <lb/><emph type="italics"/>Juvene&longs;cunt:<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Sed, quia cum Igne quid commune habet<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PVLCHER,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hoc etiam in FONTE emortuus,<emph.end type="center"/></s></p> <pb xlink:href="051/01/014.jpg"/> <p type="main"> <s><emph type="center"/>Novo prodigio Novus <lb/><emph type="italics"/>Revivi&longs;cit<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PHOENIX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Unde infelici&longs;&longs;imorum temporum <lb/>Hæc una e&longs;t felicitas, <lb/>Quod mergantur in FONTE PULCHRO, <lb/>In quo ni&longs;i tota &longs;ubmergantur, <lb/>Nunquam emergent <lb/>Feliciora.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Et Gloria hæc &longs;umma erit<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONTIS PVLCHRI,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>In ea incidi&longs;&longs;e tempora, <lb/>In quæ ni&longs;i incidi&longs;&longs;et, <lb/>Forent tempora omnino <lb/>Profligata.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De FONTE PULCHRO quid ampliùs dicam? <lb/>Fontes alij aut æ&longs;tu pro&longs;pero ex&longs;iccantur, <lb/>Aut algore &longs;ini&longs;tro congelant, <lb/>Ut fluxum &longs;i&longs;tant:<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FONS PVLCHER.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>FLUET DONEC INFLUAT <lb/>IN FONTEM <lb/>QUOCUM SALIET IN VITAM ÆTERNAM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quod vovent & precantur mecum<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>OMNES BONÆ MUSÆ <lb/>A FONTE PULCHRO <lb/>LOTÆ, RIGATÆ, POTÆ.<emph.end type="center"/></s></p> <p type="main"> <s>P. NICOLAUS MOHR è Socie­<lb/>tate JESU. </s></p> <pb xlink:href="051/01/015.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>Facultas admodum R. P.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PRÆPOSITI GENERALIS <lb/>SOCIETATIS JESU.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>GOSWINUS <lb/>NICKEL SOCIETA­<lb/>TIS JESU<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>PRÆPOSITUS GENERALIS.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>CUm Opus, quod in&longs;cribitur<emph.end type="italics"/> Mechanica <lb/>Hydraulico-pnevmatica, à P. GASPARE <lb/>SCHOTT <emph type="italics"/>noftræ Societatis Sacerdote compo&longs;i­<lb/>tum, aliquot eju&longs;dem Societatis Religio&longs;i recognove­<lb/>rint, & in lucem edi po&longs;&longs;e probaverint; facultatem <lb/>concedimus vt typis mandetur, &longs;i ijs ad quos pertinet, <lb/>ita videbitur. </s><s>In cujus rei te&longs;timonium has litteras <lb/>manu no&longs;trâ &longs;ub&longs;criptas, &longs;igillo&queacute; no&longs;tro munitas da­<lb/>mus Romæ,<emph.end type="italics"/> 23. <emph type="italics"/>Januarij<emph.end type="italics"/> 1655. </s></p> <p type="main"> <s>GOSWINUS NICKEL. </s></p> <pb xlink:href="051/01/016.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>FACULTAS<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>R. P. PROVINCIALIS <lb/>SOCIETATIS IESV<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per Rheni Superioris Provinciam Bi­<lb/>bliopolæ facta.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>CUm ex Mandato Sacræ Cæ&longs;areæ Maje&longs;tatis omnibus <lb/>& &longs;ingulis Typographis, Bibliopolis, ac aliis quamcun­<lb/>que librariam negotiationem exercentibus, &longs;eriò firmiterque in­<lb/>hibeatur, nè qui&longs;quam libros ullos<emph.end type="italics"/> à SOCIETATIS <emph type="italics"/>no&longs;træ Pa­<lb/>tribus hactenus editos, aut impo&longs;terum edendos intra S.R. Im­<lb/>perij, Regnorum, & Dominiorum Suæ Cæ&longs;areæ Maje&longs;tatis hæ­<lb/>reditariorum fines, &longs;imili aliovè charactere aut formâ, &longs;ive in <lb/>toto, &longs;ive in parte recudere, vel aliò recudendos mittere, aut ali­<lb/>bi etiam impre&longs;&longs;os adducere, vendere, & di&longs;trahere, clàm &longs;eu <lb/>palàm, citrà &longs;upradictorum Patrum con&longs;en&longs;um ac te&longs;timonium, <lb/>audeat, vel præ&longs;umat: Ego<emph.end type="italics"/> NITHARDUS BIBERUS, <lb/>SOCIETATIS JESU <emph type="italics"/>per Rheni &longs;uperioris Provinciam Pro­<lb/>vincialis, concedo<emph.end type="italics"/> Joanni Godefrido Schôn wettero <emph type="italics"/>fa­<lb/>cultatem, &longs;uis &longs;umptibus excudendi<emph.end type="italics"/> P. GASPARIS SCHOTTI <lb/>è SOCIEIATE JESU Mechanicam Hydraulico-pnev­<lb/>maticam. </s><s><emph type="italics"/>In quorum fidem hoc ei te&longs;timonium manu no&longs;trâ <lb/>&longs;ub&longs;criptum, & Sigillo munitum dare voluimus. Herbipoli<emph.end type="italics"/><lb/>21. <emph type="italics"/>Fanuarij<emph.end type="italics"/> 1656. </s></p> <p type="main"> <s>NITHARDUS BIBERUS. </s></p> <p type="main"> <s>L. S. </s></p> <pb xlink:href="051/01/017.jpg"/> <p type="main"> <s><emph type="center"/>ELENCHUS<emph.end type="center"/></s></p> <figure id="id.051.01.017.1.jpg" xlink:href="051/01/017/1.jpg"/> <p type="main"> <s><emph type="center"/>ELENCHUS TITU­<lb/>LORUM,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>Sive <lb/>SYNOPSIS OPERIS.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s>Præloquium ad Lectorem, de Operis Occa&longs;ione, Divi&longs;ione, In&longs;criptione; deque <lb/>Hydraulicorum & Pnevmaticorum Scriptoribus. pag. 1. </s></p> <p type="main"> <s><emph type="center"/>PARS I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>THEORETICA.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinarum Hydraulico-Pnevmaticarum principiis &longs;eu fundamentis. 15 </s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA I.<emph.end type="center"/></s></p> <p type="main"> <s>De vi Attractiva corporum, ad vacuum vel replendum, vel fugiendum: &longs;eu de <lb/>primo Machinarum Hydro-pnevmaticarum principio. 18 </s></p> <p type="main"> <s>§. I. Hero Alexandrinus vacuum in aëre & aqua di&longs;&longs;eminatum agno&longs;cit. 19 </s></p> <p type="main"> <s>§. II. Experimenta quibus Hero vacuum in corporibus di&longs;&longs;eminatum pro­<lb/>bat. 21 </s></p> <p type="main"> <s>§. III. Experimenta quibus vacuum nullum e&longs;&longs;e probatur. 25 </s></p> <p type="main"> <s>§. IV. Vis attractiva ob vacui metum, primum Machinarum Hydro-pnevma­<lb/>ticarum principium, quæ, & qualis, quibusvis in&longs;it corporibus. 28 </s></p> <p type="main"> <s>§. V. Experimentum, quo o&longs;tenditur vis attractiva ad aquas in altum evchen­<lb/>das, vacui vitandi causâ, per Machinas Hydro-pnevmaticas. 30 </s></p> <p type="main"> <s>§. VI. Notantur nonnulla circa prædictum Experimentum, &longs;imulque &longs;tabili­<lb/>tur, in attractione aquæ metu vacui habendam e&longs;&longs;e rationem perpendiculi <lb/>aquarum. 33 </s></p> <p type="main"> <s>§. VII. Heronis Alexandrini error in elevanda aqua vi attractiva. 36 </s></p> <p type="main"> <s>§. VIII. Alius Heronis error in elevanda aqua vi attractiva. 37 </s></p> <p type="main"> <s>§. IX. In aquarum elevatione vi attractivâ, habenda e&longs;t ratio perpendiculi &longs;olùm <lb/>illorum tuborum, per quos aqua, non per quos aër vehitur. 39 </s></p> <pb xlink:href="051/01/018.jpg"/> <p type="main"> <s><emph type="center"/>TITULORUM.<emph.end type="center"/></s></p> <p type="main"> <s>§. X. Viattractivâ elevari pote&longs;t aqua ultra perpendiculi altitudinem, aëre me­<lb/>diante. 40 </s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA II.<emph.end type="center"/></s></p> <p type="main"> <s>De vi Expul&longs;iva propter corporum impenetrabilitatem; &longs;eu de &longs;ecundo Machi­<lb/>narum Hydro-pnevmaticarum principio. 43 </s></p> <p type="main"> <s>§. I. Omnia univer&longs;i corpora &longs;unt inter &longs;e contigua. ibid. </s></p> <p type="main"> <s>§. II. Corpora &longs;e mutuò expellunt. 45 </s></p> <p type="main"> <s>§. III. Experimentum, quo o&longs;tenditur vis expul&longs;iva, propter corporum im­<lb/>penetrabilitatem, ad aquas elevandas in altum. 46 </s></p> <p type="main"> <s>§. IV. Notantur nonnulla circa prædictum Experimentum. 48 </s></p> <p type="main"> <s>§. V. Heronis error in elevando oleo vi expul&longs;ivâ in lucerna. 50 </s></p> <p type="main"> <s>§. VI. Attractione & expul&longs;ione &longs;imul aquam elevare po&longs;&longs;umus. 53 </s></p> <p type="main"> <s>§. VII. Salomon Caus meritò &longs;ugillat Heronem. 55 </s></p> <p type="main"> <s>§. VIII. Idem perpendiculum aquæ cadentis non pote&longs;t &longs;ervire &longs;imul attra­<lb/>ctioni & expul&longs;ioni. 57 </s></p> <p type="main"> <s>§. IX. Error apud Joannem Bapti&longs;tam Portam indicatur. 58 </s></p> <p type="main"> <s>§. X. Alia ratio aquam elevandi in altum propter corporum impenetrabili­<lb/>tatem. 59 </s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA III.<emph.end type="center"/></s></p> <p type="main"> <s>De vi Rarefactiva; &longs;eu de tertio Hydro-pnevmaticarum Machinarum prin­<lb/>cipio. 61 </s></p> <p type="main"> <s>§. I. Rarefactionis vis, & effectus mirabilis. ibid. </s></p> <p type="main"> <s>§. II. Alia rarefactionis exempla. 62 </s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA IV.<emph.end type="center"/></s></p> <p type="main"> <s>De fluxu aquæ naturali; &longs;eu de quarto Hydro-pnevmaticarum Machinarum <lb/>principio. 64 </s></p> <p type="main"> <s>CAPUT I. De Proprietatibus aquæ fluentis liberè. 65 </s></p> <p type="main"> <s>PROPRIETAS </s></p> <p type="main"> <s>I. Aqua tendit ad loca decliviora. 67 </s></p> <p type="main"> <s>II. Aquæ &longs;uperficies &longs;uperior, ce&longs;&longs;ante fluxu, &longs;phærica e&longs;t; reliquæ conforman­<lb/>tur va&longs;is & receptaculis. ibid. </s></p> <p type="main"> <s>III. Aqua minùs pre&longs;&longs;a expellitur à magis pre&longs;&longs;a. 68 </s></p> <p type="main"> <s>IV. Aquæ, & humidi cuiuscunque, pars unaquæque premitur humido &longs;upra <lb/>ip&longs;am exi&longs;tente ad perpendiculum, &longs;i humidum &longs;it de&longs;cendens in aliquo, aut <lb/>abalio aliquo pre&longs;&longs;um. ibid. </s></p> <p type="main"> <s>V. Aquâ in &longs;itu naturali con&longs;i&longs;tente, partes &longs;uperiores non premunt inferio­<lb/>res. 70 </s></p> <pb xlink:href="051/01/019.jpg"/> <p type="main"> <s>VI. Aquæ in &longs;itu naturali po&longs;itæ una pars non expellit alteram. 71 </s></p> <p type="main"> <s>VII. Non omnes æquæ æquales magnitudine, &longs;unt æquales pondere. ibid. </s></p> <p type="main"> <s>VIII. Aqua naturaliter non a&longs;cendit ad locum altiorem &longs;uâ origine. ibid. </s></p> <p type="main"> <s>CAPUT II. De Proprietatibus aquæ fluentis per &longs;iphones. 72 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Siphonis varias divi&longs;iones a&longs;&longs;ignare. ibid. </s></p> <p type="main"> <s>II. Siphonis erecti proprietates a&longs;&longs;ignare. 74 </s></p> <p type="main"> <s>III. Siphonis inver&longs;i proprietates a&longs;&longs;ignare. 77 </s></p> <p type="main"> <s>IV. Siphonis mixti inæqualium crurium proprietates a&longs;&longs;ignare. 81 </s></p> <p type="main"> <s>V. Siphonis mixti æqualium crurium proprietates a&longs;&longs;ignare. 84 </s></p> <p type="main"> <s>VI. Inver&longs;i &longs;iphonis, va&longs;i uno crure impo&longs;ito, proprietates a&longs;&longs;ignare. ibid. </s></p> <p type="main"> <s>VII. Cau&longs;am ad&longs;ignare, cur quando o&longs;culum externi cruris &longs;iphonis inver&longs;i e&longs;t <lb/>altius, aut æquè altum ac aquæ &longs;uperficies &longs;uprema in va&longs;e, aqua non fluat; <lb/>quando verò e&longs;t demi&longs;&longs;ius, fluat. 88 </s></p> <p type="main"> <s>VIII. Siphonem ad libram &longs;eu vectem revocare, & filtrum ad &longs;iphonem. 93 </s></p> <p type="main"> <s>IX. Diabetem &longs;piritalem de&longs;cribere, eiu&longs;que proprietates ad&longs;ignare. 94 </s></p> <p type="main"> <s>X. Siphonis inver&longs;i fluxum æqualem reddere. 96 </s></p> <p type="main"> <s>XI. Siphone inver&longs;o aquam ex uno montis latere in alterum, per verticem, de­<lb/>ducere. 98 </s></p> <p type="main"> <s>XII. Siphone inver&longs;o aquam ex montis radice ad ejus verticem elevare. 102 </s></p> <p type="main"> <s>XIII. Cau&longs;am a&longs;&longs;ignare, cur in &longs;iphone inver&longs;o interrupto perpendiculum aquæ <lb/>de&longs;cendentis debeat &longs;uperare perpendiculum aquæ a&longs;cendentis. 104 </s></p> <p type="main"> <s>XIV. Cau&longs;am a&longs;&longs;ignare, cur in Fonte Heronis perpendiculum aquæ de&longs;cen­<lb/>dentis debeat e&longs;&longs;e longius perpendiculo aquæ a&longs;cendentis. 107 </s></p> <p type="main"> <s>CAPUT III. De Proprietatibus aquæ fluentis per tubos. 110 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Aqua decurrit per tubi verticalis foramen ba&longs;is, in&longs;tar columnæ aqueæ, cuius <lb/>ba&longs;is æqualis foramini, altitudo perpendiculares à ba&longs;i erectæ; &longs;ive tubi &longs;int <lb/>&longs;emper pleni, &longs;ive non. 111 </s></p> <p type="main"> <s>II. Per tubos tam &longs;emper, quàm non &longs;emper plenos æqualis altitudinis, & æqua­<lb/>lium foraminum, effluit æqualis aquæ copia, eodem vel æquali tempore, <lb/>cujuscunque capacitatis & formæ &longs;int tubi. 113 </s></p> <p type="main"> <s>III. Per tubos tam &longs;emper, quàm non &longs;emper plenos æqualium luminum, &longs;ed <lb/>inæqualium altitudinum, effluit eodem, vel æquali tempore, inæqualis aquæ <lb/>copia. 114 </s></p> <p type="main"> <s>IV. Per tubos &longs;emper, & non &longs;emper plenos inæqualium luminum, &longs;ed æquali­<lb/>um altitudinum, effluit eodem, vel æquali tempore, inæqualis aquæ <lb/>copia. ibid. </s></p> <pb xlink:href="051/01/020.jpg"/> <p type="main"> <s>V. Per tubos æquè altos, & æqualium luminum, non &longs;emper plenos, fluit eodem <lb/>tempore æqualis aquæ copia; &longs;ed tantò fluit unus diutiùs altero, quantò <lb/>plus aquæ continet unus quàm alter. 115 </s></p> <p type="main"> <s>VI. Per tubos non &longs;emper plenos, & non æquè altos, æqualium tamen lumi­<lb/>num, eodem vel æquali tempore non fluit æqualis aquæ copia. ibid. </s></p> <p type="main"> <s>VII. Tubus altitudine quadrupedalis, cui pro ba&longs;is diametro pedis Pari&longs;ien&longs;is <lb/>uncia, aquâ &longs;emper, plenus, effundit per lumen lineare in ba&longs;i &longs;itum, aquæ <lb/>libram &longs;patio tredecim minutorum &longs;ecundorum temporis. 116 </s></p> <p type="main"> <s>VIII. Aquæ fluentes ex tubis tam &longs;emper quàm non &longs;emper plenis æqualium <lb/>foraminum, &longs;ed inæqualium altitudinum, habent rationem &longs;ubduplicatam <lb/>altitudinum tuborum; habentque dicti tubi duplicatam rationem aqua­<lb/>rum, quas fundunt. 117 </s></p> <p type="main"> <s>IX. Aqua naturali motu de&longs;cendens & effluens per tubos, imitatur leges alio­<lb/>rum gravium naturali motu de&longs;cendentium. 120 </s></p> <p type="main"> <s>X. Velocitates motus aquæ de&longs;cendentis & effluentis per tubos æqualium fo­<lb/>raminum, &longs;ed inæqualium altitudinum, habent &longs;ubduplicatam rationem <lb/>altitudinum. 125 </s></p> <p type="main"> <s>XI. Cau&longs;am a&longs;&longs;ignare, cur aquæ fluentes per tubos æqualium luminum, &longs;ed in­<lb/>æqualium altitudinum, habeant rationem &longs;ubduplicatam altitudinum tu­<lb/>borum. 126 </s></p> <p type="main"> <s>XII. Tempora quibus æqualis aquæ quantitas è tubis æqualium luminum, &longs;ed <lb/>inæqualium altitudinum effluit, habent &longs;ubduplicatam rationem tubo­<lb/>rum. ibid. </s></p> <p type="main"> <s>XIII. Si tubi, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, &longs;int ejusdem altitudinis, <lb/>&longs;ed inæqualium foraminum, e&longs;t eadem ratio aquæ ad aquam, quæ foraminis <lb/>ad foramen, phy&longs;icè &longs;eu ad &longs;en&longs;um. 127 </s></p> <p type="main"> <s>XIV. Tubi non &longs;emper pleni æquè alti, & æqualium foraminum; &longs;ed inæquali­<lb/>um ba&longs;ium, evacuantur inæqualibus temporibus, e&longs;tque eadem ratio tem­<lb/>porum, quæ ba&longs;ium. 129 </s></p> <p type="main"> <s>XV. Tempora quibus deplentur tubi non &longs;emper pleni, æquèlati, &longs;ed non æquè <lb/>alti, per æqualia foramina, &longs;unt in altitudinum ratione &longs;ubduplicata. 131 </s></p> <p type="main"> <s>XVI. Tempora quibus evacuantur tubi non &longs;emper pleni &longs;imiles, & æquales <lb/>quoad altitudines & ba&longs;es, per lumina &longs;imilia inæqualia, &longs;unt reciprocè, ut <lb/>lumina. ibid. </s></p> <p type="main"> <s>XVII. Datis altitudine & foramine tubi &longs;emper pleni, invenire quantitatem <lb/>aquæ quam dato tempore effundat; vel, datis iisdem, invenire magnitudi­<lb/>nem ci&longs;ternæ quæ dato tempore repleatur. 132 </s></p> <pb xlink:href="051/01/021.jpg"/> <p type="main"> <s>XVIII. Datis altitudine & lumine tubi &longs;emper pleni, invenire tempus quo da­<lb/>tam aquæ quantitatem effundat, &longs;ive quo datam ci&longs;ternam impleat. 135 </s></p> <p type="main"> <s>XIX. Datis tempore, quantitate aquæ, &longs;eu ci&longs;terna, & lumine tubi, invenire alti­<lb/>t&udot;dinem tubi, qui &longs;emper plenus ci&longs;ternam dato tempore repleat. 136 </s></p> <p type="main"> <s>XX. Dato va&longs;e, & foramine per quod effluit aqua, invenire tempus quo eva­<lb/>cuatur. 137 </s></p> <p type="main"> <s>XXI. Dato va&longs;e, & tempore, invenire foramen per quod evacuetur tempore <lb/>dato. 139 </s></p> <p type="main"> <s>XXII. Altitudinem &longs;caturiginis dati fontis per tubos fluentis invenire. 140 </s></p> <p type="main"> <s>XXIII. Data alicujus tubi, aut va&longs;is erogatorii altitudine, ac tempore quo deter­<lb/>minatam aquæ quantitatem è &longs;uo lumine effundit, invenire altitudinem <lb/>ejusdem aut alterius tubi, qui æquali tempore, per æquale lumen, aliam de­<lb/>terminatam aquæ quantitatem effundat. 140 </s></p> <p type="main"> <s>XXIV. In tubo &longs;eu va&longs;e &longs;emper pleno determinare &longs;patia, quæ temporibus <lb/>æqualibus &longs;ibi &longs;uccedentibus evacuantur; uti & menfuram &longs;eu pondus a­<lb/>quæ quæ effluit. 141 </s></p> <p type="main"> <s><emph type="center"/>PARERGUM CAPITIS III.<emph.end type="center"/></s></p> <p type="main"> <s>De inventione mediæ, ac tertiæ proportionalis quantitatis, in numeris, & lineis. 144. </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Inter duos numeros medium proportionalem invenire. 145 </s></p> <p type="main"> <s>II. Datis duobus numeris, tertium continuè proportionalem invenire. ibid. </s></p> <p type="main"> <s>III. Inter duas rectas lineas datas invenire tertiam proportionalem. ibid. </s></p> <p type="main"> <s>IV. Datis duabus rectis, invenire tertiam proportionalem. 146 </s></p> <p type="main"> <s>V. Aliter invenire tertiam proportionalem. 147 </s></p> <p type="main"> <s>VI. Adhuc aliter invenire tertiam proportionalem. ibid </s></p> <p type="main"> <s>VII. Datis tribus numeris invenire quartum proportionalem. 148 </s></p> <p type="main"> <s>VIII. Datis tribus rectis lineis, quartam proportionalem invenire. ibid. </s></p> <p type="main"> <s><emph type="center"/>CAPUT IV.<emph.end type="center"/></s></p> <p type="main"> <s>De proprietatibus aquæ &longs;alientis ex tubis. 149 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Salientium &longs;ive ecdromorum horizontalium, & mediorum, &longs;uper eodem ho­<lb/>rizonte, longitudines &longs;unt in ratione &longs;ubduplicata tuborum, ex quibus exi­<lb/>liunt. 151 </s></p> <p type="main"> <s>III. Salientes horizontales & mediæ, ejusdem tubi, eò &longs;unt longiores, quò lu­<lb/>men tubi fuerit altius &longs;upra horizontem. 153 </s></p> <pb xlink:href="051/01/022.jpg"/> <p type="main"> <s>III. Salientes horizontales & mediæ, eandem longitudinis rationem &longs;ervant, <lb/>quam altitudines tuborum &longs;uper eundem horizontem. 154 </s></p> <p type="main"> <s>IV. Salientium verticalium in quacunque elevatione tubi &longs;upra horizontem <lb/>&longs;emper eadem e&longs;t altitudo. 155 </s></p> <p type="main"> <s>V. Saliens verticalis nunquam adæquat aluitudinem originis. 156 </s></p> <p type="main"> <s>VI. Saliens verticalis tubi quadrupedalis proximè æquat quinque &longs;extas tubi &longs;ui <lb/>partes. ibid. </s></p> <p type="main"> <s>VII. Salientes verticales eò &longs;unt longiores, quò tubi &longs;unt longiores; &longs;ed non eâ­<lb/>dem proportione illæ ac hi cre&longs;cunt. ibid. </s></p> <p type="main"> <s>VIII. Data tubi altitudine, & &longs;upra horizontem elevatione, invenire longitudi­<lb/>nem &longs;alientis horizontalis, & mediæ. 157 </s></p> <p type="main"> <s>IX. Data longitudine &longs;alientis horizontalis, aut mediæ, invenire altitudinem tu­<lb/>bi, cognitâ ejus elevatione &longs;upra horizontem. ibid. </s></p> <p type="main"> <s>X. Ex nota &longs;caturiginis altitudine fontis unius ex tubo exilientis horizontaliter, <lb/>altitudinem &longs;caturiginis cujuscunque alterius æqualiter &longs;upra horizontem <lb/>elevati invenire. 158 </s></p> <p type="main"> <s><emph type="center"/>CAPUT V.<emph.end type="center"/></s></p> <p type="main"> <s>De fluxu aquæ per diver&longs;a ejusdem va&longs;is aut tubi foramina. 158 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Per foramina æqualia, æquè à &longs;ummo tubi di&longs;tantia, &longs;ive in ba&longs;e, &longs;ive in latere, <lb/>æquali tempore æquales fluunt aquarum quantitates. 160 </s></p> <p type="main"> <s>II. Aquæ è foraminibus æqualiter à &longs;ummo tubi di&longs;tantibus decurrentes, &longs;unt in­<lb/>ter &longs;e ut foramina. ibid. </s></p> <p type="main"> <s>III. Aqua per foramina va&longs;is eo impetu &longs;eu velocitate decurrit, quo per tubos <lb/>æqualium foraminum & altitudinum. 161 </s></p> <p type="main"> <s>IV. Velocitates aquæ decurrentis per foramina æqualia ejusdem va&longs;is, inæqua­<lb/>liter di&longs;tantia à &longs;ummo va&longs;is, &longs;unt in &longs;ubduplicata ratione di&longs;tantiæ. 162 </s></p> <p type="main"> <s>V. Aquæ per æqualia foramina inæqualiter à &longs;ummitate va&longs;is di&longs;tantia fluentes, <lb/>&longs;unt in &longs;ubduplicata ratione di&longs;tantiarum. ibid. </s></p> <p type="main"> <s>VI. Secto foramine laterali va&longs;is in partes æquales, à rectis horizontalibus, in­<lb/>venire rationes aquarum ex eis fluentium. 163 </s></p> <p type="main"> <s>VII. Secto foramine laterali va&longs;is in partes inæquales, à rectis horizontalibus, <lb/>reperire rationes aquarum effluentium ex ip&longs;is. 164 </s></p> <p type="main"> <s>VIII. Datis foraminibus inæqualibus &longs;uper eadem horizontali, venari rationes <lb/>aquarum. ibid. </s></p> <p type="main"> <s>IX. Datis foraminibus ejusdem va&longs;is, quorum unum &longs;uperius, alterum inferius, <lb/>inter easdem parallelas perpendiculares, reperire rationes aquarum. 165 </s></p> <pb xlink:href="051/01/023.jpg"/> <p type="main"> <s>X. Datis foraminibus ejusdem va&longs;is, quorum unum &longs;uperius, alterum inferius; <lb/>non inter easdem parallelas, reperire rationes aquarum. ibid. </s></p> <p type="main"> <s>XI. Dato foramine, & linea horizontali, in aliquo va&longs;e, con&longs;tituere &longs;uper illa fo­<lb/>ramen, è quo æqualis aqua fluat eodem tempore. 166 </s></p> <p type="main"> <s>XII. Dato foramine, & latere alterius in eodem va&longs;e, reperire foramen, è quo <lb/>æqualis aqua effluat. ibid. </s></p> <p type="main"> <s>XIII. Dato foramine, reperire aliud æquale in eodem va&longs;e, è quo fluat aqua in <lb/>ratione data. 167 </s></p> <p type="main"> <s>XIV. Dato foramine, aptare in eodem va&longs;e aliud datum &longs;imile, magnitudinis di­<lb/>ver&longs;æ, à quo aqua fluens cum fluente à primo, habeat rationem datam. 168 </s></p> <p type="main"> <s><emph type="center"/>CAPUT VI.<emph.end type="center"/></s></p> <p type="main"> <s>De aëris gravitate, rarefactione, & conden&longs;atione. 169 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Aëris gravitatem invenire. 169 </s></p> <p type="main"> <s>II. Quantum conden&longs;ari aër po&longs;&longs;it, invenire. 170 </s></p> <p type="main"> <s>III. Quantum rarefieri aër po&longs;&longs;it, invenire. 171 </s></p> <p type="main"> <s><emph type="center"/>PARS II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PRACTICA.<emph.end type="center"/></s></p> <p type="main"> <s>De fabrica Machinarum Hydro-pnevmaticarum ex traditis principiis. 173 </s></p> <p type="main"> <s><emph type="center"/>CLASSIS PRIMA.<emph.end type="center"/></s></p> <p type="main"> <s>De variis Hydraulicis atque Pnevmaticis Machinis. 176 </s></p> <p type="main"> <s><emph type="center"/>CAPUT I.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis quæ fiunt vi attractiva. ibid. </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Fonticulus phialæ vitreæ inclu&longs;us. 177 </s></p> <p type="main"> <s>II. Siphon inver&longs;us interruptus, aquam in determinatam altitudinem evchens. 179. </s></p> <p type="main"> <s>III. Fons Cæ&longs;areus. 181 </s></p> <p type="main"> <s>IV. Scyphus plenus per fundum effundens liquorem, non plenus retinens. 183 </s></p> <p type="main"> <s>V. Cancer vomitor. 185 </s></p> <p type="main"> <s>VI. Sphæra vitrea Aqui&longs;uga. 186 </s></p> <p type="main"> <s>VII. Siphon inver&longs;us interruptus, elevans aquam in quamvis altitudinem. ibid. </s></p> <p type="main"> <s>VIII. Navis Horologa. 188 </s></p> <p type="main"> <s>IX. Siphon inver&longs;us horologus. 189 </s></p> <pb xlink:href="051/01/024.jpg"/> <p type="main"> <s>X. Bina va&longs;a, quorum uni &longs;i aqua infundatur, alterum reddit vinum. 190 </s></p> <p type="main"> <s><emph type="center"/>CAPUT II.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis quæ fiunt vi expul&longs;iva. 191 </s></p> <p type="main"> <s>I. Fons Heronis in va&longs;is immediatis. 192 </s></p> <p type="main"> <s>Item Fonticulus &longs;imilis Fonti Heronis. 194 </s></p> <p type="main"> <s>II. Clep&longs;ydra Heroniana. 195 </s></p> <p type="main"> <s>III. Fons Heronis in va&longs;is mediatis: item &longs;cyphus diver&longs;os ejiciens liquores. 197. </s></p> <p type="main"> <s>IV. Fons novus Poly&longs;iphonius. 201 </s></p> <p type="main"> <s>V. Fons perennis, alto in loco aquam è puteo profundo &longs;ubmini&longs;trans. 203 </s></p> <p type="main"> <s>VI. Antlia, &longs;eu Cte&longs;ibia Machina. 205 </s></p> <p type="main"> <s>VII. Speculator cornu inflans. 207 </s></p> <p type="main"> <s>VIII. Fonticulus compre&longs;&longs;ione aquam &longs;pargens in altum: Baculus item viato­<lb/>rius aquivomus, & Catellus mingens. 208 </s></p> <p type="main"> <s>IX. Phiala vitrea, compre&longs;&longs;ione aquam projiciens in altum. 211 </s></p> <p type="main"> <s>X. Infundibulum pnevmatico-hydraulicum, aquam in determinatam altitudi­<lb/>nem attollens. 211 </s></p> <p type="main"> <s>XI. Infundibulum alterum pnevmatico-hydraulicum, aquam in quamlibet al­<lb/>titudinem extollens. 213 </s></p> <p type="main"> <s>XII. Fons eâdem fi&longs;tulâ di&longs;colores ejiciens liquores. 214 </s></p> <p type="main"> <s>XIII. Sclopetum Æolium &longs;eu pnevmaticum. 216 </s></p> <p type="main"> <s>XIV. Aliud &longs;clopetum Pnevmaticum. 217 </s></p> <p type="main"> <s>XV. Sedes Aquivoma. 219 </s></p> <p type="main"> <s>XVI. Heronis va&longs;a quæ vinum pro aquainfu&longs;a reddunt: &longs;eu Hydriæ Canæ Ga­<lb/>lilææ. 220 </s></p> <p type="main"> <s>XVII. Hydraconti&longs;terium antiquum. 222 </s></p> <p type="main"> <s>XVIII. Hydraconti&longs;terium novum. 223 </s></p> <p type="main"> <s><emph type="center"/>CAPUT III.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis quæ fiunt rarefactione. 226 </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Pyrobolus fons, incale&longs;centis per ignem aëris vi aquam expellens. 226 </s></p> <p type="main"> <s>II. Fons alius pyrobolus, projectum liquorem convertens in aërem, autignem. <lb/>226. Item Meteorologicæ impre&longs;&longs;iones igneæ. 229 </s></p> <p type="main"> <s>III. Thermo&longs;copium progno&longs;ticum Hybernum. 229. & Æ&longs;tivum. 231 </s></p> <p type="main"> <s>IV. In&longs;trumentum novum, gradus humidi & &longs;icci indicans. 232 </s></p> <p type="main"> <s>V. Cacabus ejiciens, & retrahens eandem aquam. 236 </s></p> <p type="main"> <s>VI. Pilæ Æoliæ. 237 </s></p> <p type="main"> <s>VII. Ci&longs;ta Æolia. 238 </s></p> <pb xlink:href="051/01/025.jpg"/> <p type="main"> <s>VIII. Æolus ventum efflans. 239 </s></p> <p type="main"> <s>IX. Memnonia &longs;tatua, citharæ, & humanæ vocis &longs;onum ad orientem &longs;olem <lb/>edens. 240 </s></p> <p type="main"> <s>X. Memnoniæ aves, voce & motu animatæ. 242 </s></p> <p type="main"> <s>XI. Ara a&longs;pide adornata, in qua igne po&longs;ito I&longs;is & O&longs;iris vinum & lac &longs;acrificant <lb/>a&longs;pis verò &longs;ibilando applaudit. 244 </s></p> <p type="main"> <s>XII. Valvæ &longs;acelli &longs;uccen&longs;o &longs;acrificii igne &longs;ponte aperibiles, & extincto clau&longs;æ. 246. </s></p> <p type="main"> <s>XIII. Ara Deorum imagines tripudiantes exhibens. 247 </s></p> <p type="main"> <s>XIV. Hydrologium horarum A&longs;tronomicarum, &longs;eu æqualium. 248 </s></p> <p type="main"> <s>XV. Fonticulus horarius. 249 </s></p> <p type="main"> <s>XVI. Præco horarius, &longs;ingulis horis cornu inflans. 252 </s></p> <p type="main"> <s><emph type="center"/>CAPUT IV.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis quæ fiunt naturali lap&longs;u aquæ. 254 </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Clep&longs;ydra Kircheriana, quæ fontis in&longs;tar ejaculatur aquam, & inver&longs;a ite­<lb/>rum fluit. 254 </s></p> <p type="main"> <s>II. Multimammia Deorum mater, lac ex uberibus promens. 256 </s></p> <p type="main"> <s>III. Rota ver&longs;atilis, aquam lu&longs;trationi nece&longs;&longs;ariam fundens. 257 </s></p> <p type="main"> <s>IV. Cycocephalus Ægyptius ex veretillo aquam fundens, quæ horas æquino­<lb/>ctiales in &longs;ubjecto va&longs;e mon&longs;trat. 259 </s></p> <p type="main"> <s>V. Hydrologium horarum antiquarum, &longs;eu inæqualium. 261 </s></p> <p type="main"> <s>VI. Hydrologium Bettinianum. 264 </s></p> <p type="main"> <s>VII. Hercules clavâ Draconem percutiens. 265 </s></p> <p type="main"> <s>VIII. Aquila horodictica. 269 </s></p> <p type="main"> <s>IX. Chorea &longs;erpentum aquivomorum. 270 </s></p> <p type="main"> <s>X. Coluber volitans. 271 </s></p> <p type="main"> <s>XI. Nauta Hydro-horologus. 272 </s></p> <p type="main"> <s>XII. Libra hydraulica horodictica. 274 </s></p> <p type="main"> <s>XIII. Hydraulicum horolabium facillimum. 275 </s></p> <p type="main"> <s>XIV. Incubus Hydro-horologus. 276 </s></p> <p type="main"> <s>XV. Hydrologium Magneticum. 277 </s></p> <p type="main"> <s><emph type="center"/>CAPUT V.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis quæ habent principium mixtum. 278 </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Avis ex&longs;putam à &longs;erpente aquam &longs;orbens è cratere. 279 </s></p> <p type="main"> <s>II. Vas hydro-pnevmaticum, omnis generis jocos exhibens. 281 </s></p> <p type="main"> <s>III. Triton buccinâ inflatâ cur&longs;um fluminum fi&longs;tens. 285 </s></p> <pb xlink:href="051/01/026.jpg"/> <p type="main"> <s>IV. Atlas cælum humeris impo&longs;itum torquens in gyrum. 289 </s></p> <p type="main"> <s>V. Lucerna Grunbergeriana. 290 </s></p> <p type="main"> <s>VI. Hydrotechnicus tubus, varia ludentis Naturæ &longs;pectacula exhibens. 291 </s></p> <p type="main"> <s><emph type="center"/>CAPUT VI.<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis hydraulicis variis. 299 </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Sphæra in aëre fu&longs;pen&longs;a, ac circa &longs;uum centrum mota. 300 </s></p> <p type="main"> <s>II. Cribrum Ve&longs;talis virginis. 303 </s></p> <p type="main"> <s>III. Tubus vitreus, aquam perpetuò incorruptam con&longs;ervans. 304 </s></p> <p type="main"> <s>IV. Phœnix hydro-botanica. ibid. </s></p> <p type="main"> <s>V. Phiala tabaci fumum refrigerans. 305 </s></p> <p type="main"> <s>VI. Torricelli & Berti tubus vacuo vacuus. 306 </s></p> <p type="main"> <s>VII. Hydropota varij coloris ac &longs;aporis aquam ex&longs;puens. 310 </s></p> <p type="main"> <s>VIII. Palingene&longs;ia Cæ&longs;area. 313 </s></p> <p type="main"> <s>IX. Vas eodem ore vinum & aquam, calidam & frigidam, hauriens ac fundens. 315 </s></p> <p type="main"> <s>X. Prochyta Heronis Alexandrini malè con&longs;tructa. 317 </s></p> <p type="main"> <s>XI. Libra hydro&longs;tatica mirabilis. 318 </s></p> <p type="main"> <s>XII. Canopus Ægyptiacus. 320 </s></p> <p type="main"> <s>XIII. Lamina plumbea plana, aquis innatans. 321 </s></p> <p type="main"> <s>XIV. Anemo&longs;copium commune. ibid. </s></p> <p type="main"> <s>XV. Anemo&longs;copium Kircherianum. 323 </s></p> <p type="main"> <s>Epilogus Cla&longs;&longs;is primæ, ubi nonnulla de fontibus Romanis, ac Tu&longs;culanis, <lb/>aliisque. 325 </s></p> <p type="main"> <s><emph type="center"/>CLASSIS SECUNDA<emph.end type="center"/></s></p> <p type="main"> <s>De Machinis motum perpetuum æmulantibus. 329 </s></p> <p type="main"> <s>PROLUSIO. De motus perpetui arte procurati impo&longs;&longs;ibilitate. ibid. </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Cochlea Archimedea motum perpetuum æmulans. 336 </s></p> <p type="main"> <s>II. Tubus &longs;piralis in plano, aquam attollens, & motum perpetuum æmulans. 341 </s></p> <p type="main"> <s>III. Horarium hydraulicum, motum perpetuum adumbrans. 346 </s></p> <p type="main"> <s>IV. Kircheriana Machinula, motus perpetui rarefactionis & conden&longs;ationis <lb/>&longs;pecimen exhibens. 351 </s></p> <p type="main"> <s>V. Fonticulus motum perpetuum vi rarefactionis & conden&longs;ationis aëris e­<lb/>mentitus. 353 </s></p> <pb xlink:href="051/01/027.jpg"/> <p type="main"> <s>VI. Horo&longs;copium Hydropnevmato-Magneticum, quo &longs;phæra Magnetica in <lb/>medio liquorum librata perpetuò circumducitur, ad mon&longs;trandas ho­<lb/>ras, circulos cœle&longs;tes, totiusque A&longs;trolabij my&longs;teria. 354 </s></p> <p type="main"> <s>VII. Machinamentum aliud hydro-pnevmatico-magneticum, perpetuans mo­<lb/>tum per ventum. 357 </s></p> <p type="main"> <s>VIII. Cte&longs;ibica Machina perpetui motus æmula. 360 </s></p> <p type="main"> <s>IX. Catona perpetuò mobilis in gyrum hydro&longs;taticâ arte, ut putabatur. 362 </s></p> <p type="main"> <s>X. Situlæ automatæ, &longs;pontaneo atque perpetuo motu aquam haurientes. 365 </s></p> <p type="main"> <s>XI. Funigiana indu&longs;tria perpetuo motu &longs;itulæ unicæ è puteis aquam hauriens. 368 </s></p> <p type="main"> <s>XII. Perennis fontium ac fluviorum in Terraqua circulatio. 371 </s></p> <p type="main"> <s>XIII. Gnomon Scheinerianus in centro mundi. 374 </s></p> <p type="main"> <s>XIV. Mobile perpetuum Chymico-hydraulicum. 376 </s></p> <p type="main"> <s>ANNOTATIO II. De Motu perpetuo quem Drebellius & alij adumbrarunt. 377 </s></p> <p type="main"> <s>ANNOTATIO III. De motu perpetuo quem Boëklerus promittit. 379 </s></p> <p type="main"> <s>ANNOTATIO IV. De motu perpetuo quem D. Har&longs;torfferus excogitavit. 381 </s></p> <p type="main"> <s><emph type="center"/>CLASSIS TERTIA.<emph.end type="center"/></s></p> <p type="main"> <s>De Organis hydraulicis, aliisque in&longs;trumentis harmonicis hydropnevma­<lb/>ticis. 383 </s></p> <p type="main"> <s>MACHINA I. Organum hydraulicum automatum & autophonum. 384 </s></p> <p type="main"> <s>PRAGMATIA I. Cameras Æolias fabricari, ad ventum organo hydraulico <lb/>&longs;ubmini&longs;trandum. ibid. </s></p> <p type="main"> <s>PRAGMATIA II. Secundus modus Æolias cameras fabricandi. 386 </s></p> <p type="main"> <s>PRAGMATIA III. Tertius modus Æolias cameras con&longs;truendi. 387 </s></p> <p type="main"> <s>PRAGMATIA IV. Ventum per folles perpetuum producere in ordine ad <lb/>Organa hydraulica. 388 </s></p> <p type="main"> <s>PRAGMATIA V. Folles aliter inflare ad in&longs;trumenta chordophôna &longs;ive <lb/>fidicina incitanda. 389 </s></p> <p type="main"> <s>PRAGMATIA VI. Cylindrum phonotacticum con&longs;truere. 390 </s></p> <p type="main"> <s>§. I. Cylindrum phonotacticum harmonicè delineare. ibid. </s></p> <p type="main"> <s>§. II. Cantilenam in Cylindrum phonotacticum harmonicè delineatum <lb/>transferre. 397 </s></p> <p type="main"> <s>§. III. Dentibus Cylindrum phonotacticum in&longs;truere. 399 </s></p> <p type="main"> <s>§. IV. Plures cantilenas in eundem cylindrum transferre. 400 </s></p> <p type="main"> <s>§. V. Cantilenas &longs;yncopatas, & <emph type="italics"/>b<emph.end type="italics"/> molli &longs;ignatas, ut & &longs;emitonia, in cylin­<lb/>drum phonotacticum transferre. 401 </s></p> <p type="main"> <s>§. VI. Minimi valoris notas cylindro phonotactico in&longs;erere. 406 <pb xlink:href="051/01/028.jpg"/> </s></p> <p type="main"> <s>PRAGMATIA VII. Cylindrum phonotacticum in gyrum movere. 407 </s></p> <p type="main"> <s>PRAGMATIA VIII. Organum hydraulicum automatum atque antophô­<lb/>num fabricare. 408 </s></p> <p type="main"> <s>MACHINA II. Organum hydraulicum Vitruvianum. 409 </s></p> <p type="main"> <s>MACHINA III. Cuculus cantans, atque tripudians. 414 </s></p> <p type="main"> <s>MACHINA IV. Gallus cantans & alas quatiens. 414 </s></p> <p type="main"> <s>MACHINA V. Diver&longs;æ volucres garrientes, ac &longs;e moventes. 417 </s></p> <p type="main"> <s>MACHINA VI. Pan Octaulum inflans, Nympha Echo reflans. 418 </s></p> <p type="main"> <s>MACHINA VII. Cyclopes automati Mu&longs;icam Pythagoricam exhibentes. 420. </s></p> <p type="main"> <s>MACHINA VIII. Clavicymbalum automatum, omnis generis in&longs;tru­<lb/>mentorum fidibus in&longs;tructorum &longs;ymphoniam exhibens. 432 </s></p> <p type="main"> <s>MACHINA IX. Automatum Kircherianum, omnis generis in&longs;trumento­<lb/>rum &longs;ymphoniam exhibens. 436 </s></p> <p type="main"> <s>MACHINA X. Ci&longs;ta pnevmato-harmonica antophóna, &longs;olo vento harmo­<lb/>nio&longs;um &longs;onum edens. 438 </s></p> <p type="main"> <s><emph type="center"/>EXPERIMENTUM NOVUM <lb/>MAGDEBURGICUM.<emph.end type="center"/></s></p> <p type="main"> <s>§. I. Experimentum quomodo fiat. 445 </s></p> <p type="main"> <s>§. II. Experimento jam invento quænam de novo addita Herbipoli. 447 </s></p> <p type="main"> <s>§. III. Argumenta ad &longs;tabiliendum vacuum ex hoc Experimento &longs;umpta. 449 </s></p> <p type="main"> <s>§. IV. Argumenta ad evertendum vacuum ex eodem Experimento deprom­<lb/>pta. 450 </s></p> <p type="main"> <s>§. V. P. Athana&longs;ii Kircheri de novo Experimento judicium. 452 </s></p> <p type="main"> <s>§. VI. Litteræ Auctoris Experimenti, ejusdemque ad varia quæ&longs;ita re&longs;pon&longs;io. 453. </s></p> <p type="main"> <s>§. VII. Ejusdem Authoris re&longs;pon&longs;io ad no&longs;trum quæ&longs;itum. 450 </s></p> <p type="main"> <s>§. VIII. P. Nicolai Zucchii è Societate Je&longs;u de novo Experimento judicium. 463. </s></p> <p type="main"> <s>§. IX. P. Melchioris Cornæi è Societate Je&longs;u de eodem Experimento judi­<lb/>cium. 465 </s></p> <figure id="id.051.01.028.1.jpg" xlink:href="051/01/028/1.jpg"/> <pb xlink:href="051/01/029.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>In<emph.end type="italics"/><lb/>MECHANICAM HYDRAU­<lb/>LICAM<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Odarion Encomia&longs;ticon.<emph.end type="center"/><lb/><emph type="italics"/>CEdat &longs;uperbas Amphitryonides <lb/>Palmas Minervæ. </s><s>Vis jacet: Artium <lb/>Tropæa clarent. </s><s>Cuncta nutus <lb/>Jam Dominæ venerantur Artis. </s><s><lb/>Non ille no&longs;tri temporis Hercules, <lb/>Qui frangit armis cornua fluminum, <lb/>Dum cana &longs;eclorum &longs;enectus <lb/>Ingeniis animis <expan abbr="&qacute;ue">que</expan> floret. </s><s><lb/>Quid? </s><s>ergò Reges nè furor incitet <lb/>Vincire Pontum. </s><s>Nil ni&longs;i fabulam <lb/>Seris propinabit nepotum <lb/>Fa&longs;tus Achæmenidæ cachinnis. </s><s><lb/>Risêre &longs;tultas æquora compedes <lb/>Manare ritu certa &longs;uo, licet <lb/>Ringatur & flagro rebelles <lb/>Mulctet aquæ male&longs;anus iras. </s><s><lb/>In&longs;anientis quid Domini minæ <lb/>Tangunt proteruum marmor? Herus jubet? <lb/>Surde&longs;cit, & plaudente fluctu <lb/>Ludificat pelagus Tyrannum. </s><s><lb/>At non & Artem vis Acheloia <lb/>Impunè ludet. </s><s>Capta &longs;uis Aqua <lb/>Technis tenetur, liberosque <lb/>Victa jocos, patiturque ri&longs;us.<emph.end type="italics"/> <pb xlink:href="051/01/030.jpg"/><emph type="italics"/>Et quas domando non potuit mari <lb/>Sevùm fremi&longs;cens ardor adoreas, <lb/>Has lenè &longs;olers Machinator <lb/>Præripuit meliore ni&longs;u. </s><s><lb/>Spectare ge&longs;tin? en tibi panditur <lb/>Hoc &longs;cena libro, quâ &longs;trepitu procul, <lb/>Quæ dulce &longs;it &longs;pecta&longs;&longs;e, &longs;pectes, <lb/>Quæque juvet didici&longs;&longs;e, di&longs;cas, <lb/>Quàm fœderatum non violabilis <lb/>Lex nectat orbem; &longs;i qua pericula <lb/>Vexent, ut imis &longs;umma, raris <lb/>Den&longs;a, levi grave det &longs;alutem. </s><s><lb/>Quò pondus vnd<gap/> vergat, & aëris; <lb/>Quod pellat; aut quod corpora jus trahat; <lb/>Cur i&longs;te gurges ructet vndas, <lb/>Quas avido bibit ales ore; <lb/>Quid mille lu&longs;us, mille jocos aquæ <lb/>Fundet, docebit<emph.end type="italics"/> SCHOTTVS <emph type="italics"/>Hydraulicæ <lb/>Con&longs;ultus artis, doctas idem <lb/>Ingenium fluitantis auræ. </s><s><lb/>Non Ille nomen fluctibus apprimat, <lb/>Quod turbet Au&longs;ter, dignus aheneis <lb/>Scribi columnis, quæ nec ævi <lb/>Dente, nec invidiæ terantur.<emph.end type="italics"/></s></p> <p type="main"> <s>L. G. S. J. </s></p> <pb xlink:href="051/01/031.jpg"/> <p type="main"> <s><emph type="center"/><emph type="italics"/>MONITIO AD LECTOREM.<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s>Opu&longs;culum hoc Appendice exceptâ Romæ <lb/>con&longs;criptum, acprælo præparatum fuit; <lb/>ideo in eo pa&longs;sim ita loquitur Auctor, <lb/>qua&longs;i Romæ adhuc degeret. </s><s>Vale, & nè <lb/>quid te moretur, errores paucos in calce <lb/>Librinotatos, priùs corrige. </s></p> <pb xlink:href="051/01/032.jpg" pagenum="1"/> <figure id="id.051.01.032.1.jpg" xlink:href="051/01/032/1.jpg"/> <p type="main"> <s><emph type="center"/>MECHANICA <lb/>HYDRAVLICO-PNEVMATICA.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PRÆLOQVIVM <lb/>AD LECTOREM;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De Operis Occa&longs;ione, Divi&longs;ione, <lb/>In&longs;criptione: <expan abbr="de&qacute;ue">deque</expan> Hydraulicorum, <lb/>& Pnevmaticorum Scripto­<lb/>ribus.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>OCCASIO OPERIS.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>MAgiam Naturalem con&longs;cribere ani-<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg1"/><lb/><emph type="italics"/>mus mihi est, benevole Lector, è Viri <lb/>Docti&longs;&longs;imi, toto&queacute; orbe noti&longs;&longs;imi Atha­<lb/>na&longs;ij Kircheri Libris, quà typo excu&longs;is, <lb/>quà exar atis manu collectam; at&que; ex omnibus eius­<lb/>dem Adver&longs;ariis ac Schediasmatis, quæ penes me <lb/>&longs;unt; nec non ex alijs probatorum Auctorum monu­<lb/>mentis, nostris&queacute; inventis, fide &longs;ummâ, pari&queacute; &longs;tudio <lb/>concinnatam, propriis&queacute; & aliorum experimentis <lb/>&longs;tabilitam: illam inquam Magiam Naturalem, cuius<emph.end type="italics"/> <pb xlink:href="051/01/033.jpg" pagenum="2"/><emph type="italics"/>in Catalogo Librorum posthàc à prædicto Docti&longs;&longs;imo <lb/>Auctore edendorum Magneticæ Arti denuò hîc Ro­<lb/>mæ nuper editæ appo&longs;ito feci mentionem. </s><s>Spartam <lb/>hanc ab ip&longs;o Auctore mihi commi&longs;&longs;am præ alijs a&longs;&longs;um­<lb/>p&longs;i excolendam, quoniam præterquàm quòd omnium <lb/>ab ip&longs;o con&longs;criptorum librorum, &longs;eu prælo <expan abbr="commi&longs;&longs;orũ">commi&longs;&longs;orum</expan>, <lb/>&longs;eu in Adver&longs;aria coniectorum, copiam habeo, quo­<lb/>tidianâ eiusdem vtor con&longs;uetudine, vtpote inre litte­<lb/>rariâ &longs;ocius; cuius proinde &longs;ententiam aut minùs <lb/>intellectam, aut breviùs &longs;ubinde explicatam, exquire­<lb/>re nullo negotio po&longs;&longs;um. </s><s>Opus erit ingens, multi&queacute; la­<lb/>boris ac &longs;tudij, nec minùs reconditâ rerum cùm natu­<lb/>ralium, tùm arte factarum refertum &longs;cientiâ. </s><s>Habe­<lb/>bis in eo varia, curio&longs;a, exotica admir andorum effe­<lb/>ctuum &longs;pectacula, reconditarúmque inventionum mi­<lb/>racula, & quæ meritò cen&longs;ebuntur magica; ab omni <lb/>tamen imposturâ, & illicitæ artis &longs;u&longs;picione aliena. </s><s><lb/>Habebis Magiam Arithmeticam; at non vulgarem: <lb/>Habebis Geometricam; at paucis perviam: Habebis <lb/>Astronomicam; at penitùs abstru&longs;am Invenies Ma­<lb/>giam Magneticam, Gnomonicam, Staticam, Opti­<lb/>cam, Dioptricam, Catoptricam, Hydraulicam, Pnev-<emph.end type="italics"/> <pb xlink:href="051/01/034.jpg" pagenum="3"/><emph type="italics"/>maticam, Pyrobolicam, <expan abbr="Harmonicã">Harmonicam</expan>, <expan abbr="Phonocampticã">Phonocampticam</expan> <lb/><expan abbr="Anacãpticã">Anacampticam</expan>, Anaclasticam, <expan abbr="Phy&longs;iognomicã">Phy&longs;iognomicam</expan>, Mecha­<lb/>nicam, Sympathicam, Steganologicam, Cryptographi­<lb/>cam, Divinatoriam, Cabalicam, Hieroglyphicam, <lb/>Sacram. </s><s>Miraberis in eodem Opere &longs;ecreta Ani­<lb/>malium, Herbarum, Plantarum, Lapidum, aliarúm­<lb/>que rerum per variam activorum cum pa&longs;&longs;ivis appli­<lb/>cationem, virtutum occultarum combinationem, Na­<lb/>turæ & Artis connubium, Paranymphâ Experientiâ. </s><s><lb/>Jdeam aliquam in fine huius Operis invenies.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg1"/>Magia Na­<lb/>turalis Au­<lb/>ctoris.</s></p> <p type="main"> <s><emph type="italics"/>Quoniam verò Opus, vt dixi, vastum erit, mul­<lb/>ti&queacute; laboris ac &longs;tudij, nec ni&longs;i &longs;ubci&longs;ivis horis, quas <lb/>ordinariis occupationibus &longs;ubtr ahere licebit, perfici­<lb/>endum; operæ pretium me facturum, gratúmque Rei­<lb/>publicæ Litterariæ existimavi, &longs;iquæ paulatim elabo­<lb/>ra&longs;&longs;em, per partes protruderem. </s><s>Ab Hydraulicis igi­<lb/>tur atque Pnevmaticis initium &longs;umere decrevi, id&queacute; <lb/>non tàm meâ, quàm aliorum voluntate. </s><s>Scribendi <lb/>occa&longs;io hæc fuit. </s><s>Est in &longs;upradicti Docti&longs;&longs;imi Auctoris<emph.end type="italics"/><lb/> <arrow.to.target n="marg2"/><lb/><emph type="italics"/>Mu&longs;eo &longs;anè celeberrimo, frequentati&longs;&longs;imóque (quod <lb/>brevi typis evulgabimus) non exigua <expan abbr="Hydraulicarũ">Hydraulicarum</expan> <lb/>ac Pnevmaticarum Machinarum copia, quas &longs;um-<emph.end type="italics"/> <pb xlink:href="051/01/035.jpg" pagenum="4"/><emph type="italics"/>mâ animi voluptate &longs;pectant atque mirantur ij, qui <lb/>ex omnibus Vrbis & Orbis partibus ad ip&longs;um vi&longs;en­<lb/>dum accurrunt Viri Principes ac Litter ati, avidé­<lb/>que &longs;cire de&longs;iderant, & Machinarum constructa­<lb/>rum rationes, & machinalium motionum cau&longs;as. </s><s>Ho­<lb/>rum de&longs;iderìo vt &longs;atisfacerem, omnium dicti Mu&longs;ej <lb/>Machinarum fabricam & qua&longs;i anatomiam edoce­<lb/>re, aut alicubi jam ab ip&longs;o Auctore edoctam enarrare, <lb/>brevi opu&longs;culo aggre&longs;&longs;us &longs;um. </s><s>Quod dum faciebam, <lb/>tam multa <expan abbr="ejusd&etilde;">ejusdem</expan> argumenti animo <expan abbr="calamóq;">calamóque</expan> occur­<lb/>rebant, quæ alibi videram, legeram, excogitaveram <lb/>ip&longs;e, nec vulgaria, nec injucunda, vt difficiliùs mihi <lb/>fuerit &longs;istere, quàm pro&longs;equi inceptum cur&longs;um; nec mi­<lb/>nor in non &longs;eribendo, quàm in &longs;cribendo labor &longs;ubeun­<lb/>dus: multóque plurafuerunt omittenda, quàm char­<lb/>tæ committenda, vt &longs;umptibus & tempori parceretur.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg2"/>Mu&longs;eum <lb/>Kircheria­<lb/>num.</s></p> <p type="main"> <s><emph type="center"/>OPERIS DIVISIO.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>Cùm verò vt in aliis &longs;cientiis & artibus, ita in Hydrauli­<lb/>cis atque Pnevmaticis, vel maximè Praxis & Theoria<emph.end type="italics"/><lb/> <arrow.to.target n="marg3"/><lb/><emph type="italics"/>conjunctionem ita ambiant, vt vna &longs;i alteram de&longs;tituat, meri­<lb/>tò vtraque cadat; & nec &longs;ola Praxis &longs;uam &longs;ine Theoria obtine­<lb/>at exi&longs;timationem, nec &longs;ine Praxi&longs;ola &longs;uam Theoria; <expan abbr="vtram&qacute;">vtramque</expan>; <lb/>coniungendam putavi; præ&longs;ertim cùm vix vllum id hactenus <lb/>factita&longs;&longs;e videam, <expan abbr="tu&qacute;ue">tuque</expan> mecum per&longs;picies, Lector, &longs;ievolves,<emph.end type="italics"/> <pb xlink:href="051/01/036.jpg" pagenum="5"/><emph type="italics"/>quotquot de Aquaticis ac Spiritalibus quoquo modo <expan abbr="tractârũt">tractârunt</expan> <lb/>Auctores, quorum Elenchum po&longs;tea dabimus. </s><s>Plerique enim <lb/>nudam duntaxat tradunt Praxin, non per&longs;criptis, ac nè indi­<lb/>catis quidem operandi principijs &longs;eu fundamentis, quæ veligno­<lb/>rarunt ip&longs;i, vel alijs inviderunt: quò fit, vt alijs &longs;æpe errandi <lb/>præbeant occa&longs;ionem, & ip&longs;i <expan abbr="nõ">non</expan> rarò pudendos committant erro­<lb/>res, vel tunc etiam, cùm aliorum errores detegere <expan abbr="at&qacute;ue">atque</expan> corri­<lb/>gere præ&longs;umptuo&longs;iùs attentant. </s><s>In duas igitur partes Opus to­<lb/>tum dividimus. </s><s>In prima theoriam damus ad omnis generis <lb/>Machinas Hydraulicas, Pnevmaticas, & Mixtas ex Vtris­<lb/>que con&longs;truendas facilitate &longs;ummâ, &longs;ucce&longs;&longs;u infallibili. </s><s>In &longs;e­<lb/>cunda fabricam docemus, & praxim exhibemus innumera­<lb/>rum Machinarum, &longs;eu purè Hydraulicarum, &longs;eu purè <lb/>Pnevmaticarum, &longs;eu Hydro-pnevmaticarum, hoc e&longs;t, ex v­<lb/>tris que Mixtarum, ex traditis principijs con&longs;tructarum, con­<lb/>&longs;truendarumvè, ad hortorum delicias, <expan abbr="domorum&qacute;ue">domorumque</expan> vtilita­<lb/>tes, commoditates, ornamenta, virorum præ&longs;ertim Principum, <lb/>qui magis oculorum inde, <expan abbr="animi&qacute;ue">animique</expan> oblectamentum, quàm rei <lb/>familiaris quæ&longs;tum ex&longs;pectant. </s><s>Nec oculos tantum modò pa­<lb/>&longs;<gap/>ere &longs;atagimus; auribus etiam &longs;ua paramus delinimenta, <expan abbr="va-ria&qacute;ue">va­<lb/>riaque</expan> Organa atque Jn&longs;trumenta automata, & autophona, <lb/>&longs;olo aquarum lap&longs;u, aëris <expan abbr="&qacute;ue">que</expan> allap&longs;u, in motum ac &longs;onum con­<lb/>citamus, non minori facilitate, quàm arte. </s><s>Et quoniam in-<emph.end type="italics"/><lb/> <arrow.to.target n="marg4"/><lb/><emph type="italics"/>credibilis e&longs;t hodie, &longs;i unquam aliàs, ne&longs;cio an manuum, an ve­<lb/>rò ingeniorum pruritus, motum, quem vocant perpetuum (quem <lb/>tot modis ac vijs <expan abbr="nõ">non</expan> pauci hactenus quæ&longs;iverunt, &longs;ed fru&longs;trà, per­<lb/>ennis quietis potiùs quàm motionis Architecti) reap&longs;e exhibendi,<emph.end type="italics"/> <pb xlink:href="051/01/037.jpg" pagenum="6"/><emph type="italics"/>& Mundo iam dudum eius exæ&longs;tuanti de&longs;iderio obtrudendi; <lb/><expan abbr="multi&qacute;ue">multique</expan> putant, non alijs &longs;aciliùs Machinis quàm hydrauli­<lb/>cis in opus deduci id po&longs;&longs;e; in vnum collegi <expan abbr="refutavi&qacute;ue">refutavique</expan>, quot­<lb/>quot videre, audire, legere potui aliorum artificia, qui eâ in re <lb/>&longs;e aliquid præ&longs;titi&longs;&longs;e putarunt, aut præ&longs;tari po&longs;&longs;e &longs;ibi per&longs;ua&longs;e­<lb/>runt; vt visâ alieni conatus vanitate, curio&longs;us Lector judi­<lb/>cium ferre de alijs queat, & à &longs;imili vano labore &longs;ibi temperet. <lb/>Tres igitur Cla&longs;&longs;es habebit Pars &longs;ecunda Operis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg3"/>Divi&longs;io O­<lb/>peris præ­<lb/>&longs;entis bi­<lb/>partita.</s></p> <p type="margin"> <s><margin.target id="marg4"/>Motus per­<lb/>petui effi­<lb/>ciendi pru­<lb/>ritus mul­<lb/>torum.</s></p> <p type="main"> <s><emph type="center"/>OPERIS INSCRIPTIO.<emph.end type="center"/><lb/> <arrow.to.target n="marg5"/></s></p> <p type="margin"> <s><margin.target id="marg5"/>In&longs;criptio <lb/>operis pr&ecedil;­<lb/>&longs;entis.</s></p> <p type="main"> <s><emph type="italics"/>MEchanicam porrò Hydraulico-pnevmaticam vocamus <lb/>hoc Opus; & Machinas Hydro pnevmaticas, &longs;eu Hydrau­<lb/>lico-pnevmaticas, quas in eodem producimus, appellamus, <lb/>quòd pleræque tales &longs;int, taliumque tradantur in prima Operis <lb/>parte principia ac regulæ; Hydraulico-pnevmaticas, inquam, <lb/>qua&longs;i dicas, Aquatico-Spiritales, hoc e&longs;t, aqua & &longs;piritu &longs;eu aëre<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg6"/><lb/><emph type="italics"/>animatas. Aquaticæ etenim Machinæ, hauriendis è profun­<lb/>do, deducendis per planitiem, educendis in altum per fi&longs;tulas ac <lb/>tubos<emph.end type="italics"/> (<foreign lang="greek">a)ul<gap/>\s</foreign> <emph type="italics"/>Græci appellant) aquis excogitatæ, triplicis &longs;unt<emph.end type="italics"/><lb/> <arrow.to.target n="marg7"/><lb/><emph type="italics"/>generis. Aliæ iumentorum, hominum, ponderum ope, rotis <lb/>variè inter &longs;e&longs;e implicatis, moventur; cuiusmodi &longs;unt tympa­<lb/>na, antliæ, cochleæ, tollenones, &longs;imiliaque, quæ Vitruvius pro­<lb/>ducit libro<emph.end type="italics"/> 10. <emph type="italics"/>Capite<emph.end type="italics"/> 9, 10, 11, 13, <emph type="italics"/>&<emph.end type="italics"/> 14. <emph type="italics"/>alijque <lb/>Auctores multi<emph.end type="italics"/> <arrow.to.target n="marg8"/><lb/><emph type="italics"/>ad nau&longs;eam vsque confarcinatis libris inculcant. Aliæ &longs;olo aqua­<lb/>rum lap&longs;u fontes exhibent amœni&longs;&longs;imos, & aquas per &longs;iphones <lb/>tubosque variè configuratos protru&longs;as nunc expandunt in &longs;ub­<lb/>tili&longs;&longs;imum lucidi&longs;&longs;imum que velum, nunc diffundunt in radios,<emph.end type="italics"/> <pb xlink:href="051/01/038.jpg" pagenum="7"/><emph type="italics"/>figurant in &longs;tellas, effingunt in flores, extendunt in iacula, cri­<lb/>&longs;pant in pluvias, conglobant in grandines, &longs;ummâ oculorum <lb/>voluptate, vt pa&longs;&longs;im in vrbanis ac &longs;uburbanis Romæ vide­<lb/>mus hortis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg6"/>Aquaticæ <lb/>Machinæ <lb/>triphcis <expan abbr="&longs;ũt">&longs;unt</expan> <lb/>generis.</s></p> <p type="margin"> <s><margin.target id="marg7"/>Tractoriæ.</s></p> <p type="margin"> <s><margin.target id="marg8"/>Hydrauli­<lb/>cæ.</s></p> <p type="main"> <s><emph type="italics"/>Aliæ denique inclu&longs;i intru&longs;ive äeris violentiâ eiaculan-<emph.end type="italics"/><lb/> <arrow.to.target n="marg9"/><lb/><emph type="italics"/>tur in altum aquas, inflant tibias, tubasque, volucrum ani­<lb/>maliumque aliorum imitantur motum ac Cantum, aliaque præ­<lb/>&longs;tant tam mira atque exotica, vix vt ab humano ingenio præ­<lb/>&longs;tari po&longs;&longs;e videantur. Eius generis fuit apud Cornelium Seve­<lb/>rum in Ætna Triton, qui aquarum a&longs;&longs;ultu auram concipiebat, <lb/>ac per buccinam ori admotam vocem edebat, &longs;ive vt ait Poëta, <lb/>irriguum Carmen. Tales etiam &longs;unt, quas magno numero, nec <lb/>minori ingenio prodit Hero in &longs;uo de Spiritalibus libello Machi­<lb/>nas, ab antiquis (quos Ægyptios interpretatur Kircherus in <lb/>Mechanica Ægyptiaca tom.<emph.end type="italics"/> 2. <emph type="italics"/>Oedipi parte<emph.end type="italics"/> 2.) <emph type="italics"/>excogitatas: <lb/>cuiusmodi &longs;unt &longs;tatuæ ad aras vinum & lac &longs;acrificantes, va­<lb/>&longs;a melancoryphi vocem edentia, Syringæ mentientes vocem a­<lb/>vicularum multarum per ordinem di&longs;po&longs;itarum, quibus a&longs;&longs;idet <lb/>noctua, quæ &longs;ua &longs;ponte ad aviculas conver&longs;a eas terret, & à <lb/>cantu ab&longs;terret; <expan abbr="aliæ&qacute;ue">aliæque</expan> multæ. Tales denique, quas toto hoc <lb/>Opere magno numero producimus.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg9"/>Hydrauli­<lb/>co-pnev­<lb/>maticæ.</s></p> <p type="main"> <s><emph type="italics"/>Primi generis Machinas appellamus nos cum alijs Tracto­<lb/>rias: & de illis non agimus hoc Opere; pertinent enim ad illam <lb/>Mechanicæ partem, quæ <expan abbr="viponderũ">viponderum</expan> atque rotarum &longs;uas perfi­<lb/>cit operationes, & &longs;ine ip&longs;ius principijs nec tradi, nec ab alijs <lb/>percipi po&longs;&longs;unt: quare Magiæ no&longs;træ Mechanicæ eas re&longs;erva­<lb/>mus. Secundi generis Machinas appellamus Hydraulicas.<emph.end type="italics"/> <pb xlink:href="051/01/039.jpg" pagenum="8"/><emph type="italics"/>Tertij denique generis Hydraulico-pnevmaticas. Quoniam <lb/>igitur pleræque Machinæ, quas producimus, huiu&longs;modi &longs;unt,<emph.end type="italics"/><lb/> <arrow.to.target n="marg10"/><lb/><emph type="italics"/>hoc e&longs;t, aquæ & aëris &longs;ub&longs;idio con&longs;tructæ; ideo Hydraulico­<lb/>pnevmaticas, vt dicebam, appellamus hoc Opere traditas <lb/>Machinas. Dico, plerasque aquæ & aëris &longs;ub&longs;idio e&longs;&longs;e con­<lb/>&longs;tructas; non omnes: &longs;unt enim & purè hydraulicæ multæ, & <lb/>purè pnevmaticæ non paucæ; imò nonnullæ, quæ licet aquæ au­<lb/>xilio fiant, hydraulicæ tamen propriè ac rigorosè, juxta &longs;en&longs;um <lb/>expo&longs;itum, cen&longs;eri non po&longs;&longs;unt, vt videbis in Operis decur&longs;u, <lb/>& ex Machinarum indice apparebit.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg10"/>Machinæ <lb/>huius Ope <lb/>ris <expan abbr="pleræq;">pleræque</expan> <lb/><expan abbr="&longs;ũt">&longs;unt</expan> hydrau­<lb/>lico-pnev­<lb/>maticæ.</s></p> <p type="main"> <s><emph type="center"/>SCRIPTORES HYDRAVLICORVM, <lb/>ET PNEVMATICORVM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>SCriptores quod attinet, qui de Hydraulicis, <expan abbr="Pnevmaticis-&qacute;ue">Pnevmaticis­<lb/>que</expan> quoquo modo &longs;crip&longs;erunt, & ad manus meas pervene­<lb/>runt, &longs;unt &longs;equentes, Alphabeti ordine.<emph.end type="italics"/> Archimedes, Atha­<lb/>na&longs;ius Kircherus, Augu&longs;tinus Ramellus, Benedictus Ca­<lb/>&longs;tellus, Daniel Lip&longs;torpius, Daniel Schvventerus, Evan­<lb/>geli&longs;ta Torricellus, Galilæus Galilæi, Ga&longs;par Ens, Ge­<lb/>orgius Agricola, Georgius Philippus Har&longs;torfferus, Ge­<lb/>orgius Valla, Hero Alexandrinus, Hieronymus Carda­<lb/>nus, Iacobus Be&longs;&longs;on, Ioannes Bapti&longs;ta Porta, Ioannes Ba­<lb/>pti&longs;ta Balianus, Ioannes Bapti&longs;ta Aleottus, Ioannes Iaco­<lb/>bus Weckerus, Ioannes Leurechon, Io&longs;ephus Ceredus, <lb/>Ioannes Branca, Marinus Ghetaldus, Marinus Mer&longs;en­<lb/>nus, Marius Bettinus, Nicolaus Cabæus, Petrus Herigo­<lb/>nius, Raphaël Magiottus, Robertus Valturius, Rober- <pb xlink:href="051/01/040.jpg" pagenum="9"/>tus à Fluctibus, Salomon Caus, Simon Stevinus, Theo­<lb/>dorus Muretus, Va&longs;&longs;or Arabs, Vitruvius, <expan abbr="eius&qacute;ue">eiusque</expan> Com­<lb/>mentatores, vt Philander, Barbarus, Cæ&longs;arinus, <expan abbr="alij&qacute;ue">alijque</expan>. <lb/><emph type="italics"/>Hæc Auctorum nomina.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Ex his Archimedes duos per&longs;crip&longs;it libros<emph.end type="italics"/> <foreign lang="greek">peri\ tw=n o)xoume/nwn</foreign>, <lb/> <arrow.to.target n="marg11"/><lb/><emph type="italics"/>hoc e&longs;t, de In&longs;identibus in humido, ex quibus pauca no&longs;tro in­<lb/>&longs;erviunt propo&longs;ito. Athana&longs;ius Kircherus Societ. Je&longs;u multa<emph.end type="italics"/><lb/> <arrow.to.target n="marg12"/><lb/><emph type="italics"/>pa&longs;&longs;im hydraulica atque pnevmatica machinamenta in&longs;erit &longs;uis <lb/>docti&longs;&longs;imis libris, præ&longs;ertim de Arte Magnetica, de Lumine & <lb/>Vmbra, de Con&longs;ono & Di&longs;&longs;ono, ac novi&longs;&longs;imè &longs;uo incompara­<lb/>bili de Ægyptiorum hieroglyphicis Operi quem Oedipum Ægy­<lb/>ptiacuin in&longs;crip&longs;it: multa quoque inter eius Manu&longs;cripta re­<lb/>peri, <expan abbr="multa&qacute;ue">multaque</expan> oretenus ab eodem percepi. Augu&longs;tinus Ra-<emph.end type="italics"/><lb/> <arrow.to.target n="marg13"/><lb/><emph type="italics"/>mellus ingens &longs;crip&longs;it Opus de Machinis Italico & Gallico idio­<lb/>mate, <expan abbr="inter&qacute;ue">interque</expan> illas ingentem habet copiam Antliarum diver&longs;is <lb/>modis con&longs;tructarum, <expan abbr="alias&qacute;ue">aliasque</expan> nonnullas praxes ad elevandas <lb/>aquas, &longs;ed omnes tractoriæ &longs;unt Machinæ ad primum pertinen­<lb/>tes genus. Benedictus Castellus, olim Mathematicus Pon-<emph.end type="italics"/><lb/> <arrow.to.target n="marg14"/><lb/><emph type="italics"/>tificius, libellum compo&longs;uit Italico idiomate de aqua cur­<lb/>rente, &longs;ed per alveos, aquæductus, & tubos inclinatos; quæ <lb/>proinde ad nos non pertinent. Daniel Lip&longs;torpius Lubecen&longs;is<emph.end type="italics"/><lb/> <arrow.to.target n="marg15"/><lb/><emph type="italics"/>edidit Specimina Philo&longs;ophiæ Carte&longs;ianæ, in cuius parte<emph.end type="italics"/> 3. <emph type="italics"/>c.<emph.end type="italics"/> 3. <lb/><emph type="italics"/>multas adducit Machinas hydraulico-pnevmaticas, easque <lb/>explicat ex Carte&longs;ij principijs. Daniel Schvventerus, & Ge-<emph.end type="italics"/><lb/> <arrow.to.target n="marg16"/><lb/><emph type="italics"/>orgius Philippus Harstorfferus Norimbergen&longs;is Patritius, in<emph.end type="italics"/><lb/> <arrow.to.target n="marg17"/><lb/><emph type="italics"/>Delicijs Mathematicis multas afferunt, <expan abbr="eas&qacute;ue">easque</expan> iucundi&longs;&longs;imas <lb/>Machinas hydraulicas, & pnevmaticas. Multas etiam in<emph.end type="italics"/> <pb xlink:href="051/01/041.jpg" pagenum="10"/> <arrow.to.target n="marg18"/><lb/><emph type="italics"/>Thaumaturgo &longs;uo Mathematico adducit ex alijs Ga&longs;par Ens;<emph.end type="italics"/><lb/> <arrow.to.target n="marg19"/><lb/><emph type="italics"/>vt & Weckerus in &longs;uis Secretis nonnullas ex Cardano de&longs;um-<emph.end type="italics"/><lb/> <arrow.to.target n="marg20"/><lb/><emph type="italics"/>ptas, quas dictus Cardanus in&longs;erit &longs;uis de &longs;ubtilitate libris. E-<emph.end type="italics"/><lb/> <arrow.to.target n="marg21"/><lb/><emph type="italics"/>vangelista Torricellus, Magni Hetruriæ Ducis Mathemati­<lb/>cus, & Benedicti Ca&longs;telli di&longs;cipulus, &longs;crip&longs;it libros<emph.end type="italics"/> 3. <emph type="italics"/>de Motu <lb/>proiectorum; quorum &longs;ecundo inter&longs;erit nonnulla de motu a­<lb/>quarum per tubos, &longs;ed quàm &longs;ubtilia, tàm parum ad praxin v-<emph.end type="italics"/><lb/> <arrow.to.target n="marg22"/><lb/><emph type="italics"/>tilia, vt ip&longs;emet fatetur. Galilæus Galilæi edidit Archimedem <lb/><expan abbr="redivivũ">redivivum</expan>, quem ex latino <expan abbr="Italicũ">Italicum</expan> fecit <expan abbr="Ioañes">Ioannes</expan> Baptista Hodierna <lb/>Siculus, Vir rerum Astronomicarum apprimè gnarus, & &longs;ide­<lb/>rum, adeoque Naturæ totius &longs;crutator indefe&longs;&longs;us, <expan abbr="amicus&qacute;ue">amicusque</expan> <lb/>&longs;inceri&longs;&longs;imus. Opu&longs;culum e&longs;t ad Hydrostaticam pertinens;<emph.end type="italics"/><lb/> <arrow.to.target n="marg23"/><lb/><emph type="italics"/>quale etiam e&longs;t Archimedes promotus Marini Ghetaldi; vt &<emph.end type="italics"/><lb/> <arrow.to.target n="marg24"/><lb/><emph type="italics"/>quæ habet Simon Stevinus; ideoque nobis nullam hîc &longs;uppetunt <lb/>materiam. Georgius Agricola libro<emph.end type="italics"/> 6. <emph type="italics"/>de rebus metallicis in-<emph.end type="italics"/><lb/> <arrow.to.target n="marg25"/><lb/><emph type="italics"/>&longs;erit nonnullas Machinas hydraulicas, nonnullas Robertus <lb/>Valturius &longs;uis de Militia libris, nonnullas Iacobus Be&longs;&longs;on Del-<emph.end type="italics"/><lb/> <arrow.to.target n="marg26"/><lb/><emph type="italics"/>phinas &longs;uo de In&longs;trumentis Mathematicis ac Mechanicis tracta­<lb/>tui; &longs;ed omnes &longs;unt tractoriæ, & alienæ à no&longs;tro instituto. Ge-<emph.end type="italics"/><lb/> <arrow.to.target n="marg27"/><lb/><emph type="italics"/>orgius Valla Placentinus libro<emph.end type="italics"/> 15. <emph type="italics"/>Expetendorum & fugiendo­<lb/>rum, qui e&longs;t &longs;extus Geometriæ, &longs;eu Spiritalium vnicus, multas <lb/>habet Machinas Spiritales, &longs;ed ad vnam omnes ex Herone Ale­<lb/>xandrino decerptas, nè nominato quidem Herone. Habebat <lb/>vir bonus, vt Io&longs;ephus Ceredus te&longs;tatur, Heronis librum græ­<lb/>cum de Spiritalibus, nondum tunc à Federico Commandino, <lb/>aliovè Latinitati donatum, <expan abbr="putabat&qacute;ue">putabatque</expan> &longs;ecurè atque impunè &longs;e <lb/>po&longs;&longs;e in alienam me&longs;&longs;em mittere falcem &longs;uam.