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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Borelli, Giovanni Alfonso</author> <title>De motionibus naturalibus a gravitate pendentibus</title> <date>1670</date> <place>Reggio di Calabria</place> <translator/> <lang>la</lang> <cvs_file>borel_demot_010_la_1670.xml</cvs_file> <cvs_version/> <locator>010.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="010/01/001.jpg"/> <p type="head"> <s id="s.000001"><emph type="center"/>DE <lb/>MOTIONIBVS <lb/>NATVRALIBVS <lb/>A GRAVITATE PENDENTIBVS<emph.end type="center"/></s> </p> <pb xlink:href="010/01/002.jpg"/> <p type="main"> <s id="s.000002">[blank] </s> </p> <pb xlink:href="010/01/003.jpg"/> <p type="main"> <s id="s.000003"><emph type="center"/>DE <lb/>MOTIONIBVS <lb/>NATVRALIBVS <lb/>A GRAVITATE PENDENTIBVS, <lb/>LIBER <lb/>IO: ALPHONSI BORRELLI <lb/>in Academia Pi&longs;ana Mathe&longs;eos profe&longs;&longs;oris.<emph.end type="center"/></s> </p> <figure id="id.010.01.003.1.jpg" xlink:href="010/01/003/1.jpg"/> <p type="main"> <s id="s.000004"><emph type="center"/>REGIO IVLIO, <lb/>In Officina Dominici Ferri. </s> <s id="s.000005">1670.<emph.end type="center"/></s> </p> <p type="main"> <s id="s.000006"><emph type="center"/><emph type="italics"/>Superiorum permi&longs;&longs;u.<emph.end type="italics"/><emph.end type="center"/></s> </p> <pb xlink:href="010/01/004.jpg"/> <p type="main"> <s id="s.000007">[blank] </s> </p> <pb xlink:href="010/01/005.jpg"/> <p type="main"> <s id="s.000008"><emph type="center"/>ILLVSTRISS. ET EXCELLENTISS. <lb/>DOMINO <lb/>D. ANDREÆ <lb/>CONCVBLET <lb/>MARCHIONI ARENÆ. <lb/></s> <s id="s.000009">IO: ALPHONSVS BORRELLVS. S.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000010">S<emph type="italics"/>I quid præclara nobilitas laudis, & commendationis mere­<lb/>tur, id profectò non filijs &longs;ed progenitoribus tribuendum e&longs;&longs;e <lb/>Sapientes non nulli cen&longs;uere; proinde qui nobilitatem iactat, de­<lb/>cus, ac bonum alienum non &longs;uum commendare dixerunt. </s> <s id="s.000011">Hoc &longs;a­<lb/>nè verum e&longs;&longs;et, &longs;i Parentes alienæ, & minimè naturales e&longs;­<lb/>&longs;ent liberorum cau&longs;æ, neque materiam, aut influxum in genera­<lb/>tione præ&longs;tarent: at &longs;ecus res &longs;e habet, &longs;icut enim plantarum ger­<lb/>mina, & fructus ip&longs;is Arboribus, ac Seminibus conformes e&longs;&longs;&etail;, <lb/>nec vnquam Ro&longs;am è papactere, aut dulcia Poma ex Quercu pro-<emph.end type="italics"/> <pb xlink:href="010/01/006.jpg"/> duci videmus; &longs;ic Parentes no&longs;tros minimè diuer&longs;am, et alteram <lb/> &longs;ibi naturam, ac Indolem procreare in liberis con&longs;entaneum e&longs;t; <lb/> Indè euenit, quod præclaris et heroicis maioribus prognati ani­<lb/> mi illam, morumque præ&longs;tantiam ut plurimum &longs;ortiantur: his <lb/> adde quod cum maior pars, et præcipua humanarum actionum <lb/> ab opinione in&longs;ita, vel acqui&longs;ita, non minus quàm à naturali in<lb/> &longs;tinctu pendeat fit ut nobilibus non leue &longs;it impo&longs;itum onus ma­<lb/>iorum ve&longs;tigijs in&longs;i&longs;tendi; per&longs;ua&longs;umque &longs;ibi habeant turpe, et <lb/> indignum e&longs;&longs;e Illustrium progenitorum eße degeneres, imo putens <lb/> præ&longs;tantiora &longs;uorum facinoribus manu, ingenio, ac prudentia ad <lb/> &longs;ui, et pro&longs;apiæ &longs;plendorem, atque patriæ utilitatem &longs;ibi e&longs;&longs;e <lb/> patranda. </s> <s id="s.000012"> has laudes iure optimo Excellenti&longs;&longs;ime Marchio tibi <lb/> deberi omnes, uno ore, fatentur; <expan abbr="quipppè">quippe</expan> qui auitam nobilitatem <lb/> ante quinque &longs;æcula inceptam longa &longs;erie Comitum Arenæ locum <lb/> vige&longs;imum quintum explens, non modo &longs;u&longs;tines, &longs;ed præclaras <lb/> eorum Virtutues &longs;uperare conatus es: et vt de Illu&longs;tribus illorum <lb/> domi, militiæque; rebus ge&longs;tis taceam, unum &longs;olummodo in <lb/> præ&longs;entia innuere erit opere prætium, curam nimirum &longs;cientia­<lb/> rum, et Virorum, qui Philosophiam colere, et nouis inuen­<lb/> tis illu&longs;trare profitentur, ex quo, luculento &longs;anè exemplo du­<lb/> ctus Aui tui Illu&longs;tri&longs;&longs;imi qui Bernardinum Tele&longs;ium &longs;upra Vul­<lb/> gum Philo&longs;ophantem eximio amore pro&longs;ecutus, tutela, et pa­<lb/> trocinio &longs;uo fouit. </s> <s id="s.000013">Tu ip&longs;e es, qui primus in præclara Vrbe Par­<lb/> tenopea, mea parente, &longs;ocietatem, &longs;eu Academiam in tuo Mu­<lb/> &longs;eo erexi&longs;ti, in qua certis, et indubitatis experimentis non ve­<lb/> rò inanibus, ac rixo&longs;is di&longs;putatiunculis, Philo&longs;ophicas Verita­<lb/> tes ad Reipublicæ litterariæ bonum, indagarentur; idque &longs;um­<lb/> ma Cura, ac Munificentia præ&longs;titi&longs;ti, in unum collectis Cla­<lb/> ri&longs;&longs;imis Docti&longs;&longs;&longs;imi&longs;que Viris, Caramuele, Thoma Cornelio, <lb/> <pb xlink:href="010/01/007.jpg"/> Franci&longs;co De Andrea, Leonardo à Capua, Luca Antonio Por­<lb/> tio, innumeri&longs;que aliis; quibus cum me quoque benignè excep­<lb/> tum, adiunxeris, ne Vacuis manibus accedam, tibi ecce Vir <lb/> Excellenti&longs;&longs;ime offero hoc meum Opus de Naturalibus Motio­<lb/> nibus à grauitate pendentibus, quod e&longs;t &longs;ecundum præcedentium <lb/> Doctrinam de Animalium motibus, in quo rationes Philo&longs;ophi­<lb/> cæ, quam plurimorum Experimentorum naturalium afferuntur, <lb/> quæ Florentiæ in Academia Experimentali Medicea Vidi, pa­<lb/> riterque accurati&longs;&longs;ime &longs;unt ob&longs;eruata in tua Neapolitana: Tu &longs;i­<lb/> quidem, Vir Optimè, in hoc libro aliqua reperies, quæ natura­<lb/>lem Scientiam, cuius &longs;anè &longs;tudio impensè teneris, promouere <lb/> valeant, iis fruere, et Vale. </s> </p> <pb xlink:href="010/01/008.jpg"/> <p type="main"> <s id="s.000014"><emph type="center"/>PROOEMIVM <lb/>AD LECTOREM.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000015">HAbes iam, erudite Lector, in hoc Libro de Motionibus Natura­<lb/>libus à grauitate pendentibus, vna cum præcedenti do Vi Per­<lb/>cu&longs;&longs;ionis ea omnia, quæ præmitti debuerant ad perfectam intelligen­<lb/>tiam doctrinæ de animalium motibus, exceptis quamplurimis mecha­<lb/>nicis lemmatibus, quæ &longs;uis locis deinceps iuxta &longs;ubiecti exigentia&mtail; <lb/>exponentur. </s> <s id="s.000016">Debeo tamen nonnulla præfari de hoc, & præcedenti <lb/>Opere, in quibus multoties afferuntur &longs;ententiæ diuer&longs;æ ab Authorum <lb/>magni nominis opinionibus. </s> <s id="s.000017">Hoc tamen &longs;umma mode&longs;tia, & modera­<lb/>tione exequutus &longs;um; quandoquidem &longs;ententias in&longs;ector, non autem <lb/>authorum nomina, aut famam attingo: quippe qui &longs;olummodo veri­<lb/>tatem quæro, &longs;eruata interim dignitate, & fama clari&longs;&longs;imorum viro­<lb/>rum: quod con&longs;tat ex eo, quod tunc &longs;olummodo viuentium autho­<lb/>rum nomina recen&longs;eo, cum laudandi eos occa&longs;io offertur; cum vero <lb/>controuer&longs;iæ agitantur nomina authorum omnino teguntur, ac &longs;ilen­<lb/>tur; quia verò hac tan religio&longs;a moderatione, & mode&longs;tia effugere non <lb/>potui contradicentium mordacitates, ideo vi&longs;um e&longs;t denuo pollicer&etail; <lb/>me ab in&longs;tituto incepto non dimoueri, nec di&longs;cedere velle, neque op­<lb/>po&longs;it oribus, &longs;i qui for&longs;an extiterint, re&longs;pon&longs;um vllum apologeticum, & <lb/>contentio&longs;um edere velle, &longs;ed tantummodo &longs;i opus fuerit meam do­<lb/>ctrinam melius, & apertius declarare, vel corrigere vbi for&longs;an huma­<lb/>no more lap&longs;us fuero. </s> <s id="s.000018">Vale. </s> </p> <pb pagenum="1" xlink:href="010/01/009.jpg"/> <p type="main"> <s id="s.000019"><emph type="center"/>DE MOTIONIBVS <lb/>NATVRALIBVS <lb/>A Grauitate pendentibus.<emph.end type="center"/></s> </p> <p type="main"> <s id="s.000020"><emph type="center"/><emph type="italics"/>LIBER<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000021"><emph type="center"/>IO: ALPHONSI BORELLI<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000022"><emph type="center"/><emph type="italics"/>Motus Corporum &longs;ublunarium in medio fluido fieri, <lb/>de quibus hactenus nemo tract auit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000023"><emph type="center"/>CAPVT I.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000024">EVidenti&longs;&longs;imum e&longs;t motus corporum <expan abbr="&longs;ub-lunariũ">&longs;ub­<lb/>lunarium</expan> fieri debere in aliquo &longs;patio, <lb/>quod minimè impleri & occupari de­<lb/>bet à corporibus duris, con&longs;i&longs;tentibus, <lb/>& omninò continuis, propterea quòd <lb/>duo corpora &longs;e mutuò penetrare nequeunt, igitur <lb/>nece&longs;&longs;e e&longs;t vt &longs;patium, in quo corpus aliquod moue­<lb/>ri debet, aut &longs;it omninò vacuum, vel &longs;altem occupe­<lb/>tur ab aliquo corpore di&longs;trahibili, & fluido, vel in <lb/>particulas &longs;ubdiui&longs;o, quod nimirum facilè expelli <lb/>po&longs;&longs;it è &longs;uo loco, vt &longs;ubintranti corpori, quod moue­<lb/>ri debet locum cedat. </s> <s id="s.000025">ab hi&longs;ce fluidis corporibus re­<lb/>gio i&longs;ta terram ambiens occupatur, vt ab aqua, aere, <lb/>& igne, in quibus fiunt motiones corporum &longs;ublu­<lb/>narium. </s> </p> <p type="main"> <s id="s.000026">De ip&longs;is porrò naturalibus motionibus corporum, <lb/>qu&etail; in medio fluido fiunt, &longs;cilicèt qua ratione, & qua-</s> </p> <pb pagenum="2" xlink:href="010/01/010.jpg"/> <p type="main"> <s id="s.000027"><arrow.to.target n="marg1"/><lb/>re corpora varias magnitudines, pondera, & di­<lb/>uer&longs;as figuras habentia, moueantur maiori, aut mi­<lb/>nori velocìtate, certa quadam proportione in medio <lb/>fluido, nemo (quod &longs;ciam) differuit. </s> <s id="s.000028">Igitur hanc <lb/>phy&longs;ico-mechanices partem hactenùs de&longs;iderata&mtail; <lb/>exponere, ac &longs;upplere animus e&longs;t; &longs;ed ne fa&longs;tidio&longs;&atail; <lb/>repetitione earum rerum, quæ ab alijs tradita &longs;unt, <lb/>lectores de tineam, &longs;upponam ea omnia, quæ in ele­<lb/>mentis mechanicis tradita &longs;unt de natura libræ, vec­<lb/>tis, trochleæ, & de reliquis ab hi&longs;ce in&longs;trumentis pen­<lb/>dentibus, eorum que naturam participantibus. </s> <s id="s.000029"><expan abbr="afferã">afferam</expan> <lb/>tantummodò aliqua quæ præcipuum v&longs;um habent in <lb/>hac doctrina de naturalibus corporum motionibus, <lb/>non de omnibus, &longs;ed de ijs &longs;olum modò, quæ à vi mo­<lb/>tiua grauitatis pendent. </s> </p> <p type="margin"> <s id="s.000030"><margin.target id="marg1"/>Cap. 1. Cor­<lb/>porum mo­<lb/>tus in medio <lb/>fluido fieri.</s> </p> <p type="main"> <s id="s.000031"><emph type="center"/><emph type="italics"/>De Momentis Grauium con&longs;istentium & fluidorum <lb/>in ij&longs;dem fluidis innatantium.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000032"><emph type="center"/>CAP. II.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000033">SVbtili&longs;&longs;imè, & præclarè Archimedes egit de in&longs;i­<lb/>dentibus humido, idip&longs;um po&longs;te a alia methodo <lb/>Galileus, & Steuinus demon&longs;trarunt, cùm veritas in­<lb/>numeris modis confirmari po&longs;&longs;it, ip&longs;e verò, non ge­<lb/>nio variandi, nouas earumdem propo&longs;itionum de­<lb/>mon&longs;trationes via longè diuer&longs;a procedendo, exco­<lb/>gitaui, & attuli, &longs;ed quia hæ valdè conducunt ad ea <lb/>quæ po&longs;terius à nobis explicanda &longs;unt. </s> <s id="s.000034">at priùs ali­<lb/>quæ hypothe&longs;es &longs;unt præmittendæ. <pb pagenum="3" xlink:href="010/01/011.jpg"/><arrow.to.target n="marg2"/></s> </p> <p type="margin"> <s id="s.000035"><margin.target id="marg2"/>Cap. 1. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000036"><emph type="center"/><emph type="italics"/>SVPPOSITIO I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000037">Suppono primò quòd quodlibet corpus, &longs;iuè den­<lb/>&longs;um, &longs;iuè fluidum, ex ijs quæ globum terra-queu&mtail; <lb/>componunt, graue e&longs;t, exercetque vim &longs;eù conatum <lb/>&longs;uæ grauitatis, etiam &longs;i in fluido &longs;ibi aut homogeneo, <lb/>aut non, con&longs;tituatur. </s> <s id="s.000038">hoc autem &longs;uo loco euidenti&longs;­<lb/>&longs;imis rationibus, ac experimentis confirmabitur. </s> </p> <p type="main"> <s id="s.000039"><emph type="center"/><emph type="italics"/>SVPPOSITIO II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000040">Secundo loco &longs;uppono vim, &longs;eù conatum, quo flui­<lb/>da nituntur &longs;e&longs;e vnire &longs;phæræ terraqueæ, effici per <lb/>lineas perpendiculares ad &longs;uperficiem horizontis. </s> <s id="s.000041">& <lb/>hoc patet quia quodlibet graue naturali in&longs;tinctu co­<lb/>natur ad centrum terræ accedere via breui&longs;&longs;ima, igi­<lb/>tur directio prædicti motus, &longs;eù conatus compre&longs;&longs;iuus <lb/>efficietur per &longs;emidiametros eiu&longs;dem terræ, hæ verò <lb/>perpendiculares &longs;unt ad &longs;uperficiem horizontalem, <lb/>quæ &longs;phæricè ip&longs;am terram comprehendit, igitur ma­<lb/>nife&longs;tum e&longs;t quòd motus &longs;eù conatus compre&longs;&longs;iuus <lb/>omnium partium fluidi per lineas ad horizontem per­<lb/>pendiculares efficitur. </s> </p> <p type="main"> <s id="s.000042"><emph type="center"/><emph type="italics"/>SVPPOSITIO III.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000043">Tertiò quod libet corpus graue e&longs;t impo&longs;&longs;ibile vt <lb/>moueatur motu &longs;pontaneo, & naturali, quando ad <expan abbr="c&etilde;-trum">cen­<lb/>trum</expan> telluris minimè approximari pote&longs;t. </s> <s id="s.000044">hoc mani­<lb/>fe&longs;tum e&longs;t quia cùm omnes partes terrenæ vt graues <lb/>naturali in&longs;tinctu ad terræ centrum accedere conen-<pb pagenum="4" xlink:href="010/01/012.jpg"/><arrow.to.target n="marg3"/><lb/>tur, hocque earum de&longs;iderium expleri minimè po&longs;&longs;it <lb/>ni&longs;i mediante motu, igitur ce&longs;&longs;ante fine nece&longs;&longs;ariò <lb/>medium quoque ce&longs;&longs;at, &longs;cilicet quando non pote&longs;t <lb/>graue aliquod magis, quàm prius ad terræ centrum <lb/>accedere, tunc nequaquam mouebitur. </s> <s id="s.000045">ex quo &longs;equi­<lb/>tur vt prædicta corpora quie&longs;cant, quandoquidem &longs;i <lb/>mouerentur, aut deberent à centro telluris recedere <lb/>& remoueri, vel lateraliter circumferri, in primo ca­<lb/>&longs;u &longs;equeretur operatio contraria naturali in&longs;tinctui <lb/>grauium, quod e&longs;t impo&longs;&longs;ibile; in &longs;ecundo verò ca&longs;u <lb/>efficeretur operatio vanæ, & &longs;i fru&longs;tratoria, nil enim <lb/>graue præterea acquireret cùm non amplius ad terræ <lb/>centru accedere po&longs;&longs;et ex hypothe&longs;i, ab&longs;urdum verò <lb/>e&longs;t atque repugnat naturam operari ca&longs;u, & ab&longs;que <lb/>fine; igitur e&longs;t impo&longs;&longs;ibile vt corpora, quæ ad <expan abbr="centrũ">centrum</expan> <lb/>terræ accedere nequeunt, vllo pacto moueantur; qua <lb/>propter nece&longs;&longs;e e&longs;t vt in eodem &longs;itu fixè quie&longs;cant in <lb/>quo prius degebant. </s> </p> <p type="margin"> <s id="s.000046"><margin.target id="marg3"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000047"><emph type="center"/><emph type="italics"/>SVPPOSITIO IV.<emph.end type="italics"/><emph.end type="center"/><lb/><arrow.to.target n="marg4"/><!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000048"><margin.target id="marg4"/>Archimedis <lb/>&longs;uppositio. </s> </p> <p type="main"> <s id="s.000049">Præterea Archimedes &longs;uppo&longs;uit vt primum prin­<lb/>cipium per &longs;e notum, quod eiu&longs;dem fluidi con&longs;i&longs;ten­<lb/>tis, partes quæ &longs;int continuat&etail; in eodem plano hori­<lb/>zontali minus pre&longs;&longs;æ debeant eijci expellique &longs;ur&longs;um <lb/><expan abbr="perp&etilde;diculariter">perpendiculariter</expan> à partibus eiu&longs;dem fluidi magis <expan abbr="cõpre&longs;&longs;is">com­<lb/>pre&longs;&longs;is</expan>, hoc verò principium, licèt veri&longs;&longs;imum &longs;it, ha­<lb/>bet tamen aliquam ob&longs;curitatem, cùm minimè eui­<lb/>dens &longs;it, quamobrem partes eiu&longs;dem fluidi po&longs;&longs;int <lb/>magis, aut minus comprimi; nec pariter euidenter </s> </p> <pb pagenum="5" xlink:href="010/01/013.jpg"/> <p type="main"> <s id="s.000050"><arrow.to.target n="marg5"/><lb/>percipitur quomodo à naturali operatione, de&longs;cen­<lb/>&longs;us nempè deor&longs;um, produci debeat operatio <expan abbr="quædã">quædam</expan> <lb/>contraria, a&longs;cen&longs;us nimirum alterius partis eiu&longs;dem <lb/>fluidi &longs;cilicet recedendo a centro telluris. </s> <s id="s.000051">erit igitur <lb/>operæpretium per&longs;picuè o&longs;tendere veritatem præ­<lb/>dictæ operationis, eamque deducere ex principijs <lb/>magis notis, & euidentibus. </s> </p> <p type="margin"> <s id="s.000052"><margin.target id="marg5"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000053"><emph type="center"/>PROPOSITIO I.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000054"><emph type="center"/><emph type="italics"/>Grauis &longs;u&longs;pen&longs;i non ex centro &longs;uæ grauitatis vna eius pars <lb/>&longs;ur&longs;um a&longs;cendit quiæ integrum graue <expan abbr="deorsũ">deorsum</expan> de&longs;cendit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000055">Sit graue AB exten&longs;um, vel compo&longs;itum ex dua­<lb/>bus partibus in extremitatibus eiu&longs;dem libræ <lb/>horizontalis AB di&longs;po&longs;itis, & commune centrum gra­<lb/>uitatis earum &longs;it D. &longs;u&longs;ti­<lb/><figure id="id.010.01.013.1.jpg" xlink:href="010/01/013/1.jpg"/><lb/>neatur po&longs;tea, fulciatur­<lb/>que tota libra ex puncto <lb/>C remoto à centro graui­<lb/>tatis D. dico quòd pars <lb/>eius oppo&longs;ita B &longs;ur&longs;u&mtail; <lb/>a&longs;cendet per arcum BF, <lb/>hac &longs;olummodo de cau&longs;&atail; <lb/>quia integrum graue AB magis, quàm prius ad cen­<lb/>trum terræ accedit. </s> <s id="s.000056">quia duæ partes graues A & B <lb/>exercent &longs;uam grauitatem & conatum compre&longs;&longs;iuum <lb/>in centro communi earum grauitatum D; e&longs;t que <lb/>prædictum centrum D remotum à fulcimento &longs;tabili <lb/>C, igitur efformabitur veluti fune-pendulum CD <pb pagenum="6" xlink:href="010/01/014.jpg"/><arrow.to.target n="marg6"/><lb/>horizontaliter con&longs;titutum, &longs;u&longs;pen&longs;um, & alligatum <lb/>in centro C & pondus vniuer&longs;um applicatum eriti&ntail; <lb/>centro D extremo fili, vel lineæ CD: &longs;ed penduli na­<lb/>tura talis e&longs;t vt conetur deor&longs;um ferri per arcum qua­<lb/>drantis DE circa centrum eius fixum C v&longs;que ad lo­<lb/>cum infimum E, quod magis ad centrum terræ appro­<lb/>ximatur, quàm in &longs;itu horizontali D & patet quòd <lb/>vniuer&longs;a hæc operatio nece&longs;&longs;aria, & naturalis e&longs;t de­<lb/>pendens à de&longs;cen&longs;u totius grauis. </s> <s id="s.000057">& e&longs;t impo&longs;&longs;ibil&etail; <lb/>vt fune pendulum CD ad in fimum &longs;itum CE perduca­<lb/>tur ab&longs;que eo quòd libra rigida &longs;itum perpendicula­<lb/>rem ad horizontem acquirat, quale e&longs;t GCF, hoc ve­<lb/>ro minimè acquiri pote&longs;t ni&longs;i pars minus grauis libræ <lb/>B &longs;ur&longs;um a&longs;cendat per arcum BF, igitur ca&longs;us, & de­<lb/>&longs;cen&longs;us totius corporis grauis AB à &longs;itu eleuato D ad <lb/>infimum E e&longs;t vera & legitima cau&longs;a a&longs;cen&longs;us corpo­<lb/>ris grauis B per arcum BF, quod fuerat o&longs;tendendum. </s> </p> <p type="margin"> <s id="s.000058"><margin.target id="marg6"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <figure id="id.010.01.014.1.jpg" xlink:href="010/01/014/1.jpg"/> <p type="main"> <s id="s.000059">Patet igitur quod &longs;im­<lb/>plex ca&longs;us, aut de&longs;cen&longs;us <lb/>corporis grauis e&longs;t vera, <lb/>& legitima cau&longs;a motus, <lb/>& a&longs;cen&longs;us alicuius partis <lb/>eius &longs;ur&longs;um, & hoc planè <lb/>contingit quotie&longs;cumque <lb/>graue vniuer&longs;um &longs;u&longs;tine­<lb/>tur ab aliquo eius puncto libræ realis, vel imagina­<lb/>riæ, it aut efficiatur commotio omnium partium eius <lb/>non quidem per lineas rectas inter &longs;e parallelas, & <lb/>horizonti perpendiculares, &longs;ed vertigino&longs;as, & cir-<pb pagenum="7" xlink:href="010/01/015.jpg"/><arrow.to.target n="marg7"/><lb/>culares quales &longs;unt illæ quæ à fune-pendulis de&longs;cri­<lb/>buntur, & in prædicto motu vertigino&longs;o e&longs;t tam ne­<lb/>ce&longs;&longs;arius, & naturalis a&longs;cen&longs;us partis minus grauis B <lb/>per arcum BF quemadmodum nece&longs;&longs;arius e&longs;t lap&longs;us <lb/>& de&longs;cen&longs;us totius grauis per arcum DE v&longs;que ad lo­<lb/>cum infimum E & licet a&longs;cen&longs;us prædictæ portionis <lb/>B vulgo cen&longs;eatur motus violentus, nihilominus &longs;i <lb/>perpendatur vertigo, & debita &longs;ituatio corporis gra­<lb/>uis quatenus naturalis e&longs;t & naturali in&longs;tinctu acqui­<lb/>&longs;ita, & producta; cùm &longs;it impo&longs;&longs;ibile vt prædicta &longs;itua­<lb/>tio debita ab&longs;olute con&longs;equatur ab&longs;que a&longs;cen&longs;u por­<lb/>tionis B &longs;itque verum quoque quod, qui vult fine&mtail; <lb/>velit quoque nece&longs;&longs;e e&longs;t media, quæ ad finem con&longs;e­<lb/>quendum nece&longs;&longs;aria <expan abbr="sũt">sunt</expan>; hinc rationabiliter inferetur <lb/>à vi naturali verè impelli minus graue &longs;ur&longs;um ver&longs;us <lb/>F, ac proindè concedendum erit a&longs;cen&longs;um per BF <lb/>naturalem pror&longs;us e&longs;&longs;e vel potius in eadem naturali <lb/>operatione includi debere violentiam motus præ­<lb/>dicti a&longs;cen&longs;us; &longs;ed vtcunque &longs;it &longs;ufficit nobis vt præ­<lb/>dicta operatio &longs;it nece&longs;&longs;aria, &longs;it que pror&longs;us impo&longs;&longs;ibi­<lb/>le vt aliter contingat; cæteri verò eam vocent &longs;iue na­<lb/>turalem, &longs;iue violentam ad eorum libitum. </s> </p> <p type="margin"> <s id="s.000060"><margin.target id="marg7"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000061"><emph type="center"/>PROP. II.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000062"><emph type="center"/><emph type="italics"/>Idip&longs;um verificatur in fluidis contentis in <lb/>eodem &longs;iphone circulari.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000063">PRæterea vt duo corpora in extremitatibus libræ <lb/>con&longs;tituantur non &longs;emper e&longs;t nece&longs;&longs;e vt corpora <pb pagenum="8" xlink:href="010/01/016.jpg"/><arrow.to.target n="marg8"/><lb/>grauia A & B affixa &longs;int virgæ alicui rigidæ & con&longs;i­<lb/>&longs;tenti vt e&longs;t ACB pote&longs;t enim concipi canalis circu­<lb/>laris AGBF qui &longs;i repleatur aqua vel quolibet alio <lb/><figure id="id.010.01.016.1.jpg" xlink:href="010/01/016/1.jpg"/><lb/>fluido liquore cuius pars dex­<lb/>tera FAG grauior &longs;it quam re­<lb/>liqua fluidi pars GBF &longs;cilicet <lb/>&longs;i fluidum FAG fuerit hydrar­<lb/>girum, FBG verò aqua com­<lb/>munis, tunc pariter efficietur <lb/>libra, & centrum grauitatis <lb/>amborum liquorum non iace­<lb/>bit in diametro FCG perpendiculari ad horizontem, <lb/>&longs;ed vltra ip&longs;um inter C & A, &longs;cilicet in puncto aliquo <lb/>D tunc pariter erit centrum totius magnitudinis flui­<lb/>di ip&longs;um C & in hoc præci&longs;e fiet &longs;u&longs;pen&longs;io totius flui­<lb/>di, quia circa ip&longs;um efficiuntur duo motus contrarij, <lb/>nempe de&longs;cen&longs;us fluidi A & a&longs;pen&longs;us alterius oppo&longs;i­<lb/>ti fluidi B cùm igitur centrum communis grauitatis D <lb/>duorum fluidorum di&longs;tet à centro &longs;u&longs;pen&longs;ionis C effi­<lb/>cietur quoque pendulum, quod circulari motu ex­<lb/>curret per arcum DE. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000064"><margin.target id="marg8"/>Cap. 3. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000065"><emph type="center"/>PROP. III.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000066"><emph type="center"/><emph type="italics"/>Organum in quo videtur motus perpetuus effici <lb/>po&longs;&longs;e exponitur, atque eius defectus, <lb/>& in&longs;ufficientia detegitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000067">ET hic breui & non omnino &longs;uperuacanea digre&longs;­<lb/>&longs;ione indicabo impo&longs;&longs;ibilitatem motus perpetui <pb pagenum="9" xlink:href="010/01/017.jpg"/><arrow.to.target n="marg9"/><lb/>in machina quæ tantam veri&longs;imilitudinis apparenti­<lb/>am habere videtur, vt quilibet iuraret tali organo <lb/>motum continuari facilè po&longs;&longs;e, huiu&longs;modi &longs;peculatio­<lb/>nem & organi &longs;tructuram mihi olim communicauit <lb/>amicus optimus Clemens &longs;eptimius Galilei alumnus. <lb/></s> <s id="s.000068">is &longs;anè cum contemplaret tympana ver&longs;atilia &longs;eu ro­<lb/>tas illas quibus nauiculæ trahuntur Pi&longs;is & in Belgio <lb/>ab vno canali ad alium à vi vnius hominis, qui inter­<lb/>nam eius periphæriam, accliuem calcando ea&mtail; <lb/>reuoluit, vt quæ à canibus eodem tympano in coqui­<lb/>nis verua rotantur, cogitauit eodem modo <expan abbr="tympanũ">tympanum</expan> <lb/>efformari po&longs;&longs;e in quo <lb/><figure id="id.010.01.017.1.jpg" xlink:href="010/01/017/1.jpg"/><lb/>perpetuò medietas eius <lb/>&longs;ini&longs;tra à fluido corpor&etail; <lb/>grauiori quam medietas <lb/>dextra occupari po&longs;&longs;et. </s> <s id="s.000069">vt <lb/>in appo&longs;ito &longs;chemat&etail;. <lb/></s> <s id="s.000070">&longs;it tympanum æreum AF <lb/>BG comprehen&longs;um à &longs;u­<lb/>perficie curua cylindrica ærea & à duabus laminis <lb/>planis circularibus inter &longs;e parallelis optimè læuiga­<lb/>tis & cum illa coaptatis conglutinati&longs;que, verùm in­<lb/>tra tympani cauitatem collocetur lamina plana FCG <lb/>quæ v&longs;um diaphragmatis præ&longs;tet & medietas cylin­<lb/>dri FCGA aqua ver hydrargiro repleatur, reliqu&atail; <lb/>verò medietas BFCG oleo velaere oppleta &longs;it; lami­<lb/>na verò FCG axi HC annexa & ferruminata intr&atail; <lb/>tympanum & circa axim fixum C manubrio aliquo <lb/>H fixè retineri & reuolui po&longs;&longs;it, hac lege vt exactè <pb pagenum="10" xlink:href="010/01/018.jpg"/><arrow.to.target n="marg10"/><lb/>tangat &longs;uperficies internas ambarum ba&longs;ium plana­<lb/>rum & cauam &longs;uperficiem curuam eiu&longs;dem tympani: <lb/>oportet autem vt ad in&longs;tar epi&longs;tomij exacti&longs;&longs;imè dia­<lb/>phragma illud reuolutum ab&longs;que vlla rima occludat <lb/>egre&longs;&longs;umque impediat aquæ vel mercurio in &longs;emicy­<lb/>lindro FAG contento, remanente reliquo &longs;patio G <lb/>BF aere, vel oleo oppleto, &longs;itque præterea moles to­<lb/>tius tympani &longs;u&longs;pen&longs;a in ip&longs;o axi C aflixo duobus ful­<lb/>cris vt liberè circumuolui tympanum po&longs;&longs;it in plano <lb/>perpendiculari ad horizontem; tunc &longs;i vi manus ma­<lb/>nubrium H eique annexum diaphragma FCG perpe­<lb/>tuò in &longs;itu verticali ad horizontem retineretur, pro­<lb/>culdubio (dicèbat amicus) haberemus in tali ca&longs;u li­<lb/>bram radiorum æqualium perpetuam imaginariam <lb/>ACB quæ ab inæqualibus ponderibus premeretur, <lb/>&longs;cilicèt à pondere emi&longs;phærij mercurialis vel aquei <lb/>FAG radius CA grauaretur, dum oppo&longs;itus radius C <lb/>B à leuiori pondere olei, vel aeris deprimeretur. </s> <s id="s.000071">& <lb/>quia horum inæqualium ponderum centrum grauita­<lb/>tis &longs;emper in aliquo puncto D intercepto inter C & <lb/>A caderet, igitur &longs;emper libra AB flecti deberet de­<lb/>or&longs;um ad partes A, vel potius con&longs;titueretur pendu­<lb/>lum horizontale CD &longs;u&longs;pen&longs;um in centro C & ideò <lb/>pendulum de&longs;cendere deberet per arcum DE; qui&atail; <lb/>verò fluidum grauius FAG de primi non po&longs;&longs;et ob im­<lb/>pedimentum diaphragmatis FCG in &longs;itu verticali à <lb/>virtute manus retenti, &longs;equeretur vt vniuer&longs;um &longs;e­<lb/>micylindricum mercurij comprimendo & calcando <lb/>curuam &longs;uperficiem tympani AG, quæ volubilis e&longs;t <pb pagenum="11" xlink:href="010/01/019.jpg"/><arrow.to.target n="marg11"/><lb/>eam impelleret, proindeque deor&longs;um conuerti debe­<lb/>ret ab A ver&longs;us G cum à nullo retinaculo impediatur, <lb/>igitur &longs;emper reuolui po&longs;&longs;et tympanum ab A ver&longs;us <lb/>G quia &longs;emper per&longs;eueraret eadem cau&longs;a vertiginis <lb/>&longs;cilicet perpetuò con&longs;eruaretur pendulum CD in &longs;itu <lb/>horizontali, & ideò &longs;emper premeret & calcaret tym­<lb/>pani &longs;uperficiem AG; quapropter tali artificio con­<lb/>&longs;equi po&longs;&longs;e videtur motus perpetuus prædicti tym­<lb/>pani. </s> </p> <p type="margin"> <s id="s.000072"><margin.target id="marg9"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000073"><margin.target id="marg10"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000074"><margin.target id="marg11"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000075">Hoc, vt dixi, tantam veri&longs;imilitudinem præ&longs;efer­<lb/>re videtur vt nemo ex pluribus amicis quibus hoc ar­<lb/>tificium communicaui fallaciam in eo latere &longs;u&longs;pica­<lb/>tus fuerit, nihilominus licèt ego, nun quam ad praxim <lb/>hoc artificium reducere curauerim, non vereor tamen <lb/>ab&longs;olutè pronunciare motus perpetuitatem hac via <lb/>con&longs;e qui non po&longs;&longs;e, quia nimirum per&longs;uadere mihi <expan abbr="nõ">non</expan> <lb/>valeo grauia corpora moueri vnquam &longs;ponte debere, <lb/>quando nè pilum quidem magis, quàm prius <expan abbr="de&longs;c&etilde;-dere">de&longs;cen­<lb/>dere</expan> valent atque ad centrum terræ accedere neque­<lb/>unt: cum itaque centrum grauitatis communis D am­<lb/>borum fluidorum &longs;emper <lb/><figure id="id.010.01.019.1.jpg" xlink:href="010/01/019/1.jpg"/><lb/>in eodem plano horizon­<lb/>tali ABCD retineatur ac <lb/>&longs;i&longs;tatur mihi omninò im­<lb/>po&longs;&longs;ibile videtur vt rot&atail; <lb/>&longs;iue tympanum AGBF <expan abbr="cõ-uertatur">con­<lb/>uertatur</expan> ad partes A ver­<lb/>&longs;us G. <!-- KEEP S--></s> <s id="s.000076">Itaque licet <expan abbr="centrũ">centrum</expan> <lb/>grauitatis communis D di&longs;tet à centro &longs;ixo vertiginis <pb pagenum="12" xlink:href="010/01/020.jpg"/><arrow.to.target n="marg12"/><lb/>C & proinde pendulum horizontale con&longs;tituat; ta­<lb/>men aio ip&longs;um retineri &longs;u&longs;pendique à vi manus, quæ <lb/>diaphragma FG retinet ne conuertatur à vi ponderis <lb/>in centro D operantis, non &longs;ecus ac &longs;i <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb/>aliquod CD à &longs;ubiecta manu &longs;u&longs;pen&longs;um deor&longs;um fer­<lb/>ri non po&longs;&longs;et per arcum DE. & licèt fune-pendulum <lb/>CD in ca&longs;u no&longs;tro non &longs;it quid continuum & <expan abbr="alligatũ">alligatum</expan> <lb/>centro C nihilominus perindè &longs;e habet, cum eius co­<lb/>natus fiat per arcum DE eo modo præcisè, ac &longs;i cen­<lb/>tro C alligatum fui&longs;&longs;et; ille verò qui prohibet de&longs;cen­<lb/>&longs;um corporis grauis D, quod &longs;olummodo moueri per <lb/>arcum DE pote&longs;t, nece&longs;&longs;ariò impedit operatione&mtail; <lb/>eius loco motiuam, ideoque fluidum FAG cum omni­<lb/>nò quie&longs;cat, non poterit impellere, & conuerter&etail; <lb/>tympanum; nullo enim modo capi pote&longs;t proiectum <lb/>impelli ab eo corpore quod omninò in quiete con&longs;i­<lb/>&longs;tit, nam &longs;emper proijciens & impellens impetu & <lb/>motu locali affectum &longs;it oportet ad hoc, vt proyecto <lb/>gradum impetus imprimere valeat, cum igitur hy­<lb/>drargyrum FAG omninò iners &longs;it & motu locali care­<lb/>at, videtur omninò impo&longs;&longs;ibile vt proiecto &longs;cilicet <lb/>tympano gradum aliquem impetus imprimere queat, <lb/>proinde que tympanum non transferetur locali motu, <lb/>quare tali artificio motus vertiginis eius nedum con­<lb/>tinuari perpetuò non poterit, &longs;ed neque motum in­<lb/>coabit. </s> <s id="s.000077">Sed relicta digre&longs;&longs;ione ad rem no&longs;tram redeo. <pb pagenum="13" xlink:href="010/01/021.jpg"/><arrow.to.target n="marg13"/></s> </p> <p type="margin"> <s id="s.000078"><margin.target id="marg12"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000079"><margin.target id="marg13"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000080"><emph type="center"/>PROP. IV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000081"><emph type="center"/><emph type="italics"/>In canali seu &longs;iphone habente duo brachia directa, & <lb/>perpendiculariter eleuata ad horizontem, fluidi <lb/>in eo de&longs;cendentis centrum grauitatis cur­<lb/>uo itinere per lineam parabolicam <lb/>de&longs;cendit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000082">IN &longs;iphone TFGV &longs;int duo canales TF & GV pa­<lb/>ralleli inter &longs;e, & erecti perpendiculariter ad ba­<lb/>&longs;im FG, & ad horizontem, & quilibet eorum æquè <lb/>cra&longs;&longs;us &longs;it; capacitas verò portionis cylindri TF &longs;u­<lb/>pra horizontalem per V eductam vt e&longs;t TA in primo <lb/>ca&longs;u, & TC in &longs;ecundo, &longs;it æqualis <lb/><figure id="id.010.01.021.1.jpg" xlink:href="010/01/021/1.jpg"/><lb/>capacitati GV, quæ &longs;ecetur i&ntail; <lb/>quotcumque partes æquales à qua <lb/>ternario men&longs;uratas in X, Y, Z, I, <lb/>L, 2, & puncta A, B, C, D, E, &longs;int <lb/>centra grauitatum cylindrorum T <lb/>F, XF, YF, ZF, & AF, vel CF, pa­<lb/>riterque H, I, K, L &longs;int centra gra­<lb/>uitatum cylindrorum GI, GL, G2, <lb/>GV, & quia centra grauitatum A, <lb/>& B, bifariam &longs;ecant cylindros T <lb/>F, XF, ergo TF ad XF &longs;e habet vt <lb/>AF, ad BF, & per conuer&longs;ione&mtail; <lb/>rationis, & permutando TF ad AF <lb/>eamdem rationem habet, quàm TX ad AB, quar&etail; <lb/>AB &longs;emi&longs;&longs;is e&longs;t ip&longs;ius TX, non &longs;ecus ac HG mediatas <pb pagenum="14" xlink:href="010/01/022.jpg"/><arrow.to.target n="marg14"/><lb/>e&longs;t cylindri IG, intelligatur aqua primò eleuari i&ntail; <lb/>&longs;itu T & deprimi in dextro canali in G, & hinc eleua­<lb/>ta aqua ad I de&longs;cendat à T ad X coniungantur qu&etail; <lb/>duæ rectæ lineæ AG, & BH &longs;e &longs;ecantes in M, eritque <lb/>punctum Min horizontali EL con&longs;titutum, propterea <lb/>quod duo cylindri aquæ AB, & HG æquales &longs;unt in­<lb/>ter &longs;e, cum &longs;emi&longs;&longs;es &longs;int cylindrorum æqualium TX & <lb/>IG, ergo altitudo AB ad HG e&longs;t vt eiu&longs;dem cylindri <lb/>ba&longs;is H ad ba&longs;im A: eadem ratione AE ad LG erit vt <lb/>ba&longs;is H ad <expan abbr="basĩ">basim</expan> A quare altitudo AE ad LG erit vt AB <lb/>ad HG, <expan abbr="sũq;">sunque</expan> duæ rectæ lineæ AE & GL <expan abbr="perp&etilde;dicula">perpendicula</expan> <lb/>res ad <expan abbr="horizontal&etilde;">horizontalem</expan> FG, vel EL, & ideò inter &longs;e paral­<lb/>lelæ, ergo ob &longs;imilitudinem triangulorum vt AM ad <lb/>MG ita erit BM ad MH, nec non EM ad ML, & ideo <lb/>rectæ AG, BH, & EL &longs;e mutuo &longs;ecabunt in eode&mtail; <lb/>puncto M. po&longs;tea vt moles aquæ XBF vnà cum GHI <lb/>ad molem aquæ IHG ita fiat di&longs;tantia HB ad BQ, & <lb/>diuidendo, vt moles aquæ XBF ad GHI ita erit di­<lb/>&longs;tantia HQ ad QB, ideoque ex elementis mechanicis <lb/>punctum Q erit centrum grauitatis aquæ XBF vnà <lb/>cum GHI. quando verò aqua erat in &longs;ummitate T & <lb/>canalis GLV omninò exhau&longs;tus erat, tunc quide&mtail; <lb/>centrum grauitatis totius aquæ TAF per&longs;i&longs;tens i&ntail; <lb/>puncto A medio eiu&longs;dem canalis perindè operare­<lb/>tur ac &longs;i &longs;u&longs;pen&longs;us fui&longs;&longs;et cylindrus èx puncto A: de­<lb/>pre&longs;&longs;a po&longs;tmodum aqua v&longs;que ad Y & eleuata v&longs;que <lb/>ad L in oppo&longs;ito canali, denuo centrum grauitatis re­<lb/>pertum prædictæ aquæ exi&longs;tet in puncto R & tandem <lb/>depre&longs;&longs;a aqua v&longs;que ad A in primo ca&longs;u & v&longs;que ad <pb pagenum="15" xlink:href="010/01/023.jpg"/><arrow.to.target n="marg15"/><lb/>Y in &longs;ecundo & &longs;ubleuata v&longs;que ad V; tunc quide&mtail; <lb/>centrum grauitatis prædictæ aquæ horizontaliter <expan abbr="cõ-&longs;titutæ">con­<lb/>&longs;titutæ</expan> præcisè incidet in <expan abbr="c&etilde;tro">centro</expan> &longs;u&longs;pen&longs;ionis M, prop­<lb/>terea quòd vt ba&longs;is V ad ba&longs;im A &longs;eù vt cylindrus a­<lb/>queus GLV ad equè altum cy­<lb/><figure id="id.010.01.023.1.jpg" xlink:href="010/01/023/1.jpg"/><lb/>lindrum AEF in primo ca&longs;u vel <lb/>ad CEF in &longs;ecundo, ita fuit reci­<lb/>procè di&longs;tantia EM ad ML. o­<lb/>&longs;tendendum modò e&longs;t punct&atail; <lb/>A, Q, R, S, M in eadèm linea pa­<lb/>rabolica e&longs;&longs;e. </s> <s id="s.000083">quia moles aquæ <lb/>TX æqualis e&longs;t æquæ moli GH <lb/>I, ergo, XBF vnà cum GHI æ­<lb/>qualis e&longs;t moli aqueæ TAF; e­<lb/>rat verò moles aquæ XBF vnà <lb/>cum GHI ad GHI vt linea HB <lb/>ad BQ &longs;eu (ducta QN parallel­<lb/>là AE) vt LE ad EN, ergo FAT <lb/>ad TX atque &longs;emi&longs;&longs;is illius FA <lb/>ad huius &longs;emi&longs;&longs;em AB eamdem <lb/>proportionem habebit qua&mtail; <lb/>LE ad EN, e&longs;t verò EA ad AF vt MA ad AG, &longs;eù vt <lb/>ME ad EL, ergo ex æqualitate ordinata EA ad AB <lb/>eamdem proportionem habebit quam ME ad EN, & <lb/>per conuer&longs;ionem rationis EA ad EB erit vt EM ad <lb/>MN, &longs;eù vt EB ad NQ, erunt igitur tres continuæ pro <lb/>portionales EA, EB, & NQ in eadem ratione qua&mtail; <lb/>habet EM ad MN, quare quadratum ex EM ad qua­<lb/>dratum ex MN eam proportionem habebit, qua&mtail; <pb pagenum="16" xlink:href="010/01/024.jpg"/><arrow.to.target n="marg16"/><lb/>AE ad NQ: ideoque puncta A & Q &longs;unt in parabol&atail; <lb/>cuius vertex M. quapropter aqua in prædicto &longs;iphone <lb/>dum ad æquilibrium de&longs;cendit mouetur eius centrum <lb/>grauitatis in linea parabolica; quod fuerat <expan abbr="o&longs;t&etilde;d&etilde;dũ">o&longs;tendendum</expan>. </s> </p> <p type="margin"> <s id="s.000084"><margin.target id="marg14"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="margin"> <s id="s.000085"><margin.target id="marg15"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000086"><margin.target id="marg16"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000087"><emph type="center"/>PROP. V.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000088"><emph type="center"/><emph type="italics"/>Ijsdem po&longs;itis &longs;i canales &longs;iphonis æquèlati angulum con&longs;ti­<lb/>tuentes æquè ad horizontem inclinati fuerint <lb/>idip&longs;um demon&longs;tratur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000089">SI po&longs;tea &longs;ipho inuer&longs;us eiu&longs;dem amplitudinis an­<lb/>gularis fuerit, vt nimirum &longs;emi&longs;&longs;es brachiorum <lb/>AF & FL æquè &longs;int ad horizontem EL inclinata effi­<lb/>ciatur què hi <lb/><figure id="id.010.01.024.1.jpg" xlink:href="010/01/024/1.jpg"/><lb/>&longs;o&longs;celium tri<lb/>angulum EF <lb/>L & brachij <lb/>&longs;upremi qua­<lb/>drans EA æ­<lb/>quale &longs;it FL, <lb/>&longs;iue FE. dico <lb/>denuò quòd <lb/>aqua totius <lb/>brachij F2. <lb/>cuius &longs;emi&longs;­<lb/>&longs;is e&longs;t AF <expan abbr="dũ">dum</expan> <lb/>fluit per canalem FL4 &longs;ur&longs;um & de&longs;cendit per 2 A; <lb/>tunc pariter eius centrum grauitatis per parabolam <lb/>deor&longs;um fertur. </s> <s id="s.000090">diui&longs;is æqualibus partibus in punctis <pb pagenum="17" xlink:href="010/01/025.jpg"/><arrow.to.target n="marg17"/><lb/>A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatu&mtail; <lb/>partium aquæ e&longs;&longs;e intelligantur vt prius, & ductis ad <lb/>horizontalem perpendicularibus AG, BV, CN, DO, <lb/>FM, H3, &c. </s> <s id="s.000091">pariterque coniunctis rectis DK, CI, <lb/>BH. quia anguli ad L, E æquales &longs;unt in i&longs;o&longs;cele, & <lb/>&longs;unt quoque anguli recti O & T, & hypothenu&longs;æ DE, <lb/>KL &longs;unt inter &longs;e æquales, ergo in &longs;imilibus triangulis <lb/>DOE, & KTL latera DO, KT æqualia erunt & recta <lb/>OE æqualis erit TL, & addita communi TE erit LE <lb/>æqualis OT quæ <expan abbr="nõ">non</expan> minus quàm DK bi&longs;&longs;ecta erit in <lb/>puncto Z, propter æquidi&longs;tantiam & æqualitatem la­<lb/>terum DO, & TK. &longs;imiliter reliquæ rectæ lineæ NY <lb/>& CI æquales erunt prioribus, & bi&longs;&longs;ectæ in puncto <lb/>P, idemque de reliquis <expan abbr="dicendũ">dicendum</expan> e&longs;t. </s> <s id="s.000092">& quia canales, <lb/>& moles aqueæ in eis contentæ AB, & FH, æquales <lb/>&longs;unt, ergo BFH æqualis e&longs;t AF; fiat iam HB ad BQ, <lb/>vt BFH ad FH, vel potius vt FA ad AB: quare &longs;emi&longs;­<lb/>&longs;es antecedentium ad ea&longs;dem con&longs;equentes in <expan abbr="ead&etilde;">eadem</expan> <lb/>ratione erunt, nempè vt EA ad AB, ita erit XB ad B <lb/>Q, & per conuer&longs;ionem rationis EA ad EB &longs;eu AG <lb/>ad BV, vel GE ad EV, & tandem vt duplum GM ad <lb/>duplum MN erit vt BX ad XQ, &longs;eu vt VX ad XN, <lb/>vel vt BV ad QN. igitur erunt tres continuæ propor­<lb/>tionales AG, BV, & QN in eadem ratione quam ha­<lb/>bet MG ad MN, quare vt quadratum MG ad quadra­<lb/>tum MN, ita erit longitudine AG ad QN ideoqu&etail; <lb/>duo puncta A & Q in parabola erunt. </s> </p> <p type="margin"> <s id="s.000093"><margin.target id="marg17"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000094">Con&longs;tat ergo quòd &longs;i brachia &longs;iphonis perpendicu­<lb/>laria fuerint ad horizontem, &longs;iuè ambo fuerint eiu&longs;-<pb pagenum="18" xlink:href="010/01/026.jpg"/><arrow.to.target n="marg18"/><lb/>dem latitudinis &longs;iuè non, &longs;emper centrum communis <lb/>grauitatis fluidi in de&longs;cen&longs;u parabolam de&longs;cribet; &longs;i <lb/>verò brachia &longs;iphonis æquè inclinata ad horizontem <lb/>fuerint, de&longs;cribet eius centrum in de&longs;cen&longs;u parabo­<lb/>lam quotie&longs;cumque brachia æquè cra&longs;&longs;a fuerint. </s> </p> <p type="margin"> <s id="s.000095"><margin.target id="marg18"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000096"><emph type="center"/>COROLLARIVM I.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000097">Siverò in eodem angulari &longs;iphone vnum brachium <lb/>dilatatum, alterum verò gracile fuerit, tunc eius <expan abbr="c&etilde;-trum">cen­<lb/>trum</expan> in de&longs;cen&longs;u curuam de&longs;cribet hyperbola&mtail; <lb/>&etail;mulantem. </s> </p> <p type="main"> <s id="s.000098"><emph type="center"/>COROLLARIVM II.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000099">Et tandem &longs;i vnum brachiorum perpendicular&etail; <lb/>fuerit ad horizontem, reliquum verò inclinatum in de­<lb/>&longs;cen&longs;u de&longs;cribet commune centrum grauitatis <expan abbr="curuã">curuam</expan> <lb/>ellip&longs;im æmulantem. </s> </p> <p type="main"> <s id="s.000100">His præmi&longs;&longs;is declarari debet altera libræ, &longs;eu &longs;i­<lb/>phonis proprietas, in quo centrum grauitatis eius <lb/>mouetur non quidem motu obliquo, & curuo, &longs;ed per <lb/>lineam rectam ad horizontem perpendicularem, pro <lb/>cuius intelligentia præmittendum e&longs;t, quod. </s> </p> <p type="main"> <s id="s.000101"><emph type="center"/>PROP. VI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000102"><emph type="center"/><emph type="italics"/>Duo pondera inæqualia fune non graui circa trochleam reuo­<lb/>luto &longs;u&longs;pen&longs;a, dum vnum eorum a&longs;cendit centrum gra­<lb/>uitatis eorum per lineam <expan abbr="rectã">rectam</expan> ad horizontem <lb/>perpendicularem deprimitur.<emph.end type="italics"/><emph.end type="center"/><pb pagenum="19" xlink:href="010/01/027.jpg"/><arrow.to.target n="marg19"/></s> </p> <p type="margin"> <s id="s.000103"><margin.target id="marg19"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000104">SIt pondus A maius, B verò minus alligata extre­<lb/>mitatibus funis ADB, qui &longs;upponatur omninò <lb/>grauitate carere, & reuoluatur circa trochleam CDE <lb/>conuertibilem circa axim fixum F. patet quòd funes <lb/>AC, & BE perpendiculariter ad ho­<lb/><figure id="id.010.01.027.1.jpg" xlink:href="010/01/027/1.jpg"/><lb/>rizontem CE prementes, & exten&longs;i <lb/>contingunt peripheriam rotæ in ter­<lb/>minis oppo&longs;itis C, & E eiu&longs;dem dia­<lb/>metri, &longs;eu libræ horizontalis, ergo <lb/>funes CA, & EB &longs;unt inter &longs;e paralle­<lb/>li; <expan abbr="coniũgatur">coniungatur</expan> po&longs;tea recta linea AB, <lb/>&longs;eceturque bifariam in G, & vt pon­<lb/>dus A ad B ita fiat di&longs;tantia BI ad IA <lb/><expan abbr="manife&longs;tũ">manife&longs;tum</expan> e&longs;t (ex mechanicis) punc­<lb/>tum I e&longs;&longs;e centrum grauitatis com­<lb/>munis duorum colligatorum ponde­<lb/>rum A & B, funis enim hanc propor­<lb/>tionem non alterat, cùm nullius gra­<lb/>uitatis &longs;upponatur: a&longs;cendat po&longs;tea <lb/>pondus minus B vbicumque ad L, & deprimatur ma­<lb/>ius pondus A v&longs;que ad K. dico quod ambo in com­<lb/>muni centro grauitatis de&longs;cendunt circa libræ cen­<lb/>trum, &longs;eu fulcimentum &longs;tabile G motu directo, & per­<lb/>pendiculari ad horizontem. </s> <s id="s.000105"><expan abbr="coniũgatur">coniungatur</expan> recta line&atail; <lb/>KL quia funis ADB æqualis, imò idem e&longs;t, quàm K <lb/>DL, igitur ablato communi ADL erit de&longs;cen&longs;us AK <lb/>æqualis a&longs;cen&longs;ui BL; quare in triangulis &longs;imilibus <lb/>ob æquidi&longs;tantiam laterum AK & BL homologorum <lb/>vt AK ad BL ita erit AG ad GB & ita pariter KML </s> </p> <pb pagenum="20" xlink:href="010/01/028.jpg"/> <p type="main"> <s id="s.000106"><arrow.to.target n="marg20"/><lb/>ad M, &longs;untque latera AK & BL æqualia inter&longs;&etail; <lb/>ergo &longs;e mutuò bifariam &longs;ecabunt rectæ coniungentes <lb/>AB, & KL in eodem puncto G; idemque continget <lb/>translatis ponderibus in N, & O, & ideo punctum G <lb/>erit centrum, &longs;eu &longs;tabile <expan abbr="fulcimentũ">fulcimentum</expan> libræ AB quo­<lb/>modolibet reuolutæ: ducatur tandem per I recta li­<lb/>nea IP parallela funibus &longs;ecans libras KL, & NO i&ntail; <lb/>punctis M, & P patet libras in eadem proportione re­<lb/>ciproca &longs;ecari in punctis I, M, P, quam habent oppo&longs;i­<lb/>ta pondera proindeque eadem puncta erunt centr&atail; <lb/>grauitatum, earumdem librarum cum ponderibus ap­<lb/>pen&longs;is; quapropter licet minus pondus B a&longs;cendat per <lb/>BLO, tamen ambo pondera A, & B in communi <expan abbr="c&etilde;-tro">cen­<lb/>tro</expan> grauitatis eorum I &longs;u&longs;pen&longs;a circa centrum <expan abbr="firmũ">firmum</expan> <lb/>G, & in extremo fune-penduli GI de&longs;cendunt no&ntail; <lb/>circulari, &longs;ed directo motu perpendiculari ad hori­<lb/>zontem ab I per M & P, quod fuerat o&longs;tendendum. </s> </p> <p type="margin"> <s id="s.000107"><margin.target id="marg20"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000108"><emph type="center"/>PROP. VII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000109"><emph type="center"/><emph type="italics"/>Id ip&longs;um osten ditur, cùm pondera in peripherijs inæqua­<lb/>libus, & concentricis eiu&longs;dem trochleæ reuoluuntur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000110">SIt trochlea CDE circa axim F conuertibilis, & in <lb/>ea &longs;it alia concentrica circumferentia RSQ, & <lb/>funi SQB alligetur pondus B, alij verò funi DEA alli­<lb/>getur pondus A <expan abbr="&longs;intq;">&longs;intque</expan> funes nullius ponderis; o&longs;ten­<lb/>detur, vt in præcedenti, funes EA, & BQ e&longs;&longs;e inter&longs;e <lb/>parallelos; po&longs;tea <expan abbr="coniũgatur">coniungatur</expan> recta AB, atque vt <expan abbr="põ-dus">pon­<lb/>dus</expan> A ad B ita reciprocè fiat di&longs;tantia BI ad IA; patet <pb pagenum="21" xlink:href="010/01/029.jpg"/><arrow.to.target n="marg21"/><lb/>punctum I e&longs;&longs;e centrum grauitatis communis ponde­<lb/>rum A, & B (cum funes nullius ponderis <expan abbr="&longs;upponãtur">&longs;upponantur</expan>) <lb/>deinde reuoluta trochlea <expan abbr="a&longs;c&etilde;dat">a&longs;cendat</expan> pondus B ad L, & <lb/>oppo&longs;itum pondus A de&longs;cendat v&longs;que ad K <expan abbr="coniũga-turque">coniunga­<lb/>turque</expan> recta KL &longs;ecans rectam AB <lb/><figure id="id.010.01.029.1.jpg" xlink:href="010/01/029/1.jpg"/><lb/>in G. dico duo pondera A, & B i&ntail; <lb/>communi eorum centro grauitatis <lb/>I circa libræ centrum &longs;tabile G mo­<lb/>tu directo, & perpendiculari ad <lb/>horizontem <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan>. </s> <s id="s.000111">quia in tro­<lb/>chleæ reuolutione <expan abbr="tãtumd&etilde;">tantumdem</expan> <expan abbr="de&longs;c&etilde;-dit">de&longs;cen­<lb/>dit</expan> terminus funis A quanta e&longs;t ex­<lb/>plicatio funis è rota CDE, & pon­<lb/>dus B a&longs;cendit quantum funis BQS <lb/>circumuoluitur circa rotam QSR <lb/>cùmque duæ rotæ concentricè con­<lb/>nexæ &longs;imul tempore <expan abbr="reuoluãtur">reuoluantur</expan> cir­<lb/>ca fixum axim F, ergo de&longs;cen&longs;us AK <lb/>ad <expan abbr="a&longs;c&etilde;&longs;um">a&longs;cen&longs;um</expan> BL eamdem proportio­<lb/>nem habet, quam peripheria CDE ad peripheriam R <lb/>SQ, &longs;eu <expan abbr="eamd&etilde;">eamdem</expan> proportionem, quam habet radius <lb/>FE ad radium <expan abbr="Fq;">Fque</expan> quare in triangulis AGK, & BGL <lb/>&longs;imilibus, ob æquidi&longs;tantiam laterum AK, & BL, erit <lb/>AG ad GB vt KG ad GL, &longs;eu vt AK ad BL; <expan abbr="proindeq;">proindeque</expan> <lb/>in eodem puncto fixo G duæ libræ AB, & KL &longs;e mutuò <lb/>&longs;ecabunt in eadem proportione, quam habent motus <lb/>eorumdem terminorum, vnde, ex mechanicis, erit <lb/>punctum G centrum, & fulcimentum firmu&mtail; <lb/>vtriu&longs;que libræ AB, & KL po&longs;tremò ducatur per I <pb pagenum="22" xlink:href="010/01/030.jpg"/><arrow.to.target n="marg22"/><lb/>rectà IM parallela funibus, &longs;eu perpendicularis ad <lb/>horizontem &longs;ecans KL in M planè &longs;ectæ erunt duæ li­<lb/>bræ prædictæ in I, & M in eadem proportione reci­<lb/>proca ponderum &longs;u&longs;pen&longs;orum, ideoque puncta I, & <lb/>M erunt centra grauitatum vtriu&longs;que libræ: quare li­<lb/>cet pondus B a&longs;cendat p BL, tamen verum e&longs;t duo <lb/>pondera AB in communi centro grauitatis I &longs;u&longs;pen&longs;a <lb/>circa centrum firmum G, & in termino fune-penduli <lb/>GI de&longs;cendere directo motu, & perpendiculari ad <lb/>horizontem per IM, & hoc erat o&longs;tendendum. </s> </p> <p type="margin"> <s id="s.000112"><margin.target id="marg21"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000113"><margin.target id="marg22"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000114">Huiu&longs;modi mechanicæ &longs;peculationes maximè <expan abbr="cõ-ferunt">con­<lb/>ferunt</expan> ad intelligentiam motus corporum in fluidis, <lb/>pro cuius declaratione primò con&longs;iderari debet. </s> </p> <p type="main"> <s id="s.000115"><emph type="center"/>PROP. VIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000116"><emph type="center"/><emph type="italics"/>Qua ratione fiat Motus fluidi in &longs;iphone continuato, <lb/>& in &longs;eip&longs;um reflexo.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000117">SIt igitur &longs;ipho ABDG in &longs;e ip&longs;um reflexus cuius <lb/>brachia lateralia BN & GO directa &longs;int, in­<lb/>ter &longs;e parallela, & ad horizontem perpendiculariter <lb/>erecta & æquè ampla. </s> <s id="s.000118">includatur po&longs;tea gutta aliqua <lb/>mercurij BC, quæ in fi&longs;tulis angu&longs;tis retinetur in eo­<lb/>dem &longs;itu collecta, reliqua verò cauitas eiu&longs;dem fi&longs;tulæ <lb/>BAGDC repleatur aqua; tunc ductis à punctis B, & <lb/>C & à <expan abbr="c&etilde;tro">centro</expan> grauitatis guttæ mercurialis H tribus li­<lb/>neis rectis parallelis horizonti BG, HI, & CF, & &longs;ec­<lb/>ta HI bifariàm in L; patet quòd duo grauia, mercu­<lb/>rius nempe BC, & aqua GF &longs;u&longs;penduntur in eade&mtail; <pb pagenum="23" xlink:href="010/01/031.jpg"/><arrow.to.target n="marg23"/><lb/>libra imaginaria HI, quia hæc duo corpora motibus <lb/>contrarijs agitantur &longs;u&longs;pendunturque ab eadem li­<lb/>bra horizontali: nec actionem eorumdem corporum <lb/>impediunt, vel adiuuant &longs;upremæ, vel infimæ aquæ <lb/>partes; quando quidem aqua AB, <lb/><figure id="id.010.01.031.1.jpg" xlink:href="010/01/031/1.jpg"/><lb/>æquilibratur collaterali AG cù&mtail; <lb/>&longs;int homogeneæ & æquè altæ, non <lb/>&longs;ecùs infimæ aquæ partes CD & F <lb/>E inter &longs;e æquilibrantur; quare ac­<lb/>tioni compre&longs;&longs;iuæ mercurij CB, <expan abbr="tã-tummodo">tan­<lb/>tummodo</expan> contraponitur pondus <lb/>aquæ FG in eodem &longs;itu horizontali <lb/>con&longs;titutæ. </s> <s id="s.000119">fiat iam vt pondus mer­<lb/>curij CB ad grauitatem aquæ FG <lb/>ita reciprocè di&longs;tantia IM ad MH, <lb/>quare punctum M erit centrum gra­<lb/>uitatis duorum corporum BC, & GF, cùmque libr&atail; <lb/>imaginaria HI fulciatur in puncto L rectæ LK per­<lb/>pendiculariter horizonti eductæ ex infimo &longs;itu fi&longs;tu­<lb/>læ, vbi bifariam libra, & magnitudines fluidæ <expan abbr="&longs;ecã-tur">&longs;ecan­<lb/>tur</expan>, igitur con&longs;tituitur fune-pendulum LM, & proin­<lb/>dè, iuxtà leges mechanices, libra flectetur <expan abbr="de&longs;cend&etilde;-do">de&longs;cenden­<lb/>do</expan> corpus BC, & a&longs;cendendo aquam FG, & hoc per­<lb/>ficitur propterea quòd centrum communis grauita­<lb/>tis M nece&longs;&longs;ariò labitur deor&longs;um iuxta penduli na­<lb/>turam. </s> <s id="s.000120">&longs;ed prædictus motus centri grauitatis M non <lb/>e&longs;t circularis, &longs;ed e&longs;t directus ad horizontem <expan abbr="perp&etilde;-dicularis">perpen­<lb/>dicularis</expan>, per lineam MQ <expan abbr="nõ">non</expan> &longs;ecùs ac in trochlea <expan abbr="cõ-tingit">con­<lb/>tingit</expan> vt dictum e&longs;t; huius operationis verò progre&longs;-<pb pagenum="24" xlink:href="010/01/032.jpg"/><arrow.to.target n="marg24"/><lb/>&longs;us talis e&longs;t, cùm primum cylindrus mercurij CB fer­<lb/>tur deorsùm transferendo eius centrum H in N, de­<lb/>nuò comparatur cum alio aquæ cylindro æquali ip&longs;i <lb/>FG è regione po&longs;ito, cuius centrum grauitatis erit <lb/>punctum O, & tunc denuò creatur noua libra <expan abbr="horizõ-talis">horizon­<lb/>talis</expan> NO &longs;ecta à rectis LP & MQ parallelis ENGO, <lb/>in P & Q cuius centrum P, quia denuò partes aquæ <lb/>collaterales &longs;upernæ & infernæ &longs;ibi ip&longs;is æquilibratæ <lb/>non adiuuant, neque impediunt duo æqualia corpo­<lb/>ra mercuriale ex N, & aqueum ex O, quæ ad inuicem <lb/>comparantur in eadem libra horizontali, <expan abbr="cumq;">cumque</expan> hæc <lb/>à parallelis lineis HN, MQ, & IO in ei&longs;dem rationi­<lb/>bus diuidatur, perductum erit centrum grauitatis pr&etail;­<lb/>dictorum corporum ad punctum Q, vnde patet de­<lb/>&longs;cendi&longs;&longs;e per rectam lineam MQ perpendicularem ad <lb/>horizontem, perdurabitque eius de&longs;cen&longs;us, <expan abbr="quou&longs;q;">quou&longs;que</expan> <lb/>corpus mercuriale CB ad &longs;itum infimum fi&longs;tulæ DE <lb/>perducatur, quando nimirum eius grauitatis <expan abbr="centrũ">centrum</expan> <lb/>H præcisè infimum &longs;itum K fi&longs;tulæ attinget. </s> </p> <p type="margin"> <s id="s.000121"><margin.target id="marg23"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000122"><margin.target id="marg24"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000123">Nec dicas fictionem e&longs;&longs;e quòd ad&longs;it libra horizon­<lb/>talis directa HI, quæ perpetuò renouetur, nam reue­<lb/>rà fulciuntur, &longs;u&longs;tentanturque duo cylindri CB, & G <lb/>F à plano aquæ &longs;ubiectæ CF quod quidem, mobile e&longs;t, <lb/>cùm cedat de&longs;cen&longs;ui mercurij CB & &longs;uperficies F <lb/>eleuetur eodem tempore & pari velocitate circa eius <lb/>punctum intermedium, igitur prædicta duo corpora <lb/>BC, & GF dum ambo premunt libram fluidam &longs;ub­<lb/>iectam &longs;uis ponderibus, & coguntur moueri &longs;imùl æ­<lb/>què velociter contrarijs lationibus nece&longs;&longs;ariò libram <pb pagenum="25" xlink:href="010/01/033.jpg"/><arrow.to.target n="marg25"/><lb/>con&longs;tituunt, quæ in &longs;uo centro grauitatis energia&mtail; <lb/>vniuer&longs;æ &longs;uæ compre&longs;&longs;ionis exercent, verum tame&ntail; <lb/>e&longs;t quòd prædicta libra non flectitur, &longs;ed continentèr <lb/>renouatur in &longs;itu horizontali, quandoquidem aqu&atail; <lb/>eleuata iam non amplius agit contra pre&longs;&longs;ionem mer­<lb/>curij CB vt dictum e&longs;t, propterea quòd æquilibratur <lb/>cum aqua collaterali &longs;upra mercurium CB eleuata. </s> </p> <p type="margin"> <s id="s.000124"><margin.target id="marg25"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000125"><emph type="center"/>PROP. IX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000126"><emph type="center"/><emph type="italics"/>Corpus aqua grauius in ea demer&longs;um dum de&longs;cendit consti­<lb/>tuit cum æqualimole collateralis fluidi libram <expan abbr="æqualiũ">æqualium</expan> <lb/>radiorum, cuius centrum grauitatis continenter <lb/>de&longs;cendende eleuat leuiorem aquam col­<lb/>lateralem, &longs;emperque renouatur <lb/>horizontalis libra.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000127">HOc præmi&longs;&longs;o intelligatur iam vas aquà plenum <lb/>RSTX, & intra eius profunditatem appona­<lb/>tur pri&longs;ma marmoreum ABCD, & producantur eius <lb/>ba&longs;es horizontales AB, & CD <lb/><figure id="id.010.01.033.1.jpg" xlink:href="010/01/033/1.jpg"/><lb/>v&longs;que ad G & H, atque planu&mtail; <lb/>AD producatur &longs;ur&longs;um, & deor­<lb/>&longs;um v&longs;que ad M, & V perpendi­<lb/>culariter ad horizontem. </s> <s id="s.000128">hic iam <lb/>habemus <expan abbr="&longs;iphon&etilde;">&longs;iphonem</expan> oblongum in &longs;e <lb/>ip&longs;um circumductum, vt in pr&etail;­<lb/>cedenti propo&longs;itione expo&longs;itum fuit, quia aqua BM <lb/>GHVC ambit pri&longs;ma &longs;upernè, lateraliter, & infernè, <lb/>nec moueri pote&longs;t <expan abbr="de&longs;c&etilde;dendo">de&longs;cendendo</expan> pri&longs;ma AC quin aqua <pb pagenum="26" xlink:href="010/01/034.jpg"/><arrow.to.target n="marg26"/><lb/>&longs;ubiecta CID è &longs;uo loco expellatur, & lateralitèr fluat <lb/>ver&longs;us P, circumferaturque &longs;ur&longs;um v&longs;que ad locu&mtail; <lb/>relictum à pr&etail;dicto pri&longs;mate lapideo in E. &longs;unt igitur <lb/>duæ partes MT, & MS veluti duo canales laterales <lb/>&longs;iphonis, qui tamen &longs;e&longs;e contingunt in communi la­<lb/>tere MV; prætereà duæ portiones aquæ &longs;upremæ XA, <lb/>& MG cùm &longs;int homogeneæ, æquè graues &longs;pecie, & <lb/>æque altæ, &longs;e mutuò æquilibrantur, pariterque duæ <lb/>portiones aqueæ &longs;ubiectæ CV, & DS pariter æquili­<lb/>brantur, vnde patet quòd tantummodo comparari <lb/>debent inter &longs;e duo corpora collateralia &longs;axum nimi­<lb/>rum BD, & aqua AH, quæ ab ei&longs;dem planis horizon­<lb/>talibus BG, & HC comprehenduntur, & hæc &longs;imiliter <lb/>fulciuntur &longs;u&longs;tentanturque à plano aquæ &longs;ubiectæ H <lb/>C <expan abbr="nõ">non</expan> firmo, & impermeabili, &longs;ed facilè à &longs;uo loco <lb/>amouibili & cedenti. </s> <s id="s.000129">in&longs;i&longs;tunt igitur prædicta duo cor­<lb/>pora BD, & AH non &longs;ecùs &longs;u&longs;pen&longs;a ac &longs;i &longs;uper libram <lb/>HC inniterentur; huius verò centrum mobile e&longs;&longs;et <lb/>punctum intermedium D, vbi nimirum libra HC bi­<lb/>fariàm &longs;ecatur, & &longs;i à centro grauitatis O &longs;axi BD ad <lb/>centrum P grauitatis aquæ AH recta linea <expan abbr="coniũga-tur">coniunga­<lb/>tur</expan>, eaque &longs;ecetur in Y reciprocè &longs;ecundùm propor­<lb/>tionem grauitatum eorumdem corporum, patet Y e&longs;­<lb/>&longs;e centrum grauitatis communis &longs;axi BD, & aquæ A <lb/>H, cùmque libra PO &longs;ecetur bifariàm à plano MV in <lb/>Q iam con&longs;urget fune-pendulum QY horizontaliter <lb/>excen&longs;um versùs O ob exce&longs;&longs;um grauitatis &longs;axi &longs;upra <lb/>aquæ pondus &longs;pecificum, igitur nece&longs;sè e&longs;t vt tot&atail; <lb/>libra flectatur <expan abbr="deorsũ">deorsum</expan>, & &longs;ic &longs;axum BD <expan abbr="de&longs;c&etilde;det">de&longs;cendet</expan>. </s> <s id="s.000130">Quia <pb pagenum="27" xlink:href="010/01/035.jpg"/><arrow.to.target n="marg27"/><lb/>verò in de&longs;cen&longs;u aqua &longs;ubiecta expul&longs;a ex I curuo iti­<lb/>nere &longs;ur&longs;um fluit per ZF v&longs;que ad E denuò renouatur <lb/>libra horizontalis, comparanturque inter &longs;e &longs;axum B <lb/>D cum aqua collaterali in nouo &longs;itu horizontali de­<lb/>pre&longs;&longs;iori exi&longs;tente, igitur denuò eadem proportione <lb/>di&longs;&longs;ecta libra imaginaria horizontali, <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb/>æquale priori eadem vi flectetur <expan abbr="deorsũ">deorsum</expan>, <expan abbr="de&longs;cendetq;">de&longs;cendetque</expan> <lb/>centrum grauitatis eius motu perpendiculari ad hori­<lb/>zontem quòu&longs;que ad fundum va&longs;is &longs;axum pertingat. </s> </p> <p type="margin"> <s id="s.000131"><margin.target id="marg26"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="margin"> <s id="s.000132"><margin.target id="marg27"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium</s> </p> <p type="main"> <s id="s.000133"><emph type="center"/>PROP. X.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000134"><emph type="center"/><emph type="italics"/>Idip&longs;um contingit, &longs;ed inuer&longs;o ordine cum corpus de­<lb/>mer&longs;um minùs graue aqua collaterali fueris.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000135">SI po&longs;tea pri&longs;ma BD fuerit ligneum, & minùs gra­<lb/>ue &longs;pecie quam aqua AH, tunc ij&longs;dem manen­<lb/>tibus &longs;olummodò centrum grauitatis communis Y <lb/>cadet ad partes aquæ inter Q & P, & proindè vniuer­<lb/>&longs;um graue compo&longs;itum ex aqua, & ligno vim faciet <lb/><expan abbr="impell&etilde;do">impellendo</expan> deor&longs;um centrum gra­<lb/><figure id="id.010.01.035.1.jpg" xlink:href="010/01/035/1.jpg"/><lb/>uitatis Y, & ideò vehementiùs <expan abbr="cõ-primetur">con­<lb/>primetur</expan> aqua &longs;ubiecta HDVS, <lb/>hæc verò ob eius continuitatem <lb/>& naturam <expan abbr="con&longs;i&longs;t&etilde;tem">con&longs;i&longs;tentem</expan>, quæ pre&longs;­<lb/>&longs;ioni non cedit, nece&longs;&longs;ariò impel­<lb/>letur versùs I, & &longs;ic vim faciet &longs;ur­<lb/>&longs;um exprimendo ligni &longs;uperficiem DC; at dum <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, oportet vt expellat è &longs;uo loco <expan abbr="incumbent&etilde;">incumbentem</expan> <lb/>aquam E, quæ tran&longs;uer&longs;ali & obliquo motu perduce-<pb pagenum="28" xlink:href="010/01/036.jpg"/><arrow.to.target n="marg28"/><lb/>tur ab E per FZ versùs I, & &longs;ic à prædicto motu circu­<lb/>lari aquæ ambientis lignum expelletur &longs;ursùm; atta­<lb/>men ratio mechanica huius actionis pendet ex eo, <lb/>quòd libra horizontalis imaginaria PO flectitur per­<lb/>petuò deorsùm quidem ad partes centri grauitatis Y <lb/>circa centrum Q, & &longs;ursùm ad partes O. &longs;ed &longs;ummo­<lb/>perè animaduertendum e&longs;t prædictam libram imagi­<lb/>nariam horizontalem renouari &longs;ucce&longs;&longs;iuè prout <expan abbr="lignũ">lignum</expan> <lb/>a&longs;cendit, <expan abbr="comparaturq;">comparaturque</expan> cum alijs lateralibus pri&longs;ma­<lb/>tibus aqueis, quæ &longs;ucce&longs;&longs;iuè offendit intercepta in­<lb/>ter prædicta plana horizontalia GB, & HC: nece&longs;sè <lb/>ergo e&longs;t vt lignum prædictum numquàm quie&longs;cat in­<lb/>tra aquam demer&longs;um quòu&longs;que ad &longs;upremam <expan abbr="libellã">libellam</expan> <lb/>aquæ RX perducatur; in&longs;uperque aliqua eius por­<lb/>tio emineat. </s> </p> <p type="margin"> <s id="s.000136"><margin.target id="marg28"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000137"><emph type="center"/>COR OLLARIVM.<emph.end type="center"/></s> </p> <p type="main"> <s id="s.000138">Hinc patet veritas Archimedei a&longs;&longs;umpti, quòd <lb/>fluidi con&longs;i&longs;tentis natura requirit vt partium eius æ­<lb/>què iacentium magis compre&longs;&longs;æ &longs;ursùm impellant <lb/>partes minus pre&longs;&longs;as perpendiculariter ad <expan abbr="horizont&etilde;">horizontem</expan>. </s> </p> <p type="main"> <s id="s.000139">Quia aqua &longs;ubiecta HCTS ob eius con&longs;i&longs;tentia&mtail; <lb/>non conden&longs;atur, & mobilis e&longs;t, quia fluida, ergo li­<lb/>bram flexibilem con&longs;tituit, <expan abbr="e&longs;tq;">e&longs;tque</expan> pars &longs;ubiecta HV <lb/>magis compre&longs;&longs;a quàm DT (propterea quòd pars a­<lb/>quea GD grauior e&longs;t ligno AC) igitur libra fluida <lb/>HDC flecti debet de&longs;cendendo HD & DC a&longs;cen­<lb/>dendo, quare tota aqua HSVD deorsùm depre&longs;&longs;a im­<lb/>pellet aquam DVTC &longs;ursùm. <pb pagenum="29" xlink:href="010/01/037.jpg"/><arrow.to.target n="marg29"/></s> </p> <p type="margin"> <s id="s.000140"><margin.target id="marg29"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000141"><emph type="center"/>PROP. XI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000142"><emph type="center"/><emph type="italics"/>Si verò corpus &longs;olidum ponitur &longs;upra aquæ libellam, <lb/>tunc de&longs;cen&longs;us communis centri grauitatis non <lb/>efficietur per lineam perpendicularem ad <lb/>horizontem &longs;ed motu curuo per <lb/>parabolam.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000143">IN progre&longs;&longs;u prædictæ operationis notabilis e&longs;t va­<lb/>riatio &longs;itus centri grauitatis eius & mechanicæ eius <lb/>operationis. </s> </p> <p type="main"> <s id="s.000144">Sit igitur in eodem va&longs;e pri&longs;ma ligneum ABCD <lb/>perductum ad &longs;upremam aquæ libellam RX, tunc &longs;i­<lb/>militer inter &longs;e comparantur duo pri&longs;mata BD ligno­<lb/>um, & AH aqueum in eodem plano horizontali &longs;u­<lb/>biecto HC in&longs;i&longs;tentes, & proindè <lb/><figure id="id.010.01.037.1.jpg" xlink:href="010/01/037/1.jpg"/><lb/>efficitur libra imaginaria PO mo­<lb/>bilis circa eius fulcimentum Q, & <lb/>centrum grauitatis <expan abbr="eorumd&etilde;">eorumdem</expan> cor­<lb/>porum cadit ad partes aquæ nem­<lb/>pè in Y inter <expan abbr="c&etilde;trum">centrum</expan> Q & extremitatem radij P. hinc <lb/>ergo &longs;e quitur vt prædicta libra flecti debeat deorsùm <lb/>ad partes Y & &longs;ur&longs;um a&longs;cendat terminus O vnà cum li­<lb/>gno versùs aquæ libellam &longs;upremam RX, igitur por­<lb/>tio aliqua ligni &longs;uprema eleuabitur &longs;upra prædictam <lb/>aquæ libellam, vt patet in po&longs;trema figura, & tunc <lb/><expan abbr="quid&etilde;">quidem</expan> &longs;ucce&longs;&longs;iuè imminuitur pri&longs;ma <expan abbr="aqueũ">aqueum</expan> GD prout <lb/>magis ligneum pri&longs;ma exurgit, eminetque &longs;upra aqu&etail; <lb/>libellam, & in prædicto a&longs;cen&longs;u dum collaterale pri&longs;-<pb pagenum="30" xlink:href="010/01/038.jpg"/><arrow.to.target n="marg30"/><lb/>ma aqueum imminuitur, pondus eius quòd prius &longs;u­<lb/>perabat grauitatem ligni BD, tandem po&longs;t <expan abbr="continuã">continuam</expan> <lb/>ponderis aquæ <expan abbr="diminution&etilde;">diminutionem</expan> reddetur præcisè æqua­<lb/>le ponderi cylindri lignei BD, & tunc coniunctis <lb/>centris grauitatum eorum à rect&atail; <lb/><figure id="id.010.01.038.1.jpg" xlink:href="010/01/038/1.jpg"/><lb/>PO hæc quidem bifariàm &longs;ecabi­<lb/>tur in termino Q & <expan abbr="ibid&etilde;">ibidem</expan> erit eius <lb/>centrum, atque fulcimentum ha­<lb/>bebitque pondus ligni BD ad <expan abbr="põ-dus">pon­<lb/>dus</expan> aquæ GD &longs;ibi æquale <expan abbr="eamd&etilde;">eamdem</expan> <lb/>proportionem, quam habet reciprocè PQ ad QO, & <lb/>proindè centrum grauitatis commune Y incidet præ­<lb/>cisè in centro &longs;eù fulcimento libræ <expan abbr="q.">que</expan> igitur æquili­<lb/>bratis prædictis ponderibus libra quie&longs;cet, nec pri&longs;­<lb/>ma ligneum BD vlteriùs <expan abbr="a&longs;c&etilde;det">a&longs;cendet</expan>, <expan abbr="neq;">neque</expan> denuò <expan abbr="deorsũ">deorsum</expan> <lb/>decidet ni&longs;i ex accidenti ratione impetus acqui&longs;iti. </s> </p> <p type="margin"> <s id="s.000145"><margin.target id="marg30"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000146">Hinc patet quòd quando primò lignum BD exur­<lb/>gere incipit &longs;upra aquæ libellam RX tunc continen­<lb/>ter magis ac magis centrum communis grauitatis Y <lb/>motu obliquo, & curuo <expan abbr="a&longs;c&etilde;dit">a&longs;cendit</expan> quòu&longs;que coniunga­<lb/>tur cum fulcimento Q libræ PO &longs;ursùm tran&longs;lat&etail;, <lb/>non &longs;ecùs, ac in &longs;iphone aqua eleuata in vno eius bra­<lb/>chio de&longs;cendendo perducit centrum grauitatis eius <lb/>per curuam lineam parabolicam, vt dictum e&longs;t; con­<lb/>cipi ergo debet &longs;ipho inæqualium brachiorum <expan abbr="quãdo">quando</expan> <lb/>primum ba&longs;is &longs;uprema AB ligni attingit aquæ libel­<lb/>lam, & quia tunc exce&longs;&longs;us grauitatis &longs;pecificæ aquæ <lb/>AH &longs;upra pondus ligni BD perindè agit ac &longs;i aliud <lb/>fluidum æquè graue &longs;pecie ligno ip&longs;i BD & maioris <pb pagenum="31" xlink:href="010/01/039.jpg"/><arrow.to.target n="marg31"/><lb/>molis &longs;upra ba&longs;im HD in&longs;i&longs;teret procul dubio ad ma­<lb/>iorem &longs;ublimitatem eleuaretur prædictum fluidu&mtail; <lb/>minùs graue &longs;pecie, quàm aqua AH, cuius <expan abbr="ab&longs;olutũ">ab&longs;olutum</expan> <lb/>pondus æquale e&longs;&longs;et ponderi eiu&longs;dem aquæ commu­<lb/>nis AH, quare ab eleuatiori loco fluidum prædictum <lb/>deorsùm excurrendo eleuaret lignum depre&longs;&longs;um BD <lb/>præcisè vt in &longs;iphone &longs;uperiùs expo&longs;ito contingeret. </s> </p> <p type="margin"> <s id="s.000147"><margin.target id="marg31"/>Cap. 2. d&etail; <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="main"> <s id="s.000148">Ex hac theoria facili negotio re&longs;olui ac <expan abbr="demõ&longs;tra-ri">demon&longs;tra­<lb/>ri</expan> po&longs;&longs;unt omnes propo&longs;itiones, quæ ab Archimed&etail; <lb/>in primo de infidentibus humido demon&longs;trantur. </s> </p> <p type="main"> <s id="s.000149"><emph type="center"/>PROP. XII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000150"><emph type="center"/><emph type="italics"/>In a&longs;cen&longs;u, vel de&longs;cen&longs;u &longs;olidi in fluide neque libra linearis <lb/>e&longs;t, neque habet centrum grauitatis in vno puncto <lb/>&longs;ed libra e&longs;&longs;e &longs;olet &longs;uperficialis, cuius fulci­<lb/>mentum e&longs;t linea circa centrum figuræ, <lb/>& grauitas communis exercetur <lb/>quoque in linea aliqua.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000151">SOlummodò indicabo <expan abbr="nõ">non</expan> &longs;emper v&longs;urpari in præ­<lb/>dicta mechanica operatione punctum, quod <expan abbr="cõ-mune">com­<lb/>mune</expan> centrum grauitatis vocari vulgò &longs;olet; propte­<lb/>rea quòd libra compo&longs;ita ex &longs;olido & fluido ambien­<lb/>te non &longs;emper linearis e&longs;t, &longs;ed &longs;uperficiem aliquando <lb/>componit, in qua nedum fulcimentum, &longs;ed etiam lo­<lb/>cus vbi exercetur communis grauitas linea e&longs;&longs;e &longs;olet <lb/>aliquando recta, aliquando curua, & multoties com­<lb/>po&longs;ita ex pluribus rectis. </s> <s id="s.000152">&longs;i enim in medio aquæ im­<lb/>mergatur directè & perpendiculariter ad <expan abbr="horizont&etilde;">horizontem</expan> <pb pagenum="32" xlink:href="010/01/040.jpg"/><arrow.to.target n="marg32"/><lb/>pri&longs;ma vel cylindrus &longs;olidus, tunc quidem dum pri&longs;­<lb/>ma de&longs;cendit, vniuer&longs;a aqua illud ambiens &longs;ur&longs;u&mtail; <lb/>eleuatur. </s> <s id="s.000153">vel illo a&longs;cendente hæc deprimitur, com­<lb/>parari ergo debet pri&longs;ma comprehen&longs;um cum anulo <lb/>&longs;eu potiùs cum fi&longs;tula fluida id ambiens, & &longs;ic effici­<lb/>tur libra quædam plana cuius fulcimentum erit linea <lb/>in confinio cylindri demer&longs;i, & fluidi ambientis ex­<lb/>ten&longs;a pariterque locus, vbi communis grauitas exer­<lb/>cetur non erit punctum, &longs;ed erit quoque linea in eo­<lb/>dem plano horizontali producta; &longs;ed facilitatis gra­<lb/>tia concipi debet &longs;ector aliquis in prædicto plano ex <lb/>centro prædictæ libræ &longs;uperficialis in axe cylindri <lb/>con&longs;tituto v&longs;que ad &longs;uperficiem aquæ ambientis, qu&etail; <lb/>contrarijs motibus vnà cum cylindro mouetur; &longs;eù <lb/>potius concipi debet radius, &longs;eù &longs;emidiameter <expan abbr="nõ">non</expan> in <lb/>diui&longs;ibilis, &longs;ed phy&longs;ica, & h&etail;c v&longs;urpari pote&longs;t vt libra <lb/>particularis cum &longs;uo fulcimento, & centro grauita­<lb/>tis, vniuer&longs;a verò libra &longs;uperficialis compo&longs;ita erit ex <lb/>pluribus, & innumeris libris radio&longs;is, vt dictum e&longs;t, <lb/>& hæc innui&longs;&longs;e modò &longs;ufficiat in hac generali præpa­<lb/>ratione, inferiùs enim accuratiùs exponentur. <pb pagenum="33" xlink:href="010/01/041.jpg"/><arrow.to.target n="marg33"/></s> </p> <p type="margin"> <s id="s.000154"><margin.target id="marg32"/>Cap. 2. de <lb/>momentis <lb/>grauium in <lb/>fluido inna­<lb/>tantium.