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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Borelli, Giovanni Alfonso</author> <title>De motionibus naturalibus a gravitate pendentibus</title> <date>1670</date> <place>Reggio di Calabria</place> <translator></translator> <lang>la</lang> <cvs_file>borel_demot_010_la_1670.xml</cvs_file> <cvs_version></cvs_version> <locator>010.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="010/01/001.jpg"></pb> <p type="head"> <s id="s.000001"><emph type="center"></emph>DE <lb></lb>MOTIONIBVS <lb></lb>NATVRALIBVS <lb></lb>A GRAVITATE PENDENTIBVS<emph.end type="center"></emph.end></s> </p> <pb xlink:href="010/01/002.jpg"></pb> <p type="main"> <s id="s.000002">[blank] </s> </p> <pb xlink:href="010/01/003.jpg"></pb> <p type="main"> <s id="s.000003"><emph type="center"></emph>DE <lb></lb>MOTIONIBVS <lb></lb>NATVRALIBVS <lb></lb>A GRAVITATE PENDENTIBVS, <lb></lb>LIBER <lb></lb>IO: ALPHONSI BORRELLI <lb></lb>in Academia Piſana Matheſeos profeſſoris.<emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.003.1.jpg" xlink:href="010/01/003/1.jpg"></figure> <p type="main"> <s id="s.000004"><emph type="center"></emph>REGIO IVLIO, <lb></lb>In Officina Dominici Ferri. </s> <s id="s.000005">1670.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000006"><emph type="center"></emph><emph type="italics"></emph>Superiorum permiſſu.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <pb xlink:href="010/01/004.jpg"></pb> <p type="main"> <s id="s.000007">[blank] </s> </p> <pb xlink:href="010/01/005.jpg"></pb> <p type="main"> <s id="s.000008"><emph type="center"></emph>ILLVSTRISS. ET EXCELLENTISS. <lb></lb>DOMINO <lb></lb>D. ANDREÆ <lb></lb>CONCVBLET <lb></lb>MARCHIONI ARENÆ. <lb></lb></s> <s id="s.000009">IO: ALPHONSVS BORRELLVS. S.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000010">S<emph type="italics"></emph>I quid præclara nobilitas laudis, & commendationis mere<lb></lb>tur, id profectò non filijs ſed progenitoribus tribuendum eſſe <lb></lb>Sapientes non nulli cenſuere; proinde qui nobilitatem iactat, de<lb></lb>cus, ac bonum alienum non ſuum commendare dixerunt. </s> <s id="s.000011">Hoc ſa<lb></lb>nè verum eſſet, ſi Parentes alienæ, & minimè naturales eſ<lb></lb>ſent liberorum cauſæ, neque materiam, aut influxum in genera<lb></lb>tione præſtarent: at ſecus res ſe habet, ſicut enim plantarum ger<lb></lb>mina, & fructus ipſis Arboribus, ac Seminibus conformes eſſę, <lb></lb>nec vnquam Roſam è papactere, aut dulcia Poma ex Quercu pro-<emph.end type="italics"></emph.end> <pb xlink:href="010/01/006.jpg"></pb> duci videmus; ſic Parentes noſtros minimè diuerſam, et alteram <lb></lb> ſibi naturam, ac Indolem procreare in liberis conſentaneum eſt; <lb></lb> Indè euenit, quod præclaris et heroicis maioribus prognati ani<lb></lb> mi illam, morumque præſtantiam ut plurimum ſortiantur: his <lb></lb> adde quod cum maior pars, et præcipua humanarum actionum <lb></lb> ab opinione inſita, vel acquiſita, non minus quàm à naturali in<lb></lb> ſtinctu pendeat fit ut nobilibus non leue ſit impoſitum onus ma<lb></lb>iorum veſtigijs inſiſtendi; perſuaſumque ſibi habeant turpe, et <lb></lb> indignum eſſe Illustrium progenitorum eße degeneres, imo putens <lb></lb> præſtantiora ſuorum facinoribus manu, ingenio, ac prudentia ad <lb></lb> ſui, et proſapiæ ſplendorem, atque patriæ utilitatem ſibi eſſe <lb></lb> patranda. </s> <s id="s.000012"> has laudes iure optimo Excellentiſſime Marchio tibi <lb></lb> deberi omnes, uno ore, fatentur; <expan abbr="quipppè">quippe</expan> qui auitam nobilitatem <lb></lb> ante quinque ſæcula inceptam longa ſerie Comitum Arenæ locum <lb></lb> vigeſimum quintum explens, non modo ſuſtines, ſed præclaras <lb></lb> eorum Virtutues ſuperare conatus es: et vt de Illuſtribus illorum <lb></lb> domi, militiæque; rebus geſtis taceam, unum ſolummodo in <lb></lb> præſentia innuere erit opere prætium, curam nimirum ſcientia<lb></lb> rum, et Virorum, qui Philosophiam colere, et nouis inuen<lb></lb> tis illuſtrare profitentur, ex quo, luculento ſanè exemplo du<lb></lb> ctus Aui tui Illuſtriſſimi qui Bernardinum Teleſium ſupra Vul<lb></lb> gum Philoſophantem eximio amore proſecutus, tutela, et pa<lb></lb> trocinio ſuo fouit. </s> <s id="s.000013">Tu ipſe es, qui primus in præclara Vrbe Par<lb></lb> tenopea, mea parente, ſocietatem, ſeu Academiam in tuo Mu<lb></lb> ſeo erexiſti, in qua certis, et indubitatis experimentis non ve<lb></lb> rò inanibus, ac rixoſis diſputatiunculis, Philoſophicas Verita<lb></lb> tes ad Reipublicæ litterariæ bonum, indagarentur; idque ſum<lb></lb> ma Cura, ac Munificentia præſtitiſti, in unum collectis Cla<lb></lb> riſſimis Doctiſſſimiſque Viris, Caramuele, Thoma Cornelio, <lb></lb> <pb xlink:href="010/01/007.jpg"></pb> Franciſco De Andrea, Leonardo à Capua, Luca Antonio Por<lb></lb> tio, innumeriſque aliis; quibus cum me quoque benignè excep<lb></lb> tum, adiunxeris, ne Vacuis manibus accedam, tibi ecce Vir <lb></lb> Excellentiſſime offero hoc meum Opus de Naturalibus Motio<lb></lb> nibus à grauitate pendentibus, quod eſt ſecundum præcedentium <lb></lb> Doctrinam de Animalium motibus, in quo rationes Philoſophi<lb></lb> cæ, quam plurimorum Experimentorum naturalium afferuntur, <lb></lb> quæ Florentiæ in Academia Experimentali Medicea Vidi, pa<lb></lb> riterque accuratiſſime ſunt obſeruata in tua Neapolitana: Tu ſi<lb></lb> quidem, Vir Optimè, in hoc libro aliqua reperies, quæ natura<lb></lb>lem Scientiam, cuius ſanè ſtudio impensè teneris, promouere <lb></lb> valeant, iis fruere, et Vale. </s> </p> <pb xlink:href="010/01/008.jpg"></pb> <p type="main"> <s id="s.000014"><emph type="center"></emph>PROOEMIVM <lb></lb>AD LECTOREM.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000015">HAbes iam, erudite Lector, in hoc Libro de Motionibus Natura<lb></lb>libus à grauitate pendentibus, vna cum præcedenti do Vi Per<lb></lb>cuſſionis ea omnia, quæ præmitti debuerant ad perfectam intelligen<lb></lb>tiam doctrinæ de animalium motibus, exceptis quamplurimis mecha<lb></lb>nicis lemmatibus, quæ ſuis locis deinceps iuxta ſubiecti exigentiam̨ <lb></lb>exponentur. </s> <s id="s.000016">Debeo tamen nonnulla præfari de hoc, & præcedenti <lb></lb>Opere, in quibus multoties afferuntur ſententiæ diuerſæ ab Authorum <lb></lb>magni nominis opinionibus. </s> <s id="s.000017">Hoc tamen ſumma modeſtia, & modera<lb></lb>tione exequutus ſum; quandoquidem ſententias inſector, non autem <lb></lb>authorum nomina, aut famam attingo: quippe qui ſolummodo veri<lb></lb>tatem quæro, ſeruata interim dignitate, & fama clariſſimorum viro<lb></lb>rum: quod conſtat ex eo, quod tunc ſolummodo viuentium autho<lb></lb>rum nomina recenſeo, cum laudandi eos occaſio offertur; cum vero <lb></lb>controuerſiæ agitantur nomina authorum omnino teguntur, ac ſilen<lb></lb>tur; quia verò hac tan religioſa moderatione, & modeſtia effugere non <lb></lb>potui contradicentium mordacitates, ideo viſum eſt denuo pollicerę <lb></lb>me ab inſtituto incepto non dimoueri, nec diſcedere velle, neque op<lb></lb>poſit oribus, ſi qui forſan extiterint, reſponſum vllum apologeticum, & <lb></lb>contentioſum edere velle, ſed tantummodo ſi opus fuerit meam do<lb></lb>ctrinam melius, & apertius declarare, vel corrigere vbi forſan huma<lb></lb>no more lapſus fuero. </s> <s id="s.000018">Vale. </s> </p> <pb pagenum="1" xlink:href="010/01/009.jpg"></pb> <p type="main"> <s id="s.000019"><emph type="center"></emph>DE MOTIONIBVS <lb></lb>NATVRALIBVS <lb></lb>A Grauitate pendentibus.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000020"><emph type="center"></emph><emph type="italics"></emph>LIBER<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000021"><emph type="center"></emph>IO: ALPHONSI BORELLI<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000022"><emph type="center"></emph><emph type="italics"></emph>Motus Corporum ſublunarium in medio fluido fieri, <lb></lb>de quibus hactenus nemo tract auit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000023"><emph type="center"></emph>CAPVT I.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000024">EVidentiſſimum eſt motus corporum <expan abbr="ſub-lunariũ">ſub<lb></lb>lunarium</expan> fieri debere in aliquo ſpatio, <lb></lb>quod minimè impleri & occupari de<lb></lb>bet à corporibus duris, conſiſtentibus, <lb></lb>& omninò continuis, propterea quòd <lb></lb>duo corpora ſe mutuò penetrare nequeunt, igitur <lb></lb>neceſſe eſt vt ſpatium, in quo corpus aliquod moue<lb></lb>ri debet, aut ſit omninò vacuum, vel ſaltem occupe<lb></lb>tur ab aliquo corpore diſtrahibili, & fluido, vel in <lb></lb>particulas ſubdiuiſo, quod nimirum facilè expelli <lb></lb>poſſit è ſuo loco, vt ſubintranti corpori, quod moue<lb></lb>ri debet locum cedat. </s> <s id="s.000025">ab hiſce fluidis corporibus re<lb></lb>gio iſta terram ambiens occupatur, vt ab aqua, aere, <lb></lb>& igne, in quibus fiunt motiones corporum ſublu<lb></lb>narium. </s> </p> <p type="main"> <s id="s.000026">De ipſis porrò naturalibus motionibus corporum, <lb></lb>quę in medio fluido fiunt, ſcilicèt qua ratione, & qua-</s> </p> <pb pagenum="2" xlink:href="010/01/010.jpg"></pb> <p type="main"> <s id="s.000027"><arrow.to.target n="marg1"></arrow.to.target><lb></lb>re corpora varias magnitudines, pondera, & di<lb></lb>uerſas figuras habentia, moueantur maiori, aut mi<lb></lb>nori velocìtate, certa quadam proportione in medio <lb></lb>fluido, nemo (quod ſciam) differuit. </s> <s id="s.000028">Igitur hanc <lb></lb>phyſico-mechanices partem hactenùs deſideratam̨ <lb></lb>exponere, ac ſupplere animus eſt; ſed ne faſtidioſą <lb></lb>repetitione earum rerum, quæ ab alijs tradita ſunt, <lb></lb>lectores de tineam, ſupponam ea omnia, quæ in ele<lb></lb>mentis mechanicis tradita ſunt de natura libræ, vec<lb></lb>tis, trochleæ, & de reliquis ab hiſce inſtrumentis pen<lb></lb>dentibus, eorum que naturam participantibus. </s> <s id="s.000029"><expan abbr="afferã">afferam</expan> <lb></lb>tantummodò aliqua quæ præcipuum vſum habent in <lb></lb>hac doctrina de naturalibus corporum motionibus, <lb></lb>non de omnibus, ſed de ijs ſolum modò, quæ à vi mo<lb></lb>tiua grauitatis pendent. </s> </p> <p type="margin"> <s id="s.000030"><margin.target id="marg1"></margin.target>Cap. 1. Cor<lb></lb>porum mo<lb></lb>tus in medio <lb></lb>fluido fieri.</s> </p> <p type="main"> <s id="s.000031"><emph type="center"></emph><emph type="italics"></emph>De Momentis Grauium conſistentium & fluidorum <lb></lb>in ijſdem fluidis innatantium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000032"><emph type="center"></emph>CAP. II.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000033">SVbtiliſſimè, & præclarè Archimedes egit de inſi<lb></lb>dentibus humido, idipſum poſte a alia methodo <lb></lb>Galileus, & Steuinus demonſtrarunt, cùm veritas in<lb></lb>numeris modis confirmari poſſit, ipſe verò, non ge<lb></lb>nio variandi, nouas earumdem propoſitionum de<lb></lb>monſtrationes via longè diuerſa procedendo, exco<lb></lb>gitaui, & attuli, ſed quia hæ valdè conducunt ad ea <lb></lb>quæ poſterius à nobis explicanda ſunt. </s> <s id="s.000034">at priùs ali<lb></lb>quæ hypotheſes ſunt præmittendæ. <pb pagenum="3" xlink:href="010/01/011.jpg"></pb><arrow.to.target n="marg2"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000035"><margin.target id="marg2"></margin.target>Cap. 1. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000036"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000037">Suppono primò quòd quodlibet corpus, ſiuè den<lb></lb>ſum, ſiuè fluidum, ex ijs quæ globum terra-queum̨ <lb></lb>componunt, graue eſt, exercetque vim ſeù conatum <lb></lb>ſuæ grauitatis, etiam ſi in fluido ſibi aut homogeneo, <lb></lb>aut non, conſtituatur. </s> <s id="s.000038">hoc autem ſuo loco euidentiſ<lb></lb>ſimis rationibus, ac experimentis confirmabitur. </s> </p> <p type="main"> <s id="s.000039"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000040">Secundo loco ſuppono vim, ſeù conatum, quo flui<lb></lb>da nituntur ſeſe vnire ſphæræ terraqueæ, effici per <lb></lb>lineas perpendiculares ad ſuperficiem horizontis. </s> <s id="s.000041">& <lb></lb>hoc patet quia quodlibet graue naturali inſtinctu co<lb></lb>natur ad centrum terræ accedere via breuiſſima, igi<lb></lb>tur directio prædicti motus, ſeù conatus compreſſiuus <lb></lb>efficietur per ſemidiametros eiuſdem terræ, hæ verò <lb></lb>perpendiculares ſunt ad ſuperficiem horizontalem, <lb></lb>quæ ſphæricè ipſam terram comprehendit, igitur ma<lb></lb>nifeſtum eſt quòd motus ſeù conatus compreſſiuus <lb></lb>omnium partium fluidi per lineas ad horizontem per<lb></lb>pendiculares efficitur. </s> </p> <p type="main"> <s id="s.000042"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000043">Tertiò quod libet corpus graue eſt impoſſibile vt <lb></lb>moueatur motu ſpontaneo, & naturali, quando ad <expan abbr="cẽ-trum">cen<lb></lb>trum</expan> telluris minimè approximari poteſt. </s> <s id="s.000044">hoc mani<lb></lb>feſtum eſt quia cùm omnes partes terrenæ vt graues <lb></lb>naturali inſtinctu ad terræ centrum accedere conen-<pb pagenum="4" xlink:href="010/01/012.jpg"></pb><arrow.to.target n="marg3"></arrow.to.target><lb></lb>tur, hocque earum deſiderium expleri minimè poſſit <lb></lb>niſi mediante motu, igitur ceſſante fine neceſſariò <lb></lb>medium quoque ceſſat, ſcilicet quando non poteſt <lb></lb>graue aliquod magis, quàm prius ad terræ centrum <lb></lb>accedere, tunc nequaquam mouebitur. </s> <s id="s.000045">ex quo ſequi<lb></lb>tur vt prædicta corpora quieſcant, quandoquidem ſi <lb></lb>mouerentur, aut deberent à centro telluris recedere <lb></lb>& remoueri, vel lateraliter circumferri, in primo ca<lb></lb>ſu ſequeretur operatio contraria naturali inſtinctui <lb></lb>grauium, quod eſt impoſſibile; in ſecundo verò caſu <lb></lb>efficeretur operatio vanæ, & ſi fruſtratoria, nil enim <lb></lb>graue præterea acquireret cùm non amplius ad terræ <lb></lb>centru accedere poſſet ex hypotheſi, abſurdum verò <lb></lb>eſt atque repugnat naturam operari caſu, & abſque <lb></lb>fine; igitur eſt impoſſibile vt corpora, quæ ad <expan abbr="centrũ">centrum</expan> <lb></lb>terræ accedere nequeunt, vllo pacto moueantur; qua <lb></lb>propter neceſſe eſt vt in eodem ſitu fixè quieſcant in <lb></lb>quo prius degebant. </s> </p> <p type="margin"> <s id="s.000046"><margin.target id="marg3"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000047"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb><arrow.to.target n="marg4"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000048"><margin.target id="marg4"></margin.target>Archimedis <lb></lb>ſuppositio. </s> </p> <p type="main"> <s id="s.000049">Præterea Archimedes ſuppoſuit vt primum prin<lb></lb>cipium per ſe notum, quod eiuſdem fluidi conſiſten<lb></lb>tis, partes quæ ſint continuatę in eodem plano hori<lb></lb>zontali minus preſſæ debeant eijci expellique ſurſum <lb></lb><expan abbr="perpẽdiculariter">perpendiculariter</expan> à partibus eiuſdem fluidi magis <expan abbr="cõpreſſis">com<lb></lb>preſſis</expan>, hoc verò principium, licèt veriſſimum ſit, ha<lb></lb>bet tamen aliquam obſcuritatem, cùm minimè eui<lb></lb>dens ſit, quamobrem partes eiuſdem fluidi poſſint <lb></lb>magis, aut minus comprimi; nec pariter euidenter </s> </p> <pb pagenum="5" xlink:href="010/01/013.jpg"></pb> <p type="main"> <s id="s.000050"><arrow.to.target n="marg5"></arrow.to.target><lb></lb>percipitur quomodo à naturali operatione, deſcen<lb></lb>ſus nempè deorſum, produci debeat operatio <expan abbr="quædã">quædam</expan> <lb></lb>contraria, aſcenſus nimirum alterius partis eiuſdem <lb></lb>fluidi ſcilicet recedendo a centro telluris. </s> <s id="s.000051">erit igitur <lb></lb>operæpretium perſpicuè oſtendere veritatem præ<lb></lb>dictæ operationis, eamque deducere ex principijs <lb></lb>magis notis, & euidentibus. </s> </p> <p type="margin"> <s id="s.000052"><margin.target id="marg5"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000053"><emph type="center"></emph>PROPOSITIO I.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000054"><emph type="center"></emph><emph type="italics"></emph>Grauis ſuſpenſi non ex centro ſuæ grauitatis vna eius pars <lb></lb>ſurſum aſcendit quiæ integrum graue <expan abbr="deorsũ">deorsum</expan> deſcendit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000055">Sit graue AB extenſum, vel compoſitum ex dua<lb></lb>bus partibus in extremitatibus eiuſdem libræ <lb></lb>horizontalis AB diſpoſitis, & commune centrum gra<lb></lb>uitatis earum ſit D. ſuſti<lb></lb><figure id="id.010.01.013.1.jpg" xlink:href="010/01/013/1.jpg"></figure><lb></lb>neatur poſtea, fulciatur<lb></lb>que tota libra ex puncto <lb></lb>C remoto à centro graui<lb></lb>tatis D. dico quòd pars <lb></lb>eius oppoſita B ſurſum̨ <lb></lb>aſcendet per arcum BF, <lb></lb>hac ſolummodo de cauſą <lb></lb>quia integrum graue AB magis, quàm prius ad cen<lb></lb>trum terræ accedit. </s> <s id="s.000056">quia duæ partes graues A & B <lb></lb>exercent ſuam grauitatem & conatum compreſſiuum <lb></lb>in centro communi earum grauitatum D; eſt que <lb></lb>prædictum centrum D remotum à fulcimento ſtabili <lb></lb>C, igitur efformabitur veluti fune-pendulum CD <pb pagenum="6" xlink:href="010/01/014.jpg"></pb><arrow.to.target n="marg6"></arrow.to.target><lb></lb>horizontaliter conſtitutum, ſuſpenſum, & alligatum <lb></lb>in centro C & pondus vniuerſum applicatum eritiņ <lb></lb>centro D extremo fili, vel lineæ CD: ſed penduli na<lb></lb>tura talis eſt vt conetur deorſum ferri per arcum qua<lb></lb>drantis DE circa centrum eius fixum C vſque ad lo<lb></lb>cum infimum E, quod magis ad centrum terræ appro<lb></lb>ximatur, quàm in ſitu horizontali D & patet quòd <lb></lb>vniuerſa hæc operatio neceſſaria, & naturalis eſt de<lb></lb>pendens à deſcenſu totius grauis. </s> <s id="s.000057">& eſt impoſſibilę <lb></lb>vt fune pendulum CD ad in fimum ſitum CE perduca<lb></lb>tur abſque eo quòd libra rigida ſitum perpendicula<lb></lb>rem ad horizontem acquirat, quale eſt GCF, hoc ve<lb></lb>ro minimè acquiri poteſt niſi pars minus grauis libræ <lb></lb>B ſurſum aſcendat per arcum BF, igitur caſus, & de<lb></lb>ſcenſus totius corporis grauis AB à ſitu eleuato D ad <lb></lb>infimum E eſt vera & legitima cauſa aſcenſus corpo<lb></lb>ris grauis B per arcum BF, quod fuerat oſtendendum. </s> </p> <p type="margin"> <s id="s.000058"><margin.target id="marg6"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <figure id="id.010.01.014.1.jpg" xlink:href="010/01/014/1.jpg"></figure> <p type="main"> <s id="s.000059">Patet igitur quod ſim<lb></lb>plex caſus, aut deſcenſus <lb></lb>corporis grauis eſt vera, <lb></lb>& legitima cauſa motus, <lb></lb>& aſcenſus alicuius partis <lb></lb>eius ſurſum, & hoc planè <lb></lb>contingit quotieſcumque <lb></lb>graue vniuerſum ſuſtine<lb></lb>tur ab aliquo eius puncto libræ realis, vel imagina<lb></lb>riæ, it aut efficiatur commotio omnium partium eius <lb></lb>non quidem per lineas rectas inter ſe parallelas, & <lb></lb>horizonti perpendiculares, ſed vertiginoſas, & cir-<pb pagenum="7" xlink:href="010/01/015.jpg"></pb><arrow.to.target n="marg7"></arrow.to.target><lb></lb>culares quales ſunt illæ quæ à fune-pendulis deſcri<lb></lb>buntur, & in prædicto motu vertiginoſo eſt tam ne<lb></lb>ceſſarius, & naturalis aſcenſus partis minus grauis B <lb></lb>per arcum BF quemadmodum neceſſarius eſt lapſus <lb></lb>& deſcenſus totius grauis per arcum DE vſque ad lo<lb></lb>cum infimum E & licet aſcenſus prædictæ portionis <lb></lb>B vulgo cenſeatur motus violentus, nihilominus ſi <lb></lb>perpendatur vertigo, & debita ſituatio corporis gra<lb></lb>uis quatenus naturalis eſt & naturali inſtinctu acqui<lb></lb>ſita, & producta; cùm ſit impoſſibile vt prædicta ſitua<lb></lb>tio debita abſolute conſequatur abſque aſcenſu por<lb></lb>tionis B ſitque verum quoque quod, qui vult finem̨ <lb></lb>velit quoque neceſſe eſt media, quæ ad finem conſe<lb></lb>quendum neceſſaria <expan abbr="sũt">sunt</expan>; hinc rationabiliter inferetur <lb></lb>à vi naturali verè impelli minus graue ſurſum verſus <lb></lb>F, ac proindè concedendum erit aſcenſum per BF <lb></lb>naturalem prorſus eſſe vel potius in eadem naturali <lb></lb>operatione includi debere violentiam motus præ<lb></lb>dicti aſcenſus; ſed vtcunque ſit ſufficit nobis vt præ<lb></lb>dicta operatio ſit neceſſaria, ſit que prorſus impoſſibi<lb></lb>le vt aliter contingat; cæteri verò eam vocent ſiue na<lb></lb>turalem, ſiue violentam ad eorum libitum. </s> </p> <p type="margin"> <s id="s.000060"><margin.target id="marg7"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000061"><emph type="center"></emph>PROP. II.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000062"><emph type="center"></emph><emph type="italics"></emph>Idipſum verificatur in fluidis contentis in <lb></lb>eodem ſiphone circulari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000063">PRæterea vt duo corpora in extremitatibus libræ <lb></lb>conſtituantur non ſemper eſt neceſſe vt corpora <pb pagenum="8" xlink:href="010/01/016.jpg"></pb><arrow.to.target n="marg8"></arrow.to.target><lb></lb>grauia A & B affixa ſint virgæ alicui rigidæ & conſi<lb></lb>ſtenti vt eſt ACB poteſt enim concipi canalis circu<lb></lb>laris AGBF qui ſi repleatur aqua vel quolibet alio <lb></lb><figure id="id.010.01.016.1.jpg" xlink:href="010/01/016/1.jpg"></figure><lb></lb>fluido liquore cuius pars dex<lb></lb>tera FAG grauior ſit quam re<lb></lb>liqua fluidi pars GBF ſcilicet <lb></lb>ſi fluidum FAG fuerit hydrar<lb></lb>girum, FBG verò aqua com<lb></lb>munis, tunc pariter efficietur <lb></lb>libra, & centrum grauitatis <lb></lb>amborum liquorum non iace<lb></lb>bit in diametro FCG perpendiculari ad horizontem, <lb></lb>ſed vltra ipſum inter C & A, ſcilicet in puncto aliquo <lb></lb>D tunc pariter erit centrum totius magnitudinis flui<lb></lb>di ipſum C & in hoc præciſe fiet ſuſpenſio totius flui<lb></lb>di, quia circa ipſum efficiuntur duo motus contrarij, <lb></lb>nempe deſcenſus fluidi A & aſpenſus alterius oppoſi<lb></lb>ti fluidi B cùm igitur centrum communis grauitatis D <lb></lb>duorum fluidorum diſtet à centro ſuſpenſionis C effi<lb></lb>cietur quoque pendulum, quod circulari motu ex<lb></lb>curret per arcum DE. </s> </p> <p type="margin"> <s id="s.000064"><margin.target id="marg8"></margin.target>Cap. 3. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000065"><emph type="center"></emph>PROP. III.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000066"><emph type="center"></emph><emph type="italics"></emph>Organum in quo videtur motus perpetuus effici <lb></lb>poſſe exponitur, atque eius defectus, <lb></lb>& inſufficientia detegitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000067">ET hic breui & non omnino ſuperuacanea digreſ<lb></lb>ſione indicabo impoſſibilitatem motus perpetui <pb pagenum="9" xlink:href="010/01/017.jpg"></pb><arrow.to.target n="marg9"></arrow.to.target><lb></lb>in machina quæ tantam veriſimilitudinis apparenti<lb></lb>am habere videtur, vt quilibet iuraret tali organo <lb></lb>motum continuari facilè poſſe, huiuſmodi ſpeculatio<lb></lb>nem & organi ſtructuram mihi olim communicauit <lb></lb>amicus optimus Clemens ſeptimius Galilei alumnus. <lb></lb></s> <s id="s.000068">is ſanè cum contemplaret tympana verſatilia ſeu ro<lb></lb>tas illas quibus nauiculæ trahuntur Piſis & in Belgio <lb></lb>ab vno canali ad alium à vi vnius hominis, qui inter<lb></lb>nam eius periphæriam, accliuem calcando eam̨ <lb></lb>reuoluit, vt quæ à canibus eodem tympano in coqui<lb></lb>nis verua rotantur, cogitauit eodem modo <expan abbr="tympanũ">tympanum</expan> <lb></lb>efformari poſſe in quo <lb></lb><figure id="id.010.01.017.1.jpg" xlink:href="010/01/017/1.jpg"></figure><lb></lb>perpetuò medietas eius <lb></lb>ſiniſtra à fluido corporę <lb></lb>grauiori quam medietas <lb></lb>dextra occupari poſſet. </s> <s id="s.000069">vt <lb></lb>in appoſito ſchematę. <lb></lb></s> <s id="s.000070">ſit tympanum æreum AF <lb></lb>BG comprehenſum à ſu<lb></lb>perficie curua cylindrica ærea & à duabus laminis <lb></lb>planis circularibus inter ſe parallelis optimè læuiga<lb></lb>tis & cum illa coaptatis conglutinatiſque, verùm in<lb></lb>tra tympani cauitatem collocetur lamina plana FCG <lb></lb>quæ vſum diaphragmatis præſtet & medietas cylin<lb></lb>dri FCGA aqua ver hydrargiro repleatur, reliquą <lb></lb>verò medietas BFCG oleo velaere oppleta ſit; lami<lb></lb>na verò FCG axi HC annexa & ferruminata intrą <lb></lb>tympanum & circa axim fixum C manubrio aliquo <lb></lb>H fixè retineri & reuolui poſſit, hac lege vt exactè <pb pagenum="10" xlink:href="010/01/018.jpg"></pb><arrow.to.target n="marg10"></arrow.to.target><lb></lb>tangat ſuperficies internas ambarum baſium plana<lb></lb>rum & cauam ſuperficiem curuam eiuſdem tympani: <lb></lb>oportet autem vt ad inſtar epiſtomij exactiſſimè dia<lb></lb>phragma illud reuolutum abſque vlla rima occludat <lb></lb>egreſſumque impediat aquæ vel mercurio in ſemicy<lb></lb>lindro FAG contento, remanente reliquo ſpatio G <lb></lb>BF aere, vel oleo oppleto, ſitque præterea moles to<lb></lb>tius tympani ſuſpenſa in ipſo axi C aflixo duobus ful<lb></lb>cris vt liberè circumuolui tympanum poſſit in plano <lb></lb>perpendiculari ad horizontem; tunc ſi vi manus ma<lb></lb>nubrium H eique annexum diaphragma FCG perpe<lb></lb>tuò in ſitu verticali ad horizontem retineretur, pro<lb></lb>culdubio (dicèbat amicus) haberemus in tali caſu li<lb></lb>bram radiorum æqualium perpetuam imaginariam <lb></lb>ACB quæ ab inæqualibus ponderibus premeretur, <lb></lb>ſcilicèt à pondere emiſphærij mercurialis vel aquei <lb></lb>FAG radius CA grauaretur, dum oppoſitus radius C <lb></lb>B à leuiori pondere olei, vel aeris deprimeretur. </s> <s id="s.000071">& <lb></lb>quia horum inæqualium ponderum centrum grauita<lb></lb>tis ſemper in aliquo puncto D intercepto inter C & <lb></lb>A caderet, igitur ſemper libra AB flecti deberet de<lb></lb>orſum ad partes A, vel potius conſtitueretur pendu<lb></lb>lum horizontale CD ſuſpenſum in centro C & ideò <lb></lb>pendulum deſcendere deberet per arcum DE; quią <lb></lb>verò fluidum grauius FAG de primi non poſſet ob im<lb></lb>pedimentum diaphragmatis FCG in ſitu verticali à <lb></lb>virtute manus retenti, ſequeretur vt vniuerſum ſe<lb></lb>micylindricum mercurij comprimendo & calcando <lb></lb>curuam ſuperficiem tympani AG, quæ volubilis eſt <pb pagenum="11" xlink:href="010/01/019.jpg"></pb><arrow.to.target n="marg11"></arrow.to.target><lb></lb>eam impelleret, proindeque deorſum conuerti debe<lb></lb>ret ab A verſus G cum à nullo retinaculo impediatur, <lb></lb>igitur ſemper reuolui poſſet tympanum ab A verſus <lb></lb>G quia ſemper perſeueraret eadem cauſa vertiginis <lb></lb>ſcilicet perpetuò conſeruaretur pendulum CD in ſitu <lb></lb>horizontali, & ideò ſemper premeret & calcaret tym<lb></lb>pani ſuperficiem AG; quapropter tali artificio con<lb></lb>ſequi poſſe videtur motus perpetuus prædicti tym<lb></lb>pani. </s> </p> <p type="margin"> <s id="s.000072"><margin.target id="marg9"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000073"><margin.target id="marg10"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000074"><margin.target id="marg11"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000075">Hoc, vt dixi, tantam veriſimilitudinem præſefer<lb></lb>re videtur vt nemo ex pluribus amicis quibus hoc ar<lb></lb>tificium communicaui fallaciam in eo latere ſuſpica<lb></lb>tus fuerit, nihilominus licèt ego, nun quam ad praxim <lb></lb>hoc artificium reducere curauerim, non vereor tamen <lb></lb>abſolutè pronunciare motus perpetuitatem hac via <lb></lb>conſe qui non poſſe, quia nimirum perſuadere mihi <expan abbr="nõ">non</expan> <lb></lb>valeo grauia corpora moueri vnquam ſponte debere, <lb></lb>quando nè pilum quidem magis, quàm prius <expan abbr="deſcẽ-dere">deſcen<lb></lb>dere</expan> valent atque ad centrum terræ accedere neque<lb></lb>unt: cum itaque centrum grauitatis communis D am<lb></lb>borum fluidorum ſemper <lb></lb><figure id="id.010.01.019.1.jpg" xlink:href="010/01/019/1.jpg"></figure><lb></lb>in eodem plano horizon<lb></lb>tali ABCD retineatur ac <lb></lb>ſiſtatur mihi omninò im<lb></lb>poſſibile videtur vt rotą <lb></lb>ſiue tympanum AGBF <expan abbr="cõ-uertatur">con<lb></lb>uertatur</expan> ad partes A ver<lb></lb>ſus G. </s> <s id="s.000076">Itaque licet <expan abbr="centrũ">centrum</expan> <lb></lb>grauitatis communis D diſtet à centro ſixo vertiginis <pb pagenum="12" xlink:href="010/01/020.jpg"></pb><arrow.to.target n="marg12"></arrow.to.target><lb></lb>C & proinde pendulum horizontale conſtituat; ta<lb></lb>men aio ipſum retineri ſuſpendique à vi manus, quæ <lb></lb>diaphragma FG retinet ne conuertatur à vi ponderis <lb></lb>in centro D operantis, non ſecus ac ſi <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb></lb>aliquod CD à ſubiecta manu ſuſpenſum deorſum fer<lb></lb>ri non poſſet per arcum DE. & licèt fune-pendulum <lb></lb>CD in caſu noſtro non ſit quid continuum & <expan abbr="alligatũ">alligatum</expan> <lb></lb>centro C nihilominus perindè ſe habet, cum eius co<lb></lb>natus fiat per arcum DE eo modo præcisè, ac ſi cen<lb></lb>tro C alligatum fuiſſet; ille verò qui prohibet deſcen<lb></lb>ſum corporis grauis D, quod ſolummodo moueri per <lb></lb>arcum DE poteſt, neceſſariò impedit operationem̨ <lb></lb>eius loco motiuam, ideoque fluidum FAG cum omni<lb></lb>nò quieſcat, non poterit impellere, & conuerterę <lb></lb>tympanum; nullo enim modo capi poteſt proiectum <lb></lb>impelli ab eo corpore quod omninò in quiete conſi<lb></lb>ſtit, nam ſemper proijciens & impellens impetu & <lb></lb>motu locali affectum ſit oportet ad hoc, vt proyecto <lb></lb>gradum impetus imprimere valeat, cum igitur hy<lb></lb>drargyrum FAG omninò iners ſit & motu locali care<lb></lb>at, videtur omninò impoſſibile vt proiecto ſcilicet <lb></lb>tympano gradum aliquem impetus imprimere queat, <lb></lb>proinde que tympanum non transferetur locali motu, <lb></lb>quare tali artificio motus vertiginis eius nedum con<lb></lb>tinuari perpetuò non poterit, ſed neque motum in<lb></lb>coabit. </s> <s id="s.000077">Sed relicta digreſſione ad rem noſtram redeo. <pb pagenum="13" xlink:href="010/01/021.jpg"></pb><arrow.to.target n="marg13"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000078"><margin.target id="marg12"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000079"><margin.target id="marg13"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000080"><emph type="center"></emph>PROP. IV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000081"><emph type="center"></emph><emph type="italics"></emph>In canali seu ſiphone habente duo brachia directa, & <lb></lb>perpendiculariter eleuata ad horizontem, fluidi <lb></lb>in eo deſcendentis centrum grauitatis cur<lb></lb>uo itinere per lineam parabolicam <lb></lb>deſcendit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000082">IN ſiphone TFGV ſint duo canales TF & GV pa<lb></lb>ralleli inter ſe, & erecti perpendiculariter ad ba<lb></lb>ſim FG, & ad horizontem, & quilibet eorum æquè <lb></lb>craſſus ſit; capacitas verò portionis cylindri TF ſu<lb></lb>pra horizontalem per V eductam vt eſt TA in primo <lb></lb>caſu, & TC in ſecundo, ſit æqualis <lb></lb><figure id="id.010.01.021.1.jpg" xlink:href="010/01/021/1.jpg"></figure><lb></lb>capacitati GV, quæ ſecetur iņ <lb></lb>quotcumque partes æquales à qua <lb></lb>ternario menſuratas in X, Y, Z, I, <lb></lb>L, 2, & puncta A, B, C, D, E, ſint <lb></lb>centra grauitatum cylindrorum T <lb></lb>F, XF, YF, ZF, & AF, vel CF, pa<lb></lb>riterque H, I, K, L ſint centra gra<lb></lb>uitatum cylindrorum GI, GL, G2, <lb></lb>GV, & quia centra grauitatum A, <lb></lb>& B, bifariam ſecant cylindros T <lb></lb>F, XF, ergo TF ad XF ſe habet vt <lb></lb>AF, ad BF, & per conuerſionem̨ <lb></lb>rationis, & permutando TF ad AF <lb></lb>eamdem rationem habet, quàm TX ad AB, quarę <lb></lb>AB ſemiſſis eſt ipſius TX, non ſecus ac HG mediatas <pb pagenum="14" xlink:href="010/01/022.jpg"></pb><arrow.to.target n="marg14"></arrow.to.target><lb></lb>eſt cylindri IG, intelligatur aqua primò eleuari iņ <lb></lb>ſitu T & deprimi in dextro canali in G, & hinc eleua<lb></lb>ta aqua ad I deſcendat à T ad X coniungantur quę <lb></lb>duæ rectæ lineæ AG, & BH ſe ſecantes in M, eritque <lb></lb>punctum Min horizontali EL conſtitutum, propterea <lb></lb>quod duo cylindri aquæ AB, & HG æquales ſunt in<lb></lb>ter ſe, cum ſemiſſes ſint cylindrorum æqualium TX & <lb></lb>IG, ergo altitudo AB ad HG eſt vt eiuſdem cylindri <lb></lb>baſis H ad baſim A: eadem ratione AE ad LG erit vt <lb></lb>baſis H ad <expan abbr="basĩ">basim</expan> A quare altitudo AE ad LG erit vt AB <lb></lb>ad HG, <expan abbr="sũq;">sunque</expan> duæ rectæ lineæ AE & GL <expan abbr="perpẽdicula">perpendicula</expan> <lb></lb>res ad <expan abbr="horizontalẽ">horizontalem</expan> FG, vel EL, & ideò inter ſe paral<lb></lb>lelæ, ergo ob ſimilitudinem triangulorum vt AM ad <lb></lb>MG ita erit BM ad MH, nec non EM ad ML, & ideo <lb></lb>rectæ AG, BH, & EL ſe mutuo ſecabunt in eodem̨ <lb></lb>puncto M. poſtea vt moles aquæ XBF vnà cum GHI <lb></lb>ad molem aquæ IHG ita fiat diſtantia HB ad BQ, & <lb></lb>diuidendo, vt moles aquæ XBF ad GHI ita erit di<lb></lb>ſtantia HQ ad QB, ideoque ex elementis mechanicis <lb></lb>punctum Q erit centrum grauitatis aquæ XBF vnà <lb></lb>cum GHI. quando verò aqua erat in ſummitate T & <lb></lb>canalis GLV omninò exhauſtus erat, tunc quidem̨ <lb></lb>centrum grauitatis totius aquæ TAF perſiſtens iņ <lb></lb>puncto A medio eiuſdem canalis perindè operare<lb></lb>tur ac ſi ſuſpenſus fuiſſet cylindrus èx puncto A: de<lb></lb>preſſa poſtmodum aqua vſque ad Y & eleuata vſque <lb></lb>ad L in oppoſito canali, denuo centrum grauitatis re<lb></lb>pertum prædictæ aquæ exiſtet in puncto R & tandem <lb></lb>depreſſa aqua vſque ad A in primo caſu & vſque ad <pb pagenum="15" xlink:href="010/01/023.jpg"></pb><arrow.to.target n="marg15"></arrow.to.target><lb></lb>Y in ſecundo & ſubleuata vſque ad V; tunc quidem̨ <lb></lb>centrum grauitatis prædictæ aquæ horizontaliter <expan abbr="cõ-ſtitutæ">con<lb></lb>ſtitutæ</expan> præcisè incidet in <expan abbr="cẽtro">centro</expan> ſuſpenſionis M, prop<lb></lb>terea quòd vt baſis V ad baſim A ſeù vt cylindrus a<lb></lb>queus GLV ad equè altum cy<lb></lb><figure id="id.010.01.023.1.jpg" xlink:href="010/01/023/1.jpg"></figure><lb></lb>lindrum AEF in primo caſu vel <lb></lb>ad CEF in ſecundo, ita fuit reci<lb></lb>procè diſtantia EM ad ML. o<lb></lb>ſtendendum modò eſt punctą <lb></lb>A, Q, R, S, M in eadèm linea pa<lb></lb>rabolica eſſe. </s> <s id="s.000083">quia moles aquæ <lb></lb>TX æqualis eſt æquæ moli GH <lb></lb>I, ergo, XBF vnà cum GHI æ<lb></lb>qualis eſt moli aqueæ TAF; e<lb></lb>rat verò moles aquæ XBF vnà <lb></lb>cum GHI ad GHI vt linea HB <lb></lb>ad BQ ſeu (ducta QN parallel<lb></lb>là AE) vt LE ad EN, ergo FAT <lb></lb>ad TX atque ſemiſſis illius FA <lb></lb>ad huius ſemiſſem AB eamdem <lb></lb>proportionem habebit quam̨ <lb></lb>LE ad EN, eſt verò EA ad AF vt MA ad AG, ſeù vt <lb></lb>ME ad EL, ergo ex æqualitate ordinata EA ad AB <lb></lb>eamdem proportionem habebit quam ME ad EN, & <lb></lb>per conuerſionem rationis EA ad EB erit vt EM ad <lb></lb>MN, ſeù vt EB ad NQ, erunt igitur tres continuæ pro <lb></lb>portionales EA, EB, & NQ in eadem ratione quam̨ <lb></lb>habet EM ad MN, quare quadratum ex EM ad qua<lb></lb>dratum ex MN eam proportionem habebit, quam̨ <pb pagenum="16" xlink:href="010/01/024.jpg"></pb><arrow.to.target n="marg16"></arrow.to.target><lb></lb>AE ad NQ: ideoque puncta A & Q ſunt in parabolą <lb></lb>cuius vertex M. quapropter aqua in prædicto ſiphone <lb></lb>dum ad æquilibrium deſcendit mouetur eius centrum <lb></lb>grauitatis in linea parabolica; quod fuerat <expan abbr="oſtẽdẽdũ">oſtendendum</expan>. </s> </p> <p type="margin"> <s id="s.000084"><margin.target id="marg14"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="margin"> <s id="s.000085"><margin.target id="marg15"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000086"><margin.target id="marg16"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000087"><emph type="center"></emph>PROP. V.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000088"><emph type="center"></emph><emph type="italics"></emph>Ijsdem poſitis ſi canales ſiphonis æquèlati angulum conſti<lb></lb>tuentes æquè ad horizontem inclinati fuerint <lb></lb>idipſum demonſtratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000089">SI poſtea ſipho inuerſus eiuſdem amplitudinis an<lb></lb>gularis fuerit, vt nimirum ſemiſſes brachiorum <lb></lb>AF & FL æquè ſint ad horizontem EL inclinata effi<lb></lb>ciatur què hi <lb></lb><figure id="id.010.01.024.1.jpg" xlink:href="010/01/024/1.jpg"></figure><lb></lb>ſoſcelium tri<lb></lb>angulum EF <lb></lb>L & brachij <lb></lb>ſupremi qua<lb></lb>drans EA æ<lb></lb>quale ſit FL, <lb></lb>ſiue FE. dico <lb></lb>denuò quòd <lb></lb>aqua totius <lb></lb>brachij F2. <lb></lb>cuius ſemiſ<lb></lb>ſis eſt AF <expan abbr="dũ">dum</expan> <lb></lb>fluit per canalem FL4 ſurſum & deſcendit per 2 A; <lb></lb>tunc pariter eius centrum grauitatis per parabolam <lb></lb>deorſum fertur. </s> <s id="s.000090">diuiſis æqualibus partibus in punctis <pb pagenum="17" xlink:href="010/01/025.jpg"></pb><arrow.to.target n="marg17"></arrow.to.target><lb></lb>A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatum̨ <lb></lb>partium aquæ eſſe intelligantur vt prius, & ductis ad <lb></lb>horizontalem perpendicularibus AG, BV, CN, DO, <lb></lb>FM, H3, &c. </s> <s id="s.000091">pariterque coniunctis rectis DK, CI, <lb></lb>BH. quia anguli ad L, E æquales ſunt in iſoſcele, & <lb></lb>ſunt quoque anguli recti O & T, & hypothenuſæ DE, <lb></lb>KL ſunt inter ſe æquales, ergo in ſimilibus triangulis <lb></lb>DOE, & KTL latera DO, KT æqualia erunt & recta <lb></lb>OE æqualis erit TL, & addita communi TE erit LE <lb></lb>æqualis OT quæ <expan abbr="nõ">non</expan> minus quàm DK biſſecta erit in <lb></lb>puncto Z, propter æquidiſtantiam & æqualitatem la<lb></lb>terum DO, & TK. ſimiliter reliquæ rectæ lineæ NY <lb></lb>& CI æquales erunt prioribus, & biſſectæ in puncto <lb></lb>P, idemque de reliquis <expan abbr="dicendũ">dicendum</expan> eſt. </s> <s id="s.000092">& quia canales, <lb></lb>& moles aqueæ in eis contentæ AB, & FH, æquales <lb></lb>ſunt, ergo BFH æqualis eſt AF; fiat iam HB ad BQ, <lb></lb>vt BFH ad FH, vel potius vt FA ad AB: quare ſemiſ<lb></lb>ſes antecedentium ad eaſdem conſequentes in <expan abbr="eadẽ">eadem</expan> <lb></lb>ratione erunt, nempè vt EA ad AB, ita erit XB ad B <lb></lb>Q, & per conuerſionem rationis EA ad EB ſeu AG <lb></lb>ad BV, vel GE ad EV, & tandem vt duplum GM ad <lb></lb>duplum MN erit vt BX ad XQ, ſeu vt VX ad XN, <lb></lb>vel vt BV ad QN. igitur erunt tres continuæ propor<lb></lb>tionales AG, BV, & QN in eadem ratione quam ha<lb></lb>bet MG ad MN, quare vt quadratum MG ad quadra<lb></lb>tum MN, ita erit longitudine AG ad QN ideoquę <lb></lb>duo puncta A & Q in parabola erunt. </s> </p> <p type="margin"> <s id="s.000093"><margin.target id="marg17"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000094">Conſtat ergo quòd ſi brachia ſiphonis perpendicu<lb></lb>laria fuerint ad horizontem, ſiuè ambo fuerint eiuſ-<pb pagenum="18" xlink:href="010/01/026.jpg"></pb><arrow.to.target n="marg18"></arrow.to.target><lb></lb>dem latitudinis ſiuè non, ſemper centrum communis <lb></lb>grauitatis fluidi in deſcenſu parabolam deſcribet; ſi <lb></lb>verò brachia ſiphonis æquè inclinata ad horizontem <lb></lb>fuerint, deſcribet eius centrum in deſcenſu parabo<lb></lb>lam quotieſcumque brachia æquè craſſa fuerint. </s> </p> <p type="margin"> <s id="s.000095"><margin.target id="marg18"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000096"><emph type="center"></emph>COROLLARIVM I.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000097">Siverò in eodem angulari ſiphone vnum brachium <lb></lb>dilatatum, alterum verò gracile fuerit, tunc eius <expan abbr="cẽ-trum">cen<lb></lb>trum</expan> in deſcenſu curuam deſcribet hyperbolam̨ <lb></lb>ęmulantem. </s> </p> <p type="main"> <s id="s.000098"><emph type="center"></emph>COROLLARIVM II.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000099">Et tandem ſi vnum brachiorum perpendicularę <lb></lb>fuerit ad horizontem, reliquum verò inclinatum in de<lb></lb>ſcenſu deſcribet commune centrum grauitatis <expan abbr="curuã">curuam</expan> <lb></lb>ellipſim æmulantem. </s> </p> <p type="main"> <s id="s.000100">His præmiſſis declarari debet altera libræ, ſeu ſi<lb></lb>phonis proprietas, in quo centrum grauitatis eius <lb></lb>mouetur non quidem motu obliquo, & curuo, ſed per <lb></lb>lineam rectam ad horizontem perpendicularem, pro <lb></lb>cuius intelligentia præmittendum eſt, quod. </s> </p> <p type="main"> <s id="s.000101"><emph type="center"></emph>PROP. VI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000102"><emph type="center"></emph><emph type="italics"></emph>Duo pondera inæqualia fune non graui circa trochleam reuo<lb></lb>luto ſuſpenſa, dum vnum eorum aſcendit centrum gra<lb></lb>uitatis eorum per lineam <expan abbr="rectã">rectam</expan> ad horizontem <lb></lb>perpendicularem deprimitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="19" xlink:href="010/01/027.jpg"></pb><arrow.to.target n="marg19"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000103"><margin.target id="marg19"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000104">SIt pondus A maius, B verò minus alligata extre<lb></lb>mitatibus funis ADB, qui ſupponatur omninò <lb></lb>grauitate carere, & reuoluatur circa trochleam CDE <lb></lb>conuertibilem circa axim fixum F. patet quòd funes <lb></lb>AC, & BE perpendiculariter ad ho<lb></lb><figure id="id.010.01.027.1.jpg" xlink:href="010/01/027/1.jpg"></figure><lb></lb>rizontem CE prementes, & extenſi <lb></lb>contingunt peripheriam rotæ in ter<lb></lb>minis oppoſitis C, & E eiuſdem dia<lb></lb>metri, ſeu libræ horizontalis, ergo <lb></lb>funes CA, & EB ſunt inter ſe paralle<lb></lb>li; <expan abbr="coniũgatur">coniungatur</expan> poſtea recta linea AB, <lb></lb>ſeceturque bifariam in G, & vt pon<lb></lb>dus A ad B ita fiat diſtantia BI ad IA <lb></lb><expan abbr="manifeſtũ">manifeſtum</expan> eſt (ex mechanicis) punc<lb></lb>tum I eſſe centrum grauitatis com<lb></lb>munis duorum colligatorum ponde<lb></lb>rum A & B, funis enim hanc propor<lb></lb>tionem non alterat, cùm nullius gra<lb></lb>uitatis ſupponatur: aſcendat poſtea <lb></lb>pondus minus B vbicumque ad L, & deprimatur ma<lb></lb>ius pondus A vſque ad K. dico quod ambo in com<lb></lb>muni centro grauitatis deſcendunt circa libræ cen<lb></lb>trum, ſeu fulcimentum ſtabile G motu directo, & per<lb></lb>pendiculari ad horizontem. </s> <s id="s.000105"><expan abbr="coniũgatur">coniungatur</expan> recta lineą <lb></lb>KL quia funis ADB æqualis, imò idem eſt, quàm K <lb></lb>DL, igitur ablato communi ADL erit deſcenſus AK <lb></lb>æqualis aſcenſui BL; quare in triangulis ſimilibus <lb></lb>ob æquidiſtantiam laterum AK & BL homologorum <lb></lb>vt AK ad BL ita erit AG ad GB & ita pariter KML </s> </p> <pb pagenum="20" xlink:href="010/01/028.jpg"></pb> <p type="main"> <s id="s.000106"><arrow.to.target n="marg20"></arrow.to.target><lb></lb>ad M, ſuntque latera AK & BL æqualia interſę <lb></lb>ergo ſe mutuò bifariam ſecabunt rectæ coniungentes <lb></lb>AB, & KL in eodem puncto G; idemque continget <lb></lb>translatis ponderibus in N, & O, & ideo punctum G <lb></lb>erit centrum, ſeu ſtabile <expan abbr="fulcimentũ">fulcimentum</expan> libræ AB quo<lb></lb>modolibet reuolutæ: ducatur tandem per I recta li<lb></lb>nea IP parallela funibus ſecans libras KL, & NO iņ <lb></lb>punctis M, & P patet libras in eadem proportione re<lb></lb>ciproca ſecari in punctis I, M, P, quam habent oppoſi<lb></lb>ta pondera proindeque eadem puncta erunt centrą <lb></lb>grauitatum, earumdem librarum cum ponderibus ap<lb></lb>penſis; quapropter licet minus pondus B aſcendat per <lb></lb>BLO, tamen ambo pondera A, & B in communi <expan abbr="cẽ-tro">cen<lb></lb>tro</expan> grauitatis eorum I ſuſpenſa circa centrum <expan abbr="firmũ">firmum</expan> <lb></lb>G, & in extremo fune-penduli GI deſcendunt noņ <lb></lb>circulari, ſed directo motu perpendiculari ad hori<lb></lb>zontem ab I per M & P, quod fuerat oſtendendum. </s> </p> <p type="margin"> <s id="s.000107"><margin.target id="marg20"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000108"><emph type="center"></emph>PROP. VII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000109"><emph type="center"></emph><emph type="italics"></emph>Id ipſum osten ditur, cùm pondera in peripherijs inæqua<lb></lb>libus, & concentricis eiuſdem trochleæ reuoluuntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000110">SIt trochlea CDE circa axim F conuertibilis, & in <lb></lb>ea ſit alia concentrica circumferentia RSQ, & <lb></lb>funi SQB alligetur pondus B, alij verò funi DEA alli<lb></lb>getur pondus A <expan abbr="ſintq;">ſintque</expan> funes nullius ponderis; oſten<lb></lb>detur, vt in præcedenti, funes EA, & BQ eſſe interſe <lb></lb>parallelos; poſtea <expan abbr="coniũgatur">coniungatur</expan> recta AB, atque vt <expan abbr="põ-dus">pon<lb></lb>dus</expan> A ad B ita reciprocè fiat diſtantia BI ad IA; patet <pb pagenum="21" xlink:href="010/01/029.jpg"></pb><arrow.to.target n="marg21"></arrow.to.target><lb></lb>punctum I eſſe centrum grauitatis communis ponde<lb></lb>rum A, & B (cum funes nullius ponderis <expan abbr="ſupponãtur">ſupponantur</expan>) <lb></lb>deinde reuoluta trochlea <expan abbr="aſcẽdat">aſcendat</expan> pondus B ad L, & <lb></lb>oppoſitum pondus A deſcendat vſque ad K <expan abbr="coniũga-turque">coniunga<lb></lb>turque</expan> recta KL ſecans rectam AB <lb></lb><figure id="id.010.01.029.1.jpg" xlink:href="010/01/029/1.jpg"></figure><lb></lb>in G. dico duo pondera A, & B iņ <lb></lb>communi eorum centro grauitatis <lb></lb>I circa libræ centrum ſtabile G mo<lb></lb>tu directo, & perpendiculari ad <lb></lb>horizontem <expan abbr="deſcẽdere">deſcendere</expan>. </s> <s id="s.000111">quia in tro<lb></lb>chleæ reuolutione <expan abbr="tãtumdẽ">tantumdem</expan> <expan abbr="deſcẽ-dit">deſcen<lb></lb>dit</expan> terminus funis A quanta eſt ex<lb></lb>plicatio funis è rota CDE, & pon<lb></lb>dus B aſcendit quantum funis BQS <lb></lb>circumuoluitur circa rotam QSR <lb></lb>cùmque duæ rotæ concentricè con<lb></lb>nexæ ſimul tempore <expan abbr="reuoluãtur">reuoluantur</expan> cir<lb></lb>ca fixum axim F, ergo deſcenſus AK <lb></lb>ad <expan abbr="aſcẽſum">aſcenſum</expan> BL eamdem proportio<lb></lb>nem habet, quam peripheria CDE ad peripheriam R <lb></lb>SQ, ſeu <expan abbr="eamdẽ">eamdem</expan> proportionem, quam habet radius <lb></lb>FE ad radium <expan abbr="Fq;">Fque</expan> quare in triangulis AGK, & BGL <lb></lb>ſimilibus, ob æquidiſtantiam laterum AK, & BL, erit <lb></lb>AG ad GB vt KG ad GL, ſeu vt AK ad BL; <expan abbr="proindeq;">proindeque</expan> <lb></lb>in eodem puncto fixo G duæ libræ AB, & KL ſe mutuò <lb></lb>ſecabunt in eadem proportione, quam habent motus <lb></lb>eorumdem terminorum, vnde, ex mechanicis, erit <lb></lb>punctum G centrum, & fulcimentum firmum̨ <lb></lb>vtriuſque libræ AB, & KL poſtremò ducatur per I <pb pagenum="22" xlink:href="010/01/030.jpg"></pb><arrow.to.target n="marg22"></arrow.to.target><lb></lb>rectà IM parallela funibus, ſeu perpendicularis ad <lb></lb>horizontem ſecans KL in M planè ſectæ erunt duæ li<lb></lb>bræ prædictæ in I, & M in eadem proportione reci<lb></lb>proca ponderum ſuſpenſorum, ideoque puncta I, & <lb></lb>M erunt centra grauitatum vtriuſque libræ: quare li<lb></lb>cet pondus B aſcendat p BL, tamen verum eſt duo <lb></lb>pondera AB in communi centro grauitatis I ſuſpenſa <lb></lb>circa centrum firmum G, & in termino fune-penduli <lb></lb>GI deſcendere directo motu, & perpendiculari ad <lb></lb>horizontem per IM, & hoc erat oſtendendum. </s> </p> <p type="margin"> <s id="s.000112"><margin.target id="marg21"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000113"><margin.target id="marg22"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000114">Huiuſmodi mechanicæ ſpeculationes maximè <expan abbr="cõ-ferunt">con<lb></lb>ferunt</expan> ad intelligentiam motus corporum in fluidis, <lb></lb>pro cuius declaratione primò conſiderari debet. </s> </p> <p type="main"> <s id="s.000115"><emph type="center"></emph>PROP. VIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000116"><emph type="center"></emph><emph type="italics"></emph>Qua ratione fiat Motus fluidi in ſiphone continuato, <lb></lb>& in ſeipſum reflexo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000117">SIt igitur ſipho ABDG in ſe ipſum reflexus cuius <lb></lb>brachia lateralia BN & GO directa ſint, in<lb></lb>ter ſe parallela, & ad horizontem perpendiculariter <lb></lb>erecta & æquè ampla. </s> <s id="s.000118">includatur poſtea gutta aliqua <lb></lb>mercurij BC, quæ in fiſtulis anguſtis retinetur in eo<lb></lb>dem ſitu collecta, reliqua verò cauitas eiuſdem fiſtulæ <lb></lb>BAGDC repleatur aqua; tunc ductis à punctis B, & <lb></lb>C & à <expan abbr="cẽtro">centro</expan> grauitatis guttæ mercurialis H tribus li<lb></lb>neis rectis parallelis horizonti BG, HI, & CF, & ſec<lb></lb>ta HI bifariàm in L; patet quòd duo grauia, mercu<lb></lb>rius nempe BC, & aqua GF ſuſpenduntur in eadem̨ <pb pagenum="23" xlink:href="010/01/031.jpg"></pb><arrow.to.target n="marg23"></arrow.to.target><lb></lb>libra imaginaria HI, quia hæc duo corpora motibus <lb></lb>contrarijs agitantur ſuſpendunturque ab eadem li<lb></lb>bra horizontali: nec actionem eorumdem corporum <lb></lb>impediunt, vel adiuuant ſupremæ, vel infimæ aquæ <lb></lb>partes; quando quidem aqua AB, <lb></lb><figure id="id.010.01.031.1.jpg" xlink:href="010/01/031/1.jpg"></figure><lb></lb>æquilibratur collaterali AG cùm̨ <lb></lb>ſint homogeneæ & æquè altæ, non <lb></lb>ſecùs infimæ aquæ partes CD & F <lb></lb>E inter ſe æquilibrantur; quare ac<lb></lb>tioni compreſſiuæ mercurij CB, <expan abbr="tã-tummodo">tan<lb></lb>tummodo</expan> contraponitur pondus <lb></lb>aquæ FG in eodem ſitu horizontali <lb></lb>conſtitutæ. </s> <s id="s.000119">fiat iam vt pondus mer<lb></lb>curij CB ad grauitatem aquæ FG <lb></lb>ita reciprocè diſtantia IM ad MH, <lb></lb>quare punctum M erit centrum gra<lb></lb>uitatis duorum corporum BC, & GF, cùmque librą <lb></lb>imaginaria HI fulciatur in puncto L rectæ LK per<lb></lb>pendiculariter horizonti eductæ ex infimo ſitu fiſtu<lb></lb>læ, vbi bifariam libra, & magnitudines fluidæ <expan abbr="ſecã-tur">ſecan<lb></lb>tur</expan>, igitur conſtituitur fune-pendulum LM, & proin<lb></lb>dè, iuxtà leges mechanices, libra flectetur <expan abbr="deſcendẽ-do">deſcenden<lb></lb>do</expan> corpus BC, & aſcendendo aquam FG, & hoc per<lb></lb>ficitur propterea quòd centrum communis grauita<lb></lb>tis M neceſſariò labitur deorſum iuxta penduli na<lb></lb>turam. </s> <s id="s.000120">ſed prædictus motus centri grauitatis M non <lb></lb>eſt circularis, ſed eſt directus ad horizontem <expan abbr="perpẽ-dicularis">perpen<lb></lb>dicularis</expan>, per lineam MQ <expan abbr="nõ">non</expan> ſecùs ac in trochlea <expan abbr="cõ-tingit">con<lb></lb>tingit</expan> vt dictum eſt; huius operationis verò progreſ-<pb pagenum="24" xlink:href="010/01/032.jpg"></pb><arrow.to.target n="marg24"></arrow.to.target><lb></lb>ſus talis eſt, cùm primum cylindrus mercurij CB fer<lb></lb>tur deorsùm transferendo eius centrum H in N, de<lb></lb>nuò comparatur cum alio aquæ cylindro æquali ipſi <lb></lb>FG è regione poſito, cuius centrum grauitatis erit <lb></lb>punctum O, & tunc denuò creatur noua libra <expan abbr="horizõ-talis">horizon<lb></lb>talis</expan> NO ſecta à rectis LP & MQ parallelis ENGO, <lb></lb>in P & Q cuius centrum P, quia denuò partes aquæ <lb></lb>collaterales ſupernæ & infernæ ſibi ipſis æquilibratæ <lb></lb>non adiuuant, neque impediunt duo æqualia corpo<lb></lb>ra mercuriale ex N, & aqueum ex O, quæ ad inuicem <lb></lb>comparantur in eadem libra horizontali, <expan abbr="cumq;">cumque</expan> hæc <lb></lb>à parallelis lineis HN, MQ, & IO in eiſdem rationi<lb></lb>bus diuidatur, perductum erit centrum grauitatis prę<lb></lb>dictorum corporum ad punctum Q, vnde patet de<lb></lb>ſcendiſſe per rectam lineam MQ perpendicularem ad <lb></lb>horizontem, perdurabitque eius deſcenſus, <expan abbr="quouſq;">quouſque</expan> <lb></lb>corpus mercuriale CB ad ſitum infimum fiſtulæ DE <lb></lb>perducatur, quando nimirum eius grauitatis <expan abbr="centrũ">centrum</expan> <lb></lb>H præcisè infimum ſitum K fiſtulæ attinget. </s> </p> <p type="margin"> <s id="s.000121"><margin.target id="marg23"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000122"><margin.target id="marg24"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000123">Nec dicas fictionem eſſe quòd adſit libra horizon<lb></lb>talis directa HI, quæ perpetuò renouetur, nam reue<lb></lb>rà fulciuntur, ſuſtentanturque duo cylindri CB, & G <lb></lb>F à plano aquæ ſubiectæ CF quod quidem, mobile eſt, <lb></lb>cùm cedat deſcenſui mercurij CB & ſuperficies F <lb></lb>eleuetur eodem tempore & pari velocitate circa eius <lb></lb>punctum intermedium, igitur prædicta duo corpora <lb></lb>BC, & GF dum ambo premunt libram fluidam ſub<lb></lb>iectam ſuis ponderibus, & coguntur moueri ſimùl æ<lb></lb>què velociter contrarijs lationibus neceſſariò libram <pb pagenum="25" xlink:href="010/01/033.jpg"></pb><arrow.to.target n="marg25"></arrow.to.target><lb></lb>conſtituunt, quæ in ſuo centro grauitatis energiam̨ <lb></lb>vniuerſæ ſuæ compreſſionis exercent, verum tameņ <lb></lb>eſt quòd prædicta libra non flectitur, ſed continentèr <lb></lb>renouatur in ſitu horizontali, quandoquidem aquą <lb></lb>eleuata iam non amplius agit contra preſſionem mer<lb></lb>curij CB vt dictum eſt, propterea quòd æquilibratur <lb></lb>cum aqua collaterali ſupra mercurium CB eleuata. </s> </p> <p type="margin"> <s id="s.000124"><margin.target id="marg25"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000125"><emph type="center"></emph>PROP. IX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000126"><emph type="center"></emph><emph type="italics"></emph>Corpus aqua grauius in ea demerſum dum deſcendit consti<lb></lb>tuit cum æqualimole collateralis fluidi libram <expan abbr="æqualiũ">æqualium</expan> <lb></lb>radiorum, cuius centrum grauitatis continenter <lb></lb>deſcendende eleuat leuiorem aquam col<lb></lb>lateralem, ſemperque renouatur <lb></lb>horizontalis libra.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000127">HOc præmiſſo intelligatur iam vas aquà plenum <lb></lb>RSTX, & intra eius profunditatem appona<lb></lb>tur priſma marmoreum ABCD, & producantur eius <lb></lb>baſes horizontales AB, & CD <lb></lb><figure id="id.010.01.033.1.jpg" xlink:href="010/01/033/1.jpg"></figure><lb></lb>vſque ad G & H, atque planum̨ <lb></lb>AD producatur ſurſum, & deor<lb></lb>ſum vſque ad M, & V perpendi<lb></lb>culariter ad horizontem. </s> <s id="s.000128">hic iam <lb></lb>habemus <expan abbr="ſiphonẽ">ſiphonem</expan> oblongum in ſe <lb></lb>ipſum circumductum, vt in prę<lb></lb>cedenti propoſitione expoſitum fuit, quia aqua BM <lb></lb>GHVC ambit priſma ſupernè, lateraliter, & infernè, <lb></lb>nec moueri poteſt <expan abbr="deſcẽdendo">deſcendendo</expan> priſma AC quin aqua <pb pagenum="26" xlink:href="010/01/034.jpg"></pb><arrow.to.target n="marg26"></arrow.to.target><lb></lb>ſubiecta CID è ſuo loco expellatur, & lateralitèr fluat <lb></lb>verſus P, circumferaturque ſurſum vſque ad locum̨ <lb></lb>relictum à prędicto priſmate lapideo in E. ſunt igitur <lb></lb>duæ partes MT, & MS veluti duo canales laterales <lb></lb>ſiphonis, qui tamen ſeſe contingunt in communi la<lb></lb>tere MV; prætereà duæ portiones aquæ ſupremæ XA, <lb></lb>& MG cùm ſint homogeneæ, æquè graues ſpecie, & <lb></lb>æque altæ, ſe mutuò æquilibrantur, pariterque duæ <lb></lb>portiones aqueæ ſubiectæ CV, & DS pariter æquili<lb></lb>brantur, vnde patet quòd tantummodo comparari <lb></lb>debent inter ſe duo corpora collateralia ſaxum nimi<lb></lb>rum BD, & aqua AH, quæ ab eiſdem planis horizon<lb></lb>talibus BG, & HC comprehenduntur, & hæc ſimiliter <lb></lb>fulciuntur ſuſtentanturque à plano aquæ ſubiectæ H <lb></lb>C <expan abbr="nõ">non</expan> firmo, & impermeabili, ſed facilè à ſuo loco <lb></lb>amouibili & cedenti. </s> <s id="s.000129">inſiſtunt igitur prædicta duo cor<lb></lb>pora BD, & AH non ſecùs ſuſpenſa ac ſi ſuper libram <lb></lb>HC inniterentur; huius verò centrum mobile eſſet <lb></lb>punctum intermedium D, vbi nimirum libra HC bi<lb></lb>fariàm ſecatur, & ſi à centro grauitatis O ſaxi BD ad <lb></lb>centrum P grauitatis aquæ AH recta linea <expan abbr="coniũga-tur">coniunga<lb></lb>tur</expan>, eaque ſecetur in Y reciprocè ſecundùm propor<lb></lb>tionem grauitatum eorumdem corporum, patet Y eſ<lb></lb>ſe centrum grauitatis communis ſaxi BD, & aquæ A <lb></lb>H, cùmque libra PO ſecetur bifariàm à plano MV in <lb></lb>Q iam conſurget fune-pendulum QY horizontaliter <lb></lb>excenſum versùs O ob exceſſum grauitatis ſaxi ſupra <lb></lb>aquæ pondus ſpecificum, igitur neceſsè eſt vt totą <lb></lb>libra flectatur <expan abbr="deorsũ">deorsum</expan>, & ſic ſaxum BD <expan abbr="deſcẽdet">deſcendet</expan>. </s> <s id="s.000130">Quia <pb pagenum="27" xlink:href="010/01/035.jpg"></pb><arrow.to.target n="marg27"></arrow.to.target><lb></lb>verò in deſcenſu aqua ſubiecta expulſa ex I curuo iti<lb></lb>nere ſurſum fluit per ZF vſque ad E denuò renouatur <lb></lb>libra horizontalis, comparanturque inter ſe ſaxum B <lb></lb>D cum aqua collaterali in nouo ſitu horizontali de<lb></lb>preſſiori exiſtente, igitur denuò eadem proportione <lb></lb>diſſecta libra imaginaria horizontali, <expan abbr="fune-pendulũ">fune-pendulum</expan> <lb></lb>æquale priori eadem vi flectetur <expan abbr="deorsũ">deorsum</expan>, <expan abbr="deſcendetq;">deſcendetque</expan> <lb></lb>centrum grauitatis eius motu perpendiculari ad hori<lb></lb>zontem quòuſque ad fundum vaſis ſaxum pertingat. </s> </p> <p type="margin"> <s id="s.000131"><margin.target id="marg26"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="margin"> <s id="s.000132"><margin.target id="marg27"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium</s> </p> <p type="main"> <s id="s.000133"><emph type="center"></emph>PROP. X.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000134"><emph type="center"></emph><emph type="italics"></emph>Idipſum contingit, ſed inuerſo ordine cum corpus de<lb></lb>merſum minùs graue aqua collaterali fueris.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000135">SI poſtea priſma BD fuerit ligneum, & minùs gra<lb></lb>ue ſpecie quam aqua AH, tunc ijſdem manen<lb></lb>tibus ſolummodò centrum grauitatis communis Y <lb></lb>cadet ad partes aquæ inter Q & P, & proindè vniuer<lb></lb>ſum graue compoſitum ex aqua, & ligno vim faciet <lb></lb><expan abbr="impellẽdo">impellendo</expan> deorſum centrum gra<lb></lb><figure id="id.010.01.035.1.jpg" xlink:href="010/01/035/1.jpg"></figure><lb></lb>uitatis Y, & ideò vehementiùs <expan abbr="cõ-primetur">con<lb></lb>primetur</expan> aqua ſubiecta HDVS, <lb></lb>hæc verò ob eius continuitatem <lb></lb>& naturam <expan abbr="conſiſtẽtem">conſiſtentem</expan>, quæ preſ<lb></lb>ſioni non cedit, neceſſariò impel<lb></lb>letur versùs I, & ſic vim faciet ſur<lb></lb>ſum exprimendo ligni ſuperficiem DC; at dum <expan abbr="lignũ">lignum</expan> <lb></lb>aſcendit, oportet vt expellat è ſuo loco <expan abbr="incumbentẽ">incumbentem</expan> <lb></lb>aquam E, quæ tranſuerſali & obliquo motu perduce-<pb pagenum="28" xlink:href="010/01/036.jpg"></pb><arrow.to.target n="marg28"></arrow.to.target><lb></lb>tur ab E per FZ versùs I, & ſic à prædicto motu circu<lb></lb>lari aquæ ambientis lignum expelletur ſursùm; atta<lb></lb>men ratio mechanica huius actionis pendet ex eo, <lb></lb>quòd libra horizontalis imaginaria PO flectitur per<lb></lb>petuò deorsùm quidem ad partes centri grauitatis Y <lb></lb>circa centrum Q, & ſursùm ad partes O. ſed ſummo<lb></lb>perè animaduertendum eſt prædictam libram imagi<lb></lb>nariam horizontalem renouari ſucceſſiuè prout <expan abbr="lignũ">lignum</expan> <lb></lb>aſcendit, <expan abbr="comparaturq;">comparaturque</expan> cum alijs lateralibus priſma<lb></lb>tibus aqueis, quæ ſucceſſiuè offendit intercepta in<lb></lb>ter prædicta plana horizontalia GB, & HC: neceſsè <lb></lb>ergo eſt vt lignum prædictum numquàm quieſcat in<lb></lb>tra aquam demerſum quòuſque ad ſupremam <expan abbr="libellã">libellam</expan> <lb></lb>aquæ RX perducatur; inſuperque aliqua eius por<lb></lb>tio emineat. </s> </p> <p type="margin"> <s id="s.000136"><margin.target id="marg28"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000137"><emph type="center"></emph>COR OLLARIVM.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000138">Hinc patet veritas Archimedei aſſumpti, quòd <lb></lb>fluidi conſiſtentis natura requirit vt partium eius æ<lb></lb>què iacentium magis compreſſæ ſursùm impellant <lb></lb>partes minus preſſas perpendiculariter ad <expan abbr="horizontẽ">horizontem</expan>. </s> </p> <p type="main"> <s id="s.000139">Quia aqua ſubiecta HCTS ob eius conſiſtentiam̨ <lb></lb>non condenſatur, & mobilis eſt, quia fluida, ergo li<lb></lb>bram flexibilem conſtituit, <expan abbr="eſtq;">eſtque</expan> pars ſubiecta HV <lb></lb>magis compreſſa quàm DT (propterea quòd pars a<lb></lb>quea GD grauior eſt ligno AC) igitur libra fluida <lb></lb>HDC flecti debet deſcendendo HD & DC aſcen<lb></lb>dendo, quare tota aqua HSVD deorsùm depreſſa im<lb></lb>pellet aquam DVTC ſursùm. <pb pagenum="29" xlink:href="010/01/037.jpg"></pb><arrow.to.target n="marg29"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000140"><margin.target id="marg29"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000141"><emph type="center"></emph>PROP. XI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000142"><emph type="center"></emph><emph type="italics"></emph>Si verò corpus ſolidum ponitur ſupra aquæ libellam, <lb></lb>tunc deſcenſus communis centri grauitatis non <lb></lb>efficietur per lineam perpendicularem ad <lb></lb>horizontem ſed motu curuo per <lb></lb>parabolam.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000143">IN progreſſu prædictæ operationis notabilis eſt va<lb></lb>riatio ſitus centri grauitatis eius & mechanicæ eius <lb></lb>operationis. </s> </p> <p type="main"> <s id="s.000144">Sit igitur in eodem vaſe priſma ligneum ABCD <lb></lb>perductum ad ſupremam aquæ libellam RX, tunc ſi<lb></lb>militer inter ſe comparantur duo priſmata BD ligno<lb></lb>um, & AH aqueum in eodem plano horizontali ſu<lb></lb>biecto HC inſiſtentes, & proindè <lb></lb><figure id="id.010.01.037.1.jpg" xlink:href="010/01/037/1.jpg"></figure><lb></lb>efficitur libra imaginaria PO mo<lb></lb>bilis circa eius fulcimentum Q, & <lb></lb>centrum grauitatis <expan abbr="eorumdẽ">eorumdem</expan> cor<lb></lb>porum cadit ad partes aquæ nem<lb></lb>pè in Y inter <expan abbr="cẽtrum">centrum</expan> Q & extremitatem radij P. hinc <lb></lb>ergo ſe quitur vt prædicta libra flecti debeat deorsùm <lb></lb>ad partes Y & ſurſum aſcendat terminus O vnà cum li<lb></lb>gno versùs aquæ libellam ſupremam RX, igitur por<lb></lb>tio aliqua ligni ſuprema eleuabitur ſupra prædictam <lb></lb>aquæ libellam, vt patet in poſtrema figura, & tunc <lb></lb><expan abbr="quidẽ">quidem</expan> ſucceſſiuè imminuitur priſma <expan abbr="aqueũ">aqueum</expan> GD prout <lb></lb>magis ligneum priſma exurgit, eminetque ſupra aquę <lb></lb>libellam, & in prædicto aſcenſu dum collaterale priſ-<pb pagenum="30" xlink:href="010/01/038.jpg"></pb><arrow.to.target n="marg30"></arrow.to.target><lb></lb>ma aqueum imminuitur, pondus eius quòd prius ſu<lb></lb>perabat grauitatem ligni BD, tandem poſt <expan abbr="continuã">continuam</expan> <lb></lb>ponderis aquæ <expan abbr="diminutionẽ">diminutionem</expan> reddetur præcisè æqua<lb></lb>le ponderi cylindri lignei BD, & tunc coniunctis <lb></lb>centris grauitatum eorum à rectą <lb></lb><figure id="id.010.01.038.1.jpg" xlink:href="010/01/038/1.jpg"></figure><lb></lb>PO hæc quidem bifariàm ſecabi<lb></lb>tur in termino Q & <expan abbr="ibidẽ">ibidem</expan> erit eius <lb></lb>centrum, atque fulcimentum ha<lb></lb>bebitque pondus ligni BD ad <expan abbr="põ-dus">pon<lb></lb>dus</expan> aquæ GD ſibi æquale <expan abbr="eamdẽ">eamdem</expan> <lb></lb>proportionem, quam habet reciprocè PQ ad QO, & <lb></lb>proindè centrum grauitatis commune Y incidet præ<lb></lb>cisè in centro ſeù fulcimento libræ <expan abbr="q.">que</expan> igitur æquili<lb></lb>bratis prædictis ponderibus libra quieſcet, nec priſ<lb></lb>ma ligneum BD vlteriùs <expan abbr="aſcẽdet">aſcendet</expan>, <expan abbr="neq;">neque</expan> denuò <expan abbr="deorsũ">deorsum</expan> <lb></lb>decidet niſi ex accidenti ratione impetus acquiſiti. </s> </p> <p type="margin"> <s id="s.000145"><margin.target id="marg30"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000146">Hinc patet quòd quando primò lignum BD exur<lb></lb>gere incipit ſupra aquæ libellam RX tunc continen<lb></lb>ter magis ac magis centrum communis grauitatis Y <lb></lb>motu obliquo, & curuo <expan abbr="aſcẽdit">aſcendit</expan> quòuſque coniunga<lb></lb>tur cum fulcimento Q libræ PO ſursùm tranſlatę, <lb></lb>non ſecùs, ac in ſiphone aqua eleuata in vno eius bra<lb></lb>chio deſcendendo perducit centrum grauitatis eius <lb></lb>per curuam lineam parabolicam, vt dictum eſt; con<lb></lb>cipi ergo debet ſipho inæqualium brachiorum <expan abbr="quãdo">quando</expan> <lb></lb>primum baſis ſuprema AB ligni attingit aquæ libel<lb></lb>lam, & quia tunc exceſſus grauitatis ſpecificæ aquæ <lb></lb>AH ſupra pondus ligni BD perindè agit ac ſi aliud <lb></lb>fluidum æquè graue ſpecie ligno ipſi BD & maioris <pb pagenum="31" xlink:href="010/01/039.jpg"></pb><arrow.to.target n="marg31"></arrow.to.target><lb></lb>molis ſupra baſim HD inſiſteret procul dubio ad ma<lb></lb>iorem ſublimitatem eleuaretur prædictum fluidum̨ <lb></lb>minùs graue ſpecie, quàm aqua AH, cuius <expan abbr="abſolutũ">abſolutum</expan> <lb></lb>pondus æquale eſſet ponderi eiuſdem aquæ commu<lb></lb>nis AH, quare ab eleuatiori loco fluidum prædictum <lb></lb>deorsùm excurrendo eleuaret lignum depreſſum BD <lb></lb>præcisè vt in ſiphone ſuperiùs expoſito contingeret. </s> </p> <p type="margin"> <s id="s.000147"><margin.target id="marg31"></margin.target>Cap. 2. dę <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="main"> <s id="s.000148">Ex hac theoria facili negotio reſolui ac <expan abbr="demõſtra-ri">demonſtra<lb></lb>ri</expan> poſſunt omnes propoſitiones, quæ ab Archimedę <lb></lb>in primo de infidentibus humido demonſtrantur. </s> </p> <p type="main"> <s id="s.000149"><emph type="center"></emph>PROP. XII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000150"><emph type="center"></emph><emph type="italics"></emph>In aſcenſu, vel deſcenſu ſolidi in fluide neque libra linearis <lb></lb>eſt, neque habet centrum grauitatis in vno puncto <lb></lb>ſed libra eſſe ſolet ſuperficialis, cuius fulci<lb></lb>mentum eſt linea circa centrum figuræ, <lb></lb>& grauitas communis exercetur <lb></lb>quoque in linea aliqua.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000151">SOlummodò indicabo <expan abbr="nõ">non</expan> ſemper vſurpari in præ<lb></lb>dicta mechanica operatione punctum, quod <expan abbr="cõ-mune">com<lb></lb>mune</expan> centrum grauitatis vocari vulgò ſolet; propte<lb></lb>rea quòd libra compoſita ex ſolido & fluido ambien<lb></lb>te non ſemper linearis eſt, ſed ſuperficiem aliquando <lb></lb>componit, in qua nedum fulcimentum, ſed etiam lo<lb></lb>cus vbi exercetur communis grauitas linea eſſe ſolet <lb></lb>aliquando recta, aliquando curua, & multoties com<lb></lb>poſita ex pluribus rectis. </s> <s id="s.000152">ſi enim in medio aquæ im<lb></lb>mergatur directè & perpendiculariter ad <expan abbr="horizontẽ">horizontem</expan> <pb pagenum="32" xlink:href="010/01/040.jpg"></pb><arrow.to.target n="marg32"></arrow.to.target><lb></lb>priſma vel cylindrus ſolidus, tunc quidem dum priſ<lb></lb>ma deſcendit, vniuerſa aqua illud ambiens ſurſum̨ <lb></lb>eleuatur. </s> <s id="s.000153">vel illo aſcendente hæc deprimitur, com<lb></lb>parari ergo debet priſma comprehenſum cum anulo <lb></lb>ſeu potiùs cum fiſtula fluida id ambiens, & ſic effici<lb></lb>tur libra quædam plana cuius fulcimentum erit linea <lb></lb>in confinio cylindri demerſi, & fluidi ambientis ex<lb></lb>tenſa pariterque locus, vbi communis grauitas exer<lb></lb>cetur non erit punctum, ſed erit quoque linea in eo<lb></lb>dem plano horizontali producta; ſed facilitatis gra<lb></lb>tia concipi debet ſector aliquis in prædicto plano ex <lb></lb>centro prædictæ libræ ſuperficialis in axe cylindri <lb></lb>conſtituto vſque ad ſuperficiem aquæ ambientis, quę <lb></lb>contrarijs motibus vnà cum cylindro mouetur; ſeù <lb></lb>potius concipi debet radius, ſeù ſemidiameter <expan abbr="nõ">non</expan> in <lb></lb>diuiſibilis, ſed phyſica, & hęc vſurpari poteſt vt libra <lb></lb>particularis cum ſuo fulcimento, & centro grauita<lb></lb>tis, vniuerſa verò libra ſuperficialis compoſita erit ex <lb></lb>pluribus, & innumeris libris radioſis, vt dictum eſt, <lb></lb>& hæc innuiſſe modò ſufficiat in hac generali præpa<lb></lb>ratione, inferiùs enim accuratiùs exponentur. <pb pagenum="33" xlink:href="010/01/041.jpg"></pb><arrow.to.target n="marg33"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000154"><margin.target id="marg32"></margin.target>Cap. 2. de <lb></lb>momentis <lb></lb>grauium in <lb></lb>fluido inna<lb></lb>tantium.</s> </p> <p type="margin"> <s id="s.000155"><margin.target id="marg33"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000156"><emph type="center"></emph><emph type="italics"></emph>Quodlibet corpus fluidum eorum quæ innituntur <lb></lb>ſuperficiei Telluris graue eſt, exercetque <lb></lb>vim ſuæ grauitatis etiam dum in <lb></lb>proprio loco, & in ipſomet <lb></lb>fluido vniuerſali ſui <lb></lb>generis conſiſtit, <lb></lb>ac quieſcit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000157"><emph type="center"></emph>CAP. III.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000158">SVppoſuimus cum Archimede aquam, & reliquą <lb></lb>corpora fluida terram ambientia vi propriæ gra<lb></lb>uitatis compreſſionem vniformem exercere verſus <lb></lb>centrum telluris, ex quo ſubindè fit vt ſphæricè circa <lb></lb>terræ centrum diſponantur. </s> <s id="s.000159">præterea ſuppoſuimus <lb></lb>cum eodem Archimede partes eiuſdem fluidi minùs <lb></lb>preſſas expelli ac ſubleuari ſurſum à partibus <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>fluidi magis compreſſis, & grauatis; ex qua hypothe<lb></lb>ſi deducitur quodliber fluidum, veluti aqua eſt, gra<lb></lb>uitatem habere eamque exercere etiam in proprio <lb></lb>loco, & naturali regione, ſcilicèt aquam ipſam dum in <lb></lb>tota aqua quieſcit tunc quoque grauitatem exercere <lb></lb>ſubiecta corpora comprimendo. <lb></lb><arrow.to.target n="marg34"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000160"><margin.target id="marg34"></margin.target>Ex Archi<lb></lb>mede dedu<lb></lb>cunt aquam <lb></lb>in ipsa aqua <lb></lb>non grauita<lb></lb>re, & id <expan abbr="ipsũ">ipsum</expan> <lb></lb>Peripatetici <lb></lb>affirmaret.</s> </p> <p type="main"> <s id="s.000161">Hoc autem à plurimis negatur qui putant Archi<lb></lb>medem oppoſitum ſenſiſſe. </s> <s id="s.000162">idipſum quoque negant <lb></lb>aliqui peripatetici qui cenſent non ſemper verum̨ <lb></lb>eſſe quòd partes ſuperiores corporis grauis compri<lb></lb>mant, & vim inferant inferioribus, & contiguis, niſi <lb></lb>infimæ partes leues ſint abſolutè, vel reſpectiuè, vnde </s> </p> <pb pagenum="34" xlink:href="010/01/042.jpg"></pb> <p type="main"> <s id="s.000163"><arrow.to.target n="marg35"></arrow.to.target><lb></lb><expan abbr="cõcedunt">concedunt</expan> terram exemp. </s> <s id="s.000164">gr. ſuper <expan abbr="aquã">aquam</expan>, aut ſuper <expan abbr="ae-rẽ">ae<lb></lb>rem</expan> poſitam, vim, & operationem grauitatis & com<lb></lb>preſſionis exercere, non itidem aquam ſupra ipſam̨ <lb></lb>terram collocatam, nec aerem aquæ incumbentem, <lb></lb>imò nec aerem ſupra aerem conſtitutum, nec aquam <lb></lb>ſupra aquam poſitam. </s> <s id="s.000165">huiuſmodi propoſitionem tali <lb></lb>ratiocinio confirmare nituntur, cum Natura cauſa, & <lb></lb>principium motus ſit, nec operetur fruſtra ſed ad cer<lb></lb>tum finem, & ad bonum, proculdubio ordinauit mo<lb></lb>tum naturalium corporum ad certum finem, & ad bo<lb></lb>num, ſcilicèt ad conſeruationem, & quia actus, ſeù <lb></lb>perfectio quam appetunt, & quam acquirere nitun<lb></lb>tur corpora grauia, & leuia dum mouentur eſt migra<lb></lb>tio, & debita conſtitutio in proprijs locis naturali<lb></lb>bus, grauium nempè de orſum, & leuium ſursùm, hine <lb></lb>ſequitur quòd poſt <expan abbr="quã">quam</expan> ad debita loca naturalia per<lb></lb>ducta ſunt, motus omninò ceſſat, vtpotè naturæ deſi<lb></lb>derio, & fine expleto, eo quòd vt ait Ariſtoteles Na<lb></lb>tura non mouet corpus aliquod vt <expan abbr="ipsũ">ipsum</expan> moueat, ſcili<lb></lb>cèt vt ipſum perpetuò, & in <expan abbr="infinitũ">infinitum</expan> agitet, ſed tan<lb></lb>tummodo vt illud ad terminum, & finem perducat <lb></lb>vt ibidem quieſcat; verùm facultates aut virtutes <lb></lb>quibus ſublunaria corpora ad propria loca feruntur <lb></lb>nil aliud ſunt, quàm grauitas aut leuitas. </s> <s id="s.000166">igitur huiuſ<lb></lb>modi facultates ordinatæ ſunt ad perducenda <expan abbr="elemẽ-taria">elemen<lb></lb>taria</expan> corpora ad propria loca vt ibidem quieſcant; <lb></lb>nec vlteriùs vſum aliquem habere poſſunt, quando<lb></lb>quidem ſi præterea motum proſe querentur in ſuis lo<lb></lb>cis perturbarent & confunderent naturalem ſituatio-<pb pagenum="35" xlink:href="010/01/043.jpg"></pb><arrow.to.target n="marg36"></arrow.to.target><lb></lb>nem eorumdem corporum. </s> <s id="s.000167">& profectò eſt conſenta<lb></lb>neum vt elementa non nitantur deſerere propria lo<lb></lb>ca, & propterea careant illo naturali ſtimulo ſeu prin<lb></lb>cipio motus quo impellebantur antequam ad ſua na<lb></lb>turalia loca perueniſſent; hinc deducitur nullum ele<lb></lb>mentum in proprio loco grauitatem, aut leuitatem <lb></lb>habere, ſed aqua in ipſa aqua poſita in propria, & na<lb></lb>turali regione degit & ſic aer in aere, ergo neutrum <lb></lb>horum elementorum grauitatem in ſuo loco habet, <lb></lb>aut exercet. </s> <s id="s.000168">& primo quoad Archimedem pertinet <lb></lb>videntur aduerſarij nequaquam tanti viri mentem̨ <lb></lb>aſſequuti ſuiſſe vt ex eius verbis ſatis <expan abbr="ſuperq;">ſuperque</expan> patet. <lb></lb></s> <s id="s.000169">vt verò Peripateticis fiat ſatis, ne dum <expan abbr="nullã">nullam</expan> lenita<lb></lb>tem poſitiuam in natura dari oſtendam, ſed præterea <lb></lb>probabo falſum eſſe quòd poſt quam corpora natura<lb></lb>lia ad ſua loca perueniunt & ibidem quieſcunt graui<lb></lb>tas vſum non habet, niſi ad perturbandum pręclarum <lb></lb>ordinem vniuerſi; nam è contra ſuadere conabor tunc <lb></lb>præcisè corpora grauitatem exercere cùm in ſuis lo<lb></lb>cis quieſcunt, imò cauſam, quare in ſuis locis quie<lb></lb>ſcunt, eſſe quia pondus exercent, ſed prius <expan abbr="perpendẽ-da">perpenden<lb></lb>da</expan> eſt actio ipſius grauitatis, & quidnam potiſſimum̨ <lb></lb>efficiat pondus dum comprimit; & profectò actio & <lb></lb>compreſſio corporis grauis non eſt tranſitus localis <lb></lb>pilæ ferreæ v.g. dum verſus terram deſcendit, nec <lb></lb>præterea eſt ſimplex contactus quo coniungitur cum <lb></lb>ſuperficie telluris ſubiectæ, ſed eſt vis, & energia, qua <lb></lb>impellitur deorſum <expan abbr="ſtringiturq;">ſtringiturque</expan> veluti prælo <expan abbr="cũ">cum</expan> ipſa <lb></lb>terra; veluti cum pondus in trutina appenditur licet <pb pagenum="36" xlink:href="010/01/044.jpg"></pb><arrow.to.target n="marg37"></arrow.to.target><lb></lb>quieſcere videatur exercet actionem quamdam <expan abbr="cõ-preſſiuam">com<lb></lb>preſſiuam</expan> tantæ energiæ quanta eſt eius grauitas; hoc <lb></lb>autem facilè percipiemus ſi fingamus duos homines <lb></lb>æquè validos & robuſtos qui totis viribus ſe mutuò <lb></lb>impellant, vbi manifeſtum eſt quòd exiſtentibus vi<lb></lb>ribus contrarijs inter ſe æqualibus, vt vna alteri noņ <lb></lb>pręualeat, tunc neuter luctantium dimouebitur è ſuo <lb></lb>loco, ſed ibidem quieſcet, licèt quilibet <expan abbr="corũ">eorum</expan> vniuer<lb></lb>ſam vim, & facultatem propriam exerceat impellen<lb></lb>do, & repellendo ſuum antagoniſtam, non ſecùs <expan abbr="quã-do">quan<lb></lb>do</expan> aliquis impellit columnam ingentem vehemen<lb></lb>ter, licèt minimè valeat eam è ſuo loco deijcere, ac <lb></lb>commouere, vt nimirum motus progreſſiuus hominis <lb></lb>impellentis, aut columnæ ſubſequatur; nihilominùs <lb></lb>negari non poteſt motus impulſiuus muſculorum, & <lb></lb>artuum hominis impellentis; nec pariter negari po<lb></lb>teſt aliqua exigua & inſenſibilis flexio eiuſdem <expan abbr="colũ-næ">colunm<lb></lb>næ</expan>, quæ ad inſtat arcus, ſeù machinæ æquali vi impul<lb></lb>ſui, & flexioni reſiſtit. </s> <s id="s.000170">ſimiliter cùm pila ferrea ſuper <lb></lb>baſim, vel laminam vitream innititur concedendum <lb></lb>omninò eſt effici conſtipationem quamdam partium <lb></lb>ferri prementis, & vitri compreſſi, vt nimirum ali<lb></lb>quantiſper eorum poroſitates <expan abbr="cõſtringantur">conſtringantur</expan>, eò quòd <lb></lb>(vt oſtenſum eſt cap. 26. de Vi percuſſionis) reperiri <lb></lb>in rerum natura corpora compoſita <expan abbr="nequeũt">nequeunt</expan> quæ ad<lb></lb>eò dura ſint vt compreſſioni cuiuslibet corporis reſi<lb></lb>ſtere valeant. </s> <s id="s.000171">quod verò prædicta compreſſio vitri ab <lb></lb>ingenti pondere fiat patet ex eo quòd augendo ma<lb></lb>gis ac magis pondus comprimens, tandem baſis vi-<pb pagenum="37" xlink:href="010/01/045.jpg"></pb><arrow.to.target n="marg38"></arrow.to.target><lb></lb>trea diſrumpitur, diſſilit, atque conteritur eo pręcisè <lb></lb>modo quo ab ictu mallei diſrumpitur; & ſi quidem <lb></lb>hoc verum non eſſet ſcilicèt ſi à pondere vtcumquę <lb></lb>multiplicato & aucto baſis vitrea non ſtringeretur & <lb></lb>comprimeretur, quælibet exiliſſima baſis vitrea to<lb></lb>leraret vim compreſſiuam ponderis cuiuſlibet <expan abbr="mõtis">montis</expan> <lb></lb>vaſti, quod procul dubio falſum eſt. </s> </p> <p type="margin"> <s id="s.000172"><margin.target id="marg35"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000173"><margin.target id="marg36"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000174"><margin.target id="marg37"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000175"><margin.target id="marg38"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000176">Hoc poſito nemo negabit quòd ſi pondus duplice<lb></lb>tur vt ſcilicèt vnum ſuper alterum ſuperponatur, <expan abbr="tũc">tunc</expan> <lb></lb>duplici vi, ac robore infima baſis vitrea comprime<lb></lb>tur ac conſtipabitur, & proindè poroſitates multò <lb></lb>magis imminuentur à duplici impulſu, quando <expan abbr="quidẽ">quidem</expan> <lb></lb>concipi non poteſt moles grauis aucta & multiplica<lb></lb>ta abſque eo quòd pondus, & proindè vis, & energia <lb></lb>compreſſiua versùs centrum telluris multiplicetur, <lb></lb>vnde fit vt partes ſolidæ & conſiſtentes <expan abbr="comprimãtur">comprimantur</expan> <lb></lb>& <expan abbr="conſtipẽtur">conſtipentur</expan> multo magis. </s> </p> <p type="main"> <s id="s.000177">At ſi hoc contingit in corporibus duriſſimis, nega<lb></lb>ri certè non poterit in corporibus fluidis, quæ noņ <lb></lb>minùs grauia ſunt & <expan abbr="cõ">comprimunt</expan> fundum vaſis in quo <lb></lb>continentur tanta vi, quanta eſt energia ponderis <lb></lb>eorum, ita ut multiplicata fluidi mole centies, & mil<lb></lb>lies vaſis fundum centies, & millies maiori vi com<lb></lb>primatur, & licèt ibidem non adſit motus progreſ<lb></lb>ſiuus, numquam tamen deficiet motus tonicus, & reſ<lb></lb>trictio pororum fundi vaſis, & compreſſio pororum <lb></lb>eiuſdem fluidi, ſi fortè poroſitates habuerit, & ſicuti <lb></lb>fluidum grauitat atque conſtringit poroſitates fundi <lb></lb>vaſis, hac de cauſa, quia ponderat, & grauitat, nulla <pb pagenum="38" xlink:href="010/01/046.jpg"></pb><arrow.to.target n="marg39"></arrow.to.target><lb></lb>ratio vetat, quin pondere ſuo comprimat infimam ſu<lb></lb>biectam laminulam eiuſdem fluidi quæ fundo vaſis <lb></lb>contigua eſt, quandoquidem minimè poſſunt ſupre<lb></lb>mæ fluidi partes fundum vaſis comprimere abſquę <lb></lb>eo quod impellant, & ſtringant infimam eiuſdem flui<lb></lb>di laminulam, cùm actio in diſtanti fieri non poſſit, ſed <lb></lb>contactu quodam remotiores impellendo eis conti<lb></lb>guas ſubiectas partes, & hæ ſubſequentes ſerie qua<lb></lb>dam ordinata quouſque fundum comprimant. </s> </p> <p type="margin"> <s id="s.000178"><margin.target id="marg39"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000179"><emph type="center"></emph>PROP. XIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000180"><emph type="center"></emph><emph type="italics"></emph>Aqua vaſis fundum çomprimit ſua grauitate.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000181">SEd hoc euidentius ſic patebit, ſit fiſtula vitrea A <lb></lb>NO perpendiculariter ad horizontem erectą, <lb></lb>repleaturquè aqua, ſeù quolibet alio fluido cor<lb></lb>pore, & ductis innumeris planis horizonti <expan abbr="æquidiſtã-tibus">æquidiſtan<lb></lb>tibus</expan> ſubdiuidatur vniuerſum fluidum iņ <lb></lb><figure id="id.010.01.046.1.jpg" xlink:href="010/01/046/1.jpg"></figure><lb></lb>laminas gracillimas ſeù membranas æquè <lb></lb>altas AB, BC, CD, DE, EF, FM, & MN. & <lb></lb>primò ſi verum eſt, vt aduerſarij credunt <lb></lb>aquam in ipſamet aqua collocatam <expan abbr="nõ">non</expan> gra<lb></lb>uitare, igitur ſuprema laminula aquea AB <lb></lb>prorſus <expan abbr="nõ">non</expan> comprimet ſubiectam <expan abbr="membra-nã">membra<lb></lb>nam</expan> aqueam BC, ſcilicet vim nullam ſuper eam exer<lb></lb>cebit (hoc enim grauitatis nomen indicat) neque eam <lb></lb>deorſum impellet perinde ac ſi aqua ſuprema AB non <lb></lb>adeſſet, proindeque hæc non augebit grauitatem in<lb></lb>ferioris laminæ BC, aliàs ſuprema aqua AB pondera-<pb pagenum="39" xlink:href="010/01/047.jpg"></pb><arrow.to.target n="marg40"></arrow.to.target><lb></lb>ret, comprimeretque ſubiectam aquam BC, quod eſt <lb></lb>contra aduerſarij hypotheſim; eadem ratione vniuer<lb></lb>ſa aqua ABC nil ponderabit, ne que comprimet ſub<lb></lb>iectam laminam aqueam CD, & tota aqua AD nec <lb></lb>etiam comprimet aut grauitatem inferet ſupra infe<lb></lb>riorem <expan abbr="aquã">aquam</expan> DE; idipſum procul dubio affirmari de<lb></lb>bet de reliquis omnibus laminulis fluidis totam alti<lb></lb>tudinem aquæ componentibus, & hoc optima ratio<lb></lb>ne de duximus, <expan abbr="quãdo">quando</expan> quidem ſeriem corporum iner<lb></lb>tium & nil prorſus deorſum impellentium nemo ſanæ <lb></lb>mentis affirmabit vim compreſſiuam deorsùm exer<lb></lb>cere, imò concedet æquè operari ac ſi eſſet vnica ſin<lb></lb>gularis laminula, vel dicet ſubiectum corpus à nihilo <lb></lb>comprimi, & è contra ſeries corporum vim <expan abbr="impulſiuã">impulſiuam</expan> <lb></lb><expan abbr="habentiũ">habentium</expan> exercet vim pro menſura multiplicati cor<lb></lb>poris, & hoc ſanè lumine naturæ <expan abbr="cõſtat">conſtat</expan>, hinc deduci<lb></lb>tur infimam laminam aqueam MN noſtri vaſis nullam <lb></lb>compreſſionem pati ab vniuerſa aqua ſuperpoſitą <lb></lb>MA non ſecùs ac ſi à nihilo premeretur vnde fit vt in<lb></lb>ferior pars aquea MN ablata qua MA tanta vi præ<lb></lb>cisè comprimat vaſis fundum NO ac ſi ſuperſtaret <lb></lb>immenſa moles aquea NA, ſed illa ob ponderis exi<lb></lb>guitatem haud ſenſibilem vim vitreo fundo infert, <lb></lb>nec ipſum inflectit, aut diſrumpit, igitur neque <expan abbr="vitrũ">vitrum</expan> <lb></lb>inflectetur aut <expan abbr="cõſtringetur">conſtringetur</expan> quando altiſſima moles a<lb></lb>quea NA ei ſuperponitur; quia verò hoc euidentiæ <lb></lb>ſenſus repugnat affirmandum eſt, aquam licèt in ipſa<lb></lb>met aqua iners & quieſcens videatur, neceſſariò gra<lb></lb>uitatem exercere. <pb pagenum="40" xlink:href="010/01/048.jpg"></pb><arrow.to.target n="marg41"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000182"><margin.target id="marg40"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000183"><margin.target id="marg41"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000184"><emph type="center"></emph>PROP. XIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000185"><emph type="center"></emph><emph type="italics"></emph>Id ipſum in ſiphone comprobatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000186">PRæterea vſurpetur idipſum vas vitreum, ſed in<lb></lb>flexum, vt eſt AMOP ſiphonis inuerſi figuram <lb></lb>referens, atque portio ANO aquą <lb></lb><figure id="id.010.01.048.1.jpg" xlink:href="010/01/048/1.jpg"></figure><lb></lb>impleatur, reliqua verò fiſtula OP o<lb></lb>leo. </s> <s id="s.000187">Et quia vt mox oſtenſum eſt ex <lb></lb>aduerſarij hypotheſi tota aqua AM <lb></lb>vim non infert neque impellit infe<lb></lb>riorem aqueam laminam MN, cùm̨ <lb></lb>nullam grauitatem ſuper eam exer<lb></lb>ceat; igitur tota moles aquea AM nil prorsùs impel<lb></lb>let terminum aquæ O & proindè ab hoc non impelle<lb></lb>tur ſurſum oleoſus cylinder OP, igitur oleum OP <lb></lb>nulla ratione ſubleuari ſursùm deberet, ſed hoc eſt <lb></lb>falſum, igitur falſa eſt quoque hypotheſis aſſumpta, <lb></lb>quòd aqua in ipſamet aqua poſita grauitatem noņ <lb></lb>exerceat. </s> </p> <p type="main"> <s id="s.000188">Et profectò methodus ac criterium dignoſcendi, <lb></lb>an corpus aliquod grauitet, atque impellat alterum, <lb></lb>erit huiuſmodi; conſiderari nimirum debent effectus <lb></lb>ab eo producti, & quanta vis contraria requiritur, <lb></lb>vt vnum à conſortio, & contactu alterius diuellatur, <lb></lb>& ſeparetur, & quia ſi nauis natando lateraliter ſco<lb></lb>pulum contingeret, poſſet à quacumque exigua vi tra<lb></lb>hi, diuelli, & ſeparari ab eodem ſcopulo, hinc in re <lb></lb>optimo inferemus nauim omninò carere vi motiua, & <pb pagenum="41" xlink:href="010/01/049.jpg"></pb><arrow.to.target n="marg42"></arrow.to.target><lb></lb>impulſiua tendendi verſus ſcopulum, è contra, quia <lb></lb>videmus, quòd pila ferrea non poteſt à contactu ſoli <lb></lb>ſeiungi, ac diuelli niſi æqualis facultas, & energią <lb></lb>contraria adhibeatur, ſcilicet niſi apponatur pondus <lb></lb>in altera extremitate libræ, quod æquale ſit grauita<lb></lb>ti prædictæ pilæ ferreę, ſicuti cùm homo robuſtus co<lb></lb>lumnam aliquam impellit, non poteſt ab ea ſeiungi, <lb></lb>niſi adhibeatur vis motiua prorsùs æqualis ei, quam <lb></lb>homo exercet; hinc de ducemus pilam vim grauitatis, <lb></lb>& hominem vim muſculorum exercere. </s> </p> <p type="margin"> <s id="s.000189"><margin.target id="marg42"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000190">Porrò effectus producti ab illa ferrea pila à paui<lb></lb>mento ſubnixa plures ſunt, ac varij, conſtringuntur <lb></lb>nempè pori ſubiecti corporis pilam ſuſtinentis, in<lb></lb>flectitur paritèr idipſum contunditurque, & multo<lb></lb>tiès diffringitur, ac diſſilit in particulas minimas, <lb></lb>igitur ſi huiuſmodi effectus ipſamet aqua operaretur, <lb></lb>abſque vlla hæſitatione aquam in ipſamet aqua gra<lb></lb>uitare affirmaremus. </s> <s id="s.000191">Modò videmus, quòd aqua ad <lb></lb>ingentem altitudinem eleuata nedùm ſolum, ac fun<lb></lb>dum vaſis inflectit, ſed ipſum multoties diffringit, & <lb></lb>hoc magis patet ſi fundum vaſis flexibile fuerit, ſi ve<lb></lb>rò conſtringi, ac condenſari poterit, illud conſtrin<lb></lb>git, atque ad minus ſpatium redigit, non ſecùs ac <lb></lb>homo robuſtus comprimeret, & ſlecteret corporą <lb></lb>flexibilia, ac cedentia, dum ea impelleret. <pb pagenum="42" xlink:href="010/01/050.jpg"></pb><arrow.to.target n="marg43"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000192"><margin.target id="marg43"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000193"><emph type="center"></emph>PROP. XV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000194"><emph type="center"></emph><emph type="italics"></emph>Alia ratione, & experimento probare compresſionem par<lb></lb>tium aquæ, & rerum in ea contentarum à pon<lb></lb>dere ipſiuſmet aquæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000195">SIt fiſtula vitrea RVX vndique clauſa <expan abbr="præterquã">præterquam</expan> <lb></lb>in ſupremo orificio R, hæc verò aqua repleatur, <lb></lb>& in ea ampullula vitrea AD immerga<lb></lb><figure id="id.010.01.050.1.jpg" xlink:href="010/01/050/1.jpg"></figure><lb></lb>tur ſitque ea plena aere, & eius pars ver<lb></lb>ſus infimum orificium apertum D graui<lb></lb>or ſit, ad hoc vt ampullula AD ſemper <lb></lb>inuerſo ſitu in ipſa aqua perſiſtat. </s> <s id="s.000196">in hac <lb></lb>machina obſeruatur quòd vexica vitrea <lb></lb>AD quò magis deprimitur infra ſupre<lb></lb>mam aquæ libellam, vel potiùs ipſamet <lb></lb>aqua altiùs infunditur, & eleuatur, tune <lb></lb>eò magis aer in ampulla contentus con<lb></lb>denſatur, <expan abbr="atq;">atque</expan> in minori ſpatio conſtrin<lb></lb>gitur, & hoc fenſu ipſo patet dum aquą <lb></lb>ingreditur per orificium D atque colli <lb></lb>ampullæ particulam aliquam implet; quod verò hu<lb></lb>iuſmodi aeris reſtrictio ſit effectus ponderis aquæ ſu<lb></lb>premæ comprimentis ſenſu ipſo dignoſcitur, <expan abbr="nã">nam</expan> quò <lb></lb>magis aquæ ſuprema ſuperficies S eleuatur versùs R <lb></lb>ſemper magis, ac magis ſucceſſiuè aeris moles præ<lb></lb>dicti tubuli conſtringitur ſubintrando nimirùm aqua <lb></lb>magis à C versùs B. </s> <s id="s.000197">Quòd verò hoc dependeat à <expan abbr="cõ-preſſione">con<lb></lb>preſſione</expan> multiplicati ponderis aquæ ſubleuatæ alià <pb pagenum="43" xlink:href="010/01/051.jpg"></pb><arrow.to.target n="marg44"></arrow.to.target><lb></lb>clariori experientia percipitur, ſi enim abſque noua <lb></lb>aquæ in fuſione in fiſtula aliqua breui, vel pollice, vel <lb></lb>ſubere comprimatur aqua orificium R attingens ſta<lb></lb>tìm apparet effectus prædictæ compreſſionis aquæ, <lb></lb>condenſatur enim, acſtringitur aer in vitrea ampul<lb></lb>la AD eodem modo præcisè, ac maior mo<lb></lb><figure id="id.010.01.051.1.jpg" xlink:href="010/01/051/1.jpg"></figure><lb></lb>les altioris aquæ eleuatæ faciebat, eſtquę <lb></lb>huiuſmodi compreſſio acris in prædictą <lb></lb>ampullula tantæ energiæ vt exiſtente ea le<lb></lb>ui, ſcilicet quæ ſponte ſua ſurſum in aquą <lb></lb>SX aſcendat poſſit è contrà <expan abbr="leuitatẽ">leuitatem</expan> amit<lb></lb>tere, atque acquirere grauitatem, moueri<lb></lb>que, ac deſcendere deorſum, <expan abbr="quotieſcumq;">quotieſcumque</expan> <lb></lb>aqua in fiſtula ad tantam altitudinem ele<lb></lb>uetur vt valdè comprimere ampullulæ aerem poſſit, <lb></lb>vt eam grauem reddat, nec vt hactenùs ſursùm, ſed <lb></lb>deorsùm vergat deſcendatque. </s> </p> <p type="margin"> <s id="s.000198"><margin.target id="marg44"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000199"><emph type="center"></emph>PROP. XVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000200"><emph type="center"></emph><emph type="italics"></emph>Alia ratione grauitatem aquæ ſuper aquam quieſcentis <lb></lb>demonſtrare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000201">HOc deducitur ex eo quòd corpora, quæ ob ex<lb></lb>cedentem eorum grauitatem demerguntur in<lb></lb>fra aquam minùs grauitant in ipſa aqua, quàm iņ <lb></lb>aere, vt ſi fuerit pila AB ferrea ſpecie grauior quàm <lb></lb>ſit aqua ipſa in vaſe RO contenta, & concipiatur IK <lb></lb>vt pondus abſolutum pilæ ferreæ AB, ſcilicèt expri<lb></lb>mat eam grauitatem quam in aere exercet, ſit que eius <pb pagenum="44" xlink:href="010/01/052.jpg"></pb><arrow.to.target n="marg45"></arrow.to.target><lb></lb>portio K grauitas abſoluta pilæ aqueæ C quæ æqua<lb></lb>lis ſit ipſi AB, ſit que pila C contenta intra eiuſdem̨ <lb></lb>aquæ RO profunditatem, vel in altera fiſtula inuerſi <lb></lb>ſiphonis, quæ cum reliqua continuetur, poſtea eadem <lb></lb>pila AB filo DA ab aliqua potentia I ſuſpenſa in me<lb></lb>dio aquæ fixè retineatur. </s> <s id="s.000202">modò ſi poſſibile eſt pilą <lb></lb>aquea C nil prorsùs ponderet in ipſamet aqua, igitur <lb></lb>in ſiphone, vel in libra DE in eius puncto medio F <lb></lb>fulta pila aquea C ſuſpenſa à termino E, quæ <expan abbr="nullã">nullam</expan> <lb></lb>prorſus grauitatem exercere in aqua ſupponitur, <expan abbr="nũ-quam">nun<lb></lb>quam</expan> imminuet pondus contrapoſitæ pilæ AB colli<lb></lb>gatæ termino libræ D, propterea quòd nihilum ab <lb></lb>aliquo pondere ſubtractum ipſum nullo pacto immi<lb></lb>nuit; nec pariter denſitas, & tenacitas aquæ gradum <lb></lb>ponderis pilæ AB diminuere poteſt, propterea quòd <lb></lb>illa reſiſtentia potis eſt retardare, & impedire mo<lb></lb>tum, non autem vim, quam graue AB in quiete con<lb></lb>ſtitutum exercet comprimendo; videmus enim, quòd <lb></lb>pila ferrea quieſcens ſiue fulciatur à molli cera, ſiue <lb></lb>à rigido adamante, ſemper eadem vi comprimit, ſci<lb></lb>licet menſurata à gradu eius <expan abbr="põderis">ponderis</expan>. </s> </p> <p type="margin"> <s id="s.000203"><margin.target id="marg45"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <figure id="id.010.01.052.1.jpg" xlink:href="010/01/052/1.jpg"></figure> <p type="main"> <s id="s.000204">His poſitis ſequitur, quòd pila fer<lb></lb>rea AB pendula intra aquam exerce<lb></lb>bit integram ſuam grauitatem IK, <lb></lb>ſcilicet eam, quam in aere exerce<lb></lb>bat, ſed hoc eſt falſum, imminuitur <lb></lb>enim præcisè pro menſura ponderis <lb></lb>K ſcilicet molis aqueæ C, & ei relin<lb></lb>quitur tantummodò pondus I, ſcili-<pb pagenum="45" xlink:href="010/01/053.jpg"></pb><arrow.to.target n="marg46"></arrow.to.target><lb></lb>cet exceſſus quo pondus eius abſolutum ſuperat gra<lb></lb>uitatem aquæ eiuſdem molis; quapropter verum <expan abbr="nõ">non</expan> <lb></lb>eſt aquam C in ipſamet aqua conſtitutam, nullam <expan abbr="cõ-preſſionem">con<lb></lb>preſſionem</expan>, aut grauitatem exercere. </s> </p> <p type="margin"> <s id="s.000205"><margin.target id="marg46"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000206"><emph type="center"></emph>PROP. XVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000207"><emph type="center"></emph><emph type="italics"></emph>Idipſum alia ratione demonſtrare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000208">VAs RO repleatur aqua, in eaque immergatur <lb></lb>pila ferrea BA quæ filo aliquo DA ſuſtineatur <lb></lb>ne ad fundum vaſis deſcendat. </s> <s id="s.000209">Manifeſtum eſt <expan abbr="potẽ-tiam">poten<lb></lb>tiam</expan> D filum, & pilam retinentem æquari ei graui<lb></lb>tati quam ipſa pila in aqua exercet, & quia in vaſe <lb></lb>aqueo RO deficit præcisè tanta aquæ quantitas, <expan abbr="quã-tum">quan<lb></lb>tum</expan> eſt ſpatium, quod corpus graue A in ipſa oc<lb></lb>cupat, collocatur verò intra aquam ne dum grauę <lb></lb>AB, ſed etiam defectus molis aquæ æqualis eidem̨ <lb></lb>AB quare ſumma poſitiuę grauitatis AB vnà cum de<lb></lb>fectiuo pondere molis aquæ expulſæ à loco AB, ſci<lb></lb>licet exceſſus ponderis AB ſupra pondus molis aquæ <lb></lb>æqualis pilæ AB æqualis erit ponderi quod exercet <lb></lb>pila AB in aqua ergò ſi huiuſmodi aquæ moles ex ſui <lb></lb>natura nil in aqua ponderat quando tollitur a ſpatio <lb></lb>AB moles aquea, quæ ipſum replebat reuerà tollitur <lb></lb>res non grauis, & quæ nil omninò ponderat; igitur à <lb></lb>pondere abſoluto ipſius AB, & à ſpatio ab ea occu<lb></lb>pato nihilum, ſeù nulla grauitas ſubtrahitur, quando <lb></lb>verò ab abſoluta grauitate IK pilæ AB nil prorſus <lb></lb>tollitur, remanet eiuſdem gradus, ac proindè pon-<pb pagenum="46" xlink:href="010/01/054.jpg"></pb><arrow.to.target n="marg47"></arrow.to.target><lb></lb>dus pilæ AB nil prorsùs imminutum erit, & æquali <lb></lb>energia ſuſtineri debet à potentia D, ac ſi eadem pi<lb></lb>la extra aquam in aere libero penderet, ſed hoc eſt <lb></lb>falſum, cùm præcisè in ipſa aqua grauitas pilæ æqua<lb></lb>lis ſit differentiæ ponderis eius abſoluti à grauitatę <lb></lb>aquæ ſibi æqualis mole, vt ex Archimede deducitur, <lb></lb>igitur neceſſariò <expan abbr="fatendũ">fatendum</expan> eſt aquam in ipſamet aqua <lb></lb>collocatam ponderare, & grauitatem exercere. </s> </p> <p type="margin"> <s id="s.000210"><margin.target id="marg47"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000211">Contra hoc euidentiſſimum ratiocinium afferri <lb></lb>ſolet difficultas valdè ſpecioſa, quam examinare, ac <lb></lb>diſſoluere erit operæ pretium, vtque ea ritè percipi<lb></lb>atur, conſideretur hæc figura. </s> <s id="s.000212">Sit vas cylindricum̨ <lb></lb><arrow.to.target n="marg48"></arrow.to.target><lb></lb>ABDC aqua plenum ſit que eius altitudo <lb></lb><figure id="id.010.01.054.1.jpg" xlink:href="010/01/054/1.jpg"></figure><lb></lb>diſſecta in quotcumque partes æquales, <lb></lb>ductis nempè planis imaginarijs MO, & <lb></lb>HI, erit igitur moles aquea AI duplą <lb></lb>aque ę molis HD; igitur pondus aquæ AI <lb></lb>duplum eſt ponderis aquæ HD. quia ve<lb></lb>rò corpus grauius minùs graue ſuperare <lb></lb>debet, hocque è ſuo loco expellere (cùm in eo conſi<lb></lb>ſtat vis, & energìa grauitatis, vt tendat deorsùm, <lb></lb>& ſic è loco infimo corpora minùs grauia expellat) & <lb></lb>poſtquàm aqua AI translata eſt ad locum HD, atque <lb></lb>aquam ibidem collocatam expulit denuò in ſitu ſu<lb></lb>periori fiſtulæ AI aqua dupli ponderis, & molis ibi<lb></lb>dem reſtituitur quæ pariter ſuperat grauitatem ſub<lb></lb>duplam aquæ, quæ ad occupandum infimum locum <lb></lb>HD ſucceſſit, igitur denuò aqua ſuprema vt grauior <lb></lb>infimam è ſuo loco extrudere, atque expellere de-<pb pagenum="47" xlink:href="010/01/055.jpg"></pb><arrow.to.target n="marg49"></arrow.to.target><lb></lb>bet, & quia hoc ſemper repetitur, ſcilicèt perpetuò <lb></lb>reſtituitur in ſuperiori loco AI aqua duplò grauior, <lb></lb>quàm ea, quæ in loco infimo HD reponitur, igitur <lb></lb>vt contingit in libra efficientur perpetuæ, & conti<lb></lb>nuatæ vibrationes, veluti in pendulo, & in aqua fie<lb></lb>ri ſolent plures vndulationes, ſic in aqua perpetuo <lb></lb>motu agitarentur eius partes aſcendendo, & deſcen<lb></lb>dendo. </s> <s id="s.000213">hoc verò ſenſus euidentia redarguit, igitur <lb></lb>fatendum eſt ſupremam aquam AI ſuſtentatam ab <lb></lb>inferiori aqua ſuper eam non exercere vim vllam̨, <lb></lb>nec preſſionem, proinde que non grauitare, hac ſcili<lb></lb>cet de cauſa, quia nimirùm in eius loco naturali col<lb></lb>locata re quieſcit, ac ſiſtitur. </s> </p> <p type="margin"> <s id="s.000214"><margin.target id="marg48"></margin.target>Contra do<lb></lb>ctrinam ſu<lb></lb>periùs addu<lb></lb>ctam adeſt <lb></lb>noua difficul<lb></lb>tas, quod ni<lb></lb>mirum mo<lb></lb>tu perpetuo <lb></lb>aqua agitari <lb></lb>deberet.</s> </p> <p type="margin"> <s id="s.000215"><margin.target id="marg49"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000216"><emph type="center"></emph>PROP. XVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000217"><emph type="center"></emph><emph type="italics"></emph>Maior aquæ moles alteri ſupe poſita non exercet maiorem <lb></lb>vim compresſiuam, quàm minor.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000218">VT verò huiuſmodi paralogiſmus detegatur, <expan abbr="animaduertẽd">a<lb></lb>nimaduertendum</expan> eſt minimè verum eſſe, quòd <lb></lb>quælibet aquæ moles maior alterà, <expan abbr="nẽpe">nempe</expan> dupla, exer<lb></lb>ceat quoque duplam vim grauitantem quotieſcum<lb></lb>que maior ſupra minorem inſiſtat, & ab ea fulciatur, <lb></lb>ſed tunc ſolummodò propoſitio verificatur quando <lb></lb>earum baſes <expan abbr="cõtiguæ">contiguæ</expan> æquales fuerint, ac inſuper in <lb></lb>eodem plano horizonti parallelo conſtiterint. </s> <s id="s.000219">Sup<lb></lb>ponatur vas cylindricum plenum aqua ABDC, ſit<lb></lb>que portio ſuprema, & ideò eius altitudo AH dupla <lb></lb>infimæ altitudinis HB, licèt ergo reuerà ſupremæ <pb pagenum="48" xlink:href="010/01/056.jpg"></pb><arrow.to.target n="marg50"></arrow.to.target><lb></lb>aquæ AI pondus duplum ſit ponderis infimæ aquæ <lb></lb>HD, non hìnc tamen inferri licet ſubiectam aquam <lb></lb>HD in tali ſitu vnicam libram tantummodò pendere <lb></lb>exiſtente ſupremo pondere AI duarum librarum, ſed <lb></lb>neceſsè eſt vt aqua HD comprimat vaſis fundum BD <lb></lb>niſu, ac vi non vnius libræ, ſed æquali ei, quæ effi<lb></lb>citur à pondere trium librarum, & ratio eſt quia ip<lb></lb>ſa aqua HD nedùm impellitur deorſum à vi propriæ <lb></lb>grauitatis vnius libræ, ſed inſuper grauatur compri<lb></lb>miturque ab incumbente pondere aquæ AI, quæ <expan abbr="cõ-preſſio">com<lb></lb>preſſio</expan> ſuperaddit aquę HD vim æqualem ei, quæ à <lb></lb>duabus libris effici poteſt; nec profectò nouum eſt ſi<lb></lb>quis centum laminas ferreas, vel lapideas, æquè <expan abbr="põ-derantes">pon<lb></lb>derantes</expan>, ſcilicet ſingulas vnius libræ vnam ſuper al<lb></lb>teram imponat, quod inſima lamina non tantummo<lb></lb>dò ſuo pondere comprimet planum ſubiectum, ſcili<lb></lb>cèt non efficiet vim æqualem centeſimæ parti totius <lb></lb>prædicti aggregati, ſed compreſſio infimę laminæ ef<lb></lb>ficiet vim centuplo maiorem ſcilicèt impellet ſubie<lb></lb>ctum planum vi æquali centum libris, & tunc <expan abbr="ſolũ-modò">ſolum<lb></lb>modò</expan> inſima lamina partem centeſimam totius ag<lb></lb>gregati ponderabit, quando illa in vna lance, reli<lb></lb>quæ verò 100. in oppoſita lance eiuſdem libræ ra<lb></lb>diorum æqualium ſuſpenderentur; ſic paritèr ſi aqua <lb></lb>HD ſupra planum ſubiectum ſiuè ſolidum, ſiuè flui<lb></lb>dum collocaretur iuxtà portionem aquæ AI, it aut ſe<lb></lb>ſe contingerent lateraliter, atque <expan abbr="earũ">earum</expan> baſes æqua<lb></lb>les in eodem plano horizontali collocarentur, tunc <lb></lb>neceſſariò dupla moles aquæ AI duplam vim com-<pb pagenum="49" xlink:href="010/01/057.jpg"></pb><arrow.to.target n="marg51"></arrow.to.target><lb></lb>preſſiuam, pro menſura duplæ grauitatis haberet. <lb></lb></s> <s id="s.000220">Verum tamen eſt, quòd alia de cauſa non eſt neceſ<lb></lb>sè, vt ſemper baſes ſint æquales, neque grauitates <lb></lb>ſint in eadem proportione dupla, dummodò altitu<lb></lb>do AH dupla ſit altitudinis ipſius HB; & ratio huius <lb></lb>diuerſitatis pendet ex alibi demonſtrandis. </s> </p> <p type="margin"> <s id="s.000221"><margin.target id="marg50"></margin.target>Cap. 3. flui<lb></lb>dum in ſue <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000222"><margin.target id="marg51"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000223">Ex ſuperiori igitur ratiocinio euinci<lb></lb><figure id="id.010.01.057.1.jpg" xlink:href="010/01/057/1.jpg"></figure><lb></lb>tur, falſum eſſe, quòd pronunciabatur, <lb></lb>nimirùm, duplam aquam AI vt grauio<lb></lb>rem, expellere deſcendendo debere ſub<lb></lb>duplam aquam ſubiectam HD, cùm ècon <lb></lb>tra hæc vt grauior, grauitate nempe pro<lb></lb>pria, & ea, quæ ei ſuperadditur ab aqua <lb></lb>ſuperincumbente AI in eodem loco infimo perma<lb></lb>nere debeat, nec vnquam à debiliori compreſſione <lb></lb>ſuperſtantis aquæ expelli poſſit, ac proindè ſequitur <lb></lb>ſumma quies, ac tranquillitas, non verò motus per<lb></lb>petuus. <lb></lb><arrow.to.target n="marg52"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000224"><margin.target id="marg52"></margin.target>Ex doctrina <lb></lb>ſuperiùs tra<lb></lb>dita videtur <lb></lb>deduci poſ<lb></lb>ſe lignum <lb></lb>infra aquam <lb></lb>poſitum ſur<lb></lb>ſum <expan abbr="aſcẽde-">aſcende<lb></lb>re</expan> non poſſe.</s> </p> <p type="main"> <s id="s.000225">Sed dices, ſi vera eſſet adducta doctrina, lignum <lb></lb>deberet in fundo aquæ paritèr retineri, proptereą <lb></lb>quòd nedum à propria grauitate comprimitur, ſed <lb></lb>etiam à pondere totius aquæ ſuperſtantis, & ideò <lb></lb>magis grauitaret quàm aqua ei ſuperpoſita, & proin<lb></lb>de lignum in fundo aquæ permanere deberet: hoc <lb></lb>autem falſum eſt, cùm experientia conſtet, lignum <lb></lb>ſursùm ferri, nec quieſcere, antequàm ad aquæ ſu<lb></lb>premam libellam perducatur. </s> </p> <pb pagenum="50" xlink:href="010/01/058.jpg"></pb> <p type="main"> <s id="s.000226"><arrow.to.target n="marg53"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000227"><margin.target id="marg53"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000228"><emph type="center"></emph>PROP. XIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000229"><emph type="center"></emph><emph type="italics"></emph>Lignum infra aquam demerſum, licèt pondus proprium, & <lb></lb>aquæ incumbentis exerceat, non proinde ibidem <lb></lb>quieſcet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000230">VT autem huius argumenti falla cia patefiat, in <lb></lb>vaſe ARSE aqua pleno demergatur priſma li<lb></lb>gneum, vel aereum HBDI ſitquę <lb></lb><figure id="id.010.01.058.1.jpg" xlink:href="010/01/058/1.jpg"></figure><lb></lb>pondus aquæ AI decem librarum̨ <lb></lb>v. g. lignum verò HD ſemilibram̨ <lb></lb>pendeat. </s> <s id="s.000231">Concedo, quòd lignum̨ <lb></lb>HD premit ſubiectam aquam BV <lb></lb>non vi ſemilibræ, ſed robore libra<lb></lb>rum decem, & ſemis, & ideo <expan abbr="lignũ">lignum</expan> <lb></lb>HD magis comprimit, ac grauitat, <lb></lb>quàm ſola aqua incumbens AI, ſed non proindè ſe<lb></lb>quitur, lignum HD quatenùs magis comprimit, ac <lb></lb>grauitat in fundo aquæ perſiſtere debere, cùm ab <lb></lb>alia cauſa ſursùm exprimatur. </s> <s id="s.000232">Secto enim priſmatę <lb></lb>aqueo CEFI æquali ipſi AI, & aqueo priſmate IG <lb></lb>cuius moles æqualis ſit ligno HD, & eius pondus <lb></lb>duas libras ſuperet; patet quòd aqua ſubiecta BV <lb></lb>premitur à pondere librarum decem, & ſemis, at <lb></lb>aqua DS comprimitur à pondere librarum duode<lb></lb>cim; ergo sipho, vel libra mobilis aquea BG flecti <lb></lb>debet eleuando lignum HD minus graue. </s> <s id="s.000233">Et hinc <lb></lb>patet, quòd ratio, quare lignum aſcendit, non eſt <lb></lb>pondus aquæ incumbentis AI, ſed eſt aqua collate-<pb pagenum="51" xlink:href="010/01/059.jpg"></pb><arrow.to.target n="marg54"></arrow.to.target><lb></lb>ralis IG, & hoc conſtat, quia ſi in ſtricta fiſtula vitrea <lb></lb>ARVC ponatur in eius fundo aqua BV in loco me<lb></lb>dio lignum HD, vel exigua aeris veſica, quæ vaſis <lb></lb>latera exactè tangat, & reliquum vaſis repleatur a<lb></lb>qua AI, tunc lignum non aſcendet ſurſum, quia nem<lb></lb>pè ſipho, vel libra mobilis <expan abbr="cũ">cum</expan> aqua collaterali crea<lb></lb>ri non poteſt. </s> </p> <p type="margin"> <s id="s.000234"><margin.target id="marg54"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000235"><emph type="center"></emph>CAP. XX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000236"><emph type="center"></emph><emph type="italics"></emph>Corpora terrena cùm è locis ſuis naturalibus remouentur <lb></lb>deſcendendo nullam grauitatem exercent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000237">SEd ſublata prædicta difficultate deuenio ad <expan abbr="oſtẽ-dendum">oſten<lb></lb>dendum</expan> quòd adeò falſum eſt corpora terrena <lb></lb>dum quieſcunt in proprijs locis non grauitare, vt è <lb></lb>contra quando à locis naturalibus ſeparata mouen<lb></lb>tur <expan abbr="tũc">tunc</expan> nullam grauitatem exerceant ſuper alias par<lb></lb>tes eiuſdem corporis, quod licèt videatur parado<lb></lb>xum, oſtendetur nihilominùs hac ratione. </s> <s id="s.000238">Conci<lb></lb>piantur primò facilitatis gratia duo lanæ inuolucra, <lb></lb>vnum ſuper alterum impoſitum ſupra planum ſubie<lb></lb>ctum, certum eſt ſupremum comprimere, & grauita<lb></lb>tem exercere ſupra ſubiectum inuolucrum, & hoc <expan abbr="cõ-ſtat">con<lb></lb>ſtat</expan> ſenſu ab effectu ouem producit pondus lanæ in<lb></lb>cumbentis, ſcilicèt ex inflexione, & compreſſionę <lb></lb>pilorum ſubiectæ lanæ, & è contra conſtat quando <lb></lb>eadem duo lanæ inuolucra collateralitèr ſeſe contin<lb></lb>gunt fulciunturque à ſubiecto plano, tunc neque pi<lb></lb>li lanei collaterales inflectuntur, nec comprimuntur, <pb pagenum="52" xlink:href="010/01/060.jpg"></pb><arrow.to.target n="marg55"></arrow.to.target><lb></lb>propterea quòd niſus grauitatis non exercetur late<lb></lb>raliter, ſed deorsùm. </s> </p> <p type="margin"> <s id="s.000239"><margin.target id="marg55"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000240">Hinc colligitur, quòd quotieſcumque ſupremum <lb></lb>lanæ inuolucrum perpendicularitèr incumbens ſu<lb></lb>peralterum, ſi ipſum non flecteret, nec ſtringeret, <lb></lb>tunc planè affirmandum eſſet lanam ſuperpoſitam̨ <lb></lb>minimè ſuper ſubiectam lanam grauitatem exercere. </s> </p> <p type="main"> <s id="s.000241">His poſitis, ſupremum lanæ inuolucrum applica<lb></lb>ri poteſt ſuper infimum dum hoc actu per aerem mo<lb></lb>uetur deſcendendo deorſum, vel dum quieſcit à pla<lb></lb>no ſtabili fultum; in primo caſu manifeſtum eſt, <lb></lb>quòd inuolucra æqualia eiuſdem lanæ æquales gra<lb></lb>dus velocitatum <expan abbr="habẽt">habent</expan>, quibus naturaliter deſcen<lb></lb>dunt; igitur ſupremum inuolucrum non deſcendet <lb></lb>tardiori, vel celeriori motu quàm ſibi <expan abbr="ſubiectũ">ſubiectum</expan>, pro<lb></lb>indeque æquali velocitare ſuprema lana compri<lb></lb>mere conatur ſubiectam lanam, ac iſta nititur effu<lb></lb>gere perſequentem; proptereaque ſe mutuo placi<lb></lb>do contactu ſolummodò exoſculantur, nec ſubiecta <lb></lb>inflectetur, aut comprimetur à ſuperſtante lana: <lb></lb>igitur, ex ſuperiùs dictis incumbens lana nequè <expan abbr="põ-dus">pon<lb></lb>dus</expan>, neque grauitatem exercebit ſupra fugientem <lb></lb>lanam ſubiectam. </s> <s id="s.000242">In ſecundo verò caſu ſi poſtquàm <lb></lb>in quiete ſubiecta lana compreſſa eſt à ſuperincum<lb></lb>bente ambas demittamus, & liberè deorſum <expan abbr="deſcẽ-dere">deſcen<lb></lb>dere</expan> concedamus, pateteas motum inchoare quan<lb></lb>do iam reſtrictæ, & conſtipatæ ſunt, & ideò in pro<lb></lb>greſſu licèt paribus velocitatibus deſcendant, reti<lb></lb>n bunt tamen eandem conſtipationem, quam prius <pb pagenum="53" xlink:href="010/01/061.jpg"></pb><arrow.to.target n="marg56"></arrow.to.target><lb></lb>habebant; ſed hinc non licet inferre, ſupremam la<lb></lb>nam dum mouetur grauitatem exercere, quia illą <lb></lb>conſtipatio non dependet ab actione grauitatis in<lb></lb>cumbentis lanæ quæ actio perſeueret exerceaturque <lb></lb>tempore deſcenſus, ſed illa conſtipatio eſt effectus <lb></lb>compreſſionis in præcedenti quiete factæ, in actu e<lb></lb>nim deſcenſus nullo pacto impellere poteſt ſuprema <lb></lb>lana ſubiectam pani velocitate ictum fugientem, & <lb></lb>ideo ſuper eam minimè pondus exercebit. </s> </p> <p type="margin"> <s id="s.000243"><margin.target id="marg56"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000244"><emph type="center"></emph>PROP. XXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000245"><emph type="center"></emph><emph type="italics"></emph>Aqua deſcendens per aerem, nullam grauitatem habet, & <lb></lb>ſolummodò eam exercet, quando quieſcit ſuper <lb></lb>aquam.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000246">SImili modo aqua non deſcendit, quando fulci<lb></lb>tur à ſuperficie terræ, & maris, ſed quando <lb></lb>extra ſuum locum peregrinatur, & mouetur, vt iņ <lb></lb>aere, & tunc ſi conſideretur cylindrus aqueus per ae<lb></lb>rem deſcendens, diuidaturque in partes æquales à <lb></lb>planis horizonti æquidiſtantibus; quia partes æqua<lb></lb>les eiuſdem aquæ ſunt æquè graues, habent impe<lb></lb>tus æquales à natura ſibi aſſignatos quibus deſcen<lb></lb>dere deorſum nituntur, igitur pars ſuprema eiuſdem <lb></lb>cylindri aquei æquè velox erit, ac pars ei ſubiecta, <lb></lb>igitur ſuprema non poterit impellere, vel compri<lb></lb>mere aquam ei ſubiectam, cùm æquali velocitatę <lb></lb>hęc ictum, & percuſſionem fugiat cum quanta à ſu<lb></lb>perincumbente inſectatur perſequiturque, ſicuti <pb pagenum="54" xlink:href="010/01/062.jpg"></pb><arrow.to.target n="marg57"></arrow.to.target><lb></lb>ſagitta exploſa minimè percutiet ſignum æquali ve<lb></lb>locitate ictum fugiens; igitur manifeſtum eſt, aquam <lb></lb>minimè grauitatem exercere ſupra ei ſubiectam a<lb></lb>quam, quando à proprio loco naturali exulat, & per <lb></lb>aerem mouetur. </s> </p> <p type="margin"> <s id="s.000247"><margin.target id="marg57"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000248">Secùs autem contingit in aqua quieſcente, iņ <lb></lb>puteo aliquo, vellacu, ſi enim diuidatur pariter in <lb></lb>laminas æque altas, patet quòd ſupremane dum <expan abbr="tã-git">tan<lb></lb>git</expan> ſimpliciter ſubiectam aquæ laminam, ſed è con<lb></lb>tra eam impellit tanta vi <expan abbr="quãta">quanta</expan> eſt energia eius gra<lb></lb>uitatis, & patet quòd infima aqua pati cogitur com<lb></lb>preſſionem, cùm ſuſtinere debeat pondus ſupremæ <lb></lb>aquæ incumbentis: & hoc accidit, quia ſua quiete <lb></lb>impedit progreſſum, & conatum compreſſiuum <expan abbr="de-orsũ">de<lb></lb>orsum</expan> ſuperpoſitæ aquę; hac de cauſa ſi habueit poro<lb></lb>ſitates hæ neceſſario conſtringentur à vi ponderis <lb></lb>incumbentis aquæ. </s> <s id="s.000249">Modò quia impulſus compreſſi<lb></lb>uus factus à ſuperiore aqua ſupra inferiorem nullo <lb></lb>alio vocabulo deſignatur, quàm grauitatis, vel <expan abbr="põ-deris">pon<lb></lb>deris</expan>, igitur verum erit, quòd aqua ſuper aquam <lb></lb><arrow.to.target n="marg58"></arrow.to.target><lb></lb>quieſcentem grauitatem exercet non quando in mo<lb></lb>tu conſtituitur, & extra ſuum naturalem locum, ſed, <lb></lb>tantummodò, quando ſiſtitur, & quieſcit in loco ſuo <lb></lb>naturali. </s> </p> <p type="margin"> <s id="s.000250"><margin.target id="marg58"></margin.target>Contra do<lb></lb>ctrinam ſu<lb></lb>periùs addu<lb></lb>ctam afferri <lb></lb>ſolet difficul<lb></lb>tas valdè <lb></lb>plauſibilis, <lb></lb>quod nimi<lb></lb>rum vrina<lb></lb>tores ingens <lb></lb>pondus aque <lb></lb>incumbentis <lb></lb>nec patian<lb></lb>tur, nec ſen<lb></lb>tiant.</s> </p> <p type="main"> <s id="s.000251">Hiſce omnibus rationibus opponi ſolet <expan abbr="experiẽ-tia">experien<lb></lb>tia</expan> ſatis vulgata, eſtque huiuſmodi: vrinatores iņ <lb></lb>profundo maris demerſi non ſentiunt, neque <expan abbr="patiũ-tur">patiun<lb></lb>tur</expan> compreſſionem ſuperincumbentis aquæ, quæ <lb></lb>multoties plures congios excedit; hinc inferunt, ſi <pb pagenum="55" xlink:href="010/01/063.jpg"></pb><arrow.to.target n="marg59"></arrow.to.target><lb></lb>aqua in ipſamet aqua pondus, & grauitatem habe<lb></lb>ret, neceſſariò vrinatores comprimerentur à vaſto <lb></lb>pondere aquæ incumbentis ſuper eorum humeros, <lb></lb>immò nec poſſet pondus tam vaſtum à viribus huma<lb></lb>nis ſuſtineri, quando videmus, ab homine robuſto <lb></lb>minus pondus ſuſtineri non poſſe; cùm ergo experi<lb></lb>entia doceat vrinatores in fundo aquæ grauitatem̨ <lb></lb>nullam percipere, igitur verum non eſt, aquam iņ <lb></lb>ipſa aqua collocatam grauitare, immò in proprio lo<lb></lb>co nil prorsùs ponderahit. </s> </p> <p type="margin"> <s id="s.000252"><margin.target id="marg59"></margin.target>Cap. 3. flui <lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000253">Huic vulgari difficultati vt fiat ſatis <expan abbr="præmittendũ">præmittendum</expan> <lb></lb>eſt, quòd aqua in ipſamet aqua conſtituta, <expan abbr="pariterq;">pariterque</expan> <lb></lb>quodlibet fluidum in ſuo homogeneo demerſum non <lb></lb>alia de cauſa quieſcit, niſi quia vndique comprimi<lb></lb>tur pari vi à grauitate ambientis fluidi, cui proprią <lb></lb>grauitate reſiſtit, vtque hoc clariùs percipiatur, o<lb></lb>ſtendemus, quod. </s> </p> <p type="main"> <s id="s.000254"><emph type="center"></emph>PROP. XXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000255"><emph type="center"></emph><emph type="italics"></emph>Corpora in bilance æquilibrata ideò quieſcunt, & torpent, <lb></lb>quia grauitatem exercent comprimunturque æquali<lb></lb>bus viribus ab ambientibus corporibus pariter <lb></lb>æquilibratis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000256">ESto libra AB radiorum æqualium in eius puncto <lb></lb>intermedio C ſuſpenſa, atque in eius extremi<lb></lb>tatibus, vtrinque quatuor laminas, vel lateres æquè <lb></lb>ponderantes ſibi mutuò incumbentes apponantur, <lb></lb>ſcilicet DE, EF,, FG, GH, ſu per A, & totidem IK, <pb pagenum="56" xlink:href="010/01/064.jpg"></pb><arrow.to.target n="marg60"></arrow.to.target><lb></lb>KL, LM, MN ſuper <expan abbr="terminũ">terminum</expan> B. </s> <s id="s.000257">Manifeſtum eſt, ag<lb></lb>gregatum ex laminis DH ibidèm retineri indifferen<lb></lb>tia quadam, nec pelli ſursùm, aut deorsùm, firmiter<lb></lb>que in tali ſitu quieſcere, vt nimirùm ſi quis infrą <lb></lb>laterem DE manum ſupponeret, minimè ab ipſis <expan abbr="cõ-primeretur">com<lb></lb>primeretur</expan>, neque vllam grauitatem perciperet, hoc <lb></lb>autem non contingit ex eo, quòd laminę lateritiæ <lb></lb>grauitatem amittant, & deorsùm nil comprimant, <lb></lb>ſed quia ab æquali vi contraria ſuſtinentur, ac ſursùm <lb></lb><expan abbr="impellũtur">impelluntur</expan> à pondere nempè oppoſito IN ſibi æquali <lb></lb>in libra AB premente. </s> <s id="s.000258">Præterea quælibet lamina in<lb></lb>termedia FE ſimilitèr quieſcit, ſiſtiturque iners, vt <lb></lb>neque ſursùm, neque deorsùm moueatur, nequę <lb></lb>ſubiectam manum, quæ lateralitèr eam retinere co<lb></lb>naretur vllatenùs comprimit, aut impellit, & hoc <lb></lb>efficitur quia lamina <lb></lb><figure id="id.010.01.064.1.jpg" xlink:href="010/01/064/1.jpg"></figure><lb></lb>FE comprimitur de<lb></lb>orſum ab incumben<lb></lb>te pondere FH, ſur<lb></lb>sùm verò impellitur <lb></lb>à ſubiecta lamina DE non virtute propria, ſed eius, <lb></lb>quam exercet contra poſitum pondus IN ſcilicet tan<lb></lb>ta vi, quanta <expan abbr="põdus">pondus</expan> IN ſuperat pondus DE; ſed quia <lb></lb>præterea lamina ipſa FE exercet vim ſui ponderis <lb></lb>contra preſſionem contrapoſiti exceſſus KN fit vt vis <lb></lb>quæ impellit ſursùm laminam FE æqualis ſit exceſſui <lb></lb>ipſius KN ſupra FE, ſcilicet æqualis ſit NL; ſuntque <lb></lb>FH, & LN inter ſe æquales; ergo viribus æqualibus <lb></lb>FE deprimitur ac ſursùm impellitur. </s> <s id="s.000259">E contra lami-<pb pagenum="57" xlink:href="010/01/065.jpg"></pb><arrow.to.target n="marg61"></arrow.to.target><lb></lb>na FE impellit deorſum laminam DE, ne dum pro<lb></lb>prio pondere, ſed etiam grauitate laminarum FH; <lb></lb>pariterque FE repellit laminas ſupremas FH noņ <lb></lb>propria virtute, ſed vi ponderis LN ſcilicet exceſſu <lb></lb>IN ſupra DF; Quaproptèr conſtat, quòd lamina la<lb></lb>teritia FE comprimitur ſupernè, & infernè à duabus <lb></lb>viribus contrarijs quæ æqualibus momentis <expan abbr="operã-tur">operan<lb></lb>tur</expan>, à quibus proindè retinetur fixè, vt nequeat ſur<lb></lb>sùm, aut deorsùm moueri. </s> <s id="s.000260">Præterea colligitur, quòd <lb></lb>reuerà lamina lateritia FE non verè in quiete inerti <lb></lb>conſtituitur, nec pondere priuatur, ſed potiùs effi<lb></lb>citur lucta quædam contrariarum virtutum <expan abbr="æqualiũ">æqualium</expan> <lb></lb>virium, vndè æquatis momentis motus tonicus, ſeù <lb></lb>quies ſubſequitur, & hìnc deducitur quòd prædicta <lb></lb>corpora ſe mutuò comprimunt, & hìnc fit, vt neuter <lb></lb><expan abbr="contrariorũ">contrariorum</expan> impellentium ſuum iter proſequi valeat, <lb></lb>proindeque cogantur fixè in eodem ſitu quieſcere. </s> </p> <p type="margin"> <s id="s.000261"><margin.target id="marg60"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000262"><margin.target id="marg61"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000263"><emph type="center"></emph>PROP. XXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000264"><emph type="center"></emph><emph type="italics"></emph>Idipſum in aqua oſtenditur exemplo ſiphonis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000265">EOdem ferè modo in aqua idem æquilibrium ef<lb></lb>fici manifeſtum eſt, proindeque partes ipſius <lb></lb>aquæ partim ſupernè comprimi à ſuperſtantibus a<lb></lb>quæ partibus, partim verò infernè ſursùm expelli, <expan abbr="nõ">non</expan> <lb></lb>propria vi, ſed pondere collateralis aquæ, quæ cum <lb></lb>illa libram imaginariam, vel ſiphonem conſtituit. <lb></lb></s> <s id="s.000266">Eſto igitur, claritatis gratia, ſipho HAB perpendi<lb></lb>cularitèr eleuatus ſupra horizontem, repletuſquę <pb pagenum="58" xlink:href="010/01/066.jpg"></pb><arrow.to.target n="marg62"></arrow.to.target><lb></lb>aqua vſque ad ſuprema orificia H & N; ſubdiuida<lb></lb>tur tota eius altitudo in partes æquales ductis nimi<lb></lb>rum planis ſuperficiebus GM, <lb></lb><figure id="id.010.01.066.1.jpg" xlink:href="010/01/066/1.jpg"></figure><lb></lb>FL, EK, DI; hic profectò aquæ <lb></lb>portio FE, licèt nullum <expan abbr="effectũ">effectum</expan> <lb></lb>grauitatis producere, <expan abbr="atq;">atque</expan> iner<lb></lb>ter quieſcere videatur, dùm in<lb></lb>differens eſt ad motum ſursùm, <lb></lb>& deorsùm, non hìnc deducere <lb></lb>licet, aquam ipſam FE in tali ſi<lb></lb>tu vim propriæ grauitatis non exercere, nec <expan abbr="cõprimi">comprimi</expan> <lb></lb>ab aqua ſuperna, & inferna: <expan abbr="cõſideretur">conſideretur</expan> enim quòd <lb></lb>FF, in parte ſuprema ab aqua FH comprimitur de<lb></lb>orsùm, è contrà à ſubiecta aqua DE expellitur ſur<lb></lb>sùm, non propria vi, ſed pondere contrapoſitę aquæ <lb></lb>NL. </s> <s id="s.000267">Hinc colligitur, quòd aqua FE reuerà impelli<lb></lb>tur deorsùm à ſuperna aqua, & ſursùm ab inferna; <lb></lb>ipſa veròmet aqua FE è contrà vim exercet contrą <lb></lb>vtramque compreſſionem, ſcilicèt contra eam, quæ <lb></lb>efficitur ab aqua ſubiecta, reſiſtit <expan abbr="põdere">pondere</expan> ſuo pro<lb></lb>prio vnà cum grauitate incumbentis aquæ FH, ſed <lb></lb>contra vim, qua comprimitur ſupernè non reſiſtit, & <lb></lb>contranititur virtute propria, ſed mediante impul<lb></lb>ſu deſcenſiuo collateralis aquæ NK, igitur huiuſmo<lb></lb>di quies aquæ, quæ in ſitu FE indifferentèr retinetur, <lb></lb>nec poteſt ſursùm, aut deorsùm moueri, eſt effectus, <lb></lb>qui neceſſariò conſequitur ad exercitium ſuæ natiuæ <lb></lb>grauitatis, & eius, quæ exercetur ab aqua ſiphonis, <lb></lb>vel ab aqua collaterali eiuſdem vaſis, in quo paritèr <pb pagenum="59" xlink:href="010/01/067.jpg"></pb><arrow.to.target n="marg63"></arrow.to.target><lb></lb>aqua operatur, veluti in ſiphone collocata fuiſſet. </s> </p> <p type="margin"> <s id="s.000268"><margin.target id="marg62"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000269"><margin.target id="marg63"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000270"><emph type="center"></emph>PROP. XXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000271"><emph type="center"></emph><emph type="italics"></emph>Aqua in ipſamet aqua demerſa undiquè comprimitur ab <lb></lb>ambiente aqua, & vtraque grauitatem exercet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000272">INtra vas ABCD aqua plenum intelligatur priſma <lb></lb>aqueum FGHE, ductiſque planis FL, & GM pa<lb></lb>rallelis horizonti. </s> <s id="s.000273">Dico, quòd aqua FH vndique pre<lb></lb>mitur ab ambiente aqua FILKG, & vtraque pondus <lb></lb>grauitatemque exercet. </s> <s id="s.000274">Quia aqua FH cum aquą <lb></lb>ambiente ſiphonem AKD conſtituit, in quo fluidum <lb></lb>ſibi homogeneum agitari poteſt, & quieſcit nihilo<lb></lb>minùs; ergo vna pars fluidi AK <lb></lb><figure id="id.010.01.067.1.jpg" xlink:href="010/01/067/1.jpg"></figure><lb></lb>æquilibratur, proindequè æquè <lb></lb>ponderat, ac pars reliqua latera<lb></lb>lis IC, portio verò aquæ FH licèt <lb></lb>motu careat, ſitque indifferens <lb></lb>ad motum ſursùm, & deorsùm, <lb></lb>haud inferre licet eam non exer<lb></lb>cere vim ſuæ grauitatis vnà cum tota aqua ambi<lb></lb>ente, quia in ſiphonis brachio AK aquæ FH ſu<lb></lb>prema facies FE deorſum impelli, & comprimi de<lb></lb>bet ab incumbente aqua AE, pariterque infimą <lb></lb>illius facies GH ſursùm impelletur à ſubiecta a<lb></lb>qua GK non virtute propria, ſed eius quam exercet <lb></lb>pondus aquæ collateralis IM; porrò nedum aqua FH <lb></lb>impellitur ſurſum ab aqua ſubiecta BH, ſed etiam, vt <lb></lb>experientia conſtat, impulſionem, & <expan abbr="conſtrictionẽ">conſtrictionem</expan> <pb pagenum="60" xlink:href="010/01/068.jpg"></pb><arrow.to.target n="marg64"></arrow.to.target><lb></lb>patietur facies eius FH ab aqua collaterali DH; <lb></lb>quod euidentius <expan abbr="oſtẽdetur">oſtendetur</expan> prop. 192. Stringitur er<lb></lb>go aqua FH veluti prælo, nec tamen iners omninò <lb></lb>eſt, repellit enim ſursùm aquam <lb></lb><figure id="id.010.01.068.1.jpg" xlink:href="010/01/068/1.jpg"></figure><lb></lb>AE vi grauitatis aquæ lateralis <lb></lb>IL, aquam verò ſubiectam repel<lb></lb>lit deorsùm vi grauitatis pro<lb></lb>priæ, & ſupremæ IE. quare quies <lb></lb>aquæ FH eſt effectus dependens <lb></lb>à compreſſione facta ab aqua am<lb></lb>biente, & ab exercitio ſuæ grauitatis, & eius quam <lb></lb>aqua ambiens ſiphonem conſtituens exercet: quod <lb></lb>erat &c. </s> </p> <p type="margin"> <s id="s.000275"><margin.target id="marg64"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000276"><emph type="center"></emph>PROP. XXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000277"><emph type="center"></emph><emph type="italics"></emph>Quodlibet corpus in aqua demerſum vndique ſtringitur <expan abbr="cõ-primiturque">con<lb></lb>primiturque</expan> ab ambiente aqua.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000278">IN eadem figura quodlibet corpus durum, molle, <lb></lb>vel <expan abbr="fluidũ">fluidum</expan> FH in aqua demerſum fixè detineatur. <lb></lb></s> <s id="s.000279">Dico ipſum vndiquè ſtringi, ac <expan abbr="cõprimi">comprimi</expan> ab ambien<lb></lb>te fluido FILHB. </s> <s id="s.000280">Quia ſolidum FH intra aquam re<lb></lb>tentum vnà cum ambiente aqua conſtituit ſiphonem <lb></lb>AKD in quo eius partes AK, & KD quieſcunt, & æ<lb></lb>quilibrantur, ergò oportet vt aqua ſuprema AE <expan abbr="cõ-primat">con<lb></lb>primat</expan>, <expan abbr="impellatq;">impellatque</expan> deorsùm ſolidi ſuperficiem FE, <lb></lb>pariterque debet aqua ſubiecta GK impellere ſur<lb></lb>ſum ſolidi ſuperficiem GH non virtute propria, ſed <lb></lb>vi ponderis aquæ collateralis IM, ſimiliter ſolidi fa-<pb pagenum="61" xlink:href="010/01/069.jpg"></pb><arrow.to.target n="marg65"></arrow.to.target><lb></lb>ciem EH ſtringet lateraliter eadem aqua IM. </s> <s id="s.000281">Igitur <lb></lb>vndique ſolidum FH ſtringitur comprimiturquè <expan abbr="tã-quam">tan<lb></lb>quam</expan> à prælo: quod erat &c. </s> </p> <p type="margin"> <s id="s.000282"><margin.target id="marg65"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000283">Et hìc notandum eſt, quòd ſi corpus FH fuerit <lb></lb>veſica flexilis repleta corpore fluido concipi poteſt <lb></lb>conſtans ex partibus non condenſabilibus, vt eſt a<lb></lb>qua, hydrargyrum, & aggregatum ex minimis ſphę<lb></lb>rulis cryſtallinis; aut componatur ex partibus adeò <lb></lb>raris, atque poroſis, vt ingentem condenſationem̨ <lb></lb>pati poſſint, cuius natura Aer eſt. </s> <s id="s.000284">In primo caſu li<lb></lb>cèt veſica FH vndique æqualibus viribus compri<lb></lb>matur ſtringaturque, nihilominùs ob duritiem par<lb></lb>tium in veſica contentarum, non poterit ipſa veſicą <lb></lb>conſtringi, <expan abbr="cõdenſarique">condenſarique</expan>, ſcilicèt minus ſpatium ex<lb></lb>plere, quàm prius occupauerat, eò quòd particulæ <lb></lb>ipſæ duriſſimæ fluidæ, vel denſæ adinuicem fulciun<lb></lb>tur, veluti columnæ, aut fornices, quæ nullo pacto <lb></lb>poſſunt frangi, vel conſtringi, cùm è contrà partes <lb></lb>aeris ob maximam earum raritatem facilè poſſint <expan abbr="cõ-ſtipari">con<lb></lb>ſtipari</expan>, proindeque veſica aera FH ad minus ſpatiûm <lb></lb>redigi poſſit conſtrictis nempè eius poroſitatibus. </s> </p> <p type="main"> <s id="s.000285">His declaratis pro reſolutione principalis proble<lb></lb><arrow.to.target n="marg66"></arrow.to.target><lb></lb>matis <expan abbr="inquirẽdũ">inquirendum</expan> eſt, quo modo, & qua ratione à com<lb></lb>preſſione ponderis incumbentis paſſio dolorifica in <lb></lb>animali ſubſequatur. </s> </p> <p type="margin"> <s id="s.000286"><margin.target id="marg66"></margin.target>Inquiritur <lb></lb>cauſa quare <lb></lb>à pondere in<lb></lb>cumbente <lb></lb>producitur <lb></lb>compreſſio, <lb></lb>ſciſſio, diui<lb></lb>ſio continui, <lb></lb>& proinde <lb></lb>dolor.</s> </p> <p type="main"> <s id="s.000287">Et primò experientia conſtat, à pondere corporis <lb></lb>manum v. g. prementis aliquando effici ſciſſionem, <lb></lb>vt ab acie ſecuris incumbentis, aliquando <expan abbr="fractionẽ">fractionem</expan>; <lb></lb>multotiès luxari, & diſrumpi articulos tractis nem-<pb pagenum="62" xlink:href="010/01/070.jpg"></pb><arrow.to.target n="marg67"></arrow.to.target><lb></lb>pè violentèr tendinibus articulos colligantibus, & <lb></lb>tandem fieri poteſt contuſio, & diffractio partium̨ <lb></lb>ſolidarum. </s> <s id="s.000288">Et hiſce omnibus modis continuitatis <lb></lb>diuiſio in animali efficitur, à quà demum diuiſionę <lb></lb>paſſionem dolorificam exoriri vulgò credunt. </s> </p> <p type="margin"> <s id="s.000289"><margin.target id="marg67"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000290">Modò oſtendendum eſt, quòd diuiſio continui, & <lb></lb>dolor procreari poteſt ab aliquo ſingulari pondere, <lb></lb>quòd ſi pondus poſtea comprimens augeatur, mul<lb></lb>tipliceturque, non proindè ſemper, & vniuersè ma<lb></lb>ior, ſed minor, immò nulla ſciſſura, vel contuſio, <lb></lb>aut fractio in animali ſub ſequi poteſt; quod quidem <lb></lb>licèt videatur paradoxum, poterit tamen facili ne<lb></lb>gotio demonſtrari. </s> </p> <p type="main"> <s id="s.000291"><emph type="center"></emph>PROP. XXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000292"><emph type="center"></emph><emph type="italics"></emph>Lamina dura, & flexibilis, quæ à pondere incumbente <lb></lb>flectitur, poterit à potentia duplicata dirigi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000293">SIt lamina chalybea AB parieti RS infixa, <expan abbr="eiq;">eique</expan> in<lb></lb>cumbat pondus C à quo lamina ipſa deorsùm̨ <lb></lb>impulſa curuitatem acquirat, <lb></lb><figure id="id.010.01.070.1.jpg" xlink:href="010/01/070/1.jpg"></figure><lb></lb>inflectaturque: adueniat po<lb></lb>ſtea vis motiua H æqualis pon<lb></lb>deri C, quæ contrario niſu ſur<lb></lb>sùm impellat eamdem <expan abbr="laminã">laminam</expan>: <lb></lb>manifeſtum eſt, quòd à duplici <lb></lb>vi C, & H, non augetur curui<lb></lb>tas ipſius laminæ, ſed ea potiùs dirigitur, quia ni<lb></lb>mirùm duæ vires contrarię æqualibus <expan abbr="momẽtis">momentis</expan> ope-<pb pagenum="63" xlink:href="010/01/071.jpg"></pb><arrow.to.target n="marg68"></arrow.to.target><lb></lb>rantes ſibi mutuò impellunt, & proindè vna alterius <lb></lb>vim, & actionem deſtruit, quantum ergo lamina in<lb></lb>flectitur deorsùm à <expan abbr="põdere">pondere</expan> C, tantumdèm ſursùm re<lb></lb>flectitur à contrario impulſu ipſius H. <margin.target id="marg68"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000294"><emph type="center"></emph>PROP. XXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000295"><emph type="center"></emph><emph type="italics"></emph>Idipſum adhibitis contrarijs ponderibus ope libræ <lb></lb>verificatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000296">APplicetur libra DE radio<lb></lb><figure id="id.010.01.071.1.jpg" xlink:href="010/01/071/1.jpg"></figure><lb></lb>rum æqualium ſuffultą <lb></lb>in F, it aut terminus D infrà ex<lb></lb>tremitatem laminæ AB collo<lb></lb>cetur, & tunc poſito pondere <lb></lb>G æquale ipſi C in altero extremo libræ E, impel<lb></lb>letur ſursùm terminus libræ, vel vectis D à vi pon<lb></lb>deris G, & ab illo lamina AB in directum retine<lb></lb>bitur contra vim compreſſiuam ponderis C, <expan abbr="quãdo-quidem">quando<lb></lb>quidem</expan> duo pondera C, & G inter ſe æqualia ſe mu<lb></lb>tuò impellunt, proindeque lamina intercepta AB, <lb></lb>neque deorsùm, neque ſursùm flectetur. </s> </p> <p type="main"> <s id="s.000297"><emph type="center"></emph>PROP. XXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000298"><emph type="center"></emph><emph type="italics"></emph>Idipſum alia ratione vſurpata libra demonſtratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000299">SI nimirùm termino E im<lb></lb><figure id="id.010.01.071.2.jpg" xlink:href="010/01/071/2.jpg"></figure><lb></lb>ponatur pondus IG du<lb></lb>plum ipſius C, atque in D ap<lb></lb>plicetur pondus M æqualę <lb></lb>eidem C, <expan abbr="manifeſtũ">manifeſtum</expan> eſt, quòd <lb></lb>pondus IG æquale eſt duo-<pb pagenum="64" xlink:href="010/01/072.jpg"></pb><arrow.to.target n="marg69"></arrow.to.target><lb></lb>bus ponderibus C & M, & ideò æquilibrium efficie<lb></lb>tur, ſcilicèt intercepta lamina AB nil prorsùs flecte<lb></lb>tur, quia licèt à pondere ſupremo C deorsùm lami<lb></lb>na pellatur, repellitur infernè à corpore M non qui<lb></lb>dem propria vi, (cùm tendat deorsùm ob eius gra<lb></lb>uitatem) ſed ab exceſſu ponderis IG ſupra M. </s> </p> <p type="margin"> <s id="s.000300"><margin.target id="marg69"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000301"><emph type="center"></emph>PROP. XXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000302"><emph type="center"></emph><emph type="italics"></emph>Animalis infra aquam demerſi membra non flectentur, <lb></lb>eò quòd vndique contrarijs viribus à fluido com<lb></lb>primuntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000303">IN ſuperiori diagrammate habemus exemplum ſi<lb></lb>mile omninò corpori animalis in aqua natantis, <lb></lb>nam licèt animalis brachium, ver. gra. AB, compri<lb></lb>matur à ſuperpoſita aqua C, non tamen flectetur de<lb></lb>orsùm, aut diſrumpetur, cùm præſtò ſit aqua ſubie<lb></lb>cta M, quæ ſursùm manum brachiumque repellat, <lb></lb>impediatque eius depreſſionem, flexionemque, <expan abbr="nõ">non</expan> <lb></lb><expan abbr="quidẽ">quidem</expan> propria vi grauitatis eius, ſed virtute <expan abbr="cõpreſ-ſiua">compreſ<lb></lb>ſiua</expan> collateralis aquæ IG, <lb></lb><figure id="id.010.01.072.1.jpg" xlink:href="010/01/072/1.jpg"></figure><lb></lb>quæ in libra, vel ſiphone i<lb></lb>maginario, eo <expan abbr="põdere">pondere</expan>, quo <lb></lb>excedit <expan abbr="grauitatẽ">grauitatem</expan> aquæ M, <lb></lb>eam ſursùm impellit, & pro<lb></lb>pterea <expan abbr="Brachiũ">Brachium</expan> AB ſuſtinet <lb></lb>ne à <expan abbr="põdere">pondere</expan> ſupremo incuruetur, aut diſrumpatur. </s> </p> <p type="main"> <s id="s.000304">Et hoc (dicet aliquis) ſufficeret ad luxationem̨ <lb></lb>membrorum animalis euitandam, ſed non proindè <pb pagenum="65" xlink:href="010/01/073.jpg"></pb><arrow.to.target n="marg70"></arrow.to.target><lb></lb>dolor compreſſiuus animalis vitari poſſet, quando<lb></lb>quidem partes carnoſæ, & tendinoſæ contunderen<lb></lb>tur diffringerenturque, atque vniuersè ſciſſuram̨ <lb></lb>aliquam paterentur. </s> </p> <p type="margin"> <s id="s.000305"><margin.target id="marg70"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000306">Vt verò fallacia huius ratiocinij detegatur. <lb></lb><arrow.to.target n="marg71"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000307"><margin.target id="marg71"></margin.target>Sed licèt lu<lb></lb>xatio non <lb></lb><expan abbr="cõſequatur">conſequatur</expan>, <lb></lb>ſaltem con<lb></lb>tuſio, & dif<lb></lb>fractio par<lb></lb>tium anima<lb></lb>lis conſequi <lb></lb>debere vi<lb></lb>detur.</s> </p> <p type="main"> <s id="s.000308"><emph type="center"></emph>PROP. XXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000309"><emph type="center"></emph><emph type="italics"></emph>Scisſio conſequens actionem Cunei, vel ſecuris <lb></lb>declaratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000310">EFfectus conſequens ad actionem cunei, & aciei <lb></lb>ſecuris, ſciſſio nuncupari ſolet, quæ efficitur <lb></lb>propterea, quòd dum cuneus intra corpus ſciſſilę <lb></lb>inſinuatur, huius partes hinc in de lateralitèr mouen<lb></lb>tur, & ab inuicem ſeparantur: hinc fit, quòd ſi par<lb></lb>tes ſubiecti corporis minimè lateralitèr moueri poſ<lb></lb>ſent, neque cuneus penetraret, nec ſciſſio fieret: <lb></lb>triplici verò modo motus laterales ſubiecti corporis <lb></lb>impediri poſſunt, primò, ſi gluten, quo partes ſubie<lb></lb>cti corporis colligantur, fuerit immenſæ virtutis, & <lb></lb>arctiſſimæ vnionis, & duritiei; ſecundò, ſi prædictæ <lb></lb>partes inter ſe diuiſæ, vt arena, <expan abbr="continerẽtur">continerentur</expan> intra vas <lb></lb>duriſſimum, cuius parietes cuilibet impulſui reſiſte<lb></lb>rent, nec præterea partes contenti corporis ſuble<lb></lb>uari ſursùm poſſent, tunc profectò nec penetratio <lb></lb>cunei, nec ſciſſio efficeretur; tertiò, ſi vaſe remoto <lb></lb>adhiberentur vires impulſiuæ lateralitèr contrariæ <lb></lb>officium vaſis ſupplentes, tunc ſimilitèr ſciſſio im<lb></lb>pediretur. <pb pagenum="66" xlink:href="010/01/074.jpg"></pb><arrow.to.target n="marg72"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000311"><margin.target id="marg72"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000312"><emph type="center"></emph>PROP. XXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000313"><emph type="center"></emph><emph type="italics"></emph>Diuiſio quæ effici poteſt à compresſione inſtrumenti non acu<lb></lb>ti, veluti eſt malleus, paritèr ad cunei actionem <lb></lb>reducitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000314">QVandoquidem particulę corporis à malleo <expan abbr="cõ-preſſæ">con<lb></lb>preſſæ</expan> inſinuantur directè, <expan abbr="promouenturq;">promouenturque</expan> <lb></lb>intra alias collaterales particulas, & quia in<lb></lb>ſinuatio prædictarum partium effici non poteſt niſi <lb></lb>collaterales particulæ non contuſæ locali motu late<lb></lb>rali tranſportentur, hinc fit, quòd particulæ illæ <expan abbr="cõ-preſſæ">con<lb></lb>preſſæ</expan> immediatè actionem cunei referant: malleus <lb></lb>verò ſit <expan abbr="inſtrumẽtalis">inſtrumentalis</expan> cauſa mediata, ſeù potiùs vir<lb></lb>tus impellens particulas compreſſas, cuneos refe<lb></lb>rentes. </s> </p> <p type="main"> <s id="s.000315"><emph type="center"></emph>PROP. XXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000316"><emph type="center"></emph><emph type="italics"></emph>Veſica arena, vel aqua repleta vndique, & in omni<lb></lb>bus partibus eius ab innumeris cuneis compreſſaneque <lb></lb>ſcindi, neque flecti, neque figuram commu<lb></lb>tare poteſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000317">SVpponatur modò veſica ABCD, quæ repleatur <lb></lb>aqua, vel hydrargyro, aut arena, vel globulis <lb></lb>cryſtallinis minutiſſimis, tunc ſi huiuſmodi veſica à <lb></lb>pauimento RS fulciatur, atque ei ſuperponatur acies <lb></lb>ſecuris, vel nouaculæ I, procùl dubio, aut veſicą <lb></lb>ſcindetur, aut ſaltèm fluidum, ſiue arena contentą <pb pagenum="67" xlink:href="010/01/075.jpg"></pb><arrow.to.target n="marg73"></arrow.to.target><lb></lb>cedet, & verſus latera veſi<lb></lb><figure id="id.010.01.075.1.jpg" xlink:href="010/01/075/1.jpg"></figure><lb></lb>cæ tranſportabitur; at ſi in<lb></lb>telligantur innumeræ acies <lb></lb>ſecurium, vndique compri<lb></lb>mentes veſicam, it aut nullą <lb></lb>eius pars intacta relinquatur: <lb></lb>primò manifeſtum eſt, ſciſſio<lb></lb>nem prohiberi, quandoquidem longa, & continua<lb></lb>ta ſeries acierum ſeſe conſequentium, & ſe mutuò <lb></lb>lateralitèr tangentium abſque vlla interruptione æ<lb></lb>quiualent corpori obtuſo, proindeque acuties illą <lb></lb>omninò deſtruitur, & Proptereà non ſequetur ſciſſio <lb></lb>quæ abſque acie acuta fieri nequit. </s> <s id="s.000318">Secundò non fi<lb></lb>et contritio, atque depreſſio alicuius partis prædi<lb></lb>ctæ veſicæ, quandoquidem non pote ſt ſuprema pars <lb></lb>eius A deprimi versùs C, quin aqua, vel arena ex<lb></lb>pulſa recipiatur ad latera B, & D, ſed hic quoquę <lb></lb>æqualibus viribus comprimitur lateralitèr veſicą, <lb></lb>igitur non poteſt ibidem perduci fluidum, vel are<lb></lb>na <expan abbr="cõpreſſa">compreſſa</expan>; & propterea veſicæ circumcircà viribus <lb></lb>æqualibus compreſsæ nulla particula cedet; & quia <lb></lb>aliundè materia ipſa fluida, vel arena talis conſiſten<lb></lb>tiæ eſt, vt ſtringi, condenſari, & ad minus ſpatium̨ <lb></lb>redigi nequeat, fit vt veſica illa, & aqua vel arena <lb></lb>in ea contenta, neque ſcindatur, neque flectatur, <lb></lb>neque vllo pacto figuram commutet quotieſcumque <lb></lb>vndique circùmcirca ab æqualibus viribus compri<lb></lb>matur. <pb pagenum="68" xlink:href="010/01/076.jpg"></pb><arrow.to.target n="marg74"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000319"><margin.target id="marg73"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000320"><margin.target id="marg74"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000321"><emph type="center"></emph>PROP. XXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000322"><emph type="center"></emph><emph type="italics"></emph>Idipſum verificatur quotieſcumque prædicta veſica in ipſa <lb></lb>aqua demergitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000323">IBi enim nedùm à perpendiculariter incumbentę <lb></lb>aqua comprimitur, ſed etiam ab infima, & colla<lb></lb>terali, vndequaque, & vniuersè æqualibus viribus <lb></lb>impellitur, conſtringitur que, vnde fit vt licèt veſi<lb></lb>ca ſit tenuiſſima, non poſſit tamen vnquam diffringi à <lb></lb>pondere licèt immenſo ſuperſtantis aquæ, vel hy<lb></lb>drargyri, nec contuſionem, aut diffractionem vllam <lb></lb>pati; & ratio eſt quia licèt tota maſſa contenta intra <lb></lb>veſicam ſit fluida, mollis, & cedens, nihilominus <lb></lb>quia minimæ particulæ fluidi, vel arenæ ſe mutuò <lb></lb>fulciunt, & natiua duritie compreſſioni reſiſtunt, fit <lb></lb>vt condenſari, aut conſtringi nequeant, & ab vni<lb></lb>uerſali circumambiente compreſſione ne minimum <lb></lb>alteretur eius figura, neque ſitus partium. </s> </p> <p type="main"> <s id="s.000324"><emph type="center"></emph>PROP. XXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000325"><emph type="center"></emph><emph type="italics"></emph>Tandem oſtenditur quare animal nullam noxam ex com<lb></lb>presſione aquæ incumbentis pati debeat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000326">NOn ſecùs in corpore animalis continentur in<lb></lb>tra eius pellem partes aliæ quidem duræ, & <lb></lb>ſolidæ, vt ſunt oſſa, aliæ molles, vt ſunt tendines, <lb></lb>nerui, membranæ, & muſculi; aliæ verò ſunt fluidæ, <lb></lb>aqueæ, vel oleaginoſæ continentes innumeras alias <pb pagenum="69" xlink:href="010/01/077.jpg"></pb><arrow.to.target n="marg75"></arrow.to.target><lb></lb>particulas ſalis, & aliorum corporum. </s> <s id="s.000327">Modò oſſa in <lb></lb>animali diſrumpi, aut iuxari non poſſunt, vt oſten<lb></lb>ſum eſt Prop. 29. niſi pondus incumbens ex vną <lb></lb>parte tantum comprimat, vt contingit in baiulis; at <lb></lb>ſi compreſſio ſubdiuidatur, vt ſphæricè, ſursùm, & <lb></lb>deorsùm, & lateraliter æqualibus viribus <expan abbr="cõprimat">comprimat</expan>, <lb></lb>ita vt nulla cutis particula libera à preſſione ſit, tunc <lb></lb>quidem eſt impoſſibile vt ſciſſio, vel luxatio ſubſe<lb></lb>quatur; idipſum dicendum eſt de neruis, ac mu<lb></lb>ſculis, qui licèt ſint molles, <expan abbr="tamẽ">tamen</expan> quia <expan abbr="cõſtãt">conſtant</expan> ex fibris <lb></lb>conſiſtentibus, & tenaciſſimis, fit vt vniuersè poſſint <lb></lb>ſe viciſſim fulcire, & reſiſtere vniuerſali, & ſphæri<lb></lb>cæ compreſſioni: idem dicendum eſt de ſanguine, <lb></lb>& alijs humoribus animalis, qui aquæ naturam par<lb></lb>ticipant, & ſicuti aqua manifeſtam condenſationem <lb></lb>non patitur, ſic quoque animalis humores in cauita<lb></lb>tibus vaſorum eius contenti contritionem pati qui<lb></lb>dem poſſunt ab impulſu facto ab vnico, vel paucis <lb></lb>locis peculiaribus; at ab vniuerſali, & circumqua<lb></lb>que facta compreſſione minimè poſſunt è ſuis vaſis <lb></lb>expelli, ac diuelli. </s> <s id="s.000328">quotieſcumque igitur partes ſo<lb></lb>lidæ, tendinoſæ, aut carnoſæ, aut humorales, ſciſſi<lb></lb>onem, luxationem, contuſionem, aut aliam quam<lb></lb>libet ſitus mutationem non patiuntur eſt impoſſibi<lb></lb>le, vt dolor, aut paſſio in animali ſubſequatur, quæ <lb></lb>à nulla alia cauſa, quàm à continui diuiſione creari <lb></lb>poteſt. </s> <s id="s.000329">Quà propter cùm vrinatores in profundo ma<lb></lb>ris demerſi ab aqua æquali vi vndique compriman<lb></lb>tur, ſupernè ſcilicèt, infernè, & lateralitèr circum-<pb pagenum="70" xlink:href="010/01/078.jpg"></pb><arrow.to.target n="marg76"></arrow.to.target><lb></lb>circa à pondere ipſius aquæ, ſequitur ex demonſtra<lb></lb>tis Prop. 29. & 32. nullam ſciſſionem, luxationem, <lb></lb>aut contuſionem in eis creari, ſcilicèt nullam conti<lb></lb>nui diuiſionem à pondere aquæ incumbentis produ<lb></lb>ci, igitur nullam noxam, nec ſenſum dolorificum̨ <lb></lb>patientur. </s> </p> <p type="margin"> <s id="s.000330"><margin.target id="marg75"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000331"><margin.target id="marg76"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000332">Sed dices, eſto nullam luxationem, fractionem, aut <lb></lb>contuſionem vrinatores ſub aqua pati debere, <expan abbr="ſaltẽ">ſaltem</expan> <lb></lb>ſenſu tactus perciperent compreſſionem ponderis <lb></lb>illius vaſtæ molis aquæ incumbentis, quam non ne<lb></lb>gamus exercere ſuam grauitatem ſupra corpus ani<lb></lb>malis demerſi. </s> <s id="s.000333">Hoc profectò eſt, quod negamus, nam <lb></lb>ratio, quare ſenſu paſſionem ab incumbente ponde<lb></lb>re illatam percipimus extra aquam poſiti eſt, quią <lb></lb>noſtræ partes ob articulorum flexilem <expan abbr="disiunctionẽ">disiunctionem</expan> <lb></lb>deorsùm pelluntur à premente graui, & ideò cogi<lb></lb>mur ingenti vi fibras muſculorum tendere, & con<lb></lb>trahere, vt lapſum membrorum impediamus; at in<lb></lb>fra aquam niſu illo laborioſo muſculorum non in<lb></lb>digemus, proptereà quòd aqua ſubiecta vices mu<lb></lb>ſculorum ſupplet repellendo æquali vi ſursùm <expan abbr="aquã">aquam</expan> <lb></lb>ſupremam vnà cum natante animali; & proinde ſu<lb></lb>prema aqua, ſuffulta à ſubiecta virtute ponderis a<lb></lb>quæ collateralis cum qua æquilibratur, nullo pacto <lb></lb>animalis partes flectere, & deprimere poteſt, & ideò <lb></lb>muſculi otioſi ſunt, & propterea nullam aliam paſ<lb></lb>ſionem animal ſentiet pręter vniuerſalem <expan abbr="cõſtrictio-nem">conſtrictio<lb></lb>nem</expan> ſui corporis; at quia, vt dictum eſt, partes durę, <lb></lb>molles, & fluidæ animalis compreſſioni non cedunt <pb pagenum="71" xlink:href="010/01/079.jpg"></pb><arrow.to.target n="marg77"></arrow.to.target><lb></lb>ob earum conſiſtentiam, hinc fit, vt nullam paſſionem <lb></lb>dolorificam ſentiant. </s> </p> <p type="margin"> <s id="s.000334"><margin.target id="marg77"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000335"><emph type="center"></emph>PROP. XXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000336"><emph type="center"></emph><emph type="italics"></emph>Vrinatores constrictionem aliquam infra aquam patiuntur <lb></lb>ob acrem in eis contentum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000337">NOn tamen negari poteſt adeſſe in animali par<lb></lb>tes aliquas aereas, & ſpiritoſas, quas <expan abbr="condẽ-ſari">conden<lb></lb>ſari</expan>, ac conſtringi poſſe manifeſtum eſt, vnde à cir<lb></lb>cumambiente conſtipatione, quam patiuntur vrina<lb></lb>tores in profundo maris conſtituti, neceſſariò aer in <lb></lb>pectoris cauitate contentus ob reſpirationis ne<lb></lb>ceſſitatem, & particulæ illæ minimæ aereæ per cor<lb></lb>pus eius diſperſæ condenſationem aliquam patiun<lb></lb>tur; proindequè motiones internæ ſpirituum forſan <lb></lb>impediuntur, & naturalis conſtitutio partium ani<lb></lb>malis perturbatur; & inde inſenſibilis tranſpiratio <lb></lb>impedita laxitudinem, & paſſionem dolorificam̨, <lb></lb>ſenſumque ſuffocationis creat; & hoc quidem expe<lb></lb>rimur quotieſcumque à veſte nimis anguſta <expan abbr="cõſtrin-gimur">conſtrin<lb></lb>gimur</expan>. </s> <s id="s.000338">Sed notandum eſt, compreſſionem veſtis non <lb></lb>eſſe vniuerſalem, & tunc quidem poteſt ſanguis ex<lb></lb>pelli versùs faciem, & partes nudatas, & à veſti<lb></lb>bus non conſtrictas, quod non contingeret ſi vni<lb></lb>uersènè minima cutis particula libera à compreſſio<lb></lb>ne eſſet. </s> <s id="s.000339">Sic cùm manus immergitur intra hydrar<lb></lb>gyrum, patimur quidem ſenſibilem compreſſionem <lb></lb>dolorificam nedùm quia partes aereæ, & ſpiritoſæ <pb pagenum="72" xlink:href="010/01/080.jpg"></pb><arrow.to.target n="marg78"></arrow.to.target><lb></lb>conſtringuntur, & condenſantur, ſed præcipuè quia <lb></lb>compreſſio efficitur in peculiari loco, & non vni<lb></lb>uersè. </s> </p> <p type="margin"> <s id="s.000340"><margin.target id="marg78"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000341">Ex qua fit vt ſanguis à venis manus extrudatur ver<lb></lb>sùs brachium non demerſum intra mercurium, & in<lb></lb>de duæ paſſiones ſubſequantur, vna quidèm conſtri<lb></lb>ctionis, altera verò eſt ea, quæ ab impedita, & in<lb></lb>terrupta ſanguinis circulatione per totam manum̨ <lb></lb>oritur. </s> </p> <p type="main"> <s id="s.000342">Sed obijciet forsàn quiſpiam exprædicta conſtri<lb></lb>ctione partium aerearum in animali <expan abbr="contẽtarum">contentarum</expan> ali<lb></lb>quam dolorificam paſſionem oriri, quam vrinatores <lb></lb>in profundo maris conſtituti percipere deberent. <lb></lb></s> <s id="s.000343">Hoc tamen vltrò conceditur, reuerà enim in profun<lb></lb>do maris paſſio aliqua conſtrictiua in vniuerſo cor<lb></lb>pore percipitur, pariterque aer in pectore animalis <lb></lb>contentus conſtringitur, & condenſatur, ſed noņ <lb></lb>proindè ingens paſſio ſuffocatiua ob craſſitiem con<lb></lb>denſati aeris in pectore contenti ſubſequetur, <expan abbr="quã-doquidem">quan<lb></lb>doquidem</expan> experimur nullam <expan abbr="noxã">noxam</expan>, aut ſenſum ſuf<lb></lb>focatiuum percipi, quotieſcumque aer inſpiratus <lb></lb>valdè attenuatur, rareſcit, aut condenſatur; ſic enim <lb></lb>in hypocauſto, atque in montis altiſſimi ſummitate <lb></lb>aer valdè rarus attenuatuſque eſt, reſpectu eius, qui <lb></lb>in profunda aliqua valle, vel in loco cenoſo reperi<lb></lb>tur, qui valdè craſſus, & condenſatus eſt, nihilomi<lb></lb>nùs, neque in ipſa reſpiratione læſio, aut paſſio ali<lb></lb>qua manifeſta percipitur, <expan abbr="neq;">neque</expan> in habitu totius cor<lb></lb>poris aer diuerſimodè rarefactus differentiam nota-<pb pagenum="73" xlink:href="010/01/081.jpg"></pb><arrow.to.target n="marg79"></arrow.to.target><lb></lb>tu dignam, & à nobis perceptibilem parit: igitur <lb></lb>vrinatores in profundo maris demerſi nullam paſſio<lb></lb>nem dolorificam percipere poſſunt licèt ſupponatur <lb></lb>quòd ab aqua incumbente ponderoſa compriman<lb></lb>tur, & condenſetur aliquo pacto aer in thorace eo<lb></lb>rum contentus. </s> <s id="s.000344">Quaproptèr ex hiſce omnibus con<lb></lb>cludere licèt <expan abbr="aquã">aquam</expan> <expan abbr="grauitatẽ">grauitatem</expan> exercere quandò quie<lb></lb>ſcit in ſuo naturali loco, nempè quando in ipſamet <lb></lb>vniuerſali aqua fulcitur, & ſuſtentatur. </s> </p> <p type="margin"> <s id="s.000345"><margin.target id="marg79"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000346">Non deſunt poſtea qui Renato Carteſio nimis <lb></lb><arrow.to.target n="marg80"></arrow.to.target><lb></lb>addicti velint partes minimas cuiuslibet fluidi, & <lb></lb>præcipuè aquæ <expan abbr="nũquàm">nunquàm</expan> quieſcere, ſed ſemper agi<lb></lb>tari, accircumuolui per <expan abbr="ipsãmet">ipsammet</expan> aquam. </s> <s id="s.000347">Hinc ſu<lb></lb>bindè inferunt partes aquæ in ipſamet aqua conſti<lb></lb>tutas, nec grauitatem, nec leuitatem habere, cùm <lb></lb>poſſint qua qu an ersùm ſursùm, atque deorsùm mo<lb></lb>ueri; nos è contrà. </s> </p> <p type="margin"> <s id="s.000348"><margin.target id="marg80"></margin.target>Carteſiani <lb></lb>cenſent par<lb></lb>tes aquæ in <lb></lb>ipſa aqua, <lb></lb>nec grauita<lb></lb>re, nec leui<lb></lb>tare, quia <lb></lb>ſursùm, & <lb></lb>deorsùm <expan abbr="cõ-tinentèr">con<lb></lb>tinentèr</expan> mo<lb></lb>uentur.