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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <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></place> <translator></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"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>A. R.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>P. GASPARIS <lb></lb>SCHOTTI<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>SOCIETATIS JESU<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>MECHANICA <lb></lb>HIDRAULICO -PNEVMATICA<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Cum<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FIGURIS ÆNÊIS, ET PRIVILEGIO SACRÆ<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Ceſaræ Majeſtatis.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>ANNO M DC LVIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end> <pb xlink:href="051/01/002.jpg"></pb> <arrow.to.target n="fig1"></arrow.to.target></s></p> <figure id="id.051.01.002.1.jpg" xlink:href="051/01/002/1.jpg"></figure> <p type="caption"> <s>MECHANICA <lb></lb>HYDRAVLICOPNEVMATICA</s></p> <p type="caption"> <s>Ad Eminentiſs: S.R.I. Principem <lb></lb>Ioannem Philippum <lb></lb>Electorem Mogunt: <lb></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><pb xlink:href="051/01/004.jpg"></pb> <p type="main"> <s><emph type="center"></emph>P. GASPARIS SCHOTTI<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>REGISCURIANI, E SOCIE<lb></lb>TATE JESU,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Olim in Panormitana Siciliæ, nunc in Herbipo<lb></lb>litana Franconiæ ejuſdem SOCIETATIS Academia <lb></lb>Matheſeos Profeſſoris,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>MECHANICA <lb></lb>HYDRAULICO-PNEV<lb></lb>MATICA,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Qua <lb></lb><emph type="italics"></emph>Præterquàm quòd Aquei elementi natura, proprietas, vis <lb></lb>motrix, atque occultus cum aëre conflictus, à primis fundamentis de<lb></lb>monſtratur; omnis quoque generis Experimenta Hydraulico-pnevmatica <lb></lb>recluduntur; & abſoluta Machinarum aquâ & aere animandarum ratio <lb></lb>ac methodus præſcribitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>OPUS BIPARTITUM,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Cujus<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s>Pars I. Mechanicæ Hydraulico-pnevmaticæ Theoriam continet. </s></p> <p type="main"> <s>Pars II. Ejuſdem Praxin exhibet, Machinasque Aquarias innumeras, uti & Organa, ali<lb></lb>aque Inſtrumenta, in motum ac ſonum concitat; nec non varia technaſinata, <lb></lb>quæ motum perpetuum vi aquæ ſpondent,exponit. </s></p> <p type="main"> <s><emph type="center"></emph>ACCESSIT<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Experimentum novum Magdeburgicum, quo vacuum alij ſta<lb></lb>bilire, alij evertere conantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Sumptu Heredum JOANNIS GODEFRIDI Schôn wetteri,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Bibliopol: Francofurtenſ.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Excudebat<emph.end type="italics"></emph.end> HENRICUS PIGRIN <emph type="italics"></emph>Typographus Herbipoli,<emph.end type="italics"></emph.end><lb></lb>ANNO M. DC. LVII.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/005.jpg"></pb> <figure id="id.051.01.005.1.jpg" xlink:href="051/01/005/1.jpg"></figure> <pb xlink:href="051/01/006.jpg"></pb> <p type="main"> <s><emph type="center"></emph>DEDICATIO.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.006.1.jpg" xlink:href="051/01/006/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Eminentiſſimo, & Reverendiſſimo Principi <lb></lb>ac Domino,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>D. JOANNI <lb></lb>PHILIPPO,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>SACRÆ SEDIS MOGUNTINÆ<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Archiepiſcopo, S. Rom. Imp. per Germani<lb></lb>am Archi-Cancellario, & Principi Electori; Epiſcopo <lb></lb>Herbipolenſi, Franciæ Orientalis Duci, <lb></lb>Domino meo clementiſſimo.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>EMINENTISSIME PRIN<lb></lb>CEPS. </s><s>Fontes quos Natura <lb></lb>producit ad hominum utilitatem, <lb></lb><emph type="italics"></emph>Mare<emph.end type="italics"></emph.end> petunt, ut fluant. </s><s><emph type="italics"></emph>Omnia quippe <lb></lb>flumina,<emph.end type="italics"></emph.end> ac proinde & fontes flumi- <pb xlink:href="051/01/007.jpg"></pb>num origines, <emph type="italics"></emph>intrant in Mare, & Mare non <lb></lb>redundat; ad locum, unde exeunt flumina, revertun<lb></lb>tur, vt iterum fluant.<emph.end type="italics"></emph.end> </s><s>Fontes quos hoc <lb></lb>in Opere produco ex Hydrotech<lb></lb>nica Arte ad Principum delecta<lb></lb>tionem, ut ſaliant, FONTEM petunt <lb></lb>PULCHRUM, Te inquam, EMI<lb></lb>NENTISSIME DOMINE, <expan abbr="Tuumq;">Tuumque</expan> <lb></lb>favorem ac benevolentiam. </s><s>Niſi <lb></lb>enim ope Tua, qui FONS es PUL<lb></lb>CHERRIMUS, foveantur, & <lb></lb>Tua augeantur ditenturque co<lb></lb>pia; exareſcant neceſſe eſt, ma<lb></lb>gno licet labore, nec minori <lb></lb>Arte, in fluxum ac ſaltum àme <lb></lb>animati. </s><s> Pateat igitur Fontibus <pb xlink:href="051/01/008.jpg"></pb>meis FONS PULCHER; <expan abbr="derivẽtur">deriventur</expan> <lb></lb>in eos Humanitatis Tuæ aquæ, ut <lb></lb>gloriari liceat, ac dicere: FONS <lb></lb>PULCHER SUFFICIT UNDAS. </s><s><lb></lb>Dixi quod volebain, & hîc finio, <lb></lb>nè peccare cogar peccatum quo <lb></lb>Scriptorum plerique reos ſe con<lb></lb>ſtituunt, dum in Mecænatum <lb></lb>ſuorum laudes ipſo in Librorum <lb></lb>veſtibulo quàm pro loci oppor<lb></lb>tunitate longiùs excurrunt. </s><s>Ma<lb></lb>jor eſt virtutum Tuarum ſplen<lb></lb>dor, majora in Eccleſiam & Im<lb></lb>perium Romanum merita, quàm <lb></lb>ut exili calamo meo, præſertim <lb></lb>hoc loco, exarentur. </s></p> <pb xlink:href="051/01/009.jpg"></pb> <p type="main"> <s>Vale PRINCEPS EMINEN<lb></lb>TISSIME, Imperii columen, <lb></lb>& Eccleſiæ decus; ae bono utrius<lb></lb>que quàm diutisſimè vive. </s><s> Ita <lb></lb>optat Herbipoli Die VIII. Julij, <lb></lb>Anno MDCL VII. </s></p> <p type="main"> <s>EMINENTISSIMÆ <lb></lb>TUÆ </s></p> <p type="main"> <s>CELSITUDINIS </s></p> <p type="main"> <s><emph type="italics"></emph>Humillimus Cliens<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Caſparus Schottè So<lb></lb>cietate JESU. </s></p> <pb xlink:href="051/01/010.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>IN FRONTEM LIBRI<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>ACROAMA EXEGETICUM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>FONS PULCHER SUFFICIT UNDAS.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <figure id="id.051.01.010.1.jpg" xlink:href="051/01/010/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Obmuteſce Antiquitas; <lb></lb>Jam dudum exaruit lympha, <lb></lb>Quam propinavit Pincerna vatum<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PEGASUS.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Riget inſtar pumicis, qui Parnaſſum irrigavit: <lb></lb>Qui infantium etiam linguas fecerat diſertas, <lb></lb>Dudum, prô pudor, eſt deſertus. </s><s><lb></lb>Pone criſtas Heliconis Nympha;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>HIPPOCRENE FUIT!<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Unde, aut ubi fluxerit olim, quis ſciat? </s><s> <lb></lb>Caſtalides ipſæ neſciunt, <lb></lb>Ex quo toties potæ cecinerunt.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Et quid mirum Helicona nuſquam apparere, <lb></lb>Si ipſa Græcia diſparuit, & migravit <lb></lb>In EUKOPAM reliquam;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>In quâ non unas numeres Athenas, <lb></lb>Quando pæne innumera vides Athenæa, <lb></lb>Suo quodque formoſum Apolline, <lb></lb>Suo quodque irriguum fonte, <lb></lb>E quo bibunt ſapientes Europæi, <lb></lb>Et entheantur.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/011.jpg"></pb> <p type="main"> <s><emph type="center"></emph>De Europa univerſa periculum facin ſola<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>GERMANIA:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De Germania verò pronuncia, <lb></lb>Si, quæ Rhenus, Mœnusve alluit, inviſas<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>ATHENÆA, <lb></lb>MOGANUM ET ARTAUNIUM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quæ, qualésve ea incolant Muſæ, <lb></lb>Diſce ex latice, qui eas reficit.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Medio bullit è Nobilitatis Rhenanæ jugo, <lb></lb>Non ſonipedis Pegaſi extuſus ungulâ; <lb></lb>Sed jubati LEONIS effoſſus ungue,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>CALLOCRENE.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc uno ambæ libant & vivunt de fonte, <lb></lb>Cælo diviſæ, non zelo,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>MOGANIDES MUSÆ ET FRANCONIDES.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>His <lb></lb>Seu ſitim arentis gutturis levent, <lb></lb>Seu barbita pulvere glorioſo ſordida lavent, <lb></lb>Seu in carmina animent Vates, <lb></lb>Seu fugientes Vatibus venas revocent, <lb></lb>Seu in pręmia lauros & palmas rigent, <lb></lb>Seu feſtivè cum Nymphis ludant <lb></lb>Apollinis honori,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PULCHER SUFFICIT UNDAS.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Verùm quid Muſas, Nymphásque memoro? <lb></lb>Ipſa adeò Natura hoc fonte haurit, <lb></lb>Ut parturientem juvet Artem:<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/012.jpg"></pb> <p type="main"> <s><emph type="center"></emph>Hinc Ars bibit, ut languentem fulciat Naturam, <lb></lb>Experti diſcimus: <lb></lb>Quod non ſola Natura audet. </s><s><lb></lb>Nec Ars ſola poteſt, <lb></lb>Et poteſt cum Arte Natura & audet. </s><s><lb></lb>Verùm deficerent, niſi ſufficeret,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PULCHER<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Undas, Animos, Vires. </s><s><lb></lb>Hoc manante animatur emortuus Æolus, <lb></lb>Et ſpirat:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc ſtillante liqueſcunt, licet ære fuſæ, Phaëtontiades, <lb></lb>Et lacrymantur:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc illabente alterni folles inflantur & efflantur, <lb></lb>Et organa reſonant:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc ſaliente Deorum ſimulacra irrorantur, <lb></lb>Et tripudiant.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Verbo, <lb></lb>Paucis multa dicam:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>CRESCIT QUODCUNQUE RIGAT, <lb></lb>VIGET QUODCUNQUE LAVAT,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PULCHER.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hinc eſt quod ſtupent obſtipi; <lb></lb>Et ægrè vident Invidi,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>HOC FONTE,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Virere lauros, Musásque vigere.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/013.jpg"></pb> <p type="main"> <s><emph type="center"></emph>FONS PULCHER.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Feras cicurat, monſtra domat: <lb></lb>Hercule felicior!<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quæ is exanimabat, hic animat;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quæ iſte clavâ fregit, ille regit <lb></lb>Suaviter influendo.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc ſtratagemate, <lb></lb><emph type="italics"></emph>Rotas Moganas<emph.end type="italics"></emph.end> firmavit, <lb></lb>Ut bene verterentur, <lb></lb>Quæ à procellis, quia rapiebantur, <lb></lb>Pæne evertebantur.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Pluris ſcilicet ſæpe eſt eſſe humanum quàm fortem, <lb></lb>Ubi gloria eſt major, <lb></lb>Vincere amoribus quàm viribus. </s><s><lb></lb>In fontibus reliquis eximium hoc habet<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PULCHER,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quòd non aquam ſolùm fundat, <lb></lb>Quâ ſuam effæta reparet Juventam<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>AQUILA;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Sed & oleum ſtillet, <lb></lb>Quo repullulantes pennas ad robur <lb></lb><emph type="italics"></emph>Ungat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Nec <emph type="italics"></emph>Aquilæ<emph.end type="italics"></emph.end> modò hoc <emph type="italics"></emph>Fonte<emph.end type="italics"></emph.end> totæ <lb></lb><emph type="italics"></emph>Juveneſcunt:<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Sed, quia cum Igne quid commune habet<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PVLCHER,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hoc etiam in FONTE emortuus,<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/014.jpg"></pb> <p type="main"> <s><emph type="center"></emph>Novo prodigio Novus <lb></lb><emph type="italics"></emph>Reviviſcit<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PHOENIX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Unde infeliciſſimorum temporum <lb></lb>Hæc una eſt felicitas, <lb></lb>Quod mergantur in FONTE PULCHRO, <lb></lb>In quo niſi tota ſubmergantur, <lb></lb>Nunquam emergent <lb></lb>Feliciora.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Et Gloria hæc ſumma erit<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONTIS PVLCHRI,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>In ea incidiſſe tempora, <lb></lb>In quæ niſi incidiſſet, <lb></lb>Forent tempora omnino <lb></lb>Profligata.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De FONTE PULCHRO quid ampliùs dicam? <lb></lb>Fontes alij aut æſtu proſpero exſiccantur, <lb></lb>Aut algore ſiniſtro congelant, <lb></lb>Ut fluxum ſiſtant:<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FONS PVLCHER.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>FLUET DONEC INFLUAT <lb></lb>IN FONTEM <lb></lb>QUOCUM SALIET IN VITAM ÆTERNAM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quod vovent & precantur mecum<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>OMNES BONÆ MUSÆ <lb></lb>A FONTE PULCHRO <lb></lb>LOTÆ, RIGATÆ, POTÆ.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>P. NICOLAUS MOHR è Socie<lb></lb>tate JESU. </s></p> <pb xlink:href="051/01/015.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Facultas admodum R. P.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PRÆPOSITI GENERALIS <lb></lb>SOCIETATIS JESU.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>GOSWINUS <lb></lb>NICKEL SOCIETA<lb></lb>TIS JESU<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>PRÆPOSITUS GENERALIS.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>CUm Opus, quod inſcribitur<emph.end type="italics"></emph.end> Mechanica <lb></lb>Hydraulico-pnevmatica, à P. GASPARE <lb></lb>SCHOTT <emph type="italics"></emph>noftræ Societatis Sacerdote compoſi<lb></lb>tum, aliquot ejuſdem Societatis Religioſi recognove<lb></lb>rint, & in lucem edi poſſe probaverint; facultatem <lb></lb>concedimus vt typis mandetur, ſi ijs ad quos pertinet, <lb></lb>ita videbitur. </s><s>In cujus rei teſtimonium has litteras <lb></lb>manu noſtrâ ſubſcriptas, ſigillo〈qué〉 noſtro munitas da<lb></lb>mus Romæ,<emph.end type="italics"></emph.end> 23. <emph type="italics"></emph>Januarij<emph.end type="italics"></emph.end> 1655. </s></p> <p type="main"> <s>GOSWINUS NICKEL. </s></p> <pb xlink:href="051/01/016.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>FACULTAS<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>R. P. PROVINCIALIS <lb></lb>SOCIETATIS IESV<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per Rheni Superioris Provinciam Bi<lb></lb>bliopolæ facta.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>CUm ex Mandato Sacræ Cæſareæ Majeſtatis omnibus <lb></lb>& ſingulis Typographis, Bibliopolis, ac aliis quamcun<lb></lb>que librariam negotiationem exercentibus, ſeriò firmiterque in<lb></lb>hibeatur, nè quiſquam libros ullos<emph.end type="italics"></emph.end> à SOCIETATIS <emph type="italics"></emph>noſtræ Pa<lb></lb>tribus hactenus editos, aut impoſterum edendos intra S.R. Im<lb></lb>perij, Regnorum, & Dominiorum Suæ Cæſareæ Majeſtatis hæ<lb></lb>reditariorum fines, ſimili aliovè charactere aut formâ, ſive in <lb></lb>toto, ſive in parte recudere, vel aliò recudendos mittere, aut ali<lb></lb>bi etiam impreſſos adducere, vendere, & diſtrahere, clàm ſeu <lb></lb>palàm, citrà ſupradictorum Patrum conſenſum ac teſtimonium, <lb></lb>audeat, vel præſumat: </s><s>Ego<emph.end type="italics"></emph.end> NITHARDUS BIBERUS, <lb></lb>SOCIETATIS JESU <emph type="italics"></emph>per Rheni ſuperioris Provinciam Pro<lb></lb>vincialis, concedo<emph.end type="italics"></emph.end> Joanni Godefrido Schôn wettero <emph type="italics"></emph>fa<lb></lb>cultatem, ſuis ſumptibus excudendi<emph.end type="italics"></emph.end> P. GASPARIS SCHOTTI <lb></lb>è SOCIEIATE JESU Mechanicam Hydraulico-pnev<lb></lb>maticam. </s><s><emph type="italics"></emph>In quorum fidem hoc ei teſtimonium manu noſtrâ <lb></lb>ſubſcriptum, & Sigillo munitum dare voluimus.</s><s>Herbipoli<emph.end type="italics"></emph.end><lb></lb>21. <emph type="italics"></emph>Fanuarij<emph.end type="italics"></emph.end> 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"></pb> <p type="main"> <s><emph type="center"></emph>ELENCHUS<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.017.1.jpg" xlink:href="051/01/017/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>ELENCHUS TITU<lb></lb>LORUM,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Sive <lb></lb>SYNOPSIS OPERIS.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s>Præloquium ad Lectorem, de Operis Occaſione, Diviſione, Inſcriptione; deque <lb></lb>Hydraulicorum & Pnevmaticorum Scriptoribus. pag. 1. </s></p> <p type="main"> <s><emph type="center"></emph>PARS I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>THEORETICA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De Machinarum Hydraulico-Pnevmaticarum principiis ſeu fundamentis. 15 </s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De vi Attractiva corporum, ad vacuum vel replendum, vel fugiendum: ſeu de <lb></lb>primo Machinarum Hydro-pnevmaticarum principio. 18 </s></p> <p type="main"> <s>§. I. Hero Alexandrinus vacuum in aëre & aqua diſſeminatum agnoſcit. 19 </s></p> <p type="main"> <s>§. II. Experimenta quibus Hero vacuum in corporibus diſſeminatum pro<lb></lb>bat. 21 </s></p> <p type="main"> <s>§. III. Experimenta quibus vacuum nullum eſſe probatur. 25 </s></p> <p type="main"> <s>§. IV. Vis attractiva ob vacui metum, primum Machinarum Hydro-pnevma<lb></lb>ticarum principium, quæ, & qualis, quibusvis inſit corporibus. 28 </s></p> <p type="main"> <s>§. V. Experimentum, quo oſtenditur vis attractiva ad aquas in altum evchen<lb></lb>das, vacui vitandi causâ, per Machinas Hydro-pnevmaticas. 30 </s></p> <p type="main"> <s>§. VI. Notantur nonnulla circa prædictum Experimentum, ſimulque ſtabili<lb></lb>tur, in attractione aquæ metu vacui habendam eſſe rationem perpendiculi <lb></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 eſt ratio perpendiculi ſolùm <lb></lb>illorum tuborum, per quos aqua, non per quos aër vehitur. 39 </s></p> <pb xlink:href="051/01/018.jpg"></pb> <p type="main"> <s><emph type="center"></emph>TITULORUM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>§. X. Viattractivâ elevari poteſt aqua ultra perpendiculi altitudinem, aëre me<lb></lb>diante. 40 </s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De vi Expulſiva propter corporum impenetrabilitatem; ſeu de ſecundo Machi<lb></lb>narum Hydro-pnevmaticarum principio. 43 </s></p> <p type="main"> <s>§. I. Omnia univerſi corpora ſunt inter ſe contigua. ibid. </s></p> <p type="main"> <s>§. II. Corpora ſe mutuò expellunt. 45 </s></p> <p type="main"> <s>§. III. Experimentum, quo oſtenditur vis expulſiva, propter corporum im<lb></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 expulſivâ in lucerna. 50 </s></p> <p type="main"> <s>§. VI. Attractione & expulſione ſimul aquam elevare poſſumus. 53 </s></p> <p type="main"> <s>§. VII. Salomon Caus meritò ſugillat Heronem. 55 </s></p> <p type="main"> <s>§. VIII. Idem perpendiculum aquæ cadentis non poteſt ſervire ſimul attra<lb></lb>ctioni & expulſioni. 57 </s></p> <p type="main"> <s>§. IX. Error apud Joannem Baptiſtam Portam indicatur. 58 </s></p> <p type="main"> <s>§. X. Alia ratio aquam elevandi in altum propter corporum impenetrabili<lb></lb>tatem. 59 </s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De vi Rarefactiva; ſeu de tertio Hydro-pnevmaticarum Machinarum prin<lb></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"></emph>PROTHEORIA IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De fluxu aquæ naturali; ſeu de quarto Hydro-pnevmaticarum Machinarum <lb></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 ſuperficies ſuperior, ceſſante fluxu, ſphærica eſt; reliquæ conforman<lb></lb>tur vaſis & receptaculis. ibid. </s></p> <p type="main"> <s>III. Aqua minùs preſſa expellitur à magis preſſa. 68 </s></p> <p type="main"> <s>IV. Aquæ, & humidi cuiuscunque, pars unaquæque premitur humido ſupra <lb></lb>ipſam exiſtente ad perpendiculum, ſi humidum ſit deſcendens in aliquo, aut <lb></lb>abalio aliquo preſſum. ibid. </s></p> <p type="main"> <s>V. Aquâ in ſitu naturali conſiſtente, partes ſuperiores non premunt inferio<lb></lb>res. 70 </s></p> <pb xlink:href="051/01/019.jpg"></pb> <p type="main"> <s>VI. Aquæ in ſitu naturali poſitæ una pars non expellit alteram. 71 </s></p> <p type="main"> <s>VII. Non omnes æquæ æquales magnitudine, ſunt æquales pondere. ibid. </s></p> <p type="main"> <s>VIII. Aqua naturaliter non aſcendit ad locum altiorem ſuâ origine. ibid. </s></p> <p type="main"> <s>CAPUT II. De Proprietatibus aquæ fluentis per ſiphones. 72 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Siphonis varias diviſiones aſſignare. ibid. </s></p> <p type="main"> <s>II. Siphonis erecti proprietates aſſignare. 74 </s></p> <p type="main"> <s>III. Siphonis inverſi proprietates aſſignare. 77 </s></p> <p type="main"> <s>IV. Siphonis mixti inæqualium crurium proprietates aſſignare. 81 </s></p> <p type="main"> <s>V. Siphonis mixti æqualium crurium proprietates aſſignare. 84 </s></p> <p type="main"> <s>VI. Inverſi ſiphonis, vaſi uno crure impoſito, proprietates aſſignare. ibid. </s></p> <p type="main"> <s>VII. Cauſam adſignare, cur quando oſculum externi cruris ſiphonis inverſi eſt <lb></lb>altius, aut æquè altum ac aquæ ſuperficies ſuprema in vaſe, aqua non fluat; <lb></lb>quando verò eſt demiſſius, fluat. 88 </s></p> <p type="main"> <s>VIII. Siphonem ad libram ſeu vectem revocare, & filtrum ad ſiphonem. 93 </s></p> <p type="main"> <s>IX. Diabetem ſpiritalem deſcribere, eiuſque proprietates adſignare. 94 </s></p> <p type="main"> <s>X. Siphonis inverſi fluxum æqualem reddere. 96 </s></p> <p type="main"> <s>XI. Siphone inverſo aquam ex uno montis latere in alterum, per verticem, de<lb></lb>ducere. 98 </s></p> <p type="main"> <s>XII. Siphone inverſo aquam ex montis radice ad ejus verticem elevare. 102 </s></p> <p type="main"> <s>XIII. Cauſam aſſignare, cur in ſiphone inverſo interrupto perpendiculum aquæ <lb></lb>deſcendentis debeat ſuperare perpendiculum aquæ aſcendentis. 104 </s></p> <p type="main"> <s>XIV. Cauſam aſſignare, cur in Fonte Heronis perpendiculum aquæ deſcen<lb></lb>dentis debeat eſſe longius perpendiculo aquæ aſcendentis. 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 baſis, inſtar columnæ aqueæ, cuius <lb></lb>baſis æqualis foramini, altitudo perpendiculares à baſi erectæ; ſive tubi ſint <lb></lb>ſemper pleni, ſive non. 111 </s></p> <p type="main"> <s>II. Per tubos tam ſemper, quàm non ſemper plenos æqualis altitudinis, & æqua<lb></lb>lium foraminum, effluit æqualis aquæ copia, eodem vel æquali tempore, <lb></lb>cujuscunque capacitatis & formæ ſint tubi. 113 </s></p> <p type="main"> <s>III. Per tubos tam ſemper, quàm non ſemper plenos æqualium luminum, ſed <lb></lb>inæqualium altitudinum, effluit eodem, vel æquali tempore, inæqualis aquæ <lb></lb>copia. 114 </s></p> <p type="main"> <s>IV. Per tubos ſemper, & non ſemper plenos inæqualium luminum, ſed æquali<lb></lb>um altitudinum, effluit eodem, vel æquali tempore, inæqualis aquæ <lb></lb>copia. ibid. </s></p> <pb xlink:href="051/01/020.jpg"></pb> <p type="main"> <s>V. Per tubos æquè altos, & æqualium luminum, non ſemper plenos, fluit eodem <lb></lb>tempore æqualis aquæ copia; ſed tantò fluit unus diutiùs altero, quantò <lb></lb>plus aquæ continet unus quàm alter. 115 </s></p> <p type="main"> <s>VI. Per tubos non ſemper plenos, & non æquè altos, æqualium tamen lumi<lb></lb>num, eodem vel æquali tempore non fluit æqualis aquæ copia. ibid. </s></p> <p type="main"> <s>VII. Tubus altitudine quadrupedalis, cui pro baſis diametro pedis Pariſienſis <lb></lb>uncia, aquâ ſemper, plenus, effundit per lumen lineare in baſi ſitum, aquæ <lb></lb>libram ſpatio tredecim minutorum ſecundorum temporis. 116 </s></p> <p type="main"> <s>VIII. Aquæ fluentes ex tubis tam ſemper quàm non ſemper plenis æqualium <lb></lb>foraminum, ſed inæqualium altitudinum, habent rationem ſubduplicatam <lb></lb>altitudinum tuborum; habentque dicti tubi duplicatam rationem aqua<lb></lb>rum, quas fundunt. 117 </s></p> <p type="main"> <s>IX. Aqua naturali motu deſcendens & effluens per tubos, imitatur leges alio<lb></lb>rum gravium naturali motu deſcendentium. 120 </s></p> <p type="main"> <s>X. Velocitates motus aquæ deſcendentis & effluentis per tubos æqualium fo<lb></lb>raminum, ſed inæqualium altitudinum, habent ſubduplicatam rationem <lb></lb>altitudinum. 125 </s></p> <p type="main"> <s>XI. Cauſam aſſignare, cur aquæ fluentes per tubos æqualium luminum, ſed in<lb></lb>æqualium altitudinum, habeant rationem ſubduplicatam altitudinum tu<lb></lb>borum. 126 </s></p> <p type="main"> <s>XII. Tempora quibus æqualis aquæ quantitas è tubis æqualium luminum, ſed <lb></lb>inæqualium altitudinum effluit, habent ſubduplicatam rationem tubo<lb></lb>rum. ibid. </s></p> <p type="main"> <s>XIII. Si tubi, ſive ſemper pleni, ſive non ſemper pleni, ſint ejusdem altitudinis, <lb></lb>ſed inæqualium foraminum, eſt eadem ratio aquæ ad aquam, quæ foraminis <lb></lb>ad foramen, phyſicè ſeu ad ſenſum. 127 </s></p> <p type="main"> <s>XIV. Tubi non ſemper pleni æquè alti, & æqualium foraminum; ſed inæquali<lb></lb>um baſium, evacuantur inæqualibus temporibus, eſtque eadem ratio tem<lb></lb>porum, quæ baſium. 129 </s></p> <p type="main"> <s>XV. Tempora quibus deplentur tubi non ſemper pleni, æquèlati, ſed non æquè <lb></lb>alti, per æqualia foramina, ſunt in altitudinum ratione ſubduplicata. 131 </s></p> <p type="main"> <s>XVI. Tempora quibus evacuantur tubi non ſemper pleni ſimiles, & æquales <lb></lb>quoad altitudines & baſes, per lumina ſimilia inæqualia, ſunt reciprocè, ut <lb></lb>lumina. ibid. </s></p> <p type="main"> <s>XVII. Datis altitudine & foramine tubi ſemper pleni, invenire quantitatem <lb></lb>aquæ quam dato tempore effundat; vel, datis iisdem, invenire magnitudi<lb></lb>nem ciſternæ quæ dato tempore repleatur. 132 </s></p> <pb xlink:href="051/01/021.jpg"></pb> <p type="main"> <s>XVIII. Datis altitudine & lumine tubi ſemper pleni, invenire tempus quo da<lb></lb>tam aquæ quantitatem effundat, ſive quo datam ciſternam impleat. 135 </s></p> <p type="main"> <s>XIX. Datis tempore, quantitate aquæ, ſeu ciſterna, & lumine tubi, invenire alti<lb></lb>tu̇dinem tubi, qui ſemper plenus ciſternam dato tempore repleat. 136 </s></p> <p type="main"> <s>XX. Dato vaſe, & foramine per quod effluit aqua, invenire tempus quo eva<lb></lb>cuatur. 137 </s></p> <p type="main"> <s>XXI. Dato vaſe, & tempore, invenire foramen per quod evacuetur tempore <lb></lb>dato. 139 </s></p> <p type="main"> <s>XXII. Altitudinem ſcaturiginis dati fontis per tubos fluentis invenire. 140 </s></p> <p type="main"> <s>XXIII. Data alicujus tubi, aut vaſis erogatorii altitudine, ac tempore quo deter<lb></lb>minatam aquæ quantitatem è ſuo lumine effundit, invenire altitudinem <lb></lb>ejusdem aut alterius tubi, qui æquali tempore, per æquale lumen, aliam de<lb></lb>terminatam aquæ quantitatem effundat. 140 </s></p> <p type="main"> <s>XXIV. In tubo ſeu vaſe ſemper pleno determinare ſpatia, quæ temporibus <lb></lb>æqualibus ſibi ſuccedentibus evacuantur; uti & menfuram ſeu pondus a<lb></lb>quæ quæ effluit. 141 </s></p> <p type="main"> <s><emph type="center"></emph>PARERGUM CAPITIS III.<emph.end type="center"></emph.end></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"></emph>CAPUT IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De proprietatibus aquæ ſalientis ex tubis. 149 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Salientium ſive ecdromorum horizontalium, & mediorum, ſuper eodem ho<lb></lb>rizonte, longitudines ſunt in ratione ſubduplicata tuborum, ex quibus exi<lb></lb>liunt. 151 </s></p> <p type="main"> <s>III. Salientes horizontales & mediæ, ejusdem tubi, eò ſunt longiores, quò lu<lb></lb>men tubi fuerit altius ſupra horizontem. 153 </s></p> <pb xlink:href="051/01/022.jpg"></pb> <p type="main"> <s>III. Salientes horizontales & mediæ, eandem longitudinis rationem ſervant, <lb></lb>quam altitudines tuborum ſuper eundem horizontem. 154 </s></p> <p type="main"> <s>IV. Salientium verticalium in quacunque elevatione tubi ſupra horizontem <lb></lb>ſemper eadem eſt 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 ſextas tubi ſui <lb></lb>partes. ibid. </s></p> <p type="main"> <s>VII. Salientes verticales eò ſunt longiores, quò tubi ſunt longiores; ſed non eâ<lb></lb>dem proportione illæ ac hi creſcunt. ibid. </s></p> <p type="main"> <s>VIII. Data tubi altitudine, & ſupra horizontem elevatione, invenire longitudi<lb></lb>nem ſalientis horizontalis, & mediæ. 157 </s></p> <p type="main"> <s>IX. Data longitudine ſalientis horizontalis, aut mediæ, invenire altitudinem tu<lb></lb>bi, cognitâ ejus elevatione ſupra horizontem. ibid. </s></p> <p type="main"> <s>X. Ex nota ſcaturiginis altitudine fontis unius ex tubo exilientis horizontaliter, <lb></lb>altitudinem ſcaturiginis cujuscunque alterius æqualiter ſupra horizontem <lb></lb>elevati invenire. 158 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De fluxu aquæ per diverſa ejusdem vaſis aut tubi foramina. 158 </s></p> <p type="main"> <s>PROPOSITIO </s></p> <p type="main"> <s>I. Per foramina æqualia, æquè à ſummo tubi diſtantia, ſive in baſe, ſive in latere, <lb></lb>æquali tempore æquales fluunt aquarum quantitates. 160 </s></p> <p type="main"> <s>II. Aquæ è foraminibus æqualiter à ſummo tubi diſtantibus decurrentes, ſunt in<lb></lb>ter ſe ut foramina. ibid. </s></p> <p type="main"> <s>III. Aqua per foramina vaſis eo impetu ſeu velocitate decurrit, quo per tubos <lb></lb>æqualium foraminum & altitudinum. 161 </s></p> <p type="main"> <s>IV. Velocitates aquæ decurrentis per foramina æqualia ejusdem vaſis, inæqua<lb></lb>liter diſtantia à ſummo vaſis, ſunt in ſubduplicata ratione diſtantiæ. 162 </s></p> <p type="main"> <s>V. Aquæ per æqualia foramina inæqualiter à ſummitate vaſis diſtantia fluentes, <lb></lb>ſunt in ſubduplicata ratione diſtantiarum. ibid. </s></p> <p type="main"> <s>VI. Secto foramine laterali vaſis in partes æquales, à rectis horizontalibus, in<lb></lb>venire rationes aquarum ex eis fluentium. 163 </s></p> <p type="main"> <s>VII. Secto foramine laterali vaſis in partes inæquales, à rectis horizontalibus, <lb></lb>reperire rationes aquarum effluentium ex ipſis. 164 </s></p> <p type="main"> <s>VIII. Datis foraminibus inæqualibus ſuper eadem horizontali, venari rationes <lb></lb>aquarum. ibid. </s></p> <p type="main"> <s>IX. Datis foraminibus ejusdem vaſis, quorum unum ſuperius, alterum inferius, <lb></lb>inter easdem parallelas perpendiculares, reperire rationes aquarum. 165 </s></p> <pb xlink:href="051/01/023.jpg"></pb> <p type="main"> <s>X. Datis foraminibus ejusdem vaſis, quorum unum ſuperius, alterum inferius; <lb></lb>non inter easdem parallelas, reperire rationes aquarum. ibid. </s></p> <p type="main"> <s>XI. Dato foramine, & linea horizontali, in aliquo vaſe, conſtituere ſuper illa fo<lb></lb>ramen, è quo æqualis aqua fluat eodem tempore. 166 </s></p> <p type="main"> <s>XII. Dato foramine, & latere alterius in eodem vaſe, reperire foramen, è quo <lb></lb>æqualis aqua effluat. ibid. </s></p> <p type="main"> <s>XIII. Dato foramine, reperire aliud æquale in eodem vaſe, è quo fluat aqua in <lb></lb>ratione data. 167 </s></p> <p type="main"> <s>XIV. Dato foramine, aptare in eodem vaſe aliud datum ſimile, magnitudinis di<lb></lb>verſæ, à quo aqua fluens cum fluente à primo, habeat rationem datam. 168 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De aëris gravitate, rarefactione, & condenſatione. 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 condenſari aër poſſit, invenire. 170 </s></p> <p type="main"> <s>III. Quantum rarefieri aër poſſit, invenire. 171 </s></p> <p type="main"> <s><emph type="center"></emph>PARS II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PRACTICA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De fabrica Machinarum Hydro-pnevmaticarum ex traditis principiis. 173 </s></p> <p type="main"> <s><emph type="center"></emph>CLASSIS PRIMA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De variis Hydraulicis atque Pnevmaticis Machinis. 176 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT I.<emph.end type="center"></emph.end></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 incluſus. 177 </s></p> <p type="main"> <s>II. Siphon inverſus interruptus, aquam in determinatam altitudinem evchens. 179. </s></p> <p type="main"> <s>III. Fons Cæſareus. 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 Aquiſuga. 186 </s></p> <p type="main"> <s>VII. Siphon inverſus 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 inverſus horologus. 189 </s></p> <pb xlink:href="051/01/024.jpg"></pb> <p type="main"> <s>X. Bina vaſa, quorum uni ſi aqua infundatur, alterum reddit vinum. 190 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De Machinis quæ fiunt vi expulſiva. 191 </s></p> <p type="main"> <s>I. Fons Heronis in vaſis immediatis. 192 </s></p> <p type="main"> <s>Item Fonticulus ſimilis Fonti Heronis. 194 </s></p> <p type="main"> <s>II. Clepſydra Heroniana. 195 </s></p> <p type="main"> <s>III. Fons Heronis in vaſis mediatis: item ſcyphus diverſos ejiciens liquores. 197 </s></p> <p type="main"> <s>IV. Fons novus Polyſiphonius. 201 </s></p> <p type="main"> <s>V. Fons perennis, alto in loco aquam è puteo profundo ſubminiſtrans. 203 </s></p> <p type="main"> <s>VI. Antlia, ſeu Cteſibia Machina. 205 </s></p> <p type="main"> <s>VII. Speculator cornu inflans. 207 </s></p> <p type="main"> <s>VIII. Fonticulus compreſſione aquam ſpargens in altum: Baculus item viato<lb></lb>rius aquivomus, & Catellus mingens. 208 </s></p> <p type="main"> <s>IX. Phiala vitrea, compreſſione aquam projiciens in altum. 211 </s></p> <p type="main"> <s>X. Infundibulum pnevmatico-hydraulicum, aquam in determinatam altitudi<lb></lb>nem attollens. 211 </s></p> <p type="main"> <s>XI. Infundibulum alterum pnevmatico-hydraulicum, aquam in quamlibet al<lb></lb>titudinem extollens. 213 </s></p> <p type="main"> <s>XII. Fons eâdem fiſtulâ diſcolores ejiciens liquores. 214 </s></p> <p type="main"> <s>XIII. Sclopetum Æolium ſeu pnevmaticum. 216 </s></p> <p type="main"> <s>XIV. Aliud ſclopetum Pnevmaticum. 217 </s></p> <p type="main"> <s>XV. Sedes Aquivoma. 219 </s></p> <p type="main"> <s>XVI. Heronis vaſa quæ vinum pro aquainfuſa reddunt: ſeu Hydriæ Canæ Ga<lb></lb>lilææ. 220 </s></p> <p type="main"> <s>XVII. Hydracontiſterium antiquum. 222 </s></p> <p type="main"> <s>XVIII. Hydracontiſterium novum. 223 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT III.<emph.end type="center"></emph.end></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, incaleſcentis per ignem aëris vi aquam expellens. 226 </s></p> <p type="main"> <s>II. Fons alius pyrobolus, projectum liquorem convertens in aërem, autignem <lb></lb>226 </s><s>Item Meteorologicæ impreſſiones igneæ. 229 </s></p> <p type="main"> <s>III. Thermoſcopium prognoſticum Hybernum. 229 </s><s>& Æſtivum. 231 </s></p> <p type="main"> <s>IV. Inſtrumentum novum, gradus humidi & ſicci 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. Ciſta Æolia. 238 </s></p> <pb xlink:href="051/01/025.jpg"></pb> <p type="main"> <s>VIII. Æolus ventum efflans. 239 </s></p> <p type="main"> <s>IX. Memnonia ſtatua, citharæ, & humanæ vocis ſonum ad orientem ſolem <lb></lb>edens. 240 </s></p> <p type="main"> <s>X. Memnoniæ aves, voce & motu animatæ. 242 </s></p> <p type="main"> <s>XI. Ara aſpide adornata, in qua igne poſito Iſis & Oſiris vinum & lac ſacrificant <lb></lb>aſpis verò ſibilando applaudit. 244 </s></p> <p type="main"> <s>XII. Valvæ ſacelli ſuccenſo ſacrificii igne ſponte aperibiles, & extincto clauſæ. 246 </s></p> <p type="main"> <s>XIII. Ara Deorum imagines tripudiantes exhibens. 247 </s></p> <p type="main"> <s>XIV. Hydrologium horarum Aſtronomicarum, ſeu æqualium. 248 </s></p> <p type="main"> <s>XV. Fonticulus horarius. 249 </s></p> <p type="main"> <s>XVI. Præco horarius, ſingulis horis cornu inflans. 252 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De Machinis quæ fiunt naturali lapſu aquæ. 254 </s></p> <p type="main"> <s>MACHINA </s></p> <p type="main"> <s>I. Clepſydra Kircheriana, quæ fontis inſtar ejaculatur aquam, & inverſa ite<lb></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 verſatilis, aquam luſtrationi neceſſariam fundens. 257 </s></p> <p type="main"> <s>IV. Cycocephalus Ægyptius ex veretillo aquam fundens, quæ horas æquino<lb></lb>ctiales in ſubjecto vaſe monſtrat. 259 </s></p> <p type="main"> <s>V. Hydrologium horarum antiquarum, ſeu 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 ſerpentum 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"></emph>CAPUT V.<emph.end type="center"></emph.end></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 exſputam à ſerpente aquam ſorbens 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 curſum fluminum fiſtens. 285 </s></p> <pb xlink:href="051/01/026.jpg"></pb> <p type="main"> <s>IV. Atlas cælum humeris impoſitum 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 ſpectacula exhibens. 291 </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT VI.<emph.end type="center"></emph.end></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 fuſpenſa, ac circa ſuum centrum mota. 300 </s></p> <p type="main"> <s>II. Cribrum Veſtalis virginis. 303 </s></p> <p type="main"> <s>III. Tubus vitreus, aquam perpetuò incorruptam conſervans. 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 ſaporis aquam exſpuens. 310 </s></p> <p type="main"> <s>VIII. Palingeneſia Cæſarea. 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 conſtructa. 317 </s></p> <p type="main"> <s>XI. Libra hydroſtatica 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. Anemoſcopium commune. ibid. </s></p> <p type="main"> <s>XV. Anemoſcopium Kircherianum. 323 </s></p> <p type="main"> <s>Epilogus Claſſis primæ, ubi nonnulla de fontibus Romanis, ac Tuſculanis, <lb></lb>aliisque. 325 </s></p> <p type="main"> <s><emph type="center"></emph>CLASSIS SECUNDA<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De Machinis motum perpetuum æmulantibus. 329 </s></p> <p type="main"> <s>PROLUSIO. De motus perpetui arte procurati impoſſibilitate. 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 ſpiralis 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 & condenſationis <lb></lb>ſpecimen exhibens. 351 </s></p> <p type="main"> <s>V. Fonticulus motum perpetuum vi rarefactionis & condenſationis aëris e<lb></lb>mentitus. 353 </s></p> <pb xlink:href="051/01/027.jpg"></pb> <p type="main"> <s>VI. Horoſcopium Hydropnevmato-Magneticum, quo ſphæra Magnetica in <lb></lb>medio liquorum librata perpetuò circumducitur, ad monſtrandas ho<lb></lb>ras, circulos cœleſtes, totiusque Aſtrolabij myſteria. 354 </s></p> <p type="main"> <s>VII. Machinamentum aliud hydro-pnevmatico-magneticum, perpetuans mo<lb></lb>tum per ventum. 357 </s></p> <p type="main"> <s>VIII. Cteſibica Machina perpetui motus æmula. 360 </s></p> <p type="main"> <s>IX. Catona perpetuò mobilis in gyrum hydroſtaticâ arte, ut putabatur. 362 </s></p> <p type="main"> <s>X. Situlæ automatæ, ſpontaneo atque perpetuo motu aquam haurientes. 365 </s></p> <p type="main"> <s>XI. Funigiana induſtria perpetuo motu ſitulæ 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. Harſtorfferus excogitavit. 381 </s></p> <p type="main"> <s><emph type="center"></emph>CLASSIS TERTIA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>De Organis hydraulicis, aliisque inſtrumentis harmonicis hydropnevma<lb></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></lb>ſubminiſtrandum. 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 conſtruendi. 387 </s></p> <p type="main"> <s>PRAGMATIA IV. Ventum per folles perpetuum producere in ordine ad <lb></lb>Organa hydraulica. 388 </s></p> <p type="main"> <s>PRAGMATIA V. Folles aliter inflare ad inſtrumenta chordophôna ſive <lb></lb>fidicina incitanda. 389 </s></p> <p type="main"> <s>PRAGMATIA VI. Cylindrum phonotacticum conſtruere. 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></lb>transferre. 397 </s></p> <p type="main"> <s>§. III. Dentibus Cylindrum phonotacticum inſtruere. 399 </s></p> <p type="main"> <s>§. IV. Plures cantilenas in eundem cylindrum transferre. 400 </s></p> <p type="main"> <s>§. V. Cantilenas ſyncopatas, & <emph type="italics"></emph>b<emph.end type="italics"></emph.end> molli ſignatas, ut & ſemitonia, in cylin<lb></lb>drum phonotacticum transferre. 401 </s></p> <p type="main"> <s>§. VI. Minimi valoris notas cylindro phonotactico inſerere. 406 <pb xlink:href="051/01/028.jpg"></pb> </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></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. Diverſæ volucres garrientes, ac ſe 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 Muſicam Pythagoricam exhibentes. 420. </s></p> <p type="main"> <s>MACHINA VIII. Clavicymbalum automatum, omnis generis inſtru<lb></lb>mentorum fidibus inſtructorum ſymphoniam exhibens. 432 </s></p> <p type="main"> <s>MACHINA IX. Automatum Kircherianum, omnis generis inſtrumento<lb></lb>rum ſymphoniam exhibens. 436 </s></p> <p type="main"> <s>MACHINA X. Ciſta pnevmato-harmonica antophóna, ſolo vento harmo<lb></lb>nioſum ſonum edens. 438 </s></p> <p type="main"> <s><emph type="center"></emph>EXPERIMENTUM NOVUM <lb></lb>MAGDEBURGICUM.<emph.end type="center"></emph.end></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 ſtabiliendum vacuum ex hoc Experimento ſumpta. 449 </s></p> <p type="main"> <s>§. IV. Argumenta ad evertendum vacuum ex eodem Experimento deprom<lb></lb>pta. 450 </s></p> <p type="main"> <s>§. V. P. Athanaſii Kircheri de novo Experimento judicium. 452 </s></p> <p type="main"> <s>§. VI. Litteræ Auctoris Experimenti, ejusdemque ad varia quæſita reſponſio. 453 </s></p> <p type="main"> <s>§. VII. Ejusdem Authoris reſponſio ad noſtrum quæſitum. 450 </s></p> <p type="main"> <s>§. VIII. P. Nicolai Zucchii è Societate Jeſu de novo Experimento judicium. 463 </s></p> <p type="main"> <s>§. IX. P. Melchioris Cornæi è Societate Jeſu de eodem Experimento judi<lb></lb>cium. 465 </s></p> <figure id="id.051.01.028.1.jpg" xlink:href="051/01/028/1.jpg"></figure> <pb xlink:href="051/01/029.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>In<emph.end type="italics"></emph.end><lb></lb>MECHANICAM HYDRAU<lb></lb>LICAM<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Odarion Encomiaſticon. </s><s><emph.end type="center"></emph.end><lb></lb><emph type="italics"></emph>CEdat ſuperbas Amphitryonides <lb></lb>Palmas Minervæ. </s><s>Vis jacet: Artium <lb></lb>Tropæa clarent. </s><s>Cuncta nutus <lb></lb>Jam Dominæ venerantur Artis. </s><s><lb></lb>Non ille noſtri temporis Hercules, <lb></lb>Qui frangit armis cornua fluminum, <lb></lb>Dum cana ſeclorum ſenectus <lb></lb>Ingeniis animis <expan abbr="q́ue">que</expan> floret. </s><s><lb></lb>Quid? </s><s>ergò Reges nè furor incitet <lb></lb>Vincire Pontum. </s><s>Nil niſi fabulam <lb></lb>Seris propinabit nepotum <lb></lb>Faſtus Achæmenidæ cachinnis. </s><lb></lb><s>Risêre ſtultas æquora compedes <lb></lb>Manare ritu certa ſuo, licet <lb></lb>Ringatur & flagro rebelles <lb></lb>Mulctet aquæ maleſanus iras. </s><lb></lb><s>Inſanientis quid Domini minæ <lb></lb>Tangunt proteruum marmor? </s><s>Herus jubet? </s><lb></lb><s>Surdeſcit, & plaudente fluctu <lb></lb>Ludificat pelagus Tyrannum. </s><lb></lb><s>At non & Artem vis Acheloia <lb></lb>Impunè ludet. </s><s>Capta ſuis Aqua <lb></lb>Technis tenetur, liberosque <lb></lb>Victa jocos, patiturque riſus.<emph.end type="italics"></emph.end> </s><s> <pb xlink:href="051/01/030.jpg"></pb><emph type="italics"></emph>Et quas domando non potuit mari <lb></lb>Sevùm fremiſcens ardor adoreas, <lb></lb>Has lenè ſolers Machinator <lb></lb>Præripuit meliore niſu. </s><s><lb></lb>Spectare geſtin? </s><s>en tibi panditur <lb></lb>Hoc ſcena libro, quâ ſtrepitu procul, <lb></lb>Quæ dulce ſit ſpectaſſe, ſpectes, <lb></lb>Quæque juvet didiciſſe, diſcas, <lb></lb>Quàm fœderatum non violabilis <lb></lb>Lex nectat orbem; ſi qua pericula <lb></lb>Vexent, ut imis ſumma, raris <lb></lb>Denſa, levi grave det ſalutem. </s><s><lb></lb>Quò pondus vndæ vergat, & aëris; <lb></lb>Quod pellat; aut quod corpora jus trahat; <lb></lb>Cur iſte gurges ructet vndas, <lb></lb>Quas avido bibit ales ore; <lb></lb>Quid mille luſus, mille jocos aquæ <lb></lb>Fundet, docebit<emph.end type="italics"></emph.end> SCHOTTVS <emph type="italics"></emph>Hydraulicæ <lb></lb>Conſultus artis, doctas idem <lb></lb>Ingenium fluitantis auræ. </s><s><lb></lb>Non Ille nomen fluctibus apprimat, <lb></lb>Quod turbet Auſter, dignus aheneis <lb></lb>Scribi columnis, quæ nec ævi <lb></lb>Dente, nec invidiæ terantur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>L. G. S. J. </s></p> <pb xlink:href="051/01/031.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>MONITIO AD LECTOREM.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s>Opuſculum hoc Appendice exceptâ Romæ <lb></lb>conſcriptum, acprælo præparatum fuit; <lb></lb>ideo in eo paſsim ita loquitur Auctor, <lb></lb>quaſi Romæ adhuc degeret. </s><s>Vale, & nè <lb></lb>quid te moretur, errores paucos in calce <lb></lb>Librinotatos, priùs corrige. </s></p> <pb xlink:href="051/01/032.jpg" pagenum="1"></pb> <figure id="id.051.01.032.1.jpg" xlink:href="051/01/032/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>MECHANICA <lb></lb>HYDRAVLICO-PNEVMATICA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PRÆLOQVIVM <lb></lb>AD LECTOREM;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De Operis Occaſione, Diviſione, <lb></lb>Inſcriptione: <expan abbr="deq́ue">deque</expan> Hydraulicorum, <lb></lb>& Pnevmaticorum Scripto<lb></lb>ribus.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>OCCASIO OPERIS.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>MAgiam Naturalem conſcribere ani-<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg1"></arrow.to.target><lb></lb><emph type="italics"></emph>mus mihi est, benevole Lector, è Viri <lb></lb>Doctiſſimi, toto〈qué〉 orbe notiſſimi Atha<lb></lb>naſij Kircheri Libris, quà typo excuſis, <lb></lb>quà exar atis manu collectam; at〈que〉 ex omnibus eius<lb></lb>dem Adverſariis ac Schediasmatis, quæ penes me <lb></lb>ſunt; nec non ex alijs probatorum Auctorum monu<lb></lb>mentis, nostris〈qué〉 inventis, fide ſummâ, pari〈qué〉 ſtudio <lb></lb>concinnatam, propriis〈qué〉 & aliorum experimentis <lb></lb>ſtabilitam: illam inquam Magiam Naturalem, cuius<emph.end type="italics"></emph.end> <pb xlink:href="051/01/033.jpg" pagenum="2"></pb><emph type="italics"></emph>in Catalogo Librorum posthàc à prædicto Doctiſſimo <lb></lb>Auctore edendorum Magneticæ Arti denuò hîc Ro<lb></lb>mæ nuper editæ appoſito feci mentionem. </s><s>Spartam <lb></lb>hanc ab ipſo Auctore mihi commiſſam præ alijs aſſum<lb></lb>pſi excolendam, quoniam præterquàm quòd omnium <lb></lb>ab ipſo conſcriptorum librorum, ſeu prælo <expan abbr="commiſſorũ">commiſſorum</expan>, <lb></lb>ſeu in Adverſaria coniectorum, copiam habeo, quo<lb></lb>tidianâ eiusdem vtor conſuetudine, vtpote inre litte<lb></lb>rariâ ſocius; cuius proinde ſententiam aut minùs <lb></lb>intellectam, aut breviùs ſubinde explicatam, exquire<lb></lb>re nullo negotio poſſum. </s><s>Opus erit ingens, multi〈qué〉 la<lb></lb>boris ac ſtudij, nec minùs reconditâ rerum cùm natu<lb></lb>ralium, tùm arte factarum refertum ſcientiâ. </s><s>Habe<lb></lb>bis in eo varia, curioſa, exotica admir andorum effe<lb></lb>ctuum ſpectacula, reconditarúmque inventionum mi<lb></lb>racula, & quæ meritò cenſebuntur magica; ab omni <lb></lb>tamen imposturâ, & illicitæ artis ſuſpicione aliena. </s><lb></lb><s>Habebis Magiam Arithmeticam; at non vulgarem: <lb></lb>Habebis Geometricam; at paucis perviam: Habebis <lb></lb>Astronomicam; at penitùs abstruſam Invenies Ma<lb></lb>giam Magneticam, Gnomonicam, Staticam, Opti<lb></lb>cam, Dioptricam, Catoptricam, Hydraulicam, Pnev-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/034.jpg" pagenum="3"></pb><emph type="italics"></emph>maticam, Pyrobolicam, <expan abbr="Harmonicã">Harmonicam</expan>, <expan abbr="Phonocampticã">Phonocampticam</expan> <lb></lb><expan abbr="Anacãpticã">Anacampticam</expan>, Anaclasticam, <expan abbr="Phyſiognomicã">Phyſiognomicam</expan>, Mecha<lb></lb>nicam, Sympathicam, Steganologicam, Cryptographi<lb></lb>cam, Divinatoriam, Cabalicam, Hieroglyphicam, <lb></lb>Sacram. </s><s>Miraberis in eodem Opere ſecreta Ani<lb></lb>malium, Herbarum, Plantarum, Lapidum, aliarúm<lb></lb>que rerum per variam activorum cum paſſivis appli<lb></lb>cationem, virtutum occultarum combinationem, Na<lb></lb>turæ & Artis connubium, Paranymphâ Experientiâ. </s><s><lb></lb>Jdeam aliquam in fine huius Operis invenies.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg1"></margin.target>Magia Na<lb></lb>turalis Au<lb></lb>ctoris.</s></p> <p type="main"> <s><emph type="italics"></emph>Quoniam verò Opus, vt dixi, vastum erit, mul<lb></lb>ti〈qué〉 laboris ac ſtudij, nec niſi ſubciſivis horis, quas <lb></lb>ordinariis occupationibus ſubtr ahere licebit, perfici<lb></lb>endum; operæ pretium me facturum, gratúmque Rei<lb></lb>publicæ Litterariæ existimavi, ſiquæ paulatim elabo<lb></lb>raſſem, per partes protruderem. </s><s>Ab Hydraulicis igi<lb></lb>tur atque Pnevmaticis initium ſumere decrevi, id〈qué〉 <lb></lb>non tàm meâ, quàm aliorum voluntate. </s><s>Scribendi <lb></lb>occaſio hæc fuit. </s><s>Est in ſupradicti Doctiſſimi Auctoris<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg2"></arrow.to.target><lb></lb><emph type="italics"></emph>Muſeo ſanè celeberrimo, frequentatiſſimóque (quod <lb></lb>brevi typis evulgabimus) non exigua <expan abbr="Hydraulicarũ">Hydraulicarum</expan> <lb></lb>ac Pnevmaticarum Machinarum copia, quas ſum-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/035.jpg" pagenum="4"></pb><emph type="italics"></emph>mâ animi voluptate ſpectant atque mirantur ij, qui <lb></lb>ex omnibus Vrbis & Orbis partibus ad ipſum viſen<lb></lb>dum accurrunt Viri Principes ac Litter ati, avidé<lb></lb>que ſcire deſiderant, & Machinarum constructa<lb></lb>rum rationes, & machinalium motionum cauſas. </s><s>Ho<lb></lb>rum deſiderìo vt ſatisfacerem, omnium dicti Muſej <lb></lb>Machinarum fabricam & quaſi anatomiam edoce<lb></lb>re, aut alicubi jam ab ipſo Auctore edoctam enarrare, <lb></lb>brevi opuſculo aggreſſus ſum. </s><s>Quod dum faciebam, <lb></lb>tam multa <expan abbr="ejusdẽ">ejusdem</expan> argumenti animo <expan abbr="calamóq;">calamóque</expan> occur<lb></lb>rebant, quæ alibi videram, legeram, excogitaveram <lb></lb>ipſe, nec vulgaria, nec injucunda, vt difficiliùs mihi <lb></lb>fuerit ſistere, quàm proſequi inceptum curſum; nec mi<lb></lb>nor in non ſeribendo, quàm in ſcribendo labor ſubeun<lb></lb>dus: multóque plurafuerunt omittenda, quàm char<lb></lb>tæ committenda, vt ſumptibus & tempori parceretur.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg2"></margin.target>Muſeum <lb></lb>Kircheria<lb></lb>num.</s></p> <p type="main"> <s><emph type="center"></emph>OPERIS DIVISIO.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Cùm verò vt in aliis ſcientiis & artibus, ita in Hydrauli<lb></lb>cis atque Pnevmaticis, vel maximè Praxis & Theoria<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg3"></arrow.to.target><lb></lb><emph type="italics"></emph>conjunctionem ita ambiant, vt vna ſi alteram deſtituat, meri<lb></lb>tò vtraque cadat; & nec ſola Praxis ſuam ſine Theoria obtine<lb></lb>at exiſtimationem, nec ſine Praxiſola ſuam Theoria; <expan abbr="vtramq́">vtramque</expan>; <lb></lb>coniungendam putavi; præſertim cùm vix vllum id hactenus <lb></lb>factitaſſe videam, <expan abbr="tuq́ue">tuque</expan> mecum perſpicies, Lector, ſievolves,<emph.end type="italics"></emph.end> <pb xlink:href="051/01/036.jpg" pagenum="5"></pb><emph type="italics"></emph>quotquot de Aquaticis ac Spiritalibus quoquo modo <expan abbr="tractârũt">tractârunt</expan> <lb></lb>Auctores, quorum Elenchum poſtea dabimus. </s><s>Plerique enim <lb></lb>nudam duntaxat tradunt Praxin, non perſcriptis, ac nè indi<lb></lb>catis quidem operandi principijs ſeu fundamentis, quæ veligno<lb></lb>rarunt ipſi, vel alijs inviderunt: quò fit, vt alijs ſæpe errandi <lb></lb>præbeant occaſionem, & ipſi <expan abbr="nõ">non</expan> rarò pudendos committant erro<lb></lb>res, vel tunc etiam, cùm aliorum errores detegere <expan abbr="atq́ue">atque</expan> corri<lb></lb>gere præſumptuoſiùs attentant. </s><s>In duas igitur partes Opus to<lb></lb>tum dividimus. </s><s>In prima theoriam damus ad omnis generis <lb></lb>Machinas Hydraulicas, Pnevmaticas, & Mixtas ex Vtris<lb></lb>que conſtruendas facilitate ſummâ, ſucceſſu infallibili. </s><s>In ſe<lb></lb>cunda fabricam docemus, & praxim exhibemus innumera<lb></lb>rum Machinarum, ſeu purè Hydraulicarum, ſeu purè <lb></lb>Pnevmaticarum, ſeu Hydro-pnevmaticarum, hoc eſt, ex v<lb></lb>tris que Mixtarum, ex traditis principijs conſtructarum, con<lb></lb>ſtruendarumvè, ad hortorum delicias, <expan abbr="domorumq́ue">domorumque</expan> vtilita<lb></lb>tes, commoditates, ornamenta, virorum præſertim Principum, <lb></lb>qui magis oculorum inde, <expan abbr="animiq́ue">animique</expan> oblectamentum, quàm rei <lb></lb>familiaris quæſtum exſpectant. </s><s>Nec oculos tantum modò pa<lb></lb>ſcere ſatagimus; auribus etiam ſua paramus delinimenta, <expan abbr="va-riaq́ue">va<lb></lb>riaque</expan> Organa atque Jnſtrumenta automata, & autophona, <lb></lb>ſolo aquarum lapſu, aëris <expan abbr="q́ue">que</expan> allapſu, in motum ac ſonum con<lb></lb>citamus, non minori facilitate, quàm arte. </s><s>Et quoniam in-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg4"></arrow.to.target><lb></lb><emph type="italics"></emph>credibilis eſt hodie, ſi unquam aliàs, neſcio an manuum, an ve<lb></lb>rò ingeniorum pruritus, motum, quem vocant perpetuum (quem <lb></lb>tot modis ac vijs <expan abbr="nõ">non</expan> pauci hactenus quæſiverunt, ſed fruſtrà, per<lb></lb>ennis quietis potiùs quàm motionis Architecti) reapſe exhibendi,<emph.end type="italics"></emph.end> <pb xlink:href="051/01/037.jpg" pagenum="6"></pb><emph type="italics"></emph>& Mundo iam dudum eius exæſtuanti deſiderio obtrudendi; <lb></lb><expan abbr="multiq́ue">multique</expan> putant, non alijs ſaciliùs Machinis quàm hydrauli<lb></lb>cis in opus deduci id poſſe; in vnum collegi <expan abbr="refutaviq́ue">refutavique</expan>, quot<lb></lb>quot videre, audire, legere potui aliorum artificia, qui eâ in re <lb></lb>ſe aliquid præſtitiſſe putarunt, aut præſtari poſſe ſibi perſuaſe<lb></lb>runt; vt visâ alieni conatus vanitate, curioſus Lector judi<lb></lb>cium ferre de alijs queat, & à ſimili vano labore ſibi temperet. </s><s><lb></lb>Tres igitur Claſſes habebit Pars ſecunda Operis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg3"></margin.target>Diviſio O<lb></lb>peris præ<lb></lb>ſentis bi<lb></lb>partita.</s></p> <p type="margin"> <s><margin.target id="marg4"></margin.target>Motus per<lb></lb>petui effi<lb></lb>ciendi pru<lb></lb>ritus mul<lb></lb>torum.</s></p> <p type="main"> <s><emph type="center"></emph>OPERIS INSCRIPTIO.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg5"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg5"></margin.target>Inſcriptio <lb></lb>operis prę<lb></lb>ſentis.</s></p> <p type="main"> <s><emph type="italics"></emph>MEchanicam porrò Hydraulico-pnevmaticam vocamus <lb></lb>hoc Opus; & Machinas Hydro pnevmaticas, ſeu Hydrau<lb></lb>lico-pnevmaticas, quas in eodem producimus, appellamus, <lb></lb>quòd pleræque tales ſint, taliumque tradantur in prima Operis <lb></lb>parte principia ac regulæ; Hydraulico-pnevmaticas, inquam, <lb></lb>quaſi dicas, Aquatico-Spiritales, hoc eſt, aqua & ſpiritu ſeu aëre<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg6"></arrow.to.target><lb></lb><emph type="italics"></emph>animatas. </s><s>Aquaticæ etenim Machinæ, hauriendis è profun<lb></lb>do, deducendis per planitiem, educendis in altum per fiſtulas ac <lb></lb>tubos<emph.end type="italics"></emph.end> (<foreign lang="grc">ἀυλοὺς</foreign> <emph type="italics"></emph>Græci appellant) aquis excogitatæ, triplicis ſunt<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg7"></arrow.to.target><lb></lb><emph type="italics"></emph>generis. </s><s>Aliæ iumentorum, hominum, ponderum ope, rotis <lb></lb>variè inter ſeſe implicatis, moventur; cuiusmodi ſunt tympa<lb></lb>na, antliæ, cochleæ, tollenones, ſimiliaque, quæ Vitruvius pro<lb></lb>ducit libro<emph.end type="italics"></emph.end> 10. <emph type="italics"></emph>Capite<emph.end type="italics"></emph.end> 9, 10, 11, 13, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 14. <emph type="italics"></emph>alijque <lb></lb>Auctores multi<emph.end type="italics"></emph.end> <arrow.to.target n="marg8"></arrow.to.target><lb></lb><emph type="italics"></emph>ad nauſeam vsque confarcinatis libris inculcant. </s><s>Aliæ ſolo aqua<lb></lb>rum lapſu fontes exhibent amœniſſimos, & aquas per ſiphones <lb></lb>tubosque variè configuratos protruſas nunc expandunt in ſub<lb></lb>tiliſſimum lucidiſſimum que velum, nunc diffundunt in radios,<emph.end type="italics"></emph.end> <pb xlink:href="051/01/038.jpg" pagenum="7"></pb><emph type="italics"></emph>figurant in ſtellas, effingunt in flores, extendunt in iacula, cri<lb></lb>ſpant in pluvias, conglobant in grandines, ſummâ oculorum <lb></lb>voluptate, vt paſſim in vrbanis ac ſuburbanis Romæ vide<lb></lb>mus hortis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg6"></margin.target>Aquaticæ <lb></lb>Machinæ <lb></lb>triphcis <expan abbr="ſũt">ſunt</expan> <lb></lb>generis.</s></p> <p type="margin"> <s><margin.target id="marg7"></margin.target>Tractoriæ.</s></p> <p type="margin"> <s><margin.target id="marg8"></margin.target>Hydrauli<lb></lb>cæ.</s></p> <p type="main"> <s><emph type="italics"></emph>Aliæ denique incluſi intruſive äeris violentiâ eiaculan-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg9"></arrow.to.target><lb></lb><emph type="italics"></emph>tur in altum aquas, inflant tibias, tubasque, volucrum ani<lb></lb>maliumque aliorum imitantur motum ac Cantum, aliaque præ<lb></lb>ſtant tam mira atque exotica, vix vt ab humano ingenio præ<lb></lb>ſtari poſſe videantur. </s><s>Eius generis fuit apud Cornelium Seve<lb></lb>rum in Ætna Triton, qui aquarum aſſultu auram concipiebat, <lb></lb>ac per buccinam ori admotam vocem edebat, ſive vt ait Poëta, <lb></lb>irriguum Carmen. </s><s>Tales etiam ſunt, quas magno numero, nec <lb></lb>minori ingenio prodit Hero in ſuo de Spiritalibus libello Machi<lb></lb>nas, ab antiquis (quos Ægyptios interpretatur Kircherus in <lb></lb>Mechanica Ægyptiaca tom.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>Oedipi parte<emph.end type="italics"></emph.end> 2.) <emph type="italics"></emph>excogitatas: <lb></lb>cuiusmodi ſunt ſtatuæ ad aras vinum & lac ſacrificantes, va<lb></lb>ſa melancoryphi vocem edentia, Syringæ mentientes vocem a<lb></lb>vicularum multarum per ordinem diſpoſitarum, quibus aſſidet <lb></lb>noctua, quæ ſua ſponte ad aviculas converſa eas terret& à <lb></lb>cantu abſterret; <expan abbr="aliæq́ue">aliæque</expan> multæ. </s><s>Tales denique, quas toto hoc <lb></lb>Opere magno numero producimus.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg9"></margin.target>Hydrauli<lb></lb>co-pnev<lb></lb>maticæ.</s></p> <p type="main"> <s><emph type="italics"></emph>Primi generis Machinas appellamus nos cum alijs Tracto<lb></lb>rias: & de illis non agimus hoc Opere; pertinent enim ad illam <lb></lb>Mechanicæ partem, quæ vi <expan abbr="ponderũ">ponderum</expan> atque rotarum ſuas perfi<lb></lb>cit operationes, & ſine ipſius principijs nec tradi, nec ab alijs <lb></lb>percipi poſſunt: quare Magiæ noſtræ Mechanicæ eas reſerva<lb></lb>mus. </s><s>Secundi generis Machinas appellamus Hydraulicas.<emph.end type="italics"></emph.end> <pb xlink:href="051/01/039.jpg" pagenum="8"></pb><emph type="italics"></emph>Tertij denique generis Hydraulico-pnevmaticas. </s><s>Quoniam <lb></lb>igitur pleræque Machinæ, quas producimus, huiuſmodi ſunt,<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg10"></arrow.to.target><lb></lb><emph type="italics"></emph>hoc eſt, aquæ & aëris ſubſidio conſtructæ; ideo Hydraulico<lb></lb>pnevmaticas, vt dicebam, appellamus hoc Opere traditas <lb></lb>Machinas. </s><s>Dico, plerasque aquæ & aëris ſubſidio eſſe con<lb></lb>ſtructas; non omnes: ſunt enim & purè hydraulicæ multæ, & <lb></lb>purè pnevmaticæ non paucæ; imò nonnullæ, quæ licet aquæ au<lb></lb>xilio fiant, hydraulicæ tamen propriè ac rigorosè, juxta ſenſum <lb></lb>expoſitum, cenſeri non poſſunt, vt videbis in Operis decurſu, <lb></lb>& ex Machinarum indice apparebit.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg10"></margin.target>Machinæ <lb></lb>huius Ope<lb></lb>ris <expan abbr="pleræq;">pleræque</expan> <lb></lb><expan abbr="ſũt">ſunt</expan> hydrau<lb></lb>lico-pnev<lb></lb>maticæ.</s></p> <p type="main"> <s><emph type="center"></emph>SCRIPTORES HYDRAVLICORVM, <lb></lb>ET PNEVMATICORVM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>SCriptores quod attinet, qui de Hydraulicis, <expan abbr="Pnevmaticis-q́ue">Pnevmaticis<lb></lb>que</expan> quoquo modo ſcripſerunt, & ad manus meas pervene<lb></lb>runt, ſunt ſequentes, Alphabeti ordine.