</s> </p> <p type="margin"> <s id="s.000155"><margin.target id="marg33"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000156"><emph type="center"/><emph type="italics"/>Quodlibet corpus fluidum eorum quæ innituntur <lb/>&longs;uperficiei Telluris graue e&longs;t, exercetque <lb/>vim &longs;uæ grauitatis etiam dum in <lb/>proprio loco, & in ip&longs;omet <lb/>fluido vniuer&longs;ali &longs;ui <lb/>generis con&longs;i&longs;tit, <lb/>ac quie&longs;cit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000157"><emph type="center"/>CAP. III.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000158">SVppo&longs;uimus cum Archimede aquam, & reliqu&atail; <lb/>corpora fluida terram ambientia vi propriæ gra<lb/>uitatis compre&longs;&longs;ionem vniformem exercere ver&longs;us <lb/>centrum telluris, ex quo &longs;ubindè fit vt &longs;phæricè circa <lb/>terræ centrum di&longs;ponantur. </s> <s id="s.000159">præterea &longs;uppo&longs;uimus <lb/>cum eodem Archimede partes eiu&longs;dem fluidi minùs <lb/>pre&longs;&longs;as expelli ac &longs;ubleuari &longs;ur&longs;um à partibus <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>fluidi magis compre&longs;&longs;is, & grauatis; ex qua hypothe­<lb/>&longs;i deducitur quodliber fluidum, veluti aqua e&longs;t, gra­<lb/>uitatem habere eamque exercere etiam in proprio <lb/>loco, & naturali regione, &longs;cilicèt aquam ip&longs;am dum in <lb/>tota aqua quie&longs;cit tunc quoque grauitatem exercere <lb/>&longs;ubiecta corpora comprimendo. <lb/><arrow.to.target n="marg34"/></s> </p> <p type="margin"> <s id="s.000160"><margin.target id="marg34"/>Ex Archi­<lb/>mede dedu­<lb/>cunt aquam <lb/>in ipsa aqua <lb/>non grauita­<lb/>re, & id <expan abbr="ipsũ">ipsum</expan> <lb/>Peripatetici <lb/>affirmaret.</s> </p> <p type="main"> <s id="s.000161">Hoc autem à plurimis negatur qui putant Archi­<lb/>medem oppo&longs;itum &longs;en&longs;i&longs;&longs;e. </s> <s id="s.000162">idip&longs;um quoque negant <lb/>aliqui peripatetici qui cen&longs;ent non &longs;emper veru&mtail; <lb/>e&longs;&longs;e quòd partes &longs;uperiores corporis grauis compri­<lb/>mant, & vim inferant inferioribus, & contiguis, ni&longs;i <lb/>infimæ partes leues &longs;int ab&longs;olutè, vel re&longs;pectiuè, vnde </s> </p> <pb pagenum="34" xlink:href="010/01/042.jpg"/> <p type="main"> <s id="s.000163"><arrow.to.target n="marg35"/><lb/><expan abbr="cõcedunt">concedunt</expan> terram exemp. </s> <s id="s.000164">gr. <!-- REMOVE S-->&longs;uper <expan abbr="aquã">aquam</expan>, aut &longs;uper <expan abbr="ae-r&etilde;">ae­<lb/>rem</expan> po&longs;itam, vim, & operationem grauitatis & com­<lb/>pre&longs;&longs;ionis exercere, non itidem aquam &longs;upra ip&longs;a&mtail; <lb/>terram collocatam, nec aerem aquæ incumbentem, <lb/>imò nec aerem &longs;upra aerem con&longs;titutum, nec aquam <lb/>&longs;upra aquam po&longs;itam. </s> <s id="s.000165">huiu&longs;modi propo&longs;itionem tali <lb/>ratiocinio confirmare nituntur, cum Natura cau&longs;a, & <lb/>principium motus &longs;it, nec operetur fru&longs;tra &longs;ed ad cer­<lb/>tum finem, & ad bonum, proculdubio ordinauit mo­<lb/>tum naturalium corporum ad certum finem, & ad bo­<lb/>num, &longs;cilicèt ad con&longs;eruationem, & quia actus, &longs;eù <lb/>perfectio quam appetunt, & quam acquirere nitun­<lb/>tur corpora grauia, & leuia dum mouentur e&longs;t migra­<lb/>tio, & debita con&longs;titutio in proprijs locis naturali­<lb/>bus, grauium nempè de or&longs;um, & leuium &longs;ursùm, hine <lb/>&longs;equitur quòd po&longs;t <expan abbr="quã">quam</expan> ad debita loca naturalia per­<lb/>ducta &longs;unt, motus omninò ce&longs;&longs;at, vtpotè naturæ de&longs;i­<lb/>derio, & fine expleto, eo quòd vt ait Ari&longs;toteles Na­<lb/>tura non mouet corpus aliquod vt <expan abbr="ipsũ">ipsum</expan> moueat, &longs;cili­<lb/>cèt vt ip&longs;um perpetuò, & in <expan abbr="infinitũ">infinitum</expan> agitet, &longs;ed tan­<lb/>tummodo vt illud ad terminum, & finem perducat <lb/>vt ibidem quie&longs;cat; verùm facultates aut virtutes <lb/>quibus &longs;ublunaria corpora ad propria loca feruntur <lb/>nil aliud &longs;unt, quàm grauitas aut leuitas. </s> <s id="s.000166">igitur huiu&longs;­<lb/>modi facultates ordinatæ &longs;unt ad perducenda <expan abbr="elem&etilde;-taria">elemen­<lb/>taria</expan> corpora ad propria loca vt ibidem quie&longs;cant; <lb/>nec vlteriùs v&longs;um aliquem habere po&longs;&longs;unt, quando­<lb/>quidem &longs;i præterea motum pro&longs;e querentur in &longs;uis lo­<lb/>cis perturbarent & confunderent naturalem &longs;ituatio-<pb pagenum="35" xlink:href="010/01/043.jpg"/><arrow.to.target n="marg36"/><lb/>nem eorumdem corporum. </s> <s id="s.000167">& profectò e&longs;t con&longs;enta­<lb/>neum vt elementa non nitantur de&longs;erere propria lo­<lb/>ca, & propterea careant illo naturali &longs;timulo &longs;eu prin­<lb/>cipio motus quo impellebantur antequam ad &longs;ua na­<lb/>turalia loca perueni&longs;&longs;ent; hinc deducitur nullum ele­<lb/>mentum in proprio loco grauitatem, aut leuitatem <lb/>habere, &longs;ed aqua in ip&longs;a aqua po&longs;ita in propria, & na­<lb/>turali regione degit & &longs;ic aer in aere, ergo neutrum <lb/>horum elementorum grauitatem in &longs;uo loco habet, <lb/>aut exercet. </s> <s id="s.000168">& primo quoad Archimedem pertinet <lb/>videntur aduer&longs;arij nequaquam tanti viri mente&mtail; <lb/>a&longs;&longs;equuti &longs;ui&longs;&longs;e vt ex eius verbis &longs;atis <expan abbr="&longs;uperq;">&longs;uperque</expan> patet. <lb/></s> <s id="s.000169">vt verò Peripateticis fiat &longs;atis, ne dum <expan abbr="nullã">nullam</expan> lenita­<lb/>tem po&longs;itiuam in natura dari o&longs;tendam, &longs;ed præterea <lb/>probabo fal&longs;um e&longs;&longs;e quòd po&longs;t quam corpora natura­<lb/>lia ad &longs;ua loca perueniunt & ibidem quie&longs;cunt graui­<lb/>tas v&longs;um non habet, ni&longs;i ad perturbandum pr&etail;clarum <lb/>ordinem vniuer&longs;i; nam è contra &longs;uadere conabor tunc <lb/>præcisè corpora grauitatem exercere cùm in &longs;uis lo­<lb/>cis quie&longs;cunt, imò cau&longs;am, quare in &longs;uis locis quie­<lb/>&longs;cunt, e&longs;&longs;e quia pondus exercent, &longs;ed prius <expan abbr="perpend&etilde;-da">perpenden­<lb/>da</expan> e&longs;t actio ip&longs;ius grauitatis, & quidnam poti&longs;&longs;imu&mtail; <lb/>efficiat pondus dum comprimit; & profectò actio & <lb/>compre&longs;&longs;io corporis grauis non e&longs;t tran&longs;itus localis <lb/>pilæ ferreæ v.g. <!-- REMOVE S-->dum ver&longs;us terram de&longs;cendit, nec <lb/>præterea e&longs;t &longs;implex contactus quo coniungitur cum <lb/>&longs;uperficie telluris &longs;ubiectæ, &longs;ed e&longs;t vis, & energia, qua <lb/>impellitur deor&longs;um <expan abbr="&longs;tringiturq;">&longs;tringiturque</expan> veluti prælo <expan abbr="cũ">cum</expan> ip&longs;a <lb/>terra; veluti cum pondus in trutina appenditur licet <pb pagenum="36" xlink:href="010/01/044.jpg"/><arrow.to.target n="marg37"/><lb/>quie&longs;cere videatur exercet actionem quamdam <expan abbr="cõ-pre&longs;&longs;iuam">com­<lb/>pre&longs;&longs;iuam</expan> tantæ energiæ quanta e&longs;t eius grauitas; hoc <lb/>autem facilè percipiemus &longs;i fingamus duos homines <lb/>æquè validos & robu&longs;tos qui totis viribus &longs;e mutuò <lb/>impellant, vbi manife&longs;tum e&longs;t quòd exi&longs;tentibus vi­<lb/>ribus contrarijs inter &longs;e æqualibus, vt vna alteri no&ntail; <lb/>pr&etail;ualeat, tunc neuter luctantium dimouebitur è &longs;uo <lb/>loco, &longs;ed ibidem quie&longs;cet, licèt quilibet <expan abbr="corũ">eorum</expan> vniuer­<lb/>&longs;am vim, & facultatem propriam exerceat impellen­<lb/>do, & repellendo &longs;uum antagoni&longs;tam, non &longs;ecùs <expan abbr="quã-do">quan­<lb/>do</expan> aliquis impellit columnam ingentem vehemen­<lb/>ter, licèt minimè valeat eam è &longs;uo loco deijcere, ac <lb/>commouere, vt nimirum motus progre&longs;&longs;iuus hominis <lb/>impellentis, aut columnæ &longs;ub&longs;equatur; nihilominùs <lb/>negari non pote&longs;t motus impul&longs;iuus mu&longs;culorum, & <lb/>artuum hominis impellentis; nec pariter negari po­<lb/>te&longs;t aliqua exigua & in&longs;en&longs;ibilis flexio eiu&longs;dem <expan abbr="colũ-næ">colunm<lb/>næ</expan>, quæ ad in&longs;tat arcus, &longs;eù machinæ æquali vi impul­<lb/>&longs;ui, & flexioni re&longs;i&longs;tit. </s> <s id="s.000170">&longs;imiliter cùm pila ferrea &longs;uper <lb/>ba&longs;im, vel laminam vitream innititur concedendum <lb/>omninò e&longs;t effici con&longs;tipationem quamdam partium <lb/>ferri prementis, & vitri compre&longs;&longs;i, vt nimirum ali­<lb/>quanti&longs;per eorum poro&longs;itates <expan abbr="cõ&longs;tringantur">con&longs;tringantur</expan>, eò quòd <lb/>(vt o&longs;ten&longs;um e&longs;t cap. 26. de Vi percu&longs;&longs;ionis) reperiri <lb/>in rerum natura corpora compo&longs;ita <expan abbr="nequeũt">nequeunt</expan> quæ ad­<lb/>eò dura &longs;int vt compre&longs;&longs;ioni cuiuslibet corporis re&longs;i­<lb/>&longs;tere valeant. </s> <s id="s.000171">quod verò prædicta compre&longs;&longs;io vitri ab <lb/>ingenti pondere fiat patet ex eo quòd augendo ma­<lb/>gis ac magis pondus comprimens, tandem ba&longs;is vi-<pb pagenum="37" xlink:href="010/01/045.jpg"/><arrow.to.target n="marg38"/><lb/>trea di&longs;rumpitur, di&longs;&longs;ilit, atque conteritur eo pr&etail;cisè <lb/>modo quo ab ictu mallei di&longs;rumpitur; & &longs;i quidem <lb/>hoc verum non e&longs;&longs;et &longs;cilicèt &longs;i à pondere vtcumqu&etail; <lb/>multiplicato & aucto ba&longs;is vitrea non &longs;tringeretur & <lb/>comprimeretur, quælibet exili&longs;&longs;ima ba&longs;is vitrea to­<lb/>leraret vim compre&longs;&longs;iuam ponderis cuiu&longs;libet <expan abbr="mõtis">montis</expan> <lb/>va&longs;ti, quod procul dubio fal&longs;um e&longs;t. </s> </p> <p type="margin"> <s id="s.000172"><margin.target id="marg35"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000173"><margin.target id="marg36"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000174"><margin.target id="marg37"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000175"><margin.target id="marg38"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000176">Hoc po&longs;ito nemo negabit quòd &longs;i pondus duplice­<lb/>tur vt &longs;cilicèt vnum &longs;uper alterum &longs;uperponatur, <expan abbr="tũc">tunc</expan> <lb/>duplici vi, ac robore infima ba&longs;is vitrea comprime­<lb/>tur ac con&longs;tipabitur, & proindè poro&longs;itates multò <lb/>magis imminuentur à duplici impul&longs;u, quando <expan abbr="quid&etilde;">quidem</expan> <lb/>concipi non pote&longs;t moles grauis aucta & multiplica­<lb/>ta ab&longs;que eo quòd pondus, & proindè vis, & energia <lb/>compre&longs;&longs;iua versùs centrum telluris multiplicetur, <lb/>vnde fit vt partes &longs;olidæ & con&longs;i&longs;tentes <expan abbr="comprimãtur">comprimantur</expan> <lb/>& <expan abbr="con&longs;tip&etilde;tur">con&longs;tipentur</expan> multo magis. </s> </p> <p type="main"> <s id="s.000177">At &longs;i hoc contingit in corporibus duri&longs;&longs;imis, nega­<lb/>ri certè non poterit in corporibus fluidis, quæ no&ntail; <lb/>minùs grauia &longs;unt & <expan abbr="cõ">comprimunt</expan> fundum va&longs;is in quo <lb/>continentur tanta vi, quanta e&longs;t energia ponderis <lb/>eorum, ita ut multiplicata fluidi mole centies, & mil­<lb/>lies va&longs;is fundum centies, & millies maiori vi com­<lb/>primatur, & licèt ibidem non ad&longs;it motus progre&longs;­<lb/>&longs;iuus, numquam tamen deficiet motus tonicus, & re&longs;­<lb/>trictio pororum fundi va&longs;is, & compre&longs;&longs;io pororum <lb/>eiu&longs;dem fluidi, &longs;i fortè poro&longs;itates habuerit, & &longs;icuti <lb/>fluidum grauitat atque con&longs;tringit poro&longs;itates fundi <lb/>va&longs;is, hac de cau&longs;a, quia ponderat, & grauitat, nulla <pb pagenum="38" xlink:href="010/01/046.jpg"/><arrow.to.target n="marg39"/><lb/>ratio vetat, quin pondere &longs;uo comprimat infimam &longs;u­<lb/>biectam laminulam eiu&longs;dem fluidi quæ fundo va&longs;is <lb/>contigua e&longs;t, quandoquidem minimè po&longs;&longs;unt &longs;upre­<lb/>mæ fluidi partes fundum va&longs;is comprimere ab&longs;qu&etail; <lb/>eo quod impellant, & &longs;tringant infimam eiu&longs;dem flui­<lb/>di laminulam, cùm actio in di&longs;tanti fieri non po&longs;&longs;it, &longs;ed <lb/>contactu quodam remotiores impellendo eis conti­<lb/>guas &longs;ubiectas partes, & hæ &longs;ub&longs;equentes &longs;erie qua­<lb/>dam ordinata quou&longs;que fundum comprimant. </s> </p> <p type="margin"> <s id="s.000178"><margin.target id="marg39"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000179"><emph type="center"/>PROP. XIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000180"><emph type="center"/><emph type="italics"/>Aqua va&longs;is fundum çomprimit &longs;ua grauitate.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000181">SEd hoc euidentius &longs;ic patebit, &longs;it fi&longs;tula vitrea A <lb/>NO perpendiculariter ad horizontem erect&atail;, <lb/>repleaturquè aqua, &longs;eù quolibet alio fluido cor­<lb/>pore, & ductis innumeris planis horizonti <expan abbr="æquidi&longs;tã-tibus">æquidi&longs;tan­<lb/>tibus</expan> &longs;ubdiuidatur vniuer&longs;um fluidum i&ntail; <lb/><figure id="id.010.01.046.1.jpg" xlink:href="010/01/046/1.jpg"/><lb/>laminas gracillimas &longs;eù membranas æquè <lb/>altas AB, BC, CD, DE, EF, FM, & MN. & <lb/>primò &longs;i verum e&longs;t, vt aduer&longs;arij credunt <lb/>aquam in ip&longs;amet aqua collocatam <expan abbr="nõ">non</expan> gra­<lb/>uitare, igitur &longs;uprema laminula aquea AB <lb/>pror&longs;us <expan abbr="nõ">non</expan> comprimet &longs;ubiectam <expan abbr="membra-nã">membra­<lb/>nam</expan> aqueam BC, &longs;cilicet vim nullam &longs;uper eam exer­<lb/>cebit (hoc enim grauitatis nomen indicat) neque eam <lb/>deor&longs;um impellet perinde ac &longs;i aqua &longs;uprema AB non <lb/>ade&longs;&longs;et, proindeque hæc non augebit grauitatem in­<lb/>ferioris laminæ BC, aliàs &longs;uprema aqua AB pondera-<pb pagenum="39" xlink:href="010/01/047.jpg"/><arrow.to.target n="marg40"/><lb/>ret, comprimeretque &longs;ubiectam aquam BC, quod e&longs;t <lb/>contra aduer&longs;arij hypothe&longs;im; eadem ratione vniuer­<lb/>&longs;a aqua ABC nil ponderabit, ne que comprimet &longs;ub­<lb/>iectam laminam aqueam CD, & tota aqua AD nec <lb/>etiam comprimet aut grauitatem inferet &longs;upra infe­<lb/>riorem <expan abbr="aquã">aquam</expan> DE; idip&longs;um procul dubio affirmari de­<lb/>bet de reliquis omnibus laminulis fluidis totam alti­<lb/>tudinem aquæ componentibus, & hoc optima ratio­<lb/>ne de duximus, <expan abbr="quãdo">quando</expan> quidem &longs;eriem corporum iner­<lb/>tium & nil pror&longs;us deor&longs;um impellentium nemo &longs;anæ <lb/>mentis affirmabit vim compre&longs;&longs;iuam deorsùm exer­<lb/>cere, imò concedet æquè operari ac &longs;i e&longs;&longs;et vnica &longs;in­<lb/>gularis laminula, vel dicet &longs;ubiectum corpus à nihilo <lb/>comprimi, & è contra &longs;eries corporum vim <expan abbr="impul&longs;iuã">impul&longs;iuam</expan> <lb/><expan abbr="habentiũ">habentium</expan> exercet vim pro men&longs;ura multiplicati cor­<lb/>poris, & hoc &longs;anè lumine naturæ <expan abbr="cõ&longs;tat">con&longs;tat</expan>, hinc deduci­<lb/>tur infimam laminam aqueam MN no&longs;tri va&longs;is nullam <lb/>compre&longs;&longs;ionem pati ab vniuer&longs;a aqua &longs;uperpo&longs;it&atail; <lb/>MA non &longs;ecùs ac &longs;i à nihilo premeretur vnde fit vt in­<lb/>ferior pars aquea MN ablata qua MA tanta vi præ­<lb/>cisè comprimat va&longs;is fundum NO ac &longs;i &longs;uper&longs;taret <lb/>immen&longs;a moles aquea NA, &longs;ed illa ob ponderis exi­<lb/>guitatem haud &longs;en&longs;ibilem vim vitreo fundo infert, <lb/>nec ip&longs;um inflectit, aut di&longs;rumpit, igitur neque <expan abbr="vitrũ">vitrum</expan> <lb/>inflectetur aut <expan abbr="cõ&longs;tringetur">con&longs;tringetur</expan> quando alti&longs;&longs;ima moles a­<lb/>quea NA ei &longs;uperponitur; quia verò hoc euidentiæ <lb/>&longs;en&longs;us repugnat affirmandum e&longs;t, aquam licèt in ip&longs;a­<lb/>met aqua iners & quie&longs;cens videatur, nece&longs;&longs;ariò gra­<lb/>uitatem exercere. <pb pagenum="40" xlink:href="010/01/048.jpg"/><arrow.to.target n="marg41"/></s> </p> <p type="margin"> <s id="s.000182"><margin.target id="marg40"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000183"><margin.target id="marg41"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000184"><emph type="center"/>PROP. XIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000185"><emph type="center"/><emph type="italics"/>Id ip&longs;um in &longs;iphone comprobatur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000186">PRæterea v&longs;urpetur idip&longs;um vas vitreum, &longs;ed in­<lb/>flexum, vt e&longs;t AMOP &longs;iphonis inuer&longs;i figuram <lb/>referens, atque portio ANO aqu&atail; <lb/><figure id="id.010.01.048.1.jpg" xlink:href="010/01/048/1.jpg"/><lb/>impleatur, reliqua verò fi&longs;tula OP o­<lb/>leo. </s> <s id="s.000187">Et quia vt mox o&longs;ten&longs;um e&longs;t ex <lb/>aduer&longs;arij hypothe&longs;i tota aqua AM <lb/>vim non infert neque impellit infe­<lb/>riorem aqueam laminam MN, cù&mtail; <lb/>nullam grauitatem &longs;uper eam exer­<lb/>ceat; igitur tota moles aquea AM nil prorsùs impel­<lb/>let terminum aquæ O & proindè ab hoc non impelle­<lb/>tur &longs;ur&longs;um oleo&longs;us cylinder OP, igitur oleum OP <lb/>nulla ratione &longs;ubleuari &longs;ursùm deberet, &longs;ed hoc e&longs;t <lb/>fal&longs;um, igitur fal&longs;a e&longs;t quoque hypothe&longs;is a&longs;&longs;umpta, <lb/>quòd aqua in ip&longs;amet aqua po&longs;ita grauitatem no&ntail; <lb/>exerceat. </s> </p> <p type="main"> <s id="s.000188">Et profectò methodus ac criterium digno&longs;cendi, <lb/>an corpus aliquod grauitet, atque impellat alterum, <lb/>erit huiu&longs;modi; con&longs;iderari nimirum debent effectus <lb/>ab eo producti, & quanta vis contraria requiritur, <lb/>vt vnum à con&longs;ortio, & contactu alterius diuellatur, <lb/>& &longs;eparetur, & quia &longs;i nauis natando lateraliter &longs;co­<lb/>pulum contingeret, po&longs;&longs;et à quacumque exigua vi tra­<lb/>hi, diuelli, & &longs;eparari ab eodem &longs;copulo, hinc in re <lb/>optimo inferemus nauim omninò carere vi motiua, & <pb pagenum="41" xlink:href="010/01/049.jpg"/><arrow.to.target n="marg42"/><lb/>impul&longs;iua tendendi ver&longs;us &longs;copulum, è contra, quia <lb/>videmus, quòd pila ferrea non pote&longs;t à contactu &longs;oli <lb/>&longs;eiungi, ac diuelli ni&longs;i æqualis facultas, & energi&atail; <lb/>contraria adhibeatur, &longs;cilicet ni&longs;i apponatur pondus <lb/>in altera extremitate libræ, quod æquale &longs;it grauita­<lb/>ti prædictæ pilæ ferre&etail;, &longs;icuti cùm homo robu&longs;tus co­<lb/>lumnam aliquam impellit, non pote&longs;t ab ea &longs;eiungi, <lb/>ni&longs;i adhibeatur vis motiua prorsùs æqualis ei, quam <lb/>homo exercet; hinc de ducemus pilam vim grauitatis, <lb/>& hominem vim mu&longs;culorum exercere. </s> </p> <p type="margin"> <s id="s.000189"><margin.target id="marg42"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000190">Porrò effectus producti ab illa ferrea pila à paui­<lb/>mento &longs;ubnixa plures &longs;unt, ac varij, con&longs;tringuntur <lb/>nempè pori &longs;ubiecti corporis pilam &longs;u&longs;tinentis, in­<lb/>flectitur paritèr idip&longs;um contunditurque, & multo­<lb/>tiès diffringitur, ac di&longs;&longs;ilit in particulas minimas, <lb/>igitur &longs;i huiu&longs;modi effectus ip&longs;amet aqua operaretur, <lb/>ab&longs;que vlla hæ&longs;itatione aquam in ip&longs;amet aqua gra­<lb/>uitare affirmaremus. </s> <s id="s.000191">Modò videmus, quòd aqua ad <lb/>ingentem altitudinem eleuata nedùm &longs;olum, ac fun­<lb/>dum va&longs;is inflectit, &longs;ed ip&longs;um multoties diffringit, & <lb/>hoc magis patet &longs;i fundum va&longs;is flexibile fuerit, &longs;i ve­<lb/>rò con&longs;tringi, ac conden&longs;ari poterit, illud con&longs;trin­<lb/>git, atque ad minus &longs;patium redigit, non &longs;ecùs ac <lb/>homo robu&longs;tus comprimeret, & &longs;lecteret corpor&atail; <lb/>flexibilia, ac cedentia, dum ea impelleret. <pb pagenum="42" xlink:href="010/01/050.jpg"/><arrow.to.target n="marg43"/></s> </p> <p type="margin"> <s id="s.000192"><margin.target id="marg43"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000193"><emph type="center"/>PROP. XV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000194"><emph type="center"/><emph type="italics"/>Alia ratione, & experimento probare compres&longs;ionem par­<lb/>tium aquæ, & rerum in ea contentarum à pon­<lb/>dere ip&longs;iu&longs;met aquæ.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000195">SIt fi&longs;tula vitrea RVX vndique clau&longs;a <expan abbr="præterquã">præterquam</expan> <lb/>in &longs;upremo orificio R, hæc verò aqua repleatur, <lb/>& in ea ampullula vitrea AD immerga­<lb/><figure id="id.010.01.050.1.jpg" xlink:href="010/01/050/1.jpg"/><lb/>tur &longs;itque ea plena aere, & eius pars ver­<lb/>&longs;us infimum orificium apertum D graui­<lb/>or &longs;it, ad hoc vt ampullula AD &longs;emper <lb/>inuer&longs;o &longs;itu in ip&longs;a aqua per&longs;i&longs;tat. </s> <s id="s.000196">in hac <lb/>machina ob&longs;eruatur quòd vexica vitrea <lb/>AD quò magis deprimitur infra &longs;upre­<lb/>mam aquæ libellam, vel potiùs ip&longs;amet <lb/>aqua altiùs infunditur, & eleuatur, tune <lb/>eò magis aer in ampulla contentus con­<lb/>den&longs;atur, <expan abbr="atq;">atque</expan> in minori &longs;patio con&longs;trin­<lb/>gitur, & hoc fen&longs;u ip&longs;o patet dum aqu&atail; <lb/>ingreditur per orificium D atque colli <lb/>ampullæ particulam aliquam implet; quod verò hu­<lb/>iu&longs;modi aeris re&longs;trictio &longs;it effectus ponderis aquæ &longs;u­<lb/>premæ comprimentis &longs;en&longs;u ip&longs;o digno&longs;citur, <expan abbr="nã">nam</expan> quò <lb/>magis aquæ &longs;uprema &longs;uperficies S eleuatur versùs R <lb/>&longs;emper magis, ac magis &longs;ucce&longs;&longs;iuè aeris moles præ­<lb/>dicti tubuli con&longs;tringitur &longs;ubintrando nimirùm aqua <lb/>magis à C versùs B. </s> <s id="s.000197">Quòd verò hoc dependeat à <expan abbr="cõ-pre&longs;&longs;ione">con­<lb/>pre&longs;&longs;ione</expan> multiplicati ponderis aquæ &longs;ubleuatæ alià <pb pagenum="43" xlink:href="010/01/051.jpg"/><arrow.to.target n="marg44"/><lb/>clariori experientia percipitur, &longs;i enim ab&longs;que noua <lb/>aquæ in fu&longs;ione in fi&longs;tula aliqua breui, vel pollice, vel <lb/>&longs;ubere comprimatur aqua orificium R attingens &longs;ta­<lb/>tìm apparet effectus prædictæ compre&longs;&longs;ionis aquæ, <lb/>conden&longs;atur enim, ac&longs;tringitur aer in vitrea ampul­<lb/>la AD eodem modo præcisè, ac maior mo­<lb/><figure id="id.010.01.051.1.jpg" xlink:href="010/01/051/1.jpg"/><lb/>les altioris aquæ eleuatæ faciebat, e&longs;tqu&etail; <lb/>huiu&longs;modi compre&longs;&longs;io acris in prædict&atail; <lb/>ampullula tantæ energiæ vt exi&longs;tente ea le­<lb/>ui, &longs;cilicet quæ &longs;ponte &longs;ua &longs;ur&longs;um in aqu&atail; <lb/>SX a&longs;cendat po&longs;&longs;it è contrà <expan abbr="leuitat&etilde;">leuitatem</expan> amit­<lb/>tere, atque acquirere grauitatem, moueri­<lb/>que, ac de&longs;cendere deor&longs;um, <expan abbr="quotie&longs;cumq;">quotie&longs;cumque</expan> <lb/>aqua in fi&longs;tula ad tantam altitudinem ele­<lb/>uetur vt valdè comprimere ampullulæ aerem po&longs;&longs;it, <lb/>vt eam grauem reddat, nec vt hactenùs &longs;ursùm, &longs;ed <lb/>deorsùm vergat de&longs;cendatque. </s> </p> <p type="margin"> <s id="s.000198"><margin.target id="marg44"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000199"><emph type="center"/>PROP. XVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000200"><emph type="center"/><emph type="italics"/>Alia ratione grauitatem aquæ &longs;uper aquam quie&longs;centis <lb/>demon&longs;trare.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000201">HOc deducitur ex eo quòd corpora, quæ ob ex­<lb/>cedentem eorum grauitatem demerguntur in­<lb/>fra aquam minùs grauitant in ip&longs;a aqua, quàm i&ntail; <lb/>aere, vt &longs;i fuerit pila AB ferrea &longs;pecie grauior quàm <lb/>&longs;it aqua ip&longs;a in va&longs;e RO contenta, & concipiatur IK <lb/>vt pondus ab&longs;olutum pilæ ferreæ AB, &longs;cilicèt expri­<lb/>mat eam grauitatem quam in aere exercet, &longs;it que eius <pb pagenum="44" xlink:href="010/01/052.jpg"/><arrow.to.target n="marg45"/><lb/>portio K grauitas ab&longs;oluta pilæ aqueæ C quæ æqua­<lb/>lis &longs;it ip&longs;i AB, &longs;it que pila C contenta intra eiu&longs;de&mtail; <lb/>aquæ RO profunditatem, vel in altera fi&longs;tula inuer&longs;i <lb/>&longs;iphonis, quæ cum reliqua continuetur, po&longs;tea eadem <lb/>pila AB filo DA ab aliqua potentia I &longs;u&longs;pen&longs;a in me­<lb/>dio aquæ fixè retineatur. </s> <s id="s.000202">modò &longs;i po&longs;&longs;ibile e&longs;t pil&atail; <lb/>aquea C nil prorsùs ponderet in ip&longs;amet aqua, igitur <lb/>in &longs;iphone, vel in libra DE in eius puncto medio F <lb/>fulta pila aquea C &longs;u&longs;pen&longs;a à termino E, quæ <expan abbr="nullã">nullam</expan> <lb/>pror&longs;us grauitatem exercere in aqua &longs;upponitur, <expan abbr="nũ-quam">nun­<lb/>quam</expan> imminuet pondus contrapo&longs;itæ pilæ AB colli­<lb/>gatæ termino libræ D, propterea quòd nihilum ab <lb/>aliquo pondere &longs;ubtractum ip&longs;um nullo pacto immi­<lb/>nuit; nec pariter den&longs;itas, & tenacitas aquæ gradum <lb/>ponderis pilæ AB diminuere pote&longs;t, propterea quòd <lb/>illa re&longs;i&longs;tentia potis e&longs;t retardare, & impedire mo­<lb/>tum, non autem vim, quam graue AB in quiete con­<lb/>&longs;titutum exercet comprimendo; videmus enim, quòd <lb/>pila ferrea quie&longs;cens &longs;iue fulciatur à molli cera, &longs;iue <lb/>à rigido adamante, &longs;emper eadem vi comprimit, &longs;ci­<lb/>licet men&longs;urata à gradu eius <expan abbr="põderis">ponderis</expan>. </s> </p> <p type="margin"> <s id="s.000203"><margin.target id="marg45"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <figure id="id.010.01.052.1.jpg" xlink:href="010/01/052/1.jpg"/> <p type="main"> <s id="s.000204">His po&longs;itis &longs;equitur, quòd pila fer­<lb/>rea AB pendula intra aquam exerce­<lb/>bit integram &longs;uam grauitatem IK, <lb/>&longs;cilicet eam, quam in aere exerce­<lb/>bat, &longs;ed hoc e&longs;t fal&longs;um, imminuitur <lb/>enim præcisè pro men&longs;ura ponderis <lb/>K &longs;cilicet molis aqueæ C, & ei relin­<lb/>quitur tantummodò pondus I, &longs;cili-<pb pagenum="45" xlink:href="010/01/053.jpg"/><arrow.to.target n="marg46"/><lb/>cet exce&longs;&longs;us quo pondus eius ab&longs;olutum &longs;uperat gra­<lb/>uitatem aquæ eiu&longs;dem molis; quapropter verum <expan abbr="nõ">non</expan> <lb/>e&longs;t aquam C in ip&longs;amet aqua con&longs;titutam, nullam <expan abbr="cõ-pre&longs;&longs;ionem">con­<lb/>pre&longs;&longs;ionem</expan>, aut grauitatem exercere. </s> </p> <p type="margin"> <s id="s.000205"><margin.target id="marg46"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000206"><emph type="center"/>PROP. XVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000207"><emph type="center"/><emph type="italics"/>Idip&longs;um alia ratione demon&longs;trare.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000208">VAs RO repleatur aqua, in eaque immergatur <lb/>pila ferrea BA quæ filo aliquo DA &longs;u&longs;tineatur <lb/>ne ad fundum va&longs;is de&longs;cendat. </s> <s id="s.000209">Manife&longs;tum e&longs;t <expan abbr="pot&etilde;-tiam">poten­<lb/>tiam</expan> D filum, & pilam retinentem æquari ei graui­<lb/>tati quam ip&longs;a pila in aqua exercet, & quia in va&longs;e <lb/>aqueo RO deficit præcisè tanta aquæ quantitas, <expan abbr="quã-tum">quan­<lb/>tum</expan> e&longs;t &longs;patium, quod corpus graue A in ip&longs;a oc­<lb/>cupat, collocatur verò intra aquam ne dum grau&etail; <lb/>AB, &longs;ed etiam defectus molis aquæ æqualis eide&mtail; <lb/>AB quare &longs;umma po&longs;itiu&etail; grauitatis AB vnà cum de­<lb/>fectiuo pondere molis aquæ expul&longs;æ à loco AB, &longs;ci­<lb/>licet exce&longs;&longs;us ponderis AB &longs;upra pondus molis aquæ <lb/>æqualis pilæ AB æqualis erit ponderi quod exercet <lb/>pila AB in aqua ergò &longs;i huiu&longs;modi aquæ moles ex &longs;ui <lb/>natura nil in aqua ponderat quando tollitur a &longs;patio <lb/>AB moles aquea, quæ ip&longs;um replebat reuerà tollitur <lb/>res non grauis, & quæ nil omninò ponderat; igitur à <lb/>pondere ab&longs;oluto ip&longs;ius AB, & à &longs;patio ab ea occu­<lb/>pato nihilum, &longs;eù nulla grauitas &longs;ubtrahitur, quando <lb/>verò ab ab&longs;oluta grauitate IK pilæ AB nil pror&longs;us <lb/>tollitur, remanet eiu&longs;dem gradus, ac proindè pon-<pb pagenum="46" xlink:href="010/01/054.jpg"/><arrow.to.target n="marg47"/><lb/>dus pilæ AB nil prorsùs imminutum erit, & æquali <lb/>energia &longs;u&longs;tineri debet à potentia D, ac &longs;i eadem pi­<lb/>la extra aquam in aere libero penderet, &longs;ed hoc e&longs;t <lb/>fal&longs;um, cùm præcisè in ip&longs;a aqua grauitas pilæ æqua­<lb/>lis &longs;it differentiæ ponderis eius ab&longs;oluti à grauitat&etail; <lb/>aquæ &longs;ibi æqualis mole, vt ex Archimede deducitur, <lb/>igitur nece&longs;&longs;ariò <expan abbr="fatendũ">fatendum</expan> e&longs;t aquam in ip&longs;amet aqua <lb/>collocatam ponderare, & grauitatem exercere. </s> </p> <p type="margin"> <s id="s.000210"><margin.target id="marg47"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000211">Contra hoc euidenti&longs;&longs;imum ratiocinium afferri <lb/>&longs;olet difficultas valdè &longs;pecio&longs;a, quam examinare, ac <lb/>di&longs;&longs;oluere erit operæ pretium, vtque ea ritè percipi­<lb/>atur, con&longs;ideretur hæc figura. </s> <s id="s.000212">Sit vas cylindricu&mtail; <lb/><arrow.to.target n="marg48"/><lb/>ABDC aqua plenum &longs;it que eius altitudo <lb/><figure id="id.010.01.054.1.jpg" xlink:href="010/01/054/1.jpg"/><lb/>di&longs;&longs;ecta in quotcumque partes æquales, <lb/>ductis nempè planis imaginarijs MO, & <lb/>HI, erit igitur moles aquea AI dupl&atail; <lb/>aque &etail; molis HD; igitur pondus aquæ AI <lb/>duplum e&longs;t ponderis aquæ HD. quia ve­<lb/>rò corpus grauius minùs graue &longs;uperare <lb/>debet, hocque è &longs;uo loco expellere (cùm in eo con&longs;i­<lb/>&longs;tat vis, & energìa grauitatis, vt tendat deorsùm, <lb/>& &longs;ic è loco infimo corpora minùs grauia expellat) & <lb/>po&longs;tquàm aqua AI translata e&longs;t ad locum HD, atque <lb/>aquam ibidem collocatam expulit denuò in &longs;itu &longs;u­<lb/>periori fi&longs;tulæ AI aqua dupli ponderis, & molis ibi­<lb/>dem re&longs;tituitur quæ pariter &longs;uperat grauitatem &longs;ub­<lb/>duplam aquæ, quæ ad occupandum infimum locum <lb/>HD &longs;ucce&longs;&longs;it, igitur denuò aqua &longs;uprema vt grauior <lb/>infimam è &longs;uo loco extrudere, atque expellere de-<pb pagenum="47" xlink:href="010/01/055.jpg"/><arrow.to.target n="marg49"/><lb/>bet, & quia hoc &longs;emper repetitur, &longs;cilicèt perpetuò <lb/>re&longs;tituitur in &longs;uperiori loco AI aqua duplò grauior, <lb/>quàm ea, quæ in loco infimo HD reponitur, igitur <lb/>vt contingit in libra efficientur perpetuæ, & conti­<lb/>nuatæ vibrationes, veluti in pendulo, & in aqua fie­<lb/>ri &longs;olent plures vndulationes, &longs;ic in aqua perpetuo <lb/>motu agitarentur eius partes a&longs;cendendo, & de&longs;cen­<lb/>dendo. </s> <s id="s.000213">hoc verò &longs;en&longs;us euidentia redarguit, igitur <lb/>fatendum e&longs;t &longs;upremam aquam AI &longs;u&longs;tentatam ab <lb/>inferiori aqua &longs;uper eam non exercere vim vlla&mtail;, <lb/>nec pre&longs;&longs;ionem, proinde que non grauitare, hac &longs;cili­<lb/>cet de cau&longs;a, quia nimirùm in eius loco naturali col­<lb/>locata re quie&longs;cit, ac &longs;i&longs;titur. </s> </p> <p type="margin"> <s id="s.000214"><margin.target id="marg48"/>Contra do­<lb/>ctrinam &longs;u­<lb/>periùs addu­<lb/>ctam ade&longs;t <lb/>noua difficul­<lb/>tas, quod ni­<lb/>mirum mo­<lb/>tu perpetuo <lb/>aqua agitari <lb/>deberet.</s> </p> <p type="margin"> <s id="s.000215"><margin.target id="marg49"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000216"><emph type="center"/>PROP. XVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000217"><emph type="center"/><emph type="italics"/>Maior aquæ moles alteri &longs;upe po&longs;ita non exercet maiorem <lb/>vim compres&longs;iuam, quàm minor.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000218">VT verò huiu&longs;modi paralogi&longs;mus detegatur, <expan abbr="animaduert&etilde;d">a­<lb/>nimaduertendum</expan> e&longs;t minimè verum e&longs;&longs;e, quòd <lb/>quælibet aquæ moles maior alterà, <expan abbr="n&etilde;pe">nempe</expan> dupla, exer­<lb/>ceat quoque duplam vim grauitantem quotie&longs;cum­<lb/>que maior &longs;upra minorem in&longs;i&longs;tat, & ab ea fulciatur, <lb/>&longs;ed tunc &longs;olummodò propo&longs;itio verificatur quando <lb/>earum ba&longs;es <expan abbr="cõtiguæ">contiguæ</expan> æquales fuerint, ac in&longs;uper in <lb/>eodem plano horizonti parallelo con&longs;titerint. </s> <s id="s.000219">Sup­<lb/>ponatur vas cylindricum plenum aqua ABDC, &longs;it­<lb/>que portio &longs;uprema, & ideò eius altitudo AH dupla <lb/>infimæ altitudinis HB, licèt ergo reuerà &longs;upremæ <pb pagenum="48" xlink:href="010/01/056.jpg"/><arrow.to.target n="marg50"/><lb/>aquæ AI pondus duplum &longs;it ponderis infimæ aquæ <lb/>HD, non hìnc tamen inferri licet &longs;ubiectam aquam <lb/>HD in tali &longs;itu vnicam libram tantummodò pendere <lb/>exi&longs;tente &longs;upremo pondere AI duarum librarum, &longs;ed <lb/>nece&longs;sè e&longs;t vt aqua HD comprimat va&longs;is fundum BD <lb/>ni&longs;u, ac vi non vnius libræ, &longs;ed æquali ei, quæ effi­<lb/>citur à pondere trium librarum, & ratio e&longs;t quia ip­<lb/>&longs;a aqua HD nedùm impellitur deor&longs;um à vi propriæ <lb/>grauitatis vnius libræ, &longs;ed in&longs;uper grauatur compri­<lb/>miturque ab incumbente pondere aquæ AI, quæ <expan abbr="cõ-pre&longs;&longs;io">com­<lb/>pre&longs;&longs;io</expan> &longs;uperaddit aqu&etail; HD vim æqualem ei, quæ à <lb/>duabus libris effici pote&longs;t; nec profectò nouum e&longs;t &longs;i­<lb/>quis centum laminas ferreas, vel lapideas, æquè <expan abbr="põ-derantes">pon­<lb/>derantes</expan>, &longs;cilicet &longs;ingulas vnius libræ vnam &longs;uper al­<lb/>teram imponat, quod in&longs;ima lamina non tantummo­<lb/>dò &longs;uo pondere comprimet planum &longs;ubiectum, &longs;cili­<lb/>cèt non efficiet vim æqualem cente&longs;imæ parti totius <lb/>prædicti aggregati, &longs;ed compre&longs;&longs;io infim&etail; laminæ ef­<lb/>ficiet vim centuplo maiorem &longs;cilicèt impellet &longs;ubie­<lb/>ctum planum vi æquali centum libris, & tunc <expan abbr="&longs;olũ-modò">&longs;olum­<lb/>modò</expan> in&longs;ima lamina partem cente&longs;imam totius ag­<lb/>gregati ponderabit, quando illa in vna lance, reli­<lb/>quæ verò 100. in oppo&longs;ita lance eiu&longs;dem libræ ra­<lb/>diorum æqualium &longs;u&longs;penderentur; &longs;ic paritèr &longs;i aqua <lb/>HD &longs;upra planum &longs;ubiectum &longs;iuè &longs;olidum, &longs;iuè flui­<lb/>dum collocaretur iuxtà portionem aquæ AI, it aut &longs;e­<lb/>&longs;e contingerent lateraliter, atque <expan abbr="earũ">earum</expan> ba&longs;es æqua­<lb/>les in eodem plano horizontali collocarentur, tunc <lb/>nece&longs;&longs;ariò dupla moles aquæ AI duplam vim com-<pb pagenum="49" xlink:href="010/01/057.jpg"/><arrow.to.target n="marg51"/><lb/>pre&longs;&longs;iuam, pro men&longs;ura duplæ grauitatis haberet. <lb/></s> <s id="s.000220">Verum tamen e&longs;t, quòd alia de cau&longs;a non e&longs;t nece&longs;­<lb/>sè, vt &longs;emper ba&longs;es &longs;int æquales, neque grauitates <lb/>&longs;int in eadem proportione dupla, dummodò altitu­<lb/>do AH dupla &longs;it altitudinis ip&longs;ius HB; & ratio huius <lb/>diuer&longs;itatis pendet ex alibi demon&longs;trandis. </s> </p> <p type="margin"> <s id="s.000221"><margin.target id="marg50"/>Cap. 3. flui­<lb/>dum in &longs;ue <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000222"><margin.target id="marg51"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000223">Ex &longs;uperiori igitur ratiocinio euinci­<lb/><figure id="id.010.01.057.1.jpg" xlink:href="010/01/057/1.jpg"/><lb/>tur, fal&longs;um e&longs;&longs;e, quòd pronunciabatur, <lb/>nimirùm, duplam aquam AI vt grauio­<lb/>rem, expellere de&longs;cendendo debere &longs;ub­<lb/>duplam aquam &longs;ubiectam HD, cùm ècon <lb/>tra hæc vt grauior, grauitate nempe pro­<lb/>pria, & ea, quæ ei &longs;uperadditur ab aqua <lb/>&longs;uperincumbente AI in eodem loco infimo perma­<lb/>nere debeat, nec vnquam à debiliori compre&longs;&longs;ione <lb/>&longs;uper&longs;tantis aquæ expelli po&longs;&longs;it, ac proindè &longs;equitur <lb/>&longs;umma quies, ac tranquillitas, non verò motus per­<lb/>petuus. <lb/><arrow.to.target n="marg52"/></s> </p> <p type="margin"> <s id="s.000224"><margin.target id="marg52"/>Ex doctrina <lb/>&longs;uperiùs tra­<lb/>dita videtur <lb/>deduci po&longs;­<lb/>&longs;e lignum <lb/>infra aquam <lb/>po&longs;itum &longs;ur­<lb/>&longs;um <expan abbr="a&longs;c&etilde;de-">a&longs;cende­<lb/>re</expan> non po&longs;&longs;e.</s> </p> <p type="main"> <s id="s.000225">Sed dices, &longs;i vera e&longs;&longs;et adducta doctrina, lignum <lb/>deberet in fundo aquæ paritèr retineri, proptere&atail; <lb/>quòd nedum à propria grauitate comprimitur, &longs;ed <lb/>etiam à pondere totius aquæ &longs;uper&longs;tantis, & ideò <lb/>magis grauitaret quàm aqua ei &longs;uperpo&longs;ita, & proin­<lb/>de lignum in fundo aquæ permanere deberet: hoc <lb/>autem fal&longs;um e&longs;t, cùm experientia con&longs;tet, lignum <lb/>&longs;ursùm ferri, nec quie&longs;cere, antequàm ad aquæ &longs;u­<lb/>premam libellam perducatur. </s> </p> <pb pagenum="50" xlink:href="010/01/058.jpg"/> <p type="main"> <s id="s.000226"><arrow.to.target n="marg53"/></s> </p> <p type="margin"> <s id="s.000227"><margin.target id="marg53"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000228"><emph type="center"/>PROP. XIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000229"><emph type="center"/><emph type="italics"/>Lignum infra aquam demer&longs;um, licèt pondus proprium, & <lb/>aquæ incumbentis exerceat, non proinde ibidem <lb/>quie&longs;cet.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000230">VT autem huius argumenti falla cia patefiat, in <lb/>va&longs;e ARSE aqua pleno demergatur pri&longs;ma li­<lb/>gneum, vel aereum HBDI &longs;itqu&etail; <lb/><figure id="id.010.01.058.1.jpg" xlink:href="010/01/058/1.jpg"/><lb/>pondus aquæ AI decem libraru&mtail; <lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->lignum verò HD &longs;emilibra&mtail; <lb/>pendeat. </s> <s id="s.000231">Concedo, quòd lignu&mtail; <lb/>HD premit &longs;ubiectam aquam BV <lb/>non vi &longs;emilibræ, &longs;ed robore libra­<lb/>rum decem, & &longs;emis, & ideo <expan abbr="lignũ">lignum</expan> <lb/>HD magis comprimit, ac grauitat, <lb/>quàm &longs;ola aqua incumbens AI, &longs;ed non proindè &longs;e­<lb/>quitur, lignum HD quatenùs magis comprimit, ac <lb/>grauitat in fundo aquæ per&longs;i&longs;tere debere, cùm ab <lb/>alia cau&longs;a &longs;ursùm exprimatur. </s> <s id="s.000232">Secto enim pri&longs;mat&etail; <lb/>aqueo CEFI æquali ip&longs;i AI, & aqueo pri&longs;mate IG <lb/>cuius moles æqualis &longs;it ligno HD, & eius pondus <lb/>duas libras &longs;uperet; patet quòd aqua &longs;ubiecta BV <lb/>premitur à pondere librarum decem, & &longs;emis, at <lb/>aqua DS comprimitur à pondere librarum duode­<lb/>cim; ergo sipho, vel libra mobilis aquea BG flecti <lb/>debet eleuando lignum HD minus graue. </s> <s id="s.000233">Et hinc <lb/>patet, quòd ratio, quare lignum a&longs;cendit, non e&longs;t <lb/>pondus aquæ incumbentis AI, &longs;ed e&longs;t aqua collate-<pb pagenum="51" xlink:href="010/01/059.jpg"/><arrow.to.target n="marg54"/><lb/>ralis IG, & hoc con&longs;tat, quia &longs;i in &longs;tricta fi&longs;tula vitrea <lb/>ARVC ponatur in eius fundo aqua BV in loco me­<lb/>dio lignum HD, vel exigua aeris ve&longs;ica, quæ va&longs;is <lb/>latera exactè tangat, & reliquum va&longs;is repleatur a­<lb/>qua AI, tunc lignum non a&longs;cendet &longs;ur&longs;um, quia nem­<lb/>pè &longs;ipho, vel libra mobilis <expan abbr="cũ">cum</expan> aqua collaterali crea­<lb/>ri non pote&longs;t. </s> </p> <p type="margin"> <s id="s.000234"><margin.target id="marg54"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000235"><emph type="center"/>CAP. XX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000236"><emph type="center"/><emph type="italics"/>Corpora terrena cùm è locis &longs;uis naturalibus remouentur <lb/>de&longs;cendendo nullam grauitatem exercent.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000237">SEd &longs;ublata prædicta difficultate deuenio ad <expan abbr="o&longs;t&etilde;-dendum">o&longs;ten­<lb/>dendum</expan> quòd adeò fal&longs;um e&longs;t corpora terrena <lb/>dum quie&longs;cunt in proprijs locis non grauitare, vt è <lb/>contra quando à locis naturalibus &longs;eparata mouen­<lb/>tur <expan abbr="tũc">tunc</expan> nullam grauitatem exerceant &longs;uper alias par­<lb/>tes eiu&longs;dem corporis, quod licèt videatur parado­<lb/>xum, o&longs;tendetur nihilominùs hac ratione. </s> <s id="s.000238">Conci­<lb/>piantur primò facilitatis gratia duo lanæ inuolucra, <lb/>vnum &longs;uper alterum impo&longs;itum &longs;upra planum &longs;ubie­<lb/>ctum, certum e&longs;t &longs;upremum comprimere, & grauita­<lb/>tem exercere &longs;upra &longs;ubiectum inuolucrum, & hoc <expan abbr="cõ-&longs;tat">con­<lb/>&longs;tat</expan> &longs;en&longs;u ab effectu ouem producit pondus lanæ in­<lb/>cumbentis, &longs;cilicèt ex inflexione, & compre&longs;&longs;ion&etail; <lb/>pilorum &longs;ubiectæ lanæ, & è contra con&longs;tat quando <lb/>eadem duo lanæ inuolucra collateralitèr &longs;e&longs;e contin­<lb/>gunt fulciunturque à &longs;ubiecto plano, tunc neque pi­<lb/>li lanei collaterales inflectuntur, nec comprimuntur, <pb pagenum="52" xlink:href="010/01/060.jpg"/><arrow.to.target n="marg55"/><lb/>propterea quòd ni&longs;us grauitatis non exercetur late­<lb/>raliter, &longs;ed deorsùm. </s> </p> <p type="margin"> <s id="s.000239"><margin.target id="marg55"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000240">Hinc colligitur, quòd quotie&longs;cumque &longs;upremum <lb/>lanæ inuolucrum perpendicularitèr incumbens &longs;u<lb/>peralterum, &longs;i ip&longs;um non flecteret, nec &longs;tringeret, <lb/>tunc planè affirmandum e&longs;&longs;et lanam &longs;uperpo&longs;ita&mtail; <lb/>minimè &longs;uper &longs;ubiectam lanam grauitatem exercere. </s> </p> <p type="main"> <s id="s.000241">His po&longs;itis, &longs;upremum lanæ inuolucrum applica­<lb/>ri pote&longs;t &longs;uper infimum dum hoc actu per aerem mo­<lb/>uetur de&longs;cendendo deor&longs;um, vel dum quie&longs;cit à pla­<lb/>no &longs;tabili fultum; in primo ca&longs;u manife&longs;tum e&longs;t, <lb/>quòd inuolucra æqualia eiu&longs;dem lanæ æquales gra­<lb/>dus velocitatum <expan abbr="hab&etilde;t">habent</expan>, quibus naturaliter de&longs;cen­<lb/>dunt; igitur &longs;upremum inuolucrum non de&longs;cendet <lb/>tardiori, vel celeriori motu quàm &longs;ibi <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan>, pro­<lb/>indeque æquali velocitare &longs;uprema lana compri­<lb/>mere conatur &longs;ubiectam lanam, ac i&longs;ta nititur effu­<lb/>gere per&longs;equentem; proptereaque &longs;e mutuo placi­<lb/>do contactu &longs;olummodò exo&longs;culantur, nec &longs;ubiecta <lb/>inflectetur, aut comprimetur à &longs;uper&longs;tante lana: <lb/>igitur, ex &longs;uperiùs dictis incumbens lana nequè <expan abbr="põ-dus">pon­<lb/>dus</expan>, neque grauitatem exercebit &longs;upra fugientem <lb/>lanam &longs;ubiectam. </s> <s id="s.000242">In &longs;ecundo verò ca&longs;u &longs;i po&longs;tquàm <lb/>in quiete &longs;ubiecta lana compre&longs;&longs;a e&longs;t à &longs;uperincum­<lb/>bente ambas demittamus, & liberè deor&longs;um <expan abbr="de&longs;c&etilde;-dere">de&longs;cen­<lb/>dere</expan> concedamus, pateteas motum inchoare quan­<lb/>do iam re&longs;trictæ, & con&longs;tipatæ &longs;unt, & ideò in pro­<lb/>gre&longs;&longs;u licèt paribus velocitatibus de&longs;cendant, reti­<lb/>n bunt tamen eandem con&longs;tipationem, quam prius <pb pagenum="53" xlink:href="010/01/061.jpg"/><arrow.to.target n="marg56"/><lb/>habebant; &longs;ed hinc non licet inferre, &longs;upremam la­<lb/>nam dum mouetur grauitatem exercere, quia ill&atail; <lb/>con&longs;tipatio non dependet ab actione grauitatis in­<lb/>cumbentis lanæ quæ actio per&longs;eueret exerceaturque <lb/>tempore de&longs;cen&longs;us, &longs;ed illa con&longs;tipatio e&longs;t effectus <lb/>compre&longs;&longs;ionis in præcedenti quiete factæ, in actu e­<lb/>nim de&longs;cen&longs;us nullo pacto impellere pote&longs;t &longs;uprema <lb/>lana &longs;ubiectam pani velocitate ictum fugientem, & <lb/>ideo &longs;uper eam minimè pondus exercebit. </s> </p> <p type="margin"> <s id="s.000243"><margin.target id="marg56"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000244"><emph type="center"/>PROP. XXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000245"><emph type="center"/><emph type="italics"/>Aqua de&longs;cendens per aerem, nullam grauitatem habet, & <lb/>&longs;olummodò eam exercet, quando quie&longs;cit &longs;uper <lb/>aquam.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000246">SImili modo aqua non de&longs;cendit, quando fulci­<lb/>tur à &longs;uperficie terræ, & maris, &longs;ed quando <lb/>extra &longs;uum locum peregrinatur, & mouetur, vt i&ntail; <lb/>aere, & tunc &longs;i con&longs;ideretur cylindrus aqueus per ae­<lb/>rem de&longs;cendens, diuidaturque in partes æquales à <lb/>planis horizonti æquidi&longs;tantibus; quia partes æqua­<lb/>les eiu&longs;dem aquæ &longs;unt æquè graues, habent impe­<lb/>tus æquales à natura &longs;ibi a&longs;&longs;ignatos quibus de&longs;cen­<lb/>dere deor&longs;um nituntur, igitur pars &longs;uprema eiu&longs;dem <lb/>cylindri aquei æquè velox erit, ac pars ei &longs;ubiecta, <lb/>igitur &longs;uprema non poterit impellere, vel compri­<lb/>mere aquam ei &longs;ubiectam, cùm æquali velocitat&etail; <lb/>h&etail;c ictum, & percu&longs;&longs;ionem fugiat cum quanta à &longs;u­<lb/>perincumbente in&longs;ectatur per&longs;equiturque, &longs;icuti <pb pagenum="54" xlink:href="010/01/062.jpg"/><arrow.to.target n="marg57"/><lb/>&longs;agitta explo&longs;a minimè percutiet &longs;ignum æquali ve­<lb/>locitate ictum fugiens; igitur manife&longs;tum e&longs;t, aquam <lb/>minimè grauitatem exercere &longs;upra ei &longs;ubiectam a­<lb/>quam, quando à proprio loco naturali exulat, & per <lb/>aerem mouetur. </s> </p> <p type="margin"> <s id="s.000247"><margin.target id="marg57"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000248">Secùs autem contingit in aqua quie&longs;cente, i&ntail; <lb/>puteo aliquo, vellacu, &longs;i enim diuidatur pariter in <lb/>laminas æque altas, patet quòd &longs;upremane dum <expan abbr="tã-git">tan­<lb/>git</expan> &longs;impliciter &longs;ubiectam aquæ laminam, &longs;ed è con­<lb/>tra eam impellit tanta vi <expan abbr="quãta">quanta</expan> e&longs;t energia eius gra­<lb/>uitatis, & patet quòd infima aqua pati cogitur com­<lb/>pre&longs;&longs;ionem, cùm &longs;u&longs;tinere debeat pondus &longs;upremæ <lb/>aquæ incumbentis: & hoc accidit, quia &longs;ua quiete <lb/>impedit progre&longs;&longs;um, & conatum compre&longs;&longs;iuum <expan abbr="de-orsũ">de­<lb/>orsum</expan> &longs;uperpo&longs;itæ aqu&etail;; hac de cau&longs;a &longs;i habueit poro­<lb/>&longs;itates hæ nece&longs;&longs;ario con&longs;tringentur à vi ponderis <lb/>incumbentis aquæ. </s> <s id="s.000249">Modò quia impul&longs;us compre&longs;&longs;i­<lb/>uus factus à &longs;uperiore aqua &longs;upra inferiorem nullo <lb/>alio vocabulo de&longs;ignatur, quàm grauitatis, vel <expan abbr="põ-deris">pon­<lb/>deris</expan>, igitur verum erit, quòd aqua &longs;uper aquam <lb/><arrow.to.target n="marg58"/><lb/>quie&longs;centem grauitatem exercet non quando in mo­<lb/>tu con&longs;tituitur, & extra &longs;uum naturalem locum, &longs;ed, <lb/>tantummodò, quando &longs;i&longs;titur, & quie&longs;cit in loco &longs;uo <lb/>naturali. </s> </p> <p type="margin"> <s id="s.000250"><margin.target id="marg58"/>Contra do­<lb/>ctrinam &longs;u­<lb/>periùs addu­<lb/>ctam afferri <lb/>&longs;olet difficul<lb/>tas valdè <lb/>plau&longs;ibilis, <lb/>quod nimi­<lb/>rum vrina­<lb/>tores ingens <lb/>pondus aque <lb/>incumbentis <lb/>nec patian­<lb/>tur, nec &longs;en­<lb/>tiant.</s> </p> <p type="main"> <s id="s.000251">Hi&longs;ce omnibus rationibus opponi &longs;olet <expan abbr="experi&etilde;-tia">experien­<lb/>tia</expan> &longs;atis vulgata, e&longs;tque huiu&longs;modi: vrinatores i&ntail; <lb/>profundo maris demer&longs;i non &longs;entiunt, neque <expan abbr="patiũ-tur">patiun­<lb/>tur</expan> compre&longs;&longs;ionem &longs;uperincumbentis aquæ, quæ <lb/>multoties plures congios excedit; hinc inferunt, &longs;i <pb pagenum="55" xlink:href="010/01/063.jpg"/><arrow.to.target n="marg59"/><lb/>aqua in ip&longs;amet aqua pondus, & grauitatem habe­<lb/>ret, nece&longs;&longs;ariò vrinatores comprimerentur à va&longs;to <lb/>pondere aquæ incumbentis &longs;uper eorum humeros, <lb/>immò nec po&longs;&longs;et pondus tam va&longs;tum à viribus huma­<lb/>nis &longs;u&longs;tineri, quando videmus, ab homine robu&longs;to <lb/>minus pondus &longs;u&longs;tineri non po&longs;&longs;e; cùm ergo experi­<lb/>entia doceat vrinatores in fundo aquæ grauitate&mtail; <lb/>nullam percipere, igitur verum non e&longs;t, aquam i&ntail; <lb/>ip&longs;a aqua collocatam grauitare, immò in proprio lo­<lb/>co nil prorsùs ponderahit. </s> </p> <p type="margin"> <s id="s.000252"><margin.target id="marg59"/>Cap. 3. flui <lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000253">Huic vulgari difficultati vt fiat &longs;atis <expan abbr="præmittendũ">præmittendum</expan> <lb/>e&longs;t, quòd aqua in ip&longs;amet aqua con&longs;tituta, <expan abbr="pariterq;">pariterque</expan> <lb/>quodlibet fluidum in &longs;uo homogeneo demer&longs;um non <lb/>alia de cau&longs;a quie&longs;cit, ni&longs;i quia vndique comprimi­<lb/>tur pari vi à grauitate ambientis fluidi, cui propri&atail; <lb/>grauitate re&longs;i&longs;tit, vtque hoc clariùs percipiatur, o­<lb/>&longs;tendemus, quod. </s> </p> <p type="main"> <s id="s.000254"><emph type="center"/>PROP. XXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000255"><emph type="center"/><emph type="italics"/>Corpora in bilance æquilibrata ideò quie&longs;cunt, & torpent, <lb/>quia grauitatem exercent comprimunturque æquali­<lb/>bus viribus ab ambientibus corporibus pariter <lb/>æquilibratis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000256">ESto libra AB radiorum æqualium in eius puncto <lb/>intermedio C &longs;u&longs;pen&longs;a, atque in eius extremi­<lb/>tatibus, vtrinque quatuor laminas, vel lateres æquè <lb/>ponderantes &longs;ibi mutuò incumbentes apponantur, <lb/>&longs;cilicet DE, EF,, FG, GH, &longs;u per A, & totidem IK, <pb pagenum="56" xlink:href="010/01/064.jpg"/><arrow.to.target n="marg60"/><lb/>KL, LM, MN &longs;uper <expan abbr="terminũ">terminum</expan> B. </s> <s id="s.000257">Manife&longs;tum e&longs;t, ag­<lb/>gregatum ex laminis DH ibidèm retineri indifferen­<lb/>tia quadam, nec pelli &longs;ursùm, aut deorsùm, firmiter­<lb/>que in tali &longs;itu quie&longs;cere, vt nimirùm &longs;i quis infr&atail; <lb/>laterem DE manum &longs;upponeret, minimè ab ip&longs;is <expan abbr="cõ-primeretur">com­<lb/>primeretur</expan>, neque vllam grauitatem perciperet, hoc <lb/>autem non contingit ex eo, quòd lamin&etail; lateritiæ <lb/>grauitatem amittant, & deorsùm nil comprimant, <lb/>&longs;ed quia ab æquali vi contraria &longs;u&longs;tinentur, ac &longs;ursùm <lb/><expan abbr="impellũtur">impelluntur</expan> à pondere nempè oppo&longs;ito IN &longs;ibi æquali <lb/>in libra AB premente. </s> <s id="s.000258">Præterea quælibet lamina in­<lb/>termedia FE &longs;imilitèr quie&longs;cit, &longs;i&longs;titurque iners, vt <lb/>neque &longs;ursùm, neque deorsùm moueatur, nequ&etail; <lb/>&longs;ubiectam manum, quæ lateralitèr eam retinere co­<lb/>naretur vllatenùs comprimit, aut impellit, & hoc <lb/>efficitur quia lamina <lb/><figure id="id.010.01.064.1.jpg" xlink:href="010/01/064/1.jpg"/><lb/>FE comprimitur de­<lb/>or&longs;um ab incumben­<lb/>te pondere FH, &longs;ur­<lb/>sùm verò impellitur <lb/>à &longs;ubiecta lamina DE non virtute propria, &longs;ed eius, <lb/>quam exercet contra po&longs;itum pondus IN &longs;cilicet tan­<lb/>ta vi, quanta <expan abbr="põdus">pondus</expan> IN &longs;uperat pondus DE; &longs;ed quia <lb/>præterea lamina ip&longs;a FE exercet vim &longs;ui ponderis <lb/>contra pre&longs;&longs;ionem contrapo&longs;iti exce&longs;&longs;us KN fit vt vis <lb/>quæ impellit &longs;ursùm laminam FE æqualis &longs;it exce&longs;&longs;ui <lb/>ip&longs;ius KN &longs;upra FE, &longs;cilicet æqualis &longs;it NL; &longs;untque <lb/>FH, & LN inter &longs;e æquales; ergo viribus æqualibus <lb/>FE deprimitur ac &longs;ursùm impellitur. </s> <s id="s.000259">E contra lami-<pb pagenum="57" xlink:href="010/01/065.jpg"/><arrow.to.target n="marg61"/><lb/>na FE impellit deor&longs;um laminam DE, ne dum pro­<lb/>prio pondere, &longs;ed etiam grauitate laminarum FH; <lb/>pariterque FE repellit laminas &longs;upremas FH no&ntail; <lb/>propria virtute, &longs;ed vi ponderis LN &longs;cilicet exce&longs;&longs;u <lb/>IN &longs;upra DF; Quaproptèr con&longs;tat, quòd lamina la­<lb/>teritia FE comprimitur &longs;upernè, & infernè à duabus <lb/>viribus contrarijs quæ æqualibus momentis <expan abbr="operã-tur">operan­<lb/>tur</expan>, à quibus proindè retinetur fixè, vt nequeat &longs;ur­<lb/>sùm, aut deorsùm moueri. </s> <s id="s.000260">Præterea colligitur, quòd <lb/>reuerà lamina lateritia FE non verè in quiete inerti <lb/>con&longs;tituitur, nec pondere priuatur, &longs;ed potiùs effi­<lb/>citur lucta quædam contrariarum virtutum <expan abbr="æqualiũ">æqualium</expan> <lb/>virium, vndè æquatis momentis motus tonicus, &longs;eù <lb/>quies &longs;ub&longs;equitur, & hìnc deducitur quòd prædicta <lb/>corpora &longs;e mutuò comprimunt, & hìnc fit, vt neuter <lb/><expan abbr="contrariorũ">contrariorum</expan> impellentium &longs;uum iter pro&longs;equi valeat, <lb/>proindeque cogantur fixè in eodem &longs;itu quie&longs;cere. </s> </p> <p type="margin"> <s id="s.000261"><margin.target id="marg60"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000262"><margin.target id="marg61"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000263"><emph type="center"/>PROP. XXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000264"><emph type="center"/><emph type="italics"/>Idip&longs;um in aqua o&longs;tenditur exemplo &longs;iphonis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000265">EOdem ferè modo in aqua idem æquilibrium ef­<lb/>fici manife&longs;tum e&longs;t, proindeque partes ip&longs;ius <lb/>aquæ partim &longs;upernè comprimi à &longs;uper&longs;tantibus a­<lb/>quæ partibus, partim verò infernè &longs;ursùm expelli, <expan abbr="nõ">non</expan> <lb/>propria vi, &longs;ed pondere collateralis aquæ, quæ cum <lb/>illa libram imaginariam, vel &longs;iphonem con&longs;tituit. <lb/></s> <s id="s.000266">E&longs;to igitur, claritatis gratia, &longs;ipho HAB perpendi­<lb/>cularitèr eleuatus &longs;upra horizontem, repletu&longs;qu&etail; <pb pagenum="58" xlink:href="010/01/066.jpg"/><arrow.to.target n="marg62"/><lb/>aqua v&longs;que ad &longs;uprema orificia H & N; &longs;ubdiuida­<lb/>tur tota eius altitudo in partes æquales ductis nimi­<lb/>rum planis &longs;uperficiebus GM, <lb/><figure id="id.010.01.066.1.jpg" xlink:href="010/01/066/1.jpg"/><lb/>FL, EK, DI; hic profectò aquæ <lb/>portio FE, licèt nullum <expan abbr="effectũ">effectum</expan> <lb/>grauitatis producere, <expan abbr="atq;">atque</expan> iner­<lb/>ter quie&longs;cere videatur, dùm in­<lb/>differens e&longs;t ad motum &longs;ursùm, <lb/>& deorsùm, non hìnc deducere <lb/>licet, aquam ip&longs;am FE in tali &longs;i­<lb/>tu vim propriæ grauitatis non exercere, nec <expan abbr="cõprimi">comprimi</expan> <lb/>ab aqua &longs;uperna, & inferna: <expan abbr="cõ&longs;ideretur">con&longs;ideretur</expan> enim quòd <lb/>FF, in parte &longs;uprema ab aqua FH comprimitur de­<lb/>orsùm, è contrà à &longs;ubiecta aqua DE expellitur &longs;ur­<lb/>sùm, non propria vi, &longs;ed pondere contrapo&longs;it&etail; aquæ <lb/>NL. </s> <s id="s.000267">Hinc colligitur, quòd aqua FE reuerà impelli­<lb/>tur deorsùm à &longs;uperna aqua, & &longs;ursùm ab inferna; <lb/>ip&longs;a veròmet aqua FE è contrà vim exercet contr&atail; <lb/>vtramque compre&longs;&longs;ionem, &longs;cilicèt contra eam, quæ <lb/>efficitur ab aqua &longs;ubiecta, re&longs;i&longs;tit <expan abbr="põdere">pondere</expan> &longs;uo pro­<lb/>prio vnà cum grauitate incumbentis aquæ FH, &longs;ed <lb/>contra vim, qua comprimitur &longs;upernè non re&longs;i&longs;tit, & <lb/>contranititur virtute propria, &longs;ed mediante impul­<lb/>&longs;u de&longs;cen&longs;iuo collateralis aquæ NK, igitur huiu&longs;mo­<lb/>di quies aquæ, quæ in &longs;itu FE indifferentèr retinetur, <lb/>nec pote&longs;t &longs;ursùm, aut deorsùm moueri, e&longs;t effectus, <lb/>qui nece&longs;&longs;ariò con&longs;equitur ad exercitium &longs;uæ natiuæ <lb/>grauitatis, & eius, quæ exercetur ab aqua &longs;iphonis, <lb/>vel ab aqua collaterali eiu&longs;dem va&longs;is, in quo paritèr <pb pagenum="59" xlink:href="010/01/067.jpg"/><arrow.to.target n="marg63"/><lb/>aqua operatur, veluti in &longs;iphone collocata fui&longs;&longs;et. </s> </p> <p type="margin"> <s id="s.000268"><margin.target id="marg62"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000269"><margin.target id="marg63"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000270"><emph type="center"/>PROP. XXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000271"><emph type="center"/><emph type="italics"/>Aqua in ip&longs;amet aqua demer&longs;a undiquè comprimitur ab <lb/>ambiente aqua, & vtraque grauitatem exercet.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000272">INtra vas ABCD aqua plenum intelligatur pri&longs;ma <lb/>aqueum FGHE, ducti&longs;que planis FL, & GM pa­<lb/>rallelis horizonti. </s> <s id="s.000273">Dico, quòd aqua FH vndique pre­<lb/>mitur ab ambiente aqua FILKG, & vtraque pondus <lb/>grauitatemque exercet. </s> <s id="s.000274">Quia aqua FH cum aqu&atail; <lb/>ambiente &longs;iphonem AKD con&longs;tituit, in quo fluidum <lb/>&longs;ibi homogeneum agitari pote&longs;t, & quie&longs;cit nihilo­<lb/>minùs; ergo vna pars fluidi AK <lb/><figure id="id.010.01.067.1.jpg" xlink:href="010/01/067/1.jpg"/><lb/>æquilibratur, proindequè æquè <lb/>ponderat, ac pars reliqua latera­<lb/>lis IC, portio verò aquæ FH licèt <lb/>motu careat, &longs;itque indifferens <lb/>ad motum &longs;ursùm, & deorsùm, <lb/>haud inferre licet eam non exer­<lb/>cere vim &longs;uæ grauitatis vnà cum tota aqua ambi­<lb/>ente, quia in &longs;iphonis brachio AK aquæ FH &longs;u­<lb/>prema facies FE deor&longs;um impelli, & comprimi de­<lb/>bet ab incumbente aqua AE, pariterque infim&atail; <lb/>illius facies GH &longs;ursùm impelletur à &longs;ubiecta a­<lb/>qua GK non virtute propria, &longs;ed eius quam exercet <lb/>pondus aquæ collateralis IM; porrò nedum aqua FH <lb/>impellitur &longs;ur&longs;um ab aqua &longs;ubiecta BH, &longs;ed etiam, vt <lb/>experientia con&longs;tat, impul&longs;ionem, & <expan abbr="con&longs;triction&etilde;">con&longs;trictionem</expan> <pb pagenum="60" xlink:href="010/01/068.jpg"/><arrow.to.target n="marg64"/><lb/>patietur facies eius FH ab aqua collaterali DH; <lb/>quod euidentius <expan abbr="o&longs;t&etilde;detur">o&longs;tendetur</expan> prop. 192. Stringitur er­<lb/>go aqua FH veluti prælo, nec tamen iners omninò <lb/>e&longs;t, repellit enim &longs;ursùm aquam <lb/><figure id="id.010.01.068.1.jpg" xlink:href="010/01/068/1.jpg"/><lb/>AE vi grauitatis aquæ lateralis <lb/>IL, aquam verò &longs;ubiectam repel­<lb/>lit deorsùm vi grauitatis pro­<lb/>priæ, & &longs;upremæ IE. quare quies <lb/>aquæ FH e&longs;t effectus dependens <lb/>à compre&longs;&longs;ione facta ab aqua am­<lb/>biente, & ab exercitio &longs;uæ grauitatis, & eius quam <lb/>aqua ambiens &longs;iphonem con&longs;tituens exercet: quod <lb/>erat &c. </s> </p> <p type="margin"> <s id="s.000275"><margin.target id="marg64"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000276"><emph type="center"/>PROP. XXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000277"><emph type="center"/><emph type="italics"/>Quodlibet corpus in aqua demer&longs;um vndique &longs;tringitur <expan abbr="cõ-primiturque">con­<lb/>primiturque</expan> ab ambiente aqua.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000278">IN eadem figura quodlibet corpus durum, molle, <lb/>vel <expan abbr="fluidũ">fluidum</expan> FH in aqua demer&longs;um fixè detineatur. <lb/></s> <s id="s.000279">Dico ip&longs;um vndiquè &longs;tringi, ac <expan abbr="cõprimi">comprimi</expan> ab ambien­<lb/>te fluido FILHB. </s> <s id="s.000280">Quia &longs;olidum FH intra aquam re­<lb/>tentum vnà cum ambiente aqua con&longs;tituit &longs;iphonem <lb/>AKD in quo eius partes AK, & KD quie&longs;cunt, & æ­<lb/>quilibrantur, ergò oportet vt aqua &longs;uprema AE <expan abbr="cõ-primat">con­<lb/>primat</expan>, <expan abbr="impellatq;">impellatque</expan> deorsùm &longs;olidi &longs;uperficiem FE, <lb/>pariterque debet aqua &longs;ubiecta GK impellere &longs;ur­<lb/>&longs;um &longs;olidi &longs;uperficiem GH non virtute propria, &longs;ed <lb/>vi ponderis aquæ collateralis IM, &longs;imiliter &longs;olidi fa-<pb pagenum="61" xlink:href="010/01/069.jpg"/><arrow.to.target n="marg65"/><lb/>ciem EH &longs;tringet lateraliter eadem aqua IM. </s> <s id="s.000281">Igitur <lb/>vndique &longs;olidum FH &longs;tringitur comprimiturquè <expan abbr="tã-quam">tan­<lb/>quam</expan> à prælo: quod erat &c. </s> </p> <p type="margin"> <s id="s.000282"><margin.target id="marg65"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000283">Et hìc notandum e&longs;t, quòd &longs;i corpus FH fuerit <lb/>ve&longs;ica flexilis repleta corpore fluido concipi pote&longs;t <lb/>con&longs;tans ex partibus non conden&longs;abilibus, vt e&longs;t a­<lb/>qua, hydrargyrum, & aggregatum ex minimis &longs;ph&etail;­<lb/>rulis cry&longs;tallinis; aut componatur ex partibus adeò <lb/>raris, atque poro&longs;is, vt ingentem conden&longs;atione&mtail; <lb/>pati po&longs;&longs;int, cuius natura Aer e&longs;t. </s> <s id="s.000284">In primo ca&longs;u li­<lb/>cèt ve&longs;ica FH vndique æqualibus viribus compri­<lb/>matur &longs;tringaturque, nihilominùs ob duritiem par­<lb/>tium in ve&longs;ica contentarum, non poterit ip&longs;a ve&longs;ic&atail; <lb/>con&longs;tringi, <expan abbr="cõden&longs;arique">conden&longs;arique</expan>, &longs;cilicèt minus &longs;patium ex­<lb/>plere, quàm prius occupauerat, eò quòd particulæ <lb/>ip&longs;æ duri&longs;&longs;imæ fluidæ, vel den&longs;æ adinuicem fulciun­<lb/>tur, veluti columnæ, aut fornices, quæ nullo pacto <lb/>po&longs;&longs;unt frangi, vel con&longs;tringi, cùm è contrà partes <lb/>aeris ob maximam earum raritatem facilè po&longs;&longs;int <expan abbr="cõ-&longs;tipari">con­<lb/>&longs;tipari</expan>, proindeque ve&longs;ica aera FH ad minus &longs;patiûm <lb/>redigi po&longs;&longs;it con&longs;trictis nempè eius poro&longs;itatibus. </s> </p> <p type="main"> <s id="s.000285">His declaratis pro re&longs;olutione principalis proble­<lb/><arrow.to.target n="marg66"/><lb/>matis <expan abbr="inquir&etilde;dũ">inquirendum</expan> e&longs;t, quo modo, & qua ratione à com­<lb/>pre&longs;&longs;ione ponderis incumbentis pa&longs;&longs;io dolorifica in <lb/>animali &longs;ub&longs;equatur. </s> </p> <p type="margin"> <s id="s.000286"><margin.target id="marg66"/>Inquiritur <lb/>cau&longs;a quare <lb/>à pondere in­<lb/>cumbente <lb/>producitur <lb/>compre&longs;&longs;io, <lb/>&longs;ci&longs;&longs;io, diui­<lb/>&longs;io continui, <lb/>& proinde <lb/>dolor.</s> </p> <p type="main"> <s id="s.000287">Et primò experientia con&longs;tat, à pondere corporis <lb/>manum v. <!-- REMOVE S-->g. <!-- REMOVE S-->prementis aliquando effici &longs;ci&longs;&longs;ionem, <lb/>vt ab acie &longs;ecuris incumbentis, aliquando <expan abbr="fraction&etilde;">fractionem</expan>; <lb/>multotiès luxari, & di&longs;rumpi articulos tractis nem-<pb pagenum="62" xlink:href="010/01/070.jpg"/><arrow.to.target n="marg67"/><lb/>pè violentèr tendinibus articulos colligantibus, & <lb/>tandem fieri pote&longs;t contu&longs;io, & diffractio partiu&mtail; <lb/>&longs;olidarum. </s> <s id="s.000288">Et hi&longs;ce omnibus modis continuitatis <lb/>diui&longs;io in animali efficitur, à quà demum diui&longs;ion&etail; <lb/>pa&longs;&longs;ionem dolorificam exoriri vulgò credunt. </s> </p> <p type="margin"> <s id="s.000289"><margin.target id="marg67"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000290">Modò o&longs;tendendum e&longs;t, quòd diui&longs;io continui, & <lb/>dolor procreari pote&longs;t ab aliquo &longs;ingulari pondere, <lb/>quòd &longs;i pondus po&longs;tea comprimens augeatur, mul­<lb/>tipliceturque, non proindè &longs;emper, & vniuersè ma­<lb/>ior, &longs;ed minor, immò nulla &longs;ci&longs;&longs;ura, vel contu&longs;io, <lb/>aut fractio in animali &longs;ub &longs;equi pote&longs;t; quod quidem <lb/>licèt videatur paradoxum, poterit tamen facili ne­<lb/>gotio demon&longs;trari. </s> </p> <p type="main"> <s id="s.000291"><emph type="center"/>PROP. XXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000292"><emph type="center"/><emph type="italics"/>Lamina dura, & flexibilis, quæ à pondere incumbente <lb/>flectitur, poterit à potentia duplicata dirigi.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000293">SIt lamina chalybea AB parieti RS infixa, <expan abbr="eiq;">eique</expan> in­<lb/>cumbat pondus C à quo lamina ip&longs;a deorsù&mtail; <lb/>impul&longs;a curuitatem acquirat, <lb/><figure id="id.010.01.070.1.jpg" xlink:href="010/01/070/1.jpg"/><lb/>inflectaturque: adueniat po­<lb/>&longs;tea vis motiua H æqualis pon­<lb/>deri C, quæ contrario ni&longs;u &longs;ur­<lb/>sùm impellat eamdem <expan abbr="laminã">laminam</expan>: <lb/>manife&longs;tum e&longs;t, quòd à duplici <lb/>vi C, & H, non augetur curui­<lb/>tas ip&longs;ius laminæ, &longs;ed ea potiùs dirigitur, quia ni­<lb/>mirùm duæ vires contrari&etail; æqualibus <expan abbr="mom&etilde;tis">momentis</expan> ope-<pb pagenum="63" xlink:href="010/01/071.jpg"/><arrow.to.target n="marg68"/><lb/>rantes &longs;ibi mutuò impellunt, & proindè vna alterius <lb/>vim, & actionem de&longs;truit, quantum ergo lamina in­<lb/>flectitur deorsùm à <expan abbr="põdere">pondere</expan> C, tantumdèm &longs;ursùm re­<lb/>flectitur à contrario impul&longs;u ip&longs;ius H. <!-- REMOVE S--><margin.target id="marg68"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000294"><emph type="center"/>PROP. XXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000295"><emph type="center"/><emph type="italics"/>Idip&longs;um adhibitis contrarijs ponderibus ope libræ <lb/>verificatur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000296">APplicetur libra DE radio­<lb/><figure id="id.010.01.071.1.jpg" xlink:href="010/01/071/1.jpg"/><lb/>rum æqualium &longs;uffult&atail; <lb/>in F, it aut terminus D infrà ex­<lb/>tremitatem laminæ AB collo­<lb/>cetur, & tunc po&longs;ito pondere <lb/>G æquale ip&longs;i C in altero extremo libræ E, impel­<lb/>letur &longs;ursùm terminus libræ, vel vectis D à vi pon­<lb/>deris G, & ab illo lamina AB in directum retine­<lb/>bitur contra vim compre&longs;&longs;iuam ponderis C, <expan abbr="quãdo-quidem">quando­<lb/>quidem</expan> duo pondera C, & G inter &longs;e æqualia &longs;e mu­<lb/>tuò impellunt, proindeque lamina intercepta AB, <lb/>neque deorsùm, neque &longs;ursùm flectetur. </s> </p> <p type="main"> <s id="s.000297"><emph type="center"/>PROP. XXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000298"><emph type="center"/><emph type="italics"/>Idip&longs;um alia ratione v&longs;urpata libra demon&longs;tratur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000299">SI nimirùm termino E im­<lb/><figure id="id.010.01.071.2.jpg" xlink:href="010/01/071/2.jpg"/><lb/>ponatur pondus IG du­<lb/>plum ip&longs;ius C, atque in D ap­<lb/>plicetur pondus M æqual&etail; <lb/>eidem C, <expan abbr="manife&longs;tũ">manife&longs;tum</expan> e&longs;t, quòd <lb/>pondus IG æquale e&longs;t duo-<pb pagenum="64" xlink:href="010/01/072.jpg"/><arrow.to.target n="marg69"/><lb/>bus ponderibus C & M, & ideò æquilibrium efficie­<lb/>tur, &longs;cilicèt intercepta lamina AB nil prorsùs flecte­<lb/>tur, quia licèt à pondere &longs;upremo C deorsùm lami­<lb/>na pellatur, repellitur infernè à corpore M non qui­<lb/>dem propria vi, (cùm tendat deorsùm ob eius gra­<lb/>uitatem) &longs;ed ab exce&longs;&longs;u ponderis IG &longs;upra M. </s> </p> <p type="margin"> <s id="s.000300"><margin.target id="marg69"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000301"><emph type="center"/>PROP. XXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000302"><emph type="center"/><emph type="italics"/>Animalis infra aquam demer&longs;i membra non flectentur, <lb/>eò quòd vndique contrarijs viribus à fluido com­<lb/>primuntur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000303">IN &longs;uperiori diagrammate habemus exemplum &longs;i­<lb/>mile omninò corpori animalis in aqua natantis, <lb/>nam licèt animalis brachium, ver. gra. AB, compri­<lb/>matur à &longs;uperpo&longs;ita aqua C, non tamen flectetur de­<lb/>orsùm, aut di&longs;rumpetur, cùm præ&longs;tò &longs;it aqua &longs;ubie­<lb/>cta M, quæ &longs;ursùm manum brachiumque repellat, <lb/>impediatque eius depre&longs;&longs;ionem, flexionemque, <expan abbr="nõ">non</expan> <lb/><expan abbr="quid&etilde;">quidem</expan> propria vi grauitatis eius, &longs;ed virtute <expan abbr="cõpre&longs;-&longs;iua">compre&longs;­<lb/>&longs;iua</expan> collateralis aquæ IG, <lb/><figure id="id.010.01.072.1.jpg" xlink:href="010/01/072/1.jpg"/><lb/>quæ in libra, vel &longs;iphone i­<lb/>maginario, eo <expan abbr="põdere">pondere</expan>, quo <lb/>excedit <expan abbr="grauitat&etilde;">grauitatem</expan> aquæ M, <lb/>eam &longs;ursùm impellit, & pro­<lb/>pterea <expan abbr="Brachiũ">Brachium</expan> AB &longs;u&longs;tinet <lb/>ne à <expan abbr="põdere">pondere</expan> &longs;upremo incuruetur, aut di&longs;rumpatur. </s> </p> <p type="main"> <s id="s.000304">Et hoc (dicet aliquis) &longs;ufficeret ad luxatione&mtail; <lb/>membrorum animalis euitandam, &longs;ed non proindè <pb pagenum="65" xlink:href="010/01/073.jpg"/><arrow.to.target n="marg70"/><lb/>dolor compre&longs;&longs;iuus animalis vitari po&longs;&longs;et, quando­<lb/>quidem partes carno&longs;æ, & tendino&longs;æ contunderen­<lb/>tur diffringerenturque, atque vniuersè &longs;ci&longs;&longs;ura&mtail; <lb/>aliquam paterentur. </s> </p> <p type="margin"> <s id="s.000305"><margin.target id="marg70"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000306">Vt verò fallacia huius ratiocinij detegatur. <lb/><arrow.to.target n="marg71"/></s> </p> <p type="margin"> <s id="s.000307"><margin.target id="marg71"/>Sed licèt lu­<lb/>xatio non <lb/><expan abbr="cõ&longs;equatur">con&longs;equatur</expan>, <lb/>&longs;altem con­<lb/>tu&longs;io, & dif­<lb/>fractio par­<lb/>tium anima­<lb/>lis con&longs;equi <lb/>debere vi­<lb/>detur.