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/042.jpg" pagenum="11"/> <p type="margin"> <s><margin.target id="marg11"/>Archime­<lb/>des.</s></p> <p type="margin"> <s><margin.target id="marg12"/>Kircherus.</s></p> <p type="margin"> <s><margin.target id="marg13"/>Ramellus.</s></p> <p type="margin"> <s><margin.target id="marg14"/>Ca&longs;tellus.</s></p> <p type="margin"> <s><margin.target id="marg15"/>Lip&longs;torpi'.</s></p> <p type="margin"> <s><margin.target id="marg16"/>Schvven­<lb/>terus.</s></p> <p type="margin"> <s><margin.target id="marg17"/>Har&longs;torffe­<lb/>rus.</s></p> <p type="margin"> <s><margin.target id="marg18"/>Ga&longs;par Ens</s></p> <p type="margin"> <s><margin.target id="marg19"/>Wecker'.</s></p> <p type="margin"> <s><margin.target id="marg20"/>Cardanus.</s></p> <p type="margin"> <s><margin.target id="marg21"/>Torricell<emph type="sup"/>9<emph.end type="sup"/>.</s></p> <p type="margin"> <s><margin.target id="marg22"/>Galilæus.</s></p> <p type="margin"> <s><margin.target id="marg23"/>Ghetaldus.</s></p> <p type="margin"> <s><margin.target id="marg24"/>Stevinus.</s></p> <p type="margin"> <s><margin.target id="marg25"/>Agricola.</s></p> <p type="margin"> <s><margin.target id="marg26"/>Valturius. <lb/>Be&longs;&longs;on.</s></p> <p type="margin"> <s><margin.target id="marg27"/>Valla.</s></p> <p type="main"> <s><emph type="italics"/>Hero Alexandrinus Auctor antiquus, græcè edidit libel-<emph.end type="italics"/><lb/> <arrow.to.target n="marg28"/><lb/><emph type="italics"/>lum de Spiritalibus, in quo quæ ab antiquis (quos Ægyptios <lb/>interpretatur Kircherus, vt &longs;uprà dicebam) tradita in illo ge­<lb/>nere fuêre, in ordinem redegit; & quæ ip&longs;emet invenit, expo­<lb/>&longs;uit: quæ quidem omnia pulcherrima &longs;unt, & ingenio plena. <lb/>Idem Auctor ait &longs;e quatuor libros con&longs;crip&longs;i&longs;&longs;e de aquaticis horo­<lb/>&longs;copijs; quos tamen temporum iniquitas nobis invidit. De-<emph.end type="italics"/><lb/> <arrow.to.target n="marg29"/><lb/><emph type="italics"/>&longs;cribit autem Hero nudam praxim, nec vllibi præcepta & regu­<lb/>las tradit, ni&longs;i quòd in principio de vacuo agat; ideoque & <lb/>ip&longs;e &longs;ubinde errat, (&longs;i tamen ip&longs;ius, & non Interpretis &longs;unt er­<lb/>rores) & alios in errorem inducit; nec omnia quæ promittit, <lb/>effectum &longs;ortiuntur. E&longs;t nihilominùs ip&longs;e de Republica litteraria <lb/>egregiè meritus, & vnicus qui ex antiquis de rebus hydraulicis<emph.end type="italics"/><lb/> <arrow.to.target n="marg30"/><lb/><emph type="italics"/>& pnevmaticis &longs;ua ad nos monumenta transmi&longs;it. Reperies <lb/>in hoc Opere no&longs;tro nonnullas ex ip&longs;o de&longs;umptas Machinas; quas <lb/>ideo adducimus, quòd aliquæ indigent correctione, vtpote fal&longs;æ: <lb/>aliquæ explicatione, vtpote ob&longs;curiùs traditæ; aliquæ excu&longs;a­<lb/>tione ac defen&longs;ione, vtpote &longs;ini&longs;trâ ab alijs cen&longs;urâ notatæ; aliæ <lb/>commendatione, vtpote no&longs;trarum ectypa; aliæ denique ad­<lb/>miratione, vtpote ingenio pleni&longs;&longs;imæ. Heronem Latinum fe­<lb/>cit Federicus Commandinus Vrbinas; Italicum Joannes Ba-<emph.end type="italics"/><lb/> <arrow.to.target n="marg31"/><lb/><emph type="italics"/>pti&longs;ta Aleottus, qui & in fine addidit quinque Problemata no­<lb/>va, &longs;anè jucundi&longs;&longs;ima, pariterque ingenio&longs;a.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg28"/>Hero.</s></p> <p type="margin"> <s><margin.target id="marg29"/>Hero Ale­<lb/>xandrinus <lb/><expan abbr="nudã">nudam</expan> pra­<lb/>xin hydrau <lb/>lico-pnev­<lb/>maticarum <lb/>Machina­<lb/>rum tradit.</s></p> <p type="margin"> <s><margin.target id="marg30"/>Eius Ma­<lb/>chinæ <expan abbr="nõ-nullæ">non­<lb/>nullæ</expan> qua­<lb/>re in hoc <lb/>Opere ad­<lb/>ducantur.</s></p> <p type="margin"> <s><margin.target id="marg31"/>Aleottus.</s></p> <p type="main"> <s><emph type="italics"/>Ioannes Bapti&longs;ta Porta Neapolitanus tres latinè &longs;crip&longs;it<emph.end type="italics"/><lb/> <arrow.to.target n="marg32"/><lb/><emph type="italics"/>egregios libellos de Spiritalibus, qui tamen pe&longs;&longs;imum nacti &longs;unt <lb/>Interpretem Joannem E&longs;crivanum Hi&longs;panum, qui eos Italicè <lb/>at que Hi&longs;panicè vertit; &longs;ed cùm Italicam linguam non calleret,<emph.end type="italics"/> <pb xlink:href="051/01/043.jpg" pagenum="12"/><emph type="italics"/>mirum e&longs;t, quàm barbarum vbique, quàm ob&longs;curum, quàm <lb/>mutilum reddiderit optimum Auctorem. Addidit nonnulla <lb/>de &longs;uo, oretenus à Porta, &longs;ed malè intellecta, & peiùs per&longs;cri­<lb/>pta, itáque alienis permixta, vt di&longs;cerni nequeant, ni&longs;i cum <lb/>genuino comparentur partu. Tradit Porta Spiritalium prin­<lb/>cipia, tradit machinamenta multa; vtraque longis experi­<lb/>mentis, nec &longs;ine expen&longs;is, confirmata. Huic ego primas inter <lb/>omnes Spiritalium Scriptores dandas cen&longs;eo. Latinum exem­<lb/>plar Neapoli impre&longs;&longs;um Anno<emph.end type="italics"/> 1601. <emph type="italics"/>innumeris &longs;catet erroribus <lb/>typographicis, qui &longs;en&longs;um &longs;æpe pror&longs;us pervertunt. Idem Au­<lb/>ctor lib.<emph.end type="italics"/> 18. <emph type="italics"/>&<emph.end type="italics"/> 19. <emph type="italics"/>Magiæ Naturalis multas alias habet Machi­<lb/>nas Hydraulicas & Pnevmaticas.<emph.end type="italics"/><lb/> <arrow.to.target n="marg33"/></s></p> <p type="margin"> <s><margin.target id="marg32"/>Port<gap/></s></p> <p type="margin"> <s><margin.target id="marg33"/>Balianus.</s></p> <p type="main"> <s><emph type="italics"/>Joannes Bapti&longs;ta Balianus Patritius Genuen&longs;is, &longs;cri­<lb/>p&longs;it libros &longs;ex de motu naturali gravium & liquidorum quorum <lb/>tres vltimi &longs;unt de liquidorum fluxu per canales & foramina; <lb/>è quorum vltimo nonnulla in Protheoriam no&longs;tram quartam<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg34"/><lb/><emph type="italics"/>derivavimus. P. Ioannes Leurechon è Societ ate no&longs;tra, Lo­<lb/>tharingus &longs;crip&longs;it gallico idiomate, tacito nomine &longs;uo, Recreatio­<lb/>nes Mathematicas; quas deinde germanicas fecit Daniel<emph.end type="italics"/><lb/> <arrow.to.target n="marg35"/><lb/><emph type="italics"/>Schvventer, latinas verò Ga&longs;par Ens. Io&longs;ephus Ceredus, <lb/>Medicus Placentinus, &longs;crip&longs;it tres egregios di&longs;cur&longs;us de Cochleæ <lb/>Archimedææ compo&longs;itione & vtilitate, ad elevandas magnâ<emph.end type="italics"/><lb/> <arrow.to.target n="marg36"/><lb/><emph type="italics"/>quantitate ac facilitate aquas. Ioannes Branca civis Roma­<lb/>nus, & Architectus Lauretanæ domus, librum &longs;crip&longs;it Italico <lb/>ac Latino &longs;ermone de Machinis, quas inter multæ &longs;unt hydrau­<lb/>licæ, & nonnullæ hydro-pnevmaticæ, at pleræque fal&longs;æ, & hy-<emph.end type="italics"/><lb/> <arrow.to.target n="marg37"/><lb/><emph type="italics"/>dro-pnevmaticis principijs contrariæ. Marinus Mer&longs;ennus<emph.end type="italics"/> <pb xlink:href="051/01/044.jpg" pagenum="13"/><emph type="italics"/>&longs;crip&longs;it Phœnomena hydraulica & pnevmatica, <expan abbr="multas&qacute;ue">multasque</expan> ex­<lb/>perientias à &longs;e in illa materia factas, ex quibu⋅ multa deducit <lb/><expan abbr="docti&longs;&longs;ima&qacute;">docti&longs;&longs;imaque</expan>; Theoremata atque Problemata; & nos <expan abbr="noñulla">nonnulla</expan> ex<emph.end type="italics"/><lb/> <arrow.to.target n="marg38"/><lb/><emph type="italics"/>ip&longs;o in&longs;eruimus quartæ no&longs;træ Protheoriæ. Nicolaus Cabæus <lb/>Commentarijs &longs;uis in Ari&longs;totelis Meteora, nonnulla habet hy-<emph.end type="italics"/><lb/> <arrow.to.target n="marg39"/><lb/><emph type="italics"/>draulica: nonnulla Marius Bettinus in Apiarijs Mathematicis <lb/>Apiario<emph.end type="italics"/> 4. <emph type="italics"/>Progymnas.<emph.end type="italics"/> 1. <emph type="italics"/>Nonnulla denique Petrus Herigo­<lb/>nius to.<emph.end type="italics"/> 3. <emph type="italics"/>Cur&longs;us Mathematici tract. de Mechanica. Raphael<emph.end type="italics"/><lb/> <arrow.to.target n="marg40"/><lb/><emph type="italics"/>Magiottus, Mathematicus Excellenti&longs;&longs;imus, Opu&longs;culum &longs;cri-<emph.end type="italics"/><lb/> <arrow.to.target n="marg41"/><lb/><emph type="italics"/>p&longs;it Italicum de aquæ Renitentia compre&longs;&longs;ioni; in quo tradit <lb/>Experimentum novum, quod nos adducimus Part.<emph.end type="italics"/> 2. <emph type="italics"/>Cla&longs;&longs;e<emph.end type="italics"/> 1. <lb/><emph type="italics"/>cap.<emph.end type="italics"/> 5. <emph type="italics"/>Machina<emph.end type="italics"/> 6. <emph type="italics"/>Robertus à Fluctibus in &longs;ua Philo&longs;ophia<emph.end type="italics"/><lb/> <arrow.to.target n="marg42"/><lb/><emph type="italics"/>Mo&longs;aica alijs&qtail; Operibus, multas pa&longs;&longs;im inter&longs;erit Machinas, a­<lb/>liâ occa&longs;ione. Salomon à Caus &longs;crip&longs;it Gallico idiomate libros tres<emph.end type="italics"/><lb/> <arrow.to.target n="marg43"/><lb/><emph type="italics"/>de hydraulicis quos ip&longs;e de viribus motricibus intitulat: Opus <lb/>est egregium, in eoque theoria aliqualiter cum praxi conjungi-<emph.end type="italics"/><lb/> <arrow.to.target n="marg44"/><lb/><emph type="italics"/>tur. Theodorus Muretus, è Societate IESV, in Pragen&longs;i Vni­<lb/>ver&longs;itate Mathematicæ Profe&longs;&longs;or, edidit Problema Mathema-<emph.end type="italics"/><lb/> <arrow.to.target n="marg45"/><lb/><emph type="italics"/>ticum de Fontibus. Vitruvius lib.<emph.end type="italics"/> 8. <emph type="italics"/>Architecturæ cap.<emph.end type="italics"/> 6 <emph type="italics"/>&<emph.end type="italics"/> 7. <lb/><emph type="italics"/>agit de perductionibus & librationibus aquarum, & in&longs;trumen­<lb/>tis ad hunc v&longs;um; & libro<emph.end type="italics"/> 10. <emph type="italics"/>varia habet in&longs;trumenta hy­<lb/>draulica, at pleraque tractoria. Va&longs;&longs;or Arabs habet varias<emph.end type="italics"/><lb/> <arrow.to.target n="marg46"/><lb/><emph type="italics"/>praxes Spiritales ad aquas in altum educendas: Liber e&longs;t Ma­<lb/>nu&longs;criptus, latinus, quem reperi inter libros P. Athana&longs;ij Kir­<lb/>cheri, at mutilum, & &longs;ine figuris nece&longs;&longs;a<gap/>ijs: Su&longs;picor e&longs;&longs;e <lb/>fragmentum Scriptoris cuiusdam Græci antiqui, à Ua&longs;&longs;ore in <lb/>Arabicam, ab alio in Latinam linguam translatum. Edidi&longs;-<emph.end type="italics"/> <pb xlink:href="051/01/045.jpg" pagenum="14"/><emph type="italics"/>&longs;em vnà cum hoc Opere, &longs;i operæ pretium me facturum judica&longs;­<lb/>&longs;em.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg34"/>Leurechon</s></p> <p type="margin"> <s><margin.target id="marg35"/>Ceredus.</s></p> <p type="margin"> <s><margin.target id="marg36"/>Branca.</s></p> <p type="margin"> <s><margin.target id="marg37"/>Mer&longs;ennus</s></p> <p type="margin"> <s><margin.target id="marg38"/>Cabæus.</s></p> <p type="margin"> <s><margin.target id="marg39"/>Bettinus.</s></p> <p type="margin"> <s><margin.target id="marg40"/>Herigoni'</s></p> <p type="margin"> <s><margin.target id="marg41"/>Magiottus</s></p> <p type="margin"> <s><margin.target id="marg42"/>Robertus <lb/>a Fluctibus</s></p> <p type="margin"> <s><margin.target id="marg43"/>Salomon à <lb/>Caus.</s></p> <p type="margin"> <s><margin.target id="marg44"/>Muretus.</s></p> <p type="margin"> <s><margin.target id="marg45"/>Vitruvius.</s></p> <p type="margin"> <s><margin.target id="marg46"/>Va&longs;&longs;or A­<lb/>rabs.</s></p> <p type="main"> <s><emph type="italics"/>Hi &longs;unt Auctores, qui de Hydraulicis atque pnevmati­<lb/>cis &longs;crip&longs;erunt, &longs;eu ex profe&longs;&longs;o, &longs;eu incidenter. Ex quibus ta­<lb/>men, &longs;i Kircherum, Portam, Mer&longs;ennum, aliosque nonnullos <lb/>excipias, pauci no&longs;trum triverunt iter, & vix vllus theoriam <lb/>cum praxi conjunxit; quod nos facimus. Aliorum Auctorum <lb/>nomina, qui vnam aut alteram Machinam &longs;uis inter&longs;erue­<lb/>runt Operibus, proferemus &longs;uis locis: Cuiusmodi &longs;unt Oron-<emph.end type="italics"/><lb/> <arrow.to.target n="marg47"/><lb/><emph type="italics"/>tius Finæus, & Bonaventura Cavallerius, eximius vterque<emph.end type="italics"/><lb/> <arrow.to.target n="marg48"/><lb/><emph type="italics"/>Mathematicus; quorum ille in fine tractatus de Horologijs <lb/>vnicam habet hydraulicam Machinam; hic alteram in fine <lb/>Exercitationis &longs;extæ Geometricæ; quarum vtram­<lb/>que nos infrà Parte<emph.end type="italics"/> 2. <emph type="italics"/>afferimus.<emph.end type="italics"/><lb/> <arrow.to.target n="fig2"/></s></p> <pb xlink:href="051/01/046.jpg" pagenum="15"/> <p type="margin"> <s><margin.target id="marg47"/>Finæus.</s></p> <p type="margin"> <s><margin.target id="marg48"/>Cavalleri'.</s></p> <figure id="id.051.01.046.1.jpg" xlink:href="051/01/046/1.jpg"/> <figure id="id.051.01.046.2.jpg" xlink:href="051/01/046/2.jpg"/> <p type="main"> <s><emph type="center"/>MECHANICÆ HYDRAVLI­<lb/>CO-PNEVMATICÆ<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PARS PRIMA <lb/>THEORETICA,<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De Machinarum Hydraulico­<lb/>pnevmaticarum principijs, <lb/>&longs;eu fundamentis.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PROœMIVM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QUatuor reperio Machinarum Hydrau-<emph.end type="italics"/><lb/> <arrow.to.target n="marg49"/><lb/><emph type="italics"/>lico-pnevmaticarum principia, quibus <lb/>ab Arte animantur in motum, illósque <lb/>præstant effectus, quos tantâ voluptate <lb/>miramur quotidie, tantâ pa&longs;&longs;im experimur vtilita-<emph.end type="italics"/><lb/> <arrow.to.target n="marg50"/><lb/><emph type="italics"/>te. Primum est vis Attractiva, ad vacuum vel fu­<lb/>giendum, velreplendum; quâ vi Aqua, elementu&mtail;<emph.end type="italics"/> <pb xlink:href="051/01/047.jpg" pagenum="16"/><emph type="italics"/>alioquingrave, iners, lentum, & humi repens, tracta <lb/>accurrit non invita, vt videtur, &longs;uæ&queacute; oblita naturæ <lb/>in &longs;ublime nititur, tripudianti &longs;imilis, vacui <expan abbr="velrepl&etilde;-">velreplen-</expan><emph.end type="italics"/><lb/> <arrow.to.target n="marg51"/><lb/><emph type="italics"/>di, vel impediendi causâ. Alterum est vis expul­<lb/>&longs;iva, ad corporum penetrationem fugiendam; quâ vi <lb/>eadem Aqua, dum aëri alterivé corpori validè in­<lb/>cumbenticedere cogitur ho&longs;pitio, expul&longs;a fugam prori­<lb/>pit eò celeriorem, excel&longs;iorémque, quò vehementiori-<emph.end type="italics"/><lb/> <arrow.to.target n="marg52"/><lb/><emph type="italics"/>bus &longs;e&longs;timulis agitatam &longs;en&longs;erit. Tertium est vis ‘Ra­<lb/>refactiva; quâ ob&longs;e&longs;&longs;um elementum in tantas &longs;ubin­<lb/>de redigitur angustias, vt dum &longs;e&longs;e, quâ data porta, <lb/>vel &longs;ubducit, vel ingerit, alas indui&longs;&longs;e videatur, abje­<lb/>ctis gravitatis propriæ compedibus. Quartum de-<emph.end type="italics"/><lb/> <arrow.to.target n="marg53"/><lb/><emph type="italics"/>ni&queacute; estgravitas Aquæ naturalis, ad decliviora loca <lb/>tendentis, & æquilibrium affectantis; quæ gravitas <lb/>non rarò (quod mirêre) in altum attollit ip&longs;am, quam <lb/>paulò antè depre&longs;&longs;er at in profundum.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg49"/>Principia <lb/><expan abbr="Machinarũ">Machinarum</expan> <lb/><expan abbr="Hydrau-lico-pnev-maticarũ">Hydrau­<lb/>lico-pnev­<lb/>maticarum</expan> <lb/>quatuor.</s></p> <p type="margin"> <s><margin.target id="marg50"/>I. Attracti­<lb/>va vis ad <lb/>vacuum <expan abbr="e-vitandũ">e­<lb/>vitandum</expan>.</s></p> <p type="margin"> <s><margin.target id="marg51"/>II. Expul&longs;i­<lb/>va vis ad <lb/>corporum <lb/>penetrati­<lb/>onem fu­<lb/>giendam:</s></p> <p type="margin"> <s><margin.target id="marg52"/>III. Rarefa­<lb/>ctio & con­<lb/>den&longs;atio, <lb/>aquam vel <lb/>expellens, <lb/>vel attra­<lb/>hens.</s></p> <p type="margin"> <s><margin.target id="marg53"/>IV. Gravi­<lb/>tas aquæ <lb/>æquilibri­<lb/>um affe­<lb/>ctantis.</s></p> <p type="main"> <s><emph type="italics"/>Hæc quatuor principia qui applicare ritè nove­<lb/>rit, quaslibet ingenio&longs;as Machinas, ad Naturæ ne&longs;cio <lb/>an æmulationem, an invidiamfabricari poterit faci­<lb/>litate &longs;ummâ, &longs;ucce&longs;&longs;u infallibili; cùm nulla Machina <lb/>hydraulica, aut pnevmatica, aut ex vtrisque mixta<emph.end type="italics"/> <pb xlink:href="051/01/048.jpg" pagenum="17"/><emph type="italics"/>ad&longs;ignari po&longs;&longs;it quæ non aliquâ harumfacultatum in-<emph.end type="italics"/><lb/> <arrow.to.target n="marg54"/><lb/><emph type="italics"/>&longs;tituatur. Jmò multis par a&longs;angis Naturæ &longs;uper abit co­<lb/>natus<emph.end type="italics"/> <foreign lang="greek">u(dro texni/ths</foreign>. <emph type="italics"/>Natura etenim non ni&longs;i vno motus <lb/>principio aquas terrâ eijcit, at&que; in fontes efformat, na­<lb/>turali videlicet fluxu aquæ <expan abbr="de&longs;cend&etilde;tis">de&longs;cendentis</expan> <expan abbr="primũ">primum</expan>, ac de­<lb/>inde a&longs;cendentis: at verò Ars non vno, &longs;ed multiplici, <lb/>vt dixi, &longs;cilicet &longs;uctu &longs;eu attractione, pre&longs;&longs;ione, dila­<lb/>tatione, præcipitatione: queis artibus, vel potiùs &longs;tra­<lb/>tagematis, in valles, in montes, in hortos, in domos de­<lb/>ducit, non fontes tantummodò, &longs;ed machinamenta a­<lb/>lia varia, jucunda, ac pror&longs;us<emph.end type="italics"/> <foreign lang="greek">qaumasiw/tata</foreign>, <emph type="italics"/>aliorum vel <lb/>nece&longs;&longs;itati, vel vtilitati, vel delectationi: Veri&longs;&longs;imum <lb/>quippe est illud Antiphontis,<emph.end type="italics"/> <foreign lang="greek">te/xnh| ga/r xratou=men, w(=n fu/sei nixw/­<lb/>meqa</foreign>. <emph type="italics"/>At hæc ip&longs;a quatuor hydro-pnevmaticarum <lb/>Machinarum principia &longs;eu fundamenta, antequam <lb/>vlteriùs progrediamur, paulô fu&longs;iùs explicare <lb/>lubet, vt &longs;ecuriùs deinde in praxi pro­<lb/>cedamus.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/049.jpg" pagenum="18"/> <p type="margin"> <s><margin.target id="marg54"/>Ars vincit <lb/>Naturam <lb/>infontibus <lb/>producen­<lb/>dis.</s></p> <p type="main"> <s><emph type="center"/>Pars I.<emph.end type="center"/></s></p> <figure id="id.051.01.049.1.jpg" xlink:href="051/01/049/1.jpg"/> <p type="main"> <s><emph type="center"/>PROTHEORIA <lb/>PRIMA<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De vi attractiva Corporum, ad vacuum vel <lb/>replendum, vel fugiendum: &longs;eu de primo Machi­<lb/>narum hydro-pnevmaticarum principio.<emph.end type="center"/><lb/> <arrow.to.target n="marg55"/></s></p> <p type="margin"> <s><margin.target id="marg55"/><emph type="italics"/><expan abbr="Vacuũ">Vacuum</expan> Phi­<lb/>lo&longs;ophorum <lb/>alij admit <lb/>tunt, alij <lb/>respuunt.<emph.end type="italics"/></s></p> <p type="main"> <s>VAcuum appellat vulgus quodlibet vas, aut lo­<lb/>cum, in quo nullum cernunt vi&longs;ibile corpus, etiam&longs;i <lb/>aëre &longs;int plena. At Philo&longs;ophi <emph type="italics"/>Vacuum<emph.end type="italics"/> definiunt <emph type="italics"/>locum <lb/>nullo repletum corpore.<emph.end type="italics"/> Hoc po&longs;terius, quod <expan abbr="&longs;olũ">&longs;olum</expan> vacui <lb/>nomen meretur propriè, non tam invi&longs;um Naturæ e&longs;t vi&longs;um De­<lb/>mocrito, Leucippo, Epicuro, alijsque, vt eliminandum penitus <lb/>cen&longs;uerint è rerum cen&longs;u. Alij verò <expan abbr="pleri&qacute;ue">plerique</expan> Philo&longs;ophi cum <lb/>Stagyrita &longs;uo adeo Naturæ adver&longs;um, adeo pernicio&longs;um exi&longs;ti­<lb/>mant Vacuum, vt ad evitandum ip&longs;um dicant, eandem <expan abbr="Naturã">Naturam</expan> <lb/><expan abbr="nullũ">nullum</expan> non movere <expan abbr="lapid&etilde;">lapidem</expan>, & omnia <expan abbr="&longs;usq;">&longs;usque</expan> <expan abbr="de&qacute;ue">deque</expan> vertere corpora, <lb/><expan abbr="ip&longs;a&qacute;ue">ip&longs;aque</expan> permi&longs;cere elementa. Qui de hydraulicis, <expan abbr="pnevma-ticis&qacute;ue">pnevma­<lb/>ticisque</expan> tractant Machinis, vnanimi con&longs;en&longs;u fatentur omnes </s></p> <p type="main"> <s> <arrow.to.target n="marg56"/><lb/>(&longs;i Lip&longs;torpium cum Carte&longs;io &longs;uo excipias) vim attractivam, <lb/>quam in Machinis nonnullis aperti&longs;&longs;im è elucere videmus, aliun­<lb/>de non provenire, ni&longs;i quòd Aqua, & Aër, Naturæ ob&longs;ecunda­<lb/>turi, accurrant tracti &longs;eu &longs;ponte, &longs;eu invitè, vel ad replendum va­<lb/>cuum quod oderunt, vel ad impediendum quod timent. Vtra­<lb/>que igitur &longs;ententia, & quæ vacuum recipit, & quæ rejicit, Hy­<lb/>draulicorum ac Pnevmaticorum Artificibus favet; ac proinde <lb/>ex vtrius que placitis vis attractiva prædicta e&longs;t explicanda. </s></p> <pb xlink:href="051/01/050.jpg" pagenum="19"/> <p type="margin"> <s><margin.target id="marg56"/><emph type="italics"/>Attractiva <lb/>vis ex appet<lb/>itu vacui <lb/>vel replen­<lb/>di, vel fu­<lb/>giendi ori­<lb/>tur in Ma­<lb/>chinis hy­<lb/>dro-pnev­<lb/>maticis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Protheoria I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>§. I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Hero Alexandrinus Vacuum in aëre & aqua <lb/>di&longs;seminatum agno&longs;cit.<emph.end type="center"/></s></p> <p type="main"> <s>HEro Alexandrinus, &longs;imul Spiritalium Magi&longs;trum agens, &longs;i­<lb/> <arrow.to.target n="marg57"/><lb/>mul Democritici, <expan abbr="Epicurei&qacute;ue">Epicureique</expan> Philo&longs;ophi per&longs;onam, prio­<lb/>rem de Vacuo &longs;ententiam doctè non minùs quàm fusè explicat, <lb/>atque tuetur, in Præfatione Libelli &longs;ui de Pnevmaticis &longs;eu Spi­<lb/>ritalibus, vbi ait<emph type="italics"/>: Alij enim vnivërsè nullum omnino vacuum e&longs;&longs;e <lb/>affirmant; alij coacervatum quidem naturâ nullum e&longs;&longs;e vacuum, &longs;ed <lb/>&longs;ecundùm exiguas partes di&longs;&longs;eminatum in aëre, humido, & igne, alijsque <lb/>corporibus; quibus maximè a&longs;&longs;entiri convenit.<emph.end type="italics"/> Vacuum coacerva­<lb/>tum veteres vocabant <foreign lang="greek">a)<gap/>n</foreign>, di&longs;&longs;eminatum verò <foreign lang="greek">parespa<gap/>me/non</foreign>, vt <lb/>notat Petrus Ga&longs;lendus in Philo&longs;ophia Epicuri; à quo Epicuro <lb/> <arrow.to.target n="marg58"/><lb/>Hero &longs;ontentiam &longs;uam mutuatus e&longs;t. <foreign lang="greek">*alla\ me\n</foreign>, inquit Epicurus <lb/>Epi&longs;tola ad <expan abbr="Herodotũ">Herodotum</expan>, <foreign lang="greek">kai\| to\ pa_n e)si\ ph_ me/n *sw_ma, ph_| de\ xeno\n</foreign> <emph type="italics"/>vniver&longs;um <lb/>autem partim quidem Corpus, partim verò inane e&longs;t.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg57"/><emph type="italics"/>Hero vacu­<lb/>um admit­<lb/>tit in aëre <lb/>& aqua di&longs; <lb/>&longs;eminatum<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg58"/><emph type="italics"/>Epicuriu <lb/>vacuum ad <lb/>mittit.<emph.end type="italics"/></s></p> <p type="main"> <s>Suam porrò de vacuo &longs;ententiam Hero tot probat rationi­<lb/>bus & experientijs, vt demon&longs;tratam exi&longs;timet, easque dignas <lb/>cen&longs;uit Marinus Mer&longs;ennus, quas Hydraulicis &longs;uis præmitteret <lb/> <arrow.to.target n="marg59"/><lb/>Phœnomenis. Ac principio quidem o&longs;tendit Hero. <emph type="italics"/>Va&longs;a, quæ <lb/>multis vacua videntur,<emph.end type="italics"/> eò quòd nullum in ijs vi&longs;ibile deprehen­<lb/>dunt Corpus, <emph type="italics"/>non e&longs;&longs;e vacua, vt putant, &longs;ed aëre plena.<emph.end type="italics"/> Quod <lb/>quidem patet ex eo, inquit Hero, quòd <emph type="italics"/>&longs;i vas, quod vacuum vide­<lb/>tur, quis inver&longs;um in aquam depre&longs;&longs;erit, rectumque &longs;ervarit, aqua in <lb/>ip&longs;um non ingredietur, quamvis totum occultatum fuerit.<emph.end type="italics"/> Vtique <lb/>non alia de Cau&longs;a, ni&longs;i quia aër, cum Corpus &longs;it, & totum vas <lb/>occupet, non permittit aquam ingredi, vt ip&longs;emet &longs;ubjungit. <lb/>Idem patetin phialis vitreis, ollis, alijsque va&longs;is, &longs;i inver&longs;a aquis <lb/>immergantur: non enim ni&longs;i difficulter admodum demergun­<lb/>tur; & dum retrahuntur, latera interiora habent &longs;icca; non ob <lb/>aliud profectò, ni&longs;i quia inclu&longs;us aër ingre&longs;&longs;um prohibuit aquæ. </s></p> <p type="margin"> <s><margin.target id="marg59"/><emph type="italics"/>Va&longs;a ina­<lb/>nia aëre e&longs;&longs;e <lb/>plena, vari­<lb/>is probatur <lb/>experimen­<lb/>tis.<emph.end type="italics"/></s></p> <p type="main"> <s>Quòd &longs;i prædictorum Va&longs;orum inver&longs;orum aquis immer­<lb/>&longs;orum <emph type="italics"/>fundum quis perforet, aqua quidem per os demer&longs;um in ip&longs;a in­<lb/>gredietur, aër verò per foramen exibit,<emph.end type="italics"/> adeo manife&longs;tè, vt non &longs;o- <pb xlink:href="051/01/051.jpg" pagenum="20"/>lùm manui admotæ &longs;en&longs;um inferat, &longs;ed etiam aures &longs;ono de­<lb/>mulceat, & quidem harmonico, &longs;i foramini aptentur fi&longs;tulæ <lb/>&longs;ono Harmonico edendo aptæ, prout ip&longs;emet Hero fieri <lb/>jubet in multis, quas de&longs;cribit in citato Libello, hydraulicis at­<lb/>que pnevmaticis Machinis. Quod etiam quotidie experimur <lb/>in Hortis Romanis, Tu&longs;culanis, Tiburtinis, & in ip&longs;o etiam <lb/>P. Athana&longs;ij Kircheri mu&longs;eo. <emph type="italics"/>Non igitur <gap/>rbitrandum e&longs;t,<emph.end type="italics"/> infert <lb/>Hero, <emph type="italics"/>in his quæ&longs;unt, vacui naturam quandam coacervatam ip&longs;am per­<lb/>&longs;e ip&longs;am exi&longs;tere &longs;ed&longs;ecundùm exiguas partes in aëre, & humido, alijsque <lb/>corporib<gap/> di&longs;&longs;eminatam,<emph.end type="italics"/> etiam in ip&longs;o adamante, duri&longs;&longs;imo licet, <lb/>den&longs;i&longs;&longs;<gap/>oque, <emph type="italics"/>quippe qui neque igniri, neque rumpi pote&longs;t, & percu&longs;­<lb/> <arrow.to.target n="marg60"/><lb/>&longs;us in incudes & malleos totus ing reditur<emph.end type="italics"/> (vt cum Pl<gap/>io putat Hero; <lb/>quod tamen, Mer&longs;enno te&longs;te, experientiæ repugnat, nam ictu <lb/>mallei in varias partes di&longs;&longs;ilit, & ita pote&longs;t iguiri, vt pereat.<emph type="italics"/>) Hoc <lb/><expan abbr="aut&etilde;">autem</expan> ip&longs;iaccidit,<emph.end type="italics"/> &longs;ubiungit Hero, <emph type="italics"/>non quòd vacuo careat, &longs;ed ob conti­<lb/>nuatam den&longs;itatem.<emph.end type="italics"/> Corpora porro illa (aëris præ&longs;ertim) quæ <lb/>partes &longs;uas habent inter &longs;e&longs;e cohærentes, <emph type="italics"/>non|tamen ex omni parte, <lb/>&longs;ed interiecta habent inter valla quædam vacua,<emph.end type="italics"/> (quæ vacuola appel­<lb/>lat Mer&longs;ennus) bellè comparat Hero arenarum cumulo, inter <lb/> <arrow.to.target n="marg61"/><lb/>cuius grana multæ aëris particulæ intercedunt; aitque, arenæ par­<lb/>ticulas particulis aëris &longs;imiles e&longs;&longs;e, <expan abbr="aër&etilde;">aërem</expan> verò, qui inter arenas in­<lb/>terjicitur, &longs;imilem vacuolis intra aërem contentis; quæ quidem <lb/>vocuola tunc di&longs;inere putat in aëre (alijsque corporibus) cùm <lb/>accedente vi quapiam conden&longs;atur aër; redire verò, cùm facta <lb/>remi&longs;&longs;ione in pri&longs;tinum ordinem re&longs;tituitur aër ob naturalem <lb/>contentionem, quâ, velut arcus inflexus, aut &longs;icca &longs;pongia vi <lb/>pre&longs;&longs;a, molem ab ip&longs;o rerum conditu &longs;ibi tributam repetit, &longs;ta­<lb/> <arrow.to.target n="marg62"/><lb/>tim atque vis externa de&longs;init. <emph type="italics"/>At aëris corpora,<emph.end type="italics"/> inquit Hero, <emph type="italics"/>inter <lb/>&longs;e&longs;e quidem cohærent, non tamen ex omni parte, &longs;edinteriecta habent <lb/>intervalla quædam vacua, &longs;icut arena, quæ e&longs;t in littoribus. Itaque a­<lb/>nimo concipiendum e&longs;t, arenæ particulas corporibus aëris &longs;imiles e&longs;&longs;e, aë­<lb/>rem vero, qui inter particulas arenæ interiicitur, &longs;imilem vacuis intra <lb/>aërem contentis. Quamobrem vi quadam accedente äerem den&longs;ari con­<lb/>tingit, & in vacuorum loca re&longs;idere, corporibus præter naturam inter <lb/>&longs;e&longs;e compre&longs;&longs;is: remi&longs;sione verò factârar&longs;us in cun dem ordinem re&longs;titui-<emph.end type="italics"/> <pb xlink:href="051/01/052.jpg" pagenum="21"/><emph type="italics"/>tur, ob naturalem Corporum contentionem; quemadmodum & in cor­<lb/>nuum ramentis, & in &longs;pongiis &longs;iccis, quæ&longs;i compre&longs;&longs;a remittantur, rur­<lb/>&longs;us in cundem locum redeunt, eandem que accipiunt molem. Similiter <lb/>&longs;i aliqua vi aëris particulæ à &longs;e in vicem di&longs;tractæ fuerint, & maior præ­<lb/>ter naturam locus vacuus fiat, rur&longs;us ad &longs;e&longs;e recurrunt, per vacuum e­<lb/>nim celerem corporum lationem fieri contingit, nullo ob&longs;tunte, aut re­<lb/>pellente, quóusque corpora ad &longs;e&longs;e applicentur.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg60"/>Adamas i­<lb/>gni & mal­<lb/>len cedit.</s></p> <p type="margin"> <s><margin.target id="marg61"/><emph type="italics"/>Vacuola He <lb/>ronis inter <lb/>aëris parti­<lb/>culas de&longs;&longs;e­<lb/>minata.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg62"/><emph type="italics"/>A<gap/>mterie <lb/>Ha habens <lb/>vacua <expan abbr="&longs;ecũ-dum">&longs;ecun­<lb/>dum</expan> Hero­<lb/>nem compa <lb/><gap/>atur are­<lb/>næ.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>§. II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Experimenta quibus Hero vacuum in Corpo­<lb/>ribus di&longs;&longs;eminatum probat.<emph.end type="center"/><lb/> <arrow.to.target n="marg63"/></s></p> <p type="margin"> <s><margin.target id="marg63"/><emph type="italics"/>Argumeta <lb/>Heronis pro <lb/>vacuo.<emph.end type="italics"/></s></p> <p type="main"> <s>HIs præmi&longs;&longs;is, multa, & pa&longs;&longs;im obvia adducit experimenta </s></p> <p type="main"> <s> <arrow.to.target n="marg64"/><lb/>Hero, quibus probat dari vacuum inter corporum, aëris præ­<lb/>&longs;ertim, particulas di&longs;&longs;eminatum; & aquam, <expan abbr="alia&qacute;ue">aliaque</expan> corpora ad <lb/>illud replendum, &longs;i nimiùm di&longs;trahantur particulæ vi externâ, ac­<lb/>currere attracta; atque adeo vim attractivam, quam primum <lb/>hydro pnevmaticarum Machinarum principium e&longs;&longs;e diximus, <lb/>tribuit Vacuo inter corpora di&longs;&longs;eminato. </s></p> <p type="margin"> <s><margin.target id="marg64"/><emph type="italics"/>Vacuum in <lb/>corporibus <lb/><expan abbr="di&longs;&longs;eminatũ">di&longs;&longs;eminatum</expan> <lb/>experimen­<lb/>tis probat <lb/>Hero.<emph.end type="italics"/></s></p> <p type="main"> <s>Primò enim, <emph type="italics"/>&longs;i quis vas levi&longs;&longs;imum & angu&longs;ti oris a&longs;&longs;umens, <lb/> <arrow.to.target n="marg65"/><lb/>atque ori admovens aërem ex&longs;uxerit, dimi&longs;erit&que;; ex labiis &longs;tatim vas <lb/>appendetur, vacuo carnem attrahente, vt locus exinanitus repleatur.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg65"/>Va&longs;a ex&longs;u­<lb/>cto aëre <expan abbr="la-biorũ">la­<lb/>biorum</expan> car­<lb/>nes attra­<lb/>hunt.</s></p> <p type="main"> <s>Secundò. <emph type="italics"/>Ova medica, quæ ex vitro con&longs;tant, & angu&longs;ti &longs;unt <lb/>oris, quando volunt humido replere, ex&longs;ugentes ore aërem, qui in ip&longs;is <lb/> <arrow.to.target n="marg66"/><lb/>continetur, o&longs;culumque digito comprehendentes, in humidum in ver­<lb/>tunt, & digito remi&longs;&longs;o in locum exin anitum attrahitur aqua, atque id­<lb/>ip&longs;um humidum præter naturam &longs;ur&longs;um fertur.<emph.end type="italics"/> Idem contingit in <lb/>Siphonibus, qui ex&longs;ucto aëre humidum è va&longs;is hauriunt, vt quo­<lb/>tidiana docet experientia, & dicemus fusè infrà Protheoria 4. <lb/>Cap. 2. Idem in multis Machinis hydraulicis, aut pnevmaticis e­<lb/>venit, vt &longs;uo loco videbimus. </s></p> <p type="margin"> <s><margin.target id="marg66"/>Ova medi­<lb/>ca quomodo <lb/>repleantur <lb/>aquá.</s></p> <p type="main"> <s>Tertò, Cucurbitæ à Chirurgis igni priùs admotæ, vt aêr <lb/> <arrow.to.target n="marg67"/><lb/>in ip&longs;is contentus rarefiat, dum corpori applicantur, <emph type="italics"/>non &longs;olùm <lb/>non excidunt, manife&longs;tam gravitatem habentes, &longs;ed adiacentem ma­<lb/>teriam per corporis raritates attrahunt, eandem ob cau&longs;am,<emph.end type="italics"/> vt &longs;cilicet <pb xlink:href="051/01/053.jpg" pagenum="22"/>locus exinanitus repleatur: <emph type="italics"/>iniectus enim ignis,<emph.end type="italics"/> &longs;ubjungit Hero, <lb/><emph type="italics"/>corrumpit & extenuat aërem, qui in ip&longs;is continetur,<emph.end type="italics"/> ideoque relin­<lb/>quitur in ip&longs;is vacuum; <emph type="italics"/>cùm verò cucurbitula re&longs;piraverit; aër in e­<lb/>vacuatum locum &longs;uccedit, materiânon ampliùs attractâ,<emph.end type="italics"/> <expan abbr="decidit&qacute;ue">deciditque</expan> <lb/>cucurbitula. <lb/> <arrow.to.target n="marg68"/></s></p> <p type="margin"> <s><margin.target id="marg67"/><emph type="italics"/>Cucurbitu­<lb/>la cur car­<lb/>nem attra­<lb/>hant.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg68"/><emph type="italics"/>Sphæra con­<lb/>cava, & aë­<lb/>replena, cur <lb/>plùs <gap/>ris <lb/>per inflatio­<lb/>nem recipi­<lb/>at <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <lb/>Heronem.<emph.end type="italics"/></s></p> <p type="main"> <s>Quartò, <emph type="italics"/>con&longs;truatur Sphæra cra&longs;&longs;itudinem habens laminæ, vt nè <lb/>facilè rumpatur, continensque circiter cotylas octo, & vndique præclu­<lb/>&longs;a;<emph.end type="italics"/> & per foramen in ip&longs;a factum immittamus <emph type="italics"/>Siphonem æreum, <lb/>hoc e&longs;t, tubum gracilem, non contingentem locum, qui puncto perfora­<lb/>to &longs;ecundùm diametrum opponitur, ita vt aqua fluere po&longs;&longs;it; alia autem <lb/>ip&longs;ius pars extra &longs;phæram emineat circiter digitos tres, ip&longs;i&queacute; diligenter <lb/>adferruminetur, ambitu foraminis circa tubum &longs;tanno præclu&longs;o, vt cùm <lb/>volumus ore per &longs;iphonem inflare, &longs;piritus ex &longs;phærâ nullo modo excidat.<emph.end type="italics"/><lb/>His factis,, <emph type="italics"/>in&longs;piciamus quæ contingunt. Aëre enim in ip&longs;a exi&longs;tente<emph.end type="italics"/><lb/>(quemadmodum & in aliis va&longs;is quæ vacua appellantur) <emph type="italics"/>totum­<lb/>que qui in ipsa locum replente, & per continuationem quandam ad eius <lb/>ambitum applicato, nullo denique loco, ut arbitrantur, penitus exi&longs;ten­<lb/>te vacuo; neque aquam immittere po&longs;&longs;emus, neque alium aërem, non <lb/>excedente priori aëre qui in ipsa erat; & &longs;i multa vi immi&longs;&longs;ionem facia­<lb/>mus, priùs di&longs;rumpetur vas, quàm aliquid &longs;u&longs;cipiat, cùm plenum &longs;it: ne­<lb/>que enim aëris corpora in minorem magnitudinem contrahi po&longs;&longs;unt: <lb/>quare nece&longs;&longs;e erit, vt in &longs;eip&longs;is habeant quædam intervalla, in quæ com­<lb/>pre&longs;&longs;a minorem obtineant molem; hoc autem veri&longs;imile non e&longs;t, nullo <lb/>penitus exi&longs;tente vacuo: & cùm corpora ad &longs;e&longs;e applicentur &longs;ecundùm <lb/>omnes &longs;uperficies, & &longs;imiliter ad va&longs;is ambitum, non po&longs;&longs;unt expul&longs;a lo­<lb/>cum alicui facere, non exi&longs;tente vacuo aliquo, quamobrem nullo modo <lb/>in &longs;phæram immittetur aliquid eorum, quæ &longs;unt extra, ni&longs;i excedat ali­<lb/>qua pars aëris priùs in ea contenti, &longs;iquidem totus locus con&longs;tipatus est, <lb/>& continuatus, vt arbitrantur. At<emph.end type="italics"/> experientiâ con&longs;tat contrari­<lb/>um: nam <emph type="italics"/>&longs;i quis &longs;iphonem ori admovens &longs;phæraminflet, multum im­<lb/>mittit &longs;piritum, non excedente aëre, qui in ea e&longs;t. Quod cùm ita &longs;em­<lb/>per contingat; manife&longs;tò o&longs;tenditur, <expan abbr="contraction&etilde;">contractionem</expan> fieri <expan abbr="corporũ">corporum</expan> in &longs;phæra <lb/>exi&longs;tentium in vacua implicata: contractio autem præter naturam fit, <lb/>ob immi&longs;&longs;ionis violentiam. Si igitur aliquis infla<gap/>, & ad ip&longs;um os ma­<lb/>num apponens, &longs;tatim digito &longs;iphonem obturet; manebit omni tempore<emph.end type="italics"/> <pb xlink:href="051/01/054.jpg" pagenum="23"/><emph type="italics"/>con&longs;tipatus aër in &longs;phæra: quod&longs;i quis aperiat, rur&longs;us extra erump<gap/>t cum <lb/><gap/>agno &longs;trepitu & clamore immi&longs;&longs;us aër, propterea quòd, vt propo&longs;uimus, <lb/>expellitur à dilatatione pr<gap/>exi&longs;tentis aëris impetu quodam factâ.<emph.end type="italics"/></s></p> <p type="main"> <s>Quintò, <emph type="italics"/>&longs;i quis velit aërem, qui in Sphæra e&longs;t, per &longs;iphonem at­</s></p> <p type="main"> <s> <arrow.to.target n="marg69"/><lb/>trahere, magna copia con&longs;equetur, nullâ aliâ&longs;ub&longs;tantiâ in &longs;phæram &longs;uc­<lb/>cedente, quemadmodum in ovo antè dictum e&longs;t. Quare ex hoc per &longs;pi­<lb/>cuè o&longs;tenditur, magnam vacui coacervationem in &longs;phæra factam e&longs;&longs;e: <lb/>non enim aëris corpora, quærelinquuntur eo tempore, maiora fieri po&longs;­<lb/>&longs;unt, ita vt expul&longs;orum corporum locum repleant: nam&longs;i augerentur, <lb/>cùm nulla ip&longs;is &longs;ub&longs;tantia extrin&longs;ecus accedat, veri&longs;imile e&longs;&longs;et, augmen­<lb/>tum fieri per rarefactionem; hoc autem e&longs;&longs;et implicatio &longs;ecundùm eva­<lb/>cuationem; &longs;ed vacuum nullum e&longs;&longs;e dicunt; non igitur augebuntur Cor­<lb/>pora; neque enim aliud augmentum ip&longs;is accidere mente concipi pote&longs;t. <lb/>Ex quibus per &longs;picuum e&longs;t, in aëris corporibus di&longs;&longs;eminata e&longs;&longs;e quædam <lb/>vacua intermedia, & vi quadam adveniente ea præter naturam in va­<lb/>cua reclinare.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg69"/>Sphæra con <lb/>cava ex&longs;u­<lb/>cto aëre, va <lb/>cua conti­<lb/>net inter­<lb/>valla <expan abbr="&longs;ecũ-dum">&longs;ecun­<lb/>dum</expan> Hero­<lb/>nem.</s></p> <p type="main"> <s>Sextò, <emph type="italics"/>vacuis non exi&longs;tentibus, neque per aquam, neque per <lb/> <arrow.to.target n="marg70"/><lb/>aërem, neque per aliud corpus vllum po&longs;&longs;et lumen tranfire, aut calidit as, <lb/>aut alia potentia<emph.end type="italics"/> &longs;eu qualitas <emph type="italics"/>corporea. Nam quomodo radij &longs;olares <lb/>per aquam in fundam va&longs;is penetrarent? Si enim aqua non haberet <lb/>poros, &longs;ed radij aquam vi &longs;cinderent, contingeret vasa plena &longs;uperfun­<lb/>di; quod fieri non videmus: Ad hæc &longs;i aquam vi &longs;cinderent, non vti­<lb/>que radiorum alij ad&longs;uperiorem locum frangerentur, alij deor&longs;um cade­<lb/>rent: nunc autem quicunque aquæ particulis occurrunt, franguntur ad <lb/>&longs;uperiorem locum; quicunque verò incidunt in aquæ vacua, paucis par­<lb/>ticulis occurrentes in va&longs;is fundum pervadunt.<emph.end type="italics"/> Adde quòd &longs;i nulla <lb/>e&longs;&longs;ent in corporibus vacua, nullum corpus per alia corpora tran­<lb/>&longs;ire po&longs;&longs;et: quod tamen oleis contingit, quorum aliqua tam &longs;ub­<lb/>tilia, &longs;unt vt omnia metalla, <expan abbr="ip&longs;um&qacute;">ip&longs;umque</expan>; <expan abbr="etiã">etiam</expan> vitrum penetrent. Idem <lb/>etiam fieri ab igne, nemo ne&longs;cit, qui ferrum, aurum, & vitrum <lb/>candentia vidit. Idem præterea à virtute magnetica fieri, quo­<lb/>tidie experimur. <lb/> <arrow.to.target n="marg71"/></s></p> <p type="margin"> <s><margin.target id="marg70"/>Corpora & <lb/>qualitates <lb/>corporeæ, pe­<lb/>netrant a­<lb/>lia corpora, <lb/>&longs;ecundùm <lb/>Heronem, <lb/>propter va­<lb/>cua interie­<lb/>cta.</s></p> <p type="margin"> <s><margin.target id="marg71"/><emph type="italics"/>Vinum mi­<lb/>&longs;cetur aquæ <lb/>ob inte<gap/>er <lb/>&longs;a vacua <lb/><gap/>uxta He­<lb/>ronem.<emph.end type="italics"/></s></p> <p type="main"> <s>Septimò, <emph type="italics"/>Vinum in aquam iniectum videtur &longs;ecundùm fu&longs;io­<lb/>nem quandam per totum aquæ locum per meare; quod non fieret, ni&longs;i va­<lb/>cua aquæ ine&longs;&longs;ent. Lumen quoque alterum per alterum fertur: nam<emph.end type="italics"/> <pb xlink:href="051/01/055.jpg" pagenum="24"/><emph type="italics"/>cùm plures lucernas quis accenderit, omnia magis illu&longs;tr abuntur, ijsdem <lb/>quoquò ver&longs;us per &longs;e invicem penetrantibus. Sed & per æs, per ferrum, <lb/>& per alia corpora omnia penetratio fit; quemadmodum & quod in tor­<lb/>pedine marina contingit.<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg72"/></s></p> <p type="margin"> <s><margin.target id="marg72"/><emph type="italics"/>Argumen­<lb/>ta aliorum <lb/><gap/>o vac<gap/>o.<emph.end type="italics"/></s></p> <p type="main"> <s>Hæ &longs;unt rationes Heronis, quibus probat. <emph type="italics"/><gap/>mne corpus ex <lb/>tenuibus con&longs;tare corporibus, inter quæ&longs;unt vacua di&longs;&longs;eminata particulis <lb/>minora.<emph.end type="italics"/> Quibus addi pote&longs;t vlteriùs, quòd eadem vacuola vi­<lb/>dentur admittenda inter aquæ partes frigore con&longs;trictas in gla­<lb/>ciem: etenim aqua in congelatione ad maius intervallum occu­<lb/>pandum extenditur; va&longs;a enim licet benè compacta, &longs;ià &longs;inu <lb/>latiori in angu&longs;tum a&longs;&longs;urgant, & repleantur aquâ ad maximam il­<lb/>lam latitudinem, vel vltra; in congelatione diffringuntur: non <lb/>&longs;ic, &longs;i infra illam latitudinem repleantur, vtdilatationi <expan abbr="&longs;patiũ">&longs;patium</expan> de­<lb/>tur. In maioribus etiam va&longs;is, &longs;ed recurvo intus labro, validius <lb/>re&longs;i&longs;tentibus, ip&longs;a glacies curvatur, &longs;ur&longs;um &longs;ecundùm convexum <lb/>elevata. Omnis etiam glacies aquæ iniecta &longs;uperna<gap/> Dila­<lb/>tatur ergo in congelatione aqua, & vacuitates parvas intus ha­<lb/>bet. </s></p> <p type="main"> <s>Addi præterea in confirmationem dictorum pote&longs;t duplex <lb/>Experimentum, vnum argenti vivi, alterum aquæ tubo inclusæ; <lb/>de quibus agemus infrà Cla&longs;se 1. cap. 6. Machina 7. Item expe­<lb/>rimentum Thermo&longs;copij, de quo ibidem cap. 3. Mach 3. </s></p> <p type="main"> <s> <arrow.to.target n="marg73"/></s></p> <p type="margin"> <s><margin.target id="marg73"/><emph type="italics"/>Vis attra­<lb/>ctiva quo­<lb/>modo ab He <lb/>rone expli­<lb/>cetur.<emph.end type="italics"/></s></p> <p type="main"> <s>Ex his alijsque argumentis atque experimentis, quæ vide­<lb/>ri po&longs;&longs;unt apud alios, præ&longs;ertim Neotericos <expan abbr="noñullos">nonnullos</expan>, <expan abbr="cõ&longs;tare">con&longs;tare</expan> po­<lb/>te&longs;t, quomodoex Heronis & <expan abbr="eorũ">eorum</expan> &longs;ententia, qui <expan abbr="vacuũ">vacuum</expan> admittunt, <lb/>Natura adnitatur trahere alia corpora, aquam præ&longs;ertim & aë­<lb/>rem, ad vacuum replendum, quod vi extrin&longs;eca præter naturam <lb/>e&longs;t alicubi coacervatum; & quomodo corporibus omnibus in­<lb/>&longs;it vis quædam attractiva, vt repleant vacuum illud; ac denique <lb/>quomodo vis attractiva corporum, aquæ inquam & aëris, cau&longs;a <lb/>e&longs;&longs;e po&longs;&longs;it ac principium Machinarum hydro-pnev­<lb/>maticarum. Lege Heronis Spiritalia. </s></p> <pb xlink:href="051/01/056.jpg" pagenum="25"/> <p type="main"> <s><emph type="center"/>§. III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Experimenta quibus vacuum nullum e&longs;&longs;e <lb/>probatur<emph.end type="center"/></s></p> <p type="main"> <s>HIs tamen non ob&longs;tantibus, communior & &longs;anior Philo&longs;o­</s></p> <p type="main"> <s> <arrow.to.target n="marg74"/><lb/>phorum Veterum ac Recentiorum &longs;en&longs;us e&longs;t, nullum in re­<lb/>rum natura vacuum e&longs;&longs;e, neque coacervatum in vnum, neque <lb/>di&longs;&longs;eminatum inter partes corporum di&longs;ci&longs;&longs;as; & neque &longs;pontè <lb/>ortum, neque productum violenter; adeoque corporum tra­<lb/>ctionem, quæ in allatis Experimentis elucet, non fieri ad replen­<lb/>dum vacuum, quod nullibi &longs;t, neque e&longs;&longs;e pote&longs;t; &longs;ed ad impe­<lb/>diendam, quam Natura tantopere abhorret, inanitatem. Sua­<lb/>dent hæc tum experientia Philo&longs;ophiæ Magi&longs;tra, tum rationes. <lb/>Experientias adducam paucas ex multis; rationes apud alios <lb/>leges. </s></p> <p type="margin"> <s><margin.target id="marg74"/><emph type="italics"/>Argumen­<lb/>ta contra <lb/>vacuum.<emph.end type="italics"/></s></p> <p type="main"> <s>Primò, Latera follium, &longs;i arctè con&longs;tricta &longs;int, & inter &longs;e <lb/> <arrow.to.target n="marg75"/><lb/>contigua, nulla vi diduci po&longs;&longs;unt, etiam Angelica, &longs;i obturetur <lb/>orificium, per quod aër inter iectum inter diducenda latera &longs;pa­<lb/>tium occupaturus &longs;ubeat. Cur hoc, ni&longs;i quia vacuum dari non <lb/>pote&longs;t? quod tamen dari deberet, &longs;i occlu&longs;o orificio aër, & <lb/>quodcunque aliud corpus &longs;ubiturum excluderetur, & tamen la­<lb/>tera diducerentur. Eâdem de cau&longs;a duæ tabulæ plani&longs;&longs;imæ, <lb/> <arrow.to.target n="marg76"/><lb/>& &longs;ibi mutuò &longs;ecundùm planitiem cohærentes, divelli non po&longs;­<lb/>&longs;unt, &longs;i ita tentetur divul&longs;io, vt aër aut aliud corpus inter &longs;uper­<lb/>ficies &longs;ubintrare tempe&longs;tivè non po&longs;&longs;it. <emph type="italics"/>Iuveni lacertorum &longs;uorum <lb/>robur iactanti<emph.end type="italics"/> (inquit P. Nicolaus Zucchius in &longs;ua de vacuo do­<lb/>cti&longs;&longs;ima Diatribe) <emph type="italics"/>propo&longs;ita-&longs;emel e&longs;t lamina ærea per an&longs;am in me­<lb/>dio extantem apprehen&longs;am elevanda è tabula marmorea, cui optimè con­<lb/>gruebat: qui primò tanquam rem ludicram puero committendam con­<lb/>temp&longs;it: tum in&longs;tantibus amicis manum vtramque admovens, cùm lu­<lb/>ctatus diu hærentem non removi&longs;&longs;et, excu&longs;avit impotentiam, obiectâ <lb/>peregrini & potenti&longs;&longs;imi glutinis interpo&longs;itione, quo forti&longs;&longs;imè copulan­<lb/>te nequiret divelli; donec vidit ab alio per tabulam facillimè laminam <lb/>deduci, & ad extrema productam, & actam in transver&longs;um, inde de­<lb/>portari.<emph.end type="italics"/> Pa&longs;&longs;im etiam experimur, dum duo corpora &longs;ecundùm <pb xlink:href="051/01/057.jpg" pagenum="26"/>planas &longs;uperficies coniuncta &longs;unt, vt vnum illorum elevatur, &longs;e­<lb/>qui etiam alterum, quantumvis grave, atque in aëre libero ve­<lb/>luti &longs;u&longs;pen&longs;um hærere. </s></p> <p type="margin"> <s><margin.target id="marg75"/><emph type="italics"/>Latera fol­<lb/>lium diauci <lb/>non po&longs;&longs;unt, <lb/>ore occlu&longs;e, <lb/>ob metum <lb/>vacus.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg76"/><emph type="italics"/>Tabulæ pla­<lb/>næ metu va <lb/>cui divelli <lb/>non po&longs;&longs;unt.<emph.end type="italics"/></s></p> <p type="main"> <s>Secundò, Si vas vitreum aquæ immergas atque impleas & <lb/> <arrow.to.target n="marg77"/><lb/>deinde intra aquam invertas, vt patens os deor&longs;um vergat, tum <lb/>æqualiter ita inver&longs;um eleves, & extrahere tentes; &longs;pectabis a­<lb/>quam illo inclu&longs;am &longs;ur&longs;um intra illud &longs;imul attolli; & &longs;i vas illud <lb/>ex parte iam extractum, & ex parte adhuc immer&longs;um, manu &longs;u­<lb/>&longs;tineas, videbis etiam aquam inclu&longs;am in illo per&longs;i&longs;tere &longs;ic eleva­<lb/>tam &longs;upra ambientis aquæ &longs;uperficiem æquilibratam, & &longs;uo et­<lb/>iam pondere manum &longs;u&longs;tinentis aggravare. Cur hoc? Quia <lb/>non pote&longs;t aër &longs;uccedere ad occupandum locum inter aquam <lb/>de&longs;cendentem, & partes va&longs;is, quæ aquâ de&longs;cendente de&longs;ere­<lb/>rentur. Idem continget in quolibet alio va&longs;e, &longs;ed in vitreo et­<lb/>iam oculis patebit experimentum. Quòd &longs;i in fundo va&longs;is fora­<lb/>men aliquod &longs;it clau&longs;um, vt po&longs;&longs;it aperiri; eo aperto, & aëre li­<lb/>berè &longs;ubintrante, aqua intra vas &longs;u&longs;pen&longs;um de&longs;cendet, & de&longs;i­<lb/>net gravare manum. <lb/> <arrow.to.target n="marg78"/></s></p> <p type="margin"> <s><margin.target id="marg77"/><emph type="italics"/>Vas inver­<lb/>&longs;um difficul <lb/>ter extrahi­<lb/>tur ex aqua <lb/>ob vacui <lb/>metum.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg78"/><emph type="italics"/>Va&longs;a &longs;ub<gap/>s <lb/>pertu&longs;a, &longs;u­<lb/>periùs occlu <lb/>&longs;a, aquam <lb/>retinent v<gap/><lb/>uí metu.<emph.end type="italics"/></s></p> <p type="main"> <s>Tertiò, In va&longs;is ad irrigandos hortos pa&longs;&longs;im adhiberi &longs;oli­<lb/>tis (cuiu&longs;modi proponimus infrà Cla&longs;s. 1. cap. 6. Mach 2, & Cri­<lb/>brum Ve&longs;talium vocamus) licet fundum ip&longs;orum &longs;it perforatum, <lb/>& multis foraminibus pervium, dum aquâ plena, æqualiter ele­<lb/>vantur in libero aëre, aqua non defluit, quàm diu digitus fora­<lb/>mini illorum &longs;upernè in collo patenti adpre&longs;&longs;us non permittit in­<lb/>gre&longs;&longs;um aëri ad replendum locum, qui, &longs;i deflueret aqua, relin­<lb/>queretur inter &longs;uperiorem va&longs;is &longs;uperficiem, & defluentem a­<lb/>quam. Et in tali con&longs;i&longs;tentia permanente aquâ intra vas, tan­<lb/>tum gravat, & deor&longs;um nititur aqua, quantum &longs;i fundo integro <lb/>& collo aperto, &longs;imul cum va&longs;e &longs;u&longs;tineretur. Remoto verò di­<lb/>gito, & permi&longs;&longs;o ingre&longs;&longs;u aëri per &longs;uperius foramen, &longs;tatim de­<lb/>fluit aqua ex fundi foraminibus. Quòd &longs;i in medio defluxu ite­<lb/>rum appo&longs;ito digito foramen ob&longs;truatur, pendet iterum aqua, <lb/>contra inclinacionem &longs;uæ gravitatis, tunc etiam manum gra­<lb/>vantis, nec defluit in apertum aërem. </s></p> <pb xlink:href="051/01/058.jpg" pagenum="27"/> <p type="main"> <s>Quartò, Si fi&longs;tulæ vnam extremitatem aquæ immergas, </s></p> <p type="main"> <s> <arrow.to.target n="marg79"/><lb/>ex altera ori admota aërem ex&longs;ugas, elevatur confe&longs;tim aqua, <lb/>&longs;ualicet gravitate reluctans, po&longs;t aërem extractum ad os ex&longs;u­<lb/>gentis; vtique nè detur vacuum in fi&longs;tula ex&longs;ucto aêre. </s></p> <p type="margin"> <s><margin.target id="marg79"/><emph type="italics"/>Fi&longs;tula ex­<lb/>&longs;ucto aëre <expan abbr="a-quã">a­<lb/>quam</expan> recipit <lb/>vacui metu<emph.end type="italics"/></s></p> <p type="main"> <s>Quintò, Si phialam cupream firmis lateribus compactam, <lb/> <arrow.to.target n="marg80"/><lb/>nè facilè rumpatur, igni admotam calefacias, vt aër intus con­<lb/>tentus vehementer rarefiat, eamque deinde frigidæ immergas, <lb/>vt aër phialæ à violenta rarefactione &longs;e recolligens conden&longs;etur, <lb/>& minorem occupet locum; intus attrahitur aqua, dum alius <lb/>aër in locum <expan abbr="relinquendũ">relinquendum</expan> &longs;uccedere non pote&longs;t, ne &longs;cilicet detur <lb/>vacuum in phiala. Sic &longs;i ex fi&longs;tula, cuius vnum orificium occlu­<lb/> <arrow.to.target n="marg81"/><lb/>&longs;um, alterum apertum, aut ex clave fœminea benè compacta, <lb/>ex&longs;ugas fortiter & continuato tractu aërem, & ce&longs;&longs;ante &longs;uctione <lb/>&longs;tatim apponas fi&longs;tulæ orificio patenti digitum aut labrum, nè <lb/>&longs;uccedat ambiens aër; attrahitur intra fi&longs;tulam, aut clavem, <lb/>caro digiti aut labri, vt notabiliter vellicet, & de carne depende­<lb/>at. Non alia de cau&longs;a, ni&longs;i quia durante ex&longs;uctione rarefit rema­<lb/>nens intus aër, & violenter <expan abbr="totũ">totum</expan> illud &longs;patium &longs;olus implet; ce&longs;­<lb/>&longs;ante verò &longs;uctu recolligit &longs;e à violenta rarefactione, & <expan abbr="minor&etilde;">minorem</expan> <lb/>locum occupans advocat aliud, quod ip&longs;i proximum e&longs;t, ad lo­<lb/>cum de&longs;ertum replendum. <expan abbr="Eadem&qacute;ue">Eademque</expan> cau&longs;a e&longs;t, cur cucurbi­<lb/> <arrow.to.target n="marg82"/><lb/>tulæ, quæ Chirurgis in v&longs;u e&longs;&longs;e &longs;olent, carnem &longs;ur&longs;um attrahant; <lb/>nimirum quia aêr, qui priùs igne incaluerat, & in raritatem abi­<lb/>erat, extincta flamma frigiditatem & den&longs;itatem recipit, atque <lb/>in minorem contractus molem inane &longs;patium relinqueret, ni&longs;i <lb/>ad id replendum caro elevaretur. </s></p> <p type="margin"> <s><margin.target id="marg80"/><emph type="italics"/>Phiala cale <lb/>facta, & a­<lb/>quæ immer­<lb/>&longs;a, attrahit <lb/>ip&longs;am va­<lb/>cui metu.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg81"/><emph type="italics"/>Fi&longs;tula ex­<lb/>tracto aëre <lb/>carnë ad­<lb/>motam tra <lb/>hunt, ne <lb/>vacuum <lb/>detur.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg82"/><emph type="italics"/>Cucurbitu­<lb/>læ carnem <lb/>attrahunt <lb/>metu vacui<emph.end type="italics"/></s></p> <p type="main"> <s>Sextò, Si &longs;clopeto æneo, aut maiori bombardæ, immit­<lb/> <arrow.to.target n="marg83"/><lb/>tas embolum interiori &longs;uperficiei benè congruentem, vt aêr in­<lb/>ter ip&longs;am & embolum &longs;ubire non po&longs;&longs;it, & deinde igniarium fo­<lb/>ramen occludas; non ni&longs;i difficulter extrahitur embolus, & vi <lb/>aliquantisper extractus retroagitur intra fi&longs;tulam: </s></p> <p type="margin"> <s><margin.target id="marg83"/><emph type="italics"/>Embolus <gap/><lb/>&longs;clopeto, <lb/>foramini i­<lb/>gniarioclau <lb/>&longs;o, difficul­<lb/>ter extrahi­<lb/>tur, vacui <lb/>metu.<emph.end type="italics"/></s></p> <p type="main"> <s>Atque hæc &longs;ecunda &longs;ententia, quæ Naturæ vacuum tan­<lb/>toperè fugientis partes tuendas &longs;u&longs;cipit, meritò à melioris notæ <lb/>Philo&longs;ophis, vt olim, ita nunc quoque præfertur: quidquid ob- <pb xlink:href="051/01/059.jpg" pagenum="28"/>ganniant Neoterici quidam, qui ne&longs;cio quo novitatis &longs;tudio in­<lb/> <arrow.to.target n="marg84"/><lb/>citati, <foreign lang="greek">xenodoci/as</foreign> vento inflati, nova quotidie dogmata cudere, <lb/>aut ob&longs;oleta <expan abbr="veterũ">veterum</expan> commenta recoquere non verecundantur. <lb/>Satiùs enim ac faciliùs e&longs;&longs;e exi&longs;timatur, admittere contra di&longs;po­<lb/>&longs;itiones particulares corporum gravium elevationem, levium <lb/>depre&longs;&longs;ionem, den&longs;iorum dilatationem, rariorum conden&longs;a­<lb/>tionem, durorum inflectionem, & &longs;imilia, quàm vacuum, quod <lb/>Naturam adeo abhorrere con&longs;picitur, vt nulla vi naturalis agen­<lb/>tis, nullo Machinæ artificio dari po&longs;&longs;it. Huiu&longs;modi autem na­<lb/>turæ pugnas & &longs;tratagemata multa &longs;pectabis manife&longs;tè infrà in <lb/>multis Machinis, quibus hæc Naturæ inanitatem fugientis &longs;o­<lb/>lertia &longs;ummam præbet commoditatem. Alia etiam paulò po&longs;t <lb/>afferam, &longs;i priùs, quæuam &longs;it vis illa Attractiva corporum, quâ <lb/>Natura vtitur ad vacuum impediendum, o&longs;tendero. </s></p> <p type="margin"> <s><margin.target id="marg84"/><emph type="italics"/>Vacuum da <lb/>rinaturali­<lb/>ter non po­<lb/>te&longs;t.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>§. IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Vis attractiva|ob vacui metum, primum Machinarum <lb/>hydro-pnevmaticarum principium, quæ, & qua­<lb/>lis, quibusvè in&longs;it corporibus.<emph.end type="center"/></s></p> <p type="main"> <s>HÆ &longs;unt binæ de vacuo &longs;ententiæ, quarum vtraque fontium <lb/>artificialium, <expan abbr="aliarum&qacute;ue">aliarumque</expan> hydro-pnevmaticarum Machina­<lb/>rum con&longs;tructioni, & effectuum mirabilium patrationi viam a­<lb/>perit & &longs;ubmini&longs;trat arma; quamvis evidentiùs &longs;ecunda, quàm <lb/>prima, cui & illam idcirco prætulimus. Quæ&longs;tio tamen non le­<lb/> <arrow.to.target n="marg85"/><lb/>vis remanet inter &longs;ecundæ huius &longs;ententiæ fautores circa vim il­<lb/>lam, quæ cogit corpora gravia accurrere ad vacuum impedi­<lb/>endum, etiam contra propriam inclinationem; <expan abbr="dubitatur&qacute;ue">dubitaturque</expan>, <lb/>quibusnam illa vis in&longs;it ceu &longs;ubiectis; trahentibusnè, an tractis <lb/>corporibus? </s></p> <p type="margin"> <s><margin.target id="marg85"/><emph type="italics"/>Vis attra­<lb/>ctiva aquæ <lb/>quibus in&longs;it <lb/>corporibus.<emph.end type="italics"/></s></p> <p type="main"> <s>Alij enim putant, e&longs;&longs;e virtutem motivam ip&longs;is corporibus <lb/> <arrow.to.target n="marg86"/><lb/>accurrentibus intrin&longs;ecam, quæ in bonum Vniver&longs;i corpora gra­<lb/>via in altum, contra con&longs;uetum modum, ad vacuum impedien­<lb/>dum, vrgeat atque impellat. At hoc experientia ip&longs;a &longs;atis con­<lb/>vellit, & fal&longs;itatis arguit; &longs;iquidem, vt benè advertunt Cabæus <pb xlink:href="051/01/060.jpg" pagenum="29"/>& Zucchius, aqua <expan abbr="a&longs;cend&etilde;s">a&longs;cendens</expan> intra tubum, ad vacuum <expan abbr="impediendũ">impediendum</expan> <lb/> <arrow.to.target n="marg87"/><lb/>(quod in &longs;equentibus Machinis frequenti&longs;&longs;imum e&longs;t) tantundem <lb/>gravat, <expan abbr="quantũ">quantum</expan> gravaret in libero aëre <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan>. Quòd benè adver­<lb/>terejubet Cabæus illos, qui &longs;pecio&longs;o nimis nomine &longs;e Ingenie­<lb/>ros appellari volunt; & Zucchius ait, &longs;e huius rei experimento <lb/>coëgi&longs;&longs;e, <emph type="italics"/>virum alioqui non ineruditum, vt fallaciam agno&longs;ceret in <lb/>via, quâ motum perpetuum &longs;e inveni&longs;&longs;e putabat, & iam dicandum Ma­<lb/>gno Principi &longs;chema in æs incidi curaverat, &longs;upponendo aquam ad impe­<lb/>diendum vacuum &longs;ua vi <expan abbr="a&longs;c&etilde;dentem">a&longs;cendentem</expan> non egere virtute æquilibrante, ne­<lb/>dum &longs;uperante pondus illius, qua eget cùm &longs;i&longs;tenda vel elevanda e&longs;t in <lb/>aëre, liberè accurrente ad replendum &longs;patium inter eam, & alia corpora <lb/>relinquendum.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg86"/><emph type="italics"/>Vis attra­<lb/>ctiva non <lb/>ine&longs;t corpo­<lb/>ribus attra <lb/>Hic.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg87"/><emph type="italics"/>Aqua in tu <lb/>bis elevata <lb/>adfugiend<gap/><lb/>vacuum <lb/>gravat.<emph.end type="italics"/></s></p> <p type="main"> <s>Alij igitur, & meliùs, exi&longs;timant, omnibus corporibus <lb/> <arrow.to.target n="marg88"/><lb/>contiguis hanc ine&longs;&longs;e vim, à Natura attributam, ad Vniver&longs;i <lb/>bonum ac con&longs;ervationem, vt quotiescunque vnum illorum lo­<lb/>co cedit, &longs;eu tractum ab extrin&longs;eco agente violenter, &longs;eu &longs;ponte <lb/>& innatâ inclinatione recedens, pondere videlicet, autlevitate: <lb/>trahat &longs;ecum alterum &longs;ibi contiguum, quantumvis reluctans, <lb/>quoties inter ip&longs;um & contiguum non pote&longs;t &longs;ubintrare corpus <lb/>aliud, quod partium Vniver&longs;i contiguitatem tueatur, & impedi­<lb/>at inanitatem; adeoque trahentibus, non tractis corporibus <lb/> <arrow.to.target n="marg89"/><lb/>vim illam motivam ine&longs;&longs;e. Et hanc vim appellant vim attracti­<lb/>vam, e&longs;tque illa ip&longs;a quam nos primum <expan abbr="Machinarũ">Machinarum</expan> hydro-pnev­<lb/>maticarum principium &longs;eu fundamentum dicimus, vnaque e&longs;t <lb/>ex cau&longs;is vacui impeditivis. Dico, vna ex cau&longs;is, non enim v­<lb/>nica e&longs;t via atque indu&longs;tria, quâ vacuum Natura evitare adni­<lb/>titur. Modò enim vtitur prædicta vi attractiva: modò ad&longs;ci&longs;cit <lb/>operam alteratricium qualitatum, quæ corpora rarefaciunt, & <lb/>in ampliorem molem diffundunt: non nunquam magno impe­<lb/>tu va&longs;a frangit, aut alia id genus media, prout occa&longs;io & nece&longs;­<lb/>&longs;itas fert, accommodat: quin etiam haud rarò nullo motu, nulla <lb/>actione, nulla denique vi effectrice, &longs;ed per negativam <expan abbr="quandã">quandam</expan> <lb/>ob&longs;i&longs;tentiam vacuo repugnat; vt cùm Iatera follium compre&longs;&longs;a <lb/>clau&longs;o orificio, vt diximus &longs;uprà, divellinon &longs;init. Semper ta- <pb xlink:href="051/01/061.jpg" pagenum="30"/>men Natura in his, vtin cæteris rebus, <expan abbr="cõpendio">compendio</expan> &longs;tudet, & quan­<lb/>tum pote&longs;t, facilioribus ac &longs;implicioribus vtitur medijs; vt &longs;i ad <lb/>fugam vacui corpus &longs;ur&longs;um attrahere, quàm den&longs;atione impedi­<lb/>re promptius &longs;it, illud præ&longs;tat, non hoc; &longs;i contrà, hoc, non il­<lb/>lud: item &longs;i per &longs;olum motum localem &longs;ine rarefactione corpus <lb/>aliunde trahere &longs;ufficit, rarefactioni parcit; alioquin vtrumque <lb/>mi&longs;cet. <lb/> <arrow.to.target n="marg90"/></s></p> <p type="margin"> <s><margin.target id="marg88"/><emph type="italics"/>Attractiva <lb/>vis trahen­<lb/>tibus corpo­<lb/>ribus ine&longs;t, <lb/>ad vacuum <lb/><expan abbr="impediendũ">impediendum</expan><emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg89"/><emph type="italics"/>Vacui cau­<lb/>&longs;a impediti­<lb/>va multi­<lb/>plex.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg90"/><emph type="italics"/>Attractiva <lb/>vis ad va­<lb/>cuum im­<lb/>pediendum <lb/>omnibus <lb/>corporibus <lb/>ine&longs;t.