<emph.end type="italics"></emph.end> </s><s>Archimedes, Atha<lb></lb>naſius Kircherus, Auguſtinus Ramellus, Benedictus Ca<lb></lb>ſtellus, Daniel Lipſtorpius, Daniel Schvventerus, Evan<lb></lb>geliſta Torricellus, Galilæus Galilæi, Gaſpar Ens, Ge<lb></lb>orgius Agricola, Georgius Philippus Harſtorfferus, Ge<lb></lb>orgius Valla, Hero Alexandrinus, Hieronymus Carda<lb></lb>nus, Iacobus Beſſon, Ioannes Baptiſta Porta, Ioannes Ba<lb></lb>ptiſta Balianus, Ioannes Baptiſta Aleottus, Ioannes Iaco<lb></lb>bus Weckerus, Ioannes Leurechon, Ioſephus Ceredus, <lb></lb>Ioannes Branca, Marinus Ghetaldus, Marinus Merſen<lb></lb>nus, Marius Bettinus, Nicolaus Cabæus, Petrus Herigo<lb></lb>nius, Raphaël Magiottus, Robertus Valturius, Rober- <pb xlink:href="051/01/040.jpg" pagenum="9"></pb>tus à Fluctibus, Salomon Caus, Simon Stevinus, Theo<lb></lb>dorus Muretus, Vaſſor Arabs, Vitruvius, <expan abbr="eiusq́ue">eiusque</expan> Com<lb></lb>mentatores, vt Philander, Barbarus, Cæſarinus, <expan abbr="alijq́ue">alijque</expan>. </s><s><lb></lb><emph type="italics"></emph>Hæc Auctorum nomina.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Ex his Archimedes duos perſcripſit libros<emph.end type="italics"></emph.end> <foreign lang="grc">περὶ τῶν ὀχουμένων</foreign>, <lb></lb> <arrow.to.target n="marg11"></arrow.to.target><lb></lb><emph type="italics"></emph>hoc eſt, de Inſidentibus in humido, ex quibus pauca noſtro in<lb></lb>ſerviunt propoſito. Athanaſius Kircherus Societ. Jeſu multa<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg12"></arrow.to.target><lb></lb><emph type="italics"></emph>paſſim hydraulica atque pnevmatica machinamenta inſerit ſuis <lb></lb>doctiſſimis libris, præſertim de Arte Magnetica, de Lumine & <lb></lb>Vmbra, de Conſono & Diſſono, ac noviſſimè ſuo incompara<lb></lb>bili de Ægyptiorum hieroglyphicis Operi quem Oedipum Ægy<lb></lb>ptiacuin inſcripſit: multa quoque inter eius Manuſcripta re<lb></lb>peri, <expan abbr="multaq́ue">multaque</expan> oretenus ab eodem percepi. </s><s>Auguſtinus Ra-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg13"></arrow.to.target><lb></lb><emph type="italics"></emph>mellus ingens ſcripſit Opus de Machinis Italico & Gallico idio<lb></lb>mate, <expan abbr="interq́ue">interque</expan> illas ingentem habet copiam Antliarum diverſis <lb></lb>modis conſtructarum, <expan abbr="aliasq́ue">aliasque</expan> nonnullas praxes ad elevandas <lb></lb>aquas, ſed omnes tractoriæ ſunt Machinæ ad primum pertinen<lb></lb>tes genus. </s><s>Benedictus Castellus, olim Mathematicus Pon-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg14"></arrow.to.target><lb></lb><emph type="italics"></emph>tificius, libellum compoſuit Italico idiomate de aqua cur<lb></lb>rente, ſed per alveos, aquæductus, & tubos inclinatos; quæ <lb></lb>proinde ad nos non pertinent. </s><s>Daniel Lipſtorpius Lubecenſis<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg15"></arrow.to.target><lb></lb><emph type="italics"></emph>edidit Specimina Philoſophiæ Carteſianæ, in cuius parte<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>c.<emph.end type="italics"></emph.end> 3. <lb></lb><emph type="italics"></emph>multas adducit Machinas hydraulico-pnevmaticas, easque <lb></lb>explicat ex Carteſij principijs. </s><s>Daniel Schvventerus, & Ge-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg16"></arrow.to.target><lb></lb><emph type="italics"></emph>orgius Philippus Harstorfferus Norimbergenſis Patritius, in<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg17"></arrow.to.target><lb></lb><emph type="italics"></emph>Delicijs Mathematicis multas afferunt, <expan abbr="easq́ue">easque</expan> iucundiſſimas <lb></lb>Machinas hydraulicas, & pnevmaticas. </s><s>Multas etiam in<emph.end type="italics"></emph.end> <pb xlink:href="051/01/041.jpg" pagenum="10"></pb> <arrow.to.target n="marg18"></arrow.to.target><lb></lb><emph type="italics"></emph>Thaumaturgo ſuo Mathematico adducit ex alijs Gaſpar Ens;<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg19"></arrow.to.target><lb></lb><emph type="italics"></emph>vt & Weckerus in ſuis Secretis nonnullas ex Cardano deſum-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg20"></arrow.to.target><lb></lb><emph type="italics"></emph>ptas, quas dictus Cardanus inſerit ſuis de ſubtilitate libris. </s><s>E-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg21"></arrow.to.target><lb></lb><emph type="italics"></emph>vangelista Torricellus, Magni Hetruriæ Ducis Mathemati<lb></lb>cus, & Benedicti Caſtelli diſcipulus, ſcripſit libros<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>de Motu <lb></lb>proiectorum; quorum ſecundo interſerit nonnulla de motu a<lb></lb>quarum per tubos, ſed quàm ſubtilia, tàm parum ad praxin v-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg22"></arrow.to.target><lb></lb><emph type="italics"></emph>tilia, vt ipſemet fatetur. </s><s>Galilæus Galilæi edidit Archimedem <lb></lb><expan abbr="redivivũ">redivivum</expan>, quem ex latino <expan abbr="Italicũ">Italicum</expan> fecit <expan abbr="Ioañes">Ioannes</expan> Baptista Hodierna <lb></lb>Siculus, Vir rerum Astronomicarum apprimè gnarus, & ſide<lb></lb>rum, adeoque Naturæ totius ſcrutator indefeſſus, <expan abbr="amicusq́ue">amicusque</expan> <lb></lb>ſinceriſſimus. </s><s>Opuſculum eſt ad Hydrostaticam pertinens;<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg23"></arrow.to.target><lb></lb><emph type="italics"></emph>quale etiam eſt Archimedes promotus Marini Ghetaldi; vt &<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg24"></arrow.to.target><lb></lb><emph type="italics"></emph>quæ habet Simon Stevinus; ideoque nobis nullam hîc ſuppetunt <lb></lb>materiam. </s><s>Georgius Agricola libro<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>de rebus metallicis in-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg25"></arrow.to.target><lb></lb><emph type="italics"></emph>ſerit nonnullas Machinas hydraulicas, nonnullas Robertus <lb></lb>Valturius ſuis de Militia libris, nonnullas Iacobus Beſſon Del-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg26"></arrow.to.target><lb></lb><emph type="italics"></emph>phinas ſuo de Inſtrumentis Mathematicis ac Mechanicis tracta<lb></lb>tui; ſed omnes ſunt tractoriæ, & alienæ à noſtro instituto. </s><s>Ge-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg27"></arrow.to.target><lb></lb><emph type="italics"></emph>orgius Valla Placentinus libro<emph.end type="italics"></emph.end> 15. <emph type="italics"></emph>Expetendorum & fugiendo<lb></lb>rum, qui eſt ſextus Geometriæ, ſeu Spiritalium vnicus, multas <lb></lb>habet Machinas Spiritales, ſed ad vnam omnes ex Herone Ale<lb></lb>xandrino decerptas, nè nominato quidem Herone. </s><s>Habebat <lb></lb>vir bonus, vt Ioſephus Ceredus teſtatur, Heronis librum græ<lb></lb>cum de Spiritalibus, nondum tunc à Federico Commandino, <lb></lb>aliovè Latinitati donatum, <expan abbr="putabatq́ue">putabatque</expan> ſecurè atque impunè ſe <lb></lb>poſſe in alienam meſſem mittere falcem ſuam.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/042.jpg" pagenum="11"></pb> <p type="margin"> <s><margin.target id="marg11"></margin.target>Archime<lb></lb>des.</s></p> <p type="margin"> <s><margin.target id="marg12"></margin.target>Kircherus.</s></p> <p type="margin"> <s><margin.target id="marg13"></margin.target>Ramellus.</s></p> <p type="margin"> <s><margin.target id="marg14"></margin.target>Caſtellus.</s></p> <p type="margin"> <s><margin.target id="marg15"></margin.target>Lipſtorpi'.</s></p> <p type="margin"> <s><margin.target id="marg16"></margin.target>Schvven<lb></lb>terus.</s></p> <p type="margin"> <s><margin.target id="marg17"></margin.target>Harſtorffe<lb></lb>rus.</s></p> <p type="margin"> <s><margin.target id="marg18"></margin.target>Gaſpar Ens</s></p> <p type="margin"> <s><margin.target id="marg19"></margin.target>Wecker'.</s></p> <p type="margin"> <s><margin.target id="marg20"></margin.target>Cardanus.</s></p> <p type="margin"> <s><margin.target id="marg21"></margin.target>Torricell<emph type="sup"></emph>9<emph.end type="sup"></emph.end>.</s></p> <p type="margin"> <s><margin.target id="marg22"></margin.target>Galilæus.</s></p> <p type="margin"> <s><margin.target id="marg23"></margin.target>Ghetaldus.</s></p> <p type="margin"> <s><margin.target id="marg24"></margin.target>Stevinus.</s></p> <p type="margin"> <s><margin.target id="marg25"></margin.target>Agricola.</s></p> <p type="margin"> <s><margin.target id="marg26"></margin.target>Valturius. <lb></lb>Beſſon.</s></p> <p type="margin"> <s><margin.target id="marg27"></margin.target>Valla.</s></p> <p type="main"> <s><emph type="italics"></emph>Hero Alexandrinus Auctor antiquus, græcè edidit libel-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg28"></arrow.to.target><lb></lb><emph type="italics"></emph>lum de Spiritalibus, in quo quæ ab antiquis (quos Ægyptios <lb></lb>interpretatur Kircherus, vt ſuprà dicebam) tradita in illo ge<lb></lb>nere fuêre, in ordinem redegit; & quæ ipſemet invenit, expo<lb></lb>ſuit: quæ quidem omnia pulcherrima ſunt, & ingenio plena. </s><s><lb></lb>Idem Auctor ait ſe quatuor libros conſcripſiſſe de aquaticis horo<lb></lb>ſcopijs; quos tamen temporum iniquitas nobis invidit. </s><s>De-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg29"></arrow.to.target><lb></lb><emph type="italics"></emph>ſcribit autem Hero nudam praxim, nec vllibi præcepta & regu<lb></lb>las tradit, niſi quòd in principio de vacuo agat; ideoque & <lb></lb>ipſe ſubinde errat, (ſi tamen ipſius, & non Interpretis ſunt er<lb></lb>rores) & alios in errorem inducit; nec omnia quæ promittit, <lb></lb>effectum ſortiuntur. </s><s>Eſt nihilominùs ipſe de Republica litteraria <lb></lb>egregiè meritus, & vnicus qui ex antiquis de rebus hydraulicis<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg30"></arrow.to.target><lb></lb><emph type="italics"></emph>& pnevmaticis ſua ad nos monumenta transmiſit. </s><s>Reperies <lb></lb>in hoc Opere noſtro nonnullas ex ipſo deſumptas Machinas; quas <lb></lb>ideo adducimus, quòd aliquæ indigent correctione, vtpote falſæ: <lb></lb>aliquæ explicatione, vtpote obſcuriùs traditæ; aliquæ excuſa<lb></lb>tione ac defenſione, vtpote ſiniſtrâ ab alijs cenſurâ notatæ; aliæ <lb></lb>commendatione, vtpote noſtrarum ectypa; aliæ denique ad<lb></lb>miratione, vtpote ingenio pleniſſimæ. </s><s>Heronem Latinum fe<lb></lb>cit Federicus Commandinus Vrbinas; Italicum Joannes Ba-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg31"></arrow.to.target><lb></lb><emph type="italics"></emph>ptiſta Aleottus, qui & in fine addidit quinque Problemata no<lb></lb>va, ſanè jucundiſſima, pariterque ingenioſa.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg28"></margin.target>Hero.</s></p> <p type="margin"> <s><margin.target id="marg29"></margin.target>Hero Ale<lb></lb>xandrinus <lb></lb><expan abbr="nudã">nudam</expan> pra<lb></lb>xin hydrau<lb></lb>lico-pnev<lb></lb>maticarum <lb></lb>Machina<lb></lb>rum tradit.</s></p> <p type="margin"> <s><margin.target id="marg30"></margin.target>Eius Ma<lb></lb>chinæ <expan abbr="nõ-nullæ">non<lb></lb>nullæ</expan> qua<lb></lb>re in hoc <lb></lb>Opere ad<lb></lb>ducantur.</s></p> <p type="margin"> <s><margin.target id="marg31"></margin.target>Aleottus.</s></p> <p type="main"> <s><emph type="italics"></emph>Ioannes Baptiſta Porta Neapolitanus tres latinè ſcripſit<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg32"></arrow.to.target><lb></lb><emph type="italics"></emph>egregios libellos de Spiritalibus, qui tamen peſſimum nacti ſunt <lb></lb>Interpretem Joannem Eſcrivanum Hiſpanum, qui eos Italicè <lb></lb>atque Hiſpanicè vertit; ſed cùm Italicam linguam non calleret,<emph.end type="italics"></emph.end> <pb xlink:href="051/01/043.jpg" pagenum="12"></pb><emph type="italics"></emph>mirum eſt, quàm barbarum vbique, quàm obſcurum, quàm <lb></lb>mutilum reddiderit optimum Auctorem. </s><s>Addidit nonnulla <lb></lb>de ſuo, oretenus à Porta, ſed malè intellecta, & peiùs perſcri<lb></lb>pta, itáque alienis permixta, vt diſcerni nequeant, niſi cum <lb></lb>genuino comparentur partu. </s><s>Tradit Porta Spiritalium prin<lb></lb>cipia, tradit machinamenta multa; vtraque longis experi<lb></lb>mentis, nec ſine expenſis, confirmata. </s><s>Huic ego primas inter <lb></lb>omnes Spiritalium Scriptores dandas cenſeo. </s><s>Latinum exem<lb></lb>plar Neapoli impreſſum Anno<emph.end type="italics"></emph.end> 1601. <emph type="italics"></emph>innumeris ſcatet erroribus <lb></lb>typographicis, qui ſenſum ſæpe prorſus pervertunt. </s><s>Idem Au<lb></lb>ctor lib.<emph.end type="italics"></emph.end> 18. <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 19. <emph type="italics"></emph>Magiæ Naturalis multas alias habet Machi<lb></lb>nas Hydraulicas & Pnevmaticas.<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg33"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg32"></margin.target>Porta.</s></p> <p type="margin"> <s><margin.target id="marg33"></margin.target>Balianus.</s></p> <p type="main"> <s><emph type="italics"></emph>Joannes Baptiſta Balianus Patritius Genuenſis, ſcri<lb></lb>pſit libros ſex de motu naturali gravium & liquidorum quorum <lb></lb>tres vltimi ſunt de liquidorum fluxu per canales & foramina; <lb></lb>è quorum vltimo nonnulla in Protheoriam noſtram quartam<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg34"></arrow.to.target><lb></lb><emph type="italics"></emph>derivavimus. </s><s>P. Ioannes Leurechon è Societ ate noſtra, Lo<lb></lb>tharingus ſcripſit gallico idiomate, tacito nomine ſuo, Recreatio<lb></lb>nes Mathematicas; quas deinde germanicas fecit Daniel<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg35"></arrow.to.target><lb></lb><emph type="italics"></emph>Schvventer, latinas verò Gaſpar Ens. </s><s>Ioſephus Ceredus, <lb></lb>Medicus Placentinus, ſcripſit tres egregios diſcurſus de Cochleæ <lb></lb>Archimedææ compoſitione & vtilitate, ad elevandas magnâ<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg36"></arrow.to.target><lb></lb><emph type="italics"></emph>quantitate ac facilitate aquas. </s><s>Ioannes Branca civis Roma<lb></lb>nus, & Architectus Lauretanæ domus, librum ſcripſit Italico <lb></lb>ac Latino ſermone de Machinis, quas inter multæ ſunt hydrau<lb></lb>licæ, & nonnullæ hydro-pnevmaticæ, at pleræque falſæ, & hy-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg37"></arrow.to.target><lb></lb><emph type="italics"></emph>dro-pnevmaticis principijs contrariæ. </s><s>Marinus Merſennus<emph.end type="italics"></emph.end> <pb xlink:href="051/01/044.jpg" pagenum="13"></pb><emph type="italics"></emph>ſcripſit Phœnomena hydraulica & pnevmatica, <expan abbr="multasq́ue">multasque</expan> ex<lb></lb>perientias à ſe in illa materia factas, ex quibuṡ multa deducit <lb></lb><expan abbr="doctiſſimaq́">doctiſſimaque</expan>; Theoremata atque Problemata; & nos <expan abbr="noñulla">nonnulla</expan> ex<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg38"></arrow.to.target><lb></lb><emph type="italics"></emph>ipſo inſeruimus quartæ noſtræ Protheoriæ. </s><s>Nicolaus Cabæus <lb></lb>Commentarijs ſuis in Ariſtotelis Meteora, nonnulla habet hy-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg39"></arrow.to.target><lb></lb><emph type="italics"></emph>draulica: nonnulla Marius Bettinus in Apiarijs Mathematicis <lb></lb>Apiario<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>Progymnas.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>Nonnulla denique Petrus Herigo<lb></lb>nius to.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>Curſus Mathematici tract. de Mechanica. </s><s>Raphael<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg40"></arrow.to.target><lb></lb><emph type="italics"></emph>Magiottus, Mathematicus Excellentiſſimus, Opuſculum ſcri-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg41"></arrow.to.target><lb></lb><emph type="italics"></emph>pſit Italicum de aquæ Renitentia compreſſioni; in quo tradit <lb></lb>Experimentum novum, quod nos adducimus Part.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>Claſſe<emph.end type="italics"></emph.end> 1. <lb></lb><emph type="italics"></emph>cap.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>Machina<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>Robertus à Fluctibus in ſua Philoſophia<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg42"></arrow.to.target><lb></lb><emph type="italics"></emph>Moſaica alijsq̨ Operibus, multas paſſim interſerit Machinas, a<lb></lb>liâ occaſione. </s><s>Salomon à Caus ſcripſit Gallico idiomate libros tres<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg43"></arrow.to.target><lb></lb><emph type="italics"></emph>de hydraulicis quos ipſe de viribus motricibus intitulat: Opus <lb></lb>est egregium, in eoque theoria aliqualiter cum praxi conjungi-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg44"></arrow.to.target><lb></lb><emph type="italics"></emph>tur. </s><s>Theodorus Muretus, è Societate IESV, in Pragenſi Vni<lb></lb>verſitate Mathematicæ Profeſſor, edidit Problema Mathema-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg45"></arrow.to.target><lb></lb><emph type="italics"></emph>ticum de Fontibus. </s><s>Vitruvius lib.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>Architecturæ cap.<emph.end type="italics"></emph.end> 6 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 7. <lb></lb><emph type="italics"></emph>agit de perductionibus & librationibus aquarum, & inſtrumen<lb></lb>tis ad hunc vſum; & libro<emph.end type="italics"></emph.end> 10. <emph type="italics"></emph>varia habet inſtrumenta hy<lb></lb>draulica, at pleraque tractoria. </s><s>Vaſſor Arabs habet varias<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg46"></arrow.to.target><lb></lb><emph type="italics"></emph>praxes Spiritales ad aquas in altum educendas: Liber eſt Ma<lb></lb>nuſcriptus, latinus, quem reperi inter libros P. Athanaſij Kir<lb></lb>cheri, at mutilum, & ſine figuris neceſſarijs: Suſpicor eſſe <lb></lb>fragmentum Scriptoris cuiusdam Græci antiqui, à Vaſſore in <lb></lb>Arabicam, ab alio in Latinam linguam translatum. </s><s>Edidiſ-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/045.jpg" pagenum="14"></pb><emph type="italics"></emph>ſem vnà cum hoc Opere, ſi operæ pretium me facturum judicaſ<lb></lb>ſem.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg34"></margin.target>Leurechon</s></p> <p type="margin"> <s><margin.target id="marg35"></margin.target>Ceredus.</s></p> <p type="margin"> <s><margin.target id="marg36"></margin.target>Branca.</s></p> <p type="margin"> <s><margin.target id="marg37"></margin.target>Merſennus</s></p> <p type="margin"> <s><margin.target id="marg38"></margin.target>Cabæus.</s></p> <p type="margin"> <s><margin.target id="marg39"></margin.target>Bettinus.</s></p> <p type="margin"> <s><margin.target id="marg40"></margin.target>Herigoni'</s></p> <p type="margin"> <s><margin.target id="marg41"></margin.target>Magiottus</s></p> <p type="margin"> <s><margin.target id="marg42"></margin.target>Robertus <lb></lb>a Fluctibus</s></p> <p type="margin"> <s><margin.target id="marg43"></margin.target>Salomon à <lb></lb>Caus.</s></p> <p type="margin"> <s><margin.target id="marg44"></margin.target>Muretus.</s></p> <p type="margin"> <s><margin.target id="marg45"></margin.target>Vitruvius.</s></p> <p type="margin"> <s><margin.target id="marg46"></margin.target>Vaſſor A<lb></lb>rabs.</s></p> <p type="main"> <s><emph type="italics"></emph>Hi ſunt Auctores, qui de Hydraulicis atque pnevmati<lb></lb>cis ſcripſerunt, ſeu ex profeſſo, ſeu incidenter. </s><s>Ex quibus ta<lb></lb>men, ſi Kircherum, Portam, Merſennum, aliosque nonnullos <lb></lb>excipias, pauci noſtrum triverunt iter, & vix vllus theoriam <lb></lb>cum praxi conjunxit; quod nos facimus. </s><s>Aliorum Auctorum <lb></lb>nomina, qui vnam aut alteram Machinam ſuis interſerue<lb></lb>runt Operibus, proferemus ſuis locis: Cuiusmodi ſunt Oron-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg47"></arrow.to.target><lb></lb><emph type="italics"></emph>tius Finæus, & Bonaventura Cavallerius, eximius vterque<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg48"></arrow.to.target><lb></lb><emph type="italics"></emph>Mathematicus; quorum ille in fine tractatus de Horologijs <lb></lb>vnicam habet hydraulicam Machinam; hic alteram in fine <lb></lb>Exercitationis ſextæ Geometricæ; quarum vtram<lb></lb>que nos infrà Parte<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>afferimus.<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="fig2"></arrow.to.target></s></p> <pb xlink:href="051/01/046.jpg" pagenum="15"></pb> <p type="margin"> <s><margin.target id="marg47"></margin.target>Finæus.</s></p> <p type="margin"> <s><margin.target id="marg48"></margin.target>Cavalleri'.</s></p> <figure id="id.051.01.046.1.jpg" xlink:href="051/01/046/1.jpg"></figure> <figure id="id.051.01.046.2.jpg" xlink:href="051/01/046/2.jpg"></figure> <p type="main"> <s><emph type="center"></emph>MECHANICÆ HYDRAVLI<lb></lb>CO-PNEVMATICÆ<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PARS PRIMA <lb></lb>THEORETICA,<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De Machinarum Hydraulico<lb></lb>pnevmaticarum principijs, <lb></lb>ſeu fundamentis.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROœMIVM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QUatuor reperio Machinarum Hydrau-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg49"></arrow.to.target><lb></lb><emph type="italics"></emph>lico-pnevmaticarum principia, quibus <lb></lb>ab Arte animantur in motum, illósque <lb></lb>præstant effectus, quos tantâ voluptate <lb></lb>miramur quotidie, tantâ paſſim experimur vtilita-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg50"></arrow.to.target><lb></lb><emph type="italics"></emph>te. </s><s>Primum est vis Attractiva, ad vacuum vel fu<lb></lb>giendum, velreplendum; quâ vi Aqua, elementum̨<emph.end type="italics"></emph.end> <pb xlink:href="051/01/047.jpg" pagenum="16"></pb><emph type="italics"></emph>alioquingrave, iners, lentum, & humi repens, tracta <lb></lb>accurrit non invita, vt videtur, ſuæ〈qué〉 oblita naturæ <lb></lb>in ſublime nititur, tripudianti ſimilis, vacui vel <expan abbr="replẽ-">replen-</expan><emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg51"></arrow.to.target><lb></lb><emph type="italics"></emph>di, vel impediendi causâ. </s><s>Alterum est vis expul<lb></lb>ſiva, ad corporum penetrationem fugiendam; quâ vi <lb></lb>eadem Aqua, dum aëri alterivé corpori validè in<lb></lb>cumbenticedere cogitur hoſpitio, expulſa fugam prori<lb></lb>pit eò celeriorem, excelſiorémque, quò vehementiori-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg52"></arrow.to.target><lb></lb><emph type="italics"></emph>bus ſeſtimulis agitatam ſenſerit. </s><s>Tertium est vis ‘Ra<lb></lb>refactiva; quâ obſeſſum elementum in tantas ſubin<lb></lb>de redigitur angustias, vt dum ſeſe, quâ data porta, <lb></lb>vel ſubducit, vel ingerit, alas induiſſe videatur, abje<lb></lb>ctis gravitatis propriæ compedibus. </s><s>Quartum de-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg53"></arrow.to.target><lb></lb><emph type="italics"></emph>ni〈qué〉 est gravitas Aquæ naturalis, ad decliviora loca <lb></lb>tendentis, & æquilibrium affectantis; quæ gravitas <lb></lb>non rarò (quod mirêre) in altum attollit ipſam, quam <lb></lb>paulò antè depreſſerat in profundum.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg49"></margin.target>Principia <lb></lb><expan abbr="Machinarũ">Machinarum</expan> <lb></lb><expan abbr="Hydrau-lico-pnev-maticarũ">Hydrau<lb></lb>lico-pnev<lb></lb>maticarum</expan> <lb></lb>quatuor.</s></p> <p type="margin"> <s><margin.target id="marg50"></margin.target>I. Attracti<lb></lb>va vis ad <lb></lb>vacuum <expan abbr="e-vitandũ">e<lb></lb>vitandum</expan>.</s></p> <p type="margin"> <s><margin.target id="marg51"></margin.target>II. Expulſi<lb></lb>va vis ad <lb></lb>corporum <lb></lb>penetrati<lb></lb>onem fu<lb></lb>giendam:</s></p> <p type="margin"> <s><margin.target id="marg52"></margin.target>III. Rarefa<lb></lb>ctio & con<lb></lb>denſatio, <lb></lb>aquam vel <lb></lb>expellens, <lb></lb>vel attra<lb></lb>hens.</s></p> <p type="margin"> <s><margin.target id="marg53"></margin.target>IV. Gravi<lb></lb>tas aquæ <lb></lb>æquilibri<lb></lb>um affe<lb></lb>ctantis.</s></p> <p type="main"> <s><emph type="italics"></emph>Hæc quatuor principia qui applicare ritè nove<lb></lb>rit, quaslibet ingenioſas Machinas, ad Naturæ neſcio <lb></lb>an æmulationem, an invidiamfabricari poterit faci<lb></lb>litate ſummâ, ſucceſſu infallibili; cùm nulla Machina <lb></lb>hydraulica, aut pnevmatica, aut ex vtrisque mixta<emph.end type="italics"></emph.end> <pb xlink:href="051/01/048.jpg" pagenum="17"></pb><emph type="italics"></emph>adſignari poſſit quæ non aliquâ harumfacultatum in-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg54"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtituatur. </s><s>Jmò multis par aſangis Naturæ ſuper abit co<lb></lb>natus<emph.end type="italics"></emph.end> <foreign lang="grc">ὑδρο τεχνίτης</foreign>. </s><s><emph type="italics"></emph>Natura etenim non niſi vno motus <lb></lb>principio aquas terrâ eijcit, at〈que〉 in fontes efformat, na<lb></lb>turali videlicet fluxu aquæ <expan abbr="deſcendẽtis">deſcendentis</expan> <expan abbr="primũ">primum</expan>, ac de<lb></lb>inde aſcendentis: at verò Ars non vno, ſed multiplici, <lb></lb>vt dixi, ſcilicet ſuctu ſeu attractione, preſſione, dila<lb></lb>tatione, præcipitatione: queis artibus, vel potiùs ſtra<lb></lb>tagematis, in valles, in montes, in hortos, in domos de<lb></lb>ducit, non fontes tantummodò, ſed machinamenta a<lb></lb>lia varia, jucunda, ac prorſus<emph.end type="italics"></emph.end> <foreign lang="grc">θαυμασιώτατα</foreign>, <emph type="italics"></emph>aliorum vel <lb></lb>neceſſitati, vel vtilitati, vel delectationi: Veriſſimum <lb></lb>quippe est illud Antiphontis,<emph.end type="italics"></emph.end> <foreign lang="grc">τέχνῃ γάρ χρατοῦμεν, ὧν φύσει νιχώ<lb></lb>μεθα</foreign>. </s><s><emph type="italics"></emph>At hæc ipſa quatuor hydro-pnevmaticarum <lb></lb>Machinarum principia ſeu fundamenta, antequam <lb></lb>vlteriùs progrediamur, paulô fuſiùs explicare <lb></lb>lubet, vt ſecuriùs deinde in praxi pro<lb></lb>cedamus.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/049.jpg" pagenum="18"></pb> <p type="margin"> <s><margin.target id="marg54"></margin.target>Ars vincit <lb></lb>Naturam <lb></lb>infontibus <lb></lb>producen<lb></lb>dis.</s></p> <p type="main"> <s><emph type="center"></emph>Pars I.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.049.1.jpg" xlink:href="051/01/049/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>PROTHEORIA <lb></lb>PRIMA<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De vi attractiva Corporum, ad vacuum vel <lb></lb>replendum, vel fugiendum: ſeu de primo Machi<lb></lb>narum hydro-pnevmaticarum principio.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg55"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg55"></margin.target><emph type="italics"></emph><expan abbr="Vacuũ">Vacuum</expan> Phi<lb></lb>loſophorum <lb></lb>alij admit<lb></lb>tunt, alij <lb></lb>respuunt.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>VAcuum appellat vulgus quodlibet vas, aut lo<lb></lb>cum, in quo nullum cernunt viſibile corpus, etiamſi <lb></lb>aëre ſint plena. </s><s>At Philoſophi <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> definiunt <emph type="italics"></emph>locum <lb></lb>nullo repletum corpore.<emph.end type="italics"></emph.end> </s><s>Hoc poſterius, quod <expan abbr="ſolũ">ſolum</expan> vacui <lb></lb>nomen meretur propriè, non tam inviſum Naturæ eſt viſum De<lb></lb>mocrito, Leucippo, Epicuro, alijsque, vt eliminandum penitus <lb></lb>cenſuerint è rerum cenſu. </s><s>Alij verò <expan abbr="pleriq́ue">plerique</expan> Philoſophi cum <lb></lb>Stagyrita ſuo adeo Naturæ adverſum, adeo pernicioſum exiſti<lb></lb>mant Vacuum, vt ad evitandum ipſum dicant, eandem <expan abbr="Naturã">Naturam</expan> <lb></lb><expan abbr="nullũ">nullum</expan> non movere <expan abbr="lapidẽ">lapidem</expan>, & omnia <expan abbr="ſusq;">ſusque</expan> <expan abbr="deq́ue">deque</expan> vertere corpora, <lb></lb><expan abbr="ipſaq́ue">ipſaque</expan> permiſcere elementa. </s><s>Qui de hydraulicis, <expan abbr="pnevma-ticisq́ue">pnevma<lb></lb>ticisque</expan> tractant Machinis, vnanimi conſenſu fatentur omnes </s></p> <p type="main"> <s> <arrow.to.target n="marg56"></arrow.to.target><lb></lb>(ſi Lipſtorpium cum Carteſio ſuo excipias) vim attractivam, <lb></lb>quam in Machinis nonnullis apertiſſim è elucere videmus, aliun<lb></lb>de non provenire, niſi quòd Aqua, & Aër, Naturæ obſecunda<lb></lb>turi, accurrant tracti ſeu ſponte, ſeu invitè, vel ad replendum va<lb></lb>cuum quod oderunt, vel ad impediendum quod timent. </s><s>Vtra<lb></lb>que igitur ſententia, & quæ vacuum recipit, & quæ rejicit, Hy<lb></lb>draulicorum ac Pnevmaticorum Artificibus favet; ac proinde <lb></lb>ex vtrius que placitis vis attractiva prædicta eſt explicanda. </s></p> <pb xlink:href="051/01/050.jpg" pagenum="19"></pb> <p type="margin"> <s><margin.target id="marg56"></margin.target><emph type="italics"></emph>Attractiva <lb></lb>vis ex appet<lb></lb>itu vacui <lb></lb>vel replen<lb></lb>di, vel fu<lb></lb>giendi ori<lb></lb>tur in Ma<lb></lb>chinis hy<lb></lb>dro-pnev<lb></lb>maticis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Protheoria I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Hero Alexandrinus Vacuum in aëre & aqua <lb></lb>diſseminatum agnoſcit.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HEro Alexandrinus, ſimul Spiritalium Magiſtrum agens, ſi<lb></lb> <arrow.to.target n="marg57"></arrow.to.target><lb></lb>mul Democritici, <expan abbr="Epicureiq́ue">Epicureique</expan> Philoſophi perſonam, prio<lb></lb>rem de Vacuo ſententiam doctè non minùs quàm fusè explicat, <lb></lb>atque tuetur, in Præfatione Libelli ſui de Pnevmaticis ſeu Spi<lb></lb>ritalibus, vbi ait<emph type="italics"></emph>: Alij enim vnivërsè nullum omnino vacuum eſſe <lb></lb>affirmant; alij coacervatum quidem naturâ nullum eſſe vacuum, ſed <lb></lb>ſecundùm exiguas partes diſſeminatum in aëre, humido, & igne, alijsque <lb></lb>corporibus; quibus maximè aſſentiri convenit. <emph.end type="italics"></emph.end> </s><s>Vacuum coacerva<lb></lb>tum veteres vocabant <foreign lang="grc">ἀ<gap></gap>ν</foreign>, diſſeminatum verò <foreign lang="grc">παρεσπα<gap></gap>μένον</foreign>, vt <lb></lb>notat Petrus Gaſlendus in Philoſophia Epicuri; à quo Epicuro <lb></lb> <arrow.to.target n="marg58"></arrow.to.target><lb></lb>Hero ſontentiam ſuam mutuatus eſt. </s><s><foreign lang="grc">Αλλὰ μὲν</foreign>, inquit Epicurus <lb></lb>Epiſtola ad <expan abbr="Herodotũ">Herodotum</expan>, <foreign lang="grc">καὶͅ τὸ πᾱν ἐσὶ πη̄ μέν Σω̄μα, πῃ̄ δὲ χενὸν</foreign> <emph type="italics"></emph>vniverſum <lb></lb>autem partim quidem Corpus, partim verò inane eſt.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg57"></margin.target><emph type="italics"></emph>Hero vacu<lb></lb>um admit<lb></lb>tit in aëre <lb></lb>& aqua diſ<lb></lb>ſeminatum<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg58"></margin.target><emph type="italics"></emph>Epicuriu <lb></lb>vacuum ad<lb></lb>mittit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Suam porrò de vacuo ſententiam Hero tot probat rationi<lb></lb>bus & experientijs, vt demonſtratam exiſtimet, easque dignas <lb></lb>cenſuit Marinus Merſennus, quas Hydraulicis ſuis præmitteret <lb></lb> <arrow.to.target n="marg59"></arrow.to.target><lb></lb>Phœnomenis. </s><s>Ac principio quidem oſtendit Hero. </s><s><emph type="italics"></emph>Vaſa, quæ <lb></lb>multis vacua videntur,<emph.end type="italics"></emph.end> eò quòd nullum in ijs viſibile deprehen<lb></lb>dunt Corpus, <emph type="italics"></emph>non eſſe vacua, vt putant, ſed aëre plena. <emph.end type="italics"></emph.end> </s><s>Quod<lb></lb>quidem patet ex eo, inquit Hero, quòd <emph type="italics"></emph>ſi vas, quod vacuum vide<lb></lb>tur, quis inverſum in aquam depreſſerit, rectumque ſervarit, aqua in <lb></lb>ipſum non ingredietur, quamvis totum occultatum fuerit.<emph.end type="italics"></emph.end> </s><s>Vtique <lb></lb>non alia de Cauſa, niſi quia aër, cum Corpus ſit, & totum vas <lb></lb>occupet, non permittit aquam ingredi, vt ipſemet ſubjungit. </s><s><lb></lb>Idem patetin phialis vitreis, ollis, alijsque vaſis, ſi inverſa aquis <lb></lb>immergantur: non enim niſi difficulter admodum demergun<lb></lb>tur; & dum retrahuntur, latera interiora habent ſicca; non ob <lb></lb>aliud profectò, niſi quia incluſus aër ingreſſum prohibuit aquæ. </s></p> <p type="margin"> <s><margin.target id="marg59"></margin.target><emph type="italics"></emph>Vaſa ina<lb></lb>nia aëre eſſe <lb></lb>plena, vari<lb></lb>is probatur <lb></lb>experimen<lb></lb>tis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Quòd ſi prædictorum Vaſorum inverſorum aquis immer<lb></lb>ſorum <emph type="italics"></emph>fundum quis perforet, aqua quidem per os demerſum in ipſa in<lb></lb>gredietur, aër verò per foramen exibit,<emph.end type="italics"></emph.end> adeo manifeſtè, vt non ſo- <pb xlink:href="051/01/051.jpg" pagenum="20"></pb>lùm manui admotæ ſenſum inferat, ſed etiam aures ſono de<lb></lb>mulceat, & quidem harmonico, ſi foramini aptentur fiſtulæ <lb></lb>ſono Harmonico edendo aptæ, prout ipſemet Hero fieri <lb></lb>jubet in multis, quas deſcribit in citato Libello, hydraulicis at<lb></lb>que pnevmaticis Machinis. </s><s>Quod etiam quotidie experimur <lb></lb>in Hortis Romanis, Tuſculanis, Tiburtinis, & in ipſo etiam <lb></lb>P. Athanaſij Kircheri muſeo. </s><s><emph type="italics"></emph>Non igitur arbitrandum eſt,<emph.end type="italics"></emph.end> infert <lb></lb>Hero, <emph type="italics"></emph>in his quæſunt, vacui naturam quandam coacervatam ipſam per<lb></lb>ſe ipſam exiſtere ſed ſecundùm exiguas partes in aëre, & humido, alijsque <lb></lb>corporibus diſſeminatam,<emph.end type="italics"></emph.end> etiam in ipſo adamante, duriſſimo licet, <lb></lb>denſiſſimoque, <emph type="italics"></emph>quippe qui neque igniri, neque rumpi poteſt, & percuſ<lb></lb> <arrow.to.target n="marg60"></arrow.to.target><lb></lb>ſus in incudes & malleos totus ingreditur<emph.end type="italics"></emph.end> (vt cum Plinio putat Hero; <lb></lb>quod tamen, Merſenno teſte, experientiæ repugnat, nam ictu <lb></lb>mallei in varias partes diſſilit, & ita poteſt igniri, vt pereat.) </s><s><emph type="italics"></emph>) Hoc <lb></lb><expan abbr="autẽ">autem</expan> ipſiaccidit,<emph.end type="italics"></emph.end> ſubiungit Hero, <emph type="italics"></emph>non quòd vacuo careat, ſed ob conti<lb></lb>nuatam denſitatem.<emph.end type="italics"></emph.end> </s><s>Corpora porro illa (aëris præſertim) quæ <lb></lb>partes ſuas habent inter ſeſe cohærentes, <emph type="italics"></emph>non|tamen ex omni parte, <lb></lb>ſed interiecta habent inter valla quædam vacua,<emph.end type="italics"></emph.end> (quæ vacuola appel<lb></lb>lat Merſennus) bellè comparat Hero arenarum cumulo, inter <lb></lb> <arrow.to.target n="marg61"></arrow.to.target><lb></lb>cuius grana multæ aëris particulæ intercedunt; aitque, arenæ par<lb></lb>ticulas particulis aëris ſimiles eſſe, <expan abbr="aërẽ">aërem</expan> verò, qui inter arenas in<lb></lb>terjicitur, ſimilem vacuolis intra aërem contentis; quæ quidem <lb></lb>vocuola tunc diſinere putat in aëre (alijsque corporibus) cùm <lb></lb>accedente vi quapiam condenſatur aër; redire verò, cùm facta <lb></lb>remiſſione in priſtinum ordinem reſtituitur aër ob naturalem <lb></lb>contentionem, quâ, velut arcus inflexus, aut ſicca ſpongia vi <lb></lb>preſſa, molem ab ipſo rerum conditu ſibi tributam repetit, ſta<lb></lb> <arrow.to.target n="marg62"></arrow.to.target><lb></lb>tim atque vis externa deſinit. </s><s><emph type="italics"></emph>At aëris corpora,<emph.end type="italics"></emph.end> inquit Hero, <emph type="italics"></emph>inter<lb></lb>ſeſe quidem cohærent, non tamen ex omni parte, ſedinteriecta habent <lb></lb>intervalla quædam vacua, ſicut arena, quæ eſt in littoribus. </s><s>Itaque a<lb></lb>nimo concipiendum eſt, arenæ particulas corporibus aëris ſimiles eſſe, aë<lb></lb>rem vero, qui inter particulas arenæ interiicitur, ſimilem vacuis intra <lb></lb>aërem contentis. </s><s>Quamobrem vi quadam accedente äerem denſari con<lb></lb>tingit, & in vacuorum loca reſidere, corporibus præter naturam inter<lb></lb>ſeſe compreſſis: remiſsione verò factârarſus in cun dem ordinem reſtitui-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/052.jpg" pagenum="21"></pb><emph type="italics"></emph>tur, ob naturalem Corporum contentionem; quemadmodum & in cor<lb></lb>nuum ramentis, & in ſpongiis ſiccis, quæſi compreſſa remittantur, rur<lb></lb>ſus in cundem locum redeunt, eandem que accipiunt molem. </s><s>Similiter <lb></lb>ſi aliqua vi aëris particulæ à ſe in vicem diſtractæ fuerint, & maior præ<lb></lb>ter naturam locus vacuus fiat, rurſus ad ſeſe recurrunt, per vacuum e<lb></lb>nim celerem corporum lationem fieri contingit, nullo obſtunte, aut re<lb></lb>pellente, quóusque corpora ad ſeſe applicentur.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg60"></margin.target>Adamas i<lb></lb>gni & mal<lb></lb>len cedit.</s></p> <p type="margin"> <s><margin.target id="marg61"></margin.target><emph type="italics"></emph>Vacuola He<lb></lb>ronis inter <lb></lb>aëris parti<lb></lb>culas deſſe<lb></lb>minata.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg62"></margin.target><emph type="italics"></emph>Aër interie<lb></lb>cta habens <lb></lb>vacua <expan abbr="ſecũ-dùm">ſecun<lb></lb>dùm</expan> Hero<lb></lb>nem compa<lb></lb>ratur are<lb></lb>næ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Experimenta quibus Hero vacuum in Corpo<lb></lb>ribus diſſeminatum probat.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg63"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg63"></margin.target><emph type="italics"></emph>Argumeta <lb></lb>Heronis pro <lb></lb>vacuo.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>HIs præmiſſis, multa, & paſſim obvia adducit experimenta </s></p> <p type="main"> <s> <arrow.to.target n="marg64"></arrow.to.target><lb></lb>Hero, quibus probat dari vacuum inter corporum, aëris præ<lb></lb>ſertim, particulas diſſeminatum; & aquam, <expan abbr="aliaq́ue">aliaque</expan> corpora ad <lb></lb>illud replendum, ſi nimiùm diſtrahantur particulæ vi externâ, ac<lb></lb>currere attracta; atque adeo vim attractivam, quam primum <lb></lb>hydropnevmaticarum Machinarum principium eſſe diximus, <lb></lb>tribuit Vacuo inter corpora diſſeminato. </s></p> <p type="margin"> <s><margin.target id="marg64"></margin.target><emph type="italics"></emph>Vacuum in <lb></lb>corporibus <lb></lb><expan abbr="diſſeminatũ">diſſeminatum</expan> <lb></lb>experimen<lb></lb>tis probat <lb></lb>Hero.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Primò enim, <emph type="italics"></emph>ſi quis vas leviſſimum & anguſti oris aſſumens, <lb></lb> <arrow.to.target n="marg65"></arrow.to.target><lb></lb>atque ori admovens aërem exſuxerit, dimiſerit〈que〉; ex labiis ſtatim vas <lb></lb>appendetur, vacuo carnem attrahente, vt locus exinanitus repleatur.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg65"></margin.target>Vaſa exſu<lb></lb>cto aëre <expan abbr="la-biorũ">la<lb></lb>biorum</expan> car<lb></lb>nes attra<lb></lb>hunt.</s></p> <p type="main"> <s>Secundò. <emph type="italics"></emph>Ova medica, quæ ex vitro conſtant, & anguſti ſunt <lb></lb>oris, quando volunt humido replere, exſugentes ore aërem, qui in ipſis <lb></lb> <arrow.to.target n="marg66"></arrow.to.target><lb></lb>continetur, oſculumque digito comprehendentes, in humidum in ver<lb></lb>tunt, & digito remiſſo in locum exin anitum attrahitur aqua, atque id<lb></lb>ipſum humidum præter naturam ſurſum fertur.<emph.end type="italics"></emph.end> </s><s>Idem contingit in <lb></lb>Siphonibus, qui exſucto aëre humidum è vaſis hauriunt, vt quo<lb></lb>tidiana docet experientia, & dicemus fusè infrà Protheoria 4. <lb></lb>Cap. 2. </s><s>Idem in multis Machinis hydraulicis, aut pnevmaticis e<lb></lb>venit, vt ſuo loco videbimus. </s></p> <p type="margin"> <s><margin.target id="marg66"></margin.target>Ova medi<lb></lb>ca quomodo <lb></lb>repleantur <lb></lb>aquá.</s></p> <p type="main"> <s>Tertò, Cucurbitæ à Chirurgis igni priùs admotæ, vt aêr <lb></lb> <arrow.to.target n="marg67"></arrow.to.target><lb></lb>in ipſis contentus rarefiat, dum corpori applicantur, <emph type="italics"></emph>non ſolùm <lb></lb>non excidunt, manifeſtam gravitatem habentes, ſed adiacentem ma<lb></lb>teriam per corporis raritates attrahunt, eandem ob cauſam,<emph.end type="italics"></emph.end> vt ſcilicet <pb xlink:href="051/01/053.jpg" pagenum="22"></pb>locus exinanitus repleatur: <emph type="italics"></emph>iniectus enim ignis,<emph.end type="italics"></emph.end> ſubjungit Hero, <lb></lb><emph type="italics"></emph>corrumpit & extenuat aërem, qui in ipſis continetur,<emph.end type="italics"></emph.end> ideoque relin<lb></lb>quitur in ipſis vacuum; <emph type="italics"></emph>cùm verò cucurbitula reſpiraverit; aër in e<lb></lb>vacuatum locum ſuccedit, materiânon ampliùs attractâ,<emph.end type="italics"></emph.end> <expan abbr="deciditq́ue">deciditque</expan> <lb></lb>cucurbitula. <lb></lb> <arrow.to.target n="marg68"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg67"></margin.target><emph type="italics"></emph>Cucurbitu<lb></lb>la cur car<lb></lb>nem attra<lb></lb>hant.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg68"></margin.target><emph type="italics"></emph>Sphæra con<lb></lb>cava, & aë<lb></lb>re plena, cur <lb></lb>plùs aeris <lb></lb>per inflatio<lb></lb>nem recipi<lb></lb>at <expan abbr="ſecundũ">ſecundum</expan> <lb></lb>Heronem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Quartò, <emph type="italics"></emph>conſtruatur Sphæra craſſitudinem habens laminæ, vt nè <lb></lb>facilè rumpatur, continensque circiter cotylas octo, & vndique præclu<lb></lb>ſa;<emph.end type="italics"></emph.end> & per foramen in ipſa factum immittamus <emph type="italics"></emph>Siphonem æreum, <lb></lb>hoc eſt, tubum gracilem, non contingentem locum, qui puncto perfora<lb></lb>to ſecundùm diametrum opponitur, ita vt aqua fluere poſſit; alia autem <lb></lb>ipſius pars extra ſphæram emineat circiter digitos tres, ipſi〈qué〉 diligenter <lb></lb>adferruminetur, ambitu foraminis circa tubum ſtanno præcluſo, vt cùm <lb></lb>volumus ore per ſiphonem inflare, ſpiritus ex ſphærâ nullo modo excidat.<emph.end type="italics"></emph.end><lb></lb> </s><s>His factis,, <emph type="italics"></emph>inſpiciamus quæ contingunt. </s><s>Aëre enim in ipſa exiſtente<emph.end type="italics"></emph.end><lb></lb>(quemadmodum & in aliis vaſis quæ vacua appellantur) <emph type="italics"></emph>totum<lb></lb>que qui in ipsa locum replente, & per continuationem quandam ad eius <lb></lb>ambitum applicato, nullo denique loco, ut arbitrantur, penitus exiſten<lb></lb>te vacuo; neque aquam immittere poſſemus, neque alium aërem, non <lb></lb>excedente priori aëre qui in ipsa erat; & ſi multa vi immiſſionem facia<lb></lb>mus, priùs diſrumpetur vas, quàm aliquid ſuſcipiat, cùm plenum ſit: ne<lb></lb>que enim aëris corpora in minorem magnitudinem contrahi poſſunt: <lb></lb>quare neceſſe erit, vt in ſeipſis habeant quædam intervalla, in quæ com<lb></lb>preſſa minorem obtineant molem; hoc autem veriſimile non eſt, nullo <lb></lb>penitus exiſtente vacuo: & cùm corpora ad ſeſe applicentur ſecundùm <lb></lb>omnes ſuperficies, & ſimiliter ad vaſis ambitum, non poſſunt expulſa lo<lb></lb>cum alicui facere, non exiſtente vacuo aliquo, quamobrem nullo modo <lb></lb>in ſphæram immittetur aliquid eorum, quæ ſunt extra, niſi excedat ali<lb></lb>qua pars aëris priùs in ea contenti, ſiquidem totus locus conſtipatus est, <lb></lb>& continuatus, vt arbitrantur. </s><s>At<emph.end type="italics"></emph.end> experientiâ conſtat contrari<lb></lb>um: nam <emph type="italics"></emph>ſi quis ſiphonem ori admovens ſphæraminflet, multum im<lb></lb>mittit ſpiritum, non excedente aëre, qui in ea eſt. </s><s>Quod cùm ita ſem<lb></lb>per contingat; manifeſtò oſtenditur, <expan abbr="contractionẽ">contractionem</expan> fieri <expan abbr="corporũ">corporum</expan> in ſphæra <lb></lb>exiſtentium in vacua implicata: contractio autem præter naturam fit, <lb></lb>ob immiſſionis violentiam. </s><s>Si igitur aliquis inflans, & ad ipſum os ma<lb></lb>num apponens, ſtatim digito ſiphonem obturet; manebit omni tempore<emph.end type="italics"></emph.end> <pb xlink:href="051/01/054.jpg" pagenum="23"></pb><emph type="italics"></emph>conſtipatus aër in ſphæra: quodſi quis aperiat, rurſus extra erumpet cum <lb></lb>magno ſtrepitu & clamore immiſſus aër, propterea quòd, vt propoſuimus, <lb></lb>expellitur à dilatatione præexiſtentis aëris impetu quodam factâ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Quintò, <emph type="italics"></emph>ſi quis velit aërem, qui in Sphæra eſt, per ſiphonem at</s></p> <p type="main"> <s> <arrow.to.target n="marg69"></arrow.to.target><lb></lb>trahere, magna copia conſequetur, nullâ aliâſubſtantiâ in ſphæram ſuc<lb></lb>cedente, quemadmodum in ovo antè dictum eſt. </s><s>Quare ex hoc per ſpi<lb></lb>cuè oſtenditur, magnam vacui coacervationem in ſphæra factam eſſe: <lb></lb>non enim aëris corpora, quærelinquuntur eo tempore, maiora fieri poſ<lb></lb>ſunt, ita vt expulſorum corporum locum repleant: namſi augerentur, <lb></lb>cùm nulla ipſis ſubſtantia extrinſecus accedat, veriſimile eſſet, augmen<lb></lb>tum fieri per rarefactionem; hoc autem eſſet implicatio ſecundùm eva<lb></lb>cuationem; ſed vacuum nullum eſſe dicunt; non igitur augebuntur Cor<lb></lb>pora; neque enim aliud augmentum ipſis accidere mente concipi poteſt. </s><s><lb></lb>Ex quibus per ſpicuum eſt, in aëris corporibus diſſeminata eſſe quædam <lb></lb>vacua intermedia, & vi quadam adveniente ea præter naturam in va<lb></lb>cua reclinare.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg69"></margin.target>Sphæra con <lb></lb>cava exſu<lb></lb>cto aëre, va<lb></lb>cua conti<lb></lb>net inter<lb></lb>valla <expan abbr="ſecũ-dum">ſecun<lb></lb>dum</expan> Hero<lb></lb>nem.</s></p> <p type="main"> <s>Sextò, <emph type="italics"></emph>vacuis non exiſtentibus, neque per aquam, neque per <lb></lb> <arrow.to.target n="marg70"></arrow.to.target><lb></lb>aërem, neque per aliud corpus vllum poſſet lumen tranfire, aut calidit as, <lb></lb>aut alia potentia<emph.end type="italics"></emph.end> ſeu qualitas <emph type="italics"></emph>corporea. </s><s>Nam quomodo radij ſolares <lb></lb>per aquam in fundam vaſis penetrarent? </s><s>Si enim aqua non haberet <lb></lb>poros, ſed radij aquam vi ſcinderent, contingeret vasa plena ſuperfun<lb></lb>di; quod fieri non videmus: Ad hæc ſi aquam vi ſcinderent, non vti<lb></lb>que radiorum alij adſuperiorem locum frangerentur, alij deorſum cade<lb></lb>rent: nunc autem quicunque aquæ particulis occurrunt, franguntur ad <lb></lb>ſuperiorem locum; quicunque verò incidunt in aquæ vacua, paucis par<lb></lb>ticulis occurrentes in vaſis fundum pervadunt.<emph.end type="italics"></emph.end> </s><s>Adde quòd ſi nulla <lb></lb>eſſent in corporibus vacua, nullum corpus per alia corpora tran<lb></lb>ſire poſſet: quod tamen oleis contingit, quorum aliqua tam ſub<lb></lb>tilia, ſunt vt omnia metalla, <expan abbr="ipſumq́">ipſumque</expan>; <expan abbr="etiã">etiam</expan> vitrum penetrent. </s><s>Idem <lb></lb>etiam fieri ab igne, nemo neſcit, qui ferrum, aurum, & vitrum <lb></lb>candentia vidit. </s><s>Idem præterea à virtute magnetica fieri, quo<lb></lb>tidie experimur. <lb></lb> <arrow.to.target n="marg71"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg70"></margin.target>Corpora & <lb></lb>qualitates <lb></lb>corporeæ, pe<lb></lb>netrant a<lb></lb>lia corpora, <lb></lb>ſecundùm <lb></lb>Heronem, <lb></lb>propter va<lb></lb>cua interie<lb></lb>cta.</s></p> <p type="margin"> <s><margin.target id="marg71"></margin.target><emph type="italics"></emph>Vinum mi<lb></lb>ſcetur aquæ <lb></lb>ob intesſper <lb></lb>ſa vacua <lb></lb>juxta He<lb></lb>ronem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Septimò, <emph type="italics"></emph>Vinum in aquam iniectum videtur ſecundùm fuſio<lb></lb>nem quandam per totum aquæ locum per meare; quod non fieret, niſi va<lb></lb>cua aquæ ineſſent. </s><s>Lumen quoque alterum per alterum fertur: nam<emph.end type="italics"></emph.end> <pb xlink:href="051/01/055.jpg" pagenum="24"></pb><emph type="italics"></emph>cùm plures lucernas quis accenderit, omnia magis illuſtr abuntur, ijsdem <lb></lb>quoquò verſus per ſe invicem penetrantibus. </s><s>Sed & per æs, per ferrum, <lb></lb>& per alia corpora omnia penetratio fit; quemadmodum & quod in tor<lb></lb>pedine marina contingit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg72"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg72"></margin.target><emph type="italics"></emph>Argumen<lb></lb>ta aliorum <lb></lb>pro vacuo.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Hæ ſunt rationes Heronis, quibus probat. </s><s><emph type="italics"></emph>omne corpus ex <lb></lb>tenuibus conſtare corporibus, inter quæſunt vacua diſſeminata particulis <lb></lb>minora.<emph.end type="italics"></emph.end> </s><s>Quibus addi poteſt vlteriùs, quòd eadem vacuola vi<lb></lb>dentur admittenda inter aquæ partes frigore conſtrictas in gla<lb></lb>ciem: etenim aqua in congelatione ad maius intervallum occu<lb></lb>pandum extenditur; vaſa enim licet benè compacta, ſià ſinu <lb></lb>latiori in anguſtum aſſurgant, & repleantur aquâ ad maximam il<lb></lb>lam latitudinem, vel vltra; in congelatione diffringuntur: non <lb></lb>ſic, ſi infra illam latitudinem repleantur, vtdilatationi <expan abbr="ſpatiũ">ſpatium</expan> de<lb></lb>tur. </s><s>In maioribus etiam vaſis, ſed recurvo intus labro, validius <lb></lb>reſiſtentibus, ipſa glacies curvatur, ſurſum ſecundùm convexum <lb></lb>elevata. </s><s>Omnis etiam glacies aquæ iniecta ſupernatat. Dila<lb></lb>tatur ergo in congelatione aqua, & vacuitates parvas intus ha<lb></lb>bet. </s></p> <p type="main"> <s>Addi præterea in confirmationem dictorum poteſt duplex <lb></lb>Experimentum, vnum argenti vivi, alterum aquæ tubo inclusæ; <lb></lb>de quibus agemus infrà Claſse 1. cap. 6. Machina 7. </s><s>Item expe<lb></lb>rimentum Thermoſcopij, de quo ibidem cap. 3. Mach 3. </s></p> <p type="main"> <s> <arrow.to.target n="marg73"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg73"></margin.target><emph type="italics"></emph>Vis attra<lb></lb>ctiva quo<lb></lb>modo ab He<lb></lb>rone expli<lb></lb>cetur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Ex his alijsque argumentis atque experimentis, quæ vide<lb></lb>ri poſſunt apud alios, præſertim Neotericos <expan abbr="noñullos">nonnullos</expan>, <expan abbr="cõſtare">conſtare</expan> po<lb></lb>teſt, quomodoex Heronis & <expan abbr="eorũ">eorum</expan> ſententia, qui <expan abbr="vacuũ">vacuum</expan> admittunt, <lb></lb>Natura adnitatur trahere alia corpora, aquam præſertim & aë<lb></lb>rem, ad vacuum replendum, quod vi extrinſeca præter naturam <lb></lb>eſt alicubi coacervatum; & quomodo corporibus omnibus in<lb></lb>ſit vis quædam attractiva, vt repleant vacuum illud; ac denique <lb></lb>quomodo vis attractiva corporum, aquæ inquam & aëris, cauſa <lb></lb>eſſe poſſit ac principium Machinarum hydro-pnev<lb></lb>maticarum. </s><s>Lege Heronis Spiritalia. </s></p> <pb xlink:href="051/01/056.jpg" pagenum="25"></pb> <p type="main"> <s><emph type="center"></emph>§. III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Experimenta quibus vacuum nullum eſſe <lb></lb>probatur<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HIs tamen non obſtantibus, communior & ſanior Philoſo</s></p> <p type="main"> <s> <arrow.to.target n="marg74"></arrow.to.target><lb></lb>phorum Veterum ac Recentiorum ſenſus eſt, nullum in re<lb></lb>rum natura vacuum eſſe, neque coacervatum in vnum, neque <lb></lb>diſſeminatum inter partes corporum diſciſſas; & neque ſpontè <lb></lb>ortum, neque productum violenter; adeoque corporum tra<lb></lb>ctionem, quæ in allatis Experimentis elucet, non fieri ad replen<lb></lb>dum vacuum, quod nullibi ſt, neque eſſe poteſt; ſed ad impe<lb></lb>diendam, quam Natura tantopere abhorret, inanitatem. </s><s>Sua<lb></lb>dent hæc tum experientia Philoſophiæ Magiſtra, tum rationes. </s><s><lb></lb>Experientias adducam paucas ex multis; rationes apud alios <lb></lb>leges. </s></p> <p type="margin"> <s><margin.target id="marg74"></margin.target><emph type="italics"></emph>Argumen<lb></lb>ta contra <lb></lb>vacuum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Primò, Latera follium, ſi arctè conſtricta ſint, & inter ſe <lb></lb> <arrow.to.target n="marg75"></arrow.to.target><lb></lb>contigua, nulla vi diduci poſſunt, etiam Angelica, ſi obturetur <lb></lb>orificium, per quod aër inter iectum inter diducenda latera ſpa<lb></lb>tium occupaturus ſubeat. </s><s>Cur hoc, niſi quia vacuum dari non <lb></lb>poteſt? </s><s>quod tamen dari deberet, ſi occluſo orificio aër, & <lb></lb>quodcunque aliud corpus ſubiturum excluderetur, & tamen la<lb></lb>tera diducerentur. </s><s>Eâdem de cauſa duæ tabulæ planiſſimæ, <lb></lb> <arrow.to.target n="marg76"></arrow.to.target><lb></lb>& ſibi mutuò ſecundùm planitiem cohærentes, divelli non poſ<lb></lb>ſunt, ſi ita tentetur divulſio, vt aër aut aliud corpus inter ſuper<lb></lb>ficies ſubintrare tempeſtivè non poſſit. </s><s><emph type="italics"></emph>Iuveni lacertorum ſuorum <lb></lb>robur iactanti<emph.end type="italics"></emph.end> (inquit P. Nicolaus Zucchius in ſua de vacuo do<lb></lb>ctiſſima Diatribe) <emph type="italics"></emph>propoſita-ſemel eſt lamina ærea per anſam in me<lb></lb>dio extantem apprehenſam elevanda è tabula marmorea, cui optimè con<lb></lb>gruebat: qui primò tanquam rem ludicram puero committendam con<lb></lb>tempſit: tum inſtantibus amicis manum vtramque admovens, cùm lu<lb></lb>ctatus diu hærentem non removiſſet, excuſavit impotentiam, obiectâ <lb></lb>peregrini & potentiſſimi glutinis interpoſitione, quo fortiſſimè copulan<lb></lb>te nequiret divelli; donec vidit ab alio per tabulam facillimè laminam <lb></lb>deduci, & ad extrema productam, & actam in transverſum, inde de<lb></lb>portari.<emph.end type="italics"></emph.end> </s><s>Paſſim etiam experimur, dum duo corpora ſecundùm <pb xlink:href="051/01/057.jpg" pagenum="26"></pb>planas ſuperficies coniuncta ſunt, vt vnum illorum elevatur, ſe<lb></lb>qui etiam alterum, quantumvis grave, atque in aëre libero ve<lb></lb>luti ſuſpenſum hærere. </s></p> <p type="margin"> <s><margin.target id="marg75"></margin.target><emph type="italics"></emph>Latera fol<lb></lb>lium diauci <lb></lb>non poſſunt, <lb></lb>ore occluſe, <lb></lb>ob metum <lb></lb>vacus.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg76"></margin.target><emph type="italics"></emph>Tabulæ pla<lb></lb>næ metu va<lb></lb>cui divelli <lb></lb>non poſſunt.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Secundò, Si vas vitreum aquæ immergas atque impleas & <lb></lb> <arrow.to.target n="marg77"></arrow.to.target><lb></lb>deinde intra aquam invertas, vt patens os deorſum vergat, tum <lb></lb>æqualiter ita inverſum eleves, & extrahere tentes; ſpectabis a<lb></lb>quam illo incluſam ſurſum intra illud ſimul attolli; & ſi vas illud <lb></lb>ex parte iam extractum, & ex parte adhuc immerſum, manu ſu<lb></lb>ſtineas, videbis etiam aquam incluſam in illo perſiſtere ſic eleva<lb></lb>tam ſupra ambientis aquæ ſuperficiem æquilibratam, & ſuo et<lb></lb>iam pondere manum ſuſtinentis aggravare. </s><s>Cur hoc? </s><s>Quia <lb></lb>non poteſt aër ſuccedere ad occupandum locum inter aquam <lb></lb>deſcendentem, & partes vaſis, quæ aquâ deſcendente deſere<lb></lb>rentur. </s><s>Idem continget in quolibet alio vaſe, ſed in vitreo et<lb></lb>iam oculis patebit experimentum. </s><s>Quòd ſi in fundo vaſis fora<lb></lb>men aliquod ſit clauſum, vt poſſit aperiri; eo aperto, & aëre li<lb></lb>berè ſubintrante, aqua intra vas ſuſpenſum deſcendet, & deſi<lb></lb>net gravare manum. <lb></lb> <arrow.to.target n="marg78"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg77"></margin.target><emph type="italics"></emph>Vas inver<lb></lb>ſum difficul<lb></lb>ter extrahi<lb></lb>tur ex aqua <lb></lb>ob vacui <lb></lb>metum.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg78"></margin.target><emph type="italics"></emph>Vaſa ſubtus <lb></lb>pertuſa, ſu<lb></lb>periùs occlu<lb></lb>ſa, aquam <lb></lb>retinent va<lb></lb>uí metu.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Tertiò, In vaſis ad irrigandos hortos paſſim adhiberi ſoli<lb></lb>tis (cuiuſmodi proponimus infrà Claſs. 1. cap. 6. Mach 2, & Cri<lb></lb>brum Veſtalium vocamus) licet fundum ipſorum ſit perforatum, <lb></lb>& multis foraminibus pervium, dum aquâ plena, æqualiter ele<lb></lb>vantur in libero aëre, aqua non defluit, quàm diu digitus fora<lb></lb>mini illorum ſupernè in collo patenti adpreſſus non permittit in<lb></lb>greſſum aëri ad replendum locum, qui, ſi deflueret aqua, relin<lb></lb>queretur inter ſuperiorem vaſis ſuperficiem, & defluentem a<lb></lb>quam. </s><s>Et in tali conſiſtentia permanente aquâ intra vas, tan<lb></lb>tum gravat, & deorſum nititur aqua, quantum ſi fundo integro <lb></lb>& collo aperto, ſimul cum vaſe ſuſtineretur. </s><s>Remoto verò di<lb></lb>gito, & permiſſo ingreſſu aëri per ſuperius foramen, ſtatim de<lb></lb>fluit aqua ex fundi foraminibus. </s><s>Quòd ſi in medio defluxu ite<lb></lb>rum appoſito digito foramen obſtruatur, pendet iterum aqua, <lb></lb>contra inclinacionem ſuæ gravitatis, tunc etiam manum gra<lb></lb>vantis, nec defluit in apertum aërem. </s></p> <pb xlink:href="051/01/058.jpg" pagenum="27"></pb> <p type="main"> <s>Quartò, Si fiſtulæ vnam extremitatem aquæ immergas, </s></p> <p type="main"> <s> <arrow.to.target n="marg79"></arrow.to.target><lb></lb>ex altera ori admota aërem exſugas, elevatur confeſtim aqua, <lb></lb>ſualicet gravitate reluctans, poſt aërem extractum ad os exſu<lb></lb>gentis; vtique nè detur vacuum in fiſtula exſucto aêre. </s></p> <p type="margin"> <s><margin.target id="marg79"></margin.target><emph type="italics"></emph>Fiſtula ex<lb></lb>ſucto aëre <expan abbr="a-quã">a<lb></lb>quam</expan> recipit <lb></lb>vacui metu<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Quintò, Si phialam cupream firmis lateribus compactam, <lb></lb> <arrow.to.target n="marg80"></arrow.to.target><lb></lb>nè facilè rumpatur, igni admotam calefacias, vt aër intus con<lb></lb>tentus vehementer rarefiat, eamque deinde frigidæ immergas, <lb></lb>vt aër phialæ à violenta rarefactione ſe recolligens condenſetur, <lb></lb>& minorem occupet locum; intus attrahitur aqua, dum alius <lb></lb>aër in locum <expan abbr="relinquendũ">relinquendum</expan> ſuccedere non poteſt, ne ſcilicet detur <lb></lb>vacuum in phiala. </s><s>Sic ſi ex fiſtula, cuius vnum orificium occlu<lb></lb> <arrow.to.target n="marg81"></arrow.to.target><lb></lb>ſum, alterum apertum, aut ex clave fœminea benè compacta, <lb></lb>exſugas fortiter & continuato tractu aërem, & ceſſante ſuctione <lb></lb>ſtatim apponas fiſtulæ orificio patenti digitum aut labrum, nè <lb></lb>ſuccedat ambiens aër; attrahitur intra fiſtulam, aut clavem, <lb></lb>caro digiti aut labri, vt notabiliter vellicet, & de carne depende<lb></lb>at. </s><s>Non alia de cauſa, niſi quia durante exſuctione rarefit rema<lb></lb>nens intus aër, & violenter <expan abbr="totũ">totum</expan> illud ſpatium ſolus implet; ceſ<lb></lb>ſante verò ſuctu recolligit ſe à violenta rarefactione, & <expan abbr="minorẽ">minorem</expan> <lb></lb>locum occupans advocat aliud, quod ipſi proximum eſt, ad lo<lb></lb>cum deſertum replendum. </s><s><expan abbr="Eademq́ue">Eademque</expan> cauſa eſt, cur cucurbi<lb></lb> <arrow.to.target n="marg82"></arrow.to.target><lb></lb>tulæ, quæ Chirurgis in vſu eſſe ſolent, carnem ſurſum attrahant; <lb></lb>nimirum quia aêr, qui priùs igne incaluerat, & in raritatem abi<lb></lb>erat, extincta flamma frigiditatem & denſitatem recipit, atque <lb></lb>in minorem contractus molem inane ſpatium relinqueret, niſi <lb></lb>ad id replendum caro elevaretur. </s></p> <p type="margin"> <s><margin.target id="marg80"></margin.target><emph type="italics"></emph>Phiala cale<lb></lb>facta, & a<lb></lb>quæ immer<lb></lb>ſa, attrahit <lb></lb>ipſam va<lb></lb>cui metu.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg81"></margin.target><emph type="italics"></emph>Fiſtula ex<lb></lb>tracto aëre <lb></lb>carnë ad<lb></lb>motam tra<lb></lb>hunt, ne <lb></lb>vacuum <lb></lb>detur.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg82"></margin.target><emph type="italics"></emph>Cucurbitu<lb></lb>læ carnem <lb></lb>attrahunt <lb></lb>metu vacui<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sextò, Si ſclopeto æneo, aut maiori bombardæ, immit<lb></lb> <arrow.to.target n="marg83"></arrow.to.target><lb></lb>tas embolum interiori ſuperficiei benè congruentem, vt aêr in<lb></lb>ter ipſam & embolum ſubire non poſſit, & deinde igniarium fo<lb></lb>ramen occludas; non niſi difficulter extrahitur embolus, & vi <lb></lb>aliquantis per extractus retroagitur intra fiſtulam: </s></p> <p type="margin"> <s><margin.target id="marg83"></margin.target><emph type="italics"></emph>Embolus è <lb></lb>ſclopeto, <lb></lb>foramini i<lb></lb>gniario clau<lb></lb>ſo, difficul<lb></lb>ter extrahi<lb></lb>tur, vacui <lb></lb>metu.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Atque hæc ſecunda ſententia, quæ Naturæ vacuum tan<lb></lb>toperè fugientis partes tuendas ſuſcipit, meritò à melioris notæ <lb></lb>Philoſophis, vt olim, ita nunc quoque præfertur: quidquid ob- <pb xlink:href="051/01/059.jpg" pagenum="28"></pb>ganniant Neoterici quidam, qui neſcio quo novitatis ſtudio in<lb></lb> <arrow.to.target n="marg84"></arrow.to.target><lb></lb>citati, <foreign lang="grc">χενοδοξίας</foreign> vento inflati, nova quotidie dogmata cudere, <lb></lb>aut obſoleta <expan abbr="veterũ">veterum</expan> commenta recoquere non verecundantur. </s><s><lb></lb>Satiùs enim ac faciliùs eſſe exiſtimatur, admittere contra diſpo<lb></lb>ſitiones particulares corporum gravium elevationem, levium <lb></lb>depreſſionem, denſiorum dilatationem, rariorum condenſa<lb></lb>tionem, durorum inflectionem, & ſimilia, quàm vacuum, quod <lb></lb>Naturam adeo abhorrere conſpicitur, vt nulla vi naturalis agen<lb></lb>tis, nullo Machinæ artificio dari poſſit. </s><s>Huiuſmodi autem na<lb></lb>turæ pugnas & ſtratagemata multa ſpectabis manifeſtè infrà in <lb></lb>multis Machinis, quibus hæc Naturæ inanitatem fugientis ſo<lb></lb>lertia ſummam præbet commoditatem. </s><s>Alia etiam paulò poſt <lb></lb>afferam, ſi priùs, quæuam ſit vis illa Attractiva corporum, quâ <lb></lb>Natura vtitur ad vacuum impediendum, oſtendero. </s></p> <p type="margin"> <s><margin.target id="marg84"></margin.target><emph type="italics"></emph>Vacuum da<lb></lb>ri naturali<lb></lb>ter non po<lb></lb>teſt.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Vis attractiva|ob vacui metum, primum Machinarum <lb></lb>hydro-pnevmaticarum principium, quæ, & qua<lb></lb>lis, quibusvè inſit corporibus.