</s> </p> <p type="main"> <s id="s.000308"><emph type="center"/>PROP. XXX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000309"><emph type="center"/><emph type="italics"/>Scis&longs;io con&longs;equens actionem Cunei, vel &longs;ecuris <lb/>declaratur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000310">EFfectus con&longs;equens ad actionem cunei, & aciei <lb/>&longs;ecuris, &longs;ci&longs;&longs;io nuncupari &longs;olet, quæ efficitur <lb/>propterea, quòd dum cuneus intra corpus &longs;ci&longs;&longs;il&etail; <lb/>in&longs;inuatur, huius partes hinc in de lateralitèr mouen­<lb/>tur, & ab inuicem &longs;eparantur: hinc fit, quòd &longs;i par­<lb/>tes &longs;ubiecti corporis minimè lateralitèr moueri po&longs;­<lb/>&longs;ent, neque cuneus penetraret, nec &longs;ci&longs;&longs;io fieret: <lb/>triplici verò modo motus laterales &longs;ubiecti corporis <lb/>impediri po&longs;&longs;unt, primò, &longs;i gluten, quo partes &longs;ubie­<lb/>cti corporis colligantur, fuerit immen&longs;æ virtutis, & <lb/>arcti&longs;&longs;imæ vnionis, & duritiei; &longs;ecundò, &longs;i prædictæ <lb/>partes inter &longs;e diui&longs;æ, vt arena, <expan abbr="continer&etilde;tur">continerentur</expan> intra vas <lb/>duri&longs;&longs;imum, cuius parietes cuilibet impul&longs;ui re&longs;i&longs;te­<lb/>rent, nec præterea partes contenti corporis &longs;uble­<lb/>uari &longs;ursùm po&longs;&longs;ent, tunc profectò nec penetratio <lb/>cunei, nec &longs;ci&longs;&longs;io efficeretur; tertiò, &longs;i va&longs;e remoto <lb/>adhiberentur vires impul&longs;iuæ lateralitèr contrariæ <lb/>officium va&longs;is &longs;upplentes, tunc &longs;imilitèr &longs;ci&longs;&longs;io im­<lb/>pediretur. <pb pagenum="66" xlink:href="010/01/074.jpg"/><arrow.to.target n="marg72"/></s> </p> <p type="margin"> <s id="s.000311"><margin.target id="marg72"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000312"><emph type="center"/>PROP. XXXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000313"><emph type="center"/><emph type="italics"/>Diui&longs;io quæ effici pote&longs;t à compres&longs;ione in&longs;trumenti non acu­<lb/>ti, veluti e&longs;t malleus, paritèr ad cunei actionem <lb/>reducitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000314">QVandoquidem particul&etail; corporis à malleo <expan abbr="cõ-pre&longs;&longs;æ">con­<lb/>pre&longs;&longs;æ</expan> in&longs;inuantur directè, <expan abbr="promouenturq;">promouenturque</expan> <lb/>intra alias collaterales particulas, & quia in­<lb/>&longs;inuatio prædictarum partium effici non pote&longs;t ni&longs;i <lb/>collaterales particulæ non contu&longs;æ locali motu late­<lb/>rali tran&longs;portentur, hinc fit, quòd particulæ illæ <expan abbr="cõ-pre&longs;&longs;æ">con­<lb/>pre&longs;&longs;æ</expan> immediatè actionem cunei referant: malleus <lb/>verò &longs;it <expan abbr="in&longs;trum&etilde;talis">in&longs;trumentalis</expan> cau&longs;a mediata, &longs;eù potiùs vir­<lb/>tus impellens particulas compre&longs;&longs;as, cuneos refe­<lb/>rentes. </s> </p> <p type="main"> <s id="s.000315"><emph type="center"/>PROP. XXXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000316"><emph type="center"/><emph type="italics"/>Ve&longs;ica arena, vel aqua repleta vndique, & in omni­<lb/>bus partibus eius ab innumeris cuneis compre&longs;&longs;aneque <lb/>&longs;cindi, neque flecti, neque figuram commu­<lb/>tare pote&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000317">SVpponatur modò ve&longs;ica ABCD, quæ repleatur <lb/>aqua, vel hydrargyro, aut arena, vel globulis <lb/>cry&longs;tallinis minuti&longs;&longs;imis, tunc &longs;i huiu&longs;modi ve&longs;ica à <lb/>pauimento RS fulciatur, atque ei &longs;uperponatur acies <lb/>&longs;ecuris, vel nouaculæ I, procùl dubio, aut ve&longs;ic&atail; <lb/>&longs;cindetur, aut &longs;altèm fluidum, &longs;iue arena content&atail; <pb pagenum="67" xlink:href="010/01/075.jpg"/><arrow.to.target n="marg73"/><lb/>cedet, & ver&longs;us latera ve&longs;i­<lb/><figure id="id.010.01.075.1.jpg" xlink:href="010/01/075/1.jpg"/><lb/>cæ tran&longs;portabitur; at &longs;i in­<lb/>telligantur innumeræ acies <lb/>&longs;ecurium, vndique compri­<lb/>mentes ve&longs;icam, it aut null&atail; <lb/>eius pars intacta relinquatur: <lb/>primò manife&longs;tum e&longs;t, &longs;ci&longs;&longs;io­<lb/>nem prohiberi, quandoquidem longa, & continua­<lb/>ta &longs;eries acierum &longs;e&longs;e con&longs;equentium, & &longs;e mutuò <lb/>lateralitèr tangentium ab&longs;que vlla interruptione æ­<lb/>quiualent corpori obtu&longs;o, proindeque acuties ill&atail; <lb/>omninò de&longs;truitur, & Proptereà non &longs;equetur &longs;ci&longs;&longs;io <lb/>quæ ab&longs;que acie acuta fieri nequit. </s> <s id="s.000318">Secundò non fi­<lb/>et contritio, atque depre&longs;&longs;io alicuius partis prædi­<lb/>ctæ ve&longs;icæ, quandoquidem non pote &longs;t &longs;uprema pars <lb/>eius A deprimi versùs C, quin aqua, vel arena ex­<lb/>pul&longs;a recipiatur ad latera B, & D, &longs;ed hic quoqu&etail; <lb/>æqualibus viribus comprimitur lateralitèr ve&longs;ic&atail;, <lb/>igitur non pote&longs;t ibidem perduci fluidum, vel are­<lb/>na <expan abbr="cõpre&longs;&longs;a">compre&longs;&longs;a</expan>; & propterea ve&longs;icæ circumcircà viribus <lb/>æqualibus compre&longs;sæ nulla particula cedet; & quia <lb/>aliundè materia ip&longs;a fluida, vel arena talis con&longs;i&longs;ten­<lb/>tiæ e&longs;t, vt &longs;tringi, conden&longs;ari, & ad minus &longs;patiu&mtail; <lb/>redigi nequeat, fit vt ve&longs;ica illa, & aqua vel arena <lb/>in ea contenta, neque &longs;cindatur, neque flectatur, <lb/>neque vllo pacto figuram commutet quotie&longs;cumque <lb/>vndique circùmcirca ab æqualibus viribus compri­<lb/>matur. <pb pagenum="68" xlink:href="010/01/076.jpg"/><arrow.to.target n="marg74"/></s> </p> <p type="margin"> <s id="s.000319"><margin.target id="marg73"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000320"><margin.target id="marg74"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000321"><emph type="center"/>PROP. XXXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000322"><emph type="center"/><emph type="italics"/>Idip&longs;um verificatur quotie&longs;cumque prædicta ve&longs;ica in ip&longs;a <lb/>aqua demergitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000323">IBi enim nedùm à perpendiculariter incumbent&etail; <lb/>aqua comprimitur, &longs;ed etiam ab infima, & colla­<lb/>terali, vndequaque, & vniuersè æqualibus viribus <lb/>impellitur, con&longs;tringitur que, vnde fit vt licèt ve&longs;i­<lb/>ca &longs;it tenui&longs;&longs;ima, non po&longs;&longs;it tamen vnquam diffringi à <lb/>pondere licèt immen&longs;o &longs;uper&longs;tantis aquæ, vel hy­<lb/>drargyri, nec contu&longs;ionem, aut diffractionem vllam <lb/>pati; & ratio e&longs;t quia licèt tota ma&longs;&longs;a contenta intra <lb/>ve&longs;icam &longs;it fluida, mollis, & cedens, nihilominus <lb/>quia minimæ particulæ fluidi, vel arenæ &longs;e mutuò <lb/>fulciunt, & natiua duritie compre&longs;&longs;ioni re&longs;i&longs;tunt, fit <lb/>vt conden&longs;ari, aut con&longs;tringi nequeant, & ab vni­<lb/>uer&longs;ali circumambiente compre&longs;&longs;ione ne minimum <lb/>alteretur eius figura, neque &longs;itus partium. </s> </p> <p type="main"> <s id="s.000324"><emph type="center"/>PROP. XXXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000325"><emph type="center"/><emph type="italics"/>Tandem o&longs;tenditur quare animal nullam noxam ex com­<lb/>pres&longs;ione aquæ incumbentis pati debeat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000326">NOn &longs;ecùs in corpore animalis continentur in­<lb/>tra eius pellem partes aliæ quidem duræ, & <lb/>&longs;olidæ, vt &longs;unt o&longs;&longs;a, aliæ molles, vt &longs;unt tendines, <lb/>nerui, membranæ, & mu&longs;culi; aliæ verò &longs;unt fluidæ, <lb/>aqueæ, vel oleagino&longs;æ continentes innumeras alias <pb pagenum="69" xlink:href="010/01/077.jpg"/><arrow.to.target n="marg75"/><lb/>particulas &longs;alis, & aliorum corporum. </s> <s id="s.000327">Modò o&longs;&longs;a in <lb/>animali di&longs;rumpi, aut iuxari non po&longs;&longs;unt, vt o&longs;ten­<lb/>&longs;um e&longs;t Prop. 29. ni&longs;i pondus incumbens ex vn&atail; <lb/>parte tantum comprimat, vt contingit in baiulis; at <lb/>&longs;i compre&longs;&longs;io &longs;ubdiuidatur, vt &longs;phæricè, &longs;ursùm, & <lb/>deorsùm, & lateraliter æqualibus viribus <expan abbr="cõprimat">comprimat</expan>, <lb/>ita vt nulla cutis particula libera à pre&longs;&longs;ione &longs;it, tunc <lb/>quidem e&longs;t impo&longs;&longs;ibile vt &longs;ci&longs;&longs;io, vel luxatio &longs;ub&longs;e­<lb/>quatur; idip&longs;um dicendum e&longs;t de neruis, ac mu­<lb/>&longs;culis, qui licèt &longs;int molles, <expan abbr="tam&etilde;">tamen</expan> quia <expan abbr="cõ&longs;tãt">con&longs;tant</expan> ex fibris <lb/>con&longs;i&longs;tentibus, & tenaci&longs;&longs;imis, fit vt vniuersè po&longs;&longs;int <lb/>&longs;e vici&longs;&longs;im fulcire, & re&longs;i&longs;tere vniuer&longs;ali, & &longs;phæri­<lb/>cæ compre&longs;&longs;ioni: idem dicendum e&longs;t de &longs;anguine, <lb/>& alijs humoribus animalis, qui aquæ naturam par­<lb/>ticipant, & &longs;icuti aqua manife&longs;tam conden&longs;ationem <lb/>non patitur, &longs;ic quoque animalis humores in cauita­<lb/>tibus va&longs;orum eius contenti contritionem pati qui­<lb/>dem po&longs;&longs;unt ab impul&longs;u facto ab vnico, vel paucis <lb/>locis peculiaribus; at ab vniuer&longs;ali, & circumqua­<lb/>que facta compre&longs;&longs;ione minimè po&longs;&longs;unt è &longs;uis va&longs;is <lb/>expelli, ac diuelli. </s> <s id="s.000328">quotie&longs;cumque igitur partes &longs;o­<lb/>lidæ, tendino&longs;æ, aut carno&longs;æ, aut humorales, &longs;ci&longs;&longs;i­<lb/>onem, luxationem, contu&longs;ionem, aut aliam quam­<lb/>libet &longs;itus mutationem non patiuntur e&longs;t impo&longs;&longs;ibi­<lb/>le, vt dolor, aut pa&longs;&longs;io in animali &longs;ub&longs;equatur, quæ <lb/>à nulla alia cau&longs;a, quàm à continui diui&longs;ione creari <lb/>pote&longs;t. </s> <s id="s.000329">Quà propter cùm vrinatores in profundo ma­<lb/>ris demer&longs;i ab aqua æquali vi vndique compriman­<lb/>tur, &longs;upernè &longs;cilicèt, infernè, & lateralitèr circum-<pb pagenum="70" xlink:href="010/01/078.jpg"/><arrow.to.target n="marg76"/><lb/>circa à pondere ip&longs;ius aquæ, &longs;equitur ex demon&longs;tra­<lb/>tis Prop. 29. & 32. nullam &longs;ci&longs;&longs;ionem, luxationem, <lb/>aut contu&longs;ionem in eis creari, &longs;cilicèt nullam conti­<lb/>nui diui&longs;ionem à pondere aquæ incumbentis produ­<lb/>ci, igitur nullam noxam, nec &longs;en&longs;um dolorificu&mtail; <lb/>patientur. </s> </p> <p type="margin"> <s id="s.000330"><margin.target id="marg75"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000331"><margin.target id="marg76"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000332">Sed dices, e&longs;to nullam luxationem, fractionem, aut <lb/>contu&longs;ionem vrinatores &longs;ub aqua pati debere, <expan abbr="&longs;alt&etilde;">&longs;altem</expan> <lb/>&longs;en&longs;u tactus perciperent compre&longs;&longs;ionem ponderis <lb/>illius va&longs;tæ molis aquæ incumbentis, quam non ne­<lb/>gamus exercere &longs;uam grauitatem &longs;upra corpus ani­<lb/>malis demer&longs;i. </s> <s id="s.000333">Hoc profectò e&longs;t, quod negamus, nam <lb/>ratio, quare &longs;en&longs;u pa&longs;&longs;ionem ab incumbente ponde­<lb/>re illatam percipimus extra aquam po&longs;iti e&longs;t, qui&atail; <lb/>no&longs;træ partes ob articulorum flexilem <expan abbr="disiunction&etilde;">disiunctionem</expan> <lb/>deorsùm pelluntur à premente graui, & ideò cogi­<lb/>mur ingenti vi fibras mu&longs;culorum tendere, & con­<lb/>trahere, vt lap&longs;um membrorum impediamus; at in­<lb/>fra aquam ni&longs;u illo laborio&longs;o mu&longs;culorum non in­<lb/>digemus, proptereà quòd aqua &longs;ubiecta vices mu­<lb/>&longs;culorum &longs;upplet repellendo æquali vi &longs;ursùm <expan abbr="aquã">aquam</expan> <lb/>&longs;upremam vnà cum natante animali; & proinde &longs;u­<lb/>prema aqua, &longs;uffulta à &longs;ubiecta virtute ponderis a­<lb/>quæ collateralis cum qua æquilibratur, nullo pacto <lb/>animalis partes flectere, & deprimere pote&longs;t, & ideò <lb/>mu&longs;culi otio&longs;i &longs;unt, & propterea nullam aliam pa&longs;­<lb/>&longs;ionem animal &longs;entiet pr&etail;ter vniuer&longs;alem <expan abbr="cõ&longs;trictio-nem">con&longs;trictio­<lb/>nem</expan> &longs;ui corporis; at quia, vt dictum e&longs;t, partes dur&etail;, <lb/>molles, & fluidæ animalis compre&longs;&longs;ioni non cedunt <pb pagenum="71" xlink:href="010/01/079.jpg"/><arrow.to.target n="marg77"/><lb/>ob earum con&longs;i&longs;tentiam, hinc fit, vt nullam pa&longs;&longs;ionem <lb/>dolorificam &longs;entiant. </s> </p> <p type="margin"> <s id="s.000334"><margin.target id="marg77"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000335"><emph type="center"/>PROP. XXXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000336"><emph type="center"/><emph type="italics"/>Vrinatores constrictionem aliquam infra aquam patiuntur <lb/>ob acrem in eis contentum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000337">NOn tamen negari pote&longs;t ade&longs;&longs;e in animali par­<lb/>tes aliquas aereas, & &longs;pirito&longs;as, quas <expan abbr="cond&etilde;-&longs;ari">conden­<lb/>&longs;ari</expan>, ac con&longs;tringi po&longs;&longs;e manife&longs;tum e&longs;t, vnde à cir­<lb/>cumambiente con&longs;tipatione, quam patiuntur vrina­<lb/>tores in profundo maris con&longs;tituti, nece&longs;&longs;ariò aer in <lb/>pectoris cauitate contentus ob re&longs;pirationis ne­<lb/>ce&longs;&longs;itatem, & particulæ illæ minimæ aereæ per cor­<lb/>pus eius di&longs;per&longs;æ conden&longs;ationem aliquam patiun­<lb/>tur; proindequè motiones internæ &longs;pirituum for&longs;an <lb/>impediuntur, & naturalis con&longs;titutio partium ani­<lb/>malis perturbatur; & inde in&longs;en&longs;ibilis tran&longs;piratio <lb/>impedita laxitudinem, & pa&longs;&longs;ionem dolorifica&mtail;, <lb/>&longs;en&longs;umque &longs;uffocationis creat; & hoc quidem expe­<lb/>rimur quotie&longs;cumque à ve&longs;te nimis angu&longs;ta <expan abbr="cõ&longs;trin-gimur">con&longs;trin­<lb/>gimur</expan>. </s> <s id="s.000338">Sed notandum e&longs;t, compre&longs;&longs;ionem ve&longs;tis non <lb/>e&longs;&longs;e vniuer&longs;alem, & tunc quidem pote&longs;t &longs;anguis ex­<lb/>pelli versùs faciem, & partes nudatas, & à ve&longs;ti­<lb/>bus non con&longs;trictas, quod non contingeret &longs;i vni­<lb/>uersènè minima cutis particula libera à compre&longs;&longs;io­<lb/>ne e&longs;&longs;et. </s> <s id="s.000339">Sic cùm manus immergitur intra hydrar­<lb/>gyrum, patimur quidem &longs;en&longs;ibilem compre&longs;&longs;ionem <lb/>dolorificam nedùm quia partes aereæ, & &longs;pirito&longs;æ <pb pagenum="72" xlink:href="010/01/080.jpg"/><arrow.to.target n="marg78"/><lb/>con&longs;tringuntur, & conden&longs;antur, &longs;ed præcipuè quia <lb/>compre&longs;&longs;io efficitur in peculiari loco, & non vni­<lb/>uersè. </s> </p> <p type="margin"> <s id="s.000340"><margin.target id="marg78"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000341">Ex qua fit vt &longs;anguis à venis manus extrudatur ver­<lb/>sùs brachium non demer&longs;um intra mercurium, & in­<lb/>de duæ pa&longs;&longs;iones &longs;ub&longs;equantur, vna quidèm con&longs;tri­<lb/>ctionis, altera verò e&longs;t ea, quæ ab impedita, & in­<lb/>terrupta &longs;anguinis circulatione per totam manu&mtail; <lb/>oritur. </s> </p> <p type="main"> <s id="s.000342">Sed obijciet forsàn qui&longs;piam exprædicta con&longs;tri­<lb/>ctione partium aerearum in animali <expan abbr="cont&etilde;tarum">contentarum</expan> ali­<lb/>quam dolorificam pa&longs;&longs;ionem oriri, quam vrinatores <lb/>in profundo maris con&longs;tituti percipere deberent. <lb/></s> <s id="s.000343">Hoc tamen vltrò conceditur, reuerà enim in profun­<lb/>do maris pa&longs;&longs;io aliqua con&longs;trictiua in vniuer&longs;o cor­<lb/>pore percipitur, pariterque aer in pectore animalis <lb/>contentus con&longs;tringitur, & conden&longs;atur, &longs;ed no&ntail; <lb/>proindè ingens pa&longs;&longs;io &longs;uffocatiua ob cra&longs;&longs;itiem con­<lb/>den&longs;ati aeris in pectore contenti &longs;ub&longs;equetur, <expan abbr="quã-doquidem">quan­<lb/>doquidem</expan> experimur nullam <expan abbr="noxã">noxam</expan>, aut &longs;en&longs;um &longs;uf­<lb/>focatiuum percipi, quotie&longs;cumque aer in&longs;piratus <lb/>valdè attenuatur, rare&longs;cit, aut conden&longs;atur; &longs;ic enim <lb/>in hypocau&longs;to, atque in montis alti&longs;&longs;imi &longs;ummitate <lb/>aer valdè rarus attenuatu&longs;que e&longs;t, re&longs;pectu eius, qui <lb/>in profunda aliqua valle, vel in loco ceno&longs;o reperi­<lb/>tur, qui valdè cra&longs;&longs;us, & conden&longs;atus e&longs;t, nihilomi­<lb/>nùs, neque in ip&longs;a re&longs;piratione læ&longs;io, aut pa&longs;&longs;io ali­<lb/>qua manife&longs;ta percipitur, <expan abbr="neq;">neque</expan> in habitu totius cor­<lb/>poris aer diuer&longs;imodè rarefactus differentiam nota-<pb pagenum="73" xlink:href="010/01/081.jpg"/><arrow.to.target n="marg79"/><lb/>tu dignam, & à nobis perceptibilem parit: igitur <lb/>vrinatores in profundo maris demer&longs;i nullam pa&longs;&longs;io­<lb/>nem dolorificam percipere po&longs;&longs;unt licèt &longs;upponatur <lb/>quòd ab aqua incumbente pondero&longs;a compriman­<lb/>tur, & conden&longs;etur aliquo pacto aer in thorace eo­<lb/>rum contentus. </s> <s id="s.000344">Quaproptèr ex hi&longs;ce omnibus con­<lb/>cludere licèt <expan abbr="aquã">aquam</expan> <expan abbr="grauitat&etilde;">grauitatem</expan> exercere quandò quie­<lb/>&longs;cit in &longs;uo naturali loco, nempè quando in ip&longs;amet <lb/>vniuer&longs;ali aqua fulcitur, & &longs;u&longs;tentatur. </s> </p> <p type="margin"> <s id="s.000345"><margin.target id="marg79"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000346">Non de&longs;unt po&longs;tea qui Renato Carte&longs;io nimis <lb/><arrow.to.target n="marg80"/><lb/>addicti velint partes minimas cuiuslibet fluidi, & <lb/>præcipuè aquæ <expan abbr="nũquàm">nunquàm</expan> quie&longs;cere, &longs;ed &longs;emper agi­<lb/>tari, accircumuolui per <expan abbr="ipsãmet">ipsammet</expan> aquam. </s> <s id="s.000347">Hinc &longs;u­<lb/>bindè inferunt partes aquæ in ip&longs;amet aqua con&longs;ti­<lb/>tutas, nec grauitatem, nec leuitatem habere, cùm <lb/>po&longs;&longs;int qua qu an ersùm &longs;ursùm, atque deorsùm mo­<lb/>ueri; nos è contrà. </s> </p> <p type="margin"> <s id="s.000348"><margin.target id="marg80"/>Carte&longs;iani <lb/>cen&longs;ent par­<lb/>tes aquæ in <lb/>ip&longs;a aqua, <lb/>nec grauita­<lb/>re, nec leui­<lb/>tare, quia <lb/>&longs;ursùm, & <lb/>deorsùm <expan abbr="cõ-tinentèr">con­<lb/>tinentèr</expan> mo­<lb/>uentur.</s> </p> <p type="main"> <s id="s.000349"><emph type="center"/>PROP. XXXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000350"><emph type="center"/><emph type="italics"/>Ostendemus, quòd licèt aqua in ip&longs;a aqua quomodolibèt con­<lb/>uoluatur, agiteturque, nihilominùs perpetuò retinet <lb/>propriam grauitatem, eamque perpetuò <lb/>exercet.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000351">INtelligatur vas aqua plenum ABCD &longs;u&longs;pen&longs;u&mtail; <lb/>in extremo termino H libræ radiorum æqualium <lb/>HL, cuius centrum I, & pendeat pondus R ab alte­<lb/>ro extremo libræ L, it aut libra quie&longs;cat, & æqueli­<lb/>bretur vas aqueum AC cum corpore R, & hoc qui-<pb pagenum="74" xlink:href="010/01/082.jpg"/><arrow.to.target n="marg81"/><lb/><figure id="id.010.01.082.1.jpg" xlink:href="010/01/082/1.jpg"/><lb/>dem verificetur, dum aqua <lb/>in prædicto va&longs;e contenta <lb/>prorsùs quie&longs;cit, &longs;altè&mtail; <lb/>quoad &longs;en&longs;us <expan abbr="apparentiã">apparentiam</expan>, <lb/>&longs;i po&longs;tea aqua agitetur, vt <lb/>nimirùm pars EF de&longs;cen­<lb/>dat ver&longs;us va&longs;is fundum, reliqua verò pars FG, &longs;ur­<lb/>sùm a&longs;cendat motu quodam vertigino&longs;o, fi veru&mtail; <lb/>e&longs;t, quòd motus a&longs;cen&longs;iuus ip&longs;ius aquæ indicat de­<lb/>fectum grauitatis eius, tunc per&longs;euerante dicto mo­<lb/>tu a&longs;cen&longs;us minui deberet pondus totius va&longs;is AC, <lb/>& propterea libra HL non quie&longs;ceret, &longs;ed deprime­<lb/>retur pondus R, quod tamen repugnat &longs;en&longs;us eui­<lb/>dentiæ; non igitur ex eo quòd aqua mouetur in ali­<lb/>quo va&longs;e carebit propria, & natiua grauitate, &longs;icuti <lb/>homo a&longs;cendens per &longs;calam extremo termino libræ <lb/>alligatam æquali momento libram premeret, ac &longs;i <lb/>idem homo in &longs;cala quie&longs;ceret, quia nimirùm dum <lb/>a&longs;cendit non minus &longs;u&longs;tentatur quàm dum quie&longs;cit. </s> </p> <p type="margin"> <s id="s.000352"><margin.target id="marg81"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000353">Sed dices, cum motus vertigino&longs;us aquæ fieri <expan abbr="nõ">non</expan> <lb/>po&longs;&longs;it ab&longs;que eo quod vna pars de&longs;cendat, & reli­<lb/>qua &longs;ubleuetur, e&longs;t valdè probabile, vt &longs;icut a&longs;cen&longs;us <lb/>aquæ FG indicat defectum grauitatis, cùm prædi­<lb/>ctus motus &longs;upponat impetum à quo &longs;ursùm propel­<lb/>latur &longs;icuti &longs;axum quod &longs;ursùm proijcitur in actu &longs;ui <lb/>a&longs;cen&longs;us, neque graue dici pote&longs;t, nec grauitatem <lb/>exercet, proptereà quòd ab impetu impre&longs;&longs;o con­<lb/>trario grauitati, vel ip&longs;amet grauitas de&longs;truitur, vel <lb/>impeditur, & ce&longs;&longs;at eius operatio. </s> <s id="s.000354">Oppo&longs;itum con-<pb pagenum="75" xlink:href="010/01/083.jpg"/><arrow.to.target n="marg82"/><lb/>tinget in aqua de&longs;cendente EF quæ videtur habere <lb/>nedùm vim propriæ grauitatis, &longs;ed in&longs;uper <expan abbr="impetũ">impetum</expan> <lb/>quo deorsùm fertur, &longs;icuti &longs;axum, quod deorsù&mtail; <lb/>proijcitur, vim, & percu&longs;&longs;ionem infert nedum men­<lb/>&longs;uratam à gradu eius ponderis, &longs;ed etiam ab impe­<lb/>tu eius de&longs;cen&longs;iuo; qua propter vis, quæ &longs;ubtrahitur <lb/>ab aqua <expan abbr="a&longs;cend&etilde;te">a&longs;cendente</expan> FG, &longs;uperadditur grauitati aquæ <lb/>de&longs;cendenti EF, & &longs;ic duplicatur vis eiu&longs;dem aquæ <lb/>de&longs;cendentis qua fundum va&longs;is BC comprimitur; <expan abbr="cũ">cum</expan> <lb/>igitur id, quod &longs;ubtrahitur ab aqua a&longs;cendente FG <lb/>&longs;uperaddatur ponderi aquæ de&longs;cendentis EF com­<lb/>pen&longs;abitur defectus cum additamento impetus <expan abbr="cõ-pre&longs;&longs;iui">con­<lb/>pre&longs;&longs;iui</expan>, proindeque non imminuetur pondus totius <lb/>aquæ in va&longs;e AC contentæ, & hæc erit cau&longs;a, quare <lb/>etiam po&longs;t aquæ agitationem pondus eius in libr&atail; <lb/>non alteratur, nec imminuitur. </s> </p> <p type="margin"> <s id="s.000355"><margin.target id="marg82"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens ponde­<lb/>rat.</s> </p> <p type="main"> <s id="s.000356"><emph type="center"/>PROP. XXXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000357"><emph type="center"/><emph type="italics"/>Reijcitur difficultas contra præcedentem propo&longs;itionem <lb/>adducta.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000358">SEd facili negotio inefficacia huius ratiocinij <expan abbr="o&longs;t&etilde;-di">o&longs;ten­<lb/>di</expan> pote&longs;t, primò experientia, &longs;ecundò ratione. <lb/></s> <s id="s.000359">Quoad primum, &longs;u&longs;pendatur vas aqueum AC duobus <lb/>filis AH, DL alligatis in extremitatibus eiu&longs;dem li­<lb/>bræ HL radiorum æqualium, &longs;u&longs;pendaturque libra <lb/>cum va&longs;e ab illius centro I, manife&longs;tum e&longs;t, quando <lb/>aqua quie&longs;cit, nec agitatur, &longs;i eri æquilibrium, qui&atail; <lb/>&longs;cilicèt centrum grauitatis M totius va&longs;is, & aquæ in-<pb pagenum="76" xlink:href="010/01/084.jpg"/><arrow.to.target n="marg83"/><lb/><figure id="id.010.01.084.1.jpg" xlink:href="010/01/084/1.jpg"/><lb/>cidit præcisè in recta linea MI <lb/>perpendiculari ad horizontem, <lb/>quæ per centrum &longs;u&longs;pen&longs;ionis <lb/>ducitur. </s> <s id="s.000360">Modò agitetur aqua va­<lb/>&longs;is, vt nimirùm pars EF de&longs;cen­<lb/>dat, pars verò KG, &longs;ursùm ten­<lb/>dat, & hoc per aliquod tempus <lb/>per&longs;eueret continuatis reuolu­<lb/>tionibus, dummodò planities libellæ, AD non alte­<lb/>retur; frigitur verum e&longs;t in tali ca&longs;u, quòd grauitas <lb/>a&longs;cendentis aquæ KG de&longs;truitur quatenus à virtute <lb/>impul&longs;iua proiectitia &longs;ursùm impellitur, & è contrà <lb/>&longs;i grauitas, & impetus aquæ de&longs;cendentis EF dupli­<lb/>catur, quia eius ponderi &longs;uperadditur vis proiectiu&atail; <lb/>deorsùm, igitur medietas va&longs;is MAB, aut leuis effi­<lb/>cietur, aut valdè eius grauitas pri&longs;tina imminut&atail; <lb/>erit, & è contrà reliqua va&longs;is medietas MDC <lb/>duplò grauior facta erit, proindeque terminus <lb/>libræ L deprimetur, eleuabiturque oppo&longs;itus ter­<lb/>minus libræ H, quod tamen fal&longs;um e&longs;t, igitur quo­<lb/>modocumque aqua agitetur, dum in ip&longs;amet aqua, & <lb/>in proprio loco continetur, neque amittit ob a&longs;cen­<lb/>&longs;um, nec acquirit ob de&longs;cen&longs;um nouam grauitate&mtail;. </s> </p> <p type="margin"> <s id="s.000361"><margin.target id="marg83"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000362">Sed faciliùs hoc experieris, &longs;i intra vas ABCD in­<lb/>&longs;eratur rota EGKF perpendicularitèr horizonti ere­<lb/>cta, & parietibus oppo&longs;itis va&longs;is infixo axe eius i&ntail; <lb/>M vt facilè rota conuerti po&longs;&longs;it. </s> <s id="s.000363">Et &longs;iquidem centrum <lb/>grauitatis totius aggregati cadit in recta line&atail; <lb/>IM perpendiculari ad horizontem, tunc &longs;iue rot&atail; <pb pagenum="77" xlink:href="010/01/085.jpg"/><arrow.to.target n="marg84"/><lb/>quie&longs;cat, &longs;iue circa eius axim <lb/><figure id="id.010.01.085.1.jpg" xlink:href="010/01/085/1.jpg"/><lb/>M conuertatur libra &longs;emper <lb/>in &longs;itu horizontali æquilibra­<lb/>ta per&longs;i&longs;tet. </s> </p> <p type="margin"> <s id="s.000364"><margin.target id="marg84"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="main"> <s id="s.000365">Vt verò ratio huius effectus <lb/>percipiatur, recurrendum e&longs;t <lb/>ad centri grauitatis definitio­<lb/>nem, ex qua habetur quòd corpus quodlibet &longs;u&longs;pen­<lb/>&longs;um à centro grauitatis eius quomodocumque reuol­<lb/>uatur circa centrum, &longs;emper æquilibrari, & haber&etail; <lb/>partes æqualium momentorum, vnde infertur, quòd <lb/>vniuer&longs;a vis, qua corpus aliquod <expan abbr="t&etilde;dit">tendit</expan> deorsùm, &longs;ci­<lb/>licet grauitas eius, exercetur in vnico illo puncto, <lb/>quod centrum grauitatis eius vocatur. </s> <s id="s.000366">Hinc deduci­<lb/>tur, quod &longs;i rota, &longs;iuè pila &longs;u&longs;tineatur ex centro gra­<lb/>uitatis eius &longs;iuè quie&longs;cat, &longs;iuè moueatur, numquam <lb/>centrum grauitatis &longs;itum commutabit, aliàs daretur <lb/>motus perpetuus, qui naturæ legibus repugnat. </s> </p> <p type="main"> <s id="s.000367">Similitèr &longs;i concipiatur fi&longs;tula vitrea inflexa ad <lb/>modum anuli, vt e&longs;t EFGK, &longs;itque prædicta fi&longs;tul&atail; <lb/>plena aqua &longs;ituata perpendiculari­<lb/><figure id="id.010.01.085.2.jpg" xlink:href="010/01/085/2.jpg"/><lb/>tèr &longs;uper planum &longs;ubiectum RS à <lb/>quo fulciatur; habebit profectò <expan abbr="c&etilde;-trum">cen­<lb/>trum</expan> grauitatis in eius puncto in­<lb/>termedio N, dum quie&longs;cit aqua i&ntail; <lb/>prædicto anulo, at &longs;i reuoluatur vt <lb/>nimirùm pars EFG de&longs;cendat, reliqua verò GKE <lb/>&longs;ursùm <expan abbr="a&longs;c&etilde;dat">a&longs;cendat</expan>, non proindè centrum grauitatis <expan abbr="trã&longs;-feretur">tran&longs;­<lb/>feretur</expan> ab N versùs O, &longs;cilicèt intra &longs;emicirculu&mtail; <pb pagenum="78" xlink:href="010/01/086.jpg"/><arrow.to.target n="marg85"/><lb/>aquæ de&longs;cendentis, nam per&longs;euerante vertigine, &longs;ci­<lb/>licèt translato centro grauitatis vltrà medium in O <lb/>&longs;emper &longs;emianulus EFG grauior e&longs;&longs;et, quàm GKE, <lb/>& propterea ille &longs;emper de&longs;cenderet, hìc verò &longs;em­<lb/>per a&longs;cenderet, proindeque anulus excurreret mo­<lb/>tu perpetuo progre&longs;&longs;iuo, quod e&longs;t fal&longs;um. </s> <s id="s.000368">per&longs;i&longs;tit <lb/>ergo centrum grauitatis &longs;emper in centro N anuli, <lb/>&longs;iue aqua in eo contenta quie&longs;cat, &longs;iuè circumduca­<lb/>tur, nam ob continguitatem partium aquæ non pote&longs;t <lb/>moueri vna pars aquæ F v. <!-- REMOVE S-->g. <!-- REMOVE S-->quin vniuer&longs;a aqu&atail; <lb/>EKG æquali velocitate reuoluatur, proindeque <expan abbr="nõ">non</expan> <lb/>vnica pars tantùm, &longs;ed aqua tota <expan abbr="impulsũ">impulsum</expan>, & impe­<lb/>tum acquirit, non &longs;ecùs ac rota lignea tota &longs;imul ic­<lb/>tum recipit atque circa <expan abbr="c&etilde;trum">centrum</expan> grauitatis eius æqui­<lb/>libratur, pari modo aqua contenta in va&longs;e AC ante <lb/>præmi&longs;&longs;æ figuræ, licèt &longs;it fluida, habet tamen pun­<lb/>ctum M circa quod partes habent æqualia momenta, <lb/>perinde ergo &longs;e habent ac &longs;i vniuer&longs;a aqua in prædi­<lb/>cto va&longs;e contenta dura e&longs;&longs;et, & con&longs;i&longs;tens vt rota li­<lb/>gnea, vel intra fi&longs;tulam anularem EFKG content&atail; <lb/>e&longs;&longs;et in qua reuoluta, &longs;iue quie&longs;cente rota, aut aqua <lb/>&longs;emper centrum grauitatis eius in eodem &longs;itu per&longs;e­<lb/>uerare debet, & proinde libra HL quie&longs;cet in <expan abbr="eod&etilde;">eodem</expan> <lb/>&longs;itu horizontali. </s> <s id="s.000369">Igitur dubitandum non e&longs;t aqua&mtail; <lb/>in &longs;uo toto collocatam, grauitatem exercere, &longs;iuè illa <lb/>omninò ibidem quie&longs;cat, &longs;iuè quomodolibet agite­<lb/>tur, & circumuoluatur. <pb pagenum="79" xlink:href="010/01/087.jpg"/><arrow.to.target n="marg86"/></s> </p> <p type="margin"> <s id="s.000370"><margin.target id="marg85"/>Cap. 3. flui­<lb/>dum in &longs;uo <lb/>toto quie­<lb/>&longs;cens pon­<lb/>derat.</s> </p> <p type="margin"> <s id="s.000371"><margin.target id="marg86"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000372"><emph type="center"/><emph type="italics"/>Po&longs;itiuam leuitatem in rerum natura <lb/>non dari.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000373"><emph type="center"/>CAP. IV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000374">HActenùs con&longs;iderauimus grauitatem non om­<lb/>nium corporum fluidorum, &longs;ed tantummodò <lb/>aquæ, hydrargyri, & &longs;imilium, de quorum pondero­<lb/>&longs;itate nemo dubitat, manife&longs;tè enim deorsùm ten­<lb/>dunt, atque de&longs;cendunt. </s> <s id="s.000375">difficultas vertitur circ&atail; <lb/>reliqua corpora, quæ &longs;ursùm a&longs;cendere videntur, vt <lb/>&longs;unt ligna, & alia corpora, quæ in aqua &longs;ursùm <expan abbr="a&longs;c&etilde;-dunt">a&longs;cen­<lb/>dunt</expan>, in his enim grauitatem ponere, videtur contra <lb/>communem conceptum; nihilominùs cum melioris <lb/>notæ Philo&longs;ophis o&longs;tendere conabimur omnia cor­<lb/>pora fluida elementaria grauitatem habere, leuita­<lb/>tem verò po&longs;itiuam ab&longs;olutè in natura non dari, ita­<lb/>que <expan abbr="o&longs;tend&etilde;dum">o&longs;tendendum</expan> e&longs;t omnia corpora elementaria ha­<lb/>bere vim &longs;e &longs;e vniendi ad efformandum no&longs;trum Sy­<lb/>&longs;tema, &longs;cilicèt habere facultatem motiuam de&longs;cen­<lb/>dendi versùs centrum globi terre&longs;tris, & huiu&longs;modi <lb/>vis vocatur grauitas. </s> <s id="s.000376">Et primo loco examinabimus <lb/>argumenta Ari&longs;totelis facta contra Platonem, & De­<lb/>mocritum prædictæ &longs;ententiæ a&longs;&longs;ertores, po&longs;tea ad <lb/>examen reuocabimus rationes eiu&longs;dem Ari&longs;totelis, <lb/>quibus leuitatem po&longs;itiuam &longs;tatuere conatur. </s> <s id="s.000377">Tertio <lb/>loco afferam demon&longs;trationes, quibus euincitur non <lb/>dari leuitatem po&longs;itiuam; & tandem con&longs;idèrabo ea <lb/>omnia, quæ pa&longs;sìm à melioribus Peripateticis con-<pb pagenum="80" xlink:href="010/01/088.jpg"/><arrow.to.target n="marg87"/><lb/>tra Platonicam &longs;ententiam afferuntur, quæ peruene­<lb/>re ad meam notitiam. </s> </p> <p type="margin"> <s id="s.000378"><margin.target id="marg87"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000379">Quòad primum Ari&longs;toteles in&longs;ectatur Democriti, <lb/>Platoni&longs;que po&longs;itionem, &longs;ed more &longs;uo, non contr&atail; <lb/><arrow.to.target n="marg88"/><lb/>&longs;ententias, at contra mera verba eorum argumenta­<lb/>tur, &longs;cilicèt quod terræ grauitas maior, quàm aeris <lb/>pendeat à copia triangulorum, quæ maior in terra, <lb/>quàm in aere exi&longs;tit, a&longs;&longs;umitque prædicta triangula, <lb/>ac &longs;i e&longs;&longs;ent &longs;uperficies planæ omninò indiui&longs;ibiles, <lb/>quod patet fal&longs;um e&longs;&longs;e, cùm in Platonica po&longs;ition&etail; <lb/>atomi triangulares &longs;int corpora, non autem &longs;uperfi­<lb/>cies indiui&longs;ibiles. </s> </p> <p type="margin"> <s id="s.000380"><margin.target id="marg88"/>Phy&longs;ic.lib.4. <lb/>cap.2.</s> </p> <p type="main"> <s id="s.000381">Præterea contra Democritum, ait, grandem aeris <lb/>ma&longs;&longs;am, veluti e&longs;&longs;et &longs;phæra aerea habens diametrum <lb/>decem cubitorum, habere maiorem copiam, & <expan abbr="abũ-dantiam">abun­<lb/>dantiam</expan> pleni, & materiei, quàm exigua pila aquea <lb/>habens diametrum vnius digiti, & proindè pila ae­<lb/>rea grauior e&longs;&longs;e deberet, & deor&longs;um de&longs;cendere, & <lb/><arrow.to.target n="marg89"/><lb/>è <expan abbr="cõtrà">contrà</expan> aquea vt leuis &longs;ursùm eleuari deberet. </s> <s id="s.000382">Hoc, <lb/>inquam, argumentum non afficit Democritum, qui <lb/>numquam tantam ab&longs;urditatem &longs;omniauit, <expan abbr="numquã">numquam</expan> <lb/>enim con&longs;iderauit plenum &longs;olitarium, &longs;ed vnà cum <lb/>pleno ingentem vacui molem augmentatam in ill&atail; <lb/>grandi aerea pila, & &longs;emper maiori cum proportio­<lb/>ne, quàm &longs;e habeat plenum aeris ad plenum aquæ. <lb/></s> <s id="s.000383">Quam exceptionem parùm &longs;incerè Ari&longs;toteles &longs;ub &longs;i­<lb/>lentio inuoluit, quoniam exi&longs;tente aere rariore, <expan abbr="quã">quam</expan> <lb/>&longs;it ip&longs;a aqua, habebit pars vacua ad partem plena&mtail; <lb/>aeris maiorem proportionem, quàm habet pars va-<pb pagenum="81" xlink:href="010/01/089.jpg"/><arrow.to.target n="marg90"/><lb/>cua ad partem plenam ip&longs;ius aquæ, & permutando, <lb/>moles vacua aeris ad molem vacuam aquæ maiorem <lb/>proportionem habebit, quàm moles plena aeris ad <lb/>molem plenam aquæ, & proindè qu&etail;libet ampla ae­<lb/>ris moles habebit <expan abbr="maior&etilde;">maiorem</expan> cau&longs;am alleuiationis <expan abbr="quã">quam</expan> <lb/>aqua, po&longs;ito quòd huiu&longs;modi cau&longs;a &longs;it vacuum, & è <lb/>contra in eodemmet aere debilior erit cau&longs;a graui­<lb/>tatis, quæ ab ip&longs;o pleno, & ab eius men&longs;ura de&longs;u­<lb/>mitur, <expan abbr="itaq;">itaque</expan> in grandi illa &longs;phæra aerea &longs;imùl <expan abbr="cũ">cum</expan> <expan abbr="aug-m&etilde;to">aug­<lb/>mento</expan> partis plenæ decies maiori, <expan abbr="quã">quam</expan> in exigua pila <lb/>aquea, &longs;uperadditur quoque cau&longs;a contraria, nempè <lb/>alleuiationis, quæ e&longs;t vacuum plu&longs;quam milliès ma­<lb/>ior, quàm &longs;it illud quod in ip&longs;a aqua continetur; <lb/>cùm igitur tàm enormiter excre&longs;cat, & &longs;uperet pro­<lb/>portio vacuitatis reliquam proportionem plenitudi­<lb/>nis in prædictis duobus elementis numquam poterit <lb/>ampla pila aerea grauior effici ob augmentum eius <lb/>plenitudinis, & partis materialis, quando ip&longs;a in &longs;e <lb/>quoque continet contrariam cau&longs;am, quæ eam <expan abbr="leu&etilde;">leuem</expan> <lb/>reddit multò magis multiplicatam, & hæc e&longs;t inani­<lb/>tas, & vacuum. </s> <s id="s.000384">Eiu&longs;dem farinæ e&longs;t longa illa &longs;eries <lb/>argumentorum toties ab Ari&longs;totele contra antiquos <lb/>adductorum. </s> </p> <p type="margin"> <s id="s.000385"><margin.target id="marg89"/>Ari&longs;t. ibid.</s> </p> <p type="margin"> <s id="s.000386"><margin.target id="marg90"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000387">Præterea verum non e&longs;t, a&longs;&longs;igna&longs;&longs;e antiquos &longs;pa­<lb/>tio vacuo motum, aut virtutem operandi, &longs;ed <expan abbr="tantũ-modò">tantun­<lb/>modò</expan> principio materiali, ac pleno eam concede­<lb/><arrow.to.target n="marg91"/><lb/>bant, quod per&longs;picuè ex <expan abbr="eod&etilde;">eodem</expan> Ari&longs;totele percipitur, <lb/>refert enim antiquos po&longs;ui&longs;&longs;e omnia corpora <expan abbr="elem&etilde;-taria">elemen­<lb/>taria</expan> grauia, & pondero&longs;a, &longs;ed magis, aut minùs, <pb pagenum="82" xlink:href="010/01/090.jpg"/><arrow.to.target n="marg92"/><lb/>prout plenum, & principium materiale deficeret, <lb/>aut abundaret in ip&longs;is; & in&longs;uper ait, quòd a&longs;cen&longs;us <lb/>&longs;ursùm aliquorum corporum, nempè ignis, <expan abbr="nõ">non</expan> à prin­<lb/>cipio aliquo po&longs;itiuo, &longs;cilicèt leuitate pendere an­<lb/>tiquì cen&longs;ebant, &longs;ed effici huiu&longs;modi a&longs;cen&longs;um per <lb/>extru&longs;ionem factam à fluidis corporibus ambienti­<lb/>bus pondero&longs;ioribus. </s> <s id="s.000388">Si igitur hæc fuit antiquoru&mtail; <lb/>&longs;ententia, quomodo eis tribui pote&longs;t tàm enormis <lb/>ab&longs;urditas, quòd nimirum vacuum moueatur, impel­<lb/>lat, habeat &longs;itum, & regionem &longs;ursùm, versùs quam <lb/>tendit? </s> <s id="s.000389">quomodò, inquam, hæc affirmare poterant il­<lb/>li, qui apertè aìebant motus omnes naturales corpo­<lb/>rum elementarium tendere deorsùm omne&longs;que pen­<lb/>dere ab vnico principio po&longs;itiuo, &longs;cilicèt à pleno, & <lb/>materia corporea? </s> <s id="s.000390">nec quia aer &longs;ursùm impellitur, <lb/>extruditurque, inde &longs;equitur, quòd vacua in aere <expan abbr="cõ-tenta">con­<lb/>tenta</expan> moueantur, atque &longs;ursùm a&longs;cendant, nam &longs;i va­<lb/>cuum nil aliud e&longs;t, quàm &longs;patium, id erit immobile, <lb/>& proindè aer &longs;ecum non a&longs;portabit vacuum ip&longs;um <lb/>&longs;ursùm, &longs;ed in ip&longs;o a&longs;cen&longs;u &longs;ucce&longs;&longs;iuè acquiret noua <lb/>&longs;patia: relinquendo præcedentia, quæ &longs;unt omninò <lb/>immobilia. </s> <s id="s.000391">at &longs;i nomen vacui meram pleni priuatio­<lb/>nem, ac nihilum &longs;ignificet, certum e&longs;t quòd nihilum <lb/>moueri non pote&longs;t, nec impellere, nec ab vno ad <lb/>alium locum migrare. </s> </p> <p type="margin"> <s id="s.000392"><margin.target id="marg91"/>Ibidem.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000393"><margin.target id="marg92"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000394">Po&longs;tquam con&longs;iderauimus Ari&longs;totelis argumenta <lb/>contra Antiquos, qui leuitatem po&longs;itiuam omninò <lb/>negabant, re&longs;tat modò vt eiu&longs;dem Ari&longs;totelis ratio­<lb/>nes pro leuitatis &longs;tabilimento, & po&longs;itione con&longs;ide-<pb pagenum="83" xlink:href="010/01/091.jpg"/><arrow.to.target n="marg93"/><lb/>remus. </s> <s id="s.000395">Præcipua eius ratio hæc e&longs;t, quia reperiun­<lb/>tur duo loca contraria in natura &longs;ursùm, & deorsùm, <lb/>&longs;cilicèt circumferentia, & centrum mundi, &longs;eu ter­<lb/>ræ; & euidentèr apparet, quòd terra infima e&longs;t, & <lb/>&longs;ubiacet omnibus alijs corporibus <expan abbr="mũdanis">mundanis</expan>, demer­<lb/>gitur enìm de&longs;cendendo infrà aerem, & infra <expan abbr="aquã">aquam</expan>, <lb/>quou&longs;que ad locum infimum perducatur, nempè ad <lb/>centrum, quando nimirum ea non impeditur; hinc <lb/>deducit, ergo terra e&longs;t ab&longs;olutè, & &longs;implicitèr gra­<lb/>uis, & non relatiuè. </s> <s id="s.000396">E contrà videmus aerem pene­<lb/>trare den&longs;itatem ip&longs;ius aquæ, & a&longs;cendere &longs;uper <expan abbr="eã">eam</expan>, <lb/>& ignem perforare <expan abbr="den&longs;itat&etilde;">den&longs;itatem</expan> <expan abbr="tũ">tum</expan> aqu&etail;, tùm aeris, per­<lb/>ducique ad &longs;upremam, & extremam &longs;uperficiem ae­<lb/>ris, veluti ad locum &longs;uum <expan abbr="natural&etilde;">naturalem</expan> &longs;upremum, vbi <lb/>tandèm quie&longs;cit, nec vlteriùs mouetur. </s> <s id="s.000397">Et quia, in­<lb/>quit, ignis omnibus &longs;upereminet, igitur e&longs;t &longs;impli­<lb/>citèr, & ab&longs;olutè leuis; terra omnibus &longs;ubijcitur, igi­<lb/>tur e&longs;t ab&longs;olutè grauis. </s> </p> <p type="margin"> <s id="s.000398"><margin.target id="marg93"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000399">Vt verò vim, & energiam Ari&longs;totelici ratiocinij <lb/>percipiamus, & exactè perpendamus, oportet vt &longs;ta­<lb/>tum controuer&longs;iæ memoremus, &longs;cilicèt the&longs;im Pla­<lb/>tonis, atque Democriti, quam Ari&longs;toteles redargue­<lb/>re profitetur, ante oculos ponamus, & po&longs;tea argu­<lb/>mentum ab Ari&longs;totele adhibitum con&longs;ideremus. </s> <s id="s.000400">Et <lb/>primò ratum per&longs;pectumque e&longs;t duplici modo fieri <lb/>po&longs;&longs;e vt ignis &longs;ursùm perducatur, & &longs;uper omnia e­<lb/>lementa emineat, aut nempè quia ignis &longs;ponte &longs;u&atail; <lb/>mouetur &longs;ursùm à principio intrin&longs;eco, & naturali, <lb/>&longs;cilicèt à leuitate, vel potiùs, quia ibidem ignis ex-<pb pagenum="84" xlink:href="010/01/092.jpg"/><arrow.to.target n="marg94"/><lb/>pellatur, extrudaturque à maiori grauitate aliorum <lb/>corporum fluidorum, veluti e&longs;t aer, & aqua; & hæc <lb/>po&longs;trema erat Platonis, & Democriti &longs;ententia, <expan abbr="quã">quam</expan> <lb/>Ari&longs;toteles redarguere tenebatur: Argumentum ve­<lb/>rò Ari&longs;totelis aliam longè diuer&longs;am propo&longs;itionem <lb/>à nemine in dubium reuocatam petit, atque in&longs;ecta­<lb/>tur; nil enim aliud obijcit, quàm phenomenon, quod <lb/>&longs;en&longs;ibus patet, & quod aduer&longs;arij vltrò <expan abbr="concedebãt">concedebant</expan>, <lb/>&longs;cilicet quòd omnes videmus ignem &longs;upra <expan abbr="aer&etilde;">aerem</expan> ele­<lb/>uari; at tenebatur potius Ari&longs;toteles demon&longs;trar&etail; <lb/>ignem a&longs;cendere non quia à medio fluido grauiori <lb/>extruditur <expan abbr="impelliturq;">impelliturque</expan> &longs;ursùm, &longs;ed quia &longs;ponte à vi <lb/>propria leuitatis mouetur, quod non præ&longs;titit, pote­<lb/>rit ergò vocari Ari&longs;totelicum ratiocinium potiùs pe­<lb/>titio, quàm demon&longs;tratio. </s> </p> <p type="margin"> <s id="s.000401"><margin.target id="marg94"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000402">Non de&longs;unt Peripatetici, qui vt <expan abbr="vigor&etilde;">vigorem</expan>, & vi&mtail; <lb/>addant Ari&longs;totelico ratiocinio, aiunt ab&longs;urdum e&longs;&longs;e <lb/>omninò corpora naturalia moueri ad propria loc&atail; <lb/>non à principio intrin&longs;eco, & eis à natura in&longs;ito, &longs;ed <lb/>à violentia externi corporis per extru&longs;ionem, vnde <lb/>deducitur, quòd natura in operationibus tàm nece&longs;­<lb/>&longs;arijs, & vtilibus fuerit deficiens, cùm nimirum in­<lb/>digeat &longs;timulis, & impul&longs;u violento, & coactione, <lb/>quæ cùm re&longs;i&longs;tentiam, & violentiam includat, vide­<lb/>tur operatio non naturalis, & propterea neque per­<lb/>petua, neque vtilis ad ordinem, & con&longs;eruationem <lb/>vniuer&longs;i. </s> </p> <p type="main"> <s id="s.000403">Huic &longs;pecio&longs;o ratiocinio re&longs;ponderi pote&longs;t, e&longs;&longs;&etail; <lb/>regulam fallacem, quòd vbicumque actiones, & o-<pb pagenum="85" xlink:href="010/01/093.jpg"/><arrow.to.target n="marg95"/><lb/>perationes non fiunt &longs;ponte, &longs;ed violentèr, tunc pro­<lb/>tunciari debeat prædictas operationes à natura, at­<lb/>que à principio naturali factas non e&longs;&longs;e. </s> </p> <p type="margin"> <s id="s.000404"><margin.target id="marg95"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000405">Vno verbo, erit quoque naturalis operatio ill&atail;, <lb/>quæ cum aliqua violentia efficitur. </s> </p> <p type="main"> <s id="s.000406"><emph type="center"/>PROP. XXXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000407"><emph type="center"/><emph type="italics"/>Licet in a&longs;cen&longs;u ligni per aquam violentia aliqua inter­<lb/>cedat, nihilominùs operatio tota naturalis erit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000408">HOc autem pote&longs;t confirmari hac ratione; &longs;i <expan abbr="verũ">verum</expan> <lb/>e&longs;&longs;et, quòd quælibet operatio in qua violentia <lb/>aliqua adhibetur reputari deberet non naturalis, &longs;e­<lb/>queretur quòd alterationum corporum <expan abbr="concretorũ">concretorum</expan> <lb/>pariterque omnium generationum vegetabilium, & <lb/>animalium nulla e&longs;&longs;et, neque vocari po&longs;&longs;et operatio <lb/>naturalis, eò quòd &longs;emper requiritur actio, & pa&longs;­<lb/>&longs;io qualitatum, & corruptio præcedentis &longs;ub&longs;tantiæ. <lb/></s> <s id="s.000409">Nec tamen dubitandum e&longs;t pa&longs;&longs;iones prædictas, & <lb/>corruptiones, operationes e&longs;&longs;e violentas, non &longs;pon­<lb/>te, &longs;ed cum di&longs;plicentia, & pa&longs;&longs;ione quadam factas, <lb/>igitur in omnibus prædictis operationibus natur&atail; <lb/>ip&longs;a violentiam exercet, & propterea confitendum <lb/>e&longs;t proprium in&longs;titutum naturæ e&longs;&longs;e violentiam exer­<lb/>cere, ita vt &longs;ine ip&longs;a nil prorsùs efficere &longs;ciat, neque <lb/>&longs;uos fines con&longs;equi valeat. </s> </p> <p type="main"> <s id="s.000410">Sed in&longs;tant, <expan abbr="accid&etilde;tale">accidentale</expan> e&longs;&longs;e, vt natura de&longs;truat præ­<lb/>cedentem formam, cùm &longs;ub &longs;equens minimè generari <lb/>po&longs;&longs;it per&longs;euerante prima, & proindè, inquiunt, pri-<pb pagenum="86" xlink:href="010/01/094.jpg"/><arrow.to.target n="marg96"/><lb/>mò, & per &longs;e naturam agere proptèr bonum, & prop­<lb/>tèr finem, generationemque, & proindè <expan abbr="præced&etilde;s">præcedens</expan> <lb/>corruptio erit veluti quædam conditio &longs;ine qua &longs;ub­<lb/>&longs;equens forma introduci, ac generari non pote&longs;t; fa­<lb/>tentur ergo, quòd &longs;altèm per accidens, natura actio­<lb/>nes violentas exercet, &longs;ed ea omnia quæ à natur&atail; <lb/>operantur, vocantur naturales actiones, igitur <expan abbr="viol&etilde;-tia">violen­<lb/>tia</expan> illa accidentalis, qua forma præcedens de&longs;trui­<lb/>tur, erit <expan abbr="quoq;">quoque</expan> vera actio, & operatio naturalis, <expan abbr="quã-doquid&etilde;">quan­<lb/>doquidem</expan>, ex vulgato axiomate, qui vult finem, velit <lb/>quoque nece&longs;sè e&longs;t media illa, quæ ad finem condu­<lb/>cunt, igitur naturalis in&longs;tinctus, quo formæ genera­<lb/>tio qu&etail;ritur, con&longs;equiturquè, nece&longs;&longs;ariò inuoluit vio­<lb/>lentiam, &longs;altem vt medium nece&longs;&longs;arium requi&longs;itum. <lb/></s> <s id="s.000411">Hinc deducere licèt non e&longs;&longs;e ab&longs;urdum, nec <expan abbr="indec&etilde;s">indecens</expan>, <lb/>quòd natura violentiam aliquam exerceat, vt ea me­<lb/>diante alia maior ab una con&longs;equatur. </s> <s id="s.000412">Si hoc, <expan abbr="inquã">inquam</expan>, <lb/>verum e&longs;t in alterationibus, & corruptionibus, mul­<lb/>tò magis hoc verificabitur in alijs &longs;uauioribus natu­<lb/>ræ actionibus, quando corpora naturalia ad &longs;ua loca <lb/>perducuntur propter bonum, & commoditatem eo­<lb/>rumdem corporum violenter agitatorum, non &longs;ecùs, <lb/>ac &longs;i quis curru, vel lectica è foro domum veheretur <lb/>ineptè quidem de coactione, & violentia quereretur, <lb/>cùm eiu&longs;modi violentia vtilitatem iucunditatemque <lb/>ei afferret. </s> <s id="s.000413">Eodem penè modo à grauibus naturaliter <lb/>de&longs;cendentibus perducerentur leuia ad debitu&mtail; <lb/>&longs;itum. <pb pagenum="87" xlink:href="010/01/095.jpg"/><arrow.to.target n="marg97"/></s> </p> <p type="margin"> <s id="s.000414"><margin.target id="marg96"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000415"><margin.target id="marg97"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000416"><emph type="center"/>PROP. XXXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000417"><emph type="center"/><emph type="italics"/>Violentia, qua lignum, & aer per aquam a&longs;cendit, dicitur <lb/>naturalis, quia e&longs;t nece&longs;&longs;aria.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000418">ET hæc quidem dicta &longs;unt iuxtà vulgarem Peri­<lb/>pateticam &longs;ententiam, &longs;ed qui&longs;quis hoc nego­<lb/>tium attentè perpenderit, is planè percipiet, quòd <lb/>vox violentiæ trahit originem metaphoricè ab illo <lb/>&longs;en&longs;u di&longs;plìcentiæ doloris, & amaritudinis, quam <lb/>patiuntur animantia, dum alterantur, & corrum­<lb/>puntur. </s> <s id="s.000419">Hinc &longs;equitur, quòd vbi deficit &longs;en&longs;us, defi­<lb/>ciat quoque dolor, & violentia nece&longs;sè e&longs;t, & proin­<lb/>dè alia regula, & norma certiori, ac tutiori di&longs;tingui <lb/>deberent operationes naturales à non naturalibus, <lb/>&longs;eù violentis, e&longs;tque huiu&longs;modi: operationes omnes <lb/>quæ ab&longs;olutè, & omninò nece&longs;&longs;ariæ &longs;unt, neque vllo <lb/>pacto fieri pote&longs;t, vt Natura eas negligat, &longs;ed cogi­<lb/>tur nece&longs;&longs;ariò eas exercere, iure naturales operatio­<lb/>nes appellari, ac cen&longs;eri debent. </s> <s id="s.000420">Modò quia ope­<lb/>ratio naturalis, qua corpora grauiora profundiùs <lb/>de&longs;cendunt, atque centro terræ propinquiora fiunt, <lb/>quàm minùs grauia nece&longs;&longs;ariò &longs;ecum inuoluit ordi­<lb/>natam di&longs;po&longs;itionem corporum, vt nimirùm grauio­<lb/>ra infimum locum po&longs;&longs;ideant; minùs grauia verò &longs;u­<lb/>premum, & in&longs;uper vniuer&longs;a huiu&longs;modi recta di&longs;po­<lb/>&longs;itio exigit vt ambo corpora moueantur tendendo <lb/><arrow.to.target n="marg98"/><lb/>deorsùm in centro communi grauitatis eorum. </s> <s id="s.000421">Non <lb/>&longs;ecùs ac in libra pre&longs;&longs;a ab in æqualibus ponderibus, <pb pagenum="88" xlink:href="010/01/096.jpg"/><arrow.to.target n="marg99"/><lb/>a&longs;cen&longs;us minoris ponderis factus à de&longs;cen&longs;u corpo­<lb/>ris grauioris alteram lancem prementis, ineptè qui­<lb/>dem, & iniuria violentia appellatur; propterea quòd <lb/>huiu&longs;modi operatio, ac di&longs;po&longs;itio nece&longs;&longs;aria, ac na­<lb/>turalis e&longs;t. </s> </p> <p type="margin"> <s id="s.000422"><margin.target id="marg98."/>Prop. 1.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000423"><margin.target id="marg99"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000424">Idip&longs;um, vel quid &longs;imile, dici debet de extru&longs;ione <lb/>cuiuslibet corporis minùs grauis facta à pre&longs;&longs;ion&etail; <lb/>ambientis fluidi grauioris, quia in tali ca&longs;u (vt &longs;uo lo­<lb/>co o&longs;tenditur) ade&longs;t libra quædam imaginaria per­<lb/><arrow.to.target n="marg100"/><lb/>petua, cuius centrum grauitatis &longs;ucce&longs;&longs;iuè deprimi­<lb/>tur, & <expan abbr="prædictũ">prædictum</expan> <expan abbr="de&longs;censũ">de&longs;censum</expan> nece&longs;&longs;ariò con&longs;equitur mo­<lb/>tus &longs;ublimationis corporis minùs grauis, hocque <expan abbr="tã">tam</expan> <lb/>diù per&longs;euerat, quou&longs;que efficiatur æquilibrium. </s> <s id="s.000425"><expan abbr="Cũ">Cum</expan> <lb/>igitur &longs;it effectus nece&longs;&longs;arius, & naturalis, extru&longs;io, <lb/>&longs;eù a&longs;cen&longs;us ligni quotie&longs;cumque circumdatur à flui­<lb/>do grauiori, non pote&longs;t, nec debet prædictus a&longs;cen­<lb/>&longs;us nuncupari, vel reputari violentus, quod erat <expan abbr="o&longs;t&etilde;-dendum">o&longs;ten­<lb/>dendum</expan>. </s> <s id="s.000426">Hoc confirmari pote&longs;t ex Galilei pulcher­<lb/>rimo ratiocinio. </s> </p> <p type="margin"> <s id="s.000427"><margin.target id="marg100"/>Prop. 9.</s> </p> <p type="main"> <s id="s.000428"><emph type="center"/>PROP. XL.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000429"><emph type="center"/><emph type="italics"/>Motus a&longs;cen&longs;us grauium non minùs naturalis e&longs;t, quàm <lb/>de&longs;cen&longs;us eorundem.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000430">FInge globum no&longs;træ terræ perforari puteo <expan abbr="perc&etilde;-trum">per cen­<lb/>trum</expan> exten&longs;o v&longs;que ad Antipodas producto, at­<lb/>que in hoc demi&longs;&longs;a pila ferrea proculdubio natura­<lb/>lis eius grauitas &longs;ucce&longs;&longs;iuè maiorem impetum acqui­<lb/>ret, quòu&longs;que ad centrum terræ pertingat, & vniuer-<pb pagenum="89" xlink:href="010/01/097.jpg"/><arrow.to.target n="marg101"/><lb/>&longs;a hæc motio naturalis cen&longs;ebitur, eò quòd pendet à <lb/>&longs;uo intrin&longs;eco principio grauitatis; &longs;ed no&longs;tqua&mtail; <lb/>pila terræ centrum attingit profectò <expan abbr="ibinõ">ibi non</expan> quie&longs;cet; <lb/>nam impetus in præcedenti de&longs;cen&longs;u acqui&longs;itus pi­<lb/>lam tran&longs;portabit vltra centrum, excurretque versùs <lb/>Antipodas. </s> <s id="s.000431">modò in hoc excur&longs;u cùm pila à centro <lb/>terræ recedat, procùl dubio &longs;ur&longs;um <expan abbr="a&longs;c&etilde;det">a&longs;cendet</expan> vocatur­<lb/>que prædictus a&longs;cen&longs;us violentus motus, & contr&atail; <lb/>eius naturam, & tamen ab operatione naturali de­<lb/>&longs;cen&longs;us dependet. </s> </p> <p type="margin"> <s id="s.000432"><margin.target id="marg101"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000433">Idip&longs;um alijs exemplis, quæ facilè po&longs;&longs;unt expe­<lb/>riri, confirmari pote&longs;t. </s> </p> <figure id="id.010.01.097.1.jpg" xlink:href="010/01/097/1.jpg"/> <p type="main"> <s id="s.000434">Sit vas aqua plenum RSXV & ha­<lb/>beatur quoque cylindrus ligneus <lb/>EF, qui in aqua demer&longs;us non de­<lb/>mergetur integrè infra &longs;upremam li­<lb/>bellam aquæ RS, &longs;ed remanebit ali­<lb/>qua eius pars GE eminens &longs;upr&atail; <lb/>aquæ libellam, propterea quòd li­<lb/>gnum minùs graue e&longs;t &longs;pecie, quàm <lb/>ip&longs;a aqua, (vt Archimedes ait.) <lb/>Si po&longs;tea eumdem ligneum cylindrum extra aqua&mtail; <lb/>&longs;ubleuauero v&longs;que ad &longs;itum AB, & hinc liberè eum <lb/>de&longs;cendere permittam, is profectò non con&longs;i&longs;tet, ne­<lb/>què quie&longs;cet in &longs;itu EF, <expan abbr="nã">nam</expan> impetus acqui&longs;itus in de­<lb/>&longs;cen&longs;u per aerem profundiùs infra aquæ libella&mtail; <lb/>motu violento cylindrum immittet v&longs;que ad &longs;itu&mtail; <lb/>CD & hinc denuò a&longs;cendendo tran&longs;gre&longs;&longs;o &longs;itu æqui­<lb/>librij EF re&longs;iliet omninò extra aquam propè &longs;itu&mtail; <pb pagenum="90" xlink:href="010/01/098.jpg"/><arrow.to.target n="marg102"/><lb/>AB, & &longs;ic denuò quou&longs;que repetitis vibrationibus <lb/>&longs;en&longs;im languendo, tandèm quie&longs;cat in &longs;itu naturali <lb/>EF. </s> </p> <p type="margin"> <s id="s.000435"><margin.target id="marg102"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <figure id="id.010.01.098.1.jpg" xlink:href="010/01/098/1.jpg"/> <p type="main"> <s id="s.000436">Pari modo &longs;umpto <expan abbr="fune-p&etilde;-dulo">fune-pen­<lb/>dulo</expan> AB quod moueri po&longs;&longs;it <lb/>circa &longs;uum centrum firmum A, <lb/>remota pila plumbea. </s> <s id="s.000437">B à &longs;itu <lb/>&longs;uo naturali, &longs;eu perpendicu­<lb/>lari ad horizontem, perducta­<lb/>que ad &longs;itum eleuatum C, illa planè vt grauis excur­<lb/>ret de&longs;cendendo arcum CB, & vniuer&longs;us is motus na­<lb/>turalis erit, vtpotè dependens ab impetu grauitatis <lb/>intrin&longs;eco, non tamen in infimo &longs;itu B pila per&longs;i&longs;tet <lb/>po&longs;tquam ibidem perducta e&longs;t, &longs;ed vlteriùs excur­<lb/>ret ferè æquali &longs;patio priori vltrà perpendiculum v&longs;­<lb/>que ad &longs;itum D, a&longs;cendendo nimirùm ab infimo &longs;itu <lb/>B per integrum arcum BD, & quia motus ille qui gi­<lb/>gnitur à principio intrin&longs;eco, & naturali non pote&longs;t <lb/>e&longs;&longs;e non naturalis, cùmque a&longs;cen&longs;us pilæ vltra cen­<lb/>trum terræ, & de&longs;cen&longs;us cylindri EF infra aquæ li­<lb/>bellam po&longs;t ca&longs;um, & a&longs;cen&longs;us pilæ plumbeæ per ar­<lb/>cum BD pendeat, creeturque ab illa naturali virtu­<lb/>te grauitatis nempè eiu&longs;dem corporis de&longs;cendentis <lb/>quatenùs de&longs;cendit: nulla enim alia cau&longs;a extrin&longs;e­<lb/>ca &longs;uperueniens excogitari pote&longs;t, quæ violentia&mtail; <lb/>in&longs;erat, & &longs;ursùm impellat prædictum graue, quàm <lb/>impetus acqui&longs;itus, & conceptus in ip&longs;o ca&longs;u natura­<lb/>litèr facto productoque à principio intrin&longs;eco graui­<lb/>tatis eius, qui procùl dubio impetus à naturali prin-<pb pagenum="91" xlink:href="010/01/099.jpg"/><arrow.to.target n="marg103"/><lb/>cipio pendens naturalis, & intrin&longs;ecus quoque erit, <lb/>igitur etiam illa operatio a&longs;cen&longs;us erit naturalis qua­<lb/>tenùs pendet creaturque à principio intrin&longs;eco, i&ntail; <lb/>eo enim &longs;olummodò ca&longs;u violenta <expan abbr="c&etilde;&longs;eri">cen&longs;eri</expan> po&longs;&longs;et <expan abbr="quã-do">quan­<lb/>do</expan> à peregrino, & <expan abbr="adu&etilde;titio">aduentitio</expan> principio procrearetur. </s> </p> <p type="margin"> <s id="s.000438"><margin.target id="marg103"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000439">Contra hoc ratiocinium in&longs;urgit in&longs;ignis Peripa­<lb/><arrow.to.target n="marg104"/><lb/>teticus, & ait, quod &longs;ub&longs;equens a&longs;cen&longs;us vltra cen­<lb/>trum terræ, vel vltra perpendiculum per arcum BD <lb/>non pendet, nec procreatur à grauitate eiu&longs;dem cor­<lb/>poris, &longs;ed ab impetu concepto per motum de&longs;cen&longs;us, <lb/>qui impetus, inquit ille, res e&longs;t, toto cœlo diuer&longs;a à <lb/>grauitate, imò prædictus impetus contra grauitatem <lb/>luctatur. </s> </p> <p type="margin"> <s id="s.000440"><margin.target id="marg104"/>Obiectiones <lb/>recentioris <lb/>authoris af­<lb/>feruntur.</s> </p> <p type="main"> <s id="s.000441">Patet ergò concedere aduer&longs;arium pilæ a&longs;cen&longs;um <lb/>po&longs;t excur&longs;um vltra centrum, vel vltra perpendicu­<lb/>lum effici, ac produci à virtute impetus impre&longs;&longs;i, qui <lb/>nimirùm immediata cau&longs;a, & principium e&longs;t prædi­<lb/>cti a&longs;cen&longs;us, &longs;eù operationis, quæ nomine leuitatis <lb/>in&longs;ignitur. </s> <s id="s.000442">At quia præter immediatam cau&longs;am illius <lb/>a&longs;cen&longs;us, &longs;cilicèt præter impetum, adnotari præte­<lb/>rea debet cau&longs;a productrix prædicti impetus, quæ <lb/>e&longs;t grauitas naturalis, & intrin&longs;eca eiu&longs;dem corpo­<lb/>ris, ergo hæc erit cau&longs;a &longs;altèm mediata illius po&longs;tre­<lb/>mi a&longs;cen&longs;us, & hìc noto quod aduer&longs;arius non negat, <lb/>nec affirmat grauitatem fui&longs;&longs;e cau&longs;am, & principium <lb/>productiuum prædicti impetus, &longs;ed tantummodò ait <lb/>valdè differre grauitatem ab impetu, imò naturas <lb/>contrarias, & &longs;e mutuo de&longs;tructiuas habere, quia ni­<lb/>mirùm non alia de cau&longs;a ce&longs;&longs;at <expan abbr="&longs;ub&longs;equ&etilde;s">&longs;ub&longs;equens</expan> motus <expan abbr="a&longs;c&etilde;-">a&longs;cen-</expan><pb pagenum="92" xlink:href="010/01/100.jpg"/><arrow.to.target n="marg105"/><lb/>&longs;us tùm pilæ, tùm fune-penduli, ni&longs;i quia grauitas pi­<lb/>læ contrario ni&longs;u vim impetus a&longs;cendentis de&longs;truit. </s> </p> <p type="margin"> <s id="s.000443"><margin.target id="marg105"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000444">Sed quid tandem hinc aduer&longs;arius deducere vel­<lb/>let? </s> <s id="s.000445">an quia ex eo, quòd natura grauitatis diuer&longs;&atail; <lb/>&longs;it ab impetu dicemus impetum prædictæ pilæ de­<lb/>&longs;cendentis v&longs;que ad centrum, vel perpendiculum ge­<lb/>nitum non fui&longs;&longs;e à vi, & exercitio grauitatis? </s> <s id="s.000446">à qu&atail; <lb/>nam ergo virtute tamquam à principio immediato <lb/>genitus fuit? </s> <s id="s.000447">profectò &longs;i &longs;en&longs;us negare non velimus, <lb/>fatendum e&longs;t à nulla alia cau&longs;a, vel principio exter­<lb/>no, &longs;ed tantummodò ab ip&longs;amet grauitate pilæ de­<lb/>&longs;cendentis impetum prædictum genitum fui&longs;&longs;e, nec <lb/>certitudo &longs;en&longs;us relinqui debet propter difficulta­<lb/>tem adductam ab aduer&longs;ario, vt præclarè Ari&longs;toteles <lb/><arrow.to.target n="marg106"/><lb/>præcipit. </s> <s id="s.000448">Si igitur grauitas pilæ e&longs;t &longs;altem <expan abbr="principiũ">principium</expan>, <lb/>& cau&longs;a mediata con&longs;equentis a&longs;cen&longs;us, nece&longs;&longs;ariò <lb/>actus, & operatio a&longs;cen&longs;us, quæ violenta, & præter <lb/>naturam &longs;axi exi&longs;timatur, efficietur procreabiturque <lb/>ab interno, & naturali principio grauitatis eius, & <lb/>proindè actus a&longs;cen&longs;us, &longs;eu motus violentus efficie­<lb/>tur à principio interno, & naturali. </s> </p> <p type="margin"> <s id="s.000449"><margin.target id="marg106"/>5. phy&longs; c. <!-- REMOVE S-->3.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000450">Et hìc obitèr mirari licèt horum philo&longs;ophoru&mtail; <lb/>&longs;ecuritatem; hìc negant impetum à grauitate pro­<lb/>creari, & inculcant valdè inter &longs;e differre, & &longs;e mu­<lb/>tuò de&longs;truere, & vnà <expan abbr="cũ">cum</expan> Ari&longs;totele in mechanicis a­<lb/><arrow.to.target n="marg107"/><lb/>pertè fatentur impetum e&longs;&longs;e grauitatem fluentem e&longs;­<lb/>&longs;eque pror&longs;us eiu&longs;dem naturæ, quia nimirum &longs;axum <lb/>impetu affectum comprimit, conterit aduer&longs;a cor­<lb/>pora eodem modo, ac ingens pondus efficit. <pb pagenum="93" xlink:href="010/01/101.jpg"/><arrow.to.target n="marg108"/></s> </p> <p type="margin"> <s id="s.000451"><margin.target id="marg107"/>Quæ&longs;t. 19.</s> </p> <p type="margin"> <s id="s.000452"><margin.target id="marg108"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000453">Sed in&longs;tat aduer&longs;arius quomodo pote&longs;t grauitas <lb/>efficere impetum quo pila a&longs;cendit &longs;i videmus <expan abbr="motũ">motum</expan> <lb/>prædictum a&longs;cen&longs;us &longs;en&longs;im debilitari, & tandem ex­<lb/>tingui &longs;olummodo propter renitentiam, & contra­<lb/>riam actionem, quam efficit pondus eiu&longs;dem pilæ? <lb/></s> <s id="s.000454">Et hìc aio, quòd exercitium eiu&longs;dem ponderis, &longs;cili­<lb/>cèt compre&longs;&longs;io eius producit duos effectus contra­<lb/>rios, primò per de&longs;cen&longs;um creat, fouet, & auget im­<lb/>petum eius, po&longs;teà per a&longs;cen&longs;um ei contranititur, <lb/>debilitat, atque de&longs;truit eum, & licèt hoc mirabil&etail; <lb/>videatur, nihilominùs idip&longs;um concedant nece&longs;sè <lb/>e&longs;t, velint, nolint, cùm &longs;en&longs;u con&longs;tet, &longs;ic eadem manus <lb/>impellendo &longs;axum dum deorsùm decidit, auget mul­<lb/>tiplicatque eius impetum, at &longs;i &longs;axum &longs;ursùm a&longs;cen­<lb/>deret eadem manus contrario motu impetum eius <lb/>debilitaret, atque de&longs;trueret. </s> <s id="s.000455">&longs;imilitèr idem calor <lb/>Solis generat, & auget plantas, & po&longs;tea eas exic­<lb/>cat extinguitque. </s> <s id="s.000456">Ex his ergò patet in&longs;ufficienti&atail; <lb/>&longs;uperiùs adducti ratiocinij. </s> </p> <p type="main"> <s id="s.000457"><emph type="center"/>PROP. XLI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000458"><emph type="center"/><emph type="italics"/>Ab eodem principio grauitatis a&longs;cen&longs;io, & &longs;ubleuatio cor­<lb/>porum leuium effici pote&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000459">SEd redeo iam ad propo&longs;itum, & alia ratione <expan abbr="eã-dem">ean­<lb/>dem</expan> propo&longs;itionem per&longs;uadere conabor. </s> <s id="s.000460">Vul­<lb/>gati&longs;&longs;imum axioma omnium <expan abbr="philo&longs;ophorũ">philo&longs;ophorum</expan> e&longs;t, quòd <lb/>natura &longs;emper producit &longs;uas operationes via breui&longs;­<lb/>&longs;ima, &longs;ummo compendio, atque abhorret à prolixi-<lb/><pb pagenum="94" xlink:href="010/01/102.jpg"/> <arrow.to.target n="marg109"/>tate, & multiplicitate cau&longs;arum quando &longs;uos effe­<lb/>ctus producere pote&longs;t via illa breuiori, & faciliori. <lb/></s> <s id="s.000461">hinc deducitur, quod &longs;i po&longs;&longs;ibile e&longs;t <expan abbr="trã&longs;portare">tran&longs;portare</expan> cor­<lb/>pora naturalia ad propria loca mediante vnica, & &longs;in­<lb/>gulari motiua virtute grauitatis, vani&longs;&longs;imè, & &longs;tultè <lb/>natura ageret, &longs;i niteretur prædictum finem a&longs;&longs;e qui <lb/>adhibitis duobus principijs &longs;cilicèt grauitate, & al­<lb/>tera oppo&longs;ita virtute, quæ leuitas nuncupatur. </s> <s id="s.000462">Quod <lb/>verò po&longs;&longs;int naturalia corpora ad &longs;ua naturalia loca <lb/>perduci à grauitate &longs;ola ab&longs;que leuitate patet ex &longs;u­<lb/>periùs dictis, nam minor grauitas, quæ ve&longs;icæ aer&etail; <lb/>plenæ tribuitur, & maior aquæ, & omnium maxima <lb/>hydrargyro, &longs;ufficienti&longs;&longs;ima cau&longs;a e&longs;t apta ad produ­<lb/>cendum <expan abbr="prædictũ">prædictum</expan> effectum, quod deducitur ex prin­<lb/><arrow.to.target n="marg110"/><lb/>cipijs, & rationibus mechanicis. </s> <s id="s.000463">Quaproptèr pro­<lb/>babili&longs;&longs;imè concedendum e&longs;t &longs;olo principio grauita­<lb/>tis ab&longs;que vlla leuitate naturam &longs;uum finem a&longs;&longs;equi <lb/>collocandi corpora terrena in debitis locis, nempè <lb/>&longs;ursùm, & deorsùm. </s> </p> <p type="margin"> <s id="s.000464"><margin.target id="marg109"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000465"><margin.target id="marg110"/>Cap. 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000466">Et hactenùs adductæ &longs;unt rationes probabiles <expan abbr="cõ-tra">con­<lb/>tra</expan> po&longs;itiuam leuitatem, re&longs;tat modò vt idip&longs;um di­<lb/>rectè o&longs;tendatur rationibus magis conuincentibus, <lb/>& efficacioribus. <pb pagenum="95" xlink:href="010/01/103.jpg"/><arrow.to.target n="marg111"/></s> </p> <p type="margin"> <s id="s.000467"><margin.target id="marg111"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000468"><emph type="center"/>PROP. XLII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000469"><emph type="center"/><emph type="italics"/>Et primò o&longs;tendemus, quòd quodlibet corpus à principio in­<lb/>trin&longs;eco, & naturali &longs;ponte translatum faciliùs, & <lb/>celeriùs mouebitur in fluido rariori, & tenuio­<lb/>ri, quàm in medio fluido cra&longs;&longs;o, & <lb/>tenaciori.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000470">SInt duo va&longs;a GHIK, alterum KILM, <expan abbr="primũ">primum</expan> aqua <lb/>repleatur, &longs;ecundum verò hydrargyro, immer­<lb/>gatur verò eadem pila lignea A in vtroque fluido, in­<lb/>telliganturque duæ moles &longs;patiales ex prædictis flui­<lb/>dis B, & C, quæ æquales &longs;int ip&longs;i A, eique <expan abbr="&longs;uperincũ-bant">&longs;uperincun­<lb/>bant</expan>, patet ergò quòd mercurij moles C grauior re­<lb/>&longs;i&longs;tentior, den&longs;ior, atque compactior e&longs;t, quàm &longs;it <lb/><figure id="id.010.01.103.1.jpg" xlink:href="010/01/103/1.jpg"/><lb/>moles aqu&etail; B. præterea pila lignea <lb/>A nullo pacto a&longs;cendere &longs;ursùm po­<lb/>te&longs;t, ni&longs;i aquam B, ab eius loco ex­<lb/>pellat vt ei locum cedat, atque mo­<lb/>les ip&longs;ius ligni A <expan abbr="trãsferatur">transferatur</expan> ad oc­<lb/>cupandum &longs;patium ei æquale B, & <lb/>hoc &longs;emper contingit, vbique enim <lb/>in <expan abbr="a&longs;c&etilde;&longs;u">a&longs;cen&longs;u</expan> cogitur continuato ni&longs;u <lb/>&longs;ursùm impellere incumbentem a­<lb/>quæ molem ei æqualem, tenacita­<lb/>temque eius penetrare, ponatur iam gradus natura­<lb/>lis impetus leuitatis ip&longs;ius ligni e&longs;&longs;e D, quia verò cor­<lb/>pus motiuum A impetu D affectum impellit corpus <lb/>B fluidum, quod in quiete con&longs;titutum &longs;ua naturali <pb pagenum="96" xlink:href="010/01/104.jpg"/><arrow.to.target n="marg112"/><lb/>inertia re&longs;i&longs;tit impul&longs;ui impellentis corporis leuis A; <lb/>ergò ex <expan abbr="demõ">demom</expan> &longs;tratis in libro de vi percu&longs;&longs;ionis <expan abbr="ead&etilde;">eadem</expan> <lb/>vis motiua leuitatis ip&longs;ius A communicatur, & <expan abbr="expã-ditur">expan­<lb/>ditur</expan> per vniuer&longs;um corpus motum, &longs;cilicèt per flui­<lb/>dum B, igitur eius impetus D valdè debilitatur re­<lb/>tardaturque, &longs;itque diminuta velocitas E, qua ni­<lb/>mirùm lignum leue A, & fluidum B mouentur. </s> <s id="s.000471">pari <lb/>ratione &longs;it F velocitas retardata, qua idem lignu&mtail; <lb/>A nec non moles hydrargyri C &longs;ibi æquali agitatur. <lb/></s> <s id="s.000472">O&longs;tendendum e&longs;t quòd velocitas, E qua nimirum li­<lb/>gnum a&longs;cendit per aquam maior &longs;it velocitate F quà <lb/>lignum per mercurium eleuatur, & habere veloci­<lb/>tatem E ad F reciprocè ferè eamdem proportionem, <lb/><figure id="id.010.01.104.1.jpg" xlink:href="010/01/104/1.jpg"/><lb/>quam habet corporea &longs;ub&longs;tantia <lb/>AC ad corpulentiam AB. <!-- KEEP S--></s> <s id="s.000473">Quia ab <lb/>eadem virtute motiua impelluntur <lb/>duo corpora A, & B à qua priùs in­<lb/>telligebatur moueri &longs;ingularis ma&longs;­<lb/>&longs;a lignea A cui naturalis gradus <lb/>impetus D conueniebat, igitur mo­<lb/>les corporea, & materialis duorum <lb/>corporum &longs;imul &longs;umptorum A & B <lb/>ad molem corpoream A reciprocè <lb/>eamdem proportionem habebit, quam eorum ve­<lb/><arrow.to.target n="marg113"/><lb/>locitates <expan abbr="hab&etilde;t">habent</expan>, & ideò <expan abbr="erũt">erunt</expan> vt D ad E. <!-- KEEP S--></s> <s id="s.000474">Simili ratio­<lb/>cinio vt moles corporea A ad molem corpoream AC <lb/>ita e&longs;t velocitas F ad D, ergo ex æqualitate pertur­<lb/>bata corporea &longs;ub&longs;tantia AB, ad AC eamdem pro­<lb/>portionem habebit, quàm velocitas F ad E, e&longs;t qu&etail; <pb pagenum="97" xlink:href="010/01/105.jpg"/><arrow.to.target n="marg114"/><lb/>&longs;ub&longs;tantia corporea AB minor ea quæ continetur in <lb/>AC, ergò impetus F minor e&longs;t quàm E; quaproptèr <lb/>lignum A intrà mercurium C <expan abbr="translatũ">translatum</expan> &longs;ursùm <expan abbr="a&longs;c&etilde;-dere">a&longs;cen­<lb/>dere</expan> debet tardiori, & minori velocitate, quàm &longs;it <lb/>velocitas E, quæ <expan abbr="cõpetit">competit</expan> ligno a&longs;cendenti in aqua B. </s> </p> <p type="margin"> <s id="s.000475"><margin.target id="marg112"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000476"><margin.target id="marg113"/>De vi per­<lb/>cu&longs;&longs;ionis pro <lb/>po&longs;it. </s> <s id="s.000477">15.