</s> </p> <p type="main"> <s id="s.000349"><emph type="center"></emph>PROP. XXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000350"><emph type="center"></emph><emph type="italics"></emph>Ostendemus, quòd licèt aqua in ipſa aqua quomodolibèt con<lb></lb>uoluatur, agiteturque, nihilominùs perpetuò retinet <lb></lb>propriam grauitatem, eamque perpetuò <lb></lb>exercet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000351">INtelligatur vas aqua plenum ABCD ſuſpenſum̨ <lb></lb>in extremo termino H libræ radiorum æqualium <lb></lb>HL, cuius centrum I, & pendeat pondus R ab alte<lb></lb>ro extremo libræ L, it aut libra quieſcat, & æqueli<lb></lb>bretur vas aqueum AC cum corpore R, & hoc qui-<pb pagenum="74" xlink:href="010/01/082.jpg"></pb><arrow.to.target n="marg81"></arrow.to.target><lb></lb><figure id="id.010.01.082.1.jpg" xlink:href="010/01/082/1.jpg"></figure><lb></lb>dem verificetur, dum aqua <lb></lb>in prædicto vaſe contenta <lb></lb>prorsùs quieſcit, ſaltèm̨ <lb></lb>quoad ſenſus <expan abbr="apparentiã">apparentiam</expan>, <lb></lb>ſi poſtea aqua agitetur, vt <lb></lb>nimirùm pars EF deſcen<lb></lb>dat verſus vaſis fundum, reliqua verò pars FG, ſur<lb></lb>sùm aſcendat motu quodam vertiginoſo, fi verum̨ <lb></lb>eſt, quòd motus aſcenſiuus ipſius aquæ indicat de<lb></lb>fectum grauitatis eius, tunc perſeuerante dicto mo<lb></lb>tu aſcenſus minui deberet pondus totius vaſis AC, <lb></lb>& propterea libra HL non quieſceret, ſed deprime<lb></lb>retur pondus R, quod tamen repugnat ſenſus eui<lb></lb>dentiæ; non igitur ex eo quòd aqua mouetur in ali<lb></lb>quo vaſe carebit propria, & natiua grauitate, ſicuti <lb></lb>homo aſcendens per ſcalam extremo termino libræ <lb></lb>alligatam æquali momento libram premeret, ac ſi <lb></lb>idem homo in ſcala quieſceret, quia nimirùm dum <lb></lb>aſcendit non minus ſuſtentatur quàm dum quieſcit. </s> </p> <p type="margin"> <s id="s.000352"><margin.target id="marg81"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000353">Sed dices, cum motus vertiginoſus aquæ fieri <expan abbr="nõ">non</expan> <lb></lb>poſſit abſque eo quod vna pars deſcendat, & reli<lb></lb>qua ſubleuetur, eſt valdè probabile, vt ſicut aſcenſus <lb></lb>aquæ FG indicat defectum grauitatis, cùm prædi<lb></lb>ctus motus ſupponat impetum à quo ſursùm propel<lb></lb>latur ſicuti ſaxum quod ſursùm proijcitur in actu ſui <lb></lb>aſcenſus, neque graue dici poteſt, nec grauitatem <lb></lb>exercet, proptereà quòd ab impetu impreſſo con<lb></lb>trario grauitati, vel ipſamet grauitas deſtruitur, vel <lb></lb>impeditur, & ceſſat eius operatio. </s> <s id="s.000354">Oppoſitum con-<pb pagenum="75" xlink:href="010/01/083.jpg"></pb><arrow.to.target n="marg82"></arrow.to.target><lb></lb>tinget in aqua deſcendente EF quæ videtur habere <lb></lb>nedùm vim propriæ grauitatis, ſed inſuper <expan abbr="impetũ">impetum</expan> <lb></lb>quo deorsùm fertur, ſicuti ſaxum, quod deorsùm̨ <lb></lb>proijcitur, vim, & percuſſionem infert nedum men<lb></lb>ſuratam à gradu eius ponderis, ſed etiam ab impe<lb></lb>tu eius deſcenſiuo; qua propter vis, quæ ſubtrahitur <lb></lb>ab aqua <expan abbr="aſcendẽte">aſcendente</expan> FG, ſuperadditur grauitati aquæ <lb></lb>deſcendenti EF, & ſic duplicatur vis eiuſdem aquæ <lb></lb>deſcendentis qua fundum vaſis BC comprimitur; <expan abbr="cũ">cum</expan> <lb></lb>igitur id, quod ſubtrahitur ab aqua aſcendente FG <lb></lb>ſuperaddatur ponderi aquæ deſcendentis EF com<lb></lb>penſabitur defectus cum additamento impetus <expan abbr="cõ-preſſiui">con<lb></lb>preſſiui</expan>, proindeque non imminuetur pondus totius <lb></lb>aquæ in vaſe AC contentæ, & hæc erit cauſa, quare <lb></lb>etiam poſt aquæ agitationem pondus eius in librą <lb></lb>non alteratur, nec imminuitur. </s> </p> <p type="margin"> <s id="s.000355"><margin.target id="marg82"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens ponde<lb></lb>rat.</s> </p> <p type="main"> <s id="s.000356"><emph type="center"></emph>PROP. XXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000357"><emph type="center"></emph><emph type="italics"></emph>Reijcitur difficultas contra præcedentem propoſitionem <lb></lb>adducta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000358">SEd facili negotio inefficacia huius ratiocinij <expan abbr="oſtẽ-di">oſten<lb></lb>di</expan> poteſt, primò experientia, ſecundò ratione. <lb></lb></s> <s id="s.000359">Quoad primum, ſuſpendatur vas aqueum AC duobus <lb></lb>filis AH, DL alligatis in extremitatibus eiuſdem li<lb></lb>bræ HL radiorum æqualium, ſuſpendaturque libra <lb></lb>cum vaſe ab illius centro I, manifeſtum eſt, quando <lb></lb>aqua quieſcit, nec agitatur, ſi eri æquilibrium, quią <lb></lb>ſcilicèt centrum grauitatis M totius vaſis, & aquæ in-<pb pagenum="76" xlink:href="010/01/084.jpg"></pb><arrow.to.target n="marg83"></arrow.to.target><lb></lb><figure id="id.010.01.084.1.jpg" xlink:href="010/01/084/1.jpg"></figure><lb></lb>cidit præcisè in recta linea MI <lb></lb>perpendiculari ad horizontem, <lb></lb>quæ per centrum ſuſpenſionis <lb></lb>ducitur. </s> <s id="s.000360">Modò agitetur aqua va<lb></lb>ſis, vt nimirùm pars EF deſcen<lb></lb>dat, pars verò KG, ſursùm ten<lb></lb>dat, & hoc per aliquod tempus <lb></lb>perſeueret continuatis reuolu<lb></lb>tionibus, dummodò planities libellæ, AD non alte<lb></lb>retur; frigitur verum eſt in tali caſu, quòd grauitas <lb></lb>aſcendentis aquæ KG deſtruitur quatenus à virtute <lb></lb>impulſiua proiectitia ſursùm impellitur, & è contrà <lb></lb>ſi grauitas, & impetus aquæ deſcendentis EF dupli<lb></lb>catur, quia eius ponderi ſuperadditur vis proiectiuą <lb></lb>deorsùm, igitur medietas vaſis MAB, aut leuis effi<lb></lb>cietur, aut valdè eius grauitas priſtina imminutą <lb></lb>erit, & è contrà reliqua vaſis medietas MDC <lb></lb>duplò grauior facta erit, proindeque terminus <lb></lb>libræ L deprimetur, eleuabiturque oppoſitus ter<lb></lb>minus libræ H, quod tamen falſum eſt, igitur quo<lb></lb>modocumque aqua agitetur, dum in ipſamet aqua, & <lb></lb>in proprio loco continetur, neque amittit ob aſcen<lb></lb>ſum, nec acquirit ob deſcenſum nouam grauitatem̨. </s> </p> <p type="margin"> <s id="s.000361"><margin.target id="marg83"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000362">Sed faciliùs hoc experieris, ſi intra vas ABCD in<lb></lb>ſeratur rota EGKF perpendicularitèr horizonti ere<lb></lb>cta, & parietibus oppoſitis vaſis infixo axe eius iņ <lb></lb>M vt facilè rota conuerti poſſit. </s> <s id="s.000363">Et ſiquidem centrum <lb></lb>grauitatis totius aggregati cadit in recta lineą <lb></lb>IM perpendiculari ad horizontem, tunc ſiue rotą <pb pagenum="77" xlink:href="010/01/085.jpg"></pb><arrow.to.target n="marg84"></arrow.to.target><lb></lb>quieſcat, ſiue circa eius axim <lb></lb><figure id="id.010.01.085.1.jpg" xlink:href="010/01/085/1.jpg"></figure><lb></lb>M conuertatur libra ſemper <lb></lb>in ſitu horizontali æquilibra<lb></lb>ta perſiſtet. </s> </p> <p type="margin"> <s id="s.000364"><margin.target id="marg84"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="main"> <s id="s.000365">Vt verò ratio huius effectus <lb></lb>percipiatur, recurrendum eſt <lb></lb>ad centri grauitatis definitio<lb></lb>nem, ex qua habetur quòd corpus quodlibet ſuſpen<lb></lb>ſum à centro grauitatis eius quomodocumque reuol<lb></lb>uatur circa centrum, ſemper æquilibrari, & haberę <lb></lb>partes æqualium momentorum, vnde infertur, quòd <lb></lb>vniuerſa vis, qua corpus aliquod <expan abbr="tẽdit">tendit</expan> deorsùm, ſci<lb></lb>licet grauitas eius, exercetur in vnico illo puncto, <lb></lb>quod centrum grauitatis eius vocatur. </s> <s id="s.000366">Hinc deduci<lb></lb>tur, quod ſi rota, ſiuè pila ſuſtineatur ex centro gra<lb></lb>uitatis eius ſiuè quieſcat, ſiuè moueatur, numquam <lb></lb>centrum grauitatis ſitum commutabit, aliàs daretur <lb></lb>motus perpetuus, qui naturæ legibus repugnat. </s> </p> <p type="main"> <s id="s.000367">Similitèr ſi concipiatur fiſtula vitrea inflexa ad <lb></lb>modum anuli, vt eſt EFGK, ſitque prædicta fiſtulą <lb></lb>plena aqua ſituata perpendiculari<lb></lb><figure id="id.010.01.085.2.jpg" xlink:href="010/01/085/2.jpg"></figure><lb></lb>tèr ſuper planum ſubiectum RS à <lb></lb>quo fulciatur; habebit profectò <expan abbr="cẽ-trum">cen<lb></lb>trum</expan> grauitatis in eius puncto in<lb></lb>termedio N, dum quieſcit aqua iņ <lb></lb>prædicto anulo, at ſi reuoluatur vt <lb></lb>nimirùm pars EFG deſcendat, reliqua verò GKE <lb></lb>ſursùm <expan abbr="aſcẽdat">aſcendat</expan>, non proindè centrum grauitatis <expan abbr="trãſ-feretur">tranſ<lb></lb>feretur</expan> ab N versùs O, ſcilicèt intra ſemicirculum̨ <pb pagenum="78" xlink:href="010/01/086.jpg"></pb><arrow.to.target n="marg85"></arrow.to.target><lb></lb>aquæ deſcendentis, nam perſeuerante vertigine, ſci<lb></lb>licèt translato centro grauitatis vltrà medium in O <lb></lb>ſemper ſemianulus EFG grauior eſſet, quàm GKE, <lb></lb>& propterea ille ſemper deſcenderet, hìc verò ſem<lb></lb>per aſcenderet, proindeque anulus excurreret mo<lb></lb>tu perpetuo progreſſiuo, quod eſt falſum. </s> <s id="s.000368">perſiſtit <lb></lb>ergo centrum grauitatis ſemper in centro N anuli, <lb></lb>ſiue aqua in eo contenta quieſcat, ſiuè circumduca<lb></lb>tur, nam ob continguitatem partium aquæ non poteſt <lb></lb>moueri vna pars aquæ F v. g. quin vniuerſa aquą <lb></lb>EKG æquali velocitate reuoluatur, proindeque <expan abbr="nõ">non</expan> <lb></lb>vnica pars tantùm, ſed aqua tota <expan abbr="impulsũ">impulsum</expan>, & impe<lb></lb>tum acquirit, non ſecùs ac rota lignea tota ſimul ic<lb></lb>tum recipit atque circa <expan abbr="cẽtrum">centrum</expan> grauitatis eius æqui<lb></lb>libratur, pari modo aqua contenta in vaſe AC ante <lb></lb>præmiſſæ figuræ, licèt ſit fluida, habet tamen pun<lb></lb>ctum M circa quod partes habent æqualia momenta, <lb></lb>perinde ergo ſe habent ac ſi vniuerſa aqua in prædi<lb></lb>cto vaſe contenta dura eſſet, & conſiſtens vt rota li<lb></lb>gnea, vel intra fiſtulam anularem EFKG contentą <lb></lb>eſſet in qua reuoluta, ſiue quieſcente rota, aut aqua <lb></lb>ſemper centrum grauitatis eius in eodem ſitu perſe<lb></lb>uerare debet, & proinde libra HL quieſcet in <expan abbr="eodẽ">eodem</expan> <lb></lb>ſitu horizontali. </s> <s id="s.000369">Igitur dubitandum non eſt aquam̨ <lb></lb>in ſuo toto collocatam, grauitatem exercere, ſiuè illa <lb></lb>omninò ibidem quieſcat, ſiuè quomodolibet agite<lb></lb>tur, & circumuoluatur. <pb pagenum="79" xlink:href="010/01/087.jpg"></pb><arrow.to.target n="marg86"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000370"><margin.target id="marg85"></margin.target>Cap. 3. flui<lb></lb>dum in ſuo <lb></lb>toto quie<lb></lb>ſcens pon<lb></lb>derat.</s> </p> <p type="margin"> <s id="s.000371"><margin.target id="marg86"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000372"><emph type="center"></emph><emph type="italics"></emph>Poſitiuam leuitatem in rerum natura <lb></lb>non dari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000373"><emph type="center"></emph>CAP. IV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000374">HActenùs conſiderauimus grauitatem non om<lb></lb>nium corporum fluidorum, ſed tantummodò <lb></lb>aquæ, hydrargyri, & ſimilium, de quorum pondero<lb></lb>ſitate nemo dubitat, manifeſtè enim deorsùm ten<lb></lb>dunt, atque deſcendunt. </s> <s id="s.000375">difficultas vertitur circą <lb></lb>reliqua corpora, quæ ſursùm aſcendere videntur, vt <lb></lb>ſunt ligna, & alia corpora, quæ in aqua ſursùm <expan abbr="aſcẽ-dunt">aſcen<lb></lb>dunt</expan>, in his enim grauitatem ponere, videtur contra <lb></lb>communem conceptum; nihilominùs cum melioris <lb></lb>notæ Philoſophis oſtendere conabimur omnia cor<lb></lb>pora fluida elementaria grauitatem habere, leuita<lb></lb>tem verò poſitiuam abſolutè in natura non dari, ita<lb></lb>que <expan abbr="oſtendẽdum">oſtendendum</expan> eſt omnia corpora elementaria ha<lb></lb>bere vim ſe ſe vniendi ad efformandum noſtrum Sy<lb></lb>ſtema, ſcilicèt habere facultatem motiuam deſcen<lb></lb>dendi versùs centrum globi terreſtris, & huiuſmodi <lb></lb>vis vocatur grauitas. </s> <s id="s.000376">Et primo loco examinabimus <lb></lb>argumenta Ariſtotelis facta contra Platonem, & De<lb></lb>mocritum prædictæ ſententiæ aſſertores, poſtea ad <lb></lb>examen reuocabimus rationes eiuſdem Ariſtotelis, <lb></lb>quibus leuitatem poſitiuam ſtatuere conatur. </s> <s id="s.000377">Tertio <lb></lb>loco afferam demonſtrationes, quibus euincitur non <lb></lb>dari leuitatem poſitiuam; & tandem conſidèrabo ea <lb></lb>omnia, quæ paſsìm à melioribus Peripateticis con-<pb pagenum="80" xlink:href="010/01/088.jpg"></pb><arrow.to.target n="marg87"></arrow.to.target><lb></lb>tra Platonicam ſententiam afferuntur, quæ peruene<lb></lb>re ad meam notitiam. </s> </p> <p type="margin"> <s id="s.000378"><margin.target id="marg87"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000379">Quòad primum Ariſtoteles inſectatur Democriti, <lb></lb>Platoniſque poſitionem, ſed more ſuo, non contrą <lb></lb><arrow.to.target n="marg88"></arrow.to.target><lb></lb>ſententias, at contra mera verba eorum argumenta<lb></lb>tur, ſcilicèt quod terræ grauitas maior, quàm aeris <lb></lb>pendeat à copia triangulorum, quæ maior in terra, <lb></lb>quàm in aere exiſtit, aſſumitque prædicta triangula, <lb></lb>ac ſi eſſent ſuperficies planæ omninò indiuiſibiles, <lb></lb>quod patet falſum eſſe, cùm in Platonica poſitionę <lb></lb>atomi triangulares ſint corpora, non autem ſuperfi<lb></lb>cies indiuiſibiles. </s> </p> <p type="margin"> <s id="s.000380"><margin.target id="marg88"></margin.target>Phyſic.lib.4. <lb></lb>cap.2.</s> </p> <p type="main"> <s id="s.000381">Præterea contra Democritum, ait, grandem aeris <lb></lb>maſſam, veluti eſſet ſphæra aerea habens diametrum <lb></lb>decem cubitorum, habere maiorem copiam, & <expan abbr="abũ-dantiam">abun<lb></lb>dantiam</expan> pleni, & materiei, quàm exigua pila aquea <lb></lb>habens diametrum vnius digiti, & proindè pila ae<lb></lb>rea grauior eſſe deberet, & deorſum deſcendere, & <lb></lb><arrow.to.target n="marg89"></arrow.to.target><lb></lb>è <expan abbr="cõtrà">contrà</expan> aquea vt leuis ſursùm eleuari deberet. </s> <s id="s.000382">Hoc, <lb></lb>inquam, argumentum non afficit Democritum, qui <lb></lb>numquam tantam abſurditatem ſomniauit, <expan abbr="numquã">numquam</expan> <lb></lb>enim conſiderauit plenum ſolitarium, ſed vnà cum <lb></lb>pleno ingentem vacui molem augmentatam in illą <lb></lb>grandi aerea pila, & ſemper maiori cum proportio<lb></lb>ne, quàm ſe habeat plenum aeris ad plenum aquæ. <lb></lb></s> <s id="s.000383">Quam exceptionem parùm ſincerè Ariſtoteles ſub ſi<lb></lb>lentio inuoluit, quoniam exiſtente aere rariore, <expan abbr="quã">quam</expan> <lb></lb>ſit ipſa aqua, habebit pars vacua ad partem plenam̨ <lb></lb>aeris maiorem proportionem, quàm habet pars va-<pb pagenum="81" xlink:href="010/01/089.jpg"></pb><arrow.to.target n="marg90"></arrow.to.target><lb></lb>cua ad partem plenam ipſius aquæ, & permutando, <lb></lb>moles vacua aeris ad molem vacuam aquæ maiorem <lb></lb>proportionem habebit, quàm moles plena aeris ad <lb></lb>molem plenam aquæ, & proindè quęlibet ampla ae<lb></lb>ris moles habebit <expan abbr="maiorẽ">maiorem</expan> cauſam alleuiationis <expan abbr="quã">quam</expan> <lb></lb>aqua, poſito quòd huiuſmodi cauſa ſit vacuum, & è <lb></lb>contra in eodemmet aere debilior erit cauſa graui<lb></lb>tatis, quæ ab ipſo pleno, & ab eius menſura deſu<lb></lb>mitur, <expan abbr="itaq;">itaque</expan> in grandi illa ſphæra aerea ſimùl <expan abbr="cũ">cum</expan> <expan abbr="aug-mẽto">aug<lb></lb>mento</expan> partis plenæ decies maiori, <expan abbr="quã">quam</expan> in exigua pila <lb></lb>aquea, ſuperadditur quoque cauſa contraria, nempè <lb></lb>alleuiationis, quæ eſt vacuum pluſquam milliès ma<lb></lb>ior, quàm ſit illud quod in ipſa aqua continetur; <lb></lb>cùm igitur tàm enormiter excreſcat, & ſuperet pro<lb></lb>portio vacuitatis reliquam proportionem plenitudi<lb></lb>nis in prædictis duobus elementis numquam poterit <lb></lb>ampla pila aerea grauior effici ob augmentum eius <lb></lb>plenitudinis, & partis materialis, quando ipſa in ſe <lb></lb>quoque continet contrariam cauſam, quæ eam <expan abbr="leuẽ">leuem</expan> <lb></lb>reddit multò magis multiplicatam, & hæc eſt inani<lb></lb>tas, & vacuum. </s> <s id="s.000384">Eiuſdem farinæ eſt longa illa ſeries <lb></lb>argumentorum toties ab Ariſtotele contra antiquos <lb></lb>adductorum. </s> </p> <p type="margin"> <s id="s.000385"><margin.target id="marg89"></margin.target>Ariſt. ibid.</s> </p> <p type="margin"> <s id="s.000386"><margin.target id="marg90"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000387">Præterea verum non eſt, aſſignaſſe antiquos ſpa<lb></lb>tio vacuo motum, aut virtutem operandi, ſed <expan abbr="tantũ-modò">tantun<lb></lb>modò</expan> principio materiali, ac pleno eam concede<lb></lb><arrow.to.target n="marg91"></arrow.to.target><lb></lb>bant, quod perſpicuè ex <expan abbr="eodẽ">eodem</expan> Ariſtotele percipitur, <lb></lb>refert enim antiquos poſuiſſe omnia corpora <expan abbr="elemẽ-taria">elemen<lb></lb>taria</expan> grauia, & ponderoſa, ſed magis, aut minùs, <pb pagenum="82" xlink:href="010/01/090.jpg"></pb><arrow.to.target n="marg92"></arrow.to.target><lb></lb>prout plenum, & principium materiale deficeret, <lb></lb>aut abundaret in ipſis; & inſuper ait, quòd aſcenſus <lb></lb>ſursùm aliquorum corporum, nempè ignis, <expan abbr="nõ">non</expan> à prin<lb></lb>cipio aliquo poſitiuo, ſcilicèt leuitate pendere an<lb></lb>tiquì cenſebant, ſed effici huiuſmodi aſcenſum per <lb></lb>extruſionem factam à fluidis corporibus ambienti<lb></lb>bus ponderoſioribus. </s> <s id="s.000388">Si igitur hæc fuit antiquorum̨ <lb></lb>ſententia, quomodo eis tribui poteſt tàm enormis <lb></lb>abſurditas, quòd nimirum vacuum moueatur, impel<lb></lb>lat, habeat ſitum, & regionem ſursùm, versùs quam <lb></lb>tendit? </s> <s id="s.000389">quomodò, inquam, hæc affirmare poterant il<lb></lb>li, qui apertè aìebant motus omnes naturales corpo<lb></lb>rum elementarium tendere deorsùm omneſque pen<lb></lb>dere ab vnico principio poſitiuo, ſcilicèt à pleno, & <lb></lb>materia corporea? </s> <s id="s.000390">nec quia aer ſursùm impellitur, <lb></lb>extruditurque, inde ſequitur, quòd vacua in aere <expan abbr="cõ-tenta">con<lb></lb>tenta</expan> moueantur, atque ſursùm aſcendant, nam ſi va<lb></lb>cuum nil aliud eſt, quàm ſpatium, id erit immobile, <lb></lb>& proindè aer ſecum non aſportabit vacuum ipſum <lb></lb>ſursùm, ſed in ipſo aſcenſu ſucceſſiuè acquiret noua <lb></lb>ſpatia: relinquendo præcedentia, quæ ſunt omninò <lb></lb>immobilia. </s> <s id="s.000391">at ſi nomen vacui meram pleni priuatio<lb></lb>nem, ac nihilum ſignificet, certum eſt quòd nihilum <lb></lb>moueri non poteſt, nec impellere, nec ab vno ad <lb></lb>alium locum migrare. </s> </p> <p type="margin"> <s id="s.000392"><margin.target id="marg91"></margin.target>Ibidem.</s> </p> <p type="margin"> <s id="s.000393"><margin.target id="marg92"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000394">Poſtquam conſiderauimus Ariſtotelis argumenta <lb></lb>contra Antiquos, qui leuitatem poſitiuam omninò <lb></lb>negabant, reſtat modò vt eiuſdem Ariſtotelis ratio<lb></lb>nes pro leuitatis ſtabilimento, & poſitione conſide-<pb pagenum="83" xlink:href="010/01/091.jpg"></pb><arrow.to.target n="marg93"></arrow.to.target><lb></lb>remus. </s> <s id="s.000395">Præcipua eius ratio hæc eſt, quia reperiun<lb></lb>tur duo loca contraria in natura ſursùm, & deorsùm, <lb></lb>ſcilicèt circumferentia, & centrum mundi, ſeu ter<lb></lb>ræ; & euidentèr apparet, quòd terra infima eſt, & <lb></lb>ſubiacet omnibus alijs corporibus <expan abbr="mũdanis">mundanis</expan>, demer<lb></lb>gitur enìm deſcendendo infrà aerem, & infra <expan abbr="aquã">aquam</expan>, <lb></lb>quouſque ad locum infimum perducatur, nempè ad <lb></lb>centrum, quando nimirum ea non impeditur; hinc <lb></lb>deducit, ergo terra eſt abſolutè, & ſimplicitèr gra<lb></lb>uis, & non relatiuè. </s> <s id="s.000396">E contrà videmus aerem pene<lb></lb>trare denſitatem ipſius aquæ, & aſcendere ſuper <expan abbr="eã">eam</expan>, <lb></lb>& ignem perforare <expan abbr="denſitatẽ">denſitatem</expan> <expan abbr="tũ">tum</expan> aquę, tùm aeris, per<lb></lb>ducique ad ſupremam, & extremam ſuperficiem ae<lb></lb>ris, veluti ad locum ſuum <expan abbr="naturalẽ">naturalem</expan> ſupremum, vbi <lb></lb>tandèm quieſcit, nec vlteriùs mouetur. </s> <s id="s.000397">Et quia, in<lb></lb>quit, ignis omnibus ſupereminet, igitur eſt ſimpli<lb></lb>citèr, & abſolutè leuis; terra omnibus ſubijcitur, igi<lb></lb>tur eſt abſolutè grauis. </s> </p> <p type="margin"> <s id="s.000398"><margin.target id="marg93"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000399">Vt verò vim, & energiam Ariſtotelici ratiocinij <lb></lb>percipiamus, & exactè perpendamus, oportet vt ſta<lb></lb>tum controuerſiæ memoremus, ſcilicèt theſim Pla<lb></lb>tonis, atque Democriti, quam Ariſtoteles redargue<lb></lb>re profitetur, ante oculos ponamus, & poſtea argu<lb></lb>mentum ab Ariſtotele adhibitum conſideremus. </s> <s id="s.000400">Et <lb></lb>primò ratum perſpectumque eſt duplici modo fieri <lb></lb>poſſe vt ignis ſursùm perducatur, & ſuper omnia e<lb></lb>lementa emineat, aut nempè quia ignis ſponte ſuą <lb></lb>mouetur ſursùm à principio intrinſeco, & naturali, <lb></lb>ſcilicèt à leuitate, vel potiùs, quia ibidem ignis ex-<pb pagenum="84" xlink:href="010/01/092.jpg"></pb><arrow.to.target n="marg94"></arrow.to.target><lb></lb>pellatur, extrudaturque à maiori grauitate aliorum <lb></lb>corporum fluidorum, veluti eſt aer, & aqua; & hæc <lb></lb>poſtrema erat Platonis, & Democriti ſententia, <expan abbr="quã">quam</expan> <lb></lb>Ariſtoteles redarguere tenebatur: Argumentum ve<lb></lb>rò Ariſtotelis aliam longè diuerſam propoſitionem <lb></lb>à nemine in dubium reuocatam petit, atque inſecta<lb></lb>tur; nil enim aliud obijcit, quàm phenomenon, quod <lb></lb>ſenſibus patet, & quod aduerſarij vltrò <expan abbr="concedebãt">concedebant</expan>, <lb></lb>ſcilicet quòd omnes videmus ignem ſupra <expan abbr="aerẽ">aerem</expan> ele<lb></lb>uari; at tenebatur potius Ariſtoteles demonſtrarę <lb></lb>ignem aſcendere non quia à medio fluido grauiori <lb></lb>extruditur <expan abbr="impelliturq;">impelliturque</expan> ſursùm, ſed quia ſponte à vi <lb></lb>propria leuitatis mouetur, quod non præſtitit, pote<lb></lb>rit ergò vocari Ariſtotelicum ratiocinium potiùs pe<lb></lb>titio, quàm demonſtratio. </s> </p> <p type="margin"> <s id="s.000401"><margin.target id="marg94"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000402">Non deſunt Peripatetici, qui vt <expan abbr="vigorẽ">vigorem</expan>, & vim̨ <lb></lb>addant Ariſtotelico ratiocinio, aiunt abſurdum eſſe <lb></lb>omninò corpora naturalia moueri ad propria locą <lb></lb>non à principio intrinſeco, & eis à natura inſito, ſed <lb></lb>à violentia externi corporis per extruſionem, vnde <lb></lb>deducitur, quòd natura in operationibus tàm neceſ<lb></lb>ſarijs, & vtilibus fuerit deficiens, cùm nimirum in<lb></lb>digeat ſtimulis, & impulſu violento, & coactione, <lb></lb>quæ cùm reſiſtentiam, & violentiam includat, vide<lb></lb>tur operatio non naturalis, & propterea neque per<lb></lb>petua, neque vtilis ad ordinem, & conſeruationem <lb></lb>vniuerſi. </s> </p> <p type="main"> <s id="s.000403">Huic ſpecioſo ratiocinio reſponderi poteſt, eſſę <lb></lb>regulam fallacem, quòd vbicumque actiones, & o-<pb pagenum="85" xlink:href="010/01/093.jpg"></pb><arrow.to.target n="marg95"></arrow.to.target><lb></lb>perationes non fiunt ſponte, ſed violentèr, tunc pro<lb></lb>tunciari debeat prædictas operationes à natura, at<lb></lb>que à principio naturali factas non eſſe. </s> </p> <p type="margin"> <s id="s.000404"><margin.target id="marg95"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000405">Vno verbo, erit quoque naturalis operatio illą, <lb></lb>quæ cum aliqua violentia efficitur. </s> </p> <p type="main"> <s id="s.000406"><emph type="center"></emph>PROP. XXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000407"><emph type="center"></emph><emph type="italics"></emph>Licet in aſcenſu ligni per aquam violentia aliqua inter<lb></lb>cedat, nihilominùs operatio tota naturalis erit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000408">HOc autem poteſt confirmari hac ratione; ſi <expan abbr="verũ">verum</expan> <lb></lb>eſſet, quòd quælibet operatio in qua violentia <lb></lb>aliqua adhibetur reputari deberet non naturalis, ſe<lb></lb>queretur quòd alterationum corporum <expan abbr="concretorũ">concretorum</expan> <lb></lb>pariterque omnium generationum vegetabilium, & <lb></lb>animalium nulla eſſet, neque vocari poſſet operatio <lb></lb>naturalis, eò quòd ſemper requiritur actio, & paſ<lb></lb>ſio qualitatum, & corruptio præcedentis ſubſtantiæ. <lb></lb></s> <s id="s.000409">Nec tamen dubitandum eſt paſſiones prædictas, & <lb></lb>corruptiones, operationes eſſe violentas, non ſpon<lb></lb>te, ſed cum diſplicentia, & paſſione quadam factas, <lb></lb>igitur in omnibus prædictis operationibus naturą <lb></lb>ipſa violentiam exercet, & propterea confitendum <lb></lb>eſt proprium inſtitutum naturæ eſſe violentiam exer<lb></lb>cere, ita vt ſine ipſa nil prorsùs efficere ſciat, neque <lb></lb>ſuos fines conſequi valeat. </s> </p> <p type="main"> <s id="s.000410">Sed inſtant, <expan abbr="accidẽtale">accidentale</expan> eſſe, vt natura deſtruat præ<lb></lb>cedentem formam, cùm ſub ſequens minimè generari <lb></lb>poſſit perſeuerante prima, & proindè, inquiunt, pri-<pb pagenum="86" xlink:href="010/01/094.jpg"></pb><arrow.to.target n="marg96"></arrow.to.target><lb></lb>mò, & per ſe naturam agere proptèr bonum, & prop<lb></lb>tèr finem, generationemque, & proindè <expan abbr="præcedẽs">præcedens</expan> <lb></lb>corruptio erit veluti quædam conditio ſine qua ſub<lb></lb>ſequens forma introduci, ac generari non poteſt; fa<lb></lb>tentur ergo, quòd ſaltèm per accidens, natura actio<lb></lb>nes violentas exercet, ſed ea omnia quæ à naturą <lb></lb>operantur, vocantur naturales actiones, igitur <expan abbr="violẽ-tia">violen<lb></lb>tia</expan> illa accidentalis, qua forma præcedens deſtrui<lb></lb>tur, erit <expan abbr="quoq;">quoque</expan> vera actio, & operatio naturalis, <expan abbr="quã-doquidẽ">quan<lb></lb>doquidem</expan>, ex vulgato axiomate, qui vult finem, velit <lb></lb>quoque neceſsè eſt media illa, quæ ad finem condu<lb></lb>cunt, igitur naturalis inſtinctus, quo formæ genera<lb></lb>tio quęritur, conſequiturquè, neceſſariò inuoluit vio<lb></lb>lentiam, ſaltem vt medium neceſſarium requiſitum. <lb></lb></s> <s id="s.000411">Hinc deducere licèt non eſſe abſurdum, nec <expan abbr="indecẽs">indecens</expan>, <lb></lb>quòd natura violentiam aliquam exerceat, vt ea me<lb></lb>diante alia maior ab una conſequatur. </s> <s id="s.000412">Si hoc, <expan abbr="inquã">inquam</expan>, <lb></lb>verum eſt in alterationibus, & corruptionibus, mul<lb></lb>tò magis hoc verificabitur in alijs ſuauioribus natu<lb></lb>ræ actionibus, quando corpora naturalia ad ſua loca <lb></lb>perducuntur propter bonum, & commoditatem eo<lb></lb>rumdem corporum violenter agitatorum, non ſecùs, <lb></lb>ac ſi quis curru, vel lectica è foro domum veheretur <lb></lb>ineptè quidem de coactione, & violentia quereretur, <lb></lb>cùm eiuſmodi violentia vtilitatem iucunditatemque <lb></lb>ei afferret. </s> <s id="s.000413">Eodem penè modo à grauibus naturaliter <lb></lb>deſcendentibus perducerentur leuia ad debitum̨ <lb></lb>ſitum. <pb pagenum="87" xlink:href="010/01/095.jpg"></pb><arrow.to.target n="marg97"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000414"><margin.target id="marg96"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000415"><margin.target id="marg97"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000416"><emph type="center"></emph>PROP. XXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000417"><emph type="center"></emph><emph type="italics"></emph>Violentia, qua lignum, & aer per aquam aſcendit, dicitur <lb></lb>naturalis, quia eſt neceſſaria.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000418">ET hæc quidem dicta ſunt iuxtà vulgarem Peri<lb></lb>pateticam ſententiam, ſed quiſquis hoc nego<lb></lb>tium attentè perpenderit, is planè percipiet, quòd <lb></lb>vox violentiæ trahit originem metaphoricè ab illo <lb></lb>ſenſu diſplìcentiæ doloris, & amaritudinis, quam <lb></lb>patiuntur animantia, dum alterantur, & corrum<lb></lb>puntur. </s> <s id="s.000419">Hinc ſequitur, quòd vbi deficit ſenſus, defi<lb></lb>ciat quoque dolor, & violentia neceſsè eſt, & proin<lb></lb>dè alia regula, & norma certiori, ac tutiori diſtingui <lb></lb>deberent operationes naturales à non naturalibus, <lb></lb>ſeù violentis, eſtque huiuſmodi: operationes omnes <lb></lb>quæ abſolutè, & omninò neceſſariæ ſunt, neque vllo <lb></lb>pacto fieri poteſt, vt Natura eas negligat, ſed cogi<lb></lb>tur neceſſariò eas exercere, iure naturales operatio<lb></lb>nes appellari, ac cenſeri debent. </s> <s id="s.000420">Modò quia ope<lb></lb>ratio naturalis, qua corpora grauiora profundiùs <lb></lb>deſcendunt, atque centro terræ propinquiora fiunt, <lb></lb>quàm minùs grauia neceſſariò ſecum inuoluit ordi<lb></lb>natam diſpoſitionem corporum, vt nimirùm grauio<lb></lb>ra infimum locum poſſideant; minùs grauia verò ſu<lb></lb>premum, & inſuper vniuerſa huiuſmodi recta diſpo<lb></lb>ſitio exigit vt ambo corpora moueantur tendendo <lb></lb><arrow.to.target n="marg98"></arrow.to.target><lb></lb>deorsùm in centro communi grauitatis eorum. </s> <s id="s.000421">Non <lb></lb>ſecùs ac in libra preſſa ab in æqualibus ponderibus, <pb pagenum="88" xlink:href="010/01/096.jpg"></pb><arrow.to.target n="marg99"></arrow.to.target><lb></lb>aſcenſus minoris ponderis factus à deſcenſu corpo<lb></lb>ris grauioris alteram lancem prementis, ineptè qui<lb></lb>dem, & iniuria violentia appellatur; propterea quòd <lb></lb>huiuſmodi operatio, ac diſpoſitio neceſſaria, ac na<lb></lb>turalis eſt. </s> </p> <p type="margin"> <s id="s.000422"><margin.target id="marg98."></margin.target>Prop. 1.</s> </p> <p type="margin"> <s id="s.000423"><margin.target id="marg99"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000424">Idipſum, vel quid ſimile, dici debet de extruſione <lb></lb>cuiuslibet corporis minùs grauis facta à preſſionę <lb></lb>ambientis fluidi grauioris, quia in tali caſu (vt ſuo lo<lb></lb>co oſtenditur) adeſt libra quædam imaginaria per<lb></lb><arrow.to.target n="marg100"></arrow.to.target><lb></lb>petua, cuius centrum grauitatis ſucceſſiuè deprimi<lb></lb>tur, & <expan abbr="prædictũ">prædictum</expan> <expan abbr="deſcensũ">deſcensum</expan> neceſſariò conſequitur mo<lb></lb>tus ſublimationis corporis minùs grauis, hocque <expan abbr="tã">tam</expan> <lb></lb>diù perſeuerat, quouſque efficiatur æquilibrium. </s> <s id="s.000425"><expan abbr="Cũ">Cum</expan> <lb></lb>igitur ſit effectus neceſſarius, & naturalis, extruſio, <lb></lb>ſeù aſcenſus ligni quotieſcumque circumdatur à flui<lb></lb>do grauiori, non poteſt, nec debet prædictus aſcen<lb></lb>ſus nuncupari, vel reputari violentus, quod erat <expan abbr="oſtẽ-dendum">oſten<lb></lb>dendum</expan>. </s> <s id="s.000426">Hoc confirmari poteſt ex Galilei pulcher<lb></lb>rimo ratiocinio. </s> </p> <p type="margin"> <s id="s.000427"><margin.target id="marg100"></margin.target>Prop. 9.</s> </p> <p type="main"> <s id="s.000428"><emph type="center"></emph>PROP. XL.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000429"><emph type="center"></emph><emph type="italics"></emph>Motus aſcenſus grauium non minùs naturalis eſt, quàm <lb></lb>deſcenſus eorundem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000430">FInge globum noſtræ terræ perforari puteo <expan abbr="percẽ-trum">per cen<lb></lb>trum</expan> extenſo vſque ad Antipodas producto, at<lb></lb>que in hoc demiſſa pila ferrea proculdubio natura<lb></lb>lis eius grauitas ſucceſſiuè maiorem impetum acqui<lb></lb>ret, quòuſque ad centrum terræ pertingat, & vniuer-<pb pagenum="89" xlink:href="010/01/097.jpg"></pb><arrow.to.target n="marg101"></arrow.to.target><lb></lb>ſa hæc motio naturalis cenſebitur, eò quòd pendet à <lb></lb>ſuo intrinſeco principio grauitatis; ſed noſtquam̨ <lb></lb>pila terræ centrum attingit profectò <expan abbr="ibinõ">ibi non</expan> quieſcet; <lb></lb>nam impetus in præcedenti deſcenſu acquiſitus pi<lb></lb>lam tranſportabit vltra centrum, excurretque versùs <lb></lb>Antipodas. </s> <s id="s.000431">modò in hoc excurſu cùm pila à centro <lb></lb>terræ recedat, procùl dubio ſurſum <expan abbr="aſcẽdet">aſcendet</expan> vocatur<lb></lb>que prædictus aſcenſus violentus motus, & contrą <lb></lb>eius naturam, & tamen ab operatione naturali de<lb></lb>ſcenſus dependet. </s> </p> <p type="margin"> <s id="s.000432"><margin.target id="marg101"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000433">Idipſum alijs exemplis, quæ facilè poſſunt expe<lb></lb>riri, confirmari poteſt. </s> </p> <figure id="id.010.01.097.1.jpg" xlink:href="010/01/097/1.jpg"></figure> <p type="main"> <s id="s.000434">Sit vas aqua plenum RSXV & ha<lb></lb>beatur quoque cylindrus ligneus <lb></lb>EF, qui in aqua demerſus non de<lb></lb>mergetur integrè infra ſupremam li<lb></lb>bellam aquæ RS, ſed remanebit ali<lb></lb>qua eius pars GE eminens ſuprą <lb></lb>aquæ libellam, propterea quòd li<lb></lb>gnum minùs graue eſt ſpecie, quàm <lb></lb>ipſa aqua, (vt Archimedes ait.) <lb></lb>Si poſtea eumdem ligneum cylindrum extra aquam̨ <lb></lb>ſubleuauero vſque ad ſitum AB, & hinc liberè eum <lb></lb>deſcendere permittam, is profectò non conſiſtet, ne<lb></lb>què quieſcet in ſitu EF, <expan abbr="nã">nam</expan> impetus acquiſitus in de<lb></lb>ſcenſu per aerem profundiùs infra aquæ libellam̨ <lb></lb>motu violento cylindrum immittet vſque ad ſitum̨ <lb></lb>CD & hinc denuò aſcendendo tranſgreſſo ſitu æqui<lb></lb>librij EF reſiliet omninò extra aquam propè ſitum̨ <pb pagenum="90" xlink:href="010/01/098.jpg"></pb><arrow.to.target n="marg102"></arrow.to.target><lb></lb>AB, & ſic denuò quouſque repetitis vibrationibus <lb></lb>ſenſim languendo, tandèm quieſcat in ſitu naturali <lb></lb>EF. </s> </p> <p type="margin"> <s id="s.000435"><margin.target id="marg102"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <figure id="id.010.01.098.1.jpg" xlink:href="010/01/098/1.jpg"></figure> <p type="main"> <s id="s.000436">Pari modo ſumpto <expan abbr="fune-pẽ-dulo">fune-pen<lb></lb>dulo</expan> AB quod moueri poſſit <lb></lb>circa ſuum centrum firmum A, <lb></lb>remota pila plumbea. </s> <s id="s.000437">B à ſitu <lb></lb>ſuo naturali, ſeu perpendicu<lb></lb>lari ad horizontem, perducta<lb></lb>que ad ſitum eleuatum C, illa planè vt grauis excur<lb></lb>ret deſcendendo arcum CB, & vniuerſus is motus na<lb></lb>turalis erit, vtpotè dependens ab impetu grauitatis <lb></lb>intrinſeco, non tamen in infimo ſitu B pila perſiſtet <lb></lb>poſtquam ibidem perducta eſt, ſed vlteriùs excur<lb></lb>ret ferè æquali ſpatio priori vltrà perpendiculum vſ<lb></lb>que ad ſitum D, aſcendendo nimirùm ab infimo ſitu <lb></lb>B per integrum arcum BD, & quia motus ille qui gi<lb></lb>gnitur à principio intrinſeco, & naturali non poteſt <lb></lb>eſſe non naturalis, cùmque aſcenſus pilæ vltra cen<lb></lb>trum terræ, & deſcenſus cylindri EF infra aquæ li<lb></lb>bellam poſt caſum, & aſcenſus pilæ plumbeæ per ar<lb></lb>cum BD pendeat, creeturque ab illa naturali virtu<lb></lb>te grauitatis nempè eiuſdem corporis deſcendentis <lb></lb>quatenùs deſcendit: nulla enim alia cauſa extrinſe<lb></lb>ca ſuperueniens excogitari poteſt, quæ violentiam̨ <lb></lb>inſerat, & ſursùm impellat prædictum graue, quàm <lb></lb>impetus acquiſitus, & conceptus in ipſo caſu natura<lb></lb>litèr facto productoque à principio intrinſeco graui<lb></lb>tatis eius, qui procùl dubio impetus à naturali prin-<pb pagenum="91" xlink:href="010/01/099.jpg"></pb><arrow.to.target n="marg103"></arrow.to.target><lb></lb>cipio pendens naturalis, & intrinſecus quoque erit, <lb></lb>igitur etiam illa operatio aſcenſus erit naturalis qua<lb></lb>tenùs pendet creaturque à principio intrinſeco, iņ <lb></lb>eo enim ſolummodò caſu violenta <expan abbr="cẽſeri">cenſeri</expan> poſſet <expan abbr="quã-do">quan<lb></lb>do</expan> à peregrino, & <expan abbr="aduẽtitio">aduentitio</expan> principio procrearetur. </s> </p> <p type="margin"> <s id="s.000438"><margin.target id="marg103"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000439">Contra hoc ratiocinium inſurgit inſignis Peripa<lb></lb><arrow.to.target n="marg104"></arrow.to.target><lb></lb>teticus, & ait, quod ſubſequens aſcenſus vltra cen<lb></lb>trum terræ, vel vltra perpendiculum per arcum BD <lb></lb>non pendet, nec procreatur à grauitate eiuſdem cor<lb></lb>poris, ſed ab impetu concepto per motum deſcenſus, <lb></lb>qui impetus, inquit ille, res eſt, toto cœlo diuerſa à <lb></lb>grauitate, imò prædictus impetus contra grauitatem <lb></lb>luctatur. </s> </p> <p type="margin"> <s id="s.000440"><margin.target id="marg104"></margin.target>Obiectiones <lb></lb>recentioris <lb></lb>authoris af<lb></lb>feruntur.</s> </p> <p type="main"> <s id="s.000441">Patet ergò concedere aduerſarium pilæ aſcenſum <lb></lb>poſt excurſum vltra centrum, vel vltra perpendicu<lb></lb>lum effici, ac produci à virtute impetus impreſſi, qui <lb></lb>nimirùm immediata cauſa, & principium eſt prædi<lb></lb>cti aſcenſus, ſeù operationis, quæ nomine leuitatis <lb></lb>inſignitur. </s> <s id="s.000442">At quia præter immediatam cauſam illius <lb></lb>aſcenſus, ſcilicèt præter impetum, adnotari præte<lb></lb>rea debet cauſa productrix prædicti impetus, quæ <lb></lb>eſt grauitas naturalis, & intrinſeca eiuſdem corpo<lb></lb>ris, ergo hæc erit cauſa ſaltèm mediata illius poſtre<lb></lb>mi aſcenſus, & hìc noto quod aduerſarius non negat, <lb></lb>nec affirmat grauitatem fuiſſe cauſam, & principium <lb></lb>productiuum prædicti impetus, ſed tantummodò ait <lb></lb>valdè differre grauitatem ab impetu, imò naturas <lb></lb>contrarias, & ſe mutuo deſtructiuas habere, quia ni<lb></lb>mirùm non alia de cauſa ceſſat <expan abbr="ſubſequẽs">ſubſequens</expan> motus <expan abbr="aſcẽ-">aſcen-</expan><pb pagenum="92" xlink:href="010/01/100.jpg"></pb><arrow.to.target n="marg105"></arrow.to.target><lb></lb>ſus tùm pilæ, tùm fune-penduli, niſi quia grauitas pi<lb></lb>læ contrario niſu vim impetus aſcendentis deſtruit. </s> </p> <p type="margin"> <s id="s.000443"><margin.target id="marg105"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000444">Sed quid tandem hinc aduerſarius deducere vel<lb></lb>let? </s> <s id="s.000445">an quia ex eo, quòd natura grauitatis diuerſą <lb></lb>ſit ab impetu dicemus impetum prædictæ pilæ de<lb></lb>ſcendentis vſque ad centrum, vel perpendiculum ge<lb></lb>nitum non fuiſſe à vi, & exercitio grauitatis? </s> <s id="s.000446">à quą <lb></lb>nam ergo virtute tamquam à principio immediato <lb></lb>genitus fuit? </s> <s id="s.000447">profectò ſi ſenſus negare non velimus, <lb></lb>fatendum eſt à nulla alia cauſa, vel principio exter<lb></lb>no, ſed tantummodò ab ipſamet grauitate pilæ de<lb></lb>ſcendentis impetum prædictum genitum fuiſſe, nec <lb></lb>certitudo ſenſus relinqui debet propter difficulta<lb></lb>tem adductam ab aduerſario, vt præclarè Ariſtoteles <lb></lb><arrow.to.target n="marg106"></arrow.to.target><lb></lb>præcipit. </s> <s id="s.000448">Si igitur grauitas pilæ eſt ſaltem <expan abbr="principiũ">principium</expan>, <lb></lb>& cauſa mediata conſequentis aſcenſus, neceſſariò <lb></lb>actus, & operatio aſcenſus, quæ violenta, & præter <lb></lb>naturam ſaxi exiſtimatur, efficietur procreabiturque <lb></lb>ab interno, & naturali principio grauitatis eius, & <lb></lb>proindè actus aſcenſus, ſeu motus violentus efficie<lb></lb>tur à principio interno, & naturali. </s> </p> <p type="margin"> <s id="s.000449"><margin.target id="marg106"></margin.target>5. phyſ c. 3.</s> </p> <p type="main"> <s id="s.000450">Et hìc obitèr mirari licèt horum philoſophorum̨ <lb></lb>ſecuritatem; hìc negant impetum à grauitate pro<lb></lb>creari, & inculcant valdè inter ſe differre, & ſe mu<lb></lb>tuò deſtruere, & vnà <expan abbr="cũ">cum</expan> Ariſtotele in mechanicis a<lb></lb><arrow.to.target n="marg107"></arrow.to.target><lb></lb>pertè fatentur impetum eſſe grauitatem fluentem eſ<lb></lb>ſeque prorſus eiuſdem naturæ, quia nimirum ſaxum <lb></lb>impetu affectum comprimit, conterit aduerſa cor<lb></lb>pora eodem modo, ac ingens pondus efficit. <pb pagenum="93" xlink:href="010/01/101.jpg"></pb><arrow.to.target n="marg108"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000451"><margin.target id="marg107"></margin.target>Quæſt. 19.</s> </p> <p type="margin"> <s id="s.000452"><margin.target id="marg108"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000453">Sed inſtat aduerſarius quomodo poteſt grauitas <lb></lb>efficere impetum quo pila aſcendit ſi videmus <expan abbr="motũ">motum</expan> <lb></lb>prædictum aſcenſus ſenſim debilitari, & tandem ex<lb></lb>tingui ſolummodo propter renitentiam, & contra<lb></lb>riam actionem, quam efficit pondus eiuſdem pilæ? <lb></lb></s> <s id="s.000454">Et hìc aio, quòd exercitium eiuſdem ponderis, ſcili<lb></lb>cèt compreſſio eius producit duos effectus contra<lb></lb>rios, primò per deſcenſum creat, fouet, & auget im<lb></lb>petum eius, poſteà per aſcenſum ei contranititur, <lb></lb>debilitat, atque deſtruit eum, & licèt hoc mirabilę <lb></lb>videatur, nihilominùs idipſum concedant neceſsè <lb></lb>eſt, velint, nolint, cùm ſenſu conſtet, ſic eadem manus <lb></lb>impellendo ſaxum dum deorsùm decidit, auget mul<lb></lb>tiplicatque eius impetum, at ſi ſaxum ſursùm aſcen<lb></lb>deret eadem manus contrario motu impetum eius <lb></lb>debilitaret, atque deſtrueret. </s> <s id="s.000455">ſimilitèr idem calor <lb></lb>Solis generat, & auget plantas, & poſtea eas exic<lb></lb>cat extinguitque. </s> <s id="s.000456">Ex his ergò patet inſufficientią <lb></lb>ſuperiùs adducti ratiocinij. </s> </p> <p type="main"> <s id="s.000457"><emph type="center"></emph>PROP. XLI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000458"><emph type="center"></emph><emph type="italics"></emph>Ab eodem principio grauitatis aſcenſio, & ſubleuatio cor<lb></lb>porum leuium effici poteſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000459">SEd redeo iam ad propoſitum, & alia ratione <expan abbr="eã-dem">ean<lb></lb>dem</expan> propoſitionem perſuadere conabor. </s> <s id="s.000460">Vul<lb></lb>gatiſſimum axioma omnium <expan abbr="philoſophorũ">philoſophorum</expan> eſt, quòd <lb></lb>natura ſemper producit ſuas operationes via breuiſ<lb></lb>ſima, ſummo compendio, atque abhorret à prolixi-<lb></lb><pb pagenum="94" xlink:href="010/01/102.jpg"></pb> <arrow.to.target n="marg109"></arrow.to.target>tate, & multiplicitate cauſarum quando ſuos effe<lb></lb>ctus producere poteſt via illa breuiori, & faciliori. <lb></lb></s> <s id="s.000461">hinc deducitur, quod ſi poſſibile eſt <expan abbr="trãſportare">tranſportare</expan> cor<lb></lb>pora naturalia ad propria loca mediante vnica, & ſin<lb></lb>gulari motiua virtute grauitatis, vaniſſimè, & ſtultè <lb></lb>natura ageret, ſi niteretur prædictum finem aſſe qui <lb></lb>adhibitis duobus principijs ſcilicèt grauitate, & al<lb></lb>tera oppoſita virtute, quæ leuitas nuncupatur. </s> <s id="s.000462">Quod <lb></lb>verò poſſint naturalia corpora ad ſua naturalia loca <lb></lb>perduci à grauitate ſola abſque leuitate patet ex ſu<lb></lb>periùs dictis, nam minor grauitas, quæ veſicæ aerę <lb></lb>plenæ tribuitur, & maior aquæ, & omnium maxima <lb></lb>hydrargyro, ſufficientiſſima cauſa eſt apta ad produ<lb></lb>cendum <expan abbr="prædictũ">prædictum</expan> effectum, quod deducitur ex prin<lb></lb><arrow.to.target n="marg110"></arrow.to.target><lb></lb>cipijs, & rationibus mechanicis. </s> <s id="s.000463">Quaproptèr pro<lb></lb>babiliſſimè concedendum eſt ſolo principio grauita<lb></lb>tis abſque vlla leuitate naturam ſuum finem aſſequi <lb></lb>collocandi corpora terrena in debitis locis, nempè <lb></lb>ſursùm, & deorsùm. </s> </p> <p type="margin"> <s id="s.000464"><margin.target id="marg109"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000465"><margin.target id="marg110"></margin.target>Cap. 2.</s> </p> <p type="main"> <s id="s.000466">Et hactenùs adductæ ſunt rationes probabiles <expan abbr="cõ-tra">con<lb></lb>tra</expan> poſitiuam leuitatem, reſtat modò vt idipſum di<lb></lb>rectè oſtendatur rationibus magis conuincentibus, <lb></lb>& efficacioribus. <pb pagenum="95" xlink:href="010/01/103.jpg"></pb><arrow.to.target n="marg111"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000467"><margin.target id="marg111"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000468"><emph type="center"></emph>PROP. XLII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000469"><emph type="center"></emph><emph type="italics"></emph>Et primò oſtendemus, quòd quodlibet corpus à principio in<lb></lb>trinſeco, & naturali ſponte translatum faciliùs, & <lb></lb>celeriùs mouebitur in fluido rariori, & tenuio<lb></lb>ri, quàm in medio fluido craſſo, & <lb></lb>tenaciori.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000470">SInt duo vaſa GHIK, alterum KILM, <expan abbr="primũ">primum</expan> aqua <lb></lb>repleatur, ſecundum verò hydrargyro, immer<lb></lb>gatur verò eadem pila lignea A in vtroque fluido, in<lb></lb>telliganturque duæ moles ſpatiales ex prædictis flui<lb></lb>dis B, & C, quæ æquales ſint ipſi A, eique <expan abbr="ſuperincũ-bant">ſuperincun<lb></lb>bant</expan>, patet ergò quòd mercurij moles C grauior re<lb></lb>ſiſtentior, denſior, atque compactior eſt, quàm ſit <lb></lb><figure id="id.010.01.103.1.jpg" xlink:href="010/01/103/1.jpg"></figure><lb></lb>moles aquę B. præterea pila lignea <lb></lb>A nullo pacto aſcendere ſursùm po<lb></lb>teſt, niſi aquam B, ab eius loco ex<lb></lb>pellat vt ei locum cedat, atque mo<lb></lb>les ipſius ligni A <expan abbr="trãsferatur">transferatur</expan> ad oc<lb></lb>cupandum ſpatium ei æquale B, & <lb></lb>hoc ſemper contingit, vbique enim <lb></lb>in <expan abbr="aſcẽſu">aſcenſu</expan> cogitur continuato niſu <lb></lb>ſursùm impellere incumbentem a<lb></lb>quæ molem ei æqualem, tenacita<lb></lb>temque eius penetrare, ponatur iam gradus natura<lb></lb>lis impetus leuitatis ipſius ligni eſſe D, quia verò cor<lb></lb>pus motiuum A impetu D affectum impellit corpus <lb></lb>B fluidum, quod in quiete conſtitutum ſua naturali <pb pagenum="96" xlink:href="010/01/104.jpg"></pb><arrow.to.target n="marg112"></arrow.to.target><lb></lb>inertia reſiſtit impulſui impellentis corporis leuis A; <lb></lb>ergò ex <expan abbr="demõ">demom</expan> ſtratis in libro de vi percuſſionis <expan abbr="eadẽ">eadem</expan> <lb></lb>vis motiua leuitatis ipſius A communicatur, & <expan abbr="expã-ditur">expan<lb></lb>ditur</expan> per vniuerſum corpus motum, ſcilicèt per flui<lb></lb>dum B, igitur eius impetus D valdè debilitatur re<lb></lb>tardaturque, ſitque diminuta velocitas E, qua ni<lb></lb>mirùm lignum leue A, & fluidum B mouentur. </s> <s id="s.000471">pari <lb></lb>ratione ſit F velocitas retardata, qua idem lignum̨ <lb></lb>A nec non moles hydrargyri C ſibi æquali agitatur. <lb></lb></s> <s id="s.000472">Oſtendendum eſt quòd velocitas, E qua nimirum li<lb></lb>gnum aſcendit per aquam maior ſit velocitate F quà <lb></lb>lignum per mercurium eleuatur, & habere veloci<lb></lb>tatem E ad F reciprocè ferè eamdem proportionem, <lb></lb><figure id="id.010.01.104.1.jpg" xlink:href="010/01/104/1.jpg"></figure><lb></lb>quam habet corporea ſubſtantia <lb></lb>AC ad corpulentiam AB. </s> <s id="s.000473">Quia ab <lb></lb>eadem virtute motiua impelluntur <lb></lb>duo corpora A, & B à qua priùs in<lb></lb>telligebatur moueri ſingularis maſ<lb></lb>ſa lignea A cui naturalis gradus <lb></lb>impetus D conueniebat, igitur mo<lb></lb>les corporea, & materialis duorum <lb></lb>corporum ſimul ſumptorum A & B <lb></lb>ad molem corpoream A reciprocè <lb></lb>eamdem proportionem habebit, quam eorum ve<lb></lb><arrow.to.target n="marg113"></arrow.to.target><lb></lb>locitates <expan abbr="habẽt">habent</expan>, & ideò <expan abbr="erũt">erunt</expan> vt D ad E. </s> <s id="s.000474">Simili ratio<lb></lb>cinio vt moles corporea A ad molem corpoream AC <lb></lb>ita eſt velocitas F ad D, ergo ex æqualitate pertur<lb></lb>bata corporea ſubſtantia AB, ad AC eamdem pro<lb></lb>portionem habebit, quàm velocitas F ad E, eſt quę <pb pagenum="97" xlink:href="010/01/105.jpg"></pb><arrow.to.target n="marg114"></arrow.to.target><lb></lb>ſubſtantia corporea AB minor ea quæ continetur in <lb></lb>AC, ergò impetus F minor eſt quàm E; quaproptèr <lb></lb>lignum A intrà mercurium C <expan abbr="translatũ">translatum</expan> ſursùm <expan abbr="aſcẽ-dere">aſcen<lb></lb>dere</expan> debet tardiori, & minori velocitate, quàm ſit <lb></lb>velocitas E, quæ <expan abbr="cõpetit">competit</expan> ligno aſcendenti in aqua B. </s> </p> <p type="margin"> <s id="s.000475"><margin.target id="marg112"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000476"><margin.target id="marg113"></margin.target>De vi per<lb></lb>cuſſionis pro <lb></lb>poſit. </s> <s id="s.000477">15.</s> </p> <p type="margin"> <s id="s.000478"><margin.target id="marg114"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000479">Et profectò euidentiſſimum eſt, quòd quodlibet <lb></lb>corpus à principio intrinſeco motu ſpontaneo trans<lb></lb>latum, multò faciliùs gradietur excurretque per me<lb></lb>dium fluidum rarius, & cedens, quàm in medio flui<lb></lb>do tenaciori, & craſſiori, vt pila aurea celeriùs per <lb></lb>aerem, quàm per aquam eiuſdem ſpatij deſcendit, & <lb></lb>per aquam velociori motu, quàm per mercurium ex<lb></lb>currit; ſic paritèr videmus animalia, quæ intrinſecą <lb></lb>vi mouentur, difficiliùs gradi poſſe, ſi infra arenam̨ <lb></lb>ſub mergantur, & minùs difficilè infrà lutum, & fa<lb></lb>ciliùs in aqua, & multò faciliùs in aere, nec <expan abbr="vnquã">vnquam</expan> <lb></lb>contrarium contingere poterit, quòd nimirùm idem <lb></lb>animal eamdem vim motiuam exercendo difficiliùs <lb></lb>& tardiùs moueatur per aerem, quàm per aquam, & <lb></lb>difficiliùs per aquam, quàm per lutum, aut per hy<lb></lb>drargyrum. </s> </p> <p type="main"> <s id="s.000480"><emph type="center"></emph>PROP. XLIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000481"><emph type="center"></emph><emph type="italics"></emph>Non moueri ſursùm corpora, quæ leuia appellantur, à vi <lb></lb>intrinſeca leuitatis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000482">HIs poſitis conſideremus modò ceram, aut veſi<lb></lb>cam aere plenam <expan abbr="aſcendẽtem">aſcendentem</expan> per diuerſa me<lb></lb>dia fluida, ſi <expan abbr="verũ">verum</expan> eſt, quòd aerea veſica ſursùm <expan abbr="aſcẽ-">aſcen-</expan><pb pagenum="98" xlink:href="010/01/106.jpg"></pb><arrow.to.target n="marg115"></arrow.to.target><lb></lb>dit in aqua; aut hydrargyro motu ſpontaneo, nempè <lb></lb>ab intrinſeca virtute motiua, quæ vocatur leuitas, <lb></lb>igitur neceſsè eſt vt in <expan abbr="aſcẽſu">aſcenſu</expan> penetret corpora flui<lb></lb>da intermedia; atque eorum tenacitatem, & denſi<lb></lb>tatem ſuperet, imò fluidum è ſuo loco expellat, vt <lb></lb>via, & tranſitus paretur, qua ſursùm aſcendere, & <lb></lb>perduci poſſit, & quia hydrargyrum magis conſti<lb></lb>patum, denſum, & graue eſt, <expan abbr="quã">quam</expan> aqua, igitur quod<lb></lb>libet corpus leue aere repletum, aut aeris naturam̨ <lb></lb>participans, vt lignum, & cera, (quæ ex aduerſario<lb></lb>rum ſententia mouentur ab intrinſeca virtute leui<lb></lb>tatis) neceſsè eſt vt maiorem reſiſtentiam <expan abbr="offendãt">offendant</expan> <lb></lb>in tranſitu per hydragyrum, à cuius tenacitate, den<lb></lb>ſitate, & pondere gradus impetus eius neceſſariò re<lb></lb>tunditur retardaturque multò magis, quàm in <expan abbr="aſcẽ-ſu">aſcen<lb></lb>ſu</expan> per aquam contingit, quæ cùm magis rara, & ce<lb></lb>dens ſit, minùs debilitat retardatque eamdem eius <lb></lb>vim motiuam, quaproptèr motus aſcenſus ligni, vel <lb></lb>ceræ per hydrargyrum multò magis retardabitur, <lb></lb>quàm ille, qui per aquam fit; quia verò hoc eſt fal<lb></lb>ſum, & contra ſenſus euidentiam, multò enim velo<lb></lb>ciòr eſt motus ligni, vel ceræ factus per <expan abbr="hydrargyrũ">hydrargyrum</expan>, <lb></lb><expan abbr="quã">quam</expan> per <expan abbr="aquã">aquam</expan>; <expan abbr="nõ">non</expan> igitur <expan abbr="verũ">verum</expan> eſt ab intrinſeco, & natu<lb></lb>rali principio ſursùm moueri, & proindè cauſa aſcen<lb></lb>ſus non erit leuitas poſitiua, ideoque nullum vſum̨ <lb></lb>habebit in natura, nec propterea exiſtet vlla leuitas. <pb pagenum="99" xlink:href="010/01/107.jpg"></pb><arrow.to.target n="marg116"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000483"><margin.target id="marg115"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000484"><margin.target id="marg116"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000485"><emph type="center"></emph>PROP. XLIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000486"><emph type="center"></emph><emph type="italics"></emph>Ratione mechanica à grauiori fluido celeriùs idem mobile <lb></lb>ſursùm exprimitur, quàm à fluido minùs graui.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000487">HViuſmodi difficultates omninò vitantur effu<lb></lb>giunturque, ſi certitudinem, & neceſſitatem <lb></lb>ex principijs mechanicis pendentem ſequamur, ſci<lb></lb>licèt poſita ſolummodò grauitate in omnibus cor<lb></lb>poribus ſublunaribus; neceſsè eſt vt <expan abbr="grauiſſimũ">grauiſſimum</expan> flui<lb></lb>dum hydrargyri maiori impetu ſursùm per extruſio<lb></lb>nem impellat lignum, quàm aliud <expan abbr="fluidũ">fluidum</expan> minùs gra<lb></lb>ue, vt eſt aqua, ſicuti in bilance pondus vnius vnciæ <lb></lb>maiori velocitate ſursùm impellitur à maiori preſ<lb></lb>ſione contraria ponderis decem librarum, quàm à <lb></lb>minori compreſſione ponderis vnius libræ. </s> <s id="s.000488">Demon<lb></lb>ſtratio verò huius rei ſuo loco exponetur, ſed inte<lb></lb>rim ſi effectus omnes qui obſeruantur in hiſce corpo<lb></lb>ribus aſcendentibus ijdem prorsùs ſunt, & ijſdem̨ <lb></lb>legibus mechanicis fiunt, ac ſi omnia corpora gra<lb></lb>uia fuiſſent, ſed inæquali grauitate donarentur, & <lb></lb>præterea in ijs non apparet phenomena motus fieri <lb></lb>ea ratione, quæ requireretur ſi præter grauitatem̨ <lb></lb>reperiretur quoque aliud principium contrarium le<lb></lb>uitatis: igitur concedendum eſt ſola grauitate natu<lb></lb>ram operari, neque leuitatem vllam exigere. </s> </p> <p type="main"> <s id="s.000489">Contra euidentiam harum rationum non deſunt, <lb></lb>qui difficultates, & ſubterfugia afferant pro <expan abbr="retinẽ-da">retinen<lb></lb>da</expan> ſuæ poſitionis in ueriſimilitudine; aiunt enim li-<pb pagenum="100" xlink:href="010/01/108.jpg"></pb><arrow.to.target n="marg117"></arrow.to.target><lb></lb>gnum tardiùs in hydrargyro aſcendere debuiſſe; <lb></lb>quàm per aquam ob maiorem illius reſiſtentiam; ſed <lb></lb>propter contrarietatem, & inimicitiam, quam habet <lb></lb>lignum cum Mercurio, ſuum curſum accelerat vt ex<lb></lb><arrow.to.target n="marg118"></arrow.to.target><lb></lb>peditè mercurium fugiat, & aquam aeremque aſſe<lb></lb>quatur; quod symbolum elementum, atque <expan abbr="amicũ">amicum</expan> <lb></lb>eſt; & propterea ceſſante odio non cogitur celerri<lb></lb>mè ab eo diſcedere. </s> <s id="s.000490">Sed vide quàm faciles ſint præ<lb></lb>dicti philoſophi; qui occaſione exigente non <expan abbr="verẽ-tur">veren<lb></lb>tur</expan> alitèr reſpondere, nam ſi ego <expan abbr="quærã">quæram</expan>, quare gra<lb></lb>uitas, quæ certè ineſt in hiſce terrenis corporibus, <lb></lb>celeriùs transfert ſaxum, quò magis ad terram acce<lb></lb>dit, atque ei approximatur; reſpondent quia vicinia <lb></lb><arrow.to.target n="marg119"></arrow.to.target><lb></lb>terræ veluti roboratur vis motiua ſaxi cadentis; ſic <lb></lb>paritèr leuitas veſicę aereę creſcere deberet in aquę <lb></lb>ſummitate, quia nempè aeri approximatur, & ideò <lb></lb>virtus eius motiua roborari quoque deberet. </s> <s id="s.000491">Sed <lb></lb>his omiſſis ſummi poſſunt diuerſa corpora, quæ na<lb></lb>turam, & temperiem diuerſam, & contrariam aquæ <lb></lb>habeant, ſimillimam verò mercurio, & talis fortaſſe <lb></lb>erit ampulla vitrea, vel veſica, quæ repleatur mercu<lb></lb>rio ſublimato, vel pręcipitato; ſic quoque vas fieri <lb></lb>poſſet ex metallo, vel alio corpore ſimillimo hy<lb></lb>drargyro, vt nimirùm efficiatur compoſitum cuius <lb></lb>natura valdè diuerſa ſit ab aqua, & ſimillima hydrar<lb></lb>gyro, & ſic omninò tolleretur inimicitia, & antipa<lb></lb>thia inter vas, & fluidum craſſius mercuriale, nihi<lb></lb>lominùs obſeruabitur prædictum vas velociùs aſcen<lb></lb>dere per hydrargyrum, tardo verò motu per aquam, <pb pagenum="101" xlink:href="010/01/109.jpg"></pb><arrow.to.target n="marg120"></arrow.to.target><lb></lb>igitur illa ſomniata inimicitia non erit cauſa prædi<lb></lb>ctæ inæqualitatis motus, ſed mechanica, & naturalis <lb></lb>neceſſitas, qua maximum pondus hydrargyrj impe<lb></lb>tuoſiore motu exprimit, & impellit ſursùm conten<lb></lb>tum vas vitreum, vel veſica, quàm impellere aquą <lb></lb>queat ſuo minori pondere. </s> </p> <p type="margin"> <s id="s.000492"><margin.target id="marg117"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000493"><margin.target id="marg118"></margin.target>Recurrunt <lb></lb>aduerſarij ad <lb></lb>maiorem <expan abbr="inimicitiã">ini<lb></lb>micitiam</expan> <expan abbr="quã">quam</expan> <lb></lb>habet <expan abbr="lignũ">lignum</expan>, <lb></lb>ſeu aer cum <lb></lb>hydrargyro, <lb></lb>quàm cum <lb></lb>aqua, vt de<lb></lb>ducant cele<lb></lb>riùs lignum <lb></lb>fugere mer<lb></lb>curium, <expan abbr="quã">quam</expan> <lb></lb><expan abbr="aquã">aquam</expan> debere.</s> </p> <p type="margin"> <s id="s.000494"><margin.target id="marg119"></margin.target>Sed reijci<lb></lb>tur.</s> </p> <p type="margin"> <s id="s.000495"><margin.target id="marg120"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000496">Id ipſum alijs exemplis confirmari poſſet, ſi nimi<lb></lb>rum ſumatur oleum à frigore condenſatum, & gla<lb></lb>ciatum, cuius temperies, & natura potiùs grauiori <lb></lb>mercurio, vel oleo tartari aſſimilatur, & è contrą <lb></lb>contrariam naturam, & diuerſam haberet ab ipſą <lb></lb>aqua, & ſic oleum prædictum ob amicitiam lento <lb></lb>motu aſcendere deberet per hydrargyrum, aut per <lb></lb>oleum tartari. </s> <s id="s.000497">Sed celerrimè in aqua currere debe<lb></lb>ret, vtpotè oleo contraria. </s> <s id="s.000498">Similitèr calx in veſica <expan abbr="cõ-tenta">con<lb></lb>tenta</expan> aquę forti ſimillima eſt ob <expan abbr="caliditatẽ">caliditatem</expan>, & acredi<lb></lb>nem ambarum, & è contrà ſummè contraria erit <expan abbr="cõ-muni">con<lb></lb>muni</expan> aquæ, & nihilominùs in illa velociſſimè aſcen<lb></lb>dit, in hac tardè. </s> <s id="s.000499">Similitèr ſumi poſſent vaſcula ex <lb></lb>cera, aut bitumine, quæ repleri poſſent puluere, ſpi<lb></lb>ritu, oleo, vel vino, vel alijs innumeris rebus, quæ <lb></lb>ſemper aſcendent velociſſimè in fluidis grauioribus, <lb></lb>vt ſunt aquæ regiæ, licèt in ſumma caliditate, & acre<lb></lb>dine ſalina conueniant, & è contra languido, & tar<lb></lb>do motu in fluidis <expan abbr="cõtrariæ">contrariæ</expan> naturæ aſcendunt, dum<lb></lb>modò minùs grauia ſint. </s> <s id="s.000500">Quaproptèr verum non eſt <lb></lb>ob inimicitiam, & contrarietatem veſicam aeream̨ <lb></lb>velociſſimè à mercurio fugere, & languido motu ex<lb></lb>currere per aquam ei ſimilem, ſed potiùs ob mecha-<pb pagenum="102" xlink:href="010/01/110.jpg"></pb><arrow.to.target n="marg121"></arrow.to.target><lb></lb>nicam rationem <expan abbr="deſumptã">deſumptam</expan> à maiori, vel minori gra<lb></lb>uitate, quæ deducitur ex Archimedis doctrina, quòd <lb></lb>ſcilicèt fluidum grauius per extruſionem impellerę <lb></lb><expan abbr="ſursũ">ſursum</expan> debeat corpora minùs grauia, & hæc eſt cauſa, <lb></lb>quare abſque poſitiua leuitate corpora ſursùm <expan abbr="aſcẽ-dere">aſcen<lb></lb>dere</expan> debent. </s> </p> <p type="margin"> <s id="s.000501"><margin.target id="marg121"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000502"><expan abbr="Cõtra">Contra</expan> <expan abbr="perſpicuitatẽ">perſpicuitatem</expan> ſupradicti ratiocinij <expan abbr="obijciũt">obijciunt</expan> <lb></lb>primò, quòd <emph type="italics"></emph>ſicuti grauiora intra minùs grauia merſa fe<lb></lb>runtur deorsùm tanta vi, quæ ſit æqualis differentiæ gra<lb></lb>uitatis mobilis ſupra grauitatem medij, constat euidentèr <lb></lb>euenturum proportion alitèr in leuioribus intra minùs leuia <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg122"></arrow.to.target><lb></lb><emph type="italics"></emph>contentis ea ſcilicèt in ordine ad leuitatem, ſursùm, non niti <lb></lb>ſecundùm menſuram exceſſus ſupra minùs leue ſursùm ni<lb></lb>ſura, vt ſimilis ratio perſuadet.<emph.end type="italics"></emph.end></s> <s id="s.000503"> Hoc ſuppoſito veluti cer<lb></lb>tum, & euidens reſpondet argumento ſuperius addu<lb></lb>cto, aitque <emph type="italics"></emph>expirationem calidam reſpectu aquæ valdè le<lb></lb>uem ſecundùm menſuram totius ſuæ leuitatis ſursùm niti <lb></lb>intra aquam, ac proindè valere ad reſiſtentiam illius cele<lb></lb>ritèr ſuperandam, at verò valdè exiguum exceſſum ſupra <lb></lb>aerem obtinentem in leuitate ſursùm niti præcisè ſecundum <lb></lb>menſuram talis exceſſus, ac proindè non eſſe mirum ſi lentè <lb></lb>per aerem aſcendat etiamſi dicatur à leuitate poſitiua in<lb></lb>trinſeca moueri.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.000504"><margin.target id="marg122"></margin.target>Denuò ad<lb></lb>miſſa leuita<lb></lb>te colligunt <lb></lb>ignem cele<lb></lb>riùs per a <lb></lb>quam, quam <lb></lb>per aerem̨ <lb></lb><expan abbr="aſcẽdere">aſcendere</expan> de<lb></lb>bere.</s> </p> <p type="main"> <s id="s.000505">Itaque ſicuti nos ex Archimedis doctrina deduci<lb></lb>mus rationem deſcenſus grauium, & aſcenſus <expan abbr="leuiũ">leuium</expan> <lb></lb>ex hac ſuppoſitione, quòd corpora omnia ſubluna<lb></lb>ria ſint grauia, ſibi perſuadent demonſtrare poſſe ea<lb></lb>dem symptomata ſupponendo nedùm corpora aſcen<lb></lb>dentia, ſed etiam medium fluidum, in quo <expan abbr="aſcendũt">aſcendunt</expan> <pb pagenum="103" xlink:href="010/01/111.jpg"></pb><arrow.to.target n="marg123"></arrow.to.target><lb></lb>eſſe leuia; quaproptèr quotieſcumque agitur de cor<lb></lb>poribus grauibus deſcendentibus comparari debent <lb></lb>grauitates tum corporis mobilis, tùm medij fluidi in <lb></lb>quo deſcendit; at è contrà cum agitur de corporibus <lb></lb>aſcendentibus, debent paritèr intèr ſe comparari le<lb></lb>uitates eorum vnà cum leuitate medij fluidi in quo <lb></lb>aſcendunt. </s> </p> <p type="margin"> <s id="s.000506"><margin.target id="marg123"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000507">Modò vt fallacia huius ratiocinij detegatur, <expan abbr="demõ-">demon<lb></lb></expan>ſtrabo priùs lemmata aliqua mechanica, ex quibus <lb></lb>poſtea adhibitis hypotheſibus ſupradictis demon<lb></lb>ſtrabo impoſſibile omninò eſſe vt impetus velocita<lb></lb>tis quo ſursùm aſcendunt corpora illa, quæ leuia ap<lb></lb>pellantur, produci poſſit atque dependeat à princi<lb></lb>pio aliquo intrinſeco à quo ſursùm impellantur re<lb></lb>moueanturque à centro terræ. </s> </p> <p type="main"> <s id="s.000508">Et primo loco obſeruo cum Ariſtotele in mecha<lb></lb>nicis, quòd. </s> </p> <p type="main"> <s id="s.000509"><emph type="center"></emph>PROP. LXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000510"><emph type="center"></emph><emph type="italics"></emph>Libræ, vel rotæ termini oppoſiti contrarijs <lb></lb>motibus circa centrum agitari <lb></lb>debent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000511">SIt libra radiorum æqualium, vel rota AIBH con<lb></lb>uertibilis circa ſuum centrum C, hic <expan abbr="manifeſtũ">manifeſtum</expan> <lb></lb>eſt, quòd ſi libram, aut rotam re uoluere velimus, ita <pb pagenum="104" xlink:href="010/01/112.jpg"></pb><arrow.to.target n="marg124"></arrow.to.target><lb></lb><figure id="id.010.01.112.1.jpg" xlink:href="010/01/112/1.jpg"></figure><lb></lb>vt terminus eius A deſcendat <lb></lb>deorsùm percurrendo arcum <lb></lb>AI neceſsè eſt vt eius oppoſi<lb></lb>tus terminus B motu contrario <lb></lb>ſursùm aſcendat percurrendo <lb></lb>arcum BH æqualem contrapo<lb></lb>ſito AI. </s> <s id="s.000512">Et <expan abbr="quotieſcumq;">quotieſcumque</expan> præ<lb></lb>dicti motus <expan abbr="cõtrarij">contrarij</expan> ſimul fie<lb></lb>ri nequeunt, tunc neceſsè eſt <lb></lb>vt libra, vel rota quieſcatiņ <lb></lb>eodem ſitu, nec agitetur. </s> </p> <p type="margin"> <s id="s.000513"><margin.target id="marg124"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000514"><emph type="center"></emph>PROP. XLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000515"><emph type="center"></emph><emph type="italics"></emph>Si eidem libræ termino applicentur potentiæ ad oppoſitas <lb></lb>partes <expan abbr="trahẽtes">trahentes</expan> mutuo <expan abbr="ſeimpediẽt">ſeimpedient</expan>, & potentia maior <lb></lb>præualebit, libram <expan abbr="flectẽdo">flectendo</expan> vi æquali dif<lb></lb>ferentiæ potentiarum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000516">APponatur poſtea pondus DE termino libræ A; <lb></lb>hoc profectò vim efficit, conaturque traherę <lb></lb>terminum libræ A per directionem AD versùs cen<lb></lb>trum telluris, at quia ſemidiameter AC in <expan abbr="cẽtro">centro</expan> librę <lb></lb>figitur immobiliter, hinc conſequetur reuolutio librę <lb></lb>fereturque terminus A non per lineam rectam AD, <lb></lb>ſed per arcum AI excurrendo integrum <expan abbr="quadrantẽ">quadrantem</expan>, <lb></lb>& quia libra AB ſupponitur continua, & rigida <expan abbr="eodẽ">eodem</expan> <lb></lb>tempore quo terminus A arcum AI pertranſit oppo<lb></lb>ſitus eius terminus B deſcribet contrapoſitum arcum <lb></lb>BH. </s> <s id="s.000517">Modò motum eiuſdem libræ, & deſcenſum pon-<pb pagenum="105" xlink:href="010/01/113.jpg"></pb><arrow.to.target n="marg125"></arrow.to.target><lb></lb>deris DE impedire poſſumus, ſi eidem termino A ap<lb></lb>plicaretur vis contraria G, quę traheret ſursùm <expan abbr="eũ">eum</expan> ip<lb></lb>ſum terminum A per eamdem rectam lineam <expan abbr="horizõ-ti">horizon<lb></lb>ti</expan> perpendicularem verſus ſupremum terminum G; <lb></lb>& ſiquidem vis, & facultas motiua G æqualis eſſet vi <lb></lb>ponderis DE, nulla ratio ſuadet quòd vna earum̨ <lb></lb>virtutum reliquam ſuperet, aut vincat, proindequę <lb></lb>terminus libræ A non deſcendet versùs I, nec aſcen<lb></lb>det versùs H, ſed omninò quieſcetin eodem ſitu. </s> <s id="s.000518">Si <lb></lb>verò <expan abbr="põdus">pondus</expan> DE ſuperaret vim <expan abbr="motiuã">motiuam</expan> G, <expan abbr="eiuſq;">eiuſque</expan> exceſ <lb></lb>ſus eſſet pondus E, tunc procùl dubio <expan abbr="põdus">pondus</expan> DE præ<lb></lb>ualeret ſuperaretque vim motiuam G, & impetus, <lb></lb>atque vis, à qua prædicta libra flecteretur deorsùm̨ <lb></lb>versùs I menſuraretur à vi ponderis E, quæ eſt diffe<lb></lb>rentia, ſeù exceſſus, quo pondus premens DE ſupe<lb></lb>rat vim eleuantem G. </s> </p> <p type="margin"> <s id="s.000519"><margin.target id="marg125"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000520"><emph type="center"></emph>PROP. XLVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000521"><emph type="center"></emph><emph type="italics"></emph>Si oppoſitos terminos libræ, vel rotæ duæ potentiæ traham, <lb></lb>ambæ deorsùm tendendo, ſe mutuò impedient, & <lb></lb>maior potentia præualebit, ſed vi æquali <lb></lb>differentiæ earum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000522">POteſt deindè alia ratione prohiberi, & impediri <lb></lb>deſcenſus ponderis DE abſque eò, quòd termi<lb></lb>no A applicetur vis aliqua animata contraria G, & <lb></lb>hoc conſequitur ſi applicetur termino oppoſito B <lb></lb>aliud pondus F, quod dùm deorsùm impellit ad eaſ<lb></lb>dem partes ad quas dirigitur pondus DE prohibetur <pb pagenum="106" xlink:href="010/01/114.jpg"></pb><arrow.to.target n="marg126"></arrow.to.target><lb></lb>quoque deſcenſus termini A eiuſdem libræ, vt <expan abbr="dictũ">dictum</expan> <lb></lb>eſt; & ſiquidem pondus F æquale fuerit ponderi <lb></lb>DE, tunc efficietur æquilibrium, quia dùm ambo <expan abbr="põ-dera">pon<lb></lb>dera</expan> conantur deſcendere deorsùm transferre quę <lb></lb>duos terminos libræ versùs infimum ſignum <expan abbr="quadrã-">quadran<lb></lb></expan><arrow.to.target n="marg127"></arrow.to.target><lb></lb>tis I, & hoc efficitur æquali vi, & impetu, procùl du<lb></lb>bio vna vis, & conatus impedit motum, & <expan abbr="defcensũ">deſcensum</expan> <lb></lb>alterius, & ex hoc mutuo <expan abbr="impedimẽto">impedimento</expan> reſultat quies <lb></lb>totius libræ in ſitu horizontali; at ſi pondus F æqua<lb></lb>Ie fuerit vni portioni D totius ponderis DE, tunc <lb></lb>præua lente maiori pondere deprimet terminum librę <lb></lb>A versùs I, aſcendetque oppoſitus terminus B versùs <lb></lb>H tanta vi quæ ſit æqualis exceſſui ponderis E. </s> <s id="s.000523">Hinc <lb></lb>colligitur quod in libra, vel rota duo æquales im<lb></lb><figure id="id.010.01.114.1.jpg" xlink:href="010/01/114/1.jpg"></figure><lb></lb>petus ad eaſdem partes <expan abbr="tendẽ-tes">tenden<lb></lb>tes</expan>, nempè deorsùm, ideoquę <lb></lb>ſimiles inter ſe, ſe mutuo impe<lb></lb>diunt, & deſtruunt, itaut quies <lb></lb>conſequatur, ſi verò eorumdem <lb></lb>ſimilium motuum <expan abbr="deſcendentiũ">deſcendentium</expan> <lb></lb>vires inæquales fuerint, præua<lb></lb>lebit maius pondus, libramque <lb></lb>reuoluet non integra ſua vi, ſed tantummodò illa dif<lb></lb>ferentia, vel exceſſu, quo maius pondus ſuperat <lb></lb>minus. <pb pagenum="107" xlink:href="010/01/115.jpg"></pb><arrow.to.target n="marg128"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000524"><margin.target id="marg126"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000525"><margin.target id="marg127"></margin.target>Prop. 45.</s> </p> <p type="margin"> <s id="s.000526"><margin.target id="marg128"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000527"><emph type="center"></emph>PROP. XLVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000528"><emph type="center"></emph><emph type="italics"></emph>Iiſdem datis, ſi ambæ potentiæ ſursùm trahant, <lb></lb>idem ſequetur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000529">ID ipſum verum quoque eſt, <lb></lb><figure id="id.010.01.115.1.jpg" xlink:href="010/01/115/1.jpg"></figure><lb></lb>ſi applicentur terminis op<lb></lb>poſitis eiuſdem libræ A, B duæ <lb></lb>vires inæquales, DE maior, & <lb></lb>F minor, quæ ambæ ſursùm ter<lb></lb>minos libræ trahant aſcenden<lb></lb>do. </s> <s id="s.000530">& hìc eodem modo oſten<lb></lb>detur, quòd libra flectetur ſur<lb></lb>sùm ab A versùs H, & reliqua <lb></lb>vis minor F ſuperabitur ab ex<lb></lb>ceſſu virtutis DE ſupra F, deſcendetque terminus B <lb></lb>versùs I. </s> </p> <p type="main"> <s id="s.000531"><emph type="center"></emph>PROP. XLIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000532"><emph type="center"></emph><emph type="italics"></emph>Si oppoſitos terminos libræ duæ potentiæ trahant vna ſur<lb></lb>sùm, altera deorsùm, ſe mutuò iuuabunt, & vis li<lb></lb>bram flectens æqualis erit ſummæ ambarum <lb></lb>potentiarum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000533">TErtio loco in eadem rota, ſeù libra AB termi<lb></lb>nus A deorsùm trahatur à <expan abbr="põdere">pondere</expan> D, ſed eius <lb></lb>oppoſitus terminus B ſursùm trahatur à vi aſcenden<lb></lb>te F, quæ minor ſit vi ponderis D, dico, quòd libra <lb></lb>non quieſcet, ſed reuoluetur eius terminus A <expan abbr="deſcẽ-">deſcen-</expan><pb pagenum="108" xlink:href="010/01/116.jpg"></pb><arrow.to.target n="marg129"></arrow.to.target><lb></lb>dendo versùs I, eleuabiturque terminus oppoſitus <lb></lb>B versùs H, & conatus, ſeù vis, quo libra reuoluitur <lb></lb>æqualis erit non differentiæ, & exceſſui ponderis D <lb></lb>ſupra vim F, ſed æquabitur aggregato ambarum vir<lb></lb><figure id="id.010.01.116.1.jpg" xlink:href="010/01/116/1.jpg"></figure><lb></lb>tutum D, & F. </s> <s id="s.000534">Applicetur termi<lb></lb>no B pondus E æquale vi ſursùm <lb></lb>impellenti F, pariterque ibidem <lb></lb><expan abbr="ſuſpẽdatur">ſuſpendatur</expan> aliud <expan abbr="põdus">pondus</expan> G æqua<lb></lb>le oppoſito ponderi D, manife<lb></lb>ſtum eſt (amotis, vel coercitis vi<lb></lb>ribus F, & E) quòd <expan abbr="põdera">pondera</expan> æqua<lb></lb>lia D, & G pendentia à terminis <lb></lb>radiorum æqualium eiuſdem li<lb></lb>bræ efficient æquilibrium, & ideò <lb></lb><arrow.to.target n="marg130"></arrow.to.target><lb></lb>libra quieſcet. </s> <s id="s.000535">Præterea quia pondus E æquatur vi <lb></lb>contrariæ ſursùm trahenti F, & ambæ applicantur <lb></lb>eidem termino B libræ AB (ab æqualibus ponderi<lb></lb><arrow.to.target n="marg131"></arrow.to.target><lb></lb>bus D, & G æquilibratæ) igitur duo pondera ſimùl <lb></lb>ſumpta G, & E libram impellunt contrario niſu, ſci<lb></lb>licet à B verſus I, & præcisè adæquant conatum pon<lb></lb>deris D, & vim trahentem F, quæ ambo deprimere <lb></lb>poſſunt terminum libræ A versùs I ſubleuando ter<lb></lb>minum B versùs H. </s> <s id="s.000536">Ergo duæ vires D, & F ſimùl <expan abbr="sũp-tæ">sump<lb></lb>tæ</expan> (amotis ponderibus G, & E) determinant vim, <lb></lb>ſeù conatum, quo libra reuolui debet ab A, versùs I. </s> </p> <p type="margin"> <s id="s.000537"><margin.target id="marg129"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000538"><margin.target id="marg130"></margin.target>Pr. 47.</s> </p> <p type="margin"> <s id="s.000539"><margin.target id="marg131"></margin.target>Pr. 46.</s> </p> <p type="main"> <s id="s.000540">Et hìc animaduertendum eſt, quòd duæ vires D, <lb></lb>& F, quæ reuerà contrariæ ſunt inter ſe (<expan abbr="cũ">cum</expan> illa deor<lb></lb>sùm comprimat, hæc verò ſursùm trahat) non ſibi <lb></lb>mutuò opponuntur, nec vna earum alteriùs motum̨ <pb pagenum="109" xlink:href="010/01/117.jpg"></pb><arrow.to.target n="marg132"></arrow.to.target><lb></lb>impedit, ſed vna promouet, adiuuat, & auget cona<lb></lb>tum, vim, & impetum alterius; & hoc accidit <expan abbr="quianõ">quia non</expan> <lb></lb>applicantur ambæ eidem termino A libræ, ſed ter<lb></lb>minis oppoſitis A, & B, qui iuxtà libræ, & rotæ pro<lb></lb>prietatem, & naturam debent moueri motibus con<lb></lb><arrow.to.target n="marg133"></arrow.to.target><lb></lb>trarijs, ſcilicèt A per arcum AI, & B per arcum BH. <lb></lb>igitur impulſus ponderis D deorsùm, & tractio facta <lb></lb>àvi F ſursùm conueniunt, & ſe mutuò adiuuant, & <lb></lb>augent, vt ab vtriſque reuolutio libræ efficiatur, quæ <lb></lb>ad eaſdem partes impellitur ab eiſdem viribus con<lb></lb>trarijs. </s> <s id="s.000541">ceſſet igitur admiratio quare duæ vires con<lb></lb>trariæ in libra ſe mutuò non <expan abbr="deſtruãt">deſtruant</expan>, ſed potiùs mu<lb></lb>tuo ſe adiuuent, ita vt ex vtriſque reſultet vna vis <expan abbr="cõ-poſita">con<lb></lb>poſita</expan>, à qua libra reuoluitur. </s> </p> <p type="margin"> <s id="s.000542"><margin.target id="marg132"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000543"><margin.target id="marg133"></margin.target>Prop. 45.</s> </p> <p type="main"> <s id="s.000544"><emph type="center"></emph>PROP. L.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000545"><emph type="center"></emph><emph type="italics"></emph>Si oppoſitos libræ terminos quatuor potentiæ trahant, duæ <lb></lb>ſursùm, & duæ deorsùm, conatus ſeù vis libram fle<lb></lb>ctens menſuratur à ſumma differentiæ aſcen<lb></lb>dentium, cum differentia deſcendentium <lb></lb>potentiarum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000546">SI tandem eadem libra à quatuor viribus impel<lb></lb>latur trahaturque, quarum duæ D, & G graues <lb></lb>ſint deorsùmque tendant, duæ verò M, & F ſursùm̨ <lb></lb>eoſdem terminos libræ trahant, ſitque energia virtu<lb></lb>tis M maior quàm F, pondus verò D minus ſit quàm <pb pagenum="110" xlink:href="010/01/118.jpg"></pb><arrow.to.target n="marg134"></arrow.to.target><lb></lb>G, <expan abbr="tũc">tunc</expan> manifeſtum eſt, terminum <lb></lb><figure id="id.010.01.118.1.jpg" xlink:href="010/01/118/1.jpg"></figure><lb></lb>A eleuari ſursùm versùs Hab ex<lb></lb>ceſſu quo vis M ſuperat faculta<lb></lb>tem motiuam F, & è contrà op<lb></lb>poſitus libræ terminus B depri<lb></lb><arrow.to.target n="marg135"></arrow.to.target><lb></lb>metur deorsùm versùs I ab ex<lb></lb>ceſſu quo pondus G ſuperat vim <lb></lb>grauitatis D; & quia prædicti <lb></lb>duo impulſus differentiales con<lb></lb>trarij ſunt, vnus quidèm ſursùm̨, <lb></lb>alter verò deorsùm, <expan abbr="applicãturque">applicanturque</expan> terminis oppoſi<lb></lb>tis eiuſdem libræ; igitur ſe mutuo adiuuant promo<lb></lb>uenturque, & proindè conatus, vis, atque impetus, <lb></lb>quo vniuerſa libra reuoluitur, æqualis erit aggrega<lb></lb>to prædictarum differentiarum. </s> </p> <p type="margin"> <s id="s.000547"><margin.target id="marg134"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000548"><margin.target id="marg135"></margin.target>Prop. 49.</s> </p> <p type="main"> <s id="s.000549"><emph type="center"></emph>PROP. LI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000550"><emph type="center"></emph><emph type="italics"></emph>Vis motiua, qua ſolidum grauius ſpecie, quàm fluidum, de<lb></lb>ſcendit, æqualis est differentiæ ponderis ſolidi ſupra <lb></lb>pondus fluidi ei æqualis mole.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.118.2.jpg" xlink:href="010/01/118/2.jpg"></figure> <p type="main"> <s id="s.000551">HIs declaratis intelligatur <lb></lb>vas RGS aqua plenum, in <lb></lb><expan abbr="eoq;">eoque</expan> immergatur corpus aliquod <lb></lb>graue durum, ac conſiſtens DE, <lb></lb>quod grauius ſit aqua collaterali <lb></lb>F patet ex dictis prop. 9. & ex <lb></lb>Archimede, duo pondera DE, & F collocari in libra <lb></lb>quadam imaginaria, & perpetua AB in qua exceſſus <pb pagenum="111" xlink:href="010/01/119.jpg"></pb><arrow.to.target n="marg136"></arrow.to.target><lb></lb>ponderis ſolidi DE ſupra grauitatem aquæ F quæ ſit <lb></lb>æqualis mole ipſi DE, ſemper idem eſt in quacumque <lb></lb>aquæ profunditate ſolidum collocetur, ſitque pon<lb></lb>dus E exceſſus quo pondus DE ſuperat grauitatem̨ <lb></lb>aquæ F, igitur conatus, vis, & impetus, quo ſolidum <lb></lb>DE deſcendit infra <expan abbr="aquã">aquam</expan> menſuratur à vi <expan abbr="põderis">ponderis</expan> E. </s> </p> <p type="margin"> <s id="s.000552"><margin.target id="marg136"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000553"><emph type="center"></emph>PROP. LII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000554"><emph type="center"></emph><emph type="italics"></emph>Vis motiua qua ſolidum leuius ſpecie, quàm fluidum aſcen<lb></lb>dit æqualis est exceſſui leuitatis ſolidi ſupra leuita<lb></lb>tem fluidi ei æqualis mole.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000555">E Contrà, ſi ſupponamus, quod lignum DE pari<lb></lb>terque aqua F careant grauitate, ſed <expan abbr="tãtummo-dò">tantummo<lb></lb>dò</expan> à vi leuitatis informentur, & ambo impulſum, & <lb></lb>impetum faciant ſursùm conenturque aſcendere, <expan abbr="nõ">non</expan> <lb></lb>ſecùs oſtendetur, quòd in libra, ſeù rota perpetua <lb></lb>ligni DE maior leuitas præualebit ſuperabitque mi<lb></lb>norem leuitatem fluidi collateralis F, proindeque <lb></lb>libra inflectetur ab A versùs R aſcendendo tanta vi, <lb></lb>quanta eſt differentia, ſeù exceſſus E, quo leuitas li<lb></lb>gni ſuperat aquæ leuitatem. </s> </p> <p type="main"> <s id="s.000556"><emph type="center"></emph>PROP. LIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000557"><emph type="center"></emph><emph type="italics"></emph>Vis motiua qua leue corpus in fluido graui aſcendit æqualis <lb></lb>eſſe debet ſummæ lenitatis ſolidi, & grauitatis <lb></lb>fluidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000558">SI verò variata hypoteſi ponamus <expan abbr="lĩgnum">lignum</expan> F leue, <lb></lb>& ſursùm ab intrinſeco principio impelli, & mo-<pb pagenum="112" xlink:href="010/01/120.jpg"></pb><arrow.to.target n="marg137"></arrow.to.target><lb></lb>ueri, at fluidum collaterale D, quòd ſit hydrargyrum <lb></lb>ſupponatur deorsùm tantummodò vim exercere, vt <lb></lb>exigit maxima eius grauitas, nec prorsùs ſursùm im<lb></lb><figure id="id.010.01.120.1.jpg" xlink:href="010/01/120/1.jpg"></figure><lb></lb>pellere, tunc quoque libra, ſeù <lb></lb>rota perpetua efformabitur iņ <lb></lb>qua ſemper terminus B trahetur <lb></lb>ſursùm à poſitiua leuitate ipſius <lb></lb>ligni F aſcendetque versùs R, <lb></lb>terminus verò oppoſitus depri<lb></lb>metur ab A versùs H vt naturą <lb></lb>grauitatis exigit, & quia hi duo motus, & conatus in <lb></lb>oppoſitis terminis libræ <expan abbr="cõtrarij">contrarij</expan> ſunt, ergò viciſſim <lb></lb>ſe non deſtruunt, nec contrariantur, ſed ſe mutuò fa<lb></lb>uent, & adiuuant. </s> <s id="s.000559">igitur conatus, & impetus quo re<lb></lb>uoluitur iam dicta libra, ſcilicèt quo lignum F aſcen<lb></lb>dit à fundo mercurij æqualis erit non differentiæ, ſed <lb></lb>aggregato ex vi leuitatis F, & ex facultate ponderis <lb></lb>mercurij D. </s> </p> <p type="margin"> <s id="s.000560"><margin.target id="marg137"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000561"><emph type="center"></emph>PROP. LIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000562"><emph type="center"></emph><emph type="italics"></emph>Si verò tam ſolidum, quàm fluidum exerceant leuitatem, <lb></lb>atque grauitatem, vis motiua, qua vnum eorum ele<lb></lb>uatur æqualis eſt aggregato ex differentia leui<lb></lb>tatum vnà cum differentia grauitatum <lb></lb>earum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000563">TAndèm ſi ſupponamus, quod lignum vim faciat <lb></lb>ſursùm vt leue, & etiam eodem tempore gra<lb></lb>uitatem eius natiuam exerceat, pariterque aqua D <pb pagenum="113" xlink:href="010/01/121.jpg"></pb><arrow.to.target n="marg138"></arrow.to.target><lb></lb>in vaſe nedùm deorsùm comprimat, vt grauis, ſed <lb></lb>etiam non omninò priuetur gradu aliquo leuitatis, <lb></lb>tunc ſimilitèr libra perpetua imaginaria efformabi<lb></lb>tur in qua terminus I deorsùm impellitur ab exceſſu <lb></lb>quo grauitas aquæ D ſuperat <lb></lb><figure id="id.010.01.121.1.jpg" xlink:href="010/01/121/1.jpg"></figure><lb></lb><expan abbr="grauitatẽ">grauitatem</expan> ligni F, & è <expan abbr="cõtràter-minus">contràter<lb></lb>minus</expan> B <expan abbr="ſursũ">ſursum</expan> eleuabitur ab ex<lb></lb>ceſſu quo leuitas ligni ſuperat <lb></lb>leuitatem ipſius aquæ. </s> <s id="s.000564">Et quia <lb></lb>prædicti impulſus ſunt contra<lb></lb>rij, applicanturque eidem li<lb></lb>bræ imaginariæ, igitur vnus impulſus alteri non op<lb></lb><arrow.to.target n="marg139"></arrow.to.target><lb></lb>ponitur, & proindè vniuerſalis conatus, & impetus <lb></lb>prædictæ libræ, ſcilicèt vis, & impetus, quo lignum <lb></lb>F aſcendit in aqua menſuratur ab vtroque exceſſu, <lb></lb>ſcilicèt ab aggregato differentiæ ponderum aquæ, <lb></lb>& ligni, vnà cum exceſſu leuitatis ligni ſupra aqueam <lb></lb>leuitatem. </s> </p> <p type="margin"> <s id="s.000565"><margin.target id="marg138"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000566"><margin.target id="marg139"></margin.target>Prop. 50.</s> </p> <p type="main"> <s id="s.000567"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000568">HIs præmiſſis ſupponamus cum aduerſarijs pri<lb></lb><arrow.to.target n="marg140"></arrow.to.target><lb></lb>mo loco, quòd reuerà præter corpora grauią <lb></lb>etiam leuia in natura exiſtant, quorum aliqua, vt ait <lb></lb>Ariſtoteles, ſint ſimplicitèr talia, alia verò reſpectiuè, <lb></lb>veluti ignis dicitur abſolutè leuis, & terra, ſeù hy<lb></lb>drargyrum, vel aliud fluidum æquè graue, ac ipſą <lb></lb>terra eſt appellabitur abſolutè graue <expan abbr="reperiũtur">reperiuntur</expan> po<lb></lb>ſtea alia corpora intermedia ſimplicia, vel mixtą, <lb></lb>quæ vocantur grauia ſimùl, & leuia reſpectiuè, ſcili-<pb pagenum="114" xlink:href="010/01/122.jpg"></pb><arrow.to.target n="marg141"></arrow.to.target><lb></lb>cèt aqua demerſa intra mercurium dicitur leuis, & <lb></lb>moueri ſursùm à principio intrinſeco, at ſi eadem̨ <lb></lb>aqua intra oleum mergatur, dicetur iam grauis, noņ <lb></lb>leuis, & moueri deorsùm à principio interno. </s> <s id="s.000569">Hoc <lb></lb>verò duplicem ſenſum habere poteſt, aut dictæ duæ <lb></lb>contrariæ qualitates ſemper in eodem corpore aquæ <lb></lb>exiſtunt, & vigent, aut ſucceſſiuè modò vna, modò <lb></lb>altera in ea reperitur, ita vt aqua in fundo hydrar<lb></lb>gyri poſita ſit reuera leuis, & nullo pacto grauis, & <lb></lb>è contià, quando eadem aqua in oleo demergitur, <lb></lb>hìc grauitatem habeat, & nullam prorsùs <expan abbr="leuitatẽ">leuitatem</expan>, <lb></lb>itaut remaneat ſopita, & extincta leuitas illa, quæ <lb></lb>tanta efficacia <expan abbr="aquã">aquam</expan> ſursùm impellebat à fundo mer<lb></lb>curij, igitur in primo ſenſu retinere aqua deberet <lb></lb>perpetuò duas contrarias qualitates, ſcilicèt leuita<lb></lb>tem, & grauitatem eodem modo, ac dicuntur mixta <lb></lb>participare ex qualitatibus extremis, calido nempè, <lb></lb>& frigido, & veluti colores medij nigre dinem, at<lb></lb>que albedinem participare <expan abbr="censẽtur">censentur</expan>, igitur dici de<lb></lb>beret, quod in igne prorsùs, & abſolutè leui qua<lb></lb>tuor integri gradus leuitatis reperiuntur, & ſimili<lb></lb>tèr in ipſa terra exiſtunt quatuor gradus grauitatis, <lb></lb>at aer habebit tres gradus leuitatis, & vnicum gra<lb></lb>dum ponderoſitatis, ſic aqua vnicum gradum lèui<lb></lb>tatis, & tres grauitatis haberet, & <expan abbr="tãdèm">tandèm</expan> aliud cor<lb></lb>pus medium inter aerem, & aquam, veluti forſan <lb></lb>eſt ſpiritus vini, habere poſſet duos gradus leuitatis, <lb></lb>& duos alios gradus grauitatis.</s> </p> <pb xlink:href="010/01/123.jpg"></pb> <p type="main"> <s id="s.000570"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000571">SVpponit præterea Aristoteles, quòd velocitas, <lb></lb>qua idem corpus aſcendit, vel deſcendit in di<lb></lb>uerſis medijs fluidis eamdem proportionem habet, <lb></lb>quam raritates, vel conſiſtentiæ eorumdem fluido<lb></lb>rum, ver. gr. ſi aer eſſet decies rarior, ac diſtrahibi<lb></lb>lior, & faciliùs penetrabilis, quam ſit aquæ, eadem <lb></lb>pila marmorea deſcendet cubitalem altitudinem ae<lb></lb>ris decies velociùs, quàm profunditatem aquę pa<lb></lb>riter cubitalem, ſcilicèt ſi prædictum aereum <expan abbr="ſatiũ">ſpatium</expan> <lb></lb>pertranſeat in vnica arteriæ pulſatione, aquæ altitu<lb></lb>dinem percurret in decem eiuſdem arteriæ pulſ<lb></lb>ationibus.</s> <s id="s.000572">Idemque in aſcenſu corporum leuium iuxtà <lb></lb>Ariſtotelis ſententiam dici debet.</s> <s id="s.000573">His præmiſſis.<lb></lb></s> </p> <p type="main"> <s id="s.000574"><emph type="center"></emph>PROP. LV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000575"><emph type="italics"></emph>Oſtendendum eſt Ignem non eſſe leuem, nec aſcendere vi <lb></lb> leuitatis eius poſitiuæ.<emph.end type="italics"></emph.end></s> <s id="s.000576">ET primò extrema corpora ſimplicia, ſcilicèt i<lb></lb>gnis & terra, vel <expan abbr="hydrargyrũ"> hydrargyrum</expan>, aut aurum fuſum, vel quodlibet aliud grauiſſimum corpus, iuxtà Ari<lb></lb>ſtotelis effatum ſi fieri poteſt, ſint abſolutè grauia, & <lb></lb>leuia itaut ignis habeat quatuor gradus leuitatis, & <lb></lb>nullam prorsùs grauitatem, è contrà terra, vel hy<lb></lb>drargyrum quatuor gradus grauitatis habeat, nullam <lb></lb> verò leuitatem, ſic enim terra erit abſolutè, & om<lb></lb>ninò grauis, ignis verò abſolutè leuis, ergò (ex prop.<pb pagenum="116" xlink:href="010/01/124.jpg"></pb> <arrow.to.target n="marg142"></arrow.to.target><lb></lb> 53.) conatus, & impetus totalis, quo ignis per mer<lb></lb>curium aſcendit, vel terra per ignem deſcendit, men<lb></lb>ſurari debet ab aggregato virium extremarum, ſci<lb></lb>licet à tota vi leuitatis cum tota vi grauitatis, quarę <lb></lb>totalis impetus erit octo graduum. </s> <s id="s.000577">Sed hoc eſt fal<lb></lb>ſum, contra aduerſarij aſſertionem, & contra Archi<lb></lb>medem, ea enim, quæ in fluido eleuantur, tanta vi <lb></lb>aſcendunt, quanta eſt grauitas qua moles fluidi mer<lb></lb>curialis æqualis corpori igneo intra ipſum demerſo <lb></lb>ſuperat huius grauitatem, quæ nulla eſt, & proindè <lb></lb>ignis impetu quatuor graduum per mercurium <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan>, quaproptèr non fertur ignis ſursùm à vi eius le<lb></lb>uitatis, & ideò leuis non erit, quod erat &c. <lb></lb><arrow.to.target n="marg143"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000578"><margin.target id="marg140"></margin.target>Suppoſitio<lb></lb>nes aliquæ <lb></lb>peripatetice <lb></lb>recenſentur.</s> </p> <p type="margin"> <s id="s.000579"><margin.target id="marg141"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000580"><margin.target id="marg142"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000581"><margin.target id="marg143"></margin.target>Dubitatur <lb></lb>de menſura <lb></lb>gradus præ<lb></lb>dicti impe<lb></lb>tus.</s> </p> <p type="main"> <s id="s.000582">Sed inſtabit denuò peripateticus, dicetque, quòd <lb></lb>ea velocitas, quæ exercetur ab igne aſcendente per <lb></lb>mercurium, aut à terra deſcendente per ignem po<lb></lb>terit cenſeri octo graduum, vel quatuor ad libitum, <lb></lb>quia non habemus certam menſuram vnius gradus <lb></lb>impetus, & ſic mediante ſenſu, & experientia non <lb></lb>poteſt eius ſententia redargui. </s> </p> <p type="main"> <s id="s.000583"><emph type="center"></emph>PROP. LVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000584"><emph type="center"></emph><emph type="italics"></emph>Reperire menſuram certi gradus impetus reſpectu cuius di<lb></lb>ſcerni valeat an impetus deſcenſus terræ per ignem, <lb></lb>vel aſcenſus ignis per mercurium ſit octo, vel <lb></lb>quatuor graduum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000585">SEd prædictùm effugium ſic refellemus: Fiat ex<lb></lb>perimentum non in mercurio ſimplicitèr graui, </s> </p> <pb pagenum="117" xlink:href="010/01/125.jpg"></pb> <p type="main"> <s id="s.000586"><arrow.to.target n="marg144"></arrow.to.target><lb></lb>ſed in aqua, vel in aere, illa enim habebit tres gradus <lb></lb>grauitatis, & vnicum leuitatis, ergo ignis per <expan abbr="aquã">aquam</expan> <lb></lb>aſcendet velocitate trium graduum; in mercurio ve<lb></lb>rò impetu octo graduum, & terra per ignem octies <lb></lb>velociùs deſcendet, quàm per aquam. </s> <s id="s.000587">Præterea aer <lb></lb>habet vnicum gradum grauitatis, & tres gradus le<lb></lb>uitatis, igitur ignis octies velociùs per mercurium <lb></lb>aſcendet, quàm per aerem, vnde hac ratione habe<lb></lb>bimus menſuram vnius gradus impetus tàm in <expan abbr="aſcẽ-ſu">aſcen<lb></lb>ſu</expan>, quàm in deſcenſu, qui comparari poteſt cum im<lb></lb>petu ignis per mercurium aſcendentis, & terræ per <lb></lb>ignem deſcendentis; & proindè facilè conijci po<lb></lb>terit, an prædictæ velocitates extremorum elemen<lb></lb>torum reuerà ſint octuplæ, vel non, comparatæ ad <lb></lb>velocitates quas exercent in intermedijs elementis.<lb></lb>& licèt experimentum non det exactam <expan abbr="præcifionẽ">præciſionem</expan>, <lb></lb>nihilominùs ſufficientiſſimè euincit falſitatem peri<lb></lb>pateticæ hypotheſis, ſed licèt reuerà vis, & energia, <lb></lb>qua corpora aſcendunt, vel deſcendunt, minimè de<lb></lb>duci poſſit ex velocitate tranſitus ſursùm, vel deor<lb></lb>sùm, vt ſuo loco apertè oſtendemus, tamen aſſumi <lb></lb>poteſt cum aduerſario ad eum redarguendum. </s> </p> <p type="margin"> <s id="s.000588"><margin.target id="marg144"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000589">Conſiderentur deindè elementa intermedia, vt <lb></lb>ſunt aer, & aqua, ſeù alia corpora mixta, quæ <expan abbr="eiſdẽ">eiſdem</expan> <lb></lb>gradibus leuitatis, & grauitatis afficiantur. </s> <s id="s.000590">Demon<lb></lb>ſtrandum eſt, nullum eorum corporum, quæ <expan abbr="aſcendũt">aſcendunt</expan> <lb></lb>ſursùm poſitiuam leuitatem habere. <pb pagenum="118" xlink:href="010/01/126.jpg"></pb><arrow.to.target n="marg145"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000591"><margin.target id="marg145"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000592"><emph type="center"></emph>PROP. LVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000593"><emph type="center"></emph><emph type="italics"></emph>Si Aer in aqua ſolummodò leuitatem exerceret, in ea non <lb></lb>aſcenderet à leuitate eius poſitiua impulſus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000594">ET primò ſupponamus prædicta elementa noņ <lb></lb>retinere ſimùl eodemque tempore duas oppo<lb></lb>ſitas facultates grauitatis, & leuitatis, ſed ſucceſſi<lb></lb>uè modò vnam, modò alteram poſſideant, prout in <lb></lb>diuerſis medijs fluidis collocantur, ſcilicèt aqua iņ <lb></lb>aere pendula ſolummodò grauis cenſeri debeat, non <lb></lb>autem leuis, ſi poſtmodum aqua infrà hydrargyrum <lb></lb>mergatur, tunc aqua leuis ſit, non autem grauis, po<lb></lb><figure id="id.010.01.126.1.jpg" xlink:href="010/01/126/1.jpg"></figure><lb></lb>natur etiam, quod aer, ſeù <expan abbr="lignũ">lignum</expan> <lb></lb>ſub aqua demerſum leue ſit, nec <lb></lb>grauitatem vllam habeat. </s> <s id="s.000595">Con<lb></lb>cipiatur poſtea vas RGHS a<lb></lb>qua D plenum, & in eo merga<lb></lb>tur maſſa aeris, vel ligni F, pa<lb></lb>tet ergò ex ſupradicta hypo<lb></lb>theſi, quod aqua D <expan abbr="nullã">nullam</expan> leuitatem, ſed tantummo<lb></lb>dò grauitatem habebit, eò quòd prædicta aqua non <lb></lb>ſupponitur demerſa intra aliud corpus fluidum den<lb></lb>ſius, & ponderoſius ipſa, ſed contigua eſt aeri. </s> <s id="s.000596">Mo<lb></lb>dò quia aer, vel lignum F ſupponitur ab aduerſarijs <lb></lb>ſursùm aſcendere à G, versùs R impulſa à poſitiua <lb></lb>leuitate eius naturali, aqua verò circumfuſa D cona<lb></lb>tum, atque impetum exercet deorsùm ab A versùs <lb></lb>H veluti natura eius grauitatis exigit, habebimus <pb pagenum="119" xlink:href="010/01/127.jpg"></pb>ergò duos impetus ad inuicem contrarios, nempè <lb></lb><arrow.to.target n="marg146"></arrow.to.target><lb></lb>leuitatis aeris F grad. 3. & grauitatis gra. </s> <s id="s.000597">3. aquæ <lb></lb>circumfuſæ D, & hæ duæ virtutes motiuæ ſimùl ſum<lb></lb>ptæ gr.6. component menſuram conatus, & impetus, <lb></lb>quo lignum F per aquam aſcendit, hoc tamen eſt fal<lb></lb><arrow.to.target n="marg147"></arrow.to.target><lb></lb>ſum, & contra conceſſionem eiuſdem aduerſarij, & <lb></lb>contra demonſtrationem Archimedis, & tandem̨ <lb></lb>contra experientiam, quia ea, quæ feruntur ſursùm <lb></lb>in aqua, tanta vi aſcendunt, quanta eſt grauitas, <lb></lb>qua moles aquæ æqualis corpori demerſo ſuperat <lb></lb>huiusmet grauitatem, quod perindè eſt, ac ſi dica<lb></lb>tur impetum ſursùm menſurari à differentia grauita<lb></lb>tum aeris, & aquæ gr. 2. non autem ab aggregato <lb></lb>gr. 6. leuitatis illius, & grauitatis huius. </s> <s id="s.000598">Quaprop<lb></lb>ter non poterit aer, vel <expan abbr="lignũ">lignum</expan> ſursùm impelli ab eius <lb></lb>leuitate poſitiua. </s> </p> <p type="margin"> <s id="s.000599"><margin.target id="marg146"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000600"><margin.target id="marg147"></margin.target>Prop. 53.</s> </p> <p type="main"> <s id="s.000601"><emph type="center"></emph>PROP. LVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000602"><emph type="center"></emph><emph type="italics"></emph>Idipſum ostendere poſito quòd aer, & aqua vtramque vim <lb></lb>leuitatis, & grauitatis exerceat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000603">SVpponamus ſecundo loco tam <expan abbr="aerẽ">aerem</expan>, quàm <expan abbr="aquã">aquam</expan> <lb></lb>ſemper retinere ambas oppoſitas qualitates, <lb></lb>ſcilicèt perpetuò afficiantur ijſdem gradibus graui<lb></lb>tatis, atque leuitatis ſitque leuitas aeris F trium gra<lb></lb>duum, & maior leuitate ipſius aquæ D vnius gradus; <lb></lb>at è contrà gradus grauitatis eiuſdem aeris F gra<lb></lb>dus vnius minor ſit pondere graduum 3. molis aquæ <lb></lb>D, quæ æqualis ſit ipſi F, habebimus profectò qua-<pb pagenum="120" xlink:href="010/01/128.jpg"></pb><arrow.to.target n="marg148"></arrow.to.target><lb></lb>tuor vires motiuas, quæ ſibi mutuò aduerſantur, & <lb></lb>in libra imaginaria BI operantur, vt nimirùm nulla <lb></lb>earum otiari queat, ſed omnes ſimùl agant, & im<lb></lb>pellant, igitur ex propoſitionibus 50. & 54. conatus, <lb></lb>ſeù impetus quo aer F impellitur ſursùm in aqua à G <lb></lb>versùs R ratione leuitatis menſurari debet ab ex<lb></lb>ceſſu 2. graduum quo leuitas eiuſdem aeris ſuperat <lb></lb>leuitatem aquæ circumfuſæ, & è <expan abbr="cõtra">contra</expan> conatus aquæ <lb></lb>contra aerem efficitur ab exceſſu grauitatis aquæ D, <lb></lb>ſupra grauitatem aeris F paritèr gr. 2. & proindè <expan abbr="dũ">dum</expan> <lb></lb>aqua deorsùm deſcendere conatur neceſſariò aerem <lb></lb>F exprimit, ac <expan abbr="ſursũm">ſursum</expan> impellit; ſuntque hæ duæ dif<lb></lb>ferentiæ, ſeù exceſſus virium contrariæ inter ſe, ſci<lb></lb>licèt vna in libra imaginaria ſursùm impellit, altera <lb></lb>verò deorsùm igitur vniuerſalis conatus, & impetus <lb></lb>totalis quo aer F aſcendit in aqua, menſurari debet <lb></lb>ab aggregato eorumdem duorum exceſſuum, quod <lb></lb><arrow.to.target n="marg149"></arrow.to.target><lb></lb>eſt gr. 4. non verò à differentia leuitatum, ſolummo<lb></lb>dò gr. 2. Sed hoc eſt falſum contra experientiam, <expan abbr="cõ-tra">con<lb></lb>tra</expan> aduerſarij aſſertum, & contra ea, quæ ab Archi<lb></lb>mede demonſtrata ſunt, quia nimirùm conatus, & <lb></lb>impetus quo fertur aerea pila ſursùm in aqua æqua<lb></lb>lis eſt differentiæ ponderum aeris, & aquę, igitur <lb></lb>verum <expan abbr="nõ">non</expan> eſt leuitatem poſitiuam in hac operati<lb></lb>one concurrere. </s> </p> <p type="margin"> <s id="s.000604"><margin.target id="marg148"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000605"><margin.target id="marg149"></margin.target>Prop. 54.</s> </p> <p type="main"> <s id="s.000606">Vſque adhùc non conſiderauimus difficultatem, <lb></lb>aut impedimentum, quod affert medium fluidum̨ <lb></lb>motui aſcenſus, vel deſcenſus corporum, quæ in ip<lb></lb>ſo feruntur, erit igitur operæpretium perpenderę <pb pagenum="121" xlink:href="010/01/129.jpg"></pb>quidnam admiſſo, vel negato prædicto peripatetico <lb></lb><arrow.to.target n="marg150"></arrow.to.target><lb></lb>aſmpto ſubſequatur. </s> </p> <p type="margin"> <s id="s.000607"><margin.target id="marg150"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000608"><emph type="center"></emph>PROP. LIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000609"><emph type="center"></emph><emph type="italics"></emph>Aliter id ipſum ostendere, poſito, quòd aer vi leuitatis per <lb></lb>diuerſa media fluida aſcendat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000610">SIt igitur idem mobile B, quod ſit lignum leuiſſi<lb></lb>mum, vel veſica aere plena, impellaturque vſque <lb></lb>ad fundum vaſis DCFE cuius medietas infima reple<lb></lb>atur aqua A, reliqua medietas ſuprema O repleatur <lb></lb>oleo, vel ſpiritu vini, & ponamus leuitatem aereæ <lb></lb>veſicæ B eſſe trium graduum, & leuitatem ſpiritus <lb></lb>vini duorum graduum, at leuitatem aquæ magis <expan abbr="dẽ-ſæ">den<lb></lb>ſæ</expan> eſſe vnius gradus. </s> <s id="s.000611">Manifeſtum eſt, quòd reſiſten<lb></lb>tia aquæ A, & partium tenacitas, quæ penetrari de<lb></lb>bet à ligno, vel veſica B dùm ſursùm aſcendit, erit <expan abbr="tã-tò">tan<lb></lb>tò</expan> maior reſiſtentia ſpiritus vi<lb></lb><figure id="id.010.01.129.1.jpg" xlink:href="010/01/129/1.jpg"></figure><lb></lb>ni O quantùm illa eſt magis <expan abbr="dẽ-ſa">den<lb></lb>ſa</expan>, & conſtipata quàm iſte, ſci<lb></lb>licèt ſi <expan abbr="ſumãtur">ſumantur</expan> moles æquales <lb></lb>eorumdem fluidorum, quantò <lb></lb>maior eſt corpulentia, & mate<lb></lb>ria, quæ prędictum aqueum ſpa<lb></lb>tium replet ea materia quæ molem ſpiritus vini oc<lb></lb>cupat, & quia <expan abbr="leuitatẽ">leuitatem</expan> ſpiritus vini ad <expan abbr="leuitatẽ">leuitatem</expan> aquæ <lb></lb>eamdem proportionem habere aiunt, quam illius <lb></lb>raritas ad huius raritatem, igitur tantò magis diſtra<lb></lb>hibilis, & minùs reſiſtens erit ſpiritus vini, quàm̨ <pb pagenum="122" xlink:href="010/01/130.jpg"></pb><arrow.to.target n="marg151"></arrow.to.target><lb></lb>aqua communis; quantò ille leuior eſt aqua commu<lb></lb>ni, ergò reſiſtentia quam aqua in fert veſicæ <expan abbr="aſcendẽ-ti">aſcenden<lb></lb>ti</expan> ad reſiſtentiam ſpiritus vini eamdem <expan abbr="proportionẽ">proportionem</expan> <lb></lb>reciprocè habet, quam ſpiritus vini leuitas ad aquæ <lb></lb>communis leuitatem. </s> <s id="s.000612">Quapropter aqua communis <lb></lb>duplò reſiſtentior erit quàm ſpiritus vini, veluti iſte <lb></lb>ſupponitur duplò leuior illo. </s> <s id="s.000613">Modò, quia aduerſarius <lb></lb>ſupponit, quòd conatus, & impetus quo aſcendit <lb></lb>aerea veſica per prædicta duo fluida menſurari de<lb></lb>beat ab exceſſu, ſeu differentia leuitatum <expan abbr="eorumdẽ">eorumdem</expan> <lb></lb>corporum, igitur aerea veſica B, quæ tres gradùs le<lb></lb>uitatis habebat, aſcendet per <expan abbr="aquã">aquam</expan> A vnum gradum <lb></lb>leuitatis habentem conatu, ſeu impetu menſurato à <lb></lb>differentia prædictarum leuitatum, quæ erit <expan abbr="duorũ">duorum</expan> <lb></lb>graduum, ſed in ſpiritu vini O qui duos gradus leui<lb></lb>tatis habebat, aſcendet, eadem pila B impetu æquali <lb></lb>differentiæ leuitatum <expan abbr="eorũdem">eorundem</expan> corporum, quæ erit <lb></lb>vnius ſolummodò gradus, & hæc quidem <expan abbr="conſequũ-tur">conſequun<lb></lb>tur</expan> ex demonſtratis in pr. 48. & 52. qua proptèr ra<lb></lb>tione differentiarum inter leuitatem corporis B, & <lb></lb>leuitates prædictorum fluidorum veſica B per aquam <lb></lb>aſcendet conatu, & impetu duplo eius, quo per ſpi<lb></lb>ritum vini eleuatur; nihilominùs velocitas qua præ<lb></lb>dicta veſica B aſcendit in aqua, non poterit eſſe du<lb></lb>pla eius, qua ſublimatur in ſpiritu vini, licèt virtus, & <lb></lb>energia, qua impellitur per aquam dupla ſit eius, <lb></lb>quæ in ſpiritu vini exercetur, proptereà quod ſuper<lb></lb>uenit noua cauſa, à qua prædicti impetus <expan abbr="retardãtur">retardantur</expan>, <lb></lb>& valdè alterantur, hæc verò eſt maior <expan abbr="dẽſitas">denſitas</expan> aquæ <pb pagenum="123" xlink:href="010/01/131.jpg"></pb>communis ſupra tenacitatem, & <expan abbr="cõſtipationem">conſtipationem</expan> ſpi<lb></lb><arrow.to.target n="marg152"></arrow.to.target><lb></lb>ritus vini; quæ, iuxtà Ariſtotelis aſſumptum, <expan abbr="maiorẽ">maiorem</expan> <lb></lb>tarditatem aſcendenti corpori affert denſitas aquæ, <lb></lb>ſcilicèt duplò maior, quàm ſit ea difficultas, qua à <lb></lb>ſpiritu vini aſcenſus eiuſdem pilæ impeditur. </s> <s id="s.000614">Hinc <lb></lb>ſequitur, quòd velocitas eiuſdem pilæ B per aquam <lb></lb>ad eam quam habere poteſt per ſpiritum vini com<lb></lb>poſita ſit ex duabus proportionibus, ſcilicèt ex pro<lb></lb>portione differentiarum leuitatum eorumdem cor<lb></lb>porum, quæ erit vt duo ad vnum, & ex propoſitio<lb></lb>ne reciproca reſiſtentiarum eorumdem mediorum̨, <lb></lb>quæ ſe habet vt vnum ad duo, ſed proportio dupla, <lb></lb>& ſubdupla componunt proportionem æqualitatis, <lb></lb>igitur æquali velocitate aſcendet eadem veſica B <lb></lb>per aquam A, & per <expan abbr="ſpiritũ">ſpiritum</expan> vini O, quod eſt <expan abbr="euidẽ-tèr">euiden<lb></lb>tèr</expan> falſum, & contra aſſertum eorumdem aduerſa<lb></lb>riorum, ergo veſica aere plena non mouetur ſursùm <lb></lb>in fluido vi leuitatis poſitiuæ, quod erat oſtenden<lb></lb>dum. </s> </p> <p type="margin"> <s id="s.000615"><margin.target id="marg151"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000616"><margin.target id="marg152"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000617">Sed antequam vlterius procedamus, <expan abbr="debẽt">debent</expan> ad exa<lb></lb>men quoque reuocari aliæ obiectiones, quæ ab au<lb></lb><arrow.to.target n="marg153"></arrow.to.target><lb></lb>thoribus clariſſimis afferuntur contra noſtram ſen<lb></lb>tentiam. </s> <s id="s.000618">Et primò quidem conſiderabo argumenta, <lb></lb>quæ deſumuntur à pyramidali figura flammæ lucer<lb></lb>næ, a qua, inquam, figura putant euidens <expan abbr="argumentũ">argumentum</expan> <lb></lb>deduci, quòd flamma ipſa ſursùm impellatur ab in<lb></lb>terno principio leuitatis, ſicque ratiocinantur: <emph type="italics"></emph>Vi<lb></lb>demus quieto, & tranquillo aere flammum ferri ſursùm <lb></lb>pyramidalitèr, cùm <expan abbr="tamẽ">tamen</expan> ſi per expresſionem hic motus fie-<emph.end type="italics"></emph.end><pb pagenum="124" xlink:href="010/01/132.jpg"></pb><arrow.to.target n="marg154"></arrow.to.target><lb></lb><emph type="italics"></emph>ret, inuerſa flammæ figuræ eſſet, aut certè inferior pars non <lb></lb>minùs quàm ſuperior acuminata, vt fit in omnibus non du<lb></lb>ris quando per expresſionem ſursùm iaciuntur. </s> <s id="s.000619"><expan abbr="Secũdò">Secundò</expan> quin<lb></lb>ta eſſentia vini in lapide accenſa ſursùm fertur non per ex<lb></lb>presſionem, ſed inſita leuitate, aer enim exprimens, vel <lb></lb>eſſet ſub baſi ignis auolantis, & illum protruderet, quod eſt <lb></lb>falſum; vel ſuperincumbens grauitando hanc <expan abbr="expresſionẽ">expresſionem</expan> <lb></lb>efficeret; neque hoc, quia ſic aer vertici ignis incumbens eum <lb></lb>deprimeret potiùs, ac reuerberaret deorsùm, quàm ſursùm.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.000620"><margin.target id="marg153"></margin.target>Noua argu<lb></lb>menta pro <lb></lb>leuitate po<lb></lb>ſitiua <expan abbr="afferũ-tur">afferun<lb></lb>tur</expan>.</s> </p> <p type="margin"> <s id="s.000621"><margin.target id="marg154"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000622"><emph type="center"></emph>PROP. LX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000623"><emph type="center"></emph><emph type="italics"></emph>Flammam in camino ab expresſione ambientis aeris <lb></lb>ſursùm impelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000624">PRimæ difficultati, quòd nimirum flamma lucer<lb></lb>næ in aere quieto, & tranquillo moueatur ſur<lb></lb>sùm ſponte, non verò per extruſionem factam ab ae<lb></lb>re ambiente, ſatisfacere nitemur adducendo experi<lb></lb>menta aliqua. </s> <s id="s.000625">Videmus enim maiores, & ampliores <lb></lb>flammas in caminis accenſas non vigere, nec diutiùs <lb></lb>perſeuerare niſi adſit aditus aeri de foris aduenienti, <lb></lb>per quem ingrediatur ventus perpetuus, qui inter <lb></lb>crura, & fœmora ignem <expan abbr="circumſtãtium">circumſtantium</expan> excurrit ver<lb></lb>sùs flammam, eſtque euidentèr ſenſibilis, nam ſi cu<lb></lb>biculi oſtium claudatur extenſo panno, vel cortina, <lb></lb>vt fieri ſolet, hęc inflatur verſus ignem camini, vt ve<lb></lb>lum nauis; imò in cubiculis vndiquè diligentèr clau<lb></lb>ſis, in quibus aer externus ſubingredi nequeat non <lb></lb>poterit flamma ſursùm impelli ab aere, quin cubi-<pb pagenum="125" xlink:href="010/01/133.jpg"></pb>culum inane remaneat, & <expan abbr="tũc">tunc</expan> ignis camini nullo pa<lb></lb><arrow.to.target n="marg155"></arrow.to.target><lb></lb>cto accendi poteſt, nec in flammam verti, aut per<lb></lb>durare, niſi oſtiolum, vel foramen aliquod in ipſo ca<lb></lb>mino aperiatur, & tunc facilè flamma accenditur, & <lb></lb>perſeuerat. </s> <s id="s.000626">Ratio huius effectus pendet nedùm ab <lb></lb>impulſu flammæ ſursùm, ſed etiam à rarefactione ae<lb></lb>ris propè ignem exiſtentis, eumque <expan abbr="ambiẽtis">ambientis</expan> per to<lb></lb>tam camini longitudinem, quia nempe aer prædictus <lb></lb>ab igne calefactus minùs grauis ſpecie redditur, <expan abbr="quã">quam</expan> <lb></lb>aer cubiculi, & externus, qui à camino diſtat; Hoc <lb></lb>autem neceſſariò aduenit ex legibus mechanicis, & <lb></lb>ex Archimedis <expan abbr="demõſtrationibus">demonſtrationibus</expan>; neceſsè enim eſt, <lb></lb>vt aer rarior, & minùs grauitans ſursùm expellatur <lb></lb>exprimaturque à grauiore aere <expan abbr="circumambiẽte">circumambiente</expan>, hinc <lb></lb>fit vt poſt aſcenſum illius aeris rarefacti per <expan abbr="caminũ">caminum</expan> <lb></lb>diminuatur moles aeris ipſius cubiculi propè, & cir<lb></lb>ca caminum. </s> <s id="s.000627">Non ergo mirum eſt, nouum aerem pro<lb></lb>fluere ad replendum cubiculi <expan abbr="ſpatiũ">ſpatium</expan>, & hæc eſt cau<lb></lb>ſa, quare percipitur ventus ille, & effluuium per<lb></lb>petuum dum flamma camini viget. </s> </p> <p type="margin"> <s id="s.000628"><margin.target id="marg155"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000629">Prædictum ratiocinium confirmari poteſt à pul<lb></lb>cherrimo experimento à D. </s> <s id="s.000630">Candido Buono Floren<lb></lb>tiæ mihi communicato. </s> </p> <p type="main"> <s id="s.000631"><emph type="center"></emph>PROP. LXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000632"><emph type="center"></emph><emph type="italics"></emph>Trutinæ æquilibratæ vna lanx excalefacta <expan abbr="ſursũ">ſursum</expan> eleuatur <lb></lb>extruſa à pondere aeris, reliquam lancem ambientis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000633">ERat enim trutina, ſeù bilanx tantæ perfectionis, <lb></lb>vt à quinquageſima parte vnius grani hordei, <pb pagenum="126" xlink:href="010/01/134.jpg"></pb><arrow.to.target n="marg156"></arrow.to.target><lb></lb>imò à multo leuiori feſtuca flecti facilè poſſet. </s> <s id="s.000634">hæc <lb></lb>quidem ſuſpenſa intra armariolum vitreum, vt à ſor<lb></lb>dibus, & venti agitatione tueretur <expan abbr="æquilibriũ">æquilibrium</expan> præ<lb></lb>cisè ſeruabat, vt eſt DE, cuius centrum C, tunc <expan abbr="sũp-ta">sump<lb></lb>ta</expan> virga ferrea IF, & igni<lb></lb><figure id="id.010.01.134.1.jpg" xlink:href="010/01/134/1.jpg"></figure><lb></lb>ta in eius extrema parte <lb></lb>F lanci A approximaba<lb></lb>tur, abſque contactu, <expan abbr="tũc">tunc</expan> <lb></lb>libra ab æquilibrio remo<lb></lb>uebatur, depreſſa nimi<lb></lb>rum lance B, & eleuata A, <lb></lb><expan abbr="idẽque">idemque</expan> <expan abbr="cõtingebat">contingebat</expan> trans<lb></lb>lato ignito ferro infra <expan abbr="lancẽ">lancem</expan>, ac priùs in ſuprema <expan abbr="lãcis">lancis</expan> <lb></lb>parte obſeruabatur: <expan abbr="rationẽ">rationem</expan> huius admirabilis <expan abbr="effect9">effectus</expan> <lb></lb><expan abbr="hãc">hanc</expan> excogitaui, & amico <expan abbr="petẽti">petenti</expan> reddidi eamque <expan abbr="cõ-municaui">com<lb></lb>municaui</expan> Societati <expan abbr="doctiſſimorũ">doctiſſimorum</expan> virorum à Sereniſs. <lb></lb>& Eminentiſs. Cardinali Leopoldo Mediceo <expan abbr="erectã">erectam</expan>, <lb></lb>quam deinceps more Italico <expan abbr="Academiã">Academiam</expan> experimen<lb></lb>talem Mediceam vocabo. </s> <s id="s.000635">Concipiantur duæ ſphæ<lb></lb>rulæ aeris inter ſe æquales LG, & HK lances <expan abbr="ambiẽ-tes">ambien<lb></lb>tes</expan>, quæ erunt æquè graues, ſcilicèt eiuſdem ſpeciei. <lb></lb></s> <s id="s.000636">Approximato poſtea ferro ignito IF procùldubio à <lb></lb>profluuio ignearum exhalationum à feruente ferro <lb></lb>emanantium, calefit nedum lanx illa metallica A, ſed <lb></lb>etiam ſphæra proximi aeris LG, quæ proindè ingen<lb></lb>tem raritatem acquirit, cùmque aer ambiens LG ar<lb></lb>ctè adhæreat <expan abbr="lãci">lanci</expan> A, <expan abbr="eiuſq;">eiuſque</expan> aſperitatibus, & foueolis, <lb></lb>colligatus componat veluti lanuginem vnitam ipſi <lb></lb>lanci, itaut nequeat moueri lanx A niſi ſecum deferat <pb pagenum="127" xlink:href="010/01/135.jpg"></pb>aeream lanuginem, ſeu cruſtam continguam, & con<lb></lb><arrow.to.target n="marg157"></arrow.to.target><lb></lb>nexam LG, verùm lanci oppoſitæ B, adhæret ſphæ<lb></lb>ra aerea HK denſior, vt potè non excalefacta à ferro <lb></lb>feruente; hinc fit vt ſumma lancis B vnà cum adnexa <lb></lb>cruſta ambientis aeris HK grauior ſit ærea lamina A <lb></lb>vnà cum rariori lanugine aeris adhærentis LG. <expan abbr="Mirũ">Mirum</expan> <lb></lb>igitur non eſt, quòd a maiori pondere libræ extremi<lb></lb>tas E deprimatur, & ei oppoſita D eleuetur. </s> <s id="s.000637">Eodem <lb></lb><arrow.to.target n="marg158"></arrow.to.target><lb></lb>ferè modo, vt dicebam priùs, aer cubiculi circą, <lb></lb>caminum cùm ſit valdè denſus, comparatus cum <expan abbr="flã-ma">flam<lb></lb>ma</expan>, & aere calefacto intra caminum exiſtente, & <lb></lb>ideò valdè rarefacto, mirum non eſt ſi proptèr illius <lb></lb>grauitatem excedentem ſursùm exprimat leuiorem <lb></lb>flammam, acremque adhærentem paritèr rarum. </s> <s id="s.000638">Eſt <lb></lb>igitur euidentiſſimum in hiſce experimentis, quòd <lb></lb>aer <expan abbr="flammã">flammam</expan> ambiens, nedùm eam exprimit, ſed <expan abbr="bonã">bonam</expan> <lb></lb>partem aeris <expan abbr="rarefactã">rarefactam</expan> vnà cum <expan abbr="flãma">flamma</expan> impellit quo<lb></lb>que ſursùm. </s> <s id="s.000639">Sed dicet aliquis, cur circa flammam̨ <lb></lb><arrow.to.target n="marg159"></arrow.to.target><lb></lb>lucernæ non obſeruatur prædictus ventus? </s> <s id="s.000640">reſpon<lb></lb>detur non eſſe æquè ſenſibilem, quia nimirum lucer<lb></lb>næ flamma non inſinuatur intra fiſtulam aliquam, vt <lb></lb>eſt canalis camini, qui exitum habet extra <expan abbr="cubiculũ">cubiculum</expan>; <lb></lb>cùm ergo lucernæ flamma vndique ambiatur ab aere <lb></lb>aperto abſque euidenti cun motione eam impellere <lb></lb>ſursùm poteſt exprimendo, nimirùm facto breui cir<lb></lb>cuitu à vertice flammæ vſque ad eius baſim, & ob <lb></lb>flammę exiguitatem parua quoque eſt moles aeris ei <lb></lb>contigua, quę agitatur, & conuoluitur, & hæc eſt <lb></lb>ratio, quare circa lucernæ flammam ventus non ob-<pb pagenum="128" xlink:href="010/01/136.jpg"></pb><arrow.to.target n="marg160"></arrow.to.target><lb></lb>ſeruatur ſimilis ei, qui propè caminum percipitur. </s> </p> <p type="margin"> <s id="s.000641"><margin.target id="marg156"></margin.target>Cap 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000642"><margin.target id="marg157"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000643"><margin.target id="marg158"></margin.target>Hæc experi<lb></lb>entia, & ra<lb></lb>tio eius ap<lb></lb>plicatur <expan abbr="flã-mæ">flanm<lb></lb>mæ</expan> camini <lb></lb>aſcendentis.</s> </p> <p type="margin"> <s id="s.000644"><margin.target id="marg159"></margin.target>Ratio quare <lb></lb>circa lucer<lb></lb>næ flammam <lb></lb>non percipi<lb></lb>tur ventus <lb></lb>ſicuti in ca<lb></lb>mino.</s> </p> <p type="margin"> <s id="s.000645"><margin.target id="marg160"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000646"><emph type="center"></emph>PROP. LXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000647"><emph type="center"></emph><emph type="italics"></emph><expan abbr="Ignẽ">Ignem</expan> non à leuitate, ſed ab extruſione ambientis aeris <expan abbr="aſcẽ-dere">aſcen<lb></lb>dere</expan>, euincitur ex deſcenſu fumi in vacuo <lb></lb>Torricelliano.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000648">SEd quòd reuerà ignis mo<lb></lb><figure id="id.010.01.136.1.jpg" xlink:href="010/01/136/1.jpg"></figure><lb></lb>ueatur <expan abbr="ſursũ">ſursum</expan> per extruſi<lb></lb>onem ambientis aeris, <expan abbr="nõ">non</expan> <expan abbr="autẽ">autem</expan> <lb></lb>aſcendat ſponte propria vir<lb></lb>tute euidentiſſimè percipitur <lb></lb>ex hoc meo <expan abbr="experimẽto">experimento</expan>, quod <lb></lb><expan abbr="Florẽtię">Florentię</expan> Sereniſſimo Leopol<lb></lb>do Cardinali Mediceo <expan abbr="cõmu-nicaui">commu<lb></lb>nicaui</expan>, comprobatumque fu<lb></lb>it in Academia Experimentali <lb></lb>Medicea, & demum Exteris <lb></lb>per Epiſtolas diuulgatum fuit. </s> </p> <p type="main"> <s id="s.000649">Sit vas vitreum AFG, cuius <lb></lb>longitudo EF duobus cubitis <lb></lb>maior ſit, habeatque <expan abbr="annexã">annexam</expan> <lb></lb>ampullam vitream CEM, ſit<lb></lb>que incuruata eius extremitas HFG, atque duæ eius <lb></lb>extremitates A, & G ſint perforatæ, & apertæ, & pri<lb></lb>ùs ſtrictè obſerato, duplici veſica ſuilla, infimo orificio <lb></lb>G repleatur vas vniuerſum hydrargyro infuſo per ſu<lb></lb>premum os AB, poſtea pilula aliqua D ex bitumine <lb></lb>aliquo atri coloris operculo ex bractea ferrea filo <pb pagenum="129" xlink:href="010/01/137.jpg"></pb>alligetur; & Orificium AB denuò veſica tegatur, <lb></lb><arrow.to.target n="marg161"></arrow.to.target><lb></lb>colligeturque ſtrictè: tandèm ſublata veſica infima <lb></lb>G concedatur egreſſus hydrargyro, vt nimirùm facta <lb></lb>ſolita vacuitate aeris remaneat hydrargyrum <expan abbr="ſuſpẽ-ſum">ſuſpen<lb></lb>ſum</expan> vſque ad O, & altitudo GO erit proximè vnius <lb></lb>cubiti, & quadrantis. </s> <s id="s.000650">His præparatis ſumatur lens <lb></lb>aliqua cryſtallina KL, & directè Soli S exponatur in <lb></lb>ea diſtantia, & ſitu in quo præcisè vertex coni radio<lb></lb>ſi à radijs Solis refractis conuergentibus formati ad <lb></lb>contactum pilæ bituminoſæ D pertingat. </s> <s id="s.000651">Idipſum̨ <lb></lb>fieri poteſt ope ſpeculi concaui vſtorij radios Solis <lb></lb>reflectentis, tunc liqueſcere incipit pila D, & fumum <lb></lb>emittit, in quo apparet mirabilis operatio, non enim <lb></lb>fumus, veluti in aere aperto accidit, ſursùm aſcen<lb></lb>dit, ſed incuruatur flectiturque deorsùm per DMN <lb></lb>non ſecùs ac virgulæ illæ aquæ cadentis è fontibus, <lb></lb>inflexas, & deorsùm tendentes lineas deſcribunt. </s> </p> <p type="margin"> <s id="s.000652"><margin.target id="marg161"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000653">Porrò quia fumum non minùs quàm flammam <expan abbr="leuẽ">leuem</expan> <lb></lb>eſſe, atque ſursùm moueri ſponte ſua à naturali prin<lb></lb>cipio impulſa, <expan abbr="cõmuniter">communiter</expan> Peripatetica Schola docet, <lb></lb>igitur neceſſario in ſpatio illo vacuo CEN, vel ſal<lb></lb>tèm in quo aer non degit niſi valdè expanſus, & rare<lb></lb>factus, fumus maiori vi ſursùm aſcendere deberet, <lb></lb>quàm in aere aperto, quia nimirùm ab aeris cor<lb></lb>pulentia aliquo pacto impeditur ipſius progreſ<lb></lb>ſus (videmus enim in aere aperto fumum ampliari, <lb></lb>diſſipari, ac diſpergi à prædicta aeris reſiſtentia,) <expan abbr="cũ-que">cun<lb></lb>que</expan> in ſpatio illo vacuo, vel à quo aer deficit poſſit <lb></lb>fumus naturali leuitate non impeditus liberiùs, & fa-<pb pagenum="130" xlink:href="010/01/138.jpg"></pb><arrow.to.target n="marg162"></arrow.to.target><lb></lb>ciliùs eleuari, igitur omninò neceſsè eſſet vt fumus <lb></lb>in prædicto vacuo ſpatio aſcenderet ſursùm, veluti <lb></lb>eius natura exigit, & è contrà eſſet impoſſibile vt <lb></lb>deorsùm deprimeretur, & caderet, vt virgulæ deci<lb></lb>dentes aquæ fontium flectuntur deorsùm; quia verò <lb></lb>hoc experientiæ repugnat non poterit dici, quòd fu<lb></lb>mus ſit leuis, ſed è contrà grauis erit. </s> <s id="s.000654">Cùm verò iņ <lb></lb>aere idem fumus ſursùm aſcendat, <expan abbr="dicẽdum">dicendum</expan> eſt quòd <lb></lb>ab aere ambiente grauiori in ſpecie, quàm ſit fumus <lb></lb>iuxtà leges mechanicas libræ aer <expan abbr="premẽs">premens</expan> per extru<lb></lb>ſionem ſursùm fumum minùs grauem expellit. </s> </p> <p type="margin"> <s id="s.000655"><margin.target id="marg162"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000656"><emph type="center"></emph>PROP. LXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000657"><emph type="center"></emph><emph type="italics"></emph>Figuram pyramidalem flammæ lucernæ non ſuadere eam à <lb></lb>vi leuitatis ſursùm impelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000658">VErùm, quod ad formam pyramidalem flammæ <lb></lb>lucernæ pertinet, non videtur, quòd eius figu<lb></lb>ra conica neceſſariò perſuadeat, & conuincat flam<lb></lb>mam ſursùm ſponte ſua, & propria virtute leuitatis <lb></lb>aſcendere, nam ſiue per extruſionem ambientis flui<lb></lb>di violenter, ſiuè ſponte à vi leuitatis ſursùm moue<lb></lb>ri ſupponamus, retinere æquè benè poſſet eamdem̨ <lb></lb>conicam <expan abbr="figurã">figuram</expan>, vt inferiùs oſtendemus. </s> <s id="s.000659">Præterea ſi <lb></lb>vera cauſa figuræ pyramidalis flammæ lucernæ eſſet <lb></lb>eius leuitas poſitiua, deberet eadem leuitas poſitiua <lb></lb>eumdem effectum producere in reliquis omnibus <lb></lb>corporibus fluidis paritèr ab ipſa impulſis, ſi tamen <lb></lb>reliqua ſint paria, ſcilicèt fumus non ſecùs ac flam-<pb pagenum="131" xlink:href="010/01/139.jpg"></pb>ma corpus fluidum, & rarum eſt, cuius continentèr <lb></lb><arrow.to.target n="marg163"></arrow.to.target><lb></lb>vna pars poſt aliam generatur, & eructatur à po<lb></lb>ris eiuſdem titionis, pariterque fumum leuitatem̨ <lb></lb>poſitiuam habere, & exercere <expan abbr="ſupponũt">ſupponunt</expan> non minùs, <lb></lb>quàm flamma habet, igitur neceſſariò fumus aſcen<lb></lb>dens, & digrediens à titione deberet formam pyra<lb></lb>midalem acquirere ſimilem ei, quam flamma lucer<lb></lb>næ habet, deberetque paritèr in acumen ſubtile ſu<lb></lb>periùs deſinere, quod profectò eſt falſum, & contra <lb></lb>ſenſus euidentiam, proſequitur enim fumus ſuum̨ <lb></lb>iter longo tractu ſursùm abſque eo quòd in acumen <lb></lb>reducatur. </s> </p> <p type="margin"> <s id="s.000660"><margin.target id="marg163"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000661">Id ipſum continget, ſi fiſtula aliqua aer in fundo <lb></lb>aquæ inſuffletur, <expan abbr="conſpiciẽtur">conſpicientur</expan> enim eleuari innume<lb></lb>ræ ampullæ aereę, quæ ab inuicem ſeparantur abſ<lb></lb>que eo quòd pyramidalem figuram acquirant, licèt <lb></lb>aer non minùs quàm flamma leuis reputetur, & ab in<lb></lb>trinſeco principio ſursùm moueri credatur, cùmque <lb></lb>vna, & eadem cauſa non poſſit diuerſos effectus pro<lb></lb>ducere, concedant neceſsè eſt, figuram, quam in <expan abbr="flã-ma">flam<lb></lb>ma</expan> obſeruamus diuerſam à figura fumi, & aeris per <lb></lb>aquam aſcendentis ab alia cauſa longè diuerſa de<lb></lb>pendere, non autem à prædicto principio intrinſeco <lb></lb>leuitatis. </s> </p> <p type="main"> <s id="s.000662">Et profectò ſi attentè perpendamus fumi, & flam<lb></lb>mæ conſiſtentias, valdè inter ſe differre reperiemus, <lb></lb>licèt ambo ſint corpora rara, & fluida. <pb pagenum="132" xlink:href="010/01/140.jpg"></pb><arrow.to.target n="marg164"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000663"><margin.target id="marg164"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000664"><emph type="center"></emph>PROP. LXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000665"><emph type="center"></emph><emph type="italics"></emph>Fumi structura, & compoſitio declaratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000666">COnſtat fumum eſſe maſſam copioſam particula<lb></lb>rum exiguarum olei, terræ, & aquæ, quæ par<lb></lb>ticulæ ab inuicem diſcretæ, & ſeparatæ nondùm̨ <lb></lb>accenſæ ſunt, licèt valdè excalefactæ ſint. </s> <s id="s.000667">hoc planè <lb></lb>confirmatur ab operatione chymica, poſſunt enim̨ <lb></lb>recolligi ex fumo partes aqueæ ſegregatæ, & diſcre<lb></lb>tæ à partibus vnctuoſis, & ſulphureis, nec non à <lb></lb>particulis terreis, & fuliginoſis, & viciſſim quæli<lb></lb>bet ex prædictis ſubſtantijs recuperari poteſt ſepa<lb></lb>rata à reliquis; præterea conſtat ſenſu, fumum noņ <lb></lb>eſſe corpus continuum, ſed aggregatum ex particu<lb></lb>lis minimis ab inuicem ſeparatis, & diſcretis, vt præ<lb></lb>clarè in nebula obſeruatur, & in alijs aqueis vapo<lb></lb>ribus, qui ſi attentè conſpiciantur in loco commodo, <lb></lb>ideſt ſi interpoſita nebula viſus dirigatur inſpiciat<lb></lb>que obſcurum, & tenebroſum aliquem locum, & in<lb></lb>terim Sol transuerſalitèr eamdem nebulam illuſtret; <lb></lb>tunc illa nebula, quæ repreſentabatur continua ap<lb></lb>paret eſſe conflata ex immenſa multitudine exiguo<lb></lb>rum granulorum aquæ, quæ lento quodam motu per <lb></lb>aerem agitantur, vt contingit in ijs fragmentis ter<lb></lb>reis minutiſſimis, quæ conſpiciuntur in radijs Solis <lb></lb>intra cubicula. </s> <s id="s.000668">Iam prædicta granula aquea copio<lb></lb>ſiſſima vagantia per aerem non facile viſibilia ſunt <lb></lb>ſigillatim ob eorum exiguitatem, ſed poſſunt tran-<pb pagenum="133" xlink:href="010/01/141.jpg"></pb>ſitum luci impedire, & componunt apparentiam il<lb></lb><arrow.to.target n="marg165"></arrow.to.target><lb></lb>lam vnius ſubſtantiæ raræ, & expanſæ, vti pariter <lb></lb>multoties accidit in tempore pluuiæ, quo guttæ <lb></lb>aquæ decidentes ab inuicem ſeparatę, ſi à loco aliquo <lb></lb>diſtanti, & remoto inſpiciantur, ſimillimæ videntur <lb></lb>nebulis, & fumo. </s> </p> <p type="margin"> <s id="s.000669"><margin.target id="marg165"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000670"><emph type="center"></emph>PROP. LXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000671"><emph type="center"></emph><emph type="italics"></emph>Fumus non eſt res accenſa, & quamobrem ab ambiente ac<lb></lb>re ſursùm exprimi poteſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000672">QVòd poſtea partes minimæ fumum componen<lb></lb>tes non ſint adhùc accenſæ, experientia <expan abbr="cõſtat">conſtat</expan>, <lb></lb>quia videmus multoties fumum accendi, atque in<lb></lb>flammari <expan abbr="quãdo">quando</expan> eum <expan abbr="tãgit">tangit</expan> flamma viua alicuius can<lb></lb>delæ, prætereà videtur quoque impoſſibile fumum <lb></lb>eſſe rem accenſam, quia nimirùm fumus gignitur in <lb></lb>cauitatibus, atque poroſitatibus internis ſigni, vel <lb></lb>cuiuslibet alterius corporis fumum eructantis, ſed <lb></lb>in hiſce locis anguſtis reſtrictiſque nedum fumus ac<lb></lb>cendi non poteſt, vt è contrà flammæ ipſæ iam <expan abbr="accẽ-ſæ">accen<lb></lb>ſæ</expan> in eiſdem locis anguſtis concluſiſque momento <lb></lb>extinguantur, ſuffocenturque; imò licet concauita<lb></lb>tes cauernoſæ ſint amplę, vt eſt cauitas alicuius later<lb></lb>næ vndique occluſæ, ſubitò <expan abbr="flãma">flamma</expan> extinguitur, <expan abbr="quã-tò">quan<lb></lb>tò</expan> magis hoc fieri debet quando cauitates, & poro<lb></lb>ſitates ſunt reſtrictæ, & anguſtiſſimæ, vt ſunt pori li<lb></lb>gni, vel alterius conſimilis corporis. </s> <s id="s.000673">Licèt ergo præ<lb></lb>dicta fragmenta exigua fumum componentia <expan abbr="nõ">non</expan> ſint <pb pagenum="134" xlink:href="010/01/142.jpg"></pb><arrow.to.target n="marg166"></arrow.to.target><lb></lb>actu accenſa, vel <expan abbr="inflãmata">inflammata</expan> nihilominùs valdè exca<lb></lb>lefacta, & rara eſſe ſolent, & hæc quidem raritas, & <lb></lb>agitatio <expan abbr="earũdẽ">earundem</expan> fumi <expan abbr="particularũ">particularum</expan>, producta ab exha<lb></lb>lationibus igneis, à quibus priùs euulſæ, & ſegre<lb></lb>gatæ fuerunt à maſſa lignea, vel alterius corporis, eſt <lb></lb>in cauſa vt non poſſint ampliùs in anguſtis illis poro<lb></lb>ſitatibus retineri, & proindè coguntur ingenti impe<lb></lb>tu eructari, effluere que per orificia patentia earum<lb></lb>dem poroſitatum, quæ orificia cùm vndique pateant, <lb></lb>fit vt fumus exeat nedùm è parte ſuprema ligni, ſed <lb></lb>etiam à parte infima, & laterali. </s> <s id="s.000674">Diffractis itaque re<lb></lb>pagulis carcerum, egreſſiſque fumi partibus in aere <lb></lb>aperto non ſine ſocietate ignearum exhalationum̨ <lb></lb>maſſam componunt minùs grauem ipſo aere <expan abbr="ambiẽ-te">ambien<lb></lb>te</expan>, & ideò poterunt ab eodem exprimi, & lento mo<lb></lb>tu impelli ſursùm atque tàm diù aſcenſus perſeuera<lb></lb>bit, quouſque exhalationes igneæ ab ipſis particulis <lb></lb>fumi non diſcedant <expan abbr="exhalẽtque">exhalentque</expan>, & pariter vſquequò <lb></lb>deficiat impetus præconceptus ab ipſo impulſu præ<lb></lb>cedenti, à quo lento quidem motu per aerem <expan abbr="fluctuã-do">fluctuan<lb></lb>do</expan> aliquantiſper fumi commoueri poterunt, cùm̨ <lb></lb>præterea exiguitas particularum eiuſdem fumi cau<lb></lb>ſa ſufficiens ſit, vt diù à qualibet minima aeris agita<lb></lb>tione <expan abbr="ſuſpẽſæ">ſuſpenſæ</expan> retineri poſſint, vt videmus puluerem <lb></lb>terreſtrem grauiſſimum per aerem diſpergi, ibiquę <lb></lb>diù retineri, vt experientia docet. <pb pagenum="135" xlink:href="010/01/143.jpg"></pb><arrow.to.target n="marg167"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000675"><margin.target id="marg166"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000676"><margin.target id="marg167"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000677"><emph type="center"></emph>PROP. LXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000678"><emph type="center"></emph><emph type="italics"></emph>Fumi non ab impetu quo eructantur ad altisſimas regiones <lb></lb>perduci poſſunt, ſed minùs graues redditi ab igniculo<lb></lb>rum commixtione exprimi ab ambiente aere <lb></lb>poſſunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000679">ET notandum eſt, quòd abſque exhalationibus <lb></lb>igneis non poſſent ad inſignem altitudinem̨ <lb></lb>fumi particulæ eleuari, quia licèt impetus ex ſui na<lb></lb>tura, quo à ligni poroſitatibus eructantur, vim per ſe <lb></lb>haberet ad eas longiùs eleuandas, nihilominùs, quia <lb></lb>huiuſmodi impetus facillimè debilitatur extingui<lb></lb>turque à particulis aeris quieſcentibus, vel prædicto <lb></lb>motu priuatis, quibus occurrunt fumi, non poſſet eius <lb></lb>aſcenſus longiùs propagari, ſed citò extingueretur. <lb></lb></s> <s id="s.000680">Vlteriùs ſi re vera fumi à ligno eructati virtute im<lb></lb>petus <expan abbr="præcõcepti">præconcepti</expan> ad <expan abbr="tãtã">tantam</expan> <expan abbr="altitudinẽ">altitudinem</expan> <expan abbr="aſcẽderẽt">aſcenderent</expan>, <expan abbr="nõ">non</expan> <expan abbr="au-tẽ">au<lb></lb>tem</expan> ob <expan abbr="ſocietatẽ">ſocietatem</expan> ignearum <expan abbr="exhalationũ">exhalationum</expan>, ſequeretur, q̨ <lb></lb><expan abbr="nõ">non</expan> ſemper fumus ad <expan abbr="eãdẽ">eandem</expan> atmoſphærę ſummitatem <lb></lb>aſcenderet, is enim qui per poros laterales ligni e<lb></lb>greditur, impetum proiectitium tranſuerſalem acqui<lb></lb>reret, & ideò proſequi ſuum motum deberet per pla<lb></lb>num horizontalem, neque ab incepto itinere tanto<lb></lb>pere deuiaret: ſimiliter fumus ille, qui ab infima par<lb></lb>te titionis in aere ſuſpenſi exit, impetum acquirit ten<lb></lb>dendi deorsùm, non ſursùm, proindeque deberet di<lb></lb>rectè profluere vſque ad pauimentum, & deinceps <lb></lb>non poſſet ad ſu premam aeris regionem perduci, <pb pagenum="136" xlink:href="010/01/144.jpg"></pb><arrow.to.target n="marg168"></arrow.to.target><lb></lb>quæ omnia falſa ſunt, & contra ſenſus euidentiam; <lb></lb>Fatendum igitur eſt, ab igneis particulis fumum ra<lb></lb>refactum eleuari ab impulſu grauioris aeris ambien<lb></lb>tis per expreſſionem. </s> </p> <p type="margin"> <s id="s.000681"><margin.target id="marg168"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000682"><emph type="center"></emph>PROP. LXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000683"><emph type="center"></emph><emph type="italics"></emph>Flamma eſt fumus accenſus magis rarefactus, qui ab aere <lb></lb>ambiente velocisſimè ſursùm exprimitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000684">PErcepta iam & declarata fumi <expan abbr="cõſtructione">conſtructione</expan> per<lb></lb>pendere modò iuuat metamorphoſim, quam̨ <lb></lb>patitur quando inflammatur. </s> <s id="s.000685">Debemus igitur con<lb></lb>cipere minimas particulas ſulphureas in fumo con<lb></lb>tentas, cùm inflammantur, maximè dilatari, rarefieri, <lb></lb>& vehementiſſimè agitari, & in hoc conſiſtere eius <lb></lb>accenſionem, ſed granula illa aquea, & terrea eiuſ<lb></lb>dem fumi, quæ ex ſua natura accenſibilia non ſunt, <lb></lb>poterunt tantummodò rarefieri multò magis, quàm <lb></lb>priùs. </s> <s id="s.000686">iam à prædicta ferè <expan abbr="momẽtanea">momentanea</expan> rarefactione, <lb></lb>agitatione, & accenſione ſubſequitur conſequen<lb></lb>tèr ſplendida, & luminoſa apparentia flammæ. </s> <s id="s.000687">Ad <lb></lb>hæc aeris ambientis grauitas, licèt exigua ſit, ſupe<lb></lb>rabit nihilominùs notabili exceſſu minimum, & in<lb></lb>ſenſibile pondus ipſius flammæ multò, & multò ma<lb></lb>gis, quàm ſuperauerat pondus <expan abbr="præcedẽtis">præcedentis</expan> fumi:hinc <lb></lb>neceſſariò flamma ab ipſo aere per extruſionem ſur<lb></lb>sùm impelletur ineffabili velocitate. </s> <s id="s.000688">Et hìc plurima <lb></lb>aduertenda ſunt. <pb pagenum="137" xlink:href="010/01/145.jpg"></pb><arrow.to.target n="marg169"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000689"><margin.target id="marg169"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000690"><emph type="center"></emph>PROP. LXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000691"><emph type="center"></emph><emph type="italics"></emph>Flamma rarior fumo minus ſpatium occupat ob <expan abbr="maximã">maximam</expan> <lb></lb>eius velocitatem, redditurque poſtea inuiſibilis noua <lb></lb>de cauſa, & tactui languida ob eius <lb></lb>diſperſionem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000692">OBſeruatur profectò titionem fumi copiam <expan abbr="ingẽ-tem">ingen<lb></lb>tem</expan> euomere, ſed ſi denuò eius flamma reui<lb></lb>uiſcat, hęc mirabili velocitate fumi illius vaſtam mo<lb></lb>lem abſumere videtur, eumque in exiguum ſpatium <lb></lb>flammæ concludere, cùm reuera non ſit reſtrictio, <lb></lb>flamma enim maiorem raritatem habet, quàm fumus, <lb></lb>pendet ergo hoc ab ineffabili velocitate partium̨ <lb></lb>flammæ. </s> <s id="s.000693">aliundè enim notum eſt per reſtrictum flu<lb></lb>minis canalem molem ampliſſimam aquæ totius flu<lb></lb>minis pertranſire, non quia in exiguo, & reſtricto illo <lb></lb>ſpatio canalis condenſetur tota aqua fluuij, ſed quia <lb></lb>velociſſimo motu per eum excurrit; cùm è contrà in <lb></lb>parte ampla fluuij aqua lentiſſimo curſu progredia<lb></lb>tur, ſic paritèr in fumo particulæ eius lento, & tardo <lb></lb>gradu excurrentes amplum, & grande ſpatium oc<lb></lb>cupabant, in flamma verò <expan abbr="eædẽ">eædem</expan> particulæ veluti per <lb></lb>ſtrictiſſimum canalem mirabili, & ineffabili veloci<lb></lb>tate currunt, & ſic poſſunt exiguum ſpatium comple<lb></lb>re. </s> <s id="s.000694">Sed quare flamma vltra verticem eius non exten<lb></lb>ditur, neque viſibilis redditur? </s> <s id="s.000695">hìc primò <expan abbr="dicendũ">dicendum</expan>, <lb></lb>quòd reuerà flamma producitur vltra eius verticem <lb></lb>per notabile ſpatium, & hoc quidem percipitur non <pb pagenum="138" xlink:href="010/01/146.jpg"></pb><arrow.to.target n="marg170"></arrow.to.target><lb></lb>viſu, ſed tactu, poſſum enim abſque noxa manum ad <lb></lb>latus flammæ approximare, vt ferè eam contingam, <lb></lb>non verò poſſum manum ſupra flammæ verticem iņ <lb></lb>notabili diſtantia vnius palmi abſque dolore, & v<lb></lb>ſtione retinere, igitur dicendum eſt, quòd ſubſtan<lb></lb>tia illa ignita vltra verticem flammæ redditur tranſ<lb></lb>parens, & ideò inuiſibilis alia noua de cauſa efficitur. <lb></lb></s> <s id="s.000696">Sed tamen negari non poteſt productio, & extenſio <lb></lb>ſubſtantiæ igneæ vltra flammam productæ, cùm hoc <lb></lb>ab ipſo tactu conuincatur. </s> <s id="s.000697">Sed dices, quare ſupra <expan abbr="flã-mæ">flam<lb></lb>mæ</expan> verticem in multò maiori altitudine non ampliùs <lb></lb>tactu percipitur effluuium calidiſſimum eius, vt pro<lb></lb>pè eius verticem percipiebatur? </s> <s id="s.000698">At forſan hoc acci<lb></lb>dit, quia ignea ſubſtantia fluidiſſima ab occurſu aeris <lb></lb>diſpergitur, & ſubdiuiditur in alias partes minores <lb></lb>ab inuicem diuiſas, & diſcretas, vt videmus aquæ <lb></lb>copiam è ſumma turri delapſam in progreſſu deſcen<lb></lb>ſus ſubdiuidi in innumeras guttulas inter ſe diſcre<lb></lb>tas, & ſicuti non æquè humectat, & madefacit pluuia <lb></lb>illa, ac maſſa integra aquæ vnita, quia nimirùm nul<lb></lb>la pars ſubiecti corporis à maſſa continua aquæ tacta <lb></lb>relinquitur arida, cùm in pluuia non omnes partes ſo<lb></lb>li <expan abbr="madefiãt">madefiant</expan> humectentur que, ita propè verticem <expan abbr="flã-mæ">flam<lb></lb>mæ</expan> ignis vnitus manum percutit, atque terebrat, <expan abbr="cũ">cum</expan> <lb></lb>è <expan abbr="cõtra">contra</expan> in remotiori altitudine ſpicula illa ignea val<lb></lb>dè diſcreta plagas exiguas, & inter ſe diſtantes iņ <lb></lb>ipſa manu inferant, & hinc minori noxa, minorique <lb></lb>dolore incurſus ignis tolerari poterit. <pb pagenum="139" xlink:href="010/01/147.jpg"></pb><arrow.to.target n="marg171"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000699"><margin.target id="marg170"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000700"><margin.target id="marg171"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000701"><emph type="center"></emph>PROP. LXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000702"><emph type="center"></emph><emph type="italics"></emph>Flammæ candelæ vertex acuminatur, quia magis accen<lb></lb>ſus, & ideò velociùs aſcendit, quàm baſis eius.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000703">PRæterea <expan abbr="ſupponẽdum">ſupponendum</expan> eſt, flammam candelæ <expan abbr="nõ">non</expan> <lb></lb>habere conſiſtentiam homogeneam, & ſimila<lb></lb>rem, pars enim infima flammulæ non eſt omninò ac<lb></lb>cenſa, quod conſtat ex eius colore ſubliuido, quia <lb></lb>nimirùm fumi oleoſi eructati ab elicnio, vel ligno <expan abbr="nõ">non</expan> <lb></lb>in inſtanti, ſed in <expan abbr="tẽpore">tempore</expan> accendi debent, igitur veri<lb></lb>ſimile eſt, quòd <expan abbr="nõ">non</expan> omnes prędicti fumi ſubitò poſt e<lb></lb>greſſum in ipſo contactu baſis flammæ ſimùl, & inte<lb></lb>grè accendantur, & propterea rarefactio, & accen<lb></lb>ſio continuatur dùm actu excurrunt illæ particulæ à <lb></lb>baſi versùs verticem flammæ. </s> <s id="s.000704">Modò ſi in baſi flam<lb></lb>mulæ fumi non ſunt omninò, & integrè accenſi, non <lb></lb>habebunt velociſſimum illum motum, cuius capax <lb></lb>eſt flammæ puræ natura, igitur in ipſa flamma conci<lb></lb>pi debet pars infima tardior, quàm ſuprema, & ver<lb></lb>ticalis, ſed ſicuti in fluuio nulla alia de cauſa tantą <lb></lb>copia aquæ in anguſtiſſimum ſpatium aluei reſtrin<lb></lb>gitur coanguſtaturque, niſi quia velociſſimè excur<lb></lb>rit, cùm è contrà in locis dilatatis, & amplis eadem <lb></lb>aquæ fluminis moles amplius ſpatium aluei ob eius <lb></lb>tarditatem occupet, ita in flamma lucernæ, quæ vt <lb></lb>fluuius ignis excurrentis concipi poteſt, mirum <expan abbr="nõ">non</expan> <lb></lb>eſt, quòd in baſi propè elicnium ob tarditatem eius <lb></lb>fluxus ampliorem ſitum occupet, quàm in eius ver-<pb pagenum="140" xlink:href="010/01/148.jpg"></pb><arrow.to.target n="marg172"></arrow.to.target><lb></lb>tice, vbi velociori curſu fugit. </s> </p> <p type="margin"> <s id="s.000705"><margin.target id="marg172"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000706">Hinc colligitur, quòd ex figura pyramidali, & a<lb></lb>cuminata flammæ lucernæ non euincitur eam à vi <lb></lb>intrinſeca leuitatis ſursùm impelli. </s> <s id="s.000707">Cùm è contrà de<lb></lb><arrow.to.target n="marg173"></arrow.to.target><lb></lb>claratum ſit, qua ratione abſque poſitiua leuitate ab <lb></lb>expreſſione aeris grauioris ambientis ſursùm expel<lb></lb>latur, pariterque oſtenſa eſt cauſa prædictæ eius fi<lb></lb>guræ acuminatæ & in verticem deſinentis, quæ non <lb></lb>pendet à leuitate propria, ſed ab expreſſione aeris <lb></lb>maxima velocitate facta in eius acumine magis <expan abbr="accẽ-ſo">accen<lb></lb>ſo</expan>, & hoc confirmatur ex eo quòd multotiès flammæ <lb></lb>candelarum non ſunt pyramidales, ſed rotundæ, aut <lb></lb>oblongæ, & ouales, & hoc clarè conſpicitur quandò <lb></lb>virga illa fumoſa, quæ eructatur ab infima lucerną <lb></lb>nupèr extincta, denuò accenditur à contactu alte<lb></lb>rius flammæ in notabili diſtantia ab inferiori cande<lb></lb>la, & tunc fumus inflammatus per longitudinem to<lb></lb>tius fumi ſubiecti deorsùm labitur vſque ad <expan abbr="elicniũ">elicnium</expan> <lb></lb><arrow.to.target n="marg174"></arrow.to.target><lb></lb>ſubiectæ lucernæ, conſpiciturque euidentèr figura <lb></lb>illius fumi <expan abbr="accẽſi">accenſi</expan> perfectè <expan abbr="rotũda">rotunda</expan>, imò <expan abbr="cũ">cum</expan> primò lu<lb></lb>cerna accenditur, eius flamma rotunda eſt, & poſtea <lb></lb>verticem conicum acquirit. </s> <s id="s.000708">in flammis verò camini <lb></lb>non obſeruantur formæ pyramydales, ſed multipli<lb></lb>citèr diuiſæ multotiès radios, ſeù linguas referunt, <lb></lb>& aliquando rotundæ conſpiciuntur, & ſic eleuan<lb></lb>tur per aliquod ſpatium. </s> <s id="s.000709">Sed de his ſatis. <pb pagenum="141" xlink:href="010/01/149.jpg"></pb><arrow.to.target n="marg175"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000710"><margin.target id="marg173"></margin.target>Concluditur <lb></lb>quod ex ſi<lb></lb>gura acumi<lb></lb>nata flammæ <lb></lb>lucernæ non <lb></lb>euincitur <lb></lb>hanc à vi le<lb></lb>uitatis <expan abbr="afcẽ-dere">afcen<lb></lb>dere</expan>.</s> </p> <p type="margin"> <s id="s.000711"><margin.target id="marg174"></margin.target>Præterea all<lb></lb>quæ flammæ <lb></lb>candelæ ſunt <lb></lb>rotundæ, & <lb></lb>flammæ ca<lb></lb>mini ſunt al <lb></lb>terius figu<lb></lb>ræ.</s> </p> <p type="margin"> <s id="s.000712"><margin.target id="marg175"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000713"><emph type="center"></emph>PROP. LXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000714"><emph type="center"></emph><emph type="italics"></emph>Flammain ſpiritu vini accenditur extra, & longè ab ipſo <lb></lb>ſpiritu, & ideò poteſt exprimi ſursùm <lb></lb>ab ambiente aere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000715">VIdeamus modò an ex accenſione vini ſpiritus <lb></lb>deducatur aſſertio leuitatis poſitiuæ. </s> <s id="s.000716">Et hic <lb></lb>denuò dico, quòd flamma ſpiritus vini non eſt actu <lb></lb>accenſa in poris internis prædicti liquoris, ſed ſicuti <lb></lb>de fumis lignorum dictum eſt, educitur è ſpiritus vi<lb></lb>ni fiuore fumoſa quædam maſſa rariſſima, quæ in po<lb></lb>roſitatibus fluoris cùm retineri nequeat, ruptis car<lb></lb>cerum repagulis ingenti impetu per orificia poroſa <lb></lb>vndique fluorem ambientia eructat, & poſtmodum̨ <lb></lb>flammam concipit, accenditurque in aliqua ſenſibi<lb></lb>li diſtantia à dicto fluore: hoc confirmatur exemplo <lb></lb>illius effluuij fumoſi, egredientis ab aliqua titionis <lb></lb>poroſitate, quod poſtmodum accenditur in diſtan<lb></lb>tia vnius digiti ab ipſo ligno, & ſpeciem præbet flu<lb></lb>oris bitumino ſi lateralitèr defluentis, qui in aerę <lb></lb>ignem concipiat. </s> <s id="s.000717">Cùm igitur ab omnibus poroſita<lb></lb>tibus ſpiritus vini, & cuiuslibet materiei accenſibi<lb></lb>lis vndequaque ſursùm, deorsùm, & lateralitèr fu<lb></lb>moſæ exhalationes egrediantur, quæ poſtea in ipſo <lb></lb>aere aperto inflammentur, & accendantur, non vi<lb></lb>detur difficile vt aer poſſit infra flammam accenſam, <lb></lb>& lateralitèr eam comprimere, & proinde expreſſio<lb></lb>ne facta eam ſursùm impellere: & <expan abbr="notandũ">notandum</expan> eſt, quòd <pb pagenum="142" xlink:href="010/01/150.jpg"></pb><arrow.to.target n="marg176"></arrow.to.target><lb></lb>expreſſio, quæ ab aere efficitur, non ſemper aſſimila<lb></lb>tur ei, quæ ex compreſſione poſtica digitorum crea<lb></lb>tur, veluti prunorum nucleos à digitis poſticè com<lb></lb>preſſis pueri proijcere longè ſolent, vtque aduerſa<lb></lb>rius exiſtimabat, ſed expulſio, & expreſſio flammæ <lb></lb><arrow.to.target n="marg177"></arrow.to.target><lb></lb>facta ab aere circumfuſo fit, vt exigit ratio mechani<lb></lb>ca ſiphonis ſursùm inuerſi vt ex elementis hidroſta<lb></lb>ticis conſtat, vtque meliùs inferiùs declarabitur vn<lb></lb>de malè infertur, quòd ſi flamma expulſa eſſet ab am<lb></lb>biente aere, deberet fieri acuminata in eius baſi, & <lb></lb>rotunda in eius vertice. </s> </p> <p type="margin"> <s id="s.000718"><margin.target id="marg176"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000719"><margin.target id="marg177"></margin.target>Cap. 2.</s> </p> <p type="main"> <s id="s.000720"><emph type="center"></emph>PROP. LXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000721"><emph type="center"></emph><emph type="italics"></emph>Flamma in ſpiritu vini accenſa non debet ab aere incum<lb></lb>bente contundi, cùm ab eius pondere non exprimatur <lb></lb>ſursùm, ſed ab aere collaterali infernè reflexo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000722">POſtrema inſtantia, quòd aer flammæ <expan abbr="ſuperincũ-bens">ſuperincun<lb></lb>bens</expan> potiùs eam deberet contundere, & dila<lb></lb>tare, & deorsùm eam diuerberare, <expan abbr="nõ">non</expan> autem in acu<lb></lb>tiem ſublimare, facilè ſoluitur, quia aer fluidus non <lb></lb>ſolùm ſupremus, & flammæ incumbens, ſed etiam̨ <lb></lb>lateralis, & infimus ob eius grauitatem ad modum̨ <lb></lb>ſiphonis, vel libræ non poteſt contundere <expan abbr="flammã">flammam</expan>, <lb></lb>ſed eam ſursùm exprimere, & impellere debet, at<lb></lb>que aer ſupernus neceſſariò ad latera excurrere de<lb></lb>bet, & tranſitum minùs ponderoſæ flammæ <expan abbr="aſcendẽ-ti">aſcenden<lb></lb>ti</expan> concedere; nec obſtaculum aliud ei inferet, præ<lb></lb>terquàm contuſionem ſupremæ aciei flammæ, vt ni-<pb pagenum="143" xlink:href="010/01/151.jpg"></pb><arrow.to.target n="marg178"></arrow.to.target><lb></lb>mirùm efficiatur vertex eius aliquo pacto rotundus, <lb></lb>& contornatus, niſi adfuerit noua alia cauſa motum <lb></lb>eius accelerans, à qua proindè eius vertex acumi<lb></lb>nari poteſt, vt ſuperiùs dictum eſt. <lb></lb><arrow.to.target n="marg179"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000723"><margin.target id="marg178"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000724">Pergamus modò ad poſtremam difficultatem ab <lb></lb>eodem authore allatam. </s> <s id="s.000725">inquit enim: <emph type="italics"></emph>ſint duæ pilæ<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000726"><arrow.to.target n="marg180"></arrow.to.target><lb></lb><emph type="italics"></emph>æneæ, vna ſolida exigui ponderis, altera maioris, ſed reple<lb></lb>ta incluſo aere, hæſine dubio aſcendit ſuper aquam, non <lb></lb>item minor, ſi ergo aqua deorsùm tendens exprimit <expan abbr="alterã">alteram</expan> <lb></lb>pilam, cur non reliquam? </s> <s id="s.000727">non igitur pila mouetur ſursùm, <lb></lb>quia exprimitur, ſed quia in ſe habet aerem natura ſua le<lb></lb>uem.<emph.end type="italics"></emph.end></s> <s id="s.000728"> Et huic profectò argumento nil aliud reſponde<lb></lb>re poſſum, ſed tantùm monere authorem eius ſe noņ <lb></lb><arrow.to.target n="marg181"></arrow.to.target><lb></lb>eſſe ſatis memorem doctrinæ Archimedis, ex quą <lb></lb>deducitur ingentem pilam æneam excauatam, & ae<lb></lb>re plenam minùs ponderare, quàm moles aquæ ei æ<lb></lb>qualis, & ideò grauitas aquæ maior velut in librą <lb></lb>ſursùm eleuare debet minus pondus prædictæ pilæ <lb></lb>æne-aereæ, cum verò comparatur ænea pila ſolida <lb></lb>licèt paruula ſit, illa tamen grauior eſt multò magis, <lb></lb>quàm ſit moles aquæ huic pilulæ æqualis, cùmque <lb></lb>comparatio fieri debeat inter duas moles æquales <lb></lb>ſolidi nempè demerſæ pilæ æneæ <expan abbr="cũ">cum</expan> mole fluidi am<lb></lb>bientis ei æquali, quia exceſſus ponderis penès pi<lb></lb>lam <expan abbr="æneã">æneam</expan> exiſtit, neceſſariò maior eius grauitas præ<lb></lb>ualebit, ideòque mergetur, & ad fundum deſcendet, <lb></lb>ex quo patet prædictum argumentum non probarę <lb></lb>pilam ęne-aeream vim leuitatis in ſe habere. </s> </p> <p type="margin"> <s id="s.000729"><margin.target id="marg180"></margin.target>Eiuſdem <lb></lb>authoris no<lb></lb>ua difficul<lb></lb>tas.</s> </p> <p type="margin"> <s id="s.000730"><margin.target id="marg181"></margin.target>Sed reijci<lb></lb>tur.</s> </p> <p type="main"> <s id="s.000731">Tandem operępretium erit diſſoluere nouas diffi-<pb pagenum="144" xlink:href="010/01/152.jpg"></pb><arrow.to.target n="marg182"></arrow.to.target><lb></lb>cultates à pręclaro authore euulgatas, quę ab hac ex<lb></lb>perientia deſumuntur; ſit fiſtula vitrea RSVX cuius <lb></lb>latitudo ſit duorum, vel trium digitorum, altitudo <lb></lb>verò ſit vnius, vel alterius cubiti, repleaturque aqua, <lb></lb><arrow.to.target n="marg183"></arrow.to.target><lb></lb>ſed remaneat in eius vertice portio aliqua aeris vni<lb></lb>us, vel alterius digiti, poſtea foramine RX perfectè <lb></lb>occluſo, vel palma manus, vel operculo aliquo re<lb></lb>uoluatur fiſtula vt eius infima baſis SV in ſupremolo<lb></lb>co emineat, videbimus aerem è fundo RX ſursùm̨ <lb></lb>aſcendere, atque incuruari ad modum arcus, ex par<lb></lb>te ſuperiori ABC, & è contrà ex parte infima AGC, <lb></lb>aut explanari, vel etiam cauitatem aliquam ad mo<lb></lb>dum ſcutellæ acquirere. </s> <s id="s.000732">Hinc prædictus Author in<lb></lb>fert certè deduci aerem ſursùm in præ<lb></lb><figure id="id.010.01.152.1.jpg" xlink:href="010/01/152/1.jpg"></figure><lb></lb>dicta fiſtula aſcendere propria virtutę <lb></lb>intrinſeca leuitatis non per <expan abbr="extruſionẽ">extruſionem</expan> <lb></lb>factam ab aqua ambiente; quia, inquit <lb></lb>ipſe, <emph type="italics"></emph>aer ſupernè fastigiatur ad modum di<lb></lb>ſculi, vt faciliùs peruadat aquam, & quaſi <lb></lb>perforet illam, quia aer est, qui turgeſcendo <lb></lb>ſursùm aquam introit, & cedere ſibi cogit <lb></lb>quaſi cuneo in illius medio adacto, alio quin <lb></lb>ſi idcircò aer ſursùm tendit quia ab aqua de<lb></lb>orsùm tendente extruditur in ſuperiora, aqua <lb></lb>potiùs peruaderet cuneatim aerem; vt con<lb></lb>tingit in pluuia, vel ſaltem retunderet ſuper<lb></lb>nè illius tumorem, & infernè illum quaſi forcipe <expan abbr="comprimẽs">comprimens</expan> <lb></lb>constringeret ad figuram conoidem eius partem infimam.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.000733"><margin.target id="marg182"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000734"><margin.target id="marg183"></margin.target>Alia argu<lb></lb>menta pro <lb></lb>leuitate po<lb></lb>ſitiua <expan abbr="desũp">desump</expan><lb></lb>ta à pulcher <lb></lb>rimo expe<lb></lb>rimento.</s> </p> <p type="main"> <s id="s.000735">Pro reſolutione harum difficultatum priùs metho-<pb pagenum="145" xlink:href="010/01/153.jpg"></pb><arrow.to.target n="marg184"></arrow.to.target><lb></lb>do generali demonſtrabimus ſuppoſito quòd aer iņ <lb></lb>aqua aſcendat <expan abbr="nõ">non</expan> virtute propriæ leuitatis, ſed per <lb></lb>extruſionem medij fluidi tunc figura aeris <expan abbr="aſcendẽ-tis">aſcenden<lb></lb>tis</expan> per aquam neceſſariò erit conuexa ſupernè, & in<lb></lb>feriùs excauata, & è contrà ſuppoſito quòd aer inter<lb></lb>no principio leuitatis per aquam aſcenderet, deberet <lb></lb>figura aeris aſcendentis tumorem, & rotunditatem̨ <lb></lb>habere tùm ex parte ſuprema, tùm ex parte ſubiecta. </s> </p> <p type="margin"> <s id="s.000736"><margin.target id="marg184"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000737"><emph type="center"></emph>PROP. LXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000738"><emph type="center"></emph><emph type="italics"></emph>Et primo oſtendendum est, quòd quodlibet fluidum intra <lb></lb>aliud fluidum tranſlatum ſiuè virtute propria, ſiuè alie<lb></lb>na violentia impulſum, dummodò eius partes non diſ<lb></lb>ſipentur in ipſo fluido in quo mouetur, ſed ſe <lb></lb>mutuò contingant, & vniantur, neceſſariò <lb></lb>tumorem, & rotundam figuram acqui<lb></lb>ret in parte anteriori mo<lb></lb>tus eius.