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HÆ ſunt binæ de vacuo ſententiæ, quarum vtraque fontium <lb></lb>artificialium, <expan abbr="aliarumq́ue">aliarumque</expan> hydro-pnevmaticarum Machina<lb></lb>rum conſtructioni, & effectuum mirabilium patrationi viam a<lb></lb>perit & ſubminiſtrat arma; quamvis evidentiùs ſecunda, quàm <lb></lb>prima, cui & illam idcirco prætulimus. </s><s>Quæſtio tamen non le<lb></lb> <arrow.to.target n="marg85"></arrow.to.target><lb></lb>vis remanet inter ſecundæ huius ſententiæ fautores circa vim il<lb></lb>lam, quæ cogit corpora gravia accurrere ad vacuum impedi<lb></lb>endum, etiam contra propriam inclinationem; <expan abbr="dubitaturq́ue">dubitaturque</expan>, <lb></lb>quibusnam illa vis inſit ceu ſubiectis; trahentibusnè, an tractis <lb></lb>corporibus? </s></p> <p type="margin"> <s><margin.target id="marg85"></margin.target><emph type="italics"></emph>Vis attra<lb></lb>ctiva aquæ <lb></lb>quibus inſit <lb></lb>corporibus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Alij enim putant, eſſe virtutem motivam ipſis corporibus <lb></lb> <arrow.to.target n="marg86"></arrow.to.target><lb></lb>accurrentibus intrinſecam, quæ in bonum Vniverſi corpora gra<lb></lb>via in altum, contra conſuetum modum, ad vacuum impedien<lb></lb>dum, vrgeat atque impellat. </s><s>At hoc experientia ipſa ſatis con<lb></lb>vellit, & falſitatis arguit; ſiquidem, vt benè advertunt Cabæus <pb xlink:href="051/01/060.jpg" pagenum="29"></pb>& Zucchius, aqua <expan abbr="aſcendẽs">aſcendens</expan> intra tubum, ad vacuum <expan abbr="impediendũ">impediendum</expan> <lb></lb> <arrow.to.target n="marg87"></arrow.to.target><lb></lb>(quod in ſequentibus Machinis frequentiſſimum eſt) tantundem <lb></lb>gravat, <expan abbr="quantũ">quantum</expan> gravaret in libero aëre <expan abbr="ſuſpẽſa">ſuſpenſa</expan>. </s><s>Quòd benè adver<lb></lb>terejubet Cabæus illos, qui ſpecioſo nimis nomine ſe Ingenie<lb></lb>ros appellari volunt; & Zucchius ait, ſe huius rei experimento <lb></lb>coëgiſſe, <emph type="italics"></emph>virum alioqui non ineruditum, vt fallaciam agnoſceret in <lb></lb>via, quâ motum perpetuum ſe inveniſſe putabat, & iam dicandum Ma<lb></lb>gno Principi ſchema in æs incidi curaverat, ſupponendo aquam ad impe<lb></lb>diendum vacuum ſua vi <expan abbr="aſcẽdentem">aſcendentem</expan> non egere virtute æquilibrante, ne<lb></lb>dum ſuperante pondus illius, qua eget cùm ſiſtenda vel elevanda eſt in <lb></lb>aëre, liberè accurrente ad replendum ſpatium inter eam, & alia corpora <lb></lb>relinquendum.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg86"></margin.target><emph type="italics"></emph>Vis attra<lb></lb>ctiva non <lb></lb>ineſt corpo<lb></lb>ribus attra <lb></lb>Hic.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg87"></margin.target><emph type="italics"></emph>Aqua in tu<lb></lb>bis elevata <lb></lb>adfugiend<gap></gap><lb></lb>vacuum <lb></lb>gravat.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Alij igitur, & meliùs, exiſtimant, omnibus corporibus <lb></lb> <arrow.to.target n="marg88"></arrow.to.target><lb></lb>contiguis hanc ineſſe vim, à Natura attributam, ad Vniverſi <lb></lb>bonum ac conſervationem, vt quotiescunque vnum illorum lo<lb></lb>co cedit, ſeu tractum ab extrinſeco agente violenter, ſeu ſponte <lb></lb>& innatâ inclinatione recedens, pondere videlicet, aut levitate: <lb></lb>trahat ſecum alterum ſibi contiguum, quantumvis reluctans, <lb></lb>quoties inter ipſum & contiguum non poteſt ſubintrare corpus <lb></lb>aliud, quod partium Vniverſi contiguitatem tueatur, & impedi<lb></lb>at inanitatem; adeoque trahentibus, non tractis corporibus <lb></lb> <arrow.to.target n="marg89"></arrow.to.target><lb></lb>vim illam motivam ineſſe. </s><s>Et hanc vim appellant vim attracti<lb></lb>vam, eſtque illa ipſa quam nos primum <expan abbr="Machinarũ">Machinarum</expan> hydro-pnev<lb></lb>maticarum principium ſeu fundamentum dicimus, vnaque eſt <lb></lb>ex cauſis vacui impeditivis. </s><s>Dico, vna ex cauſis, non enim v<lb></lb>nica eſt via atque induſtria, quâ vacuum Natura evitare adni<lb></lb>titur. </s><s>Modò enim vtitur prædicta vi attractiva: modò adſciſcit <lb></lb>operam alteratricium qualitatum, quæ corpora rarefaciunt, & <lb></lb>in ampliorem molem diffundunt: non nunquam magno impe<lb></lb>tu vaſa frangit, aut alia id genus media, prout occaſio & neceſ<lb></lb>ſitas fert, accommodat: quin etiam haud rarò nullo motu, nulla <lb></lb>actione, nulla denique vi effectrice, ſed per negativam <expan abbr="quandã">quandam</expan> <lb></lb>obſiſtentiam vacuo repugnat; vt cùm Iatera follium compreſſa <lb></lb>clauſo orificio, vt diximus ſuprà, divellinon ſinit. </s><s>Semper ta- <pb xlink:href="051/01/061.jpg" pagenum="30"></pb>men Natura in his, vtin cæteris rebus, <expan abbr="cõpendio">compendio</expan> ſtudet, & quan<lb></lb>tum poteſt, facilioribus ac ſimplicioribus vtitur medijs; vt ſi ad <lb></lb>fugam vacui corpus ſurſum attrahere, quàm denſatione impedi<lb></lb>re promptius ſit, illud præſtat, non hoc; ſi contrà, hoc, non il<lb></lb>lud: item ſi per ſolum motum localem ſine rarefactione corpus <lb></lb>aliunde trahere ſufficit, rarefactioni parcit; alioquin vtrumque <lb></lb>miſcet. <lb></lb> <arrow.to.target n="marg90"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg88"></margin.target><emph type="italics"></emph>Attractiva <lb></lb>vis trahen<lb></lb>tibus corpo<lb></lb>ribus ineſt, <lb></lb>ad vacuum <lb></lb><expan abbr="impediendũ">impediendum</expan><emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg89"></margin.target><emph type="italics"></emph>Vacui cau<lb></lb>ſa impediti<lb></lb>va multi<lb></lb>plex.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg90"></margin.target><emph type="italics"></emph>Attractiva <lb></lb>vis ad va<lb></lb>cuum im<lb></lb>pediendum <lb></lb>omnibus <lb></lb>corporibus <lb></lb>ineſt.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sed hæc accuratiús Philoſophi; nobis ſufficit varijs experi<lb></lb>entijs monſtraſſe, ineſſe corporibus Vniverſum componentibus <lb></lb>vim attractivam vel ad replendum, vel ad impediendum <expan abbr="vacuũ">vacuum</expan>; <lb></lb>quæ vis vt alia corpora, ita multò magis aërem & aquam attra<lb></lb>hat, & Machinarum Hydro-pnevmaticarum principium ac <expan abbr="fũ-damentum">fun<lb></lb>damentum</expan> primum conſtituat. </s></p> <p type="main"> <s>Nunc tempus eſt, vt experimento vnico & veluti re ipſa <lb></lb>monſtremus, quomodo vis attractiva, quam hactenus corpori<lb></lb>bus Vniverſum componentibus ineſſe oſtendimus ad vacuum <lb></lb>impediendum (vel vt Hero vult, replendum) cauſa eſſe poſſit, <lb></lb>atque principium Hydro-pnevmaticarum Machinarum. </s></p> <p type="main"> <s><emph type="center"></emph>§. V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Experimentum, quo oſtenditur vis attractiva ad aquas <lb></lb>in altum evehendas, vacui vitandi causâ, per Machinas <lb></lb>Hydro-pnevmaticas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>INfrà Claſse 1. cap. 1. Machina 11. </s><s>Modum præſcribimus <expan abbr="aquã">aquam</expan> </s></p> <p type="main"> <s> <arrow.to.target n="marg91"></arrow.to.target><lb></lb>ad certam ac determinatam aliquam altitudinem evehendi, <lb></lb>eumque appellamus Siphonem inverſum interruptum: qui mo<lb></lb>dus cùm nitatur vi Attractivâ orta ex vacui metu, multaque im<lb></lb>plicet notatu digniſſima, & ad vim Attractivam penitiùs intelli<lb></lb>gendam omninò neceſſaria, hîc eum paulò fuſiùs explicandum <lb></lb>cenſui; ibi enim breviter tantùm, & quantum ad praxin ſufficit, <lb></lb>illum proponimus. </s><s>Sit itaque in ciſterna, puteo, piſcina, aut <lb></lb>vaſe quocunque B, aquâ pleno, elevanda ad pedes ex.g.centũ (di<lb></lb>co, exempli gratia, nam alioquin non poteſt ad <expan abbr="tantã">tantam</expan> <expan abbr="altitudinẽ">altitudinem</expan> <lb></lb>attolli per vim attractivam) aqua in vas KA, quod ſit conſtitu- <pb xlink:href="051/01/062.jpg" pagenum="31"></pb> <arrow.to.target n="fig3"></arrow.to.target><lb></lb>tum in parte ſuperiore domus, <expan abbr="habeatq́ue">habeatque</expan> epiſtomium H, per <lb></lb>quod, vbi repletum fuerit vas, depleri poſſit. </s><s>Fiat vas C, cu<lb></lb>iuscunque capacitatis (quamvis meliùs ſit, vt ſit æqualis capa<lb></lb>citatis cum vaſe KA, aut ſaltem non minoris) ex eoque derive<lb></lb>tur ad vas KA, ſiphon ſeu tubus OI, qui in vaſe C, incipiat im<lb></lb>mediatè infra operculum ipſius, in vaſe verò KA, deſinat paulò <lb></lb>infra eiuſdem operculum, tantum ab illo diſtans, quantum ſuf<lb></lb>ficit vt aër permeare poſſit. </s><s>Deinde ex vaſe B, derivetur ad vas <lb></lb>KA, tubus BK; qui in vaſe B, incipiat paulò ſupra fundum ipſi- <pb xlink:href="051/01/063.jpg" pagenum="32"></pb> <arrow.to.target n="fig4"></arrow.to.target><lb></lb>us, in vaſe verò KA, deſinat paulò infra operculum; vbi etiam <lb></lb>nonnihil in curvetur, vti in figura apparet. </s><s>Tandem ex vaſe C, <lb></lb>derivetur alius tubus EF, cum epiſtomio E, habens longitudi<lb></lb>nem paulò majorem longitudine tubi BK, capacitatem verò <lb></lb>ſeu amplitudinem eidem BK, omnino æqualem. </s><s>Debent autem <lb></lb>omnes tres tubi diligentiſſimè <expan abbr="adferrũinari">adferruninari</expan> ſeu coarctari plum<lb></lb>bo, aliavè materia, ſuis vaſis in loco tranſitus; & tam vas C, quam <lb></lb>vas KA, claudi <expan abbr="obturariq́ue">obturarique</expan> vndiq, ſtudioſiſſimè, nè aërem ali<lb></lb>unde, quàm per tubos, recipere aut ejicere valeant. </s><s>His ita <pb xlink:href="051/01/064.jpg" pagenum="33"></pb>præparatis, impleatur vas C. aquâ per foramen O, immiſſo ipſi <lb></lb>foramini iufundibulo; & vbi repletum fuerit, claudatur vt di<lb></lb>ctum. </s><s>Deinde clauſo epiſtomio H, aperiatur epiſtomium E, <lb></lb>tubi EF; <expan abbr="defluetq́ue">defluetque</expan> aqua ex vaſe C, & in locum ipſius, nè va<lb></lb>cuum in vaſe admittatur, ſequetur per ſiphonem IO, aër in va<lb></lb>ſe KA, contentus; in locum verò aëris extracti è vaſe KA, ſeque<lb></lb>tur, propter vacui metum, aqua vaſis ſeu ciſternæ aut piſcinæ B, <lb></lb>per ſiphonem BK; & tam diu durabit aſcenſus aquæ per <expan abbr="ſiphonẽ">ſiphonem</expan> <lb></lb>BK, in vas KA, quàm diu deſcendet aqua per ſiphonem EF ex va<lb></lb>ſe C. </s><s>Lege quæ dicimus infrà loco cit. </s><s>En ergo, quomodo aqua, <lb></lb>ad vacuum impediendum, aſcendat contra naturalem ſuam in<lb></lb>clinationem, & quomodo propter <expan abbr="eandẽ">eandem</expan> cauſam aër deſcendat. </s></p> <p type="margin"> <s><margin.target id="marg91"></margin.target><emph type="italics"></emph>Experimen<lb></lb>tum vim <lb></lb><expan abbr="attractivã">attractivam</expan> <lb></lb>oſtendens <lb></lb>ad vacuum <lb></lb>impedien<lb></lb>dum.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.064.1.jpg" xlink:href="051/01/064/1.jpg"></figure> <figure id="id.051.01.064.2.jpg" xlink:href="051/01/064/2.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Notantur nonnulla circa prædictum experimentum, <expan abbr="ſi-mulq́">ſi<lb></lb>mulque</expan>; ſtabilitur, in attractione aquæ metu vacui habendam <lb></lb>eſſe rationem perpendiculi aquarum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DIximus, meliùs eſſe vt vas C, ſit æqualis capacitatis cum vaſe <lb></lb>KA, aut ſaltem non minoris: & præterea ſiphonem EF debe<lb></lb>re eſſe paulò longiorem ſiphone BK, capacitatis verò ſeu ampli<lb></lb>tudinis æqualis. </s><s>Ratio quoad capacitatem vaſorum & ſipho<lb></lb>num eſt, quia tamdiu aſcendit aqua per BK, quàm diu deſcen<lb></lb>dit per EF, vt dixi (tam diu enim, & non ampliùs, durat vacui <lb></lb>metus, ob quam aqua aſcendit per tubum BK:) ſi ergo vas C mi<lb></lb>nus eſſet quàm vas KA, aut tubus EF capacior quàm tubus BK; ef<lb></lb>flueret tota aqua ex C, antequam repleretur KA. </s><s>Accedit & <lb></lb>hoc commodi ex æquali vtrorumque capacitate, quòd ſcire poſ<lb></lb>ſit apud C exiſtens, quandonam plenum ſit vas KA; quando ni<lb></lb>mirum effluxerit tota aqua C. </s><s>Ratio verò cur tubus EF, debeat <lb></lb> <arrow.to.target n="marg92"></arrow.to.target><lb></lb>eſſe longior tubo BK, patebit ex dicendis Protheoria IV. capite <lb></lb>2. Propoſit. 13. interim hîc id confirmo hoc Experimento. </s><s>Ac<lb></lb>cipe vas aquâ plenum, eique inſere ſiphonem inverſum ABCD <lb></lb>æqualium crurium. </s><s>Accipe deinde tubum rectum DE aquâ <lb></lb>plenum, eumque, obturato priùs ore E, inſere extremitati D, <pb xlink:href="051/01/065.jpg" pagenum="34"></pb> <arrow.to.target n="fig5"></arrow.to.target><lb></lb>cruris CD, & diligenter coarcta in<lb></lb>ter ſeſe, nè aër inter <expan abbr="vtrumq;">vtrumque</expan> <expan abbr="trãſire">tranſire</expan> <lb></lb>poſſit. </s><s>His factis aperios inferius. </s><s><lb></lb>Et ſi quidem tubus rectus DE lon<lb></lb>gior fuerit quàm crus AB à ſupre<lb></lb>ma ſuperficie aquæ vaſis <expan abbr="vsq;">vsque</expan> ad B; <lb></lb>effluet aqua ex E, <expan abbr="aſcendetq́ue">aſcendetque</expan> a<lb></lb>qua vaſis A, per crus AB, <expan abbr="indeq́ue">indeque</expan> <lb></lb>per CD, crus deſcendet, donec <lb></lb>tota effluxerit ex ore E. </s><s>Si aut de<lb></lb>urtetur tubus DE in F, fiatque <lb></lb>æqualis cruri AB; aſendet aqua va<lb></lb>ſis A ſolùm uſque ad B, quàm diu vi<lb></lb>delicet aqua ex F effluit; quâ elapsâ, <lb></lb>relabetur aqua cruris AB intra vas <lb></lb>A, Si idem tubus DE decurtetur <lb></lb>in G, aut H, <expan abbr="fiatq́ue">fiatque</expan> brevior quàm <lb></lb>crus AB; aſcendet aqua per AB ſo<lb></lb>lùm aliquòuſque, & deinde rela<lb></lb>betur. </s><s>Experientiam quilibet fa<lb></lb>cilè poterit facere. </s></p> <p type="margin"> <s><margin.target id="marg92"></margin.target><emph type="italics"></emph>Experimë<lb></lb>tum aliud: <lb></lb>oſtendens <lb></lb>vim attra<lb></lb>ctivam a<lb></lb>quæ in <expan abbr="altũ">altum</expan>.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.065.1.jpg" xlink:href="051/01/065/1.jpg"></figure> <p type="main"> <s>Nec ſufficit vt tubus EF, ſupe<lb></lb>rioris figuræ ſit <expan abbr="quacunq;">quacunque</expan> ratione longior tubo BK, ſed neceſſari<lb></lb>um eſt, vt <expan abbr="perpendiculũ">perpendiculum</expan> ipſius EF, ſit longius quàm perpendicu<lb></lb>lum BK, hoc eſt, vt tubus EF perpendiculariter deſcendat <lb></lb>profundiùs infra vas C, quàm tubus BK aſcendat perpendi<lb></lb>culariter ſupra vas B. </s><s>Quare ſi tubus EF centum & vnius pe<lb></lb> <arrow.to.target n="marg93"></arrow.to.target><lb></lb>dum inclinaretur infra vas C, aut convolveretur in helicem, <lb></lb>vt hîc apparet, ita vt perpendiculum ipſius ſolùm eſſet pedum <lb></lb>v.g. 60. ab E vſque ad D v.g. & non vſque ad N; neutiquam <lb></lb>ſufficeret; ſed omnino neceſſarium eſt, vt perpendiculum ſit <lb></lb>etiam ad minimùm centum pedum, & pertingat vſque ad N. </s><s>Et <lb></lb>hæc perpendiculi menſura adeo eſt neceſſaria in hydraulicis hi<lb></lb>ſce operationibus, vt Natura falli nulla arte, nullo dolo, <expan abbr="nullaq́">nullaque</expan>; <lb></lb>experientia poſſit. </s><s>Ioannes Baptiſta Porta lib. 2. Spirital. cap. <pb xlink:href="051/01/066.jpg" pagenum="35"></pb> <arrow.to.target n="fig6"></arrow.to.target><lb></lb>1. ait, ſe, cúm indigeret determi<lb></lb>nato perpendiculo infra vas de<lb></lb>ſcendente, nec locum haberet <lb></lb>ad demittendum perpendicula<lb></lb>riter tubum, multis viis tentaſſe, <lb></lb>vt defectum ſuppleret; præcipuè <lb></lb>verò duabus memoratis, nimi<lb></lb>rum inclinando primùm, deinde <lb></lb>in helicem convolvendo tubum <lb></lb>requiſitæ longitudinis; ſed nun<lb></lb>quam deſideratum effectum fu<lb></lb>iſſe conſecutum, nec vnquam <lb></lb>aſcendiſſe aquam ad maiorem <lb></lb>altitudinem quàm erat perpen<lb></lb>diculum tubi inclinati, aut tor<lb></lb>tuoſi. </s><s>Demiſit etiam infra vas <lb></lb>canalem capaciorem, licet bre<lb></lb>viorem illo, qui erat ſupra vas: <lb></lb>præterea loco vnius longioris <lb></lb>demiſit multos breviores, qui ſi<lb></lb>mul ſuperabant longitudinem <lb></lb>ſuperioris; ſed vano ſemper labore. </s><s>Adeo ſui juris tenax eſt <lb></lb>Natura, & vt non fallit nos in ſuis operationibus, ita nec falli à <lb></lb>nobis vult. </s><s>Infrà tamen Claſse 1. cap. 1. Machina 7. </s><s>Modum do<lb></lb>cebo elevandi aquam ad quamvis <expan abbr="altitudinẽ">altitudinem</expan> perpendiculis bre<lb></lb>vibus multiplicatis, ſed vtrisque, deſcendentis nimirum & aſcen<lb></lb>dentis aquæ. </s><s>Notandum præterea eſt hoc loco, Tubum OI, <lb></lb>aut CI, poſſe eſſe quantævis longitudinis, vt infrà iterum dicam <lb></lb>§. IX. </s><s>Quomodo autem vi attractiva & expulſiva ſimul elevari <lb></lb>poſſit aqua ad maiorem altitudinem quàm ſit perpen<lb></lb>diculum aquæ deſcendentis, dicemus infrà <lb></lb>Protheoria II. </s></p> <pb xlink:href="051/01/067.jpg" pagenum="36"></pb> <p type="margin"> <s><margin.target id="marg93"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>lum aquæ <lb></lb>deſcenden<lb></lb>tis debet eſſe <lb></lb>longius, <lb></lb>quàm aſcen<lb></lb>dentis.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.067.1.jpg" xlink:href="051/01/067/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Heronis Alexandrini error in elevanda a<lb></lb>qua vi attractivâ.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg94"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg94"></margin.target><emph type="italics"></emph>Error He<lb></lb>ronis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>HEro Alexandrinus cap. 53. libri de Spiritalibus modum præ<lb></lb>ſcribit elevandi aquam per vim attractivam ex vacui metu; <lb></lb>ſed vehementer hallucinatur, ob perpendiculi prædicti <expan abbr="defectũ">defectum</expan>; <lb></lb>ſi tamen Heronis eſt error ille, & non potiùs interpretis, qui ſche<lb></lb>ma appoſuit, vt notavit etiam Ioannes Baptiſta Porta lib. 2. de <lb></lb>Spirital. cap. 2. </s><s>Affero verba vnà cum Schemate Heronis, ex ver<lb></lb>ſione & editione Federici Commandini Vrbinatis, qui ex Græco <lb></lb>in latinum eum tranſtulit quem errorem repetit etiam Ioannes <lb></lb>Baptiſta Aleottus in verſione Italica. </s></p> <p type="main"> <s><emph type="italics"></emph>Eſt etiam alia conſtructio,<emph.end type="italics"></emph.end> inquit Hero, <emph type="italics"></emph>in qua humidum ſen<lb></lb>ſim fertur, & manet, ita vt ſemper aſcendens videatur.<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="fig7"></arrow.to.target><lb></lb><emph type="italics"></emph> </s><s>Sit baſis<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>vndique præcluſa, quæ dia<lb></lb>phragma habeat<emph.end type="italics"></emph.end> CD, <emph type="italics"></emph>& vitreum oper<lb></lb>culum Cylindri forma<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>ſimiliter vndi<lb></lb>que præcluſum. </s><s>In operculo autem<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>ſit <lb></lb>tubus<emph.end type="italics"></emph.end> GH, <emph type="italics"></emph>ab ipſius tecto parum diſtans, <lb></lb>& ſimul perforatus cum diaphragmate. </s><s>A<lb></lb>lius etiam tubus<emph.end type="italics"></emph.end> KL <emph type="italics"></emph>ſimul perforetur cum <lb></lb>tecto baſis, & à diaphragmate parum diſtet. </s><s><lb></lb>Inſit autem baſi extra vitreum operculum <lb></lb>foramen<emph.end type="italics"></emph.end> M, <emph type="italics"></emph>per quod vas<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>impleatur: <lb></lb>& baſis<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>ad fundum canalem habeat<emph.end type="italics"></emph.end><lb></lb>N. </s><s><emph type="italics"></emph>Sit præterea alius tubus<emph.end type="italics"></emph.end> XO, <emph type="italics"></emph>ſimul <lb></lb>perforatus cum diaphragmate, parumque <lb></lb>à baſi diſtans, per quem implebitur vas<emph.end type="italics"></emph.end> CB. </s><s><lb></lb><emph type="italics"></emph>Itaque obſtructo canali<emph.end type="italics"></emph.end> N, <emph type="italics"></emph>aër qui eſt in<emph.end type="italics"></emph.end> CB, <emph type="italics"></emph>per tubos, & per fora<lb></lb>men<emph.end type="italics"></emph.end> M <emph type="italics"></emph>excedet extra. </s><s>Et cùm vas<emph.end type="italics"></emph.end> CB <emph type="italics"></emph>repletum fuerit, implebi<lb></lb>mus<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>per foramen<emph.end type="italics"></emph.end> M, <emph type="italics"></emph>aër enim qui in ipſo eſt, per idem foramen <lb></lb>excedit. </s><s>Si igitur canalem<emph.end type="italics"></emph.end> N <emph type="italics"></emph>fluere dimittamus, in locum<emph.end type="italics"></emph.end> CB <emph type="italics"></emph>exina<lb></lb>nitum, aër ex vitreo operculo procedet per tubum<emph.end type="italics"></emph.end> GH: <emph type="italics"></emph>in locum autem <lb></lb>vitrei operculi exinanitum ex<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>humidum aſcendet per tubum<emph.end type="italics"></emph.end> KL, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <pb xlink:href="051/01/068.jpg" pagenum="37"></pb><emph type="italics"></emph>aer per foramen<emph.end type="italics"></emph.end> M <emph type="italics"></emph>ingredietur. </s><s>Atque hoc vsque eò fiet, quoad vitreum <lb></lb>operculum repletum fuerit. </s><s>Oportebit autem loca<emph.end type="italics"></emph.end> AD, CB, EF, <emph type="italics"></emph>inter <lb></lb>ſe æqualia eſſe, vt ad invicem & aër, & humidum transferantur. </s><s>Quan<lb></lb>do autem vas<emph.end type="italics"></emph.end> CB <emph type="italics"></emph>exinanitum fuertt, & conſtiterit aër is continuitas, <lb></lb>rurſus ex vitreo operculo aqua in vas<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>deferetur, aëre per canalem<emph.end type="italics"></emph.end><lb></lb>N, <emph type="italics"></emph>& per<emph.end type="italics"></emph.end> GH <emph type="italics"></emph>tubum in vitreum operculum ingrediente, qui verò <lb></lb>eſt in vase<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>aër per foramen<emph.end type="italics"></emph.end> M <emph type="italics"></emph>excedet.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.068.1.jpg" xlink:href="051/01/068/1.jpg"></figure> <p type="main"> <s>Ita Hero; ſed errat autipſe, aut eius interpres: debete<lb></lb>nim canalis N deſcendere infra vas perpendiculariter ad tantam <lb></lb>profunditatem, quanta eſt longitudo KL, vt attrahatur tota a<lb></lb>qua vaſis AD; alioquin poſtquam effluxerit aliquantulum a<lb></lb>quæ ex canali N, traxeritque aliquantulum aëris ex cylindro <lb></lb>EF, & aquæ ex vaſe AD, ceſſabit omnino aquæ fluxus, ob de<lb></lb>fectum perpendiculi æqualis perpendiculo KL, ſaltem ab ſu<lb></lb>prema ſuperficie aquæ vaſis AD, vſque ad orificium K tubi <lb></lb>prædict KL. </s><s>Qui defectus ſi ſuppleatur, ſequetur effectus deſide<lb></lb>ratus. </s><s>Porta tamen loco citato, occaſione huius Heronianæ <lb></lb>induſtriæ, alium excogita vit modum elevandi vi attractiva ex <lb></lb>inferiori ad ſuperius vas aquam: quem legere poteris apud <expan abbr="ipsũ">ipsum</expan>. </s></p> <p type="main"> <s><emph type="center"></emph>§. VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Alius Heronis error in elevanda aqua <lb></lb>vi attractiva.<emph.end type="center"></emph.end></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"></arrow.to.target><lb></lb>ſi tamen & hic non eſt adſcribendus interpreti. </s><s>Docere <lb></lb>vult Hero modum elevandi atque attrahendi humidum ex vaſe <lb></lb>per ſiphonem inverſum, cuius vnum crus ſit humido <expan abbr="immerſũ">immerſum</expan>, <lb></lb>alterum extra vas promineat, non attrahendo prius per os no<lb></lb>ſtrum aërem ex ſiphone, ſed appendendo vas quodpiam aquâ <lb></lb>plenum: Sic ergo diſcurrit. </s></p> <p type="margin"> <s><margin.target id="marg95"></margin.target><emph type="italics"></emph>Error alius <lb></lb>Heronis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Sit ſmerismation aliquod, cuius maſculum quidem apponatur <lb></lb>extrinſeco ſiphonis cruri, ita vt per ipſum fluat, ſitque<emph.end type="italics"></emph.end> TV; <emph type="italics"></emph>famina ve-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/069.jpg" pagenum="38"></pb> <arrow.to.target n="fig8"></arrow.to.target><lb></lb><emph type="italics"></emph>rò<emph.end type="italics"></emph.end> TYV <emph type="italics"></emph>priùs adglutinata vaſi<emph.end type="italics"></emph.end><lb></lb>LZ, <emph type="italics"></emph>quod paulò plùs aquæ, quàm <lb></lb>ſiphon capiat; habeat autem ad <lb></lb>fundum effluxionem<emph.end type="italics"></emph.end> <foreign lang="grc">Ω</foreign> <emph type="italics"></emph>Quan<lb></lb>do igitur volumus per ſiphonem e<lb></lb>ducere aquam, quæ eſt in vaſe<emph.end type="italics"></emph.end> AB, <lb></lb><emph type="italics"></emph>effluxionem vaſis<emph.end type="italics"></emph.end> LZ <emph type="italics"></emph>digito <expan abbr="cõ-prehendentes">con<lb></lb>prehendentes</expan>, ipſum aquâ imple<lb></lb>bimus. </s><s>Poſtea fœmineum ſmeri<lb></lb>ſma maſculo aptantes effluxionem<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">Ω</foreign> <emph type="italics"></emph>dimittemus. </s><s>Evacuato au<lb></lb>tem<emph.end type="italics"></emph.end> LZ <emph type="italics"></emph>vaſe, aër in ſiphone <lb></lb>exiſtens in evacuatum locum pro<lb></lb>cedet; quem conſequetur humi<lb></lb>dum quod in vaſe<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>ita vt <expan abbr="ſiphõ">ſiphon</expan> <lb></lb>impleatur. </s><s>Deinde aufferentes <lb></lb>vas<emph.end type="italics"></emph.end> LZ <emph type="italics"></emph>Siphonem fluere ſine<lb></lb>mus. </s><s>Oportet autem ſiphonem rectè deſcendere, ſi officium ſuum præ<lb></lb>ſtare debeat; illud autem erit, quando ad vaſis<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>labrum duas regu<lb></lb>las rectas compingemus, atque inter ipſas intrinſecum ſiphonis crus <lb></lb>conſtituemus, ita vt vtrasque contingat; ad idem verò ſiphonis crus <lb></lb>intrinſecum vtrimque clauvicuulam affigemus, regulas continentem <lb></lb>parte interiori: ita enim neque obliquum, neque in anteriorem par<lb></lb>tem declinabit; rectò enim & exquiſitè deſcendet, claviculis regulas <lb></lb>atterentibus.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.069.1.jpg" xlink:href="051/01/069/1.jpg"></figure> <p type="main"> <s>Hæc Hero; quæ tamen falſa ſunt, & contraria experien<lb></lb>tiæ, rationi, & hydro-pnevmaticis principijs. </s><s>Niſi enim vaſis <lb></lb>altitudo ab V ad <foreign lang="grc">Ω</foreign> tanta ſit, quantum eſt crus internum CD <lb></lb>Siphonis; non aſcendet aqua per crus CD, niſi ad tantam al<lb></lb>titudinem, quanta eſt altitudo vaſis prædicta ab Y, vſque ad <foreign lang="grc">Ω</foreign>. </s><s><lb></lb>Et ratio eſt, quia cùm perpendiculum Y <foreign lang="grc">Ω</foreign> minus ſit, quàm <lb></lb>perpendiculum CD; non poteſt aqua attolli ad altitudinem <lb></lb>CD, ſed poſtquam aſcenderit ad altitudinem æqualem perpen<lb></lb>diculo Y <foreign lang="grc">Ω</foreign>, relabetur intra vas AB. </s><s>Ioannes Baptiſta Porta <pb xlink:href="051/01/070.jpg" pagenum="39"></pb>lib. 2. de ſpirital. cap. 3. ait. aquam non effluxuram è vaſe LZ, ab<lb></lb> <arrow.to.target n="marg96"></arrow.to.target><lb></lb>lato impedimento apud <foreign lang="grc">Ω</foreign>, propter defectum ſcilicet perpendi<lb></lb>culi prædicti. </s><s>Sed ratio & experientia convincit, effluere aquam <lb></lb>è vaſe; & aſcendere aquam per crus internum ad altitudinem ex<lb></lb>plicatam; quod ipſemet Porta alibi fatetur. </s></p> <p type="margin"> <s><margin.target id="marg96"></margin.target><emph type="italics"></emph>Error Ioan<lb></lb>nis Baptiſtæ <lb></lb>Porta.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Ut igitur ex vaſe AB extrahi poſſit aqua per ſiphonem abſ<lb></lb>que eo quòd ore attrahatur aër, oportet loco Vaſis LZ adhibere <lb></lb>tubum tantæ longitudinis, quantæ eſt crus CD, imò paulò ma<lb></lb>joris: tunc enim effluente aquâ ex tubo appenſo aſcendet paula<lb></lb>tim aqua per ſiphonem, donec pervenerit uſque ad ſignum V, <lb></lb>quod ſuppono eſſe ſemper demiſſius quàm eſt ſuprema ſuperfi<lb></lb>cies aquæ in Vaſe AB: tunc enim ſi aufferatur tubus appenſus, ef<lb></lb>fluxus aquæ ex ſiphone tam diu durabit, donec tota aqua ex <lb></lb>vaſe AB effluxerit, ſi os C ad fundum vſque vaſis pertigerit. </s><s>Vi<lb></lb>de Salomonem de Caus lib. 1. de viribus motricibus. </s><s>Vide præ<lb></lb>terea quæ ſcribimus de fluxu aquæ per ſiphones infrà Protheo<lb></lb>ria IV. Cap. 2. præſertim Propoſit. XI. ubi in Annotatione 2. no<lb></lb>tamus errorem Marini Merſenni <expan abbr="ſimilẽ">ſimilem</expan> prædicti Heronis errori. </s></p> <p type="main"> <s>Monuit hîc, & optimè, <expan abbr="acutiſſimeq́ue">acutiſſimeque</expan> P. Paulus Caſatus <lb></lb>Matheſeos in Romano noſtro Collegio Profeſſor, quæ diximus <lb></lb>contra Heronem hoc loco, tunc ſolùm haberelocum, quando <lb></lb>ſuprema aquæ ſuperficies non eſſet multùm ſupra punctum C. </s><s><lb></lb>Cæterùm ſi vas AB eſt plenum, & <expan abbr="perpendiculũ">perpendiculum</expan> <foreign lang="grc">ΨΩ</foreign> ſuperat per<lb></lb>pendiculum à ſuprema aquæ ſuperficie <expan abbr="uſq;">uſque</expan> ad D; poterit aſcen<lb></lb>dere aqua, & per crus DY defluere; quâ ſemel defluente, ſem<lb></lb>per deinde defluet, donec evacuetur vas vsque ad punctum C, <lb></lb>quoniam perpendiculum DY ſemper manebit longius quàm <lb></lb>perpendiculum CD. </s></p> <p type="main"> <s><emph type="center"></emph>§. IX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>In aquarum elevatione vi attractivâ, habenda eſt ratio <lb></lb>perpendiculi ſolùm illorum tuborum, per quos aqua, <lb></lb>non per quos aër vehitur.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg97"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg97"></margin.target><emph type="italics"></emph>Tubi per <lb></lb>quos aër de<lb></lb>fertur in<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>NOtat optimè Ioannes Baptiſta Porta lib 2. de Spiritalibus. C. 6. <lb></lb>& nos etiam ſuprà in fine §. VI. inſinuavimus, in Machinis </s></p> <pb xlink:href="051/01/071.jpg" pagenum="40"></pb> <p type="main"> <s> <arrow.to.target n="marg98"></arrow.to.target><lb></lb> <arrow.to.target n="fig9"></arrow.to.target><lb></lb>vi attractiva elevan<lb></lb>tibus aquam, haben<lb></lb>dam eſſe rationem <lb></lb>longitudinis ac bre<lb></lb>vitatis ſolùm illorum <lb></lb>tuborum ſeu canali<lb></lb>um, qui conferunt <lb></lb>ad aquarum perpen<lb></lb>diculum, & per quos <lb></lb>tranſire debet aqua, <lb></lb>atque adeo quorum <lb></lb>aquæ ſe mutuò tra<lb></lb>here ac vincere de<lb></lb>bent; non verò reli<lb></lb>quorum, per quos <lb></lb>ſolùm aër <expan abbr="trãſire ">tranſire</expan> de<lb></lb>bet. </s><s>Quod vt meli<lb></lb>ùs intelligatur, inſpi<lb></lb>clatur figura poſſit <lb></lb>ſuprà §. citato, in qua <lb></lb>figura habenda eſt <lb></lb>ſolùm ratio <expan abbr="tuborũ">tuborum</expan> <lb></lb>BK, & EF; hi enim <lb></lb>duo continent aquas <lb></lb>quarum perpendi<lb></lb>cula ad invicem pu<lb></lb>gnant, juxta dicenda infrà Protheoria IV. cap. 2. Propoſit. 13. <lb></lb>tubus verò OI poteſt eſſe quantævis longitudinis aut brevita<lb></lb>tis, ac proinde vas C poteſt eſſe & infra & ſupra vas B. </s><s>Patet <lb></lb>hoc experientia, vt dicemus loco citato; vbi etiam experientiæ <lb></lb>cauſam dabimus. </s></p> <p type="margin"> <s><margin.target id="marg98"></margin.target><emph type="italics"></emph>Machinis <lb></lb>attractivis <lb></lb>metu vacui <lb></lb>poſſunt eſſe <lb></lb>quantævis <lb></lb>longitudinis<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.071.1.jpg" xlink:href="051/01/071/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. X.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Vi attractivâ elevari poteſt aqua vltra perpen<lb></lb>culi altitudinem, aëre mediante.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/072.jpg" pagenum="41"></pb> <p type="main"> <s>Ingenioſſimum ſanè modum <expan abbr="Naturã">Naturam</expan> <expan abbr="quodam̃odo">quodammodo</expan> decipiendi, <lb></lb>& aquam vltra perpendiculi à Natura requiſiti altitudinem e<lb></lb>levandi vi attractiva, affert Porta loco proximè citato, cap. 11. <lb></lb>aitque ſe illum caſu reperiſſe inter continuas hydraulicas atque <lb></lb>pnevmaticas experientias quas fecit. </s><s>Fit hoc aëre mediante, <lb></lb>aquæ immiſto. </s><s>Hac ratione, inquit Porta, perpendiculo 50. <lb></lb>pedum elevari poteſt aqua ad altitudinem pedum 80. </s><s>Modus <lb></lb>hic eſt. </s></p> <figure id="id.051.01.072.1.jpg" xlink:href="051/01/072/1.jpg"></figure> <p type="main"> <s>Sit ex vaſe AB portatili e<lb></lb> <arrow.to.target n="marg99"></arrow.to.target><lb></lb>levanda aqua ad vas D, ad alti<lb></lb>tudinem pedum 80. </s><s>Fiat canalis <lb></lb>vitreus GK (vtſpectari, oculis<lb></lb>que percipi manifeſtè poſſitar<lb></lb>tificium) vtrimque apertus, & <lb></lb>vaſi D optimè coarctatus a<lb></lb>pud K. </s><s>Fiat deinde vas C, æ<lb></lb>qualis aut maioris capacitatis, <lb></lb>quàm vas D; <expan abbr="inſeraturq́ue">inſeraturque</expan> v<lb></lb>trique canalis PQ vtrimque a<lb></lb>pertus immediatè ſub operculis <lb></lb>ſeu tectis vaſorum. </s><s>Tandem <lb></lb>ex vaſe C deſcendat perpendi<lb></lb>culariter canalis EF quinqua<lb></lb>ginta pedum longitudinis, ha<lb></lb>bens epiſtomium E, & ſit opti<lb></lb>mè adferruminatus fundo vaſis C. </s><s>His factis, impleantur vaſa <lb></lb>AB, & C, aquâ, <expan abbr="admoveaturq́ue">admoveaturque</expan> vas AB tubo GK, ita vt o<lb></lb>ſculum G ſit aquæ immerſum, & aperiatur epiſtomium E; de<lb></lb>ſcendet aqua ex vaſe C, ſecumque trahet aërem ex tubis QP, <lb></lb>& KG, & ex vaſe D, ſimulque aquam ex vaſe AB. </s><s>Poſtquam <lb></lb>aſcenderit aqua intra canalem GK vſque ad aliquod ſpatium <lb></lb>exiguum, v.g. vſque ad H; remove aliquantulùm vas AB; & <lb></lb>aqua canalis aſcendet vlteriús, tracta ſcilicet ab aqua effluente <lb></lb>per FE) & poſt aquam ſequetur aër. </s><s>Admove deinde iterum <pb xlink:href="051/01/073.jpg" pagenum="42"></pb> <arrow.to.target n="fig10"></arrow.to.target><lb></lb>vas AB, & attrahetur alia aqua, <lb></lb><expan abbr="eritq́ue">eritque</expan> aër HI inter aquam <lb></lb>GH, & IM. </s><s>Iterum remove vas <lb></lb>AB, & ingredietur per os G alius <lb></lb>aër, ſequeturque aquam. </s><s>Quo <lb></lb>facto, ſi vas iterum admôris, <expan abbr="di-ctamq;">di<lb></lb>ctamque</expan> operationem repetive<lb></lb>ris; aſcendent tandem aqua & <lb></lb>aër miſti inter ſe, vſque ad vas D, <lb></lb>illudque replebunt, <expan abbr="antequã">antequam</expan> ef<lb></lb>fluat tota aqua vaſis C, quod ob <lb></lb>id minus eſſe debet quam vas D. </s></p> <p type="margin"> <s><margin.target id="marg99"></margin.target><emph type="italics"></emph>Experimen<lb></lb>tum Porta <lb></lb>ad aquam <lb></lb>elevandam <lb></lb>vltra <expan abbr="perpẽ-diculi">perpen<lb></lb>diculi</expan> alti<lb></lb>tudinem.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.073.1.jpg" xlink:href="051/01/073/1.jpg"></figure> <p type="main"> <s>Procedendum eſt autem <lb></lb>valde cautè in hoc negotio, nè <lb></lb>nimium aéris ingrediatur per os <lb></lb>G, & levitate ſua ſurſum ten<lb></lb>dens pellat modicam aquam <lb></lb>antea in tromiffam, repleatque totum canalem GK, ſicque de<lb></lb>ſtruatur continuitas aquæ & aëris intra canalem: hoc enim ſi <lb></lb>fieret, non repleretur vas D, niſi poſt longiſſimum tempus, & <lb></lb>multas operationes, deberetque ſæpius repleri vas C. </s><s>Nun<lb></lb>quam præterea tantum aquæ ſimul continere debet canalis <lb></lb>GK, vt ejus perpendiculum ſuperet perpendiculum aquæ ca<lb></lb>n alis EF. </s><s>Ex hac praxi deducit Porta modum mirabilem, & <lb></lb>omnibus antiquis ignotum, ut ipſe ait, elevandi per ſiphonem <lb></lb>inverſum aquam è montis radice ad ejus verticem; quem mo<lb></lb>dum afferam infrà Protheoria IV. cap. 2. Propoſit. 12. ex <lb></lb>quo etiam loco meliùs intelligetur hoc <lb></lb>præſens Experimentum. </s></p> <pb xlink:href="051/01/074.jpg" pagenum="43"></pb> <p type="main"> <s><emph type="center"></emph>Protheoria II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA <lb></lb>SECVNDA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De vi Expulſiva propter corporum impe<lb></lb>netrabilitatem; ſeu de ſecundo Machinarum Hy<lb></lb>dropnevmaticarum principio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Omnia Vniverſi corpora ſunt inter ſe <lb></lb>contigua.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COrpora omnia, quæ DEVS Optimus Maximus <lb></lb> <arrow.to.target n="marg100"></arrow.to.target><lb></lb>in prima rerum conditione intra præſtitutum in Vni<lb></lb>verſi ambitu concluſit locum, Cœlum dico, Elemen<lb></lb>ta, & Mixta, tali ſunt ordine diſpoſita, ut multi, nec <lb></lb>vulgares Philoſophi, exiſtiment, motum localem in Mundo non <lb></lb><expan abbr="futurũ">futurum</expan> ullum, niſi aut concedatur diſperſum per omnia vacuum <lb></lb>(quale vidimus invehere Heronem, alioſque nonnullos) aut <lb></lb>corporum mutua penetratio, aut rerum omnium commotio, <lb></lb>atque permixtio. </s><s>Audi Epicurum apud Diogenem Laêrtium <lb></lb>lib. 10. in Epiſtola ad Herodotum, ubi ait. </s><s><foreign lang="grc">Εἰ δὲ μὴ ἠ̄ν ὁ καὶ χενὸς, καὶ <lb></lb>χώ<gap></gap>αν, καὶ ἀναφ<gap></gap> φύσιν ὀνομάξομεν, <gap></gap>χ ἄν εἰ̄χε τὰ σώματα ὅπ<gap></gap>ν <gap></gap>δὲ δἰ <gap></gap><lb></lb>εχινεῑτο, χα<gap></gap>άπε<gap></gap> φάινετω χιν<gap></gap>μενα</foreign> <emph type="italics"></emph>Niſi verò id eſſet quoque, quod & <lb></lb>inane,<emph.end type="italics"></emph.end> ſeu vacuum, <emph type="italics"></emph>& regionem,<emph.end type="italics"></emph.end> ſeu ſpatium, <emph type="italics"></emph>ac locum & intacti<lb></lb>lem<emph.end type="italics"></emph.end> ſive in corpoream <emph type="italics"></emph>naturam vocamus; non haberent corpora ne<lb></lb>que ubi eſſent, neque quà motus ſuos obirent; cùm moveri ea quidem <lb></lb>manifeſtum ſit.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg100"></margin.target><emph type="italics"></emph>Corpora o<lb></lb>mnia Vni<lb></lb>verſi conti<lb></lb>gua inter ſe.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Hanc autem, quam petitam ex motu rationem inſinuat <lb></lb> <arrow.to.target n="marg101"></arrow.to.target><lb></lb>ſolummodò Epicurus, deducunt manifeſtiùs Democritus atque <lb></lb>Leucippus (quos ſecutus eſt Epicurus) apud Ariſtotelem lib. 4. <lb></lb>Phyſ. tex. 6. (ubi etiam alteram de corporum penetratione ur<lb></lb>gent) his verbis <foreign lang="grc"><gap></gap> γὰ<gap></gap> ἂν δοχόιη εἴναι εἰ μ<gap></gap> χενὸν. τὸ γά<gap></gap> πλ<gap></gap>ες ἀδύνα<lb></lb>τον εἴναι δέξα<gap></gap></foreign>, &c. </s><s><emph type="italics"></emph>Non videtur quippe eſſe motus, niſi ſit inane. </s><s><lb></lb>Quod enim plenum eſt, admittere in ſe mobile non poteſt. </s><s>Nam ſi ad-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/075.jpg" pagenum="44"></pb> <arrow.to.target n="marg102"></arrow.to.target><lb></lb><emph type="italics"></emph>mittat, & fuerint in eodem loco duo corpora; nihil repugnabit, quò mi<lb></lb>nùs quotquot libuerit, ſimul ſint; quia dici, cur id non valeat evenire, <lb></lb>minimè poteſt. </s><s>Sin autem eveniat, tunc quod minimum, id admittet <lb></lb>quod maximum; quando ipſum magnum multa parva eſt: adeo ut ſi <lb></lb>multa æqualia in eodem eſſe contigerit, eſſe & in æqualia contingat.<emph.end type="italics"></emph.end> </s><s>Ean<lb></lb>dem <expan abbr="conſecutionẽ">conſecutionem</expan> deducit Lucretius in ſua verſibus ligata Phi<lb></lb> <arrow.to.target n="marg103"></arrow.to.target><lb></lb>loſophia; additque non ſolùm, ſi Inane ſeu Vacuum non admit<lb></lb>tatur, rem nullam exijs quæ ſunt, moveri, ſed nec ullam denuò <lb></lb>naſci poſſe in mundo. </s></p> <p type="margin"> <s><margin.target id="marg101"></margin.target><emph type="italics"></emph>Argumen<lb></lb>tum Epicuri <lb></lb>Leucippi, ac <lb></lb>Democriti <lb></lb>pro vacuo.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg102"></margin.target><emph type="italics"></emph>Corporum <lb></lb>penetratio <lb></lb>non poteſt <lb></lb>fieri natu<lb></lb>raliter.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg103"></margin.target><emph type="italics"></emph>Vacuum <expan abbr="nõ">non</expan> <lb></lb>admittit <lb></lb>Lucretius.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Quæ ſi non eſſet Inane,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Non tam ſolicito motu privata careret, Quàm genita omninò nulla ra<lb></lb>tione fuiſſet, vndique materies quoniam ſtipata fuiſſet.<emph.end type="italics"></emph.end> </s><s>Cogita enim <lb></lb>vniverſum mundum (ait vir doctiſſimus Petrus Gaſſendus in <lb></lb>ſuis de Phyſiologia Epicuri Animad verſionibus, ex Epicuri men<lb></lb>te,) ſi nihil Inanis interſperſum habeat, confertiſſimam eſſe mo<lb></lb>lem, adeo ut nè minimum quidem corpuſculum valeat de novo <lb></lb>ſuſcipere (quod quidem aſſerendum neceſſariò eſt, ſi nullum in <lb></lb>rebus Inane, ſi nihil non plenum, ſi locus nullus reſtat complen<lb></lb>dus.). </s><s>Quare aut corpus non admittetur denuò genitum, aut in <lb></lb>illo loco collocabitur, in quo aliud jam ſitum eſt; ſicque idem <lb></lb>locus duo corpora ſeſe undique penetrantia capiet. </s><s>Quod ſanè <lb></lb>per vires Naturæ fieri poſſe non dixeris, ut ut alij id aſſerant, in<lb></lb>ducti exemplo panis, ſpongiæque ſiccæ aquam, cui injiciuntur, <lb></lb>inſugentis; & cinerum tantundem aquæ in conſortium ſuum ad<lb></lb>mittentium in vaſe, quantum ſine cineribus vas recipere poteſt. <lb></lb> <arrow.to.target n="marg104"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg104"></margin.target><emph type="italics"></emph>Argumen<lb></lb>tum Epicu<lb></lb>reorum ac <lb></lb>Democriti <lb></lb>torum pro <lb></lb>vacuo.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Si abſonum videtur vacuum admittere, ſi <foreign lang="grc">ἀδύνατον</foreign> corpo<lb></lb>rum dari penetrationem, & tamen motum admittimus localem; <lb></lb>ſuſque deque verti corpora omnia, quæ Univerſo concluduntur, <lb></lb>fateamur neceſſe eſt toties, quoties eorum unum movebitur, di<lb></lb>cet Democriticus quiſpiam, aut Epicureus: moveatur enim <lb></lb>quodcunque eorum, quæ ſunt, de ſuo quem occupat loco, alte<lb></lb>riuſque in vadere tentet ſtationem; ſanè cùm locum plenum <lb></lb>offendat, neceſſe erit, ex eo pellat, quod corpus illum occupat. </s><s><lb></lb>Illud porrò quónam concedat, ſi omnia quidem plena ſunt? </s><s>An <pb xlink:href="051/01/076.jpg" pagenum="45"></pb>non ipſum rurſus expellet aliud? </s><s>At de eo par redibit difficultas: <lb></lb>hoc enim, aliud expellere loco debebit; & illud aliud; ſicque con<lb></lb>tinuari neceſſe erit inchoatam ſomel corporum commotionem <lb></lb>in ævum, & totum commoveri Vniverſum vel ad muſcæ vola<lb></lb>tum. </s><s>Si enim vel unum corpus cedere loco non valeat, aut non <lb></lb>volet, omnis ceſſabit illicò motus, eritque unaquæque res mun<lb></lb>di ſic inſerta in aliam, ut magis è loco excedere nequeat, quàm <lb></lb>mytuli (inquit Gaſſendus paulò antè citatus) ſeu cochleæ illæ, <lb></lb>quæ intra ſilices naſcuntur. </s><s>Neque dicas, eſſe in mundo rara, <lb></lb>liquida, fluxaque corpora, quæ cedere magis quàm ſilices poſ<lb></lb>ſint. </s><s>Sint enim quantum vis rara, fluxa, & cedere nata; ſi admi<lb></lb>ſtum Inane non habent, ſi particulæ omnes illorum contiguita<lb></lb>tem undique, ſeu ſecundùm totas ſuperficies habent; tale con<lb></lb>tinuum corpus facient, ut perinde ſit ſeu ex ſilice, ſeu ex aqua, ſeu <lb></lb>ex aëre illud dicas: neque enim aër vel paucioribus, vel minùs <lb></lb>compactis ſui partibus occupabit locum minorem, quàm ſilex, <lb></lb>cùm quotcunque loci particulas feceris, tam nulla earum ſit aë<lb></lb>ris, quàm ſilicis particulæ expers. </s><s>Hactenus Democritici, & <lb></lb>Epicurei. </s></p> <p type="main"> <s><emph type="center"></emph>§. II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corpora ſe mutuò expellunt.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HIs quid reponendum, viderint Philoſophi. </s><s>Ariſtoteles certe, </s></p> <p type="main"> <s> <arrow.to.target n="marg105"></arrow.to.target><lb></lb>qui nec vacuum admittit, nec corporum penetrationem <lb></lb>mutuam, nequaquam timet rerum omnium ad quemlibet mo<lb></lb>tum commotionem; quoniam liquida non ſolùm pelluntur, ſed <lb></lb>dividuntur etiam dum urgentur; & quæ antrorſum vergebant <lb></lb>partes, latera lambentes claudunt terga. </s><s>At quidquid ſit, tam <lb></lb>evidens eſt, corpus unum expellere alterum è ſuo, quem occu<lb></lb>pat, loco, ni ſponte excedere velit, quàm eſt manifeſtum, mo<lb></lb> <arrow.to.target n="marg106"></arrow.to.target><lb></lb>tum dari localem; idque verum eſt non tantùm in duris ſoli<lb></lb>diſvé, ſed liquidis etiam ac fluidis corporibus, aëre dico, & aqua. </s><s><lb></lb>videmus enim quotidie, aquam vaſi, tuboque aëre pleno illa<lb></lb>bentem, expellere aërem, ſi exeundi locum habet; & ſi non ha<lb></lb>bet, neque aquam poſſe, aut velle infundi. </s><s>Videmus item aë- <pb xlink:href="051/01/077.jpg" pagenum="46"></pb>rem inflatum vaſi per os unum, expellere aquam per alterum, aut <lb></lb>etiam per idem, ſi elabendi detur locus; qui ſi non datur, nec aë<lb></lb>ri patere ingreſſum. </s><s>Videmus follibus compreſſis erumpere <lb></lb>aërem, & aquam etiam, ſi aquâ erant repleti. </s><s>Videmus, ſi vaſi <lb></lb>aquâ pleno operculum in medio perforatum imponamus, de<lb></lb>primamuſque, aquam preſſam, ſi inter latera vaſis & opercu<lb></lb>lum erumpere non poteſt, exſilire per foramen magno impetu. </s><s><lb></lb>Taceo centena exempla alia. </s><s>Atque hæc mutua corporum ex<lb></lb>pulſio alterum eſt Machinarum Hydro-pnevmaticarum prin<lb></lb>cipium, quo innumera, & non minùs iucunda, quàm admiran<lb></lb>da exhibentur ſpectacula paſſim, vt apparebit apertiſſimè ex ſe<lb></lb>quentibus Machinis. </s><s>Interimſequens accipe Experimentum. </s></p> <p type="margin"> <s><margin.target id="marg105"></margin.target><emph type="italics"></emph>Corpora ex<lb></lb>pellunt ſe <lb></lb>mutuò.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg106"></margin.target><emph type="italics"></emph><expan abbr="Experimẽ-ta">Experimen<lb></lb>ta</expan> varia, <lb></lb>quibus pro<lb></lb>batur cor<lb></lb>poraſe mu<lb></lb>mutuò ex<lb></lb>pellere.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Experimentum, quo oſtenditur vis expulſiva, propter <lb></lb>corporum impenetrabilitatem, ad aquas elevan<lb></lb>das in altum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.077.1.jpg" xlink:href="051/01/077/1.jpg"></figure> <p type="main"> <s>FAcexſtanno, cu<lb></lb>pro, creta, ligno, <lb></lb>aut alia quacunque <lb></lb>materia aquis reſi<lb></lb>ſtente tria vaſcula <lb></lb>A, F, & G, columnis <lb></lb>interſe diſtincta, vt <lb></lb>monſtrat figura; aut <lb></lb>alia ratione, prout <lb></lb>placuerit, aut com<lb></lb>modiùs fuerit: <expan abbr="ſint-q́ue">ſint<lb></lb>que</expan> hæc vaſcula vn<lb></lb>dique clauſa quàm <lb></lb>diligentiſſime, nè <lb></lb>aër poſſit aut ingre<lb></lb>di, aut elabi, ſaltem <lb></lb>ex A & G. </s><s>Vas infe<lb></lb>rius G habeat <expan abbr="epi-ſtomiũ">epi<lb></lb>ſtomium</expan> I. per quod <pb xlink:href="051/01/078.jpg" pagenum="47"></pb>aqua effluere poſſit. </s><s>Vaſa A & F habeant in operculis forami<lb></lb>na C & E, vt per ea infundi poſſit aqua, & iterum obturari. </s><s><lb></lb>Exvaſe A egrediatur tubulus AB vtrimque, apertus qui apud <lb></lb>A fundum vaſis non attingat, ſed tantum ab illo diſtet, vt <lb></lb>aqua interfluere poſſit: apud B verò habeat oſculum ſtrictiſſi<lb></lb>mum. </s><s>Habeat præterea epiſtomium K. </s><s>Ex eodem vaſe A de<lb></lb>ſcendat intra vas inferius G alius tubulus DN, vtrimque aper<lb></lb>tus, qui apud D non attingat operculum vaſis A, ſed tantum <lb></lb>ab illo diſtet, vt poſſit egredi aër: apud H verò tranſeat ſolum <lb></lb>operculum vaſis G, & non extendatur vlteriùs.| </s><s>Ex vaſe deni<lb></lb>que F deſcendatintra vas G alius tubus FG vtrimque aper<lb></lb>tus, qui apud F tranſeat ſolùm fundum vaſis, & non progredia<lb></lb>tur vlteriùs; apud G verò diſtet tantum à fundo, vt aqua ef<lb></lb>fluere poſſit, habeatque vas G epiſtominm L. </s><s>Hi tres tubi <lb></lb>debentita ſtanno alia vè materia coarctari, & adferruminari va<lb></lb>ſis in loco tranſitus, vt nullus aër penetrare intra vaſa, aut elabi <lb></lb>ex ijsdem poſſit. </s><s>Cavendum præterea diligenter eſt, nè tubu<lb></lb>lus AB ſit longior, aut æquè longus, ac tubulus FG; quare <lb></lb>meliùs erit, ſi inter B & K decurtetur quantum poteſt, & quàm <lb></lb>minimum extra vas A protendatur. </s></p> <p type="main"> <s>His ita ritè præparatis, repleantur aqua duo vaſa A & F, per <lb></lb>foramina C & E, & obturentur quàm diligentiſſimè, maximè <lb></lb>foramen C (foramen enim E poteſt manere apertum;) vas <lb></lb>verò G maneatvacuum; & omnia epiſtomia ſint clauſa. </s><s>De<lb></lb>inde aperiatur epiſtomium L, vt aqua vaſis F defluere poſſit <lb></lb>intra vas G: & poſtquam defluxit aliquantulum aquæ, aperia<lb></lb>tur epiſtomium K; <expan abbr="erumpetq́ue">erumpetque</expan> maximo impetu aqua va<lb></lb>ſis A per tubulum AB, proſilietque in altum, vi expulſiva, pro<lb></lb>pter corporum impetrabilitatem. </s><s>Nàm aqua vaſis F deſcen<lb></lb>dens intra vas G, expellit inde aërem per tubum HD intra vas <lb></lb>A; qui aer expellit inde aquam per tubulum AB, quoniam ne<lb></lb>que in G, neque in A, aër & aqua ſimul in eodem loco manere <lb></lb>poſſunt, ſed neceſſariò vnum corpus expellit alterum, propter <lb></lb>eorum impenetrabilitatem. </s><s>Vides igitur quomodo vis expul<lb></lb>ſiva propter corporum impenetrabilitatem ſit principium & <pb xlink:href="051/01/079.jpg" pagenum="48"></pb>cauſa Machinarum Hydro-pnevmaticarum? </s><s>Vbi deſcenderit <lb></lb>aqua vaſis F intra vas G, & exſiliuerit aqua vaſis A per tubum <lb></lb>AB; depromi poterit aqua vaſis G per epiſtomium I, & reple<lb></lb>ri iterum vaſa A & F, vt antea, & inſtitui idem luſus. </s></p> <p type="main"> <s><emph type="center"></emph>§. IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Notantur nonnulla circa prædictum <lb></lb>Experimentum.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg107"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg107"></margin.target><emph type="italics"></emph>Fundame<lb></lb>tum omni<lb></lb>um Machi<lb></lb>narum Hy<lb></lb>dropnev<lb></lb>maticarum <lb></lb>quæ fiunt vi <lb></lb>expulſiva.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>HOc experimentum eſt fundamentum omnium Hydro<lb></lb>pnevmaticarum Machinarum quæ fiunt vi expulſiva ob cor<lb></lb> <arrow.to.target n="fig11"></arrow.to.target><lb></lb>porum impenetra<lb></lb>bilitatem; ideoque <lb></lb>Tyrones diligenter <lb></lb>procurare debent, <lb></lb>vt illud intelligant: <lb></lb>quare nonnulla cir<lb></lb>ca <expan abbr="ipsũ">ipsum</expan> ſunt adver<lb></lb>tenda. </s></p> <figure id="id.051.01.079.1.jpg" xlink:href="051/01/079/1.jpg"></figure> <p type="main"> <s>Primum eſt, ex<lb></lb>pedire vt vas A non <lb></lb>ſit minùs capax <expan abbr="quã">quam</expan> <lb></lb>vas F, & vt tubus <lb></lb>FG non ſit amplior <lb></lb>tubo AB: ſic enim <lb></lb>fiet, vt quàmdiu a<lb></lb>qua ex vaſe F <expan abbr="deſcẽ-dit">deſcen<lb></lb>dit</expan> intra G, tamdiu <lb></lb>ſaliat aqua ex vase A <lb></lb>per tubum AB. </s><s>Hoc <lb></lb><expan abbr="tamẽ">tamen</expan> non eſt omni<lb></lb>nò neceſſarium. </s></p> <p type="main"> <s>Secundum eſt, Non eſſe neceſſarium, vt fiat vas F, ſed fie<lb></lb>ri poteſtſolus canalis ſeu tubus FG, qui apud F habeat infun<lb></lb>dibulum, vt aqua infundi poſſit; dummodò ſit longior quàm <lb></lb>tubus AB; vt mox dicam. </s></p> <pb xlink:href="051/01/080.jpg" pagenum="49"></pb> <p type="main"> <s>Tertium eſt, omninò <expan abbr="neceſſariũ">neceſſarium</expan> eſſe, vt tubus FG longi<lb></lb>or ſit quam tubus AB, quia, vt diximus Protheoria I. §. VI. & di<lb></lb>cemus iterum infrà Protheoria IV. cap. 2. Propoſit. 14. hîc et<lb></lb>iam, vt vbiq, in hydraulicis, perpendiculis certatur, non verò <expan abbr="a-quarũ">a<lb></lb>quarum</expan> copiâ. </s><s><expan abbr="Perpendiculũ|autẽ">Perpendiculun|autem</expan> tubi FG computatur ab F <expan abbr="vſq;">vſque</expan> ad </s></p> <p type="main"> <s> <arrow.to.target n="marg108"></arrow.to.target><lb></lb>ſupremam <expan abbr="ſuperficiẽ">ſuperficiem</expan> aquæ deſcendentis & quieſcentis in vaſe G. </s><s><lb></lb>Quò verò longius fuerit perpendiculum FG ſupra perpendicu<lb></lb>lum AB eò altiùs ſalit aqua ex oſculo B. </s><s>Quare cùm in prin<lb></lb>cipio, quando incipit deſcendere aqua intra vas G, longius ſit <lb></lb>perpendiculum FG, quàm poſtea (repleto paulatim vaſe G) <lb></lb>& id <expan abbr="ſẽper">ſemper</expan> magis ac magis minuatur; conſequens eſt, vtin prin<lb></lb>cipio altiùs ſaliat aqua ex B, quàm poſt principium, & vt ſem<lb></lb>per minùs & minùs altè exſiliat. </s><s>Vide etiam quæ dicimus in<lb></lb>frà Parte 2. Claſse I. cap. 2. Machina I. Annot. 2. </s></p> <p type="margin"> <s><margin.target id="marg108"></margin.target><emph type="italics"></emph>Perpendi<lb></lb>culis, non a<lb></lb>qudrum co<lb></lb>piâ certatur <lb></lb>in hydrau<lb></lb>licis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Quartum eſt, Non ſolùm ſervandam eſſe proportionem <lb></lb>quoad longitudinem inter tubos AB, & GF, ſed etiam quoad <lb></lb>capacitatem, nè ſcilicet AB laxior ſit quàm GF; alioquin gra<lb></lb>vior erit aqua intra ipſum, quàm vt elevari poſſit ab aëre modi<lb></lb>co intra vas A pulſo à modica aqua cadente intra vas G. </s><s>Si <lb></lb>verò FG tubus laxior eſſet quàm AB, nimis citò repleretur <lb></lb>vas G, & antequam tota aqua vaſis A expelleretur per AB. </s></p> <p type="main"> <s>Quintum eſt, Nihil referre quantæ ſit altitudinis tubus HD, <lb></lb>per quem aër defertur, quia nihil confert ad perpendiculum. </s><s>Pro<lb></lb>curandum tamen eſt, nè ſit nimis laxus, aliàs multùm aëris intra <lb></lb>ipſum abſorberetur, qui alioquin expelli deberet intra vas A. </s></p> <p type="main"> <s>Sextum eſt, prædictum artificium elevandi aquam vi ex<lb></lb>pulſiva propter corporum impenetra bilitatem, eſſe typum & <lb></lb>exemplar omnium Machinarum Hydro-pnevmaticarum præ<lb></lb>dicta virtute animatarum; ac proinde ſemperante oculos <lb></lb>in ſimilibus Machinis fabricandis eſſe habendum, <lb></lb>vt in principio dicebam. </s></p> <pb xlink:href="051/01/081.jpg" pagenum="50"></pb> <p type="main"> <s><emph type="center"></emph>§ V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Heronis error in elevando oleo vi Expulſivâ <lb></lb>in lucerna.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HEro Alexandrinus in libello de Spiritalibus cap. 72. proponit <lb></lb>hanc Machinam. </s><s><emph type="italics"></emph>Lucernæ conſtructio, vt ellychnio impo<lb></lb>ſito, quando oleum deficiat, ex aure eius oleum in ellychnium infun<lb></lb>datur, quantum quis voluerit, nullo ipſi appoſito vaſe, ex quo oleum in<lb></lb> <arrow.to.target n="marg109"></arrow.to.target><lb></lb>fluat.<emph.end type="italics"></emph.end> </s><s>Qua quidem in conſtructione errorem committit graviſ<lb></lb>ſimum (ſi tamen ipſius eſt error, & non potiùs Interpretis, qui <lb></lb>figuras appoſuit) quem hîc detegere oportet, ne alijs etiam ſit <lb></lb> <arrow.to.target n="fig12"></arrow.to.target><lb></lb>errandi occaſio. </s><s>Quod eò et<lb></lb>iam libentiùs facio, quòd nec <lb></lb>Federicus Commandinus, qui <lb></lb>ex Græco in latinum tranſtulit <lb></lb>Heronem; nec Ioannes Bapti<lb></lb>ſta Aleottus, qui Commandini <lb></lb>interpretationem red didit Itali<lb></lb>cam; nec Ioannes Baptiſta Porta, <lb></lb>qui Heronis errorem etiam ob<lb></lb>ſervavit, genuinam lucernæ de<lb></lb>lineationem dederunt. </s><s>Eam <lb></lb>verò hîc dare conabimur, allatis <lb></lb> <arrow.to.target n="marg110"></arrow.to.target><lb></lb>Heronis verbis ex Commandini <lb></lb>translatione, addendo nonnulla <lb></lb>verba majoris claritatis gratia, <lb></lb>quæ aſteriſcis in margine no<lb></lb>tantur. </s><s>Sic ergo diſcurrit Hero. </s><s><lb></lb><emph type="italics"></emph>Conſtruatur lucerna, baſim habens <lb></lb>concavam, & triangularem inſtar <lb></lb>pyramidis; ſit que baſis concava<emph.end type="italics"></emph.end> AB <lb></lb>CD, <emph type="italics"></emph>& in ea diaphragma<emph.end type="italics"></emph.end> EF. </s><s><emph type="italics"></emph>Lu<lb></lb>cernæ autem caulis ſit<emph.end type="italics"></emph.end> GH, <emph type="italics"></emph>& ipſe <lb></lb>concavus; ſupra quem ſit concavus <lb></lb>calathus<emph.end type="italics"></emph.end> KL, <emph type="italics"></emph>plurimum olei conti<lb></lb>nens. </s><s>Ex diaphragmate<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>pro-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/082.jpg" pagenum="51"></pb><emph type="italics"></emph>cedat<emph.end type="italics"></emph.end> MN <emph type="italics"></emph>tubus, ſimul cum eo perforatus, tantum diſtans à calathi <lb></lb>operculo<emph.end type="italics"></emph.end> KL <emph type="italics"></emph>(in quo ellychnium imponitur) quantum ad aër is <lb></lb>exitum ſufficiat. </s><s>Alius autem tubulus<emph.end type="italics"></emph.end> XO <emph type="italics"></emph>demittatur per opercu<lb></lb>lum<emph.end type="italics"></emph.end> KL <emph type="italics"></emph>diſtans à fundo calathi, quantum ſatis ſit ad aquæ fluxum <lb></lb>& ex operculo paululum excedens. </s><s>Exceſſui verò aptetur alius tubulus<emph.end type="italics"></emph.end><lb></lb>P <emph type="italics"></emph>habens ſuperius oſculum obſtructum; qui tubulus per fundum lychnij <lb></lb> impulſus coagmentetur lychno. </s><s>At tubum autem<emph.end type="italics"></emph.end> P <emph type="italics"></emph>adglutine<lb></lb>tur alius tubulus exilis, procedens ad extremitatem auris, & ſimul com ea <lb></lb>perforetur, vt in fluat in concavitatem ellychnij, foramen habens <lb></lb>quemadmodum & alij. </s><s>Et ſub diaphragmate<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>conglutinetur clavi<lb></lb>cula deferens in locum<emph.end type="italics"></emph.end> CDEF, <emph type="italics"></emph>ita, vt ſi aperiatur, aqua ex loco<emph.end type="italics"></emph.end><lb></lb>ABEF, <emph type="italics"></emph>in ipſum<emph.end type="italics"></emph.end> CDEF <emph type="italics"></emph>tranſeat. </s><s>Sit autem in operculo<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>par<lb></lb>rum foramen, per quod locum<emph.end type="italics"></emph.end> ABEF <emph type="italics"></emph>implebimus aquâ; & qui <lb></lb>in ipſo eſt aër, per dictum foramen excedet. </s><s>Itaque ſublato ellych<lb></lb>nio, calathum oleo imple bimus per tubum<emph.end type="italics"></emph.end> XO, <emph type="italics"></emph>aëre per<emph.end type="italics"></emph.end> NM <emph type="italics"></emph>tubulum <lb></lb>excedente, & adhuc per clavem apertam, quæ eſt in fundo<emph.end type="italics"></emph.end> C.D, <lb></lb> <emph type="italics"></emph>quando & quæ eſt in<emph.end type="italics"></emph.end> CDEF <emph type="italics"></emph>aqua effluet. </s><s>Impoſito igitur el<lb></lb>lychnio per ſmeriſma<emph.end type="italics"></emph.end> P, <emph type="italics"></emph>quando opus ſit oleum infundere, aperiemus <lb></lb>clavem, quæ in fundo<emph.end type="italics"></emph.end> CD; <emph type="italics"></emph>& aquâ ex loco<emph.end type="italics"></emph.end> ABEF <emph type="italics"></emph>in locum<emph.end type="italics"></emph.end><lb></lb> CDEF<emph type="italics"></emph> ſecedente, aër qui eſt in ipſo, per tubum<emph.end type="italics"></emph.end> MN <emph type="italics"></emph>ad cala<lb></lb>thum perveniens elidet oleum; quod quidem per tubulum<emph.end type="italics"></emph.end> XO, <emph type="italics"></emph>& <lb></lb>per alium ipſi cohærentem ad ellychnium procedet. </s><s>Quando au<lb></lb>tem non amplùs fluere volumus, clavicula claudetur, & ceſſabit; & <lb></lb>rurſus quando opus ſit, idem faciemus.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg109"></margin.target>Error He<lb></lb>ronis in lu<lb></lb>cernæ con<lb></lb>ſtructione.</s></p> <p type="margin"> <s><margin.target id="marg110"></margin.target><emph type="italics"></emph>Lucernæ <lb></lb>Heronis ge<lb></lb>auina figu<lb></lb>ra.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.082.1.jpg" xlink:href="051/01/082/1.jpg"></figure> <p type="main"> <s>Hæc Commandinus Heronis Interpres; quæ ego omni<lb></lb> <arrow.to.target n="marg111"></arrow.to.target><lb></lb>no mendoſa eſſe exiſtimo: puto enim vbique lychnum pro el<lb></lb>lychnio ponendum eſſe, & alia pleraque legenda prout in mar<lb></lb>gine ſunt poſita aſteriſcis notata. </s><s>Non potui in venire Græcum <lb></lb>Heronis textum, vt vt diù quæſiverim. </s><s>Tubuli etiam ſupra ca<lb></lb>lathi operculum diſponendi ſunt ſine dubio, vt nos diſpoſuimus, <lb></lb><expan abbr="quoniã">quoniam</expan> Heronis textus latinus apud <expan abbr="ipſum̃et">ipſumnet</expan> Commandinum id <lb></lb>exigit. </s><s>Nec mireris Lector, ſi ſuſpicet Commandini præſentem <lb></lb>Latinum de lucerna textum non eſſe vndequaque correſpon<lb></lb>dentem græco textui; poſthumum enim eſt Opus Commandini, <pb xlink:href="051/01/083.jpg" pagenum="52"></pb>nec poſtremam ipſius manum expertum, vt habetur initio libelli <lb></lb>in præfatiuncula ad Lectorem. </s><s>Eſt autem in Commandini te<lb></lb>xtu ac ſchemate inſignis error in eo, quòd clavicula R trans<lb></lb>mittit aquam quæ eſt in ABEF intra baſim EFCD per aper<lb></lb>tum ſolùm foramen ſine tubulo, qui paulò longior ſit quàm tu<lb></lb>bulus OX; quod tamen omnino requiritur, vt diximus paulò <lb></lb>antè §. IV. & cauſam dabimusintrà Protheoria IV. cap. 2. Pro<lb></lb>poſit. 14. experientia ſiquidem conſtat, cylindrum aquæ per fo<lb></lb>ramen <expan abbr="deſcendentẽ">deſcendentem</expan> (ſi quandoque deſcendit aëre ſuccedente) <lb></lb>in aêre libero non habere eandem vim, ac deſcendentem per <lb></lb>tubum; tametſi vtrobique ſit eadem aquæ quantitas, cum eodem <lb></lb>perpendiculo. </s><s>Cauſa eſt, quia ſi liberè & ſine tubo defluit a queus <lb></lb>cylindrus, <expan abbr="ſignũ">ſignum</expan> eſt aërem ſubintrare; ſi aër ſubintrat, ceſſat me<lb></lb>tus vacui, ac proinde aqua debet elevari vt <expan abbr="laborãti">laboranti</expan> Naturæ ſuc<lb></lb>currat. </s><s>Quòd ſi tam ſtrictum eſt foramen, vt aër ſubintrare non <lb></lb>poſſit, nè gutta quidem aquæ effluet, vt experientia quotidiana <lb></lb>docet, idque propter vacui metum. </s><s>Hunc tamen errorem ego <lb></lb> <arrow.to.target n="marg112"></arrow.to.target><lb></lb>nequaquam Heroni adſcribendum putem, vt Porta facit, ſed <lb></lb>exiſtimo Heronem produxiſſe tubulum R ferè vſque fundum <lb></lb>CD; ſic enim major erit quàm tubulus XO, & aqua per ipſam <lb></lb>R decideus habebit perpendiculum præponderans perpendi<lb></lb>culo aquæ ſeu olei aſcendentis per XO. </s></p> <p type="margin"> <s><margin.target id="marg111"></margin.target><emph type="italics"></emph>Heronis lo<lb></lb>cus apud <lb></lb>Comman<lb></lb>dinum men<lb></lb>doſuæ.