</s> </p> <p type="margin"> <s id="s.000478"><margin.target id="marg114"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000479">Et profectò euidenti&longs;&longs;imum e&longs;t, quòd quodlibet <lb/>corpus à principio intrin&longs;eco motu &longs;pontaneo trans­<lb/>latum, multò faciliùs gradietur excurretque per me­<lb/>dium fluidum rarius, & cedens, quàm in medio flui­<lb/>do tenaciori, & cra&longs;&longs;iori, vt pila aurea celeriùs per <lb/>aerem, quàm per aquam eiu&longs;dem &longs;patij de&longs;cendit, & <lb/>per aquam velociori motu, quàm per mercurium ex­<lb/>currit; &longs;ic paritèr videmus animalia, quæ intrin&longs;ec&atail; <lb/>vi mouentur, difficiliùs gradi po&longs;&longs;e, &longs;i infra arena&mtail; <lb/>&longs;ub mergantur, & minùs difficilè infrà lutum, & fa­<lb/>ciliùs in aqua, & multò faciliùs in aere, nec <expan abbr="vnquã">vnquam</expan> <lb/>contrarium contingere poterit, quòd nimirùm idem <lb/>animal eamdem vim motiuam exercendo difficiliùs <lb/>& tardiùs moueatur per aerem, quàm per aquam, & <lb/>difficiliùs per aquam, quàm per lutum, aut per hy­<lb/>drargyrum. </s> </p> <p type="main"> <s id="s.000480"><emph type="center"/>PROP. XLIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000481"><emph type="center"/><emph type="italics"/>Non moueri &longs;ursùm corpora, quæ leuia appellantur, à vi <lb/>intrin&longs;eca leuitatis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000482">HIs po&longs;itis con&longs;ideremus modò ceram, aut ve&longs;i­<lb/>cam aere plenam <expan abbr="a&longs;cend&etilde;tem">a&longs;cendentem</expan> per diuer&longs;a me­<lb/>dia fluida, &longs;i <expan abbr="verũ">verum</expan> e&longs;t, quòd aerea ve&longs;ica &longs;ursùm <expan abbr="a&longs;c&etilde;-">a&longs;cen-</expan><pb pagenum="98" xlink:href="010/01/106.jpg"/><arrow.to.target n="marg115"/><lb/>dit in aqua; aut hydrargyro motu &longs;pontaneo, nempè <lb/>ab intrin&longs;eca virtute motiua, quæ vocatur leuitas, <lb/>igitur nece&longs;sè e&longs;t vt in <expan abbr="a&longs;c&etilde;&longs;u">a&longs;cen&longs;u</expan> penetret corpora flui­<lb/>da intermedia; atque eorum tenacitatem, & den&longs;i­<lb/>tatem &longs;uperet, imò fluidum è &longs;uo loco expellat, vt <lb/>via, & tran&longs;itus paretur, qua &longs;ursùm a&longs;cendere, & <lb/>perduci po&longs;&longs;it, & quia hydrargyrum magis con&longs;ti­<lb/>patum, den&longs;um, & graue e&longs;t, <expan abbr="quã">quam</expan> aqua, igitur quod­<lb/>libet corpus leue aere repletum, aut aeris natura&mtail; <lb/>participans, vt lignum, & cera, (quæ ex aduer&longs;ario­<lb/>rum &longs;ententia mouentur ab intrin&longs;eca virtute leui­<lb/>tatis) nece&longs;sè e&longs;t vt maiorem re&longs;i&longs;tentiam <expan abbr="offendãt">offendant</expan> <lb/>in tran&longs;itu per hydragyrum, à cuius tenacitate, den­<lb/>&longs;itate, & pondere gradus impetus eius nece&longs;&longs;ariò re­<lb/>tunditur retardaturque multò magis, quàm in <expan abbr="a&longs;c&etilde;-&longs;u">a&longs;cen­<lb/>&longs;u</expan> per aquam contingit, quæ cùm magis rara, & ce­<lb/>dens &longs;it, minùs debilitat retardatque eamdem eius <lb/>vim motiuam, quaproptèr motus a&longs;cen&longs;us ligni, vel <lb/>ceræ per hydrargyrum multò magis retardabitur, <lb/>quàm ille, qui per aquam fit; quia verò hoc e&longs;t fal­<lb/>&longs;um, & contra &longs;en&longs;us euidentiam, multò enim velo­<lb/>ciòr e&longs;t motus ligni, vel ceræ factus per <expan abbr="hydrargyrũ">hydrargyrum</expan>, <lb/><expan abbr="quã">quam</expan> per <expan abbr="aquã">aquam</expan>; <expan abbr="nõ">non</expan> igitur <expan abbr="verũ">verum</expan> e&longs;t ab intrin&longs;eco, & natu­<lb/>rali principio &longs;ursùm moueri, & proindè cau&longs;a a&longs;cen­<lb/>&longs;us non erit leuitas po&longs;itiua, ideoque nullum v&longs;u&mtail; <lb/>habebit in natura, nec propterea exi&longs;tet vlla leuitas. <pb pagenum="99" xlink:href="010/01/107.jpg"/><arrow.to.target n="marg116"/></s> </p> <p type="margin"> <s id="s.000483"><margin.target id="marg115"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000484"><margin.target id="marg116"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000485"><emph type="center"/>PROP. XLIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000486"><emph type="center"/><emph type="italics"/>Ratione mechanica à grauiori fluido celeriùs idem mobile <lb/>&longs;ursùm exprimitur, quàm à fluido minùs graui.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000487">HViu&longs;modi difficultates omninò vitantur effu­<lb/>giunturque, &longs;i certitudinem, & nece&longs;&longs;itatem <lb/>ex principijs mechanicis pendentem &longs;equamur, &longs;ci­<lb/>licèt po&longs;ita &longs;olummodò grauitate in omnibus cor­<lb/>poribus &longs;ublunaribus; nece&longs;sè e&longs;t vt <expan abbr="graui&longs;&longs;imũ">graui&longs;&longs;imum</expan> flui­<lb/>dum hydrargyri maiori impetu &longs;ursùm per extru&longs;io­<lb/>nem impellat lignum, quàm aliud <expan abbr="fluidũ">fluidum</expan> minùs gra­<lb/>ue, vt e&longs;t aqua, &longs;icuti in bilance pondus vnius vnciæ <lb/>maiori velocitate &longs;ursùm impellitur à maiori pre&longs;­<lb/>&longs;ione contraria ponderis decem librarum, quàm à <lb/>minori compre&longs;&longs;ione ponderis vnius libræ. </s> <s id="s.000488">Demon­<lb/>&longs;tratio verò huius rei &longs;uo loco exponetur, &longs;ed inte­<lb/>rim &longs;i effectus omnes qui ob&longs;eruantur in hi&longs;ce corpo­<lb/>ribus a&longs;cendentibus ijdem prorsùs &longs;unt, & ij&longs;de&mtail; <lb/>legibus mechanicis fiunt, ac &longs;i omnia corpora gra­<lb/>uia fui&longs;&longs;ent, &longs;ed inæquali grauitate donarentur, & <lb/>præterea in ijs non apparet phenomena motus fieri <lb/>ea ratione, quæ requireretur &longs;i præter grauitate&mtail; <lb/>reperiretur quoque aliud principium contrarium le­<lb/>uitatis: igitur concedendum e&longs;t &longs;ola grauitate natu­<lb/>ram operari, neque leuitatem vllam exigere. </s> </p> <p type="main"> <s id="s.000489">Contra euidentiam harum rationum non de&longs;unt, <lb/>qui difficultates, & &longs;ubterfugia afferant pro <expan abbr="retin&etilde;-da">retinen­<lb/>da</expan> &longs;uæ po&longs;itionis in ueri&longs;imilitudine; aiunt enim li-<pb pagenum="100" xlink:href="010/01/108.jpg"/><arrow.to.target n="marg117"/><lb/>gnum tardiùs in hydrargyro a&longs;cendere debui&longs;&longs;e; <lb/>quàm per aquam ob maiorem illius re&longs;i&longs;tentiam; &longs;ed <lb/>propter contrarietatem, & inimicitiam, quam habet <lb/>lignum cum Mercurio, &longs;uum cur&longs;um accelerat vt ex­<lb/><arrow.to.target n="marg118"/><lb/>peditè mercurium fugiat, & aquam aeremque a&longs;&longs;e­<lb/>quatur; quod symbolum elementum, atque <expan abbr="amicũ">amicum</expan> <lb/>e&longs;t; & propterea ce&longs;&longs;ante odio non cogitur celerri­<lb/>mè ab eo di&longs;cedere. </s> <s id="s.000490">Sed vide quàm faciles &longs;int præ­<lb/>dicti philo&longs;ophi; qui occa&longs;ione exigente non <expan abbr="ver&etilde;-tur">veren­<lb/>tur</expan> alitèr re&longs;pondere, nam &longs;i ego <expan abbr="quærã">quæram</expan>, quare gra­<lb/>uitas, quæ certè ine&longs;t in hi&longs;ce terrenis corporibus, <lb/>celeriùs transfert &longs;axum, quò magis ad terram acce­<lb/>dit, atque ei approximatur; re&longs;pondent quia vicinia <lb/><arrow.to.target n="marg119"/><lb/>terræ veluti roboratur vis motiua &longs;axi cadentis; &longs;ic <lb/>paritèr leuitas ve&longs;ic&etail; aere&etail; cre&longs;cere deberet in aqu&etail; <lb/>&longs;ummitate, quia nempè aeri approximatur, & ideò <lb/>virtus eius motiua roborari quoque deberet. </s> <s id="s.000491">Sed <lb/>his omi&longs;&longs;is &longs;ummi po&longs;&longs;unt diuer&longs;a corpora, quæ na­<lb/>turam, & temperiem diuer&longs;am, & contrariam aquæ <lb/>habeant, &longs;imillimam verò mercurio, & talis forta&longs;&longs;e <lb/>erit ampulla vitrea, vel ve&longs;ica, quæ repleatur mercu­<lb/>rio &longs;ublimato, vel pr&etail;cipitato; &longs;ic quoque vas fieri <lb/>po&longs;&longs;et ex metallo, vel alio corpore &longs;imillimo hy­<lb/>drargyro, vt nimirùm efficiatur compo&longs;itum cuius <lb/>natura valdè diuer&longs;a &longs;it ab aqua, & &longs;imillima hydrar­<lb/>gyro, & &longs;ic omninò tolleretur inimicitia, & antipa­<lb/>thia inter vas, & fluidum cra&longs;&longs;ius mercuriale, nihi­<lb/>lominùs ob&longs;eruabitur prædictum vas velociùs a&longs;cen­<lb/>dere per hydrargyrum, tardo verò motu per aquam, <pb pagenum="101" xlink:href="010/01/109.jpg"/><arrow.to.target n="marg120"/><lb/>igitur illa &longs;omniata inimicitia non erit cau&longs;a prædi­<lb/>ctæ inæqualitatis motus, &longs;ed mechanica, & naturalis <lb/>nece&longs;&longs;itas, qua maximum pondus hydrargyrj impe­<lb/>tuo&longs;iore motu exprimit, & impellit &longs;ursùm conten­<lb/>tum vas vitreum, vel ve&longs;ica, quàm impellere aqu&atail; <lb/>queat &longs;uo minori pondere. </s> </p> <p type="margin"> <s id="s.000492"><margin.target id="marg117"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000493"><margin.target id="marg118"/>Recurrunt <lb/>aduer&longs;arij ad <lb/>maiorem <expan abbr="inimicitiã">ini<lb/>micitiam</expan> <expan abbr="quã">quam</expan> <lb/>habet <expan abbr="lignũ">lignum</expan>, <lb/>&longs;eu aer cum <lb/>hydrargyro, <lb/>quàm cum <lb/>aqua, vt de­<lb/>ducant cele­<lb/>riùs lignum <lb/>fugere mer­<lb/>curium, <expan abbr="quã">quam</expan> <lb/><expan abbr="aquã">aquam</expan> debere.</s> </p> <p type="margin"> <s id="s.000494"><margin.target id="marg119"/>Sed reijci­<lb/>tur.</s> </p> <p type="margin"> <s id="s.000495"><margin.target id="marg120"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000496">Id ip&longs;um alijs exemplis confirmari po&longs;&longs;et, &longs;i nimi­<lb/>rum &longs;umatur oleum à frigore conden&longs;atum, & gla­<lb/>ciatum, cuius temperies, & natura potiùs grauiori <lb/>mercurio, vel oleo tartari a&longs;&longs;imilatur, & è contr&atail; <lb/>contrariam naturam, & diuer&longs;am haberet ab ip&longs;&atail; <lb/>aqua, & &longs;ic oleum prædictum ob amicitiam lento <lb/>motu a&longs;cendere deberet per hydrargyrum, aut per <lb/>oleum tartari. </s> <s id="s.000497">Sed celerrimè in aqua currere debe­<lb/>ret, vtpotè oleo contraria. </s> <s id="s.000498">Similitèr calx in ve&longs;ica <expan abbr="cõ-tenta">con­<lb/>tenta</expan> aqu&etail; forti &longs;imillima e&longs;t ob <expan abbr="caliditat&etilde;">caliditatem</expan>, & acredi­<lb/>nem ambarum, & è contrà &longs;ummè contraria erit <expan abbr="cõ-muni">con­<lb/>muni</expan> aquæ, & nihilominùs in illa veloci&longs;&longs;imè a&longs;cen­<lb/>dit, in hac tardè. </s> <s id="s.000499">Similitèr &longs;umi po&longs;&longs;ent va&longs;cula ex <lb/>cera, aut bitumine, quæ repleri po&longs;&longs;ent puluere, &longs;pi­<lb/>ritu, oleo, vel vino, vel alijs innumeris rebus, quæ <lb/>&longs;emper a&longs;cendent veloci&longs;&longs;imè in fluidis grauioribus, <lb/>vt &longs;unt aquæ regiæ, licèt in &longs;umma caliditate, & acre­<lb/>dine &longs;alina conueniant, & è contra languido, & tar­<lb/>do motu in fluidis <expan abbr="cõtrariæ">contrariæ</expan> naturæ a&longs;cendunt, dum­<lb/>modò minùs grauia &longs;int. </s> <s id="s.000500">Quaproptèr verum non e&longs;t <lb/>ob inimicitiam, & contrarietatem ve&longs;icam aerea&mtail; <lb/>veloci&longs;&longs;imè à mercurio fugere, & languido motu ex­<lb/>currere per aquam ei &longs;imilem, &longs;ed potiùs ob mecha-<pb pagenum="102" xlink:href="010/01/110.jpg"/><arrow.to.target n="marg121"/><lb/>nicam rationem <expan abbr="de&longs;umptã">de&longs;umptam</expan> à maiori, vel minori gra­<lb/>uitate, quæ deducitur ex Archimedis doctrina, quòd <lb/>&longs;cilicèt fluidum grauius per extru&longs;ionem impeller&etail; <lb/><expan abbr="&longs;ursũ">&longs;ursum</expan> debeat corpora minùs grauia, & hæc e&longs;t cau&longs;a, <lb/>quare ab&longs;que po&longs;itiua leuitate corpora &longs;ursùm <expan abbr="a&longs;c&etilde;-dere">a&longs;cen­<lb/>dere</expan> debent. </s> </p> <p type="margin"> <s id="s.000501"><margin.target id="marg121"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000502"><expan abbr="Cõtra">Contra</expan> <expan abbr="per&longs;picuitat&etilde;">per&longs;picuitatem</expan> &longs;upradicti ratiocinij <expan abbr="obijciũt">obijciunt</expan> <lb/>primò, quòd <emph type="italics"/>&longs;icuti grauiora intra minùs grauia mer&longs;a fe­<lb/>runtur deorsùm tanta vi, quæ &longs;it æqualis differentiæ gra­<lb/>uitatis mobilis &longs;upra grauitatem medij, constat euidentèr <lb/>euenturum proportion alitèr in leuioribus intra minùs leuia <emph.end type="italics"/><lb/><arrow.to.target n="marg122"/><lb/><emph type="italics"/>contentis ea &longs;cilicèt in ordine ad leuitatem, &longs;ursùm, non niti <lb/>&longs;ecundùm men&longs;uram exce&longs;&longs;us &longs;upra minùs leue &longs;ursùm ni­<lb/>&longs;ura, vt &longs;imilis ratio per&longs;uadet.<emph.end type="italics"/></s> <s id="s.000503"> Hoc &longs;uppo&longs;ito veluti cer­<lb/>tum, & euidens re&longs;pondet argumento &longs;uperius addu­<lb/>cto, aitque <emph type="italics"/>expirationem calidam re&longs;pectu aquæ valdè le­<lb/>uem &longs;ecundùm men&longs;uram totius &longs;uæ leuitatis &longs;ursùm niti <lb/>intra aquam, ac proindè valere ad re&longs;i&longs;tentiam illius cele­<lb/>ritèr &longs;uperandam, at verò valdè exiguum exce&longs;&longs;um &longs;upra <lb/>aerem obtinentem in leuitate &longs;ursùm niti præcisè &longs;ecundum <lb/>men&longs;uram talis exce&longs;&longs;us, ac proindè non e&longs;&longs;e mirum &longs;i lentè <lb/>per aerem a&longs;cendat etiam&longs;i dicatur à leuitate po&longs;itiua in­<lb/>trin&longs;eca moueri.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.000504"><margin.target id="marg122"/>Denuò ad­<lb/>mi&longs;&longs;a leuita­<lb/>te colligunt <lb/>ignem cele­<lb/>riùs per a <lb/>quam, quam <lb/>per aere&mtail; <lb/><expan abbr="a&longs;c&etilde;dere">a&longs;cendere</expan> de­<lb/>bere.</s> </p> <p type="main"> <s id="s.000505">Itaque &longs;icuti nos ex Archimedis doctrina deduci­<lb/>mus rationem de&longs;cen&longs;us grauium, & a&longs;cen&longs;us <expan abbr="leuiũ">leuium</expan> <lb/>ex hac &longs;uppo&longs;itione, quòd corpora omnia &longs;ubluna­<lb/>ria &longs;int grauia, &longs;ibi per&longs;uadent demon&longs;trare po&longs;&longs;e ea­<lb/>dem symptomata &longs;upponendo nedùm corpora a&longs;cen­<lb/>dentia, &longs;ed etiam medium fluidum, in quo <expan abbr="a&longs;cendũt">a&longs;cendunt</expan> <pb pagenum="103" xlink:href="010/01/111.jpg"/><arrow.to.target n="marg123"/><lb/>e&longs;&longs;e leuia; quaproptèr quotie&longs;cumque agitur de cor­<lb/>poribus grauibus de&longs;cendentibus comparari debent <lb/>grauitates tum corporis mobilis, tùm medij fluidi in <lb/>quo de&longs;cendit; at è contrà cum agitur de corporibus <lb/>a&longs;­cendentibus, debent paritèr intèr &longs;e comparari le­<lb/>uitates eorum vnà cum leuitate medij fluidi in quo <lb/>a&longs;cendunt. </s> </p> <p type="margin"> <s id="s.000506"><margin.target id="marg123"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000507">Modò vt fallacia huius ratiocinij detegatur, <expan abbr="demõ-">demon­<lb/></expan>&longs;trabo priùs lemmata aliqua mechanica, ex quibus <lb/>po&longs;tea adhibitis hypothe&longs;ibus &longs;upradictis demon­<lb/>&longs;trabo impo&longs;&longs;ibile omninò e&longs;&longs;e vt impetus velocita­<lb/>tis quo &longs;ursùm a&longs;cendunt corpora illa, quæ leuia ap­<lb/>pellantur, produci po&longs;&longs;it atque dependeat à princi­<lb/>pio aliquo intrin&longs;eco à quo &longs;ursùm impellantur re­<lb/>moueanturque à centro terræ. </s> </p> <p type="main"> <s id="s.000508">Et primo loco ob&longs;eruo cum Ari&longs;totele in mecha­<lb/>nicis, quòd. </s> </p> <p type="main"> <s id="s.000509"><emph type="center"/>PROP. LXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000510"><emph type="center"/><emph type="italics"/>Libræ, vel rotæ termini oppo&longs;iti contrarijs <lb/>motibus circa centrum agitari <lb/>debent.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000511">SIt libra radiorum æqualium, vel rota AIBH con­<lb/>uertibilis circa &longs;uum centrum C, hic <expan abbr="manife&longs;tũ">manife&longs;tum</expan> <lb/>e&longs;t, quòd &longs;i libram, aut rotam re uoluere velimus, ita <pb pagenum="104" xlink:href="010/01/112.jpg"/><arrow.to.target n="marg124"/><lb/><figure id="id.010.01.112.1.jpg" xlink:href="010/01/112/1.jpg"/><lb/>vt terminus eius A de&longs;cendat <lb/>deorsùm percurrendo arcum <lb/>AI nece&longs;sè e&longs;t vt eius oppo&longs;i­<lb/>tus terminus B motu contrario <lb/>&longs;ursùm a&longs;cendat percurrendo <lb/>arcum BH æqualem contrapo­<lb/>&longs;ito AI. </s> <s id="s.000512">Et <expan abbr="quotie&longs;cumq;">quotie&longs;cumque</expan> præ­<lb/>dicti motus <expan abbr="cõtrarij">contrarij</expan> &longs;imul fie­<lb/>ri nequeunt, tunc nece&longs;sè e&longs;t <lb/>vt libra, vel rota quie&longs;cati&ntail; <lb/>eodem &longs;itu, nec agitetur. </s> </p> <p type="margin"> <s id="s.000513"><margin.target id="marg124"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000514"><emph type="center"/>PROP. XLVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000515"><emph type="center"/><emph type="italics"/>Si eidem libræ termino applicentur potentiæ ad oppo&longs;itas <lb/>partes <expan abbr="trah&etilde;tes">trahentes</expan> mutuo <expan abbr="&longs;eimpedi&etilde;t">&longs;eimpedient</expan>, & potentia maior <lb/>præualebit, libram <expan abbr="flect&etilde;do">flectendo</expan> vi æquali dif­<lb/>ferentiæ potentiarum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000516">APponatur po&longs;tea pondus DE termino libræ A; <lb/>hoc profectò vim efficit, conaturque traher&etail; <lb/>terminum libræ A per directionem AD versùs cen­<lb/>trum telluris, at quia &longs;emidiameter AC in <expan abbr="c&etilde;tro">centro</expan> libr&etail; <lb/>figitur immobiliter, hinc con&longs;equetur reuolutio libr&etail; <lb/>fereturque terminus A non per lineam rectam AD, <lb/>&longs;ed per arcum AI excurrendo integrum <expan abbr="quadrant&etilde;">quadrantem</expan>, <lb/>& quia libra AB &longs;upponitur continua, & rigida <expan abbr="eod&etilde;">eodem</expan> <lb/>tempore quo terminus A arcum AI pertran&longs;it oppo­<lb/>&longs;itus eius terminus B de&longs;cribet contrapo&longs;itum arcum <lb/>BH. </s> <s id="s.000517">Modò motum eiu&longs;dem libræ, & de&longs;cen&longs;um pon-<pb pagenum="105" xlink:href="010/01/113.jpg"/><arrow.to.target n="marg125"/><lb/>deris DE impedire po&longs;&longs;umus, &longs;i eidem termino A ap­<lb/>plicaretur vis contraria G, qu&etail; traheret &longs;ursùm <expan abbr="eũ">eum</expan> ip­<lb/>&longs;um terminum A per eamdem rectam lineam <expan abbr="horizõ-ti">horizon­<lb/>ti</expan> perpendicularem ver&longs;us &longs;upremum terminum G; <lb/>& &longs;iquidem vis, & facultas motiua G æqualis e&longs;&longs;et vi <lb/>ponderis DE, nulla ratio &longs;uadet quòd vna earu&mtail; <lb/>virtutum reliquam &longs;uperet, aut vincat, proindequ&etail; <lb/>terminus libræ A non de&longs;cendet versùs I, nec a&longs;cen­<lb/>det versùs H, &longs;ed omninò quie&longs;cetin eodem &longs;itu. </s> <s id="s.000518">Si <lb/>verò <expan abbr="põdus">pondus</expan> DE &longs;uperaret vim <expan abbr="motiuã">motiuam</expan> G, <expan abbr="eiu&longs;q;">eiu&longs;que</expan> exce&longs; <lb/>&longs;us e&longs;&longs;et pondus E, tunc procùl dubio <expan abbr="põdus">pondus</expan> DE præ­<lb/>ualeret &longs;uperaretque vim motiuam G, & impetus, <lb/>atque vis, à qua prædicta libra flecteretur deorsù&mtail; <lb/>versùs I men&longs;uraretur à vi ponderis E, quæ e&longs;t diffe­<lb/>rentia, &longs;eù exce&longs;&longs;us, quo pondus premens DE &longs;upe­<lb/>rat vim eleuantem G. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000519"><margin.target id="marg125"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000520"><emph type="center"/>PROP. XLVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000521"><emph type="center"/><emph type="italics"/>Si oppo&longs;itos terminos libræ, vel rotæ duæ potentiæ traham, <lb/>ambæ deorsùm tendendo, &longs;e mutuò impedient, & <lb/>maior potentia præualebit, &longs;ed vi æquali <lb/>differentiæ earum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000522">POte&longs;t deindè alia ratione prohiberi, & impediri <lb/>de&longs;cen&longs;us ponderis DE ab&longs;que eò, quòd termi­<lb/>no A applicetur vis aliqua animata contraria G, & <lb/>hoc con&longs;equitur &longs;i applicetur termino oppo&longs;ito B <lb/>aliud pondus F, quod dùm deorsùm impellit ad ea&longs;­<lb/>dem partes ad quas dirigitur pondus DE prohibetur <pb pagenum="106" xlink:href="010/01/114.jpg"/><arrow.to.target n="marg126"/><lb/>quoque de&longs;cen&longs;us termini A eiu&longs;dem libræ, vt <expan abbr="dictũ">dictum</expan> <lb/>e&longs;t; & &longs;iquidem pondus F æquale fuerit ponderi <lb/>DE, tunc efficietur æquilibrium, quia dùm ambo <expan abbr="põ-dera">pon­<lb/>dera</expan> conantur de&longs;cendere deorsùm transferre qu&etail; <lb/>duos terminos libræ versùs infimum &longs;ignum <expan abbr="quadrã-">quadran­<lb/></expan><arrow.to.target n="marg127"/><lb/>tis I, & hoc efficitur æquali vi, & impetu, procùl du­<lb/>bio vna vis, & conatus impedit motum, & <expan abbr="defcensũ">de&longs;censum</expan> <lb/>alterius, & ex hoc mutuo <expan abbr="impedim&etilde;to">impedimento</expan> re&longs;ultat quies <lb/>totius libræ in &longs;itu horizontali; at &longs;i pondus F æqua­<lb/>Ie fuerit vni portioni D totius ponderis DE, tunc <lb/>præua lente maiori pondere deprimet terminum libr&etail; <lb/>A versùs I, a&longs;cendetque oppo&longs;itus terminus B versùs <lb/>H tanta vi quæ &longs;it æqualis exce&longs;&longs;ui ponderis E. <!-- KEEP S--></s> <s id="s.000523">Hinc <lb/>colligitur quod in libra, vel rota duo æquales im­<lb/><figure id="id.010.01.114.1.jpg" xlink:href="010/01/114/1.jpg"/><lb/>petus ad ea&longs;dem partes <expan abbr="tend&etilde;-tes">tenden­<lb/>tes</expan>, nempè deorsùm, ideoqu&etail; <lb/>&longs;imiles inter &longs;e, &longs;e mutuo impe­<lb/>diunt, & de&longs;truunt, itaut quies <lb/>con&longs;equatur, &longs;i verò eorumdem <lb/>&longs;imilium motuum <expan abbr="de&longs;cendentiũ">de&longs;cendentium</expan> <lb/>vires inæquales fuerint, præua­<lb/>lebit maius pondus, libramque <lb/>reuoluet non integra &longs;ua vi, &longs;ed tantummodò illa dif­<lb/>ferentia, vel exce&longs;&longs;u, quo maius pondus &longs;uperat <lb/>minus. <pb pagenum="107" xlink:href="010/01/115.jpg"/><arrow.to.target n="marg128"/></s> </p> <p type="margin"> <s id="s.000524"><margin.target id="marg126"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000525"><margin.target id="marg127"/>Prop. 45.</s> </p> <p type="margin"> <s id="s.000526"><margin.target id="marg128"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000527"><emph type="center"/>PROP. XLVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000528"><emph type="center"/><emph type="italics"/>Ii&longs;dem datis, &longs;i ambæ potentiæ &longs;ursùm trahant, <lb/>idem &longs;equetur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000529">ID ip&longs;um verum quoque e&longs;t, <lb/><figure id="id.010.01.115.1.jpg" xlink:href="010/01/115/1.jpg"/><lb/>&longs;i applicentur terminis op­<lb/>po&longs;itis eiu&longs;dem libræ A, B duæ <lb/>vires inæquales, DE maior, & <lb/>F minor, quæ ambæ &longs;ursùm ter­<lb/>minos libræ trahant a&longs;cenden­<lb/>do. </s> <s id="s.000530">& hìc eodem modo o&longs;ten­<lb/>detur, quòd libra flectetur &longs;ur­<lb/>sùm ab A versùs H, & reliqua <lb/>vis minor F &longs;uperabitur ab ex­<lb/>ce&longs;&longs;u virtutis DE &longs;upra F, de&longs;cendetque terminus B <lb/>versùs I. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000531"><emph type="center"/>PROP. XLIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000532"><emph type="center"/><emph type="italics"/>Si oppo&longs;itos terminos libræ duæ potentiæ trahant vna &longs;ur­<lb/>sùm, altera deorsùm, &longs;e mutuò iuuabunt, & vis li­<lb/>bram flectens æqualis erit &longs;ummæ ambarum <lb/>potentiarum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000533">TErtio loco in eadem rota, &longs;eù libra AB termi­<lb/>nus A deorsùm trahatur à <expan abbr="põdere">pondere</expan> D, &longs;ed eius <lb/>oppo&longs;itus terminus B &longs;ursùm trahatur à vi a&longs;cenden­<lb/>te F, quæ minor &longs;it vi ponderis D, dico, quòd libra <lb/>non quie&longs;cet, &longs;ed reuoluetur eius terminus A <expan abbr="de&longs;c&etilde;-">de&longs;cen-</expan><pb pagenum="108" xlink:href="010/01/116.jpg"/><arrow.to.target n="marg129"/><lb/>dendo versùs I, eleuabiturque terminus oppo&longs;itus <lb/>B versùs H, & conatus, &longs;eù vis, quo libra reuoluitur <lb/>æqualis erit non differentiæ, & exce&longs;&longs;ui ponderis D <lb/>&longs;upra vim F, &longs;ed æquabitur aggregato ambarum vir­<lb/><figure id="id.010.01.116.1.jpg" xlink:href="010/01/116/1.jpg"/><lb/>tutum D, & F. <!-- KEEP S--></s> <s id="s.000534">Applicetur termi­<lb/>no B pondus E æquale vi &longs;ursùm <lb/>impellenti F, pariterque ibidem <lb/><expan abbr="&longs;u&longs;p&etilde;datur">&longs;u&longs;pendatur</expan> aliud <expan abbr="põdus">pondus</expan> G æqua­<lb/>le oppo&longs;ito ponderi D, manife­<lb/>&longs;tum e&longs;t (amotis, vel coercitis vi­<lb/>ribus F, & E) quòd <expan abbr="põdera">pondera</expan> æqua­<lb/>lia D, & G pendentia à terminis <lb/>radiorum æqualium eiu&longs;dem li­<lb/>bræ efficient æquilibrium, & ideò <lb/><arrow.to.target n="marg130"/><lb/>libra quie&longs;cet. </s> <s id="s.000535">Præterea quia pondus E æquatur vi <lb/>contrariæ &longs;ursùm trahenti F, & ambæ applicantur <lb/>eidem termino B libræ AB (ab æqualibus ponderi­<lb/><arrow.to.target n="marg131"/><lb/>bus D, & G æquilibratæ) igitur duo pondera &longs;imùl <lb/>&longs;umpta G, & E libram impellunt contrario ni&longs;u, &longs;ci­<lb/>licet à B ver&longs;us I, & præcisè adæquant conatum pon­<lb/>deris D, & vim trahentem F, quæ ambo deprimere <lb/>po&longs;&longs;unt terminum libræ A versùs I &longs;ubleuando ter­<lb/>minum B versùs H. <!-- KEEP S--></s> <s id="s.000536">Ergo duæ vires D, & F &longs;imùl <expan abbr="sũp-tæ">sump­<lb/>tæ</expan> (amotis ponderibus G, & E) determinant vim, <lb/>&longs;eù conatum, quo libra reuolui debet ab A, versùs I. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000537"><margin.target id="marg129"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000538"><margin.target id="marg130"/>Pr. <!-- REMOVE S-->47.</s> </p> <p type="margin"> <s id="s.000539"><margin.target id="marg131"/>Pr. <!-- REMOVE S-->46.</s> </p> <p type="main"> <s id="s.000540">Et hìc animaduertendum e&longs;t, quòd duæ vires D, <lb/>& F, quæ reuerà contrariæ &longs;unt inter &longs;e (<expan abbr="cũ">cum</expan> illa deor­<lb/>sùm comprimat, hæc verò &longs;ursùm trahat) non &longs;ibi <lb/>mutuò opponuntur, nec vna earum alteriùs motu&mtail; <pb pagenum="109" xlink:href="010/01/117.jpg"/><arrow.to.target n="marg132"/><lb/>impedit, &longs;ed vna promouet, adiuuat, & auget cona­<lb/>tum, vim, & impetum alterius; & hoc accidit <expan abbr="quianõ">quia non</expan> <lb/>applicantur ambæ eidem termino A libræ, &longs;ed ter­<lb/>minis oppo&longs;itis A, & B, qui iuxtà libræ, & rotæ pro­<lb/>prietatem, & naturam debent moueri motibus con­<lb/><arrow.to.target n="marg133"/><lb/>trarijs, &longs;cilicèt A per arcum AI, & B per arcum BH. <lb/>igitur impul&longs;us ponderis D deorsùm, & tractio facta <lb/>àvi F &longs;ursùm conueniunt, & &longs;e mutuò adiuuant, & <lb/>augent, vt ab vtri&longs;que reuolutio libræ efficiatur, quæ <lb/>ad ea&longs;dem partes impellitur ab ei&longs;dem viribus con­<lb/>trarijs. </s> <s id="s.000541">ce&longs;&longs;et igitur admiratio quare duæ vires con­<lb/>trariæ in libra &longs;e mutuò non <expan abbr="de&longs;truãt">de&longs;truant</expan>, &longs;ed potiùs mu­<lb/>tuo &longs;e adiuuent, ita vt ex vtri&longs;que re&longs;ultet vna vis <expan abbr="cõ-po&longs;ita">con­<lb/>po&longs;ita</expan>, à qua libra reuoluitur. </s> </p> <p type="margin"> <s id="s.000542"><margin.target id="marg132"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000543"><margin.target id="marg133"/>Prop. 45.</s> </p> <p type="main"> <s id="s.000544"><emph type="center"/>PROP. L.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000545"><emph type="center"/><emph type="italics"/>Si oppo&longs;itos libræ terminos quatuor potentiæ trahant, duæ <lb/>&longs;ursùm, & duæ deorsùm, conatus &longs;eù vis libram fle­<lb/>ctens men&longs;uratur à &longs;umma differentiæ a&longs;cen­<lb/>dentium, cum differentia de&longs;cendentium <lb/>potentiarum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000546">SI tandem eadem libra à quatuor viribus impel­<lb/>latur trahaturque, quarum duæ D, & G graues <lb/>&longs;int deorsùmque tendant, duæ verò M, & F &longs;ursù&mtail; <lb/>eo&longs;dem terminos libræ trahant, &longs;itque energia virtu­<lb/>tis M maior quàm F, pondus verò D minus &longs;it quàm <pb pagenum="110" xlink:href="010/01/118.jpg"/><arrow.to.target n="marg134"/><lb/>G, <expan abbr="tũc">tunc</expan> manife&longs;tum e&longs;t, terminum <lb/><figure id="id.010.01.118.1.jpg" xlink:href="010/01/118/1.jpg"/><lb/>A eleuari &longs;ursùm versùs Hab ex­<lb/>ce&longs;&longs;u quo vis M &longs;uperat faculta­<lb/>tem motiuam F, & è contrà op­<lb/>po&longs;itus libræ terminus B depri­<lb/><arrow.to.target n="marg135"/><lb/>metur deorsùm versùs I ab ex­<lb/>ce&longs;&longs;u quo pondus G &longs;uperat vim <lb/>grauitatis D; & quia prædicti <lb/>duo impul&longs;us differentiales con­<lb/>trarij &longs;unt, vnus quidèm &longs;ursù&mtail;, <lb/>alter verò deorsùm, <expan abbr="applicãturque">applicanturque</expan> terminis oppo&longs;i­<lb/>tis eiu&longs;dem libræ; igitur &longs;e mutuo adiuuant promo­<lb/>uenturque, & proindè conatus, vis, atque impetus, <lb/>quo vniuer&longs;a libra reuoluitur, æqualis erit aggrega­<lb/>to prædictarum differentiarum. </s> </p> <p type="margin"> <s id="s.000547"><margin.target id="marg134"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000548"><margin.target id="marg135"/>Prop. 49.</s> </p> <p type="main"> <s id="s.000549"><emph type="center"/>PROP. LI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000550"><emph type="center"/><emph type="italics"/>Vis motiua, qua &longs;olidum grauius &longs;pecie, quàm fluidum, de­<lb/>&longs;cendit, æqualis est differentiæ ponderis &longs;olidi &longs;upra <lb/>pondus fluidi ei æqualis mole.<emph.end type="italics"/><emph.end type="center"/></s> </p> <figure id="id.010.01.118.2.jpg" xlink:href="010/01/118/2.jpg"/> <p type="main"> <s id="s.000551">HIs declaratis intelligatur <lb/>vas RGS aqua plenum, in <lb/><expan abbr="eoq;">eoque</expan> immergatur corpus aliquod <lb/>graue durum, ac con&longs;i&longs;tens DE, <lb/>quod grauius &longs;it aqua collaterali <lb/>F patet ex dictis prop. 9. & ex <lb/>Archimede, duo pondera DE, & F collocari in libra <lb/>quadam imaginaria, & perpetua AB in qua exce&longs;&longs;us <pb pagenum="111" xlink:href="010/01/119.jpg"/><arrow.to.target n="marg136"/><lb/>ponderis &longs;olidi DE &longs;upra grauitatem aquæ F quæ &longs;it <lb/>æqualis mole ip&longs;i DE, &longs;emper idem e&longs;t in quacumque <lb/>aquæ profunditate &longs;olidum collocetur, &longs;itque pon­<lb/>dus E exce&longs;&longs;us quo pondus DE &longs;uperat grauitate&mtail; <lb/>aquæ F, igitur conatus, vis, & impetus, quo &longs;olidum <lb/>DE de&longs;cendit infra <expan abbr="aquã">aquam</expan> men&longs;uratur à vi <expan abbr="põderis">ponderis</expan> E. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000552"><margin.target id="marg136"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000553"><emph type="center"/>PROP. LII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000554"><emph type="center"/><emph type="italics"/>Vis motiua qua &longs;olidum leuius &longs;pecie, quàm fluidum a&longs;cen­<lb/>dit æqualis est exce&longs;&longs;ui leuitatis &longs;olidi &longs;upra leuita­<lb/>tem fluidi ei æqualis mole.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000555">E Contrà, &longs;i &longs;upponamus, quod lignum DE pari­<lb/>terque aqua F careant grauitate, &longs;ed <expan abbr="tãtummo-dò">tantummo­<lb/>dò</expan> à vi leuitatis informentur, & ambo impul&longs;um, & <lb/>impetum faciant &longs;ursùm conenturque a&longs;cendere, <expan abbr="nõ">non</expan> <lb/>&longs;ecùs o&longs;tendetur, quòd in libra, &longs;eù rota perpetua <lb/>ligni DE maior leuitas præualebit &longs;uperabitque mi­<lb/>norem leuitatem fluidi collateralis F, proindeque <lb/>libra inflectetur ab A versùs R a&longs;cendendo tanta vi, <lb/>quanta e&longs;t differentia, &longs;eù exce&longs;&longs;us E, quo leuitas li­<lb/>gni &longs;uperat aquæ leuitatem. </s> </p> <p type="main"> <s id="s.000556"><emph type="center"/>PROP. LIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000557"><emph type="center"/><emph type="italics"/>Vis motiua qua leue corpus in fluido graui a&longs;cendit æqualis <lb/>e&longs;&longs;e debet &longs;ummæ lenitatis &longs;olidi, & grauitatis <lb/>fluidi.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000558">SI verò variata hypote&longs;i ponamus <expan abbr="lĩgnum">lignum</expan> F leue, <lb/>& &longs;ursùm ab intrin&longs;eco principio impelli, & mo-<pb pagenum="112" xlink:href="010/01/120.jpg"/><arrow.to.target n="marg137"/><lb/>ueri, at fluidum collaterale D, quòd &longs;it hydrargyrum <lb/>&longs;upponatur deorsùm tantummodò vim exercere, vt <lb/>exigit maxima eius grauitas, nec prorsùs &longs;ursùm im­<lb/><figure id="id.010.01.120.1.jpg" xlink:href="010/01/120/1.jpg"/><lb/>pellere, tunc quoque libra, &longs;eù <lb/>rota perpetua efformabitur i&ntail; <lb/>qua &longs;emper terminus B trahetur <lb/>&longs;ursùm à po&longs;itiua leuitate ip&longs;ius <lb/>ligni F a&longs;cendetque versùs R, <lb/>terminus verò oppo&longs;itus depri­<lb/>metur ab A versùs H vt natur&atail; <lb/>grauitatis exigit, & quia hi duo motus, & conatus in <lb/>oppo&longs;itis terminis libræ <expan abbr="cõtrarij">contrarij</expan> &longs;unt, ergò vici&longs;&longs;im <lb/>&longs;e non de&longs;truunt, nec contrariantur, &longs;ed &longs;e mutuò fa­<lb/>uent, & adiuuant. </s> <s id="s.000559">igitur conatus, & impetus quo re­<lb/>uoluitur iam dicta libra, &longs;cilicèt quo lignum F a&longs;cen­<lb/>dit à fundo mercurij æqualis erit non differentiæ, &longs;ed <lb/>aggregato ex vi leuitatis F, & ex facultate ponderis <lb/>mercurij D. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000560"><margin.target id="marg137"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000561"><emph type="center"/>PROP. LIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000562"><emph type="center"/><emph type="italics"/>Si verò tam &longs;olidum, quàm fluidum exerceant leuitatem, <lb/>atque grauitatem, vis motiua, qua vnum eorum ele­<lb/>uatur æqualis e&longs;t aggregato ex differentia leui­<lb/>tatum vnà cum differentia grauitatum <lb/>earum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000563">TAndèm &longs;i &longs;upponamus, quod lignum vim faciat <lb/>&longs;ursùm vt leue, & etiam eodem tempore gra­<lb/>uitatem eius natiuam exerceat, pariterque aqua D <pb pagenum="113" xlink:href="010/01/121.jpg"/><arrow.to.target n="marg138"/><lb/>in va&longs;e nedùm deorsùm comprimat, vt grauis, &longs;ed <lb/>etiam non omninò priuetur gradu aliquo leuitatis, <lb/>tunc &longs;imilitèr libra perpetua imaginaria efformabi­<lb/>tur in qua terminus I deorsùm impellitur ab exce&longs;&longs;u <lb/>quo grauitas aquæ D &longs;uperat <lb/><figure id="id.010.01.121.1.jpg" xlink:href="010/01/121/1.jpg"/><lb/><expan abbr="grauitat&etilde;">grauitatem</expan> ligni F, & è <expan abbr="cõtràter-minus">contràter­<lb/>minus</expan> B <expan abbr="&longs;ursũ">&longs;ursum</expan> eleuabitur ab ex­<lb/>ce&longs;&longs;u quo leuitas ligni &longs;uperat <lb/>leuitatem ip&longs;ius aquæ. </s> <s id="s.000564">Et quia <lb/>prædicti impul&longs;us &longs;unt contra­<lb/>rij, applicanturque eidem li­<lb/>bræ imaginariæ, igitur vnus impul&longs;us alteri non op­<lb/><arrow.to.target n="marg139"/><lb/>ponitur, & proindè vniuer&longs;alis conatus, & impetus <lb/>prædictæ libræ, &longs;cilicèt vis, & impetus, quo lignum <lb/>F a&longs;cendit in aqua men&longs;uratur ab vtroque exce&longs;&longs;u, <lb/>&longs;cilicèt ab aggregato differentiæ ponderum aquæ, <lb/>& ligni, vnà cum exce&longs;&longs;u leuitatis ligni &longs;upra aqueam <lb/>leuitatem. </s> </p> <p type="margin"> <s id="s.000565"><margin.target id="marg138"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000566"><margin.target id="marg139"/>Prop. 50.</s> </p> <p type="main"> <s id="s.000567"><emph type="center"/><emph type="italics"/>SVPPOSITIO V.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000568">HIs præmi&longs;&longs;is &longs;upponamus cum aduer&longs;arijs pri­<lb/><arrow.to.target n="marg140"/><lb/>mo loco, quòd reuerà præter corpora graui&atail; <lb/>etiam leuia in natura exi&longs;tant, quorum aliqua, vt ait <lb/>Ari&longs;toteles, &longs;int &longs;implicitèr talia, alia verò re&longs;pectiuè, <lb/>veluti ignis dicitur ab&longs;olutè leuis, & terra, &longs;eù hy­<lb/>drargyrum, vel aliud fluidum æquè graue, ac ip&longs;&atail; <lb/>terra e&longs;t appellabitur ab&longs;olutè graue <expan abbr="reperiũtur">reperiuntur</expan> po­<lb/>&longs;tea alia corpora intermedia &longs;implicia, vel mixt&atail;, <lb/>quæ vocantur grauia &longs;imùl, & leuia re&longs;pectiuè, &longs;cili-<pb pagenum="114" xlink:href="010/01/122.jpg"/><arrow.to.target n="marg141"/><lb/>cèt aqua demer&longs;a intra mercurium dicitur leuis, & <lb/>moueri &longs;ursùm à principio intrin&longs;eco, at &longs;i eade&mtail; <lb/>aqua intra oleum mergatur, dicetur iam grauis, no&ntail; <lb/>leuis, & moueri deorsùm à principio interno. </s> <s id="s.000569">Hoc <lb/>verò duplicem &longs;en&longs;um habere pote&longs;t, aut dictæ duæ <lb/>contrariæ qualitates &longs;emper in eodem corpore aquæ <lb/>exi&longs;tunt, & vigent, aut &longs;ucce&longs;&longs;iuè modò vna, modò <lb/>altera in ea reperitur, ita vt aqua in fundo hydrar­<lb/>gyri po&longs;ita &longs;it reuera leuis, & nullo pacto grauis, & <lb/>è contià, quando eadem aqua in oleo demergitur, <lb/>hìc grauitatem habeat, & nullam prorsùs <expan abbr="leuitat&etilde;">leuitatem</expan>, <lb/>itaut remaneat &longs;opita, & extincta leuitas illa, quæ <lb/>tanta efficacia <expan abbr="aquã">aquam</expan> &longs;ursùm impellebat à fundo mer­<lb/>curij, igitur in primo &longs;en&longs;u retinere aqua deberet <lb/>perpetuò duas contrarias qualitates, &longs;cilicèt leuita­<lb/>tem, & grauitatem eodem modo, ac dicuntur mixta <lb/>participare ex qualitatibus extremis, calido nempè, <lb/>& frigido, & veluti colores medij nigre dinem, at­<lb/>que albedinem participare <expan abbr="cens&etilde;tur">censentur</expan>, igitur dici de­<lb/>beret, quod in igne prorsùs, & ab&longs;olutè leui qua­<lb/>tuor integri gradus leuitatis reperiuntur, & &longs;imili­<lb/>tèr in ip&longs;a terra exi&longs;tunt quatuor gradus grauitatis, <lb/>at aer habebit tres gradus leuitatis, & vnicum gra­<lb/>dum pondero&longs;itatis, &longs;ic aqua vnicum gradum lèui­<lb/>tatis, & tres grauitatis haberet, & <expan abbr="tãdèm">tandèm</expan> aliud cor­<lb/>pus medium inter aerem, & aquam, veluti for&longs;an <lb/>e&longs;t &longs;piritus vini, habere po&longs;&longs;et duos gradus leuitatis, <lb/>& duos alios gradus grauitatis.</s> </p> <pb xlink:href="010/01/123.jpg"/> <p type="main"> <s id="s.000570"><emph type="center"/><emph type="italics"/>SVPPOSITIO VI.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000571">SVpponit præterea Aristoteles, quòd velocitas, <lb/>qua idem corpus a&longs;cendit, vel de&longs;cendit in di­<lb/>uer&longs;is medijs fluidis eamdem proportionem habet, <lb/>quam raritates, vel con&longs;i&longs;tentiæ eorumdem fluido­<lb/>rum, ver. gr. &longs;i aer e&longs;&longs;et decies rarior, ac di&longs;trahibi­<lb/>lior, & faciliùs penetrabilis, quam &longs;it aquæ, eadem <lb/>pila marmorea de&longs;cendet cubitalem altitudinem ae­<lb/>ris decies velociùs, quàm profunditatem aqu&ecedil; pa­<lb/>riter cubitalem, &longs;cilicèt &longs;i prædictum aereum <expan abbr="&longs;atiũ">&longs;patium</expan> <lb/>pertran&longs;eat in vnica arteriæ pul&longs;atione, aquæ altitu­<lb/>dinem percurret in decem eiu&longs;dem arteriæ pul&longs;<lb/>ationibus.</s> <s id="s.000572">Idemque in a&longs;cen&longs;u corporum leuium iuxtà <lb/>Ari&longs;totelis &longs;ententiam dici debet.</s> <s id="s.000573">His præmi&longs;&longs;is.<lb/></s> </p> <p type="main"> <s id="s.000574"><emph type="center"/>PROP. LV.<emph.end type="center"/></s> </p> <p type="main"> <s id="s.000575"><emph type="italics"/>O&longs;tendendum e&longs;t Ignem non e&longs;&longs;e leuem, nec a&longs;cendere vi <lb/> leuitatis eius po&longs;itiuæ.<emph.end type="italics"/></s> <s id="s.000576">ET primò extrema corpora &longs;implicia, &longs;cilicèt i­<lb/>gnis & terra, vel <expan abbr="hydrargyrũ"> hydrargyrum</expan>, aut aurum fu&longs;um, vel quodlibet aliud graui&longs;&longs;imum corpus, iuxtà Ari­<lb/>&longs;totelis effatum &longs;i fieri pote&longs;t, &longs;int ab&longs;olutè grauia, & <lb/>leuia itaut ignis habeat quatuor gradus leuitatis, & <lb/>nullam prorsùs grauitatem, è contrà terra, vel hy­<lb/>drargyrum quatuor gradus grauitatis habeat, nullam <lb/> verò leuitatem, &longs;ic enim terra erit ab&longs;olutè, & om­<lb/>ninò grauis, ignis verò ab&longs;olutè leuis, ergò (ex prop.<pb pagenum="116" xlink:href="010/01/124.jpg"/> <arrow.to.target n="marg142"/><lb/> 53.) conatus, & impetus totalis, quo ignis per mer­<lb/>curium a&longs;cendit, vel terra per ignem de&longs;cendit, men­<lb/>&longs;urari debet ab aggregato virium extremarum, &longs;ci<lb/>licet à tota vi leuitatis cum tota vi grauitatis, quar&etail; <lb/>totalis impetus erit octo graduum. </s> <s id="s.000577">Sed hoc e&longs;t fal­<lb/>&longs;um, contra aduer&longs;arij a&longs;&longs;ertionem, & contra Archi­<lb/>medem, ea enim, quæ in fluido eleuantur, tanta vi <lb/>a&longs;cendunt, quanta e&longs;t grauitas qua moles fluidi mer­<lb/>curialis æqualis corpori igneo intra ip&longs;um demer&longs;o <lb/>&longs;uperat huius grauitatem, quæ nulla e&longs;t, & proindè <lb/>ignis impetu quatuor graduum per mercurium <expan abbr="a&longs;c&etilde;-dit">a&longs;cen­<lb/>dit</expan>, quaproptèr non fertur ignis &longs;ursùm à vi eius le­<lb/>uitatis, & ideò leuis non erit, quod erat &c. <lb/><arrow.to.target n="marg143"/></s> </p> <p type="margin"> <s id="s.000578"><margin.target id="marg140"/>Suppo&longs;itio­<lb/>nes aliquæ <lb/>peripatetice <lb/>recen&longs;entur.</s> </p> <p type="margin"> <s id="s.000579"><margin.target id="marg141"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000580"><margin.target id="marg142"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000581"><margin.target id="marg143"/>Dubitatur <lb/>de men&longs;ura <lb/>gradus præ­<lb/>dicti impe­<lb/>tus.</s> </p> <p type="main"> <s id="s.000582">Sed in&longs;tabit denuò peripateticus, dicetque, quòd <lb/>ea velocitas, quæ exercetur ab igne a&longs;cendente per <lb/>mercurium, aut à terra de&longs;cendente per ignem po­<lb/>terit cen&longs;eri octo graduum, vel quatuor ad libitum, <lb/>quia non habemus certam men&longs;uram vnius gradus <lb/>impetus, & &longs;ic mediante &longs;en&longs;u, & experientia non <lb/>pote&longs;t eius &longs;ententia redargui. </s> </p> <p type="main"> <s id="s.000583"><emph type="center"/>PROP. LVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000584"><emph type="center"/><emph type="italics"/>Reperire men&longs;uram certi gradus impetus re&longs;pectu cuius di­<lb/>&longs;cerni valeat an impetus de&longs;cen&longs;us terræ per ignem, <lb/>vel a&longs;cen&longs;us ignis per mercurium &longs;it octo, vel <lb/>quatuor graduum.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000585">SEd prædictùm effugium &longs;ic refellemus: Fiat ex­<lb/>perimentum non in mercurio &longs;implicitèr graui, </s> </p> <pb pagenum="117" xlink:href="010/01/125.jpg"/> <p type="main"> <s id="s.000586"><arrow.to.target n="marg144"/><lb/>&longs;ed in aqua, vel in aere, illa enim habebit tres gradus <lb/>grauitatis, & vnicum leuitatis, ergo ignis per <expan abbr="aquã">aquam</expan> <lb/>a&longs;cendet velocitate trium graduum; in mercurio ve­<lb/>rò impetu octo graduum, & terra per ignem octies <lb/>velociùs de&longs;cendet, quàm per aquam. </s> <s id="s.000587">Præterea aer <lb/>habet vnicum gradum grauitatis, & tres gradus le­<lb/>uitatis, igitur ignis octies velociùs per mercurium <lb/>a&longs;cendet, quàm per aerem, vnde hac ratione habe­<lb/>bimus men&longs;uram vnius gradus impetus tàm in <expan abbr="a&longs;c&etilde;-&longs;u">a&longs;cen­<lb/>&longs;u</expan>, quàm in de&longs;cen&longs;u, qui comparari pote&longs;t cum im­<lb/>petu ignis per mercurium a&longs;cendentis, & terræ per <lb/>ignem de&longs;cendentis; & proindè facilè conijci po­<lb/>terit, an prædictæ velocitates extremorum elemen­<lb/>torum reuerà &longs;int octuplæ, vel non, comparatæ ad <lb/>velocitates quas exercent in intermedijs elementis.<!--neuer Satz--><lb/>& licèt experimentum non det exactam <expan abbr="præcifion&etilde;">præci&longs;ionem</expan>, <lb/>nihilominùs &longs;ufficienti&longs;&longs;imè euincit fal&longs;itatem peri­<lb/>pateticæ hypothe&longs;is, &longs;ed licèt reuerà vis, & energia, <lb/>qua corpora a&longs;cendunt, vel de&longs;cendunt, minimè de­<lb/>duci po&longs;&longs;it ex velocitate tran&longs;itus &longs;ursùm, vel deor­<lb/>sùm, vt &longs;uo loco apertè o&longs;tendemus, tamen a&longs;&longs;umi <lb/>pote&longs;t cum aduer&longs;ario ad eum redarguendum. </s> </p> <p type="margin"> <s id="s.000588"><margin.target id="marg144"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000589">Con&longs;iderentur deindè elementa intermedia, vt <lb/>&longs;unt aer, & aqua, &longs;eù alia corpora mixta, quæ <expan abbr="ei&longs;d&etilde;">ei&longs;dem</expan> <lb/>gradibus leuitatis, & grauitatis afficiantur. </s> <s id="s.000590">Demon­<lb/>&longs;trandum e&longs;t, nullum eorum corporum, quæ <expan abbr="a&longs;cendũt">a&longs;cendunt</expan> <lb/>&longs;ursùm po&longs;itiuam leuitatem habere. <pb pagenum="118" xlink:href="010/01/126.jpg"/><arrow.to.target n="marg145"/></s> </p> <p type="margin"> <s id="s.000591"><margin.target id="marg145"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000592"><emph type="center"/>PROP. LVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000593"><emph type="center"/><emph type="italics"/>Si Aer in aqua &longs;olummodò leuitatem exerceret, in ea non <lb/>a&longs;cenderet à leuitate eius po&longs;itiua impul&longs;us.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000594">ET primò &longs;upponamus prædicta elementa no&ntail; <lb/>retinere &longs;imùl eodemque tempore duas oppo­<lb/>&longs;itas facultates grauitatis, & leuitatis, &longs;ed &longs;ucce&longs;&longs;i­<lb/>uè modò vnam, modò alteram po&longs;&longs;ideant, prout in <lb/>diuer&longs;is medijs fluidis collocantur, &longs;cilicèt aqua i&ntail; <lb/>aere pendula &longs;olummodò grauis cen&longs;eri debeat, non <lb/>autem leuis, &longs;i po&longs;tmodum aqua infrà hydrargyrum <lb/>mergatur, tunc aqua leuis &longs;it, non autem grauis, po­<lb/><figure id="id.010.01.126.1.jpg" xlink:href="010/01/126/1.jpg"/><lb/>natur etiam, quod aer, &longs;eù <expan abbr="lignũ">lignum</expan> <lb/>&longs;ub aqua demer&longs;um leue &longs;it, nec <lb/>grauitatem vllam habeat. </s> <s id="s.000595">Con­<lb/>cipiatur po&longs;tea vas RGHS a­<lb/>qua D plenum, & in eo merga­<lb/>tur ma&longs;&longs;a aeris, vel ligni F, pa­<lb/>tet ergò ex &longs;upradicta hypo­<lb/>the&longs;i, quod aqua D <expan abbr="nullã">nullam</expan> leuitatem, &longs;ed tantummo­<lb/>dò grauitatem habebit, eò quòd prædicta aqua non <lb/>&longs;upponitur demer&longs;a intra aliud corpus fluidum den­<lb/>&longs;ius, & pondero&longs;ius ip&longs;a, &longs;ed contigua e&longs;t aeri. </s> <s id="s.000596">Mo­<lb/>dò quia aer, vel lignum F &longs;upponitur ab aduer&longs;arijs <lb/>&longs;ursùm a&longs;cendere à G, versùs R impul&longs;a à po&longs;itiua <lb/>leuitate eius naturali, aqua verò circumfu&longs;a D cona­<lb/>tum, atque impetum exercet deorsùm ab A versùs <lb/>H veluti natura eius grauitatis exigit, habebimus <pb pagenum="119" xlink:href="010/01/127.jpg"/>ergò duos impetus ad inuicem contrarios, nempè <lb/><arrow.to.target n="marg146"/><lb/>leuitatis aeris F grad. <!-- REMOVE S-->3. & grauitatis gra. </s> <s id="s.000597">3. aquæ <lb/>circumfu&longs;æ D, & hæ duæ virtutes motiuæ &longs;imùl &longs;um­<lb/>ptæ gr.6. component men&longs;uram conatus, & impetus, <lb/>quo lignum F per aquam a&longs;cendit, hoc tamen e&longs;t fal­<lb/><arrow.to.target n="marg147"/><lb/>&longs;um, & contra conce&longs;&longs;ionem eiu&longs;dem aduer&longs;arij, & <lb/>contra demon&longs;trationem Archimedis, & tande&mtail; <lb/>contra experientiam, quia ea, quæ feruntur &longs;ursùm <lb/>in aqua, tanta vi a&longs;cendunt, quanta e&longs;t grauitas, <lb/>qua moles aquæ æqualis corpori demer&longs;o &longs;uperat <lb/>huiusmet grauitatem, quod perindè e&longs;t, ac &longs;i dica­<lb/>tur impetum &longs;ursùm men&longs;urari à differentia grauita­<lb/>tum aeris, & aquæ gr. <!-- REMOVE S-->2. non autem ab aggregato <lb/>gr. <!-- REMOVE S-->6. leuitatis illius, & grauitatis huius. </s> <s id="s.000598">Quaprop­<lb/>ter non poterit aer, vel <expan abbr="lignũ">lignum</expan> &longs;ursùm impelli ab eius <lb/>leuitate po&longs;itiua. </s> </p> <p type="margin"> <s id="s.000599"><margin.target id="marg146"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000600"><margin.target id="marg147"/>Prop. 53.</s> </p> <p type="main"> <s id="s.000601"><emph type="center"/>PROP. LVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000602"><emph type="center"/><emph type="italics"/>Idip&longs;um ostendere po&longs;ito quòd aer, & aqua vtramque vim <lb/>leuitatis, & grauitatis exerceat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000603">SVpponamus &longs;ecundo loco tam <expan abbr="aer&etilde;">aerem</expan>, quàm <expan abbr="aquã">aquam</expan> <lb/>&longs;emper retinere ambas oppo&longs;itas qualitates, <lb/>&longs;cilicèt perpetuò afficiantur ij&longs;dem gradibus graui­<lb/>tatis, atque leuitatis &longs;itque leuitas aeris F trium gra­<lb/>duum, & maior leuitate ip&longs;ius aquæ D vnius gradus; <lb/>at è contrà gradus grauitatis eiu&longs;dem aeris F gra­<lb/>dus vnius minor &longs;it pondere graduum 3. molis aquæ <lb/>D, quæ æqualis &longs;it ip&longs;i F, habebimus profectò qua-<pb pagenum="120" xlink:href="010/01/128.jpg"/><arrow.to.target n="marg148"/><lb/>tuor vires motiuas, quæ &longs;ibi mutuò aduer&longs;antur, & <lb/>in libra imaginaria BI operantur, vt nimirùm nulla <lb/>earum otiari queat, &longs;ed omnes &longs;imùl agant, & im­<lb/>pellant, igitur ex propo&longs;itionibus 50. & 54. conatus, <lb/>&longs;eù impetus quo aer F impellitur &longs;ursùm in aqua à G <lb/>versùs R ratione leuitatis men&longs;urari debet ab ex­<lb/>ce&longs;&longs;u 2. graduum quo leuitas eiu&longs;dem aeris &longs;uperat <lb/>leuitatem aquæ circumfu&longs;æ, & è <expan abbr="cõtra">contra</expan> conatus aquæ <lb/>contra aerem efficitur ab exce&longs;&longs;u grauitatis aquæ D, <lb/>&longs;upra grauitatem aeris F paritèr gr. <!-- REMOVE S-->2. & proindè <expan abbr="dũ">dum</expan> <lb/>aqua deorsùm de&longs;cendere conatur nece&longs;&longs;ariò aerem <lb/>F exprimit, ac <expan abbr="&longs;ursũm">&longs;ursum</expan> impellit; &longs;untque hæ duæ dif­<lb/>ferentiæ, &longs;eù exce&longs;&longs;us virium contrariæ inter &longs;e, &longs;ci­<lb/>licèt vna in libra imaginaria &longs;ursùm impellit, altera <lb/>verò deorsùm igitur vniuer&longs;alis conatus, & impetus <lb/>totalis quo aer F a&longs;cendit in aqua, men&longs;urari debet <lb/>ab aggregato eorumdem duorum exce&longs;&longs;uum, quod <lb/><arrow.to.target n="marg149"/><lb/>e&longs;t gr. <!-- REMOVE S-->4. non verò à differentia leuitatum, &longs;olummo­<lb/>dò gr. <!-- REMOVE S-->2. Sed hoc e&longs;t fal&longs;um contra experientiam, <expan abbr="cõ-tra">con­<lb/>tra</expan> aduer&longs;arij a&longs;&longs;ertum, & contra ea, quæ ab Archi­<lb/>mede demon&longs;trata &longs;unt, quia nimirùm conatus, & <lb/>impetus quo fertur aerea pila &longs;ursùm in aqua æqua­<lb/>lis e&longs;t differentiæ ponderum aeris, & aqu&etail;, igitur <lb/>verum <expan abbr="nõ">non</expan> e&longs;t leuitatem po&longs;itiuam in hac operati­<lb/>one concurrere. </s> </p> <p type="margin"> <s id="s.000604"><margin.target id="marg148"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000605"><margin.target id="marg149"/>Prop. 54.</s> </p> <p type="main"> <s id="s.000606">V&longs;que adhùc non con&longs;iderauimus difficultatem, <lb/>aut impedimentum, quod affert medium fluidu&mtail; <lb/>motui a&longs;cen&longs;us, vel de&longs;cen&longs;us corporum, quæ in ip­<lb/>&longs;o feruntur, erit igitur operæpretium perpender&etail; <pb pagenum="121" xlink:href="010/01/129.jpg"/>quidnam admi&longs;&longs;o, vel negato prædicto peripatetico <lb/><arrow.to.target n="marg150"/><lb/>a&longs;mpto &longs;ub&longs;equatur. </s> </p> <p type="margin"> <s id="s.000607"><margin.target id="marg150"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000608"><emph type="center"/>PROP. LIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000609"><emph type="center"/><emph type="italics"/>Aliter id ip&longs;um ostendere, po&longs;ito, quòd aer vi leuitatis per <lb/>diuer&longs;a media fluida a&longs;cendat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000610">SIt igitur idem mobile B, quod &longs;it lignum leui&longs;&longs;i­<lb/>mum, vel ve&longs;ica aere plena, impellaturque v&longs;que <lb/>ad fundum va&longs;is DCFE cuius medietas infima reple­<lb/>atur aqua A, reliqua medietas &longs;uprema O repleatur <lb/>oleo, vel &longs;piritu vini, & ponamus leuitatem aereæ <lb/>ve&longs;icæ B e&longs;&longs;e trium graduum, & leuitatem &longs;piritus <lb/>vini duorum graduum, at leuitatem aquæ magis <expan abbr="d&etilde;-&longs;æ">den­<lb/>&longs;æ</expan> e&longs;&longs;e vnius gradus. </s> <s id="s.000611">Manife&longs;tum e&longs;t, quòd re&longs;i&longs;ten­<lb/>tia aquæ A, & partium tenacitas, quæ penetrari de­<lb/>bet à ligno, vel ve&longs;ica B dùm &longs;ursùm a&longs;cendit, erit <expan abbr="tã-tò">tan­<lb/>tò</expan> maior re&longs;i&longs;tentia &longs;piritus vi­<lb/><figure id="id.010.01.129.1.jpg" xlink:href="010/01/129/1.jpg"/><lb/>ni O quantùm illa e&longs;t magis <expan abbr="d&etilde;-&longs;a">den­<lb/>&longs;a</expan>, & con&longs;tipata quàm i&longs;te, &longs;ci­<lb/>licèt &longs;i <expan abbr="&longs;umãtur">&longs;umantur</expan> moles æquales <lb/>eorumdem fluidorum, quantò <lb/>maior e&longs;t corpulentia, & mate­<lb/>ria, quæ pr&etail;dictum aqueum &longs;pa­<lb/>tium replet ea materia quæ molem &longs;piritus vini oc­<lb/>cupat, & quia <expan abbr="leuitat&etilde;">leuitatem</expan> &longs;piritus vini ad <expan abbr="leuitat&etilde;">leuitatem</expan> aquæ <lb/>eamdem proportionem habere aiunt, quam illius <lb/>raritas ad huius raritatem, igitur tantò magis di&longs;tra­<lb/>hibilis, & minùs re&longs;i&longs;tens erit &longs;piritus vini, quà&mtail; <pb pagenum="122" xlink:href="010/01/130.jpg"/><arrow.to.target n="marg151"/><lb/>aqua communis; quantò ille leuior e&longs;t aqua commu­<lb/>ni, ergò re&longs;i&longs;tentia quam aqua in fert ve&longs;icæ <expan abbr="a&longs;cend&etilde;-ti">a&longs;cenden­<lb/>ti</expan> ad re&longs;i&longs;tentiam &longs;piritus vini eamdem <expan abbr="proportion&etilde;">proportionem</expan> <lb/>reciprocè habet, quam &longs;piritus vini leuitas ad aquæ <lb/>communis leuitatem. </s> <s id="s.000612">Quapropter aqua communis <lb/>duplò re&longs;i&longs;tentior erit quàm &longs;piritus vini, veluti i&longs;te <lb/>&longs;upponitur duplò leuior illo. </s> <s id="s.000613">Modò, quia aduer&longs;arius <lb/>&longs;upponit, quòd conatus, & impetus quo a&longs;cendit <lb/>aerea ve&longs;ica per prædicta duo fluida men&longs;urari de­<lb/>beat ab exce&longs;&longs;u, &longs;eu differentia leuitatum <expan abbr="eorumd&etilde;">eorumdem</expan> <lb/>corporum, igitur aerea ve&longs;ica B, quæ tres gradùs le­<lb/>uitatis habebat, a&longs;cendet per <expan abbr="aquã">aquam</expan> A vnum gradum <lb/>leuitatis habentem conatu, &longs;eu impetu men&longs;urato à <lb/>differentia prædictarum leuitatum, quæ erit <expan abbr="duorũ">duorum</expan> <lb/>graduum, &longs;ed in &longs;piritu vini O qui duos gradus leui­<lb/>tatis habebat, a&longs;cendet, eadem pila B impetu æquali <lb/>differentiæ leuitatum <expan abbr="eorũdem">eorundem</expan> corporum, quæ erit <lb/>vnius &longs;olummodò gradus, & hæc quidem <expan abbr="con&longs;equũ-tur">con&longs;equun­<lb/>tur</expan> ex demon&longs;tratis in pr. <!-- REMOVE S-->48. & 52. qua proptèr ra­<lb/>tione differentiarum inter leuitatem corporis B, & <lb/>leuitates prædictorum fluidorum ve&longs;ica B per aquam <lb/>a&longs;cendet conatu, & impetu duplo eius, quo per &longs;pi­<lb/>ritum vini eleuatur; nihilominùs velocitas qua præ­<lb/>dicta ve&longs;ica B a&longs;cendit in aqua, non poterit e&longs;&longs;e du­<lb/>pla eius, qua &longs;ublimatur in &longs;piritu vini, licèt virtus, & <lb/>energia, qua impellitur per aquam dupla &longs;it eius, <lb/>quæ in &longs;piritu vini exercetur, proptereà quod &longs;uper­<lb/>uenit noua cau&longs;a, à qua prædicti impetus <expan abbr="retardãtur">retardantur</expan>, <lb/>& valdè alterantur, hæc verò e&longs;t maior <expan abbr="d&etilde;&longs;itas">den&longs;itas</expan> aquæ <pb pagenum="123" xlink:href="010/01/131.jpg"/>communis &longs;upra tenacitatem, & <expan abbr="cõ&longs;tipationem">con&longs;tipationem</expan> &longs;pi­<lb/><arrow.to.target n="marg152"/><lb/>ritus vini; quæ, iuxtà Ari&longs;totelis a&longs;&longs;umptum, <expan abbr="maior&etilde;">maiorem</expan> <lb/>tarditatem a&longs;cendenti corpori affert den&longs;itas aquæ, <lb/>&longs;cilicèt duplò maior, quàm &longs;it ea difficultas, qua à <lb/>&longs;piritu vini a&longs;cen&longs;us eiu&longs;dem pilæ impeditur. </s> <s id="s.000614">Hinc <lb/>&longs;equitur, quòd velocitas eiu&longs;dem pilæ B per aquam <lb/>ad eam quam habere pote&longs;t per &longs;piritum vini com­<lb/>po&longs;ita &longs;it ex duabus proportionibus, &longs;cilicèt ex pro­<lb/>portione differentiarum leuitatum eorumdem cor­<lb/>porum, quæ erit vt duo ad vnum, & ex propo&longs;itio­<lb/>ne reciproca re&longs;i&longs;tentiarum eorumdem medioru&mtail;, <lb/>quæ &longs;e habet vt vnum ad duo, &longs;ed proportio dupla, <lb/>& &longs;ubdupla componunt proportionem æqualitatis, <lb/>igitur æquali velocitate a&longs;cendet eadem ve&longs;ica B <lb/>per aquam A, & per <expan abbr="&longs;piritũ">&longs;piritum</expan> vini O, quod e&longs;t <expan abbr="euid&etilde;-tèr">euiden­<lb/>tèr</expan> fal&longs;um, & contra a&longs;&longs;ertum eorumdem aduer&longs;a­<lb/>riorum, ergo ve&longs;ica aere plena non mouetur &longs;ursùm <lb/>in fluido vi leuitatis po&longs;itiuæ, quod erat o&longs;tenden­<lb/>dum. </s> </p> <p type="margin"> <s id="s.000615"><margin.target id="marg151"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000616"><margin.target id="marg152"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000617">Sed antequam vlterius procedamus, <expan abbr="deb&etilde;t">debent</expan> ad exa­<lb/>men quoque reuocari aliæ obiectiones, quæ ab au­<lb/><arrow.to.target n="marg153"/><lb/>thoribus clari&longs;&longs;imis afferuntur contra no&longs;tram &longs;en­<lb/>tentiam. </s> <s id="s.000618">Et primò quidem con&longs;iderabo argumenta, <lb/>quæ de&longs;umuntur à pyramidali figura flammæ lucer­<lb/>næ, a qua, inquam, figura putant euidens <expan abbr="argumentũ">argumentum</expan> <lb/>deduci, quòd flamma ip&longs;a &longs;ursùm impellatur ab in­<lb/>terno principio leuitatis, &longs;icque ratiocinantur: <emph type="italics"/>Vi­<lb/>demus quieto, & tranquillo aere flammum ferri &longs;ursùm <lb/>pyramidalitèr, cùm <expan abbr="tam&etilde;">tamen</expan> &longs;i per expres&longs;ionem hic motus fie-<emph.end type="italics"/><pb pagenum="124" xlink:href="010/01/132.jpg"/><arrow.to.target n="marg154"/><lb/><emph type="italics"/>ret, inuer&longs;a flammæ figuræ e&longs;&longs;et, aut certè inferior pars non <lb/>minùs quàm &longs;uperior acuminata, vt fit in omnibus non du­<lb/>ris quando per expres&longs;ionem &longs;ursùm iaciuntur. </s> <s id="s.000619"><expan abbr="Secũdò">Secundò</expan> quin­<lb/>ta e&longs;&longs;entia vini in lapide accen&longs;a &longs;ursùm fertur non per ex­<lb/>pres&longs;ionem, &longs;ed in&longs;ita leuitate, aer enim exprimens, vel <lb/>e&longs;&longs;et &longs;ub ba&longs;i ignis auolantis, & illum protruderet, quod e&longs;t <lb/>fal&longs;um; vel &longs;uperincumbens grauitando hanc <expan abbr="expres&longs;ion&etilde;">expres&longs;ionem</expan> <lb/>efficeret; neque hoc, quia &longs;ic aer vertici ignis incumbens eum <lb/>deprimeret potiùs, ac reuerberaret deorsùm, quàm &longs;ursùm.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.000620"><margin.target id="marg153"/>Noua argu­<lb/>menta pro <lb/>leuitate po­<lb/>&longs;itiua <expan abbr="afferũ-tur">afferun­<lb/>tur</expan>.</s> </p> <p type="margin"> <s id="s.000621"><margin.target id="marg154"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000622"><emph type="center"/>PROP. LX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000623"><emph type="center"/><emph type="italics"/>Flammam in camino ab expres&longs;ione ambientis aeris <lb/>&longs;ursùm impelli.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000624">PRimæ difficultati, quòd nimirum flamma lucer­<lb/>næ in aere quieto, & tranquillo moueatur &longs;ur­<lb/>sùm &longs;ponte, non verò per extru&longs;ionem factam ab ae­<lb/>re ambiente, &longs;atisfacere nitemur adducendo experi­<lb/>menta aliqua. </s> <s id="s.000625">Videmus enim maiores, & ampliores <lb/>flammas in caminis accen&longs;as non vigere, nec diutiùs <lb/>per&longs;euerare ni&longs;i ad&longs;it aditus aeri de foris aduenienti, <lb/>per quem ingrediatur ventus perpetuus, qui inter <lb/>crura, & fœmora ignem <expan abbr="circum&longs;tãtium">circum&longs;tantium</expan> excurrit ver­<lb/>sùs flammam, e&longs;tque euidentèr &longs;en&longs;ibilis, nam &longs;i cu­<lb/>biculi o&longs;tium claudatur exten&longs;o panno, vel cortina, <lb/>vt fieri &longs;olet, h&etail;c inflatur ver&longs;us ignem camini, vt ve­<lb/>lum nauis; imò in cubiculis vndiquè diligentèr clau­<lb/>&longs;is, in quibus aer externus &longs;ubingredi nequeat non <lb/>poterit flamma &longs;ursùm impelli ab aere, quin cubi-<pb pagenum="125" xlink:href="010/01/133.jpg"/>culum inane remaneat, & <expan abbr="tũc">tunc</expan> ignis camini nullo pa­<lb/><arrow.to.target n="marg155"/><lb/>cto accendi pote&longs;t, nec in flammam verti, aut per­<lb/>durare, ni&longs;i o&longs;tiolum, vel foramen aliquod in ip&longs;o ca­<lb/>mino aperiatur, & tunc facilè flamma accenditur, & <lb/>per&longs;euerat. </s> <s id="s.000626">Ratio huius effectus pendet nedùm ab <lb/>impul&longs;u flammæ &longs;ursùm, &longs;ed etiam à rarefactione ae­<lb/>ris propè ignem exi&longs;tentis, eumque <expan abbr="ambi&etilde;tis">ambientis</expan> per to­<lb/>tam camini longitudinem, quia nempe aer prædictus <lb/>ab igne calefactus minùs grauis &longs;pecie redditur, <expan abbr="quã">quam</expan> <lb/>aer cubiculi, & externus, qui à camino di&longs;tat; Hoc <lb/>autem nece&longs;&longs;ariò aduenit ex legibus mechanicis, & <lb/>ex Archimedis <expan abbr="demõ&longs;trationibus">demon&longs;trationibus</expan>; nece&longs;sè enim e&longs;t, <lb/>vt aer rarior, & minùs grauitans &longs;ursùm expellatur <lb/>exprimaturque à grauiore aere <expan abbr="circumambi&etilde;te">circumambiente</expan>, hinc <lb/>fit vt po&longs;t a&longs;cen&longs;um illius aeris rarefacti per <expan abbr="caminũ">caminum</expan> <lb/>diminuatur moles aeris ip&longs;ius cubiculi propè, & cir­<lb/>ca caminum. </s> <s id="s.000627">Non ergo mirum e&longs;t, nouum aerem pro­<lb/>fluere ad replendum cubiculi <expan abbr="&longs;patiũ">&longs;patium</expan>, & hæc e&longs;t cau­<lb/>&longs;a, quare percipitur ventus ille, & effluuium per­<lb/>petuum dum flamma camini viget. </s> </p> <p type="margin"> <s id="s.000628"><margin.target id="marg155"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000629">Prædictum ratiocinium confirmari pote&longs;t à pul­<lb/>cherrimo experimento à D. <!-- KEEP S--></s> <s id="s.000630">Candido Buono Floren­<lb/>tiæ mihi communicato. </s> </p> <p type="main"> <s id="s.000631"><emph type="center"/>PROP. LXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000632"><emph type="center"/><emph type="italics"/>Trutinæ æquilibratæ vna lanx excalefacta <expan abbr="&longs;ursũ">&longs;ursum</expan> eleuatur <lb/>extru&longs;a à pondere aeris, reliquam lancem ambientis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000633">ERat enim trutina, &longs;eù bilanx tantæ perfectionis, <lb/>vt à quinquage&longs;ima parte vnius grani hordei, <pb pagenum="126" xlink:href="010/01/134.jpg"/><arrow.to.target n="marg156"/><lb/>imò à multo leuiori fe&longs;tuca flecti facilè po&longs;&longs;et. </s> <s id="s.000634">hæc <lb/>quidem &longs;u&longs;pen&longs;a intra armariolum vitreum, vt à &longs;or­<lb/>dibus, & venti agitatione tueretur <expan abbr="æquilibriũ">æquilibrium</expan> præ­<lb/>cisè &longs;eruabat, vt e&longs;t DE, cuius centrum C, tunc <expan abbr="sũp-ta">sump­<lb/>ta</expan> virga ferrea IF, & igni­<lb/><figure id="id.010.01.134.1.jpg" xlink:href="010/01/134/1.jpg"/><lb/>ta in eius extrema parte <lb/>F lanci A approximaba­<lb/>tur, ab&longs;que contactu, <expan abbr="tũc">tunc</expan> <lb/>libra ab æquilibrio remo­<lb/>uebatur, depre&longs;&longs;a nimi­<lb/>rum lance B, & eleuata A, <lb/><expan abbr="id&etilde;que">idemque</expan> <expan abbr="cõtingebat">contingebat</expan> trans­<lb/>lato ignito ferro infra <expan abbr="lanc&etilde;">lancem</expan>, ac priùs in &longs;uprema <expan abbr="lãcis">lancis</expan> <lb/>parte ob&longs;eruabatur: <expan abbr="ration&etilde;">rationem</expan> huius admirabilis <expan abbr="effect9">effectus</expan> <lb/><expan abbr="hãc">hanc</expan> excogitaui, & amico <expan abbr="pet&etilde;ti">petenti</expan> reddidi eamque <expan abbr="cõ-municaui">com­<lb/>municaui</expan> Societati <expan abbr="docti&longs;&longs;imorũ">docti&longs;&longs;imorum</expan> virorum à Sereni&longs;s. <lb/><!-- REMOVE S-->& Eminenti&longs;s. <!-- REMOVE S-->Cardinali Leopoldo Mediceo <expan abbr="erectã">erectam</expan>, <lb/>quam deinceps more Italico <expan abbr="Academiã">Academiam</expan> experimen­<lb/>talem Mediceam vocabo. </s> <s id="s.000635">Concipiantur duæ &longs;phæ­<lb/>rulæ aeris inter &longs;e æquales LG, & HK lances <expan abbr="ambi&etilde;-tes">ambien­<lb/>tes</expan>, quæ erunt æquè graues, &longs;cilicèt eiu&longs;dem &longs;peciei. <lb/></s> <s id="s.000636">Approximato po&longs;tea ferro ignito IF procùldubio à <lb/>profluuio ignearum exhalationum à feruente ferro <lb/>emanantium, calefit nedum lanx illa metallica A, &longs;ed <lb/>etiam &longs;phæra proximi aeris LG, quæ proindè ingen­<lb/>tem raritatem acquirit, cùmque aer ambiens LG ar­<lb/>ctè adhæreat <expan abbr="lãci">lanci</expan> A, <expan abbr="eiu&longs;q;">eiu&longs;que</expan> a&longs;peritatibus, & foueolis, <lb/>colligatus componat veluti lanuginem vnitam ip&longs;i <lb/>lanci, itaut nequeat moueri lanx A ni&longs;i &longs;ecum deferat <pb pagenum="127" xlink:href="010/01/135.jpg"/>aeream lanuginem, &longs;eu cru&longs;tam continguam, & con­<lb/><arrow.to.target n="marg157"/><lb/>nexam LG, verùm lanci oppo&longs;itæ B, adhæret &longs;phæ­<lb/>ra aerea HK den&longs;ior, vt potè non excalefacta à ferro <lb/>feruente; hinc fit vt &longs;umma lancis B vnà cum adnexa <lb/>cru&longs;ta ambientis aeris HK grauior &longs;it ærea lamina A <lb/>vnà cum rariori lanugine aeris adhærentis LG. <expan abbr="Mirũ">Mirum</expan> <lb/>igitur non e&longs;t, quòd a maiori pondere libræ extremi­<lb/>tas E deprimatur, & ei oppo&longs;ita D eleuetur. </s> <s id="s.000637">Eodem <lb/><arrow.to.target n="marg158"/><lb/>ferè modo, vt dicebam priùs, aer cubiculi circ&atail;, <lb/>caminum cùm &longs;it valdè den&longs;us, comparatus cum <expan abbr="flã-ma">flam<lb/>ma</expan>, & aere calefacto intra caminum exi&longs;tente, & <lb/>ideò valdè rarefacto, mirum non e&longs;t &longs;i proptèr illius <lb/>grauitatem excedentem &longs;ursùm exprimat leuiorem <lb/>flammam, acremque adhærentem paritèr rarum. </s> <s id="s.000638">E&longs;t <lb/>igitur euidenti&longs;&longs;imum in hi&longs;ce experimentis, quòd <lb/>aer <expan abbr="flammã">flammam</expan> ambiens, nedùm eam exprimit, &longs;ed <expan abbr="bonã">bonam</expan> <lb/>partem aeris <expan abbr="rarefactã">rarefactam</expan> vnà cum <expan abbr="flãma">flamma</expan> impellit quo­<lb/>que &longs;ursùm. </s> <s id="s.000639">Sed dicet aliquis, cur circa flamma&mtail; <lb/><arrow.to.target n="marg159"/><lb/>lucernæ non ob&longs;eruatur prædictus ventus? </s> <s id="s.000640">re&longs;pon­<lb/>detur non e&longs;&longs;e æquè &longs;en&longs;ibilem, quia nimirum lucer­<lb/>næ flamma non in&longs;inuatur intra fi&longs;tulam aliquam, vt <lb/>e&longs;t canalis camini, qui exitum habet extra <expan abbr="cubiculũ">cubiculum</expan>; <lb/>cùm ergo lucernæ flamma vndique ambiatur ab aere <lb/>aperto ab&longs;que euidenti cun motione eam impellere <lb/>&longs;ursùm pote&longs;t exprimendo, nimirùm facto breui cir­<lb/>cuitu à vertice flammæ v&longs;que ad eius ba&longs;im, & ob <lb/>flamm&etail; exiguitatem parua quoque e&longs;t moles aeris ei <lb/>contigua, qu&etail; agitatur, & conuoluitur, & hæc e&longs;t <lb/>ratio, quare circa lucernæ flammam ventus non ob-<pb pagenum="128" xlink:href="010/01/136.jpg"/><arrow.to.target n="marg160"/><lb/>&longs;eruatur &longs;imilis ei, qui propè caminum percipitur. </s> </p> <p type="margin"> <s id="s.000641"><margin.target id="marg156"/>Cap 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000642"><margin.target id="marg157"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000643"><margin.target id="marg158"/>Hæc experi<lb/>entia, & ra­<lb/>tio eius ap­<lb/>plicatur <expan abbr="flã-mæ">flanm<lb/>mæ</expan> camini <lb/>a&longs;cendentis.</s> </p> <p type="margin"> <s id="s.000644"><margin.target id="marg159"/>Ratio quare <lb/>circa lucer­<lb/>næ flammam <lb/>non percipi­<lb/>tur ventus <lb/>&longs;icuti in ca­<lb/>mino.</s> </p> <p type="margin"> <s id="s.000645"><margin.target id="marg160"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000646"><emph type="center"/>PROP. LXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000647"><emph type="center"/><emph type="italics"/><expan abbr="Ign&etilde;">Ignem</expan> non à leuitate, &longs;ed ab extru&longs;ione ambientis aeris <expan abbr="a&longs;c&etilde;-dere">a&longs;cen­<lb/>dere</expan>, euincitur ex de&longs;cen&longs;u fumi in vacuo <lb/>Torricelliano.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000648">SEd quòd reuerà ignis mo­<lb/><figure id="id.010.01.136.1.jpg" xlink:href="010/01/136/1.jpg"/><lb/>ueatur <expan abbr="&longs;ursũ">&longs;ursum</expan> per extru&longs;i­<lb/>onem ambientis aeris, <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> <lb/>a&longs;cendat &longs;ponte propria vir­<lb/>tute euidenti&longs;&longs;imè percipitur <lb/>ex hoc meo <expan abbr="experim&etilde;to">experimento</expan>, quod <lb/><expan abbr="Flor&etilde;ti&etail;">Florenti&etail;</expan> Sereni&longs;&longs;imo Leopol­<lb/>do Cardinali Mediceo <expan abbr="cõmu-nicaui">commu­<lb/>nicaui</expan>, comprobatumque fu­<lb/>it in Academia Experimentali <lb/>Medicea, & demum Exteris <lb/>per Epi&longs;tolas diuulgatum fuit. </s> </p> <p type="main"> <s id="s.000649">Sit vas vitreum AFG, cuius <lb/>longitudo EF duobus cubitis <lb/>maior &longs;it, habeatque <expan abbr="annexã">annexam</expan> <lb/>ampullam vitream CEM, &longs;it­<lb/>que incuruata eius extremitas HFG, atque duæ eius <lb/>extremitates A, & G &longs;int perforatæ, & apertæ, & pri­<lb/>ùs &longs;trictè ob&longs;erato, duplici ve&longs;ica &longs;uilla, infimo orificio <lb/>G repleatur vas vniuer&longs;um hydrargyro infu&longs;o per &longs;u­<lb/>premum os AB, po&longs;tea pilula aliqua D ex bitumine <lb/>aliquo atri coloris operculo ex bractea ferrea filo <pb pagenum="129" xlink:href="010/01/137.jpg"/>alligetur; & Orificium AB denuò ve&longs;ica tegatur, <lb/><arrow.to.target n="marg161"/><lb/>colligeturque &longs;trictè: tandèm &longs;ublata ve&longs;ica infima <lb/>G concedatur egre&longs;&longs;us hydrargyro, vt nimirùm facta <lb/>&longs;olita vacuitate aeris remaneat hydrargyrum <expan abbr="&longs;u&longs;p&etilde;-&longs;um">&longs;u&longs;pen­<lb/>&longs;um</expan> v&longs;que ad O, & altitudo GO erit proximè vnius <lb/>cubiti, & quadrantis. </s> <s id="s.000650">His præparatis &longs;umatur lens <lb/>aliqua cry&longs;tallina KL, & directè Soli S exponatur in <lb/>ea di&longs;tantia, & &longs;itu in quo præcisè vertex coni radio­<lb/>&longs;i à radijs Solis refractis conuergentibus formati ad <lb/>contactum pilæ bitumino&longs;æ D pertingat. </s> <s id="s.000651">Idip&longs;u&mtail; <lb/>fieri pote&longs;t ope &longs;peculi concaui v&longs;torij radios Solis <lb/>reflectentis, tunc lique&longs;cere incipit pila D, & fumum <lb/>emittit, in quo apparet mirabilis operatio, non enim <lb/>fumus, veluti in aere aperto accidit, &longs;ursùm a&longs;cen­<lb/>dit, &longs;ed incuruatur flectiturque deorsùm per DMN <lb/>non &longs;ecùs ac virgulæ illæ aquæ cadentis è fontibus, <lb/>inflexas, & deorsùm tendentes lineas de&longs;cribunt. </s> </p> <p type="margin"> <s id="s.000652"><margin.target id="marg161"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000653">Porrò quia fumum non minùs quàm flammam <expan abbr="leu&etilde;">leuem</expan> <lb/>e&longs;&longs;e, atque &longs;ursùm moueri &longs;ponte &longs;ua à naturali prin­<lb/>cipio impul&longs;a, <expan abbr="cõmuniter">communiter</expan> Peripatetica Schola docet, <lb/>igitur nece&longs;&longs;ario in &longs;patio illo vacuo CEN, vel &longs;al­<lb/>tèm in quo aer non degit ni&longs;i valdè expan&longs;us, & rare­<lb/>factus, fumus maiori vi &longs;ursùm a&longs;cendere deberet, <lb/>quàm in aere aperto, quia nimirùm ab aeris cor­<lb/>pulentia aliquo pacto impeditur ip&longs;ius progre&longs;­<lb/>&longs;us (videmus enim in aere aperto fumum ampliari, <lb/>di&longs;&longs;ipari, ac di&longs;pergi à prædicta aeris re&longs;i&longs;tentia,) <expan abbr="cũ-que">cun­<lb/>que</expan> in &longs;patio illo vacuo, vel à quo aer deficit po&longs;&longs;it <lb/>fumus naturali leuitate non impeditus liberiùs, & fa-<pb pagenum="130" xlink:href="010/01/138.jpg"/><arrow.to.target n="marg162"/><lb/>ciliùs eleuari, igitur omninò nece&longs;sè e&longs;&longs;et vt fumus <lb/>in prædicto vacuo &longs;patio a&longs;cenderet &longs;ursùm, veluti <lb/>eius natura exigit, & è contrà e&longs;&longs;et impo&longs;&longs;ibile vt <lb/>deorsùm deprimeretur, & caderet, vt virgulæ deci­<lb/>dentes aquæ fontium flectuntur deorsùm; quia verò <lb/>hoc experientiæ repugnat non poterit dici, quòd fu­<lb/>mus &longs;it leuis, &longs;ed è contrà grauis erit. </s> <s id="s.000654">Cùm verò i&ntail; <lb/>aere idem fumus &longs;ursùm a&longs;cendat, <expan abbr="dic&etilde;dum">dicendum</expan> e&longs;t quòd <lb/>ab aere ambiente grauiori in &longs;pecie, quàm &longs;it fumus <lb/>iuxtà leges mechanicas libræ aer <expan abbr="prem&etilde;s">premens</expan> per extru­<lb/>&longs;ionem &longs;ursùm fumum minùs grauem expellit. </s> </p> <p type="margin"> <s id="s.000655"><margin.target id="marg162"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000656"><emph type="center"/>PROP. LXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000657"><emph type="center"/><emph type="italics"/>Figuram pyramidalem flammæ lucernæ non &longs;uadere eam à <lb/>vi leuitatis &longs;ursùm impelli.