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000739">QVodlibet fluidum <expan abbr="homogeneũ">homogeneum</expan> naturali inſtin<lb></lb>ctu videtur ſponte coaleſcere, ac ſimul in ſuo <lb></lb>toto partes ſuas conglutinare, vt videmus partes ae<lb></lb>ris libentèr, & auidè viciſſim vniri, & difficiliùs ab <lb></lb>inuicem diſtrahi ſepararique, ſic quoque partes aquę <lb></lb>vniuntur, conglobanturque ſphæricè <expan abbr="quotieſcumq;">quotieſcumque</expan> <lb></lb>ſibi mutuò approximantur, itaut ex duabus guttulis <lb></lb>vna ſuper aliam excurrendo, & ſe mutuò <expan abbr="amplectẽ-do">amplecten<lb></lb>do</expan> vnicam ampliorem guttam <expan abbr="cõſtituant">conſtituant</expan>, eſtque tàm <lb></lb>tenax huiuſmodi vnio, & vinculum partium aquæ, vt <pb pagenum="146" xlink:href="010/01/154.jpg"></pb><arrow.to.target n="marg185"></arrow.to.target><lb></lb>ſi contingat aquæ guttam pendentem diſtrahi ab ali<lb></lb>qua violentia, illa attenuatur, & gracileſcit elonga<lb></lb>turque, & denuò ceſſante violentia reſtringitur re<lb></lb>colligitur, conglobaturque, ſic paritèr videmus a<lb></lb>quam ad membranæ ſubtiliſſimæ <expan abbr="extẽſionem">extenſionem</expan> redigi <lb></lb>circa aerem ſpumam componentem, vnde conſtat <lb></lb>partes aquæ inter ſe viciſſim colligari vinculo <expan abbr="quodã">quodam</expan>: <lb></lb>id ipſum obſeruamus in vitro, & metallis fuſis. </s> <s id="s.000740">Qua<lb></lb>liſcumque igitur ſit cauſa huius vinculi, & tenacita<lb></lb>tis partium homogenearum eiuſdem fluidi, vel quia <lb></lb>ab aliquo glutine, ſeù viſcoſitate vniantur, aut ab <lb></lb>aliqua alia cauſa partes <expan abbr="eiuſdẽ">eiuſdem</expan> fluidi ſe mutuò <expan abbr="am-plexẽtur">am<lb></lb>plexentur</expan>, & <expan abbr="cõnectantur">connectantur</expan>, certum eſt tamen veram eſſe <lb></lb>prædictam vnionem, quotieſcumque fluidum intrą <lb></lb>aliud fluidum alterius naturæ collocatur, vt oleum̨ <lb></lb>intra aquam, vel aer intra quodlibet aliud fluidum, <lb></lb>non diſſipabitur, ſed tenaci quadam vnione conglo<lb></lb>babitur, licet in motu poterit aliquo pacto eius figu<lb></lb>ra rotunda alterari. </s> <s id="s.000741">hoc autem non contingit in om<lb></lb>nibus fluidis cuiuſcumque naturæ ſint, nam aquą <lb></lb>intra vinum, & metalla fuſa inter ſe commixta noņ <lb></lb>ſegregantur; ſed facilè commiſcentur, confundun<lb></lb>turque inter ſe. </s> <s id="s.000742">Et in hiſce aduertendum eſt <expan abbr="adductã">adductam</expan> <lb></lb>experientiam locum non habere, ſed tantummodò <lb></lb>in fluidis priùs expoſitis non homogeneis inter ſe. </s> </p> <p type="margin"> <s id="s.000743"><margin.target id="marg185"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000744">Supponamus igitur fluidum ABC, verbi gratia ae<lb></lb>rem, vel hydrargyrum, moueri vi intrinſeca, vel vio<lb></lb>lenter impulſum in aqua intra fiſtulàm <expan abbr="ſtrictã">ſtrictam</expan> RSVX <lb></lb>contenta à termino B versùs E: & quia ſpatium DN <pb pagenum="147" xlink:href="010/01/155.jpg"></pb><arrow.to.target n="marg186"></arrow.to.target><lb></lb>LF vbi fluidum ABC tranſportari de<lb></lb><figure id="id.010.01.155.1.jpg" xlink:href="010/01/155/1.jpg"></figure><lb></lb>bet, iam repletum, & occupatum eſt <lb></lb>à medio fluido aqueo, hoc autem vt lo<lb></lb>cum cedat ſubintranti fluido ABC, ne<lb></lb>ceſsè eſt vt hinc diſcedat transferatur<lb></lb>que ad <expan abbr="occupãdum">occupandum</expan> illud ſpatium, quod <lb></lb>derelinquitur à fluido ABC, cùmquę <lb></lb>corpus ABC vnionem ſeruet, nec diſſi<lb></lb>petur, igitur anterius medium fluidum <lb></lb>debet per eius latera obliquè excur<lb></lb>rere ad occupandas partes poſticas derelictas à flui<lb></lb>do ABC, ſcilicèt fluidum ENDB mouebitur ad <expan abbr="partẽ">partem</expan> <lb></lb>ſiniſtram versùs A, & medium fluidum BFLE moue<lb></lb>bitur ad partem dexteram versùs C, eruntque prædi<lb></lb>cti motus non æquidiſtantes axi EB, ſed erunt incli<lb></lb>nati per lineas obliquas vt ſunt EA, & EC, & hoc <lb></lb>neceſſitate quadam contingit, quia fluidum è loco <lb></lb>ampliori SEBD <expan abbr="pertrãſire">pertranſire</expan> debet per anguſtam viam <lb></lb>AO, & reliqua fluidi medietas VEBF pariter ab am<lb></lb>plo ſpatio perduci, ac pertranſire debet per ſtrictum <lb></lb>locum CP, & huiuſmodi viæ anguſtæ cùm ſint lateri <lb></lb>vaſis adhærentes, neceſsè eſt vt motus, & fluxus aqua <lb></lb>à ſitu B versùs O, & P obliquo itinere fiat impellen<lb></lb>do, contundendo, & confricando ſuperficiem cor<lb></lb>poris ABC, quod compreſſioni cedit ob eius fluidi<lb></lb>tatem, igitur ABC accommodari debet ſituationi <lb></lb>obliquæ preſſionis corporum excurrentium à ſupre<lb></lb>mo loco B versùs O, & P, quapropter neceſſitatę <lb></lb>quadam acquirit fluidum ABC tumorem, & conuc-<pb pagenum="148" xlink:href="010/01/156.jpg"></pb><arrow.to.target n="marg187"></arrow.to.target><lb></lb>xitarem cuius vertex in parte eius anteriori B exiſtit. <lb></lb></s> <s id="s.000745">Et quia fluidum ABC, vt dictum eſt, diuerſæ naturę, ac <lb></lb>conſiſtentiæ eſt ab ipſo fluido ambiente in quo mo<lb></lb>uetur, ideò non commiſcentur, neque viciſſim <expan abbr="confũ-duntur">confun<lb></lb>duntur</expan> inter ſe, ſed quodlibet eorum ſeruabit vnio<lb></lb>nem, & connexionem ſuarum partium homogenea<lb></lb>rum. </s> <s id="s.000746">Hinc conſtat quòd fluidum ABC dum fertur à <lb></lb>B versùs E, neceſſariò acquirit figuram tumidam, & <lb></lb>acuminatam versùs anteriorem partem motus eius, <lb></lb>& hoc ſemperverificari debet, à quacumque virtute <lb></lb>motiua transferatur, ſiue ab intrinſeca, & naturali, <lb></lb>ſiuè ab externa: & hoc propoſitum fuerat. </s> </p> <p type="margin"> <s id="s.000747"><margin.target id="marg186"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000748"><margin.target id="marg187"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000749"><emph type="center"></emph>PROP. LXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000750"><emph type="center"></emph><emph type="italics"></emph>Poſito quòd fluidum violenter ſursùm exprimatur à fluido <lb></lb>ambiente grauiori, diuerſæque conſistentiæ, infima a<lb></lb>ſcendentis fluidi ſuperficies explanata, vel <lb></lb>concaua erit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.156.1.jpg" xlink:href="010/01/156/1.jpg"></figure> <p type="main"> <s id="s.000751">DEinde fluidum ABC, oleum v. g. <lb></lb>demerſum in fundo alterius flui<lb></lb>di grauioris, & diuerſæ conſiſtentiæ, vt <lb></lb>eſt aqua intra fiſtulam ſtrictam SX con<lb></lb>tenta, & ſuppoſito, quòd idipſum flui<lb></lb>dum ABC non aſcendat in ipſa aqua à <lb></lb>vi natiuæ eius leuitatis translatum, ſed <lb></lb>expulſum per <expan abbr="extruſionẽ">extruſionem</expan> à maiori gra<lb></lb>uitate fluidi aquæ ambientis. </s> <s id="s.000752"><expan abbr="Oſtendẽ-dum">Oſtenden<lb></lb>dum</expan> eſt in hac hypotheſi infimam, & poſticam <expan abbr="partẽ">partem</expan> <pb pagenum="149" xlink:href="010/01/157.jpg"></pb><arrow.to.target n="marg188"></arrow.to.target><lb></lb>AGC eiuſdem olei aſcendentis neceſſariò explana<lb></lb>tam, imò excauatam fore; quia ex hypotheſi pondus <lb></lb>ſpecificum aquæ ambientis ſuperat ſpecificam gra<lb></lb>uitatem olei ABC; iam ſi eſt moles aquæ collateralis <lb></lb>FQPC æqualis medietati olei BGC, proculdubio <lb></lb>aqua FQPC grauior erit oleo BGC, vel ſi moles inę<lb></lb>quales ſunt, aquæ momentum ſuperat olei <expan abbr="momentũ">momentum</expan>, <lb></lb>hiſce verò inæqualibus ponderibus ineumbunt, & <lb></lb>ſubijciuntur moles aquæ æque ponderantes, vel æ<lb></lb>qualium momentorum, ergo in ſiphone compoſito <lb></lb>ex cylindri portione aquea VXKL, & ex cylindri <lb></lb>portione EIKL compoſita ex aqua, & oleo inæqua<lb></lb>liter premuntur partes aquæ ſubiectæ GPXI. quæ li<lb></lb>bram conſtituunt, nempè aqua CPXK maiori niſu <lb></lb>comprimitur ab aqua FQPC, quam aqua GCKI pre<lb></lb>matur ab oleo BGC minus graui, & ideò ex coroll pr. <lb></lb>10. oleum BGC ſursùm impelletur ab aqua ſubiecta <lb></lb>GIKC, & talis expreſſio fiet (ex prop. 51.) tanta vi, <lb></lb>quanta eſt grauitas exceſſus ponderis aquæ FQPC <lb></lb>ſupra grauitatem olei BGC. </s> <s id="s.000753">præterea quia aqua in<lb></lb>ter EB, & LC dum fertur deorſum ad occupandum̨ <lb></lb>ſpatium ab aſcendente oleo derelictum, neceſſariò <lb></lb>comprimit contunditque ſuperficiem collateralem̨ <lb></lb>olei BC non duri, ſed cedentis, eſtque motus obli<lb></lb>quus per ſuperficiem decliuem BC, ergo ſpatium̨, <lb></lb>ſeù alueus, per quod incumbens aqua pertranſirę <lb></lb>debet comprehenſum à ſuperficie aquæ FCK dire<lb></lb>cto, & non impedito motu fluentis, & inclinatam de<lb></lb>cliuemque olei BC ſuperficiem, continentèr magis <pb pagenum="150" xlink:href="010/01/158.jpg"></pb><arrow.to.target n="marg189"></arrow.to.target><lb></lb>conſtringatur anguſteturque, & proinde incumbens <lb></lb>aqua velociori motu, & ideò impetu, & vi maiori <lb></lb>fluere cogatur per anguſtias C, quàm per amplum̨ <lb></lb>alueum <expan abbr="BFQ">BFQ</expan> quare oportet vt vehementiùs, & ma<lb></lb>iori impetu, & vi pars olei versùs C deorsùm com<lb></lb>primatur, contundaturque quàm reliquæ partes olei <lb></lb>propinquiores vertici eius B, è contra aqua ſubiecta <lb></lb>CKIG reflectitur ſursùm, impellit, atque contundit <lb></lb>infimam baſim olei GC ea vi, & impetu quo collate<lb></lb>ralis aqua FCPQ exceſſu ſuæ grauitatis ſuperat ſpe<lb></lb>cificam olei ponderoſitatem. </s> <s id="s.000754">Patet ergo quod à dua<lb></lb>bus viribus <expan abbr="cõtrarijs">contrarijs</expan>, veluti prælo, comprimitur <expan abbr="oleũ">oleum</expan> <lb></lb>BCG ſupernè ab impetu aquæ obliquè deſcenden<lb></lb>tis per BC, & infernè à vi aquæ reflexæ oleum <expan abbr="ſursũ">ſursum</expan> <lb></lb>impellentis, cùmque vis, & compreſſio, quæ ſupernè <lb></lb>infertur, inæqualis ſit, vehementiori, & validiori vi <lb></lb>facta propè terminum C, & debiliori, verſus <expan abbr="verticẽ">verticem</expan> <lb></lb>B, impulſus verò ſubiectæ aquæ IKCG licèt vnifor<lb></lb>mis ſit vbique, nihilominùs propter minorem <expan abbr="deſcẽ-dentis">deſcen<lb></lb>dentis</expan> aquæ obſiſtentiam in B, quàm versùs C ſit <lb></lb>vt vehementiùs oleum impellatur contundaturque à <lb></lb>ſubiecta aqua reflexa versùs axem IG vbi niſum <expan abbr="cõ-trarium">con<lb></lb>trarium</expan> <expan abbr="debiliorẽ">debiliorem</expan> offendit quàm versùs latera A, & <lb></lb>C, & propterea ſuperficies ſubiecta olei AGC exca<lb></lb>uata erit ad modum ſcutellæ, & hoc quidem neceſ<lb></lb>ſariò efficietur non à vi intrinſeca, & naturali leuita<lb></lb>tis ipſius olei, ſed à ſuppoſita energia grauitatis <lb></lb>fluidi ambientis, quod fuerat demonſtrandum. <pb pagenum="151" xlink:href="010/01/159.jpg"></pb><arrow.to.target n="marg190"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000755"><margin.target id="marg188"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000756"><margin.target id="marg189"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000757"><margin.target id="marg190"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000758"><emph type="center"></emph>PROP. LXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000759"><emph type="center"></emph><emph type="italics"></emph>Si fluidum ſponte à virtute intrinſeca intra aliud fluidum <lb></lb>diuerſæ conſistentiæ moueatur, in parte poſteriori, ſeù <lb></lb>termino à quo, ſui motus, non erit excauatum, <lb></lb>ſed tumidam, & conuexam figuram <lb></lb>acquiret.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000760">SVpponamus ſecundo loco fluidum <lb></lb><figure id="id.010.01.159.1.jpg" xlink:href="010/01/159/1.jpg"></figure><lb></lb>ABC, quod ſit aqua, grauius eſſę <lb></lb>ambiente fluido (quod ſit v. g. oleum) <lb></lb>manifeſtum eſt aquam ABCH deorsùm <lb></lb>in oleo deſcendere ab I versùs E ab in<lb></lb>trinſeco principio ſuæ grauitatis impnl<lb></lb>ſum. </s> <s id="s.000761">Dico iam quod eadem aqua in par<lb></lb>te poſtica ſui motus H, ſcilicèt versùs <lb></lb>terminum à quo ſui motus, non erit ex<lb></lb>cauata ad modum ſcutellæ, ſed tumida, & conuexa <lb></lb>erit. </s> <s id="s.000762">Quia cum primo aqua ABCH demergitur in<lb></lb>fra olei <expan abbr="libellã">libellam</expan> RX, & inchoat proſequiturque ſuum <lb></lb><expan abbr="deſcẽſum">deſcenſum</expan>, neceſsè eſt vt oleum ſubiectum AEC è ſuo <lb></lb>loco continenter recedat, & recurrat ad replen<lb></lb>dum locum poſticum AMKC ab aqua derelictum; er<lb></lb>go aqua AHCB, & oleum ambiens motibus contra<lb></lb>rijs agitari debent, nempe aqua deſcendet dum am<lb></lb>biens oleum aſcendit, igitur ratione motus, oleum̨ <lb></lb>poſticè recurrens non impellet aquam ictum fugien<lb></lb>tem, nec proinde eius figuram AHC contundere, & <lb></lb>explanare poterit. </s> <s id="s.000763">præterea aqua ABCH habet vim <pb pagenum="152" xlink:href="010/01/160.jpg"></pb><arrow.to.target n="marg191"></arrow.to.target><lb></lb>ſe mouendi deorsùm in oleo, hoc verò nullam facul<lb></lb>tatem ſe mouendi deorsùm in <expan abbr="eodẽ">eodem</expan> oleo habet, <expan abbr="cũ">cum</expan> in <lb></lb>fluido ſui generis iners æquilibretur, ergo hoc nomi<lb></lb>ne pariter aqua ictum fugiens, immò non impulſą, <lb></lb>nec percuſſa ab oleo poſticè recurrente non poterit <lb></lb>contundi, nec explanari, & hoc experientia patet, <lb></lb>nam ſi pila dura capillitium è filis ſericis tenuiſſimis <lb></lb>ſibi annexum habuerit, & intra aquam filo deorsùm, <lb></lb>ſursùm, vel lateraliter trahatur nunquam poſticum <lb></lb>capillitium contundetur explanabiturque, dum vni<lb></lb>formi, non verò retardata velocitate pila in aquą <lb></lb>mouetur. </s> <s id="s.000764">& ab hac experientia luculenter euinci<lb></lb>tur ſomnium illorum, qui aiunt ad vitandum <expan abbr="vacuũ">vacuum</expan> <lb></lb>rapidiſſimo motu oleum poſticè recurrere, & ſic poſ<lb></lb>ſe aquæ ſuperficiem contundere, & explanare. </s> <s id="s.000765">Qua<lb></lb>propter aqua excepto ſimplici contactu in ſuperficie <lb></lb>AHC nullam contuſionem, aut percuſſionem patie<lb></lb>tur ab oleo ſuperincumbente MACK, igitur neceſsè <lb></lb>eſt vt aqua in AHC retineat eamdem figuram, quam <lb></lb>priùs habebat, ſed eius figura intra oleum vnita, & <lb></lb>contornata eſſe ſolet ob naturalem partum eius con<lb></lb>nexionem, & vinculum, & ob compreſſionem vn<lb></lb>dequaque factam à fluido ambiente, vt dictum eſt. <lb></lb></s> <s id="s.000766">igitur dum aqua ABC deſcendit intra oleum poſtre<lb></lb>ma eius baſis AHC, ſcilicèt versùs terminum à quo <lb></lb><arrow.to.target n="marg192"></arrow.to.target><lb></lb>motus inchoat, eius figura debet eſſe tumida con<lb></lb>uexa, & contornata, cum è contra eadem aqua <expan abbr="aſcẽ-dens">aſcen<lb></lb>dens</expan> intra mercurium ſi extruderetur à fluido ambi<lb></lb>ente neceſſariò eius poſtica baſis versùs principium <pb pagenum="153" xlink:href="010/01/161.jpg"></pb><arrow.to.target n="marg193"></arrow.to.target><lb></lb>motus non tumida, ſed excauata eſſe debuerat, & <lb></lb>hæc omnia oſtendenda fuerant. </s> </p> <p type="margin"> <s id="s.000767"><margin.target id="marg191"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000768"><margin.target id="marg192"></margin.target>Ex prop. 73.</s> </p> <p type="margin"> <s id="s.000769"><margin.target id="marg193"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000770"><emph type="center"></emph>PROP. LXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000771"><emph type="center"></emph><emph type="italics"></emph>Si fluidum à principio intrinſeco moueatur intra aliud flui<lb></lb>dum diuerſæ conſistentiæ, quod valdè rarefieri, & con<lb></lb>denſari queat, tunc multò magis tumida efficie<lb></lb>tur pars postica fluidi decurrentis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000772">ET hoc quidem verum eſt quando fluidum am<lb></lb>biens, in quo aliud fluidum mouetur ſursùm, <lb></lb>vel deorsùm, non patitur ſenſibilem <expan abbr="condenſationẽ">condenſationem</expan>, <lb></lb>vel rarefactionem, veluti eſt oleum, aut aqua; at ſi <lb></lb>valdè rarefiat condenſeturque, vt aer propter velo<lb></lb>ciſſimum caſum aquæ AHCB remanet aer poſticus <lb></lb>MACK valdè rarefactus, ideoque inhabilis vt inſe<lb></lb>qui poſſit aquam cadentem, & proindè nedùm aer <lb></lb>incumbens guttam aquæ deſcendentem in H noņ <lb></lb>percutiet, cùm è contrà, ne ibidem, (vt vulgò credi<lb></lb>tur) vacuum remaneat eius vertex tumidus H valdè <lb></lb>eleuabitur <expan abbr="prominebitq;">prominebitque</expan> & ſic videmus guttas plu<lb></lb>uiales ſecum trahere veluti caudam aqueam <expan abbr="gracilẽ">gracilem</expan>, <lb></lb>tantùm abeſt vt poſticè contuſionem patiantur, aut <lb></lb>excauentur, & hoc clariùs percipitur ſi pila aliquą <lb></lb>lignea, & dura, quæ habeat comam ex filamentis, ſeù <lb></lb>pilis exiliſſimis, & nullius ferè ponderis compoſitam <lb></lb>cadat deorsùm in aere, tunc enim pili ſupremi aſſur<lb></lb>gunt efficiuntque veluti caudam fluctuantem, non <lb></lb>autem comprimuntur contundunturque versùs ſu-<pb pagenum="154" xlink:href="010/01/162.jpg"></pb><arrow.to.target n="marg194"></arrow.to.target><lb></lb>premam partem ipſius pilæ, quod eſt ſignum euidens <lb></lb>nullam vim compreſſiuam pati ab aere ſuperincum<lb></lb>bente. </s> </p> <p type="margin"> <s id="s.000773"><margin.target id="marg194"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000774"><emph type="center"></emph>PROP. LXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000775"><emph type="center"></emph><emph type="italics"></emph>Si oleum, vel aer aſcenderet in aqua ſponte à vi ſuæ leui<lb></lb>tatis impulſus non poſſet eius baſis excauari ad inſtar <lb></lb>ſcutellæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000776">TAndem demonſtrandum eſt po<lb></lb><figure id="id.010.01.162.1.jpg" xlink:href="010/01/162/1.jpg"></figure><lb></lb>ſito, quòd aer, vel oleum ABCH <lb></lb>aſcenderet in ipſa aqua à propria, & <lb></lb>intrinſeca virtute leuitatis impulſum, <lb></lb>quod eſſet abſolutè impoſſibile, vt e<lb></lb>ius baſis infima excauata eſſet ad mo<lb></lb>dum ſcutellæ; quia ex aduerſarij hypo<lb></lb>theſi oleum ABCH aſcendit in aqua contenta in fi<lb></lb>ſtula ſtricta RSVX propria virtute leuitatis ab I ver<lb></lb>sùs E, nec ab aqua infima impellitur exprimiturque <lb></lb>ſursùm, ergò aqua MACK, quæ currit ad <expan abbr="replendũ">replendum</expan> <lb></lb>ſpatium derelictum ab oleo cum ſit ex ſui natura gra<lb></lb>uis exercet vim ſui ponderis ab H verſus I premen<lb></lb>do præcisè ſuper <expan abbr="fundũ">fundum</expan> vitri RX, & nullo pacto vim <lb></lb>exercere poteſt ſursùm ab l versùs H, hoc enim eſſet <lb></lb>contra grauium naturam, & contra ipſam aduerſarij <lb></lb>hypotheſim. </s> <s id="s.000777">Præterea quia oleum ABCH, & aqua <lb></lb>ambiens motibus contrarijs agitari debent, nempè <lb></lb>oleum, vt leue, aſcendet dum aqua ambiens <expan abbr="deſcẽ-det">deſcen<lb></lb>det</expan>, igitur non ſibi occurrunt, & aduerſantur, ſed ab <pb pagenum="155" xlink:href="010/01/163.jpg"></pb><arrow.to.target n="marg195"></arrow.to.target><lb></lb>inuicem conantur recedere; quare ratione motus <lb></lb>aqua inferiùs, & poſticè recurrens non impellet <expan abbr="oleũ">oleum</expan> <lb></lb>ictum fugiens, nec proindè eius figuram AHC <expan abbr="cõ-tundere">con<lb></lb>tundere</expan>, & explanare poteſt. </s> <s id="s.000778">Igitur in hoc caſu duo <lb></lb>impetus inter ſe contrarij, & ab inuicem receden<lb></lb>tes reperiuntur leuitatis olei, nimirùm, ſursùm ab H <lb></lb>versùs E, aquæ verò conatus inferiùs tendentis ab <lb></lb>H versùs I, igitur hæc duo corpora oleum AHCB, <lb></lb>& aqua ſubiecta MACK ſe mutuò tantummodò tan<lb></lb>gent placidiſſimo amplexu abſque vlla pugna, & re<lb></lb>pulſu, vt nimirùm aqua oleum non impellat, neque <lb></lb>hoc illam repellat, igitur oleum ABCH multò minùs <lb></lb>comprimi, ac contundi debetin H ab aqua ſubie<lb></lb><arrow.to.target n="marg196"></arrow.to.target><lb></lb>cta deorsùm premente, quàm contundebatur poſticè <lb></lb>ab oleo incumbente, quando nimirum intra oleum̨ <lb></lb>deſcendebat, & pondus eiuſdem olei incumbentis <lb></lb>patiebatur (in vtroque enim caſu recurſus fluidi ad <lb></lb>ſpatium replendum æquè reperitur, & proindè ne<lb></lb>que nocet, neque adiuuat prædictum effectum) ſed <lb></lb>ex antepræmiſſa propoſitione aqua per oleum deci<lb></lb>dens à vi natiua grauitatis impulſa retinet tumorem <lb></lb>eleuationemque <expan abbr="cõuexam">conuexam</expan> in poſtica parte eius mo<lb></lb>tus, igitur multò magis eleuari deberet tumor iņ <lb></lb>oleo per aquam aſcendente in parte poſteriore mo<lb></lb>tus eius ſi ab intrinſeca leuitate eleuaretur, qua pro<lb></lb>ptèr erit omninò impoſſibile, vt oleum, vel aer dum <lb></lb>aſcendit per aquam, excauetur in parte infima eius <lb></lb>baſis, <expan abbr="quãdo">quando</expan> nimirùm ſursùm fertur ab interno prin<lb></lb>cipio leuitatis, quod demonſtrandum fuerat. <pb pagenum="156" xlink:href="010/01/164.jpg"></pb><arrow.to.target n="marg197"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000779"><margin.target id="marg195"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000780"><margin.target id="marg196"></margin.target>In prop. 74.</s> </p> <p type="margin"> <s id="s.000781"><margin.target id="marg197"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000782">His præmiſſis examinari modò debent ſigillatim̨ <lb></lb>oppoſitiones ſuperiùs adductæ. </s> </p> <p type="main"> <s id="s.000783"><emph type="center"></emph>PROP. LXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000784"><emph type="center"></emph><emph type="italics"></emph>Et primo loco dieo, quòd figura inflata, conuexa, & acumi<lb></lb>nata quam aer acquirit in fiſtula aqua plena in parte an<lb></lb>teriori eius motus dum ſursùm aſcendit, non eſt argu<lb></lb>mentum efficax, & euincens aerem ſursùm <lb></lb>moueri à principio intrinſeco ſuæ <lb></lb>leuitatis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000785">QVia demonſtratum eſt corpora fluida <expan abbr="cedẽtia">cedentia</expan>, </s> </p> <p type="main"> <s id="s.000786"><arrow.to.target n="marg198"></arrow.to.target><lb></lb>& homogenea ſi moueantur intra aliud cor<lb></lb>pus Huidum ſiue propria, & intrinſeca virtute moti<lb></lb>ua, ſiue ab impulſu facto à cauſa extrinſeca, aut ab <lb></lb>ipſo medio, neceſſariò in anteriori parte motus il<lb></lb>lius tume fieri, contornari, & aliquantiſper acumina<lb></lb>ri debere, quaproptèr tumor, qui in aere aſcenden<lb></lb>te per aquam obſeruatur, neque iuuat, neque nocet, <lb></lb>nec ſuadet, neque diſſuadet leuitatem poſitiuam̨. <lb></lb></s> <s id="s.000787">Mirum tamen eſt non animaduerſam fuiſſe cauſam <lb></lb>cauitatis eiuſdem aeris in parte poſtica eius motus, <lb></lb>à qua cauitate, ſicut oſtenſum eſt, euidentèr deduci<lb></lb>tur impoſſibile eſſe aerem ab intrinſeco principio le<lb></lb>uitatis ſursùm ferri, ſed potiùs per <expan abbr="extruſionẽ">extruſionem</expan> me<lb></lb>dij fluidi ſursùm eleuari. </s> </p> <p type="margin"> <s id="s.000788"><margin.target id="marg198"></margin.target>Prop. 72.</s> </p> <p type="main"> <s id="s.000789">Cùm poſtea inſtat aduerſarius aerem, dum per a<lb></lb>quam aſcendit, acumen eius ſursùm porrigere, vt fa<lb></lb>ciliùs terebrare, & perforare aquam vi ſuæ leuitatis <pb pagenum="157" xlink:href="010/01/165.jpg"></pb><arrow.to.target n="marg199"></arrow.to.target><lb></lb>poſſit. </s> <s id="s.000790">Hoc profectò negatur, quia licèt aer non ſit <lb></lb>leuis, ſed per extruſionem à medio fluido ſursùm̨ <lb></lb>expellatur, efformare debet quoque eminentiam il<lb></lb>lam contornatam, & acuminatam, vt demonſtratum <lb></lb>eſt. </s> </p> <p type="margin"> <s id="s.000791"><margin.target id="marg199"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000792">Sed vtile erit parumpèr circumſtantias huius ex<lb></lb><arrow.to.target n="marg200"></arrow.to.target><lb></lb>perientię accuratiùs perpendere, inquit enim, <emph type="italics"></emph>par<lb></lb>tem fistulæ ſuperiorem conuerte deorsùm, & erige fiſtulam <lb></lb>perpendicularitèr ad horizontem, videbis enim aerem, qui in <lb></lb>fundo fiſtulæ habuerat formam cylindri occupantem totam <lb></lb>cauitatem fistulæ in latum mox aſcendere, & ſic aſcendere, <lb></lb>vt ſe coarctans extendat in longum, & ſuperiorem cylindri <lb></lb>illius ſuperficiem, quæ plana erat ad modum diſculi, iam <lb></lb>conoidem factam eſſe.<emph.end type="italics"></emph.end></s> <s id="s.000793"> Itaque hic author <lb></lb><figure id="id.010.01.165.1.jpg" xlink:href="010/01/165/1.jpg"></figure><lb></lb>cenſet quòd <expan abbr="quãdo">quando</expan> fiſtula RV <expan abbr="perpẽ-dicularitèr">perpen<lb></lb>dicularitèr</expan> ad <expan abbr="horizõtem">horizontem</expan> eleuatur, ae<lb></lb>rem ROPX, quidum ſupernè conſiſte<lb></lb>bat cylindricam formam habebat, <expan abbr="etiã">etiam</expan> <lb></lb>in hoc ſitu infimo perſeuerare poſſę <lb></lb>per aliquod tempus in eadem figurą <lb></lb>cylindrica, quod profectò ſi verum eſ<lb></lb>ſet non facilè reddi ratio poſſet quare, & quemad<lb></lb>modum à compreſſione aquæ <expan abbr="ſuperincumbẽtis">ſuperincumbentis</expan> pla<lb></lb>na aeris ſuperficies OP efficiatur tumida, & conue<lb></lb>xa, veluti eſt ABC. </s> <s id="s.000794">Alia igitur longè diuerſa ratione <lb></lb>res ſe habet. <pb pagenum="158" xlink:href="010/01/166.jpg"></pb><arrow.to.target n="marg201"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000795"><margin.target id="marg200"></margin.target>Circumſtan<lb></lb>tia notatu di<lb></lb>gna in tali <lb></lb>experimen<lb></lb>to affertur <lb></lb>ab aduerſa<lb></lb>rio.</s> </p> <p type="margin"> <s id="s.000796"><margin.target id="marg201"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000797"><emph type="center"></emph>PROP. LXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000798"><emph type="center"></emph><emph type="italics"></emph>Cauſa ſeparationis aerei cylindri è fundo vaſis eſt pondus <lb></lb>aquæ ambientis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000799">INtelligatur denuò fiſtula RV plena aqua, in quą <lb></lb>exiſtat aereus cylindrus PORX in parte eius ſu<lb></lb><figure id="id.010.01.166.1.jpg" xlink:href="010/01/166/1.jpg"></figure><lb></lb>prema operculo XR <lb></lb>clauſa, poſtea circa <expan abbr="pũ-ctum">pun<lb></lb>ctum</expan> V <expan abbr="fixũ">fixum</expan> reuolua<lb></lb>tur <expan abbr="deorsũ">deorsum</expan> fiſtula <expan abbr="trãſ-ferendo">tranſ<lb></lb>ferendo</expan> nimirùm latus <lb></lb>VX in locis VF, VG, <lb></lb>VH, & VK, <expan abbr="manifeſtũ">manifeſtum</expan> <lb></lb>eſt, quod in ſitu VF pro<lb></lb>pter vaſis <expan abbr="inclinationẽ">inclinationem</expan> <lb></lb>ſuperficies PO aquæ <lb></lb>POSV non perſeuera<lb></lb>bit in eodem ſitu incli<lb></lb>nato, cùm aqua natura<lb></lb>li inſtinctu æquabili ſi<lb></lb>tu ad horizontem parallelo diſponi, redigique de<lb></lb>beat, quaproptèr à ſitu decliui PO deſcendet inferiùs <lb></lb>versùs ſuperficiem BDA horizonti parallelam, veluti <lb></lb>exigit ſitus, & pendentia fiſtulæ VFR. </s> <s id="s.000800">Hinc ſequi<lb></lb>tur, vt aqua excurrat ad occupandum <expan abbr="ſpatiũ">ſpatium</expan> ODAR, <lb></lb>à quo aer expulſus deueniet ad replendum ſpatium <lb></lb>ſupremum ab aqua derelictum, ſcilicèt PEBD. </s> <s id="s.000801">Pro<lb></lb>grediamur modò ad ſituationem fiſtulæ <expan abbr="horizontalẽ">horizontalem</expan> <pb pagenum="159" xlink:href="010/01/167.jpg"></pb><arrow.to.target n="marg202"></arrow.to.target><lb></lb>VG multò magis aqua inſinuabitur infra aerem dila<lb></lb>tando ſinum ampliorem ODAIR, & multò magis<lb></lb>incuruabitur aeris ſuperficies EBD, tum à vi qua flui<lb></lb>da ſe ſe connectunt conglobanturque, quotieſcum<lb></lb>que in fluido ipſis hetherogeneo <expan abbr="collocãtur">collocantur</expan>, cùm ab <lb></lb>acceſſu noui aeris expulſi à cauitate infima DAIRO. <lb></lb></s> <s id="s.000802">Poftquàm verò magis fiſtula deprimitur in ſitu val<lb></lb>dè inclinato VH eadem ratione profluet aqua versùs <lb></lb>partem infimam, & omninò aerem ſeparabit, diuel<lb></lb>letque à fundo vaſis, & proindè ſubintrabit ad oc<lb></lb>cupandum ſpatium ODAICHR. </s> <s id="s.000803">Poſtremò perdu<lb></lb>cta fiſtula ad inclinationem omnium maximam iņ <lb></lb>ſitu VK perpendiculari ad <expan abbr="horizontẽ">horizontem</expan> aqua, quæ iam <lb></lb>inſinuata fuerat circa, & infra aerem tumefactum, & <lb></lb>contornatum EBDC, <expan abbr="tãdèm">tandèm</expan> omninò aerem à fundo, <lb></lb>& lateribus vaſis diuellet, & proindè multò magis <lb></lb>deſcenſus, & compreſſio aquæ ambientis per latera <lb></lb>vaſis, & aeris continuari poteſt; & vniuerſa hæc o<lb></lb>peratio pendet, vt dictum eſt, non ab aere ſpontę <lb></lb>aſcendente, neque ab eius leuitate, ſed ab exceſſu <lb></lb>grauitatis fluidæ aquæ ambientis, quæ in vertigine <lb></lb>fiſtulæ neceſſariò ſeparat, atque diuellit aerem à la<lb></lb>teribus, & fundo vaſis, & ſic via ſternitur commodiſ<lb></lb>ſima, vt continuari, & proſequi preſſio aquæ poſſit, <lb></lb>vnde aer ſursùm expulſus continuare poteſt eius cur<lb></lb>ſum, ſi, inquam, hoc obſeruatum, & adnotatum fuiſ<lb></lb>ſet, proculdubiò ex mutatione figuræ planæ in tumi<lb></lb>dam in aere aſcendente per aquam non deduxiſſet <lb></lb>prædictus author aeris leuitatem poſitiuam. <pb pagenum="160" xlink:href="010/01/168.jpg"></pb><arrow.to.target n="marg203"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000804"><margin.target id="marg202"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000805"><margin.target id="marg203"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000806">Sed poſito quòd in vehementiſſima turbinatione <lb></lb>retineretur pauliſpèr aqua adhærens fundo ſupremo <lb></lb>fiſtulæ, & proinde aer infimus ſaltem per <expan abbr="breuiſſimũ">breuiſſimum</expan> <lb></lb>ſpatium cylindricam formam ORXP retineret, mani<lb></lb>feſtum eſt, quòd ſubito ceſſante impetu aqua vt gra<lb></lb>uior aere deorsùm deſcenderet, labereturque, aut <lb></lb>in loco intermedio fiſtulæ, aut ad latera, prout vndu<lb></lb>latio partium aquæ eam promoueret, & ſic ſemper à <lb></lb>deſcenſu grauioris aquę figura tumida, & conuexa <lb></lb>aeris aſcendentis crearetur, numquam verò ſpontę <lb></lb>ab ipſa leuitate aeris. </s> </p> <p type="main"> <s id="s.000807"><arrow.to.target n="marg204"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000808"><margin.target id="marg204"></margin.target>Reſponde<lb></lb>tur ſingulis <lb></lb>oppoſitioni<lb></lb>bus aduer<lb></lb>ſarij.</s> </p> <p type="main"> <s id="s.000809">Cùm verò inſtat: <emph type="italics"></emph>Si idcircò aer ſursùm tendit, quia ab <lb></lb>aqua deorsùm tendente extruditur in ſuperiora aqua potiùs <lb></lb>peruaderet cuneatim aerem, quem admodum aqua <expan abbr="decidẽs">decidens</expan> <lb></lb>extra fistulam ſubiectum aerem perrumpit, non verò illum <lb></lb>ambiens intra ſe recipit.<emph.end type="italics"></emph.end></s> <s id="s.000810"> Hic primò noto, quòd non <expan abbr="sẽ-per">sem<lb></lb>per</expan> aqua cadens aerem penetrat, nam multoties <lb></lb>penetratur ab ipſo aere quando nimirùm ſcinditur <lb></lb>in plures partes, vt contingit in pluuia, vel potiùs <lb></lb>quando è feneſtra catino aqua proijcitur. </s> </p> <p type="main"> <s id="s.000811">Sic paritèr maſſa pulueris terreſtris è turris verti<lb></lb>ce proiecta licèt in principio ſit vnita, nihilominùs <lb></lb>ab aere diſſipatur, diſpergiturque, idemque accidit <lb></lb>in fumo aſcendente per aerem. </s> <s id="s.000812">Secundò noto, quòd <lb></lb>partes aeris, vt dictum eſt, ſponte ſua connectuntur <lb></lb>colliganturque inter ſe, & proinde intra aquam po<lb></lb>ſitæ omnes vniri debent, atque ſimùl, conglobatæ <lb></lb>per aquam aſcendent, non ſecùs, ac partes aquæ in<lb></lb>tra aerem, vel oleum viciſſim vniuntur, congloban- <pb pagenum="161" xlink:href="010/01/169.jpg"></pb><arrow.to.target n="marg205"></arrow.to.target><lb></lb>turque. </s> <s id="s.000813">Et tunc ſolummodò ab inuicem ſegregantur <lb></lb>ſubdiuidunturque, quando medium fluidum vehe<lb></lb>menti, & irregulari motu fluidum per ipſum aſcen<lb></lb>dens, vel deſcendens perrumpit diuiditque, ſeù quia <lb></lb>non omnes partes prædicti fluidi excurrentis æquali <lb></lb>impetu mouentur, vel quia laterales partes fluidi ab <lb></lb>aſperitatibus, & contactibus laterum fiſtulæ retar<lb></lb>dantur, ſeù ab aliqua alia cauſa detinentur: nil igitur <lb></lb>ex hoc pro leuitate poſitiua acquiritur. </s> </p> <p type="margin"> <s id="s.000814"><margin.target id="marg205"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000815">Subdit poſtea idem author, quòd <emph type="italics"></emph>aqua ſupernè re<lb></lb>tunderet aeris tumorem, & infernè illum, quaſi forcipe <lb></lb>comprimens, conſtringeret ad figuram conoidem eius partem <lb></lb>infimam.<emph.end type="italics"></emph.end></s> <s id="s.000816"> Reſpondetur hoc falſum eſſe, quia vt iam̨ <lb></lb>demonſtratum eſt nunquam figura aeris per aquam <lb></lb>aſcendentis acuminata in eius infima parte effici poſ<lb></lb>ſet, ſed neceſsè eſt, vt ab impulſu facto ab aqua gra<lb></lb>uiori ibidem excauetur ad modum ſcutellæ, & prop<lb></lb>ter occurſum, & obſtaculum aquæ ſupremæ dum aer <lb></lb>fluidus aſcendit tumorem, & conuexitatem ſuper<lb></lb>nè acquirat. </s> </p> <p type="main"> <s id="s.000817">Cùm verò idem author ſubdit, quod <emph type="italics"></emph>ſi caſu copule<lb></lb>tur particula aliqua aeris cum oleo per aquam aſcendente, <lb></lb>conſtat quòd huiuſmodi aggregatum velociùs aſcendit per <lb></lb>aquam.<emph.end type="italics"></emph.end> <expan abbr="Nõ">non</expan> video quidnam ex hoc deduci poſſit pro <lb></lb>leuitate poſitiua, imò nego quod <emph type="italics"></emph>non posſit reddi phy<lb></lb>ſica, & ſolida ratio cur velociùs moueatur coniunctum il<lb></lb>lud ex oleo, & aere, quàm oleum ſolum.<emph.end type="italics"></emph.end></s> <s id="s.000818"> Et poſtea: <emph type="italics"></emph>neque <lb></lb>aquam citiùs deſcendendo expellere quoque citiùs oleum <lb></lb>ſursùm cum nec maior moles ſit aquæ ſupra <expan abbr="oleũ">oleum</expan>, quàm an-<emph.end type="italics"></emph.end><pb pagenum="162" xlink:href="010/01/170.jpg"></pb><arrow.to.target n="marg206"></arrow.to.target><lb></lb><emph type="italics"></emph>tea.<emph.end type="italics"></emph.end></s> <s id="s.000819"> Primò aio nil referre an moles aquæ ſit maior, <lb></lb>aut minor reſpectu olei, & aeris, ſed ſufficit vt gra<lb></lb>uitas ſpecifica aquæ, multò maior ſit reſpectu aggre<lb></lb>gati ex aere, & oleo, quàm reſpectu ſolius olei, ita<lb></lb>que in caſu noſtro moles aquæ, ſiue magna, ſiue exi<lb></lb>gua, in fiſtula poteſt comparari cum oleo tantùm, vel <lb></lb>cum aggregato ex oleo, & aere; modò ex Archime<lb></lb>dis doctrina eadem aqua grauior eſt ſpecie aggre<lb></lb>gato ex oleo & aere, quàm oleo ſolitario, & quò ma<lb></lb>ior fuerit differentia grauitatum ſpecificarum, tantò <lb></lb>maior, cęteris paribus, eſt velocitas mobilis in fluido, <lb></lb>& hinc <expan abbr="cõſtat">conſtat</expan> quòd ea quæ adducta ſunt, vt maximè <lb></lb>abſurda <expan abbr="nedũ">nedum</expan> inconuenientia non ſunt, ſed è contrà <lb></lb>neceſſitate mechanica contingere debent. </s> <s id="s.000820">Poſtremæ <lb></lb>oppoſitioni, vbi ait: <emph type="italics"></emph>Nec denique dici poteſt coniunctum <lb></lb>ex oleo, & aere eſſe aliquid leuius, quàm aquæ alterum <expan abbr="tã-tum">tan<lb></lb>tum</expan> in eadem mole, ideoque aquam illud magis in grauita<lb></lb>te excedere, quàm oleum ſeorsùm ſumptum, & proindè ci<lb></lb>tiùs illius locum occupare velle; nam ſi non datur leuitas, <lb></lb>& particula aeris habet aliquid grauitatis potiùs ex illa, & <lb></lb>oleo factum est corpus grauius, quàm est ſolum oleum.<emph.end type="italics"></emph.end></s> <s id="s.000821"> Et <lb></lb>hic nil aliud reſpondere poſſum, niſi quòd huiuſmo<lb></lb>di ratiocinia condonari poſſunt ijs, qui in doctriną <lb></lb>Archimedis minimè verſati ſunt. </s> <s id="s.000822">Affertur enim, vt <lb></lb>abſurdum, quòd aggregatum ex oleo, & aere grauius <lb></lb>ſit abſolutè ſolo oleo, quod profectò non negatur, eſt <lb></lb>enim veriſſimum, ſed tamen animaduertendum eſt, <lb></lb>quod licèt prædictum aggregatum ex oleo, & aerę <lb></lb>grauitate abſoluta magis ponderet, quàm oleum per <pb pagenum="163" xlink:href="010/01/171.jpg"></pb><arrow.to.target n="marg207"></arrow.to.target><lb></lb>ſe ſumptum, tamen ſi grauitas ſpecifica conſidere<lb></lb>tur, erit aggregatum ex oleo, & aere minùs graue, <lb></lb>quàm oleum ſolum, quia nempè pondus aggregati <lb></lb>ex oleo & aere, minorem proportionem habet ad <lb></lb>grauitatem molis aqueæ ei æqualis, quàm pondus <lb></lb>ſolius olei habeat ad <expan abbr="grauitatẽ">grauitatem</expan> aquæ molis prædicto <lb></lb>oleo æqualis, ſcilicèt ſi aggregati ex oleo, & aere <lb></lb>grauitas ſubdupla fuerit pondere molis aquæ ſibi æ<lb></lb>qualis, pondus olei ſolius maius erit medietate <expan abbr="põ-deris">pon<lb></lb>deris</expan> molis aquæ oleo æqualis, & hinc ſit vt maiori <lb></lb>impetu ſursùm per expreſſionem impellatur aggre<lb></lb>gatum ex oleo & aere à ſuperabundanti grauitate <lb></lb>aquæ circumfuſæ, quæ maiori differentia ſpecificam <lb></lb>grauitatem eius ſuperat, quàm moueatur oleum ſur<lb></lb>sùm extruſum à pondere minùs excedenti eiuſdem̨ <lb></lb>aquæ ambientis. </s> <s id="s.000823">Et hoc quidem ſi ritè percipiatur, <lb></lb>tollentur, & euaneſcent omnes difficultates, quæ <lb></lb>contra prædictam doctrinam afferri poſſunt. </s> </p> <p type="margin"> <s id="s.000824"><margin.target id="marg206"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000825"><margin.target id="marg207"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000826">Præter ea, quæ iam dicta ſunt affert idem author <lb></lb>alia experimenta ex quibus putat euidentèr deduci <lb></lb><arrow.to.target n="marg208"></arrow.to.target><lb></lb>poſſe exiſtentiam leuitatis poſitiuæ, quia inquit: <lb></lb><emph type="italics"></emph>Cylindrus ligneus è fundo aquæ ſursùm tanto impetu fertur <lb></lb>vt multotiès exiliat totus ſupra aquam ille igitur ſaltus in<lb></lb>dicium eſt impetus ab intrinſeca leuitate facti, quia aqua <lb></lb>non poteſt illud vltrà trudere quam ſit ipſi opus vt locum <lb></lb>inferiorem occupet niſi ipſa ſursùm priùs feratur, quod eſt <lb></lb>contra ipſius grauitatem.<emph.end type="italics"></emph.end><pb pagenum="164" xlink:href="010/01/172.jpg"></pb><arrow.to.target n="marg209"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000827"><margin.target id="marg208"></margin.target>Noua <expan abbr="argu-mẽta">argu<lb></lb>menta</expan> eiuſd<expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>Authoris <lb></lb>pro leuitate <lb></lb>poſitiua.</s> </p> <p type="margin"> <s id="s.000828"><margin.target id="marg209"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000829"><emph type="center"></emph>PROP. LXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000830"><emph type="center"></emph><emph type="italics"></emph>Lignum in aqua aſcendens ſaltu ſupra eius libellam exilit <lb></lb>ob impetum acquiſitum in præcedenti motu, licèt per <lb></lb>extruſionem fiat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000831">PRo reſponſione ponamus cylindrum ligneum in <lb></lb>fundo aquæ. </s> <s id="s.000832">Dico quòd ſi id moueatur ſursùm <lb></lb>ab intrinſeca vilenitatis, vel ab extruſione medij flui<lb></lb>di aquei, neceſſariò velocitas eius dum aſcendit <expan abbr="cõ-tinentèr">con<lb></lb>tinentèr</expan> augebitur, quia dum ſursùm <expan abbr="aſcẽdit">aſcendit</expan> in quo<lb></lb>libet temporis inſtanti, eadem virtus motiua, aut le<lb></lb>uitatis, aut externi impulſus, quæ ſemper eadem, & <lb></lb>eiuſdem energiæ eſt, pariterque extruſio à medio <lb></lb>fluido paritèr efficitur ab eadem virtute impulſiua, <lb></lb>quæ eſt differentia, vel exceſſus ponderis aquæ ſu<lb></lb>pra pondus ligni aſcendentis, cùmque gradus velo<lb></lb>citatum à ligno acquiſiti ob impulſiones ei illatas <expan abbr="nõ">non</expan> <lb></lb>ſubitò extinguantur, ſed perſeuerent, vt dictum eſt, <lb></lb>igitur ſubſequentes impulſiones imprimuntur ei mo<lb></lb><arrow.to.target n="marg210"></arrow.to.target><lb></lb>bili non inerti, ſed iam agitati à præcedentibus im<lb></lb>preſſis velocitatibus, & proindè ſucceſſiuo incre<lb></lb>mento augebitur gradus impetus eiuſdem ligni <expan abbr="aſcẽ-dentis">aſcen<lb></lb>dentis</expan>. </s> <s id="s.000833">Igitur mirum non eſt, cylindrum ligneum̨, <lb></lb>quando iam acquiſiuit inſignem gradum impetus à <lb></lb>continuato impulſu, & preſſione aquæ circumfuſæ, <lb></lb>ſiuè ab interna eius leuitate poſitiua, mirum, <expan abbr="inquã">inquam</expan>, <lb></lb>non eſt ſi ab aqua proſiliat, & ſursùm extra aquæ ſu<lb></lb>perficiem propellatur: non igitur ſignum <expan abbr="neceſſariũ">neceſſarium</expan> <pb pagenum="165" xlink:href="010/01/173.jpg"></pb><arrow.to.target n="marg211"></arrow.to.target><lb></lb>eſt ſaltus, & proſilitio ligni ab aqua leuitatis eius <lb></lb>poſitiuæ, quandoquidem prædictus ſaltus effici po<lb></lb>teſt in vtraque hypotheſi, ſcilicèt ſiuè admittatur, <lb></lb>ſiuè negetur leuitas poſitiua. </s> </p> <p type="margin"> <s id="s.000834"><margin.target id="marg210"></margin.target>Lib. de vi <lb></lb><gap></gap> ca. 9.</s> </p> <p type="margin"> <s id="s.000835"><margin.target id="marg211"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000836">Sed vt apertè inefficacia huius argumenti perci<lb></lb>piatur, poſſumus ijſdem ferè verbis oſtendere falſum <lb></lb><arrow.to.target n="marg212"></arrow.to.target><lb></lb>eſſe, quòd à leuitate poſitiua lignum ſursùm impel<lb></lb>latur, ait enim <emph type="italics"></emph>ſaltum dependere non poſſe ab extruſione <lb></lb>aquæ ambientis, quia aqua non potest illud vltrà trude<lb></lb>re, quàm ſit ipſi opus, vt locum inferiorem occupet.<emph.end type="italics"></emph.end></s> <s id="s.000837"> Di<lb></lb>cam ego eodem modo contra leuitatem poſitiuam, <lb></lb>quod non deberet eius leuitas propellere <expan abbr="lignũ">lignum</expan> plùs, <lb></lb>quàm requirit recta diſpoſitio, & conſtitutio natura<lb></lb>lis, quia nempè (ſubijciam) non poteſt leuitas <expan abbr="lignũ">lignum</expan> <lb></lb>vltrà ſubleuare, quàm ſit ipſi opus vt locum ſuperi<lb></lb>orem in aqua occupet, cùm ſit nempè leuitas nullą <lb></lb>alia de cauſa ligno communicata ab ipſa natura, niſi <lb></lb>vt vna pars ligni demerſa ſubſidat, altera verò ſupra <lb></lb>eam in aere emineat, non verò vt lignum integrum̨ <lb></lb>extra aquam collocetin ipſo nempè aere. </s> <s id="s.000838">igitur con<lb></lb>cedat aduerſarius neceſsè eſt non expulſum fuiſſe li<lb></lb>gnum ſursùm à leuitate poſitiua ſupra <expan abbr="ſupremã">ſupremam</expan> aquæ <lb></lb>libellam, & hinc planè conijciet ſui argumenti inef<lb></lb>ficaciam. </s> </p> <p type="margin"> <s id="s.000839"><margin.target id="marg212"></margin.target>Retorquetur <lb></lb>idipſum ar<lb></lb>gumentum <lb></lb>contra ad<lb></lb>uerſarium. </s> </p> <p type="main"> <s id="s.000840">Proſequitur deindè: <emph type="italics"></emph>quando cylindrus erat in fundo <expan abbr="noõ">non </expan><lb></lb>poteſt inueniri, quæ pars aquæ illum ſursùm trudat non illa, <lb></lb>quæ in fundo, ſuppono enim perfectum cylindrum phyſicè, <lb></lb>& fundum vaſis exactè <expan abbr="planũ">planum</expan> adeò vt nulla ſenſibilis pars <lb></lb>aquæ interlabi posſit quamdiù cylinder vi detinetur ibi.<emph.end type="italics"></emph.end><pb pagenum="166" xlink:href="010/01/174.jpg"></pb><arrow.to.target n="marg213"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000841"><margin.target id="marg213"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000842">Et hinc apertè conijcio non benè perceptum fuiſ<lb></lb>ſe modum quomodò medium fluidum ſursùm impel<lb></lb>lat <expan abbr="extrudatq;">extrudatque</expan> lignum minùs graue ipſa aqua, & ideò <lb></lb>operæpretium erit apertè, & diſtinctè hoc declarare. </s> </p> <p type="main"> <s id="s.000843"><emph type="center"></emph>PROP. LXXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000844"><emph type="center"></emph><emph type="italics"></emph>Niſi lignum, & ambiens aqua collateralis motibus contra<lb></lb>rijs ſursùm, & deorsùm ſimul tempore moueri que<lb></lb>ant, numquam lignum in aqua aſcendet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.174.1.jpg" xlink:href="010/01/174/1.jpg"></figure> <p type="main"> <s id="s.000845">SIt vas ABCD aqua plenum iņ <lb></lb>cuius fundo apponatur priſma <lb></lb>ligneum EFGB hìc adeſt aqua li<lb></lb>gno incumbens AEFH, atque aqua <lb></lb>collateralis HFID, quæ comprimit <lb></lb>ſubiectum aqueum priſma FICG, <lb></lb>Dico primò, quod ſuperincumbens <lb></lb>aqua AEFH nequaquàm ſursùm impellit ſubiectum <lb></lb>lignum, imò id comprimit: neque præterea ſuperna <lb></lb>collateralis aqua HFID prædictum lignum eleuat, <lb></lb>ſed tantummodò æquilibratur cum collaterali aqua <lb></lb>AEFH. </s> <s id="s.000846">Tantummodò ad rem noſtram facit aquą, <lb></lb>quæ ad latus ipſius ligni apponitur, FGCI, & hæc <expan abbr="nõ">non</expan> <lb></lb>ſemper ſubleuare poteſt lignum BF, niſi habuerit <lb></lb>duas conditiones, primò vt aqua FC deſcenderę <lb></lb>deorsùm valeat, ſecundò vt eodem tempore eadem <lb></lb>aqua lignum GE impellere ſursùm poſſit. </s> <s id="s.000847">At quan<lb></lb>dò huiuſmodi motus contrarij ob aliquod impedi<lb></lb>mentum fieri ſimùl <expan abbr="nõ">non</expan> poſſunt, omninò lignum quie-</s> </p> <pb pagenum="167" xlink:href="010/01/175.jpg"></pb> <p type="main"> <s id="s.000848"><arrow.to.target n="marg214"></arrow.to.target><lb></lb>ſcet in fundo ipſius aquæ, quia nimirum locum non <lb></lb>habet libræ, aut ſiphonis operatio. </s> <s id="s.000849">Hoc autem ſic <lb></lb>perſpicuum fiet: ſupponamus baſim lignei priſmatis <lb></lb>BG perfectè, & exquiſitè tangere fundum vaſis BC, <lb></lb>ſcilicèt ſi ambę ſuperficies fuerint explanatæ, & læ<lb></lb>uigatæ, tunc profectò aqua FC, licèt grauior ſit ipſo <lb></lb>ligno minimè excurrere poterit deorsùm cùm noņ <lb></lb>adſit aditus inter ligni baſim BG, & <expan abbr="fundũ">fundum</expan> putei: in<lb></lb>nititur igitur atque ſuſtentatur maius pondus aquę <lb></lb>FC à ſoliditate fundi GC eiuſdem putei, quare ne<lb></lb>ceſsè eſt vt <expan abbr="eadẽ">eadem</expan> aqua collateralis FC omninò quie<lb></lb>ſcat, & proindè lignum EG non aſcendet ſursùm, nec <lb></lb>expelletur ab aqua collaterali quieſcente, quaprop<lb></lb>ter habebimus libram BC non quidem <expan abbr="conuertibilẽ">conuertibilem</expan> <lb></lb>circa centrum G, ſed ſtabilem, & firmam, cum in ea <lb></lb>minimè contrarij motus <expan abbr="deſcẽſus">deſcenſus</expan> partis GC, & <expan abbr="aſcẽ-ſus">aſcen<lb></lb>ſus</expan> alterius radij BG fieri poſſint ſimùl, & ſemel, vn<lb></lb>de mirum non eſt lignum GE è fundo vaſis non <expan abbr="aſcẽ-dere">aſcen<lb></lb>dere</expan>. </s> </p> <p type="margin"> <s id="s.000850"><margin.target id="marg214"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000851"><emph type="center"></emph>PROP. LXXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000852"><emph type="center"></emph><emph type="italics"></emph>Vis motiua eleuans lignum in aqua eſt maius pondus colla<lb></lb>teralis aquæ, quæ deſcendere posſit, & præterea mo<lb></lb>tu reflexo infimam ligni baſim ſursùm <lb></lb>impellat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000853">PRæterea dico, quòd non ſufficit vt aqua collate<lb></lb>ralis FC ſolummodò moueri deorsùm poſſit, <lb></lb>ſed oportet prętere a vt reflectatur ſursùm infrà <expan abbr="lignũ">lignum</expan> <pb pagenum="168" xlink:href="010/01/176.jpg"></pb><arrow.to.target n="marg215"></arrow.to.target><lb></lb>GE ad hoc vt lignum è fundo vaſis aſcendat, quod <lb></lb>conſtat hac experientia: Perforetur <expan abbr="fundũ">fundum</expan> vaſis GC <lb></lb>tunc profectò aqua FG, & ei ſuperincumbens FD <lb></lb>profluet <expan abbr="deſcendẽdo">deſcendendo</expan> per <expan abbr="apertũ">apertum</expan> orificium GC, nec <lb></lb>proindè <expan abbr="lignũ">lignum</expan> GE <expan abbr="ſursũ">ſursum</expan> <expan abbr="aſcẽdet">aſcendet</expan>, ſed neceſsè eſt ob<lb></lb>turato foramine GC, vt aqua fluere, & inſinuari poſ<lb></lb>ſit inter priſmatis baſim BG, & fundum putei, & tune <lb></lb>aſcendet lignum, ſi nimirùm concipiatur putei fun<lb></lb>dum magis depreſſum vt eſt MK, & aqua FC proflu<lb></lb><figure id="id.010.01.176.1.jpg" xlink:href="010/01/176/1.jpg"></figure><lb></lb>ens repleuerit ſpatium BMLG ef<lb></lb>ficietur ſipho DKMA cuius vną <lb></lb>pars aquea HK grauìor eſt reliqua <lb></lb>parte AL, & proindè <expan abbr="maiorẽ">maiorem</expan> vim <lb></lb>compreſſiuam habebit aqua HK, <lb></lb>quàm aqua, & <expan abbr="lignũ">lignum</expan> AL, & prop<lb></lb>terea deprimetur deſcendendo a<lb></lb>qua FGK eleuabiturque motu <expan abbr="cõtrario">contrario</expan> aqua LB vnà <lb></lb>cum ligno incumbente, neceſſariò igitur requiruntur <lb></lb>hi duo motus contrarij deſcenſus aquæ grauioris FK, <lb></lb>& aſcenſus aquæ LB vt lignum eleuari poſſit. </s> <s id="s.000854">Hinc <lb></lb>colligitur, quod vis motiua, quæ impellit ligneum̨ <lb></lb>priſma GE ſursùm eſt profectò grauitas aquæ colla<lb></lb>teralis FC, ſed quatenùs moueri, atque deſcendere <lb></lb>poteſt, & præterea quatenus ſursùm impellere va<lb></lb>let aquam BL, & huic impulſui cedere debet minor <lb></lb>vis deficientis grauitatis ligni EG, & hæc eſt legiti<lb></lb>ma, & adæquata cauſa, quare lignum à maiori im<lb></lb>pulſu aquæ collateralis prementis ſursùm impelli<lb></lb>tur ab aqua, quæ infra eius baſim inſinuatur. <pb pagenum="169" xlink:href="010/01/177.jpg"></pb><arrow.to.target n="marg216"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000855"><margin.target id="marg215"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000856"><margin.target id="marg216"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000857">His declaratis accedamus iam ad difficultates ad<lb></lb>uerſarij, in quibus ſupponit, quòd dum ligneus cy<lb></lb>lindrus GE exquiſito, & immediato contactu fundo <lb></lb>vaſis adhæret, ipſumque veluti exoſculatur, licèt vas </s> </p> <p type="main"> <s id="s.000858"><arrow.to.target n="marg217"></arrow.to.target><lb></lb>repletum aqua fuerit, lignum ſponte ſua, & vi eius <lb></lb>leuitatis ſursùm aſcendere deberet. </s> <s id="s.000859">Sed quid facies, <lb></lb>ſi experimentum huic aſſertioni refragatur? </s> <s id="s.000860">Et pro<lb></lb>cùl dubio ſi experimentum ita ſe haberet, vt ab ipſo <lb></lb>refertur, ſcilicèt ſi cylindrus ligneus GE exquiſitè <lb></lb>tangens ſuperficiem fundi vaſis BG complanatam, <lb></lb>& lęuigatam, eſſetque vas aqua repletum, & nihilo<lb></lb>minus lignum ſursùm aſcenderet, neceſſariò aſſerere <lb></lb>teneremur, & confiteri, lignum, non à principio ex<lb></lb>trinſeco per extruſionem, ſed à vi naturali leuitatis <lb></lb>eius aſcendere. </s> </p> <p type="margin"> <s id="s.000861"><margin.target id="marg217"></margin.target>Experimen<lb></lb>tum falſum <lb></lb>aduerſarij <lb></lb>pro leuitate <lb></lb>poſitiua.</s> </p> <p type="main"> <s id="s.000862"><emph type="center"></emph>PROP. LXXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000863"><emph type="center"></emph><emph type="italics"></emph>Experimentis euincitur non ob defectum leuitatis poſitiuæ, <lb></lb>ſed quia extruſio à medio fluido grauiori fieri non po<lb></lb>test, lignum in aquæ fundo quieſcere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000864">VErùm quia lignum EG in aqua demerſum non <lb></lb>aſcendit è fundo vaſis cui adhæret, imò ibidem <lb></lb>ſiſtitur, & quieſcit, igitur <expan abbr="nõ">non</expan> ineſt in ligno cauſa ima<lb></lb>ginata, quæ leuitas poſitiua vocatur. </s> <s id="s.000865">E contrà quo<lb></lb>tieſcumque fieri, & exerceri poteſt extruſio medij <lb></lb>fluidi, ideſt quotieſcumque fluidum grauius fluerę <lb></lb>poteſt, & inſinuari infra cylindrum ligneum, ſemper <lb></lb>ſubſequitur effectus aſcenſus illius, at quando (vt <pb pagenum="170" xlink:href="010/01/178.jpg"></pb><arrow.to.target n="marg218"></arrow.to.target><lb></lb>in noſtro caſu accidit) aqua ſubingredi inter duas <lb></lb>ſuperficies ligni, & fundi vaſis non poteſt ob exqui<lb></lb>ſitum contactum, & congruentiam, tunc non ſequi<lb></lb>tur effectus aſcenſus eiuſdem ligni, veluti in bilance <lb></lb>pondus centum librarum non ſubleuabit contrapoſi<lb></lb>tum pondus vnciale quotieſcumque illud impeditur, <lb></lb>vt ne queat deorsùm deprimi, igitur vera cauſa <expan abbr="aſcẽ-ſus">aſcen<lb></lb>ſus</expan> ligni in aqua eſt extruſio facta à medio fluido, <expan abbr="nõ">non</expan> <lb></lb>autem leuitas poſitiua in ligno inexiſtens. </s> </p> <p type="margin"> <s id="s.000866"><margin.target id="marg218"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem non <lb></lb>dari. </s> </p> <p type="main"> <s id="s.000867">Porrò hoc experti ſumus in Academia Experimen<lb></lb>tali Medicea. </s> <s id="s.000868">Poſuimus pilam li<lb></lb><figure id="id.010.01.178.1.jpg" xlink:href="010/01/178/1.jpg"></figure><lb></lb>gneam G in fundo vaſis ABCD, <lb></lb>quæ tangebat <expan abbr="orificiũ">orificium</expan> EF conca<lb></lb>uitatis he miſphæricæ EIF in fun<lb></lb>do vaſis excauatæ, poſteà reple<lb></lb>uimus vas hydrargyro vſque ad <lb></lb>ſummitatem AD, nec tamen li<lb></lb>gnea pila G fundum reliquit a<lb></lb>ſcendendo ſursùm; & <expan abbr="notandũ">notandum</expan>, <lb></lb>quòd prædicta pila non arctè orificio vaſis adhære<lb></lb>bat, & colligabatur, ſed potiùs facillimè digitis di<lb></lb>moueri contorquerique poterat, vnde conijcitur, <lb></lb>quàm debili nexu fundum, aut orificium acumi<lb></lb>natum EF <expan abbr="tãgebat">tangebat</expan>. </s> <s id="s.000869">quia poſte à inſignis Peripateticus <lb></lb>ſuſpicabatur, quòd præcipua cauſa detinens <expan abbr="ligneã">ligneam</expan> <lb></lb>pilam demerſam infra hydrargyrum in fundo vaſis <lb></lb>erat timor, & abominium vacui, quod effici debuiſ<lb></lb>ſet in illo ſpatio quotieſcumque pila ſursùm aſcen<lb></lb>deret; proptereà, vt petijt prædictus Philoſophus <pb pagenum="171" xlink:href="010/01/179.jpg"></pb><arrow.to.target n="marg219"></arrow.to.target><lb></lb>perforauimus fundum vaſis IH, vt nimirùm è partę <lb></lb>ſubiecta aer ſuccedere poſſet ad replendum <expan abbr="vacuũ">vacuum</expan>, <lb></lb>& ſic leuitas poſitiua ligni G abſque vacui periculo <lb></lb>commodè ſursùm aſcendere poſſet; hac præparatione <lb></lb>facta, illa lignea pila fundum non dereliquit, nec ſur<lb></lb>sùm aſcendit; nec paritèr aſcendit poſtquam <expan abbr="foramẽ">foramen</expan> <lb></lb>H occluſum denuò fuit, & cauitas ſubiecta EIF, & <lb></lb>ſuprema AED repleta hydrargyro fuit. </s> <s id="s.000870">Vnde dedu<lb></lb>cere poſſumus pilam non à poſitiua leuitate eleuari, <lb></lb>ſed potiùs ab expreſſione ambientis fluidi quotieſ<lb></lb>cumque excurrere poteſt abſque impedimento in<lb></lb>fra ſuperficiem eiuſdem pilæ. </s> </p> <p type="margin"> <s id="s.000871"><margin.target id="marg219"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000872">Perpendamus tandem poſtrema verba eiuſdem̨ <lb></lb><arrow.to.target n="marg220"></arrow.to.target><lb></lb>Authoris, qui ait: <emph type="italics"></emph>Sed quid dicent aduerſarij, ſi in fundo <lb></lb>vaſis eſſet foramen amplum, anguſtius tamen cylindro, & <lb></lb>occluſum, quod eodem momento aperiretur quo manus eleuat <lb></lb>virgam? </s> <s id="s.000873">certè enim aqua efflueret deorsùm, & tamen cy<lb></lb>lindraceum lignum illud tenderet ſursùm. </s> <s id="s.000874">Agnoſcant ergò <lb></lb>in ligno illo leuitatem aliquam, quæ impetum producendo <lb></lb>ſursùm versùs priùs natura mouet, ac pellit <expan abbr="aquã">aquam</expan>, & cau<lb></lb>ſaest vt aqua corpus fluidum it a illi cedat, vt ſubintret in <lb></lb>illius locum, ne detur vacuum, eamque non exercere gra<lb></lb>uitatem actu, ſed ſuperiores quidem aquæ partes impelli à <lb></lb>cylindro ligneo, & cedere illi locum digrediendo ad latera, <lb></lb>vt locum illarum partium impleant, quæ infernè <expan abbr="ſubintrãt">ſubintrant</expan> <lb></lb>in locum cylindri.<emph.end type="italics"></emph.end></s> <s id="s.000875"> Et hic nil aliud reſpondere poſſum̨ <lb></lb>niſi mirari confidentiam, ſecuritatemque qua aſſeri<lb></lb>tur experientia non ſicuti reuera ſe habet, vtque à <lb></lb>quolibet comprobari poteſt, ſed veluti præiudica<lb></lb>ta opinio eis perſuaſerat. <pb pagenum="172" xlink:href="010/01/180.jpg"></pb><arrow.to.target n="marg221"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000876"><margin.target id="marg220"></margin.target>Aliud <expan abbr="falsũ">falsum</expan> <lb></lb><expan abbr="experimentũ">experimentum</expan> <lb></lb>ab eodé au<lb></lb>thore <expan abbr="allatũ">allatum</expan></s> </p> <p type="margin"> <s id="s.000877"><margin.target id="marg221"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <figure id="id.010.01.180.1.jpg" xlink:href="010/01/180/1.jpg"></figure> <p type="main"> <s id="s.000878">Sit igitur vas ABCD in cuius <expan abbr="fũdo">funshy;<lb></lb>do</expan> aperiatur amplum <expan abbr="foramẽ">foramen</expan> BC, <lb></lb>ſit poſtea ligneus cylindrus FE, <lb></lb>cuius baſis HE paulò amplior ſit <lb></lb>foramine vaſis, vt nimirum poſſit <lb></lb>ipſum præcisè occludere, obſtrue<lb></lb>reque ſimplici contactu; repleatur <lb></lb>poſtea vas aqua <expan abbr="vſq;">vſque</expan> ad AD, ſup<lb></lb>ponit aduerſarius, quòd cylindrus <lb></lb>FE non poſſit in fundo vaſis deti<lb></lb>neri, niſi <expan abbr="deorsũ">deorsum</expan> vi impellatur vir<lb></lb>ga quadam ferrea ML præterea <lb></lb>ait, quòd ſi occluſo infimo foramine BC, <expan abbr="eodẽ">eodem</expan> mo<lb></lb>mento temporis recludatur os infimum, remoueatur<lb></lb>que virga ML, fore vt aqua exeat per infimum os <lb></lb>BC, & lignum FE aſcendat ſursùm, <emph type="italics"></emph>quod<emph.end type="italics"></emph.end>, ſubdit ip<lb></lb>ſe, <emph type="italics"></emph>eſt argumentum certisſimum leuitatis poſitiuæ eiuſdem <lb></lb>ligni.<emph.end type="italics"></emph.end></s> <s id="s.000879"> Et hic primò obſeruo contra aduerſarij aſſer<lb></lb>tionem, quòd ſi baſis cylindri HE zona circularis <lb></lb>præcisè tangat, & exoſculetur perimetrum orificij <lb></lb>putei BC, tunc non requiritur epiſtomium vt aquą <lb></lb>è vaſe non effluat, neque requiritur impulſus virgæ <lb></lb>LM, vt prohibeatur aſcenſus cylindri FE è fundo va<lb></lb>ſis, ſed ibidem quieſcet, veluti ſi tenacitèr colliga<lb></lb>tus eſſet ab illo contactu ſimplici. </s> <s id="s.000880">Imò, quod magis <lb></lb>mirere, ſi infima zona baſis HE ipſius cylindri lignei <lb></lb>non perfectè congrueret; neque compleret vndique <lb></lb>tangendo orificium infimum BC, ſed per rimulas, <lb></lb>vel angulos aliquos aqua deorſum efflueret, tunc <pb pagenum="173" xlink:href="010/01/181.jpg"></pb><arrow.to.target n="marg222"></arrow.to.target><lb></lb>neque opus haberemus virga impellente ML vt li<lb></lb>gnum prædictum in fundo vaſis retineretur, ſed <expan abbr="ſpõ-te">ſpon<lb></lb>te</expan> ſua ibidèm quieſceret, imò ſi quis conaretur ſur<lb></lb>sùm trahere prædictum <expan abbr="cylindrũ">cylindrum</expan> FE filo aliquo ML <lb></lb>tunc nedùm vt eius baſim diuelleret à contactu orifi<lb></lb>cij BC, ſed etiam poſt eius ſeparationem à fundo per <lb></lb>aliquod exiguum interuallum, aliqua renitentia per<lb></lb>ſentiretur, et vis aliqua trahens requireretur, aliàs <lb></lb>ſponte ſua lignum ipſum decideret denuò ad occlu<lb></lb>dendum vaſis orificium BC, Hinc videat aduerſarius <lb></lb>quàm iure exclamet, cùm ait: <emph type="italics"></emph>Agnoſcant ergò in ligno <lb></lb>leuitatem aliquam, &c.<emph.end type="italics"></emph.end> quia cum experientia totum̨ <lb></lb>oppoſitum oſtendat, iurè poſſemus ei reddere verba <lb></lb>ſua: Agnoſcat ergo in ligno nullam leuitatem ineſſe. </s> </p> <p type="margin"> <s id="s.000881"><margin.target id="marg222"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000882"><emph type="center"></emph>PROP. LXXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000883"><emph type="center"></emph><emph type="italics"></emph>Supra foramen in fundo putei apertum exercetur compresſio <lb></lb>ponderis columnæ aqueæ vſque ad ſupremam eius li<lb></lb>bellam extenſæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000884">ET profectò ij, qui verſati <lb></lb><figure id="id.010.01.181.1.jpg" xlink:href="010/01/181/1.jpg"></figure><lb></lb>ſunt in hac doctrina hydro<lb></lb>ſtatica Archimedea optimè <expan abbr="no-rũt">no<lb></lb>runt</expan>, quòd quotieſcumque in præ<lb></lb>dicto vaſe aqua pleno aperitur<lb></lb>os in eius fundo BC, tunc adeſt <lb></lb>cylindrus aqueus IBCK, qui <expan abbr="cõ-primit">com<lb></lb>primit</expan>, & vim facit proprio pon<lb></lb>dere ſupra quodlibet corpus im-<pb pagenum="174" xlink:href="010/01/182.jpg"></pb><arrow.to.target n="marg223"></arrow.to.target><lb></lb>pediens exitum, ac fluxum prædictæ aquæ, quod <expan abbr="q́ui-libet">qui<lb></lb>libet</expan> experiri facilè poteſt ſi palma manus occludat <lb></lb>infimum vaſis orificium BC, percipiet enim <expan abbr="cõpreſ-ſionem">compreſ<lb></lb>ſionem</expan>, & impulſum tanta vi factum quanta eſt gra<lb></lb>uitas cylindri aquei prædicti, & hoc experitur ne<lb></lb>dùm quando palma manus vetat omninò effluxum̨ <lb></lb>aquæ, quam ſi aliquantiſper manus ſubleuetur, vt <lb></lb>poſſit aqua effluere. </s> <s id="s.000885">Hoc præmiſſo. </s> </p> <p type="margin"> <s id="s.000886"><margin.target id="marg223"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000887"><emph type="center"></emph>PROP. LXXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000888"><emph type="center"></emph><emph type="italics"></emph>Ex prædicta experientia euidentèr oſtendetur lignum in <lb></lb>aqua nullam poſitiuam leuitatem exercere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.182.1.jpg" xlink:href="010/01/182/1.jpg"></figure> <p type="main"> <s id="s.000889">SVpponamus cum Aduer<lb></lb>ſario (ſi poſſibile eſt) cy<lb></lb>lindrum ligneum FE ſub a<lb></lb>qua <expan abbr="demersũ">demersum</expan> vim exercere, <lb></lb>ac tendere ſursùm intrinſeca <lb></lb>vi ſuę leuitatis <expan abbr="dũ">dum</expan> aqua col<lb></lb>lateralis per rimulas infimas <lb></lb>H & E effluit è vaſe: Sit ve<lb></lb>rò energia leuitatis ligni (vt <lb></lb>æquum eſt) certæ, & deter<lb></lb>minatæ menſuræ, quæ expri<lb></lb>mi poterit à pondere corporis P <expan abbr="ſuſpẽſi">ſuſpenſi</expan> in libra MO <lb></lb>radiorum æqualium; Huic vi leuitatis aduerſatur <expan abbr="cõ-trario">con<lb></lb>trario</expan> niſu pondus ſuperincumbentis cylindri aquei <lb></lb>IFGK, quod paritèr intelligatur termino M eiuſdem <lb></lb>libræ ſuſpenſum. </s> <s id="s.000890">Quoniam vis leuitatis cylindri li-<pb pagenum="175" xlink:href="010/01/183.jpg"></pb><arrow.to.target n="marg224"></arrow.to.target><lb></lb>gnei FE in aqua demerſi ſemper eadem eſt, nec po<lb></lb>teſt vnquam diminui, cùm ſit æqualis vi illius ponde<lb></lb>ris, quod ſufficit ad prohibendum <expan abbr="aſcẽſum">aſcenſum</expan> prædicto <lb></lb>ligno FE (vt conſtat ex Archimede) & è contrà pon<lb></lb>dus incumbentis cylindri aquei IKGF poteſt ſucceſ<lb></lb><arrow.to.target n="marg225"></arrow.to.target><lb></lb>ſiuè diminui in infinitum prout eius altitudo IF dimi<lb></lb>nuta fuerit, ſublata nimirum aqna è vaſe ABD. fiat <lb></lb>igitur vis ponderis aquæ IG minor energia leuitatis <lb></lb>ligni FE, ſcilicèt minor ſit pondere P, quia verò mi<lb></lb>nor vis ſuperari à maiori debet, igitur neceſſariò <lb></lb>pondus P deprimet radium libræ NO, ſuperabitque <lb></lb>reſiſtentiam diminutæ aquæ IG ſuſpenſæ in altera li<lb></lb>bræ extremitate M, ſcilicèt lignum FE (quod tange<lb></lb>re orificium vaſis HE ſupponebatur) ſursùm aſcen<lb></lb>det in ipſa aqua vi maioris ſuæ leuitatis, ſed hoc eſt <lb></lb>falſum, & contra ſenſus euidentiam, numquam enim <lb></lb>prædictus cylindius ligneus fundum deſerit, nec ſur<lb></lb>sùm aſcendit; ſi tamen ſemper orificio BC inſiſtat, <lb></lb>nec incutiatur vt ad latus fundi baſis transferatur, vbi <lb></lb>maior eius baſis pars inſiſtit fundo ſtabili putei, vel <lb></lb>cylindrus ipſe tranſuersè flectatur. </s> <s id="s.000891">Igitur verum <expan abbr="nõ">non</expan> <lb></lb>eſt lignum FE exercere nè minimum gradum impe<lb></lb>tus leuitatis. </s> </p> <p type="margin"> <s id="s.000892"><margin.target id="marg224"></margin.target>Cap 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000893"><margin.target id="marg225"></margin.target>De inſidét. <lb></lb></s> <s id="s.000894">fluido lib. 1. <lb></lb>prop. 6.</s> </p> <p type="main"> <s id="s.000895"><emph type="center"></emph>PROP. LXXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000896"><emph type="center"></emph><emph type="italics"></emph>Aliter idipſum demonstrare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000897">IIſdem poſitis intelligatur præterea quòd vis leui<lb></lb>tatis prædicti ligni, ſcilicèt pondus P æqualis ſit <pb pagenum="176" xlink:href="010/01/184.jpg"></pb><arrow.to.target n="marg226"></arrow.to.target><lb></lb>energię ponderis incumbentis cylindri aquei IG: <lb></lb>tunc quælibet minima vis addita ponderi P deberet <lb></lb>eleuare vſque ad ſupremæ aquæ libellam cylindrum <lb></lb>FE, quod ſimilitèr eſt falſum, debet enim ſuperad<lb></lb>di ponderi P aliud pondus R æquale ponderi lignei <lb></lb>cylindri FE. </s> </p> <p type="margin"> <s id="s.000898"><margin.target id="marg226"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000899"><emph type="center"></emph>PROP. LXXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000900"><emph type="center"></emph><emph type="italics"></emph>Præterea alio modo idem confirmare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000901">TAndem (in eadem hypotheſi) ſit vis leuitatis <lb></lb>poſitiuæ ligni FE minor vi ponderis ſuperin<lb></lb>cumbentis cylindri aquei IG. (& maioris claritatis <lb></lb>gratia) ſupponamus pondus P æquale exceſſui gra<lb></lb>uitatis aqueæ molis cylindro FE æqualis ſupra pon<lb></lb><arrow.to.target n="marg227"></arrow.to.target><lb></lb><figure id="id.010.01.184.1.jpg" xlink:href="010/01/184/1.jpg"></figure><lb></lb>dus cylindri lignei prædicti; <lb></lb>quia ex Archimede lignum̨ <lb></lb>FE tanto impetu in aqua <expan abbr="tẽ-dit">ten<lb></lb>dit</expan> ſursùm <expan abbr="quãta">quanta</expan> eſt vis gra<lb></lb>uitatis prędicti exceſſus. </s> <s id="s.000902">Mo<lb></lb>dò <expan abbr="põdus">pondus</expan> cylindri aquei IG <lb></lb>maius eſt pondere P, ſcilicèt <lb></lb>vi leuitatis ligni FE, igitur <lb></lb>prædicta leuitas à pondere <lb></lb>aquæ incumbentis ſuperabi<lb></lb>tur vtpotè à maiori virtutę, <lb></lb>& proindè lignum detinebitur in fundo vaſis, nec a<lb></lb>ſcendet. </s> <s id="s.000903">Si poſtea eidem termino libræ O ſuſpenda<lb></lb>tur aliud pondus Q æquale exceſſui ponderis aquæ <pb pagenum="177" xlink:href="010/01/185.jpg"></pb><arrow.to.target n="marg228"></arrow.to.target><lb></lb>IG ſupra grauitatem P, patet quod vt ſuperetur im<lb></lb>pedimentum, quod reperit lignum FE ipſumque <expan abbr="a-ſcẽdere">a<lb></lb>ſcendere</expan> vetat ſufficiet vis ponderis Q, quæ eſt diffe<lb></lb>rentia ponderis aquæ prementis IG, & leuitatis li<lb></lb>gni FE. </s> <s id="s.000904">Sed hoc eſt falſum, quandoquidem pręter <lb></lb>pondus Q requiritur etiam pondus R æquale pon<lb></lb>deri abſoluto cylindri lignei FE, & inſuper requiri<lb></lb>tur pondus P quod vnà cum Q æquantur ponderi a<lb></lb>quæ IG. </s> <s id="s.000905">Quapropter adeò falſum eſt ligneum cylin<lb></lb>drum FE virtute propriæ leuitatis vim ſursùm exer<lb></lb>cere in aqua, vt potiùs deorsùm premat, vt corpus <lb></lb>graue. </s> </p> <p type="margin"> <s id="s.000906"><margin.target id="marg227"></margin.target>Ibidem.</s> </p> <p type="margin"> <s id="s.000907"><margin.target id="marg228"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000908">Et hactenùs comparauimus vires comprimentes <lb></lb>grauitatis ſuperincumbentis cylindri aquei IG & le<lb></lb>uitatis cylindri lignei FE, reſtat modò vt paritèr <expan abbr="cõ-paremus">con<lb></lb>paremus</expan> velocitates prædictorum corporum, ſcilicèt <lb></lb>videndum qua velocitate lignum FE ſursùm à vile<lb></lb>uitatis impellatur reſpectu contrariæ celeritatis, qua <lb></lb>aqua ABD per infimum foramen BC effluit: eo pro<lb></lb>pemodum modo, quo piſces contra curſum alicuius <lb></lb>fluentis fluminis mouentur, ſi enim piſcis velociùs <lb></lb>natat, quàm aqua contrario curſu currat, procùl du<lb></lb>bio piſcis reſpectu fundi, & ripæ, & ſpatij mundani <lb></lb>contra a quæ curſum reuera excurret aliquantiſper, <lb></lb>quòd ſi prædictæ duæ contrariæ velocitates æquales <lb></lb>fuerint, licèt reuera piſcis agitetur, commoueatur<lb></lb>que ſemper in eodem ſitu mundani ſpatij perſiſtet, ſi <lb></lb>tandèm velocitas piſcis minor fuerit celeritate con<lb></lb>traria fluentis, licèt piſcis natet, & verè anterius ex-<pb pagenum="178" xlink:href="010/01/186.jpg"></pb><arrow.to.target n="marg229"></arrow.to.target><lb></lb>currat in aqua, nihilominùs retrocedet reſpectu ſpa<lb></lb>tij mundani, ſed curſu magis tardo, & lento, quàm̨ <lb></lb>flumen mouetur. </s> </p> <p type="margin"> <s id="s.000909"><margin.target id="marg229"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000910"><emph type="center"></emph>PROP. LXXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000911"><emph type="center"></emph><emph type="italics"></emph>Alia ratione poſitiuam leuitatem non dari <lb></lb>oſtenditur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000912">IT aque eodem modo in vaſe ABC aqua pleno, & <lb></lb>infernè perforato in B intelligantur demerſi glo<lb></lb>buli aerei, ſed perpendiculariter imminentes ſuper <lb></lb>infimum foramen B, ſcilicèt intra cylindrum aqueum <lb></lb>DBE, qui ad modum fluminis intra <lb></lb><figure id="id.010.01.186.1.jpg" xlink:href="010/01/186/1.jpg"></figure><lb></lb>aquam vaſis repleti defluit egre<lb></lb>diturque per foramen B. </s> <s id="s.000913">Et ſuppo<lb></lb>namus maiori celeritate, ſcilicèt <lb></lb>dupla, aquam fluere à D vſque ad <lb></lb>B, quàm globus aereus G mouea<lb></lb>tur ſur sùm translatus à naturali eius <lb></lb>leuitate, itaut, quando aqua prædi<lb></lb>cti cylindri fluentis <expan abbr="trãſit">tranſit</expan> ſpatium <lb></lb>GI debeat aereus globus G ſursùm impelli, & <expan abbr="trã-ſigere">tran<lb></lb>ſigere</expan> ſpatium æquale IH ſubduplum ipſius GI, eo <lb></lb>quod medium fluidum in quo globus aereus G <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan> non eſt ſtabile, ſed deorsùm defluit, non ſecùs ac <lb></lb>flumen, igitur quando aqua ſpatium GI tranſegerit, <lb></lb>globus aereus contrario curſu medietatem itineris <lb></lb>IH perficiet, qua proptèr ex hiſce duabus contrarijs <lb></lb>velocitatibus reſultabit tertia quędam celeritas, quæ <pb pagenum="179" xlink:href="010/01/187.jpg"></pb><arrow.to.target n="marg230"></arrow.to.target><lb></lb>æqualis erit differentiæ prædictarum oppoſitarum <lb></lb>celeritatum, & ideò aer G deſcendet duplo tardiùs <lb></lb>aqua ambiente; Quòd verò hoc ſit falſum, experien<lb></lb>tia ipſa docet ſi nimirùm aqua DE atro colore tinga<lb></lb>tur, vel diſperſo puluere terreſtri pauliſper turbida <lb></lb>reddatur, tunc procùl dubio particulæ illæ arenoſæ <lb></lb>graues, aut ob exiguitatem in ipſa aqua dum quieſcit <lb></lb>non deſcendunt, vel lento motu deorsùm feruntur a <lb></lb>vi maioris grauitatis <expan abbr="earũ">earum</expan>. </s> <s id="s.000914">igitur quando aqua deor<lb></lb>sùm fluit, videtur impoſſibile vt grauiores particulæ <lb></lb>arenoſæ minori velocitate transferantur deorsùm̨, <lb></lb>quàm aqua ipſa in qua degunt, quare bulla aerea G <lb></lb>quæ vt leuis ſursùm aſcendere ſupponitur, non poſſet <lb></lb>pari velocitate ſimul <expan abbr="cũ">cum</expan> particulis terreis aquæ tur<lb></lb>bidæ deorsùm deſcendere, ſed hoc eſt falſum, cum <lb></lb>abſque vlla differentia velocitatis deorsùm feran<lb></lb>tur vnà cum aqua turbida cylindri fluentis, igitur ve<lb></lb>rum non eſt, quòd aer G moueatur ſursùm à vi natu<lb></lb>ralis leuitatis eius translatus, cùm <expan abbr="aliũdè">aliundè</expan> quando re<lb></lb>uera aer G principium motiuum leuitatis in ſe habe<lb></lb>ret non poſſet vllo pacto in aqua ipſum <expan abbr="nõ">non</expan> exercere. </s> </p> <p type="margin"> <s id="s.000915"><margin.target id="marg230"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000916"><emph type="center"></emph>PROP. LXXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000917"><emph type="center"></emph><emph type="italics"></emph>Confirmatur aerem ab ambiente aqua per extruſionem ſur<lb></lb>sùm impelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000918">EContrà quandò globus aereus G nullam pror<lb></lb>sùs leuitatem haberet, & ſolummodò per ex<lb></lb>truſionem factam à grauitate fluidi ambientis eleua-<pb pagenum="180" xlink:href="010/01/188.jpg"></pb><arrow.to.target n="marg231"></arrow.to.target><lb></lb>retur, nullo pacto in tali caſu poſſet aqua ab inferiori <lb></lb>ſitu H ſursùm impellere aerem G, propterea quod <lb></lb>aqua DB cogitur excurrere deorsùm per vaſis aper<lb></lb>tum foramen B, & ideò non poteſt motu reflexo ſur<lb></lb>sùm impellere aerem G. igitur neceſsè eſt vt globus <lb></lb>aereus G deferatur à vi fluentis aquæ, vt ipſa experi<lb></lb>entia oſtendit. </s> <s id="s.000919">Vnde colligitur, quod nullum ex ad<lb></lb>ductis, & excogitatis <expan abbr="experimẽtis">experimentis</expan> vſque adhuc euin<lb></lb>cere perſuadereque poteſt exiſtentiam leuitatis po<lb></lb>ſitiuæ, & è contrà ſemper multò magis confirmatur, <lb></lb>demonſtraturque eius non exiſtentia, quaproptèr fa<lb></lb>tendum eſt corpora, quæ leuia appellantur, ſursùm <lb></lb>impelli per extruſionem à fluidis ambientibus gra<lb></lb>uioribus. </s> </p> <p type="margin"> <s id="s.000920"><margin.target id="marg231"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000921">Sed coronidis loco afferam demonſtrationem à <lb></lb>me excogitatam, abſolutè non dari in natura <expan abbr="poſitiuã">poſitiuam</expan> <lb></lb>leuitatem, vtque commodiùs hoc efficiam primò <lb></lb>nonnullas ſuppoſitiones ſenſui manifeſtas <expan abbr="proponã">proponam</expan>, <lb></lb>& deinceps aliqua lemmata ex principijs mechani<lb></lb>cis deſumpta demonſtrabo. </s> </p> <p type="main"> <s id="s.000922"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000923">ET primò noto, quòd corpus ſiue ſimilare, & ho<lb></lb>mogeneum, ſiue heterogeneum, tunc vocatur <lb></lb>exiſtimaturque rarius ſpecie, quàm aliud, quando <lb></lb>ſumptis æqualibus molibus eorumdem illud <expan abbr="minorẽ">minorem</expan> <lb></lb>copiam materialis ſubſtantiæ corporeæ, & ſenſibi<lb></lb>lis comprehendit in eodem ſpatio, quàm iſtud, quòd <lb></lb>profectò concipi poteſt, ſi intelligatur mino: copia <pb pagenum="181" xlink:href="010/01/189.jpg"></pb><arrow.to.target n="marg232"></arrow.to.target><lb></lb>materiei ſenſibilis in maiori ſpatio corporis rarioris <lb></lb>extenſa per interpoſitionem inanium ſpatiolorum. </s> </p> <p type="margin"> <s id="s.000924"><margin.target id="marg232"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000925"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000926">SI verò moles æquales, ſiuè inæquales non con<lb></lb>ſiderentur, & raritas in vna earum <expan abbr="contẽta">contenta</expan> ma<lb></lb>ior fuerit raritate alterius, tunc dicetur illa raritas <lb></lb><arrow.to.target n="marg233"></arrow.to.target><lb></lb>abſolutè maior reliqua, ſiuè exceſſus raritatis exten<lb></lb>ſiuè in maiori mole multiplicetur, ſiuè intenſiuè iņ <lb></lb>minori mole augeatur. </s> </p> <p type="margin"> <s id="s.000927"><margin.target id="marg233"></margin.target>Sup. 8.</s> </p> <p type="main"> <s id="s.000928"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000929">PRæterea ſuppono ex Ariſtotele raritatem alicu<lb></lb>ius corporis multiplicari, & augeri in infinitum <lb></lb>poſſe prout ſubſtantialis moles corporea, quæ in eo<lb></lb>dem ſpatio continebatur, ſucceſſiuè imminuitur, & <lb></lb>poſt diminutionem extenditur expanditurque vt re<lb></lb>pleat idipſum ſpatium, quod prius à non imminuto <lb></lb>corpore occupabatur. </s> </p> <p type="main"> <s id="s.000930"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000931">SVppono præterea, quòd vis quæ requiritur ad <lb></lb>ſeparanda duo corpora ſe mutuò tangentia im<lb></lb>mediato, & exquiſito contactu, (quod accidit <expan abbr="quã-do">quan<lb></lb>do</expan> eorum ſuperficies ſunt omninò ſimiles, & optimè <lb></lb>lęuigatæ) non eſt infinita, ſed determinata, quia ni<lb></lb>mirùm ſenſus euidentia oſtendit, quod ſi potentią <lb></lb>motiua augeatur ſemper magis, ac magisne dùm cor<lb></lb>pora ſe mutuò tangentia ſeparantur, & ab inuicem <pb pagenum="182" xlink:href="010/01/190.jpg"></pb><arrow.to.target n="marg234"></arrow.to.target><lb></lb>diuelluntur, ſed etiam corpora illa, quæ continuą <lb></lb>cenſentur, vt eſt columna marmorea, vel virga me<lb></lb>tallica, tandèm à vi trahente diſtrahitur, euelliturque <lb></lb>directo motu vna pars ab altera, quæ tenaciori glu<lb></lb>tine vinculoque vniuntur, quàm illa duo corpora ſe <lb></lb>mutuò tangentia, & ſimplici contactu vnita. </s> </p> <p type="margin"> <s id="s.000932"><margin.target id="marg234"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000933"><emph type="center"></emph>PROP. LXXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000934"><emph type="center"></emph><emph type="italics"></emph>Verùm <expan abbr="prædictã">prædictam</expan> vim, quæ requiritur ad ſeparanda duo cor<lb></lb>pora ſe mutuò tangentia, posſibile eſt mediante libra <lb></lb>menſurari hac ratione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000935">SIt cylindrus CAB cuius baſis <lb></lb><figure id="id.010.01.190.1.jpg" xlink:href="010/01/190/1.jpg"></figure><lb></lb>AB perfectiſſimè explanata, <lb></lb>& lęuigata congruat exoſcule<lb></lb>turque <expan abbr="ſuperficiẽ">ſuperficiem</expan> pauimenti DE, <lb></lb>pari diligentia complanatam, & <lb></lb>lęuigatam, & cautionis gratią, <lb></lb>vttuti omninò ſimus aerem am<lb></lb>bientem penetrare, ac ingredi non poſſe inter præ<lb></lb>dictas duas complanatas ſuperficies poſſent colliga<lb></lb>ri tùm cylindro, tùm pauimento duæ laminæ vitreæ <lb></lb>AB, & DE, aut alterius ſubſtantiæ duriſſimæ, quæ in<lb></lb>ſtar ſpeculi explanatæ, & lęuigatæ ſint; poſteà com<lb></lb>primantur, vna, ſuper alteram intrà aliquod fluidum <lb></lb>viſibile veluti eſt aqua, vel hydrargyrum, vt nimi<lb></lb>rùm viſu conſtet nihil omninò intercipi inter prædi<lb></lb>ctas duas ſuperficies, dum nimirùm vna earum trahi<lb></lb>tur, vt ab altera diuellatur. </s> <s id="s.000936">Colligetur poſtea cylin-<pb pagenum="183" xlink:href="010/01/191.jpg"></pb><arrow.to.target n="marg235"></arrow.to.target><lb></lb>dri extremitas C termino H trochleæ, vel libræ HK <lb></lb>radiorum æqualium, cuius centrum I, & reliquo ex<lb></lb>tremo K ſuſpendatur pondus N æquale grauitati ab<lb></lb>ſolutæ cylindri AC. profectò manifeſtum eſt ſenſui <lb></lb>non ſufficere pondus N ad ſeparandum, & diuellen<lb></lb>dum cylindrum AC à pauimento DE, ſed requiritur <lb></lb>aliqua vis multò maior illa, quæ reperiri <expan abbr="aſſignariq;">aſſignarique</expan> <lb></lb><arrow.to.target n="marg236"></arrow.to.target><lb></lb>poterit, non enim eſt infinita, igitur ſi addatur con<lb></lb>tinentèr pondus ponderi termino K <expan abbr="tãdem">tandem</expan> deuenie<lb></lb>mus ad pondus aliquod, vt eſt O à quo cvlindrus CA <lb></lb>directa tractione diuelli à pauimento poterit. </s> <s id="s.000937">Quia <lb></lb>verò duo pondera N, & O directè diuellunt <expan abbr="cylindrũ">cylindrum</expan> <lb></lb>AC, & hic reſiſtit ſeparationi duabus viribus, pro<lb></lb>prij ſcilicèt ponderis æqualis nempè ipſi N, & vi <lb></lb>contactus, & repugnantiæ ad vacuum <expan abbr="admmittendũ">admittendum</expan>. <lb></lb></s> <s id="s.000938">igitur remanens vis ponderis O æqualis erit, & aucta <lb></lb>ſuperabit vim connexionis duarum ſuperficierum ſe <lb></lb>mutuò exquiſitè tangentium. </s> </p> <p type="margin"> <s id="s.000939"><margin.target id="marg235"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000940"><margin.target id="marg236"></margin.target>Sup. 8.</s> </p> <p type="main"> <s id="s.000941">Non defuit tamen qui hunc progreſſum in <expan abbr="dubiũ">dubium</expan> <lb></lb>reuocare auſus ſit, & ſic inutilem, ac inefficacem vni<lb></lb>uerſam demonſtrationem ſubſequentem redderę, <lb></lb>quę in prædicta experimentali operatione fundatur. <lb></lb></s> <s id="s.000942">Nucleus difficultatis talis eſt, non videri poſſibilę <lb></lb>columnam AC vnquam poſſe motu tàm directo ſur<lb></lb>sùm trahi, nec libra, nec trochlea itaut non flectatur <lb></lb>inclineturque, & hoc (inquiunt) nullo pacto huma<lb></lb>na diligentia aſſe qui poſſe; imò aſſerere auſi ſunt, <lb></lb>quòd ſi funis HC directè traheretur perpendiculari<lb></lb>tèr nimirùm ad planum horizontis, & ad baſim DE <pb pagenum="184" xlink:href="010/01/192.jpg"></pb><arrow.to.target n="marg237"></arrow.to.target><lb></lb>nunquam à quacumque vi diuelli columna poſ<lb></lb>ſet, nec ſuperari reſiſtentia ad vacuum, quod profe<lb></lb>ctò ſubſequeretur in actu violento ſeparationis ſu<lb></lb>perficierum AB, & DE. </s> <s id="s.000943">Si verò (aiunt) applicetur <lb></lb>vis tranſuerſalitèr, itaut latus BC columnæ angulum <lb></lb>conſtituat cum linea tractionis, tunc facilè ſeparari, <lb></lb>ac diuelli ab inuicem poteruut prædictę ſuperficies. </s> </p> <p type="margin"> <s id="s.000944"><margin.target id="marg237"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000945">Huiuſmodi cauilloſa reſponſio condonari poteſt <lb></lb>ijs Philoſophis, qui mathematices imperiti ſunt. </s> </p> <p type="main"> <s id="s.000946"><emph type="center"></emph>PROP. XC.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000947"><emph type="center"></emph><emph type="italics"></emph>Potest facili negotio præcisè innoteſcere <expan abbr="reſiſtẽtiailla">reſiſtentia illa</expan> abſolu<lb></lb>ta, & totalis, quæ requiritur ad ſeparationem illam di<lb></lb>rectam, & ad horizontem perpendicularem efficien<lb></lb>dam ipſius columnæ à fundo vaſis, quotieſcum<lb></lb>que constet quanta vis requiritur adeam <lb></lb>ſeparandam impetu obliquo ab <lb></lb>eodem ſolo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000948">SIt denuò cylindrus AC <lb></lb><figure id="id.010.01.192.1.jpg" xlink:href="010/01/192/1.jpg"></figure><lb></lb>cuius baſis AB lęuigatiſ<lb></lb>ſima, <expan abbr="cõtactu">contactu</expan> perfecto ſuper<lb></lb>ficiem pauimenti DE paritèr <lb></lb>lęuigatam tangat, & vis M <lb></lb>tranſuerſali directione CM <lb></lb>perpendiculari ad CB trahat <lb></lb>terminum columnæ C, & va<lb></lb>leat huiuſmodi potentia diuellere ſuperficiem AB <lb></lb>ab ipſo <expan abbr="pauimẽto">pauimento</expan>, ſitque prædicta <expan abbr="potẽtia">potentia</expan> M æqualis <pb pagenum="185" xlink:href="010/01/193.jpg"></pb><arrow.to.target n="marg238"></arrow.to.target><lb></lb>ponderi R, & <expan abbr="quã">quam</expan> proportionem habet ſemiſſis dia<lb></lb>metri AB baſis prædictæ columnæ ad ſuam altitudi<lb></lb>nem BC, eamdem habeat pondus R ad aliud pondus <lb></lb>S. oſtendendum modò eſt vim ponderis S æqualem <lb></lb>eſſe totali reſiſtentiæ contactus duarum <expan abbr="prædictarũ">prædictarum</expan> <lb></lb>ſuperficierum, ſeù potiùs æqualem eſſe vi, qua vacui <lb></lb>reſiſtentia ſuperatur, vel potiùs pondus S ſufficerę <lb></lb>ad diuellendam columnam à pauimento directa tra<lb></lb>ctione, ſcilicèt detinendo, & <expan abbr="transferẽdo">transferendo</expan> baſim AB <lb></lb>ſemper æquidiſtantem plano baſis DE. </s> <s id="s.000949">Quia in actu <lb></lb>ſeparationis ſuperficiei AB à pauimento debet pun<lb></lb>ctum eius B contingere, & inniti ipſi pauimento, & <lb></lb>angularitèr ſubleuari terminus oppoſitus A, vnà cum <lb></lb>tota baſis ſuperficie AB, efficiendo nimirùm <expan abbr="angulũ">angulum</expan> <lb></lb>cum pauimenti plano DE; & hic obſeruari debent <lb></lb>loca vbi duæ vires applicantur, ſcilicèt reſiſtentia, & <lb></lb>eius, quæ eam ſuperat, & per quam directionem tra<lb></lb>hunt & vim exercent; & pater, quòd reſiſtentia iņ <lb></lb>omnibus <expan abbr="pũctis">punctis</expan> inferioris ſuperficiei AB exiſtit, <expan abbr="sũt-que">sunt<lb></lb>que</expan> veluti totidem fibræ <expan abbr="perpẽdicularitèr">perpendicularitèr</expan> erectę ad <lb></lb>planum ſubiectum, quæ cum eo coniunguntur colli<lb></lb>ganturque; è contrà vis mouens M vectem CB adhi<lb></lb>bet circa centrum firmum B, & quia vniuerſa reſi<lb></lb>ſtentia vniformiter diſtribuitur per totam baſis ſu<lb></lb>perficiem AB, reducitur, & perindè reſiſtit ac ſi iņ <lb></lb>centro aggregati prædictarum fibrarum collocatą <lb></lb>eſſet, centrum verò omnium fibrarum prædictarum <lb></lb>idem eſt ac centrum I, quod eſt centrum eiuſdem ba<lb></lb>ſis; quaproptèr maximus conatus vniuerſæ reſiſten-<pb pagenum="186" xlink:href="010/01/194.jpg"></pb><arrow.to.target n="marg239"></arrow.to.target><lb></lb>tiæ ad diuulſionem exercetur in centro I circuli AB. <lb></lb></s> <s id="s.000950">Habebimus igitur vectem inflexum CBI in quo vis <lb></lb><expan abbr="mouẽs">mouens</expan> M applicatur in C, reſiſtentia verò applicatur <lb></lb>in I, & fulcimentum, ſeù centrum reuolutionis vectis <lb></lb>CBI eſt punctum B quod fixum perſeuerat dum cir<lb></lb>ca ipſum motus, & reuolutiones partium vectis <expan abbr="fiũt">fiunt</expan>; <lb></lb>Quaproptèr, iuxtà leges Mechanices, reſiſtentia to<lb></lb>talis ad diuulſionem, & ſeparationem ſuperficiei AB <lb></lb>ab ipſo pauimento ad vim <expan abbr="mouẽtem">mouentem</expan> M eamdem pro<lb></lb>portionem habebit, quam vectis longitudo CB ad <lb></lb>oppoſitam eius portionem BI, ſcilicèt habebit eam<lb></lb>dem proportionem. </s> <s id="s.000951">quam pondus S habet ad pondus <lb></lb>R. </s> <s id="s.000952">Verùm pondus R æquale erat potentiæ M. igitur <lb></lb>pondus S æquale erit reſiſtentię abſolutæ, & totali, <lb></lb>quam exercet ſuperficies AB quando diuelli, & ſe<lb></lb>parari debet à ſuperficie paui <expan abbr="mẽti">menti</expan> tractione directa. <lb></lb></s> <s id="s.000953">Hinc deducitur quòd ſi <expan abbr="põ-">pon<lb></lb></expan><figure id="id.010.01.194.1.jpg" xlink:href="010/01/194/1.jpg"></figure><lb></lb>dus O propoſitionis 89. di<lb></lb>uellit columnam à pauimento <lb></lb>directione, & impetu tranſ<lb></lb>uerſali, & perpendiculari ad <lb></lb>latus columnę, poterit nihilo<lb></lb>minùs indagari <expan abbr="reſiſtẽtia">reſiſtentia</expan> ab<lb></lb>ſoluta, & totalis contiguita<lb></lb>tis, vel repugnantiæ ad vacuum earumdem ſuperfi<lb></lb>cierum, eritque talis vis abſoluta tantomaior pon<lb></lb>dere O, quantò altitudo columnæ CB maior eſt ſe<lb></lb>miſſe diametri AB, & ſic ſi vis transuerſalitèr colum<lb></lb>nam diuellens æqualis eſſet ponderi trium librarum <pb pagenum="187" xlink:href="010/01/195.jpg"></pb><arrow.to.target n="marg240"></arrow.to.target><lb></lb>v. g. & altitudo columnæ CB decies maior radio ba<lb></lb>ſis, tunc totalis reſiſtentia prædictæ contiguitatis, ſeù <lb></lb>repugnantia ad vacuuum admittendum, æqualis erit <lb></lb>potentiæ ponderis triginta librarum. </s> <s id="s.000954">Quaproptèr <lb></lb>conſtat, quòd vis, quæ requiritur ad reſiſtentiam <expan abbr="cõ-tactus">con<lb></lb>tactus</expan> directè ſuperandam, licèt maior vt plurimùm <lb></lb>ſit, quàm ea quæ actu exercetur, nihilominùs finita, <lb></lb>& determinata eſt, & facili negotio indagari, men<lb></lb>ſurarique poteſt. </s> <s id="s.000955">His declaratis pergo ad <expan abbr="demõſtrã-dum">demonſtran<lb></lb>dum</expan>, quòd. </s> </p> <p type="margin"> <s id="s.000956"><margin.target id="marg238"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000957"><margin.target id="marg239"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000958"><margin.target id="marg240"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000959"><emph type="center"></emph>PROP. XCI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000960"><emph type="center"></emph><emph type="italics"></emph>Dato quolibet corpore duro homogeneo, aliudilli æquale repe<lb></lb>riri poteſt, cuius raritas abſoluta ad illius raritatem <lb></lb>maiorem proportionem qualibet dataratione <lb></lb>maioris inæqualitatis habeat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000961">SIt cylindrus ſolidus ABC, & <lb></lb><figure id="id.010.01.195.1.jpg" xlink:href="010/01/195/1.jpg"></figure><lb></lb>quælibet data ratio maioris <lb></lb>inæqualitatis T ad V, & fiat RS <lb></lb>maior quàm T. reperiri debetcy<lb></lb>linder æqualis ABC cuius rari<lb></lb>tas abſoluta ad raritatem ABC <lb></lb>ſit vt RS ad V. </s> <s id="s.000962">Secetur portio cy<lb></lb>lindrica AD, & RX proximè maior quam V, & fiat <lb></lb>cylindrus ſolidus EF æqualis AD, cuiuſ raritas in <lb></lb>ſpecie ad raritatem ipſius AC ſit vt RX ad V; poſtea <lb></lb>fiat alius cylindrus, ſiue fluidus, ſiue ſolidus FG æ<lb></lb>qualis DB, ita vt illius raritas in ſpecie ad raritatem <pb pagenum="188" xlink:href="010/01/196.jpg"></pb><arrow.to.target n="marg241"></arrow.to.target><lb></lb>eiuſdem AC ſit vt XS ad V. igitur duæ antecedentes <lb></lb>RX, & XS ad V, ſcilicet RS ad V eamdem propor<lb></lb>tionem habebit quam raritas ſpecifica aggregati ex <lb></lb>EF, & FG ad raritatem AC, ſuntquè moles EH, & <lb></lb>AC æquales, ergo eorum raritates abſolutæ ſunt pro<lb></lb>portionales ſpecificis, ſcilicèt ſe habent vt RS ad V. <lb></lb>quod erat, &c. </s> </p> <p type="margin"> <s id="s.000963"><margin.target id="marg241"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000964"><emph type="center"></emph>PROP. XCII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000965"><emph type="center"></emph><emph type="italics"></emph>Cylindrum compoſitum ex duobus cylindris inæqualitèr ra<lb></lb>ris transformare in cylindrum ſimilitèr excauatum, <lb></lb>cuius pars continens homogenea, & æqualis ſit. <lb></lb></s> <s id="s.000966">vni illorum, pars verò excauata homo<lb></lb>genea, & æqualis ſit reliquo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000967">SIt datus cylindrus ſoli<lb></lb><figure id="id.010.01.196.1.jpg" xlink:href="010/01/196/1.jpg"></figure><lb></lb>dus AC, compoſitus ex <lb></lb>duobus cylindris AD, & DB <lb></lb>inæqualitèr raris alium cy<lb></lb>lindrum ſimilitèr <expan abbr="excauatũ">excauatum</expan> <lb></lb>æqualem, & ſimilem illi de<lb></lb>ſcribere, cuius pars continens æqualis, & homoge<lb></lb>nea ſit ipſi AD, contenta verò æqualis, & homoge<lb></lb>nea ſit ipſi DB. reperto centro <expan abbr="q.">que</expan> cylindricæ figuræ <lb></lb>AC coniungantur rectæ AQ, BQ ad terminos lateris <lb></lb>cylindri AB, & fiat triangulum ENF ſimile, & æqua<lb></lb>le ipſi AQB. poſtea inter AB, & MB reperiantur duæ <lb></lb>mediæ proportionales, quarum maior ſit PB (vt do<lb></lb>cuimus lib. 5. conic. </s> <s id="s.000968">Apoll.lemm. 7.) deinde in <expan abbr="triã-">trian-</expan><pb pagenum="189" xlink:href="010/01/197.jpg"></pb><arrow.to.target n="marg242"></arrow.to.target><lb></lb>gulo ENF ducatur IK parallela EF, & æqualis ipſi <lb></lb>PB, & ducta RNS parallela ipſis EF, & IK reuolua<lb></lb>tur figura circa axim RS vt fiant duo cylindri <expan abbr="concẽ-trici">concen<lb></lb>trici</expan> EFGH, & IKLO; intelligatur modò ſpatium <lb></lb>internum IKLO repletum ſubſtantia homogenea ip<lb></lb>ſi cylindro DB, & reſiduum ambiens EFGH explea<lb></lb>tur ex eadem ſubſtantia corporea ipſius AD; & quia <lb></lb>AB ad MB, ſiuè cylinder AC ad cylindrum MC, vel <lb></lb>cylinder EG ad cylindrum IL triplicatam propor<lb></lb>tionem habet lateris AB ad PB, vel EF ad IK; ergo <lb></lb>cylinder AC ad MC eamdem proportionem habet, <lb></lb>quam integer cylindrus EG ad cauitatem cylindri<lb></lb>cam IL, & per conuerſionem rationis cylinder AC <lb></lb>ad. </s> <s id="s.000969">cylindrum AD ſe habet vt totus cylindrus EG <lb></lb>ad partem continentem EKGO. </s> <s id="s.000970">Suntque cylindri <lb></lb>AC, & EG æquales, cùm ſint ſimiles, & ſimilitèr po<lb></lb>ſiti circa latera æqualia AB, & EF, igitur cylinder <lb></lb>excauatus EKGO æqualis eſt ſibi homogeneo cylin<lb></lb>dro AD, proindeque cylinder IL æqualis, & homo<lb></lb>geneus erit ipſi MC, quod fuerat. </s> </p> <p type="margin"> <s id="s.000971"><margin.target id="marg242"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000972">His præhabitis noto, quòd cùm agitur de faculta<lb></lb><arrow.to.target n="marg243"></arrow.to.target><lb></lb>te, ſeù principio quo corpora vim faciunt tendendo <lb></lb>deorsùm, quęrimus tantummodò gradum virtutis <expan abbr="cõ-preſſiuæ">con<lb></lb>preſſiuæ</expan> eorum, quæ procùl dubio à grauitate, ſeu <lb></lb>pondere eorum menſuratur, hoc verò duplici modo <lb></lb>augeri poſſe conſtat, aut per multiplicationem eiuſ<lb></lb><arrow.to.target n="marg244"></arrow.to.target><lb></lb>dem corporis, vt cum lignea columna augetur mole, <lb></lb>aut cum <expan abbr="ſubſtãtia">ſubſtantia</expan> corporea, & plena in eodem ſpatio <lb></lb>diſſeminata, & contenta magis ſtringitur, conden-<pb pagenum="190" xlink:href="010/01/198.jpg"></pb><arrow.to.target n="marg245"></arrow.to.target><lb></lb>ſatur, conſtipaturque, & primum vocatur augmen<lb></lb>tum grauitatis extenſiuum, reliquum verò <expan abbr="intenſiuũ">intenſiuum</expan>. <lb></lb></s> <s id="s.000973">Regula verò, qua menſurari poteſt gradus prædictæ <lb></lb>grauitatis commodè deſumitur à vi contraria, quæ <lb></lb><arrow.to.target n="marg246"></arrow.to.target><lb></lb>depreſſionem eius prohibere poteſt, & hic <expan abbr="notandũ">notandum</expan> <lb></lb>eſt minimè nos ſollicitos eſſe de velocitate motus, <lb></lb>qua deorsùm eadem grauia feruntur, ſed tantummo<lb></lb>dò conſiderare vim, & conatum ponderis eius, qui <lb></lb>in libra à vi oppoſiti <expan abbr="æquipõdij">æquipondij</expan> præcisè menſuratur. <lb></lb><arrow.to.target n="marg247"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000974"><margin.target id="marg243"></margin.target>Vis compri<lb></lb>mens exten<lb></lb>ſiuè augetur <lb></lb>multiplicata <lb></lb>mole corpo<lb></lb>ris.</s> </p> <p type="margin"> <s id="s.000975"><margin.target id="marg244"></margin.target><expan abbr="Intẽſiuè">Intenſiuè</expan> ve<lb></lb>rò conſtipa<lb></lb>ta, & conden<lb></lb>ſata mate<lb></lb>ria.</s> </p> <p type="margin"> <s id="s.000976"><margin.target id="marg245"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000977"><margin.target id="marg246"></margin.target>Gradus præ<lb></lb>dictæ graui<lb></lb>tatis menſu<lb></lb>ratur à vi <expan abbr="cõtraria">con<lb></lb>traria</expan>, quæ <lb></lb><expan abbr="depreſſionẽ">depreſſionem</expan> <lb></lb>eius prohi<lb></lb>bere poteſt.</s> </p> <p type="margin"> <s id="s.000978"><margin.target id="marg247"></margin.target>Hic no agi<lb></lb>tur de velo<lb></lb>citate <expan abbr="deſcẽ-ſus">deſcen<lb></lb>ſus</expan>, ſed de vi <lb></lb><expan abbr="cõpreſſiua">compreſſiua</expan>.</s> </p> <p type="main"> <s id="s.000979"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO IX.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb><arrow.to.target n="marg248"></arrow.to.target></s> </p> <p type="margin"> <s id="s.000980"><margin.target id="marg248"></margin.target>Vis ſursùm <lb></lb><expan abbr="impellẽs">impellens</expan> quę <lb></lb>leuitas voca<lb></lb>tur augeri po<lb></lb>teſt extenſi<lb></lb>uè multipli<lb></lb>cato eodem <lb></lb>corpore le<lb></lb>ui.</s> </p> <p type="main"> <s id="s.000981">NOn ſecùs quando agitur de vi, & energia, quą <lb></lb>corpora, quæ leuia appellantur ſursùm moue<lb></lb>ri nituntur, quæritur non velocitas, ſed vis, quæ <lb></lb>ſursùm impellit, quæ leuitas appellari ſolet, & hæc <lb></lb>quoque duplici modo augeri poteſt, aut extenſiuè, <lb></lb>aut <expan abbr="intẽſiuè">intenſiuè</expan>, ſcilicèt aut <expan abbr="multiplicãdo">multiplicando</expan> molem <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>corporis leuis, vt ſphæra aeris palmaris octies <expan abbr="maio-rẽ">maio<lb></lb>rem</expan> <expan abbr="leuitatẽ">leuitatem</expan> habebit, <expan abbr="quã">quam</expan> ſphæra <expan abbr="eiuſdẽ">eiuſdem</expan> aeris ſemipal<lb></lb>maris, propterea quod vis illa leuitatis tantumdem <lb></lb>multiplicatur, quantum maſſa eius corporea exten<lb></lb>ditur, cùm omnes partes eiuſdem aeris æquè leues <lb></lb>ſint, & æquè raræ, requiraturque vis contraria pro<lb></lb>hibens illius aſcenſum octiès maior quam in huius <lb></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"></arrow.to.target><lb></lb>ri poteſt leuitas expandendo, & rarefaciendo <expan abbr="ſubſtã-">ſubſtan-</expan><pb pagenum="191" xlink:href="010/01/199.jpg"></pb><arrow.to.target n="marg250"></arrow.to.target><lb></lb>tiam corpoream, & plenam, vt nimirum maius <lb></lb>ſpatium occupet, & in hoc caſu comparari debent <lb></lb>ſpatia occupata, ſiuè moles æquales inter ſe, & <expan abbr="cũ">cum</expan> <lb></lb>medio fluido in quo leuitant, vt ſi fuerint duæ pilæ <lb></lb>æquales, vna aquea, altera aerea intra <expan abbr="mercuriũ">mercurium</expan> de<lb></lb>merſę, dicetur maior leuitas intenſiuè aeris reſpectu <lb></lb>leuitatis aquæ, & leuitates eamdem proportionem <lb></lb>habebunt, quàm raritates molium æquallum aeris, <lb></lb><arrow.to.target n="marg251"></arrow.to.target><lb></lb>& aquę in mercurio conſideratæ habent. </s> <s id="s.000984">Et hoc eui<lb></lb>dentia ſenſus ſuadet, ſi enim intra hydrargyrum de<lb></lb>mergatur ampulla vitrea plumbo repleta, huius qui<lb></lb>dem gradus leuitatis menſuratur à vi <expan abbr="cõntraria">contraria</expan>, quæ <lb></lb>aſcenſum eius in mercurio prohibere poteſt, ſitque <lb></lb>talis vis contraria pondus duarum vnciarum ſuper<lb></lb>poſitum, & intra mercutium fixè detinens <expan abbr="natantẽ">natantem</expan> <lb></lb>ampullam. </s> <s id="s.000985">Si poſtea plumbi vncia è cauitate ampul<lb></lb>læ ſubtrahatur, patet quod <expan abbr="tantũ">tantum</expan> præcisè totius am<lb></lb>pullæ raritas aucta erit, quantum diminuta fuit ſub<lb></lb>ſtantia corporea ponderoſa intra ampullam eiuſdem <lb></lb>molis, & figuræ contenta, & tunc gradus leuitatis <lb></lb>præcisè augebitur vna vncia, nam ſi velimus <expan abbr="aſcensũ">aſcensum</expan> <lb></lb>eiuſdem ampullæ prohibere ſuperponi debent non <lb></lb>duæ vt priùs, ſed tres vnciæ, poſtea ſi ampullæ rari<lb></lb>tas denuò augeatur detracta altera <expan abbr="plũbi">plumbi</expan> vncia, gra<lb></lb>dus quoque leuitatis eadem menſura creſcet vt ni<lb></lb>mirùm requirantur quatuor vnciæ ad prohibendum <lb></lb>eius aſcenſum è mercurio, idemque verificatur ſi <lb></lb>vlterius pondus internum ampullæ diminuatur; qua<lb></lb>re incrementa leuitatis proportionalia ſunt incre-<pb pagenum="192" xlink:href="010/01/200.jpg"></pb><arrow.to.target n="marg252"></arrow.to.target><lb></lb>mentis raritatis eiuſdem corporis. </s> </p> <p type="margin"> <s id="s.000986"><margin.target id="marg249"></margin.target>Intenſiuè <lb></lb>verò rarefa<lb></lb>ciendo id in <lb></lb>corpus.</s> </p> <p type="margin"> <s id="s.000987"><margin.target id="marg250"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.000988"><margin.target id="marg251"></margin.target>Incrementa <lb></lb><expan abbr="leuitatũ">leuitatum</expan> pro<lb></lb>portionalia <lb></lb><expan abbr="sũt">sunt</expan> <expan abbr="incremẽ-tis">incremen<lb></lb>tis</expan> raritatum <lb></lb>eiuſdem cor<lb></lb>poris <expan abbr="eius-dẽque">eius<lb></lb>demque</expan> molis, <lb></lb>& <expan abbr="mẽsuran-tur">mensuran<lb></lb>tur</expan> à vi <expan abbr="põderum">ponde<lb></lb>rum</expan> <expan abbr="prohibantiũ">prohi<lb></lb>bentium</expan> eleua<lb></lb>tiones.</s> </p> <p type="margin"> <s id="s.000989"><margin.target id="marg252"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000990">Hinc inferri licet, quòd ſi raritas non eſt cauſa ef<lb></lb>fectiua, motus ſursùm, ſeù leuitatis, requiritur <expan abbr="ſaltẽ">ſaltem</expan> <lb></lb>raritas tamquam affectio neceſſaria, ſine qua leuitas <lb></lb><arrow.to.target n="marg253"></arrow.to.target><lb></lb>minimè augeri poteſt, ſed oportet vt raritates in ali<lb></lb>quo medio fluido conſiderentur, non autem abſolu<lb></lb>tè, & in vacuo. </s> </p> <p type="margin"> <s id="s.000991"><margin.target id="marg253"></margin.target>Si raritas <expan abbr="nõ">non</expan> <lb></lb>eſt causa aſ<lb></lb>cenſus <expan abbr="leuiũ">leuium</expan>, <lb></lb>requiritur <lb></lb><expan abbr="tamẽ">tamen</expan> neceſ<lb></lb>ſariò</s> </p> <p type="main"> <s id="s.000992"><emph type="center"></emph>PROP. XCIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000993"><emph type="center"></emph><emph type="italics"></emph>Reperire modò poſſumus corpus, quod in dato fluido aſcendat <lb></lb>tanta vi ſursùm, quæ ſuperet quamcumque finitam <lb></lb>vim.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000994">SIt vas ABC <expan abbr="repleaturq;">repleaturque</expan> flui<lb></lb><figure id="id.010.01.200.1.jpg" xlink:href="010/01/200/1.jpg"></figure><lb></lb>do M quod ſit aqua, vel hy<lb></lb>drargyrum, & ſit quælibet va<lb></lb>ſta vis motiua R. debet reperiri <lb></lb>corpus, quod in prædicto fluido <lb></lb>innatet, atque ab eius <expan abbr="fũdo">fundo</expan> ſur<lb></lb>sum aſcendat tanta vi, & energia <lb></lb>vt ſuperet vim datam R. ſuma<lb></lb>tur cylindrus DE cuiuſcumque <lb></lb>ſolidæ materiei conſiſtentiſque, <lb></lb>earum tamen, quæ in prædicto fluido M innatant, <lb></lb>et vis qua corpus DE aſcendit è fundo fluidi M ſit S: <lb></lb>poſtea (ex duabus præcedentibus propoſitionibus) <lb></lb>reperiatur cylindrus excauatus FG, cuius externą <lb></lb>figura ſit æqualis, & ſimilis ipſi DE, itaut raritas ab<lb></lb>ſoluta ipſius FG ad <expan abbr="raritatẽ">raritatem</expan> alterius DE <expan abbr="maiorẽ">maiorem</expan> pro-<pb pagenum="193" xlink:href="010/01/201.jpg"></pb><arrow.to.target n="marg254"></arrow.to.target><lb></lb>portionem habeat, <expan abbr="quã">quam</expan> R ad S, & quia (ex 9. ſuppoſi<lb></lb>tione) impetus, & energia, qua cylindrus FG ſur<lb></lb>sùm fertur in dato fluido M ad eam vim, qua cylin<lb></lb>drus DE priori æqualis ſursùm fertur in eodem flui<lb></lb>do eamdem proportionem habet, quam raritas cor<lb></lb>poris FG ad raritatem alterius DE, habentque præ<lb></lb>dictæ raritates ne dum abſolutè, ſed etiam in medio <lb></lb>fluido mercuriali conſideratæ, maiorem proportio<lb></lb>nem, quam R ad S, igitur vis, & robur, quo cylindrus <lb></lb>FG ſursùm aſcendit in fluido M ad eam vim, qua ele<lb></lb>uatur ibidem cylindrus DE maiorem proportionem <lb></lb>habebit, quam R ad S, erat verò S vis, qua ſolidum <lb></lb>DE ſursùm transferebatur in fluido M, ergò validi<lb></lb>tas, & energia, qua aſcendit cylindrus FG in <expan abbr="eodẽ">eodem</expan> <lb></lb>fluido maior erit, quàm R, & hoc propoſitum fuerat. </s> </p> <p type="margin"> <s id="s.000995"><margin.target id="marg254"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.000996">Sed poſſumus faciliùs, & breuiori apparatu pro<lb></lb>blema abſoluere, ſi modò moles corporis innatantis <lb></lb>intra aliud fluidum ſimpliciter augeatur multiplice<lb></lb>turque. </s> </p> <p type="main"> <s id="s.000997"><emph type="center"></emph><emph type="italics"></emph>SVPPOSITIO X.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000998">VT <expan abbr="præcedẽs">præcedens</expan> problema faciliùs effici poſſit, priùs <lb></lb>præmitti debet, quòd quando agitur de vi, & <lb></lb>energia leuitatis, ſenſu conſtat duas æquales moles e<lb></lb>iuſdem corporis homogenei v.g. eiuſdem ligni æquè <lb></lb>leues eſſe, ſcilicèt exercere conatus impulſiuos <expan abbr="ſursũ">ſursum</expan> <lb></lb>inter ſe æquales in eodem fluido, in aqua nempè, ita <lb></lb>ut impelli deorsùm debeant ab æqualibus ponderi<lb></lb>bus ad hoc vt vetentur eorum aſcenſus, & fixè infra <pb pagenum="194" xlink:href="010/01/202.jpg"></pb><arrow.to.target n="marg255"></arrow.to.target><lb></lb>ſupremam aquæ libellam detineantur. </s> <s id="s.000999">paritèr <expan abbr="certũ">certum</expan> <lb></lb>eſt inæquales moles eiuſdem ligni inæquales vires <lb></lb>leuitatum in aqua habere, & inæqualibus conatibus, <lb></lb>& viribus ſursùm impellere; nam ſi ex ligno maiori <lb></lb>ſecetur auferaturque vna pars æqualis moli ligni mi<lb></lb>noris, hæ cùm ſint æquè leues, moleſque æquales ha<lb></lb>beant, vt nimirùm prohiberi eorum aſcenſus noņ <lb></lb>poſſint, niſi ab æqualibus ponderibus <expan abbr="incumbẽtibus">incumbentibus</expan>, <lb></lb>videtur impoſſibile vt exceſſus ille ligni maioris ſu<lb></lb>pra minorem (cùm ſit eiuſdem naturæ ligneæ proin<lb></lb>de que leuis) vim ſursùm non exerceat pro menſura <lb></lb>ſuæ quantitatis, & proinde requirat vim contrariam <lb></lb>alicuius ponderis incumbentis, vt eius aſcenus pro<lb></lb>hibeatur. </s> </p> <p type="margin"> <s id="s.001000"><margin.target id="marg255"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.001001"><emph type="center"></emph>PROP. XCIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001002"><emph type="center"></emph><emph type="italics"></emph>Hoc ſuppoſito demonſtrabo, quòd duæ moles eiuſdem leuis <lb></lb>corporis ſursùm impellendo in eodem fluido exercent <lb></lb>vires, quæ eamdem proportionem habent, quam <lb></lb>moles ipſæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001003">IN vaſe FDE aqua pleno, vel alio <lb></lb><figure id="id.010.01.202.1.jpg" xlink:href="010/01/202/1.jpg"></figure><lb></lb>fluido demergantur duæ inæqua<lb></lb>les moles eiuſdem ligni, quæ ſcilicèt <lb></lb>æquè rarę ſint ſpecie, vt ſunt ABC, & <lb></lb>HIK, ſit que S leuitas, ſeù vis qua li<lb></lb>gnum ABC <expan abbr="ſursũ">ſursum</expan> aſcendit; atque R <lb></lb>ſit leuitas alterius HIK. </s> <s id="s.001004">Dico quòd <lb></lb>leuitas S ad R eamdem <expan abbr="proportionẽ">proportionem</expan> <pb pagenum="195" xlink:href="010/01/203.jpg"></pb><arrow.to.target n="marg256"></arrow.to.target><lb></lb>habet, quam lignea moles ABC ad molem HIK. po<lb></lb>natur leuitas, aut vis <expan abbr="eleuãs">eleuans</expan> N, quæ habeat ad R <expan abbr="quã-libet">quan<lb></lb>libet</expan> proportionem commenſurabilem ex inſinitis, <lb></lb>quæ proponi poſſunt pariterque fiat moles BM ex <lb></lb>eodem ligno conſtans quæ ad HIK ſe habeat vt N <lb></lb>ad R. mani feſtum eſt, quòd quotieſcumque lignum <lb></lb>BM æquatur ligno ABC, runc paritèr vis leuitatis N <lb></lb>æqualis erit ipſi S (eò quòd moles æquales eiuſdem̨ <lb></lb>ligni ſursùm æquali vi leuitatis impellunt) & <expan abbr="quo-tieſcũque">quo<lb></lb>tieſcunque</expan> ligni moles BM maior fuerit, quàm ABC <lb></lb>ſemper leuitas N maior erit leuitate S, & quando li<lb></lb>gnum BM minus fuerit, quàm ABC, erit quoque le<lb></lb>uitas N minor, quàm S, & habent BM, HIK, & N & <lb></lb>R quamcumque proportionalitatem commenſurabi<lb></lb>lem, igitur (ex noſtro Euclide reſtituto) moles li<lb></lb><arrow.to.target n="marg257"></arrow.to.target><lb></lb>gnea ABC ad molem HIK eamdem proportionem̨ <lb></lb>habebit quam vis leuitatis S, qua nimirùm ABC in <lb></lb>aqua aſcendit, ad leuitatem R qua corpus HIK ele<lb></lb>uatur in eodem fluido, quòd fuerat &c. </s> </p> <p type="margin"> <s id="s.001005"><margin.target id="marg256"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.001006"><margin.target id="marg257"></margin.target>Lib. 3 prop. <lb></lb></s> <s id="s.001007">24.</s> </p> <p type="main"> <s id="s.001008">Si quis fortè ſuſpicaretur ex figurarum diuerſitate <lb></lb><arrow.to.target n="marg258"></arrow.to.target><lb></lb>prædictorum corporum leuium licèt eiuſdem conſi<lb></lb>ſtentiæ homogeneæ ſint, & eumdem gradum rarita<lb></lb>tis habeant, alterari poſſe iam dictam proportionali<lb></lb>tatem, monendus profectò eſt, quod præter Ariſtote<lb></lb><arrow.to.target n="marg259"></arrow.to.target><lb></lb>lis aſſertum, vbi ait, quod <emph type="italics"></emph>figuræ non ſunt cauſæ ſimplici<lb></lb>tèr aſcenſus, vel deſcenſus corporum in fluido, ſed tantum<lb></lb>modò tardioris, vel celerioris motus<emph.end type="italics"></emph.end>, idipſum poſtea de<lb></lb>monſtratum fuit ex Mechanicis principijs à Ghetal<lb></lb>do, & Galilæo. </s> <s id="s.001009">attamen incaſu noſtro non requirun-<pb pagenum="196" xlink:href="010/01/204.jpg"></pb><arrow.to.target n="marg260"></arrow.to.target><lb></lb>tur figuræ corporum aſcendentium omninò diuer<lb></lb>ſæ, & diſſimiles inter ſe, quia æquè benè noſtræ de<lb></lb>monſtrationi aptari poſſunt cylindri æquè alti, & in<lb></lb>æqualium baſium, ſiuè contra ſi baſes æquales ſint, <lb></lb>altitudines ſint inæquales. </s> <s id="s.001010">hoc præmiſſo libet <expan abbr="idipsũ">idipsum</expan> <lb></lb>problema alia ratione reſoluere. </s> </p> <p type="margin"> <s id="s.001011"><margin.target id="marg258"></margin.target>Diuerſitas <lb></lb><expan abbr="figuratū">figuratum</expan> non <lb></lb>alterat præ<lb></lb>dictam pro<lb></lb>portionali<lb></lb>tatem.</s> </p> <p type="margin"> <s id="s.001012"><margin.target id="marg259"></margin.target>4. de Cælo. <lb></lb></s> <s id="s.001013">cap. 6.</s> </p> <p type="margin"> <s id="s.001014"><margin.target id="marg260"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.001015"><emph type="center"></emph>PROP. XCV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001016"><emph type="center"></emph><emph type="italics"></emph>Dato quocumque fluido, in quo corpus aliquod ſolidum inna<lb></lb>tare valeat, reperiri debet moles quam habere debet, <lb></lb>vt in eadem fluido aſcendere posſit tanta vi, vt <lb></lb>ſuperet quamcumque finitam virtutem <lb></lb>motiuam.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001017">SIt vas FDE, impleaturquę <lb></lb><figure id="id.010.01.204.1.jpg" xlink:href="010/01/204/1.jpg"></figure><lb></lb>fluido M, aqua nimirùm, aut <lb></lb>quolibet alio conſiſtenti fluido. <lb></lb></s> <s id="s.001018">Sumatur poſtea ligneus cylinder <lb></lb>ABC, vel quælibet alia materia, <lb></lb>quæ in prędicto fluido innatet, ſit<lb></lb>que quælibet immenſa, ſed <expan abbr="tamẽ">tamen</expan> <lb></lb>finita vis R, debet reperiri mo<lb></lb>les, & amplitudo quam haberę <lb></lb>debet corpus aliud homogeneum <lb></lb>ipſi ABC, vt tanta vi in fluido M aſcendat quæ maior <lb></lb>ſit virtute motiua R. </s> <s id="s.001019">Immergatur in eodem fluido <lb></lb>cylindrus ABC, eiuſque leuitas in fluido, ſeu vis, qua <lb></lb>nititur in eo <expan abbr="aſcẽdere">aſcendere</expan> ſit S. </s> <s id="s.001020">Poſteà fiat cylindrus HIK <lb></lb>ſimilis homogeneus, & eiuſdem materiæ ac eſt ABC, <pb pagenum="197" xlink:href="010/01/205.jpg"></pb><arrow.to.target n="marg261"></arrow.to.target><lb></lb>& tantæ vaſtitatis, vt ad eum moles ABC minorem <lb></lb>proportionem habeat, quam S ad R, ſcilicèt ſit vt S <lb></lb>ad V, quæ maior erit quam R, & quia eiuſdem ſub<lb></lb>ſtantiæ nempè ligni factæ ſunt duæ moles ABC, & <lb></lb>HIK; igitur (ex præcedenti) vt cylindrus ABC ad <lb></lb>HIK, ita ſe habet abſoluta leuitas illius S ad huius le<lb></lb>uitatem, quæ erit V, & habet S ad R <expan abbr="maiorẽ">maiorem</expan> propor<lb></lb>tionem, quàm moles ABC ad HIK, igitur leuitas V, <lb></lb>ſeù vis, qua ſolidum HIK aſcendit in fluido M maior <lb></lb>eſt quacumque data vi finita R. </s> </p> <p type="margin"> <s id="s.001021"><margin.target id="marg261"></margin.target>Cap. 4. poſi<lb></lb>tiuam <expan abbr="leui-tatẽ">leui<lb></lb>tatem</expan> <expan abbr="nõ">non</expan> dari.</s> </p> <p type="main"> <s id="s.001022"><emph type="center"></emph>PROP. XCVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001023"><emph type="center"></emph><emph type="italics"></emph>Idipſum problema effici poſſe methodo Archimedæa ſic <lb></lb>ostendemus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001024">SVmatur lignum L, vel aliud <lb></lb><figure id="id.010.01.205.1.jpg" xlink:href="010/01/205/1.jpg"></figure><lb></lb>corpus ſibi homogeneum, <lb></lb>quod innatare poſſit intra flui<lb></lb>dum M, ponaturque quælibet <lb></lb>vis finita ponderis P, atque vt <lb></lb>pondus abſolutum molis fluidi <lb></lb>M, quæ æqualis ſit ipſi L, ad <lb></lb>pondus abſolutum ligni L, ſci<lb></lb>licèt vt grauitas ſpecifica flui<lb></lb>di M ad L, it a ſe habeat R ad S, <lb></lb>poſtea fiat cylindrus ACB <expan abbr="eiuſdẽ">eiuſdem</expan> materiei L, ad cuius <lb></lb>grauitatem abſolutam <expan abbr="põdus">pondus</expan> P minorem proportio<lb></lb>nem habeat, quàm differentia ipſarum R, & S ad S. <lb></lb></s> <s id="s.001025">Tandem immergatur cylindrus AC intra fluidum M <pb pagenum="198" xlink:href="010/01/206.jpg"></pb><arrow.to.target n="marg262"></arrow.to.target><lb></lb>contentum in vaſe FDE tantæ profunditatis, vt cy<lb></lb>lindrus AC vniuersè, & perpendicularitèr ad Hori<lb></lb>zontem mergi poſſit, vt eius baſis non contingat <expan abbr="fũ-dum">fun<lb></lb>dum</expan> vaſis FDE, atque ſupremus terminus C fluidi li<lb></lb>bellam contingat. </s> <s id="s.001026">Præterea applicari debet pondus <lb></lb>P ſupra verticem cylindri CA, itaut pondus P immi<lb></lb>neat ſupra fluidi libellam, neque aliqua eius portio <lb></lb><figure id="id.010.01.206.1.jpg" xlink:href="010/01/206/1.jpg"></figure><lb></lb>demergatur. </s> <s id="s.001027">His præparatis <lb></lb>quia exceſſus <expan abbr="põderis">ponderis</expan> R ſupra <lb></lb>S ad ipſum pondus S maiorem <lb></lb><expan abbr="proportionẽ">proportionem</expan> habet quam gra<lb></lb>uitas P ad pondus cylindri <lb></lb>ACB, ergò componendo, gra<lb></lb>uitas R ad S <expan abbr="maiorẽ">maiorem</expan> proportio <lb></lb>nem habebit quàm duo <expan abbr="põde-ra">ponde<lb></lb>ra</expan> P, & CAB, ſimul ſumpta, ad <lb></lb>pondus CAB; verùm grauitas <lb></lb>molis fluidi M æqualis ſolido AC ad pondus abſolu<lb></lb>tum eiuſdem ſolidi AC habet eamdem <expan abbr="proportionẽ">proportionem</expan>, <lb></lb>quam R ad S, ergò moles fluidi M æqualis ſolido AC <lb></lb>ad ſolidum idipſum AC, ſeù illius pondus ad graui<lb></lb>tatem huius habebit maiorem proportionem quàm <lb></lb>pondera P, & CAB ſimùl ſumpta ad pondus AC, & <lb></lb>proindè pondus abſolutum molis fluidi M æqualis <lb></lb>AC maius erit grauitate ipſius P vnà cum ponderę <lb></lb>cylindri AC. </s> <s id="s.001028">Verumtamen Archimedes demonſtra<lb></lb><arrow.to.target n="marg263"></arrow.to.target><lb></lb>uit ſolidum innatans tunc ſolummodò in fluido quie<lb></lb>ſcere quando eius pondus abſolutum æquale fuerit <lb></lb>grauitati molis fluidi ambientis, quæ ſit æqualis por-<pb pagenum="199" xlink:href="010/01/207.jpg"></pb><arrow.to.target n="marg264"></arrow.to.target><lb></lb>tioni eiuſdem ſolidi intra eiuſdem fluidi libellam de<lb></lb>merſi. </s> <s id="s.001029">Qua proptèr quando pondus abſolutum præ<lb></lb>dicti ſolidi minus fuerit pondere prædicti fluidi am<lb></lb>bientis æqualis portioni eius demerſæ neceſſariò <lb></lb>ſolidum ipſum in fluido eleuabitur vlteriuſque <expan abbr="aſcẽ-det">aſcen<lb></lb>det</expan>, igitur Cylindrus AC vnà cum ſuperincumben<lb></lb>te pondere P eique coniuncto, & continuato noņ <lb></lb>quieſcet, ſed ſursùm aſcendet, quaproptèr vis pre<lb></lb>mens ponderis P non ſufficit, nec habet tantam̨ <lb></lb>vim vt retineat ſolidum AC integrè infra fluidi <lb></lb>M libellam demerſum. </s> <s id="s.001030">Cùmque, vt Archimedes de<lb></lb><arrow.to.target n="marg265"></arrow.to.target><lb></lb>monſtrauit, energia, & vis, qua ſolidum AC cona<lb></lb>tur, & vim facit vt ſursùm aſcendat in fluido M ęqua<lb></lb>lis ſit vi illius ponderis, quod ſi ſuper id imponatur, <lb></lb>poteſt id retinere infra fluidi libellam prohibereque <lb></lb>eius aſcenſum, igitur vis, qua cylindrus AC conatur <lb></lb>ſursùm aſcendere in fluido M maior eſt quacumque <lb></lb>vi finita ponderis P, & hoc propoſitum fuerat. </s> </p> <p type="margin"> <s id="s.001031"><margin.target id="marg262"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.001032"><margin.target id="marg263"></margin.target>De <expan abbr="inſidẽt">inſident</expan>. <lb></lb>humido lib. <lb></lb>5. prop. 4.</s> </p> <p type="margin"> <s id="s.001033"><margin.target id="marg264"></margin.target>Cap. 4. poſi<lb></lb>tiuam <expan abbr="leui-tatẽ">leui<lb></lb>tatem</expan> <expan abbr="nõ">non</expan> dari.</s> </p> <p type="margin"> <s id="s.001034"><margin.target id="marg265"></margin.target>Eod. lib. 1. <lb></lb>prop. 6.</s> </p> <p type="main"> <s id="s.001035"><emph type="center"></emph>PROP. XCVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001036"><emph type="center"></emph><emph type="italics"></emph>His præmisſis deuenio iam ad propoſitionem <expan abbr="principalẽ">principalem</expan>, quòd <lb></lb>nimirùm quodlibet corpus ſursùm aſcendens in date <lb></lb>aliquo fluido non eleuatur ſponte ſua à principio <lb></lb>nempè intrinſeco leuitatis impulſum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001037">SIt L quodlibet corpus eorum, quæ à Peripateti<lb></lb>cis vocantur à prædominio aerea, vt ſunt ferè <lb></lb>omnia ligna, & alia innumera, & fluidum M in vaſe <lb></lb>FDI <expan abbr="contẽtum">contentum</expan>, ſit que prædictum fluidum, aut aqua, <pb pagenum="200" xlink:href="010/01/208.jpg"></pb><arrow.to.target n="marg266"></arrow.to.target><lb></lb>aut hydrargyrum; procùl dubio corpus L intra flui<lb></lb>dum M demerſum ſursùm aſcendet. </s> <s id="s.001038"><expan abbr="Demonſtrandũ">Demonſtrandum</expan> <lb></lb>modò eſt idipſum non ſpontaneo motu ab intrinſeco <lb></lb>principio leuitatis aſcendere. </s> <s id="s.001039">Si hoc enim verum̨ <lb></lb><figure id="id.010.01.208.1.jpg" xlink:href="010/01/208/1.jpg"></figure><lb></lb>non eſt, ſit, ſi fieri poteſt leuitas <lb></lb>corporis L naturalis cauſa, & <lb></lb>virtus à qua ſpontaneo motu <lb></lb>ſursùm impellatur in fluido M. <lb></lb></s> <s id="s.001040">Et primò pręparetur infima ba<lb></lb>ſis AB cylindri homogenei ipſi <lb></lb>L, vt nimirùm ei vniatur ferru<lb></lb>mineturque lamina aliqua vi<lb></lb>trea, vel metallica, quæ ſit op<lb></lb>timè explanata, & læuigata, & eiuſdem materiæ, at<lb></lb>que figuræ, & læuitatis ſit pauimentum, vel fundum <lb></lb>putei DE. </s> <s id="s.001041">Secundo loco reperta iam ſit <expan abbr="mẽſura">menſura</expan> cer<lb></lb><arrow.to.target n="marg267"></arrow.to.target><lb></lb>ta, & determinata illius virtutis, quæ requiritur ad <lb></lb>ſeparandam, & diuellendam ſuperficiem vitri AB ab <lb></lb>immediato contactu cum fundo putei DE, ſiuè vis <lb></lb>illa, quæ ſuperare valet reſiſtentiam prædictarum̨ <lb></lb>ſuperficierum ſe tangentium ad vacuum admitten<lb></lb>dum; ſupponamuſque huiuſmodivim eſſe æqualem̨ <lb></lb><arrow.to.target n="marg268"></arrow.to.target><lb></lb>ponderi G, atque reperiatur cylindrus AC eiuſdem <lb></lb>materiei L itaut vis leuitatis qua conatur ſursùm mo<lb></lb>ueri in fluido M vna cum vitrea lamina AB maior ſit <lb></lb>vi, & energia ponderis G, ſitque vis illa leuitatis æ<lb></lb>qualis potentię H. quapropter vis qua ſolidum AC <lb></lb>conatur, & impetum facit vt ſursùm in dato fluido <lb></lb>aſcendat, maior eſt illa vi, & facultate, quæ requi-<pb pagenum="201" xlink:href="010/01/209.jpg"></pb><arrow.to.target n="marg269"></arrow.to.target><lb></lb>ritur ad ſeparandam, & diuellendam baſim AB à fun<lb></lb>do putei DE horizonti æquidiſtante. </s> <s id="s.001042">dum igitur ba<lb></lb>ſis AB immediatè, & exquiſitè tangit fundum putei <lb></lb>DE, vt ſibi mutuò congruant, exoſculenturque, re<lb></lb>pleatur vniuerſum vas FE prædicto fluido M quouſ<lb></lb>que ſuprema fluidi libella ad ſummitatem C cylindri <lb></lb>AC demerſi pertingat. </s> <s id="s.001043">Et quia hìc iam exiſtunt, & <lb></lb>operantur duæ vires contrariæ, vna quidem H im<lb></lb>pellit ſursùm, eſtque virtus eius leuitatis, alia verò <lb></lb>G, quæ huic reſiſtit, & vim deorsùm tendendo facit, <lb></lb>eſtque energia contactus ſuperficierum AB & DE, <lb></lb>ſeù repugnantia ad vacuum admittendum qua con<lb></lb>trario niſui aſcenſus cylindri AC reſiſtit: Eſtque <expan abbr="cõ-traria">con<lb></lb>traria</expan> vis H leuitatis, prædicti cylindri maior virtu<lb></lb>te G tenacitatis, vel repugnantiæ ad vacuum, quæ <lb></lb>impetum contrarium deorsùm facit; igitur maior vis <lb></lb>leuitatis H neceſſariò ſuperare debet vim minorem <lb></lb>G, & proinde diſtrahet diuelletque cylindrum AC à <lb></lb>fundo putei DE, atque poſt ſeparationem idipſum̨ <lb></lb>ſursùm ad ſuperficiem fluidi M impellet, transferet<lb></lb>que; ſed hoc eſt falſum, & contra ſenſus <expan abbr="euidentiã">euidentiam</expan>, <lb></lb>proptereà quòd numquam contingit vt baſis colum<lb></lb>næ AB ſeparetur à <expan abbr="cõtactu">contactu</expan> fundi putei DE, licèt ſup<lb></lb>ponatur vim leuitatis quocumque exceſſu vim con<lb></lb>tactus ſuperare, igitur verum non eſt cylindrum AC <lb></lb>ſursùm impelli ab intrinſeca, & poſitiua facultatę <lb></lb>leuitatis eius, quod fuerat demonſtrandum. <pb pagenum="202" xlink:href="010/01/210.jpg"></pb><arrow.to.target n="marg270"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001044"><margin.target id="marg266"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.001045"><margin.target id="marg267"></margin.target>Prop. 88. & <lb></lb>89.</s> </p> <p type="margin"> <s id="s.001046"><margin.target id="marg268"></margin.target>Pro. 93. 95. <lb></lb>& 96.</s> </p> <p type="margin"> <s id="s.001047"><margin.target id="marg269"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="margin"> <s id="s.001048"><margin.target id="marg270"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.001049"><emph type="center"></emph>PROP. XCVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001050"><emph type="center"></emph><emph type="italics"></emph>Confirmatur eadem præcedens propoſitio.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001051">ET procùl dubio cenſeri non debet vera cauſą <lb></lb>alicuius effectus illa qua poſita, & non impe<lb></lb>dita ab excedente vi contraria, non ponitur nihilo<lb></lb>minùs, nec ſubſequitur effectus, ſed poſita leuitatę <lb></lb>poſitiua in prædicta lignea columna AC infra <expan abbr="fluidũ">fluidum</expan> <lb></lb>M demerſa, & non impedita à virtute contraria con<lb></lb>tactus, aut à timore vacui (eò quòd ex conſtructio<lb></lb>ne hæc multò minor fuerat virtute, & energia leui<lb></lb>tatis) non ſubſequitur nihilominùs effectus aſcenſus <lb></lb>columnæ in prædicto fluido, igitur leuitas poſitiuą <lb></lb>non eſt cauſa <expan abbr="aſcẽſus">aſcenſus</expan> <expan abbr="ſursũ">ſursum</expan> prædicti ligni in fluido M. </s> </p> <p type="main"> <s id="s.001052">Poſtquam oſtenſa fuit prędicta negatiua propoſi<lb></lb>tio. </s> </p> <p type="main"> <s id="s.001053"><emph type="center"></emph>PROP. XCIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001054"><emph type="center"></emph><emph type="italics"></emph>Demonſtrabitur iam quod neceſſariò admitti debet cum Pla<lb></lb>tone, & Archimede, quòd corpora omnia, quæ leuia <lb></lb>appellantur ſursùm aſcendunt ab extruſione <lb></lb>fluidorum in quibus innatant ob exceſſum <lb></lb>grauitatis eorumdem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001055">QVia illa eſt vera cauſa alicuius effectus natura<lb></lb>lis, qua poſita ſubſequitur effectus, & ablata <lb></lb>pariter effectus tollitur, ſed poſita extruſione facta <lb></lb>à corpore fluido grauiori ſubſequitur effectus aſcen-<pb pagenum="203" xlink:href="010/01/211.jpg"></pb><arrow.to.target n="marg271"></arrow.to.target><lb></lb>ſus nimirùm ſolidi minùs grauis in eo demerſi, & <lb></lb>quotieſcumque prædicta extruſio tollitur, aut im<lb></lb>peditur, aufertur quoque vetaturque aſcenſus præ<lb></lb>dicti corporis ſolidi, igitur neceſſariò prædicta ex<lb></lb>truſio grauioris fluidi ambientis eſt vera, & legitima <lb></lb>cauſa aſcenſus eorum corporum, quæ leuia <expan abbr="appellã-tur">appellan<lb></lb>tur</expan>; ſic quia in hypotheſi in propoſitione 97 expoſi<lb></lb>ta extruſio aquæ, vel hydrargyri tollitur, & impedi<lb></lb><figure id="id.010.01.211.1.jpg" xlink:href="010/01/211/1.jpg"></figure><lb></lb>tur, cùm fluidum M interlabi, <lb></lb>aut excurrere non poſſit infra <lb></lb>baſim AB prædictæ columnę ob <lb></lb>arctam connexionem contactus <lb></lb>baſis AB cum fundo putei DE, <lb></lb>licèt ambiens <expan abbr="fluidũ">fluidum</expan> multò gra<lb></lb>uius ſit prædicta <expan abbr="colũna">columna</expan> lignea, <lb></lb>& in tali caſu columna ſursùm <lb></lb>in fluido <expan abbr="nõ">non</expan> aſcendit. </s> <s id="s.001056">E contrà <lb></lb>quotieſcumque extruſio fieri poteſt, ſcilicèt quoties <lb></lb>fluidum M excurrere poteſt infra baſim AB ob con<lb></lb>cuſſionem, vel minimam dilatationem <expan abbr="ſuperficierũ">ſuperficierum</expan> <lb></lb>ſe tangentium, ſeù ob tranſitum per fiſſuram, aut fo<lb></lb>ramen aliquod collaterale, tunc ſubſequitur effectus <lb></lb>aſcenſus prædictæ columnæ, igitur neceſſariò extru<lb></lb>ſio facta à grauiori fluido M eſt vera cauſa ſublima<lb></lb>tionis, & aſcenſus prædicti ligni in fluido, quod fue<lb></lb>rat oſtendendum. </s> </p> <p type="margin"> <s id="s.001057"><margin.target id="marg271"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.001058">Et hìc ſummopere <expan abbr="animaduertẽdum">animaduertendum</expan> eſt, hallucina<lb></lb><arrow.to.target n="marg272"></arrow.to.target><lb></lb>tionem pendere ex eo quòd tribuitur effectus noņ <lb></lb>veræ cauſæ, ſed alij imaginatæ, quoniam <expan abbr="quotieſcũ-">quotieſcun-</expan><pb pagenum="204" xlink:href="010/01/212.jpg"></pb><arrow.to.target n="marg273"></arrow.to.target><lb></lb>que lignum ſursùm aſcendit in aqua ſemper verifi<lb></lb>catur id minùs grauitare, quàm moles aquæ <expan abbr="ambiẽ-tis">ambien<lb></lb>tis</expan> ei æqualis, quæ ſi liberè fluere, & excurrere po<lb></lb>teſt infra eius baſim, ſcilicèt ſi exercere poteſt ex<lb></lb>ceſſum ſui ponderis, mirum non eſt eleuare corpus <lb></lb>minoris grauitatis, ſicuti in libra videmus minus <expan abbr="põ-dus">pon<lb></lb>dus</expan> à maiori ſubleuari, quotieſcumque tamen pon<lb></lb>dus maius liberè vim ſuam exercere poteſt, at ſi fue<lb></lb>rit ſubſtentatum, vel fulciatur à pauimento pondus <lb></lb>minus eleuare non poterit. </s> <s id="s.001059">Huiuſmodi cauſa, quæ <lb></lb>certa eſt, & neceſſariò operari debet iuxtà leges me<lb></lb>chanices, <expan abbr="numquã">numquam</expan> poteſt, nec debet excludi, vt ac<lb></lb>ceptetur imaginata cauſa leuitatis poſitiuæ, quæ ſi <lb></lb>adeſſet, ſuum <expan abbr="effectũ">effectum</expan> producere deberet in caſu pro<lb></lb>poſitionis 97. vbi nil prorsùs operari oſtenſum eſt, <lb></lb>tamquàm ſcilicèt ſi non eſſet. </s> </p> <p type="margin"> <s id="s.001060"><margin.target id="marg272"></margin.target>Cauſa hallu<lb></lb>cinationiſ de<lb></lb>tegitur.</s> </p> <p type="margin"> <s id="s.001061"><margin.target id="marg273"></margin.target>Cap. 4. poſi<lb></lb>tiuam leui<lb></lb>tatem noņ <lb></lb>dari.</s> </p> <p type="main"> <s id="s.001062">Poſtquam igitur examinauimus, & reiecimus ra<lb></lb>tiones omnes Peripateticas <expan abbr="cõtra">contra</expan> Platonem, & alios <lb></lb>antiquos pro aſſertione leuitatis poſitiuæ, pariter<lb></lb>que inefficaces repertæ ſunt omnes aliæ rationes, <lb></lb>quæ pro confirmatione prædictæ <expan abbr="ſentẽtiæ">ſententiæ</expan> circumfe<lb></lb>runtur, cùmque tandem methodo demonſtratiua <expan abbr="ve-ritatẽ">ve<lb></lb>ritatem</expan> noſtræ <expan abbr="ſentẽtiæ">ſententiæ</expan> confirmauerimus, poſſumus <expan abbr="iã">iam</expan>, <lb></lb>abſque iactantia, affirmare euiciſſe nullam leuitatem <lb></lb>poſitiuam in natura dari virtute cuius naturalia cor<lb></lb>pora conentur diſcedere à noſtra terra versùs ſupe<lb></lb>riores partes, ſed è contra pronunciare poſſumus re<lb></lb>periri in omnibus corporibus ſublunaribus vim <expan abbr="quã-dam">quan<lb></lb>dam</expan> vniuerſalem ſe mutuò complectendi, & globo <pb pagenum="205" xlink:href="010/01/213.jpg"></pb><arrow.to.target n="marg274"></arrow.to.target><lb></lb>terreno adhærendi mediante facultate deſcenſiuą, <lb></lb>quæ grauitas appellatur, hæc, inquam, grauitas di<lb></lb>uerſimodè participata à corporibus terram ambien<lb></lb>tibus efficit vt minùs grauia expulſa ex inferioribus <lb></lb>locis à grauioribus illa ſursùm eleuentur, & ſic cor<lb></lb>pora elementaria optima <expan abbr="quidẽ">quidem</expan> conſtitutione <expan abbr="æqui-librẽtur">æqui<lb></lb>librentur</expan>, & ad ſua loca naturalia aſportentur vt ibi<lb></lb>dem quieſcant. </s> </p> <p type="margin"> <s id="s.001063"><margin.target id="marg274"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001064"><emph type="center"></emph><emph type="italics"></emph>De Structura, Grauitate, Æquilibrio, <lb></lb>& Vi Elateria Aeris.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001065"><emph type="center"></emph>CAP. V.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001066">IAm ſuperiùs ſatis ſuperque oſtenſum eſt aquam̨ <lb></lb>grauitare etiam in propria regione, & in ſuo toto: <lb></lb>præterea oſtendimus nullam leuitatem poſitiuam re<lb></lb>periri in corporibus mixtis, in ijs nempè, quæ à præ<lb></lb>dominio aerea vulgò appellantur, quod verò peculi<lb></lb>ariter aer grauis ſit, ne dum Ariſtot. apertè fatetur, <lb></lb>cùm ait: <emph type="italics"></emph>Omnia elementa grauitatem habere prætèr ignem<emph.end type="italics"></emph.end>, <lb></lb><arrow.to.target n="marg275"></arrow.to.target><lb></lb><emph type="italics"></emph>pariterquè omnia leuitatem habere prætèr <expan abbr="terrã">terram</expan>.<emph.end type="italics"></emph.end></s> <s id="s.001067"> Hinc in<lb></lb>fert: <emph type="italics"></emph>terram igitur, & quæ terræ habent plurimum, vbique <lb></lb>grauitatem habere eſt neceſſarium. </s> <s id="s.001068">Aquam autem vbique, <lb></lb>prætèr quàm in terra, aerem verò præterquam in aqua, & <lb></lb>terra. </s> <s id="s.001069">In ſua enim regione omnia grauitatem habent prætèr <lb></lb>ignem, etiam aer ipſe. </s> <s id="s.001070">Signum autem est quia trahit plùs in<lb></lb>flatus vter, quàm vacuus.<emph.end type="italics"></emph.end></s> <s id="s.001071"> Sed etiam demonſtrari po<lb></lb>teſt eodem modo, ijſdemque rationibus, quas in prę<lb></lb>cedenti capitulo adduximus, ſicuti enim ibi conſide-<pb pagenum="206" xlink:href="010/01/214.jpg"></pb><arrow.to.target n="marg276"></arrow.to.target><lb></lb>rauimus ligna, ampullas vitreas |, & veſicas aere ple<lb></lb>nas per aquam aſcendentes, demonſtrauimuſque eas <lb></lb>non vi leuitatis, ſed ab extruſione medij fluidi ſursùm <lb></lb>impelli, ſic pariter ſi loco ligni, aut veſicę ponatur aer <lb></lb>in <expan abbr="fũdo">fundo</expan> hydrargyri, vel aquæ, olei, vel ſpiritus vini <lb></lb><expan abbr="nõ">non</expan> ſecùs, ac priùs <expan abbr="factũ">factum</expan> eſt, <expan abbr="oſtẽdemus">oſtendemus</expan> aerem non <expan abbr="ſpõ-te">ſpon<lb></lb>te</expan> ſua aſcendere à vi leuitatis tranſlatum, ſed à preſ<lb></lb>ſione grauioris medij fluidi violenter ſursùm impel<lb></lb>lentis. </s> <s id="s.001072">licèt ergo negotium omninò confectum eſſę <lb></lb>videatur, vtile tamen erit idipſum confirmare ex æ<lb></lb>quilibrio aeris cum cæteris fluidis. </s> </p> <p type="margin"> <s id="s.001073"><margin.target id="marg275"></margin.target>4. de Cælo <lb></lb>cap. 4.</s> </p> <p type="margin"> <s id="s.001074"><margin.target id="marg276"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001075"><emph type="center"></emph>PROP. C.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001076"><emph type="center"></emph><emph type="italics"></emph>Ex ſuſpenſione mercurij in inſtrumento Torricelliano <lb></lb>ſuadetur aerem, vt grauem, æquilibrium <lb></lb>efficere cum mercurio.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001077">ET hac occaſione conſiderabimus pulcherrimum <lb></lb>profectò experimentum eorum, quæ hoc ſeculo <lb></lb>adinuenta ſunt, hydrargyri nempè eleuatio in fiſtula, <lb></lb>quam primus <expan abbr="omniũ">omnium</expan> animaduertit doctiſſimus Tor<lb></lb>ricellius, eſtque experimentum huiuſmodi: Sit fiſtu<lb></lb>la vitrea ABC perforata tantummodò in eius extre<lb></lb>mitate C, in A verò clauſa, hæc verò hydrargyro <lb></lb>repleta vſque ad ſummitatem C pulpa indicis ſtrictè <lb></lb>claudatur, inuertaturque contrario ſitu, vt nimirùm <lb></lb>os eius C inferiùs reſpiciat; ſitque poſtea præparata <lb></lb>ſcutella DHE pariter hydrargyro plena demerga<lb></lb>tur infimum orificium C fiſtulæ vnà <expan abbr="cũ">cum</expan> digito occlu-<pb pagenum="207" xlink:href="010/01/215.jpg"></pb><arrow.to.target n="marg277"></arrow.to.target><lb></lb>dente infrà ſupremam hy<lb></lb><figure id="id.010.01.215.1.jpg" xlink:href="010/01/215/1.jpg"></figure><lb></lb>drargyri libellam DE, tunc <lb></lb>ſublato digito mercurius <lb></lb>profluet ab orificio C quo<lb></lb>uſque altitudo FB extantis <lb></lb>hydrargyri ſupra libellam̨ <lb></lb>DE ſit pedum duorum, & <lb></lb>quadrantis, vel vnius cubi<lb></lb>ti, & quadrantis, nec vlte<lb></lb>rius hydrargyrum grauiſſi<lb></lb>mum deſcendit ſemperque <lb></lb>ad eamdem altitudinem̨ <lb></lb>perſeuerat, licèt inclinetur <lb></lb>fiſtula, ſcilicèt ducta recta FG parallela horizonti <expan abbr="sẽ-per">sen<lb></lb>per</expan> ſummitas hydrargyri ad eamdem horizontalem <lb></lb>FG perueniet quomodocumque fiſtula inclinetur. <lb></lb></s> <s id="s.001078">Ipſe Torricellius experimenti inuentor ſagaciſſimè <lb></lb>cauſam quoque huius effectus indagauit, animaduer<lb></lb>tit enim nos in infima profunditate oceani aerei de<lb></lb>merſos eſſe, & ſicuti maris aqua vndique fundum̨ <lb></lb>comprimit per lineas horizonti perpendiculares, ſeù <lb></lb>directas verſus centrum telluris, ſic quoque in oceano <lb></lb>aereo niſus eius grauitatis exercetur perpendiculari<lb></lb>tèr ſupra horizontis planum, vnde concipi debent cy<lb></lb>lindri aerei perpendicularitèr ſuperficiem hydrargy<lb></lb>ri DE ſupremam comprimentes; quia verò eadem̨ <lb></lb>libella mercurij DE comprimitur quoque in ſitu B à <lb></lb>ſuperficie baſis B mercurialis cylindri FB efforma<lb></lb>tur veluti libra, vel ſipho, quæ numquam quieſcit, ni-<pb pagenum="208" xlink:href="010/01/216.jpg"></pb><arrow.to.target n="marg278"></arrow.to.target><lb></lb>ſi æquilibrium momentorum efficiatur, ſcilicèt niſi <lb></lb>momentum ponderis cylindri aerei ſuperficiem DE <lb></lb>comprimentis æquale fuerit momento ponderis cy<lb></lb>lindri mercurialis BF. </s> <s id="s.001079">Huiuſmodi ſpeculatio magno <lb></lb>plauſu à viris doctis excepta fuit, alijſque <expan abbr="experimẽ-tis">experimen<lb></lb>tis</expan> pariter comprobata, quia nimirùm ſi loco hydrar<lb></lb>gyri aquam adhibeamus, vel aliud fluidum, tunc aqua <lb></lb>pura eleuatur ad altitudinem pedum 32. vel cubito<lb></lb>rum 17. proximè cuius pondus præcisè æquatur gra<lb></lb>uitati prædicti cylindri mercurialis BF vnius cubiti, <lb></lb>& quadrantis (ſumptis nimirum baſibus æqualibus) <lb></lb>& ſi fuerit oleum altius quàm aqua pura eleuatur, ſed <lb></lb>præcisè quantum exigit aquæ grauitas ei æqualis; <lb></lb>idemque continget ſi fuerit aliquis ſpiritus, vel qui<lb></lb>libet alius liquor. </s> <s id="s.001080">cùm igitur in hiſce omnibus fiſtulis <lb></lb>eleuentur varij liquores, itaut eorum partes eleuatæ <lb></lb>ſuper infimam libellam ſemper eiuſdem ſint grauita<lb></lb>tis, dicendum neceſſariò eſt ab vnica, & eadem vi <lb></lb>compreſſiua eleuari, quę ſemper eiuſdem roboris ſit: <lb></lb>at nulla alia aſſignari poteſt præter pondus cylindri <lb></lb>aerei liquori in ſcutella contento <expan abbr="incũbentis">incumbentis</expan>. </s> <s id="s.001081">igitur <lb></lb>poteſt aer incumbens eleuare prædictos liquores, hoc <lb></lb>autem minimè effici poſſet abſque eo quod in aerę <lb></lb>æquilibrium efficeretur; ſicuti in maris oceano ex eo <lb></lb>quod omnes partes aquæ æquali niſu deorſum ferun<lb></lb>tur, & premunt, fit vt eius ſuprema libella ſphæricè <lb></lb>contornetur, ſic paritèr ſuprema aeris ſuperficies <lb></lb>ſphæricè tornata erit, ex eo quod partes eius omnes <lb></lb>æquali niſu deorſum <expan abbr="grauitãtes">grauitantes</expan> æquilibrium <expan abbr="efficiũt">efficiunt</expan>. <pb pagenum="209" xlink:href="010/01/217.jpg"></pb><arrow.to.target n="marg279"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001082"><margin.target id="marg277"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001083"><margin.target id="marg278"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001084"><margin.target id="marg279"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001085"><emph type="center"></emph>PROP. CI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001086"><emph type="center"></emph><emph type="italics"></emph>Idipſum clariùs confirmatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001087">QVòd poſtea prædicta mercurij eleuatio in fi ſtu<lb></lb>la producatur ab aeris compreſſione ſuprą <lb></lb>mercurium in ſcutella contentum, confirmatur alią <lb></lb>ratione, ſed clariùs adhibito <expan abbr="inſtrumẽ-to">inſtrumen<lb></lb>to</expan> à me excogitato, quod Academiæ <lb></lb>Experimentali Mediceę communicaui, <lb></lb>eiuſque ichon habetur figura 34. libri <lb></lb>experimentorum eiuſdem Academiæ, <lb></lb>abſque enim ſcutella DE ſufficit vt in<lb></lb>fima pars fiſtulæ BC incuruetur, ſur<lb></lb>ſumque inflectatur, <expan abbr="tũc">tunc</expan> quidem reple<lb></lb>ta vt priùs vniuerſa fiſtula mercurio, <lb></lb>reuoluatur vt eius pars clauſa A & lon<lb></lb>gitudo fiſtulæ AFB perpendicularitèr <lb></lb>ad horizontem emineat, tunc quidem <lb></lb>ab orificio aperto G hydrargyrum̨ <lb></lb>profluet, vel intra amplitudinem am<lb></lb>pullæ DG reducetur, quouſque altitu<lb></lb><figure id="id.010.01.217.1.jpg" xlink:href="010/01/217/1.jpg"></figure><lb></lb>do mercurialis cylindri FB ſupra <expan abbr="libellã">libellam</expan> BD fuerit v<lb></lb>nius cubiti & quadrantis, & tunc <expan abbr="cõcipi">concipi</expan> debet cylin<lb></lb>drus aereus DS vſque ad ſupremam aeris ſuperficiem <lb></lb>S extenſus, cuius pondus æquetur grauitati cylindri <lb></lb>mercurialis FB. </s> <s id="s.001088">Quod verò à compreſſione prædicti <lb></lb>cylindri aerei DS eleuetur grauiſſimum <expan abbr="hydrargyrũ">hydrargyrum</expan> <lb></lb>FB probatur ex eo quod ſi augeatur impulſus, & com-<pb pagenum="210" xlink:href="010/01/218.jpg"></pb><arrow.to.target n="marg280"></arrow.to.target><lb></lb>preſſio ſupra ſuperficiem hydrargyri D altiùs ele<lb></lb>uatur mercurius in fiſtula BFA. ſic ſi noua fiſtula, vel <lb></lb>inſtrumento pneumatico aer inſuffletur, vt compri<lb></lb>mat ſuperficiem hydrargyri D eleuatur quoque ſu<lb></lb>prema ſuperficies F hydrargyri in fiſtula clauſa; & ſi <lb></lb>è contrà embolo retracto, velùti exugatur aer impe<lb></lb>diatur que compreſſio eius ſupra mercurium D ſpon<lb></lb>tè labetur mercurius deſcendetque deorsùm versùs <lb></lb>B. præterea ſi ſupra mercurium in D infundatur aqua, <lb></lb>quæ propagetur vique ad libellam GI, tunc quidem <lb></lb>mercurius quoque eleuatur ab F vſque ad H, & quod <lb></lb>mirum eſt, eleuatur mercurius præcisè pro menſura <lb></lb>ponderis aquæ incumbentis GD, ſcilicèt altitudo G <lb></lb>D erit quatuordeciès maior, quàm FH, quia talis re<lb></lb>ciprocè eſt proportio ponderis mercurij ad aquam. <lb></lb></s> <s id="s.001089">Si igitur in ſpatio inani nulla alia cauſa vlterioris ele<lb></lb>uationis hydrargyri FH aſſignari poteſt præter gra<lb></lb>uitatem aquæ collateralis GD cum qua mercurius F <lb></lb>H æquilibrium efficit, quare negabimus reliquum <lb></lb>mercurij FB eleuari à pondere aliquo premente ſu<lb></lb>perficiem D, quæ ſit ſemper eiuſdem roboris? </s> <s id="s.001090">cùm<lb></lb>que nullum aliud corpus grauitans aſſignari poſſit <lb></lb>prætèr aerem, igitur neceſſariò ab hoc mercurius <lb></lb>eleuatur. </s> </p> <p type="margin"> <s id="s.001091"><margin.target id="marg280"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001092">Prætermiſſis alijs experimentis excogitatis à viris <lb></lb>doctiſſimis in Italia, Gallia, & Anglia, de quibus fusè <lb></lb>agitur in libro <expan abbr="experimẽtorum">experimentorum</expan> noſtræ Academiæ ex<lb></lb>perimentalis Mediceæ nè repetamus ea, quæ iam paſ<lb></lb>ſim vulgata ſunt, tantummodò recenſebo, & ad exa-<pb pagenum="211" xlink:href="010/01/219.jpg"></pb><arrow.to.target n="marg281"></arrow.to.target><lb></lb>men reuocabo difficultates contra ratiocinium Torri<lb></lb>cellianum, & noſtrum à doctiſſimo viro allatas <expan abbr="cũ">cum</expan> ait. <lb></lb><emph type="italics"></emph>Dicebatur ſegmentum mercurij IC ſustineri à cylindro aeris <lb></lb>eiuſdem baſis, itaut perfectum ſit vtrinque æquilibrium. <lb></lb></s> <s id="s.001093">Contra hanc ſententiam nonnulla militant ſi appendatur fi<lb></lb><arrow.to.target n="marg282"></arrow.to.target><lb></lb>stula BD poſtquàm ſubducto digito deſcendit mercurius in <lb></lb>IC ſtatera fideli adhibita, & ſignetur pon<lb></lb>deris ratio, ac deindè citrà mercurij deſcen<lb></lb>ſum eadem fiſtula cum æquali quantitate <lb></lb>mercurij appendatur, eadem ratio ponderis <lb></lb>inuenietur paulò maior, æqualem quantita<lb></lb>tem mercurij intelligo <expan abbr="ſegmẽto">ſegmento</expan> IC;<emph.end type="italics"></emph.end> Et pau<lb></lb>lò infra ſubſequitur. <emph type="italics"></emph>Si mercurius IC <lb></lb>ſuſtinetur à cylindro exterioris aeris, igitur <lb></lb>cum illo perfectum æquilibrium facit, igitur <lb></lb>cum alio æquali pondere ad libram appenſo <lb></lb><figure id="id.010.01.219.1.jpg" xlink:href="010/01/219/1.jpg"></figure><lb></lb>aliud æquilibrium facere non potest. </s> <s id="s.001094">Supponemus enim mer<lb></lb>curium IC eße trium librarum, æquilibrium facit cum cy<lb></lb>lindro aeris etiam trium librarum. </s> <s id="s.001095">Si autem aliud pondus <lb></lb>trium librarum in alter a lance appendatur <expan abbr="cũ">cum</expan> hoc mercuri<lb></lb>us æquilibrium facere nequit, alioquin ſex Libris mercurius <lb></lb>æquilibraret, quod legibus staticæ repugnat.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001096"><margin.target id="marg281"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001097"><margin.target id="marg282"></margin.target>Defficulta<lb></lb>tes contra <lb></lb>noſtram do<lb></lb>ctrinam.</s> </p> <p type="main"> <s id="s.001098"><emph type="center"></emph>PROP. CII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001099"><emph type="center"></emph><emph type="italics"></emph>Euidentiſsimo exemplo in aqua <expan abbr="oſtẽditur">oſtenditur</expan> quod licèt mercu<lb></lb>rius in fiſtula ab æquipondio aquæ ſuſtineatur, nihilo<lb></lb>minùs vis eleuans fiſtulam ſustinet præterea <lb></lb>aquæ incumbentis pondus æquale <lb></lb>mercurio.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="212" xlink:href="010/01/220.jpg"></pb><arrow.to.target n="marg283"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001100"><margin.target id="marg283"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001101">QVia verò ratiocinium hoc à viro doctiſſimo af<lb></lb>fertur vt conuincens, & <expan abbr="euidẽs">euidens</expan>, conabor, amo<lb></lb>re veritatis, luculentèr exponere eius defectum, & <lb></lb>claritatis gratia operationem euidentiorem in ipſą <lb></lb>aqua conſiderabo ſimilem omninò ei quam præ ma<lb></lb>nibus habemus. </s> <s id="s.001102">Sit vas profundiſſimum RTVS aere <lb></lb>plenum in cuius fundo pona<lb></lb>tur ſcutella DF mercurio ple<lb></lb>na, ſitque poſtea fiſtula vitrea <lb></lb>AC <expan abbr="vtrinq;">vtrinque</expan> perforata, & per<lb></lb>uia cuius in fima pars C demer<lb></lb>gatur infra mercurij libellam; <lb></lb>poſtea repleatur puteus aqua <lb></lb>vt vitri ſummitatem A non at<lb></lb>tingat, & remaneat fiſtula exi<lb></lb>nanita vt prius tunc quidem <lb></lb>ſenſu conſtat eleuari hydrar<lb></lb>gyrum in fiſtula à C vſque ad <lb></lb><figure id="id.010.01.220.1.jpg" xlink:href="010/01/220/1.jpg"></figure><lb></lb>B quouſque mercurialis altitudo CB decima quarta <lb></lb>pars ſit aquæ altitudinis HG. hic iam quia effectus <lb></lb>eleuationis mercurij vſque ad B productus fuit ab a<lb></lb>qua de nouo impoſita dubitandum <expan abbr="nõ">non</expan> eſt ab eius gra<lb></lb>uitate mercurium eleuatum fuiſſe, quod præterea <lb></lb>confirmatur ex æquipondio ipſius cylindri aquæ HG <lb></lb>cum mercuriali cylindro CB eiuſdem baſis; itaque in <lb></lb>libra CEG, vel in ſiphone tunc quieſcunt duo fluida, <lb></lb>mercurius nempè & aqua, cùm præcisè efficitur <expan abbr="eorũ">eorum</expan> <lb></lb>æquilibrium; claudatur poſtea fiſtula in B interpoſita <lb></lb>nimirùm laminula non diſſimili ei, quàm in arundini-<pb pagenum="213" xlink:href="010/01/221.jpg"></pb><arrow.to.target n="marg284"></arrow.to.target><lb></lb>bus obſeruamus à qua præcisè prohibeatur tranſitus <lb></lb>fluidi per rimas laterales, poſtea impleatur reliqua <lb></lb>pars fiſtulæ AB aqua, & tandèm eadem vitrea fiſtu<lb></lb>la termino I libræ IL radiorum æqualium ſuſpenda<lb></lb>tur, atque ab oppoſito termino eius L pendeat pon<lb></lb>dus M æquale ponderi ipſius vitri AC. videndum̨ <lb></lb>modò eſt an à ſimplici pondere M ſuſtineri poſſit vi<lb></lb>trea fiſtula AC, & patet non ſufficere, quia in ſipho<lb></lb>ne ACGH pondus cylindri aquei HG æquatur præ<lb></lb>cisè ponderi mercurij BC, cumque pręterea aqua <expan abbr="cõ-tenta">con<lb></lb>tenta</expan> in ſpatio fiſtulæ AB ferè æqualis ſit aquæ HG, <lb></lb>ergò ſumma aquæ AB, & mercurij BC duplo grauior <lb></lb>eſt, quam ſit cylindrus aqueus HG vt nimirùm ſi a<lb></lb>qua HG fuerit vnius libræ erunt mercurius CB, & <lb></lb>aqua AB ferè duarum librarum (non conſiderato <expan abbr="põ-dere">pon<lb></lb>dere</expan> ipſius vitri AC,) ergò vt fiat æquilibrium de<lb></lb>bet addi ponderi M aliud pondus O, quod ſit æqua<lb></lb>le ponderi aquæ AB, & tunc in infima libra CEG, <lb></lb>ſeu ſiphone eſſicitur æquilibrium inter cylindrum a<lb></lb>queum HG, & mercurium CB, in ſuprema verò li<lb></lb>bra IL efficitur æquilibrium inter fiſtulam vitream̨ <lb></lb>AC, vnà cum aqua AB ex vna parte, & ponderæ M, <lb></lb>O ex altera parte. </s> <s id="s.001103">Igitur quia reuera mercurius CB <lb></lb>non ſuſtinetur à potentia O ſubleuante <expan abbr="librã">libram</expan> <expan abbr="ſupre-mã">ſupre<lb></lb>mam</expan>, cum nimirùm ſuſtineatur à collaterali aqua HG, <lb></lb>eſt impoſſibile fiſtulam vitream AC ſuſtineri à ſo<lb></lb>litario pondere M æquale grauitati ipſius vitri, niſi <lb></lb>inſuper addatur alia potentia O, quæ ſuſtineat cy<lb></lb>lindrum aqueum AB æquè graue ferè, ac|eſt mercu<lb></lb>rius CB. <pb pagenum="214" xlink:href="010/01/222.jpg"></pb><arrow.to.target n="marg285"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001104"><margin.target id="marg284"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001105"><margin.target id="marg285"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001106">Si poſtea fiſtula vitrea ſecetur in B, eiuſque ſupre<lb></lb>ma portio BA tollatur amoueaturque, at que pondus <lb></lb>M æquale ſit grauitati vitri decurtati CB, tunc <expan abbr="quidẽ">quidem</expan> <lb></lb>incumbit, ac innititur fiſtulę cylindrus aqueus BA <lb></lb>fiſtulamque comprimit non ſecus, ac priùs quando <lb></lb>intra cauitatem fiſtulæ AB continebatur. </s> </p> <p type="main"> <s id="s.001107"><emph type="center"></emph>PROP. CIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001108"><emph type="center"></emph><emph type="italics"></emph>Licèt Torricelliana fistula à mercurio in ea ſuſpenſo <expan abbr="nõ">non</expan> gra<lb></lb>uetur, tamen manus cogitur ſuſtinere pondus cylin<lb></lb>dri aerei fiſtulæ incumbentis, quod æquatur <expan abbr="põ-deriincluſi">pon<lb></lb>deri incluſi</expan> mercurij.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001109">IDipſum noſtræ fiſtulæ directæ in ae<lb></lb>re conſtitutæ adaptari poteſt, ſit<lb></lb>que illa AC duorum cubitorum habe<lb></lb>atque orificium C inſignis exiguitatis, <lb></lb>repleaturque mercurio deorſumquę <lb></lb>inuertatur in aere libero (non enim <lb></lb>neceſsè eſt, vt os C intra ſcutellam <lb></lb>mercurij plenam infundatur, <expan abbr="quãdo">quando</expan> <lb></lb>valdè ſtrictum eſt os eius C,) tunc <lb></lb>ab infimo orificio C mercurius in ae<lb></lb>re profluet quouſque altitudo CB <lb></lb>fuerit vnius cubiti, & quadrantis pro<lb></lb>ximè. </s> <s id="s.001110">Hic concipi debet cylindrus <lb></lb>aereus SG vſque ad ſupremam regio<lb></lb><figure id="id.010.01.222.1.jpg" xlink:href="010/01/222/1.jpg"></figure><lb></lb>nis aeris ſuperficiem extenſus, qui re<lb></lb>flexus per EC vim faciat contra preſſionem mercu<lb></lb>rij BC, eumque ſuſpendat, & ſic liberè concedo ad-<pb pagenum="215" xlink:href="010/01/223.jpg"></pb><arrow.to.target n="marg286"></arrow.to.target><lb></lb>uerſario, quòd fiſtula AC nil prorsùs ab incluſo mer<lb></lb>curio BC grauatur, & ſic de facto experimur appli<lb></lb>cata digiti pulpa ori infimo fiſtulæ; quod in partę <lb></lb>intermedia pulpæ à mercurio tacta nulla compreſſio, <lb></lb>nec <expan abbr="cõtuſio">contuſio</expan> <expan abbr="neq;">neque</expan> grauitatio perſentitur, quando præ<lb></lb>cisè mercurij altitudo BC eſt vnius cubiti, & <expan abbr="qua-drãtis">qua<lb></lb>drantis</expan> ferè; quod ſieius altitudo ſupra CB augeatur, <lb></lb><expan abbr="tũc">tunc</expan> <expan abbr="ſolũmodò">ſolummodò</expan> percipitur in medio pulpæ digiti ſub<lb></lb>iecti <expan abbr="cõpreſſio">compreſſio</expan> grauitans iuxtà <expan abbr="mẽſurã">menſuram</expan> exceſſus mer<lb></lb>curij ſupra eum qui altitudinem vnius cubiti, & qua<lb></lb>drantis occupat, & ſi è contrà mercurius deprima<lb></lb>tur violentèr infra debitam altitudinem BC, tunc ne<lb></lb>dùm ſubiecta pulpa digiti non comprimitur, ſed è <lb></lb>contrà exugitur, vt efficiunt cucurbitæ medicæ, & <lb></lb>hyrudines. </s> <s id="s.001111">Sed dicet aduerſarius ſi mercurius BC <lb></lb>nil grauitat, nec comprimit digitum, quare requi<lb></lb>ritur vis, aut libræ, aut digiti ſubiecti, quæ nedum̨ <lb></lb>æquet pondus ſolias vitri AC, ſed prætereà ſuſtine<lb></lb>re valeat duas libras v. g. quas <expan abbr="pẽdit">pendit</expan> mercurius BC? <lb></lb></s> <s id="s.001112">Reſpondeo aereum cylindrum SA fiſtulæ vitreæ in<lb></lb>cumbentem ſua grauitate agere non minùs, quàm̨ <lb></lb>collateralis cylindrus aereus SG, cumque vitrum̨ <lb></lb>CA non repellatur æquali actione contraria ſursùm <lb></lb>ab aere collaterali SG, quia huius vis exercetur, & <lb></lb>omninò expletur ſuſtentando mercurium BC; igitur <lb></lb>neceſſariò vitrum CA comprimitur deorsùm à gra<lb></lb>uitate aeris incumbentis SA, cuius pondus æqualę <lb></lb>eſt mercurio BC hinc fit vi ex præconcepta falſa opi<lb></lb>nione tribuamus compreſſionem aeris SA nobis in-<pb pagenum="216" xlink:href="010/01/224.jpg"></pb><arrow.to.target n="marg287"></arrow.to.target><lb></lb>compertam alij cauſæ nempe grauitati ipſius mer<lb></lb>curij BC intra fiſtulam contenti. </s> <s id="s.001113">Hoc profectò con<lb></lb>firmatur ex eo, quod prædicta fiſtula à digito ſuſten<lb></lb>tata exercet ſuam compreſſionem contra pulpæ di<lb></lb>giti extremitatem, quæ à perimetro orificij vitri <expan abbr="tã-gitur">tan<lb></lb>gitur</expan>, & contunditur: non autem contra mediam pul<lb></lb>pæ digiti partem, quæ ab ingenti pondere trium li<lb></lb>brarum mercurij v. g. magis, & euidentius compri<lb></lb>mi deberet quàm grauentur ambientes pulpæ digi<lb></lb>ti partes à perimetro oriſicij vitri trium vnciarum. </s> </p> <p type="margin"> <s id="s.001114"><margin.target id="marg286"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001115"><margin.target id="marg287"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001116">Hanc euidentiſſimam demonſtrationem conatur <lb></lb><arrow.to.target n="marg288"></arrow.to.target><lb></lb>aduerſarius refellere, ait enim, <emph type="italics"></emph>hoc facilè reijcitur nem<lb></lb>pè æqualis cylindrus aeris incumbit baſi ſupremæ obstructæ <lb></lb>fistulæ ſiue mercurio, ſiue aqua, ſiue aere fi<lb></lb>ſtula plena ſit, vt patet. </s> <s id="s.001117">Vnde ſi <expan abbr="quẽ">quem</expan> haberet <lb></lb>effectum, eumdem ſemper haberet, ſed hæc <lb></lb>inſtantia futilis est, quare in ea diutiùs mi<lb></lb>nimè hærendum.