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg112"></margin.target><emph type="italics"></emph>Heronis er<lb></lb>ror excuſa<lb></lb>tur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Similis error reperitur apud Heronem cap. 36. vbi docet <lb></lb>ſatyriſcum conſtruere ſuper quadam baſi, vtrem in manibus <expan abbr="te-nentẽ">te<lb></lb>nentem</expan>, cui adiacet labellum; vt infuſo in labellum humore, ita <lb></lb>vt repleatur, aqua per vtrem in idem labellum in fluat, & non ſu<lb></lb>perfundatur, quòusque tota per vtrem aqua evacuata fuerit. </s><s>Ex <lb></lb>qua quidem conſtructione deſumpta eſt praxis conſtruendi fon<lb></lb>tem Heronis, de quo infrà Parte 2. Claſse I. cap. 2. Machi<lb></lb>na 1. 2. & 3. vbi errorem Heronis detegemus; <lb></lb>ſi tamen Heronis eſt, & non In<lb></lb>terpretis. </s></p> <pb xlink:href="051/01/084.jpg" pagenum="53"></pb> <p type="main"> <s><emph type="center"></emph>§. VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Attractione & expulſione ſimul aquam ele<lb></lb>vare poſſumus.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DIximus §. IV præcedente, perpen diculum aquæ cadentis & <lb></lb>pellentis aërem, longius eſſe debere perpendiculo aquæ <lb></lb>aſcendentis per expulſionem. </s><s>Diximus præterea Protheoria I. <lb></lb>§. VI. perpendiculum aquæ cadentis & trahentis aërem, debe<lb></lb>re ſuperare longitudine perpendiculum aquæ attractæ. </s><s>Infrâ <lb></lb>Parte 2. Claſse I. cap. 1. Machina 7. & cap. 2. Machina 10. & 11. di<lb></lb>cemus, qua ratione per multiplicationem plurium <expan abbr="perpẽ">perpendicu<lb></lb>lorum</expan> brevium elevari poſſit aqua, tam per expulſionem, quàm <lb></lb>per attractionem, ad quam vis altitudinem. </s><s>Nunc ſubjiciam <lb></lb>modum attollendi aquam per attractionem & expulſionem ſi<lb></lb> <arrow.to.target n="marg113"></arrow.to.target><lb></lb>simul ad duplam altitudinem aquæ cadentis, quoniam ingenio<lb></lb>fus eſt, & ad multa poteſt eſſe vtilis. </s><s>Refert illum Porta lib. 2. <lb></lb>Spiritalium cap. 2. eumque magnificè extollit, tanquam à ſe in<lb></lb>ventum; & ait ſuperare omnem humanum intellectum, nec vn<lb></lb>quam in mentem veniſſe antiquis, ſe verò poſt expenſas multas, <lb></lb>& labores plurimos illum tandem reperiſſe. </s><s>Modus hic eſt. </s></p> <p type="margin"> <s><margin.target id="marg113"></margin.target><emph type="italics"></emph>Modus in<lb></lb>genioſus e<lb></lb>levandi <lb></lb>aquam in<lb></lb>quam vis al<lb></lb>titudinem <lb></lb>per attracti<lb></lb>onem & ex<lb></lb>pulſionem, <lb></lb>ſimul.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.084.1.jpg" xlink:href="051/01/084/1.jpg"></figure> <p type="main"> <s>Sit ex vaſe B elevanda <lb></lb>aqua vſque ad vas E, ad <lb></lb>altitudinem centum pe<lb></lb>dum, mediante perpen<lb></lb>diculo 50. pedum aquæ <lb></lb>cadentis. </s><s>Fiant alia duo <lb></lb>vaſa A, & C, in eodem <lb></lb>plano horizontali cum <lb></lb>vaſe B conſtituta, <expan abbr="ejuſdẽ">ejuſdem</expan> <lb></lb>capacitatis cum B; & in<lb></lb>fra ipſa conſtituatur vas <lb></lb>D, cujus ſuprema oper<lb></lb>culi pars diſtet à fundis di<lb></lb>ctorum vaſorum 50. pedi<lb></lb>bus. </s><s>Ex vaſe A deſcen<lb></lb>dat in vas D tubus GX, 50. <pb xlink:href="051/01/085.jpg" pagenum="54"></pb> <arrow.to.target n="fig13"></arrow.to.target><lb></lb><expan abbr="pedũ">pedum</expan>; qui tamen ab X ex<lb></lb>tendi ac prolongari poteſt <lb></lb>uſque ad H, dummodò <lb></lb>tantum diſtet à fundo, ut <lb></lb>aqua effluere poſſit. </s><s>Ha<lb></lb>beat autem hic tubus epi<lb></lb>ſtomium V. </s><s>Ex vaſe B de<lb></lb>ſcendat in idem vas D ali<lb></lb>us tubus KI, incipiens <lb></lb>paulò infra operculum <lb></lb>apud K, & deſinens pau<lb></lb>lò infra operculum apud <lb></lb>I. </s><s>Ex vaſe C deſcendat <lb></lb>tubus OP 50. pedum, <lb></lb>habens epiſtomium T. </s><s>Ex <lb></lb>vaſe E deſcendant in va<lb></lb>ſa B & C duo tubi: pri<lb></lb>mus NC, incipiens infra operculum apud N, & deſinens in<lb></lb>fra operculum apud C: alter ML, incipiens immediatè infra <lb></lb>operculum apud M, & deſinens ſupra fundum apud L. </s><s>Lon<lb></lb>gitudo verò hujus tubi ML ab operculo M uſque ad punctum <lb></lb>L ſit centum pedum. </s><s>Tria vaſa A, B, C, habeant ſua forami<lb></lb>na cum infundibulis F, per quæ aqua infundi poſſit intra vaſa, <lb></lb>& obturari. </s><s>Vas tamen A poteſt manere apertum. </s><s>Duo vaſa <lb></lb>D & E habeant ſua epiſtomia H & S. </s><s>Omnia præterea va<lb></lb>ſa, excepto A, debent eſſe undique ac diligentiſſimè clauſa; <lb></lb>ideoque tubi debent in loco tranſitus accuratiſſimè adferrumi<lb></lb>nari ipſorum vaſorum operculis, & fundis. </s><s>His ita conſtitutis, <lb></lb>repleantur tria vaſa A, B, C, aquâ, & claudantur, clauſis priùs <lb></lb>omnibus epiſtomijs omnium vaſorum ac tuborum: reliqua ve<lb></lb>rò duo vaſa, D & E, maneant vacua. </s><s>Deinde aperiatur <lb></lb>epiſtomium T; & aqua vaſis C deſcendet verſus P, ſecum<lb></lb>que trahet, ad vacuum vitandum, aërem vaſis E, per tubum <lb></lb>NC, ſimulque aquam vaſis B uſque ad altitudinem 50. pedum <pb xlink:href="051/01/086.jpg" pagenum="55"></pb>ubi V, quantum nimirum eſt perpendiculum tubl OP, per <lb></lb>quem aqua cadit. </s><s>Poſtquam verò aqua deſcenderit hinc uſque <lb></lb>ad P, inde uſque ad V, hærebit utrimque velut in æquilibrio <lb></lb>immobilis, propter perpendiculorum æqualitatem. </s><s>Tum verò <lb></lb>aperiatur epiſtomium V, & aqua vaſis A deſcendet intra vas <lb></lb>D, indeque expellet aërem per tubum IK intra vas B; qui aër <lb></lb>premet aquam, atque propellet ſurſum per tubum LM verſus <lb></lb>M, ſicque elevabitur aqua ultra punctum V, effluetque aqua <lb></lb>ex tubo OP, penituſque aſcendet aqua vaſis B, per tubum LM, <lb></lb>intra vas E; nec ceſſabit fluxus, donec tria vaſa A, B, C, ſimul <lb></lb>fuerint evacuata, totaque aqua B aſcenderitin E. </s><s>Sijam aqua <lb></lb>vaſorum D & E per ſua epiſtomia depromatur, & vaſa A, B, C, <lb></lb>denuò repleantur; inſtitui poterit eadem circulatio, idque to<lb></lb>ties, quoties libuerit. </s><s>Hæc eſt praxis Portæ; ingenioſus atque <lb></lb>induſtrius artifex addere, demere, mutare poterit, quæ libuerit, <lb></lb>ornatûs aut commoditatis gratia, modò non alteretur rel ſub<lb></lb>ſtantia, quam nos præcisè hîc dedimus. </s></p> <figure id="id.051.01.086.1.jpg" xlink:href="051/01/086/1.jpg"></figure> <p type="main"> <s>Nota hîc, ut aperto epiſtomio T deſcendat aqua vaſis C <lb></lb>verſus P, laxandum ſimul eſſe epiſtomium V vaſis A; alio<lb></lb>quin nunquam deſcendet aqua vaſis C, nè detur vacuum, ut <lb></lb>conſideranti patebit. </s></p> <p type="main"> <s>Nota præterea, quod diximus de aqua aſcendente ad alti<lb></lb>tudinem 50. pedum, tantùm gratia exempli fuiſſe dictum: nam <lb></lb>aqua non poteſt per attractionem|elevari ad tantam <expan abbr="altitudinẽ">altitudinem</expan>, <lb></lb>ut alibi fuſiùs dicemus. </s></p> <p type="main"> <s><emph type="center"></emph>§. VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salomon Caus meritò ſugillat Heronem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HEro cap. 55. Spiritalium ait, <emph type="italics"></emph>quædam vaſa à principio humore <lb></lb>injecto fluunt, intermiſſione verò facta non ampliùs fluunt injecto <lb></lb>humore, quouſ〈qué〉 ad dimidium repleta fuerint; tunc enim incipiunt flue<lb></lb>re: At intermiſſione facta, non ampliùs fluunt, quouſ〈que〉 impleantur.<emph.end type="italics"></emph.end><lb></lb> </s><s>Hujus rei probandæ gratia proponit hujuſmodi machinam.</s> <pb xlink:href="051/01/087.jpg" pagenum="56"></pb> <s><arrow.to.target n="marg114"></arrow.to.target><lb></lb> <arrow.to.target n="fig14"></arrow.to.target><lb></lb><emph type="italics"></emph></s><s>Sit enim vas<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>habens in ſeipſo <lb></lb>tres ſiphones inflexos<emph.end type="italics"></emph.end> C, D, E, <emph type="italics"></emph>in ven<lb></lb>tre occultatos, quorum altera quidem <lb></lb>crura ſint ad fundum vaſis, altera ve<lb></lb>rò extra ferantur in canales efforma<lb></lb>ta; atque eorum extremis apponantur <lb></lb>vaſa<emph.end type="italics"></emph.end> F, H, G, <emph type="italics"></emph>quorum fundum diſtet <lb></lb>ab oſculis, quantum ad aquæ fluxum ſa<lb></lb>tis ſit. </s><s>Omnia verò comprehendantur <lb></lb>alio quodam vaſe, tanquam baſi<emph.end type="italics"></emph.end> KLMN, <lb></lb><emph type="italics"></emph>quæ canalem<emph.end type="italics"></emph.end> X <emph type="italics"></emph>habeat. </s><s>Et ſiphonis <lb></lb>quidem<emph.end type="italics"></emph.end> C <emph type="italics"></emph>curvit as ſit ad fundum va<lb></lb>ſis; ſiphonis verò<emph.end type="italics"></emph.end> D <emph type="italics"></emph>curvitas ad di<lb></lb>midium altitudinis ejus & ſiphonis<emph.end type="italics"></emph.end> E <lb></lb><emph type="italics"></emph>ad ipſum collum. </s><s>Si igitur in vas<emph.end type="italics"></emph.end> AB <lb></lb><emph type="italics"></emph>aquam infundamus, à principio <expan abbr="quidẽ">quidem</expan> <lb></lb>fluet per ſiphonem<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>quoniam cur<lb></lb>vitas ipſius eſt ad fundum. </s><s>Quòd ſi <lb></lb>intermittamus, evacuabitur humidum <lb></lb>infuſum per canalem<emph.end type="italics"></emph.end> X, <emph type="italics"></emph>& vas<emph.end type="italics"></emph.end> F <emph type="italics"></emph>relin quetur aqua plenum, ſiphonis <lb></lb>verò<emph.end type="italics"></emph.end> C <emph type="italics"></emph>reliqua pars aëre plena erit. </s><s>Rurſum cùm aquam infunda<lb></lb>mus, non procedet per ſiphonem<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>propterea quòd aër in eo contine<lb></lb>tur inter aquam infuſam, & eam quæ eſt in vaſe<emph.end type="italics"></emph.end> F. </s><s><emph type="italics"></emph>Aſcendet ergo <lb></lb>humidum uſque ad ſiphonis<emph.end type="italics"></emph.end> D <emph type="italics"></emph>curvitatem, quæ eſt ad dimidium alti<lb></lb>tudinis vaſis; & tunc fluere incipiet: ſed inter miſſione facta, rurſus <lb></lb>idem continget quod in ſiphone<emph.end type="italics"></emph.end> C <emph type="italics"></emph>jam dictum eſt. </s><s>Eadem & in ſi<lb></lb>phone<emph.end type="italics"></emph.end> E <emph type="italics"></emph>intelligantur. </s><s>Oportebit autem humidum ſenſim infunde<lb></lb>re, nè aër, qui in ſiphonibus comprehenſus eſt, ſumma vi expellatur.<emph.end type="italics"></emph.end><lb></lb>Hæc Hero; Quæ tamen, & quidem optimè, atque ex Hydro<lb></lb>pnevmaticæ artis principijs, Salomon Caus in ſuis hydraulicis, <lb></lb> <arrow.to.target n="marg115"></arrow.to.target><lb></lb>ſeu lib. 1. de viribus motricibus, reprehendit, dicens effluere <lb></lb>aquam per ſiphonem C, etiam poſt ſecundam infuſionem in<lb></lb>tra vas, eò quòd aër contentus intra ſiphonem C pellatur ab <lb></lb>aqua extra inferius oſculum, erumpatque extra aquam vaſis F <pb xlink:href="051/01/088.jpg" pagenum="57"></pb>Quod quidem <expan abbr="veriſſimũ">veriſſimum</expan> eſt, cùm aqua infuſa intra vas AB per ſe<lb></lb>cundam <expan abbr="infuſionẽ">infuſionem</expan>, facillimè aſcendat per crus internum <expan abbr="uſq;">uſque</expan> ad <lb></lb><expan abbr="curvitatẽ">curvitatem</expan> C, non reſiſtente aëre; qui aër intra <expan abbr="ſiphonẽ">ſiphonem</expan> CF compreſ<lb></lb>ſus cedit aquæ aſcendenti primùm uſq, ad <expan abbr="curvitatẽ">curvitatem</expan> C, <expan abbr="indeq;">indeque</expan> <lb></lb>deſcendenti pondere ſuo, pulſo aëre, erumpente per aquam va<lb></lb>ſis F. </s><s>Adde quòd ſi tam altum eſſet vaſculum F, ut aër per ejus <lb></lb>aquam exitum non inveniret; aſcenderet is per ſiphonem aquæ <lb></lb>mixtus, prout fieri videmus in canali vitreo quantumvis gracili <lb></lb>atque longo: ſi enim aquâ aliquòusque eum repleas, & ob<lb></lb>tùrato utroque orificio invertas, ut aqua ſuperiorem, aër inferio<lb></lb>rem occupat locum; ſtatim deſcendit aqua, & aſcenditaër, aper<lb></lb>tâ ſibi vel per medias aquas viâ, ut teſtantur bullæ frequentes in<lb></lb>ter aquas erumpentes; & qui paulò antè ſuccumbebat aquæ, ei<lb></lb>dem paulò poſt incumbit aër. </s></p> <p type="margin"> <s><margin.target id="marg114"></margin.target><emph type="italics"></emph>Heronis Ma<lb></lb>china defe<lb></lb>ctuoſa.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg115"></margin.target><emph type="italics"></emph>Heronis er<lb></lb>ror.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.088.1.jpg" xlink:href="051/01/088/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Idem perpendiculum aquæ cadentis non poteſt ſervire <lb></lb>ſimul attractioni & expulſioni.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>POrta loco ſæpe citato de ſpiritalibus Cap. VIII. ait, ſe fre<lb></lb>quenter tentaſſe ut aquam eodem perpendiculo mediante <lb></lb>elevaret ad majorem altitudinem, quàm perpendiculum erat, <lb></lb>partim attractione, partim expulſione. </s><s>Eum in finem fecit vas <lb></lb>A, ex quo elevare volebat aquam uſque ad vas B, ad alti<lb></lb>tudinem pedum centum verbi gratia. </s><s>Conſtruxit igitur aliud <lb></lb>æquale vas C in eodem plano, & aliud DF demiſſius utroque <lb></lb>pedibus 50. vaſa conſtructa inſtruxit tubis & epiſtomijs, prout <lb></lb>figura monſtrat. </s><s>Hiſce peractis, replevit vaſa C & A aquis, & <lb></lb>diligenter clauſit utrumque, clauſis etiam eadem diligentia vaſis <lb></lb>B & DE. </s><s>Deinde aperuit tubum ED, ut deſcendente aqua vaſis C <lb></lb>intra vas DE, traheretur aër ex tubo CK, vaſe B, & tubo <lb></lb>IH, ſimulque attraheretur aqua vaſis A ſaltem ad L, altitu<lb></lb>dinem pedum 50; quod & factum fuit. </s><s>Sperabat|autem ut aër <lb></lb>vaſis DF pulſus per tubum EG, intra vas A, expelleret inde <pb xlink:href="051/01/089.jpg" pagenum="58"></pb> <arrow.to.target n="fig15"></arrow.to.target><lb></lb>aliam aquam, & ſublatam <lb></lb>jam antea aquam vſque ad <lb></lb>L, attolleret vlteriùs vſque <lb></lb>ad vas B; at nunquam id <lb></lb>obtinere potuit: nam poſt<lb></lb>quam aſcenderat aqua vſ<lb></lb>que ad L, hæſit ſuſpenſa, <lb></lb>& aqua vaſis C non deflu<lb></lb>xit ampliùs per tubum ED. </s><s><lb></lb>Collegit inde, idem per<lb></lb>pendiculum ED non poſ<lb></lb>ſe inſervire attractioni & <lb></lb>expulſioni ſimul, ſed vel <lb></lb>ſoli attractioni, vel ſoli ex<lb></lb>pulſioni; quod benè notan<lb></lb>dum eſt. </s><s>Cauſam dabi<lb></lb>mus infrà Protheoria IV. <lb></lb>capite 2. Propoſit. 13. & 14. <lb></lb>quam tamen ignoraſſe Por<lb></lb>ta videtur, quoniam nul<lb></lb>lam adſignat. </s></p> <figure id="id.051.01.089.1.jpg" xlink:href="051/01/089/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. IX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Error apud Ioannem Baptiſtam Portam, indicatur.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>APud Ioannem Baptiſtam Portam lib 2. Spiritalium cap. 10. <lb></lb>traditur modus elevandi aquam per expulſionem ad ſtellas <lb></lb>vſque, vt ibi dicitur, mediante ſolo vnico perpendiculo quin<lb></lb>quaginta verbi gratia pedum altitudinis: qui tamen eſt omnino <lb></lb>falſus, & repugnat doctrinæ Portæ in præcedentibus traditæ; <lb></lb>Vnde ſuſpicabar ab Hiſpano traductore fuiffe additum: crede<lb></lb>re enim nulla ratione poteram, à Porta tam enormem errorem <lb></lb>potuiſſe committi. </s><s>Reperi tamen deinde eundem modum in <pb xlink:href="051/01/090.jpg" pagenum="59"></pb> <arrow.to.target n="fig16"></arrow.to.target><lb></lb>editione latina cap. 9. Modus hic <lb></lb>eſt. </s><s>Eſto vas C, & ſupra ipſum <lb></lb>ad diſtantiam pedum verbi gratia <lb></lb>quinquaginta, vaſa D & K, cum <lb></lb>ſuis infundibulis; & ſupra hæc ali<lb></lb>ud G; aliudque ſupra hoc; & ſic <lb></lb>deinceps ad quamvis altitudinem, <lb></lb>etiam vſque ad ſtellas. </s><s>Conjun<lb></lb>gantur dicta vaſa tubis, vt mon<lb></lb>ſtrat figura, habeatque tubus DB <lb></lb>ſuum epiſtomium, vt & vas C ſu<lb></lb>um; & vaſa D & K repleantur a<lb></lb>quâ. </s><s>Deinde aperiatur epiſtomi<lb></lb>um tubi DB, & aqua deſcendens <lb></lb>intra vas C expellet inde aërem <lb></lb>per tubum FK intra vas K; qui <lb></lb>aër inde expellet aquam per tu<lb></lb>bum FG in vas G, & ex G per <lb></lb>tubum HI expelletur aqua in aliud <lb></lb>vas, & ſic vlteriùs. </s><s>Sed hæc pror<lb></lb> <arrow.to.target n="marg116"></arrow.to.target><lb></lb>ſus ſunt erronea, & contra princi<lb></lb>pia hydraulica. </s><s>Perpendiculum <lb></lb>enim DB aquæ cadentis pedum quinquaginta, non poteſt ele<lb></lb>vare aliam præter aquam vaſis K per tubum FG pedum etiam <lb></lb>50. ad ſummum, vſque ad vas G, vbi quieſcet aqua. </s><s>Dato dein<lb></lb>de quòd ex G poſſet elevari aqua eodem perpendiculo DB, de<lb></lb>beret tubus IH pertingere ferè vſque ad fundum vaſis G, vt <lb></lb>aqua preſſa intrare poſſet. </s><s>Falſus ergo eſt hic modus. </s><s>Alium nos <lb></lb>trademus infrà Claſse I. cap. 2. Machina 4. & 11. </s></p> <p type="margin"> <s><margin.target id="marg116"></margin.target><emph type="italics"></emph>Error apud <lb></lb>Portam.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.090.1.jpg" xlink:href="051/01/090/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>§. X.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Alia ratio aquam elevandi in altum propter <lb></lb>Corporum impenetrabilitatem.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg117"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg117"></margin.target><emph type="italics"></emph>Modui ele<lb></lb>vandi <expan abbr="aquã">aquam</expan> <lb></lb>etiam bru<lb></lb>tis notus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>ESt & alia ratio aquam quieſcentem atque infuſam vaſis ele<lb></lb>vandi, in altum, atque in fontes efformandi, quam vel ipſa <lb></lb>bruta do cent animalia. </s><s>De Cervis quippe Lybicis narratur, quòd <pb xlink:href="051/01/091.jpg" pagenum="60"></pb>dum ſitientes foveam offendunt <expan abbr="aquã">aquam</expan> plenam, culus tamen ſu<lb></lb>prema ſuperficies humilior <expan abbr="atq;">atque</expan> profundior eſt, quàm vt capite <lb></lb>ac collo protenſo eam attingere poſſint, calculos ore & vnguibus <lb></lb>aſportantes foveæ injiciant, vt deſidentibus in fundum lapidi<lb></lb>bus humor ſubſidentium corporum occupatione elevetur, ſu<lb></lb>perioremque elatus repleat vacuitatem; ita ſolerti machinatio<lb></lb>ne reficiuntur. </s><s>Vaſis <expan abbr="itaq;">itaque</expan> puteisque ſi ſolida injicias corpora, quæ <lb></lb>fundum petant vel ſponte, vel vi depreſſa; elevabitur aqua, & <lb></lb>per tubos ſuperiùs applicatos effluens in fontem formabitur. </s><s><lb></lb>Hoc artificio conſtructus erat olim fons ad S. Georg. Venetijs, </s></p> <p type="main"> <s> <arrow.to.target n="marg118"></arrow.to.target><lb></lb>teſte Ioſepho Ceredo Diſcurſu primo de Modo elevandi aquas <lb></lb>è locis humilibus, pag. 11. </s><s>Binæ enim fabricatæ erant ciſternæ, <lb></lb>ſeu piſcinæ, humilior ac profundior vna, altera elatior ad prioris <lb></lb>latus. </s><s>Humilior latera habebat anguſta, & putei inſtar erecta; <lb></lb>è cuius fundo vſque ad collateralis ſuprema labra deduceban<lb></lb>tur tubi plumbei. </s><s>Habebat præterea operculum ligneum atque <lb></lb>graviſſimum, quod ciſternæ latera vacua implebat, & aquæ in<lb></lb>cumbens ſuo paulatim pondere deſcendebat, atque aquam <expan abbr="cõ-primens">con<lb></lb>primens</expan> eam intra tubos compellebat; per quos aſcendens, ſub<lb></lb>ſequentibus alijs aquis pulſa, exonerabat ſeſe intra ſuperiorem <lb></lb>collateralem ciſternam, indeque pondere ſuo naturaliter dela<lb></lb>bens per fiſtulas efforma batur in fontem. </s><s>Multas alias Machi<lb></lb>nas hydraulicas eodem conſtructas artificio enumerat ibidem <lb></lb>citatus Ceredus, & vnam hac ratione adornatam Machinulam <lb></lb>Scaliger Exercitat. 42. contra Cardanum; ex qua tamen falſum <lb></lb>deducit modum oſtendendi fontium originem ex mari. </s><s>Hac <lb></lb>porrò ratione in altum elevatur aqua per antlias, quarum ingen<lb></lb>tem copiam affert Auguſtinus Ramellus inſuo de Machi<lb></lb>nis hydraulicis opere, & nos aliquas adduce<lb></lb>mus Claſse I. cap. 2. Machina 6. </s></p> <pb xlink:href="051/01/092.jpg" pagenum="61"></pb> <p type="margin"> <s><margin.target id="marg118"></margin.target><emph type="italics"></emph>Fons ad S. <lb></lb>Georgium <lb></lb>Venetijs.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Protheoria III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA <lb></lb>TERTIA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Devi Rarefactiva; ſeu de tertio Hydro-pnev<lb></lb>maticarum Machinarum Principio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>§. I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Rarefactionis vis, & effectus mirabiles.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>RArefactionem ingentes ſuppeditare vires vt <lb></lb>alijs corporibus, ita aquæ & aëri, ad ea in omnem ſi<lb></lb>tus differentiam impellendam, multòque magis ad <lb></lb>hydro-pnevmatica omnis generis technaſmata mo<lb></lb>lienda; is ſolus ignorare poteſt, qui ſtupendos ipſius effectus igno<lb></lb>rat. </s><s>videmus quotidie, miramurque, ac plangimus ſtragem, <lb></lb> <arrow.to.target n="marg119"></arrow.to.target><lb></lb>quam <foreign lang="grc">πολιο<gap></gap>χῃταὶ</foreign> nitrato & ſulphureo pulvere intra bombarda<lb></lb>rum militarium anguſtias rarefacto edunt, in ſternendis non ho<lb></lb>minibus tantùm, ſed ædibus, turribus, propugnaculis, atque <lb></lb>adeo vrbibus integris. </s><s>Non Iovis tantummodo fulmina imita<lb></lb>tur rarefactio in bombardis, ſed Plutonis etiam iras æmulatur in <lb></lb>ſubterraneis cuniculis; tantò pernicioſiore ſtrage, quantò mi<lb></lb>nùs patente. </s><s>Excavant Martiales Architecti à loco obſidionis <lb></lb> <arrow.to.target n="marg120"></arrow.to.target><lb></lb>ad vſque propugnaculum, cui ruinam minantur, viam anfra<lb></lb>ctuoſam, anguſtamque, magneticæ pixidis ductu, uti inter alios <lb></lb>docet P. Athanaſius Kircherus lib. 2. de Arte Magnet. par. 2. cap. 1. <lb></lb>Probl. 7. & nos in Pantometro Kircherianolib. 5. Ichnographi<lb></lb>co Probl. 8. </s><s>Sub loco deinde ruinæ deſtinato Cameram con<lb></lb>ſtruunt laxiorem, eamque implent pulveris tormentarij vaſis, <lb></lb>& oſtium claudunt, relicto exiguo foramine, perque viam totam <lb></lb>ignis pabulum ſternunt, & egreſſi ignem applicant; qui ſerpens <lb></lb>per viam accendit pulveris maſſam omnem Camerâ concluſam, <lb></lb>itàque rarefacit, dilatatque, ut anguſtiarum impatiens, & laxio<lb></lb>rem quærens locum, impoſitam ſibi molem diſiiciat horribili <lb></lb> <arrow.to.target n="marg121"></arrow.to.target><lb></lb>fremitu, nec minori terrore, quàm damno. </s><s>Nihil unquam <lb></lb>magis ſimile terræ motui, qui & ipſe rarefactionis eſt effectus lu- <pb xlink:href="051/01/093.jpg" pagenum="62"></pb>culentiſſimus, excogitatum fuit. </s><s>Eodem enim prorſus modo <lb></lb>in terræ concuſſione flamma ex aliqua ſubterranea fornace, vel <lb></lb>interno calore, per venulam aliquam nitri aut ſulphuris ſerpit, <lb></lb>donec perveniat ad locum, in quo maiorem huiuſce materiæ <lb></lb>copiam inveniat; quâ ſubitò accenſa & rarefactâ, dum maio<lb></lb>rem quærit locum, ſibi impoſitas concutit, & diſjicit non rarò, <lb></lb>moles. </s><s>Sæpe etiam iam antea accenſus in terræ viſceribus ignis, <lb></lb>dum nova augetur aliunde attracta materia, montes ſibi impoſi<lb></lb> <arrow.to.target n="marg122"></arrow.to.target><lb></lb>tos concutit, finditque, vt non ſemel audivi, vidique in Ætna Si<lb></lb>ciliæ, duorum annorum accola olim, & nunc hoc ipſo anno 1654. <lb></lb>quo hæc ſcribo, hîc Romæ, quam (raro exemplo) concuſſit mo<lb></lb>tus ille ingens, qui tantam Soræ ſtragem intulit, & Romam hinc <lb></lb>inde Neapolim, omnes que interiacentes regiones tremefecit. </s></p> <p type="margin"> <s><margin.target id="marg119"></margin.target><emph type="italics"></emph>Rarefactio<lb></lb>nis vis in <lb></lb>bombardis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg120"></margin.target><emph type="italics"></emph>Rarefactio<lb></lb>nis vis in <lb></lb>cuniculis <lb></lb>ſubterra<lb></lb>neis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg121"></margin.target><emph type="italics"></emph>Rarefactio<lb></lb>nis vis in <lb></lb>terræ mo<lb></lb>tibus.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg122"></margin.target><emph type="italics"></emph>Terræmo<lb></lb>tus Romæ <lb></lb>anno<emph.end type="italics"></emph.end> 1654.</s></p> <p type="main"> <s><emph type="center"></emph>§. II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Alia Rarefactionis Exempla.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg123"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg123"></margin.target><emph type="italics"></emph>Rarefactio<lb></lb>nis exempla <lb></lb>duo.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>NArrat P. Nicolaus Cabæus lib. 4. Meteor. Ariſt. text. 12. <expan abbr="q.">que</expan> 1. <lb></lb>vidiſſe ſe marmoreum vas maximum atque duriſſimum ab <lb></lb>aqua conglaciata diſciſſum, eò quòd <expan abbr="cõgelatione">congelatione</expan> rarefactæ fue<lb></lb>rint aliquæ internæ partes aquæ: factà enim illâ ſubitâ congela<lb></lb>tione, obſtiterunt attenuationi & rarefactioni partium latera va<lb></lb>ſis, <expan abbr="ceſſitq́ue">ceſſitque</expan> durities vehementiæ rarefactionis, & fractum eſt <lb></lb>vas, quod non diſrupiſſent centum juga boum, ſi in diverſas par<lb></lb>tes traxiſſent. </s><s>Idem Cabæus ibidem aſſerit, ſe vidiſſe columnam <lb></lb>marmoream, quam tres homines dilatatis brachijs ſimul non <lb></lb>poterant complecti, quamque mille juga boum, ſi in diverſas <lb></lb>partes, toto juncto impetu traxiſſent, frangere non potuiſſent, <lb></lb>fractam tamen prorſus mediam atque truncatam, eò quòd ligna <lb></lb>quædam columnæ illi proxima fuerint combuſta, ideoque ex vi<lb></lb>cino calore ſpiritulus aliquis in marmore incluſus intus in meati<lb></lb>bus fuerit rarefactus, & ex rarefactione maiorem ſibi <expan abbr="locũ">locum</expan> quæ<lb></lb>ſiverit. </s></p> <p type="main"> <s>Notum jam pœnè eſt omnibus, quod refert Petrus Caſtel<lb></lb>lus in Libello de Incendio Veſuvij Italicè conſcripto, & exipſo <lb></lb>Kircherus lib. 3. Artis Magnet, part. 2. cap. 3. circa finem, de pul- <pb xlink:href="051/01/094.jpg" pagenum="63"></pb>vere pyrio ex auro confecto, quod aurum fulminans appellat Ca</s></p> <p type="main"> <s> <arrow.to.target n="marg124"></arrow.to.target><lb></lb>ſtellus, & aurum volatile Crollius. </s><s>Eſt id nihil aliud quàm au<lb></lb>rum calcinatum aquâ forti ſeu regiâ, ſale armoniaco, & oleo tar<lb></lb>tari præcipitati. </s><s>Hæc calx quàm primùm ſentit etiam calorem <lb></lb>ignis, concipit ſponte ſua flammam, & in auras abit, cum ingenti <lb></lb>fragore & ſtrepitu: & ſi vel vnum aut alterum huius pulveris gra<lb></lb>num cultro impoſueris, & candelam infrà applicueris, vtinca. </s><s><lb></lb>leſcat; tantum edit fragorem, ac ſi magnam exploſiſſes bombar<lb></lb>dam. </s><s>Facit autem effectum contrarium ordinario pulveri pyrio, <lb></lb>quia non ſurſum, ſed deorſum tendit; vnde ſerupulus vnicus hu<lb></lb>ius volatilis auri poſitus ſupra laminam ferream <expan abbr="nõ">non</expan> modicæ craſ<lb></lb>ſitiei, & carbone deſuper applicato accenſus, penetrat & per<lb></lb>foratipſam laminam. </s></p> <p type="margin"> <s><margin.target id="marg124"></margin.target><emph type="italics"></emph>Aurum ful<lb></lb>minans.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Nolo hîc ommittere aliud rarefactionis exemplum, quo <lb></lb>ego ipſe multis in locis, coram viris etiam Principibus, exiguâ <lb></lb>machinulâ non exiguum excita vi fragorem, bombardulæ mi<lb></lb>noris fragori prorſus æqualem ac ſimilem. </s><s>Vitreas Sphærulas <lb></lb> <arrow.to.target n="marg125"></arrow.to.target><lb></lb>nucis avellanæ magnitudine, aut etiam minores, fieri curavi ad <lb></lb>lampadem Romæ à quodam Germano artifice, vitrum in omnes <lb></lb>colores omnes que figuras florum, fructuum, avium, animalium <lb></lb>omnis generis, jcuncularum quarumlibet affabrè elaboratarum <lb></lb>efformante, idemque in ſubtiliſſima fila ad rotam <expan abbr="circumactã">circumactam</expan> <lb></lb>diducente. </s><s>In eas vitreas Sphærulas acetum, aut nitratum ſa<lb></lb>lem aquâ diſſolutum ac liquefactum infundi iuſfi, & ad medieta<lb></lb>tem repleri, ac deinde hermeticè claudi ad eandem lampadem. </s><s><lb></lb>Harum ſphærularum vnam ſi carbonibus non nimiùm accenſis, <lb></lb>aut calidis cineribus (vt paulatim calefiat) impoſueris; rarefit <lb></lb>ſpiritoſa materia intus clauſa, & majorem quærens locum, poſt <lb></lb>ſpatium circiter temporis quo Pſalmus 50. <emph type="italics"></emph>Miſerere mei Deus,<emph.end type="italics"></emph.end> re<lb></lb>citari poteſt, tanto cum impetu ac fragore viam ſibi aperit, vt <lb></lb>non tantùm vitrum in mille minutiſſimas particulas diffringat, <lb></lb>ſed cineres etiam & carbones toto conclavi diſſipet, nullius <lb></lb>damno, niſi ſi quis vultum propè applicet. </s><s>Cùm experientiam <lb></lb>Romæ coram Sereniſſimi Holſatiæ Ducis Filio primogenito fa- <pb xlink:href="051/01/095.jpg" pagenum="64"></pb>cerem, foco aſſidenti more ibidem ſolito, famuli ante cubicu<lb></lb>lum præſtolantes accurrebant attoniti, bombardulam in Princi<lb></lb>pem ſuum exploſam credentes. </s><s>Alius magnus quidam Prin<lb></lb>ceps cùm nonnullas à me accepiſſet, ac domi die quodam cum <lb></lb>multis alijs nobilibus foco aſſideret, vnam oſtendit, ac videnti<lb></lb>bus omnibus igni iniecit, aſſerens, vbi calefieret, gratiſſimum <lb></lb>ſparſuram odorem. </s><s>Cùm omnes arrectis naribus, & ore hi<lb></lb>ante odorem exſpectarent, derepente fit crepitus, & carbonum <lb></lb>disiectio, diffugientibus omnibus in timorem primò, deinde in <lb></lb>riſum diſſolutis. </s><s>Alio tempore coram Cardinale quodam & <lb></lb>magno Nobilium comitatu, admonito priùs clanculum ſolo <lb></lb>Cardinale, vnam exploſi; & ita omnes alij præter dictum <lb></lb>Cardinalem territi fuêre, vt auctorem (ignorabant me eſſe) <lb></lb>ad pœnam quærerent. </s></p> <p type="margin"> <s><margin.target id="marg125"></margin.target><emph type="italics"></emph>Vitrea ſphæ<lb></lb>rula mino<lb></lb>ris bombar<lb></lb>dulæ crepi<lb></lb>tum amu<lb></lb>lantes.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Innumeros alios effectus rarefactionis, ſicut & condenſa<lb></lb>tionis, adducere poſſem; ſed hi ſufficiunt ad adſtruendam effica<lb></lb>ciam in commovendis corporibus. </s><s>Quæ efficacia ſi tanta eſt, <lb></lb>quantam vidimus; quis neget, eandem in aëre & aquis elucere <lb></lb>poſſe, dilatando & conſtringendo elementa ipſa, & in fontes a<lb></lb>liaque hydraulica, pnevmaticaque artificia animando? ſed hæc <lb></lb>evidentiſſimè oſtendemus in multis ex ſequentibus Machinis <lb></lb>Partis 2. præſertim Claſ. <expan abbr="Ĩ">I.</expan>. cap. 3. Mach. 1.2.5.6.8. & alijs multis. </s></p> <p type="main"> <s><emph type="center"></emph>PROTHEORIA<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>QVARTA.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De fluxu Aquæ naturali;<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>ſeu <lb></lb>De quarto Hydro-pnevmaticarum Machina<lb></lb>rum principio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PLurima, jucundiſſima, vtiliſſimaque circa A<lb></lb>quæ fluxum naturalem, ſeu libera ea ſit, ſeu aquædu<lb></lb>ctibus, canalibus, tubis, ſiphonibus, fiſtulis, & qui<lb></lb>bus cunque alijs meatibus conſtricta, dicenda occur<lb></lb>runt noc ioco, quæ Hydro-pnevmaticarum Machinarum Arti-</s></p> <pb xlink:href="051/01/096.jpg" pagenum="65"></pb> <p type="main"> <s><emph type="center"></emph>Protheoria IV.<emph.end type="center"></emph.end><lb></lb>ficibus non minùs neceſſaria, quàm vtilia ſunt. </s><s>Nos ex omni<lb></lb>bus ea tantùm, quæ fini noſtro conducere videbuntur, ſelegimus; <lb></lb>cætera ad Mechanicam noſtram Magiam reſervabimus. </s></p> <p type="main"> <s><emph type="center"></emph>CAPVT I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De proprietatibus Aquæ fluentis liberè.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROOEMIVM.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>LIberè fluit aqua, dum nullis conſtricta<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg126"></arrow.to.target><lb></lb><emph type="italics"></emph> eſt meatibus ceu vinculis. </s><s>Huiuſce proprie<lb></lb>tates, fini noſtro conducentes, vt aſſignem, <lb></lb>Suppono duo, quæ licet in dubium revocentur <lb></lb>ab aliquibus, conceduntur tamen à meliores <lb></lb>notæ Philoſophis & Mathematicis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg126"></margin.target>Aqua libe<lb></lb>rè fluere <lb></lb>quæ dica<lb></lb>tur.</s></p> <p type="main"> <s><emph type="italics"></emph>Primum eſt, Ordinem Elementorum, naturæ eorum con<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg127"></arrow.to.target><lb></lb><emph type="italics"></emph>gruentem hunc eſſe, vt Terra ſit in medio omnium, Aqua circa <lb></lb>Terram, circa Aquam Aër, & circa Aërem putatus ignis. </s><s>Ac <lb></lb>principio quidem rerum, quando<emph.end type="italics"></emph.end> Creavit DEVS cœlum & <lb></lb>terram, <emph type="italics"></emph>Genes. C. I. prædictum ſervarunt ordinem, vſque ad <lb></lb>diem Mundi tertium, quo die Deus benedictus Terram, anteà <lb></lb>ſphæricè rotundam, in cavitates varias deformavit, in easque <lb></lb>Aquam omnem ſubtercœleſtem, maribus, lacubus, fluminibus, <lb></lb>fontibus diſcretam, derivavit, vnumque ex Terra & Aqua <lb></lb>globum conſtituit, vnicâ contentum ſphæricâ ſuperficie, terrenâ<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg128"></arrow.to.target><lb></lb><emph type="italics"></emph> hinc, inde aqueâ, prout Aquæ diverſimodè Terram diſciſſam <lb></lb>interfluunt, aut circumfluunt. </s><s>Qui quidem globus ex Terra <lb></lb>& Aqua coagmentatus (quem ob id rectè <expan abbr="Terraqueũ">Terraqueum</expan> appellare <lb></lb>poſſumus) in prima ſui coagmentatione, quando die Mundi<emph.end type="italics"></emph.end> <pb xlink:href="051/01/097.jpg" pagenum="66"></pb><emph type="italics"></emph>tertio<emph.end type="italics"></emph.end> dixit DEUS: congre gentur aquæ, quæ ſub cœlo ſunt, <lb></lb>in locum vnum, & appareat Arida; & factum eſt ita; <emph type="italics"></emph>in <lb></lb>medio Vniverſi, hoc est, in centro ſupremi, & omnia ambien<lb></lb>tis Cæli collocatus fuiſſe videtur; in medio, inquam, non ſolùm <lb></lb>quoad ſenſum (quod nullus, aut vix vllus, ſaltem alicuius no<lb></lb>minis, negat) ſed revera ac mathematicè, ita vt centrum gra<lb></lb>vitatis Terraquæ congruerit tunc perfectè centro Vniverſi, exi-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg129"></arrow.to.target><lb></lb><emph type="italics"></emph>gente id naturali ipſius gravitate. </s><s>Nunc verò licet ob conti<lb></lb>nuam gravium in Terra Marique mutationem, centrique gra<lb></lb>vitatis variationem prædicta Terraqua non ſit fortaſſe ſemper <lb></lb>præcisè & mathematicè in Mundi medio in ſenſu dicto (non <lb></lb>enim certò constat, ad centrum gravitatis mutatum continuò, <lb></lb>ſequi continuam, licet exiguam, trepidationem ipſius, nitentis <lb></lb>ad mundi centrum) tam parum tamen ab illo centro distat, <lb></lb>quàm multùm diſtat à tota mole Terraquæ quodcunque pon<lb></lb>dus defacto additum aut ablatum de novo. </s><s>Ex quibus dedu<lb></lb>citur, ſi centrum gravitatis Terraquæ differt à centro magni<lb></lb>tudinis eiusdem (vt probabile eſt differre, cùm Terra pondero<lb></lb>ſior ſit quàm Aqua, nec omnes Terræ partes, æqualis ſint ponde<lb></lb>ris) differre ſolùm inſenſibiliter; ac proinde idem cenſeri poſſe; <lb></lb>ſaltem phyſicè & ad ſenſum, vtrumque centrum. </s><s>Sed de his <lb></lb>ſusè tractatum vide à Kirchero in Mundo ſubterranneo, libro 1. <lb></lb>de Centroſophia, & à nobis in Mechanica Vniverſali lib. 1. <lb></lb>aut in Magia Mechanica.<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg130"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg127"></margin.target>Elmento<lb></lb>rum ordo <lb></lb>naturalis;</s></p> <p type="margin"> <s><margin.target id="marg128"></margin.target>Terra que<lb></lb>us globus <lb></lb>in medio <lb></lb>mundi col<lb></lb>locat' fuit <lb></lb>die tertio <lb></lb>creationis <lb></lb>rerum.</s></p> <p type="margin"> <s><margin.target id="marg129"></margin.target>Terra qua <lb></lb>nunc non <lb></lb>eſt ſemper <lb></lb>in mundi <lb></lb>centro ma<lb></lb>thematicè.</s></p> <p type="margin"> <s><margin.target id="marg130"></margin.target>Centrum <lb></lb>commune <lb></lb>omnium <lb></lb>gravium <lb></lb>ac levium</s></p> <p type="main"> <s><emph type="italics"></emph>Alterum quod ſuppono est, centrum Vniverſi, adeoque <lb></lb>Centrum Terraquei globi, quem in Mundi medio ſtatuimus, <lb></lb>cenſeri poſſe centrum commune omnium gravium ac levium, quò<emph.end type="italics"></emph.end> <pb xlink:href="051/01/098.jpg" pagenum="67"></pb><emph type="italics"></emph>nimirum omnia gravia per ſe tendunt appetitu innato, & à quo <lb></lb>levia recedunt, vtraque per rectas ac breviſſimas lineas, niſi <lb></lb>impediantur, aut cogantur per obliquam ac longiorem viam <lb></lb>verſus illud deſcendere, vel ab illo recedere. </s><s>Cùm igitur aqua <lb></lb>omnis ſit gravis, vt experientiâ patet; tendet appetitu naturali <lb></lb>ad centrum Terraquæ, id eſt, ad centrum Vniverſi. </s><s>Idem di<lb></lb>cendum eſt de alijs liquoribus. </s><s>His præmiſſis accedimus ad <lb></lb>propoſitum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua tendit ad loca decliviora.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>AQuam, & omnem alium humorem, fluentem <lb></lb>iberè, currere ad loca decliviora, & centro Mundi ac <lb></lb>Terraquæ propinquiora, ſi patet ipſis liber aditus, ſive <lb></lb>rectus ac perpendicularis, ſive obliquus; patet expe<lb></lb>rientia quotidiana, nec indiget probatione. </s><s>Ex quo deduci<lb></lb>tur, aquæ etiam conſiſtentis partes omnes inclinare innato ap<lb></lb>petitu ad eadem loca decliviora: ideo enim de facto, ſublatis </s></p> <p type="main"> <s> <arrow.to.target n="marg131"></arrow.to.target><lb></lb>impedimentis, eò fluit aqua, quia naturaliter eò inclinat. </s><s>Con<lb></lb>ſiſtentem porrò aquam appello, quæ ſitum obtinet naturalem. </s><s><lb></lb>Situs autem ſeu poſitio naturalis aquæ eſt, quem dum naturali <lb></lb> <arrow.to.target n="marg132"></arrow.to.target><lb></lb>ſuo fluxui & conſiſtentiæ permittitur, ſua ſponte aſſumit, tam in <lb></lb>ſuperficie ſuperiore, quàm in inferiore, & lateralibus. </s></p> <p type="margin"> <s><margin.target id="marg131"></margin.target><emph type="italics"></emph>Aqua con<lb></lb>ſiſtens qua <lb></lb>dicatur.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg132"></margin.target><emph type="italics"></emph>Aqua ſitus <lb></lb>naturalis <lb></lb>quis ſit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ ſuperficies ſuperior, ceſſante fluxu, ſphærica <lb></lb>eſt; reliquæ conformantur vaſis & rece<lb></lb>ptaculis,<emph.end type="center"></emph.end></s></p> <p type="main"> <s>AQua liberè fluens tam diu fluit, donec partium continuata<lb></lb> <arrow.to.target n="marg133"></arrow.to.target><lb></lb>rum extima ſeu ſuperior ſuperficies ſphærica ſit, habens idem <lb></lb><expan abbr="centrũ">centrum</expan> cum centro Terraquæ & Vniverſi, hoc eſt, donec omnes <lb></lb>extimæ ſuperficiei partes æqualiter diſtenta Centro Mundi. </s><s>De- <pb xlink:href="051/01/099.jpg" pagenum="68"></pb>monſtrat hoc ſubtiliſſimè Archimedes lib 1. de infidentibus hu<lb></lb>mido Propoſit. 2. & Ariſtot. lib. 2. de Cœlo text. 31. & ſequitur <lb></lb>ex præcedente Proprietate. </s><s>Si enim ceſſante fluxu, & conſi<lb></lb>ſtente iam aquâ, pars vna ſuperficiei extimæ altior eſſet, & altera <lb></lb>humilior, hoc eſt, ſi non omnes æquè diſtarent à centro Mundi <lb></lb>(quod eſt ſphæricam habere ſuperficiem, habentem idem Cen<lb></lb>trum commune Mundi;) non omnes aquæ partes, ſublatis im<lb></lb>pedimentis, fluerent ad loca decliviora, nec aquæ conſiſtentis <lb></lb>partes omnes eò naturali appetitu inclinarent; aut certè violen<lb></lb>ter in tali ſtatu, & nullo præſente impedimento, detinerentur; <lb></lb> <arrow.to.target n="marg134"></arrow.to.target><lb></lb>quod incongruum eſt, & naturis rerum repugnans. </s></p> <p type="margin"> <s><margin.target id="marg133"></margin.target><emph type="italics"></emph>Aqua conſi<lb></lb>ſtentis ſuper<lb></lb>ficies ſuperi<lb></lb>or ſpharica <lb></lb>eſt.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg134"></margin.target><emph type="italics"></emph>Aquæ vaſis <lb></lb>contentæ ſu<lb></lb>perficies con<lb></lb>formantur <lb></lb>vaſorum in<lb></lb>ternis figu<lb></lb>ris.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Inferior porrò aquæ ſuperficies, & laterales, conforman<lb></lb>tur ſuperficiebus internis vaſorum & receptaculorum, quibus <lb></lb>aqua continetur: Vnde ſi vna pars fundi vaſorum ac recepta<lb></lb>culorum eſt altior alterâ (prout in mari, lacubus, fluminibus, <lb></lb>& vaſis ordinariè fit) etiam talis erit aquæ illis contentæ infe<lb></lb>rior ſuperficies. </s><s>Idem intellige de lateralibus ſuperficiebus. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma I.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg135"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg135"></margin.target><emph type="italics"></emph>Aquarum <lb></lb>omnium Su<lb></lb>perficies ſu<lb></lb>perior eſt <lb></lb>ſphærica.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur hinc, Oceani, Marium, lacuum, & aquarum qua<lb></lb>rumcunque continuatarum, & in quibuscunque receptacu<lb></lb>lis contentarum, ac conſiſtentium, ſuperficies ſuperiores atque <lb></lb>externas eſſe ſphæricas, habentes idem cum Terraquæ ſuperficie </s></p> <p type="main"> <s> <arrow.to.target n="marg136"></arrow.to.target><lb></lb><expan abbr="cõvexa">convexa</expan> centrum. </s><s>In vaſis tamen & receptaculis exiguis adeo exi<lb></lb>gua eſt & inſenſibilisſphæricitas iſtius ſuperficiei, vt meritò ſup<lb></lb>poni poſſit eſſe planam, ſeu horizonti parallelam: vnde & nos <lb></lb>in ſequentibus id nobis concedi poſtulabimus, & ita ſuppone<lb></lb>mus. </s></p> <p type="margin"> <s><margin.target id="marg136"></margin.target><emph type="italics"></emph>In vaſis ta<lb></lb>men exiguis <lb></lb>cenſeri po<lb></lb>teſt plana.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur iterum, idem vas ad turris aut montis radicem po<lb></lb> <arrow.to.target n="marg137"></arrow.to.target><lb></lb>ſitum, & aquâ omnino plenum, plùs aquæ continere, mathe<lb></lb>maticè loquendo, quàm poſitum in turris aut montis vertice, & <lb></lb>aquâ itidem omnino plenum. </s><s>Ratio eſt, quia major eſt ſphæri<lb></lb>citas aquæ in primo, quàm ſecundo caſu. </s></p> <pb xlink:href="051/01/100.jpg" pagenum="69"></pb> <p type="margin"> <s><margin.target id="marg137"></margin.target><emph type="italics"></emph>Aquæ plus <lb></lb><expan abbr="cõtinet">continet</expan> vas <lb></lb>plenù infe<lb></lb>riori, quàm <lb></lb>ſuperiori <lb></lb>loco.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur tertiò, ſi aqua ad libellam conſtituta eſſet alicubi, <lb></lb> <arrow.to.target n="marg138"></arrow.to.target><lb></lb>non poſſe conſiſtere, ſed neceſſariò moveri, quia tunc non <lb></lb>omnes partes extimæ & ſuperioris ſuperficiei eſſent æquè vicinæ <lb></lb>centro Terraquæ. </s><s>Athoc meliùs explicabitur in Pantometro <lb></lb>noſtro Kircheriano lib. 9. Hydragogico, vbi delibellatione a<lb></lb>quarum agemus, <expan abbr="iterumq;">iterumque</expan> in Mechanica noſtra Vniverſali, libro <lb></lb>quem inſcribemus Mechanicam Hydragogicam. </s></p> <p type="margin"> <s><margin.target id="marg138"></margin.target><emph type="italics"></emph>Aqua con<lb></lb>ſiſtere non <lb></lb>poteſt ad li<lb></lb>bellam con<lb></lb>ſtituta.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua minùs preſſa expellitur à magis preſſa.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>AQuæ, & humidi cuiuscunque, ea eſt natura, inquit Archi<lb></lb>medes lib. 1. de Infidentibus humido, Hypotheſi I, vt par<lb></lb>tibus ipſius æqualiter iacentibus & continuatis inter ſeſe; minùs <lb></lb>preſſa à magis preſſa expellatur; & quidem tantò fortiùs, quantò <lb></lb>aut minùs illa, aut magis hæc preſſa fuerit. </s><s>Hoc quomodo ſit in<lb></lb>telligendum, patebit ex ſequentibus Proprietatibus huius capitis, <lb></lb>& etiam ex dicendis capite ſequenti, Propoſitione 2. </s></p> <p type="main"> <s><emph type="center"></emph>Proprietas IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ, & humidi cuiuſcunque, pars vnaquæ que premi<lb></lb>tur humido ſupra ipſam exiſtente ad perpendiculum, ſi hu<lb></lb>midum ſit deſcendens in aliquo, aut ab alio ali<lb></lb>quo preſſum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ASſerit hoc Archimedes loco proximè citato. </s><s><expan abbr="Itaq;">Itaque</expan> quando <lb></lb> <arrow.to.target n="marg139"></arrow.to.target><lb></lb>humidum non eſt deſcendens in aliquo, aut non eſt ab ali<lb></lb>quo alio preſſum, ſed conſiſtit in ſuo ſitu naturali, vna pars non <lb></lb>premit alteram, vt mox dicemus. </s><s>Si autem humidum <lb></lb>eſt deſcendens in aliquo, vt ſi effluit per foramen vaſis, aut in<lb></lb>fluit in vas coniunctum: tunc partes ſupra foramen premuntur <lb></lb>à partibus ad perpendiculum ipſis incumbentibus, non verò ab <lb></lb>alijs collateralibus. </s><s>Similiter ſi humidum premitur ab aliquo, <lb></lb>partes preſſæ premunt ſolùm quæ ipſis ad perpendiculum ſub<lb></lb>ſtant. </s></p> <pb xlink:href="051/01/101.jpg" pagenum="70"></pb> <p type="margin"> <s><margin.target id="marg139"></margin.target><emph type="italics"></emph>Aquæ par<lb></lb>tes inferio<lb></lb>res <expan abbr="premũ-tur">premun<lb></lb>tur</expan> à ſupe<lb></lb>rioribus ad <lb></lb>perpendicu<lb></lb>lum incum<lb></lb>bentibus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquâ in ſitu naturali conſiſtente, partes ſuperiores non <lb></lb>premunt inferiores.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PAtet hoc ex multis ſignis. </s><s>Primò enim alioquin partes aquæ <lb></lb>inferiores eſſent denſiores ſuperioribus, quia <expan abbr="cõpreſſæ">compreſſæ</expan> eſſent. </s><s><lb></lb>Secundò, vrinatores infra aquam exiſtentes non ſentiunt pon<lb></lb>dus aquarum incumbentium ſibi. </s><s>Tertiò, herbæ leviſſimæ intra <lb></lb>aquam creſcentes, & in altum aſſurgentes, non ſternuntur ab <lb></lb>aqua ſuperincumbente. </s><s>Quartò, corpus grave fune alligatum <lb></lb>& infra aquam demerſum, ſuſtinetur à manu, & extrahitur, tan<lb></lb>ta facilitate, quanta ſuſtineretur & extraheretur, ſi nulla aqua illi <lb></lb>incumberet; imò maiorietiam facilitate, quoniam gravia mi<lb></lb>nùs ponderantintra, quàm extra aquam. </s><s>Quintò, ſitula aquâ <lb></lb>plena levior eſt intra aquam, quàm extra: Curhoc, niſi quia <lb></lb>aqua intra aquam non ponderat? </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg140"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg140"></margin.target><emph type="italics"></emph>Aquæ con<lb></lb>ſiſtentis par<lb></lb>tes ſuperio<lb></lb>res non pre<lb></lb>munt actu <lb></lb>inferiores.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur hinc, quando Archimedes, alijque dicunt, omnes <lb></lb>aquæ partes, dum ea in ſitu conſiſtit naturali, a qualiter pre<lb></lb>mi, non eſſe ſermonem de actuali preſſione, ſed ſolùm de aptitu<lb></lb>dinali. </s><s>Premi vnum ab alio aptitudinaliter, eſt, habere ſupra <lb></lb>ſe grave non ſuſtentatum; at premi actualiter eſt ita habere ſu</s></p> <p type="main"> <s> <arrow.to.target n="marg141"></arrow.to.target><lb></lb>pra ſe grave non ſuſtentatum, vt ablato impedimento cedere co<lb></lb>gatur corpori incumbenti; & niſi cedat, comprimatur. </s><s>Vel di<lb></lb>cendum eſt, premi quidem partes humidi inferiores à ſuperio<lb></lb>ribus ſibi ſuperin cumbentibus, at non comprimi. </s><s>Solùm ergo <lb></lb>partes ſuperiores aquæ actu premunt inferiores, quando vel ab <lb></lb>alio premuntur ſuperiores, vel quando ſunt altiores alijs partibus <lb></lb>contiguis in eodem vaſe, aut in duobus vaſis inter ſe communi<lb></lb>cantibus, vt videbimus, cùm de Siphonibus agetur; vel denique <lb></lb>quando infra ſe habent inferiores immediatè corpus levius ſe in <lb></lb>ſpecie, v.g. aërem, aut tenuiſſimum fundum; in omnibus enim <lb></lb>hiſce caſibus partes inferiores cedunt quidem ſuperioribus, at <lb></lb>minimè ab illis comprimuntur. </s><s>Hinc eſt, quòd aqua effluatè <lb></lb>foramine in fundo aut latere vaſis. </s><s>Hinc etiam eſt, quòd fun- <pb xlink:href="051/01/102.jpg" pagenum="71"></pb>dum tenue vaſis incurvetur, ac tandem frangatur. </s><s>Hinc deni<lb></lb>que eſt, quòd dum partes aquæ ſuperiores premuntur, & partes <lb></lb>inferiores non habent effugium aut infrà, aut è latere vaſis, rum<lb></lb>patur potiùs vas, quàm partes inferiores comprimantur. </s><s>Vide <lb></lb>quæ dicimus infrà parte 2. Claſse 1. cap. 5. Machina 6. </s></p> <p type="margin"> <s><margin.target id="marg141"></margin.target><emph type="italics"></emph>Premi actu, <lb></lb>& premi <lb></lb>aptitudina<lb></lb>liter, quid <lb></lb>ſit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ in ſitu naturali poſitæ vna pars non <lb></lb>expellit alteram.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PAtet experientia. </s><s>Et ratio eſt, quia vna non premit alteram, <lb></lb>vt dictum in præcedenti Proprietate. </s><s>Quòd ſi in vaſis con<lb></lb>jugatis altior aqua pellit minùs altam, cauſa eſt, quòd non ſit <lb></lb>poſita in ſitu naturali, quia ſcilicet non habet omnes partes æ<lb></lb>què diſtantes à centro Mundi. </s></p> <p type="main"> <s><emph type="center"></emph>Proprietas VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Non omnes aquæ æquales magnitudine, ſunt <lb></lb>æquales pondere.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SUnt enim ſalsæ graviores dulcibus, & frigidæ calidis eiuſdem <lb></lb> <arrow.to.target n="marg142"></arrow.to.target><lb></lb>ſpeciei, ſeu individui; & tam ſalsæ, quàm dulces, aliæ alijs gra<lb></lb>viores ſunt, vt patet experientia, & fatentur etiam nautæ, vi<lb></lb>dentes naves è fluminibus impuris ad pura, aut è mari ad flumina <lb></lb>transeuntes ſubſidere profundiùs, & ſubinde cum ſubmerſionis <lb></lb>periculo. </s></p> <p type="margin"> <s><margin.target id="marg142"></margin.target><emph type="italics"></emph>Aqua ſalsa <lb></lb>frigida, im<lb></lb>pura, gra<lb></lb>vior eſt <expan abbr="quã">quam</expan> <lb></lb>dulcis &c.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Proprietas VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua naturaliter non aſcendit ad locum altio<lb></lb>rem ſuâ origine.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>IMò nec fluit naturaliter ab vno ad alterum locum, niſi terminus à quo <lb></lb>altior ſit, quàm terminùs ad quem.<emph.end type="italics"></emph.end> </s><s>Vtrumque patet experientiã, <lb></lb> <arrow.to.target n="marg143"></arrow.to.target><lb></lb>& ſequitur ex dictis Proprietate I. & II. </s><s>Hinc Hydragogi aſſe<lb></lb>runt, non poſſe deduciaquam de loco in locum, ſive per alveum, <lb></lb>ſive per aquæductus, canales, ac tubos deducenda ſit, ſi ſpatium <lb></lb>ſit æquilibratum, ſeu ad libellam conſtitutum; nec ſufficere <expan abbr="Ma-thematicã">Ma<lb></lb>thematicam</expan>, aut quam cunque phyſicam declivitatem, ſed requiri <lb></lb>in ſingulis milliaribus cadentiam ſeu declivitatem quatuor ad <pb xlink:href="051/01/103.jpg" pagenum="72"></pb>minimùm vnciarum vnius pedis, (eſt vncia pars duodecima pe<lb></lb>dis) ita vt terminus ad quem in fine milliaris ſit vicinior centro <lb></lb>Terræ quatuorvncijs, quàm terminus à quo; &p oſt alterum mil<lb></lb>liare alijs quatuor vncijs ſit vicinior, & ſic deinceps ſemper, eſt<lb></lb>que hæc regula à <expan abbr="plerisq́ue">plerisque</expan> recepta tanquam Axioma hydra<lb></lb>gogicum. </s><s>Sed de hac re fusè agemus in Pantometro noſtro <lb></lb>Kircheriano lib. 9. vbi agemus ex profeſſo de Hydragogia & li. <lb></lb>bellatione aquarum; & in Mechanica Vniverſali. </s></p> <p type="margin"> <s><margin.target id="marg143"></margin.target><emph type="italics"></emph>Aqua non <lb></lb>poteſt decur<lb></lb>rere per ſpa<lb></lb>tium æqui<lb></lb>libratum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>CAPVT II. <lb></lb>DE <lb></lb>Proprietatibus Aquæ fluentis per <lb></lb>ſiphones.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>QUamvis in Machinis noſtris Hydro-pnevmati<lb></lb>cis, Parte 2. indifferenter & pro eodem fumamus no<lb></lb>men ſiphonis, & tubi, pro fiſtula ſcilicet, per quam <lb></lb>aqua fluit, ſive recta illa ſit, ſive curva; hîc tamen, <lb></lb> <arrow.to.target n="marg144"></arrow.to.target><lb></lb>maioris diſtinctionis gratia, ſiphonem à tubo diſtinguimus. </s><s><lb></lb>Eſ igitur Siphon nihil aliud quàm tubus inflexus. </s><s>Huius variæ <lb></lb>ſunt ſpecies, vt ſequitur. </s></p> <p type="margin"> <s><margin.target id="marg144"></margin.target><emph type="italics"></emph>Siphon quid<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis varias diviſiones aſſignare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIphon igitur, ſeu tubus in flexus, dividitur variè, & habet diver<lb></lb> <arrow.to.target n="marg145"></arrow.to.target><lb></lb>ſas figuras, vt apparet in appoſitis ſchematiſmis. </s><s>Alius enim <lb></lb>dicitur ſiphon erectus, alius in verſus, aliusmixtus, alius æquali<lb></lb>um, alius in æqualium crurium. <lb></lb> <arrow.to.target n="marg146"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg145"></margin.target><emph type="italics"></emph>Siphonis <lb></lb>ſpecies va<lb></lb>ria.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg146"></margin.target><emph type="italics"></emph>Siphon ere<lb></lb>ctus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Siphon erectus eſt, cuius omnia crura ſurſum ſunt. </s><s>Huius<lb></lb>modi ſunt ſeptem priores, & vltimus ex hîc appoſitis. </s></p> <p type="main"> <s> <arrow.to.target n="marg147"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg147"></margin.target><emph type="italics"></emph>Siphon in<lb></lb>verſus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Siphon inverſus eſt, cuius omnia crura deorſum ſunt. </s><s>Hu<lb></lb>iusmodi ſuntijdem, ſi inver ſi intelligantur, hoc eſt, ſi B ſurſum, <lb></lb>C & A deorſum ſpectent. </s></p> <p type="main"> <s> <arrow.to.target n="marg148"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg148"></margin.target><emph type="italics"></emph>Siphon mi<lb></lb>xtus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Siphon mixtus eſt, cuius crura partim ſurſum, partim de<lb></lb>orſum ſunt. </s><s>Huiuſmodi ſunt tres penultimi ex appoſitis, ſeu 8. 9. <lb></lb>& 10. </s></p> <pb xlink:href="051/01/104.jpg" pagenum="73"></pb> <figure id="id.051.01.104.1.jpg" xlink:href="051/01/104/1.jpg"></figure> <p type="main"> <s>Siphones tam erecti, quàm inverſi, vel habent vtrumque <lb></lb>erus æquale, vel inæquale. </s><s>Si æqualia ſunt crura, vellongitu<lb></lb>dine & capacitate ſuntæqualia, vt apparet in prima, tertia, & </s></p> <p type="main"> <s> <arrow.to.target n="marg149"></arrow.to.target><lb></lb>ſeptima figura: vel ſola longitudine æqualia, capacitate verò <lb></lb>inæqualia, vt apparet in ſecunda, quarta, quinta, ſexta, & vlti<lb></lb>ma figura. </s></p> <pb xlink:href="051/01/105.jpg" pagenum="74"></pb> <p type="margin"> <s><margin.target id="marg149"></margin.target><emph type="italics"></emph>Siphones a<lb></lb>qualium, <lb></lb>& inaqua<lb></lb>lium cruri<lb></lb>um.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Siphones mixti, vel habent omnia crura æqualia longitu<lb></lb>dine, vt in octava figura apparet; vel aliqua tantùm, ut in nona <lb></lb>figura; vel nulla, ut in decima figura patet. </s><s>Hæc eadem crura <lb></lb>poſſunt eſſe diverſæ capacitatis inter ſe. <lb></lb> <arrow.to.target n="marg150"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg150"></margin.target><emph type="italics"></emph>Siphon con<lb></lb>iugatus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Nota. Siphonem quartum aliqui vocant coniugatum, re<lb></lb>liquos verò inflexos appellant. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis erecti proprietates aſſignare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg151"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg151"></margin.target><emph type="italics"></emph>Siphonis e<lb></lb>recti proprie<lb></lb>tates.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>PRima.<emph.end type="italics"></emph.end> Aqua vni ſiphonis erecti cruri infuſa deſcendit pri<lb></lb>mùm, deinde aſcendit per alterum crus, donec ſupremæ ſu<lb></lb>perficies in vtroque <lb></lb> <arrow.to.target n="fig17"></arrow.to.target><lb></lb>crure ſint in eadem <lb></lb>linea horizontali. </s><s><lb></lb>Sint ſiphones erecti <lb></lb>ABCDEF, ſive æ<lb></lb>qualium, ſive inæ<lb></lb>qualium crurium, <lb></lb>tam quoad longitu<lb></lb>dinem, quàm quoad <lb></lb>capacitatem; <expan abbr="uniq;">vnique</expan> <lb></lb>crurium, ſive longi<lb></lb>ori, ſive breviori, <lb></lb>ſive æquali, & ſive <lb></lb>largiori, ſive ſtricti<lb></lb>ori, v.g. cruri AB, <lb></lb>infundatur aqua: <lb></lb>deſcendet ea <expan abbr="primũ">primum</expan> <lb></lb>vſque ad B, <expan abbr="indeq;">indeque</expan> <lb></lb>per C & D aſcen<lb></lb>det, donec ſupremæ <lb></lb>aquę ſuperficies ſint <lb></lb>in vtroque crure in <lb></lb>eadem linea Hori- <pb xlink:href="051/01/106.jpg" pagenum="75"></pb>zontali, v.g. in linea HIK; hoc eſt, donec omnes dictarum ſu<lb></lb>perficierum partes diſtent æqualiter à centro terræ, juxta dicta <lb></lb>cap. 1. Proprietat. 2. Ratio deſumitur ex dictis ibidem. </s><s>Ex his <lb></lb>formo ſequens. </s></p> <figure id="id.051.01.106.1.jpg" xlink:href="051/01/106/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Axioma Hydraulicum I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVantùm aqua deſcendit per vnum ſiphonis erecti crus, tantundem </s></p> <p type="main"> <s> <arrow.to.target n="marg152"></arrow.to.target><lb></lb>aſcendit per alterum.<emph.end type="italics"></emph.end> Idem contingit in omnibus canalibus, <lb></lb>alveis, & meatibus quibuscunque incurvatis. </s></p> <p type="margin"> <s><margin.target id="marg152"></margin.target>Axioma hy<lb></lb>draulicum.</s></p> <p type="main"> <s><emph type="italics"></emph>Secunda.<emph.end type="italics"></emph.end> Si vni crurium, ſive longiori, ſive breviori, ſive <lb></lb>æquali, & ſive capaciori, ſive minùs capaci, addas aliquid aquæ, <lb></lb>v.g. cruri AB; attollitur etiam alterius cruris aqua, donec rur<lb></lb>ſus ſuperficies diſtent æqualiter a centrro terræ, ſeu ſint in eadem <lb></lb>linea horizontali, v.g. in linea GFE. </s><s>Ratio eſt eadem. </s></p> <p type="main"> <s><emph type="italics"></emph>Tertia.<emph.end type="italics"></emph.end> Si cruri longiori, ſive id capacius ſit altero iam <lb></lb>pleno, ſive non, addas plùs aquæ, v.g. cruri AB; deſcendet ea <lb></lb>per B, <expan abbr="elevabitq́ue">elevabitque</expan> aquam cruris CDEF, & expellet per os <lb></lb>EF, donec ceſſante infuſione ſit iterum vtraque ſuperficies in li<lb></lb>nea GFE. </s><s>Patet experientiâ, & ratio eſt eadem, ne ſcilicet ſu<lb></lb>perficies vnius cruris diſtet plùs aut minùs, à centro terræ, quàm <lb></lb>alterius. </s></p> <p type="main"> <s><emph type="italics"></emph>Quarta.<emph.end type="italics"></emph.end> Si cruri breviori, licet capaciori, nempe cruri <lb></lb>EFCD, jam pleno addas plùs aquæ |; ea non attollet aquam <lb></lb>cruris longioris vltra punctum G, ſed effluet ex ore EF, licet <lb></lb>aqua cruris EFCD ſit longè maior & ponderoſior, quàm <lb></lb>aqua cruris AB. </s><s>Patet itidem experientiâ, & ratio eſt eadem. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur hinc primò, aquam maioris perpendiculi pellere <lb></lb> <arrow.to.target n="marg153"></arrow.to.target><lb></lb>aquam minoris perpendiculi, non obſtante maiore copia, & <lb></lb>maiore pondere huius: ideo enim aqua cruris AB primæ & tertiæ <lb></lb>figuræ expellit aquam cruris CDEF, licet longè maiorem & <lb></lb>ponderoſiorem, quia perpendiculum illius eſt maius ſeu longius, <lb></lb>quàm perpendiculum huius. </s><s>Aquæ perpendiculum hic, & in <lb></lb> <arrow.to.target n="marg154"></arrow.to.target><lb></lb>ſequentibus, appello altitudinem aquæ ſupra horizontem, ſeu <lb></lb>ſupra centrum Terræ, ita vt illa dicatur habere maius perpendi- <pb xlink:href="051/01/107.jpg" pagenum="76"></pb>culum, quàm altera, cuius altitudo ab infima ad ſupremam ſu<lb></lb>perficiem maior eſt, in eodem horizonte. </s></p> <p type="margin"> <s><margin.target id="marg153"></margin.target><emph type="italics"></emph>Aqua ma<lb></lb>ioru perpen<lb></lb>diculi pellit <lb></lb>aquam mi<lb></lb>noris perpen<lb></lb>diculi in Si<lb></lb>phonibus e<lb></lb>rectis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg154"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>lum aquæ <lb></lb>quid.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium II.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg155"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg155"></margin.target><emph type="italics"></emph>Aqua ma<lb></lb>gis aut, mi<lb></lb>nùs preſſa <lb></lb>in ſiphoni<lb></lb>bus, <expan abbr="quanã">quanam</expan> <lb></lb>dicatur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur ſecundò, Quænam aqua in ſiphone erecto dicatur <lb></lb>magis aut minùs preſſa: Nam cùm conſtet, Aquam minùs <lb></lb>preſſam expelli à magis preſſa, per dicta Capite primo, Propriet. <lb></lb>3. conſtet præterea, Aquam minoris perpendiculi in ſiphone e<lb></lb>recto premi atque expelli ab aqua maioris perpendiculi; clarum <lb></lb>eſt, Aquam minoris perpendiculi dici minùs, <expan abbr="aquã">aquam</expan> verò maioris <lb></lb>perpendiculi dici magis preſsam. </s><s>Ex his formo ſequens </s></p> <p type="main"> <s><emph type="center"></emph>Axioma Hydraulicum II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>IN hydraulicis non aquarum copiâ, ſed perpendiculis pugnatur, & vin</s></p> <p type="main"> <s> <arrow.to.target n="marg156"></arrow.to.target><lb></lb>citur.