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000658">VErùm, quod ad formam pyramidalem flammæ <lb/>lucernæ pertinet, non videtur, quòd eius figu­<lb/>ra conica nece&longs;&longs;ariò per&longs;uadeat, & conuincat flam­<lb/>mam &longs;ursùm &longs;ponte &longs;ua, & propria virtute leuitatis <lb/>a&longs;cendere, nam &longs;iue per extru&longs;ionem ambientis flui­<lb/>di violenter, &longs;iuè &longs;ponte à vi leuitatis &longs;ursùm moue­<lb/>ri &longs;upponamus, retinere æquè benè po&longs;&longs;et eamde&mtail; <lb/>conicam <expan abbr="figurã">figuram</expan>, vt inferiùs o&longs;tendemus. </s> <s id="s.000659">Præterea &longs;i <lb/>vera cau&longs;a figuræ pyramidalis flammæ lucernæ e&longs;&longs;et <lb/>eius leuitas po&longs;itiua, deberet eadem leuitas po&longs;itiua <lb/>eumdem effectum producere in reliquis omnibus <lb/>corporibus fluidis paritèr ab ip&longs;a impul&longs;is, &longs;i tamen <lb/>reliqua &longs;int paria, &longs;cilicèt fumus non &longs;ecùs ac flam-<pb pagenum="131" xlink:href="010/01/139.jpg"/>ma corpus fluidum, & rarum e&longs;t, cuius continentèr <lb/><arrow.to.target n="marg163"/><lb/>vna pars po&longs;t aliam generatur, & eructatur à po­<lb/>ris eiu&longs;dem titionis, pariterque fumum leuitate&mtail; <lb/>po&longs;itiuam habere, & exercere <expan abbr="&longs;upponũt">&longs;upponunt</expan> non minùs, <lb/>quàm flamma habet, igitur nece&longs;&longs;ariò fumus a&longs;cen­<lb/>dens, & digrediens à titione deberet formam pyra­<lb/>midalem acquirere &longs;imilem ei, quam flamma lucer­<lb/>næ habet, deberetque paritèr in acumen &longs;ubtile &longs;u­<lb/>periùs de&longs;inere, quod profectò e&longs;t fal&longs;um, & contra <lb/>&longs;en&longs;us euidentiam, pro&longs;equitur enim fumus &longs;uu&mtail; <lb/>iter longo tractu &longs;ursùm ab&longs;que eo quòd in acumen <lb/>reducatur. </s> </p> <p type="margin"> <s id="s.000660"><margin.target id="marg163"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000661">Id ip&longs;um continget, &longs;i fi&longs;tula aliqua aer in fundo <lb/>aquæ in&longs;uffletur, <expan abbr="con&longs;pici&etilde;tur">con&longs;picientur</expan> enim eleuari innume­<lb/>ræ ampullæ aere&etail;, quæ ab inuicem &longs;eparantur ab&longs;­<lb/>que eo quòd pyramidalem figuram acquirant, licèt <lb/>aer non minùs quàm flamma leuis reputetur, & ab in­<lb/>trin&longs;eco principio &longs;ursùm moueri credatur, cùmque <lb/>vna, & eadem cau&longs;a non po&longs;&longs;it diuer&longs;os effectus pro­<lb/>ducere, concedant nece&longs;sè e&longs;t, figuram, quam in <expan abbr="flã-ma">flam­<lb/>ma</expan> ob&longs;eruamus diuer&longs;am à figura fumi, & aeris per <lb/>aquam a&longs;cendentis ab alia cau&longs;a longè diuer&longs;a de­<lb/>pendere, non autem à prædicto principio intrin&longs;eco <lb/>leuitatis. </s> </p> <p type="main"> <s id="s.000662">Et profectò &longs;i attentè perpendamus fumi, & flam­<lb/>mæ con&longs;i&longs;tentias, valdè inter &longs;e differre reperiemus, <lb/>licèt ambo &longs;int corpora rara, & fluida. <pb pagenum="132" xlink:href="010/01/140.jpg"/><arrow.to.target n="marg164"/></s> </p> <p type="margin"> <s id="s.000663"><margin.target id="marg164"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000664"><emph type="center"/>PROP. LXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000665"><emph type="center"/><emph type="italics"/>Fumi structura, & compo&longs;itio declaratur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000666">COn&longs;tat fumum e&longs;&longs;e ma&longs;&longs;am copio&longs;am particula­<lb/>rum exiguarum olei, terræ, & aquæ, quæ par­<lb/>ticulæ ab inuicem di&longs;cretæ, & &longs;eparatæ nondù&mtail; <lb/>accen&longs;æ &longs;unt, licèt valdè excalefactæ &longs;int. </s> <s id="s.000667">hoc planè <lb/>confirmatur ab operatione chymica, po&longs;&longs;unt eni&mtail; <lb/>recolligi ex fumo partes aqueæ &longs;egregatæ, & di&longs;cre­<lb/>tæ à partibus vnctuo&longs;is, & &longs;ulphureis, nec non à <lb/>particulis terreis, & fuligino&longs;is, & vici&longs;&longs;im quæli­<lb/>bet ex prædictis &longs;ub&longs;tantijs recuperari pote&longs;t &longs;epa­<lb/>rata à reliquis; præterea con&longs;tat &longs;en&longs;u, fumum no&ntail; <lb/>e&longs;&longs;e corpus continuum, &longs;ed aggregatum ex particu­<lb/>lis minimis ab inuicem &longs;eparatis, & di&longs;cretis, vt præ­<lb/>clarè in nebula ob&longs;eruatur, & in alijs aqueis vapo­<lb/>ribus, qui &longs;i attentè con&longs;piciantur in loco commodo, <lb/>ide&longs;t &longs;i interpo&longs;ita nebula vi&longs;us dirigatur in&longs;piciat­<lb/>que ob&longs;curum, & tenebro&longs;um aliquem locum, & in­<lb/>terim Sol transuer&longs;alitèr eamdem nebulam illu&longs;tret; <lb/>tunc illa nebula, quæ repre&longs;entabatur continua ap­<lb/>paret e&longs;&longs;e conflata ex immen&longs;a multitudine exiguo­<lb/>rum granulorum aquæ, quæ lento quodam motu per <lb/>aerem agitantur, vt contingit in ijs fragmentis ter­<lb/>reis minuti&longs;&longs;imis, quæ con&longs;piciuntur in radijs Solis <lb/>intra cubicula. </s> <s id="s.000668">Iam prædicta granula aquea copio­<lb/>&longs;i&longs;&longs;ima vagantia per aerem non facile vi&longs;ibilia &longs;unt <lb/>&longs;igillatim ob eorum exiguitatem, &longs;ed po&longs;&longs;unt tran-<pb pagenum="133" xlink:href="010/01/141.jpg"/>&longs;itum luci impedire, & componunt apparentiam il­<lb/><arrow.to.target n="marg165"/><lb/>lam vnius &longs;ub&longs;tantiæ raræ, & expan&longs;æ, vti pariter <lb/>multoties accidit in tempore pluuiæ, quo guttæ <lb/>aquæ decidentes ab inuicem &longs;eparat&etail;, &longs;i à loco aliquo <lb/>di&longs;tanti, & remoto in&longs;piciantur, &longs;imillimæ videntur <lb/>nebulis, & fumo. </s> </p> <p type="margin"> <s id="s.000669"><margin.target id="marg165"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000670"><emph type="center"/>PROP. LXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000671"><emph type="center"/><emph type="italics"/>Fumus non e&longs;t res accen&longs;a, & quamobrem ab ambiente ac­<lb/>re &longs;ursùm exprimi pote&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000672">QVòd po&longs;tea partes minimæ fumum componen­<lb/>tes non &longs;int adhùc accen&longs;æ, experientia <expan abbr="cõ&longs;tat">con&longs;tat</expan>, <lb/>quia videmus multoties fumum accendi, atque in­<lb/>flammari <expan abbr="quãdo">quando</expan> eum <expan abbr="tãgit">tangit</expan> flamma viua alicuius can­<lb/>delæ, prætereà videtur quoque impo&longs;&longs;ibile fumum <lb/>e&longs;&longs;e rem accen&longs;am, quia nimirùm fumus gignitur in <lb/>cauitatibus, atque poro&longs;itatibus internis &longs;igni, vel <lb/>cuiuslibet alterius corporis fumum eructantis, &longs;ed <lb/>in hi&longs;ce locis angu&longs;tis re&longs;tricti&longs;que nedum fumus ac­<lb/>cendi non pote&longs;t, vt è contrà flammæ ip&longs;æ iam <expan abbr="acc&etilde;-&longs;æ">accen­<lb/>&longs;æ</expan> in ei&longs;dem locis angu&longs;tis conclu&longs;i&longs;que momento <lb/>extinguantur, &longs;uffocenturque; imò licet concauita­<lb/>tes cauerno&longs;æ &longs;int ampl&etail;, vt e&longs;t cauitas alicuius later­<lb/>næ vndique occlu&longs;æ, &longs;ubitò <expan abbr="flãma">flamma</expan> extinguitur, <expan abbr="quã-tò">quan­<lb/>tò</expan> magis hoc fieri debet quando cauitates, & poro­<lb/>&longs;itates &longs;unt re&longs;trictæ, & angu&longs;ti&longs;&longs;imæ, vt &longs;unt pori li­<lb/>gni, vel alterius con&longs;imilis corporis. </s> <s id="s.000673">Licèt ergo præ­<lb/>dicta fragmenta exigua fumum componentia <expan abbr="nõ">non</expan> &longs;int <pb pagenum="134" xlink:href="010/01/142.jpg"/><arrow.to.target n="marg166"/><lb/>actu accen&longs;a, vel <expan abbr="inflãmata">inflammata</expan> nihilominùs valdè exca­<lb/>lefacta, & rara e&longs;&longs;e &longs;olent, & hæc quidem raritas, & <lb/>agitatio <expan abbr="earũd&etilde;">earundem</expan> fumi <expan abbr="particularũ">particularum</expan>, producta ab exha­<lb/>lationibus igneis, à quibus priùs euul&longs;æ, & &longs;egre­<lb/>gatæ fuerunt à ma&longs;&longs;a lignea, vel alterius corporis, e&longs;t <lb/>in cau&longs;a vt non po&longs;&longs;int ampliùs in angu&longs;tis illis poro­<lb/>&longs;itatibus retineri, & proindè coguntur ingenti impe­<lb/>tu eructari, effluere que per orificia patentia earum­<lb/>dem poro&longs;itatum, quæ orificia cùm vndique pateant, <lb/>fit vt fumus exeat nedùm è parte &longs;uprema ligni, &longs;ed <lb/>etiam à parte infima, & laterali. </s> <s id="s.000674">Diffractis itaque re­<lb/>pagulis carcerum, egre&longs;&longs;i&longs;que fumi partibus in aere <lb/>aperto non &longs;ine &longs;ocietate ignearum exhalationu&mtail; <lb/>ma&longs;&longs;am componunt minùs grauem ip&longs;o aere <expan abbr="ambi&etilde;-te">ambien­<lb/>te</expan>, & ideò poterunt ab eodem exprimi, & lento mo­<lb/>tu impelli &longs;ursùm atque tàm diù a&longs;cen&longs;us per&longs;euera­<lb/>bit, quou&longs;que exhalationes igneæ ab ip&longs;is particulis <lb/>fumi non di&longs;cedant <expan abbr="exhal&etilde;tque">exhalentque</expan>, & pariter v&longs;quequò <lb/>deficiat impetus præconceptus ab ip&longs;o impul&longs;u præ­<lb/>cedenti, à quo lento quidem motu per aerem <expan abbr="fluctuã-do">fluctuan­<lb/>do</expan> aliquanti&longs;per fumi commoueri poterunt, cù&mtail; <lb/>præterea exiguitas particularum eiu&longs;dem fumi cau­<lb/>&longs;a &longs;ufficiens &longs;it, vt diù à qualibet minima aeris agita­<lb/>tione <expan abbr="&longs;u&longs;p&etilde;&longs;æ">&longs;u&longs;pen&longs;æ</expan> retineri po&longs;&longs;int, vt videmus puluerem <lb/>terre&longs;trem graui&longs;&longs;imum per aerem di&longs;pergi, ibiqu&etail; <lb/>diù retineri, vt experientia docet. <pb pagenum="135" xlink:href="010/01/143.jpg"/><arrow.to.target n="marg167"/></s> </p> <p type="margin"> <s id="s.000675"><margin.target id="marg166"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000676"><margin.target id="marg167"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000677"><emph type="center"/>PROP. LXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000678"><emph type="center"/><emph type="italics"/>Fumi non ab impetu quo eructantur ad altis&longs;imas regiones <lb/>perduci po&longs;&longs;unt, &longs;ed minùs graues redditi ab igniculo­<lb/>rum commixtione exprimi ab ambiente aere <lb/>po&longs;&longs;unt.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000679">ET notandum e&longs;t, quòd ab&longs;que exhalationibus <lb/>igneis non po&longs;&longs;ent ad in&longs;ignem altitudine&mtail; <lb/>fumi particulæ eleuari, quia licèt impetus ex &longs;ui na­<lb/>tura, quo à ligni poro&longs;itatibus eructantur, vim per &longs;e <lb/>haberet ad eas longiùs eleuandas, nihilominùs, quia <lb/>huiu&longs;modi impetus facillimè debilitatur extingui­<lb/>turque à particulis aeris quie&longs;centibus, vel prædicto <lb/>motu priuatis, quibus occurrunt fumi, non po&longs;&longs;et eius <lb/>a&longs;cen&longs;us longiùs propagari, &longs;ed citò extingueretur. <lb/></s> <s id="s.000680">Vlteriùs &longs;i re vera fumi à ligno eructati virtute im­<lb/>petus <expan abbr="præcõcepti">præconcepti</expan> ad <expan abbr="tãtã">tantam</expan> <expan abbr="altitudin&etilde;">altitudinem</expan> <expan abbr="a&longs;c&etilde;der&etilde;t">a&longs;cenderent</expan>, <expan abbr="nõ">non</expan> <expan abbr="au-t&etilde;">au­<lb/>tem</expan> ob <expan abbr="&longs;ocietat&etilde;">&longs;ocietatem</expan> ignearum <expan abbr="exhalationũ">exhalationum</expan>, &longs;equeretur, &qtail; <lb/><expan abbr="nõ">non</expan> &longs;emper fumus ad <expan abbr="eãd&etilde;">eandem</expan> atmo&longs;phær&etail; &longs;ummitatem <lb/>a&longs;cenderet, is enim qui per poros laterales ligni e­<lb/>greditur, impetum proiectitium tran&longs;uer&longs;alem acqui­<lb/>reret, & ideò pro&longs;equi &longs;uum motum deberet per pla­<lb/>num horizontalem, neque ab incepto itinere tanto­<lb/>pere deuiaret: &longs;imiliter fumus ille, qui ab infima par­<lb/>te titionis in aere &longs;u&longs;pen&longs;i exit, impetum acquirit ten­<lb/>dendi deorsùm, non &longs;ursùm, proindeque deberet di­<lb/>rectè profluere v&longs;que ad pauimentum, & deinceps <lb/>non po&longs;&longs;et ad &longs;u premam aeris regionem perduci, <pb pagenum="136" xlink:href="010/01/144.jpg"/><arrow.to.target n="marg168"/><lb/>quæ omnia fal&longs;a &longs;unt, & contra &longs;en&longs;us euidentiam; <lb/>Fatendum igitur e&longs;t, ab igneis particulis fumum ra­<lb/>refactum eleuari ab impul&longs;u grauioris aeris ambien­<lb/>tis per expre&longs;&longs;ionem. </s> </p> <p type="margin"> <s id="s.000681"><margin.target id="marg168"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000682"><emph type="center"/>PROP. LXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000683"><emph type="center"/><emph type="italics"/>Flamma e&longs;t fumus accen&longs;us magis rarefactus, qui ab aere <lb/>ambiente velocis&longs;imè &longs;ursùm exprimitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000684">PErcepta iam & declarata fumi <expan abbr="cõ&longs;tructione">con&longs;tructione</expan> per­<lb/>pendere modò iuuat metamorpho&longs;im, qua&mtail; <lb/>patitur quando inflammatur. </s> <s id="s.000685">Debemus igitur con­<lb/>cipere minimas particulas &longs;ulphureas in fumo con­<lb/>tentas, cùm inflammantur, maximè dilatari, rarefieri, <lb/>& vehementi&longs;&longs;imè agitari, & in hoc con&longs;i&longs;tere eius <lb/>accen&longs;ionem, &longs;ed granula illa aquea, & terrea eiu&longs;­<lb/>dem fumi, quæ ex &longs;ua natura accen&longs;ibilia non &longs;unt, <lb/>poterunt tantummodò rarefieri multò magis, quàm <lb/>priùs. </s> <s id="s.000686">iam à prædicta ferè <expan abbr="mom&etilde;tanea">momentanea</expan> rarefactione, <lb/>agitatione, & accen&longs;ione &longs;ub&longs;equitur con&longs;equen­<lb/>tèr &longs;plendida, & lumino&longs;a apparentia flammæ. </s> <s id="s.000687">Ad <lb/>hæc aeris ambientis grauitas, licèt exigua &longs;it, &longs;upe­<lb/>rabit nihilominùs notabili exce&longs;&longs;u minimum, & in­<lb/>&longs;en&longs;ibile pondus ip&longs;ius flammæ multò, & multò ma­<lb/>gis, quàm &longs;uperauerat pondus <expan abbr="præced&etilde;tis">præcedentis</expan> fumi:hinc <lb/>nece&longs;&longs;ariò flamma ab ip&longs;o aere per extru&longs;ionem &longs;ur­<lb/>sùm impelletur ineffabili velocitate. </s> <s id="s.000688">Et hìc plurima <lb/>aduertenda &longs;unt. <pb pagenum="137" xlink:href="010/01/145.jpg"/><arrow.to.target n="marg169"/></s> </p> <p type="margin"> <s id="s.000689"><margin.target id="marg169"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000690"><emph type="center"/>PROP. LXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000691"><emph type="center"/><emph type="italics"/>Flamma rarior fumo minus &longs;patium occupat ob <expan abbr="maximã">maximam</expan> <lb/>eius velocitatem, redditurque po&longs;tea inui&longs;ibilis noua <lb/>de cau&longs;a, & tactui languida ob eius <lb/>di&longs;per&longs;ionem.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000692">OB&longs;eruatur profectò titionem fumi copiam <expan abbr="ing&etilde;-tem">ingen­<lb/>tem</expan> euomere, &longs;ed &longs;i denuò eius flamma reui­<lb/>ui&longs;cat, h&etail;c mirabili velocitate fumi illius va&longs;tam mo­<lb/>lem ab&longs;umere videtur, eumque in exiguum &longs;patium <lb/>flammæ concludere, cùm reuera non &longs;it re&longs;trictio, <lb/>flamma enim maiorem raritatem habet, quàm fumus, <lb/>pendet ergo hoc ab ineffabili velocitate partiu&mtail; <lb/>flammæ. </s> <s id="s.000693">aliundè enim notum e&longs;t per re&longs;trictum flu­<lb/>minis canalem molem ampli&longs;&longs;imam aquæ totius flu­<lb/>minis pertran&longs;ire, non quia in exiguo, & re&longs;tricto illo <lb/>&longs;patio canalis conden&longs;etur tota aqua fluuij, &longs;ed quia <lb/>veloci&longs;&longs;imo motu per eum excurrit; cùm è contrà in <lb/>parte ampla fluuij aqua lenti&longs;&longs;imo cur&longs;u progredia­<lb/>tur, &longs;ic paritèr in fumo particulæ eius lento, & tardo <lb/>gradu excurrentes amplum, & grande &longs;patium oc­<lb/>cupabant, in flamma verò <expan abbr="eæd&etilde;">eædem</expan> particulæ veluti per <lb/>&longs;tricti&longs;&longs;imum canalem mirabili, & ineffabili veloci­<lb/>tate currunt, & &longs;ic po&longs;&longs;unt exiguum &longs;patium comple­<lb/>re. </s> <s id="s.000694">Sed quare flamma vltra verticem eius non exten­<lb/>ditur, neque vi&longs;ibilis redditur? </s> <s id="s.000695">hìc primò <expan abbr="dicendũ">dicendum</expan>, <lb/>quòd reuerà flamma producitur vltra eius verticem <lb/>per notabile &longs;patium, & hoc quidem percipitur non <pb pagenum="138" xlink:href="010/01/146.jpg"/><arrow.to.target n="marg170"/><lb/>vi&longs;u, &longs;ed tactu, po&longs;&longs;um enim ab&longs;que noxa manum ad <lb/>latus flammæ approximare, vt ferè eam contingam, <lb/>non verò po&longs;&longs;um manum &longs;upra flammæ verticem i&ntail; <lb/>notabili di&longs;tantia vnius palmi ab&longs;que dolore, & v­<lb/>&longs;tione retinere, igitur dicendum e&longs;t, quòd &longs;ub&longs;tan­<lb/>tia illa ignita vltra verticem flammæ redditur tran&longs;­<lb/>parens, & ideò inui&longs;ibilis alia noua de cau&longs;a efficitur. <lb/></s> <s id="s.000696">Sed tamen negari non pote&longs;t productio, & exten&longs;io <lb/>&longs;ub&longs;tantiæ igneæ vltra flammam productæ, cùm hoc <lb/>ab ip&longs;o tactu conuincatur. </s> <s id="s.000697">Sed dices, quare &longs;upra <expan abbr="flã-mæ">flam­<lb/>mæ</expan> verticem in multò maiori altitudine non ampliùs <lb/>tactu percipitur effluuium calidi&longs;&longs;imum eius, vt pro­<lb/>pè eius verticem percipiebatur? </s> <s id="s.000698">At for&longs;an hoc acci­<lb/>dit, quia ignea &longs;ub&longs;tantia fluidi&longs;&longs;ima ab occur&longs;u aeris <lb/>di&longs;pergitur, & &longs;ubdiuiditur in alias partes minores <lb/>ab inuicem diui&longs;as, & di&longs;cretas, vt videmus aquæ <lb/>copiam è &longs;umma turri delap&longs;am in progre&longs;&longs;u de&longs;cen­<lb/>&longs;us &longs;ubdiuidi in innumeras guttulas inter &longs;e di&longs;cre­<lb/>tas, & &longs;icuti non æquè humectat, & madefacit pluuia <lb/>illa, ac ma&longs;&longs;a integra aquæ vnita, quia nimirùm nul­<lb/>la pars &longs;ubiecti corporis à ma&longs;&longs;a continua aquæ tacta <lb/>relinquitur arida, cùm in pluuia non omnes partes &longs;o­<lb/>li <expan abbr="madefiãt">madefiant</expan> humectentur que, ita propè verticem <expan abbr="flã-mæ">flam<lb/>mæ</expan> ignis vnitus manum percutit, atque terebrat, <expan abbr="cũ">cum</expan> <lb/>è <expan abbr="cõtra">contra</expan> in remotiori altitudine &longs;picula illa ignea val­<lb/>dè di&longs;creta plagas exiguas, & inter &longs;e di&longs;tantes i&ntail; <lb/>ip&longs;a manu inferant, & hinc minori noxa, minorique <lb/>dolore incur&longs;us ignis tolerari poterit. <pb pagenum="139" xlink:href="010/01/147.jpg"/><arrow.to.target n="marg171"/></s> </p> <p type="margin"> <s id="s.000699"><margin.target id="marg170"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000700"><margin.target id="marg171"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000701"><emph type="center"/>PROP. LXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000702"><emph type="center"/><emph type="italics"/>Flammæ candelæ vertex acuminatur, quia magis accen­<lb/>&longs;us, & ideò velociùs a&longs;cendit, quàm ba&longs;is eius.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000703">PRæterea <expan abbr="&longs;uppon&etilde;dum">&longs;upponendum</expan> e&longs;t, flammam candelæ <expan abbr="nõ">non</expan> <lb/>habere con&longs;i&longs;tentiam homogeneam, & &longs;imila­<lb/>rem, pars enim infima flammulæ non e&longs;t omninò ac­<lb/>cen&longs;a, quod con&longs;tat ex eius colore &longs;ubliuido, quia <lb/>nimirùm fumi oleo&longs;i eructati ab elicnio, vel ligno <expan abbr="nõ">non</expan> <lb/>in in&longs;tanti, &longs;ed in <expan abbr="t&etilde;pore">tempore</expan> accendi debent, igitur veri­<lb/>&longs;imile e&longs;t, quòd <expan abbr="nõ">non</expan> omnes pr&etail;dicti fumi &longs;ubitò po&longs;t e­<lb/>gre&longs;&longs;um in ip&longs;o contactu ba&longs;is flammæ &longs;imùl, & inte­<lb/>grè accendantur, & propterea rarefactio, & accen­<lb/>&longs;io continuatur dùm actu excurrunt illæ particulæ à <lb/>ba&longs;i versùs verticem flammæ. </s> <s id="s.000704">Modò &longs;i in ba&longs;i flam­<lb/>mulæ fumi non &longs;unt omninò, & integrè accen&longs;i, non <lb/>habebunt veloci&longs;&longs;imum illum motum, cuius capax <lb/>e&longs;t flammæ puræ natura, igitur in ip&longs;a flamma conci­<lb/>pi debet pars infima tardior, quàm &longs;uprema, & ver­<lb/>ticalis, &longs;ed &longs;icuti in fluuio nulla alia de cau&longs;a tant&atail; <lb/>copia aquæ in angu&longs;ti&longs;&longs;imum &longs;patium aluei re&longs;trin­<lb/>gitur coangu&longs;taturque, ni&longs;i quia veloci&longs;&longs;imè excur­<lb/>rit, cùm è contrà in locis dilatatis, & amplis eadem <lb/>aquæ fluminis moles amplius &longs;patium aluei ob eius <lb/>tarditatem occupet, ita in flamma lucernæ, quæ vt <lb/>fluuius ignis excurrentis concipi pote&longs;t, mirum <expan abbr="nõ">non</expan> <lb/>e&longs;t, quòd in ba&longs;i propè elicnium ob tarditatem eius <lb/>fluxus ampliorem &longs;itum occupet, quàm in eius ver-<pb pagenum="140" xlink:href="010/01/148.jpg"/><arrow.to.target n="marg172"/><lb/>tice, vbi velociori cur&longs;u fugit. </s> </p> <p type="margin"> <s id="s.000705"><margin.target id="marg172"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000706">Hinc colligitur, quòd ex figura pyramidali, & a­<lb/>cuminata flammæ lucernæ non euincitur eam à vi <lb/>intrin&longs;eca leuitatis &longs;ursùm impelli. </s> <s id="s.000707">Cùm è contrà de­<lb/><arrow.to.target n="marg173"/><lb/>claratum &longs;it, qua ratione ab&longs;que po&longs;itiua leuitate ab <lb/>expre&longs;&longs;ione aeris grauioris ambientis &longs;ursùm expel­<lb/>latur, pariterque o&longs;ten&longs;a e&longs;t cau&longs;a prædictæ eius fi­<lb/>guræ acuminatæ & in verticem de&longs;inentis, quæ non <lb/>pendet à leuitate propria, &longs;ed ab expre&longs;&longs;ione aeris <lb/>maxima velocitate facta in eius acumine magis <expan abbr="acc&etilde;-&longs;o">accen­<lb/>&longs;o</expan>, & hoc confirmatur ex eo quòd multotiès flammæ <lb/>candelarum non &longs;unt pyramidales, &longs;ed rotundæ, aut <lb/>oblongæ, & ouales, & hoc clarè con&longs;picitur quandò <lb/>virga illa fumo&longs;a, quæ eructatur ab infima lucern&atail; <lb/>nupèr extincta, denuò accenditur à contactu alte­<lb/>rius flammæ in notabili di&longs;tantia ab inferiori cande­<lb/>la, & tunc fumus inflammatus per longitudinem to­<lb/>tius fumi &longs;ubiecti deorsùm labitur v&longs;que ad <expan abbr="elicniũ">elicnium</expan> <lb/><arrow.to.target n="marg174"/><lb/>&longs;ubiectæ lucernæ, con&longs;piciturque euidentèr figura <lb/>illius fumi <expan abbr="acc&etilde;&longs;i">accen&longs;i</expan> perfectè <expan abbr="rotũda">rotunda</expan>, imò <expan abbr="cũ">cum</expan> primò lu­<lb/>cerna accenditur, eius flamma rotunda e&longs;t, & po&longs;tea <lb/>verticem conicum acquirit. </s> <s id="s.000708">in flammis verò camini <lb/>non ob&longs;eruantur formæ pyramydales, &longs;ed multipli­<lb/>citèr diui&longs;æ multotiès radios, &longs;eù linguas referunt, <lb/>& aliquando rotundæ con&longs;piciuntur, & &longs;ic eleuan­<lb/>tur per aliquod &longs;patium. </s> <s id="s.000709">Sed de his &longs;atis. <pb pagenum="141" xlink:href="010/01/149.jpg"/><arrow.to.target n="marg175"/></s> </p> <p type="margin"> <s id="s.000710"><margin.target id="marg173"/>Concluditur <lb/>quod ex &longs;i­<lb/>gura acumi­<lb/>nata flammæ <lb/>lucernæ non <lb/>euincitur <lb/>hanc à vi le­<lb/>uitatis <expan abbr="afc&etilde;-dere">afcen­<lb/>dere</expan>.</s> </p> <p type="margin"> <s id="s.000711"><margin.target id="marg174"/>Præterea all­<lb/>quæ flammæ <lb/>candelæ &longs;unt <lb/>rotundæ, & <lb/>flammæ ca­<lb/>mini &longs;unt al <lb/>terius figu­<lb/>ræ.</s> </p> <p type="margin"> <s id="s.000712"><margin.target id="marg175"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000713"><emph type="center"/>PROP. LXX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000714"><emph type="center"/><emph type="italics"/>Flammain &longs;piritu vini accenditur extra, & longè ab ip&longs;o­ <lb/>&longs;piritu, & ideò pote&longs;t exprimi &longs;ursùm <lb/>ab ambiente aere.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000715">VIdeamus modò an ex accen&longs;ione vini &longs;piritus <lb/>deducatur a&longs;&longs;ertio leuitatis po&longs;itiuæ. </s> <s id="s.000716">Et hic <lb/>denuò dico, quòd flamma &longs;piritus vini non e&longs;t actu <lb/>accen&longs;a in poris internis prædicti liquoris, &longs;ed &longs;icuti <lb/>de fumis lignorum dictum e&longs;t, educitur è &longs;piritus vi­<lb/>ni fiuore fumo&longs;a quædam ma&longs;&longs;a rari&longs;&longs;ima, quæ in po­<lb/>ro&longs;itatibus fluoris cùm retineri nequeat, ruptis car­<lb/>cerum repagulis ingenti impetu per orificia poro&longs;a <lb/>vndique fluorem ambientia eructat, & po&longs;tmodu&mtail; <lb/>flammam concipit, accenditurque in aliqua &longs;en&longs;ibi­<lb/>li di&longs;tantia à dicto fluore: hoc confirmatur exemplo <lb/>illius effluuij fumo&longs;i, egredientis ab aliqua titionis <lb/>poro&longs;itate, quod po&longs;tmodum accenditur in di&longs;tan­<lb/>tia vnius digiti ab ip&longs;o ligno, & &longs;peciem præbet flu­<lb/>oris bitumino &longs;i lateralitèr defluentis, qui in aer&etail; <lb/>ignem concipiat. </s> <s id="s.000717">Cùm igitur ab omnibus poro&longs;ita­<lb/>tibus &longs;piritus vini, & cuiuslibet materiei accen&longs;ibi­<lb/>lis vndequaque &longs;ursùm, deorsùm, & lateralitèr fu­<lb/>mo&longs;æ exhalationes egrediantur, quæ po&longs;tea in ip&longs;o <lb/>aere aperto inflammentur, & accendantur, non vi­<lb/>detur difficile vt aer po&longs;&longs;it infra flammam accen&longs;am, <lb/>& lateralitèr eam comprimere, & proinde expre&longs;&longs;io­<lb/>ne facta eam &longs;ursùm impellere: & <expan abbr="notandũ">notandum</expan> e&longs;t, quòd <pb pagenum="142" xlink:href="010/01/150.jpg"/><arrow.to.target n="marg176"/><lb/>expre&longs;&longs;io, quæ ab aere efficitur, non &longs;emper a&longs;&longs;imila­<lb/>tur ei, quæ ex compre&longs;&longs;ione po&longs;tica digitorum crea­<lb/>tur, veluti prunorum nucleos à digitis po&longs;ticè com­<lb/>pre&longs;&longs;is pueri proijcere longè &longs;olent, vtque aduer&longs;a­<lb/>rius exi&longs;timabat, &longs;ed expul&longs;io, & expre&longs;&longs;io flammæ <lb/><arrow.to.target n="marg177"/><lb/>facta ab aere circumfu&longs;o fit, vt exigit ratio mechani­<lb/>ca &longs;iphonis &longs;ursùm inuer&longs;i vt ex elementis hidro&longs;ta­<lb/>ticis con&longs;tat, vtque meliùs inferiùs declarabitur vn­<lb/>de malè infertur, quòd &longs;i flamma expul&longs;a e&longs;&longs;et ab am<lb/>biente aere, deberet fieri acuminata in eius ba&longs;i, & <lb/>rotunda in eius vertice. </s> </p> <p type="margin"> <s id="s.000718"><margin.target id="marg176"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000719"><margin.target id="marg177"/>Cap. 2.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000720"><emph type="center"/>PROP. LXXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000721"><emph type="center"/><emph type="italics"/>Flamma in &longs;piritu vini accen&longs;a non debet ab aere incum­<lb/>bente contundi, cùm ab eius pondere non exprimatur <lb/>&longs;ursùm, &longs;ed ab aere collaterali infernè reflexo.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000722">PO&longs;trema in&longs;tantia, quòd aer flammæ <expan abbr="&longs;uperincũ-bens">&longs;uperincun­<lb/>bens</expan> potiùs eam deberet contundere, & dila­<lb/>tare, & deorsùm eam diuerberare, <expan abbr="nõ">non</expan> autem in acu­<lb/>tiem &longs;ublimare, facilè &longs;oluitur, quia aer fluidus non <lb/>&longs;olùm &longs;upremus, & flammæ incumbens, &longs;ed etia&mtail; <lb/>lateralis, & infimus ob eius grauitatem ad modu&mtail; <lb/>&longs;iphonis, vel libræ non pote&longs;t contundere <expan abbr="flammã">flammam</expan>, <lb/>&longs;ed eam &longs;ursùm exprimere, & impellere debet, at­<lb/>que aer &longs;upernus nece&longs;&longs;ariò ad latera excurrere de­<lb/>bet, & tran&longs;itum minùs pondero&longs;æ flammæ <expan abbr="a&longs;cend&etilde;-ti">a&longs;cenden­<lb/>ti</expan> concedere; nec ob&longs;taculum aliud ei inferet, præ­<lb/>terquàm contu&longs;ionem &longs;upremæ aciei flammæ, vt ni-<pb pagenum="143" xlink:href="010/01/151.jpg"/><arrow.to.target n="marg178"/><lb/>mirùm efficiatur vertex eius aliquo pacto rotundus, <lb/>& contornatus, ni&longs;i adfuerit noua alia cau&longs;a motum <lb/>eius accelerans, à qua proindè eius vertex acumi­<lb/>nari pote&longs;t, vt &longs;uperiùs dictum e&longs;t. <lb/><arrow.to.target n="marg179"/></s> </p> <p type="margin"> <s id="s.000723"><margin.target id="marg178"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000724">Pergamus modò ad po&longs;tremam difficultatem ab <lb/>eodem authore allatam. </s> <s id="s.000725">inquit enim: <emph type="italics"/>&longs;int duæ pilæ<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000726"><arrow.to.target n="marg180"/><lb/><emph type="italics"/>æneæ, vna &longs;olida exigui ponderis, altera maioris, &longs;ed reple­<lb/>ta inclu&longs;o aere, hæ&longs;ine dubio a&longs;cendit &longs;uper aquam, non <lb/>item minor, &longs;i ergo aqua deorsùm tendens exprimit <expan abbr="alterã">alteram</expan> <lb/>pilam, cur non reliquam? </s> <s id="s.000727">non igitur pila mouetur &longs;ursùm, <lb/>quia exprimitur, &longs;ed quia in &longs;e habet aerem natura &longs;ua le­<lb/>uem.<emph.end type="italics"/></s> <s id="s.000728"> Et huic profectò argumento nil aliud re&longs;ponde­<lb/>re po&longs;&longs;um, &longs;ed tantùm monere authorem eius &longs;e no&ntail; <lb/><arrow.to.target n="marg181"/><lb/>e&longs;&longs;e &longs;atis memorem doctrinæ Archimedis, ex qu&atail; <lb/>deducitur ingentem pilam æneam excauatam, & ae­<lb/>re plenam minùs ponderare, quàm moles aquæ ei æ­<lb/>qualis, & ideò grauitas aquæ maior velut in libr&atail; <lb/>&longs;ursùm eleuare debet minus pondus prædictæ pilæ <lb/>æne-aereæ, cum verò comparatur ænea pila &longs;olida <lb/>licèt paruula &longs;it, illa tamen grauior e&longs;t multò magis, <lb/>quàm &longs;it moles aquæ huic pilulæ æqualis, cùmque <lb/>comparatio fieri debeat inter duas moles æquales <lb/>&longs;olidi nempè demer&longs;æ pilæ æneæ <expan abbr="cũ">cum</expan> mole fluidi am­<lb/>bientis ei æquali, quia exce&longs;&longs;us ponderis penès pi­<lb/>lam <expan abbr="æneã">æneam</expan> exi&longs;tit, nece&longs;&longs;ariò maior eius grauitas præ­<lb/>ualebit, ideòque mergetur, & ad fundum de&longs;cendet, <lb/>ex quo patet prædictum argumentum non probar&etail; <lb/>pilam &etail;ne-aeream vim leuitatis in &longs;e habere. </s> </p> <p type="margin"> <s id="s.000729"><margin.target id="marg180"/>Eiu&longs;dem <lb/>authoris no­<lb/>ua difficul­<lb/>tas.</s> </p> <p type="margin"> <s id="s.000730"><margin.target id="marg181"/>Sed reijci­<lb/>tur.</s> </p> <p type="main"> <s id="s.000731">Tandem oper&etail;pretium erit di&longs;&longs;oluere nouas diffi-<pb pagenum="144" xlink:href="010/01/152.jpg"/><arrow.to.target n="marg182"/><lb/>cultates à pr&etail;claro authore euulgatas, qu&etail; ab hac ex­<lb/>perientia de&longs;umuntur; &longs;it fi&longs;tula vitrea RSVX cuius <lb/>latitudo &longs;it duorum, vel trium digitorum, altitudo <lb/>verò &longs;it vnius, vel alterius cubiti, repleaturque aqua, <lb/><arrow.to.target n="marg183"/><lb/>&longs;ed remaneat in eius vertice portio aliqua aeris vni­<lb/>us, vel alterius digiti, po&longs;tea foramine RX perfectè <lb/>occlu&longs;o, vel palma manus, vel operculo aliquo re­<lb/>uoluatur fi&longs;tula vt eius infima ba&longs;is SV in &longs;upremolo­<lb/>co emineat, videbimus aerem è fundo RX &longs;ursù&mtail; <lb/>a&longs;cendere, atque incuruari ad modum arcus, ex par­<lb/>te &longs;uperiori ABC, & è contrà ex parte infima AGC, <lb/>aut explanari, vel etiam cauitatem aliquam ad mo­<lb/>dum &longs;cutellæ acquirere. </s> <s id="s.000732">Hinc prædictus Author in­<lb/>fert certè deduci aerem &longs;ursùm in præ­<lb/><figure id="id.010.01.152.1.jpg" xlink:href="010/01/152/1.jpg"/><lb/>dicta fi&longs;tula a&longs;cendere propria virtut&etail; <lb/>intrin&longs;eca leuitatis non per <expan abbr="extru&longs;ion&etilde;">extru&longs;ionem</expan> <lb/>factam ab aqua ambiente; quia, inquit <lb/>ip&longs;e, <emph type="italics"/>aer &longs;upernè fastigiatur ad modum di­<lb/>&longs;culi, vt faciliùs peruadat aquam, & qua&longs;i <lb/>perforet illam, quia aer est, qui turge&longs;cendo <lb/>&longs;ursùm aquam introit, & cedere &longs;ibi cogit <lb/>qua&longs;i cuneo in illius medio adacto, alio quin <lb/>&longs;i idcircò aer &longs;ursùm tendit quia ab aqua de­<lb/>orsùm tendente extruditur in &longs;uperiora, aqua <lb/>potiùs peruaderet cuneatim aerem; vt con­<lb/>tingit in pluuia, vel &longs;altem retunderet &longs;uper­<lb/>nè illius tumorem, & infernè illum qua&longs;i forcipe <expan abbr="comprim&etilde;s">comprimens</expan> <lb/>constringeret ad figuram conoidem eius partem infimam.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.000733"><margin.target id="marg182"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000734"><margin.target id="marg183"/>Alia argu­<lb/>menta pro <lb/>leuitate po­<lb/>&longs;itiua <expan abbr="desũp">desump</expan><lb/>ta à pulcher <lb/>rimo expe­<lb/>rimento.</s> </p> <p type="main"> <s id="s.000735">Pro re&longs;olutione harum difficultatum priùs metho-<pb pagenum="145" xlink:href="010/01/153.jpg"/><arrow.to.target n="marg184"/><lb/>do generali demon&longs;trabimus &longs;uppo&longs;ito quòd aer i&ntail; <lb/>aqua a&longs;cendat <expan abbr="nõ">non</expan> virtute propriæ leuitatis, &longs;ed per <lb/>extru&longs;ionem medij fluidi tunc figura aeris <expan abbr="a&longs;cend&etilde;-tis">a&longs;cenden­<lb/>tis</expan> per aquam nece&longs;&longs;ariò erit conuexa &longs;upernè, & in­<lb/>feriùs excauata, & è contrà &longs;uppo&longs;ito quòd aer inter­<lb/>no principio leuitatis per aquam a&longs;cenderet, deberet <lb/>figura aeris a&longs;cendentis tumorem, & rotunditate&mtail; <lb/>habere tùm ex parte &longs;uprema, tùm ex parte &longs;ubiecta. </s> </p> <p type="margin"> <s id="s.000736"><margin.target id="marg184"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000737"><emph type="center"/>PROP. LXXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000738"><emph type="center"/><emph type="italics"/>Et primo o&longs;tendendum est, quòd quodlibet fluidum intra <lb/>aliud fluidum tran&longs;latum &longs;iuè virtute propria, &longs;iuè alie­<lb/>na violentia impul&longs;um, dummodò eius partes non di&longs;­<lb/>&longs;ipentur in ip&longs;o fluido in quo mouetur, &longs;ed &longs;e <lb/>mutuò contingant, & vniantur, nece&longs;&longs;ariò <lb/>tumorem, & rotundam figuram acqui­<lb/>ret in parte anteriori mo­<lb/>tus eius.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000739">QVodlibet fluidum <expan abbr="homogeneũ">homogeneum</expan> naturali in&longs;tin­<lb/>ctu videtur &longs;ponte coale&longs;cere, ac &longs;imul in &longs;uo <lb/>toto partes &longs;uas conglutinare, vt videmus partes ae­<lb/>ris libentèr, & auidè vici&longs;&longs;im vniri, & difficiliùs ab <lb/>inuicem di&longs;trahi &longs;epararique, &longs;ic quoque partes aqu&etail; <lb/>vniuntur, conglobanturque &longs;phæricè <expan abbr="quotie&longs;cumq;">quotie&longs;cumque</expan> <lb/>&longs;ibi mutuò approximantur, itaut ex duabus guttulis <lb/>vna &longs;uper aliam excurrendo, & &longs;e mutuò <expan abbr="amplect&etilde;-do">amplecten­<lb/>do</expan> vnicam ampliorem guttam <expan abbr="cõ&longs;tituant">con&longs;tituant</expan>, e&longs;tque tàm <lb/>tenax huiu&longs;modi vnio, & vinculum partium aquæ, vt <pb pagenum="146" xlink:href="010/01/154.jpg"/><arrow.to.target n="marg185"/><lb/>&longs;i contingat aquæ guttam pendentem di&longs;trahi ab ali­<lb/>qua violentia, illa attenuatur, & gracile&longs;cit elonga­<lb/>turque, & denuò ce&longs;&longs;ante violentia re&longs;tringitur re­<lb/>colligitur, conglobaturque, &longs;ic paritèr videmus a­<lb/>quam ad membranæ &longs;ubtili&longs;&longs;imæ <expan abbr="ext&etilde;&longs;ionem">exten&longs;ionem</expan> redigi <lb/>circa aerem &longs;pumam componentem, vnde con&longs;tat <lb/>partes aquæ inter &longs;e vici&longs;&longs;im colligari vinculo <expan abbr="quodã">quodam</expan>: <lb/>id ip&longs;um ob&longs;eruamus in vitro, & metallis fu&longs;is. </s> <s id="s.000740">Qua­<lb/>li&longs;cumque igitur &longs;it cau&longs;a huius vinculi, & tenacita­<lb/>tis partium homogenearum eiu&longs;dem fluidi, vel quia <lb/>ab aliquo glutine, &longs;eù vi&longs;co&longs;itate vniantur, aut ab <lb/>aliqua alia cau&longs;a partes <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> fluidi &longs;e mutuò <expan abbr="am-plex&etilde;tur">am­<lb/>plexentur</expan>, & <expan abbr="cõnectantur">connectantur</expan>, certum e&longs;t tamen veram e&longs;&longs;e <lb/>prædictam vnionem, quotie&longs;cumque fluidum intr&atail; <lb/>aliud fluidum alterius naturæ collocatur, vt oleu&mtail; <lb/>intra aquam, vel aer intra quodlibet aliud fluidum, <lb/>non di&longs;&longs;ipabitur, &longs;ed tenaci quadam vnione conglo­<lb/>babitur, licet in motu poterit aliquo pacto eius figu­<lb/>ra rotunda alterari. </s> <s id="s.000741">hoc autem non contingit in om­<lb/>nibus fluidis cuiu&longs;cumque naturæ &longs;int, nam aqu&atail; <lb/>intra vinum, & metalla fu&longs;a inter &longs;e commixta no&ntail; <lb/>&longs;egregantur; &longs;ed facilè commi&longs;centur, confundun­<lb/>turque inter &longs;e. </s> <s id="s.000742">Et in hi&longs;ce aduertendum e&longs;t <expan abbr="adductã">adductam</expan> <lb/>experientiam locum non habere, &longs;ed tantummodò <lb/>in fluidis priùs expo&longs;itis non homogeneis inter &longs;e. </s> </p> <p type="margin"> <s id="s.000743"><margin.target id="marg185"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000744">Supponamus igitur fluidum ABC, verbi gratia ae­<lb/>rem, vel hydrargyrum, moueri vi intrin&longs;eca, vel vio<lb/>lenter impul&longs;um in aqua intra fi&longs;tulàm <expan abbr="&longs;trictã">&longs;trictam</expan> RSVX <lb/>contenta à termino B versùs E: & quia &longs;patium DN <pb pagenum="147" xlink:href="010/01/155.jpg"/><arrow.to.target n="marg186"/><lb/>LF vbi fluidum ABC tran&longs;portari de­<lb/><figure id="id.010.01.155.1.jpg" xlink:href="010/01/155/1.jpg"/><lb/>bet, iam repletum, & occupatum e&longs;t <lb/>à medio fluido aqueo, hoc autem vt lo­<lb/>cum cedat &longs;ubintranti fluido ABC, ne­<lb/>ce&longs;sè e&longs;t vt hinc di&longs;cedat transferatur­<lb/>que ad <expan abbr="occupãdum">occupandum</expan> illud &longs;patium, quod <lb/>derelinquitur à fluido ABC, cùmqu&etail; <lb/>corpus ABC vnionem &longs;eruet, nec di&longs;&longs;i­<lb/>petur, igitur anterius medium fluidum <lb/>debet per eius latera obliquè excur­<lb/>rere ad occupandas partes po&longs;ticas derelictas à flui­<lb/>do ABC, &longs;cilicèt fluidum ENDB mouebitur ad <expan abbr="part&etilde;">partem</expan> <lb/>&longs;ini&longs;tram versùs A, & medium fluidum BFLE moue­<lb/>bitur ad partem dexteram versùs C, eruntque prædi­<lb/>cti motus non æquidi&longs;tantes axi EB, &longs;ed erunt incli­<lb/>nati per lineas obliquas vt &longs;unt EA, & EC, & hoc <lb/>nece&longs;&longs;itate quadam contingit, quia fluidum è loco <lb/>ampliori SEBD <expan abbr="pertrã&longs;ire">pertran&longs;ire</expan> debet per angu&longs;tam viam <lb/>AO, & reliqua fluidi medietas VEBF pariter ab am­<lb/>plo &longs;patio perduci, ac pertran&longs;ire debet per &longs;trictum <lb/>locum CP, & huiu&longs;modi viæ angu&longs;tæ cùm &longs;int lateri <lb/>va&longs;is adhærentes, nece&longs;sè e&longs;t vt motus, & fluxus aqua <lb/>à &longs;itu B versùs O, & P obliquo itinere fiat impellen­<lb/>do, contundendo, & confricando &longs;uperficiem cor­<lb/>poris ABC, quod compre&longs;&longs;ioni cedit ob eius fluidi­<lb/>tatem, igitur ABC accommodari debet &longs;ituationi <lb/>obliquæ pre&longs;&longs;ionis corporum excurrentium à &longs;upre­<lb/>mo loco B versùs O, & P, quapropter nece&longs;&longs;itat&etail; <lb/>quadam acquirit fluidum ABC tumorem, & conuc-<pb pagenum="148" xlink:href="010/01/156.jpg"/><arrow.to.target n="marg187"/><lb/>xitarem cuius vertex in parte eius anteriori B exi&longs;tit. <lb/></s> <s id="s.000745">Et quia fluidum ABC, vt dictum e&longs;t, diuer&longs;æ natur&etail;, ac <lb/>con&longs;i&longs;tentiæ e&longs;t ab ip&longs;o fluido ambiente in quo mo­<lb/>uetur, ideò non commi&longs;centur, neque vici&longs;&longs;im <expan abbr="confũ-duntur">confun­<lb/>duntur</expan> inter &longs;e, &longs;ed quodlibet eorum &longs;eruabit vnio­<lb/>nem, & connexionem &longs;uarum partium homogenea­<lb/>rum. </s> <s id="s.000746">Hinc con&longs;tat quòd fluidum ABC dum fertur à <lb/>B versùs E, nece&longs;&longs;ariò acquirit figuram tumidam, & <lb/>acuminatam versùs anteriorem partem motus eius, <lb/>& hoc &longs;emperverificari debet, à quacumque virtute <lb/>motiua transferatur, &longs;iue ab intrin&longs;eca, & naturali, <lb/>&longs;iuè ab externa: & hoc propo&longs;itum fuerat. </s> </p> <p type="margin"> <s id="s.000747"><margin.target id="marg186"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000748"><margin.target id="marg187"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000749"><emph type="center"/>PROP. LXXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000750"><emph type="center"/><emph type="italics"/>Po&longs;ito quòd fluidum violenter &longs;ursùm exprimatur à fluido <lb/>ambiente grauiori, diuer&longs;æque con&longs;istentiæ, infima a­<lb/>&longs;cendentis fluidi &longs;uperficies explanata, vel <lb/>concaua erit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <figure id="id.010.01.156.1.jpg" xlink:href="010/01/156/1.jpg"/> <p type="main"> <s id="s.000751">DEinde fluidum ABC, oleum v. <!-- REMOVE S-->g. <lb/><!-- REMOVE S-->demer&longs;um in fundo alterius flui­<lb/>di grauioris, & diuer&longs;æ con&longs;i&longs;tentiæ, vt <lb/>e&longs;t aqua intra fi&longs;tulam &longs;trictam SX con­<lb/>tenta, & &longs;uppo&longs;ito, quòd idip&longs;um flui­<lb/>dum ABC non a&longs;cendat in ip&longs;a aqua à <lb/>vi natiuæ eius leuitatis translatum, &longs;ed <lb/>expul&longs;um per <expan abbr="extru&longs;ion&etilde;">extru&longs;ionem</expan> à maiori gra­<lb/>uitate fluidi aquæ ambientis. </s> <s id="s.000752"><expan abbr="O&longs;tend&etilde;-dum">O&longs;tenden­<lb/>dum</expan> e&longs;t in hac hypothe&longs;i infimam, & po&longs;ticam <expan abbr="part&etilde;">partem</expan> <pb pagenum="149" xlink:href="010/01/157.jpg"/><arrow.to.target n="marg188"/><lb/>AGC eiu&longs;dem olei a&longs;cendentis nece&longs;&longs;ariò explana­<lb/>tam, imò excauatam fore; quia ex hypothe&longs;i pondus <lb/>&longs;pecificum aquæ ambientis &longs;uperat &longs;pecificam gra­<lb/>uitatem olei ABC; iam &longs;i e&longs;t moles aquæ collateralis <lb/>FQPC æqualis medietati olei BGC, proculdubio <lb/>aqua FQPC grauior erit oleo BGC, vel &longs;i moles in&etail;­<lb/>quales &longs;unt, aquæ momentum &longs;uperat olei <expan abbr="momentũ">momentum</expan>, <lb/>hi&longs;ce verò inæqualibus ponderibus ineumbunt, & <lb/>&longs;ubijciuntur moles aquæ æque ponderantes, vel æ­<lb/>qualium momentorum, ergo in &longs;iphone compo&longs;ito <lb/>ex cylindri portione aquea VXKL, & ex cylindri <lb/>portione EIKL compo&longs;ita ex aqua, & oleo inæqua­<lb/>liter premuntur partes aquæ &longs;ubiectæ GPXI. quæ li­<lb/>bram con&longs;tituunt, nempè aqua CPXK maiori ni&longs;u <lb/>comprimitur ab aqua FQPC, quam aqua GCKI pre­<lb/>matur ab oleo BGC minus graui, & ideò ex coroll pr. <lb/><!-- REMOVE S-->10. oleum BGC &longs;ursùm impelletur ab aqua &longs;ubiecta <lb/>GIKC, & talis expre&longs;&longs;io fiet (ex prop. 51.) tanta vi, <lb/>quanta e&longs;t grauitas exce&longs;&longs;us ponderis aquæ FQPC <lb/>&longs;upra grauitatem olei BGC. </s> <s id="s.000753">præterea quia aqua in­<lb/>ter EB, & LC dum fertur deor&longs;um ad occupandu&mtail; <lb/>&longs;patium ab a&longs;cendente oleo derelictum, nece&longs;&longs;ariò <lb/>comprimit contunditque &longs;uperficiem collaterale&mtail; <lb/>olei BC non duri, &longs;ed cedentis, e&longs;tque motus obli­<lb/>quus per &longs;uperficiem decliuem BC, ergo &longs;patiu&mtail;, <lb/>&longs;eù alueus, per quod incumbens aqua pertran&longs;ir&etail; <lb/>debet comprehen&longs;um à &longs;uperficie aquæ FCK dire­<lb/>cto, & non impedito motu fluentis, & inclinatam de­<lb/>cliuemque olei BC &longs;uperficiem, continentèr magis <pb pagenum="150" xlink:href="010/01/158.jpg"/><arrow.to.target n="marg189"/><lb/>con&longs;tringatur angu&longs;teturque, & proinde incumbens <lb/>aqua velociori motu, & ideò impetu, & vi maiori <lb/>fluere cogatur per angu&longs;tias C, quàm per amplu&mtail; <lb/>alueum <expan abbr="BFQ">BFQ</expan> quare oportet vt vehementiùs, & ma­<lb/>iori impetu, & vi pars olei versùs C deorsùm com­<lb/>primatur, contundaturque quàm reliquæ partes olei <lb/>propinquiores vertici eius B, è contra aqua &longs;ubiecta <lb/>CKIG reflectitur &longs;ursùm, impellit, atque contundit <lb/>infimam ba&longs;im olei GC ea vi, & impetu quo collate­<lb/>ralis aqua FCPQ exce&longs;&longs;u &longs;uæ grauitatis &longs;uperat &longs;pe­<lb/>cificam olei pondero&longs;itatem. </s> <s id="s.000754">Patet ergo quod à dua­<lb/>bus viribus <expan abbr="cõtrarijs">contrarijs</expan>, veluti prælo, comprimitur <expan abbr="oleũ">oleum</expan> <lb/>BCG &longs;upernè ab impetu aquæ obliquè de&longs;cenden­<lb/>tis per BC, & infernè à vi aquæ reflexæ oleum <expan abbr="&longs;ursũ">&longs;ursum</expan> <lb/>impellentis, cùmque vis, & compre&longs;&longs;io, quæ &longs;upernè <lb/>infertur, inæqualis &longs;it, vehementiori, & validiori vi <lb/>facta propè terminum C, & debiliori, ver&longs;us <expan abbr="vertic&etilde;">verticem</expan> <lb/>B, impul&longs;us verò &longs;ubiectæ aquæ IKCG licèt vnifor­<lb/>mis &longs;it vbique, nihilominùs propter minorem <expan abbr="de&longs;c&etilde;-dentis">de&longs;cen­<lb/>dentis</expan> aquæ ob&longs;i&longs;tentiam in B, quàm versùs C &longs;it <lb/>vt vehementiùs oleum impellatur contundaturque à <lb/>&longs;ubiecta aqua reflexa versùs axem IG vbi ni&longs;um <expan abbr="cõ-trarium">con­<lb/>trarium</expan> <expan abbr="debilior&etilde;">debiliorem</expan> offendit quàm versùs latera A, & <lb/>C, & propterea &longs;uperficies &longs;ubiecta olei AGC exca­<lb/>uata erit ad modum &longs;cutellæ, & hoc quidem nece&longs;­<lb/>&longs;ariò efficietur non à vi intrin&longs;eca, & naturali leuita­<lb/>tis ip&longs;ius olei, &longs;ed à &longs;uppo&longs;ita energia grauitatis <lb/>fluidi ambientis, quod fuerat demon&longs;trandum. <pb pagenum="151" xlink:href="010/01/159.jpg"/><arrow.to.target n="marg190"/></s> </p> <p type="margin"> <s id="s.000755"><margin.target id="marg188"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000756"><margin.target id="marg189"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000757"><margin.target id="marg190"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000758"><emph type="center"/>PROP. LXXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000759"><emph type="center"/><emph type="italics"/>Si fluidum &longs;ponte à virtute intrin&longs;eca intra aliud fluidum <lb/>diuer&longs;æ con&longs;istentiæ moueatur, in parte po&longs;teriori, &longs;eù <lb/>termino à quo, &longs;ui motus, non erit excauatum, <lb/>&longs;ed tumidam, & conuexam figuram <lb/>acquiret.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000760">SVpponamus &longs;ecundo loco fluidum <lb/><figure id="id.010.01.159.1.jpg" xlink:href="010/01/159/1.jpg"/><lb/>ABC, quod &longs;it aqua, grauius e&longs;&longs;&etail; <lb/>ambiente fluido (quod &longs;it v. <!-- REMOVE S-->g. <!-- REMOVE S-->oleum) <lb/>manife&longs;tum e&longs;t aquam ABCH deorsùm <lb/>in oleo de&longs;cendere ab I versùs E ab in­<lb/>trin&longs;eco principio &longs;uæ grauitatis impnl­<lb/>&longs;um. </s> <s id="s.000761">Dico iam quod eadem aqua in par­<lb/>te po&longs;tica &longs;ui motus H, &longs;cilicèt versùs <lb/>terminum à quo &longs;ui motus, non erit ex­<lb/>cauata ad modum &longs;cutellæ, &longs;ed tumida, & conuexa <lb/>erit. </s> <s id="s.000762">Quia cum primo aqua ABCH demergitur in­<lb/>fra olei <expan abbr="libellã">libellam</expan> RX, & inchoat pro&longs;equiturque &longs;uum <lb/><expan abbr="de&longs;c&etilde;&longs;um">de&longs;cen&longs;um</expan>, nece&longs;sè e&longs;t vt oleum &longs;ubiectum AEC è &longs;uo <lb/>loco continenter recedat, & recurrat ad replen­<lb/>dum locum po&longs;ticum AMKC ab aqua derelictum; er­<lb/>go aqua AHCB, & oleum ambiens motibus contra­<lb/>rijs agitari debent, nempe aqua de&longs;cendet dum am­<lb/>biens oleum a&longs;cendit, igitur ratione motus, oleu&mtail; <lb/>po&longs;ticè recurrens non impellet aquam ictum fugien­<lb/>tem, nec proinde eius figuram AHC contundere, & <lb/>explanare poterit. </s> <s id="s.000763">præterea aqua ABCH habet vim <pb pagenum="152" xlink:href="010/01/160.jpg"/><arrow.to.target n="marg191"/><lb/>&longs;e mouendi deorsùm in oleo, hoc verò nullam facul­<lb/>tatem &longs;e mouendi deorsùm in <expan abbr="eod&etilde;">eodem</expan> oleo habet, <expan abbr="cũ">cum</expan> in <lb/>fluido &longs;ui generis iners æquilibretur, ergo hoc nomi­<lb/>ne pariter aqua ictum fugiens, immò non impul&longs;&atail;, <lb/>nec percu&longs;&longs;a ab oleo po&longs;ticè recurrente non poterit <lb/>contundi, nec explanari, & hoc experientia patet, <lb/>nam &longs;i pila dura capillitium è filis &longs;ericis tenui&longs;&longs;imis <lb/>&longs;ibi annexum habuerit, & intra aquam filo deorsùm, <lb/>&longs;ursùm, vel lateraliter trahatur nunquam po&longs;ticum <lb/>capillitium contundetur explanabiturque, dum vni­<lb/>formi, non verò retardata velocitate pila in aqu&atail; <lb/>mouetur. </s> <s id="s.000764">& ab hac experientia luculenter euinci­<lb/>tur &longs;omnium illorum, qui aiunt ad vitandum <expan abbr="vacuũ">vacuum</expan> <lb/>rapidi&longs;&longs;imo motu oleum po&longs;ticè recurrere, & &longs;ic po&longs;­<lb/>&longs;e aquæ &longs;uperficiem contundere, & explanare. </s> <s id="s.000765">Qua­<lb/>propter aqua excepto &longs;implici contactu in &longs;uperficie <lb/>AHC nullam contu&longs;ionem, aut percu&longs;&longs;ionem patie­<lb/>tur ab oleo &longs;uperincumbente MACK, igitur nece&longs;sè <lb/>e&longs;t vt aqua in AHC retineat eamdem figuram, quam <lb/>priùs habebat, &longs;ed eius figura intra oleum vnita, & <lb/>contornata e&longs;&longs;e &longs;olet ob naturalem partum eius con­<lb/>nexionem, & vinculum, & ob compre&longs;&longs;ionem vn­<lb/>dequaque factam à fluido ambiente, vt dictum e&longs;t. <lb/></s> <s id="s.000766">igitur dum aqua ABC de&longs;cendit intra oleum po&longs;tre­<lb/>ma eius ba&longs;is AHC, &longs;cilicèt versùs terminum à quo <lb/><arrow.to.target n="marg192"/><lb/>motus inchoat, eius figura debet e&longs;&longs;e tumida con­<lb/>uexa, & contornata, cum è contra eadem aqua <expan abbr="a&longs;c&etilde;-dens">a&longs;cen­<lb/>dens</expan> intra mercurium &longs;i extruderetur à fluido ambi­<lb/>ente nece&longs;&longs;ariò eius po&longs;tica ba&longs;is versùs principium <pb pagenum="153" xlink:href="010/01/161.jpg"/><arrow.to.target n="marg193"/><lb/>motus non tumida, &longs;ed excauata e&longs;&longs;e debuerat, & <lb/>hæc omnia o&longs;tendenda fuerant. </s> </p> <p type="margin"> <s id="s.000767"><margin.target id="marg191"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000768"><margin.target id="marg192"/>Ex prop. 73.</s> </p> <p type="margin"> <s id="s.000769"><margin.target id="marg193"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000770"><emph type="center"/>PROP. LXXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000771"><emph type="center"/><emph type="italics"/>Si fluidum à principio intrin&longs;eco moueatur intra aliud flui­<lb/>dum diuer&longs;æ con&longs;istentiæ, quod valdè rarefieri, & co­n<lb/>den&longs;ari queat, tunc multò magis tumida efficie­<lb/>tur pars postica fluidi decurrentis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000772">ET hoc quidem verum e&longs;t quando fluidum am­<lb/>biens, in quo aliud fluidum mouetur &longs;ursùm, <lb/>vel deorsùm, non patitur &longs;en&longs;ibilem <expan abbr="conden&longs;ation&etilde;">conden&longs;ationem</expan>, <lb/>vel rarefactionem, veluti e&longs;t oleum, aut aqua; at &longs;i <lb/>valdè rarefiat conden&longs;eturque, vt aer propter velo­<lb/>ci&longs;&longs;imum ca&longs;um aquæ AHCB remanet aer po&longs;ticus <lb/>MACK valdè rarefactus, ideoque inhabilis vt in&longs;e­<lb/>qui po&longs;&longs;it aquam cadentem, & proindè nedùm aer <lb/>incumbens guttam aquæ de&longs;cendentem in H no&ntail; <lb/>percutiet, cùm è contrà, ne ibidem, (vt vulgò credi­<lb/>tur) vacuum remaneat eius vertex tumidus H valdè <lb/>eleuabitur <expan abbr="prominebitq;">prominebitque</expan> & &longs;ic videmus guttas plu­<lb/>uiales &longs;ecum trahere veluti caudam aqueam <expan abbr="gracil&etilde;">gracilem</expan>, <lb/>tantùm abe&longs;t vt po&longs;ticè contu&longs;ionem patiantur, aut <lb/>excauentur, & hoc clariùs percipitur &longs;i pila aliqu&atail; <lb/>lignea, & dura, quæ habeat comam ex filamentis, &longs;eù <lb/>pilis exili&longs;&longs;imis, & nullius ferè ponderis compo&longs;itam <lb/>cadat deorsùm in aere, tunc enim pili &longs;upremi a&longs;&longs;ur­<lb/>gunt efficiuntque veluti caudam fluctuantem, non <lb/>autem comprimuntur contundunturque versùs &longs;u-<pb pagenum="154" xlink:href="010/01/162.jpg"/><arrow.to.target n="marg194"/><lb/>premam partem ip&longs;ius pilæ, quod e&longs;t &longs;ignum euidens <lb/>nullam vim compre&longs;&longs;iuam pati ab aere &longs;uperincum­<lb/>bente. </s> </p> <p type="margin"> <s id="s.000773"><margin.target id="marg194"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000774"><emph type="center"/>PROP. LXXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000775"><emph type="center"/><emph type="italics"/>Si oleum, vel aer a&longs;cenderet in aqua &longs;ponte à vi &longs;uæ leui­<lb/>tatis impul&longs;us non po&longs;&longs;et eius ba&longs;is excauari ad in&longs;tar <lb/>&longs;cutellæ.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000776">TAndem demon&longs;trandum e&longs;t po­<lb/><figure id="id.010.01.162.1.jpg" xlink:href="010/01/162/1.jpg"/><lb/>&longs;ito, quòd aer, vel oleum ABCH <lb/>a&longs;cenderet in ip&longs;a aqua à propria, & <lb/>intrin&longs;eca virtute leuitatis impul&longs;um, <lb/>quod e&longs;&longs;et ab&longs;olutè impo&longs;&longs;ibile, vt e­<lb/>ius ba&longs;is infima excauata e&longs;&longs;et ad mo­<lb/>dum &longs;cutellæ; quia ex aduer&longs;arij hypo­<lb/>the&longs;i oleum ABCH a&longs;cendit in aqua contenta in fi­<lb/>&longs;tula &longs;tricta RSVX propria virtute leuitatis ab I ver­<lb/>sùs E, nec ab aqua infima impellitur exprimiturque <lb/>&longs;ursùm, ergò aqua MACK, quæ currit ad <expan abbr="replendũ">replendum</expan> <lb/>&longs;patium derelictum ab oleo cum &longs;it ex &longs;ui natura gra­<lb/>uis exercet vim &longs;ui ponderis ab H ver&longs;us I premen­<lb/>do præcisè &longs;uper <expan abbr="fundũ">fundum</expan> vitri RX, & nullo pacto vim <lb/>exercere pote&longs;t &longs;ursùm ab l versùs H, hoc enim e&longs;&longs;et <lb/>contra grauium naturam, & contra ip&longs;am aduer&longs;arij <lb/>hypothe&longs;im. </s> <s id="s.000777">Præterea quia oleum ABCH, & aqua <lb/>ambiens motibus contrarijs agitari debent, nempè <lb/>oleum, vt leue, a&longs;cendet dum aqua ambiens <expan abbr="de&longs;c&etilde;-det">de&longs;cen­<lb/>det</expan>, igitur non &longs;ibi occurrunt, & aduer&longs;antur, &longs;ed ab <pb pagenum="155" xlink:href="010/01/163.jpg"/><arrow.to.target n="marg195"/><lb/>inuicem conantur recedere; quare ratione motus <lb/>aqua inferiùs, & po&longs;ticè recurrens non impellet <expan abbr="oleũ">oleum</expan> <lb/>ictum fugiens, nec proindè eius figuram AHC <expan abbr="cõ-tundere">con­<lb/>tundere</expan>, & explanare pote&longs;t. </s> <s id="s.000778">Igitur in hoc ca&longs;u duo <lb/>impetus inter &longs;e contrarij, & ab inuicem receden­<lb/>tes reperiuntur leuitatis olei, nimirùm, &longs;ursùm ab H <lb/>versùs E, aquæ verò conatus inferiùs tendentis ab <lb/>H versùs I, igitur hæc duo corpora oleum AHCB, <lb/>& aqua &longs;ubiecta MACK &longs;e mutuò tantummodò tan­<lb/>gent placidi&longs;&longs;imo amplexu ab&longs;que vlla pugna, & re­<lb/>pul&longs;u, vt nimirùm aqua oleum non impellat, neque <lb/>hoc illam repellat, igitur oleum ABCH multò minùs <lb/>comprimi, ac contundi debetin H ab aqua &longs;ubie­<lb/><arrow.to.target n="marg196"/><lb/>cta deorsùm premente, quàm contundebatur po&longs;ticè <lb/>ab oleo incumbente, quando nimirum intra oleu&mtail; <lb/>de&longs;cendebat, & pondus eiu&longs;dem olei incumbentis <lb/>patiebatur (in vtroque enim ca&longs;u recur&longs;us fluidi ad <lb/>&longs;patium replendum æquè reperitur, & proindè ne­<lb/>que nocet, neque adiuuat prædictum effectum) &longs;ed <lb/>ex antepræmi&longs;&longs;a propo&longs;itione aqua per oleum deci­<lb/>dens à vi natiua grauitatis impul&longs;a retinet tumorem <lb/>eleuationemque <expan abbr="cõuexam">conuexam</expan> in po&longs;tica parte eius mo­<lb/>tus, igitur multò magis eleuari deberet tumor i&ntail; <lb/>oleo per aquam a&longs;cendente in parte po&longs;teriore mo­<lb/>tus eius &longs;i ab intrin&longs;eca leuitate eleuaretur, qua pro­<lb/>ptèr erit omninò impo&longs;&longs;ibile, vt oleum, vel aer dum <lb/>a&longs;cendit per aquam, excauetur in parte infima eius <lb/>ba&longs;is, <expan abbr="quãdo">quando</expan> nimirùm &longs;ursùm fertur ab interno prin­<lb/>cipio leuitatis, quod demon&longs;trandum fuerat. <pb pagenum="156" xlink:href="010/01/164.jpg"/><arrow.to.target n="marg197"/></s> </p> <p type="margin"> <s id="s.000779"><margin.target id="marg195"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000780"><margin.target id="marg196"/>In prop. 74.</s> </p> <p type="margin"> <s id="s.000781"><margin.target id="marg197"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000782">His præmi&longs;&longs;is examinari modò debent &longs;igillati&mtail; <lb/>oppo&longs;itiones &longs;uperiùs adductæ. </s> </p> <p type="main"> <s id="s.000783"><emph type="center"/>PROP. LXXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000784"><emph type="center"/><emph type="italics"/>Et primo loco dieo, quòd figura inflata, conuexa, & acumi­<lb/>nata quam aer acquirit in fi&longs;tula aqua plena in parte an­<lb/>teriori eius motus dum &longs;ursùm a&longs;cendit, non e&longs;t argu­<lb/>mentum efficax, & euincens aerem &longs;ursùm <lb/>moueri à principio intrin&longs;eco &longs;uæ <lb/>leuitatis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000785">QVia demon&longs;tratum e&longs;t corpora fluida <expan abbr="ced&etilde;tia">cedentia</expan>, </s> </p> <p type="main"> <s id="s.000786"><arrow.to.target n="marg198"/><lb/>& homogenea &longs;i moueantur intra aliud cor­<lb/>pus Huidum &longs;iue propria, & intrin&longs;eca virtute moti­<lb/>ua, &longs;iue ab impul&longs;u facto à cau&longs;a extrin&longs;eca, aut ab <lb/>ip&longs;o medio, nece&longs;&longs;ariò in anteriori parte motus il­<lb/>lius tume fieri, contornari, & aliquanti&longs;per acumina­<lb/>ri debere, quaproptèr tumor, qui in aere a&longs;cenden­<lb/>te per aquam ob&longs;eruatur, neque iuuat, neque nocet, <lb/>nec &longs;uadet, neque di&longs;&longs;uadet leuitatem po&longs;itiua&mtail;. <lb/></s> <s id="s.000787">Mirum tamen e&longs;t non animaduer&longs;am fui&longs;&longs;e cau&longs;am <lb/>cauitatis eiu&longs;dem aeris in parte po&longs;tica eius motus, <lb/>à qua cauitate, &longs;icut o&longs;ten&longs;um e&longs;t, euidentèr deduci­<lb/>tur impo&longs;&longs;ibile e&longs;&longs;e aerem ab intrin&longs;eco principio le­<lb/>uitatis &longs;ursùm ferri, &longs;ed potiùs per <expan abbr="extru&longs;ion&etilde;">extru&longs;ionem</expan> me­<lb/>dij fluidi &longs;ursùm eleuari. </s> </p> <p type="margin"> <s id="s.000788"><margin.target id="marg198"/>Prop. 72.</s> </p> <p type="main"> <s id="s.000789">Cùm po&longs;tea in&longs;tat aduer&longs;arius aerem, dum per a­<lb/>quam a&longs;cendit, acumen eius &longs;ursùm porrigere, vt fa­<lb/>ciliùs terebrare, & perforare aquam vi &longs;uæ leuitatis <pb pagenum="157" xlink:href="010/01/165.jpg"/><arrow.to.target n="marg199"/><lb/>po&longs;&longs;it. </s> <s id="s.000790">Hoc profectò negatur, quia licèt aer non &longs;it <lb/>leuis, &longs;ed per extru&longs;ionem à medio fluido &longs;ursù&mtail; <lb/>expellatur, efformare debet quoque eminentiam il­<lb/>lam contornatam, & acuminatam, vt demon&longs;tratum <lb/>e&longs;t. </s> </p> <p type="margin"> <s id="s.000791"><margin.target id="marg199"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000792">Sed vtile erit parumpèr circum&longs;tantias huius ex­<lb/><arrow.to.target n="marg200"/><lb/>perienti&etail; accuratiùs perpendere, inquit enim, <emph type="italics"/>par­<lb/>tem fistulæ &longs;uperiorem conuerte deorsùm, & erige fi&longs;tulam <lb/>perpendicularitèr ad horizontem, videbis enim aerem, qui in <lb/>fundo fi&longs;tulæ habuerat formam cylindri occupantem totam <lb/>cauitatem fistulæ in latum mox a&longs;cendere, & &longs;ic a&longs;cendere, <lb/>vt &longs;e coarctans extendat in longum, & &longs;uperiorem cylindri <lb/>illius &longs;uperficiem, quæ plana erat ad modum di&longs;culi, iam <lb/>conoidem factam e&longs;&longs;e.<emph.end type="italics"/></s> <s id="s.000793"> Itaque hic author <lb/><figure id="id.010.01.165.1.jpg" xlink:href="010/01/165/1.jpg"/><lb/>cen&longs;et quòd <expan abbr="quãdo">quando</expan> fi&longs;tula RV <expan abbr="perp&etilde;-dicularitèr">perpen­<lb/>dicularitèr</expan> ad <expan abbr="horizõtem">horizontem</expan> eleuatur, ae­<lb/>rem ROPX, quidum &longs;upernè con&longs;i&longs;te­<lb/>bat cylindricam formam habebat, <expan abbr="etiã">etiam</expan> <lb/>in hoc &longs;itu infimo per&longs;euerare po&longs;&longs;&etail; <lb/>per aliquod tempus in eadem figur&atail; <lb/>cylindrica, quod profectò &longs;i verum e&longs;­<lb/>&longs;et non facilè reddi ratio po&longs;&longs;et quare, & quemad­<lb/>modum à compre&longs;&longs;ione aquæ <expan abbr="&longs;uperincumb&etilde;tis">&longs;uperincumbentis</expan> pla­<lb/>na aeris &longs;uperficies OP efficiatur tumida, & conue­<lb/>xa, veluti e&longs;t ABC. </s> <s id="s.000794">Alia igitur longè diuer&longs;a ratione <lb/>res &longs;e habet. <pb pagenum="158" xlink:href="010/01/166.jpg"/><arrow.to.target n="marg201"/></s> </p> <p type="margin"> <s id="s.000795"><margin.target id="marg200"/>Circum&longs;tan­<lb/>tia notatu di­<lb/>gna in tali <lb/>experimen­<lb/>to affertur <lb/>ab aduer&longs;a­<lb/>rio.</s> </p> <p type="margin"> <s id="s.000796"><margin.target id="marg201"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000797"><emph type="center"/>PROP. LXXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000798"><emph type="center"/><emph type="italics"/>Cau&longs;a &longs;eparationis aerei cylindri è fundo va&longs;is e&longs;t pondus <lb/>aquæ ambientis.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000799">INtelligatur denuò fi&longs;tula RV plena aqua, in qu&atail; <lb/>exi&longs;tat aereus cylindrus PORX in parte eius &longs;u­<lb/><figure id="id.010.01.166.1.jpg" xlink:href="010/01/166/1.jpg"/><lb/>prema operculo XR <lb/>clau&longs;a, po&longs;tea circa <expan abbr="pũ-ctum">pun­<lb/>ctum</expan> V <expan abbr="fixũ">fixum</expan> reuolua­<lb/>tur <expan abbr="deorsũ">deorsum</expan> fi&longs;tula <expan abbr="trã&longs;-ferendo">tran&longs;­<lb/>ferendo</expan> nimirùm latus <lb/>VX in locis VF, VG, <lb/>VH, & VK, <expan abbr="manife&longs;tũ">manife&longs;tum</expan> <lb/>e&longs;t, quod in &longs;itu VF pro<lb/>pter va&longs;is <expan abbr="inclination&etilde;">inclinationem</expan> <lb/>&longs;uperficies PO aquæ <lb/>POSV non per&longs;euera­<lb/>bit in eodem &longs;itu incli­<lb/>nato, cùm aqua natura­<lb/>li in&longs;tinctu æquabili &longs;i­<lb/>tu ad horizontem parallelo di&longs;poni, redigique de­<lb/>beat, quaproptèr à &longs;itu decliui PO de&longs;cendet inferiùs <lb/>versùs &longs;uperficiem BDA horizonti parallelam, veluti <lb/>exigit &longs;itus, & pendentia fi&longs;tulæ VFR. </s> <s id="s.000800">Hinc &longs;equi­<lb/>tur, vt aqua excurrat ad occupandum <expan abbr="&longs;patiũ">&longs;patium</expan> ODAR, <lb/>à quo aer expul&longs;us deueniet ad replendum &longs;patium <lb/>&longs;upremum ab aqua derelictum, &longs;cilicèt PEBD. </s> <s id="s.000801">Pro­<lb/>grediamur modò ad &longs;ituationem fi&longs;tulæ <expan abbr="horizontal&etilde;">horizontalem</expan> <pb pagenum="159" xlink:href="010/01/167.jpg"/><arrow.to.target n="marg202"/><lb/>VG multò magis aqua in&longs;inuabitur infra aerem dila­<lb/>tando &longs;inum ampliorem ODAIR, & multò magis­<lb/>incuruabitur aeris &longs;uperficies EBD, tum à vi qua flui­<lb/>da &longs;e &longs;e connectunt conglobanturque, quotie&longs;cum­<lb/>que in fluido ip&longs;is hetherogeneo <expan abbr="collocãtur">collocantur</expan>, cùm ab <lb/>acce&longs;&longs;u noui aeris expul&longs;i à cauitate infima DAIRO. <lb/><!-- KEEP S--></s> <s id="s.000802">Poftquàm verò magis fi&longs;tula deprimitur in &longs;itu val­<lb/>dè inclinato VH eadem ratione profluet aqua versùs <lb/>partem infimam, & omninò aerem &longs;eparabit, diuel­<lb/>letque à fundo va&longs;is, & proindè &longs;ubintrabit ad oc­<lb/>cupandum &longs;patium ODAICHR. </s> <s id="s.000803">Po&longs;tremò perdu­<lb/>cta fi&longs;tula ad inclinationem omnium maximam i&ntail; <lb/>&longs;itu VK perpendiculari ad <expan abbr="horizont&etilde;">horizontem</expan> aqua, quæ iam <lb/>in&longs;inuata fuerat circa, & infra aerem tumefactum, & <lb/>contornatum EBDC, <expan abbr="tãdèm">tandèm</expan> omninò aerem à fundo, <lb/>& lateribus va&longs;is diuellet, & proindè multò magis <lb/>de&longs;cen&longs;us, & compre&longs;&longs;io aquæ ambientis per latera <lb/>va&longs;is, & aeris continuari pote&longs;t; & vniuer&longs;a hæc o­<lb/>peratio pendet, vt dictum e&longs;t, non ab aere &longs;pont&etail; <lb/>a&longs;cendente, neque ab eius leuitate, &longs;ed ab exce&longs;&longs;u <lb/>grauitatis fluidæ aquæ ambientis, quæ in vertigine <lb/>fi&longs;tulæ nece&longs;&longs;ariò &longs;eparat, atque diuellit aerem à la­<lb/>teribus, & fundo va&longs;is, & &longs;ic via &longs;ternitur commodi&longs;­<lb/>&longs;ima, vt continuari, & pro&longs;equi pre&longs;&longs;io aquæ po&longs;&longs;it, <lb/>vnde aer &longs;ursùm expul&longs;us continuare pote&longs;t eius cur­<lb/>&longs;um, &longs;i, inquam, hoc ob&longs;eruatum, & adnotatum fui&longs;­<lb/>&longs;et, proculdubiò ex mutatione figuræ planæ in tumi­<lb/>dam in aere a&longs;cendente per aquam non deduxi&longs;&longs;et <lb/>prædictus author aeris leuitatem po&longs;itiuam. <pb pagenum="160" xlink:href="010/01/168.jpg"/><arrow.to.target n="marg203"/></s> </p> <p type="margin"> <s id="s.000804"><margin.target id="marg202"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000805"><margin.target id="marg203"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000806">Sed po&longs;ito quòd in vehementi&longs;&longs;ima turbinatione <lb/>retineretur pauli&longs;pèr aqua adhærens fundo &longs;upremo <lb/>fi&longs;tulæ, & proinde aer infimus &longs;altem per <expan abbr="breui&longs;&longs;imũ">breui&longs;&longs;imum</expan> <lb/>&longs;patium cylindricam formam ORXP retineret, mani­<lb/>fe&longs;tum e&longs;t, quòd &longs;ubito ce&longs;&longs;ante impetu aqua vt gra­<lb/>uior aere deorsùm de&longs;cenderet, labereturque, aut <lb/>in loco intermedio fi&longs;tulæ, aut ad latera, prout vndu­<lb/>latio partium aquæ eam promoueret, & &longs;ic &longs;emper à <lb/>de&longs;cen&longs;u grauioris aqu&etail; figura tumida, & conuexa <lb/>aeris a&longs;cendentis crearetur, numquam verò &longs;pont&etail; <lb/>ab ip&longs;a leuitate aeris. </s> </p> <p type="main"> <s id="s.000807"><arrow.to.target n="marg204"/></s> </p> <p type="margin"> <s id="s.000808"><margin.target id="marg204"/>Re&longs;ponde­<lb/>tur &longs;ingulis <lb/>oppo&longs;itioni­<lb/>bus aduer­<lb/>&longs;arij.</s> </p> <p type="main"> <s id="s.000809">Cùm verò in&longs;tat: <emph type="italics"/>Si idcircò aer &longs;ursùm tendit, quia ab <lb/>aqua deorsùm tendente extruditur in &longs;uperiora aqua potiùs <lb/>peruaderet cuneatim aerem, quem admodum aqua <expan abbr="decid&etilde;s">decidens</expan> <lb/>extra fistulam &longs;ubiectum aerem perrumpit, non verò illum <lb/>ambiens intra &longs;e recipit.<emph.end type="italics"/></s> <s id="s.000810"> Hic primò noto, quòd non <expan abbr="s&etilde;-per">sem<lb/>per</expan> aqua cadens aerem penetrat, nam multoties <lb/>penetratur ab ip&longs;o aere quando nimirùm &longs;cinditur <lb/>in plures partes, vt contingit in pluuia, vel potiùs <lb/>quando è fene&longs;tra catino aqua proijcitur. </s> </p> <p type="main"> <s id="s.000811">Sic paritèr ma&longs;&longs;a pulueris terre&longs;tris è turris verti­<lb/>ce proiecta licèt in principio &longs;it vnita, nihilominùs <lb/>ab aere di&longs;&longs;ipatur, di&longs;pergiturque, idemque accidit <lb/>in fumo a&longs;cendente per aerem. </s> <s id="s.000812">Secundò noto, quòd <lb/>partes aeris, vt dictum e&longs;t, &longs;ponte &longs;ua connectuntur <lb/>colliganturque inter &longs;e, & proinde intra aquam po­<lb/>&longs;itæ omnes vniri debent, atque &longs;imùl, conglobatæ <lb/>per aquam a&longs;cendent, non &longs;ecùs, ac partes aquæ in­<lb/>tra aerem, vel oleum vici&longs;&longs;im vniuntur, congloban- <pb pagenum="161" xlink:href="010/01/169.jpg"/><arrow.to.target n="marg205"/><lb/>turque. </s> <s id="s.000813">Et tunc &longs;olummodò ab inuicem &longs;egregantur <lb/>&longs;ubdiuidunturque, quando medium fluidum vehe­<lb/>menti, & irregulari motu fluidum per ip&longs;um a&longs;cen­<lb/>dens, vel de&longs;cendens perrumpit diuiditque, &longs;eù quia <lb/>non omnes partes prædicti fluidi excurrentis æquali <lb/>impetu mouentur, vel quia laterales partes fluidi ab <lb/>a&longs;peritatibus, & contactibus laterum fi&longs;tulæ retar­<lb/>dantur, &longs;eù ab aliqua alia cau&longs;a detinentur: nil igitur <lb/>ex hoc pro leuitate po&longs;itiua acquiritur. </s> </p> <p type="margin"> <s id="s.000814"><margin.target id="marg205"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000815">Subdit po&longs;tea idem author, quòd <emph type="italics"/>aqua &longs;upernè re­<lb/>tunderet aeris tumorem, & infernè illum, qua&longs;i forcipe <lb/>comprimens, con&longs;tringeret ad figuram conoidem eius partem <lb/>infimam.<emph.end type="italics"/></s> <s id="s.000816"> Re&longs;pondetur hoc fal&longs;um e&longs;&longs;e, quia vt ia&mtail; <lb/>demon&longs;tratum e&longs;t nunquam figura aeris per aquam <lb/>a&longs;cendentis acuminata in eius infima parte effici po&longs;­<lb/>&longs;et, &longs;ed nece&longs;sè e&longs;t, vt ab impul&longs;u facto ab aqua gra­<lb/>uiori ibidem excauetur ad modum &longs;cutellæ, & prop­<lb/>ter occur&longs;um, & ob&longs;taculum aquæ &longs;upremæ dum aer <lb/>fluidus a&longs;cendit tumorem, & conuexitatem &longs;uper­<lb/>nè acquirat. </s> </p> <p type="main"> <s id="s.000817">Cùm verò idem author &longs;ubdit, quod <emph type="italics"/>&longs;i ca&longs;u copule­<lb/>tur particula aliqua aeris cum oleo per aquam a&longs;cendente, <lb/>con&longs;tat quòd huiu&longs;modi aggregatum velociùs a&longs;cendit per <lb/>aquam.<emph.end type="italics"/> <expan abbr="Nõ">non</expan> video quidnam ex hoc deduci po&longs;&longs;it pro <lb/>leuitate po&longs;itiua, imò nego quod <emph type="italics"/>non pos&longs;it reddi phy­<lb/>&longs;ica, & &longs;olida ratio cur velociùs moueatur coniunctum il­<lb/>lud ex oleo, & aere, quàm oleum &longs;olum.<emph.end type="italics"/></s> <s id="s.000818"> Et po&longs;tea: <emph type="italics"/>neque <lb/>aquam citiùs de&longs;cendendo expellere quoque citiùs oleum <lb/>&longs;ursùm cum nec maior moles &longs;it aquæ &longs;upra <expan abbr="oleũ">oleum</expan>, quàm an-<emph.end type="italics"/><pb pagenum="162" xlink:href="010/01/170.jpg"/><arrow.to.target n="marg206"/><lb/><emph type="italics"/>tea.