<emph.end type="italics"></emph.end></s> <s id="s.001118"> Sit fiſtula AC plena ae<lb></lb>re non mercurio ſuſtenteturque infer<lb></lb>nè eius orificium C à ſubiecta digiti <lb></lb>pulpa, concedo, quod ſupernè digi<lb></lb>tus premitur à columna aeris SAC, pa<lb></lb>riterque <expan abbr="cõprimitur">comprimitur</expan> à vitri fiſtula AC, <lb></lb>quidnam ex hoc deducit aduerſarius? <lb></lb></s> <s id="s.001119">dicet, quod tantumdem ponderis pa<lb></lb>teretur digitus ſubiectus <expan abbr="quãdo">quando</expan> vitrea <lb></lb>fiſtula exinanita eſt, quàm ſi <expan abbr="mercuriũ">mercurium</expan> <lb></lb><figure id="id.010.01.224.1.jpg" xlink:href="010/01/224/1.jpg"></figure><lb></lb>BC contineret, ſcilicèt ſi fiſtula pen<lb></lb>deret duas vncias, & aereus cylindrus SA <expan abbr="pẽdat">pendat</expan> tres <pb pagenum="217" xlink:href="010/01/225.jpg"></pb><arrow.to.target n="marg289"></arrow.to.target><lb></lb>libras exinanita fiſtula æquè comprimeretur ſubie<lb></lb>ctus digitus à pondere totius cylindri aerei SA <expan abbr="triũ">trium</expan> <lb></lb>librarum vnà cum duabus vncijs vitri AC, cùmque <lb></lb>hoc ſit falſum; fiſtula enim exinanita duas vncias ſo<lb></lb>lummodò pendit, non ergo ſuprema <expan abbr="colũmna">columna</expan> aerea <lb></lb>SA fiſtulam, & proindè digitum ſubiectum compri<lb></lb>mit. </s> </p> <p type="margin"> <s id="s.001120"><margin.target id="marg288"></margin.target><expan abbr="Cõtiã">Contram</expan> ſupe<lb></lb>rius <expan abbr="expoſitã">expoſitam</expan> <lb></lb><expan abbr="doctrinã">doctrinam</expan> de<lb></lb>nuo aduer<lb></lb>ſarius inſur<lb></lb>git,</s> </p> <p type="margin"> <s id="s.001121"><margin.target id="marg289"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001122"><emph type="center"></emph>PROP. CIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001123"><emph type="center"></emph><emph type="italics"></emph>Fiſtula exinanita, licèt grauetur à cylindro aereo <expan abbr="incumbẽ-te">incumben<lb></lb>te</expan> non minus, ac quando extante mercurio repletur, <lb></lb>debet tamen in primo caſu ſubiectus digitus vi<lb></lb>tri tantum pondus percipere, in ſecundo ve<lb></lb>rò præterea à pondere æquali mercurio <lb></lb>ſuſpenſo grauabitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001124">HVic difficultati <expan abbr="reſpõdetur">reſpondetur</expan>, quòd, vt multotiès <lb></lb>inſinuatum eſt, nulla alia de cauſa fluida cor<lb></lb>pora circa tellurem ſphæricè <expan abbr="cõtornantur">contornantur</expan>, niſi prop<lb></lb>tèr eorum æquilibrium, ſcilicet quia omnes eius par<lb></lb>tes æquali niſu vim faciunt tendendo deorsùm, & <lb></lb>poſtquam à ſoliditate terræ ſubiectæ eius progreſ<lb></lb>ſus deorsùm impeditur niſu reflexo veluti in ſiphone <lb></lb>viciſſim ſe mutuo <expan abbr="impellũt">impellunt</expan> quoque partes fluidi, vel <lb></lb>ſolidi eleuatæ ſursùm, itaque in caſu noſtro, concipi <lb></lb>debet nedùm columna aerea SAC, ſed etiam alia ei <lb></lb>æqualis aerea columna SG, quæ infernè per EC re<lb></lb>flectatur, & ſursùm impellat digitum ſuſtentantem <lb></lb>vitrum æquali niſu, ac ipſa ſupernè comprimitur à <pb pagenum="218" xlink:href="010/01/226.jpg"></pb><arrow.to.target n="marg290"></arrow.to.target><lb></lb>cylindro aereo SAC. digitus ergo <expan abbr="cõ-primitur">com<lb></lb>primitur</expan> à duabus æqualibus viribus <lb></lb>inter ſe contrarijs veluti forcipe, de<lb></lb>orsùm quidem à pondere aereo SAC, <lb></lb><expan abbr="ſursũ">ſursum</expan> verò a vi preſſionis aeris SG re<lb></lb>flexi per EC, <expan abbr="eodẽ">eodem</expan> ferè modo quo vri<lb></lb>natores pondus incumbentis aquæ <expan abbr="nõ">non</expan> <lb></lb>percipiunt, quia nimirùm æquali vi <lb></lb>ſursùm motu reflexo impelluntur ab a<lb></lb>qua ſubiecta, ac grauantur ab aquą <lb></lb>ſuprema <expan abbr="deſcendẽte">deſcendente</expan>, vt ſuperius <expan abbr="oſtẽ-sũ">oſten<lb></lb>sum</expan> fuit; igitur in caſu noftro digitus ſu<lb></lb>ſtinebit tantummodò grauitatem dua<lb></lb>rum vnciarum fiſtulæ vitreæ exinani<lb></lb><figure id="id.010.01.226.1.jpg" xlink:href="010/01/226/1.jpg"></figure><lb></lb>tæ AC quia nimirùm hic eſt exceſſus <lb></lb>ponderis totius columnæ aereæ, & vitreæ SAC ſupra <lb></lb>aeream <expan abbr="columnã">columnam</expan> ei ęqualem SGC: diuerſiſſimus ergo <lb></lb>eſt caſus fiſtulæ vitreæ mercurio ſtagnante repletæ, <lb></lb>quia nimirùm vis compreſſiua <expan abbr="colũnæ">columnæ</expan> aereæ SG om<lb></lb>ninò expletur abſumiturque eleuando <expan abbr="ſuſtinẽdoque">ſuſtinendoque</expan> <lb></lb>mercurium BC, & ſic remaneat aerea columna SA <lb></lb>(prætèr vitrum) non ſuſtentata à repulſione <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>aeris SG, & proindè ſuſtineri debèt à digito ſubiecto <lb></lb>eo mode, quo ſupra expoſuimus. </s> </p> <p type="margin"> <s id="s.001125"><margin.target id="marg290"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001126">Quapropter conuincens non eſt argumentum do<lb></lb>ctiſſimi viri, ideoque remanent illibatæ rationes ſu<lb></lb>periùs adductæ quibus perſuademur <expan abbr="mercuriũ">mercurium</expan> in fi<lb></lb>ſtula ſuſtineri à preſſione circumambientis aeris. </s> </p> <p type="main"> <s id="s.001127">Tranſeamus iam ad examen tertiæ rationis ab eo-<pb pagenum="219" xlink:href="010/01/227.jpg"></pb><arrow.to.target n="marg291"></arrow.to.target><lb></lb>dem viro clariſſimo adductæ, inquit <lb></lb>enim: <emph type="italics"></emph>Si ſegmentum IC mercurij ab ae<lb></lb>ris exterioris cylindro ſuſtinetur, igitur <expan abbr="cũ">cum</expan> <lb></lb>cylindrus exterior eamdem vim ſemper <lb></lb>habeat æqualem ſegmentum IC ſemper <lb></lb>ſustinet. </s> <s id="s.001128">Sed hoc experimento repugnat, <lb></lb>nam ſi tantulum aeris antequàm demit<lb></lb>tatur mercurius in fiſtula relinquatur mer<lb></lb>curius deſcendet infra C; in C autem ſuſti<lb></lb>neri deberet ſi à cylindro aeris exterioris <lb></lb>ſuſtineretur vt patet &c.<emph.end type="italics"></emph.end><lb></lb><figure id="id.010.01.227.1.jpg" xlink:href="010/01/227/1.jpg"></figure><lb></lb><arrow.to.target n="marg292"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001129"><margin.target id="marg291"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001130"><margin.target id="marg292"></margin.target>Tertium ar<lb></lb>gumentum <lb></lb>eiuſdem au<lb></lb>thoris.</s> </p> <p type="main"> <s id="s.001131">Non latuit huius argumenti authorem reſponſio à <lb></lb>fautoribus contrariæ ſententiæ allata, nimirùm <emph type="italics"></emph>illud <lb></lb>tantulum aeris infra fiſtulam relicti poſt deſcenſum mer<lb></lb>curij liberiorem nanciſci campum, ac proindè cum ante com<lb></lb>preſſus eſſet explicare ſeſe, ac dilatare, & premere ſuperfi<lb></lb>ciem mercurij, vnde hic infra C deſcendit.<emph.end type="italics"></emph.end></s> <s id="s.001132"> Sed inſtat di<lb></lb>cendo; <emph type="italics"></emph>tantam aeris compresſionem iam ſupra ſatis effi<lb></lb>cacitèr ab ipſo refutatam fuiſſe.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001133">Sed an reuerà iure refutata fuerit, poſteriùs <expan abbr="oſtẽ-demus">oſten<lb></lb>demus</expan>, modò tantam aeris dilatationem argumento <lb></lb>ab eadem experientia deducto retinebimus; <expan abbr="attamẽ">attamen</expan> <lb></lb>interea erit operæpretium exponere quomodò, & <lb></lb>quando aer intra mercurium in fiſtula relictus expli<lb></lb>cetur dilateturque. </s> </p> <figure id="id.010.01.227.2.jpg" xlink:href="010/01/227/2.jpg"></figure> <pb pagenum="220" xlink:href="010/01/228.jpg"></pb> <p type="main"> <s id="s.001134"><arrow.to.target n="marg293"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001135"><margin.target id="marg293"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001136"><emph type="center"></emph>PROP. CV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001137"><emph type="center"></emph><emph type="italics"></emph>Exponitur quare, & quando aer relictus in fiſtula Torri<lb></lb>celliana altitudinem mercurij conſuetam deprimere <lb></lb>debeat; & ſimul traditur modus menſurandi <lb></lb>maximam aeris dilatationem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001138">EX Roberuallij pulcherrima obſeruatione illius <lb></lb>veſicæ cyprinæ, quæ in vacuo fiſtulæ dilatatur <lb></lb>ego conieci reperiri facilè poſſe in eodem Torricel<lb></lb>liano inſtrumento maximam amplitudinem, ad <expan abbr="quã">quam</expan> <lb></lb>aer non compreſſus à vi externa, & in ſua libertatę <lb></lb>relictus dilatari queat, quæ dilatatio certum, ac de<lb></lb>terminatum ſpatium in vacuo Torricelliano occupa<lb></lb>ret, quod nimirum ſufficienter exciperet maximam <lb></lb>eiuſdem aeris expanſionem. </s> <s id="s.001139">Hinc poſtea <expan abbr="deducebã">deducebam</expan> <lb></lb>molem aeris, quæ præcisè ſpatium vacuum in Tor<lb></lb>ricelliano inſtrumento occuparet (quam molem me<lb></lb>diocrem appellabimus) non poſſe deorsùm impelle<lb></lb>re, & magis <expan abbr="cõprimere">comprimere</expan> ſuperficiem ſupremam mer<lb></lb>curij ſtagnantis, ac proindè omnes moles aeris mi<lb></lb>nores illa, & ideò minus ſpatium poſt totalem eo<lb></lb>rum dilatationem exigentes non poſſe prædictam <lb></lb>mercurij ſupremam ſuperficiem deprimere, <expan abbr="cũ">cum</expan> è con<lb></lb>trà moles omnes acris excedentes ſupradictam me<lb></lb>diocrem molem, & ideò exigentes amplius ſpa<lb></lb>tium deprimere neceſſariò <expan abbr="ſupremã">ſupremam</expan> mercurij ſuper<lb></lb>ficiem in fiſtula infra conſuetam altitudinem vnius <lb></lb>cubiti, & quadrantis. <pb pagenum="221" xlink:href="010/01/229.jpg"></pb><arrow.to.target n="marg294"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001140"><margin.target id="marg294"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001141">Vtque hæc experientia commodè exequi poſſet <lb></lb>efformaui fiſtulas vitreas ſextam, & ſeptimam deli<lb></lb>neatas folio 43. libri experimentorum noſtræ Aca<lb></lb>demiæ Experimentalis Mediceæ, ſed poſtea facilio<lb></lb>ri apparatu idipſum conſequi poſſe animaduerti me<lb></lb>diante hoc inſtrumento, eſtque eius artificium hu<lb></lb>iuſmodi: ampullæ vitreæ AB cuius diameter proximè <lb></lb>quatuor digitos adæquet <expan abbr="cõtinuetur">continuetur</expan> prælonga fiſtu<lb></lb>la BC maiore duorum cubitorum, quæ inflexa ſit iņ <lb></lb>eius infimo loco CEF, atque in ſupremo loco eius A <lb></lb>continuetur quoque ſtricta alia fiſtula AD cuius ex<lb></lb>tremum ſupremum orificium apertum D claudi poſ<lb></lb>ſit poſt mercurij infuſionem ſuilla veſica; poſtea ter<lb></lb>minus extremus alterius fiſtulæ FG vniatur cum al<lb></lb>tero extremo fiſtulæ incuruatæ appoſitis colligatiſ<lb></lb>que portionibus inteſtini agnini, quæ ne rumpantur <lb></lb>diffringantur que à nimio mercurij pondere pariter <lb></lb>operiantur fiſtula, vel digitali coriaceo, atque arctè <lb></lb>alligatis inteſtinis, & corio vtriſque extremitatibus <lb></lb>fiſtularum, poterit facilè fiſtula FG inflecti ſursùm, <lb></lb>& deorsùm poſt mercurij infuſionem, eriganturquę <lb></lb>perpendiculariter ad horizontem ambæ fiſtulæ DB <lb></lb>C, & GF. </s> <s id="s.001142">His præparatis per orificium D infundatur <lb></lb>hydrargyrum quouſque duæ fiſtulæ BC, FG, & am<lb></lb>pulla AB, repleantur, relinquaturque ſpatium ſupre<lb></lb>mæ fiſtulæ ID aere plenum, arctè poſteà claudatur <lb></lb>ſupremum orificium D ſuilla veſica; tandèm flecta<lb></lb>tur deorsùm fiſtula collateralis FG, ab eius ſupremo <lb></lb>ore G profluens mercurius excipiatur vaſe MN, </s> </p> <pb pagenum="222" xlink:href="010/01/230.jpg"></pb> <p type="main"> <s id="s.001143"><arrow.to.target n="marg295"></arrow.to.target><lb></lb>quouſque infima mercurij <lb></lb>libella ſit LO, & ſuprema <lb></lb>ſuperficies eiuſdem mer<lb></lb>curij ſtagnantis ſit H reli<lb></lb>cto nempè ſpatio vacuo <lb></lb>DABH, quia verò cylin<lb></lb>drus aereus DI dilatatur, <lb></lb><expan abbr="explicaturq;">explicaturque</expan> pro eius ge<lb></lb>nio in ſpatio vacuo <expan abbr="ibidẽ">ibidem</expan> <lb></lb>relicto, fit vt poſſit <expan abbr="ali-quãdo">ali<lb></lb>quando</expan> poſt eius dilatatio <lb></lb>nem integrè, & totalitèr <lb></lb>occupare <expan abbr="ſpatiũ">ſpatium</expan> DABH, <lb></lb>& tunc cum <expan abbr="nõ">non</expan> poſſit am<lb></lb>pliùs explicari ſua virtute <lb></lb><figure id="id.010.01.230.1.jpg" xlink:href="010/01/230/1.jpg"></figure><lb></lb>elatere non impellet deorsùm ſuperficiem hydrar<lb></lb>gyri H, & ideò ſumma altitudo mercurij HO erit <lb></lb>inalterata, ſcilicèt omnium maxima earum, quæ fie<lb></lb>ri poſſunt vnius cubiti & quadrantis proximè, & tunc <lb></lb>experientia conſtat aerem DI maximè dilatatum in<lb></lb>tra ſpatium DABH occupare locum 180. maiorem̨ <lb></lb>quam prius. </s> <s id="s.001144">ſuppoſita hac cognitione ab experientia <lb></lb>deducta denuò operatio repetatur, & conſtat quod <lb></lb>omnes moles aeris non excedentes ſpatium DI non <lb></lb>depriment mediocrem mercurij eleuationem OH; & <lb></lb>è contrà omnes aeris moles excedentes DI <expan abbr="cõprimẽt">compriment</expan> <lb></lb>mercurium efficientque altitudinem OK minorem̨ <lb></lb>menſura conſueta vnius cubiti, & quadrantis proxi<lb></lb>mè, & hoc profectò non fuiſſe à doctiſſimo viro ani-<pb pagenum="223" xlink:href="010/01/231.jpg"></pb><arrow.to.target n="marg296"></arrow.to.target><lb></lb>maduerſum facilè conſtat, non enim dixiſſet: <emph type="italics"></emph>ſi tantu<lb></lb>lum aeris antequam demittatur mercurius in fistula, relin<lb></lb>quatur mercurius deſcendet infra H. vbi ſuſtineri debuerat <lb></lb>ſi ab aeris cylindro ſuſtinebatur.<emph.end type="italics"></emph.end> reuerà enim quælibet <lb></lb>portiones aeris minores ſpatio ID ſummam altitudi<lb></lb>nem mercurij in fiſtula non deprimunt, quia nimirùm <lb></lb>aereus cylindrus eiuſdem roboris æquali vi compri<lb></lb>mit mercurium ſubiectum. </s> <s id="s.001145">At quando aeris moles <lb></lb>maior ID ibidem includitur, tunc virtute eius elate<lb></lb>ria, vt poſtea dicemus, vim facit contra impulſum̨ <lb></lb>aeris externi, nempè cylindrus mercurij HO æquili<lb></lb>bratus ab aere externo impellitur ſursùm ab O ver<lb></lb>sùs H, ab aere verò incluſo intra ampullam AB, dum <lb></lb>conatur ſe dilatare repellitur deorsùm ab H versùs <lb></lb>O. </s> <s id="s.001146">Vis ergo aeris comprimentis mercurium ſtagnan<lb></lb>tem L agit contra duas reſiſtentias, ſcilicèt contra <expan abbr="põ-dus">pon<lb></lb>dus</expan> mercurij HO, & contra vim exiguam aeris in<lb></lb>cluſi ſe dilatare conantis; igitur in hoc caſu minor erit <lb></lb>altitudo mercurij OK quam HO, licet producatur ab <lb></lb>eadem aeris virtute premente; Nil igitur ex hac ter<lb></lb>tia aduerſarij ratione deducitur contra aeris preſſio<lb></lb>nem, & æquilibrium cum mercurio incluſo intra fi<lb></lb>ſtulam. </s> </p> <p type="margin"> <s id="s.001147"><margin.target id="marg295"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001148"><margin.target id="marg296"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001149">Quarta ratio eadem ferè eſt cum prima, ad eamque <lb></lb><arrow.to.target n="marg297"></arrow.to.target><lb></lb>reducitur. </s> <s id="s.001150">quinta verò pendet ex eo quod ſpatium̨ <lb></lb>ſupremum fiſtulæ poſt mercurij lapſum non vacuum, <lb></lb>ſed repletum eſſe ait ex materia quadam tenuiſſima, <lb></lb>ſed valdè tenſa de qua re ſuo loco diſputabimus; in<lb></lb>terim incidenter noto eius verba dum ait, <emph type="italics"></emph>tantam ae-<emph.end type="italics"></emph.end><pb pagenum="224" xlink:href="010/01/232.jpg"></pb><arrow.to.target n="marg298"></arrow.to.target><lb></lb><emph type="italics"></emph>ris compresſionem ſenſui repugnare: cum inclinata fiſtula <lb></lb>derumeſcat veſica, antequam ſuperficies mercurij ad illam <lb></lb>perueniat.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001151"><margin.target id="marg297"></margin.target>Quarta, & <lb></lb>quinta ratio <lb></lb>eiuſdem au<lb></lb>thoris.</s> </p> <p type="margin"> <s id="s.001152"><margin.target id="marg298"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001153"><emph type="center"></emph>PROP. CVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001154"><emph type="center"></emph><emph type="italics"></emph>Veſica cyprina inflata Roberuallij in ſummitate fiſtulæ Tor<lb></lb>ricellianæ <expan abbr="nõ">non</expan> ſemper detumeſcit poſt huius inclinatio<lb></lb>nem, & ratio huius effectus redditur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001155">HOc profectò non ſemper accidit, præcipuè <expan abbr="quã-do">quan<lb></lb>do</expan> fiſtula capacem ampullam in ſummitate ha<lb></lb>bet, in ea enim commodè aliqua aeris portio, quæ <expan abbr="sẽ-per">sem<lb></lb>per</expan> in fiſtulæ ſuprema parte remanet, aut ibidem col<lb></lb>ligitur reduciturque poſtquàm ſegregatur à mercu<lb></lb>rij ſubſtantia, per quam aſcendunt innumera granula <lb></lb>aerea partim viſibilia, partim inconſpicua ob minu<lb></lb>tiem, & hæc quidem ad ſupremam mercurij ſuperfi<lb></lb>ciem aſcendunt, & prout magis ad ſpatium vacuum <lb></lb>appropinquantur, eo magis creſcunt bullæ aereæ, in<lb></lb>fianturque, & tandem expanduntur, diſſiliunt <expan abbr="rumpũ-turque">rumpun<lb></lb>turque</expan> in prædicto ſpatio vacuo, & hoc magis <expan abbr="euidẽ-ter">euiden<lb></lb>ter</expan> obſeruatur ſi ſuprema hydrargyri cylindri ſuper<lb></lb>ficies exigua aquæ portione cooperiatur, tunc gra<lb></lb>nula aerea à mercurio aſcendentia videri poſſunt in <lb></lb>tranſitu per aquam tranſpicuam, quæ ſpeciem repre<lb></lb>ſentant ebullitionis cuiuſdam compoſitæ ex prædi<lb></lb>ctis particulis aereis inflatis, & velociſſimè <expan abbr="ſursũ">ſursum</expan> ex<lb></lb>currentibus. </s> <s id="s.001156">His poſitis veſicula illa cyprina Rober<lb></lb>uallij inclinata fiſtula ſolet detumeſcere antequam̨ <pb pagenum="225" xlink:href="010/01/233.jpg"></pb><arrow.to.target n="marg299"></arrow.to.target><lb></lb>mercurius eam attingat, propterea quòd partes illæ <lb></lb>aereæ, quæ priùs ſummè dilatatæ erant in amplo ſpa<lb></lb>tio inani in ſummitate fiſtulæ, poſtea reſtricto ſpatio <lb></lb>ob mercurij aſcenſum denuò condenſantur, & proin<lb></lb>dè mirum non eſt veſicam cyprinam ab aere eam am<lb></lb>biente denſiori, quàm ſit aer intra veſicam <expan abbr="cõtentus">contentus</expan>, <lb></lb><expan abbr="compreſſionẽ">compreſſionem</expan> pati debere, & proinde detumeſcere. </s> </p> <p type="margin"> <s id="s.001157"><margin.target id="marg299"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001158">Quando verò ſubdit, quod aer intra fiſtulam im<lb></lb>miſſus dum mercurius eleuatus eſt ad prædictam al<lb></lb>titudinem cubiti vnius, & quadrantis proximè, <expan abbr="ſursũ">ſursum</expan> <lb></lb>fertur tanto impetu, vt ſupremum fiſtulæ fundum, & <lb></lb>baſis diffringatur; diſſiliatque, & quia ab exceſſu exi<lb></lb>gui ponderis tantus impetus creari non poteſt, hinc <lb></lb>deducit non poſſe à cylindro aeris ambiente, & ab <lb></lb>eius <expan abbr="põdere">pondere</expan> vllo pacto impelli neque mercurius, ne<lb></lb>que aer in prædicta fiſtula. </s> </p> <p type="main"> <s id="s.001159"><emph type="center"></emph>PROP. CVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001160"><emph type="center"></emph><emph type="italics"></emph>Aer in fiſtula Torricelliana adueniens nedùm pondere, ſed <lb></lb>vi elaſtica, & impetu in motu acquiſito diffringere <lb></lb>fundum ſupremum fistulæ poteſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001161">HVic difficultati occurro <expan abbr="cõſiderando">conſiderando</expan> quòd mer<lb></lb>curius in fiſtula ſursùm impellitur ab aere ex<lb></lb>terno non vnica, ſed triplici vi, ponderis nimirum, <lb></lb>virtutis elaſticæ ad modum machinæ, & impetus in <lb></lb>motu acquiſiti: ſed præcipua, & inſignis actio in ca<lb></lb>ſu noſtro impetui tribui debet. </s> <s id="s.001162">Quia poſtquam è <lb></lb>fiſtula cum mercurio extante in aere pendula effluit <pb pagenum="226" xlink:href="010/01/234.jpg"></pb><arrow.to.target n="marg300"></arrow.to.target><lb></lb>gutta aliqua mercurij ſubito ceſſat æquilibrium, & <lb></lb>ideò maius pondus collateralis columnæ aereæ po<lb></lb>teſt ſursùm intra fiſtulam impellere molem minus <expan abbr="põ-derãtis">pon<lb></lb>derantis</expan> mercurij incluſi; & licèt ab initio motus mer<lb></lb>curij ſursùm ſit tardus, & debilis, tamen in progreſ<lb></lb>ſu, & continuatione prædicti motus dum repetitis <lb></lb>ictibus mercurius ab aeris pondere, & vi eius elaſti<lb></lb>ca continenter impellitur, nouos gradus impetus, & <lb></lb>velocitatis creat, qui impetus ſunt integri, & <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>energiæ, non enim à vacuo intra fiſtulam incluſo de<lb></lb>bilitari poſſunt, veluti debilitantur impetus <expan abbr="corporũ">corporum</expan> <lb></lb><arrow.to.target n="marg301"></arrow.to.target><lb></lb>per aerem excurrentium; prædicti verò gradus velo<lb></lb>citatum ſimul coaceruati, tandem vim illam <expan abbr="ingentẽ">ingentem</expan> <lb></lb>componunt, quæ diffringere fundum vitreæ fiſtulæ <lb></lb>poteſt; adde quod corpora grauiſſima; vt eſt hydrar<lb></lb>gyrum validius fuſcipiunt retinentque vim impetus <lb></lb>præconcepti, & hinc ſequitur percuſſio eius validiſ<lb></lb>ſima in vitri fundum. </s> <s id="s.001163">Supradictum ratiocinium ab ip<lb></lb>ſa experientia <expan abbr="cõſirmari">confirmari</expan> videtur; ſi enim fiſtula præ<lb></lb>longa ſubtili, & gracili fundo clauſa, & mercurio ple<lb></lb>na inuerſo ore infra mercurium in ſcutella <expan abbr="ſtagnantẽ">ſtagnantem</expan> <lb></lb>demerſa, & inclinato ſitu detineatur vt mercurius <lb></lb>minus vno digito à ſupremo fundo diſtet, tunc ſu<lb></lb>ſpenſa fiſtula aer adueniens fundum eius non diffrin<lb></lb>git, at perpendiculari ſitu erecta fiſtula aer <expan abbr="ſuccedẽs">ſuccedens</expan> <lb></lb>ingenti impetu <expan abbr="diſtãtem">diſtantem</expan> à fundo mercurium propel<lb></lb>lit vt eum diffringat, quia nimirum in prolixiori mo<lb></lb>tu plures gradus impetus creari, & ſimul coaceruari <lb></lb>poſſunt. <pb pagenum="227" xlink:href="010/01/235.jpg"></pb><arrow.to.target n="marg302"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001164"><margin.target id="marg300"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001165"><margin.target id="marg301"></margin.target>De vi per<lb></lb><gap></gap>cap. 22.</s> </p> <p type="margin"> <s id="s.001166"><margin.target id="marg302"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001167">Poſtea ſubdit: <emph type="italics"></emph>Cylindrus aeris exterioris à quo (vt non<lb></lb>nulli volunt) mercurij extantis ſegmentum ſuſtinetur, ne<lb></lb>que plus, neque minus poteſt ſustinere, igitur ſi ferrum can<lb></lb>dens admoueatur ſegmento vacuo fiſtulæ, nulla eſt ratio cur <lb></lb>ſuperficies ſuprema mercurij ſubſidat. </s> <s id="s.001168">Subſidit tamen. </s> <s id="s.001169">Si<emph.end type="italics"></emph.end><arrow.to.target n="marg303"></arrow.to.target><lb></lb><emph type="italics"></emph>verò nix, vel trita glacies admoueatur, mercurius attolli<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001170"><margin.target id="marg303"></margin.target>Sextum ar<lb></lb>gumentum.</s> </p> <p type="main"> <s id="s.001171"><emph type="center"></emph>PROP. CVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001172"><emph type="center"></emph><emph type="italics"></emph>Igneæ exhalationes corporeæ vehementisſima agitatione <expan abbr="tũ">tum</expan> <lb></lb>per ſe, cum variè impellendo, & <expan abbr="torquẽdo">torquendo</expan> particulas <lb></lb>aeris in ſummitate fistulæ Torricellianæ reli<lb></lb>ctas, facilè poſſunt ſubſidentem mercu<lb></lb>rium æquilibratum deprimere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001173">REſpondeo, quòd igneæ particulæ nedùm ſe ip<lb></lb>ſas vehementèr agitant, commouentque, ſed <lb></lb>præterea aereas quoque particulas in vitri ſummita<lb></lb>te incluſas, vt dictum eſt, vehementiſſimè impellunt; <lb></lb>porrò quia quodlibet corpus æquilibratum poteſt à <lb></lb>quacumque exigua vi agitari, (vt demonſtrauimus <lb></lb>in noſtro opere de vi percuſſionis) ſitque prædictus <lb></lb>mercurius in fiſtula æquilibratus cum <expan abbr="æquiponderã-te">æquiponderan<lb></lb>te</expan> cylindro aereo externo, igitur neceſſariò ab inte<lb></lb>ſtina illa agitatione ignearum, & aerearum particu<lb></lb>larum ſuperficies mercurij percuſſa propelli poteſt, <lb></lb>& ideò deprimi infra conſuetam eius altitudinem de<lb></lb>bet, è contrà adhibita niue, vel trita glacie, ſpatium <lb></lb>illud dum igne priuatur, & deficit quoque agitatio, <lb></lb>& reuolutio nedum particularum ignis, ſed etiam̨ <pb pagenum="228" xlink:href="010/01/236.jpg"></pb><arrow.to.target n="marg304"></arrow.to.target><lb></lb>aeris contenti, propterea præualere poteſt exceſſus <lb></lb>grauitatis aeris ambientis ſupra mercurium in fiſtu<lb></lb>la eleuatum. </s> </p> <p type="margin"> <s id="s.001174"><margin.target id="marg304"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001175">Affert poſtea ſeptimam rationem: <emph type="italics"></emph>Si poſtquam mer<lb></lb>curius ſubſidit vas infimum claudatur vt nulla rima ſu-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg305"></arrow.to.target><lb></lb><emph type="italics"></emph>perſit, per quam aer ſubeat, non tamen propterea mercurius <lb></lb>ſubſidit, ſed tunc non ſuſtinetur à cylindro aeris, quia ſcili<lb></lb>cèt non est applicatus.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001176"><margin.target id="marg305"></margin.target>Septima in<lb></lb>ſtantia.</s> </p> <p type="main"> <s id="s.001177">Huic argumento primus omnium reſpondit Cla<lb></lb>riſſimus Torricellius in epiſtola ad Clariſſimum Mi<lb></lb>chaelem Angelum Riccium miſſa, quam humaniſſi<lb></lb>mè mihi communicauit anno 1658. eamque Floren<lb></lb>tiæ poſteà Sereniſſimo Principi Leopoldo tradidi, & <lb></lb>inter amicos euulgaui. </s> </p> <p type="main"> <s id="s.001178"><emph type="center"></emph>PROP. CIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001179"><emph type="center"></emph><emph type="italics"></emph>Licèt operculo impediatur aeris presſio ſupra <expan abbr="mercuriũ">mercurium</expan> ſta<lb></lb>gnantem in ſcutella, tamen quia aer relictus ibidem <lb></lb>remanet eodem modo preſſus, & conſtipatus <lb></lb>ac prius poteſt mercurium in fistula ad <lb></lb>eamdem altitudinem re<lb></lb>tinere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001180">IS habet, quod <expan abbr="quãdo">quando</expan> intercipitur prohibeturque <lb></lb>commercium inter ambientem aerem, & eum, qui <lb></lb>immediatè ſuperficiem ſtagnantis mercurij tangit <lb></lb>poſito nimirùm operculo, vt v. g. quando in fiſtulą <lb></lb>inflexa ABG mercurius eleuatur vſque ad <expan abbr="altitudinẽ">altitudinem</expan> <lb></lb>BF vnius cubiti, & quadrantis relicto ſpatio inani <pb pagenum="229" xlink:href="010/01/237.jpg"></pb><arrow.to.target n="marg306"></arrow.to.target><lb></lb>AF, & poſito quod prædicta mercurij ſublimatio de<lb></lb>pendeat à compreſſione, quam cylindrus aereus SD <lb></lb>vſque ad ſupremam aeris ſuperficiem extenſus ſuą <lb></lb>grauitate efficiat ſupra <expan abbr="ſtagnãtem">ſtagnantem</expan> mer<lb></lb><figure id="id.010.01.237.1.jpg" xlink:href="010/01/237/1.jpg"></figure><lb></lb>curium D, ſequitur, quod ſi occludatur <lb></lb>orificium G eiuſdem fiſtulæ remanebit <lb></lb>portio aerea intercepta GD <expan abbr="eodẽ">eodem</expan> mo<lb></lb>do <expan abbr="cõpreſſa">compreſſa</expan> reſtrictaque vt priùs, quia <lb></lb>nimirùm digitus, vel operculum reti<lb></lb>net conſeruatque aerem in eadem po<lb></lb>ſitione, & conſtrictione, quam prius ab <lb></lb>incumbente aere patiebatur. </s> <s id="s.001181">Eodem̨ <lb></lb>ferè modo, ac ſi loco aeris ſuperpone<lb></lb>rentur mercurio plures cylindri lapidei <lb></lb>vnus ſuper alterum incumbens, tunc <lb></lb>profectò infimus cylindrus comprime<lb></lb>ret ſuperficiem ſubiecti hydrargyri D <lb></lb>non tantùm energia ponderis proprij, <lb></lb>ſed vi conflata ex grauitate omnium incumbentium <lb></lb>cylindrorum modò ablatis ſemotiſque ſupremis om<lb></lb>nibus columnis ſi in fimus cylindrulus, tantummodò <lb></lb>tabula, vecte, aut quo cumque alio retinaculo <expan abbr="eadẽ">eadem</expan> <lb></lb>vi fixè in eodem ſitu retineretur, patet quòd æquali <lb></lb>energia comprimeret ſubiectam mercurij <expan abbr="ſuperficiẽ">ſuperficiem</expan> <lb></lb>D ac priùs premebatur à prælonga illa ſerie colum<lb></lb>narum incumbentium; Et hic dicendum eſſet, quòd <lb></lb>cauſa immediata impellens mercurium non eſt longa <lb></lb>illa ſeries columnarum SD, ſed eſt infimus cylindru<lb></lb>lus GD qui tanta vi comprimit ſubiectum <expan abbr="mercuriũ">mercurium</expan> <pb pagenum="230" xlink:href="010/01/238.jpg"></pb><arrow.to.target n="marg307"></arrow.to.target><lb></lb>quanta eſt grauitas omnium columnarum SD; itaque <lb></lb>grauitas omnium columnarum appellari poteſt cau<lb></lb>ſa productiua illius compreſſionis, quam facit infi<lb></lb>mus cylindrulus GD mercurio immediatè <expan abbr="cõtiguus">contiguus</expan>, <lb></lb>quia verò huiuſmodi effectus remanet, quando clau<lb></lb>ditur orificium G, remouenturque columnæ ſupre<lb></lb>mæ, igitur æquali vi, & æquali menſura debet mer<lb></lb>curius BF ſublimari. </s> <s id="s.001182">Id ipſum dici debet de aere SD, <lb></lb>certum profectò eſt dum orificium G eſt apertum cy<lb></lb>lindrum aereum GS vſque ad aeris ſupremam ſuper<lb></lb>ficiem extenſum comprimere cylindrulum aereum̨ <lb></lb>GD tanta vi quanta exigit energia grauitatis aeris <lb></lb>SG, quando verò digito, vel operculo impeditur <expan abbr="cõ-tactus">con<lb></lb>tactus</expan>, & compreſſio aeris ſupremi SG remanet cy<lb></lb>lindrulus aereus GD eodem modo compreſſus reſtri<lb></lb>ctuſque, ac prius igitur neceſſario eodem modo ſub<lb></lb>iectum mercurium D premet proindeque ad <expan abbr="eamdẽ">eamdem</expan> <lb></lb>altitudinem BF eum ſubleuabit. </s> </p> <p type="margin"> <s id="s.001183"><margin.target id="marg306"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001184"><margin.target id="marg307"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001185"><emph type="center"></emph>PROP. CX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001186"><emph type="center"></emph><emph type="italics"></emph>Idipſum confirmatur in aquæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001187">VEritas huius aſſerti alio experimento confirma<lb></lb>tur: Demergatur in aliquo puteo RV aqua ple<lb></lb>no eadem fiſtula ABG cum mercurio extante FB, vi<lb></lb>demus quod aliquantiſper mercurius infra libellam <lb></lb>D deprimitur à pondere <expan abbr="incũbentis">incumbentis</expan> aquæ ND, quæ <lb></lb>paritèr altiùs <expan abbr="mercuriũ">mercurium</expan> in fiſtulam ſubleuat per ſpa<lb></lb>tium BH, vt nimirùm exceſſus FH ſupra eam eleua-<pb pagenum="231" xlink:href="010/01/239.jpg"></pb><arrow.to.target n="marg308"></arrow.to.target><lb></lb>tionem, quæ in libero aere efficiebatur, ſit pars de<lb></lb>cimaquarta altitudinis aquæ ND. in hoc rerum ſta<lb></lb>tu digito, vel quolibet alio operculo claudatur fi<lb></lb>ſtulæ oſtium G hic iam ceſſat om<lb></lb><figure id="id.010.01.239.1.jpg" xlink:href="010/01/239/1.jpg"></figure><lb></lb>ninò actio, & compreſſio <expan abbr="põderis">ponderis</expan> <lb></lb>cylindri aquei NG, & tamen mer<lb></lb>curius in eodem ſigno fiſtulæ H <lb></lb>perſeuerat, igitur eodem modo <lb></lb>in aere occluſo oſtio G perſeue<lb></lb>rare, & retineri debet mercurius <lb></lb>ſubleuatus <expan abbr="vſq;">vſque</expan> ad F mediatè <expan abbr="qui-dẽ">qui<lb></lb>dem</expan> à <expan abbr="põdere">pondere</expan> aeris qui prius <expan abbr="incũ-bebat">incum<lb></lb>bebat</expan>, ſed modo immediatè ab illa compreſſione, & <lb></lb>reſtrictione, quam produxerat pondus incumbentis <lb></lb>aeris SG. vnde conſtat quod mercurius in fiſtula ele<lb></lb>uari poteſt à pondere aeris ambientis, nec adductą <lb></lb>difficultas hanc ſententiam debilitat aut deſtruit. </s> </p> <p type="margin"> <s id="s.001188"><margin.target id="marg308"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001189">Subdit poſtea pro confirmatione ſui ratiocinij: <lb></lb><arrow.to.target n="marg309"></arrow.to.target><lb></lb><emph type="italics"></emph>Iam verò facilè ostendo non ſustineri, ſeu ſuſpendi in BF eò <lb></lb>quod aer interceptus inter operculum, & ſuperficiem vlte<lb></lb>riori compreſsioni reſistat, nempè ſi admoto dicto operculo, & <lb></lb>extante mercurio in BF aperiatur foramen in A mercurius <lb></lb>illicò infra F deſcendit, idque notabili ſegmento, &c.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001190"><margin.target id="marg309"></margin.target>Hoc ratio<lb></lb>cinium cona <lb></lb>tur refellere <lb></lb>aduerſarius.</s> </p> <p type="main"> <s id="s.001191">Sibi ipſi poſtea opponit dicendo, quòd mercurius <lb></lb><expan abbr="deorsũ">deorsum</expan> impellitur duplici vi, propriæ ſcilicèt grauita<lb></lb>tis mercurij BF, & <expan abbr="põderis">ponderis</expan> aeris per <expan abbr="ſupremũ">ſupremum</expan> <expan abbr="foramẽ">foramen</expan> <lb></lb><expan abbr="fluẽtis">fluentis</expan>, quid mirum ſi præualeat, interceptumque ae<lb></lb>rem vlteriùs comprimat, & mercurium infra F depri<lb></lb>mat. </s> <s id="s.001192">poſtea huic argumento reſpondet: <emph type="italics"></emph>Dico non ma-<emph.end type="italics"></emph.end><pb pagenum="232" xlink:href="010/01/240.jpg"></pb><arrow.to.target n="marg310"></arrow.to.target><lb></lb><emph type="italics"></emph>gis comprimi aera interceptum inter D, & dictum opercu<lb></lb>lum à mercurio FB, & cylindro aeris grauitantis per fora<lb></lb>men A, quam remoto operculo, & clauſo foramine A ab eo<lb></lb>dem mercurio BF & eodem cylindro aeris exterioris, nam <lb></lb>perindè eſt ſiue tota vis preſsionis per lineam vnicam inci<lb></lb>dat, vel applicetur; ſiue ſubduplum per vnam, & ſubdu<lb></lb>plum per oppoſitam.<emph.end type="italics"></emph.end></s> <s id="s.001193"> Vnde (paucis interceptis conclu<lb></lb>dit) <emph type="italics"></emph>perſpicuè deduco non ideo admoto ſcilicet operculo in G <lb></lb>extare mercurium BF, & minimè ſubſidere, quia ſcilicet <lb></lb>dictus aer interceptus comprimi vltra non poteſt, ſed alia de <lb></lb>cauſa, &c.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001194"><margin.target id="marg310"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001195">Sed pace tanti viri, aio, verum <expan abbr="nõ">non</expan> eſſe eius aſſump<lb></lb>tum, demonſtrabo enim quod clauſo vitro in G, & a<lb></lb>perto in A vis, qua comprimitur aer FB duplò vali<lb></lb>dior eſt ea, qua comprimitur clauſo vitro in A, & a<lb></lb>perto in G, pro cuius intelligentia præmittenda eſt <lb></lb>ſequens. </s> </p> <p type="main"> <s id="s.001196"><emph type="center"></emph>PROP. CXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001197"><emph type="center"></emph><emph type="italics"></emph>Anulus, vel veſica aere plena æquè ab vnica & ſub<lb></lb>dupla potentia comprimitur conſtringiturque, <lb></lb>quàm à dupla, ſeu à duabus potentijs illi <lb></lb>æqualibus vtrinque anulum, vel <lb></lb>veſicam constringentibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001198">SIt ABC anulus calybeus, vel veſica aere plena, & <lb></lb>primò <expan abbr="cõprimatur">comprimatur</expan> à duabus <expan abbr="potẽtijs">potentijs</expan> <expan abbr="cõtrarijs">contrarijs</expan>, & <lb></lb>interſe æqualibus P, & E, ſeu G. </s> <s id="s.001199">Et quia vnaquæque <lb></lb><expan abbr="potẽtiarum">potentiarum</expan> P tunc præcisè æquilibratur reſiſtentiæ, <pb pagenum="233" xlink:href="010/01/241.jpg"></pb><arrow.to.target n="marg311"></arrow.to.target><lb></lb>ſeu energiæ compreſſionis, quam patitur pars B, <expan abbr="quã-do">quan<lb></lb>do</expan> ambo poſt flexionem, & motum quieſcunt; ergo <lb></lb>momentum <expan abbr="potẽtiæ">potentiæ</expan> P æqua<lb></lb><figure id="id.010.01.241.1.jpg" xlink:href="010/01/241/1.jpg"></figure><lb></lb>le eſt <expan abbr="momẽto">momento</expan> <expan abbr="reſiſtẽtiæ">reſiſtentiæ</expan>, ſeu <lb></lb>energiæ, compreſſionis, <expan abbr="quã">quam</expan> <lb></lb>patitur B, & fiunt niſus per <lb></lb>eamdem rectam perpendi<lb></lb>cularem ad horizontem, igi<lb></lb>tur abſoluta potentia P æ<lb></lb>qualis | eſt reſiſtentiæ abſolutæ, ſeu vi compreſſionis, <lb></lb>quam patitur B. </s> <s id="s.001200">Pari ratione abſoluta potentia E, vel <lb></lb>G æquatur reſiſtentiæ, ſeu vi compreſſionis partis op<lb></lb>poſitæ C. vnde deducitur duas potentias P & E, ſeu <lb></lb>G ſimul ſumptas æquales eſſe reſiſtentiæ integræ, ſeu <lb></lb>vi totali compreſſionis, quam patitur anulus, vel ve<lb></lb>ſica ABC. </s> </p> <p type="margin"> <s id="s.001201"><margin.target id="marg311"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001202">Poſtea ſubſtituatur pauimentum durum RS loco <lb></lb>potentiæ flectentis E, vel G, & ſolummodo ſupernè <lb></lb>anulus, vel veſica aerea comprimatur à potentia P <lb></lb>ſcilicet à ſemiſſe potentiarum P, & E. </s> <s id="s.001203">Dico anulum̨, <lb></lb>vel veſicam aeream æquè conſtringi, ac priùs à dua<lb></lb>bus potentijs contrarijs contundebatur. </s> <s id="s.001204">Quia paui<lb></lb>mentum ſtabile RS perinde reagit impediendo mo<lb></lb>tum, & deſcenſum ponderis P, ipſumque in eodem ſi<lb></lb>tu quiete ſtabili permanere cogit, ac operatur manus <lb></lb>ſubiecta E, vel pondus G mediante libra FE, ergo <lb></lb>ſtabilitatis ſoli momentum æquatur momento, & po<lb></lb>tentiæ abſolutæ ipſius E, ſeu P. quare anulus, ſeu ae<lb></lb>rea veſica BC comprimitur non à ſingulari, & ſubdu-<pb pagenum="234" xlink:href="010/01/242.jpg"></pb><arrow.to.target n="marg312"></arrow.to.target><lb></lb>pla potentia P, ſed a duplici <lb></lb><figure id="id.010.01.242.1.jpg" xlink:href="010/01/242/1.jpg"></figure><lb></lb>potentia, tanquam à forcipe, <lb></lb>vel prælo, nempè à P, & ab <lb></lb>huic æquali reſiſtentia paui<lb></lb>menti RS. </s> <s id="s.001205">Igitur æquè com<lb></lb>primetur anulus, vel veſica <lb></lb>aerea ſolo innixa à ſingulari <lb></lb>potentia P, ac ſi à duabus contrarijs potentijs P, & <lb></lb>E, vel G conſtringeretur. </s> </p> <p type="margin"> <s id="s.001206"><margin.target id="marg312"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001207"><emph type="center"></emph><emph type="italics"></emph>COROLLARIVM.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001208">HInc patet, quòd ſi duæ potentiæ æquales ſimul <lb></lb>coniunctæ comprimant eumdem ſupremum̨ <lb></lb>anuli terminum pauimento innixi, tunc momentum̨ <lb></lb>fiue energia, qua anulus contunditur ſtringiturquę <lb></lb>duplex eſt eius, qua ab ijſdem potentijs oppoſitos <lb></lb>terminos ſtringentibus comprimitur. </s> </p> <p type="main"> <s id="s.001209">Quia quotieſcum que duæ potentiæ inter ſe æqua<lb></lb>les P & G premunt ſupremum terminum B anuli BC, <lb></lb>tunc ſolum ſtabile RS in E, cui innititur idem præſtat, <lb></lb>& tanta energia operatur, ac ſi in E adeſſet potentią <lb></lb>æqualis ambabus contrarijs potentijs G & P: quare <lb></lb>vis, qua ſtringitur anulus æqualis eſt duplo potentia<lb></lb>rum G, & P. è contrà quando anulus ſtringitur ab ijſ<lb></lb>dem potentijs G, & P ſubdiuiſis, ſcilicèt à potentią <lb></lb>P in ſitu B, atque à potentia G in oppoſito eius ter<lb></lb>mino C vt in præcedenti figura videre eſt, tunc vis, <lb></lb>qua ſtringitur anulus, æqualis eſt præcisè duabus po<lb></lb>tentijs oppoſitis G, & P, igitur quando anulus ſolo <pb pagenum="235" xlink:href="010/01/243.jpg"></pb><arrow.to.target n="marg313"></arrow.to.target><lb></lb>innixus ſtringitur ab ijſdem potentijs G, & P in B du<lb></lb>plici energia conſtringitur, contunditurque quam ſi <lb></lb>ab ijſdem duabus potentijs G, & P ſubdiuiſis <expan abbr="cõſtrin-geretur">conſtrin<lb></lb>geretur</expan>. </s> </p> <p type="margin"> <s id="s.001210"><margin.target id="marg313"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001211"><emph type="center"></emph>PROP. CXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001212"><emph type="center"></emph><emph type="italics"></emph>In Torricelliana fiſtula mercurio extante, clauſo oriſicio <lb></lb>ſcutellæ, & aperta ſummitate fiſtulæ, aer in ſcu<lb></lb>tella interceptus inter mercurium, & <lb></lb>operculum à vi duplò validiori <lb></lb>comprimitur, quàm illo <lb></lb>aperto, & hoc clauſo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001213">IN fiſtula Torricelliana ACG aper<lb></lb>ta in G, & clauſa in A, facto vacuo, <lb></lb><figure id="id.010.01.243.1.jpg" xlink:href="010/01/243/1.jpg"></figure><lb></lb>more ſolito, remanente mercurio BF <lb></lb>eleuato <expan abbr="ſupralibellã">ſupra libellam</expan> BD; patet ex ip<lb></lb>ſiuſmet aduerſarij hypotheſi, quòd <lb></lb>aer in ſcutella, ſeu ampulla DG con<lb></lb>tentus ſtringitur, comprimiturque à <lb></lb>duabus potentijs contrarijs inter ſę <lb></lb>æqualibus (eò quod æquilibrantur) <lb></lb>nempè à pondere mercurij <expan abbr="extãtis">extantis</expan> BF, <lb></lb>& à pondere columnæ aereæ GS. </s> <s id="s.001214">Si <lb></lb>poſtea appoſito operculo exactè clau<lb></lb>datur orificium G, & aperiatur <expan abbr="orificiũ">orificium</expan> <lb></lb>in ſummitate fiſtulæ A aer interceptus <lb></lb>inter operculum G, & mercurium D <lb></lb>ſtringitur comprimiturque à mercurio BF, & à colum-<pb pagenum="236" xlink:href="010/01/244.jpg"></pb><arrow.to.target n="marg314"></arrow.to.target><lb></lb>na aerea FS æquali ipſi GS, tunc patet, quòd poten<lb></lb>tiæ comprimentes mercurij FB, & aeris FS æquales <lb></lb>ſunt potentiæ eiuſdem mercurij FB, & aeris SG. </s> <s id="s.001215">Iam <lb></lb>dico, quod duplò validiori vi comprimitur aer DG <lb></lb>clauſo orificio G, & aperta ſummitate A, quàm illo <lb></lb>aperto, & hoc clauſo. </s> <s id="s.001216">Quia obturato vitro in A, & a<lb></lb>perto in G ampulla aerea DG ſtringitur à duabus <lb></lb>oppoſitis potentijs, à mercurio nempè FB, & ab aeris <lb></lb><arrow.to.target n="marg315"></arrow.to.target><lb></lb>columna SG, ergo vis, qua aerea veſica DG ſtringitur <lb></lb>æqualis eſt duabus poténtijs mercurij BF, & aeris SG, <lb></lb>ſeu duplò ponderis mercurij BF. è contra clauſo ori<lb></lb>ſicio G, & aperto vitro in A duæ potentiæ mercurij <lb></lb>BF, & aeris SF comprimunt <expan abbr="aereã|veficã">aere a veſica</expan> DG in D, qui <lb></lb>aer innititur fundo ſtabili, nempè operculo G, igitur, <lb></lb>ex corollario præcedentis, propoſitionis vis, qua aer <lb></lb>DG ſtringitur æqualis eſt duplò <expan abbr="potẽtiarum">potentiarum</expan> mèrcu<lb></lb>rij BF, & aeris SF, nempèl quadruplò potentiæ mer<lb></lb>curij BF; igitur dupla vi, & energia <expan abbr="cõſtringitur">conſtringitur</expan> aer <lb></lb>DG clauſo orificio G, & aperto vitro in A, ac <expan abbr="cõpri-mebatur">compri<lb></lb>mebatur</expan> quando vitrum claudebatur in A, reſeraba<lb></lb>tur verò in G. </s> </p> <p type="margin"> <s id="s.001217"><margin.target id="marg314"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elateria <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001218"><margin.target id="marg315"></margin.target>Ex 1. parte <lb></lb>top. III. </s> <s id="s.001219">111.</s> </p> <p type="main"> <s id="s.001220">Quod verò à maiori vi compreſſiua, nempè dupla <lb></lb>magis conſtringi, condenſarique debeat aer DG, & <lb></lb>proinde mercurius deprimatur infra ſupremam ele<lb></lb>uationem F mirum profectò non eſt, imò iuxtà ordi<lb></lb>nem naturæ, & neceſſitatem, qua operatur debet <lb></lb>mercurius in prædicto caſu aliquantulum deprimi, vt <lb></lb>exigit aeris natura, quæ dilatationi, & conſtrictioni <lb></lb>obnoxia eſt. </s> <s id="s.001221">Hinc conſtat ab aere <expan abbr="cõpreſſo">compreſſo</expan> DG pro-<pb pagenum="237" xlink:href="010/01/245.jpg"></pb><arrow.to.target n="marg316"></arrow.to.target><lb></lb>hiberi deſcenſum mercurij BF, quæ compreſſio facta <lb></lb>fuit à cylindro aereo incumbente SG ope eius na<lb></lb>tiuæ grauitatis. </s> </p> <p type="margin"> <s id="s.001222"><margin.target id="marg316"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001223">Non eſt neceſsè vt hìc repetam <expan abbr="experimẽta">experimenta</expan> innu<lb></lb>mera, quæ paſſim obuia <expan abbr="sũt">sunt</expan>, de quibus Roberuallius, <lb></lb>Merſennus, Pecquetus, Boile, Gaſſendus, & plures <lb></lb>alij ſcripſerunt, & tandem prodijt liber experimen<lb></lb>torum noſtræ Academiæ Experimentalis Mediceæ; <lb></lb>ex his enim euincitur, ab aere ambiente mercurium̨ <lb></lb>in fiſtula ſubleuari, quandoquidem quotieſcumque <lb></lb>aer exſugitur, ſeu prohibetur eius compreſſio ſuper <lb></lb>ſtagnantem mercurium, tunc deprimitur mercurius <lb></lb>infra ſupremum ſignum in fiſtula, & ſi hoc fiat in ſpa<lb></lb>tio vacuo, ſcilicèt in loco à quo aer excluſus ſit, tunc <lb></lb>quidem mercurius omninò deprimitur, & è contrà <lb></lb>adueniente aere ſubitò mercurius in prædicta fiſtula <lb></lb>eleuatur. </s> <s id="s.001224">idipſum accidit in aqua. </s> </p> <p type="main"> <s id="s.001225"><emph type="center"></emph>PROP. CXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001226"><emph type="center"></emph><emph type="italics"></emph>Suadetur aeris difformis grauitas ex inæquali mercurij ele<lb></lb>uatione in fiſtula, prout altitudo aeris maior, aut mi<lb></lb>nor fuerit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001227">PRætere a euidentiſſimum eſt, mercurium in prædi<lb></lb>cta fiſtula eò magis deprimi infra altitudinem̨ <lb></lb>vnius cubiti, & quadrantis, quò magis <expan abbr="inſtrumentũ">inſtrumentum</expan> <lb></lb>eleuatur à plano ſubiecto, ſic Dominus Paſchalius in <lb></lb>montibus Aruerniæ expertus eſt in radice montis <lb></lb>mercurij altitudinem fuiſſe pollicum 27. cum tribus <pb pagenum="238" xlink:href="010/01/246.jpg"></pb><arrow.to.target n="marg317"></arrow.to.target><lb></lb>lineis: <expan abbr="trãslato">translato</expan> inſtrumento ad altitudinem pedum̨ <lb></lb>900. ſupra montis radicem, mercurij altitudo fuit ſo<lb></lb>lummodò pollicum 25. in cacumine verò montis vbi <lb></lb>altitudo ab eius radice erat pedum 3000. eleuatio <lb></lb>mercurij fuit pollicum 24. lin. 2. conſtat ergo nedùm <lb></lb>minui compreſſionem quando minuitur aeris altitu<lb></lb>do, ſed etiam euincitur difformitas grauitatis ipſius <lb></lb>aeris; conijcitur enim, quòd aer habeat conſiſtentiam <lb></lb>veluti ſpongioſam <expan abbr="ſitq;">ſitque</expan> veluti lanæ cumulus, cuius <lb></lb>partes ſuperiores dum comprimunt infimas, reddunt <lb></lb>aeris regionem difformiter grauem pro varia earum̨ <lb></lb>compreſſione, & conſtipatione, & pro varia miſtu<lb></lb>ra particularum aquæ, & terræ. </s> </p> <p type="margin"> <s id="s.001228"><margin.target id="marg317"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001229">Idipſum poſtea obſeruauimus Florentiæ in altiſſi<lb></lb>ma turri palatij, in qua aſcenſis ſolummodò cubitis <lb></lb>50. ſupra infimam plateam, & palatij atrium depreſ<lb></lb>ſus apparuit mercurius ſpatio vnius gradus, ſcilicèt <lb></lb>decima parte vnius digiti, at poſtea perducto inſtru<lb></lb>mento ad altitudinem 100. <expan abbr="cubitorũ">cubitorum</expan> depreſſio mer<lb></lb>curij minor fuit altero gradu euidenti, & notabili <lb></lb>defectu. </s> <s id="s.001230">Idemque poſtea obſeruatum fuit in monti<lb></lb>bus propè Florentiam, & ne ſuſpicio ſubiret aeris ſu<lb></lb>premi frigiditatem depreſſiſſe mercurium in fiſtulą <lb></lb>elegimus loca, & tempora commoda, ſcilicèt calefa<lb></lb>cta à ſole in turris cacumine, & vmbroſa in eius ra<lb></lb>dicibus, vt eorum temperies eadem eſſet, & hoc in<lb></lb>dicabatur adhibitis perfectiſſimis termometris, quç <lb></lb>oſtendebant aerem in ſummitate turris, aut eadem̨ <lb></lb>temperio, aut calidiori ſeruari quem in radice turris <pb pagenum="239" xlink:href="010/01/247.jpg"></pb><arrow.to.target n="marg318"></arrow.to.target><lb></lb>aut montis. </s> <s id="s.001231">& ne ſuſpicio ſubiret à concuſſione mer<lb></lb>curij in fiſtula dum transferebatur ſursùm excluſis <lb></lb>particulis minimis aereis, debuiſſe poſtea mercurium <lb></lb>aliquantiſper deprimi, curauimus etiam obturato in<lb></lb>fimo fiſtulæ orificio, ne vlla concuſſio mercurij effice<lb></lb>retur, & poſtea in ipſo deſcenſu vidimus præcisè <lb></lb>mercurium in ijſdem locis eleuatum fuiſſe ad eaſdem <lb></lb>altitudines, ad quas in aſcenſu <expan abbr="mõtis">montis</expan>, vel turris per<lb></lb>uenerat, vnde colligitur ſolummodò ab aeris varią <lb></lb>compreſſione mercurium ſuas altitudines variaſſe. <lb></lb><arrow.to.target n="marg319"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001232"><margin.target id="marg318"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001233"><margin.target id="marg319"></margin.target>Altitudo <lb></lb>mercurij in <lb></lb>fiſtula Torri<lb></lb>celliana non <lb></lb>ſemper eiuſ<lb></lb>dem menſu<lb></lb>ræ eſt.</s> </p> <p type="main"> <s id="s.001234">Vltimo loco animaduertimus non ſemper mercu<lb></lb>rium ad eamdem præcisè altitudinem in fiſtula ele<lb></lb>nari, quæ aliqua ex parte pendet à temperie aeris <lb></lb>calida, & frigida, ſed hæc quidem exigua eſt ſi vi<lb></lb>trea fiſtula in vertice eius ſupremo annexam ampul<lb></lb>lam vacuam, amplam habeat; mirabilis profectò vi<lb></lb>ſa eſt variatio illa altitudinis, quæ procùl dubio à <expan abbr="tẽ-perie">ten<lb></lb>perie</expan> calidi, & frigidi aeris non dependet, <expan abbr="cũ">cum</expan> perin<lb></lb>de obſeruata ſit temporibus æſtiuis, & hyemalibus, <lb></lb>pariter que in cubiculo ab igne excalefacto, vel fri<lb></lb>gido, et habeo penès me obſeruationes <expan abbr="duorũ">duorum</expan> anno<lb></lb>rum 1657. & 1658. <expan abbr="prædictarũ">prædictarum</expan> <expan abbr="varietatũ">varietatum</expan>, in quibus <lb></lb>ſingulis diebus <expan abbr="adnotãtur">adnotantur</expan> gradus caliditatis aeris ex <lb></lb>termometro, an dies fuerit nebuloſus, vel pluuius, <lb></lb>aut ſerenus, & quinam venti ſpirarint, quas feci mo<lb></lb>nitu, & iuſſu Sereniſs. Ferdinandi Secundi M. </s> <s id="s.001235">Ducis <lb></lb>Ætrurię, naturalium operationum ſagaciſſimi explo<lb></lb>ratoris: & tandem videtur ex pluribus obſeruatio<lb></lb>nibus ſimùl collectis deduci poſſe, quòd multoties </s> </p> <pb pagenum="240" xlink:href="010/01/248.jpg"></pb> <p type="main"> <s id="s.001236"><arrow.to.target n="marg320"></arrow.to.target><lb></lb>cùm imminet aliqua diuturna, & continuata pluuia <lb></lb>in illa regione, tunc mercurius in fiſtula per aliquos <lb></lb>gradus ſupra conſuetam altitudinem eleuatur, è con<lb></lb>trà pluuia iam actu cadente mercurius in prædicta fi<lb></lb>ſtula deprimi ſolet, nec eſt exigua prædicta differen<lb></lb>tia, multotiès enim Piſis obſeruaui in diuturnis plu<lb></lb>uioſis tempeſtatibus variaſſe mercurij altitudinem̨ <lb></lb>per duodecim gradus, ſcilicèt per latitudinem vnius <lb></lb>pollicis. </s> <s id="s.001237">Quia verò aſſeruo penès me exemplar epi<lb></lb>ſtolæ, quam Sereniſſimo Principi Leopoldo modò <lb></lb>Cardinali ampliſſimo anno 1657. ſcripſi circa hanc <lb></lb>materiam, hìc afferam breuiter ea, quæ tunc ſpecu<lb></lb>latus ſum, quod nimirùm fieri poteſt ob aeris preſ<lb></lb>ſionem ſupra mercurium ſtagnantem in fiſtula, vt an<lb></lb>te pluuiam aer multò magis grauitet, & comprimat, <lb></lb>quam in ipſo pluuiæ deſcenſu, quod vt clariùs oſten<lb></lb>dam, præmittendum eſt. </s> </p> <p type="margin"> <s id="s.001238"><margin.target id="marg320"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001239"><emph type="center"></emph>PROP. CXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001240"><emph type="center"></emph><emph type="italics"></emph>In fiſtula Torricelliana intra puteum demerſa ſi aqua <lb></lb>à grauiori ſuper addito fluido occupetur, mercu<lb></lb>rius in fistula altiùs ſubleuatur, at post <lb></lb>illius delapſum denuo mercurius <lb></lb>deprimitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001241">SVmpta fiſtula vitrea ABC flexa in B, & facto iņ <lb></lb>ea vacuo, more ſolito, mercurius eleuetur vſque <lb></lb>ad F, demittatur poſtea fiſtula intra vas vitreum cy<lb></lb>lindricum DE maximę altitudinis earum quæ exca-<pb pagenum="241" xlink:href="010/01/249.jpg"></pb><arrow.to.target n="marg321"></arrow.to.target><lb></lb>uari efformarique poſſunt, atque in eius fundo E de<lb></lb>mittatur fiſtula cum ſtagnante mercurio ABC; poſtea <lb></lb>repleatur cylindrus vitreus oleo, vel alio liquore le<lb></lb>uiori vſque ad G, conſtat à nouo pondere olei ſupra <lb></lb>mercurium ſtagnantem C incumbentis eleuari præ<lb></lb>terea mercurium ab F ad H, vt nimirum fiat æquili<lb></lb>brium inter mercurium HF, & <expan abbr="oleũ">oleum</expan> <lb></lb><figure id="id.010.01.249.1.jpg" xlink:href="010/01/249/1.jpg"></figure><lb></lb>CG; poſtea ſi ſupra olei <expan abbr="ſuperficiẽ">ſuperficiem</expan> <lb></lb>G innatet vas NO, quod arena, a<lb></lb>qua, vel alio grauiori fluido <expan abbr="nõ">non</expan> om<lb></lb>ninò impleatur, procùl dubio à no<lb></lb>uo pondere NO altiùs mercurius <lb></lb>eleuabitur in fiſtula ab H vſque ad <lb></lb>M. </s> <s id="s.001242">His peractis reuoluatur vas N <lb></lb>O, vt nimirum arena, vel a qua flue<lb></lb>re poſſit deorsùm ad modum pluuię <lb></lb>per ſpatium oleoſum GC, & dùm <lb></lb>prædicta pluuia deorsùm deſcendit <lb></lb>non deſeret mercurius <expan abbr="ſummitatẽ">ſummitatem</expan> <lb></lb>fiſtulæ M, at poſtquam arenoſa, vel aquea pluuia <expan abbr="fun-dũ">fun<lb></lb>dum</expan> cylindri EK attingit, & proindè infrà ſtagnantem <lb></lb>libellam mercurij C deprimitur, tunc mercurius non <lb></lb>ampliùs perſiſtet in ſummitate fiſtulæ M, ſed paula<lb></lb>tim deſcendet versùs H, prout maiori copia pluuią <lb></lb>aquea, vel arenoſa ad <expan abbr="fũdum">fundum</expan> vaſis EK perducitur. </s> <s id="s.001243">ra<lb></lb>tio huius rei eſt quia licèt arena, vel aqua grauior o<lb></lb>leo ſit, & proindè comprimat mercurium ſtagnantem <lb></lb>in C, eumque eleuet vſque ad M, nihilominùs quan<lb></lb>do arena, vel aqua <expan abbr="fundũ">fundum</expan> vaſis EK attingit, compri-<pb pagenum="242" xlink:href="010/01/250.jpg"></pb><arrow.to.target n="marg322"></arrow.to.target><lb></lb>mit eius fundum, non verò <expan abbr="ſuperficiẽ">ſuperficiem</expan> ſtagnantis mer<lb></lb>curij C, & ſic mercurius comprimitur tantummodò à <lb></lb>cylindro oleoſo GC. </s> </p> <p type="margin"> <s id="s.001244"><margin.target id="marg321"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001245"><margin.target id="marg322"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001246"><emph type="center"></emph>PROP. CXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001247"><emph type="center"></emph><emph type="italics"></emph>Mercurius in fiſtula Torricellian a altiùs eleuabitur <expan abbr="dũ">dum</expan> aer <lb></lb>nebulis pluuioſis impregnatur, at postquam pluuia <lb></lb>delapſa eſt, denuò mercurius in fistulæ <lb></lb>deprimitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001248">AB hoc euidentiſſimo experimento problema no<lb></lb>ſtrum ſolui poſſe cenſeo, quandoquidem quid <lb></lb>aliud ſunt nebulæ pluuioſæ, ſcilicèt aqua grauidæ, <lb></lb>quàm aggregatum ex innumeris granulis minutiſſi<lb></lb>mis aqueis? </s> <s id="s.001249">& cùm prædicta nebula in altiſſimis ae<lb></lb>ris partibus innatat, vellentiſſimo <lb></lb><figure id="id.010.01.250.1.jpg" xlink:href="010/01/250/1.jpg"></figure><lb></lb>motu aquæ particulæ eius <expan abbr="deſcen-dũt">deſcen<lb></lb>dunt</expan>, procùl dubio ſuo pondere na<lb></lb>turali augent aeris <expan abbr="grauitatẽ">grauitatem</expan>, ideo<lb></lb>que maiori niſu globum <expan abbr="terraqueũ">terraqueum</expan> <lb></lb>comprimunt, quam aer purus, & <lb></lb>aqueis guttulis omninò priuatus <lb></lb>conſtringere eum poſſit: & ideò fi<lb></lb>ſtula mercurialis ABC in infimo <lb></lb>prædicto aere conſtituta compri<lb></lb>mitur nedùm à pondere ſuperſtan<lb></lb>tis aeris, ſed præterea à ponderę <lb></lb>totius aquæ nebulam ſupremam̨ <lb></lb>componentis: itaque per aliquod tempus <expan abbr="antequã">antequam</expan> <pb pagenum="243" xlink:href="010/01/251.jpg"></pb><arrow.to.target n="marg323"></arrow.to.target><lb></lb>pluuia deſcendat, fieri poteſt vt mercurius in fiſtula <lb></lb>ſupremam illam altitudinem M pertingat, in eaque <lb></lb>permaneat, & hoc nedum à nebulis, ſed à quacum<lb></lb>que alia cauſa grauitante effici poteſt, ſi enim terre<lb></lb>ſtris puluis à vento, vel alia commotion e ſursùm im<lb></lb>pellatur, atque per aerem diſſipetur ſpargaturque <lb></lb>tunc nemo dubitat aerem grauiori niſu ſuperficiem <lb></lb>orbis terraquei comprimere. </s> <s id="s.001250">Si poſtea à qualibet <lb></lb>cauſa nebula impellatur, vt nimirùm terram attin<lb></lb>gat, ſcilicèt pluuia paulatim terram aſſequatur <expan abbr="eã-que">ean<lb></lb>que</expan> humectet, tunc patet innumera aquæ granulą <lb></lb>terræ innici, neque amplius aeris grauitatem, & <lb></lb>compreſſionem augere, & quia à terra ſubiecta ſu<lb></lb>ſtentantur, non poſſunt vt priùs ſuo naturali pondere <lb></lb>comprimere ſuperficiem infimam mercurij ſtagnan<lb></lb>tis, & propterea ſemper à minori pondere mercu<lb></lb>rius in C comprimitur prout magis pluuia ad terram <lb></lb>perducitur, & prout magis aer illo pondere alleuia<lb></lb>tur, & propterea ſuperficies eius in ſuprema fiſtulæ <lb></lb>parte ſenſim deprimitur vſque ad infimum ſitum F. <lb></lb><arrow.to.target n="marg324"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001251"><margin.target id="marg323"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001252"><margin.target id="marg324"></margin.target>Non tamen <lb></lb>conuerſa re<lb></lb>gula vera est <lb></lb>nam ab alijs <lb></lb>cauſis eleua<lb></lb>tio mercurij <lb></lb>in fiſtula va<lb></lb>riari poteſt.</s> </p> <p type="main"> <s id="s.001253">Licèt hoc verum ſit, non tamen indè elici poteſt <lb></lb>conuerſa regula generalis, vt nimirum quotieſcum<lb></lb>que mercurius in fiſtula eleuatur debeat pluuia ex<lb></lb>pectari, quando quidem poteſt huiuſmodi <expan abbr="augmentũ">augmentum</expan> <lb></lb>compreſſionis produci ab aliqua ingenti agitatione <lb></lb>ſupremæ atmoſphæræ; & ſi fortè à particulis aqueis, <lb></lb>& terreis ſubleuatis maior grauitas aeris producitur <lb></lb>fieri poteſt vt à violentia ventorum alibi tranſpor<lb></lb>tentur nebulæ, & ſic pluuia alibi translata non deci-</s> </p> <pb pagenum="244" xlink:href="010/01/252.jpg"></pb> <p type="main"> <s id="s.001254"><arrow.to.target n="marg325"></arrow.to.target><lb></lb>dat in eo loco vbi originem habuit. </s> <s id="s.001255">Atque ex his om<lb></lb>nibus concludi poteſt aerem reuera ſuo pondere, & <lb></lb>vi elaſtica comprimere mercurium in fiſtula conten<lb></lb>tum, eumque ad illam determinatam altitudinem ele<lb></lb>uare. </s> </p> <p type="margin"> <s id="s.001256"><margin.target id="marg325"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001257"><emph type="center"></emph>PROP. CXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001258"><emph type="center"></emph><emph type="italics"></emph>Aerem eſſe grauem experimentis aliorum comprobatur, & <lb></lb><expan abbr="primã">primam</expan> Merſennij <expan abbr="experientiã">experientiam</expan> ope ignis infide<lb></lb>lem eſſe.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001259">SEd multò magis patebit veritas prædictæ propo<lb></lb>ſitionis adhibitis experimentis à quibus imme<lb></lb>diatè, & directè oſtenditur aeris grauitas, & primò <lb></lb><arrow.to.target n="marg326"></arrow.to.target><lb></lb>conſtat <expan abbr="experiẽtia">experientia</expan> relata ab Ariſtotele, vbi ait, vtrem <lb></lb>inflatum maiorem grauitatem, & preſſionem exerce<lb></lb>re quàm <expan abbr="vacuũ">vacuum</expan>. </s> <s id="s.001260">hocque poſtea diligentiſſimè ab alijs <lb></lb>comprobatum eſt, & ſumma facilitate perfici poteſt <lb></lb>non quidem follibus violenter <expan abbr="inſufflãdo">inſufflando</expan> vtrem, ſed <lb></lb>leni plenitudine vtre clauſo, vel commodiùs pila lu<lb></lb>ſoria aerea ad trutinam examinata, & poſtea funicu<lb></lb>lo circa vtrem, vel pilam reuoluto violenterque con<lb></lb>ſtricto, tune quidem ob aeris condenſationem pon<lb></lb>dus vtris, aut pilæ manifeſtè ad trutinam augetur; <lb></lb>præterea, vt docuit Galilæus, intra vitream lagenam <lb></lb>violentèr aer inſufflari poteſt vt valdè condenſetur, <lb></lb>& tunc pondus prædictæ lagenæ ſenſibilitèr augetur <lb></lb><expan abbr="promẽſura">promenſura</expan> aeris ibidem condenſati, & hac <expan abbr="experiẽ-tia">experien<lb></lb>tia</expan> diligentiſſimè facta ingenioſiſſimus Antonius Oli-<pb pagenum="245" xlink:href="010/01/253.jpg"></pb><arrow.to.target n="marg327"></arrow.to.target><lb></lb>ua reperit, quòd grauitas molis aeris, quæ æqualis <lb></lb>ſit cubo aqueo vnius libræ granum vnum pendet. </s> <s id="s.001261">at <lb></lb>Merſennus in Phęnomenis pneumaticis ope ignis <expan abbr="eã-dem">ean<lb></lb>dem</expan> experientiam fecit, ſumpſit æolo pilam æream, <lb></lb>eamque vehementiſſimo igne calefecit, vt prorsùs <lb></lb><arrow.to.target n="marg328"></arrow.to.target><lb></lb>candeſceret, & ſic in bilance perſectiſſima, quæ à ſe<lb></lb>migraro ſlectebatur, examinauit pondus eiuſdem̨ <lb></lb>ęolo pilæ <expan abbr="candẽtis">candentis</expan>, eamque reperit <expan abbr="vnciarũ">vnciarum</expan> 4. drach. <lb></lb></s> <s id="s.001262">6. & gran. 15. poſtea refrigerata æolo pila eius pon<lb></lb>dus præcedentem ſuperauit gran. 4. & hinc elicit ae<lb></lb>rem incluſum in æolo pila grana 4. ponderaſſe, porrò <lb></lb>pondus aeris illius ad æqualem aquæ molem ait re<lb></lb>periſſe in proportione 1. ad 1356. </s> </p> <p type="margin"> <s id="s.001263"><margin.target id="marg326"></margin.target>4. de cęlo. <lb></lb>cap. 4.</s> </p> <p type="margin"> <s id="s.001264"><margin.target id="marg327"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001265"><margin.target id="marg328"></margin.target>Prop. 29.</s> </p> <p type="main"> <s id="s.001266">Sed prædicta experientia multis nominibus infi<lb></lb>delis eſt, primò quia corpora vehementer excalefacta <lb></lb>in bilance ſuſpenſa non oſtendunt veram grauitatem <lb></lb><arrow.to.target n="marg329"></arrow.to.target><lb></lb>eorum, ſed diminutam, quia vt ſuperiùs oſtenſum̨ <lb></lb>eſt, ignis diffuſus ab æolo pila candente valdè rare<lb></lb>facit aerem prædictam æolo pilam ambientem, cum<lb></lb>que aer ambiens fimul cum pila vnum corpus graue <lb></lb>componat intra denſiorem aerem ſuſpenſum, fit vt <lb></lb>aggregatum prædictum minùs graue ſpecie ſit, <expan abbr="quã">quam</expan> <lb></lb>prius, & proinde imminuitur grauitas æreæ æolo pi<lb></lb>læ, non ſolùm ob deſectum aeris incluſi, ſed etiam ob <lb></lb>eius ſeruentiſſimam caliditatem. </s> </p> <p type="margin"> <s id="s.001267"><margin.target id="marg329"></margin.target>c 4 prop. 61.</s> </p> <p type="main"> <s id="s.001268">Rursùs aer in ęolopila à vehementiſſimo igne am<lb></lb>pliatus expanſuſque non poteſt dici verè rarefactus, <lb></lb>quia nimirùm copia ignis vehementiſſimè agitati, & <lb></lb>circumuoluti intra æolo pilæ cauitatem diſgregat, ac <pb pagenum="246" xlink:href="010/01/254.jpg"></pb><arrow.to.target n="marg330"></arrow.to.target><lb></lb>ſe parat particulas aliquas aeris ibidem relictas, ita<lb></lb>que intercapedines, quæ ſeparant aeris particulas, <lb></lb>partim occupantur ab igne, partim ab inani ſpatio, <lb></lb>dum igneæ particulæ motu velociſſimo conuertun<lb></lb>tur, & vertigines complent, intercipiendo grandia <lb></lb>ſpatia inania; vndè malè hinc infertur raritas maxima <lb></lb>ad quam aer ampliari poteſt. </s> </p> <p type="margin"> <s id="s.001269"><margin.target id="marg330"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001270"><emph type="center"></emph>PROP. CXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001271"><emph type="center"></emph><emph type="italics"></emph>Secunda Merſenni experientia in ſclopeto pneumatico <lb></lb>fact a dubia quoque eſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001272">MElior eſt ſecunda Merſenni experientia dùm̨ <lb></lb>in bombarda, ſeu ſclopeto pneumatico ma<lb></lb>gno conatu immiſit vaſtam aeris molem, quæ in exi<lb></lb>guo ſpatio condenſata fuit, aitque pondus ſexagin<lb></lb>ta <expan abbr="granorũ">granorum</expan> aeris incluſiſſe in cauitate catapultæ, quæ <lb></lb>ab 8. vncijs aquæ impleri poterat, hinc deducit ae<lb></lb>rem in ſclopeto immiſſum adeò condenſari vt quin<lb></lb>decies ſpatium internum catapultæ expleat; proin<lb></lb>de que tres digitos cubicos aeris ferè <expan abbr="põderare">ponderare</expan> gra<lb></lb>num vnum. </s> <s id="s.001273">Sed ex tanto apparatu tandem Merſen<lb></lb>nus nil certi colligit, cùm afferat innumeras difficul<lb></lb>tates, & ingenuè fateatur, ſemper dubitari poſſe an <lb></lb>intra catapultæ cauitatem vnà cum aere inſuffletur <lb></lb>particula aliqua oleaginoſa, vel aquea, quandoqui<lb></lb>dem epiſtomium emboli humectari debetin eius ſu<lb></lb>perficie coriacea, vt omninò rimæ claudantur, vt re<lb></lb>greſſus aeris prohibeatur. <pb pagenum="247" xlink:href="010/01/255.jpg"></pb><arrow.to.target n="marg331"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001274"><margin.target id="marg331"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001275">Hiſce omnibus difficultatibus perpenſis plures <lb></lb>modi <expan abbr="inueniẽdi">inueniendi</expan> aeris <expan abbr="grauitatẽ">grauitatem</expan> in Academia Experi<lb></lb>mentali Medicea excogitati <expan abbr="fuerũt">fuerunt</expan> ab illis doctis vi<lb></lb>ris, hìc tamen referam aliquos ex multis à me ibidem <lb></lb>propoſitis. </s> </p> <p type="main"> <s id="s.001276"><emph type="center"></emph>PROP. CXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001277"><emph type="center"></emph><emph type="italics"></emph>Nouum artificium ad explorandam aeris grauitatem <lb></lb>exponitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001278">PRimò ſumatur fiſtula vitrea <lb></lb><figure id="id.010.01.255.1.jpg" xlink:href="010/01/255/1.jpg"></figure><lb></lb>ABCF inflexa propè eius <lb></lb>extremum C, in ſummitate verò <lb></lb>annexam habeat <expan abbr="vitreã">vitream</expan> ampul<lb></lb>lam AB diametro 4. digitorum̨, <lb></lb>habeatque duo orificia aperta in <lb></lb>M & F, longitudo verò eius BD <lb></lb>maior ſit ſeſqui cubito. </s> <s id="s.001279">Vas <expan abbr="præ-dictũ">præ<lb></lb>dictum</expan> hydrargyro impleatur per <lb></lb>orificium M, obturato prius oſtio <lb></lb>infimo F, & poſteà denuò veſica <lb></lb>ſuilla clauſo ſupremo orificio M <lb></lb>ibidem alligari debet æneum fi<lb></lb>lum <expan abbr="graciliſſimũ">graciliſſimum</expan> MSN, & aper<lb></lb>to infimo oſtio F, facto vacuo mo<lb></lb>re ſolito, deſcendet mercurij ſu<lb></lb>perficies vſque ad L, poſt quam̨ <lb></lb>ſcilicèt maior pars eius fluxerit ab infimo orificio F, <lb></lb>remanſerit que ſpatium ABL exinanitum, & tunc de-<pb pagenum="248" xlink:href="010/01/256.jpg"></pb><arrow.to.target n="marg332"></arrow.to.target><lb></lb>nuò duplici veſica ſuilla ſtrictè alligata claudatur <lb></lb>orificium F. </s> <s id="s.001280">Poſteà præparari debet vas profundum <lb></lb>PQR aqua plenum vſque ad ſummitatem PR, ſitque <lb></lb>eius profunditas tanta vt mergi poſſit vniuerſum in<lb></lb>ſtrumentum MAC, vt tamen eius baſis C putei fun<lb></lb>dum non attingat; demergatur fiſtula prædicta vitrea <lb></lb>vnà cum mercurio contento intra aquam; & ſi fortè <lb></lb>os ſupremum vitri M non demergitur infra aquæ ſu<lb></lb>perficiem PR, exigui anuli ænei totidem vnciæ gra<lb></lb>na pendentes in C, & in ſummitate A apponantur, <lb></lb>quouſque vniuerſa machina vitrea fiat proximè mi<lb></lb>nùs grauis ſpecie quàm aqua, ſcilicèt innatet, & emi<lb></lb>neat ſupra aquę libellam PR pars aliqua SN prædi<lb></lb>cti fili ænei vitro annexi, & in S fiat æquilibrium, & <lb></lb>quies. </s> <s id="s.001281">Deinde in aere aperiatur ſupremum os vitri <lb></lb>M, vt ſpatium inane ABL aere impleatur, <expan abbr="remane-bitq;">remane<lb></lb>bitque</expan> reliqua pars fiſtulæ plena hydrargyro, vt priùs, <lb></lb>propterea quod operculum in F impedit <expan abbr="exitũ">exitum</expan> mer<lb></lb>curio LCF. </s> <s id="s.001282">In hoc ſtatu denuò eadem ſuilla veſicą <lb></lb>claudatur arcteque ligetur vitri os ſupremum M; & <lb></lb>tandem denuò demergatur fiſtula infra <expan abbr="libellã">libellam</expan> aquæ <lb></lb>PR. </s> <s id="s.001283">Et quia in hoc caſu demergitur infra aquæ libel<lb></lb>lam moles conflata ex ijſdem corporibus, ſcilicèt ex <lb></lb>vitro ACF, ex hydrargyro LCF, & ex ijſdem veſicis, <lb></lb>& filis M & F, & ſolummodò de nouo adeſt aer ABL, <lb></lb>quo fiſtula priùs care bat; igitur neceſsè eſt, vt <expan abbr="põdus">pondus</expan> <lb></lb>totius machinæ NACF maius ſit quàm in priori ſta<lb></lb>tu quando ſpatium ABL vacuum fuerat. </s> <s id="s.001284">Quaproptèr <lb></lb>non poterit denuò ſubleuari fiſtula ad eamdem alti-<pb pagenum="249" xlink:href="010/01/257.jpg"></pb><arrow.to.target n="marg333"></arrow.to.target><lb></lb>tudinem S, niſi grauitas eius imminuatur; auferri igi<lb></lb>tur debent aliqua grana, ſeù anuli ænei è collo fiſtulæ <lb></lb>AM, vt machina ad æquilibrium <expan abbr="cũ">cum</expan> aqua redigatur, <lb></lb>mergaturque denuò <expan abbr="vſq;">vſque</expan> ad ſitum S; quot igitur gra<lb></lb>na tolluntur à fiſtulæ collo A, tot præcisè menſura<lb></lb>bunt pondus aeris ABL intra fiſtulam incluſi. </s> </p> <p type="margin"> <s id="s.001285"><margin.target id="marg332"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001286"><margin.target id="marg333"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001287">Multis modis poſtea indagari poteſt proportio <lb></lb>ponderis aeris ad aquam, ſed omnium facillimus, & <lb></lb>ſimplex erit ſi in aere perfectiſſima bilance pondere<lb></lb>tur moles aquæ æqualis ſpatio ABL, & hic compa<lb></lb>retur cum pondere iam inuento aeris eiuſdem molis <lb></lb>ABL. </s> </p> <p type="main"> <s id="s.001288"><emph type="center"></emph>PROP. CXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001289"><emph type="center"></emph><emph type="italics"></emph>Poſtea emisſis quam plurimis termostaticis à me inuentis <lb></lb>afferam instrumentum quo pondus abſolutum aeris <lb></lb>in diuerſis locis eleuatis, ac depresſis, & variè <lb></lb>temperatis reperiri poteſt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001290">FIant tres ampullæ, vel veſicæ vitreæ, vel æneæ, <lb></lb>qualis eſt AB, habeantque collum <expan abbr="ſupremũ">ſupremum</expan> CA <lb></lb>æneum perfectiſſimè contornatum, hoc autem viſco<lb></lb>ſa aliqua materia, ac tenaci vniatur ferrumineturque <lb></lb>cum ſuprema ampullæ parte; habeat poſtea <expan abbr="canalẽ">canalem</expan>, <lb></lb>ſeu colli cauitatem turbinatam conicè, & perfectiſſi<lb></lb>mè <expan abbr="læuigatã">læuigatam</expan>, huic verò cauitati adaptari poſſit aliud <lb></lb>operculum paritèr æneum, & turbinatum, & exqui<lb></lb>ſitiſſimè læuigatum, vt nimirùm nulla rimula rema<lb></lb>neat, & perfectiſſimè claudat orificium fiſtulæ C, vt <pb pagenum="250" xlink:href="010/01/258.jpg"></pb><arrow.to.target n="marg334"></arrow.to.target><lb></lb>prohibeat ingreſſum, aut exitum aquæ, vel aeri; <expan abbr="tã-dem">tan<lb></lb>dem</expan> aptetur tenuiſſimum filum æneum CFE, <expan abbr="diuisũ">diuisum</expan> <lb></lb>in particulas æquales, ſeu gra<lb></lb><figure id="id.010.01.258.1.jpg" xlink:href="010/01/258/1.jpg"></figure><lb></lb>dus. </s> <s id="s.001291">Poſtea in fundo vaſis D in<lb></lb>cludantur granula exigua plum<lb></lb>bi quouſque vniuerſam <expan abbr="ampullã">ampullam</expan> <lb></lb>CAB <expan abbr="deprimãt">deprimant</expan> infra aquæ libel<lb></lb>lam PR, ita tamen vt ampullą <lb></lb>CB <expan abbr="nõ">non</expan> pertingat ad fundum va<lb></lb>ſis Q, ſed innatet, & ſecetur fi<lb></lb>lum æneum CE à libella aquæ <lb></lb>PR in aliquo eius puncto inter<lb></lb>medio F. </s> <s id="s.001292">His præparatis <expan abbr="debẽt">debent</expan> <lb></lb>tres prędictæ ampullæ tempera<lb></lb>ri in eodem loco, & eodem vaſe aqueo, impleantur<lb></lb>que aere eiuſdem cubiculi ad <expan abbr="radicẽ">radicem</expan> turris, vel <expan abbr="mõ-tis">mon<lb></lb>tis</expan> poſiti, & in hiſce omnibus notetur ſignum fili F, <lb></lb>quod aquæ ſuperficiem tangit, & adhibitis vulgari<lb></lb>bus termometris notetur gradus caliditatis tùm ae<lb></lb>ris cubiculi, tùm aquæ <expan abbr="eiuſdẽ">eiuſdem</expan> vaſis. </s> <s id="s.001293">poſtea duæ am<lb></lb>pullæ <expan abbr="tranſportẽtur">tranſportentur</expan> vna ad ſummitatem alicuius tur<lb></lb>ris vel montis, reliquare ponatur medio loco inter <expan abbr="sũ-mitatem">sum<lb></lb>mitatem</expan>, & radicem, ſeu baſim eius, & ibidem ape<lb></lb>riantur, vt raritatem aeris montani acquirant (arti<lb></lb>ficiosè aere temperato ſi opus fuerit vt ad eumdem <lb></lb>caliditatis gradum reducantur, quem in cubiculo ha<lb></lb>buerat;) poſtea denuò ampullæ claudantur, atquę <lb></lb>intra idipſum cubiculum aſportentur, & ibidem in<lb></lb>tra aquam demerſæ, apparebunt differentiæ à primą <pb pagenum="251" xlink:href="010/01/259.jpg"></pb><arrow.to.target n="marg335"></arrow.to.target><lb></lb>ampullarum demerſione, aer enim ſupremæ turris, <lb></lb>vt minùs grauis altiùs eleuabit ſilum æneum CE, vt <lb></lb>nimirùm ſupra aquæ libellam emineat portio maior, <lb></lb>quàm EF, & ex prædicta comparatione facilè digno<lb></lb>ſci poteſt diuerſitas ponderis aeris, quæ in diuerſis <lb></lb>eleuationibus reperitur. </s> <s id="s.001294">Sic etiam reperiri poterunt <lb></lb>differentiæ grauitatum aeris diuerſorum locorum, ac <lb></lb>Vrbium. </s> </p> <p type="margin"> <s id="s.001295"><margin.target id="marg334"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001296"><margin.target id="marg335"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001297"><emph type="center"></emph>PROP. CXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001298"><emph type="center"></emph><emph type="italics"></emph>Tutisſimo, & facillimo experimento elicitur ſpecificam <lb></lb>aquæ ad aeris grauitatem ſe habere, vt<emph.end type="italics"></emph.end> 1175. <lb></lb><emph type="italics"></emph>cum<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>ſeptimis ad<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001299">SEd præcipuus, ac pulcherrimus modus <expan abbr="reperiẽ-di">reperien<lb></lb>di</expan> aeris grauitatem hic eſt, <expan abbr="quẽ">quem</expan> Acade miæ Me<lb></lb>diceæ experimentali anno 1660. communi caui, vnà <lb></lb>cum eius demonſtratione, <lb></lb><figure id="id.010.01.259.1.jpg" xlink:href="010/01/259/1.jpg"></figure><lb></lb>eumque ibidem eiuſdem <lb></lb>anni ęſtate ad praxim re<lb></lb>degi: ſumpſi plumbeam pi<lb></lb>lam cauam BC aere <expan abbr="plenã">plenam</expan>, <lb></lb>& vndique clauſam, hanc <lb></lb>quidem perfectiſſima bi<lb></lb>lance in aere ponderaui, <lb></lb>poſtea addito pondere F, <lb></lb>à quo poſſet pila BC infra <lb></lb>aquæ libellam demergi, paritèr eius pondus præci<lb></lb>ſum in aqua reperi, alligata nimirùm pila non funi-<pb pagenum="252" xlink:href="010/01/260.jpg"></pb><arrow.to.target n="marg336"></arrow.to.target><lb></lb>culis, ſed pluribus ſatis equinis à quibus eius gra<lb></lb>uitas in aqua non alteratur ſaltem differentia ſenſibi<lb></lb>li; poterit ergò ſumi additamentum ponderis F ac ſi <lb></lb>augeret craſſitiem pilæ <expan abbr="plũbeæ">plumbeæ</expan> BC; ſit ergo GE pon<lb></lb>dus totius pilæ BACL vnà cum pondere adiuncto F <lb></lb>in aere trutinato; GH verò ſit pondus eiuſdem ag<lb></lb>gregati BALCF intra <expan abbr="aquã">aquam</expan> examinatum. </s> <s id="s.001300">quia verò, <lb></lb><arrow.to.target n="marg337"></arrow.to.target><lb></lb>ex Archimede, pondus corporis intra aquam demerſi <lb></lb>imminuitur pro quantitate <expan abbr="põderis">ponderis</expan> molis aquæ quæ <lb></lb>æqualis ſit integro corpori demerſo, igitur differen<lb></lb>tia HE erit pondus molis aquæ PQ, quæ æqualis ſit <lb></lb>corpori demerſo BALCF. poſtea pilam plumbeam <lb></lb>BC eodem modo clauſam violentèr malleo contudi, <lb></lb>vt ad minus ſpatium BLC redigeretur; <expan abbr="manifeſtũ">manifeſtum</expan> <lb></lb>eſt conſtipatum reſtrictumque ſuiſſe aerem incluſum <lb></lb>vt nimirùm portio aeris A incluſa ſit in eodem ſpa<lb></lb>tio, quod occupabat reliqua aeris portio L. denuò <lb></lb>igitur pilam plumbeam contuſam BLCF ponderaui <lb></lb>in aere, & in aqua, atque in aere pondus eius fuit <lb></lb>GN maius, quàm GE, eius verò pondus in aqua fuit <lb></lb>GM, quaproptèr ponderum differentia MN erit gra<lb></lb>uitas molis aquæ RS quæ æqualis ſit corpori demer<lb></lb>ſo BLCF, & ſecetur EO æqualis MN. </s> <s id="s.001301">Quia verò aer <lb></lb>AL in ipſomet aere <expan abbr="eiuſdẽ">eiuſdem</expan> grauitatis nil grauitat ob <lb></lb>æquilibrium, igitur pondus GE tribui debet plum<lb></lb>bo BCF, cùm verò pila contuſa in aere magis graui<lb></lb>tet pro menſura nimirùm GN, tunc quoque tota gra<lb></lb>uitas GE plumbo eidem tribui debet, at exceſſus <lb></lb>grauitatis EN nullo pacto tribui poteſt portioni ae-<pb pagenum="253" xlink:href="010/01/261.jpg"></pb><arrow.to.target n="marg338"></arrow.to.target><lb></lb>reæ L, quæ priùs æquè rara erat cum ſuo ambientę, <lb></lb>ſed tribui de bet portioni aereæ A, quæ inſinuata eſt <lb></lb>in eodem ſpatio L, in quo reliqua pars aeris contine<lb></lb>batur; Poſtea quia HE eſt pondus molis aquæ PQ, <lb></lb>quæ ęqualis eſt moli BA <lb></lb><figure id="id.010.01.261.1.jpg" xlink:href="010/01/261/1.jpg"></figure><lb></lb>LCF, & EO eſt <expan abbr="põdus">pondus</expan> mo<lb></lb>lis aquæ RS æqualis inte<lb></lb>græ pilæ contuſæ BLCF; i<lb></lb>gitur differentiale pondus <lb></lb>HO pertinet ad <expan abbr="aquã">aquam</expan> VX, <lb></lb><expan abbr="nẽpè">nempè</expan> ad <expan abbr="differẽtiã">differentiam</expan> aquę PQ <lb></lb>ſupra RS, quę æqualis eſt <lb></lb>aeri A inſinuato intra <expan abbr="ſpa-tiũ">ſpa<lb></lb>tium</expan> L; igitur habemus duo <lb></lb>corpora inter ſe æqualia mole <expan abbr="nẽpè">nempè</expan> aqua VX, & aer <lb></lb>A, horum autem pondera abſoluta, ex Archimedę, <lb></lb><arrow.to.target n="marg339"></arrow.to.target><lb></lb>eamdem proportionem habent, quam eorum gra<lb></lb>uitates in ſpecie; igitur pondus HO ad OM ſiuę <lb></lb>ad ei æquale EN, eamdem <expan abbr="proportionẽ">proportionem</expan> habet, <expan abbr="quã">quam</expan> <lb></lb>grauitas in ſpecie ipſius aquæ ad grauitatem ſpecifi<lb></lb>cam aeris, reperta autem fuit EN grauitas molis ae<lb></lb>ris A ob contuſionem inſinuati intra L, igitur neceſ<lb></lb>ſariò pondus HO tribui debet aqueæ moli VX. ſi po<lb></lb>ſtea ſumatur moles aquæ Y ad quam aquæ moles VX <lb></lb>eamdem proportionem habeat, quam HO ad OM, <lb></lb>patet eamdem grauitatem habere aquam Y ac aer A. <lb></lb></s> <s id="s.001302">His demonſtratis referam iam experimentum factum <lb></lb>in noſtra Academia experimentali Medicea; pon<lb></lb>dus in aere totius pilæ, & aeris BALCF fuit GE gra-<pb pagenum="254" xlink:href="010/01/262.jpg"></pb><arrow.to.target n="marg340"></arrow.to.target><lb></lb>norum 31616. pondus verò <expan abbr="eiuſdẽ">eiuſdem</expan> in aqua fuit GH <lb></lb>gran. 4272, eorum differentia HE fuit gran. 27344. <lb></lb>Præterea pondus totius pilæ contuſæ GN fuit gra<lb></lb>norum 31623. in aere, in aqua verò fuit GM gran. <lb></lb>12508, ergò eorum differentia ſcilicèt pondus MN, <lb></lb>vel EO fuit granorum 19115. pondus EN differen<lb></lb>tiale inter GE, & GN fuit gran. 7. pondus verò dif<lb></lb>ferentiale HO erit granorum 8229. quare ex regula <lb></lb>aurea vt pondus aeris granor. </s> <s id="s.001303">7. ad pondus molis a<lb></lb>quæ ei æqualis gran. 8229. ita ſe habet 1. ad 1175. <lb></lb>cum 4. ſept. </s> <s id="s.001304">itaque vna particula aquæ æquè ponde<lb></lb>rabit, ac æſtiui aeris particulæ 1175. cum 4. ſept. <lb></lb></s> <s id="s.001305">quarum ſingulæ æquales ſint mole ipſi aquæ. </s> </p> <p type="margin"> <s id="s.001306"><margin.target id="marg336"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001307"><margin.target id="marg337"></margin.target>De infiden<lb></lb>tibus humi<lb></lb>do l. 1. pr. 7.</s> </p> <p type="margin"> <s id="s.001308"><margin.target id="marg338"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001309"><margin.target id="marg339"></margin.target>Ibidem.</s> </p> <p type="margin"> <s id="s.001310"><margin.target id="marg340"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001311">Et in hac operatione facillima, quæ fallacijs, ac <lb></lb>difficultatibus minimè obnoxia eſſe videtur, ſummo <lb></lb>compendione dùm grauitas ipſius aeris, ſed etiam̨ <lb></lb>proportio, quam habet ad aquæ grauitatem vnicą <lb></lb>operatione elicitur. </s> </p> <p type="main"> <s id="s.001312"><emph type="center"></emph>PROP. CXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001313"><emph type="center"></emph><emph type="italics"></emph>Distantia inter maximam aeris conſtrictionem, & eiuſdem <lb></lb>maximam dilatationem est vt<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> 2000. <lb></lb><emph type="italics"></emph>ferè.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001314">TAndem ex noſtris experimentis deducitur ma<lb></lb><arrow.to.target n="marg341"></arrow.to.target><lb></lb>xima aeris dilatatio. </s> <s id="s.001315">Suppoſito enim quòd in <lb></lb>catapulta pneumatica aer ad <expan abbr="decimã">decimam</expan> ſpatij eius par<lb></lb>tem redigatur, quia ſupra, ex noſtro experimento, de<lb></lb>duximus aerem rarefieri vt ſpatium expleat centies, <pb pagenum="255" xlink:href="010/01/263.jpg"></pb><arrow.to.target n="marg342"></arrow.to.target><lb></lb>& octuagies maius, quàm priùs, quia verò hic aer <lb></lb>communis ſtringi condenſarique poteſt violenter vſ<lb></lb>que ad decimam eius partem, vel decimam quintam. <lb></lb></s> <s id="s.001316">igitur diſtantia inter <expan abbr="maximã">maximam</expan> aeris denſitatem, & <lb></lb>ampliſſimam eius expanſionem, aut erit 1800. aut <lb></lb>2700. <expan abbr="eadẽ">eadem</expan> proximè, quæ à Merſenno poſita fuerat. </s> </p> <p type="margin"> <s id="s.001317"><margin.target id="marg341"></margin.target>Prop. 105.</s> </p> <p type="margin"> <s id="s.001318"><margin.target id="marg342"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001319"><emph type="center"></emph>PROP. CXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001320"><emph type="center"></emph><emph type="italics"></emph>Aer in naturali eius conſtrictione remota omni violentiæ <lb></lb>rarisſimus eſt, & ſpatium occupat bis millies maius <lb></lb>quam in ſtatu maximæ eius violentæ constri<lb></lb>ctionis, quæ ſi remoueatur ſpontè, & in<lb></lb>genti vi ad <expan abbr="pristinã">pristinam</expan> natiuam rari<lb></lb>tatem redigitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001321">QVia verò experientia conſtat aerem dilatari <lb></lb>quidem <expan abbr="ſpõte">ſponte</expan> ſua, & non ſine impetu, & cele<lb></lb>ritate maxima, & è contrà <expan abbr="numquã">numquam</expan> ſponte conſtrin<lb></lb>gi condenſarique videmus, ſed ſemper hoc efficitur <lb></lb>ab aliqua violentia externa, hinc cogimur aſſererę <lb></lb>aerem habere virtutem quamdam elaſticam, qua ni<lb></lb>mirùm quotieſcumque violentiam conſtrictiuam pa<lb></lb>titur, tunc quidem reſilire vehementerque vibrarę <lb></lb>ſeſe dilatando poſſe; hoc autem conſtat <expan abbr="luculẽto">luculento</expan> ex<lb></lb>perimento in ipſa catapulta pneumatica, in qua aer <lb></lb>magna vi incluſus in eius cauitatem poſtea amotą <lb></lb>valuula tanta violentia ruit, erumpitque, vt pilam̨ <lb></lb>plumbeam, ſeù telum impellat proijciatque, vt iņ <lb></lb>magna diſtantia tabulam oppoſitam ſatis craſſam̨ <pb pagenum="256" xlink:href="010/01/264.jpg"></pb><arrow.to.target n="marg343"></arrow.to.target><lb></lb>diſrumpat, atque terebret: hoc autem nulla rationę <lb></lb>fieri poſſet, niſi aer haberet vim, & facultatem̨ <lb></lb>ingentem ſeſe dilatandi, & amplius ſpatium̨ <lb></lb>occupandi. </s> <s id="s.001322">Cùm igitur iam ex ſuperiùs dictis inno<lb></lb>tuerit ad quamnam maximam amplitudinem aer ra<lb></lb>refieri, dilatarique poſſit, pariterque ad quem gra<lb></lb>dum conſtipationis, <expan abbr="condenſationiſq;">condenſationiſque</expan> comprimi va<lb></lb>leat, & vidimus quòd eadem aeris moles, quæ in ſua <lb></lb>maxima condenſatione fuit redacta occupabat minus <lb></lb>quam bis milleſimam partem ſpatij, quod in maxima <lb></lb>ſui dilatatione explebat, dicendum eſt aerem in ſua <lb></lb>naturali conſtitutione, ideſt remota omni violentią <lb></lb>externa, ampliſſimum ſpatium exigere, & in tali qui<lb></lb>dem <expan abbr="expãſione">expanſione</expan> conſeruari in ſuprema aeris regione, <lb></lb>vel in ſpatio vacuo, at in regione infima aeris propè <lb></lb>aquam, & terram tunc quidem varijs modis compri<lb></lb>mitur, cùm à pondere aeris incumbentis, tùm à pon<lb></lb>dere aquæ aut terræ in infimis cauitatibus, aut à qua<lb></lb>cumque alia vi motiua ad prædictam maximam con<lb></lb>ſtipationem redigitur. </s> <s id="s.001323">Sic videmus in inſtrumento <lb></lb>Torricelliano aeris granula ad latera mercurij poſi<lb></lb>ta, dum ſursùm aſcendunt quò magis ad mercurij <lb></lb>ſummitatem <expan abbr="accedũt">accedunt</expan>, eò magis moles aereorum gra<lb></lb>nulorum augeri, quouſque propè ſpatium inane ſu<lb></lb>premum ingentes ſphęras expleant: idipſum immiſſa <lb></lb>veſica cyprina propemodum exinanita intra mercu<lb></lb>rium obſeruatur, & clariùs mercurio ſuperpoſita a<lb></lb>quæ portione conſpicitur in eodem inſtrumento, <expan abbr="nã">nam</expan> <lb></lb>granula aerea intra aquam <expan abbr="contẽta">contenta</expan>, quæ hactenùs ob <pb pagenum="257" xlink:href="010/01/265.jpg"></pb><arrow.to.target n="marg344"></arrow.to.target><lb></lb>ſui exiguitatem inobſeruabilia, & inconſpicua fue<lb></lb>rant, poſtea facto vacuo, ſcilicèt ſublata incumbentis <lb></lb>aeris compreſſione, ſubitò conſpiciuntur ſenſim infla<lb></lb>ri, augerique, vt efficiant ampullas grandes per <expan abbr="aquã">aquam</expan> <lb></lb>aſcendentes, quæ ad confinium ſupremum eius per<lb></lb>ductæ diſſiliunt, euomuntque aereas particulas intra <lb></lb>prædictum ſpatium inane, cùm è contra ſi dum actu <lb></lb>eleuantur ampullæ amplæ illæ aereæ, denuò compri<lb></lb>mantur aere ſupremè introducto momento conſpi<lb></lb>cies aerem denuò ad ſtrictiſſimum, & inconſpicuum <lb></lb>ſpatium redigi; Non poteſt igitur negari, niſi negatis <lb></lb><expan abbr="euidẽtiſſimis">euidentiſſimis</expan> ſenſationibus, quod naturalis aeris <expan abbr="cõ-ſtitutio">con<lb></lb>ſtitutio</expan>, & diſpoſitio ſit illa ampliſſima, & rariſſima; & <lb></lb>præterea quòd quotieſcumque à vi externa compri<lb></lb>mitur, conſtringiturque nihilominùs habeat quoque <lb></lb>vim, & energiam naturalem ſeſe celerrimè dilatandi, <lb></lb>facta nimirum reſilitione ad modum machinæ. </s> </p> <p type="margin"> <s id="s.001324"><margin.target id="marg343"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001325"><margin.target id="marg344"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001326"><emph type="center"></emph>PROP. CXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001327"><emph type="center"></emph><emph type="italics"></emph>Aer videtur compoſitus ex machinulis, quæ ſtringi <lb></lb>quidem adhibita violentia poſsint, ſed postea <lb></lb>ſponte reſilire ad inſtar arcus valeant.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001328">HIc iam quæri poteſt, qualis nam eſſe oporteat <lb></lb>aeris ſtructura ac forma, vt prædictas opera<lb></lb>tiones efficere valeat. </s> <s id="s.001329">Et profectò ſi ſenſu, non uerò <lb></lb>phantaſticis, & chimericis hypotheſibus philoſo<lb></lb>phandum eſt, confiteri tenemur aerem componi ex <lb></lb>machinis flexibilibus, & reſilientibus ad modum ar-<pb pagenum="258" xlink:href="010/01/266.jpg"></pb><arrow.to.target n="marg345"></arrow.to.target><lb></lb>cus, quia nimirum in hiſce machinis prædictum ſymp<lb></lb>toma obſeruatur, ſcilicèt arcus, vel machinæ exigunt <lb></lb>amplam illam extenſionem, & ſi ab externa vi con<lb></lb>ſtringantur, comprimanturque, tunc ſponte ſua reſili<lb></lb>unt prioremque amplam <expan abbr="ſituationemrepetũt">ſituationemrepetunt</expan>; ſi enim <lb></lb>aereæ particulæ non eſſent machinæ profectò percipi <lb></lb>non poſſet quare, & quomodò poſt compreſſionem <expan abbr="re-ſilirẽt">re<lb></lb>ſilirent</expan>; nampoſtquam aeris particulæ compreſſæ ſunt, <lb></lb>loca non minora, ſed ſibi ipſis adęquata occupant, <expan abbr="cũ">cum</expan> <lb></lb>non poſſint corpora ſe mutuò penetrare, igitur iņ <lb></lb>prędicta conſtrictione libenter perſiſtere deberent, <lb></lb>nec quęrerent loca ampliora, quæ ab ipſis impleri oc<lb></lb>cupariquè non poſſent: deberet igitur ipſis aſſignari <lb></lb>vis quædam motiua quæ diſſociaret ſepararetque ae<lb></lb>ris particulas à ſe inuicem, hæc verò ſenſu, & cogni<lb></lb>tione quadam animaſtica percipere deberent <expan abbr="damnũ">damnum</expan> <lb></lb>quod ad <expan abbr="cõſtipationẽ">conſtipationem</expan> <expan abbr="cõſequeretur">conſequeretur</expan>, ſi enim <expan abbr="noxã">noxam</expan> non <lb></lb>perciperent, qua quæſo ratione ſe excitarent ad ope<lb></lb>randum? </s> <s id="s.001330">Quanto rationabilius eſt eam ſtructuram ae<lb></lb>reis particulis aſſignare, à qua neceſſitate cæca <expan abbr="cogã-tur">cogan<lb></lb>tur</expan> ſeſe explicare quotieſcumque contra earum natu<lb></lb>ralem exigentiam <expan abbr="cõſtringuntur">conſtringuntur</expan>; hoc autem aſſe que<lb></lb>mur ſi concipiamus aeream ſubſtantiam conflari ex <lb></lb>innumeris machinulis iuxtà ſe poſitis, & tunc quidem <lb></lb>clarè percipiemus in prædicto aggregato virtute mil<lb></lb>lam elateriam reperiri poſſe, quia nimirùm machinu<lb></lb>læ illæ poſt compreſſionem ſeſe conantur dilatare. </s> <s id="s.001331">vt <lb></lb>verò conſtet, me non ſubitò nec oſcitanter huic ſen<lb></lb>tentiæ aſſenſum prębuiſſe, referam quicquid in <expan abbr="mentẽ">mentem</expan> <lb></lb>venit circa aeris ſtructuram. <pb pagenum="259" xlink:href="010/01/267.jpg"></pb><arrow.to.target n="marg346"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001332"><margin.target id="marg345"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001333"><margin.target id="marg346"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001334"><emph type="center"></emph>PROP. CXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001335"><emph type="center"></emph><emph type="italics"></emph>Si aeris minimæ particulæ eſſent coni excauati magnetica <lb></lb>virtute affecti, ſaluari poſſent symptomatæ condenſa<lb></lb>tionis violentæ, & ſpontaneæ eius ingentis <lb></lb>rarefactionis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001336">PRimò enim excogitaui artificium, quo ſuppoſi<lb></lb>tis aereis minimis particulis non flexibilibus, <lb></lb>poſſet nihilominùs fieri prædicta aeris ſpontanea di<lb></lb>latatio. </s> <s id="s.001337">Supponebam enim minimas aeris particulas <lb></lb>eſſe conicas, ſed excauatas: <expan abbr="tũc">tunc</expan> <expan abbr="quidẽ">quidem</expan>, <expan abbr="cũ">cum</expan> vertex vnius <lb></lb>aerei coni poſſit intra <expan abbr="cauitatẽ">cauitatem</expan> alterius inſinuari, po<lb></lb>teſt planè ſaluari illa compreſſio, quæ videtur <expan abbr="incõ-prehenſibilis">incon<lb></lb>prehenſibilis</expan> aliquibus Philoſophis, quia enim pars <lb></lb>ſolida corporea, & plena prædictorum conorum po<lb></lb>teſt eſſe nedùm pars bis milleſima, ſed adhùc minor <lb></lb>ſpatio inani intra prædictos conos <expan abbr="contẽto">contento</expan>, nil enim <lb></lb>vetat corpus denſum, ac durum in graciliſſimas lami<lb></lb>nas extendi poſſe, à quibus coni excauati efformen<lb></lb>tur. </s> <s id="s.001338">ſed hic iam nodus difficillimę ſolutionis ſe offert, <lb></lb>qua, <expan abbr="inquã">inquam</expan> ratione poſtquàm vnus <lb></lb><figure id="id.010.01.267.1.jpg" xlink:href="010/01/267/1.jpg"></figure><lb></lb>conus intrà <expan abbr="aliũ">alium</expan> inſinuatus eſt, vim <lb></lb>facit ſe ab eo <expan abbr="ſeparãdi">ſeparandi</expan>, procùl du<lb></lb>bio ijs vis quędam motiua aſſigna<lb></lb>ri debet, & hæc diuerſa <expan abbr="nõ">non</expan> erit ab <lb></lb>ea, quæ in alijs corporibus terre<lb></lb>nis reperitur: <expan abbr="cõcipiantur">concipiantur</expan> ergo conuli excauati aerei <lb></lb>ABC, DCE, FGH, IHL. & ſic alij innumeri eodem <pb pagenum="260" xlink:href="010/01/268.jpg"></pb><arrow.to.target n="marg347"></arrow.to.target><lb></lb>modo diſpoſiti: animaduerti poſtea, quòd in ma<lb></lb>gnete, & in omnibus magneticis corporibus dantur <lb></lb>duo poli, borealis nempè, & auſtralis, & quotieſ<lb></lb>cumque duo corpora magnetica ſuper aquam inna<lb></lb>tantia ad ſeſe propiùs accedunt, tunc quidem polo <lb></lb>vnius auſtrali vnitur, connectitur que alterius corpo<lb></lb>ris borealis polus, & ſi contingat vt alitèr diſponan<lb></lb>tur à violentia aliqua externa, fponte ſua recedunt, <lb></lb>& indebita conſtitutione ſituantur, tum reſpectu ſui, <lb></lb>cum reſpectu poli auſtralis Orbis Terræ. </s> <s id="s.001339">cogitaiam̨ <lb></lb>conos excauatos ABC, FGH eſſe magneticos, vel <lb></lb>ferreos virtute tamen magnetica affectos, vt nimirùm <lb></lb>omnes vertices A, & F ſint poli boreales, partes ve<lb></lb>rò auſtrales ſint baſes BC, & GH, & quia baſes præ<lb></lb>dictæ ſunt cauæ poli auſtrales præcisè exiſtent in cen<lb></lb>tris circulorum BC, & GH. his poſitis innatent iam <lb></lb>prędicti conuli, ſcilicèt moueri lateralitèr poſſint abſ<lb></lb>que vllo impedimento, tunc quidem polus borealis <lb></lb>F coni FGH, ſi coniungi debet iuxtà magneticas le<lb></lb>ges cum polo auſtrali conuli ABC neceſſariò vertex <lb></lb>F cum centro circuli baſis BC coniungetur naturali <lb></lb>inſtinctu, & ideò reſiſtet externæ violentiæ, quæ <expan abbr="hãc">hanc</expan> <lb></lb>ſituationem perturbare conaretur. </s> <s id="s.001340">A dueniat iam alia <lb></lb>vis externa, quæ violentèr inſinuet verticem F intra <lb></lb>ſinuoſam cauitatem alterius versùs A, tunc quidem̨ <lb></lb>naturali niſu, ceſſante <expan abbr="violẽtia">violentia</expan> externa, recedet ver<lb></lb>tex coni FGH ab interna illa poſitione, & denuò re<lb></lb>trocedet <expan abbr="quouſq;">quouſque</expan> eius vertex F coniungatur centro <lb></lb>circuli baſis BC. </s> <s id="s.001341">Et hæc inquam eſſet vis elaſtica, quæ <pb pagenum="261" xlink:href="010/01/269.jpg"></pb><arrow.to.target n="marg348"></arrow.to.target><lb></lb>in aere reperitur, nec talis hypotheſis vt impoſſibilis <lb></lb>reprobari poſſet, cum reuera & terra, & corpora om<lb></lb>nia terrena magneticam vim habere manifeſtum ſit, <lb></lb>in quibus prædicta operatio neceſſariò ſequeretur, <lb></lb>poſita <expan abbr="nimirũ">nimirum</expan> prædicta figuratione in particulis ma<lb></lb>gneticis. </s> <s id="s.001342">Poſſent aliunde omnia alia phænomeną, <lb></lb>quæ in aere obſeruantur ſaluari ex prædicta hypo<lb></lb>theſi, igitur concedi ea deberet ſaltem vt poſſibilis. </s> </p> <p type="margin"> <s id="s.001343"><margin.target id="marg347"></margin.target>Cap. 5. de ae <lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001344"><margin.target id="marg348"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001345"><emph type="center"></emph>PROP. CXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001346"><emph type="center"></emph><emph type="italics"></emph>Meliùs aeris proprietates ſaluantur ſi eius minimæ particu<lb></lb>læ ſint duræ flexibiles, & reſilientes ad modum ma<lb></lb>chinæ, habeantque figuram tubi, vel cylindri <lb></lb>excauati compoſiti ex laminis, vel filis <lb></lb>læuibus, aut ramoſis obliquè in ſe <lb></lb>ipſos circumductis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001347">HAnc tamen hypotheſim poſtea reiicere accura<lb></lb>tiùs conſiderata; ſuppoſui enim tubulos ali<lb></lb>quos graciliſſimos multis modis componi poſſe ex <lb></lb>materia reſiliente ad modum machinæ. </s> <s id="s.001348">Primò ſuppo<lb></lb>ni poſſunt tubuli conflati ex tenuiſſima laminula iņ <lb></lb>ſe ipſam circumducta, & continuata, quæ paritèr <lb></lb>machina ſit flexibilis, & poſt compreſſionem reſilire <lb></lb>valeat, vt contingit in arcu compreſſo. </s> <s id="s.001349">hinc ſaluari <lb></lb>poteſt maxima illa aeris condenſatio quam patitur à <lb></lb>vi externa comprimente, quia nimirùm perimetrum <lb></lb>internum fiſtulæ licèt ſemper eiuſdem menſuræ ſit, <lb></lb>tamen minorem capacitatem continentèr acquirit, <pb pagenum="262" xlink:href="010/01/270.jpg"></pb><arrow.to.target n="marg349"></arrow.to.target><lb></lb>quò magis comprimitur, ſcilicèt quò magis à circu<lb></lb>lo recedit eius baſis, & ad figuram longiorem ellip<lb></lb>ticam redigitur. </s> <s id="s.001350">Alio modo componi poſſunt tubuli <lb></lb>aerei, ſi nimirùm concipiatur inuolucrum factum ex <lb></lb>lamina tenuiſſima, quæ quidem paritèr flexibilis ſit, <lb></lb>& ad modum arcus reſilire valeat, hæc, inquam, mul<lb></lb>tò magis comprimi poteſt, & ad minus ſpatium redi<lb></lb>gi, quam ſimplex tubus paulò ante expoſitus, quią <lb></lb>nimirùm internus ambitus adhùc conſtringi, & immi<lb></lb>nui poteſt, vt nimirùm perimeter baſis minor fiat, re<lb></lb>petitis nimirum conuolutionibus prædicti inuolucri, <lb></lb>& præterea, non minùs, quam antea poteſt laterali<lb></lb>tèr comprimi vt nimirùm baſis non circularis, ſed el<lb></lb>liptica fiat, & ſic duplicata cauſa reſtrictionis mul<lb></lb>tò magis minui poterit moles aeris conſtipati con<lb></lb>denſatique; Tertiò ſi ſupponantur tubuli aerei com<lb></lb>poſiti ex tenuiſſima virga ramoſa, vel faſcia obliquè <lb></lb>reuoluta, & in ſe ipſam circumducta ad modum ſpi<lb></lb>ræ, relictis nimirùm aliquibus interſtitijs inter tranſ<lb></lb>uerſales ſpiras, tunc quidem multò faciliùs tubulus <lb></lb>prædictus conſtipari poterit tribus nominibus, & <lb></lb>quia ambitus internus imminuitur, pariterque decur<lb></lb>tatur altitudo fiſtulæ, & tandem ad figuram compreſ<lb></lb>ſam ellipticam redigitur, quare ſi ſolida materia præ<lb></lb>dicti tubuli, ſeù ſpiræ ſit dura quidem, ſed flexibilis, <lb></lb>& apta ad reſiliendum vt machina, vel arcus chali<lb></lb>beus, eique naturalitèr competat ampla, & dilatatą <lb></lb>figura, poterunt profectò <expan abbr="cõſtringi">conſtringi</expan> ab externa vi, at <lb></lb>ceſſante violentia <expan abbr="ſpõte">ſponte</expan> ſua reſilient, ad prioremque <pb pagenum="263" xlink:href="010/01/271.jpg"></pb><arrow.to.target n="marg350"></arrow.to.target><lb></lb>ſtatum dilatatum, rarumque redigentur, vt videmus <lb></lb>in ijs ſerpentibus puerorum ex tenuiſſimo æneo filo <lb></lb>confectis, ſcilicèt ſpiralitèr reuolutis ad modum co<lb></lb>chleæ, in <expan abbr="ijſq;">ijſque</expan> facta compreſſione ſpatium eorum ma<lb></lb>ximè imminuitur, at poſtmodum raritatem ſuam de<lb></lb>nuò repetunt. </s> <s id="s.001351">Et hac quidem figura aſſignata aeri fa<lb></lb>cilè ſaluantur phænomena omnia, quæ in ipſo aerę <lb></lb>obſeruantur, de quibus ſigillatim ſuis in locis pecu<lb></lb>liaritèr agemus. </s> </p> <p type="margin"> <s id="s.001352"><margin.target id="marg349"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="margin"> <s id="s.001353"><margin.target id="marg350"></margin.target>Cap. 5. de ae<lb></lb>ris grauitate <lb></lb>æquilibrio, <lb></lb>ſtructura, & <lb></lb>vi elaterią <lb></lb>eius.</s> </p> <p type="main"> <s id="s.001354"><emph type="center"></emph><emph type="italics"></emph>Nullam Attractionem, nec Vim Tractiuam in <lb></lb>Natura dari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001355"><emph type="center"></emph>CAP. VI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001356">NIl frequentiùs apud Medicos, & Philoſophos <lb></lb>reperitur, quàm nomen qualitatis, ſeu virtu<lb></lb>tis attractiuæ, quæ licèt magno faſtu, & ſupercilio <lb></lb>proferatur, nil profectò abſurdiùs reperies, ſi attentè <lb></lb><expan abbr="perpẽdas">perpendas</expan> quid nomine attractionis intelligant. </s> <s id="s.001357"><expan abbr="Aiũt">Aiunt</expan> <lb></lb>igitur manifeſtè conſtare in natura attractionem da<lb></lb>ri, vt videre eſt in magnete, qui ferrum ad ſe trahit, <lb></lb>pariterque electrica omnia corpora feſtucas exiguas <lb></lb>magno impetu ad ſe adducunt, ſic paritèr calorem, <lb></lb>& dolorem in aliqua determinata parte animalis ex<lb></lb>citatum, vt in manu v. g. vel crure, attrahere à parti<lb></lb>bus longinquis nedùm ſanguinem, ſed etiam humo<lb></lb>res cæteros aiunt; non ſecùs cucurbitulæ medicæ fol<lb></lb>les, & alia inſtrumenta pneumatica dum aerem exu<lb></lb>gunt, attrahunt quoque humores adnexos; quia ve-<pb pagenum="264" xlink:href="010/01/272.jpg"></pb><arrow.to.target n="marg351"></arrow.to.target><lb></lb>rò in hiſce omnibus operationibus nullum organum <lb></lb>corporeum apparet à quo tractio effici valeat; hinc <lb></lb>concludunt vim, & qualitatem attractiuam incor<lb></lb>poream eſſe, habereque facultatem ad ſe attrahendi <lb></lb>fluida corpora ambientia. </s> <s id="s.001358">Sed quis capiet à virtutę <lb></lb>incorporea naturali vi, & immediatè, abſque organo <lb></lb>corporeo, corpus aliquod moueri, & trahi poſſe? </s> <s id="s.001359">quo<lb></lb>modo enim quod incorporeum, & proindè indiuiſi<lb></lb>bile eſt applicare ſe poteſt, apprehendere, conſtrin<lb></lb>gere, impellereque corpus extenſionem habens, cum <lb></lb>lumine naturæ conſtet nullam motionem, aut actio<lb></lb>nem phyſicam abſque contactu fieri poſſe, pariter<lb></lb>que conſtet corpus ab incorporeo minimè tangi? </s> <s id="s.001360">Igi<lb></lb>tur neceſsè eſt vt attractio fiat mediante aliquo in<lb></lb>ſtrumento corporeo. </s> </p> <p type="margin"> <s id="s.001361"><margin.target id="marg351"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001362"><emph type="center"></emph>PROP. CXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001363"><emph type="center"></emph><emph type="italics"></emph>Agens naturale niſi moueatur minimè trahere poteſt aliud <lb></lb>corpus, quod præterea fune, vel vncino alligatum <lb></lb>transferri debet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001364">QVia <expan abbr="agẽs">agens</expan> <expan abbr="corporeũ">corporeum</expan> quotieſcumque ſua vi mo<lb></lb>tiua trahit aliud corpus neceſſariò agitari <lb></lb><expan abbr="quodãmodo">quodammodo</expan>, & moueri debet ſi enim omninò iners, <lb></lb>& ſtabile agens ſupponatur, quomodò quæſo aliud <lb></lb>corpus contiguum agitabit, & è ſuo loco dimouebit? <lb></lb></s> <s id="s.001365">verùm quando agens motu locali agitatur, tunc com<lb></lb>prehendo, quòd corpus ei adnexum è regione poſi<lb></lb>tum expelli è ſuo loco debet, aliàs agens corpus non <pb pagenum="265" xlink:href="010/01/273.jpg"></pb><arrow.to.target n="marg352"></arrow.to.target><lb></lb>moueretur; & hoc <expan abbr="cõſtat">conſtat</expan> quia duo corpora ſe mutuò <lb></lb>penetrare <expan abbr="nõ">non</expan> poſſunt: igitur ſi obiectum corpus flui<lb></lb>dum fuerit, ſaltem agitari debet lateralitèr vt <expan abbr="liberũ">liberum</expan> <lb></lb>tranſitum impellenti corpori concedat, & ſi fuerit <lb></lb>durum, ac conſiſtens, integrum corpus obiectum di<lb></lb>mouebit id expellendo. </s> <s id="s.001366">Si verò corpus ambiens <lb></lb>non anteriùs motui eius obijciatur nec ipſum impe<lb></lb>diat, ſed poſticè ei adhæreat, tunc quidem ſi allige<lb></lb>tur fune, vel vncino, alioque conſimili corpore cur<lb></lb>uo, fieri poteſt, vt ad motum agentis etiam <expan abbr="colligatũ">colligatum</expan> <lb></lb>corpus ſubſequens transferatur. </s> <s id="s.001367">Et hoc quidem ea<lb></lb>dem ratione lumine naturæ deducta euincitur, quia <lb></lb>inſtrumenti tractorij pars curua, quæ anteriùs impel<lb></lb>litur ab agente, ob <expan abbr="eãdem">eandem</expan> impenetrabilitatem an<lb></lb>teriùs impellitur, & ab eius duritie, & ſoliditate cor<lb></lb>pus poſticè apprehenſum transfertur; at ſi funis, aut <lb></lb>vncinus, vel quodlibet aliud organum curuum re<lb></lb>moueatur, non video, neque percipio quomodo <expan abbr="dũ">dum</expan> <lb></lb>mouetur corpus anticum trahere ſecum debeat cor<lb></lb>pus <expan abbr="poſticũ">poſticum</expan> nullo vinculo, nec glutine ſibi <expan abbr="connexũ">connexum</expan>. </s> </p> <p type="margin"> <s id="s.001368"><margin.target id="marg352"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001369">Sed non deſunt Philoſophi, qui dicant: <emph type="italics"></emph>æquè faci<lb></lb>lè concipi corpus tenſum dum ſeſe reducit, aliud corpus, cui <lb></lb>contiguum est ſecum adducere, ac corpus compreſſum aliud <lb></lb>corpus à ſe amouere, nec alio fune opus eſt ad hunc finem, <lb></lb>cùm enim iuxtà naturæ inſtitutum omnia corpora ſint par<lb></lb>tes vniuerſi, & partes, quæ totum aliquod componunt con<lb></lb>iunctæ eße debeant, alioquin partes non eſſent ſi ſeorſim eſſe <lb></lb>poſſent, ideò vnum corpus adhæret alteri.<emph.end type="italics"></emph.end><pb pagenum="266" xlink:href="010/01/274.jpg"></pb><arrow.to.target n="marg353"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001370"><margin.target id="marg353"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001371"><emph type="center"></emph>PROP. CXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001372"><emph type="center"></emph><emph type="italics"></emph>Primò dico falſum eſſe æquè facilè corpus tenſum dum ſe re<lb></lb>ducit aliud corpus cui contiguum eſt ſecum adducere, <lb></lb>ac corpus compreſſum aliud corpus à ſe <lb></lb>amouere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001373">QVia neceſſitas huius operationis patet ex eo <lb></lb>quòd corpus moueri non poteſt ad locum al<lb></lb>terius corporis occupandum, niſi expellat illud ibi <lb></lb>degens, cùm duo corpora in eodem loco poni noņ <lb></lb>poſſint; at quod corpus dum mouetur recedendo ab <lb></lb>alterius corporis loco trahere ſecum adhærendo de<lb></lb>beat corpus poſticè ſibi contiguum à cuius contactu <lb></lb>conatur recedere, & cui non colligatur glutine, fu<lb></lb>ne, aut alio vinculo, nedùm gratis aſſeritur, <expan abbr="verũ">verum</expan> om<lb></lb>ninò impoſſibile videtur, & omnem captum ſuperat. <lb></lb></s> <s id="s.001374">Cùm verò ait <emph type="italics"></emph>naturæ <expan abbr="inſtitutũ">inſtitutum</expan> eſſe vt corpora mundana <lb></lb>ſint partes vniuerſi<emph.end type="italics"></emph.end> hoc planè ei conceditur, ſed nego, <lb></lb>quòd <emph type="italics"></emph>partes, quæ totum componunt, coniunctæ eſſe debeant, <lb></lb>& quod aliàs partes non eſſent ſi ſeorſim eſſe poſſent;<emph.end type="italics"></emph.end> nam <lb></lb>partes exercitus diſcretæ ſunt, & tamen totum exer<lb></lb>citum componunt. </s> <s id="s.001375">Similiter plures lineolę diſcretæ <lb></lb>totam longitudinem palmarem componere poſſent, <lb></lb>non ſecùs ac ſi <expan abbr="cõiunctæ">coniunctæ</expan> directæ, vel tortuoſæ eſſent. <lb></lb></s> <s id="s.001376">Et noto, quòd nomine coniunctionis hìc non intelli<lb></lb>gitur vnio, & connexio omninò firma, ſed ſimplex <lb></lb>contactus partium, qualis eſt ille quo aceruus arenæ, <lb></lb>& granorum tritici connectitur; nam aqua à <expan abbr="cõtiguo">contiguo</expan> <pb pagenum="267" xlink:href="010/01/275.jpg"></pb><arrow.to.target n="marg354"></arrow.to.target><lb></lb>aere attracta, vel ab embolo eis non connectitur vni<lb></lb>turque, ſed tantum adhæret ſimplici contactu. </s> <s id="s.001377">Modò <lb></lb>nemo eſt, ſi ſeriò, & bona fide loqui velit, qui noņ <lb></lb>percipiat eſſe impoſſibile vt grana tritici ſubſequen<lb></lb>tia trahantur ab antecedentibus granis, eorumquę <lb></lb>motum imitentur à vi ſimplicis contactus abſque vl<lb></lb>lo vinculo, vel glutine, & procùl dubio talis motus <lb></lb>effici poſſet quando grana ſubſequentia ab aliquą <lb></lb>vi motiua impellerentur, quę aut ſpontaneo motu, co<lb></lb>gnitione præuia, vt animalia, aut cæca neceſſitate, <lb></lb>vt grauia, tranſportarentur, quæ omnia in noſtro ca<lb></lb>ſu locum non habent. </s> </p> <p type="margin"> <s id="s.001378"><margin.target id="marg354"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001379">Sed ne gratis prolata verba diutiùs inſectemur, <lb></lb>noto quòd aduerſarij numquam euincent dari in na<lb></lb>tura vim, ſeu qualitatem attractiuam, niſi euidentia <lb></lb>ſenſus, aut demonſtratione oſtendant, quòd corpo<lb></lb>ra, quæ attrahi videntur non moueantur à vi intrinſe<lb></lb>ca ſpontaneo motu, neque impellantur ab externo a<lb></lb>liquo corpore. </s> <s id="s.001380">Hoc autem cùm numquam præſtite<lb></lb>rint, profectò affirmare non poſſunt dari in natura ve<lb></lb>ram attractionem, proindeque licitum erit eorum aſ<lb></lb>ſertionem negare. </s> </p> <p type="main"> <s id="s.001381">E contrà ſi nos offenderimus, quòd aliqua corpo<lb></lb>ra eorum, quæ attrahi videntur vi naturali, <expan abbr="ſpõte">ſponte</expan> mo<lb></lb>ueantur, & accedant ad alia corpora: reliqua verò vi <lb></lb>externa impellantur, planè profligata erit vis, & qua<lb></lb>litas attractiua è rerum natura. <pb pagenum="268" xlink:href="010/01/276.jpg"></pb><arrow.to.target n="marg355"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001382"><margin.target id="marg355"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001383"><emph type="center"></emph>PROP. CXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001384"><emph type="center"></emph><emph type="italics"></emph>Corpora, quæ attrahi videntur, aut ſponte, aut à vi ex<lb></lb>terna impelluntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb><arrow.to.target n="marg356"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001385"><margin.target id="marg356"></margin.target>Cap. 25.</s> </p> <p type="main"> <s id="s.001386">ET primò quoad ferrum, & magnetem pertinet, <lb></lb>iam oſtendimus (lib. de vi percuſs.) ambo hæc <lb></lb>corpora naturali vi ſpontaneo motu vnum versùs al<lb></lb>terum moueri non ſecùs, ac grauia ſponte ad terram <lb></lb>feruntur. </s> <s id="s.001387">In electricis verò iam ab alijs cauſa attra<lb></lb>ctionis tradita eſt; conſtat enim experientia, quod <lb></lb>niſi electrica corpora incaleſcant ope confricationis <lb></lb>in aliquo panno factæ non attrahunt exiguas, & leues <lb></lb>eiſque vicinas feſtucas, quæ proindè collocantur in <lb></lb>quadam veluti atmoſphæra ex fumoſis, & calidis ex<lb></lb>halationibus compoſita ambiente corpus <expan abbr="electricũ">electricum</expan>, <lb></lb>ex quo fit vt maſſa illa ex prædictis vaporibus, & fe<lb></lb>ſtucis compoſita leuior ſit aere contiguo magis re<lb></lb>moto, ideoque ab hoc maſſa illa fumoſa exprimitur, <lb></lb>conſtringiturque vndique versùs <expan abbr="ſolidũ">ſolidum</expan> corpus ele<lb></lb>ctricum, & <expan abbr="conſequẽtèr">conſequentèr</expan> ſecum <expan abbr="trãſportabit">tranſportabit</expan> feſtucas. </s> </p> <p type="main"> <s id="s.001388">In tubis pneumaticis, & cteſibianis, nec non in cu<lb></lb>cur bitulis medicis, dicendum, quòd ad eas fluida, & <lb></lb>mollia corpora feruntur non ſpontaneo motu, ſed à vi <lb></lb>externa impulſa, & hæc profectò non eſt alia quàm̨ <lb></lb>ſimplex grauitas oceani aerei <expan abbr="orbẽ">orbem</expan> terraqueum am<lb></lb>bientis, à quo aqua, & corpora mollia ſubiecta <expan abbr="cõ-primuntur">com<lb></lb>primuntur</expan>, exprimunturque, vt conſtat ex doctriną <lb></lb>hydroſtatica ſuperiùs expoſita. </s> <s id="s.001389">Hinc fit vt ſubleua-<pb pagenum="269" xlink:href="010/01/277.jpg"></pb><arrow.to.target n="marg357"></arrow.to.target><lb></lb>to embolo in tubo, vel rarefacto aere interno cucur<lb></lb>bitulæ pars fluida, & mollis ſubiecta minùs compreſ<lb></lb>ſa ab ambiente aere expelli ſursùm debeat à partę <lb></lb>magis preſſa. </s> <s id="s.001390">Stultè ergo quis recurreret ad vim, & <lb></lb>qualitatem attractiuam emboli, vel cucurbitulæ, vt <lb></lb>aquam eleuet, cùm adſit vera, & neceſſaria cauſa hu<lb></lb>ius effectus, quæ eſt columna aerea aquam <expan abbr="ſubiectã">ſubiectam</expan> <lb></lb>comprimens, à qua vi impulſiua aqua inſinuatur, ex<lb></lb>primiturque intra tubum, vel cucurbitam. <lb></lb><arrow.to.target n="marg358"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001391"><margin.target id="marg357"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001392"><margin.target id="marg358"></margin.target>Cap. 12.</s> </p> <p type="main"> <s id="s.001393">Sed hoc clariùs ſuo loco declarabitur; interim tran<lb></lb>ſeo ad difficultatem ſatis plauſibilem, quæ contra <expan abbr="hãc">hanc</expan> </s> </p> <p type="main"> <s id="s.001394"><arrow.to.target n="marg359"></arrow.to.target><lb></lb>doctrinam afferri ſolet. </s> <s id="s.001395">Inquiunt enim, quando cu<lb></lb>curbitulæ carnem attrahunt, vel fiſtula digiti <expan abbr="pulpã">pulpam</expan> <lb></lb>intra eam inſinuat, manifeſtè percipitur ſenſus dolo<lb></lb>rificus in parte illa carnis, aut digiti, quæ intra cucur<lb></lb>bitulam, vel fiſtulam inſinuatur, nulla verò paſſio, aut <lb></lb>noxa percipitur in reliqua parte corporis animalis, <lb></lb>nec in poſtica digiti parte, ſenſus verò doloris à nihi<lb></lb>lo produci non poteſt, & è contrà cauſa actiua com<lb></lb>preſſionem efficiens ſenſationem dolorificam afferre <lb></lb>deberet, igitur ſenſus doloris percipi deberet non in <lb></lb>pulpa digiti, ſed in oppoſito vngue, pariterque dolor <lb></lb>non in ſcapulis, vbi cucurbita id hæret, ſed in pecto<lb></lb>re percipi deberet, vbi reuerà efficitur compreſſio, <lb></lb>& contuſio ab extremo aere ambiente, in ipſa verò <lb></lb>pulpa carnis intra cucurbitam, vel fiſtulam inſinuata <lb></lb>nulla paſſio percipi deberet, cùm ibi deficiat cauſą <lb></lb>illa, quæ ſua violentia impellit, & comprimit <expan abbr="carnẽ">carnem</expan>. </s> </p> <p type="margin"> <s id="s.001396"><margin.target id="marg359"></margin.target>Si aeris preſ<lb></lb>ſio animalis <lb></lb>carnem intra <lb></lb>cucurbitulas <lb></lb>impelleret <lb></lb>dolor in op<lb></lb>poſita corpo<lb></lb>ris parte <expan abbr="cõ-preſſa">com<lb></lb>preſſa</expan> perci<lb></lb>pi deberet, <lb></lb>non in par<lb></lb>te attracta.</s> </p> <p type="main"> <s id="s.001397">Pro huius difficultatis ſolutione repetenda ſunt <pb pagenum="270" xlink:href="010/01/278.jpg"></pb><arrow.to.target n="marg360"></arrow.to.target><lb></lb>aliqua priùs declarata, vbi ſcilicèt quærebatur qua<lb></lb>re vrinatores in profundo maris ingentem <expan abbr="grauitatẽ">grauitatem</expan> <lb></lb>aquæ incumbentis non percipiunt, diximus hoc pro<lb></lb><arrow.to.target n="marg361"></arrow.to.target><lb></lb>uenire, ex eo, quòd partes aquæ fluidæ æquali niſu <lb></lb>grauitatis comprimunt vndequaque corpus anima<lb></lb>lis demerſum, nempè è parte ſuprema infima, & col<lb></lb><arrow.to.target n="marg362"></arrow.to.target><lb></lb>laterali, quia ibidem oſtendimus, quòd impulſio, at<lb></lb>que compreſſio in vno peculiari loco facta luxatio<lb></lb>nem, rupturam, contuſionemque efficere poteſt, & <lb></lb>è contra ſi eadem virtus compreſſiua multiplicetur, <lb></lb>vt vndique impellat, <expan abbr="cõprimatque">comprimatque</expan> corpus animalis, <lb></lb>tunc oſtendimus nedùm noxam doloremque non au<lb></lb>geri, ſed è contrà nullam luxationem, neque contu<lb></lb>ſionem, & proinde nullam paſſionem dolorificam̨ <lb></lb>procreari poſſe. </s> <s id="s.001398">Et hoc euidentiſſimum eſt ex ſupe<lb></lb>riùs demonſtratis. </s> <s id="s.001399">Præterea diximus, quòd licèt in<lb></lb>ſignis luxatio, & diuiſio continui ab vniuerſali illą <lb></lb>compreſſione fluidi non ſubſequatur, non tamen ne<lb></lb>gari poteſt conſtrictio quædam totius corporis, quæ <lb></lb>quidem in profundo oceani oportet vt ſentiatur, ob <lb></lb>nouitatem; at in aere nullo pacto animal ab vniuer<lb></lb>ſali eius compreſſione conſtrictioneque vllam paſ<lb></lb>ſionem percipere debet ob aſſuetudinem, ab ipſo e<lb></lb>nim ortu animalia ſemper eadem veſte aerea <expan abbr="ambiũ-tur">ambiun<lb></lb>tur</expan> conſtringunturque, proindeque nullam mutatio<lb></lb>nem in ipſo animali aeris compreſſio producit, & <lb></lb>propterea cenſet à nulla vi ambiente conſtringi, aut <lb></lb>comprimi, igitur à prædicta vi compreſſiua carnes, <lb></lb>vaſa, & viſcera patiuntur conſtrictionem quamdam, <pb pagenum="271" xlink:href="010/01/279.jpg"></pb><arrow.to.target n="marg363"></arrow.to.target><lb></lb>quæ profectò nullo pacto percipi poteſt ab animali<lb></lb>bus. </s> <s id="s.001400">Imò etiam conſtrictiones non perpetuæ, vt <expan abbr="sũt">sunt</expan> <lb></lb>illæ quæ fiunt à noſtris veſtimentis ob <expan abbr="conſuetudinẽ">conſuetudinem</expan>, <lb></lb>paſſionem dolorificam minimè afferre ſolent. </s> </p> <p type="margin"> <s id="s.001401"><margin.target id="marg360"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001402"><margin.target id="marg361"></margin.target>Cap. 3.</s> </p> <p type="margin"> <s id="s.001403"><margin.target id="marg362"></margin.target>Reſoluitur <lb></lb>ſuperior dif<lb></lb>ficultas.</s> </p> <p type="margin"> <s id="s.001404"><margin.target id="marg363"></margin.target>Cap. 6 non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001405"><emph type="center"></emph>PROP. CXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001406"><emph type="center"></emph><emph type="italics"></emph>Ceſſante in vna parte aeris compresſione humores, & mol<lb></lb>lis carnes impelli debent intra cucurbitulam.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001407">HIs præmiſſis animaduertendum eſt, quòd nouus <lb></lb>effectus flexionis, aut diuiſionis continui, vel <lb></lb>contuſionis in animali duplici modo produci poteſt, <lb></lb>aut quia ſuperuenit noua cauſa <expan abbr="impellẽs">impellens</expan> vnicum ani<lb></lb>malis latus, aut quia deficit ibidem vis illa compreſ<lb></lb>ſiua fluidi ambientis, quæ reliquas omnes animalis <lb></lb>partes conſtringit, comprimitque, & quæ hactenùs <lb></lb>ob conſuetudinem non percipiebatur. </s> <s id="s.001408">In primo caſu <lb></lb>mirum non eſt effectum contuſionis doloriſque tribui <lb></lb>impellenti virtuti ſuperuenienti; at in ſecundo caſu <lb></lb>fallacia oriri poteſt ex phantaſia præiudicata, ſcili<lb></lb>cèt exiſtimabitur defectum comprimentis fluidi iņ <lb></lb>vno latere tractionem, & ſuctionem procreare, <expan abbr="quã-doquidem">quan<lb></lb>doquidem</expan> nemo perſuadebitur, quòd oppoſita com<lb></lb>preſſio facta à fluido ambiente, cuius actionem num<lb></lb>quam percepit ob aſſuetudinem, contuſionem, aut <lb></lb>impulſionem ſanguinis, & carnium efficere vnquam <lb></lb>potuiſſet. </s> <s id="s.001409">Nec deſunt exempla quibus hoc confirma<lb></lb>tur. </s> <s id="s.001410">ponatur Rana infra aquam, vel hydrargyrum de<lb></lb>merſa, <expan abbr="cõſtat">conſtat</expan> eam vndique ſtringi veluti prælo à flui-<pb pagenum="272" xlink:href="010/01/280.jpg"></pb><arrow.to.target n="marg364"></arrow.to.target><lb></lb>do ambiente; ſi poſtea foramini collaterali vaſis ra<lb></lb>næ abdomen applicetur vt exactè perimetrum fora<lb></lb>minis contingat, tunc portio cutis eius comprehen<lb></lb>ſa à prædicto foramine inflari, & turgere conſpicie<lb></lb>tur, & veluti mammillam tumidam extra forameņ <lb></lb>ad partes aeris exporrigere, non quidem quia attra<lb></lb>hitur ab aere externo, ſed quia exprimitur à preſſio<lb></lb>ne grauioris fluidi ambientis: verùm cùm prædictą <lb></lb>extuberantia creari non poſſit abſque violenta tranſ<lb></lb>poſitione, & diſtractione partium in abdomine con<lb></lb>tentarum, ſcilicet inteſtinorum, membranarum, va<lb></lb>ſorum, & cutis, igitur hinc ſubſequetur paſſio dolo<lb></lb>rifica, quam rana iudicabit ab aeris externi attra<lb></lb>ctione factam fuiſſe, nec vnquam perſuaderi poſſet à <lb></lb>pondere aquæ, vel mercurij ambientis dependerę. <lb></lb></s> <s id="s.001411">Non ſecùs vniuerſalis illa aeris compreſſio continua<lb></lb>ta, & aſſidua quadam preſſione contuſioneque corpus <lb></lb>vniuerſum animalis veluti prælum ſtringit, atque ob <lb></lb>conſuetudinem nullam noxam, neque ſenſationem̨ <lb></lb>creat; ceſſante poſtea in aliqua peculiari corporis <lb></lb>parte huiuſmodi compreſſione mirum non eſt ſi hu<lb></lb>mores, & carnes ob compreſſionem factam in reliquis <lb></lb>locis animalis impellantur violentèr intra cucurbi<lb></lb>tulam, vbi actio compreſſiua aeris deficit, & ibidem <lb></lb>paſſio dolorifica ſentiatur. <lb></lb><figure id="id.010.01.280.1.jpg" xlink:href="010/01/280/1.jpg"></figure><pb pagenum="273" xlink:href="010/01/281.jpg"></pb><arrow.to.target n="marg365"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001412"><margin.target id="marg364"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001413"><margin.target id="marg365"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001414"><emph type="center"></emph>PROP. CXXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001415"><emph type="center"></emph><emph type="italics"></emph>Pluribus experimentis confirmatur à pondere ambientis <lb></lb>fluidi corpora mollia intra cucurbitulas, & fistulas <lb></lb>inſinuari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001416">QVòd poſtea reuerà caro intra cucurbitulam in<lb></lb>ſinuetur à compreſſione externi aeris <expan abbr="ambiẽ-tis">ambien<lb></lb>tis</expan>, poteſt pluribus experimentis comprobari. </s> <s id="s.001417">ſuma<lb></lb>tur veſica ſuilla aere plena, ſed non valdè tenſa, eique <lb></lb>applicetur orificium cucurbitulæ paritèr aere ple<lb></lb>næ, vt nimirùm perimetrum eius oris tangat veſicæ <lb></lb>pelliculam, poſteà veſica cum annexa cucurbitula in<lb></lb>fra aquam demergatur, videbis quò magis veſica ad <lb></lb>fundum aquæ perducitur, eò magis portionem veſi<lb></lb>cæ intra cucurbitam contentam turgere inflarique, & <lb></lb>intra cucurbitulæ cauitatem aliquantulum inſinuari, <lb></lb>perindè, ac caro noſtra turgens intra cucurbitulas <lb></lb>immitti ſolet. </s> <s id="s.001418">Et multò euidentiùs hoc continget fi <lb></lb>prædicta veſica aqua impleatur, & poſtmodum vnà <lb></lb>cum annexa cucurbitula infra <expan abbr="hydrargyrũ">hydrargyrum</expan> immitta<lb></lb>tur, videbis quòd tanta vi turgida pars veſicæ intrà <lb></lb>cucurbitulam immittitur, vt requiratur violentia ali<lb></lb>qua ad diuellendam cucurbitulam ab ipſa veſica. <lb></lb></s> <s id="s.001419">Et hoc profectò tribui non poteſt virtuti attractiuæ, <lb></lb>quam nec cucurbitula, neque aer incluſus habet, ſed <lb></lb>manifeſtè hoc efficitur à pondere aquæ, vel mercurij <lb></lb>ambientis, à quo veſica vndique comprimitur præ<lb></lb>terquàm in illo circello comprehenſo à cucurbitulæ <pb pagenum="274" xlink:href="010/01/282.jpg"></pb><arrow.to.target n="marg366"></arrow.to.target><lb></lb>orificio, ibi enim aer incluſus in cucurbitula <expan abbr="tãtum-modò">tantum<lb></lb>modò</expan> veſicam tangit, & durities vitreæ cucurbitulæ <lb></lb>veluti fornex impedit ne aqua, vel hydrargyrum am<lb></lb>biens ſubiectam veſicæ particulam comprimat con<lb></lb>tundatque. </s> </p> <p type="margin"> <s id="s.001420"><margin.target id="marg366"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001421">Idipſum hoc alio opportuniori experimento com<lb></lb>probari poteſt: in fiſtula vitrea vtrinque aperta aere <lb></lb>plena infernè aptata digiti pulpa orificium eius om<lb></lb>ninò claudatur, poſtea manus cum ei annexa, & in<lb></lb>cumbente fiſtula immergatur intra <expan abbr="aquã">aquam</expan>, vel hydrar<lb></lb>gyrum, itaut ſupremum fiſtulæ orificium extet ſu<lb></lb>pra mercurij, aut aquæ libellam; tunc caro pulpæ di<lb></lb>giti inflatur tumoremque inſinuat rubicundum intrą <lb></lb>fiſtulam, percipitur que ſenſus quidam ſuctionis, & <lb></lb>hic conſtat non adeſſe vim vllam attractiuam, cùm̨ <lb></lb>aer intra <expan abbr="fiſtulã">fiſtulam</expan> ſupernè recluſam nullam <expan abbr="attractionẽ">attractionem</expan> <lb></lb>faciat, & proindè concedendum eſt, à pondere am<lb></lb>bientis aquæ, vel mercurij, comprimi manum, atque <lb></lb>digitum, & ſic <expan abbr="ſanguinẽ">ſanguinem</expan> exprimi inſinuarique in illa <lb></lb>parte digiti, quæ non ſtringitur, nec comprimitur <lb></lb>à pondere ambientis fluidi. </s> </p> <p type="main"> <s id="s.001422"><expan abbr="Idẽ">Idem</expan> obſeruabitur, ſi homo ad inſignem <expan abbr="profũditatẽ">profunditatem</expan> <lb></lb>aquæ demerſus fiſtulam làbijs comprehenſam, & ſu<lb></lb>premo aeri communicantem ſecum deferat, vel orifi<lb></lb>cium fiſtulæ cuti manus, aut brachij applicet; is cer<lb></lb>tè videbit linguam, vel cutim intra fiſtulam parum<lb></lb>per inſinuari, & ſenſum ſuctionis patietur, ad inſtar <lb></lb>eius qui in cucurbitulis fieri ſolet. </s> </p> <p type="main"> <s id="s.001423">Idipſum experieris ſi ingentem cucurbitulàm ab-<pb pagenum="275" xlink:href="010/01/283.jpg"></pb><arrow.to.target n="marg367"></arrow.to.target><lb></lb>domini applicatam tecum deferas in <expan abbr="profũdo">profundo</expan> maris. <lb></lb></s> <s id="s.001424">Ex quibus omnibus <expan abbr="cõſtat">conſtat</expan>, quòd à compreſſione me<lb></lb>dij fluidi ambientis <expan abbr="conſtringũtur">conſtringuntur</expan> partes omnes ani<lb></lb>malis, & proindè exprimi poteſt <expan abbr="sãguis">sanguis</expan>, & caro mol<lb></lb>lis in ea cauitate cucurbitæ, in qua cutis caret com<lb></lb>preſſione cùm aer cucurbitæ rarefactus ab igne, vel <lb></lb>à ſuctione, aut emboli tractione ſit imminutus, fit vt <lb></lb>minimè comprimat cutim ſubiectam, ea validitatę, <lb></lb>qua reliquæ animalis partes ab ambiente aere con<lb></lb>tunduntur. <lb></lb><arrow.to.target n="marg368"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001425"><margin.target id="marg367"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001426"><margin.target id="marg368"></margin.target>Obijciunt <lb></lb>ſenſu perci<lb></lb>pi <expan abbr="|tractionẽ">| tractionem</expan> <lb></lb>in parte cor<lb></lb>poris conti<lb></lb>gua cucur<lb></lb>bitulæ, non <lb></lb>verò pati im<lb></lb>pulſum à flui<lb></lb>do in reli<lb></lb>quo corpore <lb></lb>factam.</s> </p> <p type="main"> <s id="s.001427">Sed, dices, ſenſu ipſo percipitur tractio quædam̨ <lb></lb>in cucurbitulis, non verò percipimus impulſionem̨ <lb></lb>factam à fluido externo <expan abbr="comprimẽte">comprimente</expan> reliquas anima<lb></lb>lis partes à cucurbitula non tactas. </s> </p> <p type="main"> <s id="s.001428"><emph type="center"></emph>PROP. CXXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001429"><emph type="center"></emph><emph type="italics"></emph>In actione cucurbitulæ ex cutis distractione, & tenſione, <lb></lb>ſenſus falsò ſe percipere ſuadetur trahi cutim, & ſan<lb></lb>guinem, cum verè tumor fiat à presſione am<lb></lb>bientis aeris.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001430">NVllus alius effectus percipitur in cucurbitulis <lb></lb>medicis præter quàm violenta quædam ex<lb></lb>preſſio, & intruſio carnis, & ſanguinis intra cucur<lb></lb>bitulæ cauitatem, à qua nimirum pellis vehementer <lb></lb>inflatur, & tumet proindeque cutis diſtenſa ſenſum <lb></lb>doloris patitur. </s> <s id="s.001431">Hoc autem triplici modo fieri poſſe <lb></lb>conſtat, aut quia funibus, & vncinis inconſpicuis cu<lb></lb>tis, caro, & ſanguis <expan abbr="trahũtur">trahuntur</expan> intra cucurbitulam, aut </s> </p> <pb pagenum="276" xlink:href="010/01/284.jpg"></pb> <p type="main"> <s id="s.001432"><arrow.to.target n="marg369"></arrow.to.target><lb></lb>quia ſpontaneo motu ad replendum vacuum ibidem <lb></lb>accurrunt, vel quia ab extrinſeca violentia preſſio<lb></lb>nis aeris ibidem exprimuntur immittunturque. </s> <s id="s.001433">pri<lb></lb>mus modus videtur omninò abſurdus, ſecundus reij<lb></lb>citur quoque, nam ſi reuerà caro, & ſanguis ſpontę <lb></lb>ſua intra cucurbitulam migrant, ergo ibidem noņ <lb></lb>attrahuntur violentèr, proindeque eſt impoſſibile, vt <lb></lb>facultas animalis percipiat ſenſum doloris ob <expan abbr="violẽ-tiam">violen<lb></lb>tiam</expan> quam non patitur, & quæ non exiſtit in natura. <lb></lb></s> <s id="s.001434">Et licèt dici poſſet dolorem creari per accidens ob <lb></lb>cutis, & carnis diſtractionem; ex hoc ipſo infertur <expan abbr="sẽ-ſitiuæ">sen<lb></lb>ſitiuæ</expan> facultatis fallacia, & deceptio, quilibet enim <lb></lb>iuraret ſenſu percipere tractionem violentam carnis, <lb></lb>non verò motum eius ſpontaneum intra <expan abbr="cucurbitulã">cucurbitulam</expan>. </s> </p> <p type="margin"> <s id="s.001435"><margin.target id="marg369"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001436">Fatendum ergo eſt, tumorem carnis, & ſanguinis <lb></lb>intra cucurbitulas produci non poſſe ab alia cauſą <lb></lb>quàm à preſſione aeris ambientis, quæ ex præmiſſis <lb></lb>propoſitionibus neceſſariò prædictum effectum cre<lb></lb>are debet, quatenùs in particula illa carnis intra cu<lb></lb>curbitulam incluſa deficit vis compreſſiua ambientis <lb></lb>aeris, hæc verò cùm minimè percipiatur, nec ad<lb></lb>uertatur ob aſſuetudinem, mirum non eſt, nouum effe<lb></lb>ctum tumoris non tribui cauſæ ignotæ licèt veræ, ſed <lb></lb>potiùs tribuatur ei cauſæ licèt ſalſæ, quæ <expan abbr="ibidẽ">ibidem</expan> adeſ<lb></lb>ſe ſenſibus conſtat, ſcilicèt cucurbitulæ exinanitæ. </s> </p> <p type="main"> <s id="s.001437">Neque nouum eſt, intra viſcera, & partes animalis <lb></lb>fieri tumores ex affluxu humorum, cùm tamen <expan abbr="nõ">non</expan> per<lb></lb>cipiamus an prædicti humores ſponte, vel vi ibidem <lb></lb>deferantur. <pb pagenum="277" xlink:href="010/01/285.jpg"></pb><arrow.to.target n="marg370"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001438"><margin.target id="marg370"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001439">Tranſeo iam ad aliud argumentum adductum pro <lb></lb>confirmatione attractionis: Sit DEF vas oblongum̨ <lb></lb>mercurio plenum, <expan abbr="ſumaturq;">ſumaturque</expan> fiſtula vi<figure id="id.010.01.285.1.jpg" xlink:href="010/01/285/1.jpg"></figure><arrow.to.target n="marg371"></arrow.to.target><lb></lb>trea vtrinque aperta AB, & immerga<lb></lb>tur intra vas DF, quouſque ſupremum <lb></lb>eius orificium A demergatur infra li<lb></lb>bellam mercurij E; <expan abbr="tũc">tunc</expan> applicetur digi<lb></lb>ti pulpa ſupremo orificio fiſtulæ A, vt <lb></lb>arctè claudatur. </s> <s id="s.001440">Iam ſi ſummitas fiſtu<lb></lb>læ A vnà cum claudente digito eleue<lb></lb>tur, percipitur manifeſta attractio di<lb></lb>giti pulpæ, quam ſuprema mercurij ſu<lb></lb>perficies tangit, hæc (inquiunt) vio<lb></lb>lentia procùl dubio efficitur à pondere <lb></lb>ſubiecti mercurij, <expan abbr="cũ">cum</expan> reuerà digitus, & <lb></lb>manus ſuſtentare debeat pondus prædicti mercurij, <lb></lb>non ſecùs, ac ſi vncino aliquo digito annecteretur, <lb></lb>hinc deducitur quòd detur in rerum natura facultas, <lb></lb>& operatio attractiua, & ſi hoc verùm eſt (inquiunt) <lb></lb>quare in cucurbitulis ſimilitèr abſque funibus, aut <lb></lb>vncinis non poteſt ſimilis attractio fieri? </s> </p> <p type="margin"> <s id="s.001441"><margin.target id="marg371"></margin.target>Aliud argu<lb></lb>mentum <expan abbr="cõ-tra">con<lb></lb>tra</expan> ſuperius <lb></lb>adductam do<lb></lb>ctrinam.</s> </p> <p type="main"> <s id="s.001442"><emph type="center"></emph>PROP. CXXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001443"><emph type="center"></emph><emph type="italics"></emph>In fiſtula vtrinque aperta mercurio plena digito ſupernè ob<lb></lb>turata, & infernè intra <expan abbr="mercuriũ">mercurium</expan> demerſa, licèt videa<lb></lb>mur percipere in digito ſenſum ſuctionis, & ponderis <lb></lb>mercurij ſustentati, tamen verè grauamur à cy<lb></lb>lindro aereo ſupra vnguem incumbente, & ſu<lb></lb>ctio pulpæ digiti à defectu presſionis aeris <lb></lb>dependet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="278" xlink:href="010/01/286.jpg"></pb><arrow.to.target n="marg372"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001444"><margin.target id="marg372"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001445">REuera Mercurius pulpæ digiti connectitur in A, <lb></lb>non vi aliqua attractiua, ſed à compreſſionę <lb></lb>aeris ambientis ſupra ſtagnans hydrargyrum E <lb></lb>vaſis ſubiecti; hoc autem confirmatur ex eo, quòd ſi <lb></lb>altiùs eleuetur fiſtula, vt nimirùm ſoli<lb></lb><figure id="id.010.01.286.1.jpg" xlink:href="010/01/286/1.jpg"></figure><lb></lb>tam altitudinem vnius cubiti, & qua<lb></lb>drantis excedat, tunc quidem ſuprema <lb></lb>mercurij ſuperficies leniſſimo motu <lb></lb>abſque vlla difficultate diuellitur, ſepa<lb></lb>raturque à digiti pulpa ſuprema A, non <lb></lb>igitur à vi attractiua mercurius digito <lb></lb>annectebatur. </s> <s id="s.001446">Sed quæres; vnde ergò <lb></lb>oritur ſenſus ille ſuctionis, & tractio<lb></lb>nis, qui in prædicta pulpa digiti perci<lb></lb>pitur, & quomodò ſuſtentat, atquę <lb></lb>percipit grauitatem mercurij ſubiecti? <lb></lb></s> <s id="s.001447">Reſpondeo, quòd à pondere aeris ma<lb></lb>nui, & digito incumbentis <expan abbr="cõprimuntur">comprimuntur</expan> omnes par<lb></lb>tes digiti, excepta illa particula, quæ orificium vitri <lb></lb>A attingit, & ab hac compreſſione exprimitur ſan<lb></lb>guis in tumore illo rubicundo pulpæ digiti, quæ in <lb></lb>orificio vitri A inſinuatur, quando ſpatium inane ibi<lb></lb>dem creatur. </s> <s id="s.001448">Præterea adeſt pondus hydrargyri in<lb></lb>tra fiſtulam contenti, quod ſuſtinetur à preſſione cy<lb></lb>lindri aerei dum comprimit mercurij ſuperficiem ſta<lb></lb>gnantis. </s> <s id="s.001449">Vnde ex vna parte habemus pondus cylin<lb></lb>dri aerei, orificium, & digitum in A comprimentis, <lb></lb>pariterque adeſt pondus vitri AB, & mercurij in ip<lb></lb>ſo contenti, ex altera verò parte adeſt grauitas alte-<pb pagenum="279" xlink:href="010/01/287.jpg"></pb><arrow.to.target n="marg373"></arrow.to.target><lb></lb>rius aerei cylindri prementis ſtagnantem ſuperfici<lb></lb>em E, & ab hoc <expan abbr="ſuſpẽditur">ſuſpenditur</expan> mercurius AB. igitur à <lb></lb>virtute manus ſuſtinetur reſiduum ponderis vltra æ<lb></lb>quilibrium, ſcilicèt pondus vitri AB vnà cum ponde<lb></lb>re cylindri aerei orificio, & digito A incumbentis, <lb></lb>licèt falsò perſuadeatur ſe ſuſtinere mercurium ſub<lb></lb>iectum, eique adnexum. </s> </p> <p type="margin"> <s id="s.001450"><margin.target id="marg373"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001451">Et profectò ab hac experientia euincitur, quòd tra<lb></lb>ctio illa, quæ in digito percipitur, non ſit vera attra<lb></lb>ctio facta ob vacui timorem, quia dum fiſtula minùs <lb></lb>cubito cum quadrante eleuatur, mercurius à digito <lb></lb>non diuellitur, & proindè ſpatium inane ibidem non <lb></lb>intercipitur, vnde nulla attractio fieri deberet, cùm <lb></lb>è contrà maxima fieret quando ob mercurij deſcen<lb></lb>ſum efficitur ſolita inanitas, & tamen hoc falſum eſt, <lb></lb>cùm in vtroque caſu ferè æquali vi digiti pulpa de<lb></lb>orſum attrahi ſentiatur. </s> </p> <p type="main"> <s id="s.001452"><expan abbr="Tãdem">Tandem</expan> examinati debet pulcherrima, & ingenio<lb></lb>ſiſſima difficultas, quam cariſſimus amicus Diony<lb></lb><arrow.to.target n="marg374"></arrow.to.target><lb></lb>ſius Guerrinus M.D. Ætrur. </s> <s id="s.001453"><expan abbr="Caſtrẽſis">Caſtrenſis</expan> Generalis pre<lb></lb>fectus mihi diſcutiendam propoſuit. </s> <s id="s.001454">Dicebat enim ſi <lb></lb>in tubis pneumaticis, ſeu cteſibijs, quibus aquam̨ <lb></lb>haurire ſolemus è puteis, aqua eleuatur, non <expan abbr="quidẽ">quidem</expan> <lb></lb>vera attractione, quatenùs embolo eleuato hauritur, <lb></lb>vel exugitur aqua ſubiecta, vt pueri calamo intrą <lb></lb>aquam immiſſo reſtricto ore, & anhelitu, & ſpiritu <lb></lb>attracto aquam ſursùm eleuant; ſed hoc contingit, <lb></lb>quia dum embolus manu ſursùm trahitur, impellitur <lb></lb>ſursùm quoque cylindrus aereus embolo <expan abbr="incumbẽs">incumbens</expan>, <pb pagenum="280" xlink:href="010/01/288.jpg"></pb><arrow.to.target n="marg375"></arrow.to.target><lb></lb>& proindè prohibetur impeditur que actio compreſ<lb></lb>ſiua prædicti aerei cylindri ſupra aquam ſubiectam. <lb></lb></s> <s id="s.001455">Vis ergo & conatus manus embolum eleuantis sem<lb></lb>per eidem reſiſtentiæ opponitur, nempèſuſpendit e<lb></lb>leuatque eumdem cylindrum aereum ſupra <expan abbr="embolũ">embolum</expan> <lb></lb>incumbentem, igitur ſemper eadem vis, idemque co<lb></lb>natus manus requiritur ad <expan abbr="ſuſtinẽdum">ſuſtinendum</expan> prædictum ae<lb></lb>reum cylindrum, & ad prohibendam eius compreſſi<lb></lb>onem ſupra aquam ſubiectam. </s> <s id="s.001456">Hinc inferebat, igitur <lb></lb>ſiue in tubo cteſibico ſupra libellam ſubiecti putei a<lb></lb>qua magis, vel minùs eleuetur ſemper eadem vi, & <lb></lb>energia manus ſuſpendere embolum, & conſequen<lb></lb>ter aquam eleuare poterimus, ſed hoc eſt falſum, & <lb></lb>contra experientiam, cùm ſemper maior vis, & cona<lb></lb>tus requiratur, quo aqua ad maiorem altitudinem in <lb></lb>tubo pneumatico eleuatur, igitur falſum eſt aquam̨ <lb></lb>eleuari, propterea quòd ſuſpenditur prohibeturque <lb></lb><expan abbr="cõpreſſio">compreſſio</expan> cylindri aerei ſupra embolum prædicti in<lb></lb>ſtrumenti. </s> <s id="s.001457">Cùm è contrà ſi reuera vi attractiua à ma<lb></lb>nu embolum trahente ſubleuatur aqua, manifeſtum̨ <lb></lb>eſt, quòd quò altiùs aſcendit maior aquæ copia, pro<lb></lb>indè grauior moles ſupra putei libellam ſuſpenditur <lb></lb>eleuaturque, mirum non eſt maius pondus aquæ à <lb></lb>maiori vi ſuſtentari eleuarique debere, quam minor <lb></lb>aquæ copia. <lb></lb><figure id="id.010.01.288.1.jpg" xlink:href="010/01/288/1.jpg"></figure><pb pagenum="281" xlink:href="010/01/289.jpg"></pb><arrow.to.target n="marg376"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001458"><margin.target id="marg374"></margin.target>Proponitur <lb></lb><expan abbr="pulcherrimũ">pulcherrimum</expan> <lb></lb><expan abbr="argumẽtum">argumentum</expan> <lb></lb>pro attracti<lb></lb>one.</s> </p> <p type="margin"> <s id="s.001459"><margin.target id="marg375"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001460"><margin.target id="marg376"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="main"> <s id="s.001461"><emph type="center"></emph>PROP. CXXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001462"><emph type="center"></emph><emph type="italics"></emph>Necesſitate mechanica in tubo pneumatico requiritur maior <lb></lb>vis ad trahendum embolum cum adhærente aqua ad <lb></lb>altitudinem maiorem, quàm ad minorem ſe<lb></lb>cundùm <expan abbr="proportionẽ">proportionem</expan> quam habent aquæ <lb></lb>ſubleuatæ pondera, vel mo<lb></lb>menta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001463">VT verò huic difficultati perſpicuè ſatisfacia<lb></lb>mus, ſupponamus in puteo, cuius ſuperficies <lb></lb>aquea BC, demergi tubum pneumaticum RB, qui <lb></lb>facilitatis gratia continuari intelligatur cum ſip ho<lb></lb>ne inuerſo BIKD; intelligatur que libra radiorum æ<lb></lb>qualium GH, cuius centrum N, & vtrinque pendeant <lb></lb>ab extremitatibus æqualia <expan abbr="põdera">pondera</expan> <lb></lb><figure id="id.010.01.289.1.jpg" xlink:href="010/01/289/1.jpg"></figure><lb></lb>E, & F, & hæc contingant <expan abbr="ſuperficiẽ">ſuperficiem</expan> <lb></lb>aquæ BC, itaut ambo grauia F, & E <lb></lb>comprimant, impellantque aquam <lb></lb>ipſam deorsùm, E <expan abbr="quidẽ">quidem</expan> immedia<lb></lb>tè, F verò mediante embolo QB, ha<lb></lb>beantque figuram cylindricam, & <lb></lb>ad modum emboli intra canales ſi<lb></lb>phonis ſtrictè, & arctè moueri <expan abbr="ſursũ">ſursum</expan>, <lb></lb>ac deorsùm poſſint, & ſupponamus <lb></lb>embolum QB grauitate carere; ad<lb></lb>ueniat poſtea externa vis, quæ ſuſtentet pondus F ip<lb></lb>ſumque ſursùm impellat, hęc profectò non debet eſſe <lb></lb>æqualis integro ponderi vaſto ipſius F, proptereą <pb pagenum="282" xlink:href="010/01/290.jpg"></pb><arrow.to.target n="marg377"></arrow.to.target><lb></lb>quòd hoc æquilibratur ab æquipondio ipſius E, & <lb></lb>proinde F nullam compreſſionem exercet, perinde, <lb></lb>ac ſi grauitate omninò careret, quare à quacumque <lb></lb>exiliſſima vi ſuſpendi, & ſursùm impelli poterit, ſit<lb></lb><figure id="id.010.01.290.1.jpg" xlink:href="010/01/290/1.jpg"></figure><lb></lb>que talis vis ſuſpenſiua, vna pars <lb></lb>quarta <expan abbr="põderis">ponderis</expan> ipſius F, igitur <expan abbr="põ-dus">pon<lb></lb>dus</expan> quod F exercet, erit tres quar<lb></lb>tæ partes totius ponderis E, igitur <lb></lb>non ampliùs fiet æquilibrium, ſed <lb></lb>pondus E exercebit quadrantem <lb></lb>totius ſui ponderis, & cum hoc <expan abbr="cõ-primet">com<lb></lb>primet</expan> <expan abbr="ſubiectã">ſubiectam</expan> a <expan abbr="quã">quam</expan> C, & proin<lb></lb>dè eleuare poterit in oppoſito tu<lb></lb>bo ſiphonis aquæ molem BM, cu<lb></lb>ius pondus vna quarta pars ſit <lb></lb>ponderis E, vel F. </s> <s id="s.001464">Poſteà denuò ſuperaddita cau<lb></lb>fa externa ſursùm F impellente, & ſuſtentante, vt <lb></lb>nimirùm remaneat vis comprimens ipſius E immi<lb></lb>nuta, & æqualis medietati ponderis E. </s> <s id="s.001465">Manifeſtum̨ <lb></lb>eſt magis æquilibrium ſuperare graue E, ſcilicèt eius <lb></lb>momentum erit æquale dimidio totius eius ponderis <lb></lb>E, vel F, proindeque eleuabit duplam aquæ molem <lb></lb>in aduerſo tubo vſque ad O, vt nimirùm moles aquæ <lb></lb>BO dupla ſit ipſius BM, & ſic vlteriùs adueniente no<lb></lb>ua vi ſuſtentante pondus F ſemper magis diminuetur <lb></lb>ipſius F compreſſio, & tantumdèm præcisè creſcet <lb></lb>momentum ponderis E, & tantundem augebitur ele<lb></lb>uatio aquæ in tubo BR, quaproptèr conſtat quod à <lb></lb>maiori vi ſursùm <expan abbr="impellẽte">impellente</expan> pondus F neceſſariò ma-<pb pagenum="283" xlink:href="010/01/291.jpg"></pb><arrow.to.target n="marg378"></arrow.to.target><lb></lb>ior moles aquæ in tubo pneumatico eleuatur, & è <expan abbr="cõ-uerſo">con<lb></lb>uerſo</expan> maior moles aquæ in tubo pneumatico BR ele<lb></lb>uata maiorem vim ſuſtentantem, & eleuantem exi<lb></lb>git. </s> <s id="s.001466">Intelligatur modò corpus FV eſſe aereum cylin<lb></lb>drum embolo AB incumbens, eumque deprimens ſu<lb></lb>pra aquæ libellam B (neglecta facilitatis gratia gra<lb></lb>uitate ipſius emboli) pariterque ſit cor<lb></lb><figure id="id.010.01.291.1.jpg" xlink:href="010/01/291/1.jpg"></figure><lb></lb>pus EX alter cylindrus aereus ſuperfi<lb></lb>ciei aquæ C incumbens, igitur quotieſ<lb></lb>cumque duo pondera aerea FV, & EX <lb></lb>æqualia ſunt, æquali vi ſubiectam <expan abbr="aquã">aquam</expan> <lb></lb>premunt, & in tali ſtatu aqua B nequę <lb></lb>eleuabitur, neque deprimetur, dum equè <lb></lb>comprimitur à <expan abbr="colũnis">columnis</expan> aereis FV, & EX <lb></lb>æquilibratis; at quando aduenit quæli<lb></lb>bet exigua vis poterit ſuſtentare <expan abbr="aereũ">aereum</expan> <lb></lb>cylindrum FV æquilibratum, & ideò <expan abbr="nõ">non</expan> <lb></lb>grauem, eumque ſursùm impellere, & <lb></lb>proindè prohibere eius preſſionem ſupra aquam B, <lb></lb>& tunc tanta præcisè erit compreſſio facta à cylindro <lb></lb>aereo EX ſupra ſubiectam aquam, quanta eſt vis, à <lb></lb>qua cylindrus aereus FV ſuſtinetur ſubleuaturque, <lb></lb>& tanta præcisè erit aquæ moles BS eleuata in tubo <lb></lb>pneumatico, igitur quantum præcisè augetur graui<lb></lb>tas ipſius aquæ BS ſubleuatæ, tantum præcisè augeri <lb></lb>debet vis illa, qua cylindrus aereus FV ſursùm im<lb></lb>pellitur, ſeù tantumdem augeri debet vis manus ſur<lb></lb>sùm embolum trahentis, à quo paritèr aereus cylin<lb></lb>drus FV ſuſtinetur impelliturque ſursùm. </s> <s id="s.001467">Et hinc pa-<pb pagenum="284" xlink:href="010/01/292.jpg"></pb><arrow.to.target n="marg379"></arrow.to.target><lb></lb>tet, quòd neceſſitate mechanica in tubo pneumatico <lb></lb>requiritur maior vis ad <expan abbr="trahẽdũ">trahendum</expan> <expan abbr="embolũ">embolum</expan> <expan abbr="quãdo">quando</expan> aqua <lb></lb><expan abbr="ſubleuãda">ſubleuanda</expan> eſt ad maiorem <expan abbr="altitudinẽ">altitudinem</expan>, <expan abbr="quã">quam</expan> ad <expan abbr="minorẽ">minorem</expan>. <lb></lb></s> <s id="s.001468">modò quia ſuperficies aquæ B premitur ab aqua BS <lb></lb>(non conſiderato embolo) & ab aere FV, & ſuperfi<lb></lb>cies aquæ C grauatur tantummodò à cylindro aereo <lb></lb>EX æquè graui ac FV (eò quòd inſignis atmoſphærę <lb></lb>ſublimitas eſt in cauſa vt exceſſus altitudinis cylin<lb></lb>dri EX ſupra cylindri FV altitudinem ſit omninò in<lb></lb>ſenſibilis, proindeque cenſeri poſſint aerei cylindri <lb></lb>EX, & FV æquè graues) ergo exceſſus grauitatis a<lb></lb><arrow.to.target n="marg380"></arrow.to.target><lb></lb>quæ BS compenſari debet à vi contraria manus A <lb></lb>embolum AI trahentis. </s> <s id="s.001469">Sed animaduertendum eſt <lb></lb>quòd vis manus embolum trahentis reuera non ele<lb></lb>uat aquam BS, quia hæc æquilibratur à ſibi æquali <lb></lb>momento aeris EX, fed tantummodò manus ſuſten<lb></lb>tat prohibetque preſſionem incumbentis aeris FV, <lb></lb>æquilibrati cum EX, cuius preſſionis <expan abbr="momẽtũ">momentum</expan> æqua<lb></lb>tur ponderi aquæ ſubleuatæ BS. hinc fit vt præiudi<lb></lb>cio decepti putemus nos ſuſtinere aquam ſubiectam <lb></lb>quando reuerà ſuſtentamus aerem incumbentem̨ <lb></lb>FV æquilibratum ipſi EX. </s> </p> <p type="margin"> <s id="s.001470"><margin.target id="marg377"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001471"><margin.target id="marg378"></margin.target>Cap. 6. non <lb></lb>dari attracti<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001472"><margin.target id="marg379"></margin.target>Cap. 6. non <lb></lb>dari attractio<lb></lb>onem.</s> </p> <p type="margin"> <s id="s.001473"><margin.target id="marg380"></margin.target>Notandum <lb></lb>tamen quod <lb></lb>vis. </s> <s id="s.001474"><expan abbr="embolũ">embolum</expan> <lb></lb> ſubleuans <expan abbr="nõ">non</expan> <lb></lb>attrahit, nec <lb></lb><expan abbr="ſuſtẽtat">ſuſtentat</expan> <expan abbr="aquã">aquam</expan> <lb></lb><expan abbr="ſubiectã">longs;ubiectam</expan> ſibi<lb></lb>que <expan abbr="adhærẽ-tem">adhæren<lb></lb>tem</expan>, ſed po<lb></lb>tiùs ſsuſtinet <lb></lb><expan abbr="aereũ">aereum</expan> cylin<lb></lb>drum <expan abbr="incũ-bentem">incum<lb></lb>bentem</expan>.</s> </p> <p type="main"> <s id="s.001475">Tandem cùm altitudo aquæ BS ad 18. cubitos fe<lb></lb>rè peruenerit, licèt deinceps embolus maiori vi alti<lb></lb>ùs trahatur nè minimum quidem aqua vlterius ſuble<lb></lb>uabitur, ex quo euincitur aquam non attrahi ab em<lb></lb>bolo, ſed impelli à pondere cylindri aerei collatera<lb></lb>lis, qui cum prædicta aquæ altitudine æquilibratur. <lb></lb></s> <s id="s.001476">Et hæc modo ſufficiant pro euerſione virtutis attrac<lb></lb>tiuæ. <pb pagenum="285" xlink:href="010/01/293.jpg"></pb><arrow.to.target n="marg381"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001477"><margin.target id="marg381"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001478"><emph type="center"></emph><emph type="italics"></emph>De Natura, & Cauſa fluiditatis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001479"><emph type="center"></emph>CAP. VII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001480">POſtquam euicimus aquam, & aerem, in eorum<lb></lb>met regionibus ponderare, & grauitatem exer<lb></lb>cere, inſuperque attractionem in natura non dari; po<lb></lb>terit <expan abbr="iã">iam</expan> natura, & vera cauſa fluiditatis <expan abbr="eorũ">eorum</expan> aſſignari. </s> </p> <p type="main"> <s id="s.001481">Et primò more noſtro de finitionem fluiditatis affe<lb></lb>remus deſumptam ab aliqua inſigni, & euidenti paſ<lb></lb>ſione eius corporis, quod fluidum appellatur. </s> <s id="s.001482">Et pro<lb></lb>fectò quotieſcumque video, atque conſidero diffe<lb></lb>rentiam inter glaciem, & aquam fluentem, obſeruo <lb></lb>in illa duritiem, & conſiſtentiam, qua iſta caret, video <lb></lb>enim immiſſo digito, quòd glacies non cedit, aquą <lb></lb>verò fluida facillimè locum præſtat ſubmerſioni, & <lb></lb>ingreſſui digiti, perfecteque circa ipſum diſponi<lb></lb>tur, & adaptatur, vt vndequaque <expan abbr="eũ">eum</expan> contingat. </s> <s id="s.001483">Video <lb></lb>inſuper non poſſe angulum glaciei impelli, aut quo<lb></lb>modolibet loco-moueri, quin tota maſſa glacialis ſi<lb></lb>mùl moueatur, cum è contrà in aqua fluida poſſit quę<lb></lb>libet eius particula impelli, circumuolui, alijſquę <lb></lb>modis agitari, quieſcentibus tamen reliquis partibus <lb></lb>eius, vel ſaltem agitatis motu tardiori, vel non ad eaſ<lb></lb>dem partes facto. </s> <s id="s.001484">Poſtremò obſeruo aquam fluidam <lb></lb>perfectiſſimè explanari, & ad libellam horizonti æ<lb></lb>quidiſtantem reduci, quod minimè fieri poſſet, niſi <lb></lb>partes eius extremæ, ſuperficialeſque æquè à medio <lb></lb>puncto telluris recederent. <pb pagenum="286" xlink:href="010/01/294.jpg"></pb><arrow.to.target n="marg382"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001485"><margin.target id="marg382"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001486">Ex hiſce omnibus phenomenis colligi poteſt paſſio <lb></lb>præcipua ex qua reliquæ omnes dependent atquę <lb></lb>exprimuntur, eritque talis: corpus fluidum erit il<arrow.to.target n="marg383"></arrow.to.target><lb></lb>lud, cuius partium æquè ponderantium poteſt vna à <lb></lb>vi externa moueri non motis reliquis, vel diuerſo mo<lb></lb>do agitatis quàm duris corporibus competit. </s> <s id="s.001487">Quæ de<lb></lb><arrow.to.target n="marg384"></arrow.to.target><lb></lb>finitio parùm differt ab ea quæ traditur ab Ariſtote<lb></lb>le, vbi ait humidum eſſe, quod facilè termino alieno <lb></lb>terminatur, & hoc accidit ex eo, quod poſſunt facil<lb></lb>limè aliquæ partes moueri, non motis teli quis, vel <lb></lb>diuerſo motu. </s> <s id="s.001488">Et hoc quidem, vt euidentiſſimum, <expan abbr="nõ">non</expan> <lb></lb>indiget vlteriori declaratione. </s> </p> <p type="margin"> <s id="s.001489"><margin.target id="marg383"></margin.target>Definitio <lb></lb>fluiditatis.</s> </p> <p type="margin"> <s id="s.001490"><margin.target id="marg384"></margin.target>De gener, & <lb></lb>corrup lib. 2. <lb></lb>cap. 3.</s> </p> <p type="main"> <s id="s.001491">Reſtat modò præcipua difficultas, an fluidum re<lb></lb>uera ſit corpus continuum, an verò ſit diſcretum, ſci<lb></lb>licèt aggregatum ex innumeris particulis ſubdiuiſis, <lb></lb>qualis eſt aceruus granorum, vel arenæ, & hoc erit <lb></lb>operę pretium accuratè examinare, idque præſtabi<lb></lb>mus oſtendendo quòd. </s> </p> <p type="main"> <s id="s.001492"><emph type="center"></emph>PROP. CXXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001493"><emph type="center"></emph><emph type="italics"></emph>Corpus ſubſtantiale componi non poteſt ex punctis <lb></lb>indiuiſibilibus, licèt numero infinitis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001494">QVia puncta indiuiſibilia non videntur exiſtere, <lb></lb>neque in ſubſtantiali corpore aſſignari poſſe, <lb></lb>niſi fictione, & mentis cogitatione, nec ſunt partes, <lb></lb>neque elementa <expan abbr="ſubſtãtiam">ſubſtantiam</expan> corpoream componen<lb></lb>tia, quod patet ex eo, quod punctum additum puncto <lb></lb>bis, decies, millies &c. </s> <s id="s.001495">non facit maius, & nil puncta <pb pagenum="287" xlink:href="010/01/295.jpg"></pb><arrow.to.target n="marg385"></arrow.to.target><lb></lb>plura differre videntur ab vnico puncto, quandoqui<lb></lb>dem, tàm ſingulare punctum, quàm eorum multitudo <lb></lb>nullum ſpatium quantum occupant, contra ac contin<lb></lb>git in vnitatibus, quæ ſimul coniunctæ creant magni<lb></lb>tudinem numericam, ex quo proinde fit, vt vnitates <lb></lb>meritò partes, & elementa numeri cenſeantur, noņ <lb></lb>verò puncta ipſius ſubſtantiæ quantæ. </s> <s id="s.001496">Hinc infertur, <lb></lb>quod ſicut ex infinitis cyfris numerus creari non po<lb></lb>reſt, & ex infinitis non entibus nequit ens confici, ſic <lb></lb>ex infinitis non quantis, quæ nec partes nec elementa <lb></lb>quantitatis ſunt, non poteſt quantum componi; ſunt<lb></lb>que puncta indiuiſibilia non quanta, nec ſunt partes <lb></lb>aut elementa <expan abbr="componẽtia">componentia</expan> quantitatem; igitur ex in<lb></lb>finitis punctis indiuiſibilibus ſubſtantia corporeą <lb></lb>quæ quanta eſt componi, crearique non poterit. </s> </p> <p type="margin"> <s id="s.001497"><margin.target id="marg385"></margin.target>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001498"><emph type="center"></emph>PROP. CXXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001499"><emph type="center"></emph><emph type="italics"></emph>Secundo loco oſtenden dum est, quòd partes quantæ <lb></lb>actu infinitæ, & eiuſdem menſuræ com<lb></lb>ponunt extenſionem infinitam;<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001500">SInt partes quantæ A, B, C, D, E, F, G, &c. </s> <s id="s.001501">actu in<lb></lb>finitæ numero, & æquales inter ſe, dico eas ex<lb></lb><figure id="id.010.01.295.1.jpg" xlink:href="010/01/295/1.jpg"></figure><lb></lb>tenſionem infinitam compone<lb></lb>re. </s> <s id="s.001502">ſumatur quælibet quantitas <lb></lb>finita cuiuſlibet vaſtitatis RS <lb></lb>eiuſdem generis cum particulis <lb></lb>A, B, C, &c. </s> <s id="s.001503">profectò aut RS. <lb></lb>multiplex eſt ipſius A, ſcilicèt <pb pagenum="288" xlink:href="010/01/296.jpg"></pb><arrow.to.target n="marg386"></arrow.to.target><lb></lb>hæc illam metitur, vel non; & primò ponamus RS ab <lb></lb>A <expan abbr="mẽſurari">menſurari</expan>, habebit ergo RS ad A eamdem propor<lb></lb> tionem, quam aliquis numerus finitus ad vnitatem,<lb></lb>& ideò in infinita multitudine partium A, B, C, &c.<lb></lb> ſumi poteſt multitudo partium, quæ maior ſit numero <lb></lb>partium ipſius RS, & prædicta maior multitudo par<lb></lb>tium efficiat <expan abbr="extenſionẽ">extenſionem</expan> X proculdubio X maior erit <lb></lb> ipſa RS, at aggregatum ex infinitis particulis A, B, C, <lb></lb>&c. maiorem extenſionem creat quam prædicta mul<lb></lb>titudo finita X, ergo multò magis aggregatum ex in<lb></lb>finitis particulis maiorem extenſionem efficit, quàm <lb></lb>habeat RS, illa verò extenſio quæ maior eſt <expan abbr="quacũq;">quacunque</expan><lb></lb>quantitate finita, neceſſariò infinita erit, ergo aggre<lb></lb>gatum ex particulis quantis numerò infinitis inter ſe <lb></lb>æqualibus efficit extenſionem infinitam. </s> </p> <p type="margin"> <s id="s.001504"><margin.target id="marg386"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001505">Secundò ſint A, & RS inter <lb></lb><figure id="id.010.01.296.1.jpg" xlink:href="010/01/296/1.jpg"></figure><lb></lb>ſe <expan abbr="incõmenſurabilia">incommenſurabilia</expan>, patet ipſi <lb></lb>RS addi poſſe portionem aliæ <lb></lb>quam SV ita vt RV multiplex <lb></lb>ſit ipſius A, & tunc <expan abbr="aggregatũ">aggregatum</expan> <lb></lb>ex infinitis particulis æqualibus <lb></lb>A, B, C, &c. </s> <s id="s.001506"> maiorem extenſionem efficiet quàm <lb></lb>RV, vt mox oſtenſum fuit, & ideò multò maiorem <lb></lb>extenſionem, quàm RS, creabit, proptereaque infi<lb></lb>nitam eſſe concludemus. <lb></lb><figure id="id.010.01.296.2.jpg" xlink:href="010/01/296/2.jpg"></figure><pb pagenum="289" xlink:href="010/01/297.jpg"></pb><arrow.to.target n="marg387"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001507"><margin.target id="marg387"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001508"><emph type="center"></emph>PROP. CXXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001509"><emph type="center"></emph><emph type="italics"></emph>Partes quantæ actu infinitæ numero, & inter ſe inæquales <lb></lb>componunt extenſionem infinitam.