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	<info>
		<author>Fabri, Honoré</author>
		<title>Tractatus physicus de motu locali</title>
		<date>1646</date>
		<place>Lyon</place>
		<translator></translator>
		<lang>la</lang>
		<cvs_file>fabri_tract_026_la_1646.xml</cvs_file>
		<cvs_version></cvs_version>
		<locator>026.xml</locator>
		<echodir>/permanent/library/UCMU9H8B</echodir>
	</info>
	<text>

	<front>
			<section>
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				<p id="N1001B" type="head">
					<s id="N1001D"><emph type="center"></emph>TRACTATVS <lb></lb>PHYSICVS <lb></lb>DE MOTV LOCALI, <lb></lb><emph type="italics"></emph>IN QVO<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1002E" type="main">
					<s id="N10030"><emph type="center"></emph>EFFECTVS OMNES, QVI AD IMPETVM, <lb></lb>Motum naturalem, violentum, &amp; mixtum pertinent, <lb></lb>explicantur, &amp; ex principiis Phyſicis <lb></lb>demonſtrantur.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1003D" type="main">
					<s id="N1003F"><emph type="center"></emph><emph type="italics"></emph>Auctore<emph.end type="italics"></emph.end> PETRO MOVSNERIO <emph type="italics"></emph>Doctore Medico:<emph.end type="italics"></emph.end><lb></lb>CVNCTA EXCERPTA<emph.end type="center"></emph.end></s>
				</p>
				<p id="N10052" type="main">
					<s id="N10054"><emph type="center"></emph><emph type="italics"></emph>Ex prælectionibus<emph.end type="italics"></emph.end> R. P. HONORATI FABRY, <lb></lb><emph type="italics"></emph>Societatis<emph.end type="italics"></emph.end> IESV.<emph.end type="center"></emph.end></s>
				</p>
				<figure id="id.026.01.001.1.jpg" xlink:href="026/01/001/1.jpg"></figure>
				<p id="N1006C" type="main">
					<s id="N1006E"><emph type="center"></emph><emph type="italics"></emph>LVGDVNI,<emph.end type="italics"></emph.end><lb></lb>Apud IOANNEM CHAMPION, <lb></lb>in foro Cambij.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1007E" type="main">
					<s id="N10080"><emph type="center"></emph><emph type="italics"></emph>M. </s>
					<s id="N10087">D C. XLVI.<emph.end type="italics"></emph.end><lb></lb>Cum Priuilegio Regis, &amp; Approbatione Doctorum.<emph.end type="center"></emph.end></s>
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			</section>
			<section>
				<pb xlink:href="026/01/003.jpg"></pb>
				<figure id="id.026.01.003.1.jpg" xlink:href="026/01/003/1.jpg"></figure>
				<p id="N1009C" type="head">
					<s id="N1009E"><emph type="center"></emph>AMPLISSIMO, <lb></lb>NOBILISSIMOQVE DOMINO,<emph.end type="center"></emph.end></s>
				</p>
				<p id="N100A7" type="main">
					<s id="N100A9"><emph type="center"></emph>D. PETRO DE SEVE, <lb></lb>DOMINO DE FLECHERES, <lb></lb>SANCTIORIS CONSILII REGIS <lb></lb>Conſiliario, in Lugdunenſi Curia Prætori prima­<lb></lb>rio, &amp; ſecundùm Mercatorum Præpoſito, &amp;c.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N100B8" type="main">
					<s id="N100BA"><emph type="center"></emph>PETRVS MOVSNERIVS,<emph.end type="center"></emph.end></s>
				</p>
				<p id="N100C1" type="main">
					<s id="N100C3"><emph type="italics"></emph>TIBI alterum noſtræ Philoſo­<lb></lb>phiæ fœtum inſcribo, cui iam <lb></lb>primum inſcripſi<emph.end type="italics"></emph.end> (PRÆTOR <lb></lb>AMPLISSIME) <emph type="italics"></emph>nempe idem <lb></lb>eſſe debeo, quia tu ſemper idem <lb></lb>es: </s>
					<s id="N100D9">non mutaſti merita, non mu­<lb></lb>tabo officia: </s>
					<s id="N100DF">multos non expoſcam Patronos, qui <lb></lb>iam omnium optimum, &amp; meritiſsimum habeo; </s>
					<s id="N100E5">neo <lb></lb>enim ſacra Philoſophiæ anathemata rudi, &amp; ru­<lb></lb>ſtico muro appendam, quæ ex ſacro tholo templi <lb></lb>Themidos amœniter pendent: </s>
					<s id="N100EF">Nec leuem toti rei li­<lb></lb>terariæ iniuriam inferrem, ſi alium illi, quàm li-<emph.end type="italics"></emph.end><pb xlink:href="026/01/004.jpg"></pb><emph type="italics"></emph>teratum Mecænatem accerſerem: </s>
					<s id="N100FD">&amp; verò Tracta­<lb></lb>tum hunc de Motu Locali, alteri quàm tibi inſcri­<lb></lb>bere non debui, cuius imperia Ludgunenſis orbis, po­<lb></lb>tiùs quàm vrbis, componunt: </s>
					<s id="N10107">Tu prudens Intelli­<lb></lb>gentia, huic orbi ſemper aſsiſtis; </s>
					<s id="N1010D">ita motibus in­<lb></lb>uigilas, vt quieti publicæ conſulas, remque ita pu­<lb></lb>blicam adminiſtras, vt ſingulis commoda procures: <lb></lb>Cæterùm dubitare non poſſum, quin hunc meum̨ <lb></lb>quantulumcumque conatum, fidemque meam iam̨ <lb></lb>tibi ſemel oppigneratam, &amp; nunc altero voto peni­<lb></lb>tus obſtrictam, æqui bonique ſis conſulturus, Valę.<emph.end type="italics"></emph.end></s>
				</p>
			</section>
			<section>
				<pb xlink:href="026/01/005.jpg"></pb>
				<figure id="id.026.01.005.1.jpg" xlink:href="026/01/005/1.jpg"></figure>
				<p id="N10129" type="head">
					<s id="N1012B"><emph type="center"></emph>PRÆFATIO.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N10132" type="main">
					<s id="N10134">NIHIL habeo præfari (Beneuole Lector) <lb></lb>in gratiam huius tractatus de Motu Locali, <lb></lb>cuius amœnitatem &amp; vtilitatem, rerum co­<lb></lb>piam &amp; ſyluam, tuo guſtui &amp; iudicio re­<lb></lb>linquo: </s>
					<s id="N10140">Multi ſanè hactenus in hac mate­<lb></lb>ria feliciter deſudarunt; </s>
					<s id="N10146">&amp; quidem præ cæteris magnus <lb></lb>ille Galileus, qui mirificâ, &amp; ferè diuinâ ingenij acie, <lb></lb>motum localem eò perduxit, quò mortalium nemo per­<lb></lb>duxerat; </s>
					<s id="N10150">quia tamen multa omiſit, quæ ad motum ſpe­<lb></lb>ctant, vt nemo neſcit; </s>
					<s id="N10156">nec ex principijs Phyſicis mira­<lb></lb>biles illos effectus demonſtrauit, ſed tantùm certis qui­<lb></lb>buſdam proportionibus ex geometricis addixit; </s>
					<s id="N1015E">vt Phy­<lb></lb>ſicæ conſulamus, aliam inimus viam: </s>
					<s id="N10164">Geometriam qui­<lb></lb>dem adhibemus, ad explicandas, exponendaſque præ­<lb></lb>dictas illas proportiones, quæ motibus inſunt; </s>
					<s id="N1016C">ſed effe­<lb></lb>ctus illos prædictis proportionibus affixos ad principia <lb></lb>Phyſica reducimus; </s>
					<s id="N10174">id eſt, cùm ſupponamus quòd ſint, <lb></lb>propter quid ſint demonſtramus: </s>
					<s id="N1017A">in votis erat motus <lb></lb>omnes vno volumine complecti; </s>
					<s id="N10180">id eſt effectus omnes <lb></lb>cuiuſuis potentiæ motricis; </s>
					<s id="N10186">tres enim agnoſcimus hu­<lb></lb>iuſmodi potentias: </s>
					<s id="N1018C">primam naturalem voco, quæ eſt <lb></lb>grauium: </s>
					<s id="N10192">alteram animalem, quæ eſt animantium: </s>
					<s id="N10196">ter­<lb></lb>tiam mediam, quæ tenſorum eſt vel compreſſorum: </s>
					<s id="N1019C">In <lb></lb>hoc tractatu tùm à motu progreſſiuo animantium, tùm <lb></lb>ab alijs motibus, qui in animato corpore, neruorum &amp; <pb xlink:href="026/01/006.jpg"></pb>muſculorum opera fiunt, penitus abſtinemus; </s>
					<s id="N101A8">cùm ſci­<lb></lb>licèt eas notiones ſupponant, quæ huius loci eſſe non <lb></lb>poſſunt, abſtinemus etiam à mirifica illa tenſorum &amp; <lb></lb>compreſſorum vi, quæ mediæ illius virtutis eſt; </s>
					<s id="N101B2">neque <lb></lb>adhuc eò rem Phyſicam adduximus; Sed hîc tantùm na­<lb></lb>turam impetus conſideramus, motus naturalis affectio­<lb></lb>nes, violenti, mixti ex rectis, reflexi, circularis, mixti <lb></lb>ex circularibus, illius qui fit in planis inclinatis ſurſum <lb></lb>&amp; deorſum, vibrationum funependuli, diuerſarum im­<lb></lb>preſſionum, centri percuſſionis, &amp;c. </s>
					<s id="N101C2">Fortè aliquis poten­<lb></lb>tias mechanicas deſideraret, lineas, motus, &amp; cæleſtes <lb></lb>ſpiras; </s>
					<s id="N101CA">ſed hæ quidquid phyſicum habent, ſingulari tra­<lb></lb>ctatui de corpore cæleſti, reliqua verò Aſtronomiæ con­<lb></lb>cedunt: potentiæ mechanicæ ad Staticam pertinent, qua­<lb></lb>re illarum tantùm phyſicum principium in hoc tractatu <lb></lb>explicamus, lineæ motus nihil phyſicum habent. </s>
					<s id="N101D6">Quare <lb></lb>ad vitandam confuſionem ad Matheſim illas remittimus, <lb></lb>cuius non modicam facient acceſſionem; igitur ſecun­<lb></lb>dum Tomum de motu locali non expectabis, qui ne <lb></lb>cuncta quidem, quæ ad motum ſpectant comprehende­<lb></lb>ret, ſed huic ſtatim Metaphyſicam demonſtratiuam ſub­<lb></lb>necto. </s>
					<s id="N101E6">Cæterùm de ſubtiliſſimo iſtorum omnium inuen­<lb></lb>torum auctore nihil dicam, qui cum ægrè tulerit paucula <lb></lb>illa quæ in prima tractatu præfatus ſum, os mihi peni­<lb></lb>tus obſtruxit: </s>
					<s id="N101F0">omitto etiam quæ in me quidam iniquè <lb></lb>certè rerum æſtimatores iactarunt: </s>
					<s id="N101F6">reponere poſſem cum <lb></lb>fænore; </s>
					<s id="N101FC">ſed nos talem conſuetudinem non habemus; </s>
					<s id="N10200">de­<lb></lb>dici hactenus pati iniurias, non inferre; quod non modò <lb></lb>moralis Philoſophia, ſed præſertim Chriſtiana Religio me <lb></lb>docet. </s>
				</p>
				<pb xlink:href="026/01/007.jpg"></pb>
				<p id="N1020D" type="main">
					<s id="N1020F">Vnum eſt, de quo te monitum velim (Amice Lector) <lb></lb>opuſculum iſtud non ſine aliquot erratis edi potuiſſe, <lb></lb>præſertim cùm in aſſignandis cuilibet figuræ ſuis chara­<lb></lb>cteribus ſæpiùs peccatum ſit; </s>
					<s id="N10219">operas excuſabis in rebus <lb></lb>Geometricis minimè verſatos: auctor tibi ſum, vt errata, <lb></lb>quæ fideliter adnotaui caſtiges, vt deinde cum maiore <lb></lb>guſtu Librum hunc perlegere poſſis. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N10226" type="main">
					<s id="N10228"><emph type="center"></emph><emph type="italics"></emph>SYNOPSIS LIBRORVM<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10233" type="main">
					<s id="N10235"><emph type="center"></emph><emph type="italics"></emph>huius tractatus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10240" type="table">
					<s id="N10242">TABELLE WAR HIER</s>
				</p>
			</section>
			<section>
				<pb xlink:href="026/01/008.jpg"></pb>
				<figure id="id.026.01.008.1.jpg" xlink:href="026/01/008/1.jpg"></figure>
				<p id="N1024F" type="head">
					<s id="N10251"><emph type="center"></emph><emph type="italics"></emph>SYNOPSIS AMPLIOR.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1025D" type="main">
					<s id="N1025F">BREVISSIMAM huius operis Epitomem hîc <lb></lb>habes (Amice Lector) quam ex Theſibus noſtri <lb></lb>Philoſophi huc traduxi, quæ tibi ampliſſimi <lb></lb>indicis loco erit. </s>
				</p>
				<figure id="id.026.01.008.2.jpg" xlink:href="026/01/008/2.jpg"></figure>
				<p id="N1026D" type="main">
					<s id="N1026F"><emph type="center"></emph><emph type="italics"></emph>De Impetu.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1027A" type="main">
					<s id="N1027C">1. IMPETVS eſt qualitas exigens motum ſui ſubiecti: </s>
					<s id="N10280"><lb></lb>datur impetus; </s>
					<s id="N10285">quia non poteſt eſſe alia cauſa exi­<lb></lb>gitiua motus: </s>
					<s id="N1028B">adde quòd, potentia motrix eſt acti­<lb></lb>ua; </s>
					<s id="N10291">igitur aliquid producit, ſed non aliud quàm <lb></lb>impetum, vt conſtat ex dictis de motu: </s>
					<s id="N10297">eſt aliquid diſtinctum à <lb></lb>ſubſtantia mobilis, quæ poteſt eſſe ſine impetu: </s>
					<s id="N1029D">non eſt modus, <lb></lb>quia diſtinguitur ab effectu ſuo formali ſecundario: </s>
					<s id="N102A3">impetus non <lb></lb>producitur in eo mobili, quod moueri non poteſt à potentia mo­<lb></lb>trice applicata: </s>
					<s id="N102AB">&amp; produci tantùm poteſt, vel in omni parte, vel <lb></lb>in nulla; </s>
					<s id="N102B1">alioquin eſſet fruſtrà; &amp; gratis ponitur neſcio quis impe­<lb></lb>tus inefficax. </s>
				</p>
				<p id="N102B7" type="main">
					<s id="N102B9">2. Primo inſtanti, quo eſt impetus, non eſt motus, ne ſimul im­<lb></lb>petus ſit in duobus locis. </s>
					<s id="N102BE">Impetus productus ad extra non produci­<lb></lb>tur à quantitate, nec virtute reſiſtitiua, nec ab alio, quàm ab impe­<lb></lb>tu, qui maximè eſt cauſa connaturalis alterius impetus: </s>
					<s id="N102C6">agit tan­<lb></lb>tùm ad extra, vt tollat impedimentum: </s>
					<s id="N102CC">hinc, cùm pro diuerſa <lb></lb>applicatione ſit diuerſum impedimentum, modò plùs, modò minùs <lb></lb>agit; </s>
					<s id="N102D4">maximè verò, cum maximum eſt impedimentum: </s>
					<s id="N102D8">hinc ictus <lb></lb>per lineam perpendicularem fortiſſimus eſt: portò omnes partes <lb></lb>impetus agunt ad extra actione communi. </s>
				</p>
				<p id="N102E0" type="main">
					<s id="N102E2">3. Impetus intenſus producere poteſt remiſſum, minoris mobi­<lb></lb>lis in maiore; </s>
					<s id="N102E8">&amp; remiſſus intenſum, maioris mobilis in minore, vt <lb></lb>patet; æqualis æqualem, æqualis mobilis in æquali, modò ſit debi-<pb xlink:href="026/01/009.jpg"></pb>ta applicatio, cum maximo impedimento, quod reuerâ tunc eſt, <lb></lb>cùm linea directionis connectit centra grauitatis vtriuſque. </s>
					<s id="N102F4">Datur <lb></lb>impetus alio impetu perfectior, &amp; imperfectior, ſine quo non po­<lb></lb>teſt explicari natura vectis: </s>
					<s id="N102FC">itaque dato quocunque dari poteſt per­<lb></lb>fectior, &amp; imperfectior: quia dato quocunque motu poteſt dari ve­<lb></lb>locior, &amp; tardior. </s>
				</p>
				<p id="N10304" type="main">
					<s id="N10306">4. Propagatur impetus vniformiter tantùm, cùm omnes partes <lb></lb>corporis mouentur motu recto æquali: </s>
					<s id="N1030C">ibi enim eſt æqualis cauſa, <lb></lb>vbi eſt æqualis effectus: </s>
					<s id="N10312">in motu circulari applicata potentia cen­<lb></lb>tro vectis, producitur æqualis perfectionis versùs circunferentiam, <lb></lb>&amp; inæqualis numerus; </s>
					<s id="N1031A">applicata verò potentia circunferentiæ, pro­<lb></lb>ducitur æqualis numerus, ſed inæqualis perfectionis versùs cen­<lb></lb>trum; </s>
					<s id="N10322">quia potentia non poteſt producere immediatè perfectiorem, <lb></lb>&amp; imperfectiorem in infinitum: </s>
					<s id="N10328">eadem potentia neceſſaria æquali­<lb></lb>bus temporibus, &amp; iiſdem circunſtantiis, producit æqualem impe­<lb></lb>tum, &amp; inæqualibus inæqualem: eſt enim hæc ratio cauſæ neceſ­<lb></lb>ſariæ. </s>
				</p>
				<p id="N10332" type="main">
					<s id="N10334">5. Impetus innatus eſt tantùm determinatus ad lineam perpen­<lb></lb>dicularem deorſum; </s>
					<s id="N1033A">alioquin ſi ad aliam determinari poſſet, primo <lb></lb>eſſet æqualis motus per inclinatam, &amp; perpendicularem; </s>
					<s id="N10340">corpus <lb></lb>graue miſſum per lineam inclinatam ab eo non declinaret; </s>
					<s id="N10346">imò im­<lb></lb>petus ſemel productus (ſi liberum eſſet medium) non deſtrueretur: </s>
					<s id="N1034C"><lb></lb>quæ omnia phyſicis hypotheſibus repugnant: omnis alius impetus, <lb></lb>etiam acquiſitus motu naturali deorſum, eſt indifferens ad omnem <lb></lb>lineam, ad vitanda infinita ferè naturæ incommoda. </s>
				</p>
				<p id="N10355" type="main">
					<s id="N10357">6. Impetus indifferens determinatur ad lineam multis modis: <lb></lb>primò, à potentia motrice: </s>
					<s id="N1035D">ſecundò, ab impetu: </s>
					<s id="N10361">tertiò, ab alio impe­<lb></lb>tu concurrente; quartò, ab obice occurrente: </s>
					<s id="N10367">quintò, ab ipſo appli­<lb></lb>cationis diuerſo modo: quæ omnia clara ſunt: hinc duo impetus ad <lb></lb>motum mixtum ſæpè concurrunt, quod ſemper fit, niſi determina­<lb></lb>tiones ſint oppoſitæ ex diametro. </s>
					<s id="N10371">Impetus eſt capax intenſionis; </s>
					<s id="N10375"><lb></lb>quia aliquando deſtruitur ex parte: </s>
					<s id="N1037A">eius extenſio commenſuratur <lb></lb>extenſioni mobilis; </s>
					<s id="N10380">quod etiam cæteris qualitatibus commune eſt: <lb></lb>impetus productus non conſeruatur à cauſa primò productiua, à <lb></lb>qua etiam ſeparatus exiſtit. </s>
				</p>
				<p id="N10388" type="main">
					<s id="N1038A">7. Impetus non eſt contrarius alteri ratione entitatis; </s>
					<s id="N1038E">quia qui­<lb></lb>libet cum quolibet in eodem ſubiecto coëxiſtere poteſt: </s>
					<s id="N10394">pugnat <lb></lb>tamen vnus cum alio ratione determinationis: </s>
					<s id="N1039A">hinc vnus impetus <lb></lb>pugnat cum alio ratione lineæ motus: </s>
					<s id="N103A0">hinc vnus videtur deſtrui ab <pb xlink:href="026/01/010.jpg"></pb>alio; </s>
					<s id="N103A8">quanquam impetus tantùm deſtruitur, cùm eſt fruſtrà: </s>
					<s id="N103AC">hinc, ſi <lb></lb>eſſet tantùm vnicus in eodem mobili, &amp; liberum eſſet medium, <lb></lb>nunquam deſtrueretur nec vnquam dici poſſet functus ſuo mune­<lb></lb>re; quod omninò gratis dicitur. </s>
				</p>
				<p id="N103B6" type="main">
					<s id="N103B8">8. Hinc, ſi ſint tantùm duo impetus in eodem mobili æquales <lb></lb>verbi gratia, vel ad eandem lineam determinantur, vel ad diverſas; </s>
					<s id="N103BE"><lb></lb>ſi ad eandem, nihil impetus deſtruitur, ſed eſt duplò velocior mo­<lb></lb>tus; </s>
					<s id="N103C5">ſi ad diuerſas, vel ſunt oppoſitæ ex diametro, vel concurrentes <lb></lb>faciunt angulum; </s>
					<s id="N103CB">ſi primum, vterque deſtruitur impetus; ſi ſe­<lb></lb>cundum, deſtruitur aliquid illius, quod determinabimus in­<lb></lb>frà. </s>
					<s id="N103D3">Impetus innatus nunquam deſtruitur: </s>
					<s id="N103D7">dici poſſet grauitas ab­<lb></lb>ſoluta; ſaltem nihil eſt, quod diſtingui ab illa probare poſſit. </s>
					<s id="N103DD">Porrò <lb></lb>nunquam deſtruitur; </s>
					<s id="N103E2">quia nunquam eſt fruſtrà; quippe eius finis, <lb></lb>vel vſus, non eſt tantùm motus deorſum, ſed grauitatio, ſeu niſus <lb></lb>quidam deorſum. </s>
					<s id="N103EA">Sed de grauitate aliàs. </s>
				</p>
				<figure id="id.026.01.010.1.jpg" xlink:href="026/01/010/1.jpg"></figure>
				<p id="N103F2" type="main">
					<s id="N103F4"><emph type="center"></emph><emph type="italics"></emph>De motu naturali deorſum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N103FF" type="main">
					<s id="N10401">1. DAtur motus naturalis grauium deorſum ab intrinſeco, <lb></lb>quippe non poteſt eſſe, vel à vi tractrice terræ vel fila­<lb></lb>mentis quibuſdam, vel materia quadam tenui expultrice. </s>
					<s id="N10408">Eius finis <lb></lb>eſt globi terreſtris compactio, &amp;c. </s>
					<s id="N1040D">Eſt autem motus naturalis ab <lb></lb>impetu: </s>
					<s id="N10413">primò, quia eius acceleratio ſine impetu explicari non po­<lb></lb>teſt: </s>
					<s id="N10419">ſecundò, quia, cùm graue deorſum cadens imprimat impetum <lb></lb>in corpore occurrente, certè debet habere impetum: nec alio ar­<lb></lb>gumento mihi probabis, Solem eſſe lucidum, ignem calidum. </s>
				</p>
				<p id="N10421" type="main">
					<s id="N10423">2. Motus hic eſt naturaliter acceleratus, ſcilicet, ab intrinſeco; <lb></lb>patet experientiâ. </s>
					<s id="N10429">Ratio eſt: </s>
					<s id="N1042C">quia, cùm in libero medio non impe­<lb></lb>diatur motus, &amp; impetus productus primo inſtanti non conſerue­<lb></lb>tur ſecundo à cauſa primò productiua, ſed ab alia, ſitque ipſa mo­<lb></lb>bilis ſubſtantia cauſa neceſſaria; </s>
					<s id="N10436">certè ſecundo inſtanti producit <lb></lb>nouum impetum: idem dica de tertio, quarto, &amp;c. </s>
					<s id="N1043C">igitur creſcit <lb></lb>cauſa motus; </s>
					<s id="N10442">igitur &amp; motus: quæ ratio clariſſima eſt: </s>
					<s id="N10446">hinc æquali­<lb></lb>bus temporibus æqualia acquiruntur velocitatis momenta; </s>
					<s id="N1044C">quia <lb></lb>cauſa neceſſaria æqualibus temporibus, æqualem effectum produ­<lb></lb>cit: quid clarius? </s>
				</p>
				<p id="N10454" type="main">
					<s id="N10456">3. Hinc non poteſt creſcere hic impetus ſecundùm porportio-<pb xlink:href="026/01/011.jpg"></pb>nem duplicatam temporum, cùm creſcat ſecundùm proportionem <lb></lb>temporum, etïam ex mente Galilei: </s>
					<s id="N10460">creſcit autem velocitas, vt im­<lb></lb>petus; </s>
					<s id="N10466">effectus, ſcilicet, vt cauſa: </s>
					<s id="N1046A">idem dico de motu, ratione velo­<lb></lb>citatis; </s>
					<s id="N10470">quippe motus ipſe eſt ſua velocitas: at verò ipſa ſpatia, <lb></lb>quæ decurruntur illo motu, ſi conſideretur crementum in inſtan­<lb></lb>tibus, creſcunt iuxta progreſſionem arithmeticam ſimplicem, <lb></lb>id eſt, ſi primo inſtanti, acquiritur vnum ſpatium, ſecundo acquiri­<lb></lb>tur vnum ſpatium, ſecundo acquiruntur duo, tertio 3. quarto 4. at­<lb></lb>que ita deinceps. </s>
				</p>
				<p id="N1047E" type="main">
					<s id="N10480">4. Hoc autem facilè poteſt <expan abbr="demõſtrari">demonſtrari</expan>: </s>
					<s id="N10488">quia, cùm velocitas creſ­<lb></lb>cat iuxta proportionem temporum, ſi primo inſtanti ſit vnus gradus <lb></lb>velocitatis, ſecundo erunt duo, tertio tres, at que ita deinceps: </s>
					<s id="N10490">igitur, <lb></lb>ſi mobile cum vno gradu velocitatis acquirit vnum ſpatium, certè <lb></lb>cum duobus acquiret duo ſpatia, cum tribus tria, atque ita dein­<lb></lb>ceps: debet autem vera progreſſio crementorum aſſumi in ſingulis <lb></lb>inſtantibus, quia reuerà ſingulis inſtantibus phyſicis (nam de iis <lb></lb>loquor) noua fit huius crementi acceſſio. </s>
				</p>
				<p id="N1049E" type="main">
					<s id="N104A0">5. Quia tamen inſtantia non ſunt ſenſibilia, vt Phyſicæ conſu­<lb></lb>latur, quæ res ſenſibiles conſiderat, aſſumi debent partes temporis <lb></lb>ſenſibiles, in quibus reuerâ progreſſio ſpatiorum non eſt arithmeti­<lb></lb>ca ſimplex; ſed tam propè accedit ad hanc numerorum imparium, <lb></lb>1. 3. 5. 7. &amp;c. </s>
					<s id="N104AC">quam Galileus excogitauit, vt ſine ſcrupulo hæc aſ­<lb></lb>ſumi poſſit: </s>
					<s id="N104B2">hinc ſpatia ſunt ferè vt temporum quadrata: dixi, ferè: </s>
					<s id="N104B6"><lb></lb>nam eſt paulò minor proportio, cùm tantùm finita ſint inſtantia <lb></lb>phyſica, quæ reuerà ſi infinita eſſent in qualibet temporis ſenſibilis <lb></lb>parte, haud dubiè ſpatia eſſent omninò in ratione duplicata tem­<lb></lb>porum: ſed, quia parum pro nihilo computatur, hanc progreſſio­<lb></lb>nem Galilei deinceps vſurpabimus in Phyſica. </s>
				</p>
				<p id="N104C4" type="main">
					<s id="N104C6">6. Hinc ratio euidens maioris ictus inflicti à corpore graui, <lb></lb>cùm ex maiori altitudine cadit. </s>
					<s id="N104CB">Sunt autem ictus, vt impetus; <lb></lb>impetus, vt tempora; hæc demum, vt radices ſpatiorum ſenſibi­<lb></lb>liter quæ omnia conſtant ex dictis. </s>
					<s id="N104D3">Impetus acquiſitus in deſcenſu <lb></lb>eſt ſemper imperfectior, ſi aſſumantur ſingula inſtantia, quæ reuerâ <lb></lb>ſunt ſemper minora; </s>
					<s id="N104DB">quia motus fit ſemper velocior: cùm graue <lb></lb>deſcendit in medio, quod reſiſtit, minùs accuratè ſeruantur prædi­<lb></lb>ctæ proportiones, quæ in vacuo modico accuratiſſimè ſeruaren­<lb></lb>tur. </s>
				</p>
				<p id="N104E5" type="main">
					<s id="N104E7">7. Reſiſtentia medij non eſt propter vllam formam improportio­<lb></lb>natam, quaſi verò impetus ſit forma improportionata aëri: </s>
					<s id="N104ED">ſed in <pb xlink:href="026/01/012.jpg"></pb>duobus præſertim conſiſtit; </s>
					<s id="N104F5">primò, eò quòd medium detrahat ali­<lb></lb>quid grauitationis corporis grauis; </s>
					<s id="N104FB">ſecundò, eò quòd partes medij <lb></lb>aliquam implicationem habeant, quæ ſolui non poteſt ſine aliqua <lb></lb>compreſſione, vel tenſione; </s>
					<s id="N10503">vtraque autem reſiſtit impetui: quod <lb></lb>ſpectat ad primum, ſi medium ſit æqualis grauitatis cum ipſo cor­<lb></lb>pore, detrahitur tota grauitatio, ſi ſubduplæ ſubduplum, &amp;c. </s>
					<s id="N1050B">de quo <lb></lb>aliàs. </s>
				</p>
				<p id="N10510" type="main">
					<s id="N10512">8. Hinc corpus graue per medium rarius, cæteris paribus, fa­<lb></lb>cilè deſcendit; non tamen ex reſiſtentia medij cognita, poteſt co­<lb></lb>gnoſci proportio grauitatis vtriuſque, propter ſecundum caput, ex <lb></lb>quo etiam petitur reſiſtentia. </s>
					<s id="N1051C">Idem corpus cum eodem medio <lb></lb>comparatum, habet tres coniugationes: nam, vel eſt grauius, vel­<lb></lb>eſt grauius, vel æquè graue, vel minùs. </s>
					<s id="N10524">Sunt etiam tres aliæ con­<lb></lb>iugationes, ſcilicet, eiuſdem mobilis cum diuerſis mediis, duorum <lb></lb>mobilium cum eodem medio, duorum mobilium cum duobus <lb></lb>mediis. </s>
				</p>
				<p id="N1052D" type="main">
					<s id="N1052F">9. Figura corporis grauis deorſum cadentis motum vel retardat <lb></lb>vel accelerat; </s>
					<s id="N10535">retardat quidem, ſi plures partes medij amouendæ <lb></lb>ſunt vel pauciores velociori motu; accelerat è contrario: </s>
					<s id="N1053B">hinc idem <lb></lb>corpus <expan abbr="parallelipedũ">parallelipedum</expan> iuxta tres diuerſos ſitus, triplici motu diuer­<lb></lb>ſo deſcendere poteſt: hinc ratio, cur acuminata tam facilè deſcen­<lb></lb>dant. </s>
					<s id="N10549">Cubus, qui deſcendit, imprimit aëri velociorem motum, <lb></lb>quàm ipſe habeat; &amp; quò maior eſt eius ſuperficies, eò velociorem. </s>
				</p>
				<p id="N1054F" type="main">
					<s id="N10551">10. Duo globi, vel cubi eiuſdem materiæ æquè velociter deſ­<lb></lb>cendunt: </s>
					<s id="N10557">ratio eſt, quia, licèt maioris vires habeant maiorem pro­<lb></lb>portionem ad molem aëris reſiſtentis, quàm vires minoris ad alte­<lb></lb>ram aëris molem, quæ proprium illius motum retardat, cùm tamen <lb></lb>aër, qui reſiſtit maiori cubo, debeat amoueri velociori motu, quàm <lb></lb>aër, qui reſiſtit minori, ſitque eadem proportio reſiſtentiæ ratione <lb></lb>motus, minoris ad maiorem, quæ eſt ratione molis, maioris ad mi­<lb></lb>norem; </s>
					<s id="N10567">certè ratio compoſita vtriuſque erit eadem in vtroque cu­<lb></lb>bo: igitur æqualiter deſcendet vterque. </s>
				</p>
				<p id="N1056D" type="main">
					<s id="N1056F">11. Si tamen ſint diuerſæ materiæ, haud dubiè, qui conſtat leuio­<lb></lb>ri materia, tardiùs deſcendet; quia eius vires habent minorem <lb></lb>proportionem ad reſiſtentiam. </s>
					<s id="N10577">Corpuſcula etiam ex grauiſſima ma­<lb></lb>teria tardiſſimè deſcendunt: </s>
					<s id="N1057D">tum, quia à filamentis illis, quibus par­<lb></lb>tes aëris implicantur, facilè detinentur; </s>
					<s id="N10583">analogiam habes in lapil­<lb></lb>lo, qui ab araneæ tela intercipitur: </s>
					<s id="N10589">tum, quia, cùm latiſſimam ali­<lb></lb>quando habeant ſuperficiem pro modica mole, minimam habent <pb xlink:href="026/01/013.jpg"></pb><expan abbr="proportionẽ">proportionem</expan> virium ad <expan abbr="reſiſtentiã">reſiſtentiam</expan>: tùm denique, quia, cùm modico <lb></lb>impetu agitari poſſint ab aëre mobili, vnus motus alium impedit. </s>
				</p>
				<p id="N1059C" type="main">
					<s id="N1059E">12. Singulis inſtantibus motus naturaliter accelerati creſcit <lb></lb>reſiſtentia; </s>
					<s id="N105A4">quia, cùm motus creſcat, æqualibus temporibus, plures <lb></lb>partes medij occurrunt; </s>
					<s id="N105AA">creſcunt tamen vires in eadem proportio­<lb></lb>ne, ſcilicet, impetus: igitur non mutatur progreſſio motus. </s>
					<s id="N105B0">Hinc <lb></lb>colligo, contra Galilæum, motum rectum ex naturaliter accelerato <lb></lb>nunquam fieri æquabilem: dixi motum rectum; quia motus corpo­<lb></lb>rum cœleſtium ex accelerato factus eſt æqualis. </s>
				</p>
				<figure id="id.026.01.013.1.jpg" xlink:href="026/01/013/1.jpg"></figure>
				<p id="N105BF" type="main">
					<s id="N105C1"><emph type="center"></emph><emph type="italics"></emph>De motu violento ſurſum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N105CC" type="main">
					<s id="N105CE">1. MOtus violentus ſurſum vulgò dicitur eſſe à principio ex­<lb></lb>trinſeco. </s>
					<s id="N105D3">Triplici modo accidere poteſt: </s>
					<s id="N105D7">primò, ſi reuerà <lb></lb>imprimatur impetus ab extrinſeco, vt, cùm mitto lapidem ſurſum: </s>
					<s id="N105DD"><lb></lb>ſecundò, ſi corpus deorſum cadens deinde reflectatur ſurſum; </s>
					<s id="N105E2">tunc <lb></lb>autem nihil eſt ab extrinſeco, niſi determinatio noua, quæ eſt à cor­<lb></lb>pore reflectente: </s>
					<s id="N105EA">tertiò, ſi terra vtrinque eſſet peruia; </s>
					<s id="N105EE">nam lapis haud <lb></lb>dubiè non ſiſteret in centro, ſaltem poſt primum deſcenſum; </s>
					<s id="N105F4">igitur <lb></lb>aſcenderet per eandem lineam; </s>
					<s id="N105FA">nullum tamen eſt principium ex­<lb></lb>trinſecum; igitur motus violentus dicit tantùm motum ſurſum <lb></lb>corporis grauis. </s>
				</p>
				<p id="N10602" type="main">
					<s id="N10604">2. Dari autem motum violentum, dubium eſſe non poteſt, qui <lb></lb>ſupponit impetum, vel impreſſum ab extrinſeco, vel in deſcenſu <lb></lb>acquiſitum, qui reuerâ ineſt ipſi mobili, cùm ipſum medium hunc <lb></lb>motum potiùs impediat, quàm iuuet: </s>
					<s id="N1060E">hinc, ſi nullus eſſet impetus <lb></lb>extrinſecus, vel acquiſitus, nullus eſſet motus violentus; quia im­<lb></lb>petus innatus illius cauſa eſſe non poteſt. </s>
					<s id="N10616">Portò hic motus non eſt <lb></lb>acceleratus, nec æqualis, alioquin <expan abbr="nunquã">nunquam</expan> rediret deorſum mobile. </s>
				</p>
				<p id="N1061F" type="main">
					<s id="N10621">3. Hinc neceſſariò eſt retardatus: </s>
					<s id="N10625">igitur deſtruitur impetus, non <lb></lb>quidem ab ipſa medij reſiſtentia; </s>
					<s id="N1062B">quippe idem medium non magis <lb></lb>reſiſtit motui ſurſum, quàm motui deorſum, vt patet: </s>
					<s id="N10631">igitur deſtrui­<lb></lb>tur ille impetus motus violenti ab impetu innato aliquo modo; </s>
					<s id="N10637">non <lb></lb>quidem vt à contrario ratione entitatis, ſed ratione determinatio­<lb></lb>nis: </s>
					<s id="N1063F">cùm enim impetus innatus exigat motum deorſum, &amp; alius ſur­<lb></lb>ſum: </s>
					<s id="N10645">hic quidem præualet, attamen fruſtrà eſt, ratione gradus <lb></lb>æqualis impetui innato: igitur deſtruitur ille gradus illo inſtanti. </s>
				</p>
				<pb xlink:href="026/01/014.jpg"></pb>
				<p id="N1064E" type="main">
					<s id="N10650">4. Hinc ſingulis temporibus æqualibus deſtruitur gradus impe­<lb></lb>tui innato; </s>
					<s id="N10656">eſt enim eadem ratio pro omnibus: </s>
					<s id="N1065A">igitur temporibus <lb></lb>æqualibus deſtruitur æqualis impetus: </s>
					<s id="N10660">igitur amittit ille motus <lb></lb>æqualia velocitatis momenta: </s>
					<s id="N10666">igitur eſt naturaliter retardatus: </s>
					<s id="N1066A">igi­<lb></lb>tur iuxta eam proportionem decreſcit motus violentus, iuxtaquam <lb></lb>creſcit naturalis: igitur dici debent de hac progreſſione retardatio­<lb></lb>nis, quæ dicta ſunt de illa progreſſione accelerationis. </s>
				</p>
				<p id="N10674" type="main">
					<s id="N10676">5. Hinc impetus imperfectior initio deſtruitur: </s>
					<s id="N1067A">quia, cùm motus <lb></lb>ille ſit velocior initio, inſtantia ſunt minora: </s>
					<s id="N10680">atqui minori tempore <lb></lb>minùs retardatur: </s>
					<s id="N10686">igitur inperfectior impetus deſtruitur; </s>
					<s id="N1068A">cùm è <lb></lb>contrario in motu acceleratio initio acquiratur imperfectior, quia <lb></lb>inſtantia ſunt maiora: vnde vides, gradus impetus eſſe heteroge­<lb></lb>neos, &amp; principium illud etiam in impetu valere, ſcilicet, ſubiectum <lb></lb>ita compleri ab vna forma, vt alterius homogeneæ non ſit ampliùs <lb></lb>capax, ſaltem naturaliter. </s>
				</p>
				<p id="N10698" type="main">
					<s id="N1069A">6. Hinc vltimus gradus impetus violenti eſt omnium perfectiſ­<lb></lb>ſimus, vt conſtat. </s>
					<s id="N1069F">Quieſceret vno inſtanti mobile iactum ſurſum, ſi <lb></lb>gradus vltimus violenti eſſet æqualis perfectionis, cum impetu in­<lb></lb>nato: </s>
					<s id="N106A7">vbi enim ventum eſſet ad inſtans æqualitatis, neutrum præ­<lb></lb>ualere poſſet: </s>
					<s id="N106AD">igitur inſtanti ſequenti eſſet quies: </s>
					<s id="N106B1">cùm tamen ſint <lb></lb>diuerſæ perfectionis, perfectior præualet: vter autem ſit perfectior, <lb></lb>dicemus infrà. </s>
				</p>
				<p id="N106B9" type="main">
					<s id="N106BB">7. Cum mobile ſurſum reflectitur, vel terra perforata ſuam lineam <lb></lb>motus ſurſum versus oppoſitam cœli plagam promouet, vel aliud <lb></lb>æqualis ponderis, vel maioris, ſurſum mouet, tunc certum eſt, inna­<lb></lb>tum eſſe perfectiorem: </s>
					<s id="N106C5">ſi verò imprimitur ab alia potentia motrice, <lb></lb>tunc etiam imperfectior eſt impetu innato; </s>
					<s id="N106CB">nam inæqualis eſt; </s>
					<s id="N106CF">alio­<lb></lb>quin, ſi eſſet æqualis, ſimul eſſent in eodem ſubiecto duo gradus <lb></lb>homogenei: </s>
					<s id="N106D7">præſtat autem eſſe imperfectiorem, quàm perfectio­<lb></lb>rem, vt plura impetus puncta à potentia imprimantur; </s>
					<s id="N106DD">quòd mul­<lb></lb>tum facit ad mouenda maiora pondera: hinc nullo inſtanti quieſ­<lb></lb>cunt proiecta ſurſum. </s>
				</p>
				<p id="N106E5" type="main">
					<s id="N106E7">8. Tandiu durat ſenſibiliter deſcenſus globi proiecti ſurſum, <lb></lb>quandiu durauit aſcenſus; </s>
					<s id="N106ED">eſt enim eadem ratio: ſagittæ verò mi­<lb></lb>nùs durat aſcenſus, quàm deſcenſus propter mixtionem materiæ. </s>
					<s id="N106F3"><lb></lb>Si motus violentus eſſet æquabilis, percurreret proiectum ſpatium <lb></lb>ferè duplum eo tempore, quo retardato percurrit ſubduplum: </s>
					<s id="N106FA">hinc <lb></lb>ſonus tam citò auditur; </s>
					<s id="N10700">quia propagatur cum particulis aëris æqua­<lb></lb>bili ferè motu: </s>
					<s id="N10706">eſſe autem ſpatium ferè duplum, probatur ex eo, <pb xlink:href="026/01/015.jpg"></pb>quòd ſpatium motu æquabili decurſum reſpondet rectangulo; </s>
					<s id="N1070E">de­<lb></lb>curſum verò motu retardato, reſpondet triangulo, ſubduplo rectan­<lb></lb>guli: aſſumpto ſcilicet, æquali tempore. </s>
				</p>
				<p id="N10716" type="main">
					<s id="N10718">9. Vites potentiæ proiicientis toto niſu reſpondent velocitati <lb></lb>acquiſitæ in toto deſcenſu corporis proiecti; <expan abbr="tantũdem">tantundem</expan> enim <lb></lb>impetus in deſcenſu acquiritur, quantùm in aſcenſu deperditur. </s>
					<s id="N10724"><lb></lb>Impetus primo inſtanti, quo eſt, agit, ſi eſt aliquod impedimen­<lb></lb>tum; </s>
					<s id="N1072B">eſt enim cauſa neceſſaria: </s>
					<s id="N1072F">primo inſtanti motus aliquid im­<lb></lb>petus deſtruitur: </s>
					<s id="N10735">ſiue præceſſerit motus violentus, ſiue non præceſ­<lb></lb>ſerit, corpus graue æquali motu deorſum cadit: </s>
					<s id="N1073B">reſiſtentia aëris eſt <lb></lb>quidem maior initio; ſed etiam ſunt maiores vires. </s>
				</p>
				<figure id="id.026.01.015.1.jpg" xlink:href="026/01/015/1.jpg"></figure>
				<p id="N10746" type="main">
					<s id="N10748"><emph type="center"></emph><emph type="italics"></emph>De motu in planis inclinatis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10753" type="main">
					<s id="N10755">1. PLanum inclinatum eſt ſurſum, vel deorſum: </s>
					<s id="N10759">in hoc deſcen­<lb></lb>dit corpus graue, niſi fortè retineatur ab aſperitate, vel pro­<lb></lb>pria, vel ipſius plani: </s>
					<s id="N10761">impeditur autem motus naturalis in plano <lb></lb>prædicto, quia impeditur eius linea: </s>
					<s id="N10767">ideò eſt tardior hic motus in <lb></lb>plano inclinato, quàm in perpendiculari: </s>
					<s id="N1076D">in ea porrò proportione <lb></lb>eſt tardior, in qua perpendiculum eſt minus linea inclinata, eiuſdem <lb></lb>ſcilicet, altitudinis; </s>
					<s id="N10775">quippe eò tardior eſt, quò magis impeditur, &amp; <lb></lb>magis impeditur, quò maius ſpatium decurrendum eſt, ad acqui­<lb></lb>rendam eandem altitudinem: igitur eadem eſt proportio impe­<lb></lb>dimenti, quæ ſpatij, &amp;c. </s>
				</p>
				<p id="N1077F" type="main">
					<s id="N10781">2. Hinc motus ſunt vt lineæ permutando: </s>
					<s id="N10785">hinc mobile deſcendit <lb></lb>per ſe in prædicto plano: </s>
					<s id="N1078B">licet enim motus impediatur, non tamen <lb></lb><expan abbr="tous">totus</expan>, impetus, qui acquiritur in eodem plano eſt imperfectior ac­<lb></lb>quiſito in perpendiculari in eadem proportione; </s>
					<s id="N10796">nam impetus ſunt <lb></lb>vt motus: </s>
					<s id="N1079C">hinc poteſt perfectio impetus imminui in infinitum, cùm <lb></lb>poſſit eſſe in infinitum linea magis, ac magis inclinata: igitur mo­<lb></lb>tum imminui poſſe in infinitum, non tantùm ex vecte, ſed etiam <lb></lb>ex planis inclinatis haberi poteſt. </s>
				</p>
				<p id="N107A6" type="main">
					<s id="N107A8">3. Hinc producit impetum imperfectiorem impetus acquiſitus <lb></lb>in hoc eodem plano, quàm acquiſitus in perpendiculari, æqualibus <lb></lb>ſcilicet temporibus, quia cauſa imperfectior imperfectiorem pro­<lb></lb>ducit effectum: </s>
					<s id="N107B2">motus in plano inclinato deorſum eſt acceleratus <lb></lb>iuxta eandem proportionem, iuxta quam acceleratur in perpendi-<pb xlink:href="026/01/016.jpg"></pb>culo: </s>
					<s id="N107BC">tempora, quibus percurruntur perpendiculum, &amp; linea plani <lb></lb>inclinati, ſunt vt lineæ; ſpatia autem, quæ in prædictis lineis acqui­<lb></lb>runtur æqualibus temporibus, ſunt vt motus, id eſt, vt lineæ per­<lb></lb>mutando, vt patet ex dictis. </s>
				</p>
				<p id="N107C6" type="main">
					<s id="N107C8">4. Ex his concludo, neceſſariò per plana omnia eiuſdem altitu­<lb></lb>dinis acquiri eandem velocitatem, quantumuis aſſumantur longiſ­<lb></lb>ſima, modò ſcilicet perpendicula ſint ſemper parallela. </s>
					<s id="N107CF">Hinc habes <lb></lb>apud Galileum, per omnes chordas circuli erecti deſcenſum fieri <lb></lb>æqualibus temporibus. </s>
					<s id="N107D6">Vires, quæ ſuſtinent pondus in plano in­<lb></lb>clinato per lineam plano <expan abbr="parallelã">parallelam</expan>, ſunt ad eas, quæ ſuſtinent in per­<lb></lb>pendiculo, vt lineæ permutando; quia debent adæquare impetum, <lb></lb>qui producitur, tùm in plano inclinato, tùm in perpendiculo. </s>
				</p>
				<p id="N107E4" type="main">
					<s id="N107E6">5. Porrò minùs grauitat in ipſum planum inclinatum corpus gra­<lb></lb>ue, quàm in planum horizontale: </s>
					<s id="N107EC">eſt autem grauitatio in horizonta­<lb></lb>li, ſeu Tangente, ad grauitationem in inclinata, ſeu ſecante, vt ipſæ <lb></lb>lineæ permutando: quod facilè demonſtramus. </s>
					<s id="N107F4">Proiicitur mobile <lb></lb>faciliùs per inclinatum planum ſurſum, quàm per ipſam perpendi­<lb></lb>cularem: patet experientia: cuius ratio eſt, quia minùs reſiſtit im­<lb></lb>petus innatus, cuius minor eſt niſus per inclinatam, vt conſtat ex <lb></lb>dictis. </s>
				</p>
				<p id="N10800" type="main">
					<s id="N10802">6. Illæ vires, quæ ſufficiunt ad eum motum ſurſum in perpendi­<lb></lb>culo, ſufficiunt ad motum ſurſum in plano inclinato eiuſdem alti­<lb></lb>tudinis: </s>
					<s id="N1080A">quia illæ vires ſufficiunt ad aſcenſum, quæ acquiruntur in <lb></lb>toto deſcenſu: ſed in deſcenſu inclinatæ, &amp; perpendiculi acquirun­<lb></lb>tur vires æquales, id eſt, velocitas æqualis, vt dictum eſt ſuprà. </s>
					<s id="N10812">Om­<lb></lb>nia puncta plani inclinati rectilinei, imò &amp; horizontalis, ſunt di­<lb></lb>uerſæ inclinationis: in iis tamen planis inclinatis quæ vulgò aſſu­<lb></lb>muntur, non mutatur ſenſibiliter inclinatio. </s>
				</p>
				<p id="N1081C" type="main">
					<s id="N1081E">7. Hinc minùs deſtruitur impetus in plano inclinato ſurſum, <lb></lb>quàm in perpendiculo; </s>
					<s id="N10824">quia diutiùs durat: </s>
					<s id="N10828">cùm enim minùs ac­<lb></lb>quiratur in deſcenſu, vt dictum eſt, minùs etiam deſtruitur in aſ­<lb></lb>cenſu: </s>
					<s id="N10830">hinc accedit propriùs hic motus ad æquabilem: </s>
					<s id="N10834">in eodem <lb></lb>plano rectilineo poteſt eſſe aſcenſus, &amp; deſcenſus, versùs eandem <lb></lb>partem: </s>
					<s id="N1083C">tale eſſet planum horizontale, in cuius vnico tantùm pun­<lb></lb>cto nulla eſt inclinatio: in quolibet puncto huius plani eſt ſingu­<lb></lb>laris inclinatio, vt patet, quæ eſt ad perpendiculum, vt Tangens ad <lb></lb>ſecantem éſtque eadem proportio motuum. </s>
				</p>
				<p id="N10846" type="main">
					<s id="N10848">8. Corpus graue in ſuperficie quadrantis caua, deorſum cadit <lb></lb>motu naturaliter accelerato; </s>
					<s id="N1084E">quia ſingulis inſtantibus accedit nouus <pb xlink:href="026/01/017.jpg"></pb>impetus; </s>
					<s id="N10856">non tamen æqualibus temporibus, acquiruntur æqualia <lb></lb>velocitatis momenta; </s>
					<s id="N1085C">quia in ſingulis punctis quadrantis, eſt diuer­<lb></lb>ſa tangens; </s>
					<s id="N10862">igitur mutatur progreſſio accelerationis, quæ certè ma­<lb></lb>jor eſt initio, &amp; ſub finem minor; quia initio tangentes acce­<lb></lb>dunt propriùs ad perpendiculum, &amp; ſub finem ad horizonta<lb></lb>lem. </s>
				</p>
				<p id="N1086C" type="main">
					<s id="N1086E">9. Deſcendit etiam in ſuperficie conuexa globi erecti motu ac­<lb></lb>celerato; </s>
					<s id="N10874">initio quidem, in minore proportione; </s>
					<s id="N10878">ſub finem, in maio­<lb></lb>re; </s>
					<s id="N1087E">vnde eſt inuerſa prioris: </s>
					<s id="N10882">poteſt etiam deſcendere corpus graue <lb></lb>vſque ad centrum terræ motu accelerato, in ſuperficie conuexa ſe­<lb></lb>micirculi: </s>
					<s id="N1088A">ſi ſuperficies terræ eſſet læuigatiſſima, corpus proje­<lb></lb>ctum moueretur in ea motu æquabili, nec deſtrueretur impetus im­<lb></lb>preſſus, vt conſtat; </s>
					<s id="N10892">poteſt quoque deſcendere per ſpiralem: ſunt in­<lb></lb>finita plana curua, in quibus faciliùs moueri poteſt, quam in ho­<lb></lb>rizontali recta. </s>
				</p>
				<figure id="id.026.01.017.1.jpg" xlink:href="026/01/017/1.jpg"></figure>
				<p id="N1089F" type="main">
					<s id="N108A1"><emph type="center"></emph><emph type="italics"></emph>De motu mixto ex rectis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N108AC" type="main">
					<s id="N108AE">1. DAri motum mixtum ille non dubitat, qui diſcum proiicit. </s>
					<s id="N108B1"><lb></lb>Mixtus ex duobus rectis æquabilibus eſt rectus, eſt que <lb></lb>diagonalis vtriuſque: </s>
					<s id="N108B8">hinc deſtruitur aliquid impetus, iuxta pro­<lb></lb>portionem differentiæ diagonalis, &amp; vtriuſque lateris ſimul ſump­<lb></lb>ti; </s>
					<s id="N108C0">quia, ſcilicet, eſt fruſtrà: </s>
					<s id="N108C4">quò maior eſt angulus, quem faciunt li­<lb></lb>neæ determinationum, minor eſt diagonalis; igitur plùs impetus <lb></lb>deſtruitur, donec tandem concurrant in oppoſitas lineas, tunc enim <lb></lb>totius impetus deſtruitur. </s>
				</p>
				<p id="N108CE" type="main">
					<s id="N108D0">2. <expan abbr="Quũ">Quum</expan> minor eſt, vel acutior prædictus angulus, minùs impetus <lb></lb>deſtruitur; </s>
					<s id="N108DA">quia diagonalis maior eſt; </s>
					<s id="N108DE">donec tandem conueniant in <lb></lb>eandem lineam, tunc enim nihil deſtruitur: </s>
					<s id="N108E4">datur de facto hic mo­<lb></lb>tus in rerum natura; </s>
					<s id="N108EA">talis eſt motus nauis à duobus ventis impreſ­<lb></lb>ſus; vel eiuſdem partis aëris; imò &amp; ipſius venti: </s>
					<s id="N108F0">motus mixtus ex <lb></lb>duobus retardatis iuxta eandem progreſſionem eſt rectus; </s>
					<s id="N108F6">quia fit <lb></lb>per hypothenuſim triangulorum proportionalium: idem dico de <lb></lb>duobus acceleratis. </s>
				</p>
				<p id="N108FE" type="main">
					<s id="N10900">3. Si mixtus ſit ex æquali, &amp; accelerato, vel ex duobus accelera­<lb></lb>tis in diuerſa progreſſione, vel ex duobus retardatis ſimiliter, fit per <lb></lb>lineam curuam, vt patet: </s>
					<s id="N10908">dum proiicitur corpus graue per horizon-<pb xlink:href="026/01/018.jpg"></pb>talem in medio libero eſt motus mixtus ex accelerato naturali, &amp; <lb></lb>retardato violento: eſt enim acceleratus naturalis, cùm deorſum <lb></lb>deorſum tendat quaſi per gradus, ſeu diuerſa plana inclinata. </s>
				</p>
				<p id="N10914" type="main">
					<s id="N10916">4. Non tamen impetus acquiſitus in eo motu eſt eiuſdem perfe­<lb></lb>ctionis cum illo, qui acquireretur in perpendiculari eiuſdem longi­<lb></lb>tudinis; </s>
					<s id="N1091E">ſed tantùm eiuſdem altitudinis: </s>
					<s id="N10922">nam perinde creſcit ille <lb></lb>impetus, atque creſceret in diuerſis planis inclinaris: </s>
					<s id="N10928">impetus verò <lb></lb>violentus in hoc motu retardatur; </s>
					<s id="N1092E">tùm, quia, ſi maneret idem, maior <lb></lb>eſſet ictus ſub finem iactus, quod eſt ridiculum; nec eſt, quòd aliqui <lb></lb>dicant, ab aëre deſtrui, qui non minùs reſiſtit naturali, quàm vio­<lb></lb>lento. </s>
				</p>
				<p id="N10938" type="main">
					<s id="N1093A">5. Adde, quòd eſt duplex determinatio: </s>
					<s id="N1093E">igitur aliquid deſtrui de­<lb></lb>bet, non acquiſiti; igitur impreſſi: </s>
					<s id="N10944">deſtrui autem non dicitur acqui­<lb></lb>ſitus, quòd, ſcilicet, plùs de nouo accedat, quàm pereat; </s>
					<s id="N1094A">eſt enim ac­<lb></lb>celeratus: </s>
					<s id="N10950">adde, quòd non infligitur tantus ictus ſub finem; </s>
					<s id="N10954">igitur <lb></lb>deſtruitur aliquid impetus, non acquiſiti, eo modo, quo diximus; </s>
					<s id="N1095A"><lb></lb>igitur impreſſi: ita tamen ſenſim deſtruitur, vt pro æquabili per ali­<lb></lb>quod ſpatium quaſi haberi poſſit. </s>
				</p>
				<p id="N10961" type="main">
					<s id="N10963">6. Hinc mobile proiectum per horizontalem, ne primo quidem <lb></lb>inſtanti per horizontalem mouetur, alioqui non eſſet motus mix­<lb></lb>tus: </s>
					<s id="N1096B">tardiùs cadit mobile ita proiectum in planùm horizontale ſub­<lb></lb>iectum, quàm cum ſua ſponte, ex eadem altitudine deſcendit: </s>
					<s id="N10971">cuius <lb></lb>rei clariſſima eſt experientia: ratio eſt; </s>
					<s id="N10977">quia impetus acquiſitus in <lb></lb>hoc iactu non eſt eiuſdem perfectionis, cùm acquiſito in perpendi­<lb></lb>culo: </s>
					<s id="N1097F">cùm proiicitur mobile per inclinatam ſurſum, mouetur motu <lb></lb>mixto ex naturali æquabili, &amp; violento retardato: patet prima pars; </s>
					<s id="N10985"><lb></lb>quia acceleratur tantùm naturalis deorſum, ſaltem in inclinata: </s>
					<s id="N1098A">ſe­<lb></lb>cunda pars etiam patet; quia ſub finem minor eſt ictus. </s>
				</p>
				<p id="N10990" type="main">
					<s id="N10992">7. Hinc linea motus eſt curua: </s>
					<s id="N10996">iuxta diuerſam progreſſionem de­<lb></lb>ſtruitur hic impetus impreſſus: </s>
					<s id="N1099C">tùm pro diuerſa inclinatione plani, <lb></lb>cuius etiam hîc habetur ratio; </s>
					<s id="N109A2">nam ſingulis inſtantibus mutatur: </s>
					<s id="N109A6"><lb></lb>tùm, quia modò plùs impetus eſt fruſtrà, modò minùs; </s>
					<s id="N109AB">plùs <lb></lb>certè, cùm linea determinationis impetus impreſſi facit obtu­<lb></lb>ſiorem: </s>
					<s id="N109B3">atqui initio eſt obtuſior; ſub finem verò aſcenſus acu­<lb></lb>tior. </s>
				</p>
				<p id="N109B9" type="main">
					<s id="N109BB">8. Aſcenſus proiecti per inclinatam diutiùs durat, quàm deſ­<lb></lb>cenſus, ratione eiuſdem plani horizontalis; </s>
					<s id="N109C1">quia, ſcilicet, aſ­<lb></lb>cenſus longior eſt, quàm deſcenſus: </s>
					<s id="N109C7">eſt autem longior; </s>
					<s id="N109CB">quia, vt <lb></lb>eſſet æqualis, nihil impetus impreſſi deberet deſtrui in aſcenſu <pb xlink:href="026/01/019.jpg"></pb>porrò in deſcenſu eſt motus mixtus ex accelerato naturali, <lb></lb>&amp; retardato violento, vt conſtat ex dictis: </s>
					<s id="N109D7">iactus per incli­<lb></lb>natam ad angulum 45. eſt omnium maximus, ratione eiuſdem <lb></lb>plani horizontalis: clara eſt experientia. </s>
					<s id="N109DF">Ratio eſt: </s>
					<s id="N109E2">quia per verti­<lb></lb>calem ſurſum, nihil acquiritur in plano horizontali, ex quo fit ia­<lb></lb>ctus; </s>
					<s id="N109EA">nihil etiam per ipſam horizontalem; igitur plùs acquiritur per <lb></lb>illam, quæ maximè ab vtraque ſimul recedit. </s>
				</p>
				<p id="N109F0" type="main">
					<s id="N109F2">9. Hæc ratio eſt verè phyſica, geometrica nulla eſt: hinc illi <lb></lb>iactus æquale ſpatium acquirunt in prædicto plano horizontali, <lb></lb>qui fiunt per inclinatas æqualiter à prædicta inclinata ad ang. 45. <lb></lb>diſtantes. </s>
					<s id="N109FC">Cùm emittitur mobile per inclinatum deorſum, in libero <lb></lb>medio, mouetur motu mixto ex naturali accelerato, &amp; impreſ­<lb></lb>ſo retardato, vt conſtat ex dictis; </s>
					<s id="N10A04">ille autem primus accelera­<lb></lb>tur per acceſſionem impetus perfectionis quàm in iactu per ho­<lb></lb>rizontalem; </s>
					<s id="N10A0C">ſed imperfectionis, quàm in perpendiculo: </s>
					<s id="N10A10">retarda­<lb></lb>tur verò impetus minùs, quàm in iactu per horizontalem; plùs ve­<lb></lb>rò, quàm in iactu per ipſum perpendiculum, in quo nihil impetus <lb></lb>deſtruitur. </s>
				</p>
				<p id="N10A1A" type="main">
					<s id="N10A1C">10. Cùm è naui mobili ſurſum mittitur corpus graue, eſt motus <lb></lb>mixtus ex tribus, in aſcenſu, ſcilicet, ex naturali æquabili, ex verti­<lb></lb>cali retardato, &amp; horizontali æquabili: </s>
					<s id="N10A24">mouetur ſurſum per cur­<lb></lb>uam, ſempérque capiti iaculatoris imminet; </s>
					<s id="N10A2A">quippe tantùm acqui­<lb></lb>rit in horizontali, quantùm nauis: </s>
					<s id="N10A30">in deſcenſu verò eſt motus <expan abbr="mix­">mixtus</expan> <lb></lb>ex horizontali retardato, &amp; naturali accelerato: </s>
					<s id="N10A3A">quia tamen bre­<lb></lb>uiſſimo illo tempore, retardatio illa horizontalis non eſt ſenſibilis, <lb></lb>ferè in ipſius iaculatoris caput deſcendit; quod certè phænomenon <lb></lb>ex noſtris principiis euincitur. </s>
				</p>
				<p id="N10A44" type="main">
					<s id="N10A46">11. Parum cautè Vfanus vniuerſim aſſerit, iaculationem pilæ ex <lb></lb>tormento, maiorem eſſe ex naui in continentem, &amp; minorem vi­<lb></lb>ciſſim, cùm vtriuſque differentia peti poſſit, vel à puluere tormen­<lb></lb>tario, vel ab eius compreſſione, vel humiditate, vel tormenti fabri­<lb></lb>ca, vel ipſius demum nauigij motu, qui pilæ motum, vel accelerat, ſi <lb></lb>versùs eandem partem eſt, vel retardat è contrario: in plano ho­<lb></lb>rizontali duro poteſt eſſe motus mixtus ex duobus, tribus, qua­<lb></lb>tuor, &amp; pluribus aliis. </s>
				</p>
				<p id="N10A58" type="main">
					<s id="N10A5A">12. Cùm è naui mobili emittitur ſagitta per horizontalem, quæ fa­<lb></lb>cit angelum rectum cum linea directionis nauis, fertur quaſi per dia­<lb></lb>gonalem vtriuſque, ſaltem per aliquod ſpatium: </s>
					<s id="N10A62">cùm verò emitti-<pb xlink:href="026/01/020.jpg"></pb>tur per horizontalem, quæ conueniat cum eadem linea directionis, <lb></lb>iactus eſt longior toto illo ſpatio, quod nauis decurrit, dum iactus <lb></lb>durat; </s>
					<s id="N10A6E">breuior tamen, ſi in partem oppoſitam fiat iactus in hoc ca­<lb></lb>ſu, ſi nauis æqualem impetum imprimeret, deorſum rectà ferretur <lb></lb>mobile motu naturali; </s>
					<s id="N10A76">imò ſagitta poſſet retorqueri in iaculatorem: </s>
					<s id="N10A7A"><lb></lb>ſi terra eſſet vtrimque peruia, lapis demiſſus per multa annorum <lb></lb>millia libraretur; non tamen eſſet motuus perpetuus. </s>
				</p>
				<figure id="id.026.01.020.1.jpg" xlink:href="026/01/020/1.jpg"></figure>
				<p id="N10A86" type="main">
					<s id="N10A88"><emph type="center"></emph><emph type="italics"></emph>De motu reflexo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10A93" type="main">
					<s id="N10A95">1. MOtus reflexi vera cauſa eſt impetus prior, ad nouam li­<lb></lb>neam determinatus ab occurrente obice; </s>
					<s id="N10A9B">planum refle­<lb></lb>ctens eſt cauſa nouæ determinationis ſuo modo; </s>
					<s id="N10AA1">cauſam enim di­<lb></lb>co eam, ex qua aliquid ſequitur: </s>
					<s id="N10AA7">ex gemina determinatione, noua, <lb></lb>ſcilicet, per ipſam perpendicularem erectam in puncto contactus, <lb></lb>&amp; priore per lineam incidentiæ, ab eodem puncto contactus pro­<lb></lb>pagatam, fit determinatio mixta per lineam reflexionis; </s>
					<s id="N10AB1">quæ omnia <lb></lb>patent ex terminis: </s>
					<s id="N10AB7">hinc nullus impetus producitur à plano refle­<lb></lb>ctente; </s>
					<s id="N10ABD">quippe prior poteſt determinari ad nouam lineam: adde, <lb></lb>quòd planum, quod caret impetu, impetum producere non poteſt. </s>
				</p>
				<p id="N10AC3" type="main">
					<s id="N10AC5">2. Imò nihil impetus deſtruitur in reflexione pura per ſe; </s>
					<s id="N10AC9">quia ni­<lb></lb>hil impetus eſt fruſtrà per ſe in pura reflexione; </s>
					<s id="N10ACF">multus tamen im­<lb></lb>petus deſtruitur per accidens, tùm ab ipſo attritu tùm mollitie <lb></lb>&amp; ceſſione, tùm preſſione: </s>
					<s id="N10AD7">hinc ſuppoſito eodem iactu, perpendi­<lb></lb>cularis reflexa eſt omnium reflexarum minima; </s>
					<s id="N10ADD">quia per eam li­<lb></lb>neam maximus ictus infligitur; </s>
					<s id="N10AE3">igitur maxima eſt partium colliſio, <lb></lb>&amp; preſſio: hinc etiam corpora duriora longiùs reflectuntur, per ipſam <lb></lb>quoque <expan abbr="perpendicularẽ">perpendicularem</expan>, dum planum reflectens ſit æquè durum. </s>
				</p>
				<p id="N10AEF" type="main">
					<s id="N10AF1">3. Determinatio noua dupla eſt prioris, poſita linea incidentiæ <lb></lb>perpendiculari, &amp; poſito etiam plano reflectente immobili; </s>
					<s id="N10AF7">quia <lb></lb>alioquin anguli reflexionis non eſſent æquales angulis incidentiæ: </s>
					<s id="N10AFD"><lb></lb>ſi globus reflectens ſit æqualis impacto, æqualis eſt ceſſio reſiſtenciæ <lb></lb>cùm ſit æquale agens reſiſtenti, perid enim reflectens reſiſtit, per <lb></lb>quod eſt: </s>
					<s id="N10B06">igitur, ſi æqualis reſiſtit, &amp; cedit, certè æqualiter ce­<lb></lb>dit, &amp; reſiſtit: </s>
					<s id="N10B0C">hinc noua determinatio æqualis eſt priori: </s>
					<s id="N10B10">hinc glo­<lb></lb>bus impactis ſiſtit immobilis; quia ex duabus determinationibus <lb></lb>oppoſitis neutra præualet. </s>
				</p>
				<pb xlink:href="026/01/021.jpg"></pb>
				<p id="N10B1B" type="main">
					<s id="N10B1D">4. Tantum eſt ab æqualitate prædicta ceſſionis, &amp; reſiſtentiæ, ad <lb></lb>nullam ceſſionem, &amp; notam reſiſtentiam, quantum eſt ad nullam <lb></lb><expan abbr="reſiſtẽtiam">reſiſtentiam</expan>, &amp; totam ceſſionem: </s>
					<s id="N10B28">hinc, cùm à tota ceſſione ad æqua­<lb></lb>litatem prædictam acquiratur tantùm noua determinato æqualis <lb></lb>priori; </s>
					<s id="N10B30">igitur ab eadem æqualitate ad nullam ceſſionem tantun­<lb></lb>dem acquiritur; </s>
					<s id="N10B36">igitur dupla prioris, vt iam ſuprà dictum eſt; </s>
					<s id="N10B3A">nulla <lb></lb>eſſet reſiſtentia in vacuo; nulla eſt ceſſio, cùm ipſum corpus refle­<lb></lb>ctens nullo modo mouetur ab ictu. </s>
				</p>
				<p id="N10B42" type="main">
					<s id="N10B44">5. Determinatio noua per lineam obliquam, eſt ad nouam per <lb></lb>lineam perpendicularem, vt ſinus rectus anguli incidentiæ, ad ſi­<lb></lb>num totum, in qualibet hypotheſi; </s>
					<s id="N10B4C">quia ſunt hæ, vt ictus, per vtran­<lb></lb>que lineam; </s>
					<s id="N10B52">ictus verò vt grauitationes in horizontale planum, &amp; <lb></lb>in planum inclinatum, ſub angulo complementi anguli incidentiæ: </s>
					<s id="N10B58"><lb></lb>hinc noua determinatio per lineam obliquam, eſt vt dupla ſinus re­<lb></lb>cti anguli incidentiæ, ad ſinum totum: </s>
					<s id="N10B5F">hinc ſupra angulum inci­<lb></lb>dentiæ 30, noua eſt maior priore, infrà minor; in ipſo angulo 30. <lb></lb>æqualis, ſuppoſita hypotheſi plani reflectentis immobilis. </s>
				</p>
				<p id="N10B67" type="main">
					<s id="N10B69">6. Ex hoc poſitiuo principio demonſtratur accuratiſſimè æqua­<lb></lb>litas anguli reflexionis, &amp; incidentiæ, quod certè demonſtratum <lb></lb>non fuit ab Ariſt. in problematis, ſect. 17. problem. 4. &amp; 13. quibus <lb></lb>in locis fusè ſatis explicatur hoc Theorema, ducta comparatione, <lb></lb>tùm à grauibus, quæ cadunt, tùm ab orbibus, quæ rotantur, rùm à <lb></lb>ſpeculis: ſed minimè demonſtratur ex certis principiis ſine petitio­<lb></lb>ne principij. </s>
					<s id="N10B79">In puncto reflexionis, poſita hypotheſi plani immo­<lb></lb>bilis reflectentis, nulla datur quies; </s>
					<s id="N10B7F">quia vnum tantùm eſt conta­<lb></lb>ctus inſtans; ſed eo inſtanti eſt motus, quo primo acquiritur locus. </s>
				</p>
				<p id="N10B85" type="main">
					<s id="N10B87">7. Omnes lineæ reflexæ per ſe ſunt æqualis longitudinis, &amp; ab <lb></lb>eodem puncto contactus, ad communem peripheriam terminan­<lb></lb>tur: </s>
					<s id="N10B8F">ſi globus impactus ſit æqualis reflectenti, ſitque linea inciden­<lb></lb>tiæ obliqua quælibet terminata ad idem punctum contactus, re­<lb></lb>flectitur prædictus globus per lineam tangentem globum refle­<lb></lb>ctentem in eodem puncto; </s>
					<s id="N10B99">quia hæc tangens eſt diagonalis com­<lb></lb>munis, &amp; determinatio mixta communis omnibus lineis inciden­<lb></lb>tiæ: eſt tamen modò longior, modò breuior linea reflexa, éſtque vt <lb></lb>vt ſinus complementi anguli incidentiæ, ad ſinum totum, qui ſit <lb></lb>determinatio prior, vt facilè demonſtramus. </s>
				</p>
				<p id="N10BA5" type="main">
					<s id="N10BA7">8. Si globus impactus ſit minor corpore reflectente, reflectitur <lb></lb>etiam per ipſam perpendicularem, &amp; determinatio noua eſt dupla­<lb></lb>prioris, minùs ratione globorum v. g. ſi globus impactus ſit ſubdu-<pb xlink:href="026/01/022.jpg"></pb>plus, determinatio noua eſt dupla prioris, minùs vna quarta, <lb></lb>&amp;c. </s>
					<s id="N10BB4">ratio eſt, quia in ea proportione globus reflectens cedit, in <lb></lb>qua mouetur, igitur tantùm detrahitur determinationis impacto <lb></lb>globo, quantùm additur motus reflectenti: at verò noua determina­<lb></lb>tio per lineam incidentiæ obliquam, eſt ad nouam per ipſam per­<lb></lb>pendicularem, vt ſinus rectus anguli incidentiæ ad ſinum totum. </s>
				</p>
				<p id="N10BC0" type="main">
					<s id="N10BC2">9. In hac hypotheſi lineæ reflexæ omnes ſunt ſupra prædictam <lb></lb>tangentem, ſeu ſectionem plani, maiores, vel minores, pro diuerſa <lb></lb>menſura diagonalis: </s>
					<s id="N10BCA">in ſuperiori verò hypotheſi æqualium globo­<lb></lb>rum, ſunt omnes in ipſa ſectione plani: ſi denique globus impactus <lb></lb>ſit maior alio, omnes ſunt infra prædictam ſectionem. </s>
					<s id="N10BD2">Porrò in hac <lb></lb>hypotheſi vltima, determinatio noua per ipſam perpendicularem <lb></lb>eſt minor priore: </s>
					<s id="N10BDA">hinc non modò nulla fit reflexio in perpendicula­<lb></lb>ri, ſed linea directa vlteriùs propagatur; quia prior determinatio <lb></lb>præualet. </s>
				</p>
				<p id="N10BE2" type="main">
					<s id="N10BE4">10. Detrahitur priori portio æqualis rationi globorum; </s>
					<s id="N10BE8">v. g. glo­<lb></lb>bus reflectens eſt ſubduplus impacto de trahitur priori determina­<lb></lb>tioni vna ſecunda; </s>
					<s id="N10BF0">eſt ſubquadruplus, vna quarta; atque ita dein­<lb></lb>ceps: </s>
					<s id="N10BF6">ratio patet ex dictis: </s>
					<s id="N10BFA">in linea verò incidentiæ obliqua, deter­<lb></lb>minatio eſt ad determinationem in perpendiculari, vt ſinus rectus <lb></lb>anguli incidentiæ ad ſinum totum: linea demum reflexa eſt modò <lb></lb>maior, modò minor pro diuerſa diagonali. </s>
				</p>
				<p id="N10C04" type="main">
					<s id="N10C06">11. Si duo globi æquales in ſe inuicem impingantur æquali mo­<lb></lb>tu, per lineam connectentem centra, vterque æquali motu priori re­<lb></lb>troagitur; </s>
					<s id="N10C0E">quia æqualis in æqualis æqualem impetum imprimit: </s>
					<s id="N10C12">non <lb></lb>eſt tamen motus reflexus; </s>
					<s id="N10C18">quia totus prior impetus deſtruitur, vt <lb></lb>patet ex dictis: </s>
					<s id="N10C1E">ſi autem inæquali motu concurrant, retroaguntur <lb></lb>iiſdem motibus, permutando; quod etiam clarum eſt: hinc egre­<lb></lb>gium paradoxum, ſi quod aliud conſequitur, ſcilicet, globum A, v. <lb></lb>g. æqualem motum imprimere globo B, ſiue hic moueatur, ſiue <lb></lb>quieſcat. </s>
				</p>
				<p id="N10C2A" type="main">
					<s id="N10C2C">12. Si verò linea incidentiæ ſit obliqua, vterque globus reflecte­<lb></lb>tur prorſus vt à plano immobili: </s>
					<s id="N10C32">hinc reflexio ſit ad angulos æqua­<lb></lb>les, &amp; lineæ omnes reflexionis ſunt æquales: ratio eſt; </s>
					<s id="N10C38">quia, quantùm <lb></lb>detrahit globus reflectens reſiſtendo, tantùm addit in partem op­<lb></lb>poſitam repellendo, poſitiuo niſu, vel impetu: quòd ſi alter globus <lb></lb>maiore, vel minore motu moueatur, vel ſi globi ſint inæquales, <lb></lb>cum æquali motu, vel inæquali, res etiam determinari poteſt ex <lb></lb>præmiſſis. </s>
				</p>
				<pb xlink:href="026/01/023.jpg"></pb>
				<p id="N10C49" type="main">
					<s id="N10C4B">13. Cum duo globi in ſeſe inuicem impinguntur æquali motu, <lb></lb>minor retroagitur velociore motu, quàm ante moueretur, vt clarum <lb></lb>eſt: </s>
					<s id="N10C53">maior verò, ſi duplus eſt alterius, ſiſtit immobilis in puncto <lb></lb>contactus; </s>
					<s id="N10C59">ſi maior duplo ſuum iter proſequitur, ſed tardiore mo­<lb></lb>tu; ſi minor duplo, retroagitur: quæ omnia facilè ex dictis demon­<lb></lb>ſtrantur. </s>
					<s id="N10C61">Poteſt impetus eſſe æqualis alteri, &amp; præualere; poteſt <lb></lb>æqualem impetum producere hoc inſtanti, &amp; ſtatim inſtanti, quod <lb></lb>ſequitur, totus deſtrui. </s>
				</p>
				<p id="N10C69" type="main">
					<s id="N10C6B">14. Poteſt globus retroagi in plano horizontali, licèt in aliud cor­<lb></lb>pus non incidat, ita vt initio tendat in ortum, verbi gratia: </s>
					<s id="N10C71">tùm <lb></lb>deinde, licèt nihil prorſus addatur, versùs occaſum; </s>
					<s id="N10C77">quod accidit, <lb></lb>cum globus vtroque motu, centri, ſcilicet, &amp; orbis, mouetur, ſed <lb></lb>contrario; primùm enim motus centri præualet, ſed facilè cedit <lb></lb>propter attritum maiorem partium. </s>
					<s id="N10C81">Nullus datur propriè motus <lb></lb>refractus: </s>
					<s id="N10C87">licèt enim incuruetur linea motus, dum per aquam ſu­<lb></lb>bit mobile; hæc tamen eſt reflexionis ſpecies. </s>
				</p>
				<p id="N10C8D" type="main">
					<s id="N10C8F">15. Globus reflectens, qui ab ictu alterius mouetur, non mouetur <lb></lb>inſtanti contactus; </s>
					<s id="N10C95">quia impetus primo inſtanti, quo eſt, non mo­<lb></lb>uetur; </s>
					<s id="N10C9B">producitur enim impetus primo inſtanti contactus: </s>
					<s id="N10C9F">ſi impe­<lb></lb>tus eſſet tantùm determinatus ad vnam lineam, nulla fieri poſſet <lb></lb>reflexio, ſed tantùm repercuſſio; </s>
					<s id="N10CA7">quia veriſſima cauſa reflexionis <lb></lb>conſiſtit in noua determinatione: </s>
					<s id="N10CAD">per reflexionem poſſunt colligi <lb></lb>plures partes aëris ſonori ad Echometriam: </s>
					<s id="N10CB3">ſagitta emiſſa per ho­<lb></lb>rizontalem ſursùm, tantillùm aſcendit per arcum; quia tantillùm <lb></lb>reflectitur ab aëre. </s>
				</p>
				<figure id="id.026.01.023.1.jpg" xlink:href="026/01/023/1.jpg"></figure>
				<p id="N10CC0" type="main">
					<s id="N10CC2"><emph type="center"></emph><emph type="italics"></emph>De motu circulari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10CCD" type="main">
					<s id="N10CCF">1. DAri motum circularem, probatur infinitis ferè experimen­<lb></lb>tis: </s>
					<s id="N10CD5">cuius ratio à priori eſt, quòd poſſint extremitates eiuſ­<lb></lb>dem cylindri in partes oppoſitas pelli; </s>
					<s id="N10CDB">vnde ſequitur neceſſariò <lb></lb>motus circularis; quem ij negare coguntur, qui ex punctis mathe­<lb></lb>maticis quantitatem componunt. </s>
					<s id="N10CE3">Motus circularis in ſublunaribus <lb></lb>oritur ex recto impedito; </s>
					<s id="N10CE9">quia, ſcilicet, determinatur tantùm im­<lb></lb>petus ad lineam rectam: </s>
					<s id="N10CEF">hinc quidam motus circularis eſt merè <lb></lb>per accidens, vt cùm retinetur extremitas funependuli, ſeu <pb xlink:href="026/01/024.jpg"></pb>fundæ, quæ ſi demittatur, ſequitur motus rectus: </s>
					<s id="N10CF9">quidam tamen <lb></lb>non eſt merè peraccidens, vt cùm pellitur extremitas cylindri in <lb></lb>plano horizontali; eſt enim, iuxta inſtitutionem naturæ, ad facili­<lb></lb>tatem motus. </s>
				</p>
				<p id="N10D03" type="main">
					<s id="N10D05">2. Quippe tale eſt naturæ inſtitutum, vt eo motu corpora mo­<lb></lb>ueantur, quo faciliùs moueri poſſunt: </s>
					<s id="N10D0B">atqui cùm pellitur altera cy­<lb></lb>lindri extremitas, in plano horizontali putà innatantis, faciliùs <lb></lb>mouetur, quàm recto, &amp; quaſi minore ſumptu, cùm minùs ſpatij <lb></lb>acquirat: æquali tempore: </s>
					<s id="N10D15">poteſt dari motus circularis mixtus ex <lb></lb>duobus rectis, quorum vnus ſit, vt ſinus recti, alius vt verſi; vix <lb></lb>tamen hoc accidit vnquàm, ſed tantùm oritur hic motus ex <lb></lb>determinatione per tangentem impedita, ratione alicuius puncti <lb></lb>immobilis. </s>
				</p>
				<p id="N10D21" type="main">
					<s id="N10D23">3. Hinc, ſi tollatur impedimentum, ſtatim per tangentem or­<lb></lb>bis fit motus, vt patet in funda: </s>
					<s id="N10D29">inæqualiter partes radij prædicti <lb></lb>orbis mouentur, iuxta proportionem diſtantiæ maioris, &amp; minoris <lb></lb>à centro: </s>
					<s id="N10D31">hinc propagatio impetus inæqualis, de qua iam ſuprà, <lb></lb>ſingulis inſtantibus &amp; punctis eſt noua determinatio; </s>
					<s id="N10D37">quia, ſcilicet, <lb></lb>ſingulis punctis ſua tangens reſpondet: </s>
					<s id="N10D3D">hinc, ſi imponatur rotæ <lb></lb>aliud corpus, ſtatim abigitur, ſine ſit in ſitu verticali, ſiue in ſitu ho­<lb></lb>rizontali; hinc dum turbo rotatur, ſi vel aquæ guttula eius ſuper­<lb></lb>ficies aſpergitur, &amp; ſtatim diſpergitur. </s>
				</p>
				<p id="N10D47" type="main">
					<s id="N10D49">4 Dari impetum in motu circulari certiſſimum eſt: </s>
					<s id="N10D4D">punctum phy­<lb></lb>ſicum eſt capax huius motus; cuius finis multiplex eſt; </s>
					<s id="N10D53">corpus mo­<lb></lb>uetur motu circulari circa centrum immobile cum motus centri <lb></lb>impeditur non tamen motus orbis, ad quem impetus facilè deter­<lb></lb>minatur, cùm ſit ad omnes lineas indifferens: </s>
					<s id="N10D5D">adde vſum vectis, <lb></lb>trochleæ, aliorúmque organorum, qui ſine motu circulari eſſe non <lb></lb>poteſt: omitto motum progreſſiuum, ipsúmque brachiorum, &amp; ti­<lb></lb>biarum vſum, qui motu circulari carere non poteſt. </s>
				</p>
				<p id="N10D67" type="main">
					<s id="N10D69">5. Motus circularis rotæ in plano verticali eſt æquabilis per ſe; </s>
					<s id="N10D6D"><lb></lb>quia nihil eſt, quod impetum ſemel impreſſum deſtruat: </s>
					<s id="N10D72">licèt enim <lb></lb>ſingulis inſtantibus ſit noua determinatio, nullus tamen impetus <lb></lb>eſt fruſtrà; </s>
					<s id="N10D7A">quippe illud ſpatium acquiritur in linea curua, quod in <lb></lb>recta, ſi nullum eſſet impedimentum, percurreret: </s>
					<s id="N10D80">quemadmodum <lb></lb>enim in reflexione, quæ fit à plano immobili, nullus deſtruitur im­<lb></lb>petus; </s>
					<s id="N10D88">ita nullus hîc deſtruitur; </s>
					<s id="N10D8C">tam enim centrum illud immobile <lb></lb>ad ſe quaſi trahit mobile, quàm planum immobile à ſe repellit; in <lb></lb>quo eſt perfectè analogia. </s>
				</p>
				<pb xlink:href="026/01/025.jpg"></pb>
				<p id="N10D97" type="main">
					<s id="N10D99">6. Hinc per ſe motus circularis integri orbis eſt perpetuus; </s>
					<s id="N10D9D">de­<lb></lb>ſtruitur tamen per accidens, ſcilicet, propter attritum axis: </s>
					<s id="N10DA3">hinc <lb></lb>tam diu durat hic motus: </s>
					<s id="N10DA9">clariſſimum experimentum habes in tur­<lb></lb>bine, cuius cuſpis læuigatiſſima in plano læuigatiſſimo rotatur; </s>
					<s id="N10DAF">nec <lb></lb>vnquam ceſſaret hic motus ſine prædicto attritu, &amp; partium aſperi­<lb></lb>tate: </s>
					<s id="N10DB7">nec quidquam obſtat, quòd aliquæ partes rotæ, quæ in circu­<lb></lb>lo verticali voluitur, aſcendant; </s>
					<s id="N10DBD">quia etiam aliquæ deſcendunt: qua­<lb></lb>re ſemper remanet perfectum æquilibrium, &amp; harum deſcenſus, il­<lb></lb>larum aſcenſum compenſat. </s>
					<s id="N10DC5">Quò diutiùs potentia motrix manet <lb></lb>applicata manubrio axis rotæ, ita vt nouum ſemper producat im­<lb></lb>petum, rotæ motus velocior eſt, atque diutiùs durat: idem prorſus <lb></lb>dico de rota circulo horizontali parallela. </s>
				</p>
				<p id="N10DCF" type="main">
					<s id="N10DD1">7. Cùm mouetur æquali niſu acus circa immobile centrum, tùm <lb></lb>in plano <expan abbr="horizõtali">horizontali</expan>, tùm in verticali, ſiue ſit <expan abbr="lõgior">longior</expan> vna, ſiue breuior <lb></lb>alia, per ſe plures gyros non deſcribit vna, quàm alia; </s>
					<s id="N10DE1">quia per ſe <lb></lb>mouetur motu æquabili: </s>
					<s id="N10DE7">per accidens tamen ſecus accidit; </s>
					<s id="N10DEB">quippe <lb></lb>maior eſt maioris attritus: </s>
					<s id="N10DF1">dixi, cùm mouetur æquali niſu; </s>
					<s id="N10DF5">nam ſæpè <lb></lb>contingit, maiore niſu potentiam motricem agere circa maiorem; </s>
					<s id="N10DFB"><lb></lb>æquali tamen tempore numerus circuitionum minoris, eſt ad nu­<lb></lb>merum circuitionum maioris per ſe vt acuum quadrata permu­<lb></lb>tando; ſunt enim motus vt ſpatia, ſpacia vt quadrata. </s>
				</p>
				<p id="N10E04" type="main">
					<s id="N10E06">8. Verbi gratia, ſit acus maior 2. minor 1. certè cùm tota area or­<lb></lb>bis maioris ſit quadrupla minoris, ſitque area maioris, ſpatium ma­<lb></lb>ioris, &amp; area minoris ſpatium minoris, haud dubiè deſcribet minor <lb></lb>quatuor circuitiones, eo tempore, quo maior decurret vnicam: </s>
					<s id="N10E10">li­<lb></lb>cèt enim extremitas minoris, quæ impellitur, habeat tantùm du­<lb></lb>plum impetum extremitatis maioris, ſitque impetus intenſio in <lb></lb>minore, dupla intenſionis impetus in maiore; </s>
					<s id="N10E1A">eſt tamen quadrupla <lb></lb>illius, quæ eſt in ſegmento maioris versùs centrum æquali minori <lb></lb>acui: porrò motus circulares æquabiles in vtraque cum eodem <lb></lb>impetu, ſunt vt motus recti. </s>
				</p>
				<p id="N10E24" type="main">
					<s id="N10E26">9. Rota in plano verticali faciliùs mouetur, quàm in horizonta­<lb></lb>li; </s>
					<s id="N10E2C">quia in illo mouetur per minimam impetus, vel potentiæ acceſ­<lb></lb>ſionem; </s>
					<s id="N10E32">ſecùs in iſto; </s>
					<s id="N10E36">quippe per minimam acceſſionem tollitur <lb></lb>æquilibrium; </s>
					<s id="N10E3C">imò moueri poteſt in plano verticali, licèt nullus im­<lb></lb>primatur impetus rotæ, v. g. per additionem minimi ponderis, vel <lb></lb>momenti, vt patet; cùm tamen in plano horizontali moueri non <lb></lb>poſſit, niſi impetus imprimatur. </s>
				</p>
				<p id="N10E4A" type="main">
					<s id="N10E4C">10. Si cylindrus in plano horizontali læuigato in altera extremi­<lb></lb>tate per tangentem impellatur, mouebitur motu circulati, ſcilicet, <pb xlink:href="026/01/026.jpg"></pb>faciliori, circa centrum, quod diſtet ab altera extremitate vna <lb></lb>quarta totius cylindri: ratio eſt: quia faciliùs mouetur circa illud <lb></lb>centrum, quàm circa alia puncta, quòd, ſcilicet, minùs ſpatij decur­<lb></lb>ratur, poſito eodem ſemper motu alterius extremitatis, cui appli­<lb></lb>catur immediatè potentia motrix. </s>
				</p>
				<p id="N10E5E" type="main">
					<s id="N10E60">11. Cùm rota mouetur in verticali, atque præponderat alter ſemi­<lb></lb>circulus, haud dubiè hic præponderans producit impetum in alio <lb></lb>ſemicirculo: </s>
					<s id="N10E68">hinc fortè eſt, quòd mirere, impetus determinatus <lb></lb>deorſum producit alium ſurſum: </s>
					<s id="N10E6E">hinc impetus vnius partis mobi­<lb></lb>lis poteſt producere ſimilem in alia parte continua; </s>
					<s id="N10E74">quod tantùm in <lb></lb>hoc caſu locum habet: </s>
					<s id="N10E7A">quando corpus incumbit plano, quod mo­<lb></lb>uetur motu recto æquabili, ab eo non ſeparatur; ſecùs verò, ſi in­<lb></lb>cumbat plano, quod mouetur motu circulari. </s>
				</p>
				<figure id="id.026.01.026.1.jpg" xlink:href="026/01/026/1.jpg"></figure>
				<p id="N10E87" type="main">
					<s id="N10E89"><emph type="center"></emph><emph type="italics"></emph>De motu funependuli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N10E94" type="main">
					<s id="N10E96">1. FVnependulum deſcendit per arcum motu naturaliter acce­<lb></lb>lerato: </s>
					<s id="N10E9C">experientia clariſſima eſt: cùm enim ex maiori ſubli­<lb></lb>mitate deſcendit, maiorem ictum infligit. </s>
					<s id="N10EA2">Ratio à priori eſt quia <lb></lb>priori impetui acquiſito nouus accedit: </s>
					<s id="N10EA8">non acceleratur in eadem <lb></lb>proportione, in qua ſuprà dictum eſt accelerari in linea recta; </s>
					<s id="N10EAE">quia <lb></lb>in hac acceleratur vniformiter, id eſt, æqualibus temporibus, <lb></lb>æqualia acquiruntur velocitatis momenta; </s>
					<s id="N10EB6">quia vel eſt ſemper ea­<lb></lb>dem inclinatio plani, vel idem perpendiculum: </s>
					<s id="N10EBC">at verò in fune­<lb></lb>pendulo in ſingulis punctis eſt noua tangens; </s>
					<s id="N10EC2">igitur noua inclina­<lb></lb>tio plani; igitur noua ratio motus. </s>
				</p>
				<p id="N10EC8" type="main">
					<s id="N10ECA">2. Initio acceleratur motus per maiora crementa, ſub finem per mi­<lb></lb>nora; </s>
					<s id="N10ED0">v.g. ſi dato tempore acquiſiuit vnum gradum impetus initio, <lb></lb>æquali deinde tempore acquiret minùs: ratio clara eſt: </s>
					<s id="N10ED8">quia, vt ac­<lb></lb>quireret æqualem, deberet eſſe eadem plani inclinatio; </s>
					<s id="N10EDE">ſed ſemper <lb></lb>creſcit Inclinatio; </s>
					<s id="N10EE4">igitur ſemper imminuitur impetus æquali <expan abbr="tẽpore">tempore</expan> <lb></lb>acquiſitus: </s>
					<s id="N10EEE">acquiritur tamen æqualis velocitas in arcu, &amp; in chor­<lb></lb>da, ſeu plano inclinato, eiuſdem altitudinis; igitur ſemper creſcit <lb></lb>motus funependuli in deſcenſu, ſed minoribus incrementis. </s>
				</p>
				<p id="N10EF6" type="main">
					<s id="N10EF8">3. Hinc breuiore tempore deſcendit per radium perpendicula­<lb></lb>rem, quàm per quadrantis arcum eiuſdem radij; </s>
					<s id="N10EFE">tùm quia breuior <lb></lb>eſt linea; tùm, quia in perpendiculari acceleratur motus per maiora <lb></lb>crementa. </s>
					<s id="N10F06">Vibratio maior eiuſdem funependuli æquali ferè tem-<pb xlink:href="026/01/027.jpg"></pb>pore cum minore perficitur: ratio eſt: </s>
					<s id="N10F0E">quia, cùm ferè decurrantur <lb></lb>arcus iuxta ſubtenſarum proportionem, certè cùm ſubtenſæ om­<lb></lb>nes æquali tempore decurrantur, idem ferè fit in ipſis arcubus: </s>
					<s id="N10F16">dixi <lb></lb>ferè: </s>
					<s id="N10F1C">nam reuerà minor vibratio citiùs, maior tardiùs perficitur, vt <lb></lb><expan abbr="cõſtat">conſtat</expan> <expan abbr="experiẽtia">experientia</expan>: neque deeſt ratio, quam in <expan abbr="analyticcã">analyticam</expan> remittimus. </s>
				</p>
				<p id="N10F2D" type="main">
					<s id="N10F2F">4. Non aſcendit funependulum ad eam altitudinem, ex qua priùs <lb></lb>deſcenderat: </s>
					<s id="N10F35">clara eſt experientia: </s>
					<s id="N10F39">neque ratio tantùm petitur ab <lb></lb>aëris reſiſtentia; </s>
					<s id="N10F3F">tam enim reſiſtit deſcenſui, quàm aſcenſui; </s>
					<s id="N10F43">ſed ex <lb></lb>eo, quòd ſingulis inſtantibus ſit quædam pugna, inter impetum in­<lb></lb>natum, &amp; alium determinatum ad arcum ſurſum: </s>
					<s id="N10F4B">quippe impetus <lb></lb>innatus ad totum deſcenſum, ſed nullo modo ad aſcenſum con­<lb></lb>currit: </s>
					<s id="N10F53">hinc in maiori vibratione imminuitur motus, &amp; ſpatium in <lb></lb>maiori proportione, quàm in minori; </s>
					<s id="N10F59">quia in hac lineæ ſingulæ aſ­<lb></lb>cenſus quaſi <expan abbr="totidẽ">totidem</expan> inclinatæ ſunt inclinatiores; in illa verò minùs. </s>
				</p>
				<p id="N10F63" type="main">
					<s id="N10F65">5. Hinc diu vibratur funependulum per minores arcus, quippe <lb></lb>facilis eſt aſcenſus per planum proximè ad horizontale accedens: </s>
					<s id="N10F6B"><lb></lb>hinc etiam in funependulo maiori diutiùs durant huiuſmodi vi­<lb></lb>brationes, idque in arcubus paulò maioribus; </s>
					<s id="N10F72">quia ſubtenſæ his <lb></lb>arcubus ſunt inclinatiores: </s>
					<s id="N10F78">hinc refutabis eos, qui dicunt, vibra­<lb></lb>tiones funependuli in vacuo fore perpetuas: </s>
					<s id="N10F7E">arcus vibratio­<lb></lb>nis aſcenſus fit motu naturaliter retardato, ſed per imminu­<lb></lb>tiones inæquales; quia pro diuerſa inclinatione plani diuerſimodè <lb></lb>retardatur. </s>
				</p>
				<p id="N10F88" type="main">
					<s id="N10F8A">6. Vltimum punctum impetus acquiſitus acquiſitum in deſcenſu, <lb></lb>nullo modo ad deſcenſum concurrit, ſed ad aſcenſum, vnico tan­<lb></lb>tùm inſtanti; </s>
					<s id="N10F92">quippe eſt omnium imperfectiſſimum; </s>
					<s id="N10F96">quod reuerà ſi <lb></lb>eſſet eiuſdem perfectionis cum innato, aſcenſus æqualis eſt deſcen­<lb></lb>ſui: </s>
					<s id="N10F9E">ſi ſint funependula inæqualia, vibrationes non ſunt æquè diu­<lb></lb>turnæ: ratio eſt: </s>
					<s id="N10FA4">quia, ſi aſſumantur, v.g. duo quadrantes inæquales, <lb></lb>ſunt ejuſdem inclinationis; igitur minor citiùs percurritur. </s>
				</p>
				<p id="N10FAA" type="main">
					<s id="N10FAC">7. Porrò tempora vibrationum ſunt in ratione ſubduplicata ar­<lb></lb>cuum ſimilium, vel chordarum ſimilium, vel radiorum; </s>
					<s id="N10FB2">id eſt, vt <lb></lb>radices ſpatiorum ſimilium: </s>
					<s id="N10FB8">verbi gratia, ſit quadruplus alterius, <lb></lb>tempus vibrationis maioris eſt duplum temporis vibrationis mino­<lb></lb>ris; </s>
					<s id="N10FC0">quod ita intelligendum eſt, vt hæc proportio conſideretur in <lb></lb>partibus temporis ſenſibilibus, vt iam dictum eſt de motu natura­<lb></lb>liter accelerato deorſum in perpendiculo, &amp; in planis inclinatis; <lb></lb>nam progreſſio arithmetica; aſſumpta in ſingulis inſtantibus, tran­<lb></lb>ſit in hanc, ſi aſſumantur partes temporis ſenſibiles, quarum ſingu­<lb></lb>læ infinitis ferè conſtent inſtantibus. </s>
				</p>
				<pb xlink:href="026/01/028.jpg"></pb>
				<p id="N10FD1" type="main">
					<s id="N10FD3">8. In maiori quadrante, circa ſupremam extremitatem, eſt minor <lb></lb>inclinatio, quàm in minore; </s>
					<s id="N10FD9">hic enim ſtatim detorquetur à perpen­<lb></lb>diculo, cum quo facit angulum maiorem: </s>
					<s id="N10FDF">at verò circa infirmam <lb></lb>extremitatem, eſt maior inclinatio in maiore, quàm in minore: </s>
					<s id="N10FE5">hinc, <lb></lb>ſi comparetur vibratio maioris, cum vibratione minoris in modico <lb></lb>arcu, tempus illius eſt paulò maius duplo, temporis huius; in maxi­<lb></lb>mo arcu paulò minùs duplo, dum, ſcilicet, longitudinum ratio <lb></lb>ſit quadrupla. </s>
				</p>
				<p id="N10FF1" type="main">
					<s id="N10FF3">9. In deſcenſu funependuli velocitas acquiſita eſt eadem cum ea, <lb></lb>quæ in ſubtenſa eiuſdem arcus acquiritur: </s>
					<s id="N10FF9">hinc ſunt ijdem ictus: </s>
					<s id="N10FFD"><lb></lb>numerus, vibrationum non eſt infinitus, licèt in vacuo vibraretur <lb></lb>funependulum; </s>
					<s id="N11004">quia, cùm ſingulæ imminuantur, &amp; infinitis pun­<lb></lb>ctis non conſtent; </s>
					<s id="N1100A">tandem ad vltimam peruenitur: </s>
					<s id="N1100E">illa autem eſt vl­<lb></lb>tima, in cuius deſcenſu acquiritur tantùm vnum punctum impetus <lb></lb>ſupra innatum; in ea tamen ſententia, quæ vel infinitas partes actu, <lb></lb>vel infinita puncta cognoſcit, certè nunquam quieſceret funepen­<lb></lb>dulum in vacuo vibratum. </s>
				</p>
				<p id="N1101A" type="main">
					<s id="N1101C">10. Funependulum in fine aſcenſus non quieſcit vno inſtanti; </s>
					<s id="N11020"><lb></lb>quia impetui innato <expan abbr="nũquam">nunquam</expan> redditur æqualis acquiſitus; </s>
					<s id="N11029">poſita ta­<lb></lb>men illa æqualitate, inſtanti ſequenti eſſet quies: </s>
					<s id="N1102F">funependulum <lb></lb>grauius citiùs deſcendit; </s>
					<s id="N11035">eſt enim eadem ratio, quæ fuit pro mo­<lb></lb>tu naturali; </s>
					<s id="N1103B">corpus oblongum ſolidum circa punctum immobile <lb></lb>in circulo verticali rotatum vibratur adinſtat funependuli; deſ­<lb></lb>cendit tamen citiùs, quàm funependulum eiuſdem longitudinis. </s>
				</p>
				<p id="N11043" type="main">
					<s id="N11045">11. Ratio facilis eſt; </s>
					<s id="N11048">quia partes ſolidæ, quæ accedunt propiùs <lb></lb>ad extremitatem immobilem, accelerant motum aliarum, quæ <lb></lb>ad mobilem extremitatem accedunt; </s>
					<s id="N11050">faciunt enim arcum mino­<lb></lb>rem: </s>
					<s id="N11056">hinc aſcenſus non peruenit ad tantam ſublimitatem; </s>
					<s id="N1105A">quia, vt <lb></lb>prædictæ partes accelerant motum aliarum in deſcenſu, ita retar­<lb></lb>dant in deſcenſu: </s>
					<s id="N11062">hinc citiùs quieſcit hoc penduli genus, quàm <lb></lb>aliud: </s>
					<s id="N11068">ex hoc colligo paradoxon, ſcilicet, corpus moueri poſſe ſua <lb></lb>ſponte velociùs in arcu deorſum, quàm in perpendiculo; v.g. ſi iuxta <lb></lb>extremitatem immobilem ſit nodus plumbeus, cuius vi, altera ex­<lb></lb>tremitas longiùs diſtans deorſum rapiatur. </s>
				</p>
				<figure id="id.026.01.028.1.jpg" xlink:href="026/01/028/1.jpg"></figure>
				<p id="N11079" type="main">
					<s id="N1107B"><emph type="center"></emph><emph type="italics"></emph>De motu mixto ex circulari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11086" type="main">
					<s id="N11088">1. ROta, quæ mouetur in ſuperficie plana, mouetur motu mixto <lb></lb>ex recto centri, &amp; circulari orbis: </s>
					<s id="N1108E">axis tantùm rotæ mouetur <lb></lb>motu recto: </s>
					<s id="N11094">punctum contactus rotæ mouetur motu tardiſſimo, <pb xlink:href="026/01/029.jpg"></pb>quando motus centri, &amp; ſuprema rotæ pars in eandem partem ſe­<lb></lb>runtur; </s>
					<s id="N1109E">punctum verò oppoſitum velociſſimo, quia in motu huius <lb></lb>rotus motus orbis additur motui centri; </s>
					<s id="N110A4">in motu verò illius, to­<lb></lb>tus motus orbis, motui centri detrahitur: quod autem detrahit mo­<lb></lb>tus orbis, nunquam æquale eſt toti motui centri. </s>
				</p>
				<p id="N110AC" type="main">
					<s id="N110AE">2. Hinc omnia puncta eiuſdem circuli rotæ mobilis in plano <lb></lb>hoc motu mixto mouentur in æquali motu: </s>
					<s id="N110B4">hoc etiam motu mo­<lb></lb>uetur globus deſcendens in plano inclinato, in quo reuerâ motu <lb></lb>hæc habes: </s>
					<s id="N110BC">primò, non modò accelerari <expan abbr="motũ">motum</expan> centri, verùm etiam <lb></lb>motum orbis; <expan abbr="ſecũdò">ſecundò</expan>, ita <expan abbr="impetũ">impetum</expan> propagari ab intrinſeco, vt ſingu­<lb></lb>lis partibus eiuſdem circuli, &amp; plani in æqualiter diſtribuatur, tertiò <lb></lb>hoc motu motum rectum non impediri à circulari, &amp; ſed iuuari. </s>
				</p>
				<p id="N110D2" type="main">
					<s id="N110D4">3. Cùm rota voluitur in ſuperficie connexa, mouetur motu mix­<lb></lb>to ex duobus circularibus: ſimilis eſt hic motus motui epicycli. </s>
					<s id="N110DA">Ca­<lb></lb>lamus volatilis, cuius miſſio frequens, &amp; repercuſſio, ludi non in­<lb></lb>grati copiam facit: </s>
					<s id="N110E2">mouetur motu mixto ex recto, &amp; circulari: </s>
					<s id="N110E6">in <lb></lb>hoc porrò motu præit calami caput, &amp; ſequuntur pennæ; </s>
					<s id="N110EC">quia aër <lb></lb>fortiùs reſiſtit pennis, quàm thecæ: hinc pennarum motum theca <lb></lb>grauior accelerat, cuius motum pennæ retardant. </s>
				</p>
				<p id="N110F4" type="main">
					<s id="N110F6">4. Hinc, ſi quando accidat, penas educi ex theca in libero medio; </s>
					<s id="N110FA"><lb></lb>ſtatim theca velociori motu mouetur, cùm tamen pennæ ipſæ ſi­<lb></lb>ſtant: </s>
					<s id="N11101">ex hac inæqualitate, ne impetus ſit fruſtrà, propter detortas <lb></lb>in alteram partem pennas ab aëre reſiſtente totum iaculum defle­<lb></lb>ctitur, agitúr que in orbem; hinc motus orbis traducitur ex theca in <lb></lb>pennas, non contrà, vt aliquis fortè exiſtimaret, licèt pennarum tar­<lb></lb>ditas, &amp; obliqua deflexio, ratione cuius ab aëre reſtante, in alteram <lb></lb>partem quaſi reflectentur, ſint neceſſaria conditio huius traductio­<lb></lb>nis. </s>
				</p>
				<p id="N11111" type="main">
					<s id="N11113">5. Hinc motu recto prædictum iaculum in vacuo tantùm mo­<lb></lb>ueretur, vt patet: hinc: </s>
					<s id="N11119">cùm pennæ ſunt explicatiores, tardiùs; </s>
					<s id="N1111D">cùm <lb></lb>verò contractiores, velociùs mouetur, etiam motu orbis; </s>
					<s id="N11123">cui non <lb></lb>minùs aër reſiſtit, in pennis, ſcilicet, quàm motui axis: </s>
					<s id="N11129">hinc, ſi theca <lb></lb>ſit grauior, velociùs; </s>
					<s id="N1112F">ſi leuior, tardiùs iaculum fertur; </s>
					<s id="N11133">etiam tenera <lb></lb>plumarum lanugo tarditatem conciliat: </s>
					<s id="N11139">porrò, ſi axis mouetur mo­<lb></lb>tu recto, quod reuerà fit, cùm iaculum deorſum demittitur in per­<lb></lb>pendiculo, hic motus eſt ſpiralis cylindricus: ex his infinita ferè <lb></lb>phænomena explicari poſſunt. </s>
				</p>
				<p id="N11143" type="main">
					<s id="N11145">6. Sunt infiniti propemodum motus mixti; </s>
					<s id="N11149">v. g. cylindri ab alte­<lb></lb>ra extremitate rotata emiſſi; </s>
					<s id="N11153">longioris haſtæ, quæ ſurſum facta cir­<lb></lb>cuitione emittitur; </s>
					<s id="N11159">brachij, gladij, &amp;c.  ſed potiſſimùm turbinis, qui <pb xlink:href="026/01/030.jpg"></pb>vel ſcutica, vel funiculo in torto circumagitur, in quo clariſſi­<lb></lb>mè apparet motus centri, &amp; orbis: </s>
					<s id="N11163">ratio motus orbis eſt impe­<lb></lb>tus impreſſus vtrique extremitati diametri vaſis in partes contra­<lb></lb>rias; </s>
					<s id="N1116B">ratio verò motus centri eſt, quia adducitur funiculo vel ex­<lb></lb>ploditur, ſeu expellitur ſcutica: </s>
					<s id="N11171">huius motus phænomena ſunt ferè <lb></lb>infinita: ſingula ex noſtris principiis facilè explicantur. </s>
				</p>
				<figure id="id.026.01.030.1.jpg" xlink:href="026/01/030/1.jpg"></figure>
				<p id="N1117C" type="main">
					<s id="N1117E"><emph type="center"></emph><emph type="italics"></emph>De diuerſis impreſſionibus motus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11189" type="main">
					<s id="N1118B">1. CVm ſuſtinetur manus, ſeu brachium, in ſitu horizontali im­<lb></lb>mobile, producitur neceſſariò impetus æqualis impetui gra­<lb></lb>uitationis; </s>
					<s id="N11193">alioquin, ſi maior eſſet, ſurſum ferretur brachium; ſi verò <lb></lb>minor, deorſum: </s>
					<s id="N11199">quia præualeret grauitatio, porrò hic impetus pro­<lb></lb>ducitur tantùm à potentia motrice animantis, in ſingulari organo; </s>
					<s id="N1119F"><lb></lb>non verò in aliis partibus, etiam animatis, niſi quando mouentur; </s>
					<s id="N111A4"><lb></lb>nec in ipſo pondere, ſi aliquod ſuſtinetur: ſic menſa in pondere ſu­<lb></lb>per poſito impetum nullum producit. </s>
					<s id="N111AB">Si anima immediatè in toto <lb></lb>corpore poſſet producere impetum, homo facilè volare poſſet. </s>
				</p>
				<p id="N111B0" type="main">
					<s id="N111B2">2. Cùm ſuſtinetur funependulum, nullus impetus producitur à <lb></lb>ſuſtinente in ipſo globo, ne ſcilicet, ſit fruſtrà; </s>
					<s id="N111B8">ſecùs verò, ſi attolla­<lb></lb>tur: </s>
					<s id="N111BE">ſic per quamlibet lineam corpus retineri poteſt ſine impetu in <lb></lb>eo corpore producto per ſe: </s>
					<s id="N111C4">hinc, cùm duo ſeſe inuicem trahunt ad­<lb></lb>uerſo niſu, neuter in altero producit impetum per ſe; </s>
					<s id="N111CA">ſed per acci­<lb></lb>dens, propter mollitiem, &amp; tenſionem partium: </s>
					<s id="N111D0">cùm verò defertur <lb></lb>aliquid coniunctum, producitur haud dubiè æqualis impetus; </s>
					<s id="N111D6">hinc <lb></lb>ſeparari non poteſt; </s>
					<s id="N111DC">quia æqualis eſt motus latoris, &amp; delati: exem­<lb></lb>plum habes in naui. </s>
				</p>
				<p id="N111E2" type="main">
					<s id="N111E4">3. Si verò nauis illicò ſiſtat, vel tardiùs moueri pergat, tunc fit ſe­<lb></lb>paratio: hinc liquida effunduntur, ſi dum feruntur, breuior quietis <lb></lb>in vaſe intercedat morula. </s>
					<s id="N111EC">Vt feratur cylindrus humeris <expan abbr="cõmodiùs">commodiùs</expan> <lb></lb>debet ſuſtineri in <expan abbr="cẽtro">centro</expan> grauitatis, ad eleuationem anguli 49. quia <lb></lb><expan abbr="tũc">tunc</expan> manui, &amp; humero æqualiter <expan abbr="põdus">pondus</expan> diſtribuitur: </s>
					<s id="N11203">ideò in circulo <lb></lb>voluitur ſcyphus aqua plenus ſine effuſione; quia impetus determi­<lb></lb>natus per tangentem circuli aquam ipſam à centro circuli remouet. </s>
				</p>
				<p id="N1120B" type="main">
					<s id="N1120D">4. Cùm trahitur aliquod corpus impetus impreſſus in vna parte <lb></lb>non producit impetum in alia, alioquin daretur proceſſus in infi­<lb></lb>nitum; </s>
					<s id="N11215">ſi chorda vtrinque trahatur, rumpetur in medio: </s>
					<s id="N11219">ſi affixa <lb></lb>extremitati immobili, trahatur à potentia applicata alteri extremi-<pb xlink:href="026/01/031.jpg"></pb>tati, rumpetur iuxta primam illam extremitatem: ſi denique pon­<lb></lb>ticulo ſuppoſito tendatur, vel pondere deprimente, in eo puncto <lb></lb>rumpetur. </s>
					<s id="N11227">Ratio communis iſtorum omnium eſt: </s>
					<s id="N1122B">quia inter illas <lb></lb>duas partes fieri debet diuiſio per ſe, quarum vna mouetur, ſecùs <lb></lb>alia; vel quarum vtraque in partes oppoſitas mouetur. </s>
				</p>
				<p id="N11233" type="main">
					<s id="N11235">5. Vt quodlibet pondus faciliùs trahatur, ſinguli equi trahere <lb></lb>debent fune communi, potiùs quàm bigati; </s>
					<s id="N1123B">quia tunc nihil ferè pe­<lb></lb>rit impetus: </s>
					<s id="N11241">cùm plures idem pondus trahunt, agunt actione com­<lb></lb>muni, alioqui ſinguli in toto pondere ſuum impetum producerent; <lb></lb>igitur ſinguli ſeorſum trahere? </s>
					<s id="N11249">eſſent, quod falſum eſt: </s>
					<s id="N1124D">ideò currus <lb></lb>paulò poſt initium motus faciliùs mouetur; </s>
					<s id="N11253">quia aliquid impetus <lb></lb>priùs producti remanet: hinc etiam rupto fune, quo trahitur currus, <lb></lb>currus ipſe modicum tempus adhuc mouetur. </s>
				</p>
				<p id="N1125B" type="main">
					<s id="N1125D">6. Si, dum quis trahit toto niſu magnum aliquod pondus, funis <lb></lb>rumpatur, pronùs corruit: quia maiorem impetum in ſe producit, <lb></lb>totum, ſcilicet, illum, quem in toto pondere produxiſſet eo inſtan­<lb></lb>ti, quo rumpitur finis, qui reuerà maior eſt, propter impedimen­<lb></lb>tum, ex præmiſſis principiis, maiorique applicatione potentiæ, ner­<lb></lb>uorum tenſione, &amp;c. </s>
					<s id="N1126B">dum trahitur vnco an nullus immobilis ver­<lb></lb>sùs nauim, nauis fertur versùs littus; dum pellitur aduersùm littus, <lb></lb>recedit à littore, quia pede, vel genu, imprimitur naui impetus in <lb></lb>contrariam pattem. </s>
				</p>
				<p id="N11275" type="main">
					<s id="N11277">7. Cùm trahitur cylindrus vtrinque æqualiter, qui neque flecti, <lb></lb>neque tendi poteſt, nullum impetum accipit; </s>
					<s id="N1127D">imò in tractione nul­<lb></lb>lus impetus eſt inutilis: </s>
					<s id="N11283">brachium infligit maiorem ictum, cùm ma­<lb></lb>iorem <expan abbr="arcũ">arcum</expan> deſcribit ſuo motu; </s>
					<s id="N1128D">quia, ſcilicet, mouetur motu natu­<lb></lb>raliter accelerato: </s>
					<s id="N11293">hinc auerſa manu validior impingitur colaphus, <lb></lb>quàm aduerſa; </s>
					<s id="N11299">quia illa maiorem arcum deſcribit: </s>
					<s id="N1129D">hinc longius bra­<lb></lb>chium cæteris paribus grauiùs ferit: hinc diu quaſi rotatur bra­<lb></lb>chium, vt longiùs mittatur lapis. </s>
				</p>
				<p id="N112A5" type="main">
					<s id="N112A7">8. Maiore fuſte maior ictus infligitur; </s>
					<s id="N112AB">quia potentia toto niſu <lb></lb>agens, diutiùs manet applicata maiori, quàm minori; </s>
					<s id="N112B1">ſuntque ictus <lb></lb>in ratione ſubduplicata vtriuſque fuſtis; </s>
					<s id="N112B7">v. g. fuſtis pendens vnam <lb></lb>libram per maximum arcum impactus, infligit ſubduplum ictum <lb></lb>alterius, quem infligit fuſtis quatuor pendens libras per eundem <lb></lb>arcum impactus: </s>
					<s id="N112C5">idem dicatur de miſſo lapide: principium huius <lb></lb>veritatis pendet ex iis, quæ diximus lib. 2. de motu naturali­<lb></lb>ter accelerate, iuxta progreſſionem numerorum imparium, <lb></lb>1. 3. 5. &amp;c. </s>
				</p>
				<p id="N112CF" type="main">
					<s id="N112D1">9. Fuſtis circa centrum immobile vibratus, maximum ictum in-<pb xlink:href="026/01/032.jpg"></pb>fligit, non quidem in centro grauitatis, id eſt, in medio, ſi ſit cy­<lb></lb>lindrus, vel parallelipedum; </s>
					<s id="N112DB">nec in extremitate mobili; </s>
					<s id="N112DF">ſed in eo <lb></lb>puncto, in quo eſt centrum impetus impreſſi, id eſt, quod æqualem <lb></lb>vtrinque dirimit impetum: ratio eſt; </s>
					<s id="N112E7">quia tunc totus impetus agit, <lb></lb>quantùm poteſt; </s>
					<s id="N112ED">illud autem punctum Geometria demonſtrat eſſe <lb></lb>terminum mediæ proportionalis, inter totum cylindrum, &amp; ſub­<lb></lb>duplum; modò nulla ratio vectis habeatur alioquin centrum pro­<lb></lb>cuſſionis diſtat 2/3 ab extremitate immobili. </s>
				</p>
				<p id="N112F7" type="main">
					<s id="N112F9">10. Cùm fuſtis inflectitur, reditque ad priſtinum ſtatum, vt <lb></lb>videre eſt in tudicula maiore, maior ictus imprimitur: </s>
					<s id="N112FF">quia non <lb></lb>tantùm agit impetus extrinſecùs adueniens; </s>
					<s id="N11305">verùm etiam potentia <lb></lb>quædam media, quæ corpora compreſſa, vel tenſa, ad priſtinum <lb></lb>ſtatum reducit: hinc maximus eſt ictus tudiculæ, cùm eo inſtanti, <lb></lb>quo reductum eſt omninò manubrium priori rectitudini, infligitur <lb></lb>ictus, quia tunc vis potentiæ mediæ eſt maxima. </s>
				</p>
				<p id="N11311" type="main">
					<s id="N11313">11. Rotato flagello ideò maxima vis ineſt, quia diutiùs potentia <lb></lb>manet applicata: </s>
					<s id="N11319">hinc vides hoc principium eſſe vniuerſaliſſimum, <lb></lb>quod iactis, pulſis, &amp; impactis competit; </s>
					<s id="N1131F">de malleorum ictu idem <lb></lb>prorſus dicendum eſt, quod de fuſte; </s>
					<s id="N11325">ſi autem mallei cadant <lb></lb>ex eadem altitudine, motu naturali accelerato, ictus ſunt vt <lb></lb>mallei, quia duplus malleus, v. g. duplum impetum acquirit: nam <lb></lb>ſingulæ partes ſeorſim æqualem impetum acquirunt. </s>
				</p>
				<p id="N11333" type="main">
					<s id="N11335">12. Si verò ex diuerſa altitudine cadant, vel ſunt æquales, vel <lb></lb>inæquales: </s>
					<s id="N1133B">ſi primum, ictus ſunt vt tempora, quibus cadunt: </s>
					<s id="N1133F">ſi <lb></lb>ſecundum, ictus ſunt in ratione compoſita temporum, &amp; mal­<lb></lb>leorum: </s>
					<s id="N11347">ſi ſunt infinitæ, partes actu, nulla eſt proportio percuſſionis <lb></lb>granuli cadentis, &amp; rupis ingentis grauitantis; </s>
					<s id="N1134D">ſed hoc vltimum fal­<lb></lb>ſum eſſe conſtat; </s>
					<s id="N11353">non poteſt tamen determinari proportio vitium <lb></lb>grauitationis, &amp; percuſſionis, niſi numerus inſtantium: quibus durat <lb></lb>motus deorſum cognoſcatur. </s>
				</p>
				<p id="N1135B" type="main">
					<s id="N1135D">13. Leuiſſimi lapides vix emittuntur ad modicam diſtantiam; </s>
					<s id="N11361"><lb></lb>quia ſtatim ſeparantur à potentia: </s>
					<s id="N11366">parallelipedum cadens de or­<lb></lb>ſum in ſitu horizontali maximum ictum infligit in centro grauita­<lb></lb>tis, id eſt, in medio; </s>
					<s id="N1136E">quia tunc totus impetus agit, totus enim impe­<lb></lb>ditur: </s>
					<s id="N11374">in aliis punctis minor eſt ictus, iuxta proportionem maioris <lb></lb>diſtantiæ à prædicto centro: ſi verò percutiatur cylindrus innatans, <lb></lb>maxima erit vis, vel effectus ictus in centro grauitatis propter ean­<lb></lb>dem rationem. </s>
				</p>
			</section>
		</front>
		<body>
			<chap id="N1137F">
				<pb pagenum="1" xlink:href="026/01/033.jpg"></pb>
				<figure id="id.026.01.033.1.jpg" xlink:href="026/01/033/1.jpg"></figure>
				<p id="N11389" type="head">
					<s id="N1138B"><emph type="center"></emph>LIBER PRIMVS, <lb></lb><emph type="italics"></emph>DE IMPETV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11398" type="main">
					<s id="N1139A">TRACTATVM hunc de motu locali <lb></lb>ab ipſo impetu auſpicamur, ex cuius <lb></lb>profectò cognitione tota res iſta de­<lb></lb>pendet; </s>
					<s id="N113A4">cum enim impetus ſit cauſa <lb></lb>immediata motus, vt fusè demonſtra­<lb></lb>bimus infrà; </s>
					<s id="N113AC">&amp; cum propter quid ſit res cognoſci <lb></lb>non poſſit, niſi eius cauſa cognoſcatur; </s>
					<s id="N113B2">dubium eſſe <lb></lb>non poteſt, quin præmittenda ſit tractatio illa, quæ <lb></lb>eſt de impetu, vt deinde affectiones ipſius motus <lb></lb>per cauſam eiuſdem demonſtrentur; immò auſim <lb></lb>dicere ex vnius impetus cognitione, non modò mo­<lb></lb>tum ipſum, verùm etiam totam rem Phyſicam pen­<lb></lb>dere. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N113C5" type="main">
					<s id="N113C7"><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 id="N113D3" type="main">
					<s id="N113D5">MOTVS <emph type="italics"></emph>localis eſt tranſitus mobilis è loco in locum continuo fluxu.<emph.end type="italics"></emph.end><lb></lb>Huius definitionis explicationem habebis in Metaphyſicâ, <lb></lb>quæ ſanè explicatio ad rem præſentem non facit. </s>
				</p>
				<p id="N113E1" type="main">
					<s id="N113E3"><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 id="N113EF" type="main">
					<s id="N113F1"><emph type="italics"></emph>Motus velox eſt quo percurritur maius ſpatium æquali tempore, vel <lb></lb>æquale ſpatium minori tempore; contrà verò motus tardus.<emph.end type="italics"></emph.end></s>
				</p>
				<pb pagenum="2" xlink:href="026/01/034.jpg"></pb>
				<p id="N113FF" type="main">
					<s id="N11401"><emph type="center"></emph><emph type="italics"></emph>Definitio III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1140D" type="main">
					<s id="N1140F"><emph type="italics"></emph>Impetus eſt qualitas exigens motum, ſeu fluxum localem ſui ſubiecti, vel <lb></lb>qua est cauſa proxima motus illius mobilis, cui ineſt, eo ſcilicet modo, quo <lb></lb>poteſt eſſe cauſa motus.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1141A" type="main">
					<s id="N1141C">Dico eſſe qualitatem ſiue diſtincta ſit, ſiue non diſtincta; </s>
					<s id="N11420">quod hîc <lb></lb>certè non diſcutio; </s>
					<s id="N11426">nec enim affirmo in hac definitione dari impetum; </s>
					<s id="N1142A"><lb></lb>ſed definio tantùm quid ſit impetus; </s>
					<s id="N1142F">qui reuera aliud non eſt, ſi eſt: </s>
					<s id="N11433"><lb></lb>quippe id tantùm concipio, cum impetum appello; </s>
					<s id="N11438">ſiue ſit, ſiue non ſit, <lb></lb>ne quis fortè initio ſtatim mihi litem intendat; </s>
					<s id="N1143E">quemadmodum definit <lb></lb>circulum Geometra; </s>
					<s id="N11444">licèt non aſſerat dari perfectum circulum; </s>
					<s id="N11448">ita Phy­<lb></lb>ſicus definit impetum, quamuis non affirmet dari impetum; </s>
					<s id="N1144E">quod tamen <lb></lb>in ſexto Theoremate demonſtrabimus; </s>
					<s id="N11454">itaque ſi eſt impetus, haud dubiè <lb></lb>nihil omninò præſtat in ſuo ſubiecto niſi motum; quod quomodò fiat, <lb></lb>explicabimus intrà in Theorematis. </s>
				</p>
				<p id="N1145D" type="main">
					<s id="N1145F"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1146B" type="main">
					<s id="N1146D"><emph type="italics"></emph>Datur motus localis<emph.end type="italics"></emph.end>; </s>
					<s id="N11476">quis enim non videt volantem auem, natantem <lb></lb>piſcem; currentem equum, rotatum globum; denique vnum corpus mi­<lb></lb>grans è loco in locum? </s>
					<s id="N1147E">ſed hoc eſt moueri per Def. 1. igitur infinitis fe­<lb></lb>rè experimentis nititur hæc hypotheſis, quam veram eſſe neceſſe eſt, ſi <lb></lb>illa vera ſunt; ſed illa certa ſunt phyſicè, neque citra miraculum fallere <lb></lb>poſſunt. </s>
				</p>
				<p id="N1148A" type="main">
					<s id="N1148C">Diceret fortè aliquis etiam motum ſubeſſe oculorum fallaciæ; cùm è <lb></lb>naui mobili littus ipſum moueri, ipſumque nauigium non moueri iudi­<lb></lb>cemus. </s>
					<s id="N11494">Quis enim oculos in Solem intendens, primo intuitu Solem ſta­<lb></lb>re non iudicet? </s>
					<s id="N11499">cum tamen deinde perniciſſimo curſu rotari demonſtre­<lb></lb>mus; </s>
					<s id="N1149F">adde alias oculorum fallacias circa motum; </s>
					<s id="N114A3">ſic rotata ſcintilla, vel <lb></lb>carbo accenſus immotum orbem deſcribere videtur; </s>
					<s id="N114A9">ſic nota inuſta <lb></lb>trocho, dum celerrimè rotatur, orbem etiam immobilem deſcribere iu­<lb></lb>dicatur; </s>
					<s id="N114B1">ſic ſtella cadens, vel exhalatio continenti ſucceſſione accenſa <lb></lb>moueri videtur; </s>
					<s id="N114B7">licet minimè moueatur; </s>
					<s id="N114BB">idem dicendum de puluere <lb></lb>tormentario, vel alia qualibet materia; quæ continuata conſecutione <lb></lb>accenditur; </s>
					<s id="N114C3">immò trochus ipſe in orbem celerrimè agitatus, quieſcere <lb></lb>videtur; </s>
					<s id="N114C9">ſic qui vertigine laborant, ea moueri exiſtimant, quæ quieſcunt; </s>
					<s id="N114CD"><lb></lb>idem exemplum habemus in ebrioſis, iracundis, in iis qui ex graui febris <lb></lb>ardore delirant, &amp; in pueris qui diu in gyros eunt, vbi verti deſierint; </s>
					<s id="N114D4"><lb></lb>ſic eorum quæ motu æquali feruntur, remotiora tardiùs moueri viden­<lb></lb>tur; </s>
					<s id="N114DB">immò ſi per eandem lineam oculus, &amp; mobile pari velocitate ince­<lb></lb>dant, ipſum mobile quieſcere videtur, plura leges apud Opticos, de <lb></lb>quibus agemus ſuo loco: Igitur ex his omnibus conſtat minimè conſta­<lb></lb>re dari motum, ex eo quòd oculis aliquid moueri videatur. </s>
				</p>
				<p id="N114E5" type="main">
					<s id="N114E7">Reſpondeo equidem fateri me, viſum ipſum plurimis ſubeſſe fraudi­<lb></lb>bus; </s>
					<s id="N114ED">attamen ſi rectè oculus admoueatur, iuſta diſtantià, nec vllum ſit <lb></lb>impedimentum exterius nec interius; </s>
					<s id="N114F3">fieri non poteſt, quin oculus mo­<lb></lb>tum obſeruet; an fortè currentis calami motus oculum meum fallere po-<pb pagenum="3" xlink:href="026/01/035.jpg"></pb>teſt? </s>
					<s id="N114FE">quidquid ſit, fateor vltrò hanc hypotheſim in eo tantùm certitudi­<lb></lb>nis gradu eſſe reponendam, in quo reponitur hæc cognitio, quâ modo <lb></lb>cognoſco me ſcribere, manuſque, &amp; calami motum obſeruo; </s>
					<s id="N11506">ſiue id tan­<lb></lb>tùm oculis fiat, ſiue intellectu ex oculis; quod aliàs diſcutiemus; ſi quis <lb></lb>fortè in Phyſica maiorem certitudinem poſtularet, cum eo certè conue­<lb></lb>nire non poſſum. </s>
				</p>
				<p id="N11510" type="main">
					<s id="N11512">Porrò quod ſpectat ad fallacias illas quæ ſupra adductæ ſunt; </s>
					<s id="N11516">certum <lb></lb>eſt vel obiectum eſſe remotius, quam par ſit; </s>
					<s id="N1151C">vel moueri celeriùs, vel <lb></lb>eſſe aliquod impedimentum interius; </s>
					<s id="N11522">præſertim in iis, qui ſeu vertigine, <lb></lb>vel alio capitis morbo laborant; ſed ne hîc opticum agere videar, harum <lb></lb>fallaciarum certiſſimas cauſas in ſuum locum remittimus. </s>
				</p>
				<p id="N1152A" type="main">
					<s id="N1152C">Cæterùm licèt ad ſtatuendam, firmandamque hanc hypoteſim, Phy­<lb></lb>ſica experimenta rectè applicato ſenſu comprobata ſufficere poſſint; <lb></lb>non deſunt tamen rationes multæ à priori, vt vulgò aiunt, quibus euin­<lb></lb>citur, non modò quid ſit motus, verùm etiam propter quid ſit. </s>
				</p>
				<p id="N11536" type="main">
					<s id="N11538">Prima duci poteſt à fine motus; </s>
					<s id="N1153C">cum enim res creatæ vbique ſimul <lb></lb>eſſe non poſſint, certè, vt illo bono gaudeant, quo fortè carent, &amp; vt <lb></lb>coniungantur ſuo fini, motu locali opus eſt; </s>
					<s id="N11544">ſitit equus, abeſt aqua, <lb></lb>certè, niſi vel hæc propinetur, vel ille accedat, ſitim leuare non pote­<lb></lb>rit; </s>
					<s id="N1154C">at neutrum ſine motu haberi poteſt: Lapis remouetur à ſuo centro, <lb></lb>à ſuo globo, à ſuo fine, vt ſeſe illi reſtituat, deorſum cadat neceſſe eſt. </s>
					<s id="N11552"><lb></lb>Itaque ad cum finem res omnes creatæ inſtitutæ ſunt, quem ſine motu <lb></lb>aſſequi non poſſunt; </s>
					<s id="N11559">igitur dari motum neceſſe eſt, vt res creatæ cum lo­<lb></lb>cum acquirant, in quo ſuo bono, ſuo fini, ſuæ perfectioni coniungan­<lb></lb>tur; vel ſaltem id muneris obeant, cui ab ipsâ naturâ deſtinantur. </s>
				</p>
				<p id="N11561" type="main">
					<s id="N11563">Secunda ratio ducitur à cauſa efficiente; niſi enim daretur motus, <lb></lb>fruſtrà daretur potentia motrix, tùm in animantibus, tùm in grauibus, <lb></lb>de quâ aliàs. </s>
				</p>
				<p id="N1156B" type="main">
					<s id="N1156D">Tertia petitur à cauſa formali; cum enim detur impetus, vt demon­<lb></lb>ſtrabimus infrà, neceſſe eſt dari motum. </s>
				</p>
				<p id="N11573" type="main">
					<s id="N11575">Quarta petitur à termino motus; </s>
					<s id="N11579">cum enim globus proiectus ſit in <lb></lb>nouo loco in quo ante non erat; </s>
					<s id="N1157F">certè nouus locus qui ſuccedit alteri <lb></lb>relicto, eſt terminus motus citra miraculum; igitur ſi eſt nouus locus, <lb></lb>eſt quoque motus. </s>
				</p>
				<p id="N11587" type="main">
					<s id="N11589">Quinta ab vſu; nec enim ſine motu flueret aqua, caderet lapis, gyros <lb></lb>agerent aſtra, flaret ventus, volarent nubes, &amp;c. </s>
				</p>
				<p id="N1158E" type="main">
					<s id="N11590">Sexta ab ipſa Mechanica, quæ organa motui miniſtrat: </s>
					<s id="N11594">quis enim ne­<lb></lb>garet maius momentum eſſe cum maiori diſtantiâ coniunctum; </s>
					<s id="N1159A">ſi verò <lb></lb>maius momentum eſt, nunquid præualebit; igitur deorſum cadet, immò <lb></lb>ſeuerior Geometria, vt omittam Aſtronomiam, motum ſupponit, cum ex <lb></lb>fluxu ſeu motu puncti infinitas fere lineas deſcribat. </s>
					<s id="N115A4">Igitur certum eſt <lb></lb>dari motum localem. </s>
				</p>
				<p id="N115A9" type="main">
					<s id="N115AB"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N115B7" type="main">
					<s id="N115B9"><emph type="italics"></emph>Datur quies, id eſt priuatio motus.<emph.end type="italics"></emph.end> Hæc hypotheſis etiam certa eſt, <pb pagenum="4" xlink:href="026/01/036.jpg"></pb>Quis enim neget ſedentem humi, vel decumbentem in lecto quieſceret <lb></lb>conſule ſenſus rectè applicatos; </s>
					<s id="N115C9">tam enim certus ſum me iam in cathe­<lb></lb>dra quieſcere, quam ſum certus Solem lucere; igitur ex certis experi­<lb></lb>mentis certa hypotheſis conſequitur. </s>
					<s id="N115D1">Non deſunt rationes à priori; nam <lb></lb>primò res aliqua ſuo bono, ſeu fini coniuncta ab eo ſeparari non poſtu­<lb></lb>lat, igitur nec moueri. </s>
					<s id="N115D9">Secundò maximum incommodum eſſet, ſi res ſe­<lb></lb>mel mota perpetuò moueretur. </s>
					<s id="N115DE">Tertiò, finis, ſeu terminus motus recti, <lb></lb>eſt quies; nam ideo lapis deorſum cadit, vt in ſuo centro ſeu globo <lb></lb>quieſcat, id eſt vt cum aliis partibus totum illud, ſeu globum componat, <lb></lb>vt dicemus aliàs. </s>
				</p>
				<p id="N115E8" type="main">
					<s id="N115EA">Diceret fortè aliquis ſententias prædictas non valere in ſententiâ <lb></lb>Copernici, quæ terræ motum adſtruit; præterea non modò falli ſenſus <lb></lb>circa motum, verùm etiam circa quietem. </s>
				</p>
				<p id="N115F2" type="main">
					<s id="N115F4">Reſpondeo primò illam Copernici ſententiam eſſe falſiſſimam, vt ſuo <lb></lb>loco oſtendemus: ſecundò, licèt terra moueretur ſecundum Coperni­<lb></lb>cum, Sol, &amp; ſtellæ quieſcerent. </s>
				</p>
				<p id="N115FC" type="main">
					<s id="N115FE">Dices iuxta hypotheſim Heraclidis Pontici, terra ipſa, Sol etiam, &amp; <lb></lb>ſtellæ mouentur. </s>
					<s id="N11603">Reſpondeo primò hypotheſim illam eſſe falſam, vt ſuo <lb></lb>loco videbimus; </s>
					<s id="N11609">ſecundò etiam data illa hypotheſi poſſet dari quies; </s>
					<s id="N1160D">ſi <lb></lb>enim globus eodem verſus occaſum impetu proiiceretur, quò verſus or­<lb></lb>tum à terra ipſa rapitur, haùd dubiè quieſceret: præterea iuxta hanc hy­<lb></lb>potheſim, quietem appellarem vnius partis cum alia connexionem in ip­<lb></lb>ſo toto ſeu globo, &amp; quieſcere dicerem lapidem, qui tantùm totius glo­<lb></lb>bi motu mouetur, ex quo profectò tota ſoluitur difficultas. </s>
				</p>
				<p id="N1161B" type="main">
					<s id="N1161D">Quod verò ſpectat ad fallacias oculi circa quietem; </s>
					<s id="N11621">eodem prorſus <lb></lb>modo ſoluendæ ſunt, quo iam ſupra ſolutæ ſunt aliæ circa motum: <lb></lb>vtrùm verò motus, &amp; quies dicant aliquid diſtinctum à mobili, dice­<lb></lb>mus infrà. </s>
				</p>
				<p id="N1162B" type="main">
					<s id="N1162D"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11639" type="main">
					<s id="N1163B"><emph type="italics"></emph>Aliquid mouetur quod incœpit moueri.<emph.end type="italics"></emph.end></s>
					<s id="N11642"> Video lapidem quieſcentem, <lb></lb>qui deinde proiectus mouetur; </s>
					<s id="N11648">igitur ante non mouebatur, igitur cum <lb></lb>deinde mouetur, cœpit moueri; mille aliis experimentis hæc hypothe­<lb></lb>ſis confirmari poteſt. </s>
				</p>
				<p id="N11650" type="main">
					<s id="N11652"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1165E" type="main">
					<s id="N11660"><emph type="italics"></emph>Aliquid mouetur quod tandem deſinit moueri, vel incipit quieſcere.<emph.end type="italics"></emph.end></s>
					<s id="N11667"> Vi­<lb></lb>deo rotatam pilam, quæ tandem quieſcit, cadentem lapidem, qui tan­<lb></lb>dem ſiſtit, &amp;c. </s>
					<s id="N1166E">igitur certa eſt hæc hypotheſis. </s>
				</p>
				<p id="N11671" type="main">
					<s id="N11673"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1167F" type="main">
					<s id="N11681"><emph type="italics"></emph>Idem mouetur modò tardiùs, modò velociùs.<emph.end type="italics"></emph.end></s>
					<s id="N11688"> Video rotatum globum, <lb></lb>qui ſenſim quieſcit: ſentio ab eodem globo modò maiorem, modò mi­<lb></lb>norem ictum infligi, &amp;c. </s>
					<s id="N11690">igitur eſt certa hypotheſis. </s>
				</p>
				<pb pagenum="5" xlink:href="026/01/037.jpg"></pb>
				<p id="N11697" type="main">
					<s id="N11699"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N116A5" type="main">
					<s id="N116A7"><emph type="italics"></emph>Corpus proiectum etiam à potentiâ motrice ſeiunctum adhuc mouetur.<emph.end type="italics"></emph.end><lb></lb>Oculos omnium teſtes appello. </s>
				</p>
				<p id="N116B0" type="main">
					<s id="N116B2"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N116BE" type="main">
					<s id="N116C0"><emph type="italics"></emph>Corpus proiectum, &amp; in aliud impactum illud ipſum impellit, &amp; mouet.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N116C7" type="main">
					<s id="N116C9"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N116D5" type="main">
					<s id="N116D7"><emph type="italics"></emph>Ignis applicatus ſubiectum aptum, cui rectè applicatur neceſſariò calefa­<lb></lb>cit, nix frigefacit, Sol illuminat, corpus in aliud impactum illud ipſum im­<lb></lb>pellit.<emph.end type="italics"></emph.end></s>
					<s id="N116E2"> Prædictæ omnes Hypotheſes certiſſimis nixæ experimentis certi­<lb></lb>tudinem phyſicam habent, &amp; citra miraculum fallere non poſſunt. </s>
				</p>
				<p id="N116E7" type="main">
					<s id="N116E9"><emph type="center"></emph><emph type="italics"></emph>Axioma I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N116F5" type="main">
					<s id="N116F7"><emph type="italics"></emph>Contradictoria ſimul eſſe non poſſunt, vel non eſſe.<emph.end type="italics"></emph.end></s>
					<s id="N116FE"> Hoc ipſum iam præ­<lb></lb>miſimus Logicæ noſtræ demonſtratiuæ, complectiturque prima illa <lb></lb>principia Metaphyſicæ. </s>
				</p>
				<p id="N11705" type="main">
					<s id="N11707">1. <emph type="italics"></emph>Impoſſibile est idem ſimul eſſe, &amp; non eſſe.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1170F" type="main">
					<s id="N11711">2. <emph type="italics"></emph>Quodlibet eſt, vel non est.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11719" type="main">
					<s id="N1171B">3. <emph type="italics"></emph>De eodem alterum contradictoriorum verè affirmatur, &amp; alterum verè <lb></lb>negatur, non ſimul vtrumque.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11725" type="main">
					<s id="N11727"><emph type="center"></emph><emph type="italics"></emph>Axioma II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11733" type="main">
					<s id="N11735"><emph type="italics"></emph>Maximum ſignum diſtinctionis realis in phyſicis est ſeparabilitas, vel op­<lb></lb>poſitio.<emph.end type="italics"></emph.end></s>
					<s id="N1173E"> Nihil enim a ſe ipſo ſeparari poſt; </s>
					<s id="N11742">quippe, vbi eſt ſeparatio, ſeu <lb></lb>diuiſio, eſt pluralitas; cur enim nummus A &amp; nummus B eiuſdem ma­<lb></lb>teriæ, formæ, ponderis, realiter diſtinguuntur? </s>
					<s id="N1174A">quia ſcilicet vnus <lb></lb>non eſt alius inquies; &amp; quare vnus non eſt alius? </s>
					<s id="N11750">quia vnus eſt hic &amp; <lb></lb>alius non eſt hic, vnum tango, &amp; alium non tango, vnus eſt meus, &amp; <lb></lb>alius non eſt meus, &amp;c. </s>
					<s id="N11757">vides prædicata contradictoria, quæ cum eidem <lb></lb>ſimul ineſſe non poſſint per Ax. 1. diuerſis, &amp; diſtinctis ineſſe neceſſe <lb></lb>eſt. </s>
				</p>
				<p id="N1175E" type="main">
					<s id="N11760">Diceret fortè aliquis hominem reproductum in duobus locis eſſe poſ­<lb></lb>ſe, &amp; dum Romæ eſt à ſe ipſo Lugduni exiſtente ſeiunctum eſſe; hoc <lb></lb>ipſum aliàs examinabimus, dum conſtet modò id totum, ſi fiat, mira­<lb></lb>culo tribuendum eſſe, cum tamen res phyſicas citra miraculum conſide­<lb></lb>remus. </s>
				</p>
				<p id="N1176C" type="main">
					<s id="N1176E"><emph type="center"></emph><emph type="italics"></emph>Axioma III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1177A" type="main">
					<s id="N1177C"><emph type="italics"></emph>Vt dicatur aliquid exiſtere, vel debet ſenſu percipi, vel aliqua ratione <lb></lb>probari.<emph.end type="italics"></emph.end></s>
					<s id="N11785"> Qui enim aſſerit rem aliquam poſitiuam exiſtere, certè poſi­<lb></lb>tiuo argumento demonſtrare debet quod ſit; </s>
					<s id="N1178B">illud porrò argumentum <lb></lb>duci poteſt vel ab experimento certo; </s>
					<s id="N11791">ſic probo exiſtere rem aliquam, <lb></lb>quam video; vel ab aliqua ratione; </s>
					<s id="N11797">ſic ex eo quòd cauſa ſit neceſſaria <lb></lb>applicata ſubiecto apto, probo effectum ipſum produci; </s>
					<s id="N1179D">vel eo quòd ſit <lb></lb>effectus probo cauſam eſſe vel ex neceſſitate, quâ aliquid eſt neceſſa­<lb></lb>rium ad aliquem finem à natura inſtitutum, quo natura ipſa ſine abſur-<pb pagenum="6" xlink:href="026/01/038.jpg"></pb>do, vel grauiſſimo incommodo carere non poteſt, probo illud ipſum <lb></lb>eſſe; </s>
					<s id="N117AC">vel demùm ex aliqua reuelatione certa in rebus fidei; </s>
					<s id="N117B0">igitur hoc <lb></lb>Axioma certum eſt phyſicè; </s>
					<s id="N117B6">quod niſi recipiatur à Philoſophis; </s>
					<s id="N117BA">cuique <lb></lb>licebit impunè mentiri; ſi enim dicam extra mundi huius fines eſſe <lb></lb>alios orbes, intra tuum muſæum, in quo ſolus fortè degis, eſſe quin­<lb></lb>quaginta homines, eſſe mille Soles, &amp; totidem Lunas in cœlo, &amp;c. </s>
					<s id="N117C4"><lb></lb>numquid ſtatim oppones Axioma iſtud, <emph type="italics"></emph>qua ratio, qua experientia, qua <lb></lb>neceſſitas, qua reuelatio?<emph.end type="italics"></emph.end> Quæſtio facti eſt, producendi ſunt teſtes: huc <lb></lb>reuoca principium illud commune. </s>
				</p>
				<p id="N117D3" type="main">
					<s id="N117D5">1. <emph type="italics"></emph>Non ſunt multiplicanda entia ſine neceſſitate, quod certè non valet niſi <lb></lb>addas, vel ſine ratione, vel ſine experientia.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N117DF" type="main">
					<s id="N117E1">2. <emph type="italics"></emph>Qui aſſerit aliquid poſitiuè, debet argumento poſitiuo probare.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N117E9" type="main">
					<s id="N117EB"><emph type="center"></emph><emph type="italics"></emph>Axioma IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N117F7" type="main">
					<s id="N117F9"><emph type="italics"></emph>Quidquid exiſtit phyſicè extra ſuas cauſas ab omni alio ſeparatum, de­<lb></lb>terminatum eſt.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11802" type="main">
					<s id="N11804">Hoc Axioma explicatione modicâ indiget: </s>
					<s id="N11808">Determinatum illud <lb></lb>apello, quod illud ipſum eſt, quod eſt, &amp; nihil aliud; </s>
					<s id="N1180E">quod eſt hoc, id <lb></lb>eſt ab omni alio diſtinctum; </s>
					<s id="N11814">atqui quidquid productum eſt, ſingulare <lb></lb>eſt, id eſt, eſt hoc; </s>
					<s id="N1181A">ſi enim producitur, alicubi producitur, &amp; ali­<lb></lb>quando, ergo dici poteſt, eſt hîc, eſt nunc; igitur determinatum eſt. </s>
					<s id="N11820"><lb></lb>Aliquis fortè ſtatim opponet mihi partes indeterminatas quantitatis: </s>
					<s id="N11825">ſed <lb></lb>proſectò nulla pars actu eſt quæ non ſit hæc, &amp; non alia; </s>
					<s id="N1182B">igitur quæ <lb></lb>non ſit determinata, de quo aliàs; quidquid ſit, ſaltem partes illæ fa­<lb></lb>ciunt aliquod totum quod eſt determinatum, quod mihi ſatis eſt modò <lb></lb>ad veritatem huius Axiomatis. </s>
					<s id="N11836">Dices aliquid poſſe eſſe nullibi; </s>
					<s id="N1183A">has <lb></lb>nugas refutabimus in Metaphyſica, quæ in mentem ſapientis viri ca­<lb></lb>dere non poſſunt; nunc ſaltem conſtat id naturali modo fieri non <lb></lb>poſſe. </s>
				</p>
				<p id="N11844" type="main">
					<s id="N11846"><emph type="center"></emph><emph type="italics"></emph>Axioma V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11852" type="main">
					<s id="N11854"><emph type="italics"></emph>Quod vnum eſt, determinatum eſt.<emph.end type="italics"></emph.end></s>
					<s id="N1185B"> Quia quod vnum eſt, eſt hoc, &amp; <lb></lb>nihil aliud; </s>
					<s id="N11861">nihil enim aliud eſt vnum, niſi indiuiſum in ſe, &amp; diui­<lb></lb>ſum à quolibet alio: </s>
					<s id="N11867">quippè indifferentia, vel indeterminatio ibi tan­<lb></lb>tum eſt, vbi ſunt plura; ſi enim tantum vnum eſt, certè non datur op­<lb></lb>tio, ſi aliqua cauſa eſt indifferens ad effectum A &amp; B, id eſt ſi non eſt, <lb></lb>cur vnum potius quàm alium producat? </s>
					<s id="N11871">plures eſſe neceſſe eſt; ſi enim <lb></lb>tantùm vnus eſt, certè indifferens non eſt. </s>
				</p>
				<p id="N11877" type="main">
					<s id="N11879"><emph type="center"></emph><emph type="italics"></emph>Axioma VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11885" type="main">
					<s id="N11887"><emph type="italics"></emph>Quidquid eſt, fruſtrà non eſt.<emph.end type="italics"></emph.end></s>
					<s id="N1188E"> Quidquid eſt, id eſt exiſtit naturaliter <lb></lb>ſcilicet, &amp; citra miraculum, fruſtrà non eſt, id eſt propter aliquem fi­<lb></lb>nem eſt ab ipſa natura inſtitutum; </s>
					<s id="N11896">finem autem rei ex ipſo vſu cogno­<lb></lb>ſcimus; </s>
					<s id="N1189C">vſum verò ipſo ferè ſenſu: </s>
					<s id="N118A0">quod vt breui inductione confirme­<lb></lb>mus, quidquid exiſtit vel eſt ſubſtantia, vel accidens; </s>
					<s id="N118A6">ſi ſubſtantia, vel <lb></lb>incorporea, vel corporea; </s>
					<s id="N118AC">ſi incorporea, vel eſt Deus, vel Angelus, vel <pb pagenum="7" xlink:href="026/01/039.jpg"></pb>Anima rationalis; </s>
					<s id="N118B5">atqui nihil horum fruſtrà eſt, vt conſtat; </s>
					<s id="N118B9">ſi corporea, <lb></lb>vel eſt corpus, vel forma; </s>
					<s id="N118BF">ſi corpus, vel elementum, vel mixtum; </s>
					<s id="N118C3"><lb></lb>vtrumque ſuum finem habet, &amp; conſtantem vſum; </s>
					<s id="N118C8">ſi forma quamdiu <lb></lb>eſt principium actionum compoſiti fruſtrà non eſt; </s>
					<s id="N118CE">quippe ad cum finem <lb></lb>eſt inſtituta; </s>
					<s id="N118D4">hinc optima ratio ducitur, cur forma materialis ſeparata <lb></lb>exiſtere non poſſit citra miraculum, quia ſcilicet fruſtrà eſſet; </s>
					<s id="N118DA">cum enim <lb></lb>non poſſit agere niſi in ſubiecto, ſi ſubiectum non eſt, fruſtrà eſt; </s>
					<s id="N118E0">at verò <lb></lb>anima rationalis, quæ aliquas actiones in organicas habet, fruſtrà non <lb></lb>eſt etiam ſeparata, igitur immortalis eſt: </s>
					<s id="N118E8">vtramque rationem ſuo loco fu­<lb></lb>sè demonſtrabimus; </s>
					<s id="N118EE">ſi verò accidens eſt, haud dubiè alteri ineſſe debet <lb></lb>propter ſuum finem intrinſecum, quem alibi effectum formalem ſecun­<lb></lb>darium appellamus; </s>
					<s id="N118F6">quem ſcilicet præſtat in ſuo ſubiecto, cui certè ſi ni­<lb></lb>hil præſtaret, in eo fruſtrà eſſet; </s>
					<s id="N118FC">ſic caloris effectus ſecundarius eſt rare­<lb></lb>factio, vel reſolutio partium ſui ſubiecti, vel aliquid aliud; impetus, <lb></lb>motus &amp;c. </s>
					<s id="N11904">Igitur tunc effet fruſtrà accidens, cum ſuo illo effectu careret; </s>
					<s id="N11908"><lb></lb>hinc rationem contrarietatis aliquando petemus, certiſſimam quidem, <lb></lb>licet nouam, &amp; inde clariſſimè conſtabit, cur, &amp; quomodo vnum contra­<lb></lb>rium ab alio deſtrui dicatur; </s>
					<s id="N11911">ſed non eſt huius loci: cùm verò audis fi­<lb></lb>nem: </s>
					<s id="N11917">ne quæſo cogites aliquid morale, nec enim illum finem intelligo, ad <lb></lb>quem ab agente rationabili deſtinatur: ſed eum dumtaxat, ad quem na­<lb></lb>tura ipſa, vel eſſentia rei ſpectat, ſed de his ſatis. </s>
				</p>
				<p id="N1191F" type="main">
					<s id="N11921">Huc reuoca Principium illud, <emph type="italics"></emph>Deus &amp; Natura nihil faciunt fruſtrà,<emph.end type="italics"></emph.end><lb></lb>id eſt quod ſuo fine careat intrinſeco. </s>
				</p>
				<p id="N1192B" type="main">
					<s id="N1192D">Dices fortè, multa videri eſſe fruſtrà, quæ tamen exiſtunt; ad quid <lb></lb>enim vel tanta aquarum copia, vel tantus ſtellarum numerus, vel tot are­<lb></lb>næ puncta? </s>
					<s id="N11935">tot fluitantes atomi? </s>
					<s id="N11938">tot inſecta? </s>
					<s id="N1193B">&amp; vermiculi: </s>
					<s id="N1193E">Reſpondeo <lb></lb>quamlibet ſtellam, quodlibet inſectum, ſeu vermiculum ſuis pollere pro­<lb></lb>prietatibus; </s>
					<s id="N11946">igitur fruſtrà non eſt, &amp; quodlibet punctum, quamlibet ato­<lb></lb>mum, &amp; quamlibet guttulam aquæ eſſe partem huius vniuerſitatis: </s>
					<s id="N1194C">quod <lb></lb>enim dices de vna, dicam de omnibus; </s>
					<s id="N11952">equidem pauciores eſſe poſſent; <lb></lb>attamen nulla eſt fruſtrà, cum quælibet ſimul cum aliis totum hoc com­<lb></lb>ponat. </s>
				</p>
				<p id="N1195A" type="main">
					<s id="N1195C"><emph type="center"></emph><emph type="italics"></emph>Axioma VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11968" type="main">
					<s id="N1196A"><emph type="italics"></emph>Tunc ponenda eſt forma distincta ſubſtantialis vel accidentalis, dum eſt ali­<lb></lb>qua proprietas ſenſibilis, quæ non poteſt tribui ipſi materiæ,<emph.end type="italics"></emph.end> hîc res tantùm <lb></lb>naturales conſidero, nec ſuper naturales attingo, quæ ſuas regulas diui­<lb></lb>næ fidei debent, non ſenſibus. </s>
				</p>
				<p id="N11978" type="main">
					<s id="N1197A">Hoc Axioma omninò certum eſt, &amp; per Ax. 3. confirmatur, vt enim <lb></lb>dicas aliquid diſtinctum ab omni alio exiſtere, vel debet id ſenſu percipi, <lb></lb>vel aliqua ratione probari quod ſit; </s>
					<s id="N11982">atqui formam ſubſtantialem ſenſu <lb></lb>non percipis immediatè; </s>
					<s id="N11988">igitur aliquem eius effectum ſenſibilem vel me­<lb></lb>diatè, vel immediatè; </s>
					<s id="N1198E">qui certè ſi tribui poſſit materiæ, haud dubiè per il­<lb></lb>lum formam non probabis, niſi formæ ipſius eſſe antè demonſtres; </s>
					<s id="N11994">ſi ve­<lb></lb>to eſt forma accidentalis, quam ſenſu percipis; certè id tantùm accidit ex <pb pagenum="8" xlink:href="026/01/040.jpg"></pb>aliqua affectione, quâ ſenſum ipſum afficit hæc forma, igitur ex effectu il­<lb></lb>lo illam percipis, quod clarum eſt. </s>
				</p>
				<p id="N119A1" type="main">
					<s id="N119A3">Huc reuoca vulgare illud principium, <emph type="italics"></emph>Frustrà fit per plura, quod po­<lb></lb>test fieri per pauciora,<emph.end type="italics"></emph.end> quod ad Tertium etiam reuocatur; </s>
					<s id="N119AF">quod ita in­<lb></lb>telligi non debet, vt ſine gutta aquæ Oceanus, ſine ſtella cœlum, ſine gra­<lb></lb>nulo arenæ terra, ſine altero oculorum homo ſtare non poſſint; </s>
					<s id="N119B7">quæ <lb></lb>omnia falſiſſima eſſe conſtat; ſed tantùm quod illud dicatur exiſtere ſiue <lb></lb>ſit ſubſtantia, ſiue accidens, quod vel experientia certa euincit, vel neceſ­<lb></lb>ſitas, vel ratio, vel diuina fides (immò &amp; humana in rebus humanis, non <lb></lb>tamen in ſcientiis.) </s>
				</p>
				<p id="N119C3" type="main">
					<s id="N119C5">Igitur nunquam claudicat hic equus Okami, vt vulgò dicitur, ſi hoc <lb></lb>fræno regatur, &amp; præſcripto ambulet paſſu. </s>
				</p>
				<p id="N119CA" type="main">
					<s id="N119CC"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N119D8" type="main">
					<s id="N119DA">Obſeruabis ſeptem præmiſſa Axiomata, licet metaphyſica ſaltem ali­<lb></lb>qua ex parte eſſe videantur, ita pertinere ad Phyſicam, vt plurimæ phy­<lb></lb>ſicæ affectiones ſine illis explicari, &amp; demonſtrari non poſſint. </s>
				</p>
				<p id="N119E1" type="main">
					<s id="N119E3">Primum certum eſt etiam certitudine metaphyſica, ſeu geometrica. </s>
					<s id="N119E6"><lb></lb>Secundum, Quartum, &amp; Quintum per Primum demonſtrari poſſunt. </s>
					<s id="N119EA"><lb></lb>Tertium eſt veluti communis poſitio, ſeu commune poſtulatum, in quo <lb></lb>docti omnes conunciunt; </s>
					<s id="N119F1">quippe nihil ſine ratione dici debet à philoſo­<lb></lb>pho; </s>
					<s id="N119F7">Sextum &amp; Septimum probari poſſunt per Tertium; ſed iam ad <lb></lb>alia, quæ propiùs ad phyſicam accedunt, veniamus. </s>
				</p>
				<p id="N119FD" type="main">
					<s id="N119FF"><emph type="center"></emph><emph type="italics"></emph>Axioma VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11A0B" type="main">
					<s id="N11A0D"><emph type="italics"></emph>Quidquid primò eſt, &amp; antè non erat, habet cauſam diſtinctam.<emph.end type="italics"></emph.end></s>
					<s id="N11A14"> Id eſt quid­<lb></lb>quid incipit eſſe ab alio eſt; </s>
					<s id="N11A1A">quippe à ſe eſſe non poteſt; </s>
					<s id="N11A1E">nihil enim à ſe <lb></lb>ipſo dependere poteſt ſeu produci; </s>
					<s id="N11A24">quia quod à ſe eſt, neceſſariò eſt, <lb></lb>quod verò neceſſariò eſt, non eſſe non poteſt, alioquin priùs eſſet, &amp; <lb></lb>poſterius, priùs vt cauſa, poſteriùs vt effectus: </s>
					<s id="N11A2C">præterea quidquid produci­<lb></lb>tur aliquando producitur, &amp; alicubi, vt certiſſimum eſt; </s>
					<s id="N11A32">ſed quia hoc ali­<lb></lb>qui negant, contendo tantùm in hoc rerum ordine, &amp; naturaliter lo­<lb></lb>quendo, quidquid producitur alicubi produci, &amp; aliquando, quod nemo <lb></lb>negabit; </s>
					<s id="N11A3C">Igitur ſi aliquid ſe producit; cur hîc potiùs quam illîc? </s>
					<s id="N11A40">cur <lb></lb>nunc potius quam antè? </s>
					<s id="N11A45">cum enim antè nullibi eſſet, cur deſinit non <lb></lb>eſſe hîc &amp; non illîc, nunc &amp; non antè? </s>
					<s id="N11A4A">hinc quod à ſe eſt, vbique, &amp; <lb></lb>ſemper eſt, ſed ne quis mihi litem intendat, licet hoc Axioma certitudi­<lb></lb>nem geometricam habeat; </s>
					<s id="N11A52">ſufficit modò habere phyſicam, quod ex om­<lb></lb>nibus hypotheſibus demonſtratur; </s>
					<s id="N11A58">ſi enim aliquid de nouo produci­<lb></lb>tur, quod certum eſt, ab alio produci video: </s>
					<s id="N11A5E">calor ab igne mediatè <lb></lb>vel immediatè, impetus à potentia motrice, vel ab alio impetu: </s>
					<s id="N11A64">cuncta <lb></lb>hæc ſi reuera producuntur de quo alibi, ab alio produci conſtat; </s>
					<s id="N11A6A">in Me­<lb></lb>taphyſica hoc ipſum geometricè demonſtrabimus; </s>
					<s id="N11A70">cum enim agere ſup­<lb></lb>ponat eſſe; </s>
					<s id="N11A76">quippe omnis actio alicuius agentis eſt; </s>
					<s id="N11A7A">&amp; cum agere termi­<lb></lb>netur ad effectum, nam fieri eſt alicuius fieri; certè agens, &amp; terminus, <lb></lb>cauſa, &amp; effectus diſtinguuntur, igitur. <emph type="italics"></emph>Quidquid primo eſt, &amp;c.<emph.end type="italics"></emph.end></s>
				</p>
				<pb pagenum="9" xlink:href="026/01/041.jpg"></pb>
				<p id="N11A8B" type="main">
					<s id="N11A8D"><emph type="center"></emph><emph type="italics"></emph>Axioma IX.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11A99" type="main">
					<s id="N11A9B"><emph type="italics"></emph>Cauſa debet exiſtere vt immediatè agat.<emph.end type="italics"></emph.end></s>
					<s id="N11AA2"> Hoc certum eſt; </s>
					<s id="N11AA5">quia agere <lb></lb>ſupponit eſſe; </s>
					<s id="N11AAB">quippe agere eſt perfectio realis actu exiſtens; igitur ali­<lb></lb>cuius actu exiſtentis; igitur certum eſt etiam Geometricè, de quo in <lb></lb>Metaph. </s>
					<s id="N11AB4">Iam vero ſufficiat certum eſſe phiſicè, vt conſtat ex omnibus <lb></lb>hypoth. </s>
					<s id="N11AB9">phyſicis; </s>
					<s id="N11ABC">nihil enim videmus agere, niſi quod eſt; </s>
					<s id="N11AC0">ſi enim age­<lb></lb>ret quod non eſt; cur potius hîc, &amp; nunc quam alibi, &amp; aliàs? </s>
					<s id="N11AC6">cur in <lb></lb>hoc ſubiecto potius quàm in alio? </s>
				</p>
				<p id="N11ACB" type="main">
					<s id="N11ACD">Dices, finis qui non eſt influit; </s>
					<s id="N11AD1">igitur agit; </s>
					<s id="N11AD5">Reſpondeo finem non <lb></lb>agere, nec influere niſi obiectiuè; </s>
					<s id="N11ADB">atqui quod non exiſtit actu, id eſt in <lb></lb>ſtatu entatiuo, &amp; reali, poteſt eſſe in ſtatu obiectiuo; </s>
					<s id="N11AE1">id eſt quod non <lb></lb>habet actum rei, poteſt habere actum obiecti, id eſt eſſe cognitum, &amp; <lb></lb>volitum, de quo aliàs; porrò hîc tantùm intelligimus cauſam efficien­<lb></lb>tem, &amp;c. </s>
				</p>
				<p id="N11AEB" type="main">
					<s id="N11AED">Dices, cauſa principalis pulli excluſi poteſt non eſſe; </s>
					<s id="N11AF1">hæc omnia di­<lb></lb>ſcutiemus ſuo loco cum de generatione animalium; </s>
					<s id="N11AF7">ſufficiat dixiſſe non <lb></lb>eſſe cauſam immediatam, de qua hîc tantum loquimur; idem reſponſum <lb></lb>eſto de rana vaga. </s>
				</p>
				<p id="N11AFF" type="main">
					<s id="N11B01"><emph type="center"></emph><emph type="italics"></emph>Axioma X.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11B0D" type="main">
					<s id="N11B0F"><emph type="italics"></emph>Cauſa debet eſſe applicata vt immediatè agat.<emph.end type="italics"></emph.end></s>
					<s id="N11B16"> Cur enim potiùs hîc <lb></lb>quam illîc; in hoc ſubiecto potiùs, quam in alio, in hac diſtantia potiùs, <lb></lb>quam in alia? </s>
					<s id="N11B1E">quidquid ſit, certum eſt phyſicè; nec enim ignis, qui eſt <lb></lb>Romæ, calefacit Lugduni. </s>
				</p>
				<p id="N11B24" type="main">
					<s id="N11B26">Dices dari fortè actionem in diſtans; </s>
					<s id="N11B2A">Reſpondeo negando, quod de­<lb></lb>monſtrabimus in Metaph.  præterea, licet daretur in productione quali­<lb></lb>tatum occultarum, &amp; ſimpathicorum quorundam effectuum, quos exa­<lb></lb>minabimus ſuo loco; </s>
					<s id="N11B34">nemo tamen dubitat quin productio caloris, lu­<lb></lb>minis, impetus; de quibus hic tantùm agimus, debeat eſſe ab applicata <lb></lb>cauſa. </s>
				</p>
				<p id="N11B3C" type="main">
					<s id="N11B3E">Dices impetum produci in extremitate perticæ, quæ non eſt applica­<lb></lb>ta, vel in globo tudiculario etiam non applicato; calorem &amp; lucem <lb></lb>produci à Sole in terra non applicata. </s>
					<s id="N11B46">Reſpondeo, eſſe applicationem <lb></lb>mediatam; nam ſi reuera hæ qualitates producuntur continuata propa­<lb></lb>gatione, diffunduntur per medium, in quo non eſt difficultas. </s>
				</p>
				<p id="N11B4E" type="main">
					<s id="N11B50">Dices etiam partes interiores cauſæ v. g. Solis agunt, ſed non agunt <lb></lb>per totum medium; alioquin agerent in alias partes Solis, à quibus <lb></lb>obteguntur. </s>
					<s id="N11B5C">Reſpondeo, diffuſionem vel propagationem actionis in­<lb></lb>choari tantum ab ipsâ ſuperficie Solis; </s>
					<s id="N11B62">quippe omnes partes agunt <lb></lb>actione communi, de quo infrà; atqui actio communis à communi me­<lb></lb>dio incipit. </s>
				</p>
				<p id="N11B6A" type="main">
					<s id="N11B6C">Dices ignem produci in parte medij remota interrupta propagatio­<lb></lb>ne, vt conſtat, ſi vitro per refractionem, vel ſpeculo per reflectionem <lb></lb>radios Solares colligas. </s>
				</p>
				<p id="N11B73" type="main">
					<s id="N11B75">Reſpondeo, ignem quidem accendi in data diſtantia; </s>
					<s id="N11B79">at non ſine <pb pagenum="10" xlink:href="026/01/042.jpg"></pb>aliqua applicatione, ſaltem virtutis, in quo non eſt difficultas; </s>
					<s id="N11B82">quomo­<lb></lb>do vero ignis accendatur, &amp; quid ſit ignem accendi, explicabimus ſuo <lb></lb>loco; quidquid ſit, certum eſt ad productionem impetus requiri ali­<lb></lb>quam applicationem, vt patet etiam in magnete. </s>
				</p>
				<p id="N11B8F" type="main">
					<s id="N11B91"><emph type="center"></emph><emph type="italics"></emph>Axioma XI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11B9D" type="main">
					<s id="N11B9F"><emph type="italics"></emph>Si cauſa vniuoca applicata, &amp; non impedita est ſufficiens ad productionem <lb></lb>effectus, non eſt ponenda alia ſcilicet æquiuoca.<emph.end type="italics"></emph.end></s>
					<s id="N11BA8"> Non dico omnem cauſam <lb></lb>eſſe vniuocam, ſed tantùm vniuocam ſufficientem, &amp; applicatam eſſe <lb></lb>cauſam, v. g. calor eſt cauſa ſufficiens caloris, vt conſtat in aqua calida; </s>
					<s id="N11BB4"><lb></lb>igitur ſi calor eſt applicatus ſubiecto, in quo producitur calor non ſupe­<lb></lb>rans vires caloris applicati; </s>
					<s id="N11BBB">dicendum eſt calorem illum ab hoc produ­<lb></lb>ci; </s>
					<s id="N11BC1">cum calor ſit cauſa neceſſaria; </s>
					<s id="N11BC5">igitur ſi ſit applicatus ſubjecto apto, <lb></lb>neceſſariò agit; </s>
					<s id="N11BCB">igitur quantum poteſt; igitur effectus non eſt tribuen­<lb></lb>dus alteri cauſæ, quam ſufficientem eſſe ignoramus. </s>
				</p>
				<p id="N11BD1" type="main">
					<s id="N11BD3">Ad hoc Axioma aliud reuoca. <emph type="italics"></emph>Si ex applicatione alicuius ſequitur ſem­<lb></lb>per effectus aliquis, illud ipſum cauſa dici debet huius effectus; </s>
					<s id="N11BDC">licet aliud ſit <lb></lb>coniunctum, ex quo ſeorſim ſumpto applicato non ſequitur effectus<emph.end type="italics"></emph.end>; </s>
					<s id="N11BE5">v. g. ex <lb></lb>applicatione aquæ calidæ ſequitur productio caloris; </s>
					<s id="N11BEF">ex applicatione ſo­<lb></lb>lius aquæ non ſequitur; </s>
					<s id="N11BF5">igitur dicendum eſt calorem hunc produci ab <lb></lb>ipſo calore, qui aquæ ineſt, non verò ab ipſa aquæ ſubſtantia; idem dico <lb></lb>de ferro frigido, &amp;c. </s>
				</p>
				<p id="N11BFD" type="main">
					<s id="N11BFF">Dices non eſſe certum calorem produci; Reſpondeo, negando; </s>
					<s id="N11C03">ſed, <lb></lb>quidquid ſit, loquor tantùm hypotheticè; dixi enim ſi producatur, à <lb></lb>calore aquæ inhærente producitur. </s>
				</p>
				<p id="N11C0B" type="main">
					<s id="N11C0D">Dices produci poſſe ab aliqua cauſa ignota poſita dumtaxat tali, vel <lb></lb>tali conditione. </s>
					<s id="N11C12">Reſpondeo, hoc reuera geometricè non probari, ſed <lb></lb>tantùm phyſicè; </s>
					<s id="N11C18">quidquid ſit, voco cauſam id, ex cuius applicatione <lb></lb>ſequitur ſemper effectus, &amp; nunquam aliàs; </s>
					<s id="N11C1E">nam phyſicè loquendo, ſiue <lb></lb>ſit alia cauſa, ſiue non, eodem modo ſe habet, ac ſi eſſet cauſa; quippe <lb></lb>certum eſt phyſicè ignem calefacere, Solem illuminare, quod ſatis eſt. </s>
				</p>
				<p id="N11C26" type="main">
					<s id="N11C28"><emph type="center"></emph><emph type="italics"></emph>Axioma XII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11C34" type="main">
					<s id="N11C36"><emph type="italics"></emph>Cauſa neceſſaria ſubiecto apto applicata, &amp; non impedita ſemper agit, &amp; <lb></lb>quantum poteſt.<emph.end type="italics"></emph.end></s>
					<s id="N11C3F"> Hoc Axioma duas partes habet; </s>
					<s id="N11C43">prima certa eſt per hy­<lb></lb>poth. 8. &amp; per definitionem cauſæ neceſſariæ, quæ in hoc differt à libe­<lb></lb>râ: Secunda pars probatur; </s>
					<s id="N11C4B">quia ſi partem effectus omitteret, quam ta­<lb></lb>men ponere poſſet; haud dubiè non eſſet cauſa neceſſaria contra hypoth. </s>
					<s id="N11C51"><lb></lb>nam ſi vnam partem effectus omittat; cur vnam potiùs quam aliam? </s>
					<s id="N11C56"><lb></lb>cur non duas? </s>
					<s id="N11C5A">cur non omnes? </s>
					<s id="N11C5D">denique video cauſam eandem eidem <lb></lb>ſubiecto eodem modo applicatam, eundem ſemper effectum producere <lb></lb>per Hyp. 8. </s>
				</p>
				<p id="N11C66" type="main">
					<s id="N11C68"><emph type="center"></emph><emph type="italics"></emph>Axioma XIII<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11C74" type="main">
					<s id="N11C76"><emph type="italics"></emph>Extenſio cauſa non intendit effectum ad intra.<emph.end type="italics"></emph.end></s>
					<s id="N11C7D"> Quælibet pars maioris <lb></lb>ignis non habet calorem intenſiorem, quàm quælibet pars minoris; idem <pb pagenum="11" xlink:href="026/01/043.jpg"></pb>dico de grauitate plumbi, &amp;c. </s>
					<s id="N11C88">nec enim libra plumbi coniuncta cum <lb></lb>alia habet diuerſam grauitatem ab eâ, quam habet ſeparata. </s>
				</p>
				<p id="N11C8D" type="main">
					<s id="N11C8F">Dixi ad intra; </s>
					<s id="N11C92">quia ad extra multum iuuat extenſio; </s>
					<s id="N11C96">ſic maior ignis <lb></lb>longiùs diffundit ſuum calorem; </s>
					<s id="N11C9C">corpus grauiùs cadens majorem ictum <lb></lb>infligit; Ad hoc Axioma reuocatur iſtud. </s>
				</p>
				<p id="N11CA2" type="main">
					<s id="N11CA4">1. <emph type="italics"></emph>Omnes partes eiuſdem cauſæ agunt ad extra actione communi,<emph.end type="italics"></emph.end> iuxta <lb></lb>eum modum quo illam explicabimus in Metaph.  nec punctum Solis ſe­<lb></lb>paratum ad eandem diſtantiam ſuam lucem, caloremque ſuum diffunde­<lb></lb>ret; </s>
					<s id="N11CB4">ad quam diffundit coniunctum cum aliis; </s>
					<s id="N11CB8">idem dico de igne maiori, <lb></lb>&amp; minori; de quibus omnibus ſuo loco. </s>
					<s id="N11CBE">Huc etiam reuoca dicta illa <lb></lb>communia. </s>
				</p>
				<p id="N11CC3" type="main">
					<s id="N11CC5">2. <emph type="italics"></emph>Plures partes cauſa plures partes effectus producunt, &amp; viciſſim.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11CCD" type="main">
					<s id="N11CCF">3. <emph type="italics"></emph>Maior, &amp; perfectior cauſa maiorem effectum producit, &amp; perfectiorem, <lb></lb>&amp; viciſſim.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11CD9" type="main">
					<s id="N11CDB">4. <emph type="italics"></emph>Perfectior effectus, vel imperfectior arguit cauſam perfectiorem, vel im­<lb></lb>perfectiorem, ſuppoſitâ eâdem applicatione; </s>
					<s id="N11CE4">ſi enim maior eſt applicatio ſine <lb></lb>ratione loci, ſiue ratione temporis; haud dubiè maior erit effectus, vt conſtat.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11CEC" type="main">
					<s id="N11CEE"><emph type="center"></emph><emph type="italics"></emph>Axioma XIV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11CFA" type="main">
					<s id="N11CFC"><emph type="italics"></emph>Quidquid deſtruitur non eſt à ſe.<emph.end type="italics"></emph.end></s>
					<s id="N11D03"> Hoc Axioma geometricum eſt; </s>
					<s id="N11D07">Quod <lb></lb>enim eſt à ſe, neceſſariò eſt; </s>
					<s id="N11D0D">cùm à libertate ſeu voluntate alterius non <lb></lb>pendeat; </s>
					<s id="N11D13">cum enim primo inſtanti quo res eſt, non ſit à ſe per Axiom. 8. <lb></lb>de ſecundo idem dici debet, quod de primo, vt patet: </s>
					<s id="N11D1B">quippe id eo <lb></lb>primo inſtanti non eſt neceſſariò, quia ita eſt illo inſtanti, vt poſſit non <lb></lb>eſſe; </s>
					<s id="N11D23">ſed etiam ſecundo inſtanti ita eſt vt poſſit non eſſe; igitur non eſt <lb></lb>neceſſariò, igitur pendet ab alio, quod poteſt facere vt non ſit. </s>
				</p>
				<p id="N11D29" type="main">
					<s id="N11D2B">Dices poſſe deſtrui ſecundo inſtanti ab aliquo contrario, à quo tamen <lb></lb>non pendet per poſitiuum influxum. </s>
					<s id="N11D30">Reſpondeo, non videri quomo­<lb></lb>do deſtrui poſſit, quod influxu poſitiuo non indiget, vt ſit; quid enim <lb></lb>faceret contrarium, quod tantùm exigere poteſt contrarij deſtructio­<lb></lb>nem, quid eſt porro deſtrui, niſi deſinere conſeruari? </s>
					<s id="N11D3A">quæ omnia fusè <lb></lb>in Metaphyſica demonſtrabimus; </s>
					<s id="N11D40">quidquid enim eſt aliquo inſtanti vel <lb></lb>eſt à ſe, vel non à ſe; ſi primùm Deus eſt; </s>
					<s id="N11D46">ſi ſecundum ab alio eſt: <lb></lb>quidquid ſit, hoc Axioma certum eſt phyſicè. </s>
				</p>
				<p id="N11D4C" type="main">
					<s id="N11D4E">Huc reuoca Axiomata ſequentia, quæ ex hoc vno deducuntur. </s>
				</p>
				<p id="N11D51" type="main">
					<s id="N11D53">1. <emph type="italics"></emph>Quidquid eſt, &amp; non eſt à ſe, eſt, ſeu pendet, ſeu conſeruatur ab alio.<emph.end type="italics"></emph.end><lb></lb>Hæc enim ſunt idem, vt conſtat. </s>
				</p>
				<p id="N11D5D" type="main">
					<s id="N11D5F">2. <emph type="italics"></emph>Quidquid destruitur, ad exigentiam alicuius deſtruitur, ſaltem totius <lb></lb>natura, ne aliquid ſit fruſtrà.<emph.end type="italics"></emph.end></s>
					<s id="N11D69"> Hoc etiam ex hypotheſibus ſequitur; </s>
					<s id="N11D6D">cum <lb></lb>enim deſtrui ſit idem ac deſinere conſeruari; </s>
					<s id="N11D73">certè qui deſinit conſer­<lb></lb>uare inſtanti A potiùs quam inſtanti B, hoc facere non poteſt niſi ali­<lb></lb>quid hoc exigat; ſcilicet iuxta leges naturæ. </s>
				</p>
				<p id="N11D7B" type="main">
					<s id="N11D7D">3. <emph type="italics"></emph>Tandiu aliquid conſeruatur, quandiu nihil exigit eius deſtructionem.<emph.end type="italics"></emph.end><lb></lb>Hoc ſequitur ex priori, id eſt quandiu eſt eadem ratio, cur ſit, &amp; con­<lb></lb>ſeruetur, quæ erat antè. </s>
				</p>
				<pb pagenum="12" xlink:href="026/01/044.jpg"></pb>
				<p id="N11D8D" type="main">
					<s id="N11D8F"><emph type="center"></emph><emph type="italics"></emph>Axioma XV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11D9B" type="main">
					<s id="N11D9D"><emph type="italics"></emph>Contraria pugnant pro rata.<emph.end type="italics"></emph.end></s>
					<s id="N11DA4"> Nec enim alia regula eſſe poteſt; </s>
					<s id="N11DA8">ſic minor <lb></lb>calor minùs deſtruit frigoris; minor impetus minùs deſtruit impetus <lb></lb>contrarij (ſi contrarium habet) quæ omnia conſtant ex hypotheſibus. </s>
					<s id="N11DB0"><lb></lb>Ratio eſt, quia plùs vel minùs contrarij deſtruere, multam habet ex­<lb></lb>tenſionem. </s>
					<s id="N11DB6">v.g. ſint duo contraria A &amp; B, ſit A vt 20. ſit B vt 5. certè ſi <lb></lb>B deſtruat A ſupra ratam, vel ſupra id, quod ſibi ex æquo reſpondet, id <lb></lb>eſt ſupra 5. cur potius 6. quam 7. 8. &amp;c. </s>
					<s id="N11DBF">Si infra, cur potius 4. quam 3. <lb></lb>2. &amp;c. </s>
					<s id="N11DC4">Igitur cum plures ſint termini tùm infra, tùm ſupra 5. cur potius <lb></lb>vnus quàm alius? </s>
					<s id="N11DC9">atqui vnus tantùm ex æquo reſpondet, ſcilicet 5. ſed <lb></lb>quod vnum eſt determinatum eſt, per Axioma 5. igitur pugnant pro <lb></lb>rata. </s>
					<s id="N11DD0">Nec dicas A totum deſtrui à B, quòd eſt contra hypotheſim, nam <lb></lb>modicum caloris non deſtruit totum frigus: </s>
					<s id="N11DD6">in impetu res eſt clariſſima; <lb></lb>adde quod minor cauſa minùs agit per Ax. 13. num. </s>
					<s id="N11DDC">3. igitur minùs exi­<lb></lb>git; porrò cum dico vnum ab alio deſtrui, intelligo tantùm ex applica­<lb></lb>tione vnius ſequi deſtructionem alterius ſaltem ex parte. </s>
				</p>
				<p id="N11DE3" type="main">
					<s id="N11DE5">Obſeruabis hæc Axiomata ſaltem maiori ex parte eſſe metaph. </s>
					<s id="N11DE8">quæ <lb></lb>nos fusè in Theorematis metaph. </s>
					<s id="N11DED">explicabimus, &amp; demonſtrabimus; </s>
					<s id="N11DF1">ſed <lb></lb>nobis hoc loco ſatis eſt, ſi parem cum phyſicis ſupponas habere cer­<lb></lb>titudinem, quod nemo negabit; conſtátque ex hypotheſibus, licèt ma­<lb></lb>iorem etiam habeant, de qua ſuo loco. </s>
				</p>
				<p id="N11DFB" type="main">
					<s id="N11DFD">Obſeruabis prætereà nos diutiùs hæſiſſe in præmittendis huic libro <lb></lb>Axiomatis, quod tamen in aliis libris non faciemus. </s>
				</p>
				<p id="N11E02" type="main">
					<s id="N11E04"><emph type="center"></emph><emph type="italics"></emph>Postulatum,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11E10" type="main">
					<s id="N11E12"><emph type="italics"></emph>Liceat datum corpus impellere, proiicere, deorſum cadens excipere, motus <lb></lb>durationem ſenſibilem, ſpatiumque ſenſibile, metiri, comparare, &amp;c.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N11E1B" type="main">
					<s id="N11E1D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N11E2A" type="main">
					<s id="N11E2C"><emph type="italics"></emph>Motus eſt aliquid realiter diſtinctum à mobili.<emph.end type="italics"></emph.end></s>
					<s id="N11E33"> Demonſtratur; Motus <lb></lb>eſt in mobili, in quo antè non erat per hypoth. </s>
					<s id="N11E38">3. &amp; deſinit eſſe in mobili, <lb></lb>in quo antè erat per hypoth.4. igitur mobile eſt, &amp; non eſt motus; </s>
					<s id="N11E3E">igi­<lb></lb>tur à motu ſeparatum; </s>
					<s id="N11E44">igitur realiter diſtinctum per Ax. 2. præterea <lb></lb>moueri, &amp; non moueri ſunt prædicata contradictoria, vt conſtat; </s>
					<s id="N11E4A">igi­<lb></lb>tur eidem ſimul ineſſe non poſſunt per Ax. 1. igitur cum eo non ſunt <lb></lb>idem; </s>
					<s id="N11E52">alioquin ſimul eſſent; </s>
					<s id="N11E56">igitur alterum illorum eſt diſtinctum à <lb></lb>mobili; </s>
					<s id="N11E5C">non quies, vt conſtat, quæ eſt tantùm negatio motus, ſeu per­<lb></lb>ſeuerantia in eodem loco; </s>
					<s id="N11E62">igitur nullam dicit mutationem; at verò <lb></lb>motus mutationem dicit, per Def. 1. hoc Theorema fusè demonſtrabo <lb></lb>in Metaph. </s>
				</p>
				<p id="N11E6D" type="main">
					<s id="N11E6F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N11E7C" type="main">
					<s id="N11E7E"><emph type="italics"></emph>Motus non poteſt dici propriè productus immediatè, vel effectus immedia­<lb></lb>tus cauſæ efficientis.<emph.end type="italics"></emph.end></s>
					<s id="N11E87"> Demonſt. </s>
					<s id="N11E8A">Motus eſt mutatio, ſeu tranſitus ex loco <lb></lb>in locum per Def. 1. ſed mutatio propriè non producitur; </s>
					<s id="N11E92">quippè pro­<lb></lb>ductio tantùm terminatur ad ens; </s>
					<s id="N11E98">nihil enim niſi ens produci poteſt; </s>
					<s id="N11E9C"><pb pagenum="13" xlink:href="026/01/045.jpg"></pb>atqui nulla mutatio dicit tantùm ens; </s>
					<s id="N11EA4">præſertim hæc, quæ tantùm dicit <lb></lb>terminum à quo, ideſt locum relictum; </s>
					<s id="N11EAA">&amp; terminum ad quem, id eſt lo­<lb></lb>cum immediatum acquiſitum; </s>
					<s id="N11EB0">nam ſeparato quocunque alio ab ipſo <lb></lb>mobili; </s>
					<s id="N11EB6">modo ſimul, id eſt eodem inſtanti relinquat primum locum, &amp; <lb></lb>nouum acquirat, omninò mouetur, ſed concretum illud ex loco relicto, <lb></lb>&amp; acquiſito produci non poteſt; </s>
					<s id="N11EBE">illud autem eſt motus, qui certè non <lb></lb>dicit tantùm locum relictum ſine acquiſito; </s>
					<s id="N11EC4">alioqui ſi mobile deſtrue­<lb></lb>retur, diceretur moueri; </s>
					<s id="N11ECA">nec etiam locum acquiſitum ſine priori relicto: </s>
					<s id="N11ECE"><lb></lb>alioqui ſi mobile primò produceretur, diceretur moueri localiter; </s>
					<s id="N11ED3">igitur <lb></lb>motus neutrum dicit ſeorſim; ſi primum, diceretur deſtructus; </s>
					<s id="N11ED9">ſi ſecun­<lb></lb>dum, diceretur aliquo modo productus, vel potiùs acquiſitus; </s>
					<s id="N11EDF">at vtrum­<lb></lb>que coniunctim, ſimulque eſſentialiter dicit motus; </s>
					<s id="N11EE5">nec enim conci­<lb></lb>pio aliud, dum concipio motum: </s>
					<s id="N11EEB">porrò vtrumque ſimul ſumptum indi­<lb></lb>uiſibiliter non poteſt dici, vel deſtructum propriè, vel productum; Di­<lb></lb>xi propriè; nam impropriè dici poteſt motus productus. </s>
				</p>
				<p id="N11EF4" type="main">
					<s id="N11EF6">Dices Motus eſt ens, non à ſe; igitur ab alio; igitur motus eſt pro­<lb></lb>ductus. </s>
					<s id="N11EFC">Reſpondeo Motum non eſſe ens abſolutum, ſed eſſe mutatio­<lb></lb>nem entis, quæ mutatio eſt concretum quoddam ex ente &amp; non ente; </s>
					<s id="N11F02"><lb></lb>quòd certè non poteſt dici propriè productum, ſed reſultans, vt relatio; </s>
					<s id="N11F07"><lb></lb>nam producatur, ſi fieri poteſt; </s>
					<s id="N11F0C">certè eſt aliquid, quod tam facilè de­<lb></lb>ſtrui poteſt, quam produci; </s>
					<s id="N11F12">igitur deſtruatur, &amp; remaneat tantùm en­<lb></lb>titas mobilis, quæ, quo inſtanti priorem locum relinquit, nouum acqui­<lb></lb>rat; certè dicitur adhuc moueri, &amp; tamen non erit motus ex ſuppoſitio­<lb></lb>ne, quod abſurdum eſt. </s>
				</p>
				<p id="N11F1C" type="main">
					<s id="N11F1E">Dices potentia motrix eſt actiua; </s>
					<s id="N11F22">igitur agit; igitur producit, ſed ni­<lb></lb>hil niſi motum. </s>
					<s id="N11F28">Reſp. potentiam motricem eſſe actiuam vt dicemus, <lb></lb>&amp; ab eâ produci impetum, qui deinde exigit motum, vt dicemus <lb></lb>infrà. </s>
				</p>
				<p id="N11F2F" type="main">
					<s id="N11F31">Nec eſt quod aliqui ita mirentur hæc à me dici; </s>
					<s id="N11F35">cum certum ſit effe­<lb></lb>ctus formales ſecundarios principum ferè qualitatum tales eſſe, vt mini­<lb></lb>mè producantur; </s>
					<s id="N11F3D">ſed quaſi reſultent ab exigentia; v. g. effectus calo­<lb></lb>ris in ſuo ſubiecto eſt eiuſdem ſubiecti rarefactio, quæ reuerâ non <lb></lb>producitur, vt conſtat. </s>
				</p>
				<p id="N11F49" type="main">
					<s id="N11F4B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N11F58" type="main">
					<s id="N11F5A"><emph type="italics"></emph>Motus eſt ab alio diſtincto in aliquo genere cauſæ.<emph.end type="italics"></emph.end></s>
					<s id="N11F61"> Demonſtratur, quia <lb></lb>motus, qui non erat, incipit eſſe per hypotheſim tertiam; ſed quod <lb></lb>huiuſmodi eſt, habet cauſam diſtinctam per Ax.8. </s>
				</p>
				<p id="N11F6A" type="main">
					<s id="N11F6C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N11F78" type="main">
					<s id="N11F7A">Obſeruabis motum localem eſſe duplicis generis; </s>
					<s id="N11F7E">primum genus mo­<lb></lb>tus eſt actio potentiæ motricis, quæ reuerà mouet, &amp; cuius exercitium <lb></lb>dicitur motus, ſeu latio, ſeu motio, ſeu actio, qua reuerâ agit, produ­<lb></lb>citque impetum, non motum; </s>
					<s id="N11F88">cum etiam ſine motu defatigetur, vt cum <lb></lb>quis alium pellit, à quo pellitur æquali niſu; </s>
					<s id="N11F8E">patet etiam in manu ſu­<lb></lb>ſtinente aliquod pondus, quæ non mouetur; </s>
					<s id="N11F94">licet reuerâ etiam ſummo <pb pagenum="14" xlink:href="026/01/046.jpg"></pb>conatu agat: </s>
					<s id="N11F9D">immò ſi potentia motrix produceret motum primum, non <lb></lb>impetum in corpore proiecto; </s>
					<s id="N11FA3">nulla deinde eſſet cauſa applicata ad pro­<lb></lb>ducendum impetum: </s>
					<s id="N11FA9">Itaque hic motus primi generis, ſi comparetur <lb></lb>cum potentia motrice, eſt verè influxus, vel actio; </s>
					<s id="N11FAF">ſi cum termino, eſt <lb></lb>eius fieri, ſeu dependentia; </s>
					<s id="N11FB5">ſi cum ſubiecto, ſeu mobili eſt paſſio; </s>
					<s id="N11FB9">nec <lb></lb>propriè dicitur produci, niſi vt quo (vt vulgò loquuntur) nec enim <lb></lb>actio eſt terminus, vel effectus, in quo ſiſtat cauſa; ſed eſt via, qua ten­<lb></lb>dit ad terminum. </s>
					<s id="N11FC3">Motus ſecundi generis eſt mutatio, ſeu tranſitus ex <lb></lb>vno loco in alium; </s>
					<s id="N11FC9">hoc eſt finis, vel effectus formalis ſecundarius, <lb></lb>quem exigit impetus; </s>
					<s id="N11FCF">&amp; fruſtrà ponitur alia entitas, quæ tantùm eſſet <lb></lb>inſtituta ad exigendam iſtam loci mutationem; Igitur ſi ſufficienter <lb></lb>exigatur ab ipſo impetu, de quo infrà, certè fruſtra ponitur quodcun­<lb></lb>que aliud per Ax.3. &amp; 7. </s>
				</p>
				<p id="N11FD9" type="main">
					<s id="N11FDB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N11FE8" type="main">
					<s id="N11FEA"><emph type="italics"></emph>Cauſa illa immediata motus, quæ non est efficiens, potest tantùm eſſe exi­<lb></lb>gens, quæ reducitur ad formalem, quæ ſuum effectum formalem ſecundarium, <lb></lb>id est ſuum finem intrinſecum exigit.<emph.end type="italics"></emph.end></s>
					<s id="N11FF5"> Sic calor exigit rarefactionem, vel <lb></lb>reſolutionem, impetus motum; </s>
					<s id="N11FFB">cum enim non ſit cauſa efficiens per Th. <lb></lb>2. ſit tamen cauſa per Th.3. nec ſit materialis, nec finalis, vt conſtat, de­<lb></lb>bet eſſe formalis, vel exigens, ſeu exigitiua; </s>
					<s id="N12004">vt patet ex ipſa cauſarum <lb></lb>enumeratione; </s>
					<s id="N1200A">non eſt materialis, quia non recipit motum, niſi ab alio; </s>
					<s id="N1200E"><lb></lb>nec finalis, quæ ſupponit alias; cum ipſa non ſit dum ponitur <lb></lb>effectus. </s>
				</p>
				<p id="N12015" type="main">
					<s id="N12017"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12024" type="main">
					<s id="N12026"><emph type="italics"></emph>Entitas ſeu ſubstantia mobilis non eſt cauſa immediata motus,<emph.end type="italics"></emph.end> Sit enim <lb></lb>lapis proiectus per Poſtul. haud dubiè ſubſtantia lapidis non eſt cauſa <lb></lb>huius motus; </s>
					<s id="N12035">quia lapis tandem ſiſtit per hypoth.4. igitur non eſt cauſa <lb></lb>motus, quia eſſet cauſa neceſſaria; </s>
					<s id="N1203B">igitur ſemper cauſaret per Ax.12. præ­<lb></lb>terea potentia motrix proiicientis verè agit, cum etiam defatigetur; </s>
					<s id="N12041">igi­<lb></lb>tur aliquid producit, non motum immediatè, qui produci non poteſt pro<lb></lb>prièper Th. 2. Adde quod motus ſecundi generis habet tantùm cauſam <lb></lb>immediatam exigentem, ſed potentia motrix non exigit; </s>
					<s id="N1204B">quia primò <lb></lb>non defatigaretur exigendo; </s>
					<s id="N12051">ſecundò quia lapis ſeparatus à manu etiam <lb></lb>mouetur, ſed non ad exigentiam potentiæ motricis, vt patet; </s>
					<s id="N12057">quia ſtatim <lb></lb>poſt ſeparationem poteſt illa potentia deſtrui, licèt lapis longo pòſt <lb></lb>tempore moueatur; ſed quod non eſt, nihil exigit. </s>
				</p>
				<p id="N1205F" type="main">
					<s id="N12061">Aliquis fortè diceret potentiam motricem exigere primam partem <lb></lb>motus, quæ deinde ſecundam exigit, &amp; ſecunda tertiam, tertia quar­<lb></lb>tam, &amp;c. </s>
					<s id="N12068">Sed contra; </s>
					<s id="N1206B">quæro quid ſit prima illa pars motus; </s>
					<s id="N1206F">nec enim <lb></lb>aliud agnoſco niſi primam mutationem loci, quæ mutatio non poteſt <lb></lb>exigere niſi quando eſt; </s>
					<s id="N12077">atqui quando eſt, nihil reale eſt actu niſi mo­<lb></lb>bile, &amp; nouus locus acquiſitus, mobile ipſum non exigit, vt demonſtra­<lb></lb>tum eſt, &amp; conceſſum, nec etiam locus de nouo acquiſitus, in quo <lb></lb>ſcilicet mobile ſiſtere poteſt: quidquid pones aliud, impetum appellabo. </s>
				</p>
				<pb pagenum="15" xlink:href="026/01/047.jpg"></pb>
				<p id="N12085" type="main">
					<s id="N12087">Dices cum graue aliquod mouetur deorſum, vel leue ſurſum, vel <lb></lb>corpus animatum ſe ipſum mouet, dici poteſt ſubſtantia corporis cauſa <lb></lb>immediata motus. </s>
					<s id="N1208E">Reſp. negando, tùm quia omnis potentia motrix <lb></lb>agit; </s>
					<s id="N12094">igitur producit aliquid aliud, quod eſt cauſa motus: præterea po­<lb></lb>tentia motrix corporis animati, agit vſque ad defatigationem, ſudorem, <lb></lb>licèt non ſit motus, igitur aliud producit, de corpore graui probabi­<lb></lb>mus infrà. </s>
				</p>
				<p id="N1209E" type="main">
					<s id="N120A0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N120AD" type="main">
					<s id="N120AF"><emph type="italics"></emph>Datur impetus.<emph.end type="italics"></emph.end></s>
					<s id="N120B6"> Demonſtro, Subſtantia mobilis non eſt cauſa imme­<lb></lb>diata motus, per Th.5. ergo aliquid aliud; igitur impetus, nam quod di­<lb></lb>ſtinctum eſt à ſubſtantia mobilis, &amp; exigit motum, eſt impetus per <lb></lb>Def.3. ſed quia hoc Theorema eſt veluti princeps huius tractatus cardo, <lb></lb>in eo paulò diutius hærendum eſt, igitur. </s>
				</p>
				<p id="N120C2" type="main">
					<s id="N120C4">Demonſtro primò dari impetum: </s>
					<s id="N120C8">Quidquid eſt, &amp; antè non erat, non <lb></lb>eſt à ſe, ſed habet cauſam per Ax.8. Motus de nouo eſt per hypotheſim <lb></lb>tertiam; </s>
					<s id="N120D0">igitur habet cauſam, ſed non aliam, quam impetum, quod pro­<lb></lb>bo: </s>
					<s id="N120D6">Lapis cadens, vel impactus in alium lapidem mouet illum per hy­<lb></lb>poth.7. ſed ſubſtantia lapidis in alium impacti non eſt cauſa huius mo­<lb></lb>tus, quia eſſet cauſa neceſſaria vt patet; </s>
					<s id="N120DE">igitur applicata eundem effe­<lb></lb>ctum produceret per Ax.12. ſed etiam applicata immediata non agit, vt <lb></lb>conſtat experientia; igitur per idem Axioma non eſt cauſa. </s>
				</p>
				<p id="N120E6" type="main">
					<s id="N120E8">Scio eſſe aliquas reſponſiones, quas infrà refellemus; nunc ſufficiat <lb></lb>dixiſſe lapidem impactum non producere motum, qui propriè non pro­<lb></lb>ducitur per Th.2. nec exigere, vt conſtat ex ſecunda probatione Th. 5. <lb></lb>igitur ſi aliquid exigit, vel producit, voco impetum. </s>
				</p>
				<p id="N120F2" type="main">
					<s id="N120F4">Secundò probatur; potentia motrix eſt actiua, quia defatigatur, quis <lb></lb>hoc neget? </s>
					<s id="N120F9">igitur aliquid producit; </s>
					<s id="N120FD">non motum, qui propriè non pro­<lb></lb>ducitur per Th.2. igitur aliquid aliud; voco impetum; </s>
					<s id="N12103">adde quod etiam <lb></lb>ſine motu agit, &amp; defatigatur vt iam dictum eſt; </s>
					<s id="N12109">igitur habet alium effe­<lb></lb>ctum immediatum; denique mouere, pellere, trahere, proiicere, percu­<lb></lb>tere, nihil niſi actionem ſonant. </s>
				</p>
				<p id="N12111" type="main">
					<s id="N12113">Tertiò probatur; pila diſiuncta à manu proiicientis diu adhuc mo­<lb></lb>uetur per hypoth.6. igitur hic motus habet cauſam per Ax. 8. quælibet <lb></lb>enim pars motus de nouo eſt, neque duæ illius partes ſimul eſſe poſſunt. </s>
					<s id="N1211A"><lb></lb>atqui potentia motrix non eſt cauſa per Ax.10. immò poteſt eſſe deſtru­<lb></lb>cta; igitur non eſt cauſa per Ax. 9. Non eſt etiam cauſa ſubſtantia pilæ <lb></lb>mobilis per Th.5.5. nec priores pattes motus per reſp. </s>
					<s id="N12125">ad primam in­<lb></lb>ſtantiam Th 5. igitur aliquid aliud; voco impetum. </s>
				</p>
				<p id="N1212B" type="main">
					<s id="N1212D">Quartò probatur; </s>
					<s id="N12130">pila proiecta ſenſim ſine ſenſu tardiore motu <lb></lb>mouetur; donec tandem moueri omnino deſinat per hypoth. </s>
					<s id="N12136">5. igitur <lb></lb>non eſt ſemper æqualis, &amp; eadem cauſa huius motus per Ax. 12. &amp; 13. <lb></lb>num.3. igitur cauſa huius motus eodem modo debilitatur, ſeu remitti­<lb></lb>tur, quo ipſe motus; </s>
					<s id="N12140">ſed decreſcit ſubſtantia mobilis, nec potentia mo-<pb pagenum="16" xlink:href="026/01/048.jpg"></pb>trix, vel corpus prius impactum; </s>
					<s id="N12149">ergo eſt alia cauſa præſens, quæ mi­<lb></lb>nuitur; voco impetum. </s>
				</p>
				<p id="N1214F" type="main">
					<s id="N12151">Quintò corpus graue deorſum cadens accelerat ſuum motum, vt patet <lb></lb>experientia; </s>
					<s id="N12157">quæ maximè clara eſt in funependulis, de qua in ſequen­<lb></lb>tibus libris; </s>
					<s id="N1215D">igitur debet eſſe cauſa huius motus velocioris; </s>
					<s id="N12161">non eſt au­<lb></lb>tem ſubſtantia lapidis, nec grauitas per Ax. 12. nec aliud quidpiam ex­<lb></lb>trinſecum, vt videbimus ſuo loco; igitur aliquid aliquid intrinſecum, <lb></lb>voco impetum. </s>
					<s id="N1216B">Igitur certum eſt dari impetum; qui certè tribui non <lb></lb>poteſt, vel vlli connotationi, vel alteri exigentiæ, vt conſtat ex <lb></lb>dictis. </s>
				</p>