<emph.end type="italics"/></s> <s id="s.000819"> Primò aio nil referre an moles aquæ &longs;it maior, <lb/>aut minor re&longs;pectu olei, & aeris, &longs;ed &longs;ufficit vt gra­<lb/>uitas &longs;pecifica aquæ, multò maior &longs;it re&longs;pectu aggre­<lb/>gati ex aere, & oleo, quàm re&longs;pectu &longs;olius olei, ita­<lb/>que in ca&longs;u no&longs;tro moles aquæ, &longs;iue magna, &longs;iue exi­<lb/>gua, in fi&longs;tula pote&longs;t comparari cum oleo tantùm, vel <lb/>cum aggregato ex oleo, & aere; modò ex Archime­<lb/>dis doctrina eadem aqua grauior e&longs;t &longs;pecie aggre­<lb/>gato ex oleo & aere, quàm oleo &longs;olitario, & quò ma­<lb/>ior fuerit differentia grauitatum &longs;pecificarum, tantò <lb/>maior, c&etail;teris paribus, e&longs;t velocitas mobilis in fluido, <lb/>& hinc <expan abbr="cõ&longs;tat">con&longs;tat</expan> quòd ea quæ adducta &longs;unt, vt maximè <lb/>ab&longs;urda <expan abbr="nedũ">nedum</expan> inconuenientia non &longs;unt, &longs;ed è contrà <lb/>nece&longs;&longs;itate mechanica contingere debent. </s> <s id="s.000820">Po&longs;tremæ <lb/>oppo&longs;itioni, vbi ait: <emph type="italics"/>Nec denique dici pote&longs;t coniunctum <lb/>ex oleo, & aere e&longs;&longs;e aliquid leuius, quàm aquæ alterum <expan abbr="tã-tum">tan­<lb/>tum</expan> in eadem mole, ideoque aquam illud magis in grauita­<lb/>te excedere, quàm oleum &longs;eorsùm &longs;umptum, & proindè ci­<lb/>tiùs illius locum occupare velle; nam &longs;i non datur leuitas, <lb/>& particula aeris habet aliquid grauitatis potiùs ex illa, & <lb/>oleo factum est corpus grauius, quàm est &longs;olum oleum.<emph.end type="italics"/></s> <s id="s.000821"> Et <lb/>hic nil aliud re&longs;pondere po&longs;&longs;um, ni&longs;i quòd huiu&longs;mo­<lb/>di ratiocinia condonari po&longs;&longs;unt ijs, qui in doctrin&atail; <lb/>Archimedis minimè ver&longs;ati &longs;unt. </s> <s id="s.000822">Affertur enim, vt <lb/>ab&longs;urdum, quòd aggregatum ex oleo, & aere grauius <lb/>&longs;it ab&longs;olutè &longs;olo oleo, quod profectò non negatur, e&longs;t <lb/>enim veri&longs;&longs;imum, &longs;ed tamen animaduertendum e&longs;t, <lb/>quod licèt prædictum aggregatum ex oleo, & aer&etail; <lb/>grauitate ab&longs;oluta magis ponderet, quàm oleum per <pb pagenum="163" xlink:href="010/01/171.jpg"/><arrow.to.target n="marg207"/><lb/>&longs;e &longs;umptum, tamen &longs;i grauitas &longs;pecifica con&longs;idere­<lb/>tur, erit aggregatum ex oleo, & aere minùs graue, <lb/>quàm oleum &longs;olum, quia nempè pondus aggregati <lb/>ex oleo & aere, minorem proportionem habet ad <lb/>grauitatem molis aqueæ ei æqualis, quàm pondus <lb/>&longs;olius olei habeat ad <expan abbr="grauitat&etilde;">grauitatem</expan> aquæ molis prædicto <lb/>oleo æqualis, &longs;cilicèt &longs;i aggregati ex oleo, & aere <lb/>grauitas &longs;ubdupla fuerit pondere molis aquæ &longs;ibi æ­<lb/>qualis, pondus olei &longs;olius maius erit medietate <expan abbr="põ-deris">pon­<lb/>deris</expan> molis aquæ oleo æqualis, & hinc &longs;it vt maiori <lb/>impetu &longs;ursùm per expre&longs;&longs;ionem impellatur aggre­<lb/>gatum ex oleo & aere à &longs;uperabundanti grauitate <lb/>aquæ circumfu&longs;æ, quæ maiori differentia &longs;pecificam <lb/>grauitatem eius &longs;uperat, quàm moueatur oleum &longs;ur­<lb/>sùm extru&longs;um à pondere minùs excedenti eiu&longs;de&mtail; <lb/>aquæ ambientis. </s> <s id="s.000823">Et hoc quidem &longs;i ritè percipiatur, <lb/>tollentur, & euane&longs;cent omnes difficultates, quæ <lb/>contra prædictam doctrinam afferri po&longs;&longs;unt. </s> </p> <p type="margin"> <s id="s.000824"><margin.target id="marg206"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000825"><margin.target id="marg207"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000826">Præter ea, quæ iam dicta &longs;unt affert idem author <lb/>alia experimenta ex quibus putat euidentèr deduci <lb/><arrow.to.target n="marg208"/><lb/>po&longs;&longs;e exi&longs;tentiam leuitatis po&longs;itiuæ, quia inquit: <lb/><emph type="italics"/>Cylindrus ligneus è fundo aquæ &longs;ursùm tanto impetu fertur <lb/>vt multotiès exiliat totus &longs;upra aquam ille igitur &longs;altus in­<lb/>dicium e&longs;t impetus ab intrin&longs;eca leuitate facti, quia aqua <lb/>non pote&longs;t illud vltrà trudere quam &longs;it ip&longs;i opus vt locum <lb/>inferiorem occupet ni&longs;i ip&longs;a &longs;ursùm priùs feratur, quod e&longs;t <lb/>contra ip&longs;ius grauitatem.<emph.end type="italics"/><pb pagenum="164" xlink:href="010/01/172.jpg"/><arrow.to.target n="marg209"/></s> </p> <p type="margin"> <s id="s.000827"><margin.target id="marg208"/>Noua <expan abbr="argu-m&etilde;ta">argu­<lb/>menta</expan> eiu&longs;d<expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>Authoris <lb/>pro leuitate <lb/>po&longs;itiua.</s> </p> <p type="margin"> <s id="s.000828"><margin.target id="marg209"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000829"><emph type="center"/>PROP. LXXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000830"><emph type="center"/><emph type="italics"/>Lignum in aqua a&longs;cendens &longs;altu &longs;upra eius libellam exilit <lb/>ob impetum acqui&longs;itum in præcedenti motu, licèt per <lb/>extru&longs;ionem fiat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000831">PRo re&longs;pon&longs;ione ponamus cylindrum ligneum in <lb/>fundo aquæ. </s> <s id="s.000832">Dico quòd &longs;i id moueatur &longs;ursùm <lb/>ab intrin&longs;eca vilenitatis, vel ab extru&longs;ione medij flui­<lb/>di aquei, nece&longs;&longs;ariò velocitas eius dum a&longs;cendit <expan abbr="cõ-tinentèr">con­<lb/>tinentèr</expan> augebitur, quia dum &longs;ursùm <expan abbr="a&longs;c&etilde;dit">a&longs;cendit</expan> in quo­<lb/>libet temporis in&longs;tanti, eadem virtus motiua, aut le­<lb/>uitatis, aut externi impul&longs;us, quæ &longs;emper eadem, & <lb/>eiu&longs;dem energiæ e&longs;t, pariterque extru&longs;io à medio <lb/>fluido paritèr efficitur ab eadem virtute impul&longs;iua, <lb/>quæ e&longs;t differentia, vel exce&longs;&longs;us ponderis aquæ &longs;u­<lb/>pra pondus ligni a&longs;cendentis, cùmque gradus velo­<lb/>citatum à ligno acqui&longs;iti ob impul&longs;iones ei illatas <expan abbr="nõ">non</expan> <lb/>&longs;ubitò extinguantur, &longs;ed per&longs;euerent, vt dictum e&longs;t, <lb/>igitur &longs;ub&longs;equentes impul&longs;iones imprimuntur ei mo­<lb/><arrow.to.target n="marg210"/><lb/>bili non inerti, &longs;ed iam agitati à præcedentibus im­<lb/>pre&longs;&longs;is velocitatibus, & proindè &longs;ucce&longs;&longs;iuo incre­<lb/>mento augebitur gradus impetus eiu&longs;dem ligni <expan abbr="a&longs;c&etilde;-dentis">a&longs;cen­<lb/>dentis</expan>. </s> <s id="s.000833">Igitur mirum non e&longs;t, cylindrum ligneu&mtail;, <lb/>quando iam acqui&longs;iuit in&longs;ignem gradum impetus à <lb/>continuato impul&longs;u, & pre&longs;&longs;ione aquæ circumfu&longs;æ, <lb/>&longs;iuè ab interna eius leuitate po&longs;itiua, mirum, <expan abbr="inquã">inquam</expan>, <lb/>non e&longs;t &longs;i ab aqua pro&longs;iliat, & &longs;ursùm extra aquæ &longs;u­<lb/>perficiem propellatur: non igitur &longs;ignum <expan abbr="nece&longs;&longs;ariũ">nece&longs;&longs;arium</expan> <pb pagenum="165" xlink:href="010/01/173.jpg"/><arrow.to.target n="marg211"/><lb/>e&longs;t &longs;altus, & pro&longs;ilitio ligni ab aqua leuitatis eius <lb/>po&longs;itiuæ, quandoquidem prædictus &longs;altus effici po­<lb/>te&longs;t in vtraque hypothe&longs;i, &longs;cilicèt &longs;iuè admittatur, <lb/>&longs;iuè negetur leuitas po&longs;itiua. </s> </p> <p type="margin"> <s id="s.000834"><margin.target id="marg210"/>Lib. de vi <lb/><gap/> ca. 9.</s> </p> <p type="margin"> <s id="s.000835"><margin.target id="marg211"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000836">Sed vt apertè inefficacia huius argumenti perci­<lb/>piatur, po&longs;&longs;umus ij&longs;dem ferè verbis o&longs;tendere fal&longs;um <lb/><arrow.to.target n="marg212"/><lb/>e&longs;&longs;e, quòd à leuitate po&longs;itiua lignum &longs;ursùm impel­<lb/>latur, ait enim <emph type="italics"/>&longs;altum dependere non po&longs;&longs;e ab extru&longs;ione <lb/>aquæ ambientis, quia aqua non potest illud vltrà trude­<lb/>re, quàm &longs;it ip&longs;i opus, vt locum inferiorem occupet.<emph.end type="italics"/></s> <s id="s.000837"> Di­<lb/>cam ego eodem modo contra leuitatem po&longs;itiuam, <lb/>quod non deberet eius leuitas propellere <expan abbr="lignũ">lignum</expan> plùs, <lb/>quàm requirit recta di&longs;po&longs;itio, & con&longs;titutio natura­<lb/>lis, quia nempè (&longs;ubijciam) non pote&longs;t leuitas <expan abbr="lignũ">lignum</expan> <lb/>vltrà &longs;ubleuare, quàm &longs;it ip&longs;i opus vt locum &longs;uperi­<lb/>orem in aqua occupet, cùm &longs;it nempè leuitas null&atail; <lb/>alia de cau&longs;a ligno communicata ab ip&longs;a natura, ni&longs;i <lb/>vt vna pars ligni demer&longs;a &longs;ub&longs;idat, altera verò &longs;upra <lb/>eam in aere emineat, non verò vt lignum integru&mtail; <lb/>extra aquam collocetin ip&longs;o nempè aere. </s> <s id="s.000838">igitur con­<lb/>cedat aduer&longs;arius nece&longs;sè e&longs;t non expul&longs;um fui&longs;&longs;e li­<lb/>gnum &longs;ursùm à leuitate po&longs;itiua &longs;upra <expan abbr="&longs;upremã">&longs;upremam</expan> aquæ <lb/>libellam, & hinc planè conijciet &longs;ui argumenti inef­<lb/>ficaciam. </s> </p> <p type="margin"> <s id="s.000839"><margin.target id="marg212"/>Retorquetur <lb/>idip&longs;um ar­<lb/>gumentum <lb/>contra ad­<lb/>uer&longs;arium. </s> </p> <p type="main"> <s id="s.000840">Pro&longs;equitur deindè: <emph type="italics"/>quando cylindrus erat in fundo <expan abbr="noõ">non </expan><lb/>pote&longs;t inueniri, quæ pars aquæ illum &longs;ursùm trudat non illa, <lb/>quæ in fundo, &longs;uppono enim perfectum cylindrum phy&longs;icè, <lb/>& fundum va&longs;is exactè <expan abbr="planũ">planum</expan> adeò vt nulla &longs;en&longs;ibilis pars <lb/>aquæ interlabi pos&longs;it quamdiù cylinder vi detinetur ibi.<emph.end type="italics"/><pb pagenum="166" xlink:href="010/01/174.jpg"/><arrow.to.target n="marg213"/></s> </p> <p type="margin"> <s id="s.000841"><margin.target id="marg213"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000842">Et hinc apertè conijcio non benè perceptum fui&longs;­<lb/>&longs;e modum quomodò medium fluidum &longs;ursùm impel­<lb/>lat <expan abbr="extrudatq;">extrudatque</expan> lignum minùs graue ip&longs;a aqua, & ideò <lb/>operæpretium erit apertè, & di&longs;tinctè hoc declarare. </s> </p> <p type="main"> <s id="s.000843"><emph type="center"/>PROP. LXXX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000844"><emph type="center"/><emph type="italics"/>Ni&longs;i lignum, & ambiens aqua collateralis motibus contra­<lb/>rijs &longs;ursùm, & deorsùm &longs;imul tempore moueri que­<lb/>ant, numquam lignum in aqua a&longs;cendet.<emph.end type="italics"/><emph.end type="center"/></s> </p> <figure id="id.010.01.174.1.jpg" xlink:href="010/01/174/1.jpg"/> <p type="main"> <s id="s.000845">SIt vas ABCD aqua plenum i&ntail; <lb/>cuius fundo apponatur pri&longs;ma <lb/>ligneum EFGB hìc ade&longs;t aqua li­<lb/>gno incumbens AEFH, atque aqua <lb/>collateralis HFID, quæ comprimit <lb/>&longs;ubiectum aqueum pri&longs;ma FICG, <lb/>Dico primò, quod &longs;uperincumbens <lb/>aqua AEFH nequaquàm &longs;ursùm impellit &longs;ubiectum <lb/>lignum, imò id comprimit: neque præterea &longs;uperna <lb/>collateralis aqua HFID prædictum lignum eleuat, <lb/>&longs;ed tantummodò æquilibratur cum collaterali aqua <lb/>AEFH. </s> <s id="s.000846">Tantummodò ad rem no&longs;tram facit aqu&atail;, <lb/>quæ ad latus ip&longs;ius ligni apponitur, FGCI, & hæc <expan abbr="nõ">non</expan> <lb/>&longs;emper &longs;ubleuare pote&longs;t lignum BF, ni&longs;i habuerit <lb/>duas conditiones, primò vt aqua FC de&longs;cender&etail; <lb/>deorsùm valeat, &longs;ecundò vt eodem tempore eadem <lb/>aqua lignum GE impellere &longs;ursùm po&longs;&longs;it. </s> <s id="s.000847">At quan­<lb/>dò huiu&longs;modi motus contrarij ob aliquod impedi­<lb/>mentum fieri &longs;imùl <expan abbr="nõ">non</expan> po&longs;&longs;unt, omninò lignum quie-</s> </p> <pb pagenum="167" xlink:href="010/01/175.jpg"/> <p type="main"> <s id="s.000848"><arrow.to.target n="marg214"/><lb/>&longs;cet in fundo ip&longs;ius aquæ, quia nimirum locum non <lb/>habet libræ, aut &longs;iphonis operatio. </s> <s id="s.000849">Hoc autem &longs;ic <lb/>per&longs;picuum fiet: &longs;upponamus ba&longs;im lignei pri&longs;matis <lb/>BG perfectè, & exqui&longs;itè tangere fundum va&longs;is BC, <lb/>&longs;cilicèt &longs;i amb&etail; &longs;uperficies fuerint explanatæ, & læ­<lb/>uigatæ, tunc profectò aqua FC, licèt grauior &longs;it ip&longs;o <lb/>ligno minimè excurrere poterit deorsùm cùm no&ntail; <lb/>ad&longs;it aditus inter ligni ba&longs;im BG, & <expan abbr="fundũ">fundum</expan> putei: in­<lb/>nititur igitur atque &longs;u&longs;tentatur maius pondus aqu&etail; <lb/>FC à &longs;oliditate fundi GC eiu&longs;dem putei, quare ne­<lb/>ce&longs;sè e&longs;t vt <expan abbr="ead&etilde;">eadem</expan> aqua collateralis FC omninò quie­<lb/>&longs;cat, & proindè lignum EG non a&longs;cendet &longs;ursùm, nec <lb/>expelletur ab aqua collaterali quie&longs;cente, quaprop­<lb/>ter habebimus libram BC non quidem <expan abbr="conuertibil&etilde;">conuertibilem</expan> <lb/>circa centrum G, &longs;ed &longs;tabilem, & firmam, cum in ea <lb/>minimè contrarij motus <expan abbr="de&longs;c&etilde;&longs;us">de&longs;cen&longs;us</expan> partis GC, & <expan abbr="a&longs;c&etilde;-&longs;us">a&longs;cen­<lb/>&longs;us</expan> alterius radij BG fieri po&longs;&longs;int &longs;imùl, & &longs;emel, vn­<lb/>de mirum non e&longs;t lignum GE è fundo va&longs;is non <expan abbr="a&longs;c&etilde;-dere">a&longs;cen­<lb/>dere</expan>. </s> </p> <p type="margin"> <s id="s.000850"><margin.target id="marg214"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000851"><emph type="center"/>PROP. LXXXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000852"><emph type="center"/><emph type="italics"/>Vis motiua eleuans lignum in aqua e&longs;t maius pondus colla­<lb/>teralis aquæ, quæ de&longs;cendere pos&longs;it, & præterea mo­<lb/>tu reflexo infimam ligni ba&longs;im &longs;ursùm <lb/>impellat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000853">PRæterea dico, quòd non &longs;ufficit vt aqua collate­<lb/>ralis FC &longs;olummodò moueri deorsùm po&longs;&longs;it, <lb/>&longs;ed oportet pr&etail;tere a vt reflectatur &longs;ursùm infrà <expan abbr="lignũ">lignum</expan> <pb pagenum="168" xlink:href="010/01/176.jpg"/><arrow.to.target n="marg215"/><lb/>GE ad hoc vt lignum è fundo va&longs;is a&longs;cendat, quod <lb/>con&longs;tat hac experientia: Perforetur <expan abbr="fundũ">fundum</expan> va&longs;is GC <lb/>tunc profectò aqua FG, & ei &longs;uperincumbens FD <lb/>profluet <expan abbr="de&longs;cend&etilde;do">de&longs;cendendo</expan> per <expan abbr="apertũ">apertum</expan> orificium GC, nec <lb/>proindè <expan abbr="lignũ">lignum</expan> GE <expan abbr="&longs;ursũ">&longs;ursum</expan> <expan abbr="a&longs;c&etilde;det">a&longs;cendet</expan>, &longs;ed nece&longs;sè e&longs;t ob­<lb/>turato foramine GC, vt aqua fluere, & in&longs;inuari po&longs;­<lb/>&longs;it inter pri&longs;matis ba&longs;im BG, & fundum putei, & tune <lb/>a&longs;cendet lignum, &longs;i nimirùm concipiatur putei fun­<lb/>dum magis depre&longs;&longs;um vt e&longs;t MK, & aqua FC proflu­<lb/><figure id="id.010.01.176.1.jpg" xlink:href="010/01/176/1.jpg"/><lb/>ens repleuerit &longs;patium BMLG ef­<lb/>ficietur &longs;ipho DKMA cuius vn&atail; <lb/>pars aquea HK grauìor e&longs;t reliqua <lb/>parte AL, & proindè <expan abbr="maior&etilde;">maiorem</expan> vim <lb/>compre&longs;&longs;iuam habebit aqua HK, <lb/>quàm aqua, & <expan abbr="lignũ">lignum</expan> AL, & prop­<lb/>terea deprimetur de&longs;cendendo a­<lb/>qua FGK eleuabiturque motu <expan abbr="cõtrario">contrario</expan> aqua LB vnà <lb/>cum ligno incumbente, nece&longs;&longs;ariò igitur requiruntur <lb/>hi duo motus contrarij de&longs;cen&longs;us aquæ grauioris FK, <lb/>& a&longs;cen&longs;us aquæ LB vt lignum eleuari po&longs;&longs;it. </s> <s id="s.000854">Hinc <lb/>colligitur, quod vis motiua, quæ impellit ligneu&mtail; <lb/>pri&longs;ma GE &longs;ursùm e&longs;t profectò grauitas aquæ colla­<lb/>teralis FC, &longs;ed quatenùs moueri, atque de&longs;cendere <lb/>pote&longs;t, & præterea quatenus &longs;ursùm impellere va­<lb/>let aquam BL, & huic impul&longs;ui cedere debet minor <lb/>vis deficientis grauitatis ligni EG, & hæc e&longs;t legiti­<lb/>ma, & adæquata cau&longs;a, quare lignum à maiori im­<lb/>pul&longs;u aquæ collateralis prementis &longs;ursùm impelli­<lb/>tur ab aqua, quæ infra eius ba&longs;im in&longs;inuatur. <pb pagenum="169" xlink:href="010/01/177.jpg"/><arrow.to.target n="marg216"/></s> </p> <p type="margin"> <s id="s.000855"><margin.target id="marg215"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000856"><margin.target id="marg216"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000857">His declaratis accedamus iam ad difficultates ad­<lb/>uer&longs;arij, in quibus &longs;upponit, quòd dum ligneus cy­<lb/>lindrus GE exqui&longs;ito, & immediato contactu fundo <lb/>va&longs;is adhæret, ip&longs;umque veluti exo&longs;culatur, licèt vas </s> </p> <p type="main"> <s id="s.000858"><arrow.to.target n="marg217"/><lb/>repletum aqua fuerit, lignum &longs;ponte &longs;ua, & vi eius <lb/>leuitatis &longs;ursùm a&longs;cendere deberet. </s> <s id="s.000859">Sed quid facies, <lb/>&longs;i experimentum huic a&longs;&longs;ertioni refragatur? </s> <s id="s.000860">Et pro­<lb/>cùl dubio &longs;i experimentum ita &longs;e haberet, vt ab ip&longs;o <lb/>refertur, &longs;cilicèt &longs;i cylindrus ligneus GE exqui&longs;itè <lb/>tangens &longs;uperficiem fundi va&longs;is BG complanatam, <lb/>& l&etail;uigatam, e&longs;&longs;etque vas aqua repletum, & nihilo­<lb/>minus lignum &longs;ursùm a&longs;cenderet, nece&longs;&longs;ariò a&longs;&longs;erere <lb/>teneremur, & confiteri, lignum, non à principio ex­<lb/>trin&longs;eco per extru&longs;ionem, &longs;ed à vi naturali leuitatis <lb/>eius a&longs;cendere. </s> </p> <p type="margin"> <s id="s.000861"><margin.target id="marg217"/>Experimen­<lb/>tum fal&longs;um <lb/>aduer&longs;arij <lb/>pro leuitate <lb/>po&longs;itiua.</s> </p> <p type="main"> <s id="s.000862"><emph type="center"/>PROP. LXXXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000863"><emph type="center"/><emph type="italics"/>Experimentis euincitur non ob defectum leuitatis po&longs;itiuæ, <lb/>&longs;ed quia extru&longs;io à medio fluido grauiori fieri non po­<lb/>test, lignum in aquæ fundo quie&longs;cere.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000864">VErùm quia lignum EG in aqua demer&longs;um non <lb/>a&longs;cendit è fundo va&longs;is cui adhæret, imò ibidem <lb/>&longs;i&longs;titur, & quie&longs;cit, igitur <expan abbr="nõ">non</expan> ine&longs;t in ligno cau&longs;a ima­<lb/>ginata, quæ leuitas po&longs;itiua vocatur. </s> <s id="s.000865">E contrà quo­<lb/>tie&longs;cumque fieri, & exerceri pote&longs;t extru&longs;io medij <lb/>fluidi, ide&longs;t quotie&longs;cumque fluidum grauius fluer&etail; <lb/>pote&longs;t, & in&longs;inuari infra cylindrum ligneum, &longs;emper <lb/>&longs;ub&longs;equitur effectus a&longs;cen&longs;us illius, at quando (vt <pb pagenum="170" xlink:href="010/01/178.jpg"/><arrow.to.target n="marg218"/><lb/>in no&longs;tro ca&longs;u accidit) aqua &longs;ubingredi inter duas <lb/>&longs;uperficies ligni, & fundi va&longs;is non pote&longs;t ob exqui­<lb/>&longs;itum contactum, & congruentiam, tunc non &longs;equi­<lb/>tur effectus a&longs;cen&longs;us eiu&longs;dem ligni, veluti in bilance <lb/>pondus centum librarum non &longs;ubleuabit contrapo&longs;i­<lb/>tum pondus vnciale quotie&longs;cumque illud impeditur, <lb/>vt ne queat deorsùm deprimi, igitur vera cau&longs;a <expan abbr="a&longs;c&etilde;-&longs;us">a&longs;cen­<lb/>&longs;us</expan> ligni in aqua e&longs;t extru&longs;io facta à medio fluido, <expan abbr="nõ">non</expan> <lb/>autem leuitas po&longs;itiua in ligno inexi&longs;tens. </s> </p> <p type="margin"> <s id="s.000866"><margin.target id="marg218"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem non <lb/>dari. </s> </p> <p type="main"> <s id="s.000867">Porrò hoc experti &longs;umus in Academia Experimen­<lb/>tali Medicea. </s> <s id="s.000868">Po&longs;uimus pilam li­<lb/><figure id="id.010.01.178.1.jpg" xlink:href="010/01/178/1.jpg"/><lb/>gneam G in fundo va&longs;is ABCD, <lb/>quæ tangebat <expan abbr="orificiũ">orificium</expan> EF conca­<lb/>uitatis he mi&longs;phæricæ EIF in fun­<lb/>do va&longs;is excauatæ, po&longs;teà reple­<lb/>uimus vas hydrargyro v&longs;que ad <lb/>&longs;ummitatem AD, nec tamen li­<lb/>gnea pila G fundum reliquit a­<lb/>&longs;cendendo &longs;ursùm; & <expan abbr="notandũ">notandum</expan>, <lb/>quòd prædicta pila non arctè orificio va&longs;is adhære­<lb/>bat, & colligabatur, &longs;ed potiùs facillimè digitis di­<lb/>moueri contorquerique poterat, vnde conijcitur, <lb/>quàm debili nexu fundum, aut orificium acumi­<lb/>natum EF <expan abbr="tãgebat">tangebat</expan>. </s> <s id="s.000869">quia po&longs;te à in&longs;ignis Peripateticus <lb/>&longs;u&longs;picabatur, quòd præcipua cau&longs;a detinens <expan abbr="ligneã">ligneam</expan> <lb/>pilam demer&longs;am infra hydrargyrum in fundo va&longs;is <lb/>erat timor, & abominium vacui, quod effici debui&longs;­<lb/>&longs;et in illo &longs;patio quotie&longs;cumque pila &longs;ursùm a&longs;cen­<lb/>deret; proptereà, vt petijt prædictus Philo&longs;ophus <pb pagenum="171" xlink:href="010/01/179.jpg"/><arrow.to.target n="marg219"/><lb/>perforauimus fundum va&longs;is IH, vt nimirùm è part&etail; <lb/>&longs;ubiecta aer &longs;uccedere po&longs;&longs;et ad replendum <expan abbr="vacuũ">vacuum</expan>, <lb/>& &longs;ic leuitas po&longs;itiua ligni G ab&longs;que vacui periculo <lb/>commodè &longs;ursùm a&longs;cendere po&longs;&longs;et; hac præparatione <lb/>facta, illa lignea pila fundum non dereliquit, nec &longs;ur­<lb/>sùm a&longs;cendit; nec paritèr a&longs;cendit po&longs;tquam <expan abbr="foram&etilde;">foramen</expan> <lb/>H occlu&longs;um denuò fuit, & cauitas &longs;ubiecta EIF, & <lb/>&longs;uprema AED repleta hydrargyro fuit. </s> <s id="s.000870">Vnde dedu­<lb/>cere po&longs;&longs;umus pilam non à po&longs;itiua leuitate eleuari, <lb/>&longs;ed potiùs ab expre&longs;&longs;ione ambientis fluidi quotie&longs;­<lb/>cumque excurrere pote&longs;t ab&longs;que impedimento in­<lb/>fra &longs;uperficiem eiu&longs;dem pilæ. </s> </p> <p type="margin"> <s id="s.000871"><margin.target id="marg219"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000872">Perpendamus tandem po&longs;trema verba eiu&longs;de&mtail; <lb/><arrow.to.target n="marg220"/><lb/>Authoris, qui ait: <emph type="italics"/>Sed quid dicent aduer&longs;arij, &longs;i in fundo <lb/>va&longs;is e&longs;&longs;et foramen amplum, angu&longs;tius tamen cylindro, & <lb/>occlu&longs;um, quod eodem momento aperiretur quo manus eleuat <lb/>virgam? </s> <s id="s.000873">certè enim aqua efflueret deorsùm, & tamen cy­<lb/>lindraceum lignum illud tenderet &longs;ursùm. </s> <s id="s.000874">Agno&longs;cant ergò <lb/>in ligno illo leuitatem aliquam, quæ impetum producendo <lb/>&longs;ursùm versùs priùs natura mouet, ac pellit <expan abbr="aquã">aquam</expan>, & cau­<lb/>&longs;aest vt aqua corpus fluidum it a illi cedat, vt &longs;ubintret in <lb/>illius locum, ne detur vacuum, eamque non exercere gra­<lb/>uitatem actu, &longs;ed &longs;uperiores quidem aquæ partes impelli à <lb/>cylindro ligneo, & cedere illi locum digrediendo ad latera, <lb/>vt locum illarum partium impleant, quæ infernè <expan abbr="&longs;ubintrãt">&longs;ubintrant</expan> <lb/>in locum cylindri.<emph.end type="italics"/></s> <s id="s.000875"> Et hic nil aliud re&longs;pondere po&longs;&longs;u&mtail; <lb/>ni&longs;i mirari confidentiam, &longs;ecuritatemque qua a&longs;&longs;eri­<lb/>tur experientia non &longs;icuti reuera &longs;e habet, vtque à <lb/>quolibet comprobari pote&longs;t, &longs;ed veluti præiudica­<lb/>ta opinio eis per&longs;ua&longs;erat. <pb pagenum="172" xlink:href="010/01/180.jpg"/><arrow.to.target n="marg221"/></s> </p> <p type="margin"> <s id="s.000876"><margin.target id="marg220"/>Aliud <expan abbr="falsũ">falsum</expan> <lb/><expan abbr="experimentũ">experimentum</expan> <lb/>ab eodé au­<lb/>thore <expan abbr="allatũ">allatum</expan></s> </p> <p type="margin"> <s id="s.000877"><margin.target id="marg221"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <figure id="id.010.01.180.1.jpg" xlink:href="010/01/180/1.jpg"/> <p type="main"> <s id="s.000878">Sit igitur vas ABCD in cuius <expan abbr="fũdo">funshy;<lb/>do</expan> aperiatur amplum <expan abbr="foram&etilde;">foramen</expan> BC, <lb/>&longs;it po&longs;tea ligneus cylindrus FE, <lb/>cuius ba&longs;is HE paulò amplior &longs;it <lb/>foramine va&longs;is, vt nimirum po&longs;&longs;it <lb/>ip&longs;um præcisè occludere, ob&longs;true­<lb/>reque &longs;implici contactu; repleatur <lb/>po&longs;tea vas aqua <expan abbr="v&longs;q;">v&longs;que</expan> ad AD, &longs;up­<lb/>ponit aduer&longs;arius, quòd cylindrus <lb/>FE non po&longs;&longs;it in fundo va&longs;is deti­<lb/>neri, ni&longs;i <expan abbr="deorsũ">deorsum</expan> vi impellatur vir­<lb/>ga quadam ferrea ML præterea <lb/>ait, quòd &longs;i occlu&longs;o infimo foramine BC, <expan abbr="eod&etilde;">eodem</expan> mo­<lb/>mento temporis recludatur os infimum, remoueatur­<lb/>que virga ML, fore vt aqua exeat per infimum os <lb/>BC, & lignum FE a&longs;cendat &longs;ursùm, <emph type="italics"/>quod<emph.end type="italics"/>, &longs;ubdit ip­<lb/>&longs;e, <emph type="italics"/>e&longs;t argumentum certis&longs;imum leuitatis po&longs;itiuæ eiu&longs;dem <lb/>ligni.<emph.end type="italics"/></s> <s id="s.000879"> Et hic primò ob&longs;eruo contra aduer&longs;arij a&longs;&longs;er­<lb/>tionem, quòd &longs;i ba&longs;is cylindri HE zona circularis <lb/>præcisè tangat, & exo&longs;culetur perimetrum orificij <lb/>putei BC, tunc non requiritur epi&longs;tomium vt aqu&atail; <lb/>è va&longs;e non effluat, neque requiritur impul&longs;us virgæ <lb/>LM, vt prohibeatur a&longs;cen&longs;us cylindri FE è fundo va­<lb/>&longs;is, &longs;ed ibidem quie&longs;cet, veluti &longs;i tenacitèr colliga­<lb/>tus e&longs;&longs;et ab illo contactu &longs;implici. </s> <s id="s.000880">Imò, quod magis <lb/>mirere, &longs;i infima zona ba&longs;is HE ip&longs;ius cylindri lignei <lb/>non perfectè congrueret; neque compleret vndique <lb/>tangendo orificium infimum BC, &longs;ed per rimulas, <lb/>vel angulos aliquos aqua deor&longs;um efflueret, tunc <pb pagenum="173" xlink:href="010/01/181.jpg"/><arrow.to.target n="marg222"/><lb/>neque opus haberemus virga impellente ML vt li­<lb/>gnum prædictum in fundo va&longs;is retineretur, &longs;ed <expan abbr="&longs;põ-te">&longs;pon­<lb/>te</expan> &longs;ua ibidèm quie&longs;ceret, imò &longs;i quis conaretur &longs;ur­<lb/>sùm trahere prædictum <expan abbr="cylindrũ">cylindrum</expan> FE filo aliquo ML <lb/>tunc nedùm vt eius ba&longs;im diuelleret à contactu orifi­<lb/>cij BC, &longs;ed etiam po&longs;t eius &longs;eparationem à fundo per <lb/>aliquod exiguum interuallum, aliqua renitentia per­<lb/>&longs;entiretur, et vis aliqua trahens requireretur, aliàs <lb/>&longs;ponte &longs;ua lignum ip&longs;um decideret denuò ad occlu­<lb/>dendum va&longs;is orificium BC, Hinc videat aduer&longs;arius <lb/>quàm iure exclamet, cùm ait: <emph type="italics"/>Agno&longs;cant ergò in ligno <lb/>leuitatem aliquam, &c.<emph.end type="italics"/> quia cum experientia totu&mtail; <lb/>oppo&longs;itum o&longs;tendat, iurè po&longs;&longs;emus ei reddere verba <lb/>&longs;ua: Agno&longs;cat ergo in ligno nullam leuitatem ine&longs;&longs;e. </s> </p> <p type="margin"> <s id="s.000881"><margin.target id="marg222"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000882"><emph type="center"/>PROP. LXXXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000883"><emph type="center"/><emph type="italics"/>Supra foramen in fundo putei apertum exercetur compres&longs;io <lb/>ponderis columnæ aqueæ v&longs;que ad &longs;upremam eius li­<lb/>bellam exten&longs;æ.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000884">ET profectò ij, qui ver&longs;ati <lb/><figure id="id.010.01.181.1.jpg" xlink:href="010/01/181/1.jpg"/><lb/>&longs;unt in hac doctrina hydro­<lb/>&longs;tatica Archimedea optimè <expan abbr="no-rũt">no­<lb/>runt</expan>, quòd quotie&longs;cumque in præ­<lb/>dicto va&longs;e aqua pleno aperitur­<lb/>os in eius fundo BC, tunc ade&longs;t <lb/>cylindrus aqueus IBCK, qui <expan abbr="cõ-primit">com­<lb/>primit</expan>, & vim facit proprio pon­<lb/>dere &longs;upra quodlibet corpus im-<pb pagenum="174" xlink:href="010/01/182.jpg"/><arrow.to.target n="marg223"/><lb/>pediens exitum, ac fluxum prædictæ aquæ, quod <expan abbr="&qacute;ui-libet">qui­<lb/>libet</expan> experiri facilè pote&longs;t &longs;i palma manus occludat <lb/>infimum va&longs;is orificium BC, percipiet enim <expan abbr="cõpre&longs;-&longs;ionem">compre&longs;­<lb/>&longs;ionem</expan>, & impul&longs;um tanta vi factum quanta e&longs;t gra­<lb/>uitas cylindri aquei prædicti, & hoc experitur ne­<lb/>dùm quando palma manus vetat omninò effluxu&mtail; <lb/>aquæ, quam &longs;i aliquanti&longs;per manus &longs;ubleuetur, vt <lb/>po&longs;&longs;it aqua effluere. </s> <s id="s.000885">Hoc præmi&longs;&longs;o. </s> </p> <p type="margin"> <s id="s.000886"><margin.target id="marg223"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000887"><emph type="center"/>PROP. LXXXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000888"><emph type="center"/><emph type="italics"/>Ex prædicta experientia euidentèr o&longs;tendetur lignum in <lb/>aqua nullam po&longs;itiuam leuitatem exercere.<emph.end type="italics"/><emph.end type="center"/></s> </p> <figure id="id.010.01.182.1.jpg" xlink:href="010/01/182/1.jpg"/> <p type="main"> <s id="s.000889">SVpponamus cum Aduer­<lb/>&longs;ario (&longs;i po&longs;&longs;ibile e&longs;t) cy­<lb/>lindrum ligneum FE &longs;ub a­<lb/>qua <expan abbr="demersũ">demersum</expan> vim exercere, <lb/>ac tendere &longs;ursùm intrin&longs;eca <lb/>vi &longs;u&etail; leuitatis <expan abbr="dũ">dum</expan> aqua col­<lb/>lateralis per rimulas infimas <lb/>H & E effluit è va&longs;e: Sit ve­<lb/>rò energia leuitatis ligni (vt <lb/>æquum e&longs;t) certæ, & deter­<lb/>minatæ men&longs;uræ, quæ expri­<lb/>mi poterit à pondere corporis P <expan abbr="&longs;u&longs;p&etilde;&longs;i">&longs;u&longs;pen&longs;i</expan> in libra MO <lb/>radiorum æqualium; Huic vi leuitatis aduer&longs;atur <expan abbr="cõ-trario">con­<lb/>trario</expan> ni&longs;u pondus &longs;uperincumbentis cylindri aquei <lb/>IFGK, quod paritèr intelligatur termino M eiu&longs;dem <lb/>libræ &longs;u&longs;pen&longs;um. </s> <s id="s.000890">Quoniam vis leuitatis cylindri li-<pb pagenum="175" xlink:href="010/01/183.jpg"/><arrow.to.target n="marg224"/><lb/>gnei FE in aqua demer&longs;i &longs;emper eadem e&longs;t, nec po­<lb/>te&longs;t vnquam diminui, cùm &longs;it æqualis vi illius ponde­<lb/>ris, quod &longs;ufficit ad prohibendum <expan abbr="a&longs;c&etilde;&longs;um">a&longs;cen&longs;um</expan> prædicto <lb/>ligno FE (vt con&longs;tat ex Archimede) & è contrà pon­<lb/>dus incumbentis cylindri aquei IKGF pote&longs;t &longs;ucce&longs;­<lb/><arrow.to.target n="marg225"/><lb/>&longs;iuè diminui in infinitum prout eius altitudo IF dimi­<lb/>nuta fuerit, &longs;ublata nimirum aqna è va&longs;e ABD. fiat <lb/>igitur vis ponderis aquæ IG minor energia leuitatis <lb/>ligni FE, &longs;cilicèt minor &longs;it pondere P, quia verò mi­<lb/>nor vis &longs;uperari à maiori debet, igitur nece&longs;&longs;ariò <lb/>pondus P deprimet radium libræ NO, &longs;uperabitque <lb/>re&longs;i&longs;tentiam diminutæ aquæ IG &longs;u&longs;pen&longs;æ in altera li­<lb/>bræ extremitate M, &longs;cilicèt lignum FE (quod tange­<lb/>re orificium va&longs;is HE &longs;upponebatur) &longs;ursùm a&longs;cen­<lb/>det in ip&longs;a aqua vi maioris &longs;uæ leuitatis, &longs;ed hoc e&longs;t <lb/>fal&longs;um, & contra &longs;en&longs;us euidentiam, numquam enim <lb/>prædictus cylindius ligneus fundum de&longs;erit, nec &longs;ur­<lb/>sùm a&longs;cendit; &longs;i tamen &longs;emper orificio BC in&longs;i&longs;tat, <lb/>nec incutiatur vt ad latus fundi ba&longs;is transferatur, vbi <lb/>maior eius ba&longs;is pars in&longs;i&longs;tit fundo &longs;tabili putei, vel <lb/>cylindrus ip&longs;e tran&longs;uersè flectatur. </s> <s id="s.000891">Igitur verum <expan abbr="nõ">non</expan> <lb/>e&longs;t lignum FE exercere nè minimum gradum impe­<lb/>tus leuitatis. </s> </p> <p type="margin"> <s id="s.000892"><margin.target id="marg224"/>Cap 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000893"><margin.target id="marg225"/>De in&longs;idét. <lb/></s> <s id="s.000894">fluido lib. 1. <lb/>prop. 6.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000895"><emph type="center"/>PROP. LXXXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000896"><emph type="center"/><emph type="italics"/>Aliter idip&longs;um demonstrare.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000897">II&longs;dem po&longs;itis intelligatur præterea quòd vis leui­<lb/>tatis prædicti ligni, &longs;cilicèt pondus P æqualis &longs;it <pb pagenum="176" xlink:href="010/01/184.jpg"/><arrow.to.target n="marg226"/><lb/>energi&etail; ponderis incumbentis cylindri aquei IG: <lb/>tunc quælibet minima vis addita ponderi P deberet <lb/>eleuare v&longs;que ad &longs;upremæ aquæ libellam cylindrum <lb/>FE, quod &longs;imilitèr e&longs;t fal&longs;um, debet enim &longs;uperad­<lb/>di ponderi P aliud pondus R æquale ponderi lignei <lb/>cylindri FE. </s> </p> <p type="margin"> <s id="s.000898"><margin.target id="marg226"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000899"><emph type="center"/>PROP. LXXXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000900"><emph type="center"/><emph type="italics"/>Præterea alio modo idem confirmare.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000901">TAndem (in eadem hypothe&longs;i) &longs;it vis leuitatis <lb/>po&longs;itiuæ ligni FE minor vi ponderis &longs;uperin­<lb/>cumbentis cylindri aquei IG. (& maioris claritatis <lb/>gratia) &longs;upponamus pondus P æquale exce&longs;&longs;ui gra­<lb/>uitatis aqueæ molis cylindro FE æqualis &longs;upra pon­<lb/><arrow.to.target n="marg227"/><lb/><figure id="id.010.01.184.1.jpg" xlink:href="010/01/184/1.jpg"/><lb/>dus cylindri lignei prædicti; <lb/>quia ex Archimede lignu&mtail; <lb/>FE tanto impetu in aqua <expan abbr="t&etilde;-dit">ten­<lb/>dit</expan> &longs;ursùm <expan abbr="quãta">quanta</expan> e&longs;t vis gra­<lb/>uitatis pr&etail;dicti exce&longs;&longs;us. </s> <s id="s.000902">Mo­<lb/>dò <expan abbr="põdus">pondus</expan> cylindri aquei IG <lb/>maius e&longs;t pondere P, &longs;cilicèt <lb/>vi leuitatis ligni FE, igitur <lb/>prædicta leuitas à pondere <lb/>aquæ incumbentis &longs;uperabi­<lb/>tur vtpotè à maiori virtut&etail;, <lb/>& proindè lignum detinebitur in fundo va&longs;is, nec a­<lb/>&longs;cendet. </s> <s id="s.000903">Si po&longs;tea eidem termino libræ O &longs;u&longs;penda­<lb/>tur aliud pondus Q æquale exce&longs;&longs;ui ponderis aquæ <pb pagenum="177" xlink:href="010/01/185.jpg"/><arrow.to.target n="marg228"/><lb/>IG &longs;upra grauitatem P, patet quod vt &longs;uperetur im­<lb/>pedimentum, quod reperit lignum FE ip&longs;umque <expan abbr="a-&longs;c&etilde;dere">a­<lb/>&longs;cendere</expan> vetat &longs;ufficiet vis ponderis Q, quæ e&longs;t diffe­<lb/>rentia ponderis aquæ prementis IG, & leuitatis li­<lb/>gni FE. </s> <s id="s.000904">Sed hoc e&longs;t fal&longs;um, quandoquidem pr&etail;ter <lb/>pondus Q requiritur etiam pondus R æquale pon­<lb/>deri ab&longs;oluto cylindri lignei FE, & in&longs;uper requiri­<lb/>tur pondus P quod vnà cum Q æquantur ponderi a­<lb/>quæ IG. </s> <s id="s.000905">Quapropter adeò fal&longs;um e&longs;t ligneum cylin­<lb/>drum FE virtute propriæ leuitatis vim &longs;ursùm exer­<lb/>cere in aqua, vt potiùs deorsùm premat, vt corpus <lb/>graue. </s> </p> <p type="margin"> <s id="s.000906"><margin.target id="marg227"/>Ibidem.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000907"><margin.target id="marg228"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000908">Et hactenùs comparauimus vires comprimentes <lb/>grauitatis &longs;uperincumbentis cylindri aquei IG & le­<lb/>uitatis cylindri lignei FE, re&longs;tat modò vt paritèr <expan abbr="cõ-paremus">con­<lb/>paremus</expan> velocitates prædictorum corporum, &longs;cilicèt <lb/>videndum qua velocitate lignum FE &longs;ursùm à vile­<lb/>uitatis impellatur re&longs;pectu contrariæ celeritatis, qua <lb/>aqua ABD per infimum foramen BC effluit: eo pro­<lb/>pemodum modo, quo pi&longs;ces contra cur&longs;um alicuius <lb/>fluentis fluminis mouentur, &longs;i enim pi&longs;cis velociùs <lb/>natat, quàm aqua contrario cur&longs;u currat, procùl du­<lb/>bio pi&longs;cis re&longs;pectu fundi, & ripæ, & &longs;patij mundani <lb/>contra a quæ cur&longs;um reuera excurret aliquanti&longs;per, <lb/>quòd &longs;i prædictæ duæ contrariæ velocitates æquales <lb/>fuerint, licèt reuera pi&longs;cis agitetur, commoueatur­<lb/>que &longs;emper in eodem &longs;itu mundani &longs;patij per&longs;i&longs;tet, &longs;i <lb/>tandèm velocitas pi&longs;cis minor fuerit celeritate con­<lb/>traria fluentis, licèt pi&longs;cis natet, & verè anterius ex-<pb pagenum="178" xlink:href="010/01/186.jpg"/><arrow.to.target n="marg229"/><lb/>currat in aqua, nihilominùs retrocedet re&longs;pectu &longs;pa­<lb/>tij mundani, &longs;ed cur&longs;u magis tardo, & lento, quà&mtail; <lb/>flumen mouetur. </s> </p> <p type="margin"> <s id="s.000909"><margin.target id="marg229"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000910"><emph type="center"/>PROP. LXXXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000911"><emph type="center"/><emph type="italics"/>Alia ratione po&longs;itiuam leuitatem non dari <lb/>o&longs;tenditur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000912">IT aque eodem modo in va&longs;e ABC aqua pleno, & <lb/>infernè perforato in B intelligantur demer&longs;i glo­<lb/>buli aerei, &longs;ed perpendiculariter imminentes &longs;uper <lb/>infimum foramen B, &longs;cilicèt intra cylindrum aqueum <lb/>DBE, qui ad modum fluminis intra <lb/><figure id="id.010.01.186.1.jpg" xlink:href="010/01/186/1.jpg"/><lb/>aquam va&longs;is repleti defluit egre­<lb/>diturque per foramen B. </s> <s id="s.000913">Et &longs;uppo­<lb/>namus maiori celeritate, &longs;cilicèt <lb/>dupla, aquam fluere à D v&longs;que ad <lb/>B, quàm globus aereus G mouea­<lb/>tur &longs;ur sùm translatus à naturali eius <lb/>leuitate, itaut, quando aqua prædi­<lb/>cti cylindri fluentis <expan abbr="trã&longs;it">tran&longs;it</expan> &longs;patium <lb/>GI debeat aereus globus G &longs;ursùm impelli, & <expan abbr="trã-&longs;igere">tran­<lb/>&longs;igere</expan> &longs;patium æquale IH &longs;ubduplum ip&longs;ius GI, eo <lb/>quod medium fluidum in quo globus aereus G <expan abbr="a&longs;c&etilde;-dit">a&longs;cen­<lb/>dit</expan> non e&longs;t &longs;tabile, &longs;ed deorsùm defluit, non &longs;ecùs ac <lb/>flumen, igitur quando aqua &longs;patium GI tran&longs;egerit, <lb/>globus aereus contrario cur&longs;u medietatem itineris <lb/>IH perficiet, qua proptèr ex hi&longs;ce duabus contrarijs <lb/>velocitatibus re&longs;ultabit tertia qu&etail;dam celeritas, quæ <pb pagenum="179" xlink:href="010/01/187.jpg"/><arrow.to.target n="marg230"/><lb/>æqualis erit differentiæ prædictarum oppo&longs;itarum <lb/>celeritatum, & ideò aer G de&longs;cendet duplo tardiùs <lb/>aqua ambiente; Quòd verò hoc &longs;it fal&longs;um, experien­<lb/>tia ip&longs;a docet &longs;i nimirùm aqua DE atro colore tinga­<lb/>tur, vel di&longs;per&longs;o puluere terre&longs;tri pauli&longs;per turbida <lb/>reddatur, tunc procùl dubio particulæ illæ areno&longs;æ <lb/>graues, aut ob exiguitatem in ip&longs;a aqua dum quie&longs;cit <lb/>non de&longs;cendunt, vel lento motu deorsùm feruntur a <lb/>vi maioris grauitatis <expan abbr="earũ">earum</expan>. </s> <s id="s.000914">igitur quando aqua deor­<lb/>sùm fluit, videtur impo&longs;&longs;ibile vt grauiores particulæ <lb/>areno&longs;æ minori velocitate transferantur deorsù&mtail;, <lb/>quàm aqua ip&longs;a in qua degunt, quare bulla aerea G <lb/>quæ vt leuis &longs;ursùm a&longs;cendere &longs;upponitur, non po&longs;&longs;et <lb/>pari velocitate &longs;imul <expan abbr="cũ">cum</expan> particulis terreis aquæ tur­<lb/>bidæ deorsùm de&longs;cendere, &longs;ed hoc e&longs;t fal&longs;um, cum <lb/>ab&longs;que vlla differentia velocitatis deorsùm feran­<lb/>tur vnà cum aqua turbida cylindri fluentis, igitur ve­<lb/>rum non e&longs;t, quòd aer G moueatur &longs;ursùm à vi natu­<lb/>ralis leuitatis eius translatus, cùm <expan abbr="aliũdè">aliundè</expan> quando re­<lb/>uera aer G principium motiuum leuitatis in &longs;e habe­<lb/>ret non po&longs;&longs;et vllo pacto in aqua ip&longs;um <expan abbr="nõ">non</expan> exercere. </s> </p> <p type="margin"> <s id="s.000915"><margin.target id="marg230"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000916"><emph type="center"/>PROP. LXXXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000917"><emph type="center"/><emph type="italics"/>Confirmatur aerem ab ambiente aqua per extru&longs;ionem &longs;ur­<lb/>sùm impelli.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000918">EContrà quandò globus aereus G nullam pror­<lb/>sùs leuitatem haberet, & &longs;olummodò per ex<lb/>tru&longs;ionem factam à grauitate fluidi ambientis eleua-<pb pagenum="180" xlink:href="010/01/188.jpg"/><arrow.to.target n="marg231"/><lb/>retur, nullo pacto in tali ca&longs;u po&longs;&longs;et aqua ab inferiori <lb/>&longs;itu H &longs;ursùm impellere aerem G, propterea quod <lb/>aqua DB cogitur excurrere deorsùm per va&longs;is aper­<lb/>tum foramen B, & ideò non pote&longs;t motu reflexo &longs;ur­<lb/>sùm impellere aerem G. igitur nece&longs;sè e&longs;t vt globus <lb/>aereus G deferatur à vi fluentis aquæ, vt ip&longs;a experi­<lb/>entia o&longs;tendit. </s> <s id="s.000919">Vnde colligitur, quod nullum ex ad­<lb/>ductis, & excogitatis <expan abbr="experim&etilde;tis">experimentis</expan> v&longs;que adhuc euin­<lb/>cere per&longs;uadereque pote&longs;t exi&longs;tentiam leuitatis po­<lb/>&longs;itiuæ, & è contrà &longs;emper multò magis confirmatur, <lb/>demon&longs;traturque eius non exi&longs;tentia, quaproptèr fa­<lb/>tendum e&longs;t corpora, quæ leuia appellantur, &longs;ursùm <lb/>impelli per extru&longs;ionem à fluidis ambientibus gra­<lb/>uioribus. </s> </p> <p type="margin"> <s id="s.000920"><margin.target id="marg231"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000921">Sed coronidis loco afferam demon&longs;trationem à <lb/>me excogitatam, ab&longs;olutè non dari in natura <expan abbr="po&longs;itiuã">po&longs;itiuam</expan> <lb/>leuitatem, vtque commodiùs hoc efficiam primò <lb/>nonnullas &longs;uppo&longs;itiones &longs;en&longs;ui manife&longs;tas <expan abbr="proponã">proponam</expan>, <lb/>& deinceps aliqua lemmata ex principijs mechani­<lb/>cis de&longs;umpta demon&longs;trabo. </s> </p> <p type="main"> <s id="s.000922"><emph type="center"/><emph type="italics"/>DEFINITIO I.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000923">ET primò noto, quòd corpus &longs;iue &longs;imilare, & ho­<lb/>mogeneum, &longs;iue heterogeneum, tunc vocatur <lb/>exi&longs;timaturque rarius &longs;pecie, quàm aliud, quando <lb/>&longs;umptis æqualibus molibus eorumdem illud <expan abbr="minor&etilde;">minorem</expan> <lb/>copiam materialis &longs;ub&longs;tantiæ corporeæ, & &longs;en&longs;ibi­<lb/>lis comprehendit in eodem &longs;patio, quàm i&longs;tud, quòd <lb/>profectò concipi pote&longs;t, &longs;i intelligatur mino: copia <pb pagenum="181" xlink:href="010/01/189.jpg"/><arrow.to.target n="marg232"/><lb/>materiei &longs;en&longs;ibilis in maiori &longs;patio corporis rarioris <lb/>exten&longs;a per interpo&longs;itionem inanium &longs;patiolorum. </s> </p> <p type="margin"> <s id="s.000924"><margin.target id="marg232"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000925"><emph type="center"/><emph type="italics"/>DEFINITIO II.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000926">SI verò moles æquales, &longs;iuè inæquales non con­<lb/>&longs;iderentur, & raritas in vna earum <expan abbr="cont&etilde;ta">contenta</expan> ma­<lb/>ior fuerit raritate alterius, tunc dicetur illa raritas <lb/><arrow.to.target n="marg233"/><lb/>ab&longs;olutè maior reliqua, &longs;iuè exce&longs;&longs;us raritatis exten­<lb/>&longs;iuè in maiori mole multiplicetur, &longs;iuè inten&longs;iuè i&ntail; <lb/>minori mole augeatur. </s> </p> <p type="margin"> <s id="s.000927"><margin.target id="marg233"/>Sup. <!-- REMOVE S-->8.</s> </p> <p type="main"> <s id="s.000928"><emph type="center"/><emph type="italics"/>SVPPOSITIO VII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000929">PRæterea &longs;uppono ex Ari&longs;totele raritatem alicu­<lb/>ius corporis multiplicari, & augeri in infinitum <lb/>po&longs;&longs;e prout &longs;ub&longs;tantialis moles corporea, quæ in eo­<lb/>dem &longs;patio continebatur, &longs;ucce&longs;&longs;iuè imminuitur, & <lb/>po&longs;t diminutionem extenditur expanditurque vt re­<lb/>pleat idip&longs;um &longs;patium, quod prius à non imminuto <lb/>corpore occupabatur. </s> </p> <p type="main"> <s id="s.000930"><emph type="center"/><emph type="italics"/>SVPPOSITIO VIII.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000931">SVppono præterea, quòd vis quæ requiritur ad <lb/>&longs;eparanda duo corpora &longs;e mutuò tangentia im­<lb/>mediato, & exqui&longs;ito contactu, (quod accidit <expan abbr="quã-do">quan­<lb/>do</expan> eorum &longs;uperficies &longs;unt omninò &longs;imiles, & optimè <lb/>l&etail;uigatæ) non e&longs;t infinita, &longs;ed determinata, quia ni­<lb/>mirùm &longs;en&longs;us euidentia o&longs;tendit, quod &longs;i potenti&atail; <lb/>motiua augeatur &longs;emper magis, ac magisne dùm cor­<lb/>pora &longs;e mutuò tangentia &longs;eparantur, & ab inuicem <pb pagenum="182" xlink:href="010/01/190.jpg"/><arrow.to.target n="marg234"/><lb/>diuelluntur, &longs;ed etiam corpora illa, quæ continu&atail; <lb/>cen&longs;entur, vt e&longs;t columna marmorea, vel virga me­<lb/>tallica, tandèm à vi trahente di&longs;trahitur, euelliturque <lb/>directo motu vna pars ab altera, quæ tenaciori glu­<lb/>tine vinculoque vniuntur, quàm illa duo corpora &longs;e <lb/>mutuò tangentia, & &longs;implici contactu vnita. </s> </p> <p type="margin"> <s id="s.000932"><margin.target id="marg234"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000933"><emph type="center"/>PROP. LXXXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000934"><emph type="center"/><emph type="italics"/>Verùm <expan abbr="prædictã">prædictam</expan> vim, quæ requiritur ad &longs;eparanda duo cor­<lb/>pora &longs;e mutuò tangentia, pos&longs;ibile e&longs;t mediante libra <lb/>men&longs;urari hac ratione.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000935">SIt cylindrus CAB cuius ba&longs;is <lb/><figure id="id.010.01.190.1.jpg" xlink:href="010/01/190/1.jpg"/><lb/>AB perfecti&longs;&longs;imè explanata, <lb/>& l&etail;uigata congruat exo&longs;cule­<lb/>turque <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> pauimenti DE, <lb/>pari diligentia complanatam, & <lb/>l&etail;uigatam, & cautionis grati&atail;, <lb/>vttuti omninò &longs;imus aerem am<lb/>bientem penetrare, ac ingredi non po&longs;&longs;e inter præ­<lb/>dictas duas complanatas &longs;uperficies po&longs;&longs;ent colliga­<lb/>ri tùm cylindro, tùm pauimento duæ laminæ vitreæ <lb/>AB, & DE, aut alterius &longs;ub&longs;tantiæ duri&longs;&longs;imæ, quæ in­<lb/>&longs;tar &longs;peculi explanatæ, & l&etail;uigatæ &longs;int; po&longs;teà com­<lb/>primantur, vna, &longs;uper alteram intrà aliquod fluidum <lb/>vi&longs;ibile veluti e&longs;t aqua, vel hydrargyrum, vt nimi­<lb/>rùm vi&longs;u con&longs;tet nihil omninò intercipi inter prædi­<lb/>ctas duas &longs;uperficies, dum nimirùm vna earum trahi­<lb/>tur, vt ab altera diuellatur. </s> <s id="s.000936">Colligetur po&longs;tea cylin-<pb pagenum="183" xlink:href="010/01/191.jpg"/><arrow.to.target n="marg235"/><lb/>dri extremitas C termino H trochleæ, vel libræ HK <lb/>radiorum æqualium, cuius centrum I, & reliquo ex­<lb/>tremo K &longs;u&longs;pendatur pondus N æquale grauitati ab­<lb/>&longs;olutæ cylindri AC. profectò manife&longs;tum e&longs;t &longs;en&longs;ui <lb/>non &longs;ufficere pondus N ad &longs;eparandum, & diuellen­<lb/>dum cylindrum AC à pauimento DE, &longs;ed requiritur <lb/>aliqua vis multò maior illa, quæ reperiri <expan abbr="a&longs;&longs;ignariq;">a&longs;&longs;ignarique</expan> <lb/><arrow.to.target n="marg236"/><lb/>poterit, non enim e&longs;t infinita, igitur &longs;i addatur con­<lb/>tinentèr pondus ponderi termino K <expan abbr="tãdem">tandem</expan> deuenie­<lb/>mus ad pondus aliquod, vt e&longs;t O à quo cvlindrus CA <lb/>directa tractione diuelli à pauimento poterit. </s> <s id="s.000937">Quia <lb/>verò duo pondera N, & O directè diuellunt <expan abbr="cylindrũ">cylindrum</expan> <lb/>AC, & hic re&longs;i&longs;tit &longs;eparationi duabus viribus, pro­<lb/>prij &longs;cilicèt ponderis æqualis nempè ip&longs;i N, & vi <lb/>contactus, & repugnantiæ ad vacuum <expan abbr="admmittendũ">admittendum</expan>. <lb/></s> <s id="s.000938">igitur remanens vis ponderis O æqualis erit, & aucta <lb/>&longs;uperabit vim connexionis duarum &longs;uperficierum &longs;e <lb/>mutuò exqui&longs;itè tangentium. </s> </p> <p type="margin"> <s id="s.000939"><margin.target id="marg235"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000940"><margin.target id="marg236"/>Sup. <!-- REMOVE S-->8.</s> </p> <p type="main"> <s id="s.000941">Non defuit tamen qui hunc progre&longs;&longs;um in <expan abbr="dubiũ">dubium</expan> <lb/>reuocare au&longs;us &longs;it, & &longs;ic inutilem, ac inefficacem vni­<lb/>uer&longs;am demon&longs;trationem &longs;ub&longs;equentem redder&etail;, <lb/>qu&etail; in prædicta experimentali operatione fundatur. <lb/></s> <s id="s.000942">Nucleus difficultatis talis e&longs;t, non videri po&longs;&longs;ibil&etail; <lb/>columnam AC vnquam po&longs;&longs;e motu tàm directo &longs;ur­<lb/>sùm trahi, nec libra, nec trochlea itaut non flectatur <lb/>inclineturque, & hoc (inquiunt) nullo pacto huma­<lb/>na diligentia a&longs;&longs;e qui po&longs;&longs;e; imò a&longs;&longs;erere au&longs;i &longs;unt, <lb/>quòd &longs;i funis HC directè traheretur perpendiculari­<lb/>tèr nimirùm ad planum horizontis, & ad ba&longs;im DE <pb pagenum="184" xlink:href="010/01/192.jpg"/><arrow.to.target n="marg237"/><lb/>nunquam à quacumque vi diuelli columna po&longs;­<lb/>&longs;et, nec &longs;uperari re&longs;i&longs;tentia ad vacuum, quod profe­<lb/>ctò &longs;ub&longs;equeretur in actu violento &longs;eparationis &longs;u­<lb/>perficierum AB, & DE. <!-- KEEP S--></s> <s id="s.000943">Si verò (aiunt) applicetur <lb/>vis tran&longs;uer&longs;alitèr, itaut latus BC columnæ angulum <lb/>con&longs;tituat cum linea tractionis, tunc facilè &longs;eparari, <lb/>ac diuelli ab inuicem poteruut prædict&etail; &longs;uperficies. </s> </p> <p type="margin"> <s id="s.000944"><margin.target id="marg237"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000945">Huiu&longs;modi cauillo&longs;a re&longs;pon&longs;io condonari pote&longs;t <lb/>ijs Philo&longs;ophis, qui mathematices imperiti &longs;unt. </s> </p> <p type="main"> <s id="s.000946"><emph type="center"/>PROP. XC.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000947"><emph type="center"/><emph type="italics"/>Potest facili negotio præcisè innote&longs;cere <expan abbr="re&longs;i&longs;t&etilde;tiailla">re&longs;i&longs;tentia illa</expan> ab&longs;olu­<lb/>ta, & totalis, quæ requiritur ad &longs;eparationem illam di­<lb/>rectam, & ad horizontem perpendicularem efficien­<lb/>dam ip&longs;ius columnæ à fundo va&longs;is, quotie&longs;cum­<lb/>que constet quanta vis requiritur adeam <lb/>&longs;eparandam impetu obliquo ab <lb/>eodem &longs;olo.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000948">SIt denuò cylindrus AC <lb/><figure id="id.010.01.192.1.jpg" xlink:href="010/01/192/1.jpg"/><lb/>cuius ba&longs;is AB l&etail;uigati&longs;­<lb/>&longs;ima, <expan abbr="cõtactu">contactu</expan> perfecto &longs;uper­<lb/>ficiem pauimenti DE paritèr <lb/>l&etail;uigatam tangat, & vis M <lb/>tran&longs;uer&longs;ali directione CM <lb/>perpendiculari ad CB trahat <lb/>terminum columnæ C, & va­<lb/>leat huiu&longs;modi potentia diuellere &longs;uperficiem AB <lb/>ab ip&longs;o <expan abbr="pauim&etilde;to">pauimento</expan>, &longs;itque prædicta <expan abbr="pot&etilde;tia">potentia</expan> M æqualis <pb pagenum="185" xlink:href="010/01/193.jpg"/><arrow.to.target n="marg238"/><lb/>ponderi R, & <expan abbr="quã">quam</expan> proportionem habet &longs;emi&longs;&longs;is dia­<lb/>metri AB ba&longs;is prædictæ columnæ ad &longs;uam altitudi­<lb/>nem BC, eamdem habeat pondus R ad aliud pondus <lb/>S. o&longs;tendendum modò e&longs;t vim ponderis S æqualem <lb/>e&longs;&longs;e totali re&longs;i&longs;tentiæ contactus duarum <expan abbr="prædictarũ">prædictarum</expan> <lb/>&longs;uperficierum, &longs;eù potiùs æqualem e&longs;&longs;e vi, qua vacui <lb/>re&longs;i&longs;tentia &longs;uperatur, vel potiùs pondus S &longs;ufficer&etail; <lb/>ad diuellendam columnam à pauimento directa tra­<lb/>ctione, &longs;cilicèt detinendo, & <expan abbr="transfer&etilde;do">transferendo</expan> ba&longs;im AB <lb/>&longs;emper æquidi&longs;tantem plano ba&longs;is DE. <!-- KEEP S--></s> <s id="s.000949">Quia in actu <lb/>&longs;eparationis &longs;uperficiei AB à pauimento debet pun­<lb/>ctum eius B contingere, & inniti ip&longs;i pauimento, & <lb/>angularitèr &longs;ubleuari terminus oppo&longs;itus A, vnà cum <lb/>tota ba&longs;is &longs;uperficie AB, efficiendo nimirùm <expan abbr="angulũ">angulum</expan> <lb/>cum pauimenti plano DE; & hic ob&longs;eruari debent <lb/>loca vbi duæ vires applicantur, &longs;cilicèt re&longs;i&longs;tentia, & <lb/>eius, quæ eam &longs;uperat, & per quam directionem tra­<lb/>hunt & vim exercent; & pater, quòd re&longs;i&longs;tentia i&ntail; <lb/>omnibus <expan abbr="pũctis">punctis</expan> inferioris &longs;uperficiei AB exi&longs;tit, <expan abbr="sũt-que">sunt­<lb/>que</expan> veluti totidem fibræ <expan abbr="perp&etilde;dicularitèr">perpendicularitèr</expan> erect&etail; ad <lb/>planum &longs;ubiectum, quæ cum eo coniunguntur colli­<lb/>ganturque; è contrà vis mouens M vectem CB adhi­<lb/>bet circa centrum firmum B, & quia vniuer&longs;a re&longs;i­<lb/>&longs;tentia vniformiter di&longs;tribuitur per totam ba&longs;is &longs;u­<lb/>perficiem AB, reducitur, & perindè re&longs;i&longs;tit ac &longs;i i&ntail; <lb/>centro aggregati prædictarum fibrarum collocat&atail; <lb/>e&longs;&longs;et, centrum verò omnium fibrarum prædictarum <lb/>idem e&longs;t ac centrum I, quod e&longs;t centrum eiu&longs;dem ba­<lb/>&longs;is; quaproptèr maximus conatus vniuer&longs;æ re&longs;i&longs;ten-<pb pagenum="186" xlink:href="010/01/194.jpg"/><arrow.to.target n="marg239"/><lb/>tiæ ad diuul&longs;ionem exercetur in centro I circuli AB. <lb/><!-- KEEP S--></s> <s id="s.000950">Habebimus igitur vectem inflexum CBI in quo vis <lb/><expan abbr="mou&etilde;s">mouens</expan> M applicatur in C, re&longs;i&longs;tentia verò applicatur <lb/>in I, & fulcimentum, &longs;eù centrum reuolutionis vectis <lb/>CBI e&longs;t punctum B quod fixum per&longs;euerat dum cir­<lb/>ca ip&longs;um motus, & reuolutiones partium vectis <expan abbr="fiũt">fiunt</expan>; <lb/>Quaproptèr, iuxtà leges Mechanices, re&longs;i&longs;tentia to­<lb/>talis ad diuul&longs;ionem, & &longs;eparationem &longs;uperficiei AB <lb/>ab ip&longs;o pauimento ad vim <expan abbr="mou&etilde;tem">mouentem</expan> M eamdem pro­<lb/>portionem habebit, quam vectis longitudo CB ad <lb/>oppo&longs;itam eius portionem BI, &longs;cilicèt habebit eam­<lb/>dem proportionem. </s> <s id="s.000951">quam pondus S habet ad pondus <lb/>R. <!-- KEEP S--></s> <s id="s.000952">Verùm pondus R æquale erat potentiæ M. igitur <lb/>pondus S æquale erit re&longs;i&longs;tenti&etail; ab&longs;olutæ, & totali, <lb/>quam exercet &longs;uperficies AB quando diuelli, & &longs;e­<lb/>parari debet à &longs;uperficie paui <expan abbr="m&etilde;ti">menti</expan> tractione directa. <lb/></s> <s id="s.000953">Hinc deducitur quòd &longs;i <expan abbr="põ-">pon­<lb/></expan><figure id="id.010.01.194.1.jpg" xlink:href="010/01/194/1.jpg"/><lb/>dus O propo&longs;itionis 89. di­<lb/>uellit columnam à pauimento <lb/>directione, & impetu tran&longs;­<lb/>uer&longs;ali, & perpendiculari ad <lb/>latus column&etail;, poterit nihilo­<lb/>minùs indagari <expan abbr="re&longs;i&longs;t&etilde;tia">re&longs;i&longs;tentia</expan> ab­<lb/>&longs;oluta, & totalis contiguita­<lb/>tis, vel repugnantiæ ad vacuum earumdem &longs;uperfi­<lb/>cierum, eritque talis vis ab&longs;oluta tantomaior pon­<lb/>dere O, quantò altitudo columnæ CB maior e&longs;t &longs;e­<lb/>mi&longs;&longs;e diametri AB, & &longs;ic &longs;i vis transuer&longs;alitèr colum­<lb/>nam diuellens æqualis e&longs;&longs;et ponderi trium librarum <pb pagenum="187" xlink:href="010/01/195.jpg"/><arrow.to.target n="marg240"/><lb/>v. <!-- REMOVE S-->g. <!-- REMOVE S-->& altitudo columnæ CB decies maior radio ba­<lb/>&longs;is, tunc totalis re&longs;i&longs;tentia prædictæ contiguitatis, &longs;eù <lb/>repugnantia ad vacuuum admittendum, æqualis erit <lb/>potentiæ ponderis triginta librarum. </s> <s id="s.000954">Quaproptèr <lb/>con&longs;tat, quòd vis, quæ requiritur ad re&longs;i&longs;tentiam <expan abbr="cõ-tactus">con­<lb/>tactus</expan> directè &longs;uperandam, licèt maior vt plurimùm <lb/>&longs;it, quàm ea quæ actu exercetur, nihilominùs finita, <lb/>& determinata e&longs;t, & facili negotio indagari, men­<lb/>&longs;urarique pote&longs;t. </s> <s id="s.000955">His declaratis pergo ad <expan abbr="demõ&longs;trã-dum">demon&longs;tran­<lb/>dum</expan>, quòd. </s> </p> <p type="margin"> <s id="s.000956"><margin.target id="marg238"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000957"><margin.target id="marg239"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000958"><margin.target id="marg240"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000959"><emph type="center"/>PROP. XCI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000960"><emph type="center"/><emph type="italics"/>Dato quolibet corpore duro homogeneo, aliudilli æquale repe­<lb/>riri pote&longs;t, cuius raritas ab&longs;oluta ad illius raritatem <lb/>maiorem proportionem qualibet dataratione <lb/>maioris inæqualitatis habeat.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000961">SIt cylindrus &longs;olidus ABC, & <lb/><figure id="id.010.01.195.1.jpg" xlink:href="010/01/195/1.jpg"/><lb/>quælibet data ratio maioris <lb/>inæqualitatis T ad V, & fiat RS <lb/>maior quàm T. reperiri debetcy­<lb/>linder æqualis ABC cuius rari­<lb/>tas ab&longs;oluta ad raritatem ABC <lb/>&longs;it vt RS ad V. <!-- KEEP S--></s> <s id="s.000962">Secetur portio cy­<lb/>lindrica AD, & RX proximè maior quam V, & fiat <lb/>cylindrus &longs;olidus EF æqualis AD, cuiu&longs; raritas in <lb/>&longs;pecie ad raritatem ip&longs;ius AC &longs;it vt RX ad V; po&longs;tea <lb/>fiat alius cylindrus, &longs;iue fluidus, &longs;iue &longs;olidus FG æ­<lb/>qualis DB, ita vt illius raritas in &longs;pecie ad raritatem <pb pagenum="188" xlink:href="010/01/196.jpg"/><arrow.to.target n="marg241"/><lb/>eiu&longs;dem AC &longs;it vt XS ad V. igitur duæ antecedentes <lb/>RX, & XS ad V, &longs;cilicet RS ad V eamdem propor­<lb/>tionem habebit quam raritas &longs;pecifica aggregati ex <lb/>EF, & FG ad raritatem AC, &longs;untquè moles EH, & <lb/>AC æquales, ergo eorum raritates ab&longs;olutæ &longs;unt pro­<lb/>portionales &longs;pecificis, &longs;cilicèt &longs;e habent vt RS ad V. <lb/>quod erat, &c. </s> </p> <p type="margin"> <s id="s.000963"><margin.target id="marg241"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000964"><emph type="center"/>PROP. XCII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000965"><emph type="center"/><emph type="italics"/>Cylindrum compo&longs;itum ex duobus cylindris inæqualitèr ra­<lb/>ris transformare in cylindrum &longs;imilitèr excauatum, <lb/>cuius pars continens homogenea, & æqualis &longs;it. <lb/></s> <s id="s.000966">vni illorum, pars verò excauata homo­<lb/>genea, & æqualis &longs;it reliquo.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000967">SIt datus cylindrus &longs;oli­<lb/><figure id="id.010.01.196.1.jpg" xlink:href="010/01/196/1.jpg"/><lb/>dus AC, compo&longs;itus ex <lb/>duobus cylindris AD, & DB <lb/>inæqualitèr raris alium cy­<lb/>lindrum &longs;imilitèr <expan abbr="excauatũ">excauatum</expan> <lb/>æqualem, & &longs;imilem illi de­<lb/>&longs;cribere, cuius pars continens æqualis, & homoge­<lb/>nea &longs;it ip&longs;i AD, contenta verò æqualis, & homoge­<lb/>nea &longs;it ip&longs;i DB. reperto centro <expan abbr="q.">que</expan> cylindricæ figuræ <lb/>AC coniungantur rectæ AQ, BQ ad terminos lateris <lb/>cylindri AB, & fiat triangulum ENF &longs;imile, & æqua­<lb/>le ip&longs;i AQB. po&longs;tea inter AB, & MB reperiantur duæ <lb/>mediæ proportionales, quarum maior &longs;it PB (vt do­<lb/>cuimus lib. 5. conic. </s> <s id="s.000968">Apoll.lemm. <!-- REMOVE S-->7.) deinde in <expan abbr="triã-">trian-</expan><pb pagenum="189" xlink:href="010/01/197.jpg"/><arrow.to.target n="marg242"/><lb/>gulo ENF ducatur IK parallela EF, & æqualis ip&longs;i <lb/>PB, & ducta RNS parallela ip&longs;is EF, & IK reuolua­<lb/>tur figura circa axim RS vt fiant duo cylindri <expan abbr="conc&etilde;-trici">concen­<lb/>trici</expan> EFGH, & IKLO; intelligatur modò &longs;patium <lb/>internum IKLO repletum &longs;ub&longs;tantia homogenea ip­<lb/>&longs;i cylindro DB, & re&longs;iduum ambiens EFGH explea­<lb/>tur ex eadem &longs;ub&longs;tantia corporea ip&longs;ius AD; & quia <lb/>AB ad MB, &longs;iuè cylinder AC ad cylindrum MC, vel <lb/>cylinder EG ad cylindrum IL triplicatam propor­<lb/>tionem habet lateris AB ad PB, vel EF ad IK; ergo <lb/>cylinder AC ad MC eamdem proportionem habet, <lb/>quam integer cylindrus EG ad cauitatem cylindri­<lb/>cam IL, & per conuer&longs;ionem rationis cylinder AC <lb/>ad.<!--kein neuer Satz, Punkt streichen--> </s> <s id="s.000969">cylindrum AD &longs;e habet vt totus cylindrus EG <lb/>ad partem continentem EKGO. </s> <s id="s.000970">Suntque cylindri <lb/>AC, & EG æquales, cùm &longs;int &longs;imiles, & &longs;imilitèr po­<lb/>&longs;iti circa latera æqualia AB, & EF, igitur cylinder <lb/>excauatus EKGO æqualis e&longs;t &longs;ibi homogeneo cylin­<lb/>dro AD, proindeque cylinder IL æqualis, & homo­<lb/>geneus erit ip&longs;i MC, quod fuerat. </s> </p> <p type="margin"> <s id="s.000971"><margin.target id="marg242"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000972">His præhabitis noto, quòd cùm agitur de faculta­<lb/><arrow.to.target n="marg243"/><lb/>te, &longs;eù principio quo corpora vim faciunt tendendo <lb/>deorsùm, qu&etail;rimus tantummodò gradum virtutis <expan abbr="cõ-pre&longs;&longs;iuæ">con­<lb/>pre&longs;&longs;iuæ</expan> eorum, quæ procùl dubio à grauitate, &longs;eu <lb/>pondere eorum men&longs;uratur, hoc verò duplici modo <lb/>augeri po&longs;&longs;e con&longs;tat, aut per multiplicationem eiu&longs;­<lb/><arrow.to.target n="marg244"/><lb/>dem corporis, vt cum lignea columna augetur mole, <lb/>aut cum <expan abbr="&longs;ub&longs;tãtia">&longs;ub&longs;tantia</expan> corporea, & plena in eodem &longs;patio <lb/>di&longs;&longs;eminata, & contenta magis &longs;tringitur, conden-<pb pagenum="190" xlink:href="010/01/198.jpg"/><arrow.to.target n="marg245"/><lb/>&longs;atur, con&longs;tipaturque, & primum vocatur augmen­<lb/>tum grauitatis exten&longs;iuum, reliquum verò <expan abbr="inten&longs;iuũ">inten&longs;iuum</expan>. <lb/></s> <s id="s.000973">Regula verò, qua men&longs;urari pote&longs;t gradus prædictæ <lb/>grauitatis commodè de&longs;umitur à vi contraria, quæ <lb/><arrow.to.target n="marg246"/><lb/>depre&longs;&longs;ionem eius prohibere pote&longs;t, & hic <expan abbr="notandũ">notandum</expan> <lb/>e&longs;t minimè nos &longs;ollicitos e&longs;&longs;e de velocitate motus, <lb/>qua deorsùm eadem grauia feruntur, &longs;ed tantummo­<lb/>dò con&longs;iderare vim, & conatum ponderis eius, qui <lb/>in libra à vi oppo&longs;iti <expan abbr="æquipõdij">æquipondij</expan> præcisè men&longs;uratur. <lb/><arrow.to.target n="marg247"/></s> </p> <p type="margin"> <s id="s.000974"><margin.target id="marg243"/>Vis compri­<lb/>mens exten­<lb/>&longs;iuè augetur <lb/>multiplicata <lb/>mole corpo­<lb/>ris.</s> </p> <p type="margin"> <s id="s.000975"><margin.target id="marg244"/><expan abbr="Int&etilde;&longs;iuè">Inten&longs;iuè</expan> ve­<lb/>rò con&longs;tip­a<lb/>ta, & conden<lb/>&longs;ata mate­<lb/>ria.</s> </p> <p type="margin"> <s id="s.000976"><margin.target id="marg245"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000977"><margin.target id="marg246"/>Gradus præ­<lb/>dictæ graui­<lb/>tatis men&longs;u­<lb/>ratur à vi <expan abbr="cõtraria">con­<lb/>traria</expan>, quæ <lb/><expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> <lb/>eius prohi­<lb/>bere pote&longs;t.</s> </p> <p type="margin"> <s id="s.000978"><margin.target id="marg247"/>Hic no agi­<lb/>tur de velo­<lb/>citate <expan abbr="de&longs;c&etilde;-&longs;us">de&longs;cen­<lb/>&longs;us</expan>, &longs;ed de vi <lb/><expan abbr="cõpre&longs;&longs;iua">compre&longs;&longs;iua</expan>.</s> </p> <p type="main"> <s id="s.000979"><emph type="center"/><emph type="italics"/>SVPPOSITIO IX.<emph.end type="italics"/><emph.end type="center"/><lb/><arrow.to.target n="marg248"/><!-- KEEP S--></s> </p> <p type="margin"> <s id="s.000980"><margin.target id="marg248"/>Vis &longs;ursùm <lb/><expan abbr="impell&etilde;s">impellens</expan> qu&etail; <lb/>leuitas voca­<lb/>tur augeri po<lb/>te&longs;t exten&longs;i­<lb/>uè multipli­<lb/>cato eodem <lb/>corpore le­<lb/>ui.</s> </p> <p type="main"> <s id="s.000981">NOn &longs;ecùs quando agitur de vi, & energia, qu&atail; <lb/>corpora, quæ leuia appellantur &longs;ursùm moue­<lb/>ri nituntur, quæritur non velocitas, &longs;ed vis, quæ <lb/>&longs;ursùm impellit, quæ leuitas appellari &longs;olet, & hæc <lb/>quoque duplici modo augeri pote&longs;t, aut exten&longs;iuè, <lb/>aut <expan abbr="int&etilde;&longs;iuè">inten&longs;iuè</expan>, &longs;cilicèt aut <expan abbr="multiplicãdo">multiplicando</expan> molem <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>corporis leuis, vt &longs;phæra aeris palmaris octies <expan abbr="maio-r&etilde;">maio­<lb/>rem</expan> <expan abbr="leuitat&etilde;">leuitatem</expan> habebit, <expan abbr="quã">quam</expan> &longs;phæra <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> aeris &longs;emipal­<lb/>maris, propterea quod vis illa leuitatis tantumdem <lb/>multiplicatur, quantum ma&longs;&longs;a eius corporea exten­<lb/>ditur, cùm omnes partes eiu&longs;dem aeris æquè leues <lb/>&longs;int, & æquè raræ, requiraturque vis contraria pro­<lb/>hibens illius a&longs;cen&longs;um octiès maior quam in huius <lb/>aeris minori mole requiratur. </s> <s id="s.000982">Secundo modo auge­</s> </p> <p type="main"> <s id="s.000983"><arrow.to.target n="marg249"/><lb/>ri pote&longs;t leuitas expandendo, & rarefaciendo <expan abbr="&longs;ub&longs;tã-">&longs;ub&longs;tan-</expan><pb pagenum="191" xlink:href="010/01/199.jpg"/><arrow.to.target n="marg250"/><lb/>tiam corpoream, & plenam, vt nimirum maius <lb/>&longs;patium occupet, & in hoc ca&longs;u comparari debent <lb/>&longs;patia occupata, &longs;iuè moles æquales inter &longs;e, & <expan abbr="cũ">cum</expan> <lb/>medio fluido in quo leuitant, vt &longs;i fuerint duæ pilæ <lb/>æquales, vna aquea, altera aerea intra <expan abbr="mercuriũ">mercurium</expan> de­<lb/>mer&longs;&etail;, dicetur maior leuitas inten&longs;iuè aeris re&longs;pectu <lb/>leuitatis aquæ, & leuitates eamdem proportionem <lb/>habebunt, quàm raritates molium æquallum aeris, <lb/><arrow.to.target n="marg251"/><lb/>& aqu&etail; in mercurio con&longs;ideratæ habent. </s> <s id="s.000984">Et hoc eui­<lb/>dentia &longs;en&longs;us &longs;uadet, &longs;i enim intra hydrargyrum de­<lb/>mergatur ampulla vitrea plumbo repleta, huius qui­<lb/>dem gradus leuitatis men&longs;uratur à vi <expan abbr="cõntraria">contraria</expan>, quæ <lb/>a&longs;cen&longs;um eius in mercurio prohibere pote&longs;t, &longs;itque <lb/>talis vis contraria pondus duarum vnciarum &longs;uper­<lb/>po&longs;itum, & intra mercutium fixè detinens <expan abbr="natant&etilde;">natantem</expan> <lb/>ampullam. </s> <s id="s.000985">Si po&longs;tea plumbi vncia è cauitate ampul­<lb/>læ &longs;ubtrahatur, patet quod <expan abbr="tantũ">tantum</expan> præcisè totius am­<lb/>pullæ raritas aucta erit, quantum diminuta fuit &longs;ub­<lb/>&longs;tantia corporea pondero&longs;a intra ampullam eiu&longs;dem <lb/>molis, & figuræ contenta, & tunc gradus leuitatis <lb/>præcisè augebitur vna vncia, nam &longs;i velimus <expan abbr="a&longs;censũ">a&longs;censum</expan> <lb/>eiu&longs;dem ampullæ prohibere &longs;uperponi debent non <lb/>duæ vt priùs, &longs;ed tres vnciæ, po&longs;tea &longs;i ampullæ rari­<lb/>tas denuò augeatur detracta altera <expan abbr="plũbi">plumbi</expan> vncia, gra­<lb/>dus quoque leuitatis eadem men&longs;ura cre&longs;cet vt ni­<lb/>mirùm requirantur quatuor vnciæ ad prohibendum <lb/>eius a&longs;cen&longs;um è mercurio, idemque verificatur &longs;i <lb/>vlterius pondus internum ampullæ diminuatur; qua­<lb/>re incrementa leuitatis proportionalia &longs;unt incre-<pb pagenum="192" xlink:href="010/01/200.jpg"/><arrow.to.target n="marg252"/><lb/>mentis raritatis eiu&longs;dem corporis. </s> </p> <p type="margin"> <s id="s.000986"><margin.target id="marg249"/>Inten&longs;iuè <lb/>verò rarefa­<lb/>ciendo id in <lb/>corpus.</s> </p> <p type="margin"> <s id="s.000987"><margin.target id="marg250"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.000988"><margin.target id="marg251"/>Incrementa <lb/><expan abbr="leuitatũ">leuitatum</expan> pro­<lb/>portionalia <lb/><expan abbr="sũt">sunt</expan> <expan abbr="increm&etilde;-tis">incremen­<lb/>tis</expan> raritatum <lb/>eiu&longs;dem cor­<lb/>poris <expan abbr="eius-d&etilde;que">eius­<lb/>demque</expan> molis, <lb/>& <expan abbr="m&etilde;suran-tur">mensuran­<lb/>tur</expan> à vi <expan abbr="põderum">ponde­<lb/>rum</expan> <expan abbr="prohibantiũ">prohi­<lb/>bentium</expan> eleua­<lb/>tiones.</s> </p> <p type="margin"> <s id="s.000989"><margin.target id="marg252"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000990">Hinc inferri licet, quòd &longs;i raritas non e&longs;t cau&longs;a ef­<lb/>fectiua, motus &longs;ursùm, &longs;eù leuitatis, requiritur <expan abbr="&longs;alt&etilde;">&longs;altem</expan> <lb/>raritas tamquam affectio nece&longs;&longs;aria, &longs;ine qua leuitas <lb/><arrow.to.target n="marg253"/><lb/>minimè augeri pote&longs;t, &longs;ed oportet vt raritates in ali­<lb/>quo medio fluido con&longs;iderentur, non autem ab&longs;olu­<lb/>tè, & in vacuo. </s> </p> <p type="margin"> <s id="s.000991"><margin.target id="marg253"/>Si raritas <expan abbr="nõ">non</expan> <lb/>e&longs;t causa a&longs;­<lb/>cen&longs;us <expan abbr="leuiũ">leuium</expan>, <lb/>requiritur <lb/><expan abbr="tam&etilde;">tamen</expan> nece&longs;­<lb/>&longs;ariò</s> </p> <p type="main"> <s id="s.000992"><emph type="center"/>PROP. XCIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000993"><emph type="center"/><emph type="italics"/>Reperire modò po&longs;&longs;umus corpus, quod in dato fluido a&longs;cendat <lb/>tanta vi &longs;ursùm, quæ &longs;uperet quamcumque finitam <lb/>vim.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.000994">SIt vas ABC <expan abbr="repleaturq;">repleaturque</expan> flui­<lb/><figure id="id.010.01.200.1.jpg" xlink:href="010/01/200/1.jpg"/><lb/>do M quod &longs;it aqua, vel hy­<lb/>drargyrum, & &longs;it quælibet va­<lb/>&longs;ta vis motiua R. debet reperiri <lb/>corpus, quod in prædicto fluido <lb/>innatet, atque ab eius <expan abbr="fũdo">fundo</expan> &longs;ur­<lb/>sum a&longs;cendat tanta vi, & energia <lb/>vt &longs;uperet vim datam R. &longs;uma­<lb/>tur cylindrus DE cuiu&longs;cumque <lb/>&longs;olidæ materiei con&longs;i&longs;tenti&longs;que, <lb/>earum tamen, quæ in prædicto fluido M innatant, <lb/>et vis qua corpus DE a&longs;cendit è fundo fluidi M &longs;it S: <lb/>po&longs;tea (ex duabus præcedentibus propo&longs;itionibus) <lb/>reperiatur cylindrus excauatus FG, cuius extern&atail; <lb/>figura &longs;it æqualis, & &longs;imilis ip&longs;i DE, itaut raritas ab­<lb/>&longs;oluta ip&longs;ius FG ad <expan abbr="raritat&etilde;">raritatem</expan> alterius DE <expan abbr="maior&etilde;">maiorem</expan> pro-<pb pagenum="193" xlink:href="010/01/201.jpg"/><arrow.to.target n="marg254"/><lb/>portionem habeat, <expan abbr="quã">quam</expan> R ad S, & quia (ex 9. &longs;uppo&longs;i­<lb/>tione) impetus, & energia, qua cylindrus FG &longs;ur­<lb/>sùm fertur in dato fluido M ad eam vim, qua cylin­<lb/>drus DE priori æqualis &longs;ursùm fertur in eodem flui­<lb/>do eamdem proportionem habet, quam raritas cor­<lb/>poris FG ad raritatem alterius DE, habentque præ­<lb/>dictæ raritates ne dum ab&longs;olutè, &longs;ed etiam in medio <lb/>fluido mercuriali con&longs;ideratæ, maiorem proportio­<lb/>nem, quam R ad S, igitur vis, & robur, quo cylindrus <lb/>FG &longs;ursùm a&longs;cendit in fluido M ad eam vim, qua ele­<lb/>uatur ibidem cylindrus DE maiorem proportionem <lb/>habebit, quam R ad S, erat verò S vis, qua &longs;olidum <lb/>DE &longs;ursùm transferebatur in fluido M, ergò validi­<lb/>tas, & energia, qua a&longs;cendit cylindrus FG in <expan abbr="eod&etilde;">eodem</expan> <lb/>fluido maior erit, quàm R, & hoc propo&longs;itum fuerat. </s> </p> <p type="margin"> <s id="s.000995"><margin.target id="marg254"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.000996">Sed po&longs;&longs;umus faciliùs, & breuiori apparatu pro­<lb/>blema ab&longs;oluere, &longs;i modò moles corporis innatantis <lb/>intra aliud fluidum &longs;impliciter augeatur multiplice­<lb/>turque. </s> </p> <p type="main"> <s id="s.000997"><emph type="center"/><emph type="italics"/>SVPPOSITIO X.