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001510">SInt partes AB, CD, EF, GH, IK, &c. </s> <s id="s.001511">numero in<lb></lb>finitæ, & inter ſe inæquales. </s> <s id="s.001512">Dico extenſionem <lb></lb>infinitam conflare. </s> <s id="s.001513">Quia dantur omnes partes quan<lb></lb>tæ numero infinitæ, ergò datur earum minima, quæ <lb></lb>ſit AB, & ex reliquis maioribus ſecentur portiones <lb></lb>CL, EM, GN, &c. </s> <s id="s.001514">ſingulæ æquales minimæ AB; & <lb></lb>quia particulæ infinitæ inæquales <lb></lb><figure id="id.010.01.297.1.jpg" xlink:href="010/01/297/1.jpg"></figure><lb></lb>AB, CD, EF, &c. </s> <s id="s.001515">maiorem exten<lb></lb>ſionem <expan abbr="componũt">componunt</expan>, quàm partes in<lb></lb>finitæ diminutæ, inter ſe æquales <lb></lb>AB, CL, EM, &c. </s> <s id="s.001516">&, ex præcedenti, <lb></lb>infinitæ particulæ quantæ eiuſdem generis AB, CL, <lb></lb>EM, &c. </s> <s id="s.001517">inter ſe æquales componunt extenſionem̨ <lb></lb>infinitam, ergò multò magis inſi initæ partes illis ma<lb></lb>iores inæquales AB, CD, EF, &c. </s> <s id="s.001518">extenſionem infi<lb></lb>nitam efficient, quod erat. </s> </p> <p type="main"> <s id="s.001519"><emph type="center"></emph>PROP. CXXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001520"><emph type="center"></emph><emph type="italics"></emph>Si eiuſdem aggregati aliquæ partes moueantur cæteris quie<lb></lb>ſcentibus, vel omnes inæqualibus motibus agitentur, <lb></lb>qui tamen non competant, nec aptari posſint <lb></lb>partibus corporis duri, & conſistentis, ne<lb></lb>ceſſariò illius aggregati partes erunt <lb></lb>actu diuiſæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="290" xlink:href="010/01/298.jpg"></pb><arrow.to.target n="marg388"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001521"><margin.target id="marg388"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001522">QVærimodo debet ſignum ex quo lumine natu<lb></lb>ræ euidentiſſimè dignoſcere valeamus an ali<lb></lb>quod corpus actu diuiſum ſit implùres partes, vel ſit <lb></lb>vnum continuum, licèt prædictæ partes ob exiguita<lb></lb>tem, vel tranſparentiam earum ſint inconſpicuæ, & <lb></lb>inobſeruabiles; hoc autem <expan abbr="ſignũerit">ſignum erit</expan> motus, & quies, <lb></lb>ſcilicèt ſi conſtat quòd vna pars A compoſiti mouetur <lb></lb>varijs modis <expan abbr="dũ">dum</expan> relique adiacentes partes B, H, E, CI, <lb></lb>&c. </s> <s id="s.001523">in eodem ſitu quieſcunt, certum erit partem <expan abbr="illã">illam</expan> <lb></lb>agitatam A à reliquis diſciſſam, & diſcretam eſſę. <lb></lb></s> <s id="s.001524">at quando omnes partes eiuſdem compoſiti mouen<lb></lb>tur, videndum qua ratione <expan abbr="euidẽtèr">euidentèr</expan> dignoſcere poſ<lb></lb>ſimus an prædictæ partes ſint continuatæ, & vnitæ, <lb></lb>vel ab inuicem diuiſæ, & profectò non ſemper inæ<lb></lb>qualitas motuum indicat diuiſionem potiùs quàm̨ <lb></lb>continuitatem, nam in vertigine rotæ ſolidæ, & du<lb></lb>ræ earum particulæ licèt tenaciter ei affixæ, & con<lb></lb>nexæ ſint, nihlominùs mouentur inæqualibus veloci<lb></lb>tatibus ſecundùm proportionem, quam habent di<lb></lb>ſtantiæ ab axi firmo eiuſdem rotæ circumductæ, igi<lb></lb>tur in aliquo fluido reuoluto ſi orbes ab eius particu<lb></lb>lis eodem tempore deſcripti maiores fuerint, quo <lb></lb>magis ab axe reuolutionis recedunt, & ſecundùm̨ <lb></lb>proportionem diſtantiarum, dubitare profectò poſ<lb></lb>ſumus an particulæ prædicti fluidi ſint continuatæ, an <lb></lb>verò actu diſcretæ. </s> </p> <p type="main"> <s id="s.001525">Hinc deducitur, quòd ſi in rotæ vertigine vna eius <lb></lb>pars magis, vel minùs, quàm priùs à centro recedat, <lb></lb>vel celeriori, aut tardiori motu feratur, quàm com-<pb pagenum="291" xlink:href="010/01/299.jpg"></pb><arrow.to.target n="marg389"></arrow.to.target><lb></lb>petit diſtantiæ eius ab axe, tunc neceſſariò talis par<lb></lb>ticula erit à rota disiuncta, & ſegregata. </s> <s id="s.001526">Vt in rotą <lb></lb><figure id="id.010.01.299.1.jpg" xlink:href="010/01/299/1.jpg"></figure><lb></lb>AEH reuoluta circa cen<lb></lb>trum D ſi eius particulæ <lb></lb>A, B, C eodem <expan abbr="tẽpore">tempore</expan> <expan abbr="de-ſcribũt">de<lb></lb>ſcribunt</expan> orbes AEH, BFI, <lb></lb>CGL, <expan abbr="eãdem">eandem</expan> proportio<lb></lb>nem habentes quam di<lb></lb>ſtantiæ à centro AD, BD, <lb></lb>& CD tunc diſtingui non <lb></lb>poteſt an prędictæ parti<lb></lb>culæ ſint diſciſſæ vt arena, <lb></lb>vel ſint agglutinatæ rotæ ſolidæ, propterea quòd id <lb></lb>ipſum ſymptoma particulis duriſſimæ rotæ competit. <lb></lb></s> <s id="s.001527">Si verò <expan abbr="circũducta">circunducta</expan> rota particula A relicto orbe AHE <lb></lb>excurrit per tangentem rectam AM, aut curuam ſpi<lb></lb>ralem AN euidentiſſimum ſignum erit particulam A <lb></lb>non eſſe annexam, & vnitam, ſed diuiſam à rota ſo<lb></lb>lida, quia continentèr à centro D magis, & magis re<lb></lb>mouetur vt in N, vel M. </s> </p> <p type="margin"> <s id="s.001528"><margin.target id="marg389"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001529">Præterea ſi particulæ eamdem à centro <expan abbr="diſtantiã">diſtantiam</expan> <lb></lb>retinuerint, & eodem tempore, quo rota integram̨ <lb></lb>reuolutionem BFB abſoluit, alia particula A, vel <lb></lb>maius, vel minus ſpatium, quàm circulum AEA per<lb></lb>ſicit, ſcilicèt percurrit arcum AEH, vel AEO, tunc <lb></lb>euidentèr conſtat particulam A non eſſe agglutina<lb></lb>tam, ſed diuiſam à rota ſolida. </s> </p> <p type="main"> <s id="s.001530">Similitèr in motu directo aggregati AEH, ſi eius <lb></lb>particulæ inæqualibus velocitatibus feruntur, ſcili-<pb pagenum="292" xlink:href="010/01/300.jpg"></pb><arrow.to.target n="marg390"></arrow.to.target><lb></lb>cèt dum A pertranſit rectam lineam AB alia pars E <lb></lb>excurrit rectam lineam EC minorem quàm AB, & alia <lb></lb>pars H excurrit ſpatium HD minùs, <lb></lb><figure id="id.010.01.300.1.jpg" xlink:href="010/01/300/1.jpg"></figure><lb></lb>quàm EC euidentiſſimum <expan abbr="ſignũ">ſignum</expan> erit <lb></lb>tales particulas A, E, H, diuiſas in<lb></lb>ter ſe eſſe. </s> </p> <p type="margin"> <s id="s.001531"><margin.target id="marg390"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001532">Hinc generaliſſima regula elici <lb></lb>poteſt, quòd <expan abbr="quotieſcũque">quotieſcunque</expan> aggre<lb></lb>gatum corporum mouetur motu di<lb></lb>recto, & eius partes inæqualibus ve<lb></lb>locitatibus feruntur, aut itinera non <lb></lb>ſunt æqui diſtantia. </s> <s id="s.001533">Vel ſi motu circulari circa <expan abbr="centrũ">centrum</expan> <lb></lb>D agitatur, omnes eius particulæ ſpiras vt AN de<lb></lb>ſcribunt, vel ſi circulos pertranſeant velocitates eo<lb></lb>rum proportionales non ſunt diſtantijs à centro: vel <lb></lb>è contra ſemper tardiores ſunt quò magis à <expan abbr="cẽtro">centro</expan> re<lb></lb>cedunt, vt ſi particula C verè tardiori motu feratur, <lb></lb>quàm D, & adhùc B tardiori, quàm C, & ſic reliquæ <lb></lb>omnes, procùl dubio ex qualibet ex prædictis inæ<lb></lb>qualitatibus euincitur particulas prædictum aggre<lb></lb>gatum componentes omninò inter ſe diſcretas, & di<lb></lb>uiſas eſſe, propterea quod hi motus non competunt, <lb></lb>nec aptari poſſunt partibus corporis continui conſi<lb></lb>ſtentis, & duri. </s> </p> <p type="main"> <s id="s.001534"><emph type="center"></emph>PROP. CXXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001535"><emph type="center"></emph><emph type="italics"></emph>Fluidi corporis partes diuiſæ inter ſe <lb></lb>eſſe debent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="293" xlink:href="010/01/301.jpg"></pb><arrow.to.target n="marg391"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001536"><margin.target id="marg391"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001537">HIs poſitis animaduerto quòd quotieſcumquę <lb></lb>corpus aliquod fluidum eſſe ſupponitur, neceſ<lb></lb>sè eſt, vt eius partes actu diuiſæ inter ſe ſint; quia flui<lb></lb>dum habere debet naturalem conformationem di<lb></lb>ſpoſitionem, & omnia requiſita vt elicere poſſit <expan abbr="illũ">illum</expan> <lb></lb>motum, quem fluxionem vocamus, ſcilicèt ſi vną <lb></lb>eius pars moueri queat cæteris quieſcentibus, vel ſi <lb></lb>omnes mouentur, percurrant motu directo inæqualia <lb></lb>ſpatia, vel ſi circularitèr ferantur, maiorem, vel mi<lb></lb>norem proportionem vertigines habeant, quam di<lb></lb>ſtantiæ à centro reuolutionis; hæ enim motiones ef<lb></lb>fici nequeunt, niſi partes fluidi actu inter ſe diuiſæ <lb></lb>ſint, vt mox <expan abbr="oſtẽſum">oſtenſum</expan> fuit, igitur quotieſcumque cor<lb></lb>pus aliquod fluidum eſſe ſupponitur, neceſſariò par<lb></lb>tes eius actu inter ſe diuiſæ erunt. </s> </p> <p type="main"> <s id="s.001538"><emph type="center"></emph>PROP. CXXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001539"><emph type="center"></emph><emph type="italics"></emph>Fluidum non poteſt habere partes connexas vnvm con<lb></lb>tinuum conſtituentes.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001540">PRæterea ſi partes fluidi non eſſent diuiſæ actu, <lb></lb>ſcilicèt ſi aqua haberet omnes eius partes planè <lb></lb>connexas, & conglutinatas vnum continuum conſti<lb></lb>tuentes, atque hæ motu directo, vel circulari moue<lb></lb>rentur intra fluidum ſui generis, ſcilicèt intrà aquam <lb></lb>ſtagnantem, cum eius particulæ minimæ eamdem in<lb></lb>uariabilem diſpoſitionem, ſituationem, ac texturam <lb></lb>retinere <expan abbr="debeãt">debeant</expan>, ac ſi partes alicuius duri corporis, <lb></lb>vel rotæ ſolidæ eſſent, procùl dubio eodem tempore </s> </p> <pb pagenum="294" xlink:href="010/01/302.jpg"></pb> <p type="main"> <s id="s.001541"><arrow.to.target n="marg392"></arrow.to.target><lb></lb><expan abbr="deſcriberẽt">deſcriberent</expan> rectas lineas æquales, vel orbes inæqua<lb></lb>les, & creſcentes in eadem proportione, quam <expan abbr="diſtã-tiæ">diſtan<lb></lb>tiæ</expan> à centro, ſeu axe firmo habent, nec aliter contin<lb></lb>gere aliquando poſſet. </s> <s id="s.001542">At quia conſtat non <expan abbr="vniuersã">vniuersam</expan> <lb></lb>aquam lacus directè æquali motu moueri, vel conuer<lb></lb>ti vnà cum interna illa portione translata, vel circum<lb></lb>ducta, ſed videmus, quòd remotiſſimæ partes placi<lb></lb>dè omninò quieſcunt, dum intermediæ excurrunt, <lb></lb>vel rotantur velociſſimo motu, nec à maxima veloci<lb></lb>tate internarum partium prædicti corporis, vel fluidę <lb></lb>rotæ immediatè tranſitur ad partes fluidi remotiores <lb></lb>prorsùs quieſcentes, quæ officium vaſis ſuppleant, <lb></lb>ſed vt videre eſt in aqua turbida, & in aere fumoſo <lb></lb>tranſitur ordinato decremento ab aquæ partibus ve<lb></lb>lociſſimè directo motu agitatis, vel reuolutis per mi<lb></lb><arrow.to.target n="marg393"></arrow.to.target><lb></lb>nùs veloces gradatim, quouſque ad extimas quie<lb></lb>ſcentes perueniatur; non igitur aqua habere poterit <lb></lb>partes connexas vnum continuum conſtituentes. </s> <s id="s.001543">His <lb></lb>præmiſſis deuenio ad propoſitionem principalem. </s> </p> <p type="margin"> <s id="s.001544"><margin.target id="marg392"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001545"><margin.target id="marg393"></margin.target>Ex pro 137.</s> </p> <p type="main"> <s id="s.001546"><emph type="center"></emph>PROP. CXL.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001547"><emph type="center"></emph><emph type="italics"></emph>Partes fluidum corpus primum componentes <lb></lb>fluidæ non ſunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001548">SI enim hoc verum non eſt, minimæ particulæ, ex <lb></lb>quibus fluidum conſtat, ſint ſemper fluidæ, ſi fie<lb></lb>ri poteſt, ergo diuidendo corpus fluidum indeſinen<lb></lb>tèr, & infinitè numquam deueniemus ad minimam̨ <lb></lb>eius particulam, quæ fluida non ſit, ſed ſemper flui-<pb pagenum="295" xlink:href="010/01/303.jpg"></pb><arrow.to.target n="marg394"></arrow.to.target><lb></lb>da erit. </s> <s id="s.001549">Et quia fluidum catenùs motum, quem fluxio<lb></lb>nem vocamus, elicere poteſt, ſcilicèt catenus fluidum <lb></lb>eſt quatenùs eius aliquæ partes mouentur cæteris <lb></lb>quieſcentibus, vel diuerſis, & inæqualibus motibus <lb></lb>agitantur ab ijs, qui competunt duris, & continuis <lb></lb>corporibus; ergò ad hoc, vt nulla particula corporis <lb></lb>fluidi care at hac paſſione fluiditatis; oportet vt ſem<lb></lb>per ei conueniat fluiditatis definitio, ſcilicèt ſemper <lb></lb>quælib et eius pars moueri poſſit cæteris quieſcenti<lb></lb>bus, vel inæqualibus motibus agitentur, quàm ſint il<lb></lb>li, qui duris, & continuis corporibus competunt. </s> <s id="s.001550">Sed <lb></lb>partes contiguæ eiuſdem maſſæ non poſſunt partim <lb></lb>moueri, partim quieſcere, vel inæqualibus motibus <lb></lb>agitari diuerſo modo, ac continuis corporibus <expan abbr="cõ-">con<lb></lb></expan><arrow.to.target n="marg395"></arrow.to.target><lb></lb>petit, niſi inter ſe ſint diuiſæ, & diſcretæ; igitur nul<lb></lb>la particula fluidi corporis quantumuis exigua aſſi<lb></lb>gnari poteſt, quæ actu diſſecta, & ſubdiuiſa non ſit in <lb></lb>plures alias particulas; qua propter nunquam perue<lb></lb>niri poterit ad finem enumerationis multitudinis par<lb></lb>tium eius, & ideò talis multitudo maior erit <expan abbr="quocũ-que">quocun<lb></lb>que</expan> numero, ſcilicèt maior quacumque quantitatę <lb></lb>finita, ergo infinita erit; at infinitæ partes actu diui<lb></lb><arrow.to.target n="marg396"></arrow.to.target><lb></lb>ſæ ſi eſſent quantæ ſiue inter ſe æquales, ſiue non, effi<lb></lb>cerent <expan abbr="extẽſionem">extenſionem</expan> in finitam, ergò ſphęra fluida pal<lb></lb>maris eſſet infinitæ magnitudinis, quod eſt falſum̨, <lb></lb>igitur non quantæ, ſed indiuiſibilia puncta erunt; hoc <lb></lb><arrow.to.target n="marg397"></arrow.to.target><lb></lb>verò eſt quoque impoſſibile, cùm infinita puncta ex<lb></lb>tenſionem quantam nequeant componere: ergò fal<lb></lb>ſum eſt, quòd minimæ particulæ ex quibus fluidum̨ <pb pagenum="296" xlink:href="010/01/304.jpg"></pb><arrow.to.target n="marg398"></arrow.to.target><lb></lb>conſtat, & in quas diuidi poteſt, ſint ſemper fluidæ, <lb></lb>quod erat oſtendendum. </s> </p> <p type="margin"> <s id="s.001551"><margin.target id="marg394"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001552"><margin.target id="marg395"></margin.target>Prop. 138.</s> </p> <p type="margin"> <s id="s.001553"><margin.target id="marg396"></margin.target>Prop. 135. & <lb></lb>136.</s> </p> <p type="margin"> <s id="s.001554"><margin.target id="marg397"></margin.target>Prop. 134.</s> </p> <p type="margin"> <s id="s.001555"><margin.target id="marg398"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001556">Hinc deducitur, quòd corpus fluidum componitur <lb></lb>ex minimis particulis non fluidis. </s> </p> <p type="main"> <s id="s.001557"><emph type="center"></emph>PROP. CXLI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001558"><emph type="center"></emph><emph type="italics"></emph>Idem aliter demonſtrare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001559">SI enim hoc verum non eſt, ſcilicèt ſi particulæ a<lb></lb>quam fluidam componentes ſemper fluidæ ſunt, <lb></lb>igitur diuidi ſemper poterit aqua ſucceſſiuè, & iņ <lb></lb>infinitum in particulas, quæ ſemper fluidæ ſint, hoc <lb></lb><arrow.to.target n="marg399"></arrow.to.target><lb></lb>tamen primò repugnat ipſimet Ariſtoteli, qui negat <lb></lb>contra Anaxagoram poſſe quodlibet corpus natura<lb></lb>le retinere eandem <expan abbr="naturã">naturam</expan> ſi ſemper magis, ac magis <lb></lb>per continuam diuiſionem ad exiguas & minimas <lb></lb>particulas reducatur; ſic diuiſa animalis carne deue<lb></lb>nietur tandem ad particulas, quæ non ampliùs carnes <lb></lb>ſint; ſic paritèr, vt habent eius expoſitores in elemen<lb></lb>tis facta conſimili diuiſione ſucceſſiua, tandem minu<lb></lb>tiſſimæ particulæ non ampliùs elementarem naturam <lb></lb>retinebunt. </s> <s id="s.001560">Hinc igitur licet inferre quòd fluido a<lb></lb>queo in infinitum ſucceſſiuè diuiſo deuenietur tan<lb></lb>dem ad particulas eius, quæ fluidæ non ſint, ſcilicèt <lb></lb>cuius vna particula non poſſit moueri quieſcentibus <lb></lb>reliquis, & propterea omnes ſimùl vnico motu agita<lb></lb>ri poterunt, ſcilicet conſiſtentiam ſolidam haberę <lb></lb>neceſsè eſt. </s> </p> <p type="margin"> <s id="s.001561"><margin.target id="marg399"></margin.target>Phyſ lib. 1 <lb></lb>cap. 4.</s> </p> <p type="main"> <s id="s.001562">Sed relicta Ariſtotelis, & Peripateticorum autho-<pb pagenum="297" xlink:href="010/01/305.jpg"></pb><arrow.to.target n="marg400"></arrow.to.target><lb></lb>ritate perpendamus rationis vim, & energiam. </s> <s id="s.001563">Si ve<lb></lb>rum eſt aquam fluidam quomodocumque diuiſam, & <lb></lb>ſubdiuiſam ſemper fluiditatem retinere, igitur ſem<lb></lb>per hiſce poſtremis particulis fluidis definitio fluidi<lb></lb>tatis ſuperiùs tradita competet, ſcilicèt aliqua mi<lb></lb>nor particula <expan abbr="eiuſdẽ">eiuſdem</expan> particulæ moueri poterit quie<lb></lb>ſcentibus collateralibus partibus. </s> <s id="s.001564">His poſitis, quią <lb></lb>corpora omnia ſublunaria innumeris poris, & forami<lb></lb>nulis peruia ſunt, ſequitur quòd aqua omnia corpora <lb></lb>concreta penetraret, nam concipiamus quemlibet <lb></lb>porum ſtrictiſſimum in vaſe ligneo, vitreo, vel metal<lb></lb>lico, certum eſt quòd portio aquea foraminulo præ<lb></lb>dicto ſuperpoſita cui adæquatur, dimenſionem, & <lb></lb>quantitatem habet æqualem amplitudini foraminis, <lb></lb>& iuxtà quantitatis naturam ſemper diuiſibilem po<lb></lb>terunt concipi particulæ centrales, & ſtrictiores, <expan abbr="quã">quam</expan> <lb></lb>ſit amplitudo eiuſdem pori, quæ particulæ aquæ <expan abbr="cẽ-trales">cen<lb></lb>trales</expan> cùm poſſint moueri quieſcentibus collaterali<lb></lb>bus, vt ſuperiùs expoſita fluidi natura exigit, ergo ne<lb></lb>ceſſariò per amplitudinem pori liberè excurrere po<lb></lb>terunt, & proindè nullum vas reperietur, per quod <lb></lb>aqua penetrare queat: & aduertendum eſt, quòd à <lb></lb>qualibet exigua vi motiua impelli, & inſinuari poſſet <lb></lb>aqua per prædictas poroſitates, ſcilicèt à vi ſuæ pro<lb></lb>priæ grauitatis, ſeù à quacumque alia vi eam <expan abbr="inſufflã-te">inſufflan<lb></lb>te</expan>, vel impellente, vt poſteriùs oſtendemus; hoc au<lb></lb>tem eſt euidenter falſum, cùm aqua communis, aut <lb></lb>ſpiritus vini ſubtiliſſimus vitri poroſitates penetrare <lb></lb>non poſſit, licèt <expan abbr="violẽtèr">violentèr</expan> impellatur, igitur falſum eſt, <pb pagenum="298" xlink:href="010/01/306.jpg"></pb><arrow.to.target n="marg401"></arrow.to.target><lb></lb>fluidum diuidi poſſe in infinitum in partes ſemper <lb></lb>fluidas; qua propter neceſsè eſt, vt tandem diuiden<lb></lb>do perueniamus ad particulas aquę, quę non ampliùs <lb></lb>fluidæ ſint, ſcilicèt in quibus non vale at moueri vną <lb></lb>eius minima particula quieſcentibus collateralibus, <lb></lb>proindeque illæ poſtremæ fluidi particulæ erunt <expan abbr="cõ-fiſtentes">con<lb></lb>ſiſtentes</expan>, quod erat oſtendendum. </s> </p> <p type="margin"> <s id="s.001565"><margin.target id="marg400"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001566"><margin.target id="marg401"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001567">Quòd verò à valdè exigua vi impelli poſſit aquą <lb></lb>per vitri poroſitates, patet ex eo, quòd videmus præ<lb></lb>longam trabem ſuper aquam ſtagnantem <expan abbr="poſitã">poſitam</expan> <expan abbr="trãſ-uersè">tranſ<lb></lb>uersè</expan> trahi poſſe à vi exigui capilli, igitur illa exigua <lb></lb>vis motiua ſuperare poreſt reſiſtentiam tot partium̨ <lb></lb>aquæ quot aſſignari poſſunt in prædicta amplitudine <lb></lb>trabis. </s> <s id="s.001568">Vnde conijcitur, quòd vis, quæ requiritur ad <lb></lb>impellendam paruam, & acutam feſtucam natantem <lb></lb>debeat eſſe ferè inſenſibilis ob eius maximam minu<lb></lb>tiem, & tamen à tam minima vi mouetur vna aquæ <lb></lb>particula non motis collateralibus, & proptereà vis <lb></lb>huic æqualis ſufficiens eſt ſu perare tenacitatem, qua <lb></lb>aquæ particulæ colligantur, vniunturque, erit igitur <lb></lb>energia tenacitatis partium aquæ minimi, & exigui <lb></lb>roboris, & propterea ſuperari poterit à puſilla vi im<lb></lb>pulſiua. </s> </p> <p type="main"> <s id="s.001569">Nec obſtat, quòd aqua communis non ſit omninò <lb></lb>ſincera, & abſque mixtura partium terreſtrium, & ſo<lb></lb>lidarum, nam licèt hoc verum ſit, nihilominùs negari <lb></lb>non poſſunt partes puræ aquæ, quæ inter minutiſſima <lb></lb>fragmenta terreſtria intercedunt, & ex ſui natura <expan abbr="cũ">cum</expan> <lb></lb>ſint fluidę, poſſent quidem penetrare interſtitia inter <pb pagenum="299" xlink:href="010/01/307.jpg"></pb><arrow.to.target n="marg402"></arrow.to.target><lb></lb>arenulas commixtas cum ipſam et aqua, imò <expan abbr="earũdẽ">earundem</expan> <lb></lb>arenularum poroſitates pertranſire valerent. </s> </p> <p type="margin"> <s id="s.001570"><margin.target id="marg402"></margin.target>Cap, 7. de <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001571">Nec præterea obſtat, quòd poroſitates vitri, aut <lb></lb>metalli non ſint directæ, ſed miris modis contortæ, & <lb></lb><arrow.to.target n="marg403"></arrow.to.target><lb></lb>anfractuoſæ, nec ſemper eiuſdem amplitudinis, nam <lb></lb>nihilominùs vetari, & impediri non poſſet tranſitus <lb></lb>fluentis aquæ, ſaltem tardiori motu, longiorique <expan abbr="tẽ-pore">ten<lb></lb>pore</expan>, quàm ſi per poroſitates directas, & æquè latas <lb></lb>pertranſire debuiſſet. </s> <s id="s.001572">Hoc autem cùm non contin<lb></lb>gat, ſcilicèt aqua intra vas vitreum diù incluſa num<lb></lb>quam exudet, concedendum eſt, minimas eius parti<lb></lb>culas non fluidas, ſed conſiſtentes eſſe. </s> </p> <p type="margin"> <s id="s.001573"><margin.target id="marg403"></margin.target>Licèt poroſi<lb></lb>tates cuius<lb></lb>libet corpo<lb></lb>ris ſint tor<lb></lb>tuoſæ tamen <lb></lb>à fluido per<lb></lb>meari poſ<lb></lb>ſunt.</s> </p> <p type="main"> <s id="s.001574">Quòd verò pori cuiuslibet vaſis permeabiles om<lb></lb>ninò ſint, nec viæ obturamentis impediantur, occlu<lb></lb>danturque, probari ſatis poteſt ex eo quod per eos <lb></lb>aliqua fluida penetrant, vt hydrargyrum per poros <lb></lb>auri, aqua, oleum, & hydrargyrum quoque per po<lb></lb>ros ligni, & vaſis fictilis, quare per eoſdem reliqua <lb></lb>omnia fluida neceſſariò pertranſire, & fluere debe<lb></lb>rent, ſaltèm tardiori motu, ſi verum eſt, quòd nulla <lb></lb>fluidi pars aſſignari poteſt, quæ paritèr fluida non <lb></lb>ſit; deberet igitur aer effluere è vaſe fictili, & ligneo <lb></lb>quotieſcumque violentèr <expan abbr="immiſſusibidẽ">immiſſus ibidem</expan> <expan abbr="cõdenſatur">condenſatur</expan>. </s> </p> <p type="main"> <s id="s.001575"><emph type="center"></emph>PROP. CXLII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001576"><emph type="center"></emph><emph type="italics"></emph>Ad fluidi conſtitutionem requiritur omnium partium diuiſio <lb></lb>in minimas particulas, talis figuræ, vt vna ſuper alte<lb></lb>ram facilè fluere posſit, & omnes æqualem vim <lb></lb>motiuam grauitatis habeant.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="300" xlink:href="010/01/308.jpg"></pb><arrow.to.target n="marg404"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001577"><margin.target id="marg404"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001578">SI modò philoſophari velimus non iuxtà homi<lb></lb>num placita, ſed <expan abbr="ſecũdùm">ſecundùm</expan> naturæ leges, quatuor <lb></lb>conditiones neceſſariæ eſſe videntur ad fluidi conſti<lb></lb>tutionem. </s> <s id="s.001579">Primùm vt ſit corpus diuiſum, & ſub diui<lb></lb>ſum in exiguas, & minimas particulas. </s> <s id="s.001580">Secundò vt <lb></lb>eius figuræ ad orbicularem formam quam proximè <lb></lb>accedant. </s> <s id="s.001581">Tertiò vt harum ſuperficies, vel ſint per<lb></lb>fectiſſimè lęuigatæ ad <expan abbr="modũ">modum</expan> ſpeculi, vel <expan abbr="ſaltẽ">ſaltem</expan> facilli<lb></lb>mè vna ſuper <expan abbr="alterã">alteram</expan> excurrere, & fluere poſſit. </s> <s id="s.001582">Et <expan abbr="tãdẽ">tandem</expan> <lb></lb>oportet vt omnes habeant <expan abbr="æqualẽ">æqualem</expan> vim motiuam qua <lb></lb>deorsùm tendant, ſcilicèt ſint æquè graues; Poſſent <lb></lb>hæc omnia (licèt rudi exemplo) non ineptè confir<lb></lb>mari ſumptis pluribus globulis cryſtallinis, <expan abbr="poſitiſq;">poſitiſque</expan> <lb></lb>in aliquo vaſe, primò prædicti globuli ad ſigaram̨ <lb></lb>vaſis adaptantur, & ſi manus vſque ad fundum vaſis <lb></lb>immittatur, tunc globuli prædicti locum cedunt, & ad <lb></lb>latera excurrunt, præterea poterit moueri vna, vel al<lb></lb>tera pila cryſtallina, quieſcentibus pilis collaterali<lb></lb>bus, vel parum motis; inſuper poſt agitationem ex<lb></lb>planarentur prædicti globuli, non enim aceruum, aut <lb></lb>montem efficerent, veluti grana frumenti, aut arenæ, <lb></lb>ſed ob eorum læuitatem facilè excurrerent deſcende<lb></lb>rentque versùs infima loca, & ſic ſuprema ſuperficies <lb></lb>explanaretur, & proximè horizonti æquidiſtantèr <lb></lb>diſponeretur. </s> <s id="s.001583">Si poſtea prædictæ ſphærulæ cryſtalli<lb></lb>næ magis exiguæ, & minutæ eſſent, tunc multò faci<lb></lb>liùs prædictæ operationes efficerentur, & ſi tandèm <lb></lb>ad ineffabilem paruitatem redigerentur, non poſſent <lb></lb>neque tactu neque viſu percipi, ſed apparentem con-<pb pagenum="301" xlink:href="010/01/309.jpg"></pb><arrow.to.target n="marg405"></arrow.to.target><lb></lb>tinuitatem repręſentarent, vt contingit in minutiſſi<lb></lb>mo puluere; & tunc quidem haberi poſſent effectus <lb></lb>omnes fluiditatis, & <expan abbr="tamẽ">tamen</expan> maſſa illa eſſet <expan abbr="aggregatũ">aggregatum</expan> ex <lb></lb>innumeris globulis cryſtallinis duris, & <expan abbr="cõſiſtentibus">conſiſtentibus</expan>. </s> </p> <p type="margin"> <s id="s.001584"><margin.target id="marg405"></margin.target>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001585">Sed audax quædam ſententia, quæ hiſce tempori<lb></lb><arrow.to.target n="marg406"></arrow.to.target><lb></lb>bus viget, meretur vt aliquantiſper in eius examinę <lb></lb>immoremur; concedunt enim fluidum componi ex <lb></lb>particulis diuiſis, exiguis, lęuigatiſque, ſed aiunt pal<lb></lb>mariam eius conditionem eſſe, vt particulæ quibus <lb></lb>conſtat, diuerſimodè agitentur, ſiue motus ille ſit ijs <lb></lb>connatus, ſiue per ſubtiliorem quamdam ſubſtantiam <lb></lb>ſuo tranſitu ipſas quaqua verſum <expan abbr="voluentẽ">voluentem</expan> efficiatur. </s> </p> <p type="margin"> <s id="s.001586"><margin.target id="marg406"></margin.target>Carteſius <lb></lb>putat præci<lb></lb>puam fluidi <lb></lb><expan abbr="conditionẽ">conditionem</expan> <lb></lb>eſſe vt om<lb></lb>nes elus par<lb></lb>tes inteſtino <lb></lb>motu <expan abbr="agitẽ-tur">agiten<lb></lb>tur</expan>.</s> </p> <p type="main"> <s id="s.001587">Duæ præcipuæ rationes afferuntur ad huius <expan abbr="ſentẽ-tiæ">ſenten<lb></lb>tiæ</expan> confirmationem, prima eſt, quia videmus in me<lb></lb><arrow.to.target n="marg407"></arrow.to.target><lb></lb>tallorum fuſione ab ignis violentia minimas particu<lb></lb>las metallicas verè agitari, idemque obſeruatur iņ <lb></lb>cera, & in reliquis alijs corporibus, quæ ab actionę <lb></lb>ignis fluida rediguntur, & profectò euidens eſt iņ <lb></lb>aqua feruente quod per lebetis poroſitates igneæ <lb></lb>exhalationes penetrantes efficiunt innumeras ſphę<lb></lb>rulas velociſſimo motu <expan abbr="excurrẽtes">excurrentes</expan> per ipſam aquam, <lb></lb>hinc ſuſpicari licet ab illa vehementi ebullitionę <lb></lb>fluxilitatem pendere, & licèt aliquando huiuſmodi <lb></lb>bullæ intra fluidum non conſpiciantur, imò corpus fu<lb></lb>ſum ſummè tranquillum, & placidum conſpiciatur, <lb></lb>vt in plumbo fuſo videre eſt, nihilominùs quia moles <lb></lb>plumbi, à fuſione valdè augetur, & inſuper ab eo fu<lb></lb>mi egredientes non paucas plumbi partes tranſpor<lb></lb>tant, manifeſtè euincitur fuſum plumbum continuè <pb pagenum="302" xlink:href="010/01/310.jpg"></pb><arrow.to.target n="marg408"></arrow.to.target><lb></lb>agitari, eiuſdemque partes varijs modis contorqueri <lb></lb>ac moueri. </s> </p> <p type="margin"> <s id="s.001588"><margin.target id="marg407"></margin.target>Hoc primò <lb></lb>probant ex <lb></lb>metallorum <lb></lb>fuſione.</s> </p> <p type="margin"> <s id="s.001589"><margin.target id="marg408"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001590">Secunda ratio deſumitur ex fermentatione; ſi enim <lb></lb><arrow.to.target n="marg409"></arrow.to.target><lb></lb>grana aliqua ſalis in fundo aquæ demergantur, aut <lb></lb>quælibet alia materia diſſolubilis, & fermentabilis, <lb></lb>videmus, quòd citò vniuerſam aquam ſapor, & tinctu<lb></lb>ra illius fermenti inficit, & alterat, hoc autem minimè <lb></lb>fieri poſſet, niſi particulæ ſalinæ <expan abbr="tranſportarẽtur">tranſportarentur</expan> per <lb></lb>vniuerſam aquam, quod abſque agitatione partium <lb></lb>eiuſdemmet aquæ nullo modo fieri poſſet. </s> </p> <p type="margin"> <s id="s.001591"><margin.target id="marg409"></margin.target>Secundò ex <lb></lb>ſalium fuſi<lb></lb>one in aqua.</s> </p> <p type="main"> <s id="s.001592"><emph type="center"></emph>PROP. CXLIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001593"><emph type="center"></emph><emph type="italics"></emph>Minutiſsimæ Corporum particulæ ab inuicem diuiſæ <lb></lb>læues, & facilè amouibiles, licèt omninò <lb></lb>quieſcant, duritiem creare non <lb></lb>poſſunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001594">ET profectò poſito, quòd corpus diuiſum ſit iņ <lb></lb>exiguas, & minimas particulas, ſi prædictæ par<lb></lb>tes diuerſimodè reuolutæ, & agitatæ fuerint, negari <lb></lb>non poteſt eas apparentiam fluidam repręſentare; <lb></lb>ſed non proinde oppoſitum verificatur, ſcilicèt quòd <lb></lb>quotieſcumque deeſt agitatio, & motus minimarum <lb></lb><expan abbr="partiũ">partium</expan> alicuius aggregati, idipſum ſit corpus durum, <lb></lb>& conſiſtens (vt apertè fatentur aliqui recentiores) <expan abbr="nã">nam</expan> <lb></lb>præcipua, & propria paſſio corporis duri non eſt eą <lb></lb>quam Carteſius affert, ſcilicet quòd omnes eius parti<lb></lb>culæ quieſcant in eodem ſitu in quo degunt; & ratio <lb></lb>eſt, quia talis paſſio non conuenit ſolummodò corpo-<pb pagenum="303" xlink:href="010/01/311.jpg"></pb><arrow.to.target n="marg410"></arrow.to.target><lb></lb>ribus duris, cum arenæ particulæ quieſcant, nec <expan abbr="tamẽ">tamen</expan> <lb></lb>cumulum ſolidum, & durum efficiant. </s> <s id="s.001595">Ex eo igitur, <lb></lb>quod videmus in corpore duro vnam eius partem̨ <lb></lb>moueri non poſſe quieſcentibus collateralibus, planè <lb></lb>deducitur, quòd non ſufficit ſimplex contactus par<lb></lb>tium immotarum, ſed præterea neceſſe eſt, vt ſint ad <lb></lb>inuicem connexæ, & agglutinatæ, vt firmitudinem, & <lb></lb>duritiem creare poſſint. </s> <s id="s.001596">& ſanè ſi reuerà corpus ſub<lb></lb>diuiſum fuerit in minutiſſimas particulas rotundas, <lb></lb>aut ad rotunditatem proximè accedentes, & careant <lb></lb>omni ſcabritie, ſintque omnes æquè graues, & in qui<lb></lb>ete conſtitutæ, tunc eſt impoſſibile, vt prædictum ag<lb></lb>gregatum durum, & conſiſtens ſit, nec poterit ſuſti<lb></lb>neri, vt arena in accliui, & <expan abbr="mõtuoſa">montuoſa</expan> eleuatione, prop<lb></lb>terea quod particularum figuræ rotundæ, & lęuigatæ <lb></lb>non poſſunt vetare excurſum, atque deſcenſum par<lb></lb>tium earundem grauium, & proindè neceſſe eſt vt ex<lb></lb>planentur, nec vna eius pars maiorem eleuationem̨ <lb></lb>ſupra planitiem horizontis habere poterit, quàm a<lb></lb>lia; præterea quodlibet corpus conſiſtens intra præ<lb></lb>dictum aggregatum demerſum ſi vim compreſſiuam, <lb></lb>ſeù grauitatem maiorem habuerit, quàm particulæ <lb></lb>illæ ſub diuiſæ, facilè poterunt impelli, ac eleuari ſu<lb></lb>pra eius libellam, & ob earum rotunditatem, & lęui<lb></lb>tatem nullo negotio excurrere circa corpus <expan abbr="demersũ">demersum</expan> <lb></lb>poſſunt, idque omni ex parte contingere, atque ad <lb></lb><arrow.to.target n="marg411"></arrow.to.target><lb></lb>eius figuram accommodari. </s> </p> <p type="margin"> <s id="s.001597"><margin.target id="marg410"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001598"><margin.target id="marg411"></margin.target><expan abbr="Argumentũ">Argumentum</expan> <lb></lb>contra ſupe<lb></lb>riorem do<lb></lb>ctrinam.</s> </p> <p type="main"> <s id="s.001599">Sed videamus qua ratione ingenioſiſſimus Author <lb></lb>neotericus hanc ſententiam confirmare nitatur, quòd <pb pagenum="304" xlink:href="010/01/312.jpg"></pb><arrow.to.target n="marg412"></arrow.to.target><lb></lb>nimirum particulæ aquæ glacialis virtute ſimplicis <lb></lb>earum quietis fluiditatem amittant; ait ipſe: <emph type="italics"></emph>multò fa<lb></lb>ciliùs moueri poſſe corpus quodlibet in motu constitutum, <expan abbr="quã">quam</expan> <lb></lb>ſi quieſcens, & stabile eſſet, quia in primo caſu non est neceſ<lb></lb>sè, vt producatur, vel creetur motus, cui corpus quodlibet ob <lb></lb>naturalem ſuam inertiam reſistit, ſed <expan abbr="tãtummodò">tantummodò</expan> vt mo<lb></lb>tus ipſe hactenùs existens, & vigens in eodem corpore diri<lb></lb>gatur.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="s.001600"><margin.target id="marg412"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001601"><emph type="center"></emph>PROP. CXLIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001602"><emph type="center"></emph><emph type="italics"></emph>Motus, & impetus non faciliùs imprimitur in corpus agi<lb></lb>tatum, quàm quieſcens, ſi tamen eius quies <lb></lb>fuerit amouibilis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001603">AT ipſe in hoc ei aſſentiri nullo modo poſſum, <lb></lb>nam licèt verum eſſet, quòd faciliùs impelli <lb></lb>poſſet corpus in motu conſtitutum, quàm quieſcens, <lb></lb>non in de ſequitur ſimplicem quietem particularum̨ <lb></lb>fluidi duritiem eius creare. </s> <s id="s.001604">nam videmus arenæ cu<lb></lb>mulum ſolummodò acquirere conſiſtentiam, & duri<lb></lb>tiem, quando glutine, vel arctiſſima vnione, & angu<lb></lb>lorum mutua inſinuatione connectuntur eius grana, <lb></lb>vt in pauimento contingit, non verò quando arenæ <lb></lb>particulę diſſolutæ placidiſſima quiete ſe mutuò tan<lb></lb>gunt, igitur eodem modo aquæ particulæ læues, diſ<lb></lb>ſolutæ, tranquilliſſima quiete ſe mutuò tangentes <expan abbr="nõ">non</expan> <lb></lb>efficient duram, & rigidam connexionem glacialem. <lb></lb></s> <s id="s.001605">Prætereà ſi corpus aliquod in quiete amouibili fuerit <lb></lb>conſtitutum, ſcilicèt ſi indifferens fuerit ad motum̨ <pb pagenum="305" xlink:href="010/01/313.jpg"></pb><arrow.to.target n="marg413"></arrow.to.target><lb></lb>quemlibet, & ad quietem non difficiliùs nouus mo<lb></lb>tus ei imprimitur, quando quieſcit, quàm quando <lb></lb>actu mouetur. </s> <s id="s.001606">hoc autem <expan abbr="oſtẽſum">oſtenſum</expan> fuit in noſtro Ope<lb></lb>re de Vi Percuſſionis: Imò ſi velimus philoſophari <lb></lb>iuxtà ſenſus euidentiam, multoties experimur, quòd <lb></lb>maiori difficultate imprimitur nouus motus in eo cor<lb></lb>pore, quod actualitèr mouetur, <expan abbr="quã">quam</expan> ſi in quiete amo<lb></lb>uibili conſtitutum fuiſſet, & hoc conſtat hac ratione: <lb></lb>quia aut motus, qui de nouo imprimi debet, ab im<lb></lb>pellente vergit, ac tendit ad eaſdem partes ad quas <lb></lb>corpus mobile ferebatur, aut ad partes oppoſitas, vel <lb></lb>tranſuersè; & patet, quod in his multò difficiliùs im<lb></lb>primitur nouus motus, quia præter inertiam corpo<lb></lb>ris mobilis, debet quoque ſuperari reſiſtentia impe<lb></lb>tus motus contrarij, & ſic videmus, quòd difficiliùs <lb></lb>reijcimus, & repercutimus pilam aduenientem, & <lb></lb>nobis occurrentem motu contrario, quàm ſi eadem̨ <lb></lb>pila omninò motu careret, & pauimento innixa quie<lb></lb>ſceret. </s> <s id="s.001607">Si poſtea motus corporis mobilis, & mouen<lb></lb>tis fiunt versùs eaſdem partes, atque velociori motu <lb></lb>mobile, quàm mouens fertur, tunc patet adeò falſum <lb></lb>eſſe faciliùs moueri poſſe corpus illud in motu velo<lb></lb>ciori conſtitutum, quàm ſi quieſceret, vt è contrà iņ <lb></lb>quiete ab illo impelli poſſet, at in fuga non poſſet à <lb></lb>tardiore impulſore vrgeri; ſi verò gradus impetus <lb></lb>mouentis corporis maior fuerit illo quo mobile <expan abbr="ictũ">ictum</expan> <lb></lb>fugit, tunc difficiliùs, ſeu tardiùs illud mouebitur, <lb></lb>quàm ſi in quiete amouibili conſtitutum fuiſſet; nam <lb></lb>in hoc caſu percuſſio fieret ab integro gradu impetus <pb pagenum="306" xlink:href="010/01/314.jpg"></pb><arrow.to.target n="marg414"></arrow.to.target><lb></lb>impellentis corporis, in illo verò caſu impulſio fie<lb></lb>ret à diminuto gradu velocitatis eius, ſcilicèt ab ex<lb></lb>ceſſu ſupra velocitatem fugientis corporis. </s> <s id="s.001608">Prætereà <lb></lb>in corporibus concretis non omninò duris, nouus mo<lb></lb>tus imprimi non poteſt in inſtanti, ſed in tempore, vt <lb></lb>alibi oſtenſum eſt, non contactu ſimplici, ſed ſociali <lb></lb>motu mouentis, & mobilis, hoc autem faciliùs con<lb></lb>ſequi poteſt in corpore aliquo quieſcente amouibi<lb></lb>litèr, quàm ſi agitetur directè, vel tranſuersè. </s> <s id="s.001609">Hinc <lb></lb>colligitur falſum eſſe, quòd faciliùs impelli poſſet <lb></lb>corpus agitatum, quàm <expan abbr="quieſcẽs">quieſcens</expan>, ſi modò quies fue<lb></lb>rit amouibilis, vt dictum eſt. </s> <s id="s.001610">Et profectò quies illą <lb></lb>particularum cuiuslibet corporis firmi, & duri noņ <lb></lb>erit amouibilis, ſcilicèt illæ particulæ non ſunt indif<lb></lb>ferentes ad motum, cum non à qualibet exigua, & mi<lb></lb>nima vi motiua moueri, & diuelli ab integra maſſą <lb></lb>dura queant, ſed requiritur inſignis <expan abbr="violẽtia">violentia</expan> vt par<lb></lb>ticulæ aquæ glaciatæ à tota maſſa ſeparentur; ex quo <lb></lb>proinde inferre licet, quòd vt plurimùm figuræ præ<lb></lb>dictarum particularum durum corpus <expan abbr="componentiũ">componentium</expan>, <lb></lb>nec ſunt regulares, nec lęuigatæ, ſed miris modis an<lb></lb>guloſæ, ramoſæ, contortæ, & vncinatæ, & proindè <lb></lb>partes eius aſperæ, & anguloſæ ſeſe contingentes, & <lb></lb>viciſſim vna intra ſpatium alterius inſinuata, poſſunt <lb></lb>mutuò ſatis benè congruere, <expan abbr="cõponereque">componereque</expan> quaſi pa<lb></lb>uimentum, & opus teſſellatum, & ſic non poteſt vna <lb></lb>particula ex toto aggregato diuelli extrahique, noņ <lb></lb>quidem propter eius quietem, aut defectum motus, <lb></lb>ſed tantummodò quia eius concatenata ſtructura dif<lb></lb>ficilè diſ ſoluitur. <pb pagenum="307" xlink:href="010/01/315.jpg"></pb><arrow.to.target n="marg415"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001611"><margin.target id="marg413"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001612"><margin.target id="marg414"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001613"><margin.target id="marg415"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001614"><emph type="center"></emph>PROP. CXLV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001615"><emph type="center"></emph><emph type="italics"></emph>Commotio partium metalli, vel vitri, ab igne fuſi per ac<lb></lb>cidens in eis fluiditatem creat, quatenùs ſcilicèt ea<lb></lb>rum figuræ anguloſæ ab inuicem ſeparantur, & <lb></lb>ob ignis interpoſitionem poſſunt vna ſuper <lb></lb><expan abbr="alterã">alteram</expan> fluere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001616">ET reuerà quotieſcum que perpendo, quanta co<lb></lb>pia, & vehementia ignis requiritur, vt areną, <lb></lb>vitrum, ferrum, aut aliud durum metallum, in <expan abbr="formã">formam</expan> <lb></lb><expan abbr="fluidã">fluidam</expan> redigatur, haud perſuaderi poſſum particulas <lb></lb>minimas <expan abbr="horũ">horum</expan> corporum poſt diuiſionem ab igne <expan abbr="fa-ctã">fa<lb></lb>ctam</expan> reduci poſſe ad figuras regulares læuigatas, & ad <lb></lb>rotunditatem accedentes, ſed puto maximè angulo<lb></lb>ſas, aſperas, & elongatas eſſe debere, & ideò difficil<lb></lb>limè poſſe contorqueri reuoluique inter contiguas <lb></lb>ſui generis particulas. </s> <s id="s.001617">in hiſce duos effectus ignem̨ <lb></lb>producere mihi veriſimile videtur, primò, quòd <expan abbr="vnã-quamque">vnan<lb></lb>quamque</expan> partem diſſociat, atque à reliqua ſeparat <lb></lb>per aliquod ſenſibile interuallum, hocque efficitur à <lb></lb>tranſitu multiplicium, & vehementiſſimarum exhala<lb></lb>tionum, & particularum ignearum interſluentium̨, <lb></lb>virtute cuius particulæ ſolidæ arenæ eodem modo <lb></lb>ab inuicem diſgregatæ diſponuntur, ac puluis terreus <lb></lb>intra aquam infuſus, & diſperſus, qui eam lutoſam, & <lb></lb>cęnoſam reddit. </s> <s id="s.001618">Quòd verò arenæ, vel ferri fuſi par<lb></lb>ticulæ reuerà per aliquod interuallum ab inuicem di<lb></lb>ſcretæ, & ſeparatæ ſint, euincitur ex eo, quòd moles <pb pagenum="308" xlink:href="010/01/316.jpg"></pb><arrow.to.target n="marg416"></arrow.to.target><lb></lb>eiuſdem ferri, vel vitri fluentis inſignitèr augetur ſu<lb></lb>pra molem, quam idem corpus durum, & conſiſtens <lb></lb>priùs habebat; ignis ergò copioſiſſimè, & vehemen<lb></lb>tiſſimè fluens inter particulas ferri, vel vitri <expan abbr="idẽ">idem</expan> pro<lb></lb>pemodum præſtat, ac rotulæ, vel cylindri ſuper quo<lb></lb>rum rotunditatem lapides anguloſi, & figuras irre<lb></lb>gulares habentes labuntur, vel vſum præſtat ſebi, <lb></lb>vel cuiuslibet alterius corporis vnctuoſi, ope cuius a<lb></lb>renulæ aſperrimæ <expan abbr="lubricitatẽ">lubricitatem</expan> acquirere poſſunt, & v<lb></lb>na particula ſuper aliam facili negotio circumuolui, <lb></lb>agitari, ac dilabi poteſt, quod perindè eſt, ac ſi præ<lb></lb>dictæ particulæ vitri, aut ferri acquiſiuiſſent figuram <lb></lb>lęuem, rotundam, vel orbicularem ęmulantem. </s> <s id="s.001619">Ve<lb></lb>rum tamen eſt, quòd huiuſmodi operatio effici nullo <lb></lb>modo poteſt abſque commotione, vertigine, & <expan abbr="trãſ-poſitione">tranſ<lb></lb>poſitione</expan> minimarum partium metalli, vel vitri, ſed <lb></lb>non indè euincitur fluiditatem in tali caſu abſolutè <lb></lb>dependere à prædicta commotione partium, niſi ex <lb></lb>accidenti, quatenus non poſſunt ſegregari, & fluere <lb></lb>particulæ aſperæ, & anguloſæ ferri, vel vitri abſque <lb></lb>ſuperabundanti, & vehementi profluuio ignis, à quo <lb></lb>demùm particulæ ipſæ ſolidæ lubricitatem, & <expan abbr="motũ">motum</expan> <lb></lb>acquirunt. </s> <s id="s.001620">Hoc autem bellè confirmatur ab experi<lb></lb><arrow.to.target n="marg417"></arrow.to.target><lb></lb>mento adducto à doctiſſimo Roberto Boile quando <lb></lb>alabaſtri <expan abbr="puluerẽ">puluerem</expan> ab igne feruenti fluxibilitatem ac<lb></lb>quiſiuiſſe ait, at poſtmodum quælibet particula eiuſ<lb></lb>dem fluoris ſupra papyrum refrigerata reperiebatur <lb></lb>aggeries arenularum minutiſſimarum, neque concre<lb></lb>tum, & ſolidum corpus efficiebat, vt in vitro, & fer-<pb pagenum="309" xlink:href="010/01/317.jpg"></pb><arrow.to.target n="marg418"></arrow.to.target><lb></lb>ro poſt fuſionem refrigerato videre eſt. </s> </p> <p type="margin"> <s id="s.001621"><margin.target id="marg416"></margin.target>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001622"><margin.target id="marg417"></margin.target>Hoc expe<lb></lb>rimento <expan abbr="cõ-probatur">con<lb></lb>probatur</expan>.</s> </p> <p type="margin"> <s id="s.001623"><margin.target id="marg418"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001624">Sed ad maiorem huius doctrinæ euidentiam con<lb></lb>ſideretur aggeries arenæ minutiſſimæ, & aridæ, hæ <lb></lb>quidem non excurrunt, neque lubricitatem habent, <lb></lb><arrow.to.target n="marg419"></arrow.to.target><lb></lb>ſi poſtea immiſſa, & intercepta aqua lutoſam <expan abbr="formã">formam</expan> <lb></lb>acquirat, <expan abbr="tũc">tunc</expan> particulæ aquæ inter arenulas intercep<lb></lb>tæ nedùm eas diſſociant, ſed veluti rotæ, vel cylin<lb></lb>druli, aut materia aliqua vnctuoſa commoditatem eis <lb></lb>præſtat, vt poſſint excurrere vna particula arenæ ſu<lb></lb>per aliam contorqueri, atque agitari, & tandem ob <lb></lb>natiuam grauitatem quælibet earum deorsùm ten<lb></lb>dendo explanantur, & ad ſuperficiem planam hori<lb></lb>zontalem rediguntur, quòd priùs abſque aqua illą <lb></lb>inter arenulas intercepta in cumulum ſatis accliuem <lb></lb>ſuſtinebatur, acquirit ergò maſſa illa arenoſa vnà <lb></lb>cum aqua conſiſtentiam fluidam, explanatur, & reci<lb></lb>pit figuram continentis vaſis, non ſecùs, ac vitrum, <lb></lb>& ferrum fuſum efformatur, & paritèr ad inſtar glo<lb></lb>bulorum cryſtallinorum, qui licèt ſint aridi abſque <lb></lb>vllo fluido admixto, & omninò quieſcant in vaſe ali<lb></lb>quo, neque agitentur, omnes tamen iam dictas flui<lb></lb>di proprietates retinere videntur. </s> </p> <p type="margin"> <s id="s.001625"><margin.target id="marg419"></margin.target>Et exemplo <lb></lb>luti <expan abbr="cõfirma-tur">confirma<lb></lb>tur</expan>.</s> </p> <p type="main"> <s id="s.001626"><emph type="center"></emph>PROP. CXLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001627"><emph type="center"></emph><emph type="italics"></emph>Requiritur vis motiua grauitatis in omnibus partibus fluidi, <lb></lb>non vt fluiditatem constituat, ſed vt explanare ho<lb></lb>rizontaliter fluidum posſit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001628">VErum tamen eſt, quòd illa præcipua conditio, & <lb></lb>proprietas fluidi, qua explanatur, & æqualitèr <pb pagenum="310" xlink:href="010/01/318.jpg"></pb><arrow.to.target n="marg420"></arrow.to.target><lb></lb>iacet in plano horizontali, nullo pacto verificari po<lb></lb>teſt, niſi in ipſo fluido ponatur virtus aliqua motiua, <lb></lb>qua ſi omninò careat, nullo pacto poterit aqua fluida <lb></lb>explanari, & ad libellam horizontalem reduci. </s> <s id="s.001629">At <lb></lb>huiuſmodi virtus motiua longè diuerſa eſt ab ea, quæ <lb></lb>exigitur à Carteſio, eiuſque ſectatoribus, non enim̨ <lb></lb>eſt motiua virtus vaga, & irregularis, quæ inordina<lb></lb>tam agitationem ſursùm, & deorsùm, & tranſuersè <lb></lb>continuato fluxu efficiat, ſed eſt tantummodò vis, at<lb></lb>que impetus naturalis grauitatis, ope cuius particu<lb></lb>læ omnes fluidi æquali niſu <expan abbr="tendũt">tendunt</expan>, ac feruntur deor<lb></lb>sùm; ſic enim æquatis momentis efficitur <expan abbr="æquilibriũ">æquilibrium</expan> <lb></lb>partium eiuſdem fluidi, vnde ſubſequitur æqualis di<lb></lb>ſpoſitio earum <expan abbr="horizõtalitèr">horizontalitèr</expan>; ſi enim huiuſmodi gra<lb></lb>uitas in fluido deficeret, non poſſet virtute æquilibrij <lb></lb>æqualitèr diſponi, ſed vna eius pars depreſſa, alia ve<lb></lb>rò ſublimis efficeret inæqualem, & aſperam ſuperfi<lb></lb>ciem externam eius, compoſitam ex vallibus, & <expan abbr="mõ-tibus">mon<lb></lb>tibus</expan>. </s> <s id="s.001630">Neceſſariò ergò fatendum eſt in hiſce fluidis <lb></lb>noſtratibus vim motiuam aliquam adeſſe vt omnes <lb></lb>æquali vi, & impetu, ad eaſdem partes, ſcilicèt deor<lb></lb>sùm tendant. </s> <s id="s.001631">Et profectò ſi ponerentur motus vagi <lb></lb>irregulares, & contrarij in eodem corpore fluido, vt <lb></lb>aduerſarij exiſtimant, ſequeretur deſtructio <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>hypotheſis, nam cùm in eadem aqua v. g. non poſ<lb></lb>ſint omnes particulæ eiuſdem aquæ ex condicto ſi<lb></lb>mul ad eaſdem partes ordinata ſeriè moueri, vt iņ <lb></lb>progreſſu alicuius cohortis, vel vt in ſupplicationi<lb></lb>bus fieri ſolet, omninò neceſsè eſt, vt aliæ partes <pb pagenum="311" xlink:href="010/01/319.jpg"></pb><arrow.to.target n="marg421"></arrow.to.target><lb></lb>ſursùm aſcendant, aliquæ verò deorsùm ferantur, & <lb></lb>proinde videtur impoſſibile, atque incredibile, vt <lb></lb>aliquando prædictæ partes motibus contrarijs ſibi <lb></lb>mutuò non occurrant, & proptereà ſe mutuò noņ <lb></lb>impediant, & ad quiet em non redigantur. </s> <s id="s.001632">Cùmque <lb></lb>abſque illa vertigine, & agitatione partium fluidi<lb></lb>tatem exiſtere negent; imò duritiem creari affirment. <lb></lb></s> <s id="s.001633">Sequitur ex eadem hypotheſi (in qua commotiones <lb></lb>partium aquæ ad fluidi conſtitutionem requiruntur) <lb></lb>effici duritiem, & conſiſtentiam, ſaltèm in illis parti<lb></lb>culis fluidi, in quibus quies creatur, quod præcisè <lb></lb>deſtruit eorum hypotheſim. </s> </p> <p type="margin"> <s id="s.001634"><margin.target id="marg420"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001635"><margin.target id="marg421"></margin.target>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001636">Inſuper ſi vera eſt prædicta vis motiua partium̨ <lb></lb>fluidi ſursùm, & deorsùm illa profectò quanta erit, <lb></lb>& certi, ac determinati gradus energiæ, quare noņ <lb></lb>poterit ſuperari à minima, & exigua vi externa eam <lb></lb><expan abbr="horizõtalitèr">horizontalitèr</expan> impellente, qualis eſt vis tenuiſſimi ca<lb></lb>pilli, quo nauim in aqua ſtagnante trahemus. </s> </p> <p type="main"> <s id="s.001637">Reſtat modò poſtrema difficultas, quomodò nimi<lb></lb>rùm aqua fluida, & quodlibet menſtruum ex vegeta<lb></lb>bilibus, ſalibus, & mineralibus tincturas extrahunt, <lb></lb>ac fermentatione quadam corpora illa diſſoluunt, <lb></lb>ac per vniuerſum fluidum ſpargunt, diffunduntque; <lb></lb>& quia huiuſmodi operatio abſque agitatione aquæ, <lb></lb>& fluidi fermentantis percipi non poteſt, hinc con<lb></lb>cludunt aquam, & fluidum quodlibet componi ex <lb></lb>particulis miris, & varijs modis agitatis, à qua tan<lb></lb>dem partium agitatione fluxibilitatem creari <expan abbr="putãt">putant</expan>. <pb pagenum="212" xlink:href="010/01/320.jpg"></pb><arrow.to.target n="marg422"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001638"><margin.target id="marg422"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001639"><emph type="center"></emph>PROP. CXLVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001640"><emph type="center"></emph><emph type="italics"></emph>Experimenta fermentationum, & diſſolutionis ſalium, li<lb></lb>cèt non omnia vera ſint, non tamen euincunt fluidi<lb></lb>tatem ſemper à continua partium agitatione <lb></lb>pendere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001641">ET hìc primò non negabo exhalationes igneas, <lb></lb>& alia corpora ſe mouentia excurrere, atquę <lb></lb>penetrare corpora omnia concreta, & ide ò <expan abbr="fluidorũ">fluidorum</expan> <lb></lb>partes commouere; ſed non proindè confiteri cogi<lb></lb>mur fluiditatem à continua agitatione partium eius <lb></lb>pendere, quandoquidem <expan abbr="nõ">non</expan> omnes experientiæ, quæ <lb></lb>ab Aduerſarijs afferuntur veræ ſunt, & illæ, quæ ve<lb></lb>ræ ſunt non euincunt partes omnes eiuſdem corpo<lb></lb>ris fluidi perpetuò agitari, atque commoueri, itaut <lb></lb>ne minima particula in aliquo angulo fluidi remane<lb></lb>at quieſcens, & abſque vlla agitatione, ſaltem per <lb></lb>aliquod breue tempus. </s> <s id="s.001642">& primum ſi granum ſalis ſo<lb></lb>lidum in fundo aquæ immergatur, verùm <expan abbr="nõ">non</expan> eſt quòd <lb></lb>citò vniuerſa aqua vaſis ſalſedine imbibitur, niſi vaſa <lb></lb>ſint ampla, & aqua ſit agitata, ſi verò ſumatur fiſtu<lb></lb>la vitrea ſatis anguſta, atque in eius fundo ſal appo<lb></lb>natur, aqua verò placidè, & ſolertèr ſali ſuperpo<lb></lb>natur, euitata, quantum fieri poteſt, agitatione, & <lb></lb>commotione eius, tunc aqua, quæ in ſummitate fiſtu<lb></lb>læ reperitur, ſalſedine non afficitur, & hoc etiam à <lb></lb>Boile experimento comprobatum fuit: vnde conij<lb></lb>citur, quòd reuerà aqua ob eius æquilibrium facilè <pb pagenum="313" xlink:href="010/01/321.jpg"></pb><arrow.to.target n="marg423"></arrow.to.target><lb></lb>poteſt commoueri, & ſic repetitis conuolutionibus <lb></lb>ſursùm, & deorsùm ſecum tranſportare valet minu<lb></lb>tiſſimas ſalis particulas, & hoc citiùs conſequitur ſi <lb></lb>agitatio <expan abbr="vehemẽs">vehemens</expan> fuerit facta, nimirùm ab impellen<lb></lb>te externo, vel ab ignis vehementia per vitri poroſi<lb></lb>tates penetrante, & per aquam aſcendente; tameņ <lb></lb>quando in fiſtula anguſta, & alta non æquè commo<lb></lb>dè, & facilè aqua agitari, vel ſemèl incepta agitatio<lb></lb>ne promoueri non poteſt, tunc ſalis particulæ non a<lb></lb>ſcendunt vſque ad <expan abbr="ſupremã">ſupremam</expan> aquæ ſummitatem, quia <lb></lb>nimirùm, licèt aqua æquilibrata à qualibet vi motiua <lb></lb>moueri, & impelli poſſit, nihilominùs quando agita<lb></lb>tio non eſt vehemens, & copioſa, citò extinguitur, <expan abbr="cũ">cum</expan> <lb></lb>reliqua moles aquæ ſuprema non impulſa ob ſui na<lb></lb>turalem inertiam, & aliqualem viſcoſitatem violen<lb></lb>tiæ motus aliquo pacto reſiſtat, proindeque impreſ<lb></lb>ſus motus in infimis aquæ particulis citò retardatur, <lb></lb>extinguitur que à reliquis aquę partibus in quiete <expan abbr="cõ-ſtitutis">con<lb></lb>ſtitutis</expan>, & hac de cauſa motus debilis in fundo factus <lb></lb><arrow.to.target n="marg424"></arrow.to.target><lb></lb>propagari vſque ad vaſis ſummitatem non poteſt. </s> </p> <p type="margin"> <s id="s.001643"><margin.target id="marg423"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001644"><margin.target id="marg424"></margin.target>Fermenta<lb></lb>tiones, & ex<lb></lb>tractiones <lb></lb>chymicæ abſ<lb></lb>que motu <lb></lb>fluidi men<lb></lb>ſtrui fieri ne<lb></lb>queunt; at du<lb></lb>bitatu an <lb></lb>motus, qui in <lb></lb>fermentatio<lb></lb>ne obſerua<lb></lb>tur, ſit cauſa <lb></lb>vel effectus <lb></lb>fermentatio<lb></lb>nis.</s> </p> <p type="main"> <s id="s.001645">Inſuper, quòd prædictæ <expan abbr="fermẽtationes">fermentationes</expan>, & tinctu<lb></lb>ræ extractionum chymicarum <expan abbr="fierinõ">fieri non</expan> poſſint abſque <lb></lb>motu, & agitatione fluidi menſtrui, <expan abbr="cõceditur">conceditur</expan>, vt cer<lb></lb>tum, & euidens, ſed dubitatur controuertiturque, <lb></lb>an motus, qui in fermentatione obſeruatur, ſit cau<lb></lb>ſa, vel effectus eiuſdem fermentationis, ſcilicèt aņ <lb></lb>motus ille antecedenter ſit proprius fluidi corporis, <lb></lb>& fluiditatem conſtituat, ſitque cauſa effectiua fer<lb></lb>mentationis, an è contrà diſſolutio ſalium, & reliquæ <pb pagenum="314" xlink:href="010/01/322.jpg"></pb><arrow.to.target n="marg425"></arrow.to.target><lb></lb>fermentationes ab alia cauſa longè diuerſa depen<lb></lb>deant, à qua producatur veluti effectus motus illę, <lb></lb>qui in fermentatione obſeruatur. </s> <s id="s.001646">Modò ſi oſtende<lb></lb>rimus, quòd ſimplex grauitas fluidi ratione quadam <lb></lb>mechanica, & iuxtà leges æquilibrij inſinuare, & im<lb></lb>pellere poteſt fluidi particulas intra poroſitates ſa<lb></lb>lium mineralium, & vegetabilium, vndè poſtea con<lb></lb>ſequatur agitatio, & ebullitio, quam in fermentatio<lb></lb>ne conſpicimus, procùl dubio non licebit ex hoc ex<lb></lb>perimento inferre motum illum antecedenter fluido <lb></lb>competere, & fluiditatem conſtituere. </s> </p> <p type="margin"> <s id="s.001647"><margin.target id="marg425"></margin.target><lb></lb>Cap, 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001648"><emph type="center"></emph>PROP. CXLVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001649"><emph type="center"></emph><emph type="italics"></emph>Commotio aquæ, quæ in ſpongiæ madefactione contingit, <lb></lb>non eſt proprin ipſius aquæ, neque fluiditatem eius co<lb></lb>ſtituit, ſed eſt effectus dependens à grauitate <lb></lb>eiuſdem fluidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001650">IMmergamus priùs in aqua fruſtum ſpongiæ, con<lb></lb>ſtat ſpongiæ ſubſtantiam <expan abbr="cõtinere">continere</expan> innumeras po<lb></lb>roſitates exiguas, & inter ſe communicantes ad inſtar <lb></lb>fiſtularum exiguarum, quæ aut aere replentur, aut <lb></lb>omninò inanes ſunt. </s> <s id="s.001651">Tunc nemo negabit aquam pro<lb></lb>prio, & naturali pondere inſinuari debere intra <expan abbr="ſpõ-giæ">ſpon<lb></lb>giæ</expan> poroſitates, quia verò hoc exequi non poteſt <lb></lb>abſque motu, & agitatione ipſius aquæ, neceſsè eſt, <lb></lb>vt ambientes partes fluidi contiguæ, & proximæ <expan abbr="cõ-ſequutiuo">con<lb></lb>ſequutiuo</expan> quodam motu <expan abbr="agitẽtur">agitentur</expan>, dum illę intra <expan abbr="ſpõ-giæ">ſpon<lb></lb>giæ</expan> poroſitates immittuntur, quæ commotiones inæ-<pb pagenum="315" xlink:href="010/01/323.jpg"></pb><arrow.to.target n="marg426"></arrow.to.target><lb></lb>quales, & variæ eſſe debent, & ad diuerſas plagas <lb></lb>tendentes, prout in ſpongiæ poroſitatibus ſupremis <lb></lb>infimis, & lateralibus aqua ingreditur; at quia ſe<lb></lb>mel aqua commota neceſſariò impetum concipit, er<lb></lb>gò neceſsè eſt, vt vis prædicti impetus impreſſi mini<lb></lb>mè otioſa ſit, proindèque percuſſiones inferat tùm <lb></lb>particulis ſolidis ipſius ſpongiæ, cùm etiam particu<lb></lb>lis aquæ contiguæ, quare non poterit extingui om<lb></lb>ninò prædicta agitatio, niſi poſt aliquod <expan abbr="tẽpus">tempus</expan>, poſt<lb></lb>quàm ſcilicèt ab impedimentis à glutine <expan abbr="partiũ">partium</expan> eiuſ<lb></lb>demmet aquæ illatis, impetus præconceptus extin<lb></lb>guatur. </s> <s id="s.001652">Patet ergò, quòd agitatio aquæ, quæ in <expan abbr="ſpõ-giæ">ſpon<lb></lb>giæ</expan> madefactione contingit, non eſt propria ipſius a<lb></lb>quæ, neque fluiditatem eius conſtituit, ſed potiùs <lb></lb>eſt effectus dependens à vi grauitatis eiuſdem fluidi, <lb></lb>quatenùs iuxtà naturæ inſtitutum, & hydroſtaticæ <lb></lb>leges inſinuari debet intra ſpongiæ poroſitates, vel <lb></lb>inanes, vel à leuiori corpore aereo occupatas. </s> </p> <p type="margin"> <s id="s.001653"><margin.target id="marg426"></margin.target><lb></lb>Cap 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001654"><emph type="center"></emph>PROP. CXLIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001655"><emph type="center"></emph><emph type="italics"></emph>Commotio aquæ ad inſtar ebullitionis, quæ in pumicis ma<lb></lb>defactione obſeruatur, non eſt propria, & conſtitu<lb></lb>tiua fluidatis eius, ſed eſt effectus dependens à <lb></lb>pondere eiuſdem fluidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001656">IMmittatur poſtea intra aquam pumex loco ſpon<lb></lb>giæ, cuius poroſitates aere refertæ ſunt, <expan abbr="tũc">tunc</expan> aqua <lb></lb>vtpotè grauior aere intra prædictas poroſitates con<lb></lb>tento ſenſim in pumicis exterioribus foraminibus in-<pb pagenum="316" xlink:href="010/01/324.jpg"></pb><arrow.to.target n="marg427"></arrow.to.target><lb></lb>ſinuari debet, & proindè aereæ particulæ, quæ poru<lb></lb>los occupabant, expelli debent, & hæ cùm in fundo <lb></lb>aquæ permanere nequeant, neceſsè eſt vt ſursùm per <lb></lb>aquam aſcendant expreſsæ à maiori pondere ipſius <lb></lb>aquæ; dum verò granula, ſeu ampullæ aereæ ſursùm <lb></lb>feruntur, & ebullitionem quamdam oculis repręſen<lb></lb>tant, fieri non poteſt, vt aqua per quam <expan abbr="trãſeunt">tranſeunt</expan>, ali<lb></lb>quo pacto non agitetur commoueaturque tum expri<lb></lb>mendo aerem, cùm etiam cedendo locum aeri tran<lb></lb>ſituro. </s> <s id="s.001657">Habemus iam nouam cauſam agitationis, & <lb></lb>commotionis ipſius aquæ præter priùs <expan abbr="expoſitã">expoſitam</expan>, <expan abbr="quã-dò">quan<lb></lb>dò</expan> nimirùm aqua vi ſuæ grauitatis inſinuabatur intra <lb></lb>ſpongiæ poros; nam præterea dum aerei globuli ex<lb></lb>preſſi, & à pumice excluſi per aquam aſcendunt, ne<lb></lb>ceſſariò aqua agitari quoque debet, igitur vniuerſa <lb></lb>illa commotio, & veluti ebullitio aquæ habet <expan abbr="causã">causam</expan> <lb></lb>efficientem, quæ eſt ſimplex aquæ grauitas, quarę <lb></lb>non licèt inferre, quòd prędictus motus ebullitionis, <lb></lb>qui in aqua poſt immerſionem pumicis conſpicitur, <lb></lb>ſit ſignum, & euincat motum illum proprium eſſe ip<lb></lb>ſius aquæ, & fluiditatem eius conſtituere. </s> </p> <p type="margin"> <s id="s.001658"><margin.target id="marg427"></margin.target><lb></lb>Cap, 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001659"><emph type="center"></emph>PROP. CL.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001660"><emph type="center"></emph><emph type="italics"></emph>Aquæ commotio à qua gleba diſſoluitur diſpergiturque per <lb></lb>eam non eſt propria, & fluiditatis conſtitutiua, ſed <lb></lb>producitur à grauitate fluidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001661">SI poſtea gleba arida intra aquam mergatur, quia <lb></lb>inter pumicem, & glebam hoc diſcriminis inter-<pb pagenum="317" xlink:href="010/01/325.jpg"></pb><arrow.to.target n="marg428"></arrow.to.target><lb></lb>cedit, quòd parietes porulorum pumicis duri <expan abbr="sũt">sunt</expan> <expan abbr="cõ-ſiſtentes">con<lb></lb>ſiſtentes</expan>, & inter ſe connexi, & vniti, è contrà in gle<lb></lb>ba parietes pororum ſunt valdè fragiles, & diſſolubi<lb></lb>les; vnde ſequitur, quòd aquæ particulæ vi grauitatis <lb></lb>intra poros glebæ inſinuatæ nedùm expellant aerem <lb></lb>ibi contentum, ſed etiam arenulas glebam conſtitu<lb></lb>entes, quæ tantummodò ſe tangunt, & nullo alio vin<lb></lb>culo, nec glutine nectuntur, facilè ab inuicem diſſo<lb></lb>cient diſpergantque. </s> <s id="s.001662">porrò cùm ad aquæ <expan abbr="immiſſionẽ">immiſſionem</expan>, <lb></lb>& aeris expreſſionem, atque aſcenſum neceſſariò mo<lb></lb>tus, & agitatio ipſius aquæ <expan abbr="cõſequatur">conſequatur</expan>, hic verò mo<lb></lb>tus abſque impetu eſſe non poſſit, qui cùm vim cuiuſ<lb></lb>cumque ponderis finiti ſuperet, vt demonſtrauimus, <lb></lb><arrow.to.target n="marg429"></arrow.to.target><lb></lb>facilè poterit exiguas illas arenulas diſſolutas nedum <lb></lb>lateraliter, ſed etiam ſursùm aliquantiſper impelle<lb></lb>re, & hinc oritur turbida quædam nebula, quæ pro<lb></lb>pè glebam demerſam conſpicitur diù <expan abbr="perſeuerãs">perſeuerans</expan>. </s> <s id="s.001663">Ex <lb></lb>vniuerſa hac naturali operatione nemo ſanæ mentis <lb></lb>eliciet aquæ particulas continuo, & vago motu agi<lb></lb>tari naturali inſtinctu, & ab hoc principio produci <lb></lb>glebæ diſſolutionem, diſperſionemque arenularum <lb></lb>eius, & feruoris, qui in aqua tunc temporis conſpici<lb></lb>tur, nam hæc omnia habent ſuam cauſam <expan abbr="neceſſariã">neceſſariam</expan>, <lb></lb>nempè aquæ grauitatem, quæ poteſt, & debet <expan abbr="nedũ">nedum</expan> <lb></lb>expellere ſursùm leues aeris particulas intra glebæ <lb></lb>poroſitates contentas, ſed etiam diſſoluere, & diſper<lb></lb>gere ſuo impetu puluerulentas glebæ particulas per <lb></lb>ipſammet aquam. <pb pagenum="318" xlink:href="010/01/326.jpg"></pb><arrow.to.target n="marg430"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001664"><margin.target id="marg428"></margin.target><lb></lb>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="margin"> <s id="s.001665"><margin.target id="marg429"></margin.target><lb></lb>In lib. <lb></lb>de p<gap></gap>. <lb></lb></s> </p> <p type="margin"> <s id="s.001666"><margin.target id="marg430"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001667"><emph type="center"></emph>PROP. CLI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001668"><emph type="center"></emph><emph type="italics"></emph>Maior, & velocior aquæ commotio, quæ in ſalium diſſolu<lb></lb>tione obſeruatur, non pendet ab intrinſece, & natura<lb></lb>li motu aquæ, ſed à ſimplici eius gra<lb></lb>uitate.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001669">COgitemus poſtea ſalem eſſe <expan abbr="glebã">glebam</expan> ab aqua diſ<lb></lb>ſolubilem, qui conſtat ex ſuis minimis parti<lb></lb>culis figuratis non vndequaque ſe tangentibus, con<lb></lb>nexiſque, & proindè ſalis gleba habet innumeros <lb></lb>porulos, & canaliculos interſperſos, qui vt <expan abbr="plurimũ">plurimum</expan> <lb></lb>non replentur, nec occupantur ab aere, cùm ſint val<lb></lb>dè exigui anguſtique, ſed aut à materia valdè tenui, <lb></lb>vel potiùs vacui omninò ſunt. </s> <s id="s.001670">Conſtat aliundè, quod <lb></lb>aqua facillimè ſali vnitur, connectitur, eiuſque po<lb></lb>roſitates penetrat, contra, ac in pumice, ligno, & alijs <lb></lb>corporibus contingit, in quibus madefactio, & a<lb></lb>quæ penetratio non fit, niſi longo tempore, & diffi<lb></lb>cilè (ſiuè hoc pendeat ab aere contento in horum̨ <lb></lb>poroſitatibus, ſiuè ab incongruentia pororum.) Ex <lb></lb>hac, inquam, maxima facilitate, qua aqua ſalibus in<lb></lb>ſinuatur, licet inferre, quòd motu velociori accurrat <lb></lb>ad occupanda illa ſalium foraminula, & ideò maio<lb></lb>ri, & vehementiori impetu diſſoluat ſe paretque par<lb></lb>ticulas ſalium, eaſque vehementius quoque impellat <lb></lb>vnà cum reliqua ambiente aqua, quæ ne dum conſe<lb></lb>quutiuo motu celeriùs agitatur, ſed etiam ab aſcenſu <lb></lb>leuiorum particularum, quæ in porulis ſalium conti-<pb pagenum="319" xlink:href="010/01/327.jpg"></pb><arrow.to.target n="marg431"></arrow.to.target><lb></lb>nebantur, commouetur. </s> <s id="s.001671">Non eſt poſtea difficile à ve<lb></lb>hementiori impetu, & motu ipſis aquæ minimas ſa<lb></lb>lis particulas ad loca remotiora diſpergi, atque <expan abbr="trãs-ferri">trans<lb></lb>ferri</expan>, quæ ſuo ſapore acri ferè vniuerſam aquam va<lb></lb>ſis ampli inficiant. </s> <s id="s.001672">Et hic quoque conſtat vniuerſam <lb></lb>hanc operationem fermentatiuam non <expan abbr="pẽdere">pendere</expan> ab in<lb></lb>teſtina motione partium aquæ fluxibilitatis conſtitu<lb></lb>tiua, ſed à ſimplici aquæ grauitate legibus mechani<lb></lb>cis operante, vt dictum eſt. <lb></lb><arrow.to.target n="marg432"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001673"><margin.target id="marg431"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="margin"> <s id="s.001674"><margin.target id="marg432"></margin.target><lb></lb>Ex hac do<lb></lb>ctrina ſequi <lb></lb>videtur, <lb></lb>quod <expan abbr="cõple-ta">comple<lb></lb>ta</expan> diſſolutio<lb></lb>ne ſalis, eius <lb></lb>particulæ, vt <lb></lb>graues ad <expan abbr="fũ-dum">fun<lb></lb>dum</expan> vaſis ca<lb></lb>derent; & ſic <lb></lb>aqua dulcis <lb></lb>redderetur, <lb></lb>quod eſt fal<lb></lb>ſum. <lb></lb></s> </p> <p type="main"> <s id="s.001675">Sed hìc difficultas oritur, ſi verum eſſet; quòd à vi <lb></lb>grauitatis aqua intra poros ſalium inſinuata <expan abbr="impetũ">impetum</expan> <lb></lb>acquireret, & ſic ſalia diſſolueret, & feruorem crea<lb></lb>ret, ergò poſtquam ſemel completa eſſet diſſolutio <lb></lb>ſalis, & extinctus feruor ebullitioque, redacta eſſet <lb></lb>aqua ſapida ad exactam tranquillitatem, non poſſent <lb></lb>ſalis particulæ grauiores ſpecie ipſa aqua ſuſpenſæ <lb></lb>retineri in ipſamet aqua, ſed ſponte ſua ſaltem tar<lb></lb>diori motu ad fundum vaſis deciderent, proindeque <lb></lb>aqua ſuprema dulcis omninò remaneret, quod eſt <lb></lb>falſum, igitur dicendum quòd non ab impetu fer<lb></lb>mentationis dependente à vi grauitatis fluidi parti<lb></lb>culæ ſalis diſperguntur, ſed potiùs ab inteſtina, & na<lb></lb>turali partium aquæ agitatione, fluiditatemque eius <lb></lb><expan abbr="conſtituẽte">conſtituente</expan> perpetuò nouis ictibus, & impulſionibus <lb></lb>ſalis particulæ retinentur natantes intrà aquæ ſub<lb></lb>ſtantiam. </s> </p> <figure id="id.010.01.327.1.jpg" xlink:href="010/01/327/1.jpg"></figure> <pb pagenum="320" xlink:href="010/01/328.jpg"></pb> <p type="main"> <s id="s.001676"><arrow.to.target n="marg433"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001677"><margin.target id="marg433"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001678"><emph type="center"></emph>PROP. CLII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001679"><emph type="center"></emph><emph type="italics"></emph>Completa diſſolutione ſalis particulæ eius innatantes non ſu<lb></lb>ſpenduntur ab intestina aquæ commotione, ſed ab eius <lb></lb>naturali glutine validiùs operante in ſuperfi<lb></lb>cieculis particularum ſalium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001680">SEd huic difficultati reſpondeo, <expan abbr="nõ">non</expan> ab impetu aquę <lb></lb>agitatæ, ſed ab alia longè diuerſa cauſa grauio<lb></lb>res particulas innatantes ſuſtineri poſſe. </s> <s id="s.001681">Certum eſt <lb></lb>corporum particulas quò tenuiores, & minutiores <lb></lb>ſunt, eò tardiùs per fluida deſcendere, vt contingit <lb></lb>in puluere terreſtri in aere, vel aqua diſperſo, quią <lb></lb>nimirùm in hiſce corpuſculis exiguis eorum ſuperfi<lb></lb>cies externa ſemper magis, ac magis creſcit in re<lb></lb>ſpectu ad ſuam grauitatem, vt alibi declarauimus; <lb></lb>quia verò menſura impedimenti fluidi externi auge<lb></lb>tur, prout prędicta ſuperficies creſcit <expan abbr="cũ">cum</expan> nullum cor<lb></lb>pus per fluidum moueri queat, quin ſucceſſiuè è loco <lb></lb>anteriori fluidum ei contiguum expellat, quotieſ<lb></lb>cumque vis impulſiua grauitatis minuitur pro molis <lb></lb>diminutione, ſuperficies verò in multo minori ſcili<lb></lb>cèt ſubduplicata proportione diminuitur, ſequitur, <lb></lb>vt fluidi impedimentum minus decreſcendo, dum̨ <lb></lb>impetus grauitatis valdè minuitur, <expan abbr="tãdem">tandem</expan> ad æqua<lb></lb>litatem, & æquilibrium quam proximè accedant, & <lb></lb>proindè hoc nomine particulæ minimæ fluido graui<lb></lb>ores motu ſemper tardiori in ipſo deſcendent quo <lb></lb>magis eorum moles imminuitur. <pb pagenum="321" xlink:href="010/01/329.jpg"></pb><arrow.to.target n="marg434"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001682"><margin.target id="marg434"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001683">Prætereà quia experientia conſtat fluidi partes <lb></lb>glutine aliquo necti interſe debere, vt poſtea fusè <lb></lb>declarabitur, atque vis, & energia prædicti glutinis <lb></lb>ſit certi ac determinati gradus, huic verò contrapo<lb></lb>nitur energia grauitatis, & velocitatis, quæ ſemper <lb></lb>magis, ac magis imminui poteſt, prout moles eius <lb></lb>ſubdiuiditur, hinc fit vt tandem ad eam exiguitatem <lb></lb>vis grauitatis, & impetus redigatur, vt æquari præ<lb></lb>cisè poſſit energiæ glutinis ipſius fluidi, proindeque <lb></lb>vna alteri præualere nequeat, vnde æquatis viribus, <lb></lb>factoque æquilibrio neceſſariò particulæ illæ graues <lb></lb>in ipſo fluido innatantes in eodem ſitu quieſcere de<lb></lb>bent. </s> <s id="s.001684">Hac ratione fieri poteſt, vt minimę ſalis parti<lb></lb>culæ per aquam diſperſæ, & innatantes æquilibrari, <lb></lb>& quieſcere in ipſa aqua poſſint, proindeque aquą <lb></lb>ſemper ſalſedinem retinere valet. </s> </p> <p type="main"> <s id="s.001685"><emph type="center"></emph>PROP. CLIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001686"><emph type="center"></emph><emph type="italics"></emph>Vehementisſima aquæ ebullitio, quæ in diſſolutione calcis <lb></lb>apparet, pendet non ab inteſtino motu aquæ, ſed ab <lb></lb>eius grauitate diſſoluente, & exprimente igneas <lb></lb>particulas, quæ in calce contine<lb></lb>bantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001687">IN calce poſtea intra <expan abbr="aquã">aquam</expan> demerſa alia noua cau<lb></lb>ſa feruoris oritur, quia in exiguis calcinati ſaxi <lb></lb>poroſitatibus, in eiuſque anfractibus includuntur in<lb></lb>numeræ particulæ ignis ibidem inſinuatæ à <expan abbr="feruẽtiſ-ſimo">feruentiſ<lb></lb>ſimo</expan> ardore fornacis, cùmque aqua ſuo pondere, & </s> </p> <pb pagenum="322" xlink:href="010/01/330.jpg"></pb> <p type="main"> <s id="s.001688"><arrow.to.target n="marg435"></arrow.to.target><lb></lb>fluxibilitate particulas calcis <expan abbr="diſſoluẽdo">diſſoluendo</expan> vinculaque <lb></lb><expan abbr="relaxãdo">relaxando</expan>, apertis oſtiolis egreſſus concedatur igneis <lb></lb>illis corpuſculis, quæ poſtea expreſſa ab excedenti <lb></lb>aquæ pondere velociori motu ſursùm per <expan abbr="aquã">aquam</expan> <expan abbr="aſcẽ-dunt">aſcen<lb></lb>dunt</expan>, proindeque in tranſitu bullularum ignearum̨ <lb></lb>aquæ partes laterales celeriùs, & vehementiùs agi<lb></lb>tantur. </s> </p> <p type="margin"> <s id="s.001689"><margin.target id="marg435"></margin.target><lb></lb>Cap, 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001690"><emph type="center"></emph>PROP. CLIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001691"><emph type="center"></emph><emph type="italics"></emph>Idipſum verificatur in diſſolutione metallorum <lb></lb>ab aqua forti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001692">IDipſum eadem ferè ratione producit aqua fortis, <lb></lb>vel regia in metallis, dum enim intra illius poro<lb></lb>ſitates vi ponderis eius inſinuatur, ſalibus quibus a<lb></lb>qua fortis referta eſt, veluti talis, ac ſcalpris abradit <lb></lb>ſolidas aliquas metalli particulas, ſimulque relaxat <lb></lb>oſtiola, egreſſumque concedit materiæ igneæ ibidem <lb></lb><expan abbr="contẽtæ">contentæ</expan>, quæ expreſſa ab inſigni grauitate aquæ for<lb></lb>tis velociſſimo motu per eamdem <expan abbr="aquã">aquam</expan> ſursùm <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan> incluſa in ampullis exiguis, & copioſiſſimis, quæ <lb></lb>ebullitionem feruentem producunt, vnà cum ingenti <lb></lb>aquæ agitatione; quæ omnia immeritò ab inteſtiną <lb></lb>partium aquæ fortis agitatione quiſquam effici cen<lb></lb>ſeret, cùm adſit neceſſaria, & euidentiſſima cauſą <lb></lb>nempè ſimplex grauitas aquæ fortis, quæ eſt impoſ<lb></lb>ſibile vt intra poroſitates inanes, aut à leuiori cor<lb></lb>pore oppletas, non inſinuetur, & proinde in eius <lb></lb>motu impetum non concipiat, cuius virtute exiguæ <pb pagenum="323" xlink:href="010/01/331.jpg"></pb><arrow.to.target n="marg436"></arrow.to.target><lb></lb>metalli particulæ corrodantur, exprimaturque ma<lb></lb>teria ignea in eo contenta, proindeque vehementiùs <lb></lb>aqua agitetur, & tandem à vi eiuſdem impetus parti<lb></lb>culę minimæ metalli, licèt aqua grauiores ſint, poſſunt <lb></lb>hinc inde diſpergi, tranſportarique, & extincto fer<lb></lb>uore à naturali partium aquæ viſcoſitate retineri in <lb></lb>media aqua poſſunt, quotieſcumque vis reſiſtentiæ <lb></lb>aquæ æqualis ſit exiliſſimo ponderi earumdem par<lb></lb>ticularum metallicarum. <lb></lb><arrow.to.target n="marg437"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001693"><margin.target id="marg436"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="margin"> <s id="s.001694"><margin.target id="marg437"></margin.target><lb></lb>Aliquæ ex<lb></lb>periẽtiæ no<lb></lb>ſtræ ſenten<lb></lb>tiæ refragati <lb></lb><expan abbr="vidẽtur">videntur</expan>, qui<lb></lb>bus inferiùm <lb></lb>ſatisfacie<lb></lb>mus. <lb></lb></s> </p> <p type="main"> <s id="s.001695">Hic poſſent innumera phęnomena afferri, quæ in <lb></lb>prædictis diſſolutionibus ſalium mineralium, & ve<lb></lb>getabilium obſeruantur, vt nimirùm cùm calx, aut <lb></lb>metallum non demergitur intra aquam, ſed eminet, <lb></lb>tangitque dumtaxat ſuperficiem eius externam, & <lb></lb>nihilominùs aqua aſcendit, ſubleuaturque penetran<lb></lb>do ſalis, & metalli poroſitates, & poſtea denuò de<lb></lb>ſcendendo diſperguntur ſolidæ particulæ efficiunt<lb></lb>que vniuerſam aquam ſapidam, vel metallo imprę<lb></lb>gnatam; non minùs videmus <expan abbr="aquã">aquam</expan> per fiſtulas tenuiſ<lb></lb>ſimas, per ſpongias aquam contingentes ſupra eius <lb></lb>ſuperficiem, aſcendere. </s> <s id="s.001696">Vnde quiſpiam dubitandi <lb></lb>anſam arripere poſſet, non pendere has operationes <lb></lb>à vi grauitatis, quæ naturæ ductu non ſursùm, ſed <lb></lb>deorsùm impellere aquam fluidam poteſt. </s> </p> <p type="main"> <s id="s.001697"><arrow.to.target n="marg438"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001698"><margin.target id="marg438"></margin.target><lb></lb>Sed interim <lb></lb>ex demon<lb></lb>ſtratis <expan abbr="euidẽ-ter">euiden<lb></lb>ter</expan> reijcitur <lb></lb>oppoſita <expan abbr="sẽ-tentia">sen<lb></lb>tentia</expan>. <lb></lb></s> </p> <p type="main"> <s id="s.001699">Sed hoc <expan abbr="nõ">non</expan> officit doctrinæ ſuperiùs expoſitæ, <expan abbr="nã">nam</expan> <lb></lb>in ſpongia, pumice, ſale, calce &c. </s> <s id="s.001700">intra aquam de<lb></lb>merſis neceſſariò vis grauitatis fluidi prædictas ope<lb></lb>rationes efficit, hæ verò diuerſæ operationes paritèr </s> </p> <p type="main"> <s id="s.001701"><arrow.to.target n="marg439"></arrow.to.target><lb></lb>producuntur ab eodem principio grauitatis, vt in-<pb pagenum="324" xlink:href="010/01/332.jpg"></pb><arrow.to.target n="marg440"></arrow.to.target><lb></lb>feriùs oſtendemus, patebitque neceſſitate quadam <lb></lb>mechanica à grauitate, & momento aquæ fluidæ <expan abbr="eã">eam</expan> <lb></lb>inſinuari intra eleuatas fiſtulas, vel intra <expan abbr="ſpongiarũ">ſpongiarum</expan>, <lb></lb>& ſalium eminentes poroſitates. </s> <s id="s.001702">Vnde elicere poſ<lb></lb>ſumus, quòd ex prædicto motu fermentationis dedu<lb></lb>ci non poteſt, quòd in fluido partes eius perpetuò in<lb></lb>teſtino motu agitentur, à qua commotione fluidi<lb></lb>tas efficiatur, & ab hac veluti à cauſa, diſſolutiones <lb></lb>ſalium metallorum, &c. </s> <s id="s.001703">non dependeant. </s> </p> <p type="margin"> <s id="s.001704"><margin.target id="marg439"></margin.target><lb></lb>Cap. 8. <lb></lb></s> </p> <p type="margin"> <s id="s.001705"><margin.target id="marg440"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001706">Deinde expendenda eſt præcipua figura particu<lb></lb>larum aquam componentium iuxtà Carteſij <expan abbr="mẽtem">mentem</expan>. <lb></lb><arrow.to.target n="marg441"></arrow.to.target><lb></lb>Putat enim prædictas particulas oblongas virgulas <lb></lb>flexibiles, & lubricas eſſe, vti ſunt anguillæ, quæ va<lb></lb>rijs modis contortæ ſe mutuò amplexentur, & <expan abbr="cõ-ponant">con<lb></lb>ponant</expan> aggeriem nodoſam, in qua varijs modis com<lb></lb>plicatæ excurrunt, varièque flectuntur, & ſic flui<lb></lb>ditatem aquæ componere, atque efficere. </s> <s id="s.001707">Et hinc ra<lb></lb>tionem eliciunt, quare guttæ aquæ è ſupremis arbo<lb></lb>rum ramis, ac folijs pendentes non decidunt, ſed te<lb></lb>naci quodam vinculo retinentur, hocque confirmare <lb></lb>nituntur tali exemplo; multotiès è caſei fragmento <lb></lb>ſursùm eleuato, & ab eius prona facie pendet agge<lb></lb>ries plurimorum vermium, qui nedùm non <expan abbr="decidũt">decidunt</expan> <lb></lb>deorsùm, ſed componunt veluti quamdam gibboſi<lb></lb>tatem deorsùm pendentem, <expan abbr="dũ">dum</expan> tamen prædicti ver<lb></lb>mes miris modis agitantur, & inflectuntur. <lb></lb><figure id="id.010.01.332.1.jpg" xlink:href="010/01/332/1.jpg"></figure><pb pagenum="325" xlink:href="010/01/333.jpg"></pb><arrow.to.target n="marg442"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001708"><margin.target id="marg441"></margin.target><lb></lb>Ex Carteſio <lb></lb>aquæ parti<lb></lb>culæ ſunt ob <lb></lb>longæ, flexi<lb></lb>biles, vt an<lb></lb>guillæ, per<lb></lb>petuò agita<lb></lb>tæ, & hinc <lb></lb>guttas aquæ <lb></lb>pendulas ſu<lb></lb>ſtineri poſſe <lb></lb>cenſent. <lb></lb></s> </p> <p type="margin"> <s id="s.001709"><margin.target id="marg442"></margin.target><lb></lb>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001710"><emph type="center"></emph>PROP. CLV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001711"><emph type="center"></emph><emph type="italics"></emph>Oſtenditur abſurditas talis poſitionis <lb></lb>Carteſianæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001712">AT ſi talis eſt aquæ natura, ſequitur vt eius par<lb></lb>ticulæ ſint animatæ, oportet enim vt percipi<lb></lb>ant, & eligant motus, & inflexiones, quæ neceſſarię <lb></lb>ſunt ad prædictum effectum producendum. </s> <s id="s.001713">Nam ſi<lb></lb>cuti illi vermes neceſsè eſt vt partim inſinuentur iņ <lb></lb>ſupremas caſei poroſitates non directè, ſed tortuosè <lb></lb>capita inflectendo, vt nimirùm efficiant hamos, vel <lb></lb>vncinos, & è contrà infimæ partes vermium <expan abbr="pendẽ-tes">penden<lb></lb>tes</expan> <expan abbr="debẽt">debent</expan> quoque inflecti, vt alios vncinos <expan abbr="efformẽt">efforment</expan>, <lb></lb>in quibus ſubſequentes vermes adrepant, debent<lb></lb>que paritèr ſubſequentes vermes non ſecùs incurua<lb></lb>ri, vt duplices vncinos <expan abbr="cõponerẽt">componerent</expan> in eius extremita<lb></lb>tibus. </s> <s id="s.001714">idipſum efficere deberent anguillæ illæ <expan abbr="aquã">aquam</expan> <lb></lb>componentes. </s> <s id="s.001715">At quomodo perſeuerare poſſet ag<lb></lb>geries prædictarum aquæ anguillularum, niſi prædi<lb></lb>ctæ earum curuitates ſumma ſolertia, & prouidentia <lb></lb>fierent, & perſeuerarent, prout neceſſitas <expan abbr="ſuſtẽtatio-nis">ſuſtentatio<lb></lb>nis</expan> ponderis earumdem exigit. </s> <s id="s.001716">Et ſi non prouiden<lb></lb>tia, ſed caſu, vt conſentaneum eſt; monentur, quomo<lb></lb>do poſſent perpetuò agitari, & inflecti quin <expan abbr="aliquã-do">aliquan<lb></lb>do</expan> vncini illi diſſoluti ſe mutuò non retinerent? </s> <s id="s.001717">vide<lb></lb>tur enim impoſſibile vt vniuerſa maſſa virgularum̨ <lb></lb>aquæ aliquando, ſaltem per breue tempus non diri<lb></lb>gatur, vel ſaltem diuerſo modo flectatur, quàm opus <pb pagenum="326" xlink:href="010/01/334.jpg"></pb><arrow.to.target n="marg443"></arrow.to.target><lb></lb>eſt, vt continuata ſeries hamorum, vel vncinorum ſe <lb></lb>viciſſim ſuſtinentium non efformetur, & ſic fieri poſ<lb></lb>ſet vt tota gutta aquæ pendens, aut aliqua eius por<lb></lb>tio ſolutis vinculis, directiſque vncinis deorsùm la<lb></lb>beretur, quod tamen eſt falſum. </s> <s id="s.001718">Tandem ſi attentè <lb></lb>conſideretur ſtructura animalium optimè percipitur <lb></lb>non poſſe vermem inflecti, ac conſeruari in aliquo ſi<lb></lb>tu curuo abſque vi, & tractione muſculorum, vt ni<lb></lb>mirùm eorum fibræ decurtentur relaxatis fibris con<lb></lb>trapoſiti muſculi. </s> <s id="s.001719">hoc autem quàm ſit durum, & in<lb></lb>comprehenſrbile in particulis ipſius aquæ ſuppone<lb></lb>re vnuſquiſque per ſe videt. </s> <s id="s.001720">Si igitur ſaluari poteſt <lb></lb>aquæ fluiditas, & tenacitas illa, qua guttæ penden<lb></lb>tes retinentur faciliori, & euidenti poſitione, vt mox <lb></lb>patebit, quis quæſo præeliget hanc violentam, diffi<lb></lb>cilemque hypotheſim? </s> <s id="s.001721">nulla igitur eſt neceſſitas po<lb></lb>nendi formam, & motionem partium aquæ tam ab<lb></lb>ſurdam <expan abbr="incomprehẽſibilẽque">incomprehenſibilenque</expan> vt facultates, & inſtru<lb></lb>menta <expan abbr="eadẽ">eadem</expan>, vel analoga ijs, quæ in animalibus natu<lb></lb>ra efformauit, ponantur. </s> </p> <p type="margin"> <s id="s.001722"><margin.target id="marg443"></margin.target><lb></lb>Cap 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="main"> <s id="s.001723"><emph type="center"></emph>PROP. CXLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001724"><emph type="center"></emph><emph type="italics"></emph>Fluida aquea habere viſcoſitatem aliquam, quæ ſaluari <lb></lb>non poteſt abſque machinulis flexibilibus, & reſilien<lb></lb>tibus, à quibus aquæ particulæ, veluti lanu<lb></lb>gine ambiuntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001725">POſtremo loco dicendum eſt de alia fluidi paſſio<lb></lb>ne, quæ in exiguis eius partibus obſeruatur, <pb pagenum="327" xlink:href="010/01/335.jpg"></pb><arrow.to.target n="marg444"></arrow.to.target><lb></lb>non autem in <expan abbr="grãdioribus">grandioribus</expan>; conſtat enim experientia <lb></lb>aquam, & cætera fluida naturam quamdam glutino<lb></lb>ſam, & viſcoſam habere, quod quidem euincitur ex <lb></lb>eo quod guttæ fluidæ ſuſpenſæ pendent è ſupremis <lb></lb>ramis arborum, & ſi quis velit particulam eiuſdem <lb></lb>guttæ à reliqua eius maſſa diuellere, perſentiet reſi<lb></lb>ſtentiam aliquam, & ceſſante vi externa denuò gutta <lb></lb>ſponte recolligitur; quòd verò prædicta operatio <lb></lb>pendeat à glutine, conſtat ex eo, quòd ſi aquæ puriſ<lb></lb>ſimæ addatur miſceaturque ſuccus, vel maſſa aliqua <lb></lb>glutinoſa, & viſcoſa, tunc quidem guttulæ penden<lb></lb>tes ampliores fiunt, in fila tenuiſſima ſatis longa ex<lb></lb>tenduntur, atque in membranas graciliſſimas attenu<lb></lb><arrow.to.target n="marg445"></arrow.to.target><lb></lb>antur quoties inſufflato aere efficiuntur bullæ <expan abbr="ingẽ-tes">ingen<lb></lb>tes</expan>, quas pueri efformare ſolent. </s> <s id="s.001726">Sic videmus <expan abbr="ſaliuã">ſaliuam</expan> <lb></lb>viſcoſam, vel aquam cum albugine oui, vel ſaponi <lb></lb>admixtam extendi in tenuiſſima fila, & denuò recol<lb></lb>ligi, qui effectus procùl dubio illi viſcoſitati admix<lb></lb>tæ tribui debet. </s> <s id="s.001727">Si igitur tam inſignis effectus pro<lb></lb>ducitur à grandi copia glutinis, vel humor is viſcoſi, <lb></lb>quis dubitabit eumdem effectum quando eſt minùs <lb></lb>inſignis productum fuiſſe à minori copia eiuſdem̨ <lb></lb>glutinis, & viſcoſi humoris? </s> <s id="s.001728">Sed nemo ferè dubitat <lb></lb>in aqua, & in reliquis fluidis viſcoſitatem, aut quid <lb></lb>analogum glutini in exiſtere, dubitatur ſolummodò <lb></lb>de cauſa prædicti glutinis, cùm hæc poſſit eſſe exter<lb></lb>na, & interna, duo enim corpora vniri poſſunt, & re<lb></lb>ſiſtere ſeparationi, cùm à cauſa externa impelluntur <lb></lb>vnum versùs aliud, vel potiùs ab aliqua vi motiua, <pb pagenum="328" xlink:href="010/01/336.jpg"></pb><arrow.to.target n="marg446"></arrow.to.target><lb></lb>qualis eſt illa, quæ in magnete, & magneticis corpo<lb></lb>ribus obſeruatur. </s> <s id="s.001729">Sed hæc inferiùs refellentur. </s> <s id="s.001730">alij <lb></lb>poſtea recurrunt ad figuras hamatas, & vncinatas <lb></lb>corporum gluten componentium. </s> <s id="s.001731">Sed meo iudicio <lb></lb>videntur huiuſmodi curuitates, & vncinos per ſę <lb></lb>minimè viſcoſitatem efficere poſſe, quia poſtquam̨ <lb></lb>actu vncini, & hami illi diſſoluti, & disiuncti ſunt, <lb></lb>nullam vim haberent ſe ſe denuò <expan abbr="recolligẽdi">recolligendi</expan>, & vni<lb></lb>endi; poſſet profectò hoc effici ſi prædictę hamatæ fi<lb></lb>guræ eſſent flexibiles, & reſilientes, vt machinæ, & <lb></lb>arcus, qui poſtquam diſtracti ſunt, vim habent ſe <expan abbr="cõ-trahendi">con<lb></lb>trahendi</expan>. </s> <s id="s.001732">Quod verò particulæ fluidi machinæ na<lb></lb>turam participent, confirmatur ex eo, quòd fluidą, <lb></lb>quæ rigida, & dura reddi poſſunt, poſt refrigeratio<lb></lb>nem flecti poſtea, & reſilire, & dirigi <expan abbr="ſpõte">ſponte</expan> videmus, <lb></lb>cum ſumuntur graciles laminæ prædicti corporis in<lb></lb>durati, vt patet in glacie, vitro, ferro, &c. </s> <s id="s.001733">Quòdque <lb></lb>præterea veriſimilis ſit prædicta poſitio machinula<lb></lb>rum in fluidis, patet exemplo aeris, qui reuerà com<lb></lb>ponitur ex particulis <expan abbr="reſiliẽtibus">reſilientibus</expan> ad modum machi<lb></lb>næ, vt ſuperiùs oſtenſum eſt, igitur non erit impoſſi<lb></lb>bile, vt eamdem naturam fluida denſiora <expan abbr="participẽt">participent</expan>, <lb></lb>ſcilicèt conſtent ex ijſdem machinulis, alitèr tameņ <lb></lb>efformatis, quàm in aere. </s> <s id="s.001734">Verum tamen eſt, quòd <lb></lb>prædictæ machinulæ in aqua, & ſimilibus fluidis de<lb></lb>bent eſſe valdè ſuperficiales, veluti lanugo quædam <lb></lb>tenuis, & debilis inueſtiens quodlibet aquæ mini<lb></lb>mum, ſcilicèt concipi debet interna, & indiuiduą <lb></lb>quælibet aquæ particula ſolida, & dura, cuius figura <pb pagenum="329" xlink:href="010/01/337.jpg"></pb><arrow.to.target n="marg447"></arrow.to.target><lb></lb>ſit octacdra, vel alterius ſimilis figuræ; hæc, inquam, <lb></lb>extrinſecè ambiri debet à tenuiſſima lanugine, quæ <lb></lb>flecti, & reſilire poſſit ad <expan abbr="modũ">modum</expan> machinæ. </s> <s id="s.001735">Sed opor<lb></lb>tet vt prædictæ machinulæ ſint breues, contortæ, & <lb></lb>exigui roboris, vt nimirùm minimam, & <expan abbr="inſenſibilẽ">inſenſibilem</expan> <lb></lb>vim habeant, nec poſſint impedimentum ſenſibilę <lb></lb>afferre fluxui interno earumdem partium aquæ. </s> </p> <p type="margin"> <s id="s.001736"><margin.target id="marg444"></margin.target><lb></lb>Cap. 7. de <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="margin"> <s id="s.001737"><margin.target id="marg445"></margin.target><lb></lb>In lib. de vi<lb></lb>percula. <lb></lb></s> </p> <p type="margin"> <s id="s.001738"><margin.target id="marg446"></margin.target><lb></lb>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis. <lb></lb></s> </p> <p type="margin"> <s id="s.001739"><margin.target id="marg447"></margin.target>Cap, 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001740">Sed circa vim prædicti glutinis fluidi <expan abbr="nõnullæ">nonnullæ</expan> dif<lb></lb><arrow.to.target n="marg448"></arrow.to.target><lb></lb>ficultates occurrunt. </s> <s id="s.001741">prima quomodo, & quare par<lb></lb>tes fluidi facilè ſuper ſe ipſas excurrere poſſint, diffi<lb></lb>cilè verò à tota maſſa fluida diuelli, ſegregariquę <lb></lb>valeant. </s> <s id="s.001742">ſecunda, quare lamina ſolida, quæ inſenſibi<lb></lb>litèr magis, vel minùs grauis fit, quàm fluidum, deor<lb></lb>sùm, aut ſursùm aſcendere poſſit in ipſomet fluido, ex <lb></lb>quo deducunt nullam viſcoſitatem in ipſo fluido re<lb></lb>periri. </s> <s id="s.001743">tertia quare aliqua fluida non miſcentur, imò <lb></lb>fugiunt alia fluida, & ſolida corpora, vti aqua noņ <lb></lb>miſcetur cum aere, neque cum oleo, neque cum hy<lb></lb>drargyro, & quodlibet ex prædictis corporibus <expan abbr="ſeiũ-gitur">ſeiun<lb></lb>gitur</expan>, & refugit reliqua corpora; quæ ſibi analogą <lb></lb>non ſint. </s> </p> <p type="margin"> <s id="s.001744"><margin.target id="marg448"></margin.target>Proponun<lb></lb>tur difficul<lb></lb>tates aliquæ <lb></lb>circa vim <lb></lb>glutinis flui<lb></lb>dorum.</s> </p> <p type="main"> <s id="s.001745"><emph type="center"></emph>PROP. CLVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001746"><emph type="center"></emph><emph type="italics"></emph>Quare partes fluidi ſuper ſeipſas fluere poſsint, <lb></lb>difficilè verò à tota maſſa fluida pen<lb></lb>dula diuelli, diſiungique queant, <lb></lb>rationem reddere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001747">QVoad primam videtur machina eius naturæ eſ<lb></lb>ſe, vt tantò maiorem energiam, aut reſiſtenti-<pb pagenum="330" xlink:href="010/01/338.jpg"></pb><arrow.to.target n="marg449"></arrow.to.target><lb></lb>am habeat, quantò à maiori violentia diſtrahatur, vt <lb></lb>conſtat <expan abbr="experiẽtia">experientia</expan>, ſi enim arcus caly beus violentiſſi<lb></lb>mè flectatur, vel dilatetur, videmus quòd ſemper ma<lb></lb>gis, ac magis reſiſtit diſtractioni maiori, & validiori <lb></lb>energia, quò magis ex plicatur, vel inflectitur machi<lb></lb>na; ſed quia partes aquæ connectuntur ad inuicem̨ <lb></lb>ſuperficie tenùs ob iam dictam lanuginem, fit vt quo<lb></lb>tieſcumque diuellere tentamus vnam aquæ partem̨ <lb></lb>ab alia, tunc prædictæ machinulæ lanuginem com<lb></lb>ponentes inter ſe connexæ violenter diſtrahantur; & <lb></lb>proindè maiorem reſiſtentiam habeant, quàm partes <lb></lb>eiuſdem aquæ, quæ ſimplici contactu ſolummodò vni<lb></lb>untur <expan abbr="abſq;">abſque</expan> eo, quòd eorum machinulæ <expan abbr="diſtractionẽ">diſtractionem</expan> <lb></lb>patiantur; vnde fit vt minori tenacitate connectan<lb></lb>tur, & ideò ob flexilitatem extremarum partium di<lb></lb>ctæ lanuginis facilè vna aquæ pars ſuper alteram mo<lb></lb>ueri, & fluere poſſit: quia vero actus, & operatio ipſa <lb></lb>diuulſionis aquæ ab aqua ſecum inuoluit violentam̨ <lb></lb>machinularum aquæ diſtractionem, non item fluxus <lb></lb>aquæ per aquam, hinc ſequitur vt in diſtractione, & <lb></lb>diuulſione reſiſtentia percipiatur, non verò in fluxu e<lb></lb>iuſdem aquæ ſuper reliquas eius partes. </s> <s id="s.001748">Similiter in <lb></lb>gutta pendente particulæ minimæ aquæ ſuperficiem <lb></lb>eius extrinſecam componentes, mutuò ſe <expan abbr="connectũt">connectunt</expan>, <lb></lb>vinciunturque, connexis nempe machinulis à quibus <lb></lb>aquæ particulæ ambiuntur, veluti à lanugine <expan abbr="quadã">quadam</expan>, <lb></lb>vt dictum eſt; quia verò prædictæ partes externæ ſu<lb></lb>ſtinent, ne dùm pondus proprium, ſed etiam grauita<lb></lb>tem omnium partium internarum eiuſdem guttæ, & <pb pagenum="331" xlink:href="010/01/339.jpg"></pb><arrow.to.target n="marg450"></arrow.to.target><lb></lb>proindè omnium maximè comprimuntur, fit vt præ<lb></lb>dictæ machinulæ externæ maximè diſtrahantur, ex<lb></lb>tendanturque, & ſic efficiant veluti reticulum te<lb></lb>nax, & conſiſtens, internæ verò partes guttulæ <lb></lb>quia minus pondus ſuſtinent immo ſuſtinentur à <lb></lb>recticulari prædicta ſuperficie externa aquæ, & noņ <lb></lb>vniuerſam ponderis vim patiuntur, vti externæ par<lb></lb>tes, ideò minùs, quàm externæ machinulæ diſtrahun<lb></lb>tur, & propterea debiliori tenacitate ſe mutuò nec<lb></lb>tunt, & hinc fit vt altera ſuper alteram excurrere fa<lb></lb>cilè poſſit, vt conſtat experientia, videmus enim in<lb></lb>ternas guttulæ partes vago motu agitari fluereque. </s> </p> <p type="margin"> <s id="s.001749"><margin.target id="marg449"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="margin"> <s id="s.001750"><margin.target id="marg450"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001751"><emph type="center"></emph>PROP. CLVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001752"><emph type="center"></emph><emph type="italics"></emph>Oſtenditur aquam vi glutinis parumper <lb></lb>reſistere penetrationi corporum ſoli<lb></lb>dorum per eam <expan abbr="discurrentiũ">discurrentium</expan>.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001753">CIrca ſecundam, dici poteſt, quòd reuerà adfit pu<lb></lb>ſilla aliqua reſiſtentia cum dura lamina fluidum <lb></lb>penetrat, & confricat laterales partes eius, quæ reſi<lb></lb>ſtentia ob ſui exiguitatem conuinci non poteſt ab ex<lb></lb>perimentis aliquorum. </s> <s id="s.001754">Et profectò ſi reuerà nullam̨ <lb></lb>viſcoſitatem fluidum haberet, nil omninò penetratio<lb></lb>ni alterius corporis reſiſteret, & ideò quodlibet cor<lb></lb>pus grauius ſpecie quàm aqua in ea deſcenderet, & <lb></lb>quodlibet minus graue ſpecificè aſcenderet ſursùm, <lb></lb>neque exceſſus perimetri, aut ſuperficiei corporis de<lb></lb>merſi reſpectu grauitatis eius poſſet omninò prohi-<pb pagenum="332" xlink:href="010/01/340.jpg"></pb><arrow.to.target n="marg451"></arrow.to.target><lb></lb>bere deſcenſum, vel aſcenſum in aqua, ſed ſolum<lb></lb>modò tarditatem afferret, non autem quietem abſo<lb></lb>lutam, vt fatentur Ghetaldus, Steuinus, & alij. </s> <s id="s.001755">Modò <lb></lb>minutiſſima grana terrea, ſalium, metallorum, & non <lb></lb>minùs particulæ minimæ corporum leuiorum ligni, <lb></lb>aeris, &c. </s> <s id="s.001756">licèt habeant excedentem, & grandem ſu<lb></lb>perficiem reſpectu puſillæ grauitatis eorum non ta<lb></lb>men poſſent omninò quieſcere in medio aquæ, ſed <expan abbr="lẽ-tiſſimo">len<lb></lb>tiſſimo</expan> motu aſcenderent, vel deſcenderent, vt exigit <lb></lb>exceſſus, vel defectus grauitatis ſpecificæ corpuſcu<lb></lb>lorum demerſorum à grauitate fluidi aquei; ſed hoc <lb></lb>eſt falſum, metalla enim, ſales, & aer in minutiſſimą <lb></lb>granula redacta immobilitèr in medio aquę <expan abbr="quieſcũt">quieſcunt</expan>, <lb></lb>& ibidem perſeuerant, igitur falfum eſt aquam gluti<lb></lb>ne omnino priuari, & nil prorsùs penetrationi reſiſte<lb></lb>re; erit igitur aliquantiſper aqua glutinoſa, <expan abbr="habebitq;">habebitque</expan> <lb></lb>ſaltem aliquam puſillam; & ſuperficialem viſcoſita<lb></lb>tem. </s> <s id="s.001757">Adde quòd partes intermediæ fluidi cùm ſint <lb></lb>æquilibratæ atque ſuſtineantur exiguam compreſſio<lb></lb>nem creant, & proindè machinulæ ſuperficiales par<lb></lb>ticularum aquæ ſubiectæ non poſſunt valde diſtrahi, <lb></lb>vel conſtringi, & ſic minimam vim reſilientem exer<lb></lb>cere poſſunt. </s> </p> <p type="margin"> <s id="s.001758"><margin.target id="marg451"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001759">Sed dices, ſi aquæ particulæ à prædicta languinę <lb></lb>ambiuntur, ergo aqua non minùs quàm aer condenſa<lb></lb>ri deberet quod repugnat experientiæ. </s> <s id="s.001760">Reſpondeo <lb></lb>quòd prædicta lanugo valdè exigua eſt reſpectu in<lb></lb>ternæ ſoliditatis cuiuſlibet globuli aquei, & ſic noņ <lb></lb>negatur quòd aliquantiſper aqua condenſari, conſti-<pb pagenum="333" xlink:href="010/01/341.jpg"></pb><arrow.to.target n="marg452"></arrow.to.target><lb></lb>parique poſſit, tamen ob inperceptibilem paruitatem <lb></lb>ſenſum fugit. </s> </p> <p type="margin"> <s id="s.001761"><margin.target id="marg452"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001762"><emph type="center"></emph>PROP. CLIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001763"><emph type="center"></emph><emph type="italics"></emph>Aquam condenſari parumper ob cedentiam lanuginis <lb></lb>eius experimento probatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001764">ET hoc ſatis concinnè confirmari poſſe videtur à <lb></lb>præclaro experimento facto in aula Sereniſſimi <lb></lb>M. D. </s> <s id="s.001765">Hetruriæ is iuſſit (vt mihi <expan abbr="relatũ">relatum</expan> fuit) cauam̨ <lb></lb>pilam <expan abbr="argẽteam">argenteam</expan> aqua repleri, atque exactiſſimè clau<lb></lb>di, ac ferruminati, quæ poſtea graui malleo contuſą <lb></lb>priorem ſphæricitatem amiſit, proindeque internum <lb></lb>eius ſpatium euidenti contractione diminutum fuit, <lb></lb>cùm conſtet <expan abbr="figurarũ">figurarum</expan> iſoperimetrarum ſphæram eſſe <lb></lb>omnium capaciſſimam, neceſsè ergo fuit vt moles a<lb></lb>quæ, quæ priùs ingens ſpatium ſphæricum replebat, <lb></lb>aliquo pacto ſtringeretur anguſtareturque, tunc mi<lb></lb>rabile ſpectaculum ſe obtulit, nimirùm vndique pila <lb></lb>argentea exſudare cæpit effundendo exiguos globu<lb></lb>los aqueos ſimiles illis, qui in cute noſtra dum ſuda<lb></lb>mus apparere ſolent. </s> <s id="s.001766">Gaſſendus poſtea refert in ſimi<lb></lb>li pila contuſa poſtquam exiguum foramen aperuiſ<lb></lb>ſet, longiùs aquam proſilientem eieciſſe. </s> <s id="s.001767">Ex his om<lb></lb>nibus videtur elici poſſe aliquantiſper aquam antę <lb></lb>exſudationem, aut eiectionem condenſatam fuiſſe. </s> </p> <p type="main"> <s id="s.001768">Et licèt reſponderi poſſet, vas prædictum poſt con<lb></lb>tuſionem violentèr ſe diſtendiſſe, & dilataſſe laterali<lb></lb>tèr, & hac ratione capacitatem eius auctam ſupplere <pb pagenum="334" xlink:href="010/01/342.jpg"></pb><arrow.to.target n="marg453"></arrow.to.target><lb></lb>potuiſſe conſtrictionem factam à contuſione, & vio<lb></lb>lentam diſtractionem illius laminæ argenteæ ad mo<lb></lb>dum machinæ ſe reſtringendo facilè potuiſſe <expan abbr="effluuiũ">effluuium</expan> <lb></lb>illud ad inſtar fonticuli, vel exſudationem per poros <lb></lb>dilatatos efficere; nihilominùs videtur incredibilę <lb></lb>in illa violentiſſima compreſſione facta in actu per<lb></lb>cuſſionis aquam ne minimum condenſatam fuiſſe ſal<lb></lb>tem per breuiſſimum tempus, quæ condenſatio præ<lb></lb>clarè ſaluatur in noſtra poſitione, quia ſcilicèt parti<lb></lb>culæ aquæ duriſſimæ ambiuntur veluti à lanugine ma<lb></lb>chinularum flexibilium, quæ parumper poſſunt com<lb></lb>primi, condenſationemque pati. </s> </p> <p type="margin"> <s id="s.001769"><margin.target id="marg453"></margin.target>Cap 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001770"><emph type="center"></emph>PROP. CLX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001771"><emph type="center"></emph><emph type="italics"></emph>Existentia lanuginis aquæ ab experimento ſuadetur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001772">EX eadem hypotheſi texturæ partium aquæ, & ae<lb></lb>ris reddi poteſt ratio alterius pulcherrimi ex<lb></lb>perimenti. </s> <s id="s.001773">Si enim <expan abbr="rotũda">rotunda</expan> phiala vitrea per anguſtiſ<lb></lb>ſimum eius foramen aqua repleatur, tunc ſi ore infe<lb></lb>riùs inuerſo ampulla reuoluatur in aere aqua non de<lb></lb>fluit, at ſi poſtea ampullæ orificium vinum (rubrum̨ <lb></lb>commoditatis gratia) contingat in ſubiecto vaſę <lb></lb>contentum, tunc videbis per idipſum foramen aquam <lb></lb>eodem tempore deſcendere, & ſimul vinum aſcende<lb></lb>re in tenuiſſima fila extenuatum; & profectò mirabi<lb></lb>le videtur poſſe vinum per medietatem orificij tranſi<lb></lb>re, dum per reliquam medietatem aqua defluit, & hoc <lb></lb>in aere ſimili modo fieri <expan abbr="nõ">non</expan> poſſe, licèt maiori exceſſu <pb pagenum="335" xlink:href="010/01/343.jpg"></pb><arrow.to.target n="marg454"></arrow.to.target><lb></lb>aquæ grauitas aerem ſuperet, quam grauitatem vi<lb></lb>ni. </s> <s id="s.001774">At hoc (ni fallor) contingit ex eo quod vinum̨ <lb></lb>aquæ naturam participat, cum non ſit vinum niſi pu<lb></lb>ra aqua cui immiſcentur plures ſpiritus, & tartara, & <lb></lb>hac de cauſa facilè particulæ vini per aquam excurre<lb></lb>re, & fluere poſſunt; at non ſic aer, qui ex grandiori<lb></lb>bus ſpiris componitur, & propterea mixtionem cum <lb></lb>aqua refugit, eiuſque effluuium impedit, quatenus <lb></lb>in fundo orificij guttula aquæ pendens quaſi <expan abbr="reticulũ">reticulum</expan> <lb></lb>ſuis villis violenter diſtractis efformat; & ſic non fa<lb></lb>cilè poſſunt diſſolui diſgregarique à grandi oribus ae<lb></lb>ris ſpiris ſimùl pariter inter ſe adnexis, intricatiſque, <lb></lb>& hac de cauſa non poteſt aqua effluere eodem <expan abbr="tẽ-pore">tem<lb></lb>pore</expan> quo aer per idem foraminulum aſcendere noņ <lb></lb>poteſt. </s> </p> <p type="margin"> <s id="s.001775"><margin.target id="marg454"></margin.target>Cap. 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001776"><emph type="center"></emph>PROP. CLXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001777"><emph type="center"></emph><emph type="italics"></emph>Eadem lanugo fluidi impedit miſcellam fluidorum <lb></lb>diuerſæ naturæ, & conſiſtentiæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001778">AD tertiam dico, quòd reuera ob defectum ana<lb></lb>logiæ non miſcentur aliqua fluida inter ſe, ne<lb></lb>que aliqua ſolida corpora madefaciunt; at prædictą <lb></lb>analogia non conſiſtit in ſimilitudine, & ſymmetrią <lb></lb>pororum corporis fluidi, nam, vt deinceps dicemus, <lb></lb>aqua per aquam penetrare, & fluere poteſt licèt eius <lb></lb>pori ſint, ob eius exiguitatem, incapaces aquearum̨ <lb></lb>particularum; igitur vera cauſa (vt puto) quare aqua <lb></lb>non miſcetur oleo, & aeri, eſt quia lanugo externą <pb pagenum="336" xlink:href="010/01/344.jpg"></pb><arrow.to.target n="marg455"></arrow.to.target><lb></lb>aquæ penetrare nequit oleum, velae rem, forſan quia <lb></lb>machinulæ pilorum lanuginis aquæ offendunt facie<lb></lb>culas, & lanugines partium olei vel aeris à quibus <lb></lb>flectuntur incuruanturque, & ſic à vi machinæ reſili<lb></lb>entis nedum prohibetur penetratio <expan abbr="prædictarũ">prædictarum</expan> aquæ <lb></lb>particularum, ſed inſuper ab inuicem ſegregantur. <lb></lb></s> <s id="s.001779">In ſolidis verò corporibus ſi adſit incongruentia po<lb></lb>rorum, partes fluidi <expan abbr="nõ">non</expan> madefacient ſolidum corpus, <lb></lb>vt hydrargyrum lignum non madefaciet, ſi verò pori <lb></lb>congruentes fuerint tamdiù retardatur miſcella, & <lb></lb>madefactio, quamdiù non explicatur lanugo <expan abbr="particu-larũ">particu<lb></lb>larum</expan> aquæ quæ in primo occurſu inflexa fuerat. </s> <s id="s.001780">Cau<lb></lb>ſa verò, & vis impulfiua, quæ impellit prædictas flui<lb></lb>di particulas intra ſolidi poroſitates, poſtea aſſigna<lb></lb>bitur. </s> </p> <p type="margin"> <s id="s.001781"><margin.target id="marg455"></margin.target>Cap 7. dę <lb></lb>natura flui<lb></lb>ditatis.</s> </p> <p type="main"> <s id="s.001782"><emph type="center"></emph><emph type="italics"></emph>Cauſam inquirere ſpontaneæ eleuationis exiguarum <lb></lb>aquæ particularum ſupra aquæ libellam <lb></lb>in ipſo aere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001783"><emph type="center"></emph>CAP. VIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001784">VEritatem Archimedeæ doctrinæ luculentèr ſu<lb></lb>periùs confirmauimus, quod ſcilicèt omnią <lb></lb>elementaria corpora ſiue fluida, fiue <expan abbr="conſiſtẽtia">conſiſtentia</expan> gra<lb></lb>uitatem habent, eamque exercent etiam in proprijs <lb></lb>locis, vnde deducitur impoſſibile eſſe vt aqua v. g. <lb></lb>leges æquilibrij tranſgrediatur, atque perturbet pul<lb></lb>cherrimum atque admirabilem ordinem, diſpoſitio<lb></lb>nemque partium vniuerſi; ſcilicèt alterando, atquę <pb pagenum="337" xlink:href="010/01/345.jpg"></pb><arrow.to.target n="marg456"></arrow.to.target><lb></lb>deformando figuram ſphæricam, vnde infertur, quòd <lb></lb>aqua nullo pacto poſſit <expan abbr="pẽdula">pendula</expan> ſuſtineri in medio ae<lb></lb>ris per aliquod tempus, neque poterit eleuari ſupra <lb></lb>ſuperficiem ſupremam totius aquæ ſubiectæ, <expan abbr="efficiẽ-do">efficien<lb></lb>do</expan> nimirùm montuoſitates aqueas, vel ſponte ſua a<lb></lb>ſcendendo per cauitates fiſtularum ſupra aquæ infi<lb></lb>mam libellam eleuatarum. </s> <s id="s.001785">Et hoc nedùm ipſa ratio <lb></lb>perſuadet, ſed etiam ſenſus euidentia oſtendit iņ <lb></lb>grandioribus aquæ portionibus. </s> </p> <p type="margin"> <s id="s.001786"><margin.target id="marg456"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001787">E contrà videmus in paruis guttulis aquæ, & reli<lb></lb><arrow.to.target n="marg457"></arrow.to.target><lb></lb>quorum fluidorum vniuerſalem regulam prædictam̨ <lb></lb>minimè verificari; aquæ enim guttæ in folijs <expan abbr="arborũ">arborum</expan> <lb></lb>non intra earum cauitates ſtagnantes quieſcunt, ex<lb></lb>plananturque, ſed tumidæ eleuantur vt monticuli, & <lb></lb>ſphæricam figuram quodammodò affectare <expan abbr="vidẽtur">videntur</expan>. <lb></lb></s> <s id="s.001788">Similiter aliæ guttæ pendulæ ſuſtinentur è ſupremis <lb></lb>ramis arborum, neque à naturali earum grauitatę <lb></lb>deorsùm impelluntur; imò ſi prædictæ guttulæ pen<lb></lb>dulæ à contactu digiti, vel feſtucæ deorsùm leuitèr <lb></lb>trahantur, ceſſante vi externa ſponte ſua aquea illą <lb></lb>mammilla retrahitur <expan abbr="ſursũ">ſursum</expan>; ſimiliter in fiſtulis tenuiſ<lb></lb>ſimis, in <expan abbr="ſpõgijs">ſpongijs</expan>, atque in filtris manifeſtè aqua <expan abbr="ſpõ-te">ſpon<lb></lb>te</expan> ſua aſcendit ſupra libellam aquæ ſubiectæ. </s> <s id="s.001789">Cùm<lb></lb>que doctrina illa vniuerſalis æquilibrij in dubium re<lb></lb>uocari nequeat, neceſsè eſt vt aliæ nouæ cauſæ, quæ <lb></lb>in hiſce guttulis fluidis operantur, efficiant <expan abbr="prædictã">prædictam</expan> <lb></lb>effectuum diuerſitatem, quam dignoſcere èrit ope<lb></lb>ræpretium. </s> </p> <p type="margin"> <s id="s.001790"><margin.target id="marg457"></margin.target>In guttis exi<lb></lb>guis pertur<lb></lb>batur vni<lb></lb>uerſalis re<lb></lb>gula, quą <lb></lb>fluida vt gra<lb></lb>uia explana<lb></lb>ri debeant.</s> </p> <p type="main"> <s id="s.001791">Et primo loco inquirenda eſt cauſa, à qua guttæ <pb pagenum="338" xlink:href="010/01/346.jpg"></pb><arrow.to.target n="marg458"></arrow.to.target><lb></lb>fluidi ſphæricè contornari, eleuari, ſuſpendique poſ<lb></lb>ſunt ad ſimilitudinem monticuli. </s> <s id="s.001792">Et procùl dubio fa<lb></lb>tendum eſt aquæ guttulas, aut vi naturali, & intrin<lb></lb>ſeca ſponte ſua vniri conglobarique, & ſic efficerę <lb></lb>ſphærulas illas aqueas, vel hoc à violentia aliquą <lb></lb>externa effici. </s> <s id="s.001793">non deſunt vtriuſque ſententiæ fauto<lb></lb>res. </s> <s id="s.001794">Aliqui enim affirmant ab aere ambiente compri<lb></lb>mi aqueas guttulas, vel pondere, vel vi elaſtica ae<lb></lb>ris, aut vtroque modo eas vndique conſtringendo, <lb></lb>& conſtipando. </s> <s id="s.001795">Quia verò numquam eædem guttæ <lb></lb>aqueæ naturalem grauitatem amittunt, ſed ſemper <lb></lb>eam exercent; fit vt in exiguis guttulis minima earum <lb></lb>grauitas ſuperari poſſit à vi compreſſiua aeris. </s> <s id="s.001796">Cùm è <lb></lb>contrà in guttis amplioribus vis grauitatis ſuperet <lb></lb>eiuſdem aeris vim compreſſiuam, & proindè depri<lb></lb>mantur explanenturque in cauitatibus terræ. </s> </p> <p type="margin"> <s id="s.001797"><margin.target id="marg458"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001798"><emph type="center"></emph>PROP. CLXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001799"><emph type="center"></emph><emph type="italics"></emph>Aeris vis compresſiua non eſt cauſa tumoris rotundi <lb></lb>guttularum fluidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001800">HÆc profectò ſententia pluribus difficultatibus <lb></lb>obnoxia eſſe videtur, quia vt animaduertit <lb></lb>ingenioſiſſimus Portius amicus noſter, vis eiuſdem̨ <lb></lb>aeris compreſſiua vnius, & eiuſdem roboris, & ener<lb></lb>gię eſſe debet, igitur ſemper eumdem effectum pro<lb></lb>ducere valet, & proindè quotieſcumque eius actio <lb></lb>exercetur contra duas inæquales reſiſtentias, maior, <lb></lb>& inſignior operatio efficietur in ſubiectum minùs <pb pagenum="339" xlink:href="010/01/347.jpg"></pb><arrow.to.target n="marg459"></arrow.to.target><lb></lb>reſiſtens, quàm in aliud. </s> <s id="s.001801">Conſiderentur modò duo <lb></lb>fluida inæqualitèr grauia ſpecie, ſcilicèt hydrargy<lb></lb>rum, & aqua communis, certum eſt guttam mercu<lb></lb>rij quatuordecies ponderoſiorem eſſe gutta aqueą <lb></lb>eiuſdem molis, quia verò vis aeris externa compri<lb></lb>mens hæc duo fluida ſemper eiuſdem roboris eſt, igi<lb></lb>tur non poterit conglobare, & ſphæricè contornare <lb></lb>guttam mercurij æquè <expan abbr="amplã">amplam</expan>, ac eſt alia gutta aquę; <lb></lb>cùm mercurius grauior, & ideò magis <expan abbr="reſiſtẽs">reſiſtens</expan> requi<lb></lb>rat maiorem vim compreſſiuam, quàm aqua minùs <lb></lb>grauis; ergo gutta mercurij, quæ ab eadem energia <lb></lb>aeris contornari debet vna pars decimaquarta opor<lb></lb>tet vt ſit amplitudinis guttæ aquæ paritèr ſphæricè <lb></lb>conglobatæ; igitur eſt omninò impoſſibile vt aer ef<lb></lb>ficiat ſphærulam mercurialem grandiorem, quàm a<lb></lb>queam; at quia hoc conſtat experientia, guttæ enim <lb></lb>mercurij, quæ ſupra tabulam planam ſphæricè con<lb></lb>tornantur, agitanturque, non minores eſſe videntur, <lb></lb>quàm guttæ aqueæ, quæ ſupra braſſicæ folia <expan abbr="cõglo-bari">conglo<lb></lb>bari</expan> ſolent: Non erit igitur aeris vis compreſſiua ve<lb></lb>ra cauſa turbinationis aquæ, vel mercurij. </s> </p> <p type="margin"> <s id="s.001802"><margin.target id="marg459"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001803"><emph type="center"></emph>PROP. CLXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001804"><emph type="center"></emph><emph type="italics"></emph>Alia experientia id ipſum confirmare.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001805">PRæterea ſi energia grauitatis, aut vis elaſtica ae<lb></lb>ris eſt illa, quæ guttas fluidi vndique <expan abbr="compri-mẽdo">compri<lb></lb>mendo</expan> eas ſphæricè tumefacit, igitur illæ guttæ, quæ <lb></lb>ab aere rariſſimo, aut infinitè expanſo ambiuntur, <pb pagenum="340" xlink:href="010/01/348.jpg"></pb><arrow.to.target n="marg460"></arrow.to.target><lb></lb>minùs comprimi deberent, quàm ab aere copioſo, & <lb></lb>maximè condenſato, igitur in vaſe Torricelliano, <lb></lb>facto vacuo, vbi nullæ, aut ſaltèm exiliſſimæ aeris <lb></lb>particulæ reperiuntur, minùs eleuari, & magis <lb></lb>contuſæ eſſe deberent, aut valdè diminutos, & <lb></lb>exiguos globulos efficere deberent prædictę aqueæ <lb></lb>guttulæ à folijs braſſicæ ſuſtentatæ, quàm illæ, quæ <lb></lb>ab aere valdè condenſato ope follium, vel <expan abbr="inſtrumẽ-ti">inſtrumen<lb></lb>ti</expan> pneumatici in aliquo vaſe, quod tamen <expan abbr="falſiſſimũ">falſiſſimum</expan> <lb></lb>eſt, ęquè enim tumidæ ſphæricè ſuſpenduntur, & ad <lb></lb>eandem altitudinem, & <expan abbr="magnitudinẽ">magnitudinem</expan> eleuantur gut<lb></lb>tæ aqueæ in vacuo Torricelliano ab aere rariſſimo, <lb></lb>quàm ab aere valdè denſo, & conſtipato, vt in Aca<lb></lb>demia experimentali Medicea experti ſumus. </s> </p> <p type="margin"> <s id="s.001806"><margin.target id="marg460"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001807"><emph type="center"></emph>PROP. CLXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001808"><emph type="center"></emph><emph type="italics"></emph>Vt partes elementi aquæ ſphæricè circa centrum terræ con<lb></lb>tornentur, oportet vt vires motiuæ earum versùs <expan abbr="cẽ-trum">cen<lb></lb>trum</expan> non ſint ſemper inter ſe æquales, ſed ha<lb></lb>beant eamdem proportionem quam ea<lb></lb>rum diſtantiæ à centro.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001809">AD hæc poterit euidenti demonſtratione (niſi <lb></lb>fallor) euinci aqueas guttas non conglobari <lb></lb>ſphæricè à vi externa aeris compreſſiua. </s> <s id="s.001810">Si enim per<lb></lb>pendamus, quare vniuerſum aquæ elementum circą <lb></lb>centrum syſtematis elementaris ſphæricè congloba<lb></lb>tur, percipiemus hoc effici quia partes aquæ habent <lb></lb>vim ſemouendi directè versùs centrum terræ, eſtque <pb pagenum="341" xlink:href="010/01/349.jpg"></pb><arrow.to.target n="marg461"></arrow.to.target><lb></lb>talis vis motiua in eodem corpore homogeneo aquæ <lb></lb>non ſemper eiuſdem gradus, niſi cùm partes exter<lb></lb>næ à centro terræ æquè recedunt. </s> </p> <p type="margin"> <s id="s.001811"><margin.target id="marg461"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001812">Sit ergo punctum E centrum globi terraquei, & <lb></lb>ſupponamus aquam ABCD inæqualitèr diſtare à <expan abbr="cẽ-tro">cen<lb></lb>tro</expan> E, ſcilicèt à vi externa, v. g. ſit eleuatus mons a<lb></lb>queus MAK ſupra reliquam eius ſuperficiem ſphæri<lb></lb>cam BCD. & ſiquidem vis <lb></lb><figure id="id.010.01.349.1.jpg" xlink:href="010/01/349/1.jpg"></figure><lb></lb>motiua deorsùm | impellens <lb></lb>versùs centrum E eſſet <expan abbr="eiuſ-dẽ">eiuſ<lb></lb>dem</expan> energiæ in aqua A, atque <lb></lb>in B, non poſſet deprimi ſu<lb></lb>prema aqua A deorsùm, ex<lb></lb>pellendo, & ſuperando <expan abbr="reſi-ſtentiã">reſi<lb></lb>ſtentiam</expan> aquæ B, vel D, quia <lb></lb>nimirùm potentia æqualis in <lb></lb><expan abbr="æqualẽ">æqualem</expan> minimè agere poteſt. </s> <s id="s.001813">Neceſsè ergò eſt vt aqua <lb></lb>eleuata MAK maiorem vim <expan abbr="compreſſiuã">compreſſiuam</expan> habeat, <expan abbr="quã">quam</expan> <lb></lb>aqua B: eſtque hoc euidentiſſimum, quia moles aquæ <lb></lb>EA, quæ altior, copioſior, & ideò grauior eſt, ſupera<lb></lb>bit reſiſtentiam minùs eleuatæ aquæ EB, & minoris <lb></lb>molis; Igitur vera cauſa, quare elementum aquæ cir<lb></lb>ca centrum terræ ſphæricè contornatur, eſt, quia par<lb></lb>tes aquæ cum reliquis continuatæ magis à centro <lb></lb>terræ eleuatæ, maiorem vim compreſſiuam habent, <lb></lb>quàm alię partes minùs à prædicto centro <expan abbr="recedẽtes">recedentes</expan>. <lb></lb><figure id="id.010.01.349.2.jpg" xlink:href="010/01/349/2.jpg"></figure><pb pagenum="342" xlink:href="010/01/350.jpg"></pb><arrow.to.target n="marg462"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001814"><margin.target id="marg462"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001815"><emph type="center"></emph>PROP. CLXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001816"><emph type="center"></emph><emph type="italics"></emph>Si circa centrum orbis elementaris duæ fluidæ ſphæræ concen<lb></lb>tricæ collocentur, quarum exterior grauis ſit, non verò <lb></lb>interior, quæ habeat montuoſitatem aliquam, <lb></lb>compresſio vniuerſalis fluidi ambientis <lb></lb>non poterit montuoſitatem <expan abbr="contẽti">contenti</expan> <lb></lb>fluidi contundere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001817">SVpponamus modò mercurium ABCD non habe<lb></lb>re vim ſe ſe vniendi, ſcilicèt non habere graui<lb></lb>tatem, patet quòd ſi prædictum hydrargyrum pone<lb></lb>retur circa centrum E totius regionis elementaris <lb></lb><expan abbr="ſpõte">ſponte</expan> ſua <expan abbr="nõ">non</expan> efficeretur ſphę<lb></lb><figure id="id.010.01.350.1.jpg" xlink:href="010/01/350/1.jpg"></figure><lb></lb>ricum, ſed retineret <expan abbr="eamdẽ">eamdem</expan> <lb></lb>montuoſitatem MAK. </s> <s id="s.001818">Sup<lb></lb>ponamus poſtea mercurium <lb></lb>à ſphæra aeris FGHI circun<lb></lb>dari, & habeat prædictum̨ <lb></lb>fluidum ambiens <expan abbr="grauitatẽ">grauitatem</expan>, <lb></lb>& principium motiuum ver<lb></lb>sùs centrum eius E, & proin<lb></lb>dè maſſa mercurialis ABCD vndique comprimetur à <lb></lb>fluido ambiente FGHI; ſitque prædictum fluidum̨ <lb></lb>ſibi homogeneum, ſcilicèt ſit vniformitèr graue. </s> <s id="s.001819">Dico <lb></lb>quod ambiens fluidum nulla ratione mercurium̨ <lb></lb>ABCD ſphæricè contornabit; quia fluidum ambiens <lb></lb>comprimit comprehenſum fluidum præcisè, <expan abbr="quantũ">quantum</expan> <lb></lb>exigit menſura grauitatis eius; eſt verò grauitas flui-<pb pagenum="343" xlink:href="010/01/351.jpg"></pb><arrow.to.target n="marg463"></arrow.to.target><lb></lb>di FA ad grauitatem alterius partis BG vt altitudo, <lb></lb>ſeu moles illius ad huius molem (cum ſupponatur <lb></lb>fluidum ſibi ipſi homogeneum) & eſt moles fluidi FA <lb></lb>minor, quàm GB, igitur fluidum FA minùs grauitat, <lb></lb>& ideò minùs comprimit ſubiectum fluidum AE, <lb></lb>quàm fluidum GB comprimat ſibi ſubiectum fluidum <lb></lb>EB; ſed eſt impoſſibile vt minor vis compreſſiua flui<lb></lb>di ambientis FA impellat deorsùm, & <expan abbr="contũdat">contundat</expan> <expan abbr="mõ-tuoſitatem">mon<lb></lb>tuoſitatem</expan> fluidi MAK, quin expellatur ſursùm hu<lb></lb>milior pars eiuſdem fluidi EB; & hæc ſursùm expelli <lb></lb>nequit niſi cædat vis compreſſiua grauitatis totius <lb></lb>fluidi GB, igitur deberet vis grauitatis maior totius <lb></lb>aquæ BG ſuperari à potentia minoris grauitatis FA, <lb></lb>quod eſt impoſſibile, ergò vis compreſſiua externą <lb></lb>aeris, vel cuiuslibet alterius fluidi, non poteſt effice<lb></lb>re tumorem illum ſphæricum, quem in guttis mercu<lb></lb>rij, & aquæ obſeruamus, quotieſcumque prædictæ <lb></lb>guttæ grauitate carerent, & in centro regionis ele<lb></lb>mentaris collocatæ eſſent. </s> </p> <p type="margin"> <s id="s.001820"><margin.target id="marg463"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001821"><emph type="center"></emph>PROP. CLXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001822"><emph type="center"></emph><emph type="italics"></emph>Non poſſe guttulas fluidi ſphæricè conglobari ab vniuerſali <lb></lb>ambientis aeris compresſione demonstratur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001823">REſtat modò vt idipſum oſtendamus in guttis a<lb></lb>queis in ſuperficie noſtræ telluris <expan abbr="exiſtẽtibus">exiſtentibus</expan>. <lb></lb></s> <s id="s.001824">Gutta aquea ABCD ſuſpenſa ſit filo GA, vt pauimen<lb></lb>tum VX non attingat, & ſuppoſito, quòd ab oceano <lb></lb>aereo RS vndique gutta ſuſpenſa contundatur, & ve-<pb pagenum="344" xlink:href="010/01/352.jpg"></pb><arrow.to.target n="marg464"></arrow.to.target><lb></lb>luti forcipe <expan abbr="cõſtringatur">conſtringatur</expan>, nempè ſupernè à columnis <lb></lb>aereis GA, lateralitèr à cylindris GH, & SD & infer<lb></lb>nè à <expan abbr="colũnis">columnis</expan> aereis reflexis RVB, & SXI. </s> <s id="s.001825">Dico ab ae<lb></lb>reo oceano minimè guttam̨ <lb></lb><figure id="id.010.01.352.1.jpg" xlink:href="010/01/352/1.jpg"></figure><lb></lb>ABCD ſphæricè contornari. <lb></lb></s> <s id="s.001826">Quia guttæ aqueæ partes AH <lb></lb>CD omninò <expan abbr="carẽt">carent</expan> vi motiua <lb></lb>qua ferantur versùs centrum <lb></lb>eiuſdem guttæ, eo quòd pars <lb></lb>eius ſuprema A trahitur <expan abbr="ſur-sũ">ſur<lb></lb>sum</expan> à filo GA, inſima verò C <lb></lb>tendit <expan abbr="deorsũ">deorsum</expan> vt grauis, ideò <lb></lb>duę partes oppoſitæ A & C <lb></lb>à ſe inuicem fugiunt, & proindè potius conantur <lb></lb>à centro ‘guttæ’ recedere, quàm ad ipſum ferri, & <lb></lb>cum eo vniri; partes verò collaterales H, & D ſiuę <lb></lb>vim grauitatis exerceant, ſiue non, <expan abbr="nunquã">nunquam</expan> tamen ho<lb></lb>rizontali motu versùs guttæ centrum naturali inſtin<lb></lb>ctu tendent, ergò ſi concipiatur <expan abbr="centrũ">centrum</expan> guttæ ABCD <lb></lb>ac ſi eſſet centrum ſy ſtematis <expan abbr="elemẽtaris">elementaris</expan> partes gut<lb></lb>tæ cenſeri poſſent non graues. </s> <s id="s.001827">His poſitis intelliga<lb></lb>tur ſuperaddita, vel eleuata eminentia, ſeu mammil<lb></lb>la aquea H in laterali loco guttæ, tunc aereus ocea<lb></lb>nus RS ne dum ſupernè ſuperficiem A, ſed etiam la<lb></lb>tera eius H, D, & infimas facieculas B, C æquali ener<lb></lb>gia comprimet, tum ratione grauitatis, cum ratione <lb></lb>virtutis elaſticæ eius. </s> <s id="s.001828">Habemus igitur caſum ſimilem <lb></lb>ei qui in <expan abbr="præcedẽti">præcedenti</expan> propoſitione ſupponebatur, ſcili<lb></lb>cèt gutta ABCD cuius partes non nituntur vniri, nec <pb pagenum="345" xlink:href="010/01/353.jpg"></pb><arrow.to.target n="marg465"></arrow.to.target><lb></lb>ſponte ferri versùs centrum eiuſdem guttæ, & ab ae<lb></lb>re æqualibus viribus vndique comprimitur; quarę <lb></lb>eſt impoſſibile, vt mammilla H contundatur, hoc e<lb></lb>nim, vt dictum eſt, exigit maiorem vim compreſſiuam <lb></lb>in H, quàm in D. <expan abbr="nõ">non</expan> poterit ergo prædicta gutta præ<lb></lb>cisè contornari, & acquirere tumorem ſphæricum. </s> </p> <p type="margin"> <s id="s.001829"><margin.target id="marg464"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001830"><margin.target id="marg465"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001831">Idipſum verificari in guttulis aqueis pauimento <lb></lb>innixis, patet ex eo, quòd ſaltem collaterales partes <lb></lb>eius H, & D carent vi motiua horizontali qua feran<lb></lb>tur versùs guttæ centrum, & tunc mammilla H noņ <lb></lb>poterit contundi ab aere GH cum eius vis <expan abbr="nõ">non</expan> ſit ma<lb></lb>ior vi compreſſiua aeris SD. </s> <s id="s.001832">Vnde colligitur, quòd <lb></lb>compreſſio fluidi aerei RSXV nullo pacto globoſita<lb></lb>tem guttularum aquæ creat, quare fatendum eſt ab <lb></lb>alia longè diuerſa cauſa hoc prouenire. </s> </p> <p type="main"> <s id="s.001833">Videndum modò eſt, an à vi intrinſeca, & natu<lb></lb>rali mercurij, vel aquæ prædictæ guttulæ <expan abbr="ſuſpendã-tur">ſuſpendan<lb></lb>tur</expan>, & tornentur. </s> </p> <p type="main"> <s id="s.001834"><emph type="center"></emph>PROP. CLXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001835"><emph type="center"></emph><emph type="italics"></emph>Guttula fluidæ non poſſunt ſponte à vi intrinſeca, & natu<lb></lb>rali tumorem, & ſphæricitatem acquirere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001836">QVia guttæ fluidæ diuerſis in locis collocari ef<lb></lb>formarique poſſunt, hinc ſequitur vt eius par<lb></lb>ticulæ componentes cogantur modò versùs vnam̨ <lb></lb>plagam, modò versùs alteram tendere, ac promoue<lb></lb>ri, prout centrum, aut ſuſpenſio guttulæ varijs in lo<lb></lb>cis transferri, ac ſituari poteſt, & tunc ſi ſenſu carent <pb pagenum="346" xlink:href="010/01/354.jpg"></pb><arrow.to.target n="marg466"></arrow.to.target><lb></lb>mirari profectò ſubit à quo Nuntio monentur, eiſque <lb></lb>oſtenditur, vbi gentium guttæ centrum exiſtat, tranſ<lb></lb>portatumque ſit, & quo ſenſu id aſſequi valeant, & <lb></lb>quo appetitu afficiantur, vt eum amplecti velint; po<lb></lb>ni ergo debet vis aliqua, quæ cæca neceſſitate tranſ<lb></lb>ferat, retineat, conglutinetque aqueas particulas <lb></lb>circa centrum guttulæ ſuſpenſæ, hæc autem vis mo<lb></lb>tiua cùm non ſit determinata ad aliquam plagam, erit <lb></lb>profectò vaga, & incerta, quæ nihilominùs certum̨ <lb></lb>gradum impetus, & proindè æqualem vim ſę <lb></lb>mouendi ſursùm, deorsùm, & ad latera habebit, <lb></lb>ergo hiſce omnibus motionibus agitari deberent a<lb></lb>quæ, vel mercurij particulæ in ipſis guttis pendenti<lb></lb>bus, & contornatis, & hoc quidem audactèr aliqui <lb></lb>recentiores pronunciant, quorum ſententia (ni fal<lb></lb>lor) non ſecùs, ac præcedens, facilè refelli poteſt, <lb></lb>quia ſi quęlibet pars fluidi in gutta æquali vi, & ener<lb></lb><arrow.to.target n="marg467"></arrow.to.target><lb></lb>gia mouetur, ſemel alterata, & perturbata eiuſdem̨ <lb></lb>guttæ rotunditate, ſcilicèt exporrecta aliqua mam<lb></lb>milla ex eodem fluido guttam componente, non poſ<lb></lb>ſet priſtinam ſphęricitatem denuò acquirere, prop<lb></lb>terea quod pars illa magis à centro remota non poſ<lb></lb>ſet centro guttæ approximari, niſi expelleret longiùs <lb></lb>à centro reliquas partes in vallibus guttæ exiſtentes, <lb></lb>nec hæ cedere locum poſſent, cùm æqualem <expan abbr="energiã">energiam</expan>, <lb></lb>ac vim habeant, ac illæ, quæ in ſummitate mammil<lb></lb>læ degunt. </s> <s id="s.001837">Si verò conſiderentur motus contrarij, & <lb></lb>diuerſi quatenùs vna portio ad infimum ſitum guttæ <lb></lb>deprimitur, altera verò eleuatur, alię lateraliter <expan abbr="ferũ-">ferun-</expan><pb pagenum="347" xlink:href="010/01/355.jpg"></pb><arrow.to.target n="marg468"></arrow.to.target><lb></lb>tur, tunc quidem quis capiet globoſam, & <expan abbr="ſphæricã">ſphæricam</expan> <lb></lb>figuram fluidi partes irregularitèr ſe mouentes com<lb></lb>ponere poſſe? </s> <s id="s.001838">Finge in hac aula pluuiam copioſam̨ <lb></lb>granulorum frumenti cadentium, & ſimùl infernè ab <lb></lb>aliqua violentia grana delapſa repelli ſursùm, & la<lb></lb>teraliter; in hac (inquam) perpetua, & confuſa agi<lb></lb>tatione, quomodò poſſent prædicta grana deciden<lb></lb>tia, & aſcendentia ſphęricam figuram conflare, & <expan abbr="nõ">non</expan> <lb></lb>potiùs quamlibet aliam figuram irregularem, vt ex<lb></lb>perientia conſtat? </s> </p> <p type="margin"> <s id="s.001839"><margin.target id="marg466"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001840"><margin.target id="marg467"></margin.target>Prop. 365.</s> </p> <p type="margin"> <s id="s.001841"><margin.target id="marg468"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001842">Recurrere ad inflexionem particularum mercurij, <lb></lb>vel aquæ, quę ad inſtar anguillarum conglobentur, & <lb></lb>vniantur, & ſic guttulas pendentes, & ſphæricas effi<lb></lb>ciant, videtur omninò abſurdum, vt ſuperiùs inſinua<lb></lb>uimus. <lb></lb><arrow.to.target n="marg469"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001843"><margin.target id="marg469"></margin.target><expan abbr="Aiũt">Aiunt</expan> ob <expan abbr="de-fectũ">de<lb></lb>fectum</expan> analo<lb></lb>giæ <expan abbr="aquã">aquam</expan>, vel <lb></lb><expan abbr="mercuriũ">mercurium</expan> in<lb></lb>tra aerem in<lb></lb>ſinuari non <lb></lb>poſſe, & i<lb></lb>deò motu re<lb></lb>flaxo in ſę <lb></lb>ipſis conglo<lb></lb>bati.</s> </p> <p type="main"> <s id="s.001844">Tantummodò conſiderabimus ea, quæ ab alijs af<lb></lb>feruntur, qui aiunt ob defectum analogiæ mercurij, <lb></lb>vel aquæ cum aere ambiente fieri, vt hydrargyrum, <lb></lb>vel aqua aerem effugiat, & aer aquam, & potiùs iņ <lb></lb>ſe ipſam ſpontaneo motu conglobetur, vniaturquę <lb></lb>non quidem à perceptione vtilis electione ſponta<lb></lb>nea, ſed neceſſitate quadam, quæ cogat vt partes <lb></lb>fluidæ ſe mouentes, & perpetuò agitatæ, dum in ae<lb></lb>re moueri nequeunt, reflectantur intra ſe ipſas, & ſic </s> </p> <p type="main"> <s id="s.001845"><arrow.to.target n="marg470"></arrow.to.target><lb></lb>guttulas illas ſphæricas efforment. </s> <s id="s.001846">Aſſignant poſtea <lb></lb>duas cauſas à quibus fluidorum diuerſa, & heteroge<lb></lb>nea natura pendet: prima eſt motuum diuerſitas, ſci<lb></lb>licèt quia pariculæ minimæ aquæ diuerſo modo agi<lb></lb>tantur, ac mouentur particulæ aeris <expan abbr="ambiẽtis">ambientis</expan>, & hinc <pb pagenum="348" xlink:href="010/01/356.jpg"></pb><arrow.to.target n="marg471"></arrow.to.target><lb></lb>pendere aiunt quod aquæ particulæ nequeant ſuam̨ <lb></lb>vim motiuam exercere intra aerem, & propterea co<lb></lb>gantur motu reflexo excurrere intra profunditatem <lb></lb>eiuſdem aqueæ guttulæ, & ex hiſce motibus reflexis <lb></lb>ſphæricam figuram guttæ efformari aiunt. </s> <s id="s.001847">Secundą <lb></lb>cauſa eſt pororum aſſimetria, inquiunt enim poroſi<lb></lb>tates aeris eius figuræ eſſe, vt particulæ aquæ nequa<lb></lb>quam poſſint per incongruentes poroſitates aeris in<lb></lb>ſinuari, & excurrere. </s> <s id="s.001848">Vndè guttula aquæ perindè ab <lb></lb>aere coercetur, ac ſi eſſet fornix marmoreus. </s> </p> <p type="margin"> <s id="s.001849"><margin.target id="marg470"></margin.target>Defectum <lb></lb>analogiæ flui<lb></lb>dorum, aut a <lb></lb>diuerſita rę <lb></lb>motuum aut <lb></lb>ab <expan abbr="incõgruẽ-tia">incongruen<lb></lb>tia</expan> pororum <lb></lb>pendere cea<lb></lb>ſcut. </s> </p> <p type="margin"> <s id="s.001850"><margin.target id="marg471"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001851"><emph type="center"></emph>PROP. CLXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001852"><emph type="center"></emph><emph type="italics"></emph>Ob motuum diuerſitatem aquæ, & aeris non poſſunt aquæ <lb></lb>guttulæ ſphæricè conglobari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001853">ET quoad motuum diuerſitatem pertinet, <expan abbr="notã-dum">notan<lb></lb>dum</expan> eſt verum non eſſe, quòd motus vnius cor<lb></lb>poris omninò impediatur à motu diuerſo alterius, <lb></lb>hoc enim contingit quando prædicti motus ſunt in<lb></lb>ter ſe contrarij per eamdem rectam lineam, & æqua<lb></lb>libus viribus, & velocitatibus facti; ſi enim non ſint <lb></lb>inter ſe contrarij, ſed ambo ad eaſdem partes <expan abbr="tẽdãt">tendant</expan>, <lb></lb>tunc non omninò impeditur motus alterius corporis, <lb></lb>ſed tantummodò alteratur quoad directionem, vel <lb></lb>circa velocitatem; quia verò aduerſarij ſupponunt <lb></lb>motiones partium tum aquæ cùm aeris, vagas, & di<lb></lb>uerſimodas ſursùm, deorsùm, & lateraliter, erit om<lb></lb>ninò impoſſibile, vt ſemper motus <expan abbr="particularũ">particularum</expan> aquæ <lb></lb>opponantur motionibus, quibus partes aeris <expan abbr="agitã-">agitan-</expan><pb pagenum="349" xlink:href="010/01/357.jpg"></pb><arrow.to.target n="marg472"></arrow.to.target><lb></lb>tur, & ſi hoc verum eſt, oportet vt ex parte, & <expan abbr="aliquã-do">aliquan<lb></lb>do</expan> impediri poſſit motus partium aquæ ab aere am<lb></lb>biente, ſed frequentiùs, & vt plurimùm nullum im<lb></lb>pedimentum motioni aquæ afferent, & tunc ſe mu<lb></lb>tuo penetrabunt, & ideò non vnientur ſphæricè gut<lb></lb>tæ aqueæ, quod eſt falſum. </s> </p> <p type="margin"> <s id="s.001854"><margin.target id="marg472"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001855">Præterea ſi aer valdè expanſus, & rarior eſt, quàm <lb></lb>aqua, & tam infirmæ, & de bilis conſiſtentiæ vt faci<lb></lb>lè à quacumque exigua vi diſſipari, & è ſuo loco di<lb></lb>moueri poſſit, veriſimile eſt vt partes aquæ denſio<lb></lb>res, & conſiſtentes poſſint, dùm mouentur, facilè ae<lb></lb>reas particulas è ſuis locis expellere, & ſic per eius <lb></lb>ſubſtantiam penetrare; quod profectò ab ipſa expe<lb></lb>rientia confirmari videtur, nam videmus vapores a<lb></lb>queos è mari, & lacubus exhalantes ſumma facilita<lb></lb>te per aerem penetrare, cùm <expan abbr="cõſtet">conſtet</expan> vapores nil aliud <lb></lb>eſſe, quàm congeriem exiliſſimarum aquæ particula<lb></lb>rum, quæ motu placido, & tranquillo ab aqua <expan abbr="difflã-tur">difflan<lb></lb>tur</expan>, tempore hyemali, abſque adiumento ignis, aut <lb></lb>alterius rapidæ violentiæ. </s> <s id="s.001856">Et profectò numquam aer <lb></lb>reperiri poteſt ſincerus abſque admiſtione minima<lb></lb>rum aquæ partium, vt conſtat ex experimentis iņ <lb></lb>noſtra Academia experimentali Medicea factis; igi<lb></lb>tur ſicuti illæ minimæ aquæ particulæ vaporem com<lb></lb>ponentes à diuerſa aeris agitatione non <expan abbr="retardãtur">retardantur</expan>, <lb></lb>nec impediuntur quin liberè, & impunè aerem pe<lb></lb>netrare poſſint, ſic paritèr particulæ illæ guttæ pen<lb></lb>dulæ terebrare poterunt aeris ambientis <expan abbr="conſiſtẽtiã">conſiſtentiam</expan>, <lb></lb>& proindè aerearum partium diuerſæ motiones non <pb pagenum="350" xlink:href="010/01/358.jpg"></pb><arrow.to.target n="marg473"></arrow.to.target><lb></lb>impedient effluuium, & motionem vagam partium <lb></lb>aquæ. </s> <s id="s.001857">Imò ſi quis hoc negotium attentè perpendat, <lb></lb>percipiet ab ijſdem partibus aqueis potius impediri <lb></lb>motiones eius, quàm ab aere externo; primò quią <lb></lb>ſunt æquè conſiſtentes, & corpulentæ, & ſic non poſ<lb></lb>ſunt viciſſim è ſuis locis dimoueri, ac expelli: inſupèr <lb></lb>cum earum motus ſint vagi, & inordinati, non <expan abbr="poſsũt">poſsunt</expan> <lb></lb>omnes ad eaſdem partes dirigi, & ideò vna pars ſu<lb></lb>per aliam incidens motu contrario, viciſſim ſe ſe iņ <lb></lb>progreſſu impedient. </s> <s id="s.001858">Ad hæc, vbi deeſt aer, deficiet <lb></lb>prorſus cauſa impediens motiones particularum a<lb></lb>quæ, proptereà quòd vbi aer non adeſt, neque eius <lb></lb>motus impedimentum afferre poterit agitationi par<lb></lb>tium aquæ. </s> <s id="s.001859">hoc autem contingit in vacuo Torricel<lb></lb>liano, vbi nullo pacto impedirentur motiones <expan abbr="earũ-dem">earun<lb></lb>dem</expan> particularum aquæ, imò faciliùs per ſpatium fe<lb></lb>rè vacuum ſpargi diſſiparique poſſent, & proindè non <lb></lb>cogerentur motu reflexo intra eaſdem guttas regre<lb></lb>di, agitari, conſtiparique, & ideò ceſſaret cauſa, & <lb></lb>neceſſitas ob quam guttulæ aquæ in vacuo, vel in ae<lb></lb>re rariſſimo ſphęricum tumorem acquirere <expan abbr="deberẽt">deberent</expan>, <lb></lb>& tamen hoc repugnat experientiæ, cùm in prædicto <lb></lb>vacuo guttulæ non minùs rotundæ, quàm in aere a<lb></lb>perto, tornentur. </s> </p> <p type="margin"> <s id="s.001860"><margin.target id="marg473"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001861"><emph type="center"></emph>PROP. CLXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001862"><emph type="center"></emph><emph type="italics"></emph>Incongruentia, & angustia pororum aeris non poſſet impedi<lb></lb>re diffuſionem particularem aquæ per <lb></lb>aerem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="351" xlink:href="010/01/359.jpg"></pb><arrow.to.target n="marg474"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001863"><margin.target id="marg474"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001864">SI poſtea conſideremus <expan abbr="incongruẽtiam">incongruentiam</expan> pororum, <lb></lb>patet verum non eſſe aduerſariorum aſſertum <expan abbr="cũ">cum</expan> <lb></lb>aiunt, ideò ab aere impediri motiones partium aquę, <lb></lb>quia orificia pororum aeris ſtrictiora ſunt, <expan abbr="quã">quam</expan> vt per <lb></lb>ea aquæ particulæ ingredi, & fluere poſſint, nam hinc <lb></lb>inferre liceret neque aqueas particulas per <expan abbr="ipsãmet">ipsammet</expan> <lb></lb>aquam cieri, & excurrere poſſe; facilè enim percipi<lb></lb>tur, quòd in aqua poroſitates non poſſunt eſſe adeò <lb></lb>amplæ, vt per eas intromitti poſſint particulæ eiuſ<lb></lb>demmet aquæ, ſed debent eſſe multò minores, ſicuti <lb></lb>interſtitia, quæ in aceruo granorum tritici, vel milij <lb></lb>intercipiuntur, ſemper minora ſunt, <expan abbr="quã">quam</expan> grana eiuſ<lb></lb>dem tritici, vel milij, aliàs facta acerui concuſſione <lb></lb>ſe mutuò magis conſtringerent amplexarentur quę <lb></lb>granula prædicta, intromiſſis nempè granulis in eiſ<lb></lb>dem amplis interſtitijs. </s> <s id="s.001865">Hinc ſequitur vt æquè diffi<lb></lb>cilè aquæ particulæ per ipſam aquam moueri, agita<lb></lb>rique poſſint, quàm per aerem, quia nempè æquè in<lb></lb>commodus eſt progreſſus aquæ per aquam, ac per ae<lb></lb>rem; ſi verum eſt requiri poroſitates in fluido tantæ <lb></lb>amplitudinis vt capaces ſint particularum aquæ ad <lb></lb>hoc vt per prædictum fluidum moueri queant. </s> <s id="s.001866">cùm<lb></lb>que aquæ anguſtæ poroſitates non impediant motum <lb></lb>particularum aquæ per ipſam aquam. </s> <s id="s.001867">ergò pariter <lb></lb>anguſtia pororum aeris non impediet motum <expan abbr="partiũ">partium</expan> <lb></lb>aquæ per aerem. </s> </p> <figure id="id.010.01.359.1.jpg" xlink:href="010/01/359/1.jpg"></figure> <pb pagenum="352" xlink:href="010/01/360.jpg"></pb> <p type="main"> <s id="s.001868"><arrow.to.target n="marg475"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001869"><margin.target id="marg475"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001870"><emph type="center"></emph>PROP. CLXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001871"><emph type="center"></emph><emph type="italics"></emph>Facilè aquæ particulæ per aerem moueri poſſunt, non quia per <lb></lb>eius poroſitates inſinuantur, ſed quia aereas particu<lb></lb>las ſolutas, & amouibiles expellere è ſuis <lb></lb>locis poßunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001872">HInc deducitur, quòd vera cauſa, quare aqua fa<lb></lb>cilè per aquam penetrare, & fluere poteſt, <expan abbr="nõ">non</expan> <lb></lb>ſit amplitudo pororum eius, ſed quia partes ipſius <lb></lb>aquæ facilè expelli poſſunt è ſuis locis vt locum ce<lb></lb>dant particulis aqueis, quæ ibidem inſinuari <expan abbr="debẽt">debent</expan>, <lb></lb>& niſi anteriores aquæ particulæ è ſuis locis expelle<lb></lb>rentur, nequaquàm aliæ partes ibidem ſuccedere, & <lb></lb>fluere poſſent. </s> <s id="s.001873">Si igitur hoc verum eſt, percipimus, <lb></lb>quòd particulæ aqueæ poſſunt quoque aerem pene<lb></lb>trare, & per eius profunditatem fluere, licèt aer po<lb></lb>ros tàm reſtrictos, & anguſtos habeat, vt aquæ parti<lb></lb>culæ per eos ingredi nequeant, ſufficit enim vt aereæ <lb></lb>particulæ poſſint è ſuis loculis expelli, vt ibidem a<lb></lb>queæ partes inſinuari poſſint, eodem modo, ac con<lb></lb>tingit in ipſamet aqua. </s> <s id="s.001874">Quod autem hoc faciliùs iņ <lb></lb>aere effici valeat, quàm in aqua, patet ex eo, quòd ae<lb></lb>reæ particulæ magis raræ, & expanſæ, & ideò minus <lb></lb>reſiſtentes ſunt, quàm partes aqueæ; non erit igitur <lb></lb>difficile vt partes aquæ ipſo aere ſolidiores è ſuis lo<lb></lb>cis expellant particulas aeris, & ſic facilè per eas a<lb></lb>qua moueatur. </s> <s id="s.001875">Adde quòd experientia <expan abbr="cõſtat">conſtat</expan> aque<lb></lb>as particulas perpetuò intra aerem inſinuari, vt ſupra <pb pagenum="353" xlink:href="010/01/361.jpg"></pb><arrow.to.target n="marg476"></arrow.to.target><lb></lb>dictum eſt de vaporibus; & reuerà nunquam reperiri <lb></lb>poteſt aer omninò aridus, & abſque vlla admixtione <lb></lb>aquæ, ſed eſt veluti ſpongia quædam. </s> </p> <p type="margin"> <s id="s.001876"><margin.target id="marg476"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001877"><emph type="center"></emph>PROP. CLXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001878"><emph type="center"></emph><emph type="italics"></emph>Licèt ob defectum analogiæ motus partium aquæ impedire<lb></lb>tur ab ambiente aere, non proindè ſphæricè <lb></lb>conglobari poſſet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001879">TAndèm dato quòd aquæ particulæ ob defectum <lb></lb>analogiæ fugerent ab aere ambiente, & impe<lb></lb>direntur tamquam à fornice, & proindè motu refle<lb></lb>xo excurrerent intrà eamdem aquam, non indè ſequi<lb></lb>tur quòd ſphæricè guttæ ipſæ efformari poſſent. </s> <s id="s.001880">Fin<lb></lb>ge enim in aliquo lacu innumeros piſciculos, vel an<lb></lb>guillulas intra vtrem, vel ſaccum raræ, & cedentis <expan abbr="cõ-ſiſtentiæ">con<lb></lb>ſiſtentiæ</expan> contineri, & æquè impediri à pelle, vel ſac<lb></lb>co cedente, & diſtrahibili, ac aquæ particulæ ab ip<lb></lb>ſo aere, quia videmus piſciculos minimè ſphæricè <lb></lb>conglobari, ſed in prædicta cauitate vtris oblongą <lb></lb>expatiari. </s> <s id="s.001881">idipſum <expan abbr="cõtingere">contingere</expan> deberet in aqueis par<lb></lb>ticulis coercitis à reti aereo, quæ licèt miris modis <lb></lb>agitarentur, nihilominùs ſphæricam rotunditatem̨ <lb></lb>acquirere non poſſent; & ratio eſt quia vt plura cor<lb></lb><arrow.to.target n="marg477"></arrow.to.target><lb></lb>pora fluida ſpontè contornentur oportet vt omnes <lb></lb>tendant directè versùs vnum punctum intermedium, <lb></lb>& præterea oportet vt vires motiuæ non ſint ſemper <lb></lb>inter ſe æquales, ſed maiorem vim impulſiuam ha<lb></lb>beant, quò magis à prædicto centro diſtant. </s> <s id="s.001882">igitur <pb pagenum="354" xlink:href="010/01/362.jpg"></pb><arrow.to.target n="marg478"></arrow.to.target><lb></lb>ex his omnibus licèt concludere, quòd neque defe<lb></lb>ctus analogiæ, nec diuerſitas motuum, neque incon<lb></lb>gruentia pororum aeris cauſa eſſe poteſt rotundita<lb></lb>tis guttularum fluidarum. </s> </p> <p type="margin"> <s id="s.001883"><margin.target id="marg477"></margin.target>Prop. 16 c.</s> </p> <p type="margin"> <s id="s.001884"><margin.target id="marg478"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001885">Poſtquam reiecimus aliorum falſas ſententias, re<lb></lb>ſtat modò vt veram cauſam huius effectus pro viribus <lb></lb>detegamus. </s> <s id="s.001886">& primò debet præmitti ſequens propo<lb></lb>ſitio mechanica. </s> </p> <p type="main"> <s id="s.001887"><emph type="center"></emph>PROP. CLXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001888"><emph type="center"></emph><emph type="italics"></emph>Si corpus anguloſum innixum parietis verticalis aſperita<lb></lb>tibus ſuſtineatur à potentia termino oppoſito, & horizon<lb></lb>tali eiuſdem corporis applicata; potentia ad corporis <lb></lb>pondus ſe habebit, vt diſtantia centri grauitatis <lb></lb>eius à fulcimento ad diſtantiam poten<lb></lb>tiæ ab eodem fulcimento.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001889">SIt corpus D à pluribus angulis comprehenſum, <lb></lb>& paries verticalis AB, cuius ſuperficies ſit a<lb></lb>ſpera, & denticulata, in huius lo<lb></lb><figure id="id.010.01.362.1.jpg" xlink:href="010/01/362/1.jpg"></figure><lb></lb>co B innitatur ſuſtineaturque ex<lb></lb>tremitas anguloſa corporis D, vt <lb></lb>nimirum minimè excurrere poſſit <lb></lb>deorſum; ſuſpendatur poſteà op<lb></lb>poſita eius extremitas E ab aliqua <lb></lb>potentia, tunc vis eleuans in E mi<lb></lb>nor erit pondere corporis D, & ad <lb></lb>eius grauitatem abſolutam <expan abbr="eamdẽ">eamdem</expan> <lb></lb>proportionem habebit, quam diſtantia BD à centro <pb pagenum="355" xlink:href="010/01/363.jpg"></pb><arrow.to.target n="marg479"></arrow.to.target><lb></lb>grauitatis prædicti ſolidi vſque ad parietem habet <lb></lb>adlongitudinem EB totius ſaxi; quia corpus graue <lb></lb>D ſuſpenditur in medio vectis <expan abbr="horizõtalis">horizontalis</expan> EB à dua<lb></lb>bus potentijs, ab illa quam exercet potentia ſuſten<lb></lb>tans E, & ab aſperitate parietis denticulati in B, er<lb></lb>gò ex mechanicis potentia E ad <expan abbr="reſiſtẽtiam">reſiſtentiam</expan> ponderis <lb></lb>D eandem rationem habet quam diſtantia DB ad to<lb></lb>tam vectis EB longitudinem. </s> </p> <p type="margin"> <s id="s.001890"><margin.target id="marg479"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001891"><emph type="center"></emph>PROP. CLXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001892"><emph type="center"></emph><emph type="italics"></emph>Iiſdem poſitis eadem potentia eleuare altiùs poterit conuer<lb></lb>tendo, & rotando corpus polihedrum regulari ſimile <lb></lb>innixum aſperitatibus eiuſdem verticalis <lb></lb>parietis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001893">SIt corpus D anguloſum, & regulari ſimile, ita vt <lb></lb>centrum grauitatis eius ſit quoque centrum ma<lb></lb>gnitudinis eiuſdem. </s> <s id="s.001894">Dico quòd eadem potentia ſub<lb></lb>dupla E poterit eleuare corpus graue D ad <expan abbr="quãlibet">quallibet</expan> <lb></lb>altitudinem parietis AC; quia cùm ſolidum D ſit re<lb></lb>gulare, & habeat figuram anguloſam, & denticula<lb></lb>tam, vt in quolibet ſitu ſuæ ſuperficiei poſſit adnecti, <lb></lb>& ſuſtineri in ſub ſequentibus aſperitatibus parietis <lb></lb>denticulati CA, ſequitur vt quomodolibet reuolua<lb></lb>tur corpus D, ſemper in ſub ſequentibus eminentijs <lb></lb>parietis aſperis AB paritèr ſuſtineatur fulciaturque, <lb></lb>atque in eodem ſitu horizontali ab ijſdem duabus <lb></lb>potentijs corpus D ſuſtinebitur, ſcilicèt à potentią <lb></lb>E, & ab aliqua denticulari eminentia parietis AC; <pb pagenum="356" xlink:href="010/01/364.jpg"></pb><arrow.to.target n="marg480"></arrow.to.target><lb></lb>cùmque ſemper eadem proportio remaneat inter eo<lb></lb>rum diſtantias à contactu, ſcilicèt inter DB ad BE, <lb></lb>igitur ſemper eadem vis E ſuſtinere, & impellerę <lb></lb>ſursùm poterit eamdem <expan abbr="reſiſtẽtiam">reſiſtentiam</expan> corporis D; qua<lb></lb>propter fiet continua vertigo ſolidi D nedùm circą <lb></lb>eius centrum, ſed etiam rotando, adhęrendoque <expan abbr="lõ-gitudini">lon<lb></lb>gitudini</expan> verticali BA, & proindè eleuabitur ad <expan abbr="quã-cum">quan<lb></lb>cum</expan> que <expan abbr="ſublimitatẽ">ſublimitatem</expan> A. </s> </p> <p type="margin"> <s id="s.001895"><margin.target id="marg480"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001896"><emph type="center"></emph>PROP. CLXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001897"><emph type="center"></emph><emph type="italics"></emph>Particulæ aquæ ſuperficiales poſſunt rotando altiùs eleuari <lb></lb>parieti vaſis adhærendo à vi ponderis aqua collate<lb></lb>ralis impulſæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001898">POſtea conſidero in vaſe XRSV in aquæ ſupremą <lb></lb>parte laminam horizontalem conflatam ex mi<lb></lb>nimis aquæ particulis A, B, D, <expan abbr="tũc">tunc</expan> <lb></lb><figure id="id.010.01.364.1.jpg" xlink:href="010/01/364/1.jpg"></figure><lb></lb>exiguum corpus A parietem fir<lb></lb>mum contingat in L, ob huius a<lb></lb>ſperitatem fulcietur, ſuſtentabi<lb></lb>tur que terminus L granuli aquei <lb></lb>A, reliqua verò portio eius ver<lb></lb>sùs C cùm non adhæreat nequę <lb></lb>ſuſtentetur ab vllo pariete, fulcietur, ſuſtinebiturque <lb></lb>à ſubiecta aqua FI, quæ non grauatur ab integro <expan abbr="põ-dere">pon<lb></lb>dere</expan> totius aquei granuli A, ſed ab eius medietatę, <lb></lb>propterea quòd concurrit ad id ſuſtentandum parie<lb></lb>tis ſcabrities L. </s> <s id="s.001899">Conſideretur poſtea conſequens mi<lb></lb>nimum granulum aqueum B, quod à pariete <expan abbr="remotũ">remotum</expan> <pb pagenum="357" xlink:href="010/01/365.jpg"></pb><arrow.to.target n="marg481"></arrow.to.target><lb></lb>integram ſuam grauitatem exercet <expan abbr="cõprimendo">comprimendo</expan> ſub<lb></lb>iectam a quam IE, & quia partium aquæ EIF, æquali<lb></lb>tèr ſcilicèt horizontalitèr iacentium, IE magis pre<lb></lb>mitur quàm FI, cùm illa duplum pondus, ſcilicèt in<lb></lb>tegrum ipſius B ſuſtineat, hæc verò ſemiſſem ponde<lb></lb>ris ipſius A, ergo pars FI minus preſſa ſursùm impel<lb></lb><arrow.to.target n="marg482"></arrow.to.target><lb></lb>letur ab EI magis preſſa, proindeque pars aquæ FI <lb></lb>vim faciet ſursùm impellendo terminum C granuli <lb></lb>aquei A; quia verò eius extremitas L foueolis aſpe<lb></lb>ris parietis adhæret, impeditur retineturque nè dire<lb></lb>cto motu ſursùm ferriqueat, ergò neceſsè eſt, vt gra<lb></lb>nulum A flectatur ad modum vectis circa firmum ter<lb></lb>minum L, cùmque tactus, & adhæſio in pariete reno<lb></lb>uetur <expan abbr="cõtinẽtèr">continentèr</expan> poſt flexionem ſursùm termini C <expan abbr="nõ">non</expan> <lb></lb>ſecùs, ac in rotis dentatis contingit, pariterque re<lb></lb>nouetur ſemper cauſa vlterioris ſuſpenſionis granuli <lb></lb>A, quæ eſt minor compreſſio ſubiectæ aquæ FI quam <lb></lb>EI; igitur ſemper renouatur flexio vectis CL ſursùm̨ <lb></lb>proindeque minutiſſimum granulum aquæ A motu <lb></lb>vertiginoſo, & reptitio aſperitatibus parietis LK <lb></lb>adhærendo eo vſque eleuabitur, quouſque fiat æqui<lb></lb>librium cum aqua collaterali. </s> </p> <p type="margin"> <s id="s.001900"><margin.target id="marg481"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001901"><margin.target id="marg482"></margin.target>Caroll. <lb></lb>Pr. 10.10.</s> </p> <p type="main"> <s id="s.001902">Videndum modò qua ratione poſſint ſaluari effe<lb></lb>ctus omnes, qui in guttis exiguis obſeruantur. </s> </p> <p type="main"> <s id="s.001903"><emph type="center"></emph>PROP. CLXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001904"><emph type="center"></emph><emph type="italics"></emph>Ratio affertur quare guttæ aquæ pendulæ è ſuperficie prona <lb></lb>ſolidi corporis ſustineantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="358" xlink:href="010/01/366.jpg"></pb><arrow.to.target n="marg483"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001905"><margin.target id="marg483"></margin.target>Cap. 8. cur <lb></lb>exiguæ aqu˛ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001906">ET primò conſideretur gutta pendula ex ſuperfi<lb></lb>cie prona rami alicuius arboris, cuius figurą <lb></lb>videtur conoidalis parabolica: reddi debet hìc cauſa <lb></lb>efficiens, & formalis huius ſuſpenſionis; concipian<lb></lb>tur externæ ſuperficiales particulæ huiuſmodi guttę, <lb></lb>quæ viciſſim connexæ à ſuis machinulis aliquo pacto <lb></lb>incuruatis ad modum arcus efficiant veluti linteum, <lb></lb>vel ſaccum in eius perimetro annexum ſummitati li<lb></lb>gni duri, & conſiſtentis; partes verò intermediæ gut<lb></lb>tulæ ſua grauitate naturali premunt, & <expan abbr="diſtrahũt">diſtrahunt</expan> lin<lb></lb>teum, vel rete ſuperficiale, at quia energia machi<lb></lb>nularum non cedit vi puſillæ grauitatis guttulæ pen<lb></lb>dentis, fit vt æquatis momentis tota gutta ſuſpenſą <lb></lb>hæreat. </s> </p> <p type="main"> <s id="s.001907"><emph type="center"></emph>PROP. CLXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001908"><emph type="center"></emph><emph type="italics"></emph>Quare globuli fluidi pendentes è filo paritèr fluido <lb></lb>ſuſtineantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001909">SEcundo loco ſit pila fluida pendula ex filo pari<lb></lb>tèr fluido, vt euidentiùs contingit in Saliua, & <lb></lb>in alijs humoribus glutinoſis; hìc iam concipi <expan abbr="debẽt">debent</expan> <lb></lb>hinc inde à filo in orbem particulæ fluidi, quæ <expan abbr="excur-rẽdo">excur<lb></lb>rendo</expan> deorsùm vt graues ad infimum fili ſitum, ibi <expan abbr="cõ-glutinatis">con<lb></lb>glutinatis</expan>, concatenatiſque externis particulis ope <lb></lb>machinularum earum efformant veluti ſacculum <expan abbr="reti-cularẽ">reti<lb></lb>cularem</expan> intra <expan abbr="quẽ">quem</expan> tanta moles fluidi contineri poteſt, <lb></lb>vt eius pondus non ſuperet robur machinularum̨ <lb></lb>glutinis. </s> </p> <pb pagenum="359" xlink:href="010/01/367.jpg"></pb> <p type="main"> <s id="s.001910"><arrow.to.target n="marg484"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001911"><margin.target id="marg484"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001912"><emph type="center"></emph>PROP. CLXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001913"><emph type="center"></emph><emph type="italics"></emph>Et cur globulus fluidus pauimento innixus; <lb></lb>ſuſtineatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001914">TErtiò pila fluida innixa pauimento paritèr ſuſti<lb></lb>netur veluti à filo, ſeù virga <expan abbr="perpẽdiculari">perpendiculari</expan> ad <lb></lb>planum ſubiectum à quo ſuſtentatur; à prædicta vir<lb></lb>ga in orbem colligantur aliæ particulæ eiuſdem flui<lb></lb>di, quæ in èxigua baſi fulciuntur à plano ſubiecto, <lb></lb>quando ob ariditatem eius, & incongruitatem po<lb></lb>rorum aqua non diffluit, nec ipſum humectat; in tali <lb></lb>caſu filum fluidum perpendiculare perinde agit, ac <lb></lb>filum pendulum; ſed guttæ figura differt aliquo pa<lb></lb>cto à præcedenti, non enim eſt ſphærica, nec oblon<lb></lb>ga oualis, ſed inferiùs dilatatur, & ſupernè acumen <lb></lb>veluti conoidale acquirit. </s> </p> <p type="main"> <s id="s.001915"><emph type="center"></emph>PROP. CLXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001916"><emph type="center"></emph><emph type="italics"></emph>Declaratur quomodò, & quouſque ex nouo affluxu guttulæ <lb></lb>augentur, & quare poſt violentam fluidi tractionem <lb></lb>denuò ſponte ſua recolliguntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001917">IN primo, & ſecundo caſu ex affluxu noui fluidi <lb></lb>augeri poteſt moles guttæ pendulæ, vt eius pon<lb></lb>dus maius ſit, quàm vt à vi glutinis ſuſtineri queat, & <lb></lb>tunc elongatur infernè, & tandem diſrumpitur, & <lb></lb>decidit, at pars reſidua oblonga recolligitur ſursùm, <lb></lb>efficitque nouam exiguam globoſitatem; cauſa verò <pb pagenum="360" xlink:href="010/01/368.jpg"></pb><arrow.to.target n="marg485"></arrow.to.target><lb></lb>huius recollectionis, & aſcenſus ſursùm hæc eſt, quia <lb></lb>à pondere, & à motu ingentis guttulæ <expan abbr="decidẽtis">decidentis</expan> ma<lb></lb>chinulæ reſiduarum partium fluidi violentèr diſtra<lb></lb>ctæ ſpontè ſua aptę natæ ſunt, denuò ſe ſe recollige<lb></lb>re, reducique ad naturalem ſitum, ſicut contingit in <lb></lb>arcu, & in qualibet machina, quæ poſt violentam̨ <lb></lb>diſtractionem, extenſionemque, denuò ſe flectit re<lb></lb>duciturque ad priſtinum ſitum, cùmque in hac vni<lb></lb>uerſali actione machinularum filum fluidum compo<lb></lb>nentium ſubſequatur motus regreſſus ſursùm, nec <lb></lb>motus fieri poſſit abſque impetu, igitur ab hoc præ<lb></lb>dictæ fluidi particulæ impelluntur altiùs quàm exi<lb></lb>gat naturalis earum grauitas, & hinc ſequitur vt de<lb></lb>nuò poſtea affluentibus circumcirca fluidi particulis, <lb></lb>denuò gutta rotunda efformetur. </s> </p> <p type="margin"> <s id="s.001918"><margin.target id="marg485"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001919">In tertio caſu Propoſit. præcedentis augeri poteſt <lb></lb>gutta duplici modo, & ex concurſu noui fluidi ſu<lb></lb>pernè ſenſim additi, quouſque vis glutinis ſufficiat, <lb></lb>vt pondus guttæ ſuſtinere valeat, nè decidat, ſed <expan abbr="dũ">dum</expan> <lb></lb>augetur, lateralitèr creſcit, ampliaturque, & ſic gut<lb></lb>ta amittit priſtinam globoſitatem. </s> </p> <p type="main"> <s id="s.001920"><emph type="center"></emph>PROP. CLXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001921"><emph type="center"></emph><emph type="italics"></emph>Quare duæ guttæ homogeneæ ſe ſe tangentes colliguntur <lb></lb>vniunturque.