				<p id="N12173" type="main">
					<s id="N12175">Diceret fortè alius hæc omnia eſſe dubia; </s>
					<s id="N12179">nam fieri poteſt vt Deus <lb></lb>tantùm moueat; </s>
					<s id="N1217F">quod ſine impetu fieri poſſe certum eſt; </s>
					<s id="N12183">Reſp. equi­<lb></lb>dem per miraculum hoc fieri poſſe; ſed quemadmadum certum eſt phy­<lb></lb>ſicè ignem applicatum calefacere, niuem frigefacere, &amp; modò calamum <lb></lb>à me hæc ſcribente moueri, ita certum oſt phyſicè ſagittam à ſagittario <lb></lb>emitti, &amp; pilam à proiiciente, &amp;c. </s>
					<s id="N1218F">adde quod Deus, vt auctor naturæ <lb></lb>eſt, agit tantùm; </s>
					<s id="N12195">vel deſinit agere iuxta exigentiam cauſarum ſecunda­<lb></lb>rum; denique cauſam phyſicè appello, ex cuius applicatione nunquam <lb></lb>non ſequitur effectus per Ax.11. num.1. </s>
				</p>
				<p id="N1219D" type="main">
					<s id="N1219F">Dicerent alij hoc totum prouenire à corpuſculis; </s>
					<s id="N121A3">vel atomis, vel fila­<lb></lb>mentis ſine vlla actione; </s>
					<s id="N121A9">equidem non reiicio corpuſcula, &amp; perennia <lb></lb>corporum effluuia: </s>
					<s id="N121AF">Dico tamen primò globum quieſcentem humi ha­<lb></lb>bere ſaltem aliquas partes quieſcentes, vel immobiles; quis hoc neget? </s>
					<s id="N121B5"><lb></lb>immò maximam ſuarum partium partem; </s>
					<s id="N121BA">igitur cum deinde proiicitur <lb></lb>idem globus, illæ partes mouentur; </s>
					<s id="N121C0">dari igitur debet cauſa huius motus <lb></lb>per Ax.8, igitur impetus: </s>
					<s id="N121C6">nec dicas moueri illas partes à corpuſculis; </s>
					<s id="N121CA">quia <lb></lb>antè erant eadem, immò plura corpuſcula; </s>
					<s id="N121D0">&amp; tamen non mouebant: </s>
					<s id="N121D4">igi­<lb></lb>tur non ſunt cauſa huius motus per Ax.12. Dices excitari; ſed quid hoc <lb></lb>eſt excitari? </s>
					<s id="N121DC">vel enim mutantur, vel non mutantur; </s>
					<s id="N121E0">ſecundum dici <lb></lb>non poteſt; </s>
					<s id="N121E6">quia vt excitentur, ex non excitatis mutari debent; igitur <lb></lb>per aliquid: </s>
					<s id="N121EC">deinde quid eſt illa excitatio, niſi impulſio; igitur ſi mouen­<lb></lb>tur illa corpuſcula, &amp; excitantur à potentia motrice, etiam partes prius <lb></lb>immobiles mouebuntur, &amp; excitabuntur per Ax.12. quia ſunt applicatæ <lb></lb>cauſæ neceſſariæ. </s>
				</p>
				<p id="N121F6" type="main">
					<s id="N121F8">Dico ſecundò minimum ex his corpuſculis non ſemper moueri; </s>
					<s id="N121FC">po­<lb></lb>teſt enim ſiſtere; quis hoc neget? </s>
					<s id="N12202">igitur ſi modò mouetur, modò quieſ­<lb></lb>cit, motus ab eo diſtinguitur per Th.1. igitur mouetur per impetum, de <lb></lb>quo infrà. </s>
				</p>
				<p id="N12209" type="main">
					<s id="N1220B">Igitur datur neceſſariò impetus, ſine quo non poſſunt explicari prædi­<lb></lb>ctæ omnes hypotheſes, contra quem ſunt quidem grauiſſimæ difficultates, <lb></lb>quas ſenſim in ſequentibus Theorematis, in quibus explicantur pro­<lb></lb>prietates huius impetus, diſcutiemus. </s>
				</p>
				<p id="N12214" type="main">
					<s id="N12216">Diceret aliquis lapidem impulſum ab aëre deinde propelli; </s>
					<s id="N1221A">ſed aër po­<lb></lb>tius reſiſtit motui; vt conſtat experientiâ; ſed hoc ſoluemus infrà. </s>
				</p>
				<pb pagenum="17" xlink:href="026/01/049.jpg"></pb>
				<p id="N12224" type="main">
					<s id="N12226"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12232" type="main">
					<s id="N12234"><emph type="italics"></emph>Impetus est aliquid distinctum à ſubstantiâ mobilis.<emph.end type="italics"></emph.end></s>
					<s id="N1223B"> Demonſtratur. </s>
					<s id="N1223E"><lb></lb>Quia ſubſtantia mobilis non eſt cauſa exigens motum per Th. 5. Impe­<lb></lb>tus eſt cauſa exigens per Def. 3. &amp; Th. 6. de eodem contradictoria dici <lb></lb>non poſſunt per Ax. 1. n. </s>
					<s id="N12248">3. Igitur impetus non eſt idem cum ſubſtantià <lb></lb>mobilis; igitur diſtinctus; deinde ſeparari poteſt à ſubſtantia mobilis <lb></lb>per Hypoth. </s>
					<s id="N12251">4. igitur eſt diſtinctus per Ax. 2. </s>
				</p>
				<p id="N12255" type="main">
					<s id="N12257"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12263" type="main">
					<s id="N12265"><emph type="italics"></emph>Impetus est accidens<emph.end type="italics"></emph.end>; </s>
					<s id="N1226E">Quippe non eſt corpus, nec forma ſubſtantia­<lb></lb>lis; quia omne corpus, &amp; omnis forma ſubſtantialis moueri poteſt, &amp; <lb></lb>non moueri, vt conſtat ex poſt. </s>
					<s id="N12276">&amp; ex Hypoth. </s>
					<s id="N1227A">3. &amp; 4. igitur diſtingui­<lb></lb>tur à motu; </s>
					<s id="N12280">igitur &amp; ab impetu per Ax. 2. igitur impetus non eſt ſub­<lb></lb>ſtantia; igitur accidens. </s>
				</p>
				<p id="N12286" type="main">
					<s id="N12288"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12294" type="main">
					<s id="N12296"><emph type="italics"></emph>Impetus non eſt modus.<emph.end type="italics"></emph.end></s>
					<s id="N1229D"> Modus duplicis generis eſſe poteſt: </s>
					<s id="N122A1">Modus <lb></lb>primi generis eſt entitas quædam diminuta, vt vulgò loquuntur, diſtin­<lb></lb>cta quidem modaliter, vt aiunt, à re, cui adhæret; ac proinde ab ca ſe­<lb></lb>parari poteſt, non tamen exiſtere ſeparata. </s>
					<s id="N122AB">Modus ſecundi generis non <lb></lb>eſt entitas quidem diſtincta; </s>
					<s id="N122B1">eſt tamen ſtatus quidam corporis; ſic ſeſſio <lb></lb>eſt modus, condenſatio, compreſſio, &amp;c. </s>
					<s id="N122B7">His poſitis Impetus non eſt mo­<lb></lb>dus primi generis; </s>
					<s id="N122BD">nihil enim probat impetum eſſe modum, quod etiam <lb></lb>non probet calorem, &amp; lucem eſſe modos; </s>
					<s id="N122C3">dicere autem omnia acci­<lb></lb>dentia eſſe modos non debemus, de quo ſuo loco; </s>
					<s id="N122C9">modus enim ita à na­<lb></lb>turâ comparatus eſt, vt ſine ſubiecto actuali ſeu fulcro non exiſtere mo­<lb></lb>dò, ſed ne concipi quidem poſſit; </s>
					<s id="N122D1">v. g. actio non poteſt concipi niſi ſit <lb></lb>alicuius actio; </s>
					<s id="N122DB">nec fieri ſine facto; </s>
					<s id="N122DF">nec via ſine termino; </s>
					<s id="N122E3">nec dependen­<lb></lb>tia ſine dependente; </s>
					<s id="N122E9">at verò poſſum concipere calorem, &amp; impetum <lb></lb>ſine alio, quod ſit actu; </s>
					<s id="N122EF">licèt enim calor exigat reſolutionem partium <lb></lb>ſui ſubiecti, ſeu rarefactionem, &amp; impetus motum; nihil tamen impe­<lb></lb>dit, quin per miraculum calor, &amp; impetus conſeruari poſſint ſine eo. </s>
					<s id="N122F7"><lb></lb>quod exigunt, hoc eſt ſine ſuo ſine; </s>
					<s id="N122FC">igitur ſine ſubiecto; </s>
					<s id="N12300">non eſt etiam <lb></lb>modus ſecundi generis vt patet, ſed de modis in Metaphyſica; vix enim <lb></lb>hoc Theorema ad rem Phyſicam quicquam facit. </s>
				</p>
				<p id="N12308" type="main">
					<s id="N1230A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12316" type="main">
					<s id="N12318"><emph type="italics"></emph>Impetus eſt qualitas Phyſica.<emph.end type="italics"></emph.end></s>
					<s id="N12320"> Sequitur ex dictis; cum nec ſit motus. </s>
					<s id="N12323"><lb></lb>nec ſubſtantia, nec modus, nec quidquam negatiuum, alioquin exige­<lb></lb>ret; </s>
					<s id="N1232A">igitur eſt aliud accidens; vocetur qualitas. </s>
				</p>
				<p id="N1232E" type="main">
					<s id="N12330"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1233C" type="main">
					<s id="N1233E"><emph type="italics"></emph>Impetus est qualitas Phyſica.<emph.end type="italics"></emph.end></s>
					<s id="N12346"> Quia impetus eſt diſtinctus realiter à ſue <lb></lb>ſubiecto per Th. 7. Eſt enim ſeparabilis per Hypoth. </s>
					<s id="N1234C">3. &amp; 4. igitur di­<lb></lb>ſtinctus per Ax. 2. ſed qualitatem realiter diſtinctam apello Phyſicam; <lb></lb>præſertim cum nec moralis ſit, nec Logica, &amp;c. </s>
				</p>
				<pb pagenum="18" xlink:href="026/01/050.jpg"></pb>
				<p id="N12358" type="main">
					<s id="N1235A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12366" type="main">
					<s id="N12368"><emph type="italics"></emph>Impetus est qualitas permanens.<emph.end type="italics"></emph.end></s>
					<s id="N1236F"> Quia lapis proiectus etiam ſeparatus <lb></lb>mouetur aliquandiu per Hyp. 6. igitur durat eius cauſa, ſcilicet impe­<lb></lb>tus; igitur eſt qualitas permanens. </s>
				</p>
				<p id="N12379" type="main">
					<s id="N1237B">Diceret fortè aliquis lapidem proiectum pelli ab aëre à tergo inſtan­<lb></lb>te, vt voluit Ariſtoteles pluribus in locis; </s>
					<s id="N12381">ſed præſertim 8. Ph.c.vlt.&amp; 7. <lb></lb>cap.2. 3.de Cœlo, cap.  3. Reſpondeo hoc dici non poſſe; </s>
					<s id="N12387">Primò quia non <lb></lb>modò non iuuat aër; </s>
					<s id="N1238D">ſed etiam impedit motum proiecti, quod de omni <lb></lb>medio neceſſariò dicendum eſt, vt patet experientiâ; </s>
					<s id="N12393">vnde quo craſſius, <lb></lb>ſeu denſius eſt <expan abbr="mediũ">medium</expan>, motum potentiùs retardat, vt videmus in proiectis <lb></lb>per aquam; </s>
					<s id="N1239F">rationem à priori afferemus infrà, cum de reſiſtentia medij: </s>
					<s id="N123A3"><lb></lb>Secundò, quis dicat pilam rotatam in ſolo moueri aëris appulſu? cum <lb></lb>alia corpora, quæ pila rotata præterlambendo quaſi allambit, nullo mo­<lb></lb>do moueantur; præſertim granula pulueris. </s>
					<s id="N123AC">Tertiò, an fortè aër id præ­<lb></lb>ſtare poteſt ſine vi impreſſa; </s>
					<s id="N123B2">igitur non minus ipſi pilæ proiectæ, quam <lb></lb>aëri ambienti imprimi poterit: </s>
					<s id="N123B8">Quartò, nullus aër à tergo pellitur; </s>
					<s id="N123BC">ſed <lb></lb>potius ipſa pila aduerſus aëra pellit, dum emittitur manu; igitur ſi aër <lb></lb>ſuccedit à tergo, id totum accidit, vel metu vacui, vel ne aër compri­<lb></lb>matur, vt videbimus infrà. </s>
					<s id="N123C6">Quintò denique, cum diu moueatur eadem <lb></lb>pars aëris, haud dubiè in ca manet vis impreſſa; igitur impetus erit ad­<lb></lb>huc qualitas permanens. </s>
				</p>
				<p id="N123CE" type="main">
					<s id="N123D0">Ad id quod obiicitur ex Ariſtotele; </s>
					<s id="N123D4">aliqui putant inclinaſſe in cam ſen­<lb></lb>tentiam; </s>
					<s id="N123DA">cùm tam en noſtram teneant illuſtres Peripatetici, quorum no­<lb></lb>minibus parco, ne tot citationes paginas impleant; vide apud Conim­<lb></lb>bric. </s>
					<s id="N123E2">l. 7. Phyſ. cap.  2. Aliqui excuſant ipſum Ariſtorelem, putantque <lb></lb>non eſſe locutum ex propriâ ſententiâ: </s>
					<s id="N123EA">Alij dicunt Ariſtotelem quidem <lb></lb>tribuiſſe aliquam vim extrinſecam aëri; </s>
					<s id="N123F0">non tamen negaſſe intrinſecam <lb></lb>impetus; </s>
					<s id="N123F6">quidquid ſit, ipſa verba Ariſtotelis demonſtrant ipſum agno­<lb></lb>uiſſe vim motricem impreſſam aëri, hoc eſt impetum (<emph type="italics"></emph>potentia enim<emph.end type="italics"></emph.end> (in­<lb></lb>quit) ſcilicet motrix, <emph type="italics"></emph>quâ pollet proijciens quaſi vim impreſſam tradit vtrique<emph.end type="italics"></emph.end>) <lb></lb>id eſt aëri ſurſum, &amp; deorſum; quid porrò eſt illa vis motrix, niſi impetus. </s>
				</p>
				<p id="N1240C" type="main">
					<s id="N1240E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1241A" type="main">
					<s id="N1241C"><emph type="italics"></emph>Impetus non producit motum.<emph.end type="italics"></emph.end></s>
					<s id="N12423"> Probatur, quia motus non dicitur pro­<lb></lb>ductus per Th. 2. Adde ſi vis rationem metaphyſicam; </s>
					<s id="N12429">quia nihil cogit <lb></lb>dicere accidens aliquod, ex iis ſcilicet, quæ ſenſu percipimus, agere ad <lb></lb>intra; </s>
					<s id="N12431">quod videtur eſſe proprium ſubſtantiæ, ſaltem naturaliter; vt <lb></lb>demonſtrabimus in Metaph. </s>
				</p>
				<p id="N12438" type="main">
					<s id="N1243A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12446" type="main">
					<s id="N12448"><emph type="italics"></emph>Impetus exigit motum, id est fluxum mobilis in loco<emph.end type="italics"></emph.end>; </s>
					<s id="N12451">quia cauſa imme­<lb></lb>diata motus eſt tantum exigens, per Th. 4. ſed impetus eſt cauſa motus <lb></lb>immediata per Th. 5. &amp; 6. igitur eſt cauſa exigens, adde quod id tantùm <lb></lb>accidens ſenſibile præſtare poteſt in ſuo ſubiecto, vt aliquam illius mu­<lb></lb>tationem præſtet, vel exigat; </s>
					<s id="N1245D">quæ vel eſt localis, hoc eſt fluxus quidam: </s>
					<s id="N12461"><pb pagenum="19" xlink:href="026/01/051.jpg"></pb>per ſpatium loci; </s>
					<s id="N12469">vel alteratiua, vt vulgò vocatur; quà ſcilicet vel re­<lb></lb>ſoluuntur partes, vel rarefiunt, vel liqueſcunt, vel concreſcunt &amp;c. </s>
					<s id="N1246F">vel <lb></lb>demùm mutant ſenſibilem ſtatum; </s>
					<s id="N12475">vel eſt perfectiua aliquo modo, qua­<lb></lb>tenus ſubiectum nouam aliquam habitudinem acquirit ad ſenſus; ſic <lb></lb>lumen illuminando obiectum reddit illud viſibile. </s>
					<s id="N1247D">&amp;c. </s>
					<s id="N12480">de quibus aliàs. </s>
				</p>
				<p id="N12483" type="main">
					<s id="N12485"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12491" type="main">
					<s id="N12493"><emph type="italics"></emph>Motus eſt effectus formalis ſecundarius impetus.<emph.end type="italics"></emph.end></s>
					<s id="N1249A"> Cum enim ſit cauſa <lb></lb>exigens per Th. 121. Voco effectum formalem ſecundarium, quem in <lb></lb>mobili exigit impetus; </s>
					<s id="N124A2">quippe, vt iam dictum eſt, cauſa exigens redu­<lb></lb>citur ad formalem; </s>
					<s id="N124A8">nec enim cauſat aliquid producendo, quod ſpectat ad <lb></lb>efficientem; </s>
					<s id="N124AE">nec mouendo, quod ſpectat ad finalem; </s>
					<s id="N124B2">nec determinando, <lb></lb>quod ſpectat ad obiectiuam; </s>
					<s id="N124B8">nec recipiendo, quod ſpectat ad materia­<lb></lb>lem; </s>
					<s id="N124BE">nec dirigendo, quod ſpectat ad idæalem, vel exemplarem; ſed <lb></lb>exigendo; </s>
					<s id="N124C4">quatenus ſcilicet ad id à natura eſt inſtituta, vt ex eius in <lb></lb>ſubiecto præſentia talis affectio, vel mutatio conſequatur; </s>
					<s id="N124CA">vocatur au­<lb></lb>tem effectus formalis ſecundarius; non verò primarius, qui eſt tantùm <lb></lb>concretum ex ipſa formâ, &amp; ſubiecto. </s>
				</p>
				<p id="N124D2" type="main">
					<s id="N124D4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N124E0" type="main">
					<s id="N124E2"><emph type="italics"></emph>Motus eſt finis intrinſecus impetus.<emph.end type="italics"></emph.end></s>
					<s id="N124E9"> Dum finem audis intrinſecum, <lb></lb>cogita quæſo aliquid phyſicum; </s>
					<s id="N124EF">eſt enim id, propter quod talis, vel ta­<lb></lb>lis forma inſtituta eſt: </s>
					<s id="N124F5">quid enim aliud eſſe poteſt; </s>
					<s id="N124F9">finem enim rerum <lb></lb>naturalium ex ipſo vſu cognoſcimus; </s>
					<s id="N124FF">immò idem eſt finis cum ipſo vſu; </s>
					<s id="N12503"><lb></lb>cum igitur impetus illum tantùm vſum habeat, quem in ipſo mobili <lb></lb>præſtare cernimus, ſcilicet motum; </s>
					<s id="N1250A">dicendum eſt motum eſſe finem in­<lb></lb>trinſecum impetus; </s>
					<s id="N12510">adde quod cum fruſtrà ſit impetus ille, qui non præ­<lb></lb>ſtat motum mediatè ſaltem in ſuo ſubiecto; quid enim aliud in ſuo ſub­<lb></lb>iecto præſtaret, quem effectum, quam mutationem? </s>
					<s id="N12518">certè ſi fruſtrà eſt, non <lb></lb>eſt, per Ax.6.igitur vt ſit, debet habere id, ſine quo eſſe non poteſt; igitur <lb></lb>maximum eius bonum eſt, igitur finis, quem natiuâ vel innatâ velut <lb></lb>appetentiâ concupiſcit, vel exigit. </s>
					<s id="N12522">Dixi mediatè, vel immediatè; </s>
					<s id="N12525">num <lb></lb>reuera datur fortè aliquis impetus, vt dicemus infrà; </s>
					<s id="N1252B">ſcilicet primus na­<lb></lb>turalis, qui ſcilicet duos fines habet diſiunctiuè; quorum alter eſt gra­<lb></lb>uitatio, alter motus deorſum. </s>
				</p>
				<p id="N12533" type="main">
					<s id="N12535"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12541" type="main">
					<s id="N12543"><emph type="italics"></emph>Niſi eſſet motus non eſſet impetus.<emph.end type="italics"></emph.end></s>
					<s id="N1254A"> Probatur quia motus eſt finis intrin­<lb></lb>ſecus impetus per Th. 16. igitur ſi nullus motus eſſe poſſet, ſuo fine ca­<lb></lb>reret impetus; </s>
					<s id="N12552">igitur non eſſet, vt patet, igitur non eſſet; </s>
					<s id="N12556">quia quod <lb></lb>fruſtrà eſt, non eſt per Ax. 6. nec obſtat quod ſuprà indicatum eſt de im <lb></lb>petu naturali primo vel innato (ſic enim deinceps appellabimus vt recti <lb></lb>diſtinguamus ab acquiſito quem vocabimus impetum accelerationis) <lb></lb>qui ſine motu conſeruatur in corpore grauitante; </s>
					<s id="N12562">quia niſi poſſibilis eſ­<lb></lb>ſet motus deorſum nulla eſſet grauitatio; </s>
					<s id="N12568">quippe grauitare eſt deor­<lb></lb>ſum inclinari, motumque inclinationis impediri; </s>
					<s id="N1256E">hinc dicemus <pb pagenum="20" xlink:href="026/01/052.jpg"></pb>in ſecundo libro impetum innatum ſæpiùs eſſe ſine motu; cum ſcilicet <lb></lb>impeditur à corpore ſuſtinente? </s>
					<s id="N12579">immò dicemus infrà primo inſtanti, <lb></lb>quo eſt impetus, nondum eſſe motum. </s>
				</p>
				<p id="N1257E" type="main">
					<s id="N12580">Obſeruabis autem certiſſimam regulam; ſcilicet ex impoſſibilitate <lb></lb>effectus formalis, ſequi impoſſibilitatem cauſæ formalis, huiuſque poſſi­<lb></lb>bilitatem ex illius poſſibilitate. </s>
				</p>
				<p id="N12588" type="main">
					<s id="N1258A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12596" type="main">
					<s id="N12598"><emph type="italics"></emph>Niſi eſſet impetus, non eſſet naturaliter motus.<emph.end type="italics"></emph.end></s>
					<s id="N1259F"> Quia niſi eſſet cauſa, non <lb></lb>eſſet naturaliter effectus per Ax. 8. Impetus enim eſt cauſa motus per <lb></lb>Th.15. Deinde omnis motus eſt ab aliqua potentia motrice, vt patet ex <lb></lb>omni hypotheſi; </s>
					<s id="N125A9">ſiue ſit naturalis in grauibus, &amp; leuibus, ſiue ſit vitalis <lb></lb>in viuentibus; </s>
					<s id="N125AF">ſiue ſit media in compreſſis, &amp; dilatatis; ſiue alia quæli­<lb></lb>bet: </s>
					<s id="N125B5">ſed omnis potentia motrix eſt actiua, quia mouet; </s>
					<s id="N125B9">ergo agit, ſed <lb></lb>motum non producit per Th. 2. Igitur impetum, qui deinde exigit mo­<lb></lb>tum per Th. 14. Dixi naturaliter; </s>
					<s id="N125C1">quia non eſt dubium, quin Deus ſine <lb></lb>impetu aliquo modo mouere poſſit; </s>
					<s id="N125C7">ideſt, facere ſine impetu, vt corpus <lb></lb>mutet locum: </s>
					<s id="N125CD">nec dicas Deum non poſſe ſupplere vices cauſæ formalis; </s>
					<s id="N125D1"><lb></lb>nam concedo id quidem pro effectu formali primario; </s>
					<s id="N125D6">nec enim Deus <lb></lb>poteſt facere, vt aliquid ſit calidum ſine calore; </s>
					<s id="N125DC">cum eſſe calidum ſit <lb></lb>idem, ac eſſe habens calorem; </s>
					<s id="N125E2">id tamen nego pro effectu ſecundario, <lb></lb>quem ſcilicet cauſa formalis exigit: </s>
					<s id="N125E8">Etenim ſicut poteſt ſummo iure non <lb></lb>ſatisfacere exigentiæ; </s>
					<s id="N125EE">ita poteſt id <expan abbr="cõferre">conferre</expan> ſine exigentiâ, quòd cum exi­<lb></lb>gentia conferre poteſt; ſic poteſt corpus reſoluere ſine calore, mouere <lb></lb>fine impetu &amp;c. </s>
					<s id="N125FA">quanquam vt verum fatear non eſſet propriè motus, ſed <lb></lb>quaſi continuæ reproductionis modus; </s>
					<s id="N12600">nam motus dicit aliquam paſ­<lb></lb>ſionem; ſcilicet actum entis in potentiâ, vt aiunt. </s>
				</p>
				<p id="N12606" type="main">
					<s id="N12608"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12614" type="main">
					<s id="N12616"><emph type="italics"></emph>Si eſſet motus naturaliter ſine impetu, corpus per ſe ipſum moueretur,<emph.end type="italics"></emph.end> id eſt, <lb></lb>exigeret motum per ſuam entitatem; </s>
					<s id="N12621">quia nullus impetus exigeret; </s>
					<s id="N12625">ergo <lb></lb>aliquid aliud, nihil diſtinctum, alioquin eſſet impetus; ergo ipſa corpo­<lb></lb>ris entitas; quanquam non eſſet motus, vt iam dictum eſt, quia non eſ­<lb></lb>ſet paſſio. </s>
				</p>
				<p id="N1262F" type="main">
					<s id="N12631"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1263D" type="main">
					<s id="N1263F"><emph type="italics"></emph>Corpus illud æquali ſemper motu ferretur per ſe<emph.end type="italics"></emph.end>; </s>
					<s id="N12648">Quia eſſet ſemper ea­<lb></lb>dem cauſa neceſſaria motus, id eſt, ipſa entitas corporis; </s>
					<s id="N1264E">igitur idem <lb></lb>effectus per Axioma 12. igitur idem, vel æqualis motus: dixi per ſe pro­<lb></lb>pter diuerſum medium. </s>
				</p>
				<p id="N12656" type="main">
					<s id="N12658"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12664" type="main">
					<s id="N12666"><emph type="italics"></emph>Si eſſet aliquod corpus eſſentialiter mobile, impetu non indigeret.<emph.end type="italics"></emph.end></s>
					<s id="N1266D"> Probatur; </s>
					<s id="N12670"><lb></lb>quia in tantum indiget mobile impetu vt impetus exigat motum; </s>
					<s id="N12675">ſed <lb></lb>corpus illud per ſuam eſſentiam exigeret motum; </s>
					<s id="N1267B">igitur non indigeret <lb></lb>impetu; </s>
					<s id="N12681">poſſet tamen impediri eius motus, vt patet; immò eſſet capax <lb></lb>recipiendi impetus., ſiue quem in ipſo produceret, ſiue quem ab alia <pb pagenum="21" xlink:href="026/01/053.jpg"></pb>cauſa extrinſeca acciperet. </s>
				</p>
				<p id="N1268C" type="main">
					<s id="N1268E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1269A" type="main">
					<s id="N1269C"><emph type="italics"></emph>Si eſſet aliquod corpus eſſentialiter immobile, eſſet incapax impetus.<emph.end type="italics"></emph.end></s>
					<s id="N126A3"> Pro­<lb></lb>batur; quia, niſi eſſet motus, non eſſet impetus per Th. 17. igitur ſubie­<lb></lb>ctum incapax motus eſt incapax impetus. </s>
				</p>
				<p id="N126AA" type="main">
					<s id="N126AC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N126B8" type="main">
					<s id="N126BA"><emph type="italics"></emph>Si eſſet aliquod ſubiectum incapax impetus, eſſet incapax motus.<emph.end type="italics"></emph.end></s>
					<s id="N126C1"> Quia <lb></lb>vbi non poteſt eſſe cauſa formalis, ibi non poteſt eſſe effectus forma­<lb></lb>lis, quod certum eſt. </s>
				</p>
				<p id="N126C8" type="main">
					<s id="N126CA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N126D6" type="main">
					<s id="N126D8"><emph type="italics"></emph>Omne corpus, quod eſt capax motus, eſt capax impetus, &amp; viciſſim.<emph.end type="italics"></emph.end><lb></lb>Probatur 1. pars; </s>
					<s id="N126E2">quia impetus in eo non eſſet fruſtrà; haberet enim <lb></lb>ſuum effectum formalem, &amp; finem intrinſecum. </s>
					<s id="N126E8">Probatur 2.pars; </s>
					<s id="N126EB">quia in <lb></lb>eo impetus non eſſet fruſtrà per Ax. 6. igitur haberet ſuum effectum; <lb></lb>igitur motum. </s>
				</p>
				<p id="N126F3" type="main">
					<s id="N126F5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12701" type="main">
					<s id="N12703"><emph type="italics"></emph>Omne corpus finitum eſt capax motus, &amp; impetus.<emph.end type="italics"></emph.end></s>
					<s id="N1270A"> Probatur 1. pars; </s>
					<s id="N1270D"><lb></lb>quia non eſt vbique, igitur poteſt transferri è loco in locum; cur enim <lb></lb>non poſſet? </s>
					<s id="N12714">Dices fortè quia affixum eſſet eſſentialiter tali, vel tali lo­<lb></lb>co, ſed contra; </s>
					<s id="N1271A">quia deſtruantur omnia, præter ipſum corpus; certè <lb></lb>nulli affixum manet. </s>
					<s id="N12720">Dices ſpatio imaginario; apage iſtas nugas: <lb></lb>de iſto ſpatio plura demonſtrabimus in Metaphy. </s>
					<s id="N12726">Probatur 2. pars; </s>
					<s id="N12729">quia <lb></lb>ſi eſt capax motus, eſt capax impetus per Th. 24. Quod dixi de corpo­<lb></lb>re; dicendum eſt de omni re creata finita permanente. </s>
				</p>
				<p id="N12731" type="main">
					<s id="N12733"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1273F" type="main">
					<s id="N12741"><emph type="italics"></emph>Quod durat tantùm vno inſtanti, eſt incapax motus, &amp; impetus.<emph.end type="italics"></emph.end></s>
					<s id="N12748"> Pro­<lb></lb>batur, quia non eſt moueri, niſi relinquat locum, &amp; acquirat alium; </s>
					<s id="N1274E">ſed <lb></lb>1. acquirere locum, eſt 1. eſſe in illo loco; </s>
					<s id="N12754">&amp; relinquere locum eſt, <lb></lb>1. non eſſe in eo loco; </s>
					<s id="N1275A">nec ſimul eſt in vtroque, quia in duobus locis <lb></lb>idem ſimul eſſe non poteſt; vt demonſtramus in Metaphyſica; </s>
					<s id="N12760">&amp; phy­<lb></lb>ſicè certum eſt ex omni hypotheſi; </s>
					<s id="N12766">igitur moueri nunc, id eſt, hoc in­<lb></lb>ſtanti, id eſt, 1. acquirere nouum locum, &amp; 1. relinquere priorem, <lb></lb>ſupponit neceſſariò antè fuiſſe in loco nunc relicto; </s>
					<s id="N1276E">ſed quod durat <lb></lb>tantùm in inſtanti, non habet antè, neque poſt; </s>
					<s id="N12774">igitur quod durat tan­<lb></lb>tùm vno inſtanti, moueri non poteſt; </s>
					<s id="N1277A">igitur eſt incapax motus; igitur <lb></lb>&amp; impetus. </s>
				</p>
				<p id="N12780" type="main">
					<s id="N12782"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1278E" type="main">
					<s id="N12790"><emph type="italics"></emph>Deus eſt incapax motus, &amp; impetus<emph.end type="italics"></emph.end>: </s>
					<s id="N12799">Tum quia vbique, eſt igitur <lb></lb>nouum locum acquirere non poteſt; </s>
					<s id="N1279F">igitur nec moueri per Definitio­<lb></lb>nem 1. tùm quia æternitas Dei tota ſimul eſt; </s>
					<s id="N127A5">igitur nec fuit antè, ne­<lb></lb>que poſt in ca; </s>
					<s id="N127AB">igitur non poteſt dici antè habuiſſe locum, quo nunc <lb></lb>caret: </s>
					<s id="N127B1">&amp; nunc non habere illum quo caret; </s>
					<s id="N127B5">tùm quia immutabilitas <pb pagenum="22" xlink:href="026/01/054.jpg"></pb>Dei hoc prohibet; </s>
					<s id="N127BE">nam moueri, eſt affici intrinſecè; </s>
					<s id="N127C2">quia etiam de­<lb></lb>ſtructis omnibus extrinſecis creatis moueri poſſem, &amp; fruſtrà recurres <lb></lb>ad partes virtuales immenſitatis Dei, quas ferè animus abhorret; apa­<lb></lb>ge partes in Deo: quis hoc ferre poſſit? </s>
					<s id="N127CC">præterea ſi ſunt, ſunt eſſentia­<lb></lb>liter immobiles; </s>
					<s id="N127D2">igitur valet ſemper ratio allata; </s>
					<s id="N127D6">igitur Deus eſt inca­<lb></lb>pax motus; igitur &amp; impetus. </s>
				</p>
				<p id="N127DC" type="main">
					<s id="N127DE">Diceret aliquis Deum quantumuis Immenſum in orbem conuolui <lb></lb>poſſe; igitur 1. ratio non probat de omni motu. </s>
					<s id="N127E4">Reſpondeo adhuc va­<lb></lb>lere, quia etiam in orbem conuolui non poteſt, niſi mutetur intrinſe­<lb></lb>cè; </s>
					<s id="N127EC">atqui ſi eſt immenſus, non poteſt mutari intrinſecè per motum; </s>
					<s id="N127F0"><lb></lb>quia nullum locum de nouo acquireret; </s>
					<s id="N127F5">ſed de hoc motu aliàs, cum de <lb></lb>infinito; </s>
					<s id="N127FB">vel de puncto phyſico mobili; quidquid ſit. </s>
					<s id="N127FF">valet ſaltem <lb></lb>1. ratio pro motu recto, &amp; aliæ duæ pro omni motu. </s>
				</p>
				<p id="N12804" type="main">
					<s id="N12806"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12812" type="main">
					<s id="N12814"><emph type="italics"></emph>Motus ipſe moueri non poteſt.<emph.end type="italics"></emph.end></s>
					<s id="N1281B"> Quia cum tantùm dicat mutationem <lb></lb>loci; </s>
					<s id="N12821">certè mutatio non eſt in loco; dicit enim tantùm locum relictum <lb></lb>eo inſtanti, quo nouus acquiritur. </s>
					<s id="N12827">Præterea quod eſt in loco dicit tan­<lb></lb>tùm ens phyſicum; </s>
					<s id="N1282D">ſed mutatio dicit etiam non ens; <emph type="italics"></emph>Hinc egregium pa­<lb></lb>radoxum; illud non mouetur per quod cuncta mouentur, quæ mouentur.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N12838" type="main">
					<s id="N1283A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12846" type="main">
					<s id="N12848"><emph type="italics"></emph>Duratio moueri non poteſt.<emph.end type="italics"></emph.end></s>
					<s id="N1284F"> Cum enim ſit ſucceſſiua, fluit per partes, <lb></lb>igitur quælibet illius pars, ſeu quod durat vna inſtanti tantùm eſt inca­<lb></lb>pax motus, per Th. 26. </s>
				</p>
				<p id="N12856" type="main">
					<s id="N12858"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12864" type="main">
					<s id="N12866"><emph type="italics"></emph>Hinc actio moueri non poteſt<emph.end type="italics"></emph.end>; </s>
					<s id="N1286F">cum enim actio per quam res conſerua­<lb></lb>tur, ſit eius duratio; vt conſtabit ex iis, quæ demonſtrabimus in Me­<lb></lb>taphyſica, &amp; cum duratio moueri non poſſit, per Th. 29. certè neque <lb></lb>actio moueri poteſt. </s>
				</p>
				<p id="N12879" type="main">
					<s id="N1287B"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12888" type="main">
					<s id="N1288A">Hinc in tanta rerum creatarum multitudine ſunt tantùm duæ, quæ <lb></lb>ſunt eſſentialiter immobiles; ſcilicet motus, &amp; actio; </s>
					<s id="N12890">quorum ille cum <lb></lb>ſit mutatio non eſt adæquatè aliquid poſitiuum; ſecus actio. </s>
				</p>
				<p id="N12896" type="main">
					<s id="N12898"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N128A5" type="main">
					<s id="N128A7">Hinc ſunt tantùm duo adæquatè poſitiua, quæ moueri non poſſunt; </s>
					<s id="N128AB"><lb></lb>ſcilicet Deus, &amp; actio; Deus, qui ſemper eſt; </s>
					<s id="N128B0">actio, quæ tantùm vno <lb></lb>inſtanti eſt; Deus vbique eſſentialiter; actio hic tantum eſſentialiter; </s>
					<s id="N128B6"><lb></lb>Deus primum ens; actio infinitum ens; </s>
					<s id="N128BB">eſt enim modus; </s>
					<s id="N128BF">Deus primum <lb></lb>mouens; actio ipſe motus; ſcilicet primi generis, de quo in ſect. </s>
					<s id="N128C5">Th.3. </s>
				</p>
				<p id="N128C8" type="main">
					<s id="N128CA"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N128D7" type="main">
					<s id="N128D9">Hinc ſi res aliqua creata per actionem tantæ perfectionis, quæ mille <lb></lb>annis eſſentialiter reſponderet, conſeruaretur; </s>
					<s id="N128DF">certè per totum illud <lb></lb>tempus moueri non poſſet; </s>
					<s id="N128E5">eſſet enim vnicum inſtans, hoc eſt duratio <pb pagenum="23" xlink:href="026/01/055.jpg"></pb>tota ſimul; </s>
					<s id="N128EE">ſed eodem inſtanti in pluribus locis eſſe non poteſt; igitur <lb></lb>nec moueri; </s>
					<s id="N128F4">adde quod per cam actionem ſum in loco, per quam ſum <lb></lb>in tempore; </s>
					<s id="N128FA">igitur ſi hæc eſt ſemper eadem, illam eandem eſſe neceſſe <lb></lb>eſt; ſed hæc ſunt metaphyſica, quæ obiter tantùm attingo, aliàs fusè <lb></lb>de monſtrabo. </s>
				</p>
				<p id="N12902" type="main">
					<s id="N12904"><emph type="center"></emph><emph type="italics"></emph>Scolium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N12910" type="main">
					<s id="N12912">Obſeruabis primò ex dictis præclarum naturæ inſtitutum; </s>
					<s id="N12916">cum enim <lb></lb>corpus moueri ſemper non debeat, (quippe hoc eſſet maximè incom­<lb></lb>modum) certè per ſuam entitatem moueri non exigit; </s>
					<s id="N1291E">alioquin ſemper <lb></lb>moueretur; </s>
					<s id="N12924">igitur per aliud ab entitate diſtinctum, id eſt per impetum; </s>
					<s id="N12928"><lb></lb>itaque licet per ſuam entitatem exigat fluxum in tempore, id eſt conſer­<lb></lb>uari, &amp; durare; </s>
					<s id="N1292F">id eſt nouam ſemper actionem conſeruatiuam; </s>
					<s id="N12933">quia <lb></lb>maximum eius bonum eſt durare vel exiſtere; </s>
					<s id="N12939">Igitur per ſe ipſum illud <lb></lb>exigit; </s>
					<s id="N1293F">quia ſemper exigit, non tamen per ſe ipſum exigit fluxum in <lb></lb>loco, id eſt motum; quia moueri non ſemper eſt bonum. </s>
				</p>
				<p id="N12945" type="main">
					<s id="N12947">Obſeruabis ſecundò, cum idem corpus aliquando velociùs, tardiùs <lb></lb>aliquando moueri exigat; </s>
					<s id="N1294D">ſi per ſuam entitatem moueri exigeret, eo­<lb></lb>dem ſemper ferretur motu; </s>
					<s id="N12953">quia eadem ſemper eſſet exigentia; </s>
					<s id="N12957">igitur <lb></lb>debet eſſe aliquid aliud; </s>
					<s id="N1295D">illud autem eſt impetus, qui aliquando maior <lb></lb>ſeu perfectior, aliquando verò minor eſt; </s>
					<s id="N12963">igitur maiorem ſeu <expan abbr="velcio­rem">velocio­<lb></lb>rem</expan> motum aliquando exigit, aliquando minorem, ſeu tardiorem; </s>
					<s id="N1296D"><lb></lb>cum enim motus ſit eius finis intrinſecus, vt reſolutio eſt finis caloris <lb></lb>vel rarefactio; </s>
					<s id="N12974">quemadmodum maior calor maiorem exigit, ſeu præ­<lb></lb>ſtat reſolutionem; ita &amp; maior, ſeu perfectior impetus maiorem, ſeu <lb></lb>velociorem motum exigit. </s>
				</p>
				<p id="N1297C" type="main">
					<s id="N1297E">Obſeruabis tertiò aliud naturæ inſtitutum, quo ſcilicet in eo tan­<lb></lb>tùm ſubiecto recipi poteſt cauſa formalis, in quo recipi poteſt eius effe­<lb></lb>ctus formalis ſecundarius: </s>
					<s id="N12986">nec alia regula, præter eam excogitari poteſt; </s>
					<s id="N1298A"><lb></lb>cum enim aliqua forma ad talem, vel talem finem à natura inſtituta eſt; </s>
					<s id="N1298F"><lb></lb>certè propter illum finem eſt, igitur in eo non eſt, in quo ſuum finem <lb></lb>conſequi non poteſt; </s>
					<s id="N12996">alioquin fruſtrà eſſet; </s>
					<s id="N1299A">&amp; contra in eo eſſe poteſt, <lb></lb>in quo fruſtrà non eſt; </s>
					<s id="N129A0">cum ſcilicet in eo ſuum finem conſequatur; </s>
					<s id="N129A4">ad­<lb></lb>de quod finis ille intrinſecus phyſicus ſcilicet, non moralis, aliquis no­<lb></lb>uus effectus eſt; </s>
					<s id="N129AC">atqui nouus effectus ſine ſua cauſa eſſe non poteſt, neque <lb></lb>cauſa neceſſaria ſine effectu; igitur ibi, ſcilicet in hoc ſubiecto, in quo <lb></lb>eſt, vel eſſe poteſt effectus formalis, cauſa formalis eſt, vel eſſe poteſt, <lb></lb>eſt inquam citra miraculum. </s>
				</p>
				<p id="N129B6" type="main">
					<s id="N129B8">Obſeruabis quartò egregiam rationem; </s>
					<s id="N129BB">propter quam res eadem in <lb></lb>pluribus locis naturaliter eſſe non poteſt; </s>
					<s id="N129C1">quippe cum res fuerit primo <lb></lb>producta in aliquo loco, illa certè nouum locum acquirere non poteſt <lb></lb>naturaliter; </s>
					<s id="N129C9">niſi per motum, atqui motus dicit neceſſario priorem lo­<lb></lb>tum relictum, &amp; nouum acquiſitum; </s>
					<s id="N129CF">igitur cum tot acquirantur loca <lb></lb>per motum, quot relinquuntur; </s>
					<s id="N129D5">ſi ante motum vnus tantùm erat eiuſ­<lb></lb>dem rei locus, poſt motum etiam vnus eſt: </s>
					<s id="N129DB">quod autem producatur tan-<pb pagenum="24" xlink:href="026/01/056.jpg"></pb>tùm res in vno loco patet; </s>
					<s id="N129E4">vel enim à cauſa prima vel ab aliqua 2. pro­<lb></lb>ducitur; </s>
					<s id="N129EA">ſi à 2. ergo ab aliqua aplicata; </s>
					<s id="N129EE">igitur ex ſuppoſitione quòd il­<lb></lb>la cauſa 2. in vno tantùm loco producta ſit, vni tantum applicari po­<lb></lb>teſt; </s>
					<s id="N129F6">quod autem cauſa 1. in pluribus locis naturaliter eundem effectum <lb></lb>non producat, certum eſt, &amp; demonſtrabimus in Metaphyſ. quia ſin­<lb></lb>gulis effectibus ſingulæ ſufficiunt actiones; </s>
					<s id="N129FE">ſingulis terminis ſingulæ <lb></lb>viæ; </s>
					<s id="N12A04">immò hoc requiri videtur, ſeu ſpectare ad huius vniuerſitatis or­<lb></lb>dinem; </s>
					<s id="N12A0A">quippe ſi res eadem in pluribus locis eſſet; cur potius in duo­<lb></lb>bus quam in tribus? </s>
					<s id="N12A10">deinde multiplex iure poſſet exiſtimari; </s>
					<s id="N12A14">denique <lb></lb>quod vnum eſt in entitate creata, ſeu dependente ab eadem cauſa, vnum <lb></lb>eſt etiam in dependentia; </s>
					<s id="N12A1C">quæ eſt actio, per quam dependet; ſed de his <lb></lb>aliàs. </s>
				</p>
				<p id="N12A22" type="main">
					<s id="N12A24"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12A30" type="main">
					<s id="N12A32"><emph type="italics"></emph>Impetus non producitur in eo mobili, quod moueri non poteſt à potentia <lb></lb>motrice applicata, licèt à fortiori moueri poſſit.<emph.end type="italics"></emph.end></s>
					<s id="N12A3B"> Probatur, quia impetus <lb></lb>eſt tantùm propter motum, qui eius effectus eſt, &amp; finis, per Th. 15. <lb></lb>&amp; 16. Igitur vbi non eſt motus, fruſtrà eſt impetus; </s>
					<s id="N12A43">ſed quod fruſtrà <lb></lb>eſt, non eſt; id eſt non eſt, quod fruſtrà eſſet, ſi eſſet per Ax. 6. Exci­<lb></lb>pio tamen impetum naturalem innatum, qui nunquam eſt fruſtrà, vt <lb></lb>dictum eſt ſuprà in Theorem. </s>
					<s id="N12A4E">17. adde quod non poteſt cognoſci <lb></lb>impetus, niſi vel ex motu, vel ex ictu, vel ex contrario niſu, vel <lb></lb>impulſu; </s>
					<s id="N12A56">ſed nihil horum cernitur in rupe quam ferio; </s>
					<s id="N12A5A">Igitur non <lb></lb>eſt dicendum in ea produci impetum, cuius rationem afferemus infrà; </s>
					<s id="N12A60"><lb></lb>nunc ſatis eſt Ax. 3. id manifeſtè probari; </s>
					<s id="N12A65">nam qui diceret in rupe im­<lb></lb>mobili impetum imprimi; </s>
					<s id="N12A6B">certè poſitiuo argumento probare tenere­<lb></lb>tur, quod tantùm duci poteſt, vel ab experimento; </s>
					<s id="N12A71">atqui hîc nullum eſt; </s>
					<s id="N12A75"><lb></lb>vel à neceſſitate, quæ nulla eſt; </s>
					<s id="N12A7A">vel ex alio quocumque capite, quod <lb></lb>nullum excogitari poteſt; </s>
					<s id="N12A80">ſed maiorem lucem huic Th. 3. ex proximè <lb></lb>ſequentibus accerſemus; </s>
					<s id="N12A86">nec eſt quòd aliqui dicant produci impetum <lb></lb>inefficacem; </s>
					<s id="N12A8C">qui cum fruſtrà ſit, ſi eſt, ex nullo capite probari poteſt: </s>
					<s id="N12A90">ad­<lb></lb>de quòd deſtruitur impetus, ne ſit fruſtrà; </s>
					<s id="N12A96">Igitur non producitur, ne ſit <lb></lb>fruſtrà; </s>
					<s id="N12A9C">nam conſeruatio eſt vera actio, vt dicemus ſuo loco; </s>
					<s id="N12AA0">Igitur ſi <lb></lb>hæc non ponitur, ne aliquid ſit fruſtrà; </s>
					<s id="N12AA6">etiam 1. productio poni non <lb></lb>debet; vnde commentum illud impetus inefficacis prorſus inefficax eſt. </s>
				</p>
				<p id="N12AAC" type="main">
					<s id="N12AAE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12ABA" type="main">
					<s id="N12ABC"><emph type="italics"></emph>Ideo potentia motrix non producit impetum in prædicta rupe.<emph.end type="italics"></emph.end> v.g. <emph type="italics"></emph>quia de­<lb></lb>bilior eſt.<emph.end type="italics"></emph.end></s>
					<s id="N12ACB"> Probatur, &amp; explicatur; quippe debilior potentia minorem ef­<lb></lb>fectum producit per. </s>
					<s id="N12AD0">Ax. 13. <emph type="italics"></emph>num.<emph.end type="italics"></emph.end> 2. igitur pauciores partes impetus <lb></lb>æquales vni certæ per idem <emph type="italics"></emph>num.<emph.end type="italics"></emph.end> 1. igitur ſi ſint plures partes ſubiecti <lb></lb>mobilis, ſeu rupis, quàm impetus; </s>
					<s id="N12AE4">cum vna pars impetus duobus parti­<lb></lb>bus ſubiecti ineſſe non poſſit; </s>
					<s id="N12AEA">licet plures vni ſimul in eſſe poſſint; </s>
					<s id="N12AEE"><lb></lb>non eſt mirum ſi nullus impetus producatur; </s>
					<s id="N12AF3">cum non poſſint tot partes <lb></lb>illius produci, quot eſſent neceſſariæ; vt ſaltem ſingulæ ſingulis ſubie­<lb></lb>cti, ſeu rupis partibus diſtribuerentur. </s>
				</p>
				<pb pagenum="25" xlink:href="026/01/057.jpg"></pb>
				<p id="N12AFF" type="main">
					<s id="N12B01">Obſeruabis autem nouum quoddam genús reſiſtentiæ; </s>
					<s id="N12B05">nam ſingulæ <lb></lb>partes rupis ab applicata potentiâ aptæ ſunt loco moueri per impreſ­<lb></lb>ſum impetum, &amp; maior potentia ſimul omnes loco moueret; </s>
					<s id="N12B0D">at verò <lb></lb>omnes ſimul, &amp; coniunctim conſideratæ; </s>
					<s id="N12B13">quatenus ſcilicet vna pars <lb></lb>non poteſt moueri ſine alia, &amp; comparatæ cum illa potentia debili di­<lb></lb>cuntur habere prædictam reſiſtentiam, quæ ſuperat potentiæ vires; </s>
					<s id="N12B1B"><lb></lb>quòd ſcilicet à maiori moueri tantùm poſſint; quia plures partes im­<lb></lb>petus poſtulantur, quam ſint eæ, quæ à prædictâ potentiâ poſſunt pro­<lb></lb>duci. </s>
				</p>
				<p id="N12B24" type="main">
					<s id="N12B26"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12B32" type="main">
					<s id="N12B34"><emph type="italics"></emph>Vel producitur impetus in omnibus ſubiecti partibus vnitis, vel in nulla; </s>
					<s id="N12B3A"><lb></lb>modò nulla fiat ſeparatio, neque compreſſio<emph.end type="italics"></emph.end>: Certum eſt enim in ijs omni­<lb></lb>bus partibus, quæ auolant ab ictu, produci impetum. </s>
					<s id="N12B44">Probatur igitur <lb></lb>1. quia ſi non producatur in omnibus partibus, &amp; nulla ſeparetur ab <lb></lb>alijs; </s>
					<s id="N12B4C">certè nulla mouetur, vt certum eſt; </s>
					<s id="N12B50">igitur nulla habet impetum; </s>
					<s id="N12B54"><lb></lb>quia ibi non eſt cauſa formalis, vbi non eſt effectus formalis; alioquin <lb></lb>eſſet fruſtrà, contra Ax. 6.2. </s>
					<s id="N12B5B">Tu dicis produci impetum in aliquot parti­<lb></lb>bus; hoc dicis, hoc proba? </s>
					<s id="N12B61">an potes dignoſcere impetum niſi ex motu? </s>
					<s id="N12B64"><lb></lb>vel conſeruaretur hîc impetus ſequentibus inſtantibus, vel ſtatim ſecun­<lb></lb>do inſtanti deſtrueretur. </s>
					<s id="N12B6A">Primum dicere abſurdum eſt; </s>
					<s id="N12B6D">quia ſi hoc eſſet <lb></lb>multisictibus repetitis tandem moueretur totum mobile; ſi verò de­<lb></lb>ſtrui dicatur. </s>
					<s id="N12B75">Secundo inſtanti; eadem ratio probat non produci. </s>
					<s id="N12B78">Pri­<lb></lb>mo inſtanti, quæ probat deſtrui. </s>
					<s id="N12B7D">Secundo nam ideo deſtruitur. </s>
					<s id="N12B80">Secun­<lb></lb>do quia eſt fruſtrà, ſed non minus eſt fruſtrà. </s>
					<s id="N12B85">Primo igitur non produ­<lb></lb>citur. </s>
					<s id="N12B8A">Primo 4. probatur; </s>
					<s id="N12B8D">quia cum non ſufficiant partes impetus, quas <lb></lb>dixi produci, vt omnibus partibus ſubiecti diſtribuantur; </s>
					<s id="N12B93">certè non eſt <lb></lb>vlla ratio, cur potiùs his quàm illis diſtribui dicantur; cum vna ſit tan­<lb></lb>tùm immediatè applicata. </s>
					<s id="N12B9B">Igitur certum eſt vel produci in omnibus, vel <lb></lb>in nulla, niſi forte aliquæ auolent, ſed tunc ſeparantur. </s>
				</p>
				<p id="N12BA0" type="main">
					<s id="N12BA2">Obiiciet aliquis 1. eſſe cauſam neceſſariam applicatam ſubiecto ap­<lb></lb>to: </s>
					<s id="N12BA8">igitur agit per Ax. 12. Reſpondeo eſſe impeditam; </s>
					<s id="N12BAC">nam reſiſtentia <lb></lb>ſubiecti ſuperat vires potentiæ vt dictum eſt; </s>
					<s id="N12BB2">immò in ipſo motu re­<lb></lb>torqueo argumentum; licèt enim ſit applicata cauſa neceſſaria mouens, <lb></lb>non tamen mouet. </s>
				</p>
				<p id="N12BBA" type="main">
					<s id="N12BBC">Obiiciet 2. Ignis applicatus agit in nonnullas partes ſubiecti, licèt <lb></lb>non agat in omnes; igitur &amp; potentia motrix. </s>
					<s id="N12BC2">Reſpondeo non eſſe pa­<lb></lb>ritatem; </s>
					<s id="N12BC8">quia vna pars poteſt calefieri, &amp; reſolui ſine alia, vt conſtat <lb></lb>non tamen vna moueri ſine alia, cui coniuncta eſt, niſi ſeparetur; igi­<lb></lb>tur nec recipere impetum ſine alia. </s>
				</p>
				<p id="N12BD0" type="main">
					<s id="N12BD2">Obiiciet. </s>
					<s id="N12BD5">3. ſint duo trahentes idem mobile; </s>
					<s id="N12BD9">ita vt ſeorſim neuter <lb></lb>trahere poſſit, coniunctim verò vterque poſſit; </s>
					<s id="N12BDF">certè ſi alter non pro­<lb></lb>ducit impetum ſeorſim, nec etiam coniunctim producet; </s>
					<s id="N12BE5">nec enim au­<lb></lb>gentur eius vires ab altero: </s>
					<s id="N12BEB">Reſpondeo vtrunque agere actione com­<lb></lb>muni; igitur non eſt mirum ſi effectus maior eſt, quem tamen neuter <pb pagenum="26" xlink:href="026/01/058.jpg"></pb>ſeorſim producere poteſt. </s>
				</p>
				<p id="N12BF6" type="main">
					<s id="N12BF8">Dices ſi vterque coniunctim producit effectum: </s>
					<s id="N12BFC">ſint v. g. 100. par­<lb></lb>tes impetus; Igitur ſinguli producunt tantùm 50. Igitur cur potiùs in <lb></lb>in his partibus ſubiecti, quàm in alijs, cum vtriuſque potentia eidem <lb></lb>ſubiecti parti poſſet eſſe applicata? </s>
					<s id="N12C0A">Reſpondeo ſingulos producere 100. <lb></lb>actione ſcilicet communi indiuiſibiliter; </s>
					<s id="N12C10">ſint enim duo trahentes A. &amp; <lb></lb>B. A. producit 100. ſed non ſolus; </s>
					<s id="N12C16">B. producit eaſdem 100. ſed non ſo­<lb></lb>lus; ſed explicabimus hunc modum actionis communis in Metaphys. <lb></lb>quod autem agant actione communi patet per Ax. 13. </s>
				</p>
				<p id="N12C1F" type="main">
					<s id="N12C21">Obiicies 4. producitur ſonus ſi ferias rupem; </s>
					<s id="N12C25">igitur &amp; impetus; </s>
					<s id="N12C29">Reſ­<lb></lb>pondeo ad ſonum ſolam aëris colliſionem ſufficere, quam fieri certum <lb></lb>eſt à prædicto ictu; </s>
					<s id="N12C31">deinde mallej motus impacti in rupem facit ſonum; </s>
					<s id="N12C35"><lb></lb>quidquid tandem ſit ſonus, de quo hîc non diſputo: </s>
					<s id="N12C3A">adde quod in ru­<lb></lb>pe ſunt ſemper aliquæ partes tremulæ, quæ modico tantùm, eoque flexi­<lb></lb>bili nexu cum alijs partibus copulantur; adde aliquam compreſſionem, <lb></lb>ex qua modicæ vibrationes ſequuntur. </s>
				</p>
				<p id="N12C44" type="main">
					<s id="N12C46">Obiicies 5. Quando aliquæ partes auolant ab ictu, haud dubiè auo­<lb></lb>lant propter impetum impreſſum: </s>
					<s id="N12C4C">Igitur prius eſt imprimi impetum, <lb></lb>quàm auolare; igitur productus eſt impetus in nonnullis partibus, &amp; <lb></lb>non in aliis, cum quibus illæ ſunt coniunctæ. </s>
					<s id="N12C54">Reſpondeo equidem im­<lb></lb>petum produci in illis partibus antequam auolent; </s>
					<s id="N12C5A">ſed ideo produci vt <lb></lb>deinde auolent nam tota ratio cur non producatur, eſt ne ſit fruſtrà; </s>
					<s id="N12C60">ſed <lb></lb>ſi auolent aliquæ partes: certè in ijs non eſt fruſtrà, in quibus habet <lb></lb>ſuum effectum, id eſt, motum. </s>
				</p>
				<p id="N12C68" type="main">
					<s id="N12C6A">Dices; </s>
					<s id="N12C6D">igitur primo inſtanti impetus ille eſt fruſtrà; </s>
					<s id="N12C71">in quo non <lb></lb>habet ſuum effectum; </s>
					<s id="N12C77">Reſpondeo nunquam primo inſtanti eſſe fruſtrà, <lb></lb>modò ſit motus ſecundo cum etiam primo inſtanti, quo eſt impetus, <lb></lb>non poſſit eſſe motus, vt demonſtrabo infrà; immò ideo ponitur im­<lb></lb>petus primo vt ſit motus ſecundo exigendo pro inſtant ſequenti, de <lb></lb>cum impetus ponat tantùm motum quo aliàs. </s>
				</p>
				<p id="N12C83" type="main">
					<s id="N12C85">Dices; </s>
					<s id="N12C88">ſed potentia motrix neſcit an poſſit pars aliqua mobilis ſepa­<lb></lb>rari; igitur non eſt quòd aliquando producat impetum, aliquando <lb></lb>non producat. </s>
					<s id="N12C90">Reſpondeo non ſtare per cauſam neceſſariam, quin ſem­<lb></lb>per agat; </s>
					<s id="N12C96">ſed per ſubiectum, quod ſi aptum eſt, &amp; capax effectus; </s>
					<s id="N12C9A">haud <lb></lb>dubiè eo ipſo cauſa neceſſaria applicata in ipſum aget; ſi verò ineptum. </s>
					<s id="N12CA0"><lb></lb>haud dubiè non aget; </s>
					<s id="N12CA4">nam ad hoc vt producatur effectus in ſubiecto; </s>
					<s id="N12CA8"><lb></lb>non ſatis eſt cauſam poſſe producere, niſi etiam ſubiectum poſſit recipe­<lb></lb>re; </s>
					<s id="N12CAF">igitur cum ſit talis ordo à natura inſtitutus, ne aliquid ſit fruſtrà; </s>
					<s id="N12CB3"><lb></lb>certè ſi impetus producibilis ſit futurus fruſtrà, hauddubiè non produ­<lb></lb>cetur; ſecus verò ſi fruſtrà non ſit futurus, in quo non eſt difficultas. </s>
				</p>
				<p id="N12CBA" type="main">
					<s id="N12CBC"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N12CC8" type="main">
					<s id="N12CCA">Obſeruabis 1. vix fieri poſſe quin ſemper aliquæ partes ſeparentur, <lb></lb>comprimantur, vel dilatentur, vt patet experientiâ. </s>
				</p>
				<p id="N12CCF" type="main">
					<s id="N12CD1">Obſeruabis 2. etiam maximam corporis molem à debili potentia mi-<pb pagenum="27" xlink:href="026/01/059.jpg"></pb>nimo etiam ictu moueri; </s>
					<s id="N12CDA">quod etiam obſeruauit Galileus in ſuis dialo­<lb></lb>gis de motu; </s>
					<s id="N12CE0">quem certè motum obſeruabis etiam inſenſibilem, tùm <lb></lb>operâ radij luminis repercuſſi, &amp; ad aliquod interuallum proiecti; </s>
					<s id="N12CE6">tùm <lb></lb>operâ ſeu piſorum in tympani membranâ tremulo quaſi motu ſubſul­<lb></lb>tantium; quâ etiam arte deprehenditur in arce obſeſſa, ſub quam muri <lb></lb>partem cuniculi agantur. </s>
				</p>
				<p id="N12CF0" type="main">
					<s id="N12CF2"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12CFF" type="main">
					<s id="N12D01">Hinc egregia ratio erui poteſt, cur ingens corporis moles à debili po­<lb></lb>tentia loco moueri non poſſit; </s>
					<s id="N12D07">cum enim tot ſaltem requirantur partes <lb></lb>impetus, quot ſunt partes ſubiecti: </s>
					<s id="N12D0D">quia vel in omnibus, vel in nulla <lb></lb>producitur; </s>
					<s id="N12D13">certè cum ſint plures partes ſubiecti, quàm vt in ſingulis <lb></lb>ab ea dumtaxat potentiâ impetus produci poſſit; quid mirum eſt, ſi mo­<lb></lb>ueri non poſſit. </s>
				</p>
				<p id="N12D1B" type="main">
					<s id="N12D1D"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12D2A" type="main">
					<s id="N12D2C">Hinc certa ratio alterius vulgaris effectus potentiæ motricis, quæ lapi­<lb></lb>dem 40. librarum tardo tantùm motu impellit, etiam cum ſummo niſu, <lb></lb>cum tamen ſaxo vnius libræ velociorem motum imprimat; </s>
					<s id="N12D34">quia ſcilicet <lb></lb>partes impetus producti diſtribuuntur pluribus partibus ſubiecti in ma­<lb></lb>iori lapide, &amp; paucioribus in minori; </s>
					<s id="N12D3C">igitur ſingulæ partes minoris <lb></lb>habent plures partes impetus, vt manifeſtè conſtat; </s>
					<s id="N12D42">ergo ille impetus <lb></lb>intenſior eſt; igitur maiorem exigit ſeu perfectiorem motum per Ax. <lb></lb>13. num.2. </s>
				</p>
				<p id="N12D4B" type="main">
					<s id="N12D4D"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12D5A" type="main">
					<s id="N12D5C">Hinc ſublata ratione diuerſæ reſiſtentiæ medij, dato pondere <lb></lb>mobilis vtriuſque, datoque niſu communi potentiæ, poteſt de­<lb></lb>terminari certus velocitatis gradus vtriuſque; </s>
					<s id="N12D64">nam ratio velocitatum <lb></lb>eſt inuerſa ponderum v. g. ſit pondùs 4. librarum; </s>
					<s id="N12D6E">fit etiam 2. librarum <lb></lb>ſit impetus impreſſus vtrique ſuppoſito communi, &amp; æquali niſu <lb></lb>potentiæ, &amp; æquali tempore; </s>
					<s id="N12D76">haud dubiè velocitas mobilis 2. libra­<lb></lb>rum erit dupla velocitatis mobilis 4. librarum; </s>
					<s id="N12D7C">quia cum ſint duplo <lb></lb>plures partes ſubiecti in hoc mobili quàm in illo (accipio enim vtrum­<lb></lb>que eiuſdem materiæ, vt omnes lites fugiam) igitur in minori eſt duplo <lb></lb>intenſior impetus: Igitur duplo velocior motus; </s>
					<s id="N12D86">dixi, ſi fiat æquali <lb></lb>niſu, &amp; æquali tempore; </s>
					<s id="N12D8C">quia reuerâ non fit in tempore æquali, ſed <lb></lb>inæquali, ſi ſupponatur idem arcus brachij v. g. iacientis; </s>
					<s id="N12D96">nam tempo­<lb></lb>ra ſunt in ratione ſubduplicata ponderum; vt demonſtrabimus lib.  10. <lb></lb>&amp; velocitates ſunt vt tempora permutando. </s>
				</p>
				<p id="N12D9E" type="main">
					<s id="N12DA0"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12DAD" type="main">
					<s id="N12DAF">Hinc facilè determinari poteſt proportio impetus impreſſi cognitâ <lb></lb>grauitate mobilium; </s>
					<s id="N12DB5">v. g. ſit mobile graue vt4. &amp; aliud graue vt 2. haud <lb></lb>dubiè vt moueatur  æquali gradu velocitatis, debet produci duplo <lb></lb>maior impetus in maiori mobili, hoc eſt, iuxta rationem maioris ad mi­<lb></lb>nus, quod clariſſimè ſequitur ex dictis; </s>
					<s id="N12DC3">vt enim tot ſint gradus impetus <pb pagenum="28" xlink:href="026/01/060.jpg"></pb>in qualibet parte minoris, quot ſunt in qualibet parte minoris; </s>
					<s id="N12DCC">haud <lb></lb>dubiè impetus maioris habet eandem rationem ad impetum minoris; <lb></lb>quam habet maius ad minus. </s>
				</p>
				<p id="N12DD4" type="main">
					<s id="N12DD6"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12DE3" type="main">
					<s id="N12DE5">Hinc quoque ducitur manifeſta ratio ſeu reſponſio ad illud præcla­<lb></lb>rum certè quorundam philoſophorum <expan abbr="commẽtum">commentum</expan>, qui volunt ex mini­<lb></lb>ma ponderis acceſſione totam terræ molem inclinari, vt in nouo æqui­<lb></lb>librio ſtatuatur; quod omninò falſum eſt; </s>
					<s id="N12DF3">nam ex ſuppotione quòd <lb></lb>terra non grauitet (vt vulgò dicitur, &amp; aliàs à nobis <expan abbr="demõſtrabitur">demonſtrabitur</expan>) illa <lb></lb>certè moueri non poteſt niſi producantur tot partes impetus quot ſunt <lb></lb>partes ſubiecti in tota terra; quæ certè maximas <expan abbr="potẽtiæ">potentiæ</expan> vires poſtulant. </s>
				</p>
				<p id="N12E05" type="main">
					<s id="N12E07"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12E13" type="main">
					<s id="N12E15"><emph type="italics"></emph>Primo inſtanti, quo est impetus, non est ille motus, cuius hic impetus eſt <lb></lb>cauſa.<emph.end type="italics"></emph.end></s>
					<s id="N12E1E"> Probatur; </s>
					<s id="N12E21">quia non poteſt eſſe motus, niſi ſit locus prior reli­<lb></lb>ctus, &amp; nouus acquiſitus, igitur ſi eodem inſtanti, quo eſt impetus, <lb></lb>haberet motum, eodem inſtanti eſſet in duobus locis, quod dici non <lb></lb>poteſt; &amp; iam diximus in Th. 26. igitur impetus primo inſtanti quo <lb></lb>eſt non habet ſuum motum. </s>
				</p>
				<p id="N12E2D" type="main">
					<s id="N12E2F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12E3B" type="main">
					<s id="N12E3D"><emph type="italics"></emph>Immò nihil eſt, quod primo inſtanti, quo eſt, moueri poſſit.<emph.end type="italics"></emph.end></s>
					<s id="N12E44"> Quia non poteſt <lb></lb>moueri, niſi acquirat nouum locum, &amp; priorem relinquat; </s>
					<s id="N12E4A">igitur, vel ſi­<lb></lb>mul in vtroque eſt, quod dici non poteſt; </s>
					<s id="N12E50">vel in relicto antè fuit; igitur <lb></lb>non eſt primum inſtans, contra ſuppoſitionem. </s>
				</p>
				<p id="N12E56" type="main">
					<s id="N12E58"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12E64" type="main">
					<s id="N12E66"><emph type="italics"></emph>Potest impetus aliquo inſtanti non moueri quo mouetur ipſum mobile, in <lb></lb>quo est.<emph.end type="italics"></emph.end></s>
					<s id="N12E6F"> Nam moueatur mobile quodlibet; </s>
					<s id="N12E73">&amp; dum mouetur, impella­<lb></lb>tur, factâ ſcilicet acceſſione noui impetus; haud dubiè hoc primo in­<lb></lb>ſtanti, quo producitur impetus in dato mobili non mouetur per Th. <lb></lb>35. quo tamen inſtanti mouetur prædictum mobile. </s>
				</p>
				<p id="N12E7E" type="main">
					<s id="N12E80"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12E8D" type="main">
					<s id="N12E8F">Hinc egregium paradoxon; <emph type="italics"></emph>Poteſt alique inſtanti moueri ſubiectum, licèt <lb></lb>non moueantur illa omnia, que eidem ſubiecto reuerâ inſunt.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N12E9A" type="main">
					<s id="N12E9C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12EA9" type="main">
					<s id="N12EAB">Hinc etiam aliud paradoxon; </s>
					<s id="N12EAF"><emph type="italics"></emph>Impetus primo inſtanti, quo eſt, non habet <lb></lb>ſuum finem, nec habere poteſt<emph.end type="italics"></emph.end>; patet, quia primo inſtanti non habet <expan abbr="motũ">motum</expan>. </s>
				</p>
				<p id="N12EBE" type="main">
					<s id="N12EC0"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12ECD" type="main">
					<s id="N12ECF">Hinc poteſt aliquid dato inſtanti carere ſuo fine; </s>
					<s id="N12ED3">licèt non ſit fruſtrà; <lb></lb>fruſtrâ enim tantùm dicitur ille impetus, qui pro inſtanti ſequenti <lb></lb>non poteſt habere motum. </s>
				</p>
				<p id="N12EDB" type="main">
					<s id="N12EDD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12EE9" type="main">
					<s id="N12EEB"><emph type="italics"></emph>Impetus pars recepta in parte ſubiecti non exigit motum aliarum partium<emph.end type="italics"></emph.end><pb pagenum="29" xlink:href="026/01/061.jpg"></pb><emph type="italics"></emph>eiuſdem ſubiecti, licèt coniunctarum.<emph.end type="italics"></emph.end></s>
					<s id="N12EFB"> Probatur 1. quia alioquin vna pars <lb></lb>impetus ſufficeret ad mouendam ingentem rupem; quod abſurdum eſt. </s>
					<s id="N12F01"><lb></lb>2. ſicut vna pars caloris non reſoluit alias partes ſubiecti; ita nec im­<lb></lb>petus. </s>
					<s id="N12F08">3. Ratio à priori eſt; quia impetus non eſt cauſa efficiens motus <lb></lb>per Th. 13. ſed tantùm cauſa formalis per Th. 15. Igitur præſtat tantùm <lb></lb>ſuum effectum formalem in eo ſubiecto, in quo eſt. </s>
				</p>
				<p id="N12F10" type="main">
					<s id="N12F12"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12F1F" type="main">
					<s id="N12F21">Hinc partes impetus non cauſant motum in ſuo ſubiecto actione, vel <lb></lb>exigentia communi; </s>
					<s id="N12F27">quia quælibet pars impetus exigit tantùm motum <lb></lb>ſui ſubiecti; </s>
					<s id="N12F2D">id eſt illius partis, quàm afficit; quod etiam probatur per <lb></lb>Ax. 13. </s>
				</p>
				<p id="N12F33" type="main">
					<s id="N12F35"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12F42" type="main">
					<s id="N12F44">Hinc corpus grauius perſe, ſaltem eiuſdem materiæ, non cadit velo­<lb></lb>ciùs, quàm leuius, vti globus plumbeus 100. librarum, quàm globus <lb></lb>vnius libræ plumbeus; </s>
					<s id="N12F4C">quia ſcilicet impetus vnius partis non iuuat mo­<lb></lb>tum alterius: </s>
					<s id="N12F52">præterea tam facilè 2, partes impetus in 2. partibus ſubie­<lb></lb>cti receptæ eaſdem mouent, quàm 100. alias 100. dixi per ſe; </s>
					<s id="N12F58">nam di­<lb></lb>uerſa eſſe poteſt medij reſiſtentia; ſed de his fuſe in 2. lib. <emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N12F69" type="main">
					<s id="N12F6B"><emph type="italics"></emph>Impetus recipitur tantùm in ipſa ſubſtantia ſubiecti naturaliter.<emph.end type="italics"></emph.end> v. g. ſi <lb></lb>mobile ſit ferrum calidum, recipitur in ipſa ſubſtantia ferri; </s>
					<s id="N12F7A">non verò <lb></lb>in ipſo calore (ex ſuppoſitione quod calor ſit accidens, vt aliàs demon­<lb></lb>ſtrabimus; </s>
					<s id="N12F82">nec in alijs accidentibus, ſi quæ ſunt, in eodem ſubiecto; </s>
					<s id="N12F86">pro­<lb></lb>batur 1. quia ſi produceretur etiam impetus in accidentibus, quo plu­<lb></lb>ra eſſent accidentia in aliquo ſubiecto; </s>
					<s id="N12F8E">plures quoque partes impetus <lb></lb>producendæ eſſent; igitur maiori potentiâ opus eſſet per Ax. 13. n. </s>
					<s id="N12F94">4. <lb></lb>Igitur difficiliùs mouerentur, quod eſt abſurdum. </s>
					<s id="N12F99">Diceret fortè ali­<lb></lb>quis eundem impetum recipi ſimul in ſubſtantia &amp; in ipſis accidenti­<lb></lb>bus; </s>
					<s id="N12FA1">ſed contra, nam reuera, ſi hoc eſſet, dum proijcitur ferrum cali­<lb></lb>dum, &amp; ſtatim frigefit, deſtrueretur totus impetus, deſtructo ſcilicet <lb></lb>eius ſubiecto: </s>
					<s id="N12FA9">2. qui hoc diceret, deberet probare; </s>
					<s id="N12FAD">nam eodem modo <lb></lb>mouetur corpus ſiue afficiatur pluribus accidentibus, ſiue paucioribus; <lb></lb>igitur non euincit experientia recipi in illis impetum, nec etiam ratio, <lb></lb>vt dicam paulò poſt. </s>
					<s id="N12FB7">Ratio à priori eſſe poteſt; </s>
					<s id="N12FBB">quia accidens cum ſuo <lb></lb>ſubiecto coniunctum exigit ſemper eſſe præſens ſubiecto, cum natura­<lb></lb>liter extra ſubiectum exiſtere non poſſit; </s>
					<s id="N12FC3">igitur cum exigat conſerua­<lb></lb>ri, &amp; exiſtere; </s>
					<s id="N12FC9">eo tantùm modo, quo poteſt naturaliter conſeruari &amp; <lb></lb>exiſtere; </s>
					<s id="N12FCF">certè exigit conſeruari, &amp; ineſſe ſubiecto; </s>
					<s id="N12FD3">igitur exiſtere in <lb></lb>eo loco, in quo exiſtit ſubiectum, vt patet; igitur, ſi ſubiectum mutet <lb></lb>locum etiam accidens cum eo coniunctum mutare debet. </s>
				</p>
				<p id="N12FDB" type="main">
					<s id="N12FDD">Dices, igitur ſimiliter dici poteſt non recipi impetum in omni­<lb></lb>bus partibus ſubiecti mobilis, ſed in vnâ dumtaxat; cui cum <lb></lb>aliæ ſint vnitæ, exigunt moueri ſine impetu ad illius motum? </s>
					<s id="N12FE5">cum <lb></lb>hoc ipſum ad omnem vnionem ſpectare videatur; </s>
					<s id="N12FEB">Reſpondeo vnam <pb pagenum="30" xlink:href="026/01/062.jpg"></pb>partem plumbi ita coniungi cum alia, vt etiam ſeparata naturaliter <lb></lb>exiſtere poſſit; </s>
					<s id="N12FF6">igitur non eſt par ratio; </s>
					<s id="N12FFA">præterea vna pars plumbi non <lb></lb>eſt in loco alterius; </s>
					<s id="N13000">nec enim inuicem penetrantur cum ſit compene­<lb></lb>tratio accidentium cum ſubiecto; </s>
					<s id="N13006">deinde, quò plures ſunt partes vnitæ, <lb></lb>maior eſt reſiſtentia, quæ ipſo etiam ſenſu percipitur; </s>
					<s id="N1300C">denique non vide­<lb></lb>tur cur potius produceretur in vna parte, quam in alia; quæ omnia <lb></lb>iam ſuprà Th. 33. demonſtrauimus. </s>
				</p>
				<p id="N13014" type="main">
					<s id="N13016">Adde quod ſi impetus produceretur in ipſis accidentibus, etiam in <lb></lb>ipſo impetu prius producto alius impetus produceretur; </s>
					<s id="N1301C">cum ſcilicet <lb></lb>noua fit impetus acceſſio; quod ſatis ridiculum eſt; quaſi verò impetus <lb></lb>indigeat impetu &amp;c. </s>
					<s id="N13024">hîc loquor tantùm de accidentibus in ſubiecto; <lb></lb>non verò de Euchariſticis, quæ à ſubiecto per miraculum ſeparata etiam <lb></lb>moueri poſſunt per impreſſum impetum. </s>
				</p>
				<p id="N1302C" type="main">
					<s id="N1302E"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1303B" type="main">
					<s id="N1303D">Hinc manifeſtè patet, quid dicendum ſit de anima bruti, quæ moue­<lb></lb>tur etiam ſine impetu; </s>
					<s id="N13043">quia exigit ſemper eſſe coniuncta corpori, à <lb></lb>quo diſiuncta naturaliter exiſtere non poteſt, vt ſuo loco dicemus; igi­<lb></lb>tur ad motum corporis, ſeu ſubiecti moueri deber. </s>
				</p>
				<p id="N1304B" type="main">
					<s id="N1304D"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1305A" type="main">
					<s id="N1305C">Idem quoque de Anima rationali dicendum eſſe videtur; </s>
					<s id="N13060">licèt <lb></lb>enim à corpore ſeparata naturaliter exiſtere poſſit; </s>
					<s id="N13066">tandiù tamen cum <lb></lb>corpore manet coniuncta, quandiu agere poteſt in organis corporeis; <lb></lb>ac proinde exigit conſeruari in corpore ipſo, quandiu ſuas operatio­<lb></lb>nes organicas in eo exercere poteſt. </s>
				</p>
				<p id="N13070" type="main">
					<s id="N13072"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1307F" type="main">
					<s id="N13081">Hinc patet ratio manifeſta ad quæſitum illud; </s>
					<s id="N13085">quomodo ſcilicet po­<lb></lb>tentia motrix materialis v.g. Taurus ſuo cornu hominem ventilare poſ­<lb></lb>ſit; nec vlla ſupereſt difficultas, dum dicas impetum non produci in <lb></lb>anima. </s>
				</p>
				<p id="N13091" type="main">
					<s id="N13093"><emph type="center"></emph><emph type="italics"></emph>Scolium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1309F" type="main">
					<s id="N130A1">Obſeruabis primò In hoc Theoremate dictum eſſe naturaliter; quia <lb></lb>per miraculum accidens ſeparatum ab omni ſubſtantia, dum ſit impe­<lb></lb>netrabile, per impetum ſibi impreſſum moueri poteſt. </s>
				</p>
				<p id="N130A9" type="main">
					<s id="N130AB">Obſeruabis ſecundò de anima bruti per miraculum ſeparatâ, idem <lb></lb>prorſus dicendum eſſe. </s>
				</p>
				<p id="N130B0" type="main">
					<s id="N130B2">Obſeruabis tertiò etiam Animam rationalem ſeparatam, modò ſit <lb></lb>cum impenetrabilitate coniuncta, capacem eſſe impetus; </s>
					<s id="N130B8">quem etiam <lb></lb>à potentia motrice corporea recipere poteſt; </s>
					<s id="N130BE">idem dictum eſto de An­<lb></lb>gelo; ſed de vtroque aliàs. </s>
				</p>
				<p id="N130C4" type="main">
					<s id="N130C6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N130D2" type="main">
					<s id="N130D4"><emph type="italics"></emph>Quando corpus pellitur ab alio corpore per impetum impreſſum; </s>
					<s id="N130DA">haud du­<lb></lb>biè impetus ille impreſſus ab aliqua cauſa efficiente producitur<emph.end type="italics"></emph.end>; patet <lb></lb>per Ax. 8. </s>
				</p>
				<pb pagenum="31" xlink:href="026/01/063.jpg"></pb>
				<p id="N130E9" type="main">
					<s id="N130EB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N130F7" type="main">
					<s id="N130F9"><emph type="italics"></emph>Ille impetus non producitur à ſubſtantia corporis in aliud impacti.<emph.end type="italics"></emph.end></s>
					<s id="N13100"> Proba­<lb></lb>tur; </s>
					<s id="N13105">quia ſi produceretur, eſſet cauſa neceſſaria vt <expan abbr="clarũ">clarum</expan> eſt; igitur appli­<lb></lb>cata, &amp; non impedita ageret per Ax. 32. quod eſt contra experientiam. </s>
					<s id="N1310F"><lb></lb>Dicunt aliqui requiri <expan abbr="motũ">motum</expan> præuium, vt agat; ſed contra; </s>
					<s id="N13118">nam motus <lb></lb>præuius non requiritur vt cauſa, vt patet; </s>
					<s id="N1311E">quia cauſa vt agat debet exi­<lb></lb>ſtere per Ax. 9. Igitur requiritur, vt conditio, quod dici non poteſt; </s>
					<s id="N13124"><lb></lb>quia primo etiam conditio debet eſſe præſens; </s>
					<s id="N13129">ſed motus præuius de <lb></lb>nihil preſenti eſt ſecundo quia non poteſt excogitari aliud munus con­<lb></lb>ditionis; </s>
					<s id="N13131">niſi vel vt tollat impedimentum, vel vt applicet cauſam ſubie­<lb></lb>cto apto; </s>
					<s id="N13137">præterea motus præuius non eſt; </s>
					<s id="N1313B">igitur eodem modo ſe <lb></lb>habet, ac ſi nunquam extitiſſet; &amp; ſi eo inſtanti quo corpus impa­<lb></lb>ctum primo tangit, amitteret totum impetum, ita vt expræterito motu <lb></lb>nihil reliquum eſſet, haud dubiè corpus aliud non pelleret. </s>
				</p>
				<p id="N13145" type="main">
					<s id="N13147">Diceret alius impetum eſſe tantùm conditionem, quæ ſemper eſt <lb></lb>de præſenti: </s>
					<s id="N1314D">ad hanc inſtantiam non valet ſuperior reſponſio; </s>
					<s id="N13151">&amp; certè <lb></lb>ſi eo ipſo inſtanti contactus noua fieret impetus acceſſio; </s>
					<s id="N13157">haud dubiè <lb></lb>maior eſſet ictus; </s>
					<s id="N1315D">licèt cum eodem motu præuio, &amp; tamen idem eſſet <lb></lb>corpus <expan abbr="impactũ">impactum</expan>, Igitur ad hanc <expan abbr="inſtantiã">inſtantiam</expan> alio modo reſpondeo, ex appli­<lb></lb>catione impetus ſemper ſequitur productio alterius impetus; </s>
					<s id="N1316D">dum ſcili­<lb></lb>cet ſubiectum, cui applicatur ſit capax motus; </s>
					<s id="N13173">ex applicatione corporis <lb></lb>ſeu ſubiecti ipſius non ſemper ſequitur; igitur dicendum eſt impetum <lb></lb>ipſum eſſe cauſam alterius per Ax. 11. n. </s>
					<s id="N1317B">1. voco enim illud cauſam, <lb></lb>ex cuius applicatione ſemper ſequitur ſimilis effectus; alioquin ſi hoc <lb></lb>neges; </s>
					<s id="N13183">proba mihi aliter ignem accendi ab alio igne; </s>
					<s id="N13187">dicam enim tibi <lb></lb>ignem applicatum eſſe tantùm conditionem, &amp; produci à cœlo; proba <lb></lb>mihi aliter calorem produci à calore? </s>
					<s id="N1318F">quo enim medio, vel argu­<lb></lb>mento id euinces? </s>
					<s id="N13194">quo etiam non euincam impetum produci ab im­<lb></lb>petu: Deinde affer rationem à priori, propter quam ſubſtantia <lb></lb>corporis producat impetum ſurſum? </s>
					<s id="N1319C">v. g. cum non exigat à ſe ipſa mo­<lb></lb>tum ſursùm, qui violentus eſt corpori graui; numquid certum eſt, vt <lb></lb>dicemus infrà impetum produci ad extra, vt tollatur impedimentum <lb></lb>motus? </s>
					<s id="N131AA">igitur illius eſt tollere impedimentum, cuius eſt exigere motum, <lb></lb>corpus ipſum graue non exigit motum ſurſum, ſed impetus; </s>
					<s id="N131B0">igitur im­<lb></lb>petus eſt tollere impedimentum ſui effectus; </s>
					<s id="N131B6">igitur producere impetum, <lb></lb>quo vno tolli tantùm poteſt: </s>
					<s id="N131BC">En tibi rationem à priori, cutum nullam <lb></lb>habeas: Præterea, cur negas impetum eſſe cauſam ſufficientem alterius <lb></lb>impetus, cum ex eius applicatione ipſo ſenſu percipiamus produci alium <lb></lb>impetum? </s>
					<s id="N131C6">quæ ratio? </s>
					<s id="N131C9">quid inde abſurdi, quid incommodi: Igitur tàm <lb></lb>certum eſt, immò certius impetum produci ab alio impetu, quàm calo­<lb></lb>rem à calore. </s>
					<s id="N131D1">Dices impetum iam habere alium effectum ſcilicet mo­<lb></lb>tum; bella profecto ratio! ſed numquid motus eſt effectus formalis im­<lb></lb>petus? </s>
					<s id="N131D9">prætereà eſt-ne effectus ad extra? </s>
					<s id="N131DC">deinde idem dico de calore; </s>
					<s id="N131E0"><pb pagenum="32" xlink:href="026/01/064.jpg"></pb>qui reuera habet effectum formalem ſecundarium ad intra, ſcilicet rare­<lb></lb>factionem, quæ eſt mutatio extenſionis; </s>
					<s id="N131EA">quemadmodum motus eſt mu­<lb></lb>tatio loci, vel vbicationis; </s>
					<s id="N131F0">igitur cum hoc | non obſtante, calor pro­<lb></lb>ducat calorem ad extra; cur impetus non producit impetum? </s>
					<s id="N131F6">cuius pro­<lb></lb>ductionem concedis virtuti corporum reſiſtitiuæ, id eſt vnioni, impe­<lb></lb>netrabilitati, &amp; cæteris huiuſmodi modorum ſuperfluorum quiſquiliis; <lb></lb>de quibus plurimi tecum contendunt. </s>
				</p>
				<p id="N13200" type="main">
					<s id="N13202"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1320E" type="main">
					<s id="N13210">Obſeruabis nonnullas eſſe difficultates, quæ communes ſunt etiam <lb></lb>illi ſententiæ, quam ſequuntur ij, qui exiſtimant impetum ad extra <lb></lb>produci à corpore impacto; quas tamen facilè ſoluemus infrà in conti­<lb></lb>nuata noſtrorum Theorematum ſerie. </s>
				</p>
				<p id="N1321A" type="main">
					<s id="N1321C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13228" type="main">
					<s id="N1322A"><emph type="italics"></emph>Aliquis impetus non producitur ab alio impetu.<emph.end type="italics"></emph.end></s>
					<s id="N13231"> Probatur, quia aliquis <lb></lb>impetus producitur ad intra à potentia motrice, vt patet. </s>
					<s id="N13236">2. cum non <lb></lb>detur progreſſus in infinitum, nec impetus idem producatur à ſe ipſo, ad <lb></lb>aliquem tandem vltimum ſeu primum deueniendum eſt, qui ab alio im­<lb></lb>petu non producatur. </s>
				</p>
				<p id="N1323F" type="main">
					<s id="N13241"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1324D" type="main">
					<s id="N1324F"><emph type="italics"></emph>Impetus producitur ſemper ad extra ab alio impetu.<emph.end type="italics"></emph.end></s>
					<s id="N13256"> Quia cum ſemper <lb></lb>ad illius productionem requiratur applicatio alterius impetus; certè <lb></lb>non eſt ponenda alia cauſa per Ax. 11. </s>
				</p>
				<p id="N1325E" type="main">
					<s id="N13260"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1326C" type="main">
					<s id="N1326E"><emph type="italics"></emph>Hinc impetus habet duplex munus cauſæ; </s>
					<s id="N13274">ſcilicet cauſæ exigentis ad intra <lb></lb>&amp; efficientis ad extra<emph.end type="italics"></emph.end>; vtrumque patet ex dictis. </s>
				</p>
				<p id="N1327D" type="main">
					<s id="N1327F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1328B" type="main">
					<s id="N1328D"><emph type="italics"></emph>Impetus agit tantùm ad extra, vt tollat impedimentum motus<emph.end type="italics"></emph.end>; </s>
					<s id="N13296">cum enim <lb></lb>motus ſit finis intrinſecus impetus; </s>
					<s id="N1329C">certè ſi nihil impediret motum, <lb></lb>haud dubiè gauderet impetus ſuo fine; </s>
					<s id="N132A2">igitur fruſtrà quidquam aliud <lb></lb>deſideraret; </s>
					<s id="N132A8">præterea licèt applicetur à tergo aliud mobile; </s>
					<s id="N132AC">non tamen <lb></lb>propterea in eo producit, vt conſtat experientiâ; </s>
					<s id="N132B2">denique cum tan­<lb></lb>tùm impetum cognoſcamus per motum; </s>
					<s id="N132B8">cum nequidem eſſet impetus, <lb></lb>ſi non eſſet motus, per Th. 17. certè totus eſt impetus propter motum <lb></lb>qui eſt eius finis; </s>
					<s id="N132C0">igitur non agit niſi propter motum: </s>
					<s id="N132C4">ſed non poteſt <lb></lb>excogitari, quid faciat propter motum, dum agit, niſi dicamus ideo <lb></lb>tantùm agere, vt tollatur impedimentum; cum certum ſit corpus im­<lb></lb>mobile, in quod impingitur aliud mobile, impedire eius motum. </s>
				</p>
				<p id="N132CE" type="main">
					<s id="N132D0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N132DC" type="main">
					<s id="N132DE"><emph type="italics"></emph>Hinc non ſimul agit impetus in orbem ſed tantùm per lineam <lb></lb>ſui motus; </s>
					<s id="N132E6">cui ſi nullum corpus occurrit reuerà non agit,<emph.end type="italics"></emph.end> Ratio eſt; </s>
					<s id="N132ED">quia li­<lb></lb>cèt aliud corpus mobili admoueatur in alia linea; </s>
					<s id="N132F3">cum non impediat <lb></lb>eius motum, vt ſuppono; </s>
					<s id="N132F9">cum agat tantùm impetus ad extra, vt tollat, <pb pagenum="33" xlink:href="026/01/065.jpg"></pb>impedimentum motu ſui ſubiecti, in eo non agit, quod non impedit; </s>
					<s id="N13302">&amp; <lb></lb>cum impediatur tantùm in vna linea, in ca tantùm agit; igitur non <lb></lb>agit in orbem. </s>
				</p>
				<p id="N1330A" type="main">
					<s id="N1330C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13318" type="main">
					<s id="N1331A">Obſeruabis primò, hanc primam eſſe difficultatem; cum in hoc im­<lb></lb>petus maximè differat ab alijs qualitatibus ſi quæ ſunt, quæ agunt in or­<lb></lb>bem, vt dicemus ſuo loco. </s>
				</p>
				<p id="N13322" type="main">
					<s id="N13324">Obſeruabis ſecundò, hanc etiam eſſe communem illorum ſententiam, <lb></lb>qui dicunt impetum ad extrà produci ab ipſo mobili, ſed ita vt ab illis <lb></lb>vix ſolui poſſit; cum tamen à nobis facilè ſoluatur. </s>
				</p>
				<p id="N1332C" type="main">
					<s id="N1332E">Obſeruabis tertiò, impetum in vtroque munere cauſæ ſubeſſe tantùm <lb></lb>vni lineæ; </s>
					<s id="N13334">ſcilicet exigit motum per vnam lineam; </s>
					<s id="N13338">cum per plures ſi­<lb></lb>mul motus eſſe non poſſit; </s>
					<s id="N1333E">ne idem mobile ſimul eſſet in pluribus lo­<lb></lb>cis; </s>
					<s id="N13344">&amp; producit impetum per vnam lineam; cum producat tantùm pro­<lb></lb>pter motum. </s>
				</p>
				<p id="N1334A" type="main">
					<s id="N1334C">Obſeruabis quartò, alias qualitates, ſi quæ ſunt, non agere ad extra, <lb></lb>vt tollant impedimentum ſui effectus ad intra; </s>
					<s id="N13352">qui ſcilicet ab impedi­<lb></lb>mento extrinſeco impediri non poteſt; </s>
					<s id="N13358">vt accidit in ipſo impetu; </s>
					<s id="N1335C">etenim <lb></lb>corpus non poteſt moueri niſi nouum locum acquirat: neque nouum <lb></lb>locum acquirere ab alio corpore occupatum, niſi corpus hoc loco ce­<lb></lb>dat, neque hoc loco cedere poteſt ſine motu, vel moueri ſine impetu, <lb></lb>igitur cum impediat motum amoueri debet, accepto dumtaxat impetu <lb></lb>ab alio mobili. </s>
				</p>
				<p id="N1336A" type="main">
					<s id="N1336C">Obſeruabis quintò nonnullos eſſe, qui volunt motum vnius corporis <lb></lb>transferri in aliud corpus; </s>
					<s id="N13372">ſed mera eſt metaphora; </s>
					<s id="N13376">nihil enim prorſus <lb></lb>eſt quod ab vno in aliud tranſeat, ſeu transferatur; nec aliud dici po­<lb></lb>teſt, niſi quod dictum eſt, impetum ſcilicet nouum produci. </s>
				</p>
				<p id="N1337E" type="main">
					<s id="N13380">Hinc etiam reiicies commentum illorum, qui dicunt ideo vnum <lb></lb>corpus ab alio moueri, quia ab vno in aliud deriuantur corpuſcula illa, <lb></lb>quæ faciunt lumen, &amp; calorem; </s>
					<s id="N13388">quia lumen, &amp; calor ſunt veræ qualita­<lb></lb>tes, non corpuſcula, vt demonſtrabimus in 5. tractatu: </s>
					<s id="N1338E">Adde quod li­<lb></lb>cet ferrum candens aliud frigidum impellat, etiam velociſſimè; </s>
					<s id="N13394">hoc ip­<lb></lb>ſum æquè frigidum manet; </s>
					<s id="N1339A">denique in craſſis tenebris nix ſeu glacies <lb></lb>frigidiſſima perniciſſimè moueri poteſt: ſed apage iſta commenta. </s>
				</p>
				<p id="N133A0" type="main">
					<s id="N133A2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N133AE" type="main">
					<s id="N133B0"><emph type="italics"></emph>Omnes partes impetus mobilis agunt ad extra actione communi.<emph.end type="italics"></emph.end></s>
					<s id="N133B7"> Probatur <lb></lb>per Ax. 13. n. </s>
					<s id="N133BC">1. niſi enim agerent actione communi ſed quælibet ſuam <lb></lb>produceret; </s>
					<s id="N133C2">cur potius in hac parte ſubiecti, quam in alia, deinde ap­<lb></lb>plicatur tantùm vna immediatè; </s>
					<s id="N133C8">Igitur agunt omnes actione commu­<lb></lb>ni; </s>
					<s id="N133CE">omnes inquam illæ, quæ impediuntur; </s>
					<s id="N133D2">cum enim impetus agat <lb></lb>tantùm ad extrà vt tollat impedimentum ſui motus; ille proſectò age­<lb></lb>re non debet, cuius motus vel effectus non impeditur. </s>
				</p>
				<pb pagenum="34" xlink:href="026/01/066.jpg"></pb>
				<p id="N133DE" type="main">
					<s id="N133E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N133EC" type="main">
					<s id="N133EE"><emph type="italics"></emph>Hinc maiora corpora putà onerariæ naues, licèt tardiſſimo motu ferantur, <lb></lb>cum in aliud corpus impinguntur maxima vi illud impellunt.<emph.end type="italics"></emph.end></s>
					<s id="N133F7"> Ratio eſt; <lb></lb>quia cum ſint plures partes impetus in pluribus partibus ſubiecti, &amp; <lb></lb>omnes agant actione communi, non mirum eſt ſi maiorem effectum <lb></lb>producant, per Ax. 13. n. </s>
					<s id="N13400">2. </s>
				</p>
				<p id="N13404" type="main">
					<s id="N13406"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13412" type="main">
					<s id="N13414">Vides primò in hoc caſu compenſari intenſionem ab extenſione; </s>
					<s id="N13418"><lb></lb>quippe quod præſtarent plures partes impetus in minore corporis mole <lb></lb>intenſæ; hoc idem præſtare poſſunt extenſæ in maiore mole. </s>
				</p>
				<p id="N1341F" type="main">
					<s id="N13421">Secundò ſicut maior moles aptior eſt ad motum imprimendum, &amp; mi­<lb></lb>nùs apta ad recipiendum ita minor contrà aptior eſt ad recipiendum, &amp; <lb></lb>minùs apta ad imprimendum. </s>
				</p>
				<p id="N13428" type="main">
					<s id="N1342A">Tertiò, Hinc corpora illa, quorum partes vel nullo vel modico nexu <lb></lb>copulantur, minimo ferè impulſu commouentur; </s>
					<s id="N13430">ſic aër &amp; aqua mini­<lb></lb>mo flante vento agitantur, nubes pelluntur; </s>
					<s id="N13436">hinc tot procellæ tempe­<lb></lb>ſtateſque cientur; nec vlla eſt alia ratio, cur minima ferè venti vis, cui <lb></lb>modicum ſaxum reſiſtit, tantam aquæ, vel aëris molem commoueat, ni­<lb></lb>ſi quia cum partes illorum corporum nullo ferè nexu coniunctæ ſint vna <lb></lb>ſine alia moueri poteſt, quod in aqua gelu concreta minimè accidit. </s>
				</p>
				<p id="N13442" type="main">
					<s id="N13444">Quartò, Hinc ſi maxima rupes ita comminueretur vt tota in pulue­<lb></lb>rem ſeu ſabulum abiret, minima vis impreſſa particulas illas moueret. </s>
				</p>
				<p id="N13449" type="main">
					<s id="N1344B">Quintò, Hinc diuino penè conſilio factum eſt, vt partes terreſtris <lb></lb>globi arctiore fibula copulentur; </s>
					<s id="N13451">ne, ſi diſiunctæ eſſent, minimo flatu <lb></lb>diſpergerentur: vt videre eſt in puluere etiam grauiſſimo, qui ab aura <lb></lb>flant e diſpergitur. </s>
				</p>
				<p id="N13459" type="main">
					<s id="N1345B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13467" type="main">
					<s id="N13469"><emph type="italics"></emph>Impetus, cuius motus non impeditur, non agit ad extrà.<emph.end type="italics"></emph.end></s>
					<s id="N13470"> Probatur per <lb></lb>Th. 44. hinc ſi aliud corpus affigas mobili à tergo, nullum impetum in <lb></lb>eo producet, cuius effectus, qui certè impetui ſingularis eſt, alia ratio <lb></lb>eſſe non poteſt; </s>
					<s id="N1347A">tam enim corpus eſt applicatum à tergo, quam in <lb></lb>ipſa fronte; &amp; nihil eſt in vno, quod non ſit in alio, niſi quod in fronte <lb></lb>impedit motum, à tergo verò non impedit. </s>
				</p>
				<p id="N13482" type="main">
					<s id="N13484"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13491" type="main">
					<s id="N13493">Hinc egregium paradoxon erui poteſt; </s>
					<s id="N13497">quod ſcilicet cauſa neceſſaria <lb></lb>etiam immediatè applicata, &amp; non impedita in ſubiecto apto non agit; </s>
					<s id="N1349D"><lb></lb>quod videtur eſſe contra Ax. 12. vnde vt agat cauſa neceſſaria, debet <lb></lb>applicari debito modo; </s>
					<s id="N134A4">ſi agat in orbem, omnis applicatio ſufficiens <lb></lb>eſt: </s>
					<s id="N134AA">ſi verò agat tantùm per vnam lineam; </s>
					<s id="N134AE">certè applicari debet in ca <lb></lb>linea; alioquin non aget defectu debitæ applicationis. </s>
				</p>
				<p id="N134B4" type="main">
					<s id="N134B6"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N134C3" type="main">
					<s id="N134C5">Hinc etiam aliud paradoxon non minus iucundum; </s>
					<s id="N134C9">cauſa neceſſaria <pb pagenum="35" xlink:href="026/01/067.jpg"></pb>applicata, &amp; non impedita non agit; </s>
					<s id="N134D2">at verò agit impedita; </s>
					<s id="N134D6">ſcilicet <lb></lb>impetus qui tantùm agit, vt tollat impedimentum; igitur, ſi non <lb></lb>impediatur non agit. </s>
				</p>
				<p id="N134DE" type="main">
					<s id="N134E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N134EC" type="main">
					<s id="N134EE"><emph type="italics"></emph>Quo minùs impeditur impetus, minùs agit ad extra, &amp; contrà; quo plùs <lb></lb>impeditur, plùs agit.<emph.end type="italics"></emph.end></s>
					<s id="N134F8"> Cum enim ideò agat ad extra, vt tollat impedi­<lb></lb>mentum; </s>
					<s id="N134FE">certè ſi nullum eſt, nihil agit, ſi minùs, minùs agit; igitur <lb></lb>agit pro rata, id eſt, pro diuerſa impedimenti ratione. </s>
				</p>
				<p id="N13504" type="main">
					<s id="N13506"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13512" type="main">
					<s id="N13514"><emph type="italics"></emph>Si linea motus, quam directionis appellant, ducatur per centrum vtriuſque <lb></lb>corporis, maximum est impedimentum,<emph.end type="italics"></emph.end> vt patet. </s>
					<s id="N1351E">ſint enim duo globi, <lb></lb>A mobilis, &amp; B. occurrens ipſi A, ſitque linea directionis DE ducta <lb></lb>per centrum vtriuſque AB, &amp; punctum contactus ſit C; </s>
					<s id="N13526">certè glo­<lb></lb>bus B maximum ponit impedimentum, quod ab eo poni poſſit; </s>
					<s id="N1352C">Igitur <lb></lb>impetus globi A agit quantùm poteſt in globum B; vt ſcilicet maxi­<lb></lb>mum impedimentum remoueat. </s>
				</p>
				<p id="N13534" type="main">
					<s id="N13536"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13542" type="main">
					<s id="N13544"><emph type="italics"></emph>Si linea motus vel ipſius parallela cadat perpendiculariter in extremam <lb></lb>diametrum globi immobilis: </s>
					<s id="N1354C">haud dubiè nihil impedit<emph.end type="italics"></emph.end>; </s>
					<s id="N13553">ſit enim globus <lb></lb>mobilis A, Immobilis B, linea directionis ſit GA, ipſi parallela FC; </s>
					<s id="N13559"><lb></lb>certè globus B. non impedit motum globi A. cum nihil loci globi B <lb></lb>occupari debeat à globo A; Igitur impetus A non agit in globum B per <lb></lb>Th. 48. </s>
				</p>
				<p id="N13562" type="main">
					<s id="N13564"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13570" type="main">
					<s id="N13572"><emph type="italics"></emph>Si linea motus ſit inter vtramque; </s>
					<s id="N13578">est minus impedimentum.<emph.end type="italics"></emph.end> ſit globus <lb></lb>immobilis BA; </s>
					<s id="N13581">ſit linea motus GC cum impedimento, de qua in Th. 50. <lb></lb>ſit alia KB cum nullo impedimento, de qua in Th. 51. ſint aliæ HD, <lb></lb>IE; </s>
					<s id="N13589">certè minus eſt impedimentum in contactu D, quàm in C; </s>
					<s id="N1358D">quia ca­<lb></lb>dit obliquè in D, perinde atque ſi caderet in tangentem NO; Igitur <lb></lb>minus impeditur; in qua vero proportione, dicemus aliàs, cum de re­<lb></lb>flexione, &amp; de motu mixto. </s>
				</p>
				<p id="N13597" type="main">
					<s id="N13599"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N135A5" type="main">
					<s id="N135A7"><emph type="italics"></emph>Hinc producitur in contactu<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>totus impetus; </s>
					<s id="N135B3">in contactu<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>minùs; </s>
					<s id="N135BD">in <lb></lb>contactu<emph.end type="italics"></emph.end> E <emph type="italics"></emph>adhuc minùs; </s>
					<s id="N135C9">in<emph.end type="italics"></emph.end> B <emph type="italics"></emph>nihil<emph.end type="italics"></emph.end>; </s>
					<s id="N135D6">quia in ea proportione producitur <lb></lb>plùs vel minùs impetus, quo plùs eſt, vel minùs impedimenti per <lb></lb>Th. 49. ſed minùs eſt impedimentum in E, quàm in C; </s>
					<s id="N135DE">&amp; in E, quàm <lb></lb>in D, per Th. 52; Igitur in D producitur minùs impetus, quàm in C, <lb></lb>&amp; minùs in E, quàm in D. </s>
				</p>
				<p id="N135E7" type="main">
					<s id="N135E9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N135F5" type="main">
					<s id="N135F7"><emph type="italics"></emph>Hinc eadem cauſa neceſſaria etiam immediate applicata diuerſum impe<emph.end type="italics"></emph.end><pb pagenum="36" xlink:href="026/01/068.jpg"></pb><emph type="italics"></emph>tum producit; vt patet in impetu, non tamen est eodem modo applicata, <lb></lb>id eſt in eadem linea.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1360A" type="main">
					<s id="N1360C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13618" type="main">
					<s id="N1361A"><emph type="italics"></emph>Hinc ratio multorum effectuum phyſicorum e. </s>
					<s id="N1361F">ui potest<emph.end type="italics"></emph.end>; </s>
					<s id="N13625">cur ſcilicet cor­<lb></lb>pus incidens in aliud perpendiculariter maximum ictum infligat; </s>
					<s id="N1362B">quia <lb></lb>ſcilicet maximum impetum producit, qui poſſit ab eo produci; </s>
					<s id="N13631">cur <lb></lb>idem corpus obliquè incidens in aliud minorem ictum infligat; cuius <lb></lb>rei alia ratio eſſe non poteſt. </s>
					<s id="N13639">Huc etiam reuoca tormenta bellica, quæ <lb></lb>vel directo, vel obliquo ictu muros verberant; </s>
					<s id="N1363F">hinc perpendicularis <lb></lb>fortiſſima eſt; licèt eadem ratio pro motu corporum non valeat, quæ <lb></lb>valet pro diffuſione, ſeu propagatione qualitatum. </s>
				</p>
				<p id="N13647" type="main">
					<s id="N13649"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13655" type="main">
					<s id="N13657">Hinc poteſt determinari quota pars impetus producatur, &amp; quantus <lb></lb>ſit ictus; </s>
					<s id="N1365D">cognito ſcilicet &amp; ſuppoſito eo impetus gradu, qui producitur, <lb></lb>cum totus producitur, vt fit in perpendiculari; </s>
					<s id="N13663">quippe tota menſura <lb></lb>impetus continetur in arcu CB; quam proportionem nos infrà demon­<lb></lb>ſtrabimus. </s>
				</p>
				<p id="N1366B" type="main">
					<s id="N1366D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13679" type="main">
					<s id="N1367B"><emph type="italics"></emph>Si linea directionis ducatur per centrum vtriuſque globi, mobilis ſcilicet <lb></lb>&amp; immobilis, impetus producit totum impetum quem poteſt producere ſiue in <lb></lb>maiori globo, ſiue in minori, ſiue in æquali<emph.end type="italics"></emph.end>; patet experientia; cuius ratio <lb></lb>eſt; </s>
					<s id="N1368A">quia impetus eſt cauſa neceſſaria; </s>
					<s id="N1368E">Igitur idem impetus eodem mo­<lb></lb>do applicatus æquali tempore, æqualem ſemper effectum producit, per <lb></lb>Ax. 12. igitur cum impetus agat tantùm, vt tollat impedimentum per <lb></lb>Th. 44. &amp; cum in prædicta linea agat quantum poteſt per Th. 50. cer­<lb></lb>tè æqualem effectum producat neceſſe eſt; ſiue in maiori ſiue in mino­<lb></lb>ri, ſiue in æquali globo immobili. </s>
				</p>
				<p id="N1369C" type="main">
					<s id="N1369E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N136AA" type="main">
					<s id="N136AC"><emph type="italics"></emph>Hinc impetus remiſſus potest producere intenſum; </s>
					<s id="N136B2">&amp; hæc eſt altera difficul­<lb></lb>tas; </s>
					<s id="N136B8">cum ſcilicet maior globus in minorem impingitur<emph.end type="italics"></emph.end>; </s>
					<s id="N136BF">cum enim omnes <lb></lb>partes impetus maioris globi agant actione communi per Th. 46. &amp; <lb></lb>cum agant quantùm maximè poſſunt; </s>
					<s id="N136C7">in minore globo, tot partes pro­<lb></lb>ducunt impetus, quot in maiore, vt patet; </s>
					<s id="N136CD">igitur in minore globo pau­<lb></lb>cioribus partibus ſubiecti diſtribuuntur plures partes impetus; </s>
					<s id="N136D3">ergo in <lb></lb>qualibet parte ſubiecti ſunt plures; </s>
					<s id="N136D9">ſed hoc eſt eſſe intenſum, vt conſtat, <lb></lb>igitur impetus remiſſus producit intenſum; quod eſt paradoxon egre­<lb></lb>gium. </s>
				</p>
				<p id="N136E1" type="main">
					<s id="N136E3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N136EF" type="main">
					<s id="N136F1"><emph type="italics"></emph>Hinc etiam impetus intenſus producit remiſſum, cum ſcilicet minor globus <lb></lb>in maiorem incidit<emph.end type="italics"></emph.end>; </s>
					<s id="N136FC">quia ſcilicet pauciores partes impetus diſtribuun­<lb></lb>tur pluribus partibus ſubiecti; </s>
					<s id="N13702">igitur quælibet ſubiecti pauciores impe­<lb></lb>tus habet; quæ omnia conſtant ex dictis. </s>
				</p>
				<pb pagenum="37" xlink:href="026/01/069.jpg"></pb>
				<p id="N1370C" type="main">
					<s id="N1370E"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1371A" type="main">
					<s id="N1371C">Obſeruabis primò, ſingularem impetus proprietatem, quæ alijs qua­<lb></lb>litatibus minimè competit; </s>
					<s id="N13722">nam aliæ qualitates v. g. calor; </s>
					<s id="N1372A">lumen in <lb></lb>eadem diſtantia effectum ſemper æquè intenſum producunt; </s>
					<s id="N13730">ſecus verò <lb></lb>impetus, qui pro maiori vel minori obice maiorem, vel minorem, hoc <lb></lb>eſt intenſiorem, vel remiſſiorem impetum in eadem diſtantia producit; </s>
					<s id="N13738"><lb></lb>cuius ratio ex eo capite petitur; </s>
					<s id="N1373D">quòd impetus agat tantùm ad extra <lb></lb>propter ſuum effectum ad intra, vt ſcilicet tollat impedimentum; </s>
					<s id="N13743">igi­<lb></lb>tur in totum, quod impedit, agit; </s>
					<s id="N13749">igitur non habet certam, &amp; deter­<lb></lb>minatam ſphæram; </s>
					<s id="N1374F">cum tantùm agat in obicem, ſiue ſit maior, ſiue <lb></lb>minor: </s>
					<s id="N13755">Quia verò eſt cauſa neceſſaria, æqualem effectum producit, id <lb></lb>eſt tot partes impetus in maiore, quot in minore, ergo, cum in mino­<lb></lb>re ſint pauciores partes ſubiecti, &amp; plures in maiore; </s>
					<s id="N1375D">haud dubiè quæli­<lb></lb>bet pars minoris habebit plures partes effectus, &amp; quælibet pars maio­<lb></lb>ris pauciores; igitur effectus erit intenſior in minore, &amp; remiſſior in <lb></lb>maiore. </s>
				</p>
				<p id="N13767" type="main">
					<s id="N13769">Prætereà, cum dixi omnes partes mobilis actione communi agere ad <lb></lb>extra; </s>
					<s id="N1376F">ita primò intelligi debet, vt omnes illæ partes moueantur: </s>
					<s id="N13773">ſecun­<lb></lb>dò, vt linea motus, ſeu directionis per centra grauitatis vtriuſque glo­<lb></lb>bi v, g. ducatur; </s>
					<s id="N1377D">alioquin, vel omnes actione communi non agunt, vel <lb></lb>minus agunt, de quo infrà; </s>
					<s id="N13783">ſufficit verò iuxta præſens inſtitutum, vt <lb></lb>globus ita impellat alium vel æqualem, vel inæqualem, vt linea dire­<lb></lb>ctionis ducatur per centrum grauitatis alterius; vide figuram. </s>
					<s id="N1378B">in qua <lb></lb>linea directionis eſt DE. </s>
				</p>
				<p id="N13790" type="main">
					<s id="N13792"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1379E" type="main">
					<s id="N137A0"><emph type="italics"></emph>Impetus globi impacti in alium globum eo modo, quo diximus, id est, linea <lb></lb>directionis ducta per centra grauitatis vtriuſque producit in eo æqualem<emph.end type="italics"></emph.end>; </s>
					<s id="N137AB">Pro­<lb></lb>batur, quia impetus eſt cauſa neceſſaria, quæ tunc agit quantum poteſt <lb></lb>per Th. 57. ſed æqualis poteſt producere æqualem: </s>
					<s id="N137B3">Probatur primò, <lb></lb>exemplo aliarum qualitatum; </s>
					<s id="N137B9">ſecundò, quia ideo agit vt tollat impedi­<lb></lb>mentum, hoc eſt vt corpus illud amoueat loco; </s>
					<s id="N137BF">igitur æquali motu per <lb></lb>ſe; </s>
					<s id="N137C5">alioquin niſi æquali motu amoueret, non tolleret impedimentum, <lb></lb>vt pater; </s>
					<s id="N137CB">tertiò ſint 30. partes impetus, certè vel producent plures vel <lb></lb>pauciores, vel totidem, non plures; </s>
					<s id="N137D1">cur enim potius 31. quam 32. <lb></lb>nec etiam pauciores; cur enim potius 20. quam 18, &amp;c. </s>
					<s id="N137D7">Igitur totidem; </s>
					<s id="N137DB"><lb></lb>quia cum ſint plures numeri plurium partium ſupra 30. &amp; pauciorum <lb></lb>infra vt patet; </s>
					<s id="N137E2">ſitque tantùm vnicus numerus æqualium; </s>
					<s id="N137E6">certè quod <lb></lb>vnum eſt, determinatum eſt, per Ax. 5. hæc ratio licèt videatur negati­<lb></lb>ua eſt tamen potentiſſima: </s>
					<s id="N137EE">quartò, quia actus ſecundus, reſpondet actui <lb></lb>primo, id eſt, effectus productus virtuti cauſæ producentis; </s>
					<s id="N137F4">itaque cum <lb></lb>virtus agendi impetus ſit eius entitas, vt patet, certè impetus productus <lb></lb>eſt per ſe æqualis impetui producenti per ſe; id eſt remoto omni <lb></lb>impedimento, &amp; facto eo contactu iuxta modum prædictum, ea quo-<pb pagenum="38" xlink:href="026/01/070.jpg"></pb>que lege, vt impetus agat quantum poteſt, &amp; omnes partes mobilis <lb></lb>moueantur æquali motu. </s>
				</p>
				<p id="N13805" type="main">
					<s id="N13807"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13814" type="main">
					<s id="N13816">Hinc reijcis illos, qui volunt à globo æquali produci in æquali ſub­<lb></lb>duplum impetum; in ſubduplo ſubtriplum; in ſubquadruplo ſubquin­<lb></lb>tuplum; ratio illorum eſt; </s>
					<s id="N1381E">quia duo globi æquales inſtanti contactus <lb></lb>perinde ſe habent, atque ſi conflarent vnum corpus; </s>
					<s id="N13824">ſed ſi conflarent <lb></lb>vnum corpus quilibet ſubduplum impetum haberet; </s>
					<s id="N1382A">ſi verò globus cum <lb></lb>alio ſubduplo faceret vnum mobile; </s>
					<s id="N13830">haud dubiè minor, id eſt, ſubduplus <lb></lb>haberet tantùm ſubtriplum impetum; atque ita deinceps; </s>
					<s id="N13836">hoc totum <lb></lb>falſiſſimum eſt; </s>
					<s id="N1383C">nam primò ſi globus æqualis acciperet tantùm ſubdu­<lb></lb>plum impetum ab alio, ſubduplo tantùm motu ferretur; </s>
					<s id="N13842">igitur ſubdu­<lb></lb>plum ſpatium decurreret, quod eſt contra experientiam, &amp; Th. 47. Se­<lb></lb>cundò, ratio propoſita nulla eſt; </s>
					<s id="N1384A">quia quando globus impactus impellit <lb></lb>alium, eſt veluti potentiâ, quæ cum tota ſua vi, &amp; cum impetu agit, <lb></lb>cuius nulla pars transfertur in alium globum; </s>
					<s id="N13852">nec enim migrat de <lb></lb>de ſubiecto in ſubiectum, ſed producit ſibi æqualem: </s>
					<s id="N13858">equidem ſi duo <lb></lb>globi æquales eſſent vel coniuncti, vel contigui in linea directionis, <lb></lb>quilibet pro rata acciperet impetus producti partem à potentia applica­<lb></lb>ta; </s>
					<s id="N13862">ſi eſſent æquales, quiſque ſubduplum: ſi alter ſubduplus ſubtri­<lb></lb>plum, &amp;c. </s>
					<s id="N13868">ſed hæc ſunt ſatis facilia. </s>
				</p>
				<p id="N1386B" type="main">
					<s id="N1386D">Obijci fortè poſſet ab aliquo primò experientia; </s>
					<s id="N13871">videmus enim ſæpè <lb></lb>globum impulſum in ludo Tudiculario moueri tardiùs globo impellen­<lb></lb>te; </s>
					<s id="N13879">reſpondeo id ſæpè accidere; </s>
					<s id="N1387D">tùm quia linea directionis non connec­<lb></lb>tit centra vtriuſque globi; </s>
					<s id="N13883">igitur minor eſt ictus per Th 52. tùm quia <lb></lb>globus impellens, vel impulſus deficiunt à perfecta ſphæra; </s>
					<s id="N13889">tùm quia <lb></lb>non eſt perfecta æqualitas globorum; adde quod quò accuratiùs prædi­<lb></lb>ctæ leges obſeruantur, ipſi motus ad æqualitatem propiùs accedunt, vt <lb></lb>conſtat experientia. </s>
				</p>
				<p id="N13893" type="main">
					<s id="N13895">Obiici poſſet ſecundò deſtrui aliquid impetus globi impellentis ab ipſo <lb></lb>ictu, vt conſtat experientia; </s>
					<s id="N1389B">igitur illa pars impetus, quæ deſtruitur, non <lb></lb>producit nouum impetum in globo impulſo; </s>
					<s id="N138A1">Reſpondeo deſtrui quidem <lb></lb>aliquid impetus in globo impacto, vt videbimus infrà; </s>
					<s id="N138A7">cum tamen de­<lb></lb>ſtruatur tantùm ſequenti poſt ictum inſtanti; </s>
					<s id="N138AD">certè cum exiſtat adhuc <lb></lb>ipſo inſtanti contactus, neceſſariò agit, quippe aliquid vltimo inſtanti <lb></lb>poteſt agere; </s>
					<s id="N138B5">adde quod illud ipſum repugnat manifeſtæ experientiæ; </s>
					<s id="N138B9"><lb></lb>licèt enim aliquando deſtruatur totus impetus in globo impacto, quod <lb></lb>ſæpè accidit in ludo Tudiculario, nam illicò ſiſtit pila eburnea; alius <lb></lb>tamen globus velociter mouetur, cuius effectus rationem infrà addu­<lb></lb>cemus. </s>
				</p>
				<p id="N138C4" type="main">
					<s id="N138C6">Obijci poſſet tertiò inde ſequi progreſſum in infinitum, nam globus <lb></lb>A impactus in globum B impellet cum æquali motu, &amp; B in C etiam <lb></lb>æquali, C in D, atque ita deinceps; </s>
					<s id="N138CE">modò illi globi ita ſtatuantur, vt <lb></lb>linea directionis per omnium centra rectà ducatur; </s>
					<s id="N138D4">Reſpondeo, vel il-<pb pagenum="39" xlink:href="026/01/071.jpg"></pb>los omnes globos ita eſſe contiguos, vt mutuo contactu ſe inuicem tan­<lb></lb>gant; </s>
					<s id="N138DF">vel aliquod ſpatium inter ſingulos intercipi; </s>
					<s id="N138E3">ſi primum, produci­<lb></lb>tur impetus à potentia motrice in omnibus, ſi ſufficiens eſt; </s>
					<s id="N138E9">non verò <lb></lb>vnus globus in alio, vt conſtat; </s>
					<s id="N138EF">ſicut duo pondera ſimul attollo, quorum <lb></lb>vnum alteri incumbit: </s>
					<s id="N138F5">ſi verò non ſe tangant, dico antequam A im­<lb></lb>pingatur in B, dum ſpatium illud interiectum percurrit, amittere aliquid <lb></lb>impetus: </s>
					<s id="N138FD">idem dico de B, &amp; C, vnde ſi nihil impetus in eo primo motu <lb></lb>periret &amp; linea directionis omnium centra perfectè connecteret; </s>
					<s id="N13903">ita vt <lb></lb>omnium ictus illi omnino ſine vlla deflexione reſponderent; </s>
					<s id="N13909">haud du­<lb></lb>biè non poſſent eſſe tot globi, quin poſſet alius addi, qui ab vltimo <lb></lb>pelleretur; </s>
					<s id="N13911">ſed vix illa omnia de quibus ſuprà poſſunt obſeruari; </s>
					<s id="N13915">Hinc <lb></lb>tamen facilè vna pars aëris aliam pellit, quod diſtinctè videmus in <lb></lb>aqua; ſed de his aliàs, ſufficiat modò propoſitam obiectionem inde <lb></lb>manere ſolutam. </s>
				</p>
				<p id="N1391F" type="main">
					<s id="N13921"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1392D" type="main">
					<s id="N1392F"><emph type="italics"></emph>Globus maior impactus in minorem imprimit illi intenſiorem impetum, &amp; <lb></lb>velociorem motum per Th.<emph.end type="italics"></emph.end> 48. <emph type="italics"></emph>&amp;<emph.end type="italics"></emph.end> 47. Nec eſt quod aliqui opponant Prin­<lb></lb>cipium illud mechanicum; </s>
					<s id="N13942">id eſt, nullum corpus poſſe maiorem veloci­<lb></lb>tatis gradum alteri corpori imprimere; </s>
					<s id="N13948">eo ſcilicet gradu, quem ipſum <lb></lb>habet; </s>
					<s id="N1394E">nec enim inuenio Principium illud apud eos Mechanicos, qui <lb></lb>mechanica momenta ſuarum demonſtrationum momentis confirmant; <lb></lb>quî porro fieri poteſt, vt principium illud admittatur, quod manifeſtæ <lb></lb>experientiæ repugnat? </s>
					<s id="N13958">Quis enim non vidit vel maius ſaxum in aliud <lb></lb>etiam tardo motu impactum maiorem motum, &amp; impetum imprimere? </s>
					<s id="N1395D"><lb></lb>quis non vidit maiores illas onerarias naues etiam pigro, &amp; tardo motu <lb></lb>labentes maximum impetum minori occurrenti cymbæ etiam impri­<lb></lb>mere? </s>
					<s id="N13965">Rationem habes in Th. 47. ſed dices; </s>
					<s id="N13969">igitur aliquis velocitatis <lb></lb>gradus nullam habet cauſam; igitur eſt à nihilo, quod dici non poteſt. </s>
					<s id="N1396F"><lb></lb>Reſpondeo, plures partes impetus non produci in minore globo, quàm <lb></lb>ſint in maiore; </s>
					<s id="N13976">igitur nulla pars eſt impetus minoris globi, quæ ſui <lb></lb>cauſam ſufficientem non habeat; </s>
					<s id="N1397C">ſed cum partes impetus maioris globi <lb></lb>diſtribuantur pluribus partibus ſubiecti, faciunt remiſſum impetum, igi­<lb></lb>tur &amp; tardum; </s>
					<s id="N13984">cum ſcilicet impetus vnius partis non iuuet motum alte­<lb></lb>rius per Th. 37. at verò cum partes impetus producti in minore globo <lb></lb>diſtribuantur paucioribus partibus ſubiecti, faciunt intenſiorem im­<lb></lb>petum; igitur velociorem motum, quippe omnes producuntur ab <lb></lb>omnibus illis actione communi per Ax. 17. num. </s>
					<s id="N13990">1. quid clarius. </s>
				</p>
				<p id="N13993" type="main">
					<s id="N13995"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N139A1" type="main">
					<s id="N139A3"><emph type="italics"></emph>Globus minor imprimit maiori remiſſiorem impetum &amp; tardiorem motum <lb></lb>&amp; æqualis, æquali æqualem<emph.end type="italics"></emph.end>; hæc omnia probantur per Th. 60. &amp; præ-, <lb></lb>cedentia. </s>
				</p>
				<pb pagenum="40" xlink:href="026/01/072.jpg"></pb>
				<p id="N139B4" type="main">
					<s id="N139B6"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N139C2" type="main">
					<s id="N139C4">Obſeruabis primò, vtrumque globum eſſe eiuſdem materiæ; </s>
					<s id="N139C8">ſi enim <lb></lb>ſint diuerſæ materiæ, ſecùs accidit, quàm diximus; </s>
					<s id="N139CE">ſi v. g. æneus mi­<lb></lb>nor pellatur ab eburneo maiore, maiorem motum hic illi non impri­<lb></lb>met; </s>
					<s id="N139DA">licèt enim ſit maior extenſio eburnei; </s>
					<s id="N139DE">eſt tamen minus pondus; <lb></lb>igitur pauciores partes. </s>
				</p>
				<p id="N139E4" type="main">
					<s id="N139E6">Secundò, eos globos accipiendos eſſe, quorum partes, vel non auo­<lb></lb>lent ab ictu, vel non comprimantur; </s>
					<s id="N139EC">comprimuntur in plumbeis, <lb></lb>æneis, &amp; auolant in vitreis; cum enim ſit compreſſio, vel partium di­<lb></lb>uiſio, deſtruitur multùm impetus. </s>
				</p>
				<p id="N139F4" type="main">
					<s id="N139F6">Tertiò reiice commentum illorum, qui dicunt corpus illud eſſe ma­<lb></lb>joris velocitatis capax, quod plures habet partes materiæ ſub eadem <lb></lb>quantitate; </s>
					<s id="N139FE">nam ſuppoſita eadem reſiſtentiæ ratione, omne corpus eſt <lb></lb>capax illius velocitatis, cuius aliud eſt capax; </s>
					<s id="N13A04">cum nullus ſit motus, quo <lb></lb>non poſſit dari velocior, &amp; tardior, vt dicemus infrà; </s>
					<s id="N13A0A">immò ſit glo­<lb></lb>bus plumbeus 12. librarum, ſit eburneus eiuſdem diametri 2. librarum, <lb></lb>v. g. haud dubiè eadem potentia producet intenſiorem impetum in <lb></lb>eburneo, vt patet experientia, &amp; ratio conſtat ex dictis; </s>
					<s id="N13A18">quaſi verò ſit <lb></lb>aliqua materiæ inertia, quæ motum reſpuat; </s>
					<s id="N13A1E">licèt fortè maior ſit pro­<lb></lb>portio reſiſtentiæ medij comparatæ cum globo eburneo, quàm compa­<lb></lb>ratæ cum plumbeo; ſed de reſiſtentia de percuſſione, &amp; de ſpatio age­<lb></lb>mus infra. </s>
				</p>
				<p id="N13A28" type="main">
					<s id="N13A2A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13A36" type="main">
					<s id="N13A38"><emph type="italics"></emph>Omnis globus, qui in alium, qui mouetur impingitur, dum hic mouetur, ve­<lb></lb>lociùs mouetur eo &amp;c. </s>
					<s id="N13A3F">in quem impingitur <emph.end type="italics"></emph.end> patet; alioquin numquam aſſequi <lb></lb>poſſet, quod ex ipſis terminis conſtat. </s>
				</p>
				<p id="N13A48" type="main">
					<s id="N13A4A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13A56" type="main">
					<s id="N13A58"><emph type="italics"></emph>Ex hac hypotheſi globus impactus producit in alie nouas partes impetus<emph.end type="italics"></emph.end>; <lb></lb>quia impeditur eius motus, igitur vt tollat impedimentum, agit ad <lb></lb>extra per Th. 44. </s>
				</p>
				<p id="N13A65" type="main">
					<s id="N13A67"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13A73" type="main">
					<s id="N13A75"><emph type="italics"></emph>Hic impetus nouus productus minor eſt eo qui produceretur in eodem globo <lb></lb>immobili<emph.end type="italics"></emph.end>: ratio eſt; </s>
					<s id="N13A80">quia ſi ſiſteret, maius eſſet impedimentum, quia <lb></lb>totum motum impediret, cuius tantùm partem impedit, dum mouetur , <lb></lb>licèt paulò tardius; igitur minus agit ad extra per Th. 49. </s>
				</p>
				<p id="N13A88" type="main">
					<s id="N13A8A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13A96" type="main">
					<s id="N13A98"><emph type="italics"></emph>Mobile adhærens alteri mobili à tergo; dum vtrumque æque velociter <lb></lb>feratur nullum producit in eo impetum.<emph.end type="italics"></emph.end></s>
					<s id="N13AA2"> Probatur, quia mobile quod præit, <lb></lb>non impedit motum ſubſequentis; igitur nullum impetum ab eo acci<lb></lb>pit per Th. 48. </s>
				</p>
				<pb pagenum="41" xlink:href="026/01/073.jpg"></pb>
				<p id="N13AAE" type="main">
					<s id="N13AB0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13ABC" type="main">
					<s id="N13ABE"><emph type="italics"></emph>Hinc paradoxon egregium ſi quod aliud; </s>
					<s id="N13AC4">globus percuſſus ab alio eadem <lb></lb>ſemper velocitate mouetur, ſiue moueretur inſtanti percuſſionis, ſiue ſi­<lb></lb>ſteret.<emph.end type="italics"></emph.end> v. g. ſit globus A quieſcens, cui imprimantur ab alio B 40. gra­<lb></lb>dus velocitatis: id eſt æqualis impetus impetui percutientis, iam verò <lb></lb>moueatur A, cum 20. grad. velocitatis, &amp; B, qui mouetur cum 40. <lb></lb>impingatur, certè cum impediatur tantùm ſubduplum motus, produce­<lb></lb>tur tantùm ſubduplum impetus, id eſt 20. qui ſi addantur 20. grad. erunt <lb></lb>40. quæ omnia conſtant per Th.49.48.&amp;c. </s>
				</p>
				<p id="N13AE1" type="main">
					<s id="N13AE3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13AF0" type="main">
					<s id="N13AF2">Hinc æquale ſemper ſpatium percuſſus globus conficit, ſiue ante per­<lb></lb>cuſſionem moueretur, ſiue quieſceret. </s>
				</p>
				<p id="N13AF7" type="main">
					<s id="N13AF9"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13B06" type="main">
					<s id="N13B08">Hinc ſi ſecundò percutiatur idem globus, ſpatium totum, quod per­<lb></lb>currit tùm à primò, tùm à ſecundo ictu eſt maius eo, quod à primo ictu <lb></lb>confeciſſet, ſi non fuiſſet ſecundò percuſſus; maius inquam ſegmento ſpa­<lb></lb>tij interiecto inter primum &amp; ſecundum ictum. </s>
				</p>
				<p id="N13B12" type="main">
					<s id="N13B14"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13B21" type="main">
					<s id="N13B23">Hinc reiicies aliquos, quorum ſententiam habes apud Doctum Mer­<lb></lb>ſennium, <emph type="italics"></emph>in prop.<emph.end type="italics"></emph.end> 20. <emph type="italics"></emph>phæn. mech. quorum ſunt hæc verba; </s>
					<s id="N13B32">ſi malleus pilam <lb></lb>currentem eodem, ac anteà modo percutiat, nonam ſui motus partem; ſi verò <lb></lb>currentem tertia vice percutiat, vnam vigeſimam ſeptimam ſui motus par­<lb></lb>tem ei tribuet, atque ita deinceps.<emph.end type="italics"></emph.end></s>
					<s id="N13B3E"> Supponit primò hæc ſententia mal­<lb></lb>leum eſſe duplum pilæ percuſſæ. </s>
					<s id="N13B43">Secundò, malleum imprimere pilæ ſub­<lb></lb>duplæ ſubtriplum motum; quod falſum eſt, vt conſtat ex Th 6. &amp; Co­<lb></lb>roll. </s>
					<s id="N13B4B">1. Præterea, licètin primà percuſſione imprimeret tantùm prædi­<lb></lb>ctæ pilæ ſubtriplum impetum, in ſecunda percuſſione maiorem impri­<lb></lb>meret poſt longiorem motum, vbi iam ad quietem propiùs accedit; </s>
					<s id="N13B53">mi­<lb></lb>norem verò paulò poſt initium motus, vt conſtat ex dictis, &amp; ex ipſa ex­<lb></lb>perientia; </s>
					<s id="N13B5B">poteſt quidem in aliquo puncto ſui motus ſecunda vice per­<lb></lb>cuti, in quo ſubtriplum tantùm motum imprimet; </s>
					<s id="N13B61">hoc eſt eo inſtanti­<lb></lb>quo tantùm amiſit tertiam fui impetus partem; </s>
					<s id="N13B67">tum deinde in tertia <lb></lb>percuſſione poteſt tantùm (1/27) motus partem illi tribuere; </s>
					<s id="N13B6D">eo ſcilicet in­<lb></lb>ſtanti, quo tantùm amiſit (1/27) ſui impetus partem; </s>
					<s id="N13B73">ſed in alijs temporis <lb></lb>punctis longè alia erit impetus producti ratio; Igitur tota hæc progreſ­<lb></lb>ſio gratis omninò fuit excogitata. </s>
				</p>
				<p id="N13B7B" type="main">
					<s id="N13B7D"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13B8A" type="main">
					<s id="N13B8C">Hinc etiam poſt ſecundam percuſſionem æquale ſpatium conficiet al­<lb></lb>teri, quod iam confecit poſt primam æqualibus temporibus; </s>
					<s id="N13B92">igitur æqua­<lb></lb>lis eſt velocitas vtriuſque motus; </s>
					<s id="N13B98">quia ſcilicet, ſi eſt æqualis impetus, eſt <lb></lb>qualis motus: Ex his maximam carum dubitationum partem ſoluere po­<lb></lb>teris quæ in eadem Merſenni propoſitione courinentur reliquas vero ex <lb></lb>dicendis infrà. </s>
				</p>
				<pb pagenum="42" xlink:href="026/01/074.jpg"></pb>
				<p id="N13BA6" type="main">
					<s id="N13BA8"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13BB5" type="main">
					<s id="N13BB7">Ex dictis etiam colliges diuerſas percuſſionum rationes ſuppoſita di­<lb></lb>uerſa ratione ponderum globi percutientis, &amp; percuſſi; </s>
					<s id="N13BBD">cum enim impe­<lb></lb>tus productus ſit æqualis per ſe impetui producenti, per Th.60. modò <lb></lb>debita fiat applicatio, de qua in Th.50. ſi percutiens ſit duplus percuſſi, <lb></lb>ſuppoſita eadem materia, motus percuſſi erit duplò velocior; quia im­<lb></lb>petus erit duplò intenſior, vt conſtat ex Th. 61. ſi verò ſit quadruplus, <lb></lb>quadruplo, &amp;c. </s>
					<s id="N13BCB">Igitur velocitates motuum ſunt in ratiòne ponderum <lb></lb>permutando. </s>
				</p>
				<p id="N13BD0" type="main">
					<s id="N13BD2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13BDE" type="main">
					<s id="N13BE0"><emph type="italics"></emph>Si corpus percuſſum ſit oblongum, &amp; percuſſio fiat in centro grauitatis eiuſ­<lb></lb>dem corporis; </s>
					<s id="N13BE8">producitur impetus in percuſſio æqualis impetui percutientis<emph.end type="italics"></emph.end>; </s>
					<s id="N13BEF">ſed <lb></lb>opus eſt aliqua figura: </s>
					<s id="N13BF5">Sit corpus AD, parallelipedum; </s>
					<s id="N13BF9">diuidatur æqua­<lb></lb>liter in E ita vt E ſit centrum grauitatis; </s>
					<s id="N13BFF">ſi percuſſio fiatin E per lineam <lb></lb>perpendicularem HE, producetur impetus in corpore AD æqualis im­<lb></lb>petui corporis percutientis; </s>
					<s id="N13C07">quia ſcilicet à corpore AD non poteſt maius <lb></lb>eſſe impedimentum; igitur agit quantùm poteſt impetus corporis per­<lb></lb>cutientis per Th.50. igitur producit æqualem per Th.69. </s>
				</p>
				<p id="N13C0F" type="main">
					<s id="N13C11"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13C1D" type="main">
					<s id="N13C1F"><emph type="italics"></emph>Si percuſſio fiat in<emph.end type="italics"></emph.end> F <emph type="italics"></emph>per lineam perpendicularem<emph.end type="italics"></emph.end> IF, <emph type="italics"></emph>minus erit impedi­<lb></lb>mentum, quàm per<emph.end type="italics"></emph.end> HE, Quia ſi per HE, moueri tantùm poteſt motu <lb></lb>recto, ſi per IF, etiam motu circulari circa aliquod centrum; </s>
					<s id="N13C38">ſed hic <lb></lb>motus eſt facilior quam ille; </s>
					<s id="N13C3E">igitur minus eſt impedimentum; </s>
					<s id="N13C42">(ſuppono <lb></lb>autem cylindrum BC vtroque modo moueri poſſe ab applicata potentia) <lb></lb>igitur minùs impetus producitur, ſi percuſſio fiat per IF, quàm ſi fiat <lb></lb>per LK: </s>
					<s id="N13C4C">In qua verò proportione ſit minus impedimentum, &amp; minori <lb></lb>opus impetu, poſito eodem potentiæ niſu, determinabimus facilè aliàs; <lb></lb>vt etiam demonſtrabimus circa quod centrum hic circularis motus fieri <lb></lb>debeat. </s>
				</p>
				<p id="N13C56" type="main">
					<s id="N13C58"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13C64" type="main">
					<s id="N13C66">Ex duobus capitibus minus eſſe poteſt impedimentum; </s>
					<s id="N13C6A">primum eſt, <lb></lb>quod petitur à puncto contactus, ſecundum à linea incidentiæ; </s>
					<s id="N13C70">v. g. ſi <lb></lb>accipiatur punctum E, in quo eſt centrum grauitatis corporis AD, &amp; in <lb></lb>eo fiat percuſſio; </s>
					<s id="N13C7C">maximum eſt impedimentum ratione puncti conta­<lb></lb>ctus, in quo fit percuſſio; </s>
					<s id="N13C82">ſi verò percuſſio fiat per lineam perpendicu­<lb></lb>larem HE, maximum eſt impedimentum, ratione lineæ; </s>
					<s id="N13C88">ſi autem ex <lb></lb>vtroque capite ſimul accidat impedimentum, maximum eſt omnium; </s>
					<s id="N13C8E"><lb></lb>iam verò ſi accipiatur punctum E, &amp; linea percuſsionis ME; </s>
					<s id="N13C93">minor eſt <lb></lb>percuſsio ratione lineæ non puncti; </s>
					<s id="N13C99">accipiatur punctum N, &amp; linea <lb></lb>percuſsionis MN, minor eſt percuſsio ratione puncti non lineæ, acci­<lb></lb>piatur punctum N, &amp; linea IN, minor eſt percuſsio ratione vtriuſque; </s>
					<s id="N13CA1"><lb></lb>ſi demum accipiatur punctum E, &amp; linea ME, minor eſt percuſsio ra­<pb pagenum="43" xlink:href="026/01/075.jpg"></pb>tione lineæ non puncti; </s>
					<s id="N13CAB">accipiatur punctum N linea percuſſionis MN, <lb></lb>minor eſt percuſſio ratione puncti non lineæ; </s>
					<s id="N13CB1">ſi accipiatur punctum N, <lb></lb>&amp; linea IN, minor eſt percuſſio ratione vtriuſque: </s>
					<s id="N13CB7">ſi demum accipia­<lb></lb>tur punctum E &amp; linea HE, maior eſt percuſſio ratione vtriuſque; </s>
					<s id="N13CBD">igi­<lb></lb>tur ſunt quatuor coniugationes; ſeu quatuor claſſes diuerſarum percuſ­<lb></lb>ſionum. </s>
				</p>
				<p id="N13CC5" type="main">
					<s id="N13CC7">Hinc compenſari poteſt ratione vnius quod deeſt ratione alterius, <lb></lb>v. g. ſi fiat percuſſio in puncto E per lineam ME, poteſt ſciri punctum <lb></lb>inter ED, in quo percuſſio per lineam perpendicularem ſit æqualis <lb></lb>percuſſioni per lineam ME; ſed de his infrà in lib.  10. cum de percuſ­<lb></lb>ſione, determinabimus enim vnde proportiones iſtæ petendæ ſint, &amp; <lb></lb>demonſtrabimus totam iſtam rem, quæ multùm curioſitatis habet, &amp; <lb></lb>vtilitatis. </s>
				</p>
				<p id="N13CDD" type="main">
					<s id="N13CDF">Determinabimus etiam dato puncto percuſſionis F v.g. cum ſequatur <lb></lb>motus vectis, quodnam ſit centrum vectis ſeu huius motus. </s>
				</p>
				<p id="N13CE6" type="main">
					<s id="N13CE8">Hinc demum ſequitur, ne hoc omittam, data minimâ percuſſione per <lb></lb>lineam MN dari poſſe adhuc minorem per lineam IN, &amp; alias incli­<lb></lb>natas; </s>
					<s id="N13CF0">&amp; data percuſſione per lineam quantumuis inclinatam, poſſe da­<lb></lb>ri æqualem per lineam perpendicularem; </s>
					<s id="N13CF6">&amp; data per lineam perpendi­<lb></lb>cularem extra centrum grauitatis E, poſſe dari æqualem; &amp; in qualibet <lb></lb>data ratione per aliquam inclinatam, quæ cadat in E, ſed de his fusè <lb></lb>ſuo loco. </s>
				</p>
				<p id="N13D00" type="main">
					<s id="N13D02"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13D0E" type="main">
					<s id="N13D10"><emph type="italics"></emph>Corpus oblongum parallelipedum percutiens aliud corpus, putà globum̨, <lb></lb>motu recto per lineam directionis, quæ producta à puncto contactus ducitur per <lb></lb>centrum globi, dum fiat contactus in centro grauitatis parallelipedi, maximum <lb></lb>ictum infligit, ſeu agit quantùm poteſt.<emph.end type="italics"></emph.end> v. g. ſit parallelipedum EB; quod <lb></lb>moueatur motu recto parallelo, lineis CD, HG, &amp;c. </s>
					<s id="N13D25">ſitque globus in <lb></lb>D; </s>
					<s id="N13D2B">haud dubiè agit quantùm poteſt, quia ſcilicet eſt maximum impedi­<lb></lb>mentum per Th.68. Tam enim globus in D impedit motum paralleli­<lb></lb>pedi, quàm parallelipedum motum globi impacti per lineam ID; </s>
					<s id="N13D33">impedit <lb></lb>inquam ratione oppoſitionis; </s>
					<s id="N13D39">quia centra grauitatis vtriuſque con­<lb></lb>currunt in eadem linea; igitur ſi maximum eſt impedimentum, agit <lb></lb>quantùm poteſt Th. 50. hinc producitur impetus æqualis per Th.60. </s>
				</p>
				<p id="N13D41" type="main">
					<s id="N13D43"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13D4F" type="main">
					<s id="N13D51"><emph type="italics"></emph>Si percuſſio fiat in G, id eſt ſi globus eſſet in G, producetur minor impetus, <lb></lb>&amp; in<emph.end type="italics"></emph.end> M <emph type="italics"></emph>adhuc minor<emph.end type="italics"></emph.end>; </s>
					<s id="N13D62">vt conſtat ex dictis in ſuperioribus Theorematis; <lb></lb>in qua vero proportione determinabimus aliàs. </s>
				</p>
				<p id="N13D68" type="main">
					<s id="N13D6A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13D76" type="main">
					<s id="N13D78"><emph type="italics"></emph>Si corpus percutiens non ſit parallelipedum, ſed alterius figuræ v.g.<emph.end type="italics"></emph.end> <emph type="italics"></emph>trigo­<lb></lb>non,<emph.end type="italics"></emph.end> ADE, ſitque maioris facilitatis gratia Orthonium; </s>
					<s id="N13D89">eiuſque motus <lb></lb>ſit parallelus lineis ED, BC: </s>
					<s id="N13D8F">ſit autem DA dupla DE; </s>
					<s id="N13D93">ſitque diuiſa to­<lb></lb>ta DA æqualiter in C, in C non erit maximus ictus; </s>
					<s id="N13D99">quia in C non <pb pagenum="44" xlink:href="026/01/076.jpg"></pb>eſt centrum grauitatis, vt patet; </s>
					<s id="N13DA2">vt autem habeatur centrum impreſſio­<lb></lb>nis; </s>
					<s id="N13DA8">aſſumatur AN media proportionalis inter totam AD, &amp; ſubdu­<lb></lb>plum AC; </s>
					<s id="N13DAE">certè cum triangulum ANO ſit ſubduplum totius ADE, <lb></lb>vt conſtat ex Geometria, &amp; æquale trapezo ND EO; </s>
					<s id="N13DB4">erit impetus in <lb></lb>vtroque æqualis; </s>
					<s id="N13DBA">igitur in N erit centrum impreſſionis, vel impetus; </s>
					<s id="N13DBE">vt <lb></lb>autem habeatur centrum percuſſionis; </s>
					<s id="N13DC4">in quo ſcilicet maximus ictus in­<lb></lb>fligitur, inueniatur centrum grauitatis H, ducaturque KHI parallela <lb></lb>DE, centrum percuſſionis erit in I; </s>
					<s id="N13DCC">quippe in I totus impeditur impetus <lb></lb>grauitatis vtrimque, cum ſit in æquilibrio; </s>
					<s id="N13DD2">quomodo verò inueniatur <lb></lb>punctum H facilè habetur ex Archimede, ductis ſcilicet AF, DB, quæ <lb></lb>diuidant bifariam æqualiter DE, EA; vel aſſumpta AI dupla ID, quod <lb></lb>demonſtrabimus in Mechan. </s>
				</p>
				<p id="N13DDD" type="main">
					<s id="N13DDF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13DEB" type="main">
					<s id="N13DED"><emph type="italics"></emph>Si circa centrum immobile rotetur corpus parallelipedum<emph.end type="italics"></emph.end> CA, <emph type="italics"></emph>diuerſa eſt <lb></lb>ratio percuſſionum ab ea, quàm ſuprà propoſuimus<emph.end type="italics"></emph.end>; </s>
					<s id="N13DFE">moueatur  enim circa <lb></lb>centrum C, fitque CA diuiſa bifariam in B, haud dubiè punctum A <lb></lb>faciet arcum AE eo tempore, quò punctum B faciet BD ſubduplum <lb></lb>AE; </s>
					<s id="N13E08">igitur punctum A duplò velociùs mouetur quàm B, vt conſtat; </s>
					<s id="N13E0C">igi­<lb></lb>tur habet duplò maiorem impetum; cum effectum habeat duplò maio­<lb></lb>rem per Ax. 13. n. </s>
					<s id="N13E14">4. igitur cum totus motus ſegmenti AB ſit ad to­<lb></lb>tum motum ſegmenti BC, vt ſpatia acquiſita; </s>
					<s id="N13E1A">certè ſpatia acquiſita <lb></lb>ſunt vt arcus; </s>
					<s id="N13E20">igitur &amp; trapezus BAED, continet 3/4 totius CAE, vt <lb></lb>conſtat; </s>
					<s id="N13E26">ſunt enim ſectores ſimilis in ratione duplicata radiorum; </s>
					<s id="N13E2A">igi­<lb></lb>tur totus motus ſegmenti BC ſubquadruplus motus totius CA; igitur <lb></lb>&amp; impetus; </s>
					<s id="N13E32">vt autem habeatur centrum impreſſionis, vel impetus; </s>
					<s id="N13E36">ſit ſe­<lb></lb>ctor CHI, ſubduplus totius CAE quod quomodo fiat, patet ex Geo­<lb></lb>metria; </s>
					<s id="N13E3E">accipiatur tantùm ſubdupla diagonalis quadrati lateris CA, igi­<lb></lb>tur in puncto H eſt centrum impreſſionis, ſeu media proportionalis in­<lb></lb>ter totam CA, &amp; ſubduplam CB: </s>
					<s id="N13E46">vt autem habeatur percuſſionis, aſ­<lb></lb>ſumatur CY dupla YA; </s>
					<s id="N13E4C">Dico punctum Y eſſe centrum percuſſionis; <lb></lb>quia perinde ſe habet, atque ſi eſſet trianguli cadentis ictus, vt demon­<lb></lb>ſtrabimus aliàs nunc tantùm indicaſſe ſufficiat. </s>
				</p>
				<p id="N13E54" type="main">
					<s id="N13E56"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13E63" type="main">
					<s id="N13E65">Hinc etiam ſoluetur, quod proponunt aliqui; ſeu potiùs quærunt; </s>
					<s id="N13E69"><lb></lb>in quà ſcilicet parte maiorem ictum infligat enſis; </s>
					<s id="N13E6E">ſi enim ſit eiuſdem <lb></lb>craſſitiei in omnibus ſuis partibus, idem dicendum eſt quod de cylin­<lb></lb>dro CA; ſi verò in mucronem deſinat, inueniemus etiam centrum <lb></lb>percuſſionis. </s>
				</p>
				<p id="N13E78" type="main">
					<s id="N13E7A"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13E87" type="main">
					<s id="N13E89">Huc etiam reuoca clauarum ictus, vel aliorum corporum, quæ ad in­<lb></lb>ſtar ſeu conorum, ſeu pyramidum verſus mucronem maiora ſunt, vel <lb></lb>denſiora; quippe ex iacto ſuprà principio iſtorum omnium effectuum <lb></lb>rationes demonſtrabimus. </s>
				</p>
				<pb pagenum="45" xlink:href="026/01/077.jpg"></pb>
				<p id="N13E97" type="main">
					<s id="N13E99"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13EA6" type="main">
					<s id="N13EA8">Colligemus etiam quid dicendum ſit de malleorum ictu; </s>
					<s id="N13EAC">ſit enim <lb></lb>malleus F æqualis malleo G (in his vna fere manubrij longitudinis ha­<lb></lb>betur ratio) ducatur arcus NM, itemque OG; </s>
					<s id="N13EB4">ictus mallei G eſt ferè <lb></lb>ſubduplus alterius, dum vterque malleus ſit æqualis; </s>
					<s id="N13EBA">dixi ferè, quia <lb></lb>motus totius mallei G non eſt omninò ſubduplus motus mallei F, quia <lb></lb>ſcilicet trapezus OD eſt minor ſubduplo alterius NE; </s>
					<s id="N13EC2">quotâ vero parte <lb></lb>ſit minor facilè poteſt ſciri opera Geometriæ: ſed hæc omnia determi­<lb></lb>nabimus. </s>
				</p>
				<p id="N13ECA" type="main">
					<s id="N13ECC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13ED8" type="main">
					<s id="N13EDA"><emph type="italics"></emph>Si daretur potentia motrix, quæ ſemper agere poſſet, impetus poſſet intendi <lb></lb>in infinitum<emph.end type="italics"></emph.end>; </s>
					<s id="N13EE5">pater, quia quocumque dato motu poteſt dari velocior in <lb></lb>infinitum; igitur poteſt dari impetus intenſior, &amp; intenſior in infinitum. </s>
				</p>
				<p id="N13EEB" type="main">
					<s id="N13EED"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13EF9" type="main">
					<s id="N13EFB">Hîc obſerua nouum diſcrimen, quod intercedit inter impetum, &amp; <lb></lb>alias qualitates; </s>
					<s id="N13F01">quæ fortè non poſſunt intendi in infinitum, ratio diſ­<lb></lb>criminis eſt, quia totus calor extenſus in maiore ſubiecto non poteſt <lb></lb>produci in minore, in quo eadem cauſa eumdem ſemper effectum pro­<lb></lb>ducit; </s>
					<s id="N13F0B">quia ſcilicet agit vniformiter difformiter; at verò impetus exten­<lb></lb>ſus in magno <expan abbr="denſoq́ue">denſoque</expan> malleo poteſt producere æqualem in maximâ <lb></lb>ferè pilâ. </s>
				</p>
				<p id="N13F17" type="main">
					<s id="N13F19"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 75.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13F25" type="main">
					<s id="N13F27"><emph type="italics"></emph>Impetus ſimilis, id eſt, ad <expan abbr="eãdem">eandem</expan> lineam determinatus, &amp; æqualis in in­<lb></lb>tenſione, non poteſt intendere alium ſimilem<emph.end type="italics"></emph.end>; </s>
					<s id="N13F36">Probatur, quia agit tantùm ad <lb></lb>extra, vt tollat impedimentum per Th. 44. ſed eorum mobilium, quæ <lb></lb>verſus <expan abbr="eãdem">eandem</expan> partem pari velocitate mouentur, neutrum impedit al­<lb></lb>terius motum, vt conſtat; igitur impetus ſimilis, &amp;c. </s>
				</p>
				<p id="N13F44" type="main">
					<s id="N13F46"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13F52" type="main">
					<s id="N13F54">Obſerua de impetu ſimili id tantùm dici; </s>
					<s id="N13F58">ſimili inquam id eſt non <lb></lb>modò eiuſdem intenſionis; </s>
					<s id="N13F5E">ſed etiam eiuſdem lineæ: </s>
					<s id="N13F62">ſi enim alterum <lb></lb>deſit, haud dubiè ſimilis impetus non eſt; </s>
					<s id="N13F68">ſic impetus quatuor grad. in­<lb></lb>tendere poteſt impetum duorum graduum; </s>
					<s id="N13F70">licèt vterque ad <expan abbr="eãdem">eandem</expan> li­<lb></lb>neam ſit determinatus; </s>
					<s id="N13F7A">ſi verò ad diuerſas lineas determinentur; etiam <lb></lb>impetus vt duo poteſt intendere impetum vt quatuor. </s>
				</p>
				<p id="N13F80" type="main">
					<s id="N13F82">Obſeruabis præterea hoc Theorema ita eſſe intelligendum, vt impe­<lb></lb>tus mobilis præeuntis nullo modo impediatur; alioquin mobile ſucce­<lb></lb>dens omninò aliud vrgeret, vt conſtat. </s>
				</p>
				<p id="N13F8A" type="main">
					<s id="N13F8C"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13F98" type="main">
					<s id="N13F9A">Hinc ſimile poteſt in aliquo caſu agere in ſimile; </s>
					<s id="N13F9E">vnde rectè colligo <lb></lb>id tantùm dictum eſſe ab Ariſtotele de qualitatibus alteratiuis; </s>
					<s id="N13FA4">quid <lb></lb>verò accidat, cum mobile graue mobili alteri ſuperponitur; dicemus <lb></lb>infrà. </s>
				</p>
				<pb pagenum="46" xlink:href="026/01/078.jpg"></pb>
				<p id="N13FB0" type="main">
					<s id="N13FB2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N13FBE" type="main">
					<s id="N13FC0"><emph type="italics"></emph>Extenſio impetus respondet extentioni ſui ſubiecti, ſcilicet mobilis<emph.end type="italics"></emph.end>; </s>
					<s id="N13FC9">cum <lb></lb>enim extra ſubjectum eſſe non poſſit, cum ſit qualitas; </s>
					<s id="N13FCF">certè ibi eſt, vbi <lb></lb>ſubjectum eſt; nam penetratur accidens cum ipſo <expan abbr="ſujecto">ſubjecto</expan>. </s>
				</p>
				<p id="N13FD9" type="main">
					<s id="N13FDB"><emph type="center"></emph><emph type="italics"></emph>Scolium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N13FE7" type="main">
					<s id="N13FE9">Obſeruabis qualitatem omnem ita ſuo ſubjecto coëxtendi, vt æqua­<lb></lb>lem omnino quodlibet eius punctum, ſeu pars extentionem habeat ex­<lb></lb>tentioni puncti, ſeu partis ſui ſubjecti; </s>
					<s id="N13FF1">nec enim aliud eſt, vnde poſſit <lb></lb>determinari extentio qualitatum, præter ipſam extenſionem ſubjecti; </s>
					<s id="N13FF7"><lb></lb>quod maximè in impetu videre eſt, cuius partes in mobili denſo minori <lb></lb>extentioni ſubjacent, quàm in mobili raro; </s>
					<s id="N13FFE">cum ex maiore ictu ſeu per­<lb></lb>cuſſione in mobili denſo plures impetus agentis partes eſſe conſtet; quia <lb></lb>ſcilicet ſunt plures partes ſubiecti. </s>
				</p>
				<p id="N14006" type="main">
					<s id="N14008"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14014" type="main">
					<s id="N14016"><emph type="italics"></emph>Datur impetus altero impetu perfectior ſecundum entitatem<emph.end type="italics"></emph.end>; dixi ſecun­<lb></lb>dum entitatem; </s>
					<s id="N14021">quia iam dictum eſt ſuprà dari perfectiorem ſecundum <lb></lb>intenſionem; </s>
					<s id="N14027">huius Theorematis veritas mihi maximè demonſtranda <lb></lb>eſt, ex quo tàm multa infrà deducemus; </s>
					<s id="N1402D">ſic autem probamus; </s>
					<s id="N14031">Quotieſ­<lb></lb>cunque mouetur corpus, producuntur ſaltem tot partes impetus quot <lb></lb>ſunt partes mobilis per Th. 33. Quotieſcunque producuntur in mobili <lb></lb>tot partes impetus quot ſunt in mobili partes ſubjecti, mouetur mobile, <lb></lb>modó non impediatur; </s>
					<s id="N1403D">quia poſita cauſa neceſſaria, &amp; non impedita per <lb></lb>Ax. 11. ponitur effectus, quod de omni cauſa, ſed de formali potiſſimum <lb></lb>dici debet; </s>
					<s id="N14045">præterea datur aliquod pondus, quod data potentia ſine me­<lb></lb>chanico organo mouere non poteſt, licèt cum organo facilè moueat; </s>
					<s id="N1404B">hæc <lb></lb>hypotheſis certa eſt; </s>
					<s id="N14051">igitur cum mouet, producit tot partes impetus quot <lb></lb>ſunt neceſſariæ, vt omnibus partibus mobilis diſtribuantur per idem Th. <lb></lb>33. cum verò non mouet, non producit tot partes impetus vt conſtat ex <lb></lb>dictis; </s>
					<s id="N1405C">igitur producit plures cum organo in mobili, quàm ſine organo; <lb></lb>igitur imperfectiores, quod demonſtro: </s>
					<s id="N14062">ſit enim vectis BF, cuius cen­<lb></lb>trum ſeu fulcrum ſit in A, potentia in B, pondus G, quod attollitur in F; </s>
					<s id="N14068"><lb></lb>plures partes impetus produci poſſunt in F, vel in E, quàm in B, ſcilicet <lb></lb>in ipſo pondere; </s>
					<s id="N1406F">quia pondus quod non poteſt attolli in B, attollitur in <lb></lb>E, vel in F, vt patet ex dictis; </s>
					<s id="N14075">præterea punctum F mouetur tardius, quàm <lb></lb>B; </s>
					<s id="N1407B">quia motus ſunt vt arcus, arcus vt ſemidiametri, hæ demum vt AF, <lb></lb>ad AB; </s>
					<s id="N14081">igitur motus puncti F, eſt tardior, vel imperfectior; </s>
					<s id="N14085">igitur im­<lb></lb>petus puncti F, eſt imperfectior impetu puncti B, per Ax. 13 num.4. atqui <lb></lb>non eſt imperfectior ratione numeri partium, igitur ratione entitatis, <lb></lb>quæ imperfectior eſt; igitur datur impetus altero impetu imperfectior. </s>
				</p>
				<p id="N1408F" type="main">
					<s id="N14091"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1409D" type="main">
					<s id="N1409F">Obſeruabis primò multa hîc ſupponi ſeu deſiderari, quæ pertinent <lb></lb>ad propagationem impetus, de quibus infrà; Secundò hoc Theorema <pb pagenum="47" xlink:href="026/01/079.jpg"></pb>per Axioma illud Metaph.  probari, <emph type="italics"></emph>Data quacumque creatura dari potest <lb></lb>perfectior, vel imperfectior.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N140B1" type="main">
					<s id="N140B3">Tertiò, ſi dato quocunque motu poteſt dari tardior: igitur dato quo­<lb></lb>cunque impetu poteſt dari imperfectior. </s>
				</p>
				<p id="N140B9" type="main">
					<s id="N140BB">Quartò, ſi daretur punctum impetus in intenſione: non poſſet dari <lb></lb>motus tardior in infinitum ſine diuerſis gradibus perfectionis. </s>
				</p>
				<p id="N140C1" type="main">
					<s id="N140C3">Quintò, ſine hac diuerſa impetus perfectione non poſſet explicari <lb></lb>productio continua impetus, quæ ſit temporibus inæqualibus, neque de­<lb></lb>ſtructio eiuſdem impetus; nec motus in diuerſis planis inclinatis, vel in­<lb></lb>diuerſis lineis citra perpendicularem, ſed de his omnibus ſuo loco. </s>
				</p>
				<p id="N140CD" type="main">
					<s id="N140CF">Sextò, Denique ratio propoſita rem iſtam euincit; </s>
					<s id="N140D3">cum enim in motu <lb></lb>vectis plures partes producantur verſus centrum, ſcilicet, in maiori pon­<lb></lb>dere, quod attollitur; &amp; cum hæ habeant motum tardiorem, ſequitur ne­<lb></lb>ceſſariò eſſe imperfectiores. </s>
				</p>
				<p id="N140DD" type="main">
					<s id="N140DF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N140EB" type="main">
					<s id="N140ED"><emph type="italics"></emph>Dato quocumque impetu dari poteſt imperfectior, &amp; imperfectior,<emph.end type="italics"></emph.end> quia da­<lb></lb>to quocumque motu dari poteſt tardior, ergo dato quocumque impetu <lb></lb>imperfectior. </s>
				</p>
				<p id="N140F9" type="main">
					<s id="N140FB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14107" type="main">
					<s id="N14109"><emph type="italics"></emph>Non poteſt explicari tarditas motus ſine diuerſa perfectione impetus, per <lb></lb>pauciores ſcilicet eiuſdem impetus partes.<emph.end type="italics"></emph.end></s>
					<s id="N14112"> Primò, quia cum retardari poſſit <lb></lb>hic motus, &amp; deſtrui ſucceſſinè hic impetus; </s>
					<s id="N14118">cumque inſtantia motus <lb></lb>velocioris ſint breuiora; </s>
					<s id="N1411E">certè initio motus, breuiori ſcilicet tempore <lb></lb>imperfectior impetus deſtrui tantùm poteſt; </s>
					<s id="N14124">cum enim æqualis æquali­<lb></lb>bus temporibus; certè inæqualis inæqualibus. </s>
					<s id="N1412A">Secundò quia vix explica­<lb></lb>ri poreſt quomodo duæ formæ homogeneæ in eodem ſubiecti puncto <lb></lb>exiſtere poſſint, quod etiam in commune eſt calori, lumini, &amp;c. </s>
				</p>
				<p id="N14131" type="main">
					<s id="N14133"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1413F" type="main">
					<s id="N14141"><emph type="italics"></emph>Cum applicatur potentia centro vectis, non producitur æqualis impetus ver­<lb></lb>ſus circumferentiam in omnibus partibus, ſed maior verſus eandem circumfe­<lb></lb>rentiam,<emph.end type="italics"></emph.end> quia eſt maior motus. </s>
				</p>
				<p id="N1414D" type="main">
					<s id="N1414F"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1415C" type="main">
					<s id="N1415E">Hinc difficiliùs attollitur pertica CA ex puncto C motu circulari, <lb></lb>quàm ex puncto B motu recto; </s>
					<s id="N14164">quia ſcilicet, cum motu recto ex puncto B <lb></lb>attollitur, omnes partes mouentur motu æquali; </s>
					<s id="N1416A">igitur impetus æqualiter <lb></lb>omnibus diſtribuitur; </s>
					<s id="N14170">igitur modò producantur tot partes impetus, quot <lb></lb>ſunt partes in mobili; </s>
					<s id="N14176">haud dubiè attolletur: </s>
					<s id="N1417A">at verò, cum motu circulari <lb></lb>ex puncto C attollitur, omnes partes inæquali motu attolluntur; </s>
					<s id="N14180">igitur <lb></lb>plures ſunt neceſſariæ, vt attollatur motu circulari; </s>
					<s id="N14186">igitur difficiliùs iuxta <lb></lb>experimentum; adde quod cum applicatur potentia in C, punctum A, <lb></lb>maius momentum habet, de quo aùàs. </s>
				</p>
				<p id="N1418E" type="main">
					<s id="N14190"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1419D" type="main">
					<s id="N1419F">Hinc ratio euidens illius experimenti, quo manifeſtè conſtat perti-<pb pagenum="48" xlink:href="026/01/080.jpg"></pb>cam CA, ex A, facilius attolli motu recto, quàm circulari; cum ſci­<lb></lb>licet cuiuſdam quaſi reflexionis opera eodem tempore vtraque extremi­<lb></lb>tas æquali motu attollitur. </s>
				</p>
				<p id="N141AC" type="main">
					<s id="N141AE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N141BA" type="main">
					<s id="N141BC"><arrow.to.target n="note1"></arrow.to.target></s>
				</p>
				<p id="N141C1" type="margin">
					<s id="N141C3"><margin.target id="note1"></margin.target><emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end>7. <lb></lb><emph type="italics"></emph>Tab.<emph.end type="italics"></emph.end>1.</s>
				</p>
				<p id="N141D5" type="main">
					<s id="N141D7"><emph type="italics"></emph>Si verò applicetur potentia extra centrum vectis v. g. in<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>poſito centro in<emph.end type="italics"></emph.end><lb></lb>A, <emph type="italics"></emph>producitur impetus minor ab<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>verſus<emph.end type="italics"></emph.end> A; </s>
					<s id="N141F7"><emph type="italics"></emph>ab verò verſus<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>producitur <lb></lb>eiuſdem perfectionis proportionaliter, cuius eſt ab<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>verſus<emph.end type="italics"></emph.end> A; denique ab E, <lb></lb>verſus B, producitur quidem vnum punctum, vel vnus gradus impetus <lb></lb>eiuſdem perfectionis cum eo, qui productus eſt in F, &amp; in E (ſupponi­<lb></lb>tur enim ex. gr. vnus tantùm gradus in F, &amp; in E, productus) at verò <lb></lb>producuntur alij imperfectiones. </s>
					<s id="N14218">v.g. in D, præter æquè perfectum pro­<lb></lb>ducuntur 3. alij adæquantes perfectionem prioris; </s>
					<s id="N14220">in C verò, præter 4. <lb></lb>ſimiles ijs, qui ſunt in D, producuntur 5. alij adæquantes prioris perfe­<lb></lb>ctionem in B7; atque ita deinceps per numeros impares, &amp; quadrata, <lb></lb>nullus tamen producitur perfectioris entitatis. </s>
				</p>
				<p id="N1422A" type="main">
					<s id="N1422C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14238" type="main">
					<s id="N1423A"><emph type="italics"></emph>Determinatur hæc diuerſa perfectio impetus à diuerſa perfectione motus, <lb></lb>quatenus fit tali modo<emph.end type="italics"></emph.end>; </s>
					<s id="N14245">quæ non poteſt explicari per impetum remiſſio­<lb></lb>rem, vel intenſiorem; </s>
					<s id="N1424B">nam cum ſit tantùm impetus inſtitutus propter <lb></lb>motum; </s>
					<s id="N14251">certè ille tantùm impetus produci poteſt, ex quo poteſt ſequi <lb></lb>motus; </s>
					<s id="N14257">igitur ſi tali tantùm motu data pars mobilis moueri poteſt; haud <lb></lb>dubiè talis tantùm impetus, ex quo ſequitur talis motus, in ea produ­<lb></lb>cetur, &amp; tali modo. </s>
				</p>
				<p id="N1425F" type="main">
					<s id="N14261"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1426D" type="main">
					<s id="N1426F"><emph type="italics"></emph>Perfectio impetus non petitur tantùm à perfectione motus ſi conſideretur <lb></lb>ſeorſim entitas eiuſdem impetus; </s>
					<s id="N14277">ſed debet comparari tota collectio omnium̨ <lb></lb>partium impetus, quæ inſunt datæ parti ſubiecti, cum tota collectione partium <lb></lb>quæ alteri parti mobilis inſunt<emph.end type="italics"></emph.end>; </s>
					<s id="N14282">quippe plures partes impetus poſſunt ha­<lb></lb>bere eum motum, vel potius eam motus perfectionem, quam pauciores <lb></lb>haberent; igitur perfectio illarum eſt ab ipſo motu, quatenus cum ipſo <lb></lb>partium numero comparatur. </s>
				</p>
				<p id="N1428C" type="main">
					<s id="N1428E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1429A" type="main">
					<s id="N1429C"><emph type="italics"></emph>Impetus perfectus producere poteſt imperfectum<emph.end type="italics"></emph.end>; patet in vecte; </s>
					<s id="N142A5">nam po­<lb></lb>tentia, ſen pondus extremitati appenſum producit in ſe impetum, à quo <lb></lb>deinde impetus in toto vecte producitur per Th.42. ſed impetus pon­<lb></lb>deris appenſi eſt eiuſdem perfectionis cum impetu producto in ipſa ve­<lb></lb>ctis extremitate, ex qua pendet; </s>
					<s id="N142B1">cum ſit vtriuſque æqualis motus; ſed <lb></lb>verſus centrum eiuſdem vectis producitur impetus imperfectior per <lb></lb>Th.82. igitur imperfectus à perfecto producitur. </s>
				</p>
				<p id="N142B9" type="main">
					<s id="N142BB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N142C7" type="main">
					<s id="N142C9"><emph type="italics"></emph>Impetus perfectus nunquam producitur ab imperfecto, per Ax.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>num.<emph.end type="italics"></emph.end> 2. <lb></lb>adde quod nunquam effectus perfectio ſuperat perfectionem cauſæ; </s>
					<s id="N142DA">dixi <lb></lb>perfectum ab imperfecto; </s>
					<s id="N142E0">ſcilicet ſi conſideretur perfectio ratione en-<pb pagenum="49" xlink:href="026/01/081.jpg"></pb>titatis; </s>
					<s id="N142E9">cum reuerâ, vt dictum eſt ſuprà, remiſſus producat intenſum, <lb></lb>quod in vecte clariſſimum eſt; </s>
					<s id="N142EF">quippe momentum applicatum in F, quod <lb></lb>tardiùs mouetur deorſum, quàm B, ſurſum, vt patet, habet impetum re­<lb></lb>miſſiorem, qui tamen producit in B, intenſiorem: </s>
					<s id="N142F7">Pro quo, obſeruabis <lb></lb>impetum imperfectum cum alio perfecto actione communi agentem <lb></lb>poſſe concurrere ad producendum perfectum, vt patet; </s>
					<s id="N142FF">non tamen in <lb></lb>ratione cauſæ totalis: </s>
					<s id="N14305">ſimiliter plures imperfecti ſimul concurrentes <lb></lb>poſſunt producere perfectum; quia plures imperfecti conjunctim adæ­<lb></lb>quant perfectionem alterius perfectioris ſinguli ſeorſim. </s>
				</p>
				<p id="N1430D" type="main">
					<s id="N1430F">Obſeruabis ſecundò præclarum naturæ inſtitutum, quo factum eſt; </s>
					<s id="N14313"><lb></lb>vt cum vires hominum maiora pondera leuare non poſſint, ſi ſeorſun <lb></lb>conſiderentur; </s>
					<s id="N1431A">cum organis tamen mechanicis conjunctæ nullum pon­<lb></lb>dus quantumuis immane leuare non poſſint; </s>
					<s id="N14320">quod certè nullo modo ac­<lb></lb>cideret, niſi plures partes impetus producerent neque plures producere <lb></lb>poſſent, niſi minoris perfectionis eſſent; quia faciliùs producitur effe­<lb></lb>ctus imperfectus, quam perfectus per Ax. 13.num.4. </s>
				</p>
				<p id="N1432A" type="main">
					<s id="N1432C">Tertiò hinc optimè à natura prouiſum eſt, vt motus tardior in infi­<lb></lb>nitum eſſe poſſit; quod reuerâ fieri non poſſet, niſi dari poſſet impetus <lb></lb>alio imperfectior. </s>
				</p>
				<p id="N14334" type="main">
					<s id="N14336">Quartò, hinc quoque benè explicatur diuerſitas impetus, quæ oritur <lb></lb>tum à diuerſo medio, tùm à plano inclinato, tùm ab aliis impedimentis, <lb></lb>tùm à diuerſo niſu eiuſdem potentiæ, tùm maximè à diuerſo applicatio­<lb></lb>nis modo; de quibus aliàs. </s>
				</p>
				<p id="N14340" type="main">
					<s id="N14342">Quintò, ſi potentia applicata mobili immediatè illud moueat motu <lb></lb>recto, vel in ſingulis punctis mobilis producitur vnum punctum impe­<lb></lb>tus, vel plura; </s>
					<s id="N1434A">ſi primum, erit primus tantùm gradus maximæ perfectio­<lb></lb>nis; </s>
					<s id="N14350">ita vt perfectiorem producere non poſſit, ad quem eſt determinata <lb></lb>potentia; </s>
					<s id="N14356">imperfectiorem tamen impetu innato, de quo infrà; ſi verò <lb></lb>ſecundum, producet in ſingulis partibus <expan abbr="eũdem">eundem</expan> gradum perfectiſſi­<lb></lb>mum cum aliis pluribus, vel paucioribus heterogeneis, &amp; imperfectio­<lb></lb>ribus. </s>
				</p>
				<p id="N14364" type="main">
					<s id="N14366"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14372" type="main">
					<s id="N14374"><emph type="italics"></emph>Potentia naturalis grauium producit tantùm vno inſtanti ad intra vnicum <lb></lb>punctum impetus in quolibet puncto ſubiecti; </s>
					<s id="N1437C">ſi tamen impetum producit, quod <lb></lb>definiam lib.<emph.end type="italics"></emph.end> 20. <emph type="italics"></emph>&amp; ſi dentur puncta ſubiecti, quod ad præſens inſtitutum non <lb></lb>pertinet<emph.end type="italics"></emph.end>; </s>
					<s id="N1438D">Probatur, quia fruſtrà eſſent plura puncta impetus; nec enim <lb></lb>ſunt multiplicandæ formæ ſine neceſſitate, ratione &amp;c. </s>
					<s id="N14393">per Ax. 7. &amp; 3. <lb></lb>n. </s>
					<s id="N14398">1. Præterea non eſt, cur potius produceret 2. quàm 3. 4. &amp;c. </s>
					<s id="N1439B">atqui <lb></lb>quod vnum eſt, determinatum eſt per Ax. 5. </s>
				</p>
				<p id="N143A1" type="main">
					<s id="N143A3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N143AF" type="main">
					<s id="N143B1"><emph type="italics"></emph>Potentia motrix animantium etiam vno inſtanti plura puncta, ſen partes <lb></lb>impetus in eadem parte ſubiecti producere potest<emph.end type="italics"></emph.end>; </s>
					<s id="N143BC">Probatur in proiectis, <lb></lb>quorum impetus aliquando plùs, aliquando minùs durat licèt ſenſim <lb></lb>ſingulis inſtantibus aliquid illius deſtruatur; </s>
					<s id="N143C4">determinatur autem <pb pagenum="50" xlink:href="026/01/082.jpg"></pb>numerus punctorum, ſeu partium ab ea potentia, cui ſubeſt potentia <lb></lb>motrix; quia modò maior eſt niſus, modò minor. </s>
				</p>
				<p id="N143CF" type="main">
					<s id="N143D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N143DD" type="main">
					<s id="N143DF"><emph type="italics"></emph>Eadem potentia inæqualibus temporibus impetum inæqualem in perfectio­<lb></lb>ne producit<emph.end type="italics"></emph.end>; </s>
					<s id="N143EA">accipiatur enim totum illud tempus, quo vnicum tantùm <lb></lb>punctum impetus producit (vocetur inſtans) de quo in Th. 86; certè <lb></lb>ſi in minori tempore agat, minùs aget, per Ax. 13. num. </s>
					<s id="N143F2">4. ſed non <lb></lb>poteſt minùs agere ratione numeri, vt patet; igitur ratione perfectio­<lb></lb>nis. </s>
				</p>
				<p id="N143FA" type="main">
					<s id="N143FC"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14408" type="main">
					<s id="N1440A">Obſeruabis ſine hoc Theoremate explicari non poſſe accelerationem <lb></lb>motus naturalis, vel augmentum impetus, vt videbimus. </s>
				</p>
				<p id="N1440F" type="main">
					<s id="N14411"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 89.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1441D" type="main">
					<s id="N1441F"><emph type="italics"></emph>Impetus violenti, qui ſenſim deſtruitur in proiectis, poſitis ijſdem circum­<lb></lb>ſtantiis medij, &amp; reſiſtentiæ, minori tempore minùs deſtruitur; </s>
					<s id="N14427">plus verò ma­<lb></lb>jori:<emph.end type="italics"></emph.end> Quia hæc deſtructio habet cauſam; nam quidquid deſtruitur, ad <lb></lb>exigentiam alicuius deſtruitur, per Ax. 14. num. </s>
					<s id="N14432">2. igitur minori <lb></lb>tempore minùs deſtruitur per Ax. 13. 4. alioquin totus ſimul debe­<lb></lb>ret deſtrui. </s>
				</p>
				<p id="N1443B" type="main">
					<s id="N1443D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14449" type="main">
					<s id="N1444B">Obſeruabis etiam ſine hoc Theoremate non poſſe explicari deſtru­<lb></lb>ctionem impetus violenti, vt videbimus infrà. </s>
				</p>
				<p id="N14450" type="main">
					<s id="N14452"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1445F" type="main">
					<s id="N14461">Hinc, quò potentia diutiùs manet applicata (putà malleo) percuſſio ma­<lb></lb>ior eſt. </s>
				</p>
				<p id="N14466" type="main">
					<s id="N14468"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14475" type="main">
					<s id="N14477">Hinc, quò impedimentum diutiùs manet applicatum, illa deſtructio <lb></lb>eſt maior. </s>
				</p>
				<p id="N1447C" type="main">
					<s id="N1447E"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1448B" type="main">
					<s id="N1448D">Hinc præclara eruitur ratio, cur maior lapis, quàm minor impactus <lb></lb>maiorem ictum infligat; </s>
					<s id="N14493">licèt tot partes impetus eodem inſtanti produ­<lb></lb>cantur in vno, quot in alio: </s>
					<s id="N14499">quia ſcilicet diutiùs manet applicatus po­<lb></lb>tentiæ; ſed hanc rationem explicabimus fusè lib.  10. cum de percuſ­<lb></lb>ſione. </s>
				</p>
				<p id="N144A1" type="main">
					<s id="N144A3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 90.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N144AF" type="main">
					<s id="N144B1"><emph type="italics"></emph>Impetus propagatur neceſſariò per totum corpus impulſum, ſeu proiectum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N144B8" type="main">
					<s id="N144BA">Probatur; </s>
					<s id="N144BD">quia cum omnes eius partes moueantur, nec vlla ſine im­<lb></lb>petu moueri poſſit per Th. 18. &amp; 33. cum etiam potentia motrix non <lb></lb>ſit omnibus immediatè applicata, vt conſtat; certè ſine propagatione, <lb></lb>vel diffuſione non poteſt explicari productio huius motus. </s>
				</p>
				<pb pagenum="51" xlink:href="026/01/083.jpg"></pb>
				<p id="N144CB" type="main">
					<s id="N144CD"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N144D9" type="main">
					<s id="N144DB">Obſeruabis propagationem impetus, vel alterius qualitatis eſſe tan­<lb></lb>tùm continuatam eiuſdem productionem, quæ incipit ab ea parte, cui <lb></lb>potentia eſt immediatè applicata, &amp; propagatur, ſeu diffunditur per <lb></lb>omnes alias donec ad vltimam perueniat eo modo, quo iam definio. </s>
				</p>
				<p id="N144E4" type="main">
					<s id="N144E6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N144F2" type="main">
					<s id="N144F4"><emph type="italics"></emph>Illa progatio non fit per motum localem, ita vt pars impetus producta in <lb></lb>prima parte ſubiecti tranſeat ad ſecundam,<emph.end type="italics"></emph.end> patet; quia cum impetus ſit ac­<lb></lb>cidens per Th. 8. de ſubiecto in ſubiectum tranſire non poteſt per deff. </s>
					<s id="N14501"><lb></lb>accidentis; de qua in Metaphyſicâ; </s>
					<s id="N14505">nec eſt quod aliqui dicant ſe <expan abbr="nõ">non</expan> poſſe <lb></lb>concipere, quomodo id fiat ſine motu locali; </s>
					<s id="N1450F">cum ipſis etiam oculis <lb></lb>quaſi cernatur; </s>
					<s id="N14515">cum enim percutis corpus oblongum AE, &amp; cadit ictus <lb></lb>in extremitatem A, corpus ipſum totum ſimul moues; igitur pars impe­<lb></lb>tus, quæ recipitur in A, non migrat in E, ſed hæc producitur in A, &amp; <lb></lb>alia in B, alia in C, atque ita deinceps. </s>
				</p>
				<p id="N1451F" type="main">
					<s id="N14521"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1452D" type="main">
					<s id="N1452F">Obſeruabis ex hac propagatione impetus per analogiam rectè om­<lb></lb>ninò explicari propagationem luminis, &amp; aliarum qualitatum, de qui­<lb></lb>bus ſuo loco. </s>
				</p>
				<p id="N14536" type="main">
					<s id="N14538"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14544" type="main">
					<s id="N14546"><emph type="italics"></emph>In propagatione impetus prima pars<emph.end type="italics"></emph.end> A v. g. <emph type="italics"></emph>non producit partem<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>&amp; <lb></lb>hæc<emph.end type="italics"></emph.end> C; </s>
					<s id="N1455F"><emph type="italics"></emph>hæc verò<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>atque ita deinceps<emph.end type="italics"></emph.end>; Probatur. </s>
					<s id="N1456F">Primò, quia ſi hoc eſſet, <lb></lb>omne corpus poſſet moueri à qualibet potentia; nam modò poſſet pro­<lb></lb>duci vnum punctum impetus, hoc etiam aliud produceret, &amp; hoc aliud, <lb></lb>atque ita deinceps. </s>
					<s id="N14579">Secundò, Minimum granum ſuperpoſitum rupi, to­<lb></lb>tam ipſam rupem mouere poſſet. </s>
					<s id="N1457E">Tertio, Quia vel in omnibus, vel in <lb></lb>nulla parte impetus producitur per Th.33. Quartò, quia impetus mobi­<lb></lb>lis projecti intenderetur; nam impetus vnius partis impetum alterius <lb></lb>intenderet. </s>
					<s id="N14588">Quintò, quia impetus partis B, tàm ageret in A, trahendo, <lb></lb>quàm in C pellendo; cum impetus vtroque modo propagetur. </s>
					<s id="N1458E">Sextò, ſi <lb></lb>applicaretur potentia in C, non video, cur impetus partis C, ageret po­<lb></lb>tius versùs E, quàm versùs A? alioquin eadem pars impetus plures pro­<lb></lb>ducere poſſet; igitur impetus potentiæ motricis ſufficiens erit cauſa ad <lb></lb>producendum totum alium. </s>
					<s id="N1459A">Septimò, tractionis impetus explicari non <lb></lb>poteſt, ſi impetus vnius partis producat in alia impetum; alioquin dare­<lb></lb>tur mutua actio infinities repetita, vt conſideranti patebit. </s>
					<s id="N145A2">Octauò, ſi <lb></lb>impetus vnius partis producit in alia; </s>
					<s id="N145A8">ſint duo globi contigui; igitur il­<lb></lb>le, qui impellit alium, reflecti poſſet, quod nunquam accidit quando <lb></lb>ſunt contigui. </s>
				</p>
				<p id="N145B0" type="main">
					<s id="N145B2">Obſeruabis illud quidem verum eſſe in motu recto, ſecus in circulari; </s>
					<s id="N145B6"><lb></lb>nam cum cylindrus circa alteram extremitatem vibratus deorſum cadit; <lb></lb>partes, quæ propiùs ad extremitatem immobilem accedunt iuuant mo­<lb></lb>tum aliarum, quæ longiùs ab eadem recedunt. </s>
				</p>
				<pb pagenum="52" xlink:href="026/01/084.jpg"></pb>
				<p id="N145C3" type="main">
					<s id="N145C5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 93.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N145D1" type="main">
					<s id="N145D3"><emph type="italics"></emph>Impetus propagatur eodem inſtanti, id eſt, ſine temporis ſucceſſione.<emph.end type="italics"></emph.end></s>
					<s id="N145DA"> Proba­<lb></lb>tur; </s>
					<s id="N145DF">ſit enim applicata potentia in A, dico ſimul produci impetum in <lb></lb>BCDE; </s>
					<s id="N145E5">quia ſi primo inſtanti produceretur in A, &amp; ſecundo in B, vel <lb></lb>A moueretur ante B, vel impetus in A eſſet fruſtrà; </s>
					<s id="N145EB">vtrumque eſt abſur­<lb></lb>dum; nam totum AE, ſimul mouetur. </s>
				</p>
				<p id="N145F1" type="main">
					<s id="N145F3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 94.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N145FF" type="main">
					<s id="N14601"><emph type="italics"></emph>Tribus tantùm modis propagari poteſt impetus ratione intenſionis.<emph.end type="italics"></emph.end></s>
					<s id="N14608"> Primò <lb></lb>ſi æqualiter omnibus partibus ſubjecti diſtribuatur; id eſt vniformiter. </s>
					<s id="N1460E"><lb></lb>Secundò, ſi plùs partibus propioribus, &amp; minùs remotioribus. </s>
					<s id="N14612">Tertiò, è <lb></lb>contra, ſi plùs remotioribus, &amp; minùs propioribus; </s>
					<s id="N14618">tribus etiam ratione <lb></lb>perfectionis eo modo, quo diximus de intenſione; </s>
					<s id="N1461E">at verò nouem mo­<lb></lb>dis propagari poteſt ratione vtriuſque; patet ex regula combinationum; </s>
					<s id="N14624"><lb></lb>ſi enim 3. ducantur in 3. habebis 9. Iam ſupereſt, vt videamus, an reue­<lb></lb>rà omnibus iſtis modis impetus re ipſa propagetur; </s>
					<s id="N1462B">quod licèt difficile <lb></lb>ſit, &amp; vix hactenus explicatum: Audeo tamen polliceri meum ſuper hac <lb></lb>re conatum non prorſus inutilem fore. </s>
				</p>
				<p id="N14633" type="main">
					<s id="N14635"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 95.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14641" type="main">
					<s id="N14643"><emph type="italics"></emph>Impetus propagatur vniformiter in mobili, cuius omnes partes mouentur <lb></lb>æquali motu<emph.end type="italics"></emph.end>; </s>
					<s id="N1464E">probatur, quia impetus non cognoſcitur niſi per motum; <lb></lb>igitur vbi eſt æqualis motus, debet eſſe æqualis impetus in omnibus par­<lb></lb>tibus, id eſt æqualis graduum heterogeneorum collectio, in quo non <lb></lb>eſt difficultas. </s>
				</p>
				<p id="N14658" type="main">
					<s id="N1465A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14666" type="main">
					<s id="N14668">Obſeruabis illud mobile moueri motu æquali ſecundum omnes ſui <lb></lb>partes, quod mouetur motu recto; quippe fieri non poteſt, quin omnes <lb></lb>partes, quæ mouentur motu recto ſimplici, motu etiam æquali mouean­<lb></lb>tur. </s>
				</p>
				<p id="N14672" type="main">
					<s id="N14674"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 96.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14680" type="main">
					<s id="N14682"><emph type="italics"></emph>Cum duo corpora ſeſe mutuò tangunt, impetus in vtroque propagatur<emph.end type="italics"></emph.end> ſint <lb></lb>v. g. globi A &amp; B, æquales ſibi inuicem contigui in C, ſit applicata po­<lb></lb>tentia in D, non modò producet impetum in globo A, ſed etiam in B: </s>
					<s id="N14693"><lb></lb>probatur primò, quia ſe habent per modum vnius, vt patet ex reſiſten­<lb></lb>tia, nec enim A moueri poteſt ſine B per lineam DE, quod certè cla­<lb></lb>riſſimum eſt; probatur ſecundò quia ſi A produceret impetum in B, duo <lb></lb>globi, vel 3. vel 5. vel infiniti tantùm reſiſterent, quantùm vnicus glo­<lb></lb>bus, quod falſum &amp; abſurdum eſt. </s>
					<s id="N146A0">Tertiò, Ratio à priori eſt; </s>
					<s id="N146A4">quia ideo <lb></lb>producitur, &amp; propagatur impetus in toto A; </s>
					<s id="N146AA">quia vna pars non poteſt <lb></lb>moueri ſine alia per Th. 33. ſed non poteſt A moueri niſi moueatur  B; <lb></lb>igitur in vtroque ſimul, &amp; æqualiter propagatur impetus. </s>
				</p>
				<p id="N146B2" type="main">
					<s id="N146B4"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N146C1" type="main">
					<s id="N146C3">Hinc ratio manifeſta cur maior ſit reſiſtentia duorum quàm vnius. </s>
				</p>
				<pb pagenum="53" xlink:href="026/01/085.jpg"></pb>
				<p id="N146CA" type="main">
					<s id="N146CC"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N146D9" type="main">
					<s id="N146DB">Hinc eadem vis requiritur ad ſuſtinenda duo pondera; ſiue vtrum­<lb></lb>que ſeorſim humeris incubet, ſiue alterum alteri ſuperponatur. </s>
				</p>
				<p id="N146E1" type="main">
					<s id="N146E3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N146F0" type="main">
					<s id="N146F2">Hinc percuſſio vel ictus globi B, cui alter A à tergo immediatè in­<lb></lb>ſiſtit maior eſt. </s>
				</p>
				<p id="N146F7" type="main">
					<s id="N146F9"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14706" type="main">
					<s id="N14708">Hinc pondus alteri ſuperpoſitum actione communi cum alio graui­<lb></lb>tat in ſuppoſitam manum. </s>
					<s id="N1470D">v. g. <emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1471E" type="main">
					<s id="N14720">Hinc potentia applicata in D, minùs impetus ſingulis imprimit. </s>
				</p>
				<p id="N14723" type="main">
					<s id="N14725"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14732" type="main">
					<s id="N14734">Hinc demum licèt impetus ratione intenſionis ſit æqualis in vtroque <lb></lb>globo; </s>
					<s id="N1473A">attamen, ſi accipiatur numerus partium vtriuſque impetus, im­<lb></lb>petus ſunt vt globi v. g. ſi B eſt æqualis A impetus productus in B eſt <lb></lb>æqualis producto in A, ſi B ſit ſubduplus, vel ſubtriplus, impetus eſt <lb></lb>ſubtriplus, vel ſubduplus; quorum omnium rationes patent ex Th.96. </s>
				</p>
				<p id="N14748" type="main">
					<s id="N1474A"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14756" type="main">
					<s id="N14758">Hinc etiam colligi poteſt manifeſtum diſcrimen, quod intercedit inter <lb></lb>propagationem impetus, &amp; aliarum qualitatum, quæ (vt vulgò dicitur) <lb></lb>vniformiter difformiter propagantur, id eſt, æqualiter in æquali <lb></lb>diſtantia, &amp; inæqualiter inæquali. </s>
				</p>
				<p id="N14761" type="main">
					<s id="N14763"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1476F" type="main">
					<s id="N14771">Hinc demum colligi poteſt non modò impetum produci in globo B <lb></lb>v. g. verùm etiam in aëre ambiente, cui ſcilicet globus contiguus eſt; </s>
					<s id="N1477B"><lb></lb>qui reuera aër facilè amouetur; </s>
					<s id="N14780">tùm quia propter raritatem pauciſſimæ <lb></lb>partes mouendæ ſunt; </s>
					<s id="N14786">tùm quia facilè diuiduntur, de quibus alias; </s>
					<s id="N1478A">tùm <lb></lb>quia, ne detur vaçuum, ſpatium à tergo relictum occupare debet, quod <lb></lb>reuerà præſtat breui peracto circuitu, vt videre eſt in aqua; </s>
					<s id="N14792">nec enim <lb></lb>totus aër agitari debet; </s>
					<s id="N14798">quis enim id conſequi poſſet; tum denique, quia <lb></lb>aër non grauitat in aëre, igitur cum non reſiſtat vlla grauitatio, facilè <lb></lb>moueri poteſt. </s>