<emph.end type="italics"/></s></p> <p type="main"> <s>Sed hæc accuratiús Philo&longs;ophi; nobis &longs;ufficit varijs experi­<lb/>entijs mon&longs;tra&longs;&longs;e, ine&longs;&longs;e corporibus Vniver&longs;um componentibus <lb/>vim attractivam vel ad replendum, vel ad impediendum <expan abbr="vacuũ">vacuum</expan>; <lb/>quæ vis vt alia corpora, ita multò magis aërem & aquam attra­<lb/>hat, & Machinarum Hydro-pnevmaticarum principium ac <expan abbr="fũ-damentum">fun­<lb/>damentum</expan> primum con&longs;tituat. </s></p> <p type="main"> <s>Nunc tempus e&longs;t, vt experimento vnico & veluti re ip&longs;a <lb/>mon&longs;tremus, quomodo vis attractiva, quam hactenus corpori­<lb/>bus Vniver&longs;um componentibus ine&longs;&longs;e o&longs;tendimus ad vacuum <lb/>impediendum (vel vt Hero vult, replendum) cau&longs;a e&longs;&longs;e po&longs;&longs;it, <lb/>atque principium Hydro-pnevmaticarum Machinarum. </s></p> <p type="main"> <s><emph type="center"/>§. V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Experimentum, quo o&longs;tenditur vis attractiva ad aquas <lb/>in altum evehendas, vacui vitandi causâ, per Machinas <lb/>Hydro-pnevmaticas.<emph.end type="center"/></s></p> <p type="main"> <s>INfrà Cla&longs;se 1. cap. 1. Machina 11. Modum præ&longs;cribimus <expan abbr="aquã">aquam</expan> </s></p> <p type="main"> <s> <arrow.to.target n="marg91"/><lb/>ad certam ac determinatam aliquam altitudinem evehendi, <lb/>eumque appellamus Siphonem inver&longs;um interruptum: qui mo­<lb/>dus cùm nitatur vi Attractivâ orta ex vacui metu, multaque im­<lb/>plicet notatu digni&longs;&longs;ima, & ad vim Attractivam penitiùs intelli­<lb/>gendam omninò nece&longs;&longs;aria, hîc eum paulò fu&longs;iùs explicandum <lb/>cen&longs;ui; ibi enim breviter tantùm, & quantum ad praxin &longs;ufficit, <lb/>illum proponimus. Sit itaque in ci&longs;terna, puteo, pi&longs;cina, aut <lb/>va&longs;e quocunque B, aquâ pleno, elevanda ad pedes ex.g.centũ (di­<lb/>co, exempli gratia, nam alioquin non pote&longs;t ad <expan abbr="tantã">tantam</expan> <expan abbr="altitudin&etilde;">altitudinem</expan> <lb/>attolli per vim attractivam) aqua in vas KA, quod &longs;it con&longs;titu- <pb xlink:href="051/01/062.jpg" pagenum="31"/> <arrow.to.target n="fig3"/><lb/>tum in parte &longs;uperiore domus, <expan abbr="habeat&qacute;ue">habeatque</expan> epi&longs;tomium H, per <lb/>quod, vbi repletum fuerit vas, depleri po&longs;&longs;it. Fiat vas C, cu­<lb/>iuscunque capacitatis (quamvis meliùs &longs;it, vt &longs;it æqualis capa­<lb/>citatis cum va&longs;e KA, aut &longs;altem non minoris) ex eoque derive­<lb/>tur ad vas KA, &longs;iphon &longs;eu tubus OI, qui in va&longs;e C, incipiat im­<lb/>mediatè infra operculum ip&longs;ius, in va&longs;e verò KA, de&longs;inat paulò <lb/>infra eiu&longs;dem operculum, tantum ab illo di&longs;tans, quantum &longs;uf­<lb/>ficit vt aër permeare po&longs;&longs;it. Deinde ex va&longs;e B, derivetur ad vas <lb/>KA, tubus BK; qui in va&longs;e B, incipiat paulò &longs;upra fundum ip&longs;i- <pb xlink:href="051/01/063.jpg" pagenum="32"/> <arrow.to.target n="fig4"/><lb/>us, in va&longs;e verò KA, de&longs;inat paulò infra operculum; vbi etiam <lb/>nonnihil in curvetur, vti in figura apparet. Tandem ex va&longs;e C, <lb/>derivetur alius tubus EF, cum epi&longs;tomio E, habens longitudi­<lb/>nem paulò majorem longitudine tubi BK, capacitatem verò <lb/>&longs;eu amplitudinem eidem BK, omnino æqualem. Debent autem <lb/>omnes tres tubi diligenti&longs;&longs;imè <expan abbr="adferrũinari">adferruninari</expan> &longs;eu coarctari plum­<lb/>bo, aliavè materia, &longs;uis va&longs;is in loco tran&longs;itus; & tam vas C, quam <lb/>vas KA, claudi <expan abbr="obturari&qacute;ue">obturarique</expan> vndiq, &longs;tudio&longs;i&longs;&longs;imè, nè aërem ali­<lb/>unde, quàm per tubos, recipere aut ejicere valeant. His ita <pb xlink:href="051/01/064.jpg" pagenum="33"/>præparatis, impleatur vas C. aquâ per foramen O, immi&longs;&longs;o ip&longs;i <lb/>foramini iufundibulo; & vbi repletum fuerit, claudatur vt di­<lb/>ctum. Deinde clau&longs;o epi&longs;tomio H, aperiatur epi&longs;tomium E, <lb/>tubi EF; <expan abbr="defluet&qacute;ue">defluetque</expan> aqua ex va&longs;e C, & in locum ip&longs;ius, nè va­<lb/>cuum in va&longs;e admittatur, &longs;equetur per &longs;iphonem IO, aër in va­<lb/>&longs;e KA, contentus; in locum verò aëris extracti è va&longs;e KA, &longs;eque­<lb/>tur, propter vacui metum, aqua va&longs;is &longs;eu ci&longs;ternæ aut pi&longs;cinæ B, <lb/>per &longs;iphonem BK; & tam diu durabit a&longs;cen<gap/>s aquæ per <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> <lb/>BK, in vas KA, quàm diu de&longs;cendet aqua per &longs;iphonem EF ex va­<lb/>&longs;e C. Lege quæ dicimus infrà loco cit. En ergo, quomodo aq ia, <lb/>ad vacuum impediendum, a&longs;cendat contra naturalem &longs;uam in­<lb/>clinationem, & quomodo propter <expan abbr="eand&etilde;">eandem</expan> cau&longs;am aër de&longs;cendat. </s></p> <p type="margin"> <s><margin.target id="marg91"/><emph type="italics"/>Experimen <lb/>tum vim <lb/><expan abbr="attractivã">attractivam</expan> <lb/>o&longs;tendens <lb/>ad vacuum <lb/>impedien­<lb/>dum.<emph.end type="italics"/></s></p> <figure id="id.051.01.064.1.jpg" xlink:href="051/01/064/1.jpg"/> <figure id="id.051.01.064.2.jpg" xlink:href="051/01/064/2.jpg"/> <p type="main"> <s><emph type="center"/>§. VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Notantur nonnulla circa prædictum experimentum, <expan abbr="&longs;i-mul&qacute;">&longs;i­<lb/>mulque</expan>; &longs;tabilitur, in attractione aquæ metu vacui habendam <lb/>e&longs;&longs;e rationem perpendiculi aquarum.<emph.end type="center"/></s></p> <p type="main"> <s>DIximus, meliùs e&longs;&longs;e vt vas C, &longs;it æq<gap/>lis capacitatis cum va&longs;e <lb/>KA, aut&longs;altem non minoris: & præterea &longs;iphonem EF debe­<lb/>re e&longs;&longs;e paulò longiorem &longs;iphone BK, capacitatis verò &longs;eu ampli­<lb/>tudinis æqualis. Ratio quoad capacitatem va&longs;orum & &longs;ipho­<lb/>num e&longs;t, quia tamdiu a&longs;cendit aqua per BK, quàm diu de&longs;cen­<lb/>dit per EF, vt dixi (tam diu enim, & non ampliùs, duratvacui <lb/>metus, ob quam aqua a&longs;cendit per tubum BK:) &longs;i ergo vas C mi­<lb/>nus e&longs;&longs;et quàm vas KA, aut tubus EF capacior quàm tubus BK; ef­<lb/>flueret tota aqua ex C, antequam repleretur KA. Accedit & <lb/>hoc commodi ex æquali vtrorumque capacitate, quòd &longs;cire po&longs;­<lb/>&longs;it apud C exi&longs;tens, quandonam plenum &longs;it vas KA; quando ni­<lb/>mirum effluxerit tota aqua C. Ratio verò cur tubus EF, debeat <lb/> <arrow.to.target n="marg92"/><lb/>e&longs;&longs;e longior tubo BK, patebit ex dicendis Protheoria IV. capite <lb/>2. Propo&longs;it. 13. interim hîc id confirmo hoc Experimento. Ac­<lb/>cipe vas aquâ plenum, eique in&longs;ere &longs;iphonem inver&longs;um ABCD <lb/>æqualium crurium. Accipe deinde tubum rectum DE aquâ <lb/>plenum, eumque, obturato priùs ore E, in&longs;ere extremitati D, <pb xlink:href="051/01/065.jpg" pagenum="34"/> <arrow.to.target n="fig5"/><lb/>cruris CD, & diligenter coarcta in­<lb/>ter &longs;e&longs;e, nè aër inter <expan abbr="vtrumq;">vtrumque</expan> <expan abbr="trã&longs;ire">tran&longs;ire</expan> <lb/>po&longs;&longs;it. His factis aperios inferius. <lb/>Et &longs;i quidem tubus rectus DE lon­<lb/>gior fuerit quàm crus AB à &longs;upre­<lb/>ma &longs;uperficie aquæ va&longs;is <expan abbr="vsq;">vsque</expan> ad B; <lb/>effluet aqua ex E, <expan abbr="a&longs;cendet&qacute;ue">a&longs;cendetque</expan> a­<lb/>qua va&longs;is A, per crus AB, <expan abbr="inde&qacute;ue">indeque</expan> <lb/>per CD, crus de&longs;cendet, donec <lb/>tota effluxerit ex ore E. Si aut de­<lb/>urtetur tubus DE in F, fiatque <lb/>æqualis cruri AB; a&longs;endet aqua va­<lb/>&longs;is A &longs;olùm u&longs;que ad B, quàm diu vi­<lb/>delicet aqua ex F effluit; quâ elapsâ, <lb/>relabetur aqua cruris AB intra vas <lb/>A, Si idem tubus DE decurtetur <lb/>in G, aut H, <expan abbr="fiat&qacute;ue">fiatque</expan> brevior quàm <lb/>crus AB; a&longs;cendet aqua per AB &longs;o­<lb/>lùm aliquòu&longs;que, & deinde rela­<lb/>betur. Experientiam quilibet fa­<lb/>cilè poterit facere. </s></p> <p type="margin"> <s><margin.target id="marg92"/><emph type="italics"/>Experimë­<lb/>tum aliud: <lb/>o&longs;tendens <lb/>vim attra­<lb/>ctivam a­<lb/>quæ in <expan abbr="altũ">altum</expan>.<emph.end type="italics"/></s></p> <figure id="id.051.01.065.1.jpg" xlink:href="051/01/065/1.jpg"/> <p type="main"> <s>Nec &longs;ufficit vt tubus EF, &longs;upe­<lb/>rioris figuræ &longs;it <expan abbr="quacunq;">quacunque</expan> ratione longior tubo BK, &longs;ed nece&longs;&longs;ari­<lb/>um e&longs;t, vt <expan abbr="perpendiculũ">perpendiculum</expan> ip&longs;ius EF, &longs;it longius quàm perpendicu­<lb/>lum BK, hoc e&longs;t, vt tubus EF perpendiculariter de&longs;cendat <lb/>profundiùs infra vas C, quàm tubus BK a&longs;cendat perpendi­<lb/>culariter &longs;upra vas B. Quare &longs;i tubus EF centum & vnius pe­<lb/> <arrow.to.target n="marg93"/><lb/>dum inclinaretur infra vas C, aut convolveretur in helicem, <lb/>vt hîc apparet, ita vt perpendiculum ip&longs;ius &longs;olùm e&longs;&longs;et pedum <lb/>v.g. 60. ab E v&longs;que ad D v.g. & non v&longs;que ad N; neutiquam <lb/>&longs;ufficeret; &longs;ed omnino nece&longs;&longs;arium e&longs;t, vt perpendiculum &longs;it <lb/>etiam ad minimùm centum pedum, & pertingat v&longs;que ad N. Et <lb/>hæc perpendiculi men&longs;ura adeo e&longs;t nece&longs;&longs;aria in hydraulicis hi­<lb/>&longs;ce operationibus, vt Natura falli nulla arte, nullo dolo, <expan abbr="nulla&qacute;">nullaque</expan>; <lb/>experientia po&longs;&longs;it. Ioannes Bapti&longs;ta Porta lib. 2. Spirital. cap. <pb xlink:href="051/01/066.jpg" pagenum="35"/> <arrow.to.target n="fig6"/><lb/>1. ait, &longs;e, cúm indigeret determi­<lb/>nato perpendiculo infra vas de­<lb/>&longs;cendente, nec locum haberet <lb/>ad demittendum perpendicula­<lb/>riter tubum, multis viis tenta&longs;&longs;e, <lb/>vt defectum &longs;uppleret; præcipuè <lb/>verò duabus memoratis, nimi­<lb/>rum inclinando primùm, deinde <lb/>in helicem convolvendo tubum <lb/>requi&longs;itæ longitudinis; &longs;ed nun­<lb/>quam de&longs;ideratum effectum fu­<lb/>i&longs;&longs;e con&longs;ecutum, nec vnquam <lb/>a&longs;cendi&longs;&longs;e aquam ad maiorem <lb/>altitudinem quàm erat perpen­<lb/>diculum tubi inclinati, aut tor­<lb/>tuo&longs;i. Demi&longs;it etiam infra vas <lb/>canalem capaciorem, licet bre­<lb/>viorem illo, qui erat &longs;upra vas: <lb/>præterea loco vnius longioris <lb/>demi&longs;it multos breviores, qui &longs;i­<lb/>mul &longs;uperabant longitudinem <lb/>&longs;uperioris; &longs;ed vano &longs;emper labore. Adeo &longs;ui juris tenax e&longs;t <lb/>Natura, & vt non fallit nos in &longs;uis operationibus, ita nec falli à <lb/>nobis vult. Infrà tamen Cla&longs;se 1. cap. 1. Machina 7. Modum do­<lb/>cebo elevandi aquam ad quamvis <expan abbr="altitudin&etilde;">altitudinem</expan> perpendiculis bre­<lb/>vibus multiplicatis, &longs;ed vtrisque, de&longs;cendentis nimirum & a&longs;cen­<lb/>dentis aquæ. Notandum præterea e&longs;t hoc loco, Tubum OI, <lb/>aut CI, po&longs;&longs;e e&longs;&longs;e quantævis longitudinis, vt infrà iterum dicam <lb/>§. IX. Quomodo autem vi attractiva & expul&longs;iva &longs;imul elevari <lb/>po&longs;&longs;it aqua ad maiorem altitudinem quàm &longs;it perpen­<lb/>diculum aquæ de&longs;cendentis, dicemus infrà <lb/>Protheoria II. </s></p> <pb xlink:href="051/01/067.jpg" pagenum="36"/> <p type="margin"> <s><margin.target id="marg93"/><emph type="italics"/>Perpendicu <lb/>lum aquæ <lb/>de&longs;cenden­<lb/>tis debet e&longs;&longs;e <lb/>longius, <lb/>quàm a&longs;cen <lb/>dentis.<emph.end type="italics"/></s></p> <figure id="id.051.01.067.1.jpg" xlink:href="051/01/067/1.jpg"/> <p type="main"> <s><emph type="center"/>§. VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Heronis Alexandrini error in elevanda a­<lb/>qua vi attractivâ.<emph.end type="center"/><lb/> <arrow.to.target n="marg94"/></s></p> <p type="margin"> <s><margin.target id="marg94"/><emph type="italics"/>Error He­<lb/>ronis.<emph.end type="italics"/></s></p> <p type="main"> <s>HEro Alexandrinus cap. 53. libri de Spiritalibus modum præ­<lb/>&longs;cribit elevandi aquam per vim attractivam ex vacui metu; <lb/>&longs;ed vehementer hallucinatur, ob perpendiculi prædicti <expan abbr="defectũ">defectum</expan>; <lb/>&longs;i tamen Heronis e&longs;t error ille, & non potiùs interpretis, qui &longs;che­<lb/>ma appo&longs;uit, vt notavit etiam Ioannes Bapti&longs;ta Porta lib. 2. de <lb/>Spirital. cap. 2. Affero verba vnà cum Schemate Heronis, ex ver­<lb/>&longs;ione & editione Federici Commandini Vrbinatis, qui ex Græco <lb/>in latinum eum tran&longs;tulit quem errorem repetit etiam Ioannes <lb/>Bapti&longs;ta Aleottus in ver&longs;ione Italica. </s></p> <p type="main"> <s><emph type="italics"/>E&longs;t etiam alia con&longs;tructio,<emph.end type="italics"/> inquit Hero, <emph type="italics"/>in qua humidum &longs;en­<lb/>&longs;im fertur, & manet, ita vt &longs;emper a&longs;cendens videatur.<emph.end type="italics"/><lb/> <arrow.to.target n="fig7"/><lb/><emph type="italics"/>Sit ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>vndique præclu&longs;a, quæ dia­<lb/>phragma habeat<emph.end type="italics"/> CD, <emph type="italics"/>& vitreum oper­<lb/>culum Cylindri forma<emph.end type="italics"/> EF <emph type="italics"/>&longs;imiliter vndi­<lb/>que præclu&longs;um. In operculo autem<emph.end type="italics"/> EF <emph type="italics"/>&longs;it <lb/>tubus<emph.end type="italics"/> GH, <emph type="italics"/>ab ip&longs;ius tecto parum di&longs;tans, <lb/>& &longs;imul perforatus cum diaphragmate. A­<lb/>lius etiam tubus<emph.end type="italics"/> KL <emph type="italics"/>&longs;imul perforetur cum <lb/>tecto ba&longs;is, & à diaphragmate parum di&longs;tet. <lb/>In&longs;it autem ba&longs;i extra vitreum operculum <lb/>foramen<emph.end type="italics"/> M, <emph type="italics"/>per quod vas<emph.end type="italics"/> AB, <emph type="italics"/>impleatur: <lb/>& ba&longs;is<emph.end type="italics"/> AB <emph type="italics"/>ad fundum canalem habeat<emph.end type="italics"/><lb/>N. <emph type="italics"/>Sit præterea alius tubus<emph.end type="italics"/> XO, <emph type="italics"/>&longs;imul <lb/>perforatus cum diaphragmate, parumque <lb/>à ba&longs;i di&longs;tans, per quem implebitur vas<emph.end type="italics"/> CB. <lb/><emph type="italics"/>Itaque ob&longs;tructo canali<emph.end type="italics"/> N, <emph type="italics"/>aër qui e&longs;t in<emph.end type="italics"/> CB, <emph type="italics"/>per tubos, & per fora­<lb/>men<emph.end type="italics"/> M <emph type="italics"/>excedet extra. Et cùm vas<emph.end type="italics"/> CB <emph type="italics"/>repletum fuerit, implebi­<lb/>mus<emph.end type="italics"/> AD <emph type="italics"/>per foramen<emph.end type="italics"/> M, <emph type="italics"/>aër enim qui in ip&longs;o e&longs;t, per idem foramen <lb/>excedit. Si igitur canalem<emph.end type="italics"/> N <emph type="italics"/>fluere dimittamus, in locum<emph.end type="italics"/> CB <emph type="italics"/>exina­<lb/>nitum, aër ex vitreo operculo procedet per tubum<emph.end type="italics"/> GH: <emph type="italics"/>in locum autem <lb/>vitrei operculi exinanitum ex<emph.end type="italics"/> AD <emph type="italics"/>humidum a&longs;cendet per tubum<emph.end type="italics"/> KL, <emph type="italics"/>&<emph.end type="italics"/> <pb xlink:href="051/01/068.jpg" pagenum="37"/><emph type="italics"/>a<gap/>r per foramen<emph.end type="italics"/> M <emph type="italics"/>ingredietur. Atque hoc vsque eò fiet, quoad vitreum <lb/>operculum repletum fuerit. Oportebit autem loca<emph.end type="italics"/> AD, CB, EF, <emph type="italics"/>inter <lb/>&longs;e æqualia e&longs;&longs;e, vt ad invicem & aër, & humidum transferantur. Quan­<lb/>do autem vas<emph.end type="italics"/> CB <emph type="italics"/>exinanitum fuertt, & con&longs;titerit aër is continuitas, <lb/>rur&longs;us ex vitreo operculo aqua in vas<emph.end type="italics"/> AD <emph type="italics"/>deferetur, aëre per canalem<emph.end type="italics"/><lb/>N, <emph type="italics"/>& per<emph.end type="italics"/> GH <emph type="italics"/>tubum in vitreum operculum ingrediente, qui verò <lb/>e&longs;t in vase<emph.end type="italics"/> AD <emph type="italics"/>aër per foramen<emph.end type="italics"/> M <emph type="italics"/>excedet.<emph.end type="italics"/></s></p> <figure id="id.051.01.068.1.jpg" xlink:href="051/01/068/1.jpg"/> <p type="main"> <s>Ita Hero; &longs;ed errat autip&longs;e, aut eius interpres: debete­<lb/>nim canalis N de&longs;cendere infra vas perpendiculariter ad tantam <lb/>profunditatem, quanta e&longs;t longitudo KL, vt attrahatur tota a­<lb/>qua va&longs;is AD; alioquin po&longs;tquam effluxerit aliquantulum a­<lb/>quæ ex canali N, traxeritque aliquantulum aëris ex cylindro <lb/>EF, & aquæ ex va&longs;e AD, ce&longs;&longs;abit omnino aquæ fluxus, ob de­<lb/>fectum perpendiculi æqualis perpendiculo KL, &longs;altem ab &longs;u­<lb/>prema &longs;uperficie aquæ va&longs;is AD, v&longs;que ad orificium K tubi <lb/>prædict KL Qui defectus &longs;i &longs;uppleatur, &longs;equetur effectus de&longs;ide­<lb/>ratus. Porta tamen loco citato, occa&longs;ione huius Heronianæ <lb/>indu&longs;triæ, alium excogita vit modum elevandi vi attractiva ex <lb/>inferiori ad &longs;uperius vas aquam: quem legere poteris apud <expan abbr="ipsũ">ipsum</expan>. </s></p> <p type="main"> <s><emph type="center"/>§. VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Alius Heronis error in elevanda aqua <lb/>vi attractiva.<emph.end type="center"/></s></p> <p type="main"> <s>ALium errorem committit Hero lib. cit. de Spiritalibus cap. 5. </s></p> <p type="main"> <s> <arrow.to.target n="marg95"/><lb/>&longs;i tamen & hic non e&longs;t ad&longs;cribendus interpreti. Docere <lb/>vult Hero modum elevandi atque attrahendi humidum ex va&longs;e <lb/>per &longs;iphonem inver&longs;um, cuius vnum crus &longs;it humido <expan abbr="immer&longs;ũ">immer&longs;um</expan>, <lb/>alterum extra vas promineat, non attrahendo prius per os no­<lb/>&longs;trum aërem ex &longs;iphone, &longs;ed appendendo vas quodpiam aquâ <lb/>plenum: Sic ergo di&longs;currit. </s></p> <p type="margin"> <s><margin.target id="marg95"/><emph type="italics"/>Error alius <lb/>Heronis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Sit &longs;merismation aliquod, cuius ma&longs;culum quidem apponatur <lb/>extrin&longs;eco &longs;iphonis cruri, ita vt per ip&longs;um fluat, &longs;itque<emph.end type="italics"/> TV; <emph type="italics"/>faminave-<emph.end type="italics"/> <pb xlink:href="051/01/069.jpg" pagenum="38"/> <arrow.to.target n="fig8"/><lb/><emph type="italics"/>rò<emph.end type="italics"/> TYV <emph type="italics"/>priùs adglutinata va&longs;i<emph.end type="italics"/><lb/>LZ, <emph type="italics"/>quod paulò plùs aquæ, quàm <lb/>&longs;iphon capiat; habeat autem ad <lb/>fundum effluxionem<emph.end type="italics"/> <foreign lang="greek">*w</foreign> <emph type="italics"/>Quan­<lb/>do igitur volumus per &longs;iphonem e­<lb/>ducere aquam, quæ e&longs;t in va&longs;e<emph.end type="italics"/> AB, <lb/><emph type="italics"/>effluxionem va&longs;is<emph.end type="italics"/> LZ <emph type="italics"/>di<gap/>ito <expan abbr="cõ-prehendentes">con­<lb/>prehendentes</expan>, ip&longs;um aquâ imple­<lb/>bimus. Po&longs;tea fœmineum &longs;meri­<lb/>&longs;ma ma&longs;culo aptantes effluxionem<emph.end type="italics"/><lb/><foreign lang="greek">*w</foreign> <emph type="italics"/>dimittemus. Evacuato au­<lb/>tem<emph.end type="italics"/> LZ <emph type="italics"/>va&longs;e, aër in &longs;iphone <lb/>exi&longs;tens in evacuatum locum pro­<lb/>cedet; quem con&longs;equetur humi­<lb/>dum quod in va&longs;e<emph.end type="italics"/> AB, <emph type="italics"/>ita vt <expan abbr="&longs;iphõ">&longs;iphom</expan> <lb/>impleatur. Deinde aufferentes <lb/>vas<emph.end type="italics"/> LZ <emph type="italics"/>Siphonem fluere &longs;ine­<lb/>mus. Oportet autem &longs;iphonem rectè de&longs;cendere, &longs;i officium &longs;uum præ­<lb/>&longs;tare debeat; illud autem erit, quando ad va&longs;is<emph.end type="italics"/> AB <emph type="italics"/>labrum duas regu­<lb/>las rectas compingemus, atque inter ip&longs;as intrin&longs;ecum &longs;iphonis crus <lb/>con&longs;tituemus, ita vt vtrasque contingat; ad idem verò &longs;iphonis crus <lb/>intrin&longs;ecum vtrimque clauvicuulam affigemus, regulas continentem <lb/>parte interiori: ita enim neque obliquum, neque in <gap/>nteriorem par­<lb/>tem declinabit; rectò enim & exqui&longs;itè de&longs;cendet, claviculis regulas <lb/>atterentibus.<emph.end type="italics"/></s></p> <figure id="id.051.01.069.1.jpg" xlink:href="051/01/069/1.jpg"/> <p type="main"> <s>Hæc Hero; quæ tamen fal&longs;a &longs;unt, & contraria experien­<lb/>tiæ, rationi, & hydro-pnevmaticis principijs. Ni&longs;i enim va&longs;is <lb/>altitudo ab V ad <foreign lang="greek">*w</foreign> tanta &longs;it, quantum e&longs;t crus internum CD <lb/>Siphonis; non a&longs;cendet aqua per crus CD, ni&longs;i ad tantam al­<lb/>titudinem, quanta e&longs;t altitudo va&longs;is prædicta ab Y, v&longs;que ad <foreign lang="greek">*w</foreign>. <lb/>Et ratio e&longs;t, quia cùm perpendiculum Y <foreign lang="greek">*w</foreign> minus &longs;it, quàm <lb/>perpendiculum CD; non pote&longs;t aqua attolli ad altitudinem <lb/>CD, &longs;ed po&longs;tquam a&longs;cenderit ad altitudinem æqualem perpen­<lb/>diculo Y <foreign lang="greek">*w</foreign>, relabetur intra vas AB. Ioannes Bapti&longs;ta Porta <pb xlink:href="051/01/070.jpg" pagenum="39"/>lib. 2. de &longs;pirital. cap. 3. ait. aquam non effluxuram è va&longs;e LZ, ab­<lb/> <arrow.to.target n="marg96"/><lb/>lato impedimento apud <foreign lang="greek">*w</foreign>, propter defectum &longs;cilicet perpendi­<lb/>culi prædicti. Sed ratio & experientia convincit, effluere aquam <lb/>è va&longs;e; & a&longs;cendere aquam per crus internum ad altitudinem ex­<lb/>plicatam; quod ip&longs;emet Porta alibi fatetur. </s></p> <p type="margin"> <s><margin.target id="marg96"/><emph type="italics"/>Error Ioan­<lb/>nis Bapti&longs;tæ <lb/>Porta.<emph.end type="italics"/></s></p> <p type="main"> <s>Ut igitur ex va&longs;e AB extrahi po&longs;&longs;it aqua per &longs;iphonem ab&longs;­<lb/>que eo quòd ore attrahatur aër, oportet loco Va&longs;is LZ adhibere <lb/>tubum tantæ longitudinis, quantæ e&longs;t crus CD, imò paulò ma­<lb/>joris: tunc enim effluente aquâ ex tubo appen&longs;o a&longs;cendet paula­<lb/>tim aqua per &longs;iphonem, donec pervenerit u&longs;que ad &longs;ignum V, <lb/>quod &longs;uppono e&longs;&longs;e &longs;emper demi&longs;&longs;ius quàm e&longs;t &longs;uprema &longs;uperfi­<lb/>cies aquæ in Va&longs;e AB: tunc enim &longs;i aufferatur tubus appen&longs;us, ef­<lb/>fluxus aquæ ex &longs;iphone tam diu durabit, donec tota aqua ex <lb/>va&longs;e AB effluxerit, &longs;i os C ad fundum v&longs;que va&longs;is pertigerit. Vi­<lb/>de Salomonem de Caus lib. 1. de viribus motricibus. Vide præ­<lb/>terea quæ &longs;cribimus de fluxu aquæ per &longs;iphones infrà Protheo­<lb/>ria IV. Cap. 2. præ&longs;ertim Propo&longs;it. XI. ubi in Annotatione 2. no­<lb/>tamus errorem Marini Mer&longs;enni <expan abbr="&longs;imil&etilde;">&longs;imilem</expan> prædicti Heronis errori. </s></p> <p type="main"> <s>Monuit hîc, & optimè, <expan abbr="acuti&longs;&longs;ime&qacute;ue">acuti&longs;&longs;imeque</expan> P. Paulus Ca&longs;atus <lb/>Mathe&longs;eos in Romano no&longs;tro Collegio Profe&longs;&longs;or, quæ diximus <lb/>contra Heronem hoc loco, tunc &longs;olùm haberelocum, quando <lb/>&longs;uprema aquæ &longs;uperficies non e&longs;&longs;et multùm &longs;upra punctum C. <lb/>Cæterùm &longs;i vas AB e&longs;t plenum, & <expan abbr="perpendiculũ">perpendiculum</expan> <foreign lang="greek">*y*w</foreign> &longs;uperat per­<lb/>pendiculum à &longs;uprema aquæ &longs;uperficie u&longs;q<gap/> ad D; poterit a&longs;cen­<lb/>dere aqua, & per crus DY defluere<gap/> quâ &longs;emel defluente, &longs;em­<lb/>per deinde defluet, donec evacuetur vas vsque ad punctum C, <lb/>quoniam perpendiculum DY &longs;emper manebit longius quàm <lb/>perpendiculum CD. </s></p> <p type="main"> <s><emph type="center"/>§. IX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>In aquarum elevatione vi attractivâ, habenda e&longs;t ratio <lb/>perpendiculi &longs;olùm illorum tuborum, per quos aqua, <lb/>non per quos aër vehitur.<emph.end type="center"/><lb/> <arrow.to.target n="marg97"/></s></p> <p type="margin"> <s><margin.target id="marg97"/><emph type="italics"/>Tubi per <lb/>quos aër de­<lb/>fertur in<emph.end type="italics"/></s></p> <p type="main"> <s>NOtat optimè Ioannes Bapti&longs;ta Porta lib 2. de Spiritalibus. C. 6. <lb/>& nos etiam &longs;uprà in fine §. VI. in&longs;inuavimus, in Machinis </s></p> <pb xlink:href="051/01/071.jpg" pagenum="40"/> <p type="main"> <s> <arrow.to.target n="marg98"/><lb/> <arrow.to.target n="fig9"/><lb/>vi attractiva elevan­<lb/>tibus aquam, haben­<lb/>dam e&longs;&longs;e rationem <lb/>longitudinis ac bre­<lb/>vitatis &longs;olùm illorum <lb/>tuborum &longs;eu canali­<lb/>um, qui conferunt <lb/>ad aquarum perpen­<lb/>diculum, & per quos <lb/>tran&longs;ire debet aqua, <lb/>atque adeo quorum <lb/>aquæ &longs;e mutuò tra­<lb/>here ac v<gap/> de­<lb/>bent, <gap/><lb/>quoru<gap/><lb/>&longs;olù<gap/><lb/>bet. <gap/>eli­<lb/>ùs intelligatur, in<gap/>­<lb/>ciat<gap/> figura porta <lb/>&longs;uprà §. citato, in qua <lb/>figura h<gap/>enda e&longs;t <lb/>&longs;olùm ratio <expan abbr="tuborũ">tuborum</expan> <lb/>BK, & EF; hi enim <lb/>duo continent aquas <lb/>quarum perpendi­<lb/>cula ad invicem pu­<lb/>gnant, juxta dicenda infrà Protheoria IV. cap. 2. Propo&longs;it. 13. <lb/>tubus verò OI pote&longs;t e&longs;&longs;e quantævis longitudinis aut brevita­<lb/>tis, ac proinde vas C pote&longs;t e&longs;&longs;e & infra & &longs;upra vas B. Patet <lb/>hoc experientia, vt dicemus loco citato; vbi etiam experientiæ <lb/>cau&longs;am dabimus. </s></p> <p type="margin"> <s><margin.target id="marg98"/><emph type="italics"/>Machinis <lb/>attractivis <lb/>metu vacui <lb/>po&longs;&longs;unt e&longs;&longs;e <lb/>quantævis <lb/>longitudinis<emph.end type="italics"/></s></p> <figure id="id.051.01.071.1.jpg" xlink:href="051/01/071/1.jpg"/> <p type="main"> <s><emph type="center"/>§. X.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Vi attractivâ elevari pote&longs;t aqua vltra perpen­<lb/>culi altitudinem, aëre mediante.<emph.end type="center"/></s></p> <pb xlink:href="051/01/072.jpg" pagenum="41"/> <p type="main"> <s>Ingenio&longs;&longs;imum &longs;anè modum <expan abbr="Naturã">Naturam</expan> quodamodo decipiendi, <lb/>& aquam vltra perpendiculi à Natura requi&longs;iti altitudinem e­<lb/>levandi vi attractiva, affert Porta loco proximè citato, cap. 11. <lb/>aitque &longs;e illum ca&longs;u reperi&longs;&longs;e inter cont<gap/>uas hydraulicas atque <lb/>pnevmaticas experientias quas fecit. Fit hoc aëre mediante, <lb/>aquæ immi&longs;to. Hac ratione, inquit Porta, perpendiculo 50. <lb/>pedum elevari pote&longs;t aqua ad altitudinem pedum 80. Modus <lb/>hic e&longs;t. </s></p> <figure id="id.051.01.072.1.jpg" xlink:href="051/01/072/1.jpg"/> <p type="main"> <s>Sit ex va&longs;e AB portatili e­<lb/> <arrow.to.target n="marg99"/><lb/>levanda aqua ad vas D, ad alti­<lb/>tudinem pedum 80. Fiat canalis <lb/>vitreus GK (vt&longs;pectari, oculis­<lb/>que percipi manife&longs;tè po&longs;&longs;itar­<lb/>tificium) vtrimque apertus, & <lb/>va&longs;i D optimè coarctatus a­<lb/>pud K. Fiat deinde vas C, æ­<lb/>qualis aut maioris capacitatis, <lb/>quàm vas D; <expan abbr="in&longs;eratur&qacute;ue">in&longs;eraturque</expan> v­<lb/>trique canalis PQ vtrimque a­<lb/>pertus immediatè &longs;ub operculis <lb/>&longs;eu tectis va&longs;orum. Tandem <lb/>ex va&longs;e C de&longs;cendat perpendi­<lb/>culariter canalis EF quinqua­<lb/>ginta pedum longitudinis, ha­<lb/>bens epi&longs;tomium E, & &longs;it opti­<lb/>mè adferruminatus fundo va&longs;is C. His factis, impleantur va&longs;a <lb/>AB, & C, aquâ, <expan abbr="admoveatur&qacute;ue">admoveaturque</expan> vas AB tubo GK, ita vt o­<lb/>&longs;culum G &longs;it aquæ immer&longs;um, & aperiatur epi&longs;tomium E; de­<lb/>&longs;cendet aqua ex va&longs;e C, &longs;ecumque trahet aërem ex tubis QP, <lb/>& KG, & ex va&longs;e D, &longs;imulque aquam ex va&longs;e AB. Po&longs;tquam <lb/>a&longs;cenderit aqua intra canalem GK v&longs;que ad aliquod &longs;patium <lb/>exiguum, v.g. v&longs;que ad H; remove aliquantulùm vas AB; & <lb/>aqua canalis a&longs;cendet vlteriús, tracta &longs;cilicet ab aqua effluente <lb/>per FE) & po&longs;t aquam &longs;equetur aër. Admove deinde iterum <pb xlink:href="051/01/073.jpg" pagenum="42"/> <arrow.to.target n="fig10"/><lb/>vas AB, & attrahetur alia aqua, <lb/><expan abbr="erit&qacute;ue">eritque</expan> aër HI inter aquam <lb/>GH, & IM. Iterum remove vas <lb/>AB, & ingredietur per os G alius <lb/>aër, &longs;equeturque aquam. Quo <lb/>facto, &longs;i vas iterum admôris, <expan abbr="di-ctamq;">di­<lb/>ctamque</expan> operationem repetive­<lb/>ris; a&longs;cendent tandem aqua & <lb/>aër mi&longs;ti inter &longs;e, v&longs;que ad vas D, <lb/>illudque replebunt, <expan abbr="antequã">antequam</expan> ef­<lb/>fluat tota aqua va&longs;is C, quod ob <lb/>id minus e&longs;&longs;e debet quam vas D. </s></p> <p type="margin"> <s><margin.target id="marg99"/><emph type="italics"/>Experimen <lb/>tum Porta <lb/>ad aquam <lb/>elevandam <lb/>vltra <expan abbr="perp&etilde;-diculi">perpen­<lb/>diculi</expan> alti­<lb/>tudinem.<emph.end type="italics"/></s></p> <figure id="id.051.01.073.1.jpg" xlink:href="051/01/073/1.jpg"/> <p type="main"> <s>Procedendum e&longs;t autem <lb/>valde cautè in hoc negotio, nè <lb/>nimium aéris ingrediatur per os <lb/>G, & levitate &longs;ua &longs;ur&longs;um ten­<lb/>dens pellat modicam aquam <lb/>antea in tromiffam, repleatque totum canalem GK, &longs;icque de­<lb/>&longs;truatur continuitas aquæ & aëris intra canalem: hoc enim &longs;i <lb/>fieret, non repleretur vas D, ni&longs;i po&longs;t longi&longs;&longs;imum tempus, & <lb/>multas operationes, deberetque &longs;æpius repleri vas C. Nun­<lb/>quam præterea tantum aquæ &longs;imul continere debet canalis <lb/>GK, vt ejus perpendiculum &longs;uperet perpendiculum aquæ ca­<lb/>n alis EF. Ex hac praxi deducit Porta modum mirabilem, & <lb/>omnibus antiquis ignotum, ut ip&longs;e ait, elevandi per &longs;iphonem <lb/>inver&longs;um aquam è montis radice ad ejus verticem; quem mo­<lb/>dum afferam infrà Protheoria IV. cap. 2. Propo&longs;it. 12. ex <lb/>quo etiam loco meliùs intelligetur hoc <lb/>præ&longs;ens Experimentum. </s></p> <pb xlink:href="051/01/074.jpg" pagenum="43"/> <p type="main"> <s><emph type="center"/>Protheoria II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA <lb/>SECVNDA.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De vi Expul&longs;iva propter corporum impe­<lb/>netrabilitatem; &longs;eu de &longs;ecundo Machinarum Hy­<lb/>dropnevmaticarum principio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>§. I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Omnia Vniver&longs;i corpora &longs;unt inter &longs;e <lb/>contigua.<emph.end type="center"/></s></p> <p type="main"> <s>COrpora omnia, quæ DEVS Optimus Maximus <lb/> <arrow.to.target n="marg100"/><lb/>in prima rerum conditione intra præ&longs;titutum in Vni­<lb/>ver&longs;i ambitu conclu&longs;it locum, Cœlum dico, Elemen­<lb/>ta, & Mixta, tali &longs;unt ordine di&longs;po&longs;ita, ut multi, nec <lb/>vulgares Philo&longs;ophi, exi&longs;timent, motum localem in Mundo non <lb/><expan abbr="futurũ">futurum</expan> ullum, ni&longs;i aut concedatur di&longs;per&longs;um per omnia vacuum <lb/>(quale vidimus invehere Heronem, alio&longs;que nonnullos) aut <lb/>corporum mutua penetratio, aut rerum omnium commotio, <lb/>atque permixtio. Audi Epicurum apud Diogenem Laêrtium <lb/>lib. 10. in Epi&longs;tola ad Herodotum, ubi ait. <foreign lang="greek">*ei) de\ mh\ h)_n o( kai\ xeno\s, kai\ <lb/>xw/<gap/>an, kai\ a)naf<gap/> fu/sin o)noma/comen, <gap/>x a)/n ei)_xe ta\ sw/mata o(/p<gap/>n <gap/>de\ di) <gap/><lb/>exinei_to, xa<gap/>a/pe<gap/> fa/inetw xin<gap/>mena</foreign> <emph type="italics"/>Ni&longs;i verò id e&longs;&longs;et quoque, quod & <lb/>inane,<emph.end type="italics"/> &longs;eu vacuum, <emph type="italics"/>& regionem,<emph.end type="italics"/> &longs;eu &longs;patium, <emph type="italics"/>ac locum & intacti­<lb/>lem<emph.end type="italics"/> &longs;ive in corpoream <emph type="italics"/>naturam vocamus; non haberent corpora ne­<lb/>que ubi e&longs;&longs;ent, neque quà motus &longs;uos obirent; cùm moveri ea quidem <lb/>manife&longs;tum &longs;it.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg100"/><emph type="italics"/>Corpora o­<lb/>mnia Vni­<lb/>ver&longs;i conti­<lb/>gua inter &longs;e.<emph.end type="italics"/></s></p> <p type="main"> <s>Hanc autem, quam petitam ex motu rationem in&longs;inuat <lb/> <arrow.to.target n="marg101"/><lb/>&longs;olummodò Epicurus, deducunt manife&longs;tiùs Democritus atque <lb/>Leucippus (quos &longs;ecutus e&longs;t Epicurus) apud Ari&longs;totelem lib. 4. <lb/>Phy&longs;. tex. 6. (ubi etiam alteram de corporum penetratione ur­<lb/>gent) his verbis <foreign lang="greek"><gap/> ga\<gap/> a)\n doxo/ih ei)/nai ei) m<gap/> xeno\n. to\ ga/<gap/> pl<gap/>es a)du/na­<lb/>ton ei)/nai de/ca<gap/></foreign>, &c. <emph type="italics"/>Non videtur quippe e&longs;&longs;e motus, ni&longs;i &longs;it inane. <lb/>Quod enim plenum e&longs;t, admittere in &longs;e mobile non pote&longs;t. Nam &longs;i ad-<emph.end type="italics"/> <pb xlink:href="051/01/075.jpg" pagenum="44"/> <arrow.to.target n="marg102"/><lb/><emph type="italics"/>mittat, & fuerint in eodem loco duo corpora; nihil repugnabit, quò mi­<lb/>nùs quotquot libuerit, &longs;imul &longs;int; quia dici, cur id non valeat evenire, <lb/>minimè pote&longs;t. Sin autem eveniat, tunc quod minimum, id admittet <lb/>quod maximum; quando ip&longs;um magnum multa parva e&longs;t: adeo ut &longs;i <lb/>multa æqualia in eodem e&longs;&longs;e contigerit, e&longs;&longs;e & in æqualia contingat.<emph.end type="italics"/> Ean­<lb/>dem <expan abbr="con&longs;ecution&etilde;">con&longs;ecutionem</expan> deducit Lucretius in &longs;ua ver&longs;ibus ligata Phi­<lb/> <arrow.to.target n="marg103"/><lb/>lo&longs;ophia; additque non &longs;olùm, &longs;i Inane &longs;eu Vacuum non admit­<lb/>tatur, rem nullam exijs quæ &longs;unt, moveri, &longs;ed nec ullam denuò <lb/>na&longs;ci po&longs;&longs;e in mundo. </s></p> <p type="margin"> <s><margin.target id="marg101"/><emph type="italics"/>Argumen­<lb/>tum Epicuri <lb/>Leucippi, ac <lb/>Democriti <lb/>pro vacuo.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg102"/><emph type="italics"/>Corporum <lb/>penetratio <lb/>non pote&longs;t <lb/>fieri natu­<lb/>raliter.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg103"/><emph type="italics"/>Vacuum <expan abbr="nõ">non</expan> <lb/>admittit <lb/>Lucretius.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/><emph type="italics"/>Quæ &longs;i non e&longs;&longs;et Inane,<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>Non tam &longs;olicito motu privata careret, Quàm genita omninò nulla ra­<lb/>tione fui&longs;&longs;et, vndique materies quoniam &longs;tipata fui&longs;&longs;et.<emph.end type="italics"/> Cogita enim <lb/>vniver&longs;um mundum (ait vir docti&longs;&longs;imus Petrus Ga&longs;&longs;endus in <lb/>&longs;uis de Phy&longs;iologia Epicuri Animad ver&longs;ionibus, ex Epicuri men­<lb/>te,) &longs;i nihil Inanis inter&longs;per&longs;um habeat, conferti&longs;&longs;imam e&longs;&longs;e mo­<lb/>lem, adeo ut nè minimum quidem corpu&longs;culum valeat de novo <lb/>&longs;u&longs;cipere (quod quidem a&longs;&longs;erendum nece&longs;&longs;ariò e&longs;t, &longs;i nullum in <lb/>rebus Inane, &longs;i nihil non plenum, &longs;i locus nullus re&longs;tat complen­<lb/>dus.) Quare aut corpus non admittetur denuò genitum, aut in <lb/>illo loco collocabitur, in quo aliud jam &longs;itum e&longs;t; &longs;icque idem <lb/>locus duo corpora &longs;e&longs;e undique penetrantia capiet. Quod &longs;anè <lb/>per vires Naturæ fieri po&longs;&longs;e non dixeris, ut ut alij id a&longs;&longs;erant, in­<lb/>ducti exemplo panis, &longs;pongiæque &longs;iccæ aquam, cui injiciuntur, <lb/>in&longs;ugentis; & cinerum tantundem aquæ in con&longs;ortium &longs;uum ad­<lb/>mittentium in va&longs;e, quantum &longs;ine cineribus vas recipere pote&longs;t. <lb/> <arrow.to.target n="marg104"/></s></p> <p type="margin"> <s><margin.target id="marg104"/><emph type="italics"/>Argumen­<lb/>tum Epicu <lb/>reorum ac <lb/>Democriti <lb/>torum pro <lb/>vacuo.<emph.end type="italics"/></s></p> <p type="main"> <s>Si ab&longs;onum videtur vacuum admittere, &longs;i <foreign lang="greek">a)du/naton</foreign> corpo­<lb/>rum dari penetrationem, & tamen motum admittimus localem; <lb/>&longs;u&longs;que deque verti corpora omnia, quæ Univer&longs;o concluduntur, <lb/>fateamur nece&longs;&longs;e e&longs;t toties, quoties eorum unum movebitur, di­<lb/>cet Democriticus qui&longs;piam, aut Epicureus: moveatur enim <lb/>quodcunque eorum, quæ &longs;unt, de &longs;uo quem occupat loco, alte­<lb/>riu&longs;que in vadere tentet &longs;tationem; &longs;anè cùm locum plenum <lb/>offendat, nece&longs;&longs;e erit, ex eo pellat, quod corpus illum occupat. <lb/>Illud porrò quónam concedat, &longs;i omnia quidem plena &longs;unt? An <pb xlink:href="051/01/076.jpg" pagenum="45"/>non ip&longs;um rur&longs;us expellet aliud? At de eo par redibit difficultas: <lb/>hoc enim, aliud expellere loco debebit; & illud aliud; &longs;icque con­<lb/>tinuari nece&longs;&longs;e erit inchoatam &longs;omel corporum commotionem <lb/>in ævum, & totum commoveri Vniver&longs;um vel ad mu&longs;cæ vola­<lb/>tum. Si enim vel unum corpus cedere loco non valeat, aut non <lb/>volet, omnis ce&longs;&longs;abit illicò motus, eritque unaquæque res mun­<lb/>di &longs;ic in&longs;erta in aliam, ut magis è loco excedere nequeat, quàm <lb/>mytuli (inquit Ga&longs;&longs;endus paulò antè citatus) &longs;eu cochleæ illæ, <lb/>quæ intra &longs;ilices na&longs;cuntur. Neque dicas, e&longs;&longs;e in mundo rara, <lb/>liquida, fluxaque corpora, quæ cedere magis quàm &longs;ilices po&longs;­<lb/>&longs;int. Sint enim quantum vis rara, fluxa, & cedere nata; &longs;i admi­<lb/>&longs;tum Inane non habent, &longs;i particulæ omnes illorum contiguita­<lb/>tem undique, &longs;eu &longs;ecundùm totas &longs;uperficies habent; tale con­<lb/>tinuum corpus facient, ut perinde &longs;it &longs;eu ex &longs;ilice, &longs;eu ex aqua, &longs;eu <lb/>ex aëre illud dicas: neque enim aër vel paucioribus, vel minùs <lb/>compactis &longs;ui partibus occupabit locum minorem, quàm &longs;ilex, <lb/>cùm quotcunque loci particulas feceris, tam nulla earum &longs;it aë­<lb/>ris, quàm &longs;ilicis particulæ expers. Hactenus Democritici, & <lb/>Epicurei. </s></p> <p type="main"> <s><emph type="center"/>§. II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Corpora &longs;e mutuò expellunt.<emph.end type="center"/></s></p> <p type="main"> <s>HIs quid reponendum, viderint Philo&longs;ophi. Ari&longs;toteles certe, </s></p> <p type="main"> <s> <arrow.to.target n="marg105"/><lb/>qui nec vacuum admittit, nec corporum penetrationem <lb/>mutuam, nequaquam timet rerum omnium ad quemlibet mo­<lb/>tum commotionem; quoniam liquida non &longs;olùm pelluntur, &longs;ed <lb/>dividuntur etiam dum urgentur; & quæ antror&longs;um vergebant <lb/>partes, latera lambentes claudunt terga. At quidquid &longs;it, tam <lb/>evidens e&longs;t, corpus unum expellere alterum è &longs;uo, quem occu­<lb/>pat, loco, ni &longs;ponte excedere velit, quàm e&longs;t manife&longs;tum, mo­<lb/> <arrow.to.target n="marg106"/><lb/>tum dari localem; idque verum e&longs;t non tantùm in duris &longs;oli­<lb/>di&longs;vé, &longs;ed liquidis etiam ac fluidis corporibus, aëre dico, & aqua. <lb/>videmus enim quotidie, aquam va&longs;i, tuboque aëre pleno illa­<lb/>bentem, expellere aërem, &longs;i exeundi locum habet; & &longs;i non ha­<lb/>bet, neque aquam po&longs;&longs;e, aut velle infundi. Videmus item aë- <pb xlink:href="051/01/077.jpg" pagenum="46"/>rem inflatum va&longs;i per os unum, expellere aquam per alterum, aut <lb/>etiam per idem, &longs;i elabendi detur locus; qui &longs;i non datur, nec aë­<lb/>ri patere ingre&longs;&longs;um. Videmus follibus compre&longs;&longs;is erumpere <lb/>aërem, & aquam etiam, &longs;i aquâ erant repleti. Videmus, &longs;i va&longs;i <lb/>aquâ pleno operculum in medio perforatum imponamus, de­<lb/>primamu&longs;que, aquam pre&longs;&longs;am, &longs;i inter latera va&longs;is & opercu­<lb/>lum erumpere non pote&longs;t, ex&longs;ilire per foramen magno impetu. <lb/>Taceo centena exempla alia. Atque hæc mutua corporum ex­<lb/>pul&longs;io alterum e&longs;t Machinarum Hydro-pnevmaticarum prin­<lb/>cipium, quo innumera, & non minùs iucunda, quàm admiran­<lb/>da exhibentur &longs;pectacula pa&longs;&longs;im, vt apparebit aperti&longs;&longs;imè ex &longs;e­<lb/>quentibus Machinis. Interim&longs;equens accipe Experimentum. </s></p> <p type="margin"> <s><margin.target id="marg105"/><emph type="italics"/>Corpora ex­<lb/>pellunt &longs;e <lb/>mutuò.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg106"/><emph type="italics"/><expan abbr="Experim&etilde;-ta">Experimen­<lb/>ta</expan> varia, <lb/>quibus pro­<lb/>batur cor­<lb/>pora&longs;e mu­<lb/>mutuò ex­<lb/>pellere.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>§. III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Experimentum, quo o&longs;tenditur vis expul&longs;iva, propter <lb/>corporum impenetrabilitatem, ad aquas elevan­<lb/>das in altum.<emph.end type="center"/></s></p> <figure id="id.051.01.077.1.jpg" xlink:href="051/01/077/1.jpg"/> <p type="main"> <s>FAcex&longs;tanno, cu­<lb/>pro, creta, ligno, <lb/>aut alia quacunque <lb/>materia aquis re&longs;i­<lb/>&longs;tente tria va&longs;cula <lb/>A, F, & G, columnis <lb/>inter&longs;e di&longs;tincta, vt <lb/>mon&longs;trat figura; aut <lb/>alia ratione, prout <lb/>placuerit, aut com­<lb/>modiùs fuerit: <expan abbr="&longs;int-&qacute;ue">&longs;int­<lb/>que</expan> hæc va&longs;cula vn­<lb/>dique clau&longs;a quàm <lb/>diligenti&longs;&longs;ime, nè <lb/>aër po&longs;&longs;it aut ingre­<lb/>di, aut elabi, &longs;altem <lb/>ex A & G. Vas infe­<lb/>rius G habeat <expan abbr="epi-&longs;tomiũ">epi­<lb/>&longs;tomium</expan> I. per quod <pb xlink:href="051/01/078.jpg" pagenum="47"/>aqua effluere po&longs;&longs;it. Va&longs;a A & F habeant in operculis forami­<lb/>na C & E, vt per ea infundi po&longs;&longs;it aqua, & iterum obturari. <lb/>Exva&longs;e A egrediatur tubulus AB vtrimque, apertus qui apud <lb/>A fundum va&longs;is non attingat, &longs;ed tantum ab illo di&longs;tet, vt <lb/>aqua interfluere po&longs;&longs;it: apud B verò habeat o&longs;culum &longs;tricti&longs;&longs;i­<lb/>mum. Habeat præterea epi&longs;tomium K. Ex eodem va&longs;e A de­<lb/>&longs;cendat intra vas inferius G alius tubulus DN, vtrimque aper­<lb/>tus, qui apud D non attingat operculum va&longs;is A, &longs;ed tantum <lb/>ab illo di&longs;tet, vt po&longs;&longs;it egredi aër: apud H verò tran&longs;eat &longs;olum <lb/>operculum va&longs;is G, & non extendatur vlteriùs.| Ex va&longs;e deni­<lb/>que F de&longs;cendatintra vas G alius tubus FG vtrimque aper­<lb/>tus, qui apud F tran&longs;eat &longs;olùm fundum va&longs;is, & non progredia­<lb/>tur vlteriùs; apud G verò di&longs;tet tantum à fundo, vt aqua ef­<lb/>fluere po&longs;&longs;it, habeatque vas G epi&longs;tominm L. Hi tres tubi <lb/>debentita &longs;tanno alia vè materia coarctari, & adferruminari va­<lb/>&longs;is in loco tran&longs;itus, vt nullus aër penetrare intra va&longs;a, aut elabi <lb/>ex ijsdem po&longs;&longs;it. Cavendum præterea diligenter e&longs;t, nè tubu­<lb/>lus AB &longs;it longior, aut æquè longus, ac tubulus FG; quare <lb/>meliùs erit, &longs;i inter B & K decurtetur quantum pote&longs;t, & quàm <lb/>minimum extra vas A protendatur. </s></p> <p type="main"> <s>His ita ritè præparatis, repleantur aqua duo va&longs;a A & F, per <lb/>foramina C & E, & obturentur quàm diligenti&longs;&longs;imè, maximè <lb/>foramen C (foramen enim E pote&longs;t manere apertum;) vas <lb/>verò G maneatvacuum; & omnia epi&longs;tomia &longs;int clau&longs;a. De­<lb/>inde aperiatur epi&longs;tomium L, vt aqua va&longs;is F defluere po&longs;&longs;it <lb/>intra vas G: & po&longs;tquam defluxit aliquantulum aquæ, aperia­<lb/>tur epi&longs;tomium K; <expan abbr="erumpet&qacute;ue">erumpetque</expan> maximo impetu aqua va­<lb/>&longs;is A per tubulum AB, pro&longs;ilietque in altum, vi expul&longs;iva, pro­<lb/>pter corporum impetrabilitatem. Nàm aqua va&longs;is F de&longs;cen­<lb/>dens intra vas G, expellit inde aërem per tubum HD intra vas <lb/>A; qui aer expellit inde aquam per tubulum AB, quoniam ne­<lb/>que in G, neque in A, aër & aqua &longs;imul in eodem loco manere <lb/>po&longs;&longs;unt, &longs;ed nece&longs;&longs;ariò vnum corpus expellit alterum, propter <lb/>eorum impenetrabilitatem. Vides igitur quomodo vis expul­<lb/>&longs;iva propter corporum impenetrabilitatem &longs;it principium & <pb xlink:href="051/01/079.jpg" pagenum="48"/>cau&longs;a Machinarum Hydro-pnevmaticarum? Vbi de&longs;cenderit <lb/>aqua va&longs;is F intra vas G, & ex&longs;iliuerit aqua va&longs;is A per tubum <lb/>AB; depromi poterit aqua va&longs;is G per epi&longs;tomium I, & reple­<lb/>ri iterum va&longs;a A & F, vt antea, & in&longs;titui idem lu&longs;us. </s></p> <p type="main"> <s><emph type="center"/>§. IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Notantur nonnulla circa prædictum <lb/>Experimentum.<emph.end type="center"/><lb/> <arrow.to.target n="marg107"/></s></p> <p type="margin"> <s><margin.target id="marg107"/><emph type="italics"/>Fundame­<lb/>tum omni­<lb/>um Machi­<lb/>narum Hy­<lb/>dro-, nev­<lb/>maticarum <lb/>quæ fiunt vi <lb/>expul&longs;iva.<emph.end type="italics"/></s></p> <p type="main"> <s>HOc experimentum e&longs;t fundamentum omnium Hydro­<lb/>pnevmaticarum Machinarum quæ fiunt vi expul&longs;iva ob cor­<lb/> <arrow.to.target n="fig11"/><lb/>porum impenetra­<lb/>bilitatem; ideoque <lb/>Tyrones diligenter <lb/>procurare debent, <lb/>vt illud intelligant: <lb/>quare nonnulla cir­<lb/>ca <expan abbr="ipsũ">ipsum</expan> &longs;unt adver­<lb/>tenda. </s></p> <figure id="id.051.01.079.1.jpg" xlink:href="051/01/079/1.jpg"/> <p type="main"> <s>Primum e&longs;t, ex­<lb/>pedire vt vas A non <lb/>&longs;it minùs capax <expan abbr="quã">quam</expan> <lb/>vas F, & vt tubus <lb/>FG non &longs;it amplior <lb/>tubo AB: &longs;ic enim <lb/>fiet, vt quàmdiu a­<lb/>qua ex va&longs;e F <expan abbr="de&longs;c&etilde;-dit">de&longs;cen­<lb/>dit</expan> intra G, tamdiu <lb/>&longs;aliat aqua ex vase A <lb/>per tubum AB. Hoc <lb/><expan abbr="tam&etilde;">tamen</expan> non e&longs;t omni­<lb/>nò nece&longs;&longs;arium. </s></p> <p type="main"> <s>Secundum e&longs;t, Non e&longs;&longs;e nece&longs;&longs;arium, vt fiat vas F, &longs;ed fie­<lb/>ri pote&longs;t&longs;olus canalis &longs;eu tubus FG, qui apud F habeat infun­<lb/>dibulum, vt aqua infundi po&longs;&longs;it; dummodò &longs;it longior quàm <lb/>tubus AB; vt mox dicam. </s></p> <pb xlink:href="051/01/080.jpg" pagenum="49"/> <p type="main"> <s>Tertium e&longs;t, omninò <expan abbr="nece&longs;&longs;ariũ">nece&longs;&longs;arium</expan> e&longs;&longs;e, vt tubus FG longi­<lb/>or &longs;it quam tubus AB, quia, vt diximus Protheoria I. §. VI. & di­<lb/>cemus iterum infrà Protheoria IV. cap. 2. Propo&longs;it. 14. hîc et­<lb/>iam, vt vbiq, in hydraulicis, perpendiculis certatur, non verò <expan abbr="a-quarũ">a­<lb/>quarum</expan> copiâ. <expan abbr="Perpendiculũ|aut&etilde;">Perpendiculun|autem</expan> tubi FG computatur ab F <expan abbr="v&longs;q;">v&longs;que</expan> ad </s></p> <p type="main"> <s> <arrow.to.target n="marg108"/><lb/>&longs;upremam <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> aquæ de&longs;cendentis & quie&longs;centis in va&longs;e G. <lb/>Quò verò longius fuerit perpendiculum FG &longs;upra perpendicu­<lb/>lum AB eò altiùs &longs;alit aqua ex o&longs;culo B. Quare cùm in prin­<lb/>cipio, quando incipit de&longs;cendere aqua intra vas G, longius &longs;it <lb/>perpendiculum FG, quàm po&longs;tea (repleto paulatim va&longs;e G) <lb/>& id <expan abbr="&longs;&etilde;per">&longs;emper</expan> magis ac magis minuatur; con&longs;equens e&longs;t, vtin prin­<lb/>cipio altiùs &longs;aliat aqua ex B, quàm po&longs;t principium, & vt &longs;em­<lb/>per minùs & minùs altè ex&longs;iliat. Vide etiam quæ dicimus in­<lb/>frà Parte 2. Cla&longs;se I. cap. 2. Machina I. Annot. 2. </s></p> <p type="margin"> <s><margin.target id="marg108"/><emph type="italics"/>Perpendi­<lb/>culis, non a­<lb/>qudrum co­<lb/>piâ certatur <lb/>in hydrau­<lb/>licis.<emph.end type="italics"/></s></p> <p type="main"> <s>Quartum e&longs;t, Non &longs;olùm &longs;ervandam e&longs;&longs;e proportionem <lb/>quoad longitudinem inter tubos AB, & GF, &longs;ed etiam quoad <lb/>capacitatem, nè &longs;cilicet AB laxior &longs;it quàm GF; alioquin gra­<lb/>vior erit aqua intra ip&longs;um, quàm vt elevari po&longs;&longs;it ab aëre modi­<lb/>co intra vas A pul&longs;o à modica aqua cadente intra vas G. Si <lb/>verò FG tubus laxior e&longs;&longs;e<gap/> quàm AB, nimis citò repleretur <lb/>vas G, & antequam tota aqua va&longs;is A expelleretur per AB. </s></p> <p type="main"> <s>Quintum e&longs;t, Nihil referre quantæ &longs;it altitudinis tubus HD, <lb/>per quem aër defertur, quia nihil confert ad perpendiculum. Pro­<lb/>curandum tamen e&longs;t, nè &longs;it nimis laxus, aliàs multùm aëris intra <lb/>ip&longs;um ab&longs;orberetur, qui alioquin expelli deberet intra vas A. </s></p> <p type="main"> <s>Sextum e&longs;t, prædictum artificium elevandi aquam vi ex­<lb/>pul&longs;iva propter corporum impenetra bilitatem, e&longs;&longs;e typum & <lb/>exemplar omnium Machinarum Hydro-pnevmaticarum præ­<lb/>dicta virtute animatarum; ac proinde &longs;emperante oculos <lb/>in &longs;imilibus Machinis fabricandis e&longs;&longs;e habendum, <lb/>vtin principio dicebam. </s></p> <pb xlink:href="051/01/081.jpg" pagenum="50"/> <p type="main"> <s><emph type="center"/>§ V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Heronis error in elevando oleo vi Expul&longs;ivâ <lb/>in lucerna.<emph.end type="center"/></s></p> <p type="main"> <s>HEro Alexandrinus in libello de Spiritalibus cap. 72. proponit <lb/>hanc Machinam. <emph type="italics"/>Lucernæ con&longs;tructio, vt ellychnio impo­<lb/>&longs;ito, quando oleum deficiat, ex aure eius oleum in ellychnium infun­<lb/>datur, quantum quis voluerit, nullo ip&longs;i appo&longs;ito va&longs;e, ex quo oleum in­<lb/> <arrow.to.target n="marg109"/><lb/>fluat.<emph.end type="italics"/> Qua quidem in con&longs;tructione errorem committit gravi&longs;­<lb/>&longs;imum (&longs;i tamen ip&longs;ius e&longs;t error, & non potiùs Interpretis, qui <lb/>figuras appo&longs;uit) quem hîc detegere oportet, ne alijs etiam &longs;it <lb/> <arrow.to.target n="fig12"/><lb/>errandi occa&longs;io. Quod eò et­<lb/>iam libentiùs facio, quòd nec <lb/>Federicus Commandinus, qui <lb/>ex Græco in latinum tran&longs;tulit <lb/>Heronem; nec Ioannes Bapti­<lb/>&longs;ta Aleottus, qui Commandini <lb/>interpretationem red didit Itali­<lb/>cam; nec Ioannes Bapti&longs;ta Porta, <lb/>qui Heronis errorem etiam ob­<lb/>&longs;ervavit, genuinam lucernæ de­<lb/>lineationem dederunt. Eam <lb/>verò hîc dare conabimur, allatis <lb/> <arrow.to.target n="marg110"/><lb/>Heronis verbis ex Commandini <lb/>translatione, addendo nonnulla <lb/>verba majoris claritatis gratia, <lb/>quæ a&longs;teri&longs;cis in margine no­<lb/>tantur. Sic ergo di&longs;currit Hero. <lb/><emph type="italics"/>Con&longs;truatur lucerna, ba&longs;im habens <lb/>concavam, & triangularem in&longs;tar <lb/>pyramidis; &longs;it que ba&longs;is concava<emph.end type="italics"/> AB <lb/>CD, <emph type="italics"/>& in ea diaphragma<emph.end type="italics"/> EF. <emph type="italics"/>Lu­<lb/>cernæ autem caulis &longs;it<emph.end type="italics"/> GH, <emph type="italics"/>& ip&longs;e <lb/>concavus; &longs;upra quem &longs;it concavus <lb/>calathus<emph.end type="italics"/> KL, <emph type="italics"/>plurimum olei conti­<lb/>nens. Ex diaphragmate<emph.end type="italics"/> EF <emph type="italics"/>pro-<emph.end type="italics"/> <pb xlink:href="051/01/082.jpg" pagenum="51"/><emph type="italics"/>cedat<emph.end type="italics"/> MN <emph type="italics"/>tubus, &longs;imul cum eo perforatus, tantum di&longs;tans à calathi <lb/>operculo<emph.end type="italics"/> KL <emph type="italics"/>(in quo ellychnium imponitur) quantum ad aër is <lb/>exitum &longs;ufficiat. Alius autem tubulus<emph.end type="italics"/> XO <emph type="italics"/>demittatur per opercu­<lb/>l<gap/>m<emph.end type="italics"/> KL <emph type="italics"/>di&longs;tans à fundo calathi, quantum &longs;atis &longs;it ad aquæ fluxum <lb/>& ex operculo paululum excedens. Exce&longs;&longs;ui verò aptetur alius tubulus<emph.end type="italics"/><lb/>P <emph type="italics"/>habens &longs;uperius o&longs;culum ob&longs;tructum; qui tubulus per fundum lychnij <lb/> impul&longs;us coagmentetur lychno. At tubum autem<emph.end type="italics"/> P <emph type="italics"/>adglutine­<lb/>tur alius tubulus exilis, procedens ad extremitatem auris, & &longs;imul com ea <lb/>perforetur, vt in fluat in concavitatem ellychnij, foramen habens <lb/>quemadmodum & alij. Et&longs;ub diaphragmate<emph.end type="italics"/> EF <emph type="italics"/>conglutinetur clavi­<lb/>cula deferens in locum<emph.end type="italics"/> CDEF, <emph type="italics"/>ita, vt &longs;i aperiatur, aqua ex loco<emph.end type="italics"/><lb/>ABEF, <emph type="italics"/>in ip&longs;um<emph.end type="italics"/> CDEF <emph type="italics"/>tran&longs;eat. Sit autem in operculo<emph.end type="italics"/> AB <emph type="italics"/>par­<lb/>rum foramen, per quod locum<emph.end type="italics"/> ABEF <emph type="italics"/>implebimus aquâ<gap/>& qui <lb/>in ip&longs;o e&longs;t aër, per dictum foramen excedet. Itaque &longs;ublato ellych­<lb/>nio, calathum oleo imple bimus per tubum<emph.end type="italics"/> XO, <emph type="italics"/>aëre per<emph.end type="italics"/> NM <emph type="italics"/>tubulum <lb/>excedente, & adhuc per clavem apertam, quæ e&longs;t in fundo<emph.end type="italics"/> C.D, <lb/> <emph type="italics"/>quando & quæ e&longs;t in<emph.end type="italics"/> CDEF <emph type="italics"/>aqua effluet. Impo&longs;ito igitur el­<lb/>lychnio per &longs;meri&longs;ma<emph.end type="italics"/> P, <emph type="italics"/>quando opus &longs;it oleum infundere, aperiemus <lb/>clavem, quæ in fundo<emph.end type="italics"/> CD; <emph type="italics"/>& aquâ ex loco<emph.end type="italics"/> ABEF <emph type="italics"/>in locum<emph.end type="italics"/><lb/>CDEF <emph type="italics"/>&longs;ecedente, aėr qui e&longs;t in ip&longs;o, per tubum<emph.end type="italics"/> MN <emph type="italics"/>ad cala­<lb/>thum perveniens elidet oleum; quod quidem per tubulum<emph.end type="italics"/> XO, <emph type="italics"/>& <lb/>per alium ip&longs;i cohærentem ad ellychnium procedet. Quando au­<lb/>tem non amplùs fluere volumus, clavicula claudetur, & ce&longs;&longs;abit; & <lb/>rur&longs;us quando opus &longs;it, idem faciemus.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg109"/>Error He­<lb/>ronis in lu­<lb/>cernæ con­<lb/>&longs;tructione.</s></p> <p type="margin"> <s><margin.target id="marg110"/><emph type="italics"/>Lucernæ <lb/>Heronis ge­<lb/>auina figu­<lb/>ra.<emph.end type="italics"/></s></p> <figure id="id.051.01.082.1.jpg" xlink:href="051/01/082/1.jpg"/> <p type="main"> <s>Hæc Commandinus Heronis Interpres; quæ ego omni­<lb/> <arrow.to.target n="marg111"/><lb/>no mendo&longs;a e&longs;&longs;e exi&longs;timo: puto enim vbique lychnum pro el­<lb/>lychnio ponendum e&longs;&longs;e, & alia pleraque legenda prout in mar­<lb/>gine &longs;unt po&longs;ita a&longs;teri&longs;cis notata. Non potui in venire Græcum <lb/>Heronis textum, vt vt diù quæ&longs;iverim. Tubuli etiam &longs;upra ca­<lb/>lathi operculum di&longs;ponendi &longs;unt &longs;ine dubio, vt nos di&longs;po&longs;uimus, <lb/><expan abbr="quoniã">quoniam</expan> Heronis textus latinus apud <expan abbr="ip&longs;u&mtilde;et">ip&longs;umnet</expan> Commandinum id <lb/>exigit. Nec mireris Lector, &longs;i &longs;u&longs;picer Commandini præ&longs;entem <lb/>Latinum de lucerna textum non e&longs;&longs;e vndequaque corre&longs;pon­<lb/>dentem græco textui; po&longs;thumum enim e&longs;t Opus Commandini, <pb xlink:href="051/01/083.jpg" pagenum="52"/>nec po&longs;tremam ip&longs;ius manum expertum, vt habetur initio libelli <lb/>in præfatiuncula ad Lectorem. E&longs;t autem in Commandini te­<lb/>xtu ac &longs;chemate in&longs;ignis error in eo, quòd clavicula R trans­<lb/>mittit aquam quæ e&longs;t in ABEF intra ba&longs;im EFCD per aper­<lb/>tum &longs;olùm foramen &longs;ine tubulo, qui paulò longior &longs;it quàm tu­<lb/>bulus OX; quod tamen omnino requiritur, vt diximus paulò <lb/>antè §. IV. & cau&longs;am dabimusintrà Protheoria IV. cap. 2. Pro­<lb/>po&longs;it. 14. experientia &longs;iquidem con&longs;tat, cylindrum aquæ per fo­<lb/>ramen <expan abbr="de&longs;cendent&etilde;">de&longs;cendentem</expan> (&longs;i quandoque de&longs;cendit aëre &longs;uccedente) <lb/>in aêre libero non habere eandem vim, ac de&longs;cendentem per <lb/>tubum; tamet&longs;i vtrobique &longs;it eadem aquæ quantitas, cum eodem <lb/>perpendiculo. Cau&longs;a e&longs;t, quia &longs;i liberè & &longs;ine tubo defluit a queus <lb/>cylindrus, <expan abbr="&longs;ignũ">&longs;ignum</expan> e&longs;t aërem &longs;ubintrare; &longs;i aër &longs;ubintrat, ce&longs;&longs;at me­<lb/>tus vacui, ac proinde aqua debet elevari vt <expan abbr="laborãti">laboranti</expan> Naturæ &longs;uc­<lb/>currat. Quòd &longs;i tam &longs;trictum e&longs;t foramen, vt aër &longs;ubintrare non <lb/>po&longs;&longs;it, nè gutta quidem aquæ effluet, vt experientia quotidiana <lb/>docet, idque propter vacui metum. Hunc tamen errorem ego <lb/> <arrow.to.target n="marg112"/><lb/>nequaquam Heroni ad&longs;cribendum putem, vt Porta facit, &longs;ed <lb/>exi&longs;timo Heronem produxi&longs;&longs;e tubulum R ferè v&longs;que fundum <lb/>CD; &longs;ic enim major erit quàm tubulus XO, & aqua per ip&longs;am <lb/>R decideus habebit perpendiculum præponderans perpendi­<lb/>culo aquæ &longs;eu olei a&longs;cendentis per XO. </s></p> <p type="margin"> <s><margin.target id="marg111"/><emph type="italics"/>Heronis lo­<lb/>cus apud <lb/>Comman­<lb/>dinum men <lb/>do&longs;<gap/>.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg112"/><emph type="italics"/>Heronis er­<lb/>ror excu&longs;a­<lb/>tur.<emph.end type="italics"/></s></p> <p type="main"> <s>Similis error reperitur apud Heronem cap. 36. vbi docet <lb/>&longs;atyri&longs;cum con&longs;truere &longs;uper quadam ba&longs;i, vtrem in manibus <expan abbr="te-nent&etilde;">te­<lb/>nentem</expan>, cui adiacet labellum; vt infu&longs;o in labellum humore, ita <lb/>vt repleatur, aqua per vtrem in idem labellum in fluat, & non &longs;u­<lb/>perfundatur, quòusque tota per vtrem aqua evacuata fuerit. Ex <lb/>qua quidem con&longs;tructione de&longs;umpta e&longs;t praxis con&longs;truendi fon­<lb/>tem Heronis, de quo infrà Parte 2. Cla&longs;se I. cap. 2. Machi­<lb/>na 1. 2. & 3. vbi errorem Heronis detegemus; <lb/>&longs;i tamen Heronis e&longs;t, & non In­<lb/>terpretis. </s></p> <pb xlink:href="051/01/084.jpg" pagenum="53"/> <p type="main"> <s><emph type="center"/>§. VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Attractione & expul&longs;ione &longs;imul aquam ele­<lb/>vare po&longs;&longs;umus.<emph.end type="center"/></s></p> <p type="main"> <s>DIximus §. IV præcedente, perpen diculum aquæ cadentis & <lb/>pellentis aërem, longius e&longs;&longs;e debere perpendiculo aquæ <lb/>a&longs;cendentis per expul&longs;ionem. Diximus præterea Protheoria I. <lb/>§. VI. perpendiculum aquæ cadentis & trahentis aërem, debe­<lb/>re &longs;uperare longitudine perpendiculum aquæ attractæ. Infrâ <lb/>Parte 2. Cla&longs;se I. cap. 1. Machina 7. & cap. 2. Machina 10. & 11. di­<lb/>cemus, qua ratione per multiplicationem plurium <expan abbr="perp&etilde;">perpem</expan> dicu­<lb/>lorum brevium elevari po&longs;&longs;it aqua, tam per expul&longs;ionem, quàm <lb/>per attractionem, ad quam vis altitudinem. Nunc &longs;ubjiciam <lb/>modum attollendi aquam per attractionem & expul&longs;ionem &longs;i­<lb/> <arrow.to.target n="marg113"/><lb/>fimul ad duplam altitudinem aquæ cadentis, quoniam ingenio­<lb/>fus e&longs;t, & ad multa pote&longs;t e&longs;&longs;e vtilis. Refert illum Porta lib. 2. <lb/>Spiritalium cap. 2. eumque magnificè extollit, tanquam à &longs;e in­<lb/>ventum; & ait &longs;uperare omnem humanum intellectum, nec vn­<lb/>quam in mentem veni&longs;&longs;e antiquis, &longs;e verò po&longs;t expen&longs;as multas, <lb/>& labores plurimos illum tandem reperi&longs;&longs;e. Modus hic e&longs;t. </s></p> <p type="margin"> <s><margin.target id="marg113"/><emph type="italics"/>Modus in­<lb/>genio&longs;us e­<lb/>levandi <lb/>aquam in <lb/>quam vis al <lb/>titudinem <lb/>per attracti <lb/>onem & ex­<lb/>pul&longs;ionem, <lb/>&longs;imul.<emph.end type="italics"/></s></p> <figure id="id.051.01.084.1.jpg" xlink:href="051/01/084/1.jpg"/> <p type="main"> <s>Sit ex va&longs;e B elevanda <lb/>aqua v&longs;que ad vas E, ad <lb/>altitudinem centum pe­<lb/>dum, mediante perpen­<lb/>diculo 50. pedum aquæ <lb/>cadentis. Fiant alia duo <lb/>va&longs;a A, & C, in eodem <lb/>plano horizontali cum <lb/>va&longs;e B con&longs;tituta, <expan abbr="eju&longs;d&etilde;">eju&longs;dem</expan> <lb/>capacitatis cum B; & in­<lb/>fra ip&longs;a con&longs;tituatur vas <lb/>D, cujus &longs;uprema oper­<lb/>culi pars di&longs;tet à fundis di­<lb/>ctorum va&longs;orum 50. pedi­<lb/>bus. Ex va&longs;e A de&longs;cen­<lb/>dat in vas D tubus GX, 50. <pb xlink:href="051/01/085.jpg" pagenum="54"/> <arrow.to.target n="fig13"/><lb/><expan abbr="pedũ">pedum</expan>; qui tamen ab X ex­<lb/>tendi ac prolongari pote&longs;t <lb/>u&longs;que ad H, dummodò <lb/>tantum di&longs;tet à fundo, ut <lb/>aqua effluere po&longs;&longs;it. Ha­<lb/>beat autem hic tubus epi­<lb/>&longs;tomium V. Ex va&longs;e B de­<lb/>&longs;cendat in idem vas D ali­<lb/>us tubus KI, incipiens <lb/>paulò infra operculum <lb/>apud K, & de&longs;inens pau­<lb/>lò infra operculum apud <lb/>I. Ex va&longs;e C de&longs;cendat <lb/>tubus OP 50. pedum, <lb/>habens epi&longs;tomium T. Ex <lb/>va&longs;e E de&longs;cendant in va­<lb/>&longs;a B & C duo tubi: pri­<lb/>mus NC, incipiens infra operculum apud N, & de&longs;inens in­<lb/>fra operculum apud C: alter ML, incipiens immediatè infra <lb/>operculum apud M, & de&longs;inens &longs;upra fundum apud L. Lon­<lb/>gitudo verò hujus tubi ML ab operculo M u&longs;que ad punctum <lb/>L &longs;it centum pedum. Tria va&longs;a A, B, C, habeant &longs;ua forami­<lb/>na cum infundibulis F, per quæ aqua infundi po&longs;&longs;it intra va&longs;a, <lb/>& obturari. Vas tamen A pote&longs;t manere apertum. Duo va&longs;a <lb/>D & E habeant &longs;ua epi&longs;tomia H & S. Omnia præterea va­<lb/>&longs;a, excepto A, debent e&longs;&longs;e undique ac diligenti&longs;&longs;imè clau&longs;a; <lb/>ideoque tubi debent in loco tran&longs;itus accurati&longs;&longs;imè adferrumi­<lb/>nari ip&longs;orum va&longs;orum operculis, & fundis. His ita con&longs;titutis, <lb/>repleantur tria va&longs;a A, B, C, aquâ, & claudantur, clau&longs;is priùs <lb/>omnibus epi&longs;tomijs omnium va&longs;orum ac tuborum: reliqua ve­<lb/>rò duo va&longs;a, D & E, maneant vacua. Deinde aperiatur <lb/>epi&longs;tomium T; & aqua va&longs;is C de&longs;cendet ver&longs;us P, &longs;ecum­<lb/>que trahet, ad vacuum vitandum, aërem va&longs;is E, per tubum <lb/>NC, &longs;imulque aquam va&longs;is B u&longs;que ad altitudinem 50. pedum <pb xlink:href="051/01/086.jpg" pagenum="55"/>ubi V, quantum nimirum e&longs;t perpendiculum tubl OP, per <lb/>quem aqua cadit. Po&longs;tquam verò aqua de&longs;cenderit hinc u&longs;que <lb/>ad P, inde u&longs;que ad V, hærebit utrimque velut in æquilibrio <lb/>immobilis, propter perpendiculorum æqualitatem. Tum verò <lb/>aperiatur epi&longs;tomium V, & aqua va&longs;is A de&longs;cendet intra vas <lb/>D, indeque expellet aërem per tubum IK intra vas B; qui aër <lb/>premet aquam, atque propellet &longs;ur&longs;um per tubum LM ver&longs;us <lb/>M, &longs;icque elevabitur aqua ultra punctum V, effluetque aqua <lb/>ex tubo OP, penitu&longs;que a&longs;cendet aqua va&longs;is B, per tubum LM, <lb/>intra vas E; nec ce&longs;&longs;abit fluxus, donec tria va&longs;a A, B, C, &longs;imul <lb/>fuerint evacuata, totaque aqua B a&longs;cenderitin E. Sijam aqua <lb/>va&longs;orum D & E per &longs;ua epi&longs;tomia depromatur, & va&longs;a A, B, C, <lb/>denuò repleantur; in&longs;titui poterit eadem circulatio, idque to­<lb/>ties, quoties libuerit. Hæc e&longs;t praxis Portæ; ingenio&longs;us atque <lb/>indu&longs;trius artifex addere, demere, mutare poterit, quæ libuerit, <lb/>ornatûs aut commoditatis gratia, modò non alteretur rel &longs;ub­<lb/>&longs;tantia, quam nos præcisè hîc dedimus. </s></p> <figure id="id.051.01.086.1.jpg" xlink:href="051/01/086/1.jpg"/> <p type="main"> <s>Nota hîc, ut aperto epi&longs;tomio T de&longs;cendat aqua va&longs;is C <lb/>ver&longs;us P, laxandum &longs;imul e&longs;&longs;e epi&longs;tomium V va&longs;is A; alio­<lb/>quin nunquam de&longs;cendet aqua va&longs;is C, nè detur vacuum, ut <lb/>con&longs;ideranti patebit. </s></p> <p type="main"> <s>Nota præterea, quod diximus de aqua a&longs;cendente ad alti­<lb/>tudinem 50. pedum, tantùm gratia exempli fui&longs;&longs;e dictum: nam <lb/>aqua non pote&longs;t per attractionem|elevari ad tantam <expan abbr="altitudin&etilde;">altitudinem</expan>, <lb/>ut alibi fu&longs;iùs dicemus. </s></p> <p type="main"> <s><emph type="center"/>§. VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salomon Caus meritò &longs;ugillat Heronem.