<emph.end type="italics"></emph.end> </s><s>Illa enim vincit pellendo, vel trahendo alteram, cuius <lb></lb>perpendiculum eſt maius. </s></p> <p type="margin"> <s><margin.target id="marg156"></margin.target>Axiomo hy<lb></lb>draulicum.</s></p> <p type="main"> <s><emph type="center"></emph>Corollarium III.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg157"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg157"></margin.target><emph type="italics"></emph>Siphonis e<lb></lb>recti ope a<lb></lb>quam ex v<lb></lb>no monte in <lb></lb>alterum de<lb></lb>rivare.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur tertiò, Quomodo ſiphonis erectiope (hoc eſt, ca<lb></lb>nale, tubo autin <expan abbr="modũ">modum</expan> ſiphonis erecti conſtructo) ex monte <lb></lb>per vallem ad alterum montem, priori paulò humiliorem, aut <lb></lb>ad locum in latere montis, derivari poſſit aqua; ſi nimirum fiat <lb></lb>ſiphon erectus, cuius os vnum immergatur aquæ montis altioris, <lb></lb>& de in ſiphon deducatur per vallem, & latera montium, usque <lb></lb>ad locum deſtinatum, humiliorem tamen origine aquæ. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg158"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg158"></margin.target><emph type="italics"></emph><expan abbr="Doliũ">Dolium</expan> quo<lb></lb>uſque ſit ple<lb></lb>num, Si<lb></lb>phone ex<lb></lb>plorare.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur quar<lb></lb> <arrow.to.target n="fig18"></arrow.to.target><lb></lb>tò, Quomodo <lb></lb>ſcire poſſis præcisè <lb></lb>quouſque dolium <lb></lb>aliquod <expan abbr="exinanitũ">exinanitum</expan> <lb></lb>ſit, manente obtu<lb></lb>ramento ſuperiore <lb></lb>clauso, <expan abbr="nulloq;">nulloque</expan> alio <lb></lb>foramine facto <lb></lb>præterid, cui epi<lb></lb>ſtomium immitti <pb xlink:href="051/01/108.jpg" pagenum="77"></pb>ſolet. </s><s>Sit enim dolium DC, exinanitum vſque ad lineam FG; <lb></lb>quod tu ignores: ſcies id, ſi tubum oblongum AB incurves in<lb></lb>feriùs iuxta B, & doleo iuxta C inſeras epiſtomij loco; liquor <lb></lb>enim dolij effluens aſcendet per tubum, donec perveniat <expan abbr="vſq;">vſque</expan> ad <lb></lb>E, & æquetur ſupremæ ſuperficiei liquoris in dolio contenti. </s></p> <figure id="id.051.01.108.1.jpg" xlink:href="051/01/108/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Corollarium V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg159"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg159"></margin.target><emph type="italics"></emph>Dolium im<lb></lb>plere per e<lb></lb>piſtomium <lb></lb>ope ſiphonis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur quintò, Quomodo repleri poſſit prædictum doli<lb></lb>um per foramen C epiſtomij. </s><s>Si enim tubum AB incur<lb></lb>vatum inſeras dolio iuxta C, & ſuperiùs iuxta A infundas li<lb></lb>quorem; aſcendet is in dolio, donec æquetur ſummitati tubi, <lb></lb>aut donec dolium ſit omnino repletum, ſi tubus altior eſt dolio. </s><s><lb></lb>Bene tamen Schvventerus monet in ſuis Recreationibus Mathe<lb></lb>maticis parte 13. quæſt. 3. debere in ſummitate dolij foramen a<lb></lb>periri, per quod aër elabatur, impediturus alioquin liquoris in<lb></lb>fuſionem, ſi non poſſit erumpere per foramen C & tubum BA. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>In Siphone erecto plurium quàm duorum crurium eadem con<lb></lb>tingunt, quæ in ſiphone duorum crurium, vt conſideranti patet.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis inverſi proprietates aſſignare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg160"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg160"></margin.target><emph type="italics"></emph>Siphonis in<lb></lb>verſi pro<lb></lb>prietates.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>PLurimas proprietates, easque plerumque miras habet Siphon<lb></lb>everſus, tam æqualium quoad longitudinem & capacitatem <lb></lb>crurium, quàm inæqualium. </s><s>Nos præcipuas referemus. </s></p> <p type="main"> <s><emph type="center"></emph>Prima Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI crura ſiphonis inverſi inæqualia ſunt quoad longitudinem, <lb></lb>& totus ſiphon repleatur aquâ, & invertatur; effluit ea tota per <lb></lb>crus longius, licet ſit minus capacitate. </s><s>Eſto Siphon inverſus <lb></lb>ABC inæqualium crurium, aquâ plenus, & crus AB longius <lb></lb>ſit quàm crus CB, hoc eſt, extremæ aquarum ſuperficies A & C <lb></lb>inæqualiter diſtent à Centro Mundi, ſcilicet AB minùs, CB <lb></lb>plùs; dico, totam aquam effluere per crus AB, licet capacitate <lb></lb>ſit minus quàm CB. </s><s>Ratio eſt, quia cùm aquæ AB perpendi<lb></lb>culum, ſit longius, quàm aquæ CB perpendiculum, ma<lb></lb>gis premitur aqua apud A, quàm apud C, per corollarlum I. </s><s> <pb xlink:href="051/01/109.jpg" pagenum="78"></pb> <arrow.to.target n="fig19"></arrow.to.target><lb></lb>Propoſitione. II. <lb></lb>præcedentis; ac pro<lb></lb>inde per Propr. III. <lb></lb>cap. 1. aqua AB ex<lb></lb>pellet aquam CB, <lb></lb>non <expan abbr="quidẽ">quidem</expan> per preſ<lb></lb>ſionem, ſed per at<lb></lb>tractionem; hoc eſt, <lb></lb>efflueta qua AB, ſe<lb></lb>cumque <expan abbr="trahetaquã">trahetaquam</expan> <lb></lb>CB, & quidem to<lb></lb>tam, tum propter <lb></lb>rationem dictam, <lb></lb>tum nè detur vacu<lb></lb>um in ſiphone. </s></p> <figure id="id.051.01.109.1.jpg" xlink:href="051/01/109/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>MOnuit hîc P. Athanaſius Kircherus, ea quæ diximus hoc loco, ſo<lb></lb>lùm eſſe intelligenda in eo caſu, in quo tubi<emph.end type="italics"></emph.end> ABC <emph type="italics"></emph>laxior portio<emph.end type="italics"></emph.end> BC <lb></lb><emph type="italics"></emph>inferiùs eſt clauſa, ſolo foramine<emph.end type="italics"></emph.end> I. <emph type="italics"></emph>relicto. </s><s>Si enim totum orificium a<lb></lb>pertum fuerit; aqua nulla ratione ſiſtipoterit quin effluat ſecumque tra<lb></lb>hat aquam cruris<emph.end type="italics"></emph.end> BA. </s><s><emph type="italics"></emph>Rationem adſignat, quia quando ſolum fora<lb></lb>men<emph.end type="italics"></emph.end> I <emph type="italics"></emph>eſt apertum, ſola columna aquea<emph.end type="italics"></emph.end> BI <emph type="italics"></emph>in fig.<emph.end type="italics"></emph.end> I. <emph type="italics"></emph>habet rationem per<lb></lb>pendiculi, eò quòd ſolum illa premat ſupra<emph.end type="italics"></emph.end> I. </s><s><emph type="italics"></emph>At quando totum orifi<lb></lb>cium eſt apertum, tota aqua<emph.end type="italics"></emph.end> BHICG <emph type="italics"></emph>habet rationem perpendiculi, <lb></lb>quia tota premit ſupra orificium apertum, ac proinde æquivalet pluribus <lb></lb>perpendiculis æqualibus perpendiculo<emph.end type="italics"></emph.end> BI; <emph type="italics"></emph>quæ ſimul ſumpta ſuperant <lb></lb>perpendiculum longius<emph.end type="italics"></emph.end> BA. </s><s><emph type="italics"></emph>Addidit, hæc ſe longa experientia didiciſſe.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Opportuna monitio, nec menti meæcontraria. </s><s>Puto tamen, a<lb></lb>quam ex orificio<emph.end type="italics"></emph.end> CI <emph type="italics"></emph>penitus aperto effluere non tam obrationem adſig<lb></lb>natam, quàm quòd aëri facillimus pateat ingreſſus ob laxitatem orificij; <lb></lb>quo ingrediente diſcontinuatur aqua, & per vtrumque orificium <expan abbr="apertũ">apertum</expan> <lb></lb>effluit.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/110.jpg" pagenum="79"></pb> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COnfirmatur hinc Axioma hydraulicum præcedens, quòd in <lb></lb>ſiphonibus (& etiam tubis, & quibuscunque vaſis) non pu<lb></lb>gnatur ponderibus, ſed altitudinibus, ſeu perpendiculis. </s><s>In<lb></lb>tellige, in caſu & ſenſu explicato. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>DIcere quis poſſet, quando ſolùm patet foramen<emph.end type="italics"></emph.end> I, <emph type="italics"></emph>tunc attracto cy<lb></lb>lindrulo aqueo<emph.end type="italics"></emph.end> BI, <emph type="italics"></emph>faciliùs ſuccedit aër per foramen attractus, <lb></lb>quàm aqua lateralis<emph.end type="italics"></emph.end> HI, <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> GI; <emph type="italics"></emph>immiſſoque aëre, aqua illa lateralis <lb></lb>facillimè effluet per foramen<emph.end type="italics"></emph.end> I. </s><s><emph type="italics"></emph>Quare in nullo caſu videtur poſſe ve<lb></lb>rificari, quòd aqua<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>attrahat totam aquam<emph.end type="italics"></emph.end> BC </s><s><emph type="italics"></emph>Nego tamen id <lb></lb>recte dici, quia aër ingrediens per foramen<emph.end type="italics"></emph.end> I <emph type="italics"></emph>adhærebit ſolùm vltimæ <lb></lb>ſuperficiei aquæ fugientis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Secunda Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI crura ſiphonis inverſi æqualia ſint quoad longitudinem, li<lb></lb>cetinæqualia capacitate (cum limitatione tamen poſita) & <lb></lb>totus repleatur aquâ, <expan abbr="invertaturq́ue">invertaturque</expan>; nihil effluit. </s><s>Decurtetur <lb></lb>in præcedente ſchemate crus AB in D, & repleatur totus ſiphon <lb></lb>aquâ, ita vt extremæ aquæ ſuperficies C & D æqualiter diſtent <lb></lb>à centro mundi; dico, nihil effluere, licet cruris CB maior aqua <lb></lb>& ponderoſior ſit, quàm aqua cruris AB. </s><s>Idem fiet, ſi absque cru<lb></lb>ris AB decurtatione, extrema aquæ ſuperficies in illo æquè di<lb></lb>ſtetà centro Mundi, atque in crure CB, vt ſi vtrobique eſſet in <lb></lb>linea horizontali CD, aut in linea GHE. </s><s>Ratio eſt, quia cùm <lb></lb>in vtroque crure æquale ſit <expan abbr="perpendiculũ">perpendiculum</expan> ſeu altitudo aquæ, pre<lb></lb>metur vtrobique æqualiter; vel ergo vtriuſque cruris aqua ſimul <lb></lb>deſcendere deberet, quod fieri non poteſt absque vacuo; vel <lb></lb>neutrius. </s><s>Exhac, & præcedente Proprietate, formari poteſt <lb></lb>aliud. </s></p> <p type="main"> <s><emph type="center"></emph>Axioma hydraulicum III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>IN hydraulicis æqualia perpendicula æqualiter premunt, inæqualia </s></p> <p type="main"> <s> <arrow.to.target n="marg161"></arrow.to.target><lb></lb>inæqualiter, ſcilicet longius plùs, brevius minùs.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/111.jpg" pagenum="80"></pb> <p type="margin"> <s><margin.target id="marg161"></margin.target>Axioma hy<lb></lb>draulicum.</s></p> <p type="main"> <s><emph type="center"></emph>Tertia Proprietas.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg162"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg162"></margin.target><emph type="italics"></emph>Aqua per <lb></lb>longius crus <lb></lb>ſiphonis ce<lb></lb>leriùs cur<lb></lb>rit, quàm <lb></lb>per brevius.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>AQua per longius crus ſiphonis inverſi eò currit celeriùs, quò <lb></lb>longius fuerit crus. </s><s>Ratio eſt, quia quò longius eſt crus, eò <lb></lb>longius eſt aquæ deſcendentis <expan abbr="perpendiculũ">perpendiculum</expan>, ac proinde eò ma<lb></lb>ius pondus incumbit aquæ prope os, eòque magis premitur a<lb></lb>qua in egreſlu, celeriúsque propterea effluit, & conſequenter ce<lb></lb>leriùs deſcendit. </s><s>Hinc formo ſequens </s></p> <p type="main"> <s><emph type="center"></emph>Axioma Hydraulicum IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg163"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg163"></margin.target><emph type="italics"></emph>Axioma hy<lb></lb>draulicum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>In hydraulicis per ſiphones & tubos longiores celeriùs fluit aqua, <lb></lb>quàm per breviores, poſito eodem, aut æquali orificio per quod effluit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quarta Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg164"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg164"></margin.target><emph type="italics"></emph>Aqua per <lb></lb><expan abbr="ſiphonẽ">ſiphonem</expan> fluit <lb></lb>difformi <lb></lb>celeritate.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>AQua per longius crus ſiphonis inverſi non effluit celeritate v<lb></lb>niformi, ſed difformi; augetur enim continuò celeritas de<lb></lb>ſcenſus, donec exhauſtum ſit crus oppoſitum: nunquam tamen <lb></lb>deſcendit tam celeriter aqua, quàm ſi liberè, hoc eſt, non per <lb></lb>ſiphonem, ſed per tubum, aut extra tubum vel canalem deſcen<lb></lb>deret. </s><s>Ratio eſt, quia aqua effluens per crus longius AB, in an<lb></lb>tea poſito, & in quocunque alio ſiphone, debet ſecum trahere <lb></lb>contranitentem aquam cruris brevioris CB, nè detur vacuum <lb></lb>intra ſiphonem; quæ aqua cruris brevioris quoniam continuò <lb></lb>minuitur effluente aqua per os A, ideo faciliùs ſemper ac faci<lb></lb>liùs attrahitur ab aqua cruris longioris AB; cuius proinde <expan abbr="deſcẽ-dentis">deſcen<lb></lb>dentis</expan> celeritas continuò intenditur, donec exhauſtum ſit to<lb></lb>tum crus CB. </s><s>Non æquat tamen celeritatem eam, quâ liberè <lb></lb>deſcenderet, non trahendo ſecum aquam alterius cruris; quia <lb></lb>quàm diu reſtat aliquid aquæ in crure breviori CB, attrahere <lb></lb>illud debet, vt poſſit effluere, ac proin de ſemper aliquid retinet <lb></lb>impedimenti; quo caret, dum liberè cadit. </s><s>Adde quòd quò <lb></lb>diutiùs aqua effluit per A, eò aquæ cruris CB ſuperficies ex<lb></lb>trema C magis aſcendit verſus B, adeoque & perpendiculum <lb></lb>aquæ cruris CB continuò minuitur, aquæ interim, quæ ex crure <lb></lb>AB fluit, perpendiculo manente eodem. </s><s>Augetur ergo aſſiduè <lb></lb>proportio perpendiculi BA ad perpendiculum BC, adeoque & <pb xlink:href="051/01/112.jpg" pagenum="81"></pb>proportio preſſionis aquæ BA ad preſſionem aquæ BC au<lb></lb>getur; ergo, &c. </s><s>Dixi, donec exhauſtum ſit totum crus CB <lb></lb>oppoſitum: nam illo exhauſto, minuitur ſemper magis ac magis <lb></lb>celeritas effluxus per os A, quoniam minuitur perpendiculum <lb></lb>aquæ, ac proinde ſemper minùs ac minùs premitur aqua apud A. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>In ſiphone inverſo pluribus tubis quàm duobus compoſito eadem. </s><s><lb></lb>& ob eandem cauſam contingunt, vt patębit conſideranti.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis mixti inæqualium crurium proprie<lb></lb>tates aſſignare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIphonum mixtorum crura vel ſunt omnia æqualia, vel omnia </s></p> <p type="main"> <s> <arrow.to.target n="marg165"></arrow.to.target><lb></lb>inæqualia, vel aliqua æqualia, aliqua inæqualia. </s><s>De proprie<lb></lb>tatibus ſiphonis, cuius omnia crura ſunt æqualia, agemus Pro<lb></lb>poſit. </s><s>ſequenti; de reliquorum proprietatibus hîc agemus. </s><s>Sit <lb></lb>igitur ſiphon AKDI. </s><s>Hic ſi integer maneat, habebit omnia cru<lb></lb>ra inæqualia: ſi truncetur in E, aut in B, habebit aliqua crura <lb></lb>æqualia, alia inæqualia: ſi truncetur in F, aut N, habebit iterum <lb></lb>omnia crura inæqualia. </s></p> <p type="margin"> <s><margin.target id="marg165"></margin.target><emph type="italics"></emph>Siphonis mi<lb></lb>xti variæ <lb></lb>ſpecies.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Prima Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI ſiphon AKDI maneat integer, & repleatur totus aquâ, efflu<lb></lb>et ea tota per os I. Ratio eſt, quia perpendiculum DI lon<lb></lb>gius eſt quàm perpendiculum DK, ut ſupponitur; ergo plùs <lb></lb>premitur aqua apud I, quàm apud K, per dicta Propoſit. III. <lb></lb>præcedente, Propriet. I. & Capite I. Propriet. III. ac proinde <lb></lb>aqua DI trahit aquam DK; quâ tractâ, ſequitur etiam aqua <lb></lb>KA, tum proprio pondere, tum ad vacuum impediendum. </s></p> <p type="main"> <s><emph type="center"></emph>Secunda Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI crus DI truncetur in B, ita vtos B ſit eiusdem altitudinis <lb></lb>ſupra horizontom cum ore A, & totus ſiphon AKDB replea<lb></lb>tur aquá; eſt qui putat non effluere ex B, ſed effluere ex A, du<lb></lb>rareque fluxum donec ſuperficies aquæ B pervenerit ad C, <lb></lb>hoc eſt, donec effluxerit tantum aquæ, quantum eſtintra BDC, <pb xlink:href="051/01/113.jpg" pagenum="82"></pb> <arrow.to.target n="fig20"></arrow.to.target><lb></lb>tunc enim, ait, ceſſabit fluxus ex A, <lb></lb>ſtabitque aqua in æquilibrio intra <lb></lb>AKC. </s><s>Quòd non effluat aqua ex B, <lb></lb>clarum eſt, quia perpendiculum BD <lb></lb>brevius eſt quàm <expan abbr="perpendiculũ">perpendiculum</expan> DK, <lb></lb>ergò aqua DB non poteſt trahere a<lb></lb>quam DK, & multò minùs <expan abbr="aquã">aquam</expan> DKA. </s><s><lb></lb>Quòd autem effluat ex A, <expan abbr="rationẽ">rationem</expan> <lb></lb>aſſignat, quia perdendiculum DK <lb></lb>longius eſt quàm perpendiculum AK; <lb></lb>ergo aqua DK fortiùs premit deor<lb></lb>ſum verſus K, quàm aqua AK, ac <lb></lb>proinde aqua AK debet cedere, & <lb></lb>effluere ex A, ac ſequi tota reliqua <lb></lb>aqua, nè vacuum detur. </s><s>Quòd de<lb></lb>nique ceſſet fluxus aquæ ex A, quan<lb></lb>do ſuperficies B pervenerit ad C, <lb></lb>rationem dat, quia tunc perpendicu<lb></lb>la CK, AK, ſunt æqualia. </s></p> <figure id="id.051.01.113.1.jpg" xlink:href="051/01/113/1.jpg"></figure> <p type="main"> <s>Experentiâ tamen conſtat, in dicto caſu <expan abbr="nullã">nullam</expan> effluere aquam <lb></lb>ex Siphone AKDB, neque per os B, neque per os A. </s><s>Rationem <lb></lb>adſigno, quia aqua quæ eſt in AKC, ita eſt librata, vt à poten<lb></lb>tia quantumvis parva moveri, & ex vna parte attolli poſſit; qua<lb></lb>re humido CD ſupra ſe poſito non reſiſtit. </s><s>I am verò quoniam <lb></lb>perpendicula crurium DC, DB æqualia ſunt, aqua in C æquè <lb></lb>premitur ac in B; quare cùm nec infra B, nec infra C vllum <lb></lb>ſit impedimentum extrinſecum, præter aërem (iam enim oſten<lb></lb>ſum eſt, aquam CKA non reſiſtere humido CD deſcendenti) <lb></lb>pariter ex A & B aqua deberet effluere; quod fieri non poteſt <lb></lb>absque vacuo. </s><s>Patet ergo cur aqua conſiſtat. </s><s>Dices, in hoc <lb></lb>diſcurſu committitur manifeſtus paralogiſmus; dividitur enim <lb></lb>mente crus DK in puncto C, & diſcurritur ac ſi realiter ibidem <lb></lb>eſſet facta diviſio; Natura non dividit aquam cruris DK in pun<lb></lb>cto C, nec propter noſtras intellectuales diviſiones mutat ope- <pb xlink:href="051/01/114.jpg" pagenum="83"></pb>randi vim, cùm non obſtante illa diviſione revera crus DK lon<lb></lb>gius ſit, quàm crus AK. </s><s>Reſpondeo, quamvis DK longius ſit <lb></lb>quàm crus AK, eius tamen activitati ſeu preſſioni deorſum non <lb></lb>ſolùm reſiſtit crus AK, ſed etiam crus DB; illud, nè aqua KA <lb></lb>pellatur ſurſum; hoc, nèaqua AD trahatur ſurſum: vnde per<lb></lb>pendiculum DK habet duplicem reſiſtentiam, ſcilicet DB, & AK; <lb></lb>quæ duæ reſiſtentiæ æquant eius activitatem, & conſequenter <lb></lb>impediunt motum aquæ DK, eiusque fluxum, ſive per os A, ſi<lb></lb>ve per os B. </s><s>Diviſio autem intellectualis cruris DK in puncto <lb></lb>C fit ſolùm ad oſten dendum quomodo duplex prædicta <expan abbr="reſiſtẽ-tia">reſiſten<lb></lb>tia</expan> æquivaleat activitati totius cruris DK. </s></p> <p type="main"> <s><emph type="center"></emph>Tertia proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI crus DI truncetur in F, vt os F ſit inferius quàm os A; <lb></lb>idem qui ſuprà putat non effluere aquam ex F, ſed ex A, du<lb></lb>rareque ut antea fluxum, donec ſuperficies F pervenerit vſque <lb></lb>ad C. </s><s>Rationem eandem dat cum illa, quam adſignavit paulò <lb></lb>antè. </s></p> <p type="main"> <s>Eâdem tamen experientiä conſtat, aquam in hoc caſu ef<lb></lb>fluere ex F, donec aqua cruris AK deſcenderit in H ad pa<lb></lb>rem cum F altitudinem. </s><s>Ratio eſt, quia humidum in F ma<lb></lb>gis premitur, quàm in C, id eſt, quàm in A, ob longius per<lb></lb>pendiculum DF, quàm DC; quare humidum in F deſcen<lb></lb>det, <expan abbr="trahetq́ue">trahetque</expan> humidum reliquum, nè detur vacuum. </s><s>Nec re<lb></lb>fert, quòd dividatur intellectu crus DK in puncto C, & compa<lb></lb>retur crus DF cum parte DC ſolùm, ac ſi & Natura ibidem <lb></lb>diviſiſſet crus DK; hoc enim ſolùm fit ob rationem paulò antè <lb></lb>allatam. </s></p> <p type="main"> <s><emph type="center"></emph>Quarta Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI crus DI truncetur in E, vt os E habeat eandem altitudinem <lb></lb>cum puncto K; ille idem qui ſuprà exiſtimat nihil effluere, <expan abbr="neq;">neque</expan> <lb></lb>ex E, neque ex A. </s><s>Ratio eius eſt, quia perpendicula DE, DK ſunt <lb></lb>æqualia; ergo aqua apud E non plùs premitur quàm apud K, nec <lb></lb>apud K plùs quàm apud E; ergo neque ex E, neque ex A <lb></lb>effluere poteſt aqua, nè æqualis potentia dicatur ſuperaſſe æ<lb></lb>qualem. </s></p> <pb xlink:href="051/01/115.jpg" pagenum="84"></pb> <p type="main"> <s>Dicendum tamen, eâdem experientiá duce, effluxuram <lb></lb>aquam ex E, duraturumque fluxum, donec ſuperficies A per<lb></lb>venlat ad K, & non vltrà. </s><s>Rationem adſigno, quia perpen<lb></lb>diculum DE longius eſt, quàm DC, dum plenus eſt tubus. </s><s>Dum <lb></lb>autem aqua deſcenderit ad K, perpendicula DK, DE ſunt æ<lb></lb>qualia. </s></p> <p type="main"> <s><emph type="center"></emph>Quinta Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Si crus DI truncetur in N, effluet aqua ex A, donec <lb></lb>ſuperficies N perveniat in C, vbi conſiſtet. </s><s>Ratio eſt, quia <lb></lb>altitudo aquæ DK, vel potiùs DC, maior eſt, quàm altitudo DN. </s></p> <p type="main"> <s><emph type="center"></emph>Sexta Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Effluxus aquæ in prædictis caſibus, ſive ex ore A, ſive ex <lb></lb>ore F, E, I, non eſt vniformis, ſed difformis, eo prorſus modo, <lb></lb>quo diximus in Propoſit. III. præced. Proprietate IV. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis mixti æqualium crurium proprieta<lb></lb>tes aſſignare.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.115.1.jpg" xlink:href="051/01/115/1.jpg"></figure> <p type="main"> <s>EX ſiphone mixto æqualium crurium, qua<lb></lb>lis eſt ABCD, in appoſito ſchemate, ſi a<lb></lb>quâ totus repleatur; effluit aqua ex D. </s><s>Ra<lb></lb>tio eſt, quia licet tam perpendicula AB, CB, <lb></lb>quàm perpendicula CD, CB, ſint æqualia; <lb></lb>quia tamen aqua CB æquilibrata eſt ab aqua <lb></lb>AB, poterit à qualibet potentia facillimè <lb></lb>moveri, ideoque ab aqua CD deorſum ni<lb></lb>tente poterittrahi, & effluere ex D; & ita de <lb></lb>facto contingit, vt experientia docet. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Inverſi Siphonis, vaſi vno crure impoſi<lb></lb>to, proprietates aſſignare.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg166"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg166"></margin.target><emph type="italics"></emph>Crus inter<lb></lb>num, & <lb></lb>crus exter<lb></lb>num ſipho<lb></lb>nis<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>OBvia ſunt quæ dicam, ideò breviter expediam. </s><s>Eſto igitur <lb></lb>vas aquâ plenum ABCD, cui inverſi ſiphonis crus vnum FE <lb></lb>immergatur, alterum FN foris maneat. </s><s>Vocetur autem crus <pb xlink:href="051/01/116.jpg" pagenum="85"></pb> <arrow.to.target n="fig21"></arrow.to.target><lb></lb>FE internum, crus verò FN <lb></lb>externum. </s><s>Huius ſiphonis <lb></lb>variæ ſunt proprietates, provt <lb></lb>variè diſponi poterit crus eius <lb></lb>externum. </s></p> <figure id="id.051.01.116.1.jpg" xlink:href="051/01/116/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Prima Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Si enim crus exter<lb></lb>num FN maneat integrum, <lb></lb>& ex ore N exſugatur aër; ſe<lb></lb>quetur aqua vaſis, ob vacui <lb></lb>metum, & tota effluet, aut pœ<lb></lb>nè tota (donec nimirum aquæ <lb></lb>ſuperficies ſuperior CD deſcen<lb></lb>derit vſque ad oſculum E) ſi <lb></lb>internum crus fundum pœnè <lb></lb>tangat. </s><s>Ratio eſt, quia per<lb></lb>pendiculum externi cruris eſt <lb></lb>longius quàm interni. </s><s>Si to<lb></lb>tus ſiphon aquâ impleatur, & <lb></lb>vtrumque orificium claudatur, ac deinde minus crus EF aquæ <lb></lb>imponatur, maiori foras prominente, & ſimul vtrumque orifi<lb></lb>cium aperiatur; idem fiet. </s></p> <p type="main"> <s>Effluet tamen inæqualiter, cum perpetuo <expan abbr="nimirũ">nimirum</expan> celerita<lb></lb>tis decremento, quia perpendiculum aquæ cruris interni, altitu<lb></lb>do nempe aquæ à puncto P uſque ad ſuperficiem ſuperiorem <lb></lb>aquæ vaſis (hæc enim ſola premit actu, reliquæ verò inferiores <lb></lb>actu non premunt, per dicta cap. 1. Proprietate V.) ſemper ma<lb></lb>gis ac magis creſcit, ac proinde ſemper magis magiſque reſiſtit <lb></lb>perpendiculo aquæ cruris externi. </s></p> <p type="main"> <s>Quò verò crus externum longius fuerit infra ſuperficiem </s></p> <p type="main"> <s> <arrow.to.target n="marg167"></arrow.to.target><lb></lb>ſuperiorem aquæ vaſis, eò fluet aqua celeriùs, & æqualibus tem<lb></lb>poribus copioſiùs: quia tunc eò magis perpendiculum externi <lb></lb>ſuperabit perpendiculum interni cruris in longitudine, & vi pre<lb></lb>mendi deorſum. </s><s>Non tamen ſufficit, ut crus externum ſit qua- <pb xlink:href="051/01/117.jpg" pagenum="86"></pb>cunque ratione longius crure interno, ſed neceſſarium omnino <lb></lb>eſt ut perpendiculum externi cruris longius ſit perpendiculo in<lb></lb>terni, juxta dicta ſuprà Protheoria I. §. VI. </s></p> <p type="margin"> <s><margin.target id="marg167"></margin.target><emph type="italics"></emph>Aqua inæ<lb></lb>quali cele<lb></lb>ritate efflu<lb></lb>it ex crure <lb></lb>externo ſi<lb></lb>phonis,<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Secunda Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Si crus externum FN decurtetur in K, & internum tan<lb></lb>gat ferè fundum in E, & ex ore K extrahatur aer; ſequetur <lb></lb>aqua uſque ad os K, propter vacui metum, & tota ferè effluet, <lb></lb>donec <expan abbr="nimirũ">nimirum</expan> perveniat ſuprema aquæ ſuperficies <expan abbr="uſq;">uſque</expan> ad oſcu<lb></lb>lum E. </s><s>Ratio eſt, quia perpendiculum cruris externi longius <lb></lb>eſt quàm interni. </s><s>At poſtquam aqua pervenerit uſque ad oſcu<lb></lb>lum E, nihil amplius effluit, quia perpendicula FE, FK ſunt <lb></lb>æqualia. </s><s>Hærebit ergo aqua in æquilibrio in utroque crure. </s></p> <p type="main"> <s><emph type="center"></emph>Tertia Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Si crus externum FN decurtetur in H, & internum ſit <lb></lb>infra lineam LM, aut pertingat ſolummodò uſque ad dictam <lb></lb>lineam; vas tamen ſit plenum uſque ad lineam CD, aut ſaltem <lb></lb>aqua ſit ſupra lineam LM; effluet aqua per os H, donec ſupre<lb></lb>ma aquæ vaſis ſuperficies perveniat uſque ad lineam LM, & non <lb></lb>ampliùs. </s><s>Ratio eſt, quia antequam dicta aquæ ſuperficies per<lb></lb>veniat ad lineam LM, perpendiculum cruris externi eſt ſem<lb></lb>per longius perpendiculo cruris interni; quando verò deſcendit <lb></lb>jam ad dictam lineam, ambo perpendicula ſunt æqualia. </s><s>Fluxus <lb></lb>porrò difformitas quoad celeritatem aut tarditatem eadem eſt, <lb></lb>quæ antea. </s></p> <p type="main"> <s><emph type="center"></emph>Quarta Proprietas.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Si crus externum decurtetur in G, ut ſit ejuſdem altitudi<lb></lb>nis ſupra Horizontem cum ſuperficie humidi CD, & aqua at<lb></lb>trahatur in G; nihil effluet, quia perpendicula ſunt æqualia: <lb></lb>quare aqua hærebit in æquilibrio in utroque crure. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Ex his colligitur primò, Si vas ſit plenum ſolummodò uſque <lb></lb> <arrow.to.target n="marg168"></arrow.to.target><lb></lb>ad lineam LM, & ſiphonis crus externum decurtetur in H, vel <lb></lb>G, vel O, internum verò pertingat uſque ad fundum; nihil <lb></lb>poſſe effluere ex crure externo. </s></p> <pb xlink:href="051/01/118.jpg" pagenum="87"></pb> <p type="margin"> <s><margin.target id="marg168"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>li exceſſum <lb></lb>tuetur Na<lb></lb>tura in a<lb></lb>quæ fluxu.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Colligitur ſecundò, quàm pertinax ſit Natura, vel conſtans <lb></lb>potiùs, in retinendo atque tuendo perpendiculi exceſſu, nè mi<lb></lb> <arrow.to.target n="marg169"></arrow.to.target><lb></lb>nor aut æqualis potentia dicatur viciſſe majorem. </s></p> <p type="margin"> <s><margin.target id="marg169"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>lo, non copia <lb></lb>aquæ Natu<lb></lb>ra pugnat, <lb></lb>ac vincit, in <lb></lb>hydrauli<lb></lb>cis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Colligitur tertiò, quomodo Natura in Hydraulicis pugnet, <lb></lb>ac ſuperet, non aquarum copiâ, ſed altitudine perpendiculari. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>Colligitur quartò, ſiphonis operationes hydraulicas ad li<lb></lb>bræ operationes commodè revocari poſle, uti mox dicemus <lb></lb>Propoſit: VIII. <expan abbr="ſeq.">ſeque</expan> </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg170"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg170"></margin.target><emph type="italics"></emph>Fonticulus <lb></lb>duplex ope <lb></lb>ſiphonis in<lb></lb>verſi.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.118.1.jpg" xlink:href="051/01/118/1.jpg"></figure> <p type="main"> <s>Hinc etiam patet, <lb></lb>qua ratione ſiphonis <lb></lb>inverſi præſidio fonti<lb></lb>culus duplex exhiberi <lb></lb>poſſit, ſi nimirum crus <lb></lb>brevius AB indatur <lb></lb>vitreo protuberanti <lb></lb>ventri BC, habeatque <lb></lb>intra ventrem ſtrictiſſi<lb></lb>mum oſculum B aper<lb></lb>tum; deinde ex eodem <lb></lb>ventre derivetur crus <lb></lb>longius DE in curva<lb></lb>tum inferiùs, & apud E <lb></lb><expan abbr="deſinẽs">deſinens</expan> in oſculum an<lb></lb>guſtum. </s><s>Si enim hu<lb></lb>juſmodi ſiphon impo<lb></lb>natur vaſi pleno, & ex <lb></lb>oſculo E ſugatur aër; <lb></lb>aſcendet aqua per crus AB, & in ventre exiliet radiosâ virgulâ <lb></lb>vix aſpectabili, indeque ſe demittet in crus alterum longius DE, <lb></lb>cogeturque ſua propendente demiſſione ad ejectionem eò altio<lb></lb>rem, quò profundiùs deſcendet. </s></p> <pb xlink:href="051/01/119.jpg" pagenum="88"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Cauſam adſignare, cur quando oſculum externi cruris <lb></lb>ſiphonis inverſi, eſt altius, aut æquè altum ac aquæ ſuperficies <lb></lb>ſuprema in vaſe, aqua non fluat; quando verò <lb></lb>eſt demiſſius, fluat.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>VIdimus, experientiam docere, quando perpendiculum cru<lb></lb>ris externi ſiphonis inverſi, eſt minus, aut æquale perpendi<lb></lb>culo cruris interni, uſque ad ſupremam aquæ ſuperficiem aquam <lb></lb>non effluere poſſe per os externi cruris, ceſſante ſuctu, ſeu attra<lb></lb>ctione; quando verò perpendiculum externi eſt majus quàm in<lb></lb>terni cruris in ſenſu expoſito, fluere donec æqualia fiant perpen<lb></lb>dicula, aut donec tota effluxerit aqua ex vaſe. </s><s>Quæritur nunc <lb></lb>hujus phænomeni cauſa. <lb></lb> <arrow.to.target n="marg171"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg171"></margin.target><emph type="italics"></emph>Siphonis <lb></lb>crus longius <lb></lb>ſuperat bre<lb></lb>vius, non <lb></lb>capacius mi<lb></lb>nus capax.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Hero Alexandrinus in libello de Spiritalibus cap 1. ait, <lb></lb>quoſdam putare, cauſam eſſe, quòd aqua cruris externi debeat <lb></lb>trahere aquam cruris interni, ac proinde illa debeat eſſe major <lb></lb>ac copioſior, quàm hæc. </s><s>Sed hoc minimè verum eſſe, patet ex <lb></lb>eo (quod etiam Hero advertit) quòd licet crus externum ſit lon<lb></lb>gè amplius atque capacius interno, <expan abbr="multoq́ue">multoque</expan> plùs aquæ conti<lb></lb>neat; ſi tamen longius non eſt, nequaquam effluit ex ipſo aqua, <lb></lb>ſed ubi ceſſat violenta ſuctio, ſeu tractio, tota refluit per crus in<lb></lb>ternum longius intra vas. </s><s>Non ergo externum crus ſuperat in<lb></lb>ternum, quòd aquæ plùs contineat. </s><s>Itaque videamus natura<lb></lb>lem cauſam & genuinam, ex Heronis primò, deinde ex noſtra <lb></lb>ſententia. </s></p> <p type="main"> <s>Diximus cap. 1. Propriet. II. aquæ continuæ & quieſcentis <lb></lb>ſuperficiem ſuperiorem eſſe ſphæricam (etiam in parvis vaſis, & <lb></lb>receptaculis, licet inſenfibiliter) centrum habentem idem quod <lb></lb>Terra, ſeu globus Terraqueus; non quieſcentem verò aquam <lb></lb>tam diu fluere, donec partes continuæ in una ſuperficie ſphærica <lb></lb>conſtituantur, hoc eſt, donec omnes extimæ ſuperficiei partes <lb></lb>continuæ æqualiter diſtent à centro Terræ. </s><s>Hoc poſito putat <lb></lb>Hero, cauſam ob quam, quando externi cruris orificium eſt <pb xlink:href="051/01/120.jpg" pagenum="89"></pb>æquè altum ac ſuperficies ſuperior aquæ vaſis, hoc eſt, quando </s></p> <p type="main"> <s> <arrow.to.target n="marg172"></arrow.to.target><lb></lb>externum crus eſt æquale interno quoad longitudinem, uſque <lb></lb>ad aquæ ſuperficiem ſupremam vaſis, aqua non effluat ex crure <lb></lb>externo, etiamſi ſiphon ſit plenus aquâ, eſſe, quia tunc aqua ſi<lb></lb>phonis continuatur cum aqua vaſis, & utriuſque ſuperficies ex<lb></lb>trema æqualiter diſtat à centro Mundi: Cauſam verò cur, quan<lb></lb>do externi cruris orificium eſt demiſſius ſuperficie extrema aquæ <lb></lb>vaſis, effluat, eſſe, quia tunc ſuperficies aquæ vaſis eſt altior, quàm <lb></lb>ſuperficies aquæ cruris externi, cum cujus aqua continuatur, ac <lb></lb>proinde tam diu fluere debet aqua vaſis, poſtquam ſemel fluere <lb></lb>cœpit, donec ſuperficies fiant æqualiter diſtantes à centro Ter<lb></lb>ræ. </s><s>Ob contrariam ergo cauſam, ſecundùm Heronem non <lb></lb>effluit aqua ex crure externo breviore, ſed refluit intra vas quia <lb></lb>nimirum ſuprema ſuperficies aquæ vaſis eſt declivior, quàm ſu<lb></lb>perficies aquæ cruris externi. </s></p> <p type="margin"> <s><margin.target id="marg172"></margin.target><emph type="italics"></emph>Heronis opi<lb></lb>nio circa a<lb></lb>quæ fluxum <lb></lb>è crure ex<lb></lb>terno ſipho<lb></lb>nis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Cœterùm cur aqua in ſecundo caſu, ex vaſe aſcendat ad <lb></lb>ſiphonis ſummitatem, contra ejus naturam, indeque deſcendat <lb></lb>ad orificium uſque externi cruris, non eſt ob cauſam jam adſigna<lb></lb>tam, ſed ut impleat, aut impediat vacuum, ſeu quia trahitur vio<lb></lb>lenter ad impediendum, aut implendum vacuum. </s><s>Quoniam <lb></lb>enim ex crure externo extrahitur aër, trahit is ſecum, nè vacuus <lb></lb>maneat ſiphon, & diſcontinuentur corpora, nempe aër & aqua, <lb></lb>trahit inquam ſecum aquam uſque ad orificium cruris externi; <lb></lb>quò ubi pervenerit, nullam ampliùs violentiam patitur ab aëre, <lb></lb>nec ab alio extrinſeco agente, ſed naturæ ſuæ relinquitur, ut pars <lb></lb>illa incipiat, aut proſequatur fluxum, cujus ſuperficies extre<lb></lb>ma minùs diſtat à centro Mundi, duretque fluxus, donec am<lb></lb>bæ ſuperficies æquales fiant. </s></p> <p type="main"> <s><emph type="center"></emph>Experimentum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ESſe porrò hanc, quam adſignavit Hero, genuinam dicti <lb></lb>phænomeni cauſam, confirmat ipſe tali Experimento. </s><s><emph type="italics"></emph>Si <lb></lb> <arrow.to.target n="marg173"></arrow.to.target><lb></lb>ſumentes,<emph.end type="italics"></emph.end> inquit, <emph type="italics"></emph>duo vaſa<emph.end type="italics"></emph.end> (cujuſmodi ſunt A & B in appo<lb></lb>ſitis figuris) <emph type="italics"></emph>injiciemus humidum in utrumque ipſorum, & implentes<emph.end type="italics"></emph.end> <pb xlink:href="051/01/121.jpg" pagenum="90"></pb><emph type="italics"></emph>ſiphonem, digitiſque ipſius oſcula comprehendentes, demittemus alte<lb></lb>rum crus in unum dictorum vaſorum adeo, ut aquâ demergatur; alte<lb></lb>rum verò in alterum vas,<emph.end type="italics"></emph.end> (ut aqua etiam demergatur, prout in <lb></lb>appoſitis figuris apparet;) <emph type="italics"></emph>fiet tota aqua continua; utrumque enim <lb></lb>humidorum, quæ ſunt in væſibus,<emph.end type="italics"></emph.end> (ita interpres) <emph type="italics"></emph>conjungitur cum eo, <lb></lb>quod eſt in ſiphone, ita ut totum continuum fiat. </s><s>Si igitur ſuperficies<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="fig22"></arrow.to.target><lb></lb><emph type="italics"></emph>humidorum, quæ priùs erant in va<lb></lb>ſibus, in una ſuperficie conſiſtant,<emph.end type="italics"></emph.end><lb></lb>ut in prima figura; <emph type="italics"></emph>quieſcet & ſic <lb></lb>utraque ipſarum demerſo ſiphone: <lb></lb>ſin minùs,<emph.end type="italics"></emph.end> ut in ſecunda figura; <lb></lb><emph type="italics"></emph>quoniam aqua continua facta eſt, <lb></lb>neceſſariò ob continuitatem in hu<lb></lb>miliorem locum fluet, quouſ〈qué〉 vel <lb></lb>omnis aqua, quæ in vaſibus, in una <lb></lb>ſuperficie ſit, vel alterum vaſorum <lb></lb><expan abbr="exinãiatur">exinaniatur</expan>,<emph.end type="italics"></emph.end> illud videlicet, quod <lb></lb>altiori fuerit loco. </s><s><emph type="italics"></emph>Fiant igitur <lb></lb>in una ſuperficie humida, quæ ſunt <lb></lb>in vaſibus; quieſcent utique, ita <lb></lb>ut etiam humidum, quod eſt in ſi<lb></lb>phone, ſimul quieſcat. </s><s>Quòd ſi<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg174"></arrow.to.target><lb></lb><emph type="italics"></emph>quis mente concipiat ſiphonem diſ<lb></lb>ſectum juxta ſuperficies humidorum, quæ ſunt in vaſibus; & ita qui<lb></lb>eſcet humidum, quod eſt in ſiphone: ergo & ſiphone ipſo ſuſpenſo, & <lb></lb>in neutram partem inclinato, rurſus quieſcet humidum, ſive æqualem <lb></lb>omnino habens latitudinem, ſive alterum crus altero multo majus ſit; <lb></lb>non enim in hoc cauſa eſt, cur humidum quieſcat, ſed in eo, quòd ip<lb></lb>ſius oſcula æqualiter jaceant.<emph.end type="italics"></emph.end> </s><s>Hæc Hero. lege etiam quæ ſequun<lb></lb>tur apud ipſum in eodem cap. 1. </s></p> <p type="margin"> <s><margin.target id="marg173"></margin.target>Experimen<lb></lb>tum circa <lb></lb>aquæ <expan abbr="fluxũ">fluxum</expan> <lb></lb>ex ſiphone.</s></p> <p type="margin"> <s><margin.target id="marg174"></margin.target>Siphon in<lb></lb>verſus æ<lb></lb>qualium <lb></lb>crurium <lb></lb>longitu di<lb></lb>ne, inæqua<lb></lb>lium capa<lb></lb>citate, reti<lb></lb>net aquam <lb></lb>ſuſpenſam <lb></lb>ſecundum <lb></lb>Heronem.</s></p> <figure id="id.051.01.121.1.jpg" xlink:href="051/01/121/1.jpg"></figure> <p type="main"> <s>Sed hæc cauſa ex Herone adſignata non videtur eſſe ve<lb></lb> <arrow.to.target n="marg175"></arrow.to.target><lb></lb>ra, aut ſaltem non eſt adæquata. </s><s>Primò enim, ſi ideo fluit <lb></lb>aqua ex crure longiore, AD, ſeu potius CD, ſecundæ figuræ, <lb></lb>quia ſuperfies extrema aquæ ipſius non eſt æqualis ſuperficiei <pb xlink:href="051/01/122.jpg" pagenum="91"></pb>extremæ aquæ alterius cruris, BF, ſeu potius EF, ſed demiſſior; <lb></lb>ergo quando ſiphon ſive æqualium, ſive inæqualium crurium, <lb></lb>aquȧ plenus, & utrimque compreſſis digitis obturatus, imponi<lb></lb>tur duobus prædictis vaſis aquȧ plenis, quorum unius ſuperficies <lb></lb>ſuprema aquæ altior eſt, quàm alterius, effluitque aqua intra vas <lb></lb>demiſſius, eò quòd alterius ſuperficies ſuprema altior eſt, & ad <lb></lb>decliviorem locum tendit, nititurque ſuperficiem ſuam adæ<lb></lb>quare ſuperficiei alterius vaſis humilioris; ergo inquam, quando <lb></lb>hoc contingit, aqua ex vaſe altiore aſcendit naturaliter & inna<lb></lb>to appetitu ad ſiphonis ſuperiorem partem, indeque deſcendit <lb></lb>intra vas humilius; naturaliter enim aquæ partes altiores fluunt <lb></lb>ad loca decliviora. </s><s>Deinde ſi illa eſt cauſa adæquata, cur quan<lb></lb>do ſiphon ina qualium crurium repletur aquâ, & ſecundùm <lb></lb>longius crus immergitur aquæ, ſecundùm brevius verò extra <lb></lb>in aëre relinquitur, cur inquam, non effluit aqua per externum, <lb></lb>ubi nullum eſt impedimentum præter aërem? </s><s>poteſt enim aqua <lb></lb>per externum fluere ad loca decliviora, & fundare unam conti<lb></lb>nuam ſuperficiem diſtinctam à ſuperficie, quæ in vaſe eſt; & <lb></lb>præterea inclinationem habet ad deſcendendum, non verò ad <lb></lb>aſcendendum. </s><s>Præterea, cur quando ſiphon inæqualium cru<lb></lb>rium repletur aqua, & tenetur inverſus in aëre, non effluit aqua <lb></lb>ex crure breviori, cum ejus aqua plùs diſtet à centro Terræ, <lb></lb>quàm aqua cruris longioris? </s><s>Alia ergo cauſa adſignari debet, cur <lb></lb>aqua cruris longioris, ſeu externi, ſeu interni, vincataquam cru<lb></lb>ris brevioris; quam paulò poſt dabimus. </s></p> <p type="margin"> <s><margin.target id="marg175"></margin.target><emph type="italics"></emph>Heronis opi<lb></lb>nio exami<lb></lb>natur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Qui tamen Heronis ſententiam tueri volet, ad has ratio<lb></lb>nes in contrarium allatas reſpondere poterit, ut ſequitur. </s><s>Nem<lb></lb>pe ad primam, aquam cruris brevioris non aſcendere naturali<lb></lb>ter, ſed tractam ab aqua cruris longioris AD, ſeu CD, ad va<lb></lb>cuum in ſiphone impediendum, & ad tuendam continuitatem <lb></lb>partium aquæ aqua enim cruris longioris AD, ſeu CD, deſcen<lb></lb>dit naturaliter (utpote tendens ad locum decliviorem) ſecum<lb></lb>que trahit reliquam aquam, quia ſuprema ſuperficies vaſis A, <lb></lb>cum qua continuatur aqua ſiphonis, & vaſis B, eſt declivior, <pb xlink:href="051/01/123.jpg" pagenum="92"></pb>ſuprema verò ſuperficies vaſis B eſt altior, & debet fieri æqua<lb></lb>litas inter ipſas: quæ non fieret, ſi aqua ſiphonis BF, ſeu EF, de<lb></lb>ſcenderet. </s></p> <p type="main"> <s>Ad ſecundam, non effluere aquam per brevius, ſed per lon<lb></lb>gius crus, quia aqua amat continuitatem ſuarum partium, & ap<lb></lb>petit habere ſuperficiem ſupremam omnium partium æqualiter <lb></lb>diſtantem à centro Terræ; quorum utrumque obtinet, ſi ef<lb></lb>fluit aqua per longius crus; neutrum, ſi per brevius. </s></p> <p type="main"> <s>Ad Tertiam, ideo non effluere aquam è crure breviore, ſed <lb></lb>è longiore, quia aqua cruris brevioris eſt altior, & aqua cruris <lb></lb>longioris declivior: curruntautem aquæ continuatæ partes alti<lb></lb> <arrow.to.target n="marg176"></arrow.to.target><lb></lb>ores ad decliviores naturaliter, & non hæ ad illas. </s></p> <p type="margin"> <s><margin.target id="marg176"></margin.target><emph type="italics"></emph>Authoris o<lb></lb>pinio circa <lb></lb>aquæ <expan abbr="fluxũ">fluxum</expan> <lb></lb>è crure ex<lb></lb>terno longio <lb></lb>re ſiphonis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sed quidquid ſit de hac Heronis ſententia, mihi magis pla<lb></lb>cet ſequens ratio allati phænomeni, quæ univerſalis eſt & in <lb></lb>omnibus ſimilibus caſibus locum habet, ut vidimus in præce<lb></lb>dentibus, & iterum videbimus infrà hoc eodem capite Propo<lb></lb>ſit. 13. & 14. </s><s>Pro qua recolendum eſt, quod diximus ſuprà Ca<lb></lb>pite 1. Proprietate IV. ex Archimede, aquæ & humidi cujuſcun<lb></lb>que partem unamquamque premi humido ſupra ipſam exiſtente <lb></lb>ad perpendiculum, ſi humidum ſit deſcendens in aliquo, aut cer<lb></lb>tè nullum habeat impedimentum, ut deſcendat. </s></p> <p type="main"> <s>Dico itaque, cauſam hujus rei eſſe eandem cum ea, quæ <lb></lb>adſignata fuit in præcedentibus, quia nimirum aqua cruris lon<lb></lb>gioris potentior eſt ad deſcendendum, ſecumque trahendum <lb></lb>aquam cruris brevioris, quàm aqua cruris alterius; & hoc ideo, <lb></lb>quia aqua premit ac premitur, dum premit ac premitur, ad per<lb></lb>pendiculum, hoc eſt, ſecundùm lineam quæ tranſit per centrum <lb></lb>Mundi. </s><s>Cujus ergo aquæ perpendiculum longius eſt, illa ma<lb></lb>gis premit ac vincit, hoc eſt, deſcendit, ſi nihil obſtet deſcen<lb></lb>ſum impediens, ut in noſtro caſu contingit. </s><s>Hîc ergo verum <lb></lb>etiam eſt, quòd <emph type="italics"></emph>in Hydraulicis pugnatur & vincitur non pondere, <lb></lb>aut copi aquarum, ſed perpendiculis,<emph.end type="italics"></emph.end> juxta Axioma hydraulicum, <lb></lb>2. quod ſuprà Propoſitione 2, formatum fuit. </s></p> <pb xlink:href="051/01/124.jpg" pagenum="93"></pb> <p type="main"> <s><emph type="center"></emph>Proprietas VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonem ad Libram ſeu vectem revocare, <lb></lb>filtrum ad ſiphonem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ESto recta linea AB, diviſa bifariam in puncto C. </s><s>Si huic <lb></lb>puncto C ſupponatur hypomochlion G, aut alligetur fi<lb></lb> <arrow.to.target n="fig23"></arrow.to.target><lb></lb>lum FG; ſtabit, hærebitque li<lb></lb>nea AB in æquilibrio horizon<lb></lb>ti parallela, & neutra pars præ<lb></lb>valebit. </s><s>Si prolongetur pars <lb></lb>CB uſque ad D, prævalebit pars <lb></lb>CD parti CA, & deſcendet. </s><s>Si <lb></lb>prolongetur eadem pars CB, uſ<lb></lb>que ad E, adhuc magis prævale<lb></lb>bit pars C parti CA, <expan abbr="cele-riuſq́ue">cele<lb></lb>riuſque</expan> deſcendet; & quò ma<lb></lb>gis prolongabitur pars longior, <lb></lb>eò magis prævalebit breviori, <lb></lb>magiſque celeriter deſcendet. </s><s><lb></lb>Linea porrò AB, aut AD, aut <lb></lb>AE, ſi hypomochlio G impo<lb></lb>natur, repræſentatvectem; ſi è <lb></lb>filo FC ſuſpendatur, repræſentat <lb></lb>libram, aut ſtateram. </s></p> <figure id="id.051.01.124.1.jpg" xlink:href="051/01/124/1.jpg"></figure> <p type="main"> <s>Eſto jam ſiphon ACB, ſive <lb></lb> <arrow.to.target n="marg177"></arrow.to.target><lb></lb>erectus, ſive inverſus, diviſus <lb></lb>mente in duas æquales partes AC, BC, & repleatur totus aquâ; <lb></lb>ex neutro crure effluet, ut vidimus atque probavimus, ſed aqua <lb></lb>ſtabit, hærebitve in duobus cruribus AC, BC, in æquilibrio. </s><s><lb></lb>Si prolongetur crus CB, uſque ad D, & repleatur totus ſi<lb></lb>phon aquâ; prævalebit crus CD, & aqua ejus in inverſo ſipho<lb></lb>ne effluens ſecum trahet reliquam; in erecto verò ſiphone de<lb></lb>ſcendet & expellet reliquam per os A. </s><s>Si prolongetur idem <lb></lb>crus CB uſque ad E, adhuc magis prævalebit crus CE, ma<lb></lb>giſque celeriter deſcendet ejus aqua, & vel ſecum trahet reli<lb></lb>quam, vel illam ſubſidendo expellet. </s></p> <pb xlink:href="051/01/125.jpg" pagenum="94"></pb> <p type="margin"> <s><margin.target id="marg177"></margin.target><emph type="italics"></emph>Siphon tam <lb></lb>erectus. </s><s><expan abbr="quãm">quam</expan> <lb></lb>inverſus, re<lb></lb>vecatur ad <lb></lb>libram.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.125.1.jpg" xlink:href="051/01/125/1.jpg"></figure> <p type="main"> <s>Patet ergo, quomodo ſiphon <lb></lb>tam erectus, quàm inverſus, re<lb></lb>vocetur ad libram, aut vectem </s></p> <p type="main"> <s>Filtrum appellamus panni <lb></lb> <arrow.to.target n="marg178"></arrow.to.target><lb></lb>laciniam ACB, pendentem ex <lb></lb>vaſe A, ita ut pars AC ſit in<lb></lb>tra vas, & aquæ immerſa, ſal<lb></lb>tem ex parte; pars verò altera <lb></lb>CB extra vas pendeat. </s><s>Hæc <lb></lb>panni lacinia ſi priùs madefiat <lb></lb>tota, deinde modo dicto ex va<lb></lb>ſe aquâ pleno ſuſpendatur; tra<lb></lb>hit aquam non ſecus ac ſiphon, <lb></lb>ſi pars exterior fuerit longior <lb></lb>quàm interior; ſi æqualis, aut <lb></lb>brevior, non trahit. </s><s>Conſtat <lb></lb>ergo, filtrum ad ſiphonem re<lb></lb>duci. </s></p> <p type="margin"> <s><margin.target id="marg178"></margin.target><emph type="italics"></emph>Filtrum re<lb></lb>vocatur ad <lb></lb>ſiphonem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Diabetem ſpiritalem deſcribere, ejuſque <lb></lb>proprietates adſignare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>EOſdem ferè effectus, quos præſtat ſiphon inflexus, cujus <lb></lb>unum crus vaſi imponitur, præſtat etiam tubus certo mo<lb></lb>do vaſi implantatus, quem Hero Alexandrinus vocat medium <lb></lb>ſpiritalem diabetem, quaſi dicas, peraſcenſorem; alij verò vo<lb></lb>cant tubum ſuffocabilem. </s><s>Sic autem conſtruitur. </s></p> <pb xlink:href="051/01/126.jpg" pagenum="95"></pb> <figure id="id.051.01.126.1.jpg" xlink:href="051/01/126/1.jpg"></figure> <p type="main"> <s>Sit vas ABCD. </s><s>Per ejus fundum <lb></lb> <arrow.to.target n="marg179"></arrow.to.target><lb></lb>CD trajiciatur tubus EF <expan abbr="utrimq;">utrimque</expan> <lb></lb>apertus, ipſi fundo coarctatus, & <lb></lb>in partem inferiorem excedens <lb></lb>apud F; at oſculum ejus ſuperi<lb></lb>us E non adæquet altitudinem <lb></lb>vaſis, ſed ſit paulò inferius. </s><s>Huic <lb></lb>tubo EF circumponatur alius tu<lb></lb>bus GHI, ſuperius clauſus, qui <lb></lb>tamen oſculum E non attingat, <lb></lb>ſed tantum ab ipſo diſtet, <expan abbr="quantũ">quantum</expan> <lb></lb>ſufficit ad aquæ ingreſſum per <lb></lb>oſculum E: inferiùs verò vel non attingat undequaque fun<lb></lb>dum vaſis; vel ſi attingit, relinquatur à latere foramen I, per <lb></lb>quod aqua intrare poſſit. </s></p> <p type="margin"> <s><margin.target id="marg179"></margin.target><emph type="italics"></emph>Diabetes <lb></lb>ſpiritalis <lb></lb>quomodo <lb></lb>conſtrua<lb></lb>tur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Si jam vas impleas aliquò uſque aquâ, v. g. uſque ad KL, in<lb></lb> <arrow.to.target n="marg180"></arrow.to.target><lb></lb>ſinuabit ſeſe illa per foramen I, & aſcendet uſque ad H, in<lb></lb>tra tubum IGH. </s><s>Si igitur per oſculum F attrahas aërem, <lb></lb>qui eſt in tubo FE; ſequetur ſimul aër, qui eſt in tubi ſuperpo<lb></lb>ſiti parte GH; & poſt aërem ſequetur aqua, quæ eſt in ejuſdem <lb></lb>tubi parte IH; nec ceſſabit fluxus ex F, donec tota aqua va<lb></lb>ſis effluxerit, alioquin daretur vacuum intra tubos, ut patet. </s><s><lb></lb>Quòd ſi totum vas impleas aquâ, aſcendet illa per foramen I, <lb></lb>intra tubum IHG, uſque dum ſupergrediatur oſculum E; quo <lb></lb>ſupergreſſo, inſinuabit ſeſe, naturali pondere, aqua per dictum <lb></lb>oſculum, & effluet per F, nec ceſſabit, donec tota effluxerit <lb></lb>aqua. </s><s>Hac arte docebimus infrà Claſſe 1. cap. 1. Machina IV. <lb></lb>conſtruere vas, quod effundat aquam per fundum, dum ple<lb></lb>num eſt; dum verò plenum non eſt, nihil effundat. </s></p> <p type="margin"> <s><margin.target id="marg180"></margin.target><emph type="italics"></emph>Diabetis <lb></lb>ſpiritalis <lb></lb>proprieta<lb></lb>tes.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>FLuxus aquæ etiam hîc inæqualis est, cum continuo celeritatis de-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/127.jpg" pagenum="96"></pb> <arrow.to.target n="fig24"></arrow.to.target><lb></lb> <arrow.to.target n="marg181"></arrow.to.target><lb></lb><emph type="italics"></emph>cremento: & quò tubus<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>lon<lb></lb>giùs exceſſerit extra fundum, eò <lb></lb>celeriùs, adeoque & copioſiùs hu<lb></lb>midum effluet. </s><s>Harum autem <lb></lb>proprietatum ratio eſt eadem cum <lb></lb>illa quæ ſuprà Propoſit.<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>pro ſi<lb></lb>phone vaſi impoſito eſt allata; tu<lb></lb>bus enim<emph.end type="italics"></emph.end> IG <emph type="italics"></emph>æquivalet cruri in<lb></lb>terno, &<emph.end type="italics"></emph.end> FE, <emph type="italics"></emph>cruri externo.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg181"></margin.target><emph type="italics"></emph>Aquæ flu<lb></lb>xus per dia<lb></lb>betem ſpiri<lb></lb>talem inæ<lb></lb>qualis eſt.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.127.1.jpg" xlink:href="051/01/127/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>IDem effectus habebitur, ſi in<lb></lb> <arrow.to.target n="marg182"></arrow.to.target><lb></lb>tra vas fiat ſiphon inverſus<emph.end type="italics"></emph.end><lb></lb>ABC, <emph type="italics"></emph>cujus dorſum<emph.end type="italics"></emph.end> B <emph type="italics"></emph>ſit paulò <lb></lb>infra ſumma labra vaſis. </s><s>Si enim aqua infundatur vaſi, aſcendet <lb></lb>ea per crus<emph.end type="italics"></emph.end> AB; <emph type="italics"></emph>& cùm ſupergreſſa fuerit dorſum<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>effluet per <lb></lb>crus<emph.end type="italics"></emph.end> BC; <emph type="italics"></emph>nec ceſſabit, donec dota effluxerit. </s><s>Vide quæ dicemus <lb></lb>infrà Parte<emph.end type="italics"></emph.end> 2. </s><s><emph type="italics"></emph>loc. cit. Machina IV. </s><s>Si verò non totum vas implea<lb></lb>tur aquâ, & aër ſugatur ex oſculo<emph.end type="italics"></emph.end> C; <emph type="italics"></emph>ſequetur ſimiliter aqua vaſis, <lb></lb>nec ceſſabit fluxus, donec tota fuerit elapſa, quoniam perpendiculum <lb></lb>aquæ cadentis (ſicut & in Diabete) majus eſt quàm perpendiculum <lb></lb>aquæ aſcendentis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg182"></margin.target>Diabetes <lb></lb>ſpiritalis a<lb></lb>lia ratione <lb></lb>conſtructus.</s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio X.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphonis inverſi fluxum æqualem <lb></lb>reddere.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SUprà Propoſit. VI. Propriet. I. oſtendimus, aquam per exter<lb></lb>num ſiphonis inverſi crus fluere inæqualiter, cum perpetuo <lb></lb>nimirum celeritatis decremento. </s><s>Oporteat igitur efficere ut <lb></lb>fluxus ſemper æqualis ſit. </s><s>Docet id Hero Alexandrinus cap. 3. <lb></lb>de ſpiritalibus in hunc ſenſum. </s></p> <pb xlink:href="051/01/128.jpg" pagenum="97"></pb> <figure id="id.051.01.128.1.jpg" xlink:href="051/01/128/1.jpg"></figure> <p type="main"> <s>Sit vas ABCD, aqua <lb></lb> <arrow.to.target n="marg183"></arrow.to.target><lb></lb>plenum vſque ad EF, gra<lb></lb>tia exempli (poteſt enim <lb></lb>plùs & minùs eſſe <expan abbr="repletũ">repletum</expan>) <lb></lb>habens ſuas anſulas LL per<lb></lb>foratas. </s><s>Fiat lebetarium <lb></lb>G, ſive apertum, ſive clau<lb></lb>ſum, quod poſſit innatare <lb></lb>ſuperficiei aquæ EF; , & per <lb></lb>eius operculum ac fundum <lb></lb>trajice ſiphonis HIK crus <lb></lb>internum ac brevius HI, & <lb></lb>ſtanno, aliavè materia ad <lb></lb>foramina benè coarcta, <lb></lb>nè aqua ſubintrare in le<lb></lb>betarium poſſit. </s><s>Alterum <lb></lb>crus externum ac longius <lb></lb>IK trajice per foramina <lb></lb>anſularum LL, ſic ut fa<lb></lb>cilè per eas moveri aſcen<lb></lb>dendo ac <expan abbr="deſcendẽdo">deſcendendo</expan> poſ<lb></lb>ſit. </s><s>His factis, ſi per oſcu<lb></lb>lum K attrahas aërem, qui <lb></lb>eſt in ſiphone, ſequetur, ob vacui fugam, aqua vaſis, eâque ſub<lb></lb>ſidente ſubſidebit ſimul & lebetarium, & ſiphon infixus lebeta<lb></lb>rio, fluetque aqua per K, donec oſculum H tangat fundum <lb></lb>CD. </s><s>Erit autem ille fluxus ſemper æqualis, eò quòd exceſſus <lb></lb>perpendiculi cruris externi & longioris ſupra perpendicu<lb></lb>lum cruris interni & brevioris, ſit ſemper æqualis, hoc <lb></lb>eſt, idem, nempe in ſchemate poſito exceſſus KM uſque <lb></lb>ad ſupremam aquæ vaſis ſuperficiem EF, propterea quòd efflu<lb></lb>ente aqua ex K, & deſcendente ſuperficie EF verſus <expan abbr="fundũ">fundum</expan> <lb></lb>vaſis, deſcendat & lebes cum ſiphone ſibi coarctato, ut dixi; quo <lb></lb>fit, ut crus IK eandem ſemper aquæ quantitatem ex vaſe per <lb></lb>crus HI attrahat, nempe illam quæ eſt in GI, à G ſuprema aquæ <pb xlink:href="051/01/129.jpg" pagenum="98"></pb> <arrow.to.target n="fig25"></arrow.to.target><lb></lb>ſuperficie, vſque ad I; ac <lb></lb>proinde eâdem ſemper fa<lb></lb>cilitate difficultatevè efflu<lb></lb>it aqua ex K<gap></gap> ergo & eâ<lb></lb>dem celeritate. </s></p> <p type="margin"> <s><margin.target id="marg183"></margin.target><emph type="italics"></emph>Aquæ flu<lb></lb>xum per <lb></lb>crus exter<lb></lb>num ſipho<lb></lb>nis æqualem <lb></lb>reddere.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.129.1.jpg" xlink:href="051/01/129/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Poteſt loco lebetarij<emph.end type="italics"></emph.end> G <lb></lb><emph type="italics"></emph>accipi ſuberis, alteriusvè leviſ<lb></lb>ſimi ligni fruſtum, & per id <lb></lb>trajici ſiphonis crus <expan abbr="internũ">internum</expan>.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg184"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg184"></margin.target><emph type="italics"></emph>Aqua effluit <lb></lb>ex crure ex<lb></lb>terno ſipho<lb></lb>nis eò cele<lb></lb>rius, quo <lb></lb>maior eſt i<lb></lb>pſi' exceſſus <lb></lb>ſupra inter<lb></lb>num crus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Quantò maior erit ex<lb></lb>ceſſus<emph.end type="italics"></emph.end> KM <emph type="italics"></emph>cruris externi, <lb></lb>tantò celeriùs effluet aqua ex<emph.end type="italics"></emph.end><lb></lb>K, <emph type="italics"></emph>ſemper tamen æqualiter. </s><s><lb></lb>Ratio eſt, quia tunc magis pre<lb></lb>mitur aqua apud oſculum<emph.end type="italics"></emph.end> K, <lb></lb><emph type="italics"></emph>& aqua cruris externi maio<lb></lb>rem exceſſum habet ſupra <expan abbr="aquã">aquam</expan> <lb></lb>cruris interni, ac proinde mi<lb></lb>norem difficultatem ad illam <lb></lb>trahendam. </s><s>Neque hoc eſt <lb></lb>contra id, quod diximus Pro<lb></lb>poſit. VII. præcedente: aliud enim eſt, cauſam dare, cur fluat aqua ex <lb></lb>crure longiore, aliud cur celeriùs fluat.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Quomodo fieri poſſit fluxus aquæ ex ſiphone partim æqualis, par<lb></lb>tim inæqualis, hoc eſt, vno tempore æqualis, altero inæqualis, pront no<lb></lb>bis placuerit, docet Hero ſupra citatus cap.<emph.end type="italics"></emph.end> 4. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphone inverſo aquam ex vno montis latere in <lb></lb>alterum, per verticem deducere.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SItmons A, in cuius latere vno ſit fons, alia vè aqua, ſeu flu<lb></lb>ens, ſeu ſtagnans B, aut C, in pede nimirum, aut in latere <pb xlink:href="051/01/130.jpg" pagenum="99"></pb> <arrow.to.target n="fig26"></arrow.to.target><lb></lb>montis; ſitque 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"></figure> <p type="main"> <s> <arrow.to.target n="marg185"></arrow.to.target><lb></lb>aqua B, aut C; & ſit in hunc locum E deducenda prædicta <lb></lb>aqua per montis verticem. </s><s>Fiat ſiphon inverſus inæqualium <lb></lb>crurium BCDE, ex plumbo, aut metallo, cuius orificium B, <lb></lb>aut C cruris brevioris ſit immerſum fonti B, aut C, alterum <lb></lb>verò orificium E cruris longioris deſinat intra ciſternam, ali<lb></lb>udvè receptorium E in loco deſtinato. </s><s>Hoc facto, obture<lb></lb>tur vtrumque ſiphonis os, & per foramen D in vertice montis <lb></lb>factum in ſiphone, repleatur totus ſiphon aqua, & foramen di<lb></lb>ligentiſſimè obturetur, nè aërem recipere poſſit. </s><s>Si iam aperia<lb></lb>tur eodem tempore ſimul vtrumque ſiphonis orificium, effluet <lb></lb>aqua per E cruris longioris intra receptaculum, <expan abbr="ſecumq;">ſecumque</expan> tra<lb></lb>het, nè vacuum intra <expan abbr="ſiphonẽ">ſiphonem</expan> fiat, aquam fontis B, aut C; nec <lb></lb>ceſſabit fluxus, quàm diu orificium B, aut C, fuerit aquæ im<lb></lb>merſum. </s><s>Ratio patet ex dictis Propoſitione 6. & alijs paſſim ex <lb></lb>præcedentibus. </s></p> <pb xlink:href="051/01/131.jpg" pagenum="100"></pb> <p type="margin"> <s><margin.target id="marg185"></margin.target><emph type="italics"></emph>Aquam per <lb></lb>montis ver<lb></lb>ticem à ba<lb></lb>ſe ad basè <lb></lb>deducere ſi<lb></lb>phone.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.131.1.jpg" xlink:href="051/01/131/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>OMninò neceſſarium eſt, ut locus<emph.end type="italics"></emph.end> E <emph type="italics"></emph>ſit humilior, ſaltem aliquan<lb></lb>tulùm, quàm locus fontis aut aquæ<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>ſeu C, ut ſiphonis crus<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>longius fieri poſſit quàm<emph.end type="italics"></emph.end> BD, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> DC. </s><s><emph type="italics"></emph>Quod ſi fieri non poſſit, ſpes <lb></lb>nulla eſt ad effectum deſideratum conſequendum. </s><s>Quare diligenter <lb></lb>priùs libellandum eſt ſpatium inter<emph.end type="italics"></emph.end> B <emph type="italics"></emph>&<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> C <emph type="italics"></emph>&<emph.end type="italics"></emph.end> E. <emph type="italics"></emph> Qu&<gap></gap>grave; <lb></lb>autem humilior fuerit locus<emph.end type="italics"></emph.end> E <emph type="italics"></emph>quàm aqua<emph.end type="italics"></emph.end> B <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>eòmcliorem res <lb></lb>ſucceſſum habebit, & eò velociùs aqua effluet ex orificio<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>vti ex di<lb></lb>ctis patet.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>POſſe etiam alia ratione trahi <expan abbr="aquã">aquam</expan> ex fonte<emph.end type="italics"></emph.end> B <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> C <emph type="italics"></emph>per ſiphonem, <lb></lb>vſque ad locum E, absque eo quòd in vertice fiat foramen<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>& ſi<lb></lb>phon repleatur aquâ nonnulli putant; ſi nimirum ex orificio<emph.end type="italics"></emph.end> E <emph type="italics"></emph>tubi<emph.end type="italics"></emph.end> <pb xlink:href="051/01/132.jpg" pagenum="101"></pb><emph type="italics"></emph>extrahatur aër follibus, aut Æolopila, quam deſcribimus infrà parte<emph.end type="italics"></emph.end> 2. <lb></lb><emph type="italics"></emph>claſſe<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>cap.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>Mach. VI. </s><s>Quam tamen <expan abbr="rationẽ">rationem</expan> nullo modo ſubſiſtere poſſe, <lb></lb>hinc oſtendo, quòd fieri non poſſit, ut follis per canalem vacuum tantum <lb></lb>aquarum pondus, quantum canalem ex attactu replere debet, attrahers <lb></lb>poſſit: montis enim inſtar <expan abbr="follẽ">follem</expan> eſſe oporteret, qui id præſtaret, cùm omnis <lb></lb>attractio proportionem ſuam babeat ad pondus attrahendum; quæ ſi im<lb></lb>parſit, rumpentur folles potiùs quàm pond<emph.end type="italics"></emph.end><emph type="sup"></emph>9<emph.end type="sup"></emph.end> <emph type="italics"></emph>attrahatur. </s><s>Vt vel hinc appæ<lb></lb>reat, quàm multa in ſpeculatione vera <expan abbr="appareãt">appareant</expan>, quæ tamen nullam effe<lb></lb>ctum in praxi exhibeant. </s><s>Marinus Merſennus in Pbænomenis Hydrau<lb></lb>licis Propoſit.