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000998">VT <expan abbr="præced&etilde;s">præcedens</expan> problema faciliùs effici po&longs;&longs;it, priùs <lb/>præmitti debet, quòd quando agitur de vi, & <lb/>energia leuitatis, &longs;en&longs;u con&longs;tat duas æquales moles e­<lb/>iu&longs;dem corporis homogenei v.g. <!-- REMOVE S-->eiu&longs;dem ligni æquè <lb/>leues e&longs;&longs;e, &longs;cilicèt exercere conatus impul&longs;iuos <expan abbr="&longs;ursũ">&longs;ursum</expan> <lb/>inter &longs;e æquales in eodem fluido, in aqua nempè, ita­ <lb/>ut impelli deorsùm debeant ab æqualibus ponderi­<lb/>bus ad hoc vt vetentur eorum a&longs;cen&longs;us, & fixè infra <pb pagenum="194" xlink:href="010/01/202.jpg"/><arrow.to.target n="marg255"/><lb/>&longs;upremam aquæ libellam detineantur. </s> <s id="s.000999">paritèr <expan abbr="certũ">certum</expan> <lb/>e&longs;t inæquales moles eiu&longs;dem ligni inæquales vires <lb/>leuitatum in aqua habere, & inæqualibus conatibus, <lb/>& viribus &longs;ursùm impellere; nam &longs;i ex ligno maiori <lb/>&longs;ecetur auferaturque vna pars æqualis moli ligni mi­<lb/>noris, hæ cùm &longs;int æquè leues, mole&longs;que æquales ha­<lb/>beant, vt nimirùm prohiberi eorum a&longs;cen&longs;us no&ntail; <lb/>po&longs;&longs;int, ni&longs;i ab æqualibus ponderibus <expan abbr="incumb&etilde;tibus">incumbentibus</expan>, <lb/>videtur impo&longs;&longs;ibile vt exce&longs;&longs;us ille ligni maioris &longs;u­<lb/>pra minorem (cùm &longs;it eiu&longs;dem naturæ ligneæ proin­<lb/>de que leuis) vim &longs;ursùm non exerceat pro men&longs;ura <lb/>&longs;uæ quantitatis, & proinde requirat vim contrariam <lb/>alicuius ponderis incumbentis, vt eius a&longs;cenus pro­<lb/>hibeatur. </s> </p> <p type="margin"> <s id="s.001000"><margin.target id="marg255"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.001001"><emph type="center"/>PROP. XCIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001002"><emph type="center"/><emph type="italics"/>Hoc &longs;uppo&longs;ito demon&longs;trabo, quòd duæ moles eiu&longs;dem leuis <lb/>corporis &longs;ursùm impellendo in eodem fluido exercent <lb/>vires, quæ eamdem proportionem habent, quam <lb/>moles ip&longs;æ.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001003">IN va&longs;e FDE aqua pleno, vel alio <lb/><figure id="id.010.01.202.1.jpg" xlink:href="010/01/202/1.jpg"/><lb/>fluido demergantur duæ inæqua­<lb/>les moles eiu&longs;dem ligni, quæ &longs;cilicèt <lb/>æquè rar&etail; &longs;int &longs;pecie, vt &longs;unt ABC, & <lb/>HIK, &longs;it que S leuitas, &longs;eù vis qua li­<lb/>gnum ABC <expan abbr="&longs;ursũ">&longs;ursum</expan> a&longs;cendit; atque R <lb/>&longs;it leuitas alterius HIK. <!-- KEEP S--></s> <s id="s.001004">Dico quòd <lb/>leuitas S ad R eamdem <expan abbr="proportion&etilde;">proportionem</expan> <pb pagenum="195" xlink:href="010/01/203.jpg"/><arrow.to.target n="marg256"/><lb/>habet, quam lignea moles ABC ad molem HIK. po­<lb/>natur leuitas, aut vis <expan abbr="eleuãs">eleuans</expan> N, quæ habeat ad R <expan abbr="quã-libet">quan­<lb/>libet</expan> proportionem commen&longs;urabilem ex in&longs;initis, <lb/>quæ proponi po&longs;&longs;unt pariterque fiat moles BM ex <lb/>eodem ligno con&longs;tans quæ ad HIK &longs;e habeat vt N <lb/>ad R. mani fe&longs;tum e&longs;t, quòd quotie&longs;cumque lignum <lb/>BM æquatur ligno ABC, runc paritèr vis leuitatis N <lb/>æqualis erit ip&longs;i S (eò quòd moles æquales eiu&longs;de&mtail; <lb/>ligni &longs;ursùm æquali vi leuitatis impellunt) & <expan abbr="quo-tie&longs;cũque">quo­<lb/>tie&longs;cunque</expan> ligni moles BM maior fuerit, quàm ABC <lb/>&longs;emper leuitas N maior erit leuitate S, & quando li­<lb/>gnum BM minus fuerit, quàm ABC, erit quoque le­<lb/>uitas N minor, quàm S, & habent BM, HIK, & N & <lb/>R quamcumque proportionalitatem commen&longs;urabi­<lb/>lem, igitur (ex no&longs;tro Euclide re&longs;tituto) moles li­<lb/><arrow.to.target n="marg257"/><lb/>gnea ABC ad molem HIK eamdem proportione&mtail; <lb/>habebit quam vis leuitatis S, qua nimirùm ABC in <lb/>aqua a&longs;cendit, ad leuitatem R qua corpus HIK ele­<lb/>uatur in eodem fluido, quòd fuerat &c. </s> </p> <p type="margin"> <s id="s.001005"><margin.target id="marg256"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.001006"><margin.target id="marg257"/>Lib. 3 prop. <lb/></s> <s id="s.001007">24.</s> </p> <p type="main"> <s id="s.001008">Si quis fortè &longs;u&longs;picaretur ex figurarum diuer&longs;itate <lb/><arrow.to.target n="marg258"/><lb/>prædictorum corporum leuium licèt eiu&longs;dem con&longs;i­<lb/>&longs;tentiæ homogeneæ &longs;int, & eumdem gradum rarita­<lb/>tis habeant, alterari po&longs;&longs;e iam dictam proportionali­<lb/>tatem, monendus profectò e&longs;t, quod præter Ari&longs;tote­<lb/><arrow.to.target n="marg259"/><lb/>lis a&longs;&longs;ertum, vbi ait, quod <emph type="italics"/>figuræ non &longs;unt cau&longs;æ &longs;implici­<lb/>tèr a&longs;cen&longs;us, vel de&longs;cen&longs;us corporum in fluido, &longs;ed tantum­<lb/>modò tardioris, vel celerioris motus<emph.end type="italics"/>, idip&longs;um po&longs;tea de­<lb/>mon&longs;tratum fuit ex Mechanicis principijs à Ghetal­<lb/>do, & Galilæo. <!-- KEEP S--></s> <s id="s.001009">attamen inca&longs;u no&longs;tro non requirun-<pb pagenum="196" xlink:href="010/01/204.jpg"/><arrow.to.target n="marg260"/><lb/>tur figuræ corporum a&longs;cendentium omninò diuer­<lb/>&longs;æ, & di&longs;&longs;imiles inter &longs;e, quia æquè benè no&longs;træ de­<lb/>mon&longs;trationi aptari po&longs;&longs;unt cylindri æquè alti, & in­<lb/>æqualium ba&longs;ium, &longs;iuè contra &longs;i ba&longs;es æquales &longs;int, <lb/>altitudines &longs;int inæquales. </s> <s id="s.001010">hoc præmi&longs;&longs;o libet <expan abbr="idipsũ">idipsum</expan> <lb/>problema alia ratione re&longs;oluere. </s> </p> <p type="margin"> <s id="s.001011"><margin.target id="marg258"/>Diuer&longs;itas <lb/><expan abbr="figuratū">figuratum</expan> non <lb/>alterat præ­<lb/>dictam pro­<lb/>portionali­<lb/>tatem.</s> </p> <p type="margin"> <s id="s.001012"><margin.target id="marg259"/>4. de Cælo. <lb/><!-- KEEP S--></s> <s id="s.001013">cap. 6.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001014"><margin.target id="marg260"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.001015"><emph type="center"/>PROP. XCV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001016"><emph type="center"/><emph type="italics"/>Dato quocumque fluido, in quo corpus aliquod &longs;olidum inna­<lb/>tare valeat, reperiri debet moles quam habere debet, <lb/>vt in eadem fluido a&longs;cendere pos&longs;it tanta vi, vt <lb/>&longs;uperet quamcumque finitam virtutem <lb/>motiuam.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001017">SIt vas FDE, impleaturqu&etail; <lb/><figure id="id.010.01.204.1.jpg" xlink:href="010/01/204/1.jpg"/><lb/>fluido M, aqua nimirùm, aut <lb/>quolibet alio con&longs;i&longs;tenti fluido. <lb/></s> <s id="s.001018">Sumatur po&longs;tea ligneus cylinder <lb/>ABC, vel quælibet alia materia, <lb/>quæ in pr&etail;dicto fluido innatet, &longs;it­<lb/>que quælibet immen&longs;a, &longs;ed <expan abbr="tam&etilde;">tamen</expan> <lb/>finita vis R, debet reperiri mo­<lb/>les, & amplitudo quam haber&etail; <lb/>debet corpus aliud homogeneum <lb/>ip&longs;i ABC, vt tanta vi in fluido M a&longs;cendat quæ maior <lb/>&longs;it virtute motiua R. <!-- KEEP S--></s> <s id="s.001019">Immergatur in eodem fluido <lb/>cylindrus ABC, eiu&longs;que leuitas in fluido, &longs;eu vis, qua <lb/>nititur in eo <expan abbr="a&longs;c&etilde;dere">a&longs;cendere</expan> &longs;it S. <!-- KEEP S--></s> <s id="s.001020">Po&longs;teà fiat cylindrus HIK <lb/>&longs;imilis homogeneus, & eiu&longs;dem materiæ ac e&longs;t ABC, <pb pagenum="197" xlink:href="010/01/205.jpg"/><arrow.to.target n="marg261"/><lb/>& tantæ va&longs;titatis, vt ad eum moles ABC minorem <lb/>proportionem habeat, quam S ad R, &longs;cilicèt &longs;it vt S <lb/>ad V, quæ maior erit quam R, & quia eiu&longs;dem &longs;ub­<lb/>&longs;tantiæ nempè ligni factæ &longs;unt duæ moles ABC, & <lb/>HIK; igitur (ex præcedenti) vt cylindrus ABC ad <lb/>HIK, ita &longs;e habet ab&longs;oluta leuitas illius S ad huius le­<lb/>uitatem, quæ erit V, & habet S ad R <expan abbr="maior&etilde;">maiorem</expan> propor­<lb/>tionem, quàm moles ABC ad HIK, igitur leuitas V, <lb/>&longs;eù vis, qua &longs;olidum HIK a&longs;cendit in fluido M maior <lb/>e&longs;t quacumque data vi finita R. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001021"><margin.target id="marg261"/>Cap. 4. po&longs;i­<lb/>tiuam <expan abbr="leui-tat&etilde;">leui­<lb/>tatem</expan> <expan abbr="nõ">non</expan> dari.</s> </p> <p type="main"> <s id="s.001022"><emph type="center"/>PROP. XCVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001023"><emph type="center"/><emph type="italics"/>Idip&longs;um problema effici po&longs;&longs;e methodo Archimedæa &longs;ic <lb/>ostendemus.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001024">SVmatur lignum L, vel aliud <lb/><figure id="id.010.01.205.1.jpg" xlink:href="010/01/205/1.jpg"/><lb/>corpus &longs;ibi homogeneum, <lb/>quod innatare po&longs;&longs;it intra flui­<lb/>dum M, ponaturque quælibet <lb/>vis finita ponderis P, atque vt <lb/>pondus ab&longs;olutum molis fluidi <lb/>M, quæ æqualis &longs;it ip&longs;i L, ad <lb/>pondus ab&longs;olutum ligni L, &longs;ci­<lb/>licèt vt grauitas &longs;pecifica flui­<lb/>di M ad L, it a &longs;e habeat R ad S, <lb/>po&longs;tea fiat cylindrus ACB <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> materiei L, ad cuius <lb/>grauitatem ab&longs;olutam <expan abbr="põdus">pondus</expan> P minorem proportio­<lb/>nem habeat, quàm differentia ip&longs;arum R, & S ad S. <lb/><!-- KEEP S--></s> <s id="s.001025">Tandem immergatur cylindrus AC intra fluidum M <pb pagenum="198" xlink:href="010/01/206.jpg"/><arrow.to.target n="marg262"/><lb/>contentum in va&longs;e FDE tantæ profunditatis, vt cy­<lb/>lindrus AC vniuersè, & perpendicularitèr ad Hori­<lb/>zontem mergi po&longs;&longs;it, vt eius ba&longs;is non contingat <expan abbr="fũ-dum">fun­<lb/>dum</expan> va&longs;is FDE, atque &longs;upremus terminus C fluidi li­<lb/>bellam contingat. </s> <s id="s.001026">Præterea applicari debet pondus <lb/>P &longs;upra verticem cylindri CA, itaut pondus P immi­<lb/>neat &longs;upra fluidi libellam, neque aliqua eius portio <lb/><figure id="id.010.01.206.1.jpg" xlink:href="010/01/206/1.jpg"/><lb/>demergatur. </s> <s id="s.001027">His præparatis <lb/>quia exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> R &longs;upra <lb/>S ad ip&longs;um pondus S maiorem <lb/><expan abbr="proportion&etilde;">proportionem</expan> habet quam gra­<lb/>uitas P ad pondus cylindri <lb/>ACB, ergò componendo, gra­<lb/>uitas R ad S <expan abbr="maior&etilde;">maiorem</expan> proportio <lb/>nem habebit quàm duo <expan abbr="põde-ra">ponde­<lb/>ra</expan> P, & CAB, &longs;imul &longs;umpta, ad <lb/>pondus CAB; verùm grauitas <lb/>molis fluidi M æqualis &longs;olido AC ad pondus ab&longs;olu­<lb/>tum eiu&longs;dem &longs;olidi AC habet eamdem <expan abbr="proportion&etilde;">proportionem</expan>, <lb/>quam R ad S, ergò moles fluidi M æqualis &longs;olido AC <lb/>ad &longs;olidum idip&longs;um AC, &longs;eù illius pondus ad graui­<lb/>tatem huius habebit maiorem proportionem quàm <lb/>pondera P, & CAB &longs;imùl &longs;umpta ad pondus AC, & <lb/>proindè pondus ab&longs;olutum molis fluidi M æqualis <lb/>AC maius erit grauitate ip&longs;ius P vnà cum ponder&etail; <lb/>cylindri AC. </s> <s id="s.001028">Verumtamen Archimedes demon&longs;tra­<lb/><arrow.to.target n="marg263"/><lb/>uit &longs;olidum innatans tunc &longs;olummodò in fluido quie­<lb/>&longs;cere quando eius pondus ab&longs;olutum æquale fuerit <lb/>grauitati molis fluidi ambientis, quæ &longs;it æqualis por-<pb pagenum="199" xlink:href="010/01/207.jpg"/><arrow.to.target n="marg264"/><lb/>tioni eiu&longs;dem &longs;olidi intra eiu&longs;dem fluidi libellam de­<lb/>mer&longs;i. </s> <s id="s.001029">Qua proptèr quando pondus ab&longs;olutum præ­<lb/>dicti &longs;olidi minus fuerit pondere prædicti fluidi am­<lb/>bientis æqualis portioni eius demer&longs;æ nece&longs;&longs;ariò <lb/>&longs;olidum ip&longs;um in fluido eleuabitur vlteriu&longs;que <expan abbr="a&longs;c&etilde;-det">a&longs;cen­<lb/>det</expan>, igitur Cylindrus AC vnà cum &longs;uperincumben­<lb/>te pondere P eique coniuncto, & continuato no&ntail; <lb/>quie&longs;cet, &longs;ed &longs;ursùm a&longs;cendet, quaproptèr vis pre­<lb/>mens ponderis P non &longs;ufficit, nec habet tanta&mtail; <lb/>vim vt retineat &longs;olidum AC integrè infra fluidi <lb/>M libellam demer&longs;um. </s> <s id="s.001030">Cùmque, vt Archimedes de­<lb/><arrow.to.target n="marg265"/><lb/>mon&longs;trauit, energia, & vis, qua &longs;olidum AC cona­<lb/>tur, & vim facit vt &longs;ursùm a&longs;cendat in fluido M &etail;qua­<lb/>lis &longs;it vi illius ponderis, quod &longs;i &longs;uper id imponatur, <lb/>pote&longs;t id retinere infra fluidi libellam prohibereque <lb/>eius a&longs;cen&longs;um, igitur vis, qua cylindrus AC conatur <lb/>&longs;ursùm a&longs;cendere in fluido M maior e&longs;t quacumque <lb/>vi finita ponderis P, & hoc propo&longs;itum fuerat. </s> </p> <p type="margin"> <s id="s.001031"><margin.target id="marg262"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.001032"><margin.target id="marg263"/>De <expan abbr="in&longs;id&etilde;t">in&longs;ident</expan>. <lb/>humido lib. <lb/><!-- REMOVE S-->5. prop. 4.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001033"><margin.target id="marg264"/>Cap. 4. po&longs;i­<lb/>tiuam <expan abbr="leui-tat&etilde;">leui­<lb/>tatem</expan> <expan abbr="nõ">non</expan> dari.</s> </p> <p type="margin"> <s id="s.001034"><margin.target id="marg265"/>Eod. <!-- REMOVE S-->lib. 1. <lb/>prop. 6.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001035"><emph type="center"/>PROP. XCVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001036"><emph type="center"/><emph type="italics"/>His præmis&longs;is deuenio iam ad propo&longs;itionem <expan abbr="principal&etilde;">principalem</expan>, quòd <lb/>nimirùm quodlibet corpus &longs;ursùm a&longs;cendens in date <lb/>aliquo fluido non eleuatur &longs;ponte &longs;ua à principio <lb/>nempè intrin&longs;eco leuitatis impul&longs;um.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001037">SIt L quodlibet corpus eorum, quæ à Peripateti­<lb/>cis vocantur à prædominio aerea, vt &longs;unt ferè <lb/>omnia ligna, & alia innumera, & fluidum M in va&longs;e <lb/>FDI <expan abbr="cont&etilde;tum">contentum</expan>, &longs;it que prædictum fluidum, aut aqua, <pb pagenum="200" xlink:href="010/01/208.jpg"/><arrow.to.target n="marg266"/><lb/>aut hydrargyrum; procùl dubio corpus L intra flui­<lb/>dum M demer&longs;um &longs;ursùm a&longs;cendet. </s> <s id="s.001038"><expan abbr="Demon&longs;trandũ">Demon&longs;trandum</expan> <lb/>modò e&longs;t idip&longs;um non &longs;pontaneo motu ab intrin&longs;eco <lb/>principio leuitatis a&longs;cendere. </s> <s id="s.001039">Si hoc enim veru&mtail; <lb/><figure id="id.010.01.208.1.jpg" xlink:href="010/01/208/1.jpg"/><lb/>non e&longs;t, &longs;it, &longs;i fieri pote&longs;t leuitas <lb/>corporis L naturalis cau&longs;a, & <lb/>virtus à qua &longs;pontaneo motu <lb/>&longs;ursùm impellatur in fluido M. <lb/></s> <s id="s.001040">Et primò pr&etail;paretur infima ba­<lb/>&longs;is AB cylindri homogenei ip&longs;i <lb/>L, vt nimirùm ei vniatur ferru­<lb/>mineturque lamina aliqua vi­<lb/>trea, vel metallica, quæ &longs;it op­<lb/>timè explanata, & læuigata, & eiu&longs;dem materiæ, at­<lb/>que figuræ, & læuitatis &longs;it pauimentum, vel fundum <lb/>putei DE. <!-- KEEP S--></s> <s id="s.001041">Secundo loco reperta iam &longs;it <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan> cer­<lb/><arrow.to.target n="marg267"/><lb/>ta, & determinata illius virtutis, quæ requiritur ad <lb/>&longs;eparandam, & diuellendam &longs;uperficiem vitri AB ab <lb/>immediato contactu cum fundo putei DE, &longs;iuè vis <lb/>illa, quæ &longs;uperare valet re&longs;i&longs;tentiam prædictaru&mtail; <lb/>&longs;uperficierum &longs;e tangentium ad vacuum admitten­<lb/>dum; &longs;upponamu&longs;que huiu&longs;modivim e&longs;&longs;e æquale&mtail; <lb/><arrow.to.target n="marg268"/><lb/>ponderi G, atque reperiatur cylindrus AC eiu&longs;dem <lb/>materiei L itaut vis leuitatis qua conatur &longs;ursùm mo­<lb/>ueri in fluido M vna cum vitrea lamina AB maior &longs;it <lb/>vi, & energia ponderis G, &longs;itque vis illa leuitatis æ­<lb/>qualis potenti&etail; H. quapropter vis qua &longs;olidum AC <lb/>conatur, & impetum facit vt &longs;ursùm in dato fluido <lb/>a&longs;cendat, maior e&longs;t illa vi, & facultate, quæ requi-<pb pagenum="201" xlink:href="010/01/209.jpg"/><arrow.to.target n="marg269"/><lb/>ritur ad &longs;eparandam, & diuellendam ba&longs;im AB à fun­<lb/>do putei DE horizonti æquidi&longs;tante. </s> <s id="s.001042">dum igitur ba­<lb/>&longs;is AB immediatè, & exqui&longs;itè tangit fundum putei <lb/>DE, vt &longs;ibi mutuò congruant, exo&longs;culenturque, re­<lb/>pleatur vniuer&longs;um vas FE prædicto fluido M quou&longs;­<lb/>que &longs;uprema fluidi libella ad &longs;ummitatem C cylindri <lb/>AC demer&longs;i pertingat. </s> <s id="s.001043">Et quia hìc iam exi&longs;tunt, & <lb/>operantur duæ vires contrariæ, vna quidem H im­<lb/>pellit &longs;ursùm, e&longs;tque virtus eius leuitatis, alia verò <lb/>G, quæ huic re&longs;i&longs;tit, & vim deorsùm tendendo facit, <lb/>e&longs;tque energia contactus &longs;uperficierum AB & DE, <lb/>&longs;eù repugnantia ad vacuum admittendum qua con­<lb/>trario ni&longs;ui a&longs;cen&longs;us cylindri AC re&longs;i&longs;tit: E&longs;tque <expan abbr="cõ-traria">con­<lb/>traria</expan> vis H leuitatis, prædicti cylindri maior virtu­<lb/>te G tenacitatis, vel repugnantiæ ad vacuum, quæ <lb/>impetum contrarium deorsùm facit; igitur maior vis <lb/>leuitatis H nece&longs;&longs;ariò &longs;uperare debet vim minorem <lb/>G, & proinde di&longs;trahet diuelletque cylindrum AC à <lb/>fundo putei DE, atque po&longs;t &longs;eparationem idip&longs;u&mtail; <lb/>&longs;ursùm ad &longs;uperficiem fluidi M impellet, transferet­<lb/>que; &longs;ed hoc e&longs;t fal&longs;um, & contra &longs;en&longs;us <expan abbr="euidentiã">euidentiam</expan>, <lb/>proptereà quòd numquam contingit vt ba&longs;is colum­<lb/>næ AB &longs;eparetur à <expan abbr="cõtactu">contactu</expan> fundi putei DE, licèt &longs;up­<lb/>ponatur vim leuitatis quocumque exce&longs;&longs;u vim con­<lb/>tactus &longs;uperare, igitur verum non e&longs;t cylindrum AC <lb/>&longs;ursùm impelli ab intrin&longs;eca, & po&longs;itiua facultat&etail; <lb/>leuitatis eius, quod fuerat demon&longs;trandum. <pb pagenum="202" xlink:href="010/01/210.jpg"/><arrow.to.target n="marg270"/></s> </p> <p type="margin"> <s id="s.001044"><margin.target id="marg266"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.001045"><margin.target id="marg267"/>Prop. 88. & <lb/>89.</s> </p> <p type="margin"> <s id="s.001046"><margin.target id="marg268"/>Pro. <!-- REMOVE S-->93. 95. <lb/>& 96.</s> </p> <p type="margin"> <s id="s.001047"><margin.target id="marg269"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="margin"> <s id="s.001048"><margin.target id="marg270"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.001049"><emph type="center"/>PROP. XCVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001050"><emph type="center"/><emph type="italics"/>Confirmatur eadem præcedens propo&longs;itio.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001051">ET procùl dubio cen&longs;eri non debet vera cau&longs;&atail; <lb/>alicuius effectus illa qua po&longs;ita, & non impe­<lb/>dita ab excedente vi contraria, non ponitur nihilo­<lb/>minùs, nec &longs;ub&longs;equitur effectus, &longs;ed po&longs;ita leuitat&etail; <lb/>po&longs;itiua in prædicta lignea columna AC infra <expan abbr="fluidũ">fluidum</expan> <lb/>M demer&longs;a, & non impedita à virtute contraria con­<lb/>tactus, aut à timore vacui (eò quòd ex con&longs;tructio­<lb/>ne hæc multò minor fuerat virtute, & energia leui­<lb/>tatis) non &longs;ub&longs;equitur nihilominùs effectus a&longs;cen&longs;us <lb/>columnæ in prædicto fluido, igitur leuitas po&longs;itiu&atail; <lb/>non e&longs;t cau&longs;a <expan abbr="a&longs;c&etilde;&longs;us">a&longs;cen&longs;us</expan> <expan abbr="&longs;ursũ">&longs;ursum</expan> prædicti ligni in fluido M. </s> </p> <p type="main"> <s id="s.001052">Po&longs;tquam o&longs;ten&longs;a fuit pr&etail;dicta negatiua propo&longs;i­<lb/>tio. </s> </p> <p type="main"> <s id="s.001053"><emph type="center"/>PROP. XCIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001054"><emph type="center"/><emph type="italics"/>Demon&longs;trabitur iam quod nece&longs;&longs;ariò admitti debet cum Pla­<lb/>tone, & Archimede, quòd corpora omnia, quæ leuia <lb/>appellantur &longs;ursùm a&longs;cendunt ab extru&longs;ione <lb/>fluidorum in quibus innatant ob exce&longs;&longs;um <lb/>grauitatis eorumdem.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001055">QVia illa e&longs;t vera cau&longs;a alicuius effectus natura­<lb/>lis, qua po&longs;ita &longs;ub&longs;equitur effectus, & ablata <lb/>pariter effectus tollitur, &longs;ed po&longs;ita extru&longs;ione facta <lb/>à corpore fluido grauiori &longs;ub&longs;equitur effectus a&longs;cen-<pb pagenum="203" xlink:href="010/01/211.jpg"/><arrow.to.target n="marg271"/><lb/>&longs;us nimirùm &longs;olidi minùs grauis in eo demer&longs;i, & <lb/>quotie&longs;cumque prædicta extru&longs;io tollitur, aut im­<lb/>peditur, aufertur quoque vetaturque a&longs;cen&longs;us præ­<lb/>dicti corporis &longs;olidi, igitur nece&longs;&longs;ariò prædicta ex­<lb/>tru&longs;io grauioris fluidi ambientis e&longs;t vera, & legitima <lb/>cau&longs;a a&longs;cen&longs;us eorum corporum, quæ leuia <expan abbr="appellã-tur">appellan­<lb/>tur</expan>; &longs;ic quia in hypothe&longs;i in propo&longs;itione 97 expo&longs;i­<lb/>ta extru&longs;io aquæ, vel hydrargyri tollitur, & impedi­<lb/><figure id="id.010.01.211.1.jpg" xlink:href="010/01/211/1.jpg"/><lb/>tur, cùm fluidum M interlabi, <lb/>aut excurrere non po&longs;&longs;it infra <lb/>ba&longs;im AB prædictæ column&etail; ob <lb/>arctam connexionem contactus <lb/>ba&longs;is AB cum fundo putei DE, <lb/>licèt ambiens <expan abbr="fluidũ">fluidum</expan> multò gra­<lb/>uius &longs;it prædicta <expan abbr="colũna">columna</expan> lignea, <lb/>& in tali ca&longs;u columna &longs;ursùm <lb/>in fluido <expan abbr="nõ">non</expan> a&longs;cendit. </s> <s id="s.001056">E contrà <lb/>quotie&longs;cumque extru&longs;io fieri pote&longs;t, &longs;cilicèt quoties <lb/>fluidum M excurrere pote&longs;t infra ba&longs;im AB ob con­<lb/>cu&longs;&longs;ionem, vel minimam dilatationem <expan abbr="&longs;uperficierũ">&longs;uperficierum</expan> <lb/>&longs;e tangentium, &longs;eù ob tran&longs;itum per fi&longs;&longs;uram, aut fo­<lb/>ramen aliquod collaterale, tunc &longs;ub&longs;equitur effectus <lb/>a&longs;cen&longs;us prædictæ columnæ, igitur nece&longs;&longs;ariò extru­<lb/>&longs;io facta à grauiori fluido M e&longs;t vera cau&longs;a &longs;ublima­<lb/>tionis, & a&longs;cen&longs;us prædicti ligni in fluido, quod fue­<lb/>rat o&longs;tendendum. </s> </p> <p type="margin"> <s id="s.001057"><margin.target id="marg271"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.001058">Et hìc &longs;ummopere <expan abbr="animaduert&etilde;dum">animaduertendum</expan> e&longs;t, hallucina­<lb/><arrow.to.target n="marg272"/><lb/>tionem pendere ex eo quòd tribuitur effectus no&ntail; <lb/>veræ cau&longs;æ, &longs;ed alij imaginatæ, quoniam <expan abbr="quotie&longs;cũ-">quotie&longs;cun-</expan><pb pagenum="204" xlink:href="010/01/212.jpg"/><arrow.to.target n="marg273"/><lb/>que lignum &longs;ursùm a&longs;cendit in aqua &longs;emper verifi­<lb/>catur id minùs grauitare, quàm moles aquæ <expan abbr="ambi&etilde;-tis">ambien­<lb/>tis</expan> ei æqualis, quæ &longs;i liberè fluere, & excurrere po­<lb/>te&longs;t infra eius ba&longs;im, &longs;cilicèt &longs;i exercere pote&longs;t ex­<lb/>ce&longs;&longs;um &longs;ui ponderis, mirum non e&longs;t eleuare corpus <lb/>minoris grauitatis, &longs;icuti in libra videmus minus <expan abbr="põ-dus">pon­<lb/>dus</expan> à maiori &longs;ubleuari, quotie&longs;cumque tamen pon­<lb/>dus maius liberè vim &longs;uam exercere pote&longs;t, at &longs;i fue­<lb/>rit &longs;ub&longs;tentatum, vel fulciatur à pauimento pondus <lb/>minus eleuare non poterit. </s> <s id="s.001059">Huiu&longs;modi cau&longs;a, quæ <lb/>certa e&longs;t, & nece&longs;&longs;ariò operari debet iuxtà leges me­<lb/>chanices, <expan abbr="numquã">numquam</expan> pote&longs;t, nec debet excludi, vt ac­<lb/>ceptetur imaginata cau&longs;a leuitatis po&longs;itiuæ, quæ &longs;i <lb/>ade&longs;&longs;et, &longs;uum <expan abbr="effectũ">effectum</expan> producere deberet in ca&longs;u pro­<lb/>po&longs;itionis 97. vbi nil prorsùs operari o&longs;ten&longs;um e&longs;t, <lb/>tamquàm &longs;cilicèt &longs;i non e&longs;&longs;et. </s> </p> <p type="margin"> <s id="s.001060"><margin.target id="marg272"/>Cau&longs;a hallu­<lb/>cinationi&longs; de­<lb/>tegitur.</s> </p> <p type="margin"> <s id="s.001061"><margin.target id="marg273"/>Cap. 4. po&longs;i­<lb/>tiuam leui­<lb/>tatem no&ntail; <lb/>dari.</s> </p> <p type="main"> <s id="s.001062">Po&longs;tquam igitur examinauimus, & reiecimus ra­<lb/>tiones omnes Peripateticas <expan abbr="cõtra">contra</expan> Platonem, & alios <lb/>antiquos pro a&longs;&longs;ertione leuitatis po&longs;itiuæ, pariter­<lb/>que inefficaces repertæ &longs;unt omnes aliæ rationes, <lb/>quæ pro confirmatione prædictæ <expan abbr="&longs;ent&etilde;tiæ">&longs;ententiæ</expan> circumfe­<lb/>runtur, cùmque tandem methodo demon&longs;tratiua <expan abbr="ve-ritat&etilde;">ve­<lb/>ritatem</expan> no&longs;træ <expan abbr="&longs;ent&etilde;tiæ">&longs;ententiæ</expan> confirmauerimus, po&longs;&longs;umus <expan abbr="iã">iam</expan>, <lb/>ab&longs;que iactantia, affirmare euici&longs;&longs;e nullam leuitatem <lb/>po&longs;itiuam in natura dari virtute cuius naturalia cor­<lb/>pora conentur di&longs;cedere à no&longs;tra terra versùs &longs;upe­<lb/>riores partes, &longs;ed è contra pronunciare po&longs;&longs;umus re­<lb/>periri in omnibus corporibus &longs;ublunaribus vim <expan abbr="quã-dam">quan­<lb/>dam</expan> vniuer&longs;alem &longs;e mutuò complectendi, & globo <pb pagenum="205" xlink:href="010/01/213.jpg"/><arrow.to.target n="marg274"/><lb/>terreno adhærendi mediante facultate de&longs;cen&longs;iu&atail;, <lb/>quæ grauitas appellatur, hæc, inquam, grauitas di­<lb/>uer&longs;imodè participata à corporibus terram ambien­<lb/>tibus efficit vt minùs grauia expul&longs;a ex inferioribus <lb/>locis à grauioribus illa &longs;ursùm eleuentur, & &longs;ic cor­<lb/>pora elementaria optima <expan abbr="quid&etilde;">quidem</expan> con&longs;titutione <expan abbr="æqui-libr&etilde;tur">æqui­<lb/>librentur</expan>, & ad &longs;ua loca naturalia a&longs;portentur vt ibi­<lb/>dem quie&longs;cant. </s> </p> <p type="margin"> <s id="s.001063"><margin.target id="marg274"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001064"><emph type="center"/><emph type="italics"/>De Structura, Grauitate, Æquilibrio, <lb/>& Vi Elateria Aeris.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001065"><emph type="center"/>CAP. V.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001066">IAm &longs;uperiùs &longs;atis &longs;uperque o&longs;ten&longs;um e&longs;t aqua&mtail; <lb/>grauitare etiam in propria regione, & in &longs;uo toto: <lb/>præterea o&longs;tendimus nullam leuitatem po&longs;itiuam re­<lb/>periri in corporibus mixtis, in ijs nempè, quæ à præ­<lb/>dominio aerea vulgò appellantur, quod verò peculi­<lb/>ariter aer grauis &longs;it, ne dum Ari&longs;tot. apertè fatetur, <lb/>cùm ait: <emph type="italics"/>Omnia elementa grauitatem habere prætèr ignem<emph.end type="italics"/>, <lb/><arrow.to.target n="marg275"/><lb/><emph type="italics"/>pariterquè omnia leuitatem habere prætèr <expan abbr="terrã">terram</expan>.<emph.end type="italics"/></s> <s id="s.001067"> Hinc in­<lb/>fert: <emph type="italics"/>terram igitur, & quæ terræ habent plurimum, vbique <lb/>grauitatem habere e&longs;t nece&longs;&longs;arium. </s> <s id="s.001068">Aquam autem vbique, <lb/>prætèr quàm in terra, aerem verò præterquam in aqua, & <lb/>terra. </s> <s id="s.001069">In &longs;ua enim regione omnia grauitatem habent prætèr <lb/>ignem, etiam aer ip&longs;e. </s> <s id="s.001070">Signum autem est quia trahit plùs in­<lb/>flatus vter, quàm vacuus.<emph.end type="italics"/></s> <s id="s.001071"> Sed etiam demon&longs;trari po­<lb/>te&longs;t eodem modo, ij&longs;demque rationibus, quas in pr&etail;­<lb/>cedenti capitulo adduximus, &longs;icuti enim ibi con&longs;ide-<pb pagenum="206" xlink:href="010/01/214.jpg"/><arrow.to.target n="marg276"/><lb/>rauimus ligna, ampullas vitreas |, & ve&longs;icas aere ple­<lb/>nas per aquam a&longs;cendentes, demon&longs;trauimu&longs;que eas <lb/>non vi leuitatis, &longs;ed ab extru&longs;ione medij fluidi &longs;ursùm <lb/>impelli, &longs;ic pariter &longs;i loco ligni, aut ve&longs;ic&etail; ponatur aer <lb/>in <expan abbr="fũdo">fundo</expan> hydrargyri, vel aquæ, olei, vel &longs;piritus vini <lb/><expan abbr="nõ">non</expan> &longs;ecùs, ac priùs <expan abbr="factũ">factum</expan> e&longs;t, <expan abbr="o&longs;t&etilde;demus">o&longs;tendemus</expan> aerem non <expan abbr="&longs;põ-te">&longs;pon­<lb/>te</expan> &longs;ua a&longs;cendere à vi leuitatis tran&longs;latum, &longs;ed à pre&longs;­<lb/>&longs;ione grauioris medij fluidi violenter &longs;ursùm impel­<lb/>lentis. </s> <s id="s.001072">licèt ergo negotium omninò confectum e&longs;&longs;&etail; <lb/>videatur, vtile tamen erit idip&longs;um confirmare ex æ­<lb/>quilibrio aeris cum cæteris fluidis. </s> </p> <p type="margin"> <s id="s.001073"><margin.target id="marg275"/>4. de Cælo <lb/>cap. 4.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001074"><margin.target id="marg276"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001075"><emph type="center"/>PROP. C.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001076"><emph type="center"/><emph type="italics"/>Ex &longs;u&longs;pen&longs;ione mercurij in in&longs;trumento Torricelliano <lb/>&longs;uadetur aerem, vt grauem, æquilibrium <lb/>efficere cum mercurio.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001077">ET hac occa&longs;ione con&longs;iderabimus pulcherrimum <lb/>profectò experimentum eorum, quæ hoc &longs;eculo <lb/>adinuenta &longs;unt, hydrargyri nempè eleuatio in fi&longs;tula, <lb/>quam primus <expan abbr="omniũ">omnium</expan> animaduertit docti&longs;&longs;imus Tor­<lb/>ricellius, e&longs;tque experimentum huiu&longs;modi: Sit fi&longs;tu­<lb/>la vitrea ABC perforata tantummodò in eius extre­<lb/>mitate C, in A verò clau&longs;a, hæc verò hydrargyro <lb/>repleta v&longs;que ad &longs;ummitatem C pulpa indicis &longs;trictè <lb/>claudatur, inuertaturque contrario &longs;itu, vt nimirùm <lb/>os eius C inferiùs re&longs;piciat; &longs;itque po&longs;tea præparata <lb/>&longs;cutella DHE pariter hydrargyro plena demerga­<lb/>tur infimum orificium C fi&longs;tulæ vnà <expan abbr="cũ">cum</expan> digito occlu-<pb pagenum="207" xlink:href="010/01/215.jpg"/><arrow.to.target n="marg277"/><lb/>dente infrà &longs;upremam hy­<lb/><figure id="id.010.01.215.1.jpg" xlink:href="010/01/215/1.jpg"/><lb/>drargyri libellam DE, tunc <lb/>&longs;ublato digito mercurius <lb/>profluet ab orificio C quo­<lb/>u&longs;que altitudo FB extantis <lb/>hydrargyri &longs;upra libella&mtail; <lb/>DE &longs;it pedum duorum, & <lb/>quadrantis, vel vnius cubi­<lb/>ti, & quadrantis, nec vlte­<lb/>rius hydrargyrum graui&longs;&longs;i­<lb/>mum de&longs;cendit &longs;emperque <lb/>ad eamdem altitudine&mtail; <lb/>per&longs;euerat, licèt inclinetur <lb/>fi&longs;tula, &longs;cilicèt ducta recta FG parallela horizonti <expan abbr="s&etilde;-per">sen­<lb/>per</expan> &longs;ummitas hydrargyri ad eamdem horizontalem <lb/>FG perueniet quomodocumque fi&longs;tula inclinetur. <lb/></s> <s id="s.001078">Ip&longs;e Torricellius experimenti inuentor &longs;agaci&longs;&longs;imè <lb/>cau&longs;am quoque huius effectus indagauit, animaduer­<lb/>tit enim nos in infima profunditate oceani aerei de­<lb/>mer&longs;os e&longs;&longs;e, & &longs;icuti maris aqua vndique fundu&mtail; <lb/>comprimit per lineas horizonti perpendiculares, &longs;eù <lb/>directas ver&longs;us centrum telluris, &longs;ic quoque in oceano <lb/>aereo ni&longs;us eius grauitatis exercetur perpendiculari­<lb/>tèr &longs;upra horizontis planum, vnde concipi debent cy­<lb/>lindri aerei perpendicularitèr &longs;uperficiem hydrargy­<lb/>ri DE &longs;upremam comprimentes; quia verò eade&mtail; <lb/>libella mercurij DE comprimitur quoque in &longs;itu B à <lb/>&longs;uperficie ba&longs;is B mercurialis cylindri FB efforma­<lb/>tur veluti libra, vel &longs;ipho, quæ numquam quie&longs;cit, ni-<pb pagenum="208" xlink:href="010/01/216.jpg"/><arrow.to.target n="marg278"/><lb/>&longs;i æquilibrium momentorum efficiatur, &longs;cilicèt ni&longs;i <lb/>momentum ponderis cylindri aerei &longs;uperficiem DE <lb/>comprimentis æquale fuerit momento ponderis cy­<lb/>lindri mercurialis BF. </s> <s id="s.001079">Huiu&longs;modi &longs;peculatio magno <lb/>plau&longs;u à viris doctis excepta fuit, alij&longs;que <expan abbr="experim&etilde;-tis">experimen­<lb/>tis</expan> pariter comprobata, quia nimirùm &longs;i loco hydrar­<lb/>gyri aquam adhibeamus, vel aliud fluidum, tunc aqua <lb/>pura eleuatur ad altitudinem pedum 32. vel cubito­<lb/>rum 17. proximè cuius pondus præcisè æquatur gra­<lb/>uitati prædicti cylindri mercurialis BF vnius cubiti, <lb/>& quadrantis (&longs;umptis nimirum ba&longs;ibus æqualibus) <lb/>& &longs;i fuerit oleum altius quàm aqua pura eleuatur, &longs;ed <lb/>præcisè quantum exigit aquæ grauitas ei æqualis; <lb/>idemque continget &longs;i fuerit aliquis &longs;piritus, vel qui­<lb/>libet alius liquor. </s> <s id="s.001080">cùm igitur in hi&longs;ce omnibus fi&longs;tulis <lb/>eleuentur varij liquores, itaut eorum partes eleuatæ <lb/>&longs;uper infimam libellam &longs;emper eiu&longs;dem &longs;int grauita­<lb/>tis, dicendum nece&longs;&longs;ariò e&longs;t ab vnica, & eadem vi <lb/>compre&longs;&longs;iua eleuari, qu&etail; &longs;emper eiu&longs;dem roboris &longs;it: <lb/>at nulla alia a&longs;&longs;ignari pote&longs;t præter pondus cylindri <lb/>aerei liquori in &longs;cutella contento <expan abbr="incũbentis">incumbentis</expan>. </s> <s id="s.001081">igitur <lb/>pote&longs;t aer incumbens eleuare prædictos liquores, hoc <lb/>autem minimè effici po&longs;&longs;et ab&longs;que eo quod in aer&etail; <lb/>æquilibrium efficeretur; &longs;icuti in maris oceano ex eo <lb/>quod omnes partes aquæ æquali ni&longs;u deor&longs;um ferun­<lb/>tur, & premunt, fit vt eius &longs;uprema libella &longs;phæricè <lb/>contornetur, &longs;ic paritèr &longs;uprema aeris &longs;uperficies <lb/>&longs;phæricè tornata erit, ex eo quod partes eius omnes <lb/>æquali ni&longs;u deor&longs;um <expan abbr="grauitãtes">grauitantes</expan> æquilibrium <expan abbr="efficiũt">efficiunt</expan>. <pb pagenum="209" xlink:href="010/01/217.jpg"/><arrow.to.target n="marg279"/></s> </p> <p type="margin"> <s id="s.001082"><margin.target id="marg277"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001083"><margin.target id="marg278"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001084"><margin.target id="marg279"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001085"><emph type="center"/>PROP. CI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001086"><emph type="center"/><emph type="italics"/>Idip&longs;um clariùs confirmatur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001087">QVòd po&longs;tea prædicta mercurij eleuatio in fi &longs;tu­<lb/>la producatur ab aeris compre&longs;&longs;ione &longs;upr&atail; <lb/>mercurium in &longs;cutella contentum, confirmatur ali&atail; <lb/>ratione, &longs;ed clariùs adhibito <expan abbr="in&longs;trum&etilde;-to">in&longs;trumen­<lb/>to</expan> à me excogitato, quod Academiæ <lb/>Experimentali Medice&etail; communicaui, <lb/>eiu&longs;que ichon habetur figura 34. libri <lb/>experimentorum eiu&longs;dem Academiæ, <lb/>ab&longs;que enim &longs;cutella DE &longs;ufficit vt in­<lb/>fima pars fi&longs;tulæ BC incuruetur, &longs;ur­<lb/>&longs;umque inflectatur, <expan abbr="tũc">tunc</expan> quidem reple­<lb/>ta vt priùs vniuer&longs;a fi&longs;tula mercurio, <lb/>reuoluatur vt eius pars clau&longs;a A & lon­<lb/>gitudo fi&longs;tulæ AFB perpendicularitèr <lb/>ad horizontem emineat, tunc quidem <lb/>ab orificio aperto G hydrargyru&mtail; <lb/>profluet, vel intra amplitudinem am­<lb/>pullæ DG reducetur, quou&longs;que altitu­<lb/><figure id="id.010.01.217.1.jpg" xlink:href="010/01/217/1.jpg"/><lb/>do mercurialis cylindri FB &longs;upra <expan abbr="libellã">libellam</expan> BD fuerit v­<lb/>nius cubiti & quadrantis, & tunc <expan abbr="cõcipi">concipi</expan> debet cylin­<lb/>drus aereus DS v&longs;que ad &longs;upremam aeris &longs;uperficiem <lb/>S exten&longs;us, cuius pondus æquetur grauitati cylindri <lb/>mercurialis FB. </s> <s id="s.001088">Quod verò à compre&longs;&longs;ione prædicti <lb/>cylindri aerei DS eleuetur graui&longs;&longs;imum <expan abbr="hydrargyrũ">hydrargyrum</expan> <lb/>FB probatur ex eo quod &longs;i augeatur impul&longs;us, & com-<pb pagenum="210" xlink:href="010/01/218.jpg"/><arrow.to.target n="marg280"/><lb/>pre&longs;&longs;io &longs;upra &longs;uperficiem hydrargyri D altiùs ele­<lb/>uatur mercurius in fi&longs;tula BFA. &longs;ic &longs;i noua fi&longs;tula, vel <lb/>in&longs;trumento pneumatico aer in&longs;uffletur, vt compri­<lb/>mat &longs;uperficiem hydrargyri D eleuatur quoque &longs;u­<lb/>prema &longs;uperficies F hydrargyri in fi&longs;tula clau&longs;a; & &longs;i <lb/>è contrà embolo retracto, velùti exugatur aer impe­<lb/>diatur que compre&longs;&longs;io eius &longs;upra mercurium D &longs;pon­<lb/>tè labetur mercurius de&longs;cendetque deorsùm versùs <lb/>B. præterea &longs;i &longs;upra mercurium in D infundatur aqua, <lb/>quæ propagetur vique ad libellam GI, tunc quidem <lb/>mercurius quoque eleuatur ab F v&longs;que ad H, & quod <lb/>mirum e&longs;t, eleuatur mercurius præcisè pro men&longs;ura <lb/>ponderis aquæ incumbentis GD, &longs;cilicèt altitudo G <lb/>D erit quatuordeciès maior, quàm FH, quia talis re­<lb/>ciprocè e&longs;t proportio ponderis mercurij ad aquam. <lb/></s> <s id="s.001089">Si igitur in &longs;patio inani nulla alia cau&longs;a vlterioris ele­<lb/>uationis hydrargyri FH a&longs;&longs;ignari pote&longs;t præter gra­<lb/>uitatem aquæ collateralis GD cum qua mercurius F <lb/>H æquilibrium efficit, quare negabimus reliquum <lb/>mercurij FB eleuari à pondere aliquo premente &longs;u­<lb/>perficiem D, quæ &longs;it &longs;emper eiu&longs;dem roboris? </s> <s id="s.001090">cùm­<lb/>que nullum aliud corpus grauitans a&longs;&longs;ignari po&longs;&longs;it <lb/>prætèr aerem, igitur nece&longs;&longs;ariò ab hoc mercurius <lb/>eleuatur. </s> </p> <p type="margin"> <s id="s.001091"><margin.target id="marg280"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001092">Prætermi&longs;&longs;is alijs experimentis excogitatis à viris <lb/>docti&longs;&longs;imis in Italia, Gallia, & Anglia, de quibus fusè <lb/>agitur in libro <expan abbr="experim&etilde;torum">experimentorum</expan> no&longs;træ Academiæ ex­<lb/>perimentalis Mediceæ nè repetamus ea, quæ iam pa&longs;­<lb/>&longs;im vulgata &longs;unt, tantummodò recen&longs;ebo, & ad exa-<pb pagenum="211" xlink:href="010/01/219.jpg"/><arrow.to.target n="marg281"/><lb/>men reuocabo difficultates contra ratiocinium Torri­<lb/>cellianum, & no&longs;trum à docti&longs;&longs;imo viro allatas <expan abbr="cũ">cum</expan> ait. <lb/><emph type="italics"/>Dicebatur &longs;egmentum mercurij IC &longs;ustineri à cylindro aeris <lb/>eiu&longs;dem ba&longs;is, itaut perfectum &longs;it vtrinque æquilibrium. <lb/></s> <s id="s.001093">Contra hanc &longs;ententiam nonnulla militant &longs;i appendatur fi­<lb/><arrow.to.target n="marg282"/><lb/>stula BD po&longs;tquàm &longs;ubducto digito de&longs;cendit mercurius in <lb/>IC &longs;tatera fideli adhibita, & &longs;ignetur pon­<lb/>deris ratio, ac deindè citrà mercurij de&longs;cen­<lb/>&longs;um eadem fi&longs;tula cum æquali quantitate <lb/>mercurij appendatur, eadem ratio ponderis <lb/>inuenietur paulò maior, æqualem quantita­<lb/>tem mercurij intelligo <expan abbr="&longs;egm&etilde;to">&longs;egmento</expan> IC;<emph.end type="italics"/> Et pau­<lb/>lò infra &longs;ub&longs;equitur. <emph type="italics"/>Si mercurius IC <lb/>&longs;u&longs;tinetur à cylindro exterioris aeris, igitur <lb/>cum illo perfectum æquilibrium facit, igitur <lb/>cum alio æquali pondere ad libram appen&longs;o <lb/><figure id="id.010.01.219.1.jpg" xlink:href="010/01/219/1.jpg"/><lb/>aliud æquilibrium facere non potest. </s> <s id="s.001094">Supponemus enim mer­<lb/>curium IC eße trium librarum, æquilibrium facit cum cy­<lb/>lindro aeris etiam trium librarum. </s> <s id="s.001095">Si autem aliud pondus <lb/>trium librarum in alter a lance appendatur <expan abbr="cũ">cum</expan> hoc mercuri­<lb/>us æquilibrium facere nequit, alioquin &longs;ex Libris mercurius <lb/>æquilibraret, quod legibus staticæ repugnat.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001096"><margin.target id="marg281"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001097"><margin.target id="marg282"/>Defficulta­<lb/>tes contra <lb/>no&longs;tram do­<lb/>ctrinam.</s> </p> <p type="main"> <s id="s.001098"><emph type="center"/>PROP. CII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001099"><emph type="center"/><emph type="italics"/>Euidenti&longs;simo exemplo in aqua <expan abbr="o&longs;t&etilde;ditur">o&longs;tenditur</expan> quod licèt mercu­<lb/>rius in fi&longs;tula ab æquipondio aquæ &longs;u&longs;tineatur, nihilo­<lb/>minùs vis eleuans fi&longs;tulam &longs;ustinet præterea <lb/>aquæ incumbentis pondus æquale <lb/>mercurio.<emph.end type="italics"/><emph.end type="center"/><pb pagenum="212" xlink:href="010/01/220.jpg"/><arrow.to.target n="marg283"/></s> </p> <p type="margin"> <s id="s.001100"><margin.target id="marg283"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001101">QVia verò ratiocinium hoc à viro docti&longs;&longs;imo af­<lb/>fertur vt conuincens, & <expan abbr="euid&etilde;s">euidens</expan>, conabor, amo­<lb/>re veritatis, luculentèr exponere eius defectum, & <lb/>claritatis gratia operationem euidentiorem in ip&longs;&atail; <lb/>aqua con&longs;iderabo &longs;imilem omninò ei quam præ ma­<lb/>nibus habemus. </s> <s id="s.001102">Sit vas profundi&longs;&longs;imum RTVS aere <lb/>plenum in cuius fundo pona­<lb/>tur &longs;cutella DF mercurio ple­<lb/>na, &longs;itque po&longs;tea fi&longs;tula vitrea <lb/>AC <expan abbr="vtrinq;">vtrinque</expan> perforata, & per­<lb/>uia cuius in fima pars C demer­<lb/>gatur infra mercurij libellam; <lb/>po&longs;tea repleatur puteus aqua <lb/>vt vitri &longs;ummitatem A non at­<lb/>tingat, & remaneat fi&longs;tula exi­<lb/>nanita vt prius tunc quidem <lb/>&longs;en&longs;u con&longs;tat eleuari hydrar­<lb/>gyrum in fi&longs;tula à C v&longs;que ad <lb/><figure id="id.010.01.220.1.jpg" xlink:href="010/01/220/1.jpg"/><lb/>B quou&longs;que mercurialis altitudo CB decima quarta <lb/>pars &longs;it aquæ altitudinis HG. hic iam quia effectus <lb/>eleuationis mercurij v&longs;que ad B productus fuit ab a­<lb/>qua de nouo impo&longs;ita dubitandum <expan abbr="nõ">non</expan> e&longs;t ab eius gra­<lb/>uitate mercurium eleuatum fui&longs;&longs;e, quod præterea <lb/>confirmatur ex æquipondio ip&longs;ius cylindri aquæ HG <lb/>cum mercuriali cylindro CB eiu&longs;dem ba&longs;is; itaque in <lb/>libra CEG, vel in &longs;iphone tunc quie&longs;cunt duo fluida, <lb/>mercurius nempè & aqua, cùm præcisè efficitur <expan abbr="eorũ">eorum</expan> <lb/>æquilibrium; claudatur po&longs;tea fi&longs;tula in B interpo&longs;ita <lb/>nimirùm laminula non di&longs;&longs;imili ei, quàm in arundini-<pb pagenum="213" xlink:href="010/01/221.jpg"/><arrow.to.target n="marg284"/><lb/>bus ob&longs;eruamus à qua præcisè prohibeatur tran&longs;itus <lb/>fluidi per rimas laterales, po&longs;tea impleatur reliqua <lb/>pars fi&longs;tulæ AB aqua, & tandèm eadem vitrea fi&longs;tu­<lb/>la termino I libræ IL radiorum æqualium &longs;u&longs;penda­<lb/>tur, atque ab oppo&longs;ito termino eius L pendeat pon­<lb/>dus M æquale ponderi ip&longs;ius vitri AC. videndu&mtail; <lb/>modò e&longs;t an à &longs;implici pondere M &longs;u&longs;tineri po&longs;&longs;it vi­<lb/>trea fi&longs;tula AC, & patet non &longs;ufficere, quia in &longs;ipho­<lb/>ne ACGH pondus cylindri aquei HG æquatur præ­<lb/>cisè ponderi mercurij BC, cumque pr&etail;terea aqua <expan abbr="cõ-tenta">con­<lb/>tenta</expan> in &longs;patio fi&longs;tulæ AB ferè æqualis &longs;it aquæ HG, <lb/>ergò &longs;umma aquæ AB, & mercurij BC duplo grauior <lb/>e&longs;t, quam &longs;it cylindrus aqueus HG vt nimirùm &longs;i a­<lb/>qua HG fuerit vnius libræ erunt mercurius CB, & <lb/>aqua AB ferè duarum librarum (non con&longs;iderato <expan abbr="põ-dere">pon­<lb/>dere</expan> ip&longs;ius vitri AC,) ergò vt fiat æquilibrium de­<lb/>bet addi ponderi M aliud pondus O, quod &longs;it æqua­<lb/>le ponderi aquæ AB, & tunc in infima libra CEG, <lb/>&longs;eu &longs;iphone e&longs;&longs;icitur æquilibrium inter cylindrum a­<lb/>queum HG, & mercurium CB, in &longs;uprema verò li­<lb/>bra IL efficitur æquilibrium inter fi&longs;tulam vitrea&mtail; <lb/>AC, vnà cum aqua AB ex vna parte, & ponderæ M, <lb/>O ex altera parte. </s> <s id="s.001103">Igitur quia reuera mercurius CB <lb/>non &longs;u&longs;tinetur à potentia O &longs;ubleuante <expan abbr="librã">libram</expan> <expan abbr="&longs;upre-mã">&longs;upre­<lb/>mam</expan>, cum nimirùm &longs;u&longs;tineatur à collaterali aqua HG, <lb/>e&longs;t impo&longs;&longs;ibile fi&longs;tulam vitream AC &longs;u&longs;tineri à &longs;o­<lb/>litario pondere M æquale grauitati ip&longs;ius vitri, ni&longs;i <lb/>in&longs;uper addatur alia potentia O, quæ &longs;u&longs;tineat cy­<lb/>lindrum aqueum AB æquè graue ferè, ac|e&longs;t mercu­<lb/>rius CB. <pb pagenum="214" xlink:href="010/01/222.jpg"/><arrow.to.target n="marg285"/></s> </p> <p type="margin"> <s id="s.001104"><margin.target id="marg284"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001105"><margin.target id="marg285"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001106">Si po&longs;tea fi&longs;tula vitrea &longs;ecetur in B, eiu&longs;que &longs;upre­<lb/>ma portio BA tollatur amoueaturque, at que pondus <lb/>M æquale &longs;it grauitati vitri decurtati CB, tunc <expan abbr="quid&etilde;">quidem</expan> <lb/>incumbit, ac innititur fi&longs;tul&etail; cylindrus aqueus BA <lb/>fi&longs;tulamque comprimit non &longs;ecus, ac priùs quando <lb/>intra cauitatem fi&longs;tulæ AB continebatur. </s> </p> <p type="main"> <s id="s.001107"><emph type="center"/>PROP. CIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001108"><emph type="center"/><emph type="italics"/>Licèt Torricelliana fistula à mercurio in ea &longs;u&longs;pen&longs;o <expan abbr="nõ">non</expan> gra­<lb/>uetur, tamen manus cogitur &longs;u&longs;tinere pondus cylin­<lb/>dri aerei fi&longs;tulæ incumbentis, quod æquatur <expan abbr="põ-deriinclu&longs;i">pon­<lb/>deri inclu&longs;i</expan> mercurij.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001109">IDip&longs;um no&longs;træ fi&longs;tulæ directæ in ae­<lb/>re con&longs;titutæ adaptari pote&longs;t, &longs;it­<lb/>que illa AC duorum cubitorum habe­<lb/>atque orificium C in&longs;ignis exiguitatis, <lb/>repleaturque mercurio deor&longs;umqu&etail; <lb/>inuertatur in aere libero (non enim <lb/>nece&longs;sè e&longs;t, vt os C intra &longs;cutellam <lb/>mercurij plenam infundatur, <expan abbr="quãdo">quando</expan> <lb/>valdè &longs;trictum e&longs;t os eius C,) tunc <lb/>ab infimo orificio C mercurius in ae­<lb/>re profluet quou&longs;que altitudo CB <lb/>fuerit vnius cubiti, & quadrantis pro­<lb/>ximè. </s> <s id="s.001110">Hic concipi debet cylindrus <lb/>aereus SG v&longs;que ad &longs;upremam regio­<lb/><figure id="id.010.01.222.1.jpg" xlink:href="010/01/222/1.jpg"/><lb/>nis aeris &longs;uperficiem exten&longs;us, qui re­<lb/>flexus per EC vim faciat contra pre&longs;&longs;ionem mercu­<lb/>rij BC, eumque &longs;u&longs;pendat, & &longs;ic liberè concedo ad-<pb pagenum="215" xlink:href="010/01/223.jpg"/><arrow.to.target n="marg286"/><lb/>uer&longs;ario, quòd fi&longs;tula AC nil prorsùs ab inclu&longs;o mer­<lb/>curio BC grauatur, & &longs;ic de facto experimur appli­<lb/>cata digiti pulpa ori infimo fi&longs;tulæ; quod in part&etail; <lb/>intermedia pulpæ à mercurio tacta nulla compre&longs;&longs;io, <lb/>nec <expan abbr="cõtu&longs;io">contu&longs;io</expan> <expan abbr="neq;">neque</expan> grauitatio per&longs;entitur, quando præ­<lb/>cisè mercurij altitudo BC e&longs;t vnius cubiti, & <expan abbr="qua-drãtis">qua­<lb/>drantis</expan> ferè; quod &longs;ieius altitudo &longs;upra CB augeatur, <lb/><expan abbr="tũc">tunc</expan> <expan abbr="&longs;olũmodò">&longs;olummodò</expan> percipitur in medio pulpæ digiti &longs;ub­<lb/>iecti <expan abbr="cõpre&longs;&longs;io">compre&longs;&longs;io</expan> grauitans iuxtà <expan abbr="m&etilde;&longs;urã">men&longs;uram</expan> exce&longs;&longs;us mer­<lb/>curij &longs;upra eum qui altitudinem vnius cubiti, & qua­<lb/>drantis occupat, & &longs;i è contrà mercurius deprima­<lb/>tur violentèr infra debitam altitudinem BC, tunc ne­<lb/>dùm &longs;ubiecta pulpa digiti non comprimitur, &longs;ed è <lb/>contrà exugitur, vt efficiunt cucurbitæ medicæ, & <lb/>hyrudines. </s> <s id="s.001111">Sed dicet aduer&longs;arius &longs;i mercurius BC <lb/>nil grauitat, nec comprimit digitum, quare requi­<lb/>ritur vis, aut libræ, aut digiti &longs;ubiecti, quæ nedu&mtail; <lb/>æquet pondus &longs;olias vitri AC, &longs;ed prætereà &longs;u&longs;tine­<lb/>re valeat duas libras v. <!-- REMOVE S-->g. <!-- REMOVE S-->quas <expan abbr="p&etilde;dit">pendit</expan> mercurius BC? <lb/></s> <s id="s.001112">Re&longs;pondeo aereum cylindrum SA fi&longs;tulæ vitreæ in­<lb/>cumbentem &longs;ua grauitate agere non minùs, quà&mtail; <lb/>collateralis cylindrus aereus SG, cumque vitru&mtail; <lb/>CA non repellatur æquali actione contraria &longs;ursùm <lb/>ab aere collaterali SG, quia huius vis exercetur, & <lb/>omninò expletur &longs;u&longs;tentando mercurium BC; igitur <lb/>nece&longs;&longs;ariò vitrum CA comprimitur deorsùm à gra­<lb/>uitate aeris incumbentis SA, cuius pondus æqual&etail; <lb/>e&longs;t mercurio BC hinc fit vi ex præconcepta fal&longs;a opi­<lb/>nione tribuamus compre&longs;&longs;ionem aeris SA nobis in-<pb pagenum="216" xlink:href="010/01/224.jpg"/><arrow.to.target n="marg287"/><lb/>compertam alij cau&longs;æ nempe grauitati ip&longs;ius mer­<lb/>curij BC intra fi&longs;tulam contenti. </s> <s id="s.001113">Hoc profectò con­<lb/>firmatur ex eo, quod prædicta fi&longs;tula à digito &longs;u&longs;ten­<lb/>tata exercet &longs;uam compre&longs;&longs;ionem contra pulpæ di­<lb/>giti extremitatem, quæ à perimetro orificij vitri <expan abbr="tã-gitur">tan­<lb/>gitur</expan>, & contunditur: non autem contra mediam pul­<lb/>pæ digiti partem, quæ ab ingenti pondere trium li­<lb/>brarum mercurij v. <!-- REMOVE S-->g. <!-- REMOVE S-->magis, & euidentius compri­<lb/>mi deberet quàm grauentur ambientes pulpæ digi­<lb/>ti partes à perimetro ori&longs;icij vitri trium vnciarum. </s> </p> <p type="margin"> <s id="s.001114"><margin.target id="marg286"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001115"><margin.target id="marg287"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001116">Hanc euidenti&longs;&longs;imam demon&longs;trationem conatur <lb/><arrow.to.target n="marg288"/><lb/>aduer&longs;arius refellere, ait enim, <emph type="italics"/>hoc facilè reijcitur nem­<lb/>pè æqualis cylindrus aeris incumbit ba&longs;i &longs;upremæ obstructæ <lb/>fistulæ &longs;iue mercurio, &longs;iue aqua, &longs;iue aere fi­<lb/>&longs;tula plena &longs;it, vt patet. </s> <s id="s.001117">Vnde &longs;i <expan abbr="qu&etilde;">quem</expan> haberet <lb/>effectum, eumdem &longs;emper haberet, &longs;ed hæc <lb/>in&longs;tantia futilis est, quare in ea diutiùs mi­<lb/>nimè hærendum.<emph.end type="italics"/></s> <s id="s.001118"> Sit fi&longs;tula AC plena ae­<lb/>re non mercurio &longs;u&longs;tenteturque infer­<lb/>nè eius orificium C à &longs;ubiecta digiti <lb/>pulpa, concedo, quod &longs;upernè digi­<lb/>tus premitur à columna aeris SAC, pa­<lb/>riterque <expan abbr="cõprimitur">comprimitur</expan> à vitri fi&longs;tula AC, <lb/>quidnam ex hoc deducit aduer&longs;arius? <lb/></s> <s id="s.001119">dicet, quod tantumdem ponderis pa­<lb/>teretur digitus &longs;ubiectus <expan abbr="quãdo">quando</expan> vitrea <lb/>fi&longs;tula exinanita e&longs;t, quàm &longs;i <expan abbr="mercuriũ">mercurium</expan> <lb/><figure id="id.010.01.224.1.jpg" xlink:href="010/01/224/1.jpg"/><lb/>BC contineret, &longs;cilicèt &longs;i fi&longs;tula pen­<lb/>deret duas vncias, & aereus cylindrus SA <expan abbr="p&etilde;dat">pendat</expan> tres <pb pagenum="217" xlink:href="010/01/225.jpg"/><arrow.to.target n="marg289"/><lb/>libras exinanita fi&longs;tula æquè comprimeretur &longs;ubie­<lb/>ctus digitus à pondere totius cylindri aerei SA <expan abbr="triũ">trium</expan> <lb/>librarum vnà cum duabus vncijs vitri AC, cùmque <lb/>hoc &longs;it fal&longs;um; fi&longs;tula enim exinanita duas vncias &longs;o­<lb/>lummodò pendit, non ergo &longs;uprema <expan abbr="colũmna">columna</expan> aerea <lb/>SA fi&longs;tulam, & proindè digitum &longs;ubiectum compri­<lb/>mit. </s> </p> <p type="margin"> <s id="s.001120"><margin.target id="marg288"/><expan abbr="Cõtiã">Contram</expan> &longs;upe­<lb/>rius <expan abbr="expo&longs;itã">expo&longs;itam</expan> <lb/><expan abbr="doctrinã">doctrinam</expan> de­<lb/>nuo aduer­<lb/>&longs;arius in&longs;ur­<lb/>git,</s> </p> <p type="margin"> <s id="s.001121"><margin.target id="marg289"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001122"><emph type="center"/>PROP. CIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001123"><emph type="center"/><emph type="italics"/>Fi&longs;tula exinanita, licèt grauetur à cylindro aereo <expan abbr="incumb&etilde;-te">incumben­<lb/>te</expan> non minus, ac quando extante mercurio repletur, <lb/>debet tamen in primo ca&longs;u &longs;ubiectus digitus vi­<lb/>tri tantum pondus percipere, in &longs;ecundo ve­<lb/>rò præterea à pondere æquali mercurio <lb/>&longs;u&longs;pen&longs;o grauabitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001124">HVic difficultati <expan abbr="re&longs;põdetur">re&longs;pondetur</expan>, quòd, vt multotiès <lb/>in&longs;inuatum e&longs;t, nulla alia de cau&longs;a fluida cor­<lb/>pora circa tellurem &longs;phæricè <expan abbr="cõtornantur">contornantur</expan>, ni&longs;i prop­<lb/>tèr eorum æquilibrium, &longs;cilicet quia omnes eius par­<lb/>tes æquali ni&longs;u vim faciunt tendendo deorsùm, & <lb/>po&longs;tquam à &longs;oliditate terræ &longs;ubiectæ eius progre&longs;­<lb/>&longs;us deorsùm impeditur ni&longs;u reflexo veluti in &longs;iphone <lb/>vici&longs;&longs;im &longs;e mutuo <expan abbr="impellũt">impellunt</expan> quoque partes fluidi, vel <lb/>&longs;olidi eleuatæ &longs;ursùm, itaque in ca&longs;u no&longs;tro, concipi <lb/>debet nedùm columna aerea SAC, &longs;ed etiam alia ei <lb/>æqualis aerea columna SG, quæ infernè per EC re­<lb/>flectatur, & &longs;ursùm impellat digitum &longs;u&longs;tentantem <lb/>vitrum æquali ni&longs;u, ac ip&longs;a &longs;upernè comprimitur à <pb pagenum="218" xlink:href="010/01/226.jpg"/><arrow.to.target n="marg290"/><lb/>cylindro aereo SAC. digitus ergo <expan abbr="cõ-primitur">com<lb/>primitur</expan> à duabus æqualibus viribus <lb/>inter &longs;e contrarijs veluti forcipe, de­<lb/>orsùm quidem à pondere aereo SAC, <lb/><expan abbr="&longs;ursũ">&longs;ursum</expan> verò a vi pre&longs;&longs;ionis aeris SG re­<lb/>flexi per EC, <expan abbr="eod&etilde;">eodem</expan> ferè modo quo vri­<lb/>natores pondus incumbentis aquæ <expan abbr="nõ">non</expan> <lb/>percipiunt, quia nimirùm æquali vi <lb/>&longs;ursùm motu reflexo impelluntur ab a­<lb/>qua &longs;ubiecta, ac grauantur ab aqu&atail; <lb/>&longs;uprema <expan abbr="de&longs;cend&etilde;te">de&longs;cendente</expan>, vt &longs;uperius <expan abbr="o&longs;t&etilde;-sũ">o&longs;ten­<lb/>sum</expan> fuit; igitur in ca&longs;u noftro digitus &longs;u­<lb/>&longs;tinebit tantummodò grauitatem dua­<lb/>rum vnciarum fi&longs;tulæ vitreæ exinani­<lb/><figure id="id.010.01.226.1.jpg" xlink:href="010/01/226/1.jpg"/><lb/>tæ AC quia nimirùm hic e&longs;t exce&longs;&longs;us <lb/>ponderis totius columnæ aereæ, & vitreæ SAC &longs;upra <lb/>aeream <expan abbr="columnã">columnam</expan> ei &etail;qualem SGC: diuer&longs;i&longs;&longs;imus ergo <lb/>e&longs;t ca&longs;us fi&longs;tulæ vitreæ mercurio &longs;tagnante repletæ, <lb/>quia nimirùm vis compre&longs;&longs;iua <expan abbr="colũnæ">columnæ</expan> aereæ SG om­<lb/>ninò expletur ab&longs;umiturque eleuando <expan abbr="&longs;u&longs;tin&etilde;doque">&longs;u&longs;tinendoque</expan> <lb/>mercurium BC, & &longs;ic remaneat aerea columna SA <lb/>(prætèr vitrum) non &longs;u&longs;tentata à repul&longs;ione <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>aeris SG, & proindè &longs;u&longs;tineri debèt à digito &longs;ubiecto <lb/>eo mode, quo &longs;upra expo&longs;uimus. </s> </p> <p type="margin"> <s id="s.001125"><margin.target id="marg290"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001126">Quapropter conuincens non e&longs;t argumentum do­<lb/>cti&longs;&longs;imi viri, ideoque remanent illibatæ rationes &longs;u­<lb/>periùs adductæ quibus per&longs;uademur <expan abbr="mercuriũ">mercurium</expan> in fi­<lb/>&longs;tula &longs;u&longs;tineri à pre&longs;&longs;ione circumambientis aeris. </s> </p> <p type="main"> <s id="s.001127">Tran&longs;eamus iam ad examen tertiæ rationis ab eo-<pb pagenum="219" xlink:href="010/01/227.jpg"/><arrow.to.target n="marg291"/><lb/>dem viro clari&longs;&longs;imo adductæ, inquit <lb/>enim: <emph type="italics"/>Si &longs;egmentum IC mercurij ab ae­<lb/>ris exterioris cylindro &longs;u&longs;tinetur, igitur <expan abbr="cũ">cum</expan> <lb/>cylindrus exterior eamdem vim &longs;emper <lb/>habeat æqualem &longs;egmentum IC &longs;emper <lb/>&longs;ustinet. </s> <s id="s.001128">Sed hoc experimento repugnat, <lb/>nam &longs;i tantulum aeris antequàm demit­<lb/>tatur mercurius in fi&longs;tula relinquatur mer­<lb/>curius de&longs;cendet infra C; in C autem &longs;u&longs;ti­<lb/>neri deberet &longs;i à cylindro aeris exterioris <lb/>&longs;u&longs;tineretur vt patet &c.<emph.end type="italics"/><lb/><figure id="id.010.01.227.1.jpg" xlink:href="010/01/227/1.jpg"/><lb/><arrow.to.target n="marg292"/></s> </p> <p type="margin"> <s id="s.001129"><margin.target id="marg291"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001130"><margin.target id="marg292"/>Tertium ar­<lb/>gumentum <lb/>eiu&longs;dem au­<lb/>thoris.</s> </p> <p type="main"> <s id="s.001131">Non latuit huius argumenti authorem re&longs;pon&longs;io à <lb/>fautoribus contrariæ &longs;ententiæ allata, nimirùm <emph type="italics"/>illud <lb/>tantulum aeris infra fi&longs;tulam relicti po&longs;t de&longs;cen&longs;um mer­<lb/>curij liberiorem nanci&longs;ci campum, ac proindè cum ante com­<lb/>pre&longs;&longs;us e&longs;&longs;et explicare &longs;e&longs;e, ac dilatare, & premere &longs;uperfi­<lb/>ciem mercurij, vnde hic infra C de&longs;cendit.<emph.end type="italics"/></s> <s id="s.001132"> Sed in&longs;tat di­<lb/>cendo; <emph type="italics"/>tantam aeris compres&longs;ionem iam &longs;upra &longs;atis effi­<lb/>cacitèr ab ip&longs;o refutatam fui&longs;&longs;e.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001133">Sed an reuerà iure refutata fuerit, po&longs;teriùs <expan abbr="o&longs;t&etilde;-demus">o&longs;ten­<lb/>demus</expan>, modò tantam aeris dilatationem argumento <lb/>ab eadem experientia deducto retinebimus; <expan abbr="attam&etilde;">attamen</expan> <lb/>interea erit operæpretium exponere quomodò, & <lb/>quando aer intra mercurium in fi&longs;tula relictus expli­<lb/>cetur dilateturque. </s> </p> <figure id="id.010.01.227.2.jpg" xlink:href="010/01/227/2.jpg"/> <pb pagenum="220" xlink:href="010/01/228.jpg"/> <p type="main"> <s id="s.001134"><arrow.to.target n="marg293"/></s> </p> <p type="margin"> <s id="s.001135"><margin.target id="marg293"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001136"><emph type="center"/>PROP. CV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001137"><emph type="center"/><emph type="italics"/>Exponitur quare, & quando aer relictus in fi&longs;tula Torri­<lb/>celliana altitudinem mercurij con&longs;uetam deprimere <lb/>debeat; & &longs;imul traditur modus men&longs;urandi <lb/>maximam aeris dilatationem.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001138">EX Roberuallij pulcherrima ob&longs;eruatione illius <lb/>ve&longs;icæ cyprinæ, quæ in vacuo fi&longs;tulæ dilatatur <lb/>ego conieci reperiri facilè po&longs;&longs;e in eodem Torricel­<lb/>liano in&longs;trumento maximam amplitudinem, ad <expan abbr="quã">quam</expan> <lb/>aer non compre&longs;&longs;us à vi externa, & in &longs;ua libertat&etail; <lb/>relictus dilatari queat, quæ dilatatio certum, ac de­<lb/>terminatum &longs;patium in vacuo Torricelliano occupa­<lb/>ret, quod nimirum &longs;ufficienter exciperet maximam <lb/>eiu&longs;dem aeris expan&longs;ionem. </s> <s id="s.001139">Hinc po&longs;tea <expan abbr="deducebã">deducebam</expan> <lb/>molem aeris, quæ præcisè &longs;patium vacuum in Tor­<lb/>ricelliano in&longs;trumento occuparet (quam molem me­<lb/>diocrem appellabimus) non po&longs;&longs;e deorsùm impelle­<lb/>re, & magis <expan abbr="cõprimere">comprimere</expan> &longs;uperficiem &longs;upremam mer­<lb/>curij &longs;tagnantis, ac proindè omnes moles aeris mi­<lb/>nores illa, & ideò minus &longs;patium po&longs;t totalem eo­<lb/>rum dilatationem exigentes non po&longs;&longs;e prædictam <lb/>mercurij &longs;upremam &longs;uperficiem deprimere, <expan abbr="cũ">cum</expan> è con­<lb/>trà moles omnes acris excedentes &longs;upradictam me­<lb/>diocrem molem, & ideò exigentes amplius &longs;pa­<lb/>tium deprimere nece&longs;&longs;ariò <expan abbr="&longs;upremã">&longs;upremam</expan> mercurij &longs;uper­<lb/>ficiem in fi&longs;tula infra con&longs;uetam altitudinem vnius <lb/>cubiti, & quadrantis. <pb pagenum="221" xlink:href="010/01/229.jpg"/><arrow.to.target n="marg294"/></s> </p> <p type="margin"> <s id="s.001140"><margin.target id="marg294"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001141">Vtque hæc experientia commodè exequi po&longs;&longs;et <lb/>efformaui fi&longs;tulas vitreas &longs;extam, & &longs;eptimam deli­<lb/>neatas folio 43. libri experimentorum no&longs;træ Aca­<lb/>demiæ Experimentalis Mediceæ, &longs;ed po&longs;tea facilio­<lb/>ri apparatu idip&longs;um con&longs;equi po&longs;&longs;e animaduerti me­<lb/>diante hoc in&longs;trumento, e&longs;tque eius artificium hu­<lb/>iu&longs;modi: ampullæ vitreæ AB cuius diameter proximè <lb/>quatuor digitos adæquet <expan abbr="cõtinuetur">continuetur</expan> prælonga fi&longs;tu­<lb/>la BC maiore duorum cubitorum, quæ inflexa &longs;it i&ntail; <lb/>eius infimo loco CEF, atque in &longs;upremo loco eius A <lb/>continuetur quoque &longs;tricta alia fi&longs;tula AD cuius ex­<lb/>tremum &longs;upremum orificium apertum D claudi po&longs;­<lb/>&longs;it po&longs;t mercurij infu&longs;ionem &longs;uilla ve&longs;ica; po&longs;tea ter­<lb/>minus extremus alterius fi&longs;tulæ FG vniatur cum al­<lb/>tero extremo fi&longs;tulæ incuruatæ appo&longs;itis colligati&longs;­<lb/>que portionibus inte&longs;tini agnini, quæ ne rumpantur <lb/>diffringantur que à nimio mercurij pondere pariter <lb/>operiantur fi&longs;tula, vel digitali coriaceo, atque arctè <lb/>alligatis inte&longs;tinis, & corio vtri&longs;que extremitatibus <lb/>fi&longs;tularum, poterit facilè fi&longs;tula FG inflecti &longs;ursùm, <lb/>& deorsùm po&longs;t mercurij infu&longs;ionem, eriganturqu&etail; <lb/>perpendiculariter ad horizontem ambæ fi&longs;tulæ DB <lb/>C, & GF. </s> <s id="s.001142">His præparatis per orificium D infundatur <lb/>hydrargyrum quou&longs;que duæ fi&longs;tulæ BC, FG, & am­<lb/>pulla AB, repleantur, relinquaturque &longs;patium &longs;upre­<lb/>mæ fi&longs;tulæ ID aere plenum, arctè po&longs;teà claudatur <lb/>&longs;upremum orificium D &longs;uilla ve&longs;ica; tandèm flecta­<lb/>tur deorsùm fi&longs;tula collateralis FG, ab eius &longs;upremo <lb/>ore G profluens mercurius excipiatur va&longs;e MN, </s> </p> <pb pagenum="222" xlink:href="010/01/230.jpg"/> <p type="main"> <s id="s.001143"><arrow.to.target n="marg295"/><lb/>quou&longs;que infima mercurij <lb/>libella &longs;it LO, & &longs;uprema <lb/>&longs;uperficies eiu&longs;dem mer­<lb/>curij &longs;tagnantis &longs;it H reli­<lb/>cto nempè &longs;patio vacuo <lb/>DABH, quia verò cylin­<lb/>drus aereus DI dilatatur, <lb/><expan abbr="explicaturq;">explicaturque</expan> pro eius ge­<lb/>nio in &longs;patio vacuo <expan abbr="ibid&etilde;">ibidem</expan> <lb/>relicto, fit vt po&longs;&longs;it <expan abbr="ali-quãdo">ali­<lb/>quando</expan> po&longs;t eius dilatatio <lb/>nem integrè, & totalitèr <lb/>occupare <expan abbr="&longs;patiũ">&longs;patium</expan> DABH, <lb/>& tunc cum <expan abbr="nõ">non</expan> po&longs;&longs;it am­<lb/>pliùs explicari &longs;ua virtute <lb/><figure id="id.010.01.230.1.jpg" xlink:href="010/01/230/1.jpg"/><lb/>elatere non impellet deorsùm &longs;uperficiem hydrar­<lb/>gyri H, & ideò &longs;umma altitudo mercurij HO erit <lb/>inalterata, &longs;cilicèt omnium maxima earum, quæ fie­<lb/>ri po&longs;&longs;unt vnius cubiti & quadrantis proximè, & tunc <lb/>experientia con&longs;tat aerem DI maximè dilatatum in­<lb/>tra &longs;patium DABH occupare locum 180. maiore&mtail; <lb/>quam prius. </s> <s id="s.001144">&longs;uppo&longs;ita hac cognitione ab experientia <lb/>deducta denuò operatio repetatur, & con&longs;tat quod <lb/>omnes moles aeris non excedentes &longs;patium DI non <lb/>depriment mediocrem mercurij eleuationem OH; & <lb/>è contrà omnes aeris moles excedentes DI <expan abbr="cõprim&etilde;t">compriment</expan> <lb/>mercurium efficientque altitudinem OK minore&mtail; <lb/>men&longs;ura con&longs;ueta vnius cubiti, & quadrantis proxi­<lb/>mè, & hoc profectò non fui&longs;&longs;e à docti&longs;&longs;imo viro ani-<pb pagenum="223" xlink:href="010/01/231.jpg"/><arrow.to.target n="marg296"/><lb/>maduer&longs;um facilè con&longs;tat, non enim dixi&longs;&longs;et: <emph type="italics"/>&longs;i tantu­<lb/>lum aeris antequam demittatur mercurius in fistula, relin­<lb/>quatur mercurius de&longs;cendet infra H. vbi &longs;u&longs;tineri debuerat <lb/>&longs;i ab aeris cylindro &longs;u&longs;tinebatur.<emph.end type="italics"/> reuerà enim quælibet <lb/>portiones aeris minores &longs;patio ID &longs;ummam altitudi­<lb/>nem mercurij in fi&longs;tula non deprimunt, quia nimirùm <lb/>aereus cylindrus eiu&longs;dem roboris æquali vi compri­<lb/>mit mercurium &longs;ubiectum. </s> <s id="s.001145">At quando aeris moles <lb/>maior ID ibidem includitur, tunc virtute eius elate­<lb/>ria, vt po&longs;tea dicemus, vim facit contra impul&longs;u&mtail; <lb/>aeris externi, nempè cylindrus mercurij HO æquili­<lb/>bratus ab aere externo impellitur &longs;ursùm ab O ver­<lb/>sùs H, ab aere verò inclu&longs;o intra ampullam AB, dum <lb/>conatur &longs;e dilatare repellitur deorsùm ab H versùs <lb/>O. <!-- KEEP S--></s> <s id="s.001146">Vis ergo aeris comprimentis mercurium &longs;tagnan­<lb/>tem L agit contra duas re&longs;i&longs;tentias, &longs;cilicèt contra <expan abbr="põ-dus">pon­<lb/>dus</expan> mercurij HO, & contra vim exiguam aeris in­<lb/>clu&longs;i &longs;e dilatare conantis; igitur in hoc ca&longs;u minor erit <lb/>altitudo mercurij OK quam HO, licet producatur ab <lb/>eadem aeris virtute premente; Nil igitur ex hac ter­<lb/>tia aduer&longs;arij ratione deducitur contra aeris pre&longs;&longs;io­<lb/>nem, & æquilibrium cum mercurio inclu&longs;o intra fi­<lb/>&longs;tulam. </s> </p> <p type="margin"> <s id="s.001147"><margin.target id="marg295"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001148"><margin.target id="marg296"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001149">Quarta ratio eadem ferè e&longs;t cum prima, ad eamque <lb/><arrow.to.target n="marg297"/><lb/>reducitur. </s> <s id="s.001150">quinta verò pendet ex eo quod &longs;patiu&mtail; <lb/>&longs;upremum fi&longs;tulæ po&longs;t mercurij lap&longs;um non vacuum, <lb/>&longs;ed repletum e&longs;&longs;e ait ex materia quadam tenui&longs;&longs;ima, <lb/>&longs;ed valdè ten&longs;a de qua re &longs;uo loco di&longs;putabimus; in­<lb/>terim incidenter noto eius verba dum ait, <emph type="italics"/>tantam ae-<emph.end type="italics"/><pb pagenum="224" xlink:href="010/01/232.jpg"/><arrow.to.target n="marg298"/><lb/><emph type="italics"/>ris compres&longs;ionem &longs;en&longs;ui repugnare: cum inclinata fi&longs;tula <lb/>derume&longs;cat ve&longs;ica, antequam &longs;uperficies mercurij ad illam <lb/>perueniat.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001151"><margin.target id="marg297"/>Quarta, & <lb/>quinta ratio <lb/>eiu&longs;dem au­<lb/>thoris.