<emph.end type="center"/></s></p> <p type="main"> <s>HEro cap. 55. Spiritalium ait, <emph type="italics"/>quædam va&longs;a à principio humore <lb/>injecto fluunt, intermi&longs;&longs;ione verò facta non ampliùs fluunt injecto <lb/>humore, quou&longs;&queacute; ad dimidium repleta fuerint; tunc enim incipiunt flue­<lb/>re: At intermi&longs;&longs;ione facta, non ampliùs fluunt, quou&longs;&que; impleantur.<emph.end type="italics"/><lb/>Hujus rei probandæ gratia proponit huju&longs;modi machinam. <pb xlink:href="051/01/087.jpg" pagenum="56"/> <arrow.to.target n="marg114"/><lb/> <arrow.to.target n="fig14"/><lb/><emph type="italics"/>Sit enim vas<emph.end type="italics"/> AB, <emph type="italics"/>habens in &longs;eip&longs;<gap/><lb/>tres &longs;iphones inflexos<emph.end type="italics"/> C, D, E, <emph type="italics"/>in ven­<lb/>tre occultatos, quorum altera quidem <lb/>crura &longs;int ad fundum va&longs;is, altera ve­<lb/>rò extra ferantur in canales efforma­<lb/>ta; atque eorum extremis apponantur <lb/>va&longs;a<emph.end type="italics"/> F, H, G, <emph type="italics"/>quorum fundum di&longs;tet <lb/>ab o&longs;culis, quantum ad aquæ fluxum &longs;a­<lb/>tis &longs;it. Omnia verò comprehendantur <lb/>alio quodam va&longs;e, tanquam ba&longs;i<emph.end type="italics"/> KLMN, <lb/><emph type="italics"/>quæ canalem<emph.end type="italics"/> X <emph type="italics"/>habeat. Et &longs;iphonis <lb/>quidem<emph.end type="italics"/> C <emph type="italics"/>curvit as &longs;it ad fundum va­<lb/>&longs;is; &longs;iphonis verò<emph.end type="italics"/> D <emph type="italics"/>curvitas ad di­<lb/>midium altitudinis ejus & &longs;iphonis<emph.end type="italics"/> E <lb/><emph type="italics"/>ad ip&longs;um collum. Si igitur in vas<emph.end type="italics"/> AB <lb/><emph type="italics"/>aquam infundamus, à principio <expan abbr="quid&etilde;">quidem</expan> <lb/>fluet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>quoniam cur­<lb/>vitas ip&longs;ius e&longs;t ad fundum. Quòd &longs;i <lb/>intermittamus, evacuabitur humidum <lb/>infu&longs;um per canalem<emph.end type="italics"/> X, <emph type="italics"/>& vas<emph.end type="italics"/> F <emph type="italics"/>relin quetur aqua plenum, &longs;iphonis <lb/>verò<emph.end type="italics"/> C <emph type="italics"/>reliqua pars aëre plena erit. Rur&longs;um cùm aquam infunda­<lb/>mus, non procedet per &longs;iphonem<emph.end type="italics"/> C, <emph type="italics"/>propterea quòd aër in eo contine­<lb/>tur inter aquam infu&longs;am, & eam quæ e&longs;t in va&longs;e<emph.end type="italics"/> F. <emph type="italics"/>A&longs;cendet ergo <lb/>humidum u&longs;que ad &longs;iphonis<emph.end type="italics"/> D <emph type="italics"/>curvitatem, quæ e&longs;t ad dimidium alti­<lb/>tudinis va&longs;is; & tunc fluere incipiet: &longs;ed inter mi&longs;&longs;ione facta, rur&longs;us <lb/>idem continget quod in &longs;iphone<emph.end type="italics"/> C <emph type="italics"/>jam dictum e&longs;t. Eadem & in &longs;i­<lb/>phone<emph.end type="italics"/> E <emph type="italics"/>intelligantur. Oportebit autem humidum &longs;en&longs;im infunde­<lb/>re, nè aër, qui in &longs;iphonibus comprehen&longs;us e&longs;t, &longs;umma vi expellatur.<emph.end type="italics"/><lb/>Hæc Hero; Quæ tamen, & quidem optimè, atque ex Hydro­<lb/>pnevmaticæ artis principijs, Salomon Caus in &longs;uis hydraulicis, <lb/> <arrow.to.target n="marg115"/><lb/>&longs;eu lib. 1. de viribus motricibus, reprehendit, dicens effluere <lb/>aquam per &longs;iphonem C, etiam po&longs;t &longs;ecundam infu&longs;ionem in­<lb/>tra vas, eò quòd aër contentus intra &longs;iphonem C pellatur ab <lb/>aqua extra inferius o&longs;culum, erumpatque extra aquam va&longs;is F <pb xlink:href="051/01/088.jpg" pagenum="57"/>Quod quidem <expan abbr="veri&longs;&longs;imũ">veri&longs;&longs;imum</expan> e&longs;t, cùm aqua infu&longs;a intra vas AB per &longs;e­<lb/>cundam <expan abbr="infu&longs;ion&etilde;">infu&longs;ionem</expan>, facillimè a&longs;cendat per crus internum <expan abbr="u&longs;q;">u&longs;que</expan> ad <lb/><expan abbr="curvitat&etilde;">curvitatem</expan> C, non re&longs;i&longs;tente aëre; qui aër intra <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> CF compre&longs;­<lb/>&longs;us cedit aquæ a&longs;cendenti primùm u&longs;q, ad <expan abbr="curvitat&etilde;">curvitatem</expan> C, <expan abbr="indeq;">indeque</expan> <lb/>de&longs;cendenti pondere &longs;uo, pul&longs;o aëre, erumpente per aquam va­<lb/>&longs;is F. Adde quòd &longs;i tam altum e&longs;&longs;et va&longs;culum F, ut aër per ejus <lb/>aquam exitum non inveniret; a&longs;cenderet is per &longs;iphonem aquæ <lb/>mixtus, prout fieri videmus in canali vitreo quantumvis gracili <lb/>atque longo: &longs;i enim aquâ aliquòusque eum repleas, & ob­<lb/>tùrato utroque orificio invertas, ut aqua &longs;uperiorem, aër inferio­<lb/>rem occupat locum; &longs;tatim de&longs;cendit aqua, & a&longs;cenditaër, aper­<lb/>tâ &longs;ibi vel per medias aquas viâ, ut te&longs;tantur bullæ frequentes in­<lb/>ter aquas erumpentes; & qui paulò antè &longs;uccumbebat aquæ, ei­<lb/>dem paulò po&longs;t incumbit aër. </s></p> <p type="margin"> <s><margin.target id="marg114"/><emph type="italics"/>Heronis Ma <lb/>china defe­<lb/>ctuo&longs;a.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg115"/><emph type="italics"/>Heronis <gap/>r­<lb/>ror.<emph.end type="italics"/></s></p> <figure id="id.051.01.088.1.jpg" xlink:href="051/01/088/1.jpg"/> <p type="main"> <s><emph type="center"/>§. VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Idem perpendiculum aquæ cadentis non pote&longs;t &longs;ervire <lb/>&longs;imul attractioni & expul&longs;ioni.<emph.end type="center"/></s></p> <p type="main"> <s>POrta loco &longs;æpe citato de &longs;piritalibus Cap. VIII. ait, &longs;e fre­<lb/>quenter tenta&longs;&longs;e ut aquam eodem perpendiculo mediante <lb/>elevaret ad majorem altitudinem, quàm perpendiculum erat, <lb/>partim attractione, partim expul&longs;ione. Eum in finem fecit vas <lb/>A, ex quo elevare volebat aquam u&longs;que ad vas B, ad alti­<lb/>tudinem pedum centum verbi gratia. Con&longs;truxit igitur aliud <lb/>æquale vas C in eodem plano, & aliud DF demi&longs;&longs;ius utroque <lb/>pedibus 50. va&longs;a con&longs;tructa in&longs;truxit tubis & epi&longs;tomijs, prout <lb/>figura mon&longs;trat. Hi&longs;ce peractis, replevit va&longs;a C & A aquis, & <lb/>diligenter clau&longs;it utrumque, clau&longs;is etiam eadem diligentia va&longs;is <lb/>B & DE. Deinde aperuit tubum ED, ut de&longs;cendente aqua va&longs;is C <lb/>intra vas DE, traheretur aër ex tubo CK, va&longs;e B, & tubo <lb/>IH, &longs;imulque attraheretur aqua va&longs;is A &longs;altem ad L, altitu­<lb/>dinem pedum 50; quod & factum fuit. Sperabat|autem ut aër <lb/>va&longs;is DF pul&longs;us per tubum EG, intra vas A, expelleret inde <pb xlink:href="051/01/089.jpg" pagenum="58"/> <arrow.to.target n="fig15"/><lb/>aliam aquam, & &longs;ublatam <lb/>jam antea aquam v&longs;que ad <lb/>L, attolleret vlteriùs v&longs;que <lb/>ad vas B; at nunquam id <lb/>obtinere potuit: nam po&longs;t­<lb/>quam a&longs;cenderat aqua v&longs;­<lb/>que ad L, hæ&longs;it &longs;u&longs;pen&longs;a, <lb/>& aqua va&longs;is C non deflu­<lb/>xit ampliùs per tubum ED. <lb/>Collegit inde, idem per­<lb/>pendiculum ED non po&longs;­<lb/>&longs;e in&longs;ervire attractioni & <lb/>expul&longs;ioni &longs;imul, &longs;ed vel <lb/>&longs;oli attractioni, vel &longs;oli ex­<lb/>pul&longs;ioni; quod benè notan­<lb/>dum e&longs;t. Cau&longs;am dabi­<lb/>mus infrà Protheoria IV. <lb/>capite 2. Propo&longs;it. 13. & 14. <lb/>quam tamen ignora&longs;&longs;e Por­<lb/>ta videtur, quoniam nul­<lb/>lam ad&longs;ignat. </s></p> <figure id="id.051.01.089.1.jpg" xlink:href="051/01/089/1.jpg"/> <p type="main"> <s><emph type="center"/>§. IX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Error apud Ioannem Bapti&longs;tam Portam, indicatur.<emph.end type="center"/></s></p> <p type="main"> <s>APud Ioannem Bapti&longs;tam Portam lib 2. Spiritalium cap. 10. <lb/>traditur modus elevandi aquam per expul&longs;ionem ad &longs;tellas <lb/>v&longs;que, vt ibi dicitur, mediante &longs;olo vnico perpendiculo quin­<lb/>quaginta verbi gratia pedum altitudinis: qui tamen e&longs;t omnino <lb/>fal&longs;us, & repugnat doctrinæ Portæ in præcedentibus traditæ; <lb/>Vnde &longs;u&longs;picabar ab Hi&longs;pano traductore fuiffe additum: crede­<lb/>re enim nulla ratione poteram, à Porta tam enormem errorem <lb/>potui&longs;&longs;e committi. Reperi tamen deinde eundem modum in <pb xlink:href="051/01/090.jpg" pagenum="59"/> <arrow.to.target n="fig16"/><lb/>editione latina cap. 9. Modus hic <lb/>e&longs;t. E&longs;to vas C, & &longs;upra ip&longs;um <lb/>ad di&longs;tantiam pedum verbi gratia <lb/>quinquaginta, va&longs;a D & K, cum <lb/>&longs;uis infundibulis; & &longs;upra hæc ali­<lb/>ud G; aliudque &longs;upra hoc; & &longs;ic <lb/>deinceps ad quamvis altitudinem, <lb/>etiam v&longs;que ad &longs;tellas. Conjun­<lb/>gantur dicta va&longs;a tubis, vt mon­<lb/>&longs;trat figura, habeatque tubus DB <lb/>&longs;uum epi&longs;tomium, vt & vas C &longs;u­<lb/>um; & va&longs;a D & K repleantur a­<lb/>quâ. Deinde aperiatur epi&longs;tomi­<lb/>um tubi DB, & aqua de&longs;cendens <lb/>intra vas C expellet inde aërem <lb/>per tubum FK intra vas K; qui <lb/>aër inde expellet aquam per tu­<lb/>bum FG in vas G, & ex G per <lb/>tubum HI expelletur aqua in aliud <lb/>vas, & &longs;ic vlteriùs. Sed hæc pror­<lb/> <arrow.to.target n="marg116"/><lb/>&longs;us &longs;unt erronea, & contra princi­<lb/>pia hydraulica. Perpendiculum <lb/>enim DB aquæ cadentis pedum quinquaginta, non pote&longs;t ele­<lb/>vare aliam præter aquam va&longs;is K per tubum FG pedum etiam <lb/>50. ad &longs;ummum, v&longs;que ad vas G, vbi quie&longs;cet aqua. Dato dein­<lb/>de quòd ex G po&longs;&longs;et elevari aqua eodem perpendiculo DB, de­<lb/>beret tubus IH pertingere ferè v&longs;que ad fundum va&longs;is G, vt <lb/>aqua pre&longs;&longs;a intrare po&longs;&longs;et. Fal&longs;us ergo e&longs;t hic modus. Alium nos <lb/>trademus infrà Cla&longs;se I. cap. 2. Machina 4. & 11. </s></p> <p type="margin"> <s><margin.target id="marg116"/><emph type="italics"/>Error apud <lb/>Portam.<emph.end type="italics"/></s></p> <figure id="id.051.01.090.1.jpg" xlink:href="051/01/090/1.jpg"/> <p type="main"> <s><emph type="center"/>§. X.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Alia ratio aquam elevandi in altum propter <lb/>Corporum impenetrabilitatem.<emph.end type="center"/><lb/> <arrow.to.target n="marg117"/></s></p> <p type="margin"> <s><margin.target id="marg117"/><emph type="italics"/>Modui ele­<lb/>vandi <expan abbr="aquã">aquam</expan> <lb/>etiam bru <lb/>tis notus.<emph.end type="italics"/></s></p> <p type="main"> <s>ESt & alia ratio aquam quie&longs;centem atque infu&longs;am va&longs;is ele­<lb/>vandi, in altum, atque in fontes efformandi, quam vel ip&longs;a <lb/>bruta do cent animalia. De Cervis quippe Lybicis narratur, quòd <pb xlink:href="051/01/091.jpg" pagenum="60"/>dum &longs;itientes foveam offendunt <expan abbr="aquã">aquam</expan> plenam, culus tamen &longs;u­<lb/>prema &longs;uperficies humilior <expan abbr="atq;">atque</expan> profundior e&longs;t, quàm vt capite <lb/>ac collo proten&longs;o eam attingere po&longs;&longs;int, calculos ore & vnguibus <lb/>a&longs;portantes foveæ injiciant, vt de&longs;identibus in fundum lapidi­<lb/>bus humor &longs;ub&longs;identium corporum occupatione elevetur, &longs;u­<lb/>perioremque elatus repleat vacuitatem; ita &longs;olerti machinatio­<lb/>ne reficiuntur. Va&longs;is <expan abbr="itaq;">itaque</expan> puteisque &longs;i &longs;olida injicias corpora, quæ <lb/>fundum petant vel &longs;ponte, vel vi depre&longs;&longs;a; elevabitur aqua, & <lb/>per tubos &longs;uperiùs applicatos effluens in fontem formabitur. <lb/>Hoc artificio con&longs;tructus erat olim fons ad S. Georg. Venetijs, </s></p> <p type="main"> <s> <arrow.to.target n="marg118"/><lb/>te&longs;te Io&longs;epho Ceredo Di&longs;cur&longs;u primo de Modo elevandi aquas <lb/>è locishumilibus, pag. 11. Binæ enim fabricatæ erant ci&longs;ternæ, <lb/>&longs;eu pi&longs;cinæ, humilior ac profundior vna, altera elatior ad prioris <lb/>latus. Humilior latera habebat angu&longs;ta, & putei in&longs;tar erecta; <lb/>è cuius fundo v&longs;que ad collateralis &longs;uprema labra deduceban­<lb/>tur tubi plumbei. Habebat præterea operculum ligneum atque <lb/>gravi&longs;&longs;imum, quod ci&longs;ternæ latera vacua implebat, & aquæ in­<lb/>cumbens &longs;uo paulatim pondere de&longs;cendebat, atque aquam <expan abbr="cõ-primens">con­<lb/>primens</expan> eam intra tubos compellebat; per quos a&longs;cendens, &longs;ub­<lb/>&longs;equentibus alijs aquis pul&longs;a, exonerabat &longs;e&longs;e intra &longs;uperiorem <lb/>collateralem ci&longs;ternam, indeque pondere &longs;uo naturaliter dela­<lb/>bens per fi&longs;tulas efforma batur in fontem. Multas alias Machi­<lb/>nas hydraulicas eodem con&longs;tructas artificio enumerat ibidem <lb/>citatus Ceredus, & vnam hac ratione adornatam Machinulam <lb/>Scaliger Exercitat. 42. contra Cardanum; ex qua tamen fal&longs;um <lb/>deducit modum o&longs;tendendi fontium originem ex mari. Hac <lb/>porrò ratione in altum elevatur aqua per antlias, quarum ingen­<lb/>tem copiam affert Augu&longs;tinus Ramellus in&longs;uo de Machi­<lb/>nis hydraulicis opere, & nos aliquas adduce­<lb/>mus Cla&longs;se I. cap. 2. Machina 6. </s></p> <pb xlink:href="051/01/092.jpg" pagenum="61"/> <p type="margin"> <s><margin.target id="marg118"/><emph type="italics"/>Fons ad S. <lb/>Georgium <lb/>Venetijs.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Protheoria III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA <lb/>TERTIA.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Devi Rarefactiva; &longs;eu de tertio Hydro-pnev­<lb/>maticarum Machinarum Principio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>§. I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Rarefactionis vis, & effectus mirabiles.<emph.end type="center"/></s></p> <p type="main"> <s>RArefactionem ingentes &longs;uppeditare vires vt <lb/>alijs corporibus, ita aquæ & aëri, ad ea in omnem &longs;i­<lb/>tus differentiam impellendam, multòque magis ad <lb/>hydro-pnevmatica omnis generis techna&longs;mata mo­<lb/>lienda; is &longs;olus ignorare pote&longs;t, qui &longs;tupendos ip&longs;ius effectus igno­<lb/>rat. videmus quotidie, miramurque, ac plangimus &longs;tragem, <lb/> <arrow.to.target n="marg119"/><lb/>quam <foreign lang="greek">polio<gap/>xh|tai\</foreign> nitrato & &longs;ulphureo pulvere intra bombarda­<lb/>rum militarium angu&longs;tias rarefacto edunt, in &longs;ternendis non ho­<lb/>minibus tantùm, fed ædibus, turribus, propugnaculis, atque <lb/>adeo vrbibus integris. Non Iovis tantummodo fulmina imita­<lb/>tur rarefactio in bombardis, &longs;ed Plutonis etiam iras æmulatur in <lb/>&longs;ubterraneis cuniculis; tantò pernicio&longs;iore &longs;trage, quantò mi­<lb/>nùs patente. Excavant Martiales Architecti à loco ob&longs;idionis <lb/> <arrow.to.target n="marg120"/><lb/>ad v&longs;que propugnaculum, cui ruinam minantur, viam anfra­<lb/>ctuo&longs;am, angu&longs;tamque, magneticæ pixidis ductu, uti inter alios <lb/>docet P. Athana&longs;ius Kircherus lib. 2. de Arte Magnet. par. 2. cap. 1. <lb/>Probl 7. & nos in Pantometro Kircherianolib. 5. Ichnographi­<lb/>co Probl. 8. Sub loco deinde ruinæ de&longs;tinato Cameram con­<lb/>&longs;truunt laxiorem, eamque implent pulveris tormentarij va&longs;is, <lb/>& o&longs;tium claudunt, relicto exiguo foramine, perque viam totam <lb/>ignis pabulum &longs;ternunt, & egre&longs;&longs;i ignem applicant; qui &longs;erpens <lb/>per viam accendit pulveris ma&longs;&longs;am omnem Camerâ conclu&longs;am, <lb/>itàque rarefacit, dilatatque, ut angu&longs;tiarum impatiens, & laxio­<lb/>rem quærens locum, impo&longs;itam &longs;ibi molem di&longs;iiciat horribili <lb/> <arrow.to.target n="marg121"/><lb/>fremitu, nec minori terrore, quàm damno. Nihil unquam <lb/>magis &longs;imile terræ motui, qui & ip&longs;e rarefactionis e&longs;t effectus lu- <pb xlink:href="051/01/093.jpg" pagenum="62"/>culenti&longs;&longs;imus, excogitatum fuit. Eodem enim pror&longs;us modo <lb/>in terræ concu&longs;&longs;ione flamma ex aliqua &longs;ubterranea fornace, vel <lb/>interno calore, per venulam aliquam nitri aut &longs;ulphuris &longs;erpit, <lb/>donec perveniat ad locum, in quo maiorem huiu&longs;ce materiæ <lb/>copiam inveniat; quâ &longs;ubitò accen&longs;a & rarefactâ, dum maio­<lb/>rem quærit locum, &longs;ibi impo&longs;itas concutit, & di&longs;jicit non rarò, <lb/>moles. Sæpe etiam iam antea accen&longs;us in terræ vi&longs;ceribus ignis, <lb/>dum nova augetur aliunde attracta materia, montes &longs;ibi impo&longs;i­<lb/> <arrow.to.target n="marg122"/><lb/>tos concutit, finditque, vt non &longs;emel audivi, vidique in Ætna Si­<lb/>ciliæ, duorum annorum accola olim, & nunc hoc ip&longs;o anno 1654. <lb/>quo hæc &longs;cribo, hîc Romæ, quam (raro exe n<gap/>o) concu&longs;&longs;it mo­<lb/>tusille ingens, qui tantam Soræ &longs;tragem <gap/>lit, & Romam hinc <lb/>inde Neapolim, omnes que interiacent<gap/> regiones tremefecit. </s></p> <p type="margin"> <s><margin.target id="marg119"/><emph type="italics"/>Rarefactio­<lb/>nis vis in <lb/>bombardis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg120"/><emph type="italics"/>Rarefactio­<lb/>nis vis in <lb/>cuniculis <lb/>&longs;ubterra­<lb/>neis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg121"/><emph type="italics"/>Rarefactio­<lb/>nis vis in <lb/>terræ mo­<lb/>tibus.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg122"/><emph type="italics"/>Terræmo­<lb/>tus Romæ <lb/>anno<emph.end type="italics"/> 1654.</s></p> <p type="main"> <s><emph type="center"/>§. II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Alia Rarefaction<gap/> Exempla.<emph.end type="center"/><lb/> <arrow.to.target n="marg123"/></s></p> <p type="margin"> <s><margin.target id="marg123"/><emph type="italics"/>Rare&longs;actio­<lb/>nis exempla <lb/>d<gap/>.<emph.end type="italics"/></s></p> <p type="main"> <s>NArrat P. Nicolaus Cabæus lib. 4. Meteor. Ari&longs;t. text. 12. <expan abbr="q.">que</expan> 1. <lb/>vidi&longs;&longs;e &longs;e marmoreum vas maximum atque duri&longs;&longs;imum ab <lb/>aqua conglaciata di&longs;ci&longs;&longs;um, eò quòd <expan abbr="cõgelatione">congelatione</expan> rarefactæ fue­<lb/>rint aliquæ internæ partes aquæ: factà enim illâ &longs;ubitâ congela­<lb/>tione, ob&longs;titerunt attenuationi & rarefactioni partium latera va­<lb/>&longs;is, <expan abbr="ce&longs;&longs;it&qacute;ue">ce&longs;&longs;itque</expan> durities vehementiæ rarefactionis, & fractum e&longs;t <lb/>vas, quod non di&longs;rupi&longs;&longs;ent centum juga boum, &longs;i in diver&longs;as par­<lb/>tes traxi&longs;&longs;ent. Idem Cabæus ibidem a&longs;&longs;erit, &longs;e vidi&longs;&longs;e columnam <lb/>marmoream, quam tres homines dilatatis brachijs &longs;imul non <lb/>poterant complecti, quamque mille juga boum, &longs;i in diver&longs;as <lb/>partes, toto juncto impetu traxi&longs;&longs;ent, frangere non potui&longs;&longs;ent, <lb/>fractam tamen pror&longs;us mediam atque truncatam, eò quòd ligna <lb/>quædam columnæ illi proxima fuerint combu&longs;ta, ideoque ex vi­<lb/>cino calore &longs;piritulus aliquis in marmore inclu&longs;us intus in meati­<lb/>bus fuerit rarefactus, & ex rarefactione maiorem &longs;ibi <expan abbr="locũ">locum</expan> quæ­<lb/>&longs;iverit. </s></p> <p type="main"> <s>Notum jam pœnè e&longs;t omnibus, quod refert Petrus Ca&longs;tel­<lb/>lus in Libello de Incendio Ve&longs;uvij Italicè con&longs;cripto, & exip&longs;o <lb/>Kircherus lib. 3. Artis Magnet, part. 2. cap. 3. circa finem, de pul- <pb xlink:href="051/01/094.jpg" pagenum="63"/>vere pyrio ex auro confecto, quod aurum fulminans appellat Ca­</s></p> <p type="main"> <s> <arrow.to.target n="marg124"/><lb/>&longs;tellus, & aurum volatile Crollius. E&longs;t id nihil aliud quàm au­<lb/>rum calcinatum aquâ forti &longs;eu regiâ, &longs;ale armoniaco, & oleo tar­<lb/>tari præcipitati. Hæc calx quàm primùm &longs;entit etiam calorem <lb/>ignis, concipit &longs;ponte &longs;ua flammam, & in auras abit, cum ingenti <lb/>fragore & &longs;trepitu: & &longs;i vel vnum aut alterum huius pulveris gra­<lb/>num cultro impo&longs;ueris, & candelam infrà applicueris, vtinca. <lb/>le&longs;cat; tantum edit fragorem, ac &longs;i magnam explo&longs;i&longs;&longs;es bombar­<lb/>dam. Facit autem effectum contrarium ordinario pulveri pyrio, <lb/>quia non &longs;ur&longs;um, &longs;ed deor&longs;um tendit; vnde &longs;erupulus vnicus hu­<lb/>ius volatilis auri po&longs;itus &longs;upra laminam ferream <expan abbr="nõ">non</expan> modicæ cra&longs;­<lb/>&longs;itiei, & carbone de&longs;uper applicato accen&longs;us, penetrat & per­<lb/>foratip&longs;am laminam. </s></p> <p type="margin"> <s><margin.target id="marg124"/><emph type="italics"/>Aurum ful­<lb/>minans.<emph.end type="italics"/></s></p> <p type="main"> <s>Nolo hîc ommittere aliud rarefactionis exemplum, quo <lb/>ego ip&longs;e multis in locis, coram viris etiam Principibus, exiguâ <lb/>machinulâ non exiguum excita vi fragorem, bombardulæ mi­<lb/>noris fragori pror&longs;us æqualem ac &longs;imilem. Vitreas Sphærulas <lb/> <arrow.to.target n="marg125"/><lb/>nucis avellanæ magnitudine, aut etiam minores, fieri curavi ad <lb/>lampadem Romæ à quodam Germano artifice, vitrum in omnes <lb/>colores omnes que figuras florum, fructuum, avium, animalium <lb/>omnis generis, jcuncularum quarumlibet affabrè elaboratarum <lb/>efformante, idemque in &longs;ubtili&longs;&longs;ima fila ad rotam <expan abbr="circumactã">circumactam</expan> <lb/>diducente. In eas vitreas Sphærulas acetum, aut nitratum &longs;a­<lb/>lem aquâ di&longs;&longs;olutum ac liquefactum infundi iu&longs;fi, & ad medieta­<lb/>tem repleri, ac deinde hermeticè claudi ad eandem lampadem. <lb/>Harum &longs;phærularum vnam &longs;i carbonibus non nimiùm accen&longs;is, <lb/>aut calidis cineribus (vt paulatim calefiat) impo&longs;ueris; rarefit <lb/>&longs;pirito&longs;a materia intus clau&longs;a, & majorem quærens locum, po&longs;t <lb/>&longs;patium circiter temporis quo P&longs;almus 50. <emph type="italics"/>Mi&longs;erere mei Deus,<emph.end type="italics"/> re­<lb/>citari pote&longs;t, tanto cum impetu ac fragore viam &longs;ibi aperit, vt <lb/>non tantùm vitrum in mille minuti&longs;&longs;imas particulas diffringat, <lb/>&longs;ed cineres etiam & carbones toto conclavi di&longs;&longs;ipet, nullius <lb/>damno, ni&longs;i &longs;i quis vultum propè applicet. Cùm experientiam <lb/>Romæ coram Sereni&longs;&longs;imi Hol&longs;atiæ Ducis Filio primogenito fa- <pb xlink:href="051/01/095.jpg" pagenum="64"/>cerem, foco a&longs;&longs;identi more ibidem &longs;olito, famuli ante cubicu­<lb/>lum præ&longs;tolantes accurrebant attoniti, bombardulam in Princi­<lb/>pem &longs;uum explo&longs;am credentes. Alius magnus quidam Prin­<lb/>ceps cùm nonnullas à me accepi&longs;&longs;et, ac domi die quodam cum <lb/>multis alijs nobilibus foco a&longs;&longs;ideret, vnam o&longs;tendit, ac videnti­<lb/>bus omnibus igni iniecit, a&longs;&longs;erens, vbi calefieret, grati&longs;&longs;imum <lb/>&longs;par&longs;uram odorem. Cùm omnes arrectis naribus, & ore hi­<lb/>ante odorem ex&longs;pectarent, derepente fit crepitus, & carbonum <lb/>disiectio, diffugientibus omnibus in timorem primò, deinde in <lb/>ri&longs;um di&longs;&longs;olutis. Alio tempore coram Cardinale quodam & <lb/>magno Nobilium comitatu, admonito priùs clanculum &longs;olo <lb/>Cardinale, vnam explo&longs;i; & ita omnes alij præter dictum <lb/>Cardinalem territi fuêre, vt auctorem (ignorabant me e&longs;&longs;e) <lb/>ad pœnam quærerent. </s></p> <p type="margin"> <s><margin.target id="marg125"/><emph type="italics"/>Vitrea &longs;phæ <lb/>rula mino­<lb/>ris bombar­<lb/>dulæ crepi­<lb/>tum amu­<lb/>lantes.<emph.end type="italics"/></s></p> <p type="main"> <s>Innumeros alios effectus rarefactionis, &longs;icut & conden&longs;a­<lb/>tionis, adducere po&longs;&longs;em; &longs;ed hi &longs;ufficiunt ad ad&longs;truendam effica­<lb/>ciam in commovendis corporibus. Quæ efficacia &longs;i tanta e&longs;t, <lb/>quantam vidimus; quis neget, eandem in aëre & aquis elucere <lb/>po&longs;&longs;e, dilatando & con&longs;tringendo elementa ip&longs;a, & in fontes a­<lb/>liaque hydraulica, pnevmaticaque artificia animando? &longs;ed hæc <lb/>evidenti&longs;&longs;imè o&longs;tendemus in multis ex &longs;equentibus Machinis <lb/>Partis 2. p<gap/>ertim Cla&longs;. <expan abbr="Ĩ">Im</expan>. cap. 3. Mach. 1.2.5.6.8. & alijsmultis. </s></p> <p type="main"> <s><emph type="center"/>PROTHEORIA<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>QVARTA.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De fluxu Aquæ naturali;<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>&longs;eu <lb/>De quarto Hydro-pnevmaticarum Machina­<lb/>rum principio.<emph.end type="center"/></s></p> <p type="main"> <s>PLurima, jucundi&longs;&longs;ima, vtili&longs;&longs;imaque circa A­<lb/>quæ fluxum naturalem, &longs;eu libera ea &longs;it, &longs;eu aquædu­<lb/>ctibus, canalibus, tubis, &longs;iphonibus, fi&longs;tulis, & qui­<lb/>bus cunque alijs meatibus con&longs;tricta, dicenda occur­<lb/>runt noc ioco, quæ Hydro-pnevmaticarum Machinarum Arti-</s></p> <pb xlink:href="051/01/096.jpg" pagenum="65"/> <p type="main"> <s><emph type="center"/>Protheoria IV.<emph.end type="center"/><lb/>ficibus non minùs nece&longs;&longs;aria, quàm vtilia &longs;unt. Nos ex omni­<lb/>bus ea tantùm, quæ fini no&longs;tro conducere videbuntur, &longs;elegimus; <lb/>cætera ad Mechanicam no&longs;tram Magiam re&longs;ervabimus. </s></p> <p type="main"> <s><emph type="center"/>CAPVT I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De proprietatibus Aquæ fluentis liberè.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PROOEMIVM.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>LIberè fluit aqua, dum nullis con&longs;tricta<emph.end type="italics"/><lb/> <arrow.to.target n="marg126"/><lb/><emph type="italics"/>e&longs;t meatibus ceu vinculis. Huiu&longs;ce proprie­<lb/>tates, fini no&longs;tro conducentes, vt a&longs;&longs;ignem, <lb/>Suppono duo, quæ licet in dubium revocentur <lb/>ab aliquibus, conceduntur tamen à me<gap/><lb/>notæ Philo&longs;ophis & Mathematicis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg126"/>Aqua libe­<lb/>rè fluere <lb/>quæ dica­<lb/>tur.</s></p> <p type="main"> <s><emph type="italics"/>Primum e&longs;t, Ordinem Elementorum, naturæ eorum con<emph.end type="italics"/><lb/> <arrow.to.target n="marg127"/><lb/><emph type="italics"/>gruentem hunc e&longs;&longs;e, vt Terra &longs;it in medio omnium, Aqua circa <lb/>Terram, circa Aquam Aër, & circa Aërem putatus lgnis. Ac <lb/>principio quidem rerum, quando<emph.end type="italics"/> Creavit DEVS cœlum & <lb/>terram, <emph type="italics"/>Genes. C. I. prædictum &longs;ervarunt ordinem, v&longs;que ad <lb/>diem Mundi tertium, quo die Deus benedictus Terram, anteà <lb/>&longs;phæricè rotundam, in cavitates varias deformavit, in easque <lb/>Aquam omnem &longs;ubtercœle&longs;tem, maribus, lacubus, fluminibus, <lb/>fontibus di&longs;cretam, derivavit, vnumque ex Terra & Aqua <lb/>globum con&longs;tituit, vnicâ contentum &longs;phæricâ &longs;uperficie, terrenâ<emph.end type="italics"/><lb/> <arrow.to.target n="marg128"/><lb/><emph type="italics"/>hinc, inde aqueâ, prout Aquæ diver&longs;imodè Terram di&longs;ci&longs;&longs;am <lb/>interfluunt, aut circumfluunt. Qui quidem globus ex Terra <lb/>& Aqua coagmentatus (quem ob id rectè <expan abbr="Terraqueũ">Terraqueum</expan> appellare <lb/>po&longs;&longs;umus) in prima &longs;ui coagmentatione, quando die Mundi<emph.end type="italics"/> <pb xlink:href="051/01/097.jpg" pagenum="66"/><emph type="italics"/>tertio<emph.end type="italics"/> dixit DEUS: congre gentur aquæ, quæ &longs;ub cœlo &longs;unt, <lb/>in locum vnum, & appareat Arida; & factum e&longs;t ita; <emph type="italics"/>in <lb/>medio Vniver&longs;i, hoc est, in centro &longs;upremi, & omnia ambien­<lb/>tis Cæli collocatus fui&longs;&longs;e videtur; in medio, inquam, non &longs;olùm <lb/>quoad &longs;en&longs;um (quod nullus, aut vix vllus, &longs;altem alicuius no­<lb/>minis, negat) &longs;ed revera ac mathematicè, ita vt centrum gra­<lb/>vitatis Terraquæ congruerit tunc perfectè centro Vniver&longs;i, exi-<emph.end type="italics"/><lb/> <arrow.to.target n="marg129"/><lb/><emph type="italics"/>gente id naturali ip&longs;ius gravitate. Nunc verò licet ob conti­<lb/>nuam gravium in Terra Marique mutationem, centrique gra­<lb/>vitatis variationem prædicta Terraqua non &longs;it forta&longs;&longs;e &longs;emper <lb/>præcisè & mathematicè in Mundi medio in &longs;en&longs;u dicto (non <lb/>enim certò constat, ad centrum gravitatis mutatum continuò, <lb/>&longs;equi continuam, licet exiguam, trepidationem ip&longs;ius, nitentis <lb/>ad mundi centrum) tam parum tamen ab illo centro distat, <lb/>quàm multùm di&longs;tat à tota mole Terraquæ quodcunque pon­<lb/>dus defacto additum aut ablatum de novo. Ex quibus dedu­<lb/>citur, &longs;i centrum gravitatis Terraquæ differt à centro magni­<lb/>tudinis eiusdem (vt probabile e&longs;t differre, cùm Terra pondero­<lb/>&longs;ior &longs;it quàm Aqua, nec omnes Terræ partes, æqualis &longs;int ponde­<lb/>ris) differre &longs;olùm in&longs;en&longs;ibiliter; ac proinde idem cen&longs;eri po&longs;&longs;e; <lb/>&longs;altem phy&longs;icè & ad &longs;en&longs;um, vtrumque centrum. Sed de his <lb/>&longs;usè tractatum vide à Kirchero in Mundo &longs;ubterranneo, libro 1. <lb/>de Centro&longs;ophia, & à nobis in Mechanica Vniver&longs;ali lib. 1. <lb/>aut in Magia Mechanica.<emph.end type="italics"/><lb/> <arrow.to.target n="marg130"/></s></p> <p type="margin"> <s><margin.target id="marg127"/><gap/>o­<lb/><gap/>do <lb/>naturalis<gap/></s></p> <p type="margin"> <s><margin.target id="marg128"/>Terraque­<lb/>us globus <lb/>in medio <lb/>muadi col <lb/>locat' fuit <lb/>die tertio <lb/>creationis <lb/>rerum.</s></p> <p type="margin"> <s><margin.target id="marg129"/>Terraqua <lb/>nnuc non <lb/>e&longs;t &longs;emper <lb/>in mundi <lb/>centro ma­<lb/>thematicè.</s></p> <p type="margin"> <s><margin.target id="marg130"/>Centrum <lb/>commune <lb/>omnium <lb/>gravium <lb/>ac levium</s></p> <p type="main"> <s><emph type="italics"/>Alterum quod &longs;uppono est, centrum Vniver&longs;i, adeoque <lb/>Centrum Terraquei globi, quem in Mundi medio &longs;tatuimus, <lb/>cen&longs;eri po&longs;&longs;e centrum commune omnium gravium ac levium, quò<emph.end type="italics"/> <pb xlink:href="051/01/098.jpg" pagenum="67"/><emph type="italics"/>nimirum omnia gravia per &longs;e tendunt appetitu innato, & à quo <lb/>levia recedunt, vtraque per rectas ac brevi&longs;&longs;imas lineas, ni&longs;i <lb/>impediantur, aut cogantur per obliquam ac longiorem viam <lb/>ver&longs;us illud de&longs;cendere, vel ab illo recedere. Cùm igitur aqua <lb/>omnis &longs;it gravis, vt experientiâ patet; tendet appetitu naturali <lb/>ad centrum Terraquæ, id e&longs;t, ad centrum Vniver&longs;i. Idem di­<lb/>cendum e&longs;t de alijs liquoribus. His præmi&longs;&longs;is accedimus ad <lb/>propo&longs;itum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua tendit ad loca decliviora.<emph.end type="center"/></s></p> <p type="main"> <s>AQuam, & omnem alium humorem, fluentem <lb/><gap/>iberè, currere ad loca decliviora, & centro Mundi ac <lb/>Terraquæ propinquiora, &longs;i patetip&longs;is liber aditus, &longs;ive <lb/><gap/>us ac perpendicularis, &longs;ive obliquus; patet expe­<lb/>rientia quotidiaua, nec indiget probatione. Ex quo deduci­<lb/>tur, aquæ etiam con&longs;i&longs;tentis partes omnes inclinare innato ap­<lb/>petitu ad eadem loca decliviora: ideo enim de facto, &longs;ublatis </s></p> <p type="main"> <s> <arrow.to.target n="marg131"/><lb/>impedimentis, eò fluit aqua, quia naturaliter eò inclinat. Con­<lb/>&longs;i&longs;tentem porrò aquam appello, quæ &longs;itum obtinet naturalem. <lb/>Situs autem &longs;eu po&longs;itio naturalis aquæ e&longs;t, quem dum naturali <lb/> <arrow.to.target n="marg132"/><lb/>&longs;uo fluxui & con&longs;i&longs;tentiæ permittitur, &longs;ua &longs;ponte a&longs;&longs;umit, tam in <lb/>&longs;uperficie &longs;uperiore, quàm in inferiore, & lateralibus. </s></p> <p type="margin"> <s><margin.target id="marg131"/><emph type="italics"/>Aqua con­<lb/>&longs;i&longs;tens qua <lb/>dicatur.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg132"/><emph type="italics"/>Aqua &longs;itus <lb/>naturalis <lb/>quis &longs;it.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ &longs;uperficies &longs;uperior, ce&longs;&longs;ante fluxu, &longs;phærica <lb/>e&longs;t; reliquæ conformantur va&longs;is & rece­<lb/>ptaculis,<emph.end type="center"/></s></p> <p type="main"> <s>AQua liberè fluens tam diu fluit, donec partium continuata­<lb/> <arrow.to.target n="marg133"/><lb/>rum extima &longs;eu &longs;uperior &longs;uperficies &longs;phærica &longs;it, habens idem <lb/><expan abbr="centrũ">centrum</expan> cum centro Terraquæ & Vniver&longs;i, hoc e&longs;t, donec omnes <lb/>extimæ &longs;uperficiei partes æqualiter di&longs;tenta Centro Mundi. De- <pb xlink:href="051/01/099.jpg" pagenum="68"/>mon&longs;trat hoc &longs;ubtili&longs;&longs;imè Archimedes lib 1. de in&longs;identibus hu­<lb/>mido Propo&longs;it. 2. & Ari&longs;tot. lib. 2. de Cœlo text. 31. & &longs;equitur <lb/>ex præcedente Proprietate. Si enim ce&longs;&longs;ante fluxu, & con&longs;i­<lb/>&longs;tente iam aquâ, pars vna &longs;uperficiei extimæ altior e&longs;&longs;et, & altera <lb/>humilior, hoc e&longs;t, &longs;i non omnes æquè di&longs;tarent à centro Mundi <lb/>(quod e&longs;t &longs;phæricam habere &longs;uperficiem, habentem idem Cen­<lb/>trum commune Mundi;) non omnes aquæ partes, &longs;ublatis im­<lb/>pedimentis, fluerent ad loca decliviora, nec aquæ con&longs;i&longs;tentis <lb/>partes omnes eò naturali appetitu inclinarent; aut certè violen­<lb/>ter in tali &longs;tatu, & nullo præ&longs;ente impedimento, detinerentur; <lb/> <arrow.to.target n="marg134"/><lb/>quod incongruum e&longs;t, & naturis rerum repugnans. </s></p> <p type="margin"> <s><margin.target id="marg133"/><emph type="italics"/>Aqua con&longs;i­<lb/>&longs;tentis &longs;uper <lb/>ficies &longs;uperi­<lb/>or &longs;pharica <lb/>e&longs;t.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg134"/><emph type="italics"/>Aquæ va&longs;is <lb/>contentæ &longs;u <lb/>perficies con <lb/>formantur <lb/>va&longs;orum in <lb/>ternis figu­<lb/>ris.<emph.end type="italics"/></s></p> <p type="main"> <s>Inferior porrò aquæ &longs;uperficies, & laterales, conforman­<lb/>tur &longs;uperficiebus internis va&longs;orum & receptaculorum, quibus <lb/>aqua continetur: Vnde &longs;i vna pars fundi va&longs;orum ac recepta­<lb/>culorum e&longs;t altior alterâ (prout in mari, lacubus, fluminibus, <lb/>& va&longs;is ordinariè fit) etiam talis erit aquæ illis contentæ infe­<lb/>rior &longs;uperficies. Idem intellige de lateralibus &longs;uperficiebus. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/><lb/> <arrow.to.target n="marg135"/></s></p> <p type="margin"> <s><margin.target id="marg135"/><emph type="italics"/>Aquarum <lb/>omnium Su <lb/>perficies &longs;u­<lb/>perior e&longs;t <lb/>&longs;phærica.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur hinc, Oceani, Marium, lacuum, & aquarum qua­<lb/>rumcunque continuatarum, & in quibuscunque receptacu­<lb/>lis contentarum, ac con&longs;i&longs;tentium, &longs;uperficies &longs;uperiores atque <lb/>externas e&longs;&longs;e &longs;phæricas, habentes idem cum Terraquæ &longs;uperficie </s></p> <p type="main"> <s> <arrow.to.target n="marg136"/><lb/><expan abbr="cõvexa">convexa</expan> centrum. In va&longs;is tamen & receptaculis exiguis adeo exi­<lb/>gua e&longs;t & in&longs;en&longs;ibilis&longs;phæricitas i&longs;tius &longs;uperficiei, vt meritò &longs;up­<lb/>poni po&longs;&longs;it e&longs;&longs;e planam, &longs;eu horizonti parallelam: vnde & nos <lb/>in &longs;equentibus id nobis concedi po&longs;tulabimus, & ita &longs;uppone­<lb/>mus. </s></p> <p type="margin"> <s><margin.target id="marg136"/><emph type="italics"/>In va&longs;is ta­<lb/>men exiguis <lb/>cen&longs;eri po­<lb/>te&longs;t plana.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur iterum, idem vas ad turris aut montis radicem po­<lb/> <arrow.to.target n="marg137"/><lb/>&longs;itum, & aquâ omnino plenum, plùs aquæ continere, mathe­<lb/>maticè loquendo, quàm po&longs;itum in turris aut montis vertice, & <lb/>aquâ itidem omnino plenum. Ratio e&longs;t, quia major e&longs;t &longs;phæri­<lb/>citas aquæ in primo, quàm &longs;ecundo ca&longs;u. </s></p> <pb xlink:href="051/01/100.jpg" pagenum="69"/> <p type="margin"> <s><margin.target id="marg137"/><emph type="italics"/>Aquæ plus <lb/><expan abbr="cõtinet">continet</expan> vas <lb/>plenù infe­<lb/>riori, quàm <lb/>&longs;uperiori <lb/>loco.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma III.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur tertiò, &longs;i aqua ad libellam con&longs;tituta e&longs;&longs;et alicubi, <lb/> <arrow.to.target n="marg138"/><lb/>non po&longs;&longs;e con&longs;i&longs;tere, &longs;ed nece&longs;&longs;ariò moveri, quia tunc non <lb/>omnes partes extimæ & &longs;uperioris &longs;uperficiei e&longs;&longs;ent æquè vicinæ <lb/>centro Terraquæ. Athoc meliùs explicabitur in Pantometro <lb/>no&longs;tro Kircheriano lib. 9. Hydragogico, vbi delibellatione a­<lb/>quarum agemus, <expan abbr="iterumq;">iterumque</expan> in Mechanica no&longs;tra Vniver&longs;ali, libro <lb/>quem in&longs;cribemus Mechanicam Hydragogicam. </s></p> <p type="margin"> <s><margin.target id="marg138"/><emph type="italics"/>Aqu<gap/> con­<lb/>&longs;i&longs;tere non <lb/>pote&longs;i ad li­<lb/>bellam con­<lb/>&longs;tituta.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua minùs pre&longs;&longs;a expellitur à magis pre&longs;&longs;a.<emph.end type="center"/></s></p> <p type="main"> <s>AQuæ, & humidi cuiuscunque, ea e&longs;t natura, inquit Archi­<lb/>medes lib. 1. de In&longs;identibus humido, Hypothe&longs;i I, vt par­<lb/>tibus ip&longs;ius æqualiter iacentibus & continuatis inter &longs;e&longs;e; minùs <lb/>pre&longs;&longs;a à magis pre&longs;&longs;a expellatur; & quidem tantò fortiùs, quantò <lb/>aut minùs illa, aut magis hæc pre&longs;&longs;a fuerit. Hoc quomodo &longs;it in­<lb/>telligendum, patebit ex &longs;equentibus Proprietatibus huius capitis, <lb/>& etiam ex dicendis capite &longs;equenti, Propo&longs;itione 2. </s></p> <p type="main"> <s><emph type="center"/>Proprietas IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ, & humidi cuiu&longs;cunque, pars vnaquæ que premi­<lb/>tur humido &longs;upra ip&longs;am exi&longs;tente ad perpendiculum, &longs;i hu­<lb/>midum &longs;it de&longs;cendens in aliquo, aut ab alio ali­<lb/>quo pre&longs;&longs;um.<emph.end type="center"/></s></p> <p type="main"> <s>AS&longs;erit hoc Archimedes loco proximè citato. <expan abbr="Itaq;">Itaque</expan> quando <lb/> <arrow.to.target n="marg139"/><lb/>humidum non e&longs;t de&longs;cendens in aliquo, aut non e&longs;t ab ali­<lb/>quo alio pre&longs;&longs;um, &longs;ed con&longs;i&longs;tit in &longs;uo &longs;itu naturali, vna pars non <lb/>premit alteram, vt mox dicemus. Si autem humidum <lb/>e&longs;t de&longs;cendens in aliquo, vt &longs;i effluit per foramen va&longs;is, aut in­<lb/>fluit in vas coniunctum: tunc partes &longs;upra foramen premuntur <lb/>à partibus ad perpendiculum ip&longs;is incumbentibus, non verò ab <lb/>alijs collateralibus. Similiter &longs;i humidum premitur ab aliquo, <lb/>partes pre&longs;&longs;æ premunt &longs;olùm quæ ip&longs;is ad perpendiculum &longs;ub­<lb/>&longs;tant. </s></p> <pb xlink:href="051/01/101.jpg" pagenum="70"/> <p type="margin"> <s><margin.target id="marg139"/><emph type="italics"/>Aquæ par­<lb/>tes inferio­<lb/>res <expan abbr="premũ-tur">premun­<lb/>tur</expan> à &longs;upe­<lb/>rioribus ad <lb/>perpendicu­<lb/>lum incum <lb/>bentibus.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquâ in &longs;itu naturali con&longs;i&longs;tente, partes &longs;uperiores non <lb/>premunt inferiores.<emph.end type="center"/></s></p> <p type="main"> <s>PAtet hoc ex multis &longs;ignis. Primò enim alioquin partes aquæ <lb/>inferiores e&longs;&longs;ent den&longs;iores &longs;uperioribus, quia <expan abbr="cõpre&longs;&longs;æ">compre&longs;&longs;æ</expan> e&longs;&longs;ent. <lb/>Secundò, vrinatores infra aquam exi&longs;tentes non &longs;entiunt pon­<lb/>dus aquarum incumbentium &longs;ibi. Tertiò, herbæ levi&longs;&longs;imæ intra <lb/>aquam cre&longs;centes, & in altum a&longs;&longs;urgentes, non &longs;ternuntur ab <lb/>aqua &longs;uperincumbente. Quartò, corpus grave fune alligatum <lb/>& infra aquam demer&longs;um, &longs;u&longs;tinetur à manu, & extrahitur, tan­<lb/>ta facilitate, quanta &longs;u&longs;tineretur & extraheretur, &longs;i nulla aqua illi <lb/>incumberet; imò maiorietiam facilitate, quoniam gravia mi­<lb/>nùs ponderantintra, quàm extra aquam. Quintò, &longs;itula aquâ <lb/>plena levior e&longs;t intra aquam, quàm extra: Curhoc, ni&longs;i quia <lb/>aqua intra aquam non ponderat? </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/> <arrow.to.target n="marg140"/></s></p> <p type="margin"> <s><margin.target id="marg140"/><emph type="italics"/>Aquæ con <lb/>&longs;i&longs;tentis par­<lb/>tes &longs;uperio­<lb/>res non pre­<lb/>munt actu <lb/>inferiores.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur hinc, quando Archimedes, alijque dicunt, omnes <lb/>aquæ partes, dum ea in &longs;itu con&longs;i&longs;tit naturali, a qualiter pre­<lb/>mi, non e&longs;&longs;e &longs;ermonem de actuali pre&longs;&longs;ione, &longs;ed &longs;olùm de aptitu­<lb/>dinali. Premi vnum ab alio aptitudinaliter, e&longs;t, habere &longs;upra <lb/>&longs;e grave non &longs;u&longs;tentatum; at premi actualiter e&longs;t ita habere &longs;u­</s></p> <p type="main"> <s> <arrow.to.target n="marg141"/><lb/>pra &longs;e grave non &longs;u&longs;tentatum, vt ablato impedimento cedere co­<lb/>gatur corpori incumbenti; & ni&longs;i cedat, comprimatur. Vel di­<lb/>cendum e&longs;t, premi quidem partes humidi inferiores à &longs;uperio­<lb/>ribus &longs;ibi &longs;uperin cumbentibus, at non comprimi. Solùm ergo <lb/>partes &longs;uperiores aquæ actu premunt inferiores, quando vel ab <lb/>alio premuntur &longs;uperiores, vel quando &longs;unt altiores alijs partibus <lb/>contiguis in eodem va&longs;e, aut in duobus va&longs;is inter &longs;e communi­<lb/>cantibus, vt videbimus, cùm de Siphonibus agetur; vel denique <lb/>quando infra &longs;e habent inferiores immediatè corpus levius &longs;e in <lb/>&longs;pecie, v.g. aërem, aut tenui&longs;&longs;imum fundum; in omnibus enim <lb/>hi&longs;ce ca&longs;ibus partes inferiores cedunt quidem &longs;uperioribus, at <lb/>minimè ab illis comprimuntur. Hinc e&longs;t, quòd aqua effluatè <lb/>foramine in fundo aut latere va&longs;is. Hinc etiam e&longs;t, quòd fun- <pb xlink:href="051/01/102.jpg" pagenum="71"/>dum tenue va&longs;is incurvetur, ac tandem frangatur. Hinc deni­<lb/>que e&longs;t, quòd dum partes aquæ &longs;uperiores premuntur, & partes <lb/>inferiores non habent effugium aut infrà, aut è latere va&longs;is, rum­<lb/>patur potiùs vas, quàm partes inferiores comprimantur. Vide <lb/>quæ dicimus infrà parte 2. Cla&longs;se 1. cap. 5. Machina 6. </s></p> <p type="margin"> <s><margin.target id="marg141"/><emph type="italics"/>Premi actu, <lb/>& premi <lb/>aptitudina­<lb/>liter, quid <lb/>&longs;it.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ in &longs;itu naturali po&longs;itæ vna pars non <lb/>expellit alteram.<emph.end type="center"/></s></p> <p type="main"> <s>PAtet experientia. Et ratio e&longs;t, quia vna non premit alteram, <lb/>vt dictum in præcedenti Proprietate. Quòd &longs;i in va&longs;is con­<lb/>jugatis altior aqua pellit minùs altam, cau&longs;a e&longs;t, quòd non &longs;it <lb/>po&longs;ita in &longs;itu naturali, quia &longs;cilicet non habet omnes partes æ­<lb/>què di&longs;tantes à centro Mundi. </s></p> <p type="main"> <s><emph type="center"/>Proprietas VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Non omnes aquæ æquales magnitudine, &longs;unt <lb/>æquales pondere.<emph.end type="center"/></s></p> <p type="main"> <s>SUnt enim &longs;alsæ graviores dulcibus, & frigidæ calidis eiu&longs;dem <lb/> <arrow.to.target n="marg142"/><lb/>&longs;peciei, &longs;eu individui; & tam &longs;alsæ, quàm dulces, aliæ alijs gra­<lb/>viores &longs;unt, vt patet experientia, & fatentur etiam nautæ, vi­<lb/>dentes naves è fluminibus impuris ad pura, aut è mari ad flumina <lb/>transeuntes &longs;ub&longs;idere profundiùs, & &longs;ubinde cum &longs;ubmer&longs;ionis <lb/>periculo. </s></p> <p type="margin"> <s><margin.target id="marg142"/><emph type="italics"/>Aqua &longs;alsa <lb/>frigida, im­<lb/>pura, gra­<lb/>vior e&longs;t <expan abbr="quã">quam</expan> <lb/>dulcis &c.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Proprietas VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua naturaliter non a&longs;cendit ad locum altio­<lb/>rem &longs;uâ origine.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>IMò nec fluit naturaliter ab vno ad alterum locum, ni&longs;i terminus à quo <lb/>altior &longs;it, quàm terminùs ad quem.<emph.end type="italics"/> Vtrumque patet experientiä, <lb/> <arrow.to.target n="marg143"/><lb/>& &longs;equitur ex dictis Proprietate I. & II. Hinc Hydragogi a&longs;&longs;e­<lb/>runt, non po&longs;&longs;e deduciaquam de loco in locum, &longs;ive per alveum, <lb/>&longs;ive per aquæductus, canales, ac tubos deducenda &longs;it, &longs;i &longs;patium <lb/>&longs;it æquilibratum, &longs;eu ad libellam con&longs;titutum; nec &longs;ufficere <expan abbr="Ma-thematicã">Ma­<lb/>thematicam</expan>, aut quam cunque phy&longs;icam declivitatem, &longs;ed requiri <lb/>in &longs;ingulis milliaribus cadentiam &longs;eu declivitatem quatuor ad <pb xlink:href="051/01/103.jpg" pagenum="72"/>minimùm vnciarum vnius pedis, (e&longs;t vncia pars duodecima pe­<lb/>dis) ita vt terminus ad quem in fine milliaris &longs;it vicinior centro <lb/>Terræ quatuorvncijs, quàm terminus à quo; &p o&longs;t alterum mil­<lb/>liare alijs quatuor vncijs &longs;it vicinior, & &longs;ic deinceps &longs;emper, e&longs;t­<lb/>que hæc regula à <expan abbr="pleris&qacute;ue">plerisque</expan> recepta tanquam Axioma hydra­<lb/>gogicum. Sed de hac re fusè agemus in Pantometro no&longs;tro <lb/>Kircheriano lib. 9. vbi agemus ex profe&longs;&longs;o de Hydragogia & li. <lb/>bellatione aquarum; & in Mechanica Vniver&longs;ali. </s></p> <p type="margin"> <s><margin.target id="marg143"/><emph type="italics"/>Aqua non <lb/>pote&longs;t decur <lb/>rereper &longs;pa­<lb/>tium æqui­<lb/>libratum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>CAPVT II. <lb/>DE <lb/>Proprietatibus Aquæ fluentis per <lb/>&longs;iphones.<emph.end type="center"/></s></p> <p type="main"> <s>QUamvis in Machinis no&longs;tris Hydro-pnevmati­<lb/>cis, Parte 2. indifferenter & pro eodem fumamus no­<lb/>men &longs;iphonis, & tubi, pro fi&longs;tula &longs;cilicet, per quam <lb/>aqua fluit, &longs;ive recta illa &longs;it, &longs;ive curva; hîc tamen, <lb/> <arrow.to.target n="marg144"/><lb/>maioris di&longs;tinctionis gratia, &longs;iphonem à tubo di&longs;tinguimus. <lb/>E<gap/>gitur Siphon nihil aliud quàm tubus inflexus. Huius variæ <lb/>&longs;unt &longs;pecies, vt &longs;equitur. </s></p> <p type="margin"> <s><margin.target id="marg144"/><emph type="italics"/>Siphon quid<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis varias divi&longs;iones a&longs;&longs;ignare.<emph.end type="center"/></s></p> <p type="main"> <s>SIphon igitur, &longs;eu tubus in flexus, dividitur variè, & habet diver­<lb/> <arrow.to.target n="marg145"/><lb/>&longs;as figuras, vt apparet in appo&longs;itis &longs;chemati&longs;mis. Alius enim <lb/>dicitur &longs;iphon erectus, alius in ver&longs;us, aliusmixtus, alius æquali­<lb/>um, alius in æqualium crurium. <lb/> <arrow.to.target n="marg146"/></s></p> <p type="margin"> <s><margin.target id="marg145"/><emph type="italics"/>Siphonis <lb/>&longs;pecies va­<lb/>ria.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg146"/><emph type="italics"/>Siphon ere­<lb/>ctus.<emph.end type="italics"/></s></p> <p type="main"> <s>Siphon erectus e&longs;t, cuius omnia crura &longs;ur&longs;um &longs;unt. Huius­<lb/>modi &longs;unt &longs;eptem priores, & vltimus ex hîc appo&longs;itis. </s></p> <p type="main"> <s> <arrow.to.target n="marg147"/></s></p> <p type="margin"> <s><margin.target id="marg147"/><emph type="italics"/>Siphon in­<lb/>ver&longs;us.<emph.end type="italics"/></s></p> <p type="main"> <s>Siphon inver&longs;us e&longs;t, cuius omnia crura deor&longs;um &longs;unt. Hu­<lb/>iusmodi &longs;untijdem, &longs;i inver &longs;i intelligantur, hoc e&longs;t, &longs;i B &longs;ur&longs;um, <lb/>C & A deor&longs;um &longs;pectent. </s></p> <p type="main"> <s> <arrow.to.target n="marg148"/></s></p> <p type="margin"> <s><margin.target id="marg148"/><emph type="italics"/>Siphon mi­<lb/>xtus.<emph.end type="italics"/></s></p> <p type="main"> <s>Siphon mixtus e&longs;t, cuius crura partim &longs;ur&longs;um, partim de­<lb/>or&longs;um &longs;unt. Huiu&longs;modi &longs;unt tres penultimi ex appo&longs;itis, &longs;eu 8. 9. <lb/>& 10. </s></p> <pb xlink:href="051/01/104.jpg" pagenum="73"/> <figure id="id.051.01.104.1.jpg" xlink:href="051/01/104/1.jpg"/> <p type="main"> <s>Siphones tam erecti, quàm inver&longs;i, vel habent vtrumque <lb/>erus æquale, vel inæquale. Si æqualia &longs;unt crura, vellongitu­<lb/>dine & capacitate &longs;untæqualia, vt apparet in prima, tertia, & </s></p> <p type="main"> <s> <arrow.to.target n="marg149"/><lb/>&longs;eptima figura: vel &longs;ola longitudine æqualia, capacitate verò <lb/>inæqualia, vt apparet in &longs;ecunda, quarta, quinta, &longs;exta, & vlti­<lb/>ma figura. </s></p> <pb xlink:href="051/01/105.jpg" pagenum="74"/> <p type="margin"> <s><margin.target id="marg149"/><emph type="italics"/>Siphones a­<lb/>qualium, <lb/>& inaqua­<lb/>lium cruri­<lb/>um.<emph.end type="italics"/></s></p> <p type="main"> <s>Siphones mixti, vel habent omnia crura æqualia longitu­<lb/>dine, vt in octava figura apparet; vel aliqua tantùm, utin nona <lb/>figura; vel nulla, ut in decima figura patet. Hæc eadem crura <lb/>po&longs;&longs;unt e&longs;&longs;e diver&longs;æ capacitatis inter &longs;e. <lb/> <arrow.to.target n="marg150"/></s></p> <p type="margin"> <s><margin.target id="marg150"/><emph type="italics"/>Siphon con­<lb/>iugatus.<emph.end type="italics"/></s></p> <p type="main"> <s>Nota. Siphonem quartum aliqui vocant coniugatum, re­<lb/>liquos verò inflexos appellant. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis erecti proprietates a&longs;&longs;ignare.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg151"/></s></p> <p type="margin"> <s><margin.target id="marg151"/><emph type="italics"/>Siphonis e­<lb/>recti proprie <lb/>tates.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>PRima.<emph.end type="italics"/> Aqua vni &longs;iphonis erecti cruri infu&longs;a de&longs;cendit pri­<lb/>mùm, deinde a&longs;cendit per alterum crus, donec &longs;upremæ &longs;u­<lb/>perficies in vtroque <lb/> <arrow.to.target n="fig17"/><lb/>crure &longs;int in eadem <lb/>linea horizontali. <lb/>Sint &longs;iphones erecti <lb/>ABCDEF, &longs;ive æ­<lb/>qualium, &longs;ive inæ­<lb/>qualium crurium, <lb/>tam quoad longitu­<lb/>dinem, quàm quoad <lb/>capacitatem; vn<gap/><expan abbr="q;">que</expan> <lb/>crutium, &longs;ive longi­<lb/>ori, &longs;ive breviori, <lb/>&longs;ive æquali, & &longs;ive <lb/>largiori, &longs;ive &longs;tricti­<lb/>ori, v.g. cruri AB, <lb/>infundatur aqua: <lb/>de&longs;cendet ea <expan abbr="primũ">primum</expan> <lb/>v&longs;que ad B, <expan abbr="indeq;">indeque</expan> <lb/>per C & D a&longs;cen­<lb/>det, donec &longs;upremæ <lb/>aqu&ecedil; &longs;uperficies &longs;int <lb/>in vtroque crure in <lb/>eadem linea Hori- <pb xlink:href="051/01/106.jpg" pagenum="75"/>zontali, v.g. in linea HIK; hoc e&longs;t, donec omnes dictarum &longs;u­<lb/>perficierum partes di&longs;tent æqualiter à centro terræ, juxta dicta <lb/>cap. 1. Proprietat. 2. Ratio de&longs;umitur ex dictis ibidem. Ex his <lb/>formo &longs;equens. </s></p> <figure id="id.051.01.106.1.jpg" xlink:href="051/01/106/1.jpg"/> <p type="main"> <s><emph type="center"/>Axioma Hydraulicum I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVantùm aqua de&longs;cendit per vnum &longs;iphonis erecti crus, tantundem </s></p> <p type="main"> <s> <arrow.to.target n="marg152"/><lb/>a&longs;cendit per alterum.<emph.end type="italics"/> Idem contingit in omnibus canalibus, <lb/>alveis, & meatibus quibuscunque incurvatis. </s></p> <p type="margin"> <s><margin.target id="marg152"/>Axioma hy <lb/>draulicum.</s></p> <p type="main"> <s><emph type="italics"/>Secunda.<emph.end type="italics"/> Si vni crurium, &longs;ive longiori, &longs;ive breviori, &longs;ive <lb/>æquali, & &longs;ive capaciori, &longs;ive minùs capaci, addas aliquid aquæ, <lb/>v.g. cruri AB; attollitur etiam alterius cruris aqua, donec rur­<lb/>&longs;us &longs;uperficies di&longs;tent æqualiter a centrro terræ, &longs;eu &longs;int in eadem <lb/>linea horizontali, v.g. in linea GFE. Ratio e&longs;t eadem. </s></p> <p type="main"> <s><emph type="italics"/>Tertia.<emph.end type="italics"/> Si cruri longiori, &longs;ive id capacius &longs;it altero iam <lb/>pleno, &longs;ive non, addas plùs aquæ, v.g. cruri AB; de&longs;cendet ea <lb/>p<gap/> B, <expan abbr="elevabit&qacute;ue">elevabitque</expan> aquam cruris CDEF, & expellet per os <lb/>EF, donec ce&longs;&longs;ante infu&longs;ione &longs;it iterum vtraque &longs;uperficies in li­<lb/>nea GFE. Patet experientiâ, & ratio e&longs;t eadem, ne &longs;cilicet &longs;u­<lb/>perficies vnius cruris di&longs;tet plùs aut minùs, à centro terræ, quàm <lb/>alterius. </s></p> <p type="main"> <s><emph type="italics"/>Quarta.<emph.end type="italics"/> Si cruri breviori, licet capaciori, nempe cruri <lb/>EFCD, jam pleno addas plùs aquæ |; ea non attollet aquam <lb/>cruris longioris vltra punctum G, &longs;ed effluet ex ore EF, licet <lb/>aqua cruris EFCD &longs;it longè maior & pondero&longs;ior, quàm <lb/>aqua cruris AB. Patet itidem experientiâ, & ratio e&longs;t eadem. </s></p> <p type="main"> <s><emph type="center"/>Corollarium I.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur hinc primò, aquam maioris perpendiculi pellere <lb/> <arrow.to.target n="marg153"/><lb/>aquam minoris perpendiculi, non ob&longs;tante maiore copia, & <lb/>maiore pondere huius: ideo enim aqua cruris AB primæ & tertiæ <lb/>figuræ expellit aquam cruris CDEF, licet longè maiorem & <lb/>pondero&longs;iorem, quia perpendiculum illius e&longs;t maius &longs;eu longius, <lb/>quàm perpendiculum huius. Aquæ perpendiculum hic, & in <lb/> <arrow.to.target n="marg154"/><lb/>&longs;equentibus, appello altitudinem aquæ &longs;upra horizontem, &longs;eu <lb/>&longs;upra centrum Terræ, ita vt illa dicatur habere maius perpendi- <pb xlink:href="051/01/107.jpg" pagenum="76"/>culum, quàm altera, cuius altitudo ab infima ad &longs;upremam &longs;u­<lb/>perficiem maior e&longs;t, in eodem horizonte. </s></p> <p type="margin"> <s><margin.target id="marg153"/><emph type="italics"/>Aqua ma­<lb/>ioru perpen­<lb/>diculi pellit <lb/>aquam mi­<lb/>noris perpen <lb/>diculi in Si­<lb/>phonibus e­<lb/>rectis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg154"/><emph type="italics"/>Perpendicu <lb/>lum aquæ <lb/>quid.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium II.<emph.end type="center"/><lb/> <arrow.to.target n="marg155"/></s></p> <p type="margin"> <s><margin.target id="marg155"/><emph type="italics"/>Aqua ma­<lb/>gis aut, mi <lb/>nùs pre&longs;&longs;a <lb/>in &longs;iphoni­<lb/>bus, <expan abbr="quanã">quanam</expan> <lb/>dicatur.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur &longs;ecundò, Quænam aqua in &longs;iphone erecto dicatur <lb/>magis aut minùs pre&longs;&longs;a: Nam cùm con&longs;tet, Aquam minùs <lb/>pre&longs;&longs;am expelli à magis pre&longs;&longs;a, per dicta Capite primo, Propriet. <lb/>3. con&longs;tet præterea, Aquam minoris perpendiculi in &longs;iphone e­<lb/>recto premi atque expelli ab aqua maioris perpendiculi; clarum <lb/>e&longs;t, Aquam minoris perpendiculi dici minùs, <expan abbr="aquã">aquam</expan> verò maioris <lb/>perpendiculi dici magis pre&longs;sam. Ex his formo &longs;equens </s></p> <p type="main"> <s><emph type="center"/>Axioma Hydraulicum II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>IN hydraulicis non aquarum copiâ, &longs;ed perpendiculis pugnatur, & vin­</s></p> <p type="main"> <s> <arrow.to.target n="marg156"/><lb/>citur.<emph.end type="italics"/> Illa enim vincit pellendo, vel trahendo alteram, cuius <lb/>perpendiculum e&longs;t maius. </s></p> <p type="margin"> <s><margin.target id="marg156"/>Axiomo hy <lb/>draulicum.</s></p> <p type="main"> <s><emph type="center"/>Corollarium III.<emph.end type="center"/><lb/> <arrow.to.target n="marg157"/></s></p> <p type="margin"> <s><margin.target id="marg157"/><emph type="italics"/>Siphonis e­<lb/>recti ope a­<lb/>quam ex v­<lb/>no monte in <lb/>alterum de <lb/>rivare.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur tertiò, Quomodo &longs;iphonis erectiope (hoc e&longs;t,<gap/>­<lb/>nale, tubo autin <expan abbr="modũ">modum</expan> &longs;iphonis erecti con&longs;tructo) ex monte <lb/>per vallem ad alterum montem, priori paulò humiliotem, aut <lb/>ad locum in latere montis, derivari po&longs;&longs;it aqua; &longs;i nimirum fiat <lb/>&longs;iphon erectus, cuius os vnum immergatur aquæ montis altioris, <lb/>& dein &longs;iphon deducatur per vallem, & latera montium, usque <lb/>adlocum de&longs;tinatum, humiliorem tamen origine aquæ. </s></p> <p type="main"> <s><emph type="center"/>Corollarium IV.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg158"/></s></p> <p type="margin"> <s><margin.target id="marg158"/><emph type="italics"/><expan abbr="Doliũ">Dolium</expan> quo­<lb/><gap/>que &longs;it ple <lb/>num, Si­<lb/>phone ex­<lb/>plorare.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligltur quar­<lb/> <arrow.to.target n="fig18"/><lb/>tò, Quomodo <lb/>&longs;cire po&longs;&longs;is præcisè <lb/>quou&longs;que dolium <lb/>aliquod <expan abbr="exinanitũ">exinanitum</expan> <lb/>&longs;it, manente obtu­<lb/>ramento &longs;uperiore <lb/>clauso, <expan abbr="nulloq;">nulloque</expan> alio <lb/>foramine facto <lb/>præterid, cui epi­<lb/>&longs;tomium immitti <pb xlink:href="051/01/108.jpg" pagenum="77"/>&longs;olet. Sit enim dolium DC, exinanitum v&longs;que ad lineam FG; <lb/>quod tu ignores: &longs;cies id, &longs;i tubum oblongum AB incurves in­<lb/>feriùs iuxta B, & doleo iuxta C in&longs;eras epi&longs;tomij loco; liquor <lb/>enim dolij effluens a&longs;cendet per tubum, donec perveniat <expan abbr="v&longs;q;">v&longs;que</expan> ad <lb/>E, & æquetur &longs;upremæ &longs;uperficiei liquoris in dolio contenti. </s></p> <figure id="id.051.01.108.1.jpg" xlink:href="051/01/108/1.jpg"/> <p type="main"> <s><emph type="center"/>Corollarium V.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg159"/></s></p> <p type="margin"> <s><margin.target id="marg159"/><emph type="italics"/>Dolium im <lb/>plere per e­<lb/>pi&longs;tomium <lb/>ope &longs;iphonis.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur quintò, Quomodo repleri po&longs;&longs;it prædictum doli­<lb/>um per foramen C epi&longs;tomij. Si enim tubum AB incur­<lb/>vatum in&longs;eras dolio iuxta C, & &longs;uperiùs iuxta A infundas li­<lb/>quorem; a&longs;cendet is in dolio, donec æquetur &longs;ummitati tubi, <lb/>aut donec dolium &longs;it omnino repletum, &longs;i tubus altior e&longs;t dolio. <lb/>Bene tamen Schvventerus monet in fuis Recreationibus Mathe­<lb/>maticis parte 13. quæ&longs;t. 3. debere in &longs;ummitate dolij foramen a­<lb/>periri, per quod aër elabatur, impediturus alioquin liquoris in­<lb/>fu&longs;ionem, &longs;i non po&longs;&longs;it erumpere per foramen C & tubum BA. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>In Siphone erecto plurium quàm duorum crurium eadem con­<lb/>tingunt, quæ in &longs;iphone duorum crurium, vt con&longs;ideranti patet.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis inver&longs;i proprietates a&longs;&longs;ignare.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg160"/></s></p> <p type="margin"> <s><margin.target id="marg160"/><emph type="italics"/>Siphonis in­<lb/>ver&longs;i pro­<lb/>prietates.