<emph.end type="italics"></emph.end> 34. <emph type="italics"></emph>addit alium modum, ſi nimirum in loco deſtinato fiat <lb></lb>piſcinæ<emph.end type="italics"></emph.end> E <emph type="italics"></emph>vndique clauſa, eaque repleatur aquâ, & orificium<emph.end type="italics"></emph.end> E <emph type="italics"></emph>ſiphonis <lb></lb>adferruminetur operculo perforato piſcinæ, ita ut aquam non attingat: <lb></lb>ſi enim reſeratur epiſtomium piſcinæ, effluet aqua, inquit, & in aquæ lo<lb></lb>cum ſuccedet aër ſiphonis, in aëris locum aqua<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>nè vacuum <lb></lb>admittatur in ſiphone: dummodò, inquit, piſcina vacua totum ſiphonis <lb></lb>aërem recipere poſſit. </s><s>Sed mirum, quantum hallucinatur Merſennus, <lb></lb>cùm, ut diximus ſuprà Protheoria I. & videbimus infrà ſuo loco, & <lb></lb>ipſemet Merſennus inſinuat, aqua fontis<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> C <emph type="italics"></emph>trahi, atque <lb></lb>aſcendere per ſiphonis crus<emph.end type="italics"></emph.end> BD, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> CD, <emph type="italics"></emph>nullatenus poſſit, niſi infra <lb></lb>piſcinam<emph.end type="italics"></emph.end> E <emph type="italics"></emph>deſcendat tubus, per quem aqua fluat, paulò maioris per<lb></lb>pendiculi quàm ſit perpendiculum<emph.end type="italics"></emph.end> BD, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> CD. <emph type="italics"></emph>quod in hac & ſimi<lb></lb>libus Machinis eſt ſummè neceſſarium, vt diximus, cùm de vi Attracti<lb></lb>va egimus, & in ſecunda Parte ſæpius repetemus, præſertim claſſe<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>cap.<emph.end type="italics"></emph.end> 1. <lb></lb><emph type="italics"></emph>Machina<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph></s><s>Poteſt tamen longitudo tubi, qui infra piſcinam<emph.end type="italics"></emph.end> E <emph type="italics"></emph>de<lb></lb>ſcendere deberet, compenſari multis brevioribus tubis, ut diximus eo<lb></lb>dem loco de vi Attractiva, & loco citato Machina<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>iterum dicemus. </s><s><lb></lb>Accedit & illud, quòd aqua in ciſterna non ſufficiat ad effectum inten<lb></lb>tum præſtandum, niſi ciſterna tantum aquæ contineat, quantæ ipſe ca<lb></lb>nalis capax eſt; at quis tantam ſabricari volet ciſternam?<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>MVlta alia circa fluxum aquæ ex ſiphone dici poſſent, præſertim <lb></lb>quòd deſcenſus aquæ fluentis per crus imitetur leges gravium de<lb></lb>ſcendentium motu naturali; ſed hæc, & ſimilia alia, intelligi facilè <lb></lb>poſſunt ex dicendis Capite ſequenti, de fluxu aquæ per tubos Propoſit.<emph.end type="italics"></emph.end> 9. </s></p> <pb xlink:href="051/01/133.jpg" pagenum="102"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio XII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Siphone inverſo aquam ex montis radice ad <lb></lb>ejus verticem elevare.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>MIrabilis eſt ſequens modus, & antiquis minimè cognitur, <lb></lb> <arrow.to.target n="marg186"></arrow.to.target><lb></lb>imò ab omnibus pro impoſſibili habitus, inquit Porta: <lb></lb>omnes enim putârunt, ſi in ſiphonis inverſi collo ſeu curvatu<lb></lb>ra ſuprema foramen fieret, & vel minimum aëris ingredere<lb></lb>tur, fore ut ſiphonis aqua diſcontinuaretur, & aqua diviſa per <lb></lb>utrumque ſiphonis crus hinc atque inde delaberetur, totuſque <lb></lb>ſiphon evacuaretur. </s><s>Contrarium monſtrat ſequens modus, <lb></lb>quem præſcribit Joannes Baptiſta Porta lib. 2. Spirital. cap. 13. <lb></lb>& 14. in hunc ſenſum. <lb></lb> <arrow.to.target n="marg187"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg186"></margin.target><emph type="italics"></emph>Vide præ <lb></lb><expan abbr="cedentẽ">cedentem</expan> <lb></lb>figuram <lb></lb>pag<emph.end type="italics"></emph.end> 99. <lb></lb><emph type="italics"></emph>vel<emph.end type="italics"></emph.end> 100.</s></p> <p type="margin"> <s><margin.target id="marg187"></margin.target><emph type="italics"></emph>Aquam è <lb></lb>montis ra<lb></lb>dice ad ver<lb></lb>ticem ele<lb></lb>vare.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sit ut antea mons A, in ejuſque radice fons B, cujus <lb></lb>aqua ſit elevanda uſque ad verticem D. </s><s>Fiat ſiphon inverſum <lb></lb>inæqualium, ut antea, crurium BDE, cujus orificium B ſit <lb></lb>immerſum fonti, orificium verò E vel liberum omninò ſit; <lb></lb>vel deſinat in piſcinam ſubjectam. </s><s>Habebit autem res tantò<lb></lb>meliorem ſucceſium, quantò longius fuerit crus DE, quàm<lb></lb>alterum DB. </s><s>Fiat deinde infra collum ſiphonis, ubi D, re<lb></lb>ceptaculum aquarum H, undique clauſum quàm diligentiſ<lb></lb>ſimè, ſuoque epiſtomio I inſtructum, ex quo depromi aqua <lb></lb>poſſit. </s><s>In hoc receptaculum derivetur ex collo ſeu curvatum <lb></lb>ſiphonis tubulus G, habens claviculam volubilem, ſitque tu<lb></lb>bulus arctiſſimè adferruminatus & ſiphonis collo, & recept<gap></gap><lb></lb>culi operculo priùs perforatis. </s><s>His factis, repleatur per infun<lb></lb>dibulum D ſiphon BDE, obſtructis priùs orificijs B & E <lb></lb>eoque repleto obturetur foramen D, & aperiatur ſimul utrum<lb></lb>que orificium B & E; dumque per tubum fluit aqua, & ex E <lb></lb>erumpit; aperiatur modiciſſimè, & momentaneâ quaſi motu<lb></lb>la clavicula tubuli G; ſtatimque per dictum tubulum deſcen<lb></lb>det modica aqua intra receptaculum H, aſcendetque modi<lb></lb>cus aër intra ſiphonem, ibique aquæ miſtus delabetur unà cum <lb></lb>ipſa per crus DE, & per os E erumpet. </s><s>Hoc ſi ſæpius fece- <pb xlink:href="051/01/134.jpg" pagenum="103"></pb>ris, tandem replebitur receptaculum H, ut aqua per ejus epi<lb></lb>ſtomium I depromi poſſit magna copia. </s><s>Hæc Porta. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>VVlt igitur Porta, tubulum<emph.end type="italics"></emph.end> G <emph type="italics"></emph>aperiendum eſſe modiciſſimè, ut ni<lb></lb>mirum ingrediatur modicus aër intra ſiphonem, & ita miſcea<lb></lb>tur aquæ, ut ea non diſcontinuetur. </s><s>Si enim ingrederetur aër copio<lb></lb>ſus, poſſet ita interrumpi aqua ſiphonis aëre interpoſito, ut perpendi<lb></lb>culum<emph.end type="italics"></emph.end> BD <emph type="italics"></emph>eſſet majus, quàm perpendiculum reliquæ aquæ intra crus<emph.end type="italics"></emph.end><lb></lb>DE; <emph type="italics"></emph>quod ubi contingeret, ſtatim diſcontinuaretur aquæ fluxus, & <lb></lb>aqua utriuſque cruris deſcenderet, unaquæque ad ſuum orificium, & <lb></lb>efflueret. </s><s>Hoc igitur incommodum ut evitetur, intromittendus eſt, <lb></lb>inquit Porta, repetitis vicibus modiciſſimus aër, ut ſine interruptio<lb></lb>nis periculo poſſit miſceri aquæ. </s><s>Nam quantumvis modicus intro<lb></lb>mittatur aër, ſi tamen is aquam cruris<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>diſcontinuat, infallibili<lb></lb>ter interrumpetur aquæ fluxus, niſi pars<emph.end type="italics"></emph.end> FE <emph type="italics"></emph>ſit paulò longior quàm <lb></lb>crus<emph.end type="italics"></emph.end> BD. </s><s><emph type="italics"></emph>Ponamus cnim aërem interceptum eſſe<emph.end type="italics"></emph.end> KF. </s><s><emph type="italics"></emph>Hic aër dum<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg188"></arrow.to.target><lb></lb><emph type="italics"></emph>erit in<emph.end type="italics"></emph.end> L, <emph type="italics"></emph>aut in<emph.end type="italics"></emph.end> M, <emph type="italics"></emph>non interrumpet quidem aquæ curſum, quia <lb></lb>perpendiculum<emph.end type="italics"></emph.end> LE, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> EM, <emph type="italics"></emph>adhuc longius eſt, ut ſuppono, quàm <lb></lb>perpendiculum<emph.end type="italics"></emph.end> DB. </s><s><emph type="italics"></emph>At quamprimùm aër<emph.end type="italics"></emph.end> KF <emph type="italics"></emph>fuerit infra<emph.end type="italics"></emph.end> M, <lb></lb><emph type="italics"></emph>jam interrumpetur aquæ fluxus, eò quòd perpendiculum aquæ ab aëre <lb></lb>uſque ad<emph.end type="italics"></emph.end> E <emph type="italics"></emph>brevius eſt, quàm perpendiculum à vertice<emph.end type="italics"></emph.end> D <emph type="italics"></emph>uſque ad<emph.end type="italics"></emph.end><lb></lb>B. </s><s><emph type="italics"></emph>Ne igitur aquæ interruptio, ſi fortè contingeret, ejus influxum <lb></lb>per ſiphonem impediat, crus<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>adeo prolongandum eſſet, ut facta <lb></lb>interruptione etiam notabili aquæ ſiphonis per interpoſitionem aëris, <lb></lb>perpendiculum tamen aquæ ab aëre uſque ad<emph.end type="italics"></emph.end> E <emph type="italics"></emph>maneret ſem<lb></lb>per longius perpendiculo cruris<emph.end type="italics"></emph.end> DB. </s><s><emph type="italics"></emph>Meliorem igitur ſucceſſum res <lb></lb>habebit, ſi fons ſit in latere montis, v. g. in<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>& non in radice<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg189"></arrow.to.target><lb></lb><emph type="italics"></emph>apud<emph.end type="italics"></emph.end> B. </s><s><emph type="italics"></emph>Praxim hanc ut dixi, docet Ioannes Baptiſta Porta lib.<emph.end type="italics"></emph.end> 2. <lb></lb><emph type="italics"></emph>Spiritalium cap.<emph.end type="italics"></emph.end> 13. <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 14. <emph type="italics"></emph>pendetque ex praxi, quam ex codem re<lb></lb>tulimus ſuprà Protheoria I. §. X. </s><s>Refert eandem praxim Merſennus <lb></lb>in hydraulicis Phænomenis Propoſit.<emph.end type="italics"></emph.end> 34. <emph type="italics"></emph>ubi tamen nonnulla de ſuo <lb></lb>adjungit non uſquequaque veritati congrua. </s><s>Veruntamen falſum <lb></lb>omnino eſt, quod habetur apud Portam loco cit. cap.<emph.end type="italics"></emph.end> 15. <emph type="italics"></emph>editionis Ita<lb></lb>licæ, de modo elevandi aquam ex flumine præterfluente per ſiphonem<emph.end type="italics"></emph.end> <pb xlink:href="051/01/135.jpg" pagenum="104"></pb><emph type="italics"></emph>uſque ad turris vicinæ altitudinem; quem quidem modum ſuſpicer <lb></lb>non eſſe ipſius Portæ, ſed eſſe interpretis ſeu traductoris ex Latino in <lb></lb>Italicum idioma Ioannis Eſcrivani Hiſpani, qui in Dedicatoria fatetur <lb></lb>ſe adjunxiſſe nonnulla, quæ oretenus ab ipſo Porta didicerat, ut ſu<lb></lb>pra in Præloquio dicebam.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg188"></margin.target><emph type="italics"></emph>Aër in tulo <lb></lb>diſcontinu<lb></lb>ans aquam, <lb></lb>interrum<lb></lb>pit <expan abbr="fluxũ">fluxum</expan> æ<lb></lb>quæ.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg189"></margin.target><emph type="italics"></emph>Portæ error <lb></lb>in elevan<lb></lb>da aqua ad <lb></lb>turris al<lb></lb>titudinem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Cauſam aſſignare, cur in ſiphone inverſo interrupto <lb></lb>perpendiculum aquæ deſcendentis debeat ſupera<lb></lb>re perpendiculum aquæ aſcendentis.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg190"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg190"></margin.target><emph type="italics"></emph>Siphon in<lb></lb>terruptus, <lb></lb>& cauſa ef<lb></lb>fectus ipſius<emph.end type="italics"></emph.end></s></p> <p type="caption"> <s><emph type="italics"></emph>I. Figura.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.135.1.jpg" xlink:href="051/01/135/1.jpg"></figure> <p type="main"> <s>INfrà Parte 2. Claſ<lb></lb>ſe 1. cap. 1. Ma<lb></lb>china 2. damus Ma<lb></lb>chinam hîc <expan abbr="poſitã">poſitam</expan>, <lb></lb>eamque appellam<emph type="sup"></emph>9<emph.end type="sup"></emph.end><lb></lb><emph type="italics"></emph>Siphonem inverſum <lb></lb>interruptum.<emph.end type="italics"></emph.end> </s><s>Ean<lb></lb>dem Machinam ex<lb></lb>hibuimus etiam ſu<lb></lb>prà Protheoria 1. <lb></lb>§. V. ubi diximus, tu<lb></lb>bum EF, per quem <lb></lb>aqua deſcendit, de<lb></lb>bere eſſe paulò lon<lb></lb>giorem tubo BK, <lb></lb>per quem aqua a<lb></lb>ſcendit. </s><s>Quod ta<lb></lb>metſi veriſſimum <lb></lb>ſit, & multis experi<lb></lb>mentis à Porta pri<lb></lb>mùm, deinde à <expan abbr="Mer-ſeño">Mer<lb></lb>ſenno</expan>, Kirchero, at<lb></lb>que à me etiam <expan abbr="cõ-probatum">con<lb></lb>probatum</expan>; ſemper <lb></lb>tamen viſum mihi <lb></lb>fuit mirabile, præ- <pb xlink:href="051/01/136.jpg" pagenum="105"></pb>ſertim, ſi de primo aquæ aſcenſu per tubum BK ſit ſermo: nec <lb></lb>ullum vidi, aut audivi unquam, qui hujus rei cauſam adſignet, <lb></lb>cui acquieſcere poſſim. </s><s>Aliam etiam Machinam hîc po</s></p> <p type="caption"> <s><emph type="italics"></emph>II. Fig.<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="fig27"></arrow.to.target><lb></lb>ſitam, & priori non multùm <lb></lb>abſimilem, adduxi eâdem Pro<lb></lb>theoria I. §. VI. quam etiam habet <lb></lb>Salomon à Caus in ſuis hydraulicis <lb></lb>lib. 1. in qua ut aqua aſcendat per <lb></lb>crus AB, debet tubus rectus DE <lb></lb>eſſe paulò longior quàm dictum <lb></lb>crus AB, ut quilibet facilè experi<lb></lb> <arrow.to.target n="marg191"></arrow.to.target><lb></lb>ri poteſt. </s><s>Quæritur igitur, quæ<lb></lb>nam ſit hujus rei cauſa in utraque <lb></lb>Machina, & in alijs hiſce ſimili<lb></lb>bus? </s><s>Neque enim hîc valetratio, <lb></lb>quam adſignavimus ſuprà Propo<lb></lb>ſit. VII. hujus capitis: nam hîc non <lb></lb>agimus de ſiphone continuato, ſeu <lb></lb><expan abbr="nõinterrupto">noninterrupto</expan>, in quo partes omnes <lb></lb>aquę ſunt continuatæ, tum inter ſe, <lb></lb>tum etiam cum aqua vaſis, ex quo <lb></lb>extrahitur aqua per crus <expan abbr="externũ">externum</expan> <lb></lb>ac longius deſcendens; ſed agimus <lb></lb>de ſiphone interrupto, in quo ſci<lb></lb>licet aër intercedit inter aquam & <lb></lb>aquam. </s><s>Adde quod hîc, licet tu<lb></lb>bi EF, & DE breviores eſſent, quàm tubus BK & crus AB; <lb></lb>tamen extrema ſuperficies aquæ illorum tuborum ſemper eſt <lb></lb>vicinior centro Mundi, ac proinde per ipſos effluere deberet <lb></lb>aqua, ſecumque trahere & aërem & aquam oppoſitam vaſorum. </s></p> <p type="margin"> <s><margin.target id="marg191"></margin.target><emph type="italics"></emph>Dubitatio. </s><s><lb></lb>& rationes <lb></lb>dubitandi <lb></lb>circa ſipho<lb></lb>nem inter<lb></lb>ruptum.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.136.1.jpg" xlink:href="051/01/136/1.jpg"></figure> <p type="main"> <s>Dices, aqua quæ trahit alteram, gravior debet eſſe aquâ <lb></lb> <arrow.to.target n="marg192"></arrow.to.target><lb></lb>quæ trahitur, ac proinde longiores debent eſſe prædicti tubi <lb></lb>EF, & DE, ut plùs aquæ contineant. </s><s>Sed contra eſt mani<lb></lb>feſta experientia allata Propoſit. III. hujus capitis Propriet. I. & <lb></lb>alia etiam allata Protheoria I. §. VIII. </s></p> <pb xlink:href="051/01/137.jpg" pagenum="106"></pb> <p type="margin"> <s><margin.target id="marg192"></margin.target><emph type="italics"></emph>Solutiones <lb></lb>inſufficien<lb></lb>tes propoſitæ <lb></lb>dubitatio<lb></lb>nis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Dices iterum, in hydraulicis pugnari ac vinci non aqua<lb></lb>rum copiâ, ſed aquarum perpendiculis, ut dictum Propoſit. 2. <lb></lb>hujus capitis in Axiomate 2. & alibi ſæpe; ideoque longiores <lb></lb>debent eſſe prædicti tubi EF, & DE, ut perpendicula aqua<lb></lb>rum deſcendentium ſint longiora, quàm perpendicula aqua<lb></lb>rum aſcendentium. </s><s>Reſoondeo, veriſſimum eſſe citatum <lb></lb>Axioma; & cauſam hujus rei, loquendo de ſiphone inverſo <lb></lb>non interrupto, adſignavimus Propoſit 7. quæ tamen cauſa in <lb></lb>caſu præſenti de ſiphone interrupto non militat; ideoque ulte<lb></lb>riùs quæritur, quænam ſit hujus rei cauſa in ſiphone interru<lb></lb>pto, atque adeo in noſtro caſu. </s><s>Difficultatem agnovit Mer<lb></lb>ſennus in Phænom. Hydraul. Propoſit 38. ſed non ſolvit. <lb></lb> <arrow.to.target n="marg193"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg193"></margin.target><emph type="italics"></emph>Solutio Au<lb></lb>ctoris ratio <lb></lb>num dubi<lb></lb>tandi circæ <lb></lb>ſiphonem in<lb></lb>terruptum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Dico igitur, cauſam eſſe, quòd aquæ pars unaquæque <lb></lb>premitur aquâ ſupra ipſam exiſtente ad perpendiculum, ſi aqua <lb></lb>illa ſit deſcendens in aliquo, (hoc eſt, ſi nullum impedimen<lb></lb>tum extrinſecum habeat, quò minùs deſcendere poſſit) pro<lb></lb>ut aſſeruimus ſuprà cap. 1. hujus Protheoriæ 4. Propriet. 4. ex <lb></lb>Archimede. </s><s>Illa igitur aqua, cujus perpendiculum eſt majus, <lb></lb>ſeu longius, magis premitur, <expan abbr="majoremq́ue">majoremque</expan> habet vim ad de<lb></lb>ſcendendum, ſi patet aditus ad deſcendendum. </s><s>Quoniam <lb></lb>igitur aperto epiſtomio E tubi EF, in I. Fig. & aperto ore <lb></lb>tubi recti DE, in II. Fig. patet aditus aquæ ad deſcendendum; <lb></lb>deſcendet illa neceſſariò, innato pondere, & intra tubum, <lb></lb>propter partes continuatas, fundabit ſuum perpendiculum; & <lb></lb>nè vacuum detur, trahet ſecum aërem, & coget aquam oppo<lb></lb>fitorum vaſorum aſcendere, <expan abbr="ſuumq́ue">ſuumque</expan> ſimiliter perpendiculum <lb></lb>fundare. </s><s>Nunquam tamen aſcendere poteſt aqua ad majus <lb></lb>ſpatium in tubo BK, & crure AB, quàm deſcenderit per tu<lb></lb>bum EF, & DE; quia ſi aſcenderet ad majus ſpatium, jam <lb></lb>perpendiculum aquæ aſcendentis majus eſſet, quàm perpen<lb></lb>diculum aquæ deſcendentis, ac proinde illa vinceret hanc, & <lb></lb>retraheret. </s><s>Itaque ſi vas C haberet in fundo foramen angu<lb></lb>itum ſine tubo adnexo, nihil aquæ efflueret, quia nullum fun<lb></lb>dare poſſet perpendiculum; ideoque nihil aſcenderet per tu- <pb xlink:href="051/01/138.jpg" pagenum="107"></pb>bum BK. </s><s>Si idem vas C haberet foramen laxum, efflueret <lb></lb>quidem aqua, ſed ſimul ſubintraret aër, ſicque ceſſante metu <lb></lb>vacui, aut diſcontinuitatis corporum, nihil aſcenderet per tu<lb></lb>bum KB. </s><s>Si tubus EF eſſet brevior tubo BK, deſcenderet aqua <lb></lb>uſque ad orificium F, & ad æquale ſpatium aſcenderet per tu<lb></lb>bum BK; ſed facta hac æqualitate, ſiſteretur utrimque aqua, <lb></lb>propter perpendiculorum æqualitatem. </s><s>Si tubus EF eſſet <lb></lb>præcisè æqualis tubo BK; deſcenderet ſimiliter aqua uſque <lb></lb>ad oſculum F, & ex parte altera aſcenderet uſque ad K, ſed <lb></lb>neutra ulteriùs pergeret, propter cauſam jam dictam de per<lb></lb>pendiculorum æqualitate. </s><s>Si denique tubus EF, eſt vel pau<lb></lb>lulum longior tubo BK, deſcendit aqua uſque ad F, & cùm <lb></lb>nullum inveniat impedimentum quò minùs egrediatur, nec <lb></lb>detineatur ab altera parte à perpendiculo æquali; effluit inna<lb></lb>to pondere ex F, & ut vitetur vacuum, <expan abbr="corporumq́ue">corporumque</expan> diſcon<lb></lb>tinuitas, ſecum rapit & aěrem vaſis KA, & aquam tubi BK, <lb></lb>vaſiſque B. </s></p> <p type="main"> <s>Notandum tamen eſt, quod jam ſæpius inculcavi, alti<lb></lb>tudinem perpendiculi aquæ tubi BK ſumendam eſſe à ſupre<lb></lb>ma aquæ vaſis B, ſuperficie, uſque ad ſupremam ſuperficiem <lb></lb>aquæ ejuſdem tubi. </s></p> <p type="main"> <s>Quod diximus de perpendiculis tuborum BK & EF, in<lb></lb>telligi etiam debet de perpendiculis AB, & DE alterius Machinæ. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XIV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Cauſam adſignare cur in Fonte Heronis perpendicu<lb></lb>lum aquæ deſcendentis debeat eſſe longius perpendi<lb></lb>culo aquæ aſcendentis.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>INfrà Parte 2. Claſſe 1. cap. 2. Machina 1. Fontem damus, </s></p> <p type="main"> <s> <arrow.to.target n="marg194"></arrow.to.target><lb></lb>eumque Fontem Heronis in vaſis immediatis appellamus; <pb xlink:href="051/01/139.jpg" pagenum="108"></pb> <arrow.to.target n="fig28"></arrow.to.target><lb></lb>& ita conſtruitur. </s><s>Vas fit <lb></lb><expan abbr="oblongũ">oblongum</expan> NOPQ, diaphra<lb></lb>gmate ſeu ſepto IM di<lb></lb>ſcriminatum in duo rece<lb></lb>ptacula ſeu vaſa, NIMQ <lb></lb>ſuperius, & IMOP inferius. </s><s><lb></lb>Superius vas labrum habet <lb></lb>aliquantulùm concavum <lb></lb>BD, in eoque foramen K. </s><s><lb></lb>In hac Machina diſponun<lb></lb>tur tubi ſeu canales ABC, <lb></lb>DEL, & GF, uti figura <lb></lb>monſtrat, & fuſius dicitur <lb></lb>loco citato; impletoque <lb></lb>receptaculo NIMQ aquâ, <lb></lb>aliove liquore per K fora<lb></lb>men, & diligenter clauſo <lb></lb>foramine K, infunditur <lb></lb>aqua labro BD, quæ per <lb></lb>canalem DEL deſcendens <lb></lb>in vas vacuum IOPM, premit ibidem aërem, atque expellit <lb></lb>per tubum FG in vas plenum <expan abbr="NIMq;">NIMque</expan> aër verò ibidem pre<lb></lb>mens aquam, expellit ipſam per tubum CBA &c. prout fu<lb></lb>fiùs dicitur loco citato. </s><s>Similes alias Machinas damus ibidem <lb></lb>Machina 2. 3. & 4. </s><s>Advertimus autem in Notis ad dictam <lb></lb>Machinam 1. tubum DEL, per quem aqua deſcendit, longio<lb></lb>rem eſſe debere tubo CBA, per quem aſcendit aqua. </s><s>Præ<lb></lb>dicto Heronis fonti omnino ſimilis eſt Lucerna, quam attuli<lb></lb>mus ſuprà Protheoria 2. §. 5. in qua tamen errorem aliquem <lb></lb>Heronis notavimus circa claviculam R, diximuſque prædi<lb></lb>ctam claviculam debere deſinere in tubulum paulò longiorem, <lb></lb>quàm eſt tubulus OX. </s><s>Quærimus nunc hujus rei cauſam. </s></p> <p type="margin"> <s><margin.target id="marg194"></margin.target><emph type="italics"></emph>Fons Hero<lb></lb>nis in vaſis <lb></lb>immediatis<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.139.1.jpg" xlink:href="051/01/139/1.jpg"></figure> <p type="main"> <s>Dicam quod ſentio. </s><s>Vt autem meliùs mentem meam in<lb></lb>telligas, Lector, recole quæ diximus ſuprà Propoſit. 2. hujus ca- <pb xlink:href="051/01/140.jpg" pagenum="109"></pb>pitis de Proprietatibus ſiphonis erecti; ubi aſſeruimus, aquam <lb></lb>cruris longioris deſcendentem elevare, atque expellere aquam <lb></lb>cruris brevioris, cogereque in altum exilire, ſi oſculum ſit an<lb></lb>guſtum. </s><s>Cauſam ejus rei diximus eſſe exceſſum perpendi<lb></lb>culi aquæ deſcendentis atque pellentis, ſupra perpendiculum <lb></lb>aquæ aſcendentis & pulſæ. </s><s>His ſuppoſitis, ita diſcurro. </s><s>Fons <lb></lb>Heronis, & Lucerna ad ipſius ſimilitudinem conſtructa, omneſ<lb></lb> <arrow.to.target n="marg195"></arrow.to.target><lb></lb>que Machinæ ſimili artificio adornatæ, nihil aliud ſunt, quàm <lb></lb>ſiphon erectus interruptus. </s><s>Nam tubus DEL habet rationem <lb></lb>cruris erecti, per quod aqua deſcendit; tubus verò CBA ha<lb></lb>bet rationem alterius cruris erecti, per quod aqua aſcendit;</s> <lb></lb><s>Aqua deſcendens per DEL, cogit aſcendere aquam per CBA, <lb></lb>mediante aëre aquam premente. </s><s>Sicut igitur in ſiphone erecto <lb></lb>non interrupto, ut aqua deſcendens per unum crus, expellat <lb></lb>aquam aſcendentem per alterum, perpendiculum aquæ de<lb></lb>ſcendentis majus debet eſſe perpendiculo aſcendentis, ideo<lb></lb>que crus, per quod aqua deſcendit, longius debet eſſe, quàm <lb></lb>crus per quod aſcendit, alioquin non effluet aqua aſcendens; <lb></lb>ita in caſu noftro tubus DEL debet eſſe longior tubo ABC, ut <lb></lb>perpendiculum aquæ deſcendentis majus fit, quàm perpendi<lb></lb>culum aquæ aſcendentis. </s><s>Tantò autem, cæteris paribus, al<lb></lb>tiùs aſcendet aqua per tubum ABC, quantò is magis ſupera<lb></lb> <arrow.to.target n="marg196"></arrow.to.target><lb></lb>bitur à tubo DEL. </s><s><expan abbr="Itaq;">Itaque</expan> hîc etiam, uti alibi <expan abbr="ubiq;">ubique</expan> in hydraulicis, <lb></lb>non aquarum copiâ, ſed perpendiculo pugnatur ac vincitur. </s></p> <p type="margin"> <s><margin.target id="marg195"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>lum aquæ <lb></lb>eadentis in <lb></lb>fonte Hero<lb></lb>nis cur exce<lb></lb>dere debeat <lb></lb>perpendicu<lb></lb>lum aquæ <lb></lb>aſcendentis<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg196"></margin.target><emph type="italics"></emph>Perpendicu<lb></lb>lo, <expan abbr="nõ">non</expan> aqua<lb></lb>rum copia, <lb></lb>pugnatur, <lb></lb>ac vincitur <lb></lb>in hydrau<lb></lb>licis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Hæc mea eſt opinio: cui meliùs quid occurrerit, profe<lb></lb>ratin medium; nullus enim adhuc rei huius cauſam attigit, quod <lb></lb>ſciam. </s><s>Non nego tamen, & aëris prementis copiam ab aquæ <lb></lb>deſcendentis copia maiore vehementiùs preſſam ac pulſam, & <lb></lb>oſculi A, vel potiùs totius tubuli CBA anguſtiam, multùm <lb></lb>conferre ad aquam altiùs ex oſculo A eiaculandam, tum ob <lb></lb>urgentis impetus incrementum, tum ob decrementum gravi<lb></lb>tatis aquæ deorſum in tubo, poſt egreſſum è tubo, nitentis. </s><s>Ne<lb></lb>go tamen, erupturam aquam è tubo CBA, ſi longior is fuerit <lb></lb>tubo DEL; idque ob rationem aſſignatam. </s></p> <pb xlink:href="051/01/141.jpg" pagenum="110"></pb> <p type="main"> <s><emph type="center"></emph>CAPVT III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De <lb></lb>Proprietatibus Aquæ fluentis per tubos.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROOEMIVM.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg197"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg197"></margin.target>Tubus <lb></lb>quid ſit.</s></p> <p type="main"> <s><emph type="italics"></emph>TVbos hîc appello Columnas concavas, ſive cylindri<lb></lb>cæ illæ ſint, ſivę priſmaticæ. </s><s>Hos in Machinis Par-<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg198"></arrow.to.target><lb></lb><emph type="italics"></emph>te<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>paſſim voco in differenter tubos, ſiphones, ca<lb></lb>nales, fiſtulas, & alijs etiam nominibus. </s><s>Foramen per quod <lb></lb>effluit aqua tubo contenta, appellat Hero Alexandrinus in <lb></lb>ſuis Pnevmaticis, os, oſculum, & orificium; Marinus verò <lb></lb>Merſennus in hydraulicis ſuis Phænomenis vocat lumen.<emph.end type="italics"></emph.end></s><lb></lb> <s><arrow.to.target n="marg199"></arrow.to.target><lb></lb><emph type="italics"></emph>Hoc foramen fieri poteſt vel in baſe tubi, vel in latere. </s><s>Fieri <lb></lb>etiam poſſunt tubi conici ad inſtar conorum truncatorum, quo<lb></lb>rum os ſeu lumen ſit vel in vertice, vel in baſi coni, prout ap<lb></lb>paret in figuris Propoſitionis primæ ſequentis.<emph.end type="italics"></emph.end> <lb></lb> <arrow.to.target n="marg200"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg198"></margin.target>Tubi fora<lb></lb>men, os, <lb></lb>oſculum, <lb></lb>lumen, <expan abbr="idẽ">idem</expan> <lb></lb>ſunt.</s></p> <p type="margin"> <s><margin.target id="marg199"></margin.target>Tuborum <lb></lb>variæ for<lb></lb>mæ.</s></p> <p type="margin"> <s><margin.target id="marg200"></margin.target>Tub' ſem<lb></lb>per plenus.</s></p> <p type="main"> <s><emph type="italics"></emph>Tubi per quos fluit aqua, aut ſunt ſemper pleni, aut non <lb></lb>ſunt ſemper pleni. </s><s>Tubum ſemper plenum vocamus, quem <lb></lb>fons aut vas aliquod ſuperimpoſitum ita implet per orificium <lb></lb>ſuperius, ut dum aqua effluit per inferius, ſemper tamen plenus <lb></lb>maneat vſque ad ſuperius orificium; quod fit, dum tantum,<emph.end type="italics"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg201"></arrow.to.target><lb></lb><emph type="italics"></emph>aut plùs influit, quàm effluit. </s><s>Tubum non ſemper plenum <lb></lb>appellamus, qui, dum effluit aqua per foramen, paulatim exin<lb></lb>anitur, nullâ interim aliâ influente aquâ.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg201"></margin.target>Tubus <expan abbr="nõ">non</expan> <lb></lb>ſemper ple<lb></lb>nus.</s></p> <p type="main"> <s><emph type="italics"></emph>Tubi quicunque, per quos aqua decurrit, aut ſunt erecti<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg202"></arrow.to.target><lb></lb><emph type="italics"></emph>perpendiculariter, aut inclinati, aut proſtrati horizontaliter. </s><s><lb></lb>Priores vocabimus verticales; medios, inclinatos; ultimos <lb></lb>horizontales.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/142.jpg" pagenum="111"></pb> <p type="margin"> <s><margin.target id="marg202"></margin.target>Tubi verti<lb></lb>cales.</s></p> <p type="main"> <s><emph type="italics"></emph>His ita expoſitis, nunc afferemus varia Phænomena, <lb></lb>id eſt, apparentias ſeu obſervationes circa fluxum aquæ per tu<lb></lb>bos verticales, cuiuscunque formæ & conditionis; ex quibus <lb></lb>deinde deducemus varia Problemata atque Theoremata; quo<lb></lb>rum multa applicari etiam poterunt fluxui aquæ per ſiphones, <lb></lb>de quibus cap. præcedente. </s><s>Agimus autem hoc Capite ſolùm <lb></lb>de fluxu aquæ per tubos ex foramine in baſi facto; de fluxu enim <lb></lb>ex foramine facto in latere, loquemur capite ſequenti.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PROPOSITIO I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>PHÆNOMENON I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua decurrit per tubi verticalis foramen baſis inſtar <lb></lb>Columnæ aqueæ, cuius baſis æqualis foramini, altitudo perpen<lb></lb>diculares à baſi erectæ; ſive tubi ſint ſemper <lb></lb>pleni, ſive non.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SInt tubi verticales, AB, cuiuscunque figuræ, haben<lb></lb> <arrow.to.target n="marg203"></arrow.to.target><lb></lb>tes foramen B in baſi. </s><s>Dico aquam decurrere per <lb></lb>foramen B inſtar columnæ aqueæ AB, cuius baſis <lb></lb>eſt foramen B, altitudo verò perpendiculares BA, <lb></lb>a baſi erectæ, ſive tubi ſint ſemper pleni, ſive non. </s><s>Patet expe<lb></lb>rientia, & ſequitur ex dictis Cap. 1. Propriet. IV. & ex doctrina <lb></lb>Archimedis lib. 1. de Inſidentibus humido, Suppoſitione I. </s></p> <p type="margin"> <s><margin.target id="marg203"></margin.target><emph type="italics"></emph>Aqua per <lb></lb>foramen ba<lb></lb>ſis tuborum <lb></lb><expan abbr="verticaliũ">verticalium</expan> <lb></lb>fluit inſtar<lb></lb>colu mnæ a<lb></lb>queæ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Ac primò quidem, ſi tubus eſt columnaris, & tota baſis eſt <lb></lb>aperta, prout eſt tubus primæ, ex appoſitis, Figuræ ad ſiniſtram; <lb></lb>manifeſta eſt experientia: videmus enim totam aquam ſimul <lb></lb>paulatim deſcendere, ſi tubus non eſt ſemper plenus. </s><s>Idem au<lb></lb>tem fit, ſi tubus eſt ſemper plenus; deſcendit enim ſemper nova <lb></lb>& nova columna aquea, & effluit ex baſi B. </s></p> <p type="main"> <s>Si autem tubus eſt quidem columnaris, ſed aqua non ef<lb></lb>fluit per totam baſim apertam, ſed per foramen in baſi factum, <pb xlink:href="051/01/143.jpg" pagenum="112"></pb> <arrow.to.target n="fig29"></arrow.to.target><lb></lb>prout apparet in ſecunda Figura; item ſi eſt conoidalis inſtar co<lb></lb>ni truncati inverſi, prout in tertia Figura apparet, idem contin<lb></lb>git: Nam videmus, effluente aquâ per B, ſubſidere paulatim <lb></lb>aquam A, <expan abbr="incumbentẽ">incumbentem</expan> ipſi B ad <expan abbr="perpendiculũ">perpendiculum</expan>, <expan abbr="fieriq́">fierique</expan>; foſſam in <lb></lb>ſuperiori ſuperficie vbi A, reliquas verò partes collaterales e A, <lb></lb>f A, confluere intra foſſam; ad eum modum, quo in arenarijs <lb></lb>horologijs, dum è ſuperiori phiala defluit arena per foramen <lb></lb>diaphragmatis in inferiorem phialam, efficitur foſſa in ſuperiori <lb></lb>arenæ ſuperficie, in eamque incidunt circumia centes arenæ par<lb></lb>tes. </s><s>Quod ſignum eſt, aquam deſcendere & effluere per B in <lb></lb>modum columnæ AB. </s><s>Et hoc quidem contingit apertè in tu<lb></lb>bis non ſemper plenis, ut experientia docet. </s><s>Idem autem con<lb></lb>tingere neceſſe eſt in tubis ſemper plenis; niſi quòd in his deſcen<lb></lb>dat ſemper nova ac nova columna aquea. </s></p> <figure id="id.051.01.143.1.jpg" xlink:href="051/01/143/1.jpg"></figure> <p type="main"> <s>Quod diximus de tubis columnaris & conoidalis figuræ; <lb></lb>intelligendum etiam eſt de columnis aliarum figurarum, pro<lb></lb>pter paritatem rationis, dummodo ſint verticaliter erecti. </s></p> <p type="main"> <s>Si foramen eſt quidem in baſi tubi (cuiuscunque figuræ <pb xlink:href="051/01/144.jpg" pagenum="113"></pb>& conditionis ſit tubus,) at ſuperior aquæ fuperficies non ſu<lb></lb>pereminet foramini ad perpendiculum, ut in appoſita Figura ap<lb></lb>paret; adhuc effluit aqua columnaliter, ſeu inſtar columnæ <lb></lb>AB, cuius baſis eſt foramen B. altitudo perpendiculares à baſi <lb></lb>uſque ad ſummitatem iſtius aquæ; quæ baſi perpendiculariter <lb></lb>imminet. </s><s>Ratio deſumitur ex dictis cap 1. Proprietate IV. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>EX his colligitur, ſolam columnam aqueam AB premere <lb></lb> <arrow.to.target n="marg204"></arrow.to.target><lb></lb>ſupra foramen B, quoniam illa ſola ad perpendiculum im<lb></lb>minet baſis foramini. </s></p> <p type="margin"> <s><margin.target id="marg204"></margin.target><emph type="italics"></emph>Columna <lb></lb>aquea ſola <lb></lb>premit ſu<lb></lb>pra <expan abbr="foramẽ">foramen</expan> <lb></lb>per quod ef<lb></lb>fluit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio II. Phænomenon II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per tubos tam ſemper, quàm non ſemper plenos æqua<lb></lb>lis altitudinis, & æqualium foraminum, effluit æqualis aquæ <lb></lb>copia, eodem vel æquali tempore, cuiuscunque capaci<lb></lb>tatis & formæ ſint tubi.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ALtitudo tuborum, tum hac, tum ſequentibus Propoſitioni <lb></lb> <arrow.to.target n="marg205"></arrow.to.target><lb></lb>bus, ſumitur à lumine ſeu foramine, uſque ad ſuperius orifi<lb></lb>cium, includendo etiam ipſius foraminis altitudinem ſeu craſ<lb></lb>ſitiem, ab interiori ad exteriorem ſuperficiem baſis, ſi in baſi ſeu <lb></lb>fundo ſit foramen. </s></p> <p type="margin"> <s><margin.target id="marg205"></margin.target><emph type="italics"></emph>Tuborum <lb></lb>altitudo vn<lb></lb>de ſumatur<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sint igitur, ut antea, tubi, AB, æquè alti, & æqualium fo<lb></lb>raminum B, ſive ſemper pleni, ſive non ſemper pleni, cuius<lb></lb>cunque capacitatis, & figuræ. </s><s>Dico, per foramina illa effluere <lb></lb>eodem, vel æquali tempore, æqualem aquæ copiam. </s><s>Quoni<lb></lb>am enim, per præcedentem Propoſitionem, ſupra foramem B <lb></lb>in omnibus æqualis aquæ copia æquali vi premit, nempe colu<lb></lb>mna aquea AB, cuius baſis eſt foramen B in omnibus æquale, <lb></lb>ut ſupponitur; & altitudo eſt perpendicularis AB, in omnibus <lb></lb>itidem æqualis; neceſſe eſt, æqualem aquæ copiam eodem tem<lb></lb>pore decurrere ex omnibus: ubi enim omnia ſunt æqualia, ef<lb></lb>fectus ſunt æquales. </s></p> <pb xlink:href="051/01/145.jpg" pagenum="114"></pb> <p type="main"> <s><emph type="center"></emph>Corollarium I.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg206"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg206"></margin.target><emph type="italics"></emph>Aquæ flux' <lb></lb>è foramine <lb></lb>vaſis non eſt <lb></lb>celerior pro<lb></lb>pter vaſis <lb></lb><expan abbr="capacitẽ">capacitatem</expan>.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>COlligitur hinc, ad aquæ effluxum maiorem, aut celeriorem <lb></lb>è foramine eodem, aut æquali, nihil facere capacitatem <lb></lb>vaſis aut tubi; adeo ut ſi totus Oceanus eſſet incluſus in uno tubo, <lb></lb>aut vaſe, & in altero modica aqua, vterque tamen tubus eſſet <lb></lb>æquè altus, & haberet æqualia foramina; æqualis aquæ copia <lb></lb>ex vtroque efflueret eodem, vel æquali tempore. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur præterea, per foramina æqualia in eadem baſi eius<lb></lb>dem tubi, æqualem aquam effluere eodem tempore. </s><s>Sed <lb></lb>de hoc agemus infrà cap. 5. Propoſ. 1. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III. Phænomenon III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per tubos tam ſemper, quàm non ſemper plenos æqua<lb></lb>lium luminum, ſed inæqualium altitudinum, effluit eodem, <lb></lb>vel æquali tempore, inæqualis aquæ copia.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>NEmpe per tubum magis altum maior, & per tubum minùs <lb></lb>altum, minor. </s><s>Ratio eſt, quia ſupra lumen altioris tubi <lb></lb>maior aquæ copia, & maiori vi ac celeritate; & ſupra lumen mi<lb></lb>noris minor, & minori vi ac celeritate premit, nempe aquea co<lb></lb>lumna magis aut minùs alta. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IV. Phænomenon IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per tubos ſemper, & non ſemper plenos inæqualium <lb></lb>luminum, ſed æqualium altitudinum, effluit eodem, vel æ<lb></lb>quali tempore, inæqualis aquæ copia.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>NEmpe per maius lumen maior, & per minus minor. </s><s>Ratio <lb></lb>eſt eadem, quia ſcilicet ſupra maius lumen premit maior a<lb></lb>quæ copia, & maiori vi; & ſupra minus minor, & minori vi, ſci<lb></lb>licet columna aquea æquè alta, ſed non æquè craſſa. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PEr tubos vtroſque, hoc eſt, tam ſemper plenos, quàm non <lb></lb>ſemper plenos, inæqualium luminum, & inæqualium altitu- <pb xlink:href="051/01/146.jpg" pagenum="115"></pb>dinum, effluere poteſt eodem, vel æquali tempore, æqualis, <lb></lb>& inæqualis aquæ copia, hoc eſt, æqualis per aliquos, inæqualis <lb></lb>per alios. </s><s>Ratio eſt, quia defectus luminis in vno poteſt ſup<lb></lb>pleri per altitudinem; & defectus altitudinis in altero poteſt ſup<lb></lb>pleri per lumen, vt experientia etiam docet. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio V. Phænomenon. V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per tubos æquè altos, & æqualium luminum, non ſem<lb></lb>per plenos, fluit eodem tempore æqualis aquæ copia; ſed tantò <lb></lb>fluit vnus diutiùs altero, quantò plùs aquæ continet <lb></lb>vnus quàm alter.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PAtet ex hactenus dictis, & experientiâ, nec indiget alia pro<lb></lb>batione. </s><s>Ille autem plùs aquæ continet, qui amplior eſt: <lb></lb>loquimur enim hîc de ijs tubis, quorum orificia ſunt æqualia, <lb></lb>etiamſi ipſi tubi ſint inæqualis amplitudinis. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ERgo & per æqualia foramina baſis eiusdem tubi, æqualis eo<lb></lb>dem tempore effluit aqua. </s><s>Vide cap. 5. Propoſ. 1. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VI. Phænomenon VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per tubos non ſemper plenos, & non æquè altos, æqua<lb></lb>lium tamen luminum, eodem vel æquali tempore <lb></lb>non fluit æqualis aquæ copia.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>EAdem eſt ratio de quibuſcunque vaſis. </s><s>Patet experientiâ, </s></p> <p type="main"> <s> <arrow.to.target n="marg207"></arrow.to.target><lb></lb>quæ monſtrat, ex altiori tubo ſeu vaſe fluere maiorem aquæ, <lb></lb>copiam tempore eodem, vel æquali, quàm ex tubo vel vaſe mi<lb></lb>nùs alto habente lumen æquale. </s><s>Et ratio eſt, quia in altiori <lb></lb>magis preinitur aqua ſupra lumen, quàm in minùs alto. </s><s>Vide <lb></lb>Propoſit. III. </s></p> <p type="margin"> <s><margin.target id="marg207"></margin.target><emph type="italics"></emph>Vas magis <lb></lb>plenum plus <lb></lb>aquæ effun<lb></lb>dit per fora<lb></lb>men, quàm <lb></lb>minus ple<lb></lb>num.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur hinc, ex eodem tubo, aut vaſe, non ſemper pleno, <lb></lb>æqualibus temporibus, non æqualem effluere aquam ex eo<lb></lb>dem foramine, ſed in ſecundo tempore minorem, quàm in pri<lb></lb>mo, & in tertio minorem, quàm in ſecundo, & ſic deinceps. </s><s><lb></lb>Vide Propoſit. 24. </s></p> <pb xlink:href="051/01/147.jpg" pagenum="116"></pb> <p type="main"> <s><emph type="center"></emph>Poriſma II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur præterea, ſpatia quæ æqualibus temporibus evacu<lb></lb>antur in dicto caſu, non eſſe æqualia, ſed ſecundum ſpatium <lb></lb>correſpondens ſecundo tempori, eſſe minus primo; & tertium <lb></lb>ſpatium correſpondens tertio tempori, minus ſecundo; & ſic de <lb></lb>cæteris. </s><s>Vide ibidem. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VII. Phænomenon VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Tubus altitudine quadrupedalis, cui pro baſis diametro <lb></lb>pedis Pariſienſis vncia, aquâ ſemper plenus, effundit per lumen <lb></lb>lineare in baſi ſitum aquæ libram ſpatio tredecim mi<lb></lb>nutorum ſecundorum temporis.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>OBſervavit hoc Marinus Merſennus, ut aſſerit ipſe in Hydrau<lb></lb>licis ſuis Phænomenis Propoſit. 1. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>VTitur autem Merſennus tam pede, quàm libra (heminam vocat ipſe)<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg208"></arrow.to.target><lb></lb><emph type="italics"></emph>Pariſienſi. </s><s>Et pedem quidem, uti in aliarum Nationum pedibus fie<lb></lb>riſolet, dividit in duodecim æquales partes, quas uncias appellat; & <lb></lb>quamlíbet vnciam ſubdividit in alias duodecim partes æquales, quas <lb></lb> <arrow.to.target n="marg209"></arrow.to.target><lb></lb>ipſe lineas, alij ſcrupulos vocant. </s><s>Vncia, ſeu duodecima pedis pars ap<lb></lb>pellatur etiam pollex; ab aliquibus verò cum Merſenno digitus: rectiùs <lb></lb>tamen digitus eſt decima ſexta pars pedis, vt conſtat ex Vitruvio, Iulio <lb></lb>Frontino, Columella, & alijs apud Villalpandum tom.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>Apparatus <lb></lb>Part.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>lib.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>cap.<emph.end type="italics"></emph.end> 16. <lb></lb> <arrow.to.target n="marg210"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg208"></margin.target><emph type="italics"></emph>Pes dividi<lb></lb>tur in vnci<lb></lb>as<emph.end type="italics"></emph.end> 12. <emph type="italics"></emph>& di<lb></lb>gitos<emph.end type="italics"></emph.end> 16.</s></p> <p type="margin"> <s><margin.target id="marg209"></margin.target>Linea eſt <lb></lb>duodecima <lb></lb>pars vncia.</s></p> <p type="margin"> <s><margin.target id="marg210"></margin.target><emph type="italics"></emph>Minuti ſe<lb></lb>cundi dura<lb></lb>tio, quanta <lb></lb>ſit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Minutum ſecundum eſt ſexageſima pars unius minuti primi, ſeu<emph.end type="italics"></emph.end><lb></lb>3600. <emph type="italics"></emph>pars vnius horæ, & proximè reſpondet lento arteriæ ſeu cordis <lb></lb>pulſui, ut Merſennus aſſerit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>NOn eſt neceſſe, ut baſis tubi quadrupedalis, quo fit obſervatio, ſit </s></p> <p type="main"> <s> <arrow.to.target n="marg211"></arrow.to.target><lb></lb>pedalis, aut uncialis, aut alterius determinatæ amplitudinis atque <lb></lb>capacitatis, ſed ſufficit quantalibet latitudo tubi, dummodò foramen ſit <lb></lb>lineare. </s><s>Ratio eſt, quia; ut vidimus Propoſitione<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>huius capitis, ea<lb></lb>dem aquæ quantitas eodem, vel æquali tempore, fluit ex tubo ſemper <lb></lb>pleno quantum vis arcto, vel lato, dummodò foramen ſit lineare, & al-<emph.end type="italics"></emph.end> <pb xlink:href="051/01/148.jpg" pagenum="117"></pb><emph type="italics"></emph>titudo ſit quadrupedalis; adeo ut ſi totus Oceanus, ut ſuprà innuimus in <lb></lb> <arrow.to.target n="marg212"></arrow.to.target><lb></lb>Corollario I. Propoſit.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>eſſet incluſus vaſi quatuor pedum æltitudinis & <lb></lb>luminis linearis, non effunderet niſi vnicam heminam ſeu libram Pari<lb></lb>ſienſem ſpatio tredecim minutorum ſecundorum; Si tamen addas, inquit <lb></lb>Merſennus, pro horis ſingulis vnam quadrageſimam quintam libræ <lb></lb>partem, quâſolet aqua marina ſuperare aquam fontium ac fluviorum in <lb></lb>pondere, & conſequenter vi premendi, & vehementiùs è foramine e<lb></lb>rumpendi.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg211"></margin.target>Vas ampli<lb></lb>us non effu<lb></lb>dit plùs a<lb></lb>quæ per fora<lb></lb>men, quàm <lb></lb>minù, am-</s></p> <p type="margin"> <s><margin.target id="marg212"></margin.target>plum, ſi al<lb></lb>titudo & fo<lb></lb>ramè æqua<lb></lb>lia ſunt.</s></p> <p type="main"> <s><emph type="center"></emph>Annotatio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVod dicit Merſennus de tubo quadrupedali, & de libra aquæ, in<lb></lb>telligi debet ſolùm loquendo de pede & libra Pariſienſi, non ve<lb></lb>rò aliarum Nationum, ſed unuſquiſque in ſua natione experientiam <lb></lb>facere debet, ut ſciat quantum aquæ, quanto tempore, ex quantæ al<lb></lb> <arrow.to.target n="marg213"></arrow.to.target><lb></lb>titudinis, quantique foraminis tubo, ejiciatur. </s><s>Cæterùm cùm diffe<lb></lb>rentia pedum, atque librarum apud diverſas Nationes tanta ſit, quan<lb></lb>ta ipſarum Nationum; cum〈qué〉 difficulter exacta menſura unius certi <lb></lb>ac determinati pedis, v. g. Romani, aut Pariſienſis, ad alias Nationes <lb></lb>tranſmitti libris impreſſis poſſit, quòd chartæ priùs madefactæ, ac dein<lb></lb>de ſiccatæ, non reddant fideliter longitudinem linearum impreſſarum; <lb></lb>nolo diutiùs huic rei inhærere, comparando pedem Pariſienſem cum <lb></lb>pedibus aliarum Nationum. </s><s>Faciat, qui volet, aut cujus intereſt, <lb></lb>experientiam, ut videat quanto tempore tubus quatuor pedum regio<lb></lb>nis ſuæ ejiciat per lumen lineare aquæ libram itidem regionis ſuæ. </s><s>De <lb></lb>exacta pedis Romani menſura, & de modo tranſmittendi illum ad <lb></lb>alias nationes, diſſeram in Pantometro Kircheriano Lib.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>Technico <lb></lb>Parte<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>Cap.<emph.end type="italics"></emph.end> 4. </s></p> <p type="margin"> <s><margin.target id="marg213"></margin.target>Podis men<lb></lb>ſura diver<lb></lb>ſa apud di<lb></lb>verſas na<lb></lb>tiones.</s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VIII. Phænomenon VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ fluentes ex tubis tam ſemper, quàm non ſem<lb></lb>per plenis æqualium foraminum, ſed inæqualium altitudinum, <lb></lb>habent rationem ſubduplicatam altitudinum tuborum; <lb></lb><expan abbr="habentq́ue">habentque</expan> dicti tubi duplicatam rationem <lb></lb>aquarum, quas fundunt.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>RAtio ſeu proportio duplicata quæcunque, eſt ratio quæ<lb></lb> <arrow.to.target n="marg214"></arrow.to.target><lb></lb>cunque ſimplex ſemel repetita, ſeu bis continuè ſumpta: <pb xlink:href="051/01/149.jpg" pagenum="118"></pb>quemadmodum ratio quæcunque triplicata, quadruplicata, &c. <lb></lb>eſt ratio quæcunque ſimplex bis, ter &c. repetita, ſeu ter, <lb></lb>quater continuè ſumpta. </s><s>Exemplum. </s><s>Inter 2 & 1 reperitur <lb></lb>ratio dupla; hæc ratio ſi ſemel repetatur, ſeu adhuc ſemel <lb></lb>accipiatur, hoc eſt, ſi bis continuè ſumatur hoc modo, 4, <lb></lb>2, 1; erit inter 4 & 1 ratio ſeu proportio duplicata illius pro<lb></lb>portionis, quæ eſt inter 2 & 1, quandoquidem inter 4 & 1 <lb></lb>reperitur ratio dupla ſemel repetita, ſeu bis continuè <lb></lb>ſumpta, hoc eſt, duplicata, ſcilicet ſemel inter 4 & 2, & ite<lb></lb>rum inter 2 & 1. </s><s>Similiter inter 8 & 1 eſt ratio triplicata il<lb></lb>lius, quæ eſt inter 2 & 1, quia inter 8 & 1, intercedit ter <lb></lb>ratio dupla, nempe 8 ad 4, 4 ad 2, 2 ad 1. </s><s>Sic 16 ad 1 ha<lb></lb>bet rationem quadruplicatam, & 32 ad 1 rationem quintu<lb></lb>plicatam rationis illius, quam habet 2 ad 1. </s><s>Aliud exemplum. </s><s><lb></lb>Inter 6 ad 4 reperitur ratio ſeſquialtera ſimplex; hæc ratio <lb></lb>duplicatur, ſi adhuc ſemel repetatur, ſeu ſi bis continuè ſuma<lb></lb>tur, ut apparet in his numeris 9, 6, 4: nam quia ut 6 ad 4, <lb></lb>ita 9 ad 6; ideo inter 9 & 4 bis reperitur ratio ſeſquialtera. </s><s><lb></lb>Si verò eadem ratio ſeſquialtera bis repetatur, ſeu ter conti<lb></lb>nuè ponatur; erit inter extremos terminos ratio ſeſqui altera <lb></lb>triplicata, ut apparet in his numeris, 13 1/4, 9, 6, 4; quam pro<lb></lb>portionem abſque fractione habebis, ſi duplicaveris hoſce <lb></lb>numeros ſic, 27, 18, 12, 8: nam ut 12 continet 8 ſemel cum <lb></lb>dimidio, ita 18 continet 12 ſemel cum dimidio, & 27 etiam <lb></lb>continet 18 ſemel cum dimidio. <lb></lb> <arrow.to.target n="marg215"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg214"></margin.target><emph type="italics"></emph>Duplicata <lb></lb>proportio <lb></lb>quæ.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg215"></margin.target><emph type="italics"></emph>Subduplica<lb></lb>ta proportio <lb></lb>quæ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Ex ratione duplicata, triplicata, quadruplicata, &c. facilè <lb></lb>intelligitur ratio ſubduplicata, ſubtriplicata, ſubquadruplica<lb></lb>ta, &c. </s><s>Nam per rationem ſubduplicatam intelligimus <expan abbr="dimidiũ">dimidium</expan> <lb></lb>rationis duplicatæ. </s><s>Verbi gratia, 4 ad 1 habet rationem dupli<lb></lb>catam rationis duplæ; 2 ad 1, aut 4 ad 2, conſtituunt dimidium <lb></lb>rationis 4 ad 1; ideo 2 ad 1, & 4 ad 2, habent rationem ſub<lb></lb>duplicatam. </s><s>Similiter 9 ad 4 habet rationem duplicatam <lb></lb>rationis ſeſquialteræ; dimidium talis rationis eſt 9 ad 6, vel <lb></lb>6 ad 4; ideo 9 ad 6, & 6 ad 4 habent rationem ſubduplica<lb></lb>tam prædictæ rationis ſeſquialteræ. </s></p> <pb xlink:href="051/01/150.jpg" pagenum="119"></pb> <figure id="id.051.01.150.1.jpg" xlink:href="051/01/150/1.jpg"></figure> <p type="main"> <s>His explicatis, eſto tubus AB unius pedis, & </s></p> <p type="main"> <s> <arrow.to.target n="marg216"></arrow.to.target><lb></lb>tubus CD quatuor pedum, æqualium foraminum, <lb></lb>& uterque ſeu ſemper, ſeu non ſemper plenus; qui <lb></lb>quidem eodem, vel æquali tempore inæqualem <lb></lb>effundunt aquæ copiam, nempe major majorem, <lb></lb>& minor minorem, ut conſtat ex Propoſitione III. <lb></lb>præcedenti. </s><s>Dico, aquam tubi CD, ad aquam <lb></lb>tubi AB eodem aut æquali tempore effuſam, ha<lb></lb>bere rationem ſubduplicatam tuborum, hoc eſt, <lb></lb>aquam effluentem è tubo CD eſſe duplam aquæ <lb></lb>effluentis è tubo BA. </s><s>Etidem dicendum eſt de qua<lb></lb>cunque alia ratione ſeu proportione; ut ſi unus tu<lb></lb>bus ſit 9 pedum, alter unius pedis, erit aqua ma<lb></lb>joris ad aquam minoris, ut 3 ad 1. </s><s>Conſtat ex <lb></lb>obſervatione, ut aſſerit Merſennus in ſuis Hydraulicis, Propo<lb></lb>ſit. 2 poſt medium. </s><s>Ratio phænomeni dependet ex velocita<lb></lb>te aquæ deſcendentis & effluentis ex tubo CD, ſupra veloci<lb></lb>tatem æquæ deſcendentis & effluentis ex tubo AB; de qua <lb></lb>vide Propoſit. IX. & X. <expan abbr="ſeq.">ſeque</expan> ubi dicemus, illam ad hanc eſſe du<lb></lb>plam, hoc eſt, ſubduplicatam altitudinum tuborum haben<lb></lb>tium æqualia foramina; quo demonſtrato, demonſtrabimus <lb></lb>deinde Propoſitione XI. hanc præſentem Propoſitionem. </s></p> <p type="margin"> <s><margin.target id="marg216"></margin.target><emph type="italics"></emph>Aquæ dupli<lb></lb>catam ra<lb></lb>tionem ha<lb></lb>bent tubo<lb></lb>rum æqua<lb></lb>lium lumi<lb></lb>num, at in<lb></lb>æqualium <lb></lb><expan abbr="altitudinũ">altitudinum</expan>.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur ex his, tuborum æqualium foraminum altitudi<lb></lb> <arrow.to.target n="marg217"></arrow.to.target><lb></lb>nes debere eſſe in duplicata ratione aquarum inæqualium <lb></lb>quas debent eodem tempore fundere. </s><s>Verbi gratia, tubus pe<lb></lb>dalis determinato tempore dat unam aquæ libram ex ſuo fo<lb></lb>ramine; ut alius tubus ex æquali foramine æquali tempore det <lb></lb>duas libras, debet habere duplicatam rationem ad illum, nem<lb></lb>pe debet eſſe altus quatuor pedibus. </s><s>Sic etiam quia tubus qua<lb></lb>tuor pedum per lineare lumen ſpatio 13 minutorum ſecundo<lb></lb>rum fundit unam libram aquæ, ut diximus Propoſit. VII. ut <lb></lb>alius tubus eodem tempore per lumen lineare fundat centum <pb xlink:href="051/01/151.jpg" pagenum="120"></pb>libras, debet habere altitudinem duplicatam 1 ad 100; nem<lb></lb>pe 40000. pedum. </s><s>Atque hæc eſt converſa præcedentis Pro<lb></lb>poſitionis. </s></p> <p type="margin"> <s><margin.target id="marg217"></margin.target><emph type="italics"></emph>Tubi æqua<lb></lb>lium lumi<lb></lb>num, at in<lb></lb>æqualium <lb></lb><expan abbr="altitudinũ">altitudinum</expan>, <lb></lb>habent du<lb></lb>plicatam <expan abbr="ra-tionẽ">ra<lb></lb>tionem</expan> aqua<lb></lb>rum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur præterea, datis tubis æqualium foraminum, at <lb></lb>inæqualium altitudinum, in numeris aut lineis, mediam <lb></lb>proportionalem dare aquas; & datis aquis in numeris aut men<lb></lb>ſuris, tertiam proportionalem dare tuborum altitudinem æqua<lb></lb>lium foraminum. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg218"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg218"></margin.target><emph type="italics"></emph>Mediæ, ac <lb></lb>Tertiæ pro<lb></lb>portionalis <lb></lb>quantitatis <lb></lb>in ventio.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>DEinventione mediæ ac tertiæ proportionalis magnitudinis in nume<lb></lb>ris ac lineis, agemus infrà in Parergo hujus capitis, & in Arith<lb></lb>metica ac Geometria practica, & in Pantometro Kircheriano lib.<emph.end type="italics"></emph.end> 8. <lb></lb><emph type="italics"></emph>cap.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>Propoſit.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 3. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IX. Theorema I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua naturali motu deſcendens & effluens per tubos, <lb></lb>imitatur leges aliorum gravium naturali <lb></lb>motu deſcendentium.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>NOn uni mirabile viſum, inquit Merſennus in Phænome<lb></lb>nis Hydraulicis Propoſit. III. quòd non ſit eadem ratio <lb></lb>quantitatis aquæ fluentis ex tubo pedali, ad aquæ quantitatem <lb></lb>ex quadrupedali tubo ſalientis, poſito æquali foramine in utro<lb></lb>que, quæ eſt 1 ad 4; cùm aqua quadrupedalis tubi quadruplo <lb></lb>magis, quàm pedalis premere videatur fundum, & aquam ex <lb></lb>lumine ſalientem. </s><s>Verùm mirari deſines, ubi noveris, aquam <lb></lb>eo ſolùm modo premere, vel ea duntaxat velocitate tubum <lb></lb>egredi, quâ moveretur, ſi ex eadem tubi altitudine cecidiſſet; <lb></lb>adeo ut ſit eadem iſtius phænomeni ratio, quæ deſcenſus aquæ <lb></lb>per tubum; & eadem hujus deſcenſus, quæ deſcenſus aliorum <lb></lb>gravium; de quo proinde hîc agendum paulò accuratiùs, quan<lb></lb>doquidem aquæ motus per tubum, & ex tubo eruptio, ſequi<lb></lb>tur leges gravium motu naturali deſcendentium. </s></p> <pb xlink:href="051/01/152.jpg" pagenum="121"></pb> <p type="main"> <s><emph type="center"></emph>Leges gravium naturali motu deſcendentium.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>LEges porrò, quas gravia in deſcenſu naturali motu facto <lb></lb> <arrow.to.target n="marg219"></arrow.to.target><lb></lb>ſervant, incredibili cura ac diligentia indagavit & obſer<lb></lb>vavit Bononiæ P. Joannes Baptiſta Ricciolus, unà cum alijs <lb></lb>è noſtra Societate Patribus, eaſque clariſſimè ac diſtinctiſſimè <lb></lb> <arrow.to.target n="marg220"></arrow.to.target><lb></lb>proponit in Tomo 1. Almageſti ſui novi; fusè quidem lib. 9. <lb></lb>ſect. 4. cap. 16. num. 24. breviter verò lib. 2. cap. 21. . </s><s>Quibus <lb></lb>Riccioli obſervationibus tantam ego fidem adhibeo, ut licet <lb></lb>hîc Romæ eaſdem repetere opportuniſſimum mihi foret, de<lb></lb>miſſis gravibus per cochleatas Divi Petri in Vaticano ſcalas <lb></lb>altiſſimas, & ab omni aëris commotione liberas, feneſtris in<lb></lb>ſuper plurimis ab ima baſi ad ſummitatem uſque refertas; no<lb></lb>luerim tamen me fruſtra fatigare, cùm nec accuratiores ad<lb></lb>hibere me poſſe putem, nec ſi adhibeam, alias præter ipſius <lb></lb>leges reperturum me certò ſciam. </s><s>Ex multis igitur deſcen<lb></lb>ſus gravium legibus à Ricciolo locis citatis adductis, duas ſe<lb></lb>quentes affero, quoniam eæ propoſito noſtro ſatisfacient. </s></p> <p type="margin"> <s><margin.target id="marg219"></margin.target><emph type="italics"></emph>Gravium <lb></lb>naturali <lb></lb>motu <expan abbr="de-ſcendentiũ">de<lb></lb>ſcendentium</expan> <lb></lb>leges.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg220"></margin.target><emph type="italics"></emph>Riccioli di<lb></lb>ligentia ex<lb></lb>acta in ob<lb></lb>ſervandis le<lb></lb>gibus gra<lb></lb>vium <expan abbr="de-ſcendentiũ">de<lb></lb>ſcendentium</expan><emph.end type="italics"></emph.end>.</s></p> <p type="main"> <s><emph type="italics"></emph>I. Gravia naturali motu per lineam perpendicularem in aëre de<lb></lb> <arrow.to.target n="marg221"></arrow.to.target><lb></lb>ſcendentia, moventur difformi velocitate, eâque majore & majore <lb></lb>verſus finem motus.<emph.end type="italics"></emph.end> </s><s>Lex hæc nota fuit jam inde à viginti & am<lb></lb>pliùs ſæculis in Academijs Phyſicorum, præſertim Peripateti<lb></lb>corum cum Ariſtotele lib. 1. de cœlo cap. 88. inquit Ricciolus, <lb></lb>patetque oculis, auribus, & tactui; videmus enim gravia de<lb></lb>ſcendentia accelerare magis ac magis motum; audimus vehe<lb></lb>mentiorem ſonum, percipimus validiorem percuſſionem, ex <lb></lb>lapſu gravis ac duri è loco altiori, quàm minùs alto. </s></p> <p type="margin"> <s><margin.target id="marg221"></margin.target>Lex I. gra<lb></lb>vium <expan abbr="de-ſcendentiũ">de<lb></lb>ſcendentium</expan>.</s></p> <p type="main"> <s><emph type="italics"></emph>II. Motus gravium naturaliter deſcendentium per aërem, cre<lb></lb> <arrow.to.target n="marg222"></arrow.to.target><lb></lb>ſcit eo incremento velocitatis, quod eſt inter numeros impares ab uni<lb></lb>tate numeratos; ſeu ita ut ſpatia æqualibus temporibus tranſmiſſa ſint <lb></lb>inter ſe, ut quadrata temporum; ſeu ita, ut ſpatia tranſmiſſa certis <lb></lb>temporibus habeant inter ſe duplicatam proportionem illius, quam ha<lb></lb>bent tempora quibus ſpatia illa menſurata fuerint.<emph.end type="italics"></emph.end> </s><s>ita Ricciolus lo<lb></lb>cis citatis, & ante ipſum Galilæus Dialogo 2. de Syſtemate <pb xlink:href="051/01/153.jpg" pagenum="122"></pb>Mundi, & Balianus lib 1. de Motu naturali gravium, Propoſit. 6. <lb></lb>(licet deinde lib. 4. à pag. 110. ad 113. aliter ſtatuat) & poſtipſos <lb></lb>Gaſſendus in Epiſtolis de motu impreſſo à motore, & Kirche<lb></lb>rus in Muſurgia lib. 6. parte 1. Lemmate 3. & conſtat experien<lb></lb> <arrow.to.target n="marg223"></arrow.to.target><lb></lb>tiâ. </s><s>Numeri pariter impares ab unitate numerati, ſunt hi: 1, <lb></lb>3, 5, 7, 9, 11, 13, 15 &c. </s><s>Itaque ſi grave aliquod deſcendens con<lb></lb>ficit in primo minuto temporis unum ſtadium ſpatij; in ſecundo <lb></lb>minuto conficiet tria ftadia, in tertio quinque, in quarto ſe<lb></lb>ptem, &c. </s><s>Sic enim ſpatia æqualibus temporibus confecta, <lb></lb>erunt inter ſe, ut quadrata temporum: nam quadratum mi<lb></lb>nuti primi eſt 1; & quadratum minuti ſecundi, 4; & quadra<lb></lb>tum minuti tertij, 9; & quadratum minuti quarti, 16 &c. ut <lb></lb>apparet inappoſita tabella. </s><s> <arrow.to.target n="table1"></arrow.to.target><lb></lb>Cùm igitur grave deſcen<lb></lb>dens in primo minuto con<lb></lb>ficiat unum ſpatium, & in <lb></lb>ſecundo minuto tria ſpatia, <lb></lb>quæ cum uno conficiunt <lb></lb>quatuor; & in tertio minu<lb></lb>to quinque ſpatia, quæ cum <lb></lb>quatuor efficiunt novem; & in quarto minuto ſeptem ſpatia, <lb></lb>quæ cum novem efficiunt ſexdecim; & in quinto minuto no<lb></lb>vem ſpatia, quæ cum ſexdecim efficiunt viginti quinque, &c. <lb></lb>apparet manifeſtè, ſpatia tranſmiſſa à gravi deſcendente, ha<lb></lb>bere ſe, ut quadrata temporum æqualium, quibus percurrun<lb></lb>tur illa ſpatia. </s><s>In idem autem recidit, ſi dicas, ſpatia tranſ<lb></lb>miſſa certis temporibus habere inter ſe duplicatam rationem <lb></lb>ſeu proportionem illius proportionis, quam habent tempora, <lb></lb>quibus ſpatia illa menſurata fuerint: nam tempus ſeu minutum <lb></lb>ſecundum ad primum, ut apparet ex tabella præcedente, ha<lb></lb>bet rationem ſeu proportionem duplam, ſpatia verò ſecundo <lb></lb>minuto confecta, nempe 1 ad 3 (quæ ſimul juncta efficiunt 4) <lb></lb>ad primum minutum habent rationem duplicatam rationis <lb></lb>duplæ. </s><s>Eadem eſt ratio de cæteris. </s><s>Lege etiam Mundum ſub- <pb xlink:href="051/01/154.jpg" pagenum="123"></pb>terraneum P. Athanaſij Kircheri, ubi in Libro Centroſophico <lb></lb>fuſiſſimè pertractat hanc materiam. </s><s>Lege præterea Joannem <lb></lb>Caramuelem in Cruce Sublimium ingeniorum. </s></p> <p type="margin"> <s><margin.target id="marg222"></margin.target>Lex II. gra<lb></lb>vium <expan abbr="de-ſcendentiũ">de<lb></lb>ſcendentium</expan>.</s></p> <p type="margin"> <s><margin.target id="marg223"></margin.target><emph type="italics"></emph>Numeri pa<lb></lb>riter impa<lb></lb>res ab unita<lb></lb>te numera<lb></lb>ti.<emph.end type="italics"></emph.end></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"></emph>Leges aquæ naturali motu deſcendentis <lb></lb>& effluentis per tubos.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt jam tubus ABCD, ſive ſemper, ſive non ſemper plenus, <lb></lb> <arrow.to.target n="marg224"></arrow.to.target><lb></lb>cujus foramen B; <expan abbr="tempuſq́ue">tempuſque</expan> in quo aqua ab A deſcendit <lb></lb>uſque ad B, dividatur in quinque æquales partes, in quarum <lb></lb>prima confecerit ſpatium A1; Dico, eandem aquam in ſe<lb></lb>cunda parte temporis conficere ſpatium A4, in tertia parte <lb></lb> <arrow.to.target n="fig30"></arrow.to.target><lb></lb>A9, in quarta ſpatium A16, in quinta ſpatium A25; <lb></lb>atque adeo ſpatia æqualibus quinque temporibus <lb></lb>confecta, habere ſe ut quadrata quinque illorum <lb></lb>temporum, ut ex appoſitis utrimque numeris ap<lb></lb>paret; ſeu velocitatem deſcenſus aquæ creſcere ſe<lb></lb>cundùm progreſſionem numerorum imparium, <lb></lb>prout indicant numeri intra tubum notati; ſeu <lb></lb>ſpatia confecta habere duplicatam rationem illius, <lb></lb>quam habent tempora, ut apparet ſi conferas nu<lb></lb>meros externos lateris AB, cum numeris lateris <lb></lb>CD. </s><s>Ratio eſt, quia aqua gravis eſt, & intra tu<lb></lb>bum naturali motu deſcendit, nullumque adeſt <lb></lb>impedimentum motus; ergo imitari debet leges aliorum gra<lb></lb>vium naturali motu deſcendentium. </s></p> <p type="margin"> <s><margin.target id="marg224"></margin.target><emph type="italics"></emph>Leges aqua <lb></lb>naturali <lb></lb>motu de<lb></lb>ſcendentis <lb></lb>per tubos.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.154.1.jpg" xlink:href="051/01/154/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Corollarium I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur hinc primò, Aquam è foramine B, tubi ſemper <lb></lb> <arrow.to.target n="marg225"></arrow.to.target><lb></lb>pleni, effluere tantâ velocitate, quantâ deſcendit ab A ad <lb></lb>B. </s><s>Ratio eſt, quia ut ſupponitur, tantum effluit per B, quan<lb></lb>tum influit per A, & è contrario tantum per A influit, quan<lb></lb>tum per B effluit, & in deſcenſu ab A ad B nulla fit inter<lb></lb>ruptio; ergo tam velociter effluit per B, quàm velociter de<lb></lb>ſcendit ab A ad B. </s></p> <pb xlink:href="051/01/155.jpg" pagenum="124"></pb> <p type="margin"> <s><margin.target id="marg225"></margin.target><emph type="italics"></emph>Leges aquæ <lb></lb>effluentis <lb></lb>per <expan abbr="foramẽ">foramen</expan> <lb></lb>tubi ſemper <lb></lb>pleni.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur ſecundò, Aquam apud B, in utroque tubo, hoc eſt, <lb></lb>ſemper & non ſemper pleno, tantâ ſolùm vi premi prope <lb></lb>foramen B, quanta eſt vis ſeu pondus aquæ à B uſque ad ſu<lb></lb>premam aquæ ſuperficiem, id eſt, columnæ aqueæ habentis <lb></lb>pro baſi latitudinem foraminis B, pro altitudine perpendicu<lb></lb>larem à B ad dictam ſuperficiem. </s><s>Ratio eſt, quia ſolùm illa <lb></lb>columna premit ſupra B, per dicta Propoſit. 1. </s><s>Intellige, niſi <lb></lb>illa aliunde impetum recipiat, ut ſi ipſi affunderetur aqua ex <lb></lb>tubo inclinato, ſive conjuncto, ſive diſiuncto. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium. III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur tertiò, Leges prædictas deſcenſus gravium ſervari <lb></lb> <arrow.to.target n="marg226"></arrow.to.target><lb></lb>ab aqua in tubo ſemper pleno, deſcendendo ab A ad B, ſo<lb></lb>lùm in primo deſcenſu, non verò in deſcenſu continuato; item <lb></lb>ſolùm à prima parte aquæ deſcendentis, <expan abbr="nõ">non</expan> à partibusipſi conti<lb></lb>guis & ſubſequentibus. </s><s>Explico Deſcendat aqua ab A ad B, effi<lb></lb>ciatque deſcenſus columnam aqueam AB, quæ dividatur in vi<lb></lb>ginti <expan abbr="quinq;">quinque</expan> æquales partes ſecundùm longitudinem ſeu altitu<lb></lb>dinem ab A ad B. </s><s>Dico, ſolùmvigeſimam quintam partem, quæ <lb></lb>eſt apud B, ſervare prædictam legem deſcenſus gravium cre<lb></lb>ſcentis in velocitate ſecundùm numeros impares ab unitate <lb></lb>numeratos; & quidem illam ſolam vigeſimam quintam par<lb></lb>tem, quæ eſt in prima columna aquea à deſcenſu aquæ for<lb></lb>mata, non verò quæ eſt in reliquis columnis ſubſequentibus. </s><s><lb></lb>Ratio eſt, quia cùm nulla pars ex viginti quinque egrediatur <lb></lb>è foramine B, quin ingrediatur alia per orificium A priori <lb></lb>æqualis; & nulla tranſeat vigeſimum quintum & ultimum ſpa<lb></lb>tiolum lateris AB, quin eodem tempore tranſeat alia æqualis <lb></lb>primum ſpatiolum, & alia ſecundum, & alia tertium, ac reli<lb></lb>qua omma; neceſsè eſt ut omnes reliquæ partes eâdem velo<lb></lb>citate conficiant ſingula ſpatiola, qua velocitate ultima con<lb></lb>ficit ultimum; & eâdem velocitate unaquæque pertranſeat <lb></lb>ſpatiolum ſibi correſpondens, qua velocitate ultima pars per<lb></lb>tranſit ultimum ſpatiolum. </s><s>Patet ergo propoſitum. </s></p> <pb xlink:href="051/01/156.jpg" pagenum="125"></pb> <p type="margin"> <s><margin.target id="marg226"></margin.target><emph type="italics"></emph>Lex deſcen<lb></lb>ſus aquæ è <lb></lb>tubo expli<lb></lb>catur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium IV.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.156.1.jpg" xlink:href="051/01/156/1.jpg"></figure> <p type="main"> <s>COlligitur quartò, Aquam è foramine B efflue<lb></lb> <arrow.to.target n="marg227"></arrow.to.target><lb></lb>re eò majori velocitate, quò altior fuerit tu<lb></lb>bus. </s><s>Ratio eſt, quia quò altior eſt tubus, eò ma<lb></lb>jorem velocitatem adquirit prima pars aquæ de<lb></lb>ſcendentis in ſuo deſcenſu, & conſequenter reli<lb></lb>quæ ſubſequentes; item quò altior eſt tubus, eò <lb></lb>altior eſt columna aquea premens apud B. ideo<lb></lb>que eò vehementiùs premit apud idem B. </s><s>Vide <lb></lb>quæ diximus Propoſit. VI. </s></p> <p type="margin"> <s><margin.target id="marg227"></margin.target><emph type="italics"></emph>Aqua è tu<lb></lb>bo eò velo<lb></lb>ciùs effluit, <lb></lb>quò altior <lb></lb>eſt tubus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur quintò, Aquam ex æqualibus tubis, quoad fora<lb></lb> <arrow.to.target n="marg228"></arrow.to.target><lb></lb>mina & altitudines, effluere æquali velocitate. </s></p> <p type="margin"> <s><margin.target id="marg228"></margin.target><emph type="italics"></emph>Aqua ex æ<lb></lb>qualibus tu<lb></lb>bis quoad o<lb></lb>mnia, æqua<lb></lb>li velocita<lb></lb>te effluit,<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio X. Theorema II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Velocitates motus aquæ deſcendentis & effluentis per <lb></lb>tubos æqualium foraminum, ſed inæqualium altitu<lb></lb>dinum, habent ſubduplicatam rationem <lb></lb>altitudinum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.156.2.jpg" xlink:href="051/01/156/2.jpg"></figure> <p type="main"> <s>ESto tubus AB altus uno pede, & alius CD al<lb></lb>tus quatuor pedibus, ſed uterque æqualium <lb></lb>foraminum, ſive ſemper, ſive non ſemper pleni, è <lb></lb>quibus effluat aqua inæquali velocitate, juxta di<lb></lb>cta Propoſitione præcedente, Corollario IV. </s><s>Dico, <lb></lb>velocitates motus & effluxus aquarum eſſe in ſub<lb></lb>duplicata ratione tuborum, hoc eſt, aquam per <lb></lb>tubum CD deſcendere, & effluere duplo velo<lb></lb>ciùs, quàm per tubum AB. </s><s>Quoniam enim aquæ <lb></lb> <arrow.to.target n="marg229"></arrow.to.target><lb></lb>motus per tubos æmulatur leges gravium deſcen<lb></lb>dentium motu naturali, per dicta Propoſit. IX. <lb></lb>præcedente, hoc eſt, creſcit in velocitate ſecun- <pb xlink:href="051/01/157.jpg" pagenum="126"></pb> <arrow.to.target n="fig31"></arrow.to.target><lb></lb>dùm progreſſionem numerorumim parium ab uni<lb></lb>tate numeratorum; ſi aqua in primo tempore de<lb></lb>terminato, v.g. in primo minuto deſcendit à C in <lb></lb>E, hoc eſt, ab A in B; in ſecundo minuto de<lb></lb>ſcendet ab E ad D, ac proinde in fine quarti pal<lb></lb>mi mota erit duplo velociùs, quàm in fine primi <lb></lb>palmi; Ergo velocitas motus aquæ per tubum CD <lb></lb>ad velocitatem aquæ per tubum AB, habet ſub<lb></lb>duplicatam rationem altitudinum. </s><s>Eadem eſt <lb></lb>ratio in alijs inæqualibus altitudinibus, quamcun<lb></lb>que habeant inter ſe proportionem. </s></p> <p type="margin"> <s><margin.target id="marg229"></margin.target><emph type="italics"></emph>Proportio <lb></lb>velocitatis <lb></lb>motus aquæ <lb></lb>deſcenden<lb></lb>tis per tubos: <lb></lb><expan abbr="inæqualiũ">inæqualium</expan> <lb></lb>foraminum.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.157.1.jpg" xlink:href="051/01/157/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end><lb></lb> </s></p> <p type="main"> <s>TUbi ergo duplicatam habent rationem illius, quam habent <lb></lb>velocitates motus deſcendentis, & effluentis per ipſos aquæ. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XI. Theorema III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Cauſam aſſignare, cur aquæ fluentes per tubos æqua<lb></lb>lium luminum, ſed inæqualium altitudinum, habeantra<lb></lb>tionem ſubduplicatam altitudinum tuborum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg230"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg230"></margin.target><emph type="italics"></emph>Proportio<lb></lb>nis prædicta <lb></lb>cauſa.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>QUod aſſeruimus Propoſit. VIII. huius capitis, demonſtran<lb></lb>;dum hîc eſt, ut fidem ibi obligatam ſolvamus. </s></p> <p type="main"> <s>Ratio igitur adſignati hîc & ibi Phænomeni eſt, quòd flu<lb></lb>xus aquæ per foramen, ſeu quantitas aquæ effluentis, pendeti <lb></lb>velocitate aquæ eiusdem deſcendentis per tubum, per dicta <lb></lb>Propoſit. IX. Corollario. I. </s><s>Velocitas autem illa eſt ſubduplicata <lb></lb>altitudinum, per dicta Propoſit. X; ergo & quantitas aquæ efflu<lb></lb>entis ex tubis inæqualium altitudinum ſubduplicata erit <expan abbr="tuborũ">tuborum</expan>. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XII. Theorema IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Tempora quibus æqualis aquæ quantitas è tubis æqua<lb></lb>lium luminum, ſed inæqualium altitudinum effluit, ha<lb></lb>bent ſubduplicatam rationem tuborum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg231"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg231"></margin.target><emph type="italics"></emph>Proportio <lb></lb>temporum <lb></lb>quibus a<lb></lb>qua effluit è <lb></lb>tubis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>SItut antea tubus AB vnius, & tubus CD quatuor pedum in <lb></lb>altitudine, ſed æqualium luminum, ſive ſemper, ſive non ſem- <pb xlink:href="051/01/158.jpg" pagenum="127"></pb>per pleni; fluatque ex tubo AB vna libra aquæ ſpatio duorum <lb></lb>minutorum. </s><s>Dico, eandem aquam effluere ex tubo CD ſpa<lb></lb>tio vnius minuti, <expan abbr="eſſeq́ue">eſſeque</expan> propterea tempus fluxus aquæ ex tubo <lb></lb>CD, ad tempus fluxus aquæ ex tubo AB, ut 1 ad 2, quæ eſt ratio <lb></lb>ſubduplicata tuborum. </s><s>Ratio ex dictis patet. </s><s>Quoniam enim <lb></lb>velocitates effluxûs aquæ ex æquali lumine habent ſubduplica<lb></lb>tam rationem tuborum, ut demonſtravimus Propoſit. X, fluet in <lb></lb>dimidio temporis tantum ex tubo CD, quantum in toto tem<lb></lb>pore ex tubo AB, poſita æqualitate luminum; ac proinde in <lb></lb>toto tempore duplum effluet ex tubo CD. </s><s>Eadem eſt ratio in <lb></lb>alijs tuborum æqualium luminum proportionibus. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>TUbi ergo quilibet æqualium luminum, ſed inæqualium alti</s></p> <p type="main"> <s> <arrow.to.target n="marg232"></arrow.to.target><lb></lb>tudinum, habent rationem duplicatam temporum, quibus <lb></lb>effluit æqualis aquæ quantitas. </s></p> <p type="margin"> <s><margin.target id="marg232"></margin.target><emph type="italics"></emph>Proportio <lb></lb>tuborum ad <lb></lb>tempora flu<lb></lb>xus aquæ.<emph.end type="italics"></emph.end> </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XIII. Theorema V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Si tubi, ſive ſemper pleni, ſive non ſemper pleni, ſint <lb></lb>eiuſdem altitudinis, ſed inæqualium foraminum, eſt eadem ra<lb></lb>tio aquæ ad aquam, quæ foraminis ad foramen, <lb></lb>phyſicè ſeu ad ſenſum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ESt Merſenni in hydraulicis Phænomenis Propoſit. IV. quem <lb></lb> <arrow.to.target n="marg233"></arrow.to.target><lb></lb>ſequitur P. Andreas Tacquet in ſuis hydraulicis Manuſcri<lb></lb>ptis cap. 4. Phænomen. 7. </s><s>Ratio eſt, quòd licet ex maiori lu<lb></lb>mine ſeu foramine fluat eodem tempore maior aquea columna <lb></lb>quàm ex minori, tantòque maior exillo quàm ex hoc, quantò <lb></lb>fuerit maius lumen ſeu <expan abbr="foramẽ">foramen</expan> illud quàm hoc, quoad aream, per <lb></lb>dicta Propoſit. 4. huius eapitis; tamen vtraque columna fluit <lb></lb>ex æquali altitudine tuborum æquâ velocitate phyſicè & ad <lb></lb>ſenſum. </s></p> <p type="margin"> <s><margin.target id="marg233"></margin.target><emph type="italics"></emph>Proportio a<lb></lb>quæ ad <expan abbr="a-quã">a<lb></lb>quam</expan> eadem <lb></lb>quæ forami<lb></lb>num in tu<lb></lb>bu æquè al<lb></lb>tis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Dixi phyſicè & ad ſenſum, quia licet gravia eiusdem ſpe<lb></lb>ciei, ſed inæqualis molis ac ponderis, ab eodem ad eundem <pb xlink:href="051/01/159.jpg" pagenum="128"></pb>terminum non deſcendant æquè velociter, revera & mathema<lb></lb>ticè, quemadmodum ſentiunt Galilæus Dialogo 2. de Syſtem. <lb></lb>Mundi, Ioannes Baptiſta Balianus lib. 1. de motu naturali gravi<lb></lb>um ſolidorum in Præfat. Nicolaus Cabæus lib. 1. Meteoror. textu <lb></lb>17. <expan abbr="q.">que</expan> 5. & 6. Arriaga diſput. 4. de Generat. ſect. 5. ſubſect. 3. <lb></lb>Maſtrius, Bellutus, & alij (quod ego falſum exiſtimo, mathe<lb></lb>maticè loquendo, cum Patre Ioanne Baptiſta Ricciolo, qui <lb></lb>tom. 1. Almageſti Novi lib. 2. cap. 21. Propoſit. 2. & lib. 9. ſect. 4. <lb></lb>num. 24. aſſerit, <emph type="italics"></emph>duorum gravium eiusdem ſpeciei & figuræ ſea inæ<lb></lb>qualis molis ac ponderis, ex eadem altitudine momento eodem dimiſ<lb></lb>ſorum, illud naturali motu citiùs deſcendere ad eundem terminum, quod <lb></lb>eſt gravius;<emph.end type="italics"></emph.end> ubi etiam Experimenta multa diverſis annis coram <lb></lb>multis viris doctis incredibili diligentiâ peracta Bononiæ refert <lb></lb>num. 13.) tamen in parvis altitudinibus, quales ſunt tuborum <lb></lb>in omni ferè caſu, tam exigua eſt differentia velocitatum, ut pro <lb></lb>eâdem ſeu æquali cenſeri meritò poſſit. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur hinc, tubos non ſemper plenos, æquales quoad alti<lb></lb>tudines, & baſes, inæquales tamen quoad foramina, evacua<lb></lb>ri inæqualibus temporibus, hoc eſt, citiùsillum, qui maius ha<lb></lb>bet lumen; <expan abbr="eſſeq́ue">eſſeque</expan> tempora, quibus evacuantur, inter ſe ut lu<lb></lb>mina, hac tamen conditione, vt per foramen maius citiùs efflu<lb></lb>at tota aqua, quàm per foramen minus, <expan abbr="tantoq́">tantoque</expan>; citiùs per majus, <lb></lb>quàm per minus, quantò foramen maius ſuperat minus. </s><s>Atque <lb></lb>hoc eſt quod dicemus Propoſit. XVI. ſequente, tempora ſcili<lb></lb>cet in dicto caſu eſſe reciprocè vt lumina. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur præterea, ex tubis non ſemper plenis, quorum æ<lb></lb>quales ſunt altitudines, at inæquales baſes, ſed totæ apertæ, <lb></lb>effluere totam aquam æquali tempore; quandoquidem vtrobi<lb></lb>que columna aquea, licet inæqualis ponderis ac molis, æquè <lb></lb>velociter deſcendit quoad ſenſum, per idem ſpatium. </s></p> <pb xlink:href="051/01/160.jpg" pagenum="129"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio XIV. Theorema VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Tubi non ſemper pleni æquè alti, & æqualium. forami<lb></lb>num, ſed inæqualium baſium, evacuantur inæqualibus <lb></lb>temporibus; <expan abbr="eſtq́ue">eſtque</expan> eadem ratio temporum, <lb></lb>quæ baſium.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PRimum patet per ſe, quia cæteris omnibus paribus major a<lb></lb> <arrow.to.target n="marg234"></arrow.to.target><lb></lb>quæ quantitas maius requirit tempus ad effluendum, quàm <lb></lb>minor. </s><s>Alterum demonſtratur, vel potiùs explicatur ſic. </s></p> <p type="margin"> <s><margin.target id="marg234"></margin.target><emph type="italics"></emph>Proportio <lb></lb>temporum <lb></lb>eadem quæ <lb></lb>baſium <expan abbr="tu-borũ">tu<lb></lb>borum</expan>, quo<lb></lb>ad aquæ flu<lb></lb>xum.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.160.1.jpg" xlink:href="051/01/160/1.jpg"></figure> <p type="main"> <s>Eſto tubus AB minoris baſis, & alius ACBD <lb></lb>majoris, uterque cylindricus, uterque æquè altus, & <lb></lb>æqualis foraminis B; ſitque diameter baſis BD tripla <lb></lb>diametri baſis B: eritigitur area baſis BD noncupla <lb></lb>areæ baſis B, quoniam circuli inter ſe ſunt, ut qua<lb></lb>drata diametrorum, per Propoſit. 2. lib. 12. Element. <lb></lb>Euclidis; quadratum <expan abbr="autẽ">autem</expan> diametri BD triplo maio<lb></lb>ris diametro B, eſt nonies maius, quàm quadratum <lb></lb>diametri B, ut ex Geometria practica patet. </s><s>Cùm <lb></lb>igitur cylindri æquè alti ſint inter ſe, ut <expan abbr="illorũ">illorum</expan> baſes, ut <lb></lb>patet ex <expan abbr="eadẽ">eadem</expan> Geomet. practica; ſequitur, aquam tubi <lb></lb>ACBD eſſe noncuplam aquæ tubi AB; ac proinde <lb></lb>tempus quo exhauritur per foramen B tubus ACDB, <lb></lb>noncuplum erit temporis, quo exhauritur per idem <lb></lb>foramen B, tubus AB, <expan abbr="quandoquidẽ">quandoquidem</expan> cylindrus aqueus ACBD, <lb></lb>non magis premit ſupra <expan abbr="foramẽ">foramen</expan> B, quàm cylindrulus aqueus AB, <lb></lb>per dicta Propoſit. II. in Corollario, & Propoſit. VII. Annot. 2. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>MErſennus in Hydraulicis Phænomenis Propoſit.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>ait, conſtare ex <lb></lb> <arrow.to.target n="marg235"></arrow.to.target><lb></lb>obſervatione, tubum quadrupedalem, cuius baſis digitalis, uno mi<lb></lb>nuto temporis totum per lineare lumen exhauriri; tubum verò quadru<lb></lb>pedalem cuius baſis pedalis, ſpatio<emph.end type="italics"></emph.end> 144. <emph type="italics"></emph>minutorum, ſeu duabus horis, &<emph.end type="italics"></emph.end><lb></lb>24. <emph type="italics"></emph>minutis. </s><s>Servatur ergò inter temporaratio baſium, vt demonſtra<lb></lb>vimus: Nam cùm pedis longitudo contineat, ex Merſenni mente, ut <lb></lb>vidimus Propoſit. VII. huius Capitis Annot. I. digiti latitudinem<emph.end type="italics"></emph.end> <pb xlink:href="051/01/161.jpg" pagenum="130"></pb><emph type="italics"></emph>duodecies; continebit quadratum pedis quadrata digiti<emph.end type="italics"></emph.end> 144. <emph type="italics"></emph>ac proinde <lb></lb>baſis pedalis baſim digitalem centies quadragies quater continebit, vt <lb></lb>diximus in Propoſitione.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg235"></margin.target>Merſenni <lb></lb>obſervatio <lb></lb>in tuborum <lb></lb>evacuati<lb></lb>one.</s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg236"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg236"></margin.target><emph type="italics"></emph>P. Pauli Ca<lb></lb>ſati dubita<lb></lb>tio contra <lb></lb>Merſenni <lb></lb>obſervatio<lb></lb>nem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>ACutiſſimè notavit hîc P.Paulus Caſatus in cenſura huius Operis, poſ<lb></lb>ſe dubitari de veritate huius Propoſitionis<emph.end type="italics"></emph.end> 14. <emph type="italics"></emph>& poſſe aliquem ſuſpi<lb></lb>cari, an experimentum allatum à Merſenno ſit in gratiam Propoſitionis <lb></lb>confictum.<emph.end type="italics"></emph.end> </s><s>Ratio dubitandi eſt, <emph type="italics"></emph>inquit,<emph.end type="italics"></emph.end> quia quo tempore par<lb></lb>vulus tubus AB exhauritur, ex maiori tubo ABCD effluit maior <lb></lb>aquæ quantitas eodem tempore, quia ſcilicet effluit in progreſſu <lb></lb>maiori velocitate ex maiori, quàm ex minori: nam in majore <lb></lb>tubo eſt maius aquæ perpendiculum in progreſſu. </s><s>Fac enim in <lb></lb>minori deſcendiſſe ſemiſſem; aquæ altitudo eſt ſolùm dimidia <lb></lb>totius altitudinis: fac ex majori eodem tempore deſcendiſſe æ<lb></lb>qualem aquam, hoc eſt (quia maior ad minorem eſt ut 9. ad 1.) <lb></lb>(1/18) totius aquæ; ergo remanet altitudo aquæ in majori (17/18) totius <lb></lb>altitudinis; ergo plus aquæ effluet vbi maior eſt velocitas ratione <lb></lb>maioris perpendiculi. </s><s>Debet igitur hæc ratio conciliari cum <lb></lb>experimento; & opus eſſet oſtendere, quomodo, licet id veri<lb></lb>ficetur in priotibus cylindrulis aquæ effluentibus, tamen maior <lb></lb>illa velocitas priorum compenſentur maiori tarditate poſterio<lb></lb>rum qui habent minus perpendiculum. </s></p> <p type="main"> <s>Hocidem dicitur de Propoſitione 16, in qua conſideratur <lb></lb>columna vt duodecupla minoris, nulla habita ratione quòd in <lb></lb>progreſſu deſcenſus fiunt altitudines valde inæquales: neque vi<lb></lb>detur valere illa argumentatio, facta præciſione per intellectum; <lb></lb>nam ſermo eſt de re prout à parte rei. </s><s><emph type="italics"></emph>Hæc P. Caſatus. </s><s>Nolui ego <lb></lb>in dubium revocare experimentum Merſenni, quoniam id nefas exiſti<lb></lb>mavi; nec experimenti cauſam indagare, ac multò minùs demonſtra<lb></lb>tionem afferre, quoniam id ad propoſitum meum nihil conducit. </s><s><lb></lb>Ratio tamen huius rei ſine dubio refundenda eſt in illam, <lb></lb>quam ipſemet Caſatus inſinuavit.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/162.jpg" pagenum="131"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio XV. Phænomenon. IX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Tempora quibus deplentur tubi non ſemper pleni æque <lb></lb>lati, ſed non æquè alti, per æqualia foramina, ſuntin al<lb></lb>titudinum ratione ſubduplicata.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>COnſtat enim ex obſervatione, inquit Merſennus in Hydrau</s></p> <p type="main"> <s> <arrow.to.target n="marg237"></arrow.to.target><lb></lb>licis Phænomenis Propoſit. IX. tubum pedalem 30 ſecundis, <lb></lb>quadrupedalem verò latitudinis eiusdem 60 ſecundis, per fora<lb></lb>men lineare, totum exhauriri. </s></p> <p type="margin"> <s><margin.target id="marg237"></margin.target><emph type="italics"></emph>Proportio <lb></lb>temporum <lb></lb>aquæ fluxus <lb></lb>ex tubis, ad <lb></lb>eorum alti<lb></lb>tudinem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Corollarium I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>HInc colligitur primò, tuborum altitudines eſſe in ratione <lb></lb>duplicata temporum, quibus deplentur æqualia lumina, vt <lb></lb>diximus etiam in Poriſmate Propoſitionis XII. præcedentis. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium <emph type="italics"></emph>II<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p> <p type="main"> <s>COlligitur ſecundò, tam tubos non ſemper plenos, quàm tu<lb></lb>bos ſemper plenos, juxta eandem rationem tribuere aquas <lb></lb>ex æqualibus foraminibus, juxta dicta hac, & octava Propo<lb></lb>ſitione. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XVI. Theorema VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Tempora quibus evacuantur tubi non ſemper pleni ſi<lb></lb>miles, & æquales quoad altitudines & baſes, per lumina ſimilia <lb></lb>inæqualia, ſunt reciprocè vt lumina.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PRopoſitio intelligenda eſt in eo ſenſu, quem explicavimus <lb></lb>in Porismate 1. Propoſit. 13. præcedentis. </s></p> <p type="main"> <s>Sint itaque tubi cylindrici ABFQ, ſimiles, & æquales in <lb></lb> <arrow.to.target n="marg238"></arrow.to.target><lb></lb>altitudinibus, humido pleni, quorum lumina ſint EC, KN, cir<lb></lb>cularia, at inæqualia (eadem eſt ratio de tubis priſmaticis, & <lb></lb>foraminibus quadratis, alteriusvè Figuræ;) ſitque lumen ſeu <lb></lb>foramen KN duodecies maius quoad aream, quàm lumen EC. </s><s><lb></lb>Dico, tempus quo exhauritur tubus AB, per lumen EC, eſſe <lb></lb>ad tempus, quo exhauritur tubus FQ, per lumen KN, ut eſt <lb></lb>reciprocèlumen KN ad lumen EC; id eſt, tantò plùs tempo<lb></lb>ris requiri ut exhauriatur tubus AB, per foramen EC, quàm <pb xlink:href="051/01/163.jpg" pagenum="132"></pb> <arrow.to.target n="fig32"></arrow.to.target><lb></lb>tubus FQ, per foramen KN, quantò <lb></lb>maius eſt lumen KN, quàm <expan abbr="lumẽ">lumen</expan> EC, <lb></lb>nempe duodecies plùs. </s></p> <p type="margin"> <s><margin.target id="marg238"></margin.target><emph type="italics"></emph>Proportio <lb></lb>temporum <lb></lb>effluxus a<lb></lb>quæ ad fora<lb></lb>mina tubo<lb></lb>rum.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.163.1.jpg" xlink:href="051/01/163/1.jpg"></figure> <p type="main"> <s>Ad hoc oſtendendum, intelligan<lb></lb>tur ſuper luminibus EC, KN, <expan abbr="tanquã">tanquam</expan> <lb></lb>ſuper baſibus, cylindri DC, LN, <expan abbr="ejuſdẽ">ejuſdem</expan> <lb></lb>altitudinis cum cylindricis tubis AB, <expan abbr="Fq.">Fque</expan> </s><s><lb></lb>Patet ex dictis Propoſit. XIII. præce<lb></lb>dente, Porismate 2, hos duos tubos <lb></lb>DC, LN, per lumina EC, KN, eodem <lb></lb>ſeu æquali tempore exhauriri. </s><s>Iam ſic. </s><s><lb></lb>Per Propoſitionem XIII, huius capi<lb></lb>tis, aqua quæ effluit ex tubo FQ, per <lb></lb>lumen KN, eſt ad aquam, quæ eodem <lb></lb>ſeu æquali tempore effluit ex tubo AB, <lb></lb>per foramen EC, ut foramen KN ad foramen EC; <lb></lb>hoc eſt, eodem ſeu æquali tempore, quo ex lumine EC effluit <lb></lb>una columna aquea DC, effluunt ex lumine KN duodecim <lb></lb>columnæ aqueæ DC: Ergo dum ex lumine KN effluxit tota <lb></lb>aqua tubi FQ, effluxit ex lumine EC ſolùm duodecima <lb></lb>pars aquæ tubi AB; ac proinde tantò plùs temporis requiritur, <lb></lb>ut evacuetur tubus AB per lumen EC, quàm ut evacuetur <lb></lb>tubus FQ per lumen KN, quantò maius eſt lumen KN quàm <lb></lb>lumen EC. </s><s>Ergo tempora ſunt reciprocè ut lumina. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur hinc, etiam converſam eſſe veram, nempe lumina, <lb></lb>per quæ evacuantur tubi prædicti, eſſeinter ſe ut reciprocè <lb></lb>tempora, quibus evacuantur: Vnde data ratione <expan abbr="temporũ">temporum</expan>, da<lb></lb>bitur ratio <expan abbr="luminũ">luminum</expan>; ſicut è contrario, data ratione <expan abbr="luminũ">luminum</expan>, datur <lb></lb>ratio temporum ſeu <expan abbr="durationũ">durationum</expan>, quibus evacuantur prædicti tubi. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XVII. Problema I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis altitudine & foramine tubi ſemper pleni, invenire <lb></lb>quantitatem aquæ quam dato tempore effundat; vel, datis <expan abbr="ijſdẽ">ijſdem</expan>, <lb></lb>invenire magnitudinem ciſternæ quæ dato tempore <lb></lb>repleatur.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/164.jpg" pagenum="133"></pb> <figure id="id.051.01.164.1.jpg" xlink:href="051/01/164/1.jpg"></figure> <p type="main"> <s>SUppono hîc id, quod notavi ſuprà Pro<lb></lb>poſit. XIII. tam exiguam eſſe differen<lb></lb>tiam inter velocitates aquarum ex tubis <lb></lb>eiusdem altitudinis, & diverſorum fora<lb></lb>minum, <expan abbr="effluentiũ">effluentium</expan>, ut cenſeri meritò poſ<lb></lb>ſit, aquam ad aquam eſſe, utforamen ad <lb></lb>foramen. </s><s>Quo poſito. <lb></lb> <arrow.to.target n="marg239"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg239"></margin.target><emph type="italics"></emph>Data alti<lb></lb>tudine & <lb></lb>foramine tu<lb></lb>bi, invenire <lb></lb>aquæ quan<lb></lb>titatem da<lb></lb>to tempore <lb></lb>effluentem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sit, exempli gratia, altitudo tubi <lb></lb>ADB pedum 64, luminis ſeu foraminis <lb></lb>diameter DB digitalis, tempus hora una. </s><s><lb></lb>Oporteat igitur reperire, quantum aquæ <lb></lb>tribuat, ſeu quantam ciſternam impleat, <lb></lb>prædictus tubus, intra unam horam. </s><s>So<lb></lb>lutio pendet ex dictis Propoſit. VII. XIII. <lb></lb>& VIII. & præterea ex Propoſit. 2. lib. 12. Eu<lb></lb>clidis. </s><s>Igitur tubum 4 pedes altum, & <lb></lb>luminis linearis, repræſentet CPK. </s><s>Ex <lb></lb>tubo ADB. ſume EDB portionem <expan abbr="etiã">etiam</expan> <lb></lb>4 pedes altam. </s><s>Et quoniam diameter DB <lb></lb>digitalis, eſt ad linearem PK, ut 12 ad 1; <lb></lb>erit per Propoſit. ſecundam lib. 12. Eucli<lb></lb>dis, lumen DB ad lumen KP, utquadra<lb></lb>tum diametri DB, ad quadratum diame<lb></lb>tri PK, hoc eſt, ut 144 ad 1. </s><s>Quare cùm <lb></lb>per Propoſit. XIII. præcedentem, in tubis <lb></lb>æquè altis & ſemper plenis, ſed inæquali<lb></lb>um luminum, aqua ab uno effuſa, fit ad a<lb></lb>quam ab altero effuſam, tempore eodem, <lb></lb>ut lumen ad lumen; dabit EDB. centies <lb></lb>quadragies quater plus aquæ, quàm det <lb></lb>eodem tempore tubus CPK: Sed tubus <lb></lb>CPK, per Propoſit. VII. præcedentem, <lb></lb>ſpatio tredecim ſecundorum temporis dat <lb></lb>unam libram aquæ: </s><s>Ergo tubus EDB <pb xlink:href="051/01/165.jpg" pagenum="134"></pb> <arrow.to.target n="fig33"></arrow.to.target><lb></lb>ſpatio tredecim ſecundorum tomporis da<lb></lb>bit 144 libras. </s><s><expan abbr="Quoniã">Quoniam</expan> autem in una hora, <lb></lb>ſeu in 60. minutis primis, hoc eſt, in 3600 <lb></lb>minutis ſecundis, tredecim ſecunda con<lb></lb>tinentur ducenties ſeptuagies ſexies, rema<lb></lb>nentque 12/<gap></gap>, ſive (facilioris calculi gratia) <lb></lb>ducenties ſeptuagies ſepties; ſi 144 libras, <lb></lb>quas tredecim ſecundis dat tubus EDB, <lb></lb>multiplices per 277, fient ferè 39888. li<lb></lb>bræ, quas horæ ſpatio fundit tubus EDB. </s><s><lb></lb>Inveniatur iam inter 64, altitudinem nem<lb></lb>pe tubi ADB, & inter 4, altitudinem ni<lb></lb>mirum portionis EDB, media proporti<lb></lb>onalis 16. </s><s>Quoniam igitur per Propoſit. <lb></lb>VIII. præcedentem, aquæ quas tubi ADB, <lb></lb>& EDB ſemper pleni, eodem tempore <lb></lb>fundunt, ſunt in ſubduplicata ratione eius <lb></lb>quam habent altitudines ADB, & EDB; <lb></lb>erit aqua quam horæ ſpatio dat tubus <lb></lb>EDB, ad aquam quam eodem tempore <lb></lb>dabit tubus ADB, ut 4 ad 16, ſeu ut 1 ad 4. </s><s><lb></lb>Itaque ſi fiat, ut 1 ad 4, ita 39888 (tot enim <lb></lb>aquæ libras iam oſtendimus horæ ſpatio <lb></lb>dare tubum EDP) ad alium numerum, <lb></lb>nempe ad 159552, quot hic continet vni<lb></lb>tates, tot aquæ libras horæ ſpatio dabit tu<lb></lb>bus ABD ſemper plenus, lumen habens <lb></lb>digitale, altitudinem pedum 64; atque <lb></lb>adeo tubus prædictus implebit horæ ſpa<lb></lb>tio ciſternam capacem librarum <lb></lb>aquæ 159552. </s></p> <pb xlink:href="051/01/166.jpg" pagenum="135"></pb> <figure id="id.051.01.166.1.jpg" xlink:href="051/01/166/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg240"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg240"></margin.target><emph type="italics"></emph>Pariſienſes <lb></lb>libra<emph.end type="italics"></emph.end> 72. <emph type="italics"></emph>ef<lb></lb>ficiunt pe<lb></lb>dem <expan abbr="cubisũ">cubisum</expan> <lb></lb>aquæ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>MErſennus ait, heminas ſeu libras Pariſienſes<emph.end type="italics"></emph.end> 72. <emph type="italics"></emph>efficere pedem <lb></lb>cubicum aquæ. </s><s>Itaque ſi placet prædictas libras ad pedes cubi<lb></lb>cos reducere, divide numerum<emph.end type="italics"></emph.end> 159552 <emph type="italics"></emph>per<emph.end type="italics"></emph.end> 72, <emph type="italics"></emph>& quotiens<emph.end type="italics"></emph.end> 2216 <emph type="italics"></emph>da<lb></lb>bit aquæ pedes cubicos quos horæ ſpatio fundet tubus<emph.end type="italics"></emph.end> ADB. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XVIII. Problema II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis altitudine & lumine tubi ſemper pleni, invenire <lb></lb>tempus quo datam aquæ quantitatem effundat, ſi<lb></lb>ve quo datam ciſternam impleat.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt tubus ſemper plenus ADB, v.g. 16 pedes altus, lumen </s></p> <p type="main"> <s> <arrow.to.target n="marg241"></arrow.to.target><lb></lb>habens digitale DB; ſit verò quantitas aquæ à tubo ADB <lb></lb>effundendæ, aut ciſterna ab eodem replenda, 3000 pedum cu<lb></lb>bicorum. </s><s>Oporteat invenire tempus quo dictam aquam ef<lb></lb>fundat, aut dictam ciſternam impleat. </s></p> <p type="margin"> <s><margin.target id="marg241"></margin.target><emph type="italics"></emph>Data alti<lb></lb>tudine & <lb></lb>foramine <lb></lb>tubi, inve<lb></lb>nire tempus <lb></lb>quo data a<lb></lb>qua effluit.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Revocentur primò 3000 pedes cubici aquæ ad heminas <lb></lb> <arrow.to.target n="fig34"></arrow.to.target><lb></lb>ſeu libras (quod fiet, ſi 3000 multiplica<lb></lb>bis per 72. fiatq, numerus librarum 216000, <lb></lb>(quandoquidem unus pes cubicus conficit <lb></lb>72 libras, ut diximus Propoſit: præceden<lb></lb>te in Annotat:) Deinde ſumatur ex ADB, <lb></lb>tubus quadrupedalis EDB: Demum inter <lb></lb>ADB altitudinem, id eſt, 16, & EDB alti<lb></lb>tudinem, id eſt, 4, inveniatur medius nu<lb></lb>merus proportionalis 8. </s><s>Igitur, per Pro<lb></lb>poſit. VIII. præcedentem, aqua fluens per <lb></lb>tubum EDB, eſt ad aquam per tubum <lb></lb>ADB eodem tempore fluentem, ut 4 ad 8, <lb></lb>in ratione videlicet ſubduplicata altitudi<lb></lb>num EDB 4 pedum, & ADB 16 pedum. </s><s><lb></lb>Quo ergo tempore dat tubus ADB 3000 <lb></lb>pedes cubicos aquæ, id eſt, 216000 hemi<lb></lb>nas ſeu libras; eodem tempore EDB dabit duplò minus, ſeu <pb xlink:href="051/01/167.jpg" pagenum="136"></pb> <arrow.to.target n="fig35"></arrow.to.target><lb></lb>heminas ſolùm 108000. </s><s>Aſſumatur jam, <lb></lb>ut antea, tubus quadrupedalis CPK lu<lb></lb>minis linearis. </s><s>Tubi EDB, CPK, ſunt æ<lb></lb>què alti; & lumina DB, PK, dantur, per 1. <lb></lb>Propoſit. lib. 12. Euclid. nempe 1, & 144 <lb></lb>lineæ quadratæ; aqua etiam quam CPK <lb></lb>fundit ſpatio 13 ſecundorum, datur, per VII. <lb></lb>præcedentem, una nimirum libra: Qua<lb></lb>re cùm quantitates aquæ à tubis æquè al<lb></lb>tis eodem tempore effuſæ ſint ut lumina, <lb></lb>per Propoſit. XIII. præcedentem, ſi fiat ut <lb></lb>lumen PK, ad lumen DB, id eſt, ut 1 ad <lb></lb>144, ita aqua unius ad aquam alterius; pro<lb></lb>ducetur numerus heminarum ſeu libra<lb></lb>rum, quas effundit tubus EDB ſpatio tre<lb></lb>decim ſecundorum, nempe 144. </s><s>Quo<lb></lb>niam igitur tubus EDB 144 libras dat ſpatio tredecim ſecundo<lb></lb>rum; libras 108000 quanto tempore dabit? </s><s>Fiat, ut 144 libræ <lb></lb>ad <gap></gap> hoc eſt, ad tredecim ſecunda, ita 108000 ad 9750; dabit <lb></lb>hic numerus ſecunda, quibus tubus EDB dat libras 108000. </s><s><lb></lb>Sed oſtenſum eſt ſuprà, quo tempote tubus EDB dat 108000 <lb></lb>libras, tubum ADB dare libras 216000, id eſt, 3000 pedes cu<lb></lb>bicos aquæ; Inventum eſt igitur tempus, quo tubus ADB ſem<lb></lb>per plenus fundit datam aquam 3000 pedum cubicorum, nem<lb></lb>pe 9750 ſecunda, ſeu 162 prima; quæ faciunt horas 2, & 42 <lb></lb>minuta prima. </s></p> <figure id="id.051.01.167.1.jpg" xlink:href="051/01/167/1.jpg"></figure> <figure id="id.051.01.167.2.jpg" xlink:href="051/01/167/2.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Propoſitio XIX. Problema III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis tempore, quantitate aquæ, ſeu Ciſternâ, & lu<lb></lb>mine tubi, invenire altitudinem tubi, qui ſemper <lb></lb>plenus ciſternam dato tempore repleat.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg242"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg242"></margin.target><emph type="italics"></emph>Dato tem<lb></lb>pore, & <lb></lb>quantitate <lb></lb>aquæ, inve<lb></lb>nire tubum <lb></lb>ex quo ef<lb></lb>fluat.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>SIt datum tempus unius horæ & 21 minutorum primorum, <lb></lb>aqua data 3000 pedum cubicorum, ſeu 216000 librarum <lb></lb>capax ciſterna, & lumen ſeu foramen tubi digitale, ſeu duo- <pb xlink:href="051/01/168.jpg" pagenum="137"></pb>decim linearum. </s><s>Oporteat invenire altitudinem tubi qui unâ <lb></lb>horâ & 21 minutis primis ex foramine digitali ejiciat 216000 <lb></lb>libras aquæ, ſeu repleat ciſteruam 3000 pedum cubicorum. </s></p> <p type="main"> <s>Quoniam tubus quadrupedalis, cujus lumen digitale, eji<lb></lb>cit tredecim ſecundorum ſpatio libras 144, ut vidimus Pro<lb></lb>poſit. XVII. præcedente, & idem tubus ſpatio duarum hora<lb></lb>rum, ac 42 minutorum primorum ejicit libras 108000, ut vi<lb></lb>dimus Propoſit. XVIII. præcedente; ergo duplum hujus aquæ, <lb></lb>hoc eſt, libræ 216000, ejicientur à tubo ejuſdem luminis alto <lb></lb>pedes 16. eò quòd tuborum æqualium foraminum altitudines <lb></lb>debeant eſſe in duplicata ratione aquarum, ut duplo plùs aquæ <lb></lb>eodem tempore fundant, prout diximus Propoſit. VIII. Pori<lb></lb>ſmate 1. </s><s>Ut verò eadem aqua effluat ex tubo ejuſdem fora<lb></lb>minis duplo velociùs, hoc eſt, intra horam unam, minuta 21; <lb></lb>debet tubus eſſe altus pedes 64, ut patet ex Poriſmate Propo<lb></lb>ſit. X. & XII. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SImili ratione datis tempore, ciſterna, & altitudine tubi, in<lb></lb>venitur foramen tubi, qui ciſternam datam repleat in illo <lb></lb>tempore. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XX. Problema IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato Vaſe, & foramine per quod effluit aqua, <lb></lb>invenire tempus quo evacuatur.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt datum vas priſmaticum ABCD, cujus tam longitudo, </s></p> <p type="main"> <s> <arrow.to.target n="marg243"></arrow.to.target><lb></lb>quàm latitudo ſit decem pedum, altitudo vero 16 pedum, <lb></lb>ac proinde capacitas totius vaſis ſit 1600 pedum cubicorum, <lb></lb>baſis verò ſit 100 pedum quadratorum; lumen denique ſeu <lb></lb>foramen E in fundo vaſis ſit digitale. </s><s>Oporteat invenire tem<lb></lb>pus quo dictum vas, ſi aquâ fuerit plenum, per lumen E eva<lb></lb>cuetur. </s></p> <pb xlink:href="051/01/169.jpg" pagenum="138"></pb> <p type="margin"> <s><margin.target id="marg243"></margin.target><emph type="italics"></emph>Dato vaſe, <lb></lb>& forami<lb></lb>ne, inveni<lb></lb>re tempus <lb></lb>quo evacua<lb></lb>tur.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.169.1.jpg" xlink:href="051/01/169/1.jpg"></figure> <p type="main"> <s>Conſtat ex dictis Pro<lb></lb>poſit. XIV. in Annotat. tu<lb></lb>bum quadrupedalem, cu<lb></lb>jus baſis pedalis, & lumen <lb></lb>lineare, ſpatio 144. minu<lb></lb>torum, ſeu duabus horis <lb></lb>& 24 minutis, totum ex<lb></lb>hauriri, ſi non ſit ſemper <lb></lb>plenus. </s><s>Conſtat præterea <lb></lb>ex eadem Propoſitione, <lb></lb>tubos non ſemper plenos, <lb></lb>æquè altos, & æqualium <lb></lb>foraminum, ſed inæqua<lb></lb>lium baſium, evacuari in<lb></lb>æqualibus temporibus; <lb></lb>& tempora quibus evacuantur, eſſe inter ſe, vt baſes. </s><s>Aſſuma<lb></lb>tur igitur tubus priſmaticus quadrupedalis KL, baſim habens <lb></lb>pedalem, & lumen lineare. </s><s>Aſſumatur præterea ex vaſe dato <lb></lb>ABCD, pars CFDH alta pedes quatuor, baſſim habens ean<lb></lb>dem cumtoto vaſe centum pedum, lumen verò 1 lineare. </s><s>Quo<lb></lb>niam igitur, per Propoſitionem XIV. dictam, tempora quibus <lb></lb>vas CFDH, & tubus KL exhauriuntur per lumen lineare, ſunt <lb></lb>inter ſe ut baſes ipſorum; baſes autem ex hypotheſi habent pro<lb></lb>portionem ut 100. ad 1; neceſſe eſt, tempus quo evacuatur vas <lb></lb>CFDH per lineare lumen 1, ad tempus quo evacuatur tubus <lb></lb>KL per lumen etiam lineare, eſſe ut 100 ad 1. </s><s>Quare cùm tu<lb></lb>bus KL per lineare lumen evacuetur ſpatio 144 minutorum, <lb></lb>ut vidimus; evacuabitur vas CFDH, per lineare lumen 1, ſpa<lb></lb>tio 14400 minutorum, (tot enim producuntur, ſi 144 multi<lb></lb>plicentur per 100) ſeu horarum 240, vel dierum decem. </s><s>Iam <lb></lb>verò quoniam per Propoſit. XVI. tempus quo effluitaqua ex va<lb></lb>ſe CFDH per lumen digitale E, ad tempus quo effluit eadem <lb></lb>aqua ex eodem vaſe per lumen lineare 1, eſt reciprocè, ſicut <lb></lb>eſt foramen 1 ad foramen E, nempe ut 1 ad 144; ſi dividatur <pb xlink:href="051/01/170.jpg" pagenum="139"></pb>tempus quo effluit aqua per foramen 1, nempe 14400 minuta, <lb></lb>per 144; hoc eſt, ſi accipiatur centeſima quadrageſima quarta <lb></lb>pars minutorum 14400, nempe minuta 100; habebitur tem<lb></lb>pus quo exhauritur vas CFDH, per digitale lumen E. </s><s>Tan<lb></lb>dem quoniam per Propoſit. XV. præcedentem, tempora qui<lb></lb>bus deplentur vaſa ABCD, CFDH. æqualium baſium, ſed non <lb></lb>æqualium altitudinum, per idem foramen E, ſunt in ſubdu<lb></lb>plicata ratione altitudinum, nempe pedum 4, & pedum 16; <lb></lb>ſi inter 4 & 16 inveniatur medius numerus proportionalis, nem<lb></lb>pe 8; erit tempus quo evacuatur vas CFDH, per lumen digita<lb></lb>le E, nimirum 100 minutorum, ad tempus quo evacuatur vas <lb></lb>ABCD per idem lumen digitale E, ut 4 ad 8, ſeu ut 1 ad 2, <lb></lb>nempe ut minuta 100, ad minuta 200, quæ efficiunt horas 3. <lb></lb>min. 20. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVod diximus de vaſe priſmatico, debet etiam intelligi de cylindrico, <lb></lb>& cuiuscunque alterius figuræ; ſed tunc aſſumi debet tubus quadru<lb></lb>pedalis vaſi ſimilis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XXI. Problema V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato vaſe, & tempore, invenire foramen per quod <lb></lb>evacuetur tempore dato.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt data ciſterna A, 1600. pe <arrow.to.target n="table1"></arrow.to.target><lb></lb> <arrow.to.target n="marg244"></arrow.to.target><lb></lb>dum cubicorum; & tempus <lb></lb>B, quo evacuandum eſt totum, <lb></lb>ſit horarum 40 & minutorum <lb></lb>16; ſitque inveniendum foramen, per quod evacuetur ciſter<lb></lb>na A data, in tempore B dato. </s><s>Aſſumatur quodvis lumen ſeu <lb></lb>foramen notæ magnitudinis, v.g. lineare; & per Propoſitionem <lb></lb>XX. præcedentem inveniatur tempus C, quo ciſterna A hu<lb></lb>mido plena, evacuetur tota per lumen lineare. </s><s>Quoniam igi<lb></lb>tur, per Propoſit. XVI. præcedentem, tempora quibus evacuan<lb></lb>tur vaſa non ſemper plena, ſimilia, & æqualia quoad altitudinem <pb xlink:href="051/01/171.jpg" pagenum="140"></pb>& baſes, per lumina ſimilia inæqualia, ſunt reciprocè ut lumina; <lb></lb>& è contrario, lumina prædictorum vaſorum ſunt reciprocè ut <lb></lb>tempora, quibus evacuantur, ut diximus in Poriſmate dictæ <lb></lb>Propoſitionis XVI; ſi fiat ut tempus B, ad tempus C, quo per <lb></lb>lineare lumen effluit ciſterna A, ita lumen lineare ad aliud; <lb></lb>hoc ipſum erit lumen quod quærebatur. </s></p> <p type="margin"> <s><margin.target id="marg244"></margin.target><emph type="italics"></emph>Dato vaſe <lb></lb>& tempore, <lb></lb>invenire <lb></lb>foramen.<emph.end type="italics"></emph.end></s></p> <table> <table.target id="table1"></table.target> <row><cell>ciſt.</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"></emph>Propoſitio XXII. Problema VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Altitudinem ſcaturiginis dati fontis per tubos <lb></lb>fluentis invenire.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg245"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg245"></margin.target><emph type="italics"></emph><expan abbr="Altitudinẽ">Altitudinem</expan> <lb></lb>Scaturigi<lb></lb>nis fontis in<lb></lb>venire per <lb></lb>tubos fluen<lb></lb>tis.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.171.1.jpg" xlink:href="051/01/171/1.jpg"></figure> <p type="main"> <s>FIat notum lumen, per quod fontis a<lb></lb>qua fluat; aut fonti lumen notæ ma<lb></lb>gnitudinis applica, v.g. lineare. </s><s>Ob<lb></lb>ſerva deinde quot aquæ libras fons per <lb></lb>lineare <expan abbr="lumẽ">lumen</expan> effundat ſpatio unius minuti primi, ſeu 60 minuto<lb></lb>rum ſecundorum; ſitque numerus ille librarum B. </s><s>Quoniam <lb></lb>igitur per Propoſit. VII. huius capitis, tubus quadrupedalis ſemper <lb></lb>plenus per lumen lineare effundit ſpatio tredecim ſecundorum <lb></lb>vnam libram, & conſequenter ſpatio 60 ſecundorum, ſeu unius <lb></lb>minuti primi, libras 4 8/13: & præterea, quoniam per Poriſma I. <lb></lb>Propoſit. VIII. huius capitis, altitudines tuborum, habentium <lb></lb>idem ſeu æquale lumen, ſunt in duplicata ratione eius quam ha<lb></lb>bent aquæ quantitates per tubos <expan abbr="eodẽ">eodem</expan> tempore effusæ: ſi fiat, ut <lb></lb>4 8/13 lib. ad numerum librarum B, ita altitudo 4 pedum, ad aliud, <lb></lb>nempe ad altitudinem numeri M; & iterum, ut 4 ad M, ita M <lb></lb>ad N; dabit numerus N altitudinem ſcaturiginis in pedibus, <lb></lb>eò quòd ratio 4 ad N ſit duplicata rationis 4 ad M, ſeu ratic<lb></lb>nis 4 8/13 ad B, nimirum aquæ ad aquam. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XXIII. Problema VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Data alicuius tubi, aut vaſis erogatorij altitudine, ac <lb></lb>tempore, quo determinatam aquæ quantitatem è ſuo lumine <lb></lb>effundit, invenire altitudinem eiusdem autalterius tubi, qui <lb></lb>æquali tempore, per æquale lumen, aliam determi<lb></lb>natam aquæ quantitatem effundat.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/172.jpg" pagenum="141"></pb> <p type="main"> <s>SIt tubi vel alterius vaſis erogatorij aquâ ſemper pleni altitudo <lb></lb> <arrow.to.target n="marg246"></arrow.to.target><lb></lb>9. pedum, ex cuius lumine ſpatio unius minuti ſaliat una aquæ <lb></lb>libra, ſit autem producenda altitudo eò uſque, ut æquali ſpatio <lb></lb>minuti, per idem aut æquale lumen effundat 16. libras aquæ. </s><s>Du<lb></lb>plicetur ratio 16 ad 1, & proveniet ratio 256 ad 1; nam 16 ducta in <lb></lb>16 efficiunt 256: cumque 9 referat unitatem, multiplica 256 per <lb></lb>9, & provenient 2304, pro tubi aut alterius vaſis quæſiti alti<lb></lb>tudine. </s><s>Ratio eſt, quia tubi habent duplicatam rationem a<lb></lb>quarum, per Propoſit. VIII. huius capitis. </s><s>Si itaque fiat, ut 1 ad <lb></lb>256, ita 9 ad aliud; provenient 2304. </s></p> <p type="margin"> <s><margin.target id="marg246"></margin.target><emph type="italics"></emph>Data tubi <lb></lb>altitudine, <lb></lb>ac tempore <lb></lb>effiuentis a<lb></lb>quæ deter<lb></lb>minatæ, in<lb></lb>venire alti<lb></lb>tudinem <lb></lb>pro alia a<lb></lb>quæ quanti<lb></lb>tate.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XXIV. Problema VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>In tubo ſeu vaſe non ſemper pleno determinare ſpatia, <lb></lb>quæ temporibus æqualibus ſibi ſuccedentibus evacuantur; <lb></lb>vti & menſuram ſeu pondus aquæ quæ effluit.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>PArte 2. Claſſe 1. cap. 4. inter alias Machinas afferemus varia liy<lb></lb>drologia, ſeu horologia aquatica, quibus per fluxum aquæ è <lb></lb> <arrow.to.target n="marg247"></arrow.to.target><lb></lb>foramine alicui<emph type="sup"></emph>9<emph.end type="sup"></emph.end> tubi, aut vaſis, metimur horas æquales ſeu ęqua<lb></lb>les temporis partes, ſignando in vaſis latere lineas determinantes <lb></lb>fluxum æqualibus temporibus correſpondentem. </s><s>At quoniam <lb></lb>ex dictis ſuprà Propoſitione VI. conſtat, ſpatia quæ æqualibus <lb></lb>temporibus evacuantur, non eſſe æqualia, ſed ſemper minora <lb></lb>atque minora evadere, eò quòd æqualibus temporibus non ef<lb></lb>fluat æqualis aquæ copia, ſed ſemper minor ac minor; ideo de<lb></lb>terminandum híc eſt, quomodo geometricè inveniendum ſit in <lb></lb>quolibet vaſe dictum ſpatiorum decrementum, ſeu quomodo <lb></lb>dividendum ſit latus vaſis, ut ſpatia adſignata æqualibus tem<lb></lb>poribus evacuentur. </s><s>Iterum quoniam per dicta eâdem Pro<lb></lb>poſitione VI, aqua quæ æqualibus temporibus effluit è dictis va<lb></lb>ſis, non eſt æqualis, ſed in æqualis; determinandum eſt, quan<lb></lb>tum quovis æquali tempore effluat. </s></p> <p type="margin"> <s><margin.target id="marg247"></margin.target><emph type="italics"></emph>In tubo de<lb></lb>terminare <lb></lb>ſpatia que <lb></lb>temporibus <lb></lb>æqualibus <lb></lb>evacuan<lb></lb>tur.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Dico itaque, aquam æqualibus temporibus effluere è tu<lb></lb>bis non ſemper plenis ea ratione, ut ſingulis temporibus decre- <pb xlink:href="051/01/173.jpg" pagenum="142"></pb>ſeat & aquæ effuſæ quantitas, & vaſis ſeu tubi evacuati ſpatium, <lb></lb>& aquæ deſcendentis ac effluentis velocitas eo decremento, <lb></lb>quod eſt inter numeros impares, verſus unitatem. </s><s>Explico. </s><s>Sit <lb></lb>vas quodcunque aquâ plenum, eius fluxus dividere debeat di<lb></lb>em, aut quam cunque diei partem, in quatuor æquales partes; <lb></lb>ſintque in vaſe 16 v.g. menſuræ ſeu libræ aquæ, quæ dato <lb></lb>tempore effluant. </s><s>Dico, primo tempore effluere ſeptem men<lb></lb>ſuras, ſecundo quinque, tertiò tres, quarto & ultimo unam. </s></p> <p type="main"> <s>Dico iterum, ſi tota vaſis altitudo ab infima ad ſupremam <lb></lb>aquæ ſuperficiem dividatur in 16 æquales partes, aquam in pri<lb></lb>mo tempore deſcendere ad 7 ſpatia, in ſecundo ad <expan abbr="quinq;">quinque</expan> in ter<lb></lb>tio ad tria, in quarto ad unum. </s><s>Dico tandem, aquam in pri<lb></lb>ma hora deſcendere <expan abbr="atq;">atque</expan> effluere ut ſeptem, in ſecunda ut quin<lb></lb>que, in tertia ut tria, in quarta ut unum. </s><s>Sequitur ex dictis <lb></lb>ſuprà Propoſitione 8, 9, & 10, quas vide. </s><s>Eadem ratio in <lb></lb>omnibus alijs eſt. </s></p> <p type="main"> <s><emph type="center"></emph>Corollarium.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg248"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg248"></margin.target><emph type="italics"></emph>Vas parare, <lb></lb>cuius flux<emph type="sup"></emph>9<emph.end type="sup"></emph.end><lb></lb>dividat da<lb></lb>tum tempus <lb></lb>in partes <lb></lb>æquales.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>EX his patet, quomodo parandum ſit vas, cuius fluxus dato <lb></lb>tempore durans dividat illud tempus in partes æquales. </s><s>Sit <lb></lb>enim vas, cuius fluxus duret per ſpatium duodecim horarum, & <lb></lb>hoc ſpatium temporis ſit dividendum, beneficio fluxus aquæ, in <lb></lb>12 æquales partes ſeu horas. Duc 12. in ſeipſa, & produces 144. <lb></lb>Deinde divide vaſis altitudinem à ſuprema ad infimam aquæ ſu<lb></lb>perficiem, in 144 partes ſeu ſpatia æqualia, & inferiùs prope <lb></lb>fundum vaſis incipiendo, deputa ultimæ horæ ex duodecim <expan abbr="vnũ">vnum</expan> <lb></lb>ſpatiolum, penultimæ tria, ante penultimæ quinque, & ſic ul<lb></lb>teriùs progredere ſecun dùm ſeriem ſeu progreſſionem numero<lb></lb>rum <expan abbr="impatiũ">impatium</expan>, prout apparet in numeris lateri dextro CD ſequen<lb></lb>tis figuræ appoſitis. </s><s>His pręſtitis, diviſum erit vas in ſpatia inęqua<lb></lb>lia, quę ſingulis æqualibus temporibus, nempe horis, evacuantur, <lb></lb>videbiſque aquam in prima hora deſcendere à ſpatio ultimo ſeu <lb></lb>144, uſque ad ſpatium 121; in ſecunda hora uſque ad ſpatium <lb></lb>100; in tertia uſque ad 81; & ſic porrò uſque ad finem; prout <pb xlink:href="051/01/174.jpg" pagenum="143"></pb> <arrow.to.target n="fig36"></arrow.to.target><lb></lb>apparet in numeris lateri ſiniſtro AB eiuſdem <lb></lb>figuræ appoſitis. </s><s>Lege Torricellum lib. 2. de <lb></lb>motu projectorum. </s></p> <figure id="id.051.01.174.1.jpg" xlink:href="051/01/174/1.jpg"></figure> <p type="main"> <s>Eadem ratione reperies, quot partes, aut <lb></lb>menſuræ certæ, ſeu pondera aquæ effluant ex va<lb></lb>ſe in ſingulis horis. </s><s>Item qua velocitate effluat <lb></lb>atque deſcendatin ijsdem, ſingulis horis. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>NVmeri dextri lateris<emph.end type="italics"></emph.end> CD <emph type="italics"></emph>indicant etiam partes <lb></lb>ſeu ſpatiola vaſis, quæ percurrit aqua ſingulis horis <lb></lb>ſuo motu deſcensûs; ſimiliter & partes aquæ, quæ ſingu<lb></lb>lis horis effluunt, & velocitatem, quâ effluunt. </s><s>Nam <lb></lb>in prima hora percurrit ſpatia<emph.end type="italics"></emph.end> 23, <emph type="italics"></emph>in ſecunda<emph.end type="italics"></emph.end> 21, <emph type="italics"></emph>in <lb></lb>tertia<emph.end type="italics"></emph.end> 19, <emph type="italics"></emph>in quarta,<emph.end type="italics"></emph.end> 17, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Numeri ſiniſtri lateris<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>ſunt duodecim qua<lb></lb>drata temporis in duodecim horas diviſi. </s><s>Nam<emph.end type="italics"></emph.end> 1 <emph type="italics"></emph>eſt <lb></lb>quadratum horæ primæ, incipiendo ab ultima;<emph.end type="italics"></emph.end> 4 <emph type="italics"></emph>eſt <lb></lb>quadratum horæ ſecundæ,<emph.end type="italics"></emph.end> 9 <emph type="italics"></emph>eſt quadratum horæ ter<lb></lb>tiæ &c. vt patet, ſi ſinguli numerimedio figuræ inſeri<lb></lb>pti multiplicentur per ſeipſos. </s><s>Et hoc eſt, quod dixi<lb></lb>mus ſuprà Propoſit.<emph.end type="italics"></emph.end> IX. <emph type="italics"></emph>in motu gravium naturaliter <lb></lb>deſcendentium ſpatia æqualibus temporibus transmiſ<lb></lb>ſa eſſe inter ſe, ut quadrata temporum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>SI vas aliquod dividere velles in partes<emph.end type="italics"></emph.end> 24, <emph type="italics"></emph>multi<lb></lb>plica<emph.end type="italics"></emph.end> 24 <emph type="italics"></emph>per<emph.end type="italics"></emph.end> 24, <emph type="italics"></emph>producentur<emph.end type="italics"></emph.end> 576. <emph type="italics"></emph>Divide ergo <lb></lb>altitudinem vaſis in<emph.end type="italics"></emph.end> 576 <emph type="italics"></emph>partes æquales, & procede <lb></lb>ut dictum in Corollario, juxta ſeriem numerorum im<lb></lb>parium. </s><s>Eadem ratione quotlibet vas in quotlibet <lb></lb>partes partieris.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVoniam quando in vaſe exigua eſt aqua, ut vix <lb></lb>fundum operiat, fluxus ipſius guttatim & non<emph.end type="italics"></emph.end> <pb xlink:href="051/01/175.jpg" pagenum="144"></pb> <arrow.to.target n="fig37"></arrow.to.target><lb></lb><emph type="italics"></emph>continuè ſit, ideo〈qué〉 aqua fluens guttulis ſuis errorem in<lb></lb>ducere poteſt; meliùs eſt, ſi duæ ultimæ diviſiones ſeu <lb></lb>ſpatiola vaſis diviſi, notata numeris<emph.end type="italics"></emph.end> 1 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 3, <emph type="italics"></emph>non ve<lb></lb>niant in numerum ſpatiolorum, & potiùs verſus prin<lb></lb>cipium adjiciantur alia duo ſpatia; ſicque vas, de quo <lb></lb>in Corollario, non dividatur in<emph.end type="italics"></emph.end> 12, <emph type="italics"></emph>ſed in<emph.end type="italics"></emph.end> 14 <emph type="italics"></emph>partes, <lb></lb>modo ibi dicto, dividendo totam ipſius altitudinem <lb></lb>in partes æquales<emph.end type="italics"></emph.end> 196 <emph type="italics"></emph>(qui numerus reſultat ex ductu <lb></lb>numeri<emph.end type="italics"></emph.end> 14 <emph type="italics"></emph>in ſeipſum) & addendo ſpatium<emph.end type="italics"></emph.end> 13, <emph type="italics"></emph>&<emph.end type="italics"></emph.end><lb></lb>14, <emph type="italics"></emph>quæ demptis duobus infimis efficiant duodecim <lb></lb>ſpatia.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.175.1.jpg" xlink:href="051/01/175/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>PARERGVM CAPITIS TERTII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De inventione mediæ, ac tertiæ propor<lb></lb>tionalis quantitatis, in numeris, & <lb></lb>lineis.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>EXdictis hoc Capite patet, quàm ſæpe neceſſa<lb></lb>ria ſit inventio mediæ, ac tertiæ, quartæque <lb></lb>proportionalis quantitatis, ut ex nota aquæ men<lb></lb>ſura, aut pondere, venire poſſimus in cognitio<lb></lb>nem deſideratæ altitudinis tubi, aut vaſis; autè <lb></lb>contrario, ut ex nota tubi altitudine veniamus in <lb></lb>cognitionem menſuræ aut ponderis aquæ, & <lb></lb>quamcunque tuborum altitudinem, aquarumvè <lb></lb>copiam reperiamus facilè per quamcunque ra<lb></lb>tionem ſubduplicatam, aut duplicatam, ſive nu<lb></lb>meris exprimi poſſit, ſive non poſſit exprimi abs<lb></lb>que ſurdis. </s><s>Operæ ergo pretium duxi, Regu<lb></lb>las breviſſimas aſſignare, vel ſaltem inſinuare, <lb></lb>prædictas quantitates inveniendi, mediam dico, <lb></lb>ac tertiam, quartamque proportionalem, tam <lb></lb>arithmeticè, quàm geometricè, libantes breviſ<lb></lb>ſimè nonnulla ex ij, quæ fuſiùs dicemus in Arith<lb></lb>metica, & in Geometria practica, ſeu in <lb></lb>Pantometro Kircheriano. </s></p> <pb xlink:href="051/01/176.jpg" pagenum="145"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Inter duos numeros medium proportiona<lb></lb>lem invenire.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DUos numeros propoſitos multiplica interſe, & ex producto </s></p> <p type="main"> <s> <arrow.to.target n="marg249"></arrow.to.target><lb></lb>erue radicem quadratam; erit hæc radix medio loco pro<lb></lb>portionalis inter duos numeros datos. </s><s>Exemplum. </s><s>Sit inter 4 <lb></lb>& 16 inveniendus medius proportionalis numerus: multiplica <lb></lb>16 per 4, fiunt 64; cuius radix quadrata eſt 8, eſtque medio <lb></lb>loco proportionalis inter 4 & 16; quia ut eſt 4 ad 8, ita 8 ad 16. </s></p> <p type="margin"> <s><margin.target id="marg249"></margin.target><emph type="italics"></emph>Numerum <lb></lb>medium in<lb></lb>ter duos in<lb></lb>venire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis duobus numeris, tertium continuè <lb></lb>proportionalem invenire.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>TRes numeri continuè proportionales dicuntur, quando eſt, <lb></lb> <arrow.to.target n="marg250"></arrow.to.target><lb></lb>ut primus ad ſecundum, ita ſecundus ad tertium. </s><s>Huiusmodi <lb></lb>ſunt 1, 3, 9, & 1, 2, 4: item 2, 4, 8: item 4, 8, 16. </s><s>Propoſitisigi<lb></lb>tur quibuscunque duobus numeris, in venietur tertius, qui ad <lb></lb>ſecundum ſit ut ipſe ſecundus ad primum, ſeu ad quem ſecun<lb></lb>dus ſit ut primus ad ſecundum; ſi ſecundum ducas in ſeipſum; <lb></lb>productus enim erit tertius proportionalis. </s></p> <p type="margin"> <s><margin.target id="marg250"></margin.target><emph type="italics"></emph>Numerum <lb></lb>tertium <expan abbr="pro-portionalẽ">pro<lb></lb>portionalem</expan> <lb></lb>poſt duos in<lb></lb>venire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Inter duas rectas lineas datas invenire mediam <lb></lb>proportionalem.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.176.1.jpg" xlink:href="051/01/176/1.jpg"></figure> <p type="main"> <s>SInt datæ duæ rectæ AB, BC, inter <lb></lb> <arrow.to.target n="marg251"></arrow.to.target><lb></lb>quas invenienda ſit media propor<lb></lb>tionalis. </s><s>Coniungantur rectæ AB, CB <lb></lb>in unam rectam continuam in puncto <lb></lb>B, ut fiat recta ABC; eâque divisâ bi<lb></lb>fariam in D, deſcribatur ſemicirculus <lb></lb>aut circulus AEC, ad intervallum <lb></lb>DA, vel DC; tandemque ex B pun<lb></lb>cto erigatur perpendicularis BE ad <lb></lb>circumferentiam uſque; eritque BE <pb xlink:href="051/01/177.jpg" pagenum="146"></pb>media proportionalis quæſita. </s><s>Demonſtrationem vide apud <lb></lb>Euclidem lib. 6. Propoſit. 13. </s></p> <p type="margin"> <s><margin.target id="marg251"></margin.target><emph type="italics"></emph>Lineam me<lb></lb>diam pro<lb></lb>portionalem <lb></lb>inter duas <lb></lb>invenire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis duabus rectis, invenire tertiam pro<lb></lb>portionalem.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg252"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg252"></margin.target><emph type="italics"></emph>Lineam ter<lb></lb>tiam propor<lb></lb>tionalem <lb></lb>poſt duas in<lb></lb>venire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>SInt datæ duæ rectæ AB, & BE, præcedentis figuræ, ſitque <lb></lb>invenienda tertia, ad quam ita ſe habeat ſecunda, ſicut pri<lb></lb>ma ad ſecundam. </s><s>Coniungantur rectæ AB, BE, in puncto B <lb></lb>ad angulum rectum, ducaturque recta EA; eáque bifariam di<lb></lb>visâ in F, ducatur recta FD perpendicularis ad AE; & facto <lb></lb>centro D, intervallo DA deſcribatur circulus, qui neceſſariò <lb></lb>tranſibit per punctum E, <emph type="italics"></emph>per quintam Quarti Euclid.<emph.end type="italics"></emph.end> Si iam <lb></lb>producatur recta AB <expan abbr="uſq;">uſque</expan> ad circumferentiam circuli, hoc eſt, <lb></lb>uſque ad punctum C; erit BC tertia proportionalis quæſita. </s></p> <p type="main"> <s>Sint iterum datæ duæ rectæ BC, & BE, ſitque invenien<lb></lb>da tertia proportionalis. </s><s>Coniungantur, ut antea, rectæ illæ <lb></lb>in B, ut efficiantangulum rectum, & ducatur recta EC; at<lb></lb>que ex puncto medio G demittatur perpendicularis GD, & <lb></lb>producta recta CB in continuum, deſcribatur centro D, in<lb></lb>tervallo DC, circulus, qui iterum tranſibit per punctum E, <lb></lb>& ſecabit rectam CB productam in A; eritque hæc recta BA <lb></lb>tertia proportionalis quæſita. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVod dictum eſt de lineis hîc poſitis, dicendum eſt de quibuscunque </s></p> <p type="main"> <s> <arrow.to.target n="marg253"></arrow.to.target><lb></lb>line is propoſitis. </s><s>Itaque ſipropoſitis duobus tubis inveniendus ſit <lb></lb>vel medius, veltertius proportionalis; coniunge lineas rectas tubis da<lb></lb>tis æquales; & operare ut dictum, & invenies quod quæris. </s><s>Quòd ſi <lb></lb>tubi propoſiti, ac lineæ ipſis æquales nimis eſſent longæ, ac proinde minùs <lb></lb>commodè circulo includi poſſent; accipe ipſarum ſubmultiplices, v.g. <lb></lb>dimidiam, tertiam, quartam, &c. partem, & cum ipſis procede <lb></lb>ut dictum; eritque inventa linea æquè ſubmultiplex <lb></lb>lineæ aut tubi quæſiti.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/178.jpg" pagenum="147"></pb> <p type="margin"> <s><margin.target id="marg253"></margin.target>Tubum me<lb></lb>dium & ter<lb></lb>tium propor<lb></lb>tionalem in<lb></lb>venire.</s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aliter invenire tertiam proportionalem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>QUod fecimus in pręcedenti Propoſitione mediante circulo, <lb></lb> <arrow.to.target n="marg254"></arrow.to.target><lb></lb>fieri poteſt faciliùs absque circulo ſic. </s></p> <p type="margin"> <s><margin.target id="marg254"></margin.target><emph type="italics"></emph>Lineam ter<lb></lb>tiam pro<lb></lb>portionalem <lb></lb>aliter inve<lb></lb>nire.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.178.1.jpg" xlink:href="051/01/178/1.jpg"></figure> <p type="main"> <s>Duæ rectæ datæ, AB, & BE, con<lb></lb>ſtituantur ad angulum rectum ABE, <lb></lb>ut dictum, & ducatur recta EA. </s><s>Pro<lb></lb>ductâ deinde AB, antecedente ſeu <lb></lb>primâ duarum datarum, ducatur ex E <lb></lb>ad AE perpendicularis EC, occur<lb></lb>rensipſi AB productæ in C; eritque <lb></lb>BC tertia proportionalis. </s></p> <p type="main"> <s>Si eſſent propoſitæ duæ rectæ CB, <lb></lb>BE, deberent ipſæ coniungi ad angu<lb></lb>lum rectum CBE, & ductâ rectâ CE, <lb></lb>productaque CB, deberet duci per<lb></lb>pendicularis AE, ad rectam CE, <expan abbr="eſſetq́ue">eſſetque</expan> AB tertia quæſita. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>INventâ alterutro modorum tertiâ continuè proportionali, ſi primam <lb></lb>omiſeris, & alijs duabus tertiam inveneris; habebis quatuor leneas <lb></lb>continuè proportionales. </s><s>Eodemque modo invenies quintam, ſextam, <lb></lb>ſeptimam, & quamcunque aliam.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Adhuc aliter invenire tertiam proportionalem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SI difficile tibi videtur ducere tot perpendiculares ad inveni<lb></lb> <arrow.to.target n="marg255"></arrow.to.target><lb></lb>endam tertiam proportionalem, uti poteris modo præſcripto <lb></lb>ab Euclide lib. 6. Propoſit. 11. ſic: </s></p> <p type="margin"> <s><margin.target id="marg255"></margin.target><emph type="italics"></emph>Adhuc ali<lb></lb>ter item pre<lb></lb>ſtare.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.178.2.jpg" xlink:href="051/01/178/2.jpg"></figure> <p type="main"> <s>Sint duæ rectæ AB, AE. </s><s><lb></lb><expan abbr="Diſponãtur">Diſponantur</expan> eæita, ut efficiant <lb></lb>angulum A quemcunque, <lb></lb>producaturque AB quam vis <lb></lb>eſſe antecedentem ſeu <expan abbr="primã">primam</expan>, <lb></lb>& capiatur BC æqualis ipſi <lb></lb>AE, quæ conſequens eſſe de- <pb xlink:href="051/01/179.jpg" pagenum="148"></pb> <arrow.to.target n="fig38"></arrow.to.target><lb></lb>bet, ſive ſecunda, aut media. </s><s><lb></lb>Deinde ductâ rectâ AB, aga<lb></lb>tur illi ex C parallela CD, <lb></lb>occurrensipſi AE productæ, <lb></lb>in D; eritque ED tertia <lb></lb>proportionalis quæſita. </s></p> <figure id="id.051.01.179.1.jpg" xlink:href="051/01/179/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>SI duæ datæſint nimis longæ, ſervetur id, quod diximus in Annota<lb></lb>tione Propoſitionis quartæ præcedentis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis tribus numeris, invenire quartum pro<lb></lb>portionalem.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg256"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg256"></margin.target><emph type="italics"></emph>Numeris <lb></lb>tribus datis <lb></lb>quartum <lb></lb>proportiona<lb></lb>lem inveni<lb></lb>re.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>UTere Regulâ proportionum apud Arithmeticos notiſſima, <lb></lb>quam Auteam vocant; & habebis intentum. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis tribus rectia lineis, quartam propor<lb></lb>tionaleminvenirc.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg257"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg257"></margin.target><emph type="italics"></emph>Lineis tri<lb></lb>bus datis, <lb></lb><expan abbr="quartã">quartam</expan> pro<lb></lb>portiona<lb></lb>lem inveni<lb></lb>re.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.179.2.jpg" xlink:href="051/01/179/2.jpg"></figure> <p type="main"> <s>SInt tres lineæ rectæ, AB, BC, <lb></lb>AD, quibus invenienda ſit <lb></lb>quarta. proportionalis, ad <lb></lb>quàm ſit tertia AD, ut eſt <lb></lb>prima AB, ad ſecundam BC. </s><s><lb></lb><expan abbr="Diſponãtur">Diſponantur</expan> primæ duæ, AB, <lb></lb>BC, ſecundùm lineam <expan abbr="rectã">rectam</expan> <lb></lb>quæ ſit AC; tertia verò AD, <lb></lb>cum prima AB, faciatangulum A quemcunque: deinde ex B <lb></lb>ad D ducatur recta BD, cui per C ducatur parallela CE, oc<lb></lb>currens rectæ AD productæ, in E puncto. </s><s>Dico, DE, eſſe <lb></lb>quartam proportionalem. </s><s>Demonſtrationem vide apud <lb></lb>Euclidem lib. 6. Propoſit. 12. </s></p> <pb xlink:href="051/01/180.jpg" pagenum="149"></pb> <p type="main"> <s><emph type="center"></emph>CAPVT IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De proprietatibus aquæ ſalientis ex tubis. </s><s><lb></lb>PROOEMIVM.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.180.1.jpg" xlink:href="051/01/180/1.jpg"></figure> <p type="main"> <s><emph type="italics"></emph>CApite præceden<lb></lb> <arrow.to.target n="marg258"></arrow.to.target><lb></lb>ti egimuo de pro<lb></lb>prietatibus a<lb></lb>quæ fluentis per tubos <lb></lb>verticales, hoc eſt, efflu<lb></lb>entis ex foramine facto in <lb></lb>baſibus tuborum: hoc Ca<lb></lb>pite agemus de proprieta<lb></lb>tibus ejuſdem aquæ ſali<lb></lb>entis ex tubis verticali<lb></lb>bus, hoc eſt, effluentis ex <lb></lb>foraminibus lateralib<emph type="sup"></emph>9<emph.end type="sup"></emph.end> <expan abbr="tu-borũ">tu<lb></lb>borum</expan>, ſeu per tubos inferi<lb></lb>ùs inflexos. </s><s>Poſſunt <expan abbr="autẽ">autem</expan> <lb></lb>tubi verticales inferiùs <lb></lb>inflecti triplici modo, ho<lb></lb> <arrow.to.target n="marg259"></arrow.to.target><lb></lb>rizontaliter, verticali<lb></lb>ter, & medio modo. </s><s>Ho<lb></lb>rizontaliter inflexus dici<lb></lb>tur, ſi pars inferior infle<lb></lb>xa ſit horizonti parallela <lb></lb>reſpectu partis reliquæ ver<emph.end type="italics"></emph.end> <pb xlink:href="051/01/181.jpg" pagenum="150"></pb> <arrow.to.target n="fig39"></arrow.to.target><lb></lb><emph type="italics"></emph>ticaliter erectæ; ſeuſi pars <lb></lb>inferior inflexa faciat cum <lb></lb>reliquæ angulum rectum. </s><s><lb></lb>Talis eſt in appoſito ſche<lb></lb>mate tubus<emph.end type="italics"></emph.end> ABC. </s><s><emph type="italics"></emph>Ver<lb></lb>ticaliter inflexus dicitur, <lb></lb>ſi pars inferior inflexa ſit <lb></lb>horizonti perpendicularis <lb></lb>reſpectu reliquæ partis et<lb></lb>iam perpendiculariter e<lb></lb>rectæ. </s><s>Talis eſt in ſche<lb></lb>mate præſenti tubus<emph.end type="italics"></emph.end> ABE. </s><s><lb></lb><emph type="italics"></emph>Medio modo inflexus di<lb></lb>citur, ſipars inferior ne<lb></lb>que parallela eſt horizon<lb></lb>ti, neque perpendicula<lb></lb>ris, ſed inter utrumque <lb></lb>ſitum facit angulum ſe<lb></lb>mirectum ſeu<emph.end type="italics"></emph.end> 45 <emph type="italics"></emph>gradu<lb></lb>um. </s><s>Talis eſt tubus<emph.end type="italics"></emph.end> ABD. </s></p> <p type="margin"> <s><margin.target id="marg258"></margin.target>Proprieta<lb></lb>tes aquæ ſa<lb></lb>lientis ex tu<lb></lb>bis vertica<lb></lb>libus.</s></p> <p type="margin"> <s><margin.target id="marg259"></margin.target>Tubi verti<lb></lb>cale, tripli<lb></lb>citer inflecti <lb></lb>poſſunt in<lb></lb>feriùs.</s></p> <figure id="id.051.01.181.1.jpg" xlink:href="051/01/181/1.jpg"></figure> <p type="main"> <s><emph type="italics"></emph>Easdem appellatio<lb></lb>nes ſubibit tubus inflexus, <lb></lb>ſi pars inferior habeat tria <lb></lb>epiſtomia,<emph.end type="italics"></emph.end> E, D, C, <emph type="italics"></emph>quorum<emph.end type="italics"></emph.end> E <emph type="italics"></emph>ſit erectum perpendiculariter,<emph.end type="italics"></emph.end><lb></lb>C <emph type="italics"></emph>proſtratum horizontaliter,<emph.end type="italics"></emph.end> D <emph type="italics"></emph>inclinatum inter utrum<lb></lb>que, ad dictum angulum. </s><s>Quod fit per tria epiſtomia dicta, <lb></lb>fieri poteſt per unum, ſi ita inſeratur parti inferiori tubi inflexi, <lb></lb>ut verti atque dirigi poſſit in quemcunque ſitum.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/182.jpg" pagenum="151"></pb> <p type="main"> <s><emph type="italics"></emph>Radij aquæ, qui ex inflexo tubo, aut ex epiſtomiis præ-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg260"></arrow.to.target><lb></lb><emph type="italics"></emph>dictis exiliunt, quales ſunt in præcedenti <expan abbr="diagram̃ate">diagrammate</expan> radij<emph.end type="italics"></emph.end> EF, <lb></lb>DI, DK, CG, CH, <emph type="italics"></emph>appellari poſſunt aqueæ virgulæ, aquei ecdro<lb></lb>mi, hoc eſt, excurſus ſeu ſaltus aquæ, & ſimilibus nominibus. </s><s><lb></lb>Marinus tamen Merſennus in Hydraulicis ſuis Phænomenis <lb></lb>appellat eos<emph.end type="italics"></emph.end> ſalientes, <emph type="italics"></emph>aitque eo nomine appellari à Iulio Fron<lb></lb>tino, aliis que veteribus; quare & nos eo vocabulo utemur.<emph.end type="italics"></emph.end> </s><lb></lb> <s><arrow.to.target n="marg261"></arrow.to.target><lb></lb><emph type="italics"></emph>Radius igitur<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>dicatur ſaliens verticalis, Radius<emph.end type="italics"></emph.end> CG, <lb></lb><emph type="italics"></emph>&<emph.end type="italics"></emph.end> CH, <emph type="italics"></emph>ſaliens Horizontalis; radius denique<emph.end type="italics"></emph.end> DI, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DK, <lb></lb><emph type="italics"></emph>ſaliens Medius, et licet ſalientes<emph.end type="italics"></emph.end> CG, CH, <emph type="italics"></emph>nonprocedant ho<lb></lb>rizontaliter, ſed ob aquæ gravitatem ſtatim deprimantur, at<lb></lb>que curventur; vocantur tamen ſalientes horizontales, propter <lb></lb>epiſtomium aut tubulum<emph.end type="italics"></emph.end> C <emph type="italics"></emph>horizontaliter diſpoſitum.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg260"></margin.target>Radij aquę <lb></lb>ex inflexo <lb></lb>tubo exili<lb></lb>entes.</s></p> <p type="margin"> <s><margin.target id="marg261"></margin.target>Salientes <lb></lb>aquæ ex tu<lb></lb>bis quid <lb></lb>ſint.</s></p> <p type="main"> <s><emph type="italics"></emph>His præmſſis, afferemus nunc nonnullas ex multis obſer-<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="marg262"></arrow.to.target><lb></lb><emph type="italics"></emph>vationes, ſeu Phænomena aquæ ſalientis ex tubis, præſertim <lb></lb>ex Marino Merſenno, qui eâ in re diligentiam multorum <lb></lb>vincit. </s><s>His deinde addemus unum aut alterum Problema. </s><s><lb></lb>Atque ex his patebunt proprietates aquæ ſalientis ex tubis.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg262"></margin.target>Phęnome<lb></lb>na aquæ ſa<lb></lb>lientis.</s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio I. Phænomenum. I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salientium ſive ecdromorum horizontalium, & medio<lb></lb>rum, ſuper eodem horizonte, longitudines ſunt in ratione ſub<lb></lb>duplicata tuborum, ex quibus exiliunt.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DIxi, <emph type="italics"></emph>ſuper eodem horizonte;<emph.end type="italics"></emph.end> nam ſuper diverſishorizon<lb></lb>tibus diverſa eſt eiuſdem ſalientis longitudo, etiam <lb></lb>reſpectu eiuſdem tubi, ut dicemus Propoſitione ſe<lb></lb>quenti. </s><s>Voco autem longitudinem horizontalium <lb></lb>ſalientium, diſtantiam in præcedenti ſchemate à puncto z v.g. <lb></lb>ad punctum H, aut G, &C. <pb xlink:href="051/01/183.jpg" pagenum="152"></pb> <arrow.to.target n="marg263"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg263"></margin.target><emph type="italics"></emph>Salientium| <lb></lb>proportio ad <lb></lb>duos tubos.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Sint igitur in præcedenti ſchemate duo tubi, BL pedalis, <lb></lb>& BA quadrupedalis; ſithorizon OHG; ſitque tubi pedalis BL <lb></lb>ſaliens horizontalis CH, tubi verò quadrupedalis BA ſaliens <lb></lb>horizontalis ſit CG. </s><s>Dico, longitudinem ſalientis tubi BL <lb></lb>pedalis, ſcilicet CH, eſſe ſubduplam ſalientis tubi BA, ſcilicet <lb></lb>CG. </s><s>Obſerva vit id Merſennus, ut aſſerit ipſe in ſuis Phænome<lb></lb>nis hydraulicis Propoſit. XVI. </s><s>Quare, ſi longitudo ſalientis tu<lb></lb>bi pedalis eſt unius pedis, longitudo ſalientis tubi quadrupedalis <lb></lb>erit duorum pedum; & longitudo ſalientis tubi ſexde cupedalis <lb></lb>erit quatuor pedum; & longitudo ſalientistubi 64 pedum erit <lb></lb>octo pedum; & ita de reliquis. </s><s>Ratio huius Phænomeni vide<lb></lb>tur deſumenda eſſe à velocitate aquæ deſcendentis per tubos, <lb></lb>quæ etiam eſt in ratione tuborum ſubduplicata, ut conſtat ex <lb></lb>Propoſit. X. Capitis præcedentis. </s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur hinc, altitudines tuborum habere duplicatam ratio<lb></lb>nem eius, quam habent longitudines ſalientium horizonta<lb></lb>lium. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVod dixi in Propoſitione de ſalientibus horizontalibus<emph.end type="italics"></emph.end> CG, CH, <lb></lb><emph type="italics"></emph>debet etiam intelligi de ſalientibus medijs<emph.end type="italics"></emph.end> DK, DI. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg264"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg264"></margin.target><emph type="italics"></emph>Salientium <lb></lb>longitudines <lb></lb>obſervare.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>LOngitudines ſælientium ſuper horizontem quemcun〈qué〉 poteſt quilibet <lb></lb>obſervare facillimè, & ubivis locorum, ſiconficiat ſibi tubulum <lb></lb>præcedentis figuræ<emph.end type="italics"></emph.end> ABC <emph type="italics"></emph>portatilem, determinatæ altitudinis & lati<lb></lb>tudinis, v.g. altumpede vno, & latum digito. </s><s>Si enim apud<emph.end type="italics"></emph.end> C <emph type="italics"></emph>epiſto<lb></lb>mium inſerat, aut etiam ſolum digitum apponat foramini<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>& de<lb></lb>inde repleto tubo epiſtomium aperiat, aut digitum amoveat, ut paucu<lb></lb>læ ſolùm guttulæ exiliant, iterumque obturet foramen; notare poterit <lb></lb>in horizonte ſignum à ſaliente impreſſum; cuiusmodi ſigna <lb></lb>ſunt in ſuperiori ſchemate<emph.end type="italics"></emph.end> K, I, H, G, &C. </s></p> <pb xlink:href="051/01/184.jpg" pagenum="153"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio II. Phænomenon II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salientes horizontales, & mediæ, ejuſdem tubi, co <lb></lb>ſunt longiores, quò lumen tubi fuerit altius ſupra <lb></lb>horizontem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIntin præcedenti diagrammate diverfi horizontes, OG, PS, </s></p> <p type="main"> <s> <arrow.to.target n="marg265"></arrow.to.target><lb></lb>QT, RV &C. ſupra quos elevatus ſit tubus ABC; Dico ſali<lb></lb>entem CHSTV (& idem intelligendum eſt de reliquis ſalienti<lb></lb>bus horizontalibus, ac medijs) ſupra horizontem RV, eſſe <lb></lb>longiorem quàm ſupra horizontem QT, & ſupra hunc longio<lb></lb>rem quàm ſupra PS, & longiorem ſupra hunc, quàm ſupra OG. </s><s><lb></lb>Creſcit itaque eò magis ſalientium horizontalium ac mediarum <lb></lb>longitudo, quo magis creſcit luminis tubi ſuper horizontem ele<lb></lb>vatio. </s><s>Si verò in ex ceſſiva altitudine orificium poneretur; cer<lb></lb>tum eſt aquæ ecdromen uſque ad terminum conſtitutum flu<lb></lb>xum non <expan abbr="continuaturã">continuaturam</expan>, ſed cum tempore in guttas, & tandem <lb></lb>in aërem reſolutum iri, ut experientia docuit in Cuppula S. Petri <lb></lb>interiori, ex quo ſcyphus plenus vino vel aqua effuſus ita evanuit <lb></lb>in intermedio aëre, ut nullum prorſus <expan abbr="veſtigiũ">veſtigium</expan> nec quidem gut<lb></lb>tarum in inferiori pavimento ijs, qui ſtudio id attendebant, ap<lb></lb>paruerit, ut P. Kircherus mihi aſſeruit. </s><s>Ex nubibus tamen de<lb></lb>cidit guttatim in terram aqua, quia in magna copia & continua<lb></lb>tæ decidunt guttæ. </s></p> <p type="margin"> <s><margin.target id="marg265"></margin.target><emph type="italics"></emph>Salientes eo <lb></lb><expan abbr="sũt">sunt</expan> longiores <lb></lb>quò altiù <lb></lb>foramen <lb></lb>tubi.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVanta verò ſit ſalientium in quavis tubi ſupra horizontem eleva<lb></lb>tione longitudo, inveſtigandum eſt obſervatione, quam quilibet <lb></lb>facilè poterit facere modo dicto Propoſitione præcedente. </s><s>Merſennus <lb></lb>in ſuis Phænomenis Propoſit.<emph.end type="italics"></emph.end> XVI. <emph type="italics"></emph>proponit paucas ex multis in ſequen<lb></lb>ti tabella, in quâ Prima Columna continet varias tubi pedalis, velpo<lb></lb>tiùs luminis tubi, ſupra horizontem elevationes in pedibus, ita ut prima <lb></lb>elevatio ſit unius pedis, ſecunda duorum pedum, &c: Secunda verò co<lb></lb>lumna exhibet ſalientium longitudines in pedibus & digitis. </s><s>Addidi<emph.end type="italics"></emph.end> <pb xlink:href="051/01/185.jpg" pagenum="154"></pb> <arrow.to.target n="marg266"></arrow.to.target><lb></lb><emph type="italics"></emph>ego ex eodem Merſenno Propoſit.<emph.end type="italics"></emph.end> 29. <emph type="italics"></emph>ſalientem tubi pedalis elevati pede <lb></lb>uno cum dimidio ſupra horizontem.<emph.end type="italics"></emph.end></s></p> <p type="margin"> <s><margin.target id="marg266"></margin.target><emph type="italics"></emph>Salientium <lb></lb>tabella ex <lb></lb>Merſenno.<emph.end type="italics"></emph.end></s></p> <table> <row><cell>Altitudines tubi ſupra Horizontem.</cell><cell>Longitudines ſalientium</cell></row> <row><cell></cell><cell>Pedes.</cell><cell></cell><cell></cell><cell>Pedes</cell><cell>Digi<gap></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 ſupra Horizontem.</cell><cell>Longitudines ſalientium</cell></row> <row><cell></cell><cell>Pedes.</cell><cell></cell><cell></cell><cell>Pedes</cell><cell>Digi<gap></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"></emph>Annotatio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>Idem Merſennus loco citato Propoſit.<emph.end type="italics"></emph.end> XVII. <emph type="italics"></emph>ait tubum quadrupeda<lb></lb>lem habentem altitudinem unius pedis ſupra horizontem, ejicere ſali <lb></lb>entem horizontalem ad pedes<emph.end type="italics"></emph.end> 3 2/3 <emph type="italics"></emph>proximè.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III. Phænomenon. III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salientes horizontales & mediæ, eandem longitudinis <lb></lb>rationem ſervant, quàm altitudines tuborum ſupra eun<lb></lb>dem horizontem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DIverſas tubi eiuſdem altitudines ſupra horizontem referant <lb></lb>in ſequenti diagrammate lineæ OG, PS, QT, RV. </s><s>Dico, ut <pb xlink:href="051/01/186.jpg" pagenum="155"></pb> <arrow.to.target n="fig40"></arrow.to.target><lb></lb>altitudo BO ad altitudi<lb></lb> <arrow.to.target n="marg267"></arrow.to.target><lb></lb>nem BR, ita eſſe longitu<lb></lb>nem ſalientis CH ad lon<lb></lb>gitudinem ſalientis CV. </s><s><lb></lb>Intelligendum autem hoc <lb></lb>eſt de illis ſalientium lon<lb></lb>gitudinibus, quas ex datis <lb></lb>altitudinibus, obſervare <lb></lb>commodè poſſumus: nam <lb></lb>cùm neſciamus, utrum, & <lb></lb>ubi ſalientium incremen<lb></lb>tum ſit deſiturum, ſi ele<lb></lb>vatio tubi ſupra horizon<lb></lb>tem æquaretur terræ ſe<lb></lb>midiametro; non poteſt <lb></lb>Propoſitio præſens eſſe u<lb></lb>niverſalis, niſi in ſenſu ex<lb></lb>explicato. </s></p> <p type="margin"> <s><margin.target id="marg267"></margin.target><emph type="italics"></emph>Salientes e<lb></lb>andem lon<lb></lb>gitudinis <lb></lb><expan abbr="proportionẽ">proportionem</expan> <lb></lb>ſervant, <lb></lb>quam tubo<lb></lb>rum altitu<lb></lb>dines.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.186.1.jpg" xlink:href="051/01/186/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Propoſitio IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Phænomenon IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salientium verticali<lb></lb>um in <expan abbr="quacunq;">quacunque</expan> elevatio<lb></lb>ne tubi ſupra horizontem <lb></lb>ſemper eadem eſt alti<lb></lb>tudo.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>ESto tubus ABC præ<lb></lb> <arrow.to.target n="marg268"></arrow.to.target><lb></lb>cedentis diagramma<lb></lb>tis, & ſaliens EF, ſitque <lb></lb>horizon RV, & tubus ſit modò in Q, modò in P, modò in O, <lb></lb>modò in B. </s><s>Dico, ſalientis EF <expan abbr="altitudinẽ">altitudinem</expan> eſſe ſemper eandem <lb></lb>in quacunque tubi elevatione ſupra horizontem RV. </s><s>In hori<lb></lb>zontalibus ſalientibus contrarium contingit, ut vidimus Pro<lb></lb>poſitione II. Ratio Phænomeni eſt, quòd altitudo ſalientis <pb xlink:href="051/01/187.jpg" pagenum="156"></pb>EF dependeat ſolùm à tubilongitudine, & lumine E, poſito <lb></lb>æquali ſemper medio ſeu aëre; at in horizontalibus longitudo <lb></lb>dependet etiam à figura ſalientis, de qua Merſennus, & Tor<lb></lb>ricellus. </s></p> <p type="margin"> <s><margin.target id="marg268"></margin.target><emph type="italics"></emph>Salientium <lb></lb>verticali<lb></lb>um altitu<lb></lb>do quæ.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio V. Phænomenon V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Saliens verticalis nunquam adæquat altitu<lb></lb>dinem originis.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg269"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg269"></margin.target><emph type="italics"></emph>Saliens ver<lb></lb>ticalis nun<lb></lb>quam adæ<lb></lb>quat altitu<lb></lb>dinem ori<lb></lb>ginis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>NUnquam enim ſaliens EF æquare poteſt altitudinem tubi <lb></lb>BA. </s><s>Et eadem eſt ratio de alijs omnibus ſalientibus, qua<lb></lb>rum altitudo nunquam æquare poteſt altitudinem originis, ſive <lb></lb>origo ſtatim tubo includatur, ſive non. </s><s>Et ratio eſt, quia gra<lb></lb>vitas humidi, & reſiſtentia aëris impediunt prædictam adæqua<lb></lb>tionem. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VI. Phænomenon VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Saliens verticalis tubi quadrupedalis proximè <lb></lb>æquat 5/6 tubi ſui.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg270"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg270"></margin.target><emph type="italics"></emph>Saliens ver<lb></lb>ticalis tubi <lb></lb>quadrupe<lb></lb>dalis.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>OBſervavit id Merſennus, aſſeritque in ſuis Phænomenis Pro<lb></lb>poſit. XVII. ubi ait, hanc ſalientem poſſe eſſe reliquarum <lb></lb>modulum, ſeu menſuram. </s><s>Vide quæ diximus Propoſitione II. <lb></lb>Annot. 2. ubi idem quod hîc aſſeruimus. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VII. Phænomenon VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Salientes verticales eò ſunt longiores, quò tubi ſunt <lb></lb>longiores; ſed non eâdem proportione illæ ac hi <lb></lb>creſcunt.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg271"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg271"></margin.target><emph type="italics"></emph>Salientium <lb></lb><expan abbr="verticaliũ">verticalium</expan> <lb></lb>longitudo <lb></lb>quȧ propor <lb></lb>tione cre<lb></lb>ſcat.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Vnde licet tuborum non adeo longorum ſalientes verticales <lb></lb>ſint proximè 5/6, aut 2/3 ſuorum tuborum; tamen in tubis <lb></lb>longis ſalientes verticales vix excedunt 1/4 tubi. </s><s>Et hoc prove<lb></lb>nit tum ob aëris reſiſtentiam, tum ob aquæ gravitatem. </s><s>Ita <lb></lb>Merſennus in Phænomenis Propoſit. XVII. </s></p> <pb xlink:href="051/01/188.jpg" pagenum="157"></pb> <p type="main"> <s><emph type="center"></emph>Propoſitio VIII. Problema I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Data tubi altitudine, & ſupra horizontem elevatione, <lb></lb>invenire longitudinem ſalientis horizontalis, <lb></lb>& mediæ.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt altitudo tubi alta pedes 9, cuius os ſit <expan abbr="elevatũ">elevatum</expan> ſupra horizon</s></p> <p type="main"> <s> <arrow.to.target n="marg272"></arrow.to.target><lb></lb>tem pedes quinque, & ſitinvenienda longitudo ſalientis hori<lb></lb>zontalis, aut mediæ, huius tubi. </s><s>Fieri hoc poteſt duplici viâ. </s><s><lb></lb>Primò per obſervationem ſic. </s><s>Applica orificio tubi epiſtomi<lb></lb>um, aut tubulum horizontaliter, aut medio modo, prout opus <lb></lb>fuerit, & nota ſalientis punctum pavimento impreſſum, iuxta <lb></lb>dicta Propoſit. 1. huius Capitis Annotat. II. </s><s>Secundò per <lb></lb>calculum ſic. </s><s>Quoniam, per Propoſitionem I. hujus Capitis, <lb></lb>ſalientium horizontalium & mediarum, ſuper eodem horizonte <lb></lb>longitudines, ſuntin ratione ſubduplicata tuborum; & per di<lb></lb>cta Propoſit. 11. huius eiuſdem Capitis, tubus pedalis pedes quin<lb></lb>que ſupra horizontem elevatus habet ſalientem longam pedes <lb></lb>quatuor; ſi inveniatur media proportionalis inter 1 & 9, nempe <lb></lb>3, erit hæc longitudo quæſita. </s></p> <p type="margin"> <s><margin.target id="marg272"></margin.target><emph type="italics"></emph>Salientis ho<lb></lb>rizontalis <lb></lb>longitudi<lb></lb>nem inve<lb></lb>nire, data <lb></lb>tubi altitu<lb></lb>dine.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IX. Problema II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Data longitudine ſalientis horizontalis, aut mediæ, <lb></lb>invenire altitudinem tubi, cognitâ eius elevatione ſu<lb></lb>pra horizontem.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SIt data longitudo ſalientis horizontalis, aut mediæ, pedum <lb></lb> <arrow.to.target n="marg273"></arrow.to.target><lb></lb>octo, ſit que tubus ipſius elevatus ſupra horizontem pedes <lb></lb>quinque, & in venienda ſit altitudo talis tubi. </s><s>Quoniam, per <lb></lb>Poriſma Propoſit. 1. huius Capitis, altitudines tuborum habent <lb></lb>duplicatam rationem eius, quam habent longitudines ſalienti<lb></lb>um horizontalium, & mediarum; & quoniam ſaliens horizon<lb></lb>talis tubi unius pedis, elevati ſupra horizontem quinque pedi<lb></lb>bus, eſt pedum quatuor; ſi rationem prædictarum ſalientium, <lb></lb>nempe 8 ad 4, duplices, ſeu bis ſumas ſic: 16, 8, 4; erit tertius <lb></lb>numerus 16, altitudo tubi quæſita, hic enim numerus 16 <lb></lb>ad 4, habet duplicatam rationem eius quam <lb></lb>habet 8 ad 4. </s></p> <pb xlink:href="051/01/189.jpg" pagenum="158"></pb> <p type="margin"> <s><margin.target id="marg273"></margin.target><emph type="italics"></emph>Salientis ho<lb></lb>rizontalis <lb></lb>longitudine <lb></lb>data inve<lb></lb>nire tubi al<lb></lb>titudinem.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio X. Problema III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Ex nota ſcaturiginis altitudine fontis unius ex tubo exi<lb></lb>lientis horizontaliter, altitudinem ſcaturiginis cuiuscun<lb></lb>que alterius æqualiter ſupra horizontem elevati <lb></lb>invenire.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg274"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg274"></margin.target><emph type="italics"></emph>Fontis alti<lb></lb>tudine ſca<lb></lb>turiginis da<lb></lb>ta, invenire <lb></lb>alias.<emph.end type="italics"></emph.end></s></p> <table> <row><cell>A</cell><cell>10.</cell><cell>B --</cell></row> <row><cell>8.</cell><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><cell>12.</cell></row> <row><cell>10.</cell><cell>15.</cell><cell>22 1/2.</cell></row></table> <p type="main"> <s>SIt ſcaturigo fontis unius A alta pedes 10; O. <lb></lb>porteat invenire altitudinem ſcaturiginis fon<lb></lb>tis B. </s><s>Idem lumen, ſeu eundem tubulum ap<lb></lb>plica horizontaliter ad utriuſque fontis oſcu<lb></lb>lum, & obſerva ſalientium horizontalium longitudinem; ſitque <lb></lb>fontis A longitudo pedum 8, fontis verò B longitudo ſit <lb></lb>pedum 12. </s><s>Fiat igitur, ut 8 ad 12, ita 10 ad aliud, nempe ad <lb></lb>15; & iterum, ut 10 ad 15, ita 15 ad aliud, nempe ad (22 3/10), ſive <lb></lb>1/2; eritque altitudo ſcaturiginis fontis B pedum 22 1/2. </s></p> <p type="main"> <s>Demonſtratio. </s><s>Per Poriſma Propoſit. 1. hujus Capitis, <lb></lb>altitudines tuborum habent duplicatam rationem ejus, quam <lb></lb>habent longitudines ſalientium horizontalium. </s><s>Quoniam ergo <lb></lb>10, nempe altitudo ſcaturiginis A, eſt ad 22 1/2 in duplicata ra<lb></lb>tione eius, quam habet 10 ad 15, hoc eſt, quam habet 8 ad 12, <lb></lb>ſaliens nempe fontis A, ad <expan abbr="ſalientẽ">ſalientem</expan> fontis B; erit neceſſariò <lb></lb>22 1/2 altitudo ſcaturiginis fontis B quæſita. </s></p> <p type="main"> <s>Atque hæc ſufficiant de tuborum ſeu fontium ſalientibus; <lb></lb>qui plura deſiderat, legat Merſennum in Hydraulicis Phæno<lb></lb>menis, & Torricellum lib. 2. de Motu projectorum à fol. 191. ubi <lb></lb>incipit agere de Motu aquarum. </s></p> <p type="main"> <s><emph type="center"></emph>CAPVT V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De fluxu Aquæ per diverſa eiuſdem vaſis <lb></lb>aut tubi foramina.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg275"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg275"></margin.target><emph type="italics"></emph>Proprieta<lb></lb>tes fluxus <lb></lb>aquæ per di<lb></lb>verſa eius<lb></lb>dem tubi <lb></lb>aut vaſis <lb></lb>foramina.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>HActenus locuti ſumus de aquæ fluxu per foramina tu<lb></lb>borum <expan abbr="verticaliũ">verticalium</expan> tum horizontalia, tum lateralia, & <lb></lb>tubos cum tubis, aquas cum aquis, foramina cum fo<lb></lb>raminibus diverſorum tuborum comparavimus; <lb></lb>nunc eiuſdem tubi & vaſis <expan abbr="cuiuſcunq;">cuiuſcunque</expan> foramina diverſa inter ſeſe <pb xlink:href="051/01/190.jpg" pagenum="159"></pb>conferemus breviter & methodicè, inſiſtentes veſtigijs Ioannis <lb></lb>Baptiſtæ Baliani lib. 6. de Motu naturali gravium & liquidorum. </s><s><lb></lb>Quibus tamen multa addi poſſunt ex dictis Capite præcedenti. </s><s><lb></lb>Sermo autem eſt hîc etiam, uti in præcedentibus, de tu<lb></lb>bis ac vaſis verticaliter erectis, ſive cylindrica illa ſint, ſive priſ<lb></lb>matica; & ſive foramina ſint rectangula, ſive circularia. </s><s>Præmit<lb></lb>tamus ergo ſequentes. </s></p> <p type="main"> <s><emph type="center"></emph>Petitiones.<emph.end type="center"></emph.end></s></p> <p type="main"> <s> <arrow.to.target n="marg276"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg276"></margin.target><emph type="italics"></emph>Petitiones <lb></lb>pro fluxu a<lb></lb>quæ ex fora <lb></lb>minibus tu<lb></lb>borum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>1. Vbi omnia ſunt æqualia, effectus ſunt æquales. </s></p> <p type="main"> <s>2. Quantitates eiusdem generis ſunt omnes commen<lb></lb>ſurabiles, <emph type="italics"></emph>ſaltem phyſicè, ut dicemus Propoſit.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>in <lb></lb>Annotat.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>3. Aqua tranſiens per tubi ſeu vaſis foramen, decurrit <lb></lb>à ſummo vaſis ad foramen, tanquam per canalem <lb></lb>columnarem, cuius baſis foramen. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>TErtia hæc Petitio eadem eſt cum Propoſit.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>Capitis tertij præceden</s></p> <p type="main"> <s> <arrow.to.target n="marg277"></arrow.to.target><lb></lb>tis. </s><s>Et licet ibi locuti tantùm fuerimus de foraminibus exiſtenti<lb></lb>bus in baſi tuborum verticaliter erectorum, hîc tamen idem concedi no<lb></lb>bis petimus etiam de foraminibus in tuborum vaſorumque lateribus exi<lb></lb>ſtentibus, propter paritatem rationis. </s><s>Petimus itaque nobis concedi, <lb></lb>quòd ſi in latere tubi, aut vaſis<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>fiat foramen<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>decurrat aqua à<emph.end type="italics"></emph.end><lb></lb> <arrow.to.target n="fig41"></arrow.to.target><lb></lb><emph type="italics"></emph>vaſis ſumitate ad foramen uſque inſtar columnæ, cu<lb></lb>ius baſis eſt æqualis foramini, altitudo perpendicula<lb></lb>res ſuper foraminis diametro erectæ, prout in appo<lb></lb>ſita figura eſt columna<emph.end type="italics"></emph.end> ABCD. </s><s><emph type="italics"></emph>Ratio poteſt eſſe, <lb></lb>quia ex dictis Capite<emph.end type="italics"></emph.end> 1 <emph type="italics"></emph>patet aquam non premere <lb></lb>niſi partes ſibi perpendiculariter ſubiectas, dum aqua <lb></lb>eſt deſcendens in aliquo, ſeu ex aliquo effluens, prout <lb></lb>hîc ſit.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="051/01/191.jpg" pagenum="160"></pb> <p type="margin"> <s><margin.target id="marg277"></margin.target>Aqua in<lb></lb>ſtar colum<lb></lb>na effluit <lb></lb>ex forami<lb></lb>ne baſis in <lb></lb>vaſe.</s></p> <figure id="id.051.01.191.1.jpg" xlink:href="051/01/191/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Propoſitio I. Theorema I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Per foramina æqualia, æquè à ſummo tubi diſtantia, <lb></lb>ſive in baſi, ſive in latere, æquali tempore æquales fluunt <lb></lb>aquarum quantitates.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.191.2.jpg" xlink:href="051/01/191/2.jpg"></figure> <p type="main"> <s>IN vaſe, ſeu tubo AB, ſint foramina C & D <lb></lb>æqualia, & horizontalia (& eadem eſt ra<lb></lb>tio, ſi lateralia eſſent, æquè à ſummitate di<lb></lb>ſtantia) per quæ aqua æquali, vel potiùs eo<lb></lb>dem tempore decurrat. </s><s>Dico, aquas de<lb></lb> <arrow.to.target n="marg278"></arrow.to.target><lb></lb>curſas (liceat ita loqui) eſſe æquales inter <lb></lb>ſe. </s><s>Vbi enim omnia ſunt æqualia, effectus <lb></lb>ſunt æquales, per Petitionem primam hujus <lb></lb>Capitis: at hîc omnia ſunt æqualia, ſcilicet foramina, columnæ <lb></lb>aqueæ, vis premendi, & ſimilia; ergo effectus, qui ſunt aquæ <lb></lb>decurſæ, æquales ſunt. </s><s>Per foramina ergo æqualia, &c. </s><s>Quod <lb></lb>erat oſten dendum. </s></p> <p type="margin"> <s><margin.target id="marg278"></margin.target><emph type="italics"></emph>Aquæ flu<lb></lb>xus exæqua<lb></lb>libus fora<lb></lb>minibus va<lb></lb>ſorum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>ET hoc verum eſt, ſive vas ſit ſemper plenum, ſive non. </s><s>Eadem eſt <lb></lb>ratio, ſi vaſa ſint cylindrica, & foramina rotunda, ut diximus et<lb></lb>iam paulò antè, & ſemper in ſequentibus dictum volumus.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Poriſma.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>SEquitur hinc, ſi ex duobus eiuſdem vaſis foraminibus æqua<lb></lb>liter à ſummo vaſis diſtantibus aquæ decurrentes eodem tem<lb></lb>pore æquales ſunt, foramina eſſe æqualia. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio II. Theorema II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ è foraminibus æqualiter à ſummo tubi diſtanti<lb></lb>bus decurrentes, ſunt inter ſe ut foramina.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>IN tubo ſeu vaſe AB, ſint duo foramina rectangula inæqualia, <lb></lb>C minus, & D maius, ſed ambo horizontalia, <expan abbr="atq;">atque</expan> adeo æ<lb></lb>quèalta, ſeu æqualiter à vaſis ſummitate remota; & aqua de<lb></lb>curſa per C ſit E, aqua verò decurſa per D ſit F. </s><s>Dico, a<lb></lb>quam E decurſam per C, habere ſe ad aquam F decurſam <pb xlink:href="051/01/192.jpg" pagenum="161"></pb> <arrow.to.target n="fig42"></arrow.to.target><lb></lb>per D, utſe habet foramen C ad foramen <lb></lb> <arrow.to.target n="marg279"></arrow.to.target><lb></lb>D. </s><s>Quoniam enim, per Petitionem ſe<lb></lb>cundam hujus, quantitates eiusdem gene<lb></lb>ris ſunt commenſurabiles, erunt longitu<lb></lb>dines C & D commenſurabiles. </s><s>Si ter<lb></lb>go communis earum menſura G, & ſecen<lb></lb>tur dictæ longitudines C & D in partes, <lb></lb>quæ ſint æquales ipſi G; quibus diviſis à <lb></lb>transverſalib<emph type="sup"></emph>9<emph.end type="sup"></emph.end> lineis <expan abbr="perpẽdicularib">perpendicularib</expan><emph type="sup"></emph>9<emph.end type="sup"></emph.end>, fiant <lb></lb>tot foramina, quot ſunt dictæ partes. </s><s>Tum <lb></lb>ſic. </s><s>Huiuſmodi foramina erunt omnia inter ſe æqualia, ex con<lb></lb>ſtructione, & per 36. Primi Euclid. </s><s>Ergo ex eis effluent eodem <lb></lb>tempore quantitates aquæ æquales, per Propoſit 1. huius. </s><s><lb></lb>Quot igitur ſunt foramina in C & D, toterunt quantitates a<lb></lb> <arrow.to.target n="fig43"></arrow.to.target><lb></lb>quarum æquales in E & F. </s><s>Cùm igitur ſint qua<lb></lb>tuor magnitudines, C, D, E, F, quarum prima <lb></lb>C eſt ad ſecundam E, ut eſt tertia D, ad quar<lb></lb>tam F; erit etiam viciſſim ſeu permutando ut C <lb></lb>ad D, ita E ad F, per decimam ſextam Quinti Euclidis. </s></p> <p type="margin"> <s><margin.target id="marg279"></margin.target><emph type="italics"></emph>Proportio <lb></lb>aquæ efflu<lb></lb>entis ad fo<lb></lb>ramina.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.192.1.jpg" xlink:href="051/01/192/1.jpg"></figure> <figure id="id.051.01.192.2.jpg" xlink:href="051/01/192/2.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Annotatio<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>QVamvis contingere poſſit, ut longitudines<emph.end type="italics"></emph.end> CD <emph type="italics"></emph>non ſint commen<lb></lb>ſurabiles, ac proinde<emph.end type="italics"></emph.end> G <emph type="italics"></emph>non ſit earum communis menſura; nihil <lb></lb>refert, quia hîc non ſumus in Mathematicis, ſed in Phyſicis, ubi non ha<lb></lb>betur ratio inſenſibilium.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III. Theorema III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aqua per foramina vaſis eo impetu ſeu velocitate de<lb></lb>currit, quo per tubos æqualium foraminum & alti<lb></lb>tudinum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.192.3.jpg" xlink:href="051/01/192/3.jpg"></figure> <p type="main"> <s>SIt vas CD, in quo foramen D, al<lb></lb>titudo vaſis CD; & ſit tubus AB <lb></lb>perpendicularis, in quo foramen <lb></lb>B ſit æquale foramini D, & altitudo <lb></lb>AB æqualis altitudini CD. </s><s>Dico, <lb></lb>in B & D impetus ſeu velocitates <pb xlink:href="051/01/193.jpg" pagenum="162"></pb> <arrow.to.target n="fig44"></arrow.to.target><lb></lb> <arrow.to.target n="marg280"></arrow.to.target><lb></lb>aquæ effluentis eſſe æquales. </s><s>Quo<lb></lb>niam enim aqua fluens è foramine D, <lb></lb>decurrit per ſpatium CD, ac ſi de<lb></lb>curreret per tubum AB perpendi<lb></lb>cularem eiusdem longitudinis, per <lb></lb>Petitionem tertiam huius; in D & B <lb></lb>ſortitur impetus ſeu velocitates ęqua<lb></lb>les, per Corollarium quintum Propoſitio. 9. Capitis III. </s></p> <p type="margin"> <s><margin.target id="marg280"></margin.target><emph type="italics"></emph>Aquæ flu<lb></lb>xus exfora<lb></lb>minibus ve<lb></lb>lociter quæ.<emph.end type="italics"></emph.end></s></p> <figure id="id.051.01.193.1.jpg" xlink:href="051/01/193/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Propoſitio IV. Theorema IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Velocitates aquæ decurrentis per foramina æqualia <lb></lb>eiuſdem vaſis, inæqualiter diſtantia à ſummo vaſis, ſunt in <lb></lb>ſubduplicata ratione diſtantiæ.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.193.2.jpg" xlink:href="051/01/193/2.jpg"></figure> <p type="main"> <s>SInt in vaſe AC foraminum æqualium <lb></lb>B & C, diſtantiæ à ſummo vaſis AB, <lb></lb>AC; ſitque media inter illas AD. </s><s>Dico, <lb></lb>impetum ſeu velocitatem in C, ad impe<lb></lb>tum ſeu velocitatem in B, eſſe ut AD ad AB. </s><s><lb></lb> <arrow.to.target n="marg281"></arrow.to.target><lb></lb>Quoniam enim, per Propoſit. tertiam hu<lb></lb>jus, aqua per foramina B & C decurrit eo <lb></lb>impetu, quo per tubos æqualium foraminum & altitudinum; <lb></lb>erunt per Propoſit. 10. Capitis tertij, velocitates aquæ in C & <lb></lb>B, ut AD ad AB, hoc eſt, velocitas apud C erit media pro<lb></lb>portionalis inter altitudines AC, AB, atque adeo ſubduplica<lb></lb>tam rationem habebit prædictarum altitudinum. </s></p> <p type="margin"> <s><margin.target id="marg281"></margin.target><emph type="italics"></emph>Proportio <lb></lb>dictæ velo<lb></lb>citatis ad <lb></lb>foraminum <lb></lb>diſtantiam.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio V. Theorema V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aquæ per æqualia foramina inæqualiter à ſummitate <lb></lb>vaſis diſtantia fluentes, ſunt in ſubduplicata ratione <lb></lb>diſtantiarum.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>IN vaſe AC, præcedentis Propoſitionis, altitudines à forami<lb></lb>nibus æqualibus B & C, ad ſummum vaſis A, ſint AB, AC, <lb></lb>quarum media ſit AD. </s><s>Dico, aquam fluentem per C, <lb></lb>ad aquam fluentem per B, eſſe ut AD, ad AB, hoc eſt, <lb></lb>eſſe mediam proportionalem, ideoque habere ſubduplicatam <pb xlink:href="051/01/194.jpg" pagenum="163"></pb>rationem altitudinum prædictarum. </s><s>Quoniam enim aqua flu<lb></lb>it per B & C veluti per tubos, per Petitionem tertiam; a<lb></lb>quæ autem per tubos æqualium altitudinum, ſunt in ſubdupli<lb></lb>cata ratione altitudinum tuborum, per propoſit. 8. Capitis <lb></lb>tertij; conſtat propoſitum. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VI. Problema I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Secto foramine laterali vaſis in partes æquales, à rectis <lb></lb>horizontalibus, invenire rationes aquarum ex eis <lb></lb>fluentium.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.194.1.jpg" xlink:href="051/01/194/1.jpg"></figure> <p type="main"> <s>IN vaſe ST ſecetur foramen <lb></lb> <arrow.to.target n="marg282"></arrow.to.target><lb></lb>laterale AB in partes æquales <lb></lb>AC, CD, DB, à rectis lineis hori<lb></lb>zontalibus, ut fiant totidem fo<lb></lb>ramina, quorum altitudines ſint <lb></lb>notæ; & per AC fluat aqua E, <lb></lb>per CD aqua F, per DB aqua <lb></lb>G, tempore æquali ſeu eodem: <lb></lb><expan abbr="oporteatq́ue">oporteatque</expan> venari proportio<lb></lb>nem aquarum E, F, G. </s><s>Fiant <lb></lb>HI, KL, MN, altitudines forami<lb></lb>num AC, CD, DB, à ſummo va<lb></lb>ſis; & inter ipſas mediæ proportionales OP, QR, per decimam <lb></lb>tertiam Sexti Euclidis, aut per propoſit. 3. Parergi Capitis tertij <lb></lb>præcedentis. </s><s>Quoniam igitur aqua E ad aquam F, eſt ut HI <lb></lb>ad OP, per Propoſit. 5. huius Capitis, nota eſt ratio aquæ E ad <lb></lb>aquam F. </s><s>Item quoniam aqua F ad aquam G, eſt ut KL ad <lb></lb>QR, per eandem Propoſit. 5. huius Capitis, nota eſt pariter ra<lb></lb>tio aquæ F ad aquam G: At ratioaquæ E ad aquam G com<lb></lb>poſita rationum inter EF & FG notarum, eſt pariter <lb></lb>nota; Reperta eſt igitur ratio aquarum <lb></lb>E, F, G. </s></p> <pb xlink:href="051/01/195.jpg" pagenum="164"></pb> <p type="margin"> <s><margin.target id="marg282"></margin.target><emph type="italics"></emph>Problemata <lb></lb>varia de flu<lb></lb>xu aquæ per <lb></lb>foramina <lb></lb>vaſorum.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VII. Problema II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Secto foramine laterali vaſis in partes inæquales, à re<lb></lb>ctis horizontalibus, reperire rationes aquarum efflu<lb></lb>entium ex ipſis.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.195.1.jpg" xlink:href="051/01/195/1.jpg"></figure> <p type="main"> <s>FOramen CD vaſis AB ſecetur à <lb></lb>recta E in partes inæquales CE, ED; <lb></lb>& effluat ex parte ſuperiore e E aqua <lb></lb>F, ex inferiori verò ED aqua G, eo<lb></lb>dem tempore. </s><s>Quæritur proportio <lb></lb>F ad G. </s><s>Si ED foramen minus non <lb></lb>menſurat CE, reperiatur eorum ma<lb></lb>xima communis menſura, per tertiam <lb></lb>Decimi Euclidis, quæ ſit H; & juxta <lb></lb>eam ſecetur CE in partes CQ, QK, KE; item ED in partes <lb></lb>EI, ID. </s><s>Quoniam igitur foramen CD ſectum eſt in partes CQ, <lb></lb>QK, KE, EI, ID, æquales per conſtructionem; reperietur per <lb></lb>Propoſit. 6. hujus Capitis, ratio aquarum per eas fluentium, <lb></lb>ac proinde aquarum fluentium per CE, & ED. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio VIII. Problema III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis foraminibus inæqualibus ſuper eadem horizon<lb></lb>tali, venari rationes aquarum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.195.2.jpg" xlink:href="051/01/195/2.jpg"></figure> <p type="main"> <s>SInt foramina AB, & CD, ſuper ho<lb></lb>rizontali BD, utrumque laterale; <lb></lb><expan abbr="Quærendaq́ue">Quærendaque</expan> ſit proportio aquarum ex <lb></lb>eis eodem tempore fluentium. </s><s>Produ<lb></lb>catur recta CEG, parallela rectæ DB, <lb></lb><expan abbr="dividaturq́ue">dividaturque</expan> foramen AB in duo fo<lb></lb>ramina AG, GB. </s><s>Quoniam igitur no<lb></lb>ta eſt ratio aquarum fluentium ex CD, <lb></lb>& GB, per Propoſit. 2. hujus Capitis; item ratio aquarum BG, <lb></lb>& GA, per Propoſit. 7. præcedentem; nota pariter eſt ratio <lb></lb>ex eis compoſita inter aquas fluentes per CD, & AG. </s><s>Cùm <pb xlink:href="051/01/196.jpg" pagenum="165"></pb>igitur nota ſit ratio aquæ fluentis per CD, ad aquam fluentem <lb></lb>per BG, & per GA partes; nota erit ratio eiuſdem ad totam <lb></lb>fluentem per AB. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio IX. Problema IV.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis foraminibus eiuſdem vaſis, quorum vnum ſu<lb></lb>perius, alterum inferius, inter easdem parallelas perpen<lb></lb>diculares, reperire rationes aquarum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.196.1.jpg" xlink:href="051/01/196/1.jpg"></figure> <p type="main"> <s>DEntur foramina AB, CD, inter parallelas <lb></lb>easdem perpendiculares AC, & BD, <expan abbr="ſitq́">ſitque</expan>; <lb></lb>venanda ratio aquarum ex eis, æquali tem<lb></lb>pore, fluentium. </s><s>Concipiatur BC, tan<lb></lb>quam foramen inter easdem parallelas. </s><s>Quo<lb></lb>niam igitur nota eſt ratio aquarum fluentium <lb></lb>ex CD, & ex CB, per Propot. 7. hujus Ca<lb></lb>pitis; item ex CB, & BA, per eandem Pro<lb></lb>poſitionem ſeptimam, nota erit pariter ratio aquarum fluenti<lb></lb>um per CD, & AB. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio X. Problema V.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Datis foraminibus eiuſdem vaſis, quorum vnum ſu<lb></lb>perius, alterum inferius, non inter eaſdem parallelas, <lb></lb>repire rationes aquarum.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.196.2.jpg" xlink:href="051/01/196/2.jpg"></figure> <p type="main"> <s>DAta ſint foramina AD, EH; oporte<lb></lb>atque reperire rationes aquarum per il<lb></lb>la æquo tempore fluentium. </s><s>Duc hori<lb></lb>zontales HI, EK, & producta DB in L, <lb></lb>concipiatur IL tanquam foramen inter <lb></lb>eaſdem parallelas cum AD; & quæratur <lb></lb>ratio aquarum per AD, IL fluentium, per <lb></lb>Propoſit. 9. hujus Capitis, & ſit ut M ad N. </s><s><lb></lb>Item quæratur ratio IL ad EH, per Pro<lb></lb>poſit. 2. hujus Capitis, & ſit ut N ad O. </s><s><lb></lb>Dico, M ad O eſſe rationem aquarum per <lb></lb>AD, & HE fluentium. </s><s>Quoniam enim ut M ad N, ita eſt AD <lb></lb>ad IL; & ut N ad O, ita IL ad EH, per conſtructionem: Erit <pb xlink:href="051/01/197.jpg" pagenum="166"></pb>ex æquo, per vigeſimam ſecundam Quinti Euclid. ut M ad O, <lb></lb>ita aqua per AD adaquam per EH fluentem. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XI. Problema VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato foramine, & linea horizontali, in aliquo vaſe, <lb></lb>conſtituere ſuper illa foramen, è quo æqualis aqua <lb></lb>fluat eodem tempore.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.197.1.jpg" xlink:href="051/01/197/1.jpg"></figure> <p type="main"> <s>SIt datum foramen AM, & hori<lb></lb>zontalis CD; ſitque deſcriben<lb></lb>dum foramen ſuper CD, è quo ef<lb></lb>fluat eodem ſeu æquali tempore, a<lb></lb>qua ut per AM. </s><s>Erigantur per<lb></lb>pendiculares AE, MC, & produ<lb></lb>catur DC in E, & ſuper EC fiat fo<lb></lb>ramen æquale foramini AM, & ſit <lb></lb>FC; & ducta FG parallela ipſi CD, <lb></lb>fiat HI media inter KB, & KE: & tandem fiat, ut HI ad KE, <lb></lb>ita DL ad EC. </s><s>Dico, foramen LG eſſe foramen quæſitum, <lb></lb>per quod æquali tempore fluat aqua ut per AM. </s><s>Quoniam e<lb></lb>nim, per Propoſit. 2. hujus Capitis, aqua foraminis LG ad a<lb></lb>quam foraminis FC, eſt ut DL ad CE, hoc eſt, HI, ad KE; & <lb></lb>per Propoſit. 5. hujus Capitis, aqua foraminis AM ad aquam <lb></lb>foraminis CF, eſt ut eadem HI, ad KE; erit ut aqua LG ad <lb></lb>CF, ita aqua AM ad CF, per undecimam Quinti Euclidis, ac <lb></lb>proinde aqua foraminis AM erit æqualis aquæ foraminis LG, <lb></lb>per nonam Quinti Euclid. & per 1. Axio. lib. 1. Euclid. </s></p> <p type="main"> <s><emph type="center"></emph>Annotatio.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="italics"></emph>POteſt tamen horizontalis data eſſe tam vicina ſummitati vaſis, ut <lb></lb>quæſitum foramen ficri non poſſit, nec hoc, nec alio modo: & tunc <lb></lb>Problema eſt inſolubile.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio XII. Problema VII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato foramine, & latere alterius in eodem vaſe, reperi<lb></lb>re foramen, è quo æqualis aqua effluat.<emph.end type="center"></emph.end></s></p> <pb xlink:href="051/01/198.jpg" pagenum="167"></pb> <figure id="id.051.01.198.1.jpg" xlink:href="051/01/198/1.jpg"></figure> <p type="main"> <s>DAtum ſit foramen AB, & latus <lb></lb>DC, in eodem vaſe; <expan abbr="oporteatq;">oporteatque</expan> <lb></lb>deſcribere foramen, cujus latus ſit <lb></lb>DC, & è quo effluat eodem tempore <lb></lb>aqua ut ab AB. </s><s>Ductis CN, & DF ho<lb></lb>rizontalibus, & p̨ducta BE, reperiatur <lb></lb>ratio <expan abbr="aquarũ">aquarum</expan> <expan abbr="fluentiũ">fluentium</expan> ex AB, & FE, <lb></lb>per Propoſit. 9. hujus Capitis, quæ ſit <lb></lb>ut G ad H; & fiat, ut H ad G, ita <lb></lb>FI ad FK, per decimam tertiam Sex<lb></lb>ti Euclid. & Propoſit. 3. Parergi Capitis 3; & à K erigatur <lb></lb>perpendicularis KL, & tandem fiat foramen, cujus latus DC, <lb></lb>æquale & ſimile ipſi FL foramini, & ſit DM. </s><s>Dico, è foramine <lb></lb>DM fluere aquam, ut ex AB foramine. </s><s>Quoniam enim aqua <lb></lb>fluens ex AB, ad aquam fluentem ex FE, eſtut G ad H, per con<lb></lb>ſtructionem; item aqua fluens per FL, ſeu ei æquale DM, ad <lb></lb>fluentem per idem FE, eſt itidem ut G ad H, per Propoſit. 2. <lb></lb>hujus Capitis; erunt aquæ fluentes per AB, & per DM, inter ſe <lb></lb>æquales, per nonam Quinti Euclidis. </s><s>Igitur DM erit foramen <lb></lb>quæſitum. </s></p> <p type="main"> <s><emph type="center"></emph>Proproſitio XIII. Problema VIII.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato foramine, reperire aliud æquale in eodem vaſe, è <lb></lb>quo fluat aqua in ratione data.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.198.2.jpg" xlink:href="051/01/198/2.jpg"></figure> <p type="main"> <s>DEtur in vaſe AB foramen C, & da<lb></lb>ta ſit ratio aquarum D, E, quarum <lb></lb>D fluat in dato tempore per foramen C; <lb></lb>reperiendum verò ſit, ubi fiat æquale <lb></lb>foramen, è quo fluat in æquali tempore <lb></lb>aqua E. </s><s>Fiat ad D, E, AC, quarta pro<lb></lb>portionalis AF, per duodecimam Sexti <lb></lb>Euclid. aut Propoſit. 8. Parergi Capitis <lb></lb>tertij præcedentis; & ad AC, AF, ter<lb></lb>tia proportionalis AG, per vndecimam <pb xlink:href="051/01/199.jpg" pagenum="168"></pb> <arrow.to.target n="fig45"></arrow.to.target><lb></lb>ſexti Euclid. aut per Propoſit. 6. Paret<lb></lb>gi citati; & in G fiat foramen, (quod <lb></lb>ſi fieri nequit, Problema eſt inſolubile.</s> <lb></lb><s>Dico, G eſſe locum foraminis quæſiti. </s><lb></lb><s>Quoniam enim aquæ fluentes per dicta <lb></lb>foramina ſunt in ſubduplicata ratione <lb></lb>altitudinum AC, AG, per Propoſit. 5. <lb></lb>hujus capitis; & aquæ D, & E ſunt pa<lb></lb>riter in ſubduplicata ratione datæ altitu<lb></lb>dinis AC, & inveniendæ altitudinis, per <lb></lb>eandem Propoſitionem 5. hujus capitis; ſequitur aquas fluen<lb></lb>tes per dicta foramina C & G, eſſe ut aquas D & E. </s></p> <figure id="id.051.01.199.1.jpg" xlink:href="051/01/199/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>Propoſitio XIV. Problema IX.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Dato foramine, aptare in eodem vaſe aliud datum ſi<lb></lb>mile, magnitudinis diverſæ, à quo aqua fluens cum <lb></lb>fluente à primo, habeat rationem datam.<emph.end type="center"></emph.end></s></p> <figure id="id.051.01.199.2.jpg" xlink:href="051/01/199/2.jpg"></figure> <p type="main"> <s>IN vaſe AB, datum ſit foramen C, & <lb></lb>aliud adſignatum D ſimile, ſed diver<lb></lb>ſæ magnitudinis, ſive majoris, ſive mi<lb></lb>noris; ratio verò aquarum data ſit E, F. </s><s><lb></lb>Aptandum ſit foramen D adſignatum <lb></lb>eâ lege, ut aqua per illud fluens, cum <lb></lb>aqua fluente ex C, ſit ut E ad F. </s><s><lb></lb>Super horizontali ducta CG, fiat fora<lb></lb>men G, æquale foramini D; & perqui<lb></lb>ratur ratio aquarum fluentium per C <lb></lb>& G, per Propoſit. 8. hujus capitis, & <lb></lb>ſit ut E ad H. </s><s>Quæ ſi eſt eadem quæ <lb></lb>eſt inter E & F, habemus intentum: <lb></lb>Sin minùs, fiat aliud foramen infra aut <lb></lb>ſupra G, ei ſimile & æquale, à quo <lb></lb>fluat aqua, quæ cum fluente ab ipſo G <lb></lb>habeat rationem ut H ad F, & ſit I, <lb></lb>Quod ſi fieri nequit, Problema eſt in- <pb xlink:href="051/01/200.jpg" pagenum="169"></pb>ſolubile.) </s><s>Dico, I eſſe foramen quæſitum. </s><s>Quoniam enim <lb></lb>aqua C ad aquam G, eſt ut E ad H; & aqua G ad aquam <lb></lb>I, eſt ut H ad F, ex conſtructione & operatione facta; erit <lb></lb>ex æquo etiam aqua C ad aquam I, ut E ad F, per vige<lb></lb>ſimam ſecundam Quinti Euclidis. </s></p> <p type="main"> <s><emph type="center"></emph>CAPUT VI.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>De Aëris gravitate, rarefactione, & <lb></lb>condenſatione.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>QUoniam in Pneumaticis ac Hydropneumaticis Ma<lb></lb>chinis magni refert, aëris naturalis pondus ſeu gra<lb></lb>vitatem, rarefactique ac condenſati quantitatem ae <lb></lb>vires cognoſcere; de ijs nonnihil parergi loco ad<lb></lb>dendum hîc cenſui. </s><s>Sit itaque </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio I.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Aëris gravitatem invenire.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>TAmetſi aêr levis ſit inter reliqua elementa, ſuaque levitate <lb></lb> <arrow.to.target n="marg283"></arrow.to.target><lb></lb>ſurſum tendat, ut ſit ſupra terram & aquam; admixtum <lb></lb>tamen habet aliquid gravitatis. </s><s>Patet ex eo, quòd folles lu<lb></lb>ſorij aëre addenſato bene inflati, ut & veſicæ inflatæ, plùs pon<lb></lb>derent, quàm flaccidi, ut exquiſita trutina aut libra deprehen<lb></lb>di poteſt. P. Joannes Baptiſta Ricciolus Tomo 1. Almgeſti <lb></lb>Novi lib. 2. cap. 5. num. 4. ait expendiſſe ſe veſicam bovinam <lb></lb>quæ flaccida erat ſcrupulorum 4, & granorum 4, & deprehen<lb></lb>diſſe inflatam fuiſſe ſcrupulorum 4, & granorum 6. </s><s>Quare <lb></lb>aër additus per inflationem, appendebat grana 2. Marinus <lb></lb>Merſennus in Phænomenis ſuis Propoſit. XXIX. aſſerit, ſe Geo<lb></lb>metris præſentibus & adjuvantibus, ponderaſſe bilance Æo<lb></lb>lopilam æneam (qualem deſcribimus infrà Parte 2. Claſſe 1. cap. 3. <lb></lb>Machina 6.) ſatis calefactam, & propemodum candentem, <pb xlink:href="051/01/201.jpg" pagenum="170"></pb>omnique humore deſtitutam, & quàm minimùm aêris conti<lb></lb>nentem; deprehendiſſeque pondus fuiſſe unciarum 4, <expan abbr="drach-marũ">drach<lb></lb>marum</expan> 6, & granorum 15: poſtquam verò naturaliter refrixiſſet <lb></lb>æolopila, & aër antea vehementer rarefactus redijſſet ad pri<lb></lb>ſtinum ac naturalem ſuum ſtatum; iterum ponderaſſe ipſam, <lb></lb>& inveniſſe pondus præcedente pondere majus fuiſſe 4 gra<lb></lb>nis. </s><s>(Apud Merſennum habetur, minus; utique typographi<lb></lb>co errore.) </s><s>Erat autem bilanx, inquit Merſennus, quæ dimi<lb></lb>dio grani perdebat æquilibrium. </s></p> <p type="margin"> <s><margin.target id="marg283"></margin.target><emph type="italics"></emph>Aëris gra<lb></lb>vitatem in<lb></lb>venire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Atque ex his patet, qua ratione aëris gravitas inveniatur. </s><s><lb></lb>Alij aliter explorant pondus aëris, præſertim Illuſtriſſimus Do<lb></lb>minus Carolus Vintimillia Eques Panormitanus in Sicilia, & Ami<lb></lb>cus Uranicus ſincei iſſimus, qui legendam mihi dedit demon<lb></lb>ſtrationem ſubtiliſſimam, praximque hydroſtaticam, qua olim <lb></lb>Adoleſcens coram Sereniſſimo Philiberto Siciliæ Prorege, No<lb></lb>bilitateque Panormitana univerſa aërem ponderaverat. </s><s>Vide <lb></lb>etiam quæ habet Daniel Lipſtorpius part. 3. Speciminum Phi<lb></lb>loſophiæ Cartheſianæ cap. 2. in fine, ubi adducit modum Galilæi <lb></lb>& Joann. Chryſoſt. Magneni.</s><s>Vide præterea Appendicem <lb></lb>in fine Operis. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio II.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quantum condenſari aër poſſit, invenire.<emph.end type="center"></emph.end><lb></lb> <arrow.to.target n="marg284"></arrow.to.target></s></p> <p type="margin"> <s><margin.target id="marg284"></margin.target>Vide infrà <lb></lb>Iconiſmi <lb></lb>VIII. Figu<lb></lb>ram IX. a.</s></p> <p type="main"> <s>ASſumatur fons pneumaticus, qualem deſcribimus infrà, <lb></lb>Parte 2. </s><s>Claſſe 1. cap. 2. Machina 8. ejuſque capacitas exactè <lb></lb>exploretur in menſura cubica aquæ. </s><s>Capiat autem dictus <lb></lb>fons, gratiâ exempli, unum pedem cubicum, ſeu libras 72. </s><s><lb></lb>In hunc fontem immitte ſyringe, per foramen C, aquam <lb></lb>quantum fieri, ſine ruptionis periculo, poteſt. </s><s>Si jam notam <lb></lb>feceris in menſura, quantitatem aquæ immiſſæ, eamque à fon</s></p> <p type="main"> <s> <arrow.to.target n="marg285"></arrow.to.target><lb></lb>tis capacitate detraxeris; reſiduum fontis indicabit locum <lb></lb>aëris condenſati, qui priùs totam fontis capacitatem imple- <pb xlink:href="051/01/202.jpg" pagenum="171"></pb>bat. </s><s>Ut ſi immiſſæ ſuntduæ tertiæ pedis cubici, occupabit aër <lb></lb>unam tertiam partem. </s></p> <p type="margin"> <s><margin.target id="marg285"></margin.target><emph type="italics"></emph>Aër quan<lb></lb>tum conden<lb></lb>ſari poſſit, <lb></lb>invenire.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Atque hæc eſt expeditiſſima ratio menſurandi conden<lb></lb>ſationem aëris. </s><s>Fieri quoque idipſum poteſt ſclopeto pneu<lb></lb>matico, de quo infrà loco cit. cap. 2. Machina 13. & 14. </s></p> <p type="main"> <s>Credunt aliqui, inquit Merſennus in Hydraulicis Propo<lb></lb>ſit. 31. aërem per condenſationem non poſſe niſi ad tertiam ſpa<lb></lb>tij, quod naturaliter occupat, partem redigi, quòd videant <lb></lb>aquam in vas infuſam tres heminas ſeu libras continens, non <lb></lb>ſuperare duas heminas, ob aërem intus manentem. </s><s>Certum <lb></lb>eſt tamen, ſubdit idem, magis condenſari poſſe; ipſeque ex<lb></lb>perientiâ didicit, poſſe ad ſpatium quindecuplo minus in ſclo<lb></lb>peto pneumatico cogi, idque ſolâ vi manus ſyringe utentis; <lb></lb>quæ vis cùm intendi multò magis poſſit, dubium non eſt, aë<lb></lb>rem adhuc multò magis condenſati poſſe. </s><s>Vide Merſennum <lb></lb>in Hydraulicis loco citato. </s></p> <p type="main"> <s><emph type="center"></emph>Propoſitio III.<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Quantum rarefieri aër poſſit, invenire.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>MArinus Merſennus loco citato Propoſit. 31. ait, conſtare, <lb></lb> <arrow.to.target n="marg286"></arrow.to.target><lb></lb>aërem ita rarefieri in ignitis æolopilis (quas deſcribimus <lb></lb>Parte 2. Claſſe 1. cap. 2. Machina 6.) ut ſeptuageſima pars aë<lb></lb>ris priùs incluſi, & nondum rarefacti, æolopilas impleat. </s><s>Hæc <lb></lb>autem rarefactionis quantitas inveniri poteſt præſidio Æolo<lb></lb>pilæ hunc in modum. </s></p> <p type="margin"> <s><margin.target id="marg286"></margin.target><emph type="italics"></emph>Aër quan<lb></lb>tum poſſit <lb></lb>rarefieri.<emph.end type="italics"></emph.end></s></p> <p type="main"> <s>Æolopila notæ capacitatis calefiat eò uſque, donec ma<lb></lb>jorem vim caloris ſuſtinere ampliùs non poſſe judicetur citra <lb></lb>liquefactionis periculum: ſic enim fiet, ut quàm minimùm aë<lb></lb>ris rarefacti totam ipſius capacitatem expleat. </s><s>Quo facto, <lb></lb>igni extracta ſtatim aquæ frigidæ immergatur. </s><s>Continget <lb></lb>enim ut aër, qui rarefactus totam Æolopilam occupabat, ad <lb></lb>naturalem redeat conſtitutionem; ac proinde Æolopila, nè <lb></lb>detur vacuum, aquam ſuget. </s><s>Hujus aquæ quantitas ſi fiat <pb xlink:href="051/01/203.jpg" pagenum="172"></pb>nota, & ab Æolopilæ capacitate detrahatur; notam relinquet <lb></lb>aëris quantitatem & nunc addenſati, & antea rarefacti. </s></p> <p type="main"> <s>Hæc ex Merſenni ſententia; quæ tamen valde incerta mi<lb></lb>hi videntur, tum quia non ſcitur quando Æolopila eſt ſummè <lb></lb>calefacta, tum quia aqua abſumitur à calore Æolopilæ ante & <lb></lb>poſt attractionem, tum denique quia conſtare non poteſt, utrum <lb></lb>aër reſiduus poſt aquæ attractionem ſit ad naturalem ſtatum re<lb></lb>dactus, an verò præter naturam addenſatus, aut rarefactus. </s><s>Vi<lb></lb>de quæ dicimus infrà in Appendice. </s></p> <p type="main"> <s><emph type="center"></emph>Concluſio<emph.end type="center"></emph.end></s></p> <p type="main"> <s><emph type="center"></emph>Protheoriæ Quartæ.<emph.end type="center"></emph.end></s></p> <p type="main"> <s>DIci hîc nonnulla poſſent de ſalientium ex fontibus pneuma<lb></lb>ticis, quos deſcribimus Parte 2. Claſſe 1. cap. 2. Machina 8. <lb></lb>longitudine, altitudineque, & cum tuborum ſalientibus compa<lb></lb>rari, ut facit Merſennus in ſuis Hydraulicis Propoſit. 28. ſed <lb></lb>quoniam valde incerta ſunt & quæ Merſennus affert, & quæ à <lb></lb>me, & à quocunque alio, varijs experientijs inventa, afferri poſ<lb></lb>ſunt; ſatiùs judicavi, omnino abſtinere. </s><s>Dependet enim ſalien<lb></lb>tium hujuſmodi longitudo atque altitudo, non à tuborumlongi<lb></lb>tudine, ſed potiſſimùm ab aëris intra fontem compreſſi vehe<lb></lb>mentia, quæ infinitis modis variari poteſt; & cùm omnia exper<lb></lb>tus fueris, dubius adhuc hærebis. </s></p> <p type="main"> <s>Dici præterea multa poſſent de fluxu aquæ per tubos incli<lb></lb>natos & horizontales; examinarique, quæ habet Joannes Bapti<lb></lb>ſta Balianus lib 4. & 5. de Motu gravium, ſeu lib. 1. & 2. de motu <lb></lb>liquidorum: at quoniam hæc non admodum conducunt fini no<lb></lb>ſtro in hoc Opere intento, & longiorem ſermonem requirunt; <lb></lb>omittenda potiùs omnino quàm paucis perſtringenda pu<lb></lb>tavi, acturus de illis in Mechanica Univerſali. </s><s>Ad <lb></lb>praxin igitur, miſsâ theoriâ, <lb></lb>procedamus. <lb></lb> <arrow.to.target n="fig46"></arrow.to.target></s></p> </chap> </body> <back></back> </text> </archimedes>