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001922">SEd dignior inquiſitione eſt recollectio duarum <lb></lb>guttularum quoties lateralitèr ſe mutuò <expan abbr="tangãt">tangant</expan>, <lb></lb>ex quibus componitur vnica gutta rotunda. </s> <s id="s.001923">Ratio <pb pagenum="361" xlink:href="010/01/369.jpg"></pb><arrow.to.target n="marg486"></arrow.to.target><lb></lb>eſt, quia partes eiuſdem fluidi homogenei facillimè <lb></lb>excurrunt ſupra, & intra ſe ipſas, dum propter ſoli <lb></lb>ariditatem, quando ipſum humectare, & madeface<lb></lb>re non poſſunt ob pororum incongruentiam, oportet <lb></lb>vt omnes ſimul <expan abbr="inſiſtãt">inſiſtant</expan> ſuper ſilum fluidum, vel ſuper <lb></lb>axim perpendicularitèr plano ſubiecto inſiſtentem, <lb></lb>& ſic in orbem, vt priùs dictum eſt, axi connectuntur, <lb></lb>& globum integrum efformant magis tamen contu<lb></lb>ſum, & depreſſum, quàm antea. </s> </p> <p type="margin"> <s id="s.001924"><margin.target id="marg486"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001925">Sed dices, quænam eſt vis motiua, quæ impellit <lb></lb>partes duarum guttularum ſe tangentium vt ſursùm <lb></lb>aſcendant in ſummitate guttulæ amplioris ex eis <expan abbr="cõ-poſitæ">con<lb></lb>poſitæ</expan>? </s> <s id="s.001926">Reſpondeo, quòd hoc <expan abbr="pẽdet">pendet</expan> ex vi compreſ<lb></lb>ſiua collateralium partium, quæ cùm <expan abbr="nõ">non</expan> poſſint pla<lb></lb>no ſubiecto vniri, & à vi glutinis ſuperatur pondus <lb></lb>partium eiuſdem fluidi, ſequitur vt ratione vectis <lb></lb>particulæ intermediæ eleuentur. </s> <s id="s.001927">Vniuerſa hæc ope<lb></lb>ratio ſic perficitur: pri<lb></lb><figure id="id.010.01.369.1.jpg" xlink:href="010/01/369/1.jpg"></figure><lb></lb>mò duo globi mercurij A <lb></lb>BCD, & EBFG innixi <lb></lb>pauimento VX in locis <lb></lb>C, & F ſe tangant latera<lb></lb>liter in B. hinc patet, <lb></lb>quòd partes fluidę BC, & <lb></lb>BF facilè intra ſe ipſas excurrendo ſe mutuò ample<lb></lb>cti poſſunt, & excludere aerem <expan abbr="intermediũ">intermedium</expan> BCF ini<lb></lb>tio facto à contactu B versùs C, & F. </s> <s id="s.001928">Idipſum accidit <lb></lb>in ſupremis partibus AB, & EB, vnde efformabitur <lb></lb>figura quaſi ſphæroidalis, & oualis HIKL, quę poſtea <pb pagenum="362" xlink:href="010/01/370.jpg"></pb><arrow.to.target n="marg487"></arrow.to.target><lb></lb>magis rotunda reddetur, ſed aliquo pacto contuſa, & <lb></lb>compreſſa remanebit, propterea quòd circa axim̨ <lb></lb>HK ad planum <expan abbr="ſubiectũ">ſubiectum</expan> <lb></lb><figure id="id.010.01.370.1.jpg" xlink:href="010/01/370/1.jpg"></figure><lb></lb>VX perpendicularem al<lb></lb>ligantur in orbem partes <lb></lb>inęqualium <expan abbr="momentorũ">momentorum</expan>, <lb></lb>quia nempè inæqualitèr, <lb></lb>ſcilicèt magis diftant ab <lb></lb>axi HK partes laterales <lb></lb>I, & L quàm anterior, & poſterior, & ideò iuxtà le<lb></lb>ges mechanices partes minùs preſsæ à magis com<lb></lb>preſſis expelli debent longiùs ab axi. </s> </p> <p type="margin"> <s id="s.001929"><margin.target id="marg487"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001930">Præterea ex dictis, ratione vectis partes fluidi I, & <lb></lb><arrow.to.target n="marg488"></arrow.to.target><lb></lb>L remotiores ab axe HK ſursùm impellent eas, quæ <lb></lb>eidem axi proximæ ſunt, ac proindè eleuabitur flui<lb></lb>da eminentia OMN, & conſequentèr latera I, & L <lb></lb>conſtringentur vt in P, & R. </s> </p> <p type="margin"> <s id="s.001931"><margin.target id="marg488"></margin.target>Prop. 173.</s> </p> <p type="main"> <s id="s.001932"><emph type="center"></emph>PROP. CLXXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001933"><emph type="center"></emph><emph type="italics"></emph>Quare filum ceræ alaccæ, vitri, aui metalli liquefacti à <lb></lb>flamma candelæ inſufflatæ ope fistulæ dum liqueſcit <lb></lb>recolligitur pilam rotundam efformans, <lb></lb>& augens.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001934">RAtio huius effectus eſt quia dum à copioſo, & <lb></lb>vehementi igne particulæ vitri diſgregantur, <lb></lb>non tamen omninò, neque ſecundùm totum, nam vni<lb></lb>cam maſſam inflatam, & fluidam componunt, & ideò <lb></lb>ex parte ſe ſe tangunt, ergo cùm habeant gluteņ, <pb pagenum="363" xlink:href="010/01/371.jpg"></pb><arrow.to.target n="marg489"></arrow.to.target><lb></lb>ſcilicèt habeant machinas flexiles, & reſilientes, ſit <lb></lb>vt à prædicta ignis penetratione violentèr diſtrahan<lb></lb>tur machinulæ illæ, vt totidem arcus, & ideò pro eo<lb></lb>rum ingenio vim habent ſe recolligendi, & ſe vnien<lb></lb>di cum reliquis partibus fili liquefacti, à quibus di<lb></lb>ſtractæ fuerant: cùmque adueniant duæ aliæ cauſæ <lb></lb>accidentales, quarum vna eſt durities, aut minor flu<lb></lb>xibilitas perimetri, aut ſuperficiei eius externæ re<lb></lb>ſpectu partium intermediarum magis fluidarum, vn<lb></lb>de efficitur veluti epidermis, & ſacculus conſiſten<lb></lb>tior; altera cauſa eſt inflatio, quam efficit ignis <expan abbr="ve-hemẽtiſſimè">ve<lb></lb>hementiſſimè</expan> agitans internas vitri partes fluidiores, <lb></lb>quæ cùm circumdentur ambianturque à perimetro, <lb></lb>& ſuperficie duriori, & tenaciori, veluti à ſacculo, <lb></lb>ſit vt à vi glutinis dum conantur ſe recolligere par<lb></lb>tes prædicti fluidi tota maſſa fuſa, & inflata retraha<lb></lb>tur, recolligaturque versùs filum, & ſic efformetur <lb></lb>globulus, & eadem ratione augeatur eius diameter, <lb></lb>at dum augetur pila creſcente pondere amittit prio<lb></lb>rem illam formam orbicularem, & efficitur gutta ob<lb></lb>longa deorsùm tendens. </s> <s id="s.001935">modò quia vis glutinis, ſeù <lb></lb>energia machinularum eſt cauſa retractionis particu<lb></lb>larum fuſarum, hoc dum ſuperat vim exigui ponde<lb></lb>ris prædictæ guttulæ facilè poterit ipſam mouere, <lb></lb>& retrahere ſiuè ſursùm, ſiuè lateralitèr. <lb></lb><figure id="id.010.01.371.1.jpg" xlink:href="010/01/371/1.jpg"></figure><pb pagenum="364" xlink:href="010/01/372.jpg"></pb><arrow.to.target n="marg490"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001936"><margin.target id="marg489"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001937"><margin.target id="marg490"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001938"><emph type="center"></emph>PROP. CLXXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001939"><emph type="center"></emph><emph type="italics"></emph>Declaratur quemadmodum lamina gracilis aqua grauior <lb></lb>ſpecie foueam efficit in aqua dum innatat, & quare <lb></lb>monticuli illi aquei non decidant.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001940">PRo clariori eiuſdem problematis intelligentią <lb></lb>inquirenda eſt ratio alterius effectus, qui in flui<lb></lb>dis obſeruatur: in vaſe BCEI <lb></lb><figure id="id.010.01.372.1.jpg" xlink:href="010/01/372/1.jpg"></figure><lb></lb>aqua pleno applicetur graci<lb></lb>liſſima lamina ænea FG ho<lb></lb>rizontalitèr, hæc quidem ſi <lb></lb>arida fuerit licèt grauior ſpe <lb></lb>cie ſit ipſa aqua, non omninò <lb></lb>demergetur, nec ad fundum vaſis feretur, ſed <expan abbr="deſcẽ-det">deſcen<lb></lb>det</expan> infra ſupremam libellam aquæ IB, ibique inna<lb></lb>tabit efficiendo argines aqueos tumidos, & eleuatos <lb></lb>GAB, & IF, qui non ſecus, ac ſi eſſent parietes im<lb></lb>pediunt effluxum ſupremæ aquæ AB vt nequeat <expan abbr="de-ſcẽdere">de<lb></lb>ſcendere</expan> in profunda fouea IFGA genita à depreſſio<lb></lb>ne eiuſdem laminæ: & hìc anima deuertendum eſt ca<lb></lb>uitatem, ſeu puteum IFGA effici tunc ſolummodò, <lb></lb>quando excurrit ad prædictum ſpatium replendum̨ <lb></lb>aliquod fluidum leuius, ſed non homogeneum ipſi <lb></lb>aquæ veluti eſt aer, vel vacuum Torricellianum: at <lb></lb>adueniente aqua, vel fluido aquæ <expan abbr="naturã">naturam</expan> participan<lb></lb>te, vt eſt vinum, tunc margines aquei GAB, & IF <expan abbr="nõ">non</expan> <lb></lb>perſiſtent, ſed diſrumpentur, & deorsùm dilapſi fo<lb></lb>ueam replebunt. </s> <s id="s.001941">Præterea notandum eſt fieri noņ <pb pagenum="365" xlink:href="010/01/373.jpg"></pb><arrow.to.target n="marg491"></arrow.to.target><lb></lb>poſſe vt argines prædicti aquei cuiuſcumque altitu<lb></lb>dinis perſiſtant, ſi enim quartam partem latitudinis <lb></lb>digiti auricularis ſuperauerint, ſubitò deorsùm præ<lb></lb>cipitantur. </s> <s id="s.001942">Ratio quæ aſſignari ſolet, huius effectus, <lb></lb>aut eſt compreſſio aeris multoties à nobis reiecta, aut <lb></lb>quia veluti in aceruo granorum tritici, vel arenæ <expan abbr="cõ-tingit">con<lb></lb>tingit</expan> efficitur montuoſitas quædam decliuis, quią <lb></lb>nimirùm ſupremæ partes fulciuntur ab inferioribus, <lb></lb>vt arginem inclinatum efforment, qui non poteſt e<lb></lb>leuari vltra angulum ſemirectum, aliàs ſubitò grana <lb></lb>ipſa deciderent deorsùm; concipiunt ergo minimą <lb></lb>aquam componentia eſſe minutiſſima quædam gra<lb></lb>nula, & proindè ad inſtar arenæ efformare poſſe ar<lb></lb>ginem prædictum. </s> <s id="s.001943">Sed hoc non videtur ſufficiens <lb></lb>duplici de cauſa, primò quia argines aquei non ele<lb></lb>uantur ad quamlibet altitudinem, vt contingit in a<lb></lb>ceruo granorum tritici, licèt enim angulus inclina<lb></lb>tionis arginis aquei, ſcilicèt complementum anguli <lb></lb>AGF, minor ſit ſemiſſe vnius anguli recti, non poteſt <lb></lb>altitudo prædicti arginis eleuari vltra altitudinem̨ <lb></lb>quadrantis latitudinis digiti auricularis, cùm oppo<lb></lb>ſitum obſeruetur in aceruo granorum tritici. </s> <s id="s.001944">Præte<lb></lb>rea argines aquei BAG, & FI ſunt curui, & gibbi, & <lb></lb>in infima eius parte G angulus inclinationis maior eſ<lb></lb>ſe ſolet ſemirecto, igitur requiritur aliqua alia cauſa <lb></lb>præter fulcimentum particularum minimarum, quod <lb></lb>in arena, & in aceruo granorum tritici <expan abbr="cõtingit">contingit</expan>. </s> <s id="s.001945">Hoc <lb></lb>egregiè ex noſtra hypotheſi ſaluatur, dum enim la<lb></lb>mina FG deſcendit infra ſupremam aquæ <expan abbr="libellã">libellam</expan> IB, <pb pagenum="366" xlink:href="010/01/374.jpg"></pb><arrow.to.target n="marg492"></arrow.to.target><lb></lb>particulæ extimæ ſuperficiei aquæ CAG, & IF quæ <lb></lb>mutuò inter ſe connectebantur, ob iam dictam lanu<lb></lb>ginem flexibilem, & <figure id="id.010.01.374.1.jpg" xlink:href="010/01/374/1.jpg"></figure><expan abbr="reſiliẽ-entem">reſilien<lb></lb>tem</expan>, poſtea diſtrahun<lb></lb>tur machinulę, & ideò fortiùs <lb></lb>ad <expan abbr="inuicẽ">inuicem</expan> vinciuntur, & pro<lb></lb>indè efformant veluti pleu<lb></lb>ram, ſeù reticulum à quo re<lb></lb>tineri, & impediri poſſunt partes aquæ prædicti <expan abbr="mõ-ticuli">mon<lb></lb>ticuli</expan> GAB, ſed non licet prædictam montuoſitatem <lb></lb>ad <expan abbr="quãcunque">quancunque</expan> altitudinem eleuare, propterea quòd <lb></lb>reſiſtentia machinularum ipſius aquæ exigui roboris <lb></lb>eſt, & proindè tamdiù perſeuerabit, quamdiù puſil<lb></lb>lam vim grauitatis ſuperat, quæ naturali inſtinctu <lb></lb>deorsùm tendere debet obliquo, & inclinato itine<lb></lb>re, & ideò eius momentum menſuratur à perpendi<lb></lb>culari altitudine ſupra planum FG, quæ valdè exi<lb></lb>gua eſt vt diximus. </s> </p> <p type="margin"> <s id="s.001946"><margin.target id="marg491"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001947"><margin.target id="marg492"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001948"><emph type="center"></emph>PROP. CLXXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001949"><emph type="center"></emph><emph type="italics"></emph>Vis impellens, & retinens argines aqueos eleuatos ſupra <lb></lb>aquæ libellam non eſt propria ipſius aquæ, neque aeris, <lb></lb>ſed eſt grauitas eiuſdem aquæ collateralis legi<lb></lb>bus mechanicis operando.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001950">DEbemus modò rationem afferre alterius phœ<lb></lb>nomeni difficilioris. </s> <s id="s.001951">ſit vas aqua <expan abbr="plenũ">plenum</expan> RDEI <lb></lb>in quo immergatur quodlibet corpus ſolidum, & du<lb></lb>rum FGK, quod ſit aridum, & non vngatur ſebo, vel <pb pagenum="367" xlink:href="010/01/375.jpg"></pb><arrow.to.target n="marg493"></arrow.to.target><lb></lb>alia ſimili vnctuoſa materia, huius verò corporis re<lb></lb>maneat vna pars FK eminens ſupra aquæ libellam̨, <lb></lb>vel emineat paries eiuſdem̨ <lb></lb><figure id="id.010.01.375.1.jpg" xlink:href="010/01/375/1.jpg"></figure><lb></lb>vaſis, tunc conſtat experientia, <lb></lb>quòd aqua non perſiſtit in in<lb></lb>fima eius libella horizontali <lb></lb>AK, ſed repit, aſcenditque per ſuperficiem <expan abbr="eleuatã">eleuatam</expan> <lb></lb>KG efformando priſma aqueum triangulare, cuius <lb></lb>ſectio eſt BGK, ibidemque retinetur ſuſpenditurque <lb></lb>mons prædictus aqucus, <expan abbr="nõ">non</expan> ſecus ac ſi à pariete cur<lb></lb>uo BG impediretur eius fluxus deorſum verſus <expan abbr="aquã">aquam</expan> <lb></lb>ſubiectam AB. </s> <s id="s.001952">Quia verò aqua non amittit <expan abbr="naturalẽ">naturalem</expan> <lb></lb>eius grauitatem, aſſignari debet cauſa à qua ſuſpenſa <lb></lb>retinetur, & quæ vis ipſam ſursùm prius impulit. <lb></lb></s> <s id="s.001953">Hæc profectò aut propria, & naturalis eſt ipſius aquę, <lb></lb>vt nimirùm ſponte ſua ſursùm aſcendat, ibidemquę <lb></lb>retineatur, aut hoc ſit ab aliqua cauſa violenta ex<lb></lb>terna. </s> <s id="s.001954">Quòd verò non ſit vis propria, & natiua ipſius <lb></lb>aquæ, patet ex ſuperiùs dictis, quia nimirùm ſemper <lb></lb>aqua grauis eſt, exercetque ſuam vim compreſſiuam <lb></lb>versùs centrum telluris, vt ſenſus euidentia conſtat. </s> </p> <p type="margin"> <s id="s.001955"><margin.target id="marg493"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001956">Alij poſtea recurrunt ad aeris vim compreſſiuam, <lb></lb>aiunt enim aerem <expan abbr="cõtiguum">contiguum</expan> interno vaſis parieti GK <lb></lb>minori energia ſubiectam aquam K comprimere, <expan abbr="quã">quam</expan> <lb></lb>aer HB à pariete remotus premat ſubiectam aquam <lb></lb>B, propterea quòd illa quodammodo ab aſperita<lb></lb>tibus parietis retinetur, ac impeditur ne libero co<lb></lb>natu, & fluxu premere queat aquam ſubiectam K <expan abbr="cũ">cum</expan> <lb></lb>hæc vniuerſam ſuam grauitatis, & virtutis elaſticæ <pb pagenum="368" xlink:href="010/01/376.jpg"></pb><arrow.to.target n="marg494"></arrow.to.target><lb></lb>energiam liberè exercere poſſit; hoc autem falſum̨ <lb></lb>eſſe ſic <expan abbr="oſtẽdemus">oſtendemus</expan>; ablata aqua repleatur vas hydrar<lb></lb>gyro, quia ex hypotheſi aduer<lb></lb><figure id="id.010.01.376.1.jpg" xlink:href="010/01/376/1.jpg"></figure><lb></lb>ſarij, aer FKG parieti vaſis <expan abbr="cõ-tiguus">con<lb></lb>tiguus</expan> minori vi <expan abbr="cõprimit">comprimit</expan> ſub<lb></lb>iectum mercurium K, quàm aer <lb></lb>HB ab <expan abbr="eodẽ">eodem</expan> pariete magis remo<lb></lb>tus premat <expan abbr="ſubiectũ">ſubiectum</expan> <expan abbr="mercuriũ">mercurium</expan> B, & præterea mercu<lb></lb>rius K, vel ęquilibratur <expan abbr="cũ">cum</expan> mercurio B, vel minori <expan abbr="mo-mẽto">mo<lb></lb>mento</expan> premit <expan abbr="ſubiectũ">ſubiectum</expan> <expan abbr="fluidũ">fluidum</expan> <expan abbr="quã">quam</expan> <expan abbr="idipsũ">idipsum</expan> B, eò quòd il<lb></lb>le à parietis aſperitatibus impeditur, hic verò libe<lb></lb>rè premit. </s> <s id="s.001957">igitur hìc <expan abbr="quoq;">quoque</expan> eleuari deberet <expan abbr="mõs">mons</expan> mer<lb></lb>curialis versùs parietem, vt in aqua contingit, quod <lb></lb>eſt falſum, & repugnat experientiæ, potiùs enim de<lb></lb>primitur in foueam BGK, non ergo ab illa inæquali <lb></lb>aeris preſſione aqueus monticulus versùs parietem̨ <lb></lb>vaſis eleuatur. </s> <s id="s.001958">Et licèt reſponderi poſſet quòd cauſa <lb></lb>huius diuerſæ operationis pendeat à defectu analo<lb></lb>giæ mercurij, & parietis vaſis, ob quem ille refugit <lb></lb>huius contactum, non tamen in dubium reuocatur ab <lb></lb>aduerſarijs inæqualis illa aeris preſſio ſupra mercu<lb></lb>rium, quare in rari caſu operatur vis illa, qua mercu<lb></lb>rius a vaſis ſuperficie interna ſeparatur vnà cum inæ<lb></lb>quali vi compreſſiua aeris, ideò in duobus vaſis cy<lb></lb>lindricis anguſtis RST, & VXZ ſit amplitudo, ſeu <lb></lb>baſis ST maior, quàm XZ in eiſque hydrargyrum in<lb></lb>fundatur vſque ad B, & E. </s> </p> <p type="margin"> <s id="s.001959"><margin.target id="marg494"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001960">Et <expan abbr="quianõ">quia non</expan> poteſt mercurij ſuprema portio à ſuper<lb></lb>ficie interna fiſtulæ ſeparari, niſi ſuſpendatur <expan abbr="efficiẽ-">efficien-</expan><pb pagenum="369" xlink:href="010/01/377.jpg"></pb><arrow.to.target n="marg495"></arrow.to.target><lb></lb>do tumidum <expan abbr="mõticulum">monticulum</expan>. </s> <s id="s.001961">Verùm minus grauis mercu<lb></lb>rij moles in ſtrictiori fiſtula contenti faciliùs ſuſpen<lb></lb>ditur, quàm grauior moles eiuſdem latiorem <expan abbr="fiſtulã">fiſtulam</expan> <lb></lb><expan abbr="occupãs">occupans</expan>; ergo faciliùs mercurius ab interna ſtrictio<lb></lb>ris fiſtulæ ſuperficie ſeparatur, <expan abbr="quã">quam</expan> ab interna latio<lb></lb>ris fiſtulæ ſuperficie, & proinde altius, vel ſaltem <expan abbr="nõ">non</expan> <lb></lb>minùs altè ſeparari deberet mercurij monticulus GF <lb></lb>quàm CA. poſtea aer perimetris in<lb></lb><figure id="id.010.01.377.1.jpg" xlink:href="010/01/377/1.jpg"></figure><lb></lb>ternis vtriuſque fiſtulæ adhærens æ<lb></lb>què impeditur, & propterea æquè <lb></lb>aeris preſſiones debilitatę viribus æ<lb></lb>qualibus ſubiectum mercurium <expan abbr="cõ-primere">con<lb></lb>primere</expan> debent; at intermediæ par<lb></lb>tes aeris versùs axes cylindrorum <expan abbr="exiſtẽtes">exiſtentes</expan> inæqua<lb></lb>les vires compreſſiuas habebunt, eò quòd inæquali<lb></lb>tèr à ſuperficiebus internis vaſorum recedunt, quare <lb></lb>aer incumbens mercurio in A maiori vi eum compri<lb></lb>met, ac contundet, quàm aer incumbens mercurio <lb></lb>in G, igitur validiori vi retundetur monticulus tumi<lb></lb>dus BAD quàm EGL, & ideo altior erit monticulus <lb></lb>mercurij EGL, quàm BAD; ſed hoc eſt falſum, multò <lb></lb>enim maior eſt altitudo CA quàm FG, ergo aeris vis <lb></lb>compreſſiua nullam inæqualitatem ſortitur, vel non <lb></lb>talis eſt vt tàm inſignes varietates producere valeat, <lb></lb>ſcilicèt non eleuarentur argines illi aquei ęquè ab ae<lb></lb>re compreſſi, ac reliqua aquæ ſuperficies horizonta<lb></lb>lis. </s> <s id="s.001962">Præterea in vacuo Torricelliano aer ibi non exi<lb></lb>ſtens <expan abbr="nõ">non</expan> poſſet eleuare argines aqueos parietibus fi<lb></lb>ſtulæ adhęrentes; vel ſi ibidem remanet minima aeris <pb pagenum="370" xlink:href="010/01/378.jpg"></pb><arrow.to.target n="marg496"></arrow.to.target><lb></lb>portio valdè expanſa, & rara erit, & ideò (ex Prop. <lb></lb>105.) eius pondus, & vis compreſſiua minor erit <expan abbr="nẽ-pè">nen<lb></lb>pè</expan> centeſima, & octuageſima pars ponderis aeris ex<lb></lb>terni eiuſdem molis: igitur illa non poterit ſupra a<lb></lb>quæ libellam eleuare <expan abbr="idẽ">idem</expan> pondus arginis aquei quod <lb></lb>in aere aperto ab huius ingenti pondere <expan abbr="ſuſpẽdeba-tur">ſuſpendeba<lb></lb>tur</expan>: cùmque hoc ſit falſum, æquè enim argines aquei <lb></lb>in prædicto vacuo ſublimantur, ac in aere aperto, igi<lb></lb>tur non ab aere ibidem non exiſtente, vel rariſſimo <lb></lb>argines prædicti ſuſpenduntur. </s> </p> <p type="margin"> <s id="s.001963"><margin.target id="marg495"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001964"><margin.target id="marg496"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001965">Alij poſtea recurrunt ad ſcabritiem, & <expan abbr="aſperitatẽ">aſperitatem</expan> <lb></lb>parietis à qua impeditur deſcenſus, ſuſpendunturque <lb></lb>particulæ aqueæ; ſed hoc minimè ſufficere videtur, <lb></lb>nam ad ſummum dicta ſcabrities commoda eſſet, & <lb></lb>apta ad retinendam aquam poſtquam ſemèl eleuata <lb></lb>fuiſſet ad illam altitudinem, quatenùs ab aſperitati<lb></lb>bus, veluti vncinis impediretur defluxus aquæ deor<lb></lb>sùm, at non poſſent aquam ſubleuare, cùm ſcabrities <lb></lb>vim motiuam non habeat; & ſanè aſperitates nedum <lb></lb>non adiuuarent, ſed potiùs impedirent aquæ eleua<lb></lb>tionem in prædictis arginibus duplici nomine, primò <lb></lb>quia eædem parietis ſcabroſitates, quæ vim habent <lb></lb>prohibendi deſcenſum aquæ, <expan abbr="impediũt">impediunt</expan> quoque eius <lb></lb>aſcenſum; præterea multò magis, & maiori vi aſcen<lb></lb>ſus aquæ impediri deberet quàm eius <expan abbr="deſcẽſus">deſcenſus</expan>, quia <lb></lb>in aſcenſu aqua præter reſiſtentiam aſperitatis parie<lb></lb>tis ſuperare debet impedimentum, & reluctantiam <lb></lb>propriæ grauitatis, cum è contra in deſcenſu ab hac <lb></lb>adiuuetur. </s> <s id="s.001966">igitur ſcabrities parietis non poteſt eſſę <pb pagenum="371" xlink:href="010/01/379.jpg"></pb><arrow.to.target n="marg497"></arrow.to.target><lb></lb>cauſa eleuationis aquæ in prædictis arginibus. </s> </p> <p type="margin"> <s id="s.001967"><margin.target id="marg497"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001968">Debet modo aſſignari virtus motiua, quæ eleuat, <lb></lb>& ſuſtinet aquam ſupra propriam libellam vſque ad <lb></lb>ſummitatem arginis, & hanc demonſtrabo eſſe ſim<lb></lb>plicem aquæ grauitatem. </s> <s id="s.001969">Quia aquæ particulæ ad<lb></lb>hærentes parieti vaſis inſinuant ramos ſuarum machi<lb></lb>nularum intra poroſitates, & foueolas parietis, à cu<lb></lb>ius eminentijs, & aſperitatibus fulciuntur extremi<lb></lb>tates particularum aquæ, quarum oppoſiti termini <lb></lb>ſuſtinentur, à ſubiecta collaterali aqua, proptereà <lb></lb>efficientur veluti totidem vectes conuertibiles circa <lb></lb>eorum fulcimenta parieti annexa. </s> <s id="s.001970">Hinc fit vt prædi<lb></lb>ctæ aquæ particulæ exiguam vim compreſſiuam exer<lb></lb>ceant, & minori momento ſubiectam aquam com<lb></lb>primant, cùm partes aquæ collateralis liberè <expan abbr="premẽ-do">premen<lb></lb>do</expan> ſupra aquam ſubiectam integram ſuam vim, & <lb></lb>momentum exerceant, igitur ex prop. 174. partes <lb></lb>minùs preſſæ ſursùm impelli debent à partibus ma<lb></lb>gis compreſſis: & licèt illæ retineantur, & impedian<lb></lb>tur ne motu ſibi ipſi æquidiſtanti ferri ſursùm <expan abbr="queãt">queant</expan>, <lb></lb>tamen eadem impedimenta <expan abbr="aſperitatũ">aſperitatum</expan> parietis præ<lb></lb>clarè adiuuant flexionem, & turbinationem earun<lb></lb>dem aquæ particularum, igitur à vi motiua grauita<lb></lb>tis maioris aquæ collateralis flecti, rotari, & impelli <lb></lb>ſursùm poſſunt parieti adhęrendo eædem aquæ par<lb></lb>ticulæ; dum verò efficitur prædicta eleuatio, ſummi<lb></lb>tates guttularum reuolutarum eminentiores reddun<lb></lb>tur quàm aliæ particulæ parieti adhærentes, igitur <lb></lb>tunc prædictæ particulæ iam eleuatæ naturali inſtin-<pb pagenum="372" xlink:href="010/01/380.jpg"></pb><arrow.to.target n="marg498"></arrow.to.target><lb></lb>ctu excurrent versùs parietem, cui ſuis villis adhæ<lb></lb>rebunt, ex qua adhæſione momentum eius grauitatis <lb></lb>denuò imminuetur, & ideò renouabitur cauſa vlte<lb></lb>rioris eius eleuationis à compreſſione laterali aquæ <lb></lb>ſuo momento non imminuto comprimentis, & hinc <lb></lb>ſequitur continuatio prædicti aſcenſus rotando, & <lb></lb>adhærendo parieti, quouſque efficiatur æquilibrium <lb></lb>cum prædicta aqua collaterali liberè premente. </s> </p> <p type="margin"> <s id="s.001971"><margin.target id="marg498"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001972">Et hìc notandum eſt, quòd vis prædictæ adhæſio<lb></lb><arrow.to.target n="marg499"></arrow.to.target><lb></lb>nis aquæ non eſt æqualis in omnibus partibus prædi<lb></lb>ctæ montuoſitatis, ſed omnium maxima eſt illa, quæ <lb></lb>retinet mini nas aquæ particulas immediatè <expan abbr="parietẽ">parietem</expan> <lb></lb>tangentes, quæ non ſecùs, ac ſi eſſent claui, vel vn<lb></lb>cini tenaci nexu ibidem inſinuantur, & minima erit <lb></lb>vis illa, quæ retinet remotiſſimas, & poſtremas par<lb></lb>ticulas dictæ montuoſitatis aquæ, aliarum verò par<lb></lb>tium illæ, quæ parieti viciniores ſunt, maiori tena<lb></lb>citate ſuſpendentur, quam aliæ partes aquæ a præ<lb></lb>dicto pariete magis remotæ. </s> <s id="s.001973">Et hinc oritur decliuitas <lb></lb>illa montis aquæ pendentis. </s> </p> <p type="margin"> <s id="s.001974"><margin.target id="marg499"></margin.target>Declinitas <lb></lb>prædicti a<lb></lb>quei montis <lb></lb>pendet ex in <lb></lb>æqualitate <lb></lb>virtutis mon<lb></lb>tium.</s> </p> <p type="main"> <s id="s.001975">Hic iam reſoluere poſſumus aliud problema val<lb></lb><arrow.to.target n="marg500"></arrow.to.target><lb></lb>dè agitatum, vnde nimirùm proueniat, quòd aquą <lb></lb>in fiſtulis tenuiſſimis vtrinque apertis ſursùm aſcen<lb></lb>dat. </s> <s id="s.001976">Et primo loco phænomena, quæ in hac opera<lb></lb>tione obſeruantur, recenſeri debent. </s> </p> <p type="margin"> <s id="s.001977"><margin.target id="marg500"></margin.target>Proponun<lb></lb>tur obſerua<lb></lb>tiones <expan abbr="aſcẽ-ſus">aſcen<lb></lb>ſus</expan> aquæ in <lb></lb>fiſula gra<lb></lb>ciliſſimis.</s> </p> <p type="main"> <s id="s.001978">Poſtquam graciliſſima fiſtula EH contingit aquæ <lb></lb><expan abbr="ſuperficiẽ">ſuperficiem</expan> RV in H videmus, quòd ſubito aqua ſen<lb></lb>ſim aſcendere incipit ad notabilem altitudinem HK <lb></lb>eiuſdem cauitatis ſupra aquæ ſubiectæ libellam RV. <pb pagenum="373" xlink:href="010/01/381.jpg"></pb><arrow.to.target n="marg501"></arrow.to.target><lb></lb>Siverò prædicta cauitas priùs humectata, & made<lb></lb>facta fuerit, & denuò exinanita ſubitò poſt <expan abbr="contactũ">contactum</expan> <lb></lb>multò altiùs, & celeriùs vſque ad G aqua perpendi<lb></lb>cularitèr eleuatur, ac aſcendebat <lb></lb><figure id="id.010.01.381.1.jpg" xlink:href="010/01/381/1.jpg"></figure><lb></lb>in priori caſu quando interna fi<lb></lb>ſtulæ cauitas arida erat. </s> <s id="s.001979">Præterea <lb></lb>ſi poſt aquæ exuctionem transfe<lb></lb>ratur fiſtula AB ab aqua ad <expan abbr="aerẽ">aerem</expan>, <lb></lb>non ſecùs in ea perpendiculari<lb></lb>ter erecta fixè retinetur eadem̨ <lb></lb>aquæ moles in eodem ſitu, & al<lb></lb>titudine CD, quàm priùs habe<lb></lb>bat. </s> <s id="s.001980">Inſuper ſi eadem exigua fi<lb></lb>ſtula interiùs madida, ſed exina<lb></lb>nita contingat paruulam guttulam aquæ F in palmą <lb></lb>manus eleuatam, ſi immediatè poſt guttæ contactum <lb></lb>fiſtula citò eleuetur, tunc videmus aquam exuctam̨ <lb></lb>non quieſcere in infimo fiſtulæ ſitu B, ſed vlteriùs <lb></lb>pauliſper ſursùm promoueri, excurrereque ſucce<lb></lb>dente aere in eius infima parte. </s> </p> <p type="margin"> <s id="s.001981"><margin.target id="marg501"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001982"><emph type="center"></emph>PROP. CLXXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001983"><emph type="center"></emph><emph type="italics"></emph>Aqua in fiſtulis non aſcendit ſpontè ſua à vi motiua particu<lb></lb>larum eius impulſa, neque inſinuatur, retineturque <lb></lb>ibidem ab æquilibrio aeris, aut ab internis ca<lb></lb>naliculi aſperitatibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001984">RElatis obſeruationibus <expan abbr="inquirendũ">inquirendum</expan> eſt, an præ<lb></lb>dicta phænomena ſaluari poſſint ex noſtris, vel <pb pagenum="374" xlink:href="010/01/382.jpg"></pb><arrow.to.target n="marg502"></arrow.to.target><lb></lb>ex aliorum Authorum principijs. </s> <s id="s.001985">Et primò ſi aquą <lb></lb>ſponte ſua aſcendit intra fiſtulæ cauitatem à vi parti<lb></lb>cularum eius ſe mouentium, igitur aut grauitate om<lb></lb>ninò carent, aut in tali caſu eam non exercent (quod <lb></lb>vltrò aliqui Authores concedunt) ſi inquam hoc ve<lb></lb>rum eſt, impoſſibile eſſet vt aqua in fiſtula immiſſą <lb></lb>perpendiculariter erecta exerceret vllam vim com<lb></lb>preſſiuam deorsùm, & ideò ſi fiſtula infernè prolon<lb></lb>garetur, nullo pacto aqua ibidem deorsùm deſcende<lb></lb>ret, quod tamen experientiæ refragatur, nam <expan abbr="eadẽ">eadem</expan> <lb></lb>fiſtula cum aqua contenta in aere translata, & per<lb></lb>pendiculariter ad horizontem erecta ſi inuerſo ſitu <lb></lb>diſponatur vt pars eius ſupina A fiat prona, aut ei alia <lb></lb>fiſtula infernè adnectatur, aqua in ea contenta celeri <lb></lb>motu deſcendit, ſi madida fuerit, quouſque prope <lb></lb>infimum orificium perducatur; igitur falſum eſt a<lb></lb>quæ in fiſtula contentæ particulas grauitate priuari, <lb></lb>proindeque ſponte ſua intra fiſtulam aſcendere. </s> <s id="s.001986"><expan abbr="Cũ">Cum</expan> <lb></lb>verò aiunt cauſam prædicti aſcenſus aquæ penderę <lb></lb>ex eo quòd eius particulæ naturali inſtinctu feruntur <lb></lb>versùs fluidum aqueum, vel aquæ analogum <expan abbr="contẽ-tum">conten<lb></lb>tum</expan> in vitri internis poroſitatibus, nec à grauitate, <lb></lb>quam negant, impediri poſſunt: ſi hoc, inquam, ve<lb></lb>rum eſſet, madefacta vniuerſa fiſtulæ interna cauita<lb></lb>te, & poſtea exinanita, atque immerſo orificio infra <lb></lb>aquæ ſubiectæ <expan abbr="libellã">libellam</expan> eleuari ſemper altiùs deberet <lb></lb>aqua vſque ad fiſtulæ ſupremum orificium, quod ta<lb></lb>men eſt falſum, non ergo ſponte ſua aqua intra fiſtu<lb></lb>lam eleuatur. <pb pagenum="375" xlink:href="010/01/383.jpg"></pb><arrow.to.target n="marg503"></arrow.to.target></s> </p> <p type="margin"> <s id="s.001987"><margin.target id="marg502"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.001988"><margin.target id="marg503"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001989">Alij poſtea aiunt quòd dum fiſtula AB <expan abbr="tãgit">tangit</expan> <expan abbr="aquã">aquam</expan> <lb></lb>vaſis RSV, vel guttulam ſuſpenſam F, tunc aer <expan abbr="ambiẽs">ambiens</expan> <lb></lb>ſuo pondere, & vi elaſtica com<lb></lb><figure id="id.010.01.383.1.jpg" xlink:href="010/01/383/1.jpg"></figure><lb></lb>primit infernè partem aquę F ex<lb></lb>tra fiſtulam exiſtentem, eamque <lb></lb>impellit versùs <expan abbr="orificiũ">orificium</expan> B, ſuper<lb></lb>nè verò aer penetrando cauita<lb></lb>tem fiſtulæ, AB contrario niſu re<lb></lb>pellit ſummitatem aquæ F intrą <lb></lb>orificium B inſinuatam: quia ve<lb></lb>rò fieri non poteſt vt contactus, <lb></lb>& aſperitates internæ fiſtulæ non <lb></lb>impediant deſcenſum, & niſum <lb></lb>compreſſiuum aeris, fit vt minori momento aer per <lb></lb>fiſtulæ canaliculum pertranſiens premat aquæ ſum<lb></lb>mitatem F, quàm liber aer externus à nullo impedi<lb></lb>mento debilitatus; igitur aqua F à validiori vi impul<lb></lb>ſiua aeris externi impelli ſursùm debet, & inſinuari <lb></lb>intra fiſtulam à B ad C. quouſque minor vis aeris per <lb></lb>AC tranſeuntis vnà cum pondere aquæ CB æquili<lb></lb>brentur momento totali aeris externi, quapropter <lb></lb>exceſſus momenti totalis aeris non impediti ſuprą <lb></lb>momentum aeris debilitati æqualis eſt ponderi aquæ <lb></lb>CD. </s> </p> <p type="main"> <s id="s.001990">Debemus modò falſitatem huius ſententiæ oſten<lb></lb>dere. </s> <s id="s.001991">Reuoluatur fiſtula AB vnà cum aqua contenta <lb></lb>CD inuerſo ſitu, vt ſupina eius pars A fiat prona, <expan abbr="tũc">tunc</expan> <lb></lb>aer infernè per prolixum canaliculum AC immiſſus <lb></lb>non ſecùs ac priùs impeditur à contactibus, & aſpe-<pb pagenum="376" xlink:href="010/01/384.jpg"></pb><arrow.to.target n="marg504"></arrow.to.target><lb></lb>ritatibus internis vitri, & ideò eodem debiliori, & <lb></lb>imminuto momento pellit aquam CD ſursùm, impe<lb></lb>ditque eius deſcenſum. </s> <s id="s.001992">E contrà aer ſupernè nil fe<lb></lb>rè impeditus premit deorsùm aquam D orificio B pe<lb></lb>nè contiguam, igitur non ſecùs, ac priùs aer totali <lb></lb>momento eius deorsùm impellit aquam DC: ab hoc <lb></lb>verò momento non ſubtrahitur, immò ei additur <expan abbr="põ-dus">pon<lb></lb>dus</expan> aquæ DC, igitur momentum, quo aqua DC im<lb></lb>pellitur deorsùm maiori exceſſu, nempè duplò ſupe<lb></lb>rat vim, qua ſursùm repellitur, ſcilicèt æqualis eſt <lb></lb>duplo ponderis aquæ DC, ſed priùs medietas prędi<lb></lb>cti exceſſus, non obſtante fiſtulæ interna ariditate, a<lb></lb>quam ſursùm celeri motu eleuauerat, igitur multò ce<lb></lb>leriùs, & faciliùs in <expan abbr="ſecũdo">ſecundo</expan> caſu à duplici exceſſu vir<lb></lb>tutis motiuę deprimi aqua DC deorsùm deberet per <lb></lb>aridum canalem CA, ſed hoc eſt falſum, nam aquą <lb></lb>DC quieſcit, aut tardiſſimo motu deſcendit versùs <lb></lb>A, ergò non eleuatur aqua in fiſtula ob inæquales ae<lb></lb>ris impulſiones. </s> </p> <p type="margin"> <s id="s.001993"><margin.target id="marg504"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001994">Tandem quod interna vitri ſcabrities non impel<lb></lb>lat illam aquæ exiguam molem, ſatis apertè confirma<lb></lb>tur ijſdem rationibus adductis in fine propoſitionis <lb></lb>183. Igitur & c. </s> </p> <p type="main"> <s id="s.001995"><emph type="center"></emph>PROP. CLXXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001996"><emph type="center"></emph><emph type="italics"></emph>Quare aqua ab ima fiſtulæ parte in aere conſtitutæ non <lb></lb>defluat rationem reddere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001997">MOdò remanet difficultas, quare ſcilicèt in infi<lb></lb>mo fiſtulæ confinio in aere conſtitutæ impe-<pb pagenum="377" xlink:href="010/01/385.jpg"></pb><arrow.to.target n="marg505"></arrow.to.target><lb></lb>ditur aquæ defluxus; & licet videatur hoc à contactu <lb></lb>aeris fieri, nihilominùs ex noſtris principijs dici po<lb></lb>teſt, quod in infimo fiſtulę orificio machinulæ lanugi<lb></lb>nis particularum aquæ inter ſe connexæ <expan abbr="diſtrahũtur">diſtrahuntur</expan>, <lb></lb>& ideo tenaciori reſiſtentia vinciuntur, & efficiunt <lb></lb>veluti rete adhærens extremo fiſtulæ, & quia vis prę<lb></lb>dictarum machinularum violenter diſtractarum ma<lb></lb>ior eſt vi ponderis exigui aquæ intra fiſtulam <expan abbr="contẽ-tæ">conten<lb></lb>tæ</expan>, hinc ſequitur aquæ quies, eodem prorſus modo, <lb></lb>ac ſuſtinentur guttæ aqueæ è ramis arborum pen<lb></lb>dentes. </s> </p> <p type="margin"> <s id="s.001998"><margin.target id="marg505"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.001999"><emph type="center"></emph>PROP. CLXXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002000"><emph type="center"></emph><emph type="italics"></emph>Reſtat modò cauſa motiua, à qua ſurſum <lb></lb>impellitur aqua in fiſtulis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002001">QVæ meo iudicio ex theoria nuper expoſita <expan abbr="pẽ-det">pen<lb></lb>det</expan>, quia nempe in cauitatibus ſubtilium fiſtu<lb></lb>larum internus aquæ contactus grandis eſt, & amplus <lb></lb>reſpectu illius aquæ moleculæ ibidem exiſtentis, er<lb></lb>go ſubitò ac infimum fiſtulæ orificium attingit <expan abbr="aquã">aquam</expan> <lb></lb>efficitur in eius interno, & cauo perimetro efficaciſ<lb></lb>ſimus contactus à cuius adhæſione fulciri ſuſtineri<lb></lb>què poteſt maius pondus, quàm habet puſilla aquæ <lb></lb>particula inſinuata, & ideo gradus prædictæ virtutis <lb></lb>ſuſpenſiuæ, & adhæſionis exercetur in aqua ſubicta, <lb></lb><arrow.to.target n="marg506"></arrow.to.target><lb></lb>& proinde ea reddetur aliquo pacto leuis, ſeu minùs <lb></lb>ponderoſa, quàm ſit aqua collateralis liberè <expan abbr="premẽs">premens</expan>. <lb></lb></s> <s id="s.002002">Et quia minimæ aquæ particulæ poroſitatibus, & aſ-<pb pagenum="378" xlink:href="010/01/386.jpg"></pb><arrow.to.target n="marg507"></arrow.to.target><lb></lb>peritaribus internis fiſtulæ innixæ efficiuntur <expan abbr="operã-turque">operan<lb></lb>turque</expan> vt <expan abbr="totidẽ">totidem</expan> vectes, quæ flecti poſſunt, & internè <lb></lb>rotari, neceſsè eſt vt partes aquæ collaterales magis <lb></lb>compreſſæ à totali energia ſui ponderis vim faciant <lb></lb><arrow.to.target n="marg508"></arrow.to.target><lb></lb>impellendo ſursùm particulas illas aquæ, quæ minùs <lb></lb>comprimuntur à vectibus ſupradictis, & ideo rotando <lb></lb>excurrere poſſunt interiùs efformando tumorem, vel <lb></lb>monticulum aqueum, qui excurrendo lateralitèr al<lb></lb>tioribus fiſtulæ poroſitatibus inſinuabitur, adhære<lb></lb>bitque, & ideò denuò imminuetur | eius vis <expan abbr="cõpreſſi-ua">compreſſi<lb></lb>ua</expan>, renouabiturque cauſa vlterioris ſuſpenſionis, & <lb></lb>proindè altiùs aqua intra fiſtulam impelletur, & ſic <lb></lb>de nouo eminentioribus lateribus adhærendo ſuc<lb></lb>ceſſiuè altius impelletur, quouſque ad ſupremam, & <lb></lb>maximam illam altitudinem aqua perducta, in quą <lb></lb>æquilibrium cum aqua collaterali liberè premente <lb></lb>efficiatur, tunc quidem quies eius ſubſequetur, nec <lb></lb>vlteriùs eleuari poterit. </s> </p> <p type="margin"> <s id="s.002003"><margin.target id="marg506"></margin.target>Ex pro. </s> <s id="s.002004">174.</s> </p> <p type="margin"> <s id="s.002005"><margin.target id="marg507"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.002006"><margin.target id="marg508"></margin.target>Prop. 182.</s> </p> <p type="main"> <s id="s.002007"><emph type="center"></emph>PROP. CLXXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002008"><emph type="center"></emph><emph type="italics"></emph>Noua phænomena ex eadem noſtra theoria ſaluantur, & <lb></lb>reijcitur vis aeris ab hac operatione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002009">SEd pro clariori huius rei intelligentia phęmenon <lb></lb>nupèr à me obſeruatum in medium adducam̨, <lb></lb>Sit fiſtula ſtricta vitrea AB hæc quidem arida <expan abbr="perpẽ-dicularitèr">perpen<lb></lb>dicularitèr</expan> aquam contingens eam eleuet per <expan abbr="ſpatiũ">ſpatium</expan> <lb></lb>BF; ſi verò internè fiſtula priùs humectata fuerit, & <lb></lb>deindè exinanita, in contactu aquæ ſubiectæ altiùs <pb pagenum="379" xlink:href="010/01/387.jpg"></pb><arrow.to.target n="marg509"></arrow.to.target><lb></lb>eleuatur per ſpatium BE; ſi poſteà eadem fiſtulą <lb></lb>profundiùs demergatur infra aquam, vel inclinetur, <lb></lb><figure id="id.010.01.387.1.jpg" xlink:href="010/01/387/1.jpg"></figure><lb></lb>aqua exucta maius ſpatium BC occupa<lb></lb>bit. </s> <s id="s.002010">His poſitis tranſportetur integra fiſtu<lb></lb>la vnà cum aqua <expan abbr="contẽta">contenta</expan> ab aqua ad aerem, <lb></lb>perpendicularitèr tamen erecta ad planum <lb></lb>horizontis tunc effluere cunctanter conſpi<lb></lb>citur ab infimo orificio B guttula quædam, <lb></lb>quæ ſenſim colligitur, tumeſcitque; & hoc <lb></lb>contingit quando valdè excedens eſt alti<lb></lb>tudo aquę BC, at ſi <expan abbr="nõ">non</expan> nimia fuerit, quieſcet <lb></lb>in ſitu perpendiculari abſque eo quòd ex <lb></lb>orificio B defluat noua aquæ gutta. </s> <s id="s.002011">Modò <lb></lb><expan abbr="dũ">dum</expan> aqua ſupra <expan abbr="terminũ">terminum</expan> E versùs C perſeuerat <expan abbr="orificiũ">orificium</expan> <lb></lb>fiſtulæ B contingat aquam vaſis, vel guttulam D ſu<lb></lb>ſpenſam à palma manus, vel adhærentem externæ, <lb></lb>& extremæ parti ipſius fiſtulæ B, videbis aquam BC <lb></lb>deprimi deorsùm vſque ad E, vbi nimirùm conſiſte<lb></lb>bat aqua exucta è vaſe, quando interna cauitas hu<lb></lb>mectata fuerat; è contrà ſi altitudo aquę internæ val<lb></lb>de diminuta fuerit, vt BG, tunc quidem in contactu <lb></lb>guttulæ inferioris augetur eius altitudo exugendo <lb></lb>nimirùm aquam ipſius guttulæ D. </s> </p> <p type="margin"> <s id="s.002012"><margin.target id="marg509"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002013">Ratio huius admirandi effectus videtur pendere <lb></lb>ex legibus æquilibrij aquæ externæ, & internæ. </s> <s id="s.002014">pri<lb></lb>mò quando gutta pendula D adhæret inſimo fiſtulæ <lb></lb>orificio, concipere debemus ſuperficiem externam̨ <lb></lb>prædictæ guttulæ pendentis eſſe veluti ſacculum, vel <lb></lb>burſam compoſitam ex machinulis aqueis variè con-<pb pagenum="380" xlink:href="010/01/388.jpg"></pb><arrow.to.target n="marg510"></arrow.to.target><lb></lb>textis, incuruatis, & diſtractis à pondere totius aquæ <lb></lb>prementis, vt alibi dictum eſt, internæ verò partes <lb></lb>eiuſdem guttulæ, ob earum lubricitatem, liberè flue<lb></lb>re poſſunt intra alias aquæ particulas, orificium vaſis <lb></lb>explentes. </s> <s id="s.002015">Hinc fit vt illæ exercendo liberè earum̨ <lb></lb>momentum grauitatis, præualeant energiæ compreſ<lb></lb>ſiuæ diminutæ, ac debilitatę particularum aquæ GB <lb></lb>intra cauitatem vitri adhærentium, & ſic ſursùm im<lb></lb>pellantur à G vſque ad F, vel ſi cauitas madida fue<lb></lb>rit vſque ad E, nempè quouſque fiat momentorum <lb></lb>æquilibrium. </s> <s id="s.002016">è contrà <expan abbr="momẽtũ">momentum</expan> altioris aquæ BC ma<lb></lb>ius erit eo, quo aqua vaſis ſubiecta, vel intra guttu<lb></lb>lam D contenta liberè premit, proindeque illa de<lb></lb>ſcendet in fiſtula à ſummitate C vſque ad E, vbi ni<lb></lb>mirùm eorum momenta adæquantur. </s> <s id="s.002017">Sed in priori <lb></lb>caſu forſan facilè ſuſpicabitur à compreſſione aeris <lb></lb>ſursùm impelli guttulam infimam à G vſque ad E, cu<lb></lb>ius inditium eſſe poteſt, quòd tota guttula D exugi<lb></lb>tur à fiſtula, imò vlteriùs promouetur aere <expan abbr="ſuccedẽ-te">ſucceden<lb></lb>te</expan>, & ſic videtur, quòd non ab aqua externa, quæ ibi<lb></lb>dem non exiſtit, & proinde operari nequit, ſed ab <lb></lb>aere impellitur. </s> <s id="s.002018">ſed reſponderi poteſt quod à vi im<lb></lb>petus, quo aqua in fiſtula aſcendit proſequi, & <expan abbr="cõ-tinuari">con<lb></lb>tinuari</expan> aliquantiſper poteſt aſcenſus poſtremæ par<lb></lb>ticulæ guttæ ipſius D, quatenus à glutine machinu<lb></lb>larum aquæ connectuntur poſtremę illæ guttulæ par<lb></lb>tes, cum præcedentibus, & ab impetu earum <expan abbr="partiũ">partium</expan>, <lb></lb>quæ actu in fiſtula mouentur ſursùm, trahantur vlte<lb></lb>riùs, & conſequentèr aer poſtea ſuccedat in ſpatio <pb pagenum="381" xlink:href="010/01/389.jpg"></pb><arrow.to.target n="marg511"></arrow.to.target><lb></lb>infimo fiſtulæ inani ab aqua derelicto. </s> </p> <p type="margin"> <s id="s.002019"><margin.target id="marg510"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="margin"> <s id="s.002020"><margin.target id="marg511"></margin.target>Cap. 8 cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002021"><emph type="center"></emph>PROP. CLXXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002022"><emph type="center"></emph><emph type="italics"></emph>Aqua in fistula magis demerſa non debet altiùs eleuari <lb></lb>quàm in ca quæ aquam, aut aerem tangit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002023">SEd procedamus ad præcipuam difficultatem, ex <lb></lb>cuius ſolutione reliquis omnibus ſatisfiet. </s> <s id="s.002024">Sit <lb></lb>vas RSV aqua plenum, ſumanturque duæ fiſtulæ æ<lb></lb>quales, & æquè amplis cauitatibus perforatæ, vtrin<lb></lb>que apertæ, vna quidem AB profundiùs demergatur <lb></lb>infra aquæ libellam RV; reliqua verò EH tantum<lb></lb>modò ſuperficiem aquæ RV contingat, & ambo per<lb></lb>pendicularitèr inſiſtant ſupremo <lb></lb><figure id="id.010.01.389.1.jpg" xlink:href="010/01/389/1.jpg"></figure><lb></lb>plano aquæ RV. </s> <s id="s.002025">Si ergo verum̨ <lb></lb>eſt, quòd aqua collateralis magis <lb></lb>compreſſa à totali eius momento <lb></lb>qualis eſt cylindrus aqueus FI <lb></lb>comparatus cum aqua BC, quæ <lb></lb>minus comprimit <expan abbr="ſubiectã">ſubiectam</expan> <expan abbr="aquã">aquam</expan>, <lb></lb>eò quòd ſuſpenditur, ſuſtentatur<lb></lb>que ab internis vitri aſperitati<lb></lb>bus, redditurque aqua CB veluti <lb></lb>virga lignea reſpectu aquæ colla<lb></lb>teralis FI; ergo quò profundiùs demergitur fiſtulą <lb></lb><arrow.to.target n="marg512"></arrow.to.target><lb></lb>longior eſt virgula minùs grauis aquea BC, & ideò, <lb></lb>ex demonſtratis, validiori vi ſursùm impelletur ab a<lb></lb>qua collaterali FI, quàm impellatur ſursùm exiguus <lb></lb>cylindrulus aquæ H, qui ſuſtinetur, & <expan abbr="cõparatur">comparatur</expan> <expan abbr="cũ">cum</expan> <pb pagenum="382" xlink:href="010/01/390.jpg"></pb><arrow.to.target n="marg513"></arrow.to.target><lb></lb>aqua ſuperficiali RV. </s> </p> <p type="margin"> <s id="s.002026"><margin.target id="marg512"></margin.target>Pr. 95.</s> </p> <p type="margin"> <s id="s.002027"><margin.target id="marg513"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002028">Sed reſpondetur, quòd aqua CB non redditur le<lb></lb>uior ob internum contactum fiſtulæ, nam interną <lb></lb>fiſtulæ ſuperficies cùm ſit madida, nihil, aut parum̨ <lb></lb>impedit vim grauitatis aquæ contentæ intra fiſtulam <lb></lb>BC, & hoc experitur cùm in aere transfertur fiſtula, <lb></lb>tunc enim aqua intra cauitatem eius madidam libe<lb></lb>rè mouetur deſcendit que; præcipuum verò impedi<lb></lb>mentum in extremo orificio fiſtulæ B experitur, non <lb></lb>intra aquam, ſed poſtquam aerem attingit; non qui<lb></lb><figure id="id.010.01.390.1.jpg" xlink:href="010/01/390/1.jpg"></figure><lb></lb>dem à vi elaſtica, vel ponderę <lb></lb>eiuſdem aeris, ſed quia tunc iņ <lb></lb>aqua ad <expan abbr="cõfinium">confinium</expan> B perducta effi<lb></lb>citur rete ſuperiùs <expan abbr="expoſitũ">expoſitum</expan>, qua<lb></lb>tenùs particulę infernæ illius aquę <lb></lb>viciſſim connexæ dum pendent à <lb></lb>vi proprię grauitatis diſtractę ea<lb></lb>rum machinulæ paritèr maiorem <lb></lb>violentiam patiuntur, & ideò ma<lb></lb>iori vi viciſſim connectuntur, & <lb></lb>ſic reſiſtere violentiæ preſſionis <lb></lb><expan abbr="aq́uæ">aquæ</expan> poſſunt; at in caſu noſtro exiſtente orificio B <lb></lb>demerſo infra aquam non poteſt effici rete illud ro<lb></lb>buſtum aptum ad ſuſtinendam aquam <expan abbr="incumbentẽ">incumbentem</expan>, <lb></lb>quia non diſtrahuntur machinulæ aquæ B exiſtentes, <lb></lb>& contingentes internam aquam vaſis RSV: hinc fit <lb></lb>vt facilè vna aquæ pars ſuper aliam ſibi contiguam̨ <lb></lb>excurrere valeat, & hinc deducitur ratio quare iņ <lb></lb>fiſtula EH vnà cum aqua HK excedente conſuetam <pb pagenum="383" xlink:href="010/01/391.jpg"></pb><arrow.to.target n="marg514"></arrow.to.target><lb></lb>altitudinem, ſi tota in aere conſtituta fuerit, altiùs <lb></lb>prædictam aquam ſuſtinebit, quàm ſi aquæ libellam <lb></lb>RV tetigerit, tunc enim deſcendit à K ad G, & HG <lb></lb>altior erit quàm DC, ſcilicèt quando fiſtula profun<lb></lb>diùs mergitur, vt in B; quia nimirum dum in aere ex<lb></lb>tabat, efficiebatur rete prædictum, cùm verò aquam <lb></lb>ſubiectam contingit, tum connexio illa tenax facilè <lb></lb>ſoluitur diffluitque, & ſic non ampliùs ſuſtinere tan<lb></lb>tum pondus incumbens poteſt. </s> </p> <p type="margin"> <s id="s.002029"><margin.target id="marg514"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquæ <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002030">Id ipſum præterea confirmatur, quia in contactu <lb></lb>aquæ in H ſuſpenditur circa fiſtulam externè monti<lb></lb>culus quidam aqueus ſupra libellam RV, quod con<lb></lb>ſequenter ſuadet aquam a vi contactus vitri externi <lb></lb>ſuſpendi niſu contrario eius, qui à grauitate aquæ <lb></lb>exercetur, & proindè aqua prædicto monticulo ſub<lb></lb>iecta, & annexa leuior redditur, igitur aqua infrą <lb></lb>orificium ſubiectum fiſtulæ ob prædictam ſuſpenſio<lb></lb>nem minùs grauis facta, neceſsè eſt, vt eleuetur ab <lb></lb>integro momento collateralis aquæ liberè premen<lb></lb>tis, & ſic inſinuetur intra cauitatem fiſtulæ ſupra a<lb></lb>quæ ſubiectæ libellam quouſque fiat momentorum <lb></lb>æquilibrium. </s> </p> <p type="main"> <s id="s.002031">Ex hac theoria facilè reſoluuntur circumſtantiæ, <lb></lb>quæ in operationibus prædictarum fiſtularum obſer<lb></lb>uantur, & ſimul magis confirmatur doctrina ſuperiùs <lb></lb>expoſita. <lb></lb><figure id="id.010.01.391.1.jpg" xlink:href="010/01/391/1.jpg"></figure><pb pagenum="384" xlink:href="010/01/392.jpg"></pb><arrow.to.target n="marg515"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002032"><margin.target id="marg515"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002033"><emph type="center"></emph>PROP. CLXXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002034"><emph type="center"></emph><emph type="italics"></emph>In fiſtulis strictioribus altiùs aqua eleuari debet, quàm in <lb></lb>latioribus, & in fistulis æqualibus, ſed in æqualiter ad <lb></lb>aquæ ſuperficiem inclinatis aqua ad eamdem <lb></lb>altitudinem eleuatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002035">ET primo loco percipitur quare in fiſtulis latio<lb></lb>ribus aqua ad minorem altitudinem eleuatur, <lb></lb>quàm in ſubtiliſſimis, & anguſtiſſimis canalibus: & <lb></lb>eſt, quia adhærentia, & connexio aquæ parietibus <lb></lb>internis canalium maiorem proportionem ad molem <lb></lb>aquæ inſinuatæ extenſiuè, & intenſiuè in canaliculis <lb></lb>ſubtiliſſimis, habet quàm in amplis, & capacioribus. <lb></lb></s> <s id="s.002036">Et quoad extenſionem pertinet, quia vis adhæſionis <lb></lb>menſuratur à contactibus, & ideò à ſuperficie inter<lb></lb>na canaliculorum, è contrà reſiſtentia menſuratur à <lb></lb>pondere cylindri aquei contenti in ijſdem canalicu<lb></lb>lis, eſtque proportio cylindrorum aqueorum <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>altitudiais duplicata eius rationis, quam habent eo<lb></lb>rum perimetri | interni, igitur quanto magis creſcit <lb></lb>interna canalis amplitudo, tantò magis minuitur ad<lb></lb>hæſio, & augetur reſiſtentia ponderis ipſius aquæ <expan abbr="cõ-tentæ">con<lb></lb>tentæ</expan>. </s> <s id="s.002037">Imminuitur poſteà gradus intenſiuus internæ <lb></lb><arrow.to.target n="marg516"></arrow.to.target><lb></lb>adhæſionis, proptereà quod, vt dictum eſt ſupra, <expan abbr="nõ">non</expan> <lb></lb>eſt æquè valida facultas, & energia adhæſionis aquę, <lb></lb>& connexionis | cum parietibus internis |in | vniuerſo <lb></lb>illo argine montuoſo, ſed eſt minus efficax, quantò <lb></lb>magis ab internis parietibus remouetur. </s> <s id="s.002038">Modò iņ <pb pagenum="385" xlink:href="010/01/393.jpg"></pb><arrow.to.target n="marg517"></arrow.to.target><lb></lb>fiſtulis amplioribus aqua contenta versùs axim caui<lb></lb>tatis eius magis recedit à ſuperficie interna fiſtulæ <lb></lb>dilatatæ, quàm in fiſtula ſtrictiori, & ideò in illa de<lb></lb>biliùs aqua ſuſtinebitur ſuſpendeturque, & quantò <lb></lb>minor eſt vis ſuſtinens, & eleuans reſpectu ponderis <lb></lb>fluidi contenti, tantò debet imminui ſublimitas eius <lb></lb>eleuationis, vbi præcisè efficitur æquilibrium ſupe<lb></lb>riùs expoſitum. </s> </p> <p type="margin"> <s id="s.002039"><margin.target id="marg516"></margin.target>In fine prop. <lb></lb></s> <s id="s.002040">182.</s> </p> <p type="margin"> <s id="s.002041"><margin.target id="marg517"></margin.target>Cap. 8. cur <lb></lb>exiguæ aquę <lb></lb>guttæ ſupra <lb></lb><expan abbr="libellã">libellam</expan> aquæ <lb></lb>aſcendunt.</s> </p> <p type="main"> <s id="s.002042">Similitèr in eodem canaliculo ad horizontem in<lb></lb>clinato longiori ſpatio eleuabitur aqua, quàm ſi per<lb></lb>pendicularitèr horizonti inſiſteret, quia nimirùm ſu<lb></lb>blimitas verticalis in <expan abbr="vtroq;">vtroque</expan> caſu eadem eſſe debet, <lb></lb>cùm in ſitu inclinato momentum aquę prementis <expan abbr="mẽ-ſuretur">men<lb></lb>ſuretur</expan> non ab vniuerſa longitudine, aut ponderę <lb></lb>abſoluto cylindri aquei ſubleuati, ſed ab eius verti<lb></lb>cali eleuatione, & propterea <expan abbr="tantumdẽ">tantumdem</expan> præcisè im<lb></lb>pelletur ab eadem cauſa eleuante non alterata, ſcili<lb></lb>cèt à pondere abſoluto aquæ collateralis liberè pre<lb></lb>mentis. <lb></lb><arrow.to.target n="marg518"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002043"><margin.target id="marg518"></margin.target>Quare præ<lb></lb>dictæ opera<lb></lb>tiones non <lb></lb>contingant <lb></lb>niſi fiſtulæ <lb></lb>ſint vtrinque <lb></lb>apertæ.</s> </p> <p type="main"> <s id="s.002044">Et hæc omnia contingere debent quotieſcumque <lb></lb>canaliculus ſupernè non clauditur; Si enim obſtru<lb></lb>ctus fuiſſet aer idem internè comprehenſus impediret <lb></lb>aquę aſcenſum, quia non poſſet aqua inſinuari abſque <lb></lb>eo quod contentus aer ſtringeretur condenſaretur<lb></lb>que, cumque aer condenſari <expan abbr="cõſtiparique">conſtiparique</expan> nequeat, <lb></lb>niſi à noua cauſa violentèr eum condenſante, cui aer <lb></lb>ſua vi elaſtica reſiſtit, igitur ſi aqua intra prædictam <lb></lb>fiſtulam ingrederetur, conſtringere <expan abbr="aerẽ">aerem</expan> internum̨ <lb></lb>deberet, & propterea idem aer ſua vi elaſtica impe<lb></lb>dict <expan abbr="prædictũ">prædictum</expan> ingreſſum. </s> </p> <pb pagenum="386" xlink:href="010/01/394.jpg"></pb> <p type="main"> <s id="s.002045"><arrow.to.target n="marg519"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002046"><margin.target id="marg519"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002047"><emph type="center"></emph><emph type="italics"></emph>De corpuſculorum innat antium mutuo amplexu, <lb></lb>atque fuga.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002048"><emph type="center"></emph>CAP. IX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002049">SVnt ferè triginta duo anni, cùm ego experiri vo<lb></lb>lui an filamenta ferrea ſuper aquam innatantią <lb></lb>in diuerſis ad meridianam inclinationibus elongata <lb></lb>retinerent eandem poſituram, ad <expan abbr="eamdẽque">eamdenque</expan> ſituatio<lb></lb>nem, directionemque redigerentur in qua fabrefacta <lb></lb>fuerant, vt Guglielmus Gilbertus ait, & dum hoc at<lb></lb>tentiùs obſeruarem, mirabile ſpectaculum ſeſe obtu<lb></lb>lit hactenùs non animaduerſum, quod nimirùm ali<lb></lb>quæ extremitates natantium corporum auido curſu <lb></lb>ſe vniebant, amplectebanturque, aliæ verò ſegrega<lb></lb>bantur non ſecùs, ac in magnete, & ferro contingit: <lb></lb>igitur ab hac nouitate excitatus idipſum comproba<lb></lb>ui adhibitis alijs corpuſculis, feſtucis, folijs <expan abbr="arborũ">arborum</expan>, <lb></lb>& innumeris alijs corporibus; cùmque ego ſummo<lb></lb>perè optarem cauſam prædicti effectus perciperę, <lb></lb>poſt innumera experimenta, animaduerti huiuſmodi <lb></lb>operationes contrarias de<lb></lb><arrow.to.target n="marg520"></arrow.to.target><lb></lb><figure id="id.010.01.394.1.jpg" xlink:href="010/01/394/1.jpg"></figure><lb></lb>pendere ab aqueis arginibus <lb></lb>circa corpora natantia adia<lb></lb>centia, aliquando eminenti<lb></lb>bus, <expan abbr="aliquãdo">aliquando</expan> depreſſis. </s> <s id="s.002050"><expan abbr="Sũpſi">Sumpſi</expan> <lb></lb>duas laminulas æreas papyro <lb></lb>graciliores, quales ſunt V, & <lb></lb>X, & in earum punctis intermedijs C, & L appoſui <pb pagenum="387" xlink:href="010/01/395.jpg"></pb><arrow.to.target n="marg521"></arrow.to.target><lb></lb>duas feſtucas CD, & LM, ibidemque cera eas ferru<lb></lb>minaui perpendicularitèr erectas ad plana laminula<lb></lb>rum. </s> <s id="s.002051">appoſui poſtea laminas ſupra <expan abbr="aquã">aquam</expan> vaſis FRSO <lb></lb>horizontali applicatione, quæ infra aquæ libellam̨ <lb></lb>innatando deprimebantur, efficiebantquè circumcir<lb></lb>cà argines aqueos EA, <lb></lb><figure id="id.010.01.395.1.jpg" xlink:href="010/01/395/1.jpg"></figure><lb></lb>GB, nec non IN, KO; <lb></lb>poſteà efformaui duas <lb></lb>aſſulas ligneas Y, & Z, <lb></lb>quarum altitudines <expan abbr="ſe-midigitũ">ſe<lb></lb>midigitum</expan> ferè <expan abbr="æquabãt">æquabant</expan>, <lb></lb><expan abbr="ijſdẽ">ijſdem</expan> <expan abbr="quoq;">quoque</expan> ſeſtucas per <lb></lb><expan abbr="pẽdiculariter">pendiculariter</expan> adaptaui, <expan abbr="poſitiſq;">poſitiſque</expan> ſuper <expan abbr="aquã">aquam</expan> <expan abbr="erigebã-tur">erigeban<lb></lb>tur</expan> circà <expan abbr="earũ">earum</expan> <expan abbr="perimetrũ">perimetrum</expan> montuoſitates <expan abbr="quædã">quædam</expan> decli<lb></lb>ues, vt EA, GB ſupra <expan abbr="vniuerſalẽ">vniuerſalem</expan> aquæ <expan abbr="libellã">libellam</expan> FHO. <lb></lb></s> <s id="s.002052">His præparatis ſolertèr digitis impuli ſummitatem̨ <lb></lb>D feſtucæ approximando laminulam V versùs X, <expan abbr="eã-que">ean<lb></lb>que</expan> firmitèr retinendo antequam ad contactum al<lb></lb>teriùs laminæ V perueniret, eratque diſtantia inter <lb></lb>laminas minor latitudine vnius digiti, tunc primò vi<lb></lb>di ſponte ſua duas laminas V, & X ſeſe mouere vną <lb></lb>versùs alteram, & licèt mediocri violentia digitis re<lb></lb>tinerentur, impedireturque acceſſus earum, poſteą <lb></lb>non minùs, quàm priùs veloci curſu ſe mutuò ample<lb></lb>ctebantur, ſed in ipſo actu coniunctionis earum om<lb></lb>ninò explanabatur <expan abbr="mõticulus">monticulus</expan> GHN aquę, quo priùs <lb></lb>ſegregabantur, poſtea me <expan abbr="cõuerti">conuerti</expan> ad aſſulas ligneas, <lb></lb>Y, & Z quæ paritèr immobiles, & inertes erant <expan abbr="quã-do">quan<lb></lb>do</expan> ab inuicem diſtabant ſpatio maiori, quàm digita-<pb pagenum="388" xlink:href="010/01/396.jpg"></pb><arrow.to.target n="marg522"></arrow.to.target><lb></lb>li, ſed magis appropinquata vna versùs alteram, ſu<lb></lb>bitò aſſulæ excurrebant ad ſe ſe amplectendum, & <lb></lb>hìc accidit operatio diuerſa à præcedenti, nam duæ <lb></lb>montuoſitates eleuatæ GB, & IN nedùm non ſe ex<lb></lb>planarunt, nec redegerunt ad aquæ ſubiectæ libellam <lb></lb>FH deſcendendo, ſed è contrà ſpatium <expan abbr="intermediũ">intermedium</expan>, <lb></lb>& cauitas BHI omninò repleta eſt vſque ad <expan abbr="ſupremũ">ſupremum</expan> <lb></lb>culmen BI. </s> <s id="s.002053">Tandem <expan abbr="coniũxi">coniunxi</expan> laminam æream V cum <lb></lb><figure id="id.010.01.396.1.jpg" xlink:href="010/01/396/1.jpg"></figure><lb></lb>aſſicula Z, & vidi, quod <lb></lb>quotieſcumque approxi<lb></lb>mabantur ad diſtantiam̨ <lb></lb>digito minorem, nedùm ſe <lb></lb>mutuò non amplecteban<lb></lb>tur, ſed è contra vna rapi<lb></lb>dè ab altera effugiebat, <lb></lb>ſegregabaturque, quaſi a<lb></lb>bominaretur <expan abbr="cõſpectum">conſpectum</expan>, & viciniam illius. </s> <s id="s.002054">Quaprop<lb></lb>ter experientia conſtat, quòd acceſſio, approximatio, <lb></lb>& amplexus laminularum, tunc ſolummodò accidit, <lb></lb>quando argines aquei ſimiles ſunt inter ſe, ſcilicèt <lb></lb><expan abbr="quãdo">quando</expan> ambo <expan abbr="sũt">sunt</expan> eleuati, vel vterque depreſſus eſt in<lb></lb>tra aquæ vaſis libellam; ſed quando argines aquei <expan abbr="sũt">sunt</expan> <lb></lb>contrario ordine diſpoſiti, vnus quidem depreſſus, <lb></lb>alter verò eleuatus ſupra aquæ libellam, tunc effici<lb></lb>tur aſſularum ſeparatio, & fuga. </s> <s id="s.002055">Et in omnibus præ<lb></lb>dictis operationibus experitur, quod ſi vna prædi<lb></lb>ctarum laminularum fixè, & in quiete retineatur, ſeù <lb></lb>potiùs in oriſicio vaſis exiſtat, reliqua laminula li<lb></lb>bera, & non retenta, aut accedet, aut fugiet conta-<pb pagenum="389" xlink:href="010/01/397.jpg"></pb><arrow.to.target n="marg523"></arrow.to.target><lb></lb>ctum alterius laminæ immobilis; cùm verò ambo li<lb></lb>berè in fluido innatant, tunc motus eſt communis in <lb></lb>vtroque corpore, cum hac tamen differentia, quòd <lb></lb>corpus minùs amplum, & minùs ponderoſum veloci<lb></lb>ori motu, aut accedit, aut refugit à reliquo, cum è <lb></lb>contrà agitatio amplioris laminæ tardiſſimo, & lan<lb></lb>guido motu fiat. </s> <s id="s.002056">Et hæc eſt vera, & accurata hiſtoria <lb></lb>huius admirandi effectus. </s> <s id="s.002057">non igitur miror <expan abbr="verã">veram</expan> cau<lb></lb>ſam huius effectus adductam non fuiſſe, cùm non <expan abbr="cõ-ftabat">con<lb></lb>ſtabat</expan> neque perfectè innotuerat hiſtoria huius ope<lb></lb>rationis, quæ tantummodò clarè, & euidentèr obſer<lb></lb>uari poteſt mediantibus ſupradictis laminulis à mę <lb></lb>excogitatis. </s> </p> <p type="margin"> <s id="s.002058"><margin.target id="marg520"></margin.target>Hiſtoriæ <lb></lb>acceſſus, & <lb></lb>receſſus cor<lb></lb>porum <expan abbr="inna-tãtium">inna<lb></lb>tantium</expan> cum <lb></lb>omnibus ſu<lb></lb>is <expan abbr="circũſtã-tijs">circumſtan<lb></lb>tijs</expan> affer<lb></lb>tur. </s> </p> <p type="margin"> <s id="s.002059"><margin.target id="marg521"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu |at<lb></lb>que fuga.</s> </p> <p type="margin"> <s id="s.002060"><margin.target id="marg522"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="margin"> <s id="s.002061"><margin.target id="marg523"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002062">Hanc experientiam Amicis communicaui, quorum <lb></lb>quamplurimi adhùc <expan abbr="viuũt">viuunt</expan>, tùm in Sicilia, tùm Romæ. <lb></lb></s> <s id="s.002063">poſte à anno 1655 Florentiæ Sereniſſimo Ferdinando <lb></lb>Magno Duci, & Principi Coſmo Hetruriæ, ac Mæ<lb></lb>cenati optimo, ſapientiſſimoque Leopoldo Cardi<lb></lb>nali Mediceo, qui humaniſſimè nuperis ſuis literis <lb></lb>huius meæ oſtenſionis, & ratiocinij à me tunc tem<lb></lb>poris adducti ſe optimè recordari ſcripſit. </s> <s id="s.002064">Inſtitutą <lb></lb>poſtea <expan abbr="Experimẽtali">Experimentali</expan> Academia Medicea publicè ſo<lb></lb>cijs illis doctiſſimis eamdem experientiam oſtendi, <lb></lb>& innumeris præclaris viris variarum nationum, qui<lb></lb>bus præcipiente Sereniſſimo Cardinali offerebatur <lb></lb>ſpectaculum ſelectiorum experimentorum prædictæ <lb></lb>Academiæ. </s> </p> <p type="main"> <s id="s.002065">Præter iam dictas nouitates <expan abbr="aliã">aliam</expan> poſtea obſeruaui <lb></lb>àcauſa longè diuerſa pendentem pro cuius intelli-<pb pagenum="390" xlink:href="010/01/398.jpg"></pb><arrow.to.target n="marg524"></arrow.to.target><lb></lb>gentia recenſeri priùs debet effectus ſatis vulgatus <lb></lb>duarum laminularum ex vitro exquiſitè explanato, & <lb></lb>lęuigato, quæ ſibi mutuò congruunt, atque exoſcu<lb></lb>lantur, amplexanturque tanta tenacitate vt ſi ſupre<lb></lb>ma horizonti parallela ſursùm eleuetur, pariter ſuc<lb></lb>cedit, trahiturque alia lamina contigua inferior, ſu<lb></lb>ſtineturque pendula, non ſecùs, ac ſi eſſet ſuperiori <lb></lb>connexa conglutinataque, quod ſi ſuperna vitrea la<lb></lb>minula pauliſpèr ad planum horizontis inclinetur, <lb></lb>tunc ſubitò inferior laminula excurret versùs partem <lb></lb>decliuem plani ſuperioris abſque eo quod à ſuprema <lb></lb>lamina diuellatur, ſed ſemper illi adhærendo deſcen<lb></lb>det impulſa ab inſtinctu naturali, quo grauia conant<lb></lb>ur ſemper magis ad centrum grauium accedere eo <lb></lb>modo, quo poſſunt, ſcilicèt via inclinata, cum directa, <lb></lb>& perpendicularis fuerit impedita. </s> </p> <p type="margin"> <s id="s.002066"><margin.target id="marg524"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002067"><emph type="center"></emph>PROP. CLXXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002068"><emph type="center"></emph><emph type="italics"></emph>Si duæ aquæ guttulæ mobiles ſe mutuo <expan abbr="tangãt">tangant</expan> lateraliter, hæ <lb></lb>non quieſcent, ſed lateralitèr excurrent quouſque ver<lb></lb>tices earum in eadem recta perpendiculari ad <lb></lb>horizontem extiterint.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002069">HOc ſuppoſito ſint duæ guttulæ aquæ ABC, vna <lb></lb><expan abbr="pẽdula">pendula</expan> ex lamina horizontali AC ſuſpenſa filo <lb></lb>DE, & alia FGH eleuata ſupra aſſulam LM <expan abbr="innatantẽ">innatantem</expan> <lb></lb>ſuper aquam RS, tunc ſi vertex B ſuperioris guttulæ <lb></lb><expan abbr="cõtinget">continget</expan> ſummitatem G guttulæ inferioris, duæ gut<lb></lb>tularum ſuperficies horizonti æquidiſtantes G, & B <pb pagenum="391" xlink:href="010/01/399.jpg"></pb><arrow.to.target n="marg525"></arrow.to.target><lb></lb>ſibi mutuò congruent, & proindè nulla ratio ſuadet <lb></lb>vt guttulæ ipſæ, & conſequen tèr aſſiculæ lateralitèr <lb></lb>moueantur, cùm earum neutra <lb></lb><figure id="id.010.01.399.1.jpg" xlink:href="010/01/399/1.jpg"></figure><lb></lb>vim motiuam habeat <expan abbr="horizõ-talem">horizon<lb></lb>talem</expan>, propterea quòd ſi mo<lb></lb>uerentur horizonti <expan abbr="æquidiſtã-ter">æquidiſtan<lb></lb>ter</expan> non magis, <expan abbr="quã">quam</expan> priùs cen<lb></lb>tro grauium <expan abbr="approximarẽtur">approximarentur</expan>, <lb></lb>neque mos eſt naturæ fruſtrà <lb></lb>operari. </s> </p> <p type="margin"> <s id="s.002070"><margin.target id="marg525"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002071">Fiat deindè contactus guttularum lateralis, ſcili<lb></lb>cèt ſuperficies ſiniſtra AB, ſupremæ pendulæ guttu<lb></lb>læ tangat ſuperficiem dextram GH inferioris guttu<lb></lb>læ, tunc efficietur contactus, & ſuperficierum con<lb></lb>gruentia, non in vnico puncto ſicuti configuratio ea<lb></lb>rum tumida, & conuexa requireret, ſed in ſatis ſen<lb></lb>ſibili ſpatio veluti eſt IK, & hìc efficitur adhæſio, & <lb></lb>congruentia inter duas aqueas partes non minori te<lb></lb>nacitate, quam duæ laminæ vitreæ ſuperiùs expoſitæ <lb></lb>ſe ſe mutuò nectebantur, itaque difficile diuelluntur <lb></lb>prædictæ aquæ vna ab altera, ſed facillimè poteſt v<lb></lb>na ſuperficies ſuper alteram excurrere, vt aquæ flu<lb></lb>xibilitas requirit, igitur quia prædictæ guttulæ effi<lb></lb>ciunt contactum IK obliquum, & decliuem versùs <lb></lb>centrum telluris, neceſsè eſt vt guttula inferior gra<lb></lb>uis FGH exerceat natiuam ſuam vim deſcenſiuam̨ <lb></lb>eo modo quo poteſt, & ideò dilabetur, fluetque de<lb></lb>orsùm ſemper tamen ſuperiori guttulæ adhærendo, <lb></lb>& hoc eò vſque fiet, quouſque ad infimum ſitum de-<pb pagenum="392" xlink:href="010/01/400.jpg"></pb><arrow.to.target n="marg526"></arrow.to.target><lb></lb>cliuitatis AB perueniatur: non poteſt verò deorsùm̨ <lb></lb>illa fluere dilabique abſque eo quod eius vertex G <lb></lb>versùs culmen B approximetur; neque huiuſmodi <lb></lb>approximatio fieri poteſt abſque eo quod laminą <lb></lb>ſubiecta LM innatando lateralitèr moueatur versùs <lb></lb>S, & ſuprema lamina AC excurrat aliquantiſpèr ver<lb></lb>sùs R, igitur neceſsè eſt, vt ambæ laminæ moueantur <lb></lb>lateralitèr, & propriùs ad ſe ſe accedant, & tunc præ<lb></lb>cisè quieſcent, nec vlteriùs ſe promouebunt, quan<lb></lb>do præcisè obliquitas deſcenſus terminatur, ſcilicèt <lb></lb><expan abbr="quãdo">quando</expan> vertex G inferioris guttulæ præcisè congruit, <lb></lb>adhæretque extremitati B guttulæ ſupremæ, & tunc <lb></lb>prędicti vertices aliquo pacto explanantur, efficiun<lb></lb>turque horizonti æquidiſtantes, quod efficitur me<lb></lb>diante vnione notabilis ſuperficiei in vtraque gut<lb></lb>tula, vnde ſequitur effectus quietis ſuperiùs expo<lb></lb>ſitus, </s> </p> <p type="margin"> <s id="s.002072"><margin.target id="marg526"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002073">Tranſeo iam ad alia experimenta difficiliora, pro <lb></lb>quorum declaratione præmitti debent aliqua lem<lb></lb>mata tum ex hydroſtaticis, cùm ex mechanicis. </s> </p> <p type="main"> <s id="s.002074"><emph type="center"></emph>PROP. CLXXXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002075"><emph type="center"></emph><emph type="italics"></emph>Corpus molle, vel fluidum intra aliud grauius fluidum de<lb></lb>merſum ne dum ab hoc ſursùm exprimitur, ſed etiam <lb></lb>later ali motu eius partes ſtringuntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002076">COnſtat ex coroll. </s> <s id="s.002077">prop. 10. fluidi naturam con<lb></lb>ſiſtentis talem eſſe vt partium eius inferiorum <lb></lb>æquabilitèr diſpoſitarum, ſcilicèt horizontalitèr in-<pb pagenum="393" xlink:href="010/01/401.jpg"></pb><arrow.to.target n="marg527"></arrow.to.target><lb></lb>ter ſe connexarum partes illæ, quæ ſunt magis preſ<lb></lb>ſæ, impellant, ac ſubleuent alias partes collaterales <lb></lb>ſursùm, ſi fuerint minùs compreſſæ. </s> <s id="s.002078">Sed oporterę <lb></lb>ait, Archimedes, vt conatus, & impulſus fluidi pre<lb></lb>mentis fiant per lineas ad horizontem perpendicu<lb></lb><arrow.to.target n="marg528"></arrow.to.target><lb></lb>lares. </s> <s id="s.002079">Hoc profectò veriſſimum eſt quotieſcumquę <lb></lb>innatet intra aquam priſma aliquod conſiſtens, & <lb></lb>durum; At ſi in vaſe BCEI aqua pleno intra ſpatium <lb></lb>AIFG collocatur <expan abbr="nõ">non</expan> priſma ligne<lb></lb><figure id="id.010.01.401.1.jpg" xlink:href="010/01/401/1.jpg"></figure><lb></lb>um, ſed aliud corpus molle, vel flui<lb></lb>dum cedens minùs graue ſpecię, <lb></lb>quàm ſit aqua collateralis, tunc ne<lb></lb>dùm fluidi IG ſursùm perpendicu<lb></lb>laritèr impelletur ſuperficies FG <lb></lb>versùs IA, ſed præterea latus eius <lb></lb>AG propelletur <expan abbr="cõſtringeturque">conſtringeturque</expan> versùs IF, itaut eo<lb></lb>dem tempore, fluidum minùs graue IG ſimùl aſcen<lb></lb>dat perpendicularitèr versùs IA, & lateralitèr quo<lb></lb>que ab AG versùs IF tranſportetur. </s> <s id="s.002080">Hinc colligitur, <lb></lb>quod aqua, ſeù quodlibet fluidum BG grauius ſpe<lb></lb>cie, quàm corpus IG <expan abbr="nedũ">nedum</expan> vim facit premendo per<lb></lb>pendicularitèr, ſed etiam vim exercet lateralitèr <expan abbr="nõ">non</expan> <lb></lb>quidem per horizontales lineas BA, & HG, ſed per <lb></lb>lineas inclinatas BK, & LG, & hoc ſuppleri Archime<lb></lb>deo aſſumpto debere cenſeo, cùm inſtinctu naturæ <lb></lb>corpora omnia grauia deſcendere conentur versùs <lb></lb>terræ centrum, quibuſcumque modis hoc ab eis con<lb></lb>ſequi poſſit, nedum itinere perpendiculari ad hori<lb></lb>zontem, ſed etiam inclinato. <pb pagenum="394" xlink:href="010/01/402.jpg"></pb><arrow.to.target n="marg529"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002081"><margin.target id="marg527"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="margin"> <s id="s.002082"><margin.target id="marg528"></margin.target>De <expan abbr="inſidẽti-bus">inſidenti<lb></lb>bus</expan> humido <lb></lb>lib. 1.</s> </p> <p type="margin"> <s id="s.002083"><margin.target id="marg529"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002084">Hoc poſito, ſi in <expan abbr="eodẽ">eodem</expan> vaſe exiſtente aqua in ſpa<lb></lb>tio ABHG intelligatur collaterale priſma AGFI ab <lb></lb>aere repleri, vel à quolibet alio fluido minùs graui <lb></lb>ſpecie, quàm ſit ipſa aqua, tunc paries aqueus AG <lb></lb>nullo pacto ſuſtinebitur in eodem ſitu erectus, ſed <lb></lb>dilabetur ſſuetque è ſupremo loco A versùs <expan abbr="infimũ">infimum</expan> <lb></lb>F, neque oppoſitum vnquàm contingere poſſet, vt <lb></lb>ſcilicèt <expan abbr="perſeuerãte">perſeuerante</expan> pariete aqueo AG erecto <expan abbr="deſcẽ-deret">deſcen<lb></lb>deret</expan> infra libellam GH, & deinde motu reflexo <lb></lb>ſursùm perpendicularitèr aquæ infimam libellam FG <lb></lb>versùs IA propelleret perpendiculari motu, profe<lb></lb>ctò hoc contigeret ſi inter aquam, & aerem adeſſet <lb></lb>paries ligneus, à quo impediretur effluuium aquæ in<lb></lb>tra foueam AF; atnullo pariete interpoſito videtur <lb></lb>omninò impoſſibile vt aqua non defluat motu incli<lb></lb>nato ad replendam cauitatem aeream AF. </s> <s id="s.002085">Hocquę <lb></lb>confirmatur euidenti experientia; fiat burſa coria<lb></lb>cea parallele pipeda ſursùm aperta ad inſtar putei, <lb></lb>& dilatatis quatuor eius angulis digitis, vel virgis, <lb></lb>immergatur burſa aere plena intra aquam; videbis, <lb></lb>quod nedùm baſis, & fundum, ſed etiam quatuor fa<lb></lb>cies collaterales burſæ incuruantur conuexè versùs <lb></lb>intermedium axim eiuſdem putei, & ſi ſimùl digiti, <lb></lb>aut virgulæ educantur, nec ampliùs vim exerceant, <lb></lb>nedùm baſis, & fundum putei aſcendet ſursùm, ſed <lb></lb>etiam eius parietes collaterales ſe ſe conſtringent, & <lb></lb>ad ſe ſe inuicem accedent, quod eſt euidentiſſimum <lb></lb>ſignum, aquam nedùm vim facere ſursùm perpendi<lb></lb>cularitèr aerem expellendo, ſed etiam lateralitèr </s> </p> <pb pagenum="395" xlink:href="010/01/403.jpg"></pb> <p type="main"> <s id="s.002086"><arrow.to.target n="marg530"></arrow.to.target><lb></lb>conari excurrere per lineas obliquas conſtringendo <lb></lb>laterales parietes prædicti putei coriacei. </s> <s id="s.002087">Hinc in<lb></lb>ferre licèt, quòd ſi magis flexibiles, & cedentes fiant <lb></lb>parietes prædicti putei, ſemperque magis <expan abbr="attenuẽ-tur">attenuen<lb></lb>tur</expan>, quouſque fiant indiuiſibiles, qualis profectò eſt <lb></lb>paries diſtinguens aquam ab aere, tunc idipſum <expan abbr="cõ-tinget">con<lb></lb>tinget</expan>, ſcilicèt aqua defluet motu tranſuerſali obli<lb></lb>quo intra cauitatem aeream AF. </s> </p> <p type="margin"> <s id="s.002088"><margin.target id="marg530"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002089">Si poſtea loco aeris repleatur eadem fouea AIFG <lb></lb>alio fluido minùs graui ſpecie, quàm ſit ipſa aquą <lb></lb>BG, v.g. repleatur oleo, dubitandum non eſt <expan abbr="idipsũ">idipsum</expan> <lb></lb>contingere, ſcilicèt nedùm baſis FG perpendicula<lb></lb>ritèr ſursùm eleuabitur, ſed etiam paries AG, ſeù <expan abbr="cõ-finium">con<lb></lb>finium</expan> aquæ communis, & olei motu tranſuerſali im<lb></lb>pelletur versùs IF. </s> </p> <p type="main"> <s id="s.002090"><emph type="center"></emph>PROP. CXCI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002091"><emph type="italics"></emph>Si vna pars eiuſdem aquæ maiori momento ſubiectum flui<lb></lb>dum compreſſerit, quàm alia eius pars collateralis, hæc <lb></lb>tranſuerſali motu ab illa impelletur, ſecum <expan abbr="tranſportã-do">tranſportan<lb></lb>do</expan> corpuſcula ſuper eam innatantia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002092">ET hìc notandum eſt non debere ſemper fluidum <lb></lb>in ſpatio AF contentum rarius, & diſtrahibilius <lb></lb>eſſe, quàm ſit fluidum AH. </s> <s id="s.002093">Sed etiam ſi fuerit maſſa <lb></lb>aquea eiuſdem conſiſtentiæ, ac eſt BG, dummodò <lb></lb>pondus, ſeù momentum fluidi BG maius ſit grauita<lb></lb>te alterius fluidi AF, impelletur quoque ſuperficies <lb></lb>AG (à qua fluida ſeparantur) tranſuerſali motu ver- <pb xlink:href="010/01/404.jpg"></pb>[missing] <pb xlink:href="010/01/405.jpg"></pb>[missing] <pb xlink:href="010/01/406.jpg"></pb>[missing] <pb xlink:href="010/01/407.jpg"></pb>[missing] <pb xlink:href="010/01/408.jpg"></pb>[missing] <pb xlink:href="010/01/409.jpg"></pb>[missing] <pb xlink:href="010/01/410.jpg"></pb>[missing] <pb xlink:href="010/01/411.jpg"></pb>[missing] <pb xlink:href="010/01/412.jpg"></pb>[missing] <pb xlink:href="010/01/413.jpg"></pb>[missing] <pb xlink:href="010/01/414.jpg"></pb>[missing] <pb xlink:href="010/01/415.jpg"></pb>[missing] <pb xlink:href="010/01/416.jpg"></pb>[missing] <pb xlink:href="010/01/417.jpg"></pb>[missing] <pb pagenum="410" xlink:href="010/01/418.jpg"></pb><arrow.to.target n="marg531"></arrow.to.target><lb></lb>nus erit momento ſectoris aſſulæ ligneæ 4 CD, & am<lb></lb>bo comprimunt partes aquæ ſubiectæ C6, & CZ æ<lb></lb>què diſpoſitas, & in directum continuatas, ſcilicèt ſu<lb></lb>pra eamdem libellam horizontalem BCY, igitur la<lb></lb>mina innatans AC approximabitur termino Y. eadem <lb></lb><arrow.to.target n="marg532"></arrow.to.target><lb></lb>ratione reliqua aſſula lignea EH tranſportabitur ver<lb></lb>sùs YT ab aqua ſubiecta RF magis preſſa, quàm col<lb></lb>lateralis aqua FZ, quaproptèr duæ aſſulæ ligneæ AC, <lb></lb>& EG neceſſariò ad ſe ſe accedent, & ſemper maiori, <lb></lb>& celeriori impetu, quò magis ſtringuntur coniun<lb></lb>gunturque, quia ſemper magis momentum aquæ in<lb></lb>terceptæ imminuitur; quod erat demonſtrandum. </s> </p> <p type="margin"> <s id="s.002094"><margin.target id="marg531"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="margin"> <s id="s.002095"><margin.target id="marg532"></margin.target>Prop. 195.</s> </p> <p type="main"> <s id="s.002096"><emph type="center"></emph>PROP. CXCIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002097"><emph type="center"></emph><emph type="italics"></emph>Tertio loco ſi duo corpora innatantia efficiant duos argines <lb></lb>aqueos conterminales, alter depreſſus, reliquus vero ſu<lb></lb>pra eiuſdem libellam eleuatus: hæc ſibi ipſis approxima<lb></lb>ta non vnientur, ſed motibus contrarijs vnum ab altero <lb></lb>fugiet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002098">IN eodem vaſe KVNL innatent duæ laminæ AC <lb></lb>ænea, & EH lignea quarum centra grauitatum 4 <lb></lb>& 7, illa deprimetur efficietque argines depreſſos K <lb></lb>A, DG, hæc verò ſuſtinebit argines eleuatos EG, & <lb></lb>IL ſupra eamdem aquæ libellam KL. & ſiquidem̨ <lb></lb>prædicta duo innatantia corpora in tanta diſtantia in<lb></lb>terſe remoueantur, vt terminus G conterminalium̨ <lb></lb>arginum DG, & GE, ſcilicèt ſummitas illius, & alte<lb></lb>rius infimus terminus pertingant præcisè vniantur-<pb pagenum="411" xlink:href="010/01/419.jpg"></pb><arrow.to.target n="marg533"></arrow.to.target><lb></lb>que in eadem libella aquæ KL vt nimirùm figuræ cur<lb></lb>uæ earum in G planitiem horizontalem conſtituant, <lb></lb>tunc conſtat expe<lb></lb><figure id="id.010.01.419.1.jpg" xlink:href="010/01/419/1.jpg"></figure><lb></lb>rientia, quod in hac <lb></lb>diſtantia, & in reli<lb></lb>quis omnibus maio<lb></lb>ribus ipſa DF omni<lb></lb>nò quieſcunt prædi<lb></lb>cta duo corpora innatantia in eodem ſitu æquilibra<lb></lb>ta, facta eadem conſtructione oſtendetur vt prius <lb></lb>(ex pr. 196.) quod momentum ſectoris 4CE æqua<lb></lb>le eſt momento portionis anuli aquei DCQG. </s> </p> <p type="margin"> <s id="s.002099"><margin.target id="marg533"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002100">Accedant poſtea ad ſe ſe lamina AC, & aſſula EH, <lb></lb>procùl dubio terminus communis duorum contermi<lb></lb>nalium arginum non habebit figuram planam hori<lb></lb>zonti parallelam conſtitutam in eadem aquę libella <lb></lb>KL, vt priùs, quando nullam decliuitatem in puncto <lb></lb>G habebant, ſed neceſsè eſt vt efficiant montuoſam <lb></lb>eleuationem ETD valdè decliuem, quæ ſecabit pla<lb></lb>num KL in T; & hoc patet, quia poſt laminarum ap<lb></lb>proximationem oportet, vt ſupremus terminus G in<lb></lb>fimæ decliuitatis DG inſinuetur versùs E, & recedat <lb></lb>ab infimo termino S ſupremæ accliuitatis SE, in quo <lb></lb>coniungebantur, & S, G in eodem plano libellæ KL, <lb></lb>exiſtunt; ergo G infra ES penetrando termino E, at<lb></lb>que S termino D approximantur, & ideò tota ſuper<lb></lb>ficies 3G cadet infra ſuperficiem S2E, & punctum 3 <lb></lb>cadet infra T, & punctum 2 ſupra idipſum, <expan abbr="cũ">cum</expan> igitur <lb></lb>decliuitas aquæ E2 in aere <expan abbr="ſuſpẽſa">ſuſpenſa</expan> hęrere nequeat, <pb pagenum="412" xlink:href="010/01/420.jpg"></pb><arrow.to.target n="marg534"></arrow.to.target><lb></lb>neceſsè eſt vt aucta decliuitate vniatur cum infimą <lb></lb>accliuitate D3, & ideò neceſsè eſt vt ſuperficies <expan abbr="cõ-poſita">con<lb></lb>poſita</expan> montis ETD ſit multò magis erecta, & accliuis <lb></lb>quam priùs; & ducta perpendiculari TY ſupra MN, <lb></lb>eam ſecet in Y & vaſis fundum in Z: & quia momen<lb></lb>tum portionis aquei anuli CDTY maius eſt momen<lb></lb>to eiuſdem ſectoris aquei anuli <expan abbr="nõ">non</expan> imminuti CDGQ <lb></lb>(non <expan abbr="quidẽ">quidem</expan> ratione molis, cùm hæc nec iuuet in hoc <lb></lb>negotio, nec noceat, vt dictum eſt, ſed quia eius <expan abbr="mõ-tuoſa">mon<lb></lb>tuoſa</expan> ſuperficies DTE facta eſt decliuior, & magis <lb></lb><arrow.to.target n="marg535"></arrow.to.target><lb></lb>ad perpendicularem <expan abbr="accedẽs">accedens</expan>, quàm priùs); erat verò <lb></lb>momentum integræ portionis anuli aquei CDGQ æ<lb></lb>quale momento ſectoris laminæ 4CD, igitur momen<lb></lb>tum portionis anuli aquei magis decliuis CDTY erit <lb></lb><figure id="id.010.01.420.1.jpg" xlink:href="010/01/420/1.jpg"></figure><lb></lb>maius momento ſe<lb></lb>ctoris laminæ 4CD, <lb></lb>& premunt ambo <lb></lb>partes aquæ ſubie<lb></lb>ctas 4P, & CZ <expan abbr="cõ-tinuatas">con<lb></lb>tinuatas</expan>, & æquali<lb></lb>ter diſpoſitas ſupra idipſum planum horizontale MB <lb></lb>CY, quapropter (ex demonſtratis) prædicta lamina <lb></lb><arrow.to.target n="marg536"></arrow.to.target><lb></lb>AC diſcedet, remouebiturque ab YZ. eadem ratio<lb></lb>ne reliqua aſſula EH remoueri debet, fugereque à vi<lb></lb>cinia YZ, cum expelli debeat lateralitèr aqua ſubie<lb></lb>cta RF vnà cum inſiſtente lamina, propterea quod à <lb></lb>magis preſſa aqua FZ expelli debet; Patet igitur duo <lb></lb>corpora AC, & EH ſegregari debere, & vnum ab al<lb></lb>tero ſugere quotieſcumque duo eorum argines con-<pb pagenum="413" xlink:href="010/01/421.jpg"></pb><arrow.to.target n="marg537"></arrow.to.target><lb></lb>trarij aquei mutuò connectuntur, quod erat demon<lb></lb>ſtrandum. </s> </p> <p type="margin"> <s id="s.002101"><margin.target id="marg534"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="margin"> <s id="s.002102"><margin.target id="marg535"></margin.target>Prop. 193.</s> </p> <p type="margin"> <s id="s.002103"><margin.target id="marg536"></margin.target>Prop. 195.</s> </p> <p type="margin"> <s id="s.002104"><margin.target id="marg537"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002105">Licèt ob facilitatem, & perſpicuitatem <expan abbr="demõſtra-tionis">demonſtra<lb></lb>tionis</expan> adducta ſint exempla corporum in quibus ar<lb></lb>gines eiuſdem figuræ ſint in ambitu eiuſdem corpo<lb></lb><arrow.to.target n="marg538"></arrow.to.target><lb></lb>ris innatantis, nihilominùs fieri poteſt, vt circa vnum <lb></lb>latus eiuſdem laminæ aqua eleuetur ſupra eius com<lb></lb>munem libellam, in altera verò parte deprimatur ef<lb></lb>ficiendo cauam montuoſitatem, hocque in laminą <lb></lb>metallica fieri poteſt inflectendo pauliſpèr angulum <lb></lb>eius: idipſum in quolibet alio corpore innatante <expan abbr="cõ-ſequi">con<lb></lb>ſequi</expan> poteſt, <expan abbr="etiã">etiam</expan> ligneo, ſi vnus eius paries ſit made<lb></lb>factus, reliquus verò aridus, quod etiam effici poteſt <lb></lb>ſi vngatur ſebo, vel aliqua alia ſimili pinguedine vna <lb></lb>eius facies, & tunc prohiberi ſolet <expan abbr="aſcẽſus">aſcenſus</expan>, & adhæ<lb></lb>rentia aquæ ſupra eius libellam; & in tali caſu contin<lb></lb>git vt idem corpus ex vna parte trahatur, ex alterą <lb></lb>verò expellatur ab alio corpore innatante, ſcilicèt <lb></lb>quando argines ſimiles ſunt, aut ambo depreſſi, aut <lb></lb>ambo eleuati, tunc efficitur acceſſus, ſed quando ar<lb></lb>gines ſunt <expan abbr="cõtrario">contrario</expan> ordine ſituati ſequitur diſceſſus, <lb></lb>& fuga vnius ab altero, & hæc omnia pendent ex ea<lb></lb>dem demonſtratione. </s> </p> <p type="margin"> <s id="s.002106"><margin.target id="marg538"></margin.target>In vno, <expan abbr="co-dẽque">co<lb></lb>denque</expan> corpo-<lb></lb>re innatante <lb></lb>fieri poſſunt <lb></lb>argines con<lb></lb>trarij.</s> </p> <p type="main"> <s id="s.002107"><emph type="center"></emph>PROP. CC.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002108"><emph type="center"></emph><emph type="italics"></emph>Sed antequam vlterius procedamus, incidentèr animaduer<lb></lb>to altitudinem foueæ in aqua genitæ à deſcenſu laminæ <lb></lb>grauioris ſpecie ipſa aqua, ad craſsitiem laminæ demerſæ <lb></lb>proportionem minorem habere quàm grauitas ſpecifica ip<lb></lb>ſius laminæ habet ad grauitatem aquæ in ſpecie.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="414" xlink:href="010/01/422.jpg"></pb><arrow.to.target n="marg539"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002109"><margin.target id="marg539"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002110">IN vaſe KVZG aqua pleno innatet lamina æneą <lb></lb>æquè craſſa ABCD, quæ efficiat in aqua foueam̨ <lb></lb>KBCG, cuius altitudo SC & RB. dico SC ad DC mi<lb></lb>norem proportionem habere quam grauitas in ſpecie <lb></lb>ipſius laminæ AC habet ad aquæ grauitatem. </s> <s id="s.002111">quia <gap></gap>x <lb></lb>hydroſtaticis moles aquæ æqua <lb></lb><figure id="id.010.01.422.1.jpg" xlink:href="010/01/422/1.jpg"></figure><lb></lb>lis ſpatio GKBC æquè ponde<lb></lb>rat, ac lamina AC vnà cum ae<lb></lb>re GKAD (qui ob inſenſibilem <lb></lb>eius grauitatem negligi poteſt) <lb></lb>& pondus abſolutum laminæ AC ad abſolutam gra<lb></lb>uitatem aquæ eiuſdem molis AC eamdem proportio<lb></lb>nem habet quam grauitas ſpecifica laminæ AC ad <lb></lb>ſpecificam grauitatem aquæ, ergo grauitas laminæ ad <lb></lb>aquæ grauitatem in ſpecie eamdem proportionem̨ <lb></lb>habet, quam pondus molis aquæ GKBC abſolutæ ad <lb></lb>pondus molis aquæ AC, ſeù proportionem, quam ha<lb></lb>bet moles GKBC ad molem AC: eſt verò priſma RB <lb></lb>CS minus ſolido inæqualium baſium GKBC, ergo <lb></lb>priſma RBCS ad AC ſeù altitudo SC ad DC minorem <lb></lb>proportionem habet, quàm laminæ AC grauitas in<lb></lb>ſpecie ad aquæ grauitatem. </s> <s id="s.002112">Itaque vulgata propoſi<lb></lb>tio vera eſſet ſi ſpatium cauitatis ab aere repletum <lb></lb>haberet parietes AK, & DG directos, & perpen<lb></lb>diculares ad horizontem, ſcilicèt ſi baſis KG æqua<lb></lb>lis foret ipſi AD; at quia ob curuitatem inſignem ſu<lb></lb>perficierum AK & DG, ſemper altitudo CS ad craſſi<lb></lb>tiem laminæ DC minorem proportionem habet <expan abbr="quã">quam</expan> <lb></lb>grauitas ſpecifica ſolidi AC ad eam, <expan abbr="quã">quam</expan> habet aqua. </s> </p> <pb pagenum="415" xlink:href="010/01/423.jpg"></pb> <p type="main"> <s id="s.002113"><arrow.to.target n="marg540"></arrow.to.target><lb></lb>& huiuſmodi proportio ſemper magis, ac magis im<lb></lb>minuitur, quò magis conſtringitur baſis laminæ AC, <lb></lb>itaut poſito quòd lamina aurea AC ſit vigeſies graui<lb></lb>or ſpecie ipſa aqua, poteſt adeò imminui baſis eius <lb></lb>AD vt altitudo arginum SD minor ſit quàm CD, cùm <lb></lb>tamen debuerat eſſe SD ad DC vt 19 ad 1, propterea <lb></lb>quod anuli triangularis SDG craſſities SG ſemper <lb></lb>eſt eiuſdem menſuræ poteſt adeo conſtringi circulus <lb></lb>baſis AD interceptus vt valdè excedat prædictum̨ <lb></lb>circulum, & cylindrum interceptum, vt facilè oſtendi <lb></lb>poſſet. </s> </p> <p type="margin"> <s id="s.002114"><margin.target id="marg540"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002115"><emph type="center"></emph>PROP. CCI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002116"><emph type="center"></emph><emph type="italics"></emph>Pondus molis aquæ æqualis portioni innatantis corporis infra <lb></lb>aquæ libellam demerſi non eſt præcisè æquale ponderi to<lb></lb>tius inn at antis corporis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002117">SEcundo loco operæpretium erit innuere quod ex <lb></lb>prædictis <expan abbr="mõtuoſitatibus">montuoſitatibus</expan> fluidi eleuatis, aut de<lb></lb>preſſis miris modis alterantur propoſitiones illæ, quæ <lb></lb>in hydroſtaticis demonſtratæ ſunt; quando enim effi<lb></lb>ciuntur argines eleuati; tunc moles aquæ æqualis ſpa<lb></lb>tio corporis <expan abbr="innatãtis">innatantis</expan> infra aquæ libellam demerſi <expan abbr="nõ">non</expan> <lb></lb>eſt eiuſdem ponderis, ac eſt corpus ipſum innatans, <lb></lb>quando quidem argines illi aquei <expan abbr="vndiq;">vndique</expan> eleuati gra<lb></lb>ues quoque ſunt, & ſuſpenduntur ob adhærentiam, & <lb></lb>connexionem cum aſperitatibus externis eiuſdem in<lb></lb>natantis corporis, at quia à prædicto pondere adiun<lb></lb>cto arginum grauius abſolutè redditur corpus præ di-<pb pagenum="416" xlink:href="010/01/424.jpg"></pb><arrow.to.target n="marg541"></arrow.to.target><lb></lb>ctum, & ideò multò magis deprimitur, quàm ſi à præ<lb></lb>dicto anulo montuoſo aquæ non grauaretur. </s> <s id="s.002118">huiuſmo<lb></lb>di verò exceſſus inſignis eſſe poteſt, ſi enim tabulą <lb></lb>grandis metallica ſupra hydrargyrum innataret, <expan abbr="mõ-tuoſitates">mon<lb></lb>tuoſitates</expan> illæ adhærentes nedùm pondus vnciarum, <lb></lb>ſed etiam aliquarum librarum excederet. </s> <s id="s.002119">Et hìc ani<lb></lb>maduertendum eſt, quòd menſura demerſionis ſumi <lb></lb>non debet ab illis ſupremis terminis, quos <expan abbr="attingũt">attingunt</expan> <lb></lb>argines aquei eleuati, cùm hoc ſit manifeſtè falſum. </s> </p> <p type="margin"> <s id="s.002120"><margin.target id="marg541"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002121"><emph type="center"></emph>PROP. CCII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002122"><emph type="center"></emph><emph type="italics"></emph>Nostra instrumenta hydroſtatica non indicant præcisè <lb></lb>fluidorum ſpecificas grauitates.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002123">PRæterea adnotari quoque debet error commu<lb></lb>nis, quem committere ſolemus dum grauitates <lb></lb>liquidorum explorare volumus inſtrumentis in no<lb></lb>ſtra Academia experimentali Medicea excogita<lb></lb>tis. </s> <s id="s.002124">vſurpari enim ſolet phiala aliqua, cuius aluus par<lb></lb>tim arena, partim aere expletur, eique adnectitur <lb></lb>ſupernè filum vitreum graciliſſimum diſtinctum, ac <lb></lb>deſignatum particulis æqualibus, quas gradus voca<lb></lb>re ſolemus, & prout magis, vel minùs deprimitur col<lb></lb>lum phialæ, ſeù filum, pronunciamus fluidum minùs <lb></lb>vel magis grauitare. </s> <s id="s.002125">Sed quia aqua adhærens prædi<lb></lb>cto collo fiſtulæ, numquam explanatè eum ſecat, ſed <lb></lb>ſemper aut deprimitur in foueolam iam dictam, vel <lb></lb>eleuatur <expan abbr="efficiẽdo">efficiendo</expan> vndique montuoſitatem aqueam; <lb></lb>hinc ſit vt prædicta aqua eleuata vel deficiens alte-<pb pagenum="417" xlink:href="010/01/425.jpg"></pb><arrow.to.target n="marg542"></arrow.to.target><lb></lb>ret menſuram præciſam grauitatis fluidi, propterea <lb></lb>quòd magis aut minùs, quàm opus eſt, deprimit <expan abbr="collũ">collum</expan> <lb></lb>prædictæ fiſtulæ, & ſic menſuram alteratam, & falla<lb></lb>cem deſignat, quæ tandem cùm in aqua vnum, vel al<lb></lb>terum granum excedere queat, in mercurio verò mul<lb></lb>tò magis, non poſſunt abſque erroris ſuſpicione vſur<lb></lb>pari cum agitur de examine ponderum exiguorum. </s> </p> <p type="margin"> <s id="s.002126"><margin.target id="marg542"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002127">Ex dictis colligitur quod fiſtula vitrea libellatoria <lb></lb>(quam hydroſtaticam libellam nonnulli <expan abbr="vocãt">vocant</expan>) non<lb></lb>nullis difficultatibus ac fallacijs obnoxia ſit. </s> <s id="s.002128">primò <lb></lb>quia ſi fiſtulæ vitreæ erectæ perpendicularitèr ad pla<lb></lb>num horizontis non fuerint præcisè æquè amplæ, <lb></lb>procùl dubio argines aqueos internos inæquales effi<lb></lb>cient, ideoque planum per ſummitates <expan abbr="arginũ">arginum</expan> aque<lb></lb>orum extenſum non erit horizonti æquidiſtans, idip<lb></lb>ſum continget ſi prædictæ duæ fiſtulæ erectæ fuerint <lb></lb>æquales inter ſe, at non ſint omninò ſordibus vnctuo<lb></lb>ſis purgatæ, & terſæ, cùm pinguedo illa prohibeat ar<lb></lb>ginis aquei eleuationem magis, aut minùs pro copią <lb></lb>aut defectu prædictæ pinguedinis. </s> <s id="s.002129">præterea ſi vna fi<lb></lb>ſtularum fuerit internè arida, reliqua verò madefacta, <lb></lb>argines quoque aquei in madida fiſtula eleuantur, <expan abbr="nõ">non</expan> <lb></lb>verò in arida. </s> </p> <p type="main"> <s id="s.002130">Alio inſuper nomine fallax eſt prædictum inſtru<lb></lb>mentum, cùm enim aqua numquam pura, & ſincerą <lb></lb>haberi poſſit, fit vt niſi bullulæ aereæ quibus num<lb></lb>quam aqua ſpoliatur, æquè diſtributæ ſint in vtraque <lb></lb>fiſtula, erunt moleculæ illæ aqueæ inæ qualitèr gra<lb></lb>ues ſpecie, & ideò earum ſummitates habebunt inæ-<pb pagenum="418" xlink:href="010/01/426.jpg"></pb><arrow.to.target n="marg543"></arrow.to.target><lb></lb>quales eleuationes, proindeque non oſtendent exa<lb></lb>ctam libellam horizontalem. </s> <s id="s.002131">Idipſum continget quo<lb></lb>tieſcumque fiſtulæ prædictæ non fuerint ab codem̨ <lb></lb>gradu caliditatis rarefactæ, nempè ſi vna à ſolaribus <lb></lb>radijs illuſtretur, reliqua verò in loco vmbroſo, aut <lb></lb>magis frigido degat. </s> <s id="s.002132">non ſecùs ſi ſordes terreæ, aut <lb></lb>ſales inæqualitèr diſtributi fuerint in vtroque canali<lb></lb>culo, nunquam præcisè organum prædictum veram̨ <lb></lb><expan abbr="horizontalẽ">horizontalem</expan> libellam indicabit. </s> <s id="s.002133">At ſi loco aquæ mer<lb></lb>curium in prædicta fiſtula incluſerimus, non effugie<lb></lb>mus omnes difficultates, nec in ſumma certi eſſe poſ<lb></lb>ſumus numquam in operationibus erraſſe quanta. </s> <s id="s.002134">eſt <lb></lb>fili alicuius tenuis craſſities; proindè conducit labo<lb></lb>rioſam hanc machinam relinquere, & more antiquo <lb></lb>regulis normalibus cum funependulo libellam hori<lb></lb>zontalem exquirere. </s> <s id="s.002135">Sed de his hactenùs. </s> </p> <p type="margin"> <s id="s.002136"><margin.target id="marg543"></margin.target>Cap. 9. de <lb></lb>corpuſculo<lb></lb>rum <expan abbr="innatã-tium">innatan<lb></lb>tium</expan> mutuo <lb></lb>amplexu at<lb></lb>que fuga.</s> </p> <p type="main"> <s id="s.002137"><emph type="center"></emph><emph type="italics"></emph>De Æquitemporanea naturali velocitate grauium <lb></lb>corporum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002138"><emph type="center"></emph>CAP. X.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002139">QVia in quolibet motu intra fluidum facto reſi<lb></lb>ſtentia exercetur, & proindè debilitatur gra<lb></lb>dus impetus naturalis quo mobile ferri deberet, ſe<lb></lb>quitur quòd gradus velocitatum non impediti, ſcili<lb></lb>cèt in vacuo, qui naturalitèr competunt corporibus <lb></lb>grauibus, neceſſariò celeriores, & vehementiores <lb></lb>ſint ijs, qui in medijs fluidis <expan abbr="exercẽtur">exercentur</expan>: ſed <expan abbr="nõ">non</expan> proin<lb></lb>dè infinitæ velocitatis, & impetus erunt, habebunt <pb pagenum="419" xlink:href="010/01/427.jpg"></pb><arrow.to.target n="marg544"></arrow.to.target><lb></lb>enim certum, & determinatum gradum velocitatis à <lb></lb>natura ipſis aſſignatum, non verò inſtantaneum. </s> <s id="s.002140">huic <lb></lb>verò <expan abbr="ſentẽtiæ">ſententiæ</expan> refragatur celebris illa Ariſtotelis de<lb></lb>monſtratio vbi contendit, quod motus in vacuo fie<lb></lb>ri deberet non in tempore, ſed in inſtanti. </s> <s id="s.002141">erit igitur <lb></lb><arrow.to.target n="marg545"></arrow.to.target><lb></lb>operæpretium ad examen vocare tale Ariſtotelicum <lb></lb><expan abbr="ratiociniũ">ratiocinium</expan>, quod <expan abbr="pẽdet">pendet</expan> ex huiuſmodi ſuppoſitione. <lb></lb><arrow.to.target n="marg546"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002142"><margin.target id="marg544"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002143"><margin.target id="marg545"></margin.target>4. phyſ. c.8.</s> </p> <p type="margin"> <s id="s.002144"><margin.target id="marg546"></margin.target><expan abbr="Eiuſdẽ">Eiuſdem</expan> mo<lb></lb>bilis veloci<lb></lb>tates reci<lb></lb>procè pro<lb></lb>port ionales <lb></lb>ſunt denſita<lb></lb>tibus fluideo<lb></lb>rum in qui<lb></lb>bus moui<lb></lb>tur. </s> <s id="s.002145">ex Atiſ. <lb></lb></s> <s id="s.002146">ibidem.</s> </p> <p type="main"> <s id="s.002147">Quod quotieſcumque idem mobile fertur per duo <lb></lb>media fluida, tunc eorum denſitates, ſeù reſiſtentiæ <lb></lb>proportionales reciprocè ſunt eiuſdem mobilis ve<lb></lb>locitatibus, quas in prædictis fluidis exercet. </s> <s id="s.002148">Itaque <lb></lb>poſito quod pila ferrea verb. </s> <s id="s.002149">gr. vna, & eadem vi mo<lb></lb>tiua ex ſui natura feratur per aquam, & per acrem, ſi <lb></lb>denſitas, & reſiſtentia ad diuiſionem aquæ centies <lb></lb>maior eſſet reſiſtentia ipſius aeris, aſſumit Philoſo<lb></lb>phus moueri pilam ferream per aerem velocitate <expan abbr="cẽ-ties">cen<lb></lb>ties</expan> maiori, quàm per aquam fertur, ſcilicèt ſi motus <lb></lb>fiant temporibus æqualibus, per <expan abbr="aerẽ">aerem</expan> excurrere ſpa<lb></lb>tium centuplum, quàm per aquam, & ſi ſpatia exa<lb></lb>cta æqualia fuerint, tempus motionis per aquam cen<lb></lb>tuplo prolixius, & tardius eſſe, quàm per aerem. </s> </p> <p type="main"> <s id="s.002150">Hoc principio ſuppoſito probat Philoſophus ve<lb></lb>locitatem cuiuslibet mobilis in vacuo eſſe <expan abbr="immẽſam">immenſam</expan>, </s> </p> <p type="main"> <s id="s.002151"><arrow.to.target n="marg547"></arrow.to.target><lb></lb>& inſtantaneam. </s> <s id="s.002152">Et profectò optimus eſſet eius pro<lb></lb>greſſus ſi prædictum <expan abbr="principiũ">principium</expan> à philoſopho aſſump<lb></lb>tum eſſet firmum, & ſtabile, ſed iam clariſs. </s> <s id="s.002153">Gali<lb></lb>leus falſum eſſe euidentiſſimè demonſtrauit in noua <lb></lb>eius ſcientia mechanica dialogo primo. <pb pagenum="420" xlink:href="010/01/428.jpg"></pb><arrow.to.target n="marg548"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002154"><margin.target id="marg547"></margin.target>Ibidem.</s> </p> <p type="margin"> <s id="s.002155"><margin.target id="marg548"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002156"><emph type="center"></emph>PROP. CCIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002157"><emph type="center"></emph><emph type="italics"></emph>Modò noua demonſtratione noſtra oſtendemus, quòd in duo<lb></lb>bus medijs fluidis inæqualitèr denſis, & reſistentibus <lb></lb>velocitates eiuſdem corporis grauis poſſunt habere maio<lb></lb>rem, eamdem, & minorem proportionem reciprocam, <lb></lb>quam habent crasſities eorumdem fluidorum, ſi tamen <lb></lb>graue in vtroque fluido deſcendat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002158">IN vaſe CF ſit fluidum M, cuius <expan abbr="dẽſitas">denſitas</expan>, craſſities, <lb></lb>vel reſiſtentia ad diſtractionem erit certæ, ac de<lb></lb>terminatæ menſuræ, ſit illa S, atque in vaſe CG po<lb></lb>natur aliud fluidum N, cuius craſſities, & reſiſtentia <lb></lb><figure id="id.010.01.428.1.jpg" xlink:href="010/01/428/1.jpg"></figure><lb></lb>R ſit maior, quàm S. præterea <lb></lb>idem mobile A, quod in vtro<lb></lb>que fluido M, & N deſcende<lb></lb>re valeat, eodem tempore T <lb></lb>percurrat ſpatium CD fluidi <lb></lb>M, ſpatium verò CE alterius <lb></lb>fluidi N. & quia vis motiuą <lb></lb>eiuſdem mobilis A vnica eſt, <lb></lb>& certi, ac determinati gra<lb></lb>dus, propterea impetus, & ve<lb></lb>locitas naturalis eiuſdem gra<lb></lb>uis A ſemper eſt <expan abbr="eadẽ">eadem</expan>, & eiuſ<lb></lb>dem gradus, ſi omninò remo<lb></lb>ueri poſſent impedimenta, quæ à medij reſiſtentią <lb></lb>afferuntur, <expan abbr="cũ">cum</expan> nulla alia de cauſa alteretur, varietur<lb></lb>que velocitas eiuſdem grauis A in diuerſis fluidis M, <pb pagenum="421" xlink:href="010/01/429.jpg"></pb><arrow.to.target n="marg549"></arrow.to.target><lb></lb>N, nifi quia prædicta fluida diuerſimodè reſiſtunt, & <lb></lb>alterant naturalem impetum, & motum eiuſdem mo<lb></lb>bilis. </s> <s id="s.002159">Supponamus igitur, quod gradus abſolutus ve<lb></lb>locitatis grauis A non retardatus, neque impeditus <lb></lb>à craſſitie alicuius medij fluidi ſit <expan abbr="tãtæ">tantæ</expan> energiæ vt <expan abbr="tẽ-pore">ten<lb></lb>pore</expan> T excurrere poſſit prolixiùs ſpatium CL; quare <lb></lb>retardatio profecta à craſſitie fluidi M impedientę <lb></lb>eius motum ſit DL, ſed à maiori craſſitie R alterius <lb></lb>fluidi N retardetur ſubtrahaturque ab integro, & na<lb></lb>turali eius fluxu ſpatium EL maius quam DL. modò <lb></lb>ſi retardatio DL facta à denſitate S fluidi M mi<lb></lb>nor fuerit ſpatio CE exacto in fluido N minori ve<lb></lb>locitate; dico, quod corporis A maior velocitas in <lb></lb>fluido M ad minorem velocitatem, quam exercet in <lb></lb>fluido N minorem proportionem habebit, quàm <expan abbr="re-ſiſtẽtia">re<lb></lb>ſiſtentia</expan>, ſeù craſſities R ad reſiſtentiam S: ſi verò DL <lb></lb>æqualis fuerit CE proportionalia erunt; & tandem̨ <lb></lb>ſi DL maior fuerit, quam CE, tunc velocitas, quam̨ <lb></lb>exercet A in M ad velocitatem, quam exercet in N <lb></lb><expan abbr="maiorẽ">maiorem</expan> <expan abbr="proportionẽ">proportionem</expan> habebit, quàm craſſities R ad S. </s> </p> <p type="margin"> <s id="s.002160"><margin.target id="marg549"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002161">Ponamus primò DL minorem eſſe, quàm CE. quia <lb></lb>eadem ED ad maiorem CE habet <expan abbr="minorẽ">minorem</expan> propor<lb></lb>tionem quàm ad minorem DL, igitur componendo <lb></lb>DC ad CE minorem proportionem habebit, quàm̨ <lb></lb>EL ad LD, ſed vt DC ad CE, ita ſe habet velocitas <lb></lb>ipſius A in fluido M ad <expan abbr="velocitatẽ">velocitatem</expan> eiuſdem in fluido <lb></lb>N, (propterea quòd velocitates eodem tempore T <lb></lb>exactè proportionales ſunt ſpatijs excurſis): & ſimi<lb></lb>litèr impedimentum, & retardatio, quam affert craſ-<pb pagenum="422" xlink:href="010/01/430.jpg"></pb><arrow.to.target n="marg550"></arrow.to.target><lb></lb>ſities R fluidi N motui corporis A ad <expan abbr="eã">eam</expan> retardatio<lb></lb>nem quam ei affert craſſities S fluidi M eodem tem<lb></lb>pore T, ſe habet vt ſpatium EL ad ſpatium DL, quæ <lb></lb>ſunt retardationes factæ in eiſdem fluidis, igitur ve<lb></lb>locitas corporis A in fluido M ad eiuſdem velocita<lb></lb>tem in fluido N habebit <expan abbr="minorẽ">minorem</expan> proportionem, <expan abbr="quã">quam</expan> <lb></lb>craſſities, & reſiſtentia fluidi N ad craſſitiem alterius <lb></lb>fluidi M. </s> </p> <p type="margin"> <s id="s.002162"><margin.target id="marg550"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002163">Ponatur poſtea DL æqualis CE, habebit ED ad <lb></lb>duas æquales eamdem proportionem, & componen<lb></lb>do DC ad CE erit vt EL ad LD, & ideò vt craſſities R, <lb></lb>ad S, ita erit velocitas corporis A in M ad <expan abbr="velocitatẽ">velocitatem</expan> <lb></lb>eiuſdem in fluido N. </s> </p> <p type="main"> <s id="s.002164"><expan abbr="Tandẽ">Tandem</expan> ponatur DL maior, quam CE, ſequitur quod <lb></lb>DC ad CE maiorem proportionem habet quam EL <lb></lb>ad LD, & ideò velocitas ipſius A in M ad eam, quam <lb></lb>habet in N maiorem proportionem habebit, quàm <lb></lb>R ad S, ſcilicèt, quàm craſſities fluidi N ad <expan abbr="craſſitiẽ">craſſitiem</expan> <lb></lb>fluidi M. </s> </p> <p type="main"> <s id="s.002165"><emph type="center"></emph><emph type="italics"></emph>COROLLARIVM.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002166">HInc ſequitur verum non eſſe quòd velocitates <lb></lb>eiuſdem corporis grauis in duobus medijs flui<lb></lb>dis ſemper reciprocè proportionales ſint reſiſtentijs <lb></lb>eorumdem fluidorum. </s> </p> <p type="main"> <s id="s.002167">Si enim ex. </s> <s id="s.002168">gr. ſupponamus globum aureum de<lb></lb><arrow.to.target n="marg551"></arrow.to.target><lb></lb>ſcendere in ſpatio inani ablatis omnibus <expan abbr="impedimẽ-tismedij">impedimen<lb></lb>tis medij</expan> abſoluta, & inalterata eius velocitate natu<lb></lb>rali, vt nimirum tempore vnius minuti ſeeundi hora-<pb pagenum="423" xlink:href="010/01/431.jpg"></pb><arrow.to.target n="marg552"></arrow.to.target><lb></lb>rij percurrat altitudinem 100. cubitorum, tunc ſi iņ <lb></lb>aqua v. g. eodem tempore deſcendendo pertranſeat <lb></lb>ſpatium nonaginta <expan abbr="cubitorũ">cubitorum</expan>, in hydrargyro verò 30. <lb></lb>cubitos vt nimirùm velocitas eius in aqua, tripla ſit <lb></lb>velocitatis quàm in hydrargyro exercet, tunc calcu<lb></lb>lus oſtendit craſſitiem hydrargyri non triplam, ſed <lb></lb>ſeptuplam eſſe craſſitiei ipſius aquæ. </s> </p> <p type="margin"> <s id="s.002169"><margin.target id="marg551"></margin.target>Exemplis id <lb></lb>ipſum com<lb></lb>probatur.</s> </p> <p type="margin"> <s id="s.002170"><margin.target id="marg552"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002171">Sumptis poſtea alijs duobus medijs fluidis magis <lb></lb>differentibus vt nimirùm in rariori percurrat eodem <lb></lb>tempore 80. cubitos in denſiori verò 20. tunc præci<lb></lb>sè eamdem quadruplam proportionem habebunt <expan abbr="dẽ-ſitates">den<lb></lb>ſitates</expan> fluidorum, quam habent velocitates. </s> <s id="s.002172">Poſtre<lb></lb>mò in alijs fluidis minùs differentibus ſi velocitates <lb></lb>habuerint proportionem duplam, eorum reſiſtentiæ <lb></lb>triplam proportionem habebunt. </s> <s id="s.002173">Vndè euidentèr <lb></lb>euincitur, falſam eſſe Ariſtotelicam ſuppoſitionem, & <lb></lb>proindè non ſequitur velocitatem cuiuslibet corpo<lb></lb>ris grauis in ſpatio inani eſſe inſtantaneam. </s> <s id="s.002174">Et profe<lb></lb>ctò ſi motus naturam perpendamus, quæ ſine tranſitu <lb></lb>locali ſucceſſiuo percipi non poteſt, planè percipi<lb></lb>mus non poſſe corpus <expan abbr="finitũ">finitum</expan> in inſtanti ab vno ad <expan abbr="aliũ">alium</expan> <lb></lb>locum migrare, eſſet enim ſimùl in termino, à quo, & <lb></lb>ad quem, ſui motus, & ſic occuparet ſpatium maius <lb></lb>ſe ipſo, & præterea tolleretur omninò conceptus ſuc<lb></lb>ceſſiuæ migrationis ab vno ad alium locum, vnde <expan abbr="cõ-cludendum">con<lb></lb>cludendum</expan> eſt, quodlibet corpus finitum à finita vir<lb></lb>tute motiua impulſum, licèt omninò remoueantur me<lb></lb>dij fluidi impedimenta, oportere, vt ſpatium <expan abbr="quantũ">quantum</expan> <lb></lb>in tempore aliquo determinato percurrat. </s> <s id="s.002175">Sed hoc <pb pagenum="424" xlink:href="010/01/432.jpg"></pb><arrow.to.target n="marg553"></arrow.to.target><lb></lb>fuſiùs & accuratiùs infra oſtendetur. </s> </p> <p type="margin"> <s id="s.002176"><margin.target id="marg553"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002177">Inquirendum modò eſt, an omnia corpora natura<lb></lb>lia æqualibus velocitatibus, an verò inęqualibus mo<lb></lb>ueri debeant in eodem inani ſpatio. </s> <s id="s.002178">& primo intuitu <lb></lb>videtur incredibile, & abſurdum æquè velocia eſſę <lb></lb>debere cùm in lationibus naturalium corporum ha<lb></lb>benda præcipuè ratio ſit facultatum motus efficienti<lb></lb>um quæ procul dubio à viribus grauitatum <expan abbr="eorumdẽ">eorumdem</expan> <lb></lb>corporum <expan abbr="pendẽt">pendent</expan>, atque hæ planè inæquales eſſe vi<lb></lb>dentur, & propterea impetus, & velocitates, ab eis <lb></lb>pendentes erunt quoque inter ſe inæquales. </s> <s id="s.002179">Hoc ab <lb></lb>Ariſtotele paſſim in phyſ. & de Cœl. aſſeritur; erit igi<lb></lb>tur operæpretium abſurditatem eius propoſitionis <lb></lb><arrow.to.target n="marg554"></arrow.to.target><lb></lb>euincere; ait ergo, grauia ſecundùm proportionem̨, <lb></lb>quam grauitates habent, moueri, pariterque leuią <lb></lb><arrow.to.target n="marg555"></arrow.to.target><lb></lb>corpora, velocitates ipſis leuitatibus proportiona<lb></lb>les habere, & quod magis mirere, ait hoc obſeruari, <lb></lb>ac ſenſibus patere, habet enim, ſi fuerint duæ moles <lb></lb>inæquales eiuſdem corporis, nempè aeris, aſcendent <lb></lb>quidem ſursùm inæqualibus velocitatibus, & ſecun<lb></lb>dùm proportionem quam habent earum magnitudi<lb></lb>nes ea prorsùs ratione (inquit ipſe) qua videmus duas <lb></lb>moles inæquales terræ (ſi cætera ſint paria) maiorem <lb></lb>deſcendere velociùs, quàm minorem, ſecundùm pro<lb></lb>portionem, quam magnitudines habent. </s> <s id="s.002180">Hoc autem <lb></lb><arrow.to.target n="marg556"></arrow.to.target><lb></lb>omninò falſum eſt, vt ſenſuum euidentia conſtat. </s> <s id="s.002181">Si <lb></lb>enim duæ pilæ ferreæ inæquales fuerint, vna ſcilicèt <lb></lb><arrow.to.target n="marg557"></arrow.to.target><lb></lb>centum vnciarum, altera vnius (ſic enim conuenien<lb></lb>tia, & paritas ſeruatur in figuris ſphæricis, ſimilibus, <pb pagenum="425" xlink:href="010/01/433.jpg"></pb><arrow.to.target n="marg558"></arrow.to.target><lb></lb>atque in vniformi, & homogenea materiæ denſitate) <lb></lb>& huiuſmodi pilæ demittantur à ſupremo termino e<lb></lb>iuſdem altitudinis centum cubitorum, vt proportio <lb></lb>velocitatum eadem ſit, quam grauitates, ſeù magni<lb></lb>tudines habent, oportet vt poſtquam pila maior per<lb></lb>tranſiuit totam altitudinem centum cubitorum, reli<lb></lb>qua pila vnius vnciæ vnicum tantummodò cubitum <lb></lb>prætergreſſa ſit, & proindè adhuc ſublimis perſiſtat <lb></lb>remota à terræ ſuperficie nonaginta nouem cubitis, <lb></lb>quando iam reliqua ad terram peruenerat, & hoc eſt, <lb></lb>quod Ariſtoteles ait, apparere, ſeu videri, quod <expan abbr="tamẽ">tamen</expan> <lb></lb>omninò experientiæ refragatur, ſenſus enim ſatis e<lb></lb>xiguam differentiam inter deſcenſus prædictorum̨ <lb></lb>corporum oſtendit. </s> <s id="s.002182">idipſum in duobus corporibus <lb></lb>non homogeneis, nec ſimilaribus obſeruatur, quæ <lb></lb>ſcilicèt habeant diuerſas grauitates in ſpecie veluti <lb></lb>eſſent duæ pilæ æquales magnitudine, vna quidem̨ <lb></lb>lignea, altera verò ferrea, hæ verò licèt ſimiles, & <lb></lb>æquales | figuras habeant, non perindè earum veloci<lb></lb>tates in deſcenſu eamdem proportionem, quam ea<lb></lb>rum pondera habent, vt Ariſtoteles cenſuit, ſed ferè <lb></lb>æquali velocitate deſcendunt. </s> </p> <p type="margin"> <s id="s.002183"><margin.target id="marg554"></margin.target>Decælo lib. <lb></lb>1. cap. 6.</s> </p> <p type="margin"> <s id="s.002184"><margin.target id="marg555"></margin.target>Ex Ariſtot. <lb></lb>grauia <expan abbr="de-ſcẽdunt">de<lb></lb>ſcendunt</expan>, & <lb></lb>leuia aſcen<lb></lb>dunt veloci<lb></lb>tatibus eam<lb></lb>dem propor<lb></lb>tionem <expan abbr="ha-bẽtibus">ha<lb></lb>bentibus</expan> <expan abbr="quã">quam</expan> <lb></lb>grauitates, <lb></lb>vel leuitates</s> </p> <p type="margin"> <s id="s.002185"><margin.target id="marg556"></margin.target>phyſ. libl 4. <lb></lb>cap. 8.</s> </p> <p type="margin"> <s id="s.002186"><margin.target id="marg557"></margin.target>Quod <expan abbr="expe-riẽtia">expe<lb></lb>rientia</expan> repro<lb></lb>batur.</s> </p> <p type="margin"> <s id="s.002187"><margin.target id="marg558"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002188">Sed non erit à noſtro inſtituto alienum oſtendere <lb></lb>defectum Ariſtotelici ratiocinij, & præcipuam <expan abbr="causã">causam</expan> <lb></lb>eius hallucinationis indicare. </s> <s id="s.002189">Ait enim, quòd mo<lb></lb>tus deſcenſus pendet à vi grauitatis, tamquàm à cau<lb></lb>ſa efficiente, quare inæquales grauitates debere quo<lb></lb>que inæquales velocitates locales efficere. <pb pagenum="426" xlink:href="010/01/434.jpg"></pb><arrow.to.target n="marg559"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002190"><margin.target id="marg559"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002191"><emph type="center"></emph>PROP. CCIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002192"><emph type="center"></emph><emph type="italics"></emph>Pondera inæqualia non producunt inæquales velocitates, ſed <lb></lb>vnam, & eamdem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002193">HOc conſtat ex dictis in noſtro libro de vi per<lb></lb>cuſſionis. </s> <s id="s.002194">Quia duorum corporum velocita<lb></lb>tes non menſurantur ab ipſis ponderibus, vt <expan abbr="nimirũ">nimirum</expan> <lb></lb>eorum velocitates proportionales ſint ponderibus, <lb></lb>quandoquidem corpora quorum grauitates valdè in<lb></lb>ter ſe differunt poſſunt vna, & eadem velocitate de<lb></lb>ſcendere, propterea quod minimæ particulæ mate<lb></lb>riales corporeæ æquè graues ſupponendæ ſunt, & hæ <lb></lb>ſibi ipſis ſuperadditæ minimè augere velocitatem̨ <lb></lb>poſſunt <expan abbr="cũ">cum</expan> vna alteram impellere nequeat, tùm quia <lb></lb>omnes habent æquales vires motiuas, cùm <expan abbr="etiã">etiam</expan> quia <lb></lb>vis æqualis in ei æqualem agere non poteſt, & ideò <lb></lb>eam non promouebit, proindeque velocitas non au<lb></lb>gebitur ſicuti decem canes venatici ęquè veloces in<lb></lb>ter ſe connexi, & ſimùl currentes non percurrent ma<lb></lb>ius ſpatium, quàm vnus eorum eodem tempore, qua<lb></lb>re licèt moles corporea augeatur, & tantumdem <expan abbr="põ-dus">pon<lb></lb>dus</expan> creſcat multipliceturque, non proindè vis moti<lb></lb>ua intenſiuè augetur, ſed tantummodò extenſiuè, <lb></lb>quatenùs expanditur vniformi diſtributione in om<lb></lb>nes materiæ grauis particulas, & ſic velocitatem au<lb></lb>gere nequeunt. </s> </p> <p type="main"> <s id="s.002195">Præterea adeo falſum eſt velocitates deſcenſuum <lb></lb>proportionales eſſe ponderibus corporum inæqua-<pb pagenum="427" xlink:href="010/01/435.jpg"></pb><arrow.to.target n="marg560"></arrow.to.target><lb></lb>lium, vt ex hac hypotheſi euidenter concludatur cor<lb></lb>pus magis graue tardius <expan abbr="deſcẽdere">deſcendere</expan> <expan abbr="quã">quam</expan> minus graue. </s> </p> <p type="margin"> <s id="s.002196"><margin.target id="marg560"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002197">Hoc elegantiſſimè demonſtratum fuit à Galileo in <lb></lb>noua ſcientia mechanica dialogo primo. <lb></lb><arrow.to.target n="marg561"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002198"><margin.target id="marg561"></margin.target>Nouæ ratio<lb></lb>nes pro Ari<lb></lb>ſtotele ad<lb></lb>ducuntur.</s> </p> <p type="main"> <s id="s.002199">Sed licèt ea, quæ huc vſque dicta ſunt, euidentiſſi<lb></lb>mè ſuadeant non habere velocitates corporum de<lb></lb>ſcendentium eamdem proportionem, quam habent <lb></lb>grauitates eorum, adeſt tamen vir clariſſimus, qui <expan abbr="sẽ-tentiam">sen<lb></lb>tentiam</expan> peripateticam ſuſtinere conatur. </s> <s id="s.002200">ait enim̨, </s> </p> <p type="main"> <s id="s.002201"><arrow.to.target n="marg562"></arrow.to.target><lb></lb><emph type="italics"></emph>ratum eſſe virtutem grauitatis efficientem cauſam eße de<lb></lb>ſcenſus corporum grauium, & quia imposſibile eſt vt motus <lb></lb>deſcenſus abſque aliqua velocitate fiat, igitur eadem graui<lb></lb>tas, quæ deſcenſum producit, erit quoque cauſa effectiua il<lb></lb>lius velocitatis, quæ naturali eius deſcenſui competit, cùm<lb></lb>que gradus grauitatis non ſit vnicus, ſed augeri, & dimi<lb></lb>nui in infinitum posſit, igitur est imposſibile vt gradus gra<lb></lb>uitatis ſummoperè diuerſi inter ſe, & inæquales eumdem <lb></lb>effectum producant, ſcilicèt eamdem præcisè velocitatem, <lb></lb>neque videntur negari poſſe prima principia notisſima, quæ <lb></lb>ſuadent omnium virtutum, & facultatum, quæ effectus <lb></lb>aliquos producere poſſunt, illam, quæ maiorem vim habet, <lb></lb>maiorem effectum producere;<emph.end type="italics"></emph.end> ſubſequitur poſtea: <lb></lb><arrow.to.target n="marg563"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002202"><margin.target id="marg562"></margin.target>I.</s> </p> <p type="margin"> <s id="s.002203"><margin.target id="marg563"></margin.target>II.</s> </p> <p type="main"> <s id="s.002204"><emph type="italics"></emph>Constat experientia ponderis in altera stateræ lance poſi<lb></lb>ti, illam, quæ ex aduerſo eſt, celeriùs attollere, quàm ſi in<lb></lb>æqualitas minor foret. </s> <s id="s.002205">aut verum celeriùs circumagi, vbi <expan abbr="põ-dus">pon<lb></lb>dus</expan> grauius machinæ illud vertenti appenditur: horologij <lb></lb>quoque curſum ſimili ponderis adiectione citatiorem fieri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002206"><arrow.to.target n="marg564"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002207"><margin.target id="marg564"></margin.target>III.</s> </p> <p type="main"> <s id="s.002208">Ait quòd <emph type="italics"></emph>ab experientia non docemur breuitatem vndu<lb></lb>lationis in pendulo leuiori à ſolo medio, non autem à graui-<emph.end type="italics"></emph.end></s> </p> <pb pagenum="428" xlink:href="010/01/436.jpg"></pb> <p type="main"> <s id="s.002209"><arrow.to.target n="marg565"></arrow.to.target><lb></lb><emph type="italics"></emph>tatis defectu prouenire, neque ſolida huius aſſertionis ratio <lb></lb>afferri potest.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg566"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002210"><margin.target id="marg565"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002211"><margin.target id="marg566"></margin.target>IV.</s> </p> <p type="main"> <s id="s.002212"><emph type="italics"></emph>Quia facilius à grauiori corpore vinci poteſt medij <expan abbr="reſiſtẽ-tia">reſiſten<lb></lb>tia</expan><emph.end type="italics"></emph.end>, ait, <emph type="italics"></emph>fore vt celerior ille grauioris corporis <expan abbr="deſcẽſus">deſcenſus</expan> à ma<lb></lb>iori eiuſdem grauitate oriatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002213"><arrow.to.target n="marg567"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002214"><margin.target id="marg567"></margin.target>V.</s> </p> <p type="main"> <s id="s.002215">Tandem Ariſtotelis argumentum validiſſimum eſ<lb></lb>ſe probat, <emph type="italics"></emph>nam cùm grauitas in certa aliqua proportione <lb></lb>reſistentiam medij ſuperet, ſequitur proportiones inter gra<lb></lb>uitatem, & medium abſque fine multiplicari poſſe, quare ſi <lb></lb>ſupponatur corpus aliquod per ſpatium imaginarium in cer<lb></lb>to velocitatis gradu, impellente grauitate deſcendere, pote<lb></lb>rit vtique dari corpus, cui talis ſit reſpectu medij realis pro<lb></lb>portio, vt pari illud velocitate tranſcurrat: infinita <expan abbr="tamẽ">tamen</expan> <lb></lb>erit diſtantia inter reſistentiam medij realis huic corpori col<lb></lb>lati, & reſiſtentiam ſpatij imaginarij comparati cum al<lb></lb>tero, quod ille æquali in eo velocitate moueri ſupponitur. </s> <s id="s.002216">Id <lb></lb>verò abſurdisſimum eſſe quilibet ſtatim pronunciabit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002217"><arrow.to.target n="marg568"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002218"><margin.target id="marg568"></margin.target>VI.</s> </p> <p type="main"> <s id="s.002219"><emph type="italics"></emph>Verſa igitur argumenti formula: quia reſiſtentia medij <lb></lb>grauitatem non nihil retardat celeriùſque fertur graue vbi <lb></lb>minùs illi reſistitur, cùm nulla ſit inter medium<emph.end type="italics"></emph.end> (plenum̨ <lb></lb>ſupple) <emph type="italics"></emph>ſpatiumque vacuum proportio, ſequetur neceſſa<lb></lb>riò neque vllam fore inter tempus in quo corpus graue de<lb></lb>terminatam medij quantitatem emetitur; & tempus in <lb></lb>quo tantumdem ſpatij vacui tranſcurrit, quare ſpatium il<lb></lb>lud vacuum in momento conficiet.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002220"><arrow.to.target n="marg569"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002221"><margin.target id="marg569"></margin.target>Reſponde<lb></lb>tur primæ <lb></lb>difficultati <lb></lb>ex ſuperiùs <lb></lb>adductis.</s> </p> <p type="main"> <s id="s.002222">Ad primam ergo difficultatem reſpondeo breui<lb></lb>tèr verum non eſſe quod effectus maioris velocitatis <lb></lb>dependeat tamquàm à cauſa efficiente à virtute ma<lb></lb>ioris grauitatis in ipſo actu deſcenſus. </s> <s id="s.002223">Quia vt oſten-<pb pagenum="429" xlink:href="010/01/437.jpg"></pb><arrow.to.target n="marg570"></arrow.to.target><lb></lb>dimus prop. 20. 21. & 204. partes æquales eiuſdem <lb></lb>grauis ex ſui natura eadem velocitate fluere deorsùm <lb></lb>debent, & deò ſuperior pari velocitate comprime<lb></lb>re nitetur inferiorem, qua hæc ictum fugit, & proin<lb></lb>de grauitas ſuperioris non augebit vim <expan abbr="compreſſiuã">compreſſiuam</expan>, <lb></lb>ſeu grauitatem inferioris; perindè ergò operatur <expan abbr="põ-dus">pon<lb></lb>dus</expan> vnius partis ac ſr æquale eſſet ponderi aggregati <lb></lb>omnium partium. </s> <s id="s.002224">ex quo fit vt in motu deſcenſus <lb></lb>quælibet corpora inæqualia æquè grauia cenſeri poſ<lb></lb>ſint; ideoque non deſcendent in æqualibus veloci<lb></lb>tatibus, neque nouum eſt vim, & energiam decem <lb></lb>hominum ſuſtinere poſſe maius pondus nempè decu<lb></lb>plum, quàm vnus eorum, ſed non indè ſequitur, quod <lb></lb>prædicti homines currere poſſint baiulando eadem̨ <lb></lb>pondera velocitate decies maiori, quam vnus <expan abbr="eorũ">eorum</expan> <lb></lb>tantùm, itaque licèt velocitas curſus dependeat à vi, <lb></lb>& energia prædictorum hominum, non proindè ve<lb></lb>locitas augetur <expan abbr="multiplicaturq;">multiplicaturque</expan> prout homines præ<lb></lb>dicti multiplicantur. </s> <s id="s.002225">Vnde patet infirmitas primæ <lb></lb>obiectionis. <lb></lb><arrow.to.target n="marg571"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002226"><margin.target id="marg570"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002227"><margin.target id="marg571"></margin.target><expan abbr="Reſpõdetur">Reſpondetur</expan> <lb></lb>ſecundæ.</s> </p> <p type="main"> <s id="s.002228">Ad ſecundam noto, nos quærere an duo corporą <lb></lb>grauia dum naturali, libero, & non impedito motu <lb></lb>feruntur inæqualibus velocitatibus deſcendant, ſci<lb></lb>licèt in eadem proportione, quam grauitates habent. <lb></lb></s> <s id="s.002229">ergo prauè, & contra logices præcepta aduerſarius <lb></lb>permutat ſubiectum problematis, cùm <expan abbr="nẽpè">nempè</expan> aſſumit <lb></lb>non duo mobilia grauia, ſed vnum, & in eo quærit <lb></lb>motus partium in ſuo toto, quæ nequeunt libero, & <lb></lb>non impedito motu deſcendere niſi ex parte. </s> <s id="s.002230">talis </s> </p> <pb pagenum="430" xlink:href="010/01/438.jpg"></pb> <p type="main"> <s id="s.002231"><arrow.to.target n="marg572"></arrow.to.target><lb></lb>profectò naturæ ſunt duo pondera ſuſpenſa, vel an<lb></lb>nexa in libra, rota, & veru, quæ componunt vnum̨ <lb></lb>mobile in centro grauitatis communis vim <expan abbr="exercẽs">exercens</expan>; <lb></lb>nec libero motu deſcendere valent, cum cogantur <lb></lb>vertiginoſo motu circa fulcimentum eius agitari <expan abbr="cõ-trarijs">con<lb></lb>trarijs</expan> lationibus. </s> <s id="s.002232">In ijs planè concedimus pondera <lb></lb>inæqualia diuerſimodè operari ob libræ <expan abbr="naturã">naturam</expan>, <expan abbr="quã">quam</expan> <lb></lb>non videtur prædictus author benè percepiſſe. </s> <s id="s.002233">Opor<lb></lb>tet ergo vt ſumamus duos globos ferreos inæquales <lb></lb>ſolutos, ſeparatoſque qui in aere demittantur, vt li<lb></lb>berè, & abſque impedimento deſcendere poſſint per <lb></lb>rectas lineas ad centrum terræ tendentes, cùmque in <lb></lb>hac <expan abbr="experiẽtia">experientia</expan> velocitates deſcenſuum ferè æquales <lb></lb>ſint licèt pondera deſcendentia ſint valdè inter ſę <lb></lb>inæqualia, facilè ſuademur quod ab aliqua circum<lb></lb>ſtantia in bilancibus, rotis, & veru impeditur, & per<lb></lb>turbatur effectus ille, qui in ſimpliciſſima operatio<lb></lb>ne obſeruabatur, quod fuſiùs in ſequenti capite de<lb></lb>clarabitur. <lb></lb><arrow.to.target n="marg573"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002234"><margin.target id="marg572"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002235"><margin.target id="marg573"></margin.target>Reſponde<lb></lb>tur tereiæ.</s> </p> <p type="main"> <s id="s.002236">Ad tertiam nego Galileum deduxiſſe grauia inæ<lb></lb>qualia deſcendere velocitatibus æqualibus debere <lb></lb>ex hac experientia, quod funependula æquè longa, <lb></lb>& inæqualiter ponderoſa efficiunt vndulationes æ<lb></lb>quitemporaneas; non enim ex hac operatione, quæ <lb></lb>difficilioris indaginis eſt, ſed ex libero <expan abbr="deſcẽſu">deſcenſu</expan> duo<lb></lb>rum inæqualium ponderum falſitatem peripatetici <lb></lb>pronunciati euidentiſſimè comprobauit. </s> <s id="s.002237">Sed interim <lb></lb>aio, quod retardatio vibrationis leuioris funependu<lb></lb>li producitur ab impedimento, & obſtaculo aeris, </s> </p> <pb pagenum="431" xlink:href="010/01/439.jpg"></pb> <p type="main"> <s id="s.002238"><arrow.to.target n="marg574"></arrow.to.target><lb></lb>non autem à defectu ponderis eius. </s> <s id="s.002239">Si enim ſuſpen<lb></lb>dantur ex filis æquè longis duæ pilæ vna plumbea, <lb></lb>altera verò lignea quarum quælibet vnam vnciam̨ <lb></lb>pendat tunc ſi æquè à perpendiculo remoueantur, ef<lb></lb>ficient vibrationes æquitemporaneas, at continen<lb></lb>tèr vndulationes ligneæ pilæ breuiores fiunt, dùm̨ <lb></lb>breuiora ſpatia hinc inde, & diminuta percurriit, hìc <lb></lb>verò <expan abbr="cõſtat">conſtat</expan> <expan abbr="tarditatẽ">tarditatem</expan> ligni <expan abbr="nõ">non</expan> à defectu <expan abbr="põderis">ponderis</expan>, cum <lb></lb>vnius quoque vnciæ ſit, ſed ab amplitudine molis e<lb></lb>ius, quatenùs ſua dilatata ſuperficie cogitur expelle<lb></lb>re <expan abbr="ampliorẽ">ampliorem</expan> aeris molem è ſuo loco, quem euidentiſ<lb></lb>ſimum eſt reſiſtere expulſioni, vt flabello, & alijs in<lb></lb>numeris modis experimur. </s> <s id="s.002240">Sed præterea ſuademur, <lb></lb>quod non à <expan abbr="põdere">pondere</expan> aucto celeritas eius motus in flui<lb></lb>do augetur; ſi enim ſupponamus ingens nauigium̨ <lb></lb>æquè velocitèr per maris ſuperficiem excurrere, ac <lb></lb>linter, manifeſtum eſt ea nullam grauitatem exercere <lb></lb>tranſuerſaliter dum in aqua <expan abbr="innatãt">innatant</expan>. </s> <s id="s.002241">adueniat poſtea <lb></lb>impedimentum externum, v. g. plures homines ſuis <lb></lb>viribus conentur impedire, & firmare curſum prædi<lb></lb>ctorum inæqualium nauigiorum, procùl dubio ener<lb></lb>gia vnius hominis tantùm ſiſtere, & ob firmare pote<lb></lb>rit lintrem, cùm è contrà nauis illa <expan abbr="ingẽs">ingens</expan> æquè velox, <lb></lb>ac nauicula <expan abbr="nõ">non</expan> poſſit impediri, neque velocitas eius <lb></lb>omninò extingui ab ingenti conatu, & repulſu <expan abbr="centũ">centum</expan> <lb></lb>hominum: cauſa huius diuerſiratis oſtenſa fuit in no<lb></lb>ſtro opere de vi percuſs. </s> <s id="s.002242">pendetque ab energia vir<lb></lb>tutis motiuæ expanſæ per vniuerſam molem nauigij <lb></lb>prægrandis, quæ tam multiplex eſt virtutis motiuæ <pb pagenum="432" xlink:href="010/01/440.jpg"></pb><arrow.to.target n="marg575"></arrow.to.target><lb></lb>nauiculæ, quantò illius moles ſuperat huius molem, <lb></lb>& ideò vis percuſſiua à maiori vi motiua <expan abbr="pendẽs">pendens</expan> mul<lb></lb>tò maior eſſe debet, quàm illa, quæ à minori virtute <lb></lb>motiua producitur; nec mirum eſt ad extinguendam <lb></lb>maiorem vim motiuam exigi validiorem vim <expan abbr="reſiſtẽ-tem">reſiſten<lb></lb>tem</expan>; hinc fit vt virtus vnius hominis impedire, & <lb></lb>extinguere poſſit vim puſillam lintrem mouentem̨, <lb></lb>non verò vaſtam vim motiuam nauigij eodem prorsùs <lb></lb>modò in pendulis pila lignea, aut minoris ponderis, <lb></lb>licèt æquè velocitèr moueatur, ac pila grauis plum<lb></lb>bear iila tamen à minori vi motiua transfertur, cui <lb></lb>aeris inertia, & corpulentia poteſt eius impetum de<lb></lb>bilitare, & extinguere, ſed non poteſt æquali reſi<lb></lb>ſtentia impedire energiam maioris virtutis motiuæ <lb></lb>grauioris pilæ plumbeæ. </s> </p> <p type="margin"> <s id="s.002243"><margin.target id="marg574"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002244"><margin.target id="marg575"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002245">Ad quartam reſponderi poteſt, falſum eſſe à maio<lb></lb>ri grauitate meliùs, & faciliùs vinci, & ſuperari me<lb></lb>dij fluidi r ſiſtentiam. </s> <s id="s.002246">nam duo funependula æqua<lb></lb>lia, & inæqualitèr grauia dum oſcillationes ſuas <expan abbr="cõfi-ciunt">confi<lb></lb>ciunt</expan> nullam prorsùs grauitatem exercent perindè, <lb></lb>ac ſi grauia non eſſent, propterea quod æquilibran<lb></lb>tur à tenacitatibus funiculorum clauibus affixorum. <lb></lb></s> <s id="s.002247">Similitèr libræ ferreæ horologiorum dum conuertun<lb></lb>tur horizontalitèr grauitate carent, ſeù eam non e<lb></lb>xercent, ſic quoque inæqualia nauigia innatantią <lb></lb>dum horizontalitèr mouentur non agunt grauitate, <lb></lb>quæ ab aqua æquilibratur, & tandem pilæ plumbeæ, <lb></lb>& ligneæ ſursùm perpendicularitèr proiectæ dum oc<lb></lb>currunt, & percutiunt ſupremum fluidum, vel corpo-<pb pagenum="433" xlink:href="010/01/441.jpg"></pb><arrow.to.target n="marg576"></arrow.to.target><lb></lb>ra ſuſpenſa, planè non agunt grauitate, quæ non ſur<lb></lb>sùm, ſed deorsùm operari, & impellere valet; et ta<lb></lb>men in ijs omnibus, quæ denſiora ſunt, aut copioſio<lb></lb>ri ſubſtantia materiali donantur magis, & faciliùs <lb></lb>medij fluidi, & obſtaculorum impedimenta <expan abbr="ſuperãt">ſuperant</expan>. <lb></lb></s> <s id="s.002248">Non igitur à grauitate, quatenùs talis eſt medij flui<lb></lb>di <expan abbr="reſiſtẽtia">reſiſtentia</expan> ſuperatur, ſed ab alia <expan abbr="cauſalõgè">cauſalongè</expan> diuerſa. </s> </p> <p type="margin"> <s id="s.002249"><margin.target id="marg576"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002250">Sed ponamus à maiori vi motiua grauiorum cor<lb></lb>porum magis, & faciliùs medij fluidi reſiſtentiam ſu<lb></lb>perari, non indè ſequetur, magis grauia celeriorem̨ <lb></lb>motum deſcenſus producere niſi ex accidenti, nam ſi <lb></lb>reuera efficiens cauſa velocitatis eſſet grauitas, ne<lb></lb>ceſſariò effectus velocitatum proportionales eſſent <lb></lb>ſuis cauſis, ſcilicèt grauitatibus, vti Aduerſarius <expan abbr="cũ">cum</expan> <lb></lb>Ariſtotele ſuſtinere tenetur. </s> <s id="s.002251">hoc autem falſum eſſę <lb></lb>manifeſtum eſt; nam duæ pilæ æquales vna aurea, al<lb></lb>tera marmorea, quæ in fluidis craſſioribus feruntur <lb></lb>velocitatibus notabili exceſſu inter ſe differentibus, <lb></lb>in aere poſtea æquè veloces eſſe videntur. </s> <s id="s.002252">igitur illa <lb></lb>inſignis differentia velocitatum ab <expan abbr="impedimẽto">impedimento</expan> me<lb></lb>dij fluidi craſſioris dependet <expan abbr="nõ">non</expan> ab inæqualibus gra<lb></lb>uitatibus, quæ æquè veloces in aere eſſe videntur. </s> </p> <p type="main"> <s id="s.002253">Sed pro clariori huius rei euidentia ſupponamus <lb></lb>validum equum æquali velocitate currere, ac canis a<lb></lb>liquis venaticus, ſubmergantur poſtea omninò am<lb></lb>bo infra aquam, vel infra lutum, procùl dubio maior <lb></lb>vis, & robur equi minùs impediri poterit à denſitate <lb></lb>aquæ, vel luti, quàm canis exigua vis impediatur, <lb></lb>& propterea equus demerſus velociùs agitari, moue-<pb pagenum="434" xlink:href="010/01/442.jpg"></pb><arrow.to.target n="marg577"></arrow.to.target><lb></lb>ri, & currere poterit; quàm canis; licèt ergo <expan abbr="mediũ">medium</expan> <lb></lb>lutoſum debilem canem magis impediat, quàm robu<lb></lb>ſtum equum, non tamen licet inferre quòd maior vis <lb></lb>motiua equi celeriorem motum producat in aere ab<lb></lb>lato impedimento luti, quàm canis, cùm æquè velo<lb></lb>ces ſupponantur. </s> </p> <p type="margin"> <s id="s.002254"><margin.target id="marg577"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002255">Demùm notari debet quàm diuerſa ſit conſtitutio <lb></lb>duorum corporum grauium in <expan abbr="æqualiũ">æqualium</expan> in medio flui<lb></lb>do magis, aut minùs denſo, & impediente quàm in <lb></lb><arrow.to.target n="marg578"></arrow.to.target><lb></lb>ſpatio prorsùs inani; namibi vt dictum eſt, graue vnà <lb></lb>cum medio fluido in quo immergitur, libram, quam<lb></lb>dam, ſeù ſiphonem conſtituit, & ideò prout efficitur <lb></lb>æquilibrium, vel mobile ſuperat, vel deficit, à gra<lb></lb>uitate fluidi ambientis effici poteſt quies, aut aſcen<lb></lb>ſus, vel deſcenſus; at in medio prorsùs inani vbi im<lb></lb>pedimentum æquilibrij prorsùs tollitur non poterit <lb></lb>vlla ratione vnica illa naturalis velocitas corporis <lb></lb>mobilis alterari, retardarique. </s> </p> <p type="margin"> <s id="s.002256"><margin.target id="marg578"></margin.target>Pr. 9. & 10.</s> </p> <p type="main"> <s id="s.002257">Ad quintum argumentum nego primo loco repe<lb></lb><arrow.to.target n="marg579"></arrow.to.target><lb></lb>riri vllum corpus poſſe quod in aliquo medio fluido <lb></lb>pleno, licèt tenuiſſimo, & rariſſimo poſſit tanta velo<lb></lb>citate moueri, quanta eſt illa, quam aliud corpus in <lb></lb>vacuo habere poſſet; nam vniuersè omnia corporą <lb></lb>terrena æquè velocia ſunt in ſpatio inani ablatis om<lb></lb>nibus impedimentis, vt mox <expan abbr="oſtẽdemus">oſtendemus</expan>, igitur quod<lb></lb>libet eorum in medio pleno conſtitutum tardiori mo<lb></lb>tu deſcendet, quàm quodlibet aliud in medio inani, <lb></lb>tantum præcisè, quantum medium prædictum <expan abbr="fluidũ">fluidum</expan> <lb></lb>ſua denſitate impedit eius naturalem motum, ergò <pb pagenum="435" xlink:href="010/01/443.jpg"></pb><arrow.to.target n="marg580"></arrow.to.target><lb></lb>non poterit reperiri aliud corpus quod in vacuo æ<lb></lb>quali tarditate feratur, ac illud in pleno excurrebat; <lb></lb>neque hoc incredibile alicui videri poteſt, niſi ijs, qui <lb></lb>à falſa perſuaſione præoccupati cenſent corpora inę<lb></lb>qualia in vacuo inæqualibus velocitatibus moueri <lb></lb>debere, quod falſum eſſe demonſtrabitur. </s> </p> <p type="margin"> <s id="s.002258"><margin.target id="marg579"></margin.target>Quintum re<lb></lb>ſpondetur.</s> </p> <p type="margin"> <s id="s.002259"><margin.target id="marg580"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002260">Ad ſextum, ſimilitèr aduerſarij hallucinatio pendet <lb></lb><arrow.to.target n="marg581"></arrow.to.target><lb></lb>ex falſa ſuppoſitione, quòd velocitates eiuſdem mo<lb></lb>bilis habeant proportionem contrario <expan abbr="reſpondentẽ">reſpondentem</expan> <lb></lb>reſiſtentijs mediorum fluidorum, verum eſt maiorem <lb></lb>medij reſiſtentiam magis velocitatem eiuſdem gra<lb></lb>uis retardare, ſed non tamen proportionalitèr hu<lb></lb>iuſmodi retardatio efficitur, vt ſupra demonſtraui<lb></lb>mus; & hìc mirari licet, quòd aduerſarius neglectą <lb></lb>Galilei demonſtratione tantummodò affert nouas <lb></lb>difficultates, qui tamen tenebatur demonſtrationem <lb></lb>adductam redarguere, & eius paralogiſmum indica<lb></lb>re, quod non præſtitit. </s> </p> <p type="margin"> <s id="s.002261"><margin.target id="marg581"></margin.target>Sexto argu<lb></lb>mento re<lb></lb>ſpondetur.</s> </p> <p type="main"> <s id="s.002262">Ad argumentum verò dico quòd ſupponendo ple<lb></lb>num denſius magis velocitatem mobilis retardarę, <lb></lb>quàm plenum rarum, pariterque poſito, plenum ad <lb></lb>vacuum nullam proportionem habere, non indè ſe<lb></lb>quitur velocitatem, quam ſaxum in vacuo exercet, <lb></lb>eſſe infinitè maiorem illo impetu, quo in aqua moue<lb></lb>retur, neque hanc velocitatem eſſe illa infinitè tar<lb></lb>diorem, poſſet enim habere proportionem finitam, <lb></lb>propterea quod diſtantia inter reſiſtentiam pleni, & <lb></lb>nullam vacui reſiſtentiam non eſt quid infinitum, ſed <lb></lb>menſuratur ab entitate finita pleni reſiſtentis, quą <pb pagenum="436" xlink:href="010/01/444.jpg"></pb><arrow.to.target n="marg582"></arrow.to.target><lb></lb>ſupra nihilum, ſeù ſupra vacuum eminet, eodem modo, <lb></lb>ac id, quod linea palmaris nihilum ſuperat, vel ſupra <lb></lb>id eminet, nil aliud planè eſt, quàm entitas finitą <lb></lb>eiuſdem lineæ palmaris. </s> </p> <p type="margin"> <s id="s.002263"><margin.target id="marg582"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002264"><emph type="center"></emph>PROP. CCV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002265"><emph type="center"></emph><emph type="italics"></emph>Hoc poſito ostendemus velocitatem cuiuslibet corporis gra<lb></lb>uis in vacuo eſſe finitam, & in tempore abſolui.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002266">SI enim fieri poteſt mobile A in vacuo infinitą <lb></lb>velocitate BC moueatur, & quia <expan abbr="nõ">non</expan> alia de cau<lb></lb>ſa in aere corpus A tardiùs mouetur, <lb></lb><figure id="id.010.01.444.1.jpg" xlink:href="010/01/444/1.jpg"></figure><lb></lb>niſi quia aer pro menſura eius denſi<lb></lb>tatis impedit, & retardat eam velo<lb></lb>citatem, quam aptum natum eſt exer<lb></lb>cere <expan abbr="idẽ">idem</expan> corpus A, remotis omnibus <lb></lb>impedimentis; eſtque aeris denſitas <lb></lb>finita, ideoque reſiſtentia, & retar<lb></lb>datio erit quid finitum; ſit illa BE, <lb></lb>ergo ab abſoluta, & totali velocita<lb></lb>te BC ablata retardatione BE rema<lb></lb>nebit velocitas EC, qua per <expan abbr="aerẽ">aerem</expan> mouebitur corpus <lb></lb>prædictum; ſed ab infinita velocitate BC ablata fini<lb></lb>ta velocitate retardationis BE, remanebit adhùc infi<lb></lb>nita velocitas EC, quare corpus A in aere mouebitur <lb></lb>infinita velocitate EC, quod eſt abſurdum, conſtat <lb></lb>enim per aerem velocitate finita, & temporanea mo<lb></lb>ueri: qua propter in vacuo non mouebitur infinitą, <lb></lb>ſeù inſtantanea velocitate, quod fuerat <expan abbr="oſtendendũ">oſtendendum</expan>. <pb pagenum="437" xlink:href="010/01/445.jpg"></pb><arrow.to.target n="marg583"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002267"><margin.target id="marg583"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002268"><emph type="center"></emph>PROP. CCVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002269"><emph type="center"></emph><emph type="italics"></emph>Idem aliter confirmatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002270">ET profectò cùm hìc non agatur de vacuo, & ple<lb></lb>no, quatenùs vacuum, & plenum ſunt, ſed qua<lb></lb>tenùs motum impediunt; propterea reſpectus, ſeù <lb></lb>proportio inter plenum, & vacuum conſideratur in <lb></lb>ordine ad impedimentum, quatenùs priuatio, & ca<lb></lb>rentia impedimenti ipſius vacui nullam <expan abbr="proportionẽ">proportionem</expan> <lb></lb>habet ad verum, & reale <expan abbr="impedimentũ">impedimentum</expan> à medio ple<lb></lb>no productum, ſicuti inter nihilum, & ens nulla da<lb></lb>tur proportio. </s> </p> <p type="main"> <s id="s.002271">Videamus modò an velocitas eiuſdem mobilis <expan abbr="tã-topere">tan<lb></lb>topere</expan> variati debeat in vacuo, & in pleno, vt reſul<lb></lb>tantes velocitates debeant infinitè inter ſe diſtare, ac <lb></lb>differre, quem ad modum carentia impedimenti, ſeù <lb></lb>nihilum ad impedimentum ipſum reale nullam pro<lb></lb>portionem habet. </s> <s id="s.002272">Et procùl dubio quoad <expan abbr="carentiã">carentiam</expan>, <lb></lb>& priuationem impedimenti pertinet, perindè eſt ſi <lb></lb>mobile in vacuo feratur, ac ſi in aliquo fluido, quod <lb></lb>eius motum nil prorsùs impediat, nec retardet, & ve<lb></lb>locitatem eius non imminuat præcisè, vt vacuum nil <lb></lb>ei obſiſtit; hoc autem præſtat aer ipſe motus, & à <expan abbr="vẽ-to">ven<lb></lb>to</expan> agitatus ad eaſdem partes, versùs quas mobile fer<lb></lb>tur, qui præterea tanta velocitate ad eaſdem partes <lb></lb>fugiat, quanta ab ipſo mobile perſequitur. </s> <s id="s.002273">tunc qui<lb></lb>dem, vt dictum eſt, nil prorsùs ab aere fluente, ſeù <lb></lb>vento illo ſecundo impeditur, vel retardatur fluxus <pb pagenum="438" xlink:href="010/01/446.jpg"></pb><arrow.to.target n="marg584"></arrow.to.target><lb></lb>prædicti mobilis, & perindè ſe habet, ac ſi in vacuo <lb></lb>moueretur. </s> </p> <p type="margin"> <s id="s.002274"><margin.target id="marg584"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002275">Modò quia impedimentum reale, quod infert aer <lb></lb>quieſcens ſua denſitate motui eiuſdem corporis ad <lb></lb>nullum, ſeù ad priuationem impedimenti aeris <expan abbr="fluẽ-tis">fluen<lb></lb>tis</expan>, ſeu venti ſecundi, (qui in diminutam eius veloci<lb></lb>tatem non minùs, ac vacuum excurrere ſinit) habebit <lb></lb>eamdem proportionem infinitam, ſeù eumdem defe<lb></lb>ctum proportionis, quam habet plenum ad vacuum̨ <lb></lb>(ex aſſumpto Peripatetico) ergo velocitas finita, & <lb></lb>temporanea eiuſdem mobilis in aere quieſcentę <lb></lb>nullam quoque proportionem habebit ad <expan abbr="velocitatẽ">velocitatem</expan> <lb></lb>eius in aere à vento ſecundo agitato, ideoque in ip<lb></lb>ſo infinita, & <expan abbr="inſtãtanea">inſtantanea</expan> velocitate moueretur, quod <lb></lb>eſt falſum, & contra experientiam. </s> <s id="s.002276">Hinc ſequitur, <lb></lb>quòd idem mobile quod in aere ſtagnante quatuor <lb></lb>gradibus velocitatis ferebatur, in vacuo poſtea vbi <lb></lb>nullum impedimentum adeſt non mouebitur infinitè <lb></lb>velociùs, & in <expan abbr="inſtãti">inſtanti</expan>. </s> <s id="s.002277">Et ratio eſt, quia <expan abbr="impedimentũ">impedimentum</expan> <lb></lb>medij fluidi retardans mobilis velocitatem non ha<lb></lb>bet infinitam energiam, ſed eſt certi, ae finiti roboris, <lb></lb>& ideo infinitatem impetus, quam in vacuo exercere <lb></lb>deberet minimè deſtruere poſſet, nam eadem vis, & <lb></lb>energia infinita requiritur, vt quantitas finita in in<lb></lb>finitum extendatur, ac è contrà requiritur vt lineą <lb></lb>verè infinita adeò decurtetur, vt extenſionem <expan abbr="finitã">finitam</expan> <lb></lb>acquirat; in vtroque enim caſu <expan abbr="trãſitus">tranſitus</expan>, & intercape<lb></lb>do infinita eſt, & propterea exigit infinitam <expan abbr="virtutẽ">virtutem</expan>. </s> </p> <p type="main"> <s id="s.002278">Præterea eadem infinita inter capedo, & carentia <pb pagenum="439" xlink:href="010/01/447.jpg"></pb><arrow.to.target n="marg585"></arrow.to.target><lb></lb>proportionis reperitur inter totale motus impedi<lb></lb>mentum, ſcilicèt inter quietem quam affert aqua de<lb></lb>ſcenſui ligni, & impedimentum quod eidem affert <lb></lb>aer quieſcens, in quo aliquo gradu velocitatis mo<lb></lb>uetur; quia verò quam proportionem habent velo<lb></lb>citates ex aduerſario, eamdem reciprocè habere de<lb></lb>bent denſitates mediorum fluidorum; diſtat verò in<lb></lb>finitè quies à motu, igitur infinitè quoque diſtarę <lb></lb>deberent inter ſe, reciprocè denſitates fluidorum, & <lb></lb>proindè aqua infinitè denſior aere eſſet, ſic enim nul<lb></lb>lam proportionem eorum denſitates haberent, quod <lb></lb>eſt omninò abſurdum; ex quibus omnibus deducitur <lb></lb>falſum eſſe aduerſarij ratiocinium. </s> </p> <p type="margin"> <s id="s.002279"><margin.target id="marg585"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002280">Poſtquam oſtendimus naturalia corpora in vacuo <lb></lb>moueri, non in inſtanti, ſed in tempore debere, & <lb></lb>præterea corpora inæqualitèr grauia non moueri ſe<lb></lb>cundum proportionem, quam habent eorum graui<lb></lb>tates, debemus poſtremo loco <expan abbr="oſtẽdere">oſtendere</expan>, quod ſi om<lb></lb>nia impedimenta, quæ dependent à medio fluido in <lb></lb>motionibus corporum grauium tolli poſſent, quod in <lb></lb>ſpatio inani verificari poſſet, tunc planè omnia cor<lb></lb>pora inæqualitèr grauia ſpecie, & mole, quibuſcum<lb></lb>que figuris prædita, eodem tempore per idem <expan abbr="ſpatiũ">ſpatium</expan> <lb></lb>deſcendere deberent. </s> <s id="s.002281">Hanc | ad mirabilem propoſitio<lb></lb>nem Galileus omnium primus protulit dialogo pri<lb></lb>mo de motu locali, & in ſuis poſtillis non dum typis <lb></lb>excuſis, eam tamen non demonſtrauit, ſed coniectu<lb></lb>ris, & probabilibus <expan abbr="tantũmodò">tantummodò</expan> rationibus confir<lb></lb>mare conatus eſt; quia verò huiuſmodi propoſitio v-<pb pagenum="440" xlink:href="010/01/448.jpg"></pb><arrow.to.target n="marg586"></arrow.to.target><lb></lb>ſum habet in hac phyſices parte, quam præ manibus <lb></lb>habemus; propterea operæpretium duxi firmis de<lb></lb>monſtrationibus eam confirmare; vt autem hoc cla<lb></lb>rè, & perſpicuè oſtendi poſſit, præmitti, & memorari <lb></lb>debent aliqua principia lumine naturæ nota, quorum <lb></lb>primum erit. <lb></lb><arrow.to.target n="marg587"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002282"><margin.target id="marg586"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002283"><margin.target id="marg587"></margin.target>Repetuntur, <lb></lb>& præmit<lb></lb>tuntur ali<lb></lb>qua princi<lb></lb>pia nota, aut <lb></lb>alibi <expan abbr="oſtẽſa">oſtenſa</expan>.</s> </p> <p type="main"> <s id="s.002284">Cuilibet corpori graui tributum, ac aſſignatum̨ <lb></lb>fuiſſe ab ipſa natura <expan abbr="gradũ">gradum</expan>, & <expan abbr="periodũ">periodum</expan> <expan abbr="determinatũ">determinatum</expan>, <lb></lb><expan abbr="præfixũ">præfixum</expan>, ac inuariabilem velocitatis, quo <expan abbr="deſcẽdere">deſcendere</expan> <lb></lb><expan abbr="deorsũ">deorsum</expan> valeat, quia nimirùm principia, & cauſæ <expan abbr="mo-tuũ">mo<lb></lb>tuum</expan> <expan abbr="naturaliũ">naturalium</expan> in <expan abbr="ijſdẽ">ijſdem</expan> corporibus <expan abbr="eædẽ">eædem</expan> omninò ſunt, </s> </p> <p type="main"> <s id="s.002285"><arrow.to.target n="marg588"></arrow.to.target><lb></lb>quæ ſuos effectus producere valent, qui non erunt <lb></lb>vagi, & indeterminati cum natura certa neceſſitate <lb></lb>operetur, ergo fieri non poteſt, vt idem corpus ex <lb></lb>ſui natura, ablatis omnibus externis impedimentis, <lb></lb>poſſit modò celeriùs, modò tardiùs, abſque vlla regu<lb></lb>la per idem ſpatium eodemque tempore moueri, ſed <lb></lb>ſemper conſtanti, ac inuariabili progreſſu vniformi<lb></lb>ter accelerato migrabit. <lb></lb><arrow.to.target n="marg589"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002286"><margin.target id="marg588"></margin.target>I.</s> </p> <p type="margin"> <s id="s.002287"><margin.target id="marg589"></margin.target>II.</s> </p> <p type="main"> <s id="s.002288">Motus eiuſdem corporis grauis à conſiſtentia me<lb></lb>dij fluidi impeditur, & retardatur prout reſiſtentią <lb></lb>maior, vel minor fuerit, contingit tamen ex acciden<lb></lb>ti, vt figura varia eiuſdem corporis grauis maius, aut <lb></lb>minus impedimentum patiatur ab eodem fluido. </s> <s id="s.002289"><expan abbr="cõ-ſtat">con<lb></lb>ſtat</expan> enim experientia, quod aer, & aqua magis obſi<lb></lb>ſtunt, impediuntque tranſitum figuræ dilatatæ alicu<lb></lb>ius laminæ, minùs verò refragantur migrationi cor<lb></lb>poris acuminati. </s> </p> <pb pagenum="441" xlink:href="010/01/449.jpg"></pb> <p type="main"> <s id="s.002290"><arrow.to.target n="marg590"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002291"><margin.target id="marg590"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002292">Hinc deducitur, quòd figura acuminata eiuſdem̨ <lb></lb>corporis grauis omninò inutilis eſt, nec motum eius <lb></lb>facilem reddit, quando motus fieri debet in ſpatio <lb></lb>prorsùs inani, non verò in medio fluido quieſcente; </s> </p> <p type="main"> <s id="s.002293"><arrow.to.target n="marg591"></arrow.to.target><lb></lb>propterea quòd vis motiua eius naturalis nullam me<lb></lb>dij reſiſtentiam ſuperare debet, ſcilicèt neque medij <lb></lb>fluidi quieſcentis ibi non exiſtentis, inertiam, aut <lb></lb>grauitatem, contiguitatem, aut glutem ſuperare de<lb></lb>bet, ſcilicèt quando nihil ei obſiſtit, nec eius <expan abbr="impetũ">impetum</expan>, <lb></lb>aut progreſſum impedire, & retardare poteſt. <lb></lb><arrow.to.target n="marg592"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002294"><margin.target id="marg591"></margin.target>III.</s> </p> <p type="margin"> <s id="s.002295"><margin.target id="marg592"></margin.target>IV.</s> </p> <p type="main"> <s id="s.002296">E contrà figura obtuſa, & ampla eiuſdem corpo<lb></lb>ris grauis nihil nocet, nec planè retardare poteſt mo<lb></lb>tum eiuſdem corporis grauis in vacuo, quia nimirum <lb></lb>nihil ei reſiſtit, neque enim <expan abbr="inertiã">inertiam</expan> medij fluidi quie<lb></lb>ſcentis ibi non exiſtentis ſuperare debet, id è ſuo lo<lb></lb>co expellendo, neque eius grauitatem, <expan abbr="contiguitatẽ">contiguitatem</expan>, <lb></lb>aut gluten ſua vi motiua vincere debet. </s> </p> <p type="main"> <s id="s.002297"><arrow.to.target n="marg593"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002298"><margin.target id="marg593"></margin.target>V.</s> </p> <p type="main"> <s id="s.002299">Cùm velocitates grauium <expan abbr="cadentiũ">cadentium</expan> non ſint æqua<lb></lb>biles, ſed vniformiter acceleratæ, ideò quando com<lb></lb>parantur inter ſe gradus velocitatum duorum corpo<lb></lb>rum deſcendentium, intelligi ſemper debent gradus <lb></lb>initiales, ſcilicèt illi, qui ab eodem termino quietis <lb></lb>temporibus æqualibus exercentur, & vniformi pro<lb></lb>greſſu creſcunt. </s> </p> <p type="main"> <s id="s.002300">His præmiſſis demonſtrari poſſunt ſequentes pro<lb></lb>poſitiones. </s> </p> <figure id="id.010.01.449.1.jpg" xlink:href="010/01/449/1.jpg"></figure> <pb pagenum="442" xlink:href="010/01/450.jpg"></pb> <p type="main"> <s id="s.002301"><arrow.to.target n="marg594"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002302"><margin.target id="marg594"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002303"><emph type="center"></emph>PROP. CCVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002304"><emph type="center"></emph><emph type="italics"></emph>Corpora homogenea commenſurabilem proportionem haben<lb></lb>tia æquè velocitèr deſcendent ablatis omnibus impe<lb></lb>dimentis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002305">SInt quęlibet duo corpora homogenea A, & B, quę <lb></lb>habeant quamcumque commenſurabilem pro<lb></lb>portionem. </s> <s id="s.002306">Dico, quod ex ſui na<lb></lb><figure id="id.010.01.450.1.jpg" xlink:href="010/01/450/1.jpg"></figure><lb></lb>tura ablatis omnibus <expan abbr="impedimẽ-tis">impedimen<lb></lb>tis</expan>, hæc duo corpora æquali velo<lb></lb>citate deſcendent, nempè eodem <lb></lb>tempore T percurrent duo ſpatia <lb></lb>D, & E inter ſe æqualia. </s> <s id="s.002307">Reperia<lb></lb>tur corpus C homogeneum ipſis <lb></lb>A, & B, quod communis menſura <lb></lb>ſit eorum; hoc verò tempore T deſcendat ſpatium F; & <lb></lb>quia duorum corporum ſimiliarium A multiplex eſt <lb></lb><arrow.to.target n="marg595"></arrow.to.target><lb></lb>ipſius C, ergo æquè velocia erunt, nempè ſpatia D, & <lb></lb>F eodem tempore T exacta æqualia ſunt inter ſe. </s> <s id="s.002308">ea<lb></lb>dem ratione duo ſpatia E, & F tranſacta eodem tem<lb></lb>pore T ab homogeneis corporibus B, & C <expan abbr="multiplicẽ">multiplicem</expan> <lb></lb>proportionem habentibus æqualia erunt inter ſę; <lb></lb>vnde ſequitur quod duo ſpatia D, & E. excurſa <expan abbr="eodẽ">eodem</expan> <lb></lb>tempore T ab homogeneis corporibus A, & B æqua<lb></lb>lia ſint inter ſe, cùm æquentur vni tertio F. </s> <s id="s.002309">Quare pa<lb></lb>tet propoſitum. <lb></lb><figure id="id.010.01.450.2.jpg" xlink:href="010/01/450/2.jpg"></figure><pb pagenum="443" xlink:href="010/01/451.jpg"></pb><arrow.to.target n="marg596"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002310"><margin.target id="marg595"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002311">cap. 5. <lb></lb>axio. 1. eiuſ<lb></lb>que corolla<lb></lb>rio.