</s> </p> <p type="margin"> <s id="s.001152"><margin.target id="marg298"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001153"><emph type="center"/>PROP. CVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001154"><emph type="center"/><emph type="italics"/>Ve&longs;ica cyprina inflata Roberuallij in &longs;ummitate fi&longs;tulæ Tor­<lb/>ricellianæ <expan abbr="nõ">non</expan> &longs;emper detume&longs;cit po&longs;t huius inclinatio­<lb/>nem, & ratio huius effectus redditur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001155">HOc profectò non &longs;emper accidit, præcipuè <expan abbr="quã-do">quan­<lb/>do</expan> fi&longs;tula capacem ampullam in &longs;ummitate ha­<lb/>bet, in ea enim commodè aliqua aeris portio, quæ <expan abbr="s&etilde;-per">sem­<lb/>per</expan> in fi&longs;tulæ &longs;uprema parte remanet, aut ibidem col­<lb/>ligitur reduciturque po&longs;tquàm &longs;egregatur à mercu­<lb/>rij &longs;ub&longs;tantia, per quam a&longs;cendunt innumera granula <lb/>aerea partim vi&longs;ibilia, partim incon&longs;picua ob minu­<lb/>tiem, & hæc quidem ad &longs;upremam mercurij &longs;uperfi­<lb/>ciem a&longs;cendunt, & prout magis ad &longs;patium vacuum <lb/>appropinquantur, eo magis cre&longs;cunt bullæ aereæ, in­<lb/>fianturque, & tandem expanduntur, di&longs;&longs;iliunt <expan abbr="rumpũ-turque">rumpun­<lb/>turque</expan> in prædicto &longs;patio vacuo, & hoc magis <expan abbr="euid&etilde;-ter">euiden­<lb/>ter</expan> ob&longs;eruatur &longs;i &longs;uprema hydrargyri cylindri &longs;uper­<lb/>ficies exigua aquæ portione cooperiatur, tunc gra­<lb/>nula aerea à mercurio a&longs;cendentia videri po&longs;&longs;unt in <lb/>tran&longs;itu per aquam tran&longs;picuam, quæ &longs;peciem repre­<lb/>&longs;entant ebullitionis cuiu&longs;dam compo&longs;itæ ex prædi­<lb/>ctis particulis aereis inflatis, & veloci&longs;&longs;imè <expan abbr="&longs;ursũ">&longs;ursum</expan> ex­<lb/>currentibus. </s> <s id="s.001156">His po&longs;itis ve&longs;icula illa cyprina Rober­<lb/>uallij inclinata fi&longs;tula &longs;olet detume&longs;cere antequa&mtail; <pb pagenum="225" xlink:href="010/01/233.jpg"/><arrow.to.target n="marg299"/><lb/>mercurius eam attingat, propterea quòd partes illæ <lb/>aereæ, quæ priùs &longs;ummè dilatatæ erant in amplo &longs;pa­<lb/>tio inani in &longs;ummitate fi&longs;tulæ, po&longs;tea re&longs;tricto &longs;patio <lb/>ob mercurij a&longs;cen&longs;um denuò conden&longs;antur, & proin­<lb/>dè mirum non e&longs;t ve&longs;icam cyprinam ab aere eam am­<lb/>biente den&longs;iori, quàm &longs;it aer intra ve&longs;icam <expan abbr="cõtentus">contentus</expan>, <lb/><expan abbr="compre&longs;&longs;ion&etilde;">compre&longs;&longs;ionem</expan> pati debere, & proinde detume&longs;cere. </s> </p> <p type="margin"> <s id="s.001157"><margin.target id="marg299"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001158">Quando verò &longs;ubdit, quod aer intra fi&longs;tulam im­<lb/>mi&longs;&longs;us dum mercurius eleuatus e&longs;t ad prædictam al­<lb/>titudinem cubiti vnius, & quadrantis proximè, <expan abbr="&longs;ursũ">&longs;ursum</expan> <lb/>fertur tanto impetu, vt &longs;upremum fi&longs;tulæ fundum, & <lb/>ba&longs;is diffringatur; di&longs;&longs;iliatque, & quia ab exce&longs;&longs;u exi­<lb/>gui ponderis tantus impetus creari non pote&longs;t, hinc <lb/>deducit non po&longs;&longs;e à cylindro aeris ambiente, & ab <lb/>eius <expan abbr="põdere">pondere</expan> vllo pacto impelli neque mercurius, ne­<lb/>que aer in prædicta fi&longs;tula. </s> </p> <p type="main"> <s id="s.001159"><emph type="center"/>PROP. CVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001160"><emph type="center"/><emph type="italics"/>Aer in fi&longs;tula Torricelliana adueniens nedùm pondere, &longs;ed <lb/>vi ela&longs;tica, & impetu in motu acqui&longs;ito diffringere <lb/>fundum &longs;upremum fistulæ pote&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001161">HVic difficultati occurro <expan abbr="cõ&longs;iderando">con&longs;iderando</expan> quòd mer­<lb/>curius in fi&longs;tula &longs;ursùm impellitur ab aere ex­<lb/>terno non vnica, &longs;ed triplici vi, ponderis nimirum, <lb/>virtutis ela&longs;ticæ ad modum machinæ, & impetus in <lb/>motu acqui&longs;iti: &longs;ed præcipua, & in&longs;ignis actio in ca­<lb/>&longs;u no&longs;tro impetui tribui debet. </s> <s id="s.001162">Quia po&longs;tquam è <lb/>fi&longs;tula cum mercurio extante in aere pendula effluit <pb pagenum="226" xlink:href="010/01/234.jpg"/><arrow.to.target n="marg300"/><lb/>gutta aliqua mercurij &longs;ubito ce&longs;&longs;at æquilibrium, & <lb/>ideò maius pondus collateralis columnæ aereæ po­<lb/>te&longs;t &longs;ursùm intra fi&longs;tulam impellere molem minus <expan abbr="põ-derãtis">pon­<lb/>derantis</expan> mercurij inclu&longs;i; & licèt ab initio motus mer­<lb/>curij &longs;ursùm &longs;it tardus, & debilis, tamen in progre&longs;­<lb/>&longs;u, & continuatione prædicti motus dum repetitis <lb/>ictibus mercurius ab aeris pondere, & vi eius ela&longs;ti­<lb/>ca continenter impellitur, nouos gradus impetus, & <lb/>velocitatis creat, qui impetus &longs;unt integri, & <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>energiæ, non enim à vacuo intra fi&longs;tulam inclu&longs;o de­<lb/>bilitari po&longs;&longs;unt, veluti debilitantur impetus <expan abbr="corporũ">corporum</expan> <lb/><arrow.to.target n="marg301"/><lb/>per aerem excurrentium; prædicti verò gradus velo­<lb/>citatum &longs;imul coaceruati, tandem vim illam <expan abbr="ingent&etilde;">ingentem</expan> <lb/>componunt, quæ diffringere fundum vitreæ fi&longs;tulæ <lb/>pote&longs;t; adde quod corpora graui&longs;&longs;ima; vt e&longs;t hydrar­<lb/>gyrum validius fu&longs;cipiunt retinentque vim impetus <lb/>præconcepti, & hinc &longs;equitur percu&longs;&longs;io eius validi&longs;­<lb/>&longs;ima in vitri fundum. </s> <s id="s.001163">Supradictum ratiocinium ab ip­<lb/>&longs;a experientia <expan abbr="cõ&longs;irmari">confirmari</expan> videtur; &longs;i enim fi&longs;tula præ­<lb/>longa &longs;ubtili, & gracili fundo clau&longs;a, & mercurio ple­<lb/>na inuer&longs;o ore infra mercurium in &longs;cutella <expan abbr="&longs;tagnant&etilde;">&longs;tagnantem</expan> <lb/>demer&longs;a, & inclinato &longs;itu detineatur vt mercurius <lb/>minus vno digito à &longs;upremo fundo di&longs;tet, tunc &longs;u­<lb/>&longs;pen&longs;a fi&longs;tula aer adueniens fundum eius non diffrin­<lb/>git, at perpendiculari &longs;itu erecta fi&longs;tula aer <expan abbr="&longs;ucced&etilde;s">&longs;uccedens</expan> <lb/>ingenti impetu <expan abbr="di&longs;tãtem">di&longs;tantem</expan> à fundo mercurium propel­<lb/>lit vt eum diffringat, quia nimirum in prolixiori mo­<lb/>tu plures gradus impetus creari, & &longs;imul coaceruari <lb/>po&longs;&longs;unt. <pb pagenum="227" xlink:href="010/01/235.jpg"/><arrow.to.target n="marg302"/></s> </p> <p type="margin"> <s id="s.001164"><margin.target id="marg300"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="margin"> <s id="s.001165"><margin.target id="marg301"/>De vi per­<lb/><gap/>cap. 22.</s> </p> <p type="margin"> <s id="s.001166"><margin.target id="marg302"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001167">Po&longs;tea &longs;ubdit: <emph type="italics"/>Cylindrus aeris exterioris à quo (vt non­<lb/>nulli volunt) mercurij extantis &longs;egmentum &longs;u&longs;tinetur, ne­<lb/>que plus, neque minus pote&longs;t &longs;ustinere, igitur &longs;i ferrum can­<lb/>dens admoueatur &longs;egmento vacuo fi&longs;tulæ, nulla e&longs;t ratio cur <lb/>&longs;uperficies &longs;uprema mercurij &longs;ub&longs;idat. </s> <s id="s.001168">Sub&longs;idit tamen. </s> <s id="s.001169">Si<emph.end type="italics"/><!-- REMOVE S--><arrow.to.target n="marg303"/><lb/><emph type="italics"/>verò nix, vel trita glacies admoueatur, mercurius attolli­<lb/>tur.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001170"><margin.target id="marg303"/>Sextum ar­<lb/>gumentum.</s> </p> <p type="main"> <s id="s.001171"><emph type="center"/>PROP. CVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001172"><emph type="center"/><emph type="italics"/>Igneæ exhalationes corporeæ vehementis&longs;ima agitatione <expan abbr="tũ">tum</expan> <lb/>per &longs;e, cum variè impellendo, & <expan abbr="torqu&etilde;do">torquendo</expan> particulas <lb/>aeris in &longs;ummitate fistulæ Torricellianæ reli­<lb/>ctas, facilè po&longs;&longs;unt &longs;ub&longs;identem mercu­<lb/>rium æquilibratum deprimere.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001173">RE&longs;pondeo, quòd igneæ particulæ nedùm &longs;e ip­<lb/>&longs;as vehementèr agitant, commouentque, &longs;ed <lb/>præterea aereas quoque particulas in vitri &longs;ummita­<lb/>te inclu&longs;as, vt dictum e&longs;t, vehementi&longs;&longs;imè impellunt; <lb/>porrò quia quodlibet corpus æquilibratum pote&longs;t à <lb/>quacumque exigua vi agitari, (vt demon&longs;trauimus <lb/>in no&longs;tro opere de vi percu&longs;&longs;ionis) &longs;itque prædictus <lb/>mercurius in fi&longs;tula æquilibratus cum <expan abbr="æquiponderã-te">æquiponderan­<lb/>te</expan> cylindro aereo externo, igitur nece&longs;&longs;ariò ab inte­<lb/>&longs;tina illa agitatione ignearum, & aerearum particu­<lb/>larum &longs;uperficies mercurij percu&longs;&longs;a propelli pote&longs;t, <lb/>& ideò deprimi infra con&longs;uetam eius altitudinem de­<lb/>bet, è contrà adhibita niue, vel trita glacie, &longs;patium <lb/>illud dum igne priuatur, & deficit quoque agitatio, <lb/>& reuolutio nedum particularum ignis, &longs;ed etia&mtail; <pb pagenum="228" xlink:href="010/01/236.jpg"/><arrow.to.target n="marg304"/><lb/>aeris contenti, propterea præualere pote&longs;t exce&longs;&longs;us <lb/>grauitatis aeris ambientis &longs;upra mercurium in fi&longs;tu­<lb/>la eleuatum. </s> </p> <p type="margin"> <s id="s.001174"><margin.target id="marg304"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001175">Affert po&longs;tea &longs;eptimam rationem: <emph type="italics"/>Si po&longs;tquam mer­<lb/>curius &longs;ub&longs;idit vas infimum claudatur vt nulla rima &longs;u-<emph.end type="italics"/><lb/><arrow.to.target n="marg305"/><lb/><emph type="italics"/>per&longs;it, per quam aer &longs;ubeat, non tamen propterea mercurius <lb/>&longs;ub&longs;idit, &longs;ed tunc non &longs;u&longs;tinetur à cylindro aeris, quia &longs;cili­<lb/>cèt non est applicatus.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001176"><margin.target id="marg305"/>Septima in­<lb/>&longs;tantia.</s> </p> <p type="main"> <s id="s.001177">Huic argumento primus omnium re&longs;pondit Cla­<lb/>ri&longs;&longs;imus Torricellius in epi&longs;tola ad Clari&longs;&longs;imum Mi­<lb/>chaelem Angelum Riccium mi&longs;&longs;a, quam humani&longs;&longs;i­<lb/>mè mihi communicauit anno 1658. eamque Floren­<lb/>tiæ po&longs;teà Sereni&longs;&longs;imo Principi Leopoldo tradidi, & <lb/>inter amicos euulgaui. </s> </p> <p type="main"> <s id="s.001178"><emph type="center"/>PROP. CIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001179"><emph type="center"/><emph type="italics"/>Licèt operculo impediatur aeris pres&longs;io &longs;upra <expan abbr="mercuriũ">mercurium</expan> &longs;ta­<lb/>gnantem in &longs;cutella, tamen quia aer relictus ibidem <lb/>remanet eodem modo pre&longs;&longs;us, & con&longs;tipatus <lb/>ac prius pote&longs;t mercurium in fistula ad <lb/>eamdem altitudinem re­<lb/>tinere.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001180">IS habet, quod <expan abbr="quãdo">quando</expan> intercipitur prohibeturque <lb/>commercium inter ambientem aerem, & eum, qui <lb/>immediatè &longs;uperficiem &longs;tagnantis mercurij tangit <lb/>po&longs;ito nimirùm operculo, vt v. <!-- REMOVE S-->g. <!-- REMOVE S-->quando in fi&longs;tul&atail; <lb/>inflexa ABG mercurius eleuatur v&longs;que ad <expan abbr="altitudin&etilde;">altitudinem</expan> <lb/>BF vnius cubiti, & quadrantis relicto &longs;patio inani <pb pagenum="229" xlink:href="010/01/237.jpg"/><arrow.to.target n="marg306"/><lb/>AF, & po&longs;ito quod prædicta mercurij &longs;ublimatio de­<lb/>pendeat à compre&longs;&longs;ione, quam cylindrus aereus SD <lb/>v&longs;que ad &longs;upremam aeris &longs;uperficiem exten&longs;us &longs;u&atail; <lb/>grauitate efficiat &longs;upra <expan abbr="&longs;tagnãtem">&longs;tagnantem</expan> mer­<lb/><figure id="id.010.01.237.1.jpg" xlink:href="010/01/237/1.jpg"/><lb/>curium D, &longs;equitur, quod &longs;i occludatur <lb/>orificium G eiu&longs;dem fi&longs;tulæ remanebit <lb/>portio aerea intercepta GD <expan abbr="eod&etilde;">eodem</expan> mo­<lb/>do <expan abbr="cõpre&longs;&longs;a">compre&longs;&longs;a</expan> re&longs;trictaque vt priùs, quia <lb/>nimirùm digitus, vel operculum reti­<lb/>net con&longs;eruatque aerem in eadem po­<lb/>&longs;itione, & con&longs;trictione, quam prius ab <lb/>incumbente aere patiebatur. </s> <s id="s.001181">Eode&mtail; <lb/>ferè modo, ac &longs;i loco aeris &longs;uperpone­<lb/>rentur mercurio plures cylindri lapidei <lb/>vnus &longs;uper alterum incumbens, tunc <lb/>profectò infimus cylindrus comprime­<lb/>ret &longs;uperficiem &longs;ubiecti hydrargyri D <lb/>non tantùm energia ponderis proprij, <lb/>&longs;ed vi conflata ex grauitate omnium incumbentium <lb/>cylindrorum modò ablatis &longs;emoti&longs;que &longs;upremis om­<lb/>nibus columnis &longs;i in fimus cylindrulus, tantummodò <lb/>tabula, vecte, aut quo cumque alio retinaculo <expan abbr="ead&etilde;">eadem</expan> <lb/>vi fixè in eodem &longs;itu retineretur, patet quòd æquali <lb/>energia comprimeret &longs;ubiectam mercurij <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> <lb/>D ac priùs premebatur à prælonga illa &longs;erie colum­<lb/>narum incumbentium; Et hic dicendum e&longs;&longs;et, quòd <lb/>cau&longs;a immediata impellens mercurium non e&longs;t longa <lb/>illa &longs;eries columnarum SD, &longs;ed e&longs;t infimus cylindru­<lb/>lus GD qui tanta vi comprimit &longs;ubiectum <expan abbr="mercuriũ">mercurium</expan> <pb pagenum="230" xlink:href="010/01/238.jpg"/><arrow.to.target n="marg307"/><lb/>quanta e&longs;t grauitas omnium columnarum SD; itaque <lb/>grauitas omnium columnarum appellari pote&longs;t cau­<lb/>&longs;a productiua illius compre&longs;&longs;ionis, quam facit infi­<lb/>mus cylindrulus GD mercurio immediatè <expan abbr="cõtiguus">contiguus</expan>, <lb/>quia verò huiu&longs;modi effectus remanet, quando clau­<lb/>ditur orificium G, remouenturque columnæ &longs;upre­<lb/>mæ, igitur æquali vi, & æquali men&longs;ura debet mer<lb/>curius BF &longs;ublimari. </s> <s id="s.001182">Id ip&longs;um dici debet de aere SD, <lb/>certum profectò e&longs;t dum orificium G e&longs;t apertum cy­<lb/>lindrum aereum GS v&longs;que ad aeris &longs;upremam &longs;uper­<lb/>ficiem exten&longs;um comprimere cylindrulum aereu&mtail; <lb/>GD tanta vi quanta exigit energia grauitatis aeris <lb/>SG, quando verò digito, vel operculo impeditur <expan abbr="cõ-tactus">con­<lb/>tactus</expan>, & compre&longs;&longs;io aeris &longs;upremi SG remanet cy­<lb/>lindrulus aereus GD eodem modo compre&longs;&longs;us re&longs;tri­<lb/>ctu&longs;que, ac prius igitur nece&longs;&longs;ario eodem modo &longs;ub­<lb/>iectum mercurium D premet proindeque ad <expan abbr="eamd&etilde;">eamdem</expan> <lb/>altitudinem BF eum &longs;ubleuabit. </s> </p> <p type="margin"> <s id="s.001183"><margin.target id="marg306"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001184"><margin.target id="marg307"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001185"><emph type="center"/>PROP. CX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001186"><emph type="center"/><emph type="italics"/>Idip&longs;um confirmatur in aquæ.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001187">VEritas huius a&longs;&longs;erti alio experimento confirma­<lb/>tur: Demergatur in aliquo puteo RV aqua ple­<lb/>no eadem fi&longs;tula ABG cum mercurio extante FB, vi­<lb/>demus quod aliquanti&longs;per mercurius infra libellam <lb/>D deprimitur à pondere <expan abbr="incũbentis">incumbentis</expan> aquæ ND, quæ <lb/>paritèr altiùs <expan abbr="mercuriũ">mercurium</expan> in fi&longs;tulam &longs;ubleuat per &longs;pa­<lb/>tium BH, vt nimirùm exce&longs;&longs;us FH &longs;upra eam eleua-<pb pagenum="231" xlink:href="010/01/239.jpg"/><arrow.to.target n="marg308"/><lb/>tionem, quæ in libero aere efficiebatur, &longs;it pars de­<lb/>cimaquarta altitudinis aquæ ND. in hoc rerum &longs;ta­<lb/>tu digito, vel quolibet alio operculo claudatur fi­<lb/>&longs;tulæ o&longs;tium G hic iam ce&longs;&longs;at om­<lb/><figure id="id.010.01.239.1.jpg" xlink:href="010/01/239/1.jpg"/><lb/>ninò actio, & compre&longs;&longs;io <expan abbr="põderis">ponderis</expan> <lb/>cylindri aquei NG, & tamen mer­<lb/>curius in eodem &longs;igno fi&longs;tulæ H <lb/>per&longs;euerat, igitur eodem modo <lb/>in aere occlu&longs;o o&longs;tio G per&longs;eue­<lb/>rare, & retineri debet mercurius <lb/>&longs;ubleuatus <expan abbr="v&longs;q;">v&longs;que</expan> ad F mediatè <expan abbr="qui-d&etilde;">qui­<lb/>dem</expan> à <expan abbr="põdere">pondere</expan> aeris qui prius <expan abbr="incũ-bebat">incum­<lb/>bebat</expan>, &longs;ed modo immediatè ab illa compre&longs;&longs;ione, & <lb/>re&longs;trictione, quam produxerat pondus incumbentis <lb/>aeris SG. vnde con&longs;tat quod mercurius in fi&longs;tula ele­<lb/>uari pote&longs;t à pondere aeris ambientis, nec adduct&atail; <lb/>difficultas hanc &longs;ententiam debilitat aut de&longs;truit. </s> </p> <p type="margin"> <s id="s.001188"><margin.target id="marg308"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001189">Subdit po&longs;tea pro confirmatione &longs;ui ratiocinij: <lb/><arrow.to.target n="marg309"/><lb/><emph type="italics"/>Iam verò facilè ostendo non &longs;ustineri, &longs;eu &longs;u&longs;pendi in BF eò <lb/>quod aer interceptus inter operculum, & &longs;uperficiem vlte­<lb/>riori compre&longs;sioni re&longs;istat, nempè &longs;i admoto dicto operculo, & <lb/>extante mercurio in BF aperiatur foramen in A mercurius <lb/>illicò infra F de&longs;cendit, idque notabili &longs;egmento, &c.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001190"><margin.target id="marg309"/>Hoc ratio­<lb/>cinium cona <lb/>tur refellere <lb/>aduer&longs;arius.</s> </p> <p type="main"> <s id="s.001191">Sibi ip&longs;i po&longs;tea opponit dicendo, quòd mercurius <lb/><expan abbr="deorsũ">deorsum</expan> impellitur duplici vi, propriæ &longs;cilicèt grauita­<lb/>tis mercurij BF, & <expan abbr="põderis">ponderis</expan> aeris per <expan abbr="&longs;upremũ">&longs;upremum</expan> <expan abbr="foram&etilde;">foramen</expan> <lb/><expan abbr="flu&etilde;tis">fluentis</expan>, quid mirum &longs;i præualeat, interceptumque ae­<lb/>rem vlteriùs comprimat, & mercurium infra F depri­<lb/>mat. </s> <s id="s.001192">po&longs;tea huic argumento re&longs;pondet: <emph type="italics"/>Dico non ma-<emph.end type="italics"/><pb pagenum="232" xlink:href="010/01/240.jpg"/><arrow.to.target n="marg310"/><lb/><emph type="italics"/>gis comprimi aera interceptum inter D, & dictum opercu­<lb/>lum à mercurio FB, & cylindro aeris grauitantis per fora­<lb/>men A, quam remoto operculo, & clau&longs;o foramine A ab eo­<lb/>dem mercurio BF & eodem cylindro aeris exterioris, nam <lb/>perindè e&longs;t &longs;iue tota vis pre&longs;sionis per lineam vnicam inci­<lb/>dat, vel applicetur; &longs;iue &longs;ubduplum per vnam, & &longs;ubdu­<lb/>plum per oppo&longs;itam.<emph.end type="italics"/></s> <s id="s.001193"> Vnde (paucis interceptis conclu­<lb/>dit) <emph type="italics"/>per&longs;picuè deduco non ideo admoto &longs;cilicet operculo in G <lb/>extare mercurium BF, & minimè &longs;ub&longs;idere, quia &longs;cilicet <lb/>dictus aer interceptus comprimi vltra non pote&longs;t, &longs;ed alia de <lb/>cau&longs;a, &c.<emph.end type="italics"/></s> </p> <p type="margin"> <s id="s.001194"><margin.target id="marg310"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001195">Sed pace tanti viri, aio, verum <expan abbr="nõ">non</expan> e&longs;&longs;e eius a&longs;&longs;ump­<lb/>tum, demon&longs;trabo enim quod clau&longs;o vitro in G, & a­<lb/>perto in A vis, qua comprimitur aer FB duplò vali­<lb/>dior e&longs;t ea, qua comprimitur clau&longs;o vitro in A, & a­<lb/>perto in G, pro cuius intelligentia præmittenda e&longs;t <lb/>&longs;equens. </s> </p> <p type="main"> <s id="s.001196"><emph type="center"/>PROP. CXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001197"><emph type="center"/><emph type="italics"/>Anulus, vel ve&longs;ica aere plena æquè ab vnica & &longs;ub­<lb/>dupla potentia comprimitur con&longs;tringiturque, <lb/>quàm à dupla, &longs;eu à duabus potentijs illi <lb/>æqualibus vtrinque anulum, vel <lb/>ve&longs;icam constringentibus.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001198">SIt ABC anulus calybeus, vel ve&longs;ica aere plena, & <lb/>primò <expan abbr="cõprimatur">comprimatur</expan> à duabus <expan abbr="pot&etilde;tijs">potentijs</expan> <expan abbr="cõtrarijs">contrarijs</expan>, & <lb/>inter&longs;e æqualibus P, & E, &longs;eu G. <!-- KEEP S--></s> <s id="s.001199">Et quia vnaquæque <lb/><expan abbr="pot&etilde;tiarum">potentiarum</expan> P tunc præcisè æquilibratur re&longs;i&longs;tentiæ, <pb pagenum="233" xlink:href="010/01/241.jpg"/><arrow.to.target n="marg311"/><lb/>&longs;eu energiæ compre&longs;&longs;ionis, quam patitur pars B, <expan abbr="quã-do">quan­<lb/>do</expan> ambo po&longs;t flexionem, & motum quie&longs;cunt; ergo <lb/>momentum <expan abbr="pot&etilde;tiæ">potentiæ</expan> P æqua­<lb/><figure id="id.010.01.241.1.jpg" xlink:href="010/01/241/1.jpg"/><lb/>le e&longs;t <expan abbr="mom&etilde;to">momento</expan> <expan abbr="re&longs;i&longs;t&etilde;tiæ">re&longs;i&longs;tentiæ</expan>, &longs;eu <lb/>energiæ, compre&longs;&longs;ionis, <expan abbr="quã">quam</expan> <lb/>patitur B, & fiunt ni&longs;us per <lb/>eamdem rectam perpendi­<lb/>cularem ad horizontem, igi­<lb/>tur ab&longs;oluta potentia P æ­<lb/>qualis | e&longs;t re&longs;i&longs;tentiæ ab&longs;olutæ, &longs;eu vi compre&longs;&longs;ionis, <lb/>quam patitur B. </s> <s id="s.001200">Pari ratione ab&longs;oluta potentia E, vel <lb/>G æquatur re&longs;i&longs;tentiæ, &longs;eu vi compre&longs;&longs;ionis partis op­<lb/>po&longs;itæ C. vnde deducitur duas potentias P & E, &longs;eu <lb/>G &longs;imul &longs;umptas æquales e&longs;&longs;e re&longs;i&longs;tentiæ integræ, &longs;eu <lb/>vi totali compre&longs;&longs;ionis, quam patitur anulus, vel ve­<lb/>&longs;ica ABC. </s> </p> <p type="margin"> <s id="s.001201"><margin.target id="marg311"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001202">Po&longs;tea &longs;ub&longs;tituatur pauimentum durum RS loco <lb/>potentiæ flectentis E, vel G, & &longs;olummodo &longs;upernè <lb/>anulus, vel ve&longs;ica aerea comprimatur à potentia P <lb/>&longs;cilicet à &longs;emi&longs;&longs;e potentiarum P, & E. <!-- KEEP S--></s> <s id="s.001203">Dico anulu&mtail;, <lb/>vel ve&longs;icam aeream æquè con&longs;tringi, ac priùs à dua­<lb/>bus potentijs contrarijs contundebatur. </s> <s id="s.001204">Quia paui­<lb/>mentum &longs;tabile RS perinde reagit impediendo mo­<lb/>tum, & de&longs;cen&longs;um ponderis P, ip&longs;umque in eodem &longs;i­<lb/>tu quiete &longs;tabili permanere cogit, ac operatur manus <lb/>&longs;ubiecta E, vel pondus G mediante libra FE, ergo <lb/>&longs;tabilitatis &longs;oli momentum æquatur momento, & po­<lb/>tentiæ ab&longs;olutæ ip&longs;ius E, &longs;eu P. quare anulus, &longs;eu ae­<lb/>rea ve&longs;ica BC comprimitur non à &longs;ingulari, & &longs;ubdu-<pb pagenum="234" xlink:href="010/01/242.jpg"/><arrow.to.target n="marg312"/><lb/>pla potentia P, &longs;ed a duplici <lb/><figure id="id.010.01.242.1.jpg" xlink:href="010/01/242/1.jpg"/><lb/>potentia, tanquam à forcipe, <lb/>vel prælo, nempè à P, & ab <lb/>huic æquali re&longs;i&longs;tentia paui­<lb/>menti RS. <!-- KEEP S--></s> <s id="s.001205">Igitur æquè com­<lb/>primetur anulus, vel ve&longs;ica <lb/>aerea &longs;olo innixa à &longs;ingulari <lb/>potentia P, ac &longs;i à duabus contrarijs potentijs P, & <lb/>E, vel G con&longs;tringeretur. </s> </p> <p type="margin"> <s id="s.001206"><margin.target id="marg312"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001207"><emph type="center"/><emph type="italics"/>COROLLARIVM.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001208">HInc patet, quòd &longs;i duæ potentiæ æquales &longs;imul <lb/>coniunctæ comprimant eumdem &longs;upremu&mtail; <lb/>anuli terminum pauimento innixi, tunc momentu&mtail; <lb/>fiue energia, qua anulus contunditur &longs;tringiturqu&etail; <lb/>duplex e&longs;t eius, qua ab ij&longs;dem potentijs oppo&longs;itos <lb/>terminos &longs;tringentibus comprimitur. </s> </p> <p type="main"> <s id="s.001209">Quia quotie&longs;cum que duæ potentiæ inter &longs;e æqua­<lb/>les P & G premunt &longs;upremum terminum B anuli BC, <lb/>tunc &longs;olum &longs;tabile RS in E, cui innititur idem præ&longs;tat, <lb/>& tanta energia operatur, ac &longs;i in E ade&longs;&longs;et potenti&atail; <lb/>æqualis ambabus contrarijs potentijs G & P: quare <lb/>vis, qua &longs;tringitur anulus æqualis e&longs;t duplo potentia­<lb/>rum G, & P. è contrà quando anulus &longs;tringitur ab ij&longs;­<lb/>dem potentijs G, & P &longs;ubdiui&longs;is, &longs;cilicèt à potenti&atail; <lb/>P in &longs;itu B, atque à potentia G in oppo&longs;ito eius ter­<lb/>mino C vt in præcedenti figura videre e&longs;t, tunc vis, <lb/>qua &longs;tringitur anulus, æqualis e&longs;t præcisè duabus po­<lb/>tentijs oppo&longs;itis G, & P, igitur quando anulus &longs;olo <pb pagenum="235" xlink:href="010/01/243.jpg"/><arrow.to.target n="marg313"/><lb/>innixus &longs;tringitur ab ij&longs;dem potentijs G, & P in B du­<lb/>plici energia con&longs;tringitur, contunditurque quam &longs;i <lb/>ab ij&longs;dem duabus potentijs G, & P &longs;ubdiui&longs;is <expan abbr="cõ&longs;trin-geretur">con&longs;trin­<lb/>geretur</expan>. </s> </p> <p type="margin"> <s id="s.001210"><margin.target id="marg313"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="main"> <s id="s.001211"><emph type="center"/>PROP. CXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001212"><emph type="center"/><emph type="italics"/>In Torricelliana fi&longs;tula mercurio extante, clau&longs;o ori&longs;icio <lb/>&longs;cutellæ, & aperta &longs;ummitate fi&longs;tulæ, aer in &longs;cu­<lb/>tella interceptus inter mercurium, & <lb/>operculum à vi duplò validiori <lb/>comprimitur, quàm illo <lb/>aperto, & hoc clau&longs;o.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001213">IN fi&longs;tula Torricelliana ACG aper­<lb/>ta in G, & clau&longs;a in A, facto vacuo, <lb/><figure id="id.010.01.243.1.jpg" xlink:href="010/01/243/1.jpg"/><lb/>more &longs;olito, remanente mercurio BF <lb/>eleuato <expan abbr="&longs;upralibellã">&longs;upra libellam</expan> BD; patet ex ip­<lb/>&longs;iu&longs;met aduer&longs;arij hypothe&longs;i, quòd <lb/>aer in &longs;cutella, &longs;eu ampulla DG con­<lb/>tentus &longs;tringitur, comprimiturque à <lb/>duabus potentijs contrarijs inter &longs;&etail; <lb/>æqualibus (eò quod æquilibrantur) <lb/>nempè à pondere mercurij <expan abbr="extãtis">extantis</expan> BF, <lb/>& à pondere columnæ aereæ GS. </s> <s id="s.001214">Si <lb/>po&longs;tea appo&longs;ito operculo exactè clau­<lb/>datur orificium G, & aperiatur <expan abbr="orificiũ">orificium</expan> <lb/>in &longs;ummitate fi&longs;tulæ A aer interceptus <lb/>inter operculum G, & mercurium D <lb/>&longs;tringitur comprimiturque à mercurio BF, & à colum-<pb pagenum="236" xlink:href="010/01/244.jpg"/><arrow.to.target n="marg314"/><lb/>na aerea FS æquali ip&longs;i GS, tunc patet, quòd poten­<lb/>tiæ comprimentes mercurij FB, & aeris FS æquales <lb/>&longs;unt potentiæ eiu&longs;dem mercurij FB, & aeris SG. </s> <s id="s.001215">Iam <lb/>dico, quod duplò validiori vi comprimitur aer DG <lb/>clau&longs;o orificio G, & aperta &longs;ummitate A, quàm illo <lb/>aperto, & hoc clau&longs;o. </s> <s id="s.001216">Quia obturato vitro in A, & a­<lb/>perto in G ampulla aerea DG &longs;tringitur à duabus <lb/>oppo&longs;itis potentijs, à mercurio nempè FB, & ab aeris <lb/><arrow.to.target n="marg315"/><lb/>columna SG, ergo vis, qua aerea ve&longs;ica DG &longs;tringitur <lb/>æqualis e&longs;t duabus poténtijs mercurij BF, & aeris SG, <lb/>&longs;eu duplò ponderis mercurij BF. è contra clau&longs;o ori­<lb/>&longs;icio G, & aperto vitro in A duæ potentiæ mercurij <lb/>BF, & aeris SF comprimunt <expan abbr="aereã|veficã">aere a ve&longs;ica</expan> DG in D, qui <lb/>aer innititur fundo &longs;tabili, nempè operculo G, igitur, <lb/>ex corollario præcedentis, propo&longs;itionis vis, qua aer <lb/>DG &longs;tringitur æqualis e&longs;t duplò <expan abbr="pot&etilde;tiarum">potentiarum</expan> mèrcu­<lb/>rij BF, & aeris SF, nempèl quadruplò potentiæ mer­<lb/>curij BF; igitur dupla vi, & energia <expan abbr="cõ&longs;tringitur">con&longs;tringitur</expan> aer <lb/>DG clau&longs;o orificio G, & aperto vitro in A, ac <expan abbr="cõpri-mebatur">compri­<lb/>mebatur</expan> quando vitrum claudebatur in A, re&longs;eraba­<lb/>tur verò in G. <!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001217"><margin.target id="marg314"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateria <lb/>eius.</s> </p> <p type="margin"> <s id="s.001218"><margin.target id="marg315"/>Ex 1. parte <lb/>top. III. </s> <s id="s.001219">111.</s> </p> <p type="main"> <s id="s.001220">Quod verò à maiori vi compre&longs;&longs;iua, nempè dupla <lb/>magis con&longs;tringi, conden&longs;arique debeat aer DG, & <lb/>proinde mercurius deprimatur infra &longs;upremam ele­<lb/>uationem F mirum profectò non e&longs;t, imò iuxtà ordi­<lb/>nem naturæ, & nece&longs;&longs;itatem, qua operatur debet <lb/>mercurius in prædicto ca&longs;u aliquantulum deprimi, vt <lb/>exigit aeris natura, quæ dilatationi, & con&longs;trictioni <lb/>obnoxia e&longs;t. </s> <s id="s.001221">Hinc con&longs;tat ab aere <expan abbr="cõpre&longs;&longs;o">compre&longs;&longs;o</expan> DG pro-<pb pagenum="237" xlink:href="010/01/245.jpg"/><arrow.to.target n="marg316"/><lb/>hiberi de&longs;cen&longs;um mercurij BF, quæ compre&longs;&longs;io facta <lb/>fuit à cylindro aereo incumbente SG ope eius na­<lb/>tiuæ grauitatis. </s> </p> <p type="margin"> <s id="s.001222"><margin.target id="marg316"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001223">Non e&longs;t nece&longs;sè vt hìc repetam <expan abbr="experim&etilde;ta">experimenta</expan> innu­<lb/>mera, quæ pa&longs;&longs;im obuia <expan abbr="sũt">sunt</expan>, de quibus Roberuallius, <lb/>Mer&longs;ennus, Pecquetus, Boile, Ga&longs;&longs;endus, & plures <lb/>alij &longs;crip&longs;erunt, & tandem prodijt liber experimen­<lb/>torum no&longs;træ Academiæ Experimentalis Mediceæ; <lb/>ex his enim euincitur, ab aere ambiente mercuriu&mtail; <lb/>in fi&longs;tula &longs;ubleuari, quandoquidem quotie&longs;cumque <lb/>aer ex&longs;ugitur, &longs;eu prohibetur eius compre&longs;&longs;io &longs;uper <lb/>&longs;tagnantem mercurium, tunc deprimitur mercurius <lb/>infra &longs;upremum &longs;ignum in fi&longs;tula, & &longs;i hoc fiat in &longs;pa­<lb/>tio vacuo, &longs;cilicèt in loco à quo aer exclu&longs;us &longs;it, tunc <lb/>quidem mercurius omninò deprimitur, & è contrà <lb/>adueniente aere &longs;ubitò mercurius in prædicta fi&longs;tula <lb/>eleuatur. </s> <s id="s.001224">idip&longs;um accidit in aqua. </s> </p> <p type="main"> <s id="s.001225"><emph type="center"/>PROP. CXIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001226"><emph type="center"/><emph type="italics"/>Suadetur aeris difformis grauitas ex inæquali mercurij ele<lb/>uatione in fi&longs;tula, prout altitudo aeris maior, aut mi­<lb/>nor fuerit.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001227">PRætere a euidenti&longs;&longs;imum e&longs;t, mercurium in prædi­<lb/>cta fi&longs;tula eò magis deprimi infra altitudine&mtail; <lb/>vnius cubiti, & quadrantis, quò magis <expan abbr="in&longs;trumentũ">in&longs;trumentum</expan> <lb/>eleuatur à plano &longs;ubiecto, &longs;ic Dominus Pa&longs;chalius in <lb/>montibus Aruerniæ expertus e&longs;t in radice montis <lb/>mercurij altitudinem fui&longs;&longs;e pollicum 27. cum tribus <pb pagenum="238" xlink:href="010/01/246.jpg"/><arrow.to.target n="marg317"/><lb/>lineis: <expan abbr="trãslato">translato</expan> in&longs;trumento ad altitudinem pedu&mtail; <lb/>900. &longs;upra montis radicem, mercurij altitudo fuit &longs;o­<lb/>lummodò pollicum 25. in cacumine verò montis vbi <lb/>altitudo ab eius radice erat pedum 3000. eleuatio <lb/>mercurij fuit pollicum 24. lin. <!-- REMOVE S-->2. con&longs;tat ergo nedùm <lb/>minui compre&longs;&longs;ionem quando minuitur aeris altitu­<lb/>do, &longs;ed etiam euincitur difformitas grauitatis ip&longs;ius <lb/>aeris; conijcitur enim, quòd aer habeat con&longs;i&longs;tentiam <lb/>veluti &longs;pongio&longs;am <expan abbr="&longs;itq;">&longs;itque</expan> veluti lanæ cumulus, cuius <lb/>partes &longs;uperiores dum comprimunt infimas, reddunt <lb/>aeris regionem difformiter grauem pro varia earu&mtail; <lb/>compre&longs;&longs;ione, & con&longs;tipatione, & pro varia mi&longs;tu­<lb/>ra particularum aquæ, & terræ. </s> </p> <p type="margin"> <s id="s.001228"><margin.target id="marg317"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001229">Idip&longs;um po&longs;tea ob&longs;eruauimus Florentiæ in alti&longs;&longs;i­<lb/>ma turri palatij, in qua a&longs;cen&longs;is &longs;olummodò cubitis <lb/>50. &longs;upra infimam plateam, & palatij atrium depre&longs;­<lb/>&longs;us apparuit mercurius &longs;patio vnius gradus, &longs;cilicèt <lb/>decima parte vnius digiti, at po&longs;tea perducto in&longs;tru­<lb/>mento ad altitudinem 100. <expan abbr="cubitorũ">cubitorum</expan> depre&longs;&longs;io mer­<lb/>curij minor fuit altero gradu euidenti, & notabili <lb/>defectu. </s> <s id="s.001230">Idemque po&longs;tea ob&longs;eruatum fuit in monti­<lb/>bus propè Florentiam, & ne &longs;u&longs;picio &longs;ubiret aeris &longs;u­<lb/>premi frigiditatem depre&longs;&longs;i&longs;&longs;e mercurium in fi&longs;tul&atail; <lb/>elegimus loca, & tempora commoda, &longs;cilicèt calefa­<lb/>cta à &longs;ole in turris cacumine, & vmbro&longs;a in eius ra­<lb/>dicibus, vt eorum temperies eadem e&longs;&longs;et, & hoc in­<lb/>dicabatur adhibitis perfecti&longs;&longs;imis termometris, quç <lb/>o&longs;tendebant aerem in &longs;ummitate turris, aut eade&mtail; <lb/>temperio, aut calidiori &longs;eruari quem in radice turris <pb pagenum="239" xlink:href="010/01/247.jpg"/><arrow.to.target n="marg318"/><lb/>aut montis. </s> <s id="s.001231">& ne &longs;u&longs;picio &longs;ubiret à concu&longs;&longs;ione mer­<lb/>curij in fi&longs;tula dum transferebatur &longs;ursùm exclu&longs;is <lb/>particulis minimis aereis, debui&longs;&longs;e po&longs;tea mercurium <lb/>aliquanti&longs;per deprimi, curauimus etiam obturato in­<lb/>fimo fi&longs;tulæ orificio, ne vlla concu&longs;&longs;io mercurij effice­<lb/>retur, & po&longs;tea in ip&longs;o de&longs;cen&longs;u vidimus præcisè <lb/>mercurium in ij&longs;dem locis eleuatum fui&longs;&longs;e ad ea&longs;dem <lb/>altitudines, ad quas in a&longs;cen&longs;u <expan abbr="mõtis">montis</expan>, vel turris per­<lb/>uenerat, vnde colligitur &longs;olummodò ab aeris vari&atail; <lb/>compre&longs;&longs;ione mercurium &longs;uas altitudines varia&longs;&longs;e. <lb/><arrow.to.target n="marg319"/></s> </p> <p type="margin"> <s id="s.001232"><margin.target id="marg318"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001233"><margin.target id="marg319"/>Altitudo <lb/>mercurij in <lb/>fi&longs;tula Torri­<lb/>celliana non <lb/>&longs;emper eiu&longs;­<lb/>dem men&longs;u­<lb/>ræ e&longs;t.</s> </p> <p type="main"> <s id="s.001234">Vltimo loco animaduertimus non &longs;emper mercu­<lb/>rium ad eamdem præcisè altitudinem in fi&longs;tula ele­<lb/>nari, quæ aliqua ex parte pendet à temperie aeris <lb/>calida, & frigida, &longs;ed hæc quidem exigua e&longs;t &longs;i vi­<lb/>trea fi&longs;tula in vertice eius &longs;upremo annexam ampul­<lb/>lam vacuam, amplam habeat; mirabilis profectò vi­<lb/>&longs;a e&longs;t variatio illa altitudinis, quæ procùl dubio à <expan abbr="t&etilde;-perie">ten­<lb/>perie</expan> calidi, & frigidi aeris non dependet, <expan abbr="cũ">cum</expan> perin­<lb/>de ob&longs;eruata &longs;it temporibus æ&longs;tiuis, & hyemalibus, <lb/>pariter que in cubiculo ab igne excalefacto, vel fri­<lb/>gido, et habeo penès me ob&longs;eruationes <expan abbr="duorũ">duorum</expan> anno­<lb/>rum 1657. & 1658. <expan abbr="prædictarũ">prædictarum</expan> <expan abbr="varietatũ">varietatum</expan>, in quibus <lb/>&longs;ingulis diebus <expan abbr="adnotãtur">adnotantur</expan> gradus caliditatis aeris ex <lb/>termometro, an dies fuerit nebulo&longs;us, vel pluuius, <lb/>aut &longs;erenus, & quinam venti &longs;pirarint, quas feci mo­<lb/>nitu, & iu&longs;&longs;u Sereni&longs;s. <!-- REMOVE S-->Ferdinandi Secundi M. </s> <s id="s.001235">Ducis <lb/>Ætruri&etail;, naturalium operationum &longs;agaci&longs;&longs;imi explo­<lb/>ratoris: & tandem videtur ex pluribus ob&longs;eruatio­<lb/>nibus &longs;imùl collectis deduci po&longs;&longs;e, quòd multoties </s> </p> <pb pagenum="240" xlink:href="010/01/248.jpg"/> <p type="main"> <s id="s.001236"><arrow.to.target n="marg320"/><lb/>cùm imminet aliqua diuturna, & continuata pluuia <lb/>in illa regione, tunc mercurius in fi&longs;tula per aliquos <lb/>gradus &longs;upra con&longs;uetam altitudinem eleuatur, è con­<lb/>trà pluuia iam actu cadente mercurius in prædicta fi­<lb/>&longs;tula deprimi &longs;olet, nec e&longs;t exigua prædicta differen­<lb/>tia, multotiès enim Pi&longs;is ob&longs;eruaui in diuturnis plu­<lb/>uio&longs;is tempe&longs;tatibus varia&longs;&longs;e mercurij altitudine&mtail; <lb/>per duodecim gradus, &longs;cilicèt per latitudinem vnius <lb/>pollicis. </s> <s id="s.001237">Quia verò a&longs;&longs;eruo penès me exemplar epi­<lb/>&longs;tolæ, quam Sereni&longs;&longs;imo Principi Leopoldo modò <lb/>Cardinali ampli&longs;&longs;imo anno 1657. &longs;crip&longs;i circa hanc <lb/>materiam, hìc afferam breuiter ea, quæ tunc &longs;pecu­<lb/>latus &longs;um, quod nimirùm fieri pote&longs;t ob aeris pre&longs;­<lb/>&longs;ionem &longs;upra mercurium &longs;tagnantem in fi&longs;tula, vt an­<lb/>te pluuiam aer multò magis grauitet, & comprimat, <lb/>quam in ip&longs;o pluuiæ de&longs;cen&longs;u, quod vt clariùs o&longs;ten­<lb/>dam, præmittendum e&longs;t. </s> </p> <p type="margin"> <s id="s.001238"><margin.target id="marg320"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001239"><emph type="center"/>PROP. CXIV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001240"><emph type="center"/><emph type="italics"/>In fi&longs;tula Torricelliana intra puteum demer&longs;a &longs;i aqua <lb/>à grauiori &longs;uper addito fluido occupetur, mercu­<lb/>rius in fistula altiùs &longs;ubleuatur, at post <lb/>illius delap&longs;um denuo mercurius <lb/>deprimitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001241">SVmpta fi&longs;tula vitrea ABC flexa in B, & facto i&ntail; <lb/>ea vacuo, more &longs;olito, mercurius eleuetur v&longs;que <lb/>ad F, demittatur po&longs;tea fi&longs;tula intra vas vitreum cy­<lb/>lindricum DE maxim&etail; altitudinis earum quæ exca-<pb pagenum="241" xlink:href="010/01/249.jpg"/><arrow.to.target n="marg321"/><lb/>uari efformarique po&longs;&longs;unt, atque in eius fundo E de­<lb/>mittatur fi&longs;tula cum &longs;tagnante mercurio ABC; po&longs;tea <lb/>repleatur cylindrus vitreus oleo, vel alio liquore le­<lb/>uiori v&longs;que ad G, con&longs;tat à nouo pondere olei &longs;upra <lb/>mercurium &longs;tagnantem C incumbentis eleuari præ­<lb/>terea mercurium ab F ad H, vt nimirum fiat æquili­<lb/>brium inter mercurium HF, & <expan abbr="oleũ">oleum</expan> <lb/><figure id="id.010.01.249.1.jpg" xlink:href="010/01/249/1.jpg"/><lb/>CG; po&longs;tea &longs;i &longs;upra olei <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> <lb/>G innatet vas NO, quod arena, a­<lb/>qua, vel alio grauiori fluido <expan abbr="nõ">non</expan> om­<lb/>ninò impleatur, procùl dubio à no­<lb/>uo pondere NO altiùs mercurius <lb/>eleuabitur in fi&longs;tula ab H v&longs;que ad <lb/>M. </s> <s id="s.001242">His peractis reuoluatur vas N <lb/>O, vt nimirum arena, vel a qua flue­<lb/>re po&longs;&longs;it deorsùm ad modum pluui&etail; <lb/>per &longs;patium oleo&longs;um GC, & dùm <lb/>prædicta pluuia deorsùm de&longs;cendit <lb/>non de&longs;eret mercurius <expan abbr="&longs;ummitat&etilde;">&longs;ummitatem</expan> <lb/>fi&longs;tulæ M, at po&longs;tquam areno&longs;a, vel aquea pluuia <expan abbr="fun-dũ">fun­<lb/>dum</expan> cylindri EK attingit, & proindè infrà &longs;tagnantem <lb/>libellam mercurij C deprimitur, tunc mercurius non <lb/>ampliùs per&longs;i&longs;tet in &longs;ummitate fi&longs;tulæ M, &longs;ed paula­<lb/>tim de&longs;cendet versùs H, prout maiori copia pluui&atail; <lb/>aquea, vel areno&longs;a ad <expan abbr="fũdum">fundum</expan> va&longs;is EK perducitur. </s> <s id="s.001243">ra­<lb/>tio huius rei e&longs;t quia licèt arena, vel aqua grauior o­<lb/>leo &longs;it, & proindè comprimat mercurium &longs;tagnantem <lb/>in C, eumque eleuet v&longs;que ad M, nihilominùs quan­<lb/>do arena, vel aqua <expan abbr="fundũ">fundum</expan> va&longs;is EK attingit, compri-<pb pagenum="242" xlink:href="010/01/250.jpg"/><arrow.to.target n="marg322"/><lb/>mit eius fundum, non verò <expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> &longs;tagnantis mer­<lb/>curij C, & &longs;ic mercurius comprimitur tantummodò à <lb/>cylindro oleo&longs;o GC. </s> </p> <p type="margin"> <s id="s.001244"><margin.target id="marg321"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001245"><margin.target id="marg322"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001246"><emph type="center"/>PROP. CXV.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001247"><emph type="center"/><emph type="italics"/>Mercurius in fi&longs;tula Torricellian a altiùs eleuabitur <expan abbr="dũ">dum</expan> aer <lb/>nebulis pluuio&longs;is impregnatur, at postquam pluuia <lb/>delap&longs;a e&longs;t, denuò mercurius in fistulæ <lb/>deprimitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001248">AB hoc euidenti&longs;&longs;imo experimento problema no­<lb/>&longs;trum &longs;olui po&longs;&longs;e cen&longs;eo, quandoquidem quid <lb/>aliud &longs;unt nebulæ pluuio&longs;æ, &longs;cilicèt aqua grauidæ, <lb/>quàm aggregatum ex innumeris granulis minuti&longs;&longs;i­<lb/>mis aqueis? </s> <s id="s.001249">& cùm prædicta nebula in alti&longs;&longs;imis ae­<lb/>ris partibus innatat, vellenti&longs;&longs;imo <lb/><figure id="id.010.01.250.1.jpg" xlink:href="010/01/250/1.jpg"/><lb/>motu aquæ particulæ eius <expan abbr="de&longs;cen-dũt">de&longs;cen­<lb/>dunt</expan>, procùl dubio &longs;uo pondere na­<lb/>turali augent aeris <expan abbr="grauitat&etilde;">grauitatem</expan>, ideo­<lb/>que maiori ni&longs;u globum <expan abbr="terraqueũ">terraqueum</expan> <lb/>comprimunt, quam aer purus, & <lb/>aqueis guttulis omninò priuatus <lb/>con&longs;tringere eum po&longs;&longs;it: & ideò fi­<lb/>&longs;tula mercurialis ABC in infimo <lb/>prædicto aere con&longs;tituta compri­<lb/>mitur nedùm à pondere &longs;uper&longs;tan­<lb/>tis aeris, &longs;ed præterea à ponder&etail; <lb/>totius aquæ nebulam &longs;uprema&mtail; <lb/>componentis: itaque per aliquod tempus <expan abbr="antequã">antequam</expan> <pb pagenum="243" xlink:href="010/01/251.jpg"/><arrow.to.target n="marg323"/><lb/>pluuia de&longs;cendat, fieri pote&longs;t vt mercurius in fi&longs;tula <lb/>&longs;upremam illam altitudinem M pertingat, in eaque <lb/>permaneat, & hoc nedum à nebulis, &longs;ed à quacum­<lb/>que alia cau&longs;a grauitante effici pote&longs;t, &longs;i enim terre­<lb/>&longs;tris puluis à vento, vel alia commotion e &longs;ursùm im­<lb/>pellatur, atque per aerem di&longs;&longs;ipetur &longs;pargaturque <lb/>tunc nemo dubitat aerem grauiori ni&longs;u &longs;uperficiem <lb/>orbis terraquei comprimere. </s> <s id="s.001250">Si po&longs;tea à qualibet <lb/>cau&longs;a nebula impellatur, vt nimirùm terram attin­<lb/>gat, &longs;cilicèt pluuia paulatim terram a&longs;&longs;equatur <expan abbr="eã-que">ean­<lb/>que</expan> humectet, tunc patet innumera aquæ granul&atail; <lb/>terræ innici, neque amplius aeris grauitatem, & <lb/>compre&longs;&longs;ionem augere, & quia à terra &longs;ubiecta &longs;u­<lb/>&longs;tentantur, non po&longs;&longs;unt vt priùs &longs;uo naturali pondere <lb/>comprimere &longs;uperficiem infimam mercurij &longs;tagnan­<lb/>tis, & propterea &longs;emper à minori pondere mercu­<lb/>rius in C comprimitur prout magis pluuia ad terram <lb/>perducitur, & prout magis aer illo pondere alleuia­<lb/>tur, & propterea &longs;uperficies eius in &longs;uprema fi&longs;tulæ <lb/>parte &longs;en&longs;im deprimitur v&longs;que ad infimum &longs;itum F. <lb/><arrow.to.target n="marg324"/><!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001251"><margin.target id="marg323"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001252"><margin.target id="marg324"/>Non tamen <lb/>conuer&longs;a re­<lb/>gula vera est <lb/>nam ab alijs <lb/>cau&longs;is eleua­<lb/>tio mercurij <lb/>in fi&longs;tula va­<lb/>riari pote&longs;t.</s> </p> <p type="main"> <s id="s.001253">Licèt hoc verum &longs;it, non tamen indè elici pote&longs;t <lb/>conuer&longs;a regula generalis, vt nimirum quotie&longs;cum­<lb/>que mercurius in fi&longs;tula eleuatur debeat pluuia ex­<lb/>pectari, quando quidem pote&longs;t huiu&longs;modi <expan abbr="augmentũ">augmentum</expan> <lb/>compre&longs;&longs;ionis produci ab aliqua ingenti agitatione <lb/>&longs;upremæ atmo&longs;phæræ; & &longs;i fortè à particulis aqueis, <lb/>& terreis &longs;ubleuatis maior grauitas aeris producitur <lb/>fieri pote&longs;t vt à violentia ventorum alibi tran&longs;por­<lb/>tentur nebulæ, & &longs;ic pluuia alibi translata non deci-</s> </p> <pb pagenum="244" xlink:href="010/01/252.jpg"/> <p type="main"> <s id="s.001254"><arrow.to.target n="marg325"/><lb/>dat in eo loco vbi originem habuit. </s> <s id="s.001255">Atque ex his om­<lb/>nibus concludi pote&longs;t aerem reuera &longs;uo pondere, & <lb/>vi ela&longs;tica comprimere mercurium in fi&longs;tula conten­<lb/>tum, eumque ad illam determinatam altitudinem ele­<lb/>uare. </s> </p> <p type="margin"> <s id="s.001256"><margin.target id="marg325"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001257"><emph type="center"/>PROP. CXVI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001258"><emph type="center"/><emph type="italics"/>Aerem e&longs;&longs;e grauem experimentis aliorum comprobatur, & <lb/><expan abbr="primã">primam</expan> Mer&longs;ennij <expan abbr="experientiã">experientiam</expan> ope ignis infide­<lb/>lem e&longs;&longs;e.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001259">SEd multò magis patebit veritas prædictæ propo­<lb/>&longs;itionis adhibitis experimentis à quibus imme­<lb/>diatè, & directè o&longs;tenditur aeris grauitas, & primò <lb/><arrow.to.target n="marg326"/><lb/>con&longs;tat <expan abbr="experi&etilde;tia">experientia</expan> relata ab Ari&longs;totele, vbi ait, vtrem <lb/>inflatum maiorem grauitatem, & pre&longs;&longs;ionem exerce­<lb/>re quàm <expan abbr="vacuũ">vacuum</expan>. </s> <s id="s.001260">hocque po&longs;tea diligenti&longs;&longs;imè ab alijs <lb/>comprobatum e&longs;t, & &longs;umma facilitate perfici pote&longs;t <lb/>non quidem follibus violenter <expan abbr="in&longs;ufflãdo">in&longs;ufflando</expan> vtrem, &longs;ed <lb/>leni plenitudine vtre clau&longs;o, vel commodiùs pila lu­<lb/>&longs;oria aerea ad trutinam examinata, & po&longs;tea funicu­<lb/>lo circa vtrem, vel pilam reuoluto violenterque con­<lb/>&longs;tricto, tune quidem ob aeris conden&longs;ationem pon­<lb/>dus vtris, aut pilæ manife&longs;tè ad trutinam augetur; <lb/>præterea, vt docuit Galilæus, intra vitream lagenam <lb/>violentèr aer in&longs;ufflari pote&longs;t vt valdè conden&longs;etur, <lb/>& tunc pondus prædictæ lagenæ &longs;en&longs;ibilitèr augetur <lb/><expan abbr="prom&etilde;&longs;ura">promen&longs;ura</expan> aeris ibidem conden&longs;ati, & hac <expan abbr="experi&etilde;-tia">experien­<lb/>tia</expan> diligenti&longs;&longs;imè facta ingenio&longs;i&longs;&longs;imus Antonius Oli-<pb pagenum="245" xlink:href="010/01/253.jpg"/><arrow.to.target n="marg327"/><lb/>ua reperit, quòd grauitas molis aeris, quæ æqualis <lb/>&longs;it cubo aqueo vnius libræ granum vnum pendet. </s> <s id="s.001261">at <lb/>Mer&longs;ennus in Ph&etail;nomenis pneumaticis ope ignis <expan abbr="eã-dem">ean­<lb/>dem</expan> experientiam fecit, &longs;ump&longs;it æolo pilam æream, <lb/>eamque vehementi&longs;&longs;imo igne calefecit, vt prorsùs <lb/><arrow.to.target n="marg328"/><lb/>cande&longs;ceret, & &longs;ic in bilance per&longs;ecti&longs;&longs;ima, quæ à &longs;e­<lb/>migraro &longs;lectebatur, examinauit pondus eiu&longs;de&mtail; <lb/>&etail;olo pilæ <expan abbr="cand&etilde;tis">candentis</expan>, eamque reperit <expan abbr="vnciarũ">vnciarum</expan> 4. drach. <lb/></s> <s id="s.001262">6. & gran. <!-- REMOVE S-->15. po&longs;tea refrigerata æolo pila eius pon­<lb/>dus præcedentem &longs;uperauit gran. <!-- REMOVE S-->4. & hinc elicit ae­<lb/>rem inclu&longs;um in æolo pila grana 4. pondera&longs;&longs;e, porrò <lb/>pondus aeris illius ad æqualem aquæ molem ait re­<lb/>peri&longs;&longs;e in proportione 1. ad 1356. </s> </p> <p type="margin"> <s id="s.001263"><margin.target id="marg326"/>4. de c&etail;lo. <lb/>cap. 4.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001264"><margin.target id="marg327"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001265"><margin.target id="marg328"/>Prop. 29.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001266">Sed prædicta experientia multis nominibus infi­<lb/>delis e&longs;t, primò quia corpora vehementer excalefacta <lb/>in bilance &longs;u&longs;pen&longs;a non o&longs;tendunt veram grauitatem <lb/><arrow.to.target n="marg329"/><lb/>eorum, &longs;ed diminutam, quia vt &longs;uperiùs o&longs;ten&longs;u&mtail; <lb/>e&longs;t, ignis diffu&longs;us ab æolo pila candente valdè rare­<lb/>facit aerem prædictam æolo pilam ambientem, cum­<lb/>que aer ambiens fimul cum pila vnum corpus graue <lb/>componat intra den&longs;iorem aerem &longs;u&longs;pen&longs;um, fit vt <lb/>aggregatum prædictum minùs graue &longs;pecie &longs;it, <expan abbr="quã">quam</expan> <lb/>prius, & proinde imminuitur grauitas æreæ æolo pi­<lb/>læ, non &longs;olùm ob de&longs;ectum aeris inclu&longs;i, &longs;ed etiam ob <lb/>eius &longs;eruenti&longs;&longs;imam caliditatem. </s> </p> <p type="margin"> <s id="s.001267"><margin.target id="marg329"/>c 4 prop. 61.</s> </p> <p type="main"> <s id="s.001268">Rursùs aer in &etail;olopila à vehementi&longs;&longs;imo igne am­<lb/>pliatus expan&longs;u&longs;que non pote&longs;t dici verè rarefactus, <lb/>quia nimirùm copia ignis vehementi&longs;&longs;imè agitati, & <lb/>circumuoluti intra æolo pilæ cauitatem di&longs;gregat, ac <pb pagenum="246" xlink:href="010/01/254.jpg"/><arrow.to.target n="marg330"/><lb/>&longs;e parat particulas aliquas aeris ibidem relictas, ita­<lb/>que intercapedines, quæ &longs;eparant aeris particulas, <lb/>partim occupantur ab igne, partim ab inani &longs;patio, <lb/>dum igneæ particulæ motu veloci&longs;&longs;imo conuertun­<lb/>tur, & vertigines complent, intercipiendo grandia <lb/>&longs;patia inania; vndè malè hinc infertur raritas maxima <lb/>ad quam aer ampliari pote&longs;t. </s> </p> <p type="margin"> <s id="s.001269"><margin.target id="marg330"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001270"><emph type="center"/>PROP. CXVII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001271"><emph type="center"/><emph type="italics"/>Secunda Mer&longs;enni experientia in &longs;clopeto pneumatico <lb/>fact a dubia quoque e&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001272">MElior e&longs;t &longs;ecunda Mer&longs;enni experientia dù&mtail; <lb/>in bombarda, &longs;eu &longs;clopeto pneumatico ma­<lb/>gno conatu immi&longs;it va&longs;tam aeris molem, quæ in exi­<lb/>guo &longs;patio conden&longs;ata fuit, aitque pondus &longs;exagin­<lb/>ta <expan abbr="granorũ">granorum</expan> aeris inclu&longs;i&longs;&longs;e in cauitate catapultæ, quæ <lb/>ab 8. vncijs aquæ impleri poterat, hinc deducit ae­<lb/>rem in &longs;clopeto immi&longs;&longs;um adeò conden&longs;ari vt quin­<lb/>decies &longs;patium internum catapultæ expleat; proin­<lb/>de que tres digitos cubicos aeris ferè <expan abbr="põderare">ponderare</expan> gra­<lb/>num vnum. </s> <s id="s.001273">Sed ex tanto apparatu tandem Mer&longs;en­<lb/>nus nil certi colligit, cùm afferat innumeras difficul­<lb/>tates, & ingenuè fateatur, &longs;emper dubitari po&longs;&longs;e an <lb/>intra catapultæ cauitatem vnà cum aere in&longs;uffletur <lb/>particula aliqua oleagino&longs;a, vel aquea, quandoqui­<lb/>dem epi&longs;tomium emboli humectari debetin eius &longs;u­<lb/>perficie coriacea, vt omninò rimæ claudantur, vt re­<lb/>gre&longs;&longs;us aeris prohibeatur. <pb pagenum="247" xlink:href="010/01/255.jpg"/><arrow.to.target n="marg331"/></s> </p> <p type="margin"> <s id="s.001274"><margin.target id="marg331"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001275">Hi&longs;ce omnibus difficultatibus perpen&longs;is plures <lb/>modi <expan abbr="inueni&etilde;di">inueniendi</expan> aeris <expan abbr="grauitat&etilde;">grauitatem</expan> in Academia Experi­<lb/>mentali Medicea excogitati <expan abbr="fuerũt">fuerunt</expan> ab illis doctis vi­<lb/>ris, hìc tamen referam aliquos ex multis à me ibidem <lb/>propo&longs;itis. </s> </p> <p type="main"> <s id="s.001276"><emph type="center"/>PROP. CXVIII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001277"><emph type="center"/><emph type="italics"/>Nouum artificium ad explorandam aeris grauitatem <lb/>exponitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001278">PRimò &longs;umatur fi&longs;tula vitrea <lb/><figure id="id.010.01.255.1.jpg" xlink:href="010/01/255/1.jpg"/><lb/>ABCF inflexa propè eius <lb/>extremum C, in &longs;ummitate verò <lb/>annexam habeat <expan abbr="vitreã">vitream</expan> ampul­<lb/>lam AB diametro 4. digitoru&mtail;, <lb/>habeatque duo orificia aperta in <lb/>M & F, longitudo verò eius BD <lb/>maior &longs;it &longs;e&longs;qui cubito. </s> <s id="s.001279">Vas <expan abbr="præ-dictũ">præ­<lb/>dictum</expan> hydrargyro impleatur per <lb/>orificium M, obturato prius o&longs;tio <lb/>infimo F, & po&longs;teà denuò ve&longs;ica <lb/>&longs;uilla clau&longs;o &longs;upremo orificio M <lb/>ibidem alligari debet æneum fi­<lb/>lum <expan abbr="gracili&longs;&longs;imũ">gracili&longs;&longs;imum</expan> MSN, & aper­<lb/>to infimo o&longs;tio F, facto vacuo mo<lb/>re &longs;olito, de&longs;cendet mercurij &longs;u­<lb/>perficies v&longs;que ad L, po&longs;t qua&mtail; <lb/>&longs;cilicèt maior pars eius fluxerit ab infimo orificio F, <lb/>reman&longs;erit que &longs;patium ABL exinanitum, & tunc de-<pb pagenum="248" xlink:href="010/01/256.jpg"/><arrow.to.target n="marg332"/><lb/>nuò duplici ve&longs;ica &longs;uilla &longs;trictè alligata claudatur <lb/>orificium F. <!-- KEEP S--></s> <s id="s.001280">Po&longs;teà præparari debet vas profundum <lb/>PQR aqua plenum v&longs;que ad &longs;ummitatem PR, &longs;itque <lb/>eius profunditas tanta vt mergi po&longs;&longs;it vniuer&longs;um in­<lb/>&longs;trumentum MAC, vt tamen eius ba&longs;is C putei fun­<lb/>dum non attingat; demergatur fi&longs;tula prædicta vitrea <lb/>vnà cum mercurio contento intra aquam; & &longs;i fortè <lb/>os &longs;upremum vitri M non demergitur infra aquæ &longs;u­<lb/>perficiem PR, exigui anuli ænei totidem vnciæ gra­<lb/>na pendentes in C, & in &longs;ummitate A apponantur, <lb/>quou&longs;que vniuer&longs;a machina vitrea fiat proximè mi­<lb/>nùs grauis &longs;pecie quàm aqua, &longs;cilicèt innatet, & emi­<lb/>neat &longs;upra aqu&etail; libellam PR pars aliqua SN prædi­<lb/>cti fili ænei vitro annexi, & in S fiat æquilibrium, & <lb/>quies. </s> <s id="s.001281">Deinde in aere aperiatur &longs;upremum os vitri <lb/>M, vt &longs;patium inane ABL aere impleatur, <expan abbr="remane-bitq;">remane­<lb/>bitque</expan> reliqua pars fi&longs;tulæ plena hydrargyro, vt priùs, <lb/>propterea quod operculum in F impedit <expan abbr="exitũ">exitum</expan> mer­<lb/>curio LCF. </s> <s id="s.001282">In hoc &longs;tatu denuò eadem &longs;uilla ve&longs;ic&atail; <lb/>claudatur arcteque ligetur vitri os &longs;upremum M; & <lb/>tandem denuò demergatur fi&longs;tula infra <expan abbr="libellã">libellam</expan> aquæ <lb/>PR. </s> <s id="s.001283">Et quia in hoc ca&longs;u demergitur infra aquæ libel­<lb/>lam moles conflata ex ij&longs;dem corporibus, &longs;cilicèt ex <lb/>vitro ACF, ex hydrargyro LCF, & ex ij&longs;dem ve&longs;icis, <lb/>& filis M & F, & &longs;olummodò de nouo ade&longs;t aer ABL, <lb/>quo fi&longs;tula priùs care bat; igitur nece&longs;sè e&longs;t, vt <expan abbr="põdus">pondus</expan> <lb/>totius machinæ NACF maius &longs;it quàm in priori &longs;ta­<lb/>tu quando &longs;patium ABL vacuum fuerat. </s> <s id="s.001284">Quaproptèr <lb/>non poterit denuò &longs;ubleuari fi&longs;tula ad eamdem alti-<pb pagenum="249" xlink:href="010/01/257.jpg"/><arrow.to.target n="marg333"/><lb/>tudinem S, ni&longs;i grauitas eius imminuatur; auferri igi­<lb/>tur debent aliqua grana, &longs;eù anuli ænei è collo fi&longs;tulæ <lb/>AM, vt machina ad æquilibrium <expan abbr="cũ">cum</expan> aqua redigatur, <lb/>mergaturque denuò <expan abbr="v&longs;q;">v&longs;que</expan> ad &longs;itum S; quot igitur gra­<lb/>na tolluntur à fi&longs;tulæ collo A, tot præcisè men&longs;ura­<lb/>bunt pondus aeris ABL intra fi&longs;tulam inclu&longs;i. </s> </p> <p type="margin"> <s id="s.001285"><margin.target id="marg332"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001286"><margin.target id="marg333"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001287">Multis modis po&longs;tea indagari pote&longs;t proportio <lb/>ponderis aeris ad aquam, &longs;ed omnium facillimus, & <lb/>&longs;implex erit &longs;i in aere perfecti&longs;&longs;ima bilance pondere­<lb/>tur moles aquæ æqualis &longs;patio ABL, & hic compa­<lb/>retur cum pondere iam inuento aeris eiu&longs;dem molis <lb/>ABL. </s> </p> <p type="main"> <s id="s.001288"><emph type="center"/>PROP. CXIX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001289"><emph type="center"/><emph type="italics"/>Po&longs;tea emis&longs;is quam plurimis termostaticis à me inuentis <lb/>afferam instrumentum quo pondus ab&longs;olutum aeris <lb/>in diuer&longs;is locis eleuatis, ac depres&longs;is, & variè <lb/>temperatis reperiri pote&longs;t.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001290">FIant tres ampullæ, vel ve&longs;icæ vitreæ, vel æneæ, <lb/>qualis e&longs;t AB, habeantque collum <expan abbr="&longs;upremũ">&longs;upremum</expan> CA <lb/>æneum perfecti&longs;&longs;imè contornatum, hoc autem vi&longs;co­<lb/>&longs;a aliqua materia, ac tenaci vniatur ferrumineturque <lb/>cum &longs;uprema ampullæ parte; habeat po&longs;tea <expan abbr="canal&etilde;">canalem</expan>, <lb/>&longs;eu colli cauitatem turbinatam conicè, & perfecti&longs;&longs;i­<lb/>mè <expan abbr="læuigatã">læuigatam</expan>, huic verò cauitati adaptari po&longs;&longs;it aliud <lb/>operculum paritèr æneum, & turbinatum, & exqui­<lb/>&longs;iti&longs;&longs;imè læuigatum, vt nimirùm nulla rimula rema­<lb/>neat, & perfecti&longs;&longs;imè claudat orificium fi&longs;tulæ C, vt <pb pagenum="250" xlink:href="010/01/258.jpg"/><arrow.to.target n="marg334"/><lb/>prohibeat ingre&longs;&longs;um, aut exitum aquæ, vel aeri; <expan abbr="tã-dem">tan­<lb/>dem</expan> aptetur tenui&longs;&longs;imum filum æneum CFE, <expan abbr="diuisũ">diuisum</expan> <lb/>in particulas æquales, &longs;eu gra­<lb/><figure id="id.010.01.258.1.jpg" xlink:href="010/01/258/1.jpg"/><lb/>dus. </s> <s id="s.001291">Po&longs;tea in fundo va&longs;is D in­<lb/>cludantur granula exigua plum­<lb/>bi quou&longs;que vniuer&longs;am <expan abbr="ampullã">ampullam</expan> <lb/>CAB <expan abbr="deprimãt">deprimant</expan> infra aquæ libel­<lb/>lam PR, ita tamen vt ampull&atail; <lb/>CB <expan abbr="nõ">non</expan> pertingat ad fundum va­<lb/>&longs;is Q, &longs;ed innatet, & &longs;ecetur fi­<lb/>lum æneum CE à libella aquæ <lb/>PR in aliquo eius puncto inter­<lb/>medio F. <!-- KEEP S--></s> <s id="s.001292">His præparatis <expan abbr="deb&etilde;t">debent</expan> <lb/>tres pr&etail;dictæ ampullæ tempera­<lb/>ri in eodem loco, & eodem va&longs;e aqueo, impleantur­<lb/>que aere eiu&longs;dem cubiculi ad <expan abbr="radic&etilde;">radicem</expan> turris, vel <expan abbr="mõ-tis">mon­<lb/>tis</expan> po&longs;iti, & in hi&longs;ce omnibus notetur &longs;ignum fili F, <lb/>quod aquæ &longs;uperficiem tangit, & adhibitis vulgari­<lb/>bus termometris notetur gradus caliditatis tùm ae­<lb/>ris cubiculi, tùm aquæ <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> va&longs;is. </s> <s id="s.001293">po&longs;tea duæ am­<lb/>pullæ <expan abbr="tran&longs;port&etilde;tur">tran&longs;portentur</expan> vna ad &longs;ummitatem alicuius tur­<lb/>ris vel montis, reliquare ponatur medio loco inter <expan abbr="sũ-mitatem">sum­<lb/>mitatem</expan>, & radicem, &longs;eu ba&longs;im eius, & ibidem ape­<lb/>riantur, vt raritatem aeris montani acquirant (arti­<lb/>ficiosè aere temperato &longs;i opus fuerit vt ad eumdem <lb/>caliditatis gradum reducantur, quem in cubiculo ha­<lb/>buerat;) po&longs;tea denuò ampullæ claudantur, atqu&etail; <lb/>intra idip&longs;um cubiculum a&longs;portentur, & ibidem in­<lb/>tra aquam demer&longs;æ, apparebunt differentiæ à prim&atail; <pb pagenum="251" xlink:href="010/01/259.jpg"/><arrow.to.target n="marg335"/><lb/>ampullarum demer&longs;ione, aer enim &longs;upremæ turris, <lb/>vt minùs grauis altiùs eleuabit &longs;ilum æneum CE, vt <lb/>nimirùm &longs;upra aquæ libellam emineat portio maior, <lb/>quàm EF, & ex prædicta comparatione facilè digno­<lb/>&longs;ci pote&longs;t diuer&longs;itas ponderis aeris, quæ in diuer&longs;is <lb/>eleuationibus reperitur. </s> <s id="s.001294">Sic etiam reperiri poterunt <lb/>differentiæ grauitatum aeris diuer&longs;orum locorum, ac <lb/>Vrbium. </s> </p> <p type="margin"> <s id="s.001295"><margin.target id="marg334"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001296"><margin.target id="marg335"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001297"><emph type="center"/>PROP. CXX.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001298"><emph type="center"/><emph type="italics"/>Tutis&longs;imo, & facillimo experimento elicitur &longs;pecificam <lb/>aquæ ad aeris grauitatem &longs;e habere, vt<emph.end type="italics"/> 1175. <lb/><emph type="italics"/>cum<emph.end type="italics"/> 4. <emph type="italics"/>&longs;eptimis ad<emph.end type="italics"/> 1.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001299">SEd præcipuus, ac pulcherrimus modus <expan abbr="reperi&etilde;-di">reperien­<lb/>di</expan> aeris grauitatem hic e&longs;t, <expan abbr="qu&etilde;">quem</expan> Acade miæ Me­<lb/>diceæ experimentali anno 1660. communi caui, vnà <lb/>cum eius demon&longs;tratione, <lb/><figure id="id.010.01.259.1.jpg" xlink:href="010/01/259/1.jpg"/><lb/>eumque ibidem eiu&longs;dem <lb/>anni &etail;&longs;tate ad praxim re­<lb/>degi: &longs;ump&longs;i plumbeam pi­<lb/>lam cauam BC aere <expan abbr="plenã">plenam</expan>, <lb/>& vndique clau&longs;am, hanc <lb/>quidem perfecti&longs;&longs;ima bi­<lb/>lance in aere ponderaui, <lb/>po&longs;tea addito pondere F, <lb/>à quo po&longs;&longs;et pila BC infra <lb/>aquæ libellam demergi, paritèr eius pondus præci­<lb/>&longs;um in aqua reperi, alligata nimirùm pila non funi-<pb pagenum="252" xlink:href="010/01/260.jpg"/><arrow.to.target n="marg336"/><lb/>culis, &longs;ed pluribus &longs;atis equinis à quibus eius gra­<lb/>uitas in aqua non alteratur &longs;altem differentia &longs;en&longs;ibi­<lb/>li; poterit ergò &longs;umi additamentum ponderis F ac &longs;i <lb/>augeret cra&longs;&longs;itiem pilæ <expan abbr="plũbeæ">plumbeæ</expan> BC; &longs;it ergo GE pon­<lb/>dus totius pilæ BACL vnà cum pondere adiuncto F <lb/>in aere trutinato; GH verò &longs;it pondus eiu&longs;dem ag­<lb/>gregati BALCF intra <expan abbr="aquã">aquam</expan> examinatum. </s> <s id="s.001300">quia verò, <lb/><arrow.to.target n="marg337"/><lb/>ex Archimede, pondus corporis intra aquam demer&longs;i <lb/>imminuitur pro quantitate <expan abbr="põderis">ponderis</expan> molis aquæ quæ <lb/>æqualis &longs;it integro corpori demer&longs;o, igitur differen­<lb/>tia HE erit pondus molis aquæ PQ, quæ æqualis &longs;it <lb/>corpori demer&longs;o BALCF. po&longs;tea pilam plumbeam <lb/>BC eodem modo clau&longs;am violentèr malleo contudi, <lb/>vt ad minus &longs;patium BLC redigeretur; <expan abbr="manife&longs;tũ">manife&longs;tum</expan> <lb/>e&longs;t con&longs;tipatum re&longs;trictumque &longs;ui&longs;&longs;e aerem inclu&longs;um <lb/>vt nimirùm portio aeris A inclu&longs;a &longs;it in eodem &longs;pa­<lb/>tio, quod occupabat reliqua aeris portio L. denuò <lb/>igitur pilam plumbeam contu&longs;am BLCF ponderaui <lb/>in aere, & in aqua, atque in aere pondus eius fuit <lb/>GN maius, quàm GE, eius verò pondus in aqua fuit <lb/>GM, quaproptèr ponderum differentia MN erit gra­<lb/>uitas molis aquæ RS quæ æqualis &longs;it corpori demer­<lb/>&longs;o BLCF, & &longs;ecetur EO æqualis MN. </s> <s id="s.001301">Quia verò aer <lb/>AL in ip&longs;omet aere <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> grauitatis nil grauitat ob <lb/>æquilibrium, igitur pondus GE tribui debet plum­<lb/>bo BCF, cùm verò pila contu&longs;a in aere magis graui­<lb/>tet pro men&longs;ura nimirùm GN, tunc quoque tota gra­<lb/>uitas GE plumbo eidem tribui debet, at exce&longs;&longs;us <lb/>grauitatis EN nullo pacto tribui pote&longs;t portioni ae-<pb pagenum="253" xlink:href="010/01/261.jpg"/><arrow.to.target n="marg338"/><lb/>reæ L, quæ priùs æquè rara erat cum &longs;uo ambient&etail;, <lb/>&longs;ed tribui de bet portioni aereæ A, quæ in&longs;inuata e&longs;t <lb/>in eodem &longs;patio L, in quo reliqua pars aeris contine­<lb/>batur; Po&longs;tea quia HE e&longs;t pondus molis aquæ PQ, <lb/>quæ &etail;qualis e&longs;t moli BA <lb/><figure id="id.010.01.261.1.jpg" xlink:href="010/01/261/1.jpg"/><lb/>LCF, & EO e&longs;t <expan abbr="põdus">pondus</expan> mo­<lb/>lis aquæ RS æqualis inte­<lb/>græ pilæ contu&longs;æ BLCF; i­<lb/>gitur differentiale pondus <lb/>HO pertinet ad <expan abbr="aquã">aquam</expan> VX, <lb/><expan abbr="n&etilde;pè">nempè</expan> ad <expan abbr="differ&etilde;tiã">differentiam</expan> aqu&etail; PQ <lb/>&longs;upra RS, qu&etail; æqualis e&longs;t <lb/>aeri A in&longs;inuato intra <expan abbr="&longs;pa-tiũ">&longs;pa­<lb/>tium</expan> L; igitur habemus duo <lb/>corpora inter &longs;e æqualia mole <expan abbr="n&etilde;pè">nempè</expan> aqua VX, & aer <lb/>A, horum autem pondera ab&longs;oluta, ex Archimed&etail;, <lb/><arrow.to.target n="marg339"/><lb/>eamdem proportionem habent, quam eorum gra­<lb/>uitates in &longs;pecie; igitur pondus HO ad OM &longs;iu&etail; <lb/>ad ei æquale EN, eamdem <expan abbr="proportion&etilde;">proportionem</expan> habet, <expan abbr="quã">quam</expan> <lb/>grauitas in &longs;pecie ip&longs;ius aquæ ad grauitatem &longs;pecifi­<lb/>cam aeris, reperta autem fuit EN grauitas molis ae­<lb/>ris A ob contu&longs;ionem in&longs;inuati intra L, igitur nece&longs;­<lb/>&longs;ariò pondus HO tribui debet aqueæ moli VX. &longs;i po­<lb/>&longs;tea &longs;umatur moles aquæ Y ad quam aquæ moles VX <lb/>eamdem proportionem habeat, quam HO ad OM, <lb/>patet eamdem grauitatem habere aquam Y ac aer A. <lb/><!-- KEEP S--></s> <s id="s.001302">His demon&longs;tratis referam iam experimentum factum <lb/>in no&longs;tra Academia experimentali Medicea; pon­<lb/>dus in aere totius pilæ, & aeris BALCF fuit GE gra-<pb pagenum="254" xlink:href="010/01/262.jpg"/><arrow.to.target n="marg340"/><lb/>norum 31616. pondus verò <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> in aqua fuit GH <lb/>gran. <!-- REMOVE S-->4272, eorum differentia HE fuit gran. <!-- REMOVE S-->27344. <lb/>Præterea pondus totius pilæ contu&longs;æ GN fuit gra­<lb/>norum 31623. in aere, in aqua verò fuit GM gran. <lb/><!-- REMOVE S-->12508, ergò eorum differentia &longs;cilicèt pondus MN, <lb/>vel EO fuit granorum 19115. pondus EN differen­<lb/>tiale inter GE, & GN fuit gran. <!-- REMOVE S-->7. pondus verò dif­<lb/>ferentiale HO erit granorum 8229. quare ex regula <lb/>aurea vt pondus aeris granor. </s> <s id="s.001303">7. ad pondus molis a­<lb/>quæ ei æqualis gran. <!-- REMOVE S-->8229. ita &longs;e habet 1. ad 1175. <lb/>cum 4. &longs;ept. </s> <s id="s.001304">itaque vna particula aquæ æquè ponde­<lb/>rabit, ac æ&longs;tiui aeris particulæ 1175. cum 4. &longs;ept. <lb/></s> <s id="s.001305">quarum &longs;ingulæ æquales &longs;int mole ip&longs;i aquæ. </s> </p> <p type="margin"> <s id="s.001306"><margin.target id="marg336"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001307"><margin.target id="marg337"/>De infiden­<lb/>tibus humi­<lb/>do l. <!-- REMOVE S-->1. pr. <!-- REMOVE S-->7.</s> </p> <p type="margin"> <s id="s.001308"><margin.target id="marg338"/>Cap. 5. de ae­<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="margin"> <s id="s.001309"><margin.target id="marg339"/>Ibidem.<!-- KEEP S--></s> </p> <p type="margin"> <s id="s.001310"><margin.target id="marg340"/>Cap. 5. de ae<lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001311">Et in hac operatione facillima, quæ fallacijs, ac <lb/>difficultatibus minimè obnoxia e&longs;&longs;e videtur, &longs;ummo <lb/>compendione dùm grauitas ip&longs;ius aeris, &longs;ed etia&mtail; <lb/>proportio, quam habet ad aquæ grauitatem vnic&atail; <lb/>operatione elicitur. </s> </p> <p type="main"> <s id="s.001312"><emph type="center"/>PROP. CXXI.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001313"><emph type="center"/><emph type="italics"/>Distantia inter maximam aeris con&longs;trictionem, & eiu&longs;dem <lb/>maximam dilatationem est vt<emph.end type="italics"/> 1. <emph type="italics"/>ad<emph.end type="italics"/> 2000. <lb/><emph type="italics"/>ferè.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001314">TAndem ex no&longs;tris experimentis deducitur ma­<lb/><arrow.to.target n="marg341"/><lb/>xima aeris dilatatio. </s> <s id="s.001315">Suppo&longs;ito enim quòd in <lb/>catapulta pneumatica aer ad <expan abbr="decimã">decimam</expan> &longs;patij eius par­<lb/>tem redigatur, quia &longs;upra, ex no&longs;tro experimento, de­<lb/>duximus aerem rarefieri vt &longs;patium expleat centies, <pb pagenum="255" xlink:href="010/01/263.jpg"/><arrow.to.target n="marg342"/><lb/>& octuagies maius, quàm priùs, quia verò hic aer <lb/>communis &longs;tringi conden&longs;arique pote&longs;t violenter v&longs;­<lb/>que ad decimam eius partem, vel decimam quintam. <lb/></s> <s id="s.001316">igitur di&longs;tantia inter <expan abbr="maximã">maximam</expan> aeris den&longs;itatem, & <lb/>ampli&longs;&longs;imam eius expan&longs;ionem, aut erit 1800. aut <lb/>2700. <expan abbr="ead&etilde;">eadem</expan> proximè, quæ à Mer&longs;enno po&longs;ita fuerat. </s> </p> <p type="margin"> <s id="s.001317"><margin.target id="marg341"/>Prop. 105.</s> </p> <p type="margin"> <s id="s.001318"><margin.target id="marg342"/>Cap. 5. de ae <lb/>ris grauitate <lb/>æquilibrio, <lb/>&longs;tructura, & <lb/>vi elateri&atail; <lb/>eius.</s> </p> <p type="main"> <s id="s.001319"><emph type="center"/>PROP. CXXII.<emph.end type="center"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.001320"><emph type="center"/><emph type="italics"/>Aer in naturali eius con&longs;trictione remota omni violentiæ <lb/>raris&longs;imus e&longs;t, & &longs;patium occupat bis millies maius <lb/>quam in &longs;tatu maximæ eius violentæ constri­<lb/>ctionis, quæ &longs;i remoueatur &longs;pontè, & in­<lb/>genti vi ad <expan abbr="pristinã">pristinam</expan> natiuam rari­<lb/>tatem redigitur.<emph.end type="italics"/><emph.end type="center"/></s> </p> <p type="main"> <s id="s.001321">QVia verò experientia con&longs;tat aerem dilatari <lb/>quidem <expan abbr="&longs;põte">&longs;ponte</expan> &longs;ua, & non &longs;ine impetu, & cele­<lb/>ritate maxima, & è contrà <expan abbr="numquã">numquam</expan> &longs;ponte con&longs;trin­<lb/>gi conden&longs;arique videmus, &longs;ed &longs;emper hoc efficitur <lb/>ab aliqua violentia externa, hinc cogimur a&longs;&longs;erer&etail; <lb/>aerem habere virtutem quamdam ela&longs;ticam, qua ni­<lb/>mirùm quotie&longs;cumque violentiam con&longs;trictiuam pa­<lb/>titur, tunc quidem re&longs;ilire vehementerque vibrar&etail; <lb/>&longs;e&longs;e dilatando po&longs;&longs;e; hoc autem con&longs;tat <expan abbr="lucul&etilde;to">luculento</expan> ex­<lb/>perimento in ip&longs;a catapulta pneumatica, in qua aer <lb/>magna vi inclu&longs;us in eius cauitatem po&longs;tea amot&atail; <lb/>valuula tanta violentia ruit, erumpitque, vt pila&mtail; <lb/>plumbeam, &longs;eù telum impellat proijciatque, vt i&ntail; <lb/>magna di&longs;tantia tabulam oppo&longs;itam &longs;atis cra&longs;&longs;a&mtail; <pb pagenum="256" xlink:href="010/01/264.jpg"/><arrow.to.target n="marg343"/><lb/>di&longs;rumpat, atque terebret: hoc autem nulla ration&etail; <lb/>fieri po&longs;&longs;et, ni&longs;i aer haberet vim, & facultate&mtail; <lb/>ingentem &longs;e&longs;e dilatandi, & amplius &longs;patiu&mtail; <lb/>occupandi. </s> <s id="s.001322">Cùm igitur iam ex &longs;uperiùs dictis inno­<lb/>tuerit ad quamnam maximam amplitudinem aer ra­<lb/>refieri, dilatarique po&longs;&longs;it, pariterque ad quem gra­<lb/>dum con&longs;tipationis, <expan abbr="conden&longs;ationi&longs;q;">conden&longs;ationi&longs;que</expan> comprimi va­<lb/>leat, & vidimus quòd eadem aeris moles, quæ in &longs;ua <lb/>maxima conden&longs;atione fuit redacta occupabat minus <lb/>quam bis mille&longs;imam partem &longs;patij, quod in maxima <lb/>&longs;ui dilatatione explebat, dicendum e&longs;t aerem in &longs;ua <lb/>naturali con&longs;titutione, ide&longs;t remota omni violenti&atail; <lb/>externa, ampli&longs;&longs;imum &longs;patium exigere, & in tali qui­<lb/>dem <expan abbr="expã&longs;ione">expan&longs;ione</expan> con&longs;eruari in &longs;uprema aeris regione, <lb/>vel in &longs;patio vacuo, at in regione infima aeris propè <lb/>aquam, & terram tunc quidem varijs modis compri­<lb/>mitur, cùm à pondere aeris incumbentis, tùm à pon­<lb/>dere aquæ aut terræ in infimis cauitatibus, aut à qua­<lb/>cumque alia vi motiua ad prædictam maximam con­<lb/>&longs;tipationem redigitur. </s> <s id="s.001323">Sic videmus in in&longs;trumento <lb/>Torricelliano aeris granula ad latera mercurij po&longs;i­<lb/>ta, dum &longs;ursùm a&longs;cendunt quò magis ad mercurij <lb/>&longs;ummitatem <expan abbr="accedũt">accedunt</expan>, eò magis moles aereorum gra­<lb/>nulorum augeri, quou&longs;que propè &longs;patium inane &longs;u­<lb/>premum ingentes &longs;ph&etail;ras expleant: idip&longs;um immi&longs;&longs;a <lb/>ve&longs;ica cyprina propemodum exinanita intra mercu­<lb/>rium ob&longs;eruatur, & clariùs mercurio &longs;uperpo&longs;ita a­<lb/>quæ portione con&longs;picitur in eodem in&longs;trumento, <expan abbr="nã">nam</expan> <lb/>granula aerea intra aquam <expan abbr="cont&etilde;ta">contenta</expan>, quæ hactenùs ob <pb pagenum="257" xlink:href="010/01/265.jpg"/><arrow.to.target n="marg344"/><lb/>&longs;ui exiguitatem inob&longs;eruabilia, & incon&longs;picua fue­<lb/>rant, po&longs;tea facto vacuo, &longs;cilicèt &longs;ublata incumbentis <lb/>aeris compre&longs;&longs;ione, &longs;ubitò con&longs;piciuntur &longs;en&longs;im infla­<lb/>ri, augerique, vt efficiant ampullas grandes per <expan abbr="aquã">aquam</expan> <lb/>a&longs;cendentes, quæ ad confinium &longs;upremum eius per­<lb/>ductæ di&longs;&longs;iliunt, euomuntque aereas particulas intra <lb/>prædictum &longs;patium inane, cùm è contra &longs;i dum actu <lb/>eleuantur ampullæ amplæ illæ aereæ, denuò compri­<lb/>mantur aere &longs;upremè introducto momento con&longs;pi­<lb/>cies aerem denuò ad &longs;tricti&longs;&longs;imum, & incon&longs;picuum <lb/>&longs;patium redigi; Non pote&longs;t igitur negari, ni&longs;i negatis <lb/><expan abbr="euid&etilde;ti&longs;&longs;imis">euidenti&longs;&longs;imis</e