				</p>
				<p id="N147A0" type="main">
					<s id="N147A2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 97.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N147AE" type="main">
					<s id="N147B0"><emph type="italics"></emph>Cum applicatur potentia centro motus circularis, ita propagatur impetus, vt <lb></lb>plures partes impetus continuò producantur verſus <expan abbr="circumferentiã">circumferentiam</expan><emph.end type="italics"></emph.end>; ſit enim <lb></lb>cylindrus CA, fig. </s>
					<s id="N147C0">Th. 73. ſit centrum motus C; </s>
					<s id="N147C4">haud dubiè plures <lb></lb>partes impetus producuntur in B, quàm in C, &amp; plures in A, quam in B; </s>
					<s id="N147CA"><lb></lb>quia, cum pars B moueatur velociùs, quàm C, &amp; A quàm B; certè, vbi eſt <lb></lb>maior motus, vel effectus, ibi debet eſſe maior impetus, vel cauſa per <lb></lb>Ax. 13. n. </s>
					<s id="N147D3">4. quod autem ſit maior motus, conſtat ex maioribus ſpatiis, <lb></lb>vel arcubus æquali tempore confectis; quod verò ſit impetus intenſior <pb pagenum="54" xlink:href="026/01/086.jpg"></pb>versùs circumferentiam, non perfectior, patet per Th. 8. </s>
				</p>
				<p id="N147DE" type="main">
					<s id="N147E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 98.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N147EC" type="main">
					<s id="N147EE"><emph type="italics"></emph>Intenſio impetus propagati iuxta hunc modum ſe habet, vt distantia à cen­<lb></lb>tro motus<emph.end type="italics"></emph.end>; </s>
					<s id="N147F9">ſint enim punctum B, &amp; punctum A: </s>
					<s id="N147FD">ita ſe habet intenſio <lb></lb>impetus puncti A ad intenſionem impetus puncti B, vt diſtantia AC <lb></lb>ad BC. Probatur, quia cum impetus ſint vt motus, motus vt ſpatia, ſpatia <lb></lb>verò ſint arcus AE. BD; </s>
					<s id="N14807">arcus ſunt, vt ſemidiametri AC, BC; igitur vt <lb></lb>diſtantiæ quòd erat demonſtrandum. </s>
				</p>
				<p id="N1480D" type="main">
					<s id="N1480F"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1481C" type="main">
					<s id="N1481E">Hinc ſi diſtantia CA eſt dupla diſtantiæ CB, impetus in A eſt du­<lb></lb>plus impetus in B: at verò impetus ſegmenti eſt ad impetum alterius, <lb></lb>vt diximus in Th. 73. </s>
				</p>
				<p id="N14826" type="main">
					<s id="N14828"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14835" type="main">
					<s id="N14837">Hinc hæc propagatio fit iuxta progreſſionem arithmeticam id eſt, ſi <lb></lb>in primâ parte verſus centrum producitur impetus vt 1. in ſecunda pro­<lb></lb>ducitur vt duo, in tertiâ vt tria, atque ita deinceps; quia proportio <lb></lb>arithmetica eſt laterum, ſeu linearum. </s>
				</p>
				<p id="N14841" type="main">
					<s id="N14843"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14850" type="main">
					<s id="N14852">Hinc hæc propagatio eſt omninò inuerſa illius, quæ aliis qualitatibus <lb></lb>competit, vt patet. </s>
				</p>
				<p id="N14857" type="main">
					<s id="N14859"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14866" type="main">
					<s id="N14868">Hinc etiam manifeſta ratio ſequitur illius experimenti, quod propo­<lb></lb>ſuimus corol. </s>
					<s id="N1486D">2. Th. 80. </s>
				</p>
				<p id="N14870" type="main">
					<s id="N14872"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1487F" type="main">
					<s id="N14881">Hinc ſi tantùm habeatur ratio impetus, facilè poteſt determinari in <lb></lb>qua proportione cylindrus faciliùs moueatur motu recto, quàm motu <lb></lb>circulari; </s>
					<s id="N14889">poſito ſcilicet centro motus in altera extremitate, cui applica­<lb></lb>tur potentia; </s>
					<s id="N1488F">quippe impetus propagatus in motu circulari eſt ſumma <lb></lb>terminorum; </s>
					<s id="N14895">propagatus verò in motu recto eſt vltimus terminorum, <lb></lb>v.g. ſint ſex puncta ſubiecti; </s>
					<s id="N1489D">in quolibet producatur impetus vt vnum; </s>
					<s id="N148A1"><lb></lb>haud dubiè erit motus rectus; </s>
					<s id="N148A6">vt verò ſit motus circularis in primo <lb></lb>puncto; </s>
					<s id="N148AC">producatur vt 1. in ſecundo vt 2. in tertio, vt 3. atque ita dein­<lb></lb>ceps; ſumma erit 21. cum tamen in motu recto eſſent tantùm 6. igitur <lb></lb>vt ſe habent 21. ad 6. ita ſe habet facilitas motus recti ad facilitatem <lb></lb>motus circularis. </s>
				</p>
				<p id="N148B6" type="main">
					<s id="N148B8">Dixi, ſi tantùm habeatur ratio impetus; </s>
					<s id="N148BC">quia ſi addatur ratio graui­<lb></lb>tationis, ſeu momenti; haud dubiè maior erit adhuc difficultas, de <lb></lb>quo infrà in Schol. <emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N148D0" type="main">
					<s id="N148D2">Hinc quò longior eſt cylindrus, v. g. creſcit proportio maioris illius <lb></lb>facilitatis, vt patet inductione; </s>
					<s id="N148DC">nam ſi ſint tantùm 2. puncta, proportio <lb></lb>erit 3. ad 2.; </s>
					<s id="N148E2">ſit tria 6. ad 3.; </s>
					<s id="N148E6">ſi 4. 10. ad 4. ſi 5. 15. ad 5.; </s>
					<s id="N148EA">ſi 6. 21. ad 6. <pb pagenum="55" xlink:href="026/01/087.jpg"></pb>ſi 7. 28. ad 7; </s>
					<s id="N148F3">ſi 8. 36. ad 8; </s>
					<s id="N148F7">ſi 9. 45. ad 9; atque ita deinceps; ex quibus primò <lb></lb>vides creſcere ſemper proportionem. </s>
					<s id="N148FD">Secundò inter duplam, &amp; triplam <lb></lb>rationem, ſcilicet 6. ad 3. &amp; 15. ad 5. intercedere 2 1/2; </s>
					<s id="N14903">inter triplam &amp; <lb></lb>quadruplam intercedere 3. 1/2; </s>
					<s id="N14909">inter quadruplam &amp; quintuplam inter­<lb></lb>cedere 4 1/2; atque ita deinceps. </s>
				</p>
				<p id="N1490F" type="main">
					<s id="N14911"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1491D" type="main">
					<s id="N1491F">Colligo denique poſſe in motu recto cum maiore niſu produci inten­<lb></lb>ſiorem impetum in data ratione; </s>
					<s id="N14925">ſit enim cylindrus AB, qui moueatur <lb></lb>circa centrum A, percurrátque B, arcum BD; </s>
					<s id="N1492B">qui accipiatur vt recta, <lb></lb>quæ à minimis arcubus ſenſu diſtingui non poteſt; </s>
					<s id="N14931">haud dubiè ſi eo <lb></lb>tempore, vel æquali, quo AB tranſit in AD; </s>
					<s id="N14937">eadem AB, vel æqualis <lb></lb>motu recto tranſeat in FD, Dico impetum huius motus eſſe duplò in­<lb></lb>tenſiorem impetu illius; </s>
					<s id="N1493F">quia impetus ſunt vt motus; </s>
					<s id="N14943">motus verò vt <lb></lb>ſpatia, quæ percurruntur æqualibus temporibus; </s>
					<s id="N14949">ſed ſpatium rectanguli <lb></lb>AD, eſt duplum trianguli ADB; </s>
					<s id="N1494F">igitur &amp; motus; </s>
					<s id="N14953">igitur &amp; impetus; </s>
					<s id="N14957">ſi <lb></lb>verò AB tranſeat in EL, ita vt AF, ſit dupla AE; </s>
					<s id="N1495D">impetus erunt <lb></lb>æquales; quia rectangulum AC, eſt æquale triangulo ABD. </s>
				</p>
				<p id="N14963" type="main">
					<s id="N14965">Dixi arcum BD, accipi vt lineam rectam; </s>
					<s id="N14969">Si enim accipiatur vt ar­<lb></lb>cus; haud dubiè motus cylindri AB, dum transfertur in FD, eſt ad mo­<lb></lb>tum eiuſdem AB, dum transfertur in AD, vt rectangulum AD, ad ſe­<lb></lb>ctorem, cuius arcus ſit æqualis rectæ BD, &amp; radius ipſi AB. </s>
				</p>
				<p id="N14974" type="main">
					<s id="N14976"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14982" type="main">
					<s id="N14984">Obſeruabis primò, id quod ſuprà dictum eſt ita eſſe intelligendum, <lb></lb>vt momentum grauitationis nullo modo conſideretur, &amp; prædictus <lb></lb>cylindrus cenſeatur potiùs moueri in plano horizontali, à quo ſuſtinea­<lb></lb>tur, quàm in circulo verticali, in quo libera ſit eius libratio, ſeu gra­<lb></lb>uitatio. </s>
				</p>
				<p id="N1498F" type="main">
					<s id="N14991">Secundò, non poſſe ſuſtineri cylindrum horizonti parallelum, niſi <lb></lb>aliqua eius portio ſeu manu, ſeu forcipe, vel alio quouis modo accipia­<lb></lb>tur, v.g. ſit cylindrus AG horizonti parallelus; vt in hoc ſitu reti­<lb></lb>neatur, debet aliqua eius portio putà AB, manu teneri, alioqui ne à po­<lb></lb>tentiâ quidem infinita ſuſtineri poſſet. </s>
				</p>
				<p id="N1499F" type="main">
					<s id="N149A1">Tertiò, ſi ſupponatur fulcitus in B; </s>
					<s id="N149A5">vt retineatur in æquilibrio, debet <lb></lb>addi momentum in A; ſeu debet retineri ab ipſa potentiâ applicata <lb></lb>in A. </s>
				</p>
				<p id="N149AE" type="main">
					<s id="N149B0">Quartò, pondus in G ſe habet ad idem pondus in A, ſtatuto centro in <lb></lb>B, vt ſegmentum GB, ad BA, id eſt, vt 5. ad 1. </s>
				</p>
				<p id="N149B6" type="main">
					<s id="N149B8">Quintò, ſi proprio pondere frangeretur BG, haud dubiè in B frange­<lb></lb>retur; </s>
					<s id="N149BE">eſt autem momentum ponderis BG, vt ſubduplum eiuſdem BG <lb></lb>poſitum in G, vt demonſtrat Galileus prop.1.de reſiſtentia corp.ſit enim <lb></lb>BG, duarum librarum, ſitque BG, diuiſa bifariam in H; </s>
					<s id="N149C6">haud dubiè <lb></lb>pondus in H, facit momentum ſubduplum eiuſdem in G, vt patet; </s>
					<s id="N149CC">ſunt <lb></lb>enim vt diſtantiæ; </s>
					<s id="N149D2">igitur cum ſegmentum HG tantùm addat momenti <lb></lb>ſupra H, quantùm detrahit HB; </s>
					<s id="N149D8">certè momentum totius ponderis BG, <pb pagenum="56" xlink:href="026/01/088.jpg"></pb>eſt tantùm ſubduplum eiuſdem poſiti in G; </s>
					<s id="N149E1">itaque ſit BG, 10. librarum, <lb></lb>æquiualet 5. libris ſtatutis in G, &amp; AB, vni libræ poſitæ in A; </s>
					<s id="N149E7">ſed hæc <lb></lb>libra in A, habet tantùm ſubquintuplum momentum eiuſdem in G, igi­<lb></lb>tur 5. libræ in A, æquiualent vni in G; </s>
					<s id="N149EF">igitur vt ſtatuatur æquilibrium, <lb></lb>debent eſſe 24. libræ in A, ſeu vires æquiualentes; </s>
					<s id="N149F5">quibus adde pondus <lb></lb>abſolutum 12. librarum; erunt 36. igitur reſiſtentia ad motum circula­<lb></lb>rem verticalem ex triplici capite oritur. </s>
					<s id="N149FD">Primò ex ipſo pondere abſolutè <lb></lb>ſumpto, quæ communis eſt motui propagationis. </s>
					<s id="N14A02">Secundò, ex momento <lb></lb>eiuſdem ponderis; </s>
					<s id="N14A08">Tertiò, ex tali genere propagationis, de quo ſuprà; <lb></lb>quæ omnia ſunt apprimè tenenda, ne quis error ſubrepat. </s>
				</p>
				<p id="N14A0E" type="main">
					<s id="N14A10"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 99.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14A1C" type="main">
					<s id="N14A1E"><emph type="italics"></emph>Cum applicatur potentia circumferentiæ motus circularis; </s>
					<s id="N14A24">ita propagatur <lb></lb>impetus, vt plures partes verſus centrum motus producantur in pondere, quod <lb></lb>attollitur<emph.end type="italics"></emph.end>; </s>
					<s id="N14A2F">ſit enim idem cylindrus CA; </s>
					<s id="N14A33">ſitque applicata potentia in <lb></lb>A, dico verſus C, plures partes produci in pondere, Probatur, quia attol­<lb></lb>litur pondus in C, quod moueri non poteſtin A, operâ vectis AC, vt con­<lb></lb>ſtat ex certa hypotheſi; igitur plures partes impetus producuntur per <lb></lb>rationem 6. &amp; 7. Th.77, </s>
				</p>
				<p id="N14A3F" type="main">
					<s id="N14A41"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14A4D" type="main">
					<s id="N14A4F">Scio quidem hoc ipſum à nemine hactenus, quod ſciam, explicatum <lb></lb>eſſe; </s>
					<s id="N14A55">atque fore vt à multis tanquam nouum, &amp; inſolens minùs fortè <lb></lb>probetur: </s>
					<s id="N14A5B">quamquam illa hypotheſis hoc ipſum euincit, vulgaris certè, <lb></lb>&amp; nemini quaſi non nota; </s>
					<s id="N14A61">qua nempè dicimus in omnibus partibus mo­<lb></lb>bilis, quod actu mouetur, impetum produci; </s>
					<s id="N14A67">&amp; ſi quando accidat corpo­<lb></lb>ris ingentem molem ab applicata potentia non poſſe moueri, illud eſſe <lb></lb>tantùm, quòd non poſſint produci tot partes impetus, quot ſunt neceſſa­<lb></lb>riæ, vt omnibus partibus ſubjecti diſtribuantur; igitur ex hac hypothe­<lb></lb>ſi, quæ ex manifeſtis ducitur experimentis, neceſſariò dicendum eſt plu­<lb></lb>res partes impetus versùs centrum vectis produci in pondere, quod at­<lb></lb>tollitur, cuius propagationis proportionem infrà demonſtrabimus. </s>
				</p>
				<p id="N14A77" type="main">
					<s id="N14A79"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 100.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14A85" type="main">
					<s id="N14A87"><emph type="italics"></emph>Impetus, qui producitur verſus centrum vectis in pondere, licèt creſcat nu­<lb></lb>mero, decreſcit tamen in perfectione.<emph.end type="italics"></emph.end></s>
					<s id="N14A90"> Probatur per Th.81. ex motu imper­<lb></lb>fectiore, cui reſpondet impetus imperfectior per Ax. 17.num.4. non ratio­<lb></lb>ne numeri, qui maior eſt per Th.99. igitur ratione entitatis, ſeu perfe­<lb></lb>ctionis entitatiuæ. </s>
				</p>
				<p id="N14A99" type="main">
					<s id="N14A9B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 101.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14AA7" type="main">
					<s id="N14AA9"><emph type="italics"></emph>Tota collectio impetus, quæ in pondere ex dato puncto vectis producitur, eſt <lb></lb>ad aliam collectionem alterius puncti in perfectione, vt distantia illius puncti <lb></lb>à centro, ad diſtantiam huius<emph.end type="italics"></emph.end>: </s>
					<s id="N14AB6">probatur, quia perfectio vnius collectionis <lb></lb>eſt ad perfectionem alterius, vt motus ad motum; motus verò ſunt vt <lb></lb>ſpatia, ſpatia vt arcus, arcus vt ſemediametri, hæ demum, vt diſtantiæ. </s>
				</p>
				<pb pagenum="57" xlink:href="026/01/089.jpg"></pb>
				<p id="N14AC2" type="main">
					<s id="N14AC4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 102.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14AD0" type="main">
					<s id="N14AD2"><emph type="italics"></emph>Impetus in ipſo vecte ſine pondere addito ita propagatur, vt ſit imperfectior <lb></lb>verſus centrum vectis<emph.end type="italics"></emph.end>; </s>
					<s id="N14ADD">probatur, quia pondus verſus centrum mouetur <lb></lb>minore motu, vt conſtat; igitur ab imperfectiore impetu; </s>
					<s id="N14AE3">ſed non eſt <lb></lb>imperfectior tantùm ratione numeri, id eſt, pauciorum partium impe­<lb></lb>tus; </s>
					<s id="N14AEB">quia ſi hoc eſſet, ſit vectis AC, motus B, eſt ſubduplus motus <lb></lb>A; </s>
					<s id="N14AF1">igitur ſi eſt impetus eiuſdem perfectionis entitatiuæ, vt ſic loquar; </s>
					<s id="N14AF5"><lb></lb>ita ſe habet numerus partium impetus in B, ad numerum partium in A, <lb></lb>vt motus B, ad motum A; </s>
					<s id="N14AFC">&amp; hic vt arcus BD, ad arcum AE; </s>
					<s id="N14B00">&amp; hic vt <lb></lb>BC, ad AC; </s>
					<s id="N14B06">igitur eſt ſubduplus; </s>
					<s id="N14B0A">igitur æqualis omninò producitur <lb></lb>impetus ab eadem potentia in vecte AC, ſiue applicetur centro C, ſiue <lb></lb>circumferentiæ A; </s>
					<s id="N14B12">igitur æquè facilè; quod eſt contra experientiam; </s>
					<s id="N14B16"><lb></lb>probatur ſecundò, quia ſi hoc eſſet, pondus idem tàm facilè attolleretur <lb></lb>in A, quàm in B; quia idem impetus produceretur, quod eſt contra ex­<lb></lb>perientiam. </s>
				</p>
				<p id="N14B1F" type="main">
					<s id="N14B21"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 103.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14B2D" type="main">
					<s id="N14B2F"><emph type="italics"></emph>Ex hoc facilè intelligitur, cur impetus propagetur faciliùs à circumferen­<lb></lb>tia ad centrum, quàm à centro ad circumferentiam, &amp; cur longior vectis ab <lb></lb>eadem potentia moueri poſſit primo modo, non ſecundo, quod clarum est.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N14B3A" type="main">
					<s id="N14B3C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 104.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14B48" type="main">
					<s id="N14B4A"><emph type="italics"></emph>Decreſcit impetus verſus centrum iuxta rationem distantiarum<emph.end type="italics"></emph.end>; </s>
					<s id="N14B53">probatur <lb></lb>quia decreſcit iuxta rationem motuum; &amp; hæc iuxta rationem diſtan­<lb></lb>tiarum. </s>
				</p>
				<p id="N14B5B" type="main">
					<s id="N14B5D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 105.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14B69" type="main">
					<s id="N14B6B"><emph type="italics"></emph>Non decreſcit numerus partium impetus à circumferentia ad centrum<emph.end type="italics"></emph.end>; </s>
					<s id="N14B74"><lb></lb>probatur, quia cum à circumferentia ad centrum ita propagetur impe­<lb></lb>tus, vt vnicum tantùm punctum producatur in ipſa extremitate mobilis; </s>
					<s id="N14B7B"><lb></lb>certè non poteſt minùs impetus produci verſus centrum ratione nume­<lb></lb>ri; </s>
					<s id="N14B82">igitur non decreſcit numerus; hinc producitur neceſſariò imperfe­<lb></lb>ctior verſus centrum. </s>
				</p>
				<p id="N14B88" type="main">
					<s id="N14B8A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 106.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14B96" type="main">
					<s id="N14B98"><emph type="italics"></emph>Non producuntur plures partes impetus in vecte verſus centrum, id est, non <lb></lb>ſunt plures in puncto vectis propiùs ad centrum accedente, quàm in co; quod <lb></lb>longiùs distat:<emph.end type="italics"></emph.end> Probatur primò, quia fruſtrà eſſent plures. </s>
					<s id="N14BA5">Secundò, cur <lb></lb>potiùs in vna proportione, quàm in alia? </s>
				</p>
				<p id="N14BAA" type="main">
					<s id="N14BAC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 107.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14BB8" type="main">
					<s id="N14BBA"><emph type="italics"></emph>Ex his constat produci impetum æqualem numero in omnibus punctis vectis <lb></lb>a circumferentia ad centrum, cum ſcilicet applicatur potentia circumferentiæ<emph.end type="italics"></emph.end>; </s>
					<s id="N14BC5"><lb></lb>probatur, quia non producitur numerus minor per Th.105. neque maior <lb></lb>per Th. 106. igitur æqualis; </s>
					<s id="N14BCC">adde quod res explicari non poteſt per ma­<lb></lb>iorem, neque per minorem; ita vt ſcilicet pondera, quæ à data potentia <lb></lb>leuantur, ſint vt diſtantiæ, de quo ſuprà. </s>
				</p>
				<pb pagenum="58" xlink:href="026/01/090.jpg"></pb>
				<p id="N14BD8" type="main">
					<s id="N14BDA"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14BE6" type="main">
					<s id="N14BE8">Obſeruabis, quod aliquando in mentem venerat; </s>
					<s id="N14BEC">ſcilicet, verſus cen­<lb></lb>trum produci maiorem numerum in ratione diſtantiarum permutando; </s>
					<s id="N14BF2"><lb></lb>&amp; imperfectiorem in ratione duplicata earumdem diſtantiarum, etiam <lb></lb>permutando, v. g. ſit idem vectis AC ſectus bifariam in B; </s>
					<s id="N14BFD">in puncto <lb></lb>B producitur numerus duplus producti in A; </s>
					<s id="N14C03">at verò perfectio impetus <lb></lb>in B eſt ad perfectionem impetus in A, vt quadratum BC ad quadra­<lb></lb>tum AC; </s>
					<s id="N14C0B">vel in ratione ſubquadrupla, licèt tota collectio impetus B <lb></lb>ſit tantùm ſubdupla perfectione collectionis impetus A; </s>
					<s id="N14C11">ſed hoc profe­<lb></lb>ctò dici non poteſt; </s>
					<s id="N14C17">nam ſint in A 4. partes impetus; igitur in B erunt <lb></lb>8. applicetur autem pondus in B. </s>
					<s id="N14C1D">Primò producentur in eo partes 8. <lb></lb>impetus perfectionis ſubquadruplæ; </s>
					<s id="N14C23">ſi comparentur cum partibus A, <lb></lb>tum producentur 16. quæ æquiualent 4 A; </s>
					<s id="N14C29">igitur 24. at verò in A pro­<lb></lb>ducentur primò 4. tum deinde 2. quæ æquiualent 8. productis in B; igitur <lb></lb>6. igitur pondus, quod leuari poteſt in B, eſt ad pondus, quod leuari poteſt <lb></lb>in A, vt 24. ad 6.id eſt, in ratione quadrupla quod omninò falſum eſt. </s>
				</p>
				<p id="N14C33" type="main">
					<s id="N14C35"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 108.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14C41" type="main">
					<s id="N14C43"><emph type="italics"></emph>Iam facilè explicatur ex dictis, quomodo, &amp; cuius rationis pondera attol­<lb></lb>lantur ex diuerſis punctis vectis<emph.end type="italics"></emph.end>; ſit enim idem vectis AC, &amp; producan­<lb></lb>tur.v.g. </s>
					<s id="N14C50">in ſingulis punctis vectis ſingula puncta impetus, ſed diuerſæ <lb></lb>perfectionis; </s>
					<s id="N14C56">haud dubiè plures partes impetus imperfecti poſſunt face­<lb></lb>re impetum æqualem in perfectione alteri, qui conſtat paucioribus, ſed <lb></lb>perfectioribus; </s>
					<s id="N14C5E">igitur cum impetus B ſit imperfectior duplò quàm im­<lb></lb>petus in A, duplò plures partes impetus producentur in B, quàm in A, er­<lb></lb>go duplò maius pondus mouebitur; atque ita deinceps; </s>
					<s id="N14C66">eum enim ap­<lb></lb>ponitur pondus in B, producuntur in eo partes impetus omnes eiuſdem <lb></lb>perfectionis; </s>
					<s id="N14C6E">quæ ſcilicet reſpondet B, id eſt, quæ eſt ſubdupla perfectio­<lb></lb>nis impetus A; </s>
					<s id="N14C74">igitur plures partes producuntur, quàm ſi eſſent perfe­<lb></lb>ctionis A; </s>
					<s id="N14C7A">ſed pauciores quàm ſi eſſent perfectionis O, quæ minor eſt; <lb></lb>quippe eadem potentia, ſeu cauſa, quæ agit quantum poteſt (quod ſup­<lb></lb>pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </s>
					<s id="N14C82"><lb></lb>4. ſed æqualis perfectio poteſt conſtare pluribus, vel paucioribus parti­<lb></lb>bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt æqualem effe­<lb></lb>ctum alteri qui conſtat 8. partibus perfectionis vt 2. quod certum eſt; ſed <lb></lb>de his plura aliàs. </s>
				</p>
				<p id="N14C8D" type="main">
					<s id="N14C8F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 109.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14C9B" type="main">
					<s id="N14C9D"><emph type="italics"></emph>Perfectio decreſcit verſus centrum iuxta diuerſam rationem longitudinum <lb></lb>vectis, ſeu distantiarum.<emph.end type="italics"></emph.end> v.g.ſit idem vectis AC, ita decreſcit ab A verſus <lb></lb>centrum C; </s>
					<s id="N14CAA">vt impetus puncti B ſit ſubduplus in perfectione, puncti R <lb></lb>ſubtriplus: </s>
					<s id="N14CB0">iam verò ſit vectis ſubduplus prioris BC, ſectus bifariam in <lb></lb>Z; </s>
					<s id="N14CB6">ſi impetus productus in B, quę eſt extremitas minoris vectis B ſit æqua­<lb></lb>lis perfectionis cum impetu producto in A (&amp; reuera ſunt æquales) ſi <lb></lb>æquali tempore percurrant arcus æquales, ſcilicet AV, &amp; BD) certè im-<pb pagenum="59" xlink:href="026/01/091.jpg"></pb>petus productus in Z eſt æqualis producto in B, cum B pertinet ad ma­<lb></lb>iorem vectem; </s>
					<s id="N14CC5">quia vt AC totus maior vectis eſt ad BC ita BC ad <lb></lb>ZC: igitur decreſcit perfectio versùs centrum iuxta rationem longi­<lb></lb>tudinum. </s>
				</p>
				<p id="N14CCD" type="main">
					<s id="N14CCF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 110.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14CDB" type="main">
					<s id="N14CDD"><emph type="italics"></emph>Minima potentia est illa, quæ in extremitate vectis, quæ procul recedit à <lb></lb>centro, vnam tantùm partem, vel vnum punctum impetus producit<emph.end type="italics"></emph.end>; nihil <lb></lb>enim minùs produci poteſt, poſito quod potentia applicata ad talem gra­<lb></lb>dum perfectionis ſit determinata, id eſt ad producendum impetum talis <lb></lb>perfectionis in ea parte ſubjecti, cui applicatur immediatè, vt ſuprà di­<lb></lb>ctum eſt. </s>
				</p>
				<p id="N14CF0" type="main">
					<s id="N14CF2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 111.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14CFE" type="main">
					<s id="N14D00"><emph type="italics"></emph>Si ſint tantum duo puncta vel duæ partes vectis, illa potentia ad illum mo­<lb></lb>uendum ſufficiens motu circulari est ad aliam ſufficientem ad illum mouen­<lb></lb>dum motu recto, vt<emph.end type="italics"></emph.end> 1/2 <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> 2. ſi ſint tria puncta vt 2. ad 3. ſi 4. vt 2. 1/2 ad 4. <lb></lb>ſi 5. vt 3. ad 5. ſi 6. vt 3. 1/2 ad 6. atque ita deinceps iuxta hanc propor­<lb></lb>tionem in quo non eſt difficultas, cum hoc totum ſequatur ex Th. 109. </s>
				</p>
				<p id="N14D16" type="main">
					<s id="N14D18"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14D24" type="main">
					<s id="N14D26">Obſerua tamen quacumque data potentia poſſe dari minorem; </s>
					<s id="N14D2A">quia <lb></lb>quocumque dato motu, etiam recto, poteſt dari tardior; </s>
					<s id="N14D30">igitur quocum­<lb></lb>que impetu imperfectior; </s>
					<s id="N14D36">igitur quando appellaui potentiam minimam; </s>
					<s id="N14D3A"><lb></lb>intellige illam quæ comparatur cum vnico puncto impetus talis perfe­<lb></lb>ctionis; hæc enim reuera minima eſt illarum omnium, quæ poſſunt pro­<lb></lb>ducere impetum talis perfectionis, ſi verò comparetur cum impetu im­<lb></lb>perfectiore, haud dubiè minima non eſt. </s>
				</p>
				<p id="N14D45" type="main">
					<s id="N14D47">Obſerua præterea ſuppoſitum eſſe hactenus in extremitate vectis ſiue <lb></lb>maioris, ſiue minoris, produci impetum eiuſdem perfectionis, eiuſque <lb></lb>vnicum punctum, ſeu partem, vnde potentia quæ applicatur maiori vecti <lb></lb>conuenit quidem cum ea, quæ applicatur minori in eo, quòd vtraque in <lb></lb>extremitate ſui vectis producat vnum punctum impetus eiuſdem perfe­<lb></lb>ctionis; differt tamen in eo, quòd illa, quæ applicatur maiori vecti, ſit <lb></lb>maior iuxta rationes prædictas in Theoremate. </s>
					<s id="N14D58">v. g. illa, quæ applicatur <lb></lb>vecti. </s>
					<s id="N14D61">2. punctorum eſt ad eam, quæ applicatur vecti trium punctorum, <lb></lb>ſcu partium, vt 1. 1/2 ad 2. &amp; ſi vectis ſit 4. punctorum ad 2. 1/2; </s>
					<s id="N14D67">ſi 5. ad 3. <lb></lb>ſi 6. ad 3. 1/2; </s>
					<s id="N14D6D">ſi 7. ad 4. ſi 8. ad 4. 1/2. Vides egregiam progreſſionem; </s>
					<s id="N14D71">ſit <lb></lb>enim vectis 2. punctorum AB, in puncto A, quod eſt extremitas, produ­<lb></lb>catur punctum impetus datæ perfectionis, in B producetur aliud, cuius <lb></lb>perfectio eſt ſubdupla prioris per Th. 109. igitur caracter, ſeu momen­<lb></lb>tum totius impetus eſt 1. 1/2. ſit porrò vectis 4. punctorum CDEF, in <lb></lb>C, quod eſt extremitas; </s>
					<s id="N14D7F">producatur vnum punctum impetus eiuſdem <lb></lb>perfectionis cum eo, quod productum eſt in A; </s>
					<s id="N14D85">certè in D producetur <lb></lb>aliud cuius perfectio erit ad priorem vt 3.ad 4. per idem Th. ſic autem <lb></lb>notetur 1/4, in E 2/4, in F 3/4, in C vero 4/4; </s>
					<s id="N14D8D">perfectiones enim ſunt vt lon-<pb pagenum="60" xlink:href="026/01/092.jpg"></pb>gitudines; </s>
					<s id="N14D96">quæ ſi colligantur, habebis characterem totius impetus, 2 1/2: </s>
					<s id="N14D9A"><lb></lb>igitur totus impetus productus in minore vecte, qui conſtat 2. punctis, <lb></lb>eſt ad impetum, qui producitur in maiore conſtante 4.punctis, vt 1. 1/2 ad <lb></lb>2. 1/2; </s>
					<s id="N14DA3">igitur vectis maior maiorem potentiam ad mouendum ipſum ve­<lb></lb>ctem requirit; non certè in deſcenſu; </s>
					<s id="N14DA9">quippe ſuo pondere deſcendit, ſed <lb></lb>in plano horizontali; </s>
					<s id="N14DAF">niſi enim potentia poſſit mouere vectem; haud <lb></lb>dubiè nullum pondus vecte mouebit. </s>
				</p>
				<p id="N14DB5" type="main">
					<s id="N14DB7">At verò ſi potentia ſit tantùm dupla minimæ, quæ datum vectem mo­<lb></lb>uere poſſit; </s>
					<s id="N14DBD">haud dubiè dato illo vecte datum ferè quodcumque pondus <lb></lb>mouere poterit; cum ipſe vectis conſtet ferè infinitis punctis in longi­<lb></lb>tudine, vt patet ex dictis, &amp; conſideranti patebit. </s>
				</p>
				<p id="N14DC5" type="main">
					<s id="N14DC7">Obſeruabis demum in mechanicis nullam ferè haberi rationem pon­<lb></lb>deris ipſius vectis; </s>
					<s id="N14DCD">parum enim pro nihilo computatur: </s>
					<s id="N14DD1">Ex his tamen <lb></lb>erui poſſunt veriſſimæ rationes Phyſicæ proportionum vectis AH; </s>
					<s id="N14DD7">ſia­<lb></lb>que A extremitas, H centrum; </s>
					<s id="N14DDD">ſitque BH 1/2. CH 1/4, DH 1/2, EH (1/16), <lb></lb>FH (1/32), GH (1/64) pondus I applicetur in A, &amp; moueatur; </s>
					<s id="N14DE3">certè in B moue­<lb></lb>bitur pondus K duplum I; </s>
					<s id="N14DE9">quia, cum impetus productus in B, ſit ſubdu­<lb></lb>plus in perfectione illius, qui producitur in A; </s>
					<s id="N14DEF">vt æqualis producatur in <lb></lb>B, &amp; in A, debent produci in B duplò plures partes impetus; </s>
					<s id="N14DF5">igitur du­<lb></lb>plò maius pondus mouebit; </s>
					<s id="N14DFB">at verò in C mouebitur pondus L quadru­<lb></lb>plum I, in D octuplum, atque ita deinceps; donec tandem in G mouea­<lb></lb>tur pondus, quod ſit ad I vt 64. ad 1. &amp; cum adhuc poſſint accipi inter <lb></lb>GH, partes aliquotæ minores, &amp; minores ferè in infinitum, non mirum <lb></lb>eſt ſi pondus maius poſſit adhuc moueri. </s>
				</p>
				<p id="N14E07" type="main">
					<s id="N14E09">Obſeruabis etiam in omni vecte abſtrahendo ab eius pondere, &amp; ap­<lb></lb>plicata eadem potentia, hoc eſſe commune; </s>
					<s id="N14E0F">vt poſſit quodcumque pon­<lb></lb>dus attolli, licèt difficiliùs in minore; </s>
					<s id="N14E15">quia hic non poteſt in tam mul­<lb></lb>tas partes aliquotas ſenſibiliter diuidi, in medio tamen vecte duplum <lb></lb>ſemper pondus mouetur; ſiue ipſe vectis ſit maior, ſiue minor. </s>
				</p>
				<p id="N14E1D" type="main">
					<s id="N14E1F">Obſeruabis deinde, ſi centrum vectis non ſit in altera extremitate, <lb></lb>ſed. </s>
					<s id="N14E24">v.g. in C; </s>
					<s id="N14E2A">haud dubiè producitur in H, &amp; in B impetus æqualis; </s>
					<s id="N14E2E">quia <lb></lb>æqualiter diſtat vtrumque punctum à centro C; </s>
					<s id="N14E34">igitur æquale pondus <lb></lb>mouebitur in B, &amp; in H; propagatur tamen nouo modo à C verſus H, de <lb></lb>quo iam ſuprà dictum eſt. </s>
				</p>
				<p id="N14E3C" type="main">
					<s id="N14E3E">Obſeruabis denique triplicem propagationem impetus eſſe legiti­<lb></lb>mam. </s>
					<s id="N14E43">Prima eſt in motu recto, cum propagatur per partes æquales, tùm <lb></lb>in perfectione, tùm in numero in ſingulis partibus ſubjecti per gradus, <lb></lb>ſcilicet heterogeneos. </s>
					<s id="N14E4A">Secunda eſt in motu circulari, applicata ſcilicet <lb></lb>potentia centro; cum propagatur per partes æquales in perfectione, &amp; <lb></lb>inæquales in numero. </s>
					<s id="N14E52">Tertia eſt in vecte, cum propagatur per partes <lb></lb>æquales in numero, &amp; inæquales in perfectione. </s>
				</p>
				<p id="N14E57" type="main">
					<s id="N14E59"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 112.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14E65" type="main">
					<s id="N14E67"><emph type="italics"></emph>Impetus debet determinari ad aliquam lineam motus<emph.end type="italics"></emph.end>; </s>
					<s id="N14E70">probatur, quia <lb></lb>non poteſt eſſe impetus, niſi exigat motum per Th.14. nec exigere mo-<pb pagenum="61" xlink:href="026/01/093.jpg"></pb>tum, niſi per aliquam lineam, vt patet; </s>
					<s id="N14E7B">ſed hoc eſt impetum eſſe de­<lb></lb>terminatum ad aliquam lineam motus; </s>
					<s id="N14E81">præterea ſi non eſt determina­<lb></lb>tus ad aliquam lineam; </s>
					<s id="N14E87">igitur indeterminatus, &amp; indifferens per Ax.1. <lb></lb>ſed indifferens manere non poteſt; cur enim potius haberet motum <lb></lb>per vnam lineam, quàm per aliam? </s>
					<s id="N14E8F">igitur debet determinari. </s>
				</p>
				<p id="N14E92" type="main">
					<s id="N14E94"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 113.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14EA0" type="main">
					<s id="N14EA2"><emph type="italics"></emph>Impetus ad plures lineas ſeorſim indifferens eſt:<emph.end type="italics"></emph.end> Probatur, quia idem im­<lb></lb>petus pilæ in aliam impactæ producit in ea impetum, qui pro diuerſo <lb></lb>contactu ad diuerſam lineam determinari poteſt; </s>
					<s id="N14EAF">præterea corpus graue <lb></lb>in diuerſis planis inclinatis deſcendit; </s>
					<s id="N14EB5">igitur per diuerſas lineas; </s>
					<s id="N14EB9">deinde <lb></lb>pila reflectitur propter impetum priorem, qui tantùm mutat lineam, vt <lb></lb>dicemus infrà; </s>
					<s id="N14EC1">adde quod funependuli vibrati impetus ſine reflexione <lb></lb>mutat lineam motus; igitur idem impetus ad plures lineas ſeorſim eſt <lb></lb>indifferens. </s>
				</p>
				<p id="N14EC9" type="main">
					<s id="N14ECB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 114.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14ED7" type="main">
					<s id="N14ED9"><emph type="italics"></emph>Hinc idem impetus ad plures lineas potest determinari ſeorſim<emph.end type="italics"></emph.end>; </s>
					<s id="N14EE2">quia ad <lb></lb>eas poteſt determinari, ad quas eſt indifferens, vt patet; ſed ad multas <lb></lb>eſt indifferens per Theorema 113. igitur ad multas poteſt determi­<lb></lb>nari. </s>
				</p>
				<p id="N14EEC" type="main">
					<s id="N14EEE"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N14EFA" type="main">
					<s id="N14EFC">Obſeruabis primò determinationem hanc nihil eſſe aliud, niſi ipſum <lb></lb>impetum cum tali linea comparatum, ſeu coniunctum; </s>
					<s id="N14F02">vnam verò li­<lb></lb>neam differre ab alia ratione terminorum v. g. illa quæ tendit verſus <lb></lb>ortum differt ab ea, quæ tendit verſus auſtrum, vel occaſum, ſcilicet <lb></lb>ratione terminorum, ſunt enim duo termini, nempè à quo, &amp; ad quem; </s>
					<s id="N14F10"><lb></lb>4. autem modis differunt termini lineæ, vel enim neuter communis eſt <lb></lb>vt AB. DC, vel terminus à quo vtrique lineæ communis eſt, vt BA. <lb></lb>BE, vel terminus ad quem vt AB, EB; vel denique viciſſim commu­<lb></lb>tantur termini, vt BE, EB, &amp; hæc terminorum coniugatio facit oppo­<lb></lb>ſitionem maximam, id eſt diametralem. </s>
				</p>
				<p id="N14F1D" type="main">
					<s id="N14F1F">Secundò obſeruabis aliquando videri eſſe vtrumque terminum com­<lb></lb>munem licèt differant lineæ; </s>
					<s id="N14F25">ſit linea recta BE, habet communes ter­<lb></lb>minos cum curua BFE, licèt omninò differat ab illa; </s>
					<s id="N14F2B">at profectò licèt <lb></lb>BE videatur eſſe vnica ſimplex linea duobus terminis clauſa; </s>
					<s id="N14F31">conſtat <lb></lb>ramen ex pluribus aliis continuata, rectáque ſerie iunctis; </s>
					<s id="N14F37">vnde, vt <lb></lb>linea dicatur eadem eſſe cum alia, debet vna cum aliâ conuenire; ita vt <lb></lb>alteri ſuperpoſita nec excedat, nec deficiat. </s>
				</p>
				<p id="N14F3F" type="main">
					<s id="N14F41">Tertiò linea motus non differt ab ipſo motu continuo tractu, ſeu <lb></lb>fluxu quaſi labenti: </s>
					<s id="N14F47">Porrò vnus motus differt ab alio, vel ratione velo­<lb></lb>citatis, vel ratione terminorum; ſed hæc parum difficultatis habent. </s>
				</p>
				<p id="N14F4D" type="main">
					<s id="N14F4F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 115.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14F5B" type="main">
					<s id="N14F5D"><emph type="italics"></emph>Impetus aliquis ad vnam tantùm lineam poteſt eſſe determinatus<emph.end type="italics"></emph.end>; </s>
					<s id="N14F66">v. g. <lb></lb><emph type="italics"></emph>impetus naturalis innatus, de quo in Th.<emph.end type="italics"></emph.end> 17. <emph type="italics"></emph>nam de acquiſito certum eſt ad<emph.end type="italics"></emph.end><pb pagenum="62" xlink:href="026/01/094.jpg"></pb><emph type="italics"></emph>plures determinari poſſe, vt videbimus cum de motu reflexo<emph.end type="italics"></emph.end>; </s>
					<s id="N14F82">probatur quia <lb></lb>motus deorſum eſt finis huius impetus; </s>
					<s id="N14F88">quia ideo corpus graue produ­<lb></lb>cit in ſe impetum (ſi tamen producit) vt tendat deorſum, vt certum eſt; </s>
					<s id="N14F8E"><lb></lb>tàm enim omne graue non impeditum tendit deorſum, quàm omnis <lb></lb>ignis eſt calidus; </s>
					<s id="N14F95">igitur ſi eſt proprietas omnis ignis eſſe calidum, quia <lb></lb>omni competit; </s>
					<s id="N14F9B">ita omni graui competit tendere infrà leuius, modò <lb></lb>non impediatur; </s>
					<s id="N14FA1">igitur eſt eius proprietas; </s>
					<s id="N14FA5">igitur ille impetus eſt de­<lb></lb>terminatus ad lineam quæ tendit deorſum; </s>
					<s id="N14FAB">ſed de hoc impetu naturali <lb></lb>innato fusè agemus infrà in ſecundò libro; nunc ſufficiat dixiſſe poſſe <lb></lb>dari aliquem impetum ita determinatum ad certam lineam, vt ad aliam <lb></lb>determinari non poſſit naturaliter, nulla eſt enim repugnantia. </s>
				</p>
				<p id="N14FB5" type="main">
					<s id="N14FB7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 116.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14FC3" type="main">
					<s id="N14FC5"><emph type="italics"></emph>Impetus determinatur aliquando ad lineam motus à potentia motrice<emph.end type="italics"></emph.end>; </s>
					<s id="N14FCE">pro­<lb></lb>batur, quia primus impetus ab ipſa potentia productus ſine impedimen­<lb></lb>to ab alio determinari non poteſt; potentia porrò motrix vel eſt gra­<lb></lb>uium, vel leuium, vel animantium, vel proiectorum, vel compreſſo­<lb></lb>rum, &amp;c. </s>
				</p>
				<p id="N14FDA" type="main">
					<s id="N14FDC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 117.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N14FE8" type="main">
					<s id="N14FEA"><emph type="italics"></emph>Potentia verò motrix determinatur vel à ſuo fine intrinſeco, vel potius ab <lb></lb>ipſa ſua natura<emph.end type="italics"></emph.end>; </s>
					<s id="N14FF5">ſic grauitas ſeu potentia motrix grauium determinata <lb></lb>eſt ad motum deorſum perpendicularem, dum in medio libero corpus <lb></lb>graue mouetur; vel à plano inclinato; </s>
					<s id="N14FFD">pro cuius diuerſa inclinatione <lb></lb>diuerſa eſt linea motus deorſum; </s>
					<s id="N15003">vel ab ipſa via, ſeu exitu patefacto; <lb></lb>ſic potentia motrix compreſſorum ſuas vires exerit, &amp; mobile ipſum <lb></lb>agit, quâ patet viâ, ſurſum, deorſum &amp;c. </s>
					<s id="N1500B">vel ab appetitu ſeu libero, ſeu <lb></lb>ſenſitiuo; </s>
					<s id="N15011">ſic potentia progreſſiua animantium cò corpus agit, quò iu­<lb></lb>bet appetitus, vel ab aliqua affectione intrinſeca intrinſecùs vel extrin­<lb></lb>ſecùs adueniente; </s>
					<s id="N15019">ſic dilatatur pupilla, vel contrahitur pro diuerſa lu­<lb></lb>minis appulſi vi, vel obiecti diſtantia: Huc reuoca motus illos natura­<lb></lb>les, qui animalibus competunt v. g. tuſſis, ſingultus, ſternutationis, &amp;c. </s>
					<s id="N15025"><lb></lb>de quibus fusè ſuo loco. </s>
				</p>
				<p id="N15029" type="main">
					<s id="N1502B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 118.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15037" type="main">
					<s id="N15039"><emph type="italics"></emph>Impetus determinatur aliquando ad lineam ab alio impetu producente<emph.end type="italics"></emph.end>; </s>
					<s id="N15042"><lb></lb>ſic impetus corporis proiecti determinatur ab impetu vel organi vel <lb></lb>manus proiicientis; </s>
					<s id="N15049">quia nihil eſt aliud à quo determinari poſſit, vt <lb></lb>patet; </s>
					<s id="N1504F">adde figuram organi, diſpoſitionem ſeu ſitum mobilis, quod ma­<lb></lb>nu tenetur; </s>
					<s id="N15055">impedimenti etiam habetur ratio v. g. corpus oblongum <lb></lb>proiici poteſt, vel motu recto ad inſtar teli, vel motu mixto ex recto <lb></lb>&amp; circulari; cum ſcilicet diuerſimodè vibratur: </s>
					<s id="N15061">ſi enim altera extremi­<lb></lb>tas adhuc hæreat in manu, dum altera mouetur, vt cum quis baculo <lb></lb>ferit; </s>
					<s id="N15069">tunc certè eſt aliquòd impedimenti genus, ex quo oritur talis li­<lb></lb>nea motus; illud autem impedimentum emergit ex diuerſa applicatione <lb></lb>diuerſaque brachij vibratione, quæ omnia ſunt ſatis clara. </s>
				</p>
				<pb pagenum="63" xlink:href="026/01/095.jpg"></pb>
				<p id="N15075" type="main">
					<s id="N15077"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 119.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15083" type="main">
					<s id="N15085"><emph type="italics"></emph>Impetus determinatus ad vnam lineam poteſt ad aliam in ſuo fluxu deter­<lb></lb>minatu<emph.end type="italics"></emph.end>; </s>
					<s id="N15090">vt patet in corpore reflexo; nec enim dici poteſt totum prio­<lb></lb>rem impetum in ipſo reflexionis puncto deſtrui, vt demonſtrabimus <lb></lb>aliàs. </s>
					<s id="N15098">Probatur etiam ex impetu proiectorum, quæ mutant lineam mo­<lb></lb>tus manente adhuc priore impetu ſaltem ex parte. </s>
				</p>
				<p id="N1509D" type="main">
					<s id="N1509F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 120.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N150AB" type="main">
					<s id="N150AD"><emph type="italics"></emph>Corpus proiectum in aliud ita illud impellit, vt determinet lineam motus <lb></lb>ratione puncti contactus<emph.end type="italics"></emph.end>; </s>
					<s id="N150B8">Sit enim, ne multiplicemus figuras, globus, <lb></lb>cuius linea directionis ſit DC, punctum contactus C, ita globus A im­<lb></lb>pellet globum B, vt linea motus, ad quam determinatur, ſit CB, id eſt <lb></lb>ducta à puncto contactus ad centrum globi impulſi; </s>
					<s id="N150C2">ſit etiam globus <lb></lb>P impactus in globum A punctum contactus ſit D, linea motus, ad <lb></lb>quam determinatur, eſt DA, quæ ſcilicet à puncto contactus ducitur <lb></lb>per centrum grauitatis corporis impulſi: </s>
					<s id="N150CC">experientia huius rei certa <lb></lb>eſt, nec ignorant qui in ludo minoris tudiculæ verſati ſunt; </s>
					<s id="N150D2">ratio au­<lb></lb>tem inde tantùm duci poteſt, quod ſcilicet ab ipſo puncto contactus ita <lb></lb>diffunditur impetus, vt hinc inde æqualiter in vtroque hemiſphærio <lb></lb>diffundatur; </s>
					<s id="N150DC">coniungitur autem vtrumque hemiſphærium circulo A, <lb></lb>vel B, in priore figura, eſtque vtriuſque communis ſectio; </s>
					<s id="N150E2">cum autem <lb></lb>vtrimque ſit æqualis impetus, nulla eſt ratio, cur linea directionis in­<lb></lb>clinet potiùs in vnum hemiſphærium, quàm in aliud: </s>
					<s id="N150EA">præterea cum <lb></lb>motus orbis globi determinetur à motu centri; </s>
					<s id="N150F0">cum ſcilicet globus in <lb></lb>globum impingitur; </s>
					<s id="N150F6">haud dubiè non poteſt eſſe alius motus centri, niſi <lb></lb>qui determinatur à puncto contactus, à quo vnica tantùm linea ad cen­<lb></lb>trum duci poteſt, vt conſtat; &amp; hæc ratio veriſſima eſt, &amp; totam rem <lb></lb>ipſam euincit. </s>
				</p>
				<p id="N15100" type="main">
					<s id="N15102"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 121.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1510E" type="main">
					<s id="N15110"><emph type="italics"></emph>Hinc licèt diuerſæ ſint linea motus globi impellentis, ſi tamen ſit idem pun­<lb></lb>ctum contactus ad <expan abbr="eãdem">eandem</expan> lineam globus impulſus determinabitur,<emph.end type="italics"></emph.end> v. g. li­<lb></lb>cet globus P. eiuſdem figuræ tangat globum A in D per lineam PD ſiue <lb></lb>per lineam HD ſiue per quamlibet aliam, globus A mouebitur ſemper <lb></lb>per lineam directionis DA propter rationem propoſitam, quod etiam <lb></lb>mille experimentis conuincitur. </s>
				</p>
				<p id="N1512A" type="main">
					<s id="N1512C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 122.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15138" type="main">
					<s id="N1513A"><emph type="italics"></emph>Determinatur impetus corporis proiecti impacti in corpus reflectens ad no­<lb></lb>uam lineam<emph.end type="italics"></emph.end>; </s>
					<s id="N15145">patet experientiâ in pilâ reflexâ; reflexionis autem ratio­<lb></lb>nem afferemus in lib.  de motu reflexo. </s>
				</p>
				<p id="N1514B" type="main">
					<s id="N1514D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 123.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15159" type="main">
					<s id="N1515B"><emph type="italics"></emph>Non determinatur tantùm ratione puncti contactus.<emph.end type="italics"></emph.end></s>
					<s id="N15162"> Probatur, quia cum <lb></lb>eodem puncto contactus poteſt eſſe determinatio ad diuerſam lineam, <lb></lb>vt manifeſtum eſt; ſit enim reflexio per angulum æqualem incidentiæ, <lb></lb>ſed diuerſi anguli poſſunt in idem punctum coire, vt patet. </s>
				</p>
				<pb pagenum="64" xlink:href="026/01/096.jpg"></pb>
				<p id="N15170" type="main">
					<s id="N15172"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 124.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1517E" type="main">
					<s id="N15180"><emph type="italics"></emph>Non determinatur noua linea in motu reflexo â priore tantùm linea <lb></lb>incidentiæ<emph.end type="italics"></emph.end>; probatur, quia poteſt eſſe eadem linea incidentiæ cum di­<lb></lb>uerſis lineis motus reflexi, vt patet. </s>
				</p>
				<p id="N1518D" type="main">
					<s id="N1518F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 125.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1519B" type="main">
					<s id="N1519D"><emph type="italics"></emph>Non determinatur noua linea motus reflexi ratione tantùm plani reflecten­<lb></lb>tis<emph.end type="italics"></emph.end>: Probatur, quia cum eodem plano reflectente diuerſæ lineæ motus <lb></lb>reflexi eſſe poſſunt, vt conſtat. </s>
				</p>
				<p id="N151AA" type="main">
					<s id="N151AC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 126.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N151B8" type="main">
					<s id="N151BA"><emph type="italics"></emph>Determinatur noua linea motus reflexi ratione lineæ prioris incidentiæ com­<lb></lb>paratæ cum plano reflectente,<emph.end type="italics"></emph.end> eſt enim angulus reflexionis æqualis angu­<lb></lb>lo incidentiæ, cuius effectus rationem aliàs afferemus, cum de motu <lb></lb>reflexo; </s>
					<s id="N151C9">&amp; verò multa hîc curſim tantùm perſtringimus, quæ in libro <lb></lb>de motu reflexo accuratiſſimè demonſtrabimus; Hìc tantùm dixiſſe ſuf­<lb></lb>ficiat determinari mobile in reflexionis puncto ad nouam lineam motus, <lb></lb>quod nemo in dubium reuocare poteſt, &amp; propter quid fiat loco citato <lb></lb>demonſtrabimus. </s>
				</p>
				<p id="N151D5" type="main">
					<s id="N151D7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 127.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N151E3" type="main">
					<s id="N151E5"><emph type="italics"></emph>Quando globus in globum æqualem ita impingitur, vt linea directionis per <lb></lb>centra vtriuſque ducatur, determinatio noua eſt æqualis priori<emph.end type="italics"></emph.end>; </s>
					<s id="N151F0">Patet ex­<lb></lb>perientia in pilis illis eburneis, quas deſiderat ludus minoris tudiculæ; </s>
					<s id="N151F6"><lb></lb>nec eſt vlla ratio, cur determinatio ſit maior potiùs, quàm minor, cum <lb></lb>vtraque pila ſit æqualis; </s>
					<s id="N151FD">ſi enim maior eſſet, vel minor; cur potiùs vno <lb></lb>gradu, quàm duobus? </s>
					<s id="N15203">quàm tribus? </s>
					<s id="N15206">Præterea, cum reſiſtens, vel im­<lb></lb>pediens eſt æquale agenti; </s>
					<s id="N1520C">certe ſicut agens refundit in paſſum totum <lb></lb>id, quod habet, id eſt æqualem impetum in intenſione, &amp; æquè velo­<lb></lb>cem motum per Th. 60. Ita reſiſtens, vel impediens refundit æquale <lb></lb>impedimentum, quod tantùm ſumi poteſt ex æqualitate mobilium; </s>
					<s id="N15218">ſed <lb></lb>ex æquali impedimento duci tantùm poteſt æqualis determinatio priori; <lb></lb>denique poteſt dari determinatio noua æqualis priori, vt conſtat, ſed <lb></lb>aliunde duci non poteſt quàm ex ipſa mobilium æqualitate, modò fiat <lb></lb>contactus per lineam connectentem centra. </s>
				</p>
				<p id="N15224" type="main">
					<s id="N15226"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 128.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15232" type="main">
					<s id="N15234"><emph type="italics"></emph>Hinc ratio manifeſta illius mirifici effectus, ſcilicet quietis pilæ impactæ<emph.end type="italics"></emph.end>; </s>
					<s id="N1523D"><lb></lb>quippe hæc quieſcet illicò ab ictu; </s>
					<s id="N15242">quia ſcilicet, cum noua determina­<lb></lb>tio ſit æqualis priori, non eſt vlla ratio, cur alterutra præualeat; </s>
					<s id="N15248">nec <lb></lb>etiam poteſt eſſe determinatio communis, ſeu mixta; cur enim potius <lb></lb>dextrorſum quam ſiniſtrorſum? </s>
					<s id="N15250">de quo infrà. </s>
				</p>
				<p id="N15253" type="main">
					<s id="N15255"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 129.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15261" type="main">
					<s id="N15263"><emph type="italics"></emph>Quando linea directionis globi impacti non connectit centra vtriuſquę <lb></lb>globi, determinatur noua linea motus tùm à priore linea incidentiæ, tùm à <lb></lb>connectente centra, quæ ſcilicet per punctum contactus à centro impacti globi<emph.end type="italics"></emph.end><pb pagenum="65" xlink:href="026/01/097.jpg"></pb><emph type="italics"></emph>ad centrum alterius ducitur<emph.end type="italics"></emph.end>; quippe nihil eſt aliud à quo determinari. </s>
					<s id="N15279"><lb></lb>poſſit, vt patet; </s>
					<s id="N1527D">non determinatur etiam ab alterutra ſeorſim, vt con­<lb></lb>ſtat, igitur ab vtraque conjunctim; </s>
					<s id="N15283">in qua verò proportione dicemus, <lb></lb>&amp; demonſtrabimus in libro de motu reflexo; ſunt enim mirificæ quæ­<lb></lb>dam reflexionum proportiones, quas ibidem explicabimus. </s>
				</p>
				<p id="N1528B" type="main">
					<s id="N1528D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 130.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15299" type="main">
					<s id="N1529B"><emph type="italics"></emph>Hinc globus ſic impactus nunquam quieſcit<emph.end type="italics"></emph.end>; </s>
					<s id="N152A4">ratio eſt, quia vtraque linea <lb></lb>determinationis cum angulum faciat, in communem lineam abit; </s>
					<s id="N152AA">nam <lb></lb>ex duabus lineis motus minimè oppoſitis ex diametro, fit alia tertia me­<lb></lb>dia pro rata; hîc etiam latent myſteria, de quibus loco citato. </s>
				</p>
				<p id="N152B2" type="main">
					<s id="N152B4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 131.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N152C0" type="main">
					<s id="N152C2"><emph type="italics"></emph>Si globus minor in maiorem impingatur per quamcumque lineam directio­<lb></lb>nis, determinatur ad nouam lineam motus reflexi<emph.end type="italics"></emph.end>; </s>
					<s id="N152CD">experientia clara eſt; ra­<lb></lb>tio eſt, quia maior globus maius eſt impedimentum, hinc nunquam <lb></lb>quieſcit minor globus impactus. </s>
				</p>
				<p id="N152D5" type="main">
					<s id="N152D7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 132.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N152E3" type="main">
					<s id="N152E5"><emph type="italics"></emph>Si globus major in minorem impingatur per lineam directionis, quæ conne­<lb></lb>ctat centra, ſeruat <expan abbr="eãdem">eandem</expan> lineam<emph.end type="italics"></emph.end>; </s>
					<s id="N152F4">patet etiam experientiâ, cuius ratio eſt <lb></lb>minor reſiſtentia minoris globi; </s>
					<s id="N152FA">ſi verò ſit alia linea directionis, omni­<lb></lb>nò reflectitur ſuo modo; </s>
					<s id="N15300">id eſt mutat lineam; </s>
					<s id="N15304">ſed de his omnibus fusè <lb></lb>aliàs; </s>
					<s id="N1530A">hîc tantùm ſufficiat indicaſſe; </s>
					<s id="N1530E">(ſuppoſita linea directionis cen­<lb></lb>trali ſeu connectente centra, ſic enim deinceps eam appellabimus, in <lb></lb>quo caſu duplex determinatio tertiam mediam conflare non poteſt) in­<lb></lb>dicaſſe inquam ſufficiat nouam determinationem, vel eſſe æqualem prio­<lb></lb>ri, vel maiorem, vel minorem; </s>
					<s id="N1531A">ſi æqualis eſt, globus impactus ſiſtit; ſi <lb></lb>maior, reflectitur; ſi minor, <expan abbr="eãdem">eandem</expan> lineam, ſed lentiùs pro rata pro­<lb></lb>ſequitur. </s>
				</p>
				<p id="N15326" type="main">
					<s id="N15328"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 133.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15334" type="main">
					<s id="N15336"><emph type="italics"></emph>Si ſit duplex impetus æqualis ad diuerſas lineas determinatus in eodem mo­<lb></lb>bili, ſique illæ ſint ex diametro oppoſitæ ſiſtere debet mobile<emph.end type="italics"></emph.end>; patet; </s>
					<s id="N15341">ſit enim <lb></lb>globus vtrimque gemino malleo percuſſus æquali ictu; </s>
					<s id="N15347">haud dubiè ſiſtit; <lb></lb>cur enim potiùs in vnam partem quam in aliam? </s>
					<s id="N1534D">cum ſimul in vtramque <lb></lb>moueri non poſſit. </s>
				</p>
				<p id="N15352" type="main">
					<s id="N15354"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 134.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15360" type="main">
					<s id="N15362"><emph type="italics"></emph>Si verò alter impetus ſit intenſior, poſito eodem caſu, haud dubiè eius de­<lb></lb>terminatio præualebit pro rata<emph.end type="italics"></emph.end>; patet etiam experientià; </s>
					<s id="N1536D">ratio eſt, quia im­<lb></lb>petus fortior debiliorem vincit; pugnant enim pro rata per Ax. 15. <lb></lb>hinc ſi ſit duplò intenſior, ſubduplum ſuæ velocitatis amittet, ſi triplè <lb></lb>ſubtriplum, &amp;c. </s>
					<s id="N15377">de quo aliàs. </s>
				</p>
				<p id="N1537A" type="main">
					<s id="N1537C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 135.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15388" type="main">
					<s id="N1538A"><emph type="italics"></emph>Si duo globi projecti ſibi inuicem occurrant in lineæ directionis connectente <lb></lb>centra, reflectitur vterque æquali motu, quo antè.<emph.end type="italics"></emph.end></s>
					<s id="N15393"> Probatur; </s>
					<s id="N15396">ſunt enim globi <pb pagenum="66" xlink:href="026/01/098.jpg"></pb>A &amp; B, &amp; A feratur per lineam DE, &amp; B per lineam ED, punctum con­<lb></lb>tactus ſit C, haud dubiè globus A impactus in B amittit totum ſuum im­<lb></lb>petum per Th.127. &amp; 128. B, item impactus in A amittit totum ſuum per <lb></lb>eandem rationem; </s>
					<s id="N153A5">globus A producit impetum in B æqualem ſuo per <lb></lb>Th.60. item B producit in A æqualem per idem Th. igitur tantùm perit <lb></lb>impetus quantùm accedit; </s>
					<s id="N153AD">igitur in vtroque globo remanet æqualis im­<lb></lb>petus priori; igitur æquali motu vterque mouetur, quod erat dem. </s>
					<s id="N153B3">&amp; hæc <lb></lb>eſt ratio veriſſima toties probatæ experientiæ. </s>
				</p>
				<p id="N153B8" type="main">
					<s id="N153BA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 136.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N153C6" type="main">
					<s id="N153C8"><emph type="italics"></emph>Hinc æquale ſpatium conficiet regrediendo poſt reflexionem, quem confeciſ­<lb></lb>ſet motu directo, ſi propagatus fuiſſet ſine obice<emph.end type="italics"></emph.end>; </s>
					<s id="N153D3">nam æquali motu æquali <lb></lb>tempore in eodem plano ſeu medio idem ſpatium decurritur; quid verò <lb></lb>accidat in aliis punctis contactus dicemus infrà, cum de reflexione. </s>
				</p>
				<p id="N153DB" type="main">
					<s id="N153DD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 137.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N153E9" type="main">
					<s id="N153EB"><emph type="italics"></emph>Si in eodem mobili duplex impetus producatur, quorum vterque ſeorſim <lb></lb>ad duas lineas ſit determinatus quæ conjunctæ faciant angulum, determinatur <lb></lb>vterque ad tertiam lineam mediam<emph.end type="italics"></emph.end>; </s>
					<s id="N153F8">ſit enim mobile in A. v. g. globus, <lb></lb>cui ſimul imprimatur impetus determinatus ad lineam AD, in plano <lb></lb>horizontali AF; </s>
					<s id="N15404">ſi vterque ſit æqualis, ad nouam lineam determinabi­<lb></lb>tur AE; </s>
					<s id="N1540A">quippe tantùm debet acquirere in horizontali AB, vel in eius <lb></lb>parallela DE, quantum acquirit in alia horizontali AD, vel in eius pa­<lb></lb>rallela BE; </s>
					<s id="N15412">igitur debet ferri in E; </s>
					<s id="N15416">igitur per diagonalem AE; </s>
					<s id="N1541A">clara eſt <lb></lb>omninò experientia; </s>
					<s id="N15420">cuius ratio à priori hæc eſt, quòd ſcilicet impetus <lb></lb>poſſit determinari ad quamlibet lineam ab alio impetu per Th.118.119. <lb></lb>igitur in eodem mobili pro rata quilibet alium determinat; </s>
					<s id="N15428">igitur ſi <lb></lb>vterque æqualis eſt, vterque æqualiter; igitur debet tantum ſpatij acqui­<lb></lb>ri in linea vnius, quantum in linea alterius. </s>
				</p>
				<p id="N15430" type="main">
					<s id="N15432">Si verò impetus per AC ſit duplus impetus per AD; </s>
					<s id="N15436">accipiatur AC <lb></lb>dupla AD, ducatur DF æqualis &amp; parallela AC; </s>
					<s id="N1543C">linea motus noua <lb></lb>erit diagonalis AF, quia vtraque determinatio concurrit ad nouam pro <lb></lb>rata; igitur debet ſpatium acquiſitum in AC eſſe duplum acquiſiti <lb></lb>in AD. </s>
				</p>
				<p id="N15447" type="main">
					<s id="N15449"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 138.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15455" type="main">
					<s id="N15457"><emph type="italics"></emph>Si ſit duplex impetus in eodem mobili ad <expan abbr="eãdem">eandem</expan> lineam determinatus, non <lb></lb>mutabitur linea; </s>
					<s id="N15463">ſed creſcet motus &amp; ſpatium<emph.end type="italics"></emph.end> Imprimatur impetus in A, <lb></lb>per AB, quo dato tempore percurratur ſpatium AB; </s>
					<s id="N1546C">deinde produca­<lb></lb>tur ſimul alius impetus æqualis priori in eodem mobili per lineam AB; </s>
					<s id="N15472"><lb></lb>Dico quod eodem tempore percurretur tota AE, dupla ſcilicet AB; </s>
					<s id="N15477"><lb></lb>quia ſcilicet dupla cauſa non impedita duplum effectum habet per Ax. <lb></lb>13. num.1. duplus impetus duplum motum; igitur duplum ſpatium; ſi <lb></lb>verò ſit triplus impetus, triplum erit ſpatium, &amp;c. </s>
				</p>
				<p id="N15481" type="main">
					<s id="N15483"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 139.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1548F" type="main">
					<s id="N15491"><emph type="italics"></emph>Si lineæ duplicis impetus, faciunt angulum acutiorem, longius erit ſpatium<emph.end type="italics"></emph.end><pb pagenum="67" xlink:href="026/01/099.jpg"></pb><emph type="italics"></emph>acquiſitum<emph.end type="italics"></emph.end>: </s>
					<s id="N154A3">ſint duæ lineæ IK IL, mobili ſcilicet ſtatuto in I; </s>
					<s id="N154A7"><lb></lb>haud dubiè noua linea erit IM; </s>
					<s id="N154AC">&amp; quo angulus KIL, erit acutior (ſup­<lb></lb>poſitis æqualibus ſemper lateribus IK IL) Diagonalis IM, erit ma­<lb></lb>ior; </s>
					<s id="N154B4">donec tandem IL &amp; IK coeant in eandem lineam; </s>
					<s id="N154B8">tunc enim li­<lb></lb>nea erit dupla IK per Th. ſuperius: </s>
					<s id="N154BE">quandiu verò eſt aliquis angulus in <lb></lb>I quantumuis acutus, linea motus erit minor dupla IK, ad quam tamen <lb></lb>propiùs ſemper accedit; quæ omnia conſtant ex elementis. </s>
				</p>
				<p id="N154C6" type="main">
					<s id="N154C8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 140.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N154D4" type="main">
					<s id="N154D6"><emph type="italics"></emph>Si lineæ duplicis impetus faciunt angulum obtuſum, ſpatium acquiſitum erit <lb></lb>breuius, &amp; eò breuius quò angulus eſt obtuſior<emph.end type="italics"></emph.end>; </s>
					<s id="N154E1">ſint enim <emph type="sup"></emph>c<emph.end type="sup"></emph.end> duæ lineæ AD <lb></lb>AB mobili ſtatuto in A, noua linea erit AC per Th. 137. &amp; ſi accipia­<lb></lb>tur angulus obtuſior HEF; </s>
					<s id="N154EF">noua linea erit EG, eo rectè breuior, <lb></lb>quò angulus eſt obtuſior, non tamen iuxta rationem angulorum; </s>
					<s id="N154F5">donec <lb></lb>tandem deſinat angulus, &amp; ED EF coëant in vnam lineam; </s>
					<s id="N154FB">tunc enim <lb></lb>nullum erit ſpatium, quia ſiſter omninò mobile per Th.133.quæ omnia <lb></lb>ipſa luce clariora eſſe conſtat; </s>
					<s id="N15503">quippe quæ cum certis experimentis, &amp; <lb></lb>clariſſimis principiis conſentiant; ſed de his plura infrà. </s>
				</p>
				<p id="N15509" type="main">
					<s id="N1550B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 141.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15517" type="main">
					<s id="N15519"><emph type="italics"></emph>Ex his neceſſaria ducitur ratio, cur impetus duplus ad diuerſas lineas de­<lb></lb>terminatus non habeat motum duplum, &amp; conſequenter ſpatium duplum<emph.end type="italics"></emph.end>; </s>
					<s id="N15524">nec <lb></lb>enim AE eſt dupla AB, vt conſtat; </s>
					<s id="N1552A">nam ſi lineæ ſint oppoſitæ ex <lb></lb>diametro vt BA BE totus deſtruitur impetus, per Th.133. ſi verò vna <lb></lb>in <expan abbr="eãdem">eandem</expan> lineam coëat cum aliâ, nihil impetus deſtruitur, nec impedi­<lb></lb>tur per Th.138. igitur quà proportione propiùs accedet ad oppoſitas; </s>
					<s id="N15538"><lb></lb>plùs deſtruetur, &amp; minus erit ſpatium; &amp; quâ proportione accedent <lb></lb>propiùs ad coëuntes, minùs deſtruetur, &amp; maius erit ſpatium, vt conſtat <lb></lb>ex dictis. </s>
				</p>
				<p id="N15541" type="main">
					<s id="N15543"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 142.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1554F" type="main">
					<s id="N15551"><emph type="italics"></emph>Hinc impetus ad diuerſas lineas determinati it a pugnant pro rata, vt mi­<lb></lb>nùs pugnent, quorum lineæ propiùs accedunt ad coëuntes; plùs verò, quorum <lb></lb>lineæ propiùs accedunt ad oppoſitas, idque iuxta proportiones Diagonalium,<emph.end type="italics"></emph.end><lb></lb>quod totum ſequitur ex dictis. </s>
				</p>
				<p id="N1555F" type="main">
					<s id="N15561"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1556D" type="main">
					<s id="N1556F">Obſeruabis vt faciliùs concipias duos impetus ad duas lineas deter­<lb></lb>minatos; </s>
					<s id="N15575">finge tibi nauim à diuerſis ventis impulſam, ſeu lapidem pro­<lb></lb>jectum è naui mobili; ſed de his plura in lib.4. cum de motu mixto. </s>
				</p>
				<p id="N1557B" type="main">
					<s id="N1557D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 143.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15589" type="main">
					<s id="N1558B"><emph type="italics"></emph>Impetus ſemel productus, quamdiu durat motus, conſeruatur.<emph.end type="italics"></emph.end></s>
					<s id="N15592"> Probatur, <lb></lb>quia non poteſt eſſe effectus, niſi ſit eius cauſa per Ax. 8. igitur ſi eſt mo­<lb></lb>tus, eſt impetus. </s>
				</p>
				<p id="N15599" type="main">
					<s id="N1559B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 144.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N155A7" type="main">
					<s id="N155A9"><emph type="italics"></emph>Impetus non conſeruatur à cauſa primò productiua.<emph.end type="italics"></emph.end></s>
					<s id="N155B0"> Probatur; quia proii-<pb pagenum="68" xlink:href="026/01/100.jpg"></pb>ciatur mobile per Poſtulatum, etiam mouetur ſeparatum à potentia mo­<lb></lb>trice per hypoth. </s>
					<s id="N155BA">6. igitur non conſeruatur à potentia motrice per Ax. <lb></lb>10. igitur nec à causâ primò productiua. </s>
				</p>
				<p id="N155C0" type="main">
					<s id="N155C2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 145.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N155CE" type="main">
					<s id="N155D0"><emph type="italics"></emph>Hinc ab alia causâ conſeruari neceſſe eſt impetum<emph.end type="italics"></emph.end>: Probatur, quia impe­<lb></lb>tus non eſt à ſe, quia deſtruitur aliquando per Ax. 14. igitur conſeruatur <lb></lb>ab alio per Ax.14. num. </s>
					<s id="N155DD">1. non à cauſa primò productiua per Th.144.igi­<lb></lb>tur ab alia, eaque applicata per Ax. 10. quæcumque tandem illa ſit, ali­<lb></lb>quando cauſam primam eſſe demonſtrabimus; </s>
					<s id="N155E7">nunc verò ſufficiat dixiſ­<lb></lb>ſe dari aliquam cauſam reuerâ applicatam, quæ ipſum conſeruat impe­<lb></lb>tum; immò ex hac ipſa rerum conſeruatione argumentum aliquando <lb></lb>ducemus, quo Deum ipſum exiſtere demonſtrabimus. </s>
				</p>
				<p id="N155F1" type="main">
					<s id="N155F3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 146.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N155FF" type="main">
					<s id="N15601"><emph type="italics"></emph>Si impetus conſeruaretur à cauſa primò productiua, nunquam deſtruere­<lb></lb>tur, quamdiu eſſet applicata.<emph.end type="italics"></emph.end></s>
					<s id="N1560A"> Demonſtratur, quia eſſet cauſa neceſſaria <lb></lb>(nam de hac ipſa loquor) igitur ſemper ageret, igitur ſemper con­<lb></lb>ſeruaret, quod eſt contra experientiam; </s>
					<s id="N15612">nam reuerâ impetus pro­<lb></lb>ductus deorſum à corpore graui motu naturaliter accelerato deſtruitur, <lb></lb>vt patet; </s>
					<s id="N1561A">præterea ſi corpus graue conſeruaret impetum primò produ­<lb></lb>ctum, non produceret nouum contra experientiam; </s>
					<s id="N15620">quippe cauſa ne­<lb></lb>ceſſaria non plùs agit vno inſtanti quàm alio, per Ax.12. adde quod im­<lb></lb>petus deſtruitur ad exigentiam alterius, quidquid tandem illud ſit per <lb></lb>Ax.14. num.2. &amp; 3. ſed cauſa primò productiua impetus non nouit rerum <lb></lb>exigentiam; </s>
					<s id="N1562C">igitur illi facere ſatis non poteſt; ex hoc etiam capite cau­<lb></lb>ſæ primæ exiſtentiam ſuo loco demonſtrabimus. </s>
				</p>
				<p id="N15632" type="main">
					<s id="N15634"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15640" type="main">
					<s id="N15642">Obſeruabis primò rem quamlibet ideo deſtrui, quia ceſſat cauſa con­<lb></lb>ſeruans illam conſeruare; </s>
					<s id="N15648">quippe quod deſtruitur eo inſtanti dicitur de­<lb></lb>ſtrui, quo primò non eſt, ſeu quo incipit primò non eſſe; atqui incipit <lb></lb>primò non eſſe ſeu deſinit eſſe, cum deſinit conſeruari. </s>
				</p>
				<p id="N15650" type="main">
					<s id="N15652">Secundò obſeruabis præclarum naturæ inſtitutum, quod etiam ex ipſis <lb></lb>hypotheſibus conſtat, quo fit vt qualitates quæ carent contrario à cauſa <lb></lb>primò productiua conſeruentur, vt lumen; </s>
					<s id="N1565A">ne ſi ab alia conſeruarentur, <lb></lb>deſtruerentur vmquam; </s>
					<s id="N15660">cum earum deſtructionem nihil exigeret per <lb></lb>Ax.14.n.2. &amp; 3. at verò qualitates, quæ contrarias habent: </s>
					<s id="N15666">ſi quæ ſunt, <lb></lb>à cauſa primò productiua minimè conſeruantur; </s>
					<s id="N1566C">cum enim ideo con­<lb></lb>trarium dicatur deſtruere contrarium, quia exigit eius deſtructionem, id <lb></lb>eſt, ne conſeruetur amplius; </s>
					<s id="N15674">certè vt cauſa conſeruans ceſſet conſeruare, <lb></lb>debet noſſe illam exigentiam; atqui nulla cognitione pollent cauſæ illæ <lb></lb>motrices naturales, de quibus eſt quæſtio. </s>
				</p>
				<p id="N1567C" type="main">
					<s id="N1567E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 147.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1568A" type="main">
					<s id="N1568C"><emph type="italics"></emph>Tamdiu conſeruatur impetus, quamdiu nihil exigit eius destructionem<emph.end type="italics"></emph.end>; </s>
					<s id="N15695">quia <lb></lb>deſtruitur tantùm ad exigentiam alicuius, quidquid tandem illud ſit, de <pb pagenum="69" xlink:href="026/01/101.jpg"></pb>quo infrà, per Ax.14.num.2. certè tamdiu non deſtruitur, quamdiu nihil <lb></lb>eſt, quod exigat eius deſtructionem; igitur tamdiu conſeruatur per Ax. <lb></lb>14.num.3. </s>
				</p>
				<p id="N156A5" type="main">
					<s id="N156A7"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N156B4" type="main">
					<s id="N156B6">Inde certa ducitur ratio, cur mobile etiam ſeparatum à manu mouea­<lb></lb>tur; </s>
					<s id="N156BC">quia ſcilicet ipſi adhuc ineſt impetus, qui eſt cauſa motus; </s>
					<s id="N156C0">quippe <lb></lb>ſuppoſui iam antè de hac hypotheſi quod ſit, non tamen propter quid ſit; <lb></lb>igitur hæc eſt germana illius ratio &amp; cauſa. </s>
				</p>
				<p id="N156C8" type="main">
					<s id="N156CA"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N156D7" type="main">
					<s id="N156D9">Hinc etiam rationem ducemus æquè præclaram in lib.2. motus natu­<lb></lb>raliter accelerati. </s>
				</p>
				<p id="N156DE" type="main">
					<s id="N156E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 148.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N156EC" type="main">
					<s id="N156EE"><emph type="italics"></emph>Impetus productus aliquando deſtruitur<emph.end type="italics"></emph.end>; Probatur, quia mobile, quod <lb></lb>antè mouebatur, deſinit tandem moueri per hyp. </s>
					<s id="N156F9">4. igitur deſtruitur <lb></lb>impetus; alioqui ſi remaneret, eſſet cauſa neceſſaria ſine effectu contra <lb></lb>Ax.12. ideo porrò deſtruitur, quia aliquid exigit eius deſtructionem, <lb></lb>quippe hæc eſt vnica deſtructionis ratio per Ax.14. num.2. </s>
				</p>
				<p id="N15703" type="main">
					<s id="N15705"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 149.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15711" type="main">
					<s id="N15713"><emph type="italics"></emph>In lineis oppoſitis impetus deſtruitur ab impetu ſuo modo<emph.end type="italics"></emph.end>; </s>
					<s id="N1571C">ſit enim globus <lb></lb>proiectus verſus auſtrum; </s>
					<s id="N15722">cui deinde imprimatur nouus impetus ver­<lb></lb>ſus Boream; </s>
					<s id="N15728">deſtruitur prior vt conſtat, igitur ad exigentiam alicuius, <lb></lb>ſed nihil eſt quod poſſit exigere, niſi nouus impetus, ſcilicet mediatè; <lb></lb>nihil enim aliud eſt applicatum, igitur nihil aliud exigit per Ax. 10. <lb></lb>hæc porrò exigentia non eſt immediata, ſed mediata, vt dixi. </s>
				</p>
				<p id="N15732" type="main">
					<s id="N15734"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 150.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15740" type="main">
					<s id="N15742"><emph type="italics"></emph>Impetus naturalis innatus exigit deſtructionem alterius, qui ab extrinſeco <lb></lb>ad diuerſam lineam corpori graui impreſſus eſt ſcilicet mediatè,<emph.end type="italics"></emph.end> experientia <lb></lb>certa eſt in proiectis, quæ tandem quieſcunt; </s>
					<s id="N1574F">igitur ad exigentiam ali­<lb></lb>cuius, ſed illud tantùm eſt impetus innatus; </s>
					<s id="N15755">nec enim eſt ſubſtantia <lb></lb>corporis; </s>
					<s id="N1575B">tùm quia qualitas ſubſtantiæ non opponitur; </s>
					<s id="N1575F">tùm quia nulla <lb></lb>eſſet ratio, cur ſubſtantia deſtrueret potiùs vno inſtanti vnum gradum, <lb></lb>quàm duos, quàm tres; </s>
					<s id="N15767">adde quod ex duobus violentis oppoſitis alte­<lb></lb>rum deſtruit; igitur impetus eſt cauſa ſufficiens deſtructiua impetus, <lb></lb>igitur non eſt ponenda alia, eo ſcilicet modo, quo diximus. </s>
				</p>
				<p id="N1576F" type="main">
					<s id="N15771"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 151.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1577D" type="main">
					<s id="N1577F"><emph type="italics"></emph>In reflexione deſtruitur aliquid impotus ſaltem per accidens<emph.end type="italics"></emph.end>; patet expe­<lb></lb>rientia, ſiue propter nouam determinationem, ſiue propter attritum, <lb></lb>vel preſſionem partium, de quo infrà. </s>
				</p>
				<p id="N1578C" type="main">
					<s id="N1578E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 152.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1579A" type="main">
					<s id="N1579C"><emph type="italics"></emph>Hinc ſi excipias tantùm impetum naturalem innatum, qui per ſuam de­<lb></lb>terminationem neceſſariam, &amp; quam nunquam mutat, pugnat cum omni<emph.end type="italics"></emph.end><pb pagenum="70" xlink:href="026/01/102.jpg"></pb><emph type="italics"></emph>extrinſeco ad aliam lineam determinato, &amp; cum ipſo acquiſito, quando mu­<lb></lb>tat lineam perpendicularem deorſum, de quo infrà; ſi hunc igitur excipias, <lb></lb>omnes aly pugnant tantùm ratione diuerſæ lineæ, ſeu determinationis, in eodem <lb></lb>mobili:<emph.end type="italics"></emph.end> Vnde ille idem, qui modo pugnat probè conueniet, ſi ad ean­<lb></lb>dem lineam determinetur. </s>
				</p>
				<p id="N157B8" type="main">
					<s id="N157BA"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N157C6" type="main">
					<s id="N157C8">Obſeruabis primò, præclarum naturæ inſtitutum, quo fit, vt impe­<lb></lb>tus perennis non ſit; vnde certè infinita propemodum emergerent ab­<lb></lb>ſurda, &amp; incommoda. </s>
				</p>
				<p id="N157D0" type="main">
					<s id="N157D2">Secundò, faciliorem modum deſtructionis impetus inſtitui non po­<lb></lb>tuiſſe, immò nec excogitari poſſe; quàm enim facilè, vel impetus op­<lb></lb>poſitus in mobili producitur, vel corpus durum opponitur &amp;c. </s>
				</p>
				<p id="N157DA" type="main">
					<s id="N157DC">Tertiò, præcipuam rationem huius deſtructionis ducendam eſſe ex <lb></lb>Ax.6. in quo dicimus nihil eſſe fruſtrà, cumque ordinem à natura eſſe <lb></lb>inſtitutum, vt potiùs aliquid deſtruatur, &amp; deſinat eſſe, quàm fruſtrà ſit, <lb></lb>&amp; dicimus deſtrui ad exigentiam totius naturæ. </s>
				</p>
				<p id="N157E5" type="main">
					<s id="N157E7">Quartò, cum impetus ſuo fine caret, fruſtrà eſt; </s>
					<s id="N157EB">finis impetus eſt mo­<lb></lb>tus, vt ſæpè diximus, ſic cum globus impactus in alium æqualem ſtatim <lb></lb>ab ictu ſiſtit immobilis; </s>
					<s id="N157F3">certe ne fruſtrà ſit impetus, deſtruitur per Ax.6. <lb></lb>&amp; per Ax. 14. num.2. cum verò determinatio altera maior eſt, certè præ­<lb></lb>ualet tantùm pro rata; </s>
					<s id="N157FB">igitur minor eſt motus; </s>
					<s id="N157FF">igitur, ne aliqui gradus <lb></lb>impetus ſint fruſtrà, deſtruuntur, cum verò ſunt duo impetus in eodem <lb></lb>mobili, vt in naui mobili ad lineas oppoſitas determinati; </s>
					<s id="N15807">haud dubiè <lb></lb>maior impetus præualet pro rata per Ax. 15. Igitur non modò totus <lb></lb>impetus minor perit, ne ſit fruſtrà; </s>
					<s id="N1580F">ſed etiam aliquot gradus maioris, ne <lb></lb>ſint etiam fruſtrà; nec enim in communem lineam coïre poſſunt. </s>
				</p>
				<p id="N15815" type="main">
					<s id="N15817">Denique quando ſunt duo impetus ad lineas diuerſas determinati, <lb></lb>ſed non oppoſitas ex diametro, pugnant pro diuerſo oppoſitionis gradu, <lb></lb>vt ſuprà fusè dictum eſt. </s>
					<s id="N1581E">Igitur cum totus impetus non habeat totum <lb></lb>motum, quod duplex illa determinatio impedit, ne aliqui gradus <lb></lb>ſint fruſtrà, deſtruuntur; </s>
					<s id="N15826">igitur vides impetum impreſſum ab ex­<lb></lb>trinſeco deſtrui tantùm ne ſit fruſtrà; faceret enim vt eſſet fruſtrà vel <lb></lb>nouus impetus, vel determinato noua, &amp; in hoc ſenſu dicitur impetus <lb></lb>deſtrui ab impetu. </s>
				</p>
				<p id="N15830" type="main">
					<s id="N15832">Quintò, ſi deſtrueretur mobile, etiam deſtrueretur impetus per idem <lb></lb>Ax. 6. quia eſſet fruſtrà ſeparatum; </s>
					<s id="N15838">immò ex hoc vno principio demon­<lb></lb>ſtramus accidentia &amp; formas ſubſtantiales materiales non poſſe natura­<lb></lb>liter conſeruari extra ſuum ſubiectum, quia ſcilicet eſſent fruſtrà; quip­<lb></lb>pe finem ſuum habent in ſubiecto. </s>
				</p>
				<p id="N15842" type="main">
					<s id="N15844">Sextò, Impetus naturalis innatus nunquam deſtruitur; </s>
					<s id="N15848">quia nunquam <lb></lb>eſt fruſtrà; quippe ſemper habet alterum ſuorum effectuum formalium, <lb></lb>id eſt vel motum deorſum, vel grauitationem, adde quod fruſtrà de­<lb></lb>ſtrueretur, cum ſit ſemper applicata potentia, id eſt ipſa grauitas, ſed de <lb></lb>his infrâ fusè. </s>
				</p>
				<pb pagenum="71" xlink:href="026/01/103.jpg"></pb>
				<p id="N15858" type="main">
					<s id="N1585A">Septimò, Impetus ſurſum deſtruitur etiam, quia eſt fruſtrà; </s>
					<s id="N1585E">quippe <lb></lb>naturalis detrahit aliquid ſpatij pro rata; </s>
					<s id="N15864">igitur ne aliquid impetus ſit <lb></lb>fruſtrà, deſtruitur; </s>
					<s id="N1586A">idem dico de impetu per inclinatam ſurſum, licèt <lb></lb>minùs deſtruatur quàm in perpendiculari ſurſum; </s>
					<s id="N15870">idem de impetu per <lb></lb>inclinatam deorſum, ſed minùs adhuc, ſed hæc acuratiori meditationi <lb></lb>ſunt relinquenda; </s>
					<s id="N15878">quod reuerâ præſtabimus in lib.4. de motu mixto; </s>
					<s id="N1587C"><lb></lb>quidquid ſit, conſtat ex dictis per idem Principium probari poſſe de­<lb></lb>ſtructionem impetus, ſcilicet ne ſit fruſtrà; ſed de his aliàs fusè. </s>
				</p>
				<p id="N15883" type="main">
					<s id="N15885"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 153.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15891" type="main">
					<s id="N15893"><emph type="italics"></emph>Impetus productus ab extrinſeco eſt tantùm contrarius ratione diuerſæ de­<lb></lb>terminationis, ſeu diuerſæ lineæ<emph.end type="italics"></emph.end>; </s>
					<s id="N1589E">Probatur primò, quia vterque ad omnem <lb></lb>lineam eſt indifferens per Th.113. igitur vnus non eſt alteri contrarius <lb></lb>ratione entitatis; </s>
					<s id="N158A6">cùm vterque ſimilem motum, immò <expan abbr="eũdem">eundem</expan> habere <lb></lb>poſſit, vt patet ex dictis: </s>
					<s id="N158B0">Igitur ratione tantùm lineæ vnus alteri eſt <lb></lb>contrarius; hinc minùs eſt contrarietatis, quo minùs eſt oppoſitionis <lb></lb>inter lineas &amp; contrà. </s>
				</p>
				<p id="N158B8" type="main">
					<s id="N158BA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 154.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N158C6" type="main">
					<s id="N158C8"><emph type="italics"></emph>Impetus naturalis acquiſitus eſt tantùm contrarius alteri extrinſeco ratio­<lb></lb>ne lineæ.<emph.end type="italics"></emph.end></s>
					<s id="N158D1"> Probatur eodem modo; quia determinari poteſt ad omnem li­<lb></lb>neam, vt patet ex reflexione grauis cadentis. </s>
				</p>
				<p id="N158D6" type="main">
					<s id="N158D8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 155.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N158E4" type="main">
					<s id="N158E6"><emph type="italics"></emph>Impetus naturalis innatus non eſt tantùm contrarius ratione lineæ<emph.end type="italics"></emph.end>; quia <lb></lb>ſcilicet non poteſt determinari ad omnem lineam, patet, alioquin cor­<lb></lb>pus graue, quod ſurſum poſt caſum reflectitur non deſcenderet amplius, <lb></lb>de quo aliàs, hæc enim curſim tantùm perſtringo, ne quid aliis libris <lb></lb>detrahatur. </s>
				</p>
				<p id="N158F7" type="main">
					<s id="N158F9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 156.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15905" type="main">
					<s id="N15907"><emph type="italics"></emph>Impetus ex naturali acquiſito poteſt fieri violentus<emph.end type="italics"></emph.end>; </s>
					<s id="N15910">vt patet in motu re­<lb></lb>flexo grauium; ratio eſt. </s>
					<s id="N15916">quia mutatur linea. </s>
				</p>
				<p id="N15919" type="main">
					<s id="N1591B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 157.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15927" type="main">
					<s id="N15929"><emph type="italics"></emph>Impetus ex non contrario eidem fit contrarius<emph.end type="italics"></emph.end>; </s>
					<s id="N15932">vt patet in eodem caſu; <lb></lb>nam impetus naturalis innatus, qui in deſcenſu non erat contrarius <lb></lb>acquiſito, in motu ſurſum reflexo fit contrarius. </s>
				</p>
				<p id="N1593A" type="main">
					<s id="N1593C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 158.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15948" type="main">
					<s id="N1594A"><emph type="italics"></emph>Impetus deorſum ab extrinſeco non eſt contrarius naturali innato ratione <lb></lb>lineæ,<emph.end type="italics"></emph.end> quia ſcilicet eſt determinatus ad eandem lineam, ſi tamen eſt con­<lb></lb>trarius, id tantùm eſt ratione propagationis impetus acquiſiti, vel ac <lb></lb>celerationis motus; quod reuerà multa, &amp; benè longâ explicatione indi­<lb></lb>get, quam conſule in lib.4. </s>
				</p>
				<p id="N1595B" type="main">
					<s id="N1595D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15969" type="main">
					<s id="N1596B">Obſeruabis cognoſci tantùm contrarietatem qualitatum ex mutua de­<lb></lb>ſtructione; </s>
					<s id="N15971">cur verò vna qualitas dicatur deſtruere aliam, &amp; cur illam <pb pagenum="72" xlink:href="026/01/104.jpg"></pb>deſtructionem exigat; </s>
					<s id="N1597A">maximum myſterium eſt, quod alibi enucleabi­<lb></lb>mus; quàm multa enim ſuper hac re tacuere Philoſophi! </s>
				</p>
				<p id="N15981" type="main">
					<s id="N15983"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 159.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1598F" type="main">
					<s id="N15991"><emph type="italics"></emph>Impetus ſibi ipſi poteſt reddi contrarius,<emph.end type="italics"></emph.end> vt reuerâ accidit in reflexione, <lb></lb>in qua deſtruitur impetus ex parte propter diuerſas determinationes; </s>
					<s id="N1599C"><lb></lb>cum ſcilicet corpus reflectens mouetur; igitur impetus prout determina­<lb></lb>tus ad lineam incidentiæ eſt aliquo modo ſibi ipſi contrarius, prout eſt <lb></lb>determinatus ad lineam reflexionis. </s>
				</p>
				<p id="N159A5" type="main">
					<s id="N159A7">Iam ferè tumultuatim, ſi quæ ſunt reliqua, Theoremata congeremus. </s>
				</p>
				<p id="N159AA" type="main">
					<s id="N159AC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 160.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N159B8" type="main">
					<s id="N159BA"><emph type="italics"></emph>Impetus violentus intendi poteſt à naturali, &amp; viciſſim<emph.end type="italics"></emph.end>; patet in projectis <lb></lb>deorſum. </s>
				</p>
				<p id="N159C5" type="main">
					<s id="N159C7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 161.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N159D3" type="main">
					<s id="N159D5">Idem impetus poteſt <expan abbr="eũdem">eundem</expan> alium aliquando plùs, aliquando minùs <lb></lb>intendere. </s>
					<s id="N159DE">v. g. 4. gradus impetus additi aliis 4. per <expan abbr="eãdem">eandem</expan> lineam <lb></lb>iidem eiſdem, minùs intendunt, vt iam ſuprà ſatis fusè dictum eſt. </s>
				</p>
				<p id="N159EB" type="main">
					<s id="N159ED"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 162.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N159F9" type="main">
					<s id="N159FB"><emph type="italics"></emph>Impetus dici poteſt propriè deſtrui ad exigentiam totius naturæ<emph.end type="italics"></emph.end> per Ax.14. <lb></lb>num.2. vt conſtat ex multis Theorematis ſuperioribus. </s>
				</p>
				<p id="N15A05" type="main">
					<s id="N15A07"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 163.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15A13" type="main">
					<s id="N15A15"><emph type="italics"></emph>Omnis dici debet incipere, &amp; deſinere intrinſecè, &amp; extrinſecè<emph.end type="italics"></emph.end>; quod enim <lb></lb>hoc inſtanti primo eſt, immediatè antecedenti vltimo non fuit, &amp; quod <lb></lb>primo non eſt hoc inſtanti, immediatè antè vltimo fuit, nec poteſt eſſe <lb></lb>immediatè pòſt, niſi ſit immediatè antè, &amp; viciſſim. </s>
				</p>
				<p id="N15A24" type="main">
					<s id="N15A26"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 164.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15A32" type="main">
					<s id="N15A34"><emph type="italics"></emph>Ideo producitur hic impetus numero potiùs, quàm alius omninò ſimilis<emph.end type="italics"></emph.end>; </s>
					<s id="N15A3D">quia <lb></lb>potentia motrix eſt determinata ad tale indiuiduum ſiue à ſe, ſiue ab <lb></lb>alio; </s>
					<s id="N15A45">idem enim de illa dicendum eſt, quod de aliis cauſis naturalibus; <lb></lb>porrò idem dici debet de deſtructione, quod de productione. </s>
				</p>
				<p id="N15A4B" type="main">
					<s id="N15A4D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15A59" type="main">
					<s id="N15A5B">Obſeruabis breuiter aliqua, quæ fortè in noſtris Theorematis fuere <lb></lb>omiſſa. </s>
				</p>
				<p id="N15A60" type="main">
					<s id="N15A62">Primò qualitates, quæ à cauſa primò productiua conſeruantur, ab ea <lb></lb>intendi non poſſe; </s>
					<s id="N15A68">quia ſingulis inſtantibus nouum effectum non pro­<lb></lb>ducit; </s>
					<s id="N15A6E">exemplum habes in luce; ſecus vero de iis dicendum eſt, quæ à <lb></lb>cauſa primò productiua non conſeruantur. </s>
				</p>
				<p id="N15A74" type="main">
					<s id="N15A76">Secundò qualitates, quæ contrarias habent, etiam deſtrui poſſe ab <lb></lb>alio, quam ab iis, ſcilicet ad exigentiam totius naturæ; ne ſcilicet ſint <lb></lb>fruſtrà. </s>
				</p>
				<p id="N15A7E" type="main">
					<s id="N15A80">Tertiò aliqua carere contrario, non tamen conſeruari à cauſa primò <lb></lb>productiua. </s>
					<s id="N15A85">v.g. anima bruti, quæ deſtruitur ad exigentiam totius natu­<lb></lb>ræ, nç ſit fruſtrà. </s>
				</p>
				<pb pagenum="73" xlink:href="026/01/105.jpg"></pb>
				<p id="N15A90" type="main">
					<s id="N15A92">Quartò, impetum intenſiorem in projectis diutiùs durare; </s>
					<s id="N15A96">quia cum <lb></lb>ſenſim deſtruatur; certè plures partes maiori tempore deſtruuntur, quàm <lb></lb>pauciores. </s>
				</p>
				<p id="N15A9E" type="main">
					<s id="N15AA0">Quintò, ſi totus impetus deſtrueretur vno inſtanti, minima reſiſtentia <lb></lb>ſufficeret ad motum impediendum: adde quod contraria pugnant pro <lb></lb>rata per Ax.15. </s>
				</p>
				<p id="N15AA8" type="main">
					<s id="N15AAA">Sextò, obſeruabis plurima in hoc libro quaſi obiter eſſe indicata, quæ <lb></lb>in aliis fusè explicata maiorem lucem accipient. </s>
				</p>
				<p id="N15AAF" type="main">
					<s id="N15AB1">Septimò, denique totam rem iſtam, quæ pertinet ad impetum paulò <lb></lb>fuſius pertractatam in hoc primo libro; </s>
					<s id="N15AB7">quòd ſcilicet ab ea reliqua ferè <lb></lb>omnia pendeant, quæ in hoc tractatu habentur; ſed de his ſatis. <lb></lb><figure id="id.026.01.105.1.jpg" xlink:href="026/01/105/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N15AC3">
				<pb pagenum="74" xlink:href="026/01/106.jpg"></pb>
				<figure id="id.026.01.106.1.jpg" xlink:href="026/01/106/1.jpg"></figure>
				<p id="N15ACD" type="head">
					<s id="N15ACF"><emph type="center"></emph>LIBER SECVNDVS, <lb></lb><emph type="italics"></emph>DE MOTV NATVRALI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15ADC" type="main">
					<s id="N15ADE">MOtus localis naturalis latè ſumptus eſt, <lb></lb>qui ab aliqua causâ naturali ponitur; </s>
					<s id="N15AE4"><lb></lb>ſtrictè verò ſumitur pro motu grauium <lb></lb>deorſum, à principio intrinſeco ſaltem <lb></lb>ſenſibiliter; </s>
					<s id="N15AED">In hoc vltimo ſenſu mo­<lb></lb>tum naturalem vſurpabo; ſit ergo. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N15AF6" type="main">
					<s id="N15AF8"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15B04" type="main">
					<s id="N15B06"><emph type="italics"></emph>MOtus localis naturalis eſt, qui eſt à grauitate deorſum.<emph.end type="italics"></emph.end> hæc defini­<lb></lb>tio vix aliqua explicatione indiget; dicitur eſſe à grauitate, <lb></lb>quidquid ſit grauitas, ſiue qualitas diſtincta, ſiue non. </s>
				</p>
				<p id="N15B13" type="main">
					<s id="N15B15"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15B22" type="main">
					<s id="N15B24"><emph type="italics"></emph>Motus æquabilis eſt, quo æqualibus quibuſcumque temporibus æqualia per­<lb></lb>curruntur ſpatia ab eodem mobili.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N15B2D" type="main">
					<s id="N15B2F"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15B3C" type="main">
					<s id="N15B3E"><emph type="italics"></emph>Motus naturaliter acceleratus eſt, quo ſecundo tempore æquali primo ma­<lb></lb>ius ſpatium acquiritur, &amp; tertio, quàm ſecundo, &amp; quarto quàm tertio, atque <lb></lb>ita deinceps; nulla ſcilicet addita vi ab extrinſeco ſaltem ſenſibiliter.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N15B4A" type="main">
					<s id="N15B4C">Definit aliter hunc motum Galileus; </s>
					<s id="N15B50">dicit enim eum eſſe, qui æquali­<lb></lb>bus temporibus æqualia acquirit velocitatis momenta; </s>
					<s id="N15B56">ſed profectò non <lb></lb>conuenit hæc definitio omni motui naturaliter accelerato, v. g. motui <lb></lb>deſcenſus funependuli, vel in orbe cauo, vel etiam in plano decliui ma­<lb></lb>ximæ longitudinis; definitio noſtra clarior eſt. </s>
				</p>
				<p id="N15B64" type="main">
					<s id="N15B66"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15B73" type="main">
					<s id="N15B75"><emph type="italics"></emph>Corpus graue cadit deorſum, &amp; cadens ex maiori altitudine maiorem ictum <lb></lb>infligit quam ſi caderet ex minore<emph.end type="italics"></emph.end>; ſi quis hoc neget hoc probet, patet ma­<lb></lb>nifeſta experientia. </s>
				</p>
				<pb pagenum="75" xlink:href="026/01/107.jpg"></pb>
				<p id="N15B86" type="main">
					<s id="N15B88"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15B95" type="main">
					<s id="N15B97"><emph type="italics"></emph>Arcus maior &amp; minor eiuſdem funependuli æqualibus ferè temporibus, <lb></lb>percurruntur<emph.end type="italics"></emph.end>; hæc etiam ſæpiùs probata eſt, &amp; ſi quis fidem detrectat, <lb></lb>probare conetur. </s>
				</p>
				<p id="N15BA4" type="main">
					<s id="N15BA6"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15BB3" type="main">
					<s id="N15BB5">Globus per planum inclinatum læuigatum deſcendens ſecundum ſpa­<lb></lb>tium citiùs percurrit, quàm primum; quod etiam ſenſu percipi poteſt, <lb></lb>&amp; tam ſæpè probatum eſt, vt nemo iam negare audeat motus naturalis <lb></lb>accelerationem. </s>
				</p>
				<p id="N15BBF" type="main">
					<s id="N15BC1"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15BCE" type="main">
					<s id="N15BD0"><emph type="italics"></emph>Omne tempus ſenſibile non eſt; </s>
					<s id="N15BD6">idem dico de ſpatio,<emph.end type="italics"></emph.end> quod nemo etiam <lb></lb>negare auſit; alioquin ſi quis negaret, dicat mihi quæſo quot ſint in mi­<lb></lb>nuto horæ inſtantia? </s>
					<s id="N15BE1">quot in apice acus puncta? </s>
				</p>
				<p id="N15BE4" type="main">
					<s id="N15BE6"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15BF3" type="main">
					<s id="N15BF5"><emph type="italics"></emph>Impetus additus alteri, &amp; determinatus ad <expan abbr="eãdem">eandem</expan> lineam, facit maiorem <lb></lb>&amp; intenſiorem impetum<emph.end type="italics"></emph.end>; patet, &amp; viciſſim, &amp; detractus alteri minorem <lb></lb>facit, &amp; viciſſim. </s>
				</p>
				<p id="N15C06" type="main">
					<s id="N15C08"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15C15" type="main">
					<s id="N15C17"><emph type="italics"></emph>Quâ proportione creſcit cauſa, eâdem creſcit effectus, &amp; viciſſim, ſi eodem <lb></lb>modo eidemque ſubjecto ſit applicata,<emph.end type="italics"></emph.end> probatur per Ax.12. l. 1. &amp; quâ pro­<lb></lb>portione illa decreſcit, hic decreſcit, &amp; viciſſim. </s>
				</p>
				<p id="N15C25" type="main">
					<s id="N15C27"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15C34" type="main">
					<s id="N15C36"><emph type="italics"></emph>Eadem cauſa neceſſaria non impedita ſubjecto apte applicata æqualibus <lb></lb>temporibus æqualem effectum producit, &amp; contrà.<emph.end type="italics"></emph.end></s>
					<s id="N15C3F"> Probatur per Ax.12.l. </s>
					<s id="N15C42">1. &amp; <lb></lb>viciſſim æqualis effectus ſupponit æqualem cauſam. </s>
				</p>
				<p id="N15C47" type="main">
					<s id="N15C49"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15C56" type="main">
					<s id="N15C58"><emph type="italics"></emph>Ille effectus, qui non producitur à causâ primâ, &amp; ad cuius productionem <lb></lb>nulla cauſa extrinſeca eſt applicata, producitur ab intrinſeco<emph.end type="italics"></emph.end>; probatur, quia <lb></lb>habere debet aliquam cauſam per Ax.8. </s>
				</p>
				<p id="N15C66" type="main">
					<s id="N15C68"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15C75" type="main">
					<s id="N15C77"><emph type="italics"></emph>Illa cauſa plus agit proportionaliter quæ habet minorem reſistentiam; minùs <lb></lb>verò, quæ maiorem, quæ demum æqualem, æquali proportione agit.<emph.end type="italics"></emph.end> v.g. cauſa, <lb></lb>cuius virtus, vel actiuitas eſt vt 20. &amp; reſiſtentia vt 10. agit in maiori <lb></lb>proportione, quàm illa cuius actiuitas eſt 30. &amp; reſiſtentia 20. in minori <lb></lb>verò quàm ea, cuius actiuitas eſt vt 3. &amp; reſiſtentia vt 1. in æquali de­<lb></lb>nique cum illa, cuius actiuitas eſt vt 4. &amp; reſiſtentia vt 2. </s>
				</p>
				<p id="N15C8D" type="main">
					<s id="N15C8F">Hoc Axioma certiſſimum eſt; </s>
					<s id="N15C93">quippe 20. faciliùs ſuperabunt 10. quàm <lb></lb>30. 20. &amp; difficiliùs quam 3. 1. &amp; æquè facilè, ac 4. 2. In motu locali <lb></lb>res eſt clariſſima; </s>
					<s id="N15C9B">quippe vires vt 12. tam facilè mouebunt 12. libras, <lb></lb>quàm vires vt 4. 4.libras; </s>
					<s id="N15CA1">ſed faciliùs, quàm vires vt 20. 30.libras, &amp; dif­<lb></lb>ficiliùs quàm vires vt 4. 3. libras; quid clarius? </s>
					<s id="N15CA7">Igitur illa cauſa faciliùs <pb pagenum="76" xlink:href="026/01/108.jpg"></pb>ſuperat reſiſtentiam impedimenti, quæ habet maiorem proportionem <lb></lb>virium cum reſiſtentia, quàm quæ minorem. </s>
				</p>
				<p id="N15CB1" type="main">
					<s id="N15CB3"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N15CBF" type="main">
					<s id="N15CC1">Si quando appellandum erit aliquod Axioma vel Theorema lib.  1.ci­<lb></lb>tabitur Liber. </s>
				</p>
				<p id="N15CC6" type="main">
					<s id="N15CC8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15CD5" type="main">
					<s id="N15CD7"><emph type="italics"></emph>Datur motus localis naturalis, iſque ab intrinſeco.<emph.end type="italics"></emph.end></s>
					<s id="N15CDE"> Probatur; corpus gra­<lb></lb>ue mouetur localiter deorſum per hypoth. </s>
					<s id="N15CE3">hic motus eſt ab intrinſeco, <lb></lb>quod probatur; </s>
					<s id="N15CE9">non eſt ab vllâ causâ extrinſecâ; igitur eſt ab intrinſeca <lb></lb>per Ax.4. antecedens probatur inductione factâ omnium extrinſecorum. </s>
					<s id="N15CEF"><lb></lb>Primò non eſt à cauſa prima, vt aliquis fortè minùs prudenter, &amp; magis <lb></lb>piè, quàm par ſit, diceret; </s>
					<s id="N15CF6">quia ille effectus tribui tantùm debet cauſæ <lb></lb>primæ, qui nullam habere poteſt cauſam ſecundam applicatam, vt patet; </s>
					<s id="N15CFC"><lb></lb>ſed hic effectus poteſt habere cauſam ſecundam applicatam, quam aſſi­<lb></lb>gnabimus infrà; </s>
					<s id="N15D03">deinde cauſa prima agit tantùm naturaliter iuxta exi­<lb></lb>gentiam cauſarum ſecundarum; </s>
					<s id="N15D09">igitur ideo moueret corpus graue deor­<lb></lb>ſum; </s>
					<s id="N15D0F">quia tunc motum corpus graue exigeret; </s>
					<s id="N15D13">ſed hoc mihi ſufficit, vt <lb></lb>dicatur hic motus eſſe ab intrinſeco; </s>
					<s id="N15D19">præterea, ſi dicatur Deus mouere <lb></lb>corpus graue deorſum iuxta illius exigentiam, dicetur etiam tùm cale­<lb></lb>facere, tùm illuminare, ad exigentiam ignis; </s>
					<s id="N15D21">quippe tàm mihi ſenſibile <lb></lb>eſt corpus graue deſcendere ſine vi impreſſa ab extrinſeco, quàm ignem <lb></lb>calefacere, &amp; ſolem lucere ſine vi extrinſeca; </s>
					<s id="N15D29">adde quod illud ſolenne <lb></lb>eſt naturæ inſtitutum, vt id, quod exigit res aliqua ad finem ſuum conſe­<lb></lb>quendum, per virtutem intrinſecam poſſit ponere, ſi dumtaxat excipias <lb></lb>concurſum diuinum, &amp; ipſam conſeruationem; </s>
					<s id="N15D33">ſic animal exigit vide­<lb></lb>re, audire, ſentire, moueri; </s>
					<s id="N15D39">igitur habet virtutem intrinſecam, per quam <lb></lb>videat, audiat, &amp; moueatur; </s>
					<s id="N15D3F">ſic ignis exigit calefacere, lucere; </s>
					<s id="N15D43">aër, vel aqua <lb></lb>frigefacere, quidquid tandem ſint iſtæ qualitates, de quibus alibi; </s>
					<s id="N15D49">ſic <lb></lb>demum corpus graue exigit moueri deorſum; quis enim neget corpori <lb></lb>graui tàm natiuum eſſe tendere deorſum, cum ſcilicet corpus leuius ſub­<lb></lb>eſt, quàm ſit animali progredi, vrere igni, lucere, &amp;c. </s>
				</p>
				<p id="N15D53" type="main">
					<s id="N15D55">Denique ſatis eſt mihi, vt dicatur aliquid cauſa, Phyſicè loquendo, ſi <lb></lb>ex illius applicatione ſemper ſequatur effectus; </s>
					<s id="N15D5B">nam non nego poſſe fie­<lb></lb>ri effectus omnes, qui noſtris ſenſibus ſubiiciuntur, ſaltem extrinſecos, <lb></lb>eſſe à cauſa prima, quippe ſi ſemper ex ignis applicatione Deus diffun­<lb></lb>deret lucem, &amp; calorem, quem ſolus ipſe produceret, igne ipſo inerte re­<lb></lb>licto, nullam prorſus mutationem perciperemus; </s>
					<s id="N15D67">&amp; nemo eſſet, qui non <lb></lb>exiſtimaret lucem hanc &amp; calorem hunc eſſe ab igne; </s>
					<s id="N15D6D">igitur Phyſicè lo­<lb></lb>quendo cauſam appellamus id, ex cuius applicatione ſemper ſequitur <lb></lb>effectus, vt iam diximus in Ax. 11.l.1. n.1. Igitur cum ex corpore graui <lb></lb>poſito in aëre libero ſequatur motus deorſum; dicendum eſt, Phyſicè lo­<lb></lb>quendò, eſſe huius motus cauſam, id eſt in ordine ad Phyſicam, perinde <lb></lb>omninò ſe habere, atque ſi eſſet cauſa, licèt cauſa non eſſet. </s>
				</p>
				<pb pagenum="77" xlink:href="026/01/109.jpg"></pb>
				<p id="N15D7F" type="main">
					<s id="N15D81">Secundò hic motus non eſt ab aëre ambiente; </s>
					<s id="N15D85">probatur, ruderet aër <lb></lb>deorſum corpus graue, quia leuior eſt, id eſt ne ſuprà ſe corpus grauius <lb></lb>haberet; </s>
					<s id="N15D8D">ſed eâdem ratione corpus graue debet remouere ſurſum aëra, <lb></lb>id eſt corpus leue, ne infrà ſe habeat corpus leuius; </s>
					<s id="N15D93">eſt enim par omni­<lb></lb>nò ratio: </s>
					<s id="N15D99">Præterea ſi aër trudit deorſinn corpus graue, quia ipſi loco <lb></lb>cedit; </s>
					<s id="N15D9F">certè ipſe aër mouetur, igitur ab intrinſeco; </s>
					<s id="N15DA3">ſi enim vna pars aë­<lb></lb>ris pellit aliam, &amp; hæc aliam, tandem ad aliquam peruenitur, quæ ſe ip­<lb></lb>ſam mouet; </s>
					<s id="N15DAB">igitur motus illius eſt ab intrinſeco; </s>
					<s id="N15DAF">igitur motus natura­<lb></lb>lis; </s>
					<s id="N15DB5">deinde non modò lapis deſcendit per aëra, ſed per mediam aquam; </s>
					<s id="N15DB9"><lb></lb>igitur ſi ab aëre truditur deorſum, idem dicendum eſt de aquâ, a qui <lb></lb>haud dubiè maiore vi truderetur; </s>
					<s id="N15DC0">nam corpus denſum maiore vi pellit, <lb></lb>quàm rarum, vt conſtat exprientiâ; </s>
					<s id="N15DC6">cum tamen corpus graue per me­<lb></lb>dium denſius difficiliùs decendat; igitur medium ipſum reſiſtit motui, <lb></lb>quis hoc neget? </s>
					<s id="N15DCE">igitur non eſt cauſa motus, quem impedit. </s>
				</p>
				<p id="N15DD1" type="main">
					<s id="N15DD3">Denique ſi corpus graue non tendit, fertur que deorſum ſuá ſponte, <lb></lb>ſed ab aëre extruſum; </s>
					<s id="N15DD9">igitur dum vix ſuſtineo manu; o. </s>
					<s id="N15DDD">libras ferri, ſeu <lb></lb>plumbi; </s>
					<s id="N15DE2">hæc vis illata manui, quam probè ſentio, eſt ab aëre impel­<lb></lb>lente plumbum, quod eſt ridiculum, cum eadem quantitas aëris incu­<lb></lb>ber, &amp; ſubſit manui, ſiue ſuſtineat plumbum, ſiue ſit vacua; ex hoc, ni <lb></lb>fallor, euincitur pondus ipſum ſui ſponte deorſum tendere. </s>
				</p>
				<p id="N15DEC" type="main">
					<s id="N15DEE">Tertiò non deſunt, qui dicant corpus graue trahi ab ipſa vi quadam <lb></lb>magneticâ, quod triplici modo fieri poteſt; </s>
					<s id="N15DF4">Primò per qualitatem <lb></lb>quamdam diffuſam, quod dici non poteſt; </s>
					<s id="N15DFA">quia capillus traheretur faci­<lb></lb>liùs, quàm ingens ſaxum, quàm maſſa, ſeu lamina; </s>
					<s id="N15E00">&amp; faciliùs eadem po­<lb></lb>tentia motrix minus pondus moueret quàm maius, cæteris paribus; </s>
					<s id="N15E06">præ­<lb></lb>terea manum meam æqualiter traheret, ſiue ſit cum aliquo pondere con­<lb></lb>iuncta, ſiue ſit nuda ſine pondere; </s>
					<s id="N15E0E">deinde illa virtus tractrix ita diffun­<lb></lb>ditur, vt in maiori diſtantia ſit infirmior, fortior in minori; </s>
					<s id="N15E14">alioqui <lb></lb>diffunderetur in infinitum, quod dici non poteſt; </s>
					<s id="N15E1A">igitur ſi idem lapis <lb></lb>demittatur ex maiore altitudine, tum ex minore; </s>
					<s id="N15E20">haud dubiè morus ille <lb></lb>primus initio eſſet tardior iſto contra experientiam; </s>
					<s id="N15E26">deinde in ſpecu al­<lb></lb>tiſſima ſubterranea trahi poſſet corpus vndequaque, ſicut in magnete; </s>
					<s id="N15E2C"><lb></lb>quæ omnia intelligi non poſſunt; denique virtutes illas ſeu qualitates <lb></lb>tractrices refellemus ſuo loco. </s>
				</p>
				<p id="N15E33" type="main">
					<s id="N15E35">Secundò, aliqui dicunt hoc totum fieri per vim quamdam ſympathi­<lb></lb>cam, quod etiam falſiſſimum eſt; </s>
					<s id="N15E3B">tùm quia hæc ſympathia explicari <lb></lb>non poteſt; </s>
					<s id="N15E41">tùm quia vel terra ipſa producit aliquid in corpore graui, <lb></lb>quod in aëre libratur; </s>
					<s id="N15E47">vel corpus in ſe ipſo; ſi primum; </s>
					<s id="N15E4B">refellitur iiſ­<lb></lb>dem omninò rationibus, quibus ipſam vim terræ tractricem ſuprà expu­<lb></lb>gnauimus; ſi verò ſecundum, hoc ipſum eſt, quod ſuprà diximus. </s>
				</p>
				<p id="N15E53" type="main">
					<s id="N15E55">Tertiò, Dixere aliqui ſubtiliùs profectò quàm veriùs, corpus graue <lb></lb>trahi deorſum, non vi quadam occultâ, vt ſuprà dictum eſt; </s>
					<s id="N15E5B">ſed filamen­<lb></lb>tis quibuſdam, ſeu ductili terræ profluuio, quod illius capillitium vo­<lb></lb>cant; </s>
					<s id="N15E63">idque tantùm fieri probant ducta ab electro analogiâ, quod pa­<lb></lb>leam &amp; minutiora corpuſcula hac eâdem arte trahit; </s>
					<s id="N15E69">ſed profectò gra-<pb pagenum="78" xlink:href="026/01/110.jpg"></pb>uiores ſunt difficultates, quam vt illis fieri ſatis queat; </s>
					<s id="N15E72">nam primò cor­<lb></lb>pus leuius ab his filamentis abripi faciliùs poſſet, vt conſtat in electro; <lb></lb>igitur citiùs deſcenderet. </s>
				</p>
				<p id="N15E7A" type="main">
					<s id="N15E7C">Secundò, corpus vicinius etiam faciliùs abriperetur. </s>
				</p>
				<p id="N15E7F" type="main">
					<s id="N15E81">Tertiò, numquid flante vento, vel imbre cadente diſſipantur hæc fi­<lb></lb>lamenta? </s>
					<s id="N15E86">quod etiam videmus in electro. </s>
				</p>
				<p id="N15E89" type="main">
					<s id="N15E8B">Quartò, manum meam æquè facilè traheret terra his funiculis ſeu <lb></lb>pondere grauatam, ſeu vacuam. </s>
				</p>
				<p id="N15E90" type="main">
					<s id="N15E92">Quintò, quemadmodum electrum ex omni parte trahit, ita terra ipſa <lb></lb>per omnem lineam traheret; immò etiam ſurſum in ſubterranea ſpecu, <lb></lb>quod eſt abſurdum. </s>
				</p>
				<p id="N15E9A" type="main">
					<s id="N15E9C">Sextò, hæc filamenta, quæ deinde reducuntur, debent habere cau­<lb></lb>ſam huius reductionis non extrinſecam; </s>
					<s id="N15EA2">igitur intrinſecam; igitur datur <lb></lb>motus naturalis. </s>
				</p>
				<p id="N15EA8" type="main">
					<s id="N15EAA">Septimò, hæc filamenta per mediam flammam non traherent, quod <lb></lb>etiam fieri videmus in electro. </s>
				</p>
				<p id="N15EAF" type="main">
					<s id="N15EB1">Quartò, motus naturalis non eſt à virtute quadam pellente, quam <lb></lb>cælo quidam affingunt; </s>
					<s id="N15EB7">nam vel ab omni parte cæli deorſum trudere­<lb></lb>tur, vel ab vnâ; ſi ab vna; </s>
					<s id="N15EBD">igitur in omni cæli plaga corpus non fertur <lb></lb>deorſum; </s>
					<s id="N15EC3">ſi ab omni, ergo cum pellatur corpus per plures lineas etiam <lb></lb>oppoſitas moueri non poteſt: </s>
					<s id="N15EC9">Præterea debilior eſſet hæc vis in maiori <lb></lb>diſtantiâ; denique vapores, &amp; alia minutiora corpuſcula in aëre fluitan­<lb></lb>tia faciliùs deorſum truderentur, contra experientiam. </s>
				</p>
				<p id="N15ED1" type="main">
					<s id="N15ED3">Sed non eſt omittendum, quod aliqui putant ex illis filamentis con­<lb></lb>texi poſſe legitimam rationem, cur atomi etiam plumbeæ materiæ non <lb></lb>ita facilè deſcendant; </s>
					<s id="N15EDB">quòd ſcilicet propter ſuam tenuitatem ab illis fi­<lb></lb>lamentis non ita intercipi vel implicari poſſint; </s>
					<s id="N15EE1">ſed quaſi piſces per fo­<lb></lb>ramina retium euadant; ſed profectò longè alia ratio eſt, quàm ſuo loco <lb></lb>afferemus, nam etiam plumæ, feſtucæ, paleæ, &amp; alia corpuſcula longio­<lb></lb>ra, ſed leuiſſima iis filamentis implicarentur, vt videre eſt in electro. </s>
				</p>
				<p id="N15EEB" type="main">
					<s id="N15EED">Quintò, aliqui recentiores exiſtimant corpora deorſum trudi ab <lb></lb>ipſa luce, quæ nihil eſt aliud, quam motio æthereæ cuiuſdam ſubſtan­<lb></lb>tiæ per poros aëris traductæ, vt ipſi volunt; ſed neque hoc probari po­<lb></lb>teſt. </s>
					<s id="N15EF7">Primò quia de nocte corpora æquali motu deorſum feruntur; pe­<lb></lb>rinde atque de die, nec minùs in obſcuriſſimo conclaui, quàm ſub dio, <lb></lb>vel aperto cælo. </s>
					<s id="N15EFF">Secundò, in ſubterraneis locis etiam grauia æquè veloci­<lb></lb>ter deſcendunt; </s>
					<s id="N15F05">licèt eò lumen non penetret; </s>
					<s id="N15F09">quod ſi aliquis obſtinatè, <lb></lb>id aſſereret; </s>
					<s id="N15F0F">haud dubiè per medium aëra maior huius materiæ copia <lb></lb>diffunditur, quàm per medias rupes, quis hoc neget; igitur pauciſſimi <lb></lb>radij vſque ad interius &amp; inferius antrum perueniunt. </s>
					<s id="N15F17">Tertiò, manum <lb></lb>meam ſiue ponderi coniunctam ſiue ab eo <expan abbr="ſeparatã">ſeparatam</expan> æqualis portio illius <lb></lb>materiæ deorſum pelleret, vt patet; igitur æquali motus vi. </s>
					<s id="N15F23">Quartò, cor­<lb></lb>pus diaphanum, per cuius poros facilè traiicitur hæc materia, eſſet leuius <lb></lb>alio quod tamen falſum eſt, vt videre eſt in vitro, cryſtallo, adamante, <lb></lb>glacie. </s>
					<s id="N15F2C">Quintò maxima huius materiæ copia collecta ſeu ſpeculi opera <pb pagenum="79" xlink:href="026/01/111.jpg"></pb>ſeu vitri, maiore vi corpora deorſum truderet; </s>
					<s id="N15F35">quia maior cauſa maio­<lb></lb>rem effectum producit per Ax.2. Sextò poſt refractionem lineam mutat <lb></lb>radius luminis; igitur deorſum rectà non pelleret. </s>
					<s id="N15F3D">Septimò radij traie­<lb></lb>cti per vitrum maiore vi deorſum pellerent quàm per lignum, vel ſpon­<lb></lb>giam; quippè per hæc corpora traiecti ſecundum authores huius ſenten­<lb></lb>tiæ diſtrahuntur propter obliquitatem pororum. </s>
					<s id="N15F47">Octauò denique radij <lb></lb>profecti à Sole iuxta ortum, vel occaſum ſunt valdè obliqui; igitur non <lb></lb>truderent deorſum rectà. </s>
				</p>
				<p id="N15F4F" type="main">
					<s id="N15F51">Nec eſt quod prædicti àuthores confugiant ad experientiam, qua <lb></lb>ſcilicet videmus tripudiantes atomos in radio ſolari immerſas; igitur <lb></lb>agitantur ab ipſo radio, quod maximè accidit in linea vſtoria, cuius <lb></lb>effectus veriſſimam rationem ſuo loco afferemus, cum de lumine. </s>
				</p>
				<p id="N15F5B" type="main">
					<s id="N15F5D">Sextò, ſunt denique multi, <expan abbr="iiq́ue">iique</expan> ex ſeuerioribus Peripateticis, qui <lb></lb>exiſtimant grauia moueri deorſum à generante, quod expreſſis verbis <lb></lb>traditum eſt ab <emph type="italics"></emph>Ariſtotele l.<emph.end type="italics"></emph.end>8. <emph type="italics"></emph>phyſ. cap.<emph.end type="italics"></emph.end>4. <emph type="italics"></emph>iuxta<emph.end type="italics"></emph.end> principium illud vniuer­<lb></lb>ſaliſſimum; <emph type="italics"></emph>Quidquid mouetur; </s>
					<s id="N15F80">ab alio mouetur<emph.end type="italics"></emph.end>; </s>
					<s id="N15F87">ſed profectò ij ipſi, qui <lb></lb>motum grauium generanti tribuunt, tanquam principi cauſæ, non ne­<lb></lb>gant ineſſe grauibus grauitatem, quæ ſit principium actiuum minus <lb></lb>principale motus; </s>
					<s id="N15F91">ad quem etiam, vt ipſi exiſtimant, forma ſubſtantialis <lb></lb>concurrit; </s>
					<s id="N15F97">In hoc quippe conueniunt omnes tùm ſectarum Principes, <lb></lb>tùm recentiores: </s>
					<s id="N15F9D">quidquid ſit etiam ex iis ipſis datur motus naturalis, <lb></lb>qui eſt à virtute proxima intrinſeca; hoc ipſum etiam ſenſit Ariſtoteles <lb></lb>lib.4. de cælo cap.  3. t. </s>
					<s id="N15FA5">25. vbi ait grauibus &amp; leuibus ineſſe principium <lb></lb>actiuum ſuorum motuum; </s>
					<s id="N15FAB">immò ſi totum cap.4. l.8. phyſ. attentè lega­<lb></lb>tur, vbi dicit moueri à generante, haud dubiè intelligetur nihil aliud in­<lb></lb>tendiſſe Ariſtotelem quàm grauia à generante, inſtanti, quo generan­<lb></lb>tur, accipere actum primum huius motus; id eſt virtutem, à qua poſ­<lb></lb>ſint reduci ad actum ſecundum, id eſt ad ipſum motum, de cuius rei ve­<lb></lb>ritate iam mihi non eſt laborandum. </s>
				</p>
				<p id="N15FB9" type="main">
					<s id="N15FBB">Igitur non mouetur corpus graue à cauſa primâ, licèt hæc concurrat <lb></lb>cum aliâ ad eius motum, nec ab aëre, nec à virtute magnetica, quæ in­<lb></lb>ſit terræ, nec adductis, reductiſque filamentis, nec à cælo pellente, nec <lb></lb>à vi ſympathicâ, nec à generante proximè &amp; immediatè; </s>
					<s id="N15FC5">quia fortè iam <lb></lb>interiit, nec ab vllo alio extrinſeco, vt conſtat inductione; </s>
					<s id="N15FCB">igitur ab ali­<lb></lb>quâ vi intrinſecâ, quidquid ſit, de qua alibi: hæc omnia paulò fuſiùs <lb></lb>tractauimus, quia in hoc vno Theoremate totam motus naturalis rem <lb></lb>verti iudicamus. </s>
				</p>
				<p id="N15FD5" type="main">
					<s id="N15FD7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N15FE4" type="main">
					<s id="N15FE6"><emph type="italics"></emph>Motus naturalis est aliquid distinctum realiter à mobili:<emph.end type="italics"></emph.end> Probatur; </s>
					<s id="N15FEF"><lb></lb>mobile ipſum aliquando quieſcit per hypoth.4.lib.1. igitur eſt ſine mo­<lb></lb>tu; </s>
					<s id="N15FF6">igitur ſeparatum à motu; </s>
					<s id="N15FFA">igitur realiter diſtinctum per Ax.2. lib.1. <lb></lb>hoc etiam probatus per Th. 1.lib.  1. Et certè mirari ſatis non poſſum <lb></lb>aliquos recentiores non poſſe concipere, vt ipſi aiunt, motum eſſe ali­<lb></lb>quid ab ipſo mobili diſtinctum; </s>
					<s id="N16004">nam quotieſcunque duo prædicata, vel <pb pagenum="80" xlink:href="026/01/112.jpg"></pb>attributa contradictoria, quorum ſcilicet vnum negat aliud, eidem ſub­<lb></lb>jecto diuerſis temporibus ineſſe dicuntur, haud dubiè alterum ſaltem ab <lb></lb>eo diſtingui realiter neceſſe eſt; </s>
					<s id="N16011">alioqui ſi vtrumque idem eſſe cum vno <lb></lb>tertio vere dicitur; </s>
					<s id="N16017"><emph type="italics"></emph>mouetur, non monetur,<emph.end type="italics"></emph.end> quæ ſunt prædicata contradi­<lb></lb>ctoria; </s>
					<s id="N16022">igitur vel moueri, vel non moueri dicit diſtinctum realiter à mo­<lb></lb>bili; Secundum eſt mera negatio; </s>
					<s id="N16028">nam eo ipſo, quod mobile eſt ſine vllo <lb></lb>addito, non mouetur; </s>
					<s id="N1602E">igitur ſuprà ipſum mobile dicit puram putam ne­<lb></lb>gationem motus; igitur moueri, dicit aliquid diſtinctum. </s>
				</p>
				<p id="N16034" type="main">
					<s id="N16036">Præterea quotieſcunque prædicatum aliquod tribuitur in propoſi­<lb></lb>tione affirmatiua falsâ; </s>
					<s id="N1603C">certè prædicatum illud non ineſt ſubiecto; </s>
					<s id="N16040">alio­<lb></lb>quin eſſet vera, vt patet; </s>
					<s id="N16046">igitur diſtinguitur à ſubiecto realiter; </s>
					<s id="N1604A">ſed hæc <lb></lb>propoſitio, <emph type="italics"></emph>lapis mouetur,<emph.end type="italics"></emph.end> dum ipſe quieſcit, eſt falſa; igitur motus non <lb></lb>ineſt mobili, igitur ab eo diſtinguitur realiter, ſeu modaliter, quæ eſt <lb></lb>diſtinctio realis minor. </s>
				</p>
				<p id="N1605A" type="main">
					<s id="N1605C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16069" type="main">
					<s id="N1606B"><emph type="italics"></emph>Metus naturalis non eſt immediatè ab entitate mobilis, ita vt nihil ſit aliud <lb></lb>vnde ſit hic motus:<emph.end type="italics"></emph.end> Probatur; lapis cadens ex maiore altitudine maiorem <lb></lb>ictum infligit perhypoth. </s>
					<s id="N16078">1. maior eſt effectus, igitur maior cauſa, id eſt <lb></lb>motus; </s>
					<s id="N1607E">igitur cauſa motus per Ax.2. ſed eſt eadem entitas mobilis, vt <lb></lb>patet; </s>
					<s id="N16084">igitur non eſt cauſa immediata motus; Præterea globus per pla­<lb></lb>num inclinatum deuolutus ſuum motum accelerat per hypotl. </s>
					<s id="N1608A">3. &amp; fune­<lb></lb>pendulum ſuam vibrationem per hypoth. </s>
					<s id="N1608F">2. igitur debet eſſe cauſa huius <lb></lb>maioris, ſeu velocioris motus per Ax.8. lib.  1. hæc porrò non eſt ſub­<lb></lb>ſtantia ipſius corporis, quæ ſemper eadem eſt, tùm initio, tùm in fine <lb></lb>motus per Ax.2. </s>
				</p>
				<p id="N16098" type="main">
					<s id="N1609A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N160A7" type="main">
					<s id="N160A9"><emph type="italics"></emph>Motus naturalis non eſt immediatè ab ipſa grauitate.<emph.end type="italics"></emph.end></s>
					<s id="N160B0"> Probatur, ſint <lb></lb>enim eædem hypoth.1.2.3. igitur maior ictus in fine motus, &amp; velocior <lb></lb>motus debent habere cauſam; ſed hæc grauitas non eſt, quæ ſemper ea­<lb></lb>dem eſt, vt patet, vtrum verò diſtinguatur grauitas ab ipſa corporis <lb></lb>ſubſtantia diſcutiemus in tractatu ſequenti. </s>
					<s id="N160BC">Fuit aliquis non infimæ no­<lb></lb>tæ Philoſophus, qui diceret maiorem illum ictum eſſe ab ipsâ corporis <lb></lb>ſubſtantiâ; ſed hoc iam refellimus Theoremate 4. lib.1. Adde quod im­<lb></lb>petu, ad extra producitur ab alio impetu per Th.42.lib.1. Dicebat etiam <lb></lb>velociorem motum eſſe ab ipsâ grauitate connotante præuium motum, <lb></lb>quod etiam refellemus infrà. </s>
				</p>
				<p id="N160CA" type="main">
					<s id="N160CC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N160D9" type="main">
					<s id="N160DB"><emph type="italics"></emph>Hinc motus naturalis eſt ab impetu.<emph.end type="italics"></emph.end></s>
					<s id="N160E2"> Probatur; eſt ab aliqua cauſa per <lb></lb>Ax.8. lib.1. ab aliqua intrinſeca per Th. 1. non à ſubſtantia corporis <lb></lb>grauis per Th. 3. non à grauitate per Th. 4. igitur ab impetu, quia <lb></lb>nihil aliud eſſe poteſt intrinſecum, à quo ſit motus per definitionem <lb></lb>3. lib.  1. </s>
				</p>
				<pb pagenum="81" xlink:href="026/01/113.jpg"></pb>
				<p id="N160F2" type="main">
					<s id="N160F4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16101" type="main">
					<s id="N16103"><emph type="italics"></emph>Ille impetus ab aliqua cauſa producitur.<emph.end type="italics"></emph.end></s>
					<s id="N1610A"> Probatur, quia quidquid de no­<lb></lb>uo eſt, habet cauſam per Ax.8. lib.  1. </s>
				</p>
				<p id="N16110" type="main">
					<s id="N16112"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1611E" type="main">
					<s id="N16120">Producitur ab aliqua cauſa intrinſeca, quia non producitur ab aliqua <lb></lb>extrinſeca; alioquin motus naturalis eſſet ab extrinſeco contra definitio­<lb></lb>nem primam, &amp; Th.1. </s>
				</p>
				<p id="N16129" type="main">
					<s id="N1612B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16137" type="main">
					<s id="N16139"><emph type="italics"></emph>Hinc produci tantùm poteſt ab ipſa ſubstantia corporis grauis; </s>
					<s id="N1613F">nam graui­<lb></lb>tas eſt ipſe impetus innatus, de qua infrà:<emph.end type="italics"></emph.end> probatur; </s>
					<s id="N16148">quia nihil eſt aliud in­<lb></lb>trinſecum, à quo produci poſſit; quòd autem non producatur ab alio im­<lb></lb>petu ad intra, patet per Th.41. lib.  1. </s>
				</p>
				<p id="N16151" type="main">
					<s id="N16153"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1615F" type="main">
					<s id="N16161"><emph type="italics"></emph>Impetus productus primo instanti durat proximè ſequenti.<emph.end type="italics"></emph.end></s>
					<s id="N16168"> Probatur pri­<lb></lb>mò; </s>
					<s id="N1616D">quia ſemper habet ſuum effectum formalem; vel grauitationis, ſi <lb></lb>impeditur; </s>
					<s id="N16173">vel motus in medio libero; </s>
					<s id="N16177">igitur non eſt fruſtrà; </s>
					<s id="N1617B">igitur <lb></lb>non deſtruitur per Th.162.lib.1. nihil enim exigit deſtructionem; </s>
					<s id="N16181">non <lb></lb>tota natura, quia non eſt fruſtrà per Ax. 6. non à contrario impetu, qui <lb></lb>ſæpè abeſt, vt cum liberè mouetur corpus graue in aëre, vel ſuſtinetur, <lb></lb>v.g. glans plumbea ab ingenti rupe: </s>
					<s id="N1618D">adde quod, licèt producatur in cor­<lb></lb>pore graui impetus violentus ſurſum, non deſtruitur, tamen innatus; alio­<lb></lb>quin nihil eſſet, quod deſtrueret violentum per Th.150. &amp; Schol. Th. <lb></lb>152.num.6.lib.1. </s>
				</p>
				<p id="N1619B" type="main">
					<s id="N1619D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N161A9" type="main">
					<s id="N161AB"><emph type="italics"></emph>Impetus ille innatus, qui durat ſecundo instanti, conſeruatur ab aliqua cau­<lb></lb>ſa<emph.end type="italics"></emph.end>; eſt certum per Ax. 14.lib.1.num.1. </s>
				</p>
				<p id="N161B7" type="main">
					<s id="N161B9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N161C5" type="main">
					<s id="N161C7"><emph type="italics"></emph>Non conſeruatur à cauſa primò productiua.<emph.end type="italics"></emph.end></s>
					<s id="N161CE"> Probatur per Th.144. lib.1. <lb></lb>alioquin non poſſet intendi ab eadem cauſa per Th. 146. lib 1. quippè <lb></lb>conſeruatio nihil eſt aliud, quàm repetita productio, vt conſtat; </s>
					<s id="N161D6">nam <lb></lb>cauſa conſeruans verè influit; </s>
					<s id="N161DC">igitur ſi eſt cauſa neceſſaria primo, &amp; ſe­<lb></lb>cundo inſtanti æquali niſu influit; </s>
					<s id="N161E2">influit enim quantum poteſt per Ax. <lb></lb>12.lib.1.quòd autem impetus intendatur, demonſtrabimus infrà; </s>
					<s id="N161E9">conſule <lb></lb>Schol.Th.146.lib.1.in quo habes rationem præclari natura inſtituti; </s>
					<s id="N161EF">quo <lb></lb>ſcilicet factum eſt, vt qualitates, quæ contrario carent à causâ primò pro­<lb></lb>ductiua; aliæ verò, quæ contrarium habent, ab alia causà conſer­<lb></lb>uentur. </s>
				</p>
				<p id="N161F9" type="main">
					<s id="N161FB"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N16207" type="main">
					<s id="N16209">Hinc ab aliâ causâ conſeruari neceſſe eſt, vt patet, eáque aplicatâ per <lb></lb>Ax.10.lib.1. quæcumque tandem illa ſit; nos aliquando cauſam primam <lb></lb>eſſe dicemus. </s>
				</p>
				<pb pagenum="82" xlink:href="026/01/114.jpg"></pb>
				<p id="N16215" type="main">
					<s id="N16217"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16223" type="main">
					<s id="N16225"><emph type="italics"></emph>Quando graue eſt in medio libero, per quod ſcilicet deſcendere poteſt, ſecun­<lb></lb>do instanti producitur nouus impetus, itemque tertio, quarto, quinto. </s>
					<s id="N1622C">&amp;c.<emph.end type="italics"></emph.end></s>
					<s id="N16231"> Pro­<lb></lb>batur primò; </s>
					<s id="N16236">quia ſecundo inſtanti eſt eadem cauſa quæ primo non ma­<lb></lb>gis impedita, eáque neceſſaria; </s>
					<s id="N1623C">igitur neceſſariò agit per Ax. 12. lib.1. <lb></lb>igitur aliquem effectum producit; ſed hic effectus non eſt impetus pro­<lb></lb>ductus primo inſtanti, quia non conſeruatur à cauſa primò productiua <lb></lb>per Th.11. igitur eſt nouus. </s>
					<s id="N16246">Probatur ſecundò; creſcit motus grauium in <lb></lb>libero medio per hypoth. </s>
					<s id="N1624B">1.2.3. igitur creſcit impetus; </s>
					<s id="N1624E">quia cum motus <lb></lb>naturalis ſit ab impetu per Th.5. quâ proportione creſcit effectus, ſcilicet <lb></lb>formalis, &amp; exigentiæ; </s>
					<s id="N16256">ſic enim motus eſt effectus impetus per Th. 15. <lb></lb>lib.1.eàdem creſcit cauſa per Ax.2. Probatur tertiò, quia corpus graue ex <lb></lb>maiore altitudine cadens maiorem quoque ictum infligit per hypoth.1. <lb></lb>igitur maior impetus imprimitur in corpore percuſſo; ſed impetus ad ex­<lb></lb>tra producitur ab alio impetu per Th.42.lib.1. igitur ſi creſcit productus <lb></lb>inpetus, creſcit impetus producens. </s>
				</p>
				<p id="N16264" type="main">
					<s id="N16266"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N16272" type="main">
					<s id="N16274">Hinc reiicies quorumdam placitum, qui volunt cauſam velocioris <lb></lb>motus eſſe grauitatem ipſam, quatenus connotat motum præuium; </s>
					<s id="N1627A">quia <lb></lb>ſcilicet grauitas non producit illum maiorem impetum ad extra, vt con­<lb></lb>ſtat; </s>
					<s id="N16282">nec ſubſtantia ipſius corporis grauis per Th.40.lib.1.igitur ipſe im­<lb></lb>petus: </s>
					<s id="N16288">præterea ſi hoc eſſet, fruſtrà requireretur impetus contra Th. 5. <lb></lb>Denique motus præuius nihil eſt amplius, cum alius ſuccedit: Vide Th. <lb></lb>40.lib.1. vbi hæc fusè diſcuſſimus. </s>
				</p>
				<p id="N16291" type="main">
					<s id="N16293"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1629F" type="main">
					<s id="N162A1"><emph type="italics"></emph>Impetus productus ſecundo instanti in medio libero conſeruatur tertio, &amp; <lb></lb>productus tertio conſeruatur, quarto, atque ita deinceps<emph.end type="italics"></emph.end>; </s>
					<s id="N162AC">quia ſcilicet nec con­<lb></lb>ſeruantur à cauſa primo productiua per Th.144.libri: </s>
					<s id="N162B2">nec aliquid exigit <lb></lb>deſtructionem; </s>
					<s id="N162B8">non contrarius impetus, quia nullus eſt applicatus, vt <lb></lb>conſtat; </s>
					<s id="N162BE">non reſiſtentia medij, quæ quidem alicuius momenti eſt; </s>
					<s id="N162C2">ſed <lb></lb>non tanti, vt impedire poſſit motum omninò, vt conſtat; </s>
					<s id="N162C8">nam ſuppono <lb></lb>liberum medium, igitur nec deſtruere impetum; </s>
					<s id="N162CE">cum tamdiu duret cau­<lb></lb>ſa quamdiu durat effectus, vt patet; </s>
					<s id="N162D4">igitur nihil eſt quod exigat impe­<lb></lb>tus huius deſtructionem; igitur non deſtruitur per Ax. 14. lib.1. <lb></lb><expan abbr="qūanta">quanta</expan> verò ſit, &amp; quid ſit cuiuſlibet medij reſiſtentia, dicemus <lb></lb>infrà. </s>
				</p>
				<p id="N162E1" type="main">
					<s id="N162E3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N162EF" type="main">
					<s id="N162F1"><emph type="italics"></emph>Si impetus innatus impeditur, ita vt moueri non poſſit corpus graue, ſe­<lb></lb>cundo instanti non producitur nouus impetus.<emph.end type="italics"></emph.end></s>
					<s id="N162FA"> Probatur primò, non creſcit <lb></lb>corporis grauis ſeu grauitas, ſeu grauitatio, vt conſtat experientiâ; </s>
					<s id="N16300">igitur <lb></lb>non creſcit impetus; </s>
					<s id="N16306">alioquin ſi creſceret cauſa, creſceret effectus per <lb></lb>Ax.2. igitur de re, quòd ſit, certum eſt, atque euidens; </s>
					<s id="N1630C">iam demonſtratur <lb></lb>propter quid ſit; </s>
					<s id="N16312">impetus ſecundo inſtanti productus eſſet fruſtrà; </s>
					<s id="N16316">careret <pb pagenum="83" xlink:href="026/01/115.jpg"></pb>enim ſuo fine, vel effectu formali, id eſt motu; igitur eſſet fruſtrà, ſed <lb></lb>quod fruſtrà eſt, non eſt per Ax.6.l.1. </s>
				</p>
				<p id="N16321" type="main">
					<s id="N16323"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1632F" type="main">
					<s id="N16331">Obſerua quæſo, quod iam ſuprà indicatum eſt, eſſe tres veluti ſpecies <lb></lb>impetus. </s>
					<s id="N16336">Prima eſt impetus naturalis innati. </s>
					<s id="N16339">Secunda naturalis acquiſiti. </s>
					<s id="N1633C"><lb></lb>Tertia violenti; </s>
					<s id="N16340">innatus eſt qui vel à generante ſimul cum corpore <lb></lb>graui productus eſt; </s>
					<s id="N16346">quiſquis tandem ſit generans, de quo aliàs; </s>
					<s id="N1634A">vel ab <lb></lb>ipſo graui quaſi profunditur, id eſt, producitur in ſe ipſo ſtatim initio, <lb></lb>quo eſt; </s>
					<s id="N16352">porrò cum in corpore graui duplex quaſi proprietas ſenſibilis <lb></lb>eſſe videatur, ſcilicet grauitas, ſeu pondus &amp; motus deorſum; </s>
					<s id="N16358">certè de­<lb></lb>bet eſſe in eo aliquid per quod tùm cognoſci poſſit eius pondus, tùm in­<lb></lb>cipiat moueri deorſum; </s>
					<s id="N16360">quippe maximè corpora ex pondere cognoſci­<lb></lb>mus, vnumque ab alio diſtinguimus; </s>
					<s id="N16366">igitur debet eſſe aliquid, quod ſen­<lb></lb>ſum afficiat, vt cognoſci poſſit; </s>
					<s id="N1636C">atqui illud ipſum non eſt ſubſtantia cor­<lb></lb>poris; </s>
					<s id="N16372">nam corpus graue meæ manui ſuſtinenti impetum imprimit; </s>
					<s id="N16376"><lb></lb>immò vim alterius impetus infringit; </s>
					<s id="N1637B">igitur operâ alterius per Th. 40. <lb></lb>&amp; 42.lib.1. Præterea illud ipſum, quod agit, ſeu deorſum pellit ſuſtinen­<lb></lb>tem manum, eſt illud ipſum quod inclinat corpus graue deorſum imme­<lb></lb>diatè, ſeu quod exigit motum naturalem deorſum; </s>
					<s id="N16385">illud autem quod <lb></lb>immediatè præſtat hunc motum, nec eſt ſubſtantia corporis grauis per <lb></lb>Th.3. igitur ipſe impetus per Th.5. adde quod primo inſtanti, quo eſt im­<lb></lb>petus, non eſt motus ille, quem exigit per Th.34. lib.1. igitur præexiſtit <lb></lb>ſemper impetus, qui ne ſit fruſtrà, habet primum effectum ſuum forma­<lb></lb>lem, id eſt grauitationem: </s>
					<s id="N16393">Ex his dicendum eſt hunc impetum natiuum <lb></lb>nunquam deſtrui, quia nunquam eſt fruſtrà, habet enim ſemper aliquem <lb></lb>effectum, primum quidem ſi caret ſecundo; </s>
					<s id="N1639B">ſecundum verò ſi caret pri­<lb></lb>mo; </s>
					<s id="N163A1">quippe vtrumque ſimul habere non poteſt; nam corporis pondus <lb></lb>cognoſci non poteſt, dum fertur deorſum accelerato motu, quot verò, <lb></lb>&amp; quanta commoda ex cognitione ponderis cuiuſlibet materiæ proce­<lb></lb>dant, vix explicari poteſt. </s>
				</p>
				<p id="N163AB" type="main">
					<s id="N163AD">Ex his verò concludendum ſupereſt impetum innatum eſſe proprie­<lb></lb>tatem quarto modo, vt vulgò aiunt, corporis grauis; </s>
					<s id="N163B3">ac proinde ab illo <lb></lb>inſeparabilem; </s>
					<s id="N163B9">quid verò fiat de illo, cum corpus graue fit leue; ſi tamen <lb></lb>hoc aliquando accidit, dicemus cum de grauitate, &amp; grauitatione, iam <lb></lb>verò ſatis eſt ad præſens inſtitutum impetum innatum ab ipſo corpori <lb></lb>graui nunquam ſeparari, quandiu remanet graue. </s>
				</p>
				<p id="N163C3" type="main">
					<s id="N163C5">Impetus naturalis acquiſitus producitur ab eodem principio intrin­<lb></lb>ſeco; </s>
					<s id="N163CB">hinc dicitur naturalis: </s>
					<s id="N163CF">dicitur verò acquiſitus, quia non eſt inna­<lb></lb>tus; </s>
					<s id="N163D5">ſed ſeparatur à corpore graui; </s>
					<s id="N163D9">quod ſemper eo caret, quandiu <lb></lb>quieſcit: </s>
					<s id="N163DF">ſed innato tantùm accedit ad motus accelerationem, &amp; ad alia <lb></lb>quamplurima, quæ ex ea ſequuntur; </s>
					<s id="N163E5">putà maiorem percuſſionem, reſi­<lb></lb>ſtentiam, vim, &amp; ad tollendum totius naturæ languidiorem; </s>
					<s id="N163EB">quo certè af­<lb></lb>ficeretur, ſi corpus graue tardiſſimo motu deorſum ferretur, de quo in­<lb></lb>frà; </s>
					<s id="N163F3">Porrò impetus acquiſitus in multis differt ab innato; primò quia <pb pagenum="84" xlink:href="026/01/116.jpg"></pb>deſtruitur à corpore reſiſtente eo modo, quo diximus, &amp; dicemus infrà. </s>
					<s id="N163FC"><lb></lb>Secundò, quia determinari poteſt ad omnem lineam. </s>
				</p>
				<p id="N16400" type="main">
					<s id="N16402">Impetus violentus eſt, qui eſt ab extrinſeco, de quo agemus infrà, &amp; <lb></lb>iam ſuprà in lib.1. multa ſunt de eo demonſtrata. </s>
				</p>
				<p id="N16407" type="main">
					<s id="N16409"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16415" type="main">
					<s id="N16417"><emph type="italics"></emph>Impetus naturalis corporis grauis intenditur dum hoc ipſum deſcendit in <lb></lb>medio libero<emph.end type="italics"></emph.end>; demonſtratur, Impetus nouus producitur in ſecundo, ter­<lb></lb>tio, quarto, &amp;c. </s>
					<s id="N16424">inſtantibus per Th.12. ſed productus in primo conſer­<lb></lb>uatur ſecundo, per Th.9. productus ſecundo conſeruatur tertio, produ­<lb></lb>ctus tertio conſeruatur quarto per Th.13. igitur ſecundus additur tertio, <lb></lb>tertius primo, ſecundo, quartus primo, ſecundo, &amp; tertio, &amp;c.ſed impetus <lb></lb>additus alteri facit intenſiorem impetum per Ax.1. igitur impetus natu­<lb></lb>ralis intenditur, quod crat demonſtrandum. </s>
				</p>
				<p id="N16431" type="main">
					<s id="N16433"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1643F" type="main">
					<s id="N16441"><emph type="italics"></emph>Hinc motus naturalis deorſum acceleratur<emph.end type="italics"></emph.end>; </s>
					<s id="N1644A">hoc ipſum ſuppoſui ſuprà <lb></lb>Quod eſſet in hyp.1.2.3. iam verò demonſtro propter quid eſt; </s>
					<s id="N16450">ſie enim <lb></lb>hypotheſis in Theorema conuerti poteſt, vt ſæpè monuimus in metho­<lb></lb>do; </s>
					<s id="N16458">igitur probatur hoc Theorema facilè; </s>
					<s id="N1645C">creſcit impetus in corpore gra­<lb></lb>ui, quod tendit deorſum in libero medio per T. 15. igitur creſcit cauſa <lb></lb>motus; </s>
					<s id="N16464">nam impetus eſt cauſa immediata motus naturalis per Th. 51. <lb></lb>ſed quâ proportione creſcit cauſa, debet creſcere effectus per Ax.2. igi­<lb></lb>tur motus naturalis deorſum creſcit, id eſt acceleratur, id eſt fit velo­<lb></lb>cior, quod erat dem: </s>
					<s id="N1646E">nec eſt quod aliquis exiſtimet hic à me committi <lb></lb>vitioſum argumentationis circulum; </s>
					<s id="N16474">quippe probaui ſuprà creſcere im­<lb></lb>petum, quia creſcit motus; </s>
					<s id="N1647A">iam verò probo creſcere motum, quia creſ­<lb></lb>cit impetus; nam primò probaui produci nouum impetum in Th.12. eo <lb></lb>quod ſecundo inſtanti. </s>
					<s id="N16482">v.g. ſit eadem cauſa neceſſaria applicata non im­<lb></lb>pedita, igitur tàm debet agere ſecundo quàm primo inſtanti, hæc fuit <lb></lb>mea probatio à priori; </s>
					<s id="N1648C">ſecundò verò probaui ex hypotheſi certa; </s>
					<s id="N16490">quia <lb></lb>ſcilicet creſcit motus, cuius veritatem cognoſco ſenſibiliter in ſe, vnde <lb></lb>ſuppono tantùm de illa quod ſit; </s>
					<s id="N16498">igitur nullus committitur circulus; nam <lb></lb>diuerſa eſt omninò cognitio. </s>
					<s id="N1649E">Prima ſcilicet qua cognoſco de motu na­<lb></lb>turaliter accelerato quod ſit, quæ mihi, &amp; ruſtico communis eſt. </s>
					<s id="N164A3">Secun­<lb></lb>da verò qua non modò cognoſco de motu illo quod ſit acceleratus, ve­<lb></lb>rùm propter quid ſit acceleratus, id eſt cauſam huius accelerationis, id <lb></lb>eſt propter quam attributum hoc ineſt ſubiecto, &amp; hæc eſt vera demon­<lb></lb>ſtratio à priori; porrò in Phyſica de effectu ſenſibili ſupponi debet quod <lb></lb>ſit, hoc enim percipitur ſenſu. </s>
					<s id="N164B1">v. g. ſupponam in Phyſica quod ſit motus <lb></lb>acceleratus, quod ignis ſit calidus, Sol lucidus, nix candida, vinum ru­<lb></lb>brum, &amp;c. </s>
					<s id="N164BC">at verò demonſtrabo propter quid hæc ſint, ſed de his <lb></lb>ſatis. </s>
				</p>
				<p id="N164C1" type="main">
					<s id="N164C3"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N164CF" type="main">
					<s id="N164D1">Obſeruabis etiam aliud naturæ inſtitutum, quo ſcilicet factum eſt, vt <pb pagenum="85" xlink:href="026/01/117.jpg"></pb>corpora grauia motu naturali accelerato deorſum ferantur; </s>
					<s id="N164DA">ſi enim motu <lb></lb>ferrentur æquabili, vel eſſet æqualis illi quem initio ſui deſcenſus ha­<lb></lb>bent, qui eſt tardiſſimus, vt conſtat ex ipſa ictuum differentia; </s>
					<s id="N164E2">atque <lb></lb>ita infinitum ferè tempus ponerent grauia in minimo etiam deſcenſu, <lb></lb>quod eſſet maximè incommodum; ſi verò motus ille eſſet æqualis mo­<lb></lb>tui v.g. quem acquiſiuit in ſpatio 3. vel 4. perticarum, pondera corpo­<lb></lb>rum creſcerent in immenſum, ideſt in ea proportione, qua ictus, qui in­<lb></lb>fligitur à corpore graui confecto 4. perticarum ſpatio maior eſt ictu, qui <lb></lb>infligitur poſt decurſum minimum omnium ſpatiorum, quod valdè in­<lb></lb>commodum eſſet. </s>
				</p>
				<p id="N164F6" type="main">
					<s id="N164F8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16504" type="main">
					<s id="N16506"><emph type="italics"></emph>Æqualibus temporibus æqualis impetus producitur, ſi ſit eadem applica­<lb></lb>tio, idemque impedimentum<emph.end type="italics"></emph.end>; </s>
					<s id="N16511">probatur, quia cauſa huius impetus eſt ne­<lb></lb>ceſſaria; ſed eadem cauſa neceſſaria æqualibus temporibus æqualem <lb></lb>impetum producit per Ax.3. </s>
				</p>
				<p id="N16519" type="main">
					<s id="N1651B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16527" type="main">
					<s id="N16529"><emph type="italics"></emph>Qua proportione creſcit impetus acceleratur motus<emph.end type="italics"></emph.end>; quia quæ proportio­<lb></lb>ne creſcit cauſa, etiam creſcit effectus per Ax.2. </s>
				</p>
				<p id="N16534" type="main">
					<s id="N16536"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16542" type="main">
					<s id="N16544"><emph type="italics"></emph>Hinc æqualibus temporibus in deſcenſu corpus graue acquirit aqualia ve­<lb></lb>locitatis, vel accelerationis momenta<emph.end type="italics"></emph.end>; </s>
					<s id="N1654F">hoc ipſum eſt quod definitionis lo­<lb></lb>co Galileus in dialogo tertio de motu naturali aſſumit; </s>
					<s id="N16555">quod tamen <lb></lb>meo iudicio fuit antè demonſtrandum quàm ſupponendum; quare ſic <lb></lb>demonſtramus, quâ proportione creſcit impetus, creſcit motus per Th. <lb></lb>18. ſed temporibus æqualibus acquiruntur æquales impetus gradus per <lb></lb>Th.17. igitur æqualia velocitatis momenta, vel incrementa. </s>
				</p>
				<p id="N16562" type="main">
					<s id="N16564"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16570" type="main">
					<s id="N16572"><emph type="italics"></emph>Spatia que per curruntur motu æquabili æqualibus temporibus ſunt æqualia<emph.end type="italics"></emph.end>; <lb></lb>Probatur per Def.2. </s>
				</p>
				<p id="N1657D" type="main">
					<s id="N1657F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1658B" type="main">
					<s id="N1658D"><emph type="italics"></emph>Duo motus æquabiles, qui durant æqualibus temporibus, ſunt vt ſpatia<emph.end type="italics"></emph.end>; <lb></lb>patet; </s>
					<s id="N16598">cùm enim impetus ſint vt motus per Ax. 2. motus ſunt vt ſpatia; <lb></lb>quippe vt ex impetu ſequitur motus, ita ex motu confectum ſpa­<lb></lb>tium. </s>
				</p>
				<p id="N165A0" type="main">
					<s id="N165A2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N165AE" type="main">
					<s id="N165B0"><emph type="italics"></emph>Duo motus æquabiles, quibus percurruntur ſpatia æqualia ſunt vt tempora <lb></lb>permutande<emph.end type="italics"></emph.end>;, patet, quia velocior eſt, quò percurritur ſpatium æquale <lb></lb>minori tempore per Def.2. l. 1. Igitur eò velocior, quò minori tem­<lb></lb>pore. </s>
				</p>
				<p id="N165C0" type="main">
					<s id="N165C2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N165CE" type="main">
					<s id="N165D0"><emph type="italics"></emph>Spatium, quod percurritur maiori tempore motu æquabili, est maius eo, <lb></lb>quod percurritur minori æquè veloci motu in ea ratione, qua vnum tempus<emph.end type="italics"></emph.end><pb pagenum="86" xlink:href="026/01/118.jpg"></pb><emph type="italics"></emph>est maius alio<emph.end type="italics"></emph.end>; </s>
					<s id="N165E4">patet, quia æqualia ſunt æqualibus temporibus per Th. <lb></lb>20. igitur inæqualibus inæqualia iuxta rationem temporum; item ſpa­<lb></lb>tium, quod idem percurritur minori tempore minus eſt. </s>
				</p>
				<p id="N165ED" type="main">
					<s id="N165EF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N165FB" type="main">
					<s id="N165FD"><emph type="italics"></emph>Tempus quo maius ſpatium percurritur eodem motu æquabili, eſt maius eò <lb></lb>quò minus conficitur iuxta rationem ſpatiorum:<emph.end type="italics"></emph.end> Si enim ſpatia ſunt vt tem­<lb></lb>pora, igitur tempora ſunt vt ſpatia; item tempus, quo minus ſpatium <lb></lb>percurritur eſt minus co, quo maius. </s>
				</p>
				<p id="N1660C" type="main">
					<s id="N1660E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1661A" type="main">
					<s id="N1661C"><emph type="italics"></emph>Spatium, quod conficitur motu velociore, eſt maius eo, quod percur­<lb></lb>ritur æquali certè tempore, ſed tardiore motu,<emph.end type="italics"></emph.end> vt conſtat per def. </s>
					<s id="N16626">2. l. 1. <lb></lb>imò eſt maius iuxta rationem velocitatis maioris, item eſt minus iuxta <lb></lb>rationem tarditatis maioris. </s>
				</p>
				<p id="N1662F" type="main">
					<s id="N16631"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1663D" type="main">
					<s id="N1663F"><emph type="italics"></emph>Tempus, quo conficitur ſpatium æquale ſed uelociore motu, est minus eo <lb></lb>quo conficitur tardiore<emph.end type="italics"></emph.end>; </s>
					<s id="N1664A">Probatur per def.2. &amp; per Th.22. idque in ratio­<lb></lb>ne velocitatum permutando; item tempus quo conficitur ſpatium æqua­<lb></lb>le tardiore motu eſt maius eo, quo conficitur velociore, patet. </s>
				</p>
				<p id="N16652" type="main">
					<s id="N16654"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16660" type="main">
					<s id="N16662"><emph type="italics"></emph>Si datum mobile eodem motu æquabili duo percurrat ſpatia, tempora mo­<lb></lb>tuum erunt vt ſpatia, &amp; viciſſim ſpatia vt tempora.<emph.end type="italics"></emph.end></s>
					<s id="N1666B"> Probatur per Th. <lb></lb>24. &amp; 23. </s>
				</p>
				<p id="N16671" type="main">
					<s id="N16673"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1667F" type="main">
					<s id="N16681"><emph type="italics"></emph>Si idem mobile temporibus æqualibus percurrat duo ſpatia motu æquabili, <lb></lb>ſed inæquali velocitate; </s>
					<s id="N16689">ſpatia erunt vt velocitates, &amp; hæ vt illa; </s>
					<s id="N1668D">imò ſi <lb></lb>ſpatia ſunt vt velocitates, tempora erunt æqualia<emph.end type="italics"></emph.end>; pater etiam per <lb></lb>Th.25. </s>
				</p>
				<p id="N16698" type="main">
					<s id="N1669A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N166A6" type="main">
					<s id="N166A8"><emph type="italics"></emph>Si percurrantur à mobili æqualia ſpatia, ſed inæquali velocitate, ipſæ ve­<lb></lb>locitates erunt in ratione permutata temporum, ideſt maior velocitas reſpon­<lb></lb>debit minori tempori, &amp; minor maiori<emph.end type="italics"></emph.end>; Probatur per Th.23. </s>
				</p>
				<p id="N166B5" type="main">
					<s id="N166B7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N166C3" type="main">
					<s id="N166C5"><emph type="italics"></emph>Si duo mobilia mouentur motu æquabili, ſed inæquali velocitate, &amp; inæqua­<lb></lb>libus temporibus, ſpatia ſunt in ratione compoſita ex ratione temporum, &amp; ex <lb></lb>ratione velocitatum,<emph.end type="italics"></emph.end> ſi enim æqualia ſint tempora, ſpatia erunt vt velo­<lb></lb>citates per Th.25. ſi æquales ſint velocitates, ſpatia erunt vt tempora, per <lb></lb>Th.29. igitur ſi nec æquales velocitates, nec æqualia tempora, erit ratio <lb></lb>ſpatiorum compoſita ex ratione temporum, &amp; ex ratione velocitatum; <lb></lb>ſit ratio temporum 3/2 ratio velocitatum 2/3 compoſita ex vtraque erit 6/2 <lb></lb>ſeu 3. vt conſtat ex ipſis elementis. </s>
				</p>
				<pb pagenum="87" xlink:href="026/01/119.jpg"></pb>
				<p id="N166E0" type="main">
					<s id="N166E2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N166EE" type="main">
					<s id="N166F0"><emph type="italics"></emph>Si duo mobilia ferantur motu æquabili per diuerſa ſpatia, &amp; diuerſa velo­<lb></lb>citate, tempora erunt in ratione compoſita ex ratione ſpatiorum &amp; ratione <lb></lb>velocitatum permutata<emph.end type="italics"></emph.end>; </s>
					<s id="N166FD">probatur eodem modo quo ſuperius Th. 30. ſit <lb></lb>ratio ſpatiorum 4/1, velocitatum 4/2; </s>
					<s id="N16703">permutetur hæc 1/4; componetur ex <lb></lb>vtraque 4/1, ideſt 1/2, quæ eſt ratio temporum. </s>
				</p>
				<p id="N16709" type="main">
					<s id="N1670B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16717" type="main">
					<s id="N16719"><emph type="italics"></emph>Si duo mobilia æquabili motu ferantur per diuerſa ſpatia, &amp; inæqualibus <lb></lb>temporibus; </s>
					<s id="N16721">ratio velocitatum erit compoſita ex ratione ſpatiorum, &amp; ex ra­<lb></lb>tione temporum permutata<emph.end type="italics"></emph.end>; Probatur eodem modo; ſit ratio ſpatiorum <lb></lb>4/2 temporum 1/2, permutetur 2/1, compoſita ex vtraque erit 2/2, ideſt 4. <lb></lb>quæ eſt ratio velocitatum. </s>
				</p>
				<p id="N1672E" type="main">
					<s id="N16730"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1673C" type="main">
					<s id="N1673E">Obſeruabis hæc omnia à vigeſimo Theoremate maiori ex parte tradi <lb></lb>à Galileo ſuo modo, optimo quidem, ſed fortè longiore quàm par ſit, <lb></lb>nulla habita ratione cauſarum phyſicarum. </s>
				</p>
				<p id="N16745" type="main">
					<s id="N16747"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16753" type="main">
					<s id="N16755"><emph type="italics"></emph>In motu naturaliter accelerato impetus nouus acquiritur ſingulis inſtanti­<lb></lb>bus<emph.end type="italics"></emph.end>; Probatur quia ſingulis inſtantibus eſt eadem cauſa neceſſaria, igi­<lb></lb>tur ſingulis inſtantibus aliquem effectum producit, per Ax. 12. l.1. ſed <lb></lb>priorem non conſeruat, vt dictum eſt ſuprà, igitur nouum producit. </s>
				</p>
				<p id="N16764" type="main">
					<s id="N16766"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16772" type="main">
					<s id="N16774"><emph type="italics"></emph>Hinc ſingulis inſtantibus æqualibus nouus impetus æqualis acquiritur,<emph.end type="italics"></emph.end> quip­<lb></lb>pe eſt æqualis, imò eadem cauſa, igitur æqualem effectum producit per <lb></lb>Ax.12. l.1. </s>
				</p>
				<p id="N16780" type="main">
					<s id="N16782"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1678E" type="main">
					<s id="N16790"><emph type="italics"></emph>Hinc ſingulis inſtantibus intenditur impetus in hoc motu<emph.end type="italics"></emph.end>; cum ſingulis <lb></lb>inſtantibus producatur nouus, &amp; prior conſeruetur, cui cum addatur, <lb></lb>intenditur per Ax. 1. </s>
				</p>
				<p id="N1679E" type="main">
					<s id="N167A0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N167AC" type="main">
					<s id="N167AE"><emph type="italics"></emph>Hinc ſingulis inſtantibus æqualiter creſcit &amp; intenditur impetus<emph.end type="italics"></emph.end> per Th. <lb></lb>34. igitur æqualiter etiam ſingulis inſtantibus creſcit velocitas motus <lb></lb>per Ax.2. </s>
				</p>
				<p id="N167BB" type="main">
					<s id="N167BD"><emph type="center"></emph><emph type="italics"></emph>Scholium<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N167C8" type="main">
					<s id="N167CA">Obſeruabis <expan abbr="dictū">dictum</expan> eſſe ſuprà <emph type="italics"></emph>instantibus æqualibus,<emph.end type="italics"></emph.end> quia temporis natura <lb></lb>aliter explicari non poteſt, quàm per inſtantia finita, vt demonſtrabimus <lb></lb>in Metaphyſica; </s>
					<s id="N167DC">quid quid ſit, voco inſtans totum illud tempus, quo res <lb></lb>aliqua ſimul producitur, ſiue ſit maius, ſiue minus, ſiue ſit pars maior, <lb></lb>vel minor, quod ad rem noſtram nihil facit penitus; </s>
					<s id="N167E4">nam dato quocun­<lb></lb>que tempore finito poteſt dari maius &amp; minus, quod certum eſt; </s>
					<s id="N167EA">igitur <lb></lb>totum illud tempus, quo producitur primus impetus acquiſitus, vo-<pb pagenum="88" xlink:href="026/01/120.jpg"></pb>co inſtans primum motus; cui æqualia deinde ſuccedunt tem­<lb></lb>pora. </s>
				</p>
				<p id="N167F7" type="main">
					<s id="N167F9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16805" type="main">
					<s id="N16807"><emph type="italics"></emph>Hinc creſcit impetus iuxta progreſſionem arithmeticam; </s>
					<s id="N1680D">cum ſingula in­<lb></lb>ſtantia æqualem impetum addant<emph.end type="italics"></emph.end>; </s>
					<s id="N16816">ſi primo inſtanti ſit vnus gradus, erunt <lb></lb>duo; productus ſcilicet alteri additus qui conſeruatur, tertio erunt;. </s>
					<s id="N1681C"><lb></lb>quarto 4. quinto 5. &amp;c. </s>
					<s id="N16820">igitur creſcit ſecundum progreſſionem arith­<lb></lb>meticam. </s>
				</p>
				<p id="N16825" type="main">
					<s id="N16827"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16833" type="main">
					<s id="N16835"><emph type="italics"></emph>Eodem modo creſcit velocitas, quia ſingulis inſtantibus æqualia acquirun­<lb></lb>tur velocitatis momenta<emph.end type="italics"></emph.end> per Ax.2. &amp; per Th.36. </s>
				</p>
				<p id="N1683F" type="main">
					<s id="N16841"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1684D" type="main">
					<s id="N1684F"><emph type="italics"></emph>Maius ſpatium acquiritur ſecundo inſtanti, quàm primo, quia ſecundo<emph.end type="italics"></emph.end><lb></lb>inſtanti motus eſt velocior per Th.36. igitur maius conficitur ſpatium, <lb></lb>tempore ſcilicet æquali per Def. 2. l. 1. idem dico de tertio, quar­<lb></lb>to, &amp;c. </s>
				</p>
				<p id="N16860" type="main">
					<s id="N16862"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1686E" type="main">
					<s id="N16870"><emph type="italics"></emph>Spatium quod acquiritur ſecundò instanti eſt ad ſpatium quod acquiritur <lb></lb>primo vt velocitas, quæ eſt ſecundo ad velocitatem, quæ eſt primo.<emph.end type="italics"></emph.end></s>
					<s id="N16879"> Patet per <lb></lb>Th.28. quia cum tempora illa ſint æqualia, ſpatia ſunt neceſſariò vt ve­<lb></lb>locitates; quippe æquali velocitati æquale ſpatium reſpondet tempore <lb></lb>æquali, igitur inæquale inæquali, igitur maius maiori, idem dico de <lb></lb>aliis inſtantibus. </s>
				</p>
				<p id="N16885" type="main">
					<s id="N16887"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16893" type="main">
					<s id="N16895"><emph type="italics"></emph>Hinc ſpatium qucd acquiritur ſecundo inſtanti eſt duplum illius, quod ac­<lb></lb>quiritur primo.<emph.end type="italics"></emph.end></s>
					<s id="N1689E"> Probatur, quia velocitas eſt dupla per Th 38. igitur ſpa­<lb></lb>tium duplum, &amp; triplum tertio, quadruplum quarto, &amp;c. </s>
				</p>
				<p id="N168A3" type="main">
					<s id="N168A5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N168B1" type="main">
					<s id="N168B3"><emph type="italics"></emph>Hinc quodlibet ſpatium creſcit æqualiter ſingulis inſtantibus æqualibus<emph.end type="italics"></emph.end>; </s>
					<s id="N168BC"><lb></lb>quia ſpatia creſcunt vt motus, ſeu vt velocitates; hæ creſcunt æqualiter <lb></lb>ſingulis inſtantibus æqualibus per Th.36. igitur æqualiter creſcunt ſin­<lb></lb>gula ſpatia per Th.40. </s>
				</p>
				<p id="N168C5" type="main">
					<s id="N168C7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N168D3" type="main">
					<s id="N168D5"><emph type="italics"></emph>Hinc ſpatia creſcunt ſingulis inſtantibus æqualibus ſecundùm progreſſio­<lb></lb>nem arithmeticam<emph.end type="italics"></emph.end>; quia creſcit vt velocitas per Th.40. hæc vt impetus <lb></lb>per Th.38. hic demum iuxta progreſſionem arithmeticam per Th. 37. <lb></lb>igitur ſi ſpatium acquiſitum primo inſtanti ſit 1. acquiſitum ſecundo erit <lb></lb>2. tertio 3. quarto 4. &amp;c. </s>
					<s id="N168E6">hinc ſpatia acquiſita ſingulis inſtantibus ſunt <lb></lb>vt ſeries numerorum, qui componunt progreſſionem ſimplicem, ſcilicet <lb></lb>1.2.3.4.5.6. &amp;c. </s>
					<s id="N168ED">dixi ſingulis inſtantibus æqualibus, quod eſt apprimè <lb></lb>tenendum; ſi enim aſſumantur partes temporis maiores, perturbatur <lb></lb>hæc progreſſio, de quo infrà. </s>
				</p>
				<pb pagenum="89" xlink:href="026/01/121.jpg"></pb>
				<p id="N168F9" type="main">
					<s id="N168FB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16907" type="main">
					<s id="N16909"><emph type="italics"></emph>Hinc peteſt dici creſcere velocitatem quolibet inſtanti iuxta rationem ſpatij <lb></lb>quod illo inſtanti decurritur<emph.end type="italics"></emph.end>; </s>
					<s id="N16914">quod certè verum eſt, dum intelligatur legi­<lb></lb>timus horum verborum ſenſus; </s>
					<s id="N1691A">quidquid reclamet Saluiatus apud <lb></lb>Galil. dialogo 3. modò aſſumatur progreſſio incrementi in ſingulis in­<lb></lb>ſtantibus, in quibus reuerà fit; cur enim potiùs in vno quàm in alio? </s>
					<s id="N16924"><lb></lb>quippe ſi comparetur velocitas vnius inſtantis cum velocitate alterius; </s>
					<s id="N16929"><lb></lb>haud dubiè erit eadem vtriuſque ratio, quæ ſpatiorum; </s>
					<s id="N1692E">ſi enim vno in­<lb></lb>ſtanti percurritur vnum ſpatium cum vno velocitatis gradu; </s>
					<s id="N16934">certè in­<lb></lb>ſtanti æquali acquiritur duplum ſpatium cum duobus velocitatis gradi­<lb></lb>bus, nec obeſt, quod obiicit Galileus tunc motus eſſe æquabiles; </s>
					<s id="N1693C">quia <lb></lb>motus qui fit in inſtanti debet conſiderari vt æquabilis; </s>
					<s id="N16942">appello enim <lb></lb>inſtans totum illud tempus, quo ſimul acquiritur aliquid impetus, ali­<lb></lb>quid enim ſimul acquiri neceſſe eſt; </s>
					<s id="N1694A">nec demum obſtat quod dicit, dari <lb></lb>non poſſe motum inſtantaneum, quod multi haud dubiè negabunt; </s>
					<s id="N16950">ego <lb></lb>in Metaphyſica explicabo quonam pacto dari poſſit motus inſtanta­<lb></lb>neus, qui reuerà datur actu, non potentiâ; </s>
					<s id="N16958">quia quacunque duratione <lb></lb>data poteſt dari minor; igitur quocunque dato motu poteſt dari minor. </s>
				</p>
				<p id="N1695E" type="main">
					<s id="N16960"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1696C" type="main">
					<s id="N1696E">Obſeruabis primò hanc ſpatiorum rationem, quæ eſt eadem cum ra­<lb></lb>tione velocitatum aſſumendam tantùm eſſe in iis ſpatiis, quæ acquirun­<lb></lb>tur ſingulis inſtantibus; </s>
					<s id="N16976">ſi enim accipiantur partes temporis maiores, quæ <lb></lb>conflentur ex multis inſtantibus; </s>
					<s id="N1697C">haud dubiè maior erit ratio ſpatio­<lb></lb>rum, quàm velocitatum.v.g.ſi primo inſtanti acquiratur primo ſpatium, <lb></lb>ſecundo, 2.tertio, 3.quarto 4.igitur ſi <expan abbr="cõparetur">comparetur</expan> velocitas primi inſtantis <lb></lb>cum velocitate quarti æqualis erit, vt ratio ſpatiorum, id eſt, vt 1. ad 4. <lb></lb>At verò ſi accipiatur pars temporis conſtans duobus inſtantibus, hæc 4. <lb></lb>inſtantia conflabunt tantùm 2. partes temporis æquales; </s>
					<s id="N1698E">in prima ac­<lb></lb>quirentur 3.ſpatia, in ſecunda 7.vt patet: </s>
					<s id="N16994">ſed quia velocitas primæ par­<lb></lb>tis temporis non eſt æquabilis, nec etiam velocitas ſecundæ; </s>
					<s id="N1699A">addantur <lb></lb>velocitates primi &amp; ſecundi inſtantis, itemque ſeorſim velocitates tertij, <lb></lb>&amp; quarti; </s>
					<s id="N169A2">certè ratio collectorum erit vt ratio ſpatiorum; ſi enim velo­<lb></lb>citas ſecundi inſtantis comparetur cum velocitate quarti eſt tantùm <lb></lb>1/2 cum tamen primum ſpatium ſit ad ſecundum in ratione 3/7. </s>
				</p>
				<p id="N169AA" type="main">
					<s id="N169AC">Secundò, ſi comparentur ſpatia cum temporibus eſt alia ratio v.g.ſpa­<lb></lb>tium acquiſitum vno inſtanti ſe habet ad ſpatium acquiſitum in duobus <lb></lb>inſtantibus, vt 1, ad 3.in tribus vt 1.ad 6.in 4. vt 1. ad 10. </s>
				</p>
				<p id="N169B3" type="main">
					<s id="N169B5">Tertiò obſeruabis, non poſſe ſenſu percipi inſtans, imò neque tempo­<lb></lb>ris partem ex mille inſtantibus conflatam; </s>
					<s id="N169BB">nec etiam ſpatium quod ac­<lb></lb>quiritur primo inſtanti; </s>
					<s id="N169C1">adhibenda ſunt tamen inſtantia neceſſariò ad <lb></lb>explicandam proportionem huius accelerationis, quæ fit in ſingulis in­<lb></lb>ſtantibus; vt verò rem iſtam reuocemus ad ſenſibilem praxim, aſſume­<lb></lb>mus proportionem aliam ſenſibilem, quæ proximè ad veram accedit, nec <lb></lb>ferè ſenſibiliter fallere poteſt, de qua infrà. </s>
				</p>
				<pb pagenum="90" xlink:href="026/01/122.jpg"></pb>
				<p id="N169D1" type="main">
					<s id="N169D3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N169DF" type="main">
					<s id="N169E1"><emph type="italics"></emph>Collectio ſpatiorum eſt ſumma terminorum huius progreſſionis arithmeticæ<emph.end type="italics"></emph.end>; <lb></lb></s>
					<s id="N169EB">Cùm enim ratio ſpatiorum ſit vt ratio velocitatum; </s>
					<s id="N169EF">dum ſcilicet hæc <lb></lb>progreſſio accipitur in inſtantibus, &amp; ratio velocitatum vt ratio incre­<lb></lb>menti impetuum; vt conſtat ex dictis, &amp; hæc ſequatur ſimplicem <lb></lb>progreſſionem 1. 2. 3. 4. &amp;c. </s>
					<s id="N169F9">certè collectio ſpatiorum eſt ſumma ter­<lb></lb>minorum. </s>
				</p>
				<p id="N169FE" type="main">
					<s id="N16A00"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16A0C" type="main">
					<s id="N16A0E"><emph type="italics"></emph>Hinc cognito primo termino, &amp; vltimo, id eſt ſpatio quod per curritur primo <lb></lb>inſtanti &amp; ſpatio quod percurritur vltimo instanti, cognoſcitur ſumma, id eſt <lb></lb>collectio ſpatiorum, id eſt, totum ſpatium confectum.<emph.end type="italics"></emph.end> v.g.ſi primus terminus, <lb></lb>ſecundus S.igitur ſumma eſt 36. quippe vltimus terminus indicat nume­<lb></lb>rum terminorum, quia primus eſt ſemper vnitas, &amp; progreſſiuus etiam <lb></lb>vnitas. </s>
				</p>
				<p id="N16A20" type="main">
					<s id="N16A22"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16A2E" type="main">
					<s id="N16A30"><emph type="italics"></emph>Hinc cognita ſumma &amp; vltimo termino cognoſcitur etiam numerus inſtan­<lb></lb>tium æqualium, qui ſemper est idem cum numero terminorum, cognoſcitur <lb></lb>etiam primus terminus, id eſt ſpatium quod primo instanti percurritur, cogno­<lb></lb>ſcuntur etiam gradus velocitatis<emph.end type="italics"></emph.end>; </s>
					<s id="N16A3F">quippe hæc omnia ſunt in eadem ratio­<lb></lb>ne; </s>
					<s id="N16A45">quæ omnia conſtant ex regulis arithmeticis præter alia multa data, <lb></lb>quæ lubens omitto; </s>
					<s id="N16A4B">tùm quia Phyſicam non ſapiunt, tùm quia hypothe­<lb></lb>ſis illa eſt impoſſibilis phyſicè; quis enim ſenſu percipere poſſit &amp; di­<lb></lb>ſtinguere vnum temporis inſtans, vel ſpatij punctum? </s>
					<s id="N16A53">licèt recenſenda <lb></lb>fuerit hæc accelerati motus proportio in inſtantibus, vt ad ſua phyſica <lb></lb>principia reduceretur. </s>
				</p>
				<p id="N16A5A" type="main">
					<s id="N16A5C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16A68" type="main">
					<s id="N16A6A"><emph type="italics"></emph>Data ſumma progreſſionis huius ſimplicis, inuenietur numerus terminorum, <lb></lb>ſi inueniatur numerus, per quem diuidatur, qui ſuperet tantùm vnitate du­<lb></lb>plum quotientis<emph.end type="italics"></emph.end>; </s>
					<s id="N16A77">quippe habebis in duplo quotientis numerum termino­<lb></lb>rum v.g. ſit ſumma 10. diuiſor ſit 5. quotiens 2. duplus 4. hic eſt nume­<lb></lb>rus terminorum datæ ſummæ; </s>
					<s id="N16A81">ſit alia ſumma 21. diuiſor ſit 7.quotiens 3. <lb></lb>numerus terminorum 6. ſit alia ſumma 36. diniſor ſit 9. quotiens 4. nu­<lb></lb>merus terminorum 8. ſit alia ſumma 45. partitor ſit 10. quotiens 4 1/2, <lb></lb>numerus terminorum 9. quomodo verò hic partitor inueniri poſſit, vi­<lb></lb>derint Arithmetici; </s>
					<s id="N16A8D">nec enim eſt huius loci, quamquam datâ ſummâ <lb></lb>huius progreſſionis ſimplicis facilè cognoſci poteſt numerus termino­<lb></lb>rum; duplicetur enim, &amp; radix 9. neglecto reſiduo dabit numerum ter­<lb></lb>minorum v.g. ſit ſumma 21. duplicetur, erit 42. rad. </s>
					<s id="N16A99">9. 6. dat numerum <lb></lb>terminorum; ſit ſumma 36. duplicetur, erit 72.rad.9.8. dabit numerum <lb></lb>terminorum. </s>
				</p>
				<p id="N16AA1" type="main">
					<s id="N16AA3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16AAF" type="main">
					<s id="N16AB1"><emph type="italics"></emph>Semper decreſcit proportio incrementi velocitatis, id est maior est proportio <lb></lb>velocitatis ſecundi inſtantis ad primum quàm tertij ad ſecundum, &amp; maior<emph.end type="italics"></emph.end><pb pagenum="91" xlink:href="026/01/123.jpg"></pb><emph type="italics"></emph>tertij ad ſecundum quàm quarti ad tertium, atque ita deinceps<emph.end type="italics"></emph.end>; </s>
					<s id="N16AC5">ſit enim <lb></lb>primo inſtanti velocitas vt 1.ſecundo erit, vt 2.tertio, vt 3.quarto, vt 4. <lb></lb>ſed maior eſt proportio 2.ad 1.quàm 3.ad 2. &amp; hæc maior quàm 4. ad 3. <lb></lb>atque ita deinceps; </s>
					<s id="N16ACF">ſimiliter maior eſt proportio ſpatij quod percurritur <lb></lb>ſecundo inſtanti ad ſpatium, quod percurritur primo, quàm ſpatij, quod <lb></lb>percurritur ſecundo inſtanti ad ſpatium, quod percurritur primo quàm <lb></lb>ſpatij quod percurritur tertio ad ſpatium, quod percurritur ſecundo, at­<lb></lb>que ita deinceps; eſt enim eadem ratio ſpatiorum quæ ſingulis inſtanti­<lb></lb>bus reſpondent, quæ velocitatum, vt demonſtratum eſt ſuprà. </s>
				</p>
				<p id="N16ADD" type="main">
					<s id="N16ADF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16AEB" type="main">
					<s id="N16AED"><emph type="italics"></emph>Minor eſt proportio totius ſpatij, quod acquiritur duobus instantibus ad to<lb></lb>tum ſpatium, quod acquiritur vno, quàm ſit illius, quod acquiritur quatuor in­<lb></lb>ſtantibus ad aliud, quod acquiritur duobus<emph.end type="italics"></emph.end>; patet ex dictis; </s>
					<s id="N16AFA">ſi enim primo <lb></lb>inſtanti acquiritur vnum ſpatium, ſecundo acquiruntur 2.igitur duobus <lb></lb>ſimul acquirantur 3. igitur proportio eſt vt 3.ad 1.Sed ſi duobus acqui­<lb></lb>runtur 3. ſpatia; </s>
					<s id="N16B04">certè 4.inſtantibus acquiruntur 10. igitur proportio eſt <lb></lb>vt 10.ad 3. ſed proportio 10/3 eſt maior 3/1, erit adhuc maior proportio ſpa­<lb></lb>tij quod acquiretur 6. inſtantibus ad illud quod acquiritur tribus; eſt <lb></lb>enim (21/6) vt patet. </s>
				</p>
				<p id="N16B0E" type="main">
					<s id="N16B10"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16B1C" type="main">
					<s id="N16B1E"><emph type="italics"></emph>Si componatur æquabilis motus ex ſubdupla velocitate maxima, &amp; mini­<lb></lb>ma, æquali tempore, idem ſpatium percurretur hoc motu naturaliter accelera­<lb></lb>to<emph.end type="italics"></emph.end>; </s>
					<s id="N16B2B">ſit enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce­<lb></lb>lerato percurrentur ſpatia 21. cuius ſummæ termini ſunt 6.igitur 6. in­<lb></lb>ſtantibus conſtat hic motus; </s>
					<s id="N16B33">accipiatur ſubduplum maximæ, &amp; minimæ <lb></lb>velocitatis, ſcilicet 3 1/2. sítque velocitas motus æquabilis inſtantium 6. <lb></lb>haud dubiè ſi ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod ſcili­<lb></lb>cet, vt habeatur ſumma progreſſionis arithmeticæ, debet addi primus <lb></lb>terminus maximo, &amp; aſſumi ſubduplum totius; </s>
					<s id="N16B3F">illudque ducere in nu­<lb></lb>merum terminorum per regulam arithmeticam; </s>
					<s id="N16B45">atqui eadem eſt ratio <lb></lb>velocitatum, quæ ſpatiorum; vt dictum eſt ſuprà; ſcilice, in ſingulis <lb></lb>inſtantibus. </s>
				</p>
				<p id="N16B4D" type="main">
					<s id="N16B4F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16B5B" type="main">
					<s id="N16B5D"><emph type="italics"></emph>Si aſſumantur partes temporis majores; quæ ſcilicet pluribus inſtantibus <lb></lb>constent, ſerueturque eadem accelerationis progreſſio arithmetica, ſpatium <lb></lb>quod ex ſumma huius progreſſionis reſultabit, erit minus vero,<emph.end type="italics"></emph.end> ſint enim 6.in­<lb></lb>ſtantia, &amp; cuilibet iuxta progreſſionem prædictam ſuum ſpatium reſpon­<lb></lb>deat, haud dubiè ſpatium ſecundi erit duplum ſpatij primi, &amp; tertium <lb></lb>triplum, &amp;c. </s>