</s> </p> <p type="margin"> <s id="s.002312"><margin.target id="marg596"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002313"><emph type="center"></emph>PROP. CCVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002314"><emph type="center"></emph><emph type="italics"></emph>Quælibet corpora homogenea inter ſe inæqualia ex ſui natu<lb></lb>ra æquè velocia ſunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002315">SInt duo quælibet corpora homogenea A, & B, <lb></lb>quorum A maius ſit quàm B; dico æquali veloci<lb></lb>tate deſcendere, ablatis <expan abbr="tamẽ">tamen</expan> <lb></lb><figure id="id.010.01.451.1.jpg" xlink:href="010/01/451/1.jpg"></figure><lb></lb>omnibus impedimentis. </s> <s id="s.002316">Si <lb></lb>enim hoc verum non eſt ma<lb></lb>ius corpus A <expan abbr="deſcẽdet">deſcendet</expan> cele<lb></lb>riùs, vel tardiùs, quàm B; & <lb></lb>primò ſi fieri poteſt, maius <lb></lb>corpus A celeriori motu fe<lb></lb>ratur, ſcilicèt eodem tempo<lb></lb>re T, percurrat A maius ſpa<lb></lb>tium C, verùm B pertranſeat <lb></lb>ſpatium minus E; ſumatur aliud corpus G homoge<lb></lb>neum ipſi A, vel B, quod maius ſit ipſo A, ſed com<lb></lb>menſurabilem proportionem habeat ipſi B, ſcilicèt <lb></lb>eius partes ſit. </s> <s id="s.002317">erunt igitur (ex præced. prop.) cor<lb></lb>pora G, & B æquè velocia, ſcilicèt eodem tempore <lb></lb>T corpus G percurret idipſum ſpatium E, quod per<lb></lb>tranſierat corpus B; eſt verò G maius, quàm A, & ei <lb></lb>homogeneum, ergo maius corpus G tardiori motu <lb></lb>deſcendit, quàm corpus minus A, ſcilicèt eodem <expan abbr="tẽ-pore">ten<lb></lb>pore</expan> T corpus maius G pertranſit minus ſpatium E, <lb></lb>atque A percurrit ſpatium maius G, quod eſt contra <lb></lb>hypotheſim, debebat enim maius corpus celeriori <pb pagenum="444" xlink:href="010/01/452.jpg"></pb><arrow.to.target n="marg597"></arrow.to.target><lb></lb>motu ferri, quàm minus igitur falſa eſt poſitio. </s> </p> <p type="margin"> <s id="s.002318"><margin.target id="marg597"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002319">Secundò, ſi fieri poteſt, eodem tempore T percur<lb></lb>rat A minus ſpatium D, quàm F tranſactum à minori <lb></lb>corpore B; & ſumatur <expan abbr="tertiũ">tertium</expan> corpus G <expan abbr="homogeneũ">homogeneum</expan> <lb></lb>ipſis A, & B, ſed maius, quàm A, quod partes ſit ip<lb></lb>ſius B; patet corpora B, G æquè velocia eſſe, igitur <lb></lb><expan abbr="eodẽ">eodem</expan> <expan abbr="tẽpore">tempore</expan> T maius corpus G percurrit maius ſpa<lb></lb>tium F, dùm minus corpus A pertranſit minus ſpa<lb></lb>tium D; quod eſt abſurdum, & contra hypotheſim, <lb></lb>debuerat enim maius corpus minus ſpatium, ſeù tar<lb></lb>diori velocitate excurrere. </s> <s id="s.002320">Quare corpus maius A, <lb></lb>neque celeriùs, neque tardiùs deſcendet, quàm B, <lb></lb>proindeque eadem velocitate feretur; quod erat &c. </s> </p> <p type="main"> <s id="s.002321"><emph type="center"></emph>PROP. CCIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002322"><emph type="center"></emph><emph type="italics"></emph>Duo corpora heterogenea æquè grauia comprehenſa ab æqua<lb></lb>libus perimetris figurarum ſimilium, & æqualium; in eo<lb></lb>dem medio fluido æquè velocitèr deſcendent ſi in ipſo mo<lb></lb>tu ſimilitèr diſpoſit a fuerint; <expan abbr="idẽque">idemque</expan> in vacuo continget.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002323">SInt duo corpora heterogenea A, & B, æquè gra<lb></lb>uia, comprehendanturque ambo ab æqualibus <lb></lb>ſuperficiebus ſphæricis, vt nimirum pila A ſit lignea, <lb></lb>& plena, altera verò B ſit phiala vitrea, cuius pars <lb></lb>extima CD ſolida ſit, <expan abbr="comprehẽſa">comprehenſa</expan> à duabus ſphæricis <lb></lb>figuris, pars verò inteſtina B ſit excauata, & ab aere <lb></lb>repleta, dico, quod hæc duo corpora in eodem me<lb></lb>dio fluido aereo v.g. æquali velocitate deſcendent. </s> </p> <p type="main"> <s id="s.002324">Quoniam, vt dictum eſt cap. 2. huius operis, cor-<pb pagenum="445" xlink:href="010/01/453.jpg"></pb><arrow.to.target n="marg598"></arrow.to.target><lb></lb>pus quod in fluido mouetur libram, vel ſiphonem <expan abbr="cõ-ſtituit">con<lb></lb>ſtituit</expan> cum <expan abbr="ambiẽte">ambiente</expan> fluido, <lb></lb><figure id="id.010.01.453.1.jpg" xlink:href="010/01/453/1.jpg"></figure><lb></lb>cuius moles æqualis ſit ſo<lb></lb>lido demerſo; igitur ſphæ<lb></lb>ra lignea A, & vitrum ca<lb></lb>uum B conſtituunt æquales <lb></lb>libras in <expan abbr="eodẽ">eodem</expan> fluido, prop<lb></lb>terea quod eorum moles æquales ſunt, & ab æquali<lb></lb>bus, & ſimilibus ſphæricis figuris comprehenduntur; <lb></lb>eſt que exceſſus ponderis ligni A ſupra pondus fluidi <lb></lb>ambientis æqualis exceſſui ponderis vitreæ phialæ <lb></lb>B ſupra pondus eiuſdem ambientis fluidi, cuius mo<lb></lb>les ſibi ipſi æqualis eſt, igitur eodem exceſſu pondus <lb></lb>ligni A, atque vitri B ſuperant pondus ambientis flui<lb></lb>di eiuſdem molis, & proindè duo corpora A, & B, <lb></lb>æquè ponderantia in eodem fluido in quo feruntur, <lb></lb>ſunt; ſed virtutes motiuæ quibus corpora A, & B de<lb></lb>orsùm feruntur, nil aliud eſſe cenſentur ab aduerſa<lb></lb>rijs quàm energiæ ponderum eorum. </s> <s id="s.002325">ergo corporą <lb></lb>A, & B in <expan abbr="eodẽ">eodem</expan> fluido habent æquales vires motiuas, <lb></lb>hæ verò ab eodem fluido æquè impediuntur, proptèr <lb></lb>ſimilitudinem, & æqualitatem figurarum, igitur eo<lb></lb>rum effectus, ſcilicèt velocitates quibus deorsùm̨ <lb></lb>feruntur, æquales prorsùs inter ſe erunt. </s> </p> <p type="margin"> <s id="s.002326"><margin.target id="marg598"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002327">In vacuo verò, quoniam duo corpora A, & B <expan abbr="com-prehẽduntur">com<lb></lb>prehenduntur</expan> ab externis ſphæricis figuris ſimilibus, <lb></lb>& æqualibus, & <expan abbr="ſupponũtur">ſupponuntur</expan> æquè grauia, igitur par<lb></lb>tes materiales nempè eorum moles corporeæ æ<lb></lb>quales ſunt inter ſe, & proindè (ex propoſ. </s> <s id="s.002328">15. de vi <pb pagenum="446" xlink:href="010/01/454.jpg"></pb><arrow.to.target n="marg599"></arrow.to.target><lb></lb>Percuſs.) vires motiuæ tam ligni A, quàm vitri exca<lb></lb>uati B æquales erunt inter ſe, quia verò à vacuo, ſeù <lb></lb>à nihilo prædictæ æquales virtutes motiuæ non impe<lb></lb>diuntur, igitur effectus ab eis dependentes nempè <lb></lb>velocitates eorum æquales erunt inter ſe. </s> </p> <p type="margin"> <s id="s.002329"><margin.target id="marg599"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002330"><emph type="center"></emph>PROP. CCX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002331"><emph type="center"></emph><emph type="italics"></emph>Idem corpus graue, quam cumque figuram habuerit, <expan abbr="deſcẽ-det">deſcen<lb></lb>det</expan> in ſpatio vacuo eadem prorsùs velocitate.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002332">SVmatur idem corpus graue, ſcilicèt maſſa ferreą <lb></lb>vnius libræ v. g. habeat que primò figuram py<lb></lb>ramidalem, vel conicam cuius vertex in A dum mo<lb></lb>uetur baſim præcedat, in B verò eius baſis antefera<lb></lb>tur; poſteà cylindricæ prolixæ longitudinis, & exi<lb></lb>guæ baſis vt eſt C, vel baſis dilatatæ vt eſt D effor<lb></lb>metur: tandem eadem maſſa ferrea tornata <expan abbr="ſphærulã">ſphærulam</expan>, <lb></lb>E efficiat, vel amplam ſphæram excauatam, aut <expan abbr="ar-millarẽ">ar<lb></lb>millarem</expan> F. </s> <s id="s.002333">Oſtendendum eſt idem graue A, B, C, &c. <lb></lb></s> <s id="s.002334">in vacuo ſemper eadem velocitate deſcendere, ſcili<lb></lb>cèt æqualibus temporibus æqualia ſpatia <expan abbr="pertrãſire">pertranſire</expan>. <lb></lb></s> <s id="s.002335">Quoniam virtus premens grauitatis cauſa eſt eius <lb></lb>motus deorsùm, porrò motus concipi non poteſt, <lb></lb>quin aliqua velocitate fiat, ſcilicèt tempore deter<lb></lb>minato ſpatium certum percurrat, vbi verò vna, & <lb></lb>eadem cauſa perſeuerat non variata, nec immutata, <lb></lb>neceſsè eſt vt <expan abbr="idẽ">idem</expan> effectus, deſcenſus nimirùm, nil <lb></lb>prorsùs variatus alteratuſque ſubſequatur, vt <expan abbr="nimirũ">nimirum</expan> <lb></lb><expan abbr="cũ">cum</expan> certa, & determinata velocitate fiat, igitur idem <pb pagenum="447" xlink:href="010/01/455.jpg"></pb><arrow.to.target n="marg600"></arrow.to.target><lb></lb>graue A, B, C, &c. </s> <s id="s.002336">vni<lb></lb><figure id="id.010.01.455.1.jpg" xlink:href="010/01/455/1.jpg"></figure><lb></lb>co, & determinato gra<lb></lb>du velocitatis moueri <lb></lb>debet, quem ſcilicèt de<lb></lb>terminato eius <expan abbr="põderi">ponderi</expan>, <lb></lb>ac conſiſtentiæ naturą <lb></lb>aſſignauit; nec figuræ <lb></lb>varietas A, B, C &c. </s> <s id="s.002337">au<lb></lb>get, aut diminuit eius <lb></lb>molem <expan abbr="quãtitatemque">quantitatemque</expan> <lb></lb>corpoream, & proindè pondus eius non variat, nec <lb></lb>alterat, igitur prædictæ diuerſæ figuræ ex ſui natu<lb></lb>ra non augent, nec minuunt effectum eiuſdem pre<lb></lb>mentis virtutis, qui quidem effectus eſt vna, & deter<lb></lb>minata velocitas. </s> <s id="s.002338">Videamus modò an figuræ varie<lb></lb>tas licèt grauitatem non variet poſſit aliquo pacto <lb></lb><expan abbr="impetũ">impetum</expan>, & celeritatem eius alterare; & profectò hoc <lb></lb>videtur impoſſibile, quia figuræ acuminatæ A, C, E <lb></lb>in vacuo nil iuuant, nec earum motum facilem, ce<lb></lb>lerioremque reddunt, quando quidem ibi nihil pene<lb></lb>trari, aut remoueri è ſuo loco debet: pariterque fi<lb></lb>guræ amplæ, ac dilatatæ B, D, & F nullum impedi<lb></lb>mentum, ac remoram motu; earum in vacuo afferunt, <lb></lb>quia nimirùm ibidem nil prorsùs obſiſtit, igitur quæ<lb></lb>libet figura, ſiuè acuminata, ſiue dilatata æquè com<lb></lb>moda erit in vacuo, nec poterit alterare <expan abbr="velocitatẽ">velocitatem</expan>, <lb></lb>quæ eidem corpori graui naturaliter competit. </s> <s id="s.002339">Qua<lb></lb>proptèr idem graue quomodolibet figuratum <expan abbr="eadẽ">eadem</expan> <lb></lb>velocitate in vacuo deſcendet, quod fuerat. </s> <s id="s.002340">Alitèr <pb pagenum="448" xlink:href="010/01/456.jpg"></pb><arrow.to.target n="marg601"></arrow.to.target><lb></lb>idem oſtendetur. </s> <s id="s.002341">Quoniam corpora homogenea, & <lb></lb>æqualia, ſed diuerſimodè figurata continent parti<lb></lb>culas homogeneas inter ſe æquales, & æquè veloces <lb></lb>ex ſui natura, ergo ſi ob figuras diuerſas inæqualibus <lb></lb>velocitatibus deſcendunt integra corpora æqualią <lb></lb>inter ſe, hoc ab aliquo impedimento procùl dubio <lb></lb>dependet, ſcilicèt ab externo corpore fluido in quo <lb></lb>moueatur, vel ipſæmet particulæ figuras varias <expan abbr="cõ-ponentes">con<lb></lb>ponentes</expan> mutuò ſe impediunt in eorum deſcenſu, ſed <lb></lb>neutro modo tranſitus impediri poſſunt, nam in va<lb></lb>cuo non adeſt fluidum impediens, & particulæ vni<lb></lb>uerſam maſſam componentes, cùm æquè veloces ex <lb></lb>ſui natura ſint, non poſſunt ſeſe mutuò retardare, ne<lb></lb>que accelerare, & proinde aggregata ipſa vnà, & <expan abbr="ca-dẽ">ca<lb></lb>dem</expan> velocitate deorsùm ferentur in vacuo, quòd fue<lb></lb>rat <expan abbr="oftẽdendum">oſtendendum</expan>. </s> <s id="s.002342">Tranſeo modò ad <expan abbr="aliã">aliam</expan> <expan abbr="propoſitionẽ">propoſitionem</expan>. </s> </p> <p type="margin"> <s id="s.002343"><margin.target id="marg600"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002344"><margin.target id="marg601"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002345"><emph type="center"></emph>PROP. CCXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002346"><emph type="center"></emph><emph type="italics"></emph>Si duo corpora æquè grauia abſolutè moles inæquales habue<lb></lb>rint, in vacuo æquè velocitèr deſcendent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002347">SInt duo corpora A, & B æquè grauia abſolutè, & <lb></lb>moles ipſius B maior ſit mole alterius A, ſcili<lb></lb>cèt ſit maſſa plumbea A vnius libræ, B verò ſit lignea <lb></lb>eiuſdem <expan abbr="põderis">ponderis</expan>, & proindè moles B maior erit, <expan abbr="quã">quam</expan> <lb></lb>A; dico, quod huiuſmodi corpora A, & B in vacuo ea<lb></lb>dem velocitate deſcendent. </s> <s id="s.002348">Sumatur moles corpo<lb></lb>rea E, quæ æquè grauis, & homogenea ſit ipſi A, ſcili<lb></lb>cèt ſit quoque plumbea, & ex ea fiat figura vnifor-<pb pagenum="449" xlink:href="010/01/457.jpg"></pb><arrow.to.target n="marg602"></arrow.to.target><lb></lb>miter excauata, itaut externa eius ſuperficies ſit om<lb></lb>ninò ſimilis, & æqualis figuræ externæ ipſius B; quo<lb></lb>niam ſubſtantia corporea ple<lb></lb><figure id="id.010.01.457.1.jpg" xlink:href="010/01/457/1.jpg"></figure><lb></lb>na ipſius E nedùm homogenea, <lb></lb>ſed prorsùs æqualis eſt ipſi A, <lb></lb>ſcilicèt vniùs libræ, erunt duo <lb></lb>corpora A, & E æqualia inter <lb></lb>ſe, & æquè grauia, licèt diuer<lb></lb>ſas, & inæquales figuras habe<lb></lb><arrow.to.target n="marg603"></arrow.to.target><lb></lb>ant, igitur A, & E in vacuo æ<lb></lb>quali velocitate deſcendent. <lb></lb></s> <s id="s.002349">poſtea quia duorum corporum B, & E pondera abſo<lb></lb>luta æquantur ponderi eiuſdem A, igitur illa æqua<lb></lb>lia <expan abbr="sũt">sunt</expan> inter ſe grauitate abſoluta, & à ſimilibus, ęqua<lb></lb>libus, & ſimiliter poſitis figuris <expan abbr="comprehẽduntur">comprehenduntur</expan>, er<lb></lb><arrow.to.target n="marg604"></arrow.to.target><lb></lb>go æqualibus velocitatibus, cum in pleno fluido, tum <lb></lb>in vacuo deſcendent. </s> <s id="s.002350">quare A, & B æquè velocia ipſi <lb></lb>E erunt, & ideò interſe. </s> </p> <p type="margin"> <s id="s.002351"><margin.target id="marg602"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002352"><margin.target id="marg603"></margin.target>Pr. 210.<margin.target id="marg604"></margin.target>Pr. 209.</s> </p> <p type="main"> <s id="s.002353"><emph type="center"></emph>PROP. CCXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002354"><emph type="center"></emph><emph type="italics"></emph>Quælibet duo corpora inæqualitèr grauia in vacuo æquè <lb></lb>velocitèr deſcendent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002355">SInt duo corpora A, & B quorum A grauius ſit, <expan abbr="quã">quam</expan> <lb></lb>B; moles verò ipſius A ponatur, vel maior, aut <lb></lb>æqualis, vel minor mole alterius B, ſcilicèt ſint præ<lb></lb>dicta corpora eiuſdem grauitatis ſpecificæ, vel non, <lb></lb>dummodò eorum pondera abſoluta inæqualia ſint. <lb></lb></s> <s id="s.002356">Dico in vacuo æquè velocia eſſe. </s> <s id="s.002357">Si hoc verum noņ <pb pagenum="450" xlink:href="010/01/458.jpg"></pb><arrow.to.target n="marg605"></arrow.to.target><lb></lb>eſt, deſcendet grauius corpus A celeriùs, vel tardiùs, <lb></lb><expan abbr="quã">quam</expan> B; & primò ſi fieri poteſt moueatur grauius cor<lb></lb>pus A in vacuo maiori celerita<lb></lb><figure id="id.010.01.458.1.jpg" xlink:href="010/01/458/1.jpg"></figure><lb></lb>te, quàm B, ſcilicèt eodem tem<lb></lb>pore G pertranſeat graue A ma<lb></lb>ius ſpatium CD corpus verò B, <lb></lb>minùs ponderans, percurrat ſpa<lb></lb>tium CE minùs, quàm CD, con<lb></lb>cipiantur poſtea duo corpora A, <lb></lb>& B ſimul colligata, aut coniun<lb></lb>cta, vt nimirum vnum ſine altero <lb></lb>moueri nequeat, & ſic connexą <lb></lb>percurrant <expan abbr="eodẽ">eodem</expan> tempore G ſpa<lb></lb>tium CF. quoniam tùm corpus A cùm B habent gra<lb></lb>dus certos, ac determinatos velocitatum ſibi à natu<lb></lb>ra aſſignatos, qui per ſe omninò inuariabiles ſunt, niſi <lb></lb>ab aliqua externa cauſa ſuperueniente alterentur, & <lb></lb>ex hypotheſi gradus naturalis velocitatis ipſius A <lb></lb><arrow.to.target n="marg606"></arrow.to.target><lb></lb>maior eſt ea, quæ competit ipſi B; igitur validior, & <lb></lb>vehementior gradus velocitatis ipſius A promouebit <lb></lb>vrgebitque tardigradum mobile B, quod proindè co<lb></lb>gatur celeriùs excurrere, quàm per ſe, & abſque illa <lb></lb>violentia latum fuiſſet. </s> <s id="s.002358">E contra corpus tardius B re<lb></lb>moram afferet velociori corpori A, quod proindè tar<lb></lb>diùs in prædicto tempore mouebitur; quaproptèr <lb></lb>duo grauia A, & B ſimul connexa, ſcilicèt amborum <lb></lb>aggregatum percurret deſcendendo eodem tempore <lb></lb>G ſpatium CF, minus quidem, quàm CD, ſed maius, <lb></lb>quàm CE, eſtque aggregatum ex A, & B grauius, <expan abbr="quã">quam</expan> <pb pagenum="451" xlink:href="010/01/459.jpg"></pb><arrow.to.target n="marg607"></arrow.to.target><lb></lb>corpus A ſolitarium, igitur grauius corpus <expan abbr="nẽ">nem</expan> pè ag<lb></lb>gregatum ex A, & B percurret eodem <expan abbr="tẽpore">tempore</expan> G ſpa<lb></lb>tium CF minus quidem, quàm CD tranſactum à ſoli<lb></lb>tario corpore A minùs graui, quod repugnat hypo<lb></lb>theſi; grauius enim in vacuo deſcendere debuerat <lb></lb>velociori motu, quàm minùs graue. </s> <s id="s.002359">Non ergo fieri <lb></lb>poteſt vt corpus grauius in vacuo celeriùs, quàm mi<lb></lb>nùs graue feratur. </s> </p> <p type="margin"> <s id="s.002360"><margin.target id="marg605"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002361"><margin.target id="marg606"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002362">cap. 5. <lb></lb>axio. </s> <s id="s.002363">3<gap></gap></s> </p> <p type="margin"> <s id="s.002364"><margin.target id="marg607"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="main"> <s id="s.002365">Secundo loco ſit grauius corpus A, ſi fieri poteſt, <lb></lb>minùs velox, quàm B, ſcilicèt A percurrat minus ſpa<lb></lb>tium CE, ſed B maius ſpatium CD eodem <expan abbr="tẽpore">tempore</expan> G; <lb></lb>& ſi cutiant ea dictum eſt, duo corpora A, & B ſimùl <lb></lb><arrow.to.target n="marg608"></arrow.to.target><lb></lb>connexa velociora erunt pigriore corpore A, & ideò <lb></lb>corpus grauius, ſcilicèt aggregatum ex A, & B velo<lb></lb>ciùs <expan abbr="deſcẽdet">deſcendet</expan>, quàm minùs graue A, quod rursùs hy<lb></lb>pothe ſi repugnat, non igitur eſt poſſibile vt corpus <lb></lb>magis ponderoſum in vacuo citiùs, aut tardiùs <expan abbr="deſcẽ-dat">deſcen<lb></lb>dat</expan>, quàm minus graue; quare neceſsè eſt, vt ambo <lb></lb>æquali velocitate in vacuo ferantur, quod fuerat de<lb></lb>monſtrandum. </s> </p> <p type="margin"> <s id="s.002366"><margin.target id="marg608"></margin.target>Ibidem.</s> </p> <p type="main"> <s id="s.002367"><emph type="center"></emph>PROP. CCXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002368"><emph type="center"></emph><emph type="italics"></emph>Idipſum aliter demonſtrabitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002369">SIt corpus BC grauius, quàm A; dico in vacuo ea<lb></lb>dem velocitate ambo deſcenſura. </s> <s id="s.002370">Reſecetur ex <lb></lb>ponderoſiori BC portio aliqua B æquè ponderans, ac <lb></lb><arrow.to.target n="marg609"></arrow.to.target><lb></lb>A, igitur licèt æquiponderantia corpora B, & A inæ<lb></lb>quales moles habebant ęquè velocia erunt in vacuo; <pb pagenum="452" xlink:href="010/01/460.jpg"></pb><arrow.to.target n="marg610"></arrow.to.target><lb></lb>præterea quia vniuerſum corpus BC, eiuſque portio <lb></lb>B ſunt ſimilia, & eiuſdem grauitatis ſpecificæ, & ſo<lb></lb>lummodò moles inæquales <expan abbr="habẽt">habent</expan>, <lb></lb><figure id="id.010.01.460.1.jpg" xlink:href="010/01/460/1.jpg"></figure><lb></lb>ſcilicèt eorum abſoluta pondera in<lb></lb>æqualia ſunt, igitur ablatis om<lb></lb>nibus impedimentis, ſcilicèt iņ <lb></lb><arrow.to.target n="marg611"></arrow.to.target><lb></lb>vacuo, eadem velocitate deſcen<lb></lb>det integrum corpus BC atque eius <lb></lb>portio B: oſtenſa autem priùs fuere <lb></lb>duo corpora A, & B in vacuo æquè velocia, igitur cor<lb></lb>pus BC, atque A, erunt quoque in vacuo æquè velo<lb></lb>cia, quod erat demonſtrandum. </s> </p> <p type="margin"> <s id="s.002371"><margin.target id="marg609"></margin.target>Pro. 211.</s> </p> <p type="margin"> <s id="s.002372"><margin.target id="marg610"></margin.target>Cap. 10. de <lb></lb>æquitempo<lb></lb>ranea natu<lb></lb>rali veloci<lb></lb>tate <expan abbr="grauiũ">grauium</expan>.</s> </p> <p type="margin"> <s id="s.002373"><margin.target id="marg611"></margin.target>Pro. 209. & <lb></lb>210.</s> </p> <p type="main"> <s id="s.002374">Ex hiſce propoſitionibus deducitur, quod omnią <lb></lb>corpora grauia, quomodocumque inter ſe differant <lb></lb>pondere, magnitudine, & figura, apta nata ſunt ex <lb></lb>ſui natura deorsùm <expan abbr="deſcẽdere">deſcendere</expan> pari velocitate, & hoc <lb></lb>procùl dnbio contingeret, quando nil prorsùs à me<lb></lb>dio fluido impedirentur, quod ſolummodò verifica<lb></lb>ri poſſetin ſpatio prorsùs inani, vbi ſi feſtuca, vel <lb></lb>pluma, & ingens maſſa ferrea ab eodem termino de<lb></lb>ſcenſum inchoarent, ſemper pari paſſu, & æquabili <lb></lb>motu excurrerent, neque aliquando ferrum <expan abbr="feſtucã">feſtucam</expan> <lb></lb>anticiparet. </s> <s id="s.002375">Propoſitio profectò admirabilis, quæ <lb></lb>paradoxum cenſeri potuerat cùm primùm à Galileo <lb></lb>coniecturalibus <expan abbr="tãtummodò">tantummodò</expan> rationibus prolata fuit, <lb></lb>quæ modò cum euidentia geometrica demonſtratą <lb></lb>fuerit, nullam anſam dubitandi relinquit. <pb pagenum="453" xlink:href="010/01/461.jpg"></pb><arrow.to.target n="marg612"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002376"><margin.target id="marg612"></margin.target>Cap. 11. gra<lb></lb>uia iu fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002377"><emph type="center"></emph><emph type="italics"></emph>Qua ratione motus grauium à medijs fluidis plenis inæqua<lb></lb>litèr veloces reddantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002378"><emph type="center"></emph>CAP. XI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002379">POſtquam oſtenſum eſt corpora omnia grauia ex <lb></lb>ſui natura æquè velocia eſſe, reſtat modò vt in<lb></lb>quiramus quomodò, & quare grauia, quæ in medijs <lb></lb>fluidis mouentur, habent velocitates inæquales; <expan abbr="hãc">hanc</expan> <lb></lb>phyſices, & mechanices partem hactenus <expan abbr="deſideratã">deſideratam</expan> <lb></lb>pro viribus ſupplere tentabimus. </s> </p> <p type="main"> <s id="s.002380"><emph type="center"></emph>PROP. CCXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002381"><emph type="center"></emph><emph type="italics"></emph>Fluida homogenoa è fistulis æquè latis, & perpendiculari<lb></lb>tèr erectis ad horizontem fluunt velocitatibus in ſubdu<lb></lb>plicata proportione longitudinum fiſtularum, ſi tamen <lb></lb>ſemper fiſtulæ repletæ ſint eodem fluido.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002382">ET priùs neceſsè eſt obſeruare, atque examina<lb></lb>re qua ratione, & quibus velocitatibus fluidą <lb></lb>in fiſtulis, ſeù ſiphonibus moueantur. </s> <s id="s.002383">Si enim ſuman<lb></lb>tur duæ fiſtulæ, quarum cauitates, & orificia æqua<lb></lb>lia ſint, & in ambabus continenter repletis fluidum̨ <lb></lb>idem exeat aqua v.g. dum fiſtulæ erectæ ad planum̨ <lb></lb>horizontale ſunt in quo orificia exiſtunt; tunc ex v<lb></lb>troque orificio defluunt aquæ moles, temporibus æ<lb></lb>qualibus, <expan abbr="nõ">non</expan> in <expan abbr="eadẽ">eadem</expan> proportione, quam habent alti<lb></lb>tudines, vt experientia docet, ſed in ſubduplicatą, <lb></lb>nempè ſi altitudo longioris fiſtulæ quadrupla fuerit <pb pagenum="454" xlink:href="010/01/462.jpg"></pb><arrow.to.target n="marg613"></arrow.to.target><lb></lb>altitudinis alterius tunc velocitas, qua aqua defluit <lb></lb>ab orificio longioris non eſt quadrupla, ſed duplą <lb></lb>tantummodò eius velocitatis, qua aqua egreditur ex <lb></lb>infimo breuioris fiſtulæ orificio. </s> <s id="s.002384">Hinc deducitur <lb></lb>quod prædicta fluida in fiſtulis erectis inæqualium̨ <lb></lb>longitudinum, <expan abbr="eãdem">eandem</expan> prorsùs naturam habent, <expan abbr="quã">quam</expan> <lb></lb>fune <expan abbr="pẽdula">pendula</expan>, quorum proprietates alibi expoſuimus. </s> </p> <p type="margin"> <s id="s.002385"><margin.target id="marg613"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002386"><emph type="center"></emph>PROP. CCXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002387"><emph type="center"></emph><emph type="italics"></emph>Fluxus æquæ intra fistulam velocior eſt circa axim, quam <lb></lb>propè internam cauam ſuperficiem eius.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002388">SEd antequam vlteriùs procedamus, animaduer<lb></lb>tendum eſt, quod aqua velociùs fluit deorsùm̨ <lb></lb>in medio cauitatis fiſtulæ, ſeù circa eius axim, quàm <lb></lb>versùs ſuperficiem eius cauam; propterea quod, vt <lb></lb>ſupra dictum eſt, gluten ipſius aquæ, quæ ſuperficiei <lb></lb>aſperæ internæ fiſtulæ adhæret magis retardat de<lb></lb>fcenſum, & fluxum aquæ, quàm in intermedia parte <lb></lb>cauitatis fiſtulæ, vbi inſenſibili tenacitate aquæ par<lb></lb>ticulæ viciſſim impediuntur, & hoc euincitur duplici <lb></lb>experimento; primò quia in ſupremo ſtrictæ fiſtulæ <lb></lb>orificio excauatur eius ſuperficies ad modum ſcutel<lb></lb>læ, è contra in egreſſu fluidi ſuperficies aquæ ad mo<lb></lb>dum conoidis, ſeu monticuli turgidi deorsùm ex<lb></lb>porrigitur, quod minimè fieri poſſet, niſi partes a<lb></lb>quæ intermediæ faciliùs fluerent, quàm partes col<lb></lb>laterales internæ ſuperficiei fiſtulæ proximę, & adhę<lb></lb>rentes, quæ vt diximus, à ſtabilibus aſperitatibus fi-<pb pagenum="455" xlink:href="010/01/463.jpg"></pb><arrow.to.target n="marg614"></arrow.to.target><lb></lb>ſtulæ retinentur aliquo pacto, & ſuſpenduntur, ideo<lb></lb>que impeditur fluxus earum. </s> </p> <p type="margin"> <s id="s.002389"><margin.target id="marg614"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002390"><emph type="center"></emph>PROP. CCXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002391"><emph type="center"></emph><emph type="italics"></emph>Quare æqua post egreſſum è fistula in aere ſubiecto non disſi<lb></lb>petur, ſed ſenſim reſtringitur quouſque diſrumpatur ra<lb></lb>tionem reddere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002392">POſtquam fluidum ab infimo orificio fiſtulæ in ae<lb></lb>re liberè effluere incipit, concipi debet, quod <lb></lb>quælibet ſuperficies, ſeu laminula prædicti fluidi <lb></lb>perducitur ad aerem liberum eo gradu velocitatis, <lb></lb>qui dependet à longitudine prædictæ fiſtulæ, ſeù <expan abbr="pẽ-duli">pen<lb></lb>duli</expan>, idemque <expan abbr="dicẽdum">dicendum</expan> eſt de reliquis omnibus ſub<lb></lb>ſequentibus aquæ laminulis, cum ad aeris confinium <lb></lb>perducuntur; deberet ergo integra laminula aquæ <lb></lb>egreſſa diuelli <expan abbr="ſeparariq;">ſepararique</expan> à ſuperficie alterius aquæ <lb></lb>laminulæ, quæ eam ſubſequitur, & ſecundo loco è fi<lb></lb>ſtula egreditur in aere libero; ratio eſt quia prima la<lb></lb>minula dum excurrit pertranſitque in aere ſpatium̨ <lb></lb>æquale craſſitiei eius in dato aliquo tempore, neceſ<lb></lb>ſariò gradum aliquem velocitatis maiorem acquiret, <lb></lb>correſpondentem motui, & tempori prædicto; ſed <lb></lb>in ſimili conſtitutione ſecunda aquæ laminula in e<lb></lb>greſſu è fiſtula caret illo gradu velocitatis, quem ac<lb></lb>quiſiuit prima laminula, igitur in ſecundo tempore <lb></lb>illi æquale prior laminula percurret ſpatium triplum <lb></lb>eius, quod priùs pertranſierat, & eius quod ſecunda <lb></lb>laminula excurrere debet, quia nimirùm in ſecundo <pb pagenum="456" xlink:href="010/01/464.jpg"></pb><arrow.to.target n="marg615"></arrow.to.target><lb></lb>illo tempore mouetur duplo <expan abbr="vehemẽtiori">vehementiori</expan> gradu ve<lb></lb>locitatis, quàm ſubſequens laminula deſcendit; ſed <lb></lb>ab initio prædictæ duæ laminulæ contiguæ inter ſę <lb></lb>erant, igitur in ſecundo tempore diuelli, ac ſeparari <lb></lb>ab inuicem deberent; quod cum non contingat, pro<lb></lb>cùl dubio ad erit aliqua cauſa, à qua colligatæ reti<lb></lb>nentur; & hæc profectò erit gluten, & viſcoſitas illa <lb></lb>exigua ſuperiùs declarata, qua partes eiuſdem fluidi <lb></lb>adinuicem adhærent, & vinciuntur. </s> <s id="s.002393">Cum verò præ<lb></lb>dictæ partes aquæ effluxæ à fiſtula inæqualibus velo<lb></lb>citatibus moueantur, & nihilominùs non poſſint ab <lb></lb>inuicem diuelli, ſepararique, ſequitur illa attenua<lb></lb>tio, & gracilitas, quæ in aqua poſt egreſſum fiſtulæ <lb></lb>obſeruatur, & propterea prædicta aqua magis, & <lb></lb>magis acuminatur, gracileſcitque. </s> <s id="s.002394">Sed hìc iam reddi <lb></lb>debet ratio, quare in progreſſu prædicta aqua fluens, <lb></lb>poſtquam ad aliquam exiguam gracilitatem redacta <lb></lb>eſt, poſtea diſrumpitur in plures partes, & guttulas; <lb></lb>& hic <expan abbr="dicendũ">dicendum</expan> eſt, quod vis, & energia prædicti glu<lb></lb>tinis cum fit exigua non poteſt tandem reſiſtere ve<lb></lb>hementiæ velocitatis continuò auctæ in ipſo aquæ <lb></lb>deſcenſu, & hæc proindè poterit diſrumpere vnio<lb></lb>nem illam aquæ, qua priùs ferebatur, eo in loco v<lb></lb>bi glutem ab aliqua cauſa externa debilitatum fue<lb></lb>rit, aut curſus velocitas variatur, retardaturque ab <lb></lb>externo impedimento. </s> </p> <p type="margin"> <s id="s.002395"><margin.target id="marg615"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002396">Quia verò ad rem noſtram nil confert motus aquę <lb></lb>fluentis in aere extra fiſtulam, propterea relicta hac <lb></lb>digreſſione, reliqua ſymptomata aquæ fluentis in fi<lb></lb>ſtulis declarari debent. <pb pagenum="457" xlink:href="010/01/465.jpg"></pb><arrow.to.target n="marg616"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002397"><margin.target id="marg616"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002398"><emph type="center"></emph>PROP. CCXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002399"><emph type="center"></emph><emph type="italics"></emph>E fiſtulis inæqualitèr amplis, & æquè altis quarum infima <lb></lb>ostiola <expan abbr="horizõt">horizont</expan> alia æqualia ſint, æquè velocitèr aquæ mo<lb></lb>les æquales effluunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002400">ET primò animaduertendum eſt, quòd in prædi<lb></lb>ctis fiſtulis orificia infima <expan abbr="perpẽdicularia">perpendicularia</expan> ad di<lb></lb>rectionem fluxus liquoris è fiſtula egredientis <expan abbr="tantũ-modò">tantunm<lb></lb>modò</expan> conſideranda veniunt, & nil refert an internæ <lb></lb>cauitates ampliores ſint orificijs ipſis (non enim hìc <lb></lb>agimus de fiſtulis infernè dilatatis ad inſtar coni); <lb></lb>quandoquidem ratio haberi debet illius portionis a<lb></lb>quæ, quæ deorsùm fluit, non verò illius, quæ in quiete <lb></lb>conſiſtit, vt v.g. ſi fuerit fiſtula aliqua vitrea ad hori<lb></lb>zontem perpendicularis, & puteus æquè altus, iņ <lb></lb>cuius fundo aperiatur foramen prorsùs æquale infi<lb></lb>mo fiſtulæ foramini, tunc aqua ab orificio putei pro<lb></lb>fluit eadem ferè velocitate, & æquali mole, ac ex il<lb></lb>la fiſtula vitrea æquè plena egreditur, proptereą <lb></lb>quòd in aqua putei concipi debet fiſtula perpendi<lb></lb>culariter horizonti erecta ab infimo foramine vſque <lb></lb>ad ſummitatem aquæ, & ſolummodò prædicta aqua <lb></lb>in fiſtula imaginaria contenta fluit, reliqua verò col<lb></lb>lateralis innititur ſuftentaturque à fundo impenetra<lb></lb>bili, & firmo ipſius putei, à quo aquæ fluxus <expan abbr="perpẽ-dicularis">perpen<lb></lb>dicularis</expan> impeditur, & ideò perindè aqua excurrit <lb></lb>perpendicularitèr, ac ſi in fiſtula vitrea contineretur. <lb></lb></s> <s id="s.002401">Verum tamen eſt, quòd ſuperficies dura interna fi<lb></lb>ſtulæ vitreæ magis ſuis aſperitatibus impedit efflu<lb></lb>uium aquæ, quàm parietes aquei in imaginaria ílla <pb pagenum="458" xlink:href="010/01/466.jpg"></pb><arrow.to.target n="marg617"></arrow.to.target><lb></lb>fiſtula putei, & hæc eſt ratio quare in anguſtiſſimis fi<lb></lb>ſtulis, & canalibus tenuiſſimis aqua nedùm tardè de<lb></lb>fluit, ſed aliquando omninò eius motus, & caſus im<lb></lb>peditur, vt ſuperiùs declarauimus. </s> </p> <p type="margin"> <s id="s.002402"><margin.target id="marg617"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002403"><emph type="center"></emph>PROP. CCXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002404"><emph type="center"></emph><emph type="italics"></emph>In eiſdem fiſtulis inæqualitèr ad horizontem inclinatis velo<lb></lb>citates aquæ fluentis ſubduplicatam proportionem <expan abbr="habẽt">habent</expan>, <lb></lb>non longitudinum, ſed ſublimitatum perpendicularium <lb></lb>carum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002405">POſtea ſi eædem duæ fiſtulæ inæqualitèr ad hori<lb></lb>zontem fuerint inclinatæ, fluxus eiuſdem fluidi <lb></lb>in eis fient velocitatibus ſubduplicatè proportiona<lb></lb>libus, non quidem longitudinibus earum, ſed vertica<lb></lb>libus altitudinibus; propterea quod demonſtrarunt <lb></lb><arrow.to.target n="marg618"></arrow.to.target><lb></lb>Galileus, & Torricellius, quòd ſi idem mobile fera<lb></lb>tur per planum inclinatum, & verticale, itaut ambo <lb></lb>eamdem eleuationem habeant, ſi tamen <expan abbr="initiũ">initium</expan> vtriuſ<lb></lb>que motus à quiete fiat, in fine vtriuſque deſcenſus, <lb></lb>acquiret mobile eumdem gradum velocitatis. </s> <s id="s.002406">Hinc <lb></lb>conſtat, quòd in duabus fiſtulis inæqualitèr ad hori<lb></lb>zontem inclinatis velocitates quibus idem fluidum̨ <lb></lb>ab infimis orificijs egreditur, correſpondere quidem <lb></lb>debeant non longitudinibus fiſtularum, ſed earum̨ <lb></lb>eleuationibus. </s> </p> <p type="margin"> <s id="s.002407"><margin.target id="marg618"></margin.target>Galil. de mo<lb></lb>tu grauium <lb></lb>deſcend. </s> <s id="s.002408">lib. <lb></lb>2. ſcol. </s> <s id="s.002409">pr. 2 <lb></lb>& Tor. lib. 1. <lb></lb>prop. 5.</s> </p> <p type="main"> <s id="s.002410"><emph type="center"></emph>PROP. CCXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002411"><emph type="center"></emph><emph type="italics"></emph>Velocitates quibus aqua egreditur ab infimis fiſtularum ori<lb></lb>ficijs illæ eædem ſunt, quibus eadem aqua intra cauitates <lb></lb>canalium mouetur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002412">OVia ſemper æqualibus temporibus æquales a-<pb pagenum="459" xlink:href="010/01/467.jpg"></pb><arrow.to.target n="marg619"></arrow.to.target><lb></lb>quæ moles ab infimo eiuſdem fiſtulæ orificio egredi<lb></lb>untur, & propterea vna, & eadem velocitate deter<lb></lb>minata ab eius ſumma altitudine aqua fluit, (ſi tamen <lb></lb>ſemper fiſtula repleta ſupponatur); ergo æqualibus <lb></lb>temporibus tanta aquæ moles ſupernè infunditur, <lb></lb>quanta inferiùs ab eadem fiſtula egreditur, quare in <lb></lb>progreſſu motus intra fiſtulam <expan abbr="eadẽ">eadem</expan> velocitate à qua <lb></lb>excurrit, qua infernè egreditur, cùmque hæc veloci<lb></lb>tas ab altitudine caſus, ſeu longitudine penduli, vel <lb></lb>fiſtulæ determinetur, igitur velocitas aquæ intra ca<lb></lb>nalem fiſtulæ ſemper eumdem gradum habet, æqua<lb></lb>lem ſcilicèt ei, qui fiſtulæ longitudini competit. </s> <s id="s.002413">po<lb></lb>ſtea, vt ſubſequentes propoſitiones demonſtrari com<lb></lb>modiùs poſſint; Primò ſupponendum eſt vt euidens, <lb></lb><arrow.to.target n="marg620"></arrow.to.target><lb></lb>quòd ab eodem fiſtulæ orificio, <expan abbr="perpẽdicularitèr">perpendicularitèr</expan> ta<lb></lb>men erecto ad directionem aquæ fluentis, duæ moles <lb></lb>æquales aquæ æqualibus temporibus egreſſæ neceſ<lb></lb>ſariò æqualibus velocitatibus egredi debent; & è <expan abbr="cõ-uerſo">con<lb></lb>uerſo</expan> ſi velocitates æquales fuerint, paritèr moles a<lb></lb>quæ æqualibus temporibus effluxæ erunt quoque in<lb></lb>ter ſe æquales. </s> <s id="s.002414">Vnde colligitur, quòd velocitatę <lb></lb>dupla eodem tempore paritèr dupla moles aquæ ab <lb></lb>æquali foramine egreditur, idemque dicendum eſt <lb></lb>de qualibet æquè multiplici proportione: paritèrque <lb></lb>ſi velocitas partes fuerit alterius velocitatis, paritèr <lb></lb>moles aquæ ab æqualibus foraminibus eodem tem<lb></lb>pore egredientes eamdem proportionem commen<lb></lb>ſurabilem habebunt, quam habent <expan abbr="earũ">earum</expan> velocitates. <lb></lb><arrow.to.target n="marg621"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002415"><margin.target id="marg619"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002416"><margin.target id="marg620"></margin.target>Supp. 1.</s> </p> <p type="margin"> <s id="s.002417"><margin.target id="marg621"></margin.target>Supp. 2.</s> </p> <p type="main"> <s id="s.002418">Non ſecùs ſi ab eodem foramine eadem velocita-<pb pagenum="460" xlink:href="010/01/468.jpg"></pb><arrow.to.target n="marg622"></arrow.to.target><lb></lb>te egrediantur duæ moles aquæ æquales, temporą <lb></lb>quoque effluxuum erunt inter ſe æqualia; & è <expan abbr="cõuer-ſo">conuer<lb></lb>ſo</expan>. </s> <s id="s.002419">Idemque dicendum eſt ſi tempora, atque moles <lb></lb>aquæ eadem velocitate dilapſæ habuerint quamlibet <lb></lb>proportionem æquè multiplicem, vel earumdem par<lb></lb>tium. </s> <s id="s.002420">His præmiſſis. </s> </p> <p type="margin"> <s id="s.002421"><margin.target id="marg622"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002422"><emph type="center"></emph>PROP. CCXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002423"><emph type="center"></emph><emph type="italics"></emph>Si ex æqualibus fistularum orificijs <expan abbr="tẽporibus">temporibus</expan> æqualibus duæ <lb></lb>aquæ moles defluant inæqualibus velocitatibus, erunt <lb></lb>aquæ moles proportionales velocitatibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002424">SInt fiſtulæ AB, & CD, quarum orificia infima B, <lb></lb>& D ſint æqualia, & <expan abbr="eorũ">eorum</expan> plana non ſit obliquè <lb></lb>inclinata ad directionem motus, quo aqua ab eis de<lb></lb>fluit, ſed eiſdem directionibus perpendiculares ſint, <lb></lb>(& hoc intelligatur in omnibus ſubſequentibus pro<lb></lb>poſitionibus), defluat poſtea moles aquæ R ex AB <lb></lb>velocitate M tempore T, & eodem <lb></lb><figure id="id.010.01.468.1.jpg" xlink:href="010/01/468/1.jpg"></figure><lb></lb>tempore minor moles aquæ S deci<lb></lb>dat ex CD velocitate N. oſtenden<lb></lb>dum eſt molem aquæ R ad S <expan abbr="eamdẽ">eamdem</expan> <lb></lb>proportionem habere quam velo<lb></lb>citas M ad N. </s> <s id="s.002425">Sumantur alia velo<lb></lb>citas H, & altera moles aquę O, hac <lb></lb>lege, vt H ipſius N, nec non O alte<lb></lb>rius S quælibet, & eædem partes <lb></lb>ſint. </s> <s id="s.002426">Patet, quòd eodem temporę <lb></lb>T ex foramine æquali ipſi B velocitate H fluet moles <lb></lb><arrow.to.target n="marg623"></arrow.to.target><lb></lb>aquæ O dum ex D velocitate N fuit aquæ moles S; & <lb></lb>ſiquidem velocitas H æqualis eſt velocitati M egre-<pb pagenum="461" xlink:href="010/01/469.jpg"></pb><arrow.to.target n="marg624"></arrow.to.target><lb></lb>dientur eodem tempore ex B prædictis duabus velo<lb></lb>citatibus H, & M duæ æquales moles aquæ O, & R; <lb></lb>ſi verò moles O fluat eodem tempore velocitate H <lb></lb>maiori, quam M, erit quoque aqua O maior, quàm̨ <lb></lb>R, & ſi velocitas H minor fuerit quàm M, erit etiam <lb></lb>moles aquæ O minor quàm R, cùm eodem tempore <lb></lb>ex foramine B <expan abbr="fluãt">fluant</expan>; quia verò ſunt quatuor quanti<lb></lb>tates M, N, R, S, & ſumuntur duæ aliæ quantitates H, <lb></lb>& O habentes quamlibet, & eamdem commenſura<lb></lb><arrow.to.target n="marg625"></arrow.to.target><lb></lb>bilem proportionem <expan abbr="conſequẽtibus">conſequentibus</expan> N, & S; ſuntque <lb></lb>vnà æquales, vel vnà maiores, aut minores antece<lb></lb>dentibus ordinatæ, igitur M ad N eamdem propor<lb></lb>tionem habebit, quam R ad S. </s> </p> <p type="margin"> <s id="s.002427"><margin.target id="marg623"></margin.target>Ex pręceden<lb></lb>ti prima ſup<lb></lb>poſitione.</s> </p> <p type="margin"> <s id="s.002428"><margin.target id="marg624"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002429"><margin.target id="marg625"></margin.target>Noſtr. Enel. <lb></lb>reſtitut. lib. <lb></lb>3. prop. 23.</s> </p> <p type="main"> <s id="s.002430"><emph type="center"></emph>PROP. CCXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002431"><emph type="center"></emph><emph type="italics"></emph>Ex eiſdem fistulis temporibus æqualibus fluent aquæ moles <lb></lb>ſubduplicatam <expan abbr="proportionẽ">proportionem</expan> habentes altitudinum <expan abbr="earũ">earum</expan>.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002432">SInt duę inæquales fiſtulæ AB maior, & CD minor <lb></lb>perpendicularitèr ad horizontem erectæ, eorum <lb></lb>foramina infima B, & D æqualia ſint inter ſe, & ſem<lb></lb>per fiſtularum plenitudine perſeue<lb></lb><figure id="id.010.01.469.1.jpg" xlink:href="010/01/469/1.jpg"></figure><lb></lb>rante, eodem tempore T egrediatur <lb></lb>ex foramine B moles aquæ R, at ex <lb></lb>foramine D alia moles aquæ S, & ſe<lb></lb>cetur altitudo EB media proportio<lb></lb>nalis inter altitudines AB, & CD; <lb></lb>patet AB ad EB proportionem ſub<lb></lb>duplicatam habere eius, quam ha<lb></lb>bet AB ad CD; dico, quòd moles a<lb></lb>quæ R ad molem S eodem tempore <pb pagenum="462" xlink:href="010/01/470.jpg"></pb><arrow.to.target n="marg626"></arrow.to.target><lb></lb>T <expan abbr="dilapsã">dilapsam</expan> eamdem proportionem habebit, quam al<lb></lb>titudo AB habet ad BE. ſit M velocitas, quæ compe<lb></lb>tit longitudini fiſtulæ AB, & ſit N velocitas fiſtulæ <lb></lb>CD; quoniam velocitas M aquæ fluentis per orifi<lb></lb>cium B, plenitudine eius perſeuerante, ad <expan abbr="velooitatẽ">velocitatem</expan> <lb></lb>N aquæ fluentis per orificium D, æquale ipſi B, ſub<lb></lb><arrow.to.target n="marg627"></arrow.to.target><lb></lb>duplicata eſt eius, quam habent fiſtularum altitudi<lb></lb>nes AB, & CD, ideoque velocitas M ad N erit vt AB <lb></lb>ad BE, ſed moles aquæ fluentes eodem tempore per <lb></lb><arrow.to.target n="marg628"></arrow.to.target><lb></lb>orificia æqualia B, D eamdem proportionem habent, <lb></lb>quàm eorum velocitates, ergo moles aquæ effluxą <lb></lb>R, ad molem S, eodem tempore T, eamdem propor<lb></lb>tionem habebit, quam altitudo AB ad EB, quod fue<lb></lb>rat oſtendendum. </s> </p> <p type="margin"> <s id="s.002433"><margin.target id="marg626"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002434"><margin.target id="marg627"></margin.target>Pr. 214.</s> </p> <p type="margin"> <s id="s.002435"><margin.target id="marg628"></margin.target>Pr. 220.</s> </p> <p type="main"> <s id="s.002436"><emph type="center"></emph>PROP. CCXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002437"><emph type="center"></emph><emph type="italics"></emph>Ab eadem fiſtula duæ moles aquæ in æquales egreſſæ eamdem <lb></lb>proportionem habent, quam tempora excurſuum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002438">AB orificio B <expan abbr="eiuſdẽ">eiuſdem</expan> fiſtulæ AB egrediatur mo<lb></lb>les aquæ R tempore T, moles verò aquæ S <expan abbr="tẽ-pore">tem<lb></lb>pore</expan> V; dico molem R, ad S <lb></lb><figure id="id.010.01.470.1.jpg" xlink:href="010/01/470/1.jpg"></figure><lb></lb>eamdem proportionem ha<lb></lb>bere, quam tempus T ad V, <lb></lb>quia perſeuerante eadem al<lb></lb>titudine fiſtulę AB ab orificio <lb></lb>eius B æquè amplo vnà, & ea<lb></lb>dem velocitate M aqua ſem<lb></lb>per fluere debet, & ſumptis, <lb></lb>vt antea H, & O, quæ eædem, & quælibet partes ſint <lb></lb><arrow.to.target n="marg629"></arrow.to.target><lb></lb><expan abbr="tẽporis">temporis</expan> V, & molis aquæ S, concludetur, quod vt <expan abbr="tẽ-">tem-<pb pagenum="463" xlink:href="010/01/471.jpg"></pb><arrow.to.target n="marg630"></arrow.to.target><lb></lb>pus</expan> T ad V, ita erit moles aquæ R ad S. </s> </p> <p type="margin"> <s id="s.002439"><margin.target id="marg629"></margin.target>Ibidem.</s> </p> <p type="margin"> <s id="s.002440"><margin.target id="marg630"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002441"><emph type="center"></emph>PROP. CCXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002442"><emph type="center"></emph><emph type="italics"></emph>Si duæ fistulæ inæqualiter altæ habuerint orificia æqualia, <lb></lb>atque ex eis egrediantur moles aquæ æquales, tempora <lb></lb>effluxuum habebunt ſubduplicatam proportionem reci<lb></lb>procam altitudinum fistularum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002443">SIt altitudo fiſtulæ AB maior, quàm CD, & eorum <lb></lb>orificia B, D æqualia, & ex B egrediatur moles <lb></lb>aquæ R tempore T, ex D verò profluat moles aquæ <lb></lb>S æqualis ipſi R tempore V, & vt priùs, ſit BE media <lb></lb>proportionalis inter AB, & <lb></lb><figure id="id.010.01.471.1.jpg" xlink:href="010/01/471/1.jpg"></figure><lb></lb>CD; dico tempus V ad T <expan abbr="eã-dem">ean<lb></lb>dem</expan> proportionem haberę, <lb></lb><expan abbr="quã">quam</expan> EB ad CD, ſit moles aquæ <lb></lb>X illa, quæ defluit ab orificio <lb></lb>D eodem tempore T, igitur <lb></lb><arrow.to.target n="marg631"></arrow.to.target><lb></lb>vt moles aquæ R ad X, ita erit <lb></lb>altitudo EB ad CD, poſteą <lb></lb>quia ab eodem oriſicio D fi<lb></lb>ſtulæ CD exeunt duæ moles <lb></lb>aqueæ X, & S temporibus T, <lb></lb><arrow.to.target n="marg632"></arrow.to.target><lb></lb>& V, igitur vt <expan abbr="tẽpus">tempus</expan> V ad T, ita ſe habet moles aquæ <lb></lb>S ad X: ſunt verò moles aquæ R, & S ex hypotheſi, <lb></lb>æquales, igitur ad eamdem molem X eamdem pro<lb></lb>portionem habent; eſt verò EB ad CD vt R ad X; <lb></lb>atque V ad T vt S ad X; igitur altitudo EB ad CD <expan abbr="eã-dem">ean<lb></lb>dem</expan> proportionem habebit, quam tempus V ad T. </s> </p> <p type="margin"> <s id="s.002444"><margin.target id="marg631"></margin.target>Prop. 221.</s> </p> <p type="margin"> <s id="s.002445"><margin.target id="marg632"></margin.target>Prop. 222.</s> </p> <p type="main"> <s id="s.002446"><emph type="center"></emph>PROP. CCXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002447"><emph type="center"></emph><emph type="italics"></emph>Duæ moles aquæ eodm tempore egredientes ex orificijs inæ-<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="464" xlink:href="010/01/472.jpg"></pb><arrow.to.target n="marg633"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002448"><margin.target id="marg633"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002449"><emph type="center"></emph><emph type="italics"></emph>qualibus fiſtularum æqualium altitudinum, æqualibus <lb></lb>velocitatibus fluent; at earum moles eamdem proportio<lb></lb>nem habebunt, quàm orificia.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002450">SInt duæ fiſtulæ AB, & CD eiuſdem altitudinis, ſed <lb></lb>orificium infimum B minus ſit alterius orificio <lb></lb>D, atque eodem tempore T fluat <lb></lb><figure id="id.010.01.472.1.jpg" xlink:href="010/01/472/1.jpg"></figure><lb></lb>ex B moles aquæ R, ex D verò ruat <lb></lb>moles aquæ S; dico eas paribus ve<lb></lb>locitatibus per fiſtulas excurrere, <lb></lb>at moles aquæ R ad S <expan abbr="eãdem">eandem</expan> pro<lb></lb>portionem habere, quam amplitu<lb></lb>do foraminis B ad ſpatium forami<lb></lb>nis D. </s> <s id="s.002451">Quia ob altitudines æquales <lb></lb>fiſtularum AB, & CD fluxus aquæ <lb></lb>æquales velocitates habent; moles verò <expan abbr="earũ">earum</expan> æqua<lb></lb>libus velocitatibus, & eodem tempore per orificią <lb></lb><arrow.to.target n="marg634"></arrow.to.target><lb></lb>inæqualia B, & D fluunt; igitur, vt amplitudo fora<lb></lb>minis B ad amplitudinem D, ita ſe habet moles aquæ <lb></lb>R ad molem S. </s> </p> <p type="margin"> <s id="s.002452"><margin.target id="marg634"></margin.target>Caſtell. de <lb></lb>menſura a<lb></lb>quæ curren<lb></lb>tis lib. 1. <lb></lb>axiom. 4.</s> </p> <p type="main"> <s id="s.002453">His præmiſſis vt velocitates quibus corpora eiuſ<lb></lb>dem grauitatis ſpecificæ aſcendunt, vel deſcendunt <lb></lb>in fluido, dignoſcere valeamus primo loco accuratiùs <lb></lb>inquirenda eſt ſtructura, & mechanica operatio ſi<lb></lb>phonis, & libræ, quam ſolidum cum fluido collatera<lb></lb>li in quo aſcendit, vel deſcendit, conſtituit. </s> </p> <p type="main"> <s id="s.002454"><emph type="center"></emph>PROP. CCXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002455"><emph type="center"></emph><emph type="italics"></emph>Cylindrus ſolidus cum æquali mole aquæ ambientis libram <lb></lb>circularem, & ſiphonem tubicum conſtituit, cuius <expan abbr="orificiũ">orificium</expan> <lb></lb>æquale eſt baſi cylindri ſolidi, & libræ fulcimentum est<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="465" xlink:href="010/01/473.jpg"></pb><arrow.to.target n="marg635"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002456"><margin.target id="marg635"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002457"><emph type="center"></emph><emph type="italics"></emph>terminus circularis fluidum à ſolido ſeparans, quæ moti<lb></lb>bus contrarijs agitantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002458">ET procedendo ad libræ, ſen ſiphonis in corpori<lb></lb>bus natantibus ſtructuram, intelligatur vas am<lb></lb>plum aqua plenum RSTX, in eoque demergatur <lb></lb>corpus ſolidum, & conſiſtens (cylindricum facilita<lb></lb>tis gratia) ABCD, quod minùs graue ſit in ſpecie <lb></lb>ipſa aqua. </s> <s id="s.002459">& quia prædictum ſolidum non poteſt ſur<lb></lb>sùm eleuari, niſi priùs incumbens aqua AKLD è ſuo <lb></lb>loco expellatur, & infernè recurrat ad replendum lo<lb></lb>cum BC à prædicto ſolido derelictum, igitur vndi<lb></lb>que per omnia eius latera AB, & DC aqua ambiens <lb></lb>deorsùm fluere debet, & propterea efficitur non v<lb></lb>nicus ſipho, ſed innumeri, vel potiùs efficitur ſipho <lb></lb><expan abbr="rotũdus">rotundus</expan> cuius pars externa aquea AFCH tubum ex<lb></lb>cauatum conſtituit, pars verò interna ſolida ABCD <lb></lb>eſt reliqua ſiphonis pars, quæ ſursùm aſcendit dum <lb></lb>aqua per tubicum ſiphonem deorsùm fluit. </s> <s id="s.002460">Et licèt <lb></lb>pateat ſenſu, in vaſis amplis, non totam aquam colla<lb></lb>teralem deſcendere dum lignum eleuatur, ſed <expan abbr="tantũ-modò">tantun<lb></lb>modò</expan> partem aliquam eius exiguam <expan abbr="adhærẽtem">adhærentem</expan> am<lb></lb>bientemque cylindrum AC, quod apertè dignoſci<lb></lb>tur in aqua turbida, itaut reliqua aqua quieſcens offi<lb></lb>cium vaſis ſuppleat, non tamen euidens eſt tubum̨ <lb></lb>aqueum AFCH ſiphonem conſtituentem præcisè æ<lb></lb>qualem eſſe ligneo cylindro AC; ideò hoc rationę <lb></lb>ſuadere conabimur. </s> <s id="s.002461">Quia tantumdem ſolidum AC <lb></lb>ſursùm aſcendit, quanta eſt moles aquæ, quæ è ſupre<lb></lb>mo loco expellitur, & quanta eſt illa, quæ infernè de-<pb pagenum="466" xlink:href="010/01/474.jpg"></pb><arrow.to.target n="marg636"></arrow.to.target><lb></lb>currit ad replendum ſpatium derelictum, ſcilicèt <expan abbr="dũ">dum</expan> <lb></lb><expan abbr="lignũ">lignum</expan> ab AD vſque ad KL mouetur expellit è ſupre<lb></lb>mo loco cylindrum aqueum AKLD, hæc verò aqua <lb></lb>antecedentem vrgendo fertur ad replendum <expan abbr="ſpatiũ">ſpatium</expan> <lb></lb>derelictum à baſi BC, non ſecùs ac in rota ſolida, vel <lb></lb>in ſiphone circulari contingit. </s> <s id="s.002462">at aqua AKLD diſce<lb></lb>dit è ſupremo loco certa, ac determinata velocitate, <lb></lb>ea ſcilicèt, qua cylindrus AC aſcendit: ergò quando <lb></lb>eadem aqua tranſportatur lateralitèr deorsùm ab A <lb></lb>G versùs FB <expan abbr="nõ">non</expan> videtur ferri debere minori, aut ma<lb></lb>iori velocitate, quam priùs conceperat, poſſidebat<lb></lb>que in ſuo diſceſſu è ſupremo loco KD, cum non im<lb></lb>pediatur, nec impellatur à collaterali aqua vaſis æ<lb></lb>quilibrata, neque à ſubiecta, quæ ſponte ſua virtu<lb></lb>te exceſſus ſui momenti in ipſo ſiphone defluit. </s> <s id="s.002463">Si igi<lb></lb>tur eodem tempore fluidum, & ſolidum ęqualia ſpa<lb></lb>tia percurrunt in ſiphone illud ſursùm aſcendendo, <lb></lb>hoc verò deorsùm deſcendendo, erunt profectò æ<lb></lb>qualia inter ſe, hoc enim minimè verificari poſſet ni<lb></lb>ſi ſiphonis canales eſſent æquales, & æ què ampli, vn<lb></lb>de deducitur, quod orificia ſiphonum ſolidi nempè, <lb></lb>& fluidi, ſcilicèt amplitudo aquæ fluentis ſit æqualis <lb></lb>amplitudini ſolidi eleuati. </s> </p> <p type="margin"> <s id="s.002464"><margin.target id="marg636"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002465">Vt verò fulcimentum prædicti ſiphonis reperiatur, <lb></lb>concipi debet radius phyſicus aquæ excurrentis, & <lb></lb>cylindri ſolidi FE, & in loco eius intermedio B di<lb></lb>ſtinguens aquam à ligno cadet fulcimentum prædi<lb></lb>ctæ libræ, quia ſcilicèt ſuper baſes æquales BE, & FB <lb></lb>inſiſtunt moles æquales ligni nempè BEQA, & aquæ <pb pagenum="467" xlink:href="010/01/475.jpg"></pb><arrow.to.target n="marg637"></arrow.to.target><lb></lb>FBAG, quæ æqualibus motibus inter ſe contrarijs <lb></lb>mouentur, tantumdem enim ſolidum aſcendit, quan<lb></lb>tum aqua collateralis deprimi<lb></lb><figure id="id.010.01.475.1.jpg" xlink:href="010/01/475/1.jpg"></figure><lb></lb>tur: & ſiquidem ſolidum eiuſ<lb></lb>dem grauitatis ſpecificæ, ac a<lb></lb>qua fuerit, tunc perindè eſt ac <lb></lb>ſi portio aquea FBAG eſſet e<lb></lb>iuſdem ſubſtantiæ, ac lignum̨ <lb></lb>BEQA, vel è contrà lignum eſ<lb></lb>ſet aqua, & tunc patet, quod <lb></lb>centrum grauitatis aggregati <lb></lb>ex ligno, & aqua collaterali ei <lb></lb>æquali inſiſtet præcisè perpen<lb></lb>dicularitèr ſuper libræ centrum, ſeu fulcimentum B, <lb></lb>& ideò nulla ratio ſuadet, quod prædictum æquili<lb></lb>brium alteretur, & proindè neque lignum aſcendet, <lb></lb>neque aqua deprimetur, vel è contrà, ſed in <expan abbr="eodẽ">eodem</expan> ſi<lb></lb>tu intra fluidum fixè perſiſtet. </s> <s id="s.002466">Si verò lignum minùs <lb></lb>graue ſpecie fuerit, quam aqua collateralis, tunc <lb></lb>patet, quod centrum communis grauitatis ſolidi, & <lb></lb>fluidi non inſiſtet vt priùs perpendicularitèr ſuprą <lb></lb>fulcimentum B libræ ſubiectæ, ſed cadet vltra ipſum <lb></lb>versùs F, & tunc iuxtà naturam penduli libram FE <lb></lb>flectetur, vel potiùs in ſiphone aqua deſcendet, & <lb></lb>lignum eleuabitur. </s> </p> <p type="margin"> <s id="s.002467"><margin.target id="marg637"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002468">Id quod dictum eſt de radio phyſico, ſeù ſe<lb></lb>ctore FE, dicendum eſt de reliquis omnibus partibus <lb></lb>tùm aquæ ambientis, cùm cylindri lignei, vndè con<lb></lb>ſtituuntur innumeræ libræ, ſeù potiùs libra ſuperfi-<pb pagenum="468" xlink:href="010/01/476.jpg"></pb><arrow.to.target n="marg638"></arrow.to.target><lb></lb>cialis, cuius fulcimentum eſt circuli periphęria ra<lb></lb>dio EB deſcripta. </s> </p> <p type="margin"> <s id="s.002469"><margin.target id="marg638"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002470">Et hoc ſemper verum eſſe videtur in vaſis amplis, <lb></lb>ſi tamen ſolida aſcendentia figuram oblongam, & æ<lb></lb>què craſſam habuerint, ſcilicèt ſi fuerint priſmatą, <lb></lb>vel cylindri, in figuris verò conicis, vel incuruatis <lb></lb>varietas aliqua reperitur, vt inferiùs patebit. </s> </p> <p type="main"> <s id="s.002471"><emph type="center"></emph>PROP. CCXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002472"><emph type="center"></emph><emph type="italics"></emph>E contra in vaſis valdè reſtrictis, & angustis amplitudo ſi<lb></lb>phonis aquei ſolidum ambientis, & deorsùm fluentis mi<lb></lb>nor eſſe debet baſi eiuſdem ſolidi, ſed contrario ordine re<lb></lb>ſpondere debent ſuis velocitatibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002473">PRo cuius intelligentia ſupponatur fiſtula, ſeù ſtri<lb></lb>ctum vas <expan abbr="vitreẽ">vitreum</expan> cylindricum RSTX aqua ple<lb></lb>num, & in eo immergatur ligneus cylindrus ABCD, <lb></lb>cuius baſis ſemidiametri QA quadratum maius ſit re<lb></lb>ctangulo KDL, tunc enim conſtat, <lb></lb><figure id="id.010.01.476.1.jpg" xlink:href="010/01/476/1.jpg"></figure><lb></lb>quod baſis circulus AD maior eſt <lb></lb>zona circulari KLDA, & propterea <lb></lb>amplitudo ſiphonis aquæ fluentis <lb></lb>minor erit amplitudine cylindri ſo<lb></lb>lidi aſcendentis; quia verò tantum<lb></lb>dem cylindrus ſolidus in aqua <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan> quanta eſt moles aquæ AGHD <lb></lb>è ſupremo loco expulſa, igitur vt <lb></lb>ſummitas cylindri AD <expan abbr="perpẽdicu-lari">perpendicu<lb></lb>lari</expan> motu feratur ad <expan abbr="locũ">locum</expan> GH opor<lb></lb>tet vt cylindrus aqueus AGHD è ſuo loco expella<lb></lb>tur, cuius baſis æqualis eſt ipſi AD; vt verò prædicta <pb pagenum="469" xlink:href="010/01/477.jpg"></pb><arrow.to.target n="marg639"></arrow.to.target><lb></lb>aqua ſuperna deorsùm feratur oportet, vt per angu<lb></lb>ſtias collaterales excurrat, & eodem tempore quo <lb></lb>aqua AGHD è ſupremo loco expellitur occupabit <lb></lb>collaterale ſpatium cylindricum excauatum AKOP <lb></lb>LD, cumque prædictus tubus aqueus æqualis ſit præ<lb></lb>dicto cylindro aqueo AGHD, oportet vt eorum ba<lb></lb>ſes reciprocè altitudinibus proportionales ſint; <lb></lb>quam ergo proportionem habet baſis tubiaquei KL <lb></lb>DA ad baſim AD cylindri aquei AH, eamdem habe<lb></lb>bit huius altitudo AG ad illius altitudinem KO, ſci<lb></lb>licèt eamdem proportionem habebit aſcenſus, ſeu <lb></lb>velocitas cylindri lignei AC ad fluxum quo deorsùm <lb></lb>deſcendit aqua in ſiphone tubico. </s> <s id="s.002474">Patet ergo, quod <lb></lb>anguſtia vaſis talis eſſe poteſt vt velocitas fluxus a<lb></lb>quæ deorsùm centies, & millies maior ſit celeritatę <lb></lb>qua cylinder ſolidus <expan abbr="aſcẽdit">aſcendit</expan>. </s> <s id="s.002475">Ex quo proindè ſequi<lb></lb>tur, quod ſi velocitas fluxus aquæ deorsùm determi<lb></lb>natur ab altitudine ſiphonis AB, ſcilicèt ſi prædictą <lb></lb>velocitas eſt vnius, & determinati gradus, vt <expan abbr="consẽ-taneum">consen<lb></lb>taneum</expan> eſt, oportet vt tanto tardiori motu ligneus <lb></lb>cylindrus in aqua aſcendat, & hoc bellè ab ipſa ex<lb></lb><arrow.to.target n="marg640"></arrow.to.target><lb></lb>perientia confirmatur. </s> <s id="s.002476">Sed præterea videtur quoque <lb></lb>ab alia cauſa velocitatem ligni aſcendentis retardari <lb></lb>debere, nempè ab aſperitatibus internæ ſuperficiei <lb></lb>vaſis, quatenùs aquæ particulæ non omninò glutine <lb></lb>priuatæ, vt dictum eſt, non facilè per prædictas angu<lb></lb>ſtias, & aſperitates fluere poſſunt, & proindè multò <lb></lb>magis ligni aſcenſum retardare valent. </s> </p> <p type="margin"> <s id="s.002477"><margin.target id="marg639"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002478"><margin.target id="marg640"></margin.target>Internę fiſtu<lb></lb>læ aſperita<lb></lb>tes motum̨, <lb></lb>cylindri re<lb></lb>tardare poſ<lb></lb>ſunt.</s> </p> <p type="main"> <s id="s.002479">His præmiſſis inquirendæ modò ſunt velocitates <pb pagenum="470" xlink:href="010/01/478.jpg"></pb><arrow.to.target n="marg641"></arrow.to.target><lb></lb>quibus cylindri inæquales in aqua aſcendunt. </s> </p> <p type="margin"> <s id="s.002480"><margin.target id="marg641"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002481">Et primo loco philoſophicus candor exigit vt fa<lb></lb>tear me non primum haſce ſpeculationes animaduer<lb></lb>tiſſe, ſed monitum, & excitatum fuiſſe ab amico An<lb></lb>tonio Oliua viro profectò perſpicaciſſimi, & ignei in<lb></lb>genij, is enim in Academia Experimentali Medicea <lb></lb>nonnulla experimenta ad hanc rem attinentia protu<lb></lb>lit, quibus confirmare conabatur, quod velocitates <lb></lb>corporum in fluido deſcendentium, vel <expan abbr="aſcendentiũ">aſcendentium</expan> <lb></lb>eamdem proportionem haberent, quam eorum alti<lb></lb>tudines. </s> <s id="s.002482">verum fundamenta, & ratiocinia quibus eius <lb></lb>opinio fulciretur hactenùs mihi ignota, & recondita <lb></lb>ſunt, propterea non verebor nouas has ſpeculatio<lb></lb>nes, quæ meæ omninò ſunt, edere, & doctiorum iudi<lb></lb>cio exponere. </s> </p> <p type="main"> <s id="s.002483"><emph type="center"></emph>PROP. CCXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002484"><emph type="center"></emph><emph type="italics"></emph>Si fuerint duo cylindri homogenei in aqua demerſi æqualium <lb></lb>baſium, & in æqualium altitudinum ſemperque eorum <lb></lb>latera perpendicularia ſint ad horizontem, tempora qui<lb></lb>bus æqualia ſpatia <expan abbr="aſcẽdendo">aſcendendo</expan>, vel <expan abbr="deſcendẽdo">deſcendendo</expan> percurrunt <lb></lb>eam dem proportionem reciprocam habebunt, quàm ſub<lb></lb>duplic at a ratio altitudinum fuerit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002485">SInt ergo duo cylindri homogenei primò aquą <lb></lb>leuiores ABC, & DEF, ſcilicèt ex eodem ligno <lb></lb>facti, quorum baſes BC, & EF æquales ſint, altitudo <lb></lb>verò AB maior ſit, quàm DE, & inter AB, & DE fiat <lb></lb>media proportionalis GB, ſintque vaſa ampla, & <expan abbr="sẽ-per">sen<lb></lb>per</expan> cylindri infra aquam demerſi retineant eorum̨ <lb></lb>latera perpendicularitèr ad horizontem erecta, (& <pb pagenum="471" xlink:href="010/01/479.jpg"></pb><arrow.to.target n="marg642"></arrow.to.target><lb></lb>hoc in ſequentibus quoque ſupponatur) ſi ſpatia æ<lb></lb>qualia X, & Z ſursùm aſcendendo percurrerint AC <lb></lb>quidem tempore T, & DF tempore V; dico tempus <lb></lb>V ad T eſſe vt AB ad GB; quia per æqualia ſpatia X, <lb></lb>& Z in aqua eleuantur ſolida AC, & DF, ergo ſuis æ<lb></lb>qualibus baſibus expellunt è locis ſupremis æquales <lb></lb>cylindros aqueos, & hæ æquales aquæ moles deor<lb></lb>sùm <expan abbr="fluũt">fluunt</expan> per ſiphones tubicos excauatos æquè craſ<lb></lb>ſos, ſcilicèt æqualium baſium, propterea quod baſes <lb></lb>BC, & EF æquales ſunt inter ſe, igitur ex ſiphonibus <lb></lb>tubicis inæqualium <expan abbr="altitudinũ">altitudinum</expan> ha<lb></lb><figure id="id.010.01.479.1.jpg" xlink:href="010/01/479/1.jpg"></figure><lb></lb>bentibus orificia, ſeu baſes æqua<lb></lb>les defluunt duæ aquæ moles inter <lb></lb>ſe æquales, ſed natura <expan abbr="prædictorũ">prædictorum</expan> <lb></lb><arrow.to.target n="marg643"></arrow.to.target><lb></lb>ſiphonum exigit, vt tempus V, quo <lb></lb>data moles aquæ profluit ab orifi<lb></lb>cio infimo ſiphonis ambientis cy<lb></lb>lindrum DF ad tempus T, quo mo<lb></lb>les aquæ illi æqualis defluit ex æ<lb></lb>quali orificio ſiphonis ambientis <lb></lb>cylindrum AC, eamdem proportionem habeat, quam <lb></lb>altitudo GB ad DE, & in prædictis temporibus tan<lb></lb>tumdem eleuantur cylindri, quantæ ſunt moles aquæ <lb></lb>ex vtriſque ſiphonibus effluxæ: igitur tempus V, quo <lb></lb>ſolidum DF eleuatur ad tempus T ſublimationis ſo<lb></lb>lidi AC eamdem <expan abbr="proportionẽ">proportionem</expan> habebit, quam altitu<lb></lb>do GC ad altitudinem DE. </s> </p> <p type="margin"> <s id="s.002486"><margin.target id="marg642"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002487"><margin.target id="marg643"></margin.target>Pr. 223.</s> </p> <p type="main"> <s id="s.002488">Secundò ſint ijdem cylindri aqua grauiores; ſimi<lb></lb>liter æquales aquæ moles ſursùm fluunt per ſiphones <pb pagenum="472" xlink:href="010/01/480.jpg"></pb><arrow.to.target n="marg644"></arrow.to.target><lb></lb>tubicos æquè craſſos, & deſcendunt cylindri AC, & <lb></lb>DF; ergo (ex prop. 223) tempus V ad tempus T e<lb></lb>rit vt altitudo GB ad DE, quod erat &c. </s> </p> <p type="margin"> <s id="s.002489"><margin.target id="marg644"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002490"><emph type="center"></emph>PROP. CCXXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002491"><emph type="center"></emph><emph type="italics"></emph>Iiſdem datis, ſi aſcenſus, vel deſcenſus fiant æqualibus <expan abbr="tẽ-poribus">tem<lb></lb>poribus</expan>, ſpatia ab eis exacta habebunt ſubduplicatam <lb></lb>proportionem altitudinum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002492">EOdem tempore T primo ſolidum AC aſcenden<lb></lb>do percurrat ſpatium X, atque <expan abbr="ſolidũ">ſolidum</expan> DF per<lb></lb>tranſeat ſpatium Z; dico, quod ſpatium X ad Z eam<lb></lb>dem proportionem habebit, quam <lb></lb><figure id="id.010.01.480.1.jpg" xlink:href="010/01/480/1.jpg"></figure><lb></lb>GB ad DE; quia eodem tempore T <lb></lb>per orificium ſiphonis <expan abbr="ambiẽtis">ambientis</expan> cy<lb></lb>lindrum AC cuius foramen æquale <lb></lb>eſt baſi BC, defluit cylindrus aqueus <lb></lb>cuius baſis æqualis eſt ipſi BC, alti<lb></lb>tudo verò X, quantum ſcilicèt <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan> prædictus cylindrus, atque tem<lb></lb>pore T per ſiphonem <expan abbr="ambiẽtem">ambientem</expan> cy<lb></lb>lindrum DF, cuius foramen æquale eſt EF, ſeu BC, <lb></lb><arrow.to.target n="marg645"></arrow.to.target><lb></lb>defluit cylindrus aqueus ſub eadem baſi, & altitudi<lb></lb>ne Z contentus; igitur moles aquæ defluxa ex priori <lb></lb>cylindro altiori ad molem aquæ egreſſam ex minori <lb></lb>cylindro, ſcilicèt altitudo X ad Z ſubduplicatam̨ <lb></lb><expan abbr="proportionẽ">proportionem</expan> habebit altitudinis AB ad DE, & proin<lb></lb>de ſpatium X aſcenſus cylindri AC ad ſpatium Z ele<lb></lb>uationis cylindri DF eodem tempore T eamdem pro<lb></lb>portionem habet, quam altitudo GB ad DE; quod <lb></lb>erat &c. <pb pagenum="473" xlink:href="010/01/481.jpg"></pb><arrow.to.target n="marg646"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002493"><margin.target id="marg645"></margin.target>Prop. 221.</s> </p> <p type="margin"> <s id="s.002494"><margin.target id="marg646"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002495">Secundò ſint cylindri AC, DF aqua grauiores; o<lb></lb>ſtendetur (ex prop. 221.) quod deſcenſus X ad de<lb></lb>ſcenſum Z, eodem tempore T factum, eſt ſicuti altitu<lb></lb>do GB ad DE, & hoc erat, &c. </s> </p> <p type="main"> <s id="s.002496"><emph type="center"></emph>PROP. CCXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002497"><emph type="center"></emph><emph type="italics"></emph>Poſtea ſi duo coni homogenei baſes æquales, & inæquales al<lb></lb>titudines habuerint, & verticibus ſursùm vergentibus, <lb></lb>itaut axes eorum ſemper inter ſe æquidistantes ſint, & <lb></lb>infra aquam exiſtentibus percurrant aſcendendo, vel <lb></lb>deſcendendo ſpatia æqualia; tempora contrario ordine re<lb></lb>ſpondebunt ſubduplicatæ proportioni altitudinum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002498">SInt duo coni eiuſdem materiei ABC, DEF, ſed <lb></lb>primò aqua leuiores, eorum baſes BC, & EF æ<lb></lb>quales ſint, altitudo verò illius maior ſit huius altitu<lb></lb>dine, inter quas ponatur GB media proportionalis; <lb></lb>tendant verò ambo ſursùm præcedendo vertices A, <lb></lb>& D, vt eorum axes paralleli ſint, <expan abbr="percurrãtque">percurrantque</expan> <expan abbr="aſcẽ-dendo">aſcen<lb></lb>dendo</expan> ſpatia æqualia AH, & DN <lb></lb><figure id="id.010.01.481.1.jpg" xlink:href="010/01/481/1.jpg"></figure><lb></lb>nempe ABC tempore T, at DEF <lb></lb>tempore V; dico tempus V ad <expan abbr="tẽ-pus">ten<lb></lb>pus</expan> T eſſe vt GB ad DE; quia æ<lb></lb>qualia ſpatia percurrunt ſursùm̨ <lb></lb>aſcendendo ſolida ABC, DEF, <lb></lb>ergo ſuis baſibus æqualibus dere<lb></lb>linquunt ſpatia æqualia, & æquè <lb></lb>alta IBCK, & OEFP, & ibidem̨ <lb></lb>fluere debent æquales aquæ moles <lb></lb>conos ambientes, quæ è ſupremis locis expelli de<lb></lb>bent, excurrunt verò prædictæ aquæ moles per ſi-<pb pagenum="474" xlink:href="010/01/482.jpg"></pb><arrow.to.target n="marg647"></arrow.to.target><lb></lb>phones, non quidem ad <expan abbr="horizõtem">horizontem</expan> perpendiculares, <lb></lb>ſed inclinatos, prout ſuperficies conorum <expan abbr="inclinãtur">inclinantur</expan>, <lb></lb>habentque ſiphones oriſicia ferè æqualia IL OM, & <lb></lb>eorum altitudines inæquales, ergo duæ moles aquæ <lb></lb>æquales deſluunt temporibus reciprocè proportio<lb></lb><arrow.to.target n="marg648"></arrow.to.target><lb></lb>nalibus ſubduplicatæ rationi altitudinum; quare <expan abbr="tẽ-pus">ten<lb></lb>pus</expan> V, quo ſolidum DEF aſcendit <expan abbr="ſpatiũ">ſpatium</expan> DN, ad <expan abbr="tẽ-pus">tem<lb></lb>pus</expan> T, quo ſolidum ABC percurrit ſpatium AH æ<lb></lb>quale ipſi DN, eamdem proportionem habebit, <expan abbr="quã">quam</expan> <lb></lb>altitudo GB ad altitudinem DE. </s> </p> <p type="margin"> <s id="s.002499"><margin.target id="marg647"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002500"><margin.target id="marg648"></margin.target>Prop. 223.</s> </p> <p type="main"> <s id="s.002501">Ijſdem poſitis ſi aſcenſus fiant æqualibus tempo<lb></lb>ribus (ſemper tamen infra aquæ libellam), ſpatia ab <lb></lb>eis exacta habebunt ſubduplicatam proportionem̨ <lb></lb>altitudinum. </s> </p> <p type="main"> <s id="s.002502">Hoc profectò facilè oſtendetur eadem methodo <lb></lb>ſuperiùs expoſita. </s> <s id="s.002503">Idemque concludetur in conorum <lb></lb>deſcenſu. </s> </p> <p type="main"> <s id="s.002504"><emph type="center"></emph>PROP. CCXXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002505"><emph type="center"></emph><emph type="italics"></emph>Iiſdem datis ſi tantummodò conorum baſes præcedant, & <lb></lb>ſursùm reſpiciant, & æquidiſtantes horizonti, & ſupre<lb></lb>mæ aquæ libellæ; idem prorsùs concludetur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002506">NAm ſemper aqua è ſuperno loco expelli debet <lb></lb>ad occupanda infima ſpatia à conis derelicta, <lb></lb>neque hoc fieri poteſt abſque eo quòd aqua circum<lb></lb>circa per ſiphones rotundos, cauos, inclinatoſquę <lb></lb>defluat, & quia celeritates fluxus aquæ in prædictis <lb></lb>ſi phonibus determinant velocitates aſcenſuum; hinc <lb></lb>ſequitur vt motus ſursùm conorum legibus <expan abbr="ſiphonũ">ſiphonum</expan> <lb></lb>ſubijciantur, ſcilicèt aſcenſus conorum eodem tem-<pb pagenum="475" xlink:href="010/01/483.jpg"></pb><arrow.to.target n="marg649"></arrow.to.target><lb></lb>pore facti ſubduplicatam proportionem habeant al<lb></lb>titudinum eorum. </s> </p> <p type="margin"> <s id="s.002507"><margin.target id="marg649"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002508"><emph type="center"></emph>PROP. CCXXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002509"><emph type="center"></emph><emph type="italics"></emph>Eorumdem conorum æquè altorum ſi vnius vertex, & al<lb></lb>terius baſis ſursùm ambo, vel deorsùm <expan abbr="reſpiciõt">reſpiciont</expan>; parum <lb></lb>celeriùs feretur is, qui mucrone præcedente fertur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002510">COmparari modò debent inter ſe duo coni æqua<lb></lb>les, ſimiles, & homogenei aqua leuiores, vel gra<lb></lb>uiores, ſed contrario ordine diſpoſiti, ſcilicèt ſi vnius <lb></lb>baſis <expan abbr="deorsũ">deorsum</expan> reſpiciat, alterius baſis ſursùm vergat, <lb></lb>ſed ambo horizonti æquidiſtantes, atque temporibus <lb></lb>æqualibus ſemper infra aquæ libellam aſcendendo, <lb></lb>vel deſcendendo ferantur; aliquantum celeriùs mo<lb></lb>uebitur is, qui vertice præcedente mouetur; quia li<lb></lb>cet expulſio ſupremæ aquæ efficiatur ab exceſſu pon<lb></lb>deris aquæ ſiphonis ſupra pondus ligni aſcendentis, <lb></lb>& ab illius motu, cui veluti appendix ſubſequitur a<lb></lb>quæ ſupernæ migratio, nihilominus illa moueri de<lb></lb>bet, ergo ſi eius motus impedimentum patietur, <expan abbr="cõ-ſequenter">con<lb></lb>ſequenter</expan> retardabitur aſcenſus ligni: modo negari <lb></lb>non poteſt reſiſtentia <expan abbr="pendẽs">pendens</expan> ab ampla translatione, <lb></lb>& diſtractione lanuginis partium aquæ, & à confri<lb></lb>catione cum aſperitatibus ligni <expan abbr="aſcendẽtis">aſcendentis</expan>; hæc pro<lb></lb>fectò magis retardare poſſe videtur baſim coni <expan abbr="ſursũ">ſursum</expan> <lb></lb>vergentem, quàm eius apicem, & hac de cauſa veri<lb></lb>ſimile videtur vt celeriùs conus ſursùm feratur quan<lb></lb>do eius vertex ſursùm reſpicit, quàm ſi inuerſo ordi<lb></lb>ne diſponatur, idemque in deſcenſu oſtendetur. </s> </p> <p type="main"> <s id="s.002511">Id quod dictum eſt de conis, verificatur etiam dę <pb pagenum="476" xlink:href="010/01/484.jpg"></pb><arrow.to.target n="marg650"></arrow.to.target><lb></lb>quibuslibet alijs figuris curuis <expan abbr="habẽtibus">habentibus</expan> baſes pla<lb></lb>nas & æquales, dummodò moles eamdem propor<lb></lb>tionem habeant, quam earum altitudines, vt ſi vna <lb></lb>eſſet hemiſphærium, reliqua verò, ſemiſphæroidalem <lb></lb>figuram æmularetur; tunc quoque ſi materiæ fuerint <lb></lb>homogeneæ, & aqua leuiores, intra ipſam <expan abbr="aſcendũt">aſcendunt</expan> <lb></lb>velocitatibus, ferè in ſubduplicata proportione <expan abbr="al-titudinũ">al<lb></lb>titudinum</expan> earumdem vt facilè ex dictis colligi poteſt. </s> </p> <p type="margin"> <s id="s.002512"><margin.target id="marg650"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002513"><emph type="center"></emph>PROP. CCXXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002514"><emph type="center"></emph><emph type="italics"></emph>Si cylindri partim in aqua, partim in aere existentes ſursùm, <lb></lb>vel deorsùm excurrerint; prædictæ proportiones velocita<lb></lb>tum valdè alterantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002515">ET hactenùs conſiderauimus aſcenſus, vel <expan abbr="deſcẽ-ſus">deſcen<lb></lb>ſus</expan> corporum dum eorum motus omninò fiunt <lb></lb>intra aquam, at quamprimùm ſupremam libellam at<lb></lb>tingunt, tunc progreſſus velocitatum valdè alteran<lb></lb>tur, debilitanturque; & ratio eſt, quia quando aliqua <lb></lb>pars ligni ſupra aquę libellam eminet tunc non <expan abbr="cõpa-rantur">compa<lb></lb>rantur</expan> amplius inter ſe duæ moles æquales aquæ, & <lb></lb>ligni, nec perſeuerat ſipho integer vt priùs, ſed <expan abbr="aliã">aliam</expan> <lb></lb>longè diuerſam naturam ſortitur, illius, inquam, cu<lb></lb>ius ex vna parte fluidum eminens continenter <expan abbr="deſcẽ-dit">deſcen<lb></lb>dit</expan> quouſque ad æquilibrium perducatur, & in hoc <lb></lb>caſu centrum communis grauitatis ſemper magis, ac <lb></lb>magis ad libræ fulcimentum accedit, motu illo curuo, <lb></lb><arrow.to.target n="marg651"></arrow.to.target><lb></lb>vt dictum eſt; & tunc propemodum ceſſat motus <expan abbr="cũ">cum</expan> <lb></lb>centrum communis grauitatis ligni, & fluidi non am<lb></lb>plius deſcendere valet, quia nempè ad ipſum fulci<lb></lb>mentum libræ perductum eſt. <pb pagenum="477" xlink:href="010/01/485.jpg"></pb><arrow.to.target n="marg652"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002516"><margin.target id="marg651"></margin.target>cap. 2. prop. 4. <lb></lb>& 11.</s> </p> <p type="margin"> <s id="s.002517"><margin.target id="marg652"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002518">Sed hoc <expan abbr="verũ">verum</expan> eſt de æquilibrio, & de vi motiua qua <lb></lb>corpus in aqua aſcendit, vel deſcendit, non verò de <lb></lb>celeritate motus eius, non enim motus eius retarda<lb></lb>tur omninò, ſed ſolummodò non augetur eodem pro<lb></lb>greſſu quo dum infra aquam poſitum ferebatur. </s> <s id="s.002519">Et <lb></lb>hoc pendet ab impetu acquiſito in præcedenti motu, <lb></lb>qui impetus perſeuerans ex ſui natura ſuum effectum <lb></lb>velocitatis producit, licet cauſa impulſiua non per<lb></lb>ſeueret eiuſdem gradus, ſed continentèr debilitetur; <lb></lb>& hæc eſt ratio quare lignum aſcendens non quieſcit <lb></lb>præcisè in eo ſitu in quo æquilibratur cum aqua col<lb></lb>laterali, ſed altiùs ab impetu præconcepto impelli<lb></lb>tur, & indè deorsùm decidendo repetitis aliquibus <lb></lb>vibrationibus, tandem in ſitu æquilibrij quieſcit. </s> </p> <p type="main"> <s id="s.002520">Et hic patet quo ſenſu intelligi debeat propoſitio </s> </p> <p type="main"> <s id="s.002521"><arrow.to.target n="marg653"></arrow.to.target><lb></lb>Archimedea, quæ habet quod tanta vi leue corpus <lb></lb>infra <expan abbr="mediũ">medium</expan> fluidum demerſum ſursùm <expan abbr="aſcẽdat">aſcendat</expan>, <expan abbr="quã-tum">quan<lb></lb>tum</expan> eſt pondus, quo fluidum æquale ipſi ſolido idip<lb></lb><arrow.to.target n="marg654"></arrow.to.target><lb></lb>ſum ſuperat. </s> <s id="s.002522">Hoc profectò verum eſt non de motu, <lb></lb>atque celeritate qua lignum ex. </s> <s id="s.002523">gr. ſursùm aſcendit, <lb></lb>ſed de energia, qua lignum in ſtatu quietis ſursùm ni<lb></lb>titur aſcendere, ſcilicèt ſi impediatur eius motus, vt <lb></lb>in bilanci contingit, tunc quidem propoſitio verifi<lb></lb>catur, non verò in actu motionis eius, nam tunc im<lb></lb>petus quo ſursùm aſcendit, auctus à præcedenti mo<lb></lb>tu ſuperabit quamcumque immenſam vim compreſſ<lb></lb>ſiuam cuiuslibet vaſtiſſimi ponderis incumbentis, vt <lb></lb>in noſtro Opere de vi percuſs. </s> <s id="s.002524">oſtenſum eſt. </s> </p> <p type="margin"> <s id="s.002525"><margin.target id="marg653"></margin.target>Incidenter <lb></lb>verus ſenſuæ <lb></lb>Archimedis <lb></lb>declaratur.</s> </p> <p type="margin"> <s id="s.002526"><margin.target id="marg654"></margin.target>De <expan abbr="inſidẽ">inſidem</expan> hu<lb></lb>mido lib. 1. <lb></lb>pr. 6.</s> </p> <p type="main"> <s id="s.002527">Præterea altera Archimedis propoſitio, quod ni<lb></lb><arrow.to.target n="marg655"></arrow.to.target><pb pagenum="478" xlink:href="010/01/486.jpg"></pb><arrow.to.target n="marg656"></arrow.to.target><lb></lb>mirùm moles fluidi æqualis ſolidi natantis parti de<lb></lb>merſæ æquè ponderet, ac ſolidum ipſum, vera eſt, <lb></lb>niſi hypotheſis varietur, oportet enim ex vi hypo<lb></lb>theſis vt ſolidum innatet ſupra vnum fluidum, nam ſi <lb></lb>omninò ſit demerſum intra rarius, & innatet ſuprą <lb></lb>aliud denſiùs fluidum propoſitio alteratur, vt docuit <lb></lb>præceptor meus Benedictus Caſtellus, qui demon<lb></lb>ſtrauit, quod ferrum ſupra mercurium natans ſi aqua <lb></lb>quoque cooperiatur, tunc quidem altiùs eleuabitur, <lb></lb>quàm priùs; propterea quod pondus aquæ collate<lb></lb>ralis auget magis hydrargyri compreſſionem, quam <lb></lb>ferri pondus augeat proindeque ferrum aliquantiſ<lb></lb>per altiùs eleuat. </s> </p> <p type="margin"> <s id="s.002528"><margin.target id="marg655"></margin.target><expan abbr="Idẽ">Idem</expan> pr. 5.</s> </p> <p type="margin"> <s id="s.002529"><margin.target id="marg656"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002530">Sed præterea animaduerti, quod alia de cauſą <lb></lb>prædictum æquilibrium alterari poteſt, nempè ex eo <lb></lb>quod aquæ libella circa ſolidum in ea natans, num<lb></lb>quam præcisè explanatur, vt docuimus cap. 9. prop. <lb></lb></s> <s id="s.002531">205. </s> </p> <p type="main"> <s id="s.002532">Porrò vt aſcenſus, vel deſcenſus cylindrorum in<lb></lb>æqualium baſium symptomata exponamus aliquæ <lb></lb>propoſitiones præmitti debent. </s> </p> <p type="main"> <s id="s.002533"><emph type="center"></emph>PROP. CCXXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002534"><emph type="center"></emph><emph type="italics"></emph>Si duo pondera inæqualia <expan abbr="ſuſpẽdũtur">ſuſpenduntur</expan> in extremitatibus dua<lb></lb>rum librarum inæqualium, ſed æqualium radiorum, ve<lb></lb>locitates reuolutionum earum ſubduplicatam proportio<lb></lb>nem habebunt radiorum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002535">SInt duæ libræ inæquales CD, & FG, quarum <expan abbr="cẽ-tra">cen<lb></lb>tra</expan> bifariam eas ſecantia ſint E, & H, & idem ma<lb></lb>ius pondus A ſuſpendatur primò in C, ſecundò in F, <pb pagenum="479" xlink:href="010/01/487.jpg"></pb><arrow.to.target n="marg657"></arrow.to.target><lb></lb>minus verò pondus B pendeat nedùm ex D, ſed <expan abbr="etiã">etiam</expan> <lb></lb>ex G; & vt A ad B, ita fiat DI ad IC, nec non GL ad <lb></lb>LF, erunt I, & L centra grauitatum librarum, fiat po<lb></lb>ſtea HN media proportionalis inter HL, & EI; <expan abbr="pa-riterq;">pa<lb></lb>riterque</expan> ponatur HO media proportionalis inter HG, <lb></lb>& ED; patet HG ad HO ſubduplicatam proportio<lb></lb>nem habere radij HG ad ED; dico velocitatem reuo<lb></lb>lutionis libræ FG ad <expan abbr="velocitatẽ">velocitatem</expan> vertiginis libræ CD <lb></lb><figure id="id.010.01.487.1.jpg" xlink:href="010/01/487/1.jpg"></figure><lb></lb>eamdem proportionem habe<lb></lb>re, quam HG ad HO; quia vt <lb></lb>A ad B, ita erat GL ad LF, <expan abbr="atq;">atque</expan> <lb></lb>DI ad IC, ergo componendo <lb></lb>GF ad FL erit vt DC ad CI, & <lb></lb>antecedentium ſemiſſes HF ad <lb></lb>FL, atque EC ad CI proporti<lb></lb>onales erunt, & per conuerſio<lb></lb>nem rationis HF ad HL erit vt CE ad EI, & permu<lb></lb>tando FH ad CE, ſeu HG ad ED erit vt LH ad IE, & <lb></lb>earum ſubduplicatæ proportiones eædem quoquę <lb></lb>erunt, nimirùm HG ad HO, vt HL ad HN; poſteą <lb></lb>quia duo pondera A, & B exercent eorum vim in <expan abbr="cẽ-tris">cen<lb></lb>tris</expan> grauitat <expan abbr="ũlibrarum">ullibrarum</expan> L, & I, & <expan abbr="ſuſpẽduntur">ſuſpenduntur</expan> ex <expan abbr="pũ-">pun<lb></lb></expan><arrow.to.target n="marg658"></arrow.to.target><lb></lb>ctis H, & E, ergo efficiunt duo funependula HL, & <lb></lb>EI, quæ conantur deſcendere per arcus LM, IK, ſed <lb></lb>pendulorum velocitates ſubduplicatam proportio<lb></lb>nem habent longitudinum eorum, igitur velocitas <lb></lb>deſcenſus libræ FG ad velocitatem deſcenſus libræ <lb></lb>CD eamdem proportionem habebit, quam LH ad <lb></lb>HN, ſeu quam habet HG ad HO, quod erat primum. <pb pagenum="480" xlink:href="010/01/488.jpg"></pb><arrow.to.target n="marg659"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002536"><margin.target id="marg657"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002537"><margin.target id="marg658"></margin.target>Cap. 2. pr. <gap></gap>.</s> </p> <p type="margin"> <s id="s.002538"><margin.target id="marg659"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002539"><emph type="center"></emph>PROP. CCXXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002540"><emph type="center"></emph><emph type="italics"></emph>Si duo ſiphones ex directis æquè altis, & contiguis fiſtulis <lb></lb>compoſiti fuerint, & in vnoquoque eorum duæ collatera<lb></lb>les fistulæ æquales ſint inter ſe, atque in ſinistris <expan abbr="ſiphonũ">ſiphonum</expan> <lb></lb>fiſtulis ponantur duo fluidi cylindruli æquè alti leuiores, <lb></lb>vel grauiores aqua, reſiduæ verò ſiphonum capacitates <lb></lb>aqua repleantur; aliquantulum tardiùs feretur cylinder <lb></lb>in ſiphone latiori, quàm in ſtrictiori.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002541">SInt duo ſiphones ABCD capaciores quàm PQRS <lb></lb>æquè alti, quorum fiſtulæ vnius AB, & CD ſint <lb></lb>æquales, & contiguæ, <expan abbr="pariterq;">pariterque</expan> duæ fiſtule PQ, & SF <lb></lb>ſint æquales, <expan abbr="cõtiguæque">contiguæque</expan>, <expan abbr="ponãturq;">ponanturque</expan> primo duæ olei <lb></lb>portiones EF, & KY æquè altæ, & proindè latitu<lb></lb>dinibus fiſtularum proportionales, reliquæ verò <lb></lb>ſiphonum capacitates aqua repleantur; dico, quod <lb></lb>oleum EF parùm tardiùs aſcendet, quàm KY. ſe<lb></lb>centur è regione, & in eiſdem planis horizonta<lb></lb><figure id="id.010.01.488.1.jpg" xlink:href="010/01/488/1.jpg"></figure><lb></lb>libus duæ aquæ portiones <lb></lb>FM, & YO, quæ æquales e<lb></lb>runt olei portionibus EF & <lb></lb>KY, & eorum centra graui<lb></lb>tatum coniungantur à rectis <lb></lb>GH, & TV, quæ bifariam̨ <lb></lb>ſectæ erunt in I, & X, atque <lb></lb>vt pondus olei EF ad <expan abbr="põdus">pondus</expan> <lb></lb>aquæ FM, velut <expan abbr="põdus">pondus</expan> olei <lb></lb>KY ad aquæ pondus YO, ita fiat HL ad LG, nec non <lb></lb>VZ ad ZT; patet perindè operari, ac premere prædi<lb></lb>cta fluida, ac ſi in libris radiorum æqualium HG, & <pb pagenum="481" xlink:href="010/01/489.jpg"></pb><arrow.to.target n="marg660"></arrow.to.target><lb></lb>TV ſuſpenſa fuiſſent, pariterque conſtat vim exerce<lb></lb>re in eorum centris grauitatum L, & Z, quæ propor<lb></lb>tionaliter libras diuidunt, & ideò in maiori libra GH <lb></lb>penduli longitudo IL maior erit longitudine penduli <lb></lb>XZ, quare impetus deſcenſus libræ & eleuatio olei <lb></lb>EF maiori velocitate fiet, quàm flexio alterius libræ <lb></lb>cum oleo KY, ſcilicèt in ſubduplicata proportionę <lb></lb><arrow.to.target n="marg661"></arrow.to.target><lb></lb>pendulorum; ſed quia hoc experientiæ repugnat, fa<lb></lb>tendum eſt ab aliquo impedimento retardari <expan abbr="aſcensũ">aſcensum</expan> <lb></lb>olei EF, & profectò nedùm ratio habenda eſt ponde<lb></lb>rum EF, FM, nec non KY, YO, quia hæc corpora in <lb></lb>libra appenſa moueri non poſſunt, quin etiam motu <lb></lb>tranſuerſali fluidum in fimum, ac ſupremum in fiſtulis <lb></lb>contentum impellant quoque motu tranſuerſali: igi<lb></lb>tur videndum quoque eſt quibus velocitatibus a<lb></lb>qua tranſuerſalitèr in vtroque ſiphone impulſa mo<lb></lb>ueri debeat; & primo quia ſpatium tranſuerſale AD <lb></lb>ad ſpatium PS duplicatam proportionem habet eius <lb></lb>quam vis motiua <expan abbr="pẽduli">penduli</expan> IL ad vim motiuam pendu<lb></lb>li XZ, ergo hoc nomine retardatur velocitas aſcenſus <lb></lb>fluidi EF: præterea tranſuerſalis fluxus aquæ in ſi<lb></lb>phone impeditur, quia non poteſt oleum EF aſcen<lb></lb>dere vſque ad 6, 7, niſi incumbens aqua E 7 ſurſum̨ <lb></lb>expellatur, colloceturque in ſpatio 6 N, & hinc aqua <lb></lb>expulſa reponatur in loco AN, & hinc excluſa aqua <expan abbr="ſi-tuationẽ">ſi<lb></lb>tuationem</expan> acquirat ND & hęc in N 8 <expan abbr="trãsferatur">transferatur</expan>, itaut <lb></lb>omnes partes aquæ AND ſimul tempore motu ſucceſ<lb></lb>ſiuo amplitudinem vaſis excurrant: huiuſmodi verò <lb></lb>tranſitus fieri non poteſt abſque eo, quòd machinulæ <pb pagenum="482" xlink:href="010/01/490.jpg"></pb><arrow.to.target n="marg662"></arrow.to.target><lb></lb>particularum fluidi non incidant in aſperitates ſuper<lb></lb>ficiei vaſis, vel fluidi quieſcentis, vnde ſubſequitur <lb></lb>confricatio, & repercuſſio partium fluidi per totam̨ <lb></lb>longitudinem canalis AD; & hac de cauſa impetus <lb></lb>fluentis aquæ tranfuerſali motu retardatur extenſiuè, <lb></lb>& intenſiuè; & quoad extenſionem pertinet, patet <lb></lb>quòd quam proportionem habet ſuperficies interna <lb></lb>vaſis AD ad ſuperficiem PS, eamdem habebit impe<lb></lb>dimentum retardans impetum fluidi AND ad impe<lb></lb>dimentum impetus fluidi P 3 S, & habet AD ad PS <lb></lb><expan abbr="duplicatã">duplicatam</expan> proportionem eius, quam habet impetus <lb></lb>aquæ fluentis AND ad impetum fluentis aquæ P 3 S. <lb></lb>verùm quoad intenſionem, patet quòd machinulæ <lb></lb>ambientes particulas fluidorum magis flectuntur, & <lb></lb>vehementiùs diſtrahuntur, quando maiori vi intra ali<lb></lb>as denſas, vel fluidas particulas agitantur, & propte<lb></lb>rea multò magis eorum impetus retardatur; Hinc fit <lb></lb>vt maior naturalis vis motiua libræ GH & ideò impe<lb></lb>tus aquæ fluentis AND magis, & intenſiuè retarde<lb></lb>tur quàm naturalis languidior impetus aquæ P 3 S, & <lb></lb>propterea oleum EF nedùm celeriùs non aſcendet, <lb></lb>quàm oleum KY, ſed præterea neceſſe eſt (vt docet ex<lb></lb>perientia) vt aliquantiſper tardius, quàm illud eleue<lb></lb>tur. </s> <s id="s.002542">idem de mercurij deſcenſu concludetur. </s> <s id="s.002543">His de<lb></lb>claratis deuenio ad Propoſitionem principalem. </s> </p> <p type="margin"> <s id="s.002544"><margin.target id="marg660"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002545"><margin.target id="marg661"></margin.target>Prop. 233.</s> </p> <p type="margin"> <s id="s.002546"><margin.target id="marg662"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002547"><emph type="center"></emph>PROP. CCXXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002548"><emph type="center"></emph><emph type="italics"></emph>Si fuerint duo cylindri homogenei, æquè alti, quorum baſes <lb></lb>inæquales, cylinder ſtrictior aliquantùm celerius <expan abbr="aſcẽdet">aſcendet</expan>, <lb></lb>vel deſcendet, quàm latior.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="483" xlink:href="010/01/491.jpg"></pb><arrow.to.target n="marg663"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002549"><margin.target id="marg663"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002550">SInt duo cylindri homogenei, primò aqua leuiores <lb></lb>ABC, & DEF, quorum altitudines AB, DE æqua<lb></lb>les ſint, baſis verò BC maior ſit, quàm EF, & <expan abbr="sẽper">semper</expan> in<lb></lb><figure id="id.010.01.491.1.jpg" xlink:href="010/01/491/1.jpg"></figure><lb></lb>fra aquam demerſi in vaſis amplis aſ<lb></lb>cendendo percurrant ſpatia æqualia <lb></lb>X & Z, AC <expan abbr="quidẽ">quidem</expan> tempore T, & DF <lb></lb>tempore V: dico quòd tempus T pa<lb></lb>rùm maius erit quàm V. quia dum in <lb></lb>aqua eleuantur ſolida AC & DF con<lb></lb>ſtituunt cum ambiente <expan abbr="cõtigua">contigua</expan> aqua <lb></lb>duos <expan abbr="ſipũones">ſiphones</expan> excauatos, æquè altos, </s> </p> <p type="main"> <s id="s.002551"><arrow.to.target n="marg664"></arrow.to.target><lb></lb>quorum fiſtulæ inæquales ſunt, nam̨ <lb></lb>craſſities fluentis aquæ circa cylindrum AC æqualis <lb></lb>eſt baſi cylindri BC, pariterque craſſities fluentis a<lb></lb>quæ circa cylindrum DF æqualis eſt craſſitiei EF: <expan abbr="erũt">erunt</expan> <lb></lb>igitur duo ſiphones ex directis, æquè altis, & conti<lb></lb>guis fiſtulis compoſiti, & in vnoquoque eorum duæ <lb></lb>collaterales fiſtulæ æquales ſunt, atque duæ internæ <lb></lb>ſiphonum fiſtulæ <expan abbr="occupãtur">occupantur</expan> à cylindris AC, & DF ho<lb></lb><arrow.to.target n="marg665"></arrow.to.target><lb></lb>mogeneis, & aqua leuioribus, & æquè altis, ergo pa<lb></lb>rùm tardiùs aſcendet craſſior cylinder AC, quàm DF, <lb></lb>ſupponuntur autem aſcendiſſe ſpatia æqualia X & Z <lb></lb>temporibus T, & V; igitur tempus T maius erit tem<lb></lb>pore V. ſi verò aſcenſus fiant æqualibus temporibus, <lb></lb>ſpatium aſcenſus latioris cylindri minus erit ſpatio <lb></lb>tranſacto à cylindro ſtrictiori: Quia cùm parum tar<lb></lb>diùs aſcendat cylinder AC quàm DF, ergo æqualibus <lb></lb>temporibus T & V percurret AC minus ſpatium X <lb></lb>dum DF maius ſpatium Z pertranſit. </s> <s id="s.002552">ſecundò ſint <expan abbr="ijdẽ">ijdem</expan> <pb pagenum="484" xlink:href="010/01/492.jpg"></pb><arrow.to.target n="marg666"></arrow.to.target><lb></lb>cylindri aqua grauiores, patet non minus ſiphones <lb></lb>conſtitui, vt in prop. 234 dictum eſt, quare eodem̨ <lb></lb>modo concludetur, quòd cylinder ſtrictior parum ce<lb></lb>lerius deſcendet quàm latior, quod erat &c. </s> <s id="s.002553"><expan abbr="Nõ">non</expan> ſecus <lb></lb>in aſcenſu vel deſcenſu prædictorum cylindrorum̨ <lb></lb>non facilè determinari poteſt menſura exceſſus velo<lb></lb>citatis cylindri DF ſupra velocitatem cylindri AC, <lb></lb>quare recurrendum eſt ad experientiam, in qua reue<lb></lb>ra obſeruatur exceſſus minimus velocitatis in cylin<lb></lb>dro DF ſupra velocitatem alterius cylindri AC; ſed <lb></lb>procùl dubio velocitas cylindri DF minorem, quàm <lb></lb>ſubduplicatam proportionem habere videtur ad ve<lb></lb>locitatem alterius cylindri AC eius quam habet baſis <lb></lb>BC ad baſim EF. </s> </p> <p type="margin"> <s id="s.002554"><margin.target id="marg664"></margin.target>Prop. 223.</s> </p> <p type="margin"> <s id="s.002555"><margin.target id="marg665"></margin.target>Prop. 334.</s> </p> <p type="margin"> <s id="s.002556"><margin.target id="marg666"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002557"><emph type="center"></emph>PROP. CCXXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002558"><emph type="center"></emph><emph type="italics"></emph>Si duo quælibet ſolida homogenea, & à ſimilibus figuris <expan abbr="cõ-prehenſa">con<lb></lb>prehenſa</expan>, ſimiliterque poſit a fuerint dum in aqua ferun<lb></lb>tur, maius celeriùs aſcendet vel deſcendet, quàm minus, <lb></lb>ſed in minori proportione quàm ſubduplicata <expan abbr="altitudinũ">altitudinum</expan>.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.010.01.492.1.jpg" xlink:href="010/01/492/1.jpg"></figure> <p type="main"> <s id="s.002559">SInt duo ſolida homogenea pri<lb></lb>mò aqua leuiora AC, & DF, quo<lb></lb>rum figuræ ſimiles ſint inter ſe, & in <lb></lb>vaſis amplis ſemper infra aquam de<lb></lb>merſa ſimiliter poſita ſint dum <expan abbr="aſcẽ-dunt">aſcen<lb></lb>dunt</expan> per ſpatia, primo æqualia X & <lb></lb>Z, ſcilicèt dum ſursùm feruntur ſem<lb></lb>per axes eorum, ſint paralleli, & æ<lb></lb>què inclinati ad planum horizontis, <lb></lb>atque AC tempore T pertranſeat ſpatium X, & DF <pb pagenum="485" xlink:href="010/01/493.jpg"></pb><arrow.to.target n="marg667"></arrow.to.target><lb></lb>tempore V percurrat ſpatium Z, & fiat IB medią <lb></lb>proportionalis inter altitudines AB, & DE. dico <expan abbr="tẽ-pus">tem<lb></lb>pus</expan> T minus eſſe <expan abbr="tẽpore">tempore</expan> V, ſed <expan abbr="tẽpus">tempus</expan> V ad T <expan abbr="minorẽ">minorem</expan> <lb></lb><expan abbr="proportionẽ">proportionem</expan> habere, <expan abbr="quã">quam</expan> IB habet ad DE; fiat vel in<lb></lb>telligatur figura GBC æquè alta, ac eſt DEF <expan abbr="eiuſdẽ-que">eiuſdem<lb></lb>que</expan> materiei habens <expan abbr="eãdẽ">eandem</expan> baſim BC, hac lege vt mo<lb></lb>les ABC ad GBC eamdem <expan abbr="proportionẽ">proportionem</expan> habeat, quam <lb></lb>altitudo AB ad GB, ſitque Y tempus, quo GBC ſur<lb></lb>ſum infra aquam aſcendendo percurrit idem ſpatium <lb></lb>X. quoniam ſunt duo folida homogenea ABC, & GB <lb></lb>C eamdem baſim BC habentia, quorum moles eam<lb></lb>dem proportionem habent, quam altitudo AB ad G <lb></lb>B, ſeù ad DE, & ſimiliter poſita ſunt dum aſcendunt <lb></lb><arrow.to.target n="marg668"></arrow.to.target><lb></lb>per ſpatia æqualia X, X; igitur tempus T, quo ABC <lb></lb>pertranſit ſpatium X ad tempus Y, quo GBC idipſum <lb></lb>ſpatium percurrit, eamdem proportionem habet, <expan abbr="quã">quam</expan> <lb></lb>DE ad IB. poſtea quia ſunt duo alia ſolida homogenea <lb></lb>æquè alta GBC, & DEF quorum baſes planæ BC, & <lb></lb>EF eamdem proportionem habent, quam moles eo<lb></lb>rum, ergo tempora Y, & V, quibus in eodem fluido <lb></lb><arrow.to.target n="marg669"></arrow.to.target><lb></lb>aqueo aſcendendo percurrunt ſpatia æqualia X, & Z <lb></lb>parùm inter ſe differunt, eritque tempus V minus <expan abbr="quã">quam</expan> <lb></lb>Y, ſed maiorem proportionem ad ipſum habet, quàm <lb></lb>DE ad IB, ac proindè tempus V maius erit, quàm T, <lb></lb>& ideò celeriùs aſcendet ABC, quàm DEF, ſed iņ <lb></lb>minori proportione, quam habet IB ad DE, idemque <lb></lb>concludetur in deſcenſu, quod erat &c. <pb pagenum="486" xlink:href="010/01/494.jpg"></pb><arrow.to.target n="marg670"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002560"><margin.target id="marg667"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002561"><margin.target id="marg668"></margin.target>Prop. 223.</s> </p> <p type="margin"> <s id="s.002562"><margin.target id="marg669"></margin.target>Prop 235.</s> </p> <p type="margin"> <s id="s.002563"><margin.target id="marg670"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002564"><emph type="center"></emph>PROP. CCXXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002565"><emph type="center"></emph><emph type="italics"></emph>Iiſdem poſitis ſi aſcenſus vel deſcenſus fiant æqualibus tem<lb></lb>poribus, ſpatium ex actum à maiori ſolido maius erit ſpa<lb></lb>tio tranſacto à ſolido minori, ſed ad <expan abbr="ipsũ">ipsum</expan> habebit <expan abbr="minorẽ">minorem</expan> <lb></lb>proportionem, quàm ſit ſubduplicata altitudinem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002566">AScendat primò ſolidum ABC ſpatium X tempo<lb></lb>re T, atque DEF percurrat ſpatium Z eodem̨ <lb></lb><figure id="id.010.01.494.1.jpg" xlink:href="010/01/494/1.jpg"></figure><lb></lb>tempore T. dico ſpatium X maius <lb></lb>eſſe, quàm Z, ſed minorem propor<lb></lb>tionem ad ipſum habere, quàm ſit <lb></lb>ſubduplicata altitudinis AB ad D <lb></lb>E; quia velocitates ſolidorum AB <lb></lb>C, & DEF eamdem proportionem <lb></lb>habent, quam ſpatia X, & Z eodem <lb></lb>tempore exacta, ergo patet propo<lb></lb>ſitum. </s> </p> <p type="main"> <s id="s.002567">Non exiguum tempus inſump<lb></lb>ſi vt experimentis expenderem ſuperiorem theori<lb></lb>am, ſed exactam præciſionem nulla diligentia, aut <lb></lb>labore adhibito aſſequi potui, hocque pendet ex <lb></lb>quamplurimis difficultatibus, ſi enim cylindrulorum <lb></lb><arrow.to.target n="marg671"></arrow.to.target><lb></lb>in fiſtulis vitreis aqua plenis aſcenſus, vel deſcen<lb></lb>ſus, obſeruentur, tunc varietates inſignes contin<lb></lb>gunt, quæ procùl dubio <expan abbr="producũtur">producuntur</expan> à vario contactu, <lb></lb>vel ab inæquali diſtantia cylindrorum à ſuperficię <lb></lb>interna vitri, quæ liberè aquam interceptam fluere <lb></lb>non ſinit. </s> <s id="s.002568">Si poſtea vaſa ampla vſurpentur, tunc li<lb></lb>cèt infimæ partes cylindrorum plumbo, vel alio pon<lb></lb>dere grauiores reddantur iuxtà proportionem altitu-<pb pagenum="487" xlink:href="010/01/495.jpg"></pb><arrow.to.target n="marg672"></arrow.to.target><lb></lb>dinum earumdem, numquam tamen cuitari poteſt <lb></lb>cylindrorum agitatio, & oſcillatio lateralis dum a<lb></lb>ſcendunt, vel deſcendunt, neque eorum axes omninò <lb></lb>ſimili poſitione moueri poſſunt, & hinc enormes va<lb></lb>rietates oriuntur; officit quoque agitatio partium̨ <lb></lb>eiuſdem aquæ quæ euitari ne quit, dum manus infrą <lb></lb>aquam immerſæ emittere cylindros debent. </s> <s id="s.002569">Hiſcę <lb></lb>difficultatibus territus, vt <expan abbr="quã">quam</expan> maximè obſtacula ef<lb></lb>fugerem, elegi ſphærulas ex eodem ligno, aut ex <expan abbr="plũ-bo">plum<lb></lb>bo</expan> confectas, in quibus ob ſimilitudinem figurarum̨ <lb></lb>in qualibet earum circumuolutione oſcillationes non <lb></lb>impediunt quin ſemper ſimili poſitione pilæ aſcen<lb></lb>dant, vel deſcendant, & tunc ex repetitis ex perimen<lb></lb>tis conſtat quod velocitates earum reuera inæquales <lb></lb>ſunt, celeriorique motu maior pila fertur, quàm mi<lb></lb>nor, ſed in minori proportione, quàm ſit ſubduplica<lb></lb>ta altitudinum, vt noſtra theoria ſuadere videtur. <lb></lb><arrow.to.target n="marg673"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002570"><margin.target id="marg671"></margin.target>Quia difficul<lb></lb>tèr hæc iņ <lb></lb>cylindris ex<lb></lb>periri <expan abbr="poſsũt">poſsunt</expan> <lb></lb>ſed faciliùs, <lb></lb>& rariùs in <lb></lb>ſphæris iņ <lb></lb>ijs noſtra <expan abbr="sẽ-tentia">sen<lb></lb>tentia</expan> com<lb></lb>probatur.</s> </p> <p type="margin"> <s id="s.002571"><margin.target id="marg672"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002572"><margin.target id="marg673"></margin.target>in valdè ra<lb></lb>ris fluidis va<lb></lb>rietates ali<lb></lb>quæ contin<lb></lb>gunt.</s> </p> <p type="main"> <s id="s.002573">Et hæc profectò valent in fluidis conſiſtentibus, & <lb></lb>non valdè <expan abbr="condẽſabilibus">condenſabilibus</expan>, vt eſt aqua, hydrargyrum, <lb></lb>oleum, & alia ſimilia, ſed in aere rariſſimo, qui ex ma<lb></lb>chinulis grandioribus, & valdè compreſſibilibus <expan abbr="cõ-ſtat">con<lb></lb>ſtat</expan>, non nullæ irregularitates contingunt in motioni<lb></lb>bus corporum per eum aſcendentium, vel <expan abbr="deſcendẽ-tium">deſcenden<lb></lb>tium</expan>; & hoc non fit eadem regula, ſcilicèt non eodem <lb></lb>modo variètur motus <expan abbr="ſolidorũ">ſolidorum</expan> in principio aſcenſus, <lb></lb>vel <expan abbr="deſcẽſus">deſcenſus</expan>, ac in progreſſu, & <expan abbr="cõtinuatione">continuatione</expan> prolixa <lb></lb><expan abbr="eorũdẽ">eorundem</expan> <expan abbr="motuũ">motuum</expan>, vt ſuo loco declarabitur. </s> <s id="s.002574"><expan abbr="Poſtquã">Poſtquam</expan> <expan abbr="cõ-parauimus">con<lb></lb>parauimus</expan> velocitates, quibus homogenea corporą <lb></lb>aſcendunt, vel deſcendunt in fluidis, expendere vlti-</s> </p> <pb pagenum="488" xlink:href="010/01/496.jpg"></pb> <p type="main"> <s id="s.002575"><arrow.to.target n="marg674"></arrow.to.target><lb></lb>mo loco debemus velocitates <expan abbr="corporũ">corporum</expan> inter ſe hete<lb></lb>rogeneorum, quæ contingunt in eodem, vel diuerſis <lb></lb>fluidis; hæc verò requirunt lemmata aliqua mechani<lb></lb>ca, quorum primum erit. </s> </p> <p type="margin"> <s id="s.002576"><margin.target id="marg674"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002577"><emph type="center"></emph>PROP. CCXXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002578"><emph type="center"></emph><emph type="italics"></emph>Si in libra radiorum æqualium duo pondera in æqualia <expan abbr="ſuſpẽ-dantur">ſuſpen<lb></lb>dantur</expan>, ſumma inæqualium ponderum ad eorum diffe<lb></lb>rentiam eamdem proportionem habebit, quam libræ ra<lb></lb>dius ad pendulum, quod constituit eadem libra.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002579">ATerminis eiuſdem libræ AB ſuſpenſæ in puncto <lb></lb>eius intermedio C <expan abbr="pendeãt">pendeant</expan> pondera inæqualia <lb></lb><figure id="id.010.01.496.1.jpg" xlink:href="010/01/496/1.jpg"></figure><lb></lb>D maius, & E minus, ſit<lb></lb>que F centrum grauita<lb></lb>tis libræ cum ponderi<lb></lb>bus appenſis, patet CF <lb></lb>eſſe longitudinem pen<lb></lb>duli. </s> <s id="s.002580">dico D plus, E ad D minus E eamdem propor<lb></lb>tionem habere, quam libræ radius AC ad penduli <lb></lb>longitudinem CF. quia F eſt centrum grauitatis librę <lb></lb>cum ponderibus ſuſpenſis D & E, ergo D ad E <expan abbr="eamdẽ">eamdem</expan> <lb></lb>proportionem habet (ex mechanicis) quàm BF ad FA, <lb></lb>& componendo D plus E ad E, pariterque duplum̨ <lb></lb>ſummæ D & E ad duplum E eamdem proportionem <lb></lb>habebit, quàm BA ad AF, igitur antecedentium ſe<lb></lb>miſſes ad conſequentes eamdem proportionem ha<lb></lb>bebunt, ſcilicèt D plus E ad duplum E erit vt ſemi <lb></lb>BA, ſeu CA ad AF, & per conuerſionem rationis D <lb></lb>plus E ad D minus E eamdem <expan abbr="proportionẽ">proportionem</expan> habebit, <lb></lb>quàm CA, ad CF, quod erat, &c. <pb pagenum="489" xlink:href="010/01/497.jpg"></pb><arrow.to.target n="marg675"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002581"><margin.target id="marg675"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002582"><emph type="center"></emph>PROP. CCXXXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002583"><emph type="center"></emph><emph type="italics"></emph>Si à terminis duarum librarum æqualium, & æqualium <lb></lb>radiorum duo pondera æqualia pendeant, ſed oppoſitis <lb></lb>minora, pendulum prioris libræ ad pendulum poſterioris <lb></lb>proportionem compoſitam habebit ex ratione differentiæ <lb></lb>priorum ponderum ad eorum ſummam, & ex ratione <lb></lb>ſummæ posteriorum ad differentiam eorumdem <expan abbr="ponderũ">ponderum</expan>.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002584">SInt duæ libræ æquales AB, & NO bifariàm ſectæ <lb></lb>in fulci mentis C, & K, atque ex A pendeat ma<lb></lb>ius pondus D, ex N verò minus pondus G, atque iņ <lb></lb><figure id="id.010.01.497.1.jpg" xlink:href="010/01/497/1.jpg"></figure><lb></lb>B, & O ſuſpendantur duo <expan abbr="põ-dera">pon<lb></lb>dera</expan> æqualia E, & M, <expan abbr="quorũ">quorum</expan> <lb></lb>ſingula minora ſint quàm D, <lb></lb>vel G; <expan abbr="reperiãturque">reperianturque</expan> duo ea<lb></lb>rum centra grauitatum F, & <lb></lb>H; dico pendulum CF ad K <lb></lb>H proportionem <expan abbr="compoſitã">compoſitam</expan> <lb></lb>habere ex ratione ponderis D minus E ad D plus E, <lb></lb>& ex ratione G plus M ad G minus M; <expan abbr="quoniã">quoniam</expan> AC ad <lb></lb>CF eſt vt D plus E ad D minus E (ex præcedenti) er<lb></lb>go inuertendo FC ad CA, ſeu ad ei æqualem KN <expan abbr="eã-dem">ean<lb></lb>dem</expan> proportionem habet <expan abbr="quã">quam</expan> D minus E ad D plus <lb></lb>E, & NK ad KH eamdem proportionem habet, <expan abbr="quã">quam</expan> <lb></lb>G plus M ad G minus M; habet verò FC ad HK pro<lb></lb>portionem compoſitam ex ratione FC ad CA, ſeu ad <lb></lb>NK, & ex ratione KN ad KH, ergo FC ad KH com<lb></lb>poſitam proportionem habebit ex ijſdem proportio<lb></lb>nibus D minus E ad D plus E, & ex G plus M ad G <lb></lb>minus M. <pb pagenum="490" xlink:href="010/01/498.jpg"></pb><arrow.to.target n="marg676"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002585"><margin.target id="marg676"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002586"><emph type="center"></emph>PROP. CCXL.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002587"><emph type="center"></emph><emph type="italics"></emph>In ijſdem trutinis datis quatuor ponderibus in illis <expan abbr="ſuſpẽſis">ſuſpenſis</expan>, <lb></lb>reperire proportionem velocitatum quibus libræ reuol<lb></lb>uuntur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002588">IN eadem figura ſint data pondera inæqualia D, & <lb></lb>G, nec non præcognita ſint pondera æqualia E, <lb></lb>& M, quæ minora prioribus ſint: reperiri debet pro<lb></lb><figure id="id.010.01.498.1.jpg" xlink:href="010/01/498/1.jpg"></figure><lb></lb>portio velocitatum qui<lb></lb>bus prædictæ libræ <expan abbr="reuol-uũtur">reuol<lb></lb>uuntur</expan>; fiat CI media pro<lb></lb>portionalis inter CF, & <lb></lb>KH; quia duo pondera D, <lb></lb>& E ſuam vim compreſſi<lb></lb>uam exercent in F centro <lb></lb>grauitatis communis eo<lb></lb>rumdem ponderum, ergo ea velocitate flectetur li<lb></lb>bra AB circa centrum fixum C, quæ competit longi<lb></lb>tudini penduli CF; eadem ratione ea velocitate fle<lb></lb><arrow.to.target n="marg677"></arrow.to.target><lb></lb>ctetur libra NO cum ponderibus G, M circa centrum <lb></lb>K, quæ competit longitudini penduli KH; & quią <lb></lb>velocitas penduli CF ad velocitatem penduli KH <expan abbr="eã-dem">ean<lb></lb>dem</expan> rationem habet quam CF ad CI; & CF ad KH <lb></lb>compoſitam proportionem habet ex ratione diffe<lb></lb><arrow.to.target n="marg678"></arrow.to.target><lb></lb>rentiæ ponderum D, & E ad eorum ſummam, & ex <lb></lb>ratione ſummæ ponderum G, M ad eorum differen<lb></lb>tiam, ergo reperire debemus <expan abbr="ſubduplicatã">ſubduplicatam</expan> propor<lb></lb>tionem prædictæ compoſitæ proportionis, vt quæſi<lb></lb>to ſatisfaciamus. </s> <s id="s.002589">Fiat modò ſumma ponderum D, & <lb></lb>E ad R, vt ſumma ponderum G, & M ad eorumdem̨ <pb pagenum="491" xlink:href="010/01/499.jpg"></pb><arrow.to.target n="marg679"></arrow.to.target><lb></lb>differentiam; & quia proportio FC ad KH compo<lb></lb>nitur ex proportione D minus E ad D plus E, & ex <lb></lb>ratione G plus M ad G minus M, ſeu ex ratione D <lb></lb>plus E ad R, ergo FC ad KH eamdem rationem ha<lb></lb>bet quam D minus E ad R, & reperta S media pro<lb></lb>portionali inter D minus E, & R erit FC ad CI, vt D <lb></lb>minus E ad S, quare factum eſt, quod propoſitum̨ <lb></lb>fuerat. </s> </p> <p type="margin"> <s id="s.002590"><margin.target id="marg677"></margin.target>Bib. noſtro <lb></lb>De vi per<lb></lb><gap></gap>cuſſionis pr. <lb></lb>92.</s> </p> <p type="margin"> <s id="s.002591"><margin.target id="marg678"></margin.target><gap></gap> 239.</s> </p> <p type="margin"> <s id="s.002592"><margin.target id="marg679"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002593"><emph type="center"></emph>PROP. CCXLI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002594"><emph type="center"></emph><emph type="italics"></emph>Datis duobus ſolidis æqualibus, eiuſdemque figuræ, ſed inæ<lb></lb>qualium grauitatum, præcognitarum, & dato quoque <lb></lb>pondere molis fluidi leuioris æqualis ſolidis demerſis: re<lb></lb>perire proportionem velocitatum quibus deſcendunt in <lb></lb>eodem fluido.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002595">SInt duæ moles ſolidæ æquales eiuſdemque figu<lb></lb>ræ AC, & GI, ſed inæqualiter graues, v. g. AC <lb></lb>ſit aurum, GI verò ſtannum, & facilitatis gratia in<lb></lb>telligantur eſſe parallelepipeda æquè alta, & æqua<lb></lb>lium baſium, & ambo in aqua EHLX demerſa <expan abbr="com-parẽtur">com<lb></lb>parentur</expan> cum æqualibus, ſimilibuſque parallelepipe<lb></lb>dis aqueis collateralibus DF, & KM cum quibus ſi<lb></lb>phones conſtituere intelligantur, tunc recta NO <expan abbr="cõ-iungens">con<lb></lb>iungens</expan> centra grauitatum auri AC, & aquæ DF li<lb></lb>bram conſtituet, quæ bifariam ſecta erit in centro, <lb></lb>ſeu fulcimento P, propter æqualitatem, & ſimilitudi<lb></lb>nem prædictorum corporum AC, DF ab eiſdem pla<lb></lb><arrow.to.target n="marg680"></arrow.to.target><lb></lb>nis horizontalibus comprehenſorum, eiuſdemquę <lb></lb>libræ centrum grauitatis ſit T, vnde patet, quod PT <lb></lb>eſt longitudo penduli à quo oritur impetus deſcen-<pb pagenum="492" xlink:href="010/01/500.jpg"></pb><arrow.to.target n="marg681"></arrow.to.target><lb></lb>ſus auri in aqua. </s> <s id="s.002596">Non ſecus <expan abbr="ſtannũ">ſtannum</expan> GI, & aqua KM <lb></lb>ei æqualis conſtituent libram QR radiorum <expan abbr="æqualiũ">æqualium</expan> <lb></lb>cuius centrum grauitatis ſit V, vnde SV erit longitu<lb></lb>do penduli, quod determinat impetum deſcenſus <lb></lb>ſtanni in aqua; & quia quatuor parallelepipeda AC, <lb></lb>DF, GI, KM æqualia ſunt inter ſe, ęquè alta, ſuper æ<lb></lb>qualibus baſibus, ergo duæ libræ NO, & QR æqua<lb></lb>les ſunt, & radiorum æqualium, atque in eorum ter<lb></lb>minis N, & Q ſuſpenduntur duo inæqualia pondera <lb></lb>aurum ſcilicèt AC, & ſtannum GI, atque in terminis <lb></lb>O, R ſuſpenduntur duo alia pondera ęqualia inter ſe, <lb></lb><figure id="id.010.01.500.1.jpg" xlink:href="010/01/500/1.jpg"></figure><lb></lb>ſed prioribus leuiora, ſcilicèt duæ <lb></lb>aquæ moles DF, & KM, & cognita <lb></lb>ſupponuntur quatuor prædicta <expan abbr="põ-dera">pon<lb></lb>dera</expan>; modò vt ſumma <expan abbr="põderum">ponderum</expan> GI, <lb></lb>& KM ad eorum differentiam ita fi<lb></lb>at ſumma ponderum AC, & DF ad <lb></lb>pondus Z, reperiaturque pondus Y <lb></lb>medium proportionale inter diffe<lb></lb>rentiam ponderum AC, DF, & pon<lb></lb><arrow.to.target n="marg682"></arrow.to.target><lb></lb>dus Z; tunc patet, quod impetus <lb></lb>quo libra NO flecti debet ad impetum quo reuolui<lb></lb>tur libra QR eamdem proportionem habebit, quam <lb></lb>differentia ponderum AC, & DF ad <expan abbr="põdus">pondus</expan> Y; & quia <lb></lb>prædicta corpora conſtituunt ſiphones æquè altos, & <lb></lb>æquè amplos, propterea quod prædicta corpora æ<lb></lb>qualia, & ſimilia ſunt inter ſe, ergo nulla alia de cau<lb></lb><arrow.to.target n="marg683"></arrow.to.target><lb></lb>ſa velocitas in prædictis ſiphonibus variari poteſt <lb></lb>præterquam à natura ipſorum <expan abbr="pendulorũ">pendulorum</expan> PT, & SV; <pb pagenum="493" xlink:href="010/01/501.jpg"></pb><arrow.to.target n="marg684"></arrow.to.target><lb></lb>quare manifeſtum eſt, quod velocitas deſcenſus auri <lb></lb>AC in aqua ad velocitatem deſcenſus ſtanni GI iņ <lb></lb>eadem aqua eamdem proportionem habebit, quam̨ <lb></lb>differentia ponderum AC, DF ad pondus Y, & hoc <lb></lb>erat quæſitum. </s> </p> <p type="margin"> <s id="s.002597"><margin.target id="marg680"></margin.target>Ca. 2.pr.10.</s> </p> <p type="margin"> <s id="s.002598"><margin.target id="marg681"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002599"><margin.target id="marg682"></margin.target>Prop. 140.</s> </p> <p type="margin"> <s id="s.002600"><margin.target id="marg683"></margin.target>Ex pr 227. <lb></lb>& 228.</s> </p> <p type="margin"> <s id="s.002601"><margin.target id="marg684"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002602">Et hinc patet neceſſitas quare ſolida ęqualia mo<lb></lb>le, ſed inæqualiter grauia licèt æquè velocia ex ſui <lb></lb>natura ſint (ſcilicèt in vacuo) <expan abbr="debẽt">debent</expan> tamen inæqua<lb></lb>libus velocitatibus in medijs fluidis deſcendere. </s> </p> <p type="main"> <s id="s.002603"><emph type="center"></emph>PROP. CCXLII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002604"><emph type="center"></emph><emph type="italics"></emph>Præterea idem ſolidum in mcdio fluido rariori, & minus <lb></lb>ponderoſo citiùs deſcendet, quàm in grauiori fluido, ſi ta<lb></lb>men vtroque fluido ſolidum grauius ſpecie fuerit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002605">SInt duo fluida DF grauius, & KM leuius, & iņ <lb></lb>vtroque immergatur idem ſolidum AC vtroque <lb></lb>fluido grauius; dico, quod AC velocius deſcendet in <lb></lb>KM, quam in DF; ſint vt prius moles, & figuræ paral<lb></lb>lelepipedæ æquales, & horizonta<lb></lb><figure id="id.010.01.501.1.jpg" xlink:href="010/01/501/1.jpg"></figure><lb></lb>liter diſpoſitæ cum æqualibus flui<lb></lb><arrow.to.target n="marg685"></arrow.to.target><lb></lb>dorum parallelepipedis. </s> <s id="s.002606">Quia, vt di<lb></lb>ctum eſt <expan abbr="cõſtituuntur">conſtituuntur</expan> duo ſiphones, <lb></lb>& duæ libræ æquales, & radiorum̨ <lb></lb>æqualium NO, & QR, quarum cen<lb></lb>tra grauitatum T, & V; & ſummą <lb></lb><arrow.to.target n="marg686"></arrow.to.target><lb></lb>ponderum AC, & DF ad horum dif<lb></lb>ferentiam eamdem proportionem̨ <lb></lb>habet quàm radius libræ PN ad <expan abbr="pẽ-duli">pen<lb></lb>duli</expan> longitudinem PT; idemque <expan abbr="dicẽdum">dicendum</expan> in reliqua <lb></lb>libra QR; & eidem ponderi AC additis, & ablatis <pb pagenum="494" xlink:href="010/01/502.jpg"></pb><arrow.to.target n="marg687"></arrow.to.target><lb></lb>inæqualibus ponderibus DF, & KM, erit ſumma eiuſ<lb></lb>dem ponderis AC, & grauioris fluidi DF maior <expan abbr="quã">quam</expan> <lb></lb>ſumma ponderis AC, & leuioris KM, at differentią, <lb></lb>ſeu exceſſus ponderis AC ſupra DF minor erit diffe<lb></lb>rentia ponderum AC, & KM, ergo maior ſumma <expan abbr="põ-derum">pon<lb></lb>derum</expan> AC, & DF ad minorem ſummam ponderum̨ <lb></lb>AC, & KM maiorem proportionem habebit, quam̨ <lb></lb>minor differentia ponderum AC, DF ad <expan abbr="differentiã">differentiam</expan> <lb></lb>maiorem ponderum AC, & KM; & permutando ſum<lb></lb>ma ponderum AC, & DF ad eorum differentiam, ſeu <lb></lb><arrow.to.target n="marg688"></arrow.to.target><lb></lb>libræ radius PN ad penduli longitudinem PT maio<lb></lb>rem proportionem habet, quam ſumma ponderum̨ <lb></lb>AC, & KM ad eorum differentiam, ſeu quam libræ <lb></lb>radius SQ ad pendulum SV, ſuntque librarum æqua<lb></lb>lium radij PN, SQ æquales inter ſe, igitur <expan abbr="pendulũ">pendulum</expan> <lb></lb>SV maioris longitudinis eſt, quàm PT, & ideò cele<lb></lb>rius deſcendet AC in rariori fluido KM quam in gra<lb></lb><arrow.to.target n="marg689"></arrow.to.target><lb></lb>uiori DF. </s> </p> <p type="margin"> <s id="s.002607"><margin.target id="marg685"></margin.target>Pr. 241.</s> </p> <p type="margin"> <s id="s.002608"><margin.target id="marg686"></margin.target>Pr. 238.</s> </p> <p type="margin"> <s id="s.002609"><margin.target id="marg687"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002610"><margin.target id="marg688"></margin.target>Pr. 238.</s> </p> <p type="margin"> <s id="s.002611"><margin.target id="marg689"></margin.target>De vi per<lb></lb>cuſſionis <lb></lb>Pr. 92.</s> </p> <p type="main"> <s id="s.002612">Et hìc pariter poteſt reperiri proportio velocita<lb></lb>tum <expan abbr="eiuſdẽ">eiuſdem</expan> ſolidi in duobus fluidis inæqualiter gra<lb></lb>uibus. </s> </p> <p type="main"> <s id="s.002613"><emph type="center"></emph>PROP. CCXLIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002614"><emph type="center"></emph><emph type="italics"></emph>Duo ſolida æqualia, & inæqualiter grauia ſi ſpecie grauiora <lb></lb>fluidis fuerint, maiori inæqualitate in medio fluido denſio<lb></lb>ri, quàm in rariori, & minùs graui fluido deſcendunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002615">QVod breuitatis gratia ex ipſo calculo collige<lb></lb>mus. </s> <s id="s.002616">Ex tabulis Doctiſſimi Marini Ghetaldi, <lb></lb>atque accuratiſſimi. </s> <s id="s.002617">P. </s> <s id="s.002618">Petiti habentur proportiones <lb></lb>grauitatum ſpecificarum plurium metallorum reſpe-<pb pagenum="495" xlink:href="010/01/503.jpg"></pb><arrow.to.target n="marg690"></arrow.to.target><lb></lb>ctu, aquæ; ſi enim ſumantur tres moles æquales auri, <lb></lb>ſtanni, & aquæ, qualium partium pondus auri fuerit <lb></lb>100. pondus ſtanni erit 39 proximè, & pondus aquæ <lb></lb>erit 5. cum triente. </s> <s id="s.002619">Verùm, ex noſtra inuentione iņ <lb></lb>Academia Experimentali Medicea explorauimus <lb></lb>proportionem ponderis ſpecifici aquæ ad aerem, quæ <lb></lb>fuit vt 1175 ad 1 proximè, igitur qualium partium <lb></lb>alicuius ſphęræ aeris pondus eſt vnius grani, erit <expan abbr="põ-dus">pon<lb></lb>dus</expan> pilæ aqueæ eiuſdem molis 1175 granorum, qua<lb></lb>re pila ſtannea eiuſdem menſuræ erit 8592 <expan abbr="granorũ">granorum</expan>, <lb></lb>at que pila aurea eiuſdem diametri erit 21406 gra<lb></lb>norum. </s> <s id="s.002620">His poſitis facto calculo, vt antepræmiſſą <lb></lb>propoſitio perſcribit, reperitur proportio <expan abbr="velocitatũ">velocitatum</expan> <lb></lb>auri, & ſtanni in aqua vt 10 ad 9 proximè; ſed in ae<lb></lb>re ſi velocitas auri fuerit 21405 erit velocitas ſtanni <lb></lb>21404 ferè; & hinc patet quare in aere corpora inę<lb></lb>qualiter grauia vt aurum, & ſtannum vniformi, & æ<lb></lb>quali ferè velocitate deſcendunt, in aqua verò inſi<lb></lb>gni exceſſu velocitas auri ſuperat ſtanni celeritatem <lb></lb>in deſcenſu. </s> </p> <p type="margin"> <s id="s.002621"><margin.target id="marg690"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002622">Sed hìc ſummoperè animaduertendum eſt, quod <lb></lb>ſuperiùs expoſita theoria verificatur in paruis altitu<lb></lb>dinibus, & in principijs deſcenſuum, non verò iņ <lb></lb>prolixiori motu, propterea quod, vt mox declarabi<lb></lb>mus, ab alia noua cauſa valdè alterantur prædictæ <lb></lb>proportiones velocitatum grauium deſcendentium, <lb></lb>pro cuius intelligentia præmittuntur hæc. </s> </p> <p type="main"> <s id="s.002623"><emph type="center"></emph>PROP. CCXLIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002624"><emph type="center"></emph><emph type="italics"></emph>Motus deſcenſus cuiuslibet grauis in fluido ſuccesſiuè retar-<emph.end type="italics"></emph.end><pb pagenum="496" xlink:href="010/01/504.jpg"></pb><arrow.to.target n="marg691"></arrow.to.target><lb></lb><emph type="italics"></emph>datat, & incrementa velocitatis eius tandem ad æqua<lb></lb>bilitatem reduci debent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="margin"> <s id="s.002625"><margin.target id="marg691"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002626">SIt vas NX omninò vacuum, & NZ ſit repletum a<lb></lb>liquo fluido aereo v.g. & intelligantur particu<lb></lb>læ temporis inter ſe æquales AB, BD, DG, GK, KN, <lb></lb>& in primo tempore AB graue deſcendens in vacuo <lb></lb>acquirat gradum impetus BC, in ſequenti verò tem<lb></lb>pore BD præter gradum DE æqualem BC, quem iņ <lb></lb>priori tempore acquiſierat, & in eo conſeruatur, ac<lb></lb>quiret quoque nouum gradum̨ <lb></lb><figure id="id.010.01.504.1.jpg" xlink:href="010/01/504/1.jpg"></figure><lb></lb>impetus EF æqualem priori BC, <lb></lb>pariterque in tertio temporę <lb></lb>prioribus æquali DG, præter im<lb></lb>petum GH ab eo acquiſitum iņ <lb></lb>tempore pręcedenti AD, acqui<lb></lb>rit nouum gradum impetus HI <lb></lb>æqualem prioribus EF, vel BC, <lb></lb>tandem in tempore GK præter <lb></lb>gradum KL, quem prius acquiſierat, denuò ei ſuper<lb></lb>additur nouus gradus impetus LM æqualis priori <lb></lb>BC; & hoc procùl dubio contingit ablatis omnibus <lb></lb>impedimentis in vaſe NX: at ſi motus ſolidi ſup<lb></lb>ponatur in medio fluido NZ fieri, ibi duplici nomi<lb></lb>ne gradus velocitatum acquirendi debilitari <expan abbr="debẽt">debent</expan>, <lb></lb>primò propter percuſſionem, quam mobile corpori <lb></lb>fluido inferre debet, ſecundò propter reſiſtentiam̨ <lb></lb>machinularum, ſeu glutinis eiuſdem fluidi; neceſsè <lb></lb>ergo eſt, vt quilibet horum graduum impetus vtpo<lb></lb>tè BC non perpetuò <expan abbr="cõſeruetur">conſeruetur</expan> integer, & illibatus, <pb pagenum="497" xlink:href="010/01/505.jpg"></pb><arrow.to.target n="marg692"></arrow.to.target><lb></lb>ſed poſt certum tempus, puta AG, à continuata fluidi <lb></lb>reſiſtentia ſenſim retardante tandem extinguatur, <lb></lb>ſubſequens verò gradus impetus acquiſitus eF <expan abbr="eadẽ">eadem</expan> <lb></lb>ratione extinguetur tempore BK æquali priori AG: <lb></lb>in hiſce verò æqualibus temporibus acquirit mobile <lb></lb>æquales gradus velocitatum, & ab his ſubtrahi de<lb></lb>bent priores illi gradus velocitatum BC, & eF inter <lb></lb>ſe æquales iam extincti, vt dictum eſt, ergo reſidui <lb></lb>gradus velocitatum Gi, & mM æquales <expan abbr="erũt">erunt</expan> inter ſe: <lb></lb>& ſic ſemper contingit in ſubſequenti tempore; <expan abbr="quã-do">quan<lb></lb>do</expan> verò perſeueratidem gradus impetus in mobile, <lb></lb>tunc motus eius æquabilis eſſe debet, ſcilicèt tem<lb></lb>poribus æqualibus percurret ſpatia æqualia, igitur <lb></lb><expan abbr="augmẽtum">augmentum</expan> impetus in mobile in progreſſu ſolius <expan abbr="tẽ-poris">ten<lb></lb>poris</expan> AG augeri poteſt, licèt non vniformi <expan abbr="incremẽ-to">incremen<lb></lb>to</expan>, & poſt tempus AG impetus non amplius creſcit, <lb></lb>& graue motu æquabili fertur, quod erat &c. </s> </p> <p type="margin"> <s id="s.002627"><margin.target id="marg692"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002628"><emph type="center"></emph>PROP. CCXLV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002629"><emph type="center"></emph><emph type="italics"></emph>Si duo corpora æqualia, & inæqualitèr grauia per fluidum <lb></lb>deſcendant prius ad æquabilitatem reducetur leuius cor<lb></lb>pus, quàm grauius.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002630">SInt duæ moles inter ſe æquales, & inæqualiter <lb></lb>graues, eiuſdemque figuræ, ſphæricæ nempè, A <lb></lb>grauior quam B, hæ verò ex ſui natura, ſcilicèt in va<lb></lb>cuo vna, & eadem velocitate ferri debent, quæ ſit V; <lb></lb>ſed duo corpora A, & B inæquali energia medium̨ <lb></lb><arrow.to.target n="marg693"></arrow.to.target><lb></lb>fluidum RSTX percutiunt, impelluntque ſecundùm <lb></lb><arrow.to.target n="marg694"></arrow.to.target><lb></lb>proportionem quam habet vis percuſſiua compoſita <lb></lb>ex vi impetus V, & ex maiori materia, ſeu maſſa cor-<pb pagenum="498" xlink:href="010/01/506.jpg"></pb><arrow.to.target n="marg695"></arrow.to.target><lb></lb>pore a contenta in grauiori corpore <lb></lb><figure id="id.010.01.506.1.jpg" xlink:href="010/01/506/1.jpg"></figure><lb></lb>A ad vim percuſſiuam compoſitam <lb></lb>ex impetu V, & ex minori materia<lb></lb>li ſubſtantia in B contenta; debilior <lb></lb>verò vis percuſſiua ab eadem <expan abbr="cõſi-">conſi<lb></lb></expan><arrow.to.target n="marg696"></arrow.to.target><lb></lb>ſtentia, & glutine eiuſdem fluidi R <lb></lb>T citiùs debilitatur extinguitur que <lb></lb>quàm magis valida vis percuſſiua <lb></lb>igitur energia percuſſiua ſolidi B ci<lb></lb>tiùs ad <expan abbr="æquabilitatẽ">æquabilitatem</expan> reducetur, <expan abbr="quã">quam</expan> <lb></lb>maior vis percuſſiua corporis A. </s> </p> <p type="margin"> <s id="s.002631"><margin.target id="marg693"></margin.target>Prop. 223.</s> </p> <p type="margin"> <s id="s.002632"><margin.target id="marg694"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002633">pr. 27.</s> </p> <p type="margin"> <s id="s.002634"><margin.target id="marg695"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002635"><margin.target id="marg696"></margin.target>Ibid. ex pro. <lb></lb><gap></gap>9. & ex cap. <lb></lb><gap></gap></s> </p> <p type="main"> <s id="s.002636"><emph type="center"></emph>PROP. CCXLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002637"><emph type="center"></emph><emph type="italics"></emph>Si comparentur velocitates corporum æqualium, & inæ<lb></lb>qualitèr grauium propè principium deſcenſus in fluido, <lb></lb>minori inæqualitate feruntur, quàm in progreſſu, & con<lb></lb>tinuatione motus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002638">SInt eadem corpora æqualia, & inæqualitèr gra<lb></lb>uia A, & B; procùl dubio ambo per aliquod <expan abbr="tẽ-pus">tenm<lb></lb>pus</expan> mouentur accelerato motu, nempè eorum ve<lb></lb>locitates ſucceſſiuè augentur, & poſtea ad æquabi<lb></lb><arrow.to.target n="marg697"></arrow.to.target><lb></lb>litatem reducuntur: in illo ergo exiguo tempore iņ <lb></lb>quo <expan abbr="amborũ">amborum</expan> velocitates à quiete ſucceſſiuè <expan abbr="creſcũt">creſcunt</expan>, <lb></lb>ſi progreſſus incrementorum non differant inſigni in<lb></lb>æqualitate, ferè <expan abbr="eadẽ">eadem</expan> velocitate deſcendent, ſcilicèt <lb></lb>percurrent temporibus æqualibus penè ſpatia æqua<lb></lb>lia; at quia leuioris corporis B impetus facilius, & <lb></lb>magis debilitatur, retunditurque, quàm impetus <lb></lb><arrow.to.target n="marg698"></arrow.to.target><lb></lb>grauioris A, igitur propè initium motus exigua dif<lb></lb>ferentia velocitatum reperitur, non ſic in progreſſu <pb pagenum="499" xlink:href="010/01/507.jpg"></pb><arrow.to.target n="marg699"></arrow.to.target><lb></lb>motus, nam poſtquam leuius corpus B ad æquabili<lb></lb>tatem redigitur, continuatur adhuc <expan abbr="incremẽtum">incrementum</expan> im<lb></lb>petus in grauiori ſolido A; totum ergo id, quod au<lb></lb>getur gradus impetus ipſius A creat notabilem ex<lb></lb>ceſſum ſupra illum gradum debilem corporis B <expan abbr="eodẽ">eodem</expan>, <lb></lb>& vniformi gradu impetus excurrentis, quare neceſ<lb></lb>sè eſt, vt propè initium motus parùm differant velo<lb></lb>citates grauium A, & B, ſcilicèt fiant ſecundùm pro<lb></lb><arrow.to.target n="marg700"></arrow.to.target><lb></lb>portiones ſuperiùs expoſitas, & poſtea in progreſſu <lb></lb>motus multò magis inter ſe differant. </s> <s id="s.002639">quod profectò <lb></lb>euincitur ex eo, quòd ſi prædicta inſignis inæqualitas <lb></lb>velocitatum, quę in progreſſu <expan abbr="motuũ">motuum</expan> eorum obſer<lb></lb>uatur, eſſet propria, & naturalis horum corporum <expan abbr="sẽ-per">sem<lb></lb>per</expan> in eodem fluido in eadem proportione fieri de<lb></lb>beret, ſcilicèt in quibuslibet temporibus æqualibus <lb></lb>moueri deberent proportionalibus velocitatibus, & <lb></lb>ſic medulla ſambuci v.g. quæ in decem minutis <expan abbr="ſecũ-dis">ſecun<lb></lb>dis</expan> horarijs pertranſit ſemiſſem itineris exacti à pila <lb></lb>marmorea, vt refert Merſennus, etiam in vno minuto <lb></lb>ſecundo illa medietatem ſpatij huius pertranſiret, <lb></lb>quod euidentèr falſum eſt. <lb></lb><arrow.to.target n="marg701"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002640"><margin.target id="marg697"></margin.target>Pro. 243. & <lb></lb>244.</s> </p> <p type="margin"> <s id="s.002641"><margin.target id="marg698"></margin.target>Pro. 245.</s> </p> <p type="margin"> <s id="s.002642"><margin.target id="marg699"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="margin"> <s id="s.002643"><margin.target id="marg700"></margin.target>Prop. 241. <lb></lb>& 243.</s> </p> <p type="margin"> <s id="s.002644"><margin.target id="marg701"></margin.target>Reſponde<lb></lb>tur experi<lb></lb>mento <expan abbr="Mer-ſẽi">Mer&shy;<lb></lb>ſeni</expan>, & alio<lb></lb>rum.</s> </p> <p type="main"> <s id="s.002645">Hinc reſoluere poſſumus difficultatem ab experi<lb></lb>méto Merſenni deſumptam; is enim ſumpſit duas pi<lb></lb>las æquales, vnam plumbeam, alteram argillaceam, <lb></lb>& in profunditate trium pedum aquæ inſumpſit <expan abbr="plũ-">plum<lb></lb><arrow.to.target n="marg702"></arrow.to.target><lb></lb>bum</expan> vnum minutum <expan abbr="ſecũdum">ſecundum</expan>, argillacea verò quin<lb></lb>que minuta ſecunda, noſter verò calculus minorem̨ <lb></lb>inæ qualitatem efficit, dum enim pila plumbea <expan abbr="deſcẽ-dit">deſcen<lb></lb>dit</expan> ſpatium aliquod in vno minuto ſecundo, argilla-<pb pagenum="500" xlink:href="010/01/508.jpg"></pb><arrow.to.target n="marg703"></arrow.to.target><lb></lb>cea inſumere debet duo minuta ſecunda tantùm, quę <lb></lb>varietas pendere videtur ex eo, quod velocitates <lb></lb>fuerunt à Merſenno obſeruatæ in valdè prolixo ſpa<lb></lb>tio, vbi medij conſiſtentia, & gluten valdè <expan abbr="alterãt">alterant</expan>, & <lb></lb><expan abbr="augẽt">augent</expan> inæqualitates velocitatum, quæ ſi propè ini<lb></lb>tium motus obſeruatæ fuiſſent, procùl dubio non ha<lb></lb>buiſſent quintuplam, ſed tantummodò duplam pro<lb></lb>portionem. </s> </p> <p type="margin"> <s id="s.002646"><margin.target id="marg702"></margin.target>Hydraul. <lb></lb>fol. 116.</s> </p> <p type="margin"> <s id="s.002647"><margin.target id="marg703"></margin.target>Cap. 11. gra<lb></lb>uia in fluido <lb></lb>velocitati<lb></lb>bus inæqua<lb></lb>libus ferri <lb></lb>debere.</s> </p> <p type="main"> <s id="s.002648">Hinc quoque deducitur imperitia eorum, qui dum <lb></lb>experiri volunt, an corpora inęqualiter grauia <expan abbr="deſcẽ-dant">deſcen<lb></lb>dant</expan> inæqualibus velocitatibus, putant hoc fieri de<lb></lb>bere non in exiguis, ſed in prolixis deſcenſibus, & <lb></lb>ideò obſeruant inæqualitates velocitatum corporum <lb></lb>in aere deſcendentium ab altiſſimis turribus vbi ve<lb></lb>locitates plumbi, & argillæ valdè differunt inter ſe, <lb></lb>cùm tamen in breuioribus altitudinibus nullo ſenſu <lb></lb>diſtingui poſſint <expan abbr="eorũ">eorum</expan> inæqualitates, cùm ambo <expan abbr="eodẽ">eodem</expan> <lb></lb>tempore ferri videantur. </s> <s id="s.002649">Et antequam vlterius pro<lb></lb>cedamus, afferemus duas experientias contra negan<lb></lb>tes motum acceleratum ſolidorum corporum intra a<lb></lb>quam; & primò in deſcenſu pilam plumbeam feta e<lb></lb>quina ſuſpendi, <expan abbr="habẽtem">habentem</expan> infernè <expan abbr="acũ">acum</expan> <expan abbr="infixã">infixam</expan>, eamque <lb></lb>demiſi intra aquam in diuerſis altitudinibus à fundo <lb></lb>cera incruſtato, <expan abbr="tũc">tunc</expan> vidi acum profundius ceram pe<lb></lb>netrare quò à ſublimiori altitudine pila decidebat. <lb></lb></s> <s id="s.002650">in aſcenſu verò ſumpſi leuiſſimum calamum <expan abbr="anſerinũ">anſerinum</expan>, <lb></lb>eiuſque infimum orificium fruſto plumbi perfectè <lb></lb>obturaui, atque bacillo demerſi calamum directè in<lb></lb>fra aquam, in maiori tamen profunditate, quàm eius <pb pagenum="501" xlink:href="010/01/509.jpg"></pb><arrow.to.target n="marg704"></arrow.to.target><lb></lb>naturalis grauitas exigebat, tunc amoto bacillo ca<lb></lb>lamus directè, & perpendicularitèr horizonti aſcen<lb></lb>dendo extra aquam proſilijt; notaui ergo <expan abbr="altitudinẽ">altitudinem</expan> <lb></lb>ſaltus, poſtea profundiùs calamum infra a quam de<lb></lb>preſſi, & notaui, remoto bacillo, ſemper <expan abbr="prolixiorẽ">prolixiorem</expan> <lb></lb>ſaltum ſupra aquam calamum effeciſſe, prout à maio<lb></lb>ri profunditate eius aſcenſus initium ſumebat; modò <lb></lb>quia non alia de cauſa calamus ſupra aquam poſilie<lb></lb>bat, quam ob impetum acquiſitum ab ipſo in aſcen<lb></lb>ſu per aquæ profunditatem, patet quod ſaltus altior <lb></lb>produci debuit à vehementiori velocitate eiuſdem <lb></lb>calami acquiſita in eius aſcenſu prolixiori. </s> </p> <p type="margin"> <s id="s.002651"><margin.target id="marg704"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002652"><emph type="center"></emph><emph type="italics"></emph>De Vacui Necesſitate.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002653"><emph type="center"></emph>CAP. XII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002654">PRæclarè mihi Ariſtoteles dixiſſe videtur, <expan abbr="Phyſicũ">Phyſicum</expan> <lb></lb>de vacuo agere debere, quia nempè nè <expan abbr="dũ">dum</expan> ſcitu <lb></lb>iucundum eſt, an detur, & quomodo, & quid ſit va<lb></lb>cuum, ſed etiam vtilis eſt huiuſmodi cognitio, vt in<lb></lb>telligantur innumeræ naturales operationes, & vt <lb></lb>percipiatur quomodo fiant motus nedùm quos in va<lb></lb>cuo fieri poſſe ſuppoſuimus, ſed etiam eos, qui iņ <lb></lb>fluido fiunt. </s> </p> <p type="main"> <s id="s.002655">Vt verò methodicè procedamus, primò <expan abbr="declaran-dũ">declaran<lb></lb>dum</expan> eſt, quid nomine vacui, & inanis intelligamus, ſe<lb></lb>cundò quot modis vſurpari, & concedi poſſit, tertiò <lb></lb>examinabimus ratiocinia, & argumenta eorum, qui <lb></lb>vacuum è rerum natura omninò tollunt, & randem̨ <lb></lb>propriam <expan abbr="ſententiã">ſententiam</expan> pro viribus confirmare nitemur. <pb pagenum="502" xlink:href="010/01/510.jpg"></pb><arrow.to.target n="marg705"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002656"><margin.target id="marg705"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002657"><emph type="center"></emph>PROP. CCXLVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002658"><emph type="center"></emph><emph type="italics"></emph>Si vacuum ſpatium ponatur entitas extenſa, & incorpo<lb></lb>rea debet concedi infinita æterna, & increata.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002659">EVidentiſſima profectò eſt nedum exiſtentia na<lb></lb>turæ corporeæ, ſed <expan abbr="etiã">etiam</expan> præcipua eius affectio <lb></lb>in definitione tradita. </s> <s id="s.002660">Dicimus enim corpus eſſę <lb></lb>ſubſtantiam triplicem extenſionem, ſeu <expan abbr="dimenſionẽ">dimenſionem</expan> <lb></lb>habentem, & ſpatium, quod à prædicto corpore oc<lb></lb>cupatur plenum vocare ſolemus, hoc porrò præiu<lb></lb>dicium pendet ex eo, quod in interna alicuius vaſis <lb></lb>capacitate poni poteſt modò terra, modò aqua, aut <lb></lb>aliud corpus fluidum, ſiue denſum, & dicimus prædi<lb></lb>ctam capacitatem vaſis repleri modò ab vno, modo <lb></lb>ab altero corporum prædictorum. </s> <s id="s.002661">Hinc concipimus <lb></lb>capacitatem <expan abbr="illã">illam</expan> vaſis eſſe quid diſtinctum, & diuer<lb></lb>ſum à corporibus id continentèr replentibus. </s> </p> <p type="main"> <s id="s.002662">Iam ex præ concepta pleni natura, & aſſectionę <lb></lb>ſtatim percipimus vacui, ſeu inanis naturam in eo <expan abbr="cõ-ſiſtere">con<lb></lb>ſiſtere</expan>, vt prędicta vaſis capacitas careat omninò cor<lb></lb>pore quolibet à quo repleri poterat. </s> <s id="s.002663">Hoc verò va<lb></lb>cuum duplici modo concipi poteſt, aut enim ſuppo<lb></lb>nitur entitas quædam incorporea non tamen indiui<lb></lb>ſibilis, ſed extenſa, & occupans triplici dimenſione <lb></lb>vniuerſam vaſis prędicti capacitatem. </s> <s id="s.002664">Alio modo <expan abbr="cõ-cipi">con<lb></lb>cipi</expan> poteſt vt mera priuatio corporum, & abſolutè <lb></lb>nihilum. </s> <s id="s.002665">priori modo conceditur à Pythagoricis, De<lb></lb>mocrito, Epicuro, & ab alijs, ratio verò quæ hanc <lb></lb>ſententiam ſuadere, & confirmare videtur, eſt quią <lb></lb>capacitas illa vaſis per ſe ſumpta, à qua ſiue re ipſa, <pb pagenum="503" xlink:href="010/01/511.jpg"></pb><arrow.to.target n="marg706"></arrow.to.target><lb></lb>ſiue mente remoueatur corpus, idipſum replens, & <lb></lb>occupans, retinere quoque videtur eaſdem dimen<lb></lb>ſiones, ſeu potius æquales dimenſionibus corporis id <lb></lb>replentis, & ſic verificari aiunt corporeas dimenſi<lb></lb>ones præcisè congruere ſpatij illius dimenſionibus; <lb></lb>quia verò concipere ſe non poſſe profitentur capaci<lb></lb>tatem illam, ſeu ſpatium dimenſionibus omninò pri<lb></lb>uatum, propterea ipſum entitatem aliquam haberę <lb></lb>licet incorpoream concedunt; conſequenter admit<lb></lb>tunt nedùm ſpatiola illa à particulis corporum com<lb></lb>prehenſa, ſed etiam integra ſpatia ſe parata extra <expan abbr="hũc">hunc</expan> <lb></lb>mundum ſenſibilem. </s> <s id="s.002666">Sed animaduerſione dignum eſt <lb></lb>prædictum ſpatium inane ſeparatum admitti debe<lb></lb>re vndique infinitè expanſum, & extenſum, quia <expan abbr="nõ">non</expan> <lb></lb>eſt maior ratio quare propè extimam mundi corpo<lb></lb>ream ſuperficiem concedatur, & non vlterius in lo<lb></lb>cis magis, ac magis à prædicta mundi ſuperficie ſe<lb></lb>paratis, diſtantibuſque. </s> <s id="s.002667">Præterea concedenda quo<lb></lb>que eſt huiuſmodi natura, ſeu entitas incorporea ſpa<lb></lb>tialis nedum infinita, ſed etiam increata, & æterna; <lb></lb>quandoquidem ante mundi creationem exiſtebant <lb></lb>prædictæ dimenſiones ſpatiales, ſcilicèt olim adhùc <lb></lb>exiſtebat longitudo, latitudo, & profunditas incor<lb></lb>porea, quod quidem libentiſſimè abſque vlla repu<lb></lb>gnantia Antiqui concedebant, vnà cum totius mundi <lb></lb>exiſtentia ab æterno; hoc verò mirum quantum or<lb></lb>thodoxos huius ſententiæ aſſertores torqueat, cùm̨ <lb></lb>cogantur ſuſtinere entitatem realem, qualis eſt illą <lb></lb>ſpatialis, nedùm inſinitè extenſam, ſed etiam ab ęter-<pb pagenum="504" xlink:href="010/01/512.jpg"></pb><arrow.to.target n="marg707"></arrow.to.target><lb></lb>no præexiſtentem, & independentem à Deo Crea<lb></lb>tore. </s> <s id="s.002668">Ideò alij cautiores non verentur concedere en<lb></lb>titatem illam ſpatialem nedùm finitam, ſed etiam à <lb></lb>Deo ab initio mundi creatam. </s> <s id="s.002669">Ijs verò opponi ſolet, <lb></lb>quod vltra confinium mundi, eiuſque ſpatij incorpo<lb></lb>rei, & ante mundum conditum remoueri nequit <expan abbr="cõ-ceptus">con<lb></lb>ceptus</expan> extenſionis incorporeæ intra, & extra ſitum̨ <lb></lb>in quo modò mundus cum eius ſpatio conditus eſt, <lb></lb>cumque prædictę dimenſiones non eſſe nihilum fate<lb></lb>antur, igitur neceſſariò admitti debet ante mundum <lb></lb>conditum ab æterno, & extra mundum ſenſibilem̨ <lb></lb>vbique eadem entitas ſpatialis. </s> <s id="s.002670">Ex quo proindè ſit, <lb></lb>vt ſpatium inane nullo modo admittendum ſit, vel ſi <lb></lb>concedatur, nullam entitatem incorpoream haberę <lb></lb>fatendum eſt. </s> <s id="s.002671">Eatenùs igitur admitti vacuum pote<lb></lb>rit, quatenùs abſoluta priuatio, & nihilum concedi<lb></lb>tur. </s> <s id="s.002672">Et in hoc ſe uſu an reuera admitti poſſit, & de<lb></lb>beat in natura videbimus. </s> </p> <p type="margin"> <s id="s.002673"><margin.target id="marg706"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002674"><margin.target id="marg707"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002675">Et primò examinari debent rationes Ariſtotelis <lb></lb>contra vacui poſitionem, & pro pleni exiſtentia, quæ <lb></lb>habentur 4. phyſic. </s> <s id="s.002676">cap. 6. 7. & 8. </s> </p> <p type="main"> <s id="s.002677"><emph type="center"></emph>PROP. CCXLVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002678"><emph type="center"></emph><emph type="italics"></emph>Soluuntur argumenta Ariſtotelis contra vacuum adducta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002679">COntra Antiquos, qui ponebant vacuum, vt cor<lb></lb>porum motus in natura fieri poſſent, ait Ariſt. <lb></lb><emph type="italics"></emph>Etiam ſi nullum ſit ſpatium ſeparabile præter corpora, quæ <lb></lb>mouentur motus fieri poterit, quod in continuorum ſicut, & <lb></lb>humidorum conuerſionibus patet.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002680">At huiuſmodi inſtantia videtur nedùm <expan abbr="inſufficiẽs">inſufficiens</expan>, <pb pagenum="505" xlink:href="010/01/513.jpg"></pb><arrow.to.target n="marg708"></arrow.to.target><lb></lb>ſed etiam nullius roboris, quia licet in motu circu<lb></lb>lari Rotæ ſolidæ <expan abbr="nõ">non</expan> appareat neceſſitas vacui, nihilo<lb></lb>minus præcipua difficultas eſt non de motu circula<lb></lb>ri, ſed de motu directo, vel per lineas curuas irregu<lb></lb>lares in fluido, in quo ſenſu non conſtat, neque de<lb></lb>monſtratur partes fluidi excurrere intra alias poſſe, <lb></lb>abſque eo quod mutuò ſe ſe confricent, inuertantur, <lb></lb>& inter ſe innumeras exiguas vacuitates admittant. <lb></lb></s> <s id="s.002681">imò in poſtrema parte huius capitis oſtendemus ne<lb></lb>ceſſariam eſſe vacui admiſſionem, ad hoc, vt fluidum, <lb></lb>vel <expan abbr="dẽſum">denſum</expan> corpus per fluidum moueri queat; ſed mo<lb></lb>dò ſatis eſt oſtendiſſe non eſſe euidens, nec demon<lb></lb>ſtratum fuiſſe, quod in motu facto in fluidis vacuum <lb></lb>neceſſario non exigatur. </s> </p> <p type="margin"> <s id="s.002682"><margin.target id="marg708"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002683">Secundò, <emph type="italics"></emph>Vacuum non eſt cauſa motus, ſed Natura, ergo <lb></lb>vacuum non datur.<emph.end type="italics"></emph.end></s> <s id="s.002684"> Cui reſponderi poteſt, neminem, <lb></lb>niſi planè delirum, ac ſtolidum, ſomniaſſe <expan abbr="vacuũ">vacuum</expan>, ſci<lb></lb>licèt nihilum, cauſam poſitiuam <expan abbr="efficiẽtem">efficientem</expan> motus eſ<lb></lb>ſe. </s> <s id="s.002685">Dixerunt certè Antiqui motum produci à natura, <lb></lb>ſiue à qualibet cauſa externa impulſiua, ſed requiri <lb></lb>vacuum veluti locus in quo motus fieri poſſit, igitur <lb></lb>Ariſtotelis <expan abbr="argumẽtum">argumentum</expan> nil officit vacui aſſertoribus. </s> </p> <p type="main"> <s id="s.002686">Tertiò ait: quod <emph type="italics"></emph>accidit dicentibus vacuum eſſe neceſ-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg709"></arrow.to.target><lb></lb><emph type="italics"></emph>ſarium, vt motus ſit contrarium potiùs, nam dato vacuo nil <lb></lb>in eo moueri poſſet, quia non eſt quo magis, aut minus mouea<lb></lb>tur, quod namque vacuum eſt, caret omni differentia<emph.end type="italics"></emph.end>, ſcili<lb></lb>cèt non habet ſursùm, neque deorsùm, nec ante, nec <lb></lb>retro, &c. </s> <s id="s.002687">Cui reſponderi poteſt, quod motus, quate<lb></lb>nus talis eſt, dicit ſolummodò migrationem, & tran-<pb pagenum="506" xlink:href="010/01/514.jpg"></pb><arrow.to.target n="marg710"></arrow.to.target><lb></lb>ſitum, qui fieri poteſt nedum in fluido, ſed etiam in <lb></lb>ſpatio inani, per quamlibet directionem, quam im<lb></lb>preſſa vis motiua deſignauerit, ergo licèt in vacuo di<lb></lb>rectiones infinitę in eo deſignabiles non ſint deter<lb></lb>minatæ, nec habeant nomina propria, non proindè <lb></lb>ſequitur non poſſe in eo deſignari, & ſic effici motus <lb></lb>per quamcumque directionem. </s> </p> <p type="margin"> <s id="s.002688"><margin.target id="marg709"></margin.target>Cap. 8.</s> </p> <p type="margin"> <s id="s.002689"><margin.target id="marg710"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002690">Quartò ſic ait, <emph type="italics"></emph>mouentur proiecta ex eo quod quando <expan abbr="nõn">non</expan> <lb></lb>tanguntur, tunc ob anthiprestaſim, aut quia pulſus aer mo<lb></lb>tu pellit celeriori, quàm ſit ea latio pulſi, at in vacuo nihil <lb></lb>horum eſſe potest, neque fit vt quicquam feratur niſi vt <lb></lb>quod vehitur.<emph.end type="italics"></emph.end></s> <s id="s.002691"> Vt pateat in efficacia argumenti Ariſto<lb></lb>telis, concedatur, quod in vacuo ob carentiam medij <lb></lb>fluidi proiectio fieri non poſſit, non inde ſequitur va<lb></lb>cuum minimè dari poſſe, nam remaneret ſolummodò <lb></lb>motus naturalis in vacuo, & hic <expan abbr="vnã">vnam</expan> cum proiectitio <lb></lb>in pleno fluido fieri poſſet, neque Ariſtot. oſtendit <lb></lb>hoc eſſe abſurdum. </s> <s id="s.002692">Omitto falſiſſimum eſſe proiecta <lb></lb><arrow.to.target n="marg711"></arrow.to.target><lb></lb>moueri à medio fluido poſtquam à proijciente deſe<lb></lb>runtur, ſed à vi motiua ipſis communicata promoue<lb></lb>ri, vnde ſequitur, quòd benè in ſpatio vacuo proie<lb></lb>ctio fieri poſſet multò meliùs quàm in ſpatio pleno <lb></lb>fluido, cum vis motiua proiecto impreſſa nullo pacto <lb></lb>impediatur ab inani ſpatio, ſicuti à medio fluido <expan abbr="sũ-mopere">sun<lb></lb>mopere</expan> impeditur retardaturque. </s> </p> <p type="margin"> <s id="s.002693"><margin.target id="marg711"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002694">c 3. & 4.</s> </p> <p type="main"> <s id="s.002695">Quintò, <emph type="italics"></emph>nemo dicere potest propter quid quod mouetur <lb></lb>stabit alicubi, cur enim magis hic, <expan abbr="quã">quam</expan> alibi; quare aut quie<lb></lb>ſcat, aut in infinitum feratur neceſsè eſt, ſi non <expan abbr="potẽtius">potentius</expan> quic<lb></lb>piam impedierit.<emph.end type="italics"></emph.end></s> <s id="s.002696"> Reſponderi poteſt optimè procede-<pb pagenum="507" xlink:href="010/01/515.jpg"></pb><arrow.to.target n="marg712"></arrow.to.target><lb></lb>re argumentum ex eo quod non datur cauſa, nec ra<lb></lb>tio quare impetus ſemel impreſſus mobili retarde<lb></lb>tur, extinguaturque, & ſic ſequitur, quod nullibi ſta<lb></lb>bit, aut quieſcet, ſed in infinitum mouebitur in va<lb></lb>cuo, niſi aliud corpus externum motum eius impe<lb></lb>diat. </s> <s id="s.002697">nec video quid incommodi ex hoc ſequatur, <lb></lb>vt proinde hac de cauſa ſpatium vacuum negari de<lb></lb>beat. </s> </p> <p type="margin"> <s id="s.002698"><margin.target id="marg712"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002699">Sextò: <emph type="italics"></emph>In vacuo propterea corpora ferri cenſentur, quia <lb></lb>cedit, at vacuum omni ex parte cedit, quare ad omnem par<lb></lb>tem feretur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002700">Si hęc ratio valeret, procul dubio, quia aqua maris <lb></lb>æquali facilitate cedit virtuti motiuę piſcis omni ex <lb></lb>parte, hinc inferre liceret, ergo piſcis fertur eodem <lb></lb>tempore ad <expan abbr="omnẽ">omnem</expan> partem, ſcilicèt ſursùm, deorsùm, <lb></lb>ante, retro, ad dextram, ſiniſtram, &c. </s> <s id="s.002701">Legitima igi<lb></lb>tur illatio eſt, quod ex eo quod ſpatium omni ex par<lb></lb>te cedit liberum eſt vt mobile per vnamquamlibet <lb></lb>directionem feratur, per eam, ſcilicèt per quam im<lb></lb>pellitur ab eius vi motiua, & ſic nil <expan abbr="incõmodi">incommodi</expan> ſequi<lb></lb>tur, proindeque vacuum non tollitur. </s> <s id="s.002702">Reliquis Ari<lb></lb>ſtot. rationibus partim cap. 10. ſatisfecimus, partim <lb></lb>verò inferiùs reſpondebimus. </s> </p> <p type="main"> <s id="s.002703">Interim libet mirari, quomodo ex huius farinæ <expan abbr="ar-gumẽtis">ar<lb></lb>gumentis</expan> tam fixè perſuaſi ſint Ariſtotelis ſectatores, <lb></lb>vt eorum nonnulli auſi ſint aſſerere Deum O. M. ſua <lb></lb>infinita virtute non poſſe in rerum natura ſpatiolum <lb></lb>aliquod vacuum coaceruare. </s> </p> <p type="main"> <s id="s.002704">Sed procedamus ad <expan abbr="argumẽtum">argumentum</expan>, quod in ore om-<pb pagenum="508" xlink:href="010/01/516.jpg"></pb><arrow.to.target n="marg713"></arrow.to.target><lb></lb>nium recentiorum verſatur, ex quo euidentiſſimè pa<lb></lb>tere aiunt vacuum non dari in rerum natura, hoc de<lb></lb>ſumitur ab innumeris experimentis, quibus conſtat <lb></lb><arrow.to.target n="marg714"></arrow.to.target><lb></lb>multa corpora moueri contra propriam, & <expan abbr="naturalẽ">naturalem</expan> <lb></lb>inclinationem ad impediendum vacuum, & quando <lb></lb>non adeſt corpus, quod accurrere poſſit ad <expan abbr="replendã">replendam</expan> <lb></lb>ſciſſuram, ſiue ſpatium quod inane remanere debe<lb></lb>ret, tunc adhibita quacumque vi externa prædictą <lb></lb>diſſolutio, & ſciſſura vacua creari non poteſt. </s> </p> <p type="margin"> <s id="s.002705"><margin.target id="marg713"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002706"><margin.target id="marg714"></margin.target>Vulgaria ex<lb></lb>perimenta <lb></lb>naturam va<lb></lb>cuum abhor<lb></lb>rere <expan abbr="probā-">proban<lb></lb></expan>tia.</s> </p> <p type="main"> <s id="s.002707">Et primò ſi <expan abbr="folliũ">follium</expan> tabellæ <expan abbr="cõprimãtur">comprimantur</expan>, aut diabetis, <lb></lb>ſeu syringæ embolum vſque ad fundum impellatur, <lb></lb>tunc retrahi non poterunt clauſo infimo orificio, vel <lb></lb>aqua ſubiecta, & contigua contra eius naturam <expan abbr="aſcẽ-det">aſcen<lb></lb>det</expan>, ne interceptum ſpatium inane remaneat. </s> </p> <p type="main"> <s id="s.002708">Id ipſum contingit in antlijs, & machinis cteſibia<lb></lb>nis, quæ vulgò <expan abbr="Trõ">Trom</expan> bæ ſpiritales vocantur, in ijs pari<lb></lb>tèr attracto embolo ſimul aqua ſubiecta ſubleuatur. </s> </p> <p type="main"> <s id="s.002709">Secundò in elepsy dra irrigatoria aqua oppleta, & <lb></lb>obturato ſuperno ore non defluit aqua per infima a<lb></lb>perta foraminula, ob vacui timorem, quod intra ca<lb></lb>uitatem vaſis remanere deberet. </s> </p> <p type="main"> <s id="s.002710">Tertiò paritèr è cucurbitula medica ſi flamma, vel <lb></lb>alio modo aer excludatur, carnibuſque applicetur, <lb></lb>caro ipſa, & ſanguis accurrunt ad replendum illud <lb></lb>ſpatium. </s> </p> <p type="main"> <s id="s.002711">Ex hiſce, & alijs huius generis experimentis, pu<lb></lb>tant euidentiſſimè comprobari, naturam vacuum ab<lb></lb>hortere, & tantummodò ſolliciti ſunt de cauſa illius <lb></lb>motus, quo partes vniuerſi accurrunt ad <expan abbr="impediendũ">impediendum</expan> <pb pagenum="509" xlink:href="010/01/517.jpg"></pb><arrow.to.target n="marg715"></arrow.to.target><lb></lb>vacuum; & in hoc mirum quantum cruciantur, alij <lb></lb>enim <expan abbr="aiũt">aiunt</expan>, Deum immediatè, alij Naturam impellere <lb></lb>corpora grauia contra eorum inſitam virtutem ad im<lb></lb>pediendum vacuum; alij poſtea aiunt partes vni<lb></lb>uerſi præter propriam vim natiuam habere nouam̨ <lb></lb>facultatem mouendi ſe quoties occaſio exigit, prop<lb></lb>ter bonum vniuerſi, ſcilicèt aqua habet inſitum prin<lb></lb>cipium grauitatis, quo perpetuò operatur <expan abbr="premẽdo">premendo</expan>, <lb></lb>& deſcendendo deorsùm, at quotieſcumque neceſ<lb></lb>ſitas vrget, vt nimirum contingat periculum ſciſſuræ, <lb></lb>& plagæ vacuæ in vniuerſo, tunc quidem alia nouą <lb></lb>virtus pariter aquæ inſita <expan abbr="eã">eam</expan> ſursùm impellit ad hoc, <lb></lb>vt malo vniuerſali medeatur. </s> </p> <p type="margin"> <s id="s.002712"><margin.target id="marg715"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002713"><emph type="center"></emph>PROP. CCXLIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002714"><emph type="center"></emph><emph type="italics"></emph>Cauſa impellens grauia ſursùm ad replendum vacuum non <lb></lb>eſt Diuina facultas, neque intrinſeca vis animaſtica, vel <lb></lb>naturalis eorumdem corporum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002715">SI actio immediata Dei admittatur in hoc caſu, e<lb></lb>rit procùl dubio operatio miraculoſa non natu<lb></lb>ralis, nam omnes naturales actiones licet diuinum v<lb></lb>niuerſalę concurſum exigant, nihilominùs exercen<lb></lb>tur phyſicis, ac naturalibus inſtrumentis, ac organis; <lb></lb>ſi verò prædictanoua virtus omnibus corporibus na<lb></lb>turalibus inſita cenſeatur, erit profectò facultas non <lb></lb>diſſimilis ei, quæ in animalibus reperitur quandoqui<lb></lb>dem tanta <expan abbr="prudẽtia">prudentia</expan> medicinam afferre malo vniuer<lb></lb>ſi concipi non poteſt abſque eo quòd aqua v. g. per<lb></lb>cipiat, & ſentiat malum illud, & deindè moueatur, <lb></lb>conetur que illud impedire; in hoc enim diſſerunt o-<pb pagenum="510" xlink:href="010/01/518.jpg"></pb><arrow.to.target n="marg716"></arrow.to.target><lb></lb>perationes naturales ab animaſticis, quod illæ cæcą <lb></lb>quadam neceſſitate perpetuò, & inceſſantèr fiunt, <expan abbr="nõ">non</expan> <lb></lb>verò quando neceſſitas exigit, vt compreſſio, & mo<lb></lb>tus deorsùm grauium ſemper exercetur, nec quando <lb></lb>ignis v. g. aquam deſtruere conatur, quia vrget ne<lb></lb>ceſſitas, aqua vnquam aufugit, & periculum euitare <lb></lb>conatur: & in ſumma non poteſt excogitari modus <lb></lb>quomodo aqua tunc ſolummodo obliuiſcatur pro<lb></lb>priæ naturæ, & ſursùm aſcendat quando periculum̨ <lb></lb>imminet ne vacuum detur, quod nec aqua percipit, <lb></lb>nec habet organa, aut inſtrumenta apta ad <expan abbr="exerendã">exerendam</expan> <lb></lb>hanc nouam operationem in illo caſu tantùm neceſſi<lb></lb>tatis, & toto reliquo tempore id non curet, & ſuam <lb></lb>propriam grauitatem exerceat. </s> </p> <p type="margin"> <s id="s.002716"><margin.target id="marg716"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002717"><emph type="center"></emph>PROP. CCL.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002718"><emph type="center"></emph><emph type="italics"></emph>Oſtenditur fallacia argumenti inſinuantis naturam <expan abbr="vacuũ">vacuum</expan> <lb></lb>abhorrere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002719">VIdendum modò eſt in quonam conſiſtat defe<lb></lb>ctus ratiocinij peripatetici, cùm aiunt, ſe vi<lb></lb>dere ſemper corpora naturalia accurrere ad impedi<lb></lb>endum vacuum, etiamſi oporteat, <expan abbr="cõtra">contra</expan> eorum natu<lb></lb>ram moueri, ergo vacuum ab ipſa natura abhorretur. <lb></lb></s> <s id="s.002720">Non negatur, id, quod ſenſibus patet, nempè aquam <lb></lb>aſcendere quotieſcumque ſpatium ſupremum exi<lb></lb>nanitur, ſed negatur aquam ſponte ſua ſursùm <expan abbr="aſcẽ-dere">aſcen<lb></lb>dere</expan> propter illum finem, ſcilicèt vt vacuum impedi<lb></lb>at. </s> <s id="s.002721">& profectò numquam certi eſſe poſſumus, an aqua <lb></lb>ſponte ſursùm feratur in illo caſu neceſſitatis, niſi <expan abbr="cõ-ſtet">con<lb></lb>ſtet</expan> <expan abbr="tũc">tunc</expan> eam ab alia cauſa externa <expan abbr="nõ">non</expan> impelli ſursùm, <pb pagenum="511" xlink:href="010/01/519.jpg"></pb><arrow.to.target n="marg717"></arrow.to.target><lb></lb>hoc autem Peripatetici numquam probarunt. </s> <s id="s.002722">& ſi re<lb></lb>uerà aqua in tali caſu impelleretur ab aliqua cauſą <lb></lb>phyſica ſursùm, tunc non per ſe, ſed per accidens <lb></lb>accurreret ad replendam illam inanitatem; per ſe ve<lb></lb>rò moueretur ob neceſſitatem violentiæ, & impulſus, <lb></lb>quem ei infert cauſa impellens. </s> </p> <p type="margin"> <s id="s.002723"><margin.target id="marg717"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002724">Quod, vt clariùs percipiatur, in <expan abbr="bilãce">bilance</expan> apponantur <lb></lb>duo pondera inæqualia, & minori ponderi ſuperpo<lb></lb>natur palma manus à qua flexio libræ prohibeatur, <lb></lb>procùl dubio ſenſim ſubleuata manu minus pondus <lb></lb>pariter ſubleuabitur manui adhærendo; tunc ſi ex eo <lb></lb>quod minus pondus aſcendere videtur, quis inferret <lb></lb>proptèr bonum vniuerſi idipſum graue obliuiſci pro<lb></lb>prię naturę, & ſursùm accurrere ad replendum ſpa<lb></lb>tium, prauè profectò, & peruersè ratiocinaretur, <lb></lb>propterea quòd aſcenſus producitur à cauſa phyſica, <lb></lb>& neceſſaria, nempè à maiori pondere contrapoſito; <lb></lb>finge modò maius pondus in prædicta bilance obue<lb></lb>latum eſſe, tunc ſi aliundè conſtet euidentèr ibi ope<lb></lb>rari maius pondus, licèt <expan abbr="incõſpicuũ">inconſpicuum</expan> ſit, <expan abbr="nõne">nonne</expan> <expan abbr="ridiculũ">ridiculum</expan> <lb></lb>eſſet confugere ad miracula, & ad machinas, tribuen<lb></lb>do | ſenſum, & perceptionem prudentem minori pon<lb></lb>deri ſubleuato, vt velit medicinam afferre imminenti <lb></lb>malo vniuerſi; igitur tota vaſta moles horum <expan abbr="argumẽ-torum">argumen<lb></lb>torum</expan> in nihilum abibit, ſi oſtenderimus aquam, & <lb></lb>cætera grauia quando aſcendunt ad <expan abbr="replendũ">replendum</expan> <expan abbr="vacuũ">vacuum</expan> <lb></lb>verè, & realitèr impelli in <expan abbr="bilãce">bilance</expan>, vel ſiphone à maiori <lb></lb>pondere contrapoſito, quod ſemper adeſt, & opera<lb></lb>tur in tali caſu, & ſic aſcenſus <expan abbr="cũ">cum</expan> habeat <expan abbr="causã">causam</expan> neceſ-<pb pagenum="512" xlink:href="010/01/520.jpg"></pb><arrow.to.target n="marg718"></arrow.to.target><lb></lb>ſariam, non poterit tribui prudenti illi cognitioni, ſeù <lb></lb>potiùs chimæricæ. </s> </p> <p type="margin"> <s id="s.002725"><margin.target id="marg718"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002726"><emph type="center"></emph>PROP. CCLI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002727"><emph type="center"></emph><emph type="italics"></emph>In ſiphone inuerſo retracto embolo aqua aſcendit <expan abbr="nõ">non</expan> ſpontè, <lb></lb>ſed impulſa à maiori pondere, vel momento aquæ alteri<lb></lb>us brachij ſiphonis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002728">VT que hoc quanta fieri poteſt perſpicuitate <lb></lb>oſtendamus, intelligatur ſipho ABCD aqua <lb></lb>repletus, cuius crura AB, & DC perpendicularitèr ad <lb></lb>horizontem erecta ſint, tunc embolum <expan abbr="cũ">cum</expan> ſuo aſſario <lb></lb>EFG, & cum fiſtula DC ſyringam <expan abbr="cõpleat">compleat</expan>, & immiſſo <lb></lb>embolo intra fiſtulam quouſque eius baſis FG <expan abbr="fundũ">fundum</expan> <lb></lb>fiſtulæ C attingat, tunc patet, quòd aqua BC officium <lb></lb><expan abbr="bilãcis">bilancis</expan> ſupplet, in cuius extremo B ſuperponitur mo<lb></lb>les aquæ grauis AB, alteri ve<lb></lb><figure id="id.010.01.520.1.jpg" xlink:href="010/01/520/1.jpg"></figure><lb></lb>rò extremitati C exigua aquæ <lb></lb>laminula FC imminet, & pro<lb></lb>indè ſi reliqua eius portio FD <lb></lb>vſque ad horizontalem AD, <lb></lb>eſſet vel aere repleta, vel om<lb></lb>ninò exinanita, & vacua, pro<lb></lb>cùl dubio aqua FC <expan abbr="ſursũ">ſursum</expan> <expan abbr="aſcẽ-deret">aſcen<lb></lb>deret</expan> versùs D, non <expan abbr="quidẽ">quidem</expan> ſponte ſua, ſed impulſa à <lb></lb><arrow.to.target n="marg719"></arrow.to.target><lb></lb>maiori contrapoſito pondere aquæ AB; propterea <lb></lb>quod in libra imaginaria fluida BC pars B magis preſ<lb></lb>ſa à maiori pondere imminentis aquæ AB expellere <lb></lb>ſursùm debet minùs grauem aquæ molem FC, quouſ<lb></lb>que ad æquilibrium in plano horizontali AD perdu<lb></lb>catur; his præmiſſis retrahatur embolum EFG ſursùm <pb pagenum="513" xlink:href="010/01/521.jpg"></pb><arrow.to.target n="marg720"></arrow.to.target><lb></lb>vt nimirùm eius baſis FG perducatur ad <expan abbr="sũmitatẽ">summitatem</expan> fi<lb></lb>ſtulæ D, ita tamen vt perfectè aſſarium FG contingat <lb></lb>internam fiſtulæ ſuperficiem, vt ne rimula quidem re<lb></lb>maneat per quam aeri ſupremo ingreſſus pateat; tunc <lb></lb>in ſpatio FD, neque aer, neque aliud corpus remane<lb></lb>ret, dum contrapoſita fiſtula AB eſt plena aquæ, & hæc <lb></lb>procùl dubio ſua naturali grauitate impellet ſursùm <lb></lb>aquam ab F vſque ad D, nulla alia de cauſa, niſi quia <lb></lb>in bilance BC maius pondus aquæ AB impellere ſur<lb></lb>sùm debet contrapoſitum minus pondus. </s> <s id="s.002729">modò iņ <lb></lb>hac operatione nonne ſtultè ratiocinaretur is, qui di<lb></lb>ceret aquam FC aſcendere ſursùm ad occupandum̨ <lb></lb>ſpatium FD contra inclinationem naturalem ſuę gra<lb></lb>uitatis, ad hoc vt repleat prædictum ſpatium ne inane <lb></lb>admittatur in natura? </s> <s id="s.002730">& ratio eſt quia non poteſt in <lb></lb>dubium reuocari cauſa phyſica, & realis, quæ author <lb></lb>eſt huius operationis, nempè maius pondus contra<lb></lb>poſitæ aquæ AB, quæ in ſiphone, & bilance neceſſita<lb></lb>te mechanica apta nata eſt impellere ſursùm aquam <lb></lb>FC vſque ad D. </s> </p> <p type="margin"> <s id="s.002731"><margin.target id="marg719"></margin.target>Cor. pro. </s> <s id="s.002732">10.</s> </p> <p type="margin"> <s id="s.002733"><margin.target id="marg720"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002734"><emph type="center"></emph>PROP. CCLII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002735"><emph type="center"></emph><emph type="italics"></emph>Si in syringa intra puteum demerſa embolum ab eius fundo <lb></lb>ſursùm retrahatur, aqua ſubiecta aſcendet, non quidem <lb></lb>ob metum vacui, ſed necesſitate mechanica à pondere co<lb></lb>lumnæ aquæ collateralis impulſa.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002736">SI poſtea non vſurpetur ſipho ſolidus ABCD, ſed <lb></lb><expan abbr="tantũmodò">tantummodò</expan> ænea syringa EDC, & hæc intra pu<lb></lb>teum RSTV perpendicularitèr ad horizontem orę <lb></lb>deorsùm vergente immittatur, quouſque infimum̨ <pb pagenum="514" xlink:href="010/01/522.jpg"></pb><arrow.to.target n="marg721"></arrow.to.target><lb></lb>eius orificium C propè fundum putei perducatur, <expan abbr="tũc">tunc</expan> <lb></lb>quia aqua intra cauitatem syringæ CF non poteſt e<lb></lb>leuari, niſi aqua collateralis IB de<lb></lb><figure id="id.010.01.522.1.jpg" xlink:href="010/01/522/1.jpg"></figure><lb></lb>ſcendat ad <expan abbr="replẽdum">replendum</expan> ſpatium ſub<lb></lb>iectum ab aqua FC relictum; nec <lb></lb>ſieri poteſt, vt illa portio aquę col<lb></lb>lateralis fundo syringæ proximą <lb></lb>IB deprimatur quin ſubſequentes <lb></lb>partes ei perpendicularitèr immi<lb></lb>nentes AI conſe quutiuo motu om<lb></lb>nes vna poſt aliam deprimantur, <lb></lb>quouſque ad ſupremam libellam̨ <lb></lb>aquæ RV perueniatur: itaque in hoc caſu adſunt ve<lb></lb>luti duæ columnæ, vna aquea AIB, quæ deorſum pre<lb></lb>mit, ac fertur, reliqua verò eſt portio aquæ CF vnà <lb></lb>cum embolo FE, & aqua imminente EH, quæ contra<lb></lb>rio motu ſursùm ſupponitur ferri; ambæ verò prædi<lb></lb>ctæ columnæ innituntur, <expan abbr="ſuſtentãturque">ſuſtentanturque</expan> ab infima la<lb></lb>mina aquea BC, quæ officium libræ ſapplet; & ſiqui<lb></lb>dem momenta quibus extremitates fluidæ libræ BC <lb></lb>premuntur à prædictis columnis AB, & HC fuerint <lb></lb>inter ſe æqualia, tunc procul dubio fiet <expan abbr="æquilibriũ">æquilibrium</expan>, <lb></lb>& quies, nec vna earum à reliqua columna ſursùm ex<lb></lb>pelletur; at ſi è fundo syringæ embolum EFG retra<lb></lb>hatur ſursùm vſque ad D, procùl dubio neceſſitatę <lb></lb>mechanica aqua ſubiecta CF ſursùm per syringæ ca<lb></lb>uitatem aſcendet, ſemper aſſario FG adhærendo, non <lb></lb>quidem ob vacui metum, ſed quia impellitur à con<lb></lb>trapoſito maiori pondere columnæ aqueæ AB. <pb pagenum="515" xlink:href="010/01/523.jpg"></pb><arrow.to.target n="marg722"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002737"><margin.target id="marg721"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002738"><margin.target id="marg722"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002739"><emph type="center"></emph>PROP. CCLIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002740"><emph type="center"></emph><emph type="italics"></emph>Iiſdem poſitis ſi præterea infimum syringæ orificium infra <lb></lb>mercurium in catino contentum mergatur, retracto em<lb></lb>bolo mercurius aſcendet non ob vacui metum, ſcd impul<lb></lb>ſus à pondere columnæ aquæ collateralis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002741">SI deinde in fundo putei RSTV ponatur catinum <lb></lb>MNO hydrargyro plenum, infra cuius libellam <lb></lb>MO orificium infimum C ſyrin<lb></lb><figure id="id.010.01.523.1.jpg" xlink:href="010/01/523/1.jpg"></figure><lb></lb>gæ immittatur, tunc paritèr re<lb></lb>tracto embolo EFG mercurius <lb></lb>in ſyringa CD aſcendet, <expan abbr="nõ">non</expan> qui<lb></lb>dem ſponte ad replendum va<lb></lb>cuum, ſed impulſus à maiori <expan abbr="põ-dere">pon<lb></lb>dere</expan> columnæ aqueæ AB, & eò <lb></lb>vſque mercurij eleuatio perſe<lb></lb>uerabit, quouſque fiat æquili<lb></lb>brium inter momentum aquæ, & <lb></lb>mercurium, ſcilicèt ſi altitudo columnæ aqueæ AB <lb></lb>fuerit 18. cubitorum, oportet, vt altitudo æquè am<lb></lb>plæ columnæ mercurij ſit cubitorum duorum, & ſe<lb></lb>mis proximè, & hæc eſt ſumma altitudo ad quam̨ <lb></lb>mercurius in prædicta syringa eleuari poteſt, at ſi vl<lb></lb>terius vi manus embolum ſubleuetur, perſiſtet tamen <lb></lb>perſeuerabitque mercurius in priori illa altitudine, <lb></lb>& potius <expan abbr="ſpatiũ">ſpatium</expan> exinanitum, ideſt <expan abbr="abſq;">abſque</expan> mercurio, & <lb></lb><expan abbr="abſq;">abſque</expan> aqua, & aere relinquet, quàm mercurius <expan abbr="pilũ">pilum</expan> <lb></lb>fubleuetur. </s> <s id="s.002742">& hinc <expan abbr="nedũ">nedum</expan> deducitur, quod mercurius <lb></lb>aſcendit quatenus, & quouſque impellitur ab oppo<lb></lb>ſito pondere fluidi AB, ſed præterea conſtat, quòd <expan abbr="nõ">non</expan> <pb pagenum="516" xlink:href="010/01/524.jpg"></pb><arrow.to.target n="marg723"></arrow.to.target><lb></lb>aſcendit ſponte ad replendum ſpatium priuatum, ſeu <lb></lb>vacuum mercurio, cùm prædictum limitem <expan abbr="cubitorũ">cubitorum</expan> <lb></lb>duorum, & ſemis non prætergrediatur, nec ſollicitus <lb></lb>ſit, quòd ſuperius ſpatium mercurio <expan abbr="vacuũ">vacuum</expan> remaneat. </s> </p> <p type="margin"> <s id="s.002743"><margin.target id="marg723"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002744"><emph type="center"></emph>PROP. CCLIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002745"><emph type="center"></emph><emph type="italics"></emph>In omnibus experimentis <expan abbr="aduerſariorũ">aduerſariorum</expan> oſtenditur violentèr <lb></lb>impelli fluidum ſursùm, & per accidens accurrere ad re<lb></lb>plendum vacuum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002746">ID quod diximus de aqua, verificari quoque in aere <lb></lb>ſatis ſuperque conſtat ex ſuperiùs dictis. </s> <s id="s.002747">Propte<lb></lb>rea quòd aer non minus, quàm aqua grauis eſt, & in <lb></lb>ſuamet regione pondus, & grauitatem exercet ſupra <lb></lb>fluida corpora ſubiecta; proindeque in aere <expan abbr="nõ">non</expan> minùs <lb></lb>quàm in aqua libra, & ſipho exercentur, in quo æqui<lb></lb>librium effici poteſt; quare retracto embolo in ſyrin<lb></lb>ga aqua ſubiecta <expan abbr="nõ">non</expan> attrahitur, neque ſugitur, neque <lb></lb>ipſa ſponte eleuatur aſſario adhærendo, ob vacui me<lb></lb>tum, ſed quia à maiori pondere colúmnæ aereæ infimo <lb></lb>fluido incumbentis eumque <expan abbr="premẽtis">prementis</expan>, neceſſitate me<lb></lb>chanica, aqua intra <expan abbr="ſyringã">ſyringam</expan> inſinuatur, & per <expan abbr="accidẽs">accidens</expan> <lb></lb>contingit, vt aqua accurrere videatur ad replendum <lb></lb>ſpatium inane. </s> <s id="s.002748">Idemque prorsùs dicendum eſt de an<lb></lb>tlijs, ac machinis Cteſibianis, & de medicis cucurbi<lb></lb>tulis, vt cap. 6. ſatis ſuperque declarauimus. </s> </p> <p type="main"> <s id="s.002749">Quòd verò tabellæ follium poſt <expan abbr="compreſſionẽ">compreſſionem</expan> ob<lb></lb>turato foramine difficile diſtrahantur, & ſic duę la<lb></lb>minę vitreę ſe tangentes, non inde ſequitur timor, & <lb></lb>ab ominium vacui, nam hoc <expan abbr="cõtingit">contingit</expan> ex eo quòd gra<lb></lb>uitas aeris ambientis, premendo ſubiectam partem <pb pagenum="517" xlink:href="010/01/525.jpg"></pb><arrow.to.target n="marg724"></arrow.to.target><lb></lb>fluidi, quę libram conſtituit, non permittit, vt tabellæ <lb></lb>facilè diſtrahantur, nam in earum ſeparatione creari <lb></lb>debet ſpatium inane, & ideò minoris ponderis quàm <lb></lb>ſit illud quo columna fluidi collateralis premit ſub<lb></lb>iectam libram fluidam, & proinde infima tabella im<lb></lb>pellitur ſursùm versùs ſupremam, vt ei adhæreat. </s> <s id="s.002750"><expan abbr="Nõ">non</expan> <lb></lb>tamen prædicta adhæſio, & vnio tabellarum eſt im<lb></lb>menſæ energiæ, vt inexperti Peripatetici cenſent, <lb></lb>præcisè enim æquat vim ponderis columnæ fluidæ <lb></lb>collateralis ſua preſſione infimam tabellam <expan abbr="ſubleuã-tis">ſubleuan<lb></lb>tis</expan>, & tunc ſi maiori vi, quàm ſit prædictum pondus <lb></lb>fluidæ columnæ vrgeas retrahendo tabellas, procùl <lb></lb>dubio ab inuicem ſeparantur, vt <expan abbr="experiẽtia">experientia</expan> docet. <lb></lb><arrow.to.target n="marg725"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002751"><margin.target id="marg724"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002752"><margin.target id="marg725"></margin.target><expan abbr="Argnmentũ">Argumentum</expan> <lb></lb>Ariſtotel. & <lb></lb>Carteſij <expan abbr="cõ-tra">con<lb></lb>tra</expan> vacuum.</s> </p> <p type="main"> <s id="s.002753">Oſtenſa nullitate præcipuorum argumentorum, <lb></lb>quæ à Peripateticis afferri ſolent contra vacui <expan abbr="exiſtẽ-tiam">exiſten<lb></lb>tiam</expan>, debet tandem ad examen reuocari <expan abbr="argumentũ">argumentum</expan> <lb></lb>valdè <expan abbr="exaggeratũ">exaggeratum</expan> ab aliquibus recentioribus, quod <lb></lb>tamen antiquitùs leuiſſimè Ariſtoteles innuerat, & <lb></lb>ſaniores Peripatetici non valdè ipſum exaggerarunt, <lb></lb>forſan exiſtimantes non eſſe tanti roboris, vt compa<lb></lb>rari poſſit rationibus ſuperiùs adductis. </s> <s id="s.002754">Dixerat Ari<lb></lb>ſtoteles cubum intra aquam immiſſum expellere ſibi </s> </p> <p type="main"> <s id="s.002755"><arrow.to.target n="marg726"></arrow.to.target><lb></lb>æqualem molem aquæ ab eo loco in quo cubus repo<lb></lb>ni debet, in vacuo autem id non <expan abbr="cõtingere">contingere</expan>, proinde<lb></lb>que ſpatium vacuum non dari, quandoquidem <expan abbr="trinã">trinam</expan> <lb></lb><expan abbr="dimẽſionem">dimenſionem</expan> haberet, ideoquè corpus eſſet, & ſic pe<lb></lb>netraretur à corpore ipſius cubi, quod eſt impoſſibi<lb></lb>le. </s> <s id="s.002756">Hanc ratiunculam in angulo phyſices Ariſtotelis <lb></lb><expan abbr="repoſitã">repoſitam</expan> ad auras reuocauit Renatus Carteſius, eiuſ-<pb pagenum="518" xlink:href="010/01/526.jpg"></pb><arrow.to.target n="marg727"></arrow.to.target><lb></lb>que aſſeclæ. </s> <s id="s.002757"><expan abbr="Inquiũt">Inquiunt</expan> enim corpus eſſe <expan abbr="rẽ">rem</expan> <expan abbr="extẽſam">extenſam</expan>, ſci<lb></lb>licèt præditam longitudine, latitudine, & profundi<lb></lb>tate, vnde vbicumque ponitur extenſio, neceſſariò <lb></lb>corpus ſubſtantiale admitti debere: hinc ſequitur <lb></lb>nullo pacto concedi poſſe ſpatium denudatum priua<lb></lb>tumque corpore ſubſtantiali, cùm dari non poſſit ex<lb></lb>tenſio ſeparata à corporibus phyſicis, & ideò aiunt, <lb></lb>quòd quicumque ſpatium vacuum admittit neceſſa<lb></lb>riò in eodem vacuo conceſſo rem, ſeu <expan abbr="ſubſtãtiam">ſubſtantiam</expan> ex<lb></lb>tenſam, ſcilicèt corpus concedat neceſsè eſt, propte<lb></lb>rea adeò verum eſt <expan abbr="vacuũ">vacuum</expan> eſſe impoſſibile, vt is, qui <lb></lb>ipſum admittit eodem ſpiritu idipſum neget. </s> <s id="s.002758">Hoc <lb></lb>porrò argumentum tantæ energiæ, & tanti robo<lb></lb>ris eſſe prædicti Authores cenſent, vt mirentur, miſe<lb></lb>reanturque debilitatem intellectus eorum, qui huic <lb></lb>argumento non acquieſcunt, & manus non dant. </s> </p> <p type="margin"> <s id="s.002759"><margin.target id="marg726"></margin.target>4. phy ſ. </s> <s id="s.002760">c. 8.</s> </p> <p type="margin"> <s id="s.002761"><margin.target id="marg727"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002762"><emph type="center"></emph>PROP. CCLV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002763"><emph type="center"></emph><emph type="italics"></emph>Dimenſiones, quæ ſpatio vacuo tribuuntur, non ſunt reales, <lb></lb>ſed meræ negationes, & priuationes.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002764">HVic obiectioni reſponderi poſſe mihi videtur, <lb></lb>quod illę, quæ dimenſiones vocantur in va<lb></lb>cuo non ſunt, neque reales, neque poſitiuæ, ſed me<lb></lb>ræ priuationes, & negationes, ſcilicèt deficit in tali <lb></lb>loco tanta longitudo, tanta latitudo, & tanta profun<lb></lb>ditas, quandoquidem ibidem deficit corpus, quod <lb></lb>rem, ſeu ſubſtantiam extenſam eſſe de finitum eſt: pa<lb></lb>ritèr falſum eſt prædictum vacuum menſurari poſſe, <lb></lb>cùm nihilum nullam dimenſionem menſurabilem ha<lb></lb>beat, ſed tantummodò intellectus noſter fictione <pb pagenum="519" xlink:href="010/01/527.jpg"></pb><arrow.to.target n="marg728"></arrow.to.target><lb></lb>quadam, & fallaci imaginatione applicat, tribuit<lb></lb>que conceptum plenitudinis ipſi vacuo, ſcilicèt ap<lb></lb>plicat conceptum, & imaginationem dimenſionum <lb></lb>eorumque menſuram vbi reuera deficit prædicta <expan abbr="mẽ-ſura">men<lb></lb>ſura</expan>; ex quo deducitur eſſe merum <expan abbr="figmẽtum">figmentum</expan>, & me<lb></lb>ram deceptionem, & fallaciam intellectus, qui nullo <lb></lb>pacto ſpoliari poteſt idea, & conceptu plenitudinis, <lb></lb>& corporis, & quantumcumque nitatur eam remo<lb></lb>uere, ſemper in eius idea, & imaginatione verſatur <lb></lb><expan abbr="phãtaſia">phantaſia</expan>, & imago entitatis <expan abbr="cuiuſdã">cuiuſdam</expan> omni ex parte <expan abbr="ex-tẽſæ">ex<lb></lb>tenſæ</expan>. </s> <s id="s.002765">Quod porrò neceſſarium eſſe videtur, nam cùm <lb></lb>nihil in intellectu concipi, aut exiſtere poſſit, quod <lb></lb>priùs à ſenſibus non hauſtum ſit; ſenſus verò nonniſi <lb></lb>res vndequa que extenſas, & corporeas ab ipſo ortu <lb></lb>per totam ætatem percipiat; hinc eſt quòd nunquam <lb></lb>intellectus quantumcumque nitatur, ideam, ſeu ima<lb></lb>ginem incorpoream, & dimenſionibus carentem ſibi <lb></lb>effingere queat; quia nimirum quando per <expan abbr="illationẽ">illationem</expan> <lb></lb>quamdam nititur ab imagine, & phantaſia corporea <lb></lb>progredi ad ideam incorporei, & vacui, tunc conatur <lb></lb>eam quodammodò extenuare, expandere, ac rarefa<lb></lb>cere, vt ſic per gradus ad conceptum vacui incorpo<lb></lb>rei perueniat; at hoc numquam aſſe qui poteſt, quią <lb></lb>ſemper eius conceptus ſiſtitur in aliqua imagine, ſeù <lb></lb>phantaſia nebulæ, ſeu auræ rariſſimæ, & valdè <expan abbr="expã-fæ">expan<lb></lb>ſæ</expan>, nunquam autem vltra limites extenſionis corpo<lb></lb>reæ tranſcendere valet. </s> <s id="s.002766">& hinc fit vt quotieſcumque <lb></lb>ſubſtantiam quamdam ſpiritualem, veluti anima eſt, <lb></lb>vel Angelus, contemplari conamur, <expan abbr="tũc">tunc</expan> quidem per-<pb pagenum="520" xlink:href="010/01/528.jpg"></pb><arrow.to.target n="marg729"></arrow.to.target><lb></lb>petuo menti obuerſatur phantaſia quædam tenuiſſi<lb></lb>mæ auræ, aut alterius ſimilis rei, quæ limites corpo<lb></lb>reos numquam progreditur. </s> <s id="s.002767">Nec ſolummodò in hoc <lb></lb>percipitur humanæ imaginationis imbecillitas, ſed <lb></lb>etiam in comprehenſione infiniti, & indiuiſibilis. <lb></lb></s> <s id="s.002768">Itaque quando vacuum cogitamus id quod verè <expan abbr="cõ-cipimus">con<lb></lb>cipimus</expan> <expan abbr="abſq;">abſque</expan> hallucinatione, eſt, quod ſi ſpatium̨ <lb></lb>vacuum eſſet plenum haberet profectò tantam <expan abbr="dimẽ-ſionem">dimen<lb></lb>ſionem</expan> longitudinis, latitudinis, atque profundita<lb></lb>tis, & hoc patet ex eò quòd non poteſt concipi <expan abbr="mẽ-ſura">men<lb></lb>ſura</expan> ſpatij alicuius vacui abſque eo quòd intellectus <lb></lb>ibidem concipiat, vel filum, vel virgam, vel rem <expan abbr="ali-quã">ali<lb></lb>quam</expan> corpoream, quæ quatenus corpus eſt, habet ve<lb></lb>ram dimenſionem; at ſi loquamur de vacuo quatenùs <lb></lb>tale eſt, in eo prorsùs negari debent, & tolli omnes <lb></lb>dimenſiones, perſuaderique debemur prædictum̨ <lb></lb>ſpatium inane carere, ſeu non habere longitudinem <lb></lb>viginti cubitorum v. g. ſcilicèt eſſe prorsùs nihilum. </s> </p> <p type="margin"> <s id="s.002769"><margin.target id="marg728"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002770"><margin.target id="marg729"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002771">Neque nouum eſt in phyſicis, ac mathematicis <expan abbr="cõ-ſiderare">con<lb></lb>ſiderare</expan> naturas, & proprietates quantitatum, & <lb></lb>numerorum defectiuorum, qui vulgò vocantur, mi<lb></lb>nus nihilo; hos profectò ne <expan abbr="dũ">dum</expan> <expan abbr="mẽſurari">menſurari</expan>, ſed <expan abbr="etiã">etiam</expan> di<lb></lb>uidi, & multiplicari poſſe <expan abbr="certũ">certum</expan> eſt, nihilominùs con<lb></lb>ſtat meras priuationes, & negationes eſſe, nec vllam <lb></lb>entitatem habere. </s> </p> <p type="main"> <s id="s.002772">Præterea vulgatum eſt, quòd dimenſiones purę, & <lb></lb>abſque ſubiecto nullam exiſtentiam in natura habent <lb></lb>niſi in imaginatione, & phantaſia noſtra, ſed tantum<lb></lb>modò reperiuntur in natura res extenſæ ſcilicèt ſub-<pb pagenum="521" xlink:href="010/01/529.jpg"></pb><arrow.to.target n="marg730"></arrow.to.target><lb></lb>ſtantiæ corporeæ; qua proptèr in vacuo vbi, ope intel<lb></lb>lectus, vel à potentia Diuina, tollitur corpus, ſcilicèt <lb></lb>res extenſa remanere non poſſunt <expan abbr="extẽſiones">extenſiones</expan> illę, ſci<lb></lb>licet longitudo, latitudo, & profunditas, ſed ſolum<lb></lb>modò priuatio, & negatio earumdem, quæ tolluntur <lb></lb>vnà cum re extenſa, nempè cum corpore. </s> </p> <p type="margin"> <s id="s.002773"><margin.target id="marg730"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002774"><emph type="center"></emph>PROP. CCLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002775"><emph type="center"></emph><emph type="italics"></emph>Dimenſiones ſpatij ſeparati, quæ extra mundum <expan abbr="concipiẽdæ">concipiendæ</expan> <lb></lb>ſunt, meræ priuationes poni debent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002776">HÆc eadem doctrina attentè conſiderata non vi<lb></lb>detur recedere à communi Peripatetico con<lb></lb>ceptu; immò expreſsè eam'affirmare tenentur, nam ex <lb></lb>Ariſtotele mundus finitus eſt, comprehenditurque à <lb></lb>perfectiſſima figura ſphærica; igitur extra mundum <lb></lb>vacuum concedant neceſsè eſt, quandoquidem ibi <lb></lb>deficit corpus, nempè res extenſa, eſtque tale <expan abbr="ſpatiũ">ſpatium</expan> <lb></lb>extra mundum menſurabile cubitis, & palmis, <expan abbr="cũ">cum</expan> ne<lb></lb>dum Intellectu, ſed etiam Author naturæ poteſt <expan abbr="ibidẽ">ibidem</expan> <lb></lb>reponere virgam quatuor cubitorum longitudinem <lb></lb>habentem, igitur prædictum ſpatium <expan abbr="ſeparatũ">ſeparatum</expan> extra <lb></lb>mundum, & omninò corpore priuatum, ſcilicèt <expan abbr="abſq;">abſque</expan> <lb></lb>re extenſa menſurari nihilominùs poteſt. </s> <s id="s.002777">quid ergo <lb></lb>prohibet, & quare tantoperè <expan abbr="horrẽt">horrent</expan>, vt ſi ab hac aula <lb></lb>omninò corpus tolleretur prædictum ſpatium <expan abbr="vacuũ">vacuum</expan> <lb></lb>cubitis, & palmis <expan abbr="mẽſurari">menſurari</expan> poſſet? </s> <s id="s.002778">Immò contra ipſos <lb></lb>retorquere argumentum poſſem <expan abbr="dicẽdo">dicendo</expan>, illa <expan abbr="lõgitudo">longitudo</expan> <lb></lb>quatuor cubitorum extra <expan abbr="mundũ">mundum</expan> eſtne vera dimen<lb></lb>ſio an non? </s> <s id="s.002779">ſi negant, potero ego quoque de hac aula, <lb></lb>ſi eſſet vacua, <expan abbr="eodẽ">eodem</expan> modo affirmare eius <expan abbr="longitudinẽ">longitudinem</expan> <pb pagenum="522" xlink:href="010/01/530.jpg"></pb><arrow.to.target n="marg731"></arrow.to.target><lb></lb>menſurabilem non eſſe veram dimenſionem, ſed tan<lb></lb>tummodò eius priuationem, & negationem, ſeù ni<lb></lb>hilum. </s> <s id="s.002780">At ſi dicent illam longitudinem 4. cubitorum <lb></lb>extra mundum eſſe verè <expan abbr="dimenſionẽ">dimenſionem</expan>, dicam ego: igi<lb></lb>tur vos <expan abbr="quoq;">quoque</expan> admittitis <expan abbr="accidẽs">accidens</expan> nempè quantitatem <lb></lb>ſine ſubiecto, ſcilicèt abſque ſubſtantia corporea, <lb></lb>quod ſi ab ſur dum eſt, debent quoque eadem mea re<lb></lb>ſponſione difficultati occurrere. </s> <s id="s.002781">Et hoc profectò <lb></lb>videtur expreſsè ab Ariſtotele concedi, cum ait extra <lb></lb>mundum non dari nec locum, nec <expan abbr="tẽpus">tempus</expan>, ſcilicèt <expan abbr="ibidẽ">ibidem</expan> <lb></lb>non reperiri dimenſiones, præter eas quas intellectus <lb></lb>falſa imaginatione ibi fingit, quod perinde eſt, ac af<lb></lb>firmare prædictas dimenſiones extra mundum eſſe <lb></lb>meras priuationes, & negationes, ſcilicèt ibidem de<lb></lb>ficere tantam longitudinem, quantam haberet cor<lb></lb>pus aliquod ſubſtantiale, quod ibidem collocatum <lb></lb>fuiſſet, & modò ibi deeſt. </s> </p> <p type="margin"> <s id="s.002782"><margin.target id="marg731"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002783">Poſtrema inſtantia, quæ ſolet afferri contra <expan abbr="vacuũ">vacuum</expan> <lb></lb>talis eſt, tam impoſſibile eſt concipere aulam hanc <lb></lb>vacuam, & prorsùs corpore priuatam, vt neceſsè ſit <lb></lb>concedere eius parietes oppoſitos, & diſcretos ſe ſe <lb></lb>mutuo tangere, propterea quod ea dicuntur ſe ſę <lb></lb>tangere, inter quæ nil intermediat, cumque inter pa<lb></lb>rietes oppoſitos prædictæ aulæ nihil intercedat, ſpa<lb></lb>tium enim vacuum nullam entitatem habere ſuppo<lb></lb>nitur; igitur parietes huius aulæ ſe mutuò tangerent, <lb></lb>quod eſt falſum. </s> </p> <p type="main"> <s id="s.002784">Econtra ea corpora dicimus inter ſe diſtare inter <lb></lb>quæ aliquid intermediat, cum igitur parietes prædi-<pb pagenum="523" xlink:href="010/01/531.jpg"></pb><arrow.to.target n="marg732"></arrow.to.target><lb></lb>ctæ aulæ inanis concedantur inter ſe diſtare, igitur <lb></lb>neceſſariò inter eos aliquid intermediet neceſsè eſt, <lb></lb>proindeque ſpatium interceptum non erit vacuum. </s> </p> <p type="margin"> <s id="s.002785"><margin.target id="marg732"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002786"><emph type="center"></emph>PROP. CCLVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002787"><emph type="center"></emph><emph type="italics"></emph>Falſum est ſolummodò ea ſe tangere, inter quæ nihil inter<lb></lb>mediat, niſi eorum extremitates coniunctæ fuerint.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002788">HVic argumento reſpondetur, verum non eſſę, <lb></lb>quòd ea ſe mutuò tangant, inter quæ nihil in<lb></lb>termediat, ſed requiritur altera conditio ad hoc vt <lb></lb>contactus fiat, ſcilicèt vt extrema corporum, quæ ſe <lb></lb>mutuò tangere debent, ſint ſimul vnita, & coniuncta, <lb></lb>ideſt eorum extremitates in eodem ſitu ſpatij mun<lb></lb>dani exiſtant, quando verò hæc conditio deficit, ſci<lb></lb>licèt quando exiſtunt in diuerſis locis, & eorum ex<lb></lb>tremitates non ſunt ſimul, tunc non ſe tangunt du<lb></lb>plici de cauſa, aut quia inter ea intercipitur aliud <lb></lb>corpus, nempè aer, aut aqua, aut quia ſeparantur ab <lb></lb>ipſomet nihilo, ſeù vacuo, & in vtroque caſu ratio <lb></lb>quare non tanguntur eſt quia termini eorum non <expan abbr="sũt">sunt</expan> <lb></lb>coniuncti, atque vniti. </s> <s id="s.002789">Vnde patet nullitas huius ar<lb></lb>gumenti. </s> </p> <p type="main"> <s id="s.002790"><emph type="center"></emph>PROP. CCLVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002791"><emph type="center"></emph><emph type="italics"></emph>Nulla ratio ſuadet mundum corporeum infinitum ponere, <lb></lb>vt vacuum omninò reijciatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002792">SAtis ſuperque percipio ante præmiſſam propoſi<lb></lb>tionem conuincere nedùm Peripateticos, ſed <lb></lb>etiam eos omnes, qui mundum finitum eſſe <expan abbr="cõcedũt">concedunt</expan>, <lb></lb>non verò eos qui mundi vniuerſitatem corpoream̨ <lb></lb>infinitam, & vndique extenſam eſſe ſibi ſuaſerunt, <pb pagenum="524" xlink:href="010/01/532.jpg"></pb><arrow.to.target n="marg733"></arrow.to.target><lb></lb>inter quos recenſeri videtur Carteſius, qui ait ſub<lb></lb>ſtantiam corpoream indefinitè extenſam mundum̨ <lb></lb>habere, & licèt non vtatur voce, infiniti, idem nihi<lb></lb>lominùs dicere videtur, niſi nos ludit, aut decipit; <lb></lb>nam inter finitum, & infinitum medium non datur, <lb></lb>quòd nimirùm maius ſit finito, & minus infinito, cùm <lb></lb>quicquid infinitum non eſt neceſſariò terminos ha<lb></lb>bere debeat; præterea idipſum ex eius verbis elici<lb></lb>tur, nullos enim extenſionis fines habere, idem eſt <lb></lb>prorsùs, ac infinitum eſſe, vtraque enim phraſi nega<lb></lb>tur vniuerſitati corporeæ finis, aut terminus. </s> <s id="s.002793">& licèt <lb></lb>ſe excuſent dicendo ſe non percipere mundum cor<lb></lb>poreum finitum eſſe poſſe, in hoc iterum nos deci<lb></lb>piunt, nam eſt prorsùs impoſſibile vt intellectus <lb></lb>humanus percipiat, & capiat entitatem <expan abbr="infinitã">infinitam</expan>, <expan abbr="quã-doquidem">quan<lb></lb>doquidem</expan> imagines, ſeùideas <expan abbr="corporũ">corporum</expan> finitas quas <lb></lb>ſenſibus hauſit licèt conetur ampliare, augere, & ex<lb></lb>tendere quocumque conatu, ſemper tamen concep<lb></lb>tus, & <expan abbr="phãtaſia">phantaſia</expan> in aliqua idæa vndique terminis clau<lb></lb>ſa permanet, & in ſumma limites infinitatis ne per <lb></lb>ſomnium quidem attingere poteſt. </s> <s id="s.002794">veriſſimumquę <lb></lb>eſt, quod dici ſolet, quod quotieſcumque infinitum <lb></lb>affirmamus, tunc quidem rei quam non capimus no<lb></lb>men obſcurum, & incompertæ ſignificationis tribui<lb></lb>mus; verum vt <expan abbr="proferã">proferam</expan> id, quod ſentio videtur Car<lb></lb>teſius aſſeruiſſe mundi corporei infinitatem non ab <lb></lb>aliqua firma ratione ductus, ſed ne diſſentiret à præ<lb></lb>iudicio facto, quod ſpatium inane dari non poſſet, <lb></lb>propterea quod ſpatium, ſcilicèt dimenſiones neceſ-<pb pagenum="525" xlink:href="010/01/533.jpg"></pb><arrow.to.target n="marg734"></arrow.to.target><lb></lb>ſariò exiſtentiam ſubſtantiæ corporeæ includere, & <lb></lb>indicare credebat, neque ſuaderi potuit fieri poſſe, <lb></lb>vt dimenſiones quas in ſpatio inani imaginamur ſint <lb></lb>non quid reale, & ſubſtantiale, ſed merè ens fictum, <lb></lb>& verè nihilum. </s> </p> <p type="margin"> <s id="s.002795"><margin.target id="marg733"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002796"><margin.target id="marg734"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002797">Alij aiunt à vacuo impediri diffuſionem lucis, & <lb></lb><arrow.to.target n="marg735"></arrow.to.target><lb></lb>influxuum celeſtium: præterea partes vniuerſi nullą <lb></lb>alia de cauſa partes eius cenſeri, niſi quia vnitatem, & <lb></lb>perfectionem mundi conſtituunt, hæ verò ſi diuiſæ <lb></lb>eſſent per vacuum partes eius non eſſent, quare va<lb></lb>cuum quatenus mundi vnitatem perfectionemquę <lb></lb>diſſoluit, dari non poſſe concludunt. </s> </p> <p type="margin"> <s id="s.002798"><margin.target id="marg735"></margin.target>Nona argu<lb></lb>menta con<lb></lb>tra vacuum</s> </p> <p type="main"> <s id="s.002799">Reſponderi poteſt benè in vacuo diffuſionem lu<lb></lb>cis, & influxuum fieri poſſe; nam per vacuum motus <lb></lb>corporum fieri diximus, quibus prædictæ actiones <lb></lb>perfici queunt; præterea nego mundi vniuerſitatem <lb></lb>continuam partium vnionem habere neceſſariò de<lb></lb>bere, poterit enim vocari mundus perfectus, & vnus <lb></lb>licet plures porulos vacuos habeat, ſicuti animal per<lb></lb>fectum, & vnum dicimus licet non ſit omninò conti<lb></lb>nuum, & habeat innumeras poroſitates. </s> </p> <p type="main"> <s id="s.002800">Tandem recentiores aliqui ad hominem contrą <lb></lb>vacui aſſertores ſic arguunt. </s> <s id="s.002801">Si aer nulla alia de cauſa <lb></lb>condenſatur, & rarefit, niſi quia vacua intercepta, <lb></lb>aut ſtrictiora, aut ampliora efficiuntur, cum aer inef<lb></lb>fabilem rarefactionem, & condenſationem patiatur, <lb></lb>eo quod in ſtatu rariſſimo occupet ſpatium ferè bis <lb></lb>millies maius quam in ſtatu maximæ condenſationis, <lb></lb>ſequitur quod pars ſolida, & plena aeris ſit vna pars <pb pagenum="526" xlink:href="010/01/534.jpg"></pb><arrow.to.target n="marg736"></arrow.to.target><lb></lb>bis milleſima ſpatij vacui ab eo occupati, hoc <expan abbr="autẽ">autem</expan> <lb></lb>videtur impoſſibile. </s> </p> <p type="margin"> <s id="s.002802"><margin.target id="marg736"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002803"><emph type="center"></emph>PROP. CCLIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002804"><emph type="center"></emph><emph type="italics"></emph>Ex ingenti ſpatio inani in particulis aeris contento non euin<lb></lb>citur vacui imposſibilitas.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002805">REſpondetur primò non eſſe neceſſarium vt vni<lb></lb>uerſum ſpatium intra aeris particulas conten<lb></lb>tum ſit prorsùs inane, poſſunt enim ibidem innume<lb></lb>ræ particulæ corporeæ ramoſæ, & ſolutæ exiſtere, & <lb></lb>vagari, vt ſunt exhalationes aqueæ, terreæ, igneæ, <lb></lb>& innumeræ aliæ. </s> </p> <p type="main"> <s id="s.002806">Secundò licèt prædictæ corporeæ particulæ, & <lb></lb>exhalationes in aere non adeſſent, non proinde eſ<lb></lb>ſet impoſſibilis exceſſus ille ſpatij vacui ſupra <expan abbr="plenã">plenam</expan> <lb></lb>aeris partem; nam, vt ſupra dictum eſt, valdè proba<lb></lb>bile eſt aeris particulas habere figuram tubi, ſeu ſpi<lb></lb>ræ ramoſæ, quæ nedùm bis milleſimum ſoliditatis, <lb></lb>ſed multò maius ſpatium comprehendere queant, <lb></lb>cuius rei non deſunt exempla in natura, ampullæ e<lb></lb>nim aqueæ, quas pueri efformare ſolent incompara<lb></lb>bile maius ſpatium cauum comprehendunt, quam̨ <lb></lb>ſit ſolida aquæ pars. </s> <s id="s.002807">Idipſum in ampullis vitreis <expan abbr="cõ-tingit">con<lb></lb>tingit</expan>, igitur non videtur tam abſurda, & impoſſibi<lb></lb>lis illa aeris figura, quæ poſſit prædictum grande ſpa<lb></lb>tium continere; quare nil probat hoc argumentum̨ <lb></lb>contra vacui poſitionem. </s> </p> <p type="main"> <s id="s.002808">Ex his omnibus concludere licet rationes hacte<lb></lb>nus excogitatas contra vacui poſitionem <expan abbr="conuincẽ-tes">conuincen<lb></lb>tes</expan> non eſſe. </s> <s id="s.002809">Reſtat modò vt directè oſtendamus ne-<pb pagenum="527" xlink:href="010/01/535.jpg"></pb><arrow.to.target n="marg737"></arrow.to.target><lb></lb>ceſſariò vacuum admitti debere, ad hoc autem <expan abbr="oſtẽ-dendum">oſten<lb></lb>dendum</expan> repetenda ſunt aliqua priùs expoſita, & af<lb></lb>ferenda alia ſunt, quæ ad noſtrum inſtitutum condu<lb></lb>cunt. <lb></lb><arrow.to.target n="marg738"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002810"><margin.target id="marg737"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002811"><margin.target id="marg738"></margin.target>Directè de<lb></lb>monſtratur <lb></lb><expan abbr="vacuiexiſtẽ-tia">vacui exiſten<lb></lb>tia</expan>.</s> </p> <p type="main"> <s id="s.002812">Et primò ni fallor ſatis apertè oſtendimus fluida <lb></lb>corpora diuidi non poſſe ſemper in partes, quæ pari<lb></lb>tèr fluidæ ſint, ſed neceſſariò deueniendum eſſe ad </s> </p> <p type="main"> <s id="s.002813"><arrow.to.target n="marg739"></arrow.to.target><lb></lb>particulas quantas, & figuratas; hæ verò neceſsè eſt, <lb></lb>vt vel molles, & flexibiles, aut omninò rigidæ, & du<lb></lb>ræ ſint. </s> <s id="s.002814">Igitur ſi oſtenderimus, quod corpora mollia, <lb></lb>& flexibilia neceſſariò componuntur ex particulis <lb></lb>quantis figuratiſque non mollibus, nec flexibilibus, <lb></lb>procùl dubio duræ conſiſtentes, & rigidæ erunt, & <lb></lb>proinde fluidum reſolui tandem debet in particulas <lb></lb>prorsùs duras. </s> </p> <p type="margin"> <s id="s.002815"><margin.target id="marg739"></margin.target>Cap. 7. prop. <lb></lb></s> <s id="s.002816">140. & 141.</s> </p> <p type="main"> <s id="s.002817"><emph type="center"></emph>PROP. CCLX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002818"><emph type="center"></emph><emph type="italics"></emph>Et primò oſtendendum eſt, quod minimæ particulæ corpus <lb></lb>molle componentes non poſſunt eſſe molles.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002819">SI enim hoc verum non eſt, ſint particulæ primum <lb></lb>molle corpus componentes non duræ, ſed mol<lb></lb>les; ergo diuidendo corpus molle numquam deue<lb></lb>niemus ad aliquam minimam eius particulam <expan abbr="durã">duram</expan>, <lb></lb>ſed ſemper mollis erit, (nam ſi ad rigidas perueniri <lb></lb>poſſet ex his profectò componeretur, quod non po<lb></lb>nitur) & quia eatenus tale corpus cedit mollitiem<lb></lb>que habet, quatenùs aliquæ eius partes quieſcunt <lb></lb>reliquis ab vno ad alium locum translatis, vel dę <lb></lb>verſo, & inæquali motu agitantur ab eo, quo reliquę <lb></lb><arrow.to.target n="marg740"></arrow.to.target><lb></lb>eius partes mouentur, ſed in maiori, aut minori pro-<pb pagenum="528" xlink:href="010/01/536.jpg"></pb><arrow.to.target n="marg741"></arrow.to.target><lb></lb>portione, quam partes rotæ ſolidę agitantur, vt <expan abbr="dictũ">dictum</expan> <lb></lb>eſt; vt <expan abbr="autẽ">autem</expan> <expan abbr="verũ">verum</expan> ſit nullam <expan abbr="particulã">particulam</expan> corporis mollis <lb></lb>carere hac paſſione mollitiei, neceſsè eſt, vt ſemper <lb></lb>ei conueniat mollitiei definitio, ſcilicèt ſemper quę<lb></lb>libet eius partes moueri queant, illo inæquali, & di<lb></lb><arrow.to.target n="marg742"></arrow.to.target><lb></lb>uerſo motu à cæteris contiguis; cumque contiguæ e<lb></lb>iuſdem concreti partes non poſſint diuerſis, & omni<lb></lb>bus inæqualibus motionibus agitari, niſi ſint diſſectę, <lb></lb>& inter ſe diuiſæ actu; ergo nulla particula mollis <lb></lb>corporis aſſignari poteſt, quæ non ſit ſubdiuiſa actu <lb></lb>in plures alias particulas, quare numquam perueniri <lb></lb>poterit ad finem enumerationis multitudinis parti<lb></lb>cularum actu diuiſarum in prædicto <expan abbr="cõpoſito">compoſito</expan> molli, <lb></lb>& ideò talis multitudo maior erit <expan abbr="quocũque">quocunque</expan> numero, <lb></lb>ſcilicèt maior erit quacumque finita quantitate: igi<lb></lb><arrow.to.target n="marg743"></arrow.to.target><lb></lb>tur infinita erit. </s> <s id="s.002820">At infinitæ partes ſi eſſent quantæ <lb></lb>actu diuiſæ <expan abbr="cõponerent">componerent</expan> extenſionem infinitam; ergo <lb></lb>quodlibet exiguum corpus eſſet infinitum, quod ſen<lb></lb>ſus euidentiæ repugnat, ſequitur ergo, quod prædictę <lb></lb>particulæ infinitæ non quantæ, & proinde puncta <lb></lb><arrow.to.target n="marg744"></arrow.to.target><lb></lb>indiuiſibilia ſint, hoc verò eſt impoſſibile, vt priùs <lb></lb>oſtenſum eſt; igitur partes molle corpus primum <expan abbr="cõ-ponentes">con<lb></lb>ponentes</expan> non ſunt molles, ſed aut flexibiles, aut om<lb></lb>ninò duræ, & rigidæ erunt. </s> </p> <p type="margin"> <s id="s.002821"><margin.target id="marg740"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002822">cap. 26.</s> </p> <p type="margin"> <s id="s.002823"><margin.target id="marg741"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002824"><margin.target id="marg742"></margin.target>Pro. 137.</s> </p> <p type="margin"> <s id="s.002825"><margin.target id="marg743"></margin.target>Prop. 135. & <lb></lb>136.</s> </p> <p type="margin"> <s id="s.002826"><margin.target id="marg744"></margin.target>Prop. </s> <s id="s.002827">134.</s> </p> <p type="main"> <s id="s.002828"><emph type="center"></emph>PROP. CCLXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002829"><emph type="center"></emph><emph type="italics"></emph>Eodem progreſſu oſtendemus, quod minimæ partes flexibile <lb></lb>corpus primum componentes omninò inflexibiles, <lb></lb>rigidæ, & duræ eſſe debent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002830">NAm ſi hoc verum non eſt, ſint prædictæ primæ <pb pagenum="529" xlink:href="010/01/537.jpg"></pb><arrow.to.target n="marg745"></arrow.to.target><lb></lb>particulæ componentes corpus flexibile non duræ, <lb></lb>ſed flexibiles; ergo <expan abbr="diuidẽdo">diuidendo</expan> prædictum corpus fle<lb></lb>xibile numquam deueniemus ad particulam eius, <lb></lb><arrow.to.target n="marg746"></arrow.to.target><lb></lb>quæ rigida ſit, ſed ſemper flecti poterit; & quia cau<lb></lb>ſa, quare prædictum corpus flectitur, eſt quia aliquę <lb></lb>eius partes mouentur reliquis quieſcentibus, vel di<lb></lb>uerſo, & inæquali motu, continuo corpori non com<lb></lb>petenti, ab eo quo reliquæ contiguæ partes agitan<lb></lb>tur; nec concipi poſſit nullam particulam flexibilis <lb></lb>corporis carere hac paſſione flexibilitatis, niſi ſem<lb></lb>per ei flexibilitatis definitio competat, ſcilicèt niſi <lb></lb>ſemper quælibet eius particulæ moueri queant inæ<lb></lb>quali motu diuerſo (& non proprio corporis conti<lb></lb>nui, & vniti) à cæteris contiguis; & partes contiguæ <lb></lb><arrow.to.target n="marg747"></arrow.to.target><lb></lb>eiuſdem concreti non poſſunt prædictis motibus di<lb></lb>uerſis agitari, niſi actu diuiſæ inter ſe ſint, ergo nul<lb></lb>la particula flexibilis corporis aſſignari poteſt, quæ <lb></lb>actu non ſit ſubdiuiſa in plures alias particulas; qua<lb></lb>re numquam perueniri poterit ad finem enumerati<lb></lb>onis multitudinis particularum actu diuiſarum, qua<lb></lb>propter talis multitudo maior erit quocumque nu<lb></lb><arrow.to.target n="marg748"></arrow.to.target><lb></lb>mero, ideoque infinita erit. </s> <s id="s.002831">Verùm prædictæ partes <lb></lb>infinitæ ſi eſſent quantæ, actu inter ſe diuiſæ compo<lb></lb>nerent extenſionem infinitam, ergo corpus aliquod <lb></lb>palmare v.g. infinitam extenſionem haberet, quod <lb></lb>eſt falſum; non igitur quantæ, ſed puncta indiuiſibi<lb></lb>lia erunt, quod cum ſit impoſſibile, vt dictum eſt, ſe<lb></lb><arrow.to.target n="marg749"></arrow.to.target><lb></lb>quitur, quod partes flexibile corpus componentes <lb></lb>non ſint flexibiles, proindeque duræ, & rigidæ eſſe <pb pagenum="530" xlink:href="010/01/538.jpg"></pb><arrow.to.target n="marg750"></arrow.to.target><lb></lb>debent, quod fuerat oſtendendum. </s> </p> <p type="margin"> <s id="s.002832"><margin.target id="marg745"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002833"><margin.target id="marg746"></margin.target>De vi per<lb></lb>cuſs. </s> <s id="s.002834">cap. 26.</s> </p> <p type="margin"> <s id="s.002835"><margin.target id="marg747"></margin.target>Pr. 137.</s> </p> <p type="margin"> <s id="s.002836"><margin.target id="marg748"></margin.target>Prn. 135. & <lb></lb>136.</s> </p> <p type="margin"> <s id="s.002837"><margin.target id="marg749"></margin.target>Pr. 134.</s> </p> <p type="margin"> <s id="s.002838"><margin.target id="marg750"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002839">Hinc ſequitur quòd partes minimæ <expan abbr="corporũ">corporum</expan> flui<lb></lb>dorum, mollium, & flexibilium figuram aliquam̨ <lb></lb>habere debent, omninò rigidam, duriſſimamquę. <lb></lb></s> <s id="s.002840">Pręterea deducitur, quòd in flexibili corpore flexio <lb></lb>eius fieri, continuarique poteſt, quouſque ad parti<lb></lb>culas omninò duras perueniatur, quæ poſtea nullo <lb></lb>pacto flecti poſſunt; quia quodlibet corpus durum, <lb></lb>quantum ſuos fines, ac terminos habere debet, igi<lb></lb>tur neceſſariò aliqua figura comprehenditur, ac ter<lb></lb>minatur, & ideò aut habebit figuram curuam, & ro<lb></lb>tundam, aut polihedram, aut mixtam, neque abſque <lb></lb>aliqua ex his concipi poteſt. </s> </p> <p type="main"> <s id="s.002841">His præmiſſis vlteriùs procedendo examinemus <lb></lb>quænam figuræ ſpatium implere poſſunt, & quæ <expan abbr="nõ">non</expan>. </s> </p> <p type="main"> <s id="s.002842">Vulgare eſt, angulos, qui ab vno <expan abbr="pũcto">puncto</expan> plani ſub<lb></lb><arrow.to.target n="marg751"></arrow.to.target><lb></lb>iecti circumcirca effici poſſunt, æquales eſſe quatuor <lb></lb>rectis angulis planis, ſi verò prædicti anguli minores <lb></lb>quatuor rectis fuerint, neceſſariò hiatum, & ſpatium <lb></lb>aliquod relinqui debere ab ijſdem angulis non re<lb></lb>pletum. </s> </p> <p type="margin"> <s id="s.002843"><margin.target id="marg751"></margin.target>De figuris <lb></lb>ſpatium im<lb></lb>plentibus <lb></lb>hypotheſes.</s> </p> <p type="main"> <s id="s.002844">Paritèr <expan abbr="notũ">notum</expan> eſt angulos ſolidos, qui ab vno pun<lb></lb>cto ſpatij trinam dimenſionem habentis vndiquę <lb></lb>effici poſſunt, æquales eſſe octo angulis rectis ſolidis <lb></lb>à qua ſumma ſi defecerint, procùl dubio hiatus, & <lb></lb>ſpatia aliqua inania trinam dimenſionem habentią <lb></lb>remanere debent. </s> </p> <p type="main"> <s id="s.002845"><emph type="center"></emph>PROP. CCLXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002846"><emph type="center"></emph><emph type="italics"></emph>Quænam figuræ planæ, & ſolidæ ſuis angulis <expan abbr="ſpatiũ">ſpatium</expan> implere <lb></lb>posſint.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="531" xlink:href="010/01/539.jpg"></pb><arrow.to.target n="marg752"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002847"><margin.target id="marg752"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002848">HInc deducitur, quòd ſi concurrant apices angu<lb></lb>lorum plurium figurarum planarum ad vnum <lb></lb>punctum plani ſubiecti, illę ſpatium omninò com<lb></lb>plebunt, quotieſcumque æquales quatuor angulis <lb></lb>rectis fuerint, ſin minùs aut penetratio in exceſſu, aut <lb></lb>interſtitia inania in defectu relinquere debent. </s> <s id="s.002849">Quia <lb></lb>verò figurarum planarum aliæ regulares ſunt, ſcilicèt <lb></lb>æquiangulæ, & æquilaterę, aliæ irregulares, <expan abbr="cõſtat">conſtat</expan> <lb></lb>ex Theone, Pappo, Maurolico, & alijs, ſex angulos <lb></lb>regularium triangulorum ad vnum punctum plani <lb></lb>ſubiecti concurrentes ſpatium implere, eò quòd <expan abbr="sũ-mam">sum<lb></lb>mam</expan> quatuor rectorum adæquant, ſic etiam apices <lb></lb>quatuor angulorum quadratarum figurarum ad <expan abbr="vnũ">vnum</expan> <lb></lb>punctum eiuſdem plani concurrentes ſpatium com<lb></lb>plent, non ſecùs apices trium angulorum hexagona<lb></lb>lium figurarum, paritèr ſpatium adimplent, & nullæ <lb></lb>aliæ; figurarum verò irregularium anguli ad vnum̨ <lb></lb>punctum ſpatij plani concurrentes, qui ſpatium <expan abbr="cõ-plere">con<lb></lb>plere</expan> poſſunt propemodum infinitę ſunt, ſcilicèt om<lb></lb>nes illæ, quorum anguli conuenientes ſummam qua<lb></lb>tuor rectorum æquant. </s> </p> <p type="main"> <s id="s.002850">Eaſdem proprietates habent anguli ſolidi, qui in <lb></lb>vno plano ſuis faciebus adaptari poſſunt, vt ſunt priſ<lb></lb>mata rectangula, & nonnulla alia, quorum baſes, aut <lb></lb>ſunt poligona regularia, aut non, & quando anguli <lb></lb>baſium ad vnum punctum plani ſubiecti concurren<lb></lb>tes ſpatium prædictum planum complent, etiam ſu<lb></lb>perficies planæ laterales in communi latere erecto <lb></lb>conueniunt, & tunc componunt, veluti <expan abbr="pauimentũ">pauimentum</expan>, </s> </p> <pb pagenum="532" xlink:href="010/01/540.jpg"></pb> <p type="main"> <s id="s.002851"><arrow.to.target n="marg753"></arrow.to.target><lb></lb>aut opus teſſellatum, vel muſiuum, itaque ſex priſ<lb></lb>mata rectangula triangularia, & æquilatera ad vnum <lb></lb>punctum plani ſubiecti ad aptata ſpatium omninò <expan abbr="cõ-plent">con<lb></lb>plent</expan>; ſic quoque quatuor priſmata quadrata, & non <lb></lb>minùs tria priſmata hexagonalia, & nulla alia præ<lb></lb>ter hæc, niſi baſes irregulares fuerint. </s> </p> <p type="margin"> <s id="s.002852"><margin.target id="marg753"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002853">Si verò conſiderentur corpora, quæ regularia ap<lb></lb>pellantur; patet, quod octo cubi ſuis angulis ad <expan abbr="vnũ">vnum</expan> <lb></lb>punctum conuenientibus ſpatium complent, & nullæ <lb></lb>aliæ figuræ, quę regulares ſint, & eiuſdem generis id<lb></lb>ipſum efficere poſſunt, hoc <expan abbr="autẽ">autem</expan> ingenioſiſſimè Mau<lb></lb>rolicus demonſtrauit, in ſuo Opuſculo nondùm edito <lb></lb>de figuris ſpatium implentibus, qui præterea hallu<lb></lb>cinationem Ariſtotelis, & Auerrois patefecit, noņ <lb></lb>enim duodecim anguli pyramidum ſpatium implere <lb></lb>poſſunt, ſed oportet vt octo anguli pyramidum ſex <lb></lb>angulis octahedrorum aptè vniantur ad vnum pun<lb></lb>ctum, vt ſpatium omninò expleant, & nullæ aliæ figu<lb></lb>ræ præter iam dictas. </s> </p> <p type="main"> <s id="s.002854">His præmiſſis conſiderari debent motus <expan abbr="earumdẽ">earumdem</expan> <lb></lb>figurarum, & ſymptomata, quæ in earum agitatione <lb></lb>contingunt. </s> </p> <p type="main"> <s id="s.002855"><emph type="center"></emph>PROP. CCLXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002856"><emph type="center"></emph><emph type="italics"></emph>Enumerantur figuræ ſolidæ, quæ intra alias agitatæ ſpatium <lb></lb>implere, aut non implere poſſunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002857">ET primò facilè conſtat, quod priſmata, & Cylin<lb></lb>dri moueri poſſunt motu directo axi <expan abbr="ęquidiſtã-ti">ęquidiſtan<lb></lb>ti</expan> intra cauitatem alterius corporis abſque pertur<lb></lb>batione figuræ ambientis corporis, vt gladius intra <pb pagenum="533" xlink:href="010/01/541.jpg"></pb><arrow.to.target n="marg754"></arrow.to.target><lb></lb>vaginam extrahi, & immitti poteſt; vnde patet, quod <lb></lb>in tali motu ſpatia inania non admittuntur. </s> </p> <p type="margin"> <s id="s.002858"><margin.target id="marg754"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002859">Præterea ſphæræ, coni, conoides, & cæteræ re<lb></lb>gulares figuræ curuæ motu vertiginis circa proprium <lb></lb><expan abbr="axẽ">axem</expan> rotari poſſunt, abſque perturbatione figuræ am<lb></lb>bientis corporis, & proinde <expan abbr="abſq;">abſque</expan> vacui admixtione. </s> </p> <p type="main"> <s id="s.002860">At figuræ polihedræ non priſmaticæ directè mo<lb></lb>ueri non poſſunt abſque perturbatione figuræ, ſitua<lb></lb>tionis, & diſpoſitionis ambientium <expan abbr="corporũ">corporum</expan>; & prop<lb></lb>terea neceſsè eſt vt non permaneat illa conſtipatą <lb></lb>vnio ſolidorum angulorum, quæ neceſſaria eſt ad ſpa<lb></lb>tium omninò replendum. </s> </p> <p type="main"> <s id="s.002861">Priſmata, cylindri, ſphæræ, coni, & nonnullæ aliæ <lb></lb>transferri tranſuersè motu directo, & inclinato ad a<lb></lb>xim non poſſunt, niſi figura, quam anguli ſolidi cor<lb></lb>porum ambientium repletam, & conſtipatam conſti<lb></lb>tuebant omninò perturbetur, admiſceaturque noņ <lb></lb>nihil vacui. </s> </p> <p type="main"> <s id="s.002862">| Præterea figuræ polihedræ circa aliquam lineam <lb></lb>tamquam axim circumduci <expan abbr="nequeũt">nequeunt</expan>, niſi perturbetur <lb></lb>diſpoſitio conſtipata corporum ambientium, vt iņ <lb></lb><expan abbr="pauimẽto">pauimento</expan> non poteſt vnum laterculum rotari niſi am<lb></lb>bientes laterculi ſitum, & ordinem conſtipatum mu<lb></lb>tando ſpatia inania admittant. </s> <s id="s.002863">Alia symptomata o<lb></lb>mittuntur, cùm hæc tantummodò in caſu noſtro ſuf<lb></lb>ficiant. </s> </p> <p type="main"> <s id="s.002864">Poſtea in ijs motibus in quibus inania ſpatia crea<lb></lb>ri debent videndum reſtat an poſſint, & <expan abbr="quomodotã-ta">quomodotan<lb></lb>ta</expan> celeritate prædicta inania ſpatia repleri, vt <expan abbr="nũquã">nunquam</expan> <lb></lb>vacuum admittant. <pb pagenum="534" xlink:href="010/01/542.jpg"></pb><arrow.to.target n="marg755"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002865"><margin.target id="marg755"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002866"><emph type="center"></emph>PROP. CCLXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002867"><emph type="center"></emph><emph type="italics"></emph>Primò ſi duæ ſuperficies planæ duorum corporum inflexibi<lb></lb>lium ſeſe tangant, & poſtea ſeparari debeant, aut illo <lb></lb>motu, quo plana ſemper ad inuicem æquidiſtant, aut an<lb></lb>gularitèr inclinentur, neceſſariò vacuum admitti debet.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002868">SInt duæ laminæ omninò duræ, & inflexibiles AB <lb></lb>C, & FEH, quæ ſuis planis ſuperficiebus ADC, <lb></lb>& GEH ſe mutuo tangant. </s> <s id="s.002869">aio, <lb></lb><figure id="id.010.01.542.1.jpg" xlink:href="010/01/542/1.jpg"></figure><lb></lb>quod ſi ſuprema lamina ſubleue<lb></lb>tur, aut flectendo angularitèr, aut <lb></lb>transferendo ſursùm ſuperficiem <lb></lb>GEH motu ſibi ipſi æquidiſtanti, <lb></lb>neceſſariò <expan abbr="vacuũ">vacuum</expan> admitti debet; <lb></lb>quia ob rigidam inflexibilemque <lb></lb>duritiem corporum ABC, & FEH ſuperficies ADC, <lb></lb>& GEH ſemper eamdem directam planitiem <expan abbr="retinẽt">retinent</expan>, <lb></lb>ſiuè quieſcant, ſiuè moueantur, ergo in actu ſepara<lb></lb>tionis fieri non poteſt vt pars plani GEH diuellatur, <lb></lb>ſepareturque à ſubiecto plano perſeuerante <expan abbr="cõtactu">contactu</expan> <lb></lb>reliquæ partis, aliàs duo plana haberent ſegmentum <lb></lb>commune, quod eſt impoſſibile. </s> <s id="s.002870">Hinc ſequitur, quod <lb></lb>diuulſio, & ſeparatio planarum ſuperficierum ADC, <lb></lb>& GEH fieri debeat non ſucceſſiuè, & in tempore, v<lb></lb>na pars poſt aliam, ſed tota ſimùl in vnico inſtanti, <lb></lb>itaut omnes partes ſupremæ ſuperficiei ſimul diuelli, <lb></lb>ſepararique debeant ab omnibus partibus ſuperfi<lb></lb>ciei infimæ; quaproptèr neceſsè eſt, vt in illo vnico <lb></lb>inſtanti ſeparationis creetur ſpatium interceptum̨, <lb></lb>cuius figura, aut parallelepipeda erit, (ſi ſuperficie-<pb pagenum="535" xlink:href="010/01/543.jpg"></pb><arrow.to.target n="marg756"></arrow.to.target><lb></lb>rum ſeparatio fiat motu perpendiculari ad eaſdem, <lb></lb>ſcilicèt ſi planum ſupremum ſemper ſibi ipſi æquidi<lb></lb>ſtando feratur) vel figuræ priſmatis triangularis (ſi <lb></lb>motus circularis ſit circa axim firmum, quieſcentem<lb></lb>que AG;) hoc verò ſpatium ſi repleri debet à cor<lb></lb>pore ſolido, vel fluido, quod ambiat prædictæ cor<lb></lb>pora, neceſsè eſt vt inſinuetur intra prædictum <expan abbr="hiatũ">hiatum</expan> <lb></lb>motu ſucceſſiuo, qui quantacumque celerita re fieri <lb></lb>fingatur, ſemper exigit tempus, numquam verò iņ <lb></lb>in ſtanti fiet, & proindè ſaltem per aliquod exiguum <lb></lb>tempus internæ partes prædictæ cauitatis in inſtanti <lb></lb>creatæ, remanebunt prorsùs inanes, quapropter ibi<lb></lb>dem verè vacuum admitti debet. </s> </p> <p type="margin"> <s id="s.002871"><margin.target id="marg756"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002872">Si poſtea conſideretur eiuſdem ſpatij vacui figura <lb></lb>dum fit motus ſeparationis, procùl dubio <expan abbr="cõtinentèr">continentèr</expan> <lb></lb>creſcit, aut altitudinem, aut angulum DAH <expan abbr="ampliã-do">amplian<lb></lb>do</expan>, ergo in qualibet particula temporis, in quo mo<lb></lb>tus <expan abbr="tabularũ">tabularum</expan> fit, creatur noua, & maior figura vacua, <lb></lb>& ideò in quolibet minimo tempore debet inſinuari <lb></lb>noua materia fluida, vel dura, vt replere valeat præ<lb></lb>dictum ſpatium, quæ materia ſi componitur ex par<lb></lb>tibus quantis, & duris, videtur impoſſibile accom<lb></lb>modari poſſe, vt pręcisè impleat prædicta ſpatia cre<lb></lb>ſcentia, & varias figuras habentia. </s> </p> <p type="main"> <s id="s.002873"><emph type="center"></emph>PROP. CCLXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002874"><emph type="center"></emph><emph type="italics"></emph>In ſeparatione corporum durorum contiguorum, vel conti<lb></lb>nuorum licèt aer intercipiatur, & rarefiat, vacuum eui<lb></lb>tari non potest.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><pb pagenum="536" xlink:href="010/01/544.jpg"></pb><arrow.to.target n="marg757"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002875"><margin.target id="marg757"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002876">SI quis verò recurrat ad poroſitates <expan abbr="tabularũ">tabularum</expan> aere <lb></lb>repletas, vel per quas materia fluida penetran<lb></lb>do præſtò accurrere poſſit ad replendum <expan abbr="vacuũ">vacuum</expan> cre<lb></lb>atum in inſtanti; refelli poteſt ex eò quòd tabulæ <expan abbr="nõ">non</expan> <lb></lb>vbique; & vniuersè perforatæ ſunt, alias nullam <expan abbr="dẽ-ſitatem">den<lb></lb>ſitatem</expan> haberent, & proindè neceſsè eſt, vt habeant <lb></lb>aliqua interſtitia ſolida non poroſa, quæ neceſſariò <lb></lb>quanta erunt, inter quæ interſtitia ſpatia relicta ina<lb></lb>nia in inſtanti ſeparationis, non poſſunt repleri, niſi <lb></lb>in tempore, quia fluidum accurrens motu locali ſuc<lb></lb>ceſſiuo ſpatium quantum pertranſire debet, ergo ne<lb></lb>ceſsè eſt, vt <expan abbr="ſaltẽ">ſaltem</expan> per aliquod <expan abbr="tẽpus">tempus</expan> inane remaneat. </s> </p> <p type="main"> <s id="s.002877">Et licèt aduerſarij in gratis <expan abbr="aſsũpta">aſsumpta</expan> hypotheſi <expan abbr="per-ſiſtãt">per<lb></lb>ſiſtant</expan> dicendo, quod ſemper inter duo corpora ſe tan<lb></lb>gentia fluidum intercedit, ſaltem admittere debent, <lb></lb>quod inter duas vitri portiones, quæ vnitæ, & vnum <lb></lb>continuum componere <expan abbr="aiũt">aiunt</expan>, antequam diffringantur, <lb></lb><expan abbr="ſcindãturque">ſcindanturque</expan>, neque aer, neque æther intercipiatur; <lb></lb>& in tali caſu ratio ſuperiùs adducta euincit in vitri <lb></lb>ſciſſura vacuum admitti debere. </s> <s id="s.002878">poſtea capi non po<lb></lb>teſt abſque nouo corpore forinſecùs adueniente exi<lb></lb>guam aeris <expan abbr="particulã">particulam</expan> maius ſpatium occupare poſſe, <lb></lb>ſe vndique dilatando <expan abbr="cũ">cum</expan> rarefit; & licet hoc interim <lb></lb>admittatur patet, quod prædicta ampliatio molis il<lb></lb>lius corporis, quod rarefit, ſine motu locali ſucceſſiuò <lb></lb>fieri non poſſit, transferuntur enim eius partes ab <lb></lb>exiguo, & reſtricto loco ad ampliorem, ergo dilatatio <lb></lb>illa rarefactionis neceſſariò in tempore peragi, & ab<lb></lb>ſolui debet, at illud ſpatium inane in <expan abbr="inſtãti">inſtanti</expan> creatum </s> </p> <pb pagenum="537" xlink:href="010/01/545.jpg"></pb> <p type="main"> <s id="s.002879"><arrow.to.target n="marg758"></arrow.to.target><lb></lb>fuerat, ergo à temporanea aeris rarefactione, & dila<lb></lb>tatione <expan abbr="ſpatiũ">ſpatium</expan> illud <expan abbr="vacuũ">vacuum</expan> repleri omninò non poteſt, <lb></lb>& ideo vacuum procùl dubio remanebit. </s> </p> <p type="margin"> <s id="s.002880"><margin.target id="marg758"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002881">His declaratis oſtendendum eſt neceſſariò <expan abbr="vacuũ">vacuum</expan> <lb></lb>diſperſum intra exiguas corporum particulas admit<lb></lb>ti debere. </s> </p> <p type="main"> <s id="s.002882">Quia manifeſtum eſt motum in rerum natura dari <lb></lb>intra corpora fluida, ſi oſtenderimus motus aliquos <lb></lb>fieri non poſſe abſque vacui intermixtione, erit pro<lb></lb>fectò certum vacuum admitti debere. </s> </p> <p type="main"> <s id="s.002883"><emph type="center"></emph>PROP. CCLXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002884"><emph type="center"></emph><emph type="italics"></emph>In diſciſsione corporis flexibilis, dum partes tractione ſepa<lb></lb>rantur, neceſſariò vacuum intercipitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002885">ET primò conſideremus <expan abbr="motũ">motum</expan>, quo diuelluntur, <lb></lb>ſcinduntur, & ſe parantur duo <expan abbr="fragmẽta">fragmenta</expan> ſaxi du<lb></lb>riſſimi ab aliqua valida percuſſione diffracti, vel à vi <lb></lb>cunei, aut vectis exſciſſi, in ijs duę ſuperficies <expan abbr="fragmẽ-torũ">fragmen<lb></lb>torum</expan>, quę arctiſſimè <expan abbr="cõnexę">connexę</expan> & vnitę <expan abbr="erãt">erant</expan>, licèt in <expan abbr="inſtã-ti">inſtan<lb></lb>ti</expan> videantur ab <expan abbr="inuicẽ">inuicem</expan> ſeparari, tamen fatendum eſt <lb></lb>in tempore breuiſſimo diuiſionem peragi; atque hoc <lb></lb>contingere ex flexione quam <expan abbr="patiũtur">patiuntur</expan> prædicta frag<lb></lb>menta, licèt ſint marmorea, aut adamantina, ex qua <lb></lb>inflexione fit vt prædicta <expan abbr="fragmẽta">fragmenta</expan> in actu diuiſionis <lb></lb>aliquantiſper incuruentur, & ſic non tota ſimùl in <expan abbr="in-ſtãti">in<lb></lb>ſtanti</expan> à ſubiecta ſuperficie diuellatur, ſed ſucceſſi<lb></lb>uè vna pars poſt aliam; vt ſi duæ laminæ marmoreæ <lb></lb><expan abbr="vniãtur">vniantur</expan> duabus planis ſuperficiebus AB, & CB, cum <lb></lb>diuellere planum CB aliqua potentia conatur, ſi CB <lb></lb>flexibilis ſupponatur, patet quod diſiuncta particula <pb pagenum="538" xlink:href="010/01/546.jpg"></pb><arrow.to.target n="marg759"></arrow.to.target><lb></lb>CD ab AM, adhùc reliqua tota eius portio DB ne<lb></lb>ctitur, <expan abbr="tãgitque">tangitque</expan> <expan abbr="portionẽ">portionem</expan> ſubiectam MB; poſtea per<lb></lb>ſeuerante violentia diuelli<lb></lb><figure id="id.010.01.546.1.jpg" xlink:href="010/01/546/1.jpg"></figure><lb></lb>tur ſecunda particula DE ab <lb></lb>MN, <expan abbr="perſeuerãte">perſeuerante</expan> contactu in <lb></lb>tota longitudine EB, deinde <lb></lb>tertia particula EF ſolummo<lb></lb>dò ab NO ſegregatur, & ſic <lb></lb>conſequentes reliquæ omnes <lb></lb>particulæ vna poſt aliam: Et <lb></lb>hìc <expan abbr="notãdũ">notandum</expan> eſt, quòd ſi in plano CB particulę CD, DE, <lb></lb>EF; non eſſent quantæ, ſed lineæ tranſuerſales, aut <lb></lb>puncta indiuiſibilia, quæ conſequentèr diuelleren<lb></lb>tur in ſingulis inſtantibus <expan abbr="tẽporis">temporis</expan>, procùl dubio pla<lb></lb>nities CB degeneraret transformaretur que in <expan abbr="curuã">curuam</expan> <lb></lb>ſuperficiem, quod profectò contingere <expan abbr="nõ">non</expan> poſſet, niſi <lb></lb>ſolida lamina CB conſtaret ex lineis tranſuerſalibus, <lb></lb>aut ex punctis actu inter ſe diuiſis contiguiſque, eò <lb></lb>quòd diuerſimodè moueri, & <expan abbr="trãſponi">tranſponi</expan>, <expan abbr="debẽt">debent</expan> ad hoc <lb></lb>vt perfectam <expan abbr="curuitatẽ">curuitatem</expan> acquirere poſſint. </s> <s id="s.002886">At ſi lami<lb></lb>na ex particulis quantis corporeis conſtaret, <expan abbr="quarũ">quarum</expan> <lb></lb>quælibet omninò dura, & inflexibilis fuiſſet, licèt <lb></lb>poſt inflexionem curuitatis apparentiam <expan abbr="sẽſibus">senſibus</expan> re<lb></lb>pręſentaret, tamen figuram quamdam polyhedram <lb></lb>ex pluribus planis CD, DE, EF, &c: <expan abbr="compoſitã">compoſitam</expan> effi<lb></lb>ceret, & tunc licèt prædictæ planitieculæ ſucceſſiuo <lb></lb>motu vna poſt aliam à ſubiecto plano diuellerentur, <lb></lb><expan abbr="tamẽ">tamen</expan> vnaquæque earum ob natiuam eius duritiem <lb></lb>inflexibilem tota ſimùl, & in inſtanti ſepararetur à <lb></lb>ſubiecto plano. <pb pagenum="539" xlink:href="010/01/547.jpg"></pb><arrow.to.target n="marg760"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002887"><margin.target id="marg759"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002888"><margin.target id="marg760"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002889">Cogitemus modò CB eſſe <expan abbr="laminã">laminam</expan>, ſen <expan abbr="fragmentũ">fragmentum</expan>, <lb></lb>quod ex integro marmore AB <expan abbr="diſrũpitur">diſrumpitur</expan>, licèt in actu <lb></lb>diuulſionis inflectatur lamina CB, tamen non acqui<lb></lb>rit perfectam curuitatem, quia non componitur ex <lb></lb>punctis actu inter ſe diſcretis, & inæqualibus moti<lb></lb>bus agitatis, ſed conſtat ex partibus quantis, figura</s> </p> <p type="main"> <s id="s.002890"><arrow.to.target n="marg761"></arrow.to.target><lb></lb>tis, omninò duris, & rigidis, vt oſtenſum eſt; ideoque <lb></lb>in eius inflexione acquiret figuram ex pluribus fa<lb></lb>cieculis, & ex pluribus angulis ſolidis compoſitam, <lb></lb>& ſic verum eſt, quòd integra diſtractio, & diuulſio <lb></lb>ſucceſſiuè, & in tempore abſoluitur, at vnaquæque <lb></lb>ex illis facieculis inflexibilibus à ſubiecta lamina, <expan abbr="cũ">cum</expan> <lb></lb>qua vnita, & conglutinata erat, diuelli debet, non in <lb></lb><arrow.to.target n="marg762"></arrow.to.target><lb></lb>tempore, ſed in inſtanti, vt ex dictis deducitur; mo<lb></lb>dò, quia ſpatiola illa vacua priſmatica <expan abbr="triãgularia">triangularia</expan>, in <lb></lb>inſtanti creata, nequeunt in inſtanti repleri neque à <lb></lb>ſolido, neque à fluido, ambiente corpore etiam ra<lb></lb><arrow.to.target n="marg763"></arrow.to.target><lb></lb>refacto, quandoquidem motus, quo accurrere de<lb></lb>bent ad illud ſpatium replendum in inſtanti fieri non <lb></lb>poteſt; ergo neceſſariò vacuum in illis interſtitijs ſal<lb></lb>tem per aliquod breue tempus admitti debet, & hoc <lb></lb>ſufficit ad <expan abbr="probãdum">probandum</expan>, nedùm vacuum impoſſibile <expan abbr="nõ">non</expan> <lb></lb>eſſe, ſed neceſſariò requiri ad talem motum <expan abbr="efficiẽdũ">efficiendum</expan>. </s> </p> <p type="margin"> <s id="s.002891"><margin.target id="marg761"></margin.target>Prop. 251. <lb></lb><gap></gap><expan abbr="uſq;">uſque</expan> Cor<gap></gap></s> </p> <p type="margin"> <s id="s.002892"><margin.target id="marg762"></margin.target>Prop. 264.</s> </p> <p type="margin"> <s id="s.002893"><margin.target id="marg763"></margin.target>Prop. 265.</s> </p> <p type="main"> <s id="s.002894"><emph type="center"></emph>PROP. CCLXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002895"><emph type="center"></emph><emph type="italics"></emph>In eadem ſcisſione non poteſt fluidum ambiens omninò crea<lb></lb>ta ſpatia vacua replere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002896">COnſideremus poſtea materiam corpoream, quæ <lb></lb>accurrere debet ad replendum illud ſpatium̨ <lb></lb>vacuum, quod continentèr augetur mutando <expan abbr="figurã">figuram</expan>; <pb pagenum="540" xlink:href="010/01/548.jpg"></pb><arrow.to.target n="marg764"></arrow.to.target><lb></lb>hæc profectò materia, aut mollis, vel flexibilis, aut <lb></lb>fluida ſit, oportet; & procùl dubio non poterit quam<lb></lb>libet figuram acquirere, cùm non componatur ex <expan abbr="pũ-ctis">pun<lb></lb>ctis</expan> indiuiſibilibus, ſed ex partibus quantis, duris, <lb></lb>& figuratis, & ideò non poterit accommodari ad fi<lb></lb>guram vaſis, ſeu ſpatij de nouo creati, itaut omninò, <lb></lb>& præcisè omnes eius angulos repleat; finge enim̨ <lb></lb>apicem alicuius particulæ duræ fluidum componen<lb></lb>tis præcisè accommodari, replereque angulum ſpatij <lb></lb>creati, poſtea ampliato pauliſpèr angulo ſpatij opor<lb></lb>teret, vt angulus ſolidus illius particulæ fluidæ ob<lb></lb>tuſior fieret, vel ibidem accurrere deberet angulus <lb></lb>alterius particulæ aptus ad replendum augmentum <lb></lb>prædictum angulare, quod aliundè cùm continentèr <lb></lb>creſcere, ampliarique ſupponatur, deberent accur<lb></lb>rere apices particularum fluidum componentium̨, <lb></lb>quæ haberent angulos ſolidos infinitis modis inter <lb></lb>ſe inæquales, & differentes, & hi poſtea vndequaque <lb></lb>accurrere deberent inſtantaneo motu ad replendą <lb></lb>innumera ſpatiola de nouo creata, quod profectò <lb></lb>omnem humanum captum ſuperat. </s> </p> <p type="margin"> <s id="s.002897"><margin.target id="marg764"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002898"><emph type="center"></emph>PROP. CCLXVIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002899"><emph type="center"></emph><emph type="italics"></emph>In motu fluidi intra fluidum vacua ſpatiola creantur per <lb></lb>breue tempus perſeuerantes.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002900">PErpendamus deindè motum fluidi intra ei homo<lb></lb><arrow.to.target n="marg765"></arrow.to.target><lb></lb>geneum fluidum, & quia, vt oſtenſum eſt, par<lb></lb>ticulæ primum fluidum componentes <expan abbr="nõ">non</expan> ſunt fluidæ, <lb></lb>nec indiuiſibiles, nec molles, aut flexibiles, cùm ſem<lb></lb>per in vnoquoque <expan abbr="deueniendũ">deueniendum</expan> ſit ad particulas <expan abbr="quã-">quan-</expan><pb pagenum="541" xlink:href="010/01/549.jpg"></pb><arrow.to.target n="marg766"></arrow.to.target><lb></lb>tas figuratas non molles, nec fluidas, quæ proindè <lb></lb>omninò rigidæ, & duræ eſſe debent certis, ac deter<lb></lb>minatis figuris præditæ; imaginemur modò huiuſmo<lb></lb>di duras particulas fluidum <expan abbr="componẽtes">componentes</expan> ſic coapta<lb></lb>ri, ac conſtipari vt omninò ſpatium repleant, patet <lb></lb>apices angulorum earumdem ad vnum punctum <expan abbr="cõ-uenientes">con<lb></lb>uenientes</expan> dum in quiete conſiſtunt præcisè octo an<lb></lb>gulos rectos ſolidos æquare, aliàs ſpatium omninò <lb></lb>non implerent; qualemcumque poſtea figuram ha<lb></lb>bere particulas duras fluidum componentes ſuppo<lb></lb>namus, ſi illæ omnibus varijſque motionibus agiten<lb></lb>tur, certum eſt, quod textura, ordo, & difpoſitio con<lb></lb><arrow.to.target n="marg767"></arrow.to.target><lb></lb>ſtipata particularum fluidi perturbatur, diſſoluitur<lb></lb>que, vt innumera ſpatiola vacua in inſtanti creentur. <lb></lb></s> <s id="s.002901">Hoc profectò patet exemplo pauimenti ſpicati, ſiuè <lb></lb>rexellati, ex laterculis, ſiuè lapillis angularibus po<lb></lb>lygonis variè figuratis contextum; hi ſanè concinnè <lb></lb>adaptati ſpatia lateralia omninò implent, quamdiù <lb></lb>in quiete conſiſtunt, at ſi quis velit vnum ſolummodo <lb></lb>laterculum reuoluere, aut directè horizontali motu <lb></lb>transferre inter alia latercula, neceſsè eſt vt diſſoluat <lb></lb>conſtipatam illam texturam ambientium laterculo<lb></lb>rum, quæ contorqueri, & è ſuis locis expelli debent <lb></lb>diuerſis, & contrarijs reuolutionibus, & <expan abbr="tũc">tunc</expan> eſt pror<lb></lb>sùs impoſſibile, vt anguli ſolidi ad vnum <expan abbr="pũctum">punctum</expan> <expan abbr="cõ-uenientes">con<lb></lb>uenientes</expan> æquales ſint, ſicuti priùs octo angulis re<lb></lb>ctis ſolidis, ſed neceſsè eſt, vt plura interſtitia inania, <lb></lb>ſeù à laterculis non occupata remaneant. </s> <s id="s.002902">Idem pror<lb></lb>sùs in particulis fluidum componentibus euenturum <pb pagenum="542" xlink:href="010/01/550.jpg"></pb><arrow.to.target n="marg768"></arrow.to.target><lb></lb>eſſe manifeſtum eſt. </s> <s id="s.002903">His poſitis, quia, vt antea inſinua<lb></lb>uimus, eſt impoſſibile, vt aliud corpus fluidum accur<lb></lb>rere poſſit ad replenda prædicta ſpatia vacua, quæ <lb></lb>creantur in inſtanti dum motus, aut diſgregatio flui<lb></lb>di, quod conatur ſpatia illa replere, fieri debeat, in <expan abbr="tẽ-pore">tem<lb></lb>pore</expan>; igitur eſt impoſſibile, vt ſubitò ſpatia prædicta <lb></lb>repleantur. </s> <s id="s.002904">Præterea figuræ ſolidæ, & duræ particu<lb></lb>larum eiuſdem fluidi accurrentis ineptæ ſunt ad re<lb></lb>plenda pręcisè ſpatiola vacua infinitarum figurarum, <lb></lb>quæ in motu partium prædicti fluidi creantur, igitur <lb></lb>ſi vna, vel plures partes fluidi intra alias moueri de<lb></lb>beant (vt certum eſt moueri) neceſſariò vacuitates <lb></lb>aliquæ ſaltem per aliquod breue tempus admitti de<lb></lb>bent. </s> </p> <p type="margin"> <s id="s.002905"><margin.target id="marg765"></margin.target><gap></gap> coro<gap></gap><lb></lb>pr. 262.</s> </p> <p type="margin"> <s id="s.002906"><margin.target id="marg766"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="margin"> <s id="s.002907"><margin.target id="marg767"></margin.target>Prop. 263.</s> </p> <p type="margin"> <s id="s.002908"><margin.target id="marg768"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002909">Sed dicent Carteſiani, corpora omnia dura, & flui<lb></lb>da facilè permeari à ſubſtantia quadam ſummè rara, <lb></lb>tenui, & penetranti, quæ æther appellatur, hæc ne<lb></lb>dùm poroſitates omnium conſiſtentium <expan abbr="corporũ">corporum</expan> oc<lb></lb>cupat, ſed pręſtò accurrere poſſe aiunt ad replendas <lb></lb>quaſcumque vacuitates. </s> </p> <p type="main"> <s id="s.002910"><emph type="center"></emph>PROP. CCLXIX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002911"><emph type="center"></emph><emph type="italics"></emph>Admiſſa ſubstantia ætherea ſubtilisſima, & penetrantisſi<lb></lb>ma, <expan abbr="nõ">non</expan> poſſet ipſa, vel quodlibet aliud corpus, moueri abſ<lb></lb>que vacui interpoſitione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002912"><expan abbr="COncedẽdum">COncedendum</expan> eſt primò illam ſubſtantiam æthe<lb></lb>ream fluidum quoque corpus eſſe, & ideo <expan abbr="cõ-poni">con<lb></lb>poni</expan> quoque debere ex ſuis minimis particulis noņ <lb></lb>fluidis, ſed duris, quantis, & figuratis, quæ in tem<lb></lb>pore velint, nolint, accurrere debent ad replendą <pb pagenum="543" xlink:href="010/01/551.jpg"></pb><arrow.to.target n="marg769"></arrow.to.target><lb></lb>ſpatia illa vacua in inſtanti creata; & præterea ob fi<lb></lb>guras ſolidas non poſſunt omninò replere inanitates <lb></lb>illas vt priùs dictum eſt. </s> </p> <p type="margin"> <s id="s.002913"><margin.target id="marg769"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002914">Secundò omiſſo motu partium aquæ, vel aeris, lo<lb></lb>quamur de motu partium <expan abbr="eiuſdẽ">eiuſdem</expan> fluidi ætherei, <expan abbr="oſtẽ-detur">oſten<lb></lb>detur</expan>, vt priùs ad motiones varias <expan abbr="particularũ">particularum</expan> æthe<lb></lb>ris neceſſariò vacuitates in eorum motu oriri debe<lb></lb>re, cùm non minùs ætheris particulæ ex quibus pri<lb></lb><arrow.to.target n="marg770"></arrow.to.target><lb></lb>mùm componitur, quantæ, figuratæ, & duræ ſint. </s> </p> <p type="margin"> <s id="s.002915"><margin.target id="marg770"></margin.target>Ex corolli <lb></lb>pr. 261.</s> </p> <p type="main"> <s id="s.002916">Poſſumus ergo ex his omnibus non ineptè <expan abbr="cõclu-dere">conclu<lb></lb>dere</expan>, quod ex eò quòd datur motus, admitti quoque <lb></lb>debeat vacuum diſſeminatum intra particulas com<lb></lb>ponentes corpora conſiſtentia, & fluida, ſaltem <expan abbr="tũc">tunc</expan> <lb></lb>temporis, cùm motus efficitur. </s> </p> <p type="main"> <s id="s.002917"><emph type="center"></emph>PROP. CCLXX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002918"><emph type="center"></emph><emph type="italics"></emph>Etiam corpora quieſcentia intra eorum poroſitates innu<lb></lb>mera ſpatiola vacua admittere debere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002919">QVia ſi non repugnat, immò <expan abbr="neceſſariũ">neceſſarium</expan> eſt, vacua <lb></lb>ſpatiola admitti debere, tunc temporis cùm <lb></lb>motus efficitur, quid vetat <expan abbr="eadẽ">eadem</expan> vacua diutiùs perſe<lb></lb>uerare extincto motu, dum fluidum omninò quieſcit? <lb></lb></s> <s id="s.002920">hoc profectò in fluido omnium rariſſimo, & ſubtiliſ<lb></lb>ſimo, qualis eſt ſubſtantia ætherea, affirmari debere <lb></lb>videtur planè neceſſarium, & conſequentèr in alijs <lb></lb>corporibus à prædicto æthere repletis: nam cùm eius <lb></lb>minimæ particulæ ſint quantæ, duræ, & varijs figuris <lb></lb>præditæ, videtur impoſſibile, vt exacta vnione ad in<lb></lb>uicem conſtipari ſemper, & vbique queant, vt pror<lb></lb>sùs ſpatium compleant, cùm cuſpides earum ad <expan abbr="vnũ">vnum</expan> <pb pagenum="544" xlink:href="010/01/552.jpg"></pb><arrow.to.target n="marg771"></arrow.to.target><lb></lb>punctum conuenientes ſummam octo ſolidorum an<lb></lb>gulorum rectorum numquam, vel rarò complere poſ<lb></lb>ſe videantur; veluti aceruus, & cumulus arenæ, aut <lb></lb>tritici concipi non poteſt abſque eò quòd ſpatiolą <lb></lb>innumera inter grana prædicta intercipiantur, quæ <lb></lb>ſpatiola augeri, & reſtringi poſſe experientia con<lb></lb>ſtat, quatenùs ſuccuſſo modio meliùs, & ſtrictiùs <lb></lb>granula accommodari poſſunt. </s> <s id="s.002921">Et licèt gratis conce<lb></lb>datur alicubi partes ætheris omninò ſpatium imple<lb></lb>re, ſaltem poſt eius agitationem, & commotionem̨ <lb></lb>vacua ſpatiola creari debere conſtat, vt dictum eſt; <lb></lb>cùmque eadem partium diſpoſitio perſeuerare poſ<lb></lb>ſit in ſubſequenti quiete eiuſdem fluidi ætherei, per<lb></lb>ſeuerabunt quoque poroſitates illæ vacuæ. </s> </p> <p type="margin"> <s id="s.002922"><margin.target id="marg771"></margin.target>Cap. 12. dę <lb></lb>vacui neceſ<lb></lb>ſitate.</s> </p> <p type="main"> <s id="s.002923">Huiuſmodi porrò vacua ſpatiola intra corporą <lb></lb>mundana diſperſa, & diſſeminata præclarum vſum̨ <lb></lb>habent in natura, non minùs ac pori, qui in plantis, & <lb></lb>animalibus reperiuntur; ſicuti enim per eos effluere, <lb></lb>& penetrare poſſunt exhalationes igneę, ſucci, & alia <lb></lb>corpuſcula, à quibus viuificantur, nutriuntur, & cre<lb></lb>ſcunt, ita per inanes mundanorum corporum poroſi<lb></lb>tates effluuia ignea lucida, & alia innumera pene<lb></lb>trando rerum naturalis ordo, & periodus conſerua<lb></lb>tur. </s> <s id="s.002924">Præterea ex vacuis prædictis diſſeminatis ha<lb></lb>betur facilis, & perceptibilis modus quomodo cor<lb></lb>pora fluida, mollia, & flexibilia fluere, cedere, & <lb></lb>flecti poſſint, & quomodo ſecari, diuidi, condenſa<lb></lb>ri, & rarefieri queant, ſine quibus hæ omnes operati<lb></lb>ones nullo modo percipi, & explicari poſſint. <pb pagenum="545" xlink:href="010/01/553.jpg"></pb><arrow.to.target n="marg772"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002925"><margin.target id="marg772"></margin.target>Cap. 13. cau<lb></lb>ſa rarefuncti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002926">Ex his omnibus concludere licet, nedùm extra <expan abbr="mũ-dum">mun<lb></lb>dum</expan> ſenſibilem ſpatium vacuum admitti debere, vt <lb></lb>ſupra oſtenſum eſt, ſed etiam intra corpora diſſemi<lb></lb>nata ſpatiola omninò vacua neceſſariò ponenda eſſe, <lb></lb>vt propoſitum fuerat. </s> </p> <p type="main"> <s id="s.002927"><emph type="center"></emph><emph type="italics"></emph>Quare inter fluida ſola aquea corpora cùm <expan abbr="cõgelantur">congelantur</expan> ingen<lb></lb>ti vi augeantur mole rationem reddere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002928"><emph type="center"></emph>CAP. XIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002929">EX doctrina ſuperiùs tradita, coronidis loco, ten<lb></lb>tabimus rationem reddere problematis admi<lb></lb>rabilis; quare ſola aqua, & cætera fluida aquæ <expan abbr="naturã">naturam</expan> <lb></lb>participantia, vt ſunt vinum, humores animalium, <lb></lb>& plantarum, ab intenſo frigore nedùm non conſtrin<lb></lb>guntur, & ad minus ſpatium rediguntur, vt contingit <lb></lb>in reliquis corporibus duris, mollibus, & fluidis; ſed <lb></lb>præterea <expan abbr="augẽtur">augentur</expan> mole <expan abbr="ampliãturque">amplianturque</expan>, ſcilicèt rarefi<lb></lb>unt, & hoc fit ingenti vi. </s> <s id="s.002930">Cùm ex vulgi loquendi vſu <lb></lb>denſitas à duritie non diſtinguatur, & fluida corpora <lb></lb>cenſeantur rariora eſſe corporibus denſis, & duris, <lb></lb>facilè ſuadentur nonnulli <expan abbr="quotieſcũque">quotieſcunque</expan> corpus flui<lb></lb>dum, vt aqua induratur, & glaciei <expan abbr="conſiſtentiã">conſiſtentiam</expan> acqui<lb></lb>rit; à vi frigoris, condenſatam fuiſſe, non verò rarefa<lb></lb>ctam; quia verò inter rare factionem, & <expan abbr="condenſatio-nẽ">condenſatio<lb></lb>nem</expan> hoc diſcriminis intercedit, vt in illa parua materia <lb></lb>ſeu ſubſtantia corporea grande ſpatium occupet, <expan abbr="cũ">cum</expan> <lb></lb>in hac è contra copioſior ſubſtantia corporea minus <lb></lb>ſpatium, & magis reſtrictum expleat; cùmque <expan abbr="euidẽ-tiſſimè">euiden<lb></lb>tiſſimè</expan> corpora omnia tum dura, cum fluida ab actio<lb></lb>ne, & vi caloris, & ignis rarefiant, & maiorem fluidi-<pb pagenum="546" xlink:href="010/01/554.jpg"></pb><arrow.to.target n="marg773"></arrow.to.target><lb></lb><expan abbr="tatẽ">tatem</expan> <expan abbr="acquirãt">acquirant</expan>, & è <expan abbr="cõtrà">contrà</expan> à frigiditate <expan abbr="cõdenſentur">condenſentur</expan> in<lb></lb>durenturque, videtur illis omninò impoſſibile vt ma<lb></lb>xima, & intenſiſſima actio frigiditatis, quæ eſt conge<lb></lb>latio eam paſſionem producere debeat, quæ propria <lb></lb>caliditatis eſt, & propterea negant aquam glaciatam <lb></lb>rarefactam eſſe debere. </s> </p> <p type="margin"> <s id="s.002931"><margin.target id="marg773"></margin.target>Cap. 13. cau<lb></lb>ſa rarefunctio<lb></lb>nis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002932"><emph type="center"></emph>PROP. CCLXXI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002933"><emph type="center"></emph><emph type="italics"></emph>Experientia conſtat fluida aquæ naturam participantia <lb></lb>ab intenſo frigore in actu congelationis ingenti vi rare<lb></lb>fieri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002934">NAm glacies ſuper aquam fluidam innatat, ergo <lb></lb><arrow.to.target n="marg774"></arrow.to.target><lb></lb>minùs grauis eſt ipſa aqua fluida, proindeque <lb></lb>rarior ipſa aqua erit, quod ex princi<lb></lb><figure id="id.010.01.554.1.jpg" xlink:href="010/01/554/1.jpg"></figure><lb></lb>pijs Archimedis euidentèr deducitur. </s> </p> <p type="margin"> <s id="s.002935"><margin.target id="marg774"></margin.target>Sed prædicti <lb></lb>ratiocinij fal<lb></lb>laciam Gali<lb></lb>leus olim de<lb></lb>texit.</s> </p> <p type="main"> <s id="s.002936">Poſtea in Academia experimentali <lb></lb>Medicea innumeris experimentis eui<lb></lb>cimus glaciem amplius ſpatium occu<lb></lb>pare, quàm aqua fluida, quæ omnia legi <lb></lb>poſſunt in prædicto libro <expan abbr="experimen-torũ">experimen<lb></lb>torum</expan> à fol. </s> <s id="s.002937">127. vſque ad fol. 165. vbi <lb></lb>habetur progreſſus congelationis aquæ <lb></lb><expan abbr="cõmunis">communis</expan>, tum à frigore artificiali niuis <lb></lb>producto, cùm à frigido naturali aeris; <lb></lb>& in artificiali <expan abbr="cõgelatione">congelatione</expan> ſemper ve<lb></lb>rum eſt, quod in principio immerſionis <lb></lb>vaſis vitrei ABD intra niuem RSTV <lb></lb>ſale aſper<gap></gap>ſam, primo aqua à puncto E, <lb></lb>ſcilicèt à gradu 142. breui ſaltu trium ferè graduum <lb></lb>eleuatur vſque ad F, & hìc licèt videatur augeri, & <pb pagenum="547" xlink:href="010/01/555.jpg"></pb><arrow.to.target n="marg775"></arrow.to.target><lb></lb>rarefieri moles aquæ ipſius vaſis<gap></gap>, nihilominùs ego <lb></lb>animaduerti, & docui hoc contingere à reſtrictione <lb></lb>eiuſdem vitrei vaſis; poſtea à puncto F continuato <lb></lb>motu moles aquæ decreſcit, condenſaturque, quouſ<lb></lb><arrow.to.target n="marg776"></arrow.to.target><lb></lb>que deprimatur ad punctum G graduum 120. & hìc <lb></lb>pauliſper videtur quieſcere, poſtea denuò moles <lb></lb>aquæ fluidæ augeri incipit, ſubleuaturque ab infimo <lb></lb>ſigno G vſque ad punctum H, ſcilicèt vſque ad gra<lb></lb>dum 130. & paulò poſt vehementiſſimum ſaltum a<lb></lb>qua efficit vſque ad gradum 166. in I, & tunc præ<lb></lb>cisè obtenebratur veluti nebula aqua in vaſe AB <expan abbr="cõ-tenta">con<lb></lb>tenta</expan>, & in glaciem vertitur, eodem illo exiguo, & <lb></lb>imperceptibili tempore, quo velociſſimus aquæ ſal<lb></lb>tus efficitur; præterea dum maiorem duritiem gla<lb></lb>cies acquirit, & aliquæ partes fluidæ propè colli ex<lb></lb>tremitatem AC gelantur, proſequitur fluxus aquæ <lb></lb>ſupra ſignum I verſus D, ibidemque profluit egredi<lb></lb>turque aqua extra vas; ex qua hiſtoria (relictis innu<lb></lb>meris alijs experimentis) euidentiſſimè conſtat, <expan abbr="aquã">aquam</expan> <lb></lb>in actu congelationis rarefieri, ſcilicèt expandi, & ad <lb></lb>ſpatium amplius redigi, idemque obſeruatur iņ <lb></lb>aquis ſtillatitijs; thermalibus, in vino, in aceto, in li<lb></lb>monum acredine, & in ſpiritu vitrioli; & ſolummo<lb></lb>dò aer, ſpiritus vini, olea, & hydrargyrum ab hac <lb></lb>communi lege eximuntur, quæ ab intenſiori gradu <lb></lb>frigoris ſemper magis mole imminuuntur ſtringun<lb></lb>turque, licèt oleum aliquo pacto conſiſtentiam ſoli<lb></lb>ditatemque acquirat, <expan abbr="cũ">cum</expan> aer, ſpiritus vini, & hydrar<lb></lb>gyrum ſemper fluida remaneant. <pb pagenum="548" xlink:href="010/01/556.jpg"></pb><arrow.to.target n="marg777"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002938"><margin.target id="marg775"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="margin"> <s id="s.002939"><margin.target id="marg776"></margin.target>De vi per<lb></lb>cuſs. cap. 31. <lb></lb>pr. 105.</s> </p> <p type="margin"> <s id="s.002940"><margin.target id="marg777"></margin.target>Cap. 13. cau<lb></lb>ſa rarefactio<lb></lb>nis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002941">Quòd verò vis, qua aqua dilatatur, in actu conge<lb></lb>lationis ſit propemodum immenſa, conſtat ex experi<lb></lb>mentis ibidem traditis, vaſa enim vitrea vndiquę <lb></lb>clauſa in actu congelationis aquæ incluſæ diffringun<lb></lb>tur, & vaſa ærea paritèr clauſa, licèt eius parietes <lb></lb>craſſitiem ſemidigiti auricularis habeant, nihilomi<lb></lb>nùs etiam diſcinduntur, diffringunturque, quod qui<lb></lb>dem à vi, & energia cunei compreſſi à vaſto ponde<lb></lb>re præſtari minimè poſſet. </s> </p> <p type="main"> <s id="s.002942">Ex recentioribus aliqui tentarunt cauſam rarefa<lb></lb>ctionis glaciei reddere; primò ex principijs Gaſſen<lb></lb>di, qui expreſsè negat frigiditatem eſſe meram calo<lb></lb>ris priuationem: ſed ſicuti in natura dantur corpuſcu<lb></lb>la ignea caliditatem producentia, fic quoque dari <lb></lb>corpuſcula aliqua tetraedica, quæ frigorifica, ſiuę <lb></lb>alinitralia à Gaſſendo appellantur; hæc dum intrą <lb></lb>aquam inſinuantur, molis amplitudinem, <expan abbr="cõnexionẽ">connexionem</expan>, <lb></lb>& duritiem creare putant, vnà cum ingenti frigidita<lb></lb>te, & hanc eſſe cauſam rarefactionis, ſeù ampliatio<lb></lb>nis, quam aqua glaciata acquirit. </s> </p> <p type="main"> <s id="s.002943"><emph type="center"></emph>PROP. CCLXXII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002944"><emph type="center"></emph><emph type="italics"></emph>Rarefactio, & augmentum molis aquæ glaciatæ non effici<lb></lb>tur à mixtione, & interpoſitione corpuſculorum frigidi<lb></lb>tatem creantium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002945">SEd hoc duplici modo redargui mihi poſſe vide<lb></lb>tur; primò, quia ſalia prædicta aquæ admixtą <lb></lb>pondus, & grauitatem eius augere aliquo pacto de<lb></lb>berent, quod quidem <expan abbr="experiẽtiæ">experientiæ</expan> repugnat, cùm cya<lb></lb>thus aquæ fluidæ vnius libræ v.g. poſt eius congela-<pb pagenum="549" xlink:href="010/01/557.jpg"></pb><arrow.to.target n="marg778"></arrow.to.target><lb></lb>tionem ad exactiſſimam trutinam examinatus nè mi<lb></lb>nimum quidem nouum pondus acquirat. </s> <s id="s.002946">His adde, <lb></lb>quòd non parua moles ſalis requiritur ad congelan<lb></lb>dam eamdem aqueam maſſam, <expan abbr="tãtopere">tantopere</expan> ampliatam, <lb></lb>quia deberet ſal per vniuerſas aquæ particulas di<lb></lb>ſpergi, vt prædictam vnionem, condenſationemque <lb></lb><expan abbr="vniuerſalẽ">vniuerſalem</expan> crearet: <expan abbr="cũmque">cumque</expan> ſalia ex ſui natura graui<lb></lb>ora ſint ipſa aqua, igitur valdè augeri deberet pon<lb></lb>dus in aqua glaciata; nec valet effugium, quòd parti<lb></lb>culæ illæ ſalinę ſint volatiles, <expan abbr="nã">nam</expan> ex obſeruationibus <lb></lb>in Academia experimentali Medicea factis conſtat <lb></lb>ſal volatile non differre ſubſtantia, conſiſtentia, & <lb></lb>figura à ſale fixo eiuſdem generis. </s> </p> <p type="margin"> <s id="s.002947"><margin.target id="marg778"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002948">Præterea ſi aqua in glaciem verſa mole augetur, <lb></lb>quia intra eius ſubſtantiam inſinuantur, <expan abbr="miſcenturq;">miſcenturque</expan> <lb></lb>corpora frigorifica, vel ſalina, profectò omnia cor<lb></lb>pora fluida ab eodem gradu frigiditatis æquè auge<lb></lb>ri mole, & ampliari deberent, ac aqua glaciata; cùm <lb></lb>ex hypotheſi nulla alia de cauſa corpora frigida red<lb></lb>dantur niſi quia replentur, & impręgnantur ab illis <lb></lb>corpuſculis, ſiue ſalibus frigorificis, ſed hoc eſt fal<lb></lb>ſum, nam aer, ſpiritus vini, oleum, & hydrargyrum <lb></lb>licèt eidem boreali vento exponantur, non augentur <lb></lb>mole, imò multò magis condenſantur, imminuuntur<lb></lb>que, & ſi præterea intenſiori gradu frigoris affician<lb></lb>tur, quàm ſit ille, qui aquam glaciare valet, perſeue<lb></lb>rat nihilominùs in illis fluiditas, & continentèr, ma<lb></lb>gis, ac magis mole imminuuntur, ſcilicèt ſemper mi<lb></lb>nus, ac minus ſpatium occupant, igitur rarefactio, & <pb pagenum="550" xlink:href="010/01/558.jpg"></pb><arrow.to.target n="marg779"></arrow.to.target><lb></lb>augmentum molis glaciei non efficitur ab aſperſione, <lb></lb>& miſtione corpuſculorum, & ſalium <expan abbr="frigorificorũ">frigorificorum</expan>, <lb></lb>ſed ab alia longè diuerſa cauſa phænomenon hoc de<lb></lb>pendet. </s> </p> <p type="margin"> <s id="s.002949"><margin.target id="marg779"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002950">Hoc Gaſſendus indicaſſe videtur, cùm ait, in glacie <lb></lb>non paucas aeris particulas commiſceri, proptereą <lb></lb>quòd videmus congelationem aquæ initium habere <lb></lb>in eius ſummitate, quæ aerem contingit, & hinc po<lb></lb>ſtea inferiùs propagari versùs fundum; & hinc ait <expan abbr="pẽ-dere">pen<lb></lb>dere</expan>, quòd glacies ſuper aquam innatat, cùm ſit aere <lb></lb>impręgnata; à quo poſtea veriſimile eſt perſuaſum̨ <lb></lb>fuiſſe ampliari poſſe molem aquæ glaciatæ, & hoc <lb></lb>conijcitur ex eius verbis, dum ait, <emph type="italics"></emph>cùm verum ſit <expan abbr="aquã">aquam</expan> <lb></lb>calefactam refrigeſcendo citiùs fortiuſque conglaciare, <expan abbr="quã">quam</expan> <lb></lb>frigidam, ecquam aliam putemus cauſam, quàm quia facta <lb></lb>maiore <expan abbr="quadã">quadam</expan> partium aquæ laxitate, ipſe aer faciliùs ſub<lb></lb>ingreditur, & vehementiùs ſtringit particulas aquæ, qui<lb></lb>bus commiſcetur?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.002951">Ex quibus Gaſſendi verbis elicitur, quòd ab aere <lb></lb>deforis adueniente in actu congelationis aqua infle<lb></lb>tur, & rarefiat. </s> </p> <p type="main"> <s id="s.002952"><emph type="center"></emph>PROP. CCLXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002953"><emph type="center"></emph><emph type="italics"></emph>Nec paritér augetur aquæ moles ànouo aere de foris adueni<lb></lb>ente in actu congelationis eius, neque à directione, & <expan abbr="tẽ-ſione">ten<lb></lb>ſione</expan> anguillularum aquæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002954">SI hoc verum eſſet, cùm omninò prohibetur aeris <lb></lb>ingreſſus intra aquam, non deberet in actu con<lb></lb>gelationis rarefieri, & ampliari eius moles, vtcùm̨ <lb></lb>vas plumbeum, vel aureum aqua plenum, & <expan abbr="vndiq;">vndique</expan> <pb pagenum="551" xlink:href="010/01/559.jpg"></pb><arrow.to.target n="marg780"></arrow.to.target><lb></lb>clauſum aeri frigidiſſimo exponitur, vel intra niuem <lb></lb>ſali admixtam demergitur, omninò à metalli <expan abbr="conſiſtẽ-tia">conſiſten<lb></lb>tia</expan> prohiberetur impedireturque ingreſſus aeris in<lb></lb>tra aquam, quaproptèr tunc <expan abbr="nõ">non</expan> deberet aqua in actu <lb></lb>congelationis rarefieri, & ampliari mole, quod <expan abbr="tamẽ">tamen</expan> <lb></lb>experientiæ repugnat; euidentiſſimè enim ampullą <lb></lb>illa plumbea, vel aurea ſua mollitie cedendo expan<lb></lb>ſioni internæ glaciei inflatur efficiturque ſphæra ma<lb></lb>ioris diametri. </s> <s id="s.002955">præterea proximè ante aquæ conge<lb></lb>lationem è profundiori aqua vaſis aſcendunt aereą <lb></lb>grana, non ab extrinſeco aere intra eiuſdem vaſis a<lb></lb>quam demergi granula illa conſpiciuntur; non igitur <lb></lb>à nouo aere ſubingrediente, & penetrante aquæ ſub<lb></lb>ſtantiam rare fieri, inflarique poteſt aqua glacialis. </s> </p> <p type="margin"> <s id="s.002956"><margin.target id="marg780"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002957">Nec rarefit ob directionem anguillularum aquam <lb></lb><expan abbr="componentiũ">componentium</expan>, vt putat Carteſius: hęc enim ſententia <lb></lb>improbabilis eſſe videtur, primò ob poſitionis ab<lb></lb>ſurditatem, non enim poteſt aqua <expan abbr="cõponi">componi</expan> ex anguil<lb></lb><arrow.to.target n="marg781"></arrow.to.target><lb></lb>lulis illis, vt ſuperiùs inſinuauimus; Inſuper ſenſu <lb></lb>conſtat in glacie innumera granula aerea de nouo <lb></lb>apparere, quæ priùs inconſpicua erant; quaproptèr <lb></lb>non à directione, & tenſione anguillalarum, ſed ab <lb></lb>illo aere, vel ab alia concomitante cauſa <expan abbr="aquã">aquam</expan> infla<lb></lb>ri, & rare fieri debere fatendum eſt. <lb></lb><arrow.to.target n="marg782"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002958"><margin.target id="marg781"></margin.target>Prop. 155.</s> </p> <p type="margin"> <s id="s.002959"><margin.target id="marg782"></margin.target>Intra aquæ <lb></lb>ſubitantiam <lb></lb>in<gap></gap>nummerae<gap></gap> ae<lb></lb>ris parti<gap></gap>cule <lb></lb><gap></gap>eommixtæ <lb></lb>r<gap></gap> periuntur</s> </p> <p type="main"> <s id="s.002960">Modò animaduertendum eſt pro ſolutione huius <lb></lb>problematis, quòd in aqua fluida innumerę aeris par<lb></lb>ticulæ admixtæ, & diſſeminatæ perpetuò reperiun<lb></lb>tur; ſiuè hoc contingat ex eo quod aqua aeri <expan abbr="cõtermi-na">contermi<lb></lb>na</expan> in varia eius agitatione aeris aliquas particulas in<pb pagenum="552" xlink:href="010/01/560.jpg"></pb><arrow.to.target n="marg783"></arrow.to.target><lb></lb>tercipit, retinetque intra ſe <expan abbr="ipsã">ipsam</expan>; vel quia ex ſubiecta <lb></lb>terra vnà cum exhalationibus igneis per eius poros <lb></lb>expirantes transferuntur inſinuanturque intra <expan abbr="aqueã">aqueam</expan> <lb></lb>maſſam innumeræ eiuſdem aeris particulæ, quæ ſi <lb></lb>grandiorem molem conſtituunt, multis <expan abbr="nimirũ">nimirum</expan> par<lb></lb>ticulis ſimul aggregatis, tunc globulos, ſiuè ampul<lb></lb>las aliquas aereas <expan abbr="cõponũt">componunt</expan>, quæ è fundo aquæ <expan abbr="cõti-nuato">conti<lb></lb>nuato</expan> motu ad <expan abbr="ſupremũ">ſupremum</expan> eius confinium feruntur; & <lb></lb>hoc paſſim obſeruatur in littore maris ijs in locis vbi <lb></lb>ſolum eſt lutoſum, præſertim æſtate, exiſtente mari <lb></lb>tranquillo, apparet enim ſeries plurium <expan abbr="ampullularũ">ampullularum</expan> <lb></lb>è fundo aſcendere varijs in locis; ſed <expan abbr="qualiſcũque">qualiſcunque</expan> ſit <lb></lb>cauſa huius admiſtionis, euidentiſſimum eſt <expan abbr="ingentẽ">ingentem</expan> <lb></lb>copiam aerearum <expan abbr="particularũ">particularum</expan> in ipſa aqua reperiri, <lb></lb>licèt viſu non percipiantur; quod confirmari poteſt <lb></lb>pulcherrimo <expan abbr="inſtrumẽto">inſtrumento</expan> Torricelliano, in quo <expan abbr="vacuũ">vacuum</expan> <lb></lb>mediante aqua efficitur, nam dum aqua deſcendit ad <lb></lb>ſolitam depreſſionem 17. cubitorum proximè, tunc <lb></lb>videmus ab aqua tantam <expan abbr="copiã">copiam</expan> ampullarum <expan abbr="aerearũ">aerearum</expan> <lb></lb>egredi, vt repręſentet ebullitionem, <expan abbr="quã">quam</expan> efficere ſolet <lb></lb>feruor ignis in eadem aqua; & hoc pendet ex eo <lb></lb>quòd particulæ minimæ aeris ibidem non vt priùs <lb></lb>comprimuntur ab ingenti pondere aereæ regionis, <lb></lb>ſed ſolummodò ab exigua grauitate aquæ <expan abbr="incumbẽ-tis">incumben<lb></lb>tis</expan>, quod perſuadetur ex eo, quòd profundiora gra<lb></lb>nula aeris, quæ ob paruitatem ferè inconſpicua <expan abbr="erãt">erant</expan>, <lb></lb>quò magis ad ſummitatem aquæ accedunt, eò magis <lb></lb>ampliantur inflantur, grandioreſque ampullas <expan abbr="cõſti-tuunt">conſti<lb></lb>tuunt</expan>, quarum aliquæ nucis magnitudinem æquant, <pb pagenum="553" xlink:href="010/01/561.jpg"></pb><arrow.to.target n="marg784"></arrow.to.target><lb></lb>prout magis vis elaſtica aeris libertatem nacta am<lb></lb>pliare dilatareque eaſdem ampullas poteſt. </s> <s id="s.002961">certiſſi<lb></lb>mum ergo eſt intra aquam contineri innumeras aeris <lb></lb>particulas ſenſui non manifeſtas, aliquando magis, <lb></lb>aliquando minùs copioſas; nec mirum eſt, aerem le<lb></lb>uem intra grauius fluidum retineri poſſe, cùm no<lb></lb>uum non ſit ob molis minutiem corpuſcula varia, tum <lb></lb>grauiſſima, cum leuiſſima intra aquam retineri, & <lb></lb>quieſcere poſſe, vt ſuperius inſinuatum eſt. </s> </p> <p type="margin"> <s id="s.002962"><margin.target id="marg783"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="margin"> <s id="s.002963"><margin.target id="marg784"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002964">Inſuper ſenſu conſtat, quòd in glacie innumeræ <lb></lb>ampullæ aere refertæ ſparſim reperiuntur, vt pluri<lb></lb>mùm ſphæricæ, ſi paruulæ fuerint, conformantur, at ſi <lb></lb>grandiores fuerint, oblongæ ſunt, & multoties <expan abbr="ſeriẽ">ſeriem</expan> <lb></lb>plurium fiſtularum repręſentant, quæ aliquando me<lb></lb>dietatem ſpatij totius glaciei adęquant; vt verò con<lb></lb>ſtaret an prædictæ ampullæ glaciei eſſent vacuæ, vel <lb></lb>aere plenæ, eiuſdem glaciei fruſtum intra aquam flui<lb></lb>dam demerſi, poſtea ſtylo ferreo acuto diligentèr e<lb></lb>ius cruſtam ſolidam perforaui vſque ad ampullas, & <lb></lb>tunc remoto ſtylo egrediebatur ab illo ſpatio am<lb></lb>pulla corporea aerea, quæ in tranſitu per aquam flui<lb></lb>dam ſuum ſpatium ſphęricum | occupabat, quouſquę <lb></lb>ad aeris confinium perducta ibidem difflaret, & cum <lb></lb>eo commiſceretur. </s> </p> <p type="main"> <s id="s.002965"><emph type="center"></emph>PROP. CCLXXIV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002966"><emph type="center"></emph><emph type="italics"></emph>Minimæ particulæ aquam componentes minores ſunt par<lb></lb>ticulis aerem componentibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002967">HOc plurima experimenta perſuadent; videmus <lb></lb>enim, quod aquæ particulæ per vaſis fictilis, <pb pagenum="554" xlink:href="010/01/562.jpg"></pb><arrow.to.target n="marg785"></arrow.to.target><lb></lb>aut lignei poroſitates exudare, & egredi poſſunt, <lb></lb>per quas aer tranſire nequit, ſic paritèr in burſa co<lb></lb>riacea aqua per eius poroſitates, licèt motu tardo, <lb></lb>permeare poteſt, cùm aer ibidem contentus, licèt in<lb></lb>genti vi comprimatur, egredi non poſſit; erunt igitur <lb></lb>particulæ aereæ grandiores, quàm aqueæ particulæ, <lb></lb>cùm per prædicta foraminula pertranſire nequeant, <lb></lb>licèt poſtea aeris partes, vtpote ipſa aqua rariores <lb></lb>contineant intra ſeipſas ingentia ſpatia vacua ſi <expan abbr="cõ-parentur">con<lb></lb>parentur</expan> cum ſua mole denſa, & plena; vnde ſupra <lb></lb>coniecimus, particulas aeris eſſe veluti ſpiras, vel in<lb></lb>uolucra ex ſubtiliſſimis laminis contortis, inuolutiſ<lb></lb>que efformatas; è contra aquæ minimas particulas <lb></lb>habere figuram plenam, & ſolidam, vel <expan abbr="octaedrã">octaedram</expan>, <lb></lb>vel alterius figuræ ad rotunditatem accedentis, quæ <lb></lb>tamen habent exiguam lanuginem eas ambientem, vt <lb></lb>hactenùs inſinuauimus. <lb></lb><arrow.to.target n="marg786"></arrow.to.target></s> </p> <p type="margin"> <s id="s.002968"><margin.target id="marg785"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="margin"> <s id="s.002969"><margin.target id="marg786"></margin.target>Poſſibile eſt <lb></lb>minimas a<lb></lb>quæ particu<lb></lb>las intra va<lb></lb>cuos tubu<lb></lb>los aerem̨ <lb></lb>componen<lb></lb>tium inſinu<lb></lb>ari poſſe.</s> </p> <p type="main"> <s id="s.002970">Hinc deducitur non eſſe impoſſibile, nec à verita<lb></lb>te omninò alienum, vt particulæ minimæ aquæ tam̨ <lb></lb>minutæ ſint, vt poſſint intra vacuas capacitates aere<lb></lb>arum particularum, ſcilicèt intra tubulos illos conti<lb></lb>neri; & ideò ab aliqua vi poſſint ibidem inſinuari, <lb></lb>quare vt poſſibilis huiuſmodi hypotheſis admitti <lb></lb>poſſe videtur. </s> </p> <p type="main"> <s id="s.002971">Ad hæc <expan abbr="ſupponendũ">ſupponendum</expan> quoque eſt aeris inuolucra, <lb></lb>vel ſpiras non componi ex laminulis graciliſſimis om<lb></lb>ninò læuibus, explanatiſque, vt ſpeculum, ſed habere <lb></lb>villos aliquos non diſſimiles ijs, quos in extima ſuper<lb></lb>ficie particularum aquæ reperiri diximus, huiuſmodi <pb pagenum="555" xlink:href="010/01/563.jpg"></pb><arrow.to.target n="marg787"></arrow.to.target><lb></lb>verò villi non eſt impoſſibile, vt in interna ampla ca<lb></lb>uitate cylindrulorum, vel ſpirarum, ramos proten<lb></lb>dant, itaut internè habeant veluti capillitium com<lb></lb>poſitum ex villis flexibilibus, & reſilientibus ad mo<lb></lb>dum machinæ, eiuſdem naturæ, ac eſt tota aeris ſub<lb></lb>ſtantia, & non minus quam habet aquæ capillitium, <lb></lb>ſed oportet vt villi interni aereorum inuolucrorum̨ <lb></lb>facilè poſſint à calido molleſcere, vt omninò flectan<lb></lb>tur, & rigiditatem amittant, & è contra à frigido, ſeù <lb></lb>à defectu caliditatis rigiditatem, & tenſionem eius <lb></lb>naturalem reaſſumant, & acquirant; cuius rei non de<lb></lb>ſunt exempla in natura; videmus enim <expan abbr="cerã">ceram</expan>, metalla, <lb></lb>& innumera alia concreta, quæ à caliditate, ſcilicèt <lb></lb>ab incurſu igniculorum mollia, cedentia, & flexilia <lb></lb>redduntur; è contra diſcedente caliditate ſpontę <lb></lb>ſua priſtinam duritiem, tenſionemque acquirunt: non <lb></lb>igitur erit impoſſibile, vt eiuſdem naturæ ſint villi, <lb></lb>qui intra tubulorum aereorum capacitatem <expan abbr="diramã-tur">diraman<lb></lb>tur</expan>, protendunturque. </s> </p> <p type="margin"> <s id="s.002972"><margin.target id="marg787"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002973"><emph type="center"></emph>PROP. CCLXXV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002974"><emph type="center"></emph><emph type="italics"></emph>His præmisſis inquirenda eſt ratio, & cauſa quare aqua in <lb></lb>actu congelationis rarefit, <expan abbr="ampliorẽque">ampliorenque</expan> molem acquirit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002975">EVidentiſſimum eſt, quòd in actu congelationis <lb></lb>exurgunt de nouo intra aquę ſubſtantiam innu<lb></lb>meræ ampullæ aere plenæ, quæ prius non <expan abbr="apparebãt">apparebant</expan>: <lb></lb>hæ procùl dubio non adueniunt deforis, ſed origi<lb></lb>nem, & ortum habere videntur in ipſamet aqua, vt <lb></lb>dictum eſt: & quia ridiculum eſt à frigore intra gla<lb></lb><arrow.to.target n="marg788"></arrow.to.target><lb></lb>ciem de nouo aerem gigni, fatendum eſt aeris innu-<pb pagenum="556" xlink:href="010/01/564.jpg"></pb><arrow.to.target n="marg789"></arrow.to.target><lb></lb>meras particulas ita commiſceri aquæ fluidæ, vt om<lb></lb>ninò <expan abbr="lateãt">lateant</expan>, eo modo quo particulæ terreæ vrinæ ad<lb></lb>miſtæ, vel metallicæ in aquis corroſiuis diſperſæ, <lb></lb>prorsùs inconſpicuæ ſunt, vt tranſpicuitatem liquo<lb></lb>rum non perturbent. </s> <s id="s.002976">Sed licèt hoc facilè <expan abbr="cõcedi">concedi</expan> poſ<lb></lb>ſit, nihilominùs remanet præcipua, & maxima diffi<lb></lb>cultas, quomodo, & qua diſpoſitione intra <expan abbr="aquã">aquam</expan> col<lb></lb>locari, ſit uarique poſſint aereæ particulæ, vt poſtmo<lb></lb>dum in actu congelationis extenſionem, & <expan abbr="inflationẽ">inflationem</expan> <lb></lb>ipſius aquæ efficere poſſit. </s> </p> <p type="margin"> <s id="s.002977"><margin.target id="marg788"></margin.target>Pr. 173.</s> </p> <p type="margin"> <s id="s.002978"><margin.target id="marg789"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002979">Huic difficultati occurri mihi poſſe videtur, <expan abbr="expẽ-dendo">expen<lb></lb>dendo</expan> figuras, & moles particularum aeris, & aquæ. <lb></lb></s> <s id="s.002980">quia, vt ſupra innuimus, aeris particulę compoſitæ vi<lb></lb>dentur ex laminulis tenuiſſimis ramoſis, & villoſis <lb></lb>ſpiralitèr contortis, quæ proinde grande ſpatium va<lb></lb>cuum intra ſe comprehendant; è contra particulæ <lb></lb>aquæ minutiores eſſe videntur, vt nimirum poſſint in<lb></lb>gredi inſinuarique intra inanes cauitates tubulorum <lb></lb>aereorum, propterea cauitates aerearum particula<lb></lb>rum infra aquam fluidam exiſtentium facilè repleri <lb></lb>poſſunt à minutioribus aqueis particulis, & ſic aqua <lb></lb>communis fluida in ſtatu eius naturali quid ſimile fo<lb></lb>ret cumulo tritici intra quem plures tubi arundinei <lb></lb>eodem tritico pleni continerentur: & hìc conſtat, <lb></lb>quod amplitudo, & moles prædicti cumuli compone<lb></lb>retur ex ſub ſtantia corporea granulorum, & <expan abbr="ſolidarũ">ſolidarum</expan> <lb></lb>partium eorumdem tubulorum. </s> <s id="s.002981">fingamus modò ab <lb></lb>aliqua virtute expelli à cauitatibus tubulorum triti<lb></lb>cum, quod in ipſis continebatur, vt nimirùm tubuli <pb pagenum="557" xlink:href="010/01/565.jpg"></pb><arrow.to.target n="marg790"></arrow.to.target><lb></lb>omnes vacui omninò remaneant; nonne ſequitur ne<lb></lb>ceſſariò ampliatio molis totius cumuli; non quidem <lb></lb>à dilatatione facta ab ipſis <expan abbr="arũdinibus">arundinibus</expan>, ſed ex eo quod <lb></lb>grana frumenti expulſa ſpatium ſibi æquale intra tri<lb></lb>ticum occupare debent, & ſic tota maſſa conſtans ex <lb></lb>ijſdem granulis frumenti corporeis, & ex ſpatijs va<lb></lb>cuis in arundinibus relictis, procùl dubio maius ſpa<lb></lb>tium occupare deberet, quàm priùs, & proindè am<lb></lb>pliaretur moles totius aggregati, & rarefieri videre<lb></lb>tur. </s> <s id="s.002982">Non ſecùs in aqua pura fluida ſpiræ, vel tubuli <lb></lb>aerei, qui priùs à particulis aquæ replebantur ſi po<lb></lb>ſtea ab aliqua neceſſitate exinanirentur, expulſa ni<lb></lb>mirùm aqua, quæ ibidem coercebatur, profectò per<lb></lb>cipimus molem totius aquæ ampliari augerique de<lb></lb>bere, propterea quod inſurgerent denuo tot ſpatio<lb></lb>la vacua quot ſunt ſpiræ, vel tubuli aerei, & hæc vnà <lb></lb>cum ſolidis particulis aquæ amplius ſpatium re<lb></lb>quirerent, & ideò moles aquea aucta, & rarefactą <lb></lb>videretur. </s> </p> <p type="margin"> <s id="s.002983"><margin.target id="marg790"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002984">Eò igitur difficultas redacta eſt, vt oſtendamus in <lb></lb>actu congelationis aquæ huiuſmodi operationem̨ <lb></lb>fieri poſſe, & indagemus modum, neceſſitatem, & <lb></lb>vim motiuam huius operationis. </s> </p> <p type="main"> <s id="s.002985">Et primò duplici modo inſinuari mihi poſſe viden<lb></lb>tur aquæ particulæ intra cauitates ſpirarum, ſiuè tu<lb></lb>bulorum aeris, aut à violentia externa, aut <expan abbr="ſpõte">ſponte</expan> ſua; <lb></lb>vtroque modo fieri poſſe non videtur improbabile; <lb></lb>certum enim eſt ignis particulas, ſeù exhalationes <lb></lb>perpetuo diſcurrere, fluere que per omnia corporą <pb pagenum="558" xlink:href="010/01/566.jpg"></pb><arrow.to.target n="marg791"></arrow.to.target><lb></lb>tàm denſa, quàm fluida, igitur quò maior erit copia <lb></lb><expan abbr="diſcurrẽtium">diſcurrentium</expan> igniculorum, eò magis corpora inertia, <lb></lb>vt ſunt aquę particulæ intra aquam æquilibratæ, agi<lb></lb>tari impellique poſſunt; perſeuerante igitur aqua in <lb></lb>ſtatu fluido procùl dubio per <expan abbr="eã">eam</expan> maior copia ignicu<lb></lb>lorum diffunditur agitaturque, quàm dum coaleſcit, <lb></lb>& ab ingenti frigore congelatur, nam frigiditas, aut <lb></lb>eſt mera priuatio igniculorum, aut ſine eorum defe<lb></lb>ctu, & abſentia, nec exiſtere, neque operari poteſt; <lb></lb>non ergò limites probabilitatis tranſcendit vt in ſta<lb></lb>tu fluiditatis maior copia igniculorum, vel exhalati<lb></lb>onum ignearum impellere poſſit minimas aquæ par<lb></lb>ticulas, eaſque inſinuare intra vacua ſpatia <expan abbr="tubulorũ">tubulorum</expan> <lb></lb>aereorum, in quibus villi interni eorumdem non ri<lb></lb>gidam omninò tenſionem habere poſſunt, & proindè <lb></lb>vehementię maiori, qua igniculi particulas aquæ im<lb></lb>pellunt cedere poſſint; & in hoc caſu ceſſante copią <lb></lb>igniculorum, ſcilicèt in ſtatu algoris, & ingentis fri<lb></lb>giditatis, aut nullo pacto, aut debiliori conatu parti<lb></lb>culæ aqueæ impelli poſſent, & proindè villi interni <lb></lb>tubulorum aereorum, vt totidem machinulæ valen<lb></lb>tiori vi ſuæ <expan abbr="tẽſionis">tenſionis</expan> expellere aquæ particulas è præ<lb></lb>dictis cauitatibus fiſtularum poſſent. </s> </p> <p type="margin"> <s id="s.002986"><margin.target id="marg791"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002987">At ſi ſupponamus non impelli violenter aquę par<lb></lb>ticulas intra aereos tubulos, ſed ſponte ſua vi graui<lb></lb>tatis fluere inſinuarique intra ſpatiola vacua eorum<lb></lb>dem tubulorum; tunc ſupponendum eſt, vt ſuperiùs <lb></lb>inſinuauimus, villos internos tubulorum aeris à frigi<lb></lb>ditate, ſeù ab igniculorum abſentia rigidiores, & <expan abbr="tẽ-">ten-</expan><pb pagenum="559" xlink:href="010/01/567.jpg"></pb><arrow.to.target n="marg792"></arrow.to.target><lb></lb>ſiores reddi poſſe, & è contra à caliditate molliores, <lb></lb>& flexiliores effici. </s> <s id="s.002988">His poſitis, quia dùm aqua fluida <lb></lb>eſt, caliditas in aqua viget, & proindè villi interni <lb></lb>ſpirarum, ſeù tubulorum <expan abbr="aereorũ">aereorum</expan> molliores, flexilio<lb></lb>reſque redditi facilè cedere poſſunt vi ponderis flu<lb></lb>entis aquæ, ideò tubuli prædicti repleri poſſunt; <lb></lb>adueniente poſtea ingenti gradu frigoris, nempè de<lb></lb>ficiente copia igniculorum, ſponte ſua villi interni <lb></lb>ſpirarum aeris tenſiores, directiores, & rigidiores <lb></lb>reddi poſſunt, & ideò ad inſtar machinularum expel<lb></lb>lere poſſunt ibidem contentas aquæ particulas, & <lb></lb>proindè tubuli prædicti exinaniri poſſunt. </s> </p> <p type="margin"> <s id="s.002989"><margin.target id="marg792"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002990">Poſtea quia dum efficitur huiuſmodi expulſio, non <lb></lb>adhùc aqua congelata indurataque eſt, vel <expan abbr="ſaltẽ">ſaltem</expan> ma<lb></lb>iori ex parte fluiditatem retinet, fit vt prædictæ ſpi<lb></lb>ræ aereæ non vt priùs aqua impręgnatæ, ſed vacuæ <lb></lb>relictæ, facilè poſſint ab ambiente fluido agitari, ex<lb></lb>pellique, & ſic poſſunt plures ſpiræ aereæ coaceruari, <lb></lb>& cum vicinis vniri, & ſic aliquas ampullas aereas <lb></lb>conſpicuas componere poſſunt, & hæc erunt forſan <lb></lb>grana illa aerea, quæ propè initium, & in actu con<lb></lb>gelationis ibidem oriri videntur. </s> </p> <p type="main"> <s id="s.002991">Contra hanc theoriam dici poſſet, quòd particu<lb></lb>læ ſpiritus vini, olei, & mercurij cùm exiguæ, & mi<lb></lb>nutiores quam ſint aeris particulæ concedi debeant, <lb></lb>non ſecùs, ac aqua intra tubulos aereos inſinuari poſ<lb></lb>ſent, & hinc quoque ab eadem neceſſitate ſuperiùs <lb></lb>expoſita valdè refrigeratis fluidis expelli quoque è <lb></lb>tubulis prædictis deberent, proindeque fluida præ-<pb pagenum="560" xlink:href="010/01/568.jpg"></pb><arrow.to.target n="marg793"></arrow.to.target><lb></lb>dicta ampliarentur, <expan abbr="ingẽtioraque">ingentioraque</expan> ſpatia occuparent, <lb></lb>quod repugnat experientiæ. </s> </p> <p type="margin"> <s id="s.002992"><margin.target id="marg793"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002993">Cui reſpondere poſſumus, quòd particulæ minimę <lb></lb>ſpiritus vini, & mercúrij ſi reuera tubulos aereos <lb></lb>replent, tamen à feruentiſſimo frigore expelli, & ex<lb></lb>cludi non poſſe videntur à prædictis cauitatibus, ſiuè <lb></lb>quia particulæ ſpiritus vini, & olei natiuo eorum ca<lb></lb>lore ſemper mollitiem, & flexilitatem villulorum ae<lb></lb>ris conſeruant, ſiue quia eorum particulæ ſunt adeò <lb></lb>exiguæ vt inter interſtitia eorumdem villulorum ſpi<lb></lb>rarum aeris remanere queant, vel ſaltem impulſæ <lb></lb>facilè circumuolutione facta inter villulos regredi<lb></lb>antur, & ſic capillitium illud perpetuò madefaciant, <lb></lb>proinde que numquam exinanitio tubulorum <expan abbr="aereorũ">aereorum</expan> <lb></lb>in ſpiritu vini, oleo, vel mercurio <expan abbr="cõtingat">contingat</expan>; & ſic <expan abbr="nũ-quam">nun<lb></lb>quam</expan> poterit <expan abbr="eorũ">eorum</expan> moles ampliari, aut inflari ab in<lb></lb>genti gradu frigoris, vt in aqua accidit. </s> </p> <p type="main"> <s id="s.002994">Pręterea obijcere <expan abbr="quiſquã">quiſquam</expan> poſſet, quod reuera ab ini <lb></lb>tio <expan abbr="dũ">dum</expan> aqua frigefit eius moles diminuitur <expan abbr="cõdẽſatur-que">condenſatur<lb></lb>que</expan> ergo ſi à frigiditate villi interni <expan abbr="tubulorũ">tubulorum</expan> <expan abbr="aereorũ">aereorum</expan> <lb></lb>rigidi, & tenſi redduntur, & proindè aquam è cauita<lb></lb>tibus illis expellunt, deberet in principio refrigera<lb></lb>tionis totius aquæ moles augeri, quod eſt falſum. </s> </p> <p type="main"> <s id="s.002995">Sed <expan abbr="reſpõderi">reſponderi</expan> poteſt quod ampliatio molis ipſius <lb></lb>aquæ nedum efficitur à prædicta expulſione particu<lb></lb>larum aquæ, è tubulis aereis, ſed multò magis celeri<lb></lb>us, & euidentiùs, à pręſentia, & <expan abbr="cõmotione">commotione</expan> exhala<lb></lb>tionum ignearum, quę ſuis ictibus ſeparant aquę ſoli<lb></lb>das particulas; è contra dum aqua frigefit, diſcedunt, <pb pagenum="561" xlink:href="010/01/569.jpg"></pb><arrow.to.target n="marg794"></arrow.to.target><lb></lb>& exhalant igniculi eorumque agitationes ab ipſą <lb></lb>aqua, & proinde aqua ſponte ſua ſtringitur <expan abbr="cõſtipa-tur">conſtipa<lb></lb>tur</expan>, minoremque molem acquirit. </s> <s id="s.002996">Hoc poſito, incipi<lb></lb>ente operatione frigiditatis, nempè remotis paucis <lb></lb>aliquibus igniculis, fiet conſtrictio, & condenſatio <lb></lb>aquæ, quæ valdè inſignis, & euidens erit; in progreſſu <lb></lb>verò frigefactionis, ſcilicèt magis, ac magis diminu<lb></lb>ta præſentia igniculorum, licèt reuera villi interni <lb></lb>fiſtularum aeris incipiant tendi, ac dirigi, & proindè <lb></lb>aliquantiſper expellant aquam à prædictis tubulis, <lb></lb>nihilominùs quia maior eſt diminutio molis depen<lb></lb>dens à diſceſſu, fuga, & defectu agitationis exhalati<lb></lb>onum ignearum, quàm ſit rarefactio producta à villis <lb></lb>aereis expellentibus aliquas aquæ particulas è ſuis <lb></lb>tubulis, ſequitur vt actio ſuperexcedens condenſa<lb></lb>tionis productæ à diſceſſu ignis occultet aliquandiu <lb></lb>minùs inſignem <expan abbr="expanſionẽ">expanſionem</expan> factam à prædictis villis; <lb></lb>cùmque progreſſus prædictarum contrariarum ope<lb></lb>rationum non ſint vniformes, ſed contrario ordinę <lb></lb>condenſatio ab ignis diſceſſu pendens ſemper mino<lb></lb>ri, & minori decremento fiat, & è contra rarefactio <lb></lb>pendens ex inanitione tubulorum aeris ſemper ma<lb></lb>ioribus incrementis progrediatur, (eo quod maiori <lb></lb>proportione creſcit impetus in villis tubulorum ae<lb></lb>reorum continenter agitatis, vt motus natura exigit, <lb></lb>quam deficiat ob ſucceſſiuam igniculorum priuatio<lb></lb>nem) fit vt apparentia diminutionis, & conſtrictionis <lb></lb>aquæ tandem deſinat, & facto quaſi æquilibrio <expan abbr="ali-quãtiſper">ali<lb></lb>quantiſper</expan> videatur in eadem amplitudine aqua per-<pb pagenum="562" xlink:href="010/01/570.jpg"></pb><arrow.to.target n="marg795"></arrow.to.target><lb></lb>ſeuerare, & deinceps denuò augeri, rarefierique in<lb></lb>cipiat, & ſic proſequatur per plures gradus quouſ<lb></lb>que multiplicata, & aucta tenſione illa villulorum, & <lb></lb>expulſione innumerarum aquæ particularum è tubu<lb></lb>lis aeris, <expan abbr="cõſequatur">conſequatur</expan> <expan abbr="vehemẽtiſſimus">vehementiſſimus</expan> ille ſaltus aquæ, <lb></lb>& maxima rarefactio eius, tunc præcisè, quando ma<lb></lb>iori ex parte glaciei conſiſtentiam acquirit. </s> </p> <p type="margin"> <s id="s.002997"><margin.target id="marg794"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="margin"> <s id="s.002998"><margin.target id="marg795"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.002999"><emph type="center"></emph>PROP. CCLXXVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.003000"><emph type="center"></emph><emph type="italics"></emph>Quare aqua, dum gelaſcit, duritiem acquirit, non autem aer, <lb></lb>oleum, ſpiritus vini, & Alercurius.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.003001">ET hoc loco aliqua afferre de <expan abbr="Cõſiſtentia">Conſiſtentia</expan>, & du<lb></lb>ritie, quam aqua acquirit in actu congelationis <lb></lb>ſuperuacaneum non erit. </s> <s id="s.003002">Cùm ex tradita theoria ab <lb></lb><expan abbr="ingẽti">ingenti</expan> gradu frigiditatis debeat aqua mole ampliari, <lb></lb>mirari licet quare aer, ſpiritus vini, <expan abbr="oleũ">oleum</expan>, atque mer<lb></lb>curius fluida ſemper permaneant, dum ſemper magis <lb></lb>condenſentur, vniantur, & minus ſpatium <expan abbr="occupẽt">occupent</expan>, <lb></lb>& è contra aqua, quæ in progreſſu frigefactionis am<lb></lb>pliatur, & rarefit, ſcilicèt partes eius magis ab inui<lb></lb>cem diſgregantur, debeant tamen conſolidari, ac in<lb></lb>durari, & conſiſtentiam glaciei acquirere. </s> </p> <p type="main"> <s id="s.003003">Et hìc primò occurrendum eſt, quod licèt aqua in <lb></lb>tali caſu rarefiat, ſcilicèt maius ſpatium acquirat, <lb></lb>non proindè cenſendum eſt omnes minimas eius par<lb></lb>ticulas laxiores reddi, & ab inuicem ſeparari, & in<lb></lb>ter ſe diſtare, nam rarefactio eius pendet à ſpatiolis <lb></lb>vacuis contentis intra tubulos aereos, non verò quia <lb></lb>particulæ aquæ ab inuicem recedant, itaque conci<lb></lb>piendum eſt aquæ particulas inter ſe connecti tena-<pb pagenum="563" xlink:href="010/01/571.jpg"></pb><arrow.to.target n="marg796"></arrow.to.target><lb></lb>ciſſima vnione, efformareque veluti fornices conti<lb></lb>nentes ſpatiola vacua, non ſecùs ac pumicis ſolidæ <lb></lb>particulæ duræ ſunt, & tenacitèr inter ſe connexæ, <lb></lb>licet innumeras poroſitates admittant. </s> <s id="s.003004">itaque benè <lb></lb>ſaluari poteſt durities aquæ glaciatæ cum expanſio<lb></lb>ne, ſeu rarefactione eius pendente ab innumeris po<lb></lb>ris vacuis, qui ſunt cauitates tubulorum aereorum̨ <lb></lb>intra aquam contentorum. </s> </p> <p type="margin"> <s id="s.003005"><margin.target id="marg796"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.003006">Sed adhùc remanet difficultas, quare particulæ a<lb></lb>quæ modo expoſito <expan abbr="cõnexæ">connexæ</expan> ſaxeam duritiem acqui<lb></lb>rant, & contra aer, ſpiritus vini, &c. </s> <s id="s.003007">fluida ſemper re<lb></lb>maneant, hoc profectò pendere videtur à diuerſą <lb></lb>conformatione particularum eorumdem fluidorum, <lb></lb>nam ſi villi externi particularum aquæ ab inſigni fri<lb></lb>gidate rigidi redduntur, non eſt impoſſibile, vt itą <lb></lb>interſe nectantur, vt non poſſint ab inuicem facilè <lb></lb>ſeparari, & ſic conſiſtentiam <expan abbr="duritiẽq;">duritienque</expan> creent; è con<lb></lb>tra ſi externi villi olei, ſpiritus vini, &c. </s> <s id="s.003008">non habeant <lb></lb>eamdem naturam, & conſiſtentiam, vt nimirum ab in<lb></lb>ſigni frigidate tenſionem, & rigiditatem non acqui<lb></lb>rant, tunc mirum non erit non poſſe ad inuicem con<lb></lb>glutinari, & texturam ſolidam, & duram efficere, & <lb></lb>hoc ſatis veriſimile eſſe videtur in oleo, & ſpiritu vi<lb></lb>ni, quæ cùm ex particulis igneis componantur, faci<lb></lb>lè villi externi flexibiles, & cedentes conſeruari poſ<lb></lb>ſunt; at in aere forſan villi externi, aut exigui ſunt, <lb></lb>aut non incuruati, aut lubrici, itaut forti vnione inter <lb></lb>ſe mutuò connecti nequeant. </s> <s id="s.003009"><expan abbr="Idipsũ">Idipsum</expan> dici poteſt dę <lb></lb>particulis hydrargyri; vnde mirum non eſt huiuſmo-<pb pagenum="564" xlink:href="010/01/572.jpg"></pb><arrow.to.target n="marg797"></arrow.to.target><lb></lb>di fluida licèt maximè frigefacta, duritiem <expan abbr="nõ">non</expan> acqui<lb></lb>rere, ſed poſtea iurare non poſſumus, quòd à vehe<lb></lb>mentiſſimo gradu frigoris in regionibus maximè bo<lb></lb>realibus, tandem non concreſcant, & duritiem noņ <lb></lb>acquirant; Sed interim ſufficit vt nuclei <expan abbr="particularũ">particularum</expan> <lb></lb>mercurij, aut ſint rotundi, aut <expan abbr="quã">quam</expan> maximè ad rotun<lb></lb>ditatem accedant, & è contra particulæ ſolidæ aquæ <lb></lb>figuram angularem habeant, vt ſint octaedræ ſua la<lb></lb>nugine coopertæ, quæ inter ſe connecti, adaptarique <lb></lb>poſſint, vt ſolidam texturam efficere valeant, non ſe<lb></lb>cùs ac lateres pauimenti ſolidam texturam <expan abbr="cõponere">componere</expan> <lb></lb>poſſunt. </s> <s id="s.003010">Conſtat ergo, quòd huiuſmodi differentią <lb></lb>fluidorum, vel alia ſimilis diſcrepantia efficere poteſt <lb></lb>duritiem glacialem in aqua, non verò in reliquis flui<lb></lb>dis ſuperius expoſitis. </s> </p> <p type="margin"> <s id="s.003011"><margin.target id="marg797"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.003012"><emph type="center"></emph>PROP. CCLXXVII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.003013"><emph type="center"></emph><emph type="italics"></emph>Remanet poſtremo loco inquirenda cauſa ingentis, & vali<lb></lb>disſimæ virtutis, qua aqua in actu congelationis eius <lb></lb>diſrumpit, ac frangit vaſa ænea conſiſtentia, & du<lb></lb>risſima.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.003014">HOc verò minimè mihi negotium faceſſit, cùm <expan abbr="de-mõſtrauerim">de<lb></lb>monſtrauerim</expan> in opere de vi percuſſionis, quòd <lb></lb>quælibet vis motus, & impetus ſuperare valet quam<lb></lb>cumque <expan abbr="reſiſtẽtiam">reſiſtentiam</expan> vaſti corporis abſque motu pre<lb></lb>mentis. </s> <s id="s.003015">Cogitemus particulas aqueas intra tubulos <lb></lb>aereos contentas retineri ibidem, & reſiſtere ex<lb></lb>pulſioni, ne dum vi ponderis totius aquæ <expan abbr="incũbentis">incumbentis</expan>, <lb></lb>ſed multò magis vnione partium pilæ, vel vaſis ænei <lb></lb>tenacis, & duri: hæc profectò reſiſtentia non agit <pb pagenum="565" xlink:href="010/01/573.jpg"></pb><arrow.to.target n="marg798"></arrow.to.target><lb></lb>motu, & impetu, cùm in quiete conſiſtat; ergo perin<lb></lb>de reſiſtit ſciſſioni durities vaſis ænei, ac ſi ingens, & <lb></lb>vaſta moles ponderis incumbentis ſuſpendi, & ele<lb></lb>uari deberet. </s> <s id="s.003016">E contra cogitemus villos internos tu<lb></lb>bulorum aereorum ob rigiditatem, & tenſionem ac<lb></lb>quiſitam à frigore vim motiuam habere, & actu mo<lb></lb>ueri, quatenus aqua exiguam conſtrictionem, & v<lb></lb>nionem pati poteſt; & proinde operari debent <expan abbr="eodẽ">eodem</expan> <lb></lb>propemodum modo, ac totidem arcus nedum tenſi, <lb></lb>ſed qui motum <expan abbr="inchoarũt">inchoarunt</expan>. </s> <s id="s.003017">Ita que habemus corpora, <lb></lb>quæ vi motiua, & impetu agunt contra grauitatem̨ <lb></lb>quieſcentem ipſius aquæ, & reſiſtentiam inertem̨ <lb></lb>tenacitatis vaſis; cùmque vis impetus maior ſit qua<lb></lb>cumque reſiſtentia quieſcente, hinc fit vt neceſſariò <lb></lb>illa vis motiua hanc quantumcumque vaſtam <expan abbr="reſiſtẽ-">reſiſten<lb></lb></expan><arrow.to.target n="marg799"></arrow.to.target><lb></lb>tiam ſuperare queat. </s> <s id="s.003018">Et quia huiuſmodi machinulæ <lb></lb>villoſæ impetum habentes innumerabiles ſunt, quæ <lb></lb>ſimul, & continenter ſuam impulſionem percuſſio<lb></lb>nemque efficiunt, mirum non eſt ſi ad inſtar pulueris <lb></lb>pyrij accenſi innumeris ictibus ſimùl percutiendo <lb></lb>fornices cuniculorum crepet, ac diſrumpat, atquę <lb></lb>ingentia pondera ſubleuet; & ſicuti ipſamet aquą <lb></lb>fluida intra innumeros poros funis inſinuata motu <lb></lb>ſuo ſubleuare poteſt ingentia pondera, ſic quoquę <lb></lb>copioſiſſimi, & innumerabiles ictus facti à villis in<lb></lb>ternis tubulorum aereorum poſſint pondera, & reſi<lb></lb>ſtentias inertes quieſcenteſque, licèt ingentes, ſupe<lb></lb>rare; ac proindè facile vaſa illa ænea frangere, ac <lb></lb>diſrumpere poterit aqua in actu congelationis eius, <pb pagenum="566" xlink:href="010/01/574.jpg"></pb><arrow.to.target n="marg800"></arrow.to.target><lb></lb>do nimirùm vehementiſſimo motu rarefit, & innume<lb></lb>ris percuſſionibus à villis prædictis aeris aquam im<lb></lb>pellit. </s> <s id="s.003019">hæc, ni fallor, veriſimilis cauſa huius <expan abbr="admirã-di">admiran<lb></lb>di</expan> effectus eſſe videtur. </s> </p> <p type="margin"> <s id="s.003020"><margin.target id="marg798"></margin.target>Cap. 13. cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="margin"> <s id="s.003021"><margin.target id="marg799"></margin.target>De vi per<lb></lb>cuſs.pro.90.</s> </p> <p type="margin"> <s id="s.003022"><margin.target id="marg800"></margin.target>Cap. 13 cau<lb></lb>ſa rarefacti<lb></lb>onis glaciei <lb></lb>affertur.</s> </p> <p type="main"> <s id="s.003023">Et hæc de motionibus dependentibus à vi natiua <lb></lb>grauitatis modo ſufficiant; non enim viſum eſt vlte<lb></lb>rius hanc præparationem extendere, & editionem̨ <lb></lb>principalis argumenti de animalium motibus diutiùs <lb></lb>retardare, cùm ſenectus, & valetudo me aſſiduè mo<lb></lb>neant ſatiùs eſſe pauca, & minùs elaborata quàm ni<lb></lb>hil ad poſteros tranſmittere. </s> </p> <p type="main"> <s id="s.003024"><emph type="center"></emph>FINIS.<emph.end type="center"></emph.end></s> </p> <pb xlink:href="010/01/575.jpg"></pb> <p type="main"> <s id="s.003025"><emph type="center"></emph>INDEX<emph.end type="center"></emph.end><emph type="center"></emph>RERVM PRÆCIPVARVM.<emph.end type="center"></emph.end><lb></lb></s> </p> <p type="main"> <s id="s.003026"><emph type="italics"></emph>AQua vaſis fundum ſua gra<lb></lb>uitate comprimit. </s> <s id="s.003027">fol.<emph.end type="italics"></emph.end> 38. </s> </p> <p type="main"> <s id="s.003028"><emph type="italics"></emph>Aqua, & quodlibet ſolidum in ipſa<lb></lb>met aqua demerſum vndique <expan abbr="cõ-primitur">com<lb></lb>primitur</expan>. </s> <s id="s.003029">fol.<emph.end type="italics"></emph.end> 59. </s> </p> <p type="main"> <s id="s.003030"><emph type="italics"></emph>Et quomodolibet reuoluta graui<lb></lb>tatem exercet.<emph.end type="italics"></emph.end> 73. </s> </p> <p type="main"> <s id="s.003031"><emph type="italics"></emph>Aqua vi glutinis parumper reſi<lb></lb>ſtit penetrationi corporum per <lb></lb><expan abbr="eã">eam</expan> excurrentium.<emph.end type="italics"></emph.end> 331. </s> </p> <p type="main"> <s id="s.003032"><emph type="italics"></emph>Et parum condenſatur ob lanugi<lb></lb>nis ceſſionem.<emph.end type="italics"></emph.end> 333. </s> </p> <p type="main"> <s id="s.003033"><emph type="italics"></emph>Aquæ particulæ ſuperficiales poſ<lb></lb>ſunt rotando altius eleuari pa<lb></lb>rieti vaſis adhærendo à vi pon<lb></lb>deris aquæ collateralis.<emph.end type="italics"></emph.end> 356. </s> </p> <p type="main"> <s id="s.003034"><emph type="italics"></emph>Quare aquæ guttulæ varijs mo<lb></lb>dis agitantur, & ſuſpenduntur.<emph.end type="italics"></emph.end><lb></lb>357. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 362. </s> </p> <p type="main"> <s id="s.003035"><emph type="italics"></emph>Aqua in fiſtulis non aſcendit ſpon<lb></lb>te, <expan abbr="neq;">neque</expan> impellitur ab aere.<emph.end type="italics"></emph.end> 373. </s> </p> <p type="main"> <s id="s.003036"><emph type="italics"></emph>Affertur cauſa motiua impellens <lb></lb>aquam intra ſubtiliſſimas fiſtu<lb></lb>las.<emph.end type="italics"></emph.end> 377. </s> </p> <p type="main"> <s id="s.003037"><emph type="italics"></emph>Et noua Phænomena ſaluantur.<emph.end type="italics"></emph.end><lb></lb>378. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 385. </s> </p> <p type="main"> <s id="s.003038"><emph type="italics"></emph>Aquea fluida in actu congelatio<lb></lb>nis rarefiunt.<emph.end type="italics"></emph.end> 546. </s> </p> <p type="main"> <s id="s.003039"><emph type="italics"></emph>Aeris maxima dilatatio reperitur.<emph.end type="italics"></emph.end><lb></lb>221. </s> </p> <p type="main"> <s id="s.003040"><emph type="italics"></emph>Estque vt<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> 2000. 254. <lb></lb></s> </p> <p type="main"> <s id="s.003041"><emph type="italics"></emph>Aeris difformis grauitas conijci<lb></lb>tur.<emph.end type="italics"></emph.end> 237. </s> </p> <p type="main"> <s id="s.003042"><emph type="italics"></emph><expan abbr="Eiuſq;">Eiuſque</expan> pondus venatur<emph.end type="italics"></emph.end> 244 <emph type="italics"></emph>& <expan abbr="ſeq.">ſeque</expan><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003043"><emph type="italics"></emph>Eſtque Aeris pondus ad pondus a<lb></lb>quæ ei æqualis mole, vt<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>1175. 251. </s> </p> <p type="main"> <s id="s.003044"><emph type="italics"></emph>Aer videtur compoſitus ex machi<lb></lb>nulis compreſſibilibus, & reſi<lb></lb>lientibus, quarum figuræ ſunt <lb></lb>cylindricæ, excauatæ, compoſi<lb></lb>tæ ex laminis ramoſis, obliquè <lb></lb>circumductis<emph.end type="italics"></emph.end> 257. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 261 </s> </p> <p type="main"> <s id="s.003045"><emph type="italics"></emph>Animalis membra ab aqua <expan abbr="incũ-bente">incum<lb></lb>bente</expan> non flectuntur, nec <expan abbr="luxã-tur">luxan<lb></lb>tur</expan>, quia vndique à contrarijs <lb></lb>viribus fluidi <expan abbr="comprimũtur">comprimuntur</expan>.<emph.end type="italics"></emph.end> 64. </s> </p> <p type="main"> <s id="s.003046"><emph type="italics"></emph>Animal à compreſſione aquæ am<lb></lb>bientis nullam noxam patietur.<emph.end type="italics"></emph.end><lb></lb>68. </s> </p> <p type="main"> <s id="s.003047"><emph type="italics"></emph>Argines depresſi aquæ, quare non <lb></lb>defluunt.<emph.end type="italics"></emph.end> 364. </s> </p> <p type="main"> <s id="s.003048"><emph type="italics"></emph>Et vis aquam eleuans non eſt pro<lb></lb>pria aquæ, nec aeris, ſed eſt aquæ <lb></lb>collateralis præſſio<emph.end type="italics"></emph.end> 366. </s> </p> <p type="main"> <s id="s.003049"><emph type="italics"></emph>Duæ laminulæ efficientes argines <lb></lb>proximos aqueos depreſſos infra <lb></lb>aquæ libellam in determinata <lb></lb>diſtantia ad inuicem approxi<lb></lb>mari debent.<emph.end type="italics"></emph.end> 403, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 4<gap></gap>7. </s> </p> <p type="main"> <s id="s.003050"><emph type="italics"></emph>Similiter ſi argines conterminales <lb></lb>eleuati ſuper libellam aquæ fue-<emph.end type="italics"></emph.end><pb xlink:href="010/01/576.jpg"></pb><lb></lb><emph type="italics"></emph>rint; pariter ad inuicem <expan abbr="accedẽt">accedent</expan>.<emph.end type="italics"></emph.end><lb></lb>408. </s> </p> <p type="main"> <s id="s.003051"><emph type="italics"></emph>Si verò arginum alter depreſſus, <lb></lb>reliquus verò ſupra aquæ libel<lb></lb>lam eleuatus fuerit, laminæ ab <lb></lb>inuicem recedent.<emph.end type="italics"></emph.end> 410. </s> </p> <p type="main"> <s id="s.003052"><emph type="italics"></emph>Incidenter propoſitiones aliquę hy<lb></lb>drostaticæ perpenduntur<emph.end type="italics"></emph.end> 413. <lb></lb><emph type="italics"></emph>vſq: ad<emph.end type="italics"></emph.end> 417. </s> </p> <p type="main"> <s id="s.003053"><emph type="italics"></emph>Agens naturale ni ſi moueatur, at<lb></lb>trahere non poteſt aliud corpus <lb></lb>fune, vel vncino ſibi non alliga<lb></lb>tum.<emph.end type="italics"></emph.end> 264. </s> </p> <p type="main"> <s id="s.003054"><emph type="italics"></emph>Et rationibus in contrarium ad<lb></lb>ductis ſatisfit.<emph.end type="italics"></emph.end> 266. </s> </p> <p type="main"> <s id="s.003055"><emph type="italics"></emph>Corpora, quæ attrahi videntur, aut <lb></lb>ſponte, aut vi externa <expan abbr="impellũ-tur">impellun<lb></lb>tur</expan>.<emph.end type="italics"></emph.end> 268. </s> </p> <p type="main"> <s id="s.003056"><emph type="italics"></emph><expan abbr="Nõ">non</expan> <expan abbr="attrabũtur">attrahuntur</expan> carnes, & humores <lb></lb>à cucurbitulis, ſed ceſſante in <lb></lb>vna parte aeris compresſionę <lb></lb>ibidem impelli debent.<emph.end type="italics"></emph.end> 272. </s> </p> <p type="main"> <s id="s.003057"><emph type="italics"></emph>Idip ſum pluribus experimentis <expan abbr="cõ-firmatur">con<lb></lb>firmatur</expan>.<emph.end type="italics"></emph.end> 273. </s> </p> <p type="main"> <s id="s.003058"><emph type="italics"></emph>Et hìc ſen ſus decipitur, cùm putat <lb></lb>cutim attrahi, <expan abbr="cũ">cum</expan> ab aere expri<lb></lb>matur.<emph.end type="italics"></emph.end> 275. </s> </p> <p type="main"> <s id="s.003059"><emph type="italics"></emph>Duobus experimentis <expan abbr="attractionẽ">attractionem</expan> <lb></lb>con firmantibus reſpondetur.<emph.end type="italics"></emph.end><lb></lb>277. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 284. </s> </p> <p type="main"> <s id="s.003060"><emph type="italics"></emph>Æquilibrata corpora ideo quie<lb></lb>ſcunt, quia grauitant.<emph.end type="italics"></emph.end> 55. </s> </p> <p type="main"> <s id="s.003061"><emph type="italics"></emph>Centrum grauitatis fluidi in ſi<lb></lb>phone viam parabolicam quan<lb></lb>do deſcribit.<emph.end type="italics"></emph.end> 13. <lb></lb></s> </p> <p type="main"> <s id="s.003062"><emph type="italics"></emph>Corpora terrena extra ſua natu<lb></lb>ralia loca dum mouentur <expan abbr="nullã">nullam</expan> <lb></lb>grauitatem exercent.<emph.end type="italics"></emph.end> 51. </s> </p> <p type="main"> <s id="s.003063"><emph type="italics"></emph>Corpus ſubstantiale componi non <lb></lb>potest ex in finitis punctis indi<lb></lb>uiduis.<emph.end type="italics"></emph.end> 186. </s> </p> <p type="main"> <s id="s.003064"><emph type="italics"></emph>Corporum minutisſimæ particulæ <lb></lb>inter ſe diuiſæ, & quieſcentes <lb></lb>duritiem non efficiunt.<emph.end type="italics"></emph.end> 302. </s> </p> <p type="main"> <s id="s.003065"><emph type="italics"></emph>Argumenta contraria reijciun<lb></lb>tur.<emph.end type="italics"></emph.end> 304. </s> </p> <p type="main"> <s id="s.003066"><emph type="italics"></emph>In fistulis, quibus velocitatibus a<lb></lb>qua defluat.<emph.end type="italics"></emph.end> 453. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 464. </s> </p> <p type="main"> <s id="s.003067"><emph type="italics"></emph>De fluiditatis natura.c.<emph.end type="italics"></emph.end>7. 285. </s> </p> <p type="main"> <s id="s.003068"><emph type="italics"></emph>Fluidum cum ſolido demerſo <expan abbr="librã">libram</expan> <lb></lb>constituit, cuius centrum gra<lb></lb>uitatis ſemper deſcendit.<emph.end type="italics"></emph.end> 25. </s> </p> <p type="main"> <s id="s.003069"><emph type="italics"></emph>Per lineam curuam parabolicam, <lb></lb>quando ſolidi pars demerſa eſt.<emph.end type="italics"></emph.end><lb></lb>29. </s> </p> <p type="main"> <s id="s.003070"><emph type="italics"></emph>Fluidi in fluido, cui non miſcetur <lb></lb>translati, pars eius anterior tu<lb></lb>mida fiet.<emph.end type="italics"></emph.end> 145. </s> </p> <p type="main"> <s id="s.003071"><emph type="italics"></emph>Quod ſi violenter ab ambientę <lb></lb>fluido exprimatur posterior e<lb></lb>ius pars caua erit.<emph.end type="italics"></emph.end> 148. </s> </p> <p type="main"> <s id="s.003072"><emph type="italics"></emph>Et ſi ſponte feratur posterior eius <lb></lb>pars conuexa erit.<emph.end type="italics"></emph.end> 151.154. </s> </p> <p type="main"> <s id="s.003073"><emph type="italics"></emph>Fluidi corporis partes inter ſe di<lb></lb>uiſæ eße debent.<emph.end type="italics"></emph.end> 293. </s> </p> <p type="main"> <s id="s.003074"><emph type="italics"></emph>Et minimæ fluidi partes non ſunt <lb></lb>fluidæ.<emph.end type="italics"></emph.end> 294. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 299. </s> </p> <p type="main"> <s id="s.003075"><emph type="italics"></emph>Per accidens fluiditatem creat <expan abbr="cõ-motio">conm<lb></lb>motio</expan> <expan abbr="partiũ">partium</expan> metalli fu ſi.<emph.end type="italics"></emph.end> 307. </s> </p> <p type="main"> <s id="s.003076"><emph type="italics"></emph>In fluidis requiritur grauitas, vt<emph.end type="italics"></emph.end><pb xlink:href="010/01/577.jpg"></pb><lb></lb><emph type="italics"></emph>explanari poſſint.<emph.end type="italics"></emph.end> 309. </s> </p> <p type="main"> <s id="s.003077"><emph type="italics"></emph>Ex ſalium diſſolutione non proba<lb></lb>tur fluiditatem à partium agi<lb></lb>tatione pendere.<emph.end type="italics"></emph.end> 317. </s> </p> <p type="main"> <s id="s.003078"><emph type="italics"></emph>Fluidi commotio, dum ſpongia, pu<lb></lb>mex, aut gleba, calx, &c. </s> <s id="s.003079">hume<lb></lb>ctantur, & diſſoluuntur, non est <lb></lb>cauſa, & fluiditatis conſtituti<lb></lb>ua, ſed est effectus dependens à <lb></lb>grauitate fluidi<emph.end type="italics"></emph.end> 314. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end><lb></lb>324. </s> </p> <p type="main"> <s id="s.003080"><emph type="italics"></emph>Fluida aquea habere <expan abbr="viſcoſitatẽ">viſcoſitatem</expan>, <lb></lb>ſcilicet lanuginem flexibilem, <lb></lb>& reſidientem.<emph.end type="italics"></emph.end> 326. </s> </p> <p type="main"> <s id="s.003081"><emph type="italics"></emph>Et hoc confirmatur.<emph.end type="italics"></emph.end> 329, </s> </p> <p type="main"> <s id="s.003082"><emph type="italics"></emph>Fluidi <expan abbr="guttænõ">guttæ non</expan> <expan abbr="cõglobantur">conglobantur</expan> ſphæ<lb></lb>ricè ab aeris compresſione.<emph.end type="italics"></emph.end> 238. </s> </p> <p type="main"> <s id="s.003083"><emph type="italics"></emph>Et experimentis <expan abbr="cõprobatur">comprobatur</expan>.<emph.end type="italics"></emph.end> 339. </s> </p> <p type="main"> <s id="s.003084"><emph type="italics"></emph>Et tandem hoc demonſtratur<emph.end type="italics"></emph.end> 343. </s> </p> <p type="main"> <s id="s.003085"><emph type="italics"></emph>Neque ſponte guttulæ fluidæ con<lb></lb>globantur.<emph.end type="italics"></emph.end> 345. </s> </p> <p type="main"> <s id="s.003086"><emph type="italics"></emph>Neque ob diuerſitatem motuum̨ <lb></lb>aquæ, & aeris.<emph.end type="italics"></emph.end> 348. </s> </p> <p type="main"> <s id="s.003087"><emph type="italics"></emph>Neque ob incongruentiam <expan abbr="pororũ">pororum</expan> <lb></lb>aer, & aqua ſe mutuò non pene<lb></lb>trant.<emph.end type="italics"></emph.end> 350. </s> </p> <p type="main"> <s id="s.003088"><emph type="italics"></emph>Flammam in camino ab expresſio<lb></lb>ne aeris ſurſum pelli.<emph.end type="italics"></emph.end> 124. </s> </p> <p type="main"> <s id="s.003089"><emph type="italics"></emph>Flammæ candelæ figura pyrami<lb></lb>dalis non euincit eius <expan abbr="leuitatẽ">leuitatem</expan>.<emph.end type="italics"></emph.end><lb></lb>130. </s> </p> <p type="main"> <s id="s.003090"><emph type="italics"></emph>Et quare acuminatur.<emph.end type="italics"></emph.end> 139. </s> </p> <p type="main"> <s id="s.003091"><emph type="italics"></emph>Flamma est fumus accenſus ab ae<lb></lb>re ſurſum expreſſus.<emph.end type="italics"></emph.end> 136.141. </s> </p> <p type="main"> <s id="s.003092"><emph type="italics"></emph>Ex fumi deſcenſu in vacuo Torri-<emph.end type="italics"></emph.end><lb></lb><lb></lb><emph type="italics"></emph>celliano ignis grauitas ſuade<lb></lb>tur.<emph.end type="italics"></emph.end> 128. </s> </p> <p type="main"> <s id="s.003093"><emph type="italics"></emph>Fumi structura, & motus decla<lb></lb>ratur.<emph.end type="italics"></emph.end> 13<gap></gap>. </s> </p> <p type="main"> <s id="s.003094"><emph type="italics"></emph>Figurarum quænam ſpatium <expan abbr="cõ-plere">con<lb></lb>plere</expan> poſſunt.<emph.end type="italics"></emph.end> 531.532. </s> </p> <p type="main"> <s id="s.003095"><emph type="italics"></emph>Grauium inæqualium circa tro<lb></lb>chleum reuolutorum <expan abbr="centrũ">centrum</expan> gra<lb></lb>uitatis per rectam, perpendicu<lb></lb>larem ad horizontem deſcendit.<emph.end type="italics"></emph.end><lb></lb>18. </s> </p> <p type="main"> <s id="s.003096"><emph type="italics"></emph>A grauiori fluido ratione mecha<lb></lb>nica celerius idem mobile <expan abbr="ſursũ">ſursum</expan> <lb></lb>exprimitur, quam à minus gra<lb></lb>ui.<emph.end type="italics"></emph.end> 99. </s> </p> <p type="main"> <s id="s.003097"><emph type="italics"></emph>Eiuſdem grauis velocitates in duo<lb></lb>bus fluidis non ſemper propor<lb></lb>tionales ſunt reſistentijs <expan abbr="eorũ-dem">eorun<lb></lb>dem</expan> fluidorum.<emph.end type="italics"></emph.end> 420. </s> </p> <p type="main"> <s id="s.003098"><emph type="italics"></emph>Inæqualia grauia non producunt <lb></lb>inæquales velocitates, ſed <expan abbr="vnã">vnam</expan>, <lb></lb>& eamdem.<emph.end type="italics"></emph.end> 426. </s> </p> <p type="main"> <s id="s.003099"><emph type="italics"></emph>Argumentis in contrarium addu<lb></lb>ctis reſpondetur.<emph.end type="italics"></emph.end> 428. <emph type="italics"></emph>vſque <lb></lb>ad<emph.end type="italics"></emph.end> 435. </s> </p> <p type="main"> <s id="s.003100"><emph type="italics"></emph>Aſcenſus grauium <expan abbr="nõ">non</expan> minus natu<lb></lb>ralis est, quam eorum <expan abbr="deſcẽſus">deſcenſus</expan>.<emph.end type="italics"></emph.end><lb></lb>88. </s> </p> <p type="main"> <s id="s.003101"><emph type="italics"></emph>Motus grauium in fluido fiunt.<emph.end type="italics"></emph.end> 1. </s> </p> <p type="main"> <s id="s.003102"><emph type="italics"></emph>Glaciei rarefactio non efficitur à <lb></lb>ſalium admixtione.<emph.end type="italics"></emph.end> 548. <emph type="italics"></emph>neque <lb></lb>ab aere de foris <expan abbr="adueniẽte">adueniente</expan>.<emph.end type="italics"></emph.end> 550. </s> </p> <p type="main"> <s id="s.003103"><emph type="italics"></emph>Quare aqua in actu congelationis <lb></lb>mole augetur.<emph.end type="italics"></emph.end> 555. </s> </p> <p type="main"> <s id="s.003104"><emph type="italics"></emph>Et quære duritiem acquirit, noņ<emph.end type="italics"></emph.end><pb xlink:href="010/01/578.jpg"></pb><lb></lb><emph type="italics"></emph>verò alia fluida?<emph.end type="italics"></emph.end> 162, <emph type="italics"></emph>& vnde <lb></lb>vis illa ingens, qua vaſa ænea <lb></lb>disrumpuntur, dum aqua gela<lb></lb>tur.<emph.end type="italics"></emph.end> 564. </s> </p> <p type="main"> <s id="s.003105"><emph type="italics"></emph>Hydrargyrum in Torricellianą <lb></lb>fistula ab æquilibrio aeris ſu<lb></lb>ſpenditur.<emph.end type="italics"></emph.end> 206. <emph type="italics"></emph>& argumentis <lb></lb>in contrarium adductis ſatisfit.<emph.end type="italics"></emph.end><lb></lb>211.225. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 235. </s> </p> <p type="main"> <s id="s.003106"><emph type="italics"></emph>Lamina, quæ à ſingulari pondere <lb></lb>flectitur dirigi poteſt à duplica<lb></lb>ta potentia.<emph.end type="italics"></emph.end> 602. </s> </p> <p type="main"> <s id="s.003107"><emph type="italics"></emph>In libra pars minus grauis aſcen<lb></lb>dit, quia totum deſcendit.<emph.end type="italics"></emph.end> 5. </s> </p> <p type="main"> <s id="s.003108"><emph type="italics"></emph>Si libræ, vel rotæ terminos duæ po<lb></lb>tentiæ ſimul deorſum, vel ſur<lb></lb>ſum <expan abbr="trabãt">trahant</expan>, mutuo ſe <expan abbr="impediẽt">impedient</expan>, <lb></lb>& eorum exceſſus metitur vim <lb></lb>flexionis.<emph.end type="italics"></emph.end> 105. </s> </p> <p type="main"> <s id="s.003109"><emph type="italics"></emph>Et ſi vna potentia ſurſum, altera <lb></lb>deorſum trahant eoſdem oppoſi<lb></lb>tos libræ terminos ſe mutuo ad<lb></lb>iuuabunt, & vis flectens æqua<lb></lb>bitur ſummæ <expan abbr="potentiarũ">potentiarum</expan>.<emph.end type="italics"></emph.end> 107. </s> </p> <p type="main"> <s id="s.003110"><emph type="italics"></emph>Leuium ſubleuatio ab eodem prin<lb></lb>cipio grauitatis effici potest.<emph.end type="italics"></emph.end> 93. </s> </p> <p type="main"> <s id="s.003111"><emph type="italics"></emph>Leuia appellata non <expan abbr="ferũtur">feruntur</expan> <expan abbr="ſur-sũ">ſur<lb></lb>sum</expan> à vi intrinſeca leuitatis.<emph.end type="italics"></emph.end> 97. </s> </p> <p type="main"> <s id="s.003112"><emph type="italics"></emph>Ignem, aerem, &c. </s> <s id="s.003113">non eſſe leuią <lb></lb>ex principijs Peripateticis <expan abbr="ostẽ-ditur">osten<lb></lb>ditur</expan><emph.end type="italics"></emph.end> 115. <emph type="italics"></emph>& <expan abbr="ſeq.">ſeque</expan><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003114"><emph type="italics"></emph>Refelluntur argumenta pro leui<lb></lb>tate poſitiua adducta.<emph.end type="italics"></emph.end> 157. <emph type="italics"></emph>& <lb></lb>ſequentibus.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.003115"><emph type="italics"></emph>Leuitatem poſitiuam non dari de-<emph.end type="italics"></emph.end><lb></lb><lb></lb><emph type="italics"></emph>monſtratur.<emph.end type="italics"></emph.end> 180. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 202, </s> </p> <p type="main"> <s id="s.003116"><emph type="italics"></emph>Lignum in fundo aquæ quieſcit, <lb></lb>quando extruſio à medio fluido <lb></lb>fieri non poteſt.<emph.end type="italics"></emph.end> 169. </s> </p> <p type="main"> <s id="s.003117"><emph type="italics"></emph>Lignum, & æerem in fundo aquæ <lb></lb>poſitiuam leuitatem non exer<lb></lb>cere, experimentis confirma<lb></lb>tur.<emph.end type="italics"></emph.end> 147. </s> </p> <p type="main"> <s id="s.003118"><emph type="italics"></emph>Motus perpetuus reijcitur.<emph.end type="italics"></emph.end> 8. </s> </p> <p type="main"> <s id="s.003119"><emph type="italics"></emph>Motiua vis, qua ſolidum grauius <lb></lb>ſpecie, quam fluidum deſcendit <lb></lb>æquatur differentiæ ponderum <lb></lb>ſpecificorum.<emph.end type="italics"></emph.end> 110. <emph type="italics"></emph>idemque di<lb></lb>cendum in leuibus.<emph.end type="italics"></emph.end> 111. </s> </p> <p type="main"> <s id="s.003120"><emph type="italics"></emph>Vis motiua qua leue in fluido gra<lb></lb>ui aſcendit, æquatur ſummæ le<lb></lb>uitatis, & grauitatis ſpecifica<lb></lb>rum.<emph.end type="italics"></emph.end> 111. </s> </p> <p type="main"> <s id="s.003121"><emph type="italics"></emph>Mollia, & flexibilia corpora com<lb></lb>ponuntur ex particulis duris, & <lb></lb>inflexibilibus.<emph.end type="italics"></emph.end> 227.228. </s> </p> <p type="main"> <s id="s.003122"><emph type="italics"></emph>Natantium corpuſculorum histo<lb></lb>ria.<emph.end type="italics"></emph.end> 368. </s> </p> <p type="main"> <s id="s.003123"><emph type="italics"></emph>Partes quantæ actu infinitè ex<lb></lb>tenſionem infinitam <expan abbr="componũt">componunt</expan>.<emph.end type="italics"></emph.end><lb></lb>287. </s> </p> <p type="main"> <s id="s.003124"><emph type="italics"></emph>Si partes eiuſdem aggregati moue<lb></lb>antur cæteris quieſcentibus, vel <lb></lb>inæqualibus motibus diuerſis, <lb></lb>ab ijs, qui duris corporibus <expan abbr="cõ-petunt">con<lb></lb>petunt</expan>, erunt illius aggregati <lb></lb>partes actu diuiſæ.<emph.end type="italics"></emph.end> 289. </s> </p> <p type="main"> <s id="s.003125"><emph type="italics"></emph>Siphonem tubicum, vel libram cir<lb></lb>cularem efficit cylindrus ſolidus <lb></lb>cum æquali mole aquæ ambien-<emph.end type="italics"></emph.end><pb xlink:href="010/01/579.jpg"></pb><lb></lb><emph type="italics"></emph>tis.<emph.end type="italics"></emph.end> 464. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 468. </s> </p> <p type="main"> <s id="s.003126"><emph type="italics"></emph>Trutinæ æquilibratæ <expan abbr="lãx">lanx</expan> excale<lb></lb>facta ſurſum extruditur ab ae<lb></lb>ris pondere.<emph.end type="italics"></emph.end> 125. </s> </p> <p type="main"> <s id="s.003127"><emph type="italics"></emph>Veſica aere plena ab innumeris <lb></lb>cuneis compreſſa non ſcindetur, <lb></lb>neque flectetur.<emph.end type="italics"></emph.end> 66. </s> </p> <p type="main"> <s id="s.003128"><emph type="italics"></emph>Violentia, qua aer per aquam <expan abbr="aſcẽ-dit">aſcen<lb></lb>dit</expan>, est naturalis, quia eſt ne<lb></lb>ceſſaria.<emph.end type="italics"></emph.end> 85. 87. </s> </p> <p type="main"> <s id="s.003129"><emph type="italics"></emph><expan abbr="Velocitatẽ">Velocitatem</expan> cuiuſlibet corporis gra<lb></lb>uis in vacuo eſſe finitam, et in <lb></lb>tempore abſolui.<emph.end type="italics"></emph.end> 436. </s> </p> <p type="main"> <s id="s.003130"><emph type="italics"></emph>Velocitates cylindrorum homege<lb></lb>neorum in fluido aſcendentium, <lb></lb>vel deſcendentium indicantur.<emph.end type="italics"></emph.end><lb></lb>470. 482. 484. </s> </p> <p type="main"> <s id="s.003131"><emph type="italics"></emph>Velocitates conorum, vel pyrami<lb></lb>dum in fluido æſcendentium̨, <lb></lb>vel deſcendentium exponuntur.<emph.end type="italics"></emph.end><lb></lb>473. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 478. </s> </p> <p type="main"> <s id="s.003132"><emph type="italics"></emph>Velocitates aſcenſus, vel deſcenſus <lb></lb>corporum bætberogeneorum̨, <lb></lb>quæ in eodem, vel diuerſis flui<lb></lb>dis fiunt indicantur.<emph.end type="italics"></emph.end> 488. <emph type="italics"></emph>vſque <lb></lb>ad<emph.end type="italics"></emph.end> 494. <lb></lb></s> </p> <p type="main"> <s id="s.003133"><emph type="italics"></emph>In eodem fluido <expan abbr="velocitatũ">velocitatum</expan> incre<lb></lb>menta continenter <expan abbr="retardãtur">retardantur</expan>, <lb></lb>& ad æquabilitatem reducun<lb></lb>tur.<emph.end type="italics"></emph.end> 496. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 500. </s> </p> <p type="main"> <s id="s.003134"><emph type="italics"></emph>In vacuo quælibet corpora in ęqua<lb></lb>lia mole, & pendere, & figura <lb></lb>eodem tempore æqualia ſpatią <lb></lb>percurrerent<emph.end type="italics"></emph.end> 439. <emph type="italics"></emph><expan abbr="vſq;">vſque</expan> ad<emph.end type="italics"></emph.end> 451. </s> </p> <p type="main"> <s id="s.003135"><emph type="italics"></emph>Vacuum priuatio entis poni debet.<emph.end type="italics"></emph.end><lb></lb>502. </s> </p> <p type="main"> <s id="s.003136"><emph type="italics"></emph>Argumenta Arist. contra vacuum <lb></lb>ſoluuntur.<emph.end type="italics"></emph.end> 504. </s> </p> <p type="main"> <s id="s.003137"><emph type="italics"></emph>Corpora non accurrunt ſponte ad <lb></lb>replendum vacuum, ſed impel<lb></lb>luntur à fluidi externi pondere, <lb></lb>& per accidens ad vacuum im<lb></lb>pediendum mouentur.<emph.end type="italics"></emph.end> 511. <emph type="italics"></emph>vſ<lb></lb>que ad<emph.end type="italics"></emph.end> 516. </s> </p> <p type="main"> <s id="s.003138"><emph type="italics"></emph>Dimenſiones quæ vacuo ſpatio tri<lb></lb>buuntur ſunt meræ priuatio<lb></lb>nes, & non entia; & argumen<lb></lb>tis in contrarium adductis ſa<lb></lb>tisfit<emph.end type="italics"></emph.end> 518. <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 526. </s> </p> <p type="main"> <s id="s.003139"><emph type="italics"></emph>In ſeparatione, & ſciſſione corpo<lb></lb>rum vacuum intercipi debet, & <lb></lb>etiam intra fluidum<emph.end type="italics"></emph.end> 534.543. <lb></lb><figure id="id.010.01.579.1.jpg" xlink:href="010/01/579/1.jpg"></figure></s> </p> </chap> </body> <back></back> </text> </archimedes>