<emph.end type="italics"/></s></p> <p type="main"> <s>PLurimas proprietates, easque plerumque miras habet Siphon <lb/>ever&longs;us, tam æqualium quoad longitudinem & capacitatem <lb/>crurium, quàm inæqualium. Nos præcipuas referemus. </s></p> <p type="main"> <s><emph type="center"/>Prima Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI crura &longs;iphonis inver&longs;i inæqualia &longs;unt quoad longitudinem, <lb/>& totus &longs;iphon repleatur aquâ, & invertatur; effluit ea tota per <lb/>cruslongius, licet &longs;it minus capacitate. E&longs;to Siphon inver&longs;us <lb/>ABC inæqualium crurium, aquâ plenus, & crus AB longius <lb/>&longs;it quàm crus CB, hoc e&longs;t, extremæ aquarum &longs;uperficies A & C <lb/>inæqualiter di&longs;tent à Centro Mundi, &longs;cilicet AB minùs, CB <lb/>plùs; dico, totam aquam effluere per crus AB, licet capacitate <lb/>&longs;it minus quàm CB. Ratio e&longs;t, quia cùm aquæ AB perpendi­<lb/>culum, &longs;it longius, quàm aquæ CB perpendiculum, ma­<lb/>gis premitur aqua apud A, quàm apud C, per corollarlum I. <pb xlink:href="051/01/109.jpg" pagenum="78"/> <arrow.to.target n="fig19"/><lb/>Propo&longs;itione. II. <lb/>præcedentis; ac pro­<lb/>indeper Propr. III. <lb/>cap. 1. aqua AB ex­<lb/>pellet aquam CB, <lb/>non <expan abbr="quid&etilde;">quidem</expan> per pre&longs;­<lb/>&longs;ionem, &longs;ed per at­<lb/>tractionem; hoc e&longs;t, <lb/>effluetaqua AB, &longs;e­<lb/>cumque <expan abbr="trahetaquã">trahetaquam</expan> <lb/>CB, & quidem to­<lb/>tam, tum propter <lb/>rationem dictam, <lb/>tum nè detur vacu­<lb/>um in &longs;iphone. </s></p> <figure id="id.051.01.109.1.jpg" xlink:href="051/01/109/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>MOnuit hîc P. Athana&longs;ius Kircherus, ea quæ diximus hoc loco, &longs;o­<lb/>lùm e&longs;&longs;e intelligenda in eo ca&longs;u, in quo tubi<emph.end type="italics"/> ABC <emph type="italics"/>laxior portio<emph.end type="italics"/> BC <lb/><emph type="italics"/>inferiùs e&longs;t clau&longs;a, &longs;olo foramine<emph.end type="italics"/> I. <emph type="italics"/>relicto. Si enim totum orificium a­<lb/>pertum fuerit; aqua nulla ratione &longs;i&longs;tipoterit quin effluat &longs;ecumque tra­<lb/>hat aquam cruris<emph.end type="italics"/> BA. <emph type="italics"/>Rationem ad&longs;ignat, quia quando &longs;olum fora­<lb/>men<emph.end type="italics"/> I <emph type="italics"/>e&longs;t apertum, &longs;ola columna aquea<emph.end type="italics"/> BI <emph type="italics"/>in fig.<emph.end type="italics"/> I. <emph type="italics"/>habet rationem per­<lb/>pendiculi, eò quòd &longs;olum illa premat &longs;upra<emph.end type="italics"/> I. <emph type="italics"/>At quando totum orifi­<lb/>cium e&longs;t apertum, tota aqua<emph.end type="italics"/> BHICG <emph type="italics"/>habet rationem perpendiculi, <lb/>quia tota premit &longs;upra orificium apertum, ac proinde æquivalet pluribus <lb/>perpendiculis æqualibus perpendiculo<emph.end type="italics"/> BI; <emph type="italics"/>quæ &longs;imul &longs;umpta &longs;uperant <lb/>perpendiculum longius<emph.end type="italics"/> BA. <emph type="italics"/>Addidit, hæc &longs;e longa experientia didici&longs;&longs;e.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Opportuna monitio, nec menti meæcontraria. Puto tamen, a­<lb/>quam ex orificio<emph.end type="italics"/> CI <emph type="italics"/>penitus aperto effluere non tam obrationem ad&longs;ig­<lb/>natam, quàm quòd aëri facillimus pateat ingre&longs;&longs;us ob laxitatem orificij; <lb/>quo ingrediente di&longs;continuatur aqua, & per vtrumque orificium <expan abbr="apertũ">apertum</expan> <lb/>effluit.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/110.jpg" pagenum="79"/> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>COnfirmatur hinc Axioma hydraulicum præcedens, quòd in <lb/>&longs;iphonibus (& etiam tubis, & quibuscunque va&longs;is) non pu­<lb/>gnatur ponderibus, &longs;ed altitudinibus, &longs;eu perpendiculis. In­<lb/>tellige, in ca&longs;u & &longs;en&longs;u explicato. </s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>DIcere quis po&longs;&longs;et, quando &longs;olùm patet foramen<emph.end type="italics"/> I, <emph type="italics"/>tunc attracto cy­<lb/>lindrulo aqueo<emph.end type="italics"/> BI, <emph type="italics"/>faciliùs &longs;uccedit aër per foramen attractus, <lb/>quàm aqua lateralis<emph.end type="italics"/> HI, <emph type="italics"/>vel<emph.end type="italics"/> GI; <emph type="italics"/>immi&longs;&longs;oque aëre, aqua illa lateralis <lb/>facillimè effluet per foramen<emph.end type="italics"/> I. <emph type="italics"/>Quare in nullo ca&longs;u videtur po&longs;&longs;e ve­<lb/>rificari, quòd aqua<emph.end type="italics"/> AB <emph type="italics"/>attrahat totam aquam<emph.end type="italics"/> BC <emph type="italics"/>Nego tamen id <lb/>recte dici, quia aër ingrediens per foramen<emph.end type="italics"/> I <emph type="italics"/>adhærebit &longs;olùm vltimæ <lb/>&longs;uperficiei aquæ fugientis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Secunda Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI crura &longs;iphonis inver&longs;i æqualia &longs;int quoad longitudinem, li­<lb/>cetinæqualia capacitate (cum limitatione tamen po&longs;ita) & <lb/>totus repleatur aquâ, <expan abbr="invertatur&qacute;ue">invertaturque</expan>; nihil effluit. Decurtetur <lb/>in præcedente &longs;chemate crus AB in D, & repleatur totus&longs;iphon <lb/>aquâ, ita vt extremæ aquæ &longs;uperficies C & D æqualiter di&longs;tent <lb/>à centro mundi; dico, nihil effluere, licet cruris CB maior aqua <lb/>& pondero&longs;ior &longs;it, quàm aqua cruris AB. Idem fiet, &longs;i absque cru­<lb/>ris AB decurtatione, extrema aquæ &longs;uperficies in illo æquè di­<lb/>&longs;tetà centro Mundi, atque in crure CB, vt &longs;i vtro<gap/> e&longs;&longs;et in <lb/>linea horizontali CD, aut in linea GHE. Ratio e&longs;t, quia cùm <lb/>in vtroque crure æquale &longs;it <expan abbr="perpendiculũ">perpendiculum</expan> &longs;eu altitudo aquæ, pre­<lb/>metur vtrobique æqualiter; vel ergo vtriu&longs;que cruris aqua &longs;imul <lb/>de&longs;cendere deberet, quod fieri non pote&longs;t absque vacuo; vel <lb/>neutrius. Exhac, & præcedente Proprietate, formari pote&longs;t <lb/>aliud. </s></p> <p type="main"> <s><emph type="center"/>Axioma hydraulicum III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>IN hydraulicis æqualia perpendicula æqualiter premunt, inæqualia </s></p> <p type="main"> <s> <arrow.to.target n="marg161"/><lb/>inæqualiter, &longs;cilicet longius plùs, brevius minùs.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/111.jpg" pagenum="80"/> <p type="margin"> <s><margin.target id="marg161"/>Axioma by <lb/>draulicum.</s></p> <p type="main"> <s><emph type="center"/>Tertia Proprietas.<emph.end type="center"/><lb/> <arrow.to.target n="marg162"/></s></p> <p type="margin"> <s><margin.target id="marg162"/><emph type="italics"/>Aqua per <lb/>longius crus <lb/>&longs;iphonis ce­<lb/>leriùs cur­<lb/>rit, quàm <lb/>per brevius.<emph.end type="italics"/></s></p> <p type="main"> <s>AQua per longius crus &longs;iphonis inver&longs;i eò currit celeriùs, quò <lb/>longius fuerit crus. Ratio e&longs;t, quia quò longius e&longs;t crus, eò <lb/>longius e&longs;t aquæ de&longs;cendentis <expan abbr="perpendiculũ">perpendiculum</expan>, ac proinde eò ma­<lb/>ius pondus incumbit aquæ prope os, eòque magis premitur a­<lb/>qua in egre&longs;lu, celeriúsque propterea effluit, & con&longs;equenter ce­<lb/>leriùs de&longs;cendit. Hinc formo &longs;equens </s></p> <p type="main"> <s><emph type="center"/>Axioma Hydraulicum IV.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg163"/></s></p> <p type="margin"> <s><margin.target id="marg163"/><emph type="italics"/>Axioma hy <lb/>draulicum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>In hydraulicis per &longs;iphones & tubos longiores celeriùs fluit aqua, <lb/>quàm per breviores, po&longs;ito eodem, aut æquali orificio per quod effluit.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Quarta Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg164"/></s></p> <p type="margin"> <s><margin.target id="marg164"/><emph type="italics"/>Aqua per <lb/><expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> fluit <lb/>difformi <lb/>celeritate.<emph.end type="italics"/></s></p> <p type="main"> <s>AQua per longius crus &longs;iphonis inver&longs;i non effluit celeritate v­<lb/>niformi, &longs;ed difformi; augetur enim continuò celeritas de­<lb/>&longs;cen&longs;us, donec exhau&longs;tum &longs;it crus oppo&longs;itum: nunquam tamen <lb/>de&longs;cendit tam celeriter aqua, quàm &longs;i liberè, hoc e&longs;t, non per <lb/>&longs;iphonem, &longs;ed per tubum, aut extra tubum vel canalem de&longs;cen­<lb/>deret. Ratio e&longs;t, quia aqua effluens per crus longius AB, in an­<lb/>tea po&longs;ito, & in quocunque alio &longs;iphone, debet &longs;ecum trahere <lb/>contranitentem aquam cruris brevioris CB, nè detur vacuum <lb/>intra &longs;iphonem; quæ aqua cruris brevioris quoniam continuò <lb/>minuitur effluente aqua per os A, ideo faciliùs &longs;emper ac faci­<lb/>liùs attrahitur ab aqua cruris longioris AB; cuius proinde <expan abbr="de&longs;c&etilde;-dentis">de&longs;cen­<lb/>dentis</expan> celeritas continuò intenditur, donec exhau&longs;tum &longs;it to­<lb/>tum crus CB. Non æquat tamen celeritatem eam, quâ liberè <lb/>de&longs;cenderet, non trahendo &longs;ecum aquam alterius cruris; quia <lb/>quàm diu re&longs;tat aliquid aquæ in crure breviori CB, attrahere <lb/>illud debet, vt po&longs;&longs;it effluere, ac proin de &longs;emper aliquid retinet <lb/>impedimenti; quo caret, dum liberè cadit. Adde quòd quò <lb/>diutiùs aqua effluit per A, eò aquæ cruris CB &longs;uperficies ex­<lb/>trema C magis a&longs;cendit ver&longs;us B, adeoque & perpendiculum <lb/>aquæ cruris CB continuò minuitur, aquæ interim, quæ ex crure <lb/>AB fluit, perpendiculo manente eodem. Augetur ergo a&longs;&longs;iduè <lb/>proportio perpendiculi BA ad perpendiculum BC, adeoque & <pb xlink:href="051/01/112.jpg" pagenum="81"/>proportio pre&longs;&longs;ionis aquæ BA ad pre&longs;&longs;ionem aquæ BC au­<lb/>getur; ergo, &c. Dixi, donec exhau&longs;tum &longs;it totum crus CB <lb/>oppo&longs;itum: nam illo exhau&longs;to, minuitur &longs;emper magis ac magis <lb/>celeritas effluxus per os A, quoniam minuitur perpendiculum <lb/>aquæ, ac proinde &longs;emper minùs ac minùs premitur aqua apud A. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>In &longs;iphone inver&longs;o pluribus tubis quàm duobus compo&longs;ito eadem. <lb/>& ob eandem cau&longs;am contingunt, vt pat&ecedil;bit con&longs;ideranti.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis mixti inæqualium crurium proprie­<lb/>tates a&longs;&longs;ignare.<emph.end type="center"/></s></p> <p type="main"> <s>SIphonum mixtorum crura vel &longs;unt omnia æqualia, vel omnia </s></p> <p type="main"> <s> <arrow.to.target n="marg165"/><lb/>inæqualia, vel aliqua æqualia, aliqua inæqualia. De proprie­<lb/>tatibus &longs;iphonis, cuius omnia crura &longs;unt æqualia, agemus Pro­<lb/>po&longs;it. &longs;equenti; de reliquorum proprietatibus hîc agemus. Sit <lb/>igitur &longs;iphon AKDI. Hic &longs;i integer maneat, habebit omnia cru­<lb/>ra inæqualia: &longs;i truncetur in E, aut in B, habebit aliqua crura <lb/>æqualia, alia inæqualia: &longs;i truncetur in F, aut N, habebit iterum <lb/>omnia crura inæqualia. </s></p> <p type="margin"> <s><margin.target id="marg165"/><emph type="italics"/>Siphonis mi­<lb/>xti variæ <lb/>&longs;pecies.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Prima Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI&longs;iphon AKDI maneatinteger, & repleatur totus aquâ, efflu­<lb/>et ea totaper os I. Ratio e&longs;t, quia perpendiculum DI lon­<lb/>gius e&longs;t quàm perpendiculum DK, ut &longs;upponitur; ergo plùs <lb/>premitur aqua apud I, quàm apud K, per dicta Propo&longs;it. III. <lb/>præcedente, Propriet. I. & Capite I. Propriet. III. ac proinde <lb/>aqua DI trahit aquam DK; quâ tractâ, &longs;equitur etiam aqu<gap/><lb/>KA, tum proprio pondere, tum ad vacuum impediendum. </s></p> <p type="main"> <s><emph type="center"/>Secunda Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI crus DI truncetur in B, ita vtos B &longs;it eiusdem altitudinis <lb/>&longs;upra horizontom cum ore A, & totus &longs;iphon AKDB replea­<lb/>tur aquá; e&longs;t qui putat non effluere ex B, &longs;ed effluere ex A, du­<lb/>rareque fluxum donec &longs;uperficies aquæ B pervenerit ad C, <lb/>hoc e&longs;t, donec effluxerit tantum aquæ, quantum e&longs;tintra BDC, <pb xlink:href="051/01/113.jpg" pagenum="82"/> <arrow.to.target n="fig20"/><lb/>tunc enim, ait, ce&longs;&longs;abit fluxus ex A, <lb/>&longs;tabitque aqua in æquilibrio intra <lb/>AKC. Quòd non effluat aqua ex B, <lb/>clarum e&longs;t, quia perpendiculum BD <lb/>brevius e&longs;t quàm <expan abbr="perpendiculũ">perpendiculum</expan> DK, <lb/>ergò aqua DB non pote&longs;t trahere a­<lb/>quam DK, & multò minùs <expan abbr="aquã">aquam</expan> DKA. <lb/>Quòd autem effluat ex A, <expan abbr="ration&etilde;">rationem</expan> <lb/>a&longs;&longs;ignat, quia perdendiculum DK <lb/>longius e&longs;t quàm perpendiculum AK; <lb/>ergo aqua DK fortiùs premit deor­<lb/>&longs;um ver&longs;us K, quàm aqua AK, ac <lb/>proinde aqua AK debet cedere, & <lb/>effluere ex A, ac &longs;equi tota reliqua <lb/>aqua, nè vacuum detur. Quòd de­<lb/>nique ce&longs;&longs;et fluxus aquæ ex A, quan­<lb/>do &longs;uperficies B pervenerit ad C, <lb/>rationem dat, quia tunc perpendicu­<lb/>la CK, AK, &longs;unt æqualia. </s></p> <figure id="id.051.01.113.1.jpg" xlink:href="051/01/113/1.jpg"/> <p type="main"> <s>Experentiâ tamen con&longs;tat, in dicto ca&longs;u <expan abbr="nullã">nullam</expan> effluere aquam <lb/>ex Siphone AKDB, neque per os B, neque per os A. Rationem <lb/>ad&longs;igno, quia aqua quæ e&longs;t in AKC, ita e&longs;t librata, vt à poten­<lb/>tia quantumvis parva moveri, & ex vna parte attolli po&longs;&longs;it; qua­<lb/>re humido CD &longs;upra &longs;e po&longs;ito non re&longs;i&longs;tit. I am verò quoniam <lb/>perpendicula crurium DC, DB æqualia &longs;unt, aqua in C æquè <lb/>premitur ac in B; quare cùm nec infra B, nec infra C vllum <lb/>&longs;it impedimentum extrin&longs;ecum, præter aërem (iam enim o&longs;ten­<lb/>&longs;um e&longs;t, aquam CKA non re&longs;i&longs;tere humido CD de&longs;cendenti) <lb/>pariter ex A & B aqua deberet effluere; quod fieri non pote&longs;t <lb/>absque vacuo. Patet ergo cur aqua con&longs;i&longs;tat. Dices, in hoc <lb/>di&longs;cur&longs;u committitur manife&longs;tus paralogi&longs;mus; dividitur enim <lb/>mente crus DK in puncto C, & di&longs;curritur ac &longs;i realiter ibidem <lb/>e&longs;&longs;et facta divi&longs;io; Natura non dividit aquam cruris DK in pun­<lb/>cto C, nec propter no&longs;tras intellectuales divi&longs;iones mutat ope- <pb xlink:href="051/01/114.jpg" pagenum="83"/>randi vim, cùm non ob&longs;tante illa divi&longs;ione revera crus DK lon­<lb/>gius &longs;it, quàm crus AK. Re&longs;pondeo, quamvis DK longius &longs;it <lb/>quàm crus AK, eius tamen activitati &longs;eu pre&longs;&longs;ioni deor&longs;um non <lb/>&longs;olùm re&longs;i&longs;tit crus AK, &longs;ed etiam crus DB; illud, nè aqua KA <lb/>pellatur &longs;ur&longs;um; hoc, nèaqua AD trahatur &longs;ur&longs;um: vnde per­<lb/>pendiculum DK habet duplicem re&longs;i&longs;tentiam, &longs;cilicet DB, & AK; <lb/>quæ duæ re&longs;i&longs;tentiæ æquant eius activitatem, & con&longs;equenter <lb/>impediunt motum aquæ DK, eiusque fluxum, &longs;ive per os A, &longs;i­<lb/>ve per os B. Divi&longs;io autem intellectualis cruris DK in puncto <lb/>C fit &longs;olùm ad o&longs;ten dendum quomodo duplex prædicta <expan abbr="re&longs;i&longs;t&etilde;-tia">re&longs;i&longs;ten­<lb/>tia</expan> æquivaleat activitati totius cruris DK. </s></p> <p type="main"> <s><emph type="center"/>Tertia proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI crus DI truncetur in F, vt os F &longs;it inferius quàm os A; <lb/>idem qui &longs;uprà putat non effluere aquam ex F, &longs;ed ex A, du­<lb/>rareque ut antea fluxum, donec &longs;uperficies F pervenerit v&longs;que <lb/>ad C. Rationem eandem dat cum illa, quam ad&longs;ignavit paulò <lb/>antè. </s></p> <p type="main"> <s>Eâdem tamen experientiä con&longs;tat, aquam in hoc ca&longs;u ef­<lb/>fluere ex F, donec aqua cruris AK de&longs;cenderit in H ad pa­<lb/>rem cum F altitudinem. Ratio e&longs;t, quia humidum in F ma­<lb/>gis premitur, quàm in C, id e&longs;t, quàm in A, ob longius per­<lb/>pendiculum DF, quàm DC; quare humidum in F de&longs;cen­<lb/>det, <expan abbr="trahet&qacute;ue">trahetque</expan> humidum reliquum, nè detur vacuum. Nec re­<lb/>fert, quòd dividatur intellectu crus DK in puncto C, & compa­<lb/>retur crus DF cum parte DC &longs;olùm, ac &longs;i & Natura ibidem <lb/>divi&longs;i&longs;&longs;et crus DK; hoc enim &longs;olùm fit ob rationem paulò antè <lb/>allatam. </s></p> <p type="main"> <s><emph type="center"/>Quarta Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>SI crus DI truncetur in E, vt os E habeat eandem altitudinem <lb/>cum puncto K; ille idem qui &longs;uprà exi&longs;timat nihil effluere, <expan abbr="neq;">neque</expan> <lb/>ex E, neque ex A. Ratio eius e&longs;t, quia perpendicula DE, DK &longs;unt <lb/>æqualia; ergo aqua apud E non plùs premitur quàm apud K, nec <lb/>apud K plùs quàm apud E; ergo neque ex E, neque ex A <lb/>effluere pote&longs;t aqua, nè æqualis potentia dicatur &longs;upera&longs;&longs;e æ­<lb/>qualem. </s></p> <pb xlink:href="051/01/115.jpg" pagenum="84"/> <p type="main"> <s>Dicendum tamen, eâdem experientiá duce, effluxuram <lb/>aquam ex E, duraturumque fluxum, donec &longs;uperficies A per­<lb/>venlat ad K, & non vltrà. Rationem ad&longs;igno, quia perpen­<lb/>diculum DE longius e&longs;t, quàm DC, dum plenus e&longs;t tubus. Dum <lb/>autem aqua de&longs;cenderit ad K, perpendicula DK, DE &longs;unt æ­<lb/>qualia. </s></p> <p type="main"> <s><emph type="center"/>Quinta Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Si crus DI truncetur in N, effluet aqua ex A, donec <lb/>&longs;uperficies N perveniat in C, vbi con&longs;i&longs;tet. Ratio e&longs;t, quia <lb/>altitudo aquæ DK, vel potiùs DC, maior e&longs;t, quàm altitudo DN. </s></p> <p type="main"> <s><emph type="center"/>Sexta Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Effluxus aquæ in prædictis ca&longs;ibus, &longs;ive ex ore A, &longs;ive ex <lb/>ore F, E, I, non e&longs;t vniformis, &longs;ed difformis, eo pror&longs;us modo, <lb/>quo diximus in Propo&longs;it. III. præced. Proprietate IV. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis mixti æqualium crurium proprieta­<lb/>tes a&longs;&longs;ignare.<emph.end type="center"/></s></p> <figure id="id.051.01.115.1.jpg" xlink:href="051/01/115/1.jpg"/> <p type="main"> <s>EX &longs;iphone mixto æqualium crurium, qua­<lb/>lis e&longs;t ABCD, in appo&longs;ito &longs;chemate, &longs;i a­<lb/>quâ totus repleatur; effluit aqua ex D. Ra­<lb/>tio e&longs;t, quia licet tam perpendicula AB, CB, <lb/>quàm perpendicula CD, CB, &longs;int æqualia; <lb/>quia tamen aqua CB æquilibrata e&longs;t ab aqua <lb/>AB, poterit à qualibet potentia facillimè <lb/>moveri, ideoque ab aqua CD deor&longs;um ni­<lb/>tente poterittrahi, & effluere ex D; & ita de <lb/>facto contingit, vt experientia docet. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Inver&longs;i Siphonis, va&longs;i vno crure impo&longs;i­<lb/>to, proprietates a&longs;&longs;ignare.<emph.end type="center"/><lb/> <arrow.to.target n="marg166"/></s></p> <p type="margin"> <s><margin.target id="marg166"/><emph type="italics"/>Crus inter­<lb/>num, & <lb/>crus exter­<lb/>num &longs;ipho­<lb/>nis<emph.end type="italics"/></s></p> <p type="main"> <s>OBvia &longs;unt quæ dicam, ideò breviter expediam. E&longs;to igitur <lb/>vas aquâ plenum ABCD, cui inver&longs;i &longs;iphonis crus vnum FE <lb/>immergatur, alterum FN foris maneat. Vocetur autem crus <pb xlink:href="051/01/116.jpg" pagenum="85"/> <arrow.to.target n="fig21"/><lb/>FE internum, crus verò FN <lb/>externum. Huius fiphonis <lb/>variæ &longs;unt proprietates, provt <lb/>variè difponi poterit crus eius <lb/>externum. </s></p> <figure id="id.051.01.116.1.jpg" xlink:href="051/01/116/1.jpg"/> <p type="main"> <s><emph type="center"/>Prima Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Si enim crus exter­<lb/>num FN maneat integrum, <lb/>& ex ore N ex&longs;ugatur aër; &longs;e­<lb/>quetur a<gap/> va&longs;is, ob vacui <lb/>metum, & tota effluet, aut pœ­<lb/>nè tota (donec nimirum aquæ <lb/>&longs;uperficies &longs;uperior CD de&longs;cen­<lb/>derit v&longs;que ad o&longs;culum E) &longs;i <lb/>internum crus fundum pœnè <lb/>tangat. Ratio e&longs;t, quia per­<lb/>pendiculum externi cruris e&longs;t <lb/>longius quàm interni. Si to­<lb/>tus &longs;iphon aquâ impleatur, & <lb/>vtrumque orificium claudatur, ac deinde minus crus EF aquæ <lb/>imponatur, maiori foras prominente, & &longs;imul vtrumque orifi­<lb/>cium aperiatur; idem fiet. </s></p> <p type="main"> <s>Effluet tamen inæqualiter, cum perpetuo <expan abbr="nimirũ">nimirum</expan> celerita­<lb/>tis decremento, quia perpendiculum aquæ cruris interni, altitu­<lb/>do nempe aquæ à puncto P u&longs;que ad &longs;uperficiem &longs;uperiorem <lb/>aquæ va&longs;is (hæc enim &longs;ola premit actu, reliquæ verò inferiores <lb/>actu non premunt, per dicta cap. 1. Proprietate V.) &longs;emper ma­<lb/>gis ac magis cre&longs;cit, ac proinde &longs;emper magis magi&longs;que re&longs;i&longs;tit <lb/>perpendiculo aquæ cruris externi. </s></p> <p type="main"> <s>Quò verò crus externum longius fuerit infra &longs;uperficiem </s></p> <p type="main"> <s> <arrow.to.target n="marg167"/><lb/>&longs;uperiorem aquæ va&longs;is, eò fluet aqua celeriùs, & æqualibus tem­<lb/>poribus copio&longs;iùs: quia tunc eò magis perpendiculum externi <lb/>&longs;uperabit perpendiculum interni cruris in longitudine, & vi pre­<lb/>mendi deor&longs;um. Non tamen &longs;ufficit, ut crus externum &longs;it qua- <pb xlink:href="051/01/117.jpg" pagenum="86"/>cunque ratione longius crure interno, &longs;ed nece&longs;&longs;arium omnino <lb/>e&longs;t ut perpendiculum externi cruris longius &longs;it perpendiculo in­<lb/>terni, juxta dicta &longs;uprà Protheoria I. §. VI. </s></p> <p type="margin"> <s><margin.target id="marg167"/><emph type="italics"/>Aqua in<gap/><lb/>quali cele­<lb/>ritate efflu­<lb/>it ex crure <lb/>externo &longs;i­<lb/>phonis,<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Secunda Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Si crus externum FN decurtetur in K, & internum tan­<lb/>gat ferè fundum in E, & ex ore K extrahatur aer; &longs;equetur <lb/>aqua u&longs;que ad os K, propter vacui metum, & tota ferè effluet, <lb/>donec <expan abbr="nimirũ">nimirum</expan> perveniat &longs;uprema aquæ &longs;uperficies <expan abbr="u&longs;q;">u&longs;que</expan> ad o&longs;cu­<lb/>lum E. Ratio e&longs;t, quia perpendiculum cruris externi longius <lb/>e&longs;t quàm interni. At po&longs;tquam aqua pervenerit u&longs;que ad o&longs;cu­<lb/>lum E, nihil amplius effluit, quia perpendicula FE, FK &longs;unt <lb/>æqualia. Hærebit ergo aqua in æquilibrio in utroque crure. </s></p> <p type="main"> <s><emph type="center"/>Tertia Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Si crus externum FN decurtetur in H, & internum <gap/><lb/>infra lineam LM, aut pertingat &longs;olummodò u&longs;que ad d<gap/><lb/>lineam; vas tamen &longs;it plenum u&longs;que ad lineam CD, aut<gap/><lb/>aqua &longs;it &longs;upra lineam LM; effluet aqua per os H, donec &longs;upre­<lb/>ma aquæ va&longs;is &longs;uperficies perveniat u&longs;que ad lineam LM, & non <lb/>ampliùs. Ratio e&longs;t, quia antequam dicta aquæ &longs;uperficies per­<lb/>veniat ad lineam LM, perpendiculum cruris externi e&longs;t &longs;em­<lb/>per longius perpendiculo cruris interni; quando verò de&longs;cendit <lb/>jam ad dictam lineam, am bo perpendicula &longs;untæqualia. Fluxus <lb/>porrò difformitas quoad celeritatem aut tarditatem eadem e&longs;t, <lb/>quæ antea. </s></p> <p type="main"> <s><emph type="center"/>Quarta Proprietas.<emph.end type="center"/></s></p> <p type="main"> <s>Si crus externum decurtetur in G, ut &longs;it eju&longs;dem altitudi­<lb/>nis &longs;upra Horizontem cum &longs;uperficie humidi CD, & aqua at­<lb/>trahatur in G; nihil effluet, quia perpendicula &longs;unt æqualia: <lb/>quare aqua hærebit in æquilibrio in utroque crure. </s></p> <p type="main"> <s><emph type="center"/>Corollarium I.<emph.end type="center"/></s></p> <p type="main"> <s>Ex his colligitur primò, Si vas &longs;it plenum &longs;olummodò u&longs;que <lb/> <arrow.to.target n="marg168"/><lb/>ad lineam LM, & &longs;iphonis crus externum decurtetur in H, vel <lb/>G, vel O, internum verò pertingat u&longs;que ad fundum; nihil <lb/>po&longs;&longs;e effluere ex crure externo. </s></p> <pb xlink:href="051/01/118.jpg" pagenum="87"/> <p type="margin"> <s><margin.target id="marg168"/><emph type="italics"/>Perpendicu <lb/>li exce&longs;&longs;um <lb/>tuetur Na­<lb/>tura in a­<lb/>quæ fluxu.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium II.<emph.end type="center"/></s></p> <p type="main"> <s>Colligitur &longs;ecundò, quàm pertinax &longs;it Natura, vel con&longs;tans <lb/>potiùs, in retinendo atque tuendo perpendiculi exce&longs;&longs;u, nè mi­<lb/> <arrow.to.target n="marg169"/><lb/>nor aut æqualis potentia dicatur vici&longs;&longs;e majorem. </s></p> <p type="margin"> <s><margin.target id="marg169"/><emph type="italics"/>Perpendicu­<lb/>lo, non copia <lb/>aquæ Natu­<lb/>ra pugnat, <lb/>ac vincit, in <lb/>hydrauli­<lb/>cis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium III.<emph.end type="center"/></s></p> <p type="main"> <s>Colligitur tertiò, quomodo Natura in Hydraulicis pugnet, <lb/>ac &longs;uperet, non aquarum copiâ, &longs;ed altitudine perpendiculari. </s></p> <p type="main"> <s><emph type="center"/>Corollarium IV.<emph.end type="center"/></s></p> <p type="main"> <s>Colligitur quartò, &longs;iphonis operationes hydraulicas ad li­<lb/>bræ operationes commodè revocari po&longs;le, uti mox dicemus <lb/>Propo&longs;it: VIII. <expan abbr="&longs;eq.">&longs;eque</expan> </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/> <arrow.to.target n="marg170"/></s></p> <p type="margin"> <s><margin.target id="marg170"/><emph type="italics"/>Fonticulus <lb/>duplex ope <lb/>&longs;iphonis in­<lb/>ver&longs;i.<emph.end type="italics"/></s></p> <figure id="id.051.01.118.1.jpg" xlink:href="051/01/118/1.jpg"/> <p type="main"> <s>Hinc etiam patet, <lb/>qua ratione &longs;iphonis <lb/>inver&longs;i præ&longs;idio fonti­<lb/>culus duplex exhiberi <lb/>po&longs;&longs;it, &longs;i nimirum crus <lb/>brevius AB indatur <lb/>vitreo protuberanti <lb/>ventri BC, habeatque <lb/>intra ventrem &longs;tricti&longs;&longs;i­<lb/>mum o&longs;culum B aper­<lb/>tum; deinde ex eodem <lb/>ventre derivetur crus <lb/>longius DE in curva­<lb/>tum inferiùs, & apud E <lb/><expan abbr="de&longs;in&etilde;s">de&longs;inens</expan> in o&longs;culum an­<lb/>gu&longs;tum. Si enim hu­<lb/>ju&longs;modi &longs;iphon impo­<lb/>natur va&longs;i pleno, & ex <lb/>o&longs;culo E &longs;ugatur aër; <lb/>a&longs;cendet aqua per crus AB, & in ventre exiliet radiosâ virgulâ <lb/>vix a&longs;pectabili, indeque &longs;e demittet in crus alterum longius DE, <lb/>cogeturque &longs;ua propendente demi&longs;&longs;ione ad ejectionem eò altio­<lb/>rem, quò profundiùs de&longs;cendet. </s></p> <pb xlink:href="051/01/119.jpg" pagenum="88"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Cau&longs;am ad&longs;ignare, cur quando o&longs;culum externi cruris <lb/>&longs;iphonis inver&longs;i, e&longs;t altius, aut æquè altum ac aquæ &longs;uperficies <lb/>&longs;uprema in va&longs;e, aqua non fluat; quando verò <lb/>e&longs;t demi&longs;&longs;ius, fluat.<emph.end type="center"/></s></p> <p type="main"> <s>VIdimus, experientiam docere, quando perpendiculum cru­<lb/>ris externi &longs;iphonis inver&longs;i, e&longs;t minus, aut æquale perpendi­<lb/>culo cruris interni, u&longs;que ad &longs;upremam aquæ &longs;uperficiem aquam <lb/>non effluere po&longs;&longs;e per os externi cruris, ce&longs;&longs;ante &longs;uctu, &longs;eu attra­<lb/>ctione; quando verò perpendiculum externi e&longs;t majus quàm in­<lb/>terni cruris in &longs;en&longs;u expo&longs;ito, fluere donec æqualia fiant perpen­<lb/>dicula, aut donec tota effluxerit aqua ex va&longs;e. Quæritur nunc <lb/>hujus phænomeni cau&longs;a. <lb/> <arrow.to.target n="marg171"/></s></p> <p type="margin"> <s><margin.target id="marg171"/><emph type="italics"/>Siphonis <lb/>crus longius <lb/>&longs;uperat bre­<lb/>vius, non <lb/>capacius mi <lb/><gap/> capax.<emph.end type="italics"/></s></p> <p type="main"> <s>Hero Alexandrinus in libello de Spiritalibus cap 1. ait, <lb/>quo&longs;dam putare, cau&longs;am e&longs;&longs;e, quòd aqua cruris externi debeat <lb/>trahere aquam cruris interni, ac proinde illa debeat e&longs;&longs;e major <lb/>ac copio&longs;ior, quàm hæc. Sed hoc minimè verum e&longs;&longs;e, patet ex <lb/>eo (quod etiam Hero advertit) quòd licet crus externum &longs;it lon­<lb/>gè amplius atque capacius interno, <expan abbr="multo&qacute;ue">multoque</expan> plùs aquæ conti­<lb/>neat; &longs;i tamen longius non e&longs;t, nequaquam effluit ex ip&longs;o aqua, <lb/>&longs;ed ubi ce&longs;&longs;at violenta &longs;uctio, &longs;eu tractio, tota refluit per crus in­<lb/>ternum longius intra vas. Non ergo externum crus &longs;uperat in­<lb/>ternum, quòd aquæ plùs contineat. Itaque videamus natura­<lb/>lem cau&longs;am & genuinam, ex Heronis primò, deinde ex no&longs;tra <lb/>&longs;ententia. </s></p> <p type="main"> <s>Diximus cap. 1. Propriet. II. aquæ continuæ & quie&longs;centis <lb/>&longs;uperficiem &longs;uperiorem e&longs;&longs;e &longs;phæricam (etiam in parvis va&longs;is, & <lb/>receptaculis, licet in&longs;enfibiliter) centrum habentem idem quod <lb/>Terra, &longs;eu globus Terraqueus; non quie&longs;centem verò aquam <lb/>tam diu fluere, donec partes continuæ in una &longs;uperficie &longs;phærica <lb/>con&longs;tituantur, hoc e&longs;t, donec omnes extimæ &longs;uperficiei partes <lb/>continuæ æqualiter di&longs;tent à centro Terræ. Hoc po&longs;ito putat <lb/>Hero, cau&longs;am ob quam, quando externi cruris orificium e&longs;t <pb xlink:href="051/01/120.jpg" pagenum="89"/>æquè altum ac &longs;uperficies &longs;uperior aquæ va&longs;is, hoc e&longs;t, quando </s></p> <p type="main"> <s> <arrow.to.target n="marg172"/><lb/>externum crus e&longs;t æquale interno quoad longitudinem, u&longs;que <lb/>ad aquæ &longs;uperficiem &longs;upremam va&longs;is, aqua non effluat ex crure <lb/>externo, etiam&longs;i &longs;iphon &longs;it plenus aquâ, e&longs;&longs;e, quia tunc aqua &longs;i­<lb/>phonis continuatur cum aqua va&longs;is, & utriu&longs;que &longs;uperficies ex­<lb/>trema æqualiter di&longs;tat à centro Mundi: Cau&longs;am verò cur, quan­<lb/>do externi cruris orificium e&longs;t demi&longs;&longs;ius &longs;uperficie extrema aquæ <lb/>va&longs;is, effluat, e&longs;&longs;e, quia tunc &longs;uperficies aquæ va&longs;is e&longs;t altior, quàm <lb/>&longs;uperficies aquæ cruris externi, cum cujus aqua continuatur, ac <lb/>proinde tam diu fluere debet aqua va&longs;is, po&longs;tquam &longs;emel fluere <lb/>cœpit, donec &longs;uperficies fiant æqualiter di&longs;tantes à centro Ter­<lb/>ræ. Ob contrariam ergo cau&longs;am, &longs;ecundùm Heronem non <lb/>effluit aqua ex crure externo breviore, &longs;ed refluit intra vas quia <lb/>nimirum &longs;uprema &longs;uperficies aquæ va&longs;is e&longs;t declivior, quàm &longs;u­<lb/>perficies aquæ cruris externi. </s></p> <p type="margin"> <s><margin.target id="marg172"/><emph type="italics"/>Heronis opi­<lb/>nio circa a­<lb/>quæ fluxum <lb/>è crure ex­<lb/>terno &longs;ipho­<lb/>nis.<emph.end type="italics"/></s></p> <p type="main"> <s>Cœterùm cur aqua in &longs;ecundo ca&longs;u, ex va&longs;e a&longs;cendat ad <lb/>&longs;iphonis &longs;ummitatem, contra ejus naturam, indeque de&longs;cendat <lb/>ad orificium u&longs;que externi cruris, non e&longs;t ob cau&longs;am jam ad&longs;igna­<lb/>tam, &longs;ed ut impleat, aut impediat vacuum, &longs;eu quia trahitur vio­<lb/>lenter ad impediendum, aut implendum vacuum. Quoniam <lb/>enim ex crure externo extrahitur aër, trahit is &longs;ecum, nè vacuus <lb/>maneat &longs;iphon, & di&longs;continuentur corpora, nempe aër & aqua, <lb/>trahit inquam &longs;ecum aquam u&longs;que ad orificium cruris externi; <lb/>quò ubi pervenerit, nullam ampliùs violentiam patitur ab aëre, <lb/>nec ab alio extrin&longs;eco agente, &longs;ed naturæ &longs;uæ relinquitur, ut pars <lb/>illa incipiat, aut pro&longs;equatur fluxum, cujus &longs;uperficies extre­<lb/>ma minùs di&longs;tat à centro Mundi, duretque fluxus, donec am­<lb/>bæ &longs;uperficies æquales fiant. </s></p> <p type="main"> <s><emph type="center"/>Experimentum.<emph.end type="center"/></s></p> <p type="main"> <s>ES&longs;e porrò hanc, quam ad&longs;ignavit Hero, genuinam dicti <lb/>phænomeni cau&longs;am, confirmat ip&longs;e tali Experimento. <emph type="italics"/>Si <lb/> <arrow.to.target n="marg173"/><lb/>&longs;umentes,<emph.end type="italics"/> inquit, <emph type="italics"/>duo va&longs;a<emph.end type="italics"/> (cuju&longs;modi &longs;unt A & B in appo­<lb/>&longs;itis figuris) <emph type="italics"/>injiciemus humidum in utrumque ip&longs;orum, & implentes<emph.end type="italics"/> <pb xlink:href="051/01/121.jpg" pagenum="90"/><emph type="italics"/>&longs;iphonem, digiti&longs;que ip&longs;ius o&longs;cula comprehendentes, demittemus alte­<lb/>rum crus in unum dictorum va&longs;orum adeo, ut aquâ demergatur; alte­<lb/>rum verò in alterum vas,<emph.end type="italics"/> (ut aqua etiam demergatur, prout in <lb/>appo&longs;itis figuris apparet;) <emph type="italics"/>fiet tota aqua continua; utrumque enim <lb/>humidorum, quæ &longs;unt in væ&longs;ibus,<emph.end type="italics"/> (ita interpres) <emph type="italics"/>conjungitur cum eo, <lb/>quod e&longs;t in &longs;iphone, ita ut totum continuum fiat. Si igitur &longs;uperficies<emph.end type="italics"/><lb/> <arrow.to.target n="fig22"/><lb/><emph type="italics"/>humidorum, quæ priùs erant in va­<lb/>&longs;ibus, in una &longs;uperficie con&longs;i&longs;tant,<emph.end type="italics"/><lb/>ut in prima figura; <emph type="italics"/>quie&longs;cet & &longs;ic <lb/>utraque ip&longs;arum demer&longs;o &longs;iphone: <lb/>&longs;in minùs,<emph.end type="italics"/> ut in &longs;ecunda figura; <lb/><emph type="italics"/>quoniam aqua continua facta e&longs;t, <lb/>nece&longs;&longs;ariò ob continuitatem in hu­<lb/>miliorem locum fluet, quou&longs;&queacute; vel <lb/>omnis aqua, quæ in va&longs;ibus, in una <lb/>&longs;uperficie &longs;it, vel alterum va&longs;orum <lb/><expan abbr="exinãiat">exinaniat</expan><gap/>r,<emph.end type="italics"/> illud videlicet, quod <lb/>altiori fuerit loco. <emph type="italics"/>Fiant igitur <lb/>in una &longs;uperficie humida, quæ &longs;unt <lb/>in va&longs;ibus; quie&longs;cent utique, ita <lb/>ut etiam humidum, quod e&longs;t in &longs;i­<lb/>phone, &longs;imul quie&longs;cat. Quòd &longs;i<emph.end type="italics"/><lb/> <arrow.to.target n="marg174"/><lb/><emph type="italics"/>quis mente concipiat &longs;iphonem <gap/>&longs;­<lb/>&longs;ectum juxta &longs;uperficies humidorum, quæ &longs;unt in va&longs;ibus; & ita qui­<lb/>e&longs;cet humidum, quod e&longs;t in &longs;iphone: ergo & &longs;iphone ip&longs;o &longs;u&longs;pen&longs;o, & <lb/>in neutram partem inclinato, rur&longs;us quie&longs;cet humidum, &longs;ive æqualem <lb/>omnino habens latitudinem, &longs;ive alterum crus altero multo majus &longs;it; <lb/>non enim in hoc cau&longs;a e&longs;t, cur humidum quie&longs;cat, &longs;ed in eo, quòd ip­<lb/>&longs;ius o&longs;cula æqualiter jaceant.<emph.end type="italics"/> Hæc Hero. lege etiam quæ &longs;equun­<lb/>tur apud ip&longs;um in eodem cap. 1. </s></p> <p type="margin"> <s><margin.target id="marg173"/>Experimen <lb/>tum circa <lb/>aquæ <expan abbr="fluxũ">fluxum</expan> <lb/>ex &longs;iphone.</s></p> <p type="margin"> <s><margin.target id="marg174"/>Siphon in­<lb/>ver&longs;us æ­<lb/>qualium <lb/>crurium <lb/>longitu di­<lb/>ne, inæqua <lb/>lium capa­<lb/>citate, reti­<lb/>net aquam <lb/>&longs;u&longs;pen&longs;am <lb/>&longs;ecundum <lb/>Heronem.</s></p> <figure id="id.051.01.121.1.jpg" xlink:href="051/01/121/1.jpg"/> <p type="main"> <s>Sed hæc cau&longs;a ex Herone ad&longs;ignata non videtur e&longs;&longs;e ve­<lb/> <arrow.to.target n="marg175"/><lb/>ra, aut &longs;altem non e&longs;t adæquata. Primò enim, &longs;i ideo fluit <lb/>aqua ex crure longiore, AD, &longs;eu potius CD, &longs;ecundæ figuræ, <lb/>quia &longs;uperfies extrema aquæ ip&longs;ius non e&longs;t æqualis &longs;uperficiei <pb xlink:href="051/01/122.jpg" pagenum="91"/>extremæ aquæ alterius cruris, BF, &longs;eu potius EF, &longs;ed demi&longs;&longs;ior; <lb/>ergo quando &longs;iphon &longs;ive æqualium, &longs;ive inæqualium crurium, <lb/>aqu&adot; plenus, & utrimque compre&longs;&longs;is digitis obturatus, imponi­<lb/>tur duobus prædictis va&longs;is aqu&adot; plenis, quorum unius &longs;uperficies <lb/>&longs;uprema aquæ altior e&longs;t, quàm alterius, effluitque aqua intra vas <lb/>demi&longs;&longs;ius, eò quòd alterius &longs;uperficies &longs;uprema altior e&longs;t, & ad <lb/>decliviorem locum tendit, nititurque &longs;uperficiem &longs;uam adæ­<lb/>quare &longs;uperficiei alterius va&longs;is humilioris; ergo inquam, quando <lb/>hoc contingit, aqua ex va&longs;e altiore a&longs;cendit naturaliter & inna­<lb/>to appetitu ad &longs;iphonis &longs;uperiorem partem, indeque de&longs;cendit <lb/>intra vas humilius; naturaliter enim aquæ partes altiores fluunt <lb/>ad loca decliviora. Deinde &longs;i illa e&longs;t cau&longs;a adæquata, cur quan­<lb/>do &longs;iphon ina qualium crurium repletur aquâ, & &longs;ecundùm <lb/>longius crus immergitur aquæ, <gap/>revius verò extra <lb/>in aëre relinquitur, cur<gap/>quam, no<gap/>uit aqua per externum, <lb/>ubi nullum e&longs;t impedimentum pr<gap/>te<gap/>erem? pote&longs;t enim aqua <lb/>per exte num fluere <gap/>d loca decliviora, & fundare unam conti­<lb/>nuam &longs;uperficiem di&longs;tinctam à &longs;uperficie, quæ in va&longs;e e&longs;t; & <lb/>præterea inclinationem habet ad de&longs;cendendum, non verò ad <lb/>a&longs;cendendum. Præterea, cur quando &longs;iphon inæqualium cru­<lb/>rium repletur aqua, & tenetur inver&longs;us in aëre, non effluit aqua <lb/>ex crure breviori, cum ejus aqua plùs di&longs;tet à centro Terræ, <lb/>quàm aqua cruris longioris? Alia ergo cau&longs;a ad&longs;ignari debet, cur <lb/>aqua cruris longioris, &longs;eu externi, &longs;eu interni, vincataquam cru­<lb/>ris brevioris; quam paulò po&longs;t dabimus. </s></p> <p type="margin"> <s><margin.target id="marg175"/><emph type="italics"/>Heronis opi­<lb/>nio exami­<lb/>natur.<emph.end type="italics"/></s></p> <p type="main"> <s>Qui tamen Heronis &longs;ententiam tueri volet, ad has ratio­<lb/>nes in contrarium allatas re&longs;pondere poterit, ut &longs;equitur. Nem­<lb/>pe ad primam, aquam cruris brevioris non a&longs;cendere naturali­<lb/>ter, &longs;ed tractam ab aqua cruris longioris AD, &longs;eu CD, ad va­<lb/>cuum in &longs;iphone impediendum, & ad tuendam continuitatem <lb/>partium aquæ aqua enim cruris longioris AD, &longs;eu CD, de&longs;cen­<lb/>dit naturaliter (utpote tendens ad locum decliviorem) &longs;ecum­<lb/>que trahit reliquam aquam, quia &longs;uprema &longs;uperficies va&longs;is A, <lb/>cum qua continuatur aqua &longs;iphonis, & va&longs;is B, e&longs;t declivior, <pb xlink:href="051/01/123.jpg" pagenum="92"/>&longs;uprema verò &longs;uperficies va&longs;is B e&longs;t altior, & debet fieri æqua­<lb/>litas inter ip&longs;as: quæ non fieret, &longs;i aqua &longs;iphonis BF, &longs;eu EF, de­<lb/>&longs;cenderet. </s></p> <p type="main"> <s>Ad &longs;ecundam, non effluere aquam per brevius, &longs;ed per lon­<lb/>gius crus, quia aqua amat continuitatem &longs;uarum partium, & ap­<lb/>petit habere &longs;uperficiem &longs;upremam omnium partium æqualiter <lb/>di&longs;tantem à centro Terræ; quorum utrumque obtinet, &longs;i ef­<lb/>fluit aqua per longius crus; neutrum, &longs;i per brevius. </s></p> <p type="main"> <s>Ad Tertiam, ideo non effluere aquam è crure breviore, &longs;ed <lb/>è longiore, quia aqua cruris brevioris e&longs;t altior, & aqua cruris <lb/>longioris declivior: curruntautem aquæ continuatæ partes alti­<lb/> <arrow.to.target n="marg176"/><lb/>ores ad decliviores naturaliter, & non hæ ad illas. </s></p> <p type="margin"> <s><margin.target id="marg176"/><emph type="italics"/>Authoris o­<lb/>pinio circa <lb/>aquæ <expan abbr="fluxũ">fluxum</expan> <lb/>è crure ex­<lb/>terno longio <lb/>re &longs;iphonis.<emph.end type="italics"/></s></p> <p type="main"> <s>Sed quidquid &longs;it de hac Heronis &longs;ententia, mihi magis pla­<lb/>cet &longs;equens ratio allati phænomeni, quæ univer&longs;alis e&longs;t & in <lb/>omnibus &longs;imilibus ca&longs;ibus locum habet, ut vidimus in præce­<lb/>dentibus, & iterum videbimus infrà hoc eodem capite Propo­<lb/>&longs;it. 13. & 14. Pro qua recolendum e&longs;t, quod diximus &longs;uprà Ca­<lb/>pite 1. Proprietate IV. ex Archimede, aquæ & humidi cuju&longs;cun­<lb/>que partem unamquamque premi humido &longs;upra ip&longs;am exi&longs;tente <lb/>ad perpendiculum, &longs;i humidum &longs;it de&longs;cendens in aliquo, aut cer­<lb/>tè nullum habeat impedimentum, ut de&longs;cendat. </s></p> <p type="main"> <s>Dico itaque, cau&longs;am hujus rei e&longs;&longs;e eandem cum ea, quæ <lb/>ad&longs;ignata fuit in præcedentibus, quia nimirum aqua cruris lon­<lb/>gioris potentior e&longs;t ad de&longs;cendendum, &longs;ecumque trahendum <lb/>aquam cruris brevioris, quàm aqua cruris alterius; & hoc ideo, <lb/>quia aqua premit ac premitur, dum premit ac premitur, ad per­<lb/>pendiculum, hoc e&longs;t, &longs;ecundùm lineam quæ tran&longs;it per centrum <lb/>Mundi. Cujus ergo aquæ perpendiculum longius e&longs;t, illa ma­<lb/>gis premit ac vincit, hoc e&longs;t, de&longs;cendit, &longs;i nihil ob&longs;tet de&longs;cen­<lb/>&longs;um impediens, ut in no&longs;tro ca&longs;u contingit. Hîc ergo verum <lb/>etiam e&longs;t, quòd <emph type="italics"/>in Hydraulicis pugnatur & vincitur non pondere, <lb/>aut copi aquarum, &longs;ed perpendiculis,<emph.end type="italics"/> juxta Axioma hydraulicum, <lb/>2. quod &longs;uprà Propo&longs;itione 2, formatum fuit. </s></p> <pb xlink:href="051/01/124.jpg" pagenum="93"/> <p type="main"> <s><emph type="center"/>Proprietas VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonem ad Libram &longs;eu vectem revocare, <lb/>filtrum ad &longs;iphonem.<emph.end type="center"/></s></p> <p type="main"> <s>ESto recta linea AB, divi&longs;a bifariam in puncto C. Si huic <lb/>puncto C &longs;upponatur hypomochlion G, aut alligetur fi­<lb/> <arrow.to.target n="fig23"/><lb/>lum FG; &longs;tabit, hærebitque li­<lb/>nea AB in æquilibrio horizon­<lb/>ti parallela, & neutra pars præ­<lb/>valebit. Si prolongetur pars <lb/>CB u&longs;que ad D, prævalebit pars <lb/>CD parti CA, & de&longs;cendet. Si <lb/>prolongetur eadem pars CB, u&longs;­<lb/>que ad E, adhuc magis prævale­<lb/>bit pars C parti CA, <expan abbr="cele-riu&longs;&qacute;ue">cele­<lb/>riu&longs;que</expan> de&longs;cendet; & quò ma­<lb/>gis prolongabitur pars longior, <lb/>eò magis prævalebit breviori, <lb/>magi&longs;que celeriter de&longs;cendet. <lb/>Linea porrò AB, aut AD, aut <lb/>AE, &longs;i hypomochlio G impo­<lb/>natur, repræ&longs;entatvectem; &longs;i è <lb/>filo FC &longs;u&longs;pendatur, repræ&longs;entat <lb/>libram, aut &longs;tateram. </s></p> <figure id="id.051.01.124.1.jpg" xlink:href="051/01/124/1.jpg"/> <p type="main"> <s>E&longs;to jam &longs;iphon ACB, &longs;ive <lb/> <arrow.to.target n="marg177"/><lb/>erectus, &longs;ive inver&longs;us, divi&longs;us <lb/>mente in duas æquales partes AC, BC, & repleatur totus aquâ; <lb/>ex neutro crure effluet, ut vidimus atque probavimus, &longs;ed aqua <lb/>&longs;tabit, hærebitve in duobus cruribus AC, BC, in æquilibrio. <lb/>Si prolongetur crus CB, u&longs;que ad D, & repleatur totus &longs;i­<lb/>phon aquâ; prævalebit crus CD, & aqua ejus in inver&longs;o &longs;ipho­<lb/>ne effluens &longs;ecum trahet reliquam; in erecto verò &longs;iphone de­<lb/>&longs;cendet & expellet reliquam per os A. Si prolongetur idem <lb/>crus CB u&longs;que ad E, adhuc magis prævalebit crus CE, ma­<lb/>gi&longs;que celeriter de&longs;cendet ejus aqua, & vel &longs;ecum trahet reli­<lb/>quam, vel illam &longs;ub&longs;idendo expellet. </s></p> <pb xlink:href="051/01/125.jpg" pagenum="94"/> <p type="margin"> <s><margin.target id="marg177"/><emph type="italics"/>Siphon tam <lb/>erectus. qu<gap/><lb/>inver&longs;us, re <lb/>vecatur ad <lb/>libram.<emph.end type="italics"/></s></p> <figure id="id.051.01.125.1.jpg" xlink:href="051/01/125/1.jpg"/> <p type="main"> <s>Patet ergo, quomodo &longs;iphon <lb/>tam erectus, quàm inver&longs;us, re­<lb/>vocetur ad libram, aut vectem </s></p> <p type="main"> <s>Filtrum appellamus panni <lb/> <arrow.to.target n="marg178"/><lb/>laciniam ACB, pendentem ex <lb/>va&longs;e A, ita ut pars AC &longs;it in­<lb/>tra vas, & aquæ immer&longs;a, &longs;al­<lb/>tem ex parte; pars verò altera <lb/>CB extra vas pendeat. Hæc <lb/>panni lacinia &longs;i priùs madefiat <lb/>tota, deinde modo dicto ex va­<lb/>&longs;e aquâ pleno &longs;u&longs;pendatur; tra­<lb/>hit aquam non &longs;ecus ac &longs;iphon, <lb/>&longs;i pars exterior fuerit longior <lb/>quàm interior; &longs;i æqualis, aut <lb/>brevior, non trahit. Con&longs;tat <lb/>ergo, filtrum ad &longs;iphonem re­<lb/>duci. </s></p> <p type="margin"> <s><margin.target id="marg178"/><emph type="italics"/>Filtrum re­<lb/>vocatur ad <lb/>&longs;iphonem.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Diabetem &longs;piritalem de&longs;cribere, eju&longs;que <lb/>proprietates ad&longs;ignare.<emph.end type="center"/></s></p> <p type="main"> <s>EO&longs;dem ferè effectus, quos præ&longs;tat &longs;iphon inflexus, cujus <lb/>unum crus va&longs;i imponitur, præ&longs;tat etiam tubus certo mo­<lb/>do va&longs;i implantatus, quem Hero Alexandrinus vocat medium <lb/>&longs;piritalem diabetem, qua&longs;i dicas, pera&longs;cen&longs;orem; alij verò vo­<lb/>cant tubum &longs;uffocabilem. Sic autem con&longs;truitur. </s></p> <pb xlink:href="051/01/126.jpg" pagenum="95"/> <figure id="id.051.01.126.1.jpg" xlink:href="051/01/126/1.jpg"/> <p type="main"> <s>Sit vas ABCD. Per ejus fundum <lb/> <arrow.to.target n="marg179"/><lb/>CD trajiciatur tubus EF <expan abbr="utrimq;">utrimque</expan> <lb/>apertus, ip&longs;i fundo coarctatus, & <lb/>in partem inferiorem excedens <lb/>apud F; at o&longs;culum ejus &longs;uperi­<lb/>us E non adæquet altitudinem <lb/>va&longs;is, &longs;ed &longs;it paulò inferius. Huic <lb/>tubo EF circumponatur alius tu­<lb/>bus GHI, &longs;uperius clau&longs;us, qui <lb/>tamen o&longs;culum E non attingat, <lb/>&longs;ed tantum ab ip&longs;o di&longs;tet, <expan abbr="quantũ">quantum</expan> <lb/>&longs;ufficit ad aquæ ingre&longs;&longs;um per <lb/>o&longs;culum E: inferiùs verò vel non attingat undequaque fun­<lb/>dum va&longs;is; vel<gap/> attingit, relinquatur à latere foramen I, per <lb/>quod aqua intrare po&longs;&longs;it. </s></p> <p type="margin"> <s><margin.target id="marg179"/><emph type="italics"/>Diabetes <lb/>&longs;piritalis <lb/>quomodo <lb/>con&longs;trua­<lb/>tur.<emph.end type="italics"/></s></p> <p type="main"> <s>Si jam vas impleas aliquò u&longs;que aquâ, v. g. u&longs;que ad KL, in­<lb/> <arrow.to.target n="marg180"/><lb/>&longs;inuabit &longs;e&longs;e illa per foramen I, & a&longs;cendet u&longs;que ad H, in­<lb/>tra tubum IGH. Si igitur per o&longs;culum F attrahas aërem, <lb/>qui e&longs;t in tubo FE; &longs;equetur &longs;imul aër, qui e&longs;t in tubi &longs;uperpo­<lb/>&longs;iti parte GH; & po&longs;t aërem &longs;equetur aqua, quæ e&longs;t in eju&longs;dem <lb/>tubi parte IH; nec ce&longs;&longs;abit fluxus ex F, donec tota aqua va­<lb/>&longs;is effluxerit, alioquin daretur vacuum intra tubos, ut patet. <lb/>Quòd &longs;i totum vas impleas aquâ, a&longs;cendet illa per foramen I, <lb/>intra tubum IHG, u&longs;que dum &longs;upergrediatur o&longs;culum E; quo <lb/>&longs;upergre&longs;&longs;o, in&longs;inuabit &longs;e&longs;e, naturali pondere, aqua per dictum <lb/>o&longs;culum, & effluet per F, nec ce&longs;&longs;abit, donec tota effluxerit <lb/>aqua. Hac arte docebimus infrà Cla&longs;&longs;e 1. cap. 1. Machina IV. <lb/>con&longs;truere vas, quod effundat aquam per fundum, dum ple­<lb/>num e&longs;t; dum verò plenum non e&longs;t, nihil effundat. </s></p> <p type="margin"> <s><margin.target id="marg180"/><emph type="italics"/>Diabetis <lb/>&longs;piritalis <lb/>proprieta­<lb/>tes.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>FLuxus aquæ etiam hîc inæqualis est, cum continuo celeritatis de-<emph.end type="italics"/> <pb xlink:href="051/01/127.jpg" pagenum="96"/> <arrow.to.target n="fig24"/><lb/> <arrow.to.target n="marg181"/><lb/><emph type="italics"/>cremento: & quò tubus<emph.end type="italics"/> EF <emph type="italics"/>lon­<lb/>giùs exce&longs;&longs;erit extra fundum, eò <lb/>celeriùs, adeoque & copio&longs;iùs hu­<lb/>midum effluet. Harum autem <lb/>proprietatum ratio e&longs;t eadem cum <lb/>illa quæ &longs;uprà Propo&longs;it.<emph.end type="italics"/> 7. <emph type="italics"/>pro &longs;i­<lb/>phone va&longs;i impo&longs;ito e&longs;t allata; tu­<lb/>bus enim<emph.end type="italics"/> IG <emph type="italics"/>æquivalet cruri in­<lb/>terno, &<emph.end type="italics"/> FE, <emph type="italics"/>cruri externo.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg181"/><emph type="italics"/>Aquæ flu­<lb/>xus per dia­<lb/>betem &longs;piri­<lb/>talem inæ­<lb/>qualis e&longs;t.<emph.end type="italics"/></s></p> <figure id="id.051.01.127.1.jpg" xlink:href="051/01/127/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>IDem effectus habebitur, &longs;i in­<lb/> <arrow.to.target n="marg182"/><lb/>tra vas fi<gap/> &longs;iphon inver&longs;us<emph.end type="italics"/><lb/>ABC, <emph type="italics"/>cujus dor&longs;um<emph.end type="italics"/> B <emph type="italics"/>&longs;it paulò <lb/>infra &longs;umma labra va&longs;is. Si enim aqua infundatur va&longs;i, a&longs;cendet <lb/>ea per crus<emph.end type="italics"/> AB; <emph type="italics"/>& cùm &longs;upergre&longs;&longs;a fuerit dor&longs;um<emph.end type="italics"/> B, <emph type="italics"/>effluet per <lb/>crus<emph.end type="italics"/> BC; <emph type="italics"/>nec ce&longs;&longs;abit, donec dota effluxerit. Vide quæ dicemus <lb/>infrà Parte<emph.end type="italics"/> 2. <emph type="italics"/>loc. cit. Machina IV. Si verò non totum vas implea­<lb/>tur aquâ, & aër &longs;ugatur ex o&longs;culo<emph.end type="italics"/> C; <emph type="italics"/>&longs;equetur &longs;imiliter aqua va&longs;is, <lb/>nec ce&longs;&longs;abit fluxus, donec tota fuerit elap&longs;a, quoniam perpendiculum <lb/>aquæ cadentis (&longs;icut & in Diabete) majus e&longs;t quàm perpendiculum <lb/>aquæ a&longs;cendentis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg182"/>Diabetes <lb/>&longs;piritalis a­<lb/>lia ratione <lb/>con&longs;tructus.</s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio X.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphonis inver&longs;i fluxum æqualem <lb/>reddere.<emph.end type="center"/></s></p> <p type="main"> <s>SUprà Propo&longs;it. VI. Propriet. I. o&longs;tendimus, aquam per exter­<lb/>num &longs;iphonis inver&longs;i crus fluere inæqualiter, cum perpetuo <lb/>nimirum celeritatis decremento. Oporteat igitur efficere ut <lb/>fluxus &longs;emper æqualis &longs;it. Docet id Hero Alexandrinus cap. 3. <lb/>de &longs;piritalibus in hunc &longs;en&longs;um. </s></p> <pb xlink:href="051/01/128.jpg" pagenum="97"/> <figure id="id.051.01.128.1.jpg" xlink:href="051/01/128/1.jpg"/> <p type="main"> <s>Sit vas ABCD, aqua <lb/> <arrow.to.target n="marg183"/><lb/>plenum v&longs;que ad EF, gra­<lb/>tia exempli (pote&longs;t enim <lb/>plùs & minùs e&longs;&longs;e <expan abbr="repletũ">repletum</expan>) <lb/>habens &longs;uas an&longs;ulas LL per­<lb/>foratas. Fiat lebetarium <lb/>G, &longs;ive apertum, &longs;ive clau­<lb/>&longs;um, quod po&longs;&longs;it innatare <lb/>&longs;uperficiei aquæ EF; <gap/> per <lb/>eius operculum ac fundum <lb/>trajice &longs;iphonis HIK crus <lb/>internum ac brevius HI, & <lb/>&longs;tanno, aliavè materia ad <lb/>foramina benè coarcta, <lb/>nè aqua &longs;ubintrare in le­<lb/>betarium po&longs;&longs;it. Alterum <lb/>crus externum ac longius <lb/>IK trajice per foramina <lb/>an&longs;ularum LL, &longs;ic ut fa­<lb/>cilè per eas moveri a&longs;cen­<lb/>dendo ac <expan abbr="de&longs;cend&etilde;do">de&longs;cendendo</expan> po&longs;­<lb/>&longs;it. His factis, &longs;i per o&longs;cu­<lb/>lum K attrahas aërem, qui <lb/>e&longs;t in &longs;iphone, &longs;equetur, ob vacui fugam, aqua va&longs;is, eâque &longs;ub­<lb/>&longs;idente &longs;ub&longs;idebit &longs;imul & lebetarium, & &longs;iphon infixus lebeta­<lb/>rio, fluetque aqua per K, donec o&longs;culum H tangat fundum <lb/>CD. Erit autem ille fluxus &longs;emper æqualis, eò quòd exce&longs;&longs;us <lb/>perpendiculi cruris externi & longioris &longs;upra perpendicu­<lb/>lum cruris interni & brevioris, &longs;it &longs;emper æqualis, hoc <lb/>e&longs;t, idem, nempe in &longs;chemate po&longs;ito exce&longs;&longs;us KM u&longs;que <lb/>ad &longs;upremam aquæ va&longs;is &longs;uperficiem EF, propterea quòd efflu­<lb/>ente aqua ex K, & de&longs;cendente &longs;uperficie EF ver&longs;us <expan abbr="fundũ">fundum</expan> <lb/>va&longs;is, de&longs;cendat & lebes cum &longs;iphone &longs;ibicoarctato, ut dixi; quo <lb/>fit, ut crus IK eandem &longs;emper aquæ quantitatem ex va&longs;e per <lb/>crus HI attrahat, nempe illam quæ e&longs;t in GI, à G &longs;uprema aquæ <pb xlink:href="051/01/129.jpg" pagenum="98"/> <arrow.to.target n="fig25"/><lb/>&longs;uperficie, v&longs;que ad 1; ac <lb/>proinde eâdem &longs;emper fa­<lb/>cilitate difficultatevè efflu­<lb/>it aqua ex K<gap/> ergo & eâ­<lb/>dem celeritate. </s></p> <p type="margin"> <s><margin.target id="marg183"/><emph type="italics"/>Aquæ flu­<lb/>xum per <lb/>crus exter­<lb/>num &longs;ipho­<lb/>nis æqualem <lb/>reddere.<emph.end type="italics"/></s></p> <figure id="id.051.01.129.1.jpg" xlink:href="051/01/129/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>Pote&longs;t loco lebetarij<emph.end type="italics"/> G <lb/><emph type="italics"/>accipi &longs;uberis, alteriusvè levi&longs;­<lb/>&longs;imi ligni fru&longs;tum, & per id <lb/>trajici &longs;iphonis crus <expan abbr="internũ">internum</expan>.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/><lb/> <arrow.to.target n="marg184"/></s></p> <p type="margin"> <s><margin.target id="marg184"/><emph type="italics"/>Aquaeffluit <lb/>ex crure ex­<lb/>terno &longs;ipho­<lb/>nis eò cele­<lb/>rius, quo <lb/>maior e&longs;t i­<lb/>p&longs;i' exce&longs;&longs;us <lb/>&longs;upra inter­<lb/>num crus.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Quantò maior erit ex­<lb/>ce&longs;&longs;us<emph.end type="italics"/> KM <emph type="italics"/>cruris externi, <lb/>tantò celeriùs effluet aqua ex<emph.end type="italics"/><lb/>K, <emph type="italics"/>&longs;emper tamen æqualiter. <lb/>Ratio e&longs;t, quia tunc magis pre­<lb/>mitur aqua apud o&longs;culum<emph.end type="italics"/> K, <lb/><emph type="italics"/>& aqua cruris externi maio­<lb/>rem exce&longs;&longs;um habet &longs;upra <expan abbr="aquã">aquam</expan> <lb/>cruris interni, ac proinde mi­<lb/>norem difficultatem ad illam <lb/>trahendam. Neque hoc e&longs;t <lb/>contra id, quod diximus Pro­<lb/>po&longs;it. VII. præcedente: aliud enim e&longs;t, cau&longs;am dare, cur fluat aqua ex <lb/>crure longiore, aliud cur celeriùs fluat.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>Quomodo fieri po&longs;&longs;it fluxus aquæ ex &longs;iphone partim æqualis, par­<lb/>tim inæqualis, hoc e&longs;t, vno tempore æqualis, altero inæqualis, pront no­<lb/>bis placuerit, docet Hero &longs;upra citatus cap.<emph.end type="italics"/> 4. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphone inver&longs;o aquam ex vno montis latere in <lb/>alterum, per verticem deducere.<emph.end type="center"/></s></p> <p type="main"> <s>SItmons A, in cuius latere vno &longs;it fons, alia vè aqua, &longs;eu flu­<lb/>ens, &longs;eu &longs;tagnans B, aut C, in pede nimirum, aut in latere <pb xlink:href="051/01/130.jpg" pagenum="99"/> <arrow.to.target n="fig26"/><lb/>montis; &longs;itque in latere altero locus E paulò humilior, quàm </s></p> <figure id="id.051.01.130.1.jpg" xlink:href="051/01/130/1.jpg"/> <p type="main"> <s> <arrow.to.target n="marg185"/><lb/>aqua B, aut C; & &longs;it in hunc locum E deducenda prædicta <lb/>aqua per montis verticem. Fiat &longs;iphon inver&longs;us inæqualium <lb/>crurium BCDE, ex plumbo, aut metallo, cuius orificium B, <lb/>aut C cruris brevioris &longs;it immer&longs;um fonti B, aut C, alterum <lb/>verò orificium E cruris longioris de&longs;inat intra ci&longs;ternam, ali­<lb/>udvè receptorium E in loco de&longs;tinato. Hoc facto, obture­<lb/>tur vtrumque &longs;iphonis os, & per foramen D in vertice montis <lb/>factum in &longs;iphone, repleatur totus &longs;iphon aqua, & foramen di­<lb/>ligenti&longs;&longs;imè obturetur, nè aërem recipere po&longs;&longs;it. Si iam aperia­<lb/>tur eodem tempore &longs;imul vtrumque &longs;iphonis orificium, effluet <lb/>aqua per E cruris longioris intra receptaculum, <expan abbr="&longs;ecumq;">&longs;ecumque</expan> tra­<lb/>het, nè vacuum intra <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> fiat, aquam fontis B, aut C; nec <lb/>ce&longs;&longs;abit fluxus, quàm diu orificium B, aut C, fuerit aquæ im­<lb/>mer&longs;um. Ratio patet ex dictis Propo&longs;itione 6. & alijs pa&longs;&longs;im ex <lb/>præcedentibus. </s></p> <pb xlink:href="051/01/131.jpg" pagenum="100"/> <p type="margin"> <s><margin.target id="marg185"/><emph type="italics"/>Aquam per <lb/>montis ver­<lb/>ticem à ba­<lb/>&longs;e ad basè <lb/>deducere &longs;<gap/><lb/>phone.<emph.end type="italics"/></s></p> <figure id="id.051.01.131.1.jpg" xlink:href="051/01/131/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>OMninò nece&longs;&longs;arium e&longs;t, ut locus<emph.end type="italics"/> E <emph type="italics"/>&longs;it humilior, &longs;altem aliquan­<lb/>tulùm, quàm locus fontis aut aquæ<emph.end type="italics"/> B, <emph type="italics"/>&longs;eu <gap/>, ut &longs;iphonis crus<emph.end type="italics"/> DE <lb/><emph type="italics"/>longius fieri po&longs;&longs;it quàm<emph.end type="italics"/> BD, <emph type="italics"/>aut<emph.end type="italics"/> DC. <emph type="italics"/>Quod &longs;i fieri non po&longs;&longs;it, &longs;pes <lb/>nulla e&longs;t ad effectum de&longs;ideratum con&longs;equendum. Quare diligenter <lb/>priùs libellandum e&longs;t &longs;patium inter<emph.end type="italics"/> B <emph type="italics"/>&<emph.end type="italics"/> E, <emph type="italics"/>aut<emph.end type="italics"/> C <emph type="italics"/>&<emph.end type="italics"/> E. <emph type="italics"/>Qu&<gap/>grave; <lb/>autem humilior fuerit locus<emph.end type="italics"/> E <emph type="italics"/>quàm aqua<emph.end type="italics"/> B <emph type="italics"/>aut<emph.end type="italics"/> C, <emph type="italics"/>eòmcliorem res <lb/>&longs;ucce&longs;&longs;um habebit, & eò velociùs <gap/>qua effluet ex orificio<emph.end type="italics"/> E, <emph type="italics"/>vti ex di­<lb/>ctis patet.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>PO&longs;&longs;e etiam alia ratione trahi <expan abbr="aquã">aquam</expan> exfonte<emph.end type="italics"/> <gap/> <emph type="italics"/>aut<emph.end type="italics"/> C <emph type="italics"/>per &longs;iphonem, <lb/>v&longs;que ad locum <gap/>, absque eo quòd in vertice &longs;<gap/>t foramen<emph.end type="italics"/> D, <emph type="italics"/>& &longs;i­<lb/>phon repleatur aqu<gap/>nulli p<gap/>; &longs;i nimirum ex orificio<emph.end type="italics"/> E <emph type="italics"/>tubi<emph.end type="italics"/> <pb xlink:href="051/01/132.jpg" pagenum="101"/><emph type="italics"/>extrahatur aër follibus, aut Æolopila, quam de&longs;cribimus infrà parte<emph.end type="italics"/> 2. <lb/><emph type="italics"/>cla&longs;&longs;e<emph.end type="italics"/> 1. <emph type="italics"/>cap.<emph.end type="italics"/> 3. <emph type="italics"/>Mach. VI. Quam tamen <expan abbr="ration&etilde;">rationem</expan> nullo modo &longs;ub&longs;i&longs;tere po&longs;&longs;e, <lb/>hinc o&longs;tendo, quòd fieri non po&longs;&longs;it, ut follis per canalem vacuum tantum <lb/>aquarum pondus, quantum canalem ex attactu replere debet, attrahers <lb/>po&longs;&longs;it: montis enim in&longs;tar <expan abbr="foll&etilde;">follem</expan> e&longs;&longs;e oporteret, qui id præ&longs;taret, cùm omnis <lb/>attractio proportionem &longs;uam babeat ad pondus attrahendum; quæ &longs;i im­<lb/>par&longs;it, rumpentur folles potiùs quàm pond<emph.end type="italics"/><emph type="sup"/>9<emph.end type="sup"/> <emph type="italics"/>attrahatur. Vt vel hinc appæ­<lb/>reat, quàm multa in &longs;peculatione vera <expan abbr="appareãt">appareant</expan>, quæ tamen nullam effe­<lb/>ctum in praxi exhibeant. Marinus Mer&longs;ennus in Pbænomenis Hydrau­<lb/>licis Propo&longs;it.<emph.end type="italics"/> 34. <emph type="italics"/>addit alium modum, &longs;i nimirum in loco de&longs;tinato fiat <lb/>pi&longs;cinæ<emph.end type="italics"/> E <emph type="italics"/>vndique clau&longs;a, eaque repleatur aquâ, & orificium<emph.end type="italics"/> E <emph type="italics"/>&longs;iphonis <lb/>adferruminetur operculo perforato pi&longs;cinæ, ita ut aquam non attingat: <lb/>&longs;i enim re&longs;eratur epi&longs;tomium pi&longs;cinæ, effluet aqua, inquit, & in aquæ lo­<lb/>cum &longs;uccedet aër &longs;iphonis, in aëris locum aqua<emph.end type="italics"/> B, <emph type="italics"/>aut<emph.end type="italics"/> C, <emph type="italics"/>nè vacuum <lb/>admittatur in &longs;iphone: dummodò, inquit, pi&longs;cina vacua totum &longs;iphonis <lb/>aërem recipere po&longs;&longs;it. Sed mirum, quantum hallucinatur Mer&longs;ennus, <lb/>cùm, ut diximus &longs;uprà Protheoria I. & videbimus infrà &longs;uo loco, & <lb/>ip&longs;emet Mer&longs;ennus in&longs;inuat, aqua fontis<emph.end type="italics"/> B, <emph type="italics"/>aut<emph.end type="italics"/> C <emph type="italics"/>trahi, atque <lb/>a&longs;cendere per &longs;iphonis crus<emph.end type="italics"/> BD, <emph type="italics"/>aut<emph.end type="italics"/> CD, <emph type="italics"/>nullatenus po&longs;&longs;it, ni&longs;i infra <lb/>pi&longs;cinam<emph.end type="italics"/> E <emph type="italics"/>de&longs;cendat tubus, per quem aqua fluat, paulò maioris per­<lb/>pendiculi quàm &longs;it perpendiculum<emph.end type="italics"/> BD, <emph type="italics"/>aut<emph.end type="italics"/> CD. <emph type="italics"/>quod in hac & &longs;imi­<lb/>libus Machinis e&longs;t &longs;ummè nece&longs;&longs;arium, vt diximus, cùm de vi Attracti­<lb/>va egimus, & in &longs;ecunda Parte &longs;æpius repetemus, præ&longs;ertim cla&longs;&longs;e<emph.end type="italics"/> 1. <emph type="italics"/>cap.<emph.end type="italics"/> 1. <lb/><emph type="italics"/>Machina<emph.end type="italics"/> 2. <emph type="italics"/>Pote&longs;t tamen longitudo tubi, qui infra pi&longs;cinam<emph.end type="italics"/> E <emph type="italics"/>de­<lb/>&longs;cendere deberet, compen&longs;ari multis brevioribus tubis, ut diximus eo­<lb/>dem loco de vi Attractiva, & loco citato Machina<emph.end type="italics"/> 7. <emph type="italics"/>iterum dicemus. <lb/>Accedit & illud, quòd aqua in ci&longs;terna non &longs;ufficiat ad effectum inten­<lb/>tum præ&longs;tandum, ni&longs;i ci&longs;terna tantum aquæ contineat, quantæ ip&longs;e ca­<lb/>nalis capax e&longs;t; at quis tantam &longs;abricari volet ci&longs;ternam?<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>MVlta alia circa fluxum aquæ ex &longs;iphone dici po&longs;&longs;ent, præ&longs;ertim <lb/>quòd de&longs;cen&longs;us aquæ fluentis per crus imitetur leges gravium de­<lb/>&longs;cendentium motu naturali; &longs;ed hæc, & &longs;imilia alia, intelligi facilè <lb/>po&longs;&longs;unt ex dicendis Capite &longs;equenti, de fluxu aquæ per tubos Propo&longs;it.<emph.end type="italics"/> 9. </s></p> <pb xlink:href="051/01/133.jpg" pagenum="102"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio XII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Siphone inver&longs;o aquam ex montis radice ad <lb/>ejus verticem elevare.<emph.end type="center"/></s></p> <p type="main"> <s>MIrabilis e&longs;t &longs;equens modus, & antiquis minimè cognit<gap/><lb/> <arrow.to.target n="marg186"/><lb/>imò ab omnibus pro impo&longs;&longs;ibili habitus, inquit Port<gap/><lb/>omnes enim putârunt, &longs;i in &longs;iphonis inver&longs;i collo &longs;eu curva<gap/><lb/>ra &longs;uprema foramen fieret, & vel minimum aëris ingrede<gap/><lb/>tur, fore ut &longs;iphonis aqua di&longs;continuaretur, & aqua divi&longs;a p<gap/><lb/>utrumque &longs;iphonis crus hinc atque inde delaberetur, totu&longs;q<gap/><lb/>&longs;iphon evacuaretur. Contrarium mon&longs;trat &longs;equens mod<gap/><lb/>quem præ&longs;cribit Joannes Bapti&longs;ta Porta lib. 2. Spirital. cap. <gap/><lb/>& 14. in hunc &longs;en&longs;um. <lb/> <arrow.to.target n="marg187"/></s></p> <p type="margin"> <s><margin.target id="marg186"/><emph type="italics"/>Vide præ <lb/><expan abbr="cedent&etilde;">cedentem</expan> <lb/>figuram <lb/>pag<emph.end type="italics"/> 99. <lb/><emph type="italics"/>vel<emph.end type="italics"/> 100.</s></p> <p type="margin"> <s><margin.target id="marg187"/><emph type="italics"/>Aquam è <lb/>montis ra­<lb/>dice ad ver­<lb/>ticem ele­<lb/>vare.<emph.end type="italics"/></s></p> <p type="main"> <s>Sit ut antea mons A, in eju&longs;que radice fons B, cuj<gap/><lb/>aqua &longs;it elevanda u&longs;que ad verticem D. Fiat &longs;iphon inver<gap/><lb/>inæqualium, ut antea, crurium BDE, cujus orificium B <gap/><lb/>immer&longs;um fonti, orificium verò E vel liberum omninò <gap/><lb/>vel de&longs;inat in pi&longs;cinam &longs;ubjectam. Habebit autem res tan<gap/><lb/>meliorem &longs;ucce&longs;ium, quantò longius fuerit crus DE, quà<gap/><lb/>alterum DB. Fiat deinde infra collum &longs;iphonis, ubi D, <gap/><lb/>ceptaculum aquarum H, undique clau&longs;um quàm diligent <gap/><lb/>&longs;imè, &longs;uoque epi&longs;tomio I in&longs;tructum, ex quo depromi aq<gap/><lb/>po&longs;&longs;it. In hoc receptaculum derivetur ex collo &longs;eu curvatu<gap/><lb/>&longs;iphonis tubulus G, habens cla viculam volubilem, &longs;itque t<gap/><lb/>bulus arcti&longs;&longs;imè adferruminatus & &longs;iphonis collo, & recept<gap/><lb/>culi operculo priùs perforatis. His factis, repleatur per infu<gap/><lb/>dibulum D &longs;iphon BDE, ob&longs;tructis priùs orificijs B & <gap/><lb/>eoque repleto obturetur foramen D, & aperiatur &longs;imul utru<gap/><lb/>que orificium B & E; dumque per tubum fluit aqua, & ex<gap/><lb/>erumpit; aperiatur modici&longs;&longs;imè, & momentaneâ qua&longs;i mo<gap/><lb/>la clavicula tubuli G; &longs;tatimque per dictum tubulum de&longs;ce<gap/><lb/>det modica aqua intra receptaculum H, a&longs;cendetque mo<gap/><lb/>cus aër intra &longs;iphonem, ibique aquæ mi&longs;tus delabetur unà cu<gap/><lb/>ip&longs;a per crus DE, & per os E erumpet. Hoc &longs;i &longs;æpius fec<gap/> <pb xlink:href="051/01/134.jpg" pagenum="103"/>ris, tandem replebitur receptaculum H, ut aqua per ejus epi <lb/>&longs;tomium I depromi po&longs;&longs;it magna copia. Hæc Porta. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>VVlt igitur Porta, tubulum<emph.end type="italics"/> G <emph type="italics"/>aperiendum e&longs;&longs;e modici&longs;&longs;imè, ut ni­<lb/>mirum ingrediatur modicus aër intra &longs;iphonem, & ita mi&longs;cea­<lb/>tur aquæ, ut ea non di&longs;continuetur. Si enim ingrederetur aër copio­<lb/>&longs;us, po&longs;&longs;et ita interrumpi aqua &longs;iphonis aëre interpo&longs;ito, ut perpendi­<lb/>culum<emph.end type="italics"/> BD <emph type="italics"/>e&longs;&longs;et majus, quàm perpendiculum reliquæ aquæ intra crus<emph.end type="italics"/><lb/>DE; <emph type="italics"/>quod ubi contingeret, &longs;tatim di&longs;continuaretur aquæ fluxus, & <lb/>aqua utriu&longs;que cruris de&longs;cenderet, unaquæque ad &longs;uum orificium, & <lb/>efflueret. Hoc igitur incommodum ut evitetur, intromittendus e&longs;t, <lb/>inquit Porta, repetitis vicibus modici&longs;&longs;imus aër, ut &longs;ine interruptio­<lb/>nis periculo po&longs;&longs;it mi&longs;ceri aquæ. Nam quantumvis modicus intro­<lb/>mittatur aër, &longs;i tamen is aquam cruris<emph.end type="italics"/> DE <emph type="italics"/>di&longs;continuat, infallibili­<lb/>ter interrumpetur aquæ fluxus, ni&longs;i pars<emph.end type="italics"/> FE <emph type="italics"/>&longs;it paulò longior quàm <lb/>crus<emph.end type="italics"/> BD. <emph type="italics"/>Ponamus cnim aërem interceptum e&longs;&longs;e<emph.end type="italics"/> KF. <emph type="italics"/>Hic aër dum<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg188"/><lb/><emph type="italics"/>erit in<emph.end type="italics"/> L, <emph type="italics"/>aut in<emph.end type="italics"/> M, <emph type="italics"/>non interrumpet quidem aquæ cur&longs;um, quia <lb/>perpendiculum<emph.end type="italics"/> LE, <emph type="italics"/>aut<emph.end type="italics"/> EM, <emph type="italics"/>adhuc longius e&longs;t, ut &longs;uppono, quàm <lb/>perpendiculum<emph.end type="italics"/> DB. <emph type="italics"/>At quamprimùm aër<emph.end type="italics"/> KF <emph type="italics"/>fuerit infra<emph.end type="italics"/> M, <lb/><emph type="italics"/>jam interrumpetur aquæ fluxus, eò quòd perpendiculum aquæ ab aëre <lb/>u&longs;que ad<emph.end type="italics"/> E <emph type="italics"/>brevius e&longs;t, quàm perpendiculum à vertice<emph.end type="italics"/> D <emph type="italics"/>u&longs;que ad<emph.end type="italics"/><lb/>B. <emph type="italics"/>Ne igitur aquæ interruptio, &longs;i fortè contingeret, ejus influxum <lb/>per &longs;iphonem impediat, crus<emph.end type="italics"/> DE <emph type="italics"/>adeo prolongandum e&longs;&longs;et, ut facta <lb/>interruptione etiam notabili aquæ &longs;iphonis per interpo&longs;itionem aëris, <lb/>perpendiculum tamen aquæ ab aëre u&longs;que ad<emph.end type="italics"/> E <emph type="italics"/>maneret &longs;em­<lb/>per longius perpendiculo cruris<emph.end type="italics"/> DB. <emph type="italics"/>Meliorem igitur &longs;ucce&longs;&longs;um res <lb/>habebit, &longs;i fons &longs;it in latere montis, v. g. in<emph.end type="italics"/> C, <emph type="italics"/>& non in radice<emph.end type="italics"/><lb/> <arrow.to.target n="marg189"/><lb/><emph type="italics"/>apud<emph.end type="italics"/> B. <emph type="italics"/>Praxim hanc ut dixi, docet Ioannes Bapti&longs;ta Porta lib.<emph.end type="italics"/> 2. <lb/><emph type="italics"/>Spiritalium cap.<emph.end type="italics"/> 13. <emph type="italics"/>&<emph.end type="italics"/> 14. <emph type="italics"/>pendetque ex praxi, quam ex codem re­<lb/>tulimus &longs;uprà Protheoria I. §. X. Refert eandem praxim Mer&longs;ennus <lb/>in hydraulicis Phænomenis Propo&longs;it.<emph.end type="italics"/> 34. <emph type="italics"/>ubi tamen nonnulla de &longs;uo <lb/>adjungit non u&longs;quequaque veritati congrua. Veruntamen fal&longs;um <lb/>omnino e&longs;t, quod habetur apud Portam loco cit. cap.<emph.end type="italics"/> 15. <emph type="italics"/>editionis Ita­<lb/>licæ, de modo elevandi aquam ex flumine præterfluente per &longs;iphonem<emph.end type="italics"/> <pb xlink:href="051/01/135.jpg" pagenum="104"/><emph type="italics"/>u&longs;que ad turris vicinæ altitudinem; quem quidem modum &longs;u&longs;picer <lb/>non e&longs;&longs;e ip&longs;ius Portæ, &longs;ed e&longs;&longs;e interpretis &longs;eu traductoris ex Latino in <lb/>Italicum idioma Ioannis E&longs;crivani Hi&longs;pani, qui in Dedicatoria fatetur <lb/>&longs;e adjunxi&longs;&longs;e nonnulla, quæ oretenus ab ip&longs;o Porta didicerat, ut &longs;u­<lb/>pra in Præloquio dicebam.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg188"/><emph type="italics"/>Aër in tulo <lb/>di&longs;continu­<lb/>ans aquam, <lb/>interrum­<lb/>pit <expan abbr="fluxũ">fluxum</expan> æ­<lb/>quæ.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg189"/><emph type="italics"/>Portæ error <lb/>in elevan­<lb/>da aqua ad <lb/>turris al­<lb/>titudinem.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Cau&longs;am a&longs;&longs;ignare, cur in &longs;iphone inver&longs;o interrupto <lb/>perpendiculum aquæ de&longs;cendentis debeat &longs;upera­<lb/>re perpendiculum aquæ a&longs;cendentis.<emph.end type="center"/><lb/> <arrow.to.target n="marg190"/></s></p> <p type="margin"> <s><margin.target id="marg190"/><emph type="italics"/>Siphon in­<lb/>terruptus. <lb/>& cau&longs;a ef­<lb/>fectus ip&longs;ius<emph.end type="italics"/></s></p> <p type="caption"> <s><emph type="italics"/>I. Figura.<emph.end type="italics"/></s></p> <figure id="id.051.01.135.1.jpg" xlink:href="051/01/135/1.jpg"/> <p type="main"> <s>INfrà Parte 2. Cla&longs;­<lb/>&longs;e 1. cap. 1. Ma­<lb/>china 2. damus Ma­<lb/>chinam hîc <expan abbr="po&longs;itã">po&longs;itam</expan>, <lb/>eamque appellam<emph type="sup"/>9<emph.end type="sup"/><lb/><emph type="italics"/>Siphonem inver&longs;um <lb/>interruptum.<emph.end type="italics"/> Ean­<lb/>dem Machinam ex­<lb/>hibuimus etiam &longs;u­<lb/>prà Protheoria 1. <lb/>§. V. ubi diximus, tu­<lb/>bum EF, per quem <lb/>aqua de&longs;cendit, de­<lb/>bere e&longs;&longs;e paulò lon­<lb/>giorem tubo BK, <lb/>per quem aqua a­<lb/>&longs;cendit. Quod ta­<lb/>met&longs;i veri&longs;&longs;imum <lb/>&longs;it, & multis experi­<lb/>mentis à Porta pri­<lb/>mùm, deinde à Mer <lb/><expan abbr="&longs;eño">&longs;enno</expan>, Kirchero, at­<lb/>que à me etiam <expan abbr="cõ-probatum">con­<lb/>probatum</expan>; &longs;emper <lb/>tamen vi&longs;um mihi <lb/>fuit mirabile, præ- <pb xlink:href="051/01/136.jpg" pagenum="105"/>&longs;ertim, &longs;i de primo aquæ a&longs;cen&longs;u per tubum BK &longs;it &longs;ermo: nec <lb/>ullum vidi, aut audivi unquam, qui hujus rei cau&longs;am ad&longs;ignet, <lb/>cui acquie&longs;cere po&longs;&longs;im. Aliam etiam Machinam hîc po­</s></p> <p type="caption"> <s><emph type="italics"/>II. Fig.<emph.end type="italics"/><lb/> <arrow.to.target n="fig27"/><lb/>&longs;itam, & priori non multùm <lb/>ab&longs;imilem, adduxi eâdem Pro­<lb/>theoria I. §. VI. quam etiam habet <lb/>Salomon à Caus in &longs;uis hydraulicis <lb/>lib. 1. in qua ut aqua a&longs;cendat per <lb/>crus AB, debet tubus rectus DE <lb/>e&longs;&longs;e paulò longior quàm dictum <lb/>crus AB, ut quilibet facilè experi­<lb/> <arrow.to.target n="marg191"/><lb/>ri pote&longs;t. Quæritur igitur, quæ­<lb/>nam &longs;it hujus rei cau&longs;a in utraque <lb/>Machina, & in alijs hi&longs;ce &longs;imili­<lb/>bus? Neque enim hîc valetratio, <lb/>quam ad&longs;ignavimus &longs;uprà Propo­<lb/>&longs;it. VII. hujus capitis: nam hîc non <lb/>agimus de &longs;iphone continuato, &longs;eu <lb/><expan abbr="nõinterrupto">noninterrupto</expan>, in quo partes omnes <lb/>aqu&ecedil; &longs;unt continuatæ, tum inter &longs;e, <lb/>tum etiam cum aqua va&longs;is, ex quo <lb/>extrahitur aqua per crus <expan abbr="externũ">externum</expan> <lb/>ac longius de&longs;cendens; &longs;ed agimus <lb/>de &longs;iphone interrupto, in quo &longs;ci­<lb/>licet aër intercedit inter aquam & <lb/>aquam. Adde quod hîc, licet tu­<lb/>bi EF, & DE breviores e&longs;&longs;ent, quàm tubus BK & crus AB; <lb/>tamen extrema &longs;uperficies aquæ illorum tuborum &longs;emper e&longs;t <lb/>vicinior centro Mundi, ac proinde per ip&longs;os effluere deberet <lb/>aqua, &longs;ecumque trahere & aërem & aquam oppo&longs;itam va&longs;orum. </s></p> <p type="margin"> <s><margin.target id="marg191"/><emph type="italics"/>Dubitatio. <lb/>& rationes <lb/>dubitandi <lb/>circa &longs;ipho­<lb/>nem inter­<lb/>ruptum.<emph.end type="italics"/></s></p> <figure id="id.051.01.136.1.jpg" xlink:href="051/01/136/1.jpg"/> <p type="main"> <s>Dices, aqua quæ trahit alteram, gravior debet e&longs;&longs;e aquâ <lb/> <arrow.to.target n="marg192"/><lb/>quæ trahitur, ac proinde longiores debent e&longs;&longs;e prædicti tubi <lb/>EF, & DE, ut plùs aquæ contineant. Sed contra e&longs;t mani­<lb/>fe&longs;ta experientia allata Propo&longs;it. III. hujus capitis Propriet. I. & <lb/>alia etiam allata Protheoria I. §. VIII. </s></p> <pb xlink:href="051/01/137.jpg" pagenum="106"/> <p type="margin"> <s><margin.target id="marg192"/><emph type="italics"/>Solutiones <lb/>in&longs;ufficien­<lb/>tes propo&longs;itæ <lb/>dubitatio­<lb/>nis.<emph.end type="italics"/></s></p> <p type="main"> <s>Dices iterum, in hydraulicis pugnari ac vinci non aqua­<lb/>rum copiâ, &longs;ed aquarum perpendiculis, ut dictum Propo&longs;it. 2. <lb/>hujus capitis in Axiomate 2. & alibi &longs;æpe; ideoque longiores <lb/>debent e&longs;&longs;e prædicti tubi EF, & DE, ut perpendicula aqua­<lb/>rum de&longs;cendentium &longs;int longiora, quàm perpendicula aqua­<lb/>rum a&longs;cendentium. Re&longs;oondeo, veri&longs;&longs;imum e&longs;&longs;e citatum <lb/>Axioma; & cau&longs;am hujus rei, loquendo de &longs;iphone inver&longs;o <lb/>non interrupto, ad&longs;ignavimus Propo&longs;it 7. quæ tamen cau&longs;a in <lb/>ca&longs;u præ&longs;enti de &longs;iphone interrupto non militat; ideoque ulte­<lb/>riùs quæritur, quænam &longs;it hujus rei cau&longs;a in &longs;iphone interru­<lb/>pto, atque adeo in no&longs;tro ca&longs;u. Difficultatem agnovit Mer­<lb/>&longs;ennus in Phænom. Hydraul. Propo&longs;it 38. &longs;ed non &longs;olvit. <lb/> <arrow.to.target n="marg193"/></s></p> <p type="margin"> <s><margin.target id="marg193"/><emph type="italics"/>Solutio Au­<lb/>ctoris ratio <lb/>num dubi­<lb/>tandi circæ <lb/>&longs;iphonem in <lb/>terruptum.<emph.end type="italics"/></s></p> <p type="main"> <s>Dico igitur, cau&longs;am e&longs;&longs;e, quòd aquæ pars unaquæque <lb/>premitur aquâ &longs;upra ip&longs;am exi&longs;tente ad perpendiculum, &longs;i aqua <lb/>illa &longs;it de&longs;cendens in aliquo, (hoc e&longs;t, &longs;i nullum impedimen­<lb/>tum extrin&longs;ecum habeat, quò minùs de&longs;cendere po&longs;&longs;it) pro­<lb/>ut a&longs;&longs;eruimus &longs;uprà cap. 1. hujus Protheoriæ 4. Propriet. 4. ex <lb/>Archimede. Illa igitur aqua, cujus perpendiculum e&longs;t majus, <lb/>&longs;eu longius, magis premitur, <expan abbr="majorem&qacute;ue">majoremque</expan> habet vim ad de­<lb/>&longs;cendendum, &longs;i patet aditus ad de&longs;cendendum. Quoniam <lb/>igitur aperto epi&longs;tomio E tubi EF, in I. Fig. & aperto ore <lb/>tubi recti DE, in II. Fig. patet aditus aquæ ad defcendendum; <lb/>de&longs;cendet illa nece&longs;&longs;ariò, innato pondere, & intra tubum, <lb/>propter partes continuatas, fundabit &longs;uum perpendiculum; & <lb/>nè vacuum detur, trahet &longs;ecum aërem, & coget aquam oppo­<lb/>fitorum va&longs;orum a&longs;cendere, <expan abbr="&longs;uum&qacute;ue">&longs;uumque</expan> &longs;imiliter perpendiculum <lb/>fundare. Nunquam tamen a&longs;cendere pote&longs;t aqua ad majus <lb/>&longs;patium in tubo BK, & crure AB, quàm de&longs;cenderit per tu­<lb/>bum EF, & DE; quia &longs;i a&longs;cenderet ad majus &longs;patium, jam <lb/>perpendiculum aquæ a&longs;cendentis majus e&longs;&longs;et, quàm perpen­<lb/>diculum aquæ de&longs;cendentis, ac proinde illa vinceret hanc, & <lb/>retraheret. Itaque &longs;i vas C haberet in fundo foramen angu­<lb/>itum &longs;ine tubo adnexo, nihil aquæ efflueret, quia nullum fun­<lb/>dare po&longs;&longs;et perpendiculum; ideoque nihil a&longs;cenderet per tu- <pb xlink:href="051/01/138.jpg" pagenum="107"/>bum BK. Si idem vas C haberet foramen laxum, efflueret <lb/>quidem aqua, &longs;ed &longs;imul &longs;ubintraret aër, &longs;icque ce&longs;&longs;ante metu <lb/>vacui, aut di&longs;continuitatis corporum, nihil a&longs;cenderet per tu­<lb/>bum KB. Si tubus EF e&longs;&longs;et brevic<gap/>tubo BK, de&longs;cenderet aqua <lb/>u&longs;que ad orificium F, & ad æquale &longs;patium a&longs;cenderet per tu­<lb/>bum BK; &longs;ed facta hac æqualitate, &longs;i&longs;teretur utrimque aqua, <lb/>propter perpendiculorum æqualitatem. Si tubus EF e&longs;&longs;et <lb/>præcisè æqualis tubo BK; de&longs;cenderet &longs;imiliter aqua u&longs;que <lb/>ad o&longs;culum F, & ex parte altera a&longs;cenderet u&longs;que ad K, &longs;ed <lb/>neutra ulteriùs pergeret, propter cau&longs;am jam dictam de per­<lb/>pendiculorum æqualitate. Si denique tubus EF, e&longs;t vel pau­<lb/>lulum longior tubo BK, de&longs;cendit aqua u&longs;que ad F, & cùm <lb/>nullum inveniat impedimentum quò minùs egrediatur, nec <lb/>detineatur ab altera parte à perpendiculo æquali; effluit inna­<lb/>to pondere ex F, & ut vitetur vacuum, <expan abbr="corporum&qacute;ue">corporumque</expan> di&longs;con­<lb/>tinuitas, &longs;ecum rapit & aěrem va&longs;is KA, & aquam tubi BK, <lb/>va&longs;i&longs;que B. </s></p> <p type="main"> <s>Notandum tamen e&longs;t, quod jam &longs;æpius inculcavi, alti­<lb/>tudinem perpendiculi aquæ tubi BK &longs;umendam e&longs;&longs;e à &longs;upre­<lb/>ma aquæ va&longs;is B, &longs;uperficie, u&longs;que ad &longs;upremam &longs;uperficiem <lb/>aquæ eju&longs;dem tubi. </s></p> <p type="main"> <s>Quod diximus de perpendiculis tuborum BK & EF, in­<lb/>telligi etiam debet de perpendiculis AB, & DE alterius Machinæ. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Cau&longs;am ad&longs;ignare cur in Fonte Heronis perpendicu­<lb/>lum aquæ de&longs;cendentis debeat e&longs;&longs;e longius perpendi­<lb/>culo aquæ a&longs;cendentis.<emph.end type="center"/></s></p> <p type="main"> <s>INfrà Parte 2. Cla&longs;&longs;e 1. cap. 2. Machina 1. Fontem damus, </s></p> <p type="main"> <s> <arrow.to.target n="marg194"/><lb/>eumque Fontem Heronis in va&longs;is immediatis appellamus; <pb xlink:href="051/01/139.jpg" pagenum="108"/> <arrow.to.target n="fig28"/><lb/>& ita con&longs;truitur. Vas fit <lb/><expan abbr="oblongũ">oblongum</expan> NOPQ, diaphra­<lb/>gmate &longs;eu &longs;epto IM di­<lb/>&longs;criminatum in duo rece­<lb/>ptacula &longs;eu va&longs;a, NIMQ <lb/>&longs;uperius, & IMOP inferius. <lb/>Superius vas labrum habet <lb/>aliquantulùm concavum <lb/>BD, in eoque foramen K. <lb/>In hac Machina di&longs;ponun­<lb/>tur tubi &longs;eu canales ABC, <lb/>DEL, & GF, uti figura <lb/>mon&longs;trat, & fu&longs;ius dicitur <lb/>loco citato; impletoque <lb/>receptaculo NIMQ aquâ, <lb/>aliove liquore per K fora­<lb/>men, & diligenter clau&longs;o <lb/>foramine K, infunditur <lb/>aqua labro BD, quæ per <lb/>canalem DEL de&longs;cendens <lb/>in vas vacuum IOPM, premit ibidem aërem, atque expellit <lb/>per tubum FG in vas plenum <expan abbr="NIMq;">NIMque</expan> aër verò ibidem pre­<lb/>mens aquam, expellit ip&longs;am per tubum CBA &c. prout fu­<lb/>fiùs dicitur loco citato. Similes alias Machinas damus ibidem <lb/>Machina 2. 3. & 4. Advertimus autem in Notis ad dictam <lb/>Machinam 1. tubum DEL, per quem aqua de&longs;cendit, longio­<lb/>rem e&longs;&longs;e debere tubo CBA, per quem afcendit aqua. Præ­<lb/>dicto Heronis fonti omnino &longs;imilis e&longs;t Lucerna, quam attuli­<lb/>mus &longs;uprà Protheoria 2. §. 5. in qua tamen errorem aliquem <lb/>Heronis notavimus circa claviculam R, diximu&longs;que prædi­<lb/>ctam claviculam debere de&longs;inere in tubulum paulò longiorem, <lb/>quàm e&longs;t tubulus OX. Quærimus nunc hujus rei cau&longs;am. </s></p> <p type="margin"> <s><margin.target id="marg194"/><emph type="italics"/>Fons Hero­<lb/>nis in va&longs;is <lb/>immediatis<emph.end type="italics"/></s></p> <figure id="id.051.01.139.1.jpg" xlink:href="051/01/139/1.jpg"/> <p type="main"> <s>Dicam quod &longs;entio. Vt autem meliùs mentem meam in­<lb/>telligas, Lector, recole quæ diximus &longs;uprà Propo&longs;it. 2. hujus ca- <pb xlink:href="051/01/140.jpg" pagenum="109"/>pitis de Proprietatibus &longs;iphonis erecti; ubi a&longs;&longs;eruimus, aquam <lb/>cruris longioris de&longs;cendentem elevare, atque expellere aquam <lb/>cruris brevioris, cogereque in altum exilire, &longs;i o&longs;culum &longs;it an­<lb/>gu&longs;tum. Cau&longs;am ejus rei diximus e&longs;&longs;e exce&longs;&longs;um perpendi­<lb/>culi aquæ de&longs;cendentis atque pellentis, &longs;upra perpendiculum <lb/>aquæ a&longs;cendentis & pul&longs;æ. His &longs;uppo&longs;itis, ita di&longs;curro. Fons <lb/>Heronis, & Lucerna ad ip&longs;ius &longs;imilitudinem con&longs;tructa, omne&longs;­<lb/> <arrow.to.target n="marg195"/><lb/>que Machinæ &longs;imili artificio adornatæ, nihil aliud &longs;unt, quàm <lb/>&longs;iphon erectus interruptus. Nam tubus DEL habet rationem <lb/>cruris erecti, per quod aqua de&longs;cendit; tubus verò CBA ha­<lb/>bet rationem alterius cruris erecti, per quod aqua a&longs;cendit; <lb/>Aqua de&longs;cendens per DEL, cogit a&longs;cendere aquam per CBA, <lb/>mediante aëre aquam premente. Sicut igitur in &longs;iphone erecto <lb/>non interrupto, ut aqua de&longs;cendens per unum crus, expellat <lb/>aquam a&longs;cendentem per alterum, perpendiculum aquæ de­<lb/>&longs;cendentis majus debet e&longs;&longs;e perpendiculo a&longs;cendentis, ideo­<lb/>que crus, per quod aqua de&longs;cendit, longius debet e&longs;&longs;e, quàm <lb/>crus per quod a&longs;cendit, alioquin non effluet aqua a&longs;cendens; <lb/>ita in ca&longs;u noftro tubus DEL debet e&longs;&longs;e longior tubo ABC, ut <lb/>perpendiculum aquæ de&longs;cendentis majus fit, quàm perpendi­<lb/>culum aquæ a&longs;cendentis. Tantò autem, cæteris paribus, al­<lb/>tiùs a&longs;cendet aqua per tubum ABC, quantò is magis &longs;upera­<lb/> <arrow.to.target n="marg196"/><lb/>bitur à tubo DEL. <expan abbr="Itaq;">Itaque</expan> hîc etiam, uti alibi <expan abbr="ubiq;">ubique</expan> in hydraulicis, <lb/>non aquarum copiâ, fed perpendiculo pugnatur ac vincitur. </s></p> <p type="margin"> <s><margin.target id="marg195"/><emph type="italics"/>Perpendicu <lb/>lum aquæ <lb/>eadentis in <lb/>fonte Hero­<lb/>nis cur exce <lb/>dere debeat <lb/>perpendicu <lb/>lum aquæ <lb/>a&longs;cendentis<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg196"/><emph type="italics"/>Perpendicu <lb/>lo, <expan abbr="nõ">non</expan> aqua­<lb/>rum copia, <lb/>pugnatur, <lb/>ac vincitur <lb/>in hydrau­<lb/>licis.<emph.end type="italics"/></s></p> <p type="main"> <s>Hæc mea e&longs;t opinio: cui meliùs quid occurrerit, profe <lb/>ratin medium; nullus enim adhuc rei huius cau&longs;am attigit, quod <lb/>&longs;ciam. Non nego tamen, & aëris prementis copiam ab aquæ <lb/>de&longs;cendentis copia maiore vehementiùs pre&longs;&longs;am ac pul&longs;am, & <lb/>o&longs;culi A, vel potiùs totius tubuli CBA angu&longs;tiam, multùm <lb/>conferre ad aquam altiùs ex ofculo A eiaculandam, tum ob <lb/>urgentis impetus incrementum, tum ob decrementum gravi­<lb/>tatis aquæ deor&longs;um in tubo, po&longs;t egre&longs;&longs;um è tubo, nitentis. Ne­<lb/>go tamen, erupturam aquam è tubo CBA, &longs;i longior is fuerit <lb/>tubo DEL; idque ob rationem a&longs;&longs;ignatam. </s></p> <pb xlink:href="051/01/141.jpg" pagenum="110"/> <p type="main"> <s><emph type="center"/>CAPVT III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De <lb/>Proprietatibus Aquæ fluentis per tubos.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PROOEMIVM.<emph.end type="center"/><lb/> <arrow.to.target n="marg197"/></s></p> <p type="margin"> <s><margin.target id="marg197"/>Tubus <lb/>quid &longs;it.</s></p> <p type="main"> <s><emph type="italics"/>TVbos hîc appello Columnas concavas, &longs;ive cylindri­<lb/>cæ illæ &longs;int, &longs;iv&ecedil; pri&longs;maticæ. Hos in Machinis Par-<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg198"/><lb/><emph type="italics"/>te<emph.end type="italics"/> 2. <emph type="italics"/>pa&longs;&longs;im voco in differenter tubos, &longs;iphones, ca­<lb/>nales, fi&longs;tulas, & alijs etiam nominibus. Foramen per quod <lb/>effluit aqua tubo contenta, appellat Hero Alexandrinus in <lb/>&longs;uis Pnevmaticis, os, o&longs;culum, & orificium; Marinus verò <lb/>Mer&longs;ennus in hydraulicis &longs;uis Phænomenis vocat lumen.<emph.end type="italics"/><lb/> <arrow.to.target n="marg199"/><lb/><emph type="italics"/>Hoc foramen fieri pote&longs;t vel in ba&longs;e tubi, vel in latere. Fieri <lb/>etiam po&longs;&longs;unt tubi conici ad in&longs;tar conorum truncatorum, quo­<lb/>rum os &longs;eu lumen &longs;it vel in vertice, vel in ba&longs;i coni, prout ap­<lb/>paret in figuris Propo&longs;itionis primæ &longs;equentis.<emph.end type="italics"/><lb/> <arrow.to.target n="marg200"/></s></p> <p type="margin"> <s><margin.target id="marg198"/>Tubi fora­<lb/>men, os, <lb/>o&longs;culum, <lb/>lumen, <expan abbr="id&etilde;">idem</expan> <lb/>&longs;unt.</s></p> <p type="margin"> <s><margin.target id="marg199"/>Tuborum <lb/>variæ for­<lb/>mæ.</s></p> <p type="margin"> <s><margin.target id="marg200"/>Tub' &longs;em­<lb/>per plenus.</s></p> <p type="main"> <s><emph type="italics"/>Tubi per quos fluit aqua, aut &longs;unt &longs;emper pleni, aut non <lb/>&longs;unt &longs;emper pleni. Tubum &longs;emper plenum vocamus, quem <lb/>fons aut vas aliquod &longs;uperimpo&longs;itum ita implet per orificium <lb/>&longs;uperius, ut dum aqua effluit per inferius, &longs;emper tamen plenus <lb/>maneat v&longs;que ad &longs;uperius orificium; quod fit, dum tantum,<emph.end type="italics"/></s></p> <p type="main"> <s> <arrow.to.target n="marg201"/><lb/><emph type="italics"/>aut plùs influit, quàm effluit. Tubum non &longs;emper plenum <lb/>appellamus, qui, dum effluit aqua per foramen, paulatim exin­<lb/>anitur, nullâ interim aliâ influente aquâ.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg201"/>Tubus <expan abbr="nõ">non</expan> <lb/>&longs;emper ple <lb/>nus.</s></p> <p type="main"> <s><emph type="italics"/>Tubi quicunque, per quos aqua decurrit, aut &longs;unt erecti<emph.end type="italics"/><lb/> <arrow.to.target n="marg202"/><lb/><emph type="italics"/>perpendiculariter, aut inclinati, aut pro&longs;trati horizontaliter. <lb/>Priores vocabimus verticales; medios, inclinatos; ultimos <lb/>horizontales.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/142.jpg" pagenum="111"/> <p type="margin"> <s><margin.target id="marg202"/>Tubi verti <lb/><gap/>ales.</s></p> <p type="main"> <s><emph type="italics"/>His ita expo&longs;itis, nunc afferemus varia Phænomena, <lb/>id e&longs;t, apparentias &longs;eu ob&longs;ervationes circa fluxum aquæ per tu­<lb/>bos verticales, cuiuscunque formæ & conditionis; ex quibus <lb/>deinde deducemus varia Problemata atque Theoremata; quo­<lb/>rum multa applicari etiam poterunt fluxui aquæ per &longs;iphones, <lb/>de quibus cap. præcedente. Agimus autem hoc Capite &longs;olùm <lb/>de fluxu aquæ per tubos ex foramine in ba&longs;i facto; de fluxu enim <lb/>ex foramine facto in latere, loquemur capite &longs;equenti.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>PROPOSITIO I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>PHÆNOMENON I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua decurrit per tubi verticalis foramen ba&longs;is in&longs;tar <lb/>Columnæ aqueæ, cuius ba&longs;is æqualis foramini, altitudo perpen­<lb/>diculares à ba&longs;i erectæ; &longs;ive tubi &longs;int &longs;emper <lb/>pleni, &longs;ive non.<emph.end type="center"/></s></p> <p type="main"> <s>SInt tubi verticales, AB, cuiuscunque figuræ, haben­<lb/> <arrow.to.target n="marg203"/><lb/>tes foramen B in ba&longs;i. Dico aquam decurrere per <lb/>foramen B in&longs;tar columnæ aqueæ AB, cuius ba&longs;is <lb/>e&longs;t foramen B, altitudo verò perpendiculares BA, <lb/>a ba&longs;i erectæ, &longs;ive tubi &longs;int &longs;emper pleni, &longs;ive non. Patet expe­<lb/>rientia, & &longs;equitur ex dictis Cap. 1. Propriet. IV. & ex doctrina <lb/>Archimedis lib. 1. de In&longs;identibus humido, Suppo&longs;itione I. </s></p> <p type="margin"> <s><margin.target id="marg203"/><emph type="italics"/>Aqua per <lb/>foramen ba <lb/>&longs;is tuborum <lb/><expan abbr="verticaliũ">verticalium</expan> <lb/>fluit in&longs;tar­<lb/>colu mnæ a­<lb/>queæ.<emph.end type="italics"/></s></p> <p type="main"> <s>Ac primò quidem, &longs;i tubus e&longs;t columnaris, & tota ba&longs;is e&longs;t <lb/>aperta, prout e&longs;t tubus primæ, ex appo&longs;itis, Figuræ ad &longs;ini&longs;tram; <lb/>manife&longs;ta e&longs;t experientia: videmus enim totam aquam &longs;imul <lb/>paulatim de&longs;cendere, &longs;i tubus non e&longs;t &longs;emper plenus. Idem au­<lb/>tem fit, &longs;i tubus e&longs;t &longs;emper plenus; de&longs;cendit enim &longs;emper nova <lb/>& nova columna aquea, & effluit ex ba&longs;i B. </s></p> <p type="main"> <s>Si autem tubus e&longs;t quidem columnaris, &longs;ed aqua non ef­<lb/>fluit per totam ba&longs;im apertam, &longs;ed per foramen in ba&longs;i factum, <pb xlink:href="051/01/143.jpg" pagenum="112"/> <arrow.to.target n="fig29"/><lb/>prout apparet in &longs;ecunda Figura; item &longs;i e&longs;t conoidalis in&longs;tar co­<lb/>ni truncati inver&longs;i, prout in tertia Figura apparet, idem contin­<lb/>git: Nam videmus, effluente aquâ per B, &longs;ub&longs;idere paulatim <lb/>aquam A, <expan abbr="incumbent&etilde;">incumbentem</expan> ip&longs;i B ad <expan abbr="perpendiculũ">perpendiculum</expan>, <expan abbr="fieri&qacute;">fierique</expan>; fo&longs;&longs;am in <lb/>&longs;uperiori &longs;uperficie vbi A, reliquas verò partes collaterales e A, <lb/>f A, confluere intra fo&longs;&longs;am; ad eum modum, quo in arenarijs <lb/>horologijs, dum è &longs;uperiori phiala defluit arena per foramen <lb/>diaphragmatis in inferiorem phialam, efficitur fo&longs;&longs;a in &longs;uperiori <lb/>arenæ &longs;uperficie, in eamque incidunt circumia centes arenæ par­<lb/>tes. Quod &longs;ignum e&longs;t, aquam de&longs;cendere & effluere per B in <lb/>modum columnæ AB. Et hoc quidem contingit apertè in tu­<lb/>bis non &longs;emper plenis, ut experientia docet. Idem autem con­<lb/>tingere nece&longs;&longs;e e&longs;t in tubis &longs;emper plenis; ni&longs;i quòd in his de&longs;cen­<lb/>dat &longs;emper nova ac nova columna aquea. </s></p> <figure id="id.051.01.143.1.jpg" xlink:href="051/01/143/1.jpg"/> <p type="main"> <s>Quod diximus de tubis columnaris & conoidalis figuræ; <lb/>intelligendum etiam e&longs;t de columnis aliarum figurarum, pro­<lb/>pter paritatem rationis, dummodo &longs;int verticaliter erecti. </s></p> <p type="main"> <s>Si foramen e&longs;t quidem in ba&longs;i tubi (cuiuscunque figuræ <pb xlink:href="051/01/144.jpg" pagenum="113"/>& conditionis &longs;it tubus,) at &longs;uperior aquæ fuperficies non &longs;u­<lb/>pereminet foramini ad perpendiculum, ut in appo&longs;ita Figura ap­<lb/>paret; adhuc effluit aqua columnaliter, &longs;eu in&longs;tar columnæ <lb/>AB, cuius ba&longs;is e&longs;t foramen B. altitudo perpendiculares à ba&longs;i <lb/>u&longs;que ad &longs;ummitatem i&longs;tius aquæ; quæ ba&longs;i perpendiculariter <lb/>imminet. Ratio de&longs;umitur ex dictis cap 1. Proprietate IV. </s></p> <p type="main"> <s><emph type="center"/>Corollarium.<emph.end type="center"/></s></p> <p type="main"> <s>EX his colligitur, &longs;olam columnam aqueam AB premere <lb/> <arrow.to.target n="marg204"/><lb/>&longs;upra foramen B, quoniam illa &longs;ola ad perpendiculum im­<lb/>minet ba&longs;is foramini. </s></p> <p type="margin"> <s><margin.target id="marg204"/><emph type="italics"/>Columna <lb/>aquea &longs;ola <lb/>premit &longs;u­<lb/>pra <expan abbr="foram&etilde;">foramen</expan> <lb/>per quod ef­<lb/>fluit.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio II. Phænomenon II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per tubos tam &longs;emper, quàm non &longs;emper plenos æqua­<lb/>lis altitudinis, & æqualium foraminum, effluit æqualis aquæ <lb/>copia, eodem vel æquali tempore, cuiuscunque capaci­<lb/>tatis & formæ &longs;int tubi.<emph.end type="center"/></s></p> <p type="main"> <s>ALtitudo tuborum, tum hac, tum &longs;equentibus Propo&longs;itioni <lb/> <arrow.to.target n="marg205"/><lb/>bus, &longs;umitur à lumine &longs;eu foramine, u&longs;que ad &longs;uperius orifi­<lb/>cium, includendo etiam ip&longs;ius foraminis altitudinem &longs;eu cra&longs;­<lb/>&longs;itiem, ab interiori ad exteriorem &longs;uperficiem ba&longs;is, &longs;i in ba&longs;i &longs;eu <lb/>fundo &longs;it foramen. </s></p> <p type="margin"> <s><margin.target id="marg205"/><emph type="italics"/>Tuborum <lb/>altitudo v<gap/><lb/>de &longs;umatur<emph.end type="italics"/></s></p> <p type="main"> <s>Sint igitur, ut antea, tubi, AB, æquè al<gap/>i, & æqualium fo­<lb/>raminum B, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, cuius­<lb/>cunque capacitatis, & figuræ. Dico, per foramina illa effluere <lb/>eodem, vel æquali tempore, æqualem aquæ copiam. Quoni­<lb/>am enim, per præcedentem Propo&longs;itionem, &longs;upra foramem B <lb/>in omnibus æqualis aquæ copia æquali vi premit, nempe colu­<lb/>mna aquea AB, cuius ba&longs;is e&longs;t foramen B in omnibus æquale, <lb/>ut &longs;upponitur; & altitudo e&longs;t perpendicularis AB, in omnibus <lb/>itidem æqualis; nece&longs;&longs;e e&longs;t, æqualem aquæ copiam eodem tem­<lb/>pore decurrere ex omnibus: ubi enim omnia &longs;unt æqualia, ef­<lb/>fectus &longs;unt æquales. </s></p> <pb xlink:href="051/01/145.jpg" pagenum="114"/> <p type="main"> <s><emph type="center"/>Corollarium I.<emph.end type="center"/><lb/> <arrow.to.target n="marg206"/></s></p> <p type="margin"> <s><margin.target id="marg206"/><emph type="italics"/>Aquæ flux' <lb/>è foramine <lb/>va&longs;is non e&longs;t <lb/>celerior pro­<lb/>pter va&longs;is <lb/>capacit<gap/><expan abbr="&etilde;">em</expan>.<emph.end type="italics"/></s></p> <p type="main"> <s>COlligitur hinc, ad aquæ effluxum maiorem, aut celeriorem <lb/>è foramine eodem, aut æquali, nihil facere capacitatem <lb/>va&longs;is aut tubi; adeo ut &longs;i totus Oceanus e&longs;&longs;et inclu&longs;us in uno tubo, <lb/>aut va&longs;e, & in altero modica aqua, vterque tamen tubus e&longs;&longs;et <lb/>æquè altus, & haberet æqualia foramina; æqualis aquæ copia <lb/>ex vtroque efflueret eodem, vel æquali tempore. </s></p> <p type="main"> <s><emph type="center"/>Corollarium II.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur præterea, per foramina æqualia in eadem ba&longs;i eius­<lb/>dem tubi, æqualem aquam effluere eodem tempore. Sed <lb/>de hoc agemus infrà cap. 5. Propo&longs;. 1. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III. Phænomenon III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per tubos tam &longs;emper, quàm non &longs;emper plenos æqua­<lb/>lium luminum, &longs;ed inæqualium altitudinum, effluit eodem, <lb/>vel æquali tempore, inæqualis aquæ copia.<emph.end type="center"/></s></p> <p type="main"> <s>NEmpe per tubum magis altum maior, & per tubum minùs <lb/>altum, minor. Ratio e&longs;t, quia &longs;upra lumen altioris tubi <lb/>maior aquæ copia, & maiori vi ac celeritate; & &longs;upra lumen mi­<lb/>noris minor, & minori vi ac celeritate premit, nempe aquea co­<lb/>lumna magis aut minùs alta. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IV. Phænomenon IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per tubos &longs;emper, & non &longs;emper plenos inæqualium <lb/>luminum, &longs;ed æqualium altitudinum, effluit eodem, vel æ­<lb/>quali tempore, inæqualis aquæ copia.<emph.end type="center"/></s></p> <p type="main"> <s>NEmpe per maius lumen maior, & per minus minor. Ratio <lb/>e&longs;t eadem, quia &longs;cilicet &longs;upra maius lumen premit maior a­<lb/>quæ copia, & maiori vi; & &longs;upra minus minor, & minori vi, &longs;ci­<lb/>licet columna aquea æquè alta, &longs;ed non æquè cra&longs;&longs;a. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>PEr tubos vtro&longs;que, hoc e&longs;t, tam &longs;emper plenos, quàm non <lb/>&longs;emper plenos, inæqualium luminum, & inæqualium altitu- <pb xlink:href="051/01/146.jpg" pagenum="115"/>dinum, effluere pote&longs;t eodem, vel æquali tempore, æqualis, <lb/>& inæqualis aquæ copia, hoc e&longs;t, æqualis per aliquos, inæqualis <lb/>per alios. Ratio e&longs;t, quia defectus luminis in vno pote&longs;t &longs;up­<lb/>pleri per altitudinem; & defectus altitudinis in altero pote&longs;t &longs;up­<lb/>pleri per lumen, vt experientia etiam docet. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio V. Phænomenon. V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per tubos æquè altos, & æqualium luminum, non &longs;em­<lb/>per plenos, fluit eodem tempore æqualis aquæ copia; &longs;ed tantò <lb/>fluit vnus diutiùs altero, quantò plùs aquæ continet <lb/>vnus quàm alter.<emph.end type="center"/></s></p> <p type="main"> <s>PAtet ex hactenus dictis, & experientiâ, nec indiget alia pro­<lb/>batione. Ille autem plùs aquæ continet, qui amplior e&longs;t: <lb/>loquimur enim hîc de ijs tubis, quorum orificia &longs;unt æqualia, <lb/>etiam&longs;i ip&longs;i tubi &longs;int inæqualis amplitudinis. </s></p> <p type="main"> <s><emph type="center"/>Corollarium.<emph.end type="center"/></s></p> <p type="main"> <s>ERgo & per æqualia foramina ba&longs;is eiusdem tubi, æqualis eo­<lb/>dem tempore effluit aqua. Vide cap. 5. Propo&longs;. 1. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VI. Phænomenon VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per tubos non &longs;emper plenos, & non æquè altos, æqua­<lb/>lium tamen luminum, eodem vel æquali tempore <lb/>non fluit æqualis aquæ copia.<emph.end type="center"/></s></p> <p type="main"> <s>EAdem e&longs;t ratio de quibu&longs;cunque va&longs;is. Patet experientiâ, </s></p> <p type="main"> <s> <arrow.to.target n="marg207"/><lb/>quæ mon&longs;trat, ex altiori tubo &longs;eu va&longs;e fluere maiorem aquæ, <lb/>copiam tempore eodem, vel æquali, quàm ex tubo vel va&longs;e mi­<lb/>nùs alto habente lumen æquale. Et ratio e&longs;t, quia in altiori <lb/>magis preinitur aqua &longs;upra lumen, quàm in minùs alto. Vide <lb/>Propo&longs;it. III. </s></p> <p type="margin"> <s><margin.target id="marg207"/><emph type="italics"/>Vas magis <lb/>plenum plus <lb/>aquæ effun­<lb/>dit per fora­<lb/>men, quàm <lb/>minus ple­<lb/>num.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur hinc, ex eodem tubo, aut va&longs;e, non &longs;emper pleno, <lb/>æqualibus temporibus, non æqualem effluere aquam ex eo­<lb/>dem foramine, &longs;ed in &longs;ecundo tempore minorem, quàm in pri­<lb/>mo, & in tertio minorem, quàm in &longs;ecundo, & &longs;ic deinceps. <lb/>Vide Propo&longs;it. 24. </s></p> <pb xlink:href="051/01/147.jpg" pagenum="116"/> <p type="main"> <s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur præterea, &longs;patia quæ æqualibus temporibus evacu­<lb/>antur in dicto ca&longs;u, non e&longs;&longs;e æqualia, &longs;ed &longs;ecundum &longs;patium <lb/>corre&longs;pondens &longs;ecundo tempori, e&longs;&longs;e minus primo; & tertium <lb/>&longs;patium corre&longs;pondens tertio tempori, minus &longs;ecundo; & &longs;ic de <lb/>cæteris. Vide ibidem. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VII. Phænomenon VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Tubus altitudine quadrupedalis, cui pro ba&longs;is diametro <lb/>pedis Pari&longs;ien&longs;is vncia, aquâ &longs;emper plenus, effundit per lumen <lb/>lineare in ba&longs;i &longs;itum aquæ libram &longs;patio tredecim mi­<lb/>nutorum &longs;ecundorum temporis.<emph.end type="center"/></s></p> <p type="main"> <s>OB&longs;ervavit hoc Marinus Mer&longs;ennus, ut a&longs;&longs;erit ip&longs;e in Hydrau­<lb/>licis &longs;uis Phænomenis Propo&longs;it. 1. </s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>VTitur autem Mer&longs;ennus tam pede, quàm libra (heminam vocat ip&longs;e)<emph.end type="italics"/><lb/> <arrow.to.target n="marg208"/><lb/><emph type="italics"/>Pari&longs;ien&longs;i. Et pedem quidem, uti in aliarum Nationum pedibus fie­<lb/>ri&longs;olet, dividit in duodecim æquales partes, quas uncias appellat; & <lb/>quamlíbet vnciam &longs;ubdividit in alias duodecim partes æquales, quas <lb/> <arrow.to.target n="marg209"/><lb/>ip&longs;e lineas, alij &longs;crupulos vocant. Vncia, &longs;eu duodecima pedis pars ap­<lb/>pellatur etiam pollex; ab aliquibus verò cum Mer&longs;enno digitus: rectiùs <lb/>tamen digitus e&longs;t decima &longs;exta pars pedis, vt con&longs;tat ex Vitruvio, Iulio <lb/>Frontino, Columella, & alijs apud Villalpandum tom.<emph.end type="italics"/> 3. <emph type="italics"/>Apparatus <lb/>Part.<emph.end type="italics"/> 2. <emph type="italics"/>lib.<emph.end type="italics"/> 3. <emph type="italics"/>cap.<emph.end type="italics"/> 16. <lb/> <arrow.to.target n="marg210"/></s></p> <p type="margin"> <s><margin.target id="marg208"/><emph type="italics"/>Pes dividi<lb/>tur in vnci­<lb/><gap/><emph.end type="italics"/> 12. <emph type="italics"/>& di­<lb/>gitos<emph.end type="italics"/> 16.</s></p> <p type="margin"> <s><margin.target id="marg209"/>Linea e&longs;t <lb/>duodecima <lb/>pars vncia.</s></p> <p type="margin"> <s><margin.target id="marg210"/><emph type="italics"/>Minuti &longs;e­<lb/><gap/>undi dura <lb/>tio, quanta <lb/>&longs;it.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Minutum &longs;ecundum e&longs;t &longs;exage&longs;ima pars unius minuti primi, &longs;eu<emph.end type="italics"/><lb/>3600. <emph type="italics"/>pars vnius horæ, & proximè re&longs;pondet lento arteriæ &longs;eu cordis <lb/>pul&longs;ui, ut Mer&longs;ennus a&longs;&longs;erit.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>NOn e&longs;t nece&longs;&longs;e, ut ba&longs;is tubi quadrupedalis, quo fit ob&longs;ervatio, &longs;it </s></p> <p type="main"> <s> <arrow.to.target n="marg211"/><lb/>pedalis, aut uncialis, aut alterius determinatæ amplitudinis atque <lb/>capacitatis, &longs;ed &longs;ufficit quantalibet latitudo tubi, dummodò foramen &longs;it <lb/>lineare. Ratio e&longs;t, quia; ut vidimus Propo&longs;itione<emph.end type="italics"/> 2. <emph type="italics"/>huius capitis, ea­<lb/>dem aquæ quantitas eodem, vel æquali tempore, fluit ex tubo &longs;emper <lb/>pleno quantum vis arcto, vel lato, dummodò foramen &longs;it lineare, & al-<emph.end type="italics"/> <pb xlink:href="051/01/148.jpg" pagenum="117"/><emph type="italics"/>titudo &longs;it quadrupedalis; adeo ut &longs;i totus Oceanus, ut &longs;uprà innuimus in <lb/> <arrow.to.target n="marg212"/><lb/>Corollario I. Propo&longs;it.<emph.end type="italics"/> 2. <emph type="italics"/>e&longs;&longs;et inclu&longs;us va&longs;i quatuor pedum æltitudinis & <lb/>luminis linearis, non effunderet ni&longs;i vnicam heminam &longs;eu libram Pari­<lb/>&longs;ien&longs;em &longs;patio tredecim minutorum &longs;ecundorum; Si tamen addas, inquit <lb/>Mer&longs;ennus, pro horis &longs;ingulis vnam quadrage&longs;imam quintam libræ <lb/>partem, quâ&longs;olet aqua marina &longs;uperare aquam fontium ac fluviorum in <lb/>pondere, & con&longs;equenter vi premendi, & vehementiùs è foramine e­<lb/>rumpendi.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg211"/>Vas ampli­<lb/>us non effu­<lb/>dit plùs a <lb/>quæ per fora <lb/>men, quàm <lb/>minù, am-</s></p> <p type="margin"> <s><margin.target id="marg212"/>plum, &longs;i al­<lb/>titudo & fo­<lb/>ramè æqua <lb/>lia &longs;unt.</s></p> <p type="main"> <s><emph type="center"/>Annotatio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVod dicit Mer&longs;ennus de tubo quadrupedali, & de libra aquæ, in­<lb/>telligi debet &longs;olùm loquendo de pede & libra Pari&longs;ien&longs;i, non ve­<lb/>rò aliarum Nationum, &longs;ed unu&longs;qui&longs;que in &longs;ua natione experientiam <lb/>facere debet, ut &longs;ciat quantum aquæ, quanto tempore, ex quantæ al­<lb/> <arrow.to.target n="marg213"/><lb/>titudinis, quantique foraminis tubo, ejiciatur. Cæterùm cùm diffe­<lb/>rentia pedum, atque librarum apud diver&longs;as Nationes tanta &longs;it, quan­<lb/>ta ip&longs;arum Nationum; cum&queacute; difficulter exacta men&longs;ura unius certi <lb/>ac determinati pedis, v. g. Romani, aut Pari&longs;ien&longs;is, ad alias Nationes <lb/>tran&longs;mitti libris impre&longs;&longs;is po&longs;&longs;it, quòd chartæ priùs madefactæ, ac dein­<lb/>de &longs;iccatæ, non reddant fideliter longitudinem linearum impre&longs;&longs;arum; <lb/>nolo diutiùs huic rei inhærere, comparando pedem Pari&longs;ien&longs;em cum <lb/>pedibus aliarum Nationum. Faciat, qui volet, aut cujus intere&longs;t, <lb/>experientiam, ut videat quanto tempore tubus quatuor pedum regio­<lb/>nis &longs;uæ ejiciat per lumen lineare aquæ libram itidem regionis &longs;uæ. De <lb/>exacta pedis Romani men&longs;ura, & de modo tran&longs;mittendi illum ad <lb/>alias nationes, di&longs;&longs;eram in Pantometro Kircheriano Lib.<emph.end type="italics"/> 1. <emph type="italics"/>Technico <lb/>Parte<emph.end type="italics"/> 2. <emph type="italics"/>Cap.<emph.end type="italics"/> 4. </s></p> <p type="margin"> <s><margin.target id="marg213"/>Podis men­<lb/>&longs;ura diver­<lb/>&longs;a apud di­<lb/>ver&longs;as na­<lb/>tiones.</s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VIII. Phænomenon VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ fluentes ex tubis tam &longs;emper, quàm non &longs;em­<lb/>per plenis æqualium foraminum, &longs;ed inæqualium altitudinum, <lb/>habent rationem &longs;ubduplicatam altitudinum tuborum; <lb/><expan abbr="habent&qacute;ue">habentque</expan> dicti tubi duplicatam rationem <lb/>aquarum, quas fundunt.<emph.end type="center"/></s></p> <p type="main"> <s>RAtio &longs;eu proportio duplicata quæcunque, e&longs;t ratio quæ­<lb/> <arrow.to.target n="marg214"/><lb/>cunque &longs;implex &longs;emel repetita, &longs;eu bis continuè &longs;umpta: <pb xlink:href="051/01/149.jpg" pagenum="118"/>quemadmodum ratio quæcunque triplicata, quadruplicata, &c. <lb/>e&longs;t ratio quæcunque &longs;implex bis, ter &c. repetita, &longs;eu ter, <lb/>quater continuè &longs;umpta. Exemplum. Inter 2 & 1 reperitur <lb/>ratio dupla; hæc ratio &longs;i &longs;emel repetatur, &longs;eu adhuc &longs;emel <lb/>accipiatur, hoc e&longs;t, &longs;i bis continuè &longs;umatur hoc modo, 4, <lb/>2, 1; erit inter 4 & 1 ratio &longs;eu proportio duplicata illius pro­<lb/>portionis, quæ e&longs;t inter 2 & 1, quandoquidem inter 4 & 1 <lb/>reperitur ratio dupla &longs;emel repetita, &longs;eu bis continuè <lb/>&longs;umpta, hoc e&longs;t, duplicata, &longs;cilicet &longs;emel inter 4 & 2, & ite­<lb/>rum inter 2 & 1. Similiter inter 8 & 1 e&longs;t ratio triplicata il­<lb/>lius, quæ e&longs;t inter 2 & 1, quia inter 8 & 1, intercedit ter <lb/>ratio dupla, nempe 8 ad 4, 4 ad 2, 2 ad 1. Sic 16 ad 1 ha­<lb/>bet rationem quadruplicatam, & 32 ad 1 rationem quintu­<lb/>plicatam rationis illius, quam habet 2 ad 1. Aliud exemplum. <lb/>Inter 6 ad 4 reperitur ratio &longs;e&longs;quialtera &longs;implex; hæc ratio <lb/>duplicatur, &longs;i adhuc &longs;emel repetatur, &longs;eu &longs;i bis continuè &longs;uma­<lb/>tur, ut apparet in his numeris 9, 6, 4: nam quia ut 6 ad 4, <lb/>ita 9 ad 6; ideo inter 9 & 4 bis reperitur ratio &longs;e&longs;quialtera. <lb/>Si verò eadem ratio &longs;e&longs;quialtera bis repetatur, &longs;eu ter conti­<lb/>nuè ponatur; erit inter extremos terminos ratio &longs;e&longs;quialtera <lb/>triplicata, ut apparet in his numeris, 13<gap/>, 9, 6, 4; quam pro­<lb/>portionem ab&longs;que fractione habebis, &longs;i duplicaveris ho&longs;ce <lb/>numeros &longs;ic, 27, 18, 12, 8: nam ut 12 continet 8 &longs;emel cum <lb/>dimidio, ita 18 continet 12 &longs;emel cum dimidio, & 27 etiam <lb/>continet 18 &longs;emel cum dimidio. <lb/> <arrow.to.target n="marg215"/></s></p> <p type="margin"> <s><margin.target id="marg214"/><emph type="italics"/>Duplicat<gap/><lb/>proportio <lb/>quæ.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg215"/><emph type="italics"/>Subduplica <lb/>ta proportio <lb/>quæ.<emph.end type="italics"/></s></p> <p type="main"> <s>Ex ratione duplicata, triplicata, quadruplicata, &c. facilè <lb/>intelligitur ratio &longs;ubduplicata, &longs;ubtriplicata, &longs;ubquadruplica­<lb/>ta, &c. Nam per rationem &longs;ubduplicatam intelligimus <expan abbr="dimidiũ">dimidium</expan> <lb/>rationis duplicatæ. Verbi gratia, 4 ad 1 habet rationem dupli­<lb/>catam rationis duplæ; 2 ad 1, aut 4 ad 2, con&longs;tituunt dimidium <lb/>rationis 4 ad 1; ideo 2 ad 1, & 4 ad 2, habent rationem &longs;ub­<lb/>duplicatam. Similiter 9 ad 4 habet rationem duplicatam <lb/>rationis &longs;e&longs;quialteræ; dimidium talis rationis e&longs;t 9 ad 6, vel <lb/>6 ad 4; ideo 9 ad 6, & 6 ad 4 habent rationem &longs;ubduplica­<lb/>tam prædictæ rationis &longs;e&longs;quialteræ. </s></p> <pb xlink:href="051/01/150.jpg" pagenum="119"/> <figure id="id.051.01.150.1.jpg" xlink:href="051/01/150/1.jpg"/> <p type="main"> <s>His explicatis, e&longs;to tubus AB unius pedis, & </s></p> <p type="main"> <s> <arrow.to.target n="marg216"/><lb/>tubus CD quatuor pedum, æqualium foraminum, <lb/>& uterque &longs;eu &longs;emper, &longs;eu non &longs;emper plenus; qui <lb/>quidem eodem, vel æquali tempore inæqualem <lb/>effundunt aquæ copiam, nempe major majorem, <lb/>& minor minorem, ut con&longs;tat ex Propo&longs;itione III. <lb/>præcedenti. Dico, aquam tubi CD, ad aquam <lb/>tubi AB eodem aut æquali tempore effu&longs;am, ha­<lb/>bere rationem &longs;ubduplicatam tuborum, hoc e&longs;t, <lb/>aquam effluentem è tubo CD e&longs;&longs;e duplam aquæ <lb/>effluentis è tubo BA. Etidem dicendum e&longs;t de qua­<lb/>cunque alia ratione &longs;eu proportione; ut &longs;i unus tu­<lb/>bus &longs;it 9 pedum, alter unius pedis, erit aqua ma­<lb/>joris ad aquam minoris, ut 3 ad 1. Con&longs;tat ex <lb/>ob&longs;ervatione, ut a&longs;&longs;erit Mer&longs;ennus in &longs;uis Hydraulicis, Propo­<lb/>&longs;it. 2 po&longs;t medium. Ratio phænomeni dependet ex velocita­<lb/>te aquæ de&longs;cendentis & effluentis ex tubo CD, &longs;upra veloci­<lb/>tatem æquæ de&longs;cendentis & effluentis ex tubo AB; de qua <lb/>vide Propo&longs;it. IX. & X. <expan abbr="&longs;eq.">&longs;eque</expan> ubi dicemus, illam ad hanc e&longs;&longs;e du­<lb/>plam, hoc e&longs;t, &longs;ubduplicatam altitudinum tuborum haben­<lb/>tium æqualia foramina; quo demon&longs;trato, demon&longs;trabimus <lb/>deinde Propo&longs;itione XI. hanc præ&longs;entem Propo&longs;itionem. </s></p> <p type="margin"> <s><margin.target id="marg216"/><emph type="italics"/>Aquæ dupli <lb/>catam ra­<lb/>tionem ha­<lb/>bent tubo­<lb/>rum æqua­<lb/>lium lumi­<lb/>num, at in­<lb/>æqualium <lb/><expan abbr="altitudinũ">altitudinum</expan>.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur ex his, tuborum æqualium foraminum altitudi­<lb/> <arrow.to.target n="marg217"/><lb/>nes debere e&longs;&longs;e in duplicata ratione aquarum inæqualium <lb/>quas debent eodem tempore fundere. Verbi gratia, tubus pe­<lb/>dalis determinato tempore dat unam aquæ libram ex &longs;uo fo­<lb/>ramine; ut alius tubus ex æquali foramine æquali tempore det <lb/>duas libras, debet habere duplicatam rationem ad illum, nem­<lb/>pe debet e&longs;&longs;e altus quatuor pedibus. Sic etiam quia tubus qua­<lb/>tuor pedum per lineare lumen &longs;patio 13 minutorum &longs;ecundo­<lb/>rum fundit unam libram aquæ, ut diximus Propo&longs;it. VII. ut <lb/>alius tubus eodem tempore per lumen lineare fundat centum <pb xlink:href="051/01/151.jpg" pagenum="120"/>libras, debet habere altitudinem duplicatam 1 ad 100; nem­<lb/>pe 40000. pedum. Atque hæc e&longs;t conver&longs;a præcedentis Pro­<lb/>po&longs;itionis. </s></p> <p type="margin"> <s><margin.target id="marg217"/><emph type="italics"/>Tubi æqua­<lb/>lium lumi­<lb/>num, at in­<lb/>æqualium <lb/><expan abbr="altitudinũ">altitudinum</expan>, <lb/>habent du­<lb/>plicatam <expan abbr="ra-tion&etilde;">ra­<lb/>tionem</expan> aqua­<lb/>rum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur præterea, datis tubis æqualium foraminum, at <lb/>inæqualium altitudinum, in numeris aut lineis, mediam <lb/>proportionalem dare aquas; & datis aquis in numeris aut men­<lb/>&longs;uris, tertiam proportionalem dare tuborum altitudinem æqua­<lb/>lium foraminum. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/><lb/> <arrow.to.target n="marg218"/></s></p> <p type="margin"> <s><margin.target id="marg218"/><emph type="italics"/>Mediæ, ac <lb/>Tertiæ pro­<lb/>portionalis <lb/>quantitatis <lb/>in ventio.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>DEinventione mediæ ac tertiæ proportionalis magnitudinis in nume­<lb/>ris ac lineis, agemus infrà in Parergo hujus capitis, & in Arith­<lb/>metica ac Geometria practica, & in Pantometro Kircheriano lib.<emph.end type="italics"/> 8. <lb/><emph type="italics"/>cap.<emph.end type="italics"/> 1. <emph type="italics"/>Propo&longs;it.<emph.end type="italics"/> 1. <emph type="italics"/>&<emph.end type="italics"/> 3. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IX. Theorema I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua naturali motu de&longs;cendens & effluens per tubos, <lb/>imitatur leges aliorum gravium naturali <lb/>motu de&longs;cendentium.<emph.end type="center"/></s></p> <p type="main"> <s>NOn uni mirabile vi&longs;um, inquit Mer&longs;ennus in Phænome­<lb/>nis Hydraulicis Propo&longs;it. III. quòd non &longs;it eadem ratio <lb/>quantitatis aquæ fluentis ex tubo pedali, ad aquæ quantitatem <lb/>ex quadrupedali tubo &longs;alientis, po&longs;ito æquali foramine in utro­<lb/>que, quæ e&longs;t 1 ad 4; cùm aqua quadrupedalis tubi quadruplo <lb/>magis, quàm pedalis premere videatur fundum, & aquam ex <lb/>lumine &longs;alientem. Verùm mirari de&longs;ines, ubi noveris, aquam <lb/>eo &longs;olùm modo premere, vel ea duntaxat velocitate tubum <lb/>egredi, quâ moveretur, &longs;i ex eadem tubi altitudine cecidi&longs;&longs;et; <lb/>adeo ut &longs;it eadem i&longs;tius phænomeni ratio, quæ de&longs;cen&longs;us aquæ <lb/>per tubum; & eadem hujus de&longs;cen&longs;us, quæ de&longs;cen&longs;us aliorum <lb/><gap/>m; de quo proinde hîc agendum paulò accuratiùs, quan­<lb/><gap/>dem aquæ motus per tubum, & ex tubo eruptio, &longs;equi­<lb/><gap/>ges gravium motu naturali de&longs;cendentium. </s></p> <pb xlink:href="051/01/152.jpg" pagenum="121"/> <p type="main"> <s><emph type="center"/>Leges gravium naturali motu de&longs;cendentium.<emph.end type="center"/></s></p> <p type="main"> <s>LEges porrò, quas gravia in de&longs;cen&longs;u naturali motu facto <lb/> <arrow.to.target n="marg219"/><lb/>&longs;ervant, incredibili cura ac diligentia indagavit & ob&longs;er­<lb/>vavit Bononiæ P. Joannes Bapti&longs;ta Ricciolus, unà cum alijs <lb/>è no&longs;tra Societate Patribus, ea&longs;que clari&longs;&longs;imè ac di&longs;tincti&longs;&longs;imè <lb/> <arrow.to.target n="marg220"/><lb/>proponit in Tomo 1. Almage&longs;ti &longs;ui novi; fusè quidem lib. 9. <lb/>&longs;ect. 4. cap. 16. num. 24. breviter verò lib. 2. cap. 21. Quibus <lb/>Riccioli ob&longs;ervationibus tantam ego fidem adhibeo, ut licet <lb/>hîc Romæ ea&longs;dem repetere opportuni&longs;&longs;imum mihi foret, de­<lb/>mi&longs;&longs;is gravibus per cochleatas Divi Petri in Vaticano &longs;calas <lb/>alti&longs;&longs;imas, & ab omni aëris commotione liberas, fene&longs;tris in <lb/>&longs;uper plurimis ab ima ba&longs;i ad &longs;ummitatem u&longs;que refertas; n<gap/>­<lb/>luerim tamen me fru&longs;tra fatigare, cùm nec accuratiores ad­<lb/>hibere me po&longs;&longs;e putem, nec &longs;i adhibeam, alias præter ip&longs;ius <lb/>leges reperturum me certò &longs;ciam. Ex multis igitur de&longs;cen­<lb/>&longs;us gravium legibus à Ricciolo locis citatis adductis, duas &longs;e­<lb/>quentes affero, quoniam eæ propo&longs;ito no&longs;tro &longs;atisfacient. </s></p> <p type="margin"> <s><margin.target id="marg219"/><emph type="italics"/>Gravium <lb/>naturali <lb/>motu <expan abbr="de-&longs;cendentiũ">de­<lb/>&longs;cendentium</expan> <lb/>leges.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg220"/><emph type="italics"/>Riccioli di­<lb/>ligentia ex­<lb/>acta in ob­<lb/>&longs;ervandis le <lb/>gibus gra­<lb/>viu<gap/><emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>I. Gravia naturali motu per lineam perpendicularem in aëre de­<lb/> <arrow.to.target n="marg221"/><lb/>&longs;cendentia, moventur difformi velocitate, eâque majore & majore <lb/>ver&longs;us finem motus.<emph.end type="italics"/> Lex hæc nota fuit jam inde à viginti & am­<lb/>pliùs &longs;æculis in Academijs Phy&longs;icorum, præ&longs;ertim Peripateti­<lb/>corum cum Ari&longs;totele lib. 1. de cœlo cap. 88. inquit Ricciolus, <lb/>patetque oculis, auribus, & tactui; videmus enim gravia de­<lb/>&longs;cendentia accelerare magis ac magis motum; audimus vehe­<lb/>mentiorem &longs;onum, percipimus validiorem percu&longs;&longs;ionem, ex <lb/>lap&longs;u gravis ac duri è loco altiori, quàm minùs alto. </s></p> <p type="margin"> <s><margin.target id="marg221"/>Lex I. gra­<lb/>vium <expan abbr="de-&longs;cendentiũ">de­<lb/>&longs;cendentium</expan>.</s></p> <p type="main"> <s><emph type="italics"/>II. Motus gravium naturaliter de&longs;cendentium per aërem, cre­<lb/> <arrow.to.target n="marg222"/><lb/>&longs;cit eo incremento velocitatis, quod e&longs;t inter numeros impares ab uni­<lb/>tate numeratos; &longs;eu ita ut &longs;patia æqualibus temporibus tran&longs;mi&longs;&longs;a &longs;int <lb/>inter &longs;e, ut quadrata temporum; &longs;eu ita, ut &longs;patia tran&longs;mi&longs;&longs;a certis <lb/>temporibus habeant inter &longs;e duplicatam proportionem illius, quam ha­<lb/>bent tempora quibus &longs;patia illa men&longs;urata fuerint.<emph.end type="italics"/> ita Ricciolus lo­<lb/>cis citatis, & ante ip&longs;um Galilæus Dialogo 2. de Sy&longs;temate <pb xlink:href="051/01/153.jpg" pagenum="122"/>Mundi, & Balianus lib 1. de Motu naturali gravium, Propo&longs;it. 6. <lb/>(licet deinde lib. 4. à pag. 110. ad 113. aliter &longs;tatuat) & po&longs;tip&longs;os <lb/>Ga&longs;&longs;endus in Epi&longs;tolis de motu impre&longs;&longs;o à motore, & Kirche­<lb/>rus in Mu&longs;urgia lib. 6. parte 1. Lemmate 3. & con&longs;tat experien­<lb/> <arrow.to.target n="marg223"/><lb/>tiâ. Numeri pariter impares ab unitate numerati, &longs;unt hi: 1, <lb/>3, 5, 7, 9, 11, 13, 15 &c. Itaque &longs;i grave aliquod de&longs;cendens con­<lb/>ficit in primo minuto temporis unum &longs;tadium &longs;patij; in &longs;ecundo <lb/>minuto conficiet tria ftadia, in tertio quinque, in quarto &longs;e­<lb/>ptem, &c. Sic enim &longs;patia æqualibus temporibus confecta, <lb/>erunt inter &longs;e, ut quadrata temporum: nam quadratum mi­<lb/>nuti primi e&longs;t 1; & quadratum minuti &longs;ecundi, 4; & quadra­<lb/>tum minuti tertij, 9; & quadratum minuti quarti, 16 &c. ut <lb/>apparet inappo&longs;ita tabella. <arrow.to.target n="table1"/><lb/>Cùm igitur grave de&longs;cen­<lb/>dens in primo minuto con­<lb/>ficiat unum &longs;patium, & in <lb/>&longs;ecundo minuto tria &longs;patia, <lb/>quæ cum uno conficiunt <lb/>quatuor; & in tertio minu­<lb/>to quinque &longs;patia, quæ cum <lb/>quatuor efficiunt novem; & in quarto minuto &longs;eptem &longs;patia, <lb/>quæ cum novem efficiunt &longs;exdecim; & in quinto minuto no­<lb/>vem &longs;patia, quæ cum &longs;exdecim efficiunt viginti quinque, &c. <lb/>apparet manife&longs;tè, &longs;patia tran&longs;mi&longs;&longs;a à gravi de&longs;cendente, ha­<lb/>bere &longs;e, ut quadrata temporum æqualium, quibus percurrun­<lb/>tur illa &longs;patia. In idem autem recidit, &longs;i dicas, &longs;patia tran&longs;­<lb/>mi&longs;&longs;a certis temporibus habere inter &longs;e duplicatam rationem <lb/>&longs;eu proportionem illius proportionis, quam habent tempora, <lb/>quibus &longs;patia illa men&longs;urata fuerint: nam tempus &longs;eu minutum <lb/>&longs;ecundum ad primum, ut apparet ex tabella præcedente, ha­<lb/>bet rationem &longs;eu proportionem duplam, &longs;patia verò &longs;ecundo <lb/>minuto confecta, nempe 1 ad 3 (quæ &longs;imul juncta efficiunt 4) <lb/>ad primum minutum habent rationem duplicatam rationis <lb/><gap/>plæ. Eadem e&longs;t ratio de cæteris. Lege etiam Mundum &longs;u<gap/>- <pb xlink:href="051/01/154.jpg" pagenum="123"/>terraneum P. Athana&longs;ij Kircheri, ubi in Libro Centro&longs;ophico <lb/>fu&longs;i&longs;&longs;imè pertractat hanc materiam. Lege præterea Joannem <lb/>Caramuelem in Cruce Sublimium ingeniorum. </s></p> <p type="margin"> <s><margin.target id="marg222"/>Lex II. gra­<lb/>vium <expan abbr="de-&longs;cendentiũ">de­<lb/>&longs;cendentium</expan>.</s></p> <p type="margin"> <s><margin.target id="marg223"/><emph type="italics"/>Numeri pa­<lb/>riter impa­<lb/>res ab unita <lb/>te numera­<lb/>ti.<emph.end type="italics"/></s></p> <table> <row><cell>Tempora</cell><cell>Quadrata</cell><cell>Spatia</cell></row> <row><cell>1</cell><cell>1</cell><cell>1</cell></row> <row><cell>2</cell><cell>4</cell><cell>3</cell></row> <row><cell>3</cell><cell>9</cell><cell>5</cell></row> <row><cell>4</cell><cell>16</cell><cell>7</cell></row> <row><cell>5</cell><cell>25</cell><cell>9</cell></row> <row><cell>6</cell><cell>36</cell><cell>11</cell></row></table> <p type="main"> <s><emph type="center"/>Leges aquæ naturali motu de&longs;cendentis <lb/>& effluentis per tubos.<emph.end type="center"/></s></p> <p type="main"> <s>SIt jam tubus ABCD, &longs;ive &longs;emper, &longs;ive non &longs;emper plenus, <lb/> <arrow.to.target n="marg224"/><lb/>cujus foramen B; <expan abbr="tempu&longs;&qacute;ue">tempu&longs;que</expan> in quo aqua ab A de&longs;cendit <lb/>u&longs;que ad B, dividatur in quinque æquales partes, in quarum <lb/>prima confecerit &longs;patium A1; Dico, eandem aquam in &longs;e­<lb/>cunda parte temporis conficere &longs;patium A4, in tertia parte <lb/> <arrow.to.target n="fig30"/><lb/>A9, in quarta &longs;patium A16, in quinta &longs;patium A25; <lb/>atque adeo &longs;patia æqualibus quinque temporibus <lb/>confecta, habere &longs;e ut quadrata quinque illorum <lb/>temporum, ut ex appo&longs;itis utrimque numeris ap­<lb/>paret; &longs;eu velocitatem de&longs;cen&longs;us aquæ cre&longs;cere &longs;e­<lb/>cundùm progre&longs;&longs;ionem numerorum imparium, <lb/>prout indicant numeri intra tubum notati; &longs;eu <lb/>&longs;patia confecta habere duplicatam rationem illius, <lb/>quam habent tempora, ut apparet &longs;i conferas nu­<lb/>meros externos lateris AB, cum numeris lateris <lb/>CD. Ratio e&longs;t, quia aqua gravis e&longs;t, & intra tu­<lb/>bum naturali motu de&longs;cendit, nullumque ade&longs;t <lb/>impedimentum motus; ergo imitari debet leges aliorum gra­<lb/>vium naturali motu de&longs;cendentium. </s></p> <p type="margin"> <s><margin.target id="marg224"/><emph type="italics"/>Leges aqua <lb/>naturali <lb/>motu de­<lb/>&longs;cendentis <lb/>per tubos.<emph.end type="italics"/></s></p> <figure id="id.051.01.154.1.jpg" xlink:href="051/01/154/1.jpg"/> <p type="main"> <s><emph type="center"/>Corollarium I.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur hinc primò, Aquam è foramine B, tubi &longs;emper <lb/> <arrow.to.target n="marg225"/><lb/>pleni, effluere tantâ velocitate, quantâ de&longs;cendit ab A ad <lb/>B. Ratio e&longs;t, quia ut &longs;upponitur, tantum effluit per B, quan­<lb/>tum influit per A, & è contrario tantum per A influit, quan­<lb/>tum per B effluit, & in de&longs;cen&longs;u ab A ad B nulla fit inter­<lb/>ruptio; ergo tam velociter effluit per B, quàm velociter de­<lb/>&longs;cendit ab A ad B. </s></p> <pb xlink:href="051/01/155.jpg" pagenum="124"/> <p type="margin"> <s><margin.target id="marg225"/><emph type="italics"/>Leges aquæ <lb/>effluentis <lb/>per <expan abbr="foram&etilde;">foramen</expan> <lb/>tubi &longs;emper <lb/>pleni.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium II.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur &longs;ecundò, Aquam apud B, in utroque tubo, hoc e&longs;t, <lb/>&longs;emper & non &longs;emper pleno, tantâ &longs;olùm vi premi prope <lb/>foramen B, quanta e&longs;t vis &longs;eu pondus aquæ à B u&longs;que ad &longs;u­<lb/>premam aquæ &longs;uperficiem, id e&longs;t, columnæ aqueæ habentis <lb/>pro ba&longs;i latitudinem foraminis B, pro altitudine perpendicu­<lb/>larem à B ad dictam &longs;uperficiem. Ratio e&longs;t, quia &longs;olùm illa <lb/>columna premit &longs;upra B, per dicta Propo&longs;it. 1. Intellige, ni&longs;i <lb/>illa aliunde impetum recipiat, ut &longs;i ip&longs;i affunderetur aqua ex <lb/>tubo inclinato, &longs;ive conjuncto, &longs;ive di&longs;iuncto. </s></p> <p type="main"> <s><emph type="center"/>Corollarium. III.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur tertiò, Leges prædictas de&longs;cen&longs;us gravium &longs;ervari <lb/> <arrow.to.target n="marg226"/><lb/>ab aqua in tubo &longs;emper pleno, de&longs;cendendo ab A ad B, &longs;o­<lb/>lùm in primo de&longs;cen&longs;u, non verò in de&longs;cen&longs;u continuato; item <lb/>&longs;olùm à prima parte aquæ de&longs;cendentis, <expan abbr="nõ">non</expan> à partibusip&longs;i conti­<lb/>guis & &longs;ub&longs;equentibus. Explico De&longs;cendat aqua ab A ad B, effi­<lb/>ciatque de&longs;cen&longs;us columnam aqueam AB, quæ dividatur in vi­<lb/>ginti <expan abbr="quinq;">quinque</expan> æquales partes &longs;ecundùm longitudinem &longs;eu altitu­<lb/>dinem ab A ad B. Dico, &longs;olùmvige&longs;imam quintam partem, quæ <lb/>e&longs;t apud B, &longs;ervare prædictam legem de&longs;cen&longs;us gravium cre­<lb/>&longs;centis in velocitate &longs;ecundùm numeros impares ab unitate <lb/>numeratos; & quidem illam &longs;olam vige&longs;imam quintam par­<lb/>tem, quæ e&longs;t in prima columna aquea à de&longs;cen&longs;u aquæ for­<lb/>mata, non verò quæ e&longs;t in reliquis columnis &longs;ub&longs;equentibus. <lb/>Ratio e&longs;t, quia cùm nulla pars ex viginti quinque egrediatur <lb/>è foramine B, quin ingrediatur alia per orificium A priori <lb/>æqualis; & nulla tran&longs;eat vige&longs;imum quintum & ultimum &longs;pa­<lb/>tiolum lateris AB, quin eodem tempore tran&longs;eat alia æqualis <lb/>primum &longs;patiolum, & alia &longs;ecundum, & alia tertium, ac reli­<lb/>qua omma; nece&longs;sè e&longs;t ut omnes reliquæ partes eâdem velo­<lb/>citate conficiant &longs;ingula &longs;patiola, qua velocitate ultima con­<lb/>ficit ultimum; & eâdem velocitate unaquæque pertran&longs;eat <lb/>&longs;patiolum &longs;ibi corre&longs;pondens, qua velocitate ultima pars per­<lb/>tran&longs;it ultimum &longs;patiolum. Patet ergo propo&longs;itum. </s></p> <pb xlink:href="051/01/156.jpg" pagenum="125"/> <p type="margin"> <s><margin.target id="marg226"/><emph type="italics"/>Lex de&longs;cen <lb/>&longs;us aquæ è <lb/>tubo expli­<lb/>catur.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium IV.<emph.end type="center"/></s></p> <figure id="id.051.01.156.1.jpg" xlink:href="051/01/156/1.jpg"/> <p type="main"> <s>COlligitur quartò, Aquam è foramine B efflue­<lb/> <arrow.to.target n="marg227"/><lb/>re eò majori velocitate, quò altior fuerit tu­<lb/>bus. Ratio e&longs;t, quia quò altior e&longs;t tubus, eò ma­<lb/>jorem velocitatem adquirit prima pars aquæ de­<lb/>&longs;cendentis in &longs;uo de&longs;cen&longs;u, & con&longs;equenter reli­<lb/>quæ &longs;ub&longs;equentes; item quò altior e&longs;t tubus, eò <lb/>altior e&longs;t columna aquea premens apud B. ideo­<lb/>que eò vehementiùs premit apud idem B. Vide <lb/>quæ diximus Propo&longs;it. VI. </s></p> <p type="margin"> <s><margin.target id="marg227"/><emph type="italics"/>Aqua è tu­<lb/>bo eò velo­<lb/>ciùs effluit, <lb/>quò altior <lb/>e&longs;t tubus.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium V.<emph.end type="center"/></s></p> <p type="main"> <s>COlligitur quintò, Aquam ex æqualibus tubis, quoad fora­<lb/> <arrow.to.target n="marg228"/><lb/>mina & altitudines, effluere æquali velocitate. </s></p> <p type="margin"> <s><margin.target id="marg228"/><emph type="italics"/>Aqua ex æ­<lb/>qualibus tu­<lb/>bis quoad o­<lb/>mnia, æqua­<lb/>li velocita­<lb/>te effluit,<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio X. Theorema II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Velocitates motus aquæ de&longs;cendentis & effluentis per <lb/>tubos æqualium foraminum, &longs;ed inæqualium altitu­<lb/>dinum, habent &longs;ubduplicatam rationem <lb/>altitudinum.<emph.end type="center"/></s></p> <figure id="id.051.01.156.2.jpg" xlink:href="051/01/156/2.jpg"/> <p type="main"> <s>ESto tubus AB altus uno pede, & alius CD al­<lb/>tus quatuor pedibus, &longs;ed uterque æqualium <lb/>foraminum, &longs;ive &longs;emper, &longs;ive non &longs;emper pleni, è <lb/>quibus effluat aqua inæquali velocitate, juxta di­<lb/>cta Propo&longs;itione præcedente, Corollario IV. Dico, <lb/>velocitates motus & effluxus aquarum e&longs;&longs;e in &longs;ub­<lb/>duplicata ratione tuborum, hoc e&longs;t, aquam per <lb/>tubum CD de&longs;cendere, & effluere duplo velo­<lb/>ciùs, quàm per tubum AB. Quoniam enim aquæ <lb/> <arrow.to.target n="marg229"/><lb/>motus per tubos æmulatur leges gravium de&longs;cen­<lb/>dentium motu naturali, per dicta Propo&longs;it. IX. <lb/>præcedente, hoc e&longs;t, cre&longs;cit in velocitate &longs;ecun- <pb xlink:href="051/01/157.jpg" pagenum="126"/> <arrow.to.target n="fig31"/><lb/>dùm progre&longs;&longs;ionem numerorumim parium ab un<gap/><lb/>tate numeratorum; &longs;i aqua in primo tempore d<gap/><lb/>terminato, v.g. in primo minuto de&longs;cendit à C i<gap/><lb/>E, hoc e&longs;t, ab A in B; in &longs;ecundo minuto d<gap/><lb/>&longs;cendet ab E ad D, ac proinde in fine quarti pa<gap/><lb/>mi mota erit duplo velociùs, quàm in fine prin<gap/><lb/>palmi; Ergo velocitas motus aquæ per tubum CI<gap/><lb/>ad velocitatem aquæ per tubum AB, habet &longs;ul<gap/><lb/>duplicatam rationem altitudinum. Eadem e<gap/><lb/>ratio in alijs inæqualibus altitudinibus, quamcu<gap/><lb/>que habeant inter &longs;e proportionem. </s></p> <p type="margin"> <s><margin.target id="marg229"/><emph type="italics"/>Proportio <lb/>velocitatis <lb/>motus aquæ <lb/>de&longs;cenden­<lb/>tis per tubos: <lb/><expan abbr="inæqualiũ">inæqualium</expan> <lb/>foraminum.<emph.end type="italics"/></s></p> <figure id="id.051.01.157.1.jpg" xlink:href="051/01/157/1.jpg"/> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/><lb/> </s></p> <p type="main"> <s>TUbi ergo duplicatam habent rationem illius, quam haben<gap/><lb/>velocitates motus de&longs;cendentis, & effluentis per ip&longs;os aquæ<gap/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XI. Theorema III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Cau&longs;am a&longs;&longs;ignare, cur aquæ fluentes per tubos æqua <lb/>lium luminum, &longs;ed inæqualium altitudinum, habeantra­<lb/>tionem &longs;ubduplicatam altitudinum tuborum.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg230"/></s></p> <p type="margin"> <s><margin.target id="marg230"/><emph type="italics"/>Proportio­<lb/>nis prædicta <lb/>cau&longs;a.<emph.end type="italics"/></s></p> <p type="main"> <s>QUod a&longs;&longs;eruimus Propo&longs;it. VIII. huius capitis, demon&longs;tran<gap/><lb/>dum hîc e&longs;t, utfidemibi obligatam &longs;olvamus. </s></p> <p type="main"> <s>Ratio igitur ad&longs;ignati hîc & ibi Phænomeni e&longs;t, quòd flu<gap/><lb/>xus aquæ per foramen, &longs;eu quantitas aquæ effluentis, pendet<gap/><lb/>velocitate aquæ eiusdem de&longs;cendentis per tubum, per dict<gap/><lb/>Propo&longs;it. IX. Corollario. I. Velocitas autem illa e&longs;t &longs;ubduplicata<gap/><lb/>altitudinum, per dicta Propo&longs;it. X; ergo & quantitas aquæ efflu­<lb/>entis ex tubis inæqualium altitudinum &longs;ubduplicata erit <expan abbr="tuborũ">tuborum</expan>. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XII. Theorema IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Tempora quibus æqualis aquæ quantitas è tubis æqua­<lb/>lium luminum, &longs;ed inæqualium altitudinum effluit, ha­<lb/>bent &longs;ubduplicatam rationem tuborum.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg231"/></s></p> <p type="margin"> <s><margin.target id="marg231"/><emph type="italics"/>Proportio <lb/>temporum <lb/>quibus a­<lb/>qua effluit è <lb/>tubis.<emph.end type="italics"/></s></p> <p type="main"> <s>SItut antea tubus AB vnius, & tubus CD quatuor pedum in <lb/>altitudine, &longs;ed æqualium luminum, &longs;ive &longs;emper, &longs;ive non &longs;em- <pb xlink:href="051/01/158.jpg" pagenum="127"/>per pleni; fluatque ex tubo AB vna libra aquæ &longs;patio duorum <lb/>minutorum. Dico, eandem aquam effluere ex tubo CD &longs;pa­<lb/>tio vnius minuti, <expan abbr="e&longs;&longs;e&qacute;ue">e&longs;&longs;eque</expan> propterea tempus fluxus aquæ ex tubo <lb/>CD, ad tempus fluxus aquæ ex tubo AB, ut 1 ad 2, quæ e&longs;t ratio <lb/>&longs;ubduplicata tuborum. Ratio ex dictis patet. Quoniam enim <lb/>velocitates effluxûs aquæ ex æquali lumine habent &longs;ubduplica­<lb/>tam rationem tuborum, ut demon&longs;travimus Propo&longs;it. X, fluet in <lb/>dimidio temporis tantum ex tubo CD, quantum in toto tem­<lb/>pore ex tubo AB, po&longs;ita æqualitate luminum; ac proinde in <lb/>toto tempore duplum effluet ex tubo CD. Eadem e&longs;t ratio in <lb/>alijs tuborum æqualium luminum proportionibus. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>TUbi ergo quilibet æqualium luminum, &longs;ed inæqualium alti­</s></p> <p type="main"> <s> <arrow.to.target n="marg232"/><lb/>tudinum, habent rationem duplicatam temporum, quibus <lb/>effluit æqualis aquæ quantitas. </s></p> <p type="margin"> <s><margin.target id="marg232"/><emph type="italics"/>Proportio <lb/>tuborum <gap/><lb/>tempora fl<gap/><lb/>xus aquæ.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIII. Theorema V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Si tubi, &longs;ive &longs;emper pleni, &longs;ive non &longs;emper pleni, &longs;int <lb/>eiu&longs;dem altitudinis, &longs;ed inæqualium foraminum, e&longs;t eadem ra­<lb/>tio aquæ ad aquam, quæ foraminis ad foramen, <lb/>phy&longs;icè &longs;eu ad &longs;en&longs;um.<emph.end type="center"/></s></p> <p type="main"> <s>ESt Mer&longs;enni in hydraulicis Phænomenis Propo&longs;it. IV. quem <lb/> <arrow.to.target n="marg233"/><lb/>&longs;equitur P. Andreas Tacquet in &longs;uis hydraulicis Manu&longs;cri­<lb/>ptis cap. 4. Phænomen. 7. Ratio e&longs;t, quòd licet ex maiori lu­<lb/>mine &longs;eu foramine fluat eodem tempore maior aquea columna <lb/>quàm ex minori, tantòque maior exillo quàm ex hoc, quantò <lb/>fuerit maius lumen &longs;eu <expan abbr="foram&etilde;">foramen</expan> illud quàm hoc, quoad aream, per <lb/>dicta Propo&longs;it. 4. huius eapitis; tamen vtraque columna fluit <lb/>ex æquali altitudine tuborum æquâ velocitate phy&longs;icè & ad <lb/>&longs;en&longs;um. </s></p> <p type="margin"> <s><margin.target id="marg233"/><emph type="italics"/>Proportio <gap/><lb/>quæ ad <gap/><lb/><expan abbr="quã">quam</expan> eadem. <lb/>quæ forami­<lb/>num in tu­<lb/>bu æquè <gap/>­<lb/>tis.<emph.end type="italics"/></s></p> <p type="main"> <s>Dixi phy&longs;icè & ad &longs;en&longs;um, quia licet gravia eiusdem &longs;pe­<lb/>ciei, &longs;ed inæqualis molis ac ponderis, ab eodem ad eundem <pb xlink:href="051/01/159.jpg" pagenum="128"/>terminum non de&longs;cendant æquè velociter, revera & mathema­<lb/>ticè, quemadmodum &longs;entiunt Galilæus Dialogo 2. de Sy&longs;tem. <lb/>Mundi, Ioannes Bapti&longs;ta Balianus lib. 1. de motu naturali gravi­<lb/>um &longs;olidorum in Præfat. Nicolaus Cabæus lib. 1. Meteoror. textu <lb/>17. <expan abbr="q.">que</expan> 5. & 6. Arriaga di&longs;put. 4. de Generat. &longs;ect. 5. &longs;ub&longs;ect. 3. <lb/>Ma&longs;trius, Bellutus, & alij (quod ego fal&longs;um exi&longs;timo, mathe. <lb/>maticè loquendo, cum Patre Ioanne Bapti&longs;ta Ricciolo, qui <lb/>tom. 1. Almage&longs;ti Novi lib. 2. cap. 21. Propo&longs;it. 2. & lib. 9. &longs;ect. 4. <lb/>num. 24. a&longs;&longs;erit, <emph type="italics"/>duorum gravium eiusdem &longs;peciei & figuræ &longs;ea inæ­<lb/>qualis molis ac ponderis, ex eadem altitudine momento eodem dimi&longs;­<lb/>&longs;orum, illud naturali motu citiùs de&longs;cendere ad eundem terminum, quod <lb/>e&longs;t gravius;<emph.end type="italics"/> ubi etiam Experimenta multa diver&longs;is annis coram <lb/>multis viris doctis incredibili diligentiâ peracta Bononiæ refert <lb/>num. 13.) tamen in parvis altitudinibus, quales &longs;unt tuborum <lb/>in omni ferè ca&longs;u, tam exigua e&longs;t differentia velocitatum, ut pro <lb/>eâdem &longs;eu æquali cen&longs;eri meritò po&longs;&longs;it. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma I.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur hinc, tubos non &longs;emper plenos, æquales quoad alti­<lb/>tudines, & ba&longs;es, inæquales tamen quoad foramina, evacua­<lb/>ri inæqualibus temporibus, hoc e&longs;t, citiùsillum, qui maius ha­<lb/>bet lumen; <expan abbr="e&longs;&longs;e&qacute;ue">e&longs;&longs;eque</expan> tempora, quibus evacuantur, inter &longs;e ut lu­<lb/>mina, hac tamen conditione, vt per foramen maius citiùs efflu­<lb/>at tota aqua, quàm per foramen minus, <expan abbr="tanto&qacute;">tantoque</expan>; citiùs per majus, <lb/>quàm per minus, quantò foramen maius &longs;uperat minus. Atque <lb/>hoc e&longs;t quod dicemus Propo&longs;it. XVI. &longs;equente, tempora &longs;cili­<lb/>cetin dicto ca&longs;u e&longs;&longs;e reciprocè vt lumina. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma II.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur præterea, ex tubis non &longs;emper plenis, quorum æ­<lb/>quales &longs;unt altitudines, at inæquales ba&longs;es, &longs;ed totæ apertæ, <lb/>effluere totam aquam æquali tempore; quandoquidem vtrobi­<lb/>que columna aquea, licet inæqualis ponderis ac molis, æquè <lb/>velociter de&longs;cendit quoad &longs;en&longs;um, per idem &longs;patium. </s></p> <pb xlink:href="051/01/160.jpg" pagenum="129"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIV. Theorema VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Tubinon &longs;emper pleni æquè alti, & æqualium. forami­<lb/>num, &longs;ed inæqualium ba&longs;ium, evacuantur inæqualibus <lb/>temporibus; <expan abbr="e&longs;t&qacute;ue">e&longs;tque</expan> eadem ratio temporum, <lb/>quæ ba&longs;ium.<emph.end type="center"/></s></p> <p type="main"> <s>PRimum patet per &longs;e, quia cæteris omnibus paribus major a­<lb/> <arrow.to.target n="marg234"/><lb/>quæ quantitas maius requirit tempus ad effluendum, quàm <lb/>minor. Alterum demon&longs;tratur, vel potiùs explicatur &longs;ic. </s></p> <p type="margin"> <s><margin.target id="marg234"/><emph type="italics"/>Proportio <lb/>temporum <lb/>eadem quæ <lb/>ba&longs;ium <expan abbr="tu-borũ">tu­<lb/>borum</expan>, quo­<lb/>ad aquæ flu<lb/>xum.<emph.end type="italics"/></s></p> <figure id="id.051.01.160.1.jpg" xlink:href="051/01/160/1.jpg"/> <p type="main"> <s>E&longs;to tubus AB minoris ba&longs;is, & alius ACBD <lb/>majoris, uterque cylindricus, uterque æquè altus, & <lb/>æqualis foraminis B; &longs;itque diameter ba&longs;is BD tripla <lb/>diametri ba&longs;is B: eritigitur area ba&longs;is BD noncupla <lb/>areæ ba&longs;is B, quoniam circuli inter &longs;e &longs;unt, ut qua­<lb/>drata diametrorum, per Propo&longs;it. 2. lib. 12. Element. <lb/>Euclidis; quadratum <expan abbr="aut&etilde;">autem</expan> diametri BD triplo maio­<lb/>ris diametro B, e&longs;t nonies maius, quàm quadratum <lb/>diametri B, ut ex Geometria practica patet. Cùm <lb/>igitur cylindri æquè alti &longs;int inter &longs;e, ut <expan abbr="illorũ">illorum</expan> ba&longs;es, ut <lb/>patet ex <expan abbr="ead&etilde;">eadem</expan> Geomet. practica; &longs;equitur, aquam tubi <lb/>ACBD e&longs;&longs;e noncuplam aquæ tubi AB; ac proinde <lb/>tempus quo exhauritur per foramen B tubus ACDB, <lb/>noncuplum erit temporis, quo exhauritur per idem <lb/>foramen B, tubus AB, <expan abbr="quandoquid&etilde;">quandoquidem</expan> cylindrus aqueus ACBD, <lb/>non magis premit &longs;upra <expan abbr="foram&etilde;">foramen</expan> B, quàm cylindrulus aqueus AB, <lb/>per dicta Propo&longs;it. II. in Corollario, & Propo&longs;it. VII. Annot. 2. </s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>MEr&longs;ennus in Hydraulicis Phænomenis Propo&longs;it.<emph.end type="italics"/> 8. <emph type="italics"/>ait, con&longs;tare ex <lb/> <arrow.to.target n="marg235"/><lb/>ob&longs;ervatione, tubum quadrupedalem, cuius ba&longs;is digitalis, uno mi­<lb/>nuto temporis totum per lineare lumen exhauriri; tubum verò quadru­<lb/>pedalem cuius ba&longs;is pedalis, &longs;patio<emph.end type="italics"/> 144. <emph type="italics"/>minutorum, &longs;eu duabus horis, &<emph.end type="italics"/><lb/>24. <emph type="italics"/>minutis. Servatur ergò inter temporaratio ba&longs;ium, vt demon&longs;tra­<lb/>vimus: Nam cùm pedis longitudo contineat, ex Mer&longs;enni mente, ut <lb/>vidimus Propo&longs;it. VII. huius Capitis Annot. I. digiti latitudinem<emph.end type="italics"/> <pb xlink:href="051/01/161.jpg" pagenum="130"/><emph type="italics"/>duodecies; continebit quadratum pedis quadrata digiti<emph.end type="italics"/> 144. <emph type="italics"/>ac proinde <lb/>ba&longs;is pedalis ba&longs;im digitalem centies quadragies quater continebit, <gap/><lb/>diximus in Propo&longs;itione.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg235"/>Mer&longs;enni <lb/>ob&longs;ervatio <lb/>in tuborum <lb/>evacuati­<lb/>one.</s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/><lb/> <arrow.to.target n="marg236"/></s></p> <p type="margin"> <s><margin.target id="marg236"/><emph type="italics"/>P. Pauli Ca <lb/>&longs;ati dubita­<lb/>tio contra <lb/>Mer&longs;enni <lb/>ob&longs;ervatio­<lb/>nem.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>ACuti&longs;&longs;imè notavit hîc P.Paulus Ca&longs;atus in cen&longs;ura huius Operis, po&longs;­<lb/>&longs;e dubitari de veritate huius Propo&longs;itionis<emph.end type="italics"/> 14. <emph type="italics"/>& po&longs;&longs;e aliquem &longs;u&longs;pi­<lb/>cari, an experimentum allatum à Mer&longs;enno &longs;it in gratiam Propo&longs;itionis <lb/>confictum.<emph.end type="italics"/> Ratio dubitandi e&longs;t, <emph type="italics"/>inquit,<emph.end type="italics"/> quia quo tempore par­<lb/>vulus tubus AB exhauritur, ex maiori tubo ABCD effluit maior <lb/>aquæ quantitas eodem tempore, quia &longs;cilicet effluit in progre&longs;&longs;u <lb/>maiori velocitate ex maiori, quàm ex minori: nam in majore <lb/>tubo e&longs;t maius aquæ perpendiculum in progre&longs;&longs;u. Fac enim in <lb/>minori de&longs;cendi&longs;&longs;e &longs;emi&longs;&longs;em; aquæ altitudo e&longs;t &longs;olùm dimidia <lb/>totius altitudinis: fac ex majori eodem tempore de&longs;cendi&longs;&longs;e æ­<lb/>qualem aquam, hoc e&longs;t (quia maior ad minorem e&longs;t ut 9. ad 1.) <lb/>(1/18) totius aquæ; ergo remanet altitudo aquæ in majori (17/18) totius <lb/>altitudinis; ergo plus aquæ effluet vbi maior e&longs;t velocitas ratione <lb/>maioris perpendiculi. Debet igitur hæc ratio conciliari cum <lb/>experimento; & opus e&longs;&longs;et o&longs;tendere, quomodo, licet id veri­<lb/>ficetur in priotibus cylindrulis aquæ effluentibus, tamen maior <lb/>illa velocitas priorum compen&longs;entur maiori tarditate po&longs;terio­<lb/>rum qui habent minus perpendiculum. </s></p> <p type="main"> <s>Hocidem dicitur de Propo&longs;itione 16, in qua con&longs;ideratur <lb/>columna vt duodecupla minoris, nulla habita ratione quòd in <lb/>progre&longs;&longs;u de&longs;cen&longs;us fiunt altitudines valde inæquales: neque vi­<lb/>detur valere illa argumentatio, facta præci&longs;ione per intellectum; <lb/>nam &longs;ermo e&longs;t de re prout à parte rei. <emph type="italics"/>Hæc P. Ca&longs;atus. Nolui ego <lb/>in dubium revocare experimentum Mer&longs;enni, quoniam id nefas exi&longs;ti­<lb/>mavi; nec experimenti cau&longs;am indagare, ac multò minùs demon&longs;tra­<lb/>tionem afferre, quoniam id ad propo&longs;itum meum nihil conducit. <lb/>Ratio tamen huius rei &longs;ine dubio refundenda e&longs;t in illam, <lb/>quam ip&longs;emet Ca&longs;atus in&longs;inuavit.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/162.jpg" pagenum="131"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio XV. Phænomenon. IX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Tempora quibus deplentur tubi non &longs;emper pleni æque <lb/>lati, &longs;ed non æquè alti, per æqualia foramina, &longs;untin al­<lb/>titudinum ratione &longs;ubduplicata.<emph.end type="center"/></s></p> <p type="main"> <s>COn&longs;tat enim ex ob&longs;ervatione, inquit Mer&longs;ennus in Hydrau­</s></p> <p type="main"> <s> <arrow.to.target n="marg237"/><lb/>licis Phænomenis Propo&longs;it. IX. tubum pedalem 30 &longs;ecundis, <lb/>quadrupedalem verò latitudinis eiusdem 60 &longs;ecundis, per fora­<lb/>men lineare, totum exhauriri. </s></p> <p type="margin"> <s><margin.target id="marg237"/><emph type="italics"/>Proportio <lb/>temporum <lb/>aquæ fluxus <lb/>ex tubis, ad <lb/>eorum alti­<lb/>tudinem.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Corollarium I.<emph.end type="center"/></s></p> <p type="main"> <s>HInc colligitur primò, tuborum altitudines e&longs;&longs;e in ratione <lb/>duplicata temporum, quibus deplentur æqualia lumina, vt <lb/>diximus etiam in Pori&longs;mate Propo&longs;itionis XII. præcedentis. </s></p> <p type="main"> <s><emph type="center"/>Corollarium <emph type="italics"/>II<emph.end type="italics"/><emph.end type="center"/></s></p> <p type="main"> <s>COlligitur &longs;ecundò, tam tubos non &longs;emper plenos, quàm tu­<lb/>bos &longs;emper plenos, juxta eandem rationem tribuere aquas <lb/>ex æqualibus foraminibus, juxta dicta hac, & octava Propo­<lb/>&longs;itione. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XVI. Theorema VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Tempora quibus evacuantur tubi non &longs;emper pleni &longs;i­<lb/>miles, & æquales quoad altitudines & ba&longs;es, per lumina &longs;imilia <lb/>inæqualia, &longs;unt reciprocè vt lumina.<emph.end type="center"/></s></p> <p type="main"> <s>PRopo&longs;itio intelligenda e&longs;t in eo &longs;en&longs;u, quem explicavimus <lb/>in Porismate 1. Propo&longs;it. 13. præcedentis. </s></p> <p type="main"> <s>Sint itaque tubi cylindrici ABFQ, &longs;imiles, & æquales in <lb/> <arrow.to.target n="marg238"/><lb/>altitudinibus, humido pleni, quorum lumina &longs;int EC, KN, cir­<lb/>cularia, at inæqualia (eadem e&longs;t ratio de tubis pri&longs;maticis, & <lb/>foraminibus quadratis, alteriusvè Figuræ;) &longs;itque lumen &longs;eu <lb/>foramen KN duodecies maius quoad aream, quàm lumen EC. <lb/>Dico, tempus quo exhauritur tubus AB, per lumen EC, e&longs;&longs;e <lb/>ad tempus, quo exhauritur tubus FQ, per lumen KN, ut e&longs;t <lb/>reciprocèlumen KN ad lumen EC; id e&longs;t, tantò plùs tempo­<lb/>ris requiri ut exhauriatur tubus AB, per foramen EC, quàm <pb xlink:href="051/01/163.jpg" pagenum="132"/> <arrow.to.target n="fig32"/><lb/>tubus FQ, per foramen KN, quantò <lb/>maius e&longs;t lumen KN, quàm <expan abbr="lum&etilde;">lumen</expan> EC, <lb/>nempe duodecies plùs. </s></p> <p type="margin"> <s><margin.target id="marg238"/><emph type="italics"/>Proportio <lb/>temporum <lb/>effluxus a­<lb/>quæ ad fora <lb/>mina tubo­<lb/>rum.<emph.end type="italics"/></s></p> <figure id="id.051.01.163.1.jpg" xlink:href="051/01/163/1.jpg"/> <p type="main"> <s>Ad hoc o&longs;tendendum, intelligan­<lb/>tur &longs;uper luminibus EC, KN, <expan abbr="tanquã">tanquam</expan> <lb/>&longs;uper ba&longs;ibus, cylindri DC, LN, <expan abbr="eju&longs;d&etilde;">eju&longs;dem</expan> <lb/>altitudinis cum cylindricis tubis AB, <expan abbr="Fq.">Fque</expan> <lb/>Patet ex dictis Propo&longs;it. XIII. præce­<lb/>dente, Porismate 2, hos duos tubos <lb/>DC, LN, per lumina EC, KN, eodem <lb/>&longs;eu æquali tempore exhauriri. Iam &longs;ic. <lb/>Per Propo&longs;itionem XIII, huius capi­<lb/>tis, aqua quæ effluit ex tubo FQ, per <lb/>lumen KN, e&longs;t ad aquam, quæ eodem <lb/>&longs;eu æquali tempore effluit ex tubo AB, <lb/>per foramen EC, ut foramen KN ad foramen EC; <lb/>hoc e&longs;t, eodem &longs;eu æquali tempore, quo ex lumine EC effluit <lb/>una columna aquea DC, effluunt ex lumine KN duodecim <lb/>columnæ aqueæ DC: Ergo dum ex lumine KN effluxit tota <lb/>aqua tubi FQ, effluxit ex lumine EC &longs;olùm duodecima <lb/>pars aquæ tubi AB; ac proinde tantò plùs temporis requiritur, <lb/>ut evacuetur tubus AB per lumen EC, quàm ut evacuetur <lb/>tubus FQ per lumen KN, quantò maius e&longs;t lumen KN quàm <lb/>lumen EC. Ergo tempora &longs;unt reciprocè ut lumina. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur hinc, etiam conver&longs;am e&longs;&longs;e veram, nempe lumina, <lb/>per quæ evacuantur tubi prædicti, e&longs;&longs;einter &longs;e ut reciprocè <lb/>tempora, quibus evacuantur: Vnde data ratione <expan abbr="temporũ">temporum</expan>, da­<lb/>bitur ratio <expan abbr="luminũ">luminum</expan>; &longs;icut è contrario, data ratione <expan abbr="luminũ">luminum</expan>, datur <lb/>ratio temporum &longs;eu <expan abbr="durationũ">durationum</expan>, quibus evacuantur prædicti tubi. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XVII. Problema I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis altitudine & foramine tubi &longs;emper pleni, invenire <lb/>quantitatem aquæ quam dato tempore effundat; vel, datis <expan abbr="ij&longs;d&etilde;">ij&longs;dem</expan>, <lb/>invenire magnitudinem ci&longs;ternæ quæ dato tempore <lb/>repleatur.<emph.end type="center"/></s></p> <pb xlink:href="051/01/164.jpg" pagenum="133"/> <figure id="id.051.01.164.1.jpg" xlink:href="051/01/164/1.jpg"/> <p type="main"> <s>SUppono hîc id, quod notavi &longs;uprà Pro­<lb/>po&longs;it. XIII. tam exiguam e&longs;&longs;e differen­<lb/>tiam inter velocitates aquarum ex tubis <lb/>eiusdem altitudinis, & diver&longs;orum fora­<lb/>minum, <expan abbr="effluentiũ">effluentium</expan>, ut cen&longs;eri meritò po&longs;­<lb/>&longs;it, aquam ad aquam e&longs;&longs;e, utforamen ad <lb/>foramen. Quo po&longs;ito. <lb/> <arrow.to.target n="marg239"/></s></p> <p type="margin"> <s><margin.target id="marg239"/><emph type="italics"/>Data alti­<lb/>tudine & <lb/>foramine tu <lb/>bi, invenire <lb/>aquæ quan­<lb/>titatem da­<lb/>to tempore <lb/>effluentem.<emph.end type="italics"/></s></p> <p type="main"> <s>Sit, exempli gratia, altitudo tubi <lb/>ADB pedum 64, luminis &longs;eu foraminis <lb/>diameter DB digitalis, tempus hora una. <lb/>Oporteat igitur reperire, quantum aquæ <lb/>tribuat, &longs;eu quantam ci&longs;ternam impleat, <lb/>prædictus tubus, intra unam horam. So­<lb/>lutio pendet ex dictis Propo&longs;it. VII. XIII. <lb/>& VIII. & præterea ex Propo&longs;it. 2. lib. 12. Eu­<lb/>clidis. Igitur tubum 4 pedes altum, & <lb/>luminis linearis, repræ&longs;entet CPK. Ex <lb/>tubo ADB. &longs;ume EDB portionem <expan abbr="etiã">etiam</expan> <lb/>4 pedes altam. Et quoniam diameter DB <lb/>digitalis, e&longs;t ad linearem PK, ut 12 ad 1; <lb/>eritper Propo&longs;it. &longs;ecundam lib. 12. Eucli­<lb/>dis, lumen DB ad lumen KP, utquadra­<lb/>tum diametri DB, ad quadratum diame­<lb/>tri PK, hoc e&longs;t, ut 144 ad 1. Quare cùm <lb/>per Propo&longs;it. XIII. præcedentem, in tubis <lb/>æquè altis & &longs;emper plenis, &longs;ed inæquali­<lb/>um luminum, aqua ab uno effu&longs;a, fit ad a­<lb/>quam ab altero effu&longs;am, tempore eodem, <lb/>utlumen ad lumen; dabit EDB. centies <lb/>quadragies quater plus aquæ, quàm det <lb/>eodem tempore tubus CPK: Sed tubus <lb/>CPK, per Propo&longs;it. VII. præcedentem, <lb/>&longs;patio tredecim &longs;ecundorum temporis dat <lb/>unam libram aquæ: Ergo tubus EDB <pb xlink:href="051/01/165.jpg" pagenum="134"/> <arrow.to.target n="fig33"/><lb/>&longs;patio tredecim &longs;ecundorum tomporis da­<lb/>bit 144 libras. <expan abbr="Quoniã">Quoniam</expan> autem in una hora, <lb/>&longs;eu in 60. minutis primis, hoc e&longs;t, in 3600 <lb/>minutis &longs;ecundis, tredecim &longs;ecunda con­<lb/>tinentur ducenties &longs;eptuagies &longs;exies, rema­<lb/>nentque <gap/>, &longs;ive (facilioris calculi gratia) <lb/>ducenties &longs;eptuagies &longs;epties; &longs;i 144 libras, <lb/>quas tredecim &longs;ecundis dat tubus EDB, <lb/>multiplices per 277, fient ferè 39888. li­<lb/>bræ, quas horæ &longs;patio fundit tubus EDB. <lb/>Inveniatur iam inter 64, altitudinem nem­<lb/>pe tubi ADB, & inter 4, altitudinem ni­<lb/>mirum portionis EDB, media proporti­<lb/>onalis 16. Quoniam igitur per Propo&longs;it. <lb/>VIII. præcedentem, aquæ quas tubi ADB, <lb/>& EDB &longs;emper pleni, eodem tempore <lb/>fundunt, &longs;unt in &longs;ubduplicata ratione eius <lb/>quam habent altitudines ADB, & EDB; <lb/>erit aqua quam horæ &longs;patio dat tubus <lb/>EDB, ad aquam quam eodem tempore <lb/>dabit tubus ADB, ut 4 ad 16, &longs;eu ut 1 ad 4. <lb/>Itaque &longs;i fiat, ut 1 ad 4, ita 39888 (tot enim <lb/>aquæ libras iam o&longs;tendimus horæ &longs;patio <lb/>dare tubum EDP) ad alium numerum, <lb/>nempe ad 159552, quot hic continet vni­<lb/>tates, tot aquæ libras horæ &longs;patio dabit tu­<lb/>bus ABD &longs;emper plenus, lumen habens <lb/>digitale, altitudinem pedum 64; atque <lb/>adeo tubus prædictus implebit horæ &longs;pa­<lb/>tio ci&longs;ternam capacem librarum <lb/>aquæ 159552. </s></p> <pb xlink:href="051/01/166.jpg" pagenum="135"/> <figure id="id.051.01.166.1.jpg" xlink:href="051/01/166/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg240"/></s></p> <p type="margin"> <s><margin.target id="marg240"/><emph type="italics"/>Pari&longs;ien&longs;es <lb/>libra<emph.end type="italics"/> 72. <emph type="italics"/>ef­<lb/>ficiunt pe­<lb/>dem <expan abbr="cubisũ">cubisum</expan> <lb/>aquæ.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>MEr&longs;ennus ait, heminas &longs;eu libras Pari&longs;ien&longs;es<emph.end type="italics"/> 72. <emph type="italics"/>efficere pedem <lb/>cubicum aquæ. Itaque &longs;i placet prædictas libras ad pedes cubi­<lb/>cos reducere, divide numerum<emph.end type="italics"/> 159552 <emph type="italics"/>per<emph.end type="italics"/> 72, <emph type="italics"/>& quotiens<emph.end type="italics"/> 2216 <emph type="italics"/>da­<lb/>bit aquæ pedes cubicos quos horæ &longs;patio fundet tubus<emph.end type="italics"/> ADB. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XVIII. Problema II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis altitudine & lumine tubi &longs;emper pleni, invenire <lb/>tempus quo datam aquæ quantitatem effundat, &longs;i­<lb/>ve quo datam ci&longs;ternam impleat.<emph.end type="center"/></s></p> <p type="main"> <s>SIt tubus &longs;emper plenus ADB, v.g. 16 pedes altus, lumen </s></p> <p type="main"> <s> <arrow.to.target n="marg241"/><lb/>habens digitale DB; &longs;it verò quantitas aquæ à tubo ADB <lb/>effundendæ, aut ci&longs;terna ab eodem replenda, 3000 pedum cu­<lb/>bicorum. Oporteat invenire tempus quo dictam aquam ef­<lb/>fundat, aut dictam ci&longs;ternam impleat. </s></p> <p type="margin"> <s><margin.target id="marg241"/><emph type="italics"/>Data alti­<lb/>tudine & <lb/>foramine <lb/>tubi, inve­<lb/>nire tempus <lb/>quo data a­<lb/>qua effluit.<emph.end type="italics"/></s></p> <p type="main"> <s>Revocentur primò 3000 pedes cubici aquæ ad heminas <lb/> <arrow.to.target n="fig34"/><lb/>&longs;eu libras (quod fiet, &longs;i 3000 multiplica­<lb/>bis per 72. fiatq, numerus librarum 216000, <lb/>(quandoquidem unus pes cubicus conficit <lb/>72 libras, ut diximus Propo&longs;it: præceden­<lb/>te in Annotat:) Deinde &longs;umatur ex ADB, <lb/>tubus quadrupedalis EDB: Demum inter <lb/>ADB altitudinem, id e&longs;t, 16, & EDB alti­<lb/>tudinem, id e&longs;t, 4, inveniatur medius nu­<lb/>merus proportionalis 8. Igitur, per Pro­<lb/>po&longs;it. VIII. præcedentem, aqua fluens per <lb/>tubum EDB, e&longs;t ad aquam per tubum <lb/>ADB eodem tempore fluentem, ut 4 ad 8, <lb/>in ratione videlicet &longs;ubduplicata altitudi­<lb/>num EDB 4 pedum, & ADB 16 pedum. <lb/>Quo ergo tempore dat tubus ADB 3000 <lb/>pedes cubicos aquæ, id e&longs;t, 216000 hemi­<lb/>nas &longs;eu libras; eodem tempore EDB dabit duplò minus, &longs;eu <pb xlink:href="051/01/167.jpg" pagenum="136"/> <arrow.to.target n="fig35"/><lb/>heminas &longs;olùm 108000. A&longs;&longs;umatur jam, <lb/>ut antea, tubus quadrupedalis CPK lu­<lb/>minis linearis. Tubi EDB, CPK, &longs;unt æ­<lb/>què alti; & lumina DB, PK, dantur, per <gap/><lb/>Propo&longs;it. lib. 12. Euclid. nempe 1, & 144 <lb/>lineæ quadratæ; aqua etiam quam CPK <lb/>fundit&longs;patio 13 &longs;ecundorum, datur, per VII. <lb/>præcedentem, una nimirum libra: Qua­<lb/>re cùm quantitates aquæ à tubis æquè al­<lb/>tis eodem tempore effu&longs;æ &longs;int ut lumina, <lb/>per Propo&longs;it. XIII. præcedentem, &longs;i fiat ut <lb/>lumen PK, ad lumen DB, id e&longs;t, ut 1 ad <lb/>144, ita aqua unius ad aquam alterius; pro­<lb/>ducetur numerus heminarum &longs;eu libra­<lb/>rum, quas effundit tubus EDB &longs;patio tre­<lb/>decim &longs;ecundorum, nempe 144. Quo­<lb/>niam igitur tubus EDB 144 libras dat &longs;patio tredecim &longs;ecundo­<lb/>rum; libras 108000 quanto tempore dabit? Fiat, ut 144 libræ <lb/>ad <gap/> hoc e&longs;t, ad tredecim &longs;ecunda, ita 108000 ad 9750; dabit <lb/>hic numerus &longs;ecunda, quibus tubus EDB dat libras 108000. <lb/>Sed o&longs;ten&longs;um e&longs;t &longs;uprà, quo tempote tubus EDB dat 108000 <lb/>libras, tubum ADB dare libras 216000, id e&longs;t, 3000 pedes cu­<lb/>bicos aquæ; Inventum e&longs;t igitur tempus, quo tubus ADB &longs;em­<lb/>per plenus fundit datam aquam 3000 pedum cubicorum, nem­<lb/>pe 9750 &longs;ecunda, &longs;eu 162 prima; quæ faciunt horas 2, & 42 <lb/>minuta prima. </s></p> <figure id="id.051.01.167.1.jpg" xlink:href="051/01/167/1.jpg"/> <figure id="id.051.01.167.2.jpg" xlink:href="051/01/167/2.jpg"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIX. Problema III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis tempore, quantitate aquæ, &longs;eu Ci&longs;ternâ, & lu­<lb/>mine tubi, invenire altitudinem tubi, qui &longs;emper <lb/>plenus ci&longs;ternam dato tempore repleat.<emph.end type="center"/><lb/> <arrow.to.target n="marg242"/></s></p> <p type="margin"> <s><margin.target id="marg242"/><emph type="italics"/>Dato tem­<lb/>pore, & <lb/>quantitate <lb/>aquæ, inve­<lb/>nire tubum <lb/>ex quo ef­<lb/>fluat.<emph.end type="italics"/></s></p> <p type="main"> <s>SIt datum tempus unius horæ & 21 minutorum primorum, <lb/>aqua data 3000 pedum cubicorum, &longs;eu 216000 librarum <lb/>capax ci&longs;terna, & lumen &longs;eu foramen tubi digitale, &longs;eu duo- <pb xlink:href="051/01/168.jpg" pagenum="137"/>decim linearum. Oporteat invenire altitudinem tubi qui unâ <lb/>horâ & 21 minutis primis ex foramine digitali ejiciat 216000 <lb/>libras aquæ, &longs;eu repleat ci&longs;teruam 3000 pedum cubicorum. </s></p> <p type="main"> <s>Quoniam tubus quadrupedalis, cujus lumen digitale, eji­<lb/>cit tredecim &longs;ecundorum &longs;patio libras 144, ut vidimus Pro­<lb/>po&longs;it. XVII. præcedente, & idem tubus &longs;patio duarum hora­<lb/>rum, ac 42 minutorum primorum ejicit libras 108000, ut vi­<lb/>dimus Propo&longs;it. XVIII. præcedente; ergo duplum hujus aquæ, <lb/>hoc e&longs;t, libræ 216000, ejicientur à tubo eju&longs;dem luminis alto <lb/>pedes 16. eò quòd tuborum æqualium foraminum altitudines <lb/>debeant e&longs;&longs;e in duplicata ratione aquarum, ut duplo plùs aquæ <lb/>eodem tempore fundant, prout diximus Propo&longs;it. VIII. Pori­<lb/>&longs;mate 1. Ut verò eadem aqua effluat ex tubo eju&longs;dem fora­<lb/>minis duplo velociùs, hoc e&longs;t, intra horam unam, minuta 21; <lb/>debet tubus e&longs;&longs;e altus pedes 64, ut patet ex Pori&longs;mate Propo­<lb/>&longs;it. X. & XII. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>SImili ratione datis tempore, ci&longs;terna, & altitudine tubi, in­<lb/>venitur foramen tubi, qui ci&longs;ternam datam repleat in illo <lb/>tempore. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XX. Problema IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato Va&longs;e, & foramine per quod effluit aqua, <lb/>invenire tempus quo evacuatur.<emph.end type="center"/></s></p> <p type="main"> <s>SIt datum vas pri&longs;maticum ABCD, cujus tam longitudo, </s></p> <p type="main"> <s> <arrow.to.target n="marg243"/><lb/>quàm latitudo &longs;it decem pedum, altitudo vero 16 pedum, <lb/>ac proinde capacitas totius va&longs;is &longs;it 1600 pedum cubicorum, <lb/>ba&longs;is verò &longs;it 100 pedum quadratorum; lumen denique &longs;eu <lb/>foramen E in fundo va&longs;is &longs;it digitale. Oporteat invenire tem­<lb/>pus quo dictum vas, &longs;i aquâ fuerit plenum, per lumen E eva­<lb/>cuetur. </s></p> <pb xlink:href="051/01/169.jpg" pagenum="138"/> <p type="margin"> <s><margin.target id="marg243"/><emph type="italics"/>Dato va&longs;e, <lb/>& forami­<lb/>ne, inveni­<lb/>re tempus <lb/>quo evacua <lb/>tur.<emph.end type="italics"/></s></p> <figure id="id.051.01.169.1.jpg" xlink:href="051/01/169/1.jpg"/> <p type="main"> <s>Con&longs;tat ex dictis Pro­<lb/>po&longs;it. XIV. in Annotat. tu­<lb/>bum quadrupedalem, cu­<lb/>jus ba&longs;is pedalis, & lumen <lb/>lineare, &longs;patio 144. minu­<lb/>torum, &longs;eu duabus horis <lb/>& 24 minutis, totum ex­<lb/>hauriri, &longs;i non &longs;it &longs;emper <lb/>plenus. Con&longs;tat præterea <lb/>ex eadem Propo&longs;itione, <lb/>tubos non &longs;emper plenos, <lb/>æquè altos, & æqualium <lb/>foraminum, &longs;ed inæqua­<lb/>lium ba&longs;ium, evacuari in­<lb/>æqualibus temporibus; <lb/>& tempora quibus evacuantur, e&longs;&longs;e inter &longs;e, vt ba&longs;es. A&longs;&longs;uma­<lb/>tur igitur tubus pri&longs;maticus quadrupedalis KL, ba&longs;im habens <lb/>pedalem, & lumen lineare. A&longs;&longs;umatur præterea ex va&longs;e dato <lb/>ABCD, pars CFDH alta pedes quatuor, ba&longs;&longs;im habens ean­<lb/>dem cumtoto va&longs;e centum pedum, lumen verò 1 lineare. Quo­<lb/>niam igitur, per Propo&longs;itionem XIV. dictam, tempora quibus <lb/>vas CFDH, & tubus KL exhauriuntur per lumen lineare, &longs;unt <lb/>inter &longs;e ut ba&longs;es ip&longs;orum; ba&longs;es autem ex hypothe&longs;i habent pro­<lb/>portionem ut 100. ad 1; nece&longs;&longs;e e&longs;t, tempus quo evacuatur vas <lb/>CFDH per lineare lumen 1, ad tempus quo evacuatur tubus <lb/>KL per lumen etiam lineare, e&longs;&longs;e ut 100 ad 1. Quare cùm tu­<lb/>bus KL per lineare lumen evacuetur &longs;patio 144 minutorum, <lb/>ut vidimus; evacuabitur vas CFDH, per lineare lumen 1, &longs;pa­<lb/>tio 14400 minutorum, (tot enim producuntur, &longs;i 144 multi­<lb/>plicentur per 100) &longs;eu horarum 240, vel dierum decem. Iam <lb/>verò quoniam per Propo&longs;it. XVI. tempus quo effluitaqua ex va­<lb/>&longs;e CFDH per lumen digitale E, ad tempus quo effluit eadem <lb/>aqua ex eodem va&longs;e per lumen lineare 1, e&longs;t reciprocè, &longs;icut <lb/>e&longs;t foramen 1 ad foramen E, nempe ut 1 ad 144; &longs;i dividatur <pb xlink:href="051/01/170.jpg" pagenum="139"/>tempus quo effluit aqua per foramen 1, nempe 14400 minuta, <lb/>per 144; hoc e&longs;t, &longs;i accipiatur cente&longs;ima quadrage&longs;ima quarta <lb/>pars minutorum 14400, nempe minuta 100; habebitur tem­<lb/>pus quo exhauritur vas CFDH, per digitale lumen E. Tan­<lb/>dem quoniam per Propo&longs;it. XV. præcedentem, tempora qui­<lb/>bus deplentur va&longs;a ABCD, CFDH. æqualium ba&longs;ium, &longs;ed non <lb/>æqualium altitudinum, per idem foramen E, &longs;unt in &longs;ubdu­<lb/>plicata ratione altitudinum, nempe pedum 4, & pedum 16; <lb/>&longs;i inter 4 & 16 inveniatur medius numerus proportionalis, nem­<lb/>pe 8; erit tempus quo evacuatur vas CFDH, per lumen digita­<lb/>le E, nimirum 100 minutorum, ad tempus quo evacuatur vas <lb/>ABCD per idem lumen digitale E, ut 4 ad 8, &longs;eu ut 1 ad 2, <lb/>nempe ut minuta 100, ad minuta 200, quæ efficiunt horas 3. <lb/>min. 20. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVod diximus de va&longs;e pri&longs;matico, debet etiam intelligi de cylindrico, <lb/>& cuiuscunque alterius figuræ; &longs;ed tunc a&longs;&longs;umi debet tubus quadru­<lb/>pedalis va&longs;i &longs;imilis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XXI. Problema V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato va&longs;e, & tempore, invenire foramen per quod <lb/>evacuetur tempore dato.<emph.end type="center"/></s></p> <p type="main"> <s>SIt data ci&longs;terna A, 1600. pe­ <arrow.to.target n="table1"/><lb/> <arrow.to.target n="marg244"/><lb/>dum cubicorum; & tempus <lb/>B, quo evacuandum e&longs;t totum, <lb/>&longs;it horarum 40 & minutorum <lb/>16; &longs;itque inveniendum foramen, per quod evacuetur ci&longs;ter­<lb/>na A data, in tempore B dato. A&longs;&longs;umatur quodvis lumen &longs;eu <lb/>foramen notæ magnitudinis, v.g. lineare; & per Propo&longs;itionem <lb/>XX. præcedentem inveniatur tempus C, quo ci&longs;terna A hu­<lb/>mido plena, evacuetur tota per lumen lineare. Quoniam igi­<lb/>tur, per Propo&longs;it. XVI. præcedentem, tempora quibus evacuan­<lb/>tur va&longs;a non &longs;emper plena, &longs;imilia, & æqualia quoad altitudinem <pb xlink:href="051/01/171.jpg" pagenum="140"/>& ba&longs;es, per lumina &longs;imilia inæqualia, &longs;unt reciprocè ut lumina; <lb/>& è contrario, lumina prædictorum va&longs;orum &longs;unt reciprocè ut <lb/>tempora, quibus evacuantur, ut diximus in Pori&longs;mate dictæ <lb/>Propo&longs;itionis XVI; &longs;i fiat ut tempus B, ad tempus C, quo per <lb/>lineare lumen effluit ci&longs;terna A, ita lumen lineare ad aliud; <lb/>hoc ip&longs;um erit lumen quod quærebatur. </s></p> <p type="margin"> <s><margin.target id="marg244"/><emph type="italics"/>Dato va&longs;e <lb/>& tempore, <lb/>invenire <lb/>foramen.<emph.end type="italics"/></s></p> <table> <table.target id="table1"/> <row><cell>ci&longs;t.</cell><cell>temp.</cell><cell>temp.</cell></row> <row><cell>-----</cell><cell>-----</cell><cell>-----</cell></row> <row><cell>A</cell><cell>B</cell><cell>C</cell></row></table> <p type="main"> <s><emph type="center"/>Propo&longs;itio XXII. Problema VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Altitudinem &longs;caturiginis dati fontis per tubos <lb/>fluentis invenire.<emph.end type="center"/><lb/> <arrow.to.target n="marg245"/></s></p> <p type="margin"> <s><margin.target id="marg245"/><emph type="italics"/><expan abbr="Altitudin&etilde;">Altitudinem</expan> <lb/>Scaturigi­<lb/>nis fontis in <lb/>venire per <lb/>tubos fluen­<lb/>tis.<emph.end type="italics"/></s></p> <figure id="id.051.01.171.1.jpg" xlink:href="051/01/171/1.jpg"/> <p type="main"> <s>FIat notum lumen, per quod fontis a­<lb/>qua fluat; aut fonti lumen notæ ma­<lb/>gnitudinis applica, v.g. lineare. Ob­<lb/>&longs;erva deinde quot aquæ libras fons per <lb/>lineare <expan abbr="lum&etilde;">lumen</expan> effundat &longs;patio unius minuti primi, &longs;eu 60 minuto­<lb/>rum &longs;ecundorum; &longs;itque numerus ille librarum B. Quoniam <lb/>igitur per Propo&longs;it. VII. huius capitis, tubus qua drupedalis &longs;emper <lb/>plenus per lumen lineare effundit &longs;patio tiedecim &longs;ecundorum <lb/>vnam libram, & con&longs;equenter &longs;patio 60 &longs;ecundorum, &longs;eu unius <lb/>minuti primi, libras 4<gap/>: & præterea, quoniam per Pori&longs;ma I. <lb/>Propo&longs;it. VIII. huius capitis, altitudines tuborum, habentium <lb/>idem &longs;eu æquale lumen, &longs;unt in duplicata ratione eius quam ha­<lb/>bent aquæ quantitates per tubos <expan abbr="eod&etilde;">eodem</expan> tempore effusæ: &longs;i fiat, ut <lb/>4<gap/> lib. ad numerum librarum B, ita altitudo 4 pedum, ad aliud, <lb/>nempe ad altitudinem numeri M; & iterum, ut 4 ad M, ita M <lb/>ad N; dabit numerus N altitudinem &longs;caturiginis in pedibus, <lb/>eò quòd ratio 4 ad N &longs;it duplicata rationis 4 ad M, &longs;eu ratic­<lb/>nis 4<gap/> ad B, nimirum aquæ ad aquam. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XXIII. Problema VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Data alicuius tubi, aut va&longs;is erogatorij altitudine, ac <lb/>tempore, quo determinatam aquæ quantitatem è &longs;uo lumine <lb/>effundit, invenire altitudinem eiusdem autalterius tubi, qui <lb/>æquali tempore, per æquale lumen, aliam determi­<lb/>natam aquæ quantitatem effundat.<emph.end type="center"/></s></p> <pb xlink:href="051/01/172.jpg" pagenum="141"/> <p type="main"> <s>SIt tubi vel alterius va&longs;is erogatorij aquâ &longs;emper pleni altitudo <lb/> <arrow.to.target n="marg246"/><lb/>9. pedum, ex cuius lumine &longs;patio unius minuti &longs;aliat una aquæ <lb/>libra, &longs;it autem producenda altitudo eò u&longs;que, ut æquali &longs;patio <lb/>minuti, per idem aut æquale lumen effundat 16. libras aquæ. Du­<lb/>plicetur ratio 16 ad 1, & proveniet ratio 256 ad 1; nam 16 ducta in <lb/>16 efficiunt 256: cumque 9 referat unitatem, multiplica 256 per <lb/>9, & provenient 2304, pro tubi aut alterius va&longs;is quæ&longs;iti alti­<lb/>tudine. Ratio e&longs;t, quia tubi habent duplicatam rationem a­<lb/>quarum, per Propo&longs;it. VIII. huius capitis. Si itaque fiat, ut 1 ad <lb/>256, ita 9 ad aliud; provenient 2304. </s></p> <p type="margin"> <s><margin.target id="marg246"/><emph type="italics"/>Data tubi <lb/>altitudine, <lb/>ac tempore <lb/>effiuentis a­<lb/>quæ deter­<lb/>minatæ, in­<lb/>venire alti­<lb/>tudinem <lb/>pro alia a­<lb/>quæ quanti­<lb/>tate.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XXIV. Problema VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>In tubo &longs;eu va&longs;e non &longs;emper pleno determinare &longs;patia, <lb/>quæ temporibus æqualibus &longs;ibi &longs;ucced entibus evacuantur; <lb/>vti & men&longs;uram &longs;eu pondus aquæ quæ effluit.<emph.end type="center"/></s></p> <p type="main"> <s>PArte 2. Cla&longs;&longs;e 1. cap. 4. inter alias Machinas afferemus varia liy­<lb/>drologia, &longs;eu horologia aquatica, quibus per fluxum aquæ è <lb/> <arrow.to.target n="marg247"/><lb/>foramine alicui<emph type="sup"/>9<emph.end type="sup"/> tubi, aut va&longs;is, metimur horas æquales &longs;eu &ecedil;qua­<lb/>les temporis partes, &longs;ignando in va&longs;is latere lineas determinantes <lb/>fluxum æqualibus temporibus corre&longs;pondentem. At quoniam <lb/>ex dictis &longs;uprà Propo&longs;itione VI. con&longs;tat, &longs;patia quæ æqualibus <lb/>temporibus evacuantur, non e&longs;&longs;e æqualia, &longs;ed &longs;emper minora <lb/>atque minora evadere, eò quòd æqualibus temporibus non ef­<lb/>fluat æqualis aquæ copia, &longs;ed &longs;emper minor ac minor; ideo de­<lb/>terminandum híc e&longs;t, quomodo geometricè inveniendum &longs;it in <lb/>quolibet va&longs;e dictum &longs;patiorum decrementum, &longs;eu quomodo <lb/>dividendum &longs;it latus va&longs;is, ut &longs;patia ad&longs;ignata æqualibus tem­<lb/>poribus evacuentur. Iterum quoniam per dicta eâdem Pro­<lb/>po&longs;itione VI, aqua quæ æqualibus temporibus effluit è dictis va­<lb/>&longs;is, non e&longs;t æqualis, &longs;ed in æqualis; determinandum e&longs;t, quan­<lb/>tum quovis æquali tempore effluat. </s></p> <p type="margin"> <s><margin.target id="marg247"/><emph type="italics"/>In tubo de­<lb/>terminare <lb/>&longs;patia que <lb/>temporibus <lb/>æqualibus <lb/>evacuan­<lb/>tur.<emph.end type="italics"/></s></p> <p type="main"> <s>Dico itaque, aquam æqualibus temporibus effluere è tu­<lb/>bis non &longs;emper plenis ea ratione, ut &longs;ingulis temporibus decre- <pb xlink:href="051/01/173.jpg" pagenum="142"/>&longs;eat & aquæ effu&longs;æ quantitas, & va&longs;is &longs;eu tubi evacuati &longs;patium, <lb/>& aquæ de&longs;cendentis ac effluentis velocitas eo decremento, <lb/>quod e&longs;t inter numeros impares, ver&longs;us unitatem. Explico. Sit <lb/>vas quodcunque aquâ plenum, eius fluxus dividere debeat di­<lb/>em, aut quam cunque diei partem, in quatuor æquales partes; <lb/>&longs;intque in va&longs;e 16 v.g. men&longs;uræ &longs;eu libræ aquæ, quæ dato <lb/>tempore effluant. Dico, primo tempore effluere &longs;eptem men­<lb/>&longs;uras, &longs;ecundo quinque, tertiò tres, quarto & ultimo unam. </s></p> <p type="main"> <s>Dico iterum, &longs;i tota va&longs;is altitudo ab infima ad &longs;upremam <lb/>aquæ &longs;uperficiem dividatur in 16 æquales partes, aquam in pri­<lb/>mo tempore de&longs;cendere ad 7 &longs;patia, in &longs;ecundo ad <expan abbr="quinq;">quinque</expan> in ter­<lb/>tio ad tria, in quarto ad unum. Dico tandem, aquam in pri­<lb/>ma hora de&longs;cendere <expan abbr="atq;">atque</expan> effluere ut &longs;eptem, in &longs;ecunda ut quin­<lb/>que, in tertia ut tria, in quarta ut unum. Sequitur ex dictis <lb/>&longs;uprà Propo&longs;itione 8, 9, & 10, quas vide. Eadem ratio in <lb/>omnibus alijs e&longs;t. </s></p> <p type="main"> <s><emph type="center"/>Corollarium.<emph.end type="center"/><lb/> <arrow.to.target n="marg248"/></s></p> <p type="margin"> <s><margin.target id="marg248"/><emph type="italics"/>Vas parare, <lb/>cuius flux<emph type="sup"/>9<emph.end type="sup"/><lb/>dividat da­<lb/>tum tempus <lb/>in partes <lb/>æquales.<emph.end type="italics"/></s></p> <p type="main"> <s>EX his patet, quomodo parandum &longs;it vas, cuius fluxus dato <lb/>tempore durans dividat illud tempus in partes æquales. Sit <lb/>enim vas, cuius fluxus duret per &longs;patium duodecim horarum, & <lb/>hoc &longs;patium temporis &longs;it dividendum, beneficio fluxus aquæ, in <lb/>12 æquales partes &longs;eu horas. Duc 12. in &longs;eip&longs;a, & produces 144. <lb/>Deinde divide va&longs;is altitudinem à &longs;uprema ad infimam aquæ &longs;u­<lb/>perficiem, in 144 partes &longs;eu &longs;patia æqualia, & inferiùs prope <lb/>fundum va&longs;is incipiendo, deputa ultimæ horæ ex duodecim <expan abbr="vnũ">vnum</expan> <lb/>&longs;patiolum, penultimæ tria, ante penultimæ quinque, & &longs;ic ul­<lb/>teriùs progredere &longs;ecun dùm &longs;eriem &longs;eu progre&longs;&longs;ionem numero­<lb/>rum <expan abbr="impatiũ">impatium</expan>, prout apparet in numeris lateri dextro CD &longs;equen­<lb/>tis figuræ appo&longs;itis. His pr&ecedil;&longs;titis, divi&longs;um erit vas in &longs;patia in&ecedil;qua­<lb/>lia, qu&ecedil; &longs;ingulis æqualibus temporibus, nempe horis, evacuantur, <lb/>videbi&longs;que aquam in prima hora de&longs;cendere à &longs;patio ultimo &longs;eu <lb/>144, u&longs;que ad &longs;patium 121; in &longs;ecunda hora u&longs;que ad &longs;patium <lb/>100; in tertia u&longs;que ad 81; & &longs;ic porrò u&longs;que ad finem; prout <pb xlink:href="051/01/174.jpg" pagenum="143"/> <arrow.to.target n="fig36"/><lb/>apparet in numeris lateri &longs;ini&longs;tro AB eiu&longs;dem <lb/>figuræ appo&longs;itis. Lege Torricellum lib. 2. de <lb/>motu projectorum. </s></p> <figure id="id.051.01.174.1.jpg" xlink:href="051/01/174/1.jpg"/> <p type="main"> <s>Eadem ratione reperies, quot partes, aut <lb/>men&longs;uræ certæ, &longs;eu pondera aquæ effluant ex va­<lb/>&longs;e in &longs;ingulis horis. Item qua velocitate effluat <lb/>atque de&longs;cendatin ijsdem, &longs;ingulis horis. </s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>NVmeri dextri lateris<emph.end type="italics"/> CD <emph type="italics"/>indicant etiam partes <lb/>&longs;eu &longs;patiola va&longs;is, quæ percurrit aqua &longs;ingulis horis <lb/>&longs;uo motu de&longs;censûs; &longs;imiliter & partes aquæ, quæ &longs;ingu­<lb/>lis horis effluunt, & velocitatem, quâ effluunt. Nam <lb/>in prima hora percurrit &longs;patia<emph.end type="italics"/> 23, <emph type="italics"/>in &longs;ecunda<emph.end type="italics"/> 21, <emph type="italics"/>in <lb/>tertia<emph.end type="italics"/> 19, <emph type="italics"/>in quarta,<emph.end type="italics"/> 17, <emph type="italics"/>&c.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>Numeri &longs;ini&longs;tri lateris<emph.end type="italics"/> AB <emph type="italics"/>&longs;unt duodecim qua­<lb/>drata temporis in duodecim horas divi&longs;i. Nam<emph.end type="italics"/> 1 <emph type="italics"/>e&longs;t <lb/>quadratum horæ primæ, incipiendo ab ultima;<emph.end type="italics"/> 4 <emph type="italics"/>e&longs;t <lb/>quadratum horæ &longs;ecundæ,<emph.end type="italics"/> 9 <emph type="italics"/>e&longs;t quadratum horæ ter­<lb/>tiæ &c. vt patet, &longs;i &longs;inguli numerimedio figuræ in&longs;eri­<lb/>pti multiplicentur per &longs;eip&longs;os. Et hoc e&longs;t, quod dixi­<lb/>mus &longs;uprà Propo&longs;it.<emph.end type="italics"/> IX. <emph type="italics"/>in motu gravium naturaliter <lb/>de&longs;cendentium &longs;patia æqualibus temporibus transmi&longs;­<lb/>&longs;a e&longs;&longs;e inter &longs;e, ut quadrata temporum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>SI vas aliquod dividere velles in partes<emph.end type="italics"/> 24, <emph type="italics"/>multi­<lb/>plica<emph.end type="italics"/> 24 <emph type="italics"/>per<emph.end type="italics"/> 24, <emph type="italics"/>producentur<emph.end type="italics"/> 576. <emph type="italics"/>Divide ergo <lb/>altitudinem va&longs;is in<emph.end type="italics"/> 576 <emph type="italics"/>partes æquales, & procede <lb/>ut dictum in Corollario, juxta &longs;eriem numerorum im­<lb/>parium. Eadem ratione quotlibet vas in quotlibet <lb/>partes partieris.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVoniam quando in va&longs;e exigua e&longs;t aqua, ut vix <lb/>fundum operiat, fluxus ip&longs;ius guttatim & non<emph.end type="italics"/> <pb xlink:href="051/01/175.jpg" pagenum="144"/> <arrow.to.target n="fig37"/><lb/><emph type="italics"/>continuè &longs;it, ideo&queacute; aqua fluens guttulis &longs;uis errorem in­<lb/>ducere pote&longs;t; meliùs e&longs;t, &longs;i duæ ultimæ divi&longs;iones &longs;eu <lb/>&longs;patiola va&longs;is divi&longs;i, notata numeris<emph.end type="italics"/> 1 <emph type="italics"/>&<emph.end type="italics"/> 3, <emph type="italics"/>non ve­<lb/>niant in numerum &longs;patiolorum, & potiùs ver&longs;us prin­<lb/>cipium adjiciantur alia duo &longs;patia; &longs;icque vas, de quo <lb/>in Corollario, non dividatur in<emph.end type="italics"/> 12, <emph type="italics"/>&longs;ed in<emph.end type="italics"/> 14 <emph type="italics"/>partes, <lb/>modo ibi dicto, dividendo totam ip&longs;ius altitudinem <lb/>in partes æquales<emph.end type="italics"/> 196 <emph type="italics"/>(qui numerus re&longs;ultat ex ductu <lb/>numeri<emph.end type="italics"/> 14 <emph type="italics"/>in &longs;eip&longs;um) & addendo &longs;patium<emph.end type="italics"/> 13, <emph type="italics"/>&<emph.end type="italics"/><lb/>14, <emph type="italics"/>quæ demptis duobus infimis efficiant duodecim <lb/>&longs;patia.<emph.end type="italics"/></s></p> <figure id="id.051.01.175.1.jpg" xlink:href="051/01/175/1.jpg"/> <p type="main"> <s><emph type="center"/>PARERGVM CAPITIS TERTII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De inventione mediæ, ac tertiæ propor­<lb/>tionalis quantitatis, in numeris, & <lb/>lineis.<emph.end type="center"/></s></p> <p type="main"> <s>EXdictis hoc Capite patet, quàm &longs;æpe nece&longs;&longs;a­<lb/>ria &longs;it inventio mediæ, ac tertiæ, quartæque <lb/>proportionalis quantitatis, ut ex nota aquæ men­<lb/>&longs;ura, aut pondere, venire po&longs;&longs;imus in cognitio­<lb/>nem de&longs;ideratæ altitudinis tubi, aut va&longs;is; autè <lb/>contrario, ut ex nota tubi altitudine veniamus in <lb/>cognitionem men&longs;uræ aut ponderis aquæ, & <lb/>quamcunque tuborum altitudinem, aquarumvè <lb/>copiam reperiamus facilè per quamcunque ra­<lb/>tionem &longs;ubduplicatam, aut duplicatam, &longs;ive nu­<lb/>meris exprimi po&longs;&longs;it, &longs;ive non po&longs;&longs;it exprimi abs­<lb/>que &longs;urdis. Operæ ergo pretium duxi, Regu­<lb/>las brevi&longs;&longs;imas a&longs;&longs;ignare, vel &longs;altem in&longs;inuare, <lb/>prædictas quantitates inveniendi, mediam dico, <lb/>ac tertiam, quartamque proportionalem, tam <lb/>arithmeticè, quàm geometricè, libantes brevi&longs;­<lb/>&longs;imè nonnulla ex ij, quæ fu&longs;iùs dicemus in Arith­<lb/>metica, & in Geometria practica, &longs;euin <lb/>Pantometro Kircheriano. </s></p> <pb xlink:href="051/01/176.jpg" pagenum="145"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Inter duos numeros medium proportiona­<lb/>lem invenire.<emph.end type="center"/></s></p> <p type="main"> <s>DUos numeros propo&longs;itos multiplica inter&longs;e, & ex producto </s></p> <p type="main"> <s> <arrow.to.target n="marg249"/><lb/>erue radicem quadratam; erit hæc radix medio loco pro­<lb/>portionalis inter duos numeros datos. Exemplum. Sit inter 4 <lb/>& 16 inveniendus medius proportionalis numerus: multiplica <lb/>16 per 4, fiunt 64; cuius radix quadrata e&longs;t 8, e&longs;tque medio <lb/>loco proportionalis inter 4 & 16; quia ut e&longs;t 4 ad 8, ita 8 ad 16. </s></p> <p type="margin"> <s><margin.target id="marg249"/><emph type="italics"/>Numerum <lb/>medium in­<lb/>ter duos in­<lb/>venire.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis duobus numeris, tertium continuè <lb/>proportionalem invenire.<emph.end type="center"/></s></p> <p type="main"> <s>TRes numeri continuè proportionales dicuntur, quando e&longs;t, <lb/> <arrow.to.target n="marg250"/><lb/>ut primus ad &longs;ecundum, ita &longs;ecundus ad tertium. Huiusmodi <lb/>&longs;unt 1, 3, 9, & 1, 2, 4: item 2, 4, 8: item 4, 8, 16. Propo&longs;itisigi­<lb/>tur quibuscunque duobus numeris, in venietur tertius, qui ad <lb/>&longs;ecundum &longs;it ut ip&longs;e &longs;ecundus ad primum, &longs;eu ad quem &longs;ecun­<lb/>dus &longs;it ut primus ad &longs;ecundum; &longs;i &longs;ecundum ducas in &longs;eip&longs;um; <lb/>productus enim erit tertius proportionalis. </s></p> <p type="margin"> <s><margin.target id="marg250"/><emph type="italics"/>Numerum <lb/>tertium pro <lb/><expan abbr="portional&etilde;">portionalem</expan> <lb/>po&longs;t duos in­<lb/>venire.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Inter duas rectas lineas datas invenire mediam <lb/>proportionalem.<emph.end type="center"/></s></p> <figure id="id.051.01.176.1.jpg" xlink:href="051/01/176/1.jpg"/> <p type="main"> <s>SInt datæ duæ rectæ AB, BC, inter <lb/> <arrow.to.target n="marg251"/><lb/>quas invenienda &longs;it media propor­<lb/>tionalis. Coniungantur rectæ AB, CB <lb/>in unam rectam continuam in puncto <lb/>B, ut fiat recta ABC; eâque divisâ bi­<lb/>fariam in D, de&longs;cribatur &longs;emicirculus <lb/>aut circulus AEC, ad intervallum <lb/>DA, vel DC; tandemque ex B pun­<lb/>cto erigatur perpendicularis BE ad <lb/>circumferentiam u&longs;que; eritque BE <pb xlink:href="051/01/177.jpg" pagenum="146"/>media proportionalis quæ&longs;ita. Demon&longs;trationem vide apud <lb/>Euclidem lib. 6. Propo&longs;it. 13. </s></p> <p type="margin"> <s><margin.target id="marg251"/><emph type="italics"/>Lineam me <lb/>diam pro­<lb/>portionalem <lb/>inter duas <lb/>invenire.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis duabus rectis, invenire tertiam pro­<lb/>portionalem.<emph.end type="center"/><lb/> <arrow.to.target n="marg252"/></s></p> <p type="margin"> <s><margin.target id="marg252"/><emph type="italics"/>Lineam ter <lb/>tiam propor <lb/>tionalem <lb/>po&longs;t duas in <lb/>venire.<emph.end type="italics"/></s></p> <p type="main"> <s>SInt datæ duæ rectæ AB, & BE, præcedentis figuræ, &longs;itque <lb/>invenienda tertia, ad quam ita &longs;e habeat &longs;ecunda, &longs;icut pri­<lb/>ma ad &longs;ecundam. Coniungantur rectæ AB, BE, in puncto B <lb/>ad angulum rectum, ducaturque recta EA; eáque bifariam di­<lb/>visâ in F, ducatur recta FD perpendicularis ad AE; & facto <lb/>centro D, intervallo DA de&longs;cribatur circulus, qui nece&longs;&longs;ariò <lb/>tran&longs;ibit per punctum E, <emph type="italics"/>per quintam Quarti Euclid.<emph.end type="italics"/> Siiam <lb/>producatur recta AB <expan abbr="u&longs;q;">u&longs;que</expan> ad circumferentiam circuli, hoc e&longs;t, <lb/>u&longs;que ad punctum C; erit BC tertia proportionalis quæ&longs;ita. </s></p> <p type="main"> <s>Sint iterum datæ duæ rectæ BC, & BE, &longs;itque invenien­<lb/>da tertia proportionalis. Coniungantur, ut antea, rectæ illæ <lb/>in B, ut efficiantangulum rectum, & ducatur recta EC; at­<lb/>que ex puncto medio G demittatur perpendicularis GD, & <lb/>producta recta CB in continuum, de&longs;cribatur centro D, in­<lb/>tervallo DC, circulus, qui iterum tran&longs;ibit per punctum E, <lb/>& &longs;ecabit rectam CB productam in A; eritque hæc recta BA <lb/>tertia proportionalis quæ&longs;ita. </s></p> <p type="main"> <s><emph type="center"/>Annotatio<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVod dictum e&longs;t de lineis hîc po&longs;itis, dicendum e&longs;t de quibuscunque </s></p> <p type="main"> <s> <arrow.to.target n="marg253"/><lb/>line is propo&longs;itis. Itaque &longs;ipropo&longs;itis duobus tubis inveniendus &longs;it <lb/>velmedius, veltertius proportionalis; coniunge lineas rectas tubis da­<lb/>tis æquales; & operare ut dictum, & invenies quod quæris. Quòd &longs;i <lb/>tubi propo&longs;iti, ac lineæ ip&longs;is æquales nimis e&longs;&longs;ent longæ, ac proinde minùs <lb/>commodè circulo includi po&longs;&longs;ent; accipe ip&longs;arum &longs;ubmultiplices, v.g. <lb/>dimidiam, tertiam, quartam, &c. partem, & cum ip&longs;is procede <lb/>ut dictum; eritque inventa linea æquè &longs;ubmultiplex <lb/>lineæ aut tubi quæ&longs;iti.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/178.jpg" pagenum="147"/> <p type="margin"> <s><margin.target id="marg253"/>Tubum me <lb/>dium <gap/> t<gap/>­<lb/>tium p<gap/>r <lb/>tionalem in <lb/>venire.</s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aliter invenire tertiam proportionalem.<emph.end type="center"/></s></p> <p type="main"> <s>QUod fecimus in pr&ecedil;cedenti Propo&longs;itione mediante circulo, <lb/> <arrow.to.target n="marg254"/><lb/>fieri pote&longs;t faciliùs absque circulo &longs;ic. </s></p> <p type="margin"> <s><margin.target id="marg254"/><emph type="italics"/>Lineam ter <lb/>tiam pro­<lb/>portionalem <lb/>aliter inve­<lb/>nire.<emph.end type="italics"/></s></p> <figure id="id.051.01.178.1.jpg" xlink:href="051/01/178/1.jpg"/> <p type="main"> <s>Duæ rectæ datæ, AB, & BE, con­<lb/>&longs;tituantur ad angulum rectum ABE, <lb/>ut dictum, & ducatur recta EA. Pro­<lb/>ductâ deinde AB, antecedente &longs;eu <lb/>primâ duarum datarum, ducatur ex E <lb/>ad AE perpendicularis EC, occur­<lb/>rensip&longs;i AB productæ in C; eritque <lb/>BC tertia proportionalis. </s></p> <p type="main"> <s>Si e&longs;&longs;ent propo&longs;itæ duæ rectæ CB, <lb/>BE, deberent ip&longs;æ coniungi ad angu­<lb/>lum rectum CBE, & ductâ rectâ CE, <lb/>productaque CB, deberet duci per­<lb/>pendicularis AE, ad rectam CE, <expan abbr="e&longs;&longs;et&qacute;ue">e&longs;&longs;etque</expan> AB tertia quæ&longs;ita. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>INventâ alterutro modorum tertiâ continuè proportionali, &longs;i primam <lb/>omi&longs;eris, & alijs duabus tertiam inveneris; habebis quatuor leneas <lb/>continuè proportionales. Eodemque modo invenies quintam, &longs;extam, <lb/>&longs;eptimam, & quamcunque aliam.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Adhuc aliter invenire tertiam proportionalem.<emph.end type="center"/></s></p> <p type="main"> <s>SI difficile tibi videtur ducere tot perpendiculares ad inveni­<lb/> <arrow.to.target n="marg255"/><lb/>endamtertiam proportionalem, uti poteris modo præ&longs;cripto <lb/>ab Euclide lib. 6. Propo&longs;it. 11. &longs;ic: </s></p> <p type="margin"> <s><margin.target id="marg255"/><emph type="italics"/>Adhuc ali­<lb/>ter item pre <lb/>&longs;tare.<emph.end type="italics"/></s></p> <figure id="id.051.01.178.2.jpg" xlink:href="051/01/178/2.jpg"/> <p type="main"> <s>Sint duæ rectæ AB, AE. <lb/><expan abbr="Di&longs;ponãtur">Di&longs;ponantur</expan> eæita, ut efficiant <lb/>angulum A quemcunque, <lb/>producaturque AB quam vis <lb/>e&longs;&longs;e antecedentem &longs;eu <expan abbr="primã">primam</expan>, <lb/>& capiatur BC æqualis ip&longs;i <lb/>AE, quæ con&longs;equens e&longs;&longs;e de- <pb xlink:href="051/01/179.jpg" pagenum="148"/> <arrow.to.target n="fig38"/><lb/>bet, &longs;ive &longs;ecunda, aut media. <lb/>Deinde ductâ rectâ AB, aga­<lb/>tur illi ex C parallela CD, <lb/>occurrensip&longs;i AE productæ, <lb/>in D; eritque ED tertia <lb/>proportionalis quæ&longs;ita. </s></p> <figure id="id.051.01.179.1.jpg" xlink:href="051/01/179/1.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>SIduæ datæ&longs;int nimis longæ, &longs;ervetur id, quod diximus in Annota­<lb/>tione Propo&longs;itionis quartæ præcedentis.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis tribus numeris, invenire quartum pro­<lb/>portionalem.<emph.end type="center"/><lb/> <arrow.to.target n="marg256"/></s></p> <p type="margin"> <s><margin.target id="marg256"/><emph type="italics"/>Numeris <lb/>tribus datis <lb/>quartum <lb/>proportiona­<lb/>lem inveni­<lb/>re.<emph.end type="italics"/></s></p> <p type="main"> <s>UTere Regulâ proportionum apud Arithmeticos noti&longs;&longs;ima, <lb/>quam Auteam vocant; & habebis intentum. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis tribus rectia lineis, quartam propor­<lb/>tionaleminvenirc.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg257"/></s></p> <p type="margin"> <s><margin.target id="marg257"/><emph type="italics"/>Lineis tri­<lb/>bus datis, <lb/><expan abbr="quartã">quartam</expan> pro­<lb/>portiona­<lb/>lem inveni­<lb/>re.<emph.end type="italics"/></s></p> <figure id="id.051.01.179.2.jpg" xlink:href="051/01/179/2.jpg"/> <p type="main"> <s>SInt tres lineæ rectæ, AB, BC, <lb/>AD, quibus invenienda &longs;it <lb/>quarta. proportionalis, ad <lb/>quàm &longs;it tertia AD, ut e&longs;t <lb/>prima AB, ad &longs;ecundam BC. <lb/><expan abbr="Di&longs;ponãtur">Di&longs;ponantur</expan> primæ duæ, AB, <lb/>BC, &longs;ecundùm lineam <expan abbr="rectã">rectam</expan> <lb/>quæ &longs;it AC; tertia verò AD, <lb/>cum prima AB, faciatangulum A quemcunque: deinde ex B <lb/>ad D ducatur recta BD, cui per C ducatur parallela CE, oc­<lb/>currens rectæ AD productæ, in E puncto. Dico, DE, e&longs;&longs;e <lb/>quartam proportionalem. Demon&longs;trationem vide apud <lb/>Euclidem lib. 6. Propo&longs;it. 12. </s></p> <pb xlink:href="051/01/180.jpg" pagenum="149"/> <p type="main"> <s><emph type="center"/>CAPVT IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De proprietatibus aquæ &longs;alientis ex tubis. <lb/>PROOEMIVM.<emph.end type="center"/></s></p> <figure id="id.051.01.180.1.jpg" xlink:href="051/01/180/1.jpg"/> <p type="main"> <s><emph type="italics"/>CApite præceden­<lb/> <arrow.to.target n="marg258"/><lb/>ti egimuo de pro­<lb/>prietatibus a­<lb/>quæ fluentis per tubos <lb/>verticales, hoc e&longs;t, efflu­<lb/>entis ex foramine facto in <lb/>ba&longs;ibus tuborum: hoc Ca­<lb/>pite agemus de proprieta­<lb/>tibus eju&longs;dem aquæ &longs;ali­<lb/>entis ex tubis verticali­<lb/>bus, hoc e&longs;t, effluentis ex <lb/>foraminibus lateralib<emph type="sup"/>9<emph.end type="sup"/> <expan abbr="tu-borũ">tu­<lb/>borum</expan>, &longs;eu per tubos inferi­<lb/>ùs inflexos. Po&longs;&longs;unt <expan abbr="aut&etilde;">autem</expan> <lb/>tubi verticales inferiùs <lb/>inflecti triplici modo, ho­<lb/> <arrow.to.target n="marg259"/><lb/>rizontaliter, verticali­<lb/>ter, & medio modo. Ho­<lb/>rizontaliter inflexus dici­<lb/>tur, &longs;i pars inferior infle­<lb/>xa &longs;it horizonti parallela <lb/>re&longs;pectupartis reliquæ ver<emph.end type="italics"/> <pb xlink:href="051/01/181.jpg" pagenum="150"/> <arrow.to.target n="fig39"/><lb/><emph type="italics"/>ticaliter erectæ; &longs;eu&longs;i pars <lb/>inferior inflexa faciat cum <lb/>reliquæ angulum rectum. <lb/>Talis e&longs;t in appo&longs;ito &longs;che­<lb/>mate tubus<emph.end type="italics"/> ABC. <emph type="italics"/>Ver­<lb/>ticaliter inflexus dicitur, <lb/>&longs;i pars inferior inflexa &longs;it <lb/>horizonti perpendicularis <lb/>re&longs;pectu reliquæ partis et­<lb/>iam perpendiculariter e­<lb/>rectæ. Talis e&longs;t in &longs;che­<lb/>mate præ&longs;enti tubus<emph.end type="italics"/> ABE. <lb/><emph type="italics"/>Medio modo inflexus di­<lb/>citur, &longs;ipars inferior ne­<lb/>que parallela e&longs;t horizon­<lb/>ti, neque perpendicula­<lb/>ris, &longs;ed inter utrumque <lb/>&longs;itum facit angulum &longs;e­<lb/>mirectum &longs;eu<emph.end type="italics"/> 45 <emph type="italics"/>gradu­<lb/>um. Talis e&longs;t tubus<emph.end type="italics"/> ABD. </s></p> <p type="margin"> <s><margin.target id="marg258"/>Proprieta­<lb/>tes aquæ &longs;a­<lb/>lientis ex tu <lb/>bis vertica­<lb/>libus.</s></p> <p type="margin"> <s><margin.target id="marg259"/>Tubi verti­<lb/>cale, tripli­<lb/>citer inflecti <lb/>po&longs;&longs;unt in­<lb/>feriùs.</s></p> <figure id="id.051.01.181.1.jpg" xlink:href="051/01/181/1.jpg"/> <p type="main"> <s><emph type="italics"/>Easdem appellatio­<lb/>nes &longs;ubibit tubusinflexus, <lb/>&longs;i pars inferior habeat tria <lb/>epi&longs;tomia,<emph.end type="italics"/> E, D, C, <emph type="italics"/>quorum<emph.end type="italics"/> E <emph type="italics"/>&longs;it erectum perpendiculariter,<emph.end type="italics"/><lb/>C <emph type="italics"/>pro&longs;tratum horizontaliter,<emph.end type="italics"/> D <emph type="italics"/>inclinatum inter utrum­<lb/>que, ad dictum angulum. Quod fit per tria epi&longs;tomia dicta, <lb/>fieri pote&longs;t per unum, &longs;i ita in&longs;eratur parti inferiori tubi inflexi, <lb/>ut verti atque dirigi po&longs;&longs;it in quemcunque &longs;itum.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/182.jpg" pagenum="151"/> <p type="main"> <s><emph type="italics"/>Radij aquæ, qui ex inflexo tubo, aut ex epi&longs;tomiis præ-<emph.end type="italics"/><lb/> <arrow.to.target n="marg260"/><lb/><emph type="italics"/>dictis exiliunt, quales &longs;unt in præcedenti <expan abbr="diagra&mtilde;ate">diagramnate</expan> radij<emph.end type="italics"/> EF, <lb/>DI, DK, CG, CH, <emph type="italics"/>appellari po&longs;&longs;unt aqueæ virgulæ, aquei ecdro­<lb/>mi, hoc e&longs;t, excur&longs;us &longs;eu &longs;altus aquæ, & &longs;imilibus nominibus. <lb/>Marinus tamen Mer&longs;ennus in Hydraulicis &longs;uis Phænomenis <lb/>appellat eos<emph.end type="italics"/> &longs;alientes, <emph type="italics"/>aitque eo nomine appellari à Iulio Fron­<lb/>tino, aliis que veteribus; quare & nos eo vocabulo utemur.<emph.end type="italics"/><lb/> <arrow.to.target n="marg261"/><lb/><emph type="italics"/>Radius igitur<emph.end type="italics"/> EF <emph type="italics"/>dicatur &longs;aliens verticalis, Radius<emph.end type="italics"/> CG, <lb/><emph type="italics"/>&<emph.end type="italics"/> CH, <emph type="italics"/>&longs;aliens Horizontalis; radius denique<emph.end type="italics"/> DI, <emph type="italics"/>&<emph.end type="italics"/> DK, <lb/><emph type="italics"/>&longs;aliens Medius, et licet &longs;alientes<emph.end type="italics"/> CG, CH, <emph type="italics"/>nonprocedant ho­<lb/>rizontaliter, &longs;ed ob aquæ gravitatem &longs;tatim deprimantur, at­<lb/>que curventur; vocantur tamen &longs;alientes horizontales, propter <lb/>epi&longs;tomium aut tubulum<emph.end type="italics"/> C <emph type="italics"/>horizontaliter di&longs;po&longs;itum.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg260"/>Radij aqu&ecedil; <lb/>ex inflexo <lb/>tubo exili­<lb/>entes.</s></p> <p type="margin"> <s><margin.target id="marg261"/>Salientes <lb/>aquæ ex tu <lb/>bis quid <lb/>&longs;int.</s></p> <p type="main"> <s><emph type="italics"/>His præm&longs;&longs;is, afferemus nunc nonnullas ex multis ob&longs;er-<emph.end type="italics"/><lb/> <arrow.to.target n="marg262"/><lb/><emph type="italics"/>vationes, &longs;eu Phænomena aquæ &longs;alientis ex tubis, præ&longs;ertim <lb/>ex Marino Mer&longs;enno, qui eâ in re diligentiam multorum <lb/>vincit. His deinde addemus unum aut alterum Problema. <lb/>Atque ex his patebunt proprietates aquæ &longs;alientis ex tubis.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg262"/>Ph&ecedil;nome­<lb/>na aquæ &longs;a <lb/>lientis.</s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio I. Phænomenum. I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salientium &longs;ive ecdromorum horizontalium, & medio­<lb/>rum, &longs;uper eodem horizonte, longitudines &longs;unt in ratione &longs;ub­<lb/>duplicata tuborum, ex quibus exiliunt.<emph.end type="center"/></s></p> <p type="main"> <s>DIxi, <emph type="italics"/>&longs;uper eodem horizonte;<emph.end type="italics"/> nam &longs;uper diver&longs;ishorizon­<lb/>tibus diver&longs;a e&longs;t eiu&longs;dem &longs;alientis longitudo, etiam <lb/>re&longs;pectu eiu&longs;dem tubi, ut dicemus Propo&longs;itione &longs;e­<lb/>quenti. Voco autem longitudinem horizontalium <lb/>&longs;alientium, di&longs;tantiam in præcedenti &longs;chemate à puncto z v.g. <lb/>adpunctum H, aut G, &C. <pb xlink:href="051/01/183.jpg" pagenum="152"/> <arrow.to.target n="marg263"/></s></p> <p type="margin"> <s><margin.target id="marg263"/><emph type="italics"/>Salientium| <lb/>proportio ad <lb/>duos tubos.<emph.end type="italics"/></s></p> <p type="main"> <s>Sint igitur in præcedenti &longs;chemate duo tubi, BL pedalis, <lb/>& BA quadrupedalis; &longs;ithorizon OHG; &longs;itque tubi pedalis BL <lb/>&longs;aliens horizontalis CH, tubi verò quadrupedalis BA &longs;aliens <lb/>horizontalis &longs;it CG. Dico, longitudinem &longs;alientis tubi BL <lb/>pedalis, &longs;cilicet CH, e&longs;&longs;e &longs;ubduplam &longs;alientis tubi BA, &longs;cilicet <lb/>CG. Ob&longs;erva vit id Mer&longs;ennus, ut a&longs;&longs;erit ip&longs;e in &longs;uis Phænome­<lb/>nis hydraulicis Propo&longs;it. XVI. Quare, &longs;i longitudo &longs;alientis tu­<lb/>bi pedalis e&longs;t unius pedis, longitudo &longs;alientis tubi quadrupedalis <lb/>erit duorum pedum; & longitudo &longs;alientis tubi &longs;exde cupedalis <lb/>erit quatuor pedum; & longitudo &longs;alientistubi 64 pedum erit <lb/>octo pedum; & ita de reliquis. Ratio huius Phænomeni vide­<lb/>tur de&longs;umenda e&longs;&longs;e à velocitate aquæ de&longs;cendentis per tubos, <lb/>quæ etiam e&longs;t in ratione tuborum &longs;ubduplicata, ut con&longs;tat ex <lb/>Propo&longs;it. X. Capitis præcedentis. </s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur hinc, altitudines tuborum habere duplicatam ratio­<lb/>nem eius, quam habent longitudines &longs;alientium horizonta­<lb/>lium. </s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVod dixi in Propo&longs;itione de &longs;alientibus horizontalibus<emph.end type="italics"/> CG, CH, <lb/><emph type="italics"/>debet etiam intelligi de &longs;alientibus medijs<emph.end type="italics"/> DK, DI. </s></p> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg264"/></s></p> <p type="margin"> <s><margin.target id="marg264"/><emph type="italics"/>Salientium <lb/>longitudines <lb/>ob&longs;ervare.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="italics"/>LOngitudines &longs;ælientium &longs;uper horizontem quemcun&queacute; pote&longs;t quilibet <lb/>ob&longs;ervare facillimè, & ubivis locorum, &longs;iconficiat &longs;ibi tubulum <lb/>præcedentis figuræ<emph.end type="italics"/> ABC <emph type="italics"/>portatilem, determinatæ altitudinis & lati­<lb/>tudinis, v.g. altumpede vno, & latum digito. Si enim apud<emph.end type="italics"/> C <emph type="italics"/>epi&longs;to­<lb/>mium in&longs;erat, aut etiam &longs;olum digitum apponat foramini<emph.end type="italics"/> C, <emph type="italics"/>& de­<lb/>inde repleto tubo epi&longs;tomium aperiat, aut digitum amoveat, ut paucu­<lb/>læ &longs;olùm guttulæ exiliant, iterumque obturet foramen; notare poterit <lb/>in horizonte &longs;ignum à &longs;aliente impre&longs;&longs;um; cuiusmodi &longs;igna <lb/>&longs;unt in &longs;uperiori &longs;chemate<emph.end type="italics"/> K, I, H, G, &C. </s></p> <pb xlink:href="051/01/184.jpg" pagenum="153"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio II. Phænomenon II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salientes horizontales, & mediæ, eju&longs;dem tubi, co <lb/>&longs;unt longiores, quò lumen tubi fuerit altius &longs;upra <lb/>horizontem.<emph.end type="center"/></s></p> <p type="main"> <s>SIntin præcedenti diagrammate diverfi horizontes, OG, PS, </s></p> <p type="main"> <s> <arrow.to.target n="marg265"/><lb/>QT, RV &C. &longs;upra quos elevatus &longs;it tubus ABC; Dico &longs;ali­<lb/>entem CHSTV (& idem intelligendum e&longs;t de reliquis &longs;alienti­<lb/>bus horizontalibus, ac medijs) &longs;upra horizontem RV, e&longs;&longs;e <lb/>longiorem quàm &longs;upra horizontem QT, & &longs;upra hunc longio­<lb/>rem quàm &longs;upra PS, & longiorem &longs;upra hunc, quàm &longs;upra OG. <lb/>Cre&longs;cit itaque eò magis &longs;alientium horizontalium ac mediarum <lb/>longitudo, quo magis cre&longs;cit luminis tubi &longs;uper horizontem ele­<lb/>vatio. Si verò in ex ce&longs;&longs;iva altitudine orificium poneretur; cer­<lb/>tum e&longs;t aquæ ecdromen u&longs;que ad terminum con&longs;titutum flu­<lb/>xum non <expan abbr="continuaturã">continuaturam</expan>, &longs;ed cum tempore in guttas, & tandem <lb/>in aërem re&longs;olutum iri, ut experientia docuit in Cuppula S. Petri <lb/>interiori, ex quo &longs;cyphus plenus vino vel aqua effu&longs;us ita evanuit <lb/>in intermedio aëre, ut nullum pror&longs;us <expan abbr="ve&longs;tigiũ">ve&longs;tigium</expan> nec quidem gut­<lb/>tarum in inferiori pavimento ijs, qui &longs;tudio id attendebant, ap­<lb/>paruerit, ut P. Kircherus mihi a&longs;&longs;eruit. Ex nubibus tamen de­<lb/>cidit guttatim in terram aqua, quia in magna copia & continua­<lb/>tæ decidunt guttæ. </s></p> <p type="margin"> <s><margin.target id="marg265"/><emph type="italics"/>Salientes eo <lb/><expan abbr="sũt">sunt</expan> longiores <lb/>quò altiù <lb/>foramen <lb/>tubi.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVanta verò &longs;it &longs;alientium in quavis tubi &longs;upra horizontem eleva­<lb/>tione longitudo, inve&longs;tigandum e&longs;t ob&longs;ervatione, quam quilibet <lb/>facilè poterit facere modo dicto Propo&longs;itione præcedente. Mer&longs;ennus <lb/>in &longs;uis Phænomenis Propo&longs;it.<emph.end type="italics"/> XVI. <emph type="italics"/>proponit paucas ex multis in &longs;equen­<lb/>ti tabella, in quâ Prima Columna continet varias tubi pedalis, velpo­<lb/>tiùs luminis tubi, &longs;upra horizontem elevationes in pedibus, ita ut prima <lb/>elevatio &longs;it unius pedis, &longs;ecunda duorum pedum, &c: Secunda verò co­<lb/>lumna exhibet &longs;alientium longitudines in pedibus & digitis. Addidi<emph.end type="italics"/> <pb xlink:href="051/01/185.jpg" pagenum="154"/> <arrow.to.target n="marg266"/><lb/><emph type="italics"/>ego ex eodem Mer&longs;enno Propo&longs;it.<emph.end type="italics"/> 29. <emph type="italics"/>&longs;alientem tubi pedalis elevati p<gap/><lb/>uno cum dimidio &longs;upra horizontem.<emph.end type="italics"/></s></p> <p type="margin"> <s><margin.target id="marg266"/><emph type="italics"/>Salientium <lb/>tabella ex <lb/>Mer&longs;enno.<emph.end type="italics"/></s></p> <table> <row><cell>Altitudines tubi &longs;upra Horizontem.</cell><cell>Longitudines &longs;alientium</cell></row> <row><cell/><cell>Pedes.</cell><cell/><cell/><cell>Pedes</cell><cell>Digi<gap/></cell></row> <row><cell>1</cell><cell>----------</cell><cell>----------</cell><cell>1</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>1 1/2</cell><cell>----------</cell><cell>----------</cell><cell>2</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>2</cell><cell>----------</cell><cell>----------</cell><cell>2</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>3</cell><cell>----------</cell><cell>----------</cell><cell>3</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>4</cell><cell>----------</cell><cell>----------</cell><cell>3</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>5</cell><cell>----------</cell><cell>----------</cell><cell>4</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>6</cell><cell>----------</cell><cell>----------</cell><cell>4</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>12</cell><cell>----------</cell><cell>----------</cell><cell>5</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>18</cell><cell>----------</cell><cell>----------</cell><cell>6</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>26</cell><cell>----------</cell><cell>----------</cell><cell>8</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>50</cell><cell>----------</cell><cell>----------</cell><cell>10</cell><cell>----------</cell><cell>----------</cell></row></table> <table> <row><cell>Altitudines tubi &longs;upra Horizontem.</cell><cell>Longitudines &longs;alientium</cell></row> <row><cell/><cell>Pedes.</cell><cell/><cell/><cell>Pedes</cell><cell>Digi<gap/></cell></row> <row><cell>1</cell><cell>----------</cell><cell>----------</cell><cell>1</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>1 1/2</cell><cell>----------</cell><cell>----------</cell><cell>2</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>2</cell><cell>----------</cell><cell>----------</cell><cell>2</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>3</cell><cell>----------</cell><cell>----------</cell><cell>3</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>4</cell><cell>----------</cell><cell>----------</cell><cell>3</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>5</cell><cell>----------</cell><cell>----------</cell><cell>4</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>6</cell><cell>----------</cell><cell>----------</cell><cell>4</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>12</cell><cell>----------</cell><cell>----------</cell><cell>5</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>18</cell><cell>----------</cell><cell>----------</cell><cell>6</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>26</cell><cell>----------</cell><cell>----------</cell><cell>8</cell><cell>----------</cell><cell>----------</cell></row> <row><cell>50</cell><cell>----------</cell><cell>----------</cell><cell>10</cell><cell>----------</cell><cell>----------</cell></row></table> <p type="main"> <s><emph type="center"/>Annotatio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>Idem Mer&longs;ennus loco citato Propo&longs;it.<emph.end type="italics"/> XVII. <emph type="italics"/>ait tubum quadrupeda <lb/>lem habentem altitudinem unius pedis &longs;upra horizontem, ejicere &longs;ali <lb/>entem horizontalem ad pedes<emph.end type="italics"/> 3 2/3 <emph type="italics"/>proximè.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III. Phænomenon. III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salientes horizontales & mediæ, eandem longitudinis <lb/>rationem &longs;ervant, quàm altitudines tuborum &longs;upra eun­<lb/>dem horizontem.<emph.end type="center"/></s></p> <p type="main"> <s>DIver&longs;as tubi eiu&longs;dem altitudines &longs;upra horizontem referant <lb/>in &longs;equenti diagrammate lineæ OG, PS, QT, RV. Dico, ut <pb xlink:href="051/01/186.jpg" pagenum="155"/> <arrow.to.target n="fig40"/><lb/>altitudo BO ad altitudi­<lb/> <arrow.to.target n="marg267"/><lb/>nem BR, ita e&longs;&longs;e longitu­<lb/>nem &longs;alientis CH ad lon­<lb/>gitudinem &longs;alientis CV. <lb/>Intelligendum autem hoc <lb/>e&longs;t de illis &longs;alientium lon­<lb/>gitudinibus, quas ex datis <lb/>altitudinibus, ob&longs;ervare <lb/>commodè po&longs;&longs;umus: nam <lb/>cùm ne&longs;ciamus, utrum, & <lb/>ubi &longs;alientium incremen­<lb/>tum &longs;it de&longs;iturum, &longs;i ele­<lb/>vatio tubi &longs;upra horizon­<lb/>tem æquaretur terræ &longs;e­<lb/>midiametro; non pote&longs;t <lb/>Propo&longs;itio præ&longs;ens e&longs;&longs;e u­<lb/>niver&longs;alis, ni&longs;i in &longs;en&longs;u ex­<lb/>explicato. </s></p> <p type="margin"> <s><margin.target id="marg267"/><emph type="italics"/>Salientes e­<lb/>andem lon­<lb/>gitudinis <lb/><expan abbr="proportion&etilde;">proportionem</expan> <lb/>&longs;ervant, <lb/>quam tubo­<lb/>rum altitu­<lb/>dines.<emph.end type="italics"/></s></p> <figure id="id.051.01.186.1.jpg" xlink:href="051/01/186/1.jpg"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Phænomenon IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salientium verticali­<lb/>um in <expan abbr="quacunq;">quacunque</expan> elevatio­<lb/>ne tubi &longs;upra horizontem <lb/>&longs;emper eadem e&longs;t alti­<lb/>tudo.<emph.end type="center"/></s></p> <p type="main"> <s>ESto tubus ABC præ­<lb/> <arrow.to.target n="marg268"/><lb/>cedentis diagramma­<lb/>tis, & &longs;aliens EF, &longs;itque <lb/>horizon RV, & tubus &longs;it modò in Q, modò in P, modò in O, <lb/>modò in B. Dico, &longs;alientis EF <expan abbr="altitudin&etilde;">altitudinem</expan> e&longs;&longs;e &longs;emper eandem <lb/>in quacunque tubi elevatione &longs;upra horizontem RV. In hori­<lb/>zontalibus &longs;alientibus contrarium contingit, ut vidimus Pro­<lb/>po&longs;itione II. Ratio Phænomeni e&longs;t, quòd altitudo &longs;alientis <pb xlink:href="051/01/187.jpg" pagenum="156"/>EF dependeat &longs;olùm à tubilongitudine, & lumine E, po&longs;ito <lb/>æquali &longs;emper medio &longs;eu aëre; at in horizontalibus longitudo <lb/>dependet etiam à figura &longs;alientis, de qua Mer&longs;ennus, & Tor­<lb/>ricellus. </s></p> <p type="margin"> <s><margin.target id="marg268"/><emph type="italics"/>Salientium <lb/>verticali­<lb/>um altitu­<lb/>do quæ.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio V. Phænomenon V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Saliens verticalis nunquam adæquat altitu­<lb/>dinem originis.<emph.end type="center"/><lb/> <arrow.to.target n="marg269"/></s></p> <p type="margin"> <s><margin.target id="marg269"/><emph type="italics"/>Saliens ver <lb/>ticalis nun­<lb/>quam adæ­<lb/>quat altitu <lb/>dinem ori­<lb/>ginis.<emph.end type="italics"/></s></p> <p type="main"> <s>NUnquam enim &longs;aliens EF æquare pote&longs;t altitudinem tubi <lb/>BA. Et eadem e&longs;t ratio de alijs omnibus &longs;alientibus, qua­<lb/>rum altitudo nunquam æquare pote&longs;t altitudinem originis, &longs;ive <lb/>origo &longs;tatim tubo includatur, &longs;ive non. Et ratio e&longs;t, quia gra­<lb/>vitas humidi, & re&longs;i&longs;tentia aëris impediunt prædictam adæqua­<lb/>tionem. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VI. Phænomenon VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Saliens verticalis tubi quadrupedalis proximè <lb/>æquat 5/6 tubi &longs;ui.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg270"/></s></p> <p type="margin"> <s><margin.target id="marg270"/><emph type="italics"/>Saliens ver <lb/>ticalis tubi <lb/>quadrupe­<lb/>dalis.<emph.end type="italics"/></s></p> <p type="main"> <s>OB&longs;ervavit id Mer&longs;ennus, a&longs;&longs;eritque in &longs;uis Phænomenis Pro­<lb/>po&longs;it. XVII. ubi ait, hanc &longs;alientem po&longs;&longs;e e&longs;&longs;e reliquarum <lb/>modulum, &longs;eu men&longs;uram. Vide quæ diximus Propo&longs;itione II. <lb/>Annot. 2. ubi idem quod hîc a&longs;&longs;eruimus. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VII. Phænomenon VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Salientes verticales eò &longs;unt longiores, quò tubi &longs;unt <lb/>longiores; &longs;ed non eâdem proportione illæ ac hi <lb/>cre&longs;cunt.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg271"/></s></p> <p type="margin"> <s><margin.target id="marg271"/><emph type="italics"/>Salientium <lb/><expan abbr="verticaliũ">verticalium</expan> <lb/>longitudo <lb/>qu&adot; propor <lb/>tione cre­<lb/>&longs;cat.<emph.end type="italics"/></s></p> <p type="main"> <s>Vnde licet tuborum non adeo longorum &longs;alientes verticales <lb/>&longs;int proximè 5/6, aut 2/3 &longs;uorum tuborum; tamen in tubis <lb/>longis &longs;alientes verticales vix excedunt 1/4 tubi. Et hoc prove­<lb/>nit tum ob aëris re&longs;i&longs;tentiam, tum ob aquæ gravitatem. Ita <lb/>Mer&longs;ennus in Phænomenis Propo&longs;it. XVII. </s></p> <pb xlink:href="051/01/188.jpg" pagenum="157"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio VIII. Problema I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Data tubi altitudine, & &longs;upra horizontem elevatione, <lb/>invenire longitudinem &longs;alientis horizontalis, <lb/>& mediæ.<emph.end type="center"/></s></p> <p type="main"> <s>SIt altitudo tubi alta pedes 9, cuius os &longs;it <expan abbr="elevatũ">elevatum</expan> &longs;upra horizon­</s></p> <p type="main"> <s> <arrow.to.target n="marg272"/><lb/>tem pedes quinque, & &longs;itinvenienda longitudo &longs;alientis hori­<lb/>zontalis, aut mediæ, huius tubi. Fieri hoc pote&longs;t duplici viâ. <lb/>Primò per ob&longs;ervationem &longs;ic. Applica orificio tubi epi&longs;tomi­<lb/>um, aut tubulum horizontaliter, aut medio modo, prout opus <lb/>fuerit, & nota &longs;alientis punctum pavimento impre&longs;&longs;um, iuxta <lb/>dicta Propo&longs;it. 1. huius Capitis Annotat. II. Secundò per <lb/>calculum &longs;ic. Quoniam, per Propo&longs;itionem I. hujus Capitis, <lb/>&longs;alientium horizontalium & mediarum, &longs;uper eodem horizonte <lb/>longitudines, &longs;untin ratione &longs;ubduplicata tuborum; & per di­<lb/>cta Propo&longs;it. 11. huius eiu&longs;dem Capitis, tubus pedalis pedes quin­<lb/>que &longs;upra horizontem elevatus habet &longs;alientem longam pedes <lb/>quatuor; &longs;i inveniatur media proportionalis inter 1 & 9, nempe <lb/>3, erit hæc longitudo quæ&longs;ita. </s></p> <p type="margin"> <s><margin.target id="marg272"/><emph type="italics"/>Salientis ho <lb/>rizontalis <lb/>longitudi­<lb/>nem inve­<lb/>nire, data <lb/>tubi altitu­<lb/>dine.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IX. Problema II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Data longitudine &longs;alientis horizontalis, aut mediæ, <lb/>invenire altitudinem tubi, cognitâ eius elevatione &longs;u­<lb/>pra horizontem.<emph.end type="center"/></s></p> <p type="main"> <s>SIt data longitudo &longs;alientis horizontalis, aut mediæ, pedum <lb/> <arrow.to.target n="marg273"/><lb/>octo, &longs;it que tubus ip&longs;ius elevatus &longs;upra horizontem pedes <lb/>quinque, & in venienda &longs;it altitudo talis tubi. Quoniam, per <lb/>Pori&longs;ma Propo&longs;it. 1. huius Capitis, altitudines tuborum habent <lb/>duplicatam rationem eius, quam habent longitudines &longs;alienti­<lb/>um horizontalium, & mediarum; & quoniam &longs;aliens horizon­<lb/>talis tubi unius pedis, elevati &longs;upra horizontem quinque pedi­<lb/>bus, e&longs;t pedum quatuor; &longs;i rationem prædictarum &longs;alientium, <lb/>nempe 8 ad 4, duplices, &longs;eu bis &longs;umas &longs;ic: 16, 8. 4; erit tertius <lb/>numerus 16, altitudo tubi quæ&longs;ita, hic enim numerus 16 <lb/>ad 4, habet duplicatam rationem eius quam <lb/>habet 8 ad 4. </s></p> <pb xlink:href="051/01/189.jpg" pagenum="158"/> <p type="margin"> <s><margin.target id="marg273"/><emph type="italics"/>Salientis ho <lb/>rizontalis <lb/>longitudine <lb/>data inve­<lb/>nire tubi al <lb/>titudinem.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio X. Problema III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Ex nota &longs;caturiginis altitudine fontis unius ex tubo exi­<lb/>lientis horizontaliter, altitudinem &longs;caturiginis cuiuscun­<lb/>que alterius æqualiter &longs;upra horizontem elevati <lb/>invenire.<emph.end type="center"/><lb/> <arrow.to.target n="marg274"/></s></p> <p type="margin"> <s><margin.target id="marg274"/><emph type="italics"/>Fontis alti­<lb/>tudine &longs;ca­<lb/>turiginis da <lb/>ta, in venire <lb/>alias.<emph.end type="italics"/></s></p> <table> <row><cell>A</cell><cell>10.</cell><cell>B --</cell></row> <row><cell>8.</cell><cell/><cell>12.</cell></row> <row><cell>10.</cell><cell>15.</cell><cell>22 1/2.</cell></row></table> <table> <row><cell>A</cell><cell>10.</cell><cell>B --</cell></row> <row><cell>8.</cell><cell/><cell>12.</cell></row> <row><cell>10.</cell><cell>15.</cell><cell>22 1/2.</cell></row></table> <p type="main"> <s>SIt &longs;caturigo fontis unius A alta pedes 10; O. <lb/>porteat invenire altitudinem &longs;caturiginis fon­<lb/>tis B. Idem lumen, &longs;eu eundem tubulum ap­<lb/>plica horizontaliter ad utriu&longs;que fontis o&longs;cu­<lb/>lum, & ob&longs;erva &longs;alientium horizontalium longitudinem; &longs;itque <lb/>fontis A longitudo pedum 8, fontis verò B longitudo &longs;it <lb/>pedum 12. Fiat igitur, ut 8 ad 12, ita 10 ad aliud, nempe ad <lb/>15; & iterum, ut 10 ad 15, ita 15 ad aliud, nempe ad (22 3/10), &longs;ive <lb/>1/2; eritque altitudo &longs;caturiginis fontis B pedum 22 1/2. </s></p> <p type="main"> <s>Demon&longs;tratio. Per Pori&longs;ma Propo&longs;it. 1. hujus Capitis, <lb/>altitudines tuborum habent duplicatam rationem ejus, quam <lb/>habent longitudines &longs;alientium horizontalium. Quoniam ergo <lb/>10, nempe altitudo &longs;caturiginis A, e&longs;t ad 22 1/2 in duplicata ra­<lb/>tione eius, quam habet 10 ad 15, hoc e&longs;t, quam habet 8 ad 12, <lb/>&longs;aliens nempe fontis A, ad <expan abbr="&longs;alient&etilde;">&longs;alientem</expan> fontis B; erit nece&longs;&longs;ariò <lb/>22 1/2 altitudo &longs;caturiginis fontis B quæ&longs;ita. </s></p> <p type="main"> <s>Atque hæc &longs;ufficiant de tuborum &longs;eu fontium &longs;alientibus; <lb/>qui plura de&longs;iderat, legat Mer&longs;ennum in Hydraulicis Phæno­<lb/>menis, & Torricellum lib. 2. de Motu projectorum à fol. 191. ubi <lb/>incipit agere de Motu aquarum. </s></p> <p type="main"> <s><emph type="center"/>CAPVT V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De fluxu Aquæ per diver&longs;a eiu&longs;dem va&longs;is <lb/>aut tubi foramina.<emph.end type="center"/><lb/> <arrow.to.target n="marg275"/></s></p> <p type="margin"> <s><margin.target id="marg275"/><emph type="italics"/>Proprieta­<lb/>tes <gap/>uxus <lb/>aqu<gap/> per di­<lb/>ver&longs;a eius­<lb/>dem tubs <lb/>au: va&longs;is <lb/>foramma.<emph.end type="italics"/></s></p> <p type="main"> <s>HActenus locuti &longs;umus de aquæ fluxu per foramina tu­<lb/>borum <expan abbr="verticaliũ">verticalium</expan> tum horizontalia, tum lateralia, & <lb/>tubos cum tubis, aquas cum aquis, foramina cum fo­<lb/>raminibus diver&longs;orum tuborum comparavimus; <lb/>nunc eiu&longs;dem tubi & va&longs;is <expan abbr="cuiu&longs;cunq;">cuiu&longs;cunque</expan> foramina diver&longs;a inter &longs;e&longs;e <pb xlink:href="051/01/190.jpg" pagenum="159"/>conferemus breviter & methodicè, in&longs;i&longs;tentes ve&longs;tigijs Ioannis <lb/>Bapti&longs;tæ Baliani lib. 6. de Motu naturali gravium & liquidorum. <lb/>Quibus tamen multa addi po&longs;&longs;unt ex dictis Capite præcedenti. <lb/>Sermo autem e&longs;t hîc etiam, uti in præcedentibus, de tu­<lb/>bis ac va&longs;is verticaliter erectis, &longs;ive cylindrica illa &longs;int, &longs;ive pri&longs;­<lb/>matica; & &longs;ive foramina &longs;int rectangula, &longs;ive circularia. Præmit­<lb/>tamus ergo &longs;equentes. </s></p> <p type="main"> <s><emph type="center"/>Petitiones.<emph.end type="center"/></s></p> <p type="main"> <s> <arrow.to.target n="marg276"/></s></p> <p type="margin"> <s><margin.target id="marg276"/><emph type="italics"/>Petitiones <lb/>pro fluxu a­<lb/>quæ ex fora <lb/>minibus tu <lb/>borum.<emph.end type="italics"/></s></p> <p type="main"> <s>1. Vbi omnia &longs;unt æqualia, effectus &longs;unt æquales. </s></p> <p type="main"> <s>2. Quantitates eiusdem generis &longs;unt omnes commen­<lb/>&longs;urabiles, <emph type="italics"/>&longs;altem phy&longs;icè, ut dicemus Propo&longs;it.<emph.end type="italics"/> 2. <emph type="italics"/>in <lb/>Annotat.<emph.end type="italics"/></s></p> <p type="main"> <s>3. Aqua tran&longs;iens per tubi &longs;eu va&longs;is foramen, decurrit <lb/>à &longs;ummo va&longs;is ad foramen, tanquam per canalem <lb/>columnarem, cuius ba&longs;is foramen. </s></p> <p type="main"> <s><emph type="center"/>Annotatio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>TErtia hæc Petitio eadem e&longs;t cum Propo&longs;it.<emph.end type="italics"/> 1. <emph type="italics"/>Capitis tertij præceden­</s></p> <p type="main"> <s> <arrow.to.target n="marg277"/><lb/>tis. Et licet ibi locuti tantùm fuerimus de foraminibus exi&longs;tenti­<lb/>bus in ba&longs;i tuborum verticaliter erectorum, hîc tamen idem concedi no­<lb/>bis petimus etiam de foraminibus in tuborum va&longs;orumque lateribus exi­<lb/>&longs;tentibus, propter paritatem rationis. Petimus itaque nobis concedi, <lb/>quòd &longs;i in latere tubi, aut va&longs;is<emph.end type="italics"/> AB <emph type="italics"/>fiat foramen<emph.end type="italics"/> B, <emph type="italics"/>decurrat aqua à<emph.end type="italics"/><lb/> <arrow.to.target n="fig41"/><lb/><emph type="italics"/>va&longs;is &longs;umitate ad foramen u&longs;que in&longs;tar columnæ, cu­<lb/>ius ba&longs;is e&longs;t æqualis foramini, altitudo perpendicula­<lb/>res &longs;uper foraminis diametro erectæ, prout in appo­<lb/>&longs;ita figura e&longs;t columna<emph.end type="italics"/> ABCD. <emph type="italics"/>Ratio pote&longs;t e&longs;&longs;e, <lb/>quia ex dictis Capite<emph.end type="italics"/> 1 <emph type="italics"/>patet aquam non premere <lb/>ni&longs;i partes &longs;ibi perpendiculariter &longs;ubiectas, dum aqua <lb/>e&longs;t de&longs;cendens in aliquo, &longs;eu ex aliquo effluens, prout <lb/>hîc &longs;it.<emph.end type="italics"/></s></p> <pb xlink:href="051/01/191.jpg" pagenum="160"/> <p type="margin"> <s><margin.target id="marg277"/>Aqua in­<lb/>&longs;tar colum­<lb/>na effluit <lb/>ex forami­<lb/>ne ba&longs;is in <lb/>va&longs;e.</s></p> <figure id="id.051.01.191.1.jpg" xlink:href="051/01/191/1.jpg"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio I. Theorema I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Per foramina æqualia, æquè à &longs;ummo tubi di&longs;tantia, <lb/>&longs;ive in ba&longs;i, &longs;ive in latere, æquali tempore æquales fluunt <lb/>aquarum quantitates.<emph.end type="center"/></s></p> <figure id="id.051.01.191.2.jpg" xlink:href="051/01/191/2.jpg"/> <p type="main"> <s>IN va&longs;e, &longs;eu tubo AB, &longs;int foramina C & D <lb/>æqualia, & horizontalia (& eadem e&longs;t ra­<lb/>tio, &longs;i lateralia e&longs;&longs;ent, æquè à &longs;ummitate di­<lb/>&longs;tantia) per quæ aqua æquali, vel potiùs eo­<lb/>dem tempore decurrat. Dico, aquas de­<lb/> <arrow.to.target n="marg278"/><lb/>cur&longs;as (liceat ita loqui) e&longs;&longs;e æquales inter <lb/>&longs;e. Vbi enim omnia &longs;unt æqualia, effectus <lb/>&longs;unt æquales, per Petitionem primam hujus <lb/>Capitis: at hîc omnia &longs;unt æqualia, &longs;cilicet foramina, columnæ <lb/>aqueæ, vis premendi, & &longs;imilia; ergo effectus, qui &longs;unt aquæ <lb/>decur&longs;æ, æquales &longs;unt. Per foramina ergo æqualia, &c. Quod <lb/>erat o&longs;ten dendum. </s></p> <p type="margin"> <s><margin.target id="marg278"/><emph type="italics"/>Aquæ flu­<lb/>xus exæqua <lb/>libus fora­<lb/>minibus va <lb/>forum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>ET hoc verum e&longs;t, &longs;ive vas &longs;it &longs;emper plenum, &longs;ive non. Eadem e&longs;t <lb/>ratio, &longs;i va&longs;a &longs;int cylindrica, & foramina rotunda, ut diximus et­<lb/>iam paulò antè, & &longs;emper in &longs;equentibus dictum volumus.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Pori&longs;ma.<emph.end type="center"/></s></p> <p type="main"> <s>SEquitur hinc, &longs;i ex duobus eiu&longs;dem va&longs;is foraminibus æqua­<lb/>liter à &longs;ummo va&longs;is di&longs;tantibus aquæ decurrentes eodem tem­<lb/>pore æquales &longs;unt, foramina e&longs;&longs;e æqualia. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio II. Theorema II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ è foraminibus æqualiter à &longs;ummo tubi di&longs;tanti­<lb/>bus decurrentes, &longs;unt inter &longs;e ut foramina.<emph.end type="center"/></s></p> <p type="main"> <s>IN tubo &longs;eu va&longs;e AB, &longs;int duo foramina rectangula inæqualia, <lb/>C minus, & D maius, &longs;ed ambo horizontalia, <expan abbr="atq;">atque</expan> adeo æ­<lb/>quèalta, &longs;eu æqualiter à va&longs;is &longs;ummitate remota; & aqua de­<lb/>cur&longs;a per C &longs;it E, aqua verò decur&longs;a per D &longs;it F. Dico, a­<lb/>quam E decur&longs;am per C, habere &longs;e ad aquam F decur&longs;am <pb xlink:href="051/01/192.jpg" pagenum="161"/> <arrow.to.target n="fig42"/><lb/>per D, ut&longs;e habet foramen C ad foramen <lb/> <arrow.to.target n="marg279"/><lb/>D. Quoniam enim, per Petitionem &longs;e­<lb/>cundam hujus, quantitates eiusdem gene­<lb/>ris &longs;unt commen&longs;urabiles, erunt longitu­<lb/>dines C & D commen&longs;urabiles. Siter­<lb/>go communis earum men&longs;ura G, & &longs;ecen­<lb/>tur dictæ longitudines C & D in partes, <lb/>quæ &longs;int æquales ip&longs;i G; quibus divi&longs;is à <lb/>transver&longs;alib<emph type="sup"/>9<emph.end type="sup"/> lineis <expan abbr="perp&etilde;dicularib">perpendicularib</expan><emph type="sup"/>9<emph.end type="sup"/>, fiant <lb/>totforamina, quot &longs;unt dictæ partes. Tum <lb/>&longs;ic. Huiu&longs;modi foramina erunt omnia inter &longs;e æqualia, ex con­<lb/>&longs;tructione, & per 36. Primi Euclid. Ergo ex eis effluent eodem <lb/>tempore quantitates aquæ æquales, per Propo&longs;it 1. huius. <lb/>Quot igitur &longs;unt foramina in C & D, toterunt quantitates a­<lb/> <arrow.to.target n="fig43"/><lb/>quarum æquales in E & F. Cùm igitur &longs;int qua­<lb/>tuor magnitudines, C, D, E, F, quarum prima <lb/>C e&longs;t ad &longs;ecundam E, ut e&longs;t tertia D, ad quar­<lb/>tam F; erit etiam vici&longs;&longs;im &longs;eu permutando ut C <lb/>ad D, ita E ad F, per decimam &longs;extam Quinti Euclidis. </s></p> <p type="margin"> <s><margin.target id="marg279"/><emph type="italics"/>Proportio <lb/>aquæ efflu­<lb/>entis ad fo­<lb/>ramina.<emph.end type="italics"/></s></p> <figure id="id.051.01.192.1.jpg" xlink:href="051/01/192/1.jpg"/> <figure id="id.051.01.192.2.jpg" xlink:href="051/01/192/2.jpg"/> <p type="main"> <s><emph type="center"/>Annotatio<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>QVamvis contingere po&longs;&longs;it, ut longitudines<emph.end type="italics"/> CD <emph type="italics"/>non &longs;int commen­<lb/>&longs;urabiles, ac proinde<emph.end type="italics"/> G <emph type="italics"/>non &longs;it earum communis men&longs;ura; nihil <lb/>refert, quia hîc non &longs;umus in Mathematicis, &longs;ed in Phy&longs;icis, ubi non ha­<lb/>betur ratio in&longs;en&longs;ibilium.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III. Theorema III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aqua per foramina va&longs;is eo impetu &longs;eu velocitate de­<lb/>currit, quo per tubos æqualium foraminum & alti­<lb/>tudinum.<emph.end type="center"/></s></p> <figure id="id.051.01.192.3.jpg" xlink:href="051/01/192/3.jpg"/> <p type="main"> <s>SIt vas CD, in quo foramen D, al­<lb/>titudo va&longs;is CD; & &longs;it tubus AB <lb/>perpendicularis, in quo foramen <lb/>B &longs;it æquale foramini D, & altitudo <lb/>AB æqualis altitudini CD. Dico, <lb/>in B & D impetus &longs;eu velocitates <pb xlink:href="051/01/193.jpg" pagenum="162"/> <arrow.to.target n="fig44"/><lb/> <arrow.to.target n="marg280"/><lb/>aquæ effluentis e&longs;&longs;e æquales. Quo­<lb/>niam enim aqua fluens è foramine D, <lb/>decurrit per &longs;patium CD, ac &longs;i de­<lb/>curreret per tubum AB perpendi­<lb/>cularem eiusdem longitudinis, per <lb/>Petitionem tertiam huius; in D & B <lb/>&longs;ortitur impetus &longs;eu velocitates &ecedil;qua­<lb/>les, per Corollarium quintum Propo&longs;itio. 9. Capitis III. </s></p> <p type="margin"> <s><margin.target id="marg280"/><emph type="italics"/>Aquæ flu­<lb/>xus exfora­<lb/>minibus ve <lb/>lociter quæ.<emph.end type="italics"/></s></p> <figure id="id.051.01.193.1.jpg" xlink:href="051/01/193/1.jpg"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio IV. Theorema IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Velocitates aquæ decurrentis per foramina æqualia <lb/>eiu&longs;dem va&longs;is, inæqualiter di&longs;tantia à &longs;ummo va&longs;is, &longs;untin <lb/>&longs;ubduplicata ratione di&longs;tantiæ.<emph.end type="center"/></s></p> <figure id="id.051.01.193.2.jpg" xlink:href="051/01/193/2.jpg"/> <p type="main"> <s>SInt in va&longs;e AC foraminum æqualium <lb/>B & C, di&longs;tantiæ à &longs;ummo va&longs;is AB, <lb/>AC; &longs;itque media inter illas AD. Dico, <lb/>impetum &longs;eu velocitatem in C, ad impe­<lb/>tum &longs;eu velocitatem in B, e&longs;&longs;e ut AD ad AB. <lb/> <arrow.to.target n="marg281"/><lb/>Quoniam enim, per Propo&longs;it. tertiam hu­<lb/>jus, aqua per foramina B & C decurrit eo <lb/>impetu, quo per tubos æqualium foraminum & altitudinum; <lb/>erunt per Propo&longs;it. 10. Capitis tertij, velocitates aquæ in C & <lb/>B, ut AD ad AB, hoc e&longs;t, velocitas apud C erit media pro­<lb/>portionalis inter altitudines AC, AB, atque adeo &longs;ubduplica­<lb/>tam rationem habebit prædictarum altitudinum. </s></p> <p type="margin"> <s><margin.target id="marg281"/><emph type="italics"/>Proportio <lb/>dictæ velo­<lb/>citatis ad <lb/>foraminum <lb/>di&longs;tantiam.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio V. Theorema V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aquæ per æqualia foramina inæqualiter à &longs;ummitate <lb/>va&longs;is di&longs;tantia fluentes, &longs;unt in &longs;ubduplicata ratione <lb/>di&longs;tantiarum.<emph.end type="center"/></s></p> <p type="main"> <s>IN va&longs;e AC, præcedentis Propo&longs;itionis, altitudines à forami­<lb/>nibus æqualibus B & C, ad &longs;ummum va&longs;is A, &longs;int AB, AC, <lb/>quarum media &longs;it AD. Dico, aquam fluentem per C, <lb/>ad aquam fluentem per B, e&longs;&longs;e ut AD, ad AB, hoc e&longs;t, <lb/>e&longs;&longs;e mediam proportionalem, ideoque habere &longs;ubduplicatam <pb xlink:href="051/01/194.jpg" pagenum="163"/>rationem altitudinum prædictarum. Quoniam enim aqua flu­<lb/>it per B & C veluti per tubos, per Petitionem tertiam; a­<lb/>quæ autem per tubos æqualium altitudinum, &longs;unt in &longs;ubdupli­<lb/>cata ratione altitudinum tuborum, per propo&longs;it. 8. Capitis <lb/>tertij; con&longs;tat propo&longs;itum. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VI. Problema I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Secto foramine laterali va&longs;is in partes æquales, à rectis <lb/>horizontalibus, invenire rationes aquarum ex eis <lb/>fluentium.<emph.end type="center"/></s></p> <figure id="id.051.01.194.1.jpg" xlink:href="051/01/194/1.jpg"/> <p type="main"> <s>IN va&longs;e ST &longs;ecetur foramen <lb/> <arrow.to.target n="marg282"/><lb/>laterale AB in partes æquales <lb/>AC, CD, DB, à rectis lineis hori­<lb/>zontalibus, ut fiant totidem fo <lb/>ramina, quorum altitudines &longs;int <lb/>notæ; & per AC fluat aqua E, <lb/>per CD aqua F, per DB aqua <lb/>G, tempore æquali &longs;eu eodem: <lb/><expan abbr="oporteat&qacute;ue">oporteatque</expan> venari proportio­<lb/>nem aquarum E, F, G. Fiant <lb/>HI, KL, MN, altitudines forami­<lb/>num AC, CD, DB, à &longs;ummo va­<lb/>&longs;is; & inter ip&longs;as mediæ proportionales OP, QR, per decimam <lb/>tertiam Sexti Euclidis, aut per propo&longs;it. 3. Parergi Capitis tertij <lb/>præcedentis. Quoniam igitur aqua E ad aquam F, e&longs;t ut HI <lb/>ad OP, per Propo&longs;it. 5. huius Capitis, nota e&longs;t ratio aquæ E ad <lb/>aquam F. Item quoniam aqua F ad aquam G, e&longs;t ut KL ad <lb/>QR, per eandem Propo&longs;it. 5. huius Capitis, nota e&longs;t pariter ra­<lb/>tio aquæ F ad aquam G: At ratioaquæ E ad aquam G com­<lb/>po&longs;ita rationum inter EF & FG notarum, e&longs;t pariter <lb/>nota; Reperta e&longs;t igitur ratio aquarum <lb/>E, F, G. </s></p> <pb xlink:href="051/01/195.jpg" pagenum="164"/> <p type="margin"> <s><margin.target id="marg282"/><emph type="italics"/>Problemata <lb/>varia de flu<lb/>xu aquæ per <lb/>foramina <lb/>va&longs;orum.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VII. Problema II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Secto foramine laterali va&longs;is in partes inæquales, à re­<lb/>ctis horizontalibus, reperire rationes aquarum efflu <lb/>entium ex ip&longs;is.<emph.end type="center"/></s></p> <figure id="id.051.01.195.1.jpg" xlink:href="051/01/195/1.jpg"/> <p type="main"> <s>FOramen CD va&longs;is AB &longs;ecetur à <lb/>recta E in partes inæquales CE, ED; <lb/>& effluat ex parte &longs;uperiore e E aqua <lb/>F, ex inferiori verò ED aqua G, eo­<lb/>dem tempore. Quæritur proportio <lb/>F ad G. Si ED foramen minus non <lb/>men&longs;urat CE, reperiatur eorum ma­<lb/>xima communis men&longs;ura, per tertiam <lb/>Decimi Euclidis, quæ &longs;it H; & juxta <lb/>eam &longs;ecetur CE in partes CQ, QK, KE; item ED in partes <lb/>EI, ID. Quoniam igitur foramen CD &longs;ectum e&longs;t in partes CQ, <lb/>QK, KE, EI, ID, æquales per con&longs;tructionem; reperietur per <lb/>Propo&longs;it. 6. hujus Capitis, ratio aquarum per eas fluentium, <lb/>ac proinde aquarum fluentium per CE, & ED. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio VIII. Problema III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis foraminibus inæqualibus &longs;uper eadem horizon­<lb/>tali, venari rationes aquarum.<emph.end type="center"/></s></p> <figure id="id.051.01.195.2.jpg" xlink:href="051/01/195/2.jpg"/> <p type="main"> <s>SInt foramina AB, & CD, &longs;uper ho­<lb/>rizontali BD, utrumque laterale; <lb/><expan abbr="Quærenda&qacute;ue">Quærendaque</expan> &longs;it proportio aquarum ex <lb/>eis eodem tempore fluentium. Produ­<lb/>catur recta CEG, parallela rectæ DB, <lb/><expan abbr="dividatur&qacute;ue">dividaturque</expan> foramen AB in duo fo­<lb/>ramina AG, GB. Quoniam igitur no­<lb/>ta e&longs;t ratio aquarum fluentium ex CD, <lb/>& GB, per Propo&longs;it. 2. hujus Capitis; item ratio aquarum BG, <lb/>& GA, per Propo&longs;it. 7. præcedentem; nota pariter e&longs;t ratio <lb/>ex eis compo&longs;ita inter aquas fluentes per CD, & AG. Cùm <pb xlink:href="051/01/196.jpg" pagenum="165"/>igitur nota &longs;it ratio aquæ fluentis per CD, ad aquam fluentem <lb/>per BG, & per GA partes; nota erit ratio eiu&longs;dem ad totam <lb/>fluentem per AB. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio IX. Problema IV.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis foraminibus eiu&longs;dem va&longs;is, quorum vnum &longs;u­<lb/>perius, alterum inferius, inter easdem parallelas perpen­<lb/>diculares, reperire rationes aquarum.<emph.end type="center"/></s></p> <figure id="id.051.01.196.1.jpg" xlink:href="051/01/196/1.jpg"/> <p type="main"> <s>DEntur foramina AB, CD, inter parallelas <lb/>easdem perpendiculares AC, & BD, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; <lb/>venanda ratio aquarum ex eis, æquali tem­<lb/>pore, fluentium. Concipiatur BC, tan­<lb/>quam foramen inter easdem parallelas. Quo­<lb/>niam igitur nota e&longs;t ratio aquarum fluentium <lb/>ex CD, & ex CB, per Propot. 7. hujus Ca­<lb/>pitis; item ex CB, & BA, per eandem Pro­<lb/>po&longs;itionem &longs;eptimam, nota erit pariter ratio aquarum fluenti­<lb/>um per CD, & AB. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio X. Problema V.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Datis foraminibus eiu&longs;dem va&longs;is, quorum vnum &longs;u­<lb/>perius, alterum inferius, non inter ea&longs;dem parallelas, <lb/>repire rationes aquarum.<emph.end type="center"/></s></p> <figure id="id.051.01.196.2.jpg" xlink:href="051/01/196/2.jpg"/> <p type="main"> <s>DAta &longs;int foramina AD, EH; oporte­<lb/>atque reperire rationes aquarum per il­<lb/>la æquo tempore fluentium. Duc hori­<lb/>zontales HI, EK, & producta DB in L, <lb/>concipiatur IL tanquam foramen inter <lb/>ea&longs;dem parallelas cum AD; & quæratur <lb/>ratio aquarum per AD, IL fluentium, per <lb/>Propo&longs;it. 9. hujus Capitis, & &longs;it ut M ad N. <lb/>Item quæratur ratio IL ad EH, per Pro­<lb/>po&longs;it. 2. hujus Capitis, & &longs;it ut N ad O. <lb/>Dico, M ad O e&longs;&longs;e rationem aquarum per <lb/>AD, & HE fluentium. Quoniam enim ut M ad N, ita e&longs;t AD <lb/>ad IL; & ut N ad O, ita IL ad EH, per con&longs;tructionem: Erit <pb xlink:href="051/01/197.jpg" pagenum="166"/>ex æquo, per vige&longs;imam &longs;ecundam Quinti Euclid. ut M ad O, <lb/>ita aqua per AD adaquam per EH fluentem. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XI. Problema VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato foramine, & linea horizontali, in aliquo va&longs;e, <lb/>con&longs;tituere &longs;uper illa foramen, è quo æqualis aqua <lb/>fluat eodem tempore.<emph.end type="center"/></s></p> <figure id="id.051.01.197.1.jpg" xlink:href="051/01/197/1.jpg"/> <p type="main"> <s>SIt datum foramen AM, & hori­<lb/>zontalis CD; &longs;itque de&longs;criben­<lb/>dum foramen &longs;uper CD, è quo ef­<lb/>fluat eodem &longs;eu æquali tempore, a­<lb/>qua ut per AM. Erigantur per­<lb/>pendiculares AE, MC, & produ­<lb/>catur DC in E, & &longs;uper EC fiat fo­<lb/>ramen æquale foramini AM, & &longs;it <lb/>FC; & ducta FG parallela ip&longs;i CD, <lb/>fiat HI media inter KB, & KE: & tandem fiat, ut HI ad KE, <lb/>ita DL ad EC. Dico, foramen LG e&longs;&longs;e foramen quæ&longs;itum, <lb/>per quod æquali tempore fluat aqua ut per AM. Quoniam e­<lb/>nim, per Propo&longs;it. 2. hujus Capitis, aqua foraminis LG ad a­<lb/>quam foraminis FC, e&longs;t ut DL ad CE, hoc e&longs;t, HI, ad KE; & <lb/>per Propo&longs;it. 5. hujus Capitis, aqua foraminis AM ad aquam <lb/>foraminis CF, e&longs;t ut eadem HI, ad KE; erit ut aqua LG ad <lb/>CF, ita aqua AM ad CF, per undecimam Quinti Euclidis, ac <lb/>proinde aqua foraminis AM erit æqualis aquæ foraminis LG, <lb/>per nonam Quinti Euclid. & per 1. Axio. lib. 1. Euclid. </s></p> <p type="main"> <s><emph type="center"/>Annotatio.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="italics"/>POte&longs;t tamen horizontalis data e&longs;&longs;e tam vicina &longs;ummitati va&longs;is, ut <lb/>quæ&longs;itum foramen ficri non po&longs;&longs;it, nec hoc, nec alio modo: & tunc <lb/>Problema e&longs;t in&longs;olubile.<emph.end type="italics"/></s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio XII. Problema VII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato foramine, & latere alterius in eodem va&longs;e, reperi­<lb/>re foramen, è quo æqualis aqua effluat.<emph.end type="center"/></s></p> <pb xlink:href="051/01/198.jpg" pagenum="167"/> <figure id="id.051.01.198.1.jpg" xlink:href="051/01/198/1.jpg"/> <p type="main"> <s>DAtum &longs;it foramen AB, & latus <lb/>DC, in eodem va&longs;e; <expan abbr="oporteatq;">oporteatque</expan> <lb/>de&longs;cribere foramen, cujus latus &longs;it <lb/>DC, & è quo effluat eodem tempore <lb/>aqua ut ab AB. Ductis CN, & DF ho­<lb/>rizontalibus, & &ptail;ducta BE, reperiatur <lb/>ratio <expan abbr="aquarũ">aquarum</expan> <expan abbr="fluentiũ">fluentium</expan> ex AB, & FE, <lb/>per Propo&longs;it. 9. hujus Capitis, quæ &longs;it <lb/>ut G ad H; & fiat, ut H ad G, ita <lb/>FI ad FK, per decimam tertiam Sex­<lb/>ti Euclid. & Propo&longs;it. 3. Parergi Capitis 3; & à K erigatur <lb/>perpendicularis KL, & tandem fiat foramen, cujus latus DC, <lb/>æquale & &longs;imile ip&longs;i FL foramini, & &longs;it DM. Dico, è foramine <lb/>DM fluere aquam, ut ex AB foramine. Quoniam enim aqua <lb/>fluens ex AB, ad aquam fluentem ex FE, e&longs;tut G ad H, per con­<lb/>&longs;tructionem; item aqua fluens per FL, &longs;eu ei æquale DM, ad <lb/>fluentem per idem FE, e&longs;t itidem ut G ad H, per Propo&longs;it. 2. <lb/>hujus Capitis; erunt aquæ fluentes per AB, & per DM, inter &longs;e <lb/>æquales, per nonam Quinti Euclidis. Igitur DM erit foramen <lb/>quæ&longs;itum. </s></p> <p type="main"> <s><emph type="center"/>Propro&longs;itio XIII. Problema VIII.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato foramine, reperire aliud æquale in eodem va&longs;e, è <lb/>quo fluat aqua in ratione data.<emph.end type="center"/></s></p> <figure id="id.051.01.198.2.jpg" xlink:href="051/01/198/2.jpg"/> <p type="main"> <s>DEtur in va&longs;e AB foramen C, & da­<lb/>ta &longs;it ratio aquarum D, E, quarum <lb/>D fluat in dato tempore per foramen C; <lb/>reperiendum verò &longs;it, ubi fiat æquale <lb/>foramen, è quo fluat in æquali tempore <lb/>aqua E. Fiat ad D, E, AC, quarta pro­<lb/>portionalis AF, per duodecimam Sexti <lb/>Euclid. aut Propo&longs;it. 8. Parergi Capitis <lb/>tertij præcedentis; & ad AC, AF, ter­<lb/>tia proportionalis AG, per vndecimam <pb xlink:href="051/01/199.jpg" pagenum="168"/> <arrow.to.target n="fig45"/><lb/>&longs;exti Euclid. aut per Propo&longs;it. 6. Paret­<lb/>gi citati; & in G fiat foramen, (quod <lb/>&longs;i fieri nequit, Problema e&longs;t in&longs;olubile.) <lb/>Dico, G e&longs;&longs;e locum foraminis quæ&longs;iti. <lb/>Quoniam enim aquæ fluentes per dicta <lb/>foramina &longs;unt in &longs;ubduplicata ratione <lb/>altitudinum AC, AG, per Propo&longs;it. 5. <lb/>hujus capitis; & aquæ D, & E &longs;unt pa­<lb/>riter in &longs;ubduplicata ratione datæ altitu­<lb/>dinis AC, & inveniendæ altitudinis, per <lb/>eandem Propo&longs;itionem 5. hujus capitis; &longs;equitur aquas fluen­<lb/>tes per dicta foramina C & G, e&longs;&longs;e ut aquas D & E. </s></p> <figure id="id.051.01.199.1.jpg" xlink:href="051/01/199/1.jpg"/> <p type="main"> <s><emph type="center"/>Propo&longs;itio XIV. Problema IX.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Dato foramine, aptare in eodem va&longs;e aliud datum &longs;i­<lb/>mile, magnitudinis diver&longs;æ, à quo aqua fluens cum <lb/>fluente à primo, habeat rationem datam.<emph.end type="center"/></s></p> <figure id="id.051.01.199.2.jpg" xlink:href="051/01/199/2.jpg"/> <p type="main"> <s>IN va&longs;e AB, datum &longs;it foramen C, & <lb/>aliud ad&longs;ignatum D &longs;imile, &longs;ed diver­<lb/>&longs;æ magnitudinis, &longs;ive majoris, &longs;ive mi­<lb/>noris; ratio verò aquarum data &longs;it E, F. <lb/>Aptandum &longs;it foramen D ad&longs;ignatum <lb/>eâ lege, ut aqua per illud fluens, cum <lb/>aqua fluente ex C, &longs;it ut E ad F. <lb/>Super horizontali ducta CG, fiat fora­<lb/>men G, æquale foramini D; & perqui­<lb/>ratur ratio aquarum fluentium per C <lb/>& G, per Propo&longs;it. 8. hujus capitis, & <lb/>&longs;it ut E ad H. Quæ &longs;i e&longs;t eadem quæ <lb/>e&longs;t inter E & F, habemus intentum: <lb/>Sin minùs, fiat aliud foramen infra aut <lb/>&longs;upra G, ei &longs;imile & æquale, à quo <lb/>fluat aqua, quæ cum fluente ab ip&longs;o G <lb/>habeat rationem ut H ad F, & &longs;it I, <lb/>Quod &longs;i fieri nequit, Problema e&longs;t in- <pb xlink:href="051/01/200.jpg" pagenum="169"/>&longs;olubile.) Dico, I e&longs;&longs;e foramen quæ&longs;itum. Quoniam enim <lb/>aqua C ad aquam G, e&longs;t ut E ad H; & aqua G ad aquam <lb/>I, e&longs;t ut H ad F, ex con&longs;tructione & operatione facta; erit <lb/>ex æquo etiam aqua C ad aquam I, ut E ad F, per vige­<lb/>&longs;imam &longs;ecundam Quinti Euclidis. </s></p> <p type="main"> <s><emph type="center"/>CAPUT VI.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>De Aëris gravitate, rarefactione, & <lb/>conden&longs;atione.<emph.end type="center"/></s></p> <p type="main"> <s>QUoniam in Pneumaticis ac Hydropneumaticis Ma­<lb/>chinis magni refert, aëris naturalis pondus &longs;eu gra­<lb/>vitatem, rarefactique ac conden&longs;ati quantitatem ae <lb/>vires cogno&longs;cere; de ijs nonnihil parergi loco ad­<lb/>dendum hîc cen&longs;ui. Sit itaque </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio I.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Aëris gravitatem invenire.<emph.end type="center"/></s></p> <p type="main"> <s>TAmet&longs;i aêr levis &longs;it inter reliqua elementa, &longs;uaque levitate <lb/> <arrow.to.target n="marg283"/><lb/>&longs;ur&longs;um tendat, ut &longs;it &longs;upra terram & aquam; admixtum <lb/>tamen habet aliquid gravitatis. Patet ex eo, quòd folles lu­<lb/>&longs;orij aëre adden&longs;ato bene inflati, ut & ve&longs;icæ inflatæ, plùs pon­<lb/>derent, quàm flaccidi, ut exqui&longs;ita trutina aut libra deprehen­<lb/>di pote&longs;t. P. Joannes Bapti&longs;ta Ricciolus Tomo 1. Almge&longs;ti <lb/>Novi lib. 2. cap. 5. num. 4. ait expendi&longs;&longs;e &longs;e ve&longs;icam bovinam <lb/>quæ flaccida erat &longs;crupulorum 4, & granorum 4, & deprehen­<lb/>di&longs;&longs;e inflatam fui&longs;&longs;e &longs;crupulorum 4, & granorum 6. Quare <lb/>aër additus per inflationem, appendebat grana 2. Marinus <lb/>Mer&longs;ennus in Phænomenis &longs;uis Propo&longs;it. XXIX. a&longs;&longs;erit, &longs;e Geo­<lb/>metris præ&longs;entibus & adjuvantibus, pondera&longs;&longs;e bilance Æo­<lb/>lopilam æneam (qualem de&longs;cribimus infrà Parte 2. Cla&longs;&longs;e 1. cap. 3. <lb/>Machina 6.) &longs;atis calefactam, & propemodum candentem, <pb xlink:href="051/01/201.jpg" pagenum="170"/>omnique humore de&longs;titutam, & quàm minimùm aêris conti­<lb/>nentem; deprehendi&longs;&longs;eque pondus fui&longs;&longs;e unciarum 4, <expan abbr="drach-marũ">drach­<lb/>marum</expan> 6, & granorum 15: po&longs;tquam verò naturaliter refrixi&longs;&longs;et <lb/>æolopila, & aër antea vehementer rarefactus redij&longs;&longs;et ad pri­<lb/>&longs;tinum ac naturalem &longs;uum &longs;tatum; iterum pondera&longs;&longs;e ip&longs;am, <lb/>& inveni&longs;&longs;e pondus præcedente pondere majus fui&longs;&longs;e 4 gra­<lb/>nis. (Apud Mer&longs;ennum habetur, minus; utique typographi­<lb/>co errore.) Erat autem bilanx, inquit Mer&longs;ennus, quæ dimi­<lb/>dio grani perdebat æquilibrium. </s></p> <p type="margin"> <s><margin.target id="marg283"/><emph type="italics"/>Aëris gra­<lb/>vitatem in­<lb/>venire.<emph.end type="italics"/></s></p> <p type="main"> <s>Atque ex his patet, qua ratione aëris gravitas inveniatur. <lb/>Alij aliter explorant pondus aëris, præ&longs;ertim Illu&longs;tri&longs;&longs;imus Do­<lb/>minus Carolus Vintimillia Eques Panormitanus in Sicilia, & Ami­<lb/>cus Uranicus &longs;incei i&longs;&longs;imus, qui legendam mihi dedit demon­<lb/>&longs;trationem &longs;ubtili&longs;&longs;imam, praximque hydro&longs;taticam, qua olim <lb/>Adole&longs;cens coram Sereni&longs;&longs;imo Philiberto Siciliæ Prorege, No­<lb/>bilitateque Panormitana univer&longs;a aërem ponderaverat. Vide <lb/>etiam quæ habet Daniel Lip&longs;torpius part. 3. Speciminum Phi­<lb/>lo&longs;ophiæ Carthe&longs;ianæ cap. 2. in fine, ubiadducit modum Galilæi <lb/>& Joann. Chry&longs;o&longs;t. Magneni. Vide præterea Appendicem <lb/>in fine Operis. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio II.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quantum conden&longs;ari aër po&longs;&longs;it, invenire.<emph.end type="center"/><lb/> <arrow.to.target n="marg284"/></s></p> <p type="margin"> <s><margin.target id="marg284"/>Vide infrà <lb/>Iconi&longs;mi <lb/>VIII. Figu­<lb/>ram IX. a.</s></p> <p type="main"> <s>AS&longs;umatur fons pneumaticus, qualem de&longs;cribimus infrà, <lb/>Parte 2. Cla&longs;&longs;e 1. cap. 2. Machina 8. eju&longs;que capacitas exactè <lb/>exploretur in men&longs;ura cubica aquæ. Capiat autem dictus <lb/>fons, gratiâ exempli, unum pedem cubicum, &longs;eu libras 72. <lb/>In hunc fontem immitte &longs;yringe, per foramen C, aquam <lb/>quantum fieri, &longs;ine ruptionis periculo, pote&longs;t. Si jam notam <lb/>feceris in men&longs;ura, quantitatem aquæ immi&longs;&longs;æ, eamque à fon­</s></p> <p type="main"> <s> <arrow.to.target n="marg285"/><lb/>tis capacitate detraxeris; re&longs;iduum fontis indicabit locum <lb/>aëris conden&longs;ati, qui priùs totam fontis capacitatem imple- <pb xlink:href="051/01/202.jpg" pagenum="171"/>bat. Ut &longs;i immi&longs;&longs;æ &longs;untduæ tertiæ pedis cubici, occupabit aër <lb/>unam tertiam partem. </s></p> <p type="margin"> <s><margin.target id="marg285"/><emph type="italics"/>Aër quan­<lb/>tum conden <lb/>&longs;ari po&longs;&longs;it, <lb/>invenire.<emph.end type="italics"/></s></p> <p type="main"> <s>Atque hæc e&longs;t expediti&longs;&longs;ima ratio men&longs;urandi conden­<lb/>&longs;ationem aëris. Fieri quoque idip&longs;um pote&longs;t &longs;clopeto pneu­<lb/>matico, de quo infrà loco cit. cap. 2. Machina 13. & 14. </s></p> <p type="main"> <s>Credunt aliqui, inquit Mer&longs;ennus in Hydraulicis Propo­<lb/>&longs;it. 31. aërem per conden&longs;ationem non po&longs;&longs;e ni&longs;i ad tertiam &longs;pa­<lb/>tij, quod naturaliter occupat, partem redigi, quòd videant <lb/>aquam in vas infu&longs;am tres heminas &longs;eu libras continens, non <lb/>&longs;uperare duas heminas, ob aërem intus manentem. Certum <lb/>e&longs;t tamen, &longs;ubdit idem, magis conden&longs;ari po&longs;&longs;e; ip&longs;eque ex­<lb/>perientiâ didicit, po&longs;&longs;e ad &longs;patium quindecuplo minus in &longs;clo­<lb/>peto pneumatico cogi, idque &longs;olâ vi manus &longs;yringe utentis; <lb/>quæ vis cùm intendi multò magis po&longs;&longs;it, dubium non e&longs;t, aë­<lb/>rem adhuc multò magis conden&longs;ati po&longs;&longs;e. Vide Mer&longs;ennum <lb/>in Hydraulicis loco citato. </s></p> <p type="main"> <s><emph type="center"/>Propo&longs;itio III.<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Quantum rarefieri aër po&longs;&longs;it, invenire.<emph.end type="center"/></s></p> <p type="main"> <s>MArinus Mer&longs;ennus loco citato Propo&longs;it. 31. ait, con&longs;tare, <lb/> <arrow.to.target n="marg286"/><lb/>aërem ita rarefieri in ignitis æolopilis (quas de&longs;cribimus <lb/>Parte 2. Cla&longs;&longs;e 1. cap. 2. Machina 6.) ut &longs;eptuage&longs;ima pars aë­<lb/>ris priùs inclu&longs;i, & nondum rarefacti, æolopilas impleat. Hæc <lb/>autem rarefactionis quantitas inveniri pote&longs;t præ&longs;idio Æolo­<lb/>pilæ hunc in modum. </s></p> <p type="margin"> <s><margin.target id="marg286"/><emph type="italics"/>Aër quan­<lb/>tum po&longs;&longs;it <lb/>rarefieri.<emph.end type="italics"/></s></p> <p type="main"> <s>Æolopila notæ capacitatis calefiat eò u&longs;que, donec ma­<lb/>jorem vim caloris &longs;u&longs;tinere ampliùs non po&longs;&longs;e judicetur citra <lb/>liquefactionis periculum: &longs;ic enim fiet, ut quàm minimùm aë­<lb/>ris rarefacti totam ip&longs;ius capacitatem expleat. Quo facto, <lb/>igni extracta &longs;tatim aquæ frigidæ immergatur. Continget <lb/>enim ut aër, qui rarefactus totam Æolopilam occupabat, ad <lb/>naturalem redeat con&longs;titutionem; ac proinde Æolopila, nè <lb/>detur vacuum, aquam &longs;uget. Hujus aquæ quantitas &longs;i fiat <pb xlink:href="051/01/203.jpg" pagenum="172"/>nota, & ab Æolopilæ capacitate detrahatur; notam relinquet <lb/>aëris quantitatem & nunc adden&longs;ati, & antea rarefacti. </s></p> <p type="main"> <s>Hæc ex Mer&longs;enni &longs;ententia; quæ tamen valde incerta mi­<lb/>hi videntur, tum quia non &longs;citur quando Æolopila e&longs;t &longs;ummè <lb/>calefacta, tum quia aqua ab&longs;umitur à calore Æolopilæ ante & <lb/>po&longs;t attractionem, tum denique quia con&longs;tare non pote&longs;t, utrum <lb/>aër re&longs;iduus po&longs;t aquæ attractionem &longs;it ad naturalem &longs;tatum re­<lb/>dactus, an verò præter naturam adden&longs;atus, aut rarefactus. Vi­<lb/>de quæ dicimus infrà in Appendice. </s></p> <p type="main"> <s><emph type="center"/>Conclu&longs;io<emph.end type="center"/></s></p> <p type="main"> <s><emph type="center"/>Protheoriæ Quartæ.<emph.end type="center"/></s></p> <p type="main"> <s>DIci hîc nonnulla po&longs;&longs;ent de &longs;alientium ex fontibus pneuma­<lb/>ticis, quos de&longs;cribimus Parte 2. Cla&longs;&longs;e 1. cap. 2. Machina 8. <lb/>longitudine, altitudineque, & cum tuborum &longs;alientibus compa­<lb/>rari, ut facit Mer&longs;ennus in &longs;uis Hydraulicis Propo&longs;it. 28. &longs;ed <lb/>quoniam valde incerta &longs;unt & quæ Mer&longs;ennus affert, & quæ à <lb/>me, & à quocunque alio, varijs experientijs inventa, afferri po&longs;­<lb/>&longs;unt; &longs;atiùs judicavi, omnino ab&longs;tinere. Dependet enim &longs;alien­<lb/>tium huju&longs;modi longitudo atque altitudo, non à tuborumlongi­<lb/>tudine, &longs;ed poti&longs;&longs;imùm ab aëris intra fontem compre&longs;&longs;i vehe­<lb/>mentia, quæ infinitis modis variari pote&longs;t; & cùm omnia exper­<lb/>tus fueris, dubius adhuc hærebis. </s></p> <p type="main"> <s>Dici præterea multa po&longs;&longs;ent de fluxu aquæ per tubos incli­<lb/>natos & horizontales; examinarique, quæ habet Joannes Bapti­<lb/>&longs;ta Balianus lib 4. & 5. de Motu gravium, &longs;eu lib. 1. & 2. de motu <lb/>liquidorum: at quoniam hæc non admodum conducunt fini no­<lb/>&longs;tro in hoc Opere intento, & longiorem &longs;ermonem requirunt; <lb/>omittenda potiùs omnino quàm paucis per&longs;tringenda pu­<lb/>tavi, acturus de illis in Mechanica Univer&longs;ali. Ad <lb/>praxin igitur, mi&longs;sâ theoriâ, <lb/>procedamus. <lb/> <arrow.to.target n="fig46"/></s></p> </chap> </body> <back/> </text> </archimedes>