					<s id="N16B70">vt conſtat ex dictis; </s>
					<s id="N16B73">igitur erunt ſpatia 21. iam verò aſſu­<lb></lb>mantur 3. partes temporis, quarum quælibet ex 2. conſtet inſtantibus; </s>
					<s id="N16B79"><lb></lb>primæ parti tria ex prædictis ſpatiis reſpondeant; </s>
					<s id="N16B7E">certè ſi ſeruetur pro­<lb></lb>greſſio arithmetica, ſecundæ reſpondebunt 6. &amp; tertiæ 9. igitur totum <lb></lb>ſpatium erit 18. minus vero quod erat 21. ſi verò aſſumantur tantùm 2. <lb></lb>partes, quarum quælibet tribus inſtantibus conſtet; </s>
					<s id="N16B88">primæ parti reſpon-<pb pagenum="92" xlink:href="026/01/124.jpg"></pb>debunt 6. ſecundæ 12. igitur ſumma erit 18. minor vero ſpatio ſcilicet <lb></lb>21.hinc vides ſuppoſito eodem inſtantium numero ſpatium eſſe ſemper <lb></lb>æquale, ſiue aſſumantur partes maiores temporis, ſiue minores, v. g. ſup­<lb></lb>poſitis 6.inſtantibus, ex quibus totum ſpatium 21.conſequitur, ſiue aſſu­<lb></lb>mantur tres partes, quarum quælibet conſtet 2. inſtantibus, ſiue duæ, <lb></lb>quarum quælibet conſtet tribus, ſpatium quod ex illis reſultat, eſt ſem­<lb></lb>per idem ſcilicet 18. aſſumptis verò 8. inſtantibus, &amp; totali ſpatio, quod <lb></lb>illis reſpondet 36. ſpatium quod ex partibus reſultabit erit 30. ſiue ſint <lb></lb>duæ partes, quarum quælibet conſtet 4. inſtantibus, ſiue ſint 4. quarum <lb></lb>quælibet conſtet duobus: </s>
					<s id="N16BA7">hinc rurſus vides aſſumpto maiori inſtantium <lb></lb>numero ſpatium verum habere maiorem rationem ad non verum, quàm <lb></lb>aſſumpto minori inſtantium numero, v.g.aſſumantur 4.inſtantia, ſumma <lb></lb>ſpatiorum erit 10. ſi verò aſſumantur 2.partes temporis, quarum quæli­<lb></lb>bet duobus inſtantibus reſpondeat; </s>
					<s id="N16BB3">ſumma ſpatij erit 9.igitur ratio ve­<lb></lb>ri ſpatij ad non verum eſt (10/9). aſſumantur 6. inſtantia ſpatij veri, ſumma <lb></lb>erit 21.non veri 18. igitur ratio (21/18) ſeu 7/6 quæ maior eſt priori: denique <lb></lb>aſſumantur 8. inſtantia ſpatij veri, ſumma erit 36. non veri 30 igitur ra­<lb></lb>tio (36/30) ſeu 6/3 quæ maior eſt prioribus, atque ita deinceps. </s>
				</p>
				<p id="N16BBF" type="main">
					<s id="N16BC1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16BCD" type="main">
					<s id="N16BCF"><emph type="italics"></emph>Datis duabus partibus temporis, &amp; cognito ſpatio quod percurritur in prima, <lb></lb>matius ſpatium reſpondebit ſecundæ quo vtraque in plures partes minores diui­<lb></lb>detur, ſuppoſita ſemper eadem progreſſione arithmetica in ipſo incremento<emph.end type="italics"></emph.end>; </s>
					<s id="N16BDC"><lb></lb>ſint enim duæ partes temporis ſenſibiles æquales AG. GH. &amp; ſpa­<lb></lb>tium quod percurritur prima parte temporis AG ſit HI; </s>
					<s id="N16BE3">in ſecunda <lb></lb>percurretur IO, id eſt, duplum HI; </s>
					<s id="N16BE9">at verò diuidatur pars temporis <lb></lb>AG in duas æquales AF, FG, &amp; conſequenter totum tempus AH in 4. <lb></lb>æquales; </s>
					<s id="N16BF1">haud dubiè in prima AF percurretur NP ſubtripla HI, &amp; in <lb></lb>ſecunda FG percurretur PK dupla NP; </s>
					<s id="N16BF7">igitur in 4. partibus temporis <lb></lb>AH percurretur ſpatium decuplum PN, ſed HO eſt tantùm nonecupla <lb></lb>NP; </s>
					<s id="N16BFF">igitur reſultabit maius ſpatium in 4.partibus temporis, quam in dua­<lb></lb>bus; licèt duæ æquiualeant 4. iuxta progreſſionem arithmeticam. </s>
				</p>
				<p id="N16C05" type="main">
					<s id="N16C07">Similiter AF diuidatur bifariam in E. &amp; tota AH in 8. æquales AE; </s>
					<s id="N16C0B"><lb></lb>certè primis 4.percurretur idem ſpatium ML æquale NK &amp; HI; </s>
					<s id="N16C10">igitur <lb></lb>in prima AE percurretur MR. cuius ML ſit decupla; </s>
					<s id="N16C16">nam 4. terminis <lb></lb>reſpondet ſumma 10. ſed 8. terminis id eſt 8.partibus temporis reſpon­<lb></lb>det ſumma; </s>
					<s id="N16C1E">6. æqualium RM; </s>
					<s id="N16C22">ſed HO tripla ML eſt tantum 30. <lb></lb>æqualium MR; igitur in 8.partibus reſultabit maius ſpatium, quàm in <lb></lb>4.quæ æquiualent 8. </s>
				</p>
				<p id="N16C2A" type="main">
					<s id="N16C2C">Ex quibus etiam conſtat quo plures accipientur partes temporis ma­<lb></lb>ius ſpatium reſultare, donec tandem perueniatur ad vltima inſtantia, ex <lb></lb>quibus reſultat maximum; </s>
					<s id="N16C34">&amp; ſi accipias AG partes temporis AG. GH. <lb></lb>habebitur HO; </s>
					<s id="N16C3A">ſi verò 4.æquales AF, creſcet ſpatium ſeu ſumma 1/9 HO; </s>
					<s id="N16C3E"><lb></lb>ſi autem 8. æquales AE creſcet 1/5 HO; </s>
					<s id="N16C43">ſi porrò 16. æquales AD creſ­<lb></lb>cet (22/108) ſi 32. æquales AC creſcet (120/408); ſi 64. æquales AB creſcet (496/1584). </s>
				</p>
				<pb pagenum="93" xlink:href="026/01/125.jpg"></pb>
				<p id="N16C4D" type="main">
					<s id="N16C4F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16C5B" type="main">
					<s id="N16C5D"><emph type="italics"></emph>In progreſſione arithmetica ſi diuidatur numerus terminorum bifariam æ­<lb></lb>qualiter nunquam ſumma poſterioris ſegmenti eſt tripla prioris<emph.end type="italics"></emph.end>; ſed ſi acci­<lb></lb>piantur duo termini eſt tantùm 2/1, ſi 4. eſt 7/3 ſi 6. eſt (15/6), ſi 8. eſt (26/10), ſi 10­<lb></lb>(40/15), ſi 12. (57/21), ſi 14. (77/28), atque ita deinceps. </s>
				</p>
				<p id="N16C6C" type="main">
					<s id="N16C6E">Ex quo obſerua mirabilem conſequutionem; </s>
					<s id="N16C72">quippe ſi aſſumantur <lb></lb>tantùm duo termini, &amp; diuidantur bifariam, ſumma poſterioris medie­<lb></lb>tatis eſt tripla primæ minùs vnitate; </s>
					<s id="N16C7A">ſi accipiantur 4. eſt tripla minùs <lb></lb>2. ſi 6. minùs 3. ſi 8. minùs 4. ſi 10. minùs 5. ſi 12. minùs 6. ſi 14. mi­<lb></lb>nùs 7. atque ita deinceps; vnde ſumma poſterioris medietatis eſt ſemper <lb></lb>tripla minùs numero ſuorum terminorum, vel quod clarum eſt minùs <lb></lb>ſubduplo vltimi, ſeu maximi termini, vel numeri terminorum totius <lb></lb>progreſſionis, quod probè omninò tenendum eſt, vt omnes experientiæ <lb></lb>explica ri poſſint, quod infrà faciemus. </s>
				</p>
				<p id="N16C8A" type="main">
					<s id="N16C8C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16C98" type="main">
					<s id="N16C9A"><emph type="italics"></emph>Ex dictis hactenus facilè redditur ratio maioris ictus eiuſdem corporis im­<lb></lb>pacti quod cadit ex maiori altitudine<emph.end type="italics"></emph.end>; fuit hyp. </s>
					<s id="N16CA5">1. ſed ideò eſt maior ictus, <lb></lb>quia maior imprimitur impetus, vt patet, at ideò maior impetus impri­<lb></lb>mitur, quia maior eſt imprimens per Ax. 2. creſcit enim impetus, vt <lb></lb>conſtat ex dictis. </s>
				</p>
				<p id="N16CAE" type="main">
					<s id="N16CB0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16CBC" type="main">
					<s id="N16CBE"><emph type="italics"></emph>Hinc quoque ratio maximæ percuſſionis ex ſolo pondere cadentis illius arie­<lb></lb>tis inflictæ<emph.end type="italics"></emph.end>; quâ ſcilicet altè infiguntur lignei pali, quibus in mediis <lb></lb>aquis tanquam iacto fundamini ſuperædificatur ingens ſæpè ædificij <lb></lb>moles. </s>
				</p>
				<p id="N16CCD" type="main">
					<s id="N16CCF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16CDB" type="main">
					<s id="N16CDD"><emph type="italics"></emph>Hinc ex minima altitudine cadens corpus graue minimum ferè ictum in­<lb></lb>fligit<emph.end type="italics"></emph.end>; quia primus impetus valdè debilis eſt, qui tamen deinde facta <lb></lb>acceſſione maximus ferè euadit. </s>
				</p>
				<p id="N16CEA" type="main">
					<s id="N16CEC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16CF8" type="main">
					<s id="N16CFA"><emph type="italics"></emph>Hinc ratio, cur tanta ſit differentia impetus grauitationis, &amp; percuſſionis <lb></lb>ab eodem mobili<emph.end type="italics"></emph.end>; </s>
					<s id="N16D05">quia ſcilicet quantumuis tempore breuiſſimo mouea­<lb></lb>tur, plurimis tamen eius motus durat inſtantibus; atqui quolibet inſtan­<lb></lb>ti motus acquiritur impetus æqualis primo impetui grauitationis, vt <lb></lb>conſtat ex dictis. </s>
					<s id="N16D0F">v. g. ſit mobile quod moueatur per mille inſtantia <lb></lb>(modicum certè tempus &amp; minimè ſenſibile) poſt hunc motum impetus <lb></lb>erit millecuplus; </s>
					<s id="N16D1B">igitur effectus etiam millecuplus; quæ omnia conſtant <lb></lb>ex dictis. </s>
				</p>
				<p id="N16D21" type="main">
					<s id="N16D23"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16D2F" type="main">
					<s id="N16D31"><emph type="italics"></emph>Hinc percuſſio quæ fit in primo inſtanti contactus creſcit vt tempus<emph.end type="italics"></emph.end>; </s>
					<s id="N16D3A">quia <lb></lb>cùm ſingulis inſtantibus creſcat impetus per partes æquales, &amp; cùm per­<lb></lb>cuſſio ſit vt impetus; etiam erit vt tempus; </s>
					<s id="N16D42">igitur percuſſio, quæ fit poſt <lb></lb>duo inſtantia motus eiuſdem corporis grauis deorſum cadentis eſt du-<pb pagenum="94" xlink:href="026/01/126.jpg"></pb>pla illius, quæ ſit poſt vnum inſtans motus, &amp; quæ fit poſt tria tripla, poſt <lb></lb>4. quadrupla, atque ita deinceps; cùm enim æqualibus temporibus æqua­<lb></lb>lia acquirantur velocitatis momenta, id eſt æquales impetus, impetus <lb></lb>erunt vt tempora, percuſſiones vt impetus, igitur percuſſiones vt tem­<lb></lb>pora. </s>
				</p>
				<p id="N16D55" type="main">
					<s id="N16D57">Dixi in primo inſtanti contactus; nam reuerâ ſecundò inſtanti con­<lb></lb>tactus, niſi fiat reflexio, augetur vis ictus, quia cauſa neceſſaria eſt ap­<lb></lb>plicata. </s>
				</p>
				<p id="N16D5F" type="main">
					<s id="N16D61"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16D6D" type="main">
					<s id="N16D6F"><emph type="italics"></emph>Hinc poſſunt comparari duæ percuſſiones duorum grauium inæqualium <lb></lb>dum cadunt deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N16D7A">ſi enim cadunt æqualibus temporibus, percuſſio­<lb></lb>nes erunt vt corpora ſeu grauitates, vt patet v.g. corpus 2. librarum poſt <lb></lb>2. inſtantia motus infligit duplam percuſſionem illius, quam infligit cor­<lb></lb>pus vnius libræ poſt 2. inſtantia motus; </s>
					<s id="N16D86">ſi verò tempora motus ſunt inæ­<lb></lb>qualia, &amp; grauitates æquales, percuſſiones erunt vt tempora; </s>
					<s id="N16D8C">ſi demum <lb></lb>grauitates inæquales, &amp; tempora motus inæqualia, percuſſiones erunt <lb></lb>in ratione compoſita ex ratione grauitatum &amp; temporum, quæ omnia <lb></lb>patent ex dictis in Th. ſuperioribus, v. g. ſit corpus duarum librarum, <lb></lb>&amp; alterum trium librarum; </s>
					<s id="N16D9C">primum moueatur per 5. inſtantia, &amp; ſecun­<lb></lb>dum 2.per 5. ratio grauitatum eſt 3/2; </s>
					<s id="N16DA2">ratio temporum eſt 7/5; </s>
					<s id="N16DA6">compoſita <lb></lb>ex vtraque erit (21/10); &amp; hæc eſt ratio percuſſionum. </s>
				</p>
				<p id="N16DAC" type="main">
					<s id="N16DAE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16DBA" type="main">
					<s id="N16DBC"><emph type="italics"></emph>Hinc poteſt ſciri ratio percuſſionis. </s>
					<s id="N16DC1">&amp; grauitationis eiuſdem mobilis in pri­<lb></lb>mo inſtanti vtriuſque, ſi cognoſcatur numerus inſtantium motus<emph.end type="italics"></emph.end>; </s>
					<s id="N16DCA">cum enim <lb></lb>ſingulis inſtantibus æqualis impetus accedat, vt ſæpè dictum eſt; </s>
					<s id="N16DD0">certè <lb></lb>erit percuſſio ad grauitationem, vt numerus inſtantium motus ad vnita­<lb></lb>tem, v.g. grauitatio ſit vt 4.ſitq́ue motus eiuſdem corporis per 8. inſtan­<lb></lb>tia; percuſſio erit ad grauitationem, vt 32. ad 4.vel vt 8.ad 1.quæ om­<lb></lb>nia conſtant ex dictis. </s>
				</p>
				<p id="N16DDE" type="main">
					<s id="N16DE0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16DEC" type="main">
					<s id="N16DEE"><emph type="italics"></emph>Hinc data percuſſione, ſi cognoſceretur probè numerus inſtantium motus, <lb></lb>dari poſſet grauitatio ipſi æqualis<emph.end type="italics"></emph.end>; </s>
					<s id="N16DF9">v.g. ſit percuſſio dati corporis cadentis <lb></lb>per 8.inſtantia, eius percuſſio eſt octupla grauitationis eiuſdem per Th. <lb></lb>56. igitur ſi detur grauitatio octupla huius, erit æqualis datæ percuſ­<lb></lb>ſioni; dabitur autem grauitatio octupla, ſi detur corpus eiuſdem mate­<lb></lb>riæ octuplò grauius, vt conſtat. </s>
				</p>
				<p id="N16E08" type="main">
					<s id="N16E0A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16E16" type="main">
					<s id="N16E18"><emph type="italics"></emph>Hinc primo inſtanti grauitationis nullum ferè ſentitur pondus,<emph.end type="italics"></emph.end> quia mini­<lb></lb>ma vis eſt, quæ conſequentibus inſtantibus augetur, hinc licèt corpus <lb></lb>breui tempore quis ſuſtineat, paulò poſt tamen ponderi cedit, ratio eſt <lb></lb>clara ex dictis. </s>
				</p>
				<pb pagenum="95" xlink:href="026/01/127.jpg"></pb>
				<p id="N16E2A" type="main">
					<s id="N16E2C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N16E38" type="main">
					<s id="N16E3A">Obſeruabis primò numerum inſtantium non poſſe à quoquam ſenſu <lb></lb>percipi, nec in calculos vocari, vt patet; </s>
					<s id="N16E40">vnde Theoremata non poſſunt <lb></lb>ad praxim reduci defectu huius cognitionis; quam ſupra adhibui hypo­<lb></lb>theſeos loco. </s>
				</p>
				<p id="N16E48" type="main">
					<s id="N16E4A">Secundò non poteſt ad amuſſim tempus cum tempore componi ad <lb></lb>æqualitatem, vel aliam datam rationem; </s>
					<s id="N16E50">licèt enim vnum tempus ſenſi­<lb></lb>bile haberet mille inſtantia ſupra aliud; </s>
					<s id="N16E56">illa tamen inæqualitas ſenſu <lb></lb>minimè perciperetur; idem dico de aliis rationibus, in quo, ni fallor, <lb></lb>maximè peccant, qui temporum æqualitatem perfectam obſeruari poſſe <lb></lb>contendunt. </s>
				</p>
				<p id="N16E60" type="main">
					<s id="N16E62">Tertiò, idem dico de percuſſionum ratione; </s>
					<s id="N16E66">quippe non poteſt ſenſu <lb></lb>percipi inæqualitas duarum percuſſionum, licèt vires vnius præualeant <lb></lb>mille punctis ſeu gradibus inſenſibilibus; </s>
					<s id="N16E6E">quippe non poteſt diſtingui <lb></lb>ab alia niſi vel ex ſpatio; </s>
					<s id="N16E74">atqui diſcerni non poteſt, an vnum ſpatium <lb></lb>ſuperet aliud mille punctis; vel ex ſono; </s>
					<s id="N16E7A">atqui ſonus poteſt diuidi in in­<lb></lb>finitos ferè gradus ſenſu minimè perceptibiles; </s>
					<s id="N16E80">igitur nulla hypotheſis <lb></lb>in his experimentis ſtatui poteſt, quibus æqualitas vel temporum, vel <lb></lb>ſpatiorum cognoſci dicatur; </s>
					<s id="N16E88">nec dicas aliquot inſtantia parùm diſeri­<lb></lb>minis importare, nam cùm ſingulis inſtantibus fiat æqualis impetus ac­<lb></lb>ceſſio, mille inſtantia reddunt percuſſionem millecuplam grauitationis; </s>
					<s id="N16E90"><lb></lb>hinc certum eſt ex numero inſtantium cognito cognoſci tantùm poſſe <lb></lb>numerum punctorum, &amp; viciſſim; </s>
					<s id="N16E97">at certè neuter ſenſu percipi poteſt; ne­<lb></lb>que tanti eſt hoc ſcire. </s>
				</p>
				<p id="N16E9D" type="main">
					<s id="N16E9F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16EAB" type="main">
					<s id="N16EAD"><emph type="italics"></emph>Hinc ſi corpus graue deſcenderet motu æquabili eoque æquali motui primi <lb></lb>inſtantis; </s>
					<s id="N16EB5">certè vix modicum ſpatium post multos annos decurreret<emph.end type="italics"></emph.end>; </s>
					<s id="N16EBC">ſuppo­<lb></lb>namus enim quod plures habent, licèt accuratè experimento ſubii­<lb></lb>ci non poſſit, ſcilicet vno ſecundo minuto temporis decurri à corpore <lb></lb>graui deorſum 12. pedes ſpatij; </s>
					<s id="N16EC6">in ſecundo minuto ſupponamus eſſe <lb></lb>mille inſtantia, quamuis infinita penè contineat; </s>
					<s id="N16ECC">ſitque in primo in­<lb></lb>ſtanti motus vnus gradus impetus; </s>
					<s id="N16ED2">ſic enim vocetur illa pars impetus, que <lb></lb>producitur primo inſtanti; </s>
					<s id="N16ED8">certè poſt mille inſtantia motus, erunt mille <lb></lb>gradus impetus; </s>
					<s id="N16EDE">iam vcrò ſi accipiatur ſubduplum maximæ &amp; minimæ <lb></lb>velocitatis; </s>
					<s id="N16EE4">id eſt vnius gradus, &amp; mille graduum, ſcilicet 500. 1/2 tri­<lb></lb>buaturque motui æquabili; </s>
					<s id="N16EEA">haud dubiè vno fecundo minuto percur­<lb></lb>rentur 12. pedes ſpatij per Th. 46. Igitur ſi cum velocitate vt 500, 1/2 <lb></lb>percurrentur 12. pedes 1.minuto, cum velocitate vt 1. percurrentur <lb></lb>12. pedes 500.ſecundis minutis, &amp;; 30. tertiis; </s>
					<s id="N16EF4">ſi verò accipiantur plura <lb></lb>inſtantia, v.g. 1000000.inſtantia, percurrentur 12. pedes 500000. ſe­<lb></lb>cundis minutis; </s>
					<s id="N16EFE">ſi verò 1000000000000. percurremur 500000000000. <lb></lb>ſecundis, id eſt 8333333333. minutis, id eſt 138888888. horis <pb pagenum="96" xlink:href="026/01/128.jpg"></pb>id eſt 5787037. diebus id eſt 89031. annis, omitto minutias; atqui lon­<lb></lb>gè adhuc plura in vno minuto continentur inſtantia. </s>
				</p>
				<p id="N16F0B" type="main">
					<s id="N16F0D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16F19" type="main">
					<s id="N16F1B"><emph type="italics"></emph>Si corpus graue deſcenderet motu æquabili, eoque æquali motui vltimi in­<lb></lb>stantis, duplum ferè ſpatium æquali tempore conficeret illius quod conficit <lb></lb>motu accelerato, duplum inquam ferè ſcilicet paulò minùs<emph.end type="italics"></emph.end>; </s>
					<s id="N16F28">quia conficit <lb></lb>idem motu æquabili; </s>
					<s id="N16F2E">cuius velocitas eſt ſubdupla maximæ &amp; minimæ; </s>
					<s id="N16F32"><lb></lb>ſed minima velocitas primi inſtantis pro nihilo reputatur; </s>
					<s id="N16F37">igitur acci­<lb></lb>piatur tantùm ſubduplum maximæ, igitur cum velocitate æquali maxi­<lb></lb>mæ, eodem tempore duplum ſpatium percurretur; </s>
					<s id="N16F3F">igitur in vno minuto <lb></lb>ſecundo, v.g. 24. pedes; </s>
					<s id="N16F47">igitur in vno minuto primo eodem motu æqua­<lb></lb>bili 1440. pedes percurrentur; </s>
					<s id="N16F4D">igitur in vna hora 86400. pedes; hinc <lb></lb>non eſt quod aliqui adeo mirentur, ſeu potiùs reiiciant hanc motus <lb></lb>accelerationem quod ex ea tùm tardiſſimus motus, tùm velociſſimus <lb></lb>conſequatur. </s>
				</p>
				<p id="N16F57" type="main">
					<s id="N16F59"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16F65" type="main">
					<s id="N16F67"><emph type="italics"></emph>Motus naturaliter acceleratus non propagatur per omnes tarditatis gra­<lb></lb>dus<emph.end type="italics"></emph.end>; </s>
					<s id="N16F72">quia tot ſunt huius propagationis gradus, quot ſunt inſtantia, <lb></lb>quibus durat hic motus, cum ſingulis inſtantibus noua fiat impetus ac­<lb></lb>ceſſio, ſed non ſunt infinita inſtantia, vt demonſtrabimus in Metaphy­<lb></lb>ſica; </s>
					<s id="N16F7C">prætereà licèt eſſent infinita inſtantia, non fieret adhuc per omnes <lb></lb>tarditatis gradus hæc propagatio; </s>
					<s id="N16F82">quia daretur aliquis gradus tarditatis, <lb></lb>quem non comprehenderet hæc graduum ſeries; </s>
					<s id="N16F88">nam incipit moueri <lb></lb>tardiùs in plano inclinato quàm in libero medio rectà deorſum, vt con­<lb></lb>ſtat, &amp; in medio denſo quàm in raro v.g. in aqua quàm in aëre; igitur <lb></lb>hic tarditatis gradus, quo incipit moueri in plano tantillùm inclinato, <lb></lb>non continetur inter illos, quibus mouetur rectà deorſum. </s>
				</p>
				<p id="N16F96" type="main">
					<s id="N16F98">Hinc duplici nomine reiice Galilæum qui hoc aſſerit. </s>
					<s id="N16F9B">Primò, quia <lb></lb>fruſtrà ponit infinita inſtantia ſine neceſſitate; </s>
					<s id="N16FA1">ſecundò, quia ratio, quam <lb></lb>habet, non conuincit; </s>
					<s id="N16FA7">vocat enim quietem tarditatem infinitam; </s>
					<s id="N16FAB">à qua <lb></lb>dum recedit mobile, haud dubiè per omnes tarditatis gradus propagari <lb></lb>poteſt eius motus; ſed contrà primò, nam reuerà quies non eſt tarditas, <lb></lb>quæ motui tantùm ineſſe poteſt. </s>
					<s id="N16FB5">Secundò, quia tàm ex quiete ſequi po­<lb></lb>teſt immediatè velox motus, quàm tardus, vt patet in proiectis. </s>
					<s id="N16FBA">Tertiò, <lb></lb>quia motus incipit; </s>
					<s id="N16FBF">igitur per aliquid ſui, igitur ille primus motus à <lb></lb>quiete infinitè non diſtat; denique rationes ſuprà propoſitæ rem iſtam <lb></lb>euincunt. </s>
				</p>
				<p id="N16FC7" type="main">
					<s id="N16FC9"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N16FD5" type="main">
					<s id="N16FD7">Obſeruabis conſideratum eſſe hactenus hunc motum nulla habita <lb></lb>ratione reſiſtentiæ medij, quæ haud dubiè hanc propoſitionem motus <lb></lb>accelerati tantillùm impedit, ſed de reſiſtentià medij agemus infrà. </s>
				</p>
				<p id="N16FDE" type="main">
					<s id="N16FE0"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N16FED" type="main">
					<s id="N16FEF">Ex dictis facilè reiicies primò ſententiam illorum, qui negant mo-<pb pagenum="97" xlink:href="026/01/129.jpg"></pb>tum naturalem accelerari, quos non ratio modò euidentiſſima, ſed adeò <lb></lb>ſenſibile experimentum omninò conuincere poteſt. </s>
				</p>
				<p id="N16FF9" type="main">
					<s id="N16FFB"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17008" type="main">
					<s id="N1700A">Secundò reiicies illos, qui volunt accelerationem motus eſſe, vel à vi <lb></lb>magnetica, quâ terra trahit ad ſe omnia grauia; </s>
					<s id="N17010">vel ab alia vi occulta, <lb></lb>quâ cœlum pellit deorſum; </s>
					<s id="N17016">vel à cœleſti illa, imò potiùs fabulosâ mate­<lb></lb>riâ; </s>
					<s id="N1701C">vel demum ab ipſa vi ſympathicâ, quâ corpus ſuo centro propiùs <lb></lb>factum totas ſuas vires exerit, vt ei ſe conjungat; quæ omnia gratis di­<lb></lb>cuntur, &amp; ex dictis pluſquam efficaciter refelli poſſunt, ne fruſtrà tempus <lb></lb>in iis iterum refellendis teramus. </s>
				</p>
				<p id="N17026" type="main">
					<s id="N17028"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17035" type="main">
					<s id="N17037">Tertiò reiicies, qui volunt motum accelerari ex aëris à tergo impel­<lb></lb>lentis appulſu, quod ridiculum eſt: </s>
					<s id="N1703D">licèt enim Ariſtoteles videatur illud <lb></lb>ſenſiſſe de projectis, quod examinabimus ſuo loco; </s>
					<s id="N17043">nunquam tamen hoc <lb></lb>dixit de motu naturali; </s>
					<s id="N17049">quin potiùs antiquorum fuit omnium hic ſen­<lb></lb>ſus, fieri <expan abbr="acceſſionẽ">acceſſionem</expan> mobili alicuius, vnde reddatur motus velocior; </s>
					<s id="N17053">hinc <lb></lb>dictum illud vulgare, <emph type="italics"></emph>vireſque acquirit eundo<emph.end type="italics"></emph.end>; </s>
					<s id="N1705F">nihil porrò intelligi poteſt <lb></lb>nomine virium, niſi id, ex quo maior ictus, ſeu percuſſio ſequitur; illud <lb></lb>autem eſſe impetum conſtat. </s>
				</p>
				<p id="N17067" type="main">
					<s id="N17069"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17076" type="main">
					<s id="N17078">Quartò ex his ſententia Ariſtotelica de motu accelerato optimè vin­<lb></lb>dicatur; </s>
					<s id="N1707E">quòd ſcilicet grauia ſub finem ſui motus velociùs ſerantur ver­<lb></lb>sùs centrum; quod ex dictis, &amp; ſimpliciſſimis, certiſſimiſque principiis <lb></lb>demonſtratum fuit. </s>
				</p>
				<p id="N17086" type="main">
					<s id="N17088"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17095" type="main">
					<s id="N17097">Quintò reiicies etiam illorum ſententiam, qui hanc accelerationem <lb></lb>tribuunt vel medio minùs reſiſtenti, vel grauitatis augmento, vel impe­<lb></lb>tui violento priùs impreſſo dum corpus graue attollitur, quod meo iudi­<lb></lb>cio ridiculum eſt; quaſi verò fruſtum rupis deciſum, deorſumque ruens <lb></lb>impetum violentum aliquando habuerit. </s>
				</p>
				<p id="N170A3" type="main">
					<s id="N170A5"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N170B2" type="main">
					<s id="N170B4">Sextò reiicies illorum ſententiam, qui volunt accelerationem motus <lb></lb>naturalis ita fieri, vt ſpatia temporibus æqualibus acquiſita ſequantur ſe­<lb></lb>riem numerorum imparium 1.3.5.7.9.11.13. &amp;c. </s>
					<s id="N170BB">&amp; ſpatia ſint vt <lb></lb>quadrata temporum v. g. ſi primo inſtanti acquiritur 1.ſpatium: ſecundo <lb></lb>acquiruntur 3. tertio 5. quarto 7. &amp;c. </s>
					<s id="N170C7">fique vno inſtanti acquiritur 1. <lb></lb>ſpatium, duobus acquiruntur 4. tribus 9. quatuor 16. atque ita deinceps <lb></lb>per quadrata, quæ omnia ex dictis falſa eſſe conſtat; </s>
					<s id="N170CF">quippe ſi æqualibus <lb></lb>temporibus acquiruntur æqualia velocitatis momenta; igitur ſi primo <lb></lb>inſtanti eſt 1.gradus, ſecundo erunt 2. igitur ſecundo tempore cum duo­<lb></lb>bus gradibus velocitatis vel impetus percurrentur duo tantùm ſpatia, ſi <lb></lb>primò inſtanti æquali cum vno gradu percurritur vnus, ſed de his fusè <lb></lb>infrà. </s>
				</p>
				<pb pagenum="98" xlink:href="026/01/130.jpg"></pb>
				<p id="N170E1" type="main">
					<s id="N170E3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N170EF" type="main">
					<s id="N170F1">Septimò reiicies etiam aliquos recentiores, qui volunt fieri hanc pro­<lb></lb>greſſionem ſpatiorum æqualibus temporibus reſpondentium ſecundùm <lb></lb>progreſſionem Geometricam, duplam, ſcilicet iuxta hos numeros 1. 2. 4. <lb></lb>8. 16. 32. &amp;c. </s>
					<s id="N170FA">quod etiam ex eadem ratione facilè confutatur: </s>
					<s id="N170FE">reiicies <lb></lb>etiam alium recentiorem, qui vult hanc progreſſionem ſumi ex linea <lb></lb>proportionaliter ſectâ, id eſt in mediam &amp; extremam rationem; </s>
					<s id="N17106">ſed de <lb></lb>his omnibus in diſſertatione ſequenti fusè diſputamus; quippe rem hanc <lb></lb>tanti eſſe putamus, vt nihil omittendum ſit, quod ad eius pleniſſimam <lb></lb>confirmationem pertineat. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N17113" type="main">
					<s id="N17115"><emph type="center"></emph>DISSERTATIO<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1711C" type="main">
					<s id="N1711E"><emph type="center"></emph><emph type="italics"></emph>De Motu naturaliter accelerato.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N17129" type="main">
					<s id="N1712B">DVæ ſunt potiſſimùm in hac materia celebres ſententiæ; </s>
					<s id="N1712F">Prima eſt <lb></lb>Galilei, &amp; ferè omnium recentiorum, qui poſt Galileum de motu <lb></lb>ſcripſerunt; </s>
					<s id="N17137">inter quos, ne omittam Genuenſem Patricium, Balianum; </s>
					<s id="N1713B"><lb></lb>Doctus Merſennus, &amp; eruditus Gaſſendus primum locum obtinent; </s>
					<s id="N17140"><lb></lb>quorum ille hanc ſententiam multis in locis, ſcilicet in ſuis quæſtioni­<lb></lb>bus Phyſicis, in ſua Galilei verſione, in harmonia vniuerſali, &amp; demum <lb></lb>in ſua Baliſtica paſſim, tùm fusè proponit, &amp; explicat, tùm etiam ſuis ra­<lb></lb>tionibus confirmat; Galileus verò illam habet tùm in gemino ſyſtema­<lb></lb>te, tùm in dialogo tertio de motu locali. </s>
				</p>
				<p id="N1714D" type="main">
					<s id="N1714F">Secunda ſententia noſtra eſt, de qua non ſemel diſputandum fuit à <lb></lb>Magiſtro, tùm verbis tùm etiam litteris ſcriptis; &amp; ne quid fortè diſſimu­<lb></lb>lem, illa eſt ſententia quam anonimo Philoſophe (quem non ſine laude <lb></lb>appellat idem Merſennus) tribuit. </s>
					<s id="N17159">prop.18.ſuæ Baliſticæ ſub finem; illa <lb></lb>eſt inquam ſententia, quam hactenus meo iudicio ſatis luculenter de­<lb></lb>monſtrauimus. </s>
				</p>
				<p id="N17161" type="main">
					<s id="N17163">Sunt tres aliæ ſententiæ, quæ ab eodem Merſenno referuntur; prima <lb></lb>eſt quæ progreſſionem ſpatiorum <expan abbr="eãdem">eandem</expan> eſſe vult cum eâ, quæ eſt ſi­<lb></lb>nuum verſorum, centro quadrantis poſito in centro terræ, &amp; altero ex­<lb></lb>tremo ſinus totius in eo punctò, in quo incipit motus. </s>
					<s id="N17171">Secunda eſt quo­<lb></lb>rumdam, qui volunt progreſſionem ſpatiorum, quæ ſingulis temporibus <lb></lb>reſpondent, eſſe in progreſſione geometrica dupla iuxta hos numeros, <lb></lb>1.2.4.8.32. Tertia eſt alicuius, qui voluit eſſe iuxta proportionem lineæ <lb></lb>ſectæ in mediam, &amp; extremam rationem. </s>
				</p>
				<p id="N1717C" type="main">
					<s id="N1717E">Tres vltimæ ſententiæ nullo prorſus nituntur fundamento; igitur vel <lb></lb>inde maximè confutantur, quòd gratis ſine vllo prorſus vel rationis vel <lb></lb>experimenti momento excogitatæ ſint. </s>
					<s id="N17186">Igitur in hac diſſertatione duæ <lb></lb>tantùm primæ diſcutiendæ ſunt Sententiæ Galilei ſchema hic habes <lb></lb>in linea AF, in qua aſſumitur AB, ſpatium ſcilicet, quod dato tempore <pb pagenum="99" xlink:href="026/01/131.jpg"></pb>corpus graue ſuo motu percurrit; </s>
					<s id="N17193">&amp; ſecundo tempore æquali BC, quæ <lb></lb>tripla eſt AB, tertio CD quintupla quarto DE ſeptupla, quinto EF <lb></lb>nonecupla; vides primò ſeriem numerorum imparium 1. 3. 5. 7. 9.atque <lb></lb>ita deinceps. </s>
					<s id="N1719D">Secundò vides ſpatia eſſe in ratione duplicata temporum, <lb></lb>hoc eſt vt temporum quadrata. </s>
					<s id="N171A2">v.g. ſi accipiatur ſpatium AB primo tem­<lb></lb>pore peractum, &amp; ſpatium AC duobus temporibus confectum: ratio hu­<lb></lb>ius ad illud eſt vt 4.ad 1.id eſt vt quadratum 2.ad quadratum 1. ſimiliter, <lb></lb>ſi accipiatur ſpatium AD confectum tribus temporibus, erit 9.id eſt qua­<lb></lb>dratum 3, ſpatium AE confectum 4.temporibus erit 16.id eſt quadratum <lb></lb>4. &amp; AF 25. quadratum 5. </s>
				</p>
				<p id="N171B3" type="main">
					<s id="N171B5">Hæc ſententia ingeniosè à Galileo excogitata ex duplici capite à ſuis <lb></lb>auctoribus confirmatur; primò experientiâ, ſecundò ratione. </s>
					<s id="N171BB">Experien­<lb></lb>tia tribus potiſſimum experimentis fulcitur; primum eſt in motu deor­<lb></lb>ſum per lineam perpendicularem. </s>
					<s id="N171C3">v. g. in linea AF; </s>
					<s id="N171CB">nam reuerà multi <lb></lb>ſunt, iique grauiſſimi auctores in rebus tùm philoſophicis, tùm mathe­<lb></lb>maticis verſatiſſimi, qui ſæpiùs ſenſu ipſo probarunt, repetitis vſque ad <lb></lb>nauſeam experimentis, tempore vnius ſecundi minuti corpus graue in <lb></lb>libero aëre 12. pedes ſpatij motu naturali deorſum percurrere; in 2.ve­<lb></lb>rò ſecundis 48. in 3.ſecundis 108.ſed ſpatia iſta ſunt vt temporum qua­<lb></lb>drata, vt conſtat. </s>
				</p>
				<p id="N171DB" type="main">
					<s id="N171DD">Secundum experimentum eſt in plano inclinato, in quo corpus graue <lb></lb>deſcendit iuxta prædictam progreſſionem, quod expreſſis verbis teſtatur <lb></lb>Galileus à ſe fuiſſe probatum ſæpiùs, nec vnquam à vero ne tantillùm <lb></lb>quidem aberraſſe. </s>
					<s id="N171E6">ſed in perpendiculari deorſum eadem proportione <lb></lb>creſcit motus, quâ in plano inclinato; licèt in plano inclinato tardior ſit <lb></lb>motus, vt demonſtrabimus aliàs. </s>
				</p>
				<p id="N171EE" type="main">
					<s id="N171F0">Tertium experimentum petitur ex funependulis; </s>
					<s id="N171F4">in quibus ſæpiùs <lb></lb>obſeruatum eſt longitudinem funis, &amp; conſequenter arcum quadrantis <lb></lb>longioris funependuli eſſe ad longitudinem, ſeu quadrantem alterius <lb></lb>breuioris, vt quadratum temporis, quo perficitur vibratio maioris ad <lb></lb>quadratum temporis, quo perficitur vibratio minoris.v.g.ſit longitudo <lb></lb>funependuli maioris, CG minoris verò ſubquadrupla CF; </s>
					<s id="N17202">eleuetur vter­<lb></lb>que funis, cui pondus æquale ſit appenſum vſque ad horizontalem <lb></lb>CDE &amp; alterum ex D; </s>
					<s id="N1720A">alterum verò ex E demiſſum cadat deorſum; haud <lb></lb>dubiè funependulum CE duplum temporis collocabit in decurrendo <lb></lb>quadrante EG, &amp; funependulum ED ſubduplum. </s>
					<s id="N17212">v. g. ſi CD conficit <lb></lb>ſuam vibrationem DF vno ſecundo, EG conficiet ſuam EG duobus, vt <lb></lb>centies obſeruatum eſt; </s>
					<s id="N1721E">ſed EG eſt quadruplus DF, vt patet; igitur EG <lb></lb>&amp; DF ſunt vt quadrata temporum, quibus percurritur EG &amp; DF ſed vt <lb></lb>deſcendit graue per DF &amp; EG, ita deſcendit per CF &amp; CG, quippe <lb></lb>DF &amp; EG habent rationem plani inclinati deorſum. </s>
				</p>
				<p id="N17228" type="main">
					<s id="N1722A">Adde quod, vt ſe habet tempus, quo deſcendit per totum quadrantem <lb></lb>DF, ad tempus, quo deſcendit per totum quadrantem EG. ſic ſe habet <lb></lb>tempus, quo deſcendit per arcum DL ſubduplum DF ad tempus, quo <lb></lb>deſcendit per arcum EI ſubduplum EG; </s>
					<s id="N17234">item tempus, quo deſcendit <pb pagenum="100" xlink:href="026/01/132.jpg"></pb>per arcum DM ſubquadruplum DF.ad tempus, quo deſcendit per arcum <lb></lb>EK ſubquadruplum EG; </s>
					<s id="N1723F">denique vt tempus, quo per minimum ar­<lb></lb>cum quadrantis DF, ad tempus, quo deſcendit per alium proportiona­<lb></lb>lem, ſcilicet quadruplum in quadrante EG; </s>
					<s id="N17247">atqui tam parui arcus poſ­<lb></lb>ſunt aſſumi, vt ſint ad inſtar lineæ rectæ deorſum tangentis ſcilicet in D <lb></lb>&amp; in E; </s>
					<s id="N1724F">igitur in his rectis deſcendunt grauia iuxta progreſſionem præ­<lb></lb>dictam; </s>
					<s id="N17255">id eſt, cum arcus minimus aſſumptus ab E, qui æquiualet rectæ, <lb></lb>ſit quadruplus arcus minimi aſſumpti à puncto D, tempus, quo percurri­<lb></lb>tur ille primus, eſt ad tempus, quo percurritur hic ſubquadruplus, vt tem­<lb></lb>pus, quo percurritur EG ad tempus, quo percurritur DF vt dictum eſt; </s>
					<s id="N1725F"><lb></lb>ſed tempus, quo percurritur EG eſt duplum illius, quo percurritur DF; </s>
					<s id="N17264"><lb></lb>igitur tempus, quo percurritur minimus arcus aſſumptus ab E, &amp; qui eſt <lb></lb>ad inſtar rectæ, eſt duplum temporis quo percurritur minimus arcus aſ­<lb></lb>ſumptus à puncto D ſubquadruplus prioris, &amp; qui eſt etiam ad inſtar re­<lb></lb>ctæ; igitur ſpatia ſunt vt temporum quadrata. </s>
				</p>
				<p id="N1726F" type="main">
					<s id="N17271">Quod autem tempus, quo percurritur EG ſit duplum illius, quo per­<lb></lb>curritur DF, patet experientiâ; </s>
					<s id="N17277">nam ſi numerentur ducentæ vibrationes <lb></lb>funependuli CD; </s>
					<s id="N1727D">eodem tempore numerabuntur centum vibrationes <lb></lb>maioris CE; </s>
					<s id="N17283">igitur vibrationum minoris numerus eſt duplus numeri vi­<lb></lb>brationum maioris, dum ſimul vibrantur; </s>
					<s id="N17289">igitur eo tempore, quo fiunt <lb></lb>100.maioris, fient 200. minoris; nam omnes vibrationes eiuſdem fune­<lb></lb>penduli ſunt æquò diuturnæ, licèt fiant per arcus inæquales eiuſdem. </s>
					<s id="N17291"><lb></lb>quadrantis, vt ſæpè obſeruatum eſt. </s>
					<s id="N17295">In his tribus potiſſimum experimen­<lb></lb>tis fundatur hæc hypotheſis Galilei, quæ nec clariùs meo. </s>
					<s id="N1729A">iudicio, nec <lb></lb>ſinceriùs exponi poſſunt. </s>
				</p>
				<p id="N1729F" type="main">
					<s id="N172A1">Antequam rationes, quæ pro hac ſententia facere videntur, propona­<lb></lb>mus, refellamuſque; </s>
					<s id="N172A7">oſtendo primò quomodo cum his experimentis <lb></lb>ſtare poſſit noſtra hypotheſis; </s>
					<s id="N172AD">igitur ex iis hypotheſis Galilei rectè de­<lb></lb>duci non poteſt: </s>
					<s id="N172B3">quippe hæc eſt certiſſima regula, quam nemo Philoſo­<lb></lb>phus negare auſit: </s>
					<s id="N172B9">Quotieſcumque aliquod experimentum tale eſt, vt <lb></lb>cum eo ſtare poſſint contrariæ hypotheſes; </s>
					<s id="N172BF">ex eo certè neutra deduci po­<lb></lb>teſt; igitur ex propoſitis experimentis ſuam hypotheſim Galileus non <lb></lb>legitimè deducit, quod vt clariſſimè oſtendam. </s>
				</p>
				<p id="N172C7" type="main">
					<s id="N172C9">Suppono, quando dicitur ſecundum ſpatium eſſe triplum primi ſup­<lb></lb>poſitis æqualibus temporibus, non ita Geometricè, certaque, &amp; acuratâ <lb></lb>aſſertione hoc dici; </s>
					<s id="N172D1">quin vel aliqua puncta in ſpatiis, vel inſtantia in <lb></lb>temporibus deſint, vel ſuperſint; </s>
					<s id="N172D7">ſi enim quis diceret ſpatium eſſe tri­<lb></lb>plum primi minus 100000. punctis, vel ſecundum tempus eſſe maius <lb></lb>primo 100000. inſtantibus; quis hanc, vel ſpatij, vel temporis differen­<lb></lb>tiam ſenſu percipiat? </s>
					<s id="N172E1">cum tamen experimentum omne phyſicum ſenſui <lb></lb>ſubeſſe poſſit; </s>
					<s id="N172E7">nec eſt quod aliquis dicat hoc idem toties obſeruatum <lb></lb>eſſe, tam multis locis temporibus, totque ac tantis etiam teſtibus, vt mi­<lb></lb>nimè fraus aliqua, vel error ſubrepere potuerit; nam cum parua ſit, &amp; <lb></lb>inſenſibilis tùm ſpatiorum, tùm temporum differentia, maius vel minus <lb></lb>æquali tempus, pro æquali, maius.vel minus triplò ſpatium pro triplo <pb pagenum="101" xlink:href="026/01/133.jpg"></pb>facilè accipi poteſt, cum nullum diſcrimen ſenſibile eſt. </s>
				</p>
				<p id="N172F8" type="main">
					<s id="N172FA">Adde quod non deſunt viri grauiſſimi qui dicant ſe vix obſeruare po­<lb></lb>tuiſſe hanc ſpatiorum progreſſionem; </s>
					<s id="N17300">plures appellare poſſem; </s>
					<s id="N17304">vnus <lb></lb>Gaſſendus eſt inſtar omnium; </s>
					<s id="N1730A">qui ſanè in obſeruando fuit acuratiſſimus, <lb></lb>qui literis ſcriptis, quas ego vidi, expreſſis verbis aſſerit progreſſionem <lb></lb>hanc non eſſe omninò iuxta hos numeros 1.3.5.7. ſed ſingulis addendas <lb></lb>eſſe ſuas minutias, quas ipſe habet; </s>
					<s id="N17314">ſed ego omitto, quia etiam ſua incer­<lb></lb>titudine laborant; </s>
					<s id="N1731A">igitur nullo experimento ad amuſſim concludes, <lb></lb>vel <expan abbr="æqualitatẽ">æqualitatem</expan> vel aliam accuratam tùm temporum tùm ſpatiorum pro­<lb></lb>portionem: </s>
					<s id="N17326">Equidem ſenſu percipio practicam hanc eſſe maiorem pede; </s>
					<s id="N1732A"><lb></lb>at tot lineis vel <expan abbr="pũctis">punctis</expan> ſuperare ne Argus quidem certò, ac diſtinctè cer­<lb></lb>neret: </s>
					<s id="N17335">Sed efficaciter, meo iudicio, hanc Galilei hypotheſim refello; </s>
					<s id="N17339">ſint <lb></lb> 2.partes temporis æquales AE, EF, eæque ſenſibiles; </s>
					<s id="N1733F">nec enim aliæ aſ­<lb></lb>ſumi poſſunt; </s>
					<s id="N17345">ſintque minimæ omnium ſenſibilium; </s>
					<s id="N17349">haud dubiè conſtant <lb></lb>ſingulæ infinitis ferè aliis inſenſibilibus, vt patet; </s>
					<s id="N1734F">igitur ſic ratiocinatur <lb></lb>Galileus; </s>
					<s id="N17355">in prima parte temporis AE corpus graue percurrit ſpatium <lb></lb>GH, &amp; in ſecunda æquali EF percurrit ſpatium HL triplum prioris; </s>
					<s id="N1735B"><lb></lb>igitur ſpatia ſunt vt quadrata temporum, rectè; ſed antequam vlterius <lb></lb>progrediar;</s>
					<s id="N17362"> Quæro vel à Galileo, vel à quolibet alto, vtrum ſpatium <lb></lb>HL ſit omnino triplum? </s>
					<s id="N17367">&amp; ſi aliquis contenderet deeſſe (1/1000000) GH <lb></lb>vtrum experimento præſenti conuinci poſſit? </s>
					<s id="N1736C">nemo, vt puto, id aſſerere <lb></lb>auſit; </s>
					<s id="N17372">hoc poſito, aſſumptaque progreſſione arithmetica <expan abbr="quã">quam</expan> noſtra ſen­<lb></lb>tentia in ſpatiis adſtruit; </s>
					<s id="N1737C">ſi prima parte temporis AE percurratur ſpa­<lb></lb>tium GH, ſecunda EF. percurretur tantùm HK duplum GH; </s>
					<s id="N17382">igitur <lb></lb>minus eſt hoc ſpatium vero ſpatio 1/4. ſcilicet tota KL; </s>
					<s id="N17388">res prorſus de­<lb></lb>monſtrata eſſet, ſi termini proportionis vnius eſſent tantùm 2. id eſt, ſi <lb></lb>progreſſio fieret in partibus temporis ſenſibilibus; </s>
					<s id="N17390">at poſito quod ſint <lb></lb>plures termini, vt reuerâ ſunt; </s>
					<s id="N17396">nam in totidem terminis fit progreſſio, in <lb></lb>quibus fit augmentum impetus, vel accelerationis acceſſio; </s>
					<s id="N1739C">atqui hæc <lb></lb>fit in ſingulis inſtantibus, licèt finitis, igitur &amp; progreſſio; </s>
					<s id="N173A2">Quare duæ <lb></lb>partes temporis AE, EF diuidantur in 4. æquales AD; certè in duabus <lb></lb>primis percurretur ſpatium. </s>
					<s id="N173AA">VQ æquale GH; igitur duabus vltimis per­<lb></lb>curretur QK, quæ ſit ad QV vt 7. ad 3. nam prima parte percurritur 1. <lb></lb>ſpatium. </s>
					<s id="N173B1">ſecunda 2. igitur QV continet tria ſpatia; </s>
					<s id="N173B5">tertia verò 3. quarta <lb></lb>4.ergo hæ duæ vltimæ 7. ſed QM eſt dupla QV; </s>
					<s id="N173BB">igitur continet 6. igi­<lb></lb>tur MK eſt 1/3 VQ, vel KL; </s>
					<s id="N173C1">igitur KM eſt (1/12) GL; </s>
					<s id="N173C5">igitur 12. L (1/10), vel <lb></lb>1/6, igitur VK eſt ad GL vt 10.ad 12. igitur totum ſpatium VK eſt mi­<lb></lb>nus vero 1/6. Præterea 2. partes temporis AE EF diuidantur in 8. partes <lb></lb>æquales AE; </s>
					<s id="N173CF">haud dubiè 4. primis percurretur ſpatium XT æquale <lb></lb>GH, quod debet diuidi in 10. ſpatia; </s>
					<s id="N173D5">nam 4. terminis, ſeu temporibus <lb></lb>reſpondent ſpatia 10. quibus æqualia ſunt 40. in teta GL, cuius XT eſt <lb></lb>(1/14), ſed ſi in 4.primis acquiruntur 10. 4. vltimis EF acquiruntur 26.ſcili­<lb></lb>cet T 5; igitur tota X 5. eſt 6. igitur eſt ad GL vt 36. ad 40. ſeu 9. ad <lb></lb>10. igitur X 5. eſt ſpatium minus vero (1/10). </s>
				</p>
				<p id="N173E1" type="main">
					<s id="N173E3">Præterea diuidatur tempus AF in 16. partes æquales AB; </s>
					<s id="N173E7">haud dubiè <pb pagenum="102" xlink:href="026/01/134.jpg"></pb>8 primis acquiritur ſpatium YS æquale GH; quod debet diuidi in ſpa­<lb></lb>tiola 36, quæ reſpondent 8. temporibus, ſeu terminis huius progreſſio­<lb></lb>nis, quibus æqualia ſunt 144. in GL, cuius YS eſt 1/4, ſed ſi in 8. primis <lb></lb>acquiruntur 36. in 8. vltimis acquirentur 100. igitur S 6. eſt 100. igitur <lb></lb>Y6. eſt 136. igitur eſt ad GL vt 136. ad 144.ſeu 17.ad 18.igitur Y6.eſt <lb></lb>ſpatium totale minus vero (1/18). </s>
				</p>
				<p id="N173FA" type="main">
					<s id="N173FC">Deinde diuidatur adhuc tempus AF in partes 32. æquales, 16. pri­<lb></lb>mis acquiritur ZR æquale GH, quod debet diuidi in ſpatiola 136.quæ <lb></lb>reſpondent 16. temporibus quibus æqualia ſunt 544. in tota GL, cuius <lb></lb>ZR eſt 1/4 ſed ſi in 16. primis temporibus acquiruntur 136. in vltimis <lb></lb>16. acquiruntur 392. igitur R 7. eſt 392. &amp; ZR 136. igitur Z 7.528. <lb></lb>igitur Z 7. eſt ad GL, vt 528. ad 544. ſeu vt 33. ad 34. igitur Z 7 eſt <lb></lb>ſpatium minus verò (1/34) </s>
				</p>
				<p id="N1740B" type="main">
					<s id="N1740D">Denique ſi diuidatur tempus AF in partes 64.ſpatium acquiſitum erit <lb></lb>minus vero, aſſumpto ſcilicet tota HL (1/66), ſi diuidatur in 128. partes, erit <lb></lb>minus (1/130) ſi diuidatur in 256. partes, erit minus (1/258) ſed temporis par­<lb></lb>tes 2.AE. EF minimè ſenſibilium diuidi poſſunt in infinita ferè inſtan­<lb></lb>tia; ſint tantùm ex.g. </s>
					<s id="N17419">1000000. igitur ſpatium tunc acquiſitum erit mi­<lb></lb>nus ſuppoſito vero HL (1/1000002), quæ ſi deſit tantùm ſpatio KL vt ſit 1/4 <lb></lb>totius GL, quis hoc diſcernat? </s>
					<s id="N17420">igitur etiam ſuppoſita progreſſione arith­<lb></lb>metica, quæ fiat in finitis inſtantibus; </s>
					<s id="N17426">ſi obſeruetur acuratiſſimè ſpatium, <lb></lb>quod percurritur in vna parte temporis ſenſibili v. g. ſpatium GH in <lb></lb>parte temporis AE; </s>
					<s id="N17432">ſpatium, quod acquiretur in tempore ſecundo æqua­<lb></lb>li tàm propè accedet ad ſpatium HL, id eſt ad triplum prioris GH, vt <lb></lb>nullus mortalium diſcernere poſſit; igitur cum hoc experimento tàm <lb></lb>poteſt ſtare noſtra hypotheſis, quàm alia Galilei, igitur neutra ex eo tan­<lb></lb>tùm euinci poteſt. </s>
				</p>
				<p id="N1743E" type="main">
					<s id="N17440">Hinc obiter obſerua progreſſionem differentiarum; </s>
					<s id="N17444">quippe ſi ſint <lb></lb>tantùm 2. partes temporis, differentia eſt 1/4; </s>
					<s id="N1744A">ſi 4.1/6 ſi 8. (1/10); ſi 16.(1/18); ſi 32. <lb></lb>(1/34); </s>
					<s id="N17450">ſi 64.(1/66) nam primò denominator fractionis ſuperat tantùm binario <lb></lb>numerum partium temporis; ſecundò differentiæ denominatorum ſunt <lb></lb>in progreſſione geometrica dupla numerorum 2. 4. 8. 16. 32. 64. <lb></lb>128. &amp;c. </s>
				</p>
				<p id="N1745A" type="main">
					<s id="N1745C">Eodem modo ſoluendum eſt ſecundum experimentum rotati globi in <lb></lb>plano decliui; </s>
					<s id="N17462">præſertim cum globus ab incurſu aſperiorum partium <lb></lb>tùm globi, tùm plani ſaltuatim deſcendat; </s>
					<s id="N17468">quod dubium eſſe non poteſt, <lb></lb>&amp; quò decliuius erit, faciliùs reſiliet a plano, vt patet; ſed de motu in <lb></lb>planis inclinatis fusè agemus infrà libro integro. </s>
				</p>
				<p id="N17470" type="main">
					<s id="N17472">Quod ſpectat ad tertium experimentum; </s>
					<s id="N17476">multa in eo ſupponuntur <lb></lb>vel falſa, vel ſaltem dubia: vel ea quæ cum noſtra hypotheſi optimè con­<lb></lb>ueniant. </s>
					<s id="N1747E">Primum eſt, quando dicuntur omnes vibrationes eiuſdem fune­<lb></lb>penduli, ſiue maiores, ſiue minores eſſe æquediuturnæ, quod manifeſtis <lb></lb>experimentis repugnat; </s>
					<s id="N17486">quippe vibratio maior plùs temporis; </s>
					<s id="N1748A">minor ve­<lb></lb>rò minùs in ſuo deſcenſu ponit; </s>
					<s id="N17490">dimittantur enim duo funependula æ­<lb></lb>qualia; </s>
					<s id="N17496">alterum quidem ex altitudine 90.graduum, alterum ex altitudine <pb pagenum="103" xlink:href="026/01/135.jpg"></pb>10. vel 15.graduum; </s>
					<s id="N1749F">ita vt ſimul vibrationes ſuas incipiant; </s>
					<s id="N174A3">numerentur <lb></lb>vibrationes vtriuſque, vbi 100. è minoribus numeratę fuerint, numera­<lb></lb>buntur circiter 97. è maioribus, quod ſæpiùs obſeruaui teſtibus etiam <lb></lb>adhibitis; </s>
					<s id="N174AD">hoc ipſum etiam obſeruarunt alij; </s>
					<s id="N174B1">atque adeo ipſe P.Merſen­<lb></lb>nus, qui L. 2. ſuæ verſionis, Ar.17. Galileum arguit parùm acurati ſtu­<lb></lb>dij in his obſeruationibus adhibiti: </s>
					<s id="N174B9">rationem huius effectus in libro de <lb></lb>funependulis explicabimus; </s>
					<s id="N174BF">immò ſi omnes vibratìones maiores primæ <lb></lb>vibrationi 90. grad. eſſent æquales, &amp; aliæ minores alterius funependu­<lb></lb>li ſenſun, vt ſit, minuerentur; </s>
					<s id="N174C9">vix 90. maiores numerare poſſes, iam enu­<lb></lb>meratis 100. ex minoribus; </s>
					<s id="N174CF">ſed de his omnibus ſuo loco; </s>
					<s id="N174D3">in vna tamen <lb></lb>vel altera vibratione vix aliquod diſcrimen obſeruatur; quod tamen ob­<lb></lb>ſeruari facilè poſſet in maioribus funependulis. </s>
				</p>
				<p id="N174DB" type="main">
					<s id="N174DD">Secundum, quod ſupponitur, eſt quod longitudines funependulorum <lb></lb>ſint prorſus, vt quadrata temporum, quibus vibrationes ſingulorum <lb></lb>fiunt, v.g. funependulum longitudinis 4. pedum facere vnam vibratio­<lb></lb>nem eo tempore, quo funependulum longitudinis vnius pedis facit duas; </s>
					<s id="N174E9"><lb></lb>quod primò in multis vibrationibus non tàm accuratè obſeruatur; </s>
					<s id="N174EE"><expan abbr="ſecū-dò">ſecun­<lb></lb>dò</expan> licèt obſeruaretur ſenſibiliter, idem reſponderi debet, quod ſuprà in <lb></lb>ſingulis vibrationibus eſſe tantùm diſcrimen; </s>
					<s id="N174F9">quod etiam in multis ſenſi­<lb></lb>bile non eſt; ſi enim diſcrimen primarum vibrationem v.g.ſit (1/100000000) <lb></lb>certè vltimarum adhuc inſenſibile erit. </s>
				</p>
				<p id="N17501" type="main">
					<s id="N17503">Tertium ſuppoſitum fuit, minimum arcum minoris quadrantis aſſum­<lb></lb>ptum, &amp; alium minoris quadrantis eſſe ad inſtar perpendicularium; </s>
					<s id="N17509">cùm <lb></lb>tamen diuerſa ſit inclinatio minoris, &amp; maioris quadrantis: </s>
					<s id="N1750F">quippe <lb></lb>principium maioris accedit propiùs ad perpendicularem; </s>
					<s id="N17515">facit enim <lb></lb>angulum contingentiæ minorem; </s>
					<s id="N1751B">alia verò extremitas accedit propiùs <lb></lb>ad horizontalem propter rationem prædictam; </s>
					<s id="N17521">hinc illa extremitas ma­<lb></lb>ioris, vnde eſt initium motus, planum decliuius facit; altera verò minùs <lb></lb>decliue; ſed hæc fusè proſequar ſuo loco. </s>
				</p>
				<p id="N17529" type="main">
					<s id="N1752B">Quartum, quod ſupponitur eſt, accelerationem motus fieri in qua­<lb></lb>drante in ea ratione, in qua fit per plana chordarum inclinata, quod <lb></lb>etiam falſum eſt; </s>
					<s id="N17533">quia in eodem plano inclinato ſupponitur eadem <lb></lb>inclinatio; </s>
					<s id="N17539">ſecus in quadrante, cuius ſingula puncta nouam faciunt in­<lb></lb>clinationem: </s>
					<s id="N1753F">adde quod quarta pars quadrantis maioris EK non facit <lb></lb>eandem inclinationem, quam totus quadrans minor DF ipſi EK æqua­<lb></lb>lis; quamquam hoc ipſi vltrò concedent aduerſarij. </s>
				</p>
				<p id="N17547" type="main">
					<s id="N17549">Præterea, ſit ita vt ſupponitur; </s>
					<s id="N1754D">ita vt ſenſibiliter differentia huius <lb></lb>progreſſionis percipi non poſſit, ſintque numeratæ omnes vibrationes <lb></lb>ſenſibiles dati funependuli ex altitudine 90, grad. demiſſi; </s>
					<s id="N17557">quæ vix eſſe <lb></lb>poſſunt 1800; </s>
					<s id="N1755D">ſint autem plures ſcilicet 2000. dicis confectas eſſe 2000 <lb></lb>minoris funependuli eo tempore, quo 1000. tantùm in quadruplo fune­<lb></lb>pendulo numerantur; </s>
					<s id="N17565">annuo quidem, ſi res tantùm ſenſibiliter conſide­<lb></lb>retur; </s>
					<s id="N1756B">ſin verò ſecùs, id pernego; ſed dico deeſſe v. g. 1000000. puncta <lb></lb>ſpatij, quæ diſcerni non poſſunt, ita vt primæ vibrationi 1000. pun­<lb></lb>cta ſecundæ, 2000. tertiæ 3000. &amp;c. </s>
					<s id="N17577">vltimæ verò, ſeu milleſimæ <pb pagenum="104" xlink:href="026/01/136.jpg"></pb>1000000. quæ omnia ſunt inſenſibilia, neque maiorem habent diffi­<lb></lb>cultatem, quàm in motu perpendiculari, de quo ſuprà; etiam conceſſis <lb></lb>vltrò omnibus experimétis propoſitis. </s>
					<s id="N17584">Igitur ſuppoſitâ progreſſione ſpa­<lb></lb>tiorum arithmetica in inſtantibus, tàm propè accedit ad aliam, quàm <lb></lb>Galileus ponit, ſiue in perpendiculari deorſum, ſiue in quadrante fune­<lb></lb>penduli; </s>
					<s id="N1758E">aſſumptis ſcilicet partibus temporis ſenſibilibus, vt differentia <lb></lb>diſcernit non poſſit; </s>
					<s id="N17594">immò nec duplum differentiæ, nec centuplum, nec <lb></lb>millecuplum; </s>
					<s id="N1759A">ſed de his ſatis quæ ex dictis ſuprà facilè intelligi poſſunt: <lb></lb>quare veniemus iam ad rationes. </s>
				</p>
				<p id="N175A0" type="main">
					<s id="N175A2">Prima ratio, quam affert Galileus eſt; </s>
					<s id="N175A6">quia cum natura in ſuis opera­<lb></lb>tionibus adhibeat ſimpliciſſima media; </s>
					<s id="N175AC">&amp; cum acceleratio motus natu­<lb></lb>ralis non poſſit fieri iuxta faciliorem, vel ſimpliciorem progreſſionem, <lb></lb>quàm ſit-ea quæ fit per quadrata; </s>
					<s id="N175B4">non eſt dubium, quin iuxta illam pro­<lb></lb>greſſio motus naturaliter accelerati fieri debeat; præſertim cùm omni­<lb></lb>bus experimentis conſentiat, &amp; in ea omnia phænomena explicari <lb></lb>poſſint. </s>
				</p>
				<p id="N175BE" type="main">
					<s id="N175C0">Reſp. Primò progreſſionem arithmeticam ſimplicem iuxta hos nu­<lb></lb>meros 1.2.3.4. longè ſimpliciorem eſſe alia quæ fit iuxta illos 1.3.5.7.vt <lb></lb>nemo non iudicabit. </s>
					<s id="N175C7">Secundò <expan abbr="cũ">cum</expan> accidit duas hypotheſes conuenire cum <lb></lb>omnibus experimentis ſeu phænomonis, debet eſſe aliqua ratio, cur ad­<lb></lb>hibeatur vna potiùs quàm alia; </s>
					<s id="N175D3">ſed nulla eſt ratio, cur Galileus adhibeat <lb></lb>ſuam, vti videbimus; </s>
					<s id="N175D9">nos verò ratione demonſtratiuâ probamus noſtram; </s>
					<s id="N175DD"><lb></lb>igitur noſtra eſt præferenda pro theorica rei veritate; quia verò alia in <lb></lb>temporibus ſenſibilibus proximè ad verum accedit eam adhibendam eſſe <lb></lb>decernemus infrà ad praxim, &amp; communem iſtorum motuum men­<lb></lb>ſuram. </s>
				</p>
				<p id="N175E8" type="main">
					<s id="N175EA">Secunda ratio eſt; </s>
					<s id="N175ED">quia, ſi accipiatur ſubduplum maximæ, &amp; minimæ <lb></lb>velocitatis; ſitque ex his quaſi conflata velocitas motus æquabilis, hoc <lb></lb>motu æquabili æquali tempore pèrcurretur ſpatium idem, quod antè <lb></lb>motu naturaliter accelerato v.g. ſint numeri datæ progreſſionis 1.3.5.7. <lb></lb>9.11. certè ſumma terminorum ſeu totum ſpatium erit 36. accipiatur <lb></lb>ſubduplum primi 1/2 &amp; ſexti 5. 1/2 habebitur velocitas vt 6. igitur cum <lb></lb>velocitate vt 6. æquali tempore percurretur ſpatium 36. quod rectè de­<lb></lb>monſtrauit Galileus. </s>
				</p>
				<p id="N17602" type="main">
					<s id="N17604">Reſpondeo non minùs noſtram hypotheſim cum hoc ipſo ſtare, quàm <lb></lb>ſtet hypotheſis Galilei: </s>
					<s id="N1760A">ſint enim 6. inſtantia, &amp; ſingulis ſua tribuantur <lb></lb>ſpatiola more dicto 1 2 3 4 5 6. ſumma ſpatiorum eſt 21. aſſumatur ſub­<lb></lb>duplum velocitatis primi inſtantis 1/2, &amp; ſubduplum ſexti inſtantis, ſcili­<lb></lb>cet 3. conflatum ex vtroque 3 1/3; </s>
					<s id="N17614">ducatur in 6.id eſt in numerum termi­<lb></lb>norum, vel inſtantium; ſumma erit 21. igitur quod tribuit Galileus ſuæ <lb></lb>progreſſioni, etiam noſtræ competit. </s>
				</p>
				<p id="N1761C" type="main">
					<s id="N1761E">Tertia ratio petitur ex matheſi ſit enim linea AE diuiſa in quatuor <lb></lb>partes æquales, quæ nobis repreſentent 4. partes temporis æquales; </s>
					<s id="N17624"><lb></lb>haud dubiè, cùm acquirantur temporibus æqualibus æqualia velocitatis <lb></lb>momenta; </s>
					<s id="N1762B">haud dubiè, inquam, his 4. temporibus AB, BC, CD, DE, ac-<pb pagenum="105" xlink:href="026/01/137.jpg"></pb>quirentur æquales velocitatis gradus; </s>
					<s id="N17634">ſit autem BI, menſura velocitatis, <lb></lb>quam acquirit mobile cadens ex ſua quiete in fine primæ partis tempo­<lb></lb>ris AB; </s>
					<s id="N1763C">certè in fine ſecundæ partis temporis BC acquiret velocitatem, <lb></lb>quæ coniuncta cum priore BI faciet duplam CH, &amp; in fine tertiæ par­<lb></lb>tiæ CD triplam DG; </s>
					<s id="N17644">denique in fine quartæ DE quadruplam EF; </s>
					<s id="N17648">quip­<lb></lb>pe cum in parte BC remaneat tota velocitas B, &amp; acquiratur æqualis; </s>
					<s id="N1764E"><lb></lb>certè in fine BC eſt velocitas CH dupla illius quæ commenſuratur BI. <lb></lb>ſimiliter in parte CD remanebit vtraque, &amp; accedet altera; </s>
					<s id="N17655">igitur eſt ve­<lb></lb>locitas DG tripla BI, &amp; EF eſt quadrupla: Similiter ita ſe ratio habet <lb></lb>cuiuſlibet alterius partis inter AB ad aliam alterius partis inter BC, vt <lb></lb>lineæ ductæ parallelæ BICH, &amp;c. </s>
					<s id="N1765F">igitur cum ſpatium acquiſitum reſ­<lb></lb>pondeat exercitio huius velocitatis; </s>
					<s id="N17665">ſitque inſtanti B vt BI, &amp; inſtanti <lb></lb>C vt CH; </s>
					<s id="N1766B">certè tempore AB eſt vt triangulum AIB; </s>
					<s id="N1766F">nam ſpatium AIB <lb></lb>eſt collectio omnium linearum, quæ duci poſſunt parallelæ in tempore <lb></lb>AB; </s>
					<s id="N17677">idem dico de trapezo CBIH, qui eſt triplus trianguli IBA; </s>
					<s id="N1767B">&amp; de <lb></lb>trapezo GDCH, qui eſt quintuplus; </s>
					<s id="N17681">igitur triangulum HCA eſt qua­<lb></lb>druplum IBA; </s>
					<s id="N17687">quia hæc triangula ſunt vt quadrata laterum; </s>
					<s id="N1768B">igitur ſpa­<lb></lb>tium acquiſitum temporibus AB, BC, eſt ad ſpatium acquiſitum tempo­<lb></lb>re AB, vt triangulum HCB ad triangulum IBA; </s>
					<s id="N17693">igitur vt quadratum <lb></lb>AB ad quadratum AC; </s>
					<s id="N17699">igitur vt quadratum temporis AB ad quadra­<lb></lb>tum temporis AC; igitur ſpatia diuerſis temporibus decurſa ſunt vt qua­<lb></lb>drata temporum, quibus ſingula decurruntur. </s>
				</p>
				<p id="N176A1" type="main">
					<s id="N176A3">Hæc ratio ad ſpeciem videtur eſſe demonſtratiua, deficit tamen à ve­<lb></lb>ra demonſtratione; </s>
					<s id="N176A9">primo, quia ſupponit inſtantia infinita, quæ multi <lb></lb>paſſim negabunt in tempore; </s>
					<s id="N176AF">immò aliquis vltrò demonſtrare tentaret <lb></lb>non eſſe infinita; </s>
					<s id="N176B5">itaque ex ſuppoſitione quod ſint tantùm finita inſtan­<lb></lb>tia aſſumantur 4. æqualia AC, CD, DE, EF, certè cum inſtans ſit to­<lb></lb>rum ſimul, velocitatem habet æquabilem ſibi toti reſpondentem; </s>
					<s id="N176BD">igitur <lb></lb>inſtanti AC reſpondeat velocitas, cuius menſura ſit ABCG; </s>
					<s id="N176C3">haud du­<lb></lb>biè inſtanti CD reſpondebit velocitas CH, ſcilicet dupla AB; </s>
					<s id="N176C9">nam re­<lb></lb>manet primus velocitatis gradus acquiſitus primo inſtanti: </s>
					<s id="N176CF">ſed alter æ­<lb></lb>qualis acquiritur; </s>
					<s id="N176D5">igitur eſt duplus prioris; </s>
					<s id="N176D9">igitur reſpondet lineæ DK. <lb></lb>quæ tripla eſt AB, &amp; quarto lineæ FN, quæ eſt quadrupla AB; </s>
					<s id="N176DF">igitur <lb></lb>creſcit ſpatium, vt rectangula CB, DH, EK, FM; </s>
					<s id="N176E5">ſed hæc creſcunt iuxta <lb></lb>progreſſionem numerorum 1.2.3.4. nec aliter res eſſe poteſt ex ſuppoſi­<lb></lb>tione quod ſint inſtantia finita; </s>
					<s id="N176ED">quod alibi ex profeſſo tractamus: </s>
					<s id="N176F1">quippe <lb></lb>illa quæſtio pertinet ad Metaphyſicam, non verò ad phyſicun; </s>
					<s id="N176F7">nam vel <lb></lb>ſingula aliquid addunt, vel nihil: aliquid addunt haud dubiè; </s>
					<s id="N176FD">igitur con­<lb></lb>ſiderantur tantùm 4. inſtantia prima AC, CD, DE, EF, in ſua ſcrie; </s>
					<s id="N17703">certè <lb></lb>non poſſunt aliam progreſſionem facere quàm eam, quæ eſt iuxta hos <lb></lb>numeros 1.2.3.4.vnde non fit per triangula ſed per rectangula minima; <lb></lb>igitur linea AF præcedentis figuræ non eſt recta, ſed denticulata, qualis <lb></lb>eſſet ABGHIKLMN, ſed longè minoribus gradibus, ſeu denticulis. </s>
					<s id="N1770F"><lb></lb>Hinc quò rectangula CB, DH, &amp;c. </s>
					<s id="N17713">fient maiora in partibus ſcilicet tem­<lb></lb>poris ſenſibilibus, ſeruata ſcilicet in illis progreſſione numerorum 1.2.3. <pb pagenum="106" xlink:href="026/01/138.jpg"></pb>4.progreſſio longiùs diſcedet à vera; </s>
					<s id="N1771E">vt ſuprà iam totius repetitum fuit: </s>
					<s id="N17722"><lb></lb>quippe hæc progreſſio in puris inſtantibus fieri tantùm poteſt, cum ſin­<lb></lb>gulis inſtantibus noua fiat acceſſio velocitatis, in hoc enim eſt error, <lb></lb>quòd in tota parte temporis AC ponatur æquabilis velocitas, eiuſque <lb></lb>principium A, ſit æquale fini C; </s>
					<s id="N1772D">nam AB, &amp; GH ſunt æquales; </s>
					<s id="N17731">cùm ta­<lb></lb>men ſit minor velocitas in A, quàm in C, niſi AC ſit tantùm <expan abbr="inſtãs">inſtans</expan>; </s>
					<s id="N1773B">vnde <lb></lb>tota velocitas in hypotheſi Galilei acquiſita in 4.partibus temporis aſ­<lb></lb>ſumptis eſt, vt triangulum AFN; </s>
					<s id="N17743">acquiſita verò in noſtra hypotheſi eſt vt <lb></lb>ſumma rectangulorum CB, CI, EK, EN, quæ ſumma eſt ad triangulum <lb></lb>AFN, vt 10, ad 8. vel vt 5.ad 4. igitur maior 1/4; nam prima pars tempo­<lb></lb>ris addit triangulum ABG, ſecunda GHI. &amp;c. </s>
				</p>
				<p id="N1774D" type="main">
					<s id="N1774F">Si tamen diuidantur iſtæ partes temporis in minores v. g. in 8. tunc <lb></lb>ſumma rectangulorum erit tantùm maior 1/8; </s>
					<s id="N17759">ſi in 16. (1/16) ſi in 32. (1/32); </s>
					<s id="N1775D">ſi in <lb></lb>64.(11/64), cuius ſehema hîc habes; ſint enim 3.partes temporis ſenſibiles A <lb></lb>CDFE, &amp; ſpatium vt triangulum AFN, ſpatia verò acquiſita in ſingulis <lb></lb>partibus, vt portiones trianguli prædicti, quæ ipſis reſpondent v. g. ac­<lb></lb>quiſitum in prima parte ad acquiſitum in ſecunda tantùm, vt triangu­<lb></lb>lum ACG ad trapezum GCDI &amp;c. </s>
					<s id="N1776F">denique acquiſitum in temporibus <lb></lb>inæqualibus, vt quadrata temporum v. g. acquiſitum in prima parte ad <lb></lb>acquiſitum in duabus, vt triangulum ACG ad triangulum ADI; </s>
					<s id="N1777B">id eſt <lb></lb>quadratum CA ad quadratum DA; </s>
					<s id="N17781">in noſtra verò hypotheſi, ſi velocitas <lb></lb>in tota prima parte AC ponatur vt CG æquabiliter; </s>
					<s id="N17787">haud dubiè ſpatium <lb></lb>acquiſitum in prædictis 4. temporibus erit, vt ſumma rectangulorum C <lb></lb>B, CI, EK, EN, quæ maior eſt toto triangulo, AFN, 4. triangulis ABG, <lb></lb>GHI, IKL, LMN, ie eſt 1/4 totius trianguli AFN; atque ita ſumma re­<lb></lb>ctangulorum continet 10. quadrata æqualia quadrato CB, &amp; triangu­<lb></lb>lum AFN, continet. </s>
					<s id="N17795">tantùm 8. </s>
				</p>
				<p id="N17798" type="main">
					<s id="N1779A">Iam verò diuidantur 4. partes temporis AF, in 8. æquales; </s>
					<s id="N1779E">in ſenten­<lb></lb>tia Galilei totum ſpatium erit ſemper triangulum AFN, id eſt vt ſubdu­<lb></lb>plum quadrati ſub AF; </s>
					<s id="N177A6">quæ cùm ſit 8. quadratum erit 64.&amp; ſubduplum <lb></lb>quadrati 32. at verò ſumma rectangulorum eſt 36. id eſt continet 36. <lb></lb>quadrata æqualia quadrato XA; cùm tamen triangulum AFN, conti­<lb></lb>neat tantùm 32. igitur ſumma prædicta eſt ad triangulum AFN, vt 36. <lb></lb>ad 32. id eſt vt 9.ad 8. igitur ſumma eſt maior triangulo 1/8, quæ omnia <lb></lb>conſtant. </s>
				</p>
				<p id="N177B4" type="main">
					<s id="N177B6">Præterea diuidatur vlteriùs tempus AF in 16. æquales partes; </s>
					<s id="N177BA">qua­<lb></lb>dratum 16. cum ſit 256. accipiatur ſubduplum id eſt 128. &amp; erit trian­<lb></lb>gulum AFN, cui ſemper reſpondet totum ſpatium acquiſitum in ſenten­<lb></lb>tia Galilei; </s>
					<s id="N177C4">at verò ſumma rectangulorum erit 136. igitur ſumma eſt ad <lb></lb>ſummam vt 136.ad 128.id eſt vt 17.ad 16. igitur eſt maior ſumma trian­<lb></lb>gulo (1/16) atque ita deinceps; </s>
					<s id="N177CC">ſi vlteriùs diuidas prædictum tempus in par­<lb></lb>tes minores: quot porrò erunt, antequam fiat tota reſolutio in inſtan­<lb></lb>tia, ſint enim v. g. in tempore AF inſtantia 1000000. ſumma quæ reſ­<lb></lb>pondet noſtræ progreſſioni, erit maior altera, quæ reſpondet progreſſio­<lb></lb>ni Galilei (1/1000000) quis hoc percipiat? </s>
				</p>
				<pb pagenum="107" xlink:href="026/01/139.jpg"></pb>
				<p id="N177E0" type="main">
					<s id="N177E2">Si verò in noſtra hypotheſi ſpatium, quod reſpondet primæ parti tem­<lb></lb>poris AC ſit idem cum illo, quod reſpondet eidem parti in ſententia <lb></lb>Galilei, id eſt æquale triangulo CAG, ſumma ſpatiorum erit minor in <lb></lb>noſtra hypotheſi triangulo AFN ſex triangulis æqualibus triangulo <lb></lb>ACG; igitur erit vt 10.ad 16. igitur minor 1/8. </s>
					<s id="N177EE">ſi verò diuidantur in 8. <lb></lb>temporis partes, triangulum AFN continebit 64. triangula æqualia <lb></lb>AXQ: </s>
					<s id="N177F6">at verò ſumma quæ reſpondet noſtræ hypotheſi 36.igitur minor <lb></lb>(7/16). denique ſi diuidantur in 16. partes, triangulum AFN continebit <lb></lb>256. triangula æqualia AYZ; at verò ſumma noſtra 136. igitur minor <lb></lb>(15/52) ſed nunquam erit minor 1/2. </s>
				</p>
				<p id="N17800" type="main">
					<s id="N17802">Obſeruabis obiter dictum eſſe ſuprà ſummam rectangulorum CB CI <lb></lb>EK EN eſſe maiorem triangulo AFN, 2.quadratis æqualibus CB; </s>
					<s id="N17808">ſi <lb></lb>verò diuidatur tempus in 8. partes, ſumma rectangulorum eſt minor præ­<lb></lb>cedenti ſummâ, toto quadrato æquali CB, id eſt 4.quadratis æqualibus <lb></lb>XB, id eſt 1/2 primæ differentiæ, quæ eſt ſumma duorum quadratorum <lb></lb>æqualium CB; </s>
					<s id="N17814">at ſi diuidatur in 16. partes, tempus AF, ſumma rectan­<lb></lb>gulorum eſt minor præcedente 8. quadratis æqualibus QZ, vel ſubdu­<lb></lb>plo quadrati CB, id eſt 1/4 primæ differentiæ quæ eſt ſumma duorum <lb></lb>quadratorum æqualium CB; </s>
					<s id="N1781E">ſi 4. partes temporis diuidantur in 8. de­<lb></lb>trahitur 1/2 differentiæ, quæ eſt inter ſummam primam rectangulorum, <lb></lb>&amp; triangulum AFN; </s>
					<s id="N17826">ſi diuidantur in 16. detrahitur 1/4 eiuſdem diffe­<lb></lb>rentiæ; </s>
					<s id="N1782C">ſi diuidantur in 32. detrahitur 1/8, ſi in 64. (1/16); </s>
					<s id="N17830">atque ita deinceps, <lb></lb>&amp; nunquam hæ minutiæ ſubtractæ in infinitum totam differentiam ex­<lb></lb>haurient; hinc minutiæ iſtæ 1/2 1/4 1/8 (1/16) (1/32) (1/64) &amp;c. </s>
					<s id="N17838">in infinitum non fa­<lb></lb>ciunt vnum integrum; ſed hæc ſunt facilia. </s>
				</p>
				<p id="N1783E" type="main">
					<s id="N17840">Quarta ratio, quam afferunt aliqui, eſt; </s>
					<s id="N17844">quia ſi cum eadem velocita­<lb></lb>te acquiſita in fine temporis dati ſine augmento nouo moueatur mobi­<lb></lb>le; </s>
					<s id="N1784C">haud dubiè acquiret duplum ſpatium tempore æquali tempori dato; </s>
					<s id="N17850"><lb></lb>v. g. ſit triangulum AFE; </s>
					<s id="N17859">ſitque velocitas acquiſita EF in 4. parti­<lb></lb>bus temporis AE, vt iam ſuprà dictum eſt, ne cogar repetere: </s>
					<s id="N1785F">certè ſi du­<lb></lb>catur velocitas EF in tempus AE, vel EL æquale; </s>
					<s id="N17865">habebitur rectan­<lb></lb>gulum EK duplum trianguli AFE: </s>
					<s id="N1786B">ſed triangulum AFE eſt ſumma <lb></lb>ſpatiorum motus accelerati tempore AE, &amp; rectangulum EK eſt ſum­<lb></lb>ma ſpatiorum motus æquabilis cum velocitate EF; igitur duplum eſt <lb></lb>ſpatium motus æquabilis, quod erat demonſtrandum. </s>
					<s id="N17875">Præterea ſi diui­<lb></lb>datur velocitas EF, &amp; eius ſubdupla ducatur in tempus AE; habebitur <lb></lb>rectangulum æquale triangulo AFE, vt conſtat. </s>
					<s id="N1787D">Reſpondeo facilè ex di­<lb></lb>ctis, hoc ipſum etiam ex noſtra hypotheſi proxime ſequi; </s>
					<s id="N17883">ſint enim duo <lb></lb>inſtantia; </s>
					<s id="N17889">haud dubie ſi non creſcit velocitas, ſecundo inſtanti æquale <lb></lb>ſpatium percurretur; </s>
					<s id="N1788F">ſi vero ſecundo inſtanti creſcat, percurrentur illo <lb></lb>motu 3.ſpatia; </s>
					<s id="N17895">&amp; cùm velocitas <expan abbr="ſecũdi">ſecundi</expan> <expan abbr="inſtãtis">inſtantis</expan> ſit dupla velocitatis primi <lb></lb>inſtantis, primo inſtanti ſit 1.gradus v.g. ſecundo erunt 2. gradus; </s>
					<s id="N178A5">igi­<lb></lb>tur moueatur per duo inſtantia motu æquabili veloci vt 2. percurrentur <lb></lb>4. ſpatia; </s>
					<s id="N178AD">igitur totum ſpatium, quod percurritur motu veloci vt 2. per <lb></lb>2.inſtantia eſt ad totum ſpatium, quod percurritur æquali tempore mo-<pb pagenum="108" xlink:href="026/01/140.jpg"></pb>tu naturaliter accelerato vt 4. ad 3. igitur continet illud 1. (11/3); </s>
					<s id="N178B8">ſi verò <lb></lb>ſint 3. inſtantis continet illud, 1/2; ſi 4. continet 1. 3/5, ſi 5. continet 1.2/3 <lb></lb>ſi 5. continet 1 2/3. ſi 6. continet 1 5/7. ſi 7. continet 1 3/4. ſi 8. continet <lb></lb>1 7/9. ſi 9. continet 1 (4/11). ſi 10. continet 1 9/5 ſic quo plura erunt inſtantia <lb></lb>accedet propiùs ad rationem duplam, nunquam tamen ad illam perue­<lb></lb>niet. </s>
					<s id="N178C6">Ex dictis multa tumultuatim Corollaria congeri poſſunt; </s>
				</p>
				<p id="N178CA" type="main">
					<s id="N178CC"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N178D9" type="main">
					<s id="N178DB">Etiamſi non ſint partes infinitæ temporis; </s>
					<s id="N178DF">in ordine tamen ad praxim <lb></lb>eodem modo ſe habent, ac ſi eſſent infinitæ; quia licèt finitæ ſint, nume­<lb></lb>rari tamen non poſſunt. </s>
				</p>
				<p id="N178E7" type="main">
					<s id="N178E9"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N178F6" type="main">
					<s id="N178F8">Etiam ſi non ſint infiniti tarditatis gradus, vt conſtat ex dictis, ſed fi­<lb></lb>niti; </s>
					<s id="N178FE">in ordine tamen ad praxim eodem modo ſe habent, ac ſi eſſent in­<lb></lb>finiti; quia non poteſt diſtingui primus, &amp; minimus ab omnibus <lb></lb>aliis. </s>
				</p>
				<p id="N17906" type="main">
					<s id="N17908"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17915" type="main">
					<s id="N17917">Licèt hypotheſis Galilei ſit falſa in hypotheſi inſtantium finitorum; </s>
					<s id="N1791B"><lb></lb>nam ſingulis inſtantibus noua fit velocitatis acceſſio; </s>
					<s id="N17920">phyſicè tamen lo­<lb></lb>quendo eodem modo ſe habet, ac ſi eſſet vera; </s>
					<s id="N17926">quia cum non poſſit pro­<lb></lb>bari, niſi in partibus temporis ſenſibilibus; </s>
					<s id="N1792C">certà, cùm quælibet pars <lb></lb>ſenſibilis innumera ferè inſtantia contineat, in quibus fit progreſſio; </s>
					<s id="N17932"><lb></lb>differentia vtriuſque ſenſibilis eſſe non poteſt; </s>
					<s id="N17937">igitur linea denticulata <lb></lb> eodem modo ſe habet phyſicè, hoc eſt ſenſibiliter, ac ſi eſſet recta; </s>
					<s id="N1793D">ſic­<lb></lb>que progreſſio arithmetica in multis terminis reducitur ſenſibiliter ad <lb></lb>Geometriam in paucioribus terminis; immò in communi illa ſententia. </s>
					<s id="N17945"><lb></lb>in qua dicitur tempus conſtare ex partibus actu infinitis, progreſſio Ga­<lb></lb>lilei tantùm locum habere peteſt; </s>
					<s id="N1794C">igitur hæc eſto clauis huius difficul­<lb></lb>tatis; </s>
					<s id="N17952">progreſſio ſimplex principium phyſicum habet, non experimen­<lb></lb>tum; </s>
					<s id="N17958">progreſſio numerorum imparium experimentum non principium; </s>
					<s id="N1795C"><lb></lb>vtramque cum principio &amp; experimento componimus; prima enim ſi. </s>
					<s id="N17961"><lb></lb>aſſumantur partes temporis ſenſibiles tranſit in ſecundam, ſecunda in <lb></lb>primam, ſi vltima aſſumantur inſtantia. </s>
				</p>
				<p id="N17967" type="main">
					<s id="N17969"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17976" type="main">
					<s id="N17978">Cognito ſpatio quod percurritur in data parte temporis ſenſibili, co­<lb></lb>gnoſci poteſt ſpatium quod in duabus æqualibus vel 3.vel 4.&amp;c.percurri <lb></lb>poteſt.v.g. </s>
					<s id="N1797F">multi probarunt ſæpiùs primo ſecundo minuto corpus graue <lb></lb>percurrere 12. pedes; igitur duobus percurreret 48. accipe enim 9. 2. <lb></lb>id eſt 4. &amp; in 4. duces 12. vt habeas 48. 4. verò minutis percurret 192. <lb></lb>nam accipe 9. 4. id eſt 16. &amp; in 16. duces 12.vt habeat 192. res omninò <lb></lb>facilis. </s>
				</p>
				<p id="N1798B" type="main">
					<s id="N1798D"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1799A" type="main">
					<s id="N1799C">Similiter cognito ſpatio quod percurrit 4. ſecundis minutis, cogno­<lb></lb>ſces ſpatium, quod percurret 2. vel 1. v.g. percurrit 4. ſecundis 192. pe-<pb pagenum="109" xlink:href="026/01/141.jpg"></pb>des; </s>
					<s id="N179A9">accipe 9.4. id eſt 16. &amp; per 16. diuide 192. quotíens dabit 12. pro <lb></lb>primo ſecundo: accipe 9.2. id eſt, 4. &amp; diuide 192. per 4.quotiens dabit <lb></lb>48. pro duobus minutis, atque ita deinceps. </s>
				</p>
				<p id="N179B1" type="main">
					<s id="N179B3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N179C0" type="main">
					<s id="N179C2">Similiter cognito tempore cognoſci poteſt ſpatium decurſum; </s>
					<s id="N179C6">quia <lb></lb>ſpatia ſunt vt quadrata temporum; </s>
					<s id="N179CC">vel cognito ſpatio cognoſci poteſt <lb></lb>tempus; quia tempora ſunt, vt radices ſpatiorum, hæc elementa ſaltem <lb></lb>Arithmetices deſiderant. </s>
				</p>
				<p id="N179D4" type="main">
					<s id="N179D6">Sed iam reſtat, vt ſoluamus objectiones aliquas, quæ contra motus ac­<lb></lb>celerationem pugnare videntur. </s>
				</p>
				<p id="N179DB" type="main">
					<s id="N179DD">Prima objectio eſt; </s>
					<s id="N179E0">ſi motus acceleratio fieret in inſtantibus, ſecundo <lb></lb>inſtanti idem corpus eſſet in duobus locis adæquatis quod ſic oſtendo: </s>
					<s id="N179E6"><lb></lb> ſit ſpatium AB quod percurrit corpus graue primo inſtanti; </s>
					<s id="N179EB">haud du­<lb></lb>biè AB, eſt eius locus adæquatus; </s>
					<s id="N179F1">ſecundo inſtanti percurrit BC duplum <lb></lb>AB; </s>
					<s id="N179F7">igitur eodem inſtanti reſpondet loco BD, &amp; DC, quorum vterque <lb></lb>eſt æqualis AB; igitur ſecundo inſtanti eſt in duobus locis, ſcilicet BD <lb></lb>&amp; DC, quod dici non poteſt. </s>
				</p>
				<p id="N179FF" type="main">
					<s id="N17A01">Hæc objectio impugnat omnem velocitatem; </s>
					<s id="N17A05">hoc eſt, non modò eam, <lb></lb>quæ motui naturaliter accelerato competit; </s>
					<s id="N17A0B">verùm etiam illam, quæ <lb></lb>ineſt motui violento; igitur vt reſpondeam faciliùs; </s>
					<s id="N17A11">ſuppono punctum <lb></lb>phyſicum, mobile ſcilicet A; </s>
					<s id="N17A17">aut ſi mauis Angelum coëxtenſum quadra­<lb></lb>to A; </s>
					<s id="N17A1D">qui ſcilicet moueatur motu accelerato, &amp; primo inſtanti acquirat <lb></lb>locum immediatum æqualem priori, ſcilicet AB; </s>
					<s id="N17A23">licèt enim poſſet ac­<lb></lb>quirere vibrationem participantem de priori; </s>
					<s id="N17A29">quia tamen acquireret <lb></lb>tandem non participantem, id eſt, quæ tota ſit extra illam, cui eſt imme­<lb></lb>diata, qualis eſt AB. ſuppono hîc acquiri vibrationem non participan­<lb></lb>tem de priori, id eſt ſpatium AB, æquale priori, in quo erat A, &amp; pror­<lb></lb>ſus extra illud poſitum licèt immediatum; </s>
					<s id="N17A35">hoc poſito, primo inſtanti pun­<lb></lb>ctum A acquirit AB tanquam locum adæquatum, vt certum eſt: </s>
					<s id="N17A3B">certum <lb></lb>eſt etiam loca BC, CD, eſſe adæquata: </s>
					<s id="N17A41">igitur ſimul, id eſt eodem in­<lb></lb>ſtanti in vtroque eſſe non poteſt; </s>
					<s id="N17A47">nam inſtans ſimul totum eſt; </s>
					<s id="N17A4B">igitur <lb></lb>ſecundo inſtanti non percurrit BC, ſed ſecundo tempore æquali primo; </s>
					<s id="N17A51"><lb></lb>hoc enim ſecundum tempus conſtat duobus inſtantibus, quod ſimul <lb></lb>vtrumque reſpondet primo: </s>
					<s id="N17A58">quippe dari poſſunt inſtantia phyſica; </s>
					<s id="N17A5C">igitur <lb></lb>primum inſtans quo percurritur AB eſt æquale duobus aliis, quibus <lb></lb>percurruntur BD, &amp; CD; vnde quando dixi primo inſtanti acquiri ſpa­<lb></lb>tium duplum primi, idem eſt, ac ſi dixiſſem ſecundo tempore æquali pri­<lb></lb>mo, quod reuerà tempus conſtat 2. inſtantibus, quorum alterum reſpon­<lb></lb>det ſpatio BC, &amp; alterum ſpatio DC. </s>
				</p>
				<p id="N17A6B" type="main">
					<s id="N17A6D">Secunda objectio; </s>
					<s id="N17A70">Sed inquiet aliquis, igitur non eſt continua acce­<lb></lb>leratio motus; nam inſtans quo percurritur ſecundum ſpatium BD, cùm <lb></lb>ſit æquale inſtanti quo percurritur tertium ſpatium DC, in vtroque ſpa­<lb></lb>tio eſt æquabilis motus. </s>
					<s id="N17A7A">Reſpondeo inſtans quo percurritur ſecundum <lb></lb>ſpatium BD, eſſe maius inſtanti, quo percurritur tertium ſpatium DC; </s>
					<s id="N17A80"><lb></lb>tà tamen lege, vt vtrumque ſimul ſumptum ſit omninò equale inſtanti, <pb pagenum="110" xlink:href="026/01/142.jpg"></pb>quo percurritur primum ſpatíum AB; </s>
					<s id="N17A8A">ſimiliter totum ſpatium CG ita <lb></lb>percurritur tertio tempore, vt ſingula ſpatia CE. EI. FG. ſingulis in­<lb></lb>ſtantibus percurrantur; </s>
					<s id="N17A92">ſed hæc tria inſtantia ſimul ſumpta ſunt æqualia <lb></lb>primo inſtanti, quo percurritur ſpatium; licèt primum quo percurritur <lb></lb>CE ſit maius ſecundo, quo percurritur EF, &amp; hoc maius tertio, quo per­<lb></lb>curritur FG, atque ita deinceps. </s>
				</p>
				<p id="N17A9C" type="main">
					<s id="N17A9E">Obſeruabis poſſe velocitatem motus explicari duobus modis. </s>
					<s id="N17AA1">Primò, <lb></lb>ſi aſſumantur tempora æqualia, &amp; ſpatia inæqualia in ea progreſſione, <lb></lb>quam hactenus explicuimus. </s>
					<s id="N17AA8">Secundò ſi accipiantur ſpatia æqualia &amp; <lb></lb>tempora inæqualia, quod duobus modis fieri tantùm poteſt. </s>
					<s id="N17AAD">Primò ſi ac­<lb></lb>cipiantur ſpatia æqualia primo ſpatio, quod percurritur primo inſtanti. </s>
					<s id="N17AB2"><lb></lb>Secundò ſi accipiantur ſpatia æqualia alteri ſpatio, quod in parte tempo­<lb></lb>ris ſenſibili percurritur; </s>
					<s id="N17AB9">in qua verò proportione tempora fiant ſemper <lb></lb>minora, &#039;dicemus infrà; </s>
					<s id="N17ABF">nec dicas durum eſſe dicere inſtans eſſe poſſe <lb></lb>minus inſtanti; </s>
					<s id="N17AC5">nam equidem fateor inſtanti mathematico nihil eſſe <lb></lb>poſſe minus; </s>
					<s id="N17ACB">ſecus verò inſtanti phyſico, quod eſt diuiſibile potentiâ, vt <lb></lb>dicemus aliàs; nomine inſtantis phyſici intelligo durationem indiuiſi­<lb></lb>bilem, hoc eſt, cuius entitas tota ſimul eſt. </s>
				</p>
				<p id="N17AD3" type="main">
					<s id="N17AD5">Tertia objectio. </s>
					<s id="N17AD8">Sed inquies, igitur ſecundo tempore æquali primo <lb></lb>acquiruntur 2.gradus velocitatis, vel impetus; </s>
					<s id="N17ADE">igitur tria ſpatia ſecun­<lb></lb>do tempore percurruntur, quod eſt contra hypotheſim; </s>
					<s id="N17AE4">quippe duo gra­<lb></lb>dus impetus accedunt primo, ſimiliter tertio tempore producentur tres <lb></lb>gradus impetus; </s>
					<s id="N17AEC">qui ſi iungantur tribus præcedentibus, erunt 6. Igitur <lb></lb>percurrentur tertio tempore 6. ſpatia, &amp; quarto 10.quinto 15. quia ſin­<lb></lb>gulis inſtantibus debet produci impetus; eſt enim cauſa neceſſaria ap­<lb></lb>plicata. </s>
				</p>
				<p id="N17AF6" type="main">
					<s id="N17AF8">Reſpondęo, equidem eo inſtanti, quo percurritur ſpatium BD, pro­<lb></lb>duci aliquid impetus, &amp; aliquid eo inſtanti, quo percurritur ſpatium <lb></lb>DC; </s>
					<s id="N17B00">ita vt tamen totus ille impetus, qui producitur his duobus inſtan­<lb></lb>tibus, ſit æqualis illi, qui producitur primo inſtanti, quo ſcilicet percurri­<lb></lb>tur ſpatium AB; </s>
					<s id="N17B08">quia duo illa inſtantia ſimul ſumpta faciunt tempus <lb></lb>æquale primo inſtanti; </s>
					<s id="N17B0E">atqui temporibus æqualibus eadem cauſa neceſ­<lb></lb>ſaria non impedita æqualem effectum producit per Ax.3.hinc vides ſin­<lb></lb>gulis inſtantibus eadem proportione decreſcere impetum in perfectio­<lb></lb>ne, qua tempus eſt breuius, ſeu velocior motus; ſed de hoc infrà. </s>
				</p>
				<p id="N17B18" type="main">
					<s id="N17B1A">Quarta objectio; </s>
					<s id="N17B1D">ſi impetus ſingulis inſtantibus creſceret, vel intende­<lb></lb>retur, augeretur grauitatio: </s>
					<s id="N17B23">quippe ſi grauitas primo inſtanti producat <lb></lb>vnum gradum impetus; </s>
					<s id="N17B29">ſecundo æqualem producet, &amp; tertio, atque ita <lb></lb>deinceps, quod eſſet abſurdum; alioqui minima atomus quodlibet cor­<lb></lb>pus graue adæquaret, quod eſt abſurdum. </s>
				</p>
				<p id="N17B31" type="main">
					<s id="N17B33">Reſpondeo nunquam impetum intendi, niſi ſit motus, qui eſt illius fi­<lb></lb>nis; </s>
					<s id="N17B39">alioquin fruſtra eſſet per plura inſtantia; </s>
					<s id="N17B3D">igitur deſtrui deberet; </s>
					<s id="N17B41">nec <lb></lb>dicas impetum naturalem etiam fruſtrà eſſe ſine motu; </s>
					<s id="N17B47">quia cum mo­<lb></lb>tus non ſit eius finis adæquatus; </s>
					<s id="N17B4D">non mirum eſt ſi poſſit eſſe ſine motu; </s>
					<s id="N17B51"><lb></lb>atqui iam diximus ſuprà habere duos fines, quorum alterum ſemper ha-<pb pagenum="111" xlink:href="026/01/143.jpg"></pb>bet; </s>
					<s id="N17B5B">primus eſt grauitatio, ſeu niſus verſus centrum; ſecundus motus <lb></lb>deorſum; </s>
					<s id="N17B61">cùm tamen impetus additivius motum tantùm pro fine habeat; <lb></lb>igitur ſi impeditur totus motus, non producitur hic impetus. </s>
				</p>
				<p id="N17B67" type="main">
					<s id="N17B69">Quinta objectio; </s>
					<s id="N17B6C">ſi impetum ſuum intendit corpus graue; </s>
					<s id="N17B70">ſimiliter <lb></lb>Ignis diceretur intendere calorem; Sol lucem, &amp;c. </s>
					<s id="N17B76">Reſpondeo primò de <lb></lb>luce ſingularem eſſe rationem; </s>
					<s id="N17B7C">quia ſcilicet conſeruatur à cauſa ſua pri­<lb></lb>mo productiua; quidquid ſit; </s>
					<s id="N17B82">ſi viderem effectum caloris, vel frigoris <lb></lb>perpetuò creſcere; </s>
					<s id="N17B88">haud dubiè dicerem etiam cauſas ipſas intendi; </s>
					<s id="N17B8C">atqui <lb></lb>hoc ipſum video in motu naturali, qui effectus impetus eſt; </s>
					<s id="N17B92">adde quod <lb></lb>argumentum à pari debile eſt; </s>
					<s id="N17B98">cum enim ſint diuerſi naturæ fines, diuer­<lb></lb>ſæ ſunt viæ quibus ſuos fines conſequítur; </s>
					<s id="N17B9E">denique contrarietas caloris, <lb></lb>&amp; frigoris impedit fortè, ne vlterius vtraque qualitas intendatur, de qua <lb></lb>fusè ſuo loco; </s>
					<s id="N17BA6">porrò dicemus Tomo ſexto calorem conſeruari à cauſa ſua <lb></lb>primo productiua; quo poſito ceſſat difficultas; quod licèt alicui durum <lb></lb>videri poſſit, demonſtrabo tamen. </s>
				</p>
				<p id="N17BAE" type="main">
					<s id="N17BB0">Sexta objectio; igitur ſi ex infinita diſtantia lapis deſcenderet, inten­<lb></lb>deret etiam ſuum motum. </s>
					<s id="N17BB5">Reſpondeo primò, non poſſe dari infinitam il­<lb></lb>lam diſtantiam. </s>
					<s id="N17BBA">Secundò etiamſi daretur lapis, ex ea non caderet; </s>
					<s id="N17BBE">fruſtrà <lb></lb>enim eſſet ille motus: </s>
					<s id="N17BC4">Tertiò, ſi daretur motus infinitus, haud dubiè eſſet <lb></lb>æquabilis; </s>
					<s id="N17BCA">qualis eſt motus circularis corporum cœleſtium; </s>
					<s id="N17BCE">at verò <lb></lb>motus naturalis deorſum corporum grauium debet eſſe acceleratus ne <lb></lb>vel deſcenderent tardiùs, ſi cum primo tantùm velocitatis gradu deſcen­<lb></lb>derent; </s>
					<s id="N17BD8">vel ſuſtineri vix poſſent, ſi impetum innatum intentiorem habe­<lb></lb>rent; vtrum verò ſemper intendatur, &amp; ex quacumque altitudine cadat <lb></lb>corpus graue, videbimus infrà. </s>
				</p>
				<p id="N17BE0" type="main">
					<s id="N17BE2">Ex dictis hactenus facilè refelluntur aliæ ſententiæ de proportione <lb></lb>motus naturaliter accelerati. </s>
				</p>
				<p id="N17BE7" type="main">
					<s id="N17BE9">Et primò quidem illa, quæ vult fieri ſecundum rationem ſinuum <lb></lb>verſorum, licèt initio tàm propè accedat ad proportionem Galilei, vt <lb></lb>diſcerni ſenſibiliter ab ea non poſſit; </s>
					<s id="N17BF1">quare tutò ſatis aſſumi po­<lb></lb>terit, ſi quando ſit opus illius loco, quod nos in explicandis motibus cœ­<lb></lb>leſtibus præſtabimus; </s>
					<s id="N17BF9">interim quia faciliùs explicatur in motu recto per <lb></lb>rationem quadratorum quàm ſinuum, illam retinebimus; </s>
					<s id="N17BFF">præſertim cùm <lb></lb>vtraque ad noſtram reducatur; modò progreſſio fiat in inſtantibus. </s>
					<s id="N17C05"><lb></lb>Secundò reiicitur ſententia illorum qui volunt hanc progreſſionem fie­<lb></lb>ri iuxta proportionem geometricam, quam vides in his numeris 1.2.4.8. <lb></lb>16. quæ licèt initio minùs recedat à vera, in progreſſu tamen multùm <lb></lb>aberrat, nec eſt vlla ratio quæ pro illa faciat: </s>
					<s id="N17C10">Et verò nulla in mentem <lb></lb>venire poteſt; niſi fortè dicatur, cùm ſecundo inſtanti ſit dupla velocitas, <lb></lb>tertio <expan abbr="ponẽdam">ponendam</expan> eſſe quadruplam, &amp; 4°. </s>
					<s id="N17C1C">octuplam; </s>
					<s id="N17C1F">quia vt velocitas pri­<lb></lb>mi inſtantis eſt ad velocitatem ſecundi, ita velocitas huius ad velocita­<lb></lb>tem tertij, &amp; velocitas huius ad velocitatem quarti; </s>
					<s id="N17C27">igitur ſequitur pro­<lb></lb>greſſionem rationis geometricæ duplæ; cur enim eſſet maior ratio pri­<lb></lb>mi inſtantis ad ſecundum quàm ſecundi ad tertium tertij ad quartum? <lb></lb></s>
					<s id="N17C30">&amp;c. </s>
					<s id="N17C33">ſed profectò vix vlla apparet rationis ſpecies, cùm nulla ſit cauſa, <pb pagenum="112" xlink:href="026/01/144.jpg"></pb>quæ 3° inſtanti, &amp; 4° plùs agat <expan abbr="quã">quam</expan> primo, &amp; ſecundo; </s>
					<s id="N17C40">igitur eſt peculiaris <lb></lb>cauſa huius inæqualitatis rationum; </s>
					<s id="N17C46">quòd ſcilicet æqualibus temporibus <lb></lb>æqualia acquirantur velocitatis momenta; vt ſuprà demonſtrauimus; </s>
					<s id="N17C4C"><lb></lb>quippe id præſtari debet in explicandis inæqualitatibus motuum recto­<lb></lb>rum naturalium, quod præſtant Aſtronomi in explicanda inæqualitate <lb></lb>motuum cæleſtium; qui ſemper æqualitatem aliquam ſupponunt, nec eſt <lb></lb>quòd hanc ſententiam nonnullis experimentis ictuum quiſquam con­<lb></lb>firmet, in quibus multa fraus ſubeſſe poteſt. </s>
				</p>
				<p id="N17C59" type="main">
					<s id="N17C5B">Tertiò reiicitur illa quoque ſententia, quæ proportionem lineæ ſectæ <lb></lb>in mediam, &amp; extremam rationem huic lineæ tribuit, quam ferè in his <lb></lb>numeris vides 1.2.3.5.8, 13. 21. 34. 55. quæ ſub finem etiam longiſſimè <lb></lb>aberrat, vt videre eſt, quare iiſdem rationibus impugnatur, quibus iam <lb></lb>aliam impugnauimus. </s>
				</p>
				<p id="N17C66" type="main">
					<s id="N17C68">Scio eſſe alias multas rationes, quibus aliqui recentiores motus natu­<lb></lb>ralis accelerationem explicare nituntur, ſed iam ſuprà ſatis ſuperque re­<lb></lb>iectæ fuerunt, vel profectò eæ ſunt, quæ ne quidem inter fabuloſa poë­<lb></lb>tarum commenta locum aliquem habere poſſint: </s>
					<s id="N17C72">Et verò niſi me ani­<lb></lb>mus fallit in re clariſſima, rationem huius effectus ex communibus <lb></lb>principiis deductam cum ipſis etiam experimentis conſentire hactenus <lb></lb>ita demonſtrauimus, vt iam vix vllus dubitationi locus relinquatur; ſed <lb></lb>interruptam Theorematum ſeriem tandem repetimus. </s>
				</p>
				<p id="N17C7E" type="main">
					<s id="N17C80"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17C8C" type="main">
					<s id="N17C8E"><emph type="italics"></emph>Si accipiantur ſpatia æqualia primo ſpatio, quod vno inſtanti percurritur, <lb></lb>inſtantia ſunt inæqualia in motu natur aliter accelerato<emph.end type="italics"></emph.end>; </s>
					<s id="N17C99">probatur, quia ſe­<lb></lb>cundum ſpatium æquale primo percurritur motu velociore, quàm pri­<lb></lb>mo, &amp; tertium quam ſecundo: </s>
					<s id="N17CA1">ergo minori tempore per Def.2.l.1. ſed <lb></lb>primum ſpatium conficitur vno inſtanti; </s>
					<s id="N17CA7">igitur ſecundum vno inſtanti, <lb></lb>ſed minore; idem dico de tertio. </s>
				</p>
				<p id="N17CAD" type="main">
					<s id="N17CAF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17CBB" type="main">
					<s id="N17CBD"><emph type="italics"></emph>In ea proportione decreſcunt hæc instantia,<emph.end type="italics"></emph.end> vt primum ſit maius ſecundo, <lb></lb>ſecundum tertio, tertium quarto, quartum quinto, quintum ſexto, <lb></lb>atque ita deinceps; ita vt ſecundum &amp; tertium ſimul ſumpta, item quar­<lb></lb>tum, quintum, ſextum, ſeptimum, item octauum, nonum, decimum, ſimul <lb></lb>ſumpta adæquent primum, hoc eſt vt vnum, duo, tria, quatuor, quinque, <lb></lb>ſex, &amp;c. </s>
					<s id="N17CD0">faciant ſemper tempora æqualia, quia temporibus æqualibus æ­<lb></lb>qualia acquiruntur velocitatis momenta? </s>
					<s id="N17CD5">igitur ſi primo inſtanti per­<lb></lb>curritur vnum ſpatium; </s>
					<s id="N17CDB">ſecundo tempore æquali percurruntur duo ſpa­<lb></lb>tia æqualia primo, &amp; tertio, tria; atque deinceps; </s>
					<s id="N17CE1">ſed vt ſuprà dictum eſt <lb></lb>in reſponſ. ad obiect. primam, vno, &amp; <expan abbr="eodẽ">eodem</expan> inſtanti non poteſt idem cor­<lb></lb>pus percurrere duo ſpatia, ne ſimul eſſet in duobus locis; </s>
					<s id="N17CED">igitur ſingula <lb></lb>ſpatia reſpondent ſingulis inſtantibus licèt minoribus; </s>
					<s id="N17CF3">ſed ſecundo tem­<lb></lb>pore æquali primo inſtanti percurruntur duo ſpatia æqualia primo ſpa­<lb></lb>tio; </s>
					<s id="N17CFB">igitur ſecundum, &amp; tertium inſtans debent ſimul ſumpta adæquare <pb pagenum="113" xlink:href="026/01/145.jpg"></pb>primum, ſed non ſunt æqualia, vt conſtat; </s>
					<s id="N17D04">alioquin duobus illis inſtanti<lb></lb>bus motus eſſet æquabilis; igitur ſecundum eſt maius tertio, ita vt tamen <lb></lb>ex vtroque tempus fiat æquale primo inſtanti. </s>
				</p>
				<p id="N17D0C" type="main">
					<s id="N17D0E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17D1A" type="main">
					<s id="N17D1C"><emph type="italics"></emph>Non decreſcunt illa inſtantia ſecundum lineam ſextam in extremam &amp; <lb></lb>mediam rationem propagatam; </s>
					<s id="N17D24">ita vt primum ſit ad ſecundum, vt ſecundum <lb></lb>ad tertium, tertium ad quartum, quartum ad quintum at que ita deinceps<emph.end type="italics"></emph.end>; </s>
					<s id="N17D2D"><lb></lb>ſit enim aliqua ſeries numerorum, qui aliquo modo accedant ad prædi­<lb></lb>ctam proportionem 1.2.3.5.8.13.21.34.55. ſitque primum inſtans vlti­<lb></lb>mus numerus 55. ſecundum 34.tertium 21. atque ita deinceps: </s>
					<s id="N17D36">Equidem <lb></lb>ſecundum, &amp; tertium adæquant primum; </s>
					<s id="N17D3C">at verò quartum, quintum, <lb></lb>ſextum nullo modo adæquant; </s>
					<s id="N17D42">immò ne quidem eius ſubduplum, &amp; <lb></lb>multò minus 3. alij addito primo: </s>
					<s id="N17D48">immò ſi linea data duodecies propor­<lb></lb>tionaliter diuidatur, vltimum ſegmentum vix eſſet ſubcentuplum primi, <lb></lb>vt conſtat; igitur reiici debet hæc propoſitio. </s>
				</p>
				<p id="N17D50" type="main">
					<s id="N17D52"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17D5E" type="main">
					<s id="N17D60"><emph type="italics"></emph>Inſtans primum non eſt ad ſecundum vt numerus ad numerum; </s>
					<s id="N17D66">nec ad <lb></lb>tertium, quartum, quintum, ſextum, &amp;c.<emph.end type="italics"></emph.end> probatur, quia nullus numerus <lb></lb>excogitari poteſt quo deſignari poſſit quantitas, ſeu perfectio, ſeu va­<lb></lb>lor iſtorum inſtantium; </s>
					<s id="N17D73">ſit enim primum inſtans ſecundum ſit 3/5. tertium <lb></lb>2/5 quartum 4/9 quintum 2/9 ſextum 2/9. Equidem ſecundum, &amp; tertium adę­<lb></lb>quant primum; </s>
					<s id="N17D7D">adde quod non poteſt amplius ſeries propagari per nu­<lb></lb>meros rationales; </s>
					<s id="N17D83">ſit autem ſecundum (6/11) 3. (5/11) cum tribus aliis 4/9 1/9 7/9; </s>
					<s id="N17D87"><lb></lb>equidem ſi reducantur hæ 5. minutiæ, reſpondebunt his (54/99) (45/99) (44/99) (12/99) (26/99): </s>
					<s id="N17D8C"><lb></lb>igitur ſecunda erit maior quarta; </s>
					<s id="N17D91">at prima ſuperat ſecundam (9/999) ſecunda <lb></lb>tertiam (1/99) tertia quartam (11/99) quarta quintam (12/99). Cur porrò hæc inæqua­<lb></lb>litas, igitur numeri poſſunt aſſignari; non poſſunt etiam poni in ſerie <lb></lb>geometrica ſubdupla 1. 1/2 1/4 1/8 &amp;c. </s>
					<s id="N17D9B">quia ſecunda. </s>
					<s id="N17D9E">&amp; tertia non adæquant <lb></lb>primam idem dicendum eſt potiori iure de tribus aliis; </s>
					<s id="N17DA4">nec etiam in ſe­<lb></lb>rie arithmetica ſimplici 1. 1/2 1/3 1/4 2/5 1/6; quia ſecunda, &amp; tertia ſunt mi­<lb></lb>nores prima 1/6, vt quarta, quinta, ſexta ſunt minores prima (26/74). </s>
				</p>
				<p id="N17DAC" type="main">
					<s id="N17DAE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17DBA" type="main">
					<s id="N17DBC"><emph type="italics"></emph>Datur aliquis ſeries numerorum irrationabilium, ſeu ſurdorum minorum, &amp; <lb></lb>minorum<emph.end type="italics"></emph.end>; quorum primus ita ſuperet ſecundum, ſecundus tertium, <lb></lb>tertius quartum, &amp;c. </s>
					<s id="N17DC9">vt ſecundus, &amp; tertius adæquent primum, item <lb></lb>quartus, quintus, ſextus. </s>
					<s id="N17DCE">item 4. alij, qui ſequuntur, item 5. item 6. &amp;c. </s>
					<s id="N17DD1"><lb></lb>v. g. poteſt dari linea AG conſtans tribus partibus æqualibus, ſcilicet <lb></lb>AB, BC, CG, &amp; ſecunda BC duabus BD maiore, &amp; DC minore, &amp; ter­<lb></lb>tia tribus prima CE minore ED, ſed maiore EF, ſecunda EF maiore F <lb></lb>G, atque ita deinceps; </s>
					<s id="N17DE0">addi poteſt quartum ſegmentum æquale AB; </s>
					<s id="N17DE4">quod <lb></lb>ſubdiuidetur in 4. partes, quarum prima ſit maior ſecunda, &amp; <expan abbr="hęc">haec</expan> tertia <lb></lb>&amp; hæc quarta, &amp; omnes minores FG; </s>
					<s id="N17DF0">ita autem ſuperant primæ ſequen­<lb></lb>tes, vt differentia primæ, &amp; ſecundæ ſit maior differentia ſecundæ, &amp; <pb pagenum="114" xlink:href="026/01/146.jpg"></pb>tertiæ, &amp; hæc maior differentia tertiæ, &amp; quartæ; atque ita deinceps, nec <lb></lb>aliter res eſſe poteſt. </s>
				</p>
				<p id="N17DFD" type="main">
					<s id="N17DFF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17E0B" type="main">
					<s id="N17E0D"><emph type="italics"></emph>Hinc partes, quo fiunt minores, accedunt propiùs ad æqualitatem,<emph.end type="italics"></emph.end> v.g. BD, <lb></lb>&amp; DC accedunt propiùs ad æqualitatem quàm AB, BD, &amp; DC, CE, pro­<lb></lb>piùs quàm CD, DB, &amp; CE, EF, quàm EC, CD, atque ita deinceps, vt patet; <lb></lb>hinc poſt aliquot inſtantia motus, æqualia ferè redduntur inſtantia, vt <lb></lb>conſtat. </s>
				</p>
				<p id="N17E20" type="main">
					<s id="N17E22"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17E2E" type="main">
					<s id="N17E30"><emph type="italics"></emph>Hinc qua proportione decreſcunt instantia, decreſcit etiam perfectio <lb></lb>impetus<emph.end type="italics"></emph.end>; </s>
					<s id="N17E3B">quia temporibus æqualibus eadem cauſa neceſſaria æqualem ef­<lb></lb>fectum producit per Ax. tertium igitur inæqualem inæqualibus, per Ax. <lb></lb>13. num.4. igitur minorem minore tempore; </s>
					<s id="N17E44">igitur minorem in eadem <lb></lb>proportione, in qua tempus eſt; igitur qua proportione, &amp;c. </s>
				</p>
				<p id="N17E4A" type="main">
					<s id="N17E4C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17E58" type="main">
					<s id="N17E5A"><emph type="italics"></emph>Hinc vides quâm ſit neceſſaria illa diuerſa perfectio impetus, quam indi­<lb></lb>cauimus lib.<emph.end type="italics"></emph.end>1. hinc impetus productus ſecundo, &amp; tertio inſtanti adæ­<lb></lb>quat impetum productum primo, quem etiam adæquat productus quar­<lb></lb>to, quinto, ſexto, item productus ſeptimo, octauo, nono; decimo, atque ita <lb></lb>deinceps; </s>
					<s id="N17E6B">hinc eſt eadem differentia impetuum, quæ <expan abbr="inſtãtium">inſtantium</expan>; </s>
					<s id="N17E73">hinc ſin­<lb></lb>gulis ſpatiis æqualibus primo ſpatio, quod percurritur primo inſtanti; </s>
					<s id="N17E79"><lb></lb>reſpondent ſingula inſtantia, &amp; ſingulis inſtantibus ſinguli, &amp; ſingulares <lb></lb>impetus; </s>
					<s id="N17E80">hinc non eſt quod primo inſtanti dicantur produci plura pun­<lb></lb>cta impetus in eodem puncto corporis grauis; </s>
					<s id="N17E86">ſed vnicum tantùm pun­<lb></lb>ctum talis perfectionis ſcilicet phyſicum; cur enim potius duo puncta, <lb></lb>quam tria? </s>
					<s id="N17E8E">ſed quod vnum eſt determinatum eſt per Ax. 5. lib.  1. hinc <lb></lb>optima ratio cur potius tali inſtanti producatur impetus talis perfectio­<lb></lb>nis quàm alterius? </s>
					<s id="N17E95">quippe perfectio impetus ſequitur perfectionem in­<lb></lb>ſtantis quo producitur; </s>
					<s id="N17E9B">hinc dicendum videtur omnia puncta impetus <lb></lb>eſſe diuerſæ perfectionis, vel heterogenea; vt vulgò aiunt Philoſophi; </s>
					<s id="N17EA1"><lb></lb>cuius rationem demonſtratiuam afferemus lib.  ſequenti cum de motu <lb></lb>violento; </s>
					<s id="N17EA8">hinc vides duplicem progreſſionem; </s>
					<s id="N17EAC">primam ſcilicet, qua ex <lb></lb>ſuppoſitis temporibus æqualibus acquiruntur ſpatia inæqualia, de qua <lb></lb>fusè ſuprà; </s>
					<s id="N17EB4">in hac enim velocitas eadem proportione cum impetu creſ­<lb></lb>cit, &amp; cum ipſo tempore; </s>
					<s id="N17EBA">hoc eſt tempore triplo eſt tripla, quadruplo <lb></lb>quadrupla; </s>
					<s id="N17EC0">item impetus in duplo tempore eſt duplus, in triplo triplus; </s>
					<s id="N17EC4"><lb></lb>modò progreſſio fiat in temporibus primo inſtanti æqualibus; </s>
					<s id="N17EC9">ſecunda <lb></lb>progreſſio eſt qua ex ſuppoſitis ſpatiis æqualibus tempora fluunt inæ­<lb></lb>qualia, hoc eſt minora &amp; minora; </s>
					<s id="N17ED1">quibus etiam reſpondet impetus im­<lb></lb>perfectior in eadem proportione temporum; prima fit per differentias <lb></lb>æquales, &amp; proportiones inæquales, ſecunda verò per differentias inæ­<lb></lb>quales, &amp; proportiones inæquales. </s>
				</p>
				<pb pagenum="115" xlink:href="026/01/147.jpg"></pb>
				<p id="N17EDF" type="main">
					<s id="N17EE1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17EED" type="main">
					<s id="N17EEF"><emph type="italics"></emph>Si aſſumantur ſpatia ſenſibilia æqualia, tempora ſunt ferè in ratione ſubdu­<lb></lb>plicata ſpatiorum<emph.end type="italics"></emph.end>; </s>
					<s id="N17EFA">crun enim ſpatia ſint vt quadrata <expan abbr="tẽporum">temporum</expan> ſenſibiliter; </s>
					<s id="N17F02"><lb></lb>certè tempora ſunt, vt radices iſtorum quadratorum, ſcilicet ſpatiorum; </s>
					<s id="N17F07"><lb></lb>ſint enim quæcunque ſpatia æqualia in linea AF; </s>
					<s id="N17F0C">ſintque ſpatia AC 4. <lb></lb>AE 16. radix quadr.4. eſt 2.16. verò 4. igitur tempora ſunt vt 4.2.ſi ve­<lb></lb>rò accipiatur primum ſpatium, quod vno tempore percurritur; </s>
					<s id="N17F14">tempus <lb></lb>quo percurruntur duo ſpatia æqualia primum eſt v.2.quo percurruntur <lb></lb>tria v.3.quo percurruntur 4.ſpatia, 2. atque ita deinceps; igitur in praxi <lb></lb>quæ tantùm fit in ſpatiis ſenſibilibus hæc progreſſio adhibenda eſt, il­<lb></lb>lamque deinceps, ſi quando opus eſt, adhibebimus. </s>
				</p>
				<p id="N17F20" type="main">
					<s id="N17F22"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17F2E" type="main">
					<s id="N17F30"><emph type="italics"></emph>In vacuo ſi corpus graue deſcenderet, prædictæ proportiones accuratiſſimè <lb></lb>ſeruarentur<emph.end type="italics"></emph.end>; </s>
					<s id="N17F3B">quia ſcilicet nullum eſſe impedimentum; </s>
					<s id="N17F3F">at verò ſi aliquod <lb></lb>intercedit impedimentum; </s>
					<s id="N17F45">haud dubiè non ſeruantur accuratè; eſt autem <lb></lb>aliquod impedimentum in medio, quantumuis liberum eſſe videatur, <lb></lb>quæ omnia conſtant. </s>
				</p>
				<p id="N17F4D" type="main">
					<s id="N17F4F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17F5B" type="main">
					<s id="N17F5D"><emph type="italics"></emph>Impetus naturalis addititius deſtruitur<emph.end type="italics"></emph.end>; patet experientiâ; </s>
					<s id="N17F66">quippe pila <lb></lb>deorſum cadens tandem quieſcit, licèt à terra reflectatur ratione impe­<lb></lb>dimenti, ex quo reſultat duplex determinatio, ratione cuius idem im­<lb></lb>petus ſibi aliquo modo redditur <expan abbr="cõtrarius">contrarius</expan>; </s>
					<s id="N17F74">ſed de his fusè in primo libro <lb></lb>à Th.148. ad finem vſque libri: </s>
					<s id="N17F7A">nam reuerâ duæ determinationes op­<lb></lb>poſitæ pugnant pro rata per Ax. 15.l.1. &amp; quotieſcunque idem impetus <lb></lb>eſt ad lineas oppoſitas determinatus eodem modo ſe habet, ac ſi duplex <lb></lb>eſſet, &amp; quilibet ſuæ ſubeſſet determinationi; </s>
					<s id="N17F84">atqui ſi duplex eſſet oppo­<lb></lb>ſitus, pugnarent pro rata; </s>
					<s id="N17F8A">igitur tàm pugnant duæ determinationes op­<lb></lb>poſitæ in eodem impetu, quàm duo impetus ad oppoſitas lineas deter­<lb></lb>minati; igitur impetus naturalis aduentitius deſtruitur, &amp;c. </s>
				</p>
				<p id="N17F92" type="main">
					<s id="N17F94"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 73.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17FA0" type="main">
					<s id="N17FA2"><emph type="italics"></emph>Impetus naturalis innatus nunquam deſtruitur<emph.end type="italics"></emph.end>; </s>
					<s id="N17FAB">Probatur, quia nihil eſte <lb></lb>quod exigat eius deſtructionem, quia ſcilicet nunquam eſt fruſtrà; </s>
					<s id="N17FB1">nam <lb></lb>vel habet motum deorſum, vel grauitationis effectum, vel deſtruit impe­<lb></lb>tum extrinſecum in motu violento; igitur nunquam eſt fruſtrà, cum ſem­<lb></lb>per habeat aliquem effectum. </s>
				</p>
				<p id="N17FBB" type="main">
					<s id="N17FBD">Dices lignum vi extrinſeca in aqua immerſum ſua ſponte aſcendit; </s>
					<s id="N17FC1"><lb></lb>igitur ille gradus impetus grauitationis deſtruitur, &amp; alius producitur; <lb></lb>hæc quæſtio ad præſens inſtitutum non pertinet, ſed ad librum de gra­<lb></lb>uitate, &amp; leuitate. </s>
					<s id="N17FCA">Igitur breuiter reſpondeo illum impetum nunquam <lb></lb>deſtrui, quandiu mobile grauitat, vel grauitatione ſingulari, (ſic corpus <lb></lb>grauitat in manum ſuſtinentis,) vel grauitatione communi, (ſic lignum <lb></lb>humori innatans grauitat, non quidem in aquam, at ſimul cum aqua;) <lb></lb>ſed de grauitate, &amp; grauitatione in Tomo de ſtatibus corporum ſenſibi-<pb pagenum="116" xlink:href="026/01/148.jpg"></pb>libus, in quo oſtendemus ideo lignum ſurſum emergere, quia ab aqua <lb></lb>extenditur, &amp; ideo corpora ſurſum ire, quia alia deorſum eunt. </s>
				</p>
				<p id="N17FDC" type="main">
					<s id="N17FDE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N17FEA" type="main">
					<s id="N17FEC"><emph type="italics"></emph>Quando lapis deſcendit per medium aëra, impeditur aliquantulum eius <lb></lb>motus<emph.end type="italics"></emph.end>: </s>
					<s id="N17FF7">Probatur primò experientiâ, quæ certa eſt; </s>
					<s id="N17FFB">tàm enim aër impe­<lb></lb>dit motum deorſum, quàm ſurſum, vt videre eſt in mobili leuiore ſeu ra­<lb></lb>riore, quod etiam flante vento obſeruare omnes poſſunt; </s>
					<s id="N18003">quomodo ve­<lb></lb>rò impediat, dicemus aliàs; </s>
					<s id="N18009">ſecundò corpus immobile, in quod mobile <lb></lb>impingitur, motum illius impedit; </s>
					<s id="N1800F">ſed in diuerſas partes aëris corpus <lb></lb>graue impingitur in deſcenſu; igitur aliquantulum impeditur eius <lb></lb>motus. </s>
				</p>
				<p id="N18017" type="main">
					<s id="N18019"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 75.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18025" type="main">
					<s id="N18027"><emph type="italics"></emph>Hinc motus naturalis deorſum aliquantulum retardatur,<emph.end type="italics"></emph.end> quia nihil aliud <lb></lb>præſtare poteſt huiuſmodi impedimentum, niſi aliquam retardationem; <lb></lb>igitur motus inde redditur tardior. </s>
				</p>
				<p id="N18034" type="main">
					<s id="N18036"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18042" type="main">
					<s id="N18044"><emph type="italics"></emph>Hinc etiam impetus producitur imperfectior<emph.end type="italics"></emph.end>; quia ex imperfectione ef­<lb></lb>fectus requiritur imperfectio cauſæ per Ax. 13.l. </s>
					<s id="N1804F">1. &amp; quâ proportione <lb></lb>eſt tardior motus eâdem impetus eſt imperfectior, per Ax. 5. excipe ta­<lb></lb>men impetum innatum, qui ſemper habet eundem effectum grauitatio­<lb></lb>nis, vel ſingularis, quâ grauitas cum ipſo medio, ſi reuerâ medium gra­<lb></lb>uitat, de quo aliàs. </s>
				</p>
				<p id="N1805C" type="main">
					<s id="N1805E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1806A" type="main">
					<s id="N1806C"><emph type="italics"></emph>Quo medium denſius eſt plus impedit motum deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N18075">Probatur, quia ſi <lb></lb>motum impedit; certè non totum; quis enim hoc dicat; </s>
					<s id="N1807B">ſed eæ dumta­<lb></lb>xat partes, quibus incubat corpus graue; </s>
					<s id="N18081">igitur quò ſunt plures huiuſ­<lb></lb>modi partes, maius eſt impedimentum; </s>
					<s id="N18087">ſed in medio denſiori plures ſunt <lb></lb>cum minore extenſione; </s>
					<s id="N1808D">hoc enim eſt, quod voco denſius; igitur me­<lb></lb>dium denſius plùs impedit. </s>
				</p>
				<p id="N18093" type="main">
					<s id="N18095"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N180A1" type="main">
					<s id="N180A3"><emph type="italics"></emph>Hinc tardiùs deſcendit mobile per mediam aquam, quàm per medium <lb></lb>aëra,<emph.end type="italics"></emph.end> quia aqua eſt denſior aëre. </s>
				</p>
				<p id="N180AD" type="main">
					<s id="N180AF"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N180BB" type="main">
					<s id="N180BD">Obſerua eſſe aliqua corpora minus denſa, quæ motum omninò im­<lb></lb>pediunt; </s>
					<s id="N180C3">quippe certum eſt aquam eſſe denſiorem ligno; </s>
					<s id="N180C7">atqui li­<lb></lb>gnum deſcenſum lapidis impedit, non verò aqua; </s>
					<s id="N180CD">quia ſcilicet lignum <lb></lb>non eſt medium, vt aqua; </s>
					<s id="N180D3">vt enim aliquod corpus ſit medium, debet eſſe <lb></lb>liquidum, vt, aqua &amp; alij liquores; vel ſpirabile vt aër, vapor, &amp;c. </s>
					<s id="N180D9">ratio <lb></lb>eſt, quia partes ligni, vel alterius corporis durioris, ita ſunt inter ſe con­<lb></lb>junctæ, vel implicatæ, vt omnem tranſitum intercludant, niſi corpus ip­<lb></lb>ſum graue valido ictu vel impetu ſibi viam aperiat; </s>
					<s id="N180E3">igitur vt corpus ali­<lb></lb>quod vice medij defungatur, debet in eo ſtatu eſſe, in quo eius partes <pb pagenum="117" xlink:href="026/01/149.jpg"></pb>modico ferè niſu ſeiungantur, &amp; loco cedant; </s>
					<s id="N180EE">ſed de his ſtatibus cor­<lb></lb>porum fusè agemus Tomo 5. adde quod ad medium ſufficit vacuum ſi <lb></lb>motus in vacuo eſſe poteſt, de quo alibi; quod certè eſt omnium me­<lb></lb>diorum optimum, cum nullo modo reſiſtar mobili. </s>
				</p>
				<p id="N180F8" type="main">
					<s id="N180FA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18106" type="main">
					<s id="N18108"><emph type="italics"></emph>Hinc producitur impetus imperfectior in medio denſiore:<emph.end type="italics"></emph.end> quia in eo tar­<lb></lb>dior eſt motus, ex cuius tarditate arguitur imperfectio impetus per Ax. <lb></lb>13.num.4. </s>
				</p>
				<p id="N18115" type="main">
					<s id="N18117"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N18123" type="main">
					<s id="N18125">Obſerua denſitatem medij cognoſci ex eius grauitate; </s>
					<s id="N18129">illud enim <lb></lb>denſius eſt, quod eſt grauius &amp; viciſſim; </s>
					<s id="N1812F">quod fusè explicabimus ſuo lo­<lb></lb>co; </s>
					<s id="N18135">eſt enim grauitas quædam <emph type="italics"></emph>denſitas, vt ait<emph.end type="italics"></emph.end> Philoſophus <emph type="italics"></emph>tùm l.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>pb.c.<emph.end type="italics"></emph.end><lb></lb>9.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>85. &amp; 86. <emph type="italics"></emph>denſum &amp; rarum,<emph.end type="italics"></emph.end> inquit, <emph type="italics"></emph>ſunt lationis efficientia,<emph.end type="italics"></emph.end> &amp; paulò ſu­<lb></lb>periùs; </s>
					<s id="N18160"><emph type="italics"></emph>eſt autem denſum graue, rarum verò leue, &amp; l.<emph.end type="italics"></emph.end>8.<emph type="italics"></emph>c.<emph.end type="italics"></emph.end>7.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>55. <emph type="italics"></emph>hæc habet, <lb></lb>graue &amp; leue; molle &amp; durum denſitates quædam eſſe, &amp; raritates videntur,<emph.end type="italics"></emph.end><lb></lb>quæ adnotare volui, vt vel inde conſtet doctrinam hanc cum Peripate­<lb></lb>tica optimè conſentire. </s>
				</p>
				<p id="N18180" type="main">
					<s id="N18182">Obſeruabis etiam hîc à me non diſcuti, in quo conſiſtat denſitas, vel <lb></lb>raritas, grauitas, vel leuitas; </s>
					<s id="N18188">ſuppono tantùm graue illud eſſe, quod ten­<lb></lb>dit deorſum; </s>
					<s id="N1818E">leue illud, quod tendit ſurſum ſiue pellatur à grauiori, ſiue <lb></lb>non, denſum verò eſſe id quod multùm materia habet ſub parua exten­<lb></lb>ſione, rarum è contrario; quorum omnium cauſas, &amp; rationes ſuo loco <lb></lb>explicabimus. </s>
				</p>
				<p id="N18198" type="main">
					<s id="N1819A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N181A6" type="main">
					<s id="N181A8"><emph type="italics"></emph>Sub medium leuius corpus graue deſcendit<emph.end type="italics"></emph.end>; </s>
					<s id="N181B1">certa eſt hypotheſis, niſi for­<lb></lb>tè aliquando per accidens ſecus accidat; </s>
					<s id="N181B7">ratio porrò petitur ex ipſa <lb></lb>grauitatis natura, quâ corpus graue tendit deorſum; </s>
					<s id="N181BD">nihil enim aliud <lb></lb>grauitas eſt, quidquid tandem illa ſit; </s>
					<s id="N181C3">quippe corpus graue deſcendit, <lb></lb>quando medium liberum habet, idemque leuius, per quod deſcendat; </s>
					<s id="N181C9"><lb></lb>quod certè ſi grauius eſſet, haud dubiè non deſcenderet; </s>
					<s id="N181CE">ſic ferrum, &amp; <lb></lb>ſaxum plumbo liquato innatant; </s>
					<s id="N181D4">cum tamen per mediam aquam de­<lb></lb>ſcendant; </s>
					<s id="N181DA">fic lignum aquæ ſupernatat, quod per liberum aëra deſcendit; </s>
					<s id="N181DE"><lb></lb>ratio eſt, quia grauius deſcendit ſub medium leuius; </s>
					<s id="N181E3">cur autem id fiat <lb></lb>fusè alibi explicabo; id tantùm obiter indico. </s>
					<s id="N181E9">Omnis motus, qui fit à <lb></lb>principio intrinſeco per lineam rectam propter locum eſt, vt patet; quis <lb></lb>enim neget corpus graue ideo deſcendere ſub leuius, vt occupet aliquem <lb></lb>locum quo prius carebat, qui tamen illi connaturalis eſt in hoc rerum <lb></lb>ordine? </s>
					<s id="N181F5">cum à natura acceperit vim illam intrinſecam, quâ in eum lo­<lb></lb>cum ſeſe recipere poteſt; </s>
					<s id="N181FB">quam certè vim intrinſecam nunquam à na­<lb></lb>tura rebus creatis inſitam eſſe conſtat, niſi ad eum finem conſequendum, <lb></lb>cui à natura deſtinantur; </s>
					<s id="N18203">cur verò locus connaturalis corporis grauio­<lb></lb>ris ſit ille, in quo leuiori ſubeſt, non diu hærebit animus, quin ſtatim ra­<lb></lb>tio affulgeat; </s>
					<s id="N1820B">cum enim corpus, quod eſt ſuprà, ſuſtineatur ab eo quod eſt <lb></lb>infrà; </s>
					<s id="N18211">illud certè infra eſſe connaturalius eſt, quod aptius eſt ad ſuſtinen-<pb pagenum="118" xlink:href="026/01/150.jpg"></pb>dum; </s>
					<s id="N1821A">atqui denſum aptius eſt ad id munus, quia plures partes ſuſtinentis <lb></lb>pauciores ſuſtinent alterius leuioris, ſeu rarioris, vt conſtat; </s>
					<s id="N18220">v.g. certum <lb></lb>eſt <expan abbr="cãdem">eandem</expan> aëris partem pluribus aquæ partibus reſpondere; </s>
					<s id="N1822C">ſed de hoc <lb></lb>alias fusè; </s>
					<s id="N18232">hæc interim ſufficiat indicaſſe, vt vel aliqua ratio affulgeat; </s>
					<s id="N18236"><lb></lb>cur ſcilicet corpus graue ſub medium leuius ſua ſponte deſcendat; </s>
					<s id="N1823B">adde <lb></lb>quod cum omne corpus graue tendat deorſum, tunc vnum infra aliud de­<lb></lb>ſcendit, cum ſunt plures partes pellentis, quàm pulſi; denique per va­<lb></lb>cuum modicum ſine vlla reſiſtentia deſcenderet. </s>
				</p>
				<p id="N18245" type="main">
					<s id="N18247"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18253" type="main">
					<s id="N18255"><emph type="italics"></emph>Sub medium grauius corpus leuius minimè deſcendit, ſed huic inna­<lb></lb>tat<emph.end type="italics"></emph.end>; </s>
					<s id="N18260">v.g. lignum aquæ, ferrum plumbo liquato; </s>
					<s id="N18266">certa eſt hypotheſis: </s>
					<s id="N1826A">ratio <lb></lb>eſt, quia ideo deſcendit graue ſub medium, quia grauius ſeu denſius eſt <lb></lb>medio; </s>
					<s id="N18272">igitur, ſi denſius eſt ipſum medium, non deſcendet; clarum eſt; <lb></lb>cur verò aſcendat ſupra medium. </s>
					<s id="N18278">v.g. cur lignum aquæ immerſum tan­<lb></lb>dem emergat hîc non diſcutio, ſed tantùm indico ab ipſa aqua ſurſum <lb></lb>extendi; quanta verò parte lignum emergat, dicemus aliàs, cum de in­<lb></lb>natantibus humido. </s>
				</p>
				<p id="N18284" type="main">
					<s id="N18286"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18292" type="main">
					<s id="N18294"><emph type="italics"></emph>Sub medium æquè graue corpus non deſcendit, nec etiam ſupra aſcendit<emph.end type="italics"></emph.end>; </s>
					<s id="N1829D">ra­<lb></lb>tio eſt, quia ideo deſcendit ſub medium, quia medium leuius eſt, ideo <lb></lb>aſcendit ſupra, quia medium grauius eſt; </s>
					<s id="N182A5">igitur ſi nec ſit grauius nec <lb></lb>leuius, non eſt quod aſcendat vel deſcendat; </s>
					<s id="N182AB">nihil tamen illius ſupra <lb></lb>primam medij ſuperficiem extare poterit; alioqui eſſet leuius medio, <lb></lb>contra ſuppoſitionem. </s>
				</p>
				<p id="N182B3" type="main">
					<s id="N182B5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N182C1" type="main">
					<s id="N182C3"><emph type="italics"></emph>Aër ſuam grauitatem habet<emph.end type="italics"></emph.end>; </s>
					<s id="N182CC">quod iam à nullo in dubium reuocari po­<lb></lb>teſt; </s>
					<s id="N182D2">nam ſi comprimatur intra vas æneum v.g. etiam minimæ craſſitu­<lb></lb>dinis; </s>
					<s id="N182DA">ſi deinde ponderetur, maius eſt haud dubiè pondus, quo maior <lb></lb>eſt aëris copia intruſa; </s>
					<s id="N182E0">atqui non modo triplum totius aëris, qui ante <lb></lb>compreſſionem totam vaſis capacitatem occupabat intrudi poteſt, vel <lb></lb>decuplum; </s>
					<s id="N182E8">verùm etiam vigecuplum; </s>
					<s id="N182EC">immò centuplum, &amp; millecuplum <lb></lb>adhibita cochleâ, vel alio mechanico organo, &amp; aucta vaſis craſſitudine, <lb></lb>de quo aliàs: </s>
					<s id="N182F4">quanta verò ſit grauitas aëris comparata cum grauitate <lb></lb>aquæ, cenſet Galileus eſſe ferè vt 1. ad 400. Merſennus verò vt 1. ad <lb></lb>1356. vel ſaltem vt 1.ad 1300. Nos maiorem illà; </s>
					<s id="N182FC">hâc vero minorem <lb></lb>eſſe obſeruauimus, de quo aliàs; </s>
					<s id="N18302">nec enim eſt præſentis inſtituti, pro <lb></lb>quo ſufficiat modò, aëri aliquam ineſſe grauitatem; </s>
					<s id="N18308">nec dicas aëra le­<lb></lb>uem eſſe; </s>
					<s id="N1830E">nam reuerâ leuis eſt, ſi comparetur cum aqua; </s>
					<s id="N18312">grauis autem ſi <lb></lb>comparetur cum aſcendente halitu, vel fortè cum vacuo; </s>
					<s id="N18318">nec eſt quod <lb></lb>aliquis fortè metuat, ne ſi aër ſit grauis, ab eo tandem opprimatur, nam <lb></lb>etiamſi aqua ſit grauis non tamen opprimit vrinatores, cuius rei veriſſi­<lb></lb>mam rationem ſuo loco afferemus; </s>
					<s id="N18322">denique non eſt quod aliqui ſatis <lb></lb>incautè reſpondeant, ipſum aëra non eſſe grauem, ſed tantùm ſentiri ali­<lb></lb>quod pondus craſſioris vaporis immixti; </s>
					<s id="N1832A">nam de alio aëre non affirmo <pb pagenum="119" xlink:href="026/01/151.jpg"></pb>grauem eſſe, niſi tantùm de illo, quem ſpiramus, in quo ambulamus, qui <lb></lb>nos ambit: </s>
					<s id="N18335">adde quod Ariſtoteles l.4. <emph type="italics"></emph>de Cœlo, c.<emph.end type="italics"></emph.end>5.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>36. tribuit aëri gra­<lb></lb>uitatem his verbis; <emph type="italics"></emph>quapropter<emph.end type="italics"></emph.end> inquit, <emph type="italics"></emph>aër, &amp; aqua habent &amp; leuitatem, &amp; <lb></lb>grauitatem.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N18354" type="main">
					<s id="N18356"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18362" type="main">
					<s id="N18364"><emph type="italics"></emph>Medium eiuſdem grauitatis cum dato corpore graui detrahit totam eius <lb></lb>grauitationem ſingularem; </s>
					<s id="N1836C">hoc eſt corpus graue in medium æquè graue non <lb></lb>grauitat<emph.end type="italics"></emph.end>; </s>
					<s id="N18375">quia ſi grauitaret deſcenderet; </s>
					<s id="N18379">ſic pars aquæ in aliam partem <lb></lb>aquæ non grauitat, &amp; ſi aqua ponderetur in aqua, nullius ponderis eſt; </s>
					<s id="N1837F"><lb></lb>cum enim nulla ſit ratio cur vna ſit infrà potiùs, quàm alia, vna certè al­<lb></lb>terius locum non ambit; igitur caret grauitatione ſingulari. </s>
				</p>
				<p id="N18386" type="main">
					<s id="N18388"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18394" type="main">
					<s id="N18396"><emph type="italics"></emph>Medium graue detrahit aliquid de ſingulari grauitatione corporis grauio­<lb></lb>ris<emph.end type="italics"></emph.end>; </s>
					<s id="N183A1">certa eſt hypotheſis; </s>
					<s id="N183A5">nec enim plumbum eſt eius ponderis ſingula­<lb></lb>ris in aqua, cuius eſt in aëre; dixi ſingularis; </s>
					<s id="N183AB">nam ſi plumbum &amp; ipſa <lb></lb>aqua ſimul appendantur, haud dubiè totum habebis pondus plumbi, &amp; <lb></lb>totum pondus aquæ; </s>
					<s id="N183B3">ratio verò huius effectus non eſt huius loci; </s>
					<s id="N183B7">quid­<lb></lb>quid ſit, ſi æqualis grauitas medij tollit totam æqualem alterius corpo­<lb></lb>ris; certè maiorem alterius corporis totam non tollit per Th. 80. ſed <lb></lb>tantùm aliquid illius, quod quomodo fiat, dicemus Tomo quinto cum de <lb></lb>graui, &amp; leui. </s>
				</p>
				<p id="N183C3" type="main">
					<s id="N183C5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N183D1" type="main">
					<s id="N183D3"><emph type="italics"></emph>Medium graue detrahit eam partem grauitationis corporis grauioris, quæ <lb></lb>eſt æqualis ſuæ grauitationi.<emph.end type="italics"></emph.end> v. g. ſi medij grauitas eſt ſubdupla, detrahit <lb></lb>ſubduplum grauitationis; </s>
					<s id="N183E4">ſi ſubdecupla, ſubdecuplum, atque ita dein­<lb></lb>ceps; hoc iam olim ſuppoſuit magnus Archim. </s>
					<s id="N183EB">ſupponunt etiam reliqui <lb></lb>omnes, præſertim recentior Galileus; </s>
					<s id="N183F1">ſi enim æqualis ſuperat æqualem, <lb></lb>ergo inæqualis pro rata; ſcilicet ſubdupla ſubduplum ſubtripla, &amp;c. </s>
					<s id="N183F7">Præ­<lb></lb>terea, cum detrahat aliquam partem grauitationis maioris per Th.85.nec <lb></lb>detrahat inæqualem maiorem, per Th.80.nec inæqualem minorem; cur <lb></lb>enim potius vnam minorem quam aliam? </s>
					<s id="N18401">certè æqualem tantùm <lb></lb>detrahere poteſt, quod ſuo loco per Principium poſitiuum demonſtra­<lb></lb>bimus. </s>
				</p>
				<p id="N18408" type="main">
					<s id="N1840A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18416" type="main">
					<s id="N18418"><emph type="italics"></emph>Hinc ratio cur grauia deſcendant tardius in aqua, quàm in aëre, &amp; in <lb></lb>aëre, quàm in vacuo<emph.end type="italics"></emph.end>; </s>
					<s id="N18423">hinc etiam maioris ſunt ponderis in aëre quam in <lb></lb>aqua; </s>
					<s id="N18429">hinc ſi grauitas alicuius corporis ſit ad grauitatem aëris vt 100. <lb></lb>ad 1. haud dubiè decreſcet eius pondus in aëre (1/100); </s>
					<s id="N1842F">id eſt, ſi penderet 100. <lb></lb>libras in vacuo, in aëre penderet 99. &amp; eo tempore quo in vacuo decur­<lb></lb>reret 100. paſſus, in aëre decurreret 99. ſi nulla ſit aliunde reſiſtentia, <lb></lb>qualis reuerâ eſt, vt dicam infrà; </s>
					<s id="N18439">ſimiliter ſi grauitas alicuius corporis <lb></lb>ſit ad grauitatem aquæ, vt 10. ad 1. decreſcet eius pondus in aqua (1/10), &amp; <lb></lb>eo tempore quo decurreret in vacuo 10. palmos ſpatij, in aqua decurre <pb pagenum="120" xlink:href="026/01/152.jpg"></pb>ret tantùm 9. poſito quod non ſit aliud quod reſiſtat; </s>
					<s id="N18448">quanta verò ſit <lb></lb>grauitas omnium corporum tùm duriorum, qualia ſunt metalla, tùm li­<lb></lb>quidorum, tùm ſpirabilium, dicemus ſuo loco; illorum tabulas habes <lb></lb>apud Gethaldum, &amp; Merſennum. </s>
				</p>
				<p id="N18452" type="main">
					<s id="N18454"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18460" type="main">
					<s id="N18462"><emph type="italics"></emph>Hinc, ſi nihil aliud deſcenſum corporum grauium impediret, cognito pen­<lb></lb>dere vtriuſque, medij &amp; corporis grauis, ſpatio, quod in vno illorum conficit, <lb></lb>cognoſci poſſet ſpatium, quod in alio conficeret æquali tempore<emph.end type="italics"></emph.end>, v. g. ſuppona­<lb></lb>mus grauitatem aquæ eſſe ad grauitatem aëris vt 400. ad 1. ſitque corpus, <lb></lb>cuius grauitas ſit dupla grauitatis aquæ; </s>
					<s id="N18477">haud dubiè eo tempore, quo <lb></lb>conficit in aëre 799. ſpatia, in aqua conf;iciet tantùm 400. quia in vacuo <lb></lb>conficeret 800. aër autem detrahit (1/800), &amp; aqua 1/2, vt conſtat ex dictis; </s>
					<s id="N1847F">ſi­<lb></lb>militer cognitis ſpatiis in vtroque medio confectis, &amp; grauitate vtriuſque <lb></lb>medij cognoſceretur grauitas corporis deſcendentis; quia tamen eſt alia <lb></lb>reſiſtentiæ ratio, hîc non hæreo. </s>
				</p>
				<p id="N18489" type="main">
					<s id="N1848B"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N18497" type="main">
					<s id="N18499">Obſeruabis dictum eſſe hactenus; </s>
					<s id="N1849D">ſi nihil aliud deſcenſum corporis <lb></lb>grauis impedit; </s>
					<s id="N184A3">nam certè aliud eſt, de quo infrà, ex cuius ignoratione <lb></lb>plures haud dubiè in inueſtigandis grauitatum medij rationibus hallu­<lb></lb>cinarentur; </s>
					<s id="N184AB">cum enim obſeruatum ſit globum plumbeum, cuius graui­<lb></lb>tas eſt ferè dodecupla grauitatis aquæ, conficere in libero aëre 48. pedes <lb></lb>ſpatij tempore duorum ſecundorum, in aqua verò 12. pedes eodem tem­<lb></lb>pore; </s>
					<s id="N184B5">certè in vacuo ipſo moueretur tardiùs quàm in aëre; </s>
					<s id="N184B9">quia eo tem­<lb></lb>pore, quo conficit in aqua 12.pedes in vacuo conficeret (13 1/21), ſi tantùm <lb></lb>detrahitur (1/12) grauitationis, &amp; deſcenſus; </s>
					<s id="N184C1">atqui in aëre eodem tempore <lb></lb>conficit 48. pedes; </s>
					<s id="N184C7">igitur velociùs moueretur in aëre quàm in vacuo; </s>
					<s id="N184CB"><lb></lb>igitur eſt aliquid aliud quod impedit motum; </s>
					<s id="N184D0">vt enim optimè monet <lb></lb>Merſennus, ſi grauitas aquæ ſit ad grauitatem aëris vt 400 ad 1.&amp; graui­<lb></lb>tas plumbi ad grauitatem aquæ vt 12. ad 1.eadem grauitas plumbi eſt ad <lb></lb>grauitatem aëris vt 4800. igitur ſi ſpatium, quod decurrit plumbum in <lb></lb>vacuo diuidatur in 4800. partes, decurret in aëre 4799. partes; </s>
					<s id="N184DC">in aqua <lb></lb>verò 4400. quod eſt contra experientiam; </s>
					<s id="N184E2">nam ſpatium, quod decurrit <lb></lb>in aëre eſt maius ſpatio, quod decurrit in aqua 3/4; </s>
					<s id="N184E8">quippe conficit 12. <lb></lb>pedes in aqua eodem tempore, quo in aëre conficit 48; </s>
					<s id="N184EE">igitur in aqua <lb></lb>amittit 3/4 ſuæ grauitationis, &amp; ſui motus; igitur 3600. partes; </s>
					<s id="N184F4">igitur <lb></lb>plumbi grauitas eſſet ad grauitatem aquæ vt 4.ad 3.&amp; ad grauitatem aë­<lb></lb>ris vt 3600. ad 1. atqui vtrumque falſum eſſe conſtat; </s>
					<s id="N184FC">igitur eſt aliquid <lb></lb>aliud, quod etiam impedit motum; nec ex motu diuerſo per diuerſa me­<lb></lb>dia cognoſci poteſt eorum grauitas. </s>
				</p>
				<p id="N18504" type="main">
					<s id="N18506"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 89.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18512" type="main">
					<s id="N18514"><emph type="italics"></emph>Hinc potiori iure reiicies illorum ſententiam, qui volunt impediri motum <lb></lb>corporis deſcendentis per diuerſa media pro diuerſa ratione grauitatum vtriuſ­<lb></lb>que medy<emph.end type="italics"></emph.end>; quod certè falſum eſt; </s>
					<s id="N18521">nam aqua ſit ad grauitatem aëris vt <lb></lb>400. ad 1. deberet omne corpus deſcendere velociùs in aëre quadrin-<pb pagenum="121" xlink:href="026/01/153.jpg"></pb>genteſies, quàm in aqua, quod falſum eſt; cum aliquod corpus nullo mo­<lb></lb>do deſcendat in aqua, quod deſcendit in aëre, vt lignum. </s>
				</p>
				<p id="N1852E" type="main">
					<s id="N18530"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 90.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1853C" type="main">
					<s id="N1853E"><emph type="italics"></emph>Non poteſt corpus graue per medium corporeum deſcendere, niſi vel totum <lb></lb>medium loco cedat, vel aliquæ partes eiuſdem medij,<emph.end type="italics"></emph.end> patet; quia vnum cor­<lb></lb>pus non poteſt penetrari cum alio. </s>
				</p>
				<p id="N1854B" type="main">
					<s id="N1854D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 91.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18559" type="main">
					<s id="N1855B"><emph type="italics"></emph>Totum medium loco non cedit in deſcenſu grauium<emph.end type="italics"></emph.end>; </s>
					<s id="N18564">patet etiam, tùm <lb></lb>quia ad mouendum totum medium exigua vis corporis grauis non ſuffi­<lb></lb>cit; </s>
					<s id="N1856C">tùm quia tàm facilè per medium durum eiuſdem grauitatis deſcen­<lb></lb>deret; denique patet manifeſtâ experientiâ. </s>
				</p>
				<p id="N18572" type="main">
					<s id="N18574"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18580" type="main">
					<s id="N18582"><emph type="italics"></emph>Hinc aliqua tantùm partes medij loco cedunt<emph.end type="italics"></emph.end>; probatur, quia vel totum <lb></lb>medium, vel aliquæ eius partes, per Th.90.non primum per Th.91. igitur <lb></lb>ſecundum, in his certè non eſt vlla difficultas. </s>
				</p>
				<p id="N1858F" type="main">
					<s id="N18591"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 93.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1859D" type="main">
					<s id="N1859F"><emph type="italics"></emph>Non poſſunt illæ partes loco cedere ſine motu; </s>
					<s id="N185A5">nec moueri ſine impetu, nec <lb></lb>habere impetum, niſi producatur in illis à cauſa aliqua applicata; quæ certè <lb></lb>alia noneſt quàm impetus corporis deſcendentis,<emph.end type="italics"></emph.end> vt conſtat ex iis, quæ dixi­<lb></lb>mus primo lib. <emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 94.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N185BD" type="main">
					<s id="N185BF"><emph type="italics"></emph>Illæ partes, quæ loco cedunt deſcendenti corpori graui, neceſſariò ab aliis <lb></lb>ſeparantur, &amp; ſuo appulſu, vel impulſu alias multas impellunt, ac ſeparant,<emph.end type="italics"></emph.end><lb></lb>atqui ſeparari non poſſunt ab aliis, niſi ſoluatur vnio, ſeu nexus, <lb></lb>quo cum aliis deuinciuntur; quidquid tandem ſit illa vnio, de qua <lb></lb>aliàs. </s>
				</p>
				<p id="N185CF" type="main">
					<s id="N185D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 95.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N185DD" type="main">
					<s id="N185DF"><emph type="italics"></emph>Hinc quò arctior eſt ille nexus, difficilius ſoluitur<emph.end type="italics"></emph.end>; igitur maiore vi, vel <lb></lb>impetu opus eſt, vt ſolui poſſit, vt conſtat. </s>
				</p>
				<p id="N185EA" type="main">
					<s id="N185EC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 96.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N185F8" type="main">
					<s id="N185FA"><emph type="italics"></emph>Hinc corpus grauius ſustinetur à leuiore.<emph.end type="italics"></emph.end> v.g. plumbum à ligno propter <lb></lb>arctiorem nexum partium ligni, qui ab impetu plumbi quantumuis gra­<lb></lb>uiſſimi ſuperari non poteſt; </s>
					<s id="N18609">hinc corpus illud, medium tantùm appello <lb></lb>in quo poſſint corpora moueri, cuius nexus ſuperari poteſt à corpore <lb></lb>grauiori in aliqua ſaltem figura, vel ſitu; </s>
					<s id="N18611">hinc corpora dura non poſſunt <lb></lb>eſſe medium; </s>
					<s id="N18617">immò neque mollia, vt cera, argilla; ſed vel liquida, vel <lb></lb>ſpirabilia. </s>
				</p>
				<p id="N1861D" type="main">
					<s id="N1861F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 97.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1862B" type="main">
					<s id="N1862D"><emph type="italics"></emph>Hinc ducitur euidens ratio, cur medium impediat motum ſi dumtaxat ha­<lb></lb>beat arctiorum partium implicationem &amp; nexum<emph.end type="italics"></emph.end>; </s>
					<s id="N18638">quia non modo partes <pb pagenum="122" xlink:href="026/01/154.jpg"></pb>medij amouendæ ſunt è ſuo loco; </s>
					<s id="N18641">verùm etiam nexus ille partium ſol­<lb></lb>uendus; igitur ex vtroque capite impeditur motus. </s>
				</p>
				<p id="N18647" type="main">
					<s id="N18649"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 98.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18655" type="main">
					<s id="N18657"><emph type="italics"></emph>Quo ſubtiliores ſunt partes difficilius inter ſe implicari poſſunt ſeu ligari <lb></lb>quibuſdam filamentis<emph.end type="italics"></emph.end>, conſtat; </s>
					<s id="N18662">igitur cum aëris partes ſint magis lubricæ, <lb></lb>quàm partes aquæ, &amp; faciliùs per obuia quæque foramina irrepere poſ­<lb></lb>ſint, non poſſunt ita contineri; </s>
					<s id="N1866A">ſic videmus multùm aquæ hauriri, dum <lb></lb>arctioribus retibus attollitur; </s>
					<s id="N18670">immò dum aquam manu ſtringimus, ali­<lb></lb>quam reſiſtentiam ſenſu percipimus; quæ certè nulla eſt, dum aëra ſtrin­<lb></lb>gimus. </s>
				</p>
				<p id="N18678" type="main">
					<s id="N1867A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N18686" type="main">
					<s id="N18688">Obſeruabis vnionem continuatiuam corporum aliquando poſitam <lb></lb>eſſe in plexu, vel implicatione partium, vt videmus in fune, ligno, carne, <lb></lb>oſſibus, &amp;c. </s>
					<s id="N1868F">aliquando in vacui metu; </s>
					<s id="N18692">ſic aqua, vt ſuo vaſi adhæreat, <lb></lb>aſcendit, vel ſurſum attollitur, ne detur vacuum; </s>
					<s id="N18698">aliquando in coitione <lb></lb>quadam magnetica; </s>
					<s id="N1869E">porrò hic plexus conſtat ex infinitis ferè tenuiſſi­<lb></lb>morum filamentorum voluminibus, vel aduncis ſiue hamatis partibus, <lb></lb>ſeu corpuſculis: </s>
					<s id="N186A6">Vtrum verò præter hæc requiratur alius vnionis mo­<lb></lb>dus, diſcutiemus fusè Tomo 5. quidquid ſit; certum eſt medium illud, <lb></lb>cuius partes arctiori maiorique nexu copulantur, longè difficiliùs per­<lb></lb>curri poſſe, ſeu perrumpi. </s>
				</p>
				<p id="N186B0" type="main">
					<s id="N186B2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 99.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N186BE" type="main">
					<s id="N186C0"><emph type="italics"></emph>Hinc non modò aqua detrahit plumbo<emph.end type="italics"></emph.end> (1/22) <emph type="italics"></emph>ſui motus, quod ſcilicet plumbi gra­<lb></lb>uitas ſit dedecupla grauitatis aquæ, verùm etiam propter reſistentiam petitam <lb></lb>ex alio capite aliquid adhuc detrahere poteſt<emph.end type="italics"></emph.end>; </s>
					<s id="N186D3">ſcilicet quia partes aquæ non <lb></lb>poſſunt amoueri, niſi ab aliis ſeparentur; </s>
					<s id="N186D9">atqui maiore vi opus eſt ad­<lb></lb>ſoluendum ſtrictiorem nexum; </s>
					<s id="N186DF">immò licèt partes aquæ nullo penitus <lb></lb>nexu vniantur, ſed tantùm vel vacui metu, vel alio modo, quod alibi ex­<lb></lb>plicabimus; </s>
					<s id="N186E7">omninò detraherent adhuc plumbo (1/12) motus; </s>
					<s id="N186EB">igitur, ſi <lb></lb>præter illud impedimentum, quod petitur à comparatione grauitatis <lb></lb>corporis mobilis cum grauitate medij, addatur aliud longè robuſtius; <lb></lb>non mirum eſt, ſi maior inde ſequatur effectus, id eſt maior imminutio <lb></lb>motus, qui quaſi frangitur ab impedimento. </s>
				</p>
				<p id="N186F7" type="main">
					<s id="N186F9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 100.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18705" type="main">
					<s id="N18707"><emph type="italics"></emph>Hinc petitur ratio illius experimenti, ſi verum eſt, duobus ſecundis per­<lb></lb>currere plumbeam pilam in aëre<emph.end type="italics"></emph.end> 48. <emph type="italics"></emph>ſpatij pedes, in aqua verò<emph.end type="italics"></emph.end> 12. <emph type="italics"></emph>pedes<emph.end type="italics"></emph.end>; </s>
					<s id="N1871E">hinc <lb></lb>tenui nexu partes aëris copulantur; </s>
					<s id="N18724">partes verò aquæ firmiori; </s>
					<s id="N18728">hinc aër <lb></lb>minùs reſiſtit etiam motibus violentis; </s>
					<s id="N1872E">hinc vix poteſt quiſpiam in aqua <lb></lb>currere propter maiorem aquæ reſiſtentiam; </s>
					<s id="N18734">hinc poteſt dici quota parte <lb></lb>firmior ſit nexus vnius corporis quàm alterius; </s>
					<s id="N1873A">hinc non tantùm copu­<lb></lb>lantur partes metu vacui; </s>
					<s id="N18740">alioquin æquè reſiſterent partes aëris, ac par­<lb></lb>tes aquæ ratione nexus; </s>
					<s id="N18746">hinc videntur guttulæ illæ ſphericæ inuolui te­<lb></lb>nui quaſi membranula, ſeu ſuperficie, cuius analogiam videmus in aqua <pb pagenum="123" xlink:href="026/01/155.jpg"></pb>feruente; </s>
					<s id="N18752">in bullis, quæ ex guttis pluuiæ reſilientibus naſci videntur; </s>
					<s id="N18756">in <lb></lb>bullis etiam illis ſaponariis, quas leui calamo pueri inter ludendum in­<lb></lb>flant; </s>
					<s id="N1875E">hinc ex minimo ferè contactu guttula ſpargitur, niſi fortè cum <lb></lb>multo aſperſa puluere cruſtam quamdam induit ſolidiorem; </s>
					<s id="N18764">ſic bullæ il­<lb></lb>læ ad minimum etiam contactum diſſipantur; </s>
					<s id="N1876A">hinc ipſa ſuperficies <lb></lb>aquæ plus videtur reſiſtere quod multis experimentis comprobatur; </s>
					<s id="N18770">ſed <lb></lb>illo maximè, quo videmus findi à remo cum quodam quaſi ſtridulo cre­<lb></lb>pitu reſiſtentiæ maioris teſte; </s>
					<s id="N18778">immò cum ab ipſa naui quaſi ſulcatur, <lb></lb>idem ſtridor auditur, maximè in iis tractibus; </s>
					<s id="N1877E">in quibus nullis fluctibus <lb></lb>agitata læuigatiſſimam faciem præfert; </s>
					<s id="N18784">habes analogiam in illa cruſta, <lb></lb>quæ concreſcit in ſuperficie liquorum, ſed præſertim oſſarum: </s>
					<s id="N1878A">adde quod <lb></lb>aër paulò compreſſior vndique guttulam premens æquali niſu eam miri­<lb></lb>ficè tornat: </s>
					<s id="N18792">hæc tantùm tumultuatim congeſta alibi fusè pertractabi­<lb></lb>mus, &amp; ex ſimpliciſſimis principiis demonſtrabimus; plura hîc de graui­<lb></lb>tate crant dicenda, &amp; de grauitatione, quæ tantùm indicaſſe ſufficiat, vt <lb></lb>deinde Tomo quinto fusè explicentur. </s>
				</p>
				<p id="N1879C" type="main">
					<s id="N1879E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 101.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N187AA" type="main">
					<s id="N187AC"><emph type="italics"></emph>Non reſistit medium propter compreſſionem partium inferiorum, quas nullo <lb></lb>modo comprimi neceſſe eſt, vel inſenſibiliter<emph.end type="italics"></emph.end>; </s>
					<s id="N187B7">cum enim tantus relinquatur <lb></lb>locus retrò, quantus acquiritur antè, nulla opus eſt compreſſione; </s>
					<s id="N187BD">ſed <lb></lb>partes à fronte pulſæ factâ circuitione retrorſum eunt, non certè tramite <lb></lb>recto; </s>
					<s id="N187C5">ſi enim frons ipſius lata ſit, haud dubiè partes pulſæ alias pellunt, <lb></lb>&amp; hæ viciſſim alias longo circuitu, vt patet experientia; nulla tamen, vel <lb></lb>modica fieri videtur compreſſio. </s>
				</p>
				<p id="N187CD" type="main">
					<s id="N187CF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 102.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N187DB" type="main">
					<s id="N187DD"><emph type="italics"></emph>Hinc quo ſunt plures partes diuidendæ, quæ antè uniebantur, maior eſt reſi­<lb></lb>ſtentia<emph.end type="italics"></emph.end>; </s>
					<s id="N187E8">igitur maiore vi opus eſt, igitur maiore grauitate; </s>
					<s id="N187EC">ſed in medio <lb></lb>denſiore ab eodem mobili plures ſeparantur quàm in rariore; </s>
					<s id="N187F2">quia ſci­<lb></lb>licet corpus denſum plures habet ſub minori extenſione, &amp; rarum è con­<lb></lb>trario, vt videbimus ſuo loco; </s>
					<s id="N187FA">igitur in medio denſiore idem mobile ma­<lb></lb>jorem reſiſtentiam inuenit, quàm in rariore; </s>
					<s id="N18800">licèt vtriuſque partes <lb></lb>æquali nexu ſeu fibula copulentur; </s>
					<s id="N18806">quia ſcilicet plures ſunt diuidendæ <lb></lb>in denſiore; </s>
					<s id="N1880C">quia plures ſcilicet in æquali ſpatio occurrunt, quàm in ra­<lb></lb>riore; igitur maiore vi grauitatis opus eſt. </s>
				</p>
				<p id="N18812" type="main">
					<s id="N18814"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 103.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18820" type="main">
					<s id="N18822"><emph type="italics"></emph>Hinc medium poteſt comparari cum alio in<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>capitibus<emph.end type="italics"></emph.end>; </s>
					<s id="N18831">Primum eſt in <lb></lb>grauitate, vel denſitate, nam reuerâ ex maiori denſitate maiorem gra­<lb></lb>uitatem reducimus; </s>
					<s id="N18839">Secundum eſt in maiori, vel minori partium nexu, <lb></lb>ex quo 4. ſequuntur combinationes 2.mediorum; </s>
					<s id="N1883F">nam vel ſunt eiuſdem <lb></lb>grauitatis, &amp; mollitiei; </s>
					<s id="N18845">vel eiuſdem grauitatis &amp; diuerſæ mollitiei; </s>
					<s id="N18849">vel <lb></lb>eiuſdem mollitiei, &amp; diuerſæ grauitatis; </s>
					<s id="N1884F">vel diuerſæ grauitatis, &amp; eiuſ­<lb></lb>dem mollitiei; </s>
					<s id="N18855">mollius autem illud appello, cuius partes laxiori nexu <lb></lb>copulantur; </s>
					<s id="N1885B">porrò 4. iſtæ combinationes ſupponunt <expan abbr="idẽ">idem</expan> mobile <expan abbr="invtroq;">in vtroque</expan> <lb></lb>medio; </s>
					<s id="N18869">ſi ſit prima combinatio, motus eſt æqualis in vtroque; </s>
					<s id="N1886D">ſi ſecunda <pb pagenum="124" xlink:href="026/01/156.jpg"></pb>maior eſt in molliori; </s>
					<s id="N18876">ſi tertia maior in grauiori; </s>
					<s id="N1887A">ſi verò quarta ſubdi­<lb></lb>uidi poteſt in duas; </s>
					<s id="N18880">nam vel grauius eſt conjunctum cum maiori molli­<lb></lb>tie, vel leuius; </s>
					<s id="N18886">ſi leuius, haud dubiè maior eſt motus in leuiore; </s>
					<s id="N1888A">ſi gra­<lb></lb>uius &amp; mollities compenſet grauitatem, id eſt, ſi vt ſe habet grauitas gra­<lb></lb>uioris ad leuitatem leuioris; </s>
					<s id="N18892">ita ſe habet mollities illius ad mollitiem <lb></lb>huius, æqualis eſt in vtroque; ſi ſecus, pro rata; </s>
					<s id="N18898">hinc poteſt eſſe æqualis <lb></lb>motus in grauiore &amp; leuiore medio, &amp; in æquè graui poteſt eſſe maior <lb></lb>in grauiore; &amp; minor; </s>
					<s id="N188A0">maior quidem, ſi maior ſit ratio mollitiei gra­<lb></lb>uioris ad mollitiem leuioris, quàm grauitatis ad grauitatem; </s>
					<s id="N188A6">minor ve­<lb></lb>rò, ſi maior ſit ratio grauitatis ad grauitatem, quàm mollitiei ad molli­<lb></lb>tiem; </s>
					<s id="N188AE">æqualis denique ſi æqualis ratio; </s>
					<s id="N188B2">&amp; his regulis cuncta facilè ex­<lb></lb>plicari poſſunt; </s>
					<s id="N188B8">hîc porrò ſuppono idem mobile, quod per vtrumque me­<lb></lb>dium deſcendere poſſit, id eſt, quod ſit vtroque grauius, medium autem <lb></lb>appello illud, per quod mobile grauius per ſe deſcendit; dixi per ſe quia <lb></lb>nonnunquam accidit, vt vel ratione figuræ, vel alterius impedimenti non <lb></lb>deſcendat. </s>
				</p>
				<p id="N188C4" type="main">
					<s id="N188C6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 104.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N188D2" type="main">
					<s id="N188D4"><emph type="italics"></emph>Sunt tres combinationes mobilis cum medio<emph.end type="italics"></emph.end>; </s>
					<s id="N188DD">prima, ſi ſit idem mobile <lb></lb>cum diuerſis mediis; </s>
					<s id="N188E3">ſecunda, ſi idem medium cum diuerſis mobilibus; </s>
					<s id="N188E7"><lb></lb>tertia ſi diuerſa mobïlia cum diuerſis mediis; </s>
					<s id="N188EC">de primâ actum eſt iam <lb></lb>ſuprà; ſecunda ſubeſt 4. combinationibus. </s>
					<s id="N188F2">Prima ſi mobilia ſint eiuſ­<lb></lb>dem materiæ, ſed diuerſæ figuræ; Secunda eiuſdem figuræ &amp; diuerſæ <lb></lb>materiæ. </s>
					<s id="N188FA">Quarta diuerſæ materiæ &amp; figuræ; </s>
					<s id="N188FE">ſi prima &amp; ſecunda, vel ſunt <lb></lb>figuræ æquales, vel inæquales; </s>
					<s id="N18904">ſi primum ſunt eiuſdem grauitatis; ſi ſe­<lb></lb>cundum diuerſæ; </s>
					<s id="N1890A">quippe figuræ ſimiles poſſunt eſſe æquales, vel inæ­<lb></lb>quales; </s>
					<s id="N18910">&amp; figuræ æquales poſſunt eſſe ſimiles, vel diſſimiles; </s>
					<s id="N18914">ſi ſit tertia <lb></lb>combinatio, in qua ſint eiuſdem figuræ, &amp; diuerſæ materiæ, diuerſæ in­<lb></lb>quam in grauitate; </s>
					<s id="N1891C">ſi figuræ ſunt æquales, ſemper eſt diuerſa grauitas; </s>
					<s id="N18920">ſi <lb></lb>inæquales poteſt eſſe vel eadem, vel tertia; </s>
					<s id="N18926">in quarta combinatione di­<lb></lb>uerſa compenſatio fieri poteſt; idem dicendum eſt de tertia combinatio­<lb></lb>ne diuerſorum mobilium, &amp; mediorum, de quibus omnibus ſeorſim iam <lb></lb>dicemus. </s>
				</p>
				<p id="N18930" type="main">
					<s id="N18932"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 105.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1893E" type="main">
					<s id="N18940"><emph type="italics"></emph>Si mobilia duo eiuſdem materiæ, figuræ, &amp; grauitatis in eodem medio de­<lb></lb>ſcendant, æquali motu feruntur<emph.end type="italics"></emph.end> dem. </s>
					<s id="N1894A">vbi eſt eadem proportio cauſæ &amp; reſi­<lb></lb>ſtentiæ ibi eſt idem effectus, per Ax. 5. ſed in hoc caſu eadem eſt illa pro­<lb></lb>portio; </s>
					<s id="N18952">nam eſt æqualis cauſa, ſcilicet grauitas; </s>
					<s id="N18956">idem medium æqualiter <lb></lb>vtrique reſiſtens, cum non plures medij partes reſiſtant vni, quam alteri; <lb></lb>igitur æqualis proportio. </s>
				</p>
				<p id="N1895E" type="main">
					<s id="N18960"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 106.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1896C" type="main">
					<s id="N1896E"><emph type="italics"></emph>Maior eſt reſistentia eiuſdem medij ratione ſcilicet partium, cum plures <lb></lb>eius partes reſistunt quàm cum pauciores<emph.end type="italics"></emph.end>; patet, quia maior effectus re­<lb></lb>ſpondet pluribus partibus cauſæ per Ax.13.l.1. num.2. </s>
				</p>
				<pb pagenum="125" xlink:href="026/01/157.jpg"></pb>
				<p id="N1897F" type="main">
					<s id="N18981"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 107.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1898D" type="main">
					<s id="N1898F"><emph type="italics"></emph>Plures partes reſistunt, quando plures pelluntur à mobili deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N18998">quip­<lb></lb>pe in tantum reſiſtunt, in quantum ab aliis ſeparantur; </s>
					<s id="N1899E">atqui in tantum <lb></lb>ſeparantur, in quantum amouentur è ſuo loco; </s>
					<s id="N189A4">ſed ideo amouentur è <lb></lb>ſuo loco, in quantum pelluntur; </s>
					<s id="N189AA">igitur cum plures pelluntur tunc plures <lb></lb>reſiſtunt; igitur tunc maior eſt reſiſtentia. </s>
				</p>
				<p id="N189B0" type="main">
					<s id="N189B2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 108.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N189BE" type="main">
					<s id="N189C0"><emph type="italics"></emph>Plures pelluntur à maiori ſuperficie, quàm à minori, quæ tendit deorſum <lb></lb>parallela horizonti.<emph.end type="italics"></emph.end> v.g. à ſuperficie cubi maioris, quàm minoris; quippe <lb></lb>tot pelluntur quot reſpondent primæ faciei, ſeu primo plano, quod eſt in <lb></lb>fronte. </s>
				</p>
				<p id="N189D1" type="main">
					<s id="N189D3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 109.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N189DF" type="main">
					<s id="N189E1"><emph type="italics"></emph>Si diuidatur cubus in cubos minores, ratio ſuperficierum erit duplicat a la­<lb></lb>terum, &amp; ratio ſolidorum triplicata,<emph.end type="italics"></emph.end> conſtat ex Geometria, ſit enim cubus </s>
				</p>
				<p id="N189EB" type="main">
					<s id="N189ED"><arrow.to.target n="note2"></arrow.to.target><lb></lb>GK, nam in gratiam eorum qui Geometriam ignorant hoc ipſum ocu­<lb></lb>lis ſubiiciendum eſſe videtur; diuidantur 6. eius facies in 4. quadrata <lb></lb>æqualia v. g. facies AI in quad. </s>
					<s id="N189FD">AE. EC. EG. EI. idem fiat in aliis <lb></lb>5. faciebus, quarum duæ hîc tantum apparent; ſcilicet AK. KL; </s>
					<s id="N18A03">ſed <lb></lb>tribus aliis parallelis; </s>
					<s id="N18A09">his tribus cædem diuiſiones reſpondent; </s>
					<s id="N18A0D">haud <lb></lb>dubiè erunt cubi minores, quorum latus ſit æquale AB, &amp; quælibet fa­<lb></lb>cies æqualis quadrato AE, ſed facies maior AI, eſt quadrupla minoris <lb></lb>AE, ergo AI eſt ad AE vt quadratum lateris AG ad quadratum lateris <lb></lb>AD; ſed hæc eſt ratio duplicata laterum 1. 2. 4. ſimiliter cubus maior <lb></lb>GK eſt octuplum minoris DN, igitur vt cubus lateris AG ad cubum <lb></lb>lateris AD. ſed hæc eſt ratio triplicata. </s>
					<s id="N18A1D">1.2.4.8. </s>
				</p>
				<p id="N18A20" type="margin">
					<s id="N18A22"><margin.target id="note2"></margin.target>a <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end>26 <lb></lb><emph type="italics"></emph>Tab.<emph.end type="italics"></emph.end>1.</s>
				</p>
				<p id="N18A35" type="main">
					<s id="N18A37"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 110.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18A43" type="main">
					<s id="N18A45"><emph type="italics"></emph>Hinc plùs minuitur ſolidum in diuerſione cubi quam facies, &amp; plùs facies <lb></lb>quàm latus<emph.end type="italics"></emph.end>; </s>
					<s id="N18A50">patet ex dictis, nam latus minoris cubi eſt tantùm ſubdu­<lb></lb>plum lateris maioris, &amp; facies ſubquadrupla; ſolidum verò ſub­<lb></lb>octuplum. </s>
				</p>
				<p id="N18A58" type="main">
					<s id="N18A5A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 111.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18A66" type="main">
					<s id="N18A68"><emph type="italics"></emph>Hinc plùs minuitur grauitas, quàm reſiſtentia minoris cubi<emph.end type="italics"></emph.end>; </s>
					<s id="N18A71">quia grauitas <lb></lb>reſpondet ſolido, &amp; reſiſtentia primę faciei; </s>
					<s id="N18A77">reſiſtentia <expan abbr="inquā">inquam</expan> ratione par­<lb></lb>tium medij; </s>
					<s id="N18A81">ſed ſolidum plus minuitur quàm facies, vt dictum eſt; </s>
					<s id="N18A85">igitur <lb></lb>plus minuitur grauitas, quæ eſt cauſa virium quàm hæc reſiſtentia; ergo <lb></lb>decreſcunt vires in maiore proportione quàm hæc reſiſtentia, quod be­<lb></lb>nè obſeruauit Galileus in dìalogis. </s>
				</p>
				<p id="N18A8F" type="main">
					<s id="N18A91">Hinc concludit Galileus duos cubos eiuſdem materiæ, ſed inæquales <lb></lb>deſcendere inæquali motu; </s>
					<s id="N18A97">maiorem ſcilicet velociùs minori; </s>
					<s id="N18A9B">demon­<lb></lb>ſtrare videtur, quia maior habet maiorem proportionem virium ad re­<lb></lb>ſiſtentiam, quàm minor; igitur maiorem habet effectum per Ax. 5. igi­<lb></lb>tur maiorem, &amp; velociorem motum. </s>
				</p>
				<p id="N18AA5" type="main">
					<s id="N18AA7">Scio non deeſſe multos viros doctos qui acriter in hanc ſententiam <pb pagenum="126" xlink:href="026/01/158.jpg"></pb>inſurgant: </s>
					<s id="N18AB0">Obiicient fortè primò, experientiam eſſe contrariam; </s>
					<s id="N18AB4">ſi enim <lb></lb>accipiantur duo cubi maior, &amp; minor eiuſdem materiæ, &amp; dimittantur <lb></lb>ex eadem altitudine eodem prorſus momento terram ferient; </s>
					<s id="N18ABC">Reſponde­<lb></lb>ri poteſt momentum illud ſenſu percipi non poſſe; ſi enim dicam ma­<lb></lb>iorem tangere terram 1000. inſtantibus ante minorem, an fortè ſenſu <lb></lb>hoc percipies, viſu ſcilicet vel auditu? </s>
					<s id="N18AC6">igitur in maxima altitudine hæc <lb></lb>ſpatiorum inæqualitas, &amp; temporum ſenſu percipi poſſet, quæ in minori <lb></lb>ſub ſenſum non cadit: præterea accipe pulueris granulum eiuſdem ma­<lb></lb>teriæ, tuncque etiam ſenſibilem motuum differentiam videbîs, atqui <lb></lb>eſt eadem ratio de omni minore. </s>
				</p>
				<p id="N18AD2" type="main">
					<s id="N18AD4">Secundò obiicient, ſi ſuperponatur cubus minor maiori in ſuo motu <lb></lb>nunquam ſeparantur; igitur æquali motu deſcendunt. </s>
					<s id="N18ADA">Reſp. videri po­<lb></lb>teſt equidem æquali motu deſcendere quia ſunt veluti partes eiuſdem <lb></lb>corporis, &amp; grauitant grauitatione communi, neque minor habet ſingu­<lb></lb>larem reſiſtentiam ſuperandam; </s>
					<s id="N18AE4">immò ſi ſuperponatur minor maiori, <lb></lb>vel maior minori, motus eſt velocior quàm eſſet ſolius maioris; </s>
					<s id="N18AEA">quia <lb></lb>cum non ſit maior reſiſtentia, maiores illi vires opponuntur; igitur fa­<lb></lb>ciliùs ſuperatur. </s>
				</p>
				<p id="N18AF2" type="main">
					<s id="N18AF4">Tertiò obiicient; </s>
					<s id="N18AF7">eſt eadem ſpecie grauitas; </s>
					<s id="N18AFB">igitur eadem grauitatio, <lb></lb>idemque motus deorſum; </s>
					<s id="N18B01">Reſponderi poſſet concedendo antecedens, <lb></lb>vnde in vacuo omnia grauia æquè velociter deſcenderent, ſi in eo mo­<lb></lb>tus eſſet; at verò altera duarum cauſarum eiuſdem ſpeciei, quæ habet mi­<lb></lb>norem proportionem actiuitatis ad reſiſtentiam, profectò minùs agit, <lb></lb>quod certum eſt. </s>
				</p>
				<p id="N18B0D" type="main">
					<s id="N18B0F">Quartò obij:igitur motus poſſet eſſe velocior, &amp; velocior in infini­<lb></lb>tum; </s>
					<s id="N18B15">ſi enim maior cubus deſcenderet velociùs; </s>
					<s id="N18B19">igitur ſi detur maior ad­<lb></lb>huc velociùs, atque ita deinceps: </s>
					<s id="N18B1F">Reſp. inanem prorſus eſſe difficulta­<lb></lb>tem; </s>
					<s id="N18B25">quia cubus ille quantumuis maximus in vacuo deſcendit velociùs <lb></lb>quàm in aliquo medio v.g.in aëre, igitur nunquam augmentum veloci­<lb></lb>tatis infinitum eſt; quippe inter duos gradus velocitatis infiniti ſunt <lb></lb>poſſibiles. </s>
					<s id="N18B2F">v. g. ſit velocitas, quam habet in vacuo vt 2. illa verò quàm <lb></lb>habet in aëre vt 1. ſi creſcat velocitas iuxta has minutias ſingulis inſtan­<lb></lb>tibus 1/2 1/4 1/8 (1/16) (1/32), atque ita deinceps; quàm porrò multæ ſunt huiuſmodi <lb></lb>progreſſiones 1/3 1/6 (1/12) (1/24) &amp;c. </s>
					<s id="N18B3D">igitur obiectiones illæ non euertunt Gali­<lb></lb>lei ſententiam. </s>
				</p>
				<p id="N18B42" type="main">
					<s id="N18B44">Inde idem Galileus oſtendere videtur cur atomi materiæ etiam gra­<lb></lb>uiſſimæ, ſeu granula pulueris motu tardiſſimo deſcendant in aëre vel in <lb></lb>aqua; quia ſcilicet per illam diuiſionem ita imminutæ ſunt vires graui­<lb></lb>tatis, vt iam reſiſtentiam medij ſuperare non poſſint. </s>
				</p>
				<p id="N18B4E" type="main">
					<s id="N18B50">Sed videtur eſſe grauiſſima difficultas, ſint enim duo cubi, maior B <lb></lb>F, minor GM, &amp; vterque innatet medio liquido duplo grauiori; </s>
					<s id="N18B56">certè ex­<lb></lb>tabit maior toto rectangulo CA æquali CF, &amp; minor toto rectangulo <lb></lb>KH æquali KM; </s>
					<s id="N18B5E">igitur eſt eadem proportio grauitatis maioris ad reſi­<lb></lb>ſtentiam medij in grauitatione, quæ eſt minoris; igitur &amp; in motu. </s>
				</p>
				<p id="N18B64" type="main">
					<s id="N18B66">Reſponderi poteſt eſſe maximam diſparitatem inter grauitationem, &amp; <pb pagenum="127" xlink:href="026/01/159.jpg"></pb>motum; </s>
					<s id="N18B6F">ſit enim cubus BD qui deſcendat per totam AH; </s>
					<s id="N18B73">haud dubiè <lb></lb>cum ſpatium DI, contineat 3. cubos medij æquales DB, eos debet remo­<lb></lb>uere in ſuo deſcenſu; </s>
					<s id="N18B7B">ſit autem cubus BG; </s>
					<s id="N18B7F">haud dubiè, cum ſit eadem pro­<lb></lb>portio cubi AE ad cubum medij DM, quæ eſt cubi BG ad cubum me­<lb></lb>dij FL, eodem tempore vterque cubum medij ſuppoſiti è ſuo loco extru­<lb></lb>det; igitur eo tempore, quo AE expellet 3. DI, FL extrudet 3. EO, ergo <lb></lb>æquabili tempore inæquale ſpatium percurrunt. </s>
				</p>
				<p id="N18B8B" type="main">
					<s id="N18B8D">Dices ergo ſpatia ſunt vt latera: </s>
					<s id="N18B91">Reſponderi poteſt hoc reuerâ per ſe <lb></lb>eſſe debere; </s>
					<s id="N18B97">ſed quia cubus DM vt extrudatur, maiorem debet facere cir­<lb></lb>cuitionem, vt à fronte retrò eat, velociori motu extrudi debet; </s>
					<s id="N18B9D">igitur vi­<lb></lb>res ſuas in eo conſumit maiori ex parte cubus AE; hinc compenſatio eſſe <lb></lb>videtur. </s>
				</p>
				<p id="N18BA5" type="main">
					<s id="N18BA7">Vt ſolui poſſit præſens difficultas, quæ cettè maxima eſt, totam rem <lb></lb>iſtam paulò fuſiùs eſſe explicandam iudico. </s>
					<s id="N18BAC">Primò itaque certum eſt <lb></lb>partes medij, quæ prius in fronte erant, retroire; </s>
					<s id="N18BB2">hoc ipſum videmus in <lb></lb>naui quæ ſulcat aquas, hoc ipſum accidit in omni corpore natante etiam <lb></lb>immobili, quippe partes aquæ retinentur ab illa membranula, de qua ſu­<lb></lb>prà; </s>
					<s id="N18BBC">ſic enim ſæpè aſſurgunt, &amp; intumeſcunt ſupra labra vaſis; </s>
					<s id="N18BC0">cur verò <lb></lb>continui penè circulares limbi dilatentur: </s>
					<s id="N18BC6">Reſp. nullo flante vento <lb></lb>vix aliquem circulum huiuſmodi in ſuperficie aquæ apparere à fronte, <lb></lb>ſed tantùm à tergo, &amp; lateribus, quaſi ad inſtar pyramidis; ſed de his aliàs <lb></lb>fusè. </s>
				</p>
				<p id="N18BD0" type="main">
					<s id="N18BD2">Secundò certum eſt numerum partium, quas impellit maior cubus A <lb></lb>E; </s>
					<s id="N18BD8">eſſe quadruplum numeri partium, quas impellit cubus BG: </s>
					<s id="N18BDC">ſint autem <lb></lb>v.g.8. partes reſiſtentes cubo maiori, ſunt duæ reſiſtentes cubo minoris; <lb></lb>ſed vires cubi maioris ſunt ad vires cubi minoris vt 8. ad 1. igitur vires <lb></lb>vt 8. ſuperabunt faciliùs reſiſtentiam vt 8. quam vires vt 1. reſiſtentiam <lb></lb>vt 2.vnde duplò velociùs moueretur, niſi aër duplò velociori motu amo­<lb></lb>uendus eſſet, quod vt clarius explicetur;</s>
				</p>
				<p id="N18BEA" type="main">
					<s id="N18BEC">Sit cubus maior AF octuplus cubi GI, vt iam dictum eſt; </s>
					<s id="N18BF0">haud <lb></lb>dubiè aër qui ſubſtat cubo AF eſt quadruplus aëris, qui ſubſtat cubo GI, <lb></lb>vnde ſi vires cubi AF eſſent quadruplæ virium cubi GI, eſſet æqualis <lb></lb>proportio in vtroque virium, &amp; reſiſtentiæ; </s>
					<s id="N18BFA">ſed ſunt octuplæ; </s>
					<s id="N18BFE">igitur faci­<lb></lb>liùs vincetur reſiſtentia; </s>
					<s id="N18C04">igitur amouebitur aër faciliùs; ſit autem aër <lb></lb>expreſſus in globulis EFB, &amp;c. </s>
					<s id="N18C0A">cuius ſuperficies cum relinquatur retrò <lb></lb>verſus AB, &amp; occupetur illa quæ eſt in fronte EF; </s>
					<s id="N18C10">haud dubiè partes <lb></lb>hinc inde diuiduntur in D, &amp; ſegmentum NB tranſit in locum relicti <lb></lb>loci BC, FN tranſit in NB, &amp; DF, in FN; </s>
					<s id="N18C18">idem dico de ſegmentis oppo­<lb></lb>ſitis; </s>
					<s id="N18C1E">idem prorſus dico de minori globo; </s>
					<s id="N18C22">nam MH tranſit in HQ, &amp; H <lb></lb>Q in QG, &amp; QG in GL, idem dico de ſegmentis oppoſitis; </s>
					<s id="N18C28">igitur hæc <lb></lb>eſt circuitio partium medij, quàm ſuprà indicauimus; hinc aër, qui amo­<lb></lb>uetur à corpore graui deſcendente moueri debet neceſſariò velociùs <lb></lb>quàm ipſum corpus graue, quod deſcendit. </s>
				</p>
				<p id="N18C32" type="main">
					<s id="N18C34">In hoc porrò obſerua ſegmentum MH moueri tardiùs quàm DF; </s>
					<s id="N18C38">quia <lb></lb>conficit ſubduplum ſpatium, eo tempore, quo DF conficit duplum; </s>
					<s id="N18C3E"><pb pagenum="128" xlink:href="026/01/160.jpg"></pb>nam DF &amp; FN ſunt duplæ MH &amp; &amp; HQ igitur dupla vi motrice opus <lb></lb>eſt; </s>
					<s id="N18C48">ſed vires cubi AF ſunt ad vires cubi GI, vt 8. ad 1. partes verò aëris, <lb></lb>quas impellit AF, ſunt ad partes aëris, quas impellit GI, vt 4.ad 1. igitur <lb></lb>ſi partes aëris mouerentur æquali motu cum ipſis cubis, à quibus mo­<lb></lb>uentur; </s>
					<s id="N18C52">certè maior moueretur motu velociori; </s>
					<s id="N18C56">vt autem moueantur par­<lb></lb>tes DF duplò velociore motu, quàm partes MH; </s>
					<s id="N18C5C">debent vires, quæ mo­<lb></lb>nent DF, eſſe in ratione dupla ad illas, quæ mouent MH, id eſt eo tem­<lb></lb>pore, quo vires vt 8.mouebunt mobile vt 4. motu vt 2. vires vt 1.moue­<lb></lb>bunt mobile vt 1. motu vt 1. licèt enim ſuperficies aëris EF moueatur <lb></lb>deorſum; attamen ab alio aëere inferiore ita repertitur, vt ſurſum verſus <lb></lb>FN repellatur. </s>
				</p>
				<p id="N18C6A" type="main">
					<s id="N18C6C">Equidem tota ſuperficies aëris DF, cum pluribus partibus conſtet, <lb></lb>non poteſt ſimul tranſire in FN; </s>
					<s id="N18C72">quia pars D antequam perueniat ad F <lb></lb>tranſit per medium DF; igitur ſucceſſiuè per mea ad illud ſpatium DF, <lb></lb>quo tempore quieſceret globus AF, quod ridiculum eſt. </s>
				</p>
				<p id="N18C7A" type="main">
					<s id="N18C7C">Quare fit neceſſariò aliqua circuitio, &amp; partium aëris commixtio, <lb></lb>ſeu conflictus; </s>
					<s id="N18C82">ita vt retroeant pulſæ prius &amp; repercuſſæ; </s>
					<s id="N18C86">non quidem <lb></lb>tramite recto, ſed cum aliqua circuitione; </s>
					<s id="N18C8C">quod certè facilè concipi po­<lb></lb>teſt, quæ circuitio eò maior eſt, quo latera cuborum ſunt maiora; ita­<lb></lb>que cum hæc ſatis fusè videantur eſſe explicata, ſit. </s>
				</p>
				<p id="N18C94" type="main">
					<s id="N18C96"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 112.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18CA2" type="main">
					<s id="N18CA4"><emph type="italics"></emph>Duo cubi eiuſde<emph.end type="italics"></emph.end>m <emph type="italics"></emph>materiæ, &amp; diuerſæ grauitatis æquali motu per ſe deſ­<lb></lb>cendunt<emph.end type="italics"></emph.end>; </s>
					<s id="N18CB5">probatur, quia licèt ſit maior proportio actiuitatis minus ad <lb></lb>ſuam reſiſtentiam, quàm alterius; </s>
					<s id="N18CBB">illud tamen compenſatur; </s>
					<s id="N18CBF">eóque par­<lb></lb>tes aëris velociùs moueri debeant iuxta rationem laterum, vt patet ex <lb></lb>dictis; </s>
					<s id="N18CC7">vnde neceſſariò ſequitur motus æqualis in vtroque cubo; </s>
					<s id="N18CCB">igitur <lb></lb>licèt maioris cubi vires habeant maiorem proportionem ad molem, <lb></lb>quæ præcipuum illius motus retardat; </s>
					<s id="N18CD3">tum tamen aër, qui reſiſtit maiori <lb></lb>cubo debeat amoueri, vt dictum eſt velociore motu quam aër, qui reſi­<lb></lb>ſtit minori, ſitque eadem proportio reſiſtentiæ ratione motus minoris <lb></lb>ad maiorem, quæ eſt ratione molis maioris ad minorem; </s>
					<s id="N18CDD">certè ratio <lb></lb>compoſita vtriuſquè erit eadem in vtroque cubo; </s>
					<s id="N18CE3">igitur æquè velociter <lb></lb>vterque deſcendet: </s>
					<s id="N18CE9">hinc ſatís facilè ſoluitur ratio Galilei, quam multi <lb></lb>parum cauti pro demonſtratione venditarunt, ad aliam verò rationem, <lb></lb>quam ex minuto puluere ducere videtur, etiam facilè reſponderi poteſt; </s>
					<s id="N18CF1"><lb></lb>ideo corpuſcula illa diu fluitare in aëre, tùm quòd minimo ferè tenuis <lb></lb>auræ flatu agitentur; </s>
					<s id="N18CF8">ſic pulueris nubes medius ventus agit; </s>
					<s id="N18CFC">quis enim <lb></lb>neſcit aëris partes agitari perpetuò; </s>
					<s id="N18D02">immò &amp; aquæ inter ſe miſceri; </s>
					<s id="N18D06">igi­<lb></lb>tur ab agitationis veluti impreſſione fluitant illa corpuſcula, cum mini­<lb></lb>mus ferè impetus extrinſecus illa commouere poſſit; </s>
					<s id="N18D0E">tùm etiam quòd à <lb></lb>filamentis illis, quibus partes aëris implicantur facilè detineantur; ana­<lb></lb>logiam habes in lapillo, qui ab araneæ tela intercipitur. </s>
				</p>
				<pb pagenum="129" xlink:href="026/01/161.jpg"></pb>
				<p id="N18D1A" type="main">
					<s id="N18D1C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 113.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18D28" type="main">
					<s id="N18D2A"><emph type="italics"></emph>Duo globi eiuſdem materiæ, &amp; diuerſæ diametri deſcendunt etiam æquali <lb></lb>motu propter <expan abbr="eãdem">eandem</expan> rationem<emph.end type="italics"></emph.end>; </s>
					<s id="N18D39">immò eſt perfectior æqualitas in globis, <lb></lb>quàm in cubis; </s>
					<s id="N18D3F">quia perfectior fit circuitio, vt conſideranti patebit; <lb></lb>hinc globus eiuſdem materiæ, &amp; grauitatis cum cubo deſcendit velociùs <lb></lb>quia ſcilicet aër in deſcenſu globi faciliùs agitur retrò, vt conſtat. </s>
				</p>
				<p id="N18D47" type="main">
					<s id="N18D49"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 114.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18D55" type="main">
					<s id="N18D57"><emph type="italics"></emph>Corpus vtrimque in mucronem deſinens faciliùs adhuc deſcendit, <lb></lb>quâm globus eiuſdem materiæ<emph.end type="italics"></emph.end>; ratio eſt; </s>
					<s id="N18D62">quia breuiore circuitu partes re­<lb></lb>troeunt; </s>
					<s id="N18D68">quippe tunc maxima eſt facilitas in pellendo aëre, qui eſt à fron­<lb></lb>te mobilis, cum velociùs moueri non debet ipſo mobili; </s>
					<s id="N18D6E">atqui hoc ip­<lb></lb>ſum eſt quod accidit mobili vtrimque aucto; </s>
					<s id="N18D74">nam linea curua DBA, <lb></lb>quam percurrit deſcriptum mobile, non eſt multò longior; </s>
					<s id="N18D7A">at verò in <lb></lb>quadrato ſuperiori AF maiori eſt duplò; in circulo quidem minor dia­<lb></lb>meter ſemiperipheriæ, ſed non duplò. </s>
				</p>
				<p id="N18D82" type="main">
					<s id="N18D84"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 115.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18D90" type="main">
					<s id="N18D92"><emph type="italics"></emph>Idem corpus diuerſo motu deſcendere poteſt,<emph.end type="italics"></emph.end> v. g. parallipedum A, ſi re­<lb></lb>ctangulum BF ſit in fronte tardiùs deſcendet, quàm ſi in fronte ſit re­<lb></lb>ctangulum CE, vel rectangulum FH; </s>
					<s id="N18DA3">hinc tribus motibus diuerſis deſ­<lb></lb>cendere poteſt idem parallipedum, modò habeat ſemper alteram facie­<lb></lb>rum horizonti parallelam; </s>
					<s id="N18DAB">hinc cylindrus eiuſdem grauitatis deſcendet <lb></lb>velociùs quàm parallelipedum, vt patet ex dictis; </s>
					<s id="N18DB1">ex quibus facilè intel­<lb></lb>ligi poteſt, quænam corpora faciliùs quàm alia deſcendant; quippe illa <lb></lb>regula eſt certiſſima quàm ſuprà attulimus. </s>
					<s id="N18DB9">Porrò obſeruabis omne <lb></lb>corpus difficiliùs pelli per lineam perpendicularem quàm per obliquam; </s>
					<s id="N18DBF"><lb></lb>hinc globus pellit tantùm vnicum punctum perpendiculariter; </s>
					<s id="N18DC4">idem di­<lb></lb>co de cono; cylindrus verò vnam lineam, cubus integrum planum. </s>
				</p>
				<p id="N18DCA" type="main">
					<s id="N18DCC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 116.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18DD8" type="main">
					<s id="N18DDA"><emph type="italics"></emph>Hinc duo corpora eiuſdem grauitatis, ſed quorum alterum<emph.end type="italics"></emph.end> f<emph type="italics"></emph>aciem, quæ eſt <lb></lb>in fronte, habet maiorem, inæquali motu deſcendunt<emph.end type="italics"></emph.end>; patet ex dictis; quia in <lb></lb>vtroque ſunt æquales vires, ſed diuerſa reſiſtentia. </s>
				</p>
				<p id="N18DED" type="main">
					<s id="N18DEF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 117.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18DFB" type="main">
					<s id="N18DFD"><emph type="italics"></emph>Hinc tenues illæ ſuperficies corporum etiam materiæ grauiſſimæ, vel in <lb></lb>aëre fluitant, vel aquis innatant<emph.end type="italics"></emph.end>; ratio eſt, quia reſiſtentia ſuperat <lb></lb>vires. </s>
				</p>
				<p id="N18E0A" type="main">
					<s id="N18E0C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N18E18" type="main">
					<s id="N18E1A">Obſeruabis primam ſuperficiem aquæ habere maiorem quamdam re­<lb></lb>ſiſtentiam propter illam, quaſi membranulam, de qua ſuprà; </s>
					<s id="N18E20">vnde aſſur­<lb></lb>git quiddam lymbus in margine bracteæ ferri, vel auri innatantis; vel <lb></lb>etiam globuli paulò grauioris aquâ, igitur vt immergatur corpus debet <lb></lb>eſſe grauius totâ illâ aquâ, quæ capacitatem illam non cauam occu­<lb></lb>paret. </s>
				</p>
				<pb pagenum="130" xlink:href="026/01/162.jpg"></pb>
				<p id="N18E30" type="main">
					<s id="N18E32"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 118.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18E3E" type="main">
					<s id="N18E40"><emph type="italics"></emph>Globi æquales diuerſæ materiæ inæqualiter deſcendunt<emph.end type="italics"></emph.end>; </s>
					<s id="N18E49">quia ſcilicet alte­<lb></lb>rum eſt grauius, quod ſuppono; </s>
					<s id="N18E4F">igitur æqualis eſt reſiſtentia, &amp; vires <lb></lb>inæquales; </s>
					<s id="N18E55">igitur non eſt eadem proportio actiuitatis: &amp; reſiſtentiæ; igi­<lb></lb>tur non eſt æqualis motus per Ax.5. </s>
				</p>
				<p id="N18E5C" type="main">
					<s id="N18E5E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 119.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18E6A" type="main">
					<s id="N18E6C"><emph type="italics"></emph>Globi otiam inæquales diuerſæ materiæ inæqualiter deſcendunt<emph.end type="italics"></emph.end>; quod de­<lb></lb>monſtro; </s>
					<s id="N18E77">quia globi eiuſdem materiæ inæqualiter deſcendunt per Th. <lb></lb>113. ſed duo globi æquales diuerſæ materiæ deſcendunt inæqualiter per <lb></lb>Th.118. igitur, &amp; inæquales; quod dico de globis&#039;, dicatur de cubis, &amp; <lb></lb>aliis figuris ſimilibus. </s>
				</p>
				<p id="N18E82" type="main">
					<s id="N18E84"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 120.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18E90" type="main">
					<s id="N18E92"><emph type="italics"></emph>Globus materiæ leuioris poteſt deſcendere velociori motu quam parallelipe­<lb></lb>dum grauioris<emph.end type="italics"></emph.end>; </s>
					<s id="N18E9D">conſtat experientia; ratio eſt, quia cum globus ferreus deſ­<lb></lb>cendat velociùs, quàm ligneus per Th. 118. in data ratione, putà (1/100) <lb></lb>haud dubiè bractea ferri non modo (1/100) tardiùs deſcendet, verùm etiam <lb></lb>(20/100) in quo non eſt difficultas. </s>
				</p>
				<p id="N18EA7" type="main">
					<s id="N18EA9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 121.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18EB5" type="main">
					<s id="N18EB7"><emph type="italics"></emph>Hinc ſi mutetur figura poſſunt grauia diuerſæ materiæ ita deſcendere, vn <lb></lb>vel grauius, vel leuius, vel grauioris materiæ, vel leuioris velociùs deſcendat<emph.end type="italics"></emph.end>; <lb></lb>vt conſtat ex regulis præſcriptis. </s>
				</p>
				<p id="N18EC4" type="main">
					<s id="N18EC6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 122.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18ED2" type="main">
					<s id="N18ED4"><emph type="italics"></emph>Globi æquales diuerſæ materiæ,<emph.end type="italics"></emph.end> v. g. ligneus, &amp; plumbeus deſcendunt <lb></lb>inæqualiter iuxta proportionem grauitatis, &amp; reſiſtentiæ medij compa­<lb></lb>ratæ cum vtroque, v.g. plumbo detrahitur (1/4800); ligno verò (8/300) v. g. ſi <lb></lb>grauitas ligni ſit ad grauitatem aëris vt 300.ad 1. &amp; plumbi vt 4800. ad <lb></lb>1. ſit enim altitudo 33. pedum 4. digit. </s>
					<s id="N18EEF">reducantur in digitos erunt 400. <lb></lb>in lineas 4800. igitur detrahetur vna linea ſpatij plumbeo globo; </s>
					<s id="N18EF5">ligneo <lb></lb>verò vnus digitus cum 4. lineis; ſed quis hoc obſeruet? </s>
				</p>
				<p id="N18EFB" type="main">
					<s id="N18EFD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 123.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18F09" type="main">
					<s id="N18F0B"><emph type="italics"></emph>Corpus graue ſpongioſum longè tardiùs deſcendit<emph.end type="italics"></emph.end>; </s>
					<s id="N18F14">quia aër in perexigua <lb></lb>illa foramina intenſus frangitur, reſilit, ac proinde motum impedit; talis <lb></lb>eſt medulla ſambuci, ſpongia, ſtupa, &amp;c. </s>
					<s id="N18F1C">immò aſperum corpus tardiùs <lb></lb>deſcendit, quòd ſcilicet aër ab aſperioribus illis ſalebris reſiliens mo­<lb></lb>tum retardet, hinc ſibilus ille auditur &amp;c. </s>
				</p>
				<p id="N18F23" type="main">
					<s id="N18F25"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N18F31" type="main">
					<s id="N18F33">Ex his conſtat quid dicendum ſit de motu corporum grauium in <lb></lb>medio, ſiue ſint eiuſdem materiæ, &amp; ſimilis figuræ, maioris vel minoris, <lb></lb>vel æqualis; </s>
					<s id="N18F3B">tunc enim deſcendunt æqualiter contra Galileum, ſiue <lb></lb>ſint diuerſæ materiæ, &amp; ſimilis figuræ, æqualis, vel inæqualis, <pb pagenum="131" xlink:href="026/01/163.jpg"></pb>tunc enim deſcendunt inæqualiter, ſiue diuerſæ materiæ &amp; diuerſæ fi­<lb></lb>guræ; </s>
					<s id="N18F48">tunc enim deſcendunt modò æqualiter, modò inæqualiter; </s>
					<s id="N18F4C">æquali­<lb></lb>ter certè, cum figura compenſat materiam; </s>
					<s id="N18F52">cum verò non compenſat, <lb></lb>inæqualiter pro rata; </s>
					<s id="N18F58">denique ſi comparentur duo corpora cum diuerſis <lb></lb>mediis; primo inuenienda eſt proportio motuum vtriuſque in eodem <lb></lb>tùm ſingulorum in diuerſis mediis, vt ſuprà dictum eſt. </s>
				</p>
				<p id="N18F60" type="main">
					<s id="N18F62"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 124.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18F6E" type="main">
					<s id="N18F70"><emph type="italics"></emph>In modico vacuo omnia æquè velociter deſcenderent<emph.end type="italics"></emph.end>: </s>
					<s id="N18F79">Probatur, quia tota <lb></lb>diuerſitas vel inæqualitas mediorum petitur à diuerſa proportione acti­<lb></lb>uitatis cum reſiſtentia medij per Ax. 5. ſed in vacuo nulla eſt reſiſten­<lb></lb>tia; </s>
					<s id="N18F83">igitur nulla proportio; igitur nulla ratio motus inæqualis. </s>
				</p>
				<p id="N18F87" type="main">
					<s id="N18F89"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 125.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18F95" type="main">
					<s id="N18F97"><emph type="italics"></emph>In motu natur aliter accelerato deorſum creſcit reſistentia medij ſingulis in­<lb></lb>ſtantibus<emph.end type="italics"></emph.end>: </s>
					<s id="N18FA2">probatur, quia ſingulis inſtantibus plures partes medij ſunt <lb></lb>ſuperandæ; </s>
					<s id="N18FA8">creſcunt enim ſpatia, vt conſtat ex dictis; igitur creſcit reſi­<lb></lb>ſtentia ſingulis inſtantibus. </s>
				</p>
				<p id="N18FAE" type="main">
					<s id="N18FB0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 126.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18FBC" type="main">
					<s id="N18FBE"><emph type="italics"></emph>Creſcit reſistentia iuxta rationem ſpatiorum,<emph.end type="italics"></emph.end> probatur; </s>
					<s id="N18FC7">quia creſcit iux­<lb></lb>ta rationem plurium partium medij, quæ temporibus æqualibus percur­<lb></lb>runtur; ſed eæ creſcunt iuxta rationem ſpatiorum, vt conſtat. </s>
				</p>
				<p id="N18FCF" type="main">
					<s id="N18FD1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 127.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N18FDD" type="main">
					<s id="N18FDF"><emph type="italics"></emph>Hinc creſcit reſiſtentia iuxta rationem velocitatum ſingulis instantibus<emph.end type="italics"></emph.end>; </s>
					<s id="N18FE8"><lb></lb>quæ ratio ſequitur progreſſionem arithmeticam ſimplicem numerorum <lb></lb>1.2.3.4.5.6. ex ſuppoſitione quòd tempus conſtet ex partibus finitis actu; </s>
					<s id="N18FEF"><lb></lb>nam eodem modo creſcit velocitas, quo creſcunt numeri prædicti; </s>
					<s id="N18FF4">ſed <lb></lb>eodem modo creſcunt ſpatia, ſi dumtaxat accipiantur in ſingulis inſtan­<lb></lb>tibus; </s>
					<s id="N18FFC">reſiſtentia creſcit iuxta rationem ſpatiorum; igitur iuxta ratio­<lb></lb>nem velocitatum. </s>
				</p>
				<p id="N19002" type="main">
					<s id="N19004"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N19010" type="main">
					<s id="N19012">Obſeruabis, ſi tempus conſtet ex infinitis actu partibus, ita vt ſingu­<lb></lb>læ partes motus ſingulis partibus temporis &amp; infinitæ infinitis reſpon­<lb></lb>deant; </s>
					<s id="N1901A">non poteſt eſſe alia progreſſio, in qua fiat acceleratio motus na­<lb></lb>turalis, quàm illa Galilei iuxta hos numeros 1. 3. 5. 7. vt conſtat ex dictis <lb></lb>per illud Principium; </s>
					<s id="N19022"><emph type="italics"></emph>æqualibus temporibus æqualia acquiruntur velocita­<lb></lb>tis momenta<emph.end type="italics"></emph.end>; </s>
					<s id="N1902D">ſi verò tempus conſtat ex finitis inſtantibus æqualibus, nul­<lb></lb>la datur progreſſio motus naturaliter accelerati; </s>
					<s id="N19033">quia motus accelerari <lb></lb>non poteſt; </s>
					<s id="N19039">ne ſcilicet eodem inſtanti mobile ſit in pluribus locis adæ­<lb></lb>quatis; denique ſi tempus conſtat ex finitis inſtantibus actu, &amp; infinitis <lb></lb>potentiâ, non poteſt eſſe alia progreſſio huius accelerationis, quam hæc <lb></lb>noſtra iuxta numeros toties repetitos 1.2.3.4.5. attamen quia illa finita <lb></lb>inſtantia ſunt ferè innumera in qualibet parte ſenſibili temporis, in <lb></lb>praxi ſine ſenſibili errore in partibus temporis ſenſibilibus poſſumus <pb pagenum="132" xlink:href="026/01/164.jpg"></pb>adhibere priorem progreſſionem Galilei, &amp; in hoc cardine tota verri­<lb></lb>tur, meo iudicio, propoſitæ quæſtionis difficultas. </s>
				</p>
				<p id="N1904E" type="main">
					<s id="N19050"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 128.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1905C" type="main">
					<s id="N1905E"><emph type="italics"></emph>Hinc creſcit reſistentia iuxta rationem crementi impetus<emph.end type="italics"></emph.end>; cum enim cre­<lb></lb>ſcant impetus in ratione velocitatum, vt conſtat, &amp; creſcat reſiſtentia <lb></lb>medij in eadem ratione per Theor. 127. creſcit etiam in ratione im­<lb></lb>petuum. </s>
				</p>
				<p id="N1906F" type="main">
					<s id="N19071"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 129.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1907D" type="main">
					<s id="N1907F"><emph type="italics"></emph>Hinc creſcit reſistentia medij in eadem ratione, in qua creſcunt vires mobi­<lb></lb>lis<emph.end type="italics"></emph.end>; demonſtr. </s>
					<s id="N1908A">quia creſcunt vires, vt creſcit impetus; nam impetus eſt <lb></lb>vis illa, quâ mobile ſuperat reſiſtentiam medij vt conſtat, ſed reſiſten­<lb></lb>tia creſcit vt impetus per Th. 128. igitur creſcit in ratione virium. </s>
				</p>
				<p id="N19092" type="main">
					<s id="N19094"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 130.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N190A0" type="main">
					<s id="N190A2"><emph type="italics"></emph>Si creſcit reſiſtentia in eadem ratione in qua creſcunt vires, non mutatur <lb></lb>progreſſio effectuum.<emph.end type="italics"></emph.end> v.g. primo inſtanti impetus ſit vt 1.ſitque 1.ſpatium, <lb></lb>in quo eſt reſiſtentia, vt 1. Secundo inſtanti ſit impetus vt 2. reſiſtentia in <lb></lb>2. ſpatiis vt 2. haud dubiè ſi vno inſtanti vnus gradus impetus ſuperat <lb></lb>reſiſtentiam vt 1. dum percurrit 1.ſpatium; </s>
					<s id="N190B5">certè 2. gradus impetus vno <lb></lb>inſtanti ſuperabunt reſiſtentiam vt 2. dum conficit mobile 2. ſpatia; at­<lb></lb>que ita deinceps. </s>
				</p>
				<p id="N190BD" type="main">
					<s id="N190BF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 132.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N190CB" type="main">
					<s id="N190CD"><emph type="italics"></emph>Hinc certè concludo contra Galileum, &amp; alios quoſdam motum grauium <lb></lb>poſt aliquod ſpatium decurſum ex naturaliter accelerato non fieri æquabilem,<emph.end type="italics"></emph.end><lb></lb>quia in tantum fieret æquabilis in quantum tanta eſſet reſiſtentia, vt no­<lb></lb>uam accelerationem impediret; </s>
					<s id="N190DB">ſed hæc ratio nulla eſt; </s>
					<s id="N190DF">quia in eadem <lb></lb>ratione creſcit reſiſtentia, in qua creſcunt vires per Th. 129. igitur non <lb></lb>mutatur progreſſio motuum per Th. 130. igitur nec acceleratio; </s>
					<s id="N190E7">igitur <lb></lb>motus naturalis ex accelerato non fit æquabilis: Equidem, vt iam ſuprà <lb></lb>dictum eſt, in minori ſemper ratione creſcit velocitas, itémque ipſa reſi­<lb></lb>ſtentia quod in omni progreſſione arithmetica iuxta numeros 1.2.3.4.5. </s>
				</p>
				<p id="N190F1" type="main">
					<s id="N190F3"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N190FF" type="main">
					<s id="N19101">Obſeruabis remitti à nobis motum leuium ſurſum in 5. Tomum, in cu­<lb></lb>ius tertio libro agemus de graui, &amp; leui; quia ideo corpus aſcendit, quia <lb></lb>ab alio deſcendente truditur ſurſum. </s>
				</p>
			</chap>
			<chap id="N19109">
				<pb pagenum="133" xlink:href="026/01/165.jpg"></pb>
				<figure id="id.026.01.165.1.jpg" xlink:href="026/01/165/1.jpg"></figure>
				<p id="N19113" type="head">
					<s id="N19115"><emph type="center"></emph>LIBER TERTIVS, <lb></lb><emph type="italics"></emph>DE MOTV VIOLENTO <lb></lb>ſurſum Perpendiculariter.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N19124" type="main">
					<s id="N19126">OMnis certè motus, qui eſt à principio ex­<lb></lb>trinſeco, violentus appellari poteſt, attamen <lb></lb>hîc non ago de omni violento, ſed dumta­<lb></lb>xat de illo, qui fit ſursùm per lineam verticalem; </s>
					<s id="N19130">quia <lb></lb>ſcilicet ex diametro opponitur motui naturali, qui <lb></lb>fit deorsùm perpendiculariter; igitur cum de hoc <lb></lb>ipſo in ſecundo Libro egerimus, de illo in hoc non <lb></lb>agemus. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N1913F" type="main">
					<s id="N19141"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1914D" type="main">
					<s id="N1914F"><emph type="italics"></emph>MOtus violentus eſt, quo corpus graue mouetur ſursùm per li­<lb></lb>neam verticalem à principio extrinſeco mediatè, vel immediatè vt <lb></lb>plurimùm.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1915A" type="main">
					<s id="N1915C">Dixi à principio extrinſeco, ſiue conjuncto, vt cum manu attollo ſur­<lb></lb>ſum corpus graue, ſiue non conjuncto, vt cum quis proiicit lapidem ſur­<lb></lb>sùm, ſiue ſit verum principium effectiuum, vt cum impetus, quem poten­<lb></lb>tia motrix producit in manu, producit alium in mobili; </s>
					<s id="N19166">ſiue non ſit <lb></lb>principium effectiuum, ſed tantùm determinans, vt cum mobile quod <lb></lb>cadit deorſum, ſurſum deinde repercutitur; </s>
					<s id="N1916E">nec enim corpus repercu­<lb></lb>tiens producit impetum nouum, vt dicemus cum de motu reflexo; </s>
					<s id="N19174">quin <lb></lb>potiùs producti partem deſtruit per accidens, &amp; quidquid illius ſupereſt, <lb></lb>ad nouam lineam determinat; quod quomodo fiat fusè ſuo loco expli­<lb></lb>cabimus, igitur licèt corpus reflectens ſit tantùm principium nouæ de­<lb></lb>terminationis, non verò alicuius impetus producti, dici poteſt princi­<lb></lb>pium huius motus violenti. </s>
				</p>
				<p id="N19182" type="main">
					<s id="N19184">Dixi vt plurimùm, nam ſi terra ducto per centrum foramine eſſet <lb></lb>peruia, haud dubiè lapis demiſſus versùs centrum iret motu naturaliter <pb pagenum="134" xlink:href="026/01/166.jpg"></pb>accelerato, tùm deinde propter impetus acquiſiti vim, à centro versùs <lb></lb>oppoſitum circumferentiæ punctum iret, motu certè violento, qui ta­<lb></lb>men ab extrinſeco non eſſet. </s>
				</p>
				<p id="N19192" type="main">
					<s id="N19194"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N191A1" type="main">
					<s id="N191A3"><emph type="italics"></emph>Corpus graue projectum ſurſum tandem redit<emph.end type="italics"></emph.end>; Hæc hypotheſis certa eſt, <lb></lb>&amp; nemo eſt qui eam in dubium vocet. </s>
				</p>
				<p id="N191AE" type="main">
					<s id="N191B0"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N191BD" type="main">
					<s id="N191BF"><emph type="italics"></emph>Quidquid erat, &amp; deſinit eſſe deſtruitur<emph.end type="italics"></emph.end>; Hoc Axioma certum eſt, quip­<lb></lb>pe deſtrui hoc tantùm dicitur, quod deſinit eſſe. </s>
				</p>
				<p id="N191CA" type="main">
					<s id="N191CC"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N191D9" type="main">
					<s id="N191DB"><emph type="italics"></emph>Quidquid destruitur, ad exigentiam alicuius destruitur, ſaltem totius na­<lb></lb>turæ.<emph.end type="italics"></emph.end></s>
					<s id="N191E4"> Hoc Axioma idem eſt cum Axiom. 14. l. 1. n. </s>
					<s id="N191EB">2. vnde alia expli­<lb></lb>catione minimè indiget; hoc ipſum etiam demonſtraui in Th.147.149. <lb></lb>150,&amp;c. </s>
					<s id="N191F3">l. 1. </s>
				</p>
				<p id="N191F9" type="main">
					<s id="N191FB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19208" type="main">
					<s id="N1920A"><emph type="italics"></emph>Datur motus violentus<emph.end type="italics"></emph.end>; demonſtro; corpus proiicitur per lineam ver­<lb></lb>ticalem per hyp. </s>
					<s id="N19215">1. ſed hic motus eſt à principio extrinſeco, igitur eſt <lb></lb>violentus per def.1. probatur minor; Primò, quia illud eſt principium, <lb></lb>ſeu cauſa motus, ex cuius applicatione ſemper ſequitur motus per Ax.11. <lb></lb>l. 1.n. </s>
					<s id="N19221">1. ſed ex applicatione potentiæ extrinſecæ v. g. arcus, manus, &amp;c. </s>
					<s id="N19228"><lb></lb>ad lineam ſurſum ſemper ſequitur motus ſurſum; igitur eſt illius cauſa. </s>
					<s id="N1922D"><lb></lb>Secundò probatur, quia mobile projectum ſursùm mouetur adhuc ſepa­<lb></lb>ratum à potentia motrice per hyp. </s>
					<s id="N19233">6.l.1. igitur potentia motrix impreſ­<lb></lb>ſit aliquid mobili, vi cuius deinde mouetur, igitur hic motus eſt à prin­<lb></lb>cipio extrinſeco. </s>
				</p>
				<p id="N1923A" type="main">
					<s id="N1923C">Diceret fortè aliquis produci hunc motum ab ipſo mobili; ſed con­<lb></lb>trà; </s>
					<s id="N19242">igitur ſemper produceret, quod abſurdum eſt: </s>
					<s id="N19246">dicet, ad hoc vt pro­<lb></lb>ducat determinari debere ab aliquo, ſed contrà; </s>
					<s id="N1924C">illud à quo determina­<lb></lb>tur vel eſt extrinſecum, vel intrinſecum, ſi primum, ergo hic motus eſt <lb></lb>ſemper à principio extrinſeco, quod ſatis eſt eſſe determinans per def.1. <lb></lb>ſi verò eſt intrinſecum; igitur ſemper eſſet hic motus, quamdiu eſſet <lb></lb>ipſum mobile, quod eſt contra hyp. </s>
					<s id="N19258">1. nam reuera non ſemper mo­<lb></lb>uetur. </s>
				</p>
				<p id="N1925D" type="main">
					<s id="N1925F">Diceret fortè alius excitari quædam corpuſcula, à quibus mouetur <lb></lb>corpus graue ſursùm; ſed contrà; </s>
					<s id="N19265">nam vel ſunt in ipſo mobili illa cor­<lb></lb>puſcula, vel extra mobile; ſi primum; </s>
					<s id="N1926B">igitur hic motus ſemper erit ab <lb></lb>extrinſeco mediatè, cum ab extrinſeco excitentur; </s>
					<s id="N19271">ſed hoc ſufficit ad <lb></lb>hoc; vt motus dicatur violentus per def. </s>
					<s id="N19277">1. ſi verò ſunt extra mobile; <lb></lb>igitur motus ille eſt ſemper ab extrinſeco, idque duplici nomine. </s>
				</p>
				<p id="N1927D" type="main">
					<s id="N1927F">Denique diceret alius ex ſuppoſitione, quod terra moueatur non poſ­<lb></lb>ſe corpus graue proiici ſursùm per lineam verticalem, niſi tantùm ad <lb></lb>ſpeciem; </s>
					<s id="N19287">vt ſi quis è naui mobili ſurſum proiiceret pilam rectà omni­<lb></lb>nò, quoad eius fieri poſſit; videbitur enim iis, qui vehuntur eadem naui <pb pagenum="135" xlink:href="026/01/167.jpg"></pb>ſurſum ferri per lineam verticalem, aliis verò inſtantibus videbitur cla­<lb></lb>riſſimè ferri per lineam nouam inclinatam. </s>
				</p>
				<p id="N19294" type="main">
					<s id="N19296">Reſpondeo etiam admiſſa ſuppoſitione dici à me motum illum ſur­<lb></lb>ſum eſſe per lineam verticalem, quando eadem linea recta connectit <lb></lb>ſemper hæc tria puncta; </s>
					<s id="N1929E">ſcilicet centrum terræ, idem punctum ſuperfi­<lb></lb>ciei terræ, &amp; ipſam pilam; </s>
					<s id="N192A4">ad illud verò quod dicitur de naui, non diffi­<lb></lb>teor verum eſſe; ſed dico non eſſe propriè motum violentum, de quo hîc <lb></lb>tantùm eſt quæſtio, ſed eſſe motum mixtum, de quo fusè ſuo loco. </s>
					<s id="N192AC">Obſer­<lb></lb>uabis autem hîc me abſtinere à refellendis abſurdis illis ſuppoſitioni­<lb></lb>bus, quibus præmiſſæ objectiones innituntur; nam, cui quæſo in men­<lb></lb>tem venire poteſt ab ipſa entitate corporis grauis produci motum in ſe? </s>
					<s id="N192B6"><lb></lb>quis credat produci frigus ab igne? </s>
					<s id="N192BA">calorem à niue? </s>
					<s id="N192BD">lucem à tenebris? </s>
					<s id="N192C0"><lb></lb>quæ porrò fabulæ, quæ commenta, quæ ſomnia excogitari poſſunt, quæ <lb></lb>non vileſcant ſi cum his comparentur. </s>
				</p>
				<p id="N192C6" type="main">
					<s id="N192C8">Illa quoque corpuſcula excitata leuiora ſunt, quàm vt aliquod præfe­<lb></lb>rant rationis momentum; cum mera ſint philoſophiæ ludibria. </s>
				</p>
				<p id="N192CE" type="main">
					<s id="N192D0">Denique illa hypotheſis de terræ motu nullis demonſtrationibus fir­<lb></lb>mata eſt, vt videbimus ſuo loco. </s>
				</p>
				<p id="N192D5" type="main">
					<s id="N192D7">Vnum fortè eſt, quod difficilius obiici poteſt; </s>
					<s id="N192DB">ſit enim linea vertica­<lb></lb>lis AC, ſitque globus in A æqualiter impulſus per lineas AD &amp; AB; </s>
					<s id="N192E1"><lb></lb>haud dubiè ſi anguli DAC, BAC ſint æquales: certè mobile feretur <lb></lb>per lineam verticalem AC, vt conſtat ex dictis. </s>
					<s id="N192E8">Reſpondeo motum illum <lb></lb>eſſe violentum; eſt enim à principio extrinſeco, coque gemino, ſeu mix­<lb></lb>to, in quo non eſt difficultas. </s>
				</p>
				<p id="N192F0" type="main">
					<s id="N192F2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N192FF" type="main">
					<s id="N19301"><emph type="italics"></emph>Motus violentus habet cauſam<emph.end type="italics"></emph.end>; quia de nouo eſt, &amp; tandem deſinit per <lb></lb>hypoth. </s>
					<s id="N1930C">1. igitur habet cauſam per Ax.8.l.1. </s>
				</p>
				<p id="N1930F" type="main">
					<s id="N19311"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1931E" type="main">
					<s id="N19320"><emph type="italics"></emph>Iſte motus ſupponit impetum<emph.end type="italics"></emph.end>; quia niſi eſſet impetus non eſſet natura­<lb></lb>liter motus per Th.18.l.1. </s>
				</p>
				<p id="N1932B" type="main">
					<s id="N1932D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1933A" type="main">
					<s id="N1933C"><emph type="italics"></emph>Iſte impetus debet eſſe in mobili projecto ſurſum<emph.end type="italics"></emph.end>; </s>
					<s id="N19345">quia ibi eſt cauſa, vbi <lb></lb>eſt effectus formalis, ſed motus eſt effectus formalis ſecundarius impe­<lb></lb>tus per Th.15.l.1. igitur cum motus ſit in projecto ſurſum, in eo eſt etiam <lb></lb>impetus: </s>
					<s id="N1934F">præterea ſecunda pars motus non ponitur à potentia motrice; <lb></lb>quia illa non eſt applicata mobili cum ponitur noua pars motus, igitur <lb></lb>ab alia cauſa applicata, ſed nulla eſt extrinſeca, vt patet, nulla intrinſeca <lb></lb>præter impetum. </s>
				</p>
				<p id="N19359" type="main">
					<s id="N1935B">Diceret aliquis ab aëre extrinſecùs ambiente mobile ipſum propelli; </s>
					<s id="N1935F"><lb></lb>ſed contra, nam aër, &amp; omne aliud medium reſiſtit potiùs quàm iuuet, vt <lb></lb>demonſtrauimus l. ſecundo Th. 1. Nec dicas fuiſſe mentem Ariſtotelis, <lb></lb>cum nobiles Peripatetici contrâ ſentiant; </s>
					<s id="N1936A">Albertus Magnus, Toletus, <lb></lb>Scaliger, Suarius, &amp; recentiores; </s>
					<s id="N19370">neque hoc negauit vnquam Ariſtote-<pb pagenum="136" xlink:href="026/01/168.jpg"></pb>les, ſed in hoc non multùm laboramus; nec dicas hinc ſequi motum <lb></lb>violentum eſſe à principio intrinſeco contra def. </s>
					<s id="N1937B">1. nam eſt quidem à <lb></lb>principio intrinſeco formali, non tamen à principio intrinſeco mouen­<lb></lb>te vel agente; </s>
					<s id="N19383">nec enim impetus eſt cauſa efficiens motus ſui ſubjecti; <lb></lb>ſed cauſa formalis vt ſæpè explicuimus. </s>
				</p>
				<p id="N19389" type="main">
					<s id="N1938B">Diceret fortè alius primam partem motus produci à potentiâ motri­<lb></lb>ce, ſecundam verò ab entitate ipſius corporis; ſed contrà; </s>
					<s id="N19391">igitur corpus <lb></lb>eſſet cauſa neceſſaria; igitur ſemper produceret. </s>
					<s id="N19397">Dices ſemper producere <lb></lb>ſi determinetur, ſed contrà; à quo determinatur ad producendam ſecun­<lb></lb>dam partem? </s>
					<s id="N1939F">nihil eſt enim applicatum, à quo determinari poſſit; </s>
					<s id="N193A3">Dices <lb></lb>accepiſſe determinationem; ſed contrà; quid eſt illa determinatio? </s>
					<s id="N193A9"><lb></lb>Dices eſſe modum; </s>
					<s id="N193AE">igitur permanentem; igitur eſt cauſa motus per Ax. <lb></lb>1. l. 1. n. </s>
					<s id="N193B7">1. igitur eſt impetus per def. </s>
					<s id="N193BA">3. l. 1. Dices determinari à priori <lb></lb>parte motus; ſed contrà primò, nam reuerâ non eſt illa pars cum deter­<lb></lb>minatur corpus. </s>
					<s id="N193C4">Secundò, quid eſt illa prima pars motus, niſi migratio è <lb></lb>loco in locum, quæ reuerâ à potentia motrice produci propriè non po­<lb></lb>teſt per Th.2. l. 1. ſed de his iam fusè actum eſt in toto ferè libro primo, <lb></lb>ſed præſertim in Th.6. </s>
				</p>
				<p id="N193CF" type="main">
					<s id="N193D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N193DE" type="main">
					<s id="N193E0"><emph type="italics"></emph>Ille impetus eſt vera qualitas Phyſica abſoluta<emph.end type="italics"></emph.end>; </s>
					<s id="N193E9">hoc iam ſuprà demon­<lb></lb>ſtratum eſt, ſcilicet phyſicè; immò ex motu violento maximè probatur <lb></lb>dari impetum, &amp; vix quidquam eſt in rerum naturâ, quod clariùs euin­<lb></lb>cat aliquid de nouo produci. </s>
				</p>
				<p id="N193F3" type="main">
					<s id="N193F5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19402" type="main">
					<s id="N19404"><emph type="italics"></emph>Iſte impetus producitur ab aliqua cauſa<emph.end type="italics"></emph.end>; </s>
					<s id="N1940D">Probatur, quia eſt de nouo; </s>
					<s id="N19411">igi­<lb></lb>tur non eſt à ſe per Ax. 8. l. 1. igitur eſt ab alio; igitur ab aliqua <lb></lb>cauſa. </s>
				</p>
				<p id="N1941B" type="main">
					<s id="N1941D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19429" type="main">
					<s id="N1942B"><emph type="italics"></emph>Producitur ab aliqua cauſa extrinſeca<emph.end type="italics"></emph.end>; </s>
					<s id="N19434">Probatur primò, quia aliquis <lb></lb>motus violentus eſt à cauſa extrinſeca per def.1. Secundò, eſt ab aliqua <lb></lb>cauſa applicata, ſed eſt tantùm applicata potentia motrix; </s>
					<s id="N1943C">igitur eſt cau­<lb></lb>ſa, per Ax. 11. l. 1. nec enim producitur hic impetus ab entitate corpo­<lb></lb>ris projecti, quod pluſquàm certum eſt ex dictis; hîc enim tantùm <lb></lb>eſt quæſtio de illo motu, qui extrinſecùs aduenit, non vero de reflexo <lb></lb>ſursùm, &amp;c. </s>
				</p>
				<p id="N1944A" type="main">
					<s id="N1944C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19458" type="main">
					<s id="N1945A"><emph type="italics"></emph>Producitur ab alio impetu<emph.end type="italics"></emph.end>; </s>
					<s id="N19463">quia potentia motrix non agit ad extra niſi <lb></lb>per impetum productum in organo, vt patet; præterea ſi eſt cauſa vni­<lb></lb>uoca ſufficiens applicata, non eſt ponenda æquiuoca per Ax.11.l.1. adde <lb></lb>quod impetus producitur ſemper ad extra ab alio impetu per Th. 42. <lb></lb>l.1.nec in his hactenus propoſitis vlla eſt difficultas. </s>
				</p>
				<p id="N1946F" type="main">
					<s id="N19471"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1947D" type="main">
					<s id="N1947F"><emph type="italics"></emph>Impetus impreſſus mobili ſurſum conſeruatur per aliquod tempus<emph.end type="italics"></emph.end>; </s>
					<s id="N19488">Probatur, <pb pagenum="137" xlink:href="026/01/169.jpg"></pb>quia mobile ſeparatum à potentia motrice adhuc mouetur per hyp.6.l.1, <lb></lb>igitur ille motus habet cauſam, vt ſæpè dictum eſt; </s>
					<s id="N19493">non aliam, quàm im­<lb></lb>petum per Th.4. non productum de nouo, quippe nulla eſt cauſa mobili <lb></lb>applicata per Th. 7. &amp; 8. igitur iam antè productam; igitur conſer­<lb></lb>uatur. </s>
				</p>
				<p id="N1949D" type="main">
					<s id="N1949F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N194AB" type="main">
					<s id="N194AD"><emph type="italics"></emph>Conſeruatur ab aliqua cauſa extrinſeca applicata<emph.end type="italics"></emph.end>; </s>
					<s id="N194B6">vt patet ex dictis, non <lb></lb>ab aëre; </s>
					<s id="N194BC">igitur à nullo corpore; </s>
					<s id="N194C0">igitur ab alia causâ inſenſibili; </s>
					<s id="N194C4">igitur <lb></lb>illam eſſe oportet, &amp; noſſe rerum omnium exigentias, &amp; poſſe cuncta <lb></lb>producere; </s>
					<s id="N194CC">quippe conſeruatio eſt repetita productio; </s>
					<s id="N194D0">immò conſerua­<lb></lb>re per actionem, per quam ſit res in tali loco, &amp; tali tempore; </s>
					<s id="N194D6">illa porrò <lb></lb>cauſa inſenſibilis incorporea, quæ vbique eſt, &amp; ſemper, Deus eſt: Nec <lb></lb>puta poſſe exiſtentiam cauſæ primæ probari ſenſibiliori, vt ſic loquar, <lb></lb>argumento, quàm eo, quod petitur ex motu projectorum, quorum motus <lb></lb>durat etiamſi à potentia motrice mobile ipſum ſit ſeparatum. </s>
				</p>
				<p id="N194E2" type="main">
					<s id="N194E4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N194F0" type="main">
					<s id="N194F2"><emph type="italics"></emph>Hinc multa colligi poſſunt.<emph.end type="italics"></emph.end></s>
					<s id="N194F9"> Primò, ſi nullus eſſet impetus extrinſecus, <lb></lb>vel acquiſitus, nullus eſſet motus violentus, niſi tantùm motus reflexus <lb></lb>cadentium deorsùm. </s>
					<s id="N19500">Secundò, ſi nullus eſſet Deus, nullus eſſet motus <lb></lb>violentus; immò nec vllus naturaliter acceleratus. </s>
					<s id="N19506">Tertiò, ſi impetus eſ­<lb></lb>ſet fluens vt motus, nullus eſſet motus violentus. </s>
					<s id="N1950B">Quartò, ſi ſingulæ par­<lb></lb>tes motus produci debent ab aliquâ causâ efficiente, nullus etiam eſſet <lb></lb>motus violentus. </s>
				</p>
				<p id="N19512" type="main">
					<s id="N19514"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19520" type="main">
					<s id="N19522"><emph type="italics"></emph>Vt ſit motus violentus debent produci plures partes impetus violenti <lb></lb>quàm ſint partes impetus naturalis<emph.end type="italics"></emph.end>; </s>
					<s id="N1952D">Probatur, quia ſi eſſent plures natura­<lb></lb>lis deorsùm, quàm ſint violenti ſurſum, corpus tenderet deorſum; ſed <lb></lb>tardiùs per Th.134.l.1. &amp; ſi tot eſſent vnius, quot alterius, mobile ipſum <lb></lb>non moueretur per Th.133.l.1. </s>
				</p>
				<p id="N19537" type="main">
					<s id="N19539"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19545" type="main">
					<s id="N19547"><emph type="italics"></emph>Motus violentus non eſt acceleratus<emph.end type="italics"></emph.end>; probatur primò experientiâ, quæ <lb></lb>certa eſt. </s>
					<s id="N19552">Secundò, quia ſi ſemper creſceret, numquam rediret mobile <lb></lb>contra hyp.1. nec enim ab vllo reflectitur; ſi enim reflecteretur ab aëre <lb></lb>intenſus, multò magis remiſſus. </s>
				</p>
				<p id="N1955A" type="main">
					<s id="N1955C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19568" type="main">
					<s id="N1956A"><emph type="italics"></emph>Hinc impetus in mobili ſurſum projecto non intenditur,<emph.end type="italics"></emph.end> quia non inten­<lb></lb>ditur effectus per Th.13. igitur nec cauſa per Ax.2.l.2. </s>
				</p>
				<p id="N19574" type="main">
					<s id="N19576"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19582" type="main">
					<s id="N19584"><emph type="italics"></emph>Motus violentus non eſt æquabilis<emph.end type="italics"></emph.end>; </s>
					<s id="N1958D">quia mobile tandem redit per hyp.1. <lb></lb>ſed numquam rediret, ſi eſſet æquabilis; cur enim potiùs hoc inſtanti <lb></lb>quàm alio? </s>
					<s id="N19595">cur ab hoc puncto ſpatij potiùs, quàm ab alio? </s>
				</p>
				<pb pagenum="138" xlink:href="026/01/170.jpg"></pb>
				<p id="N1959C" type="main">
					<s id="N1959E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N195AA" type="main">
					<s id="N195AC"><emph type="italics"></emph>Hinc non conſeruatur intactus impetus<emph.end type="italics"></emph.end>; </s>
					<s id="N195B5">quia ſi eſſet intactus, eſſet ſem­<lb></lb>per æqualis; igitur haberet ſemper æqualem motum per Ax.3.l.2. igitur <lb></lb>motus eſſet æquabilis, contra Th.15. </s>
				</p>
				<p id="N195BD" type="main">
					<s id="N195BF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N195CB" type="main">
					<s id="N195CD"><emph type="italics"></emph>Hinc neceſſe eſt aliquid impetus destrui<emph.end type="italics"></emph.end>; </s>
					<s id="N195D6">cum enim non remaneat inta­<lb></lb>ctus, &amp; æqualis; nec fiat maior per Th.14. certè fit minor, igitur detra­<lb></lb>ctione aliqua per Ax.1.l.2. </s>
				</p>
				<p id="N195DE" type="main">
					<s id="N195E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N195EC" type="main">
					<s id="N195EE"><emph type="italics"></emph>Singulis inſtantibus aliquid deſtruitur impetus impreſſi<emph.end type="italics"></emph.end>; probatur quia <lb></lb>cur potiùs vno quam alio? </s>
					<s id="N195F9">quippe illa ratio, quæ probat de vno probat <lb></lb>de ſingulis. </s>
				</p>
				<p id="N195FE" type="main">
					<s id="N19600"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1960C" type="main">
					<s id="N1960E"><emph type="italics"></emph>Hinc neceſſariè eadem vel aqualis cauſa deſtructionis debet eſſe applicata<emph.end type="italics"></emph.end>; <lb></lb>probatur, quia æqualis effectus æqualem cauſam ſupponit, per Ax. <lb></lb>3. l. 2. </s>
				</p>
				<p id="N1961F" type="main">
					<s id="N19621"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1962D" type="main">
					<s id="N1962F"><emph type="italics"></emph>Illa cauſa non eſt tantùm aër ambiens vt volunt aliqui<emph.end type="italics"></emph.end>; </s>
					<s id="N19638">quia licèt reſi­<lb></lb>ſtat motui, ſeu potius mobili, non tamen eſt ea reſiſtentia, quæ poſſit <lb></lb>impetum tam citò deſtruere; </s>
					<s id="N19640">probatur primò, quia ſi hoc eſſet, deſtrue­<lb></lb>retur æquali tempore per omnem lineam ſurſum, quod eſt contra expe­<lb></lb>rientiam, vt dicemus infrà; </s>
					<s id="N19648">eſſet enim eadem cauſa applicata; </s>
					<s id="N1964C">igitur idem <lb></lb>&amp; æqualis effectus; </s>
					<s id="N19652">probatur ſecundò, quia non deſtruit aër primum il­<lb></lb>lum gradum impetus naturalis acquiſiti, vt conſtat in motu deorſum, qui <lb></lb>tamen eſt imperfectiſſimus; igitur non eſt ſufficiens ad deſtruendum im­<lb></lb>petum violentum, niſi longo tempore. </s>
					<s id="N1965C">Tertiò, globus ſursùm projectus <lb></lb>aſcendit, &amp; deinde deſcendit æquali tempore; </s>
					<s id="N19662">igitur ſaltem ſingulis in­<lb></lb>ſtantibus deſtruitur vnus gradus impetus violenti æqualis primo gradui <lb></lb>innato; </s>
					<s id="N1966A">atqui aër non poteſt vno inſtanti deſtruere impetum æqualem <lb></lb>primo innato; alioqui non intenderetur motus naturalis. </s>
					<s id="N19670">Quartò, &amp; hæc <lb></lb>eſt ratio à priori, quotieſcumque ſunt in eodem mobili duo impetus ad <lb></lb>oppoſitas lineas determinati, pugnant pro rata, vt demonſtrauimus l.1. <lb></lb>Th. 149. 150. 152. &amp; in toto Schol. &amp; multis aliis paſſim; atqui conſer­<lb></lb>uatur ſemper impetus naturalis innatus per Sch. Th.152.n.6.l.1.per Th. <lb></lb>9. &amp; Schol.Th.14. &amp; Th.73.l.2. </s>
				</p>
				<p id="N19683" type="main">
					<s id="N19685"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19691" type="main">
					<s id="N19693"><emph type="italics"></emph>Illa cauſa non eſt entitas corporis mobilis, vel ipſa grauitas, diſtincta ſcili­<lb></lb>cet ab impetu innato ſi quæ eſt de quæ alias,<emph.end type="italics"></emph.end> probatur, quia non eſſet potior <lb></lb>ratio cur vno inſtanti deſtruerentur duo gradus impetus, quàm 3. 4. 5. <lb></lb>quippe grauitas exigeret deſtructionem omnium: præterea omnis impe­<lb></lb>tus deſtruitur ne ſit fruſtrà per Schol, Th.152. &amp; Th.162.l.1. denique ſi <pb pagenum="139" xlink:href="026/01/171.jpg"></pb>adeſt contrarius impetus deſtructiuus eo modo, quo explicuimus l. 1. non <lb></lb>eſt ponenda alia cauſa deſtructiua. </s>
				</p>
				<p id="N196AD" type="main">
					<s id="N196AF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N196BB" type="main">
					<s id="N196BD"><emph type="italics"></emph>Hinc neceſſe eſt impetum violentum deſtrui ab impetu naturali innato<emph.end type="italics"></emph.end>; </s>
					<s id="N196C6">pro­<lb></lb>batur, quia nulla eſt cauſa extrinſeca deſtructiua ſaltem adæquatè per hT. <lb></lb>20.igitur eſt intrinſeca per Ax.4. l.2. ſed intrinſeca vel eſt mobilis enti­<lb></lb>tas, vel grauitas, vel impetus innatus; </s>
					<s id="N196D0">ſed mobilis entitas non eſt cauſa <lb></lb>deſtructiua; nec etiam ipſa grauitas per Th.21. igitur impetus naturalis <lb></lb>innatus. </s>
				</p>
				<p id="N196D8" type="main">
					<s id="N196DA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N196E6" type="main">
					<s id="N196E8"><emph type="italics"></emph>Hinc vera ratio cur ſingulis inſtantibus aliquid deſtruatur,<emph.end type="italics"></emph.end> quia ſingulis <lb></lb>inſtantibus eſt cauſa deſtructiua applicata, igitur ſingulis inſtantibus de­<lb></lb>ſtruit per Ax. 12. l. 1. </s>
				</p>
				<p id="N196F7" type="main">
					<s id="N196F9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19705" type="main">
					<s id="N19707"><emph type="italics"></emph>Hinc etiam ratio cur ſingulis instantibus, ſeu æqualibus temporibus æqua­<lb></lb>liter deſtruatur<emph.end type="italics"></emph.end>; </s>
					<s id="N19712">quia ſingulis inſtantibus eſt eadem cauſa deſtructiua ap­<lb></lb>plicata; igitur ſingulis inſtantibus æqualiter deſtruit per Ax.3.l.2.porrò <lb></lb>in tantum deſtruit in quantum efficit, vt aliquid ſit fruſtrà, vt fusè di­<lb></lb>ctum eſt lib.1.vel in quantum exigit eius <expan abbr="deſtructionẽ">deſtructionem</expan>, nam perinde eſt. </s>
				</p>
				<p id="N19720" type="main">
					<s id="N19722"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1972E" type="main">
					<s id="N19730"><emph type="italics"></emph>Hinc etiam petitur ratio, propter quam talis portio impetus violenti de­<lb></lb>ſtruatur vne inſtanti<emph.end type="italics"></emph.end>; quia ſcilicet contraria pugnant prorata per Ax.15. <lb></lb>&amp; per Th.134.l.1. </s>
				</p>
				<p id="N1973D" type="main">
					<s id="N1973F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1974B" type="main">
					<s id="N1974D"><emph type="italics"></emph>Hinc illa inuerſa communis dicti, æqualibus temporibus æqualia deſtruun­<lb></lb>tur velocitatis momenta in motu violento<emph.end type="italics"></emph.end>; quippe eadem cauſa eidem ſub­<lb></lb>jecto applicata æqualibus temporibus æqualem effectum producit per <lb></lb>Ax.3.l.2. ſed impetus innatus eſt cauſa deſtructiua impetus violenti per <lb></lb>Th. 22. igitur æqualibus temporibus, &amp;c. </s>
				</p>
				<p id="N1975E" type="main">
					<s id="N19760"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1976C" type="main">
					<s id="N1976E"><emph type="italics"></emph>In eadem proportione retardatur motus violentus, in qua naturalis accele­<lb></lb>ratur<emph.end type="italics"></emph.end>: </s>
					<s id="N19779">probatur quia ſingulis inſtantibus æqualibus acquiritur æqualis <lb></lb>gradus impetus, vt ſæpè dictum eſt ſuprà; </s>
					<s id="N1977F">atqui ſingulis inſtantibus de­<lb></lb>ſtruitur vnus gradus impetus violenti per Th.24. ſed ille gradus reſpon­<lb></lb>det impetui innato per Th. 25. igitur æqualibus temporibus tantùm de­<lb></lb>ſtruitur violenti, quantùm acquiritur naturalis; cum enim primo in­<lb></lb>ſtanti ſit impetus naturalis, &amp; ſecundo tempore æquali acquiratur æqua­<lb></lb>lis, item tertio, quarto, &amp;c. </s>
					<s id="N1978D">certè cum impetus innatus pugnet cum vio­<lb></lb>lento pro rata; </s>
					<s id="N19793">nec ſit potior ratio cur maiorem portionem quàm mino­<lb></lb>rem deſtruat, æqualem certè deſtruit, itemque ſecundo inſtanti æqua­<lb></lb>lem, item tertio, quarto; igitur in eadem proportione decreſcit violentus, <lb></lb>ſeu retardatur, in qua naturalis acceleratur. </s>
				</p>
				<pb pagenum="140" xlink:href="026/01/172.jpg"></pb>
				<p id="N197A1" type="main">
					<s id="N197A3">Hinc inuertenda eſt progreſſionis linea; </s>
					<s id="N197A7">quippe linea AE repræſen­<lb></lb>tat nobis progreſſionem motus accelerati, quæ fit in inſtantibus, &amp; li­<lb></lb>nea FK progreſſionem motus, quæ fit in partibus temporis ſenſibilibus; </s>
					<s id="N197AF"><lb></lb>in illa primo inſtanti decurritur primum ſpatium AB, ſecundo tempore <lb></lb>æquali BC, tertio CD, quarto DE: </s>
					<s id="N197B6">in hac vero prima parte acquiritur <lb></lb>ſpatium FG ſecunda æquali primæ GH, tertia HI, quarta IK; </s>
					<s id="N197BC">igitur ſi ac­<lb></lb>cipiatur linea AE, progrediendo ab A verſus E, vel linea FK progre­<lb></lb>diendo ab F verſus K habebitur progreſſio motus naturaliter accelerati; </s>
					<s id="N197C4"><lb></lb>ſi verò accipiatur EA, vel KF, progrediendo ſcilicet ab E verſus A, vel à <lb></lb>K verſus F, erit progreſſio motus violenti naturaliter retardati; </s>
					<s id="N197CB">vt con­<lb></lb>ſtat ex præcedèntibus Theorematis; &amp; quemadmodum progreſſio acce­<lb></lb>lerationis in inſtantibus finitis fit iuxta ſeriem iſtorum numerorum 1.2. <lb></lb>3.4. in partibus verò temporis ſenſibilibus iuxta ſeriem iſtorum 1.3.5.7. <lb></lb>ita fit omninò progreſſio retardationis in inſtantibus iuxta hos nume­<lb></lb>ros 4.3.2.1. in partibus temporis ſenſibilibus iuxta hos 7.5. 3. 1. </s>
				</p>
				<p id="N197DA" type="main">
					<s id="N197DC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N197E8" type="main">
					<s id="N197EA"><emph type="italics"></emph>Motus violentus durat tot inſtantibus ſcilicet æquiualentibus quot ſunt ij <lb></lb>gradus impetus quibus violentus ſuperat innatum,<emph.end type="italics"></emph.end> v.g. ſit vnus gradus im­<lb></lb>petus innati; </s>
					<s id="N197F9">producantur 5. gradus violenti, quorum ſinguli ſint æqua­<lb></lb>les innato etiam <expan abbr="æquiualẽter">æquiualenter</expan>, motus durabit 4. inſtantibus etiam æqui­<lb></lb>ualenter id eſt 4. temporibus, quorum ſingula erunt æqualia primo in­<lb></lb>ſtanti motus naturalis, probatur, cum ſingulis inſtantibus æqualibus de­<lb></lb>ſtruatur vnus gradus; certè 4. inſtantibus durat motus. </s>
				</p>
				<p id="N19809" type="main">
					<s id="N1980B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19817" type="main">
					<s id="N19819"><emph type="italics"></emph>Si accipiantur ſpatia æqualia in hac progreſſione retardationis, eſt inuerſa <lb></lb>illius, quàm tribuimus ſuprà accelerationi, aſſumptis ſcilicet ſpatiis æqualibus; </s>
					<s id="N19821"><lb></lb>tum ſi accipiantur ſpatia æqualia prime ſpatie quod decurritur prime inſtan­<lb></lb>ti metus naturalis, tum ſi accipiantur ſpatia æqualia date ſpatie quod in par­<lb></lb>te temporis ſenſibili percurritur<emph.end type="italics"></emph.end>; </s>
					<s id="N1982D">quippe quemadmodum in progreſſione <lb></lb>accelerationis decreſcunt tempora; </s>
					<s id="N19833">ſic in progreſſione retardationis <lb></lb>creſcunt, aſſumptis ſcilicet ſpatiis æqualibus; quare ne iam dicta hic re­<lb></lb>petam, conſule quæ diximus lib.2. de hac progreſſione. </s>
				</p>
				<p id="N1983B" type="main">
					<s id="N1983D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19849" type="main">
					<s id="N1984B"><emph type="italics"></emph>Hinc instantia initio huius metus ſunt minora ſicut initio motus naturalis <lb></lb>ſunt maiora; </s>
					<s id="N19853">&amp; ſub finem in motu violente ſunt maiora, in naturali ſunt mi­<lb></lb>nora<emph.end type="italics"></emph.end>; </s>
					<s id="N1985C">quia ſcilicet hic acceleratur, ille retardatur: </s>
					<s id="N19860">igitur velo­<lb></lb>citas accelerati creſcit; </s>
					<s id="N19866">igitur ſi accipiantur ſpatia æqualia, decreſcit tem­<lb></lb>pus; </s>
					<s id="N1986C">at verò velocitas retardati decreſcit, igitur aſſumptis ſpatiis æquali­<lb></lb>bus, creſcit tempus; </s>
					<s id="N19872">igitur ſi accipiatur ſpatium, quod percurritur primo <lb></lb>inſtanti huius motus, &amp; deinde alia huic æqualia; </s>
					<s id="N19878">haud dubiè, cum ſe­<lb></lb>cundo inſtanti motus ſit tardior, ſitque aſſumptum æquale ſpatium; haud <lb></lb>dubiè inquam inſtans ſecundum erit maius primo, &amp; tertium ſecundo, <lb></lb>atque ita deinceps. </s>
				</p>
				<pb pagenum="141" xlink:href="026/01/173.jpg"></pb>
				<p id="N19886" type="main">
					<s id="N19888"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19894" type="main">
					<s id="N19896"><emph type="italics"></emph>Hinc primo inſtanti motus violenti deſtruitur minor gradus impetus quàm <lb></lb>ſecundo,<emph.end type="italics"></emph.end> quod demonſtro; </s>
					<s id="N198A1">quia eadem cauſa breuiore tempore minùs agit <lb></lb>per Ax.3.l.2. &amp; Ax. 13.l.1. num.4. igitur minùs impetus deſtruitur pri­<lb></lb>mo, quàm ſecundo, &amp; minùs ſecundo quàm tertio, atque ita deinceps; <lb></lb>idem enim dici debet de cauſa deſtructiua, quod de productiua. </s>
				</p>
				<p id="N198AB" type="main">
					<s id="N198AD">Dices, igitur idem impetus deſtruitur primo inſtanti, quo eſt, ſi deſtrui­<lb></lb>tur primo inſtanti motus. </s>
					<s id="N198B2">Reſpondeo negando; quia primo inſtanti, quo <lb></lb>eſt impetus, non eſt motus per Th.34.l.1. </s>
				</p>
				<p id="N198B8" type="main">
					<s id="N198BA">Dices, igitur impetus ille eſt fruſtrà, quia nullus effectus, ſeu motus <lb></lb>ex eo ſequitur; Reſpondeo negando; nam omnes gradus impetus qui ei­<lb></lb>dem parti mobilis inſunt, communi quaſi actione, vel exigentia indi­<lb></lb>uiſibiliter exigunt motum. </s>
				</p>
				<p id="N198C4" type="main">
					<s id="N198C6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N198D2" type="main">
					<s id="N198D4"><emph type="italics"></emph>Hinc gradus omnes producti in eadem parte ſubiecti ſunt inæquales in­<lb></lb>perfectione<emph.end type="italics"></emph.end>; </s>
					<s id="N198DF">cum enim ſinguli ſingulis inſtantibus deſtruantur, vt dictum <lb></lb>eſt; quippe eſt tantùm vnus gradus impetus innati, &amp; cum ſingula in­<lb></lb>ſtantia ſint inæqualia, etiam ſinguli gradus illius impetus ſunt inæquales <lb></lb>in perfectione. </s>
				</p>
				<p id="N198E9" type="main">
					<s id="N198EB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N198F7" type="main">
					<s id="N198F9"><emph type="italics"></emph>Hinc redditur optima ratio, cur tot producantur potiùs quàm plures, quæ <lb></lb>alioquin minimè afferri poteſt<emph.end type="italics"></emph.end>; </s>
					<s id="N19904">immò, niſi hoc eſſet, nulla eſſet huiuſmodi <lb></lb>naturalis retardatio; nam producantur, ſi fieri poteſt, omnes æquales, ſint­<lb></lb>que v.g.20. nunquid poſſunt eſſe 40. perfectionis ſubduplæ, vel 10. du­<lb></lb>plæ, vel 5. quadruplæ &amp;c. </s>
					<s id="N1990E">cur autem potiùs vnum dices quàm aliud? </s>
					<s id="N19911">at <lb></lb>verò optimam inde reddo rationem quòd cum ſint omnes inæquales, cò <lb></lb>plures ſunt, quò maior eſt niſus; pauciores verò, quò minor. </s>
				</p>
				<p id="N19919" type="main">
					<s id="N1991B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19927" type="main">
					<s id="N19929"><emph type="italics"></emph>Hinc ſunt inæquales in eâdem proportione, in quæ inſtantia ſunt inæqualia<emph.end type="italics"></emph.end><lb></lb>v. </s>
					<s id="N19932">g. quà proportione primum inſtans eſt minus ſecundo, &amp; ſecundum <lb></lb>tertio, ita ille gradus impetus, qui deſtruitur primo inſtanti, eſt minor <lb></lb>vel imperfectior co, qui deſtruitur ſecundo, &amp; qui deſtruitur ſecundo <lb></lb>imperfectior co, qui deſtruitur tertio, atque ita deinceps. </s>
				</p>
				<p id="N1993D" type="main">
					<s id="N1993F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1994B" type="main">
					<s id="N1994D"><emph type="italics"></emph>Hinc perfectiſſimus omnium graduum ille eſt qui deſtruitur vltimo inſtan­<lb></lb>ti, de quo infrá<emph.end type="italics"></emph.end>; </s>
					<s id="N19958">quod ſequitur ex dictis neceſſariò: vtrùm verò ille ſit æ­<lb></lb>qualis omninò in perfectione impetui naturali innato, dicemus <lb></lb>infrà. </s>
				</p>
				<p id="N19960" type="main">
					<s id="N19962"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1996E" type="main">
					<s id="N19970">Hic obſeruabis mirabilem ſanæ naturæ prouidentiam, quæ motus <lb></lb>omnes cum ipſo naturali ita compoſuit, vt ſit veluti regula omnium mo­<lb></lb>tuum, ſitque vnum quaſi principium perfectionis totius impetus; </s>
					<s id="N19978">tùm in <pb pagenum="142" xlink:href="026/01/174.jpg"></pb>motu naturali, in cuius progreſſione producitur ſemper imperfectior, <lb></lb>tùm in violento, in cuius progreſſione deſtruitur ſemper perfectior; </s>
					<s id="N19983"><lb></lb>producitur imperfectior ab eadem cauſa in minoribus temporibus, &amp; <lb></lb>deſtruitur perfectior ab eadem cauſa in maioribus temporibus; </s>
					<s id="N1998A">&amp; cum <lb></lb>impetus innatus ſit cauſa deſtructiua impetus violenti, habet inæqualem <lb></lb>proportionem cum ſuo effectu pro temporibus inæqualibus; </s>
					<s id="N19992">&amp; cum <lb></lb>idem impetus innatus ſit quaſi principium crementi, vel accelerationis, <lb></lb>ſicut eſt principium retardationis; </s>
					<s id="N1999A">certè pro inæqualitate temporum eſt <lb></lb>diuerſa proportio crementorum; quo nihil clarius in hac materia meo <lb></lb>iudicio dici poteſt. </s>
				</p>
				<p id="N199A2" type="main">
					<s id="N199A4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N199B0" type="main">
					<s id="N199B2"><emph type="italics"></emph>Hinc finis motus naturalis omninò conuenit cum principio motus violenti; </s>
					<s id="N199B8"><lb></lb>&amp; finis huius cum principio illius<emph.end type="italics"></emph.end>; quæcumque tandem progreſſio accipia­<lb></lb>tur; </s>
					<s id="N199C2">ſiue temporum æqualium in ſpatiis inæqualibus; ſiue ſpatio­<lb></lb>rum æqualium in temporibus inæqualibus, ſiue aſſumantur inſtan­<lb></lb>tia in progreſſione arithmetica ſimplici iuxta hos numeros 1.2.3.4. ſiue <lb></lb>aſſumantur temporis partes ſenſibiles in progreſſione Galilei iuxta hos <lb></lb>numeros 1.3.5.7. quæ omnia ex dictis neceſſariò conſequuntur. </s>
				</p>
				<p id="N199CE" type="main">
					<s id="N199D0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N199DC" type="main">
					<s id="N199DE"><emph type="italics"></emph>Nec modò conuenit principium vnius cum alterius fine, &amp; viciſſim, ſed <lb></lb>etiam aliæ partes motus in diſtantiis æqualibus<emph.end type="italics"></emph.end> ſit enim linea AG, quam <lb></lb>percurrit mobile demiſſum ex puncto A deorſum motu naturaliter ac­<lb></lb>celerato, &amp; moueatur per 6. inſtantia, ſeu 6. tempora æqualia: </s>
					<s id="N199ED">Primo <lb></lb>inſtanti, quo percurrit ſpatium AB; </s>
					<s id="N199F3">haud dubiè, quando peruenit ad pun­<lb></lb>ctum G, habet 7. gradus impetus æquales, quia ante motum AB habebat <lb></lb>innatum; </s>
					<s id="N199FB">ſed in motu illo fluunt 6. tempora æqualia, vt dictum eſt; </s>
					<s id="N199FF">igitur <lb></lb>6. acquirit gradus impetus, quorum quidem vltimò acquiſitus nullum <lb></lb>adhuc habuit motum; </s>
					<s id="N19A07">ſed haud dubiè haberet, ſi vlteriùs hic motus pro­<lb></lb>pagaretur: </s>
					<s id="N19A0D">his poſitis imprimantur mobili in O 7.gradus impetus æqua­<lb></lb>les prioribus ſursùm motu violento, per lineam OH; </s>
					<s id="N19A13">certè primo inſtan­<lb></lb>ti motus, ſeu tempore æquali prioribus percurret ON, id eſt 6. ſpatiola; </s>
					<s id="N19A19"><lb></lb>quia licèt ſint 7.gradus; </s>
					<s id="N19A1E">attamen impetus innatus corporis grauis detra­<lb></lb>hit vnum ſpatium, ſimulque deſtruit vnum gradum, ſecundo tempore <lb></lb>percurret NM 5. tertio ML 4. quarto LK 3. quinto KI 2. ſexto IH 1. <lb></lb>igitur primum violenti ON reſpondet vltimo naturali FG ſeu ſecun­<lb></lb>dum illius quinto huius, tertium illius quarto huius, quartum tertio, <lb></lb>quintum ſecundo ſextum primo, &amp; viciſſim; idem prorſus in progreſſione <lb></lb>Galilei accidit, aſſumptis ſcilicet partibus temporis ſenſibilibus. </s>
				</p>
				<p id="N19A2E" type="main">
					<s id="N19A30"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19A3C" type="main">
					<s id="N19A3E"><emph type="italics"></emph>Hinc ad eam altitudinem aſcendit motu violento cum iis gradibus impe­<lb></lb>tus, quos habuit ab eadem altitudine decidens motu naturali<emph.end type="italics"></emph.end>; conſtat ex <lb></lb>dictis. </s>
				</p>
				<pb pagenum="143" xlink:href="026/01/175.jpg"></pb>
				<p id="N19A4F" type="main">
					<s id="N19A51"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19A5D" type="main">
					<s id="N19A5F"><emph type="italics"></emph>Hinc ſi motus violentus, &amp; naturalis durent æqualibus temporibus, ſpatia <lb></lb>vtriuſque erunt æqualia<emph.end type="italics"></emph.end>; </s>
					<s id="N19A6A">conſtat etiam ex dictis v.g. corpus graue, motu <lb></lb>naturali in libero aëre tempore duorum ſecundorum percurrit 48. pe­<lb></lb>des, igitur ſi moueatur ſurſum æquali tempore percurret 48. pedes per <lb></lb>ſe, dico per ſe; quippe ratione figuræ corporis ſecus accidere poteſt, vt <lb></lb>plurimùm etiam accedit ratione motus mixti ex motu centri recto, &amp; <lb></lb>motu orbis circulari, de quo infrà. </s>
				</p>
				<p id="N19A7A" type="main">
					<s id="N19A7C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19A88" type="main">
					<s id="N19A8A"><emph type="italics"></emph>Hinc, vt ſpatia vtroque motu diuerſa ſunt æqualia, ita tempora quibus de­<lb></lb>curruntur ſunt æqualia,<emph.end type="italics"></emph.end> &amp; impetus acquiſitus in fine naturalis cum in­<lb></lb>nato eſt æqualis impetui producta in principio violenti. </s>
				</p>
				<p id="N19A96" type="main">
					<s id="N19A98"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19AA4" type="main">
					<s id="N19AA6"><emph type="italics"></emph>Hinc tandiu durat deſcenſus mobilis proiecti ſursùm motu violento, quan­<lb></lb>diu durat eiuſdem aſcenſus, &amp; tot habet gradus impetus in fine deſcenſus, <lb></lb>quot habet in principio aſcenſus<emph.end type="italics"></emph.end>; </s>
					<s id="N19AB3">eſt enim æquale ſpatium; </s>
					<s id="N19AB7">igitur æquale <lb></lb>tempus; igitur æqualis vtrobique impetus. </s>
					<s id="N19ABD">Sed hîc duo obiici poſſunt, <lb></lb>primò ſagittam per lineam verticalem vibratam poſuiſſe tantùm in aſ­<lb></lb>cenſu 3. ſecunda, in deſcenſu verò 5. vt ſæpiùs obſeruatum eſt, teſte Mer­<lb></lb>ſenno; </s>
					<s id="N19AC7">ſecundò, ſi eodem tempore corpus graue ſursùm proiectum motu <lb></lb>violento aſcenderet, quo deinde deſcendit, in fine deſcenſus æqualis <lb></lb>eſſet ictus, ſeu percuſſio vtriuſque; cum tamen illa ſit maior, quæ infli­<lb></lb>gitur motu violento, vt conſtat multis experimentis. </s>
				</p>
				<p id="N19AD1" type="main">
					<s id="N19AD3">Reſpondeo ad primum etiam teſte Merſenno globum ferreum trium <lb></lb>aut 4. librarum ſurſum exploſum è breuiore tormento ſed latiore, æqua­<lb></lb>le tempus in aſcenſu, &amp; in deſcenſu inſumpſiſſe; </s>
					<s id="N19ADB">quod reuerâ ſecùs acci­<lb></lb>dit ſagittæ, cuius differentia aſcenſus, &amp; deſcenſus ſenſu etiam percipi <lb></lb>poteſt; </s>
					<s id="N19AE3">tùm quia lignea materia multò leuior eſt ferro, tùm quia leuiſſi­<lb></lb>mæ illæ pennæ, quibus inſtruitur, motum retardant in deſcenſu; </s>
					<s id="N19AE9">quod <lb></lb>maximè confirmatur ex eo quod pluma facilè anhelitu ſurſum pellatur <lb></lb>ſatis veloci motu, quæ deinde tardiſſimo ſua ſponte deſcendit: </s>
					<s id="N19AF1">præterea <lb></lb>mucro ferreus, quo ſagitta armatur, ſemper præire debet, cuius rei ratio­<lb></lb>nem afferemus infrà; </s>
					<s id="N19AF9">igitur cum in aſcenſu præeat, vt præeat in deſcen­<lb></lb>ſu, altera extremitas ſemicirculum ſuo motu facere debet, qui certè ad <lb></lb>naturalem motum pertinet, altera tamen extremitas, quæ mouetur mo­<lb></lb>tu contrario alterius motum retardat; ad ſecundam obiectionem <lb></lb>reſpondebo Th.44. </s>
				</p>
				<p id="N19B05" type="main">
					<s id="N19B07"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19B13" type="main">
					<s id="N19B15"><emph type="italics"></emph>Si motus violentus eſſet æquabilis, ſpatium eſſet ferè duplum illius, quod <lb></lb>percurritur motu naturaliter retardato, aſſumptis ſcilicet <expan abbr="tẽporibus">temporibus</expan> æqualibus<emph.end type="italics"></emph.end>; </s>
					<s id="N19B24"><lb></lb>cum enim motu æquabili compoſito ex ſubdupla velocitate maximæ, &amp; <lb></lb>minimæ motus accelerati æquali tempore percurratur æquale ſpatium, <lb></lb>ſubduplum minimæ pro nihilo ferè habetur; </s>
					<s id="N19B2D">igitur poteſt tantùm aſſu-<pb pagenum="144" xlink:href="026/01/176.jpg"></pb>mi ſubduplum maximæ; igitur velocitas motus ſit æqualis maximæ, haud <lb></lb>dubiè ſpatium duplum percurretur. </s>
				</p>
				<p id="N19B38" type="main">
					<s id="N19B3A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19B46" type="main">
					<s id="N19B48"><emph type="italics"></emph>Hinc benè à naturâ inſtitutum fuit impetum naturalem innatum ſemper <lb></lb>conſeruari<emph.end type="italics"></emph.end>; </s>
					<s id="N19B53">alioqui violentus eſſet æquabilis, igitur nunquam deſineret: <lb></lb>quantum abſurdum! quale incommodum &amp;c. </s>
				</p>
				<p id="N19B59" type="main">
					<s id="N19B5B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19B67" type="main">
					<s id="N19B69"><emph type="italics"></emph>Eadem eſt ratio ſeu proportio ictuum, &amp; percuſſionum, quæ integrorum <lb></lb>ſpatiorum quæ ſcilicet toto motu percurruntur in aſcenſu &amp; deſcenſu,<emph.end type="italics"></emph.end> v. g. <lb></lb>corpus graue cadens ex data altitudine 48 pedum æqualem ictum infli­<lb></lb>git in fine deſcenſus, &amp; in principio aſcenſus, quo ſcilicet ad <expan abbr="eãdem">eandem</expan> <lb></lb>altitudinem aſcenderet; </s>
					<s id="N19B81">probatur, quia æqualis acquiritur impetus in <lb></lb>deſcenſu alteri, qui deſtruitur in aſcenſu, aſſumptis dumtaxat ſpatiis illis <lb></lb>æqualibus; </s>
					<s id="N19B89">igitur æqualis eſt in fine deſcenſus, in quo eſt totus acquiſi­<lb></lb>tus, atque in principio aſcenſus, in quo nullus eſt deſtructus: </s>
					<s id="N19B8F">ad id verò, <lb></lb>quod dicebatur ſuprà de ſagitta, cuius ictus maior eſt initio aſcenſus, <lb></lb>quàm in fine deſcenſus non diffiteor; </s>
					<s id="N19B97">quia materia ſagittæ, tùm lignea <lb></lb>tùm plumea motum ſatis ſuperque retardat, vt differentia ictuum ſenſu <lb></lb>ipſo percipi poſſit; quæ tamen nulla perciperetur in aſcenſu deſcenſu­<lb></lb>que globi ferrei. </s>
				</p>
				<p id="N19BA1" type="main">
					<s id="N19BA3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19BAF" type="main">
					<s id="N19BB1"><emph type="italics"></emph>Hinc reiicies Galileum, &amp; alios eius ſectatores qui volunt impetum corpori <lb></lb>impreſſum deſtrui tantùm ab aëre<emph.end type="italics"></emph.end>; </s>
					<s id="N19BBC">quod pluſquàm falſum eſſe comper­<lb></lb>tum eſt, vt demonſtrauimus ſuprà Th. 20. quaſi verò non adſit aliqua <lb></lb>cauſa neceſſaria deſtructiua, ſcilicet impetus innatus; </s>
					<s id="N19BC4">hinc etiam eum­<lb></lb>dem reiicies, qui vult numquam fieri poſſe, vt motu naturaliter accelera­<lb></lb>to tanta acquiratur velocitas, quanta imprimitur in motu violento; </s>
					<s id="N19BCC">vult <lb></lb>enim motum acceleratum tranſire in æquabilem, cuius contrarium de­<lb></lb>monſtrauimus ſuprà Th. 131, l. 2. igitur cum creſcat ſemper velocitas, <lb></lb>nullus eſt finitus gradus, quem tandem non aſſequatur; immò vt dictum <lb></lb>eſt in præcedenti Th. aſſumptis æqualibus ſpatiis, impetus, qui eſt in <lb></lb>principio aſcenſus, æqualis eſt cum eo, qui eſt in fine deſcenſus. </s>
				</p>
				<p id="N19BDC" type="main">
					<s id="N19BDE">Diceret fortè aliquis cadentem globum ex altiſſimæ turris apice de­<lb></lb>clinare à perpendiculari antequam terram feriat, vt conſtat ex multis <lb></lb>experimentis; </s>
					<s id="N19BE6">igitur præualet tandem reſiſtentia aëris: </s>
					<s id="N19BEA">ſed reſpondeo id <lb></lb>tantùm accidere propter currentem illac aëris tractum; alioquin non <lb></lb>eſſet potiùs ratio, cur in vnam partem declinaret, quàm in aliam. </s>
				</p>
				<p id="N19BF2" type="main">
					<s id="N19BF4"><emph type="center"></emph><emph type="italics"></emph>Theoroma<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19C00" type="main">
					<s id="N19C02"><emph type="italics"></emph>Non eſt eadem ratio ictuum, ſeu percuſſionum, quæ eſt ſegmentorum in­<lb></lb>tegri ſpatij<emph.end type="italics"></emph.end>; </s>
					<s id="N19C0D">v.g. in ſubduplo ſpatij ſegmento non eſt ſubduplus ictus, ſit <lb></lb> enim ſpatium integrum motus vîolenti OH, &amp; principium motus ſit <lb></lb>in O, finis in H; </s>
					<s id="N19C17">accipiatur ſegmentum OM, quod eſt quaſi ſubduplum O <lb></lb>H, ictus in M non eſt profectò ſubduplus ictus in O, ſed tantùm in L, vt <pb pagenum="145" xlink:href="026/01/177.jpg"></pb>conſtat ex dictis; igitur rationes ictuum non ſunt, vt rationes ſegmen­<lb></lb>torum integri ſpatij. </s>
				</p>
				<p id="N19C24" type="main">
					<s id="N19C26"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19C32" type="main">
					<s id="N19C34"><emph type="italics"></emph>Vt in praxi determinentur rationes ictuum<emph.end type="italics"></emph.end>; </s>
					<s id="N19C3D">aſſumatur progreſſio Gali­<lb></lb>lei in AF, ita vt ſi prima parte temporis ſenſibili percurratur ſpatium <lb></lb>FE 9 partium æqualium; </s>
					<s id="N19C45">ſecunda percurratur ED. 7. partium, tertia <lb></lb>DC 5. quarta CB 3; </s>
					<s id="N19C4B">quinta BA 1. hoc poſito facilè erit determinare <lb></lb>rationes ictuum; </s>
					<s id="N19C51">nam in deſcenſu ictus ſunt vt velocitates, &amp; hæ vt tem­<lb></lb>pora; </s>
					<s id="N19C57">igitur ſi AB percurritur in dato tempore, &amp; AC in duobus prio­<lb></lb>ri æqualibus; </s>
					<s id="N19C5D">certè ictus in deſcenſu AC eſt duplus ictus in deſcenſu <lb></lb>AB; in AD triplus, &amp;c. </s>
					<s id="N19C63">Igitur in aſcenſu ictus in F erit quintuplus, <lb></lb>ictus in E quadruplus in D triplus, &amp;c. </s>
					<s id="N19C68">igitur ictus ſunt in ratione dupli­<lb></lb>cata ſpatiorum facto ſpatij initio à ſummo puncto A. </s>
				</p>
				<p id="N19C6E" type="main">
					<s id="N19C70"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19C7C" type="main">
					<s id="N19C7E"><emph type="italics"></emph>Hinc cognitis viribus, quibus corpus graue proijcitur ad datam altitudi­<lb></lb>nem, cognoſci poſſunt vires, quibus ad aliam quamcumque proijciatur<emph.end type="italics"></emph.end>; </s>
					<s id="N19C89">v. g. <lb></lb>proiiciatur corpus graue ad altitudinem 48. pedum; </s>
					<s id="N19C92">vires ſunt iis æqua­<lb></lb>les, quas acquirit in deſcenſu eiuſdem altitudinis 48. pedum; </s>
					<s id="N19C98">ſit alia di­<lb></lb>ſtantia 100. pedum; haud dubiè vires neceſſariæ ad motum hunc violen­<lb></lb>tum ſunt æquales iis, quas acquireret in deſcenſu 100. pedum per Th. <lb></lb>40. atqui ita ſe habent vires acquiſitæ in deſcenſu 48. pedum ad vires <lb></lb>acquiſitas in deſcenſu 100. vt v.g. 48. ad v.g. 100. id eſt ferè vt 7. <lb></lb>ad 10. </s>
				</p>
				<p id="N19CAB" type="main">
					<s id="N19CAD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19CB9" type="main">
					<s id="N19CBB"><emph type="italics"></emph>Cognitis etiam ſpatiis cognoſcetur tempus<emph.end type="italics"></emph.end>; </s>
					<s id="N19CC4">ſit enim decurſum idem ſpa­<lb></lb>tium 48. pedum motu violento ſurſum; </s>
					<s id="N19CCA">idque v. g. tempore 2. ſecundo­<lb></lb>rum, quod ferè cum experientia conſentit; </s>
					<s id="N19CD4">ſit aliud ſpatium 100. tempus <lb></lb>primi motus eſt ad tempus ſecundi vt v. g. 48. ad v. g. 100. quia ſpatia <lb></lb>ſunt vt quadrata temporum; </s>
					<s id="N19CE4">igitur tempora vt radices 4. hinc vires ſunt <lb></lb>in ratione temporum; </s>
					<s id="N19CEA">quia vt temporibus æqualibus acquiruntur æqua­<lb></lb>lia velocitatis momenta in motu naturali, ita &amp; deſtruuntur æqualia in <lb></lb>motu violento, quæ omnia conſtant; igitur ictus ſunt vt vires, vires vt <lb></lb>tempora, tempora denique, vt radices <expan abbr="q.">que</expan> ſpatiorum. </s>
				</p>
				<p id="N19CF8" type="main">
					<s id="N19CFA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 150.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19D06" type="main">
					<s id="N19D08"><emph type="italics"></emph>In vltimo contactu motus violenti nullus eſt ictus, v. g. mobile projectum <lb></lb>ſurſum<emph.end type="italics"></emph.end> <emph type="italics"></emph>per lineam<emph.end type="italics"></emph.end> FA <emph type="italics"></emph>nullam percuſſionem infligeret in<emph.end type="italics"></emph.end> A; </s>
					<s id="N19D23">probatur <lb></lb>quia non tendit vlteriùs; </s>
					<s id="N19D29">igitur non impeditur eius motus à ſuperficie <lb></lb>corporis terminati ad punctum A; igitur nullum impetum in eo produ­<lb></lb>cit, qui tantùm producitur ad tollendum impedimentum per Th.44.l.1. <lb></lb>igitur nullum ictum infligit, qui tantùm infligitur per impetum, vt <lb></lb>conſtat. </s>
				</p>
				<p id="N19D35" type="main">
					<s id="N19D37"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19D43" type="main">
					<s id="N19D45"><emph type="italics"></emph>Ex his ſatis facilè comparari poſſunt rationes percuſſionis,<emph.end type="italics"></emph.end> quæ infliguntur <pb pagenum="146" xlink:href="026/01/178.jpg"></pb>tùm ex caſu corporis grauis cadentis, tùm ex vi mallei impacti, tùm ex <lb></lb>impetu corporis projecti, tùm ex grauitatione corporis grauis incum­<lb></lb>bentis, quæ omnia hîc fuſiùs eſſent tractanda, niſi locum proprium infrà <lb></lb>ſibi vendicarent. </s>
				</p>
				<p id="N19D58" type="main">
					<s id="N19D5A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19D66" type="main">
					<s id="N19D68"><emph type="italics"></emph>Ad motum violentum non concurrit impetus innatus,<emph.end type="italics"></emph.end> probatur, quia im­<lb></lb>petus ad lineas oppoſitas ex diametro determinati ad communem li­<lb></lb>neam determinari non poſſunt, cur enim potiùs dextrorſum quam ſini­<lb></lb>strorſum? </s>
					<s id="N19D76">igitur non concurrunt ad communem motum, niſi dicatur <lb></lb>impetus innatus valeo nomine concurrere ad violentum, quod eius li­<lb></lb>neam ſingulis temporibus quaſi caſtiget, vltróque, vel vlteriùs currentem <lb></lb>contineat. </s>
				</p>
				<p id="N19D7F" type="main">
					<s id="N19D81"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19D8D" type="main">
					<s id="N19D8F"><emph type="italics"></emph>Hinc ad motum violentum impetus ab exteriore potentia mobili impreſſus <lb></lb>tantùm concurrit<emph.end type="italics"></emph.end>; </s>
					<s id="N19D9A">patet, cum enim in mobili projecto ſurſum ſit tantùm <lb></lb>ille impetus præter innatum, nec innatus concurrat per Th. 52. illum <lb></lb>tantùm concurrere neceſſe eſt: excipe ſemper impetum acquiſitum, de <lb></lb>quo iam ſuprà. </s>
				</p>
				<p id="N19DA4" type="main">
					<s id="N19DA6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19DB2" type="main">
					<s id="N19DB4"><emph type="italics"></emph>Primo instanti quo producitur impetus ille à potentia motrice in mobili, me­<lb></lb>diante ſcilicet impetu producto in organo proprio, non eſt motus<emph.end type="italics"></emph.end>; probatur, <lb></lb>quia primo inſtanti, quo eſt impetus, non eſt motus, per Th.34.l.1. </s>
				</p>
				<p id="N19DC2" type="main">
					<s id="N19DC4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19DD0" type="main">
					<s id="N19DD2"><emph type="italics"></emph>Impetus productus in manu producit impetum in organo vel in mobili pri­<lb></lb>mo inſtanti, quo eſt<emph.end type="italics"></emph.end>; </s>
					<s id="N19DDD">probatur, quia ſecundo inſtanti exigit motum ſui ſub­<lb></lb>jecti; </s>
					<s id="N19DE3">igitur tolli etiam impedimentum; </s>
					<s id="N19DE7">igitur per motum medij; </s>
					<s id="N19DEB">igitur <lb></lb>priori inſtanti in eodem mobili debet eſſe impetus; </s>
					<s id="N19DF1">igitur produci ab <lb></lb>impetu organi; igitur &amp; in organo ab impetu manus. </s>
				</p>
				<p id="N19DF7" type="main">
					<s id="N19DF9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19E05" type="main">
					<s id="N19E07"><emph type="italics"></emph>Primo inſtanti, quo producitur impetus in motu violento, nullus eius gra­<lb></lb>dus deſtruitur<emph.end type="italics"></emph.end>; probatur, quia alioquin ſimul eodem inſtanti, quo eſſe in­<lb></lb>ciperet, eſſe deſineret, quod dici non poteſt. </s>
				</p>
				<p id="N19E14" type="main">
					<s id="N19E16"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19E22" type="main">
					<s id="N19E24"><emph type="italics"></emph>Impetus innatus impedit ne producatur tantus impetus in motu violento,<emph.end type="italics"></emph.end><lb></lb>probatur, quia certè tàm impedit primam productionem, quàm conſer­<lb></lb>uationem, vt patet; </s>
					<s id="N19E30">eſt enim par vtrobique ratio; præterea agit in ipſam <lb></lb>manum. </s>
				</p>
				<p id="N19E36" type="main">
					<s id="N19E38"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19E44" type="main">
					<s id="N19E46"><emph type="italics"></emph>Impetus violentus producitur minor, quàm produceretur vno dumtaxat gra­<lb></lb>du aquali ipſi impetui innato<emph.end type="italics"></emph.end>; </s>
					<s id="N19E51">quippe ſicut deſtruit ſingulis inſtantibus <lb></lb>æqualibus vnum gradum; </s>
					<s id="N19E57">quia pugnat pro rata; </s>
					<s id="N19E5B">ita prorſus impedit, ne <pb pagenum="147" xlink:href="026/01/179.jpg"></pb>producatur vnus gradus ſibi æqualis primo inſtanti; cur enim duo po­<lb></lb>tiùs, quàm tres? </s>
				</p>
				<p id="N19E66" type="main">
					<s id="N19E68"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19E74" type="main">
					<s id="N19E76"><emph type="italics"></emph>Secundo ſtatim inſtanti deſtruit alterum gradum<emph.end type="italics"></emph.end>: </s>
					<s id="N19E7F">quippe eſt cauſa ne­<lb></lb>ceſſaria; </s>
					<s id="N19E85">igitur ſtatim primo inſtanti exigit deſtructionem; </s>
					<s id="N19E89">non certè <lb></lb>pro primo inſtanti per Th.56.igitur pro ſecundo, atque ita pro aliis dein­<lb></lb>ceps; deſtruitur autem, ne ſit fruſtrà eo modo, quo diximus ſuprà. </s>
				</p>
				<p id="N19E91" type="main">
					<s id="N19E93"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19E9F" type="main">
					<s id="N19EA1"><emph type="italics"></emph>Hinc optima ratio illius instituti naturæ, quo factum eſt, vt impetus innatus <lb></lb>numquam destruatur<emph.end type="italics"></emph.end>; </s>
					<s id="N19EAC">ne ſi aliquando deſtrueretur, nulla eſſet cauſa de­<lb></lb>ſtructiua impetus violenti; ac proinde æquabilis eſſet, ſemperque dura­<lb></lb>ret, deſtructiua inquam ſuo modo. </s>
				</p>
				<p id="N19EB4" type="main">
					<s id="N19EB6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19EC2" type="main">
					<s id="N19EC4"><emph type="italics"></emph>Hinc corpus quod non grauitat, facilè proijcitur, vel impellitur<emph.end type="italics"></emph.end>: </s>
					<s id="N19ECD">ſic na­<lb></lb>uis aquis innatans, nubes in aëre liberatæ; halitus, atque adeo ipſæ partes <lb></lb>aquæ, quas perexiguus lapillus in orbes penè innumeros agit, ne quid <lb></lb>dicam de partibus aëris, quæ tam citò &amp; procul mouentur, vt conſtat in <lb></lb>ſono, motu ſcilicet ferè æquabili. </s>
				</p>
				<p id="N19ED9" type="main">
					<s id="N19EDB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19EE7" type="main">
					<s id="N19EE9"><emph type="italics"></emph>Hinc etiam è contrario corpus grauius difficiliùs ſurſum proijcitur<emph.end type="italics"></emph.end>: </s>
					<s id="N19EF2">tùm <lb></lb>quia plures partes impetus ſunt producendæ in ſubjecto grauiore quod <lb></lb>pluribus partibus conſtat, tùm impetus innatus maior eſt, non quidem in <lb></lb>intenſione ſed in extenſione, ac proinde impedit ne plures gradus pro­<lb></lb>ducantur; quippe maius impedimentum plus impedit, quis hoc neget? </s>
				</p>
				<p id="N19EFE" type="main">
					<s id="N19F00"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19F0C" type="main">
					<s id="N19F0E"><emph type="italics"></emph>Omnes partes impetus productæ in mobili primo instanti concurrunt ad <lb></lb>motum ſecundi instantis<emph.end type="italics"></emph.end>; probatur, quia alioqui aliqua eſſet fruſtrà, quod <lb></lb>dici non debet. </s>
				</p>
				<p id="N19F1B" type="main">
					<s id="N19F1D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19F29" type="main">
					<s id="N19F2B"><emph type="italics"></emph>Concurrunt omnes illæ, quæ inſunt eidem parti ſeu puncto mobilis <expan abbr="commun">communes</expan> <lb></lb>quaſi actione vel exigentia<emph.end type="italics"></emph.end>; patet ex dictis de impetu, quia concurrunt ad <lb></lb>velocitatem, quæ eſt indiuiſibilis actu. </s>
				</p>
				<p id="N19F3C" type="main">
					<s id="N19F3E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19F4A" type="main">
					<s id="N19F4C"><emph type="italics"></emph>Non ponitur tamen totus motus ſecundo instanti, quem exigunt primo; <emph.end type="italics"></emph.end><lb></lb>quia impetus innatus aliquid detrahit, cum exigat motum deorſum per <lb></lb>lineam oppoſitam, igitur imminuitur motus pro rata. </s>
				</p>
				<p id="N19F58" type="main">
					<s id="N19F5A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19F66" type="main">
					<s id="N19F68"><emph type="italics"></emph>Hinc ille gradus motus qui non ponitur ſecundo instanti respondet gradus <lb></lb>impetus qui destruitur<emph.end type="italics"></emph.end>; cum vterque habeat <expan abbr="eãdem">eandem</expan> menſuram, ſcilicet <lb></lb>impetum innatum. </s>
				</p>
				<pb pagenum="148" xlink:href="026/01/180.jpg"></pb>
				<p id="N19F7D" type="main">
					<s id="N19F7F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19F8B" type="main">
					<s id="N19F8D"><emph type="italics"></emph>Hinc effectus peteſt eſſe eo instanti quo non existit eius cauſa partialis<emph.end type="italics"></emph.end>; </s>
					<s id="N19F96">v.g. <lb></lb>motus qui ponitur ſecundo inſtanti non minùs exigitur ab eo gradu im­<lb></lb>petus qui deſtruitur ſecundò inſtanti, quàm ab aliis, non exigitur qui­<lb></lb>dem ſecundo ſed primo pro ſecundo; </s>
					<s id="N19FA1">vnde dixi cauſam partialem, quia <lb></lb>etiam exigitur ab aliis gradibus impetus, qui non deſtruuntur exigentiâ <lb></lb>communi; </s>
					<s id="N19FA9">quippe impetus non exigit niſi pro ſecundo inſtanti; </s>
					<s id="N19FAD">nec vl­<lb></lb>lum abſurdum eſt eo inſtanti cauſam exigentiæ non exiſtere cum poni­<lb></lb>tur eius effectus, ſcilicet id quod exigebat priori inſtanti quo erat; </s>
					<s id="N19FB5">nul­<lb></lb>lus eſt enim influxus huius cauſæ; præſertim cum non ſit cauſa <lb></lb>totalis. </s>
				</p>
				<p id="N19FBD" type="main">
					<s id="N19FBF">Vnde cum effectus qui ponitur ſecundo inſtanti non reſpondeat per­<lb></lb>fectioni cauſæ totius propter impedimentum, aliquis gradus cauſæ eſſet <lb></lb>fruſtrà; </s>
					<s id="N19FC7">igitur eodem inſtanti ſecundo deſtrui debet, alioqui niſi deſtrue­<lb></lb>retur ſingulis inſtantibus poneretur effectus non reſpondens perfectioni <lb></lb>cauſæ; </s>
					<s id="N19FCF">immò numquam deſtrueretur totus motus violentus, vt conſtat; </s>
					<s id="N19FD3"><lb></lb>itaque primo inſtanti omnes gradus impetus qui ſunt exigunt motum <lb></lb>pro ſecundo ne aliquis eo inſtanti ſit fruſtrà ſi non exigeret, &amp; ſecundo <lb></lb>inſtanti aliquis gradus impetus deſtruitur, ne ſit fruſtrà eodem inſtanti <lb></lb>ſecundo, cum ſcilicet non ſint tot gradus motus, quot ſunt gradus impe­<lb></lb>tus; atque ita deinceps tertio inſtanti deſtruitur vnus gradus, vt iam ſu­<lb></lb>prà dictum eſt. </s>
				</p>
				<p id="N19FE2" type="main">
					<s id="N19FE4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N19FF0" type="main">
					<s id="N19FF2"><emph type="italics"></emph>Ideo deſtruitur potiùs vnus gradus impetus quàm alius ſecundo inſtanti, <lb></lb>tertioque, &amp;c. </s>
					<s id="N19FF9">quia talis eſt perfectionis<emph.end type="italics"></emph.end>; </s>
					<s id="N1A000">hoc iam ſuprà explicatum eſt; quia <lb></lb>cum motus initio ſit velocior, inſtantia ſunt minora, igitur minùs im­<lb></lb>petus in ſingulis deſtruitur, pater ex dictis. </s>
				</p>
				<p id="N1A008" type="main">
					<s id="N1A00A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A016" type="main">
					<s id="N1A018"><emph type="italics"></emph>Ille gradus impetus qui deſtruitur ſecundo inſtanti non concurrit ad motum <lb></lb>tertij inſtantis<emph.end type="italics"></emph.end>; </s>
					<s id="N1A023">quia non poteſt concurrere ad motum niſi exigendo; </s>
					<s id="N1A027">at­<lb></lb>qui exigere tantùm poteſt, quando eſt; </s>
					<s id="N1A02D">quod enim non eſt non exigit, <lb></lb>ſed motus tertij inſtantis exigitur ſecundo; </s>
					<s id="N1A033">ſic enim tota res motus pro­<lb></lb>cedit vt impetus primo inſtanti exigat motum pro ſecundo; </s>
					<s id="N1A039">&amp; ſecundo <lb></lb>pro tertio; </s>
					<s id="N1A03F">&amp; tertio pro quarto, atque ita deinceps; </s>
					<s id="N1A043">igitur impetus ille <lb></lb>qui deſtruitur; ſecundo inſtanti non exigit motum pro tertio, &amp; qui de­<lb></lb>ſtruitur tertio non exigit pro quarto, atque ita deinceps. </s>
				</p>
				<p id="N1A04B" type="main">
					<s id="N1A04D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A059" type="main">
					<s id="N1A05B"><emph type="italics"></emph>Hinc impetus innatus non concurrit ad motum violentum,<emph.end type="italics"></emph.end> vt dictum eſt, <lb></lb>ſed tantùm impedit, immediatè quidem, quia cum exigat motum deor­<lb></lb>sùm, facit vt non ſit tantus motus ſurſum; </s>
					<s id="N1A068">mediatè verò, quia cum non <lb></lb>ſit tantus motus ſursùm, quantus eſſet, haud dubiè non reſpondet adæ­<lb></lb>quatè cauſæ; </s>
					<s id="N1A070">igitur aliquid cauſæ fruſtrà eſt; </s>
					<s id="N1A074">igitur deſtrui debet; hinc <pb pagenum="149" xlink:href="026/01/181.jpg"></pb>deſtruitur etiam hic impetus per principium commune, ne aliquid ſit <lb></lb>fruſtrà. </s>
				</p>
				<p id="N1A07F" type="main">
					<s id="N1A081"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A08D" type="main">
					<s id="N1A08F"><emph type="italics"></emph>Linea motus ſurſum determinatur à potentia motrice<emph.end type="italics"></emph.end>; </s>
					<s id="N1A098">probatur, quia hæc <lb></lb>determinat impetum productum in manu vel in organo; </s>
					<s id="N1A09E">hic verò im­<lb></lb>petum, quem producit in mobili ſursùm projecto; patet, quia nulla eſt <lb></lb>alia cauſa applicata. </s>
				</p>
				<p id="N1A0A6" type="main">
					<s id="N1A0A8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A0B4" type="main">
					<s id="N1A0B6"><emph type="italics"></emph>Tandem duo impetus violentus, ſcilicet, &amp; innatus ad æqualitatem perue­<lb></lb>nirent, ſi vel vnus gradus violenti eſſet æqualis perfectionis cum innato<emph.end type="italics"></emph.end>; </s>
					<s id="N1A0C1">cum <lb></lb>enim detrahatur ſemper pars aliquota alicuius totius, tandem perueni­<lb></lb>tur ad vltimam; </s>
					<s id="N1A0C9">igitur ſint 100. gradus impetus violenti, quorum quili­<lb></lb>bet ſit æqualis impetui innato; </s>
					<s id="N1A0CF">certè cum temporibus æqualibus æqua­<lb></lb>lis gradus impetus deſtruatur; </s>
					<s id="N1A0D5">accipiatur illud tempus, in quo deſtrui­<lb></lb>tur vnus, haud dubiè 100. æqualibus temporibus deſtruentur omnes 100. <lb></lb>igitur 99. inſtantibus deſtruentur 99. gradus; </s>
					<s id="N1A0DD">igitur ſupereſt vnus; igitur <lb></lb>duo illi impetus perueniunt tandem ad æqualitatem. </s>
				</p>
				<p id="N1A0E3" type="main">
					<s id="N1A0E5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 73.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A0F1" type="main">
					<s id="N1A0F3"><emph type="italics"></emph>Vbi vterque perueniſſet ad æqualitatem, non eſſet potior ratio cur mobile mo­<lb></lb>ueretur ſursùm quàm deorſum inſtanti ſequenti<emph.end type="italics"></emph.end>; </s>
					<s id="N1A0FE">probatur, quia tàm gra­<lb></lb>dus impetus innati exigit motum deorſum quàm gradus impetus vio­<lb></lb>lenti ſursùm; igitur neuter habebit motum per Th.133.l. </s>
					<s id="N1A106">1. </s>
				</p>
				<p id="N1A10A" type="main">
					<s id="N1A10C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A118" type="main">
					<s id="N1A11A"><emph type="italics"></emph>Hinc ipſo inſtanti, quo eſſet æqualitas, eſſet adhuc motus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A123">quia inſtanti <lb></lb>immediatè antecedenti erant duo gradus impetus violenti, &amp; vnus in­<lb></lb>nati; igitur duo illi præualent pro inſtanti ſequenti, in quo eſt æqua­<lb></lb>litas. </s>
				</p>
				<p id="N1A12D" type="main">
					<s id="N1A12F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 75.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A13B" type="main">
					<s id="N1A13D"><emph type="italics"></emph>Itaque quieſceret mobile ipſo ſtatim inſtanti, quod inſtanti æqualitatis ſuc­<lb></lb>cedit<emph.end type="italics"></emph.end>; patet, quia neuter impetus pro illo inſtanti præualere poſſet per <lb></lb>Th. 73. </s>
				</p>
				<p id="N1A14A" type="main">
					<s id="N1A14C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A158" type="main">
					<s id="N1A15A"><emph type="italics"></emph>Igitur inſtanti quietis nullus eſſet ampliùs impetus violentus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A163">cum enim <lb></lb>ſingulis inſtantibus deſtruatur vnus gradus, v. g inſtanti illo, quod ſe­<lb></lb>quitur poſt inſtans æqualitatis, deſtruitur ille gradus, qui ſupereſt; </s>
					<s id="N1A16D">nec <lb></lb>poteſt vel plùs, vel minùs deſtrui; </s>
					<s id="N1A173">pugnant enim pro rata; quod certè <lb></lb>cuiquam fortè paradoxor videbitur, ſcilicet nullum tune eſſe motum <lb></lb>propter pugnam, cum tamen nulla eſt amplius pugna. </s>
				</p>
				<p id="N1A17B" type="main">
					<s id="N1A17D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A189" type="main">
					<s id="N1A18B"><emph type="italics"></emph>Quies illa duraret tantùm vno inſtanti,<emph.end type="italics"></emph.end> probatur, quia cum inſtanti quie­<lb></lb>tis ſit tantùm impetus innatus per Th. 76. certè non impeditur quomi­<lb></lb>nus habeat motum pro inſtanti ſequenti, quem reuerà exigit; </s>
					<s id="N1A198">igitur pro <pb pagenum="150" xlink:href="026/01/182.jpg"></pb>inſtanti ſequenti moueritur; </s>
					<s id="N1A1A1">ſed pro alio antecedente mouebatur; igi­<lb></lb>tur quies illa durat tantùm vno inſtanti. </s>
				</p>
				<p id="N1A1A7" type="main">
					<s id="N1A1A9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A1B5" type="main">
					<s id="N1A1B7"><emph type="italics"></emph>Quies illa non fit propter aliquam reflexionem, vt aliqui dicunt<emph.end type="italics"></emph.end>; </s>
					<s id="N1A1C0">quia nul­<lb></lb>la prorſus eſt reflexio, vbi nullum eſt reflectens; </s>
					<s id="N1A1C6">atqui nullum eſt refle­<lb></lb>ctens, vt patet, quia nullum eſt corpus impediens motus propagationem; </s>
					<s id="N1A1CC"><lb></lb>licèt enim medium impediat, non tamen per modum reflectentis pro­<lb></lb>priè; </s>
					<s id="N1A1D3">immo vt dicemus infrà in puncto reflexionis nulla datur quies; ſed <lb></lb>motus reflexus ſibi vendicat librum ſingularem. </s>
				</p>
				<p id="N1A1D9" type="main">
					<s id="N1A1DB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A1E7" type="main">
					<s id="N1A1E9"><emph type="italics"></emph>Hinc ſiue præceſſerit motus violentus, ſiue non, corpus graue eodem vel æ­<lb></lb>quali motu deorſum cadit,<emph.end type="italics"></emph.end> quia nullus amplius remanet impetus violen­<lb></lb>tus in fine motus violenti, per Th.76. igitur ſolus impetus naturalis li­<lb></lb>bero motu deorsùm fertur. </s>
				</p>
				<p id="N1A1F7" type="main">
					<s id="N1A1F9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A205" type="main">
					<s id="N1A207"><emph type="italics"></emph>Hinc reiicies aliquos apud Galileum, qui volunt ideo motum naturalem <lb></lb>accelerari, quia ſenſim deſtruitur impetus violentus antè impreſſus,<emph.end type="italics"></emph.end> quod pe­<lb></lb>nitus ridiculum eſt; quia lapis deciſus è rupe etiam motu naturaliter <lb></lb>accelerato deorſum cadit, licèt eò nunquam motu violento euectus <lb></lb>fuerit. </s>
				</p>
				<p id="N1A218" type="main">
					<s id="N1A21A">Obſeruabis hanc hypotheſim gradus impetus violenti æqualis perfe­<lb></lb>ctionis cum innato eſſe falſam. </s>
					<s id="N1A21F">Primò, quia commodius eſt potentiæ <lb></lb>motrici producere imperfectiorem impetum, ſic enim plures illius gra­<lb></lb>dus producere poteſt. </s>
					<s id="N1A226">Secundò, quia in reflexo ſurſum vltimus gradus <lb></lb>qui deſtruitur eſt imperfectior innato, eſt enim acquiſitus; igitur in omni <lb></lb>alio motu ſursùm. </s>
					<s id="N1A22E">Tertiò, quia violentus eſt cum innato in eadem ſubie­<lb></lb>cti parte; ſed idem ſubiectum formas homogeneas non patitur, de quò <lb></lb>aliàs, hinc dicendum ſupereſt non quieſcere mobile in fine motus </s>
				</p>
				<p id="N1A236" type="main">
					<s id="N1A238"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A244" type="main">
					<s id="N1A246"><emph type="italics"></emph>Corpus quod non grauitat proiicitur ſurſum motu æquabili per ſe<emph.end type="italics"></emph.end>; </s>
					<s id="N1A24F">patet, quia <lb></lb>nihil eſt quod deſtruat ipſum impetum; </s>
					<s id="N1A255">igitur ſemper moueretur, niſi <lb></lb>per accidens ab ipſo medio eius motus retardaretur; </s>
					<s id="N1A25B">vnde dixi <emph type="italics"></emph>per ſe,<emph.end type="italics"></emph.end><lb></lb>cum ratione medij retardetur; immò quò leuius eſt, faciliùs à medio re­<lb></lb>tinetur, vide Th.61. </s>
				</p>
				<p id="N1A268" type="main">
					<s id="N1A26A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A276" type="main">
					<s id="N1A278"><emph type="italics"></emph>Non creſcit impetus naturalis in motu violento ſurſum<emph.end type="italics"></emph.end>; probatur primò, <lb></lb>quia impetus naturalis aduentitius ſupponit motum deorſum, ad cuius <lb></lb>intenſionem à natura fuit inſtitutus per reſp. </s>
					<s id="N1A285">ad quartam obiect. </s>
					<s id="N1A288">in diſ­<lb></lb>ſert.l.2. adde quod tardiùs aſcenderet, quàm deſcenderet; </s>
					<s id="N1A28E">deinde velo­<lb></lb>ciùs deſcenderet poſtmotum violentum corpus graue, quàm ſi nullo mo­<lb></lb>tu violento præuio demitteretur deorſum, quæ omnia experimentis <pb pagenum="151" xlink:href="026/01/183.jpg"></pb><expan abbr="etiã">etiam</expan> vulgaribus repugnant; immò &amp; cunctis ferè præmiſſis Theorematis. </s>
				</p>
				<p id="N1A29F" type="main">
					<s id="N1A2A1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A2AD" type="main">
					<s id="N1A2AF"><emph type="italics"></emph>Motus violentus non tendit ad quietem per omnes tarditatis gradus, vt <lb></lb>paſſim aſſerit Galileus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A2BA">Primò, quia non ſunt infinita inſtantia, ſed retarda­<lb></lb>tur tantùm ſingulis inſtantibus; </s>
					<s id="N1A2C0">Secundò in medio denſiore minùs du­<lb></lb>rat; </s>
					<s id="N1A2C6">igitur non tranſit per tot gradus tarditatis; </s>
					<s id="N1A2CA">præterea in plano incli­<lb></lb>nato ſurſum în minore proportione retardatur motus, quod etiam in <lb></lb>plano horizontali certiſſimum eſt; quorum omnium rationes ſuo loco <lb></lb>videbimus. </s>
				</p>
				<p id="N1A2D4" type="main">
					<s id="N1A2D6">Nec eſt quod aliqui dicant infinito tribui non poſſe hæc prædicata <lb></lb>æqualitatis vel inæqualitatis, quod falſum eſt, loquamur de infinito actu; </s>
					<s id="N1A2DC"><lb></lb>ſi enim eſſet numerus infinitus hominum, nunquid verum eſſet dicere <lb></lb>numerum oculorum eſſe maiorem numero hominum; </s>
					<s id="N1A2E3">nec eſt quod ali­<lb></lb>qui confugiant ad diſiunctiones; </s>
					<s id="N1A2E9">nos rem iſtam ſuo loco fusè tractabi­<lb></lb>mus &amp; demonſtrabimus, ni fallor, cum Ariſtotele, fieri non pòſſe vt ſit <lb></lb>aliquod creatum infinitum actu; </s>
					<s id="N1A2F1">licèt vltrò concedamus plura eſſe infi­<lb></lb>nita potentiâ; &amp; verò certum eſt infinito potentiâ non ineſſe huiuſmodi <lb></lb>prædicata æqualitatis, vel inæqualitatis. </s>
				</p>
				<p id="N1A2F9" type="main">
					<s id="N1A2FB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A307" type="main">
					<s id="N1A309"><emph type="italics"></emph>Immò ſi tranſiret mobile ſursùm proiectum per omnes tarditatis gradus, <lb></lb>nunquam profectò deſcenderat<emph.end type="italics"></emph.end>; </s>
					<s id="N1A314">quia cum ſingulis inſtantibus ſinguli gra­<lb></lb>dus reſpondeant, &amp; duo inſtantia ſimul eſſe non poſſint; </s>
					<s id="N1A31A">nunquam certè <lb></lb>verum eſſet dicere fluxiſſe infinita; </s>
					<s id="N1A320">igitur nec mobile per infinitos tar­<lb></lb>ditatis gradus ad quietem perueniſſe; hoc Theorema ſupponit eſſe tan­<lb></lb>tùm finita inſtantia. </s>
				</p>
				<p id="N1A328" type="main">
					<s id="N1A32A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A336" type="main">
					<s id="N1A338"><emph type="italics"></emph>Reſiſtentia aëris est maior initio, quàm in fine motus violenti,<emph.end type="italics"></emph.end> vt conſtat ex <lb></lb>dictis, quia initio motus eſt velocior, igitur plures partes aëris æquali <lb></lb>tempore reſiſtunt; in fine verò è contrario. </s>
				</p>
				<p id="N1A345" type="main">
					<s id="N1A347"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A353" type="main">
					<s id="N1A355"><emph type="italics"></emph>Hinc oppoſita eſt omninò ratio reſistentia, quæ ſequitur ex motu violento illi, <lb></lb>quæ cum naturali eſt coniuncta,<emph.end type="italics"></emph.end> hæc enim initio minor, in fine maior, illa <lb></lb>verò initio maior, &amp; in fine minor; hinc prima creſcit cam ſuo motu, <lb></lb>ſecunda cum ſuo decreſcit. </s>
				</p>
				<p id="N1A364" type="main">
					<s id="N1A366"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A372" type="main">
					<s id="N1A374"><emph type="italics"></emph>Decreſcit igitur impetus eadem proportione, qua decreſcit reſiſtentia<emph.end type="italics"></emph.end>; vt pa­<lb></lb>tet ex dictis; igitur in toto motu eadem eſt reſiſtentiæ proportio. </s>
				</p>
				<p id="N1A37F" type="main">
					<s id="N1A381"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A38D" type="main">
					<s id="N1A38F"><emph type="italics"></emph>Variæ ſunt potentiæ motrices, à quibus mobile ſurſum proiici potest motu <lb></lb>violento,<emph.end type="italics"></emph.end> v.g. potentia motrix animantium, potentia motrix grauium mo­<lb></lb>bili ſcilicet ſurſum repercuſſo; potentia motrix, quæ ſequitur ex com­<lb></lb>preſſione &amp; rarefactione corporum, ſed de his omnibus aliàs. </s>
				</p>
				<pb pagenum="152" xlink:href="026/01/184.jpg"></pb>
				<p id="N1A3A4" type="main">
					<s id="N1A3A6"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A3B2" type="main">
					<s id="N1A3B4">Obſeruabis primò ſi aliquando accidat, vt aliqui volunt ictum, qui <lb></lb>ſtatim initio motus violenti infligitur, non eſſe maximum, ſed minorem <lb></lb>eo, qui poſt aliquod confectum ſpatium infligitur; </s>
					<s id="N1A3BC">quod probant in pila <lb></lb>ex fiſtula ænea ſurſum emiſſa, quæ <expan abbr="moiorẽ">maiorem</expan> ictum infligit in data diſtantia, <lb></lb>quod ſanè ſi verum eſt, hæc vnica eſt, ſeu ratio, ſeu cauſa, quòd ſcilicet ſur­<lb></lb>ſum pila pellatur ab igne, qui ab ore fiſtulæ erumpens per aliquod ſpa­<lb></lb>tium à tergo vrget; igni enim innatum eſt ſurſum euolare. </s>
				</p>
				<p id="N1A3CC" type="main">
					<s id="N1A3CE">Obſeruabis ſecundò, vix poſſe manu mobile ſurſum rectà proiici, quia <lb></lb>ſcilicet manus extremitas motu mixto mouetur ex duobus vel pluribus <lb></lb>circularibus, de quo infrà. </s>
				</p>
				<p id="N1A3D5" type="main">
					<s id="N1A3D7">Obſerua tertiò, non tantùm propter grauitationem conſeruari impe­<lb></lb>tum naturalem innatum, ſed etiam vt motui violento reſiſtat; at verò <lb></lb>non reſiſteret, niſi grauitaret. </s>
				</p>
				<p id="N1A3DF" type="main">
					<s id="N1A3E1">Obſerua quartò, reciprocas rationes motus naturalis &amp; violenti; in <lb></lb>quibus mirabile prorſus fuit naturæ inſtitutum, cum idem in vtroque il­<lb></lb>larum ſit principium. </s>
				</p>
				<p id="N1A3E9" type="main">
					<s id="N1A3EB">Obſerua quintò, finem motus violenti eſſe multiplicem, nullum ta­<lb></lb>men à natura inſtitutum; </s>
					<s id="N1A3F1">quippe potentia motrix, quæ agit ex appetitu <lb></lb>elicito, (vt vulgò aiunt,) ſeu cum cognitione, finem ſibi proponit ad libi­<lb></lb>tùm; </s>
					<s id="N1A3F9">illa verò quæ vi compreſſionis excitatur per accidens ſurſum agit <lb></lb>mobile potiùs, quàm per aliam lineam; repercuſſa ſursùm videntur eſſe <lb></lb>magis iuxta inſtitutum naturæ. <lb></lb><figure id="id.026.01.184.1.jpg" xlink:href="026/01/184/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N1A407">
				<pb pagenum="153" xlink:href="026/01/185.jpg"></pb>
				<figure id="id.026.01.185.1.jpg" xlink:href="026/01/185/1.jpg"></figure>
				<p id="N1A411" type="head">
					<s id="N1A413"><emph type="center"></emph>LIBER QVARTVS,  <lb></lb><emph type="italics"></emph>DE MOTV MIXTO EX <lb></lb>duobus, vel pluribus rectis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A422" type="main">
					<s id="N1A424">MOTVM mixtum eum eſſe non dico, qui <lb></lb>ex pluribus aliis motibus componatur; <lb></lb>ſeu miſceatur; </s>
					<s id="N1A42C">nec enim plures motus <lb></lb>ſimul eſſe poſſunt in eodem mobili; </s>
					<s id="N1A432">cùm <lb></lb>tantùm eſſe poſſit vno dumtaxat inſtan­<lb></lb>ti vnica migratio ex loco in locum; </s>
					<s id="N1A43A">nec plura loca <lb></lb>naturali virtute ſimul acquiri poſſunt; </s>
					<s id="N1A440">Igitur nec ſi­<lb></lb>mul eſſe duo motus; </s>
					<s id="N1A446">Itaque motus mixtus ſimplex <lb></lb>eſt, ſi conſideretur ratio, &amp; linea motus; </s>
					<s id="N1A44C">mixtus verò <lb></lb>dicitur, quod ex pluribus reſultet, qui reuerâ non <lb></lb>ſunt, ſed cùm eſſe poſſint, quaſi confluunt in tertium <lb></lb>motum communi ſumptu quaſi de vtroque partici­<lb></lb>pantem, quod totum fit propter diuerſos impetus, <lb></lb>vel <expan abbr="eũdem">eundem</expan> ad diuerſas lineas determinatum, vt fusè <lb></lb>explicabimus infrà: Porrò in hoc Libro explicamus <lb></lb>tantùm motum mixtum, qui reſultat ex pluribus re­<lb></lb>ctis, vt titulus ipſe præfert. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N1A467" type="main">
					<s id="N1A469"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A475" type="main">
					<s id="N1A477"><emph type="italics"></emph>MOtus mixtus eſt, qui ſequitur ex multiplici impetu ad <expan abbr="eãdem">eandem</expan>, vel di­<lb></lb>uerſas lineas determinato, vel eodem ad diuerſas<emph.end type="italics"></emph.end>; </s>
					<s id="N1A486">hæc definitio cla­<lb></lb>ra eſt; </s>
					<s id="N1A48C">obſeruabis tantùm ad motum mixtum ſufficere duplicem impe-<pb pagenum="154" xlink:href="026/01/186.jpg"></pb>tum ad <expan abbr="eãdem">eandem</expan> lineam determinatam, deorſum, v.g. in mobili proiecto; </s>
					<s id="N1A49B"><lb></lb>nec enim eſt motus purè naturalis, nec etiam violentus, vt conſtat; igi­<lb></lb>tur mixtus. </s>
				</p>
				<p id="N1A4A2" type="main">
					<s id="N1A4A4"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A4B1" type="main">
					<s id="N1A4B3"><emph type="italics"></emph>Cum proiicitur corpus per lineam horizontalem, vel inclinatum ſurſum, <lb></lb>vel deorſum mobile percurrit lineam curuam<emph.end type="italics"></emph.end>; quod etiam pueri ſciunt, qui <lb></lb>diſco ludunt. </s>
				</p>
				<p id="N1A4C0" type="main">
					<s id="N1A4C2"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A4CF" type="main">
					<s id="N1A4D1"><emph type="italics"></emph>Globus etiam plumbeus è ſummo malo malo mobilis nauis demiſſus per <lb></lb>lineam perpendicularem deorſum minimè cadit, ſed per curuam inclinatam<emph.end type="italics"></emph.end>: </s>
					<s id="N1A4DC"><lb></lb>hæc hypotheſis mille ſaltem nititur experimentis; </s>
					<s id="N1A4E1">modò ſufficiat quod <lb></lb>ſit; nam propter quid ſit, demonſtrabo. </s>
				</p>
				<p id="N1A4E7" type="main">
					<s id="N1A4E9"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A4F6" type="main">
					<s id="N1A4F8"><emph type="italics"></emph>Proiectum per horizontalem ſub finem motus minùs ferit quàm initio, imò <lb></lb>&amp; proiectum per inclinatam deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1A503">hæc hypotheſis centies probata fuit; <lb></lb>nec in dubium reuocari poteſt. </s>
				</p>
				<p id="N1A509" type="main">
					<s id="N1A50B"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A518" type="main">
					<s id="N1A51A"><emph type="italics"></emph>Omnis impetus qui mobili ineſt dum ipſum mouetur, præſtat aliquid ad mo­<lb></lb>tum<emph.end type="italics"></emph.end>; </s>
					<s id="N1A525">vel enim retardat, vt impetus innatus retardat violentum, vt ſuprà <lb></lb>diximus; vel ad motum vnà cum alio, vel ſolus concurrit. </s>
					<s id="N1A52B">Ax.2. </s>
				</p>
				<p id="N1A52E" type="main">
					<s id="N1A530"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A53D" type="main">
					<s id="N1A53F"><emph type="italics"></emph>Ille impetus qui alium retardat, haud dubiè retardat tantùm pro rata<emph.end type="italics"></emph.end>; <lb></lb>hoc etiam ſuprà demonſtrauimus, &amp; qui deſtruitur, deſtruitur quoque <lb></lb>pro rata, ne ſit fruſtrà qui deſtruitur. </s>
				</p>
				<p id="N1A54C" type="main">
					<s id="N1A54E"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A55B" type="main">
					<s id="N1A55D"><emph type="italics"></emph>Ille impetus qui cum alio ad <expan abbr="eũdem">eundem</expan> motum concurrit, concurrit etiam pro <lb></lb>rata<emph.end type="italics"></emph.end>; hoc etiam ſuprà demonſtratum eſt, eſt enim cauſa neceſſaria, igitur <lb></lb>quantum poteſt concurrit, igitur pro rata ſuæ virtutis. </s>
				</p>
				<p id="N1A56E" type="main">
					<s id="N1A570"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A57D" type="main">
					<s id="N1A57F"><emph type="italics"></emph>Licèt ſint plures impetus in eodem mobili, non ſunt tamen plures ſimul li­<lb></lb>neæ motus<emph.end type="italics"></emph.end>; ne mobile ſit ſimul in pluribus locis. </s>
				</p>
				<p id="N1A58A" type="main">
					<s id="N1A58C"><emph type="center"></emph><emph type="italics"></emph>Poſtulatum<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A599" type="main">
					<s id="N1A59B"><emph type="italics"></emph>Liceat aſſumere quamlibet coniugationem motuum,<emph.end type="italics"></emph.end> v. g. vel duorum æ­<lb></lb>quabilium, vel alterius æquabilis, &amp; alterius retardati, vel alterius æqua­<lb></lb>bilis, &amp; alterius accelerati, vel alterius retardati, &amp; alterius accelera­<lb></lb>ti, &amp;c. </s>
				</p>
				<p id="N1A5AD" type="main">
					<s id="N1A5AF"><emph type="center"></emph><emph type="italics"></emph>Poſtulatum<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A5BC" type="main">
					<s id="N1A5BE"><emph type="italics"></emph>Illa linea vocetur curua quæ conſtat infinitis prope lateribus polygoni.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1A5C5" type="main">
					<s id="N1A5C7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A5D4" type="main">
					<s id="N1A5D6"><emph type="italics"></emph>Motus mixtus ex duobus æquabilibus æqualibus eſt rectus<emph.end type="italics"></emph.end>; ſit enim mo-<pb pagenum="155" xlink:href="026/01/187.jpg"></pb>bile in A, ſitque impetus per AB, &amp; alter æqualis per AD, motus mixtus <lb></lb>fiet per AE, aſſumpta ſcilicet DE æquali, &amp; parallela AB, quod probatur <lb></lb>per Th.137.l.1. </s>
				</p>
				<p id="N1A5E9" type="main">
					<s id="N1A5EB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A5F8" type="main">
					<s id="N1A5FA"><emph type="italics"></emph>Linea AE eſt diagonalis quadrati, quotieſcumque vterque impetus eſt æ­<lb></lb>qualis, &amp; lineæ determinationum decuſſantur ad angulos rectos<emph.end type="italics"></emph.end>; probatur per <lb></lb>idem Th.137. </s>
				</p>
				<p id="N1A608" type="main">
					<s id="N1A60A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A617" type="main">
					<s id="N1A619"><emph type="italics"></emph>Hinc deſtruitur aliquid impetus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A622">alioquin motus eſſet duplus cuiuſli­<lb></lb>bet ſeorſim ſumpti, quod falſum eſt; </s>
					<s id="N1A628">nam motus ſunt vt lineæ ſed diago­<lb></lb>nalis quadrati non eſt dupla lateris; hoc etiam probatur per Th. 141. <lb></lb>&amp; 142.l.1. </s>
				</p>
				<p id="N1A630" type="main">
					<s id="N1A632"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A63F" type="main">
					<s id="N1A641"><emph type="italics"></emph>Motus mixtus ex duobus æquabilibus inæqualibus est etiam rectus<emph.end type="italics"></emph.end>; ſit <lb></lb>enim mobile in A eadem figura ſitque impetus per AC, &amp; alter ſubdu­<lb></lb>plus prioris per AD, motus fiet per AF ducta DF æquali, &amp; parallela AC, <lb></lb>quod probatur per Th.137.l.1. </s>
				</p>
				<p id="N1A651" type="main">
					<s id="N1A653"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A660" type="main">
					<s id="N1A662"><emph type="italics"></emph>Linea AF eſt diagonalis rectanguli, quotieſcunque lineæ determinationum <lb></lb>decuſſantur ad angulos rectos<emph.end type="italics"></emph.end>; probatur per idem Th.137. </s>
				</p>
				<p id="N1A66E" type="main">
					<s id="N1A670"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A67D" type="main">
					<s id="N1A67F"><emph type="italics"></emph>Hinc deſtruitur aliquid impetus per Th.<emph.end type="italics"></emph.end>141. &amp; 142.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. idque pro rata <lb></lb>ne aliquid ſit fruſtrà per Ax.2. &amp; ſæpè iam probatum eſt. </s>
				</p>
				<p id="N1A68F" type="main">
					<s id="N1A691"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A69D" type="main">
					<s id="N1A69F"><emph type="italics"></emph>Hinc determinari poteſt portio vtriuſque impetus destructi,<emph.end type="italics"></emph.end> v.g. ſi ſint æ­<lb></lb>quales, portio detracta vtrique æqualibus temporibus eſt differentia <lb></lb>diagonalis &amp; compoſitæ ex DA, AB, quod clarum eſt; ſi vero impetus <lb></lb>ſint inæquales, portio deſtructa erit ſemper differentia diagonalis, v.g. <lb></lb>AF &amp; compoſitæ ex AC.AD. </s>
				</p>
				<p id="N1A6B3" type="main">
					<s id="N1A6B5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A6C1" type="main">
					<s id="N1A6C3"><emph type="italics"></emph>Aliquando impetus qui remanet in motu mixto est rationalis<emph.end type="italics"></emph.end>; </s>
					<s id="N1A6CC">id eſt habet <lb></lb>proportionem ad vtrumque, quæ appellari poteſt, aliquando ad neutrum, <lb></lb><expan abbr="aliquãdo">aliquando</expan> ad alterutrum; </s>
					<s id="N1A6D7">ad vtrumque v.g. ſi alter impetuum ſit 8.alter 6. <lb></lb>haud dubiè linea motus mixti erit 10. ad neutrum vt in diagonali qua­<lb></lb>drati, &amp; in multis aliis; </s>
					<s id="N1A6E1">ad alterum denique v. g. ſi alter ſit ſubduplus la­<lb></lb>teris æquilateri; alter verò eiuſdem perpendicularis; nam diagonalis, ſeu <lb></lb>linea motus mixti erit latus ipſum æquilateri. </s>
				</p>
				<p id="N1A6ED" type="main">
					<s id="N1A6EF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A6FB" type="main">
					<s id="N1A6FD"><emph type="italics"></emph>Si lineæ determinationum decuſſentur ad angulum obtuſum, ſintque æqua­<lb></lb>les impetus, linea motus mixti erit diagonalis Rhombi<emph.end type="italics"></emph.end>; </s>
					<s id="N1A708">vt patet per Th.140. <lb></lb>l.1. poteſt autem hæc diagonalis eſſe vel æqualis alteri laterum, vel ma-<pb pagenum="156" xlink:href="026/01/188.jpg"></pb>ior, vel minor; eſt æqualis, quando angulus maior Rhombi eſt 120. eſt <lb></lb>minor cùm angulus minor eſt 60. denique eſt maior, cùm maior angu­<lb></lb>lus eſt minor 120, quæ omnia conſtant ex Geometria. </s>
				</p>
				<p id="N1A718" type="main">
					<s id="N1A71A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A726" type="main">
					<s id="N1A728"><emph type="italics"></emph>Si lineæ determinationum decuſſentur ad angulum acutum, &amp; ſint æqua­<lb></lb>les impetus, linea motus mixti erit diagonalis Rhombi<emph.end type="italics"></emph.end>; quæ certè eò longior <lb></lb>erit, quò angulus erit acutior per Th. 139. l.1. porrò eſt ſemper maior <lb></lb>lateribus ſeorſim ſumptis. </s>
				</p>
				<p id="N1A737" type="main">
					<s id="N1A739"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A745" type="main">
					<s id="N1A747">Obſerua in Rhombo eſſe duas diagonales inæquales, vt conſtat; </s>
					<s id="N1A74B">igi­<lb></lb>tur cùm lineæ determinationum decuſſantur ad angulum obtuſum, linea <lb></lb>motus mixti ſemper eſt diagonalis minor; cùm verò decuſſantur ad an­<lb></lb>gulum acutum, ſemper eſt diagonalis maior. </s>
				</p>
				<p id="N1A755" type="main">
					<s id="N1A757"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A764" type="main">
					<s id="N1A766">Hinc quò acutior eſt angulus diagonalis accedit propiùs ad duplum <lb></lb>lateris, donec tandem vtraque linea coëat; tunc enim linea motus eſt du­<lb></lb>pla lateris. </s>
				</p>
				<p id="N1A76E" type="main">
					<s id="N1A770"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A77D" type="main">
					<s id="N1A77F">Hinc quoque quò angulus eſt obtuſior diagonalis accedit propiùs ad <lb></lb>nullam, vt ſic loquar, donec tandem vtraque linea concurrat in rectam, <lb></lb>tunc enim nulla eſt diagonalis; igitur nulla linea motus. </s>
				</p>
				<p id="N1A787" type="main">
					<s id="N1A789"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A795" type="main">
					<s id="N1A797"><emph type="italics"></emph>Cum alter impetuum eſt maior, linea motus eſt diagonalis Rhomboidis, mi­<lb></lb>nor quidem ſi lineæ decuſſentur ad angulum obtuſum; </s>
					<s id="N1A79F">maior verò ſi decuſſen­<lb></lb>tur ad angulum acutum<emph.end type="italics"></emph.end>; vt patet ex dictis. </s>
				</p>
				<p id="N1A7A8" type="main">
					<s id="N1A7AA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A7B6" type="main">
					<s id="N1A7B8"><emph type="italics"></emph>Cum alter impetus in motu mixto est maior, linea motus mixti accedit <lb></lb>proprius ad lineam maioris; </s>
					<s id="N1A7C0">hoc est facit angulum acutiorem cum illa<emph.end type="italics"></emph.end>; v.g. in <lb></lb>eadem figura ſit linea impetus maioris AC, &amp; minoris AD, linea motus <lb></lb>mixti eſt diagonalis AF, quæ accedit propiùs ad AC, quàm ad AD, id eſt <lb></lb>facit angulum acutiorem cum AC, vt patet ex dictis. </s>
				</p>
				<p id="N1A7CF" type="main">
					<s id="N1A7D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A7DD" type="main">
					<s id="N1A7DF"><emph type="italics"></emph>Cum verò impetus ſunt æquales, linea motus mixti facit angulum æqualem <lb></lb>cum linea vtriuſque<emph.end type="italics"></emph.end>; vt AE in eadem figura quod etiam dici debet, licèt <lb></lb>lineæ determinationum decuſſentur ad angulum obtuſum vel acutum, <lb></lb> vt AC, EG. IM. </s>
				</p>
				<p id="N1A7EE" type="main">
					<s id="N1A7F0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A7FC" type="main">
					<s id="N1A7FE"><emph type="italics"></emph>Non creſcit, vel decreſcit in eadem ratione, in quæ vnus impetus ſuperat <lb></lb>alium<emph.end type="italics"></emph.end>; </s>
					<s id="N1A809">cum enim impetus ſint vt lineæ, ſub quibus fiunt rectangula vel <lb></lb>Rhomboides; v.g. impetus AC eſt duplus impetus AD, ſed angulus D <lb></lb>AF non eſt duplus anguli FAC, vt conſtat ex Geometria. </s>
				</p>
				<pb pagenum="157" xlink:href="026/01/189.jpg"></pb>
				<p id="N1A818" type="main">
					<s id="N1A81A"><emph type="center"></emph><emph type="italics"></emph>Scolium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A826" type="main">
					<s id="N1A828">Obſeruabis dari de facto hunc motum mixtum ex duobus æquabilibus <lb></lb>in rerum natura; </s>
					<s id="N1A82E">talis eſt motus nauis, quam geminus ventus impellit in <lb></lb>mari, vel nubis, imò aëris pars in medio aëre, atque adeo ipſius venti, <lb></lb>ſunt enim hi motus æquabiles per ſe; quippe retardantur ſolummodo <lb></lb>propter reſiſtentiam medij, non verò propter vllam grauitationem. </s>
				</p>
				<p id="N1A838" type="main">
					<s id="N1A83A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A846" type="main">
					<s id="N1A848"><emph type="italics"></emph>Motus mixtus ex duobus retardatis eſt rectus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A851">ſit enim duplex impetus <lb></lb>per AE &amp; AH æqualis; </s>
					<s id="N1A857">ita vt in dato tempore percurrat ſeorſim AE mo­<lb></lb>tu retardato; </s>
					<s id="N1A85D">item AH iuxta proportionem Galilei; </s>
					<s id="N1A861">certè eo tempore quo <lb></lb>percurreret AD in AE, &amp; AI in AH percurrit AG motu mîxto per Th. <lb></lb>5. Similiter eo tempore quo percurreret AE ſeorſim, &amp; AH, percurrit <lb></lb>AF per Th.5. Igitur hic motus mixtus eſt rectus, dum ſit vterque retar­<lb></lb>datus iuxta <expan abbr="eãdem">eandem</expan> progreſſionem; </s>
					<s id="N1A872">ſimiliter ſi alter impetus impetus <lb></lb>ſit inæqualis, vt patet in ſequenti figura, ſit enim impetus per AE, &amp; <lb></lb>alter minor per AH, certè ex AD, AI fit AG, &amp; ex AE, AH fit AF, quam <lb></lb>rectam eſſe conſtat ex Geometria; nec vlla eſt difficultas, quæ ex ſupe­<lb></lb>rioribus Theorematis facilè ſolui non poſſit. </s>
				</p>
				<p id="N1A87E" type="main">
					<s id="N1A880"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A88D" type="main">
					<s id="N1A88F">Hinc linea motus mixti ex duobus retardatis ſiue æqualibus, ſiue <lb></lb>inæqualibus eſt diagonalis parallelogrammatis ſub lineis determina­<lb></lb>tionum. </s>
				</p>
				<p id="N1A896" type="main">
					<s id="N1A898"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A8A4" type="main">
					<s id="N1A8A6">Obſeruabis dari de facto hunc motum in rerum natura, ſi v. g. in pla­<lb></lb>no horizontali idem globus, vel ſimul gemino ictu impellatur, vel ſi iam <lb></lb>impulſum mobile per nouam lineam impellatur. </s>
				</p>
				<p id="N1A8B1" type="main">
					<s id="N1A8B3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A8BF" type="main">
					<s id="N1A8C1"><emph type="italics"></emph>Motus mixtus ex duobus acceleratis uniformiter eſt etiam rectus<emph.end type="italics"></emph.end>; </s>
					<s id="N1A8CA">Proba­<lb></lb>tur, quia debet tantùm inuerti linea prioris ſcilicet mixti ex duobus re­<lb></lb>tardatis; </s>
					<s id="N1A8D2">ſi enim à puncto F pellatur per FE, FH, motu accelerato, ita <lb></lb>primo, tempori reſpondeat FM, FN, ſecundo NH, ME; </s>
					<s id="N1A8D8">haud dubiè li­<lb></lb>nea motus mixti erit FA; nam primò tempori reſpondebit FG, &amp; duo­<lb></lb>bus FA, vt conſtat ex dictis, ſiue vterque impetus ſit æqualis, ſiue alter <lb></lb>maior altero. </s>
				</p>
				<p id="N1A8E2" type="main">
					<s id="N1A8E4"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A8F1" type="main">
					<s id="N1A8F3">Hinc etiam linea motus mixti ex duobus acceleratis eſt diagonalis, <lb></lb>vt iam ſuprà dictum eſt de omnibus aliis. </s>
				</p>
				<p id="N1A8F8" type="main">
					<s id="N1A8FA"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A906" type="main">
					<s id="N1A908">Obſeruabis hunc motum dari in rerum natura ſaltem in corporibus <lb></lb>ſublunaribus; nec enim eſt acceleratus niſi ſit motus naturalis, qui à <lb></lb>duplici impetu eſſe non poteſt. </s>
				</p>
				<pb pagenum="158" xlink:href="026/01/190.jpg"></pb>
				<p id="N1A914" type="main">
					<s id="N1A916"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A922" type="main">
					<s id="N1A924"><emph type="italics"></emph>Si motus mixtus conſtet ex æquabili, &amp; accelerato naturaliter ſit per li­<lb></lb>neam curuam<emph.end type="italics"></emph.end>; </s>
					<s id="N1A92F">ſit enim impetus per AF motu æquabili, &amp; per AC motu <lb></lb>accelerato naturaliter, ita vt eo tempore quo percurritur ſeorſim ſpa­<lb></lb>tium AB percurratur AD triplum; </s>
					<s id="N1A937">certè ex vtroque primo tempore re­<lb></lb>ſultat linea motus mixti AE, ſecundo tempore EG, ſed AEG non eſt <lb></lb>recta; alioquin duo triangula ABE, ACG eſſent proportionalia, quod <lb></lb>eſt abſurdum. </s>
				</p>
				<p id="N1A941" type="main">
					<s id="N1A943"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A94F" type="main">
					<s id="N1A951"><emph type="italics"></emph>Hæc linea eſt Parabola<emph.end type="italics"></emph.end>; </s>
					<s id="N1A95A">quod ipſe Galileus toties inſinuauit, &amp; quiuis <lb></lb>etiam rudior Geometra intelliget; in quo diutiùs non hæreo, præſertim <lb></lb>cùm nullus ſit motus, qui conſtet ex æquabili, &amp; naturaliter accelerato, <lb></lb>vt demonſtrabimus infrà. </s>
				</p>
				<p id="N1A964" type="main">
					<s id="N1A966"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A972" type="main">
					<s id="N1A974"><emph type="italics"></emph>Si motus mixtus conſtet ex æquabili &amp; naturaliter retardato, fit per lineam <lb></lb>curuam<emph.end type="italics"></emph.end>; ſi enim eo <expan abbr="tẽpore">tempore</expan> quo per NE ſurſum proiicitur corpus graue <lb></lb>&amp; conſequenter motu naturaliter retardato impellatur per NI motu <lb></lb>æquabili, diuidatur NI in 4. partes æquales v.g. ductis parallelis RD, <lb></lb>NE, PC, &amp;c. </s>
					<s id="N1A98B">aſſumatur NS vel RM, cui affigatur quilibet numerus impar; </s>
					<s id="N1A98F"><lb></lb>putà 7. itaque RM ſint 7. ducatur HM parallelæ IN, aſſumatur QL 5. <lb></lb>ducatur GL parallela, accipiatur VK 3. ducatur FK: </s>
					<s id="N1A996">denique aſſumatur <lb></lb>FAI ducaturque AE parallela IN, &amp; deſcribatur per puncta AKLMN, <lb></lb>linea curua; </s>
					<s id="N1A99E">hæc eſt Parabola, vt conſtat ex Geometria; </s>
					<s id="N1A9A2">nam ſi BK eſt 1. <lb></lb>CL erit 4. DM 9. EV 16. ſed æquales ſunt AF.AG.AH.AI. prioribus vt <lb></lb>patet; </s>
					<s id="N1A9AA">igitur ſagittæ ſunt vt quadrata <expan abbr="applicatarũ">applicatarum</expan>; </s>
					<s id="N1A9B2">igitur hæc eſt Parabola; <lb></lb>igitur curua, atqui motus mixtus prædictus fieret per hanc lineam, nam <lb></lb>eo tempore quo mobile eſſet in S, erit in M, concurrit enim vterque im­<lb></lb>petus pro rata, &amp; eo tempore, quo eſſet in K erit in L, atque ita <lb></lb>deinceps. </s>
				</p>
				<p id="N1A9BE" type="main">
					<s id="N1A9C0"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1A9CC" type="main">
					<s id="N1A9CE">Obſeruabis eſſe prorſus inuerſam prioris, quæ ſit ex motu æquabili, &amp; <lb></lb>naturaliter accelerato; </s>
					<s id="N1A9D4">ſi enim per AE ſit æquabilis &amp; æqualis priori <lb></lb>per NI, &amp; per AI ſit acceleratus, ſi quo tempore peruenit in B motu æ­<lb></lb>quabili perueniat in F motu accelerato; haud dubiè perueniet in K, mox <lb></lb>in L, &amp;c. </s>
					<s id="N1A9DE">quia eadem proportione, ſed inuerſa quâ retardatur, <lb></lb>acceleratur; </s>
					<s id="N1A9E4">igitur ſi vltimo tempore retardati acquirit tantùm <lb></lb>YE; </s>
					<s id="N1A9EA">primo tempore æquali ſcilicet accelerati acquiret AF, atque ita <lb></lb>deinceps ſi per NE ſit retardatus, &amp; per NI æquabilis linea motus mixti <lb></lb>erit NLA; </s>
					<s id="N1A9F2">ſi verò ſit per AI acceleratus, &amp; per AE æquabilis æqualis <lb></lb>priori per NI, lineamosus mixti erit ALN eadem ſcilicet cum priori <lb></lb>mutatis tantùm terminis à quo, &amp; ad quem; vtrùm verò in rerum natu­<lb></lb>ra ſit huiuſmodi motus videbimus infrà. </s>
				</p>
				<pb pagenum="159" xlink:href="026/01/191.jpg"></pb>
				<p id="N1AA00" type="main">
					<s id="N1AA02"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AA0E" type="main">
					<s id="N1AA10"><emph type="italics"></emph>Si conſtet ex retardato &amp; accelerato, vt fit in perpendiculari ſurſum, &amp; <lb></lb>deorſum motus mixtus, linea per quam fit eſt curua,<emph.end type="italics"></emph.end> ſit enim retardatus <lb></lb>per AD, ſit acceleratus per AG, aſſumatur AB cum numero impari, putà <lb></lb>5.BC.3. CD.1. accipiatur AE.1. EF.3. ducantur parallelæ BK. CL. DI. <lb></lb>&amp; aliæ EM. FH. GI. &amp; per puncta AM. HI. ducatur linea curua, hæc eſt <lb></lb>linea motus mixti ex retardato &amp; accelerato; hæc porrò non eſt Parabo­<lb></lb>la, vt conſtat, quia quadratum AE non eſt ad ad quadratum AF, vt qua­<lb></lb>dratum AB, vel EM ad quadratum FH, vel AC. </s>
				</p>
				<p id="N1AA28" type="main">
					<s id="N1AA2A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AA36" type="main">
					<s id="N1AA38">Obſeruabis in fine huius motus amplitudinem, ſeu ſinum rectum li­<lb></lb>neæ ſcilicet GI, eſſe æqualem altitudini ſeu ſinui verſo, vel ſagittæ AG; </s>
					<s id="N1AA3E"><lb></lb>cùm enim motus naturaliter acceleratus in eadem proportione creſcat, <lb></lb>quod hic ſuppono, in qua retardatus decreſcit; </s>
					<s id="N1AA45">certè AG quæ eſt linea <lb></lb>accelerati eſt æqualis GI, quæ eſt linea retardati: non tamen dicendum <lb></lb>eſt lineam AI eſſe circulum, alioquin GH eſſet æqualis GI, ſed GH eſt, v. <lb></lb>g. 89. cum GI ſit radix quadr.81. eſt enim 9. licèt GM ſit æqualis GH. <lb></lb>ſed de his lineis infrà. </s>
					<s id="N1AA54">Vtrùm verò ſit aliquis motus huiuſmodi, videbi­<lb></lb>mus in ſequentibus Theorematis. </s>
				</p>
				<p id="N1AA5A" type="main">
					<s id="N1AA5C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AA68" type="main">
					<s id="N1AA6A"><emph type="italics"></emph>Quando corpus proiicitur per horizontalem in aëre libero, mouetur motu <lb></lb>mixto<emph.end type="italics"></emph.end>; </s>
					<s id="N1AA75">probatur, quia ſunt duo impetus in eo corpore, ſcilicet innatus <lb></lb>deorſum, &amp; impreſſus per horizontalem, vt patet; igitur vterque aliquid <lb></lb>præſtat ad illum motum per Ax. 1. igitur eſt motus mixtus per def. </s>
					<s id="N1AA7D">1. </s>
				</p>
				<p id="N1AA81" type="main">
					<s id="N1AA83"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AA8F" type="main">
					<s id="N1AA91"><emph type="italics"></emph>Ille motus non eſt mixtus ex vtroque æquabili.<emph.end type="italics"></emph.end></s>
					<s id="N1AA98"> Demonſtro; motus mixtus <lb></lb>ex vtroque æquabili eſt rectus per Th.1.&amp; 4. ſed hic motus proiecti per <lb></lb>horizontalem non eſt rectus per hyp.1. </s>
				</p>
				<p id="N1AA9F" type="main">
					<s id="N1AAA1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AAAD" type="main">
					<s id="N1AAAF"><emph type="italics"></emph>Ille motus non eſt mixtus ex naturali æquabili &amp; alio accelerato<emph.end type="italics"></emph.end>; patet, <lb></lb>quia nulla eſt cauſa, à qua violentus poſſit accelerari. </s>
				</p>
				<p id="N1AABA" type="main">
					<s id="N1AABC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AAC8" type="main">
					<s id="N1AACA"><emph type="italics"></emph>Non est mixtus ex naturali æquabili &amp; violento retardato<emph.end type="italics"></emph.end>; </s>
					<s id="N1AAD3">Primò, quia <lb></lb>cùm pro tata concurrant poſt integrum quadrantem vix ſpatium vnius <lb></lb>palmi confeciſſet in perpendiculari deorſum per Th.59.l.2.quod tamen <lb></lb>eſt contra experientiam.Secundò, quia ad aliquod tandem punctum per­<lb></lb>ueniretur, in quo mobile haberet tantùm impetum innatun; igitur nul­<lb></lb>lus eſſet ictus contra experientiam. </s>
					<s id="N1AAE1">Tertiò, quia naturalis impetus in­<lb></lb>tenditur in plano inclinato; </s>
					<s id="N1AAE7">igitur in motu per inclinatam, eſt enim <lb></lb>motus deorſum; igitur intenditur impetus naturalis, vt patet ex lib.  2. <lb></lb>igitur non eſt mixtus. </s>
				</p>
				<pb pagenum="160" xlink:href="026/01/192.jpg"></pb>
				<p id="N1AAF3" type="main">
					<s id="N1AAF5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AB01" type="main">
					<s id="N1AB03"><emph type="italics"></emph>Motus ille non eſt mixtus ex naturali retardator &amp; violento æquabili, vel <lb></lb>accelerato<emph.end type="italics"></emph.end>; quia numquam deſtruitur impetus innatus, vt ſæpiùs dictum <lb></lb>eſt ſuprà, tùm primo, tùm ſecundo libro, nec in hoc eſt vlla diffi­<lb></lb>cultas. </s>
				</p>
				<p id="N1AB12" type="main">
					<s id="N1AB14"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AB20" type="main">
					<s id="N1AB22"><emph type="italics"></emph>Non est mixtus ex naturali accelerato &amp; violento æquabili<emph.end type="italics"></emph.end>; </s>
					<s id="N1AB2B">demonſtra­<lb></lb>tur, primò, quia ſub finem motus eſſet maior impetus; </s>
					<s id="N1AB31">quippè nihil de­<lb></lb>traheretur violento, ſed multùm accederet naturali; igitur eſſet maior, <lb></lb>igitur eſſet maior ictus contra hyp. </s>
					<s id="N1AB39">3. ſecundò, quotieſcunque ſunt duo <lb></lb>impetus in eodem mobili ad diuerſas lineas determinati, aliquid illo­<lb></lb>rum deſtruitur per Th.141.l.1.tertiò ſi eſſet vterque æquabilis, aliquid <lb></lb>deſtrueretur per Theorema 6. igitur potiori iure, ſi impetus naturalis <lb></lb>creſcat. </s>
				</p>
				<p id="N1AB44" type="main">
					<s id="N1AB46">Diceret fortè aliquis impetum deſtrui ab aëre, ſed iam ſuprà reſpon­<lb></lb>ſum eſt modicum inde imminui; </s>
					<s id="N1AB4C">nec enim vnquam aër in corpore graui <lb></lb>deſtruit tantùm impetus, quantùm producitur naturalis ſi ſit acceleratus; <lb></lb>alioquin motus deorſum non creſceret contra experientiam, &amp; ſuprà in <lb></lb>toto ferè 2.lib.  demonſtrauimus. </s>
				</p>
				<p id="N1AB56" type="main">
					<s id="N1AB58"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AB64" type="main">
					<s id="N1AB66"><emph type="italics"></emph>Hinc linea huius motus non eſt Parabola<emph.end type="italics"></emph.end>; quia vt ſit Parabola, debet ille <lb></lb>motus conſtare vel ex naturali æquabili, &amp; violento retardato per Th. <lb></lb>19. vel ex naturali accelerato &amp; violento æquabili per Th. 18. ſed hic <lb></lb>motus neuter eſt, non primum per Th. 25. non ſecundum per Theo­<lb></lb>rema 26. </s>
				</p>
				<p id="N1AB7C" type="main">
					<s id="N1AB7E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AB8A" type="main">
					<s id="N1AB8C"><emph type="italics"></emph>Hinc reiicies Galileum,<emph.end type="italics"></emph.end> qui in dialogis hæc ſemper ſuppoſuit, ſed nun­<lb></lb>quam probauit, nec probare vnquam potuit; </s>
					<s id="N1AB97">hoc etiam ſupponunt <lb></lb>multi Galilei ſectatores, qui cenſent impetum nunquam deſtrui niſi à <lb></lb>reſiſtentia medij; </s>
					<s id="N1AB9F">ſed quæro ab illis quodnam medium deſtruat partem <lb></lb>impetus in motu mixto; </s>
					<s id="N1ABA5">nec enim linea motus mixti adæquat duas alias <lb></lb>ex quibus quaſi reſultat; </s>
					<s id="N1ABAB">certè hoc non poteſt explicari cum infinitis fetè <lb></lb>aliis, niſi dicatur impetum deſtrui ab alio impetu, eo modo quo ſæpè <lb></lb>diximus, hoc eſt ne ſit fruſtrà; igitur impetus violentus deſtruitur ab in­<lb></lb>nato, non tamen innatus à violento, vt ſæpiùs inculcauimus. </s>
				</p>
				<p id="N1ABB5" type="main">
					<s id="N1ABB7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ABC3" type="main">
					<s id="N1ABC5"><emph type="italics"></emph>Non eſt mixtus ex naturali accelerato eo modo quo acceleratur deorſum per <lb></lb>lineam perpendicularem &amp; ex violento retardato<emph.end type="italics"></emph.end>: </s>
					<s id="N1ABD0">Probatur, ſi ita eſt, <expan abbr="tãtùm">tantùm</expan> <lb></lb>additur naturali, quantum detrahitur violento, imò plùs; </s>
					<s id="N1ABDA">igitur ſemper <lb></lb>eſt in eo mobili æqualis vel maior impetus; igitur æqualis eſt ſemper, <lb></lb>vel maior ictus contra hyp. </s>
					<s id="N1ABE2">3. adde quod non minùs impeditur ab im­<lb></lb>petu violento naturalis motus, quàm ab inclinato plano; </s>
					<s id="N1ABE8">ſed in plano <pb pagenum="161" xlink:href="026/01/193.jpg"></pb>inclinato non acceleratur motus cum eadem acceſſione, qua ſcilicet in­<lb></lb>tenditur in perpendiculari deorsùm; </s>
					<s id="N1ABF3">nec enim tam citò deſcendit mobi­<lb></lb>le, quod certum eſt, &amp; in lib.de planis inclinatis demonſtrabo, cum tan­<lb></lb>tùm hîc ſupponam ad inſtar phyſicæ hypotheſeos; adde quod idem mo­<lb></lb>bile proiectum per horizontalem in data diſtantia minùs ferit, quàm pro­<lb></lb>iectum per inclinatam deorſum. </s>
				</p>
				<p id="N1ABFF" type="main">
					<s id="N1AC01"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AC0D" type="main">
					<s id="N1AC0F"><emph type="italics"></emph>Itaque motus prædictus mixtus est ex violento retardato &amp; naturali acce­<lb></lb>lerato, non eo quidem modo quo acceleratur in perpendiculari, ſed eo quo acce­<lb></lb>leratur in plano inclinato, quod hic ſingulis <expan abbr="inſtãtibus">inſtantibus</expan> mutatur<emph.end type="italics"></emph.end>; </s>
					<s id="N1AC20">probatur pri­<lb></lb>mo, quia inductione facta non <expan abbr="cõſtat">conſtat</expan> ex omnibus aliis; </s>
					<s id="N1AC2A">ſunt enim tantùm <lb></lb>9 combinationes, quia ſunt tres differentiæ, ſcilicet æquabilibus, retarda­<lb></lb>tio, acceleratio; </s>
					<s id="N1AC32">igitur ſi 3.ducantur in 3. ſunt 9. ſunt autem prima ex na­<lb></lb>turali, quem deinceps voco primum, æquabili &amp; violento (quem voca­<lb></lb>bo ſecundum) æquabili, ſecunda ex prima æquabili &amp; ſecundo accelera­<lb></lb>to, tertia ex primo æquabili &amp; ſecundo retardato, quarta ex primo acce­<lb></lb>lerato &amp; ſecundo æquabili, quinta ex primo accelerato &amp; ſecundo acce­<lb></lb>lerato, ſexta ex primo accelerato &amp; ſecundo retardato, ſeptima ex primo <lb></lb>retardato &amp; ſecundo æquabili, octaua ex primo retardato &amp; ſecundo ac­<lb></lb>celerato, nona ex primo retardato, &amp; ſecundo retardato: non eſt prima <lb></lb>per Th.22. non ſecunda per Th. 21. non tertia per Th. 24. non quarta, <lb></lb>per Th.26. non quinta per T.2h.23. non ſexta per Th.29. eo modo quo <lb></lb>diximus, non ſeptima per Th. 25. non octaua per Th. 25. non denique <lb></lb>nona per Th.25. igitur debet eſſe alius motus, ſed alius excogitari non <lb></lb>poteſt præter illum quem adduxi. </s>
					<s id="N1AC4E">Probatur ſecundò, quia non minùs <lb></lb>impeditur ab impetu violento impetus naturalis acquiſitus quàm à pla­<lb></lb>no inclinato vt iam dictum eſt; </s>
					<s id="N1AC56">igitur acceleratur quidem ſed minùs; </s>
					<s id="N1AC5A">nec <lb></lb>enim vterque eſt æquabilis, nam linea eſſet recta per Th.4. &amp; naturalis <lb></lb>creſcit quia deſcendit deorſum; præterea per Th.24. non poteſt impetus <lb></lb>naturalis eſſe æquabilis, igitur non poteſt violentus eſſe vel æquabilis, <lb></lb>vel acceleratus, igitur retardatus. </s>
				</p>
				<p id="N1AC66" type="main">
					<s id="N1AC68"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AC74" type="main">
					<s id="N1AC76"><emph type="italics"></emph>Motus naturalis acceleratus ex quo hic motus conſtat acceleratur in alia <lb></lb>proportione quàm fit ea, in qua acceleratur, dum per idem planum inclina­<lb></lb>tum deſcendit<emph.end type="italics"></emph.end>; </s>
					<s id="N1AC83">probatur, quia ſingulis inſtantibus mutatur inclinatio pla­<lb></lb>ni ſeu lineæ; igitur ſingulis inſtantibus mutatur proportio accelera­<lb></lb>tionis. </s>
				</p>
				<p id="N1AC8B" type="main">
					<s id="N1AC8D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AC99" type="main">
					<s id="N1AC9B"><emph type="italics"></emph>Hinc perpetuò creſcit proportio accelerationis, quia ſemper creſcit inclina­<lb></lb>tio plani,<emph.end type="italics"></emph.end> vt patet, cùm enîm ſit linea curua per hyp. </s>
					<s id="N1ACA5">1. quo magis incur­<lb></lb>uatur, accedit propiùs ad perpendicularem, igitur motus magis accele­<lb></lb>ratur. </s>
				</p>
				<pb pagenum="162" xlink:href="026/01/194.jpg"></pb>
				<p id="N1ACB0" type="main">
					<s id="N1ACB2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ACBE" type="main">
					<s id="N1ACC0"><emph type="italics"></emph>Hinc ratio hypotheſeos primæ,<emph.end type="italics"></emph.end> cùm enim conſtet hic motus ex accelera­<lb></lb>to &amp; retardato, eius linea eſt curua per Th.20. non tamen eſt Parabola, <lb></lb>vt conſtat ex eodem Th.20. Vnde reiicies Galileum, qui vult lineam mo­<lb></lb>tus proiecti per horizontalem in aëre libero eſſe Parabolam. </s>
				</p>
				<p id="N1ACCF" type="main">
					<s id="N1ACD1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ACDD" type="main">
					<s id="N1ACDF"><emph type="italics"></emph>In hoc motu retardatur in maiori proportione violentus quàm acceleretur <lb></lb>natur alis<emph.end type="italics"></emph.end>; </s>
					<s id="N1ACEA">probatur, non in minore, quia plùs impetus adderetur quàm de­<lb></lb>traheretur; igitur maior eſſet in fine motus quàm initio, igitur maior <lb></lb>ictus contra hyp.;. </s>
					<s id="N1ACF2">non in æquali, quia ſemper eſſet æqualis ictus con­<lb></lb>tra hyp.3.&amp; contra Th.29. </s>
				</p>
				<p id="N1ACF7" type="main">
					<s id="N1ACF9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AD05" type="main">
					<s id="N1AD07"><emph type="italics"></emph>Hinc plùs detrahitur impetus quàm addatur,<emph.end type="italics"></emph.end> quia ſcilicet detrahitur <lb></lb>pro rata, vt dicemus infrà; at verò cùm acceleretur tantùm naturalis <lb></lb>iuxta rationem motus, &amp; motus ſit iuxta rationem plani, minùs accele­<lb></lb>ratur quàm ſi caderet mobile perpendiculariter deorſum. </s>
				</p>
				<p id="N1AD16" type="main">
					<s id="N1AD18"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AD24" type="main">
					<s id="N1AD26"><emph type="italics"></emph>Hinc ratio clara cur ſit minor ictus in ſine huius motus<emph.end type="italics"></emph.end>; </s>
					<s id="N1AD2F">quia ſcilicet eſt <lb></lb>minùs impetus, quia plùs detractum eſt quàm additum; </s>
					<s id="N1AD35">nec eſt quod <lb></lb>tribuant hanc retardationem medio; </s>
					<s id="N1AD3B">quippe aër non plùs reſiſtit motui <lb></lb>violento quàm naturali; </s>
					<s id="N1AD41">ſed id quod detrahitur ab aëre corpori graui, v. <lb></lb>g. pilæ plumbeæ eſt inſenſibile, vt fatentur omnes; igitur idem <expan abbr="dicen-dū">dicen­<lb></lb>dum</expan> eſt de motu violento &amp; mixto, hinc hoc ipſum etiam fieret in vacuo. </s>
				</p>
				<p id="N1AD50" type="main">
					<s id="N1AD52"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AD5E" type="main">
					<s id="N1AD60"><emph type="italics"></emph>Impetus naturalis concurrit ad hunc motum<emph.end type="italics"></emph.end>; probatur, quia alioquin <lb></lb>eſſet rectus contra hyp. </s>
					<s id="N1AD6B">3. prætereà poteſt concurrere; </s>
					<s id="N1AD6E">nec enim ſunt li­<lb></lb>neæ determinationum oppoſitæ; igitur concurrit per Th.137.l.1. </s>
				</p>
				<p id="N1AD75" type="main">
					<s id="N1AD77"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AD83" type="main">
					<s id="N1AD85"><emph type="italics"></emph>Si impetus naturalis non concurreret ad hunc motum, proiectum moueretur <lb></lb>per lineam horizontalem rectam, vt conſtat, motu æquabili<emph.end type="italics"></emph.end>; poſito quod non <lb></lb>retardaretur in horizontali, eodem modo moueretur quo in verticali <lb></lb>ſurſum, quæ omnia conſtant ex dictis ſuprà. </s>
				</p>
				<p id="N1AD94" type="main">
					<s id="N1AD96"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ADA2" type="main">
					<s id="N1ADA4"><emph type="italics"></emph>Patest vtrimque deſcribi linea curua huius motus<emph.end type="italics"></emph.end>; </s>
					<s id="N1ADAD">ſit enim mobile pro­<lb></lb>jectum ex E per horizontalem EI <expan abbr="eã">eam</expan> ſcilicet velocitate, quam acquiſiuiſ­<lb></lb>ſet motu naturaliter accelerato deſcendendo ex A in E; </s>
					<s id="N1ADB9"><expan abbr="ſitq́ue">ſitque</expan> AB ſpa­<lb></lb>tium acquiſitum primo inſtanti deſcenſus; BC duplum, CD triplum, &amp;c. </s>
					<s id="N1ADC2"><lb></lb>iuxta progreſſionem arithmeticam, ſit EI æqualis EA, diuidatur que eo­<lb></lb>dem modo in 4. ſpatia vt diuiſa eſt EA; </s>
					<s id="N1ADC9">aſſumpta EO æqualis AB, ducan­<lb></lb>tur FN. GM. HL. IK. parallelæ EV; </s>
					<s id="N1ADCF">aſſumatur OP æqualis OE, &amp; PQ,<lb></lb>quæ ſit ad OE, vt OE ad hypothenuſim ſeu planum inclinatum EN, aſ-<pb pagenum="163" xlink:href="026/01/195.jpg"></pb>ſinuatur QR æqualis OE, tum RS quæ ſit ad OE vt OQ ad planum incli­<lb></lb>natum NM; </s>
					<s id="N1ADDC">denique aſſumatur ST æqualis OE, tum TV, quæ ſit ad OF, <lb></lb>vt QS ad inclinatam ML; ducantur ON. QM. SL. VK. parallelæ EI, <lb></lb>tùm per puncta E.N.M.L.X ducatur curua, hæc eſt linea prædicti motus, <lb></lb>demonſtratur. </s>
				</p>
				<p id="N1ADE6" type="main">
					<s id="N1ADE8">Impetus violentus percurrit EF eo tempore, quo naturalis percurrit <lb></lb>EO; </s>
					<s id="N1ADEE">igitur linea motus mixti ex vtroque ducitur per punctum N, &amp; licèt <lb></lb>videatur eſſe recta EN, ſcilicet diagonalis rectanguli OF, eſt tamen cur­<lb></lb>ua, quia mobile non percurrit EF vno inſtanti; </s>
					<s id="N1ADF6">igitur nec EO, igitur <lb></lb>motu æqualiter accelerato percurrit EO; </s>
					<s id="N1ADFC">igitur EN non eſt recta per <lb></lb>Th.20. Præterea.Secundo tempore impetus innatus remanet; </s>
					<s id="N1AE02">igitur per­<lb></lb>curratur OP cui addit ut PQ, quia impetus naturalis minùs creſcit, vt di­<lb></lb>ctum eſt in Th.34. quippe creſcit iuxta rationem plani inclinati EN.ad <lb></lb>EO permutando, quæ ſit v.g. ſubquadrupla; </s>
					<s id="N1AE0E">igitur PQ eſt ſubquadrupla <lb></lb>EO; </s>
					<s id="N1AE14">&amp; cùm deſtrui ſupponatur vnus gradus violenti, v.g. ſuperſunt tan­<lb></lb>tùm 3. quibus percurritur FG; igitur linea huius motus duci debet per <lb></lb>punctum M, idem dico de punctis L &amp; K, igitur hæc eſt linea motus <lb></lb>mixti, quàm ſcilicet corpus graue proiectum per horizontalem ſuo fluxu <lb></lb>deſcribit, &amp; cuius alias proprietates demonſtrabimus. </s>
				</p>
				<p id="N1AE22" type="main">
					<s id="N1AE24"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AE30" type="main">
					<s id="N1AE32"><emph type="italics"></emph>Hinc impetus naturalis in motu mixto creſcit ſemper in maiori proportione<emph.end type="italics"></emph.end><lb></lb>v.g. </s>
					<s id="N1AE3B">Oq.eſt maior EO, &amp; QS maior OQ atque ita deinceps. </s>
				</p>
				<p id="N1AE3E" type="main">
					<s id="N1AE40"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AE4C" type="main">
					<s id="N1AE4E"><emph type="italics"></emph>Impetus violentus hîc ſupponitur decreſcere ſemper in eadem proportione<emph.end type="italics"></emph.end>; </s>
					<s id="N1AE57"><lb></lb>v.g. FG eſt minor EF vno ſpatio, GH minor EF vno ſpatio; HI minor <lb></lb>GH vno ſpatio, quæ omnia conſtant. </s>
					<s id="N1AE60">Vtrùm verò id fiat, dicemus infrà, <lb></lb>&amp; exempli gratia tantùm dictum eſſe volo. </s>
				</p>
				<p id="N1AE65" type="main">
					<s id="N1AE67"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AE73" type="main">
					<s id="N1AE75"><emph type="italics"></emph>Hinc quò maior eſt impetus violentus in hoc motu, amplitudo huius linea <lb></lb>eſt maior<emph.end type="italics"></emph.end> v.g. VK, quæ ſemper maior eſt altitudine VE, vt enim eſſet æ­<lb></lb>qualis, impetus naturalis deberet creſcere in eadem proportione, in qua <lb></lb>decreſcit violentus, vt dictum eſt ſuprà. </s>
				</p>
				<p id="N1AE85" type="main">
					<s id="N1AE87"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AE93" type="main">
					<s id="N1AE95"><emph type="italics"></emph>Determinari poſſet hæc amplitudo, ſi decreſcat violentus in EI, vt decre­<lb></lb>ſcit in verticali EA<emph.end type="italics"></emph.end>; </s>
					<s id="N1AEA0">nam EI &amp; EA ſunt æquales, ſed EI &amp; VK ſunt æqua­<lb></lb>les, AE verò eſt linea, vel quam conficit mobile proiectum ſurſum cum <lb></lb>eodem, vel æquali impetu alteri quo proiicitur per horizontalem; ſeu <lb></lb>eſt linea quam percurrit corpus graue deorſum, dum acquirit æqualem <lb></lb>impetum alteri impreſſo eidem mobili per horizontalem EI. </s>
				</p>
				<p id="N1AEAC" type="main">
					<s id="N1AEAE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AEBA" type="main">
					<s id="N1AEBC"><emph type="italics"></emph>Hinc non poteſt proijci in libero medio mobile graue per rectam horizonta­<lb></lb>lem<emph.end type="italics"></emph.end>; </s>
					<s id="N1AEC7">quippe moueri non poteſt niſi motu mixto ex naturali accelerato <pb pagenum="164" xlink:href="026/01/196.jpg"></pb>eo modo quo diximus, &amp; violento retardato; </s>
					<s id="N1AED0">igitur linea eſt curua; dixi <lb></lb>in medio libero, cùm in plano duro horizontali per lineam rectam pro­<lb></lb>iici poſſit. </s>
				</p>
				<p id="N1AED8" type="main">
					<s id="N1AEDA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AEE6" type="main">
					<s id="N1AEE8"><emph type="italics"></emph>Hinc funis tenſus, cuius ſcilicet vtraque extremitas immobiliter affixa eſt, <lb></lb>nunquam eſt rectus, ſed inflectitur<emph.end type="italics"></emph.end>; </s>
					<s id="N1AEF3">ratio eſt, quia haud dubiè grauitat, igi­<lb></lb>tur incuruatur; vtrùm verò faciat Parabolam hæc linea curua, vt vult <lb></lb>Galileus, examinabimus in libro de lineis motus. </s>
				</p>
				<p id="N1AEFB" type="main">
					<s id="N1AEFD"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AF09" type="main">
					<s id="N1AF0B">Obſeruabis funem tenſum ſemper incuruari, niſi fortè ex maxima tra­<lb></lb>ctione ſuam flexibilitatem amittat, cuius ope tantùm curuatur, imò ita <lb></lb>tendi poteſt, vt tenſioni cedens frangatur: Equidem poſito quod vel in­<lb></lb>flecti poſſit, vel reduci, neceſſariò inflectetur in medio, vt benè demon­<lb></lb>ſtrat Galileus in dialogis, noſque infrà ad potentiam vectis reducemus, <lb></lb>ne multiplicemus figuras. </s>
				</p>
				<p id="N1AF19" type="main">
					<s id="N1AF1B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1AF27" type="main">
					<s id="N1AF29"><emph type="italics"></emph>Hinc ducitur optima ratio, cur proiectum per lineam horizontalem, v.g.pi­<lb></lb>la è tormento exploſa, vel ſagitta arcu emiſſa per plura ſecunda minuta mo­<lb></lb>ueatur in medio aëre antequam terram attingat<emph.end type="italics"></emph.end>; </s>
					<s id="N1AF36">quod pluſquàm mille ex­<lb></lb>perimentis comprobatum eſt; </s>
					<s id="N1AF3C">plura leges apud Merſennum, v. g. ſit tor­<lb></lb>mentum horizonti parallelum extans ſupra horizontem tribus pedibus; </s>
					<s id="N1AF46"><lb></lb>certum eſt ſpatium illud trium pedum confici à globo perpendiculariter <lb></lb>demiſſo tempore 30. tertiorum; </s>
					<s id="N1AF4D">cùm tamen exploſus per lineam hori­<lb></lb>zontalem terram tantùm attingat poſt 4. ſecunda, ideſt 240. tertia; </s>
					<s id="N1AF53">ita <lb></lb>Merſennus l.2. de motu Prop. vltima, imò l. 5. ſuæ verſionis art.5. con­<lb></lb>tra Galileum oſtendit glandem emiſſam è tormento minori conficere <lb></lb>75. exapedas, tempore vnius ſecundi minuti in linea, quæ parùm decli­<lb></lb>nat ab horizontali; </s>
					<s id="N1AF61">atqui tempore vnius ſecundi minuti conficit 2.exa­<lb></lb>pedas in perpendiculari deorſum; </s>
					<s id="N1AF67">igitur deberet glans infrà ſcopum de­<lb></lb>ſcendere notabiliter, id eſt, toto 12. pedum interuallo, cùm tamen vix <lb></lb>tantillùm aberret à ſcopo 1.Idem Merſennus habet in Baliſtica Prop.25. <lb></lb>globum è maiore tormento horizonti parallelo emiſſum in aëre tractu <lb></lb>continuo volaſſe toto tempore 8. ſecundorum, antequam planum hori­<lb></lb>zontale attigiſſet, cùm tamen ſex tantùm exapedis tormentum extaret <lb></lb>ſupra horizontem; </s>
					<s id="N1AF77">alter globus ex alio tormento exploſus 6. tantum ſe­<lb></lb>cunda in aëre conſumpſit; </s>
					<s id="N1AF7D">imò bombardarum globi aliquando tota 14. <lb></lb>ſecunda poſuerunt; </s>
					<s id="N1AF83">habet idem Merſennus alia plura, quorum fides ſit <lb></lb>penes authores à quibus accepit; </s>
					<s id="N1AF89">nam vt dicam quod res eſt vix accu­<lb></lb>ratè minima illa tempora metiri poſſumus; </s>
					<s id="N1AF8F">quidquid ſit, ex illis ſaltem <lb></lb>euinco mobile projectum per horizontalem plùs temporis inſumere in <lb></lb>ſuo fluxu, quam ſi ex eadem altitudine perpendiculariter demittatur; vt <lb></lb>vult Galileus; </s>
					<s id="N1AF99">cuius ratio alia non eſt ab ea, quàm ſuprà indicauimus, <lb></lb>quòd ſcilicet motus naturalis minùs creſcat in motu mixto quàm in na-<pb pagenum="165" xlink:href="026/01/197.jpg"></pb>turali, vt ſuprà demonſtrauimus; </s>
					<s id="N1AFA4">imò ſi creſceret vt vult Galileus, ictus; <lb></lb>haud dubiè eſſet maior in fine motus quàm initio, quod omninò expe­<lb></lb>rientiæ repugnat. </s>
				</p>
				<p id="N1AFAC" type="main">
					<s id="N1AFAE">Nec eſt quod aliquis dicat glandem emiſſam per horizontalem tan­<lb></lb>tillùm aſcendere; </s>
					<s id="N1AFB4">vnde plus temporis in aſcenſu ſimul &amp; deſcenſu col­<lb></lb>locatur, quàm in ſolo deſcenſu; </s>
					<s id="N1AFBA">nam primò vix hoc aliquis ſibi perſua­<lb></lb>ſerit, cùm experimento percipi non poſſit; </s>
					<s id="N1AFC0">Secundò licèt verum eſſet, <lb></lb>non tamen eſt tantus aſcenſus, quin adhuc plùs temporis ponat in aſ­<lb></lb>cenſu, atqué in deſcenſu, quàm in altiſſima perpendiculari quadruplæ al­<lb></lb>titudinis, vt conſtat; </s>
					<s id="N1AFCA">ſit enim horizontalis AF, diſtans à plano hori­<lb></lb>zontali altitudine BA; </s>
					<s id="N1AFD0">ſit tormentum directum per lineam AF, &amp; glo­<lb></lb>bus percurrat lineam curuam AEF, idque ſpatio 8.ſecundorum minu­<lb></lb>torum; </s>
					<s id="N1AFD8">ſitque DE 3. pedum; </s>
					<s id="N1AFDC">certè eo tempore quo conficit AE, ſi in <lb></lb>perpendiculari conficiat ED, cum ED conficiat tempore 30tʹ; </s>
					<s id="N1AFE2">haud <lb></lb>dubiè AE eodem tempore conficere deberet; </s>
					<s id="N1AFE8">ſed conficit AE tempore <lb></lb>4. ſecundorum, vt conſtat ex ipſis multorum obſeruationibus; </s>
					<s id="N1AFEE">igitur to­<lb></lb>tam AEF deberet percurrere tempore 1″, id eſt eo tempore quo in per­<lb></lb>pendiculari deorſum percurruntur 12. pedes; </s>
					<s id="N1AFF6">denique ſi verum ſit glo­<lb></lb>bum aſcendere tantillùm dum emittitur è tormento horizonti paralle­<lb></lb>lo; </s>
					<s id="N1AFFE">crediderim id eſſe tùm ex aliqua repercuſſione aëris, tùm eo quod à <lb></lb>flamma ſurſum aſcendente ſurſum etiam aliquantulum inclinetur; </s>
					<s id="N1B004">quod <lb></lb>verò ſpectat ad ſagittam, alia cauſa non eſt niſi modica aëris repercuſſio; </s>
					<s id="N1B00A"><lb></lb>eſt enim leuior ſagittæ materia; ſed de repercuſſione fusè agemus <lb></lb>infrà. </s>
				</p>
				<p id="N1B011" type="main">
					<s id="N1B013"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B01F" type="main">
					<s id="N1B021"><emph type="italics"></emph>Motus projecti ſurſum per inclinatam eſt mixtus<emph.end type="italics"></emph.end>; </s>
					<s id="N1B02A">probatur, quia conſtat <lb></lb>ex naturali, &amp; violenti; qui cùm non ſint in oppoſitis lineis, ad commu­<lb></lb>nem motum concurrunt, vt patet. </s>
				</p>
				<p id="N1B032" type="main">
					<s id="N1B034"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B040" type="main">
					<s id="N1B042"><emph type="italics"></emph>Non eſt mixtus ex vtroque æquabili<emph.end type="italics"></emph.end>; quia linea eſſet recta per Th.1.ſed <lb></lb>linea huius motus eſt curua per hyp. </s>
					<s id="N1B04D">non pertinet etiam hic motus ad <lb></lb>ſecundam combinationem de qua Th. 30. nec ad quintam, nec ad <lb></lb>octauam, nec ad nonam, de aliis videbimus infrà. </s>
				</p>
				<p id="N1B054" type="main">
					<s id="N1B056"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B062" type="main">
					<s id="N1B064"><emph type="italics"></emph>Non eſt mixtus ex naturali accelerato, &amp; violento æquabili<emph.end type="italics"></emph.end>; </s>
					<s id="N1B06D">probatur, <lb></lb>quia in fine motus eſſet maior impetus, igitur eſſet maior ictus contra ex­<lb></lb>perientiam; </s>
					<s id="N1B075">imò longè maior quàm ſi mobile proiiceretur per horizon­<lb></lb>talem, quia diutiùs durat ille motus; </s>
					<s id="N1B07B">igitur plures gradus impetus na­<lb></lb>turalis acquiruntur; </s>
					<s id="N1B081">igitur longè maior eſt ictus; prætereà ſi impetus <lb></lb>naturalis deſtruit impetum ſurſum in verticali, cur non in inclinata? </s>
					<s id="N1B087">nam <lb></lb>eſt eadem omninò ratio; </s>
					<s id="N1B08D">quippe ideò deſtruitur in verticali, quia cor­<lb></lb>pus graue ſurſum attollitur; </s>
					<s id="N1B093">cùm tamen ſua ſponte deorſum ferri debe­<lb></lb>ret; </s>
					<s id="N1B099">ſed non minùs, cùm per inclinatam ſurſum proiicitur, remouetur à <pb pagenum="166" xlink:href="026/01/198.jpg"></pb>ſuo centro, &amp; ſurſum rapitur; </s>
					<s id="N1B0A2">nec obſtat oppoſitio lineæ verticalis ſur­<lb></lb>ſum cum perpendiculari deorſum; quia etiam per inclinatam deorſum <lb></lb>fertur in plano inclinato, quæ opponitur ex diametro alteri inclinatæ <lb></lb>ſurſum. </s>
				</p>
				<p id="N1B0AC" type="main">
					<s id="N1B0AE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B0BA" type="main">
					<s id="N1B0BC"><emph type="italics"></emph>Non eſt mixtus in aſcenſu ex primo accelerato &amp; ſecundo retardato, acce­<lb></lb>lerato inquam eo modo quo acceleratur in perpendiculari deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1B0C7">probatur <lb></lb>primò, quia motus ille eſſet ſemper æqualis, quia tantùm adderetur im­<lb></lb>petus quantùm detraheretur, igitur eſſet idem ictus in fine qui in princi­<lb></lb>pio; Secundò, quia tempora motuum eſſent breuiora quàm par ſit con­<lb></lb>tra experientiam, vt patet ex Th.46. </s>
				</p>
				<p id="N1B0D3" type="main">
					<s id="N1B0D5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B0E1" type="main">
					<s id="N1B0E3"><emph type="italics"></emph>Non eſt mixtus in aſcenſu ex violento retardato, &amp; naturali accelerato, eo <lb></lb>modo quo diximus in Th.<emph.end type="italics"></emph.end> 30. probatur, quia cùm acceleretur iuxta ratio­<lb></lb>nem plani inclinati deorſum, vt dictum eſt, ſupra horizontalem; </s>
					<s id="N1B0F0">nullum <lb></lb>eſt ampliùs planum inclinatum deorſum; </s>
					<s id="N1B0F6">igitur nulla acceleratio, imò <lb></lb>impetus naturalis, vt iam ſuprà dictum eſt creſcit tantùm vt motus deor­<lb></lb>ſum acceleretur; </s>
					<s id="N1B0FE">ſed nullus eſt hîc motus deorſum; </s>
					<s id="N1B102">modicùm figuræ <lb></lb>rem ob oculos ponit; </s>
					<s id="N1B108">motus in plano AB eſt ad motum in AC vt <lb></lb>AC ad AB, &amp; in AD, vt AD ad AB, &amp; in AE, vt AE ad AB; </s>
					<s id="N1B10E">igitur immi­<lb></lb>nuitur in infinitum; ſed acceleratur in inclinata deorſum iuxta hanc ra­<lb></lb>tionem, igitur nulla ſupereſt ampliùs proportio, ſecundum quam acce­<lb></lb>lerari poſſet in inclinata ſurſum. </s>
				</p>
				<p id="N1B118" type="main">
					<s id="N1B11A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B126" type="main">
					<s id="N1B128"><emph type="italics"></emph>Hic motus eſt mixtus ex naturali æquabili, &amp; violento retardato in aſcen­<lb></lb>ſu<emph.end type="italics"></emph.end>; </s>
					<s id="N1B133">probatur, quia nulla alia combinatio præter hanc ſupereſt, quam <lb></lb>tertio loco ſuprà collocauimus in Th. 30. ratio à priori eſt, quia natura­<lb></lb>lis innatus non retardatur; </s>
					<s id="N1B13B">quia nunquam deſtruitur, nec acceleratur; </s>
					<s id="N1B13F"><lb></lb>quia ſurſum tendit mobile; </s>
					<s id="N1B144">igitur ſupereſt tantùm quod ſit æquabilis, <lb></lb>violentus verò non acceleratur, vt patet, quia nulla eſt cauſa: </s>
					<s id="N1B14A">non eſt <lb></lb>æquabilis, quia coniunctus eſt cum cauſa deſtructiua; igitur eſt re­<lb></lb>tardatus. </s>
				</p>
				<p id="N1B152" type="main">
					<s id="N1B154"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B160" type="main">
					<s id="N1B162"><emph type="italics"></emph>Hic motus eſt mixtus in arcu deſcenſus ex naturali accelerato eo modo, quo <lb></lb>diximus ſuprà in Th.<emph.end type="italics"></emph.end> 30. <emph type="italics"></emph>&amp; violento retardato<emph.end type="italics"></emph.end>; </s>
					<s id="N1B173">probatur per idem Th.eſt <lb></lb>enim par vtrique motui ratio; quippe hic perinde ſe habet, atque ſi mo­<lb></lb>bile per horizontalem proiiceretur, nam præuius motus <expan abbr="nequidquã">nequidquam</expan> facit. </s>
				</p>
				<p id="N1B17F" type="main">
					<s id="N1B181"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B18D" type="main">
					<s id="N1B18F"><emph type="italics"></emph>Arcus vterque constat linea curua<emph.end type="italics"></emph.end>; probatur per Th.19. non eſt tamen <lb></lb>Parabola linea arcus deſcenſus per Th.20.&amp; 27. </s>
				</p>
				<p id="N1B19A" type="main">
					<s id="N1B19C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B1A8" type="main">
					<s id="N1B1AA"><emph type="italics"></emph>Poteſt hac linea vtcumque deſcribi, ſuppoſita retardatione violenti in pro<emph.end type="italics"></emph.end>-<pb pagenum="167" xlink:href="026/01/199.jpg"></pb><emph type="italics"></emph>portione arithmetica ſimplici<emph.end type="italics"></emph.end>; </s>
					<s id="N1B1BD">ſit enim verticalis, AG horizontalis AN, <lb></lb>linea projectionis AD; </s>
					<s id="N1B1C3">ſitque primum ſegmentum AD, quod ſcilicet <lb></lb>percurritur eo tempore quo in perpendiculari deorſum percurritur DF, <lb></lb>id eſt, v.g. ſexta eius pars, ducatur AFG, ſitque FG 5. partium, quarum <lb></lb>ſcilicet AD eſt 6. aſſumatur GH æqualis DF, ducaturque FHI; </s>
					<s id="N1B1CF">ſitque <lb></lb>HI 4. partium, aſſumatur IP æqualis GH, ducaturque HP; </s>
					<s id="N1B1D5">accipiatur <lb></lb>PK 3. partium; </s>
					<s id="N1B1DB">iam motus naturalis acceleratur eo modo quo ſuprà di­<lb></lb>ctum eſt iuxta rationem inclinationis deorſum; </s>
					<s id="N1B1E1">itaque aſſumatur KL <lb></lb>paulo maior IP; ſimiliter ducatur PLM, ſitque LM duarum partium, <lb></lb>&amp; MN paulò maior KL, tum ſit LNO, ſitque NO 1. partis, &amp; OB ma­<lb></lb>ior MN, &amp; ducatur curua per puncta A.F.H.P.L.N.B. &amp; habebis <lb></lb>intentum. </s>
				</p>
				<p id="N1B1ED" type="main">
					<s id="N1B1EF">Porrò hæc linea non eſt parabolica, vt conſtat ex Geometria &amp; plura <lb></lb>puncta habebis ſi minora ſpatiola aſſumas; ſuppono enim DF eſſe tan­<lb></lb>tùm id ſpatij quod primo inſtanti in perpendiculari deorſum à corpore <lb></lb>graui percurritur. </s>
				</p>
				<p id="N1B1F9" type="main">
					<s id="N1B1FB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B207" type="main">
					<s id="N1B209"><emph type="italics"></emph>Aliter hæc linea poteſt deſcribi ſuppoſita retardatione per numeros impa­<lb></lb>res; vt habes in fig.<emph.end type="italics"></emph.end> 46.T.1. in qua AC eſt verticalis, AB horizontalis, <lb></lb>AD inclinata 9. partium, FG 7. HI 5. reliqua vt ſuprà dictum eſt. </s>
				</p>
				<p id="N1B216" type="main">
					<s id="N1B218">Si verò linea inclinata recedat longiùs ab horizontali, &amp; accedat pro­<lb></lb>piùs ad verticalem; vt habeantur puncta, transferantur eadem ſpatia, &amp; <lb></lb>habebis puncta, per quæ deſcribes prædictam lineam. </s>
				</p>
				<p id="N1B220" type="main">
					<s id="N1B222">Denique ſi inclinata accedat propiùs ad horizontalem, transferantur <lb></lb>ſimiliter ſpatia vnius in alteram. </s>
				</p>
				<p id="N1B227" type="main">
					<s id="N1B229">Obſeruabis autem crementa deſcenſus in GH. IB eſſe iuxta nume­<lb></lb>ros impares 1.3.5.7.&amp;c. </s>
					<s id="N1B22E">quandoquidem aſſumitur ſpatium quod confi­<lb></lb>citur in tempore ſenſibili, habita tamen ſemper ratione accelerationis, <lb></lb>quæ fit in plano inclinato, vnde creſcit ſemper proportio acceleratio­<lb></lb>nis, vt ſuprà demonſtrauimus; quæ certè proportionum inæqualitas ef­<lb></lb>ficit, ne poſſint accuratè deſcribi prædictæ lineæ, ſed tantùm rudi Miner­<lb></lb>uâ, cum ſingulis inſtantibus mutetur proportio accelerationis. </s>
				</p>
				<p id="N1B23C" type="main">
					<s id="N1B23E"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B24A" type="main">
					<s id="N1B24C">Obſeruabis nondum eſſe à nobis determinatam proportionem illam, <lb></lb>in qua deſtruitur impetus violentus in motu mixto, quæ tamen ex dictis <lb></lb>ſuprà poteſt colligi; quippe deſtruitur pro rata, ideſt qua proportione <lb></lb>linea motus mixti eſt minor linea compoſita ex vtroque, ſit ergo. </s>
				</p>
				<p id="N1B256" type="main">
					<s id="N1B258"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B264" type="main">
					<s id="N1B266"><emph type="italics"></emph>Impetus violentus ſolus deſtruitur in arcu aſcenſus<emph.end type="italics"></emph.end>; </s>
					<s id="N1B26F">probatur, quia natu­<lb></lb>ralis non creſcit, vt patet; conſtat enim arcus aſcenſus ex naturali æqua­<lb></lb>bili, ſed aliquis impetus decreſcit, vt conſtat ex dictis, igitur ſolus <lb></lb>violentus. </s>
				</p>
				<pb pagenum="168" xlink:href="026/01/200.jpg"></pb>
				<p id="N1B27D" type="main">
					<s id="N1B27F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B28B" type="main">
					<s id="N1B28D"><emph type="italics"></emph>Impetus naturalis non decreſcit etiam in arcu deſcenſus<emph.end type="italics"></emph.end>; probatur quia <lb></lb>creſcit, vt dictum eſt ſuprà, igitur non decreſcit. </s>
				</p>
				<p id="N1B298" type="main">
					<s id="N1B29A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B2A6" type="main">
					<s id="N1B2A8"><emph type="italics"></emph>Deſtruitur impetus violentus pro rata. </s>
					<s id="N1B2AD">id eſt, qua proportione eſt frustrà;<emph.end type="italics"></emph.end><lb></lb>v.g. </s>
					<s id="N1B2B4">ſit impetus per AD inclinatam ſurſum, &amp; alius per AB perpendi­<lb></lb>cularem deorſum; </s>
					<s id="N1B2BA">haud dubiè motus erit per AC; </s>
					<s id="N1B2BE">igitur concurrunt <lb></lb>ad motum AC motus AB &amp; AD, vel potiùs impetus; </s>
					<s id="N1B2C4">igitur debet de­<lb></lb>ſtrui impetus in ea proportione, in qua AC eſt minor AG, id eſt com­<lb></lb>poſita ex AD, DC, quod impetus AB non poſſit deſtrui; </s>
					<s id="N1B2CC">totum id <lb></lb>quod deſtruetur detrahetur impetui AD; </s>
					<s id="N1B2D2">igitur aſſumatur DF ſcilicet <lb></lb>differentia AC, &amp; AG; impetus deſtructus ita ſe habet ad impetum <lb></lb>AD, vt DF ad AD, &amp; ad reſiduum impetum ex AD, vt DF ad FA, <lb></lb>quæ omnia conſtant ex Th.7. ſit ergo AC fig. </s>
					<s id="N1B2DC">49. perpendicularis ſur­<lb></lb>ſum, AD inclinata, AB horizontalis; ſit impetus violentus reſpondens <lb></lb>AD, &amp; naturalis DG, ducatur AGK, ex AD detrahatur DF, id eſt <lb></lb>differentia AG &amp; compoſitæ ex AD. DG, ſupereſt AF, cui aſſumitur <lb></lb>æqualis GK, ex qua detrahitur KH, id eſt differentia GL, &amp; compoſitæ <lb></lb>ex GK, KL, ſupereſt GH, cui LO accipitur æqualis, cui detrahitur <lb></lb>OM, id eſt differentia LP &amp; compoſitæ ex LO, OP, ſupereſt ML, cui <lb></lb>æqualis accipitur PR, atque ita deinceps. </s>
					<s id="N1B2EE">Porrò demonſtratur deſtrui <lb></lb>impetum violentum iuxta hanc proportionem; </s>
					<s id="N1B2F4">quia deſtruitur, qua <lb></lb>proportione eſt fruſtrà, pro rata per Ax.2.&amp; Th.7.ſed totus impetus qui <lb></lb>concurrit ad ſecundam lineam AG, eſt compoſitus ex AD, GD; </s>
					<s id="N1B2FC">quia ſi <lb></lb>naturalis ſolus eſſet, percurreret ſpatium æquale DG; </s>
					<s id="N1B302">ſi verò ſolus eſſet <lb></lb>violentus percurreret ſpatium æquale AD; </s>
					<s id="N1B308">igitur vterque ſimul ſumptus <lb></lb>eſt vt <expan abbr="cõpoſita">compoſita</expan>, ex AG. DG. igitur ſi ea proportione eſt fruſtrà, qua motus <lb></lb>deficit, cùm AG ſit motus; </s>
					<s id="N1B314">certè motus eſt ad impetum, vt AG ad <expan abbr="compo-ſitã">compo­<lb></lb>ſitam</expan> ex AD. DG; </s>
					<s id="N1B31E">igitur deficit motus tota DF quæ eſt differentia AG &amp; <lb></lb><expan abbr="cõpoſitæ">compoſitæ</expan> ex AD. DG; </s>
					<s id="N1B327">igitur impetus eſt fruſtrà in ratione DF; </s>
					<s id="N1B32B">igitur de­<lb></lb>bet deſtrui in ratione DF; </s>
					<s id="N1B331">ſed impetus DG ſeu naturalis nihil deſtrui­<lb></lb>tur per Th.57. &amp; 58. igitur ex violento AD deſtruitur DF; </s>
					<s id="N1B337">igitur ſu­<lb></lb>pereſt tantum AF vel æqualis GK; </s>
					<s id="N1B33D">ſimiliter impetui GK &amp; KL re­<lb></lb>ſpondet motus GL, ſed GL eſt minor compoſita ex GK &amp; KL ſeg­<lb></lb>mento KH; </s>
					<s id="N1B345">igitur eſt fruſtrà impetus in ratione KH; </s>
					<s id="N1B349">igitur deſtruitur <lb></lb>in eadem ratione KH, non ex naturali KL; </s>
					<s id="N1B34F">igitur ex violento GK; <lb></lb>igitur ſupereſt tantum GH, vel æqualis LO, in qua ſimiliter procedi­<lb></lb>tur. </s>
					<s id="N1B357">&amp; ſupereſt LM vel æqualis PR, atque ita deinceps. </s>
				</p>
				<p id="N1B35A" type="main">
					<s id="N1B35C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B369" type="main">
					<s id="N1B36B">Hinc deſtruitur impetus initio motus in maiori quantitate, quia <pb pagenum="169" xlink:href="026/01/201.jpg"></pb>DF. v. g. eſt maxima omnium differentiarum. </s>
				</p>
				<p id="N1B377" type="main">
					<s id="N1B379"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B386" type="main">
					<s id="N1B388">Hinc ſub finem differentia lineæ motus v. g. TB ſemper eſt maius <lb></lb>latus trianguli TXB; </s>
					<s id="N1B392">idem dico de aliis; igitur differentia lineæ motus <lb></lb>&amp; compoſitæ ex duplici impetu eſt ſemper minor &amp; minor in in­<lb></lb>finitum. </s>
				</p>
				<p id="N1B39A" type="main">
					<s id="N1B39C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B3A9" type="main">
					<s id="N1B3AB">Poſſunt determinari à Geometria omnes anguli triangulorum ADG. <lb></lb>GKL. OLP. nam ADG eſt æqualis CAD, at verò GKL æqualis <lb></lb>KGD, &amp; hic duobus ſimul ADG &amp; DAG, igitur determinari facilè <lb></lb>poterunt ex doctrina triangulorum. </s>
				</p>
				<p id="N1B3B4" type="main">
					<s id="N1B3B6"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B3C3" type="main">
					<s id="N1B3C5">Hinc etiam ſciri poterit in quo puncto linea motus v.g. LP cum per­<lb></lb>pendiculari OP faciat angulum rectum, quod ſatis eſt indicaſſe, nam hic <lb></lb>Geometram non ago. </s>
				</p>
				<p id="N1B3CE" type="main">
					<s id="N1B3D0"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B3DD" type="main">
					<s id="N1B3DF">Hinc quoque ſciri poteſt maxima altitudo huius projectionis, quæ <lb></lb>ſcilicet in eo puncto eſt, in quo linea motus cum perpendiculari deor­<lb></lb>ſum facit angulum rectum, v.g. in puncto P, ſi angulus LPO eſt <lb></lb>rectus. </s>
				</p>
				<p id="N1B3EA" type="main">
					<s id="N1B3EC"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B3F9" type="main">
					<s id="N1B3FB">Hinc poteſt etiam ſciri altitudo operâ triangulorum productorum <lb></lb>AG 2. GK 3. OLP. quod quiuis Geometra facilè intelliget; hîc quo­<lb></lb>que obiter obſerua vnum, quod ſæpè aliàs indicauimus, quanti videlicet <lb></lb>momenti ſit Geometria in rebus phyſicis. </s>
				</p>
				<p id="N1B405" type="main">
					<s id="N1B407"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B413" type="main">
					<s id="N1B415">Hinc etiam colligo arcum aſcenſus maiorem eſſe arcu deſcenſus ſu­<lb></lb>pra idem planum horizontale AB; </s>
					<s id="N1B41B">quia in arcu deſcenſus acceleratur <lb></lb>pro ratione diuerſæ inclinationis impetus naturalis; </s>
					<s id="N1B421">igitur lineam mo­<lb></lb>tus addunt propiùs ad perpendicularem, vt vides in TB; </s>
					<s id="N1B427">igitur minùs <lb></lb>acquirit in horizontali; </s>
					<s id="N1B42D">igitur minor amplitudo horizontalis ſubeſt ar­<lb></lb>cui deſcenſus projectorum quàm arcui aſcenſus; dixi ſuprà idem pla­<lb></lb>num, quia arcus deſcenſus infra planum AB propagatur ferè in infi­<lb></lb>nitum. </s>
				</p>
				<p id="N1B437" type="main">
					<s id="N1B439"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B445" type="main">
					<s id="N1B447">Hinc reiicio Galileum qui nulla prorſus fultus ratione phyſica vult <lb></lb>vtrumque eſſe æqualem, quod tamen omnibus experimentis repugnat, &amp; <lb></lb>ipſi etiam pueri, qui diſco ludunt obſeruare poſſunt arcum deſcenſus ſui <lb></lb>diſci eſſe longè minorem, nec eſt quod ad ſuam Parabolam confugiat, <lb></lb>quæ duo falſa ſupponit principia, ſcilicet æquabilitatem motus violen­<lb></lb>ti, &amp; accelerationem naturalis eo ſcilicet modo quo fieret in perpendi­<lb></lb>culari; at vtrumque falſum eſſe ſuprà demonſtrauimus, adde quod vt iam <pb pagenum="170" xlink:href="026/01/202.jpg"></pb>dixi in ſagitta emiſſa, projecto diſco, &amp;c. </s>
					<s id="N1B45C">omnes obſeruare poſſunt ar­<lb></lb>cum aſcenſus maiorem eſſe arcu deſcenſus, quod etiam ſupponunt om­<lb></lb>nes, qui de re tormentaria ſcripſerunt; præſertim Vfanus tract. 3. <lb></lb>c. 13. </s>
				</p>
				<p id="N1B46A" type="main">
					<s id="N1B46C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B478" type="main">
					<s id="N1B47A">Hinc etiam colliges contra Vfanum globum è tormento emiſſum per <lb></lb>inclinatam ſurſum non ferri primò per lineam rectam, quia mouetur <lb></lb>motu mixto, qui rectus eſſe non poteſt in hoc caſu per Th.54. </s>
				</p>
				<p id="N1B481" type="main">
					<s id="N1B483"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B48F" type="main">
					<s id="N1B491">Motus mixtus arcus deſcenſus vſque ad centrum terræ durare poſſet <lb></lb>ſi producerentur tot partes impetus quot ſunt inſtantia illius motus; quia <lb></lb>cùm ſemper deſtruatur minor impetus, &amp; minor in infinitum, poſt ali­<lb></lb>quod ſpatium deſcenſus tam parùm deſtruitur vſque ad centrum terræ vt <lb></lb>non adæquet totus ille impetus primam partem primo inſtanti deſtru­<lb></lb>ctam, at tunc linea motus à perpendiculari deorſum diſtingui non <lb></lb>poteſt. </s>
				</p>
				<p id="N1B4A1" type="main">
					<s id="N1B4A3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B4AF" type="main">
					<s id="N1B4B1">Sed ne Geometriam omninò deſpicere videar, in circulo demonſtro <lb></lb>proportiones omnes in quibus decreſcit motus violentus per quamlibet <lb></lb>lineam inclinatam ſurſum, vel deorſum; </s>
					<s id="N1B4B9">ſit ergo circulus ADGQ cen­<lb></lb>tro B; </s>
					<s id="N1B4BF">ſit motus violentus ſurſum BD coniunctus cum naturali BR, ſint­<lb></lb>que ex gr. BR. RQ æquales; </s>
					<s id="N1B4C7">haud dubiè linea motus erit BC, quia na­<lb></lb>turalis BR pugnat pro rata per Th.134.l.1. eritque BC ſubdupla BD; <lb></lb>igitur centro R. ſemidiametro RC deſcribatur circulus CLPS, erit <lb></lb>æqualis priori, ducanturque ex centro B infinitæ lineæ BE. BF. BK. <lb></lb>BN, &amp; vt res fit clarior, ſint omnes anguli DBE. EBF. FBG, &amp;c. <lb></lb></s>
					<s id="N1B4D4">æquales ſcilicet grad. 30. &amp; ex punctis E.F.G.K.N.q. </s>
					<s id="N1B4D9">ducantur lineæ <lb></lb>ad circunferentiam circuli CLPS. parallelæ DP.Dico omnes eſſe æqua­<lb></lb>les DC; </s>
					<s id="N1B4E1">nam primò FH. GL. KM. QP ſunt æquales, vt patet: </s>
					<s id="N1B4E5">deinde <lb></lb>CE &amp; QO ſunt æquales; </s>
					<s id="N1B4EB">igitur EV. OX, quod etiam certum eſt; igi­<lb></lb>tur ſi ſupponatur idem motus violentus æqualis BD per omnes inclina­<lb></lb>tas BE. BF, &amp;c. </s>
					<s id="N1B4F3">coniunctus naturali æquali BR; </s>
					<s id="N1B4F6">primum ſpatium erit <lb></lb>BC, ſecundum BV, tertium BH, quartum BL, quintum BM, ſextum <lb></lb>BO<emph type="sub"></emph>2<emph.end type="sub"></emph.end> ſeptimum BP. quod certè mirabile eſt; </s>
					<s id="N1B504">nam ex BE. EV. fit BV per <lb></lb>Th.5. ſimiliter ex BF. FH. fit BH, ex BG. GL. fit BL; </s>
					<s id="N1B50A">denique ex <lb></lb><expan abbr="Bq.">Bque</expan> QP fit BP; iam verò proportiones iſtarum linearum ex Trigo­<lb></lb>nometria facilè intelligi poſſunt. </s>
				</p>
				<p id="N1B515" type="main">
					<s id="N1B517"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B523" type="main">
					<s id="N1B525"><emph type="italics"></emph>Iactus per horizontalem, &amp; per verticalem nihil acquirit per ſe in eodem <lb></lb>plane horizontali, vnde incipit iactus<emph.end type="italics"></emph.end>; </s>
					<s id="N1B530">probatur, quia verticalis iactus per <lb></lb><expan abbr="eãdem">eandem</expan> lineam redit; </s>
					<s id="N1B539">horizontalis verò ſtatim deſcendit; quia motus <pb pagenum="171" xlink:href="026/01/203.jpg"></pb>mixtus eſt per Th.44. dixi per ſe, nam fortè per accidens fieri poteſt, vt <lb></lb>iactus horizontalis habeat arcum aſcenſus, &amp; deſcenſus. </s>
				</p>
				<p id="N1B544" type="main">
					<s id="N1B546"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B552" type="main">
					<s id="N1B554"><emph type="italics"></emph>Hinc quò iactus propiùs accedit ad horizontalem ſeu verticalem, minùs <lb></lb>acquirit in eodem plano horizontali, ſcilicet in eo à cuius extremitate inci­<lb></lb>pit iactus<emph.end type="italics"></emph.end>; </s>
					<s id="N1B561">probatur, quia cùm iactus verticalis nihil prorſus acqui­<lb></lb>rat in horizontali plano per Theorema 60. certè quò propiùs ad illum <lb></lb>iactus inclinatus accedet, minùs acquiret; idem dico de iactu hori­<lb></lb>zontali. </s>
				</p>
				<p id="N1B56B" type="main">
					<s id="N1B56D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B579" type="main">
					<s id="N1B57B"><emph type="italics"></emph>Hinc quò iactus longiùs recedit ab vtroque ſcilicet à verticali, &amp; hori­<lb></lb>zontali, plùs acquiret in eodem plano horizontali<emph.end type="italics"></emph.end>; ſi enim quò plùs ac­<lb></lb>cedit ad vtrumque, minùs acquirit, igitur plùs acquirit, quò plùs re­<lb></lb>cedit. </s>
				</p>
				<p id="N1B58A" type="main">
					<s id="N1B58C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B598" type="main">
					<s id="N1B59A"><emph type="italics"></emph>Hinc iactus medius ſeu per inclinatam qua cum verticali, vel horizontali <lb></lb>facit angulum<emph.end type="italics"></emph.end> 45.<emph type="italics"></emph>ſeu ſemirectum, eſt omnium maximus, id eſt plùs acqui­<lb></lb>rit in eodem plano horizontali, quàm reliqui omnes<emph.end type="italics"></emph.end>; </s>
					<s id="N1B5AD">experientia certiſſima <lb></lb>eſt, ratio eſt quia ab horizontali &amp; verticali maximè omnium diſtat; <lb></lb>igitur maximus eſt per Theorema 62. nec eſt vlla alia ratio geome­<lb></lb>trica. </s>
				</p>
				<p id="N1B5B7" type="main">
					<s id="N1B5B9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B5C5" type="main">
					<s id="N1B5C7"><emph type="italics"></emph>Iactus qui æqualiter ab horizontali &amp; verticali diſtant, ſunt æquales<emph.end type="italics"></emph.end>; </s>
					<s id="N1B5D0"><lb></lb>probatur, quia qua proportione ad horizontalem ſeu verticalem acce­<lb></lb>dit iactus, in ea proportione minor eſt; </s>
					<s id="N1B5D7">igitur qui æqualiter acce­<lb></lb>dunt in proportione æquali, minores ſunt; </s>
					<s id="N1B5DD">igitur æquales, quod mo­<lb></lb>dica figura ob oculos ponet; </s>
					<s id="N1B5E3">ſit enim quadrans ABF, iactus verti­<lb></lb>calis AB, horizontalis AF, medius AD, hic maximus omnium <lb></lb>erit; at verò AC, &amp; AE, qui ab AD æqualiter diſtant, erunt æ­<lb></lb>quales. </s>
				</p>
				<p id="N1B5ED" type="main">
					<s id="N1B5EF"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B5FB" type="main">
					<s id="N1B5FD">Obſeruabis primò, omitti à me multa quæ ſuis Parabolis aliqui af­<lb></lb>fingunt, quæ nec experimentis, nec vllis rationibus conſen­<lb></lb>tiunt. </s>
				</p>
				<p id="N1B604" type="main">
					<s id="N1B606">Secundò rationem iſtorum omnium Theorematum; </s>
					<s id="N1B60A">quia quo iactus <lb></lb>ad verticalem propiùs accedit, maior quantitas impetus deſtruitur <lb></lb> v.g. in AD plùs quàm in GK; </s>
					<s id="N1B614">igitur citò deficiunt vires huic iactui; </s>
					<s id="N1B618"><lb></lb>adde quod acquirit in verticali, quod alius acquirit in horizontali; </s>
					<s id="N1B61D">at <pb pagenum="172" xlink:href="026/01/204.jpg"></pb>verò qui propiùs accedit ad horizontalem citò deſcendit infra planum <lb></lb>horizontale, tùm quia propior eſt, tum quia citò naturalis impetus <lb></lb>acceleratur; </s>
					<s id="N1B62A">igitur plùs acquirit in perpendiculari deorſum, quàm in <lb></lb>horizontali; quæ omnia ex certis principiis, non fictitiis dedu­<lb></lb>cuntur. </s>
				</p>
				<p id="N1B632" type="main">
					<s id="N1B634">Tertiò, obſeruabis talem eſſe hypotheſim illam Paraboliſtarum, de <lb></lb>qua ſuprà; </s>
					<s id="N1B63A">ſit enim iactus verticalis EA; </s>
					<s id="N1B63E">medius EB; </s>
					<s id="N1B642">certè ex eorum <lb></lb>etiam principio eo tempore, quo motu æquabili percurreret mobile ſpa­<lb></lb>tium EA, motu naturaliter retardato percurreret ſpatium EG ſubdu­<lb></lb>plum; </s>
					<s id="N1B64C">atqui percurrit EG eo tempore, quo idem percurreret GE motu <lb></lb>naturaliter accelerato; </s>
					<s id="N1B652">ſed percurret inclinatam EC eo tempore quo <lb></lb>percurret EA, ſcilicet motu æquabili; </s>
					<s id="N1B658">ſunt enim æquales: Volunt autem <lb></lb>FE diuidi in 16. partes, &amp; ED in 8. ducique parallelas HQ IP, &amp;c. </s>
					<s id="N1B65E">&amp; ac­<lb></lb>cipi VR (1/16) FE, ita vt RQ ſit ad RH vt 9.ad 7. &amp; PS (4/16) &amp; NT (9/16), vel O <lb></lb>T (1/16) PS (4/16) PR (9/16); </s>
					<s id="N1B666">igitur eo tempore, quo mobile eſſet in IX, erit in M; </s>
					<s id="N1B66A"><lb></lb>igitur motus naturalis acquiſiuit XM, id eſt 1/4 AE; </s>
					<s id="N1B66F">igitur eo tempore quo <lb></lb>eſſet in B erit in D; </s>
					<s id="N1B675">igitur motus naturalis acquiſiuit BD quadruplum X <lb></lb>M; </s>
					<s id="N1B67B">nam ſi vno tempore motu æquabili conficit EX, duobus conficit E <lb></lb>D &amp; ſi motu naturaliter accelerato conficit vno tempore XM, duobus <lb></lb>conficit BD iuxta proportionem Galilei, in qua ſpatia ſunt vt temporum <lb></lb>quadrata; </s>
					<s id="N1B685">&amp; quo tempore motu æquabili conficeret EA, vel EB naturali <lb></lb>conficeret GE vel CZ æqualem GE; ducatur igitur linea per puncta E. <lb></lb>RS, OM, hæc eſt ſemiparabola cui ſi addas MZD, habebis totam ampli­<lb></lb>tudinem Parabolæ ED, hoc eſt totum ſpatium, quod acquirit in plano <lb></lb>horizontali ED iactus medius EB. </s>
				</p>
				<p id="N1B692" type="main">
					<s id="N1B694">Si verò ſit inclinata EY; </s>
					<s id="N1B698">vt habeatur iuxta hanc hypotheſim amplitu­<lb></lb>do horizontalis; </s>
					<s id="N1B69E">fiat ſemicirculus centro G, ſemidiametro GE; </s>
					<s id="N1B6A2">ſit per­<lb></lb>pendicularis YK, erit ſubdupla amplitudo; </s>
					<s id="N1B6A8">ſicut perpendicularis XL de­<lb></lb>finit ſubduplam amplitudinem LE iactus EB; </s>
					<s id="N1B6AE">ſimiliter YK definit ſubdu­<lb></lb>plam amplitudinem iactus E 4.3. nam arcus YX eſt æqualis arcui X 4. <lb></lb>igitur anguli YEC, CE. 3. ſunt æquales; hinc iactus ſunt æquales ſupra, &amp; <lb></lb>infra grad.45. vt autem habeatur altitudo Parabolæ ſubdupla XL eſt al­<lb></lb>titudo Parabolæ iactus EC, ſubdupla YX eſt altitudo iactus EY, ſubdu­<lb></lb>pla 4.K eſt altitudo iactus E 3. </s>
				</p>
				<p id="N1B6BD" type="main">
					<s id="N1B6BF">Ex his facilè iuxta hypetheſim tabulæ omnium iactuum, cuiuſlibet <lb></lb>eleuationis conſtrui poſſunt; </s>
					<s id="N1B6C5">de quibus habes plura apud Galileum in <lb></lb>dialogis, &amp; plurima apud Merſennum in Baliſtica; </s>
					<s id="N1B6CB">quare ab illis abſti­<lb></lb>neo: præſertim cum ſit falſa illa hypotheſis, eiuſque ſectatores vltrò fa­<lb></lb>teantur tabulas illas non parum à vero abeſſe, de quo vide Merſennum <lb></lb>prop.  30. Baliſt. </s>
				</p>
				<p id="N1B6D6" type="main">
					<s id="N1B6D8">Quartò, poſſunt iuxta noſtram hypotheſim tabulæ nouæ conſtrui, quod <lb></lb>&amp; ego præſtarem, niſi prorſus inutiles eſſent; </s>
					<s id="N1B6DE">quare prudenter omiſſas <lb></lb>eſſe prudentes omnes cenſebunt, cum hîc calculatorem non <expan abbr="agã">agam</expan>, ſed phi­<lb></lb>loſophum; </s>
					<s id="N1B6EA">id certè tolerari potuit in analyticis, quæ ſine calculationibus <lb></lb>intelligi non poſſunt; </s>
					<s id="N1B6F0">ſed minimè ferendum in Phyſica, quæ ſucculen-<pb pagenum="173" xlink:href="026/01/205.jpg"></pb>tior eſt, quàm vt numeris tantùm, <expan abbr="ſicciſq́ue">ſicciſque</expan> calculis nutriatur; </s>
					<s id="N1B6FD">adde quod <lb></lb>Praxis Theoricæ in his omninò præferenda eſt; </s>
					<s id="N1B703">quamquam huic etiam <lb></lb>parti deeſſe nolumus, ſed in ſingularem libellum omnes iſtas tabulas &amp; <lb></lb>alias huiuſmodi remittimus; cum hic tantùm rerum phyſicarum cauſas <lb></lb>explicemus. </s>
				</p>
				<p id="N1B70D" type="main">
					<s id="N1B70F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B71B" type="main">
					<s id="N1B71D"><emph type="italics"></emph>Si accipiatur planum horizontale intra illud vnde incipit iactus haud du­<lb></lb>biè iactus omnium maximus erit horizontalis in vtraque hypotheſi.<emph.end type="italics"></emph.end></s>
					<s id="N1B726"> Primo in <lb></lb>hypotheſi Galilci, in qua Parabola GD figurâ ſuperiore habet maximum <lb></lb>omnium amplitudinem; </s>
					<s id="N1B72E">licèt iactus per GX; </s>
					<s id="N1B732">ex quo ſequitur, non ha­<lb></lb>beat impetum maiorem, quâm iactus per EY, vel EX; </s>
					<s id="N1B738">in noſtra verò, ia­<lb></lb>ctus per BG primo tempore plùs acquirit in horizontali BG, quàm ia­<lb></lb>ctus per BF; </s>
					<s id="N1B740">igitur plùs etiam ſecundo tempore; </s>
					<s id="N1B744">nam BF acquirit tantùm <lb></lb>primo tempore BH, at verò BG acquirit RL; </s>
					<s id="N1B74A">adde quod minùs perit ex <lb></lb>iactu BG; </s>
					<s id="N1B750">quippe aſſumatur BL in B 2. &amp; GL in 2. 3. detrahitur tantùm <lb></lb>G. 3.ex BG; </s>
					<s id="N1B756">at verò aſſumatur BH in B 4. &amp; FH in 4.5. detrahitur F 5.ex <lb></lb>BF; </s>
					<s id="N1B75C">igitur plùs ex BF quàm ex BG; quæ omnia ex ſuperioribus regulis <lb></lb>iuſta noſtram hypotheſim præſcriptis conſequuntur. </s>
				</p>
				<p id="N1B762" type="main">
					<s id="N1B764"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B770" type="main">
					<s id="N1B772"><emph type="italics"></emph>Immò probabile eſt æquales fore iactus per inclinatas ſurſum, &amp; deorſum <lb></lb>æqualiter ab horizontali, vnde incipit iactus, distantes; </s>
					<s id="N1B77A">æquales inquam in ali­<lb></lb>quo plano horizontali, inferiore<emph.end type="italics"></emph.end>; </s>
					<s id="N1B783">ſi enim iactus fiat per BD eadem figura &amp; <lb></lb>BP nihil acquiritur in horizontali, vt conſtat; </s>
					<s id="N1B789">ſi verò iactus ſit per BG <lb></lb>maximum ſpatium acquirunt in horizontali plano inferiore; </s>
					<s id="N1B78F">igitur qua <lb></lb>proportione propiùs accedent lineæ ſeu iactus ad BD, PP minùs acqui­<lb></lb>rent; </s>
					<s id="N1B797">qua verò proportione propiùs accedent ad RG plùs acquirent; </s>
					<s id="N1B79B">igi­<lb></lb>tur æqualiter plùs, &amp; minùs hinc inde, ſi æqualiter hinc inde diſtent; </s>
					<s id="N1B7A1">im­<lb></lb>mò hoc ipſum præſentibus oculis intueri licèt; </s>
					<s id="N1B7A7">ſi enim iactus BF compa­<lb></lb>retur cum iactu BK; </s>
					<s id="N1B7AD">certè BK acquirit RK, BF acquirit BH æqualem B <lb></lb>K; </s>
					<s id="N1B7B3">ſed BF &amp; BK æqualiter diſtant ab horizontali BG; </s>
					<s id="N1B7B7">nam arcus GF, &amp; <lb></lb>GK ſunt æquales, vt conſtat: idem dico de iactu BE, &amp; BX, qui acquirunt <lb></lb>æquale ſpatium in horizontali æquale ſcilicet BZ. </s>
				</p>
				<p id="N1B7BF" type="main">
					<s id="N1B7C1"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B7CD" type="main">
					<s id="N1B7CF">Obſeruabis hoc omninò licèt mirum cuiquam fortè videatur, certè <lb></lb>inſtitutum eſſe à natura; </s>
					<s id="N1B7D5">ſi enim comparentur omnes iactus ſuprà hori­<lb></lb>zontalem BG, haud dubiè cum duo extremi ſcilicet BD, &amp; BG nihil <lb></lb>prorſus acquirant, vt conſtat ex dictis, iactus medius ſcilicet ad gradum <lb></lb>45.erit omnium maximus, quia æqualiter ab vtraque extremitate diſtat, <lb></lb>vt demonſtrauimus ſuprà; </s>
					<s id="N1B7E1">ſi verò comparentur omnes iactus, qui poſ­<lb></lb>ſunt fieri à centro B per totum ſemicirculum <expan abbr="DGq;">DGque</expan> certè cum duo ex­<lb></lb>tremi BD, BQ nihil prorſus acquirant, vt conſtat, iactus medius, ſcilicet <lb></lb>ad gradum 90.qui eſt BG erit omnium maximus, quia æqualiter ab vtra-<pb pagenum="174" xlink:href="026/01/206.jpg"></pb>que diſtat extremitate; ſimiliter quemadmodum iactus æqualiter à me­<lb></lb>dio iactu 45. diſtantes æqualem amplitudinem acquirunt in horizontali <lb></lb>BG, ita qui æqualiter diſtant à medio iactu 90.vel horizontali BG æqua­<lb></lb>lem amplitudinem acquirunt in aliquo plano horizontali, ſcilicet in eo <lb></lb>vnde vterque iactus deſinit in perpendicularem deorſum. </s>
				</p>
				<p id="N1B7FC" type="main">
					<s id="N1B7FE">Obſeruabis ſecundo, omnes perpendiculares deorſum perinde accipi, <lb></lb>atque ſi eſſent parallelæ propter inſenſibilem differentium; </s>
					<s id="N1B804">quod certè <lb></lb>ab omnibus admittitur; quomodo verò per diuerſa plana deorſum cor­<lb></lb>pus tendere poſſit, vſque ad centrum terræ, Libro ſequenti explica­<lb></lb>bimus. </s>
				</p>
				<p id="N1B80E" type="main">
					<s id="N1B810"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B81C" type="main">
					<s id="N1B81E"><emph type="italics"></emph>In iactu per inclinatam deorſum dato tempore minùs detrahitur de impetu <lb></lb>violento, quàm in iactu per inclinatam ſurſum<emph.end type="italics"></emph.end> ſit enim circulus centro A <lb></lb>ſemidiametro AG; </s>
					<s id="N1B82B">ſitque AG horizontalis, &amp; AO perpendiculatis deor­<lb></lb>ſum; </s>
					<s id="N1B831">ſit iactus per inclinatam ſurſum AD, ſitque impetus violentus vt A <lb></lb>D, &amp; naturalis deorſum vt DE; </s>
					<s id="N1B837">linea motus erit DAE; </s>
					<s id="N1B83B">igitur aſſumatur A <lb></lb>E in AC, &amp; DE in CB, ex impetu AD detrahitur DB, vt conſtat ex dictis <lb></lb>quia totius ille fruſtrà eſt; </s>
					<s id="N1B843">ſit autem inclinata deorſum cum impetu vio­<lb></lb>lento æquali AI æqualis AD, ſitque naturalis deorſum acceleratus pro <lb></lb>rata plani inclinati vt IL, linea motus erit AL; </s>
					<s id="N1B84B">aſſumatur AK, vt AL, &amp; <lb></lb>KH vt IL, detrahitur tantùm IH, ſed IH eſt minor DB; igitur tempore <lb></lb>ſequenti æquali impetus violentus inclinatæ ſurſum erit vt EF æqualis <lb></lb>AB inclinatæ deorſum, vt LM, quæ maior eſt EF, quia eſt æqua­<lb></lb>lis AH. </s>
				</p>
				<p id="N1B857" type="main">
					<s id="N1B859">Ratio à priori eſt, quia cum inclinata deorſum faciat acutum angu­<lb></lb>lum cum perpendiculari deorſum, cum quo obtuſum facit inclinata ſur­<lb></lb>ſum, maior eſt in illa linea motus; </s>
					<s id="N1B861">eſt enim maior diagonalis, in hac ve­<lb></lb>rò minor, igitur in illa minùs impetus eſt fruſtrà, in iſta verò plùs, igitur <lb></lb>minùs impetus in illa deſtruitur, plùs in iſta; quæ omnia conſtant ex <lb></lb>Th. 110. &amp; 139. &amp; 140. l.1. habes etiam in qua proportione decreſcat <lb></lb>impetus. </s>
				</p>
				<p id="N1B86D" type="main">
					<s id="N1B86F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B87B" type="main">
					<s id="N1B87D"><emph type="italics"></emph>Hinc in iactu qui fit per inclinatam deorſum minùs detrahitur,<emph.end type="italics"></emph.end> &amp; in eo <lb></lb>qui fit per inclinationem ſurſum plùs detrahitur, in perpendiculari deor­<lb></lb>ſum nihil detrahitur, in perpendiculari ſurſum totus detrahitur qui po­<lb></lb>teſt extrahi, id eſt ex collectione vtriuſque naturalis, &amp; violenti dupli <lb></lb>naturalis in prima linea motus; hæc omnia ſequuntur ex dictis. </s>
				</p>
				<p id="N1B88E" type="main">
					<s id="N1B890">Obiici poteſt vnum ſatis difficile; quia ſi in perpendiculari deorſum <lb></lb>purà in AP nihil detrahitur impetus violenti, igitur creſcit ſemper vis <lb></lb>ictus, quod videtur eſſe contra experientiam. </s>
				</p>
				<p id="N1B898" type="main">
					<s id="N1B89A">Reſp. me aliquando fuiſſe in ea ſententiâ, vt reuerâ exiſtimarem de­<lb></lb>creſcere impetum violentum in iactu perpendiculari deorſum; </s>
					<s id="N1B8A0">cum <lb></lb>etiam exiſtimarem decreſcere vim ictus; </s>
					<s id="N1B8A6">ſed re melius conſiderata, cum <lb></lb>nunquam id experiri potuerim; </s>
					<s id="N1B8AC">nam ſemper ſentio vim ictus maiorem, <pb pagenum="175" xlink:href="026/01/207.jpg"></pb>cum deorſum mobile proiicitur, quàm cum ſua ſponte ex eadem altitu­<lb></lb>dine deſcendit; certè ni fallor cum ratio demonſtratiua pro hac ſen­<lb></lb>tentia faciat, non dubitaui ampliùs priorem ſententiam immutare. </s>
				</p>
				<p id="N1B8B9" type="main">
					<s id="N1B8BB">Porrò ratio, quæ pro hac ſententia facit, remque ipſam euincit, talis <lb></lb>eſt; </s>
					<s id="N1B8C1">certum eſt impetum violentum deſtrui à naturali aliquando in ma­<lb></lb>iori, aliquando in minori proportione, vt conſtat ex dictis; </s>
					<s id="N1B8C7">illa autem, <lb></lb>ſeu maior, ſeu minor proportio aliam regulam non habet præter illam <lb></lb>quam toties inculcauimus, id eſt impetum deſtrui pro rata, id eſt qua <lb></lb>proportione eſt fruſtrà, id eſt qua proportione eſt minor motus eo, qui <lb></lb>eſſet ab vtroque impetu ſi ad <expan abbr="eãdem">eandem</expan> lineam vterque determinatus eſſet <lb></lb>atqui cum proiicitur mobile deorſum, vterque impetus ad <expan abbr="eãdem">eandem</expan> li­<lb></lb>neam eſt determinatus; </s>
					<s id="N1B8DF">igitur nihil motus deeſt per Th.138.l.1. igitur <lb></lb>nihil impetus eſt fruſtrà; igitur nihil impetus illius deſtruitur. </s>
				</p>
				<p id="N1B8E5" type="main">
					<s id="N1B8E7">Quod dictum eſſe velim non conſiderata medij reſiſtentiâ, quæ certè <lb></lb>aliquid impetus deſtruit, quod tamen inſenſibile eſt in medio libero, pu­<lb></lb>tà in aëre; </s>
					<s id="N1B8EF">ſi enim inſenſibilis eſt hæc reſiſtentia in motu naturali; </s>
					<s id="N1B8F3">dum <lb></lb>mobile ſit eius ſoliditatis, quæ ſuperet facilè vim aëris; certè etiam in­<lb></lb>ſenſibilis eſt in motu proiectorum, præſertim in mediocri ſpatio, eſt <lb></lb>enim par vtrobique ratio. </s>
				</p>
				<p id="N1B8FD" type="main">
					<s id="N1B8FF">Equidem fateor in longiſſimo ſpatio poſſe tandem deſtrui totum im­<lb></lb>petum violentum; </s>
					<s id="N1B905">nam ſi aliquid in dato ſpatio deſtruitur; </s>
					<s id="N1B909">igitur in ma­<lb></lb>iore piùs deſtruitur; </s>
					<s id="N1B90F">atque ita deinceps, donec tandem totus deſtructus <lb></lb>ſit; at verò in iis altitudinibus, ex quibus corpus deorſum proiicere poſ­<lb></lb>ſumus, vix quidquam facit prædicta reſiſtentia. </s>
				</p>
				<p id="N1B917" type="main">
					<s id="N1B919">Nec eſt quod aliquis dicat ab hac reſiſtentia non deſtrui impetum <lb></lb>naturalem in motu naturaliter accelerato, vt dictum eſt in ſecundo lib. </s>
					<s id="N1B91F"><lb></lb>Igitur nec deſtrui violentum; </s>
					<s id="N1B923">nam qua proportione creſcit medij reſi­<lb></lb>ſtentia, creſcunt vires impetus, qui perpetuò augetur; </s>
					<s id="N1B929">vnde cum <lb></lb>remaneat ſemper eadem reſiſtentiæ proportio ſicut primo tempore mo­<lb></lb>tus impedit hæc reſiſtentia, ne tantillùm impetus producatur; </s>
					<s id="N1B931">ita ſecun­<lb></lb>do tempore impedit ne tantillùm æquale producatur; </s>
					<s id="N1B937">igitur nihil pro­<lb></lb>ducti impetus ab illa deſtruitur propter augmentum continuum: </s>
					<s id="N1B93D">at ve­<lb></lb>rò cum impetus violentus non intendatur; </s>
					<s id="N1B943">certè ſi tantillùm illus perit, <lb></lb>primo vel ſecundo inſtanti motus, propter medij reſiſtentis, tantillùm <lb></lb>æquale ſingulis temporibus æqualibus deſtruitur; igitur cum infinitus <lb></lb>non ſit poſt longiſſimum ſpatij tractum totus tandem deſtruetur vio­<lb></lb>lentus ſolo ſuperſtite naturali. </s>
				</p>
				<p id="N1B94F" type="main">
					<s id="N1B951">Hinc fortè ſagitta ex notabili altitudine minùs ferit; </s>
					<s id="N1B955">quia materia illa <lb></lb>lignea, &amp; plumea, ex qua conſtat, multùm ab aëre reſiſtente accipit de­<lb></lb>trimenti: </s>
					<s id="N1B95D">adde quod licèt initio deorſum rectà emittatur; </s>
					<s id="N1B961">attamen mini­<lb></lb>mo aëris flatu declinat tantillùm obliqua; hæc verò obliquitas maximam <lb></lb>ictus vim infringit, &amp; conflictus impetuum quaſi ipſum ictum diſtrahit, <lb></lb>quod facilè probabis, ſi modico ferè tactu cadentem perpendiculariter <lb></lb>ſagittam à ſuo tramite deturbes. </s>
				</p>
				<p id="N1B96D" type="main">
					<s id="N1B96F">Dices, etiam in glande è tormento exploſa hoc ipſum cernitur </s>
				</p>
				<pb pagenum="176" xlink:href="026/01/208.jpg"></pb>
				<p id="N1B976" type="main">
					<s id="N1B978">Reſp. eſt minor vis ictus inflicti à glande deorſum, quàm ſurſum vt <lb></lb>aliqui putant; </s>
					<s id="N1B97E">id autem ex duplici capite procedere; </s>
					<s id="N1B982">primum eſt, cum fe­<lb></lb>ratur glans ab igne per aliquod tempus, non eſt dubium, quin vis ignis <lb></lb>ſurſum maior ſit quàm deorſum; </s>
					<s id="N1B98A">cum ſurſum gemino quaſi impetu fera­<lb></lb>tur, deorſum verò impetu tantùm exploſionis; </s>
					<s id="N1B990">ſecundum eſt, quia cum <lb></lb>glans iam deorſum ſua ſponte deſcendat, haud dubiè ab igne minus eò <lb></lb>impelli poteſt, vt ſæpè diximus ſuprà; quidquid ſit, ſi proiiciatur deorſum <lb></lb>globus plumbeus vel arcu, vel manu, obſeruabitur maiorem ab eo ictum <lb></lb>infligi, quàm ſi ſua ſponte deſcenderet. </s>
				</p>
				<p id="N1B99C" type="main">
					<s id="N1B99E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B9AA" type="main">
					<s id="N1B9AC"><emph type="italics"></emph>Si corpus moueatur deorſum perpendiculariter motu mixto, eo tempore que <lb></lb>motu naturali acquireret illum impetum quem habet motu violento, acquirit <lb></lb>triplum illius ſpatium<emph.end type="italics"></emph.end> v.g. in figura ſuperiore ſit linea perpendiculatis <lb></lb>deorſum A E, in qua motu naturali dato tempore acquiratur AB, &amp; ſe­<lb></lb>cundo tempore æquali BC; </s>
					<s id="N1B9BF">ſitque impetus violentus vt AC: </s>
					<s id="N1B9C3">Dico quod <lb></lb>æquali tempore prioribus acquireret AE triplum AC, quia motu ve­<lb></lb>loci vt AC acquirit CE eo tempore, quo motu veloci vt AB acquirit A <lb></lb>B, &amp; veloci vt BC acquirit BC; </s>
					<s id="N1B9CD">nam eo tempore, quo acquirit AB acqui­<lb></lb>rit CD, &amp; eo tempore, quo acquirit BC acquirit DE; </s>
					<s id="N1B9D3">ergo eo tempore, <lb></lb>quo acquirit AC acquirit CE; </s>
					<s id="N1B9D9">ergo ſi iungatur motus naturalis violento, <lb></lb>eo tempore, quo motu naturali acquiretur tantùm AC, motu mixto ex <lb></lb>naturali &amp; tali violento acquiretur AE, id eſt triplum: </s>
					<s id="N1B9E1">ſi verò moueatur <lb></lb>duobus temporibus, ita vt primò acquirat AC, &amp; altero triplum AC, <lb></lb>ſitque coniunctus impetus violentus vt AC; certè duobus temporibus <lb></lb>acquiretur motu mixto octuplum AC, ſed hæc ſunt facilia. </s>
				</p>
				<p id="N1B9EB" type="main">
					<s id="N1B9ED"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1B9F9" type="main">
					<s id="N1B9FB"><emph type="italics"></emph>Si corpus graue proiiciatur deorſum per medium aëra, qui reſiſtat, cum <lb></lb>tandem deſtruatur impetus violentus, vbi totus deſtructus eſt, minor eſt ictus <lb></lb>quàm eſſet. </s>
					<s id="N1BA04">ſi corpus graue ſolo impetu natur ali eò deſcendiſſet<emph.end type="italics"></emph.end>; </s>
					<s id="N1BA0B">quod demon­<lb></lb>ſtro, ſit enim ſpatium AD, quod percurrit motu mixto eo tempore, quo <lb></lb>motu naturali puro ſpatium BC idem mobile percurreret, ſitque deſtru­<lb></lb>ctus in puncto D totus impetus violentus; </s>
					<s id="N1BA15">certè remanet tantùm natu­<lb></lb>ralis acquiſitus eo tempore, quo mobile percurrit BC; </s>
					<s id="N1BA1B">ſed temporibus æ­<lb></lb>qualibus acquiruntur æqualia velocitatis momenta; </s>
					<s id="N1BA21">igitur æqualis im­<lb></lb>petus; </s>
					<s id="N1BA27">igitur in C tantùm ille impetus, qui eſſet in E vel in D; </s>
					<s id="N1BA2B">ſed dum <lb></lb>percurreret ED motu puro naturali, augetur impetus; </s>
					<s id="N1BA31">igitur maior eſſet <lb></lb>impetus in D ſub finem motus naturalis per AD, quam motus mixti per <lb></lb>eamdem AD; </s>
					<s id="N1BA39">igitur maior ictus ſub finem naturalis; igitur minus ſub fi­<lb></lb>nem violenti. </s>
				</p>
				<p id="N1BA3F" type="main">
					<s id="N1BA41"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BA4D" type="main">
					<s id="N1BA4F"><emph type="italics"></emph>Hinc paradoxon egregium; </s>
					<s id="N1BA54">mobile proiectum in data diſtantia minùs ferit <lb></lb>quàm ſua ſponte demiſſum<emph.end type="italics"></emph.end>; quod neceſſariò ſequitur ex dictis. </s>
				</p>
				<p id="N1BA5D" type="main">
					<s id="N1BA5F">Obſeruabis ſcrupulum adhuc fortè hærere, cur ſcilicet impetus <pb pagenum="177" xlink:href="026/01/209.jpg"></pb>violentus non deſtruatur à naturali, cuius ſcilicet iuſtam impedit propa­<lb></lb>gationem; </s>
					<s id="N1BA6A">ſed profectò nullo modo impetus ille violentus impedit effe­<lb></lb>ctum impetus naturalis innati vel addititij; </s>
					<s id="N1BA70">quia vterque totum ſuum ef­<lb></lb>fectum ſortitur; </s>
					<s id="N1BA76">quod autem ſpectat ad propagationem; certè ita propa­<lb></lb>gatur, vt temporibus æqualibus æqualis impetus accedat. </s>
				</p>
				<p id="N1BA7C" type="main">
					<s id="N1BA7E">Dices, debes quidem nouus impetus accedere, ſed non tali <lb></lb>modo. </s>
				</p>
				<p id="N1BA83" type="main">
					<s id="N1BA85">Reſp. non eſſe alium modum à natura inſtitutum, niſi vt temporibus <lb></lb>æqualibus æqualia velocitatis momenta acquirantur. </s>
				</p>
				<p id="N1BA8A" type="main">
					<s id="N1BA8C">Dices præterea, fruſtrà accedit nouus impetus naturalis, cum iam ad­<lb></lb>ſit violentus, qui eius munere defungi poteſt. </s>
				</p>
				<p id="N1BA91" type="main">
					<s id="N1BA93">Reſp. cauſam neceſſariam neceſſariò agere; igitur corpus graue perpe­<lb></lb>tuò in medio libero ſuum motum intendit. </s>
				</p>
				<p id="N1BA99" type="main">
					<s id="N1BA9B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BAA7" type="main">
					<s id="N1BAA9"><emph type="italics"></emph>Poteſt vtcumque delineari linea motus mixti per inclinatam deorſum<emph.end type="italics"></emph.end> ſit <lb></lb>enim perpendicularis deorſum AB ſit iactus per inclinatam AF; </s>
					<s id="N1BAB4">ſitque <lb></lb>impetus violentus vt AE naturalis vt EC, linea motus erit AC; </s>
					<s id="N1BABA">aſſumatur <lb></lb>AF æqualis AC, &amp; DF æqualis EC, ſitque CH vt AD, &amp; impetus natu­<lb></lb>ralis auctus vt HK, linea motus erit CK; </s>
					<s id="N1BAC2">ſit CI æqualis DK, &amp; IG æqua­<lb></lb>lis HK, &amp; KL æqualis CG; </s>
					<s id="N1BAC8">ſit que impetus naturalis ſecundò auctus vt L <lb></lb>M; </s>
					<s id="N1BACE">linea motus erit KM; igitur connectantur puncta AC, KM per lineam <lb></lb>curuam, hæc eſt linea quæſita, vt conſtat ex dictis ſuprà. </s>
				</p>
				<p id="N1BAD4" type="main">
					<s id="N1BAD6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 73.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BAE2" type="main">
					<s id="N1BAE4"><emph type="italics"></emph>Hinc poteſt aliquo tempore tantùm impetus violenti deſtrui quantùm pro­<lb></lb>ducitur naturalis<emph.end type="italics"></emph.end>; igitur ſi non conſideres reſiſtentiam medij, tunc æqua­<lb></lb>lis eſſet ictus, &amp; æquabilis motus. </s>
				</p>
				<p id="N1BAF1" type="main">
					<s id="N1BAF3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BAFF" type="main">
					<s id="N1BB01"><emph type="italics"></emph>Quando mobile peruenit in M, &amp; acquiſiuit in perpendiculari deorſum to­<lb></lb>tam altitudinem AR, non habet totum impetum naturalem, quem acquireret <lb></lb>motu naturali per totam AR, ſed tantùm illum, quem acquireret in compoſita <lb></lb>ex ſegmentis NO, PB, QR<emph.end type="italics"></emph.end>; quia ad motum iſtum deorſum non tantùm <lb></lb>concurrit impetus naturalis, ſed etiam violentus vt conſtat. </s>
				</p>
				<p id="N1BB12" type="main">
					<s id="N1BB14"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 75.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BB20" type="main">
					<s id="N1BB22"><emph type="italics"></emph>Hinc reiicies Galileum, &amp; alios,<emph.end type="italics"></emph.end> qui volunt in linea motus AC ac­<lb></lb>quiri <expan abbr="tantũdem">tantundem</expan> impetus naturalis quantum in perpendiculari AB ac­<lb></lb>quireretur. </s>
				</p>
				<p id="N1BB32" type="main">
					<s id="N1BB34"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BB40" type="main">
					<s id="N1BB42"><emph type="italics"></emph>In naui mobili ſi è ſummo malo remittatur corpus graue, deſcendit motu <emph.end type="italics"></emph.end><pb pagenum="178" xlink:href="026/01/210.jpg"></pb><emph type="italics"></emph>mixto<emph.end type="italics"></emph.end>; probatur, quia duplex impetus concurrit ad illum motum, ſcilicet <lb></lb>naturalis deorſum, &amp; horizontalis impreſſus à naui, vt conſtat ex defini­<lb></lb>tione 1.hyp.2. &amp; Ax.1. </s>
				</p>
				<p id="N1BB58" type="main">
					<s id="N1BB5A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BB66" type="main">
					<s id="N1BB68"><emph type="italics"></emph>Ille motus eſt mixtus ex naturali accelerato, &amp; violento per horizontalem <lb></lb>retardato<emph.end type="italics"></emph.end>; quod eodem modo probatur, quo ſuprà probatum eſt in mobi­<lb></lb>li proiecto per horizontalem Th.30. eſt enim prorſus eadem, cum à na­<lb></lb>ui reuera imprimatur impetus iis omnibus, quæ motu nauis fe­<lb></lb>runtur. </s>
				</p>
				<p id="N1BB79" type="main">
					<s id="N1BB7B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BB87" type="main">
					<s id="N1BB89"><emph type="italics"></emph>Hinc reiicio omnes alias combinationes recepta ſexta; </s>
					<s id="N1BB8F">immò ſextam <lb></lb>ipſam ex parte<emph.end type="italics"></emph.end>; nec enim naturalis acceleratur in hoc motu in ea <lb></lb>proportione, in qua acceleratur per lineam perpendicularem deor­<lb></lb>ſum per Th. 29.ſed iuxta rationem planorum inclinatorum per Theo­<lb></lb>rema 31. nec etiam violentus deſtruitur vniformiter, ſed pro rata per <lb></lb>Th. 39. </s>
				</p>
				<p id="N1BBA0" type="main">
					<s id="N1BBA2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BBAE" type="main">
					<s id="N1BBB0"><emph type="italics"></emph>Hinc initio plùs detrahitur violenti, &amp; minùs additur naturalis, in <lb></lb>fine plùs additur naturalis &amp; minùs detrahitur violenti<emph.end type="italics"></emph.end>; hinc minor eſt <lb></lb>ictus in fine niſi malus nauis ad eam altitudinem aſcenderet, ad quam <lb></lb>profectò nullus aſcendit, quæ omnia conſtant per Theorema 34. <lb></lb>35. 36. </s>
				</p>
				<p id="N1BBC1" type="main">
					<s id="N1BBC3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BBCF" type="main">
					<s id="N1BBD1"><emph type="italics"></emph>Hinc ratio curuitatis huius lineæ, vel hypotheſis ſecundæ<emph.end type="italics"></emph.end>; </s>
					<s id="N1BBDA">quæ tamen non <lb></lb>eſt Parabola vt volunt aliqui; </s>
					<s id="N1BBE0">hinc non eo tempore deſcendit in nauim <lb></lb>prædictus globus, quo deſcenderet per ipſam perpendicularem motu <lb></lb>purè naturali ex eadem altitudine, ſed maiore tempore; quia motu mix­<lb></lb>to non acceleratur iuxta proportionem motus naturalis puri per Th. <lb></lb>77. quod confirmatur illis omnibus experimentis, quæ ſuprà adduxi <lb></lb>Th. 46. </s>
				</p>
				<p id="N1BBF1" type="main">
					<s id="N1BBF3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BBFF" type="main">
					<s id="N1BC01"><emph type="italics"></emph>Hinc ſi nauis moueretur eadem velocitate, qua funis arcus cum re­<lb></lb>dit, eſſetque aptata ſagitta, &amp; directa horizontaliter in naui; </s>
					<s id="N1BC09">haud <lb></lb>dubiè ſi poſt aliquod tempus ſtaret illicò immota nauis: </s>
					<s id="N1BC0F">emitteretur ſa­<lb></lb>gita, non minore certè vi quàm ab ipſo arcu<emph.end type="italics"></emph.end>; </s>
					<s id="N1BC18">hinc etiam cum <lb></lb>nauis appellitur ad littus, ſi ſtatim ſubſiſtat; </s>
					<s id="N1BC1E">omnia quæ ſunt in <lb></lb>naui ſuccutiuntur &amp; <expan abbr="pleriq;">plerique</expan> cadunt incauti in partem aduerſam propter <pb pagenum="179" xlink:href="026/01/211.jpg"></pb>impetum à naui acceptum; ex quo certè experimento maximè confir­<lb></lb>matur hic impetus à naui impreſſus, per quem Galileus ex hypotheſi mo­<lb></lb>tus æſtum maris explicat exemplo appulſarum nauium ad littus, quæ <lb></lb>aquam vehunt. </s>
				</p>
				<p id="N1BC33" type="main">
					<s id="N1BC35"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BC41" type="main">
					<s id="N1BC43"><emph type="italics"></emph>Hinc demiſſus globus plumbeus, vel alterius materiæ, quæ facilè vim aëris <lb></lb>infringat è ſummo malo nauis ad imum ferè malum deſcendit,<emph.end type="italics"></emph.end> hæc eſt ex­<lb></lb>perientia à Galileo producta, non tamen adinuenta, à Gaſſendo do­<lb></lb>ctiſſimè &amp; elegantiſſimè explicata, ab omnibus Copernici ſectatoribus <lb></lb>toties decantata, quæ vulgus ignobile ad admirationem adducit; </s>
					<s id="N1BC54">imò <lb></lb>plures è Philoſophis fuere, qui eam in dubium adducerent, cum cam ſuis <lb></lb>principiis, ne dicam fortè ſomniis aduerſari putarent; certiſſimum tamen <lb></lb>eſt illud experimentum centies, imò millies comprobatum, totis etiam <lb></lb>vrbibus ſpectantibus. </s>
					<s id="N1BC60">Nec ratio huius experimenti adeo abſtruſa eſt, <lb></lb>vel recondita, quin à vulgari, ne dicam triobolari Philoſopho ſtatim ex­<lb></lb>plicari poſſit; </s>
					<s id="N1BC68">cum enim imprimatur à naui mobili impetus pendulo <lb></lb>globo per horizontalem, &amp; alius ab ipſa grauitate deorſum per Th. 71. <lb></lb>certè mouetur globus demiſſus reſecto funiculo motu mixto ex hori­<lb></lb>zontali nauis, naturali corporis grauis; </s>
					<s id="N1BC72">igitur per lineam curuam, quæ <lb></lb>ferè ad imum malum terminatur ſed modicum figuræ adhibendum eſt; </s>
					<s id="N1BC78"><lb></lb>ſit planum aquæ <expan abbr="horizõtale">horizontale</expan>, cui innatat nauis IH; </s>
					<s id="N1BC81">ſit malus IA perpen­<lb></lb>dicularis altus 48. pedes; </s>
					<s id="N1BC87">diuidatur in 4. partes æquales; </s>
					<s id="N1BC8B">corpus graue <lb></lb>conficiat ſpatium illud duobus ſecundis, v.g.igitur AK vno ſecundo; </s>
					<s id="N1BC91">eſt <lb></lb>autem VK 12. pedum; </s>
					<s id="N1BC97">iam verò moueatur nauis per horizontalem IH, <lb></lb>vel AL maxima quaſi velocitate qua triremis moueri poteſt; </s>
					<s id="N1BC9D">ita vt vna <lb></lb>hora faciat 16. milliaria Germanica, &amp; 15′.4. milliaria, 3′ 800. paſſus, <lb></lb>1′ 266. 1″ 4. paſſus &amp; (13/30); </s>
					<s id="N1BCA5">ſupponamus 1″ conficere 18. pedes, ſitque AC <lb></lb>18. &amp; AK vel CE 12. haud dubiè motu mixto faciet lineam AE, &amp; ſe­<lb></lb>cundo tempore lineam EH, donec tandem cadat in punctum H nauis, <lb></lb>quò ferè peruenit punctum I; </s>
					<s id="N1BCAF">nam eodem modo retardatur motus <lb></lb>nauis; </s>
					<s id="N1BCB5">immò plùs quàm motus globi; </s>
					<s id="N1BCB9">quod ſcilicet partes aquæ, quæ à <lb></lb>naui diuiduntur multum reſiſtant; </s>
					<s id="N1BCBF">vnde fit compenſatio; </s>
					<s id="N1BCC3">nam initio <lb></lb>motus violentus, quaſi ſecum rapit motum naturalem initio tardiſſi­<lb></lb>mum; præſertim cum non acceleretur, niſi iuxta rationem plani incli­<lb></lb>nati, vt ſuprà dictum eſt, &amp; in fine naturalis rapit violentum. </s>
				</p>
				<p id="N1BCCD" type="main">
					<s id="N1BCCF">Dixi ad imum ferè malum; </s>
					<s id="N1BCD3">nam reuera aliquid deeſt quod tamen in­<lb></lb>ſenſibile eſt; </s>
					<s id="N1BCD9">ſed quia modico tempore globus deſcendit; </s>
					<s id="N1BCDD">ſit enim malus <lb></lb>108. pedum altitudinis, deſcendit globus tempore 3″; </s>
					<s id="N1BCE3">ſit 192.4; </s>
					<s id="N1BCE7">ſit ſi <lb></lb>fieri poteſt 432. deſcendet 6″, ſed nunquam accedit ad tantam altitudi­<lb></lb>nem, igitur duobus vel tribus ſecundis deſcendit; </s>
					<s id="N1BCEF">igitur modico tem­<lb></lb>pore; </s>
					<s id="N1BCF5">igitur violentus motus cenſeri debet eo tempore æquabilis ſenſi­<lb></lb>biliter; </s>
					<s id="N1BCFB">&amp; cum motus nauis nunquam ſit eiuſdem velocitatis cum illa <lb></lb>quæ acquiritur tempore 2″ in deſcenſu, quia cum in deſcenſu acquiran­<lb></lb>tur, hoc dato tempore ferè 48. pedes ſpatij; </s>
					<s id="N1BD03">certè motu æquabili cuius <pb pagenum="180" xlink:href="026/01/212.jpg"></pb>eſſet eadem velocitas acquirerentur 96. ſed vix acquirerentur 24.vt di­<lb></lb>ctum eſt ſuprà; </s>
					<s id="N1BD0E">igitur vix nauis percurrit in horizontali æqualem lineam <lb></lb>longitudini mali eo tempore, quo globus nauim attingit ſit enim <lb></lb>altitudo mali FA 48. pedum; </s>
					<s id="N1BD16">ſit amplitudo ſpatij horizontalis æqualis <lb></lb>FA; haud dubiè 1″ percurret AD, id eſt 12.pedes ferè, quo tempore per­<lb></lb>currat FG. 24. pedes &amp; 20″ percurret DF, &amp; GI. ſi motus ſumatur vt <lb></lb>æquabilis, vel GH, ſi retardatur, igitur 1°″ mobile percurrit ſegmentum <lb></lb>curuæ AE &amp; 2° EH. </s>
				</p>
				<p id="N1BD22" type="main">
					<s id="N1BD24">Et licèt videatur tantùm acquirere MI, quæ eſt minor DF 15. per­<lb></lb>pendiculari deorſum, acquirit totam EH, quæ non modo eſt à motu na­<lb></lb>turali, verùm etiam à motu violento; </s>
					<s id="N1BD2C">nec enim motu naturali dum mi­<lb></lb>ſcetur cum alio, tantùm acquiritur deorſum, quantùm reuerâ acquiritur <lb></lb>motu naturali puro, vt ſuprà monuimus; </s>
					<s id="N1BD34">quia tamen etiam deorſum mo­<lb></lb>tus violentus deflectitur, etiam aliquid ſpatij ratione violenti deorſum <lb></lb>acquiritur; </s>
					<s id="N1BD3C">ſi enim vbi peruenit in E vterque impetus intactus remane­<lb></lb>ret ſine acceſſione, ſine imminutione; </s>
					<s id="N1BD42">haud dubiè per <expan abbr="eãdem">eandem</expan> EM, quæ <lb></lb>ſit tangens huius curuæ AEH ſuum curſum proſequeretur; </s>
					<s id="N1BD4C">igitur ac­<lb></lb>quireret deorſum totam DN, vel EO propter impetum naturalem præ­<lb></lb>uium; ſi verò aliquid naturalis accedat, quid mirum ſi ratione illius ac­<lb></lb>quiratur MI, vel NF? </s>
				</p>
				<p id="N1BD56" type="main">
					<s id="N1BD58">Dices non deſcendit tam citò motu naturali accelerato, mixto cum <lb></lb>violento, quàm motu puro naturali. </s>
				</p>
				<p id="N1BD5D" type="main">
					<s id="N1BD5F">Reſpondeo concedo; </s>
					<s id="N1BD63">vnde nunquam ex A in H 2″ deſcendit; </s>
					<s id="N1BD67">ſed <lb></lb>tardiùs, licèt FA ſit 48. ped. ſed parùm abeſt tùm propter minorem reſi­<lb></lb>ſtentiam huius impetus violenti, qui facilè detorquetur, &amp; conſequen­<lb></lb>tur minùs illius perit, tùm quia etiam deſtruitur aliquid violenti; igitur <lb></lb>paulò plùs temporis collocat in GI, quàm in FG. </s>
				</p>
				<p id="N1BD75" type="main">
					<s id="N1BD77"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BD83" type="main">
					<s id="N1BD85">Obſeruabis primò, ſi nouus impetus accedat, non eſſe expectandum <lb></lb>hunc effectum; quippe nihil accipit à naui globus deinceps, vbi ſemel <lb></lb>reſecto fune ab ea quaſi ſeparatur. </s>
				</p>
				<p id="N1BD8D" type="main">
					<s id="N1BD8F">Secundò, ſi ſtatim ſiſtat nauis demiſſo globo ad vnum malum nullo <lb></lb>modo deſcendet, vt patet, ſed antè. </s>
				</p>
				<p id="N1BD94" type="main">
					<s id="N1BD96">Tertiò, ſi demittatur globus dum ſiſtit nauis, tùm deinde, vbi <lb></lb>demiſſus eſt, impellatur nauis; non deſcendet etiam ad radicem, ſed <lb></lb>retrò. </s>
				</p>
				<p id="N1BD9E" type="main">
					<s id="N1BDA0">Quartò, motus nauis non eſt æquabilis, quidquid dicat Galileus; </s>
					<s id="N1BDA4">alio­<lb></lb>quin vna remorum impulſione opus eſſet, vt ſemper eodem motu moue­<lb></lb>retur, aut certè ſi continua remigatione impellatur; </s>
					<s id="N1BDAC">creſceret in infini­<lb></lb>tum velocitas motus, ſi nihil de priori, velocitate detraheretur; </s>
					<s id="N1BDB2">retarda­<lb></lb>tur igitur ille nauis motus propter reſiſtentiam aquæ, cuius partes &amp; im­<lb></lb>pellendæ &amp; ſulcandæ, ſeu diuidendæ ſunt; </s>
					<s id="N1BDBA">hinc fiunt roſtratæ naues <lb></lb>vel cuſpidatæ vt faciliùs aquam findere poſſint; </s>
					<s id="N1BDC0">igitur ille motus nauis <lb></lb>non eſt æquabilis; Idem prorſus dicendum eſt de impetu impreſſo in <pb pagenum="181" xlink:href="026/01/213.jpg"></pb>globo, cuius aliquæ partes deſtruuntur, ne ſint fruſtrà, quod ſuprà de pro­<lb></lb>jecto per horizontalem vel inclinatam luculenter demonſtrauimus. </s>
				</p>
				<p id="N1BDCD" type="main">
					<s id="N1BDCF">Quintò ſi demittatur ex alia naui proxima immobili perpendiculari­<lb></lb>ter omninò deſcendet; </s>
					<s id="N1BDD5">Vnde valde hallucinantur ij, qui exiſtimant hunc <lb></lb>motum eſſe ab aëre quem nauis commouet, quod falſiſſimum eſt, quia <lb></lb>pertica ad inſtar mali parùm aëris commouet; </s>
					<s id="N1BDDD">adde quod aër retrò agi­<lb></lb>tur, vt patet in aqua; </s>
					<s id="N1BDE3">præterea ſi è curru immobili demittatur globus eo <lb></lb>tempore, quo alius currus præteruolat, deſcendit perpendiculariter; </s>
					<s id="N1BDE9">ſi ve­<lb></lb>rò è curru mobili etiam in maiori diſtantia porrecta ſcilicet maximè <lb></lb>extra currum demittente dextera; </s>
					<s id="N1BDF1">globus ab ipſo curru capietur; </s>
					<s id="N1BDF5">hîc <lb></lb>etiam obſeruabis idem prorſus accidere in curru mobili, quod in naui; </s>
					<s id="N1BDFB">ſi <lb></lb>enim è feneſtra currus mobilis demittas pilam, ſemper cadet ex aduerſo; <lb></lb>idem dico de currente equo, cui inſidens demittat globum, imò ſi locus <lb></lb>ſit planus &amp; politus, pila per aliquod tempus currum, vel equitem inſe­<lb></lb>quetur, quod quiſque probare poterit, vt reuerâ centies probatum <lb></lb>fuit. </s>
				</p>
				<p id="N1BE09" type="main">
					<s id="N1BE0B">Sextò ad rationem Galilei, qui contendit motum circularem circa <lb></lb>centrum terræ eſſe æquabilem, quia ſcilicet mobile non recedit à centro: <lb></lb>leuis eſt omninò ratio; </s>
					<s id="N1BE13">quia globus in medio aëre motu mixto mouetur, <lb></lb>id eſt habet impetum partim deorſum, partim per tangentem, &amp; nullo <lb></lb>modo per circularem, vt certum eſt; </s>
					<s id="N1BE1B">nec enim rotata alium impetum im­<lb></lb>primunt, igitur violentus eſt; </s>
					<s id="N1BE21">igitur deſtrui debet etiam iuxta commu­<lb></lb>nia principia: </s>
					<s id="N1BE27">adde quod motus mixtus fit per Diagonalem quod etiam <lb></lb>ipſe admittit; </s>
					<s id="N1BE2D">igitur totus impetus æqualem motum non habet; </s>
					<s id="N1BE31">nec enim <lb></lb>Diagonalis æqualis eſt vnquam duobus lateribus; </s>
					<s id="N1BE37">igitur aliquid illius <lb></lb>fruſtrà eſt; </s>
					<s id="N1BE3D">igitur deſtrui debet; </s>
					<s id="N1BE41">præterea licèt motus circularis ſit peren­<lb></lb>nis circa centrum mundi; </s>
					<s id="N1BE47">nam de illo tantùm eſt quæſtio, hoc ipſum <lb></lb>ſupponit primò motum illum eſſe ſimplicem; </s>
					<s id="N1BE4D">ſecundò, nullam prorſus <lb></lb>eſſe reſiſtentiam; </s>
					<s id="N1BE53">atqui in hoc caſu vtrumque deficit; </s>
					<s id="N1BE57">nam motus ille <lb></lb>circularis non eſt ſimplex ſed mixtus, &amp; obeſt reſiſtentia aquæ, vt ſuprà <lb></lb><expan abbr="dictũ">dictum</expan> eſt; niſi verò conſideres <expan abbr="deſcendentẽ">deſcendentem</expan> globum è ſummo malo, quis <lb></lb>dicat eſſe circularem? </s>
					<s id="N1BE68">adde quod nauis imprimit tantùm rectum per <lb></lb>tangentem, vt iam ſuprà dictum eſt; </s>
					<s id="N1BE6E">porrò ad illud, quod dicit non de­<lb></lb>ſtrui motum circularem à naturali, cui non eſt contrarius, cum non re­<lb></lb>moueat longiùs à centro; </s>
					<s id="N1BE76">videtur omninò diſſimulare cauſam impetus <lb></lb><expan abbr="deſtructiuã">deſtructiuam</expan>, quæ cettè in <expan abbr="cõtrarietate">contrarietate</expan> tantùm determinationis poſita eſt, <lb></lb>vt ſuprà dictum eſt; </s>
					<s id="N1BE85">ex qua ſequitur aliquid impetus fruſtrà eſſe; </s>
					<s id="N1BE89">ac pro­<lb></lb>inde deſtrui per Axioma illud toties decantatum, <emph type="italics"></emph>Quod frustrà eſt, non eſt<emph.end type="italics"></emph.end>: </s>
					<s id="N1BE95"><lb></lb>Præterea non video quomodo hanc rationem proponat magnus Gali­<lb></lb>leus, qui nullum alium impetum violentum deſtrui putat, nîſi tantùm il­<lb></lb>lum, qui eſt per lineam verticalem ſurſum; nam ex motu illo impreſſo <lb></lb>æquabili, &amp; naturali accelerato ſuas Parabolas adſtruit. </s>
				</p>
				<p id="N1BEA0" type="main">
					<s id="N1BEA2">Septimò, non eſt tamen quod diffitear ingeniosè excogitatum ab eo <lb></lb>fuiſſe, ideo globum è ſummo malo demiſſum ad imum deſcendere, quod <lb></lb>ſcilicet deſcendat motu mixto ex naturali accelerato, &amp; violento æqua-<pb pagenum="182" xlink:href="026/01/214.jpg"></pb>bili, quod vt breuiter ob oculos ponatur ſit malus nauis mobilis IA, <lb></lb>quæ eo tempore, quo corpus graue deſcendit ab A in D motu naturali, <lb></lb>percurrit FG æquabili motu, &amp; conſequenter GI æqualem FG eo tem­<lb></lb>pore, quo idem corpus graue percurrit DF triplam AD; </s>
					<s id="N1BEB5">igitur globus <lb></lb>demiſſus ex A ſuo motu deſcribit Parabolam AEH; quod etiam accidet <lb></lb>aſſumpta quacunque altitudine mali vel quocunque ſpatio confecto à <lb></lb>naui mobili eo tempore, quo corpus graue motu naturali accelerato <lb></lb>conficit ſpatium æquale altitudini mali. </s>
				</p>
				<p id="N1BEC1" type="main">
					<s id="N1BEC3">Octauò, non eſt tamen diſſimulandum, quod etiam non diſſimulauit <lb></lb>Merſennus, talem non fore deſcenſum, ſi nauis v. g. eadem cum emiſſa <lb></lb>ſagitta, vel exploſa è tormento glande velocitate moueretur; </s>
					<s id="N1BECF">non quod <lb></lb>aër vel medium obſiſtat, vt ipſi dicunt; </s>
					<s id="N1BED5">hoc enim iam ſuprà rejecimus; </s>
					<s id="N1BED9"><lb></lb>ſed quod major impetus violentus efficiat, vt iam ſuprà dictum eſt, ne in <lb></lb>tanta proportione naturalis acceleretur; </s>
					<s id="N1BEE0">quod etiam ſuo boatu intonant <lb></lb>tormenta maiora, è quibus horizontaliter directis exploſæ pilæ per plu­<lb></lb>ra ſecunda in libero aëre moueantur, licèt os tormenti à plano horizon­<lb></lb>tis vix tribus pedibus abſit; </s>
					<s id="N1BEEA">igitur non deſcribunt ſuo motu Parabolas; </s>
					<s id="N1BEEE"><lb></lb>hinc ſub finem minor eſt ictus; hinc etiam fatetur idem Merſennus ſe­<lb></lb>cundum ſpatium horizontale confici tardiore motu quàm primum &amp; <lb></lb>tertium quàm ſecundum, atque ita deinceps. </s>
				</p>
				<p id="N1BEF7" type="main">
					<s id="N1BEF9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BF05" type="main">
					<s id="N1BF07"><emph type="italics"></emph>Si corpus graue proiiciatur ſurſum perpendiculariter è naui mobili, ſunt tres <lb></lb>impetus qui concurrunt ad illum motum<emph.end type="italics"></emph.end> ſit enim nauis mobilis per hori­<lb></lb>zontalem LF, è qua ſurſum rectâ per lineam perpendicularem LA pro­<lb></lb>iiciatur corpus graue; </s>
					<s id="N1BF16">huic certè ineſt triplus impetus, ſcilicet duo vio­<lb></lb>lenti, alter per verticalem LA impreſſus à proiiciente; </s>
					<s id="N1BF1C">alter per horizon­<lb></lb>talem LF impreſſus à naui; </s>
					<s id="N1BF22">tertius denique naturalis per ipſam perpen­<lb></lb>dicularem deorſum LP; </s>
					<s id="N1BF28">igitur tres iſti impetus ſuo modo concurrunt <lb></lb>ad motum per Ax.1.certè ſi ineſſent tantùm duo impetus ſcilicet LA, &amp; <lb></lb>LF, motus fieret per inclinatam rectam LC; </s>
					<s id="N1BF30">vel ſi tantùm duo LP, &amp; <lb></lb>LA fieret per ipſam LA motus retardatus; </s>
					<s id="N1BF36">vel ſi LF &amp; LP fieret per <lb></lb>curuam deorſum, vt conſtat ex dictis; igitur per aliam lineam fieri de­<lb></lb>bet ad quam tres illi impetus concurrunt. </s>
				</p>
				<p id="N1BF3E" type="main">
					<s id="N1BF40"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BF4C" type="main">
					<s id="N1BF4E"><emph type="italics"></emph>Tam pugnat impetus naturalis per LP cum verticali LA quando eſt con­<lb></lb>junctus cum horizontali LF, quàm cum nullus eſt horizontalis,<emph.end type="italics"></emph.end> probatur, <lb></lb>quia ſemper mobile deorſum trahit, vt patet. </s>
				</p>
				<p id="N1BF5A" type="main">
					<s id="N1BF5C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BF68" type="main">
					<s id="N1BF6A"><emph type="italics"></emph>Hinc naturalis eſt æquabilis, &amp; violentus ſurſum eſt retardatus; </s>
					<s id="N1BF70">horizon­<lb></lb>talis verò eſt æquabilis ſaltem æquiualenter<emph.end type="italics"></emph.end>; </s>
					<s id="N1BF79">quia cum illo non pugnat ho­<lb></lb>rizontalis, in aſcenſu ſaltem perinde ſe habet; </s>
					<s id="N1BF7F">immò cum illo conuenit <lb></lb>ad deſtruendum violentum ſurſum, id eſt ad deflectendum deorſum <lb></lb>mobile vt conſtat; </s>
					<s id="N1BF87">igitur hic motus conſtat ex naturali &amp; horizontali <pb pagenum="183" xlink:href="026/01/215.jpg"></pb>æquabilibus, &amp; violento retardato ſint enim tres impetus ab eodem <lb></lb>puncto E ſcilicet EF, ED, EA; </s>
					<s id="N1BF92">ex EA ED fit mixtus EG, ex EA, <lb></lb>EF, violentus EB; denique ex mixto EG à naturali EF fit EC, quæ <lb></lb>omnia ſunt clara. </s>
				</p>
				<p id="N1BF9A" type="main">
					<s id="N1BF9C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BFA8" type="main">
					<s id="N1BFAA"><emph type="italics"></emph>Aſcendit mobile ad <expan abbr="eãdem">eandem</expan> altitudinem hoc motu, ad quem aſcenderet <lb></lb>ſine horizontali<emph.end type="italics"></emph.end> v. g. ſine horizontali aſcendit in B, cum horizontali <lb></lb>aſcendit in C, ſed DC, &amp; EB ſunt eiuſdem altitudinis. </s>
				</p>
				<p id="N1BFBE" type="main">
					<s id="N1BFC0"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1BFCC" type="main">
					<s id="N1BFCE">Obſeruabis, licèt iſte motus non fiat per lineam parabolicam, vt ſuprà <lb></lb>demonſtrauimus Th. 54. &amp; reliquis; quia tamen ſenſibiliter proximè <lb></lb>accedit, deinceps vtemur Parabola vt in fig. </s>
					<s id="N1BFD6">Th. 83. &amp; horizontalem <lb></lb>motum accipiemus pro æquabili; </s>
					<s id="N1BFDC">licèt omninò æquabilis non ſit; </s>
					<s id="N1BFE0">niſi <lb></lb>tantùm æquiualenter; </s>
					<s id="N1BFE6">dixi æquiualenter, quia eodem modo ſe habet hic <lb></lb>motus, ac ſi per inclinatam ſurſum LC impetu ſcilicet LC mobile pro­<lb></lb>iiceretur; </s>
					<s id="N1BFEE">ſed in hoc caſu deſtrueretur impetus ille per inclinatam ſim­<lb></lb>plex; </s>
					<s id="N1BFF4">igitur &amp; mixtus; </s>
					<s id="N1BFF8">quia tamen ille qui remanet partim ex LA, par­<lb></lb>tim ex LF eodem modo ferè ſe habet ac ſi totus LF intactus maneret; <lb></lb>hinc dictum eſt ſuprà æquiualenter eſſe æquabilem. </s>
				</p>
				<p id="N1C000" type="main">
					<s id="N1C002"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C00E" type="main">
					<s id="N1C010"><emph type="italics"></emph>Aſcendit hoc motu ad ſubduplam altitudinem illius, ad quam motu mixto <lb></lb>tantum ex verticali &amp; horizontali ſine naturali aſcenderet<emph.end type="italics"></emph.end>; quippe aſcende­<lb></lb>ret in C fig. </s>
					<s id="N1C01D">Th.83. ſine impetu naturali, ſed FC &amp; LA æquales ſunt; </s>
					<s id="N1C021"><lb></lb>atqui motu violento puro, niſi naturalis obeſſet, aſcenderet in A; </s>
					<s id="N1C026">at ve­<lb></lb>rò ſi obeſt naturalis; </s>
					<s id="N1C02C">aſcendit tantùm motu violento in K, &amp; mixto in <lb></lb>in D; </s>
					<s id="N1C032">quia ex K in L motu naturali tot acquireret mobile gradus impe­<lb></lb>tus naturalis quot amittit in motu violento ab L in K; </s>
					<s id="N1C038">ſed cum in impe­<lb></lb>tu acquiſito à K in L motu æquabili aſcenderet ab L in A, quæ eſt dupla <lb></lb>LK vt oſtendimus in ſecundo libro; </s>
					<s id="N1C040">ſed motu mixto, &amp; verticali, &amp; ho­<lb></lb>rizontali aſcenderet in C; </s>
					<s id="N1C046">ſed FD eſt ſubdupla FE; igitur motu mixto <lb></lb>aſcendit ad ſubduplam altitudinem, &amp;c. </s>
				</p>
				<p id="N1C04C" type="main">
					<s id="N1C04E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C05A" type="main">
					<s id="N1C05C"><emph type="italics"></emph>Mobile projectum è naui mobili, vbi ad ſummam altitudinem peruenit mo­<lb></lb>tu mixto ex verticali retardato, horizontali æquabili, &amp; naturali item æqua­<lb></lb>bili, deſcendit etiam motu mixto ex horizontali retardato ſaltem æquiualenter, <lb></lb>&amp; naturali accelerato<emph.end type="italics"></emph.end>; </s>
					<s id="N1C06B">dixi æquiualenter, quia vt dixi in Sch. Th.86. licèt <lb></lb>remaneat aliquid impetus verticalis qui in communem lineam abit cum <lb></lb>horizontali; </s>
					<s id="N1C075">res tamen perinde ſe habet atque ſi totus verticalis deſtrue­<lb></lb>retur, &amp; totus horizontalis intactus permaneret; igitur deſcenſus fit mo­<lb></lb>tu mixto ex naturali accelerato &amp; horizontali retardato per Th.30. quia <lb></lb>tamen modico illo tempore parùm retardatur, vt ſuprà monui, ſenſibili­<lb></lb>ter accipi poteſt pro æquabili. </s>
				</p>
				<pb pagenum="184" xlink:href="026/01/216.jpg"></pb>
				<p id="N1C085" type="main">
					<s id="N1C087"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 89.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C093" type="main">
					<s id="N1C095"><emph type="italics"></emph>Hinc ſenſibiliter ex aſcenſu &amp; deſcenſu fit<emph.end type="italics"></emph.end> <emph type="italics"></emph>integra Parabola<emph.end type="italics"></emph.end>; </s>
					<s id="N1C0A4">nam pro­<lb></lb>iiciatur ex L in A, eo tempore, quo nauis mouetur ex L in F, certè ſi <lb></lb>tempus illud diuidatur bifariam prima parte mobile percurret LI tri­<lb></lb>plam IK in verticali, &amp; LM ſubduplam LF in horizontali; </s>
					<s id="N1C0AE">igitur erit <lb></lb>in G; </s>
					<s id="N1C0B4">ſecunda verò parte temporis in verticali percurrit IK, &amp; MF in <lb></lb>horizontali; </s>
					<s id="N1C0BA">igitur erit in D; </s>
					<s id="N1C0BE">præterea ſi accipiantur duæ aliæ partes tem­<lb></lb>poris æquales; </s>
					<s id="N1C0C4">prima in perpendiculari deorſum percurret DE æqua­<lb></lb>lem LK, &amp; in horizontali DO; </s>
					<s id="N1C0CA">igitur erit in N; </s>
					<s id="N1C0CE">ſecunda vero in per­<lb></lb>pendiculari percurret NQ triplam NO, &amp; NR in horizontali; igitur <lb></lb>erit in S; </s>
					<s id="N1C0D6">ſed hæc eſt Parabola; </s>
					<s id="N1C0DA">nam vt ſe habent quadrata applicatarum <lb></lb>v.g. EG, FL, ita ſagittæ DE, DF; dixi ſenſibiliter, nam vt ſuprà mo­<lb></lb>nui eſt alia linea, quæ tamen proximè accedit ad Parabolam. </s>
				</p>
				<p id="N1C0E5" type="main">
					<s id="N1C0E7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 90.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C0F3" type="main">
					<s id="N1C0F5"><emph type="italics"></emph>Hinc ferè recedit mobile in idem punctum nauis, è quo ſurſum proiectum <lb></lb>eſt<emph.end type="italics"></emph.end>; </s>
					<s id="N1C100">dixi ferè, quia non eſt omninò Parabola; immò ſupponitur motus <lb></lb>horizontalis tùm nauis tùm mobilis omninò æquabilis, à quo tamen <lb></lb>tantillùm deficit, ſed in tam breui tempore non eſt ſenſibile. </s>
				</p>
				<p id="N1C108" type="main">
					<s id="N1C10A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 91.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C116" type="main">
					<s id="N1C118"><emph type="italics"></emph>Hinc quantùm initio detrahit horizontali verticalis intenſior, &amp; ſub finem <lb></lb>remittit, tantùm initio remittit horizontali naturalis tardior, &amp; ſub finem ve­<lb></lb>locior detrahit<emph.end type="italics"></emph.end>; </s>
					<s id="N1C125">ſic in aſcenſu linea curua LD, initio parùm recedit à ver­<lb></lb>ticali LK, &amp; multùm ſub finem; in deſcenſu verò curua DS accedit <lb></lb>propiùs ad horizontalem DT, à qua multùm recedit ſub finem. </s>
				</p>
				<p id="N1C12D" type="main">
					<s id="N1C12F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C13B" type="main">
					<s id="N1C13D"><emph type="italics"></emph>Hinc eadem, quâ mobilis proijcitur ſurſum è naui mobili, recipitur manu<emph.end type="italics"></emph.end>; <lb></lb>probata centies experientia; idem dico de ſagitta, arcu emiſſa, glande <lb></lb>tormento exploſa, &amp;c. </s>
					<s id="N1C14A">ſic dum demittis manu in eadem naui aliquod <lb></lb>graue deorſum, eadem ſemper à te diſtantia cadit; ſic in rhodis currenti­<lb></lb>bus poma odorifera, ſurſum modica vi projecta eadem ſemper excipiun­<lb></lb>tur manu, perinde atque ſi currus ipſe ſtaret. </s>
					<s id="N1C154">Ita prorſus ſe res habet <lb></lb>dum inſidens equo etiam perniciſſimè currenti ludis huiuſmodi moti­<lb></lb>bus; </s>
					<s id="N1C15C">quorum nullum prorſus diſcrimen obſeruabis in naui, ſiue ſtet ſiue <lb></lb>moueatur ſolito curſu; </s>
					<s id="N1C162">ſi enim eadem velocitate, qua vel emiſſa ſagitta, <lb></lb>vel glans exploſa moueretur; haud dubiè maximum diſcrimen inter­<lb></lb>cederet. </s>
				</p>
				<p id="N1C16A" type="main">
					<s id="N1C16C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 93.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C178" type="main">
					<s id="N1C17A"><emph type="italics"></emph>Hinc ſi pilam projectam è naui mobili continuo intuitu proſequaris ſurſum <lb></lb>rectà ferri iudicabis<emph.end type="italics"></emph.end>; </s>
					<s id="N1C185">quippe cum perpetuò mutes perpendicularem pro­<lb></lb>pter motum nauis, in eadem ſemper eſſe putas, in qua pila ſemper <lb></lb>occurrat; </s>
					<s id="N1C18D">licèt reuerâ qui ſunt in naui immobili rem aliter eſſe <pb pagenum="185" xlink:href="026/01/217.jpg"></pb>iudicent; </s>
					<s id="N1C196">quippe vident pilam ſuo motu deſcribere curuam non ſimi­<lb></lb>lem illi, quam diſcus per lineam inclinatam ſurſum proiectus ſuo mo­<lb></lb>tu deſcriberet; neque mirum eſt, cum ſint eædem vtriuſque rationes, cum <lb></lb>hac tantum differentia, quòd inclinata diſci ſit motus ſimplicis, inclina­<lb></lb>ta verò pilæ aſcendentis ſit motus mixti ex horizontali &amp; verticali, æ­<lb></lb>quabili quidem in aſcenſus accelerato in deſcenſu. </s>
				</p>
				<p id="N1C1A4" type="main">
					<s id="N1C1A6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 94.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C1B2" type="main">
					<s id="N1C1B4"><emph type="italics"></emph>Ex his vides non valere vulgarem rationem, quæ vulgò affertur contra mo­<lb></lb>tum terræ, ſequi ſcilicet ex eo lapidem proiectum ſurſum per verticalem longo <lb></lb>interuallo verſus occaſum retrò deſcenſurum,<emph.end type="italics"></emph.end> quod tamen etiam ex motu <lb></lb>terræ ſuppoſito non ſequeretur, cum non ſequatur ex motu nauis. </s>
				</p>
				<p id="N1C1C2" type="main">
					<s id="N1C1C4">Igitur alia ratione impugnari debet hypotheſis illa, quæ terræ motum <lb></lb>deſtruit; </s>
					<s id="N1C1CA">quod certè ſi à me fieri poſſit, in tractatu de corporibus cœleſti­<lb></lb>bus, vel de nouo ſyſtemate aliquando præſtabimus; </s>
					<s id="N1C1D0">non tamen eſt quod <lb></lb>hîc diſſimulem aliquorum agendi methodum, qui ex hoc phœnome­<lb></lb>no conſtanter aſſerunt terram moueri; </s>
					<s id="N1C1D8">nam primò, ſequeretur tantùm <lb></lb>moueri circa centrum id eſt motu orbis, non verò motu centri; quæ eſt <lb></lb>hypotheſis Origani. </s>
					<s id="N1C1E0">Secundò ex quiete terræ hoc idem phœnomenon <lb></lb>ſequitur; </s>
					<s id="N1C1E6">quippe, ſi terra quieſcit, eadem manu cadentem excipio lapi­<lb></lb>dem, quæ ſurſum rectà proiicit; </s>
					<s id="N1C1EC">igitur quemadmodum ex hoc non infero <lb></lb>terræ quietem, ſed aliunde; </s>
					<s id="N1C1F2">ita neque ex hoc inferri poteſt terræ motus; </s>
					<s id="N1C1F6"><lb></lb>cum enim duplex hypotheſis eodem phœnomeno ſtare poteſt, neutra ex <lb></lb>eo euincitur; igitur ſicuti fateor ex hoc phœnomeno minimè demon­<lb></lb>ſtrari terræ quietem ita &amp; tu fateri debes ex eo minimè adſtrui poſſe <lb></lb>terræ motum. </s>
				</p>
				<p id="N1C201" type="main">
					<s id="N1C203">Adde quod, haud dubiè ſi terra quieſcit citiùs proiectus lapis ſurſum <lb></lb>deſcendit, quàm ſi mouetur; </s>
					<s id="N1C209">nec enim vt dictum eſt ſuprà proiecta velo­<lb></lb>ciſſimo motu per horizontalem deſcendunt eo tempore, quo ex eadem <lb></lb>altitudine motu purè naturali deſcenderent; </s>
					<s id="N1C211">quod multis euincitur ex­<lb></lb>perimentis, vt vidimus in Th.46. atqui punctum terræ ſub æquatore ve­<lb></lb>lociſſimè moueretur, quod vno temporis ſecundo conficeret 1250.pedes <lb></lb>geometricos ſi 5. pedes geometrici tribuantur paſſui, 4000. paſſus leucæ <lb></lb>germanicæ, 15. leucæ germanicæ gradui Æquatoris, toti demum Æqua­<lb></lb>tori 360. gradus; </s>
					<s id="N1C21F">cum autem iactus medius tormenti validiſſimi ſit <lb></lb>15000. pedum, duretque 30″ temporis; </s>
					<s id="N1C225">certè 30″ temporis conſicit pun­<lb></lb>ctum æquatoris 37500. pedes; </s>
					<s id="N1C22B">igitur mouetur velociùs exploſa glande; </s>
					<s id="N1C22F"><lb></lb>igitur ſi hæc velocitas glandis impedit, ne tàm citò deorſum cadat, ma­<lb></lb>jor velocitas motus terræ potiori iure illud ipſum impediet; igitur ſi <lb></lb>terra quieſcit, globus ſurſum proiectus velociùs recidet in terram, etſi <lb></lb>terra moueatur tardiùs. </s>
				</p>
				<p id="N1C23A" type="main">
					<s id="N1C23C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C248" type="main">
					<s id="N1C24A">Obſeruabis duos tantùm motus in naui mobili fuiſſe hactenus explica­<lb></lb>tos; </s>
					<s id="N1C250">primus eſt, quo demittitur plumbea pila è ſummo mali; </s>
					<s id="N1C254">ſecundus eſt, <lb></lb>quo ex <expan abbr="sũmo">summo</expan> malo, vel ex alio nauis mobilis puncto proiicitur <expan abbr="ſursũ">ſursum</expan> cor-<pb pagenum="186" xlink:href="026/01/218.jpg"></pb>pus graue per lineam verticalem; </s>
					<s id="N1C267">ſunt autem plures alij motus, tot ſcili­<lb></lb>cet, quot poſſunt duci lineæ è ſummo malo in orbem quoquo verſum; <lb></lb>quarum hæ ſunt præcipuæ. </s>
					<s id="N1C26F">ſit apex mali B; </s>
					<s id="N1C273">circa quem deſcribatur cir­<lb></lb>culus ACDE, ſitque primò circulus ille verticalis parallelus ſcilicet li­<lb></lb>neæ directionis nauis BA, quæ ſit v. g. verſus Boream; </s>
					<s id="N1C27F">primò habes li­<lb></lb>neam verticalem ſurſum BE; </s>
					<s id="N1C285">ſecundò perpendicularem deorſum BC; </s>
					<s id="N1C289"><lb></lb>tertiò lineam directionis verſus Boream BA; </s>
					<s id="N1C28E">quartò illi oppoſitum <lb></lb>verſus Auſtrum BD; tùm voluatur circulus circa axem immobilem AD <lb></lb>per quadrantem integrum, dum ſcilicet BE ſit ad Ortum, quæ eſt quinta <lb></lb>linea, &amp; BC ipſi oppoſita ad Occaſum, quæ eſt ſexta. </s>
					<s id="N1C298">Igitur habes 6. li­<lb></lb>neas; </s>
					<s id="N1C29D">ſcilicet ſurſum, deorſum, verſus Boream &amp; Auſtrum, verſus Ortum, <lb></lb>&amp; Occaſum; linea quæ tendit deorſum poteſt dupliciter conſiderari, vel <lb></lb>enim demittitur ſua ſponte, vel proiicitur. </s>
				</p>
				<p id="N1C2A5" type="main">
					<s id="N1C2A7">Iam verò inter <expan abbr="Boreã">Boream</expan>, &amp; Occaſum habes lineas triplicis generis, primò <lb></lb>horizonti parallelas, quæ vt conſiderentur; </s>
					<s id="N1C2B1">cenſeatur prædictus circulus <lb></lb>parallelus horizonti, ita vt ex centro B ducantur ad <expan abbr="circumferentiã">circumferentiam</expan> tot <lb></lb>lineæ, quot ſunt puncta in circumferentia; </s>
					<s id="N1C2BD">ſecundò inclinatas ſurſum &amp; <lb></lb>inclinatas deorſum; </s>
					<s id="N1C2C3">ſimiliter inter Occaſum &amp; Auſtrum, inter Auſtrum <lb></lb>&amp; Ortum, inter Ortum &amp; Boream; porrò exprimes omnes lineas, ſi api­<lb></lb>cem mali fingas centrum globi, ſeu ſi in circulo prædicto verticali à <lb></lb>centro B ad circumferentiam ducantur tot lineæ quot poſſunt duci, <lb></lb>tuncque circa axem EC immobilem voluatur circulus, &amp;c. </s>
					<s id="N1C2CF">his poſi­<lb></lb>tis ſit. </s>
				</p>
				<p id="N1C2D4" type="main">
					<s id="N1C2D6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 95.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C2E2" type="main">
					<s id="N1C2E4"><emph type="italics"></emph>Si proijciatur globus deorſum à ſummo malo, deſcendet ferè ad imum ma­<lb></lb>lum<emph.end type="italics"></emph.end>; </s>
					<s id="N1C2EF">probatur, quia deſcendet quidem velociùs quàm ſi motu naturali <lb></lb>deſcenderet vt conſtat per Th. 69. ſed profectò nihil acquiret in hori­<lb></lb>zontali globus, quod non acquirat nauis; </s>
					<s id="N1C2F7">igitur imùm ferè malum attin­<lb></lb>git ſed opus eſt aliqua figurâ; </s>
					<s id="N1C2FD">ſit enim apex mali A, deſcendatque pri­<lb></lb>mò ex A ſua ſponte in H; </s>
					<s id="N1C303">haud dubiè ſi eo tempore, quo motu na­<lb></lb>turali conficit AD, mixto deorſum conficit AF, eo tempore cadet in G <lb></lb>ex A ſi hic impetus deorſum adueniat; </s>
					<s id="N1C30B">ſed res eſt clara; </s>
					<s id="N1C30F">hæc porrò figura <lb></lb>non eſt Parabola, licèt ſit curua; </s>
					<s id="N1C315">conſtat autem hîc motus ex naturali <lb></lb>accelerato, ex impreſſo deorſum æquabili per ſe, &amp; horizontali ſenſi­<lb></lb>biliter æquabili; poteſt autem deſignari hæc linea motus ex ſuprà <lb></lb>dictis. </s>
				</p>
				<p id="N1C31F" type="main">
					<s id="N1C321"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 96.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C32D" type="main">
					<s id="N1C32F"><emph type="italics"></emph>Si in circulo verticali prædicto proijciatur per lineam horizontalem ver­<lb></lb>ſus Boream, mouebitur globus motu mixto ex duplici horizontali per <expan abbr="eãdem">eandem</expan> <lb></lb>lineam ferè æquabili; </s>
					<s id="N1C33D">id eſt ſenſibiliter, licèt geometricè loquendo retardetur, <lb></lb>&amp; naturali accelerato<emph.end type="italics"></emph.end>; </s>
					<s id="N1C346">ſit perpendicularis deorſum AH, <expan abbr="horizōtalis">horizontalis</expan> AC, <lb></lb>quam conficiat eo tempore, quo conficit AH motu naturali, motu mixto <lb></lb>perueniet in K; </s>
					<s id="N1C352">ſi verò duplicetur horizontalis, ita vt eo tempore quo <lb></lb>conficit AH, conficiat AD, motu mixto perueniet in L; </s>
					<s id="N1C358">hæc autem curua <pb pagenum="187" xlink:href="026/01/219.jpg"></pb>HL accedit ad Parabolam licèt non ſit vera Parabola; quia quando ia­<lb></lb>ctus horizontalis eſt velociſſimus, qualis in arce, vel in tormentis belli­<lb></lb>cis, eodem tempore mobile non decidit in terram, quo deſcenderet mo­<lb></lb>tu purè naturali ex eadem altitudine. </s>
				</p>
				<p id="N1C367" type="main">
					<s id="N1C369"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 97.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C375" type="main">
					<s id="N1C377"><emph type="italics"></emph>Hinc, ſi motus nauis eſſet æqualis motui ſagittæ, motus ex vtroque mixtus <lb></lb>duplam amplitudinem in plano hòrizontali acquireret, v.g. ſi<emph.end type="italics"></emph.end> tantùm ſagitta <lb></lb>emiſſa arcu extra nauim ex A perueniret in K, in naui mobili perueniret <lb></lb>in L; </s>
					<s id="N1C388">ſi verò nauis, vt reuerâ fit, tardiùs moueatur, ſagitta è naui emiſſa <lb></lb>verſus Boream ſcilicet acquiret pro rata, id eſt ſi nauis motus ſit tantùm <lb></lb>ſubduplus perueniret in M; ſi ſubquadruplus in N &amp;c. </s>
				</p>
				<p id="N1C390" type="main">
					<s id="N1C392"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 98.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C39E" type="main">
					<s id="N1C3A0"><emph type="italics"></emph>Hinc tormentum bellicum quod eſt in prora directum ad <expan abbr="eãdem">eandem</expan> lineam, <lb></lb>quam ſuo motu conficit nauis maiorem iactum habebit, non tamen ſenſibiliter<emph.end type="italics"></emph.end>; </s>
					<s id="N1C3AF"><lb></lb>quia motus nauis parum addit; </s>
					<s id="N1C3B4">obſeruabis tamen non videri maiorem <lb></lb>quàm ſi nauis quieſceret, quia eo tempore, quo ſagitta ex A peruenit in <lb></lb>L, nauis ex H peruenit in K; </s>
					<s id="N1C3BC">igitur videtur ſemper eſſe idem iactus, ſiue <lb></lb>moueatur nauis ſiue non, quia eſt ſemper eadem diſtantia nauis, &amp; ter­<lb></lb>mini iactus; cum nauis id totum acquirat ſpatij, quod motui ſagittæ <lb></lb>accedit. </s>
				</p>
				<p id="N1C3C6" type="main">
					<s id="N1C3C8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 99.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C3D4" type="main">
					<s id="N1C3D6"><emph type="italics"></emph>Hinc vt quis maiore niſu lapidem v. g. proijciat, tùm longiore tempore <lb></lb>brachium rotat, tùm præuio curſu impetum auget,<emph.end type="italics"></emph.end> quia non tantùm impe­<lb></lb>tus brachij imprimitur mobili, ſed etiam impetus totius corporis; </s>
					<s id="N1C3E7">hinc <lb></lb>etiam ſi præmittatur curſus longiore ſaltu in plano horizontali maius <lb></lb>ſpatium traiicitur; quæ omnia ex iiſdem principiis manifeſtè ſe­<lb></lb>quuntur. </s>
				</p>
				<p id="N1C3F3" type="main">
					<s id="N1C3F5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 100.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C401" type="main">
					<s id="N1C403"><emph type="italics"></emph>Si verò per oppoſitam lineam verſus Auſtrum proijcitur mobile, mouebitur <lb></lb>motu mixto ex duobus horizontalibus ad oppoſitas lineas, &amp; ex naturali ac­<lb></lb>celerato<emph.end type="italics"></emph.end>; </s>
					<s id="N1C410">ſit proiectio per AB, ita vt mobilè perueniat in L niſi impedia­<lb></lb>tur; </s>
					<s id="N1C416">certè ſi nauis motu ſubduplo in oppoſitam partem feratur, peruenit <lb></lb>tantùm in K, quæ omnia conſtant ex dictis; </s>
					<s id="N1C41C">nam impetus oppoſiti pu­<lb></lb>gnant pro rata, vt ſæpè diximus; </s>
					<s id="N1C422">videbitur tamen eſſe æqualis iactus; </s>
					<s id="N1C426">ſi <lb></lb>enim eo tempore, quo ſagitta peruenit in K, nauis fertur in oppoſitam <lb></lb>partem ſpatio æquali KL, haud dubiè diſtantia ſemper erit æqualis; tan­<lb></lb>tùm enim recedit verſus Boream nauis, quantùm ſagitta à puncto L ad <lb></lb>punctum K reducitur. </s>
				</p>
				<p id="N1C432" type="main">
					<s id="N1C434"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 101.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C440" type="main">
					<s id="N1C442"><emph type="italics"></emph>Si motus nauis eſſet æqualis motui ſagittæ v. g.<emph.end type="italics"></emph.end> <emph type="italics"></emph>ſi nauis ferretur per <lb></lb>lineam GC ſeu TA verſus Boream, &amp; ſagitta è ſummo malo emitteretur <lb></lb>per lineam TO verſus Auſtrum, deſcenderet per lineam T.G. nec quidquam<emph.end type="italics"></emph.end><pb pagenum="188" xlink:href="026/01/220.jpg"></pb><emph type="italics"></emph>acquireret in horizontali<emph.end type="italics"></emph.end>; </s>
					<s id="N1C460">quod probatur per Th. 133. l.1. ſic globus tor­<lb></lb>menti etiam ne latum quidem vnguem pertranſiret in horizontali, vide­<lb></lb>tur tamen ſemper eſſe idem iactus; </s>
					<s id="N1C468">nam eo tempore, quo ſagitta caderet <lb></lb>à T in G, nauis eſſet in C, atqui CG &amp; GM ſunt aſſumptæ æquales; hinc <lb></lb>potiùs arcus eſſet emiſſus quàm ſagitta, &amp; tormentum exploſum quàm <lb></lb>globus. </s>
				</p>
				<p id="N1C472" type="main">
					<s id="N1C474"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C480" type="main">
					<s id="N1C482">Obſeruabis, ſi nauis motus ſit ad motum ſagittæ v. g. in ratione ſub­<lb></lb>dupla, ſcilicet vt FG, vel LM ad GM peruenit in L per Parabolam TL; </s>
					<s id="N1C48C">ſt <lb></lb>vt EG vel KM ad GL peruenit in K per Parabolam TK; ſi vt DG vel I <lb></lb>M ad GM peruenitin I per Parabolam TI, &amp;c. </s>
					<s id="N1C494">vnde vides Parabolas <lb></lb>iſtas ſemper in infinitum contrahi, donec tandem in rectam TG deſi­<lb></lb>nant vbi motus nauis eſt æqualis motui ſagittæ: Parabolas dixi ſenſibi­<lb></lb>liter, ſcilicet eo modo, quo ſuprà. </s>
				</p>
				<p id="N1C49E" type="main">
					<s id="N1C4A0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 102.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C4AC" type="main">
					<s id="N1C4AE"><emph type="italics"></emph>Si verò motus nauis eſſet maior motu ſagittæ, ſagitta fèrretur in <expan abbr="eãdem">eandem</expan> <lb></lb>partem in quam fertur nauis per ſpatium æquale differentia illorum motuum,<emph.end type="italics"></emph.end><lb></lb>v.g. </s>
					<s id="N1C4BD">ſi nauis moueatur per GM &amp; ſagitta per TA, ſitque motus nauis ad <lb></lb>motum ſagittæ, vt GM, ad IM; eo tempore quo nauis attinget M, ſagitta <lb></lb>cadet in I, &amp; ſi motus ſit vt GM ad KM cadet in K vel vt GM ad GL <lb></lb>cadet in L. per Parabolas, quæ omnia conſtant ex dictis, &amp; ex Theore­<lb></lb>mate per 134. l.1. </s>
				</p>
				<p id="N1C4C9" type="main">
					<s id="N1C4CB"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C4D8" type="main">
					<s id="N1C4DA"><emph type="italics"></emph>Ex illa hypotheſi ſequitur egregium paradoxon ſcilicet ſagittam retorqueri <lb></lb>in ſagittarium<emph.end type="italics"></emph.end>; </s>
					<s id="N1C4E5">ſit enim motus nauis ad motum ſagittæ vt GM ad LM; </s>
					<s id="N1C4E9"><lb></lb>haud dubiè per Th. ſuperius eo tempore, quo nauis peruenit ad M ſa­<lb></lb>gitta attinget punctum L, &amp; eo tempore quo nauis eſſet in L ſagitta eſ­<lb></lb>ſet in puncto Y, ſi cum nauis peruenit in L illicò ſiſtat ſagitta, cadet in <lb></lb>ipſam nauim; </s>
					<s id="N1C4F4">nam cadet in L quod clarum eſt: </s>
					<s id="N1C4F8">dixi ſi nauis ſiſtat poſt <lb></lb>emiſſam ſagittam, ſi enim nauis ſemper moueatur, æquabilis ſemper eſſe <lb></lb>videbitur ſagittæ iactus, ſi enim è naui immobili emiſſa fuiſſet prædicta <lb></lb>ſagitta per horizontalem TO, acquiſiuiſſet ſpatium vel amplitudinem G <lb></lb>L; </s>
					<s id="N1C504">ſed videtur confeciſſe ML, cum nauis mouetur; atqui ML eſt æqualis <lb></lb>LG, quid clarius? </s>
				</p>
				<p id="N1C50A" type="main">
					<s id="N1C50C">Hinc ſi quis in naui currat per lineam directionis id eſt verſus eain <lb></lb>partem, in quam mouetur nauis, curret velociùs; </s>
					<s id="N1C512">immò ſi ambulet, ingen­<lb></lb>tes faciet paſſus ſeu ſaltus v.g.ſi nauis conficit ſpatium GM eo tempore <lb></lb>quo aliquis ſaltat ex G in H; </s>
					<s id="N1C51A">haud dubiè amplitudo eius ſaltus erit com­<lb></lb>poſita ex tota GM &amp; GH; </s>
					<s id="N1C520">ſi verò in partem oppoſitam verſus C currat: </s>
					<s id="N1C524"><lb></lb>vel currit velociùs, vel tardiùs, vel æquali motu: </s>
					<s id="N1C529">ſi primum, aliquid ſpatij <lb></lb>acquiret verſus C æqualis ſcilicet <expan abbr="differẽtiæ">differentiæ</expan> motuum; </s>
					<s id="N1C533">ſi <expan abbr="ſecundũ">ſecundum</expan>, recedet <lb></lb>verſus M ſpatio æquali eidem differentiæ; ſi tertium, nec accedet, nec re­<lb></lb>cedet, ſed totis viribus currens ſeu tentans currere in eodem ſemper lo-<pb pagenum="189" xlink:href="026/01/221.jpg"></pb>co ſtabit, vel ſi ſit rotatus globus in tabulato nauis mouebitur motu or­<lb></lb>bis circa centrum immobile. </s>
				</p>
				<p id="N1C546" type="main">
					<s id="N1C548"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 103.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C554" type="main">
					<s id="N1C556"><emph type="italics"></emph>Si proiiciatur mobile per lineam inclinatam deorſum, quæ ſit hypothenuſis <lb></lb>trianguli orthogonij, cuius baſis ſit horizontalis &amp; perpendiculum ſpatium,<emph.end type="italics"></emph.end><lb></lb>quod percurritur motu naturali æquali tempore, idque in naui mobili <lb></lb>in eam <expan abbr="partẽ">partem</expan>, verſus quam mouetur nauis, erit motus mixtus ex naturali <lb></lb>accelerato &amp; inclinato mixto ex horizontali &amp; alio inclinato ſit enim <lb></lb>horizontalis AD, perpendicularis AMK, ſit AM ſpatium quod percurri­<lb></lb>tur in perpendiculari motu purè naturali, eo tempore, quo percurritur <lb></lb>AC ſubdupla AD, ſitque AM ſubdupla AC, &amp; ſecundo tempore æquali <lb></lb>percurratur in horizontali CD, &amp; in perpendiculari MK tripla AM; </s>
					<s id="N1C572"><lb></lb>erit motus mixtus per lineam parabolicam ANH; </s>
					<s id="N1C577">nam ſuppono hori­<lb></lb>zontalem æquabilem, cùm parùm ab eo abſit, vt ſupradictum eſt; præſer­<lb></lb>tim cum ſenſibiliter hæc linea ſit parabolica. </s>
				</p>
				<p id="N1C57F" type="main">
					<s id="N1C581">Iam verò in eadem naui proiiciatur mobile per inclinatam AP, quæ <lb></lb>ſit diagonalis quadrati AP, &amp; impetus perinclinatam AP ſit ad impetum <lb></lb>per horizontalem AC, vt AP ad AC; </s>
					<s id="N1C589">ducatur LPF parallela MN, &amp; CF <lb></lb>parallela AP; </s>
					<s id="N1C58F">denique diagonalis AF: </s>
					<s id="N1C593">haud dubiè ML eſt æqualis AM, vt <lb></lb>patet; </s>
					<s id="N1C599">&amp; ſi motus eſſet tantum mixtus ex AC &amp; AP fieret per diagona­<lb></lb>lem AF, quam mobile eodem tempore percurreret quo vel AC vel AP; </s>
					<s id="N1C59F"><lb></lb>igitur ſi dum percurrit AF percurrit AM, motu naturali, certè dum per­<lb></lb>currit AN ſubdupla AF, percurret tantùm ſubquadruplam AM; </s>
					<s id="N1C5A6">aſſuma­<lb></lb>tur ergo NO æqualis AS, &amp; FG æqualis AM; <expan abbr="ducaturq;">ducaturque</expan> curua AOG, hæc <lb></lb>eſt linea quęſita. </s>
				</p>
				<p id="N1C5B2" type="main">
					<s id="N1C5B4">Itaque idem dicendum eſt de his inclinatis, quod de aliis ſuprà di­<lb></lb>ctum eſt Th.72. niſi quod accipitur inclinata mixta ex horizontali &amp; da­<lb></lb>ta inclinata, v.g. ANF ex AC &amp; AP; </s>
					<s id="N1C5BE">hæc autem linea non eſt Parabolica, <lb></lb>quia quadratum MN, vel VO eſt ad quadratum RG vt 1.ad 4.at verò ſa­<lb></lb>gitta AV eſt ad ſagittam AP, vt 5.ad 12.porrò hæc linea ſecat Parabolam <lb></lb>vt patet; ſi verò accipiatur inclinatata AI, mixta inclinata erit AH igitur <lb></lb>aſſumatur HX æqualis AM, &amp; PZ æqualis AS ducetur linea huius mo­<lb></lb>tus per AZX. quænam verò ſint hç lineæ, dicemus aliàs Tomo ſequenti. </s>
				</p>
				<p id="N1C5CC" type="main">
					<s id="N1C5CE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 104.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C5DA" type="main">
					<s id="N1C5DC"><emph type="italics"></emph>Si proiiciatur per inclinatam ſurſum in eam partem, in quam mouetur nauis, <lb></lb>erit etiam mixtus ex naturali, &amp; inclinato ex horizontali, &amp; data inclinata<emph.end type="italics"></emph.end>; <lb></lb>vnde idem prorſus <expan abbr="dicẽduin">dicendum</expan> eſt de mixta inclinata, quod de ſimplici in­<lb></lb>clinata, de qua multa ſuprà dicta ſunt à Th.47. ſuppoſito tamen motu na­<lb></lb>turali accelerato, ad quem proximè accedit propter mutationem perpe­<lb></lb>tuam lineæ. </s>
					<s id="N1C5F3">ſit enim inclinata ſurſum AB, quæ percurratur motu <lb></lb>æquabili eo tempore, quo horizontalis AE, vel quo motu naturali LA; </s>
					<s id="N1C5F9"><lb></lb>diuidatur AE bifariam in D; </s>
					<s id="N1C5FE">ducatur DG, tùm DC, AC, hæc eſt linea mo­<lb></lb>tus mixti ex inclinata AG, &amp; horizontali AD; </s>
					<s id="N1C604">ſequitur deinde Parabola; </s>
					<s id="N1C608"><lb></lb>nam ſi eo tempore quo percurritur AD, percurritur AG, &amp; LM vel FA; </s>
					<s id="N1C60D"><pb pagenum="190" xlink:href="026/01/222.jpg"></pb>certè eodem percurritur AC, igitur ſubduplo tempore <expan abbr="percurrẽtur">percurrentur</expan> AN; </s>
					<s id="N1C619"><lb></lb>igitur FO, quæ eſt ſubquadrupla FA; </s>
					<s id="N1C61E">igitur aſſumatur NH æqualis FO, &amp; <lb></lb>CK æqualis FA, &amp; ducatur curua per puncta AHK; hæc eſt ſemiparabo­<lb></lb>la, nam KI eſt ad KE vt quadratum IH ad quadratum EA. </s>
				</p>
				<p id="N1C626" type="main">
					<s id="N1C628">Vnde vides omnes inclinatas ſurſum vſque ab horizontali DB ad <lb></lb>verticalem DA incluſiuè eſſe Parabolas; omnes verò inclinatas ab ea­<lb></lb>dem horizontali DB ad perpendicularem DC incluſiuè non eſſe Para­<lb></lb>bolas, ſed propiùs accedere ad rectam, vnde aliquis ſuſpicari poſſet eſſe <lb></lb>Hyperbolas. </s>
				</p>
				<p id="N1C634" type="main">
					<s id="N1C636"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 105.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C642" type="main">
					<s id="N1C644"><emph type="italics"></emph>Si proijciatur mobile per inclinatam ſurſum vel deorſum in partem oppoſi­<lb></lb>tam directionis nauis,<emph.end type="italics"></emph.end> <emph type="italics"></emph>ſcilicet per diagonales deſcendit &amp; aſcendit per li­<lb></lb>neam rectam, ſurſum vel deorſum, v.g.<emph.end type="italics"></emph.end> ſit horizontalis KL, inclinata <lb></lb>deorſum KB, mixta erit KL; </s>
					<s id="N1C659">ſit etiam inclinata KL, &amp; horizontalis <lb></lb>CH; </s>
					<s id="N1C65F">mixta erit KH, cui addatur in eadem KF portio ſpatij, quod motu <lb></lb>naturali percurritur; idem dico de aliis inclinatis. </s>
				</p>
				<p id="N1C665" type="main">
					<s id="N1C667">Præterea ſit horizontalis VX, inclinata <expan abbr="ſursũ">ſursum</expan> VN; </s>
					<s id="N1C66F">mixta erit VY; </s>
					<s id="N1C673">ſic <lb></lb>ex VOVX fiet VS detracta ſcilicet portioni ſpatij, quod detrahitur à <lb></lb>motu naturali; ſi verò ſit vel major motus horizontalis, vel minor eo, <lb></lb>quem aſſumpſimus, non percurrit mobile lineam rectam ſed vel Para­<lb></lb>bolam ſi ſurſum proiiciatur, vel ſi deorſum aliam nouam, quam ad Hy­<lb></lb>perbolam accedere ſuprà diximus. </s>
				</p>
				<p id="N1C681" type="main">
					<s id="N1C683">Hinc certè, quod mirabile dictu eſt, ſi è puncto nauis V ſurſum per <lb></lb>inclinatam VO proiiciatur, ſtatimque poſt proiectionem ſiſtat nauis, in <lb></lb>ipſam nauim deſcendet mobile; </s>
					<s id="N1C68B">atque ita ex his habeo omnes motus cir­<lb></lb>culi verticalis paralleli lineæ directionis; </s>
					<s id="N1C691">quare ſupereſt vt explicemus <lb></lb>alios motus; ac primò quidem per circulum horizontalem, cuius habeo <lb></lb>quoque duas lineas, ſcilicet communes ſectiones horizontalis &amp; prio­<lb></lb>ris verticalis, id eſt lineam directionis verſus Boream, &amp; oppoſitam ver­<lb></lb>ſus Auſtrum. </s>
				</p>
				<p id="N1C69E" type="main">
					<s id="N1C6A0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 106.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C6AC" type="main">
					<s id="N1C6AE"><emph type="italics"></emph>Si proijciatur mobile per horizontalem verſus Ortum è naui mobili, <lb></lb>monebitur motu mixto ex duplici horizontali, &amp; naturali deorſum<emph.end type="italics"></emph.end>, ſit <lb></lb>enim horizontalis verſus Boream AC, &amp; alia horizontalis AH verſus <lb></lb>ortum in eodem plano horizontali; </s>
					<s id="N1C6BD">certè ex vtraque fit mixta AK, quæ <lb></lb>ſi percurratur æquali tempore cum AC, &amp; eius ſubdupla cum AB, AC <lb></lb>verò æquali tempore cum AF; </s>
					<s id="N1C6C5">quamquàm ſuppono iam eſſe perpendi­<lb></lb>cularem deorſum AB; </s>
					<s id="N1C6CB">denique cum AG ſubquadrupla AF aſſumatur <lb></lb>ED æqualis AG perpendiculariter ducta in AD, &amp; KL æqualis AF <lb></lb>parallela ED, &amp; per puncta AEL ducatur curua, hæc eſt linea motus <lb></lb>quæſita; </s>
					<s id="N1C6D5">voluatur autem triangulum AKL, donec ſit parallelum circulo <lb></lb>verticali vel alteri, ACO erit in proprio ſitu; </s>
					<s id="N1C6DB">vnde eo tempore, quo eſ­<lb></lb>ſet in DE punctum nauis A eſſet in B, &amp; eo, quo eſſet in KL, punctum A <lb></lb>eſſet in C; hoc eſt ſingula puncta AK, è regione AC ductis parallelis <pb pagenum="191" xlink:href="026/01/223.jpg"></pb>BD, CK, ac proinde nauis &amp; mobile ſemper eſſent è regione in linea <lb></lb>verſus ortum. </s>
				</p>
				<p id="N1C6EA" type="main">
					<s id="N1C6EC">Hinc ſi ex A dirigas <expan abbr="ſagittã">ſagittam</expan> in H feris punctum K, quam artem probè <lb></lb>noſſe debent rei tormentariæ præfecti; </s>
					<s id="N1C6F6">quippe ſagitta aberrabit à ſcopo <lb></lb>verſus Boream declinans toto eo ſpatio, quod conficit nauis eodem tem­<lb></lb>pore, quo mouetur ſagitta; ita prorſus ſi moueatur H verſus K, vt attin­<lb></lb>gas ex puncto immobili A debes dirigere ictum in K, ſi quo tempore <lb></lb>ſagitta conficit AK ſcopus H percurrit HK.Idem prorſus dicendum eſt <lb></lb>de iaculatione per lineam oppoſitam verſus occaſum. </s>
				</p>
				<p id="N1C704" type="main">
					<s id="N1C706">Si verò proiiciatur mobile per lineam inter Boream, &amp; Ortum, linea <lb></lb>motus erit Parabola cuius Tangens erit mixta ex horizontali verſus <lb></lb>Boream, &amp; declinante verſus Ortum, v. g. ſit horizontalis verſus Boream <lb></lb>AF, quam hactenus aſſumpſi pro linea directionis; </s>
					<s id="N1C714">ſit linea verſus <lb></lb>Ortum AC; </s>
					<s id="N1C71A">ſit declinans verſus Boream AL; </s>
					<s id="N1C71E">ſitque impetus AL, ad <lb></lb>AE vt AL ad AE, quod hactenus ſuppoſui; </s>
					<s id="N1C724">ſit LG æqualis AE, AG <lb></lb>eſt mixta ex AE, AL; </s>
					<s id="N1C72A">aſſumatur KI, &amp; GH vt iam diximus; fiatque <lb></lb>Parabola AIH, quæ circa axem AE ita voluatur, vt ſit perpendicularis <lb></lb>plano horizontali LF. </s>
				</p>
				<p id="N1C732" type="main">
					<s id="N1C734">Idem dico de omni alia declinante vel à Borea ad Ortum, vel ad Oc­<lb></lb>caſum. </s>
				</p>
				<p id="N1C739" type="main">
					<s id="N1C73B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 107.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C747" type="main">
					<s id="N1C749"><emph type="italics"></emph>Si mobile proiiciatur per declinantem ab Austro ad Ortum, cuius impetus <lb></lb>ſit vt linea; </s>
					<s id="N1C751">conficit lineam parabolicam, cuius tangens vel amplitudo eſt re­<lb></lb>sta ad Ortum<emph.end type="italics"></emph.end>; </s>
					<s id="N1C75A">ſit enim NF ad Boream, NA ad Auſtrum, NI ad Or­<lb></lb>tum, ND ad Occaſum; </s>
					<s id="N1C760">ſit NL declinans ab auſtro ad Ortum, ſitque im­<lb></lb>petus per NL ad impetum per NF, vt NL ad NF; </s>
					<s id="N1C766">mixta ex NF NL <lb></lb>eſt HK; </s>
					<s id="N1C76C">ſit autem KH æqualis ſpatio, quod conficitur motu naturali eo <lb></lb>tempore, quo percurritur NF, ſit KI æqualis NK, &amp; IG quadrupla KH; <lb></lb>Parabola NHG eſt linea motus quæſita dum voluatur NIG circa axem <lb></lb>NI, dum IG pendeat perpendicularitur ex plano horizontali ON. </s>
				</p>
				<p id="N1C776" type="main">
					<s id="N1C778">Idem fiet, ſi proiiciatur per declinantem NB ab Auſtro ſcilicet ad <lb></lb>Occaſum. </s>
				</p>
				<p id="N1C77E" type="main">
					<s id="N1C780"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 108.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C78C" type="main">
					<s id="N1C78E"><emph type="italics"></emph>Si mobile proiiciatur per inclinantem ſurſum in circulo verticali, cuius ſe­<lb></lb>ctio cum horizontali tendit ad Ortum, conficit lineam parabolicam, cuius am­<lb></lb>plitudo eſt mixta ex horizontali verſus Boream, &amp; horizontali verſus Ortum,<emph.end type="italics"></emph.end><lb></lb> ſit linea verſus Boream AB, verſus Ortum AK, mixta ex vtraque AF, <lb></lb>linea inclinata ſurſum AP, Parabola AMN, quæ vertatur circa A do­<lb></lb>nec incubet AFG, denique AFG circa FA voluatur, donec incubet <lb></lb>perpendiculariter plano; porrò perinde eſt, ſiue proiiciatur per inclina­<lb></lb>tam ſurſum verſus Ortum, ſiue verſus Occaſum. </s>
				</p>
				<p id="N1C7A5" type="main">
					<s id="N1C7A7">Si verò proiiciatur per inclinatam deorſum verſus Ortum, deſcribit <lb></lb>lineam, quæ non eſt Parabola, ſed propiùs accedit ad Hyperbolam, cuius <pb pagenum="192" xlink:href="026/01/224.jpg"></pb>tangens eſt mixta ex inclinata deorſum ex horizontali verſus Boream, <lb></lb> ſit enim AC verſus Boream, AB verſus Ortum, AD inclinata deor­<lb></lb>ſum ſub horizontali AB, AG quæ eſt in eodem plano cum AD DG, <lb></lb>mixta ex AD, &amp; AC; </s>
					<s id="N1C7B8">aſſumatur EF æqualis ſpatio, quod conficitur <lb></lb>motu naturali eo tempore, quo conficitur AE, &amp; GH æqualis ſpatio, <lb></lb>quod conficitur motu naturali eo tempore, quo percurritur AG; </s>
					<s id="N1C7C0">duca­<lb></lb>tur curua AFH, cuius ſitus vt habeatur ſit AB verſus Ortum, ex qua <lb></lb>pendeat perpendiculariter deorſum triangulum ABH, tùm circa axem <lb></lb>AD voluatur triangulum ADH, donec HD ſit parallela horizonti; </s>
					<s id="N1C7CA">tùm <lb></lb>circa axem AG voluatur triangulum AGH, dum GH ſit perpendicu­<lb></lb>laris deorſum, tunc enim linea motus AFH habebit proprium ſitum; <lb></lb>idem fiet ſi proiiciatur per inclinatam deorſum verſus Occaſum. </s>
				</p>
				<p id="N1C7D5" type="main">
					<s id="N1C7D7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 109.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C7E3" type="main">
					<s id="N1C7E5"><emph type="italics"></emph>Si proijciatur per inclinatam ſurſum, &amp; declinantem ad Ortum, linea mo­<lb></lb>tus erit Parabola, cuius amplitudo erit mixta ex declinante horizontali, &amp; <lb></lb>horizontali verſus Boream,<emph.end type="italics"></emph.end> ſit enim horizontalis verſus Boream AK, <lb></lb>horizontalis verſus Ortum AR, declinans à Borea in Ortum AD, mixta <lb></lb>ex AD, AK ſit AI, ſitque Rhomboides AE parallelus horizonti; </s>
					<s id="N1C7F6">ſit <lb></lb>EG perpendicularis ſurſum, ſit HD parallela GE; differentia ſpatij, <lb></lb>quod acquiritur motu naturali eo tempore, quo percurritur AI, &amp; FC, <lb></lb>quæ ſit ſubdupla EG. </s>
					<s id="N1C800">Dico lineam motus AHF eſſe parabolicam, quæ <lb></lb>omnia conſtant ex dictis; </s>
					<s id="N1C806">idemque dictum eſto de omni alia inclinata <lb></lb>ſurſum ſimul, &amp; declinante, ſeu verſus Ortum ſeu verſus Occaſum; </s>
					<s id="N1C80C">porrò <lb></lb>triangulum AEG incubat <expan abbr="perpẽdiculariter">perpendiculariter</expan> plano horizontali ADEK; </s>
					<s id="N1C816"><lb></lb>ſi verò proiiciatur per inclinatam deorſum voluatur AKE, dum KO <lb></lb>ſit perpendicularis deorſum; </s>
					<s id="N1C81D">ſit planum RK horizontale, voluatur <lb></lb>AKE circa A, ita vt KO ſit ſemper perpendicularis deorſum, donec <lb></lb>AE ſecet planum RK in AD ſint IO. &amp; EA vt EF, GH in ſuperio­<lb></lb>re figura, &amp; per puncta AOM ducatur curua; hæc eſt linea motus <lb></lb>quæſita. </s>
				</p>
				<p id="N1C829" type="main">
					<s id="N1C82B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 110.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C837" type="main">
					<s id="N1C839"><emph type="italics"></emph>Si proiiciatur per declinantem ab Austro ad Ortum &amp; inclinatam ſurſum, <lb></lb>deſcribet Parabolam, cuius amplitudo erit mixta ex horizontali verſus Bo­<lb></lb>ream &amp; declinante horizontali ab Auſtro ad Ortum<emph.end type="italics"></emph.end> ſit AF horizontalis <lb></lb>verſus Boream, AG verſus Ortum, AI declinans ab Auſtro ad Ortum, <lb></lb>AG mixta ex AF AI AL inclinata, ANK Parabola; </s>
					<s id="N1C84A">ſit enim planum <lb></lb>FI horizontale cui triangulum ALI incubet perpendiculariter in ſe­<lb></lb>ctione AG, reliqua ſunt facilia; </s>
					<s id="N1C852">idem dico de inclinata ſurſum ſimul, &amp; <lb></lb>declinante ab Auſtro ad Occaſum; </s>
					<s id="N1C858">ſi verò ſit inclinata deorſum, ſit pla­<lb></lb>num ACB horizontale, AB ſit declinans, AC ſit mixta ex AB &amp; ho­<lb></lb>rizontali verſus Boream AF; ſit AD inclinata deorſum, fiatque cur­<lb></lb>ua AQE more ſolito, ita vt triangulum ACE perpendiculariter <lb></lb>deorſum pendeat ex plano horizontali ACB, reliqua ſunt facilia. </s>
				</p>
				<pb pagenum="193" xlink:href="026/01/225.jpg"></pb>
				<p id="N1C868" type="main">
					<s id="N1C86A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C876" type="main">
					<s id="N1C878">Obſeruabis aſſumptam eſſe à me hactenus Parabolam, licèt accurate <lb></lb>non ſint parabolicæ lineæ, quia proximè ad Parabolas accedunt; <lb></lb>certè Phyſicè loquendo &amp; ſenſibiliter pro Parabolis aſſumi poſſe ni­<lb></lb>hil vetat. </s>
				</p>
				<p id="N1C882" type="main">
					<s id="N1C884"><emph type="center"></emph><emph type="italics"></emph>Corollaria.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C88F" type="main">
					<s id="N1C891">Ex his colligis mirabilium motuum rationem. </s>
					<s id="N1C894">Primò mobile proje­<lb></lb>ctum per lineam declinantem ab Ortu ferri poſſe rectà ad Ortum. </s>
				</p>
				<p id="N1C899" type="main">
					<s id="N1C89B">Secundò projectum per inclinatam deorſum, ferri poſſe per ipſam <lb></lb>perpendicularem deorſum. </s>
				</p>
				<p id="N1C8A0" type="main">
					<s id="N1C8A2">Tertiò projectum per inclinatam ſurſum, ferri poſſe per verti­<lb></lb>calem. </s>
				</p>
				<p id="N1C8A7" type="main">
					<s id="N1C8A9">Quartò, rationem à priori habes, cur ſi ex equo vel ſpuas, vel ali­<lb></lb>quid demittas deorſum, rectà perpendiculariter non cadat, ſed ſemper <lb></lb>è regione, quod maximè videre eſt cum purgatur nauis mobilis, eiecta <lb></lb>ſcilicet aquâ, quæ ſemper nauim inſequi videtur, imò &amp; cum quis pe­<lb></lb>dem effert in naui hunc motum quoque obſeruat. </s>
				</p>
				<p id="N1C8B4" type="main">
					<s id="N1C8B6">Quintò non erit etiam iniucundum inde elicere quomodo in maiore <lb></lb>naui, diſco ludere vel pila quis poſſit, licèt nauis motus nullo modo lu­<lb></lb>dum impediat; quæ omnia ex iis, quæ diximus neceſſariò conſequuntur, <lb></lb>&amp; quæ manifeſtum probat experimentum. </s>
				</p>
				<p id="N1C8C0" type="main">
					<s id="N1C8C2">Sextò, inde etiam eruuntur rationes motuum mixtorum ex pluribus <lb></lb>motibus v.g.4.5.6.7.&amp;c.in infinitum ſiue in eodem plano, ſiue in diuer­<lb></lb>ſis; </s>
					<s id="N1C8CA">In diuerſis vt hactenus explicuimus; </s>
					<s id="N1C8CE">in eodem vero ſiv.g.per BC, <lb></lb>BE, BA ſimul imprimantur impetus eidem mobili qui ſint vt ipſæ li­<lb></lb>neæ; </s>
					<s id="N1C8D6">primò fiat ex BA BC mixta BD, &amp; ex BD BE, mixta BF, vel ex <lb></lb>BE BC mixta BG, &amp; ex BG BA mixta BF, vel ex BE BA mixta <lb></lb>BH, &amp; ex BH BC mixta BF; </s>
					<s id="N1C8DE">vides ſemper eſſe <expan abbr="cãdem">eandem</expan> vltimam <lb></lb>mixtam in diuerſis planis; iam oſtendimus eſſe plures ſuprà in naui <lb></lb>mobili v.g. per planum verticale, horizontale, &amp; inclinatum. </s>
				</p>
				<p id="N1C8EC" type="main">
					<s id="N1C8EE">Septimò, ſi in naui mobili curreret equus, vel currus, eſſet motus mix­<lb></lb>tus ex quatuor aliis, &amp; ſi terra moueretur in naui mobili eſſent quatuor <lb></lb>motus, ſi ex ea aliquod mobile proiiceretur; inuenitur autem linea mix­<lb></lb>ta in diuerſis planis per quamdam planorum circuitionem, de qua <lb></lb>ſuprà. </s>
				</p>
				<p id="N1C8FA" type="main">
					<s id="N1C8FC">Octauò, poſſet facilè in eodem plano motus mixtus conflari ex qua­<lb></lb>tuor aliis vel etiam pluribus, ſint enim quatuor in eodem plano AD <lb></lb>AE. AF. AH. ex AD AE fit AB, ex AB, A fi fit AC, ex AC AH <lb></lb>fit AG, quæ eſt longior AC, &amp; AC longior AB: poſſes etiam compo­<lb></lb>nere ex AH AF, atque ita deinceps eodem ordine, &amp; ſemper vltima <lb></lb>linea erit AG, quod certè mirabile eſt, &amp; à Geometris demonſtrari <lb></lb>poteſt. </s>
				</p>
				<p id="N1C90C" type="main">
					<s id="N1C90E">Nonò, ex his motibus mixtis educi poſſunt rationes multorum effe-<pb pagenum="194" xlink:href="026/01/226.jpg"></pb>ctuum naturalium, qui obſeruantur in rebus naturalibus, quales ſunt v.g. <lb></lb>nubium, vaporum, ventorumque motus, qui ſæpè turbinatim procellas <lb></lb>agunt, quorum turbinum ratio referri non debet, vt videbimus ſuo loco, <lb></lb>in repercuſſionem aliquam, quæ fiat à concauis montibus, qui longiſſi­<lb></lb>mo interuallo ſæpiùs abſunt; </s>
					<s id="N1C920">ſed potiùs petenda eſt ab ipſa mixti motus <lb></lb>naturâ; </s>
					<s id="N1C926">quippè rara materies venti facilè recipit omnem impetum; </s>
					<s id="N1C92A">ita­<lb></lb>que ex prægnantibus ſæpè nubibus conferta tenuiſſimorum halituum <lb></lb>examina fractis quaſi carceribus quacumque linea erumpunt; <lb></lb>hinc infiniti propemodum motus, hinc turbines illi, &amp;c. </s>
					<s id="N1C934"><lb></lb>atque hæc de motu mixto ex pluribus <lb></lb>rectis ſint ſatis. <lb></lb><figure id="id.026.01.226.1.jpg" xlink:href="026/01/226/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N1C940">
				<pb pagenum="195" xlink:href="026/01/227.jpg"></pb>
				<figure id="id.026.01.227.1.jpg" xlink:href="026/01/227/1.jpg"></figure>
				<p id="N1C94A" type="head">
					<s id="N1C94C"><emph type="center"></emph>LIBER QVINTVS, <lb></lb><emph type="italics"></emph>DE MOTV IN DIVERSIS <lb></lb>Planis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C95B" type="main">
					<s id="N1C95D">HACTENVS conſiderauimus motum in libe­<lb></lb>ro medio; iam verò conſiderabimus in planis <lb></lb>durioribus, in quibus mobilè feratur vel ſua <lb></lb>ſponte vel ab extrinſeco impulſum. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N1C96A" type="main">
					<s id="N1C96C"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C978" type="main">
					<s id="N1C97A"><emph type="italics"></emph>PLanum inclinatum eſt corpus durum læuigatiſſimum, in quo mobile quod­<lb></lb>piam moueri poſſit, quod nec ſit verticale ſurſum, nec perpendiculare deor­<lb></lb>ſum,<emph.end type="italics"></emph.end> non addo, nec horizonti parallelum; quia planum rectilineum hori­<lb></lb>zontale eſt etiam decliue, vt ſuo loco videbimus. </s>
				</p>
				<p id="N1C989" type="main">
					<s id="N1C98B"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C998" type="main">
					<s id="N1C99A"><emph type="italics"></emph>Corpus graue per planum inclinatum deſcendit, &amp; quidem velociùs per illud <lb></lb>planum, quod minùs recedit à perpendiculari, tardiùs verò per illud, quod plùs <lb></lb>recedit.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1C9A5" type="main">
					<s id="N1C9A7"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C9B4" type="main">
					<s id="N1C9B6"><emph type="italics"></emph>Corpus graue in plano inclinato minùs grauitat, id eſt faciliùs ſustinetur, &amp; <lb></lb>tardiore motu deſcendit, quàm in perpendiculari deorſum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1C9BF" type="main">
					<s id="N1C9C1">Vtraque hypotheſis certa eſt, &amp; de vtraque ſupponimus tantùm, quòd <lb></lb>ſit, nam demonſtrabimus infrà propter quid ſit. </s>
				</p>
				<p id="N1C9C6" type="main">
					<s id="N1C9C8"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1C9D5" type="main">
					<s id="N1C9D7"><emph type="italics"></emph>Corpus graue ideò tantùm mouetur ſua ſponte, vt deorſum tendat<emph.end type="italics"></emph.end>: </s>
					<s id="N1C9E0">hoc <lb></lb>Axioma conſtat ex iis, quæ fusè demonſtraui ſecundò lib.  adde quod, <lb></lb>deorſum tendere, &amp; corpus graue ſua ſponte moueri idem prorſus ſonare <lb></lb>videntur; </s>
					<s id="N1C9EA">nec enim loquor de potentiâ motrice animantium, vel de alia <lb></lb>quacumque magneticâ, ſed de potentiâ motrice grauium; </s>
					<s id="N1C9F0">graue autem <lb></lb>illud appello, quod in medio rariore poſitum deorſum tendit, niſi impe­<lb></lb>diatur, denique hîc ſuppono dari motum naturalem grauium deorſum <pb pagenum="196" xlink:href="026/01/228.jpg"></pb>quod demonſtratum eſt ſecundo lib.  &amp; verò ſi tibi adhuc non fiat ſatis, <lb></lb>probetur hoc Axioma per hypotheſim primam; nam reuerâ ſuppono <lb></lb>quòd omnibus experimentis comprobatur, ſcilicet corpus graue per pla­<lb></lb>num Inclinatum deorſum ſua ſponte deſcendere, non verò aſcendere niſi <lb></lb>propter aliquam reflexionem. </s>
				</p>
				<p id="N1CA05" type="main">
					<s id="N1CA07"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CA14" type="main">
					<s id="N1CA16"><emph type="italics"></emph>Motus, qui impeditur, imminuitur, idque pro rata, &amp; viciſſim impeditur <lb></lb>qui imminuitur<emph.end type="italics"></emph.end>; cur enim imminueretur ſeu retardaretur, ſi nullum ſit <lb></lb>impedimentum? </s>
				</p>
				<p id="N1CA23" type="main">
					<s id="N1CA25"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CA32" type="main">
					<s id="N1CA34"><emph type="italics"></emph>Omne quod impedit motum, debet eſſe applicatum mobili vel per ſe, vel <lb></lb>per ſuam virtutem<emph.end type="italics"></emph.end>; hoc Axioma etiam certum eſt. </s>
				</p>
				<p id="N1CA3F" type="main">
					<s id="N1CA41"><emph type="center"></emph><emph type="italics"></emph>Poſtulatum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CA4D" type="main">
					<s id="N1CA4F"><emph type="italics"></emph>Liceat accipere in perpendiculari deorſum, parallelas, cum ſcilicet aſſumi­<lb></lb>tur modica altitudo<emph.end type="italics"></emph.end>; licèt enim non ſint parallelę, quia tamen inſenſibili <lb></lb>interuallo ad ſeſe inuicem accedunt, pro parallelis accipiuntur. </s>
				</p>
				<p id="N1CA5C" type="main">
					<s id="N1CA5E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CA6B" type="main">
					<s id="N1CA6D"><emph type="italics"></emph>Impeditur motus corporis in plano inclinato<emph.end type="italics"></emph.end>; certum eſt quod impedia­<lb></lb>tur, quia tardiore motu deſcendit mobile per hyp. </s>
					<s id="N1CA78">2. igitur impeditur <lb></lb>per Axio.2. </s>
				</p>
				<p id="N1CA7D" type="main">
					<s id="N1CA7F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CA8C" type="main">
					<s id="N1CA8E"><emph type="italics"></emph>Ideo impeditur, quia impeditur linea ad quam determinatus eſt impetus <lb></lb>innatus<emph.end type="italics"></emph.end>; cum ſit determinatus ad lineam perpendicularem deorſum per <lb></lb>Ax.1. cur enim potiùs ad vnam lineam quàm ad aliam? </s>
					<s id="N1CA9B">atqui id tan­<lb></lb>tùm planum inclinatum efficit, vel impedit, ne deorſum rectà tendere <lb></lb>poſſit; igitur ex eo tantùm capite impedit. </s>
				</p>
				<p id="N1CAA3" type="main">
					<s id="N1CAA5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CAB2" type="main">
					<s id="N1CAB4"><emph type="italics"></emph>Non totus impeditur motus in plano inclinato<emph.end type="italics"></emph.end>; </s>
					<s id="N1CABD">quia ſi totus impediretur, <lb></lb>nullus eſſet omninò motus ſuper eodem plano, ſed per planum inclina­<lb></lb>tum mobile deorſum mouetur per hyp.1.igitur totus motus non impedi­<lb></lb>tur; hinc ratio à priori primæ hypotheſeos. </s>
				</p>
				<p id="N1CAC7" type="main">
					<s id="N1CAC9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CAD6" type="main">
					<s id="N1CAD8"><emph type="italics"></emph>In ea proportione minùs mouetur, in quæ plùs impeditur<emph.end type="italics"></emph.end>; </s>
					<s id="N1CAE1">probatur per <lb></lb>Axioma 2.cum enim motus imminuatur, quia impeditur per idem Axio­<lb></lb>ma; </s>
					<s id="N1CAE9">certè quò plùs impeditur, plùs imminuitur; ſed quò plùs imminui­<lb></lb>tur, minor eſt, ergo quò plùs impeditur, minor eſt. </s>
				</p>
				<p id="N1CAEF" type="main">
					<s id="N1CAF1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CAFE" type="main">
					<s id="N1CB00"><emph type="italics"></emph>Eò plùs impeditur motus, quò maius ſpatium conficiendum eſt ad ac­<lb></lb>quirendam <expan abbr="eãdem">eandem</expan> altitudinem, ſeu diſtantiam à centro, illo ſpatio, <lb></lb>quod conficitur in perpendiculari deorſum<emph.end type="italics"></emph.end>; hoc Theor. vt clariùs <lb></lb>demonſtretur, aliquid figuræ tribuendum eſt. </s>
					<s id="N1CB15">ſit perpendicularis deor-<pb pagenum="197" xlink:href="026/01/229.jpg"></pb>ſum, AB, ſit planum inclinatum AE duplum AB; </s>
					<s id="N1CB1E">certè vbi mobile ex A <lb></lb>peruenit in E per planum AE, diſtat æquè à centro, ac ſi eſſet in B; </s>
					<s id="N1CB24">ſup­<lb></lb>pono enim perpendiculares omnes deorſum eſſe parallelas per poſtula­<lb></lb>tum; </s>
					<s id="N1CB2C">igitur non acceſſit propiùs ad centrum confecto ſpatio AE, quàm <lb></lb>confecto AB; </s>
					<s id="N1CB32">igitur impeditur in plano AE in ea proportione, in qua <lb></lb>AB eſt minor AE, nam haud dubiè AE eſt maior AB, ſit autem dupla v.g. <lb></lb>igitur impeditur non quidem totus motus ſed ſubduplus; </s>
					<s id="N1CB3B">in plano verò <lb></lb>AD impeditur iuxta cam proportionem in qua AB eſt minor AD, nec <lb></lb>enim aliunde poteſt impediri, cum ſcilicet impediatur tantùm, quia im­<lb></lb>peditur linea ad quam ab ipſa natura determinatus eſt per Th.2. v. g.li­<lb></lb>nea deorſum AB; </s>
					<s id="N1CB49">quippè lineæ comparantur inter ſe v.g. AE cum AB, <lb></lb>nam impedimentum lineæ AE in eo tantùm poſitum eſt, quòd difficiliùs <lb></lb>per illam quàm per AB ad <expan abbr="cẽtrum">centrum</expan> feratur mobile, quod certum eſt, cum <lb></lb>imperimentum petatur a difficultate; </s>
					<s id="N1CB59">atqui difficultas motus, qui fit per <lb></lb>lineam AE in eo tantùm eſt, quòd ſit maius ſpatium conficiendum, igi­<lb></lb>tur quò maius ſpatium eſt, maior difficultas eſt; igitur quò maior linea <lb></lb>eſt, maius impedimentum eſt. </s>
				</p>
				<p id="N1CB63" type="main">
					<s id="N1CB65">Adde quod vel impedimenti proportio petitur ab angulis vel à Tan­<lb></lb>gentibus, vel à ſecantibus; </s>
					<s id="N1CB6B">nihil enim aliud adeſſe poteſt; </s>
					<s id="N1CB6F">igitur per Ax. <lb></lb>3. poteſt tantùm impediri ab his; </s>
					<s id="N1CB76">ſed proportio impedimenti non poteſt <lb></lb>eſſe ab angulis; </s>
					<s id="N1CB7C">quod probatur primò, quia ſi ego quæram à te in qua <lb></lb>proportione motus per AE eſt tardior motu per AB; </s>
					<s id="N1CB82">dices in ea, in qua <lb></lb>angulus EAB eſt maior nullo angulo, quod eſt ridiculum: </s>
					<s id="N1CB88">Equidem di­<lb></lb>ceres motum per AD eſſe velociorem motu per AE in ea proportione, <lb></lb>in qua angulus EAB eſt maior angulo BAD, quod tamen falſum eſt; </s>
					<s id="N1CB90">eſſet <lb></lb>enim ferè duplò maior, quod repugnat <expan abbr="experimẽtis">experimentis</expan> omnibus; </s>
					<s id="N1CB9A">at ſi <expan abbr="accipiã">accipiam</expan> <lb></lb>angulum BA, qui ſit tantùm vnius gradus ſeu minuti, ſitque EAB angu­<lb></lb>lus 60. grad. ſi velocitas motus per AI eſſet ad velocitatem motus per <lb></lb>AE vt angulus EAB ad angulum BAI, motus per AI eſſet ſexagecuplò <lb></lb>velocior, quàm per AE, quod eſt abſurdum: Diceret fortè aliquis in to­<lb></lb>to angulo 90. GAB diſtribui huius impedimenti motum v.g. ſi angulus <lb></lb>BAI ſit 1.grad. </s>
					<s id="N1CBB2">motus per AI amittit tantùm (1/90) ſui motus; ſi angulus D <lb></lb>AB circiter 40.grad. </s>
					<s id="N1CBB8">motus per AD amittit tantùm (40/90), &amp; per AE (60/90); cum <lb></lb>ſit angulus BAE 60. grad. igitur motus per AB eſt ad motum per AE <lb></lb>vt 3.ad 1. quod omnibus experimentis repugnat. </s>
				</p>
				<p id="N1CBC2" type="main">
					<s id="N1CBC4">Secundò probatur, quia ſi fiat inclinata proximè accedens ad AG v. <lb></lb>g.4′.&amp; aſſumatur alia accedens 3′. </s>
					<s id="N1CBCA">differentia anguli erit tantùm 2′. </s>
					<s id="N1CBCD">cum <lb></lb>tamen differentia longitudinis plani ſeu ſecantis huius, &amp; illius, ſit ma­<lb></lb>xima, vt conſtat ex canone ſinuum, igitur non imminueretur motus in <lb></lb>plano inclinato ratione impedimenti contra Th.4. quis enim neget eſſe <lb></lb>maximum impedimentum motus tantum ſpatium, quod <expan abbr="conficiendũ">conficiendum</expan> eſt. </s>
				</p>
				<p id="N1CBDC" type="main">
					<s id="N1CBDE">Tertiò, omnia experimenta conſentiunt huic Theoremati, &amp; repu­<lb></lb>gnant huic propoſitioni quæ petitur ab angulis; </s>
					<s id="N1CBE4">adde quod angulus ni­<lb></lb>hil prorſus facit ad motum, ſed linea ſeu ſpatium; denique hoc ipſum eſt <lb></lb>quod ab omnibus Mechanicis vulgò ſupponitur perinde quaſi prima <pb pagenum="198" xlink:href="026/01/230.jpg"></pb>notio, quæ tamen aliquâ demonſtratione indiget. </s>
				</p>
				<p id="N1CBF1" type="main">
					<s id="N1CBF3">Equidem explicari poteſt hæc demonſtratio operâ libræ; </s>
					<s id="N1CBF7">ſit enim <lb></lb>libra CG cuius centrum immobile eſt A; </s>
					<s id="N1CBFD">ſit autem diameter libræ CG, <lb></lb>pondus in C ſe habet ad pondus in D, tranſlata ſcilicet diametro in DH <lb></lb>vt CA, ad BA; </s>
					<s id="N1CC05">igitur pondus in D grauitaret minùs in planum inclina­<lb></lb>tum DA, quàm in horizontali CAI; </s>
					<s id="N1CC0B">nam pondus in D idem præſtat, quod <lb></lb>præſtaret appenſum in D fune DE; </s>
					<s id="N1CC11">igitur grauitatio in C eſt ad grauita­<lb></lb>tionem in D, vt CA, vel DA ad BA; </s>
					<s id="N1CC17">ſed quâ proportione decreſcit graui­<lb></lb>tatio in planum, creſcit motus in plano inclinato, quia minùs impeditur <lb></lb>per Th.4. igitur in perpendiculari ea nulla eſt gtauitatio in planum; </s>
					<s id="N1CC1F">nec <lb></lb>impeditur vllo modo motus, igitur ab E verſus C ita impeditur motus, vt <lb></lb>AC verſus C impeditur grauitatio in planum, ſed impeditur grauitatio <lb></lb>in D v.g. in ratione totius CA ad EA, vel DA ad DI; igitur impeditur <lb></lb>motus in eadem proportione v.g. in plano DA ad DB vel AI, igitur in <lb></lb>ratione plani inclinati ad perpendicularem. </s>
				</p>
				<p id="N1CC31" type="main">
					<s id="N1CC33">Hæc omnia veriſſima ſunt; </s>
					<s id="N1CC37">ſupereſt tamen vt ſciatur ratio phyſica cur <lb></lb>pondus in D æquiualeat ponderi in B quod ſupponunt quidem omnes <lb></lb>Mechanici, &amp; omnibus experimentis congruit: </s>
					<s id="N1CC3F">Equidem pondus pendu­<lb></lb>lum ex D fune DB, vel longiore, eſt eiuſdem momenti, cuius eſt affixum <lb></lb>in D, ita vt linea directionis, quæ ducitur ab eius centro reſpondeat fu­<lb></lb>ni DB; </s>
					<s id="N1CC49">vnde rectè concluditur ab Archimede idem pondus affixum bra­<lb></lb>chio BA eiuſdem eſſe momenti cum pendulo DB, vel affixo puncto D, <lb></lb>quod certè veriſſumum eſt, nondum tamen rationem phyſicam video; </s>
					<s id="N1CC51"><lb></lb>verum quidem eſt idem pondus pendulum fune DB minoris eſſe <lb></lb>momenti, quàm ſi eſſet affixum puncto C; </s>
					<s id="N1CC58">nam ſuppono CG eſſe libram <lb></lb>in ſitu horizontali; </s>
					<s id="N1CC5E">tum quia pondus illud DB trahit deorſum extremum <lb></lb>libræ D per arcum DC longo circuitu, maximè declinante à ſua linea <lb></lb>directionis DB; </s>
					<s id="N1CC66">tùm quia ex hoc ſequitur neceſſariò pondus B deflecti <lb></lb>à ſua perpendiculari curua linea; </s>
					<s id="N1CC6C">tùm quia linea DA, quæ rigida ſuppo­<lb></lb>nitur, reſiſtit motui DB &amp; patet; in qua verò proportione, dictum eſt <lb></lb>certè hactenus, ſed phyſicè non demonſtratum. </s>
				</p>
				<p id="N1CC74" type="main">
					<s id="N1CC76">Pater Merſennus multis locis ex doctiſſimo Roberuallo demonſtrat <lb></lb>rem iſtam ingenioſiſſimè; </s>
					<s id="N1CC7C">ſit enim circulus centro R; </s>
					<s id="N1CC80">ſint vectes æqua­<lb></lb>les BF horizonti, DN perpendiculari paralleli; </s>
					<s id="N1CC86">tùm CL, FO, æqualiter <lb></lb>inclinati, ducantur CO EL; </s>
					<s id="N1CC8C">haud dubiè ſi pondera C &amp; L ſint æqualia <lb></lb>erit æquilibrium; </s>
					<s id="N1CC92">quod certum eſt, &amp; demonſtrabimus cum de libra; </s>
					<s id="N1CC96">eſt <lb></lb>enim quarta propoſitio Vbaldi de libra; </s>
					<s id="N1CC9C">ſed pondus in O pendulum ſci­<lb></lb>licet filo CO eſt eiuſdem momenti, cuius eſt pondus in P; </s>
					<s id="N1CCA2">igitur pon­<lb></lb>dus in P æquale ponderi O ſuſtineret pondus ML, ſed pondus in P <lb></lb>eſt ad pondus in B vel in F, ad hoc, vt ſit æquilibrium, RF ad R <lb></lb>P; </s>
					<s id="N1CCAC">igitur pondus in A vel in R, quod erit ad pondus in L, vt P ad R <lb></lb>L, ſuſtinebit pondus in L; </s>
					<s id="N1CCB2">ſed ſi applicetur potentia in C quæ trahat per <lb></lb>tangentem CT, faciet idem momentum quod faceret in B trahens per <lb></lb>tangentem BA; </s>
					<s id="N1CCBA">at vicem illius potentiæ gerit pondus B vel A, quod gra­<lb></lb>uitat per BA; </s>
					<s id="N1CCC0">igitur potentia applicata C per CT, æqualis ponderi A <pb pagenum="199" xlink:href="026/01/231.jpg"></pb>retineret pondus in L; </s>
					<s id="N1CCC9">ducatur autem KLG Tangens parallela CT; </s>
					<s id="N1CCCD">certè <lb></lb>eadem potentia in L per LG retinebit pondus in L; </s>
					<s id="N1CCD3">quæ idem retine­<lb></lb>ret applicata in C per CT; </s>
					<s id="N1CCD9">cum enim RC &amp; RL ſint æquales ſi ſint ap­<lb></lb>plicatæ duæ potentiæ æquales in C quidem per CT, &amp; in L per LG; </s>
					<s id="N1CCDF"><lb></lb>haud dubiè erit perfectum æquilibrium; </s>
					<s id="N1CCE4">igitur ſi pondus A pendeat in <lb></lb>H fune LGH, retinebit pondus L in plano inclinato GLK; </s>
					<s id="N1CCEA">eſt autem <lb></lb>pondus H ad pondus LN SR ad RL; </s>
					<s id="N1CCF0">ſed triangula RSL, &amp; GKI <lb></lb>ſunt proportionalia; </s>
					<s id="N1CCF6">igitur pondus in H eſt ad pondus L, vt GI ad G <lb></lb>K; </s>
					<s id="N1CCFC">igitur ſi vires, quæ retinent pondus in plano inclinato GK ſunt ad vi­<lb></lb>res, quæ retinent pondus in perpendiculari GI, vt GI ad GK; igitur im­<lb></lb>petus ſeu motus mobilis in plano GK eſt ad impetum, ſeu motum eiuſ­<lb></lb>dem in perpendiculo GI, vt GI ad GK. </s>
				</p>
				<p id="N1CD06" type="main">
					<s id="N1CD08">Hæc omnia veriſſima ſunt, ſemper tamen deſiderari videtur ratio phy­<lb></lb>ſica, cur idem pondus pendulum ex C in O, ſit eiuſdem momenti cum <lb></lb>pondere affixo puncto P, ſeu brachio libræ horizontalis PS. quod certè <lb></lb>Mechanica Axiomatis, vel hypotheſeos loco iure aſſumere poteſt; </s>
					<s id="N1CD12">at ve­<lb></lb>rò phyſica non ſatis habet de re cognoſcere quod ſit, niſi ſciat propter <lb></lb>quid ſit; igitur nos aliquam afferre conabimur. </s>
					<s id="N1CD1A">Suppono tantùm tunc <lb></lb>eſſe æquilibrium perfectum duorum ponderum æqualium cum <expan abbr="vtrimq;">vtrimque</expan> <lb></lb>æqualia illa pondera ita ſunt appenſa, vt linea directionis vnius æqua­<lb></lb>lis ſit lineæ directionis alterius, cur enim alterum præualeret ſi ſint æ­<lb></lb>qualia? </s>
					<s id="N1CD29">hoc poſito. </s>
				</p>
				<p id="N1CD2C" type="main">
					<s id="N1CD2E">Dico pondus affixum P æquale ponderi L facere æquilibrium; cum <lb></lb>enim linea directionis ſit PO, ſi deſcenderet liberè per PO. </s>
					<s id="N1CD34">L eodem <lb></lb>tempore attolleretur per LS, quod certè applicatis planis SL PO facilè <lb></lb>fieri poſſet; </s>
					<s id="N1CD3C">ſed eodem modo P grauitat, quo ſi deſcenderet per PO; </s>
					<s id="N1CD40">eſt <lb></lb>enim eius linea directionis; </s>
					<s id="N1CD46">atqui tunc faceret æquilibrium, quod oſten­<lb></lb>do; </s>
					<s id="N1CD4C">æquale ſpatium conficeret L, per LS aſcendendo, quod P per PO <lb></lb>deſcendendo; </s>
					<s id="N1CD52">igitur ſi attolleret L in S, ſimiliter pondus L æquale P in S <lb></lb>attolleret pondus P ex O in P, igitur neutrum præualere poteſt; ſed quia <lb></lb>hæc fuſiùs explicabimus cum de libra, nunc tantùm indicaſſe ſufficiat. </s>
				</p>
				<p id="N1CD5A" type="main">
					<s id="N1CD5C">Supereſt vt breuiter oſtendamus accipi non poſſe hanc proportio­<lb></lb>nem imminutionis motus in plano inclinato à Tangente BE tùm <lb></lb>quia; </s>
					<s id="N1CD64">iam à ſecante accipi oſtendimus, tùm quia ſit Tangens BD æqualis <lb></lb>ſumi toti ſeu perpendiculari AB; </s>
					<s id="N1CD6A">ſequeretur motum per AD æqualem <lb></lb>eſſe motui per AB; </s>
					<s id="N1CD70">Equidem in maxima diſtantia accedit Tangens ad <lb></lb>ſecantem; igitur eò plùs impeditur motus, quò maius ſpatium conficien­<lb></lb>dum eſt, &amp;c. </s>
				</p>
				<p id="N1CD78" type="main">
					<s id="N1CD7A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CD87" type="main">
					<s id="N1CD89"><emph type="italics"></emph>Ex hoc ſequitur neceſſariò motum in plano inclinato eſſe ad motum in per­<lb></lb>pendiculari, vt ipſa perpendicularis ad ipſum planum inclinatum,<emph.end type="italics"></emph.end> v.g. velo­<lb></lb>citas motus per AE eſt ad velocitatem motus per AB, vt ipſa AB eſt <lb></lb>ad ipſam AE, ſit enim AE dupla AB, velocitas per AB eſt dupla veloci­<lb></lb>tatis per AE. </s>
				</p>
				<pb pagenum="200" xlink:href="026/01/232.jpg"></pb>
				<p id="N1CDA0" type="main">
					<s id="N1CDA2">Obſerua quæſo, cum dico motum in plano inclinato eſſe ad motum <lb></lb>in perpendiculo, vt ipſæ lineæ permutando, ita intelligendum eſſe, vt <lb></lb>vel aſſumatur motus in ſingulis inſtantibus, ita vt eo inſtanti, quo datum <lb></lb>ſpatium in inclinata acquiritur, acquiratur duplum in perpendiculo; </s>
					<s id="N1CDAC">quo <lb></lb>poſito valet certè tantùm illa proportio ratione motus æquabilis, ſi ſer­<lb></lb>uari debet; nam perinde ſe habet phyſicè, atque ſi eſſet, vt iam fusè ex­<lb></lb>plicatum eſt lib.2. in re ſimili. </s>
				</p>
				<p id="N1CDB6" type="main">
					<s id="N1CDB8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CDC4" type="main">
					<s id="N1CDC6"><emph type="italics"></emph>Hinc deſcendit mobile per ſe in plano inclinato<emph.end type="italics"></emph.end>; </s>
					<s id="N1CDCF">ratio eſt, quia totus mo­<lb></lb>tus non impeditur, cum ſit eadem proportio, quæ eſt perpendicularis <lb></lb>ad inclinatam; dixi per ſe, nam per accidens in plano ſcabro tantillùm <lb></lb>inclinato mobile deſcendit, adde quod corpus graue tamdiu mouetur <lb></lb>quandiu accedere poteſt ad centrum terræ. </s>
				</p>
				<p id="N1CDDB" type="main">
					<s id="N1CDDD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CDE9" type="main">
					<s id="N1CDEB"><emph type="italics"></emph>Motus in infinitum imminui poteſt,<emph.end type="italics"></emph.end> probatur, quia proportio perpen­<lb></lb>dicularis ad inclinatam poteſt eſſe minor in infinitum, quia inclinata <lb></lb>poteſt eſſe longior, &amp; in infinitum. </s>
				</p>
				<p id="N1CDF7" type="main">
					<s id="N1CDF9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CE05" type="main">
					<s id="N1CE07"><emph type="italics"></emph>Ex his vera redditur ratio cur in plano inclinato ad angulum BG motus ſit <lb></lb>ſubduplus illius qui fit in perpendiculari<emph.end type="italics"></emph.end>; v.g. ſit angulus BAE 60. certè <lb></lb>AE eſt dupla AB, ſed motus in AB eſt ad motum in AE vt AE ad AB <lb></lb>per Th.6. igitur eſt duplus. </s>
				</p>
				<p id="N1CE18" type="main">
					<s id="N1CE1A">Ex his reiicies quoque Cardanum, &amp; alios quoſdam, qui diuerſam <lb></lb>proportionem motuum in planis inclinatis deducunt ex diuerſis angu­<lb></lb>lis inclinationis; iuxta quam proportionem motus in AE eſſet ſubtri­<lb></lb>plus in AB contra experimentum. </s>
				</p>
				<p id="N1CE24" type="main">
					<s id="N1CE26"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CE32" type="main">
					<s id="N1CE34"><emph type="italics"></emph>Motus acceleratur in plano inclinato<emph.end type="italics"></emph.end>; </s>
					<s id="N1CE3D">experientia clariſſima eſt, ratio <lb></lb>eadem cum illa, quam adduximus lib.3. cum de motu naturali, quia ſci­<lb></lb>licet prior impetus conſeruatur, &amp; acquiritur nouus, Imò acceleratur <lb></lb>iuxta <expan abbr="eãdem">eandem</expan> proportionem, vel noſtram ſingulis inſtantibus, vel Gali­<lb></lb>lei in partibus temporum ſenſibilibus; vnde aſſumemus deinceps iſtam <lb></lb>Galilei proportionem, quia ſcilicet partes temporis ſenſibiles tantùm <lb></lb>aſſumere poſſumus. </s>
				</p>
				<p id="N1CE51" type="main">
					<s id="N1CE53"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CE5F" type="main">
					<s id="N1CE61"><emph type="italics"></emph>In plano inclinato eſt idem impetus innatus qui est in perpendiculari,<emph.end type="italics"></emph.end> ſed <lb></lb>in hac habet totum ſuum motum, non verò in illa, quia impeditur, niſi <lb></lb>enim totus eſſet, non grauitaret corpus illud in planum inclinatum; </s>
					<s id="N1CE6E"><lb></lb>quippe ſuas omnes vires impetus ille exereret circa motum; </s>
					<s id="N1CE73">igitur ali­<lb></lb>quid illarum exerit circa motum aliquid circa planum, in quod ex parte <lb></lb>grauitat; igitur idem eſt impetus innatus, adde quod ille eſt inſepa­<lb></lb>rabilis. </s>
				</p>
				<pb pagenum="201" xlink:href="026/01/233.jpg"></pb>
				<p id="N1CE81" type="main">
					<s id="N1CE83"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CE8F" type="main">
					<s id="N1CE91"><emph type="italics"></emph>Impetus naturalis aduentitius productus à corpore graui in plano inclinato <lb></lb>eſt minor eo, qui producitur in perpendiculari<emph.end type="italics"></emph.end>; </s>
					<s id="N1CE9C">probatur, quia eſt minor <lb></lb>motus, igitur minor impetus, vt ſæpè diximus; </s>
					<s id="N1CEA2">ſecundò (hæc eſt ratio <lb></lb>à priori;) quia cum ideo producatur impetus iſte aduentitius, vt motus <lb></lb>acceleretur; </s>
					<s id="N1CEAA">certè debet reſpondere motui, qui competit impetui innati; </s>
					<s id="N1CEAE"><lb></lb>ſi enim nullum habet motum, nullus accedit de nouo impetus, è con­<lb></lb>tra verò ſi eſt motus, ſed maior, ſi maior eſt motus, &amp; minor ſi eſt minor; <lb></lb>quia hic impetus tantùm eſt propter motum. </s>
				</p>
				<p id="N1CEB7" type="main">
					<s id="N1CEB9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CEC5" type="main">
					<s id="N1CEC7"><emph type="italics"></emph>Impetus qui producitur in acceleratione motus habet totum motum quem <lb></lb>exigit (præſcindendo à reſiſtentia medij)<emph.end type="italics"></emph.end>; </s>
					<s id="N1CED2">nec enim per illum mobile graui­<lb></lb>tat in planum; </s>
					<s id="N1CED8">alioquin creſceret ſemper grauitatio; </s>
					<s id="N1CEDC">igitur totus exerce­<lb></lb>tur circa motum; </s>
					<s id="N1CEE2">ratio eſt quia hic impetus addititius non eſt inſtitutus <lb></lb>propter grauitationem, ſed tantùm propter motum: adde quod ad om­<lb></lb>nem lineam determinari poteſt, ſecùs verò naturalis ſaltem om­<lb></lb>ninò. </s>
				</p>
				<p id="N1CEEC" type="main">
					<s id="N1CEEE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CEFA" type="main">
					<s id="N1CEFC"><emph type="italics"></emph>Imminuitur motu illo grauitatio corporis in planum<emph.end type="italics"></emph.end>; ratio eſt primò; </s>
					<s id="N1CF05">quia <lb></lb>quò velociùs mouetur in plano, breuiori tempore ſingulis partibus in­<lb></lb>cumbit: </s>
					<s id="N1CF0D">ſecundò quia motu illo accelerato quaſi diſtrahitur mobile ab <lb></lb>illa linea grauitationis in planum; hinc mobile celeri motu moueretur <lb></lb>in plano illo inclinato, quod eiuſdem ſubſiſtentis grauitationi &amp; ponde­<lb></lb>ri vltrò cederet. </s>
				</p>
				<p id="N1CF17" type="main">
					<s id="N1CF19"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CF25" type="main">
					<s id="N1CF27"><emph type="italics"></emph>Impetus innatus ex ſe eſt ſemper determinatus ad lineam perpendicularem <lb></lb>deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1CF32">quia grauitas tendit ad commune centrum, vt videbimus tra­<lb></lb>ctatu ſequenti; </s>
					<s id="N1CF38">tamen ratione plani quaſi detorquetur ad lineam plani <lb></lb>ad quam tamen omninò non determinatur, alioquin non grauitaret in <lb></lb>planum: </s>
					<s id="N1CF40">vnde dixi, detorquetur ſeu quaſi diuiditur, perinde quaſi eſſet <lb></lb>duplex impetus, quorum alter per lineam perpendicularem deorſum <lb></lb>eſſet determinatus, in quo non eſt difficultas; impetus tamen aduenti­<lb></lb>tius determinatur omninò ad lineam plani. </s>
				</p>
				<p id="N1CF4A" type="main">
					<s id="N1CF4C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1CF58" type="main">
					<s id="N1CF5A">Dubitari poteſt an grauitatio in planum inclinatum ſit vt reſiduum <lb></lb>plani, cui detrahitur perpendiculum v.g. ſit planum inclinatum CD ad <lb></lb>angulum ACD 60. potentia quæ ſuſtinet pondus B per EB eſt ad præ­<lb></lb>dictum pondus vt CA ad CD; </s>
					<s id="N1CF66">detrahitur CA ex CD, ſupereſt FD æqua­<lb></lb>lis ſcilicet CA; </s>
					<s id="N1CF6C">an fortè grauitatio ponderis B in planum inclinatum C <lb></lb>D eſt ad grauitationem eiuſdem in planum horizontale; </s>
					<s id="N1CF72">quæ eſt graui­<lb></lb>tatio tota, id eſt nihil imminuta vt DF ad DC; </s>
					<s id="N1CF78">attollatur enim totum <lb></lb>triangulum CAD in eadem ſitu altera manu, &amp; altera filo EB paralle-<pb pagenum="202" xlink:href="026/01/234.jpg"></pb>lo CF, retineatur pondus B ne ſcilicet deorſum cadat; </s>
					<s id="N1CF83">tùm ſubtrahatur <lb></lb>pondus trianguli CAD; nunquid fortè altera manus ſuſtinebit tantùm <lb></lb>ſubduplum ponderis B? &amp; altera ſubduplum? </s>
					<s id="N1CF8B">igitur vt habeatur quod <lb></lb>ſuſtinet ſuppoſita dextra v.g. debet ſubſtrahi, quod ſuſtinet ſiniſtra, ſed <lb></lb>quod ſuſtinet ſiniſtra, eſt vt ipſa potentia, id eſt vt CA ad CD; igitur <lb></lb>tota CD repræſentat totum pondus, ſegmentum CF partem ponderis <lb></lb>quæ competit potentiæ E, FD verò partem quæ ſuſtinetur à pla­<lb></lb>no CF. </s>
				</p>
				<p id="N1CF9C" type="main">
					<s id="N1CF9E">Hinc facilè poſſet determinari quota pars ponderis incubet plano,<lb></lb>ſit enim planum inclinatum AC, perpendiculum AB, accipiatur AB <lb></lb>æqualis AB, ſitque AC tripla AB, duæ tertiæ ponderis incubant plano <lb></lb>ſi verò ſit horizontale planum, totum pondus grauitat in illud; </s>
					<s id="N1CFA8">nulla eſt <lb></lb>enim perpendicularis, ſi ſit perpendiculare planum, nihil prorſus gra­<lb></lb>uitat; </s>
					<s id="N1CFB0">quia nulla eſt inclinata, &amp; quò propiùs accedit planum inclina­<lb></lb>tum ad horizontalem plùs grauitat pondus in illud, minùs verò; quò <lb></lb>propiùs accedit ad perpendicularem. </s>
				</p>
				<p id="N1CFB8" type="main">
					<s id="N1CFBA">Hinc eſſet oppoſita ratio grauitationis, &amp; motus, in plano inclinato; </s>
					<s id="N1CFBE"><lb></lb>nam quò plùs eſt grauitationis minùs eſt motus, quò plùs motus, minùs <lb></lb>grauitationis; </s>
					<s id="N1CFC5">quando verò planum inclinatum eſt duplum perpendicu­<lb></lb>culi vt planum CFD, tunc <expan abbr="tantũdem">tantundem</expan> detrahitur de grauitatione in <lb></lb>planum quantùm de motu in eodem plano; </s>
					<s id="N1CFD1">ideſt vtrique ſubduplum, <lb></lb>ſi verò vt in plano ADC perpendiculum eſt ſubtriplum plani, detrahun­<lb></lb>tur de motu 2/3 &amp; de grauitatione 1/3, idem dico de aliis, quæ certè omnia <lb></lb>ex veris principiis phyſicis conſequi videntur, quò enim plus grauitat <lb></lb>mobile in planum, plùs ſuſtinetur; </s>
					<s id="N1CFDD">quò plùs ſuſtinetur, plùs impeditur il­<lb></lb>lius motus; </s>
					<s id="N1CFE3">ſed hoc repugnat communi Mechanicorum ſententiæ, qui <lb></lb>cenſent grauitationem in planum inclinatum eſſe ad grauitationem in <lb></lb>horizontale, vt Tangens eſt ad ſecantem, quæ ſit linea plani inclinati, <lb></lb>v.g. vt AB ad CD, quod certè omnes ſupponunt, ſed minimè <expan abbr="demon-ſtrãt">demon­<lb></lb>ſtrant</expan>, ſi quid video ſaltem phyſicè; </s>
					<s id="N1CFF5">nec enim illud nemonſtrant propriè ex <lb></lb>eo quòd pondus in extremitate libræ affixum habeat diuerſa momenta <lb></lb>iuxta rationem Tangentium ad ſecantes, v.g. in ſecunda figura Th.5. <lb></lb>pondus in D eſt ad pondus in C vt BA ad DA, quod veriſſimum eſt, &amp; <lb></lb>ſuprà demonſtrauimus; </s>
					<s id="N1D003">quippe hoc pertinet ad rationem momenti, non <lb></lb>verò grauitationis in planum; </s>
					<s id="N1D009">adde quod affixum eſt pondus vecti; </s>
					<s id="N1D00D">igi­<lb></lb>tur vectis ſuſtinet totum illius pondus; </s>
					<s id="N1D013">vtrùm verò ſi pondus in plano <lb></lb>inclinato veluti in vecte moueatur pondus quo grauitat in planum ſit <lb></lb>ad pondus quo grauitat in horizontali vt Tangens ad ſecantem, certè <lb></lb>non demonſtrant; </s>
					<s id="N1D01D">attamen ita res prorſus ſe habet; quare fit. </s>
				</p>
				<p id="N1D021" type="main">
					<s id="N1D023"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D02F" type="main">
					<s id="N1D031"><emph type="italics"></emph>Grauitatio ponderis in planum inclinatum eſt ad grauitationem eiuſdem <lb></lb>in planum horizontale, vt Tangens, vel horizontalis ad ſecantem, vel incli­<lb></lb>natam,<emph.end type="italics"></emph.end> quod demonſtro. </s>
					<s id="N1D03D">Primò ſit planum inclinatum GD, pondus in-<pb pagenum="203" xlink:href="026/01/235.jpg"></pb>cubans F; </s>
					<s id="N1D046">dico grauitationem ponderis F in inclinatam GD eſſe ad gra­<lb></lb>uitationem in horizontalem CD vt CD ad GD; </s>
					<s id="N1D04C">quia pondus F pellit <lb></lb>planum per lineam FE ſeu GB Tangentem; </s>
					<s id="N1D052">quia determinari non po­<lb></lb>teſt ſeu percuſſio, ſeu impreſſio ex alio capite quàm ex linea ducta à <lb></lb>centro grauitatis perpendiculariter in planum, vt demonſtrauimus <lb></lb>in Th. 120. l. 1. atqui libræ extremitas G initio deſcendit per Tangen­<lb></lb>tem GB, id eſt per minimum arcum, qui ferè concurrit cum Tangente; </s>
					<s id="N1D060"><lb></lb>ſed ideò deſcendit in AB, quia pellitur deorſum à pondere; </s>
					<s id="N1D065">igitur men­<lb></lb>ſura grauitationis eſt deſcenſus libræ, ſed libra faciliùs deſcendit ex A <lb></lb>deorſum quàm ex G in proportione AD ad CD vel GD ad CD; </s>
					<s id="N1D06D">igitur <lb></lb>grauitatio ponderis in A eſt ad grauitationem eiuſdem in G, vt GD ad <lb></lb>CD; quia rationes cauſarum ſunt eædem cum rationibus effectuum. </s>
				</p>
				<p id="N1D075" type="main">
					<s id="N1D077">Præterea ſit planum inclinatum GD, ſit IF parallela GD; </s>
					<s id="N1D07B">ſint IK, I <lb></lb>M &amp; quadrans KFR; </s>
					<s id="N1D081">punctum I ſit centrum libræ immobile; </s>
					<s id="N1D085">certè ſi ſit <lb></lb>alterum brachium libræ æquale IF inſtructum æquali pondere F, erit æ­<lb></lb>quilibrium; ſed pondus illud in F eſt ad idem in R, vt IM ad IF, ſeu vt <lb></lb>CD ad GD, quod erat dem. </s>
				</p>
				<p id="N1D08F" type="main">
					<s id="N1D091"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D09D" type="main">
					<s id="N1D09F">Obſeruabis poſſe facilè ex dictis explicari diuerſas potentias applica­<lb></lb>tas ponderi F in eodem plano GD, primò ſi accipiatur IHF parallela <lb></lb>GH cum centro immobili I pondus retinebitur, ſi potentia in I ſit ad <lb></lb>globum vt GC ad GD, vt demonſtratum eſt; ſi verò pellat potentia per <lb></lb>lineam IF, globus deſcendet, vt patet. </s>
				</p>
				<p id="N1D0AB" type="main">
					<s id="N1D0AD">Hinc ſecundò ſuſtinens MF totum pondus F ſuſtinet, patet, quia ſi­<lb></lb>ue planum inclinatum pondus ipſum tangat, ſiue perpendiculare, totum <lb></lb>ſuſtinet pondus; ſubſtracto enim plano pondus immobile manet, adde <lb></lb>quod non poteſt pondus F ſuſtineri in brachio IM, niſi æquale pondus <lb></lb>ex æquali brachio oppoſito pendeat. </s>
				</p>
				<p id="N1D0B9" type="main">
					<s id="N1D0BB">Tertiò ex puncto T lineâ TFE non poteſt ſuſtineri pondus licèt po­<lb></lb>tentia in T eſſet infinita, quia ex TE deſcendet in TV, patet; idem <lb></lb>dico de omnibus aliis lineis ductis ab F ad aliquod punctum inter <lb></lb>TM. </s>
				</p>
				<p id="N1D0C5" type="main">
					<s id="N1D0C7">Quartò ex puncto X linea XF ſuſtinebitur pondus dum potentia ap­<lb></lb>plicetur in X, maior quidem potentia applicata in I, ſed minor applica­<lb></lb>ta in M; </s>
					<s id="N1D0CF">nam potentia M eſt ad potentiam I vt IF ad MF; </s>
					<s id="N1D0D3">igitur poten­<lb></lb>tia X eſt ad potentiam M vt MF ad XF; ad potentiam verò I vt IF <lb></lb>ad XF. </s>
				</p>
				<p id="N1D0DC" type="main">
					<s id="N1D0DE">Quintò, cùm triangula IF M.HF 4. ſint proportionalia, potentia M <lb></lb>eſt ad potentiam I vt HF ad 4. F. </s>
				</p>
				<p id="N1D0E4" type="main">
					<s id="N1D0E6">Sextò, ſi applicetur potentia, vel in T pellendo per lineam TFE, quæ <lb></lb>cadit perpendiculariter in planum GD, vel ſi applicetur in A per lineam <lb></lb>AE trahendo, non poterit retineri globus, quæcunque tandem poten­<lb></lb>tia applicetur; </s>
					<s id="N1D0F0">quia ſemper per GD globus rotari poterit nullo cor­<lb></lb>pore impediente; </s>
					<s id="N1D0F6">ſuppono enim tùm planum tùm globum eſſe perfectè <pb pagenum="204" xlink:href="026/01/236.jpg"></pb>politum, quod tamen nobis deeſſe certum eſt ad experimentum, ſuppo­<lb></lb>no nullam eſſe partium compreſſionem, qua vna pars in aliam quaſi pe­<lb></lb>netret; </s>
					<s id="N1D103">ſi enim totus locus datur ad deſcenſum; </s>
					<s id="N1D107">certè non eſt vlla ratio <lb></lb>propter quam non deſcendat; </s>
					<s id="N1D10D">nec dicas affigi plano GD ab ipſa vi ex­<lb></lb>teriùs affigente; </s>
					<s id="N1D113">quia nullo modo impeditur motus, per datam lineam, <lb></lb>niſi vel aliquod corpus opponatur, vel alius impetus detrahat ab eadem <lb></lb>linea; atqui nihil horum prorsùs eſt in hoc caſu. </s>
				</p>
				<p id="N1D11B" type="main">
					<s id="N1D11D">Si potentia applicetur in N per lineam NF, maior eſſe debet quàm in <lb></lb>I, ſed minor quàm in A; </s>
					<s id="N1D123">eſt autem ad potentiam in I vt IF ad NF; </s>
					<s id="N1D127"><lb></lb>quippe reſiſtit planum GD huic potentiæ in N, non tamen reſiſtit in I; </s>
					<s id="N1D12C"><lb></lb>igitur illa maior eſſe debet, quod autem potentia in N ſit ad potentiam <lb></lb>in I, vt IF ad NF (poſito ſcilicet quod vtraque pondus E ſuſtineat) plùs <lb></lb>quàm certum eſt; </s>
					<s id="N1D135">quia cùm pondus poſſit tantùm moueri per EG ſeu per <lb></lb>lineam FI potentia NF trahit per FN; </s>
					<s id="N1D13B">igitur potentia in N ſuſtinens <lb></lb>pondus F eſt ad potentiam in I ſuſtinentem idem pondus, vt IF ad NF; <lb></lb>ſimiliter potentia in K ſuſtinens idem pondus F eſt ad potentiam in I vt <lb></lb>IF ad ZF, nam IZ eſt perpendicularis in KF, donec tandem potentia <lb></lb>ſit in A applicata per AF in quam IF cadit perpendiculariter, igitur po­<lb></lb>tentia in A debet eſſe infinita. </s>
				</p>
				<p id="N1D149" type="main">
					<s id="N1D14B">Octauò, ſi pellatur pondus F per omnes lineas contentas ſiniſtrorſum <lb></lb>inter FT &amp; FA deorſum faciliùs cadet; </s>
					<s id="N1D151">ſi verò trahatur per lineas con­<lb></lb>tentas inter TF &amp; FA dextrorſum, etiam deorſum cadit; </s>
					<s id="N1D157">quia perinde <lb></lb>eſt ſiue trahatur per lineam IF, ſiue pellatur æquali niſu per lineam VF <lb></lb>quæ concurrit cum FI; </s>
					<s id="N1D15F">&amp; perinde eſt ſiue pellatur per IF, ſiue trahatur <lb></lb>per FV; idem dictum ſit de omnibus aliis lineis, quæ per centrum F <lb></lb>hinc inde ducuntur. </s>
				</p>
				<p id="N1D167" type="main">
					<s id="N1D169">Vnum eſt, quod deſiderari videtur ex quo reliqua ferè omnia depen­<lb></lb>dent, quomodo ſcilicet potentia in N trahens per FN ſit ad potentiam <lb></lb>in I trahentem per FI vt FI eſt ad FN, quod ſic breuiter demonſtro: </s>
					<s id="N1D171"><lb></lb> ſit horizontalis BD, &amp; triangulum ECD; ex centro D ducatur arcus <lb></lb>BE, qui ſit v.g. 30.grad. </s>
					<s id="N1D17A">vt CE ſit ſubdupla ED; </s>
					<s id="N1D17E">certè potentia in B <lb></lb>eſt ad potentiam in E per EC vt BD, vel ED ad CD; </s>
					<s id="N1D184">ſed potentia in E <lb></lb>per EA Tangentem eſt æqualis potentiæ in B; </s>
					<s id="N1D18A">ſit autem planum EA, &amp; <lb></lb>connectatur AC; </s>
					<s id="N1D190">triangula AEC &amp; ECD ſunt proportionalia; </s>
					<s id="N1D194">igitur <lb></lb>ſit AC verticalis, EC horizontalis, &amp; AE inclinata; </s>
					<s id="N1D19A">ſit potentia in A <lb></lb>per AE trahens pondus E; </s>
					<s id="N1D1A0">ſit potentia C trahens per CE; </s>
					<s id="N1D1A4">dico quod <lb></lb>impeditur tractio toto angulo AEC, ſicut ante impediebatur grauitatio <lb></lb>toto angulo AEC; </s>
					<s id="N1D1AC">igitur vtrobique eſt æquale impedimentum; </s>
					<s id="N1D1B0">ſed in <lb></lb>primo caſu ratione impedimenti ita ſe habet potentia in E per EA ad <lb></lb>potentiam in E per EC, vt ED ad CD, vel vt EA ad EC; igitur in ſe­<lb></lb>cundo in quo eſt idem impedimentum potentia in A per EA eſt ad po­<lb></lb>tentiam in C per EC, vt ipſa inclinata AE ad EC. </s>
				</p>
				<p id="N1D1BD" type="main">
					<s id="N1D1BF">Nonò denique obſeruabis, egregium eſſe apud Merſennum tractatum <lb></lb>authore doctiſſimo Roberuallo ſuper hac tota re, in quo certè Geome-<pb pagenum="205" xlink:href="026/01/237.jpg"></pb>tria nihil deſiderare poteſt; </s>
					<s id="N1D1CA">licèt phyſica fortè aliquid deſiderare poſſit; <lb></lb>adde quod implicatior illa figura infinitis ferè contexta lineis, quam ha­<lb></lb>bet, equidem erudito Geometræ faciet ſatis, non tamen rudiori Tyroni, <lb></lb>qui vix in hoc labyrintho tutum ſe eſſe putabit. </s>
				</p>
				<p id="N1D1D4" type="main">
					<s id="N1D1D6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D1E2" type="main">
					<s id="N1D1E4"><emph type="italics"></emph>Si globus incumbat<emph.end type="italics"></emph.end> <emph type="italics"></emph>plano inclinato rotatur neceſſariò deorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1D1F3">ſit enim <lb></lb>globus F in plano ED; </s>
					<s id="N1D1F9">ducatur FH perpendicularis deorſum; </s>
					<s id="N1D1FD">hæc eſt <lb></lb>linea directionis centri grauitatis, vt conſtat; </s>
					<s id="N1D203">igitur cùm non ſuſtinea­<lb></lb>tur in prædicta linea, nec enim terminatur ad punctum contactus G, cer­<lb></lb>tè debet rotari; </s>
					<s id="N1D20B">adde quod non eſt in æquilibrio, vt patet, ratio autem <lb></lb>inæqualitatis eſt vt GF ad FN, nec vlla eſt difficultas; igitur duplici <lb></lb>quaſi motu deſcendet in prædicto plano ille globus, ſcilicet motu centri <lb></lb>propter inclinationem plani, &amp; motu orbis, tùm quia non eſt in æqui­<lb></lb>librio, tùm quia in linea directionis FH non ſuſtinetur à plano. </s>
				</p>
				<p id="N1D217" type="main">
					<s id="N1D219"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D225" type="main">
					<s id="N1D227"><emph type="italics"></emph>Si corpus aliquod incumbat<emph.end type="italics"></emph.end> <emph type="italics"></emph>plano inclinato, ſique linea directionis <lb></lb>centri grauitatis ſecet ipſum planum intra baſim corpus repit quidem in <lb></lb>prædicto plano ſed non rotatur, ſi verò cadat extra baſim rotatur, non repit<emph.end type="italics"></emph.end>; </s>
					<s id="N1D23A"><lb></lb>ſit enim planum inclinatum BC, cui incubet cubus DL, cuius cen­<lb></lb>trum grauitatis ſit I; </s>
					<s id="N1D241">ducatur RG perpendicularis deorſum per cen­<lb></lb>trum grauitatis I cadit in punctum G intra baſim BG; </s>
					<s id="N1D247">igitur non ro­<lb></lb>tabitur, ſed repet; </s>
					<s id="N1D24D">quia ſi ſuſtinetur in G remoto ſenſim plano BC; <lb></lb>haud dubiè portio GD non præponderat portioni GL, vt patet ex <lb></lb>libra. </s>
				</p>
				<p id="N1D255" type="main">
					<s id="N1D257">Sit quoque parallelipedum EK, centrum grauitatis N, perpendicu­<lb></lb>laris ducta per centrum HNM cadit intra baſim; </s>
					<s id="N1D25D">igitur non rotabi­<lb></lb>tur, quia ſubmoto plano BC non ſuſtinetur quidem in M, ſed minimè <lb></lb>inclinabitur dextrorſum; igitur non rotabitur. </s>
					<s id="N1D265">Si verò cadat extra ba­<lb></lb>ſim haud dubiè rotabitur, ſit enim planum inclinatum AC, cui in­<lb></lb>cumbat parallelipedum FN, cuius centrum grauitatis ſit L; </s>
					<s id="N1D26D">ducatur L <lb></lb>perpendicularis, cadit in E extra baſim FD; </s>
					<s id="N1D273">certè latus DN inclinabi­<lb></lb>tur deorſum; igitur rotabitur, quia eodem modo ſe habet, quo ſe ha­<lb></lb>beret, ſi ſubmoto plano ſuſtineretur in linea DX, ſed trapezus DX <lb></lb>PN triangulo FXD præponderat per regulas libræ, de quibus ſuo <lb></lb>loco. </s>
				</p>
				<p id="N1D27F" type="main">
					<s id="N1D281">Obſeruabis autem primò ſciri poſſe data plani inclinatione &amp; baſi <lb></lb>parallelipedi maximam illius altitudinem, qua poſita non rotetur; </s>
					<s id="N1D287"><lb></lb>ſecus verò poſita quacunque alia maiore; </s>
					<s id="N1D28C">ſit enim planum AC, ba­<lb></lb>ſis parallelipedi FD; </s>
					<s id="N1D292">erigantur FO, DN perpendiculares in <pb pagenum="206" xlink:href="026/01/238.jpg"></pb>AC; </s>
					<s id="N1D29B">tùm erigatur perpendicularis DX parallela AB; </s>
					<s id="N1D29F">connectantur R <lb></lb>M: dico FX eſſe maximam altitudinem, vt conſtat ex dictis. </s>
				</p>
				<p id="N1D2A5" type="main">
					<s id="N1D2A7">Secundò, quotieſcunque rectangulum, ita eſt ſitum, vt eius <lb></lb>diagonalis ſit perpendicularis; </s>
					<s id="N1D2AD">dico eſſe in perfecto æquilibrio; </s>
					<s id="N1D2B1"><lb></lb>ſit enim rectangulum BE, cuius diagonalis BE perpendicula­<lb></lb>riter cadit in horizontalem AC; </s>
					<s id="N1D2B8">certè erit in æqualibrio; </s>
					<s id="N1D2BC">ſit enim <lb></lb>diuiſum per lineam BE ita vt FH vel KI ſit libra quæ ſuſtineatur in ful­<lb></lb>cro BG; ſitque totum pondus trianguli BED appenſum brachio GH, <lb></lb>&amp; aliud BET appenſum brachio æquali GF, erit perfectum æquili­<lb></lb>brium per regulas libræ, ſed duo triangula eodem modo ſe habent <lb></lb>conjuncta, quo ſe haberent ſeparata &amp; appenſa, vt patet. </s>
				</p>
				<p id="N1D2CA" type="main">
					<s id="N1D2CC">Tertiò, omnia rectangula proportionalia in eodem æquilibrio rema­<lb></lb>nerent v.g. rectangulum BG cum rectangulo BE, idem dico de Rhom­<lb></lb>bo, Rhomboide, &amp;c. </s>
				</p>
				<p id="N1D2D5" type="main">
					<s id="N1D2D7">Quartò, inde etiam cognoſcitur in qua proportione minuatur pondus. </s>
					<s id="N1D2DA"><lb></lb>v. g. ſit enim cylindrus AE horizontalis, ſuſtineaturque in A immo­<lb></lb>biliter, itemque in E; </s>
					<s id="N1D2E5">certè qui ſuſtinet in E æqualiter ſuſtinet; </s>
					<s id="N1D2E9">at verò <lb></lb>ſi attollatur in AD; </s>
					<s id="N1D2EF">certè potentia quæ in D ſuſtinet, eſt ad potentiam <lb></lb>quæ ſuſtinet in E, vt AF ad AE, quia pondus grauitaret in D &amp; in E in <lb></lb>eadem ratione per Th. 16. ſed potentia ſuſtinens adæquat ponderis ra­<lb></lb>tionem, ſuſtinens inquam, per DH; </s>
					<s id="N1D2F9">nam reuerà ſuſtinens per DF æqua­<lb></lb>lis eſſe debet potentiæ in E: </s>
					<s id="N1D2FF">idem dico ſi attollatur in AP, nam potentia <lb></lb>trahens in P, per CP, eſt ad potentiam in E, vt QA ad AP, vel AE; <lb></lb>igitur pondus in D eſt ad pondus in P vt FA ad QA. </s>
				</p>
				<p id="N1D307" type="main">
					<s id="N1D309">Quintò, hinc ſi duo ferant parallelipedum in ſitu inclinato v.g.vt AD, <lb></lb>ferunt inæqualiter, ſcilicet in ratione AD FA, itemque ſi ferant in ſitu <lb></lb>inclinato AP, vel AC, donec tandem AE attollatur in B, nihil amplius <lb></lb>ſuſtinet potentia in B, &amp; potentia in A totum ſuſtinet. </s>
				</p>
				<p id="N1D312" type="main">
					<s id="N1D314">Sextò, hinc cùm attollitur cylindrus continuò minùs ſentitur pondus <lb></lb>&amp; faciliùs attollitur; ſic qui attollunt pontes illos verſatiles, initio maxi­<lb></lb>mo niſu, &amp; modico ſub finem trahunt. </s>
				</p>
				<p id="N1D31C" type="main">
					<s id="N1D31E">Septimò obſeruabis, ſi circa centrum immobile A attollatur cylindrus <lb></lb>AE fune BE, potentia poſita in B, vel fune EO, potentia poſita in O; </s>
					<s id="N1D324"><lb></lb>hæc deber eſſe minor quàm poſita in B, vt autem cognoſcatur propor­<lb></lb>tio, fiat angulus PAE æqualis angulo OEB; </s>
					<s id="N1D32B">ducatur PQ; </s>
					<s id="N1D32F">dico poten­<lb></lb>tiam in O eſſe ad potentiam B, vt AQ ad AP, quia ſi anguli OEB &amp; <lb></lb>PAQ ſunt æquales etiam anguli APQ &amp; AEB ſunt æquales; igitur <lb></lb>perinde eſt ſiue trahatur PA circa A per lineam PQ, ſiue trahatur EA <lb></lb>circa A per lineam EB. </s>
					<s id="N1D33C">Idem dictum ſit de aliis lincis. </s>
				</p>
				<p id="N1D33F" type="main">
					<s id="N1D341">Octauò ſi attollendum ſit rectangulum non quidem circa axem; </s>
					<s id="N1D345">ſed <lb></lb>circa angulum immobilem, etiam decreſcit proportio ponderis, ſit enim <lb></lb>v.g. <expan abbr="quadratũ">quadratum</expan> ACFD, ſitque AD horizontalis, AI perpendicularis, duca­<lb></lb>tur diagonalis AF, attollatur circa punctum A, ita vt transferatur in AG, <lb></lb>ducatur GB perpendicularis: </s>
					<s id="N1D355">dico potentiam in G eſſe ad potentiam in <lb></lb>in A, vt AB ad AD; quippe res eodem modo ſe habet, ac ſi AF aſcenderet <pb pagenum="207" xlink:href="026/01/239.jpg"></pb>per arcum FM, donec vbi AF traducta ſit in AM, tunc enim nulla erit <lb></lb>potentia in M propter æquilibrium. </s>
				</p>
				<p id="N1D362" type="main">
					<s id="N1D364">Nonò, hinc initio decreſcit in maiori proportione ratione præpon­<lb></lb>derantiæ; </s>
					<s id="N1D36A">quia poſita baſi KN, angulus KAN eſt omnium maximus; at <lb></lb>verò decreſcit in minori proportione initio ratione ſegmenti horizon­<lb></lb>talis AD, in quam cadit perpendicularis. </s>
				</p>
				<p id="N1D372" type="main">
					<s id="N1D374">Decimò, ſi ſit rectangulum oblongum horizontale vt AE diffici­<lb></lb>liùs attolletur; </s>
					<s id="N1D37A">quia quadratum AF figuræ prioris debet tantùm attolli <lb></lb>per arcum FM, vt ſtatuatur in æquilibro; </s>
					<s id="N1D380">at verò rectangulum AE fi­<lb></lb>guræ huius attolli debet per arcum EC longè maiorem; </s>
					<s id="N1D386">igitur difficiliùs: <lb></lb>porrò potentia in D eſt ad potentiam in F vt AG ad AF, vt conſtat ex <lb></lb>dictis. </s>
				</p>
				<p id="N1D38E" type="main">
					<s id="N1D390">Vndecimò, denique, ſi ſit rectangulum oblongum, ſed verticale vt <lb></lb>HK longè faciliùs attolletur, quia diagonalis HK debet tantùm percur­<lb></lb>rere arcum KM vt ſtatuatur in æquilibrio; </s>
					<s id="N1D398">igitur minorem, igitur longè <lb></lb>faciliùs; porrò hæc omnia omnibus experimentis conſentiunt, &amp; ex <lb></lb>principiis facillimis demonſtrantur. </s>
					<s id="N1D3A0">Hæc paulò fuſiùs proſequutus ſum, <lb></lb>quia pertinent ad rationem plani inclinati. </s>
				</p>
				<p id="N1D3A5" type="main">
					<s id="N1D3A7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D3B3" type="main">
					<s id="N1D3B5"><emph type="italics"></emph>In plano inclinato acceleratur motus in eadem proportione qua acceleratur <lb></lb>in perpendiculari<emph.end type="italics"></emph.end>; </s>
					<s id="N1D3C0">ſit enim planum inclinatum AC, perpendicularis A <lb></lb>E, in qua primo tempore ſenſibili percurrat AD; </s>
					<s id="N1D3C6">ſecundò DE; </s>
					<s id="N1D3CA">certè dato <lb></lb>etiam tempore licèt maiore percurret AB; </s>
					<s id="N1D3D0">igitur alio æquali percurret <lb></lb>CB; </s>
					<s id="N1D3D6">nam vt ſe habet AE ad AG; </s>
					<s id="N1D3DA">ita ſe habet AD ad AB, &amp; DE ad BC; <lb></lb>quæ omnia ſunt certa. </s>
				</p>
				<p id="N1D3E0" type="main">
					<s id="N1D3E2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D3EE" type="main">
					<s id="N1D3F0"><emph type="italics"></emph>Hinc æqualis ineſt velocitas mobili decurſa AC, inclinata &amp; decurſa AE <lb></lb>perpendiculari,<emph.end type="italics"></emph.end> probatur, motus per AC eſt ad motum per AE, vt AE, ad <lb></lb>AC per Th.6.igitur motus per AC eſt tardior; </s>
					<s id="N1D3FD">ſed motu tardiore minùs <lb></lb>ſpatium conficitur æquali tempore in ca proportione, in qua motus eſt <lb></lb>tardior; </s>
					<s id="N1D405">ſed proportio velocitatis eſt vt AC ad AE: </s>
					<s id="N1D409">atqui quâ propor­<lb></lb>tione motus eſt tardior alio, maius ſpatium decurri debet, vt motu acce­<lb></lb>lerato per minora crementa acquiratur velocitas alteri æqualis; </s>
					<s id="N1D411">igitur <lb></lb>eò ſpatium debet eſſe maius, quò motus erit tardior; </s>
					<s id="N1D417">igitur debet percur­<lb></lb>ri AC in inclinata, &amp; AE in perpendiculari, vt ſit æqualis velocitas; </s>
					<s id="N1D41D"><lb></lb>ſit autem v.g. AC dupla AE, certè motus per AC eſt ſubduplus motus <lb></lb>pes AE; </s>
					<s id="N1D426">ducatur EB perpendicularis, certè AB eſt ſubdupla AE; </s>
					<s id="N1D42A">igitur <lb></lb>eo tempore, quo percurret AE, percurret tantùm AB ſubduplum ſcili­<lb></lb>cet motu ſubduplo; </s>
					<s id="N1D432">igitur tempore æquali BC triplam AB; </s>
					<s id="N1D436">ſed tem­<lb></lb>poribus æqualibus acquiruntur æqualia velocitatis momenta; </s>
					<s id="N1D43C">igitur ve­<lb></lb>locitas in C eſt dupla illius, quæ erat in B; </s>
					<s id="N1D442">ſed quæ eſt in E eſt dupla il­<lb></lb>lius, quæ eſt in B; igitur quæ eſt in E eſt æqualis illi, quæ eſt in C. </s>
					<s id="N1D449">Adde <lb></lb>quod in ea proportione in qua motus eſt tardior, ſpatium eſt maius, vt <lb></lb>æqualis velocitas acquiratur; </s>
					<s id="N1D451">igitur ſi quælibet pars ſpatij motum auget <pb pagenum="208" xlink:href="026/01/240.jpg"></pb>minùs quidem qua proportione motus eſt tardior, &amp; ſi ſpatium AC ma­<lb></lb>jus eſt ſpatio AE in ca proportione in qua motus per AE eſt velocior; </s>
					<s id="N1D45C"><lb></lb>pauciores partes ſpatij AE augent motum, ſed plùs ſingulæ, &amp; plures <lb></lb>ſpatij AC augent motum, ſed minùs ſingulæ; </s>
					<s id="N1D463">ſed cum ſint plures in ea­<lb></lb>dem proportione, in qua minùs augent; certè plures quarum ſingulæ mi­<lb></lb>nùs augent, ſimul ſumptæ æqualiter augent, v.g. ſint AC 4. partes, &amp; AE <lb></lb>2. ſingulæ AE augeant motum vt 4. &amp; ſingulæ AC vt 2. quia in ca pro­<lb></lb>portione minùs augent in qua 2. ſunt ad 4. certè 2. ſimul ſumptæ augent <lb></lb>motum vt 8. &amp; 4. ſimul ſumptæ etiam vt 8. quæ dicta ſunt in gratiam <lb></lb>Geometrarum, ſed meliùs adhuc ex dictis patebit. </s>
				</p>
				<p id="N1D475" type="main">
					<s id="N1D477"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D483" type="main">
					<s id="N1D485"><emph type="italics"></emph>Hinc aqualis eſſet ictus ab eodem mobili poſt motum per AE. AF. AC. <lb></lb>AG.<emph.end type="italics"></emph.end> quia eſſet acquiſitus æqualis impetus; igitur eſſet æqualis ictus, <lb></lb>quod certè mirabile eſt. </s>
				</p>
				<p id="N1D492" type="main">
					<s id="N1D494"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D4A0" type="main">
					<s id="N1D4A2"><emph type="italics"></emph>Hinc poteſt determinari ſpatij quæcunque petita proportio ad ſpatium da­<lb></lb>tum<emph.end type="italics"></emph.end>; </s>
					<s id="N1D4AD">v. g. ſit ictus inflictus à mobili decurſa perpendiculari AE: </s>
					<s id="N1D4B5">vis æ­<lb></lb>qualem ictum ſed confecto ſpatio duplo; </s>
					<s id="N1D4BB">accipe AC duplam AE: vis æ­<lb></lb>qualem ictum ſed confecto ſpatio triplo, accipe AG triplam AE. </s>
				</p>
				<p id="N1D4C2" type="main">
					<s id="N1D4C4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D4D0" type="main">
					<s id="N1D4D2"><emph type="italics"></emph>Tempora quibus percurruntur ſpatia planorum ſunt vt planorum longitu­<lb></lb>dines,<emph.end type="italics"></emph.end> v.g.tempus quo percurritur planum inclinatum AC eſt ad tempus <lb></lb>quo percurritur perpendicularis AE, vt AC ad AE; </s>
					<s id="N1D4DF">probatur, cùm enim <lb></lb>mobile in C &amp; in E habeat æqualem impetum ſeu velocitatem per Th. <lb></lb>20. certè cùm motus in AC ſit ſubduplus v.g. motus in AE, eſt enim <lb></lb>vt AE ad AC per Th.6. igitur cum ſubduplo motu æquali tempore ac­<lb></lb>quiritur ſubduplus impetus; </s>
					<s id="N1D4EE">igitur tempore duplo æqualis impetus; </s>
					<s id="N1D4F2">at­<lb></lb>qui tempus motus per AC eſt ad tempus motus per AE vt AC ad AE, <lb></lb>ideſt duplum; </s>
					<s id="N1D4FA">adde quod ſi æqualis impetus eſt in C &amp; in E; </s>
					<s id="N1D4FE">igitur æqua­<lb></lb>lis in D &amp; in B, ſed AB eſt ad BC vt AD ad DE; </s>
					<s id="N1D504">igitur ſi creſcit impe­<lb></lb>tus per partes ſubduplas in AC, neceſſariò creſcit per partes duplas in <lb></lb>ſpatio, atque in tempore; </s>
					<s id="N1D50C">cùm enim motus ſit ſubduplus, tarditas eſt ſub­<lb></lb>dupla; </s>
					<s id="N1D512">igitur acquiritur in AC ſpatium AB ſubduplum AE eo tempore, <lb></lb>quo percurritur AE, ſi enim accipiantur æqualia tempora, ſpatia ſunt vt <lb></lb>motus; </s>
					<s id="N1D51A">ſed motus per AC eſt ſubduplus; </s>
					<s id="N1D51E">igitur ſpatium AB eſt ſubdu­<lb></lb>plum AE; </s>
					<s id="N1D524">ſed tempore æquali conficit BC triplum AB, igitur tota AC <lb></lb>eſt dupla AE; </s>
					<s id="N1D52A">ſed percurritur tempore duplo; </s>
					<s id="N1D52E">igitur tempora ſunt vt <lb></lb><expan abbr="lõgitudines">longitudines</expan> planorum; </s>
					<s id="N1D537">ſed clariùs, &amp; breuiùs illud demonſtro; </s>
					<s id="N1D53B">In ea pro­<lb></lb>portione erit maius tempus per AC quàm per AE, in qua minor eſt <lb></lb>motus per AC quàm per AE; </s>
					<s id="N1D543">ſi enim motus per AF eſſet ad motum per <lb></lb>AE vt AF ad AE, certè æquali tempore AF &amp; AE percurrerentur; </s>
					<s id="N1D549">igitur <lb></lb>qua proportione motus per AF eſt minor, tempus eſt maius; </s>
					<s id="N1D54F"><expan abbr="tantũdem">tantundem</expan> <lb></lb>enim additur tempori, quantum detrahitur motui; igitur tempora ſunt <pb pagenum="209" xlink:href="026/01/241.jpg"></pb>vt lineæ. </s>
					<s id="N1D55D">Hinc acquiritur velocitas æqualis, vt dictum eſt Th. 20. quia <lb></lb>ſi tantùm addit tempus per AF ſupra tempus per AE, quantum addit <lb></lb>motus per AE ſupra motum per AF, haud dubiè eſt æqualitas. </s>
				</p>
				<p id="N1D564" type="main">
					<s id="N1D566"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D572" type="main">
					<s id="N1D574"><emph type="italics"></emph>Hinc poteſt determinari longitudo plani, quæ dato tempore percurratur,<emph.end type="italics"></emph.end> v. <lb></lb>g. perpendicularis 3. pedum percurritur 30tʹ. </s>
					<s id="N1D581">igitur ſi aſſumas planum <lb></lb>inclinatum 6. pedum, percurretur 1″. </s>
					<s id="N1D586">ſi 12. 2′. </s>
					<s id="N1D589">ſi 24. 4″. </s>
					<s id="N1D58C">atque ita dein­<lb></lb>ceps; </s>
					<s id="N1D591">hinc poſſet dari planum inclinatum quod tantùm 100. annis per­<lb></lb>curretur, ſcilicet ſi longitudo plani aſſumpti ſit æque multiplex longitu­<lb></lb>dinis 12. pedum atque 100. anni vnius ſecundi; quod facilè eſt, imò da­<lb></lb>to plano cuiuſcunque longitudinis, poteſt dari tempus quodcunque quo <lb></lb>percurratur, de quo infrà. </s>
				</p>
				<p id="N1D59D" type="main">
					<s id="N1D59F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D5AB" type="main">
					<s id="N1D5AD"><emph type="italics"></emph>Determinari poteſt quantum ſpatium conficiat mobile in plano inclinato; <lb></lb>dum conficit perpendicularem<emph.end type="italics"></emph.end>; </s>
					<s id="N1D5B8">ſit enim perpendiculum AE, inclinata AC; </s>
					<s id="N1D5BC"><lb></lb>ducatus, EB perpendicularis in AC; </s>
					<s id="N1D5C1">dico quod eodem tempore percur­<lb></lb>ret AE &amp; AB, quod demonſtro; </s>
					<s id="N1D5C7">quia triangula EAB, EAC ſunt pro­<lb></lb>portionalia: </s>
					<s id="N1D5CD">igitur AB eſt ad AE vt AE ad AC; </s>
					<s id="N1D5D1">igitur motus in AB <lb></lb>eſt ad motum in DE vt AB ad AE; </s>
					<s id="N1D5D7">igitur ſi tempora aſſumantur æqua­<lb></lb>lia ſpatia erunt vt motus, vt patet, id eſt motu ſubduplo acquiritur ſpa­<lb></lb>tium ſubduplum: </s>
					<s id="N1D5DF">nec alia eſſe poteſt regula tarditatis, igitur ſpatia <lb></lb>erunt vt AB ad AE, id eſt in ratione motuum; </s>
					<s id="N1D5E5">licèt enim motus veloci­<lb></lb>tas creſcat, attamen ſi accipiatur velocitas compoſita ex ſubdupla maxi­<lb></lb>mæ &amp; minimæ, percurretur AE motu æquabili æquali tempore; ſed <lb></lb>compoſita ex ſubdupla maximæ &amp; minimæ per AB habet <expan abbr="eãdem">eandem</expan> ra­<lb></lb>tionem ad priorem compoſitam, quàm motus per AB ad motum per AE. <lb></lb>&amp; hic quam habet AB ad AE. </s>
					<s id="N1D5F8">Sed hæc ſunt clara. </s>
				</p>
				<p id="N1D5FB" type="main">
					<s id="N1D5FD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D609" type="main">
					<s id="N1D60B"><emph type="italics"></emph>Hinc æquali tempore deſcendit per inclinatam BE,<emph.end type="italics"></emph.end> ſit enim inclinata <lb></lb>AG, perpendicularis AE; ſit quoque FC perpendicularis in AG, &amp; FD, <lb></lb>in CF. </s>
					<s id="N1D619">Dico quòd eo tempore, quo conficit CD perpendicularem <lb></lb>conficit CF inclinatam per Th.24. eſt enim DF perpendicularis in IC. <lb></lb>ſicut FC in AG, ſed CD eſt æqualis AF, vt patet. </s>
				</p>
				<p id="N1D620" type="main">
					<s id="N1D622"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D62E" type="main">
					<s id="N1D630"><emph type="italics"></emph>Hinc cognito ſpatio quod percurritur in plano inclinato, cognoſcitur ſpa­<lb></lb>tium quod conficeretur tempore æquali in perpendiculari,<emph.end type="italics"></emph.end> ſit enim tempus <lb></lb>quo percurritur AC; ducatur ex C perpendicularis CF. </s>
					<s id="N1D63E">Dico confici AF <lb></lb>in perpendiculari eo tempore, quo percurritur AC: </s>
					<s id="N1D644">vel ſit inclinata C <lb></lb>F, ducatur ex F perpendicularis FD; percurretur CD eo tempore, quo <lb></lb>percurritur CF, quæ probantur per Th.24.&amp; 25. </s>
				</p>
				<pb pagenum="210" xlink:href="026/01/242.jpg"></pb>
				<p id="N1D650" type="main">
					<s id="N1D652"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D65E" type="main">
					<s id="N1D660"><emph type="italics"></emph>Hinc per omnes chordas inſcriptas circulo ad alteram extremitatem, <lb></lb>diametri perpendicularis terminatas deſcendit mobile æquali tempore<emph.end type="italics"></emph.end>; </s>
					<s id="N1D66B">a ſit <lb></lb>enim circulus centro B; </s>
					<s id="N1D671">ſit diameter AE perpendicularis deorſum; </s>
					<s id="N1D675">du­<lb></lb>catur AC inclinata, tùm CE; </s>
					<s id="N1D67B">deſcendat haud dubiè æquali tempore <lb></lb>per AC.CE.AE. per Th.24.25.26. idem dico de omnibus aliis AD.D <lb></lb>E. AG.GE.AF.FE; </s>
					<s id="N1D683">eſt enim eadem omnibus ratio; hinc non poteſt da­<lb></lb>ri planum tam paruæ longitudinis, quo non poſſit dari minus, quod dato <lb></lb>tempore percurratur. </s>
					<s id="N1D68B">Hæc eſt illa propoſitio toties à Galileo enuncia­<lb></lb>ta; </s>
					<s id="N1D691">cum enim motus per BE ſit ad motum per GE vt GE ad BE, &amp; tem­<lb></lb>pus per BE ad tempus per GE vt BE ad GE; </s>
					<s id="N1D697">cumque ſit vt BE ad GE <lb></lb>rita GE ad AE; </s>
					<s id="N1D69D">certè motus per AE eſt ad motum per GE vt AE ad G <lb></lb>E; </s>
					<s id="N1D6A3">igitur tantùm addit AE ſupra GE ratione ſpatij, quantum ratione <lb></lb>motus: igitur tempore æquali per AE. &amp; GE fiet motus, idem dico de <lb></lb>aliis chordis. </s>
				</p>
				<p id="N1D6AB" type="main">
					<s id="N1D6AD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D6B9" type="main">
					<s id="N1D6BB"><emph type="italics"></emph>Hinc datis duabus inclinatis æqualibus poteſt determinari ratio tempo­<lb></lb>rum, in quibus percurruntur<emph.end type="italics"></emph.end>; </s>
					<s id="N1D6C6">ſint enim AG.AH æquales, ſed diuerſæ incli­<lb></lb>nationis; haud dubiè cum æquali tempore AG. AF percurrantur per <lb></lb>Th. 27. tempora quibus percurruntur AGAH erunt vt tempora quibus <lb></lb>percurruntur AF AH, &amp; hæc vt tempora quibus percurruntur AE. A <lb></lb>K, &amp; hæc vt radices quadratæ illorum ſpatiorum AE. AK, cum autem <lb></lb>ſpatia ſint vt quadrata temporum, vel in duplicata ratione, ſi inter AE <lb></lb>&amp; AK ſit media proportionalis AN. v. g. tempus quo percurretur AE <lb></lb>erit ad tempus, quo percurretur AK vt AE ad AN, vel AN ad AK. </s>
				</p>
				<p id="N1D6DE" type="main">
					<s id="N1D6E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D6EC" type="main">
					<s id="N1D6EE"><emph type="italics"></emph>Hinc cognito tempore quo percurritur data portio linea cognoſci potest <lb></lb>tempus, quo percurritur aliud ſpatium vel alia portio,<emph.end type="italics"></emph.end> v. g. cognoſco tem­<lb></lb>pus quo percurritur AK, &amp; volo cognoſcere tempus quo percurritur K <lb></lb>E, conſequenti motu ex AK, ſcio tempus quo percurritur ſola AE, quod <lb></lb>eſt ad tempus quo percurritur AK vt AE ad AN per Th. 28. igitur <lb></lb>tempus quo percurritur KE conſequenti motu ex AK eſt ad tempus, <lb></lb>quo percurritur AK vt EN ad NA, vel vt NK, ad NA. </s>
				</p>
				<p id="N1D706" type="main">
					<s id="N1D708"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1D714" type="main">
					<s id="N1D716"><emph type="italics"></emph>Hinc in planis inæqualibus tùm in longitudine, tùns in inclinatione, <lb></lb>poteſt ſciri ratio temporum, quibus percurruntur<emph.end type="italics"></emph.end>; </s>
					<s id="N1D721">ſint enim AC AR duo pla­<lb></lb>na; </s>
					<s id="N1D727">ſit autem AE perpendicularis indefinita; </s>
					<s id="N1D72B">diuidatur AC bifariam <lb></lb>in V ducta perpendiculari VB; </s>
					<s id="N1D731">ex B fiat circulus, ſecabit puncta <lb></lb>ACE; </s>
					<s id="N1D737">ſecat etiam AR; </s>
					<s id="N1D73B">in D igitur AC, &amp; AD percurruntur æquali <lb></lb>tempore per Th. 27. ſimiliter fiat circulus ART eodem modos certè A <lb></lb>R &amp; AT percurruntur æqualibus temporibus per Th. 27. igitur tempus, <lb></lb>quo per curritur AR, vel AD eſt ad tempus, quo percurritur AR vt <lb></lb>tempus, quo percurritur AE ad tempus, quo percurritur AT; </s>
					<s id="N1D747">ſed hæc <pb pagenum="211" xlink:href="026/01/243.jpg"></pb>ſunt vt radices AEAT, id eſt tempus quo percurritur AE eſt ad tem­<lb></lb>pus, quo percurritur AT, vt AE ad mediam proportionalem inter AE <lb></lb>AT, vel vt AD ad mediam proportionalem inter AD AR; quippe AD <lb></lb>eſt ad AR vt AE ad AT. </s>
				</p>
				<p id="N1D756" type="main">
					<s id="N1D758">Galileus verò demonſtrat rationem iſtorum temporum eſſe compoſi­<lb></lb>tam ex ratione longitudinem planorum &amp; ex ratione ſubduplicata al­<lb></lb>titudinum eorumdem permutatim accepta: pro quo obſerua à Galileo <lb></lb>rationem duplicatam appellari duplam, &amp; ſubduplicatam appellari ſub­<lb></lb>duplam. </s>
				</p>
				<p id="N1D764" type="main">
					<s id="N1D766">Obſeruabis denique plurima ex his colligi poſſe præſertim ex Th. 27. <lb></lb>quæ quia ſunt purè geometrica, certè phyſicę minimè competunt; aliqua <lb></lb>tamen omittere non poſſum. </s>
				</p>
				<p id="N1D76E" type="main">
					<s id="N1D770">Primò, ſi ſint duo plana inæqualia ad angulum rectum, qui ſuſtinea­<lb></lb>tur ab horizontali, determinari poſſunt tempora deſcenſuum ſit enim <lb></lb>triangulum orthogonium ABE, ita vt AE ſit horizontalis; </s>
					<s id="N1D778">ducatur B <lb></lb>G indefinita perpendicularis in baſim AE; </s>
					<s id="N1D77E">tùm FA perpendicularis in <lb></lb>AB; </s>
					<s id="N1D784">tùm FC perpendicularis in BE; </s>
					<s id="N1D788">tùm denique GE in BE; </s>
					<s id="N1D78C">dico BA <lb></lb>BFBC percurri temporibus æqualibus, item BE, BG, EG, etiam æqua­<lb></lb>libus; </s>
					<s id="N1D794">igitur tempus, quo percurritur BA eſt ad tempus quo percurri­<lb></lb>tur BE, vt tempus, quo percurritur BF ad tempus quo percurritur BG; <lb></lb>hæc porrò ſunt in ſubduplicata ratione BFBG vel BC, &amp; BE. </s>
				</p>
				<p id="N1D79D" type="main">
					<s id="N1D79F">Secundò, ſi planum ſuſtinens angulum rectum non ſit parallelum <lb></lb>horizonti 6. res ſimiliter determinari poterit; </s>
					<s id="N1D7A5">ſit enim triangulum or­<lb></lb>thogonium ABC ex B, ducatur perpendicularis deorſum indefinitè BF, <lb></lb>tùm EA in AB, tùm DC in CB, tùm EH parallela DC, tùm GC in A <lb></lb>C; </s>
					<s id="N1D7AF">denique AG parallela BF; dico quod BABEHE AE percurren­<lb></lb>tur æqualibus temporibus item BCCDBD. </s>
				</p>
				<p id="N1D7B5" type="main">
					<s id="N1D7B7">Tertiò, ſiue deſcendat ex B in C per lineam perpendicularem BC, <lb></lb>ſiue ex A per inclinatam AC, eodem modo deſcendet ſiue per CD, ſiue <lb></lb>per CE; ratio eſt clara, quia acquirit æqualem velocitatem ſiue ex A ſi­<lb></lb>ue ex B deſcendat pet Th. 20. erit autem tempus per CE ad tempus per <lb></lb>CD, vt CE ad CD per Th.23.&amp; motus per CE ad motum per CD, vt <lb></lb>CD ad CE per Th.6. poſito initio motus in C. </s>
				</p>
				<p id="N1D7C6" type="main">
					<s id="N1D7C8">Quartò, præuio motu ex A vel ex B ad C poteſt inueniri inclinata, <lb></lb>per quam mobile pergat moueri motu ſcilicet naturaliter accelerato, ita <lb></lb>vt æquali tempore illam conficiat; </s>
					<s id="N1D7D0">ſi enim BC conficiet dato tempore; </s>
					<s id="N1D7D4"><lb></lb>igitur CF triplum CB conficiet tempore æquali; </s>
					<s id="N1D7D9">ſit autem planum ho­<lb></lb>rizontale EDK ad quod ex C ducendum ſit planum inclinatum, quod <lb></lb>eodem tempore percurratur, quo CF, diuidatur CF bifariam in H, &amp; ex <lb></lb>puncto H fiat arcus CK, ducaturque CK: </s>
					<s id="N1D7E3">Dico CF &amp; CK æquali tem­<lb></lb>pore confici per Th. 27. modò ex quiete C procedat motus: </s>
					<s id="N1D7E9">ſimiliter aſ­<lb></lb>ſumi poteſt alia horizontalis LM ducto arcu LF ex centro H; </s>
					<s id="N1D7EF">nam CL <lb></lb>&amp; CF æquali tempore percurruntur; </s>
					<s id="N1D7F5">ſi verò præſupponatur motus præ­<lb></lb>uius ex A vel ex B, haud dubiè CK breuiori tempore percurretur, quàm <lb></lb>CF, idem dico de CL; </s>
					<s id="N1D7FD">alioqui CE &amp; CI eodem præuio motu ſuppo <pb pagenum="212" xlink:href="026/01/244.jpg"></pb>ſito æquali tempore percurrerentur, quod falſum eſt; </s>
					<s id="N1D806">nam ſit AC ad A <lb></lb>N vt AN ad AE; </s>
					<s id="N1D80C">ſitque BC ad BO vt BO ad BI; </s>
					<s id="N1D810">certè tempus, quo <lb></lb>percurritur BC eſt ad tempus, quo percurritur CI vt CB ad CO, &amp; <lb></lb>tempus quo percurritur BC eſt ad tempus quo percurritur CE vt BC ad <lb></lb>CN; </s>
					<s id="N1D81A">ſed CN eſt minor quàm CO, vt conſtat ex Geometria, quod bre­<lb></lb>uiter in tironum <expan abbr="gratiã">gratiam</expan> in terminis rationabilibus oſtendo, ſit planum <lb></lb>inclinatum AE 9. ſitque AE id eſt 9. ad AD. 6. vt AD ad AC 4. ex <lb></lb>centro C aſſumpta CH 3. ducatur arcus HB &amp; ex A ad prædictum ar­<lb></lb>cum Tangens AB, tùm ex BC G indefinitè &amp; ex E, EG perpendicularis <lb></lb>in EA; </s>
					<s id="N1D82C">haud dubiè triangula CGE, CAB ſunt proportionalia; </s>
					<s id="N1D830">igitur vt <lb></lb>CB;.ad CA. 4.ita CE 5. ad CG 6. 2/3; </s>
					<s id="N1D836">igitur tota BG eſt 9. 2/3; ſitque B <lb></lb>G ad BF, vt BF ad DC, quod vt fiat BG 9. 2/3 in BC 3. productum erit <lb></lb>29. igitur BF eſt Rad. </s>
					<s id="N1D83E">quad. </s>
					<s id="N1D841">29.igitur eſt maior 5. ſed ſi eſſet maior 5. C <lb></lb>M &amp; CD eſſent æquales; </s>
					<s id="N1D847">igitur CF eſt maior CD; </s>
					<s id="N1D84B">eſt enim BF ferè 3. <lb></lb>1/2 paulò minùs: </s>
					<s id="N1D851">vt autem reperiatur linea inclinata, quæ percurratur æ­<lb></lb>quali tempore cum BC ſuppoſito præuio motu per BC, aſſumatur CK <lb></lb>æqualis CB id eſt 3.partium, <expan abbr="fiatq́ue">fiatque</expan> vt AC ad AK, ita AK ad AN; </s>
					<s id="N1D85D">haud <lb></lb>dubiè percurret CN æquali tempore, quo BC; </s>
					<s id="N1D863">vt verò habeatur pun­<lb></lb>ctum in horizontali, ſit AF perpendicularis bifariam diuiſa in K, ſit K <lb></lb>F diuiſa in 4. partes æquales, quibus addatur FP 1/4 KFEK V dupla FA, <lb></lb>&amp; producatur in X; </s>
					<s id="N1D86D">ita vt EX ſit 1/4 EK: </s>
					<s id="N1D871">dico quod præuio motu ex A in <lb></lb>K, &amp; deinde deflexo per KX conficietur KX æquali tempore cum AK; </s>
					<s id="N1D877"><lb></lb>ſi enim caderet mobile ex V primo tempore percurreret VL, id eſt 1/4 V <lb></lb>K eo tempore, quo percurreret AK per Th.6. igitur ſecundo tempore <lb></lb>æquali LK, id eſt 3/4 VK; </s>
					<s id="N1D880">igitur tertio tempore æquali KX 5/4 VK; nam eo­<lb></lb>dem modo ſe habet in k ſiue deſcendat ex V, ſiue ex A per Th.20. </s>
				</p>
				<p id="N1D886" type="main">
					<s id="N1D888">Porrò vt habeatur in horizontali FS; </s>
					<s id="N1D88C">ſit FR æqualis KF; </s>
					<s id="N1D890">ſit FT æ­<lb></lb>qualis KR; </s>
					<s id="N1D896">ſit arcus TS ex k: </s>
					<s id="N1D89A">Dico quod ks eſt linea quæſita; </s>
					<s id="N1D89E">nam ſi ſit <lb></lb>vt BS ad BZ, ita BZ ad BK, kz erit æqualis KF, vel AK; </s>
					<s id="N1D8A4">ſed tempus <lb></lb>quo percurritur AK eſt ad tempus quo percurritur Dk vt BK ad AK <lb></lb>per Th.23.&amp; ad tempus, quo percurritur BS, vt Bk ad BZ, &amp; ad tem­<lb></lb>pus quo percurritur ks vt Bk ad kz; ergo Ak &amp; ks percurruntur æ­<lb></lb>quali tempore, ſi kz ſit æqualis KF, quod ſic breuiter demonſtro, cùm <lb></lb>figura apud Galileum deſideretur. </s>
					<s id="N1D8B2">ſint AFFE æquales; </s>
					<s id="N1D8B6">ducatur AE <lb></lb>quæ transferatur iu FG, ſitque GI æqualis AG, ſic tota AG mihi repræ­<lb></lb>ſentat totam BS ſuperioris figuræ, vt conſtat; </s>
					<s id="N1D8BE">ſit autem AG ad AH vt A <lb></lb>H ad AI: </s>
					<s id="N1D8C4">Dico GH eſſe æqualem AF; </s>
					<s id="N1D8C8">ſit enim quadratum HD mediæ <lb></lb>proportionalis: </s>
					<s id="N1D8CE">Dico eſſe æquale rectangulo IC, dùm AC ſit æqualis A <lb></lb>G; </s>
					<s id="N1D8D4">igitur quadratum PR cuius latus eſt æquale FG, ſeu AE continet <lb></lb>duo quadrata RDSN; </s>
					<s id="N1D8DA">ergo GH eſt æqualis VN; igitur GH quod erat <lb></lb>demonſtrandum. </s>
				</p>
				<p id="N1D8E0" type="main">
					<s id="N1D8E2">Quintò, hinc nunquam ks vel kx poteſt eſſe tripla Ak donec tan­<lb></lb>dem perueniatur ad perpendiculum kH; </s>
					<s id="N1D8E8">nam ſecundo tempore percur­<lb></lb>ritur kH triplum Ak, ſi primo percurritur Ak; </s>
					<s id="N1D8EE">nunquam etiam ks vel <lb></lb>vlla alia inclinata poteſt eſſe dupla tantùm Ak; </s>
					<s id="N1D8F4">ſed ſemper eſt maior, do-<pb pagenum="213" xlink:href="026/01/245.jpg"></pb>nec tandem perueniat ad horizontalem KY, quæ eſt dupla AK, quia in <lb></lb>horizontali non acceleratur motus; </s>
					<s id="N1D8FF">igitur cum impetu acquiſito in deſ­<lb></lb>cenſu AK, conficiet motu æquabili KY duplum AK per Th.42.l.3. poſito <lb></lb>quòd non deſtruatur; atque ex his ſatis facilè intelligentur, quæcumque <lb></lb>habes apud Galileum in dialog.3.à propoſitione 3.ad 23. </s>
				</p>
				<p id="N1D909" type="main">
					<s id="N1D90B">Sextò non probat Galileus, ſed tantùm ſupponit mobile ad <expan abbr="eãdem">eandem</expan> <expan abbr="alti-tudinẽ">alti­<lb></lb>tudinem</expan> aſcendere poſſe motu reflexo ex qua deſcendit, quod examinabi­<lb></lb>mus lib. <expan abbr="ſequẽti">ſequenti</expan>, hinc non laborabimus in <expan abbr="examinãdis">examinandis</expan> prop.  24.25.26.27. </s>
				</p>
				<p id="N1D923" type="main">
					<s id="N1D925">Septimò, cognito tempore, quo percurrit mobile perpendiculum EC <lb></lb>quod ſit diameter circuli; </s>
					<s id="N1D92B">ſciri poteſt quo tempore percurrat duas chor­<lb></lb>das ſimul EGGC; </s>
					<s id="N1D931">ſit enim Tangens EF, ſitque vt FG ad FD, ita FD ad <lb></lb>FC; </s>
					<s id="N1D937">cum EG &amp; EC deſcendat æquali tempore per Th.27. cum in G ſit <lb></lb>idem motus, ſiue ex E, ſiue ex F deſcendat per Th.20. certè ſi deſcendit <lb></lb>per EG dato tempore, quod ſit vt EG, deſcendit per GC tempore, quod <lb></lb>eſt vt GD; igitur tempus, quo deſcendit per EC eſt ad tempus, quo deſ­<lb></lb>cendit per EGC, vt EG ad EGD. </s>
				</p>
				<p id="N1D943" type="main">
					<s id="N1D945">Obſeruabis autem GF eſſe ad EF vt EF ad FC; </s>
					<s id="N1D949">igitur FD eſt media <lb></lb>inter FC GF, &amp; eſt æqualis FE, igitur anguli FDE.FED æquales; </s>
					<s id="N1D94F">ſed FD <lb></lb>E eſt æqualis duobus DCE.DEC, &amp; FEG, eſt æqualis DCE; igitur duo G <lb></lb>DE DEC ſunt æquales. </s>
				</p>
				<p id="N1D957" type="main">
					<s id="N1D959">Octauò, ſi accipiantur æquales horizontalis, &amp; perpendicularis, v.g. <lb></lb>BA AC, ducaturque BC: </s>
					<s id="N1D960">Dico nullum duci poſſe planum inclinatum à <lb></lb>puncto B ad perpendiculum AEM, quod breuiori tempore percurratur, <lb></lb>quàm BC, nec intra angulum vt BR, nec extra vt BM; </s>
					<s id="N1D968">ſit enim vt BC ad <lb></lb>BI ita BI ad BH, eſt autem BI æqualis BA, igitur ſi BA, ſit 4.BC eſt v.g. <lb></lb>32. &amp; BH radix q.8.igitur HI eſt ferè I paulò plùs; igitur cum BH percur­<lb></lb>ratur æquali tempore cum AC, eſt tempus, quo percurritur BH ad tem­<lb></lb>pus quo percurritur HC vt BH ad HI. </s>
				</p>
				<p id="N1D976" type="main">
					<s id="N1D978">Sit autem BR dupla AR, ſitque perpendicularis AK in BR; </s>
					<s id="N1D97C">certè KR <lb></lb>eſt ſubquadrupla BR; </s>
					<s id="N1D982">igitur percurritur BL æqualis KR eo tempore quo <lb></lb>percurritur AR; </s>
					<s id="N1D988">igitur BL ſit ad BV vt BV ad BR; </s>
					<s id="N1D98C">igitur temporibus æ­<lb></lb>qualibus percurruntur BL LR; </s>
					<s id="N1D992">igitur ſi tempus quo percurritur BL ſit vt <lb></lb>BH, tempus quo percurretur LR erit etiam vt BH; </s>
					<s id="N1D998">igitur totum tempus <lb></lb>quo percurritur tota BR erit vt tota BE, ſed tempus quo percurritur tota <lb></lb>BC eſt tantum vt BI quę eſt minor BC; </s>
					<s id="N1D9A0">igitur BC breuiori tempore per­<lb></lb>curritur quàm BR; ſit <expan abbr="etiã">etiam</expan> vt BP ad BX ita BX ad BM, ſi BO eſt 4. OP 2. <lb></lb>certè BP eſt rad.q. </s>
					<s id="N1D9AC">12.id eſt ferè 3.1/2 paulò minùs, BM verò eſt dupla BA <lb></lb>vel BO; </s>
					<s id="N1D9B2">igitur eſt 8. ducatur ergo 8. in 4. 1/3 productum erit 28. cuius radix <lb></lb>eſt ferè 5.1/3 paulò minùs; </s>
					<s id="N1D9B8">igitur BX eſt 5.1/3 paulò minùs; </s>
					<s id="N1D9BC">cum autem BH <lb></lb>ſit 2.q.8.eſt ferè 2.5/6, paulò minùs; </s>
					<s id="N1D9C2">igitur ſit vt BP 3.1/2 ad BX 5.1/3, ita BH <lb></lb>2.5/6 ad aliam; </s>
					<s id="N1D9C8">certè erit 144. id eſt 4.(26/63), licèt minùs acceptum ſit; </s>
					<s id="N1D9CC">igitur <lb></lb>126.eſt maior BI, quæ eſt tantùm 4; igitur BE breuiori tempore percur­<lb></lb>ritur, quàm BM. </s>
				</p>
				<p id="N1D9D4" type="main">
					<s id="N1D9D6">Nonò, per duas chordas quadrantis deſcendit breuiori tempore mo­<lb></lb>bile, quàm per alteram tantùm inferiorem ſcilicet ſit enim tantùm <pb pagenum="214" xlink:href="026/01/246.jpg"></pb>quadrans ABG in quo ſint duæ chordæ GC, CB: </s>
					<s id="N1D9E1">Dico quòd per vtram­<lb></lb>que ex G breuiori tempore deſcendit, quàm per inferiorem CB; </s>
					<s id="N1D9E7">quia <lb></lb>per CB, &amp; GB æquali tempore deſcendit per Th.27.ſed per GCB bre­<lb></lb>uiori tempore deſcendit, quàm per GB; </s>
					<s id="N1D9EF">ſit enim GD perpendicularis <lb></lb>parallela AB; </s>
					<s id="N1D9F5">ſit ED perpendicularis in CG, &amp; per 3. puncta GCD <lb></lb>ducatur circulus: </s>
					<s id="N1D9FB">his poſitis, GH &amp; GC eodem tempore percurrentur, <lb></lb>&amp; in C idem erit motus, ſiue ex G per GE, ſiue ex E per EC deſcen­<lb></lb>dat mobile per Th.27.&amp; 20. ſit autem EB ad EK vt EK ad EC, ſitque <lb></lb>BE v.g, dupla BE vel BA: </s>
					<s id="N1DA05">dico EK eſſe æqualem BG; </s>
					<s id="N1DA09">eſt autem BH <lb></lb>maior BC vel AB, vel HG minor CK; </s>
					<s id="N1DA0F">ſit etiam GH ad GI, ita GI <lb></lb>ad GB: </s>
					<s id="N1DA15">dico tempus, quo deſcendit per GCB eſſe ad tempus quo de­<lb></lb>ſcendit per GB vt GCK ad compoſitam ex GC, HI; </s>
					<s id="N1DA1B">ſed hæc eſt ma­<lb></lb>ior illa, vt patet ex Geometria, &amp; analytica; </s>
					<s id="N1DA21">igitur breuiori tempore de­<lb></lb>ſcendit per GCB, quàm per GB; ſed de hoc aliàs. </s>
				</p>
				<p id="N1DA27" type="main">
					<s id="N1DA29">Sit enim EB 8. dupla ſcilicet AB; </s>
					<s id="N1DA2D">ſit autem EE ſubdupla EB ad <lb></lb>EK vt EK ad EB; </s>
					<s id="N1DA33">aſſumatur GE, ſitque tempus, quo continetur GC. <lb></lb>vt GC, &amp; quo conficitur BC vt CK; </s>
					<s id="N1DA39">igitur quo conficitur GCB vt <lb></lb>GCK: </s>
					<s id="N1DA3F">ſimiliter ſit ſecunda linea GB, ſitque tempus, quo percurritur <lb></lb>GH vt GC, vel NO æqualis GC, ſitque vt GH ad GN, ita GN ad <lb></lb>GB certè ſi GH decurratur tempore GH, AB decurretur tempore <lb></lb>HN; </s>
					<s id="N1DA49">ſed HN maior eſt MB, vel CG, vt conſtat ex analytica; </s>
					<s id="N1DA4D">adde quod <lb></lb>in figura prima ſit GI ad GM vt GM ad GB; </s>
					<s id="N1DA53">certè ſi tempore GI <lb></lb>percurratur GI, percurretur GB tempore GM; </s>
					<s id="N1DA59">eſt autem GM æqua­<lb></lb>lis AB, vel EC; </s>
					<s id="N1DA5F">ſimiliter ſit EC ad EK vt EK ad EB, ſi percurratur <lb></lb>EC tempore EC, percurretur EB tempore EK; </s>
					<s id="N1DA65">ſed GC percurretur <lb></lb>tempore GC ſed GCK minor eſt GIM; </s>
					<s id="N1DA6B">ſit enim GM. 4. EK R. <expan abbr="q.">que</expan> <lb></lb>32. id eſt, 5 7/8 paulò minùs, quibus ſi ſubtrahas CE 4. &amp; ſubſtituas CG <lb></lb>2. paulò plùs habebis 3 7/8; igitur GCK minor eſt GIM. </s>
					<s id="N1DA77">Ex his habes <lb></lb>omnes Galilei propoſitiones de motu in planis inclinatis numero 38. in <lb></lb>quo ſtudio, vt verum fatear, maximam ſibi laudem peperit; </s>
					<s id="N1DA7F">in quo ta­<lb></lb>men opere duo deſiderari videntur, <expan abbr="alterũ">alterum</expan> à Philoſophis, quod ita phyſi­<lb></lb>cæ partes omnes neglexerit, vt ferè vni Geometriæ ſatisfaceret; alterum <lb></lb>ab Geometris quod Geometriam equidem accuratè tractarit. </s>
					<s id="N1DA8D">Sed minùs <lb></lb>ad captum Tyronum: atque hæc de his ſint ſatis, vt tandem noſtrorum <lb></lb>Theorematum ſeriem interruptam repetamus. </s>
				</p>
				<p id="N1DA95" type="main">
					<s id="N1DA97"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DAA3" type="main">
					<s id="N1DAA5"><emph type="italics"></emph>Ex dictis ſequitur pondus centum librarum poſſe habere tantùm grauitatio­<lb></lb>nem vnius libræ<emph.end type="italics"></emph.end>; </s>
					<s id="N1DAB0">ſit enim planum inclinatum centuplum horizontalis, id <lb></lb>eſt, ſecans centupla Tangentis; haud dubiè grauitatio in prædictum pla­<lb></lb>num erit tantùm ſubcentupla per Th.16. </s>
				</p>
				<p id="N1DAB9" type="main">
					<s id="N1DABB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DAC7" type="main">
					<s id="N1DAC9"><emph type="italics"></emph>Ex duobus ferentibus idem parallelipedum in ſitu inclinato poteſt alter fer­<lb></lb>re tantùm vnam libram, licèt pendat centum libras<emph.end type="italics"></emph.end>; </s>
					<s id="N1DAD4">ſit enim ita inclina-<pb pagenum="215" xlink:href="026/01/247.jpg"></pb>tum, vt linea inclinationis ſit centupla horizontalis oppoſitæ; certè qui <lb></lb>ſuſtinet in altera extremitate eleuata (1/100) tantùm ſuſtinet ponderis par­<lb></lb>tem per Th. 18. alius verò ſuſtinet in altera extremitate, quæ deorſum <lb></lb>eſt (93/100). </s>
				</p>
				<p id="N1DAE3" type="main">
					<s id="N1DAE5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DAF1" type="main">
					<s id="N1DAF3"><emph type="italics"></emph>Qui poteſt tantùm datum pondus ſurſum attollere per lineam verticalem, <lb></lb>centuplum per inclinatum planum ad <expan abbr="eãdem">eandem</expan> altitudinem attollet<emph.end type="italics"></emph.end>; </s>
					<s id="N1DB02">ſi enim ſit <lb></lb>inclinata ad perpendiculum in ratione centupla; haud dubiè qui attollit <lb></lb>datum pondus per ipſum perpendiculum ſine viribus auctis per inclina­<lb></lb>tum planum, pondus centuplò maius attollet, quia potentia per inclina­<lb></lb>tam eſt ad potentiam per ipſum perpendiculum vel altitudo ad inclina­<lb></lb>tam per Theor. 6. igitur ſi æqualis vtrobique applicetur potentia, pon­<lb></lb>dus centuplò maius attollet per inclinatam, ſeu pellendo, ſeu tra­<lb></lb>hendo. </s>
				</p>
				<p id="N1DB16" type="main">
					<s id="N1DB18"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DB24" type="main">
					<s id="N1DB26"><emph type="italics"></emph>Hinc ratio plani inclinati demonſtrat<emph.end type="italics"></emph.end> <emph type="italics"></emph>cochleæ vires.<emph.end type="italics"></emph.end> v.g. pellitur ſurſum <lb></lb>per DE inclinatam faciliùs quàm verticalem DH in ratione DE ad <lb></lb>DH, quæ ſi eſt tripla, eadem potentia quæ datum pondus attollit per <lb></lb>DH, triplò maius attollet per DE, vel ſi attollat per DA verticalem, <lb></lb>triplò maius attollet per ſpiras vel Helices DE EC, CF, &amp;c. </s>
					<s id="N1DB3E">vſque ad <lb></lb>A; hinc quò Helix erit inclinatior, potentia maius pondus illius operâ <lb></lb>attollet. </s>
				</p>
				<p id="N1DB45" type="main">
					<s id="N1DB47"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DB53" type="main">
					<s id="N1DB55"><emph type="italics"></emph>Hinc clarè vides compenſari longitudinem motus, ſpatij vel temporis, pon­<lb></lb>deris acceſſione,<emph.end type="italics"></emph.end> v.g. triplò maius pondus attollitur per DE quàm per <lb></lb>DH; </s>
					<s id="N1DB64">quia ſpatium DE eſt triplum DH; igitur motus triplus, ſcilicet in <lb></lb>duratione, (loquor enim de motu æquabili quo ſurſum corpus, vel tra­<lb></lb>hitur, vel continuò pellitur.) </s>
				</p>
				<p id="N1DB6C" type="main">
					<s id="N1DB6E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DB7A" type="main">
					<s id="N1DB7C"><emph type="italics"></emph>Hinc nullus mons eſſe poteſt quantumuis arduus, ad cuius apicem via faci­<lb></lb>li in modum cochleæ ſtrata pertingi non poſſit<emph.end type="italics"></emph.end>; &amp; quò plures erunt ſpiræ, eo <lb></lb>facilior erit &amp; minùs decliuis via. </s>
				</p>
				<p id="N1DB89" type="main">
					<s id="N1DB8B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DB97" type="main">
					<s id="N1DB99"><emph type="italics"></emph>Quando deſcendit mobile per multas ſpiras, ſeu volutas, poteſt determinari <lb></lb>altitudo perpendicularis, ex qua eodem tempore deſcenderet<emph.end type="italics"></emph.end>; </s>
					<s id="N1DBA4">ſit enim ſpira <lb></lb>ſeu cochlea AFCHD, &amp; perpendiculum AD; </s>
					<s id="N1DBAA">certè eodem tempore <lb></lb>deſcendit per AFC, quo deſcenderet per AG duplam AF; </s>
					<s id="N1DBB0">ſed eo tem­<lb></lb>pore, quo deſcendit per AF inclinatam, conficit AD per Th.27. quæ eſt <lb></lb>ad AF vt AF ad BA; </s>
					<s id="N1DBB8">ſit autem dupla: </s>
					<s id="N1DBBC">ſimiliter eodem tempore conficit <lb></lb>AFG vel AFG, quo conficit AE duplam AG; denique eo tempore, <lb></lb>quo conficit AF CHD, vel AGD, conficit duplam AE. </s>
				</p>
				<pb pagenum="216" xlink:href="026/01/248.jpg"></pb>
				<p id="N1DBC9" type="main">
					<s id="N1DBCB">Sic etiam eo tempore, quo in perpendiculo conficit AD conficit ſub­<lb></lb>duplam ſcilicet AF, ſed hæc ſunt clara. </s>
				</p>
				<p id="N1DBD0" type="main">
					<s id="N1DBD2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DBDE" type="main">
					<s id="N1DBE0"><emph type="italics"></emph>Quando proiicitur mobile per planum inclinatum ſurſum in ea proportione <lb></lb>proiicitur longiùs, quò inclinata ipſa longior eſt perpendiculari.<emph.end type="italics"></emph.end> v.g. ſi proii­<lb></lb>citur per BA in verticali, illa eadem <expan abbr="potẽtia">potentia</expan> quæ proiicit in A ex B, pro­<lb></lb>iiciet <expan abbr="quoq;">quoque</expan> ex F in A, ex M in A, atque ita deinceps ex ſingulis punctis <lb></lb>horizontalis BM; </s>
					<s id="N1DBFB">ratio eſt, quia in ea proportione deſtruitur impetus <lb></lb>per BA, in qua motus per AB deſcendit; </s>
					<s id="N1DC01">nam impetus innatus deor­<lb></lb>ſum quaſi trahit mobile graue; </s>
					<s id="N1DC07">impetus verò impreſſus ſurſum attollit; </s>
					<s id="N1DC0B"><lb></lb>igitur pugnant pro rata, vt ſæpè diximus in tertio libro, &amp; alibi: </s>
					<s id="N1DC10">ſimiliter <lb></lb>in inclinata FA impetus innatus quaſi reducit mobile deorſum dum <lb></lb>impreſſus violentus ſurſum promouet; </s>
					<s id="N1DC18">igitur ſi impetus innatus per AB, <lb></lb>&amp; per AT æqualem vim haberet, haud dubiè æquale ſpatium contine­<lb></lb>ret mobile projectum per BA &amp; FA; </s>
					<s id="N1DC20">nam eadem potentia cum æquali <lb></lb>reſiſtentia idem præſtat &amp; inæqualiter deſcendit per AB AF, &amp; motus <lb></lb>per AF eſt ad motum per AB, vt AB ad AF. v.g. ſubduplus; </s>
					<s id="N1DC2A">igitur re­<lb></lb>ſiſtentia per BA erit dupla reſiſtentiæ per FA; </s>
					<s id="N1DC30">igitur ſpatium per FA <lb></lb>erit duplum; </s>
					<s id="N1DC36">igitur ex F aſcendet in A, quo cum eo impetu ex B aſcendet <lb></lb>in A, ſuppoſita eadem potentia; </s>
					<s id="N1DC3C">idem etiam dicendum de aliis punctis <lb></lb>horizontalis BM: </s>
					<s id="N1DC42">præterea ille impetus ſufficit ad motum ſurſum per <lb></lb>FA, qui accipitur in deſcenſu AF, vt conſtat ex dictis; </s>
					<s id="N1DC48">itemque ſufficit <lb></lb>ad motum ſurſum per BA qui acquiritur in deſcenſu AB; ſed æqualis ve­<lb></lb>locitas, vel impetus acquiritur in vtroque deſcenſu AB AF per Th. 20. <lb></lb>igitur idem impetus ſufficit ad deſcenſum BA FA. </s>
				</p>
				<p id="N1DC52" type="main">
					<s id="N1DC54"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DC60" type="main">
					<s id="N1DC62"><emph type="italics"></emph>Hinc dicendum eſt impetum naturalem per inclinatam FA vel MA non <lb></lb>ſurſum intendi, ſeu creſcere<emph.end type="italics"></emph.end>; </s>
					<s id="N1DC6D">alioqui ex A mobile deſcenderet citiùs in F, <lb></lb>poſtquàm ex F proiectum eſſet in A, quàm ſi tantùm ex A in F demit­<lb></lb>teretur, quod eſt contra experientiam; adde quòd impetus naturalis ſur­<lb></lb>ſum non creſcit, vt iam ſæpè dictum eſt. </s>
				</p>
				<p id="N1DC77" type="main">
					<s id="N1DC79"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DC85" type="main">
					<s id="N1DC87"><emph type="italics"></emph>Destruitur aliquid impetus impreſſi in mobili per planum inclinatum.<emph.end type="italics"></emph.end><lb></lb>Probatur, quia tandem quieſcit mobile; </s>
					<s id="N1DC91">igitur ceſſat motus; </s>
					<s id="N1DC95">igitur &amp; im­<lb></lb>petus: </s>
					<s id="N1DC9B">nec dicas id fieri ab aëre, vel plani ſcabritie; </s>
					<s id="N1DC9F">nam, ſi hoc eſſet, <lb></lb>æquale ſpatium conficeret in FA &amp; LA; </s>
					<s id="N1DCA5">quippe æqualis portio plani <lb></lb>æqualiter reſiſtit; Idem dico de aëre; igitur deſtruitur impetus impreſ­<lb></lb>ſus ab impetu naturali. </s>
				</p>
				<p id="N1DCAD" type="main">
					<s id="N1DCAF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DCBB" type="main">
					<s id="N1DCBD"><emph type="italics"></emph>Destruitur tantùm pro rata, hoc eſt in ratione, quam habet perpendiculum <lb></lb>ad inclinatam.<emph.end type="italics"></emph.end> v.g. ſit perpendiculum FCA; </s>
					<s id="N1DCCA">haud dubiè ſi non deſtrue­<lb></lb>retur motus ſurſum cum eo gradu impetus, quo ex F aſcendit in C motu <lb></lb>retardato, aſcenderet in A motu æquabili, &amp; eodem tempore; </s>
					<s id="N1DCD2">igitur eo <pb pagenum="217" xlink:href="026/01/249.jpg"></pb>tempore deſtruitur totus impetus; </s>
					<s id="N1DCDB">ſi verò proiiciatur per LC; </s>
					<s id="N1DCDF">certè im­<lb></lb>petus totus non deſtruitur per LC, eo tempore, quo ex F aſcenderet in <lb></lb>C, ſed pro rata, id eſt in ratione FC ad LC, quæ ſit ſubdupla v.g. igitur <lb></lb>impetus deſtruitur tantùm ſubduplus; </s>
					<s id="N1DCEB">igitur eo tempore, quo ex F aſcen­<lb></lb>dit in C, ex L aſcendet in K, ita vt LM æquali FC addatur MK æqua­<lb></lb>lis EB; eſt autem EB ſubdupla CA vel EF. </s>
					<s id="N1DCF3">Similiter ſit perpendicu­<lb></lb>lum FG, &amp; inclinata HF tripla FG; </s>
					<s id="N1DCF9">aſſumatur FC æqualis FG, item­<lb></lb>que HO æqualis GF; </s>
					<s id="N1DCFF">certè eo tempore, quo perpendiculari detrahitur <lb></lb>totus impetus, detrahitur tantùm ſubtriplum per inclinatam HF; </s>
					<s id="N1DD05">igitur <lb></lb>aſſumatur ER ſubtripla EF; </s>
					<s id="N1DD0B">&amp; addatur OP æqualis FR: </s>
					<s id="N1DD0F">dico quod eo <lb></lb>tempore, quo ex G aſcendit in F, ex H aſcendit in P; </s>
					<s id="N1DD15">quippe aſcenderet <lb></lb>in O, ſi eo tempore totus impetus deſtrueretur, &amp; in S ſi nullus; </s>
					<s id="N1DD1B">igitur <lb></lb>in P, ſi ſubtriplus tantùm deſtruatur, deſtruitur porrò ſubtriplus, quia vis <lb></lb>impetus innati per FH eſt tantùm ſubtripla eiuſdem per FG; </s>
					<s id="N1DD23">atqui de­<lb></lb>ſtruitur tantùm ab impetu innato, quæ omnia certiſſimè conſtant; Ex <lb></lb>quo habes tempora eſſe vt lineas. </s>
				</p>
				<p id="N1DD2B" type="main">
					<s id="N1DD2D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DD39" type="main">
					<s id="N1DD3B"><emph type="italics"></emph>Hinc poteſt dici quo tempore conficiatur tota inclinata ſurſum ſcilicet eo <lb></lb>tempore quo inclinata deorſum percurritur.<emph.end type="italics"></emph.end> v.g, CL dupla CF percurritur <lb></lb>tempore duplo illius, quo percurritur CF; </s>
					<s id="N1DD48">igitur mobile proiectum ex <lb></lb>L in C percurrit LC eodem tempore aſcendendo, quo percurrit EL de­<lb></lb>ſcendendo; ſed percurrit EL deſcendendo eodem tempore, quo percur­<lb></lb>rit perpendicularem quadruplam CF, vt ſuprà diximus. </s>
				</p>
				<p id="N1DD52" type="main">
					<s id="N1DD54"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DD60" type="main">
					<s id="N1DD62"><emph type="italics"></emph>Hinc nunquam in inclinata ſurſum proiectum mobile acquirit duplum ſpa­<lb></lb>tium illius quod acquirit idem proiectum in verticali ſurſum,<emph.end type="italics"></emph.end> v. g. ex H pro­<lb></lb>iectum nunquam acquiret in HF duplum ſpatium GF, poſito quòd ex <lb></lb>G proiiciatur tantùm in F dato tempore, ſitque eadem potentia per HF. <lb></lb>Probatur, quia ſemper deſtruitur aliquid impetus iuxta proportionem <lb></lb>FG ad FH per Th.40. ſed ſi nullus deſtruitur impetus, duplum ſpatium <lb></lb>conficit; </s>
					<s id="N1DD7B">igitur ſi aliquid deſtruitur, duplum ſpatium non conficitur: po­<lb></lb>teſt tamen propiùs in infinitum ad duplum accedere. </s>
				</p>
				<p id="N1DD81" type="main">
					<s id="N1DD83"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DD8F" type="main">
					<s id="N1DD91"><emph type="italics"></emph>Hinc erecta perpendiculari<emph.end type="italics"></emph.end> FC, <emph type="italics"></emph>ductaque horizontali<emph.end type="italics"></emph.end> FL, <emph type="italics"></emph>productaque <lb></lb>in infinitum, ſi ex quolibet illius puncto eleuetur planum inclinatum termina­<lb></lb>tum ad<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>eadem potentia que ex<emph.end type="italics"></emph.end> F <emph type="italics"></emph>in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>mobile proiiciet, etiam ex quolibet <lb></lb>puncto deſignato in horizontali proiiciet in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>per planum inclinatum<emph.end type="italics"></emph.end>; quod <lb></lb>probatur per Th. 38. </s>
				</p>
				<p id="N1DDC6" type="main">
					<s id="N1DDC8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DDD4" type="main">
					<s id="N1DDD6"><emph type="italics"></emph>Ex his etiam probatur proiici ex<emph.end type="italics"></emph.end> L <emph type="italics"></emph>in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>ab ea potentia, quæ ex<emph.end type="italics"></emph.end> F <emph type="italics"></emph>proiicit in<emph.end type="italics"></emph.end><lb></lb>C; </s>
					<s id="N1DDF2">cum enim primo tempore proiiciat ex L in K (ſuppono enim LC <lb></lb>eſſe quadruplam KC) certè ſecundo conficit tantùm KC; </s>
					<s id="N1DDF8">eſt enim mo­<lb></lb>tus violentus ſurſum retardatus inuerſus motus deorſum accelerati; </s>
					<s id="N1DDFE">at-<pb pagenum="218" xlink:href="026/01/250.jpg"></pb>qui motu naturaliter accelerato ſi primo tempore conficit KC, ſecun­<lb></lb>do conficit KL triplum CK; igitur ſi motu retardato primo tempore <lb></lb>conficit LK, ſecundo conficit KC ſubtriplum LK. </s>
				</p>
				<p id="N1DE0C" type="main">
					<s id="N1DE0E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DE1A" type="main">
					<s id="N1DE1C"><emph type="italics"></emph>Si proiiciatur in horizontali motus per ſe eſt æqualis in ſpatio modico<emph.end type="italics"></emph.end>: </s>
					<s id="N1DE25">Pro­<lb></lb>batur, quia in nulla proportione deſtruitur, vt patet; </s>
					<s id="N1DE2B">dixi per ſe, quia re­<lb></lb>uera nullum eſt planum perfectè lęuigatum, nec etiam mobile: </s>
					<s id="N1DE31">vnde cum <lb></lb>aſperitas plani reſiſtat, inde maximè motus retardatur; dixi in ſpatio <lb></lb>modico, nam planum horizontale rectilineum longius, eſt planum incli­<lb></lb>natum, de quo infrà, vnde vt motus ſit æqualis, debet proiici in ſuperfi­<lb></lb>cie curua æqualiter diſtante à centro mundi. </s>
				</p>
				<p id="N1DE3D" type="main">
					<s id="N1DE3F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DE4B" type="main">
					<s id="N1DE4D"><emph type="italics"></emph>Si proiiciatur mobile deorſum per inclinatum planum, mouetur velociùs<emph.end type="italics"></emph.end> B; <lb></lb>certum eſt, &amp; acquirit maius ſpatium ſingulis temporibus iuxta ratio­<lb></lb>nem impetus accepti. </s>
					<s id="N1DE5A">v.g. ſit planum ABE, in quo primo dato tem­<lb></lb>pore mobile acquirat AB, ſitque impetus impreſſus æqualis împetui, <lb></lb>quem acquirit dum percurrit ſpatium AB; </s>
					<s id="N1DE64">haud dubiè primo tempore <lb></lb>ratione vtriuſque impetus percurrit AC, ſcilicet, duo ſpatia; </s>
					<s id="N1DE6A">ſecundo <lb></lb>CD, id eſt 4. ſpatia; </s>
					<s id="N1DE70">tertio DE, id eſt 6. ſpatia; atque ita deinceps: vn­<lb></lb>de vides proportionem arithmeticam, quæ naſcitur ex acceſſione quan­<lb></lb>tumuis modica noui impetus. </s>
				</p>
				<p id="N1DE78" type="main">
					<s id="N1DE7A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DE86" type="main">
					<s id="N1DE88"><emph type="italics"></emph>In plano inclinato non deſtruitur impetus impreſſus, quia non eſt frustrà<emph.end type="italics"></emph.end>; <lb></lb>igitur non deſtruitur per Sch. Th.152.lib.1. ſic diximus in Theoremate <lb></lb>68. l.4. in proiecto deorſum per lineam perpendicularem deorſum non <lb></lb>deſtrui quidquam impetus impreſſi, licèt deſtruatur in proiecto per in­<lb></lb>clinatam deorſum in libero medio, vt diximus in Th.67. lib.4. vide Th. <lb></lb>68.lib.4. </s>
				</p>
				<p id="N1DE9E" type="main">
					<s id="N1DEA0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DEAC" type="main">
					<s id="N1DEAE"><emph type="italics"></emph>Poteſt determinari quantus impetus imprimi debeat mobili per planum in­<lb></lb>clinatum, vt æquali velocitate moueatur quo mouetur in perpendiculari ſuæ <lb></lb>ſponte,<emph.end type="italics"></emph.end> hoc eſt vt æquali tempore æquale ſpatium vtrimque acquiratur, <lb></lb>aſſumpto ſcilicet ſpatio totali, quod toti motui competit, non verò eius <lb></lb>tantùm parte; debet enim aſſumi impetus iuxta proportionem differen­<lb></lb>tiæ ſpatij, quod acquiritur in perpendiculari, &amp; alterius ſpatij, quod ac­<lb></lb>quiritur in perpendiculari, &amp; alterius ſpatij, quod acquiritur in inclina­<lb></lb>ta. </s>
					<s id="N1DEC5">v.g. ſit planum inclinatum AH, perpendiculum verò AE; </s>
					<s id="N1DECB">ducatur <lb></lb>EB perpendicularis in AH, mobile percurrit AB in inclinata eo tem­<lb></lb>pore, quo percurrit AE in perpendiculo; </s>
					<s id="N1DED3">aſſumatur AC æqualis AE; </s>
					<s id="N1DED7"><lb></lb>ſi imprimatur impetus, qui ſit ad acquiſitum in ſpatio AB vt BC ad AB: </s>
					<s id="N1DEDC"><lb></lb>dico quod mobile eodem tempore percurret AE, &amp; AC, vt conſtat; </s>
					<s id="N1DEE1"><lb></lb>quia impetus in C eſt æqualis impetui in E; </s>
					<s id="N1DEE6">vt verò percurrat in incli­<lb></lb>nata AH æquale ſpatium AG, æquali tempore, quo percurrit AG; </s>
					<s id="N1DEEC">aſ-<pb pagenum="219" xlink:href="026/01/251.jpg"></pb>ſumatur AF æqualis AH, addaturque impetus, qui ſit ad acquiſitum in <lb></lb>H, vt GF ad FA, vel AH, &amp; habebitur intentum: </s>
					<s id="N1DEF7">dixi totum ſpatium re­<lb></lb>ſpondens ſcilicet toti motui; </s>
					<s id="N1DEFD">alioqui ſi pars tantùm accipiatur tùm ſpa­<lb></lb>tij, tùm motus, res procul dubio ſecus accidet; ſit enim impetus impreſ­<lb></lb>ſus vt BC ad AB. </s>
					<s id="N1DF06">Equidem primò tempore, quo in perpendiculari con­<lb></lb>citur AE, conficitur AC æqualis; </s>
					<s id="N1DF0C">at verò ſecundo, quo conficitur EG <lb></lb>triplum AE in perpendiculari, conficitur CI quadruplum AC, vel <lb></lb>AE; </s>
					<s id="N1DF14">igitur non ſunt æqualia ſpatia; ſed hæc ſunt ſatis facilia. </s>
				</p>
				<p id="N1DF18" type="main">
					<s id="N1DF1A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DF26" type="main">
					<s id="N1DF28"><emph type="italics"></emph>Si planum horizontale ſit perfectè læuigatum in vne tantùm illius puncto ſi­<lb></lb>ſtere poteſt mobile graue<emph.end type="italics"></emph.end>; </s>
					<s id="N1DF33">ſit enim globus terræ centro A ſemidiametro <lb></lb>AE; </s>
					<s id="N1DF39">ſitque planum horizontale FEGN læuigatiſſimum: dico quòd in <lb></lb>puncto contactus E quieſcet mobile. </s>
					<s id="N1DF3F">Probatur, quia ex omni alio puncto <lb></lb>mobile poteſt deſcendere; </s>
					<s id="N1DF45">ſit enim in G. v.g. haud dubiè GA maior eſt <lb></lb>AE; </s>
					<s id="N1DF4D">igitur GE planum eſt inclinatum, id eſt, E propiùs accedet ad cen­<lb></lb>trum terræ A; ſed per planum inclinatum mobile deſcendit per hyp. </s>
					<s id="N1DF53">1. <lb></lb>idem dico de omni alio plani puncto, excepto puncto E, ex quo non <lb></lb>poteſt moueri, niſi aſcendat, id eſt à centro A recedat; igitur in eo <lb></lb>quieſcet. </s>
				</p>
				<p id="N1DF5D" type="main">
					<s id="N1DF5F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DF6B" type="main">
					<s id="N1DF6D"><emph type="italics"></emph>Hinc in menſa lauigatiſſima globus vel eburneus, vel cryſtallinus vix vn­<lb></lb>quam ſistit, niſi in eius centro,<emph.end type="italics"></emph.end> quod multis experimentis comprobatum <lb></lb>eſt, &amp; ratio luce meridianâ clarior à rudioribus etiam primo ſtatim ob­<lb></lb>tutu cernitur. </s>
				</p>
				<p id="N1DF7B" type="main">
					<s id="N1DF7D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DF89" type="main">
					<s id="N1DF8B"><emph type="italics"></emph>Hinc ridiculum ſeu joculare paradoxon, quo ſcilicet dici poteſt duorum alter <lb></lb>in eodem plano aſcendere, alter deſcendere, licèt in <expan abbr="eãdem">eandem</expan> cœli plagam con­<lb></lb>uerſi ambulent<emph.end type="italics"></emph.end>; </s>
					<s id="N1DF9C">ſi enim alter ex G in E; </s>
					<s id="N1DFA0">alter verò ex E in F tenderet; </s>
					<s id="N1DFA4">hic <lb></lb>certè aſcenderet, quia recederet à terræ centro A; </s>
					<s id="N1DFAA">ille verò deſcende­<lb></lb>ret, quia ad centrum accederet; &amp; ſi in partes oppoſitas ambulent, in <lb></lb>hoc eodem plano vterque ſimul aſcendere, vel ſimul deſcendere poteſt. </s>
				</p>
				<p id="N1DFB2" type="main">
					<s id="N1DFB4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DFC0" type="main">
					<s id="N1DFC2"><emph type="italics"></emph>Eſt etiam aliud paradoxon, ſcilicet in eodem puncto E duo plana eadem li­<lb></lb>neâ contenta hinc inde aſcendere; </s>
					<s id="N1DFCA">vel duos montes altiſſimos in eadem recta <lb></lb>linea contineri; </s>
					<s id="N1DFD0">vel mediam vallem, &amp; gemines montes linea rectiſſima ſimul <lb></lb>connecti<emph.end type="italics"></emph.end>; hæc porrò ſunt ſatis facilia, &amp; vix ſupra vulgi captum. </s>
				</p>
				<p id="N1DFD9" type="main">
					<s id="N1DFDB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1DFE7" type="main">
					<s id="N1DFE9"><emph type="italics"></emph>Adde aliud paradoxon ſcilicet idem mobile per duo plana parallela inæ­<lb></lb>quali motu deſcendere.<emph.end type="italics"></emph.end> v.g. per plana XFB, VEA, nam VEA eſt per­<lb></lb>pendiculum; at verò XFB eſt horizontale, vt clarum eſt. </s>
				</p>
				<p id="N1DFF8" type="main">
					<s id="N1DFFA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E006" type="main">
					<s id="N1E008"><emph type="italics"></emph>Poteſt determinari motus proportio cuiuſlibet puncti aſſignati in plano EN<emph.end type="italics"></emph.end>; </s>
					<s id="N1E011"><pb pagenum="220" xlink:href="026/01/252.jpg"></pb>ſit enim punctum G; </s>
					<s id="N1E019">ducatur à centro A recta AGH; </s>
					<s id="N1E01D">haud dubiè eſt per­<lb></lb>pendicularis; </s>
					<s id="N1E023">ducatur IGK ſecans GH; ad angulos rectos; </s>
					<s id="N1E027">hæc eſt ho­<lb></lb>rizontalis, quæ ad hanc perpendicularem pertinet; </s>
					<s id="N1E02D">ducatur HI parallela <lb></lb>EG; </s>
					<s id="N1E033">hæc eſt inclinata, vt patet ex dictis; immò per ipſam deff. </s>
					<s id="N1E037">1. ſed mo­<lb></lb>tus in inclinata eſt vt ipſum perpendiculum ad inclinatam per Th. 6. <lb></lb>igitur motus per HI in ipſo puncto H, vel per GE in ipſo puncto G eſt <lb></lb>ad motum per HG, vt HG ad HI. </s>
				</p>
				<p id="N1E041" type="main">
					<s id="N1E043">Aliter ducatur HZ perpendicularis IH; </s>
					<s id="N1E047">dico motum in G vel ex G <lb></lb>initio eſſe ad motum per VE vel GL vt GH ad GZ; ſunt enim duo <lb></lb>triangula IGH, ZGH proportionalia. </s>
				</p>
				<p id="N1E04F" type="main">
					<s id="N1E051">Aliter ducatur LK parallela GG; </s>
					<s id="N1E055">triangula GKL, GHI ſunt propor­<lb></lb>tionalia; igitur motus per GE eſt ad motum per HG, vt LG ad LK. </s>
				</p>
				<p id="N1E05C" type="main">
					<s id="N1E05E">Aliter ducatur QL, triangula QLA, LGK ſunt proportionalia; </s>
					<s id="N1E062">igi­<lb></lb>tur motus per GE eſt ad motum per HG vt QL ad AL; igitur vt ſinus <lb></lb>rectus anguli QAL ad totum. </s>
					<s id="N1E06A">Idem dico de puncto O, &amp; omnibus alia <lb></lb>in quibus eſt eadem praxis. </s>
				</p>
				<p id="N1E06F" type="main">
					<s id="N1E071"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E07D" type="main">
					<s id="N1E07F"><emph type="italics"></emph>In ſingulis punctis plani EN eſt diuerſus motus<emph.end type="italics"></emph.end>; </s>
					<s id="N1E088">nam in puncto E nullus <lb></lb>eſt motus per Th. 50.atqui in puncto G eſt motus; </s>
					<s id="N1E08E">idem dico de puncto <lb></lb>O, atqui in puncto O eſt maior motus, quàm in G, ſcilicet initio, id eſt <lb></lb>velocior incipit motus in O, quàm in G; </s>
					<s id="N1E096">probatur quia in G eſt ad mo­<lb></lb>tum maximum qui fit in perpendiculari vt QL ad LA, &amp; in puncto O <lb></lb>vt YP ad PA, ſed YP eſt maior QL, vt conſtat; </s>
					<s id="N1E09E">igitur initio eſt maior <lb></lb>motus in O quàm in G; igitur quâ proportione horizontalis EN erit <lb></lb>longior, puncta, quæ longiùs diſtabunt, habebunt rationem plani ma­<lb></lb>gis inclinati. </s>
				</p>
				<p id="N1E0A8" type="main">
					<s id="N1E0AA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E0B6" type="main">
					<s id="N1E0B8"><emph type="italics"></emph>Poteſt determinari grauitatio in ſingulis punctis plani EN<emph.end type="italics"></emph.end>; </s>
					<s id="N1E0C1">cum enim <lb></lb>grauitatio in plano inclinato ſit ad grauitationem in horizontali vt <lb></lb>Tangens ad ſecantem, vel vt horizontalis, in quam ſcilicet cadit perpen­<lb></lb>lum ad inclinatam per Th. 16. ſit punctum, G grauitatio in eo puncto <lb></lb>eſt ad grauitationem in puncto E, vt QA ad AL, &amp; in puncto O ve YA <lb></lb>ad AP: idem dico de aliis punctis. </s>
				</p>
				<p id="N1E0CF" type="main">
					<s id="N1E0D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E0DD" type="main">
					<s id="N1E0DF"><emph type="italics"></emph>Hinc eò minor eſt grauitatio, quò maior eſt diſtantia ab E<emph.end type="italics"></emph.end>; </s>
					<s id="N1E0E8">atque ita ab E <lb></lb>verſus N creſcit motus, &amp; decreſcit grauitatio; at verò ab N verſus B <lb></lb>creſcit grauitatio, &amp; decreſcit motus. </s>
				</p>
				<p id="N1E0F0" type="main">
					<s id="N1E0F2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E0FE" type="main">
					<s id="N1E100"><emph type="italics"></emph>Globus ab O verſus E rotatus ſemper acceleraret ſuum motum.<emph.end type="italics"></emph.end></s>
					<s id="N1E107"> Demon­<lb></lb>ſtro, quia impetus productus in O conſeruaretur etiam in G, &amp; nouus <lb></lb>produceretur, igitur acceleraret ſuum motum; </s>
					<s id="N1E10F">ſuppono enim planum E <lb></lb>N eſſe læuigatiſſimum; </s>
					<s id="N1E115">igitur nihil eſſet, à quo deſtrueretur: </s>
					<s id="N1E119">adde quòd <pb pagenum="221" xlink:href="026/01/253.jpg"></pb>ſemper haberet ſuum effectum; </s>
					<s id="N1E122">igitur non eſſet fruſtrà; igitur per Schol. <lb></lb>Th.152.l.1. </s>
				</p>
				<p id="N1E129" type="main">
					<s id="N1E12B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E137" type="main">
					<s id="N1E139"><emph type="italics"></emph>Ille motus acceleratur per partes inæquales<emph.end type="italics"></emph.end>; </s>
					<s id="N1E142">quia ſcilicet motus additus <lb></lb>in O minor eſſet quàm in N, &amp; in G quàm in O per Th. 56. igitur per <lb></lb>partes inæquales acceleraretur, immò poteſt determinari proportio cre­<lb></lb>menti motus in ſingulis; </s>
					<s id="N1E14C">cum enim in O ſit vt YP, in QL. in Yvt T <foreign lang="grc">δ</foreign><lb></lb>ad AC; certè creſcit in proportione ſinuum rectorum ad ſinum totum. </s>
				</p>
				<p id="N1E155" type="main">
					<s id="N1E157"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E163" type="main">
					<s id="N1E165"><emph type="italics"></emph>Mobile deſcendens ex O in E tranſit per tot plana inclinata diuerſa, quot <lb></lb>ſunt puncta in tota EO vt conſtat, vel potiùs quot poſſunt duci Tangentes di­<lb></lb>uerſæ in toto arcu PE<emph.end type="italics"></emph.end>; quippe Tangens puncti P eſſet parallela IG, idem <lb></lb>dico de omnibus aliis punctis arcus PE. </s>
				</p>
				<p id="N1E174" type="main">
					<s id="N1E176"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E182" type="main">
					<s id="N1E184"><emph type="italics"></emph>Motus funependuli in quolibet puncto arcus, per quem deſcendit, eſt ad mo­<lb></lb>tum in perpendiculari, vt ſinus reſidui arcus ad ſemidiametrum<emph.end type="italics"></emph.end>; </s>
					<s id="N1E18F">v.g. ſit fune­<lb></lb>pendulum AD in perpendiculari, quod vibrari poſſit circa punctum im­<lb></lb>mobile A, eleuetur in A<foreign lang="grc">β</foreign>, ducatur Tangens <foreign lang="grc">β</foreign> V motus funependiculi in <lb></lb>puncto <foreign lang="grc">β</foreign> ſcilicet initio, idem eſt, qui eſſet in plano inclinato <foreign lang="grc">β</foreign>V vt patet, <lb></lb>atqui motus in inclinato plano <foreign lang="grc">β</foreign> V eſt ad motum in <expan abbr="perpẽdiculari">perpendiculari</expan> vt <foreign lang="grc">α</foreign> V. <lb></lb>ad <foreign lang="grc">β</foreign> V, ſed <foreign lang="grc">α</foreign>V eſt ad <foreign lang="grc">β</foreign>V vt <foreign lang="grc">αβ</foreign> ad A<foreign lang="grc">β</foreign>, ſunt enim triangula proportionalia; <lb></lb>igitur motus initio ſcilicet in puncto arcus putà B eſt ad motum in per­<lb></lb>pendiculari etiam initio conſideratum, vt ſinus rectus reſidui arcus, putà <lb></lb><foreign lang="grc">β</foreign> D ad ſemidiametrum, vel ſinum totum, id eſt <foreign lang="grc">α β</foreign> ad A <foreign lang="grc">β</foreign>, idem dico de <lb></lb>omnibus aliis punctis. </s>
				</p>
				<p id="N1E1E2" type="main">
					<s id="N1E1E4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E1F0" type="main">
					<s id="N1E1F2"><emph type="italics"></emph>Hinc proportio accelerationis motus in deſcenſu funependuli ſeu incremen­<lb></lb>ti in ſingulis punctis additi eſt in proportione huiuſmodi ſinuum minorum ſem­<lb></lb>per &amp; minorum<emph.end type="italics"></emph.end>; v.g. motus in puncto B eſt vt BA ſemidiameter in <foreign lang="grc">τ</foreign> vt <foreign lang="grc">τ</foreign><lb></lb><foreign lang="grc">μ</foreign> in <foreign lang="grc">β</foreign> vt <foreign lang="grc">β α</foreign>, id eſt licèt maior ſit motus in <foreign lang="grc">τ</foreign> quàm in B, cum ſcilicet <lb></lb>deſcendit ex B in <foreign lang="grc">τ</foreign>, vt illa portio crementi quæ in ipſo puncto <foreign lang="grc">τ</foreign> addi­<lb></lb>tur eſt ad primam in B vt <foreign lang="grc">τ μ</foreign> ad BA. </s>
				</p>
				<p id="N1E229" type="main">
					<s id="N1E22B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E237" type="main">
					<s id="N1E239"><emph type="italics"></emph>Hinc velocitas acquiſita in arcu BT eſt ad acquiſitam in arcu B <foreign lang="grc">β</foreign>, vt <lb></lb>omnes ſinus eiuſdem arcus B <foreign lang="grc">τ</foreign> ad omnes ſinus arcus B <foreign lang="grc">β</foreign>, &amp; hæc ad acquiſi­<lb></lb>tum in toto quadrante BD, vt hi ad omnes ſinus quadrantis<emph.end type="italics"></emph.end>; </s>
					<s id="N1E252">ſimiliter poteſt <lb></lb>comparari acquiſita tantùm in arcu BT, cum acquiſita in arcu <foreign lang="grc">τ β</foreign> vel <foreign lang="grc">β</foreign><lb></lb>D, quod probatur; quia motus, qui reſpondet ſingulis punctis arcus initio <lb></lb>eſt in proportione ſinuum ſeu tranſuerſarum BA, <foreign lang="grc">τ μ, β α</foreign>, &amp;c. </s>
					<s id="N1E267">igitur ſi <lb></lb>à ſingulis punctis arcus quadrantis in rectam lineam compoſiti duce­<lb></lb>rentur; </s>
					<s id="N1E26F">haùd dubiè prædictam aream quaſi occupabunt; igitur acquiſita <lb></lb>in vno puncto eſt ad acquiſitam in alio puncto vt linea tranſuerſa ad <pb pagenum="222" xlink:href="026/01/254.jpg"></pb>tranſuerſam v. g. acquiſita in ſolo puncto <foreign lang="grc">τ</foreign> nulla habita ratione ſupe­<lb></lb>riorum ad acquiſitam in ſolo puncto <foreign lang="grc">β</foreign> vt <foreign lang="grc">τμ</foreign> ad <foreign lang="grc">βα</foreign> ita acquiſita in arcu <lb></lb>B <foreign lang="grc">τ</foreign> eſt ad acquiſitam in arcu <foreign lang="grc">τ β</foreign>, vt area ſinuum B <foreign lang="grc">τ α</foreign>, ad aream ſinum <lb></lb>arcus <foreign lang="grc">τ β. </foreign></s>
				</p>
				<p id="N1E2A3" type="main">
					<s id="N1E2A5"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E2B1" type="main">
					<s id="N1E2B3">Obſeruabis prædicta ita intelligenda eſſe, vt aſſumantur arcus extenſi <lb></lb>in lineam rectam, ne ſcilicet ſinus plùs æquo contrahantur, ſeu potius <lb></lb>aliquo modo compenetrentur; </s>
					<s id="N1E2BB">ſemper enim accidet trapezus mixtus, v. <lb></lb>g. ſit trapezus A <foreign lang="grc">τ</foreign> aſſumatur recta æqualia arcui B <foreign lang="grc">τ</foreign> &amp; duæ rectæ æqua­<lb></lb>les duabus BA <foreign lang="grc">τ μ</foreign>, quarta erit curua; igitur erit trapezus mixtus, quæ cer­<lb></lb>tè cautio adhibenda eſt, alioquin falſum eſſet ſuperius Theorema, ſed de <lb></lb>funependulis infrà. </s>
				</p>
				<p id="N1E2D6" type="main">
					<s id="N1E2D8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E2E4" type="main">
					<s id="N1E2E6"><emph type="italics"></emph>In plano horizontali E O motus incrementa in diuerſis punctis habent <lb></lb><expan abbr="eãdem">eandem</expan> proportionem quam habent in motu funependuli per arcum ſuum<emph.end type="italics"></emph.end> v. g. <lb></lb>fit planum EO ducatur AP O, motus in O eſt ad motum in perpendicu­<lb></lb>lari vt PX ad AE, ſit funependulum AP cuius centrum; </s>
					<s id="N1E2FB">cui affixa eſt im­<lb></lb>mobiliter extremitas funis, ſit A &amp; punctum quietis ſit E, motus illius in <lb></lb>puncto P eſt ad motum in puncto C vt PX ad AB: </s>
					<s id="N1E303">ſimiliter motus in G <lb></lb>puncto plani eſt ad motum in perpendiculari vt LQ ad AE per Th.55. <lb></lb><expan abbr="itemq́ue">itemque</expan> ſit funependulum in L, motus in L eſt ad motum in C vt LQ <lb></lb>ad AE, idem dico de punctis T &amp; Y &amp; omnibus aliis; igitur crementa <lb></lb>motus tùm in motu tùm in arcu ſunt in eadem proportione. </s>
				</p>
				<p id="N1E312" type="main">
					<s id="N1E314"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E320" type="main">
					<s id="N1E322"><emph type="italics"></emph>Determinari poteſt velocitas acquiſita in deſcenſu OE,<emph.end type="italics"></emph.end> eſt enim vt trian­<lb></lb>gulum <expan abbr="mixtũ">mixtum</expan> cuius alterum latus rectum ſit ad OE, alterum ad angulos <lb></lb>rectos PX, tertium curua connectens ſinus rectos infra PX verſus vt E <lb></lb>vides in figura EO 4. eſt autem hæc velocitas ad velocitatem acquiſi­<lb></lb>tam in perpendiculari æquali OE vt prædictum triangulum EO 4. ad <lb></lb>rectangulum ſub OEA. </s>
				</p>
				<p id="N1E338" type="main">
					<s id="N1E33A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E346" type="main">
					<s id="N1E348"><emph type="italics"></emph>Non deſcendit mobile per per OE &amp; GE æquali tempore vt patet,<emph.end type="italics"></emph.end> quia <lb></lb>hæc Tangens EO poteſt eſſe longior in infinitum; ſed has proportiones <lb></lb>demonſtrabimus Tom, ſequenti, quia multam Geometriam deſide­<lb></lb>rant. </s>
				</p>
				<p id="N1E357" type="main">
					<s id="N1E359"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E365" type="main">
					<s id="N1E367"><emph type="italics"></emph>Omne planum quod ad aliquod punctum circumferentiæ globi terreſtris <lb></lb>terminatur, &amp; productum vlterius non ſecat centrum poteſt plænum inclina­<lb></lb>tum eſſe,<emph.end type="italics"></emph.end> v.g. in planum LD vel YD, immò nullum eſt planum quod non <lb></lb>ſit horizontale, id eſt quod non cadat perpendiculariter in aliquem ra­<lb></lb>dium vel in aliquod perpendiculum v.g. LD eſt horizontalis quia ca-<pb pagenum="223" xlink:href="026/01/255.jpg"></pb>dit perpendiculariter in perpendiculum AD, idem dico de plano YD, <lb></lb>cuius perpendiculum vt inueniatur, ex centro A adducatur perpendicu­<lb></lb>laris in YD: </s>
					<s id="N1E385">hinc non poteſt deſcendere corpus ad centrum terræ per <lb></lb>planum inclinatum rectilineum quia linea recta quæ ducitur ad cen­<lb></lb>trum eſt perpendiculum; igitur non eſt planum inclinatum. </s>
				</p>
				<p id="N1E38D" type="main">
					<s id="N1E38F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E39B" type="main">
					<s id="N1E39D"><emph type="italics"></emph>Poteſt determinari motus duorum planorum inclinatorum quorum idem <lb></lb>est perpendiculum,<emph.end type="italics"></emph.end> ſit enim arcus terræ GFC centro A; </s>
					<s id="N1E3A8">ſint duo plana <lb></lb>FK GFL quorum idem eſt perpendiculum LA; </s>
					<s id="N1E3AE">motus in K per KF initio <lb></lb>eſt ad motum per K vt DC ad DCA; </s>
					<s id="N1E3B4">ducatur autem AH perpendicula­<lb></lb>ris in GL, &amp; centro A ducatur arcus HE, ducaturque vel HO perpendi­<lb></lb>cularis in AL vel CP in AH; </s>
					<s id="N1E3BC">dico motum in L eſſe vt PC ad CA: ſed <lb></lb>hæc ſunt facilia. </s>
				</p>
				<p id="N1E3C2" type="main">
					<s id="N1E3C4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E3D0" type="main">
					<s id="N1E3D2"><emph type="italics"></emph>Nullus gradus impetus deſtruitur in deſcenſu KF vel MF per ſe<emph.end type="italics"></emph.end>; </s>
					<s id="N1E3DB">quia nihil <lb></lb>eſt à quo deſtruatur, dixi per ſe; nam per accidens aliquid deſtrui poteſt <lb></lb>tùm ratione plani ſcabri tùm etiam ratione aëris. </s>
				</p>
				<p id="N1E3E3" type="main">
					<s id="N1E3E5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E3F1" type="main">
					<s id="N1E3F3"><emph type="italics"></emph>Omnes gradus acquiſiti in deſcenſu concurrunt ad deſcenſum præter vnum <lb></lb>ſcilicet præter acquiſitum vltimo instanti deſcenſus<emph.end type="italics"></emph.end>; quia impetus non con­<lb></lb>currit ad motum primo inſtanti quo eſt, per Th. 34. lib.1. de omnibus <lb></lb>aliis certum eſt quod concurrant, quia non impediuntur, igitur concur­<lb></lb>runt per Ax.12. lib.1. </s>
				</p>
				<p id="N1E405" type="main">
					<s id="N1E407"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E413" type="main">
					<s id="N1E415"><emph type="italics"></emph>Omnes gradus impetus qui concurrunt ad deſcenſum, concurrunt ad aſcen­<lb></lb>ſum præter vnum<emph.end type="italics"></emph.end>; </s>
					<s id="N1E420">probatur, quia ſi omnes concurrerent, maior eſſet aſ­<lb></lb>cenſus deſcenſu quod eſt abſurdum: adde quod impetus innatus ad li­<lb></lb>neam ſurſum determinari non poteſt per Th.12. ſed impetus innatus <lb></lb>concurrit ad deſcenſum, vt patet. </s>
				</p>
				<p id="N1E42A" type="main">
					<s id="N1E42C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 73.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E438" type="main">
					<s id="N1E43A"><emph type="italics"></emph>Hinc tot concurrunt ad aſcenſum quot ad deſcenſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1E443">nam ad aſcenſum <lb></lb>omnes præter vltimum, ad deſcenſum omnes præter primum; igitur tot <lb></lb>concurrunt ad aſcenſum, quot ad deſcenſum. </s>
				</p>
				<p id="N1E44B" type="main">
					<s id="N1E44D">Dices, primo inſtanti aſcenſus aliquis gradus deſtruitur. </s>
					<s id="N1E450">Reſponderet <lb></lb>aliquis, tranſeat antecedens, quia cùm inſtanti vltimo deſcenſus omnes <lb></lb>gradus præter innatum exigant motus pro ſequenti inſtanti, quod eſt pri­<lb></lb>mum inſtans aſcenſus; certè tot concurrunt ad primum inſtans aſcenſus, <lb></lb>quot ad vltimum deſcenſus, licèt aliquis gradus deſtruatur pro primo in­<lb></lb>ſtanti aſcenſus. </s>
					<s id="N1E45E">Reſponderet alius, cùm primo inſtanti aſcenſus gradus <lb></lb>ille qui vltimo deſcenſus productus eſt concurrat ad motum, igitur illo <lb></lb>inſtanti fruſtrà non eſſe, igitur non debere deſtrui, cùm eo tantùm no­<lb></lb>mine deſtruatur impetus; </s>
					<s id="N1E468">igitur primo inſtanti aſcenſus non deſtrui <pb pagenum="224" xlink:href="026/01/256.jpg"></pb>vllum <expan abbr="gradũ">gradum</expan> impetus, quia ſcilicet impetus innatus in omnibus inſtan­<lb></lb>tibus præcedentibus habuit motum <expan abbr="deorsũ">deorsum</expan>; </s>
					<s id="N1E47B">igitur nullo <expan abbr="inſtãti">inſtanti</expan> præteri­<lb></lb>to exigebat motum oppoſitum: adde quod vltimo inſtanti deſcenſus quo <lb></lb>mobile ponitur in F impetus naturalis non exigit ampliùs motum, cur <lb></lb>enim potius verſus M quàm verſus N, igitur primo tantùm inſtanti aſ­<lb></lb>cenſus quo mobile fertur verſus N, impetus naturalis exigit mobile re­<lb></lb>dire in F. </s>
				</p>
				<p id="N1E48E" type="main">
					<s id="N1E490">Dices, ſi primo inſtanti aſcenſus nullus gradus impetus deſtruitur; igi­<lb></lb>tur nec ſecundo neque tertio, non eſt enim potior ratio pro vno quàm <lb></lb>pro altero. </s>
					<s id="N1E498">Reſponderet negando, nam ideo, vt iam indicaui, primo <expan abbr="inſtã-ti">inſtan­<lb></lb>ti</expan> aſcenſus nullus gradus deſtruitur, quia inſtanti immediatè <expan abbr="antecedẽti">antecedenti</expan>, <lb></lb>quod erat vltimum deſcenſus, impetus innatus non exigebat quidquam <lb></lb>ampliùs, igitur nullus gradus eſt fruſtrà, igitur nullus deſtruitur, at verò <lb></lb>inſtanti aſcenſus impetus innatus exigit pro ſequente, quod eſt ſecun­<lb></lb>dum aſcenſus mobile redire in F, igitur ex illa pugna ſecundi inſtantis <lb></lb>deſtruitur aliquid impetus; </s>
					<s id="N1E4B0">ſed profectò primo aſcenſus deſtruitur ali­<lb></lb>quid impetus, quia aliquid motus remittitur, propter impetum inna­<lb></lb>tum; </s>
					<s id="N1E4B8">igitur aliquis impetus eſt fruſtrà: </s>
					<s id="N1E4BC">non tamen hoc facit, quin omnes <lb></lb>gradus in deſcenſu acquiſiti concurrant ad aſcenſum; igitur tot concur­<lb></lb>runt ad aſcenſum, quot ad deſcenſum, cum hac tamen differentia, quod <lb></lb>impetus innatus, qui concurrit ad deſcenſum, non ad aſcenſum ſit longè <lb></lb>velocior vltimo inſtanti motus acquiſito, qui concurrit ad deſcenſum, <lb></lb>non ad aſcenſum, </s>
				</p>
				<p id="N1E4CA" type="main">
					<s id="N1E4CC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E4D8" type="main">
					<s id="N1E4DA"><emph type="italics"></emph>Hinc in ea proportione creſcit impetus in deſcenſu, qua decreſcit in aſcenſu, <lb></lb>&amp; in eadem creſcit, &amp; decreſcit motus in eadem creſcunt, &amp; decreſcunt ſpa­<lb></lb>tia,<emph.end type="italics"></emph.end> v.g. ſint ſex inſtantia deſcenſus iuxta proportionem ſcilicet inſtan­<lb></lb>tium, in qua res iſta faciliùs explicatur: </s>
					<s id="N1E4EB">primo inſtanti motus ſunt duo <lb></lb>gradus impetus, quorum alter tantùm concurrit, ſcilicet qui præextitit; </s>
					<s id="N1E4F1"><lb></lb>qui enim producitur primo illo inſtanti, non concurrit ad illum motum <lb></lb>per Th. 34. lib.  1. igitur primo inſtanti ſunt duo gradus impetus, vnus <lb></lb>gradus motus, &amp; vnum ſpatium; </s>
					<s id="N1E4FA">ſecundo verò inſtanti ſunt tres gradus <lb></lb>impetus quorum vnus non concurrit, 2. gradus motus, 2.ſpatia, atque ita <lb></lb>deinceps; donec tandem ſexto eo vltimo inſtanti deſcenſus ſint 7. gra­<lb></lb>dus impetus, quorum vnus non concurrit, 6. gradus motus, &amp; 6. <lb></lb>ſpatia. </s>
				</p>
				<p id="N1E506" type="main">
					<s id="N1E508">Similiter primo inſtanti aſcenſus ſunt 7. gradus impetus, quorum <lb></lb>vnus non concurrit ſcilicet innatus, 6. gradus motus, 6. ſpatia; ſecundo <lb></lb>6.gradus impetus, quorum vnus non concurrit ſcilicet innatus, 5.gradus <lb></lb>motus, 5.ſpatia, atque ita deinceps. </s>
				</p>
				<p id="N1E512" type="main">
					<s id="N1E514"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E520" type="main">
					<s id="N1E522"><emph type="italics"></emph>Hinc æqualia ferè vtrimque ſunt ſpatia deſcenſus ſcilicet, &amp; aſcenſus<emph.end type="italics"></emph.end>; v.g. <lb></lb>MF æquale FN, quia eſt ſumma eorumdem terminorum per Th. 74. <lb></lb>igitur ex F mobile aſcendit ad altitudinem FN æqualem altitudini FM, <pb pagenum="225" xlink:href="026/01/257.jpg"></pb>ex qua priùs deſcenderat dixi ferè, quia cum innatus ſit perfectior vlti­<lb></lb>mo acquiſito paulò plùs ſpatij acquiritur in deſcenſu, quàm in aſcenſu, <lb></lb>ſed minimum eſt ſenſibile. </s>
				</p>
				<p id="N1E539" type="main">
					<s id="N1E53B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E547" type="main">
					<s id="N1E549"><emph type="italics"></emph>Hinc æqualibus temporibus aſcendit ferè ab F in N, &amp; deſcendit ex M <lb></lb>in F,<emph.end type="italics"></emph.end> quia numerus terminorum æqualis eſt numero inſtantium. </s>
				</p>
				<p id="N1E553" type="main">
					<s id="N1E555"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E561" type="main">
					<s id="N1E563"><emph type="italics"></emph>Hinc motum haberet ferè perpetuum ab M in F ab F in N, ab N ite­<lb></lb>rum in F, &amp;c.<emph.end type="italics"></emph.end> ſi enim deſcendens ex M in F aſcendit ad æqualem altitu­<lb></lb>dinem FN, ita &amp; deſcendens ex N in F aſcendet ad æqualem altitudi­<lb></lb>nem FM, atque ita deinceps; </s>
					<s id="N1E572">igitur motus erit ferè perpetuus; </s>
					<s id="N1E576">ſed pro­<lb></lb>fectò nullum eſt corpus tàm læuigatum, quod motum non impediat: dixi <lb></lb>ferè, quia deſcenſus tantillùm ſuperat aſcenſum, ſed vix intra mille an­<lb></lb>nos ſenſu id percipi poſſet. </s>
				</p>
				<p id="N1E580" type="main">
					<s id="N1E582"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E58E" type="main">
					<s id="N1E590"><emph type="italics"></emph>Hinc ſi terrestris globus eſſet perforatus in perpendiculo FAI, ſi ex puncto <lb></lb>F demitteretur globus plumbeus per FAI deſcenderet ex F in A, tum ex <lb></lb>Aaſcenderet in I æquali ferè tempore<emph.end type="italics"></emph.end>; </s>
					<s id="N1E59D">quod neceſſariò ſequitur ex dictis; </s>
					<s id="N1E5A1"><lb></lb>quia omnes gradus qui concurrent ad aſcenſum, etiam concurrerent ad <lb></lb>deſcenſum, præter vnum, ſcilicet vltimo inſtanti deſcenſus acquiſitum; </s>
					<s id="N1E5A8"><lb></lb>&amp; omnes, qui concurrerent ad deſcenſum, concurrerent etiam ad aſcen­<lb></lb>ſum præter vnum, ſcilicet primum vel innatum; </s>
					<s id="N1E5AF">igitur æquale ſpatium <lb></lb>æquali tempore percurreretur; </s>
					<s id="N1E5B5">quod certè dictum ſit abſtrahendo à re­<lb></lb>ſiſtentia aëris, quæ fortè modica eſſet; </s>
					<s id="N1E5BB">Ex hac perpetua vibrationum ſe­<lb></lb>rie aliquando explicabimus cauſas phyſicas apogæi &amp; perigæi Solis, &amp; <lb></lb>aliorum planetarum; adhibe <expan abbr="cãdem">eandem</expan> cautionem, de qua ſuprà. </s>
				</p>
				<p id="N1E5C7" type="main">
					<s id="N1E5C9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E5D5" type="main">
					<s id="N1E5D7"><emph type="italics"></emph>Si duo plana inclinata faciunt angulum eſt ferè æqualis aſcenſus deſcenſui.<emph.end type="italics"></emph.end><lb></lb>v. </s>
					<s id="N1E5E0">g. deſcendat per LF dico quod aſcendet per FR ad altitudinem ferè <lb></lb>æqualem LF, quia licèt in angulo illo LFR ſit noua determinatio ad <lb></lb>nouam lineam motus, id eſt quaſi reflexio; </s>
					<s id="N1E5EA">nihil eſt tamen quod deſtruat <lb></lb>impetum; nam in reflexione ſeu noua determinatione non perit aliquid <lb></lb>impetus neceſſariò vt lib.  ſequenti demonſtrabimus. </s>
				</p>
				<p id="N1E5F2" type="main">
					<s id="N1E5F4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E600" type="main">
					<s id="N1E602"><emph type="italics"></emph>Eſt tamen alia ratio de motu funependuli quâ euincemus aſcenſum eſſe mi­<lb></lb>norem deſcenſu,<emph.end type="italics"></emph.end> de qua infrà. </s>
				</p>
				<p id="N1E60C" type="main">
					<s id="N1E60E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E61A" type="main">
					<s id="N1E61C"><emph type="italics"></emph>Initio aſcenſus per FN deſtruuntur gradus impetus producti ſub finem de­<lb></lb>ſcenſus, &amp; ſub finem aſcenſus destruuntur producti initio deſcenſus:<emph.end type="italics"></emph.end> ratio eſt <lb></lb>clara, quia producti ſub finem deſcenſus ſunt imperfectiores, cùm plùs <lb></lb>recedant à perpendiculari, per Th. 55. ſimiliter initio aſcenſus longiùs <lb></lb>recedit linea à verticali; </s>
					<s id="N1E62D">igitur minùs deſtruetur impetus, vt ſæpè incul-<pb pagenum="226" xlink:href="026/01/258.jpg"></pb>cauimus; nam idem deſtruitur in dato puncto aſcenſus, qui producere­<lb></lb>tur in eodem puncto deſcenſus. </s>
				</p>
				<p id="N1E638" type="main">
					<s id="N1E63A">Dices, gradus productus vltimo inſtanti deſcenſus non deſtruitur pri­<lb></lb>mo aſcenſus. </s>
					<s id="N1E63F">Reſpondeo deſtrui; </s>
					<s id="N1E643">hinc eadem cauſa idem deſtruit primo <lb></lb>inſtanti aſcenſus quod produxit vltimo inſtanti deſcenſus; deſtruit in­<lb></lb>quam mediatè. </s>
				</p>
				<p id="N1E64B" type="main">
					<s id="N1E64D">Hîc obſeruabis ſingulare diſcrimen, quod intercedit inter cauſam <lb></lb>producentem, &amp; exigentem; </s>
					<s id="N1E653">nam producens verè agit, exigens verò tan­<lb></lb>tùm exigit; </s>
					<s id="N1E659">illa conſequitur effectum eo inſtanti quo agit; </s>
					<s id="N1E65D">hæc verò non <lb></lb>habet effectum eo inſtanti, quo exigit, ſed pro ſequenti; </s>
					<s id="N1E663">eſt tamen cauſa <lb></lb>eo inſtanti, quo exigit, non certè agens, ſed exigens: </s>
					<s id="N1E669">exemplum habes <lb></lb>in impetu, qui non habet motum eo inſtanti quo exigit, ſed tantùm ſe­<lb></lb>quenti pro quo exigit; </s>
					<s id="N1E671">igitur eſt cauſa motus antequàm ſit motus, non <lb></lb>agens ſed exigens; at verò cum impetus alium impetum producit eſt <lb></lb>tantùm cauſa illius cum agit. </s>
				</p>
				<p id="N1E679" type="main">
					<s id="N1E67B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E687" type="main">
					<s id="N1E689"><emph type="italics"></emph>Vltimo inſtanti aſcenſus ſunt duo gradus impetus, ſcilicet productus primo <lb></lb>inſtanti deſcenſus cum innato<emph.end type="italics"></emph.end>; </s>
					<s id="N1E694">igitur inſtanti ſequenti erit motus, id eſt, <lb></lb>deſcenſus, quia præualet innatus qui perfectior eſt, vt conſtat ex dictis; </s>
					<s id="N1E69A"><lb></lb>igitur nullum erit inſtans quietis; quæ omnia explicari debent eodem <lb></lb>modo, quo iam explicuimus in motu violento, lib.3. eſt enim eadem ra­<lb></lb>tio, &amp;c. </s>
					<s id="N1E6A3">quæ omitto ne multa hîc repetere cogar. </s>
				</p>
				<p id="N1E6A6" type="main">
					<s id="N1E6A8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E6B4" type="main">
					<s id="N1E6B6"><emph type="italics"></emph>Ictus eſſent ferè æquales in ſegmentis æqualibus aſcenſus &amp; deſcenſus,<emph.end type="italics"></emph.end> quia <lb></lb>motus eſſet æqualis in illis; igitur ictus æquales, quod facilè eſt. </s>
				</p>
				<p id="N1E6C1" type="main">
					<s id="N1E6C3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E6CF" type="main">
					<s id="N1E6D1"><emph type="italics"></emph>In planis eiuſdem inclinationis idem corpus graue eſt eiuſdem ponderis<emph.end type="italics"></emph.end> v. <lb></lb>g. ſint plana FE. GD. HO eiuſdem inclinationis cum communi ſci­<lb></lb>licet perpendiculo ODEA; </s>
					<s id="N1E6E1">certè pondus corporis in O eſt ad pondus <lb></lb>eiuſdem in H vt AH ad AO per Th.57. &amp; pondus corporis eiuſdem in <lb></lb>D eſt ad pondus eiuſdem in G vt AG ad AD, &amp; in E vt AF ad AE; </s>
					<s id="N1E6E9"><lb></lb>ſed AF eſt ad AE vt AG ad AD, vt AH ad AO; ſunt enim triangula <lb></lb>proportionalia. </s>
				</p>
				<p id="N1E6F0" type="main">
					<s id="N1E6F2">Hinc reiice quorumdam recentiorum ſententiam, qui volunt corpus, <lb></lb>quod propiùs ad centrum terræ accedit, eſſe minùs graue, &amp; grauius quod <lb></lb>longiùs à centro recedit, quod de grauitate corporis abſolutè ſumpti nul­<lb></lb>latenus dici poteſt vt conſtat, vtrum verò ſi cum alio in eadem libra ſta­<lb></lb>tuatur hinc inde, videbimus ſuo loco. </s>
				</p>
				<p id="N1E6FD" type="main">
					<s id="N1E6FF">Diceret fortè aliquis in ipſo centro ſpoliari ſua tota grauitate; </s>
					<s id="N1E703">igitur <lb></lb>quo propiùs accedit ad centrum maiori grauitatis portione multatur; </s>
					<s id="N1E709">ſed <lb></lb>nego conſequentiam; </s>
					<s id="N1E70F">nec enim ſequitur priuari parte grauitatis dum <lb></lb>abeſt à centro, licèt tota priuetur cum eſt in centro ſed de hac quæſtione <lb></lb>plura aliàs; nec enim huius loci eſt. </s>
				</p>
				<pb pagenum="227" xlink:href="026/01/259.jpg"></pb>
				<p id="N1E71B" type="main">
					<s id="N1E71D">Sed ne hoc fortè excidat ſi Globus CGLH deſcendat ex A ad cen­<lb></lb>trum mundi ſeu grauium E, quæri poteſt vtrum omnes partes mouean­<lb></lb>tur ſua ſponte verſus L etiam illæ quæ vltra centrum E proceſſerunt, ſeu <lb></lb>quod idem eſt, vtrum globus CGLH, cuius centrum E eſt coniun­<lb></lb>ctum cum centro grauium E tranſlatus in IFKB eiuſdem ſit ponderis, <lb></lb>cuius eſſet in A. v.g. Reſp. primò globum prædictum, cuius centrum eſt in E, nullius eſſe <lb></lb>ponderis, vt conſtat; nec enim potiùs in vnam partem, quàm in aliam <lb></lb>inclinat. </s>
				</p>
				<p id="N1E731" type="main">
					<s id="N1E733">Reſpondeo ſecundò globum <expan abbr="eũdem">eundem</expan>, cuius centrum eſt D ex­<lb></lb>tra centrum grauium E grauitare, quia inclinat verſus E.R eſpondeo ter­<lb></lb>tiò non æqualiter grauitare, ſiue ſit in D, ſiue ſit in A; </s>
					<s id="N1E73F">quia grauitat per <lb></lb>ſuam entitatem quatenus coniuncta eſt cum inclinatione; </s>
					<s id="N1E745">ſed non eſt ea­<lb></lb>dem entitas in A quæ in D cum eadem inclinatione, igitur nec eadem <lb></lb>grauitas; </s>
					<s id="N1E74D">non enim grauitat inde ſecundum totam ſuam entitatem; <lb></lb>quia ſcilicet ſectio MFNE non poteſt ampliùs grauitare infrà E, quan­<lb></lb>doquidem E eſt locus infimus. </s>
				</p>
				<p id="N1E755" type="main">
					<s id="N1E757">Dices grauitare grauitatione communi. </s>
					<s id="N1E75A">Reſpondeo ad extra conce­<lb></lb>do, ſcilicet ad producendum impetum in corpore quod impedit motum, <lb></lb>ſecus verò grauitatione intrinſecâ; vnde ſi ſuſtineretur globus in F non <lb></lb>ſuſtineretur totus, ſed fortè detraheretur de toto pondere, primò ſectio <lb></lb>MFNE, quæ non grauitat verſus F &amp; altera æqualis quæ ab ea ſuſtine­<lb></lb>retur. </s>
					<s id="N1E768">v.g. ſi ſectio OCPD immediatè incumberet ſectioni MFNE, <lb></lb>ita vt corda OP iungeretur cordæ MN; </s>
					<s id="N1E770">certè vtraque conſiſteret; dixi <lb></lb>fortè, quia non eſt ita certum, vt videbimus alias. </s>
					<s id="N1E776">Dices igitur ſi globus <lb></lb>ille eſſet in centro, minima vi adhibita amoueretur; </s>
					<s id="N1E77C">igitur idem timen­<lb></lb>dum eſſet de toto terreſtri globo; </s>
					<s id="N1E782">ſed noli timere quæſo tàm facilè terræ <lb></lb>motum; </s>
					<s id="N1E788">immò ſi globus ille ſemel occuparet centrum E., cum non tan­<lb></lb>tum hemiſpherium GLH contra nitatur GCH; </s>
					<s id="N1E78E">verùm etiam CGL, <lb></lb>CHL, &amp; infinita alia; </s>
					<s id="N1E794">certè vt moueatur vbi ſemel centrum E occupat, <lb></lb>debent tot ferè produci gradus impetus, quot produci deberent vt mo­<lb></lb>ueretur extra centrum, vt probabimus cum de grauitate ſcilicet in tra­<lb></lb>ctatu ſequenti phyſicæ ſingulari: Interim dicendum eſt ſingulas partes <lb></lb>huius globi ſeorſim grauitare, cum centrum occupat, excepto illo puncto <lb></lb>quod in centro eſt. </s>
				</p>
				<p id="N1E7A2" type="main">
					<s id="N1E7A4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E7B0" type="main">
					<s id="N1E7B2"><emph type="italics"></emph>Poteſt, corpus graue deſcendere ad centrum terræ per planum conuexum <lb></lb>quadrantis,<emph.end type="italics"></emph.end> ſit enim globus terræ GBCK, centrum A; deſcribatur ex <lb></lb>K ſemidiametro KA quadrans KLA. </s>
					<s id="N1E7BF">Dico quòd corpus graue deſcen­<lb></lb>det per conuexum arcum LVA, non tamen per concauum. </s>
					<s id="N1E7C4">Probatur <lb></lb>prima pars, quia à puncto L per arcum LVA ſemper accedit propiùs ad <lb></lb>centrum A; </s>
					<s id="N1E7CC">igitur per illam deſcendet, quia nulla eſt alia linea minor <lb></lb>dextrorſum; </s>
					<s id="N1E7D2">ſi enim eſſet aliqua, eſſet LCA; </s>
					<s id="N1E7D6">quia poſſunt tantùm duci <lb></lb>duæ illæ rectæ breuiſſimæ, quæ terminentur ad puncta LC vt patet; </s>
					<s id="N1E7DC">ſed <lb></lb>LCA eſt maior arcu LVA: </s>
					<s id="N1E7E2">Probatur ſecunda pars, quia ab L in A in-<pb pagenum="228" xlink:href="026/01/260.jpg"></pb>trorſum poteſt duci linea LA breuior arcu LVA; igitur per concauum <lb></lb>LVA non deſcenderet mobile. </s>
				</p>
				<p id="N1E7ED" type="main">
					<s id="N1E7EF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E7FB" type="main">
					<s id="N1E7FD"><emph type="italics"></emph>Motus puncti L initio eſſet minor motu puncti V initio; </s>
					<s id="N1E803">id eſt poſito quod <lb></lb>demittatur ex V verſus A<emph.end type="italics"></emph.end>; </s>
					<s id="N1E80C">demonſtro, quia eodem modo ſe habet in L, <lb></lb>atque ſi eſſet in puncto L <expan abbr="Tãgentis">Tangentis</expan> LC, vt pater; </s>
					<s id="N1E816">ſed motus per LC ini­<lb></lb>tio eſt ad motum per LA vt ND ad NA vel vt LC ad LA per Th.55. <lb></lb>at verò motus in V vel in F initio per FE <expan abbr="Tãgentem">Tangentem</expan> eſt ad motum per­<lb></lb>pendiculi FA vt FE ad FA; </s>
					<s id="N1E824">ſed eſt maior ratio FE ad FA, quàm LE <lb></lb>ad LA, vt conſtat; igitur motus initio in V eſt minor quàm in L <lb></lb>initio. </s>
				</p>
				<p id="N1E82C" type="main">
					<s id="N1E82E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E83A" type="main">
					<s id="N1E83C"><emph type="italics"></emph>Hinc eſt inuerſa ratio motus funependuli vulgaris &amp; plani inclinati recti,<emph.end type="italics"></emph.end><lb></lb>in quibus motus ſupremi puncti eſt maior motu cuiuſlibet alterius pun­<lb></lb>cti, vnde inciperet motus, cum tamen hic ſit minor: porrò poſſet eſſe <lb></lb>funependulum KLA dum vel LVA eſſet orbis durus quem media di­<lb></lb>uideret rima quaſi ecliptica globi penduli ex K fune extenſo, &amp; per ri­<lb></lb>mam incerto KL, vel quod faciliùs eſſet ſi KL eſſet priſma durum, quod <lb></lb>circa K immobile moueri ſeu volui poſſet. </s>
				</p>
				<p id="N1E850" type="main">
					<s id="N1E852"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E85E" type="main">
					<s id="N1E860"><emph type="italics"></emph>Alia via facilior occurrit, quæ mihi videtur non eſſe omittenda qua propor­<lb></lb>tiones illæ diuerſi motus demonstrari poſſent,<emph.end type="italics"></emph.end> ſit. </s>
					<s id="N1E86A">v.g. punctum L; </s>
					<s id="N1E870">aſſumatur <lb></lb>arcus LQ æqualis arcui LA; </s>
					<s id="N1E876">ducatur recta AQ, in quam ducatur LK <lb></lb>perpendicularis: </s>
					<s id="N1E87C">dico motum in L per arcum LVA initio eſſe ad motum <lb></lb>per LA vt KA ad LA: </s>
					<s id="N1E882">ſimiliter ſit punctum V; </s>
					<s id="N1E886">aſſumatur VL æqualis <lb></lb>arcui VA; </s>
					<s id="N1E88C">&amp; in hanc perpendicularis VX.dico motum in V per arcum <lb></lb>VA eſſe ad motum per ipſum perpendiculum VA vt XA ad rectam <lb></lb>VA; </s>
					<s id="N1E894">idem dico de omnibus aliis: </s>
					<s id="N1E898">Ratio eſt, quia Tangens, quæ ducere­<lb></lb>tur in V eſſet parallela AX; igitur triangula vtrimque eſſent æqualia. </s>
					<s id="N1E89E"><lb></lb>v.g. FEA &amp; FYA: item motus in P eſt ad motum per ipſum perpen­<lb></lb>diculum, vt Tangens PM ad PA, vt conſtat ex dictis. </s>
				</p>
				<p id="N1E8A7" type="main">
					<s id="N1E8A9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 89.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E8B5" type="main">
					<s id="N1E8B7"><emph type="italics"></emph>Hinc totus motus per LA perpendiculum eſt ad totum motum per arcum <lb></lb>LVA, vt omnes chordæ ductæ ab A ad omnia puncta quadrantis AVL <lb></lb>ſimul ſumptæ ad totidem ſubduplas chordarum ductarum ab A ad alterna <lb></lb>puncta totius ſemicirculi ALQ vel ad totidem <expan abbr="Tãgentes">Tangentes</expan> ſimul ſumptas<emph.end type="italics"></emph.end>: </s>
					<s id="N1E8CA">cum <lb></lb>enim motus in L per arcum LVA ſit ad motum in L por ipſum perpen­<lb></lb>diculum LA vt ſubdupla AQ ad LA, &amp; motus in V per arcum in A <lb></lb>ſit ad motum in V per rectam VA, vt ſubdupla chordæ AL ad rectam <lb></lb>VA, atque ita deinceps per Th.88. certè omnia antecedentis ſimul ſum­<lb></lb>pta habent illam rationem ad omnia conſequentia ſimul ſumpta, vt con­<lb></lb>ſtat; igitur totus motus, &amp;c. </s>
				</p>
				<pb pagenum="229" xlink:href="026/01/261.jpg"></pb>
				<p id="N1E8DE" type="main">
					<s id="N1E8E0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 90.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E8EC" type="main">
					<s id="N1E8EE"><emph type="italics"></emph>Globus deſcendens B per conuexum arcum LVA in quo A eſt centrum <lb></lb>terræ aſcenderet denuò per quadrantem oppoſitum AFS<emph.end type="italics"></emph.end>; </s>
					<s id="N1E8F9">patet, quia totus <lb></lb>impetus non deſtrueretur in centro A, qui ſcilicet eſſet intenſior pro­<lb></lb>pter accelerationem deſcenſus, quàm vt in momento deſtruatur; quod <lb></lb>probatur ex aliis funependulis, &amp; reflexis. </s>
				</p>
				<p id="N1E903" type="main">
					<s id="N1E905"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 91.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E911" type="main">
					<s id="N1E913"><emph type="italics"></emph>Non aſcenderet per totum arcum AFS<emph.end type="italics"></emph.end>; </s>
					<s id="N1E91C">hoc Theorema probabitur cum <lb></lb>de motu funependuli, eſt enim eadem pro vtroque ratio; quæ in eo po­<lb></lb>ſita eſt, quòd in aſcenſu aliquid impetus deſtruatur. </s>
				</p>
				<p id="N1E924" type="main">
					<s id="N1E926"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E932" type="main">
					<s id="N1E934"><emph type="italics"></emph>Velociùs deſcenderet per arcum maiorem LVA quam per minorem XA; </s>
					<s id="N1E93A"><lb></lb>velociùs, inquam, pro rata<emph.end type="italics"></emph.end>; </s>
					<s id="N1E942">nam arcum XA citiùs percurreret; </s>
					<s id="N1E946">ratio eſt, <lb></lb>quia modicus XA eſt magis curuus, vt patet; </s>
					<s id="N1E94C">igitur determinatio­<lb></lb>nis mutatio maior eſt: adde quod maior arcus accedit propiùs ad <lb></lb>rectam. </s>
				</p>
				<p id="N1E954" type="main">
					<s id="N1E956"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 93.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E962" type="main">
					<s id="N1E964"><emph type="italics"></emph>Non modo per quadrantem circuli deſcendere poteſt in centrum terræ, ſed <lb></lb>etiam per ſemicirculum<emph.end type="italics"></emph.end>; </s>
					<s id="N1E96F">vt videre eſt in eadem figura, nam ſi globus ſta­<lb></lb>tueretur iuxta Quantulùm, ſcilicet, extra perpendiculum AQ dextror­<lb></lb>ſum, v.g. versùs P; </s>
					<s id="N1E979">certè deſcenderet vſque ad A per conuexum ſemicir­<lb></lb>culi QLA; per conuexum, inquam, non per concauum, vt dictum eſt <lb></lb>de quadrante LVA. </s>
					<s id="N1E981">Ratio eſt, quia accederet ſemper propiùs ad cen­<lb></lb>trum A; </s>
					<s id="N1E987">igitur eſſet planum inclinatum per Th. 2. igitur per illud de­<lb></lb>ſcenderet, nec vlla eſſet difficultas; </s>
					<s id="N1E98D">quod autem accedat ſemper propiùs <lb></lb>ad A per ſemicirculum QLA, certum eſt; </s>
					<s id="N1E993">quia PA minor eſt QA; nam <lb></lb>diameter eſt maxima ſubtenſarum in circulo. </s>
					<s id="N1E999">Immò per alium ſemi­<lb></lb>circulum ASQ aſcenderet denuóque deſcenderet repetitis pluribus vi­<lb></lb>brationibus; nunquam tamen aſcenderet vſque ad punctum Q propter <lb></lb>tamdem rationem, quam in Theoremate 92. adduximus. </s>
				</p>
				<p id="N1E9A3" type="main">
					<s id="N1E9A5">Obſeruabis præterea non tantùm corpus graue poſſe deſcendere per <lb></lb>ſemicirculum, qui ſecet centrum mundi A, ſed etiam per plures alios. </s>
					<s id="N1E9AA"><lb></lb>v.g. per ſemicirculum ROB, quia ſcilicet ab R verſus BO &amp; ab O <lb></lb>verſus B ſemper deſcendit, aſcenditque propiùs ad A, cùm nulla linea in­<lb></lb>ter AOB duci poſſit ad punctum A, quæ non ſit maior BA, vt <lb></lb>conſtat. </s>
				</p>
				<p id="N1E9B6" type="main">
					<s id="N1E9B8">Vt autem habeas iſtos circulos; accipe centrum ſuprà A verſus K, mo­<lb></lb>do radius ſeu ſemidiameter deſcendat infrà A. v.g. IB vel KB, &amp;c. </s>
				</p>
				<p id="N1E9C0" type="main">
					<s id="N1E9C2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 94.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E9CE" type="main">
					<s id="N1E9D0"><emph type="italics"></emph>Hinc poteſt aliquis dimidium globum terreſtrem percurrere, licèt ſemper <lb></lb>deſcendat<emph.end type="italics"></emph.end>; </s>
					<s id="N1E9DB">vtſi conficiat ſemicirculum ROB, &amp; licet ſemper aſcendat, <pb pagenum="230" xlink:href="026/01/262.jpg"></pb>vt ſi conficiat ſemicirculum BIIR; hæc ita clara ſunt, vt oculis tantùm <lb></lb>indigeant. </s>
				</p>
				<p id="N1E9E6" type="main">
					<s id="N1E9E8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1E9F4" type="main">
					<s id="N1E9F6"><emph type="italics"></emph>Hinc poteſt eſſe mons per quem aliquis aſcendat, licèt ſub planum horizon­<lb></lb>tale deſcendat.<emph.end type="italics"></emph.end> v.g. ſit Tangens in puncto B; </s>
					<s id="N1EA03">haud dubiè qui ex B verſus <lb></lb>H procederet per arcum BH, haud dubiè aſcenderet, quia recederet <lb></lb>ſemper à centro mundi A; </s>
					<s id="N1EA0B">deſcenderet tamen infra Tangentem in B; </s>
					<s id="N1EA0F">igi­<lb></lb>tur mons eſſet infra horizontale planum; montem enim appello tractum <lb></lb>arduum, in quo dum aliquis ambulat, aſcendit, hoc eſt recedit à terræ <lb></lb>centro. </s>
				</p>
				<p id="N1EA19" type="main">
					<s id="N1EA1B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 96.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EA27" type="main">
					<s id="N1EA29"><emph type="italics"></emph>Diuerſæ eſſent rationes motus in deſcenſu per ſemicirculum QLA<emph.end type="italics"></emph.end>; </s>
					<s id="N1EA32">ſcilicet <lb></lb>in iis punctis, quæ propiùs accedunt ad A motus eſſet velocior initio <lb></lb>ſcilicet; </s>
					<s id="N1EA3A">poteſt autem haberi hæc proportio ductis Tangentibus, vt ſæpè <lb></lb>iam dixi; </s>
					<s id="N1EA40">at verò in ſemicirculo ROB in puncto T eſſet velociſſimus mo­<lb></lb>tus initio, quia angulus ITA eſt maximus eorum omnium, qui poſſunt <lb></lb>fieri ductis duabus rectis ab A &amp; I coëuntibus in ſemicirculo ROB, igi­<lb></lb>tur &amp; illi oppoſitus; </s>
					<s id="N1EA4A">igitur perpendiculum AT accedit propiùs ad Tan­<lb></lb>gentem; </s>
					<s id="N1EA50">igitur planum inclinatius eſt; </s>
					<s id="N1EA54">igitur in puncto T eſt velocior mo­<lb></lb>tus initio quàm in aliis; igitur acceleratur motus ab R in T per cre­<lb></lb>menta ſemper maiora, &amp; ab ipſo T ad B per crementa minora. </s>
				</p>
				<p id="N1EA5C" type="main">
					<s id="N1EA5E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 97.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EA6A" type="main">
					<s id="N1EA6C"><emph type="italics"></emph>Poteſt deſcendere corpus graue v.g. globus vſque ad centrum terræ per He­<lb></lb>licem<emph.end type="italics"></emph.end>; </s>
					<s id="N1EA79">ſit enim globus terræ AEQO, centrum K; </s>
					<s id="N1EA7D">diuidatur QK in 4. <lb></lb>partes æquales QR.RP.PS.SK; </s>
					<s id="N1EA83">aſſumatur EH æqualis QR, &amp; AC æqua­<lb></lb>lis QP, &amp; OM æqualis QS; </s>
					<s id="N1EA89">tùm per ſignata puncta deſcribatur helix Q <lb></lb>HCZMK: </s>
					<s id="N1EA8F">dico quod per eius conuexum globus deſcenderet ex Q, ad <lb></lb>centrum terræ; </s>
					<s id="N1EA95">quia ſemper accedit propiùs ad centrum; </s>
					<s id="N1EA99">immò per plura <lb></lb>volumina deſcendere poteſt; ſit enim QK diuiſa in 8. partes æquales Q <lb></lb>TTR, &amp;c. </s>
					<s id="N1EAA1">tùm aſſumatur EF æqualis QT, AB æqualis QR, ON æqualis <lb></lb>QV tùm QR in ipſa QK, &amp; æqualis QY, ED, a qualis QS, &amp; OL æqualis <lb></lb>QX; &amp; per puncta aſſignata deſcribatur Helix QFBNPIDLK, per cam <lb></lb>deſcenderet globus ad centrum terræ K poſt duas circumuolutiones. </s>
				</p>
				<p id="N1EAAB" type="main">
					<s id="N1EAAD">Per aliam quoque ſpiralem compoſitam ex ſemicirculis deſcendere <lb></lb>poteſt ad centrum terræ B; </s>
					<s id="N1EAB3">ſit enim centrum terræ F &amp; globus terræ A <lb></lb>CMD; </s>
					<s id="N1EAB9">accipiantur duo puncta hinc inde HK ad libitum; </s>
					<s id="N1EABD">tunc ex H <lb></lb>fiat ſemicirculus MB; </s>
					<s id="N1EAC3">haud dubiè globus poſitus in M deſcendet in B per <lb></lb>conuexum ſemicirculi in B; </s>
					<s id="N1EAC9">quia B inter omnia illius puncta accedit pro­<lb></lb>ximè ad F; </s>
					<s id="N1EACF">tùm ex K ducatur ſemicirculus BI; </s>
					<s id="N1EAD3">certè ex B deſcenderet in I <lb></lb>propter <expan abbr="eãdem">eandem</expan> rationem, tùm ex H deſcribatur ſemicirculus IF; </s>
					<s id="N1EADD">certè <lb></lb>ex I deſcendet in F, quæ omnia patent ex dictis; </s>
					<s id="N1EAE3">poſſunt autem multipli­<lb></lb>cari iſtæ ſpiræ in infinitum: Hinc licèt globus ſingulis horis 100000. leu­<lb></lb>cas conficeret in deſcenſu, non tamen attingeret centrum niſi poſt 1000. <lb></lb>annos, immò plures ſecundùm numerum ſpirarum. </s>
				</p>
				<pb pagenum="231" xlink:href="026/01/263.jpg"></pb>
				<p id="N1EAF1" type="main">
					<s id="N1EAF3">Denique poteſt deſcendere per plura plana inclinata AKLMNO <lb></lb>PQRST, ſiue ducantur perpendiculariter, ſcilicet AK in BC, KL in B <lb></lb>D, atque ita deinceps; </s>
					<s id="N1EAFB">ſiue non perpendiculariter, modò DL ſit maior C <lb></lb>K, EM maior DL, at que ita deinceps; attamen vltimum planum TB non <lb></lb>erit inclinatum, ſed perpendiculum, vt patet. </s>
				</p>
				<p id="N1EB03" type="main">
					<s id="N1EB05"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 98.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EB11" type="main">
					<s id="N1EB13"><emph type="italics"></emph>Poſſunt eſſe infinita plana inter orbem terræ, &amp; horizontale per quæ globus <lb></lb>ſeu corpus graue non deſcendet<emph.end type="italics"></emph.end>; </s>
					<s id="N1EB1E">ſit enim centrum terræ C, ex quo deſcri­<lb></lb>batur arcus QMH ducta diametro MCA in M; </s>
					<s id="N1EB24">ducatur Tangens NM <lb></lb>L; </s>
					<s id="N1EB2A">hæc erit horizontale planum, vt conſtat; </s>
					<s id="N1EB2E">tùm ex aliquo puncto infra C <lb></lb>putà ex A deſcribatur arcus SMK; </s>
					<s id="N1EB34">cercè ſi ponatur globus in M non <lb></lb>deſcendet per arcum MG, quia potiùs aſcenderet; </s>
					<s id="N1EB3A">immò ſi ponatur <lb></lb>in T deſcendet in M, immò faciliùs pelleretur corpus graue per arcum <lb></lb>MT, quàm per horizontalem MN, vt patet; </s>
					<s id="N1EB42">igitur potentia illa, quæ per <lb></lb>horizontalem pellit non eſt omnium minima, quæ per arcum MQ pel­<lb></lb>lit; quia in eo nullo modo globus aſcendit, ſed ſemper à centro C æqui­<lb></lb>diſtat. </s>
					<s id="N1EB4C">Si verò aſſumas quæcumque centra ſupra B putà D, &amp; E, &amp; ducas <lb></lb>arcus TMGPOMF; </s>
					<s id="N1EB52">certè globus deſcendet per MO, &amp; MP, vt manife­<lb></lb>ſtum eſt ex dictis, &amp; hoc fortè ludicrum cuiquam videbitur; </s>
					<s id="N1EB58">ſi enim col­<lb></lb>locetur globus in T, deſcendit verſus M; </s>
					<s id="N1EB5E">ſi verò in Y deſcendet verſus <lb></lb>P; </s>
					<s id="N1EB64">licèt V &amp; T non diſtét pollice; </s>
					<s id="N1EB68">poſſunt enim accipi minima illa ſpatia <lb></lb>verſus M, vbi eſt angulus contingentiæ; </s>
					<s id="N1EB6E">nulla tamen poteſt duci recta ab <lb></lb>M infra MN, per quam globus non deſcendat velociùs initio, quàm per <lb></lb>vllum arcum, ſiue MP, ſiue MO, ſiue quemcumque alium quamtumuis <lb></lb>maximè incuruatum vel inclinatum; </s>
					<s id="N1EB78">quia ſcilicet recta illa ducta ex M <lb></lb>infra MN ſecat omnes illos arcus, vt patet; </s>
					<s id="N1EB7E">igitur initio facit planum <lb></lb>inclinatius: dixi initio, quia deinde in arcu multùm inualeſcit motus, <lb></lb>cum ſemper deficiat in recta, vt diximus abundè ſuprà. </s>
				</p>
				<p id="N1EB86" type="main">
					<s id="N1EB88"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 99.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EB94" type="main">
					<s id="N1EB96"><emph type="italics"></emph>Si quadrans ita diſtet à centro mundi, vt tùm alter eius radius, tùm Tan­<lb></lb>gens ipſi parallela cenſeantur perpendiculares, globus deſcendet ex eius vertice <lb></lb>per arcum<emph.end type="italics"></emph.end>: </s>
					<s id="N1EBA3">Sit enim quadrans ATE erectus ſupra horizontem, ita vt <lb></lb>AE ſit horizontalis, &amp; tùm TA, tùm 3. A perpendiculares; </s>
					<s id="N1EBA9">certè deſcen­<lb></lb>det globus per eius conuexum VBA in eadem proportione, in qua deſ­<lb></lb>cerdit per ſemicirculum, de quo ſuprà; </s>
					<s id="N1EBB1">Igitur motus per quadrantem T <lb></lb>BE eſt ad motum per ipſum perpendiculum in eadem ratione, in qua eſt <lb></lb>ad motum per ſemicirculum; </s>
					<s id="N1EBB9">quippe motus in T nullus eſt per arcum TE; </s>
					<s id="N1EBBD"><lb></lb>5.verò motus per arcum 5.E, initio ſcilicet, vt ſæpè dictum eſt, eſt ad mo­<lb></lb>tum per ipſam perpendicularem vt A 7.ad A 5.in 4.vt A 7.ad A 4. in B <lb></lb>vt A <foreign lang="grc">δ</foreign> ad AB, in D vt AH ad AD in X vt AF ad AX, in E, vt AE ad A <lb></lb>E; </s>
					<s id="N1EBCC">vides autem tranſire motum hunc ferè per omnes gradus tarditatis: </s>
					<s id="N1EBD0">di­<lb></lb>co ferè, quia reuerâ non tranſit per omnes; quippe ſi fieret maior qua­<lb></lb>drans tangens iſtum in T, motus eſſet iuxta initium præſertim tar­<lb></lb>dior. </s>
				</p>
				<pb pagenum="232" xlink:href="026/01/264.jpg"></pb>
				<p id="N1EBDE" type="main">
					<s id="N1EBE0">Obſeruaſti iam vt puto motum per Arcum TBE eſſe inuerſum vul­<lb></lb>garis funependuli; </s>
					<s id="N1EBE6">quippe in illo motuum incrementa initio ſunt mino­<lb></lb>ra, &amp; ſemper creſcunt; at verò in hoc initio ſunt maiora, &amp; ſemper de­<lb></lb>creſcunt. </s>
				</p>
				<p id="N1EBEE" type="main">
					<s id="N1EBF0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 100.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EBFC" type="main">
					<s id="N1EBFE"><emph type="italics"></emph>Poſſunt determinari vires, quæ ſuſtinere poſſunt datum pondus collocatum̨<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>in arcu erecto ATE<emph.end type="italics"></emph.end>: </s>
					<s id="N1EC0D">quippe ad ſuſtinendum pondus in T nullæ vires <lb></lb>requiruntur, ad ſuſtinendum in E æqualis potentia ponderi requiritur; </s>
					<s id="N1EC13"><lb></lb>at verò potentia, quæ ſuſtinet in 5. ſe habet ad æqualem vt A 7.ad AE, <lb></lb>in 4.vt A Z.ad AE, in B vt A<foreign lang="grc">δ</foreign> ad AE, in D vt AH ad AE, in X vt AF ad <lb></lb>AE; </s>
					<s id="N1EC20">denique in E vt AE ad AE; ratio eſt, quia potentia debet eſſe pro­<lb></lb>portionata momento ponderis, ſeu motus, ſed motus in B.v.g.per BE eſt <lb></lb>ad motum qui fit per perpendicularem vt A<foreign lang="grc">δ</foreign> ad AB vel AE, igitur po­<lb></lb>tentia quæ impedit hunc motum, id eſt quæ ſuſtinet pondus in B eſt ad <lb></lb>illam quæ ſuſtinet in E vt A <foreign lang="grc">δ</foreign> ad AE. </s>
				</p>
				<p id="N1EC35" type="main">
					<s id="N1EC37">Debet autem ſuſtineri pondus vel per Tangentem ductam ad punctum <lb></lb>B vel ipſi parallelam in certo dumtaxat funiculo, vt fit in trochleis; vnde <lb></lb>ſi ſemicirculus A 2.E ſit trochlea, &amp; pondus pendeat ex E, <expan abbr="adhibeaturq;">adhibeaturque</expan> <lb></lb>potentia trahens in A, debet eſſe æqualis ponderi, ſed de trochleis fusè <lb></lb>lib.  11. </s>
				</p>
				<p id="N1EC47" type="main">
					<s id="N1EC49">Hinc etiam facilè determinari poteſt quomodo deſtruatur impetus, <lb></lb>ſi proiiciatur globus per arcum EBT ſurſum; </s>
					<s id="N1EC4F">nam in eadem proportione <lb></lb>deſtruetur in aſcendendo, qua acceleratur deſcendendo; </s>
					<s id="N1EC55">neque eſt hîc <lb></lb>ſingularis difficultas; </s>
					<s id="N1EC5B">quemadmodum enim in deſcenſu ſemper accele­<lb></lb>ratur per incrementa inæqualia iuxta rationem explicatam; </s>
					<s id="N1EC61">ita in aſcen­<lb></lb>ſu ſemper retardatur per detractiones inæquales; </s>
					<s id="N1EC67">in deſcenſu quidem per <lb></lb>incrementa initio minora, &amp; maiora ſub finem; in aſcenſu è contrario <lb></lb>per detractiones initio maiores ſub finem minores. </s>
				</p>
				<p id="N1EC6F" type="main">
					<s id="N1EC71">Hinc denique determinari poteſt quantùm corpus grauitet in toto <lb></lb>arcu TBE; </s>
					<s id="N1EC77">in E nihil grauitat, in T totum grauitat; igitur grauitatio in <lb></lb>T, ſeu tota eſt ad grauitationem in E, vt TA ad nihil, in 5. verò vt AT <lb></lb>ad AT, in 4. vt AT ad AA, in B vt AT ad AS, atque ita deinceps, quæ <lb></lb>conſtant ex dictis. </s>
				</p>
				<p id="N1EC81" type="main">
					<s id="N1EC83">Inſuper obſerua corpus graue incumbens arcui TBE, per varias lineas <lb></lb>poſſe pelli, vel trahi, de quibus idem prorſus dicendum eſt, quod dictum <lb></lb>eſt in Th.5. &amp; Sch.Th.16. </s>
				</p>
				<p id="N1EC8A" type="main">
					<s id="N1EC8C">Adde quod omiſimus, ſed facilè ex dictis lib.  1. intelligi poteſt, im­<lb></lb>petum qui producitur in acceleratione motus per planum inclinatum <lb></lb>eſſe imperfectiorem ex duplici capite; primò ratione minoris temporis, <lb></lb>quo producitur ex ratione maioris vel minoris inclinationis, ſeu longi­<lb></lb>tudinis. </s>
					<s id="N1EC98">v.g. ſit planum inclinatum AC; </s>
					<s id="N1EC9E">certè cum poſt motum per A <lb></lb>E, &amp; per AB ſit æqualis ictus vel impetus; </s>
					<s id="N1ECA4">&amp; cùm tempus quo deſcendit <lb></lb>per AE ſit duplum temporis, quo deſcendit per AB; </s>
					<s id="N1ECAA">certè ſingulis inſtan­<lb></lb>tibus, quibus durat motus per AC, producitur impetus ſubduplus tan-<pb pagenum="233" xlink:href="026/01/265.jpg"></pb>tùm in perfectione illius, qui producitur per AB; ſi enim æqualis perfe­<lb></lb>ctionis; </s>
					<s id="N1ECB7">igitur impetus poſt deſcenſum per AC eſſet duplus illius qui ha­<lb></lb>betur in B poſt deſcenſum per AB; </s>
					<s id="N1ECBD">ſi autem eſſet minor ſubduplo; </s>
					<s id="N1ECC1">igitur <lb></lb>in C, vel impetus eſſet minor quam in B contra hypotheſim; </s>
					<s id="N1ECC7">igitur debet <lb></lb>ſubduplus; </s>
					<s id="N1ECCD">igitur duplò plures ſunt gradus impetus in C quàm in B, cùm <lb></lb>ſcilicet ſinguli gradus impetus in B æquiualeant duobus impetus in A: <lb></lb>his adde aliqua breuia Corollaria, quæ quiſque ex dictis facilè colligere <lb></lb>poterit. </s>
				</p>
				<p id="N1ECD7" type="main">
					<s id="N1ECD9"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ECE6" type="main">
					<s id="N1ECE8">Ex his primò vides perfectam analogiam impetus in omni motu, qui <lb></lb>reuera explicari non poteſt, niſi detur impetus alio imperfectior: </s>
					<s id="N1ECEE">Porrò <lb></lb>multa hîc deſiderantur, quæ ad motum in planis inclinatis pertinent, que <lb></lb>in Tomum ſequentem remittimus; quia potiori iure ad Mathematicam <lb></lb>ſpectant, quàm ad Phyſicam. </s>
				</p>
				<p id="N1ECF8" type="main">
					<s id="N1ECFA"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ED07" type="main">
					<s id="N1ED09">Secundò, impetus poſſe in infinitum decreſcere perfectionem quod <lb></lb>primò conſtat ex eo, quòd infra horizontalem poſſint duci lineæ minùs <lb></lb>&amp; minùs inclinatæ: ſecundò ex eo, quòd poſſint inter quamlibet inclina­<lb></lb>tam deorſum rectam, &amp; ſuperficiem orbis terræ deſcribi infiniti orbes, <lb></lb>quorum centrum ſit ſupra centrum terræ, quorum arcus initio faciunt <lb></lb>minorem, &amp; minorem inclinationem. </s>
				</p>
				<p id="N1ED17" type="main">
					<s id="N1ED19"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ED26" type="main">
					<s id="N1ED28">Tertiò, hinc colliges impetum qui producitur in primo puncto deſ­<lb></lb>cenſus illorum arcuum eſſe prorſus alogum cum illo, qui producitur in <lb></lb>primo puncto deſcenſus cuiuſlibet rectæ inclinatæ, &amp; illum qui à pro­<lb></lb>ximo puncto verſus punctum contactus in Tangente producitur <lb></lb>eſſe etiam alogum cum illo, qui in proximo puncto verſus idem pun­<lb></lb>ctum contactus producitur in circumferentia circuli, cuius centrum ſit <lb></lb>infra centrum terræ, id eſt cuius radius ſit longior radio orbis terræ, </s>
				</p>
				<p id="N1ED37" type="main">
					<s id="N1ED39"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ED46" type="main">
					<s id="N1ED48">Quartò, quid mirabilius quam ad idem punctum contactus poſſe du­<lb></lb>ci infinitos circulos quorum arcus omnes in eaſdem partes incuruan­<lb></lb>tur, licèt ſint infiniti? </s>
					<s id="N1ED4F">quia ſumpto termino in eodem puncto contactus <lb></lb>omninò aſcendant ſcilicet ij, qui maiores ſunt orbe terræ, &amp; infiniti, qui <lb></lb>deſcendunt, ij ſcilicet qui minores ſunt; &amp; vnicus tantùm medius, qui <lb></lb>nec aſcendat nec deſcendat, qui eſt orbis terræ. </s>
				</p>
				<p id="N1ED59" type="main">
					<s id="N1ED5B"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ED68" type="main">
					<s id="N1ED6A">Quintò, non poſſe faciliùs globum moueri, quàm in ſuperficie terræ, <lb></lb>ſi probè læuigata eſſet; </s>
					<s id="N1ED70">nullum enim eſt planum ſupra ſiue rectum, ſiue <lb></lb>curuum, quod non aſcendat; </s>
					<s id="N1ED76">nullum infrà quod non deſcendat: hinc mo­<lb></lb>tus eſſet æquabilis. </s>
				</p>
				<pb pagenum="234" xlink:href="026/01/266.jpg"></pb>
				<p id="N1ED80" type="main">
					<s id="N1ED82"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1ED8F" type="main">
					<s id="N1ED91">Sextò, cum globus rotatur in plano inclinato mouetur motu mixto, <lb></lb>ſcilicet ex motu orbis &amp; centri, <expan abbr="moueturq́ue">moueturque</expan> velociùs quàm cubus eiuſ­<lb></lb>dem ponderis; </s>
					<s id="N1ED9D">quia pauciores partes plani fricantur à globo; </s>
					<s id="N1EDA1">ſed hæc ra­<lb></lb>tio non valet, niſi ſupponatur planum non eſſe perfectè læuigatum; </s>
					<s id="N1EDA7">igi­<lb></lb>tur eſt alia ratio: an quia cubus mouetur motu centri? </s>
					<s id="N1EDAD">globus verò motu <lb></lb>centri &amp; orbis; </s>
					<s id="N1EDB3">ſed motus orbis iuuat motum centri; </s>
					<s id="N1EDB7">ſed hæc ratio nulla <lb></lb>eſt, quia <expan abbr="tantũdem">tantundem</expan> pars ſuperior globi addit motui centri quantùm <lb></lb>inferior detrahit; </s>
					<s id="N1EDC3">igitur alia ratio eſt, ſcilicet non tantùm globum deſ­<lb></lb>cendere in plano inclinato per grauitatem abſolutam, ſed etiam per reſ­<lb></lb>pectiuam, <expan abbr="eſtq́ue">eſtque</expan> veluti potentia Mechanica admota, ſcilicet vectis, cu­<lb></lb>jus quaſi vicem gerit ſemidiameter circuli: </s>
					<s id="N1EDD1">porrò vectis centrum eſt <lb></lb>punctum contactus; </s>
					<s id="N1EDD7">dixi ſemidiametrum, non verò diametrum; </s>
					<s id="N1EDDB">quia to­<lb></lb>tum pondus globi non eſt appenſum extremæ diametro, ſed extremæ ſe­<lb></lb>midiametro in hoc caſu; illa autem extremitas eſt centrum grauitatis <lb></lb>globi. </s>
				</p>
				<p id="N1EDE5" type="main">
					<s id="N1EDE7"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EDF3" type="main">
					<s id="N1EDF5">Septimò, hinc etiam apparet analogia impetus imperfectioris, qui pro­<lb></lb>ducitur verſus centrum vectis, &amp; illius, qui producitur in mobili per <lb></lb>planum inclinatum; </s>
					<s id="N1EDFD">nam ideo eſt imperfectior, qui producitur verſus <lb></lb>centrum vectis, quia temporibus æqualibus partes mobiles vectis, quæ <lb></lb>ſunt verſus centrum acquirunt ſpatia inæqualia ſcilicet, minora, &amp; mi­<lb></lb>nora in infinitum; </s>
					<s id="N1EE07">ita prorſus in planis inclinatis cum acquirantur tem­<lb></lb>poribus æqualibus ſpatia inæqualia; </s>
					<s id="N1EE0D">minora certè in longioribus, ſup­<lb></lb>poſita dumtaxat eadem perpendiculi altitudine debet produci impetus <lb></lb>imperfectior; nam ex imperfectione effectus id eſt motus, benè colligitur <lb></lb>imperfectio cauſæ id eſt impetus. </s>
				</p>
				<p id="N1EE17" type="main">
					<s id="N1EE19"><emph type="center"></emph><emph type="italics"></emph>Collorarium<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EE25" type="main">
					<s id="N1EE27">Octauò denique, mirabile eſt, quî fieri poſſit, vt eadem potentia quæ <lb></lb>totas ſuas vires exerens globum proiicit per lineam verticalem ad al­<lb></lb>titudinem vnius pollicis, id eſt quæ proiicere tantùm poteſt per ſpatium <lb></lb>digitale, per omnes tamen inclinatas, quæ ad extremitatem huius per­<lb></lb>pendiculi duci poſſunt, cuiuſcunque ſint longitudinis, non auctis viri­<lb></lb>bus proiiciat; quis hoc crederet? </s>
					<s id="N1EE35">niſi manifeſta cogeret demonſtratio, <lb></lb>quam habes in Th.20.27. &amp;c. </s>
				</p>
			</chap>
			<chap id="N1EE3A">
				<pb pagenum="235" xlink:href="026/01/267.jpg"></pb>
				<figure id="id.026.01.267.1.jpg" xlink:href="026/01/267/1.jpg"></figure>
				<p id="N1EE44" type="head">
					<s id="N1EE46"><emph type="center"></emph>LIBER SEXTVS, <lb></lb><emph type="italics"></emph>DE MOTV REFLEXO.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EE53" type="main">
					<s id="N1EE55">DE motu reflexo agendum eſſe videtur hoc <lb></lb>loco; præmittenduſque eſt motui circula­<lb></lb>ri, qui fortè ſine motu reflexo nunquam fit, <lb></lb>vt dicemus infrà. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N1EE62" type="main">
					<s id="N1EE64"><emph type="center"></emph><emph type="italics"></emph>DEPINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EE70" type="main">
					<s id="N1EE72"><emph type="italics"></emph>MOtus reflexus eſt reditus mobilis ratione corporis impedientis primam <lb></lb>lineam motus.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1EE7B" type="main">
					<s id="N1EE7D">Hæc definitio eſt clara; </s>
					<s id="N1EE81">dicitur reditus, quia reuerâ mobile, quod re­<lb></lb>percutitur, ſeu reflectitur, quaſi redit, ſeu retrò agitur; </s>
					<s id="N1EE87">ſiue id fiat per <lb></lb>eandem lineam, quâ appulſum fuit; ſiue per aliam: </s>
					<s id="N1EE8D">ſic pila in murum <lb></lb>impacta reflecti dicitur, ita vt eius linea frangatur in ipſa muri ſuperfi­<lb></lb>cie, quod duobus tantùm modis fieri poteſt: primò ſine angulo, vt cum <lb></lb>redit mobile per eandem lineam, per quam priùs acceſſerat, ſicque linea <lb></lb>reflexionis opponi videtur ex diametro lineæ incidentiæ. </s>
					<s id="N1EE99">Secundò cum <lb></lb>angulo, quòd ſcilicet in puncto reflexionis linea reflexionis cum linea <lb></lb>incidentiæ faciat angulum. </s>
				</p>
				<p id="N1EEA0" type="main">
					<s id="N1EEA2"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EEAF" type="main">
					<s id="N1EEB1"><emph type="italics"></emph>Corpus reflectens eſt, quod motum liberum alterius corporis impacti non <lb></lb>permittit vlteriùs per eandem lineam propagari, ſed illius lineam frangit, &amp; <lb></lb>inflectit,<emph.end type="italics"></emph.end> &amp;c. </s>
					<s id="N1EEBD">huius corporis conditiones in ſequentibus Theorematis <lb></lb>definiemus. </s>
				</p>
				<p id="N1EEC2" type="main">
					<s id="N1EEC4"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EED1" type="main">
					<s id="N1EED3"><emph type="italics"></emph>Punctum reflexionis eſt punctum illud plani reflectentis, in quo linea refle­<lb></lb>xionis, &amp; linea incidentiæ coëunt.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1EEDC" type="main">
					<s id="N1EEDE"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EEEB" type="main">
					<s id="N1EEED"><emph type="italics"></emph>Linea incidentiæ eſt illa linea motus. </s>
					<s id="N1EEF2">per quam mobile ante reflexionem ap­<lb></lb>pellitur ad planum reflectens.<emph.end type="italics"></emph.end></s>
				</p>
				<pb pagenum="236" xlink:href="026/01/268.jpg"></pb>
				<p id="N1EEFD" type="main">
					<s id="N1EEFF"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EF0C" type="main">
					<s id="N1EF0E"><emph type="italics"></emph>Linea reflexionis eſt illa linea motus, per quam mobile poſt reflexionem re­<lb></lb>cedit à plano inclinato<emph.end type="italics"></emph.end>; hinc vides punctum reflexionis eſſe terminum ad <lb></lb>quem illius lineæ, &amp; terminum à quo huius. </s>
				</p>
				<p id="N1EF1B" type="main">
					<s id="N1EF1D"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EF2A" type="main">
					<s id="N1EF2C"><emph type="italics"></emph>Angulus incidentiæ eſt, quem facit cum plano reflectente linea inci­<lb></lb>dentiæ.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1EF35" type="main">
					<s id="N1EF37"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EF43" type="main">
					<s id="N1EF45"><emph type="italics"></emph>Angulus reflexionis eſt, quem facit linea reflexionis cum eodem plano.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1EF4C" type="main">
					<s id="N1EF4E"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EF5A" type="main">
					<s id="N1EF5C"><emph type="italics"></emph>Cathetus eſt linea perpendiculariter cadens in planum reflectens ducta ab <lb></lb>aliquo puncto linea incidentia<emph.end type="italics"></emph.end>; </s>
					<s id="N1EF67">&amp; tunc dicitur Cathetus incidentiæ; </s>
					<s id="N1EF6B">vel <lb></lb>ab aliquo lineæ reflexionis, &amp; tunc dicitur Cathetus reflexionis; hæc <lb></lb>omnia ſunt facilia, quæ in gratiam Tyronum breuiter in figura <lb></lb>propono. </s>
				</p>
				<p id="N1EF75" type="main">
					<s id="N1EF77">Sit FB linea plani reflectentis; </s>
					<s id="N1EF7B">ſit D punctum reflexionis; ſit AD <lb></lb>linea incidentiæ, DH linea reflexionis, AB Cathetus incidentiæ, HF <lb></lb>Cathetus reflexionis, ADB angulus incidentiæ, EDF oppoſitus, <lb></lb>HDF angulus reflexionis, CDB oppoſitus, ADH angulus aperturæ <lb></lb>vel pyramidis reflexionis, EDC oppoſitus, ADE angulus ſupplementi <lb></lb>anguli incidentiæ, HDG angulus complementi anguli reflexionis, re­<lb></lb>ctangulum BH ſuperficies reflexionis, BF ſectio plani reflectentis, &amp; <lb></lb>prædictæ ſuperficiei. </s>
				</p>
				<p id="N1EF8D" type="main">
					<s id="N1EF8F"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EF9C" type="main">
					<s id="N1EF9E"><emph type="italics"></emph>Aliquod corpus in aliud cum impetu impaction reflectitur,<emph.end type="italics"></emph.end> hæc hypothe­<lb></lb>ſis certa eſt. </s>
				</p>
				<p id="N1EFA8" type="main">
					<s id="N1EFAA"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EFB7" type="main">
					<s id="N1EFB9"><emph type="italics"></emph>Corpus reflexum in aliud impactum aliquando illud mouet<emph.end type="italics"></emph.end>; ſic pila ab <lb></lb>aliquo corpore reflexa in aliam incidens mouet illam. </s>
				</p>
				<p id="N1EFC4" type="main">
					<s id="N1EFC6"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EFD3" type="main">
					<s id="N1EFD5"><emph type="italics"></emph>Quo motus directus, ſcilicet qui ſis per lineam incidentia, eſt maior, maior <lb></lb>eſt quoque motus reflexus<emph.end type="italics"></emph.end>; ſi enim maiore vi pila appellitur in parietem <lb></lb>maiore vi etiam retorquctur. </s>
				</p>
				<p id="N1EFE2" type="main">
					<s id="N1EFE4"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1EFF1" type="main">
					<s id="N1EFF3"><emph type="italics"></emph>Idem impetus ad plures lineas determinari pereſt ſeorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1EFFC">hoc Axima <lb></lb>certum eſt; probatum eſt in libro 1. Th.113.114. &amp;c. </s>
					<s id="N1F002">dixi ſeorſim, nam <lb></lb>plures ſimul lineas habere non poteſt per Th.115.l.1. </s>
				</p>
				<p id="N1F007" type="main">
					<s id="N1F009"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F016" type="main">
					<s id="N1F018"><emph type="italics"></emph>Vbi eſt effectus, ibi eſt cauſa, effectus inquam formalis,<emph.end type="italics"></emph.end> v. g. vbi eſt album, <lb></lb>ibi eſt id, quod exigit motum, ſeu præſtat illum motum in mobili; </s>
					<s id="N1F027">id eſt <pb pagenum="237" xlink:href="026/01/269.jpg"></pb>impetus: quippe omnis motus eſt ab impetu, quod ſæpiùs in toto libro <lb></lb>primo demonſtratum eſt. </s>
				</p>
				<p id="N1F032" type="main">
					<s id="N1F034"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F041" type="main">
					<s id="N1F043"><emph type="italics"></emph>Impetus destruitur tantùm ne ſit frustra per Sch. Theor.<emph.end type="italics"></emph.end>152.<emph type="italics"></emph>&amp; alia multa <lb></lb>libro primò,<emph.end type="italics"></emph.end> ſi enim impetus ſuum poſſet habere effectum reuerâ non de­<lb></lb>ſtrueretur. </s>
				</p>
				<p id="N1F057" type="main">
					<s id="N1F059"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F066" type="main">
					<s id="N1F068"><emph type="italics"></emph>Tunc dici non poteſt tota cauſa destructa (cauſa inquam formalis) cum <lb></lb>tuus effectus non eſt deſtructus<emph.end type="italics"></emph.end>; ſeu tunc non debet dici deſtructus totus <lb></lb>impetus cum totus motus non eſt deſtructus. </s>
				</p>
				<p id="N1F075" type="main">
					<s id="N1F077"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F084" type="main">
					<s id="N1F086"><emph type="italics"></emph>Datur motus reflexus<emph.end type="italics"></emph.end>; </s>
					<s id="N1F08F">nemo dubitat: </s>
					<s id="N1F093">quippe aliquod corpus in aliud <lb></lb>impactum reflectitur per Ax. primum ſed ſi corpus reflectitur eſt motus <lb></lb>reflexus; </s>
					<s id="N1F09B">igitur certum eſt de motu reflexo quod ſit; infrà verò videbi­<lb></lb>mus propter quid ſit. </s>
				</p>
				<p id="N1F0A1" type="main">
					<s id="N1F0A3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F0B0" type="main">
					<s id="N1F0B2"><emph type="italics"></emph>In motu reflexo eſt impetus<emph.end type="italics"></emph.end>; probatur, quia vbi eſt motus, ibi eſt impe­<lb></lb>tus per Axioma 2. </s>
				</p>
				<p id="N1F0BE" type="main">
					<s id="N1F0C0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F0CD" type="main">
					<s id="N1F0CF"><emph type="italics"></emph>Hinc cauſa motus reflexi eſt impetus qui ineſt corpori reflexo<emph.end type="italics"></emph.end>; </s>
					<s id="N1F0D8">nec enim eſt <lb></lb>quidquam aliud applicatum cum mobile ſeparatum tùm à corpore refle­<lb></lb>ctente, tùm à manu proiicientis etiam moueatur; </s>
					<s id="N1F0E0">igitur nihil extrinſe­<lb></lb>cum poteſt eſſe cauſa huius motus; </s>
					<s id="N1F0E6">igitur aliquod intrinſecum, voco <lb></lb>impetum; </s>
					<s id="N1F0EC">hîc diutiùs non hæreo, quia ſimile argumentum habes in ter­<lb></lb>tio libro, in quo fusè probaui requiri impetum ad motum violentum, <lb></lb>atqui nullus motus reflexus eſt naturalis; igitur violentus vel mixtus, <lb></lb>igitur requirit neceſſariò impetum. </s>
				</p>
				<p id="N1F0F6" type="main">
					<s id="N1F0F8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F105" type="main">
					<s id="N1F107"><emph type="italics"></emph>Ille impetus vel producitur nouus, vel conſeruatur prauius<emph.end type="italics"></emph.end>; clarum eſt, <lb></lb>nec aliud excogitari poteſt. </s>
				</p>
				<p id="N1F112" type="main">
					<s id="N1F114"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F121" type="main">
					<s id="N1F123"><emph type="italics"></emph>Ille impetus non producitur à corpore reflectente<emph.end type="italics"></emph.end>: </s>
					<s id="N1F12C">probatur primò, quia <lb></lb>omnis impetus producitur ad extra ab alio impetu per Theor. 42. lib.1. <lb></lb>Secundò probatur, quia corpus reflectens ſemper produceret impetum <lb></lb>in alio corpore applicato; </s>
					<s id="N1F138">eſſet enim cauſa neceſſaria; </s>
					<s id="N1F13C">igitur neceſſariò <lb></lb>ageret per Ax.12. lib.1. nec eſt quod dicas agere tantùm poſita tali con­<lb></lb>ditione: </s>
					<s id="N1F144">hoc eſt poſito motu præuio, quod ſatis ridiculum eſt, vt iam <lb></lb>aliàs monui; </s>
					<s id="N1F14A">quia conditio nihil aliud præſtat in cauſa quàm applicatio­<lb></lb>nem ſubiecti apti, in quo agat, &amp; ſubtractionem omnis impedimenti; </s>
					<s id="N1F150"><lb></lb>atqui cum proximè pila parieti adhæret, eſt omninò applicata, &amp; abeſt <lb></lb>omne impedimentum: </s>
					<s id="N1F157">præterea ſi corpus reflectens ageret; </s>
					<s id="N1F15B">haud dubiè <pb pagenum="238" xlink:href="026/01/270.jpg"></pb>ſi maius eſt maiorem impetum produceret; </s>
					<s id="N1F164">nec enim agit tantùm pars, <lb></lb>quæ tangitur; </s>
					<s id="N1F16A">alioqui globus qui tangit tantùm in puncto minimè re­<lb></lb>flecteretur; quid enim punctum agere poteſt? </s>
					<s id="N1F170">Igitur ſi tantùm agit, quo <lb></lb>maius eſt plùs agit; quæ omnia ſunt perabſurda; Igitur non producitur <lb></lb>ille impetus à corpore reflectente. </s>
					<s id="N1F178">Vide Th. 40.lib.1.&amp;c. </s>
				</p>
				<p id="N1F17B" type="main">
					<s id="N1F17D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F18A" type="main">
					<s id="N1F18C"><emph type="italics"></emph>Non producitur ab vllo alio extrinſeco<emph.end type="italics"></emph.end>; </s>
					<s id="N1F195">non ab aëre, qui motui obſi­<lb></lb>ſtit; </s>
					<s id="N1F19B">ſed nihil eſt aliud extrinſecum applicatum; </s>
					<s id="N1F19F">Igitur non producitur <lb></lb>ab vlla cauſa extrinſeca: </s>
					<s id="N1F1A5">adde ſi vis rationem euidentiſſimam, quæ Theo­<lb></lb>rema ſuperius mirificè confirmat; </s>
					<s id="N1F1AB">quia ſcilicet maximè applicatur mo­<lb></lb>bile corpori reflectenti per lineam perpendicularem; </s>
					<s id="N1F1B1">igitur per illam <lb></lb>maximè deberet agere: </s>
					<s id="N1F1B7">quippè per lineam obliquam quaſi tantùm allam­<lb></lb>bitur corpus reflectens; </s>
					<s id="N1F1BD">atqui linea reflexionis perpendicularis minima <lb></lb>eſt omnium quamuis per accidens, vt conſtat experientiâ, &amp; nos infrà <lb></lb>demonſtrabimus; </s>
					<s id="N1F1C5">cùm tamen deberet eſſe maxima; </s>
					<s id="N1F1C9">igitur impetus non <lb></lb>producitur in mobili reflexo, nec ab ipſo corpore reflectente, nec ab vllo <lb></lb>alio extrinſeco; quia nihil prorſus aliud applicatum eſt, à quo produci <lb></lb>poſſit. </s>
					<s id="N1F1D3">Reſpondent aliqui produci à generante; ſed quodnam eſt illud <lb></lb>generans? </s>
					<s id="N1F1D9">non cauſa ſecunda, vt patet; an verò prima? </s>
					<s id="N1F1DD">ſed quis dicat <lb></lb>moueri tantùm à Deo pilam à muro repercuſſam? </s>
					<s id="N1F1E2">ſed quidquid moue­<lb></lb>tur, inquies, ab alio mouetur, vt vult Philoſophus. </s>
					<s id="N1F1E8">Reſpondeo mediatè <lb></lb>ſcilicet, vel immediatè; </s>
					<s id="N1F1EE">quippe illa pila à ſe ipſa non mouetur, ſed ab <lb></lb>impulſore mediante, ſcilicet, impetu impreſſo; ſed hæc alibi iam indi­<lb></lb>cauimus. </s>
				</p>
				<p id="N1F1F6" type="main">
					<s id="N1F1F8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F204" type="main">
					<s id="N1F206"><emph type="italics"></emph>Non producitur ille impetus ab ipſo mobili,<emph.end type="italics"></emph.end> vt conſtat nec enim exigit <lb></lb>moueri illo motu; </s>
					<s id="N1F211">adde quod eſt cauſa neceſſaria; </s>
					<s id="N1F215">igitur nulla eſſet ra­<lb></lb>tio, cur modò maiorem, modò minorem effectum, hoc eſt impetum pro­<lb></lb>duceret; quod tamen accidit; ſed hæc ſunt facilia. </s>
				</p>
				<p id="N1F21D" type="main">
					<s id="N1F21F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F22B" type="main">
					<s id="N1F22D"><emph type="italics"></emph>Non producitur nouus impetus in reflectione pura:<emph.end type="italics"></emph.end> probatur, quia produ­<lb></lb>ceretur ab aliqua cauſa: </s>
					<s id="N1F238">illa autem eſſet vel extrinſeca, vel intrinſeca; </s>
					<s id="N1F23C"><lb></lb>non producitur ab vlla causâ extrinſecà per Theor.6.nec ab vlla intrin­<lb></lb>ſecâ per Th.7. igitur à nulla; </s>
					<s id="N1F243">igitur nullus producitur; </s>
					<s id="N1F247">dixi in reflexio­<lb></lb>ne purâ, quia præter reflexionem fieri poteſt, vt corpus reflectens mobi­<lb></lb>le impellat; </s>
					<s id="N1F24F">vt cum duo globi mutuò colliduntur, vel vt ſit aliqua com­<lb></lb>preſſio, quâ poſitâ nouus impetus producetur; </s>
					<s id="N1F255">non eſt tamen quòd ali­<lb></lb>quis dicat motum reflexum eſſe tantùm à compreſſione; </s>
					<s id="N1F25B">quia quò corpus <lb></lb>durius eſt; </s>
					<s id="N1F261">&amp; minùs redit, meliùs reflectitur; ſic marmor à marmore fa­<lb></lb>cilè reflectitur. </s>
				</p>
				<p id="N1F267" type="main">
					<s id="N1F269"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F275" type="main">
					<s id="N1F277"><emph type="italics"></emph>Hinc impetus ille, qui eſt cauſa motus reflexi, eſt idem cum præuio conſer<emph.end type="italics"></emph.end>-<pb pagenum="239" xlink:href="026/01/271.jpg"></pb><emph type="italics"></emph>uato<emph.end type="italics"></emph.end>; quia vel eſt productus de nouo, vel præuius, per Th. 4. non pri­<lb></lb>mum per Th.8.igitur eſt præuius. </s>
				</p>
				<p id="N1F28C" type="main">
					<s id="N1F28E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F29A" type="main">
					<s id="N1F29C"><emph type="italics"></emph>Hinc potentia motrix, quæ priùs impegit mobile in corpus reflectens eſt cau­<lb></lb>ſa huius motus reflexi<emph.end type="italics"></emph.end>; </s>
					<s id="N1F2A7">quia ſcilicet eſt cauſa impetus, vi cuius mobile <lb></lb>mouetur etiam motu reflexo; hinc qui ludit pilá, verè dicitur cauſa re­<lb></lb>flexionis pilæ, cauſa inquam, ſed mouens. </s>
				</p>
				<p id="N1F2AF" type="main">
					<s id="N1F2B1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F2BD" type="main">
					<s id="N1F2BF"><emph type="italics"></emph>Corpus reflectens dici poteſt aliquo modo cauſa reflexionis, id eſt, cauſa no­<lb></lb>uæ determinationis lineæ motus<emph.end type="italics"></emph.end>; niſi enim occurreret paries. </s>
					<s id="N1F2CA">v.g. non re­<lb></lb>flecteretur pila; quamquam dici debet potiùs occaſio, immò impedi­<lb></lb>mentum prioris lineæ, ex quo neceſſariò ſequitur noua linea, ve dicam <lb></lb>infrà. </s>
				</p>
				<p id="N1F2D6" type="main">
					<s id="N1F2D8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F2E4" type="main">
					<s id="N1F2E6"><emph type="italics"></emph>Hinc habetur veriſſima cauſa reflexionis<emph.end type="italics"></emph.end>; </s>
					<s id="N1F2EF">cum enim impetus non con­<lb></lb>ſeruetur à cauſa primò producente, vt ſæpè dictum eſt ſuprà, nec deſtrui <lb></lb>poſſit ſaltem totus à corpore reflectente; </s>
					<s id="N1F2F7">certè debet ſuum motum vlte­<lb></lb>riùs propagare; </s>
					<s id="N1F2FD">igitur per aliquam lineam; quomodo verò determine­<lb></lb>tur linea reflexionis, dicemus infrà. </s>
				</p>
				<p id="N1F303" type="main">
					<s id="N1F305"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F311" type="main">
					<s id="N1F313"><emph type="italics"></emph>Hinc non destruitur totus impetus in puncto reflexionis.<emph.end type="italics"></emph.end></s>
					<s id="N1F31A"> Probatur primò, <lb></lb>quia motus reflexus eſt ab impetu per Th. 3. ſed non producitur nouus <lb></lb>impetus per Theorema 8. igitur eſt impetus, qui erat ante reflexionem <lb></lb>per Th.9. igitur non deſtruitur totus, ſaltem per ſe, in puncto reflexio­<lb></lb>nis. </s>
					<s id="N1F325">Probatur ſecundò à priori; </s>
					<s id="N1F328">quia nunquam deſtruitur impetus, niſi <lb></lb>quando eſt fruſtra per Ax.3.ſed corpus reflectens non facit, vt ſit fruſtrà, <lb></lb>quia non impedit omnem lineam motus; </s>
					<s id="N1F330">igitur ſi ad aliquam determi­<lb></lb>nari poteſt, impetus non erit fruſtrà: ad quam autem determinari de­<lb></lb>beat, dicemus infrà. </s>
				</p>
				<p id="N1F338" type="main">
					<s id="N1F33A">Dixi, non deſtruitur totus impetus; </s>
					<s id="N1F33E">quia fortè aliqua pars illius de­<lb></lb>ſtruitur in reflexione vt demonſtrabo, ſcilicet per accidens: dixi præterea <lb></lb>per ſe, quia per accidens poteſt accidere vt totus impetus deſtruatur pro­<lb></lb>pter mollitiem vel corporis reflexi, vel propter aliam cauſam, de quo <lb></lb>aliàs. </s>
				</p>
				<p id="N1F34A" type="main">
					<s id="N1F34C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F358" type="main">
					<s id="N1F35A"><emph type="italics"></emph>Ex hoc etiam habetur impetum non eſſe ſucceſſiuum ſed qualitatem perma­<lb></lb>nentem eamque durare, licèt à cauſa primò producente non conſeruetur ſed ab <lb></lb>alia<emph.end type="italics"></emph.end>; vt iam alias demonſtrauimus. </s>
				</p>
				<p id="N1F367" type="main">
					<s id="N1F369"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F375" type="main">
					<s id="N1F377">In omni reflexione determinatur noua linea motus; </s>
					<s id="N1F37B">clarum eſt, quia <lb></lb>non eſt motus ſine linea determinata, vt patet; </s>
					<s id="N1F381">ſed non remanet prior <pb pagenum="240" xlink:href="026/01/272.jpg"></pb>linea; </s>
					<s id="N1F38A">igitur eſt noua, igitur illa determinatur; cur enim potiùs, quàm <lb></lb>alia, niſi determinaretur vna. </s>
				</p>
				<p id="N1F390" type="main">
					<s id="N1F392"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F39E" type="main">
					<s id="N1F3A0"><emph type="italics"></emph>Non determinatur à puncto contactus <expan abbr="tamũm">tantum</expan><emph.end type="italics"></emph.end>; </s>
					<s id="N1F3AC">quia ab eodem puncto <lb></lb>plures lineæ reflexionis procedere poſſunt; </s>
					<s id="N1F3B2">non à linea incidentiæ tan­<lb></lb>tùm; </s>
					<s id="N1F3B8">quia ſi tantillùm inclinetur planum eadem linea incidentiæ poteſt <lb></lb>habere diuerſas lineas reflexionis; </s>
					<s id="N1F3BE">non determinatur <expan abbr="deniq;">denique</expan> ab ipſo plano <lb></lb>inclinato quod diuerſas lineas reflectit; </s>
					<s id="N1F3C8">non determinatur, inquam, ab <lb></lb>his omnibus ſeorſim ſumptis, vt patet, ſed ab omnibus coniunctim: </s>
					<s id="N1F3CE"><lb></lb>quippe ab his determinatur linea motus, ex quibus poſitis, &amp; applicatis <lb></lb>neceſſariò ſequitur; </s>
					<s id="N1F3D5">ſed ex applicatione iſtorum omnium ſeorſim non ſe­<lb></lb>quitur talis linea; </s>
					<s id="N1F3DB">quæ tamen ſequitur ex applicatione omnium coniun­<lb></lb>ctim, vt patet; igitur ab his coniunctim ſumptis determinatur linea. </s>
				</p>
				<p id="N1F3E1" type="main">
					<s id="N1F3E3">Dices, linea incidentiæ non eſt ampliùs, quando linea reflexionis <lb></lb>determinatur; igitur non poteſt illam determinare. </s>
					<s id="N1F3E9">Reſpondeo deter­<lb></lb>minationem in eo eſſe poſitam tantùm, quòd impetus poſito tali angulo <lb></lb>incidentiæ non poſſit aliam inire lineam, præter illam vnicam; </s>
					<s id="N1F3F1">cùm enim <lb></lb>impetus ex ſe ſit indifferens ad omnes lineas, eo ipſo determinatur ad <lb></lb>vnam, quo impeditur ne per alias motus propagetur; </s>
					<s id="N1F3F9">atqui angulus inci­<lb></lb>dentiæ non modò dicit lineam incidentiæ, ſed lineam plani, atque adeo <lb></lb>apicem anguli qui eſt in puncto contactus; igitur poſito illo angulo <lb></lb>incidentiæ impetus determinatur ad lineam reflexionis. </s>
				</p>
				<p id="N1F403" type="main">
					<s id="N1F405">Porrò quod impediatur omnis alia linea, patet ex eo, quod primo ipſa <lb></lb>linea incidentiæ impeditur ne vlteriùs producatur ab impenetrabilita­<lb></lb>te; &amp; duritie plani reflectentis; immò &amp; omnes aliæ impediuntur, quæ <lb></lb>per ipſum planum duci poſſunt. </s>
				</p>
				<p id="N1F40F" type="main">
					<s id="N1F411">Secundò, quod ſpectat ad alias, quæ citra planum reflectens à pun­<lb></lb>cto contactus duci quoque poſſunt, omnes præter vnam impediuntur, <lb></lb>quæ ſcilicet facit angulum cum plano æqualem angulo incidentiæ, vt <lb></lb>demonſtrabimus infrà. </s>
				</p>
				<p id="N1F41A" type="main">
					<s id="N1F41C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F428" type="main">
					<s id="N1F42A"><emph type="italics"></emph>Ideo determinatur impetus ad omnem lineam, quia impeditur prior linea<emph.end type="italics"></emph.end>; <lb></lb>clarum eſt; niſi enim impediretur prior; </s>
					<s id="N1F435">certè non determinaretur ad <lb></lb>nouam, quod certum eſt: </s>
					<s id="N1F43B">adde quod planum reflectens perinde ſe habet, <lb></lb>que ſi mobile impelleret cum eo impetus gradu, quem ipſum mobile <lb></lb>iam habet; </s>
					<s id="N1F443">impelleret autem per lineam perpendicularem in puncto <lb></lb>contactus erectam; ſed propter priorem determinationem fit noua linea <lb></lb>mixta, de qua infrà. </s>
				</p>
				<p id="N1F44B" type="main">
					<s id="N1F44D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F459" type="main">
					<s id="N1F45B"><emph type="italics"></emph>Corpus reflectens impedit motum<emph.end type="italics"></emph.end>; </s>
					<s id="N1F464">quia eſt impenetrabile, durum, den­<lb></lb>ſum; ſed de his infrà, quando conſiderabimus impedimenta ratione <lb></lb>materiæ. </s>
				</p>
				<pb pagenum="241" xlink:href="026/01/273.jpg"></pb>
				<p id="N1F470" type="main">
					<s id="N1F472"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F47E" type="main">
					<s id="N1F480"><emph type="italics"></emph>Corpus reflectens plùs, vel minùs impedit motum ratione diuerſæ appulſio­<lb></lb>nis:<emph.end type="italics"></emph.end> probatur, quia motus reflexus aliquando eſt maior, aliquando eſt <lb></lb>minor, de quo infrà. </s>
				</p>
				<p id="N1F48C" type="main">
					<s id="N1F48E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F49A" type="main">
					<s id="N1F49C"><emph type="italics"></emph>Si corpus reflectens impingeretur in mobile, cui nullus prius ineſſet impetus, <lb></lb>punctum contactus determinaret lineam motus<emph.end type="italics"></emph.end>; vt demonſtrauimus lib.10. <lb></lb><expan abbr="moueretq́ue">moueretque</expan> globum, v.g. per lineam perpendicularem ductam à puncto <lb></lb>contactus per centrum globi per Th.120.&amp; 121. lib.1. </s>
				</p>
				<p id="N1F4B1" type="main">
					<s id="N1F4B3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F4BF" type="main">
					<s id="N1F4C1"><emph type="italics"></emph>Quò maiorem ictum infligit mobile per lineam incidentiæ corpori refle­<lb></lb>ctenti, eſt maius impedimentum<emph.end type="italics"></emph.end>; </s>
					<s id="N1F4CC">cum enim impetus agat tantùm ad extra, <lb></lb>vt tollat impedimentum; </s>
					<s id="N1F4D2">certè quò maior eſt ictus, plùs agit impetus; </s>
					<s id="N1F4D6"><lb></lb>igitur quò maior eſt ictus, eſt maius impedimentum, &amp; viciſſim quò <lb></lb>maius eſt impedimentum eſt maior ictus; &amp; contrà, quò minor eſt ictus, <lb></lb>eſt minus impedimentum, &amp; viciſſim ſuppoſita ſcilicet eadem potentiâ <lb></lb>impellente, vt demonſtratum eſt libro primo. </s>
				</p>
				<p id="N1F4E1" type="main">
					<s id="N1F4E3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F4EF" type="main">
					<s id="N1F4F1"><emph type="italics"></emph>Quando linea incidentiæ cadit perpendiculariter in planum reflectens eſt <lb></lb>maximum impedimentum<emph.end type="italics"></emph.end>; quia ſcilicet eſt maximus ictus, vt probauimus <lb></lb>lib.1. </s>
				</p>
				<p id="N1F4FF" type="main">
					<s id="N1F501"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F50D" type="main">
					<s id="N1F50F"><emph type="italics"></emph>Quò linea incidentiæ cadit obliquiùs in <expan abbr="planũ">planum</expan>, eſt minùs <expan abbr="impedimentũ">impedimentum</expan>,<emph.end type="italics"></emph.end> quia <lb></lb>eſt minor ictus. </s>
					<s id="N1F521">v.g.in fig. </s>
					<s id="N1F524">Definitione.8. ictus per lineam GD eſt ad <lb></lb>ictum per lineam AD, vt AD ad AB; </s>
					<s id="N1F52A">nec in his immoror, quæ lib.1. <lb></lb>&amp; aliis ſufficienter demonſtrata ſunt; </s>
					<s id="N1F530">præſertim cum de planis inclina­<lb></lb>tis; </s>
					<s id="N1F536">nam perinde ſe habet inflictus ictus, atque grauitatio in ipſum pla­<lb></lb>num; </s>
					<s id="N1F53C">eſt enim grauitatio in planum inclinatum, vt ſuprà fusè dictum eſt <lb></lb>in Th.16. lib.5.ad grauitationem in horizontale, vt Tangens horizonta­<lb></lb>les ad ſecantem, id eſt, vt AB ad AD; </s>
					<s id="N1F544">nam BD eſt quaſi perpendicu­<lb></lb>laris; igitur ictus ſunt, vt ſinus anguli incidentiæ ad ſinum totum. </s>
					<s id="N1F54A">v. g. <lb></lb>vt AB, ad AD hinc per lineam, AD, eſt minùs impedimentum quàm <lb></lb>per GD immò eadem eſt ratio impedimentorum &amp; ictuum; igitur im­<lb></lb>pedimentum in linea, GD eſt ad impedimentum per lineam, AD, vt <lb></lb>AD, ad AB. </s>
				</p>
				<p id="N1F55A" type="main">
					<s id="N1F55C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F568" type="main">
					<s id="N1F56A"><emph type="italics"></emph>Hinc plùs, vel minùs determinat nouam lineam motus planum reflectens<emph.end type="italics"></emph.end>; </s>
					<s id="N1F573"><lb></lb>cum enim ideo determinetur impetus ad nouam lineam, quia impeditur <lb></lb>prior per Theorema 17. certè in eadem proportione determinatur ad <lb></lb>nouam, in qua impeditur prior; </s>
					<s id="N1F57C">ſed plùs vel minùs impeditur per Th. <lb></lb>23. igitur plùs vel minùs determinatur impetus; </s>
					<s id="N1F583">igitur plùs vel minùs <lb></lb>determinat planum reflectens: porrò planum BD, determinat mobile <pb pagenum="242" xlink:href="026/01/274.jpg"></pb>quod reflectit per lineam DG, &amp; niſi eſſet alia determinatio per DG <lb></lb>reflecteretur mobile, vt reuerâ fit, cum linea incidentiæ eſt perpen­<lb></lb>dicularis. </s>
				</p>
				<p id="N1F592" type="main">
					<s id="N1F594"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F5A0" type="main">
					<s id="N1F5A2"><emph type="italics"></emph>Hinc planum reflectens maximè determinat impetum ad nouam lineam <lb></lb>cum linea incidentiæ eſt perpendicularis<emph.end type="italics"></emph.end>; </s>
					<s id="N1F5AD">quia tunc eſt maximum impedi­<lb></lb>mentum per Th.22.igitur maximè determinat per Th.24. &amp; contrà, quò <lb></lb>linea incidentiæ eſt obliquior, minor eſt determinatio ad lineam no­<lb></lb>uam; igitur hæc tria ſunt in eadem proportione, ſcilicet ictus, impedi­<lb></lb>mentum, determinatio noua. </s>
				</p>
				<p id="N1F5B9" type="main">
					<s id="N1F5BB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F5C7" type="main">
					<s id="N1F5C9"><emph type="italics"></emph>Maxima determinatio, quâ planum reflectens poſſit impetum, mobili im­<lb></lb>preſſum, quaſi retorquere, eſt illa, quæ fit per lineam perpendicularem.<emph.end type="italics"></emph.end> v.g.per <lb></lb>DG; </s>
					<s id="N1F5D6">ſi enim planum ipſum mobile impelleret à puncto contactus D; <lb></lb>certè impelleret tantùm per lineam perpendicularem, ſeu per lineam <lb></lb>ductam à puncto D per centrum globi, ſi v. g. eſſet globus, vt demon­<lb></lb>ſtrauimus in primo lib.1. Igitur maxima determinatio, quæ poſſit inferri <lb></lb>à plano eſt in ipſa perpendiculari. </s>
				</p>
				<p id="N1F5E6" type="main">
					<s id="N1F5E8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F5F4" type="main">
					<s id="N1F5F6"><emph type="italics"></emph>Hinc, ſi linea incidentiæ eſt perpendicularis GD, linea quoque reflexionis <lb></lb>eſt eadem DG<emph.end type="italics"></emph.end>; </s>
					<s id="N1F601">quia huic eſt maximum impedimentum, quia ſcilicet eſt <lb></lb>maximus ictus; igitur maxima determinatio per Th. 25. ſed maxima eſt <lb></lb>illa, quâ mobile per ipſam perpendicularem DG à puncto contactus D <lb></lb>retorquetur per Th.26. Igitur ſi linea incidentiæ, &amp;c. </s>
					<s id="N1F60B">quod erat proban­<lb></lb>dum. </s>
					<s id="N1F610">Probatur præterea, quia ſi linea incidentiæ eſt perpendicularis <lb></lb>GD, non eſt potior ratio, cur linea reflexionis inclinet dextrorſum ver­<lb></lb>ſus A, quàm ſiniſtrorſum verſus H; igitur debet eſſe perpendicu­<lb></lb>laris. </s>
				</p>
				<p id="N1F61A" type="main">
					<s id="N1F61C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F628" type="main">
					<s id="N1F62A"><emph type="italics"></emph>Si linea incidentiæ cadat obliquè in planum, linea reflexionis non erit per­<lb></lb>pendicularis<emph.end type="italics"></emph.end> v. g. ſit linea incidentia AD, linea reflexionis non eſt per­<lb></lb>pendicularis DG; quia tunc non eſt maximus ictus, nec maximum im­<lb></lb>pedimentum per Th.23.igitur nec maxima determinatio per Theor.24. <lb></lb>igitur non fit per ipſam perpendicularem DG per Th. 26. </s>
				</p>
				<p id="N1F63F" type="main">
					<s id="N1F641"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F64D" type="main">
					<s id="N1F64F"><emph type="italics"></emph>Hinc linea reflexionis, quæ ſequitur lineam incidentiæ obliquè cadentem in <lb></lb>planum non tantùm determinatur à plane reflectente ſed participat aliquid de <lb></lb>priori determinatione.<emph.end type="italics"></emph.end> v. g. ſit linea incidentiæ AD, linea reflexionis <lb></lb>DH; </s>
					<s id="N1F662">non tantùm determinatur hæc linea à plano FB, alioqui eſſet DG, <lb></lb>nec eſt eadem cum prima; alioqui eſſet DE, ſed partim determinatur à <lb></lb>plano FB per DG partimque reti nec aliquid primæ determinationis, &amp; <lb></lb>ex vtraque fit DH, vt conſtat, quia quò linea incidentiæ eſt obliquior, <lb></lb>planum minùs determinat per Th. 25. </s>
				</p>
				<pb pagenum="243" xlink:href="026/01/275.jpg"></pb>
				<p id="N1F672" type="main">
					<s id="N1F674"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F680" type="main">
					<s id="N1F682"><emph type="italics"></emph>Hinc quâ proportione planum minùs confert ad nouam determinationem, <lb></lb>plùs remanet prioris determinationis; </s>
					<s id="N1F68A">quò verò plùs illud confert, huius minùs <lb></lb>restat<emph.end type="italics"></emph.end>; </s>
					<s id="N1F693">hinc, cum planum totam confert <expan abbr="nouã">nouam</expan> <expan abbr="determinationẽ">determinationem</expan> vt in per­<lb></lb>pendiculari DD, nihil prioris remanet; </s>
					<s id="N1F6A1">hinc ſi linea incidentiæ ſit pa­<lb></lb>rallela plano BF nulla fiet noua determinatio, tota priore intacta; </s>
					<s id="N1F6A7">ſi ve­<lb></lb>rò ſit perpendicularis GD, tota determinatio eſt noua, &amp; nihil prioris <lb></lb>remanet; ſi demum lineæ incidentiæ ſint aliæ, confert vtrumque ad no­<lb></lb>uam determinationem pro rata. </s>
				</p>
				<p id="N1F6B1" type="main">
					<s id="N1F6B3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F6BF" type="main">
					<s id="N1F6C1"><emph type="italics"></emph>Si pellatur mobile per AD in planum FB, determinatio lineæ reflexionis <lb></lb>erit quaſi mixta ſinistrorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N1F6CC">ſi enim ex D propagaretur motus in E rectè <lb></lb>ſiniſtrorſum acquireret DF in linea BF, vt patet; </s>
					<s id="N1F6D2">igitur ſi ſit linea inci­<lb></lb>dentiæ AD, noua determinatio per DH conſtabit partim ex eo, quòd <lb></lb>planum reflectens confert partim ex eo, quod remanet prioris determi­<lb></lb>nationis, quod reſpondet DF, &amp; ex eo quod confert planum FB, quod <lb></lb>reſpondet DP; </s>
					<s id="N1F6DE">quia ictus per AD eſt ad ictum per GD, vt PD ad DP <lb></lb>vel DG; </s>
					<s id="N1F6E4">ſed eſt eadem ratio impedimenti eademque determinationis <lb></lb>per Theoremata ſuperiora; atqui ex DPDF fit DHGO. igitur deter­<lb></lb>minatio lineæ reflexæ eſt mixta, quod erat probandum. </s>
				</p>
				<p id="N1F6EC" type="main">
					<s id="N1F6EE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F6FA" type="main">
					<s id="N1F6FC"><emph type="italics"></emph>Hinc decreſcit determinatio, quam confert planum iuxta rationem ſinuum <lb></lb>verſorum in<emph.end type="italics"></emph.end> GD. v. g. ſi ſit linea incidentiæ AD; </s>
					<s id="N1F70B">ducatur APH paral­<lb></lb>lela FB, determinatio quam confert planum, decreſcit ſinu verſo PG; </s>
					<s id="N1F711">ſi <lb></lb>verò ſit linea incidentiæ ID, decreſcit ſinu verſo LG; atque ita dein­<lb></lb>ceps; at verò creſcit portio prioris determinationis lineæ incidentiæ <lb></lb>iuxta rationem ſinuum rectorum in DB v. g. ſi ſit linea incidentiæ AD, <lb></lb>creſcit ſinu recto AP æquali BD ſi ſit IL creſcit ſinu recto IL vel RD. </s>
				</p>
				<p id="N1F721" type="main">
					<s id="N1F723"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F72F" type="main">
					<s id="N1F731"><emph type="italics"></emph>Hinc angulus reflexionis eſt æqualis angulo incidentiæ, &amp; hoc eſt principium <lb></lb>poſitiuum huius æqualitatis angulorum.<emph.end type="italics"></emph.end> ſit enim linea incidentiæ AD, du­<lb></lb>catur APH, AB, HF; </s>
					<s id="N1F73E">certè DF &amp; DB ſunt æquales APPH; </s>
					<s id="N1F742">item­<lb></lb>que ABPDHF ſunt æquales; </s>
					<s id="N1F748">atqui determinatio lineæ reflexionis <lb></lb>eſt mixta ex DFH; </s>
					<s id="N1F74E">igitur erit DH; </s>
					<s id="N1F752">ſed triangula DFH, DAB ſunt <lb></lb>æqualia &amp; anguli HDFADB ſunt æquales: </s>
					<s id="N1F758">ſimiliter ſit linea inciden­<lb></lb>tiæ ID, ducatur IN parallela AHIRNM; </s>
					<s id="N1F75E">certè duo anguli IDR, <lb></lb>NDM ſunt æquales; </s>
					<s id="N1F764">idem dico de omnibus aliis lineis incidentiæ, &amp; <lb></lb>hæc eſt vera ratio poſitiua à priori, de qua plura infrà; </s>
					<s id="N1F76A">non deeſt etiam <lb></lb>negatiua, quia ſcilicet poſita linea incidentiæ AD cùm ſiniſtrorſum ſint <lb></lb>infiniti anguli inæquales angulo incidentiæ; </s>
					<s id="N1F772">non eſt potior ratio, cur <lb></lb>per vnum fiat quàm per alium, &amp; cum ſit tantùm vnus æqualis HDM in <lb></lb>eodem ſcilicet plano; </s>
					<s id="N1F77A">certè per illum fieri debet; </s>
					<s id="N1F77E">quippe quod vnum <lb></lb>eſt, determinatum eſt, vt ſæpè diximus aliàs; </s>
					<s id="N1F784">nec eſt quòd aliqui delica-<pb pagenum="244" xlink:href="026/01/276.jpg"></pb>tioris ſthomachi rationem hanc negatiuam, cum tanta nauſea reſpuant, <lb></lb>cum optima ſit; </s>
					<s id="N1F78F">nec vlli fallaciæ ſubiiciatur, non tamen ſolitariam eſſe <lb></lb>oportuit; quippe effectus poſitiuus per principium poſitiuum ad ſuam <lb></lb>cauſam reducendus eſt. </s>
				</p>
				<p id="N1F797" type="main">
					<s id="N1F799"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F7A5" type="main">
					<s id="N1F7A7"><emph type="italics"></emph>Hinc vides eſſe ſemper quatuor angulos æquales,<emph.end type="italics"></emph.end> ſcilicet, angulum inci­<lb></lb>dentiæ, angulum reflexionis &amp; duos his oppoſitos; allos verò quatuor <lb></lb>etiam inter ſe æquales, ſcilicet duos angulos complementi &amp; duos his <lb></lb>oppoſitos. </s>
				</p>
				<p id="N1F7B6" type="main">
					<s id="N1F7B8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F7C4" type="main">
					<s id="N1F7C6"><emph type="italics"></emph>Hinc quoque reiicies illos, qui nolunt in reflexione impetum produci in mo­<lb></lb>bili à plano reflectente<emph.end type="italics"></emph.end>; quod reuerâ, ſi fieret nulla eſſet ratio æqualitatis <lb></lb>angulorum incidentiæ, &amp; reflexionis, reiicies quoque aliquos apud Mer­<lb></lb>ſennum in phænom. </s>
					<s id="N1F7D5">Balliſt. prop.  24. qui ponunt duo qualitatum gene­<lb></lb>ra, quarum aliæ mobile firmiter affigant plano, aliæ à plano remoueant, <lb></lb>quod pluſquàm ridiculum eſt; </s>
					<s id="N1F7DF">itemque alios ibidem, qui nolunt circa <lb></lb>punctum reflexionis ab impreſſione mobilis foſſulam fieri, ſed non ſine <lb></lb>compreſſione, cuius deinde vi repellitur idem mobile; </s>
					<s id="N1F7E7">ſed in duro mar­<lb></lb>more nullum omninò apparet veſtigium huius foſſulæ, adde quod ſi hoc <lb></lb>eſſet, ſemper reflexio fieret per ipſam perpendicularem; </s>
					<s id="N1F7EF">quod vero perti­<lb></lb>net ad illas qualitates magneticas, quarum aliæ retinent, aliæ repellunt <lb></lb>mobile, pœnitus in hoc caſu inſulſæ ſunt; </s>
					<s id="N1F7F7">alioqui etiam ſine motu præ­<lb></lb>uio repellerent: vtrum verò in magnete admittendæ ſint, fusè diſputa­<lb></lb>bimus ſuo loco. </s>
				</p>
				<p id="N1F7FF" type="main">
					<s id="N1F801"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F80D" type="main">
					<s id="N1F80F"><emph type="italics"></emph>Ex hac angulorum æqualitate tùm Captotrica infinita ferè Theoremata de­<lb></lb>monstrat in radiis viſilibus, in ſpeculis vſtoriis, tùm Echometria in reflexione <lb></lb>ſonorum.<emph.end type="italics"></emph.end></s>
					<s id="N1F81A"> Et verò noua Catoptrica poteſt eſſe in motu, quæ eadem pror­<lb></lb>ſus demonſtrabit, tùm in ſpeculis parabolicis, à quibus omnia miſſilia <lb></lb>projecta per parallelas axi Parabolæ in idem punctum reflectentur; </s>
					<s id="N1F822">vel <lb></lb>Ellipticis, à quibus omnia miſſilia projecta à dato puncto per omnes li­<lb></lb>neas ad idem punctum reflectentur; </s>
					<s id="N1F82A">vel Hyperbolicis, à quibus miſſilia <lb></lb>projecta per plures lineas ad idem punctum ad aliud punctum omnes re­<lb></lb>flectuntur; </s>
					<s id="N1F832">vel Sphæricis concauis, à quibus miſſilia projecta per plures <lb></lb>lineas decuſſatas in eodem puncto ad idem punctum reflectuntur; vel <lb></lb>Sphæricis conuexis, à quibus miſſile proiectum à quolibet puncto dato <lb></lb>ad quodlibet aliud datum reflectitur. </s>
					<s id="N1F83C">Ratio eſt, quia in circulo ſunt om­<lb></lb>nia plana; </s>
					<s id="N1F842">quælibet enim Tangens planum eſt; ſiue denique in Cylin­<lb></lb>dricis, Conicis, &amp;c. </s>
					<s id="N1F848">quæ omnia ex principiis Catoptricis demonſtrari <lb></lb>poſſunt: </s>
					<s id="N1F84E">adde ſi vis in hac Catoptrica verſatos eſſe debere, qui pilâ lu­<lb></lb>dunt, quos nunquam falleret ictus, ſi hanc rationem angulorum non mo­<lb></lb>dò perfectè callerent, verùm etiam ad praxim reducerent: immò poſſet <lb></lb>eſſe aliqua portio muri talis figuræ, vt ſemper inde reflexa pila per da­<lb></lb>tum cuniculum rectà traiiceretur. </s>
				</p>
				<pb pagenum="245" xlink:href="026/01/277.jpg"></pb>
				<p id="N1F85E" type="main">
					<s id="N1F860"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F86C" type="main">
					<s id="N1F86E"><emph type="italics"></emph>In reflexione destruitur aliquid impetus, ſi talis ſit vtriuſque determina­<lb></lb>tionis pugna, vt aliquid impetus ſit frustrà<emph.end type="italics"></emph.end>; </s>
					<s id="N1F879">vt conſtat ex his, quæ diximus <lb></lb>libro primo; </s>
					<s id="N1F87F">conſtat autem in reflexione eſſe determinationum pugnam <lb></lb>per Th 31. &amp; 32. pugnat enim ſuo modo prior determinatio per GD <lb></lb>cum ſecunda oppoſita per DG; igitur aliquid impetus deſtruitur, ſi ex <lb></lb>tali pugna aliquid ſit fruſtrà. </s>
					<s id="N1F889">Obſeruabis autem eundem impetum in eo­<lb></lb>dem mobili cum duplici determinatione perinde ſe habere in ordine <lb></lb>ad nouam, vt patet, lineam, atque ſi eſſent duo impetus in ratione deter­<lb></lb>minationum: vtrùm autem aliquid impetus ſit fruſtrà per ſe, determina­<lb></lb>bimus infrà. </s>
				</p>
				<p id="N1F895" type="main">
					<s id="N1F897"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F8A3" type="main">
					<s id="N1F8A5"><emph type="italics"></emph>Si totus impetus destrueretur nulla eſſet reflexio<emph.end type="italics"></emph.end>; </s>
					<s id="N1F8AE">quod maximè eſſet ab­<lb></lb>ſurdum &amp; incommodum toti naturæ; </s>
					<s id="N1F8B4">ſi verò nullus impetus deſtruere­<lb></lb>tur, ſeu per ſe, ſeu per accidens, daretur motus perpetuus; </s>
					<s id="N1F8BA">quippe mo­<lb></lb>bile ad eandem altitudinem aſcenderet poſt reflexionem, iterumque de­<lb></lb>ſcendens ad <expan abbr="eãdem">eandem</expan> aſcenderet atque ita deinceps; igitur motus eſſet <lb></lb>perpetuus, &amp; nunquam corpus illud quieſceret, quod eſt contra inſtitu­<lb></lb>tum naturæ. </s>
				</p>
				<p id="N1F8CA" type="main">
					<s id="N1F8CC"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F8D8" type="main">
					<s id="N1F8DA">Obſerua primò ex hypotheſi certa haberi, dari motum reflexum, ex <lb></lb>qua colligo totum impetum non deſtrui. </s>
					<s id="N1F8DF">Secundò ex hypotheſi certa <lb></lb>haberi, motum reflexum eſſe minorem directo vlteriùs propagato, vt <lb></lb>conſtat experientiâ, ex qua colligo aliquam portionem impetus deſtrui, <lb></lb>ſaltem per accidens propter compreſſionem, &amp; alliſionem partium. </s>
				</p>
				<p id="N1F8E8" type="main">
					<s id="N1F8EA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F8F6" type="main">
					<s id="N1F8F8"><emph type="italics"></emph>Maior eſt determinatio, quæ confertur à plano mobili per lineam perpendi­<lb></lb>cularem incidenti, quàm prior, quæ inerat mobili<emph.end type="italics"></emph.end>; </s>
					<s id="N1F903">probatur, quia nec eſt <lb></lb>minor, nec æqualis, non minor; </s>
					<s id="N1F909">alioquin prior vinceret; </s>
					<s id="N1F90D">non æqualis, <lb></lb>quia neutra præualeret; </s>
					<s id="N1F913">igitur eſt maior; </s>
					<s id="N1F917">ſi vtraque determinatio eſſet <lb></lb>aqualis totus impetus deſtrui deberet; </s>
					<s id="N1F91D">igitur eadem eſt proportio impe­<lb></lb>tus remanentis, quæ eſt mixtæ determinationis ex priori, &amp; noua; </s>
					<s id="N1F923">nul­<lb></lb>lus enim impetus eſſe poteſt ſine determinatione; </s>
					<s id="N1F929">igitur ſi tota perit de­<lb></lb>terminatio, totus etiam perit impetus, qui illi reſpondet; </s>
					<s id="N1F92F">&amp; ſi remanet <lb></lb>aliquid determinationis mixtæ, aliquid etiam impetus remanet, qui eſt <lb></lb>ad priorem impetum, vt hæc determinatio reſidua ad priorem determi­<lb></lb>nationem; quantum verò remaneat prioris impetus, dicam infrà. </s>
				</p>
				<p id="N1F939" type="main">
					<s id="N1F93B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1F947" type="main">
					<s id="N1F949"><emph type="italics"></emph>Determinatio per DG à plano eſt dupla determinationis prioris per lineam <lb></lb>incidentiæ GD<emph.end type="italics"></emph.end>; quod ſic demonſtro; </s>
					<s id="N1F954">ſit linea incidentiæ ID, linea re­<lb></lb>flexionis erit DN, ſcilicet ad angulos æquales, per Th. 33. ſit autem an­<lb></lb>gulus NDM 30. graduum, &amp; NDG 60. ducatur NO parallela GD; </s>
					<s id="N1F95C"><pb pagenum="246" xlink:href="026/01/278.jpg"></pb>tùm ID producatur in O, denique ducatur NG: </s>
					<s id="N1F964">prima determinatio <lb></lb>lineæ incidentiæ ID, eſt per DO, determinatio plani eſt per DG; </s>
					<s id="N1F96A">ſed <lb></lb>DO eſt æqualis DG; </s>
					<s id="N1F970">nam DON, DNG ſunt æquilatera æqualia; </s>
					<s id="N1F974"><lb></lb>hinc determinatio mixta eſt per DN, diuidens angulum GDO bifa­<lb></lb>riam; </s>
					<s id="N1F97B">igitur ſi ſit linea incidentiæ ID &amp; angulus ID B. 30. graduum, <lb></lb>æqualis eſt determinatio plani determinationi prioris lineæ; </s>
					<s id="N1F981">hinc angu­<lb></lb>lus diuiditur æqualiter bifariam; </s>
					<s id="N1F987">ſit verò linea incidentiæ AD produ­<lb></lb>cta vſque ad E, linea reflexionis DH; </s>
					<s id="N1F98D">ducatur HE; </s>
					<s id="N1F991">aſſumatur DT <lb></lb>æqualis EH: </s>
					<s id="N1F997">dico determinationem plani eſſe ad determinationem <lb></lb>prioris lineæ AD vel DE, vt DT ad DE; </s>
					<s id="N1F99D">cum enim determinatio mix­<lb></lb>ta ſit per DH; </s>
					<s id="N1F9A3">certè DH accedit propiùs ADDG, quàm ad DE; </s>
					<s id="N1F9A7">igi­<lb></lb>tur determinatio per DG eſt ad determinationem, per DE vt DT <lb></lb>æqualis HE ad DE; nam perinde ſe habent, atque ſi eſſent duo impe­<lb></lb>tus determinati ad duas lineas, de quibus hoc ipſum demonſtrauimus <lb></lb>tùm libro 1. Th.137. 138. 139. &amp;c. </s>
					<s id="N1F9B3">tùm lib.4. à Th. 1. ad Th.14.quippe <lb></lb>linea determinationis mixtæ eſt diagonalis, vt ſæpè probauimus: </s>
					<s id="N1F9B9">deinde <lb></lb>ſit linea incidentiæ per KD; </s>
					<s id="N1F9BF">ſit DX linea reflexionis; </s>
					<s id="N1F9C3">ſit XQ, ipſique <lb></lb>æqualis DZ, dico determinationem per DG eſſe ad determinationem <lb></lb>per DQ vt DZ ad DQ, ſed XQ eſt minor GS, vt conſtat; </s>
					<s id="N1F9CB">igitur quò <lb></lb>linea incidentiæ accedit propiùs ad perpendicularem GD, determinatio <lb></lb>plani eſt maior, eſtque vt chordæ NO, HE, <expan abbr="Xq;">Xque</expan> igitur ſi tandem li­<lb></lb>nea incidentiæ ſit perpendicularis GD, determinatio plani eſt ad deter­<lb></lb>minationem lineæ incidentiæ, vt DY æqualis GS ad DG: </s>
					<s id="N1F9DB">ſed cum ex <lb></lb>Th.4. multa lux reliquis conſequentibus immò &amp; antecedentibus afful­<lb></lb>gere poſſit, paulò fuſiùs explicandum, &amp; demonſtrandum eſſe videtur: </s>
					<s id="N1F9E3"><lb></lb>itaque duobus modis, primò ex hypotheſi anguli reflexionis æqualis an­<lb></lb>gulo incidentiæ, quod iam reuerâ præſtitum eſt; ſed cum ex hoc Theo­<lb></lb>remate prædicta æqualitas angulorum reflexionis tanquam per princi­<lb></lb>pium immediatum poſitiuum demonſtrari poſſit, ne ſit aliqua circuli <lb></lb>ſpecies, quo determinatio noua dupla prioris poſita linea incidentiæ <lb></lb>perpendiculari per æqualitatem anguli reflexionis, &amp; hæc æqualitas per <lb></lb>illam eandem determinationem duplam demonſtretur, aliam viam inire <lb></lb>oportet, vnde intima totius reflexionis principia eruantur, quod vt <lb></lb>fiat. </s>
				</p>
				<p id="N1F9F8" type="main">
					<s id="N1F9FA">Primò certum eſt, corpus reflectens in perpendiculari, (quæ eſt cum <lb></lb>linea incidentiæ terminata ad punctum contactus ducitur per centrum <lb></lb>grauitatis globi reflexi) certum eſt inquam corpus reflectens in prædi­<lb></lb>cta linea aliquando cedere, aliquando non cedere; </s>
					<s id="N1FA04">cedere autem dici­<lb></lb>tur cùm vel amouetur à corpore impacto, vel ſaltem concutitur: <lb></lb>tunc autem nullo modo cedere dicitur, cum ab ictu nullo modo mo­<lb></lb>uetur. </s>
				</p>
				<p id="N1FA0E" type="main">
					<s id="N1FA10">Secundò, ceſſio, &amp; reſiſtentia ita poſſunt comparari, vt vel ceſſio ſit <lb></lb>æqualis reſiſtentiæ, vel ceſſio ſine reſiſtentia, vel reſiſtentia ſine ceſſione: </s>
					<s id="N1FA16"><lb></lb>porrò tunc eſt ceſſio tota, cum nulla eſt reſiſtentia, quod tantum accide­<lb></lb>ret, ſi corpus moueretur in vacuo; </s>
					<s id="N1FA1D">quippe nullum eſt medium quamtum-<pb pagenum="247" xlink:href="026/01/279.jpg"></pb>uis rarum, &amp; tenue, quod aliquantulum non reſiſtat, vt clarum eſt; </s>
					<s id="N1FA26">tunc <lb></lb>quoque eſt reſiſtentia ſine ceſſione, ſeu tota reſiſtentia, cum ipſum cor­<lb></lb>pus reſiſtens nullo modo cedit; </s>
					<s id="N1FA2E">id eſt nullo modo mouetur ab ictu; </s>
					<s id="N1FA32">neque <lb></lb>enim excogitari poteſt maior reſiſtentia; </s>
					<s id="N1FA38">denique tunc eſt æqualis ceſ­<lb></lb>ſio reſiſtentiæ, cum ipſum corpus, in quod aliud impingitur (vocetur re­<lb></lb>flectens) tantùm cedit quantum reſiſtit; </s>
					<s id="N1FA40">cedit autem per motum; </s>
					<s id="N1FA44">igitur <lb></lb>ſi reflectenti imprimitur æqualis motus ab impacto reflectens æqualiter <lb></lb>cedit, &amp; reſiſtit, ſi minor minùs cedit, &amp; plùs reſiſtit, ſi nullus nullo mo­<lb></lb>do cedit, ſed tantùm reſiſtit; ſi maior plùs cedit, &amp; minùs reſiſtit, ſcili­<lb></lb>cet in infinitum, donec tandem in vacuo ſit tantum ceſſio, nulla reſi­<lb></lb>ſtentia. </s>
				</p>
				<p id="N1FA52" type="main">
					<s id="N1FA54">Tertiò, tunc impactum motum æqualem imprimit reflectenti, cum <lb></lb>impactum æquale eſt reflectenti, tùm mole, tùm pondere v.g. globus A <lb></lb>impactus in globum B eiuſdem materiæ, &amp; diametri, modo nullus fiat <lb></lb>attritus partium, ſeu compreſſio, ſitque linea directionis connectens <lb></lb>centra per punctum contactus, quod in primo libro iam demonſtratum <lb></lb>eſt; </s>
					<s id="N1FA64">cum enim totus impetus globi A agat, &amp; quantum poteſt; </s>
					<s id="N1FA68">certè pro­<lb></lb>ducit æqualem; </s>
					<s id="N1FA6E">nec enim aliunde determinari poteſt æqualitas effectus <lb></lb>quàm ab æqualitate cauſæ poſitis iiſdem circumſtantiis, &amp; cum impetus <lb></lb>in B impreſſus diſtribuatur tot partibus quot producens æqualis in A, <lb></lb>vterque impetus eſt æquè intenſus; </s>
					<s id="N1FA78">igitur æquè velox motus per ſe; </s>
					<s id="N1FA7C">cum <lb></lb>per accidens aliquando ſecus accidat; </s>
					<s id="N1FA82">ſi verò reflectens ſit minor, idem <lb></lb>impetus paucioribus partibus diſtribuitur; </s>
					<s id="N1FA88">igitur intenſior eſt; </s>
					<s id="N1FA8C">igitur <lb></lb>velocior motus, ſecus verò cum maior eſt, donec tandem tanta ſit moles, <lb></lb>vt plura ſint puncta in reflectente, quàm ſint in impacto puncta impe­<lb></lb>tus; tunc enim nullus imprimitur impetus, vt conſtat ex dictis lib.  1. </s>
				</p>
				<p id="N1FA97" type="main">
					<s id="N1FA99">Quartò, quod autem ſit æqualis reſiſtentia, &amp; ceſſio globi B æqualis <lb></lb>globo A etiam certum eſt; </s>
					<s id="N1FA9F">tùm quia, ſi æqualiter mouetur, æqualiter ce­<lb></lb>dit, vt iam dixi ſi æqualiter cedit, æqualiter reſiſtit; </s>
					<s id="N1FAA5">nam quâ proportio­<lb></lb>ne minùs cedit, plùs reſiſtit; </s>
					<s id="N1FAAB">igitur qua proportione ceſſio augetur, reſi­<lb></lb>ſtentia imminuitur: præterea cum reſiſtat per ſuam entitatem impene­<lb></lb>trabilem, duram &amp;c. </s>
					<s id="N1FAB3">certè ſi eſt æqualis entitas, eſt æqualis reſiſtentia; </s>
					<s id="N1FAB7"><lb></lb>quod etiam videmus in corporibus immerſis eiuſdem grauitatis cum <lb></lb>medio, ita vt tot ſint partes impellentes, quot impulſæ; </s>
					<s id="N1FABE">denique illud <lb></lb>experimentum quo videmus globum A impactum in B æqualem per li­<lb></lb>neam connectentem centra immobilem ſiſtere, rem iſtam euincit; </s>
					<s id="N1FAC6">nam <lb></lb>ideo ſiſtit, quia eſt æqualis determinatio noua priori; </s>
					<s id="N1FACC">nam vt ſe habet <lb></lb>reſiſtentia reflectentis, ita ſe habet noua determinatio, quam ſuo modo <lb></lb>confert impacto, vt ſuprà demonſtratum eſt: </s>
					<s id="N1FAD4">&amp; cùm ſint ad lineas op­<lb></lb>poſitas ex diametro hæ duæ determinationes, neutra præualere poteſt; <lb></lb>igitur neceſſe eſt ſiſtere globum impactum. </s>
				</p>
				<p id="N1FADC" type="main">
					<s id="N1FADE">Quintò, certum eſt determinationem nouam eſſe iuxta proportionem <lb></lb>reſiſtentiæ, &amp; hanc iuxta proportionem minoris ceſſionis; </s>
					<s id="N1FAE4">vnde cum <lb></lb>nulla eſt reſiſtentia, ſed tantùm ceſsio, nulla prorſus eſt noua determina­<lb></lb>tio igitur à termino nullius reſiſtentiæ, &amp; totius ceſsionis ad terminum <pb pagenum="248" xlink:href="026/01/280.jpg"></pb>æqualis ceſſionis, &amp; reſiſtentiæ, acquiritur tantùm noua determinatio <lb></lb>æqualis priori: </s>
					<s id="N1FAF3">ſimiliter à termino nullius ceſſionis, &amp; totius reſiſtentiæ <lb></lb>ad terminum æqualis reſiſtentiæ, &amp; ceſſionis, acquiritur tantùm æqualis <lb></lb>ceſſio; </s>
					<s id="N1FAFB">ſed qua proportione creſcit ceſſio, imminuitur reſiſtentia, &amp; vi­<lb></lb>ciſsim; </s>
					<s id="N1FB01">igitur cum æqualis ceſsio, &amp; reſiſtentia ſint in communi medio; </s>
					<s id="N1FB05"><lb></lb>tantùm enim eſt ab æquali reſiſtentia &amp; æquali ceſsione ad totam ceſ­<lb></lb>ſionem, &amp; nullam reſiſtentiam, quantùm eſt ab æquali reſiſtentia &amp; ceſ­<lb></lb>ſione æquali ad totam reſiſtentiam, &amp; nullam ceſsionem; </s>
					<s id="N1FB0E">&amp; cum à nulla <lb></lb>reſiſtentia ad æqualem acquiritur noua determinatio æqualis priori; </s>
					<s id="N1FB14">cer­<lb></lb>tè ab æquali ad totam acquiretur <expan abbr="tantũdem">tantundem</expan> determinationis nouæ; igi­<lb></lb>tur tunc erit dupla prioris, quod erat demonſtrandum. </s>
				</p>
				<p id="N1FB20" type="main">
					<s id="N1FB22">Sextò, præterea globus A impactus ſine acceſsione noui impetus non <lb></lb>poteſt velociùs moueri, quàm antè moueretur; </s>
					<s id="N1FB28">ſed per reflexionem non <lb></lb>acquirit maiorem impetum, vt conſtat; </s>
					<s id="N1FB2E">igitur velociùs, quàm antè non <lb></lb>mouetur; </s>
					<s id="N1FB34">igitur ſi conſideretur globus A impactus; </s>
					<s id="N1FB38">ſi eſt æqualis reſi­<lb></lb>ſtentia, nullo modo mouetur; </s>
					<s id="N1FB3E">ſi eſt maior reſiſtentia, ſed non tota; </s>
					<s id="N1FB42">mo­<lb></lb>uetur quidem motu reflexo; </s>
					<s id="N1FB48">ſed inæquali priori, ſi adhuc maior moue­<lb></lb>tur etiam, ſed velociore motu, donec tandem in tota reſiſtentia toto <lb></lb>priore motu moueatur per ſe, vt dicemus paulò pòſt; </s>
					<s id="N1FB50">ſi verò ſit minor <lb></lb>reſiſtentia ceſsione, mouetur quidem per eandem lineam, ſed tardiore <lb></lb>motu, ſi adhuc minor mouetur quoque, ſed velociore motu, donec tan­<lb></lb>dem in nulla reſiſtentia ſit totus prior motus; </s>
					<s id="N1FB5A">ſi verò conſideretur glo­<lb></lb>bus reflectens, ſi eſt æqualis reſiſtentia mouetur æquali motu; ſi maior <lb></lb>minore; ſi tota nullo; </s>
					<s id="N1FB62">ſi vero ſit minor reſiſtentia mouetur motu velo­<lb></lb>ciore, atque ita deinceps; ſi nulla quaſi infinito: </s>
					<s id="N1FB68">dico quaſi, quia ſi va­<lb></lb>cuum moueri poſſet per impoſsibile, certè cum non reſiſtat, infinitè ce­<lb></lb>deret; igitur infinito motu quaſi moueretur. </s>
				</p>
				<p id="N1FB70" type="main">
					<s id="N1FB72">Septimò, vnde vides ab illo communi medio verſus vtrumque extre­<lb></lb>mum creſcere ſemper motum globi impacti; </s>
					<s id="N1FB78">donec tandem in vtroque <lb></lb>extremo æquali motu moueatur, quo iam priùs mouebatur in linea inci­<lb></lb>dentiæ; </s>
					<s id="N1FB80">at verò globi reflectentis verſus extremum nullius ceſsionis im­<lb></lb>minui motum, donec tandem in illo extremo nullus ſit; </s>
					<s id="N1FB86">creſcere vero <lb></lb>verſus aliud extremum, donec tandem in illo infinitus ſit, eo modo, quo <lb></lb>diximus, id eſt infinita ceſsio, quam accipio ad inſtar motus infinitæ ve­<lb></lb>locitatis; quemadmodum accipi poteſt nulla ceſsio, ſeu tota reſiſtentia <lb></lb>ad inſtar motus infinitæ tarditatis. </s>
				</p>
				<p id="N1FB92" type="main">
					<s id="N1FB94">Octauò, globus impactus imprimit ſemper æqualem impetum refle­<lb></lb>ctenti, qui pro diuerſa huius mole diuerſum modum præſtat; </s>
					<s id="N1FB9A">ſi refle­<lb></lb>ctens æqualis eſt æqualem, ſi maior minorem, ſi minor maiorem; </s>
					<s id="N1FBA0">quippe <lb></lb>idem impetus in paucioribus partibus facit maiorem motum, in totidem <lb></lb>æqualem, in pluribus minorem, donec tandem ſi plures ſint partes ſub­<lb></lb>jecti quàm partes impetus, nullus ſit motus; igitur nullus impetus, vt <lb></lb>conſtat ex his, quæ diximus lib.1. </s>
				</p>
				<p id="N1FBAD" type="main">
					<s id="N1FBAF">Nonò, hinc motus reflexus in perpendiculari minor eſt ea parte mo­<lb></lb>tus, quæ reflectenti imprimitur; </s>
					<s id="N1FBB5">vel enim imprimitur motus æqualis, <pb pagenum="249" xlink:href="026/01/281.jpg"></pb>vel inæqualis, ſi æqualis, certè toto motu multatur globus impactus; </s>
					<s id="N1FBBE">ſi <lb></lb>inæqualis, vel minor, vel maior; </s>
					<s id="N1FBC4">ſi minor, certè eſt aliquis motus refle­<lb></lb>xus æqualis priori minùs ea parte, quæ reflectenti imprimitur, donec <lb></lb>tandem nullus imprimatur motus; </s>
					<s id="N1FBCC">tunc enim reflexus eſt priori æqua­<lb></lb>lis; ſi verò maior imprimitur, fortè nullus eſt reflexus poſito ſcilicet ra­<lb></lb>dio incidentiæ perpendiculari, minor tamen erit idem motus globi im­<lb></lb>pacti vlteriùs per eandem lineam propagati. </s>
					<s id="N1FBD6">v.g.ſi ſit duplus detrahitur <lb></lb>priori motui 1/2, ſi triplus 1/3, ſi quadruplus 1/4, atque ita deinceps; ſi de­<lb></lb>nique infinities velocior ex ſuppoſitione impoſsibili detrahitur aliquid, <lb></lb>quod habet ad priorem motum proportionem minoris inæqualitatis in­<lb></lb>finitam. </s>
				</p>
				<p id="N1FBE2" type="main">
					<s id="N1FBE4">Decimò, ex his rectè concludi poteſt non produci infinita puncta im­<lb></lb>petus, nec eſſe infinitas partes ſubjecti actu; </s>
					<s id="N1FBEA">alioqui punctum mouere­<lb></lb>tur motu infinito, qui repugnat: </s>
					<s id="N1FBF0">præterea nullum eſſet corpus quamtum­<lb></lb>nis magnum, cui modico ictu non imprimatur impetus, ſi impetus con­<lb></lb>flat infinitis partibus; </s>
					<s id="N1FBF8">quare in vtraque progreſsione ſiſtendum eſt; <lb></lb>primò in nulla ceſsione &amp; tota reſiſtentia, cum ſcilicet plura ſunt pun­<lb></lb>cta ſubjecti, quàm impetus. </s>
					<s id="N1FC00">Secundò cum reflectens tantùm conſtat <lb></lb>vnico puncto, in quo ſcilicet impetus finitus impreſſus præſtat velociſ­<lb></lb>ſimum motum quem præſtare poteſt; </s>
					<s id="N1FC08">licèt enim dato quocunque motu <lb></lb>poſsit dari velocior, non tamen cum dato impetu finito determinato ſi­<lb></lb>ne acceſsione alterius; ſed iam interruptam noſtrorum Theorematum ſe­<lb></lb>riem proſequamur. </s>
				</p>
				<p id="N1FC12" type="main">
					<s id="N1FC14"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FC20" type="main">
					<s id="N1FC22"><emph type="italics"></emph>Determinatio noua cuiuſlibet alterius anguli incidentiæ obliqui, vel acuti, <lb></lb>eſt ad priorem, vt duplum ſinus recti eiuſdem anguli ad ſinum totum.<emph.end type="italics"></emph.end> v. g. <lb></lb> ſit radius incidentiæ AD in <expan abbr="planũ">planum</expan> immobile BDF: </s>
					<s id="N1FC35">dico nouam de­<lb></lb>terminationem eſſe ad priorem, vt duplum AB, id eſt BC ad DA. De­<lb></lb>monſtro; </s>
					<s id="N1FC3D">cum enim ictus per AD obliquam ſit ad ictum per AB per­<lb></lb>pendicularem, vt AB ad AD, vt conſtat ex dictis, tùm ſupra, tùm in lib. <lb></lb>de planis inclinatis; </s>
					<s id="N1FC45">ictus enim habent eam proportionem, quam ha­<lb></lb>bent grauitationes; </s>
					<s id="N1FC4B">ſed grauitatio in inclinatam AD eſt ad grauitatio­<lb></lb>nem in horizontalem DB, vt DB ad DA; </s>
					<s id="N1FC51">igitur ictus inflictus plano <lb></lb>DB per inclinatam AD eſt ad inflictum per ipſam perpendicularem <lb></lb>GD vt PR æqualem AB ad DA; </s>
					<s id="N1FC59">nam ictus in planum AD per GD <lb></lb>idem eſt cum ictu in DB per AD: </s>
					<s id="N1FC5F">ſimiliter ſit incidens KD, ſitque an­<lb></lb>gulus IDR æqualis KDG, ictus in ID per GD eſt æqualis ictui in <lb></lb>DR per KD; </s>
					<s id="N1FC67">ſunt enim GDI, KDR æquales; </s>
					<s id="N1FC6B">ſed ictus in ID eſt, vt <lb></lb>grauitatio in eandem ID; </s>
					<s id="N1FC71">hæc autem in inclinatam DI, ad aliam in <lb></lb>horizontalem DR vt DR ad DI; </s>
					<s id="N1FC77">igitur ictus in DI per GD eſt ad <lb></lb>ictum in DR per GD, vt DR vel LI ad ID; </s>
					<s id="N1FC7D">ſed K <foreign lang="grc">β</foreign> eſt æqualis IL; </s>
					<s id="N1FC85"><lb></lb>nam arcus KG &amp; IR ſunt æquales; </s>
					<s id="N1FC8A">igitur ictus per GD in DR eſt ad <lb></lb>ictum in DR per KD eſt vt DK ad K <foreign lang="grc">β</foreign>; ſed impedimentum eſt vt ictus. </s>
					<s id="N1FC94"><lb></lb>reſiſtentia vt impedimentum, determinatio noua, vt reſiſtentia; </s>
					<s id="N1FC99">igitur <pb pagenum="250" xlink:href="026/01/282.jpg"></pb>determinatio noua in linea incidentiæ GD eſt ad nouam in linea inci­<lb></lb>dentiæ KD, vt GD vel KD ad K <foreign lang="grc">β</foreign>, &amp; in linea incidentiæ AD vt AD <lb></lb>ad AB; </s>
					<s id="N1FCAA">igitur vt ſinus totus ad ſinum rectum dati anguli incidentiæ; </s>
					<s id="N1FCAE">ſed <lb></lb>in linea incidentiæ perpendiculari GD, determinatio noua eſt ad pri o­<lb></lb>rem in ratione dupla; </s>
					<s id="N1FCB6">igitur vt G <foreign lang="grc">δ</foreign> ad GD; </s>
					<s id="N1FCBE">ergo noua per KD eſt <lb></lb>ad nouam per DG, vt K <foreign lang="grc">θ</foreign>, ad G <foreign lang="grc">δ</foreign>; </s>
					<s id="N1FCCC">nam vt eſt K <foreign lang="grc">β</foreign> ad GD ita K <foreign lang="grc">θ</foreign> ad <lb></lb>G <foreign lang="grc">δ</foreign>; </s>
					<s id="N1FCDE">ergo noua per KD eſt ad priorem vt K <foreign lang="grc">θ</foreign> ad KD, &amp; noua per <lb></lb>AD, vt AC ad AD, atque ita deinceps; ergo determinatio noua per <lb></lb>lineam incidentiæ obliquam eſt ad priorem, vt duplum ſinus recti an­<lb></lb>guli incidentiæ ad ſinum totum, quod erat demonſtrandum. </s>
				</p>
				<p id="N1FCEC" type="main">
					<s id="N1FCEE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FCFA" type="main">
					<s id="N1FCFC"><emph type="italics"></emph>Hinc in ipſo angulo<emph.end type="italics"></emph.end> 60. <emph type="italics"></emph>determinatio noua eſt æqualis priori, id eſt in an­<lb></lb>gulo incidentiæ<emph.end type="italics"></emph.end> 30. ſit enim prædictus angulus IDR; </s>
					<s id="N1FD0D">certè RI eſt ſubdu­<lb></lb>pla ID, vt conſtat; </s>
					<s id="N1FD13">ſed determinatio noua per ID eſt ad priorem, vt <lb></lb>dupla IR ad ID; ergo vt æqualis ad æqualem. </s>
				</p>
				<p id="N1FD19" type="main">
					<s id="N1FD1B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FD27" type="main">
					<s id="N1FD29"><emph type="italics"></emph>Hinc ſupra angulum<emph.end type="italics"></emph.end> 30.<emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end> 90. <emph type="italics"></emph>noua determinatio eſt maior priore,<emph.end type="italics"></emph.end><lb></lb>donec tandem in ipſa GD vel in ipſo angulo GDR 90. ſit dupla prio­<lb></lb>ris, infrà verò angulum 30. eſt minor priore, donec tandem in ipſa ſe­<lb></lb>ctione plani FDB nulla ſit noua. </s>
				</p>
				<p id="N1FD42" type="main">
					<s id="N1FD44"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FD50" type="main">
					<s id="N1FD52"><emph type="italics"></emph>Ex his demonstratur acuratiſſimè æqualitas anguli reflexionis cum ſuo an­<lb></lb>gulo incidentiæ<emph.end type="italics"></emph.end>; </s>
					<s id="N1FD5D">ſit enim linea incidentiæ KD v. g. determinatio noua <lb></lb>per DG eſt ad priorem per DQ, vt K <foreign lang="grc">θ</foreign> vel XQ æqualis ad DQ; igi­<lb></lb>tur vt DZ æqualis QX ad DX; </s>
					<s id="N1FD71">ſed quotieſcumque ſunt duæ determi­<lb></lb>nationes, fit mixta per diagonalem Parallelo grammatis; </s>
					<s id="N1FD77">ſed QZ eſt pa­<lb></lb>rallelogramma, &amp; DX diagonalis; </s>
					<s id="N1FD7D">igitur determinatio mixta ex vtra­<lb></lb>que eſt per DX; </s>
					<s id="N1FD83">ſed angulus XDG eſt æqualis KDG, vt patet, nam <lb></lb>XDG eſt æqualis DXQ, &amp; hic DQX, &amp; hic QD <foreign lang="grc">δ</foreign>, &amp; hic QDK; </s>
					<s id="N1FD8D"><lb></lb>igitur KDR, qui eſt angulus incidentiæ eſt æqualis angulo XDF, qui <lb></lb>eſt angulus reflexionis: idem dico de omni alio. </s>
				</p>
				<p id="N1FD94" type="main">
					<s id="N1FD96">Obſeruaſti iam ni fallor primò determinationes nouas eſſe vt chor­<lb></lb>das arcus ſubdupli incidentiæ. </s>
					<s id="N1FD9B">Secundò planum reflectens quaſi repelle­<lb></lb>re omnes ictus per DG, id eſt per lineam, quæ à puncto contactus duci­<lb></lb>tur per centrum grauitatis, vt demonſtratum eſt lib.1. Th.120.121. </s>
				</p>
				<p id="N1FDA2" type="main">
					<s id="N1FDA4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FDB0" type="main">
					<s id="N1FDB2"><emph type="italics"></emph>Nullus impetus deſtruitur per ſe in pura reflexione<emph.end type="italics"></emph.end>; </s>
					<s id="N1FDBB">nam per accidens vt <lb></lb>plurimùm deſtruitur, vt dicemus infrà: </s>
					<s id="N1FDC1">dixi in pura reflexione; </s>
					<s id="N1FDC5">quia cum <lb></lb>fit aliqua compreſſio, vel repellitur corpus impactus niſu poſitiuo, etiam <lb></lb>deſtruitur impetus; </s>
					<s id="N1FDCD">demonſtratur Th. quia nihil impetus eſt fruſtrà; </s>
					<s id="N1FDD1"><lb></lb>igitur nihil deſtruitur: </s>
					<s id="N1FDD6">conſequentia patet ex dictis; probatur antece­<lb></lb>dens, quia linea determinationis mixtæ eſt ſemper æqualis lineæ prioris <lb></lb>determinationis, ſi remoto obice fuiſſet propagata. </s>
					<s id="N1FDDE">v.g. ſit linea inciden-<pb pagenum="251" xlink:href="026/01/283.jpg"></pb>tiæ AD, quæ vlteriùs producta ſine reflexione ſit, vt DE; </s>
					<s id="N1FDE9">certè deter­<lb></lb>minatio, ſeu motus eſt vt DE, vt patet: </s>
					<s id="N1FDEF">iam reflectatur in D à plano <lb></lb>BF; </s>
					<s id="N1FDF5">noua determinatio per DG eſt ad priorem, vt DT æqualis HE ad <lb></lb>DE; </s>
					<s id="N1FDFB">igitur determinatio mixta per DH eſt vt DH, ſed DH eſt æqua­<lb></lb>lis DE; </s>
					<s id="N1FE01">igitur determinatio mixta eſt æqualis priori; </s>
					<s id="N1FE05">igitur nihil im­<lb></lb>petus eſt fruſtrà; </s>
					<s id="N1FE0B">igitur nihil illius deſtruitur, quod erat demonſtrandum: </s>
					<s id="N1FE0F"><lb></lb>Idem demonſtrari poteſt in quacunque lineâ; in perpendiculo verò <lb></lb>GD; </s>
					<s id="N1FE16">cùm noua per DG ſit dupla prioris per D <foreign lang="grc">δ</foreign>, id eſt, vt DY æqua­<lb></lb>lis GD, ad DA; certè mixta erit DG æqualis DA. </s>
				</p>
				<p id="N1FE21" type="main">
					<s id="N1FE23"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FE2F" type="main">
					<s id="N1FE31"><emph type="italics"></emph>Hinc omnes lineæ reflexæ per ſe ſunt æquales,<emph.end type="italics"></emph.end> quia ſunt ſemidiametri eiuſ­<lb></lb>dem circuli; </s>
					<s id="N1FE3C">dico per ſe; </s>
					<s id="N1FE40">nam per accidens ſecùs accidit; </s>
					<s id="N1FE44">hinc malè di­<lb></lb>citur reflexam perpendicularem eſſe omnium reflexarum breuiſſimam <lb></lb>per ſe; quod licèt ita eſſe videatur, illud reuerâ eſt per accidens. </s>
				</p>
				<p id="N1FE4C" type="main">
					<s id="N1FE4E">Obiiceret fortè aliquis <expan abbr="pilã">pilam</expan> reflexam nunquam ad eam aſcendere <expan abbr="ſubli-mitatẽ">ſubli­<lb></lb>mitatem</expan> ex qua priùs demiſſa fuerat. </s>
					<s id="N1FE5B">Reſp. hoc <expan abbr="veriſſimũ">veriſſimum</expan> eſſe ſed per acci­<lb></lb>dens hoc ita fieri certum eſt propter diuiſionem, attritum, compreſſio­<lb></lb>nem, ceſſionemque partium; </s>
					<s id="N1FE67">vnde pila eò altiùs aſcendit, quò durior, &amp; <lb></lb>leuigatior eſt illa materia, ex qua conſtat, planumque ipſum leuigatius, <lb></lb>durius &amp; ad libellam acuratius ita compoſitum, vt ſit omninò horizonti <lb></lb>parallelum: </s>
					<s id="N1FE71">adde quod planum debet eſſe prorſus immobile; ſi enim mo­<lb></lb>bile ſit, multus impetus deſtruitur. </s>
				</p>
				<p id="N1FE77" type="main">
					<s id="N1FE79"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FE85" type="main">
					<s id="N1FE87"><emph type="italics"></emph>Hinc licèt non poſſit eſſe motus mixtus ex duplici impetu ad diuerſas lineas <lb></lb>determinato, niſi aliquid impetus destruatur, vt constat ex dictis; </s>
					<s id="N1FE8F">poteſt ta­<lb></lb>men eſſe linea motus quaſi mixta ex duabus cum eodem ſcilicet impetu licèt <lb></lb>nihil impetus destruatur; eſt enim maximum diſcrimen vtriuſque, vt <lb></lb>patet.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N1FE9B" type="main">
					<s id="N1FE9D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FEA9" type="main">
					<s id="N1FEAB"><emph type="italics"></emph>Ideo perpendicularis reflexa eſt reflexarum minima, non quidem per ſe, <lb></lb>ſed per accidens<emph.end type="italics"></emph.end>; </s>
					<s id="N1FEB6">quia cum perpendicularis maximum ictum infligat, fit <lb></lb>maior compreſſio partium, attritus, diuiſio; ex quibus neceſſariò ſequi­<lb></lb>tur plùs impetus deſtrui. </s>
				</p>
				<p id="N1FEBE" type="main">
					<s id="N1FEC0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FECC" type="main">
					<s id="N1FECE"><emph type="italics"></emph>Motus reflexus non eſt mixtus ex motu plani pellentis &amp; alio<emph.end type="italics"></emph.end>; </s>
					<s id="N1FED7">quia reue­<lb></lb>rà planum nullum imprimit impetum, quod etiam ex dictis neceſſariò <lb></lb>ſequitur; </s>
					<s id="N1FEDF">ſed eſt veluti occaſio, ex qua reſultat noua determinatio mix­<lb></lb>ta, ratione ſcilicet impedimenti, eo modo, quo diximus; ſi enim pla­<lb></lb>num ipſum nouum impetum imprimeret mobili, non eſſet pura reflexio. </s>
					<s id="N1FEE7"><lb></lb>de qua modo agimus, ſed alia, de qua infrà. </s>
				</p>
				<p id="N1FEEB" type="main">
					<s id="N1FEED"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FEF9" type="main">
					<s id="N1FEFB"><emph type="italics"></emph>Non datur quies vlla in puncto reflexionis<emph.end type="italics"></emph.end>; </s>
					<s id="N1FF04">appello puram reflexionem, <pb pagenum="252" xlink:href="026/01/284.jpg"></pb>in qua nullus ſit attritus nec <expan abbr="cõpreſſio">compreſſio</expan>, vel in mobili impacto, vel in pla­<lb></lb>no reflectente; prob. </s>
					<s id="N1FF13">quia mobile vno tantùm inſtanti tangit <expan abbr="planũ">planum</expan>; </s>
					<s id="N1FF1B">igitur <lb></lb>nullo inſtanti quieſcit; </s>
					<s id="N1FF21">antecedens certum eſt, quia eo inſtanti, quo primò <lb></lb>tangit, habet <expan abbr="impetũ">impetum</expan>; </s>
					<s id="N1FF2B">nec enim deſtruitur totus per Th.38.igitur inſtanti <lb></lb>ſequenti habebit ſuum effectum, ergo motum; </s>
					<s id="N1FF31">ergo vno tantùm inſtanti <lb></lb>tangit; </s>
					<s id="N1FF37">nec dicas impetum illum impediri; </s>
					<s id="N1FF3B">nam ideo impediretur motus <lb></lb>pro ſequenti inſtanti, quia tangitur planum primo inſtanti; </s>
					<s id="N1FF41">igitur ſimi­<lb></lb>liter, non moueretur tertio inſtanti, quia priori, id eſt ſecundo planum <lb></lb>tangeretur; idem dico de quarto, quinto &amp;c. </s>
					<s id="N1FF49">ergo mobile omninò quie­<lb></lb>ſceret, nec reflecteretur, quod eſt contra Th.1.igitur vno tantùm inſtanti <lb></lb>tangit mobile planum, quod erat antecedens propoſitum: Iam verò pro­<lb></lb>batur conſequentia; </s>
					<s id="N1FF53">ſi quieſcit in puncto reflexionis mobile; </s>
					<s id="N1FF57">igitur eo <lb></lb>inſtanti, quo tangit illud punctum; </s>
					<s id="N1FF5D">ſed eo inſtanti non quieſcit, quo reue­<lb></lb>râ mouetur; </s>
					<s id="N1FF63">atqui eo inſtanti quo tangit reuerâ mouetur; quia moueri, eſt <lb></lb>nouum locum primò acquirere per def.1. l.1. </s>
				</p>
				<p id="N1FF69" type="main">
					<s id="N1FF6B">Obiicies, primo inſtanti contactus mobile tangit planum quieſcens, <lb></lb>ergo non mouetur. </s>
					<s id="N1FF70">Reſpondeo negando <expan abbr="conſeq̃uens">conſequens</expan>, nam reuerâ poteſt <lb></lb>mobile in plano immobili moueri. </s>
				</p>
				<p id="N1FF79" type="main">
					<s id="N1FF7B">Obiicies ſecundò, mobile in puncto non mouetur; igitur in puncto <lb></lb>reflexionis non mouetur. </s>
					<s id="N1FF81">Reſpondeo primò negando antecedens; qui <lb></lb>enim admittunt puncta phyſica, dicent acquiri poſſe motu punctum phy­<lb></lb>ſicum ſpatij. </s>
					<s id="N1FF88">Reſpondeo ſecundò eandem eſſe difficultatem pro motu ſe­<lb></lb>quentis inſtantis, quidquid ſit, ſiue dentur puncta ſiue non, cuius diſcuſ­<lb></lb>ſio pertinet ad Metaphyſicam, ne.no negabit motum reuerâ eſſe, cum pri­<lb></lb>mo nouus locus acquiritur, in quo non eſt difficultas. </s>
				</p>
				<p id="N1FF91" type="main">
					<s id="N1FF93">Obiicies tertiò, in puncto nulla eſt ſucceſſio; igitur neque motus. </s>
					<s id="N1FF97"><lb></lb>Reſpondeo primò, nulla eſt ſucceſsio actu, concedo, potentia, nego; </s>
					<s id="N1FF9C">Re­<lb></lb>ſpondeo ſecundò, concedo antecedens, diſtinguo conſequens; </s>
					<s id="N1FFA2">nullus eſt <lb></lb>motus ſucceſsiuus, concedo; inſtantaneus, nego. </s>
				</p>
				<p id="N1FFA8" type="main">
					<s id="N1FFAA">Obiicies quartò, nullus datur motus inſtantaneus. </s>
					<s id="N1FFAD">Reſpondeo, nullus <lb></lb>datur inſtantaneus actu nego, potentiâ concedo; quia quocunque dato <lb></lb>motu poteſt dari minor. </s>
				</p>
				<p id="N1FFB5" type="main">
					<s id="N1FFB7">Obiicies quintò, igitur motus in eo puncto non poteſt eſſe tardior, &amp; <lb></lb>velocior. </s>
					<s id="N1FFBC">Reſpondeo primo negando; nam vno motu inſtantaneo actu <lb></lb>poteſt dari velocior, vel tardior, quæ omnia facilè in Metaphyſicis expli­<lb></lb>cantur, &amp; demonſtrantur, ex quibus certè res iſta phyſica minimè de­<lb></lb>pendet. </s>
				</p>
				<p id="N1FFC5" type="main">
					<s id="N1FFC7">Obiicies ſextò, authoritatem Ariſtotelis. </s>
					<s id="N1FFCB">Reſpondeo Ariſtotelem in­<lb></lb>telligendum eſſe de corpore projecto ſurſum motu violento, quod ante­<lb></lb>quam deſcendat vno inſtanti quieſcit; quod etiam demonſtraui lib.  3.Im­<lb></lb>mò plerique ſunt inter Peripateticos qui tenent in puncto reflexionis <lb></lb>non dari quietem, in hoc ſcilicet reflexionis genere, de quo hîc agimus, <lb></lb>qui fusè hanc quæſtionem diſcutiunt, nos breuiore methodo vſi rem <lb></lb>ipſam, ni fallor ex noſtris principiis demonſtrauimus. </s>
				</p>
				<pb pagenum="253" xlink:href="026/01/285.jpg"></pb>
				<p id="N1FFDF" type="main">
					<s id="N1FFE1"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N1FFED" type="main">
					<s id="N1FFEF">Obſerua primò, ſi planum reflectens cedit, vel mobile ipſum, rem <lb></lb>aliter eſſe explicandam. </s>
				</p>
				<p id="N1FFF4" type="main">
					<s id="N1FFF6">Secundò tribus modis <expan abbr="planũ">planum</expan> cedere, primò per <expan abbr="diuiſionẽ">diuiſionem</expan> partium ſi fran<lb></lb>gantur; 2° per diuiſionem ſine fractione propriè ſumpta, ſed <expan abbr="cũ">cum</expan> ceſsione. </s>
				</p>
				<p id="N20008" type="main">
					<s id="N2000A">Tertiò, ſine diuiſione, ſed non ſine compreſsione. </s>
				</p>
				<p id="N2000D" type="main">
					<s id="N2000F"><expan abbr="Exẽplum">Exemplum</expan> primi generis habes in charta, ſeu vitro, quæ <expan abbr="dũ">dum</expan> reflectit fran­<lb></lb>gitur: </s>
					<s id="N2001C"><expan abbr="exemplũ">exemplum</expan> ſecundi in cera molli, vel pingui terrâ; </s>
					<s id="N20023">tertii <expan abbr="deniq;">denique</expan> in <expan abbr="mẽ-brana">men­<lb></lb>brana</expan> tenſa, vel fune tenſo: </s>
					<s id="N20031">ſimiliter mobile ipſum tribus modis cedere <lb></lb>poteſt 1° <expan abbr="cũ">cum</expan> diuiſione partium, &amp; fractione, ſic <expan abbr="dũ">dum</expan> <expan abbr="vitrũ">vitrum</expan> à marmore refle­<lb></lb>ctitur in mille partes abit.2° ſine fractione, ſed non ſine depreſsione; ſic <lb></lb>plumbum deprimitur in corpus durum impactum, aut cera mollis. </s>
					<s id="N20047">3° ſine <lb></lb>diuiſione, ſed <expan abbr="nõ">non</expan> ſine aliqua compreſsione, ſic veſicca inflata reflectitur. </s>
				</p>
				<p id="N20050" type="main">
					<s id="N20052">Itaque duo ſunt planorum genera. </s>
					<s id="N20055">Primum eſt eorum, quæ non cedunt <lb></lb>præ duritie. </s>
					<s id="N2005A">Secundum eorum, quæ cedunt vel per fractionem, vel per de­<lb></lb>preſsionem, vel per compreſsionem: </s>
					<s id="N20060">per fractionem dupliciter; </s>
					<s id="N20064">primò ſi <lb></lb>alterantur tantùm aliquæ partes minutiores, vt fit in molliori lapide; </s>
					<s id="N2006A"><lb></lb>Secundò ſi per fractionem corpus diuidatur in partes notabiles, vt fit in <lb></lb>vitro, glacie; adde totidem genera mobilium. </s>
				</p>
				<p id="N20071" type="main">
					<s id="N20073">Obſerua tertiò eſſe tres alias combinationes; </s>
					<s id="N20077">vel enim mobile reflecti­<lb></lb>tur à mobili, ſed non pellitur à plano, &amp; hæc eſt pura reflexio; vel pellitur <lb></lb>à plano ſine motu præuio, vel ſimul reflectitur, &amp; pellitur à plano, quod <lb></lb>ſimul mouetur. </s>
					<s id="N20081">Obſerua 4° <expan abbr="cũ">cum</expan> mouetur corpus reflectens à mobili im­<lb></lb>pacto tres eſſe quoque <expan abbr="cõbinationes">combinationes</expan>, vel enim cum mouetur corpus refle­<lb></lb>ctens, reflectitur, ſeu retroagitur mobile impactum, vel <expan abbr="cõſiſtit">conſiſtit</expan>, ſeu quie­<lb></lb>ſcit, vel non retroagitur, ſed idem iter proſequitur. </s>
					<s id="N20096">Obſerua 5° <expan abbr="cū">cum</expan> ſint <lb></lb>quinque veluti ſtatus corporis reflectentis; </s>
					<s id="N200A0">nam vel eſt molle, vel preſsi­<lb></lb>bile, vel durum vel fragile, vel friabile, &amp; totidem ſtatus mobilis, eſſe 25. <lb></lb>combinationes, vt patet ex regula combinationum, in quo non eſt diffi­<lb></lb>cultas; igitur deinceps conſiderabo reflexionem ratione potiùs materiæ <lb></lb>corporis, tùm reflexi, tùm reflectentis, ſit ergo. </s>
				</p>
				<p id="N200AC" type="main">
					<s id="N200AE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N200BA" type="main">
					<s id="N200BC"><emph type="italics"></emph>Deſtruitur impetus in reflexione ex multis capitibus<emph.end type="italics"></emph.end>: primò, ratione diuer­<lb></lb>ſæ determinationis, ſi talis eſt vt aliquid impetus ſit fruſtrà, ſuppoſita <lb></lb>etiam perfecta duritie mobilis, &amp; plani &amp; figura apta. </s>
					<s id="N200C9">Secundò, ratione <lb></lb>diuiſionis partium vel plani, vel mobilis, vel vtriuſque; </s>
					<s id="N200CF">ſi enim alteran­<lb></lb>tur partes, fit quaſi foſſula, quam ſenſim ſubit mobile, cumque ſingulis <lb></lb>inſtantibus ſit noua difficultas ſuperanda, ſemper inde imminuitur impe­<lb></lb>tus: </s>
					<s id="N200D9">adde quod minor eſt determinatio plani quod cadit; </s>
					<s id="N200DD">igitur minor <lb></lb>eſt motus reflexus; </s>
					<s id="N200E3">igitur plùs impetus eſt fruſtrà; </s>
					<s id="N200E7">igitur plùs deſtruitur; </s>
					<s id="N200EB"><lb></lb>ſi autem planum vel ipſum mobile propter fragilitatem in partes diſsi­<lb></lb>liat, etiam deſtruitur aliquid impetus; Tertio ratione impreſsionis; <lb></lb>Quarto ratione compreſsionis; Quintò ratione repulſionis; Sextò ra­<lb></lb>tione liberioris ceſsionis; ſed hæc omnia minutiùs videntur eſſe ex­<lb></lb>plicanda. </s>
				</p>
				<pb pagenum="254" xlink:href="026/01/286.jpg"></pb>
				<p id="N200FC" type="main">
					<s id="N200FE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2010A" type="main">
					<s id="N2010C"><emph type="italics"></emph>Deſtruitur impetus cum ſcilicet mobili impacto in planum atteruntur par­<lb></lb>tes vel plani, vel mobilis, vel vtriuſque,<emph.end type="italics"></emph.end> ſic cum ſaxum alliditur molliori la­<lb></lb>pidi, prima ſuperficies reſiſtit quidem; </s>
					<s id="N20119">at certè minùs quàm par ſit, vt <lb></lb>ſiſtat mobile; </s>
					<s id="N2011F">deſtruitur tamen aliquid impetus, quia impeditur tantil­<lb></lb>lùm ſaltem prima illa determinatio; </s>
					<s id="N20125">Secunda ſuperficies reſiſtit etiam in <lb></lb>maiori ſcilicet proportione, tùm quia impetus euaſit infirmior ex primo <lb></lb>quaſi conflictu, tùm quia paulò durior eſt ſecunda ſuperficies quàm pri­<lb></lb>ma, quod ſcilicet aliquæ partes quaſi intrudantur in vacuitates interce­<lb></lb>ptas; </s>
					<s id="N20131">ſic pila lignea multis ictibus confuſa durior eſt; </s>
					<s id="N20135">denique tertia ſu­<lb></lb>perficies reſiſtit in maiori proportione quàm ſecunda &amp; quarta quàm <lb></lb>tertia; </s>
					<s id="N2013D">atque ita deinceps, donec tandem, vel totus impetus vincatur, vel <lb></lb>determinatio prior ſuperetur: </s>
					<s id="N20143">hinc ſi alterantur partes plani tantùm, mi­<lb></lb>nùs impetus deſtruetur, quàm ſi atterantur partes mobilis; quia impetus <lb></lb>partium mobilis attritarum totus deſinit, nec vllam vim ampliùs facit, <lb></lb>quod potiori iure dicendum eſt, ſi atterantur partes vtriuſque. </s>
				</p>
				<p id="N2014D" type="main">
					<s id="N2014F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2015B" type="main">
					<s id="N2015D"><emph type="italics"></emph>Hinc pluribus licèt inſtantibus mobile tangat planum, non tamen vllo quie­<lb></lb>ſcit<emph.end type="italics"></emph.end>; alioqui ſemper quieſceret per Th.50. </s>
				</p>
				<p id="N20168" type="main">
					<s id="N2016A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20176" type="main">
					<s id="N20178"><emph type="italics"></emph>Hinc cum atteruntur partes plani ab impactione mobilis, minor eſt reflexio<emph.end type="italics"></emph.end>; </s>
					<s id="N20181"><lb></lb>quia minor eſt cauſa, ſcilicet impetus, quæ minor eſt adhuc ſi atterantur <lb></lb>partes mobilis, &amp; minor adhuc, ſi partes vtriuſque; quæ omnia conſtant <lb></lb>ex dictis. </s>
				</p>
				<p id="N2018A" type="main">
					<s id="N2018C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20198" type="main">
					<s id="N2019A"><emph type="italics"></emph>Cum reſiliunt partes mobilis, destruitur impetus pen ſe, quia ſcilicet illa di­<lb></lb>uiſio, vel ſolutio continuitatis ſeu plexus reſiſtit<emph.end type="italics"></emph.end>; </s>
					<s id="N201A5">igitur impedit, ſed omne im­<lb></lb>pedimentum detrahit aliquid impetus: </s>
					<s id="N201AB">dixi per ſe, nam per accidens fieri <lb></lb>poteſt, vt aliqua particula reſiliens maiore cum impetu moueatur, vt pa­<lb></lb>tet aliquando experientiâ; quia præter priorem impetum, qui cum aliis <lb></lb>partibus illi communis erat, additur alius propter nouam alliſionem, ſeu, <lb></lb>quod mirabilius eſt, cum aliqua particula ex maiore maſsâ diuellitur, im­<lb></lb>petus totius mobilis quaſi migrat in particulam illam, perinde quaſi ab <lb></lb>eo emitteretur, id eſt cum antè totum mobile velociſſimo motu ferretur, <lb></lb>particula auulſa, eodem deinde mouetur. </s>
				</p>
				<p id="N201BD" type="main">
					<s id="N201BF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N201CB" type="main">
					<s id="N201CD"><emph type="italics"></emph>Porrò reſiliunt particulæ mobilis per omnes ferè lineas, quæ determinantur <lb></lb>per accidens à forma vel ſectione diuiſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N201D8">quæ enim dextrorſum ſeparan­<lb></lb>tur, dextrorſum eunt; </s>
					<s id="N201DE">atque ita in omnem partem ſine alia regula; </s>
					<s id="N201E2">cur <lb></lb>verò ab ictu diuellantur partes, non eſt huius loci diſcutere; </s>
					<s id="N201E8">ſic enim <lb></lb>quaſi finditur ſaxum ex colliſione; </s>
					<s id="N201EE">tùm quia ex illo omnium partium <lb></lb>ſuccuſſu ſoluitur illarum nexus; </s>
					<s id="N201F4">tùm quia intruduntur aliquæ partes, <pb pagenum="255" xlink:href="026/01/287.jpg"></pb>quaſi ad inſtar cunei, quæ aliàs diuidunt; </s>
					<s id="N201FD">tùm denique, quia eſt aliqua <lb></lb>compreſſio, cuius vires certè maximæ ſunt, vt dicemus alibi: </s>
					<s id="N20203">Exemplum <lb></lb>habes tùm in corpore duro, quale eſt vitrum, cuius modicam laminam ſi <lb></lb>duriori pauimento impingas, hinc inde mille particulæ tumultuatim re­<lb></lb>ſilient; tùm in corpore liquido, vt in aqua, quæ etiam ad corpus durum <lb></lb>alliſa in mille guttulas diſpergitur, quia eius partes facilè ſeparantur. </s>
				</p>
				<p id="N2020F" type="main">
					<s id="N20211"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2021D" type="main">
					<s id="N2021F"><emph type="italics"></emph>Si vel mobile eſt mollius, vel ipſum planum, vel vtrumque, ita vt non atte­<lb></lb>rantur partes, ſed tantùm citra compreſſionem cedant, deſtruitur etiam multus <lb></lb>impetus<emph.end type="italics"></emph.end>; </s>
					<s id="N2022C">ſit enim v.g.pila ex molliori cera, haud dubiè ex impactione non <lb></lb>comprimitur quidem, ſed deprimitur, nec amplius figuram ſphæræ, ſed <lb></lb>portionis habet: </s>
					<s id="N20234">in qua reuerâ depreſſione multus eſt conflictus, nec ſuf­<lb></lb>ficienter prima ſuperficies reſiſtit, licèt aliquid impetus deſtruat, nec <lb></lb>etiam ſecunda, nec tertia, quæ tamen reſiſtunt ſemper in maiori propor­<lb></lb>tione; </s>
					<s id="N2023E">donec tandem vel totus ictus quaſi extinguatur, vel determinatio <lb></lb>prior ſuperetur; </s>
					<s id="N20244">ex quo ſequitur reflexio, ſed minor: </s>
					<s id="N20248">porrò minor refle­<lb></lb>xio reſultat ex mollitie mobilis, quam plani, cæteris paribus, &amp; minor <lb></lb>adhuc ex mollitie vtriuſque; in quo verò conſiſtat mollities corpo­<lb></lb>rum, &amp; quomodo deprimantur ſine compreſſione, explicabimus tra­<lb></lb>ctatu ſequenti. </s>
				</p>
				<p id="N20254" type="main">
					<s id="N20256"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20262" type="main">
					<s id="N20264"><emph type="italics"></emph>Hinc plumbum ad reflexionem minùs aptum eſt,<emph.end type="italics"></emph.end> quia ſcilicet eius partes <lb></lb>difficiliùs auelluntur, &amp; à maiore ictu, qui ex grauitate maiore reſultat, <lb></lb>faciliùs deprimuntur; </s>
					<s id="N20271">hinc cum in molliorem terram pila alliditur, quaſi <lb></lb>emoritur eius ſaltus; </s>
					<s id="N20277">hinc, ſi grauior ictus eſt, qualis eſt maioris vel mi­<lb></lb>noris pilæ è tormento exploſæ, &amp; mollior terra, qualis eſt illa quâ vulgò <lb></lb>aggeres munitionum farciuntur, pila terram ipſam facto foramine pene­<lb></lb>trat, cùm facilè cedat materia; nec inde amplius reſultat, cuius rei ratio <lb></lb>eſt clariſſima quia ſenſim extinguitur impetus, nec anguſtiæ foraminis <lb></lb>reditum patiuntur. </s>
				</p>
				<p id="N20285" type="main">
					<s id="N20287">Hinc multâ lanâ muniuntur latera nauium contra maiora tormenta; </s>
					<s id="N2028B"><lb></lb>quippe globi vis ſenſim emoritur in lana, quia ſinguli pili reſiſtunt; &amp; <lb></lb>quia facilè cedunt difficiliùs diuiduntur, ſed fallenti illa ceſſione ictum <lb></lb>quoque fallunt, in quo non eſt difficultas. </s>
				</p>
				<p id="N20294" type="main">
					<s id="N20296"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N202A2" type="main">
					<s id="N202A4"><emph type="italics"></emph>Quando fit aliqua compreſſio, distribuitur etiam impetus<emph.end type="italics"></emph.end>; </s>
					<s id="N202AD">eſt enim con­<lb></lb>flictus, &amp; pugna partium inter ſe; </s>
					<s id="N202B3">ſit enim veſicca in pauimentum alli­<lb></lb>ſa, partes anticæ aëris, quo veſicca inflatur, comprimunt, &amp; quaſi poſti­<lb></lb>cas repellunt, à quibus mutuò retruduntur; </s>
					<s id="N202BB">vides pugnam; </s>
					<s id="N202BF">igitur de­<lb></lb>ſtruitur impetus: </s>
					<s id="N202C5">ſed reſtituitur ſtatim à potentia motrice media, quâ <lb></lb>ſcilicet corpus omne compreſſum plùs æquo, vt ſeſe in priſtinum exten­<lb></lb>ſionis ſtatum reſtituat, producit in ſe impetum: porrò de hac potentiâ <pb pagenum="254" xlink:href="026/01/288.jpg"></pb>agemus fusè tractatu ſequenti lib.2. porrò vel comprimitur tantum mo­<lb></lb>bile, vel tantùm ipſum planum, vel ſimul vtrumque. </s>
				</p>
				<p id="N202D4" type="main">
					<s id="N202D6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N202E2" type="main">
					<s id="N202E4"><emph type="italics"></emph>Ex hac compreſſione ſequitur aliqua reflexio<emph.end type="italics"></emph.end>; </s>
					<s id="N202ED">ſiue tantùm mobile com­<lb></lb>primatur, vt veſicca inflata vel pila; </s>
					<s id="N202F3">quippe præter reflexionem puram, <lb></lb>id eſt præter priorem impetum, qui tamen ex parte deſtruitur, fit acceſſio <lb></lb>noui impetus; </s>
					<s id="N202FB">igitur maior eſt motus qui reuerâ impetus maior eſt, quò <lb></lb>maior eſt compreſſio, quæ maior eſt, quò maior eſt ictus; </s>
					<s id="N20301">hinc maximè <lb></lb>apta eſt ad reflexionem pila, &amp; veſicca; </s>
					<s id="N20307">ſi tamen excipias mobile duriſ­<lb></lb>ſimum in planum duriſſimum impactum; </s>
					<s id="N2030D">tunc enim maxima eſt reflexio, <lb></lb>experientiâ teſte; </s>
					<s id="N20313">ſi verò planum ipſum comprimatur, ex illa quoque <lb></lb>compreſſione ſequitur noui impetus acceſſio: </s>
					<s id="N20319">Exemplum habes in fune <lb></lb>tenſo, vel in membrana timpani bellici, in qua piſa tam facilè ſubſultant; </s>
					<s id="N2031F"><lb></lb>emoritur tamen ferè totus prior impetus propter ceſſionem plani; </s>
					<s id="N20324">&amp; niſi <lb></lb>nouus accederet, haud dubiè vel nulla penitus vei minima fieret refle­<lb></lb>xio; </s>
					<s id="N2032C">denique fieri poteſt compreſſio tùm in mobili, tùm in plano v.g. ſi <lb></lb>veſicca inflata repercutiatur à membrana tympani maximè tenſa, in hoc <lb></lb>caſu maxima fit noui impetus acceſſio ex duplici compreſſione; </s>
					<s id="N20336">ſed ma­<lb></lb>xima fit etiam prioris impetus imminutio ex duplici etiam capite, nem­<lb></lb>pè ex compreſſione, eaque duplici, &amp; noua determinatione; ſed hæc ſunt <lb></lb>facilia. </s>
				</p>
				<p id="N20340" type="main">
					<s id="N20342"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2034E" type="main">
					<s id="N20350"><emph type="italics"></emph>Si corpus in aliud impactum repellatur per productionem impetus. </s>
					<s id="N20355">v.g. ſi <lb></lb>duo globi mutuò impellantur, deſtruitur etiam impetus ex hoc capite,<emph.end type="italics"></emph.end> vt patet <lb></lb>experientia: </s>
					<s id="N20362">immò ſi globus in æqualem globum impingatur deſtruitur <lb></lb>totus impetus prior; </s>
					<s id="N20368">vt dictum eſt alibi, de quo etiam infrà: </s>
					<s id="N2036C">Ratio huius <lb></lb>Theorematis eſt, quia aliqua impetus portio eſt fruſtrà; </s>
					<s id="N20372">quia non poteſt <lb></lb>habere ſuum effectum; igitur deſtrui debet. </s>
				</p>
				<p id="N20378" type="main">
					<s id="N2037A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20386" type="main">
					<s id="N20388"><emph type="italics"></emph>Si globus in alium æqualem impingitur, ita vt punctum contactus, &amp; cen­<lb></lb>trum vtriuſque ſint in eadem linea, multa <expan abbr="ſequũtur">ſequuntur</expan> phænomena, quæ iam atti­<lb></lb>gimus lib.<emph.end type="italics"></emph.end>1.<emph type="italics"></emph>à Th.<emph.end type="italics"></emph.end>60.Primò, æqualis impetus in globo, in quem impactus <lb></lb>eſt, producitur per Th.60.lib.1. Secundò, æqualis eſt determinatio noua <lb></lb>priori; </s>
					<s id="N203A3">probatur per Th.127.lib.1. Tertiò, deſtruitur totus impetus prior <lb></lb>per Th.128. hinc quieſcit globus impactus; </s>
					<s id="N203A9">cuius rei non poteſt eſſe alia <lb></lb>cauſa; </s>
					<s id="N203AF">nec enim dicas deſtrui totum impetum illum (vt reuerâ totus de­<lb></lb>ſtruitur) ratione reſiſtentiæ, quæ minor eſt, quàm eſſet, ſi in parietem il­<lb></lb>lideretur; </s>
					<s id="N203B7">igitur tota ratio, cur deſtruatur totus impetus, duci tantùm <lb></lb>poteſt ex eo, quod ſit fruſtrà; </s>
					<s id="N203BD">eſt autem fruſtrà, quia cum prior deter­<lb></lb>minatio ferat globum impactùm per eandem lineam, &amp; noua per oppo­<lb></lb>ſitam; </s>
					<s id="N203C5">vtraque certè æqualis eſt; </s>
					<s id="N203C9">igitur neutra præualet; </s>
					<s id="N203CD">igitur globus <lb></lb>conſiſtit; </s>
					<s id="N203D3">ſi quis enim diceret non eſſe æquales; </s>
					<s id="N203D7">igitur altera maior eſt; </s>
					<s id="N203DB"><lb></lb>igitur debet præualere; </s>
					<s id="N203E0">igitur ſi prior eſt, debet vlteriùs propagari motus <pb pagenum="255" xlink:href="026/01/289.jpg"></pb>in eadem linea; </s>
					<s id="N203E9">ſi noua, igitur debet tantillùm reflecti; igitur cum nec <lb></lb>vlteriùs producatur motus, nec retrò agatur mobile, vtraque determi­<lb></lb>natio neceſſariò æqualis eſt. </s>
					<s id="N203F1">Quænam verò ſit huius æqualitatis ratio à <lb></lb>priori, difficilè dictu eſt; </s>
					<s id="N203F7">dico tamen petendam eſſe ab æqualitate glo­<lb></lb>borum; </s>
					<s id="N203FD">cum enim determinatio noua ſit duplò maior à plano immobili <lb></lb>&amp; duro; </s>
					<s id="N20403">certè à plano mobili minor eſt, vt conſtat, quia cedit; </s>
					<s id="N20407">igitur <lb></lb>quâ proportione plùs, vel minùs cedit, eſt minor dupla; </s>
					<s id="N2040D">ſed maior glo­<lb></lb>bus minùs cedit, quàm æqualis; </s>
					<s id="N20413">quia ceſſio eſt minor impulſione; </s>
					<s id="N20417">igitur <lb></lb>quando ceſſio eſt æqualis impulſioni, æquales ſunt determinationes; </s>
					<s id="N2041D">at­<lb></lb>qui cum producitur æqualis impetus, &amp; imprimitur æqualis motus, <lb></lb>æqualis eſt ceſſiò impulſioni, id eſt æquè cedit, ac impellitur; cum tamen, <lb></lb>ſi maior ſit globus, non æquè citò cedat, quia tardior motus imprimitur, <lb></lb>&amp; hæc eſt, ni fallor, vera ratio huius æqualitatis determinationum, &amp; <lb></lb>hæc vera cauſa quietis globi impacti, de qua iam ſuprà Th. 40. </s>
				</p>
				<p id="N2042B" type="main">
					<s id="N2042D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 63.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20439" type="main">
					<s id="N2043B"><emph type="italics"></emph>Cum verò globus impellitur in globum æqualem per lineam obliquam, num­<lb></lb>quam quieſcit<emph.end type="italics"></emph.end>; </s>
					<s id="N20446">quod demonſtratur, quia ſemper eſt determinatio mixta; </s>
					<s id="N2044A"><lb></lb>quod vt meliùs intelligatur, opus eſt nouâ figurâ ſit ergo punctum con­<lb></lb>tactus duorum globorum B, &amp; ipſa CBN ſit Tangens communis, ſeu <lb></lb>ſectio plani, quæ gerit vicem plani reflectentis; </s>
					<s id="N20453">fit autem primò linea <lb></lb>incidentiæ connectens centra FBA; </s>
					<s id="N20459">nulla fit in ea reflexio per Th. 61. <lb></lb>quia ſcilicet determinatio noua per lineam BF eſt æqualis priori per <lb></lb>FB; </s>
					<s id="N20461">ſit EB linea incidentiæ faciens angulum EBC cum Tangente <lb></lb>NC; </s>
					<s id="N20467">determinatio noua eſt ad determinationem priorem vt BG vel <lb></lb>ER ad BE, &amp; ſi ſit linea incidentiæ DB vt BH, vel SD ad BD; </s>
					<s id="N2046D">deni­<lb></lb>que ſi ſit BV vt TV ad BV, donec tandem linea incidentiæ ſit CB, quâ <lb></lb>poſitâ nulla eſt determinatio noua; </s>
					<s id="N20475">vides eſſe eandem viam proportio­<lb></lb>num quæ fuit ſuprà; </s>
					<s id="N2047B">licèt non ſit futura eadem angulorum reflexionis <lb></lb>proportio, quia determinationum nouarum rationes non ſunt eædem; <lb></lb>producatur enim EBL DBM &amp;c. </s>
					<s id="N20483">determinatio prior per EB eſt ad <lb></lb>nouam per BF, vt BE ad BG; </s>
					<s id="N20489">igitur ducantur EP PL; </s>
					<s id="N2048D">aſſumatur LI <lb></lb>æqualis BG, &amp; GI, BL æqualis BE; </s>
					<s id="N20493">denique ducatur BI: dico BI eſſe <lb></lb>lineam reflexionis ſeu determinationem mixtam ex BG BL per Th. <lb></lb>137.lib.1.&amp;c. </s>
					<s id="N2049D">Similiter ſi ſit linea incidentiæ DBN, ducanturque DO. <lb></lb>OM, &amp; aſſumatur MK æqualis BH, vel SD, dico lineam BK eſſe de­<lb></lb>terminationem mixtam ex BH BM, ex quibus etiam longitudo omnium <lb></lb>reflexarum facilè determinari poteſt; quippe longitudo eſt vt linea de­<lb></lb>terminationis mixtæ. </s>
					<s id="N204A9">v.g. BI, BK; </s>
					<s id="N204AF">demonſtratur autem hæc determi­<lb></lb>nationum progreſſio, quia determinatio per EB eſt ad determinationem <lb></lb>per FB vt ictus per EB ad ictum per FB, vt iam ſæpè dictum eſt; </s>
					<s id="N204B7">ſed <lb></lb>ictus per EB in CN eſt ad ictum per FB vt ER ad FB vel EB, id eſt, vt <lb></lb>ſinus rectus anguli incidentiæ ad ſinum totum; </s>
					<s id="N204BF">ſed determinatio noua <lb></lb>in perpendiculo FB eſt ad priorem, vt FB ad BF per Th.62. igitur noua <lb></lb>determinatio per EB eſt ad priorem vt ER ſeu ſinus rectus anguli EBC <pb pagenum="256" xlink:href="026/01/290.jpg"></pb>ad ſinum totum EB, &amp; per DB vt DS ad DB: idem dico de aliis. </s>
				</p>
				<p id="N204CC" type="main">
					<s id="N204CE">Hinc colligo primò, omnes determinationes nouas in hypotheſi glo­<lb></lb>borum æqualium eſſe ſubduplas in eiſdem angulis priorum determina­<lb></lb>tionum in hypotheſi corporis reflectentis immobilis. </s>
				</p>
				<p id="N204D5" type="main">
					<s id="N204D7">Colligo ſecundò, omnes reflexiones fieri neceſſariò per eandem li­<lb></lb>neam, quæ ſcilicet eſt Tangens puncti contactus globi reflectentis, quod <lb></lb>valdè mirificum eſt, &amp; facilè obſeruabunt, qui Tudicula minore ludunt. </s>
					<s id="N204DE"><lb></lb>Colligo ſexto, cum angulus incidentiæ eſt 60. lineam reflexam eſſe ſub­<lb></lb>duplam directæ quæ vlteriùs produceretur; infrà verò ſexto eſſe maio­<lb></lb>rem, ſuprà verò eſſe minorem, eſt autem longitudo lineæ ſinus comple­<lb></lb>menti anguli incidentiæ. </s>
					<s id="N204E9">v.g. ſi linea incidentiæ ſit EB eſt EG, ſi DB <lb></lb>eſt DH, ſi VB eſt VX. </s>
				</p>
				<p id="N204F0" type="main">
					<s id="N204F2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 64.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N204FE" type="main">
					<s id="N20500"><emph type="italics"></emph>Si globus minor in maiorem impingatur, qui ab eo tamen moueatur per li­<lb></lb>neam connectentem centra vtriuſque impactus, reflectitur<emph.end type="italics"></emph.end>; </s>
					<s id="N2050B">ratio eſt, quia ma­<lb></lb>ior globus eſt maius impedimentum, vt iam diximus Th. 131.lib.1.id <lb></lb>eſt, vt clariùs hic explicetur, quæ ibidem tantùm obiter indicauimus, <lb></lb>noua determinatio maior eſt priore, quia ceſsio eſt minor impulſione; ſit <lb></lb>autem. </s>
					<s id="N20517">v.g. globus reflectens duplus impacto; </s>
					<s id="N2051D">igitur motus eſt ſubduplus, <lb></lb>quia ſcilicet impetus diſtribuitur pluribus partibus ſubjecti; </s>
					<s id="N20523">igitur ſin­<lb></lb>gulæ minùs habent; </s>
					<s id="N20529">igitur impetus eſt remiſsior; </s>
					<s id="N2052D">igitur motus tardior; </s>
					<s id="N20531"><lb></lb>igitur ceſsio minor ſubduplo; </s>
					<s id="N20536">igitur determinatio noua eſt maior æqua­<lb></lb>li 1/2 hinc debet neceſſariò reflecti, quia quotieſcunque ad lineas op­<lb></lb>poſitas ex diametro determinatur impetus, maior determinatio præua­<lb></lb>let pro rata per Th.134.lib.1. nam perinde ſe habet, atque ſi eſſet duplex <lb></lb>impetus; </s>
					<s id="N20542">quanta porrò eſſe debeat linea reflexa, determinari poteſt; </s>
					<s id="N20546">ſi <lb></lb>enim determinatio noua eſſet ſolilaria mobile cum eo impetu, quem ha­<lb></lb>bet <expan abbr="cõficeret">conficeret</expan> v.g. BA vel BF; </s>
					<s id="N20554">diuidatur BF in duas partes æquales in <foreign lang="grc">υ</foreign>, <lb></lb>determinatio noua eſt ad priorem vt 3. ad 2. aſſumatur F<foreign lang="grc">β</foreign> æqualis B<foreign lang="grc">υ</foreign>; </s>
					<s id="N20566"><lb></lb>igitur propter determinationem priorem oppoſitam ſcilicet BA detra­<lb></lb>hi debent duæ partes toti B<foreign lang="grc">β</foreign> ſcilicet <foreign lang="grc">βυ</foreign> æqualis BA; </s>
					<s id="N20575">igitur linea re­<lb></lb>flexa erit B<foreign lang="grc">υ</foreign> dupla totius BF; </s>
					<s id="N2057F">ſit etiam globus reflectens, qui mouetur <lb></lb>ab impacto, quadruplus, determinatio noua erit ad priorem vt 7. ad 4. <lb></lb>fit B<foreign lang="grc">δ</foreign> ad BA vt 7. ad 4. ex B<foreign lang="grc">δ</foreign> detrahatur DH æqualis BA, ſupereſt <lb></lb>HB id eſt 3/4 totius BF; non poteſt autem eſſe maior determinatio no­<lb></lb>ua priore quàm in ratione dupla, vt diximus ſuprà. </s>
					<s id="N20593">Ratio eſt, quia eò mi­<lb></lb>nor eſt determinatio noua, quò maior eſt motus impreſſus globo maiori <lb></lb>reflectenti; </s>
					<s id="N2059B">igitur tantum detrahitur duplæ, quantum additur motus; </s>
					<s id="N2059F">ſi <lb></lb>motus eſt æqualis, detrahitur duplæ æqualis priori; </s>
					<s id="N205A5">igitur ſupereſt æqua­<lb></lb>lis; </s>
					<s id="N205AB">ſi motus eſt ſubduplus, detrahitur duplæ ſubdupla prioris; </s>
					<s id="N205AF">igitur ſu­<lb></lb>pereſt 1/2 ſi ſubquadruplus detrahitur duplæ ſubquadrupla prioris, igitur <lb></lb>ſupereſt 1 3/4 ſi ſit duplus motus, determinatio noua eſt ſubdupla; </s>
					<s id="N205B7">igitur <lb></lb>priori detrahitur 1/2 de quo infrà; </s>
					<s id="N205BD">quod autem ſpectat ad longitudi­<lb></lb>nes linearum non eſt difficultas; quippe determinatio minor detrahi <lb></lb>deber maiori. </s>
				</p>
				<pb pagenum="257" xlink:href="026/01/291.jpg"></pb>
				<p id="N205C9" type="main">
					<s id="N205CB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 65.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N205D7" type="main">
					<s id="N205D9"><emph type="italics"></emph>Si globus minor in maiorem impingatur per lineam obliquam incidentiæ, <lb></lb>ſemper reflectitur<emph.end type="italics"></emph.end>; </s>
					<s id="N205E4">quippè ſit determinatio mixta ex priore, &amp; noua, quæ <lb></lb>determinari poteſt, ſi aliquid à nouæ figuræ deſcribatur; </s>
					<s id="N205EA">ſit circulus <lb></lb>FQCD; </s>
					<s id="N205F0">ſint diametri QD, FC; </s>
					<s id="N205F4">ſit AI dupla AF, ſitque determi­<lb></lb>natio prior vt FA, ſi ſecunda ſit vt AI, erit dupla prioris; </s>
					<s id="N205FA">igitur corpus <lb></lb>reflectens erit immobile; </s>
					<s id="N20600">igitur ſi linea incidentiæ ſit EA, reflexa erit <lb></lb>AT, ita vt anguli TAF, EAF ſint æquales; </s>
					<s id="N20606">ſi autem determinatio no­<lb></lb>ua ſit ad priorem vt AH ad AF, id eſt, v.g. vt 3. ad 2. poſitâ ſcilicet li­<lb></lb>neâ incidentiæ perpendiculari FA in planum reflectens QD, quod certè <lb></lb>mouebitur per Th. 64. aliter procedendum eſt vt inueniatur linea re­<lb></lb>flexa reſpondens lineæ incidentiæ obliquæ; </s>
					<s id="N20614">diuidatur FAMK ita vt <lb></lb>KN ſit ad AF vt 3.ad 2. ac proinde AH ſit diuiſa bifariam in K; </s>
					<s id="N2061A">de­<lb></lb>ſcribatur circulus KMNR, ſit linea quælibet incidentiæ obliqua EA; </s>
					<s id="N20620"><lb></lb>producatur in B; </s>
					<s id="N20625">ducantur OX BT parallelæ AH; </s>
					<s id="N20629">aſſumatur AG æqua­<lb></lb>lis OX, &amp; GS æqualis AB; </s>
					<s id="N2062F">certè BS erit æqualis OX vel AG; </s>
					<s id="N20633">duca­<lb></lb>tur AS, hæc erit reflexa quæſita: </s>
					<s id="N20639">idem dico de omnibus aliis lineis in­<lb></lb>cidentiæ; demonſtratur eodem modo quo ſuprà in Th. 30. 31. 32. quæ <lb></lb>conſule, ne hic repetere cogar. </s>
				</p>
				<p id="N20641" type="main">
					<s id="N20643"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 66.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2064F" type="main">
					<s id="N20651"><emph type="italics"></emph>Si globus maior impingatur in minorem, per lineam incidentiæ connecten­<lb></lb>tem centra nullo modo reflectitur ſed per eandem lineam primum motum pro­<lb></lb>pagat licèt tardiùs per Th.<emph.end type="italics"></emph.end>132. lib.1. in qua verò proportione retardetur <lb></lb>motus non ita facilè dictu eſt; dici tamen poteſt &amp; explicari in fig. </s>
					<s id="N20660">Th. <lb></lb>63. ſi enim globi ſunt æquales, ceſſio æqualis eſt impulſioni; </s>
					<s id="N20667">ſi globus <lb></lb>impactus ſit maior, ceſſio eſt maior impulſione, vt conſtat; </s>
					<s id="N2066D">igitur, ſi globus <lb></lb>eſt ad globum vt FB ad FB; </s>
					<s id="N20673">determinatio noua erit ad priorem vt FB <lb></lb>ad FB; </s>
					<s id="N20679">igitur quieſcet globus impactus per Th. 62. ſi verò globus impa­<lb></lb>ctus ſit ad alium vt EB ad ER; </s>
					<s id="N2067F">determinatio noua erit ad priorem, vt <lb></lb>BG ad BF; </s>
					<s id="N20685">igitur motus retardatus globi impacti eſt ad non retardatum <lb></lb>vt FG ad FB; </s>
					<s id="N2068B">quod ſi globus impactus eſt ad alium vt DB ad DS, deter­<lb></lb>minatio noua eſt ad priorem vt BH ad BF; </s>
					<s id="N20691">ſi ſit vt TV, ad VB, deter­<lb></lb>minatio noua erit ad priorem vt BX ad BF, donec tandem nullus ſit <lb></lb>globus reſiſtens; neque res aliter eſſe poteſt. </s>
				</p>
				<p id="N20699" type="main">
					<s id="N2069B">Hinc vides duos terminos oppoſitos, qui ſunt, nulla reſiſtentia, &amp; infi­<lb></lb>nita reſiſtentia; </s>
					<s id="N206A1">nulla eſt reſiſtentia, cum globus impactus in nullum in­<lb></lb>cidit, ſed eſt veluti infinita ceſſio; </s>
					<s id="N206A7">cum verò globus in corpus immobile <lb></lb>impingitur, eſt veluti infinita reſiſtentia ratione huius motus; </s>
					<s id="N206AD">cum verò <lb></lb>globus in alium globum, quem mouet, impingitur, ſi vterque æqualis eſt; </s>
					<s id="N206B3"><lb></lb>eſt etiam æqualis ceſſio reſiſtentiæ; </s>
					<s id="N206B8">igitur globus impactus quieſcit, &amp; <lb></lb>hoc eſt iuſtum medium extremorum prædictorum, id eſt, inter nullam <lb></lb>ceſſionem, &amp; infinitam ceſſionem; </s>
					<s id="N206C0">media eſt æqualis ceſſio; </s>
					<s id="N206C4">&amp; inter nul­<lb></lb>lam reſiſtentiam &amp; infinitam reſiſtentiam media eſt æqualis reſiſtentia; </s>
					<s id="N206CA"><pb pagenum="258" xlink:href="026/01/292.jpg"></pb>reſiſtentia autem conſideratur in globo impacto, cuius reſiſtitur motui; </s>
					<s id="N206D2"><lb></lb>ceſſio verò in alio, qui motui cedit; </s>
					<s id="N206D7">appello autem infinitam reſiſten­<lb></lb>tiam cui nulla reſpondet ceſſio; </s>
					<s id="N206DD">nihil enim aliud præſtaret infinita; </s>
					<s id="N206E1">por­<lb></lb>rò cum nulla eſt ceſſio, determinatio noua eſt dupla prioris, vt demon­<lb></lb>ſtratum eſt ſuprà; </s>
					<s id="N206E9">igitur nihil prioris remanet; </s>
					<s id="N206ED">cum verò nulla eſt reſi­<lb></lb>ſtentia, tota prior remanet, &amp; nulla eſt noua: </s>
					<s id="N206F3">denique cum ceſſio æqua­<lb></lb>lis eſt reſiſtentiæ, tantùm remanet prioris quantùm eſt nouæ; </s>
					<s id="N206F9">igitur <lb></lb>vtraque æqualis eſt: Vnde vides, ni fallor, perfectam analogiam, &amp;c. </s>
					<s id="N206FF">Ob­<lb></lb>ſeruaſti ni fallor, quod in hac re potiſſimum eſt. </s>
					<s id="N20704">Primò, tunc eſſe infini­<lb></lb>tam reſiſtentiam, cum nulla eſt ceſſio: vt in corpore reflectente prorſus <lb></lb>immobili. </s>
					<s id="N2070C">Secundò, tunc eſſe infinitam ceſſionem, cum nulla eſt reſi­<lb></lb>ſtentia vt in vacuo. </s>
					<s id="N20711">Tertiò, æqualitatem ceſſionis, &amp; reſiſtentiæ æquali­<lb></lb>ter ab vtroque diſtare; tantùm enim eſt inter æqualitatem illam, &amp; in­<lb></lb>finitam ceſſionem quantum inter eandem æqualitatem, &amp; infinitam re­<lb></lb>ſiſtentiam. </s>
					<s id="N2071B">Quartò ab infinita ceſſione ad æqualitatem accedere nouam <lb></lb>determinationem æqualem priori. </s>
					<s id="N20720">Quintò, ab eadem æqualitate ad in­<lb></lb>finitam reſiſtentiam <expan abbr="tantũdem">tantundem</expan> accedere, ac proinde nouam determi­<lb></lb>nationem eſſe duplam prioris; ex quo etiam probatur æqualitas angulo­<lb></lb>rum incidentiæ, &amp; reflexionis. </s>
				</p>
				<p id="N2072E" type="main">
					<s id="N20730"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 67.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2073C" type="main">
					<s id="N2073E"><emph type="italics"></emph>Si globus maior impingatur in minorem per lineam obliquam ſemper re­<lb></lb>flectitur, licèt aliquando inſenſibiliter, quia fit determinatio mixta ex noua &amp; <lb></lb>priore, cuius proportio determinari poteſt<emph.end type="italics"></emph.end>; ſit enim determinatio noua ad <lb></lb>priorem in linea incidentiæ perpendiculari vt C<foreign lang="grc">δ</foreign> ad CA fig. </s>
					<s id="N20751">Th. 65. <lb></lb> vel vt AZ ad AF, ſit linea incidentiæ obliqua EA producta in B; </s>
					<s id="N20757"><lb></lb>certè ſi determinatio noua per lineam incidentiæ obliquam EA eſt ad <lb></lb>priorem, vt AZ ad AF; </s>
					<s id="N2075E">ſumatur B<foreign lang="grc">υ</foreign> æqualis AY; </s>
					<s id="N20766">ducantur Y<foreign lang="grc">υ</foreign> A<foreign lang="grc">υ</foreign><lb></lb>dico A<foreign lang="grc">υ</foreign> eſſe lineam reflexionis, quia eſt mixta ex AY &amp; AB, vt con­<lb></lb>ſtat ex dictis; Idem dico de aliis incidentiæ. </s>
				</p>
				<p id="N20779" type="main">
					<s id="N2077B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 68.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20787" type="main">
					<s id="N20789"><emph type="italics"></emph>Si globus in æqualem globum impingatur, qui æquali impetu in eum etiam <lb></lb>impingitur per lineam connectentem centra<emph.end type="italics"></emph.end>; </s>
					<s id="N20794">vterque retro agitur æquali <lb></lb>pœnitus motu, quo ſuam lineam vlteriùs propagaſſet, ſi in alterum glo­<lb></lb>bum non incidiſſet per Th.137.lib.1.ſi autem inæquali impetu mouean­<lb></lb>tur, non eſt determinatum ſuprà; poteſt autem ſit determinari, fig. </s>
					<s id="N2079E">1. <lb></lb>Tab.1.ſit globus A impactus in alium B motu vt 4. eodem tempore, quo <lb></lb>globus B impingitur in A motu vt 2. certè globus B retrò agetur motu vt <lb></lb>4. quippè ſiue moueatur æquali motu, ſiue minori, ſiue etiam quieſcat, <lb></lb>ſemper æquali motu à globo A impelletur; quod certè mirabile eſt; pri­<lb></lb>mum conſtat per Th. 135.lib.  tertium conſtat per Theor.128.lib.1. </s>
					<s id="N207AC">Igi­<lb></lb>tur ſecundum conſtat, ſi enim impellitur motu vt 4.dum in contrariam <lb></lb>partem mouetur vt 4. multò magis ſi tantùm mouetur vt 2. &amp; ſi tantùm <lb></lb>impellitur motu vt 4. dum quieſcit multò magis motu vt 4. dum in <pb pagenum="259" xlink:href="026/01/293.jpg"></pb>contrariam partem mouetur motu vt 2. at verò globus A non retro age­<lb></lb>tur: </s>
					<s id="N207BD">motu vt 4. ſed tantùm motu vt 2. vt patet; </s>
					<s id="N207C1">quippe omninò conſiſteret, <lb></lb>ſi globus B nullum præuium impetum habuiſſet; ſi verò habuiſſet mo­<lb></lb>tum vt 4. tùm etiam A retroageretur motu vt 4. igitur motu vt duo, ſi <lb></lb>B impreſſit impetum vt duo. </s>
				</p>
				<p id="N207CB" type="main">
					<s id="N207CD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 69.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N207D9" type="main">
					<s id="N207DB"><emph type="italics"></emph>Si globus A inæqualem globum impingatur per lineam obliquam, ita vt al­<lb></lb>ter in alterum impetu mutuo impingatur, determinari poteſt motus vtriuſque <lb></lb>vterque reflectetur<emph.end type="italics"></emph.end>; </s>
					<s id="N207E8">certum eſt, fit enim determinatio mixta ex noua, &amp; <lb></lb>priore; </s>
					<s id="N207EE">igitur eſt motus, quod duobus modis fieri poteſt; </s>
					<s id="N207F2">primò ſi æqua­<lb></lb>lis vtriuſque ſit motus, ſit linea incidentiæ EB producta in L fig.Th.63. <lb></lb> per quam globus A ab E proiicitur in globum B; </s>
					<s id="N207FA">eſtque LB linea in­<lb></lb>cidentiæ, per quam globus proiicitur in globum A, ita vt punctum con­<lb></lb>tactus ſit B, &amp; linea connectens centra ABF; </s>
					<s id="N20802">ſi globus B conſiſteret in <lb></lb>puncto B globus A reflecteretur per lineam BI, vt demonſtratum eſt in <lb></lb>Theoremate 63. quia determinatio prior eſt, vt BL, noua vt BG; </s>
					<s id="N2080A">igitur <lb></lb>ex vtraque fit BI; </s>
					<s id="N20810">at verò ſi globus B imprimat impetum in globo A <lb></lb>æqualem quidem, ſi linea incidentiæ eſſet perpendicularis, minorem ta­<lb></lb>men, quia eſt obliqua qui eſt ad æqualem vt BG ad BF; </s>
					<s id="N20818">certè determina­<lb></lb>tio noua eſt dupla BG; </s>
					<s id="N2081E">quippe ratione reflexionis eſt vt BG, ratione <lb></lb>impulſionis vt BG; </s>
					<s id="N20824">igitur compoſita ex vtraque vt B<foreign lang="grc">δ</foreign> dupla BG; </s>
					<s id="N2082C">aſſu­<lb></lb>matur LP æqualis; </s>
					<s id="N20832">haud dubiè B<foreign lang="grc">δ</foreign>, &amp; P<foreign lang="grc">δ</foreign> BL; certè determinatio mix­<lb></lb>ta ex B<foreign lang="grc">δ</foreign>, BL erit BP, quæ erit linea reflexionis. </s>
					<s id="N20844">Hinc egregium Corol­<lb></lb>larium deduco quod ſcilicet reflectatur globus A per angulos æquales, <lb></lb>quotieſcunque globo æquali impetu contranitente repellitur; </s>
					<s id="N2084C">quippe <lb></lb>angulus PBF eſt æqualis angulo EBF: alterum etiam deduco, omnes li­<lb></lb>neas reflexionis ad quoſcunque angulos ſiue rectos, ſiue obliquos dum <lb></lb>vterque globus mutuo impetu ab æquali potentia in ſeſe inuicem impin­<lb></lb>guntur, eſſe æquales, quod certè mirabile eſt. </s>
					<s id="N20858">Secundò, ſi non ſit æqualis <lb></lb>vtriuſque motus, ſed motus globi DB ſit ad motum globi A vt AZ ad <lb></lb>AF fig. </s>
					<s id="N2085F">Th.65. res ferè eodem modo determinari poteſt; </s>
					<s id="N20863">quippè mo­<lb></lb>tus impreſſus à globo B per lineam perpendicularem eſt ad motum im­<lb></lb>preſſum A per inclinatam EA vt AZ ad AY; ſit autem linea inci­<lb></lb>dentiæ DB fig. </s>
					<s id="N2086D">Th. 63. eiuſdem incidentiæ cum EA fig. </s>
					<s id="N20870">Th. 65. igitur <lb></lb>globus A incidat per DB, &amp; globus B per MB, ita vt punctum conta­<lb></lb>ctus ſit B, &amp; linea connectens centra FA; determinatio noua ratione in­<lb></lb>cidentiæ eſt vt BH, cui addatur HF æqualis AY fig. </s>
					<s id="N2087A">alterius ratione <lb></lb>motus impreſſi à globo B; </s>
					<s id="N20880">tota determinatio erit BF; </s>
					<s id="N20884">aſſumatur MT <lb></lb>æqualis BF: dico nouam lineam quæſitam eſſe B<foreign lang="grc">θ</foreign> mixtam ſcilicet ex <lb></lb>BF BM, quod probatur vt ſuprà. </s>
				</p>
				<p id="N20890" type="main">
					<s id="N20892"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 70.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2089E" type="main">
					<s id="N208A0"><emph type="italics"></emph>Si duo globi inæquales inuicem impingantur per lineam connectentem cen­<lb></lb>tra diuerſimodè <expan abbr="poſsũt">poſsunt</expan> reflecti<emph.end type="italics"></emph.end>; </s>
					<s id="N208AF">Primò, ſi motus vtriuſque eſt æqualis, minor <lb></lb>globus retroagetur; </s>
					<s id="N208B5">accipit enim totum impetum maioris globi, id eſt, <pb pagenum="260" xlink:href="026/01/294.jpg"></pb>impetum æqualem; </s>
					<s id="N208BE">igitur retro agitur velociore motu in eadem propor­<lb></lb>tione qua alter globus maior eſt altero, v.g. ſi maior eſt duplus, retroa­<lb></lb>getur motu duplo illius, quo ſuum iter proſequeretur, niſi maior globus <lb></lb>occurreret; </s>
					<s id="N208CA">at verò globus maior duplus ſcilicet alterius non retroage­<lb></lb>tur; </s>
					<s id="N208D0">quippè ſi minor globus conſiſteret in puncto contactus, maior glo­<lb></lb>bus ſuum iter proſequeretur motu ſubduplo; </s>
					<s id="N208D6">quippe determinatio noua <lb></lb>eſſet ſubdupla prioris, vt patet ex Th.66. ſed accipit etiam impetum ſub­<lb></lb>duplum illius, quem habet, igitur determinatio noua eſt compoſita ex <lb></lb>duabus ſubduplis; </s>
					<s id="N208E0">igitur eſt æqualis priori; </s>
					<s id="N208E4">igitur <expan abbr="nõ">non</expan> retroagetur, ſed con­<lb></lb>ſiſtet ſi duplus eſt; ſi verò maior duplo ſuum iter proſequetur ſed minore <lb></lb>motu pro rata, ſi minor duplo retroagetur. </s>
					<s id="N208F0">Hinc egregium effatum, ſi duo <lb></lb>globi in ſe ſe inuicem allidantur æquali motu, ſi maior duplus eſt, conſi­<lb></lb>ſtet ad punctum contactus; </s>
					<s id="N208F8">ſi maior duplo ſuum iter proſequetur; ſi mi­<lb></lb>nor reflectetur; </s>
					<s id="N208FE">quod ſi motu inæquali mouentur, vel maior mouetur <lb></lb>maiori motu, vel minor; </s>
					<s id="N20904">ſi maior, minor retroagetur, maior verò vel re­<lb></lb>troagetur, vel conſiſtet, vel eadem via mouebitur; </s>
					<s id="N2090A">retroagetur quidem, ſi <lb></lb>noua determinatio compoſita ſcilicet ex impetu impreſſo à minore glo­<lb></lb>bo, &amp; determinatione reflexionis quam conferet globus minor, etiamſi <lb></lb>quieſceret; </s>
					<s id="N20914">ſi noua inquam determinatio ſit maior priore; </s>
					<s id="N20918">conſiſtet verò, <lb></lb>ſi fit æqualis; </s>
					<s id="N2091E">ſuum denique iter proſequetur, ſi ſit minor: quæ omnia ex <lb></lb>dictis facilè determinari poſſunt. </s>
				</p>
				<p id="N20924" type="main">
					<s id="N20926"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 71.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20932" type="main">
					<s id="N20934"><emph type="italics"></emph>Si verò duo globi inæquales in ſeſe inuicem impingantur per lineas obliquas, <lb></lb>ſunt quoque tres combinationes<emph.end type="italics"></emph.end>; </s>
					<s id="N2093F">vel enim vterque impingitur motu æquali, <lb></lb>vel maior globus maiore motu, vel minor; vt autem habeatur linea, ſeu <lb></lb>determinatio cuiuſlibet globi, ſupponi debet primò linea incidentiæ al­<lb></lb>terius v.g. maioris. </s>
					<s id="N2094B"><expan abbr="Secũdò">Secundò</expan> ſupponi debet minor quieſcere. </s>
					<s id="N20951">Tertiò, inue­<lb></lb>niri noua determinatio, quæ confertur maiori à minore quieſcente, quæ <lb></lb>facilè inueniri poteſt cognita determinatione noua, quam conferret ſi <lb></lb>linea incidentiæ eſſet perpendicularis; Quartò, debet inueniri determi­<lb></lb>natio noua quæ confertur à minore maiori ratione impetus, quæ facilè <lb></lb>inueniri poteſt cognita determinatione huius impetus per lineam per­<lb></lb>pendicularem. </s>
					<s id="N20961">Quintò, debet componi determinatio noua ex vtraque. </s>
					<s id="N20964"><lb></lb>Sextò denique, ex his habebitur determinatio mixta ex hac compoſita, &amp; <lb></lb>linea incidentiæ producta, quod facilè ex dictis intelligitur; ſimiliter, vt <lb></lb>habeatur reflexo minoris, debent eadem præſupponi in maiore. </s>
				</p>
				<p id="N2096D" type="main">
					<s id="N2096F">Obiiceret hic ſortè aliquis mirari ſe quamobrem duo globi æquales <lb></lb>in ſeſe inuicem æquali motu impinguntur vterque retroagatur, cùm po­<lb></lb>tiùs vterque conſiſtere deberet: quemadmodum quieſcit globus cui im­<lb></lb>primuntur duo impetus contrarij, hoc eſt ad lineas oppoſitas determi­<lb></lb>nati. </s>
					<s id="N2097B">Reſpondeo cum eodem inſtanti eidem globo duplex ille impetus <lb></lb>imprimitur, non videri vllam rationem, cur alter præualeat; </s>
					<s id="N20981">at verò vbi <lb></lb>iam impetus eſt productus, poteſt ad aliam lineam determinari, vt patet; </s>
					<s id="N20987"><lb></lb>igitur ratione determinationis nouæ, quæ eſt æqualis priori deſtruitur; </s>
					<s id="N2098C"><pb pagenum="261" xlink:href="026/01/295.jpg"></pb>igitur, ſi nihil aliud eſſet, globus quieſceret; at verò ratione impetus <lb></lb>noui producti ab alio globo, vel eius impetu, retroagitur. </s>
				</p>
				<p id="N20996" type="main">
					<s id="N20998"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 72.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N209A4" type="main">
					<s id="N209A6"><emph type="italics"></emph>Poteſt globus retroagi, licèt in aliud corpus non incidat<emph.end type="italics"></emph.end>: hoc eſt vulgare, <lb></lb>mirificum tamen experimentum, ſit enim globus ECBL incubans <lb></lb>plano horizontali MLG, in quem deſcendat planum, quod niſi globi <lb></lb>reſiſteret materies, reſecaret ſectionem DHE. </s>
					<s id="N209B5">Dico quod ab iſto ictu <lb></lb>globus determinabitur ad duos motus, alterum centri K verſus A, alte­<lb></lb>rum orbis puncti D ſcilicet, vel C verſus E, ita vt initio motus centri <lb></lb>præualeat verſus A, qui citò deſtruitur propter affrictum partium plani; </s>
					<s id="N209BF"><lb></lb>vnde remanet tantùm motus orbis, quo ſcilicet globus rotatur verſus F; </s>
					<s id="N209C4"><lb></lb>nec eſt alia ratio huius experimenti, in quo habetur quædam reflexio ſi­<lb></lb>ne corpore reflectente: pro quo obſerua fore vt experimentum meliùs <lb></lb>ſuccedat, ſi cadat ictus propiùs ad punctum C, quia diutiùs voluitur <lb></lb>orbis. </s>
				</p>
				<p id="N209CF" type="main">
					<s id="N209D1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 73.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N209DD" type="main">
					<s id="N209DF"><emph type="italics"></emph>Hinc etiam ratio euidentiſſima alterius experimenti, quod valdè familiare <lb></lb>eſt iis, qui breuioribus globulis ludunt<emph.end type="italics"></emph.end>; </s>
					<s id="N209EA">ſi enim ita proiiciatur per medium <lb></lb>aëra globulus, vt eius hemiſphærium ſuperiùs moueatur contrario motu <lb></lb>motui centri, vel vt Aſtronomi loquuntur in Antecedentia, vbi globulus <lb></lb>terræ planum attingit, vel illico conſiſtit, vel retroagitur, niſi aliqua <lb></lb>portio plani inæqualis aliò reflectat; </s>
					<s id="N209F6">cuius rei ratio eſt duplex ille mo­<lb></lb>tus, quorum ſi determinatio æqualis eſt, conſiſtit globus; </s>
					<s id="N209FC">ſi verò determi­<lb></lb>natio motus orbis ſit maior, quod ſemper accidit in breuiore ictu; certè <lb></lb>cum præualeat, globum retroire neceſſe eſt. </s>
				</p>
				<p id="N20A04" type="main">
					<s id="N20A06"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 74.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20A12" type="main">
					<s id="N20A14"><emph type="italics"></emph>Globulus eburneus in alium impactus conſistit quidem ſi centrum respicias<emph.end type="italics"></emph.end>; </s>
					<s id="N20A1D"><lb></lb>at verò ſæpè accidit globulum circa centrum ſuum immobile motu cir­<lb></lb>culari &amp; horizontali ad inſtar vorticis conuolui; </s>
					<s id="N20A24">cuius effectus ratio eſt, <lb></lb>quia cùm prior impetus ideo tantùm deſtruatur, quia eſt fruſtrà, &amp; fru­<lb></lb>ſtrà eſt, quia æqualis eſt determinatio vtraque per lineas oppoſitas, de­<lb></lb>terminatio inquam motus centri; </s>
					<s id="N20A2E">ſi tamen globi deficiat æquilibrium, vt <lb></lb>ſemper reuerâ tantillùm deficit, in partem illam globus voluitur, vt vide­<lb></lb>mus in corpore oblongo, cuius dum vna extremitas pellitur circa cen­<lb></lb>trum aliquod voluitur; </s>
					<s id="N20A38">ſed de motu circulari infrà; ſed tantiſper ſphæ­<lb></lb>riſterium ingredi placuit, vt alios effectus motus reflexi demon­<lb></lb>ſtremus. </s>
				</p>
				<p id="N20A40" type="main">
					<s id="N20A42"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 75.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20A4E" type="main">
					<s id="N20A50"><emph type="italics"></emph>Cum pila coniicitur in parietem ad latus, reſilit in pauimentum, vnde ite­<lb></lb>rum repercutitur fallente ſaltu<emph.end type="italics"></emph.end>; </s>
					<s id="N20A5B">ratio eſt clara, quia quadruplici quaſi <lb></lb>motu mouetur pila in vltimo ſaltu; </s>
					<s id="N20A61">Primus eſt motus centri bis reflexus; </s>
					<s id="N20A65"><pb pagenum="262" xlink:href="026/01/296.jpg"></pb>Secundus primus motus orbis, quo ſcilicet primum in parietem illiſa eſt, <lb></lb>Tertius motus orbus mixtus, quo ex pariete reſiſtit; </s>
					<s id="N20A6F">Quartus denique <lb></lb>motus orbis, quo mouetur poſt quàm à pauimento repercuſſa eſt, exem­<lb></lb>plum habes in pila rotata per planum horizontale, quæ obliquè in aduer­<lb></lb>ſum planum impingitur; </s>
					<s id="N20A79">ſtatim enim obſeruas nouum motum orbis mix­<lb></lb>tum ex priori &amp; nouo, in quo eſt quidem maxima difficultas; ſed de his <lb></lb>motibus mixtis agemus infrà lib.  9. </s>
				</p>
				<p id="N20A81" type="main">
					<s id="N20A83"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 76.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20A8F" type="main">
					<s id="N20A91"><emph type="italics"></emph>Cum pila emittitur rotato ſurſum pilari reticulo ſaltus vt plurimùm fallit, <lb></lb>ſecus verò ſi emittatur reticulo deorſum acto<emph.end type="italics"></emph.end>; </s>
					<s id="N20A9C">ratio eſt, quia in primo caſu <lb></lb>motus orbis pilæ eſt contrarius motui centri, vt patet; inde fraus ſaltus, <lb></lb>ſecus verò in ſecundo caſu. </s>
				</p>
				<p id="N20AA4" type="main">
					<s id="N20AA6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 77.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20AB2" type="main">
					<s id="N20AB4"><emph type="italics"></emph>Cum pila velociſſimè ita emittitur, vt linea incidentiæ faciat angulum acu­<lb></lb>tiſſimum cum pauimento, nullus ferè eſt ſaltus<emph.end type="italics"></emph.end>; </s>
					<s id="N20ABF">quia cum parùm valeat vis <lb></lb>reflexiua ad angulum acutiſſimum; </s>
					<s id="N20AC5">quia prior determinatio ferè præua­<lb></lb>let, &amp; remanet tota, non quidem intacta, ſed vix ſaucia; </s>
					<s id="N20ACB">determinatio <lb></lb>motus orbis, qui promouet motum centri, iuuat priorem determina­<lb></lb>tionem motus centri; igitur vel nullus, vel modicus, iſque celerrimus <lb></lb>fit ſaltus. </s>
				</p>
				<p id="N20AD5" type="main">
					<s id="N20AD7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 78.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20AE3" type="main">
					<s id="N20AE5"><emph type="italics"></emph>Cum pila cadit obliqua linea in pauimentum non longo à pariete interuallo, <lb></lb>in quem linea ſurſum inclinata poſt ſaltum ſtatim impingitur longè altiùs <lb></lb>aſcendit pilæ ſaltus,<emph.end type="italics"></emph.end> ratio petitur à noua reflexione, quod facilè eſt. </s>
				</p>
				<p id="N20AF1" type="main">
					<s id="N20AF3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 79.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20AFF" type="main">
					<s id="N20B01"><emph type="italics"></emph>Cum pila obliquè cadit in iuncturam parietis &amp; pauimenti, non reflectitur, <lb></lb>&amp; tunc maximè fallit ſaltus<emph.end type="italics"></emph.end>; </s>
					<s id="N20B0C">ratio eſt, quia eſt duplex punctum conta­<lb></lb>ctus; </s>
					<s id="N20B12">igitur determinationum nouarum conflictus; </s>
					<s id="N20B16">quippè paries verſus <lb></lb>pauimentum; </s>
					<s id="N20B1C">hoc verò verſus parietem repellit; igitur tantùm ſupereſt, <lb></lb>vt in pauimento rotetur ſine ſaltu, quod accidit ad omnem angulum in­<lb></lb>cidentiæ obliquum, vt patet experientiâ, cuius ratio communis eſt. </s>
				</p>
				<p id="N20B24" type="main">
					<s id="N20B26"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 80.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20B32" type="main">
					<s id="N20B34"><emph type="italics"></emph>Cum leniore affrictu pilæ funis perstringitur vel, vt aiunt, crispatur, ſaltus <lb></lb>etiam ludentis manum frustratur<emph.end type="italics"></emph.end>; quia motus orbis mutatur in illo funis <lb></lb>incuſſu, vt patet. </s>
				</p>
				<p id="N20B41" type="main">
					<s id="N20B43"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 81.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20B4F" type="main">
					<s id="N20B51"><emph type="italics"></emph>Denique, cum reticulo motus orbis is a intorquetur, vt vel circulo horizon­<lb></lb>tali, vel alteri inclinato ſit parallelus, ſaltus pilæ fallaciæ ſubeſt<emph.end type="italics"></emph.end>; </s>
					<s id="N20B5C">quippe à <lb></lb>priori determinatione motus orbis tuebatur; </s>
					<s id="N20B62">omitto inæqualitatem pa­<lb></lb>uimenti, quæ ſaltum pilæ ſæpiſſimè à ſua linea detorquet; ſed fortè ſatis <lb></lb>luſum eſt. </s>
				</p>
				<pb pagenum="263" xlink:href="026/01/297.jpg"></pb>
				<p id="N20B6E" type="main">
					<s id="N20B70"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 82.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20B7C" type="main">
					<s id="N20B7E"><emph type="italics"></emph>Cum planus lapis per lineam incidentiæ valdè obliquam in ſuperficiem <lb></lb>aquæ proijcitur, quaſi repit lapis in ipſa ſuperficie ſeu plurimo ſaltu diſcurrit<emph.end type="italics"></emph.end>; </s>
					<s id="N20B89"><lb></lb>quia ſcilicet modica reſiſtentia ſufficit ad reflexionem, cum angulus in­<lb></lb>cidentiæ eſt obliquior, vt conſtat ex dictis; </s>
					<s id="N20B90">vt tamen longiorem tractum <lb></lb>percurrat lapis, ita proiiciendus eſt, vt eius horizonti planior ſuperficies <lb></lb>ſit parallela; </s>
					<s id="N20B98">immò tantillùm portio anthica attollatur: cur autem, &amp; <lb></lb>quomodo reſiſtat ſuperficies aquæ, dicemus ſuo loco. </s>
				</p>
				<p id="N20B9E" type="main">
					<s id="N20BA0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 83.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20BAC" type="main">
					<s id="N20BAE"><emph type="italics"></emph>Immò ſæpiùs accidit maiorum tormentorum pilas ab aqua reflecti aliquo­<lb></lb>ties, vt multis experimentis comprobatum eſt<emph.end type="italics"></emph.end>; </s>
					<s id="N20BB9">nec enim ab interiore maris <lb></lb>fundo reflecti poſſunt, ſed lineam incidentiæ valdè obliquam eſſe neceſ­<lb></lb>ſe eſt; habes egregium experimentum apud Mercennum in phœn. </s>
					<s id="N20BC1"><lb></lb>Balliſt propoſitione 25. ab illuſtri viro petro Petito obſeruatum, quo <lb></lb>duntaxat aſſerit pilam è tormento ferreo 10 pedes longo, &amp; horizontali <lb></lb>parallelo emiſſam, quinquies à ſuperficie Oceani reflexam fuiſſe; ſed de <lb></lb>hoc paulò pòſt. </s>
				</p>
				<p id="N20BCC" type="main">
					<s id="N20BCE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 84.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20BDA" type="main">
					<s id="N20BDC"><emph type="italics"></emph>Addo vnum, quod ſæpiùs obſeruatum eſt in illo iactu planorum lapidum, <lb></lb>quòd ſcilicet ſub finem iactus quaſi in orbem dextrorſum reflectantur<emph.end type="italics"></emph.end>; </s>
					<s id="N20BE7">cuius <lb></lb>ratio manifeſta eſt motus orbis horizontali parallelus, qui præter motum <lb></lb>centri lapidi impreſſus eſt; </s>
					<s id="N20BEF">quia faciliùs deſtruitur motus centri, quàm <lb></lb>motus orbis; </s>
					<s id="N20BF5">vnde ſub finem hic illum in ſuas partes trahit, dextrorſum <lb></lb>ſcilicet, ſi dextra proiiciatur lapis; </s>
					<s id="N20BFB">quia duobus primis digitis poſterior <lb></lb>lapidis portio ſiniſtrorſum inflectitur; igitur anterior dextrorſum, in <lb></lb>quo non eſt difficultas. </s>
				</p>
				<p id="N20C03" type="main">
					<s id="N20C05"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 85.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20C11" type="main">
					<s id="N20C13"><emph type="italics"></emph>Cum proiicitur globus in aquam per lineam incidentiæ obliquam, ſi non re­<lb></lb>flectitur ab ipſa ſuperficie aquæ; </s>
					<s id="N20C1B">incuruatur eius linea producta per mediam <lb></lb>aquam,<emph.end type="italics"></emph.end> v.g. ſit vas ABD G, ſolidum aquæ vaſe contentum CBDF; </s>
					<s id="N20C26">li­<lb></lb>nea obliqua incidentiæ globi projecti IH, producta HD: </s>
					<s id="N20C2C">dico quod <lb></lb>frangetur in H, &amp; quaſi refringetur in HE; </s>
					<s id="N20C32">experientia certiſſima eſt; </s>
					<s id="N20C36"><lb></lb>ratio verò eſt, quia cùm vis reflexiua puncti H ſit aliqua, hoc eſt, cùm ſit <lb></lb>aliquid determinationis nouæ, quæ haud dubiè minor eſt priore, debet <lb></lb>neceſſariò mutari linea; </s>
					<s id="N20C3F">quod autem ſit aliquid determinationis nouæ <lb></lb>in H, patet ex eo quod angulus incidentiæ ſit valdè obliquus, reflectitur <lb></lb>globus; igitur in altero angulo incidentiæ debet eſſe aliquid nouæ de­<lb></lb>terminationis. </s>
					<s id="N20C49">Secundò, quia plùs reſiſtit aqua, quàm aër; </s>
					<s id="N20C4D">igitur fran­<lb></lb>gitur prior determinatio, &amp; hæc eſt vera ratio huius effectus, quem ali­<lb></lb>qui obſeruarunt; </s>
					<s id="N20C55">Et fortè dici poſſet refractio motus, quæ prorſus eſt <lb></lb>contraria refractioni luminis; </s>
					<s id="N20C5B">quippe refractio luminis talis eſt, vt radius <lb></lb>primo medio raro in denſum incidens incuruetur ad perpendicularem, <lb></lb>cum tamen linea motus obliquè incidens è medio raro in denſum incur-<pb pagenum="264" xlink:href="026/01/298.jpg"></pb>uetur à perpendiculari: </s>
					<s id="N20C68">An fortè etiam ex hoc phænomeno duci poteſt <lb></lb>vera menſura, ſeu regula refractionum, quod ingenioſiſſimè excogitauit <lb></lb>vir illuſtris Renatus Deſcartes in ſua Dioptrica; </s>
					<s id="N20C70">ſed diſcrimen maximum <lb></lb>eſt, quòd luminis diffuſio ſeu propagatio nullum dicat motum localem, <lb></lb>vt ſuo loco demonſtrabimus; </s>
					<s id="N20C78">quippe lumen qualitas eſt, vt impetus; quod <lb></lb>tamen ad rem præſentem nihil prorſus facit. </s>
				</p>
				<p id="N20C7E" type="main">
					<s id="N20C80"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 86.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20C8C" type="main">
					<s id="N20C8E"><emph type="italics"></emph>Linea refractionis motus non eſt recta (ſic eam deinceps appellabimus.)<emph.end type="italics"></emph.end><lb></lb><expan abbr="Cũ">Cum</expan> enim ideo deflectat à recta HD, quia <expan abbr="planũ">planum</expan> in H reſiſtit motui globi; <lb></lb>igitur etiam in K deflectet à recta KE, quia etiam medium in K reſiſtit. </s>
				</p>
				<p id="N20CA1" type="main">
					<s id="N20CA3">Obſeruabis tamen primò, vix hoc diſcerni poſſe, niſi ſit maxima vis <lb></lb>motus; </s>
					<s id="N20CA9">quippe grauitas corporis defert corpus deorſum; vnde vis illa <lb></lb>grauitationis impedit, ne corpus reflectat ſeu reſiliat ſurſum Secundò, ſi <lb></lb>corpus in aquam projectum ſit leuius aqua, non modò hæc refractio ſen­<lb></lb>ſibilis eſt, verùm etiam illa perpetua refractionum ſeries, quia aqua ſem­<lb></lb>per attollit ſurſum corpus leuius. </s>
					<s id="N20CB5">Tertiò, in corpore oblongo hoc expe­<lb></lb>rimentum maximè probatur, quia plures partes aquæ ſimul reflectunt. </s>
				</p>
				<p id="N20CBA" type="main">
					<s id="N20CBC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 87.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20CC8" type="main">
					<s id="N20CCA"><emph type="italics"></emph>Linea motus refracti non eſt recta,<emph.end type="italics"></emph.end> prob. </s>
					<s id="N20CD2">quia cum in ſingulis punctis <lb></lb>aquæ ferè mutetur, curuam eſſe neceſſe eſt. </s>
				</p>
				<p id="N20CD7" type="main">
					<s id="N20CD9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 88.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20CE5" type="main">
					<s id="N20CE7"><emph type="italics"></emph>Hinc optima ratio ducitur, cur globus ex tormento excuſſus ad angulum <lb></lb>incidentiæ valdè acutum ſuperficiem aquæ penetret<emph.end type="italics"></emph.end>; </s>
					<s id="N20CF2">ex qua denuò emergit <lb></lb>quaſi per arcum primum deorſum; </s>
					<s id="N20CF8">tùm demum ſurſum inflexum immò <lb></lb>plures accidunt huiuſmodi repetitæ emerſiones: </s>
					<s id="N20CFE">hinc valdè falluntur, <lb></lb>qui credunt ab ipſo fundo maris globum repercuti; quod pluſquàm ri­<lb></lb>diculum eſt; hoc quoque <expan abbr="experimentũ">experimentum</expan> in projectis ſaxis ſæpiùs obſeruaui. </s>
				</p>
				<p id="N20D0A" type="main">
					<s id="N20D0C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 89.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20D18" type="main">
					<s id="N20D1A"><emph type="italics"></emph>Hinc cum ſaxa planiora ſunt in medio aëre ſimile obſeruari poteſt experi­<lb></lb>mentum<emph.end type="italics"></emph.end>; </s>
					<s id="N20D25">nam poſt aliquem deſcenſum iterum aſcendit ſaxum; nec eſt <lb></lb>quod aliquis vento flanti cauſam huius effectus tribuat, qui ſemper acci­<lb></lb>dit etiam valdè ſereno cœlo. </s>
				</p>
				<p id="N20D2D" type="main">
					<s id="N20D2F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 90.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20D3B" type="main">
					<s id="N20D3D"><emph type="italics"></emph>Hinc cauſa euidens illius aſcenſus ſagittæ quamtumuis per lineam horizon­<lb></lb>ti parallelam emitatur<emph.end type="italics"></emph.end>; </s>
					<s id="N20D48">quippè ab aëre inferiori quaſi repercutitur, ali­<lb></lb>quid ſimile coniicio in glandibus ex tormento exploſis; </s>
					<s id="N20D4E">eſt enim aliquis <lb></lb>quamuis inſenſibilis aſcenſus; </s>
					<s id="N20D54">hinc fortè ratio, cur in ſcopum lineas di­<lb></lb>rectionis horizonti parallelæ reſpondentem globus incidat, cùm infra <lb></lb>ſcopum cadere deberet, vt reuerâ fit in notabili diſtantia propter mo­<lb></lb>tum mixtum; </s>
					<s id="N20D5E">exemplum huius effectus clariſſimum video in illis auicu­<lb></lb>lis, quæ per ſaltus, vel arcus huiuſmodi volant; primò enim deſcendere <lb></lb>videntur, ſed vix aſcendunt. </s>
				</p>
				<pb pagenum="265" xlink:href="026/01/299.jpg"></pb>
				<p id="N20D6A" type="main">
					<s id="N20D6C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 91.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20D78" type="main">
					<s id="N20D7A"><emph type="italics"></emph>Poteſt determinari proportio anguli huius refractionis motus, ſi cognoſcatur <lb></lb>reſiſtentia, qua medium reſistit perpendiculari<emph.end type="italics"></emph.end>; </s>
					<s id="N20D85">v. g. ſi globus plumbeus ex <lb></lb>aëre perpendiculariter cadat in ſuperficiem aquæ, haud dubiè ipſam <lb></lb>aquam ſubit, ſed minore motu; </s>
					<s id="N20D91">quippe frangitur ab ipſa denſitate aquæ <lb></lb>vis primi impetus, quo ſcilicet per liberiorem aëra priùs ferebatur: </s>
					<s id="N20D97">vnde <lb></lb>ſi habeatur proportio reſiſtentiæ aquæ poſita linea incidentiæ perpendi­<lb></lb>culari, non eſt dubium, quin habeatur etiam reſiſtentia poſita linea in­<lb></lb>cidentiæ obliqua; nam eodem modo hoc determinandum eſt, quo ſuprà <lb></lb>determinatum fuit Th. 66. 67. v. g. in fig. </s>
					<s id="N20DA7">Th. 65. determinatio noua <lb></lb>poſita perpendiculari ſit ad priorem vt AZ ad AF, ita vt per mediam <lb></lb>aquam conficiat tantùm ſpatium A<foreign lang="grc">δ</foreign> v. g. eo tempore, quo in libero aë­<lb></lb>re conficit AC; </s>
					<s id="N20DB9">certè ſi linea incidentiæ ſit inclinata EA, determinatio <lb></lb>noua erit ad priorem, vt AY ad AE, vel AB; </s>
					<s id="N20DBF">igitur fiet mixta ex AY <lb></lb>AB, ſcilicet A<foreign lang="grc">υ</foreign>; </s>
					<s id="N20DC9">non tamen eo tempore conficiet A<foreign lang="grc">υ</foreign>, quo conficiet <lb></lb>A<foreign lang="grc">δ</foreign>; </s>
					<s id="N20DD7">quia ſcilicet omnes partes aquæ reſiſtunt, vt conſtat; </s>
					<s id="N20DDB">igitur con­<lb></lb>ficietur A <foreign lang="grc">θ</foreign> æqualis A<foreign lang="grc">δ</foreign>; quæ porrò ſit proportio reſiſtentiæ, quæ mobi­<lb></lb>le retardat in aqua, &amp; reſiſtentiæ, quæ idem retardat in aëre determina­<lb></lb>ri non poteſt, niſi primò cognoſcatur proportio grauitatis vtriuſque. </s>
					<s id="N20DEB"><lb></lb>Secundò, niſi ſciatur in quo poſita ſit hæc reſiſtentia: Tertiò, niſi per­<lb></lb>ſpectum ſit, an maiore nexu partes aquæ inter ſe copulentur, an mino­<lb></lb>re, vel æquali, de quo alias. </s>
					<s id="N20DF4">Equidem P. Merſennus lib.1.a.15. ſuæ ver­<lb></lb>ſionis aſſerit corpus graue per mediam aquam conficere 12. pedes ſpatij <lb></lb>eo <expan abbr="tẽpore">tempore</expan>, quo 48. percurrit in aëre, id eſt, tempore duorum ſecundorum. </s>
				</p>
				<p id="N20E01" type="main">
					<s id="N20E03">Obſeruabis autem hîc tantùm conſideratam fuiſſe lineam A<foreign lang="grc">θ</foreign> rectam <lb></lb>ſine noua determinatione, quæ ſcilicet inſenſibilis eſt, quando linea in­<lb></lb>cidentiæ non eſt tam obliqua, nec impetus tantarum virium. </s>
					<s id="N20E0E">Denique <lb></lb>obſeruabis cognito vno angulo motus refracti ad datum angulum inci­<lb></lb>dentiæ cognoſci facilè quemlibet alium, qui alteri angulo incidentiæ re­<lb></lb>ſpondeat, vt patet ex dictis: </s>
					<s id="N20E18">Vtrum verò anguli refractionum motus ex <lb></lb>aëre in aquam ſint iidem cum angulis refractionum luminis ex aqua in <lb></lb>aëra, examinabimus alibi: </s>
					<s id="N20E20">hæc interim ſufficiant de motu refracto; quem <lb></lb>tamen adhuc reflexum eſſe contendo, immò nulla eſt refractio in motu, <lb></lb>quæ non ſit reflexio, &amp; nulla reflexio in lumine, quæ non ſit refractio, de <lb></lb>quo fusè alibi. </s>
				</p>
				<p id="N20E2A" type="main">
					<s id="N20E2C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 92.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20E38" type="main">
					<s id="N20E3A"><emph type="italics"></emph>Aqua, quæ cadit in planum durum reſilit in mille partes quoquo verſum<emph.end type="italics"></emph.end>; </s>
					<s id="N20E43"><lb></lb>non certè, quòd partes inferiores pellantur à ſuperioribus, vt volunt ali­<lb></lb>qui; </s>
					<s id="N20E4A">ſed quòd facilè ſeparentur partes aquæ; </s>
					<s id="N20E4E">vnde non mirum eſt, ſi vel <lb></lb>modico impetu diſpergantur; </s>
					<s id="N20E54">quippe, vt corpus aliquod reflectatur in­<lb></lb>tegrum, id eſt ſine partium diſperſione, debet reſiſtentia vnionis partium <lb></lb>eſſe maior tota vi impetus ad nouam lineam determinati; </s>
					<s id="N20E5C">cur verò po­<lb></lb>tiùs vna guttula dextrorſum repercutiatur, quàm ſiniſtrorſum; </s>
					<s id="N20E62">certè alia <lb></lb>ratio eſſe non poteſt, niſi primò diuerſa figura tùm aquæ impactæ, tùm <pb pagenum="266" xlink:href="026/01/300.jpg"></pb>plani reflectentis; Secundò aër reſiliens; </s>
					<s id="N20E6D">Tertiò ſectio ipſa, vt ſic lo­<lb></lb>quar, diuiſionis, ſeu conflictus aliarum partium: idem, cæteris paribus, de <lb></lb>lapide, cuius mille particulæ reſiliunt. </s>
				</p>
				<p id="N20E75" type="main">
					<s id="N20E77"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 93.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20E83" type="main">
					<s id="N20E85"><emph type="italics"></emph>Globus reflectens, qui ab ictu alterius mouetur, non mouetur ipſo instanti con­<lb></lb>tactus<emph.end type="italics"></emph.end>; prob. </s>
					<s id="N20E90">quia eo primum inſtanti ab alio globo accipit impetum; ſed <lb></lb>primo inſtanti, quo eſt impetus, non eſt motus, vt demonſtratum eſt lib. <lb></lb>1.igitur globus reflectens, &amp;c. </s>
					<s id="N20E99">mouetur tamen. </s>
					<s id="N20E9C">Secundò inſtans; vnde <lb></lb>vno tantùm inſtanti contactus eſt. </s>
				</p>
				<p id="N20EA1" type="main">
					<s id="N20EA3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 94.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20EAF" type="main">
					<s id="N20EB1"><emph type="italics"></emph>Hinc colligo produci illum impetum ipſo inſtanti contactus<emph.end type="italics"></emph.end>; </s>
					<s id="N20EBA">alioqui inſtan­<lb></lb>ti ſequenti non eſſet motus; </s>
					<s id="N20EC0">immò daretur quies in puncto reflexionis; </s>
					<s id="N20EC4"><lb></lb>quippe, ſi tantùm ſecundo inſtanti produceretur, fieret contactus in duo­<lb></lb>bus inſtantibus; igitur eſſet quies. </s>
				</p>
				<p id="N20ECB" type="main">
					<s id="N20ECD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 95.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20ED9" type="main">
					<s id="N20EDB"><emph type="italics"></emph>Figura corporis impacti variare poteſt reflexionem<emph.end type="italics"></emph.end>; ſi enim corpus impa­<lb></lb>ctum ſit parallelipedum v. g. multiplex eſſe poteſt reflexionis variatio <lb></lb>pro diuerſo appulſu, vt conſideranti patebit. </s>
				</p>
				<p id="N20EEC" type="main">
					<s id="N20EEE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 96.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20EFA" type="main">
					<s id="N20EFC"><emph type="italics"></emph>Si impetus eſſet tantùm determinatus ad vnam lineam; </s>
					<s id="N20F02">nulla daretur re­<lb></lb>flexio<emph.end type="italics"></emph.end>; patet, quia nulla daretur cauſa reflexionis, quæ tantùm eſt impe­<lb></lb>tus prior ad nouam lineam determinatus ratio plani oppoſiti. </s>
				</p>
				<p id="N20F0D" type="main">
					<s id="N20F0F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 97.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N20F1B" type="main">
					<s id="N20F1D"><emph type="italics"></emph>Quò angulus incidentiæ eſt obliquior, faciliùs fit reflexio<emph.end type="italics"></emph.end>; </s>
					<s id="N20F26">quia minor por­<lb></lb>tio impetus deſtruitur quamuis per accidens; </s>
					<s id="N20F2C">igitur motus propagatur <lb></lb>faciliùs; adde quod noua determinatio minùs recedit à priori. </s>
				</p>
				<p id="N20F32" type="main">
					<s id="N20F34"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N20F40" type="main">
					<s id="N20F42">Primò obſeruabis cauſæ reflexionis eſſe multiplices; </s>
					<s id="N20F46">ſcilicet planum <lb></lb>reflectens, priorem impetum permanentem, nouam determinationem: </s>
					<s id="N20F4C">in <lb></lb>plano verò reflectente conſiderantur impenetrabilitas, durities, &amp; im­<lb></lb>mobilitas: </s>
					<s id="N20F54">in priore impetu conſideratur capacitas ad nouam lineam <lb></lb>motus, &amp; ſufficiens intenſio ad hoc, vt aliquid impetus ab ictu vel con­<lb></lb>tactu remaneat; </s>
					<s id="N20F5C">denique noua determinatio, ſi radius incidentiæ ſit <lb></lb>perpendicularis, debet eſſe maior priore; </s>
					<s id="N20F62">alioqui nulla erit reflexio; ſi <lb></lb>verò linea incidentiæ ſit obliqua, poteſt eſſe maior, vel minor, vel <lb></lb>æqualis. </s>
				</p>
				<p id="N20F6A" type="main">
					<s id="N20F6C">Secundò obſeruabis veriſſimam cauſam reflexionis poſitam eſſe in de­<lb></lb>terminatione noua, ratione cuius poteſt eſſe motus; </s>
					<s id="N20F72">igitur impetus non <lb></lb>eſt fruſtrà; igitur non debet deſtrui ſecundùm illam portionem, quæ <lb></lb>non eſt fruſtrà. </s>
				</p>
				<pb pagenum="267" xlink:href="026/01/301.jpg"></pb>
				<p id="N20F7E" type="main">
					<s id="N20F80">Tertiò, quod ſpectat ad æqualitatem anguli reflexionis, &amp; anguli in­<lb></lb>cidentiæ, non eſt alia huius æqualitatis ratio præter illam, quam attuli­<lb></lb>mus; </s>
					<s id="N20F88">nec eſt quod aliqui aliam rationem comminiſcantur, cuius prin­<lb></lb>cipia theſim ipſam ſupponunt; </s>
					<s id="N20F8E">nam primò ſupponunt omnem virtutem <lb></lb>quantumuis impeditam eniti maximè quantum poteſt, vt producat ef­<lb></lb>fectum ſecundùm intenſionem agentis; </s>
					<s id="N20F96">cùm fortè Geometra admitte­<lb></lb>ret hoc principium ſine alia probatione: an fortè virtus ipſa cognoſcit <lb></lb>intentionem, agentis, id eſt impetus potentiæ motricis? </s>
					<s id="N20F9E">numquid impe­<lb></lb>tus ipſe determinari debet ab ipſa potentia motrice? </s>
					<s id="N20FA3">numquid eſt deter­<lb></lb>minatio noua à plano reflectente? </s>
					<s id="N20FA8">an fortè potentia motrix intendit <lb></lb>motum per aliam lineam, quàm per lineam incidentiæ? </s>
					<s id="N20FAD">cum ipſa linea <lb></lb>reflexionis ſemper accidat præter intentionem potentiæ motricis natu­<lb></lb>ralis; denique licèt hoc totum verum eſſet, vnde probatur poſſe impe­<lb></lb>tum ad angulum reflexionis æqualem ſe ipſum determinare? </s>
					<s id="N20FB7">Secundò, <lb></lb>ſupponunt impetum eſſe indifferentem ad diuerſas lineas, quod ſanè ve­<lb></lb>rum eſt; </s>
					<s id="N20FBF">probare tamen deberent, &amp; diſcernere impetum innatum ab <lb></lb>omni aliò, at, eſto id verum ſit; cur potiùs determinatur ad lineam quæ <lb></lb>faciat angulum æqualem, quàm inæqualem angulo incidentiæ? </s>
					<s id="N20FC7">ex hoc <lb></lb>enim principio non probatur hæc æqualitas. </s>
				</p>
				<p id="N20FCC" type="main">
					<s id="N20FCE">Tertiò, ſupponunt dextra fieri ſiniſtra in reflexione, &amp; transferri an­<lb></lb>gulos, idque in eodem plano; </s>
					<s id="N20FD4">benè eſt; </s>
					<s id="N20FD8">rem factam ſupponunt, quam <lb></lb>nemo negat; </s>
					<s id="N20FDE">ſed propter quid fiat demonſtrandum eſſet; ſi enim quæ­<lb></lb>ram, cur in eodem plano ſint radius incidentiæ. </s>
					<s id="N20FE4">radius reflexus, &amp; ſe­<lb></lb>ctio communis plani reflectentis? </s>
					<s id="N20FE9">non video quonam modo demon­<lb></lb>ſtrent. </s>
					<s id="N20FEE">Dicent fortè, quia ita fit in lumine; </s>
					<s id="N20FF2">belle! obſcurum per obſcu­<lb></lb>rius; </s>
					<s id="N20FF8">quippe ratio reflexionis clarior eſt in motu, quàm in flumine, vt <lb></lb>ſuo loco videbimus; </s>
					<s id="N20FFE">igitur negari poſſet de lumine, licèt verum ſit, do­<lb></lb>nec ſit demonſtratum; immò quamuis probatum eſſet de lumine, quis <lb></lb>vnquam deduxit à pari argumentum demonſtratiuum? </s>
					<s id="N21006">Dicent non eſſe <lb></lb>potiùs rationem, cur fiat per vnum planum ex aliis infinitis, quàm per <lb></lb>aliud; </s>
					<s id="N2100E">benè eſt, iam vtuntur illa negatiua ratione, quam paulò antè re­<lb></lb>ſpuebant, licèt optima ſit, nec quidquam in contrarium afferunt; </s>
					<s id="N21014">at ſo­<lb></lb>litariam eſſe non oportet; quippe vt iam ſuprà monui, effectus po­<lb></lb>ſitiuus per principium poſitiuum ad ſuam cauſam reducendus eſt. </s>
				</p>
				<p id="N2101C" type="main">
					<s id="N2101E">Denique dicent hanc eſſe demonſtrationem <emph type="italics"></emph>Aristotelis in Problematis <lb></lb>ſect.<emph.end type="italics"></emph.end>17.<emph type="italics"></emph>Probl.<emph.end type="italics"></emph.end>13. quod vt palam fiat, textum ipſum deſcribo, <emph type="italics"></emph>quamobrem,<emph.end type="italics"></emph.end><lb></lb>inquit, <emph type="italics"></emph>corpora, quæ feruntur, vbi alicubi occurrerunt, reſilire in partem con­<lb></lb>trariam ſolent, nec niſi ad ſimiles angulos, an quod non ſolum eo feruntur im­<lb></lb>petu, quo pro ſua parte ipſa fieri aptiſſima ſunt, verùm etiam illo, qui à mittente <lb></lb>proficiſcitur; </s>
					<s id="N21040">ſuus igitur ceſſat cuique impetus, cum ſuum ad locum peruene­<lb></lb>rint, omnia namque requieſcere ſolent vbi in eam ſedem ſeſe contulerunt, quam <lb></lb>ſuapte naturâ deſiderant; </s>
					<s id="N21048">ſed externo illo, quem habent, impetu neceſſitas ori­<lb></lb>tur amplius mouendi; </s>
					<s id="N2104E">quod cùm in partem priorem effici neque at, quia re pro­<lb></lb>hibetur objecta, vel in latus, vel in rectum agi neceſſe eſt; </s>
					<s id="N21054">omnia autem in an­<lb></lb>gulos reſiliunt ſimiles, quoniam eodem ferri cogantur, quò motus ducat; </s>
					<s id="N2105A">quem<emph.end type="italics"></emph.end><pb pagenum="268" xlink:href="026/01/302.jpg"></pb><emph type="italics"></emph>is dedit, qui miſerit; </s>
					<s id="N21067">eo autem vt angulo, vel acuto, vel recto ferantur omninò <lb></lb>incidit; vt igitur in ſpeculis extremum lineæ rectæ, &amp;c. </s>
					<s id="N2106D">itaque feruntur, &amp;c. </s>
					<s id="N21070"><lb></lb>cum angulo tanto retorqueantur, quanto vertex conſtiterit,<emph.end type="italics"></emph.end> &amp;c Sed quæſo, quis <lb></lb>vmquam agnoſcet demonſtrationem in mera comparatione præſertim <lb></lb>in problematis quorum rationes Ariſtoteles, vel alter, vt aliqui volunt, <lb></lb>illorum auctor dubitanter tantùm proponit? </s>
					<s id="N2107D">Igitur vix auſim aſſerere ab <lb></lb>Ariſtotele hoc ipſum fuiſſe demonſtratum; </s>
					<s id="N21083">ſed aliam demonſtrationem <lb></lb>aggrediuntur, pro qua ſupponunt primò determinationem eſſe formam, <lb></lb>ſeu formalitatem, ſeu connotationem; </s>
					<s id="N2108B">quam parùm hæc phyſicam ſa­<lb></lb>piunt, &amp; demonſtrationem olent! Secundò, vnumquodque per ſe deter­<lb></lb>minare ad aliud, ad quod eſt determinatum, &amp; determinationem fieri <lb></lb>per id, quod eſt maximè determinatum; </s>
					<s id="N21095">quia propter quod vnumquod­<lb></lb>que tale eſt, &amp; illud magis; </s>
					<s id="N2109B">quam debile fulcrum! Tertiò ſupponunt, <lb></lb>principium determinans effectum ſecundum genus, &amp; ſpeciem ſimilem <lb></lb>ſibi reddere in vtroque, etiam Logicè; </s>
					<s id="N210A3">Quartò, ſupponunt ex duobus <lb></lb>indeterminatis poſſe fieri determinatum; quid inde? </s>
					<s id="N210A9">Quintò, ſuppo­<lb></lb>nunt angulum reflexionis determinari ab angulo incidentiæ; ſed hæc eſt <lb></lb>theſis. </s>
					<s id="N210B1">Ex his principiis primò concludunt reflexionem fieri per angulos <lb></lb>æquales, idque in eodem plano; </s>
					<s id="N210B7">ſcio quidem de re quod ſit, ſed non vi­<lb></lb>deo demonſtrari propter quid ſit ex his principiis, vt conſideranti pate­<lb></lb>bit; </s>
					<s id="N210BF">nec eſt quod vlteriùs in iis refutandis immoremur; </s>
					<s id="N210C3">præſertim cùm <lb></lb>rem hanc acuratiſſimè demonſtrauerimus ſuprà; </s>
					<s id="N210C9">ſed antequam ab hoc <lb></lb>motu reflexo diſcedam, alia demonſtratio reiicienda eſt, quæ ſic propo­<lb></lb>nitur ſit planum reflectens immobile, MR, ſit linea incidentiæ KD; </s>
					<s id="N210D1"><lb></lb>hæc eſt, vt aiunt, determinatio mixta ex duabus K<foreign lang="grc">β</foreign>, K<foreign lang="grc">θ</foreign>: </s>
					<s id="N210DE">hoc poſito, li­<lb></lb>nea reflexa erit DX, mixta ſcilicet ex D<foreign lang="grc">θ</foreign> D<foreign lang="grc">υ</foreign>; </s>
					<s id="N210EC">ſed profectò non video, <lb></lb>nec ſentio vim huius determinationis; </s>
					<s id="N210F2">primò enim nego motum per <lb></lb>KD eſſe mixtum; </s>
					<s id="N210F8">eſt enim tantùm vnicum principium determinationis; </s>
					<s id="N210FC"><lb></lb>igitur vna tantùm eſt determinatio; </s>
					<s id="N21101">nam primò hæc eadem linea KD <lb></lb>poſſet eſſe mixta ex pluribus aliis; </s>
					<s id="N21107">quippè poſſunt eſſe infinita Paralle­<lb></lb>logrammata, quibus hæc diagonalis KD communis eſſe poſſit; cur au­<lb></lb>tem potiùs erit diagonalis vnius quàm alterius. </s>
					<s id="N2110F">Secundò, ſi cadat deor­<lb></lb>ſum corpus graue impingaturque in planum inclinatum, nunquid eſt <lb></lb>motus ſimplex, &amp; purus naturalis? </s>
					<s id="N21116">quis eſt qui hoc neget, ſi terminos <lb></lb>ipſos capiat? </s>
					<s id="N2111B">ſed dicunt, ſi proiiciatur mobile per inclinatam in planum <lb></lb>horizontale, eſt motus mixtus ex naturali accelerato, &amp; impreſſo; </s>
					<s id="N21121">equi­<lb></lb>dem hic motus mixtus eſt, ſed tota linea curua; </s>
					<s id="N21127">quæ non eſt parabolica, <lb></lb>vt conſtat ex dictis ſuprà lib.4.non facit lineam directionis, ſed vltimum <lb></lb>illius ſegmentum, ſeu vltima Tangens, quæ tanquam recta aſſumitur: <lb></lb>præterea quis vmquam lineam incidentiæ aſſumpſit niſi rectum? </s>
					<s id="N21131">igitur <lb></lb>licèt linea incidentiæ poſſit eſſe mixta ex duabus aliis, quod negari non <lb></lb>poteſt; </s>
					<s id="N21139">poteſt tamen eſſe ſimplex, quod nemo etiam negabit; </s>
					<s id="N2113D">igitur hoc <lb></lb>ipſum nihil facit ad hanc incidentiæ lineam; </s>
					<s id="N21143">igitur illud primum an­<lb></lb>tecedens eſt falſum, in quo habetur lineam incidentiæ eſſe mixtam; </s>
					<s id="N21149">quia <lb></lb>cùm debeat eſſe vniuerſale, vt ſcilicet vniuerſaliter concludat; </s>
					<s id="N2114F">certè, ſi <pb pagenum="269" xlink:href="026/01/303.jpg"></pb>vniuerſale eſt, falſum eſſe conſtat; addunt aliqui eſſe mixtam æquiualen­<lb></lb>ter. </s>
					<s id="N2115A">Tertiò, cum ſit eadem potentia motrix applicata, tùm in K, tùm in <lb></lb>A; </s>
					<s id="N21160">certè debet eſſe idem impetus; </s>
					<s id="N21164">cum autem duæ lineæ K <foreign lang="grc">θ</foreign> K <foreign lang="grc">β</foreign> repræ­<lb></lb>ſentent duos impetus, qui concurrunt ad motum mixtum per KD (nam <lb></lb>hoc ipſi dicunt) certè duo ABAP ſimul ſumpti æquales eſſe deberent <lb></lb>duobus K <foreign lang="grc">θ</foreign> K <foreign lang="grc">β</foreign>, quod falſum eſt; quia KD ſit 4. ſitque angulus GDK <lb></lb>30.grad. </s>
					<s id="N21180">K <foreign lang="grc">θ</foreign> eſt 2. igitur collecta <foreign lang="grc">θ</foreign> K <foreign lang="grc">β</foreign> eſt 6. &amp; eius quadratum 36. at <lb></lb>verò quadratum AB eſt 18. ergo quadratum collectæ ex ABAP eſt <lb></lb>32. igitur illa maior eſt. </s>
				</p>
				<p id="N21193" type="main">
					<s id="N21195">Sed iam ad aliam propoſitionem venio, in qua dicitur linea reflexio­<lb></lb>nis DX eſſe mixta ex D <foreign lang="grc">θ</foreign> D <foreign lang="grc">υ</foreign> quod falſum eſt; </s>
					<s id="N211A3">nam primò hoc dicis, <lb></lb>hoc proba poſitiuo argumento: </s>
					<s id="N211A9">Dices, quia non poteſt aliter explicari <lb></lb>æqualitas anguli reflexionis; </s>
					<s id="N211AF">bellè! nego antecedens; nam licèt nondum <lb></lb>verus illius modus explicatus non eſſet, proba tuum eſſe verum. </s>
					<s id="N211B5">Secundò <lb></lb>vel aliquid prioris determinationis manet, vel nihil; </s>
					<s id="N211BB">non primum, vt ipſi <lb></lb>volunt; </s>
					<s id="N211C1">alioqui DX eſſet mixta ex tribus ſcilicet DQ, D <foreign lang="grc">θ</foreign>, D <foreign lang="grc">υ</foreign>, quod <lb></lb>abſurdum eſt; </s>
					<s id="N211CF">quod ſi nihil remaneat prioris determinationis; </s>
					<s id="N211D3">ergo ni­<lb></lb>hil prioris impetus, quod etiam concedunt; </s>
					<s id="N211D9">igitur producitur nouus, ſci­<lb></lb>licet propter compreſſionem aëris, corporis reflexi, &amp; reflectentis; </s>
					<s id="N211DF">ſed <lb></lb>profectò, licèt hoc totum verum eſſet, cùm illa compreſſio fieret in linea <lb></lb>quæ per centrum globi producitur, ſcilicet à puncto contactus, ſcilicet <lb></lb>in linea DG; </s>
					<s id="N211E9">certè per illam fieret repercuſſio; </s>
					<s id="N211ED">Tertiò tunc maxima eſt <lb></lb>percuſſio, cum linea incidentiæ eſt perpendicularis; </s>
					<s id="N211F3">igitur tunc eſſe de­<lb></lb>bet maxima vis compreſſionis; </s>
					<s id="N211F9">igitur maxima vis repercuſſionis, ſed eſt <lb></lb>tantùm vt DG; at verò, ſi linea incidentiæ ſit AD, vis repercuſſionis <lb></lb>erit, vt collecta ex DFDP quæ maior eſt priore. </s>
					<s id="N21201">Quartò, cur DX erit <lb></lb>potiùs mixta ex duabus D <foreign lang="grc">θ</foreign>, D <foreign lang="grc">υ</foreign>, quàm ex duabus aliis? </s>
					<s id="N2120E">Quintò, perinde <lb></lb>ſe habet planum reflectens, atque ſi globum ipſum pelleret, cùm nihil de­<lb></lb>terminationis prioris remaneat, vt ipſi volunt, ſed pelleret per ipſam <lb></lb>DG. Sextò, proba argumento poſitiuo eſſe mixtam DX ex D <foreign lang="grc">υ</foreign>, D <foreign lang="grc">θ</foreign>; nam <lb></lb>hoc reuerâ fingis ſine ratione. </s>
					<s id="N21222">Septimò, præterea ſi corpus eſſet duriſſi­<lb></lb>mum minùs reflecti poſſet à plano duriſſimo, ſi nulla fieret compreſſio. </s>
					<s id="N21227"><lb></lb>Octauò proba mihi impetum priorem deſtrui per ſe; </s>
					<s id="N2122C">nam cùm ſit indif­<lb></lb>ferens ad omnes lineas, nunquam deſtruitur, niſi ſit fruſtrà; </s>
					<s id="N21232">hic autem <lb></lb>fruſtrà non eſt: </s>
					<s id="N21238">Itaque manifeſtum efficitur, non modò ex his principiis <lb></lb>non demonſtrari æqualitatem anguli reflexionis, ſed ne argumento qui­<lb></lb>dem probabili comprobari; quia tamen in noſtra demonſtratione multa <lb></lb>ſunt, quæ ipſis non probantur, breuiter recenſeo. </s>
				</p>
				<p id="N21242" type="main">
					<s id="N21244">Suppono primò, planum reflectens eſſe principium nouæ determina­<lb></lb>tionis, quod nemo inficiebitur. </s>
					<s id="N21249">Secundò, eſſe tantùm principium vnius <lb></lb>determinationis quia vnum principium eſt. </s>
					<s id="N2124E">Tertiò, per quamcunque li­<lb></lb>neam incidat globus in punctum D plani ſcilicet immobilis, eſt ſemper <lb></lb>idem punctum contactus &amp; eadem <expan abbr="Tãgens">Tangens</expan>. </s>
					<s id="N2125A">Quartò, à puncto contactus <lb></lb>globi duci tantùm poſſe vnicam lineam ad centrum. </s>
					<s id="N2125F">Quintò, cum deter­<lb></lb>minationis terminus à quo ſit illud punctum contactus, per illam tan-<pb pagenum="270" xlink:href="026/01/304.jpg"></pb>tum lineam fieri poteſt; </s>
					<s id="N2126A">nam perinde ſe habet globus ille, atque ſi re­<lb></lb>pelleretur à plano; </s>
					<s id="N21270">nec alia eſſe poteſt linea directionis globi, vt fusè <lb></lb>probauimus, cum de impetu; </s>
					<s id="N21276">nec in hoc eſt vlla difficultas, quia cen­<lb></lb>trum grauitatis dirigit lineam motus; hoc poſito. </s>
				</p>
				<p id="N2127C" type="main">
					<s id="N2127E">Si nulla eſſet determinatio præter hanc, haud dubiè globus per DG <lb></lb>moueretur, vt reuerâ ſit cum linea incidentiæ eſt perpendicularis; </s>
					<s id="N21284">quia <lb></lb>duæ lineæ oppoſitæ non faciunt determinationem mixtam; </s>
					<s id="N2128A">ſecus verò <lb></lb>omnes alias; </s>
					<s id="N21290">cum igitur globus prædictus reflectatur per DX, illud ſit <lb></lb>neceſſariò per determinationem mixtam, quod etiam fatentur omnes: </s>
					<s id="N21296"><lb></lb>mixta eſſe non poteſt niſi ex duabus ſit, vnica tantùm à plano reflecten­<lb></lb>te eſt, ſcilicet per DG; </s>
					<s id="N2129D">igitur altera eſſe debet, eáque prior per KDQ; </s>
					<s id="N212A1"><lb></lb>cùm enim prior determinatio ſupponatur, vt KD vel vt DQ: eſt enim <lb></lb>ſemper eadem, &amp; cùm noua ſit per DG, poſita diagonali DX, quis non <lb></lb>videt eſſe mixtam ex DQ &amp; DZ æquali QX? nam perinde ſe habet <lb></lb>globus in D, atque ſi pelleretur hinc per DQ, hinc per DZ, ita vt impe­<lb></lb>tus eſſent vt lineæ DZ DQ. </s>
				</p>
				<p id="N212AE" type="main">
					<s id="N212B0">Ex his concludo determinationem nouam eſſe ad priorem poſitâ li­<lb></lb>neâ incidentiæ KD, vt DZ vel QX ad DQ poſitâ verò lineâ inciden­<lb></lb>tiæ AD, vt EH ad DE; </s>
					<s id="N212B8">denique in perpendiculari GD, vt <foreign lang="grc">δ</foreign> G ad DG, <lb></lb>id eſt, in ratione dupla; </s>
					<s id="N212C2">&amp; nemo eſt meo iudicio, qui rem iſtam attentè <lb></lb>conſiderans non concedat vltrò de re quod ſit, ex hypotheſi æqualitatis <lb></lb>angulorum reflexionis cum aliis incidentiæ; vt autem demonſtretur <lb></lb>propter quid ſit, aliud principium adhibendum eſt, quod fusè præſtiti­<lb></lb>mus ſuprà. </s>
					<s id="N212CE">Sed obiiciunt iſtam determinationem nouam quæ fit à plano <lb></lb>eſſe fictitiam, &amp; chymericam; </s>
					<s id="N212D4">ſed meo iudicio chymeram facit, qui rem <lb></lb>tam claram non capit; </s>
					<s id="N212DA">cum enim non negent nouam determinationem <lb></lb>eſſe in motu reflexo, nam impetus eſt indifferens, vt ſuprà probatum eſt <lb></lb>abundè, &amp; ex motu funependuli euincitur; </s>
					<s id="N212E2">certè ſi noua eſt, à plano eſt: </s>
					<s id="N212E6"><lb></lb>ſed à plano eſt per ipſam perpendicularem vt demonſtratum eſt ſuprà; <lb></lb>igitur hæc noua determinatio fictitia non eſt. </s>
				</p>
				<p id="N212ED" type="main">
					<s id="N212EF">Sed dicunt ab eodem plano eſſe non poſſe determinationem inæqua­<lb></lb>lem; quia idem principium eundem effectum habet. </s>
					<s id="N212F5">Reſp. negando ante­<lb></lb>cedens; </s>
					<s id="N212FA">cùm enim pro diuerſa reſiſtentia diuerſa ſit determinatio, &amp; <lb></lb>cùm planum prædictum modò plùs, modò minùs reſiſtat; quid mirum ſi <lb></lb>diuerſa ſit etiam determinatio? </s>
				</p>
				<p id="N21302" type="main">
					<s id="N21304">Inſtant, lineam determinationis eiuſdem impetus eſſe ſemper æqua­<lb></lb>lem. </s>
					<s id="N21309">Reſp. negando; </s>
					<s id="N2130C">quia idem impetus ad duas lineas poteſt determi­<lb></lb>nari ſimul, quæ faciant determinationem mixtam; vnde licèt idem im­<lb></lb>petus habeat eandem lineam ſpatij, non tamen eandem lineam determi­<lb></lb>nationis. </s>
					<s id="N21316">v.g. quando dico determinationem nouam in perpendiculari <lb></lb>eſſe ad priorem vt DY ad DG; </s>
					<s id="N2131E">non dico propterea DY eſſe lineam ſpa­<lb></lb>tij; ſed cùm duæ determinationes comparantur, aſſumi poſſunt lineæ, <lb></lb>quæ deſignent proportionem ſeu rationem determinationum, quid fa­<lb></lb>cilius? </s>
				</p>
				<p id="N21328" type="main">
					<s id="N2132A">Quæres, quid ſit illa determinatio: facilis quæſtio. </s>
					<s id="N2132E">Reſp. eſſe ipſum <pb pagenum="271" xlink:href="026/01/305.jpg"></pb>impetum cum habitudine actuali ad talem vel talem lineam; </s>
					<s id="N21337">quod au­<lb></lb>tem poſſit eſſe plùs vel minùs determinatus ad vnam, quàm ad aliam, du­<lb></lb>bium eſſe non poteſt, nec in dubium reuocari, &amp; benè diſtinguitur li­<lb></lb>nea quanta in ratione determinationis, &amp; quanta in ratione ſpatij: </s>
					<s id="N21341">immò <lb></lb>hoc ipſi ſupponunt; nam ſi KD eſt mixta ex K <foreign lang="grc">β</foreign> &amp; K <foreign lang="grc">θ</foreign>, quis non vi­<lb></lb>det eſſe eundem impetum cum determinatione duplici inæquali? </s>
					<s id="N21351">præ­<lb></lb>terea, quis neget globum impactum perpendiculariter in alium æqua­<lb></lb>lem quieſcere? </s>
					<s id="N21358">cur verò quieſcit, niſi quia impetus eſt fruſtrà; <lb></lb>cur autem eſt fruſtrà, niſi quia cum determinatio <lb></lb>noua ſit æqualis priori? </s>
					<s id="N21360">ſed de <lb></lb>his ſatis. <lb></lb><figure id="id.026.01.305.1.jpg" xlink:href="026/01/305/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N2136B">
				<pb pagenum="272" xlink:href="026/01/306.jpg"></pb>
				<figure id="id.026.01.306.1.jpg" xlink:href="026/01/306/1.jpg"></figure>
				<p id="N21375" type="head">
					<s id="N21377"><emph type="center"></emph>LIBER SEPTIMVS, <lb></lb><emph type="italics"></emph>DE MOTV CIRCVLARI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N21385" type="main">
					<s id="N21387">CVM in natura minimè deſideretur motus cir­<lb></lb>cularis, eius affectiones breuiter in hoc libro <lb></lb>demonſtrantur. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N21391" type="main">
					<s id="N21393"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO 1.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2139F" type="main">
					<s id="N213A1"><emph type="italics"></emph>MOtus circularis eſt, cuius linea æqualiter in omnibus ſuis punctis à com­<lb></lb>muni centro distat.<emph.end type="italics"></emph.end> v. g. ſi punctum in periphæria circuli moue­<lb></lb>retur. </s>
				</p>
				<p id="N213B1" type="main">
					<s id="N213B3"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N213C0" type="main">
					<s id="N213C2"><emph type="italics"></emph>Radius motus eſt linea recta ducta ab illo communi centro ad periphæ­<lb></lb>riam.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N213CB" type="main">
					<s id="N213CD"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N213DA" type="main">
					<s id="N213DC"><emph type="italics"></emph>Arcus eſt pars periphæria maior, vel minor.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N213E3" type="main">
					<s id="N213E5"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N213F2" type="main">
					<s id="N213F4"><emph type="italics"></emph>Tangens eſt linea, quæ tangit periphæriam in vnico puncto, quam tamen <lb></lb>non ſecat<emph.end type="italics"></emph.end>; hæc omnia clara ſunt, immò vulgaria. </s>
				</p>
				<p id="N213FF" type="main">
					<s id="N21401"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2140E" type="main">
					<s id="N21410"><emph type="italics"></emph>Si dum rota vertitur imponatur eius ſumma ſuperficiei aliquod mobile, <lb></lb>proijcitur à rota, ſeu potiùs amouetur<emph.end type="italics"></emph.end>; res clara eſt in molari lapide, in <lb></lb>funda, &amp;c. </s>
				</p>
				<p id="N2141D" type="main">
					<s id="N2141F"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2142C" type="main">
					<s id="N2142E"><emph type="italics"></emph>Illa mouentur æqualiter, quæ temporibus æqualibus aqualia ſpatia percur­<lb></lb>runt; inæqualiter verò qua inæqualia; qua maiora, celeriùs; tardiùs, qua <lb></lb>minora.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2143A" type="main">
					<s id="N2143C"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21449" type="main">
					<s id="N2144B"><emph type="italics"></emph>Qua ſimul incipiunt moueri, &amp; deſinunt, aquali tempore mouentur.<emph.end type="italics"></emph.end></s>
				</p>
				<pb pagenum="273" xlink:href="026/01/307.jpg"></pb>
				<p id="N21456" type="main">
					<s id="N21458"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21465" type="main">
					<s id="N21467"><emph type="italics"></emph>Datur motus circularis.<emph.end type="italics"></emph.end></s>
					<s id="N2146E"> Probatur infinitis ferè experimentis; primò in <lb></lb>librâ cuius brachia motu tantùm circulari deſcendunt. </s>
					<s id="N21474">Secundò in ve­<lb></lb>cte, qui etiam mouetur circulari motu; </s>
					<s id="N2147A">Tertiò in turbine, rota molari, <lb></lb>liquore contento intra vas ſphæricum; Quartò in funependulo vibrato. </s>
					<s id="N21480"><lb></lb>Probatur ſecundò; </s>
					<s id="N21485">quia poteſt imprimi impetus vtrique extremitati ci­<lb></lb>lindri in partes oppoſitas, ſit enim cilindrus, vel parallelipedum LC, <lb></lb>cuius extremitati imprimatur impetus, per lineam CP, itemque extre­<lb></lb>mitati L æqualis per lineam LG oppoſitam CP. Dico, quod mouebitur <lb></lb>circulariter circa centrum K, ita vt extremitas L conficiat arcum LB &amp; <lb></lb>C arcum CE; </s>
					<s id="N21493">nec enim C moueri poteſt per CP neque L per LM; </s>
					<s id="N21497"><lb></lb>quippe cùm ſit æqualis impetus, neutra extremitas præualere poteſt: </s>
					<s id="N2149C">non <lb></lb>vtraque, quia MP eſt maior LC; </s>
					<s id="N214A2">nec dici poteſt neutram moueri, cum <lb></lb>moueri poſſit L per arcum LT, &amp; C per arcum CS; </s>
					<s id="N214A8">quippe impetus <lb></lb>eſt indifferens ad omnem lineam; &amp; hæc eſt ratio à priori circularis <lb></lb>motus de qua fusè infrà. </s>
				</p>
				<p id="N214B0" type="main">
					<s id="N214B2">Obſeruabis motum circularem ab iis negari, qui ex punctis mathema­<lb></lb>ticis continuum componunt; </s>
					<s id="N214B8">quia ex eo ſequeretur non poſſe dari mo­<lb></lb>tum continuum velociorem, vel tardiorem, quod ridiculum eſt; </s>
					<s id="N214BE">ſi enim <lb></lb>punctum Q æquali tempore moueatur cum puncto C certè arcus QR <lb></lb>quem percurrit eo tempore, quo C percurrit arcum CS, eſſet æqualis <lb></lb>arcui CS, quod eſt abſurdum; </s>
					<s id="N214C8">quod certè ne admittere cogantur, mo­<lb></lb>tum circularem negant, quod æquè abſurdum eſt; </s>
					<s id="N214CE">præſertim eum ad vi­<lb></lb>tandum motum circularem infinita quoque abſurda deglutiant, ma­<lb></lb>nifeſtis experimentis contradicant, oculos ipſos intuentium præſtigiis <lb></lb>illudi aſſerant, ferreum vectem dum mouetur in mille partes diffringi <lb></lb>etiam iurent; ſed hæc omitto. </s>
				</p>
				<p id="N214DA" type="main">
					<s id="N214DC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N214E9" type="main">
					<s id="N214EB"><emph type="italics"></emph>Niſi impediretur impetus determinatio per lineam rectam, non daretur mo­<lb></lb>tus circularis ſaltem in ſublunaribus.<emph.end type="italics"></emph.end> v. g. niſi impediretur determinatio <lb></lb>impetus, qui ineſt puncto L per lineam LM; </s>
					<s id="N214FC">haud dubiè non mouere­<lb></lb>tur per arcum LB, ſed per rectam LM; igitur ille motus non eſſet cir­<lb></lb>cularis. </s>
				</p>
				<p id="N21504" type="main">
					<s id="N21506"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21513" type="main">
					<s id="N21515"><emph type="italics"></emph>Hinc motus circularis oritur ex recto impedito in ſingulis punctis<emph.end type="italics"></emph.end>: </s>
					<s id="N2151E">dixi in <lb></lb>ſingulis punctis; </s>
					<s id="N21524">quia licèt in puncto L impediretur, non tamen in ſe­<lb></lb>quenti; </s>
					<s id="N2152A">eſſet quidem noua linea determinationis, non tamen curua; ſi <lb></lb>tamen in ſingulis punctis impediatur æquali ſemper radio, haud dubiè <lb></lb>eſt circularis. </s>
				</p>
				<p id="N21532" type="main">
					<s id="N21534">Obſeruabis dictum eſſe ſupra in ſublunaribus quia corpora cœleſtia <lb></lb>mouentur motu circulari non habita vlla ratione motus recti, de quo <lb></lb>ſuo loco. </s>
				</p>
				<pb pagenum="274" xlink:href="026/01/308.jpg"></pb>
				<p id="N2153F" type="main">
					<s id="N21541"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2154E" type="main">
					<s id="N21550"><emph type="italics"></emph>Hinc ſingulis instantibus punctum dum mouetur circa centrum<emph.end type="italics"></emph.end> K <emph type="italics"></emph>deter­<lb></lb>minatur ad nouam lineam<emph.end type="italics"></emph.end>; </s>
					<s id="N21561">quia ſcilicet ſingulis inſtantibus impeditur; </s>
					<s id="N21565"><lb></lb>igitur ſingulis inſtantibus nouam determinationem accipit; eſt enim ea­<lb></lb>dem ratio pro ſecundo inſtanti, quæ eſt pro primo, itemque pro tertio, <lb></lb>quarto, &amp;c. </s>
				</p>
				<p id="N2156E" type="main">
					<s id="N21570"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2157D" type="main">
					<s id="N2157F"><emph type="italics"></emph>Hinc tot ſunt determinationes ſingulis inſtantibus reſpondentes, quot ſunt <lb></lb>Tangentes in circulo<emph.end type="italics"></emph.end>; </s>
					<s id="N2158A">quippè in ſingulis punctis determinatur ad Tan­<lb></lb>gentem; </s>
					<s id="N21590">ſed impeditur denuò pro ſequenti inſtanti; </s>
					<s id="N21594">igitur ad nouam <lb></lb>Tangentem determinatur; </s>
					<s id="N2159A">eſt autem hæc veriſſima motus circularis ra­<lb></lb>tio; </s>
					<s id="N215A0">quod ſcilicet cum ſingulis inſtantibus æqualiter impediatur motus <lb></lb>rectus; </s>
					<s id="N215A6">quia altera mobilis extremitas accedere non poteſt, ſingulis quo­<lb></lb>que inſtantibus ad nouam Tangentem determinatur æquali ſemper ra­<lb></lb>dio; vnde neceſſariò ſequitur motus circularis. </s>
				</p>
				<p id="N215AE" type="main">
					<s id="N215B0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N215BD" type="main">
					<s id="N215BF"><emph type="italics"></emph>Hinc reiicies aliquem recentiorem, qui vult motum circularem eſſe mixtum <lb></lb>ex duobus rectis, quorum alter ſit vt ſinus recti, alter verò vt ſinus verſi,<emph.end type="italics"></emph.end> ſit <lb></lb>enim quadrans KCE; ſit impetus per EK, &amp; per EO, vel duplex, vel <lb></lb>idem determinatus ad duas iſtas lineas, ita vt determinatio per EK ſit <lb></lb>ad determinationem EO, vt ſinus verſi ad rectos. </s>
					<s id="N215D0">v. g. aſſumpto arcu <lb></lb>EM, vt EN ad NM; certè hoc poſito debet moueri punctum E per li­<lb></lb>neam circularem EMC. </s>
					<s id="N215DC">Equidem ſi eſſet duplex impetus, vel vnus tan­<lb></lb>tùm cum duplici illa determinatione, ex eo ſequeretur motus circularis <lb></lb>mixtus ex duobus rectis; </s>
					<s id="N215E4">ſicut rectus poteſt ex duobus circularibus ori­<lb></lb>ri, vt dicemus aliàs; </s>
					<s id="N215EA">non tamen inde ſequitur omnem motum circula­<lb></lb>rem eſſe mixtum ex duobus rectis, quod nemo non videt: </s>
					<s id="N215F0">quippe poſito <lb></lb>quòd radius KE ſit affixus immobiliter centro K, licèt pellatur tantùm, <lb></lb>per Tangentem EO etiam cum valido impetu, nihilo tamen minus mo­<lb></lb>tu circulari mouebitur: </s>
					<s id="N215FA">Adde quod difficile eſſet duos impetus ita attem­<lb></lb>perare, vt creſceret vnus in ratione ſinuum verſorum, &amp; alter in ratione <lb></lb>ſinuum rectorum; </s>
					<s id="N21602">nec enim motus illi recti, ex quibus circularis quaſi <lb></lb>naſceretur, æquales eſſe poſſunt; </s>
					<s id="N21608">igitur ſufficit vnius impetus ad vnam <lb></lb>tantùm lineam primo inſtanti determinatus v.g. ad Tangentem EO, qui <lb></lb>ratione impedimenti in K ſuum effectum habere non poteſt, ſed reduci­<lb></lb>tur continuò verſus K æquali ſemper diſtantia; </s>
					<s id="N21614">ex quo ſequitur neceſſa­<lb></lb>riò motus circularis, ſcilicet ex illa quaſi funis adductione; </s>
					<s id="N2161A">ſi enim ex <lb></lb>puncto K laxaretur habena ſegmentis æqualibus; </s>
					<s id="N21620">differentiæ ſinus totius <lb></lb>&amp; ſecantis v. g. ſegmento VO in arcu EP; certè E moueretur per <lb></lb>rectam EO. </s>
				</p>
				<p id="N2162C" type="main">
					<s id="N2162E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2163A" type="main">
					<s id="N2163C"><emph type="italics"></emph>Hinc optimè intelligitur ratio hypotheſeos primæ<emph.end type="italics"></emph.end>; </s>
					<s id="N21645">ſi enim punctum E ſepara-<pb pagenum="275" xlink:href="026/01/309.jpg"></pb>retur à recta EK eo inſtanti, quo imprimitur impetus; </s>
					<s id="N2164E">haud dubiè per <lb></lb>rectam EO moueretur; </s>
					<s id="N21654">quia ſcilicet impetus puncti E determinatus eſt <lb></lb>in puncto E ad motum per Tangentem EO; </s>
					<s id="N2165A">&amp; ſi nullum eſſet impedi­<lb></lb>mentum per rectam EO, moueretur; </s>
					<s id="N21660">atqui ſi ſeparetur punctum E, ceſ­<lb></lb>ſat impedimentum, vt patet; </s>
					<s id="N21666">nec enim amplius retinetur ex puncto K; </s>
					<s id="N2166A"><lb></lb>igitur ceſſat ratio motus circularis; </s>
					<s id="N2166F">igitur motu recto per rectam EO <lb></lb>mouebitur; </s>
					<s id="N21675">ſic lapis impoſitus rotæ dum maximo cum impetu vertitur, <lb></lb>per Tangentem proiicitur; </s>
					<s id="N2167B">ſic gutta aquæ, quæ cadit in volubilem tro­<lb></lb>chum etiam diſpergitur; </s>
					<s id="N21681">ſic rota ipſa, cuius aliqua pars præ nimia vi <lb></lb>motus diffringitur, illam quaſi proiicit per rectam; </s>
					<s id="N21687">hinc ratio vnica <lb></lb>proiectionis quæ fit operâ fundarum; </s>
					<s id="N2168D">ſit enim funda KE vel KL, quæ <lb></lb>moueatur per arcum LE; </s>
					<s id="N21693">certè, ſi lapis demittatur in puncto E, lapis <lb></lb>proiicietur per rectam LO; </s>
					<s id="N21699">nec enim ad aliam lineam lapis, dum eſt in <lb></lb>puncto E, eſt determinatus, niſi ad Tangentem EO, ad quam dumtaxat <lb></lb>impetus puncti EA eſt determinatus; in hoc igitur Fundibularij tan­<lb></lb>tùm inſiſtit induſtria, quâ ſcilicet ſaxum in funda rotatum ſcopum cui <lb></lb>deſtinatur, attingat, vt illam Tangentem inueniat quæ à prædicto ſcopo <lb></lb>in circulum, quem ſuo motu deſcribit, funda ducitur. </s>
					<s id="N216A7">v.g. ſit radius fun­<lb></lb>dæ KL hypomoclium K, circulus quem deſcribit funda LEC; </s>
					<s id="N216AF">ſit ſco­<lb></lb>pus O, ducatur tangens EO; </s>
					<s id="N216B5">certè, ſi vbi funda peruenit in E, dimit­<lb></lb>tat lapidem, prædictum ſcopum non illicò feriet; </s>
					<s id="N216BB">hinc etiam ratio, cur in <lb></lb>naui dum motu recto mouetur  facilè conſiſtamus; cum tamen (quod in <lb></lb>longioribus illis nauiculis facilè contingere poteſt) ſi circa centrum <lb></lb>ſuum nauis vertatur, quod accidit cum vtraque extremitas in partes op­<lb></lb>poſitas, vel remo, vel pertica pellitur, nec in ca conſiſtamus. </s>
				</p>
				<p id="N216C7" type="main">
					<s id="N216C9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N216D5" type="main">
					<s id="N216D7"><emph type="italics"></emph>Si rota plana in circulo horizontali voluatur, ſitque pondus plano rotæ incu­<lb></lb>bans, in eo producetur impetus<emph.end type="italics"></emph.end>; vt certum eſt; </s>
					<s id="N216E2">an verò pondus retroagi de­<lb></lb>beat, præſertim ſi ſit globus, vel aqua; </s>
					<s id="N216E8">an verò per Tangentem proiici, <lb></lb>dubium eſſe poteſt; </s>
					<s id="N216EE">videntur enim pro vtraque hypotheſi facere expe­<lb></lb>rientiæ; </s>
					<s id="N216F4">pro prima quidem, ſi rotetur rota concaua ſeu ſcutella plena <lb></lb>aqua; </s>
					<s id="N216FA">aqua enim in partem contrariam volui videbitur; &amp;, ſi plano <lb></lb>quod in circulo horizontali voluitur imponatur globus leuigatiſſimus, <lb></lb>certè in partem oppoſitam ibit. </s>
					<s id="N21702">Secundæ hypotheſi alia videntur fauere <lb></lb>experimenta; </s>
					<s id="N21708">ſi enim trochus volubilis, vel aqua, vel puluere aſperga­<lb></lb>tur, ſtatim aqua reſilit per Tangentem, idem dico de puluere, ſi funda in <lb></lb>circulo horizontali voluatur, lapis demiſſus per Tangentem ibit: ſed <lb></lb>hæc omnia, quæ ad proiectiones pertinent, licèt illæ ſequantur ex motu <lb></lb>circulari, examinabimus &amp; demonſtrabimus lib.  10. cum de proiectis. </s>
				</p>
				<p id="N21714" type="main">
					<s id="N21716"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21722" type="main">
					<s id="N21724"><emph type="italics"></emph>Cauſa motus circularis eſt ea, quæ cum tali impedimento coniuncta eſt<emph.end type="italics"></emph.end>; </s>
					<s id="N2172D">ex <lb></lb>quo accidit diametrum mobilis in aliquo ſui puncto retineri immobi­<lb></lb>lem; ſunt autem varij modi huius applicationis. </s>
					<s id="N21735">Primus eſt ille, quem <lb></lb>indicauimus ſuprà Th.1.cum ſcilicet vtraque extremitas cylindri æquali <pb pagenum="276" xlink:href="026/01/310.jpg"></pb>impetu in partes oppoſitas pellitur. </s>
					<s id="N2173F">v.g. C per CP, L per LG. Secundus<lb></lb>eſt, cum affigitur altera extremitas. </s>
					<s id="N21746">v.g. punctum K affigitur, ita vt tamen <lb></lb>propter flexibilitatem radij KL, idem radius moueri poſſit circa cen­<lb></lb>trum K, vt videmus in funependulis. </s>
					<s id="N2174F">Tertius eſt, ſi diameter fulcro K <lb></lb>inſeratur, vt in obelis ferri, vel magnetica acu: huc reuoca rotas omnes, <lb></lb>quæ in circulo horizontali, &amp; verticali voluuntur. </s>
					<s id="N21757">Quartus, ſi cum ali­<lb></lb>qua exploſione digitorum motus imprimatur, vel globo, vel trocho, vel <lb></lb>iis cubis, quibus inſcripti numeri poſt girationem ſortem indicant. </s>
					<s id="N2175E"><lb></lb>Quintus, ſi cum flagello trochus agatur; </s>
					<s id="N21763">cum enim implicetur flagel­<lb></lb>lum trocho, vbi retrahitur, in gyros agitur trochus; </s>
					<s id="N21769">huc reuoca funem <lb></lb>illum plicatilem, quibus armatus ferro trochus voluitur: </s>
					<s id="N2176F">adde his refle­<lb></lb>xionem variam ex qua ſæpè oritur hæc turbinatio; </s>
					<s id="N21775">tùm etiam figuram <lb></lb>vaſis; </s>
					<s id="N2177B">ſic aqua intra vas ſphæricum voluitur; </s>
					<s id="N2177F">ſic in vorticibus voluitur <lb></lb>aqua propter præruptum deſcenſum aluei; </s>
					<s id="N21785">ſic etiam turbinatim deſcen­<lb></lb>dit aqua per tubum infundibuli; cætera omitto, quæ ex his facilè intel­<lb></lb>ligi poſſunt. </s>
				</p>
				<p id="N2178D" type="main">
					<s id="N2178F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2179B" type="main">
					<s id="N2179D"><emph type="italics"></emph>Datur impetus in motu circulari<emph.end type="italics"></emph.end>; </s>
					<s id="N217A6">probatur facilè, quia etiam abſente <lb></lb>potentia motrice durat motus; </s>
					<s id="N217AC">igitur adeſſe debet illius cauſa; igitur <lb></lb>impetus, clarum eſt; </s>
					<s id="N217B2">debet autem eſſe hic impetus ita determinatus, vt <lb></lb>determinatio vnius puncti impediat determinationem alteriùs; ſed aliam <lb></lb>permittat, alioqui deſtrueretur totus impetus, &amp; hæc viciſſim illam. </s>
				</p>
				<p id="N217BA" type="main">
					<s id="N217BC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N217C8" type="main">
					<s id="N217CA"><emph type="italics"></emph>Subjectum huius impetus eſt omne mobile<emph.end type="italics"></emph.end>; </s>
					<s id="N217D3">non eſt difficultas pro mobili <lb></lb>corporeo, quod pluribus partibus conſtat; </s>
					<s id="N217D9">quippe impetus vnius partis <lb></lb>poteſt impedire impetum alterius; </s>
					<s id="N217DF">at difficilius eſt dictu, an punctum, <lb></lb>ſi detur, moueri poſſit circulariter: de puncto phyſico loquor? </s>
					<s id="N217E5">cui cer­<lb></lb>tè non repugnat motus circularis; quippè licèt careat partibus actu, non <lb></lb>tamen caret partibus potentiâ. </s>
					<s id="N217ED">Dices, non mutat locum; </s>
					<s id="N217F1">igitur non mo­<lb></lb>uetur: </s>
					<s id="N217F7">antecedens conſtare videtur, quia ſemper remanet in eodem loco: </s>
					<s id="N217FB"><lb></lb>conſequentia etiam videtur eſſe clara per Def.1. lib.  1. Reſpondeo pri­<lb></lb>mò mutare locum reſpectiuum; </s>
					<s id="N21802">quippe licèt punctum phyſicum non ha­<lb></lb>beat partes, habet tamen facies; </s>
					<s id="N21808">vnde facies conuertuntur per motum <lb></lb>circularem; </s>
					<s id="N2180E">igitur non habent ampliùs eundem reſpectum; igitur nec <lb></lb>eundem locum reſpectiuum. </s>
					<s id="N21814">Reſpondeo ſecundò, punctum phyſicum ha­<lb></lb>bere partes potentiâ, non actu; </s>
					<s id="N2181A">vnde mutat locum, dum voluitur; </s>
					<s id="N2181E">quia <lb></lb>quælibet pars potentiâ diuerſæ parti ſpatij potentiâ reſpondet; </s>
					<s id="N21824">ſed hîc <lb></lb>non diſcutio quæſtionem illam, an dentur puncta phyſica; </s>
					<s id="N2182A">ſed tantùm <lb></lb>aſſero, ex ſuppoſitione quòd detur punctum phyſicum moueri poſſe mo­<lb></lb>tu circulari: </s>
					<s id="N21832">Idem de Angelo dici poteſt, non tamen de puncto mathe­<lb></lb>matico, cuius motus concipi non poteſt; </s>
					<s id="N21838">vnde optimè negat Ariſtoteles <lb></lb>punctum mathematicum moueri poſſe; </s>
					<s id="N2183E">immò nos aliquando repugnare <lb></lb>dari punctum mathematicum oſtendemus; igitur ex dictis patet, omne <pb pagenum="277" xlink:href="026/01/311.jpg"></pb>mobile, quod ſcilicet moueri poteſt motu recto, motu circulari etiam <lb></lb>moueri poſſe. </s>
				</p>
				<p id="N2184B" type="main">
					<s id="N2184D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21859" type="main">
					<s id="N2185B"><emph type="italics"></emph>Finis huius motus varius eſt in naturâ, &amp; multiplex vſus<emph.end type="italics"></emph.end>; primò enim <lb></lb>ex motu circulari fit, vt impetus qui eſt ad omnem lineam indifferens <lb></lb>habeat ſuum effectum, cum omnes lineæ impediuntur præter vnam, &amp; <lb></lb>hoc eſt vera ratio à priori huius motus. </s>
					<s id="N2186A">Secundò nulla libratio, ſeu vi­<lb></lb>bratio eſſe poſſet, niſi motus circularis eſſet; hinc nullus libræ vſus, ve­<lb></lb>ctis, trochleæ, aliorumque organorum mechanicorum quorum opera <lb></lb>inutilis eſſet ſine motu circulari. </s>
					<s id="N21874">Tertiò, omitto gyros, &amp; ſpiras, turbi­<lb></lb>num, rotarum, lapidum molarium, immò &amp; ſyderum orbitas, fundarum <lb></lb>librationes; </s>
					<s id="N2187C">immò &amp; ipſorum brachiorum; digitorum, tybiarum vſum; <lb></lb>immò auſim dicere motum circularem non minùs toti naturæ vtilem <lb></lb>eſſe, quàm rectum. </s>
				</p>
				<p id="N21884" type="main">
					<s id="N21886"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21892" type="main">
					<s id="N21894"><emph type="italics"></emph>Motus circularis poteſt appellari ſimplex<emph.end type="italics"></emph.end>; </s>
					<s id="N2189D">quia ex pluribus mixtus non <lb></lb>eſt omnis motus circularis, licèt aliquis motus circularis poſſit eſſe mixtus <lb></lb>ex duobus rectis, vt dictum eſt ſuprà; </s>
					<s id="N218A5">non minùs quàm rectus poteſt eſſe <lb></lb>mixtus ex duobus circularibus; </s>
					<s id="N218AB">non eſt tamen propterea dicendum om­<lb></lb>nem circularem eſſe mixtum; </s>
					<s id="N218B1">cum ſcilicet in mobili, quod circulari mo­<lb></lb>tu mouetur, non fit duplex impetus; quis autem dicat motum funepen­<lb></lb>duli ſurſum vibrati eſſe mixtum? </s>
					<s id="N218B9">equidem in ſublunaribus nullus eſt mo­<lb></lb>tus circularis qui ex multiplici determinatione non conſtet, vt dictum <lb></lb>eſt ſuprà; </s>
					<s id="N218C1">Vnde fortè vel eo nomine mixtus dici poſſet, ſed propter ean­<lb></lb>dem rationem motus reflexus mixtus dici poſſet; </s>
					<s id="N218C7">quidquid ſit, dum rem <lb></lb>intelligas, loquere vt voles; </s>
					<s id="N218CD">dixi in ſublunaribus, quia corpora cœleſtia <lb></lb>ita ſunt à natura inſtituta, vt circulari motu rotari poſtulent; de quo ſuo <lb></lb>loco: </s>
					<s id="N218D5">Et verò hæc legitima videtur eſſe Ariſtotelis ſententia, qui motum <lb></lb>naturalem rectum grauibus, &amp; leuibus tribuit, circularem verò cœleſti­<lb></lb>bus; </s>
					<s id="N218DD">ex quo etiam motu tanquam ex natiua proprietate quintam cœlo­<lb></lb>rum eſſentiam concludit; denique nulla videtur eſſe repugnantia, nul­<lb></lb>lumque abſurdum, ſi motus circularis alicui corpori competat. </s>
					<s id="N218E5">Vtrum <lb></lb>verò motus circularis dici poſſit naturalis, dubium eſſe non poteſt, pro <lb></lb>cœleſtibus illis corporibus, ſi à principio intrinſeco rotantur; </s>
					<s id="N218ED">pro ſub­<lb></lb>lunaribus aliquod fortè dubium eſſet; ſed quæſo te cum funependulum <lb></lb>ſua ſponte vibratum deſcendit, quo nomine motum illum appellas? </s>
					<s id="N218F5">Nun­<lb></lb>quid eſt à principio intrinſeco? </s>
					<s id="N218FA">cur igitur naturalem appellare detrectas? </s>
					<s id="N218FD"><lb></lb>rem intelligis, loquere vt voles. </s>
				</p>
				<p id="N21901" type="main">
					<s id="N21903"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2190F" type="main">
					<s id="N21911"><emph type="italics"></emph>Omnia puncta eiuſdem circuli mouentur æquali motu.<emph.end type="italics"></emph.end></s>
					<s id="N21918"> Probatur quia <lb></lb>æqualibus temporibus æquales arcus percurrunt, vt conſtat; igitur mo­<lb></lb>uentur æquali motu, id eſt æquè velociter per Axioma 1. </s>
				</p>
				<pb pagenum="278" xlink:href="026/01/312.jpg"></pb>
				<p id="N21925" type="main">
					<s id="N21927"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21933" type="main">
					<s id="N21935"><emph type="italics"></emph>Puncta diuerſorum circulorum mouentur inæquali motu<emph.end type="italics"></emph.end>; </s>
					<s id="N2193E">quia tempori­<lb></lb>bus æqualibus inæquales percurrunt arcus; </s>
					<s id="N21944">igitur inæquali motu per <lb></lb>Axio. 1. v.g. puncta L &amp; C quæ diſtant æqualiter à centro K, mouentur <lb></lb>æquali motu, quia æquali tempore conficiunt æquales arcus CS, LT; at <lb></lb>verò puncta CQ inæquali motu mouentur, quia æquali tempore arcus <lb></lb>inæquales percurrunt, ſcilicet CS, QX. </s>
				</p>
				<p id="N21954" type="main">
					<s id="N21956"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21962" type="main">
					<s id="N21964"><emph type="italics"></emph>Hinc puncta, quæ accedunt propiùs ad centrum mouentur tardiùs, quæ lon­<lb></lb>giùs recedunt, mouentur velociùs.<emph.end type="italics"></emph.end> v.g. C velociùs, quia conficit arcum ma­<lb></lb>iorem; </s>
					<s id="N21973">CSQ tardiùs, quia æquali tempore conficit arcum minorem <lb></lb>QR ſunt autem arcus ſimiles, vt radij, id eſt QR eſt ad CS, vt radius <lb></lb>KQ ad QC, ſed motus ſunt vt arcus; igitur motus, vt radij, vel diſtantiæ <lb></lb>à centro communi. </s>
				</p>
				<p id="N2197D" type="main">
					<s id="N2197F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2198B" type="main">
					<s id="N2198D"><emph type="italics"></emph>Ex his constat impetum, qui præstat motum circularem distribui in mobili <lb></lb>vniformiter, id eſt æqualem in eodem circulo, vel in distantia æquali, &amp; dif­<lb></lb>formiter, id eſt inæqualem in diuerſis circulis, vel in diuerſa distantia<emph.end type="italics"></emph.end>; </s>
					<s id="N2199A">quia <lb></lb>ex inæqualitate motus cognoſci tantùm poteſt inæqualitas impetus; </s>
					<s id="N219A0">fit <lb></lb>autem hæc diffuſio, ſeu propagatio in ratione longitudinum v. g. impe­<lb></lb>tus in Q eſt ad impetum in C, vt longitudo KQ ad KC, vt conſtat ex <lb></lb>dictis; </s>
					<s id="N219AE">accipio autem omnes partes impetus, quæ ſunt in Q, &amp; compa­<lb></lb>ro omnes illas cum omnibus illis, quæ inſunt puncto C; </s>
					<s id="N219B4">nam certum eſt <lb></lb>ex his quæ fusè diximus lib.1.non produci plures partes impetus in C, <expan abbr="quã">quam</expan> <lb></lb>in <expan abbr="q;">que</expan> ſed perfectiorem impetum produci in C, quàm in Q: </s>
					<s id="N219C4">recole quæ <lb></lb>diximus lib.1. à Th. 99. ad Th.112. in quibus habes totam propagatio­<lb></lb>nem impetus determinati ad motum circularem; </s>
					<s id="N219CC">ſiue applicetur po­<lb></lb>tentia centro, id eſt iuxta centrum; ſiue circumferentiæ. </s>
				</p>
				<p id="N219D2" type="main">
					<s id="N219D4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N219E0" type="main">
					<s id="N219E2"><emph type="italics"></emph>Motus puncti C non eſt velocior motu puncti Q ratione temporis, ſed ſpatij<emph.end type="italics"></emph.end>; </s>
					<s id="N219EB"><lb></lb>quia vtrumque mouetur ſemper æquali tempore, quia ſunt in eodem ra­<lb></lb>dio; </s>
					<s id="N219F2">recole etiam, quæ diximus alibi, ſcilicet lib.  2. in comparatione <lb></lb>motuum, vel aſſumi poſſe ſpatia æqualia cum temporibus inæqualibus, <lb></lb>vel tempora æqualia cum ſpatiis inæqualibus; </s>
					<s id="N219FA">atqui in motu circulari <lb></lb>cum omnes partes eiuſdem mobilis ſimul moueantur, id eſt ſimul inci­<lb></lb>piant, &amp; deſinant moueri; </s>
					<s id="N21A02">certè æquali tempore mouentur; </s>
					<s id="N21A06">ſed motus <lb></lb>eſt inæqualis; igitur non ratione temporis, quod æquale eſt, ſed <lb></lb>ſpatij. </s>
				</p>
				<p id="N21A0E" type="main">
					<s id="N21A10">Hic fortè aliquis deſideraret ſolutionem illius argumenti, quod vul­<lb></lb>gò ducitur ex motu circulari contra puncta phyſica, quod ſic breuiter <lb></lb>proponi poteſt. </s>
					<s id="N21A17">Sit punctum Q, quod acquirat punctum ſpatij verſus R <lb></lb>vno inſtanti; </s>
					<s id="N21A1D">certe punctum C, quod mouetur verſus S, acquiret eodem <pb pagenum="279" xlink:href="026/01/313.jpg"></pb>illo inſtanti pluſquam punctum ſpatij; </s>
					<s id="N21A26">igitur eodem inſtanti erit in <lb></lb>duobus loris, quod eſt abſurdum; </s>
					<s id="N21A2C">nec poteſt dici punctum C moueri <lb></lb>duobus inſtantibus, ſed minoribus, quæ ſcilicet reſpondeant inſtanti, quo <lb></lb>mouetur punctum <expan abbr="q;">que</expan> quia ſi poſt primum inſtans C ſiſteret, Q mouere­<lb></lb>tur adhuc, quod eſt abſurdum; nam ſimul incipit, &amp; deſinit moueri, <lb></lb>cum puncto C. </s>
					<s id="N21A3D">Equidem non poteſt explicari maior velocitas motus C <lb></lb>per inſtantia minora, vt patet; igitur per ſpatia maiora. </s>
					<s id="N21A43">Itaque reſpon­<lb></lb>deo ſi C &amp; Q mouentur in eodem radio conjunctim non poſſe pun­<lb></lb>ctum K acquirere punctum ſpatij nullo modo participans cum priori, <lb></lb>ſed participans; </s>
					<s id="N21A4D">licèt enim punctum ſpatij careat partibus actu, habet <lb></lb>tamen partes potentia, vt explicabimus fusè ſuo loco; </s>
					<s id="N21A53">ſunt enim vbica­<lb></lb>tiones communicantes, &amp; non communicantes, quod explico in Ange­<lb></lb>lo ſit enim Angelus coëxtenſus quadrato FC, (quam hypotheſim <lb></lb>nemo negabit;) ſit alius æqualis extenſionis coëxtenſus quadrato HE, <lb></lb>qui conſiſtat dum primus Angelus mouetur; </s>
					<s id="N21A5F">certè ita moueri poteſt, vt <lb></lb>primo inſtanti occupet ſpatium CK, &amp; coëxtendatur alteri Angelo, vt <lb></lb>certum eſt; </s>
					<s id="N21A67">quippè vnico inſtanti locum ſibi adæquatum occupare po­<lb></lb>teſt; </s>
					<s id="N21A6D">vel ita moueri poteſt, vt primo inſtanti occupet ſpatium GD, &amp; <lb></lb>coëxtendatur quidem alteri Angelo ſed inadæquatè: </s>
					<s id="N21A73">his poſitis, ſpatium <lb></lb>HE comparatum cum ſpatio FC eſt non communicans; </s>
					<s id="N21A79">ſpatium verò <lb></lb>GD communicans, tum cum HE, tum cum HA, poſſunt autem dari <lb></lb>huiuſmodi ſpatia in infinitum plùs vel minùs participantia v. g. LM <lb></lb>plus participat de AC quam BD, &amp; BD pluſquam NO; </s>
					<s id="N21A87">igitur non <lb></lb>eſt dubium quin Angelus moueatur eo tardiùs, ſuppoſito æquali tempo­<lb></lb>re, quo acquirit ſpatium plùs participans de priore; </s>
					<s id="N21A8F">vnde quando vno <lb></lb>inſtanti acquirit ſpatium non communicans HE, non poteſt velociùs <lb></lb>moueri illo inſtanti, vel æquali; </s>
					<s id="N21A97">nec poteſt motus eſſe velocior ratione <lb></lb>ſpatij, licèt poſſit eſſe ratione temporis; quia ſpatium HE acquirere po­<lb></lb>teſt minore inſtanti. </s>
					<s id="N21A9F">Quod dicitur de Angelo, dicatur de puncto phyſi­<lb></lb>co; cuius extenſio eſt quidem indiuiſibilis actu vt extenſio Angeli diui­<lb></lb>ſibilis tamen potentia in infinitum. </s>
				</p>
				<p id="N21AA7" type="main">
					<s id="N21AA9">His poſitis, motus extremitatis radij dirigit motum aliorum puncto­<lb></lb>rum verſus centrum; ſed punctum extremitatis radij non poteſt <lb></lb>dato inſtanti moueri velociùs quàm ſi punctum ſpatij non communi­<lb></lb>cans acquirat, quo poſito nullum aliud punctum radij acquirit eodem <lb></lb>inſtanti ſpatium non communicans. </s>
				</p>
				<p id="N21AB5" type="main">
					<s id="N21AB7">Dices, ponamus punctum extremitatis facta acceſſione noui ſegmenti <lb></lb>moueri eadem velocitate, quâ priùs mouebatur, cum terminabat radium; </s>
					<s id="N21ABD"><lb></lb>igitur acquirit punctum ſpatij non participans; igitur extremitas noua <lb></lb>illo inſtanti acquirit pluſquam punctum. </s>
					<s id="N21AC4">Reſpondeo, ſi addatur extremi­<lb></lb>tas noua facta ſcilicet acceſſione noui ſegmenti, poſito quod punctum <lb></lb>prioris extremitatis moueatur æquè velociter ac priùs; </s>
					<s id="N21ACC">certè noua ex­<lb></lb>tremitas velociùs mouebitur priore, vt conſtat; </s>
					<s id="N21AD2">igitur inſtanti minore <lb></lb>acquiret ſpatium non communicans; igitur hoc inſtanti minore prior <lb></lb>extremitas acquirit ſpatium communicans. </s>
					<s id="N21ADA">Ex his vides velocitatem <pb pagenum="280" xlink:href="026/01/314.jpg"></pb>motus circularis ratione eiuſdem radij, vel mobilis explicari per ſpatia <lb></lb>magis, vel minùs communicantia; </s>
					<s id="N21AE5">at verò velocitatem motus recti per <lb></lb>inſtantia maiora, &amp; minora: </s>
					<s id="N21AEB">Sed hæc fusè in Metaphyſica explicabimus; </s>
					<s id="N21AEF"><lb></lb>neque hîc contendimus dari vel puncta, vel inſtantia; </s>
					<s id="N21AF4">ſed tantùm poſito <lb></lb>quod dentur, ita ſolui poſſe argumentum illud, quod vulgò ducitur ex <lb></lb>motu circulari, quo reuerâ puncta Mathematica non tamen phyſica pro­<lb></lb>fligantur: </s>
					<s id="N21AFE">ſimiliter ſolues argumentum illud vix triobolare, quo dicuntur <lb></lb>eſſe tot puncta in minore circulo, quot in maiore, eo quod iidem radij <lb></lb>vtrumque ſecent, quia ſi duo radij ad duo puncta immediata maioris <lb></lb>terminentur, penetrantur inadæquatè in ſectione minoris circuli; ſed <lb></lb>de hoc aliàs. </s>
				</p>
				<p id="N21B0A" type="main">
					<s id="N21B0C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21B18" type="main">
					<s id="N21B1A"><emph type="italics"></emph>Motus circularis poteſt eſſe velocior, &amp; tardior in infinitum<emph.end type="italics"></emph.end>; </s>
					<s id="N21B23">quia quocun­<lb></lb>que dato radio poteſt dari maior, &amp; minor; </s>
					<s id="N21B29">immò poteſt compenſari <lb></lb>motus; </s>
					<s id="N21B2F">ſit enim radius EC diuiſus bifariam in H; </s>
					<s id="N21B33">certè ſi moueatur <lb></lb>EC circa centrum E; </s>
					<s id="N21B39">C mouebitur duplo velociùs quàm H, quia arcus <lb></lb>CN eſt duplus HT; </s>
					<s id="N21B3F">ſi tamen ſit radius AH; </s>
					<s id="N21B43">certè ſi poteſt moueri <lb></lb>æquè velociter, ſi enim aſſumatur H <foreign lang="grc">μ</foreign> æqualis HT, &amp; percurrat H <foreign lang="grc">μ</foreign><lb></lb>eo tempore, quo alter radius EC percurrit CN, motus erit æqualis; </s>
					<s id="N21B52">quia <lb></lb>arcus CN &amp; H <foreign lang="grc">μ</foreign> ſunt æquales, vt conſtat: </s>
					<s id="N21B5C">poteſt etiam vectis longio­<lb></lb>ris extremitas moueri motu æquali cum extremitate minoris; </s>
					<s id="N21B62">ſi enim <lb></lb>H extremitas HE percurrit H <foreign lang="grc">μ</foreign>, &amp; aſſumatur vectis duplus EC, diuida­<lb></lb>tur H <foreign lang="grc">μ</foreign> bifariam in T ducaturque ETN; </s>
					<s id="N21B72">certè ſi C conficiat CN co­<lb></lb>dem tempore, vtraque extremitas C &amp; H æquè velociter mouebitur; </s>
					<s id="N21B78">ſi <lb></lb>autem duplicetur adhuc longitudo radij, diuidatur HT bifariam in X, <lb></lb>ducaturque linea, atque ita deinceps; quæ omnia ſunt trita. </s>
				</p>
				<p id="N21B80" type="main">
					<s id="N21B82">Ex his habes principium motus tardioris, &amp; velocioris in infinitum; </s>
					<s id="N21B86">ſi <lb></lb>enim punctum H ſemper æquali tempore conficiat arcum H <foreign lang="grc">μ</foreign>; </s>
					<s id="N21B90">certè <lb></lb>punctum C conficiet arcum C <foreign lang="grc">β</foreign> duplum prioris; </s>
					<s id="N21B9A">quia EC eſt dupla <lb></lb>EH; </s>
					<s id="N21BA0">ſi verò accipiatur tripla, conficiet triplum, atque ita deinceps; </s>
					<s id="N21BA4">ſed <lb></lb>poteſt vectis eſſe longior, &amp; longior in infinitum; </s>
					<s id="N21BAA">igitur motus velo­<lb></lb>cior, &amp; velocior; </s>
					<s id="N21BB0">ſi verò punctum C conficiat tantùm arcum CN æqua­<lb></lb>lem H <foreign lang="grc">μ</foreign>; haud dubiè punctum H mouebitur duplò tardiùs, &amp; ſi acci­<lb></lb>piatur vectis duplus CE, cuius extremitas percurrat arcum æqualem <lb></lb>CN, punctum H mouebitur quadruplò tardiùs, atque ita deinceps. </s>
				</p>
				<p id="N21BBE" type="main">
					<s id="N21BC0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21BCC" type="main">
					<s id="N21BCE"><emph type="italics"></emph>Motus circularis non eſt naturaliter acceleratus.<emph.end type="italics"></emph.end></s>
					<s id="N21BD5"> Probatur, quia in infi­<lb></lb>nitum intenderetur, quod eſſet abſurdum in natura; </s>
					<s id="N21BDB">caret enim termino: </s>
					<s id="N21BDF"><lb></lb>non eſt difficultas pro motu circulari violento quo v.g. vertitur rota in <lb></lb>circulo verticali, vel mixto, quo ſcilicet lapis ſphæricus ita deſcendit, vt <lb></lb>circa ſuum centrum etiam voluatur, vel indifferenti, quo recta vertitur <lb></lb>in circulo horizontali; </s>
					<s id="N21BEC">quia nullum eſt principium accelerationis iſto­<lb></lb>rum motuum; </s>
					<s id="N21BF2">igitur eſt tantùm difficultas pro naturali circulari, quo <pb pagenum="281" xlink:href="026/01/315.jpg"></pb>fortè ſydera rotantur; qui tamen non eſt acceleratus per ſe, propter ra­<lb></lb>tionem prædictam. </s>
				</p>
				<p id="N21BFD" type="main">
					<s id="N21BFF">Obiiceret fortè aliquis; </s>
					<s id="N21C02">eadem ratio quæ probat motum naturalem <lb></lb>deorſum accelerari, eadem probat circularem naturalem etiam intendi: <lb></lb>quippè ſemper adeſt principium intrinſecum applicatum. </s>
					<s id="N21C0A">Reſpondeo <lb></lb>negandam eſſe paritatem; </s>
					<s id="N21C10">quia naturalis motus grauium non accelera­<lb></lb>tur fruſtrà; </s>
					<s id="N21C16">Nunquam enim recedit à ſuo fine; </s>
					<s id="N21C1A">at verò, ſi motus circula­<lb></lb>ris ſyderum acceleraretur, tandem abiret in infinitum, quod reuerâ eſſet <lb></lb>contra finem à natura inſtitutum; quippè carerent ſuo fine, &amp; vſu corpo­<lb></lb>ra cœleſtia, ſi longè celeriori motu rotarentur. </s>
				</p>
				<p id="N21C24" type="main">
					<s id="N21C26">Obiiceret alius, motus circularis naturalis non acceleraretur, igitur <lb></lb>tardiſſimus eſſet, qualis reuerâ motus naturalis grauium deorſum, quod <lb></lb>eſt contra experientiam. </s>
					<s id="N21C2D">Reſpondeo, vel determinatum impetus gradum, <lb></lb>eumque valdè intentum produxiſſe iuxta inſtitutum ſuæ naturæ, vel per <lb></lb>aliquot minuta ſeſe mouiſſe motu recto naturaliter accelerato; ſed de <lb></lb>hoc motu ſyderum agemus fusè aliquando, cum de cauſis corporum cœ­<lb></lb>leſtium. </s>
				</p>
				<p id="N21C39" type="main">
					<s id="N21C3B">Obiicies deſcenſum funependuli, qui eſt naturaliter acceleratus; ſed <lb></lb>profectò ille motus eſt tantùm per accidens circularis. </s>
				</p>
				<p id="N21C41" type="main">
					<s id="N21C43"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N21C4F" type="main">
					<s id="N21C51">Obſeruabis ex dictis ſatis conſtare, quàm temerè mirentur aliqui tan­<lb></lb>tam motuum cœleſtium celeritatem, cum motus circularis velocitas in <lb></lb>infinitum augeri poſſit: Obſeruabis præterea, ſi fortè motus rectus corpo­<lb></lb>rum cœleſtium præceſſit per aliquot minuta, motum illum, qui deinde <lb></lb>ſucceſſit, non eſſe perfectè circularem, ſed mixtum, quem aliquando ex­<lb></lb>plicabimus, &amp; ex eo cauſas Apogæi, Perigæi, declinationis, &amp;c. </s>
					<s id="N21C5F">omnéſ­<lb></lb>que anomalias deducemus ſuo loco. </s>
				</p>
				<p id="N21C64" type="main">
					<s id="N21C66"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21C72" type="main">
					<s id="N21C74"><emph type="italics"></emph>Rota circulo verticali parallela circa axem mobilis addito minimo im­<lb></lb>petu per ſe moueri poteſt<emph.end type="italics"></emph.end>; </s>
					<s id="N21C7F">ſit enim ABCD plano verticali parallela circa <lb></lb>centrum E volubilis; </s>
					<s id="N21C85">ſitque in perfecto æquilibrio, &amp; accedat minima <lb></lb>vis impetus in A v.g. haud dubiè punctum E deſcendet deorſum, alio­<lb></lb>quin maneret æquilibrium, &amp; non maneret: dixi per ſe; </s>
					<s id="N21C8F">nam cùm non <lb></lb>poſſit volui circa centrum E, niſi vel cum mobili axe duobus hinc inde <lb></lb>lunatis fulcris ſuſtentato, vel facto foramine circa axem immobilem, vel <lb></lb>circa geminos apices conicos immiſſos iuſtis apothecis in plano rotæ <lb></lb>excauatis, quales videmus in acu magnetica; atqui non poteſt volui rota <lb></lb>ſiue primo, ſiue ſecundo, ſiue tertio modo voluatur ſine multa compreſ­<lb></lb>ſione partium, id eſt, ſine aliquo affrictu, in quo multæ particulæ vnius <lb></lb>plani cum particulis alterius quaſi pectinatim commiſſæ, motum &amp; im­<lb></lb>petunt ſiſtunt. </s>
				</p>
				<p id="N21CA3" type="main">
					<s id="N21CA5"><emph type="center"></emph><emph type="italics"></emph>Theorèma<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21CB1" type="main">
					<s id="N21CB3"><emph type="italics"></emph>Rota minor in eodem ſitu de quo ſuprà æquè facilè moueri poteſt, ac maior<emph.end type="italics"></emph.end><pb pagenum="282" xlink:href="026/01/316.jpg"></pb><emph type="italics"></emph>per ſe.<emph.end type="italics"></emph.end></s>
					<s id="N21CC3"> Probatur primò, quia vtraque minimo impetu moueri poteſt per <lb></lb>Th. 21. Secundò, quia addita minima vi impetus in F, &amp; minima in A <lb></lb>tàm facilè maior rota deſcendit, quàm minor, quia æqualiter tollitur <lb></lb>æquilibrium vtriuſque: dixi per ſe, quia maior rota propter maius pon­<lb></lb>dus maiore affrictu motum impedit. </s>
				</p>
				<p id="N21CCF" type="main">
					<s id="N21CD1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21CDD" type="main">
					<s id="N21CDF"><emph type="italics"></emph>Poteſt vis aliqua applicata rotæ in A v.g. rotam mouere in eodem ſitu ver­<lb></lb>ticali; licèt nullum impetum producat.<emph.end type="italics"></emph.end></s>
					<s id="N21CEB"> Probatur, quia vis minima poteſt <lb></lb>deprimere rotam ABCD. v.g. per Th.21. ſed vis minima non poteſt <lb></lb>producere impetum in qualibet rota, vt patet; </s>
					<s id="N21CF5">nec enim producere po­<lb></lb>teſt, niſi in tota rota producat per Th.33. lib.  primo; ſed vis minima im­<lb></lb>petus tot partes impetus, producere non poteſt, quot eſſent neceſſariæ, vt <lb></lb>omnibus partibus rotæ diſtribuerentur. </s>
				</p>
				<p id="N21CFF" type="main">
					<s id="N21D01"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21D0D" type="main">
					<s id="N21D0F"><emph type="italics"></emph>Hinc egregium paradoxum; </s>
					<s id="N21D14">poteſt aliquid mouere rotam, &amp; non agere in <lb></lb>rotam<emph.end type="italics"></emph.end>; </s>
					<s id="N21D1D">quia vis mouens non poteſt in rotam agere, niſi impetum in ea <lb></lb>producat, vt patet; </s>
					<s id="N21D23">ſed poteſt illa vis rotam mouere licèt impetum in ea <lb></lb>non producat per Th.23. igitur mouere, &amp; non agere: </s>
					<s id="N21D29">quod quomodo <lb></lb>fiat facilè explicari poteſt; quippè illa vis ponderis. </s>
					<s id="N21D2F">v.g. quæ accedit pun­<lb></lb>cto A cum toto pondere ſemicirculi BA DE, grauitatione communi <lb></lb>præualet grauitationi alterius ſemicirculi rotæ BC DE; </s>
					<s id="N21D39">quia ſcilicet <lb></lb>maior eſt; ſic pondus vnius ſcrupuli ſuperpoſitum ingenti rupi non pro­<lb></lb>ducit in rupe impetum, ſed ſi fortè appendatur rupes, ſimul cum illa gra­<lb></lb>uitat, quod facilè concipi poteſt. </s>
				</p>
				<p id="N21D43" type="main">
					<s id="N21D45"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21D51" type="main">
					<s id="N21D53"><emph type="italics"></emph>Cum deſcendit deorſum ſemicirculus BA DE, attollitur ſurſum ſemicir­<lb></lb>culus oppoſitus<emph.end type="italics"></emph.end>; </s>
					<s id="N21D5E">quia ſcilicet impetus illius producit in iſto alium impe­<lb></lb>tum; </s>
					<s id="N21D64">nec enim corpus graue aſcendit ſurſum ſua ſponte in medio leuio­<lb></lb>re; igitur ab extrinſeco; </s>
					<s id="N21D6A">ſed nulla eſt alia cauſa applicata præter impe­<lb></lb>tum ſemicirculi deſcendentis; </s>
					<s id="N21D70">igitur ab eo producitur hic impetus, <lb></lb>iſque omninò æqualis; quia ſcilicet vterque mouetur motu æquali. </s>
				</p>
				<p id="N21D76" type="main">
					<s id="N21D78"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21D84" type="main">
					<s id="N21D86"><emph type="italics"></emph>Hinc impetus deorſum producere poteſt impetum ſurſum<emph.end type="italics"></emph.end>; quippe <lb></lb>ad aliam lineam determinare non poteſt, quod valdè paradoxum eſt. </s>
				</p>
				<p id="N21D91" type="main">
					<s id="N21D93"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21D9F" type="main">
					<s id="N21DA1"><emph type="italics"></emph>Hinc impetus vnius partis mobilis continui poteſt impetum ſimilem produ­<lb></lb>cere in alia parte eiuſdem mobilis<emph.end type="italics"></emph.end>; vt patet ex dictis, quod tantùm locum <lb></lb>habet in motu circulari. </s>
					<s id="N21DAE">Diceret aliquis, igitur in motu recto etiam lo­<lb></lb>cum habebit. </s>
					<s id="N21DB3">Reſpondeo negando, alioqui minima potentia quodlibet <lb></lb>pondus motu recto moueret etiam nullo adhibito mechanico organo; </s>
					<s id="N21DB9"><lb></lb>quia modo produceretur tantulus impetus in aliqua parte, hic produce­<lb></lb>ret alium, &amp; hic alium, immò vterque ſecundo inſtanti alium produce-<pb pagenum="283" xlink:href="026/01/317.jpg"></pb>ret: </s>
					<s id="N21DC5">eſſet enim cauſa neceſſaria; </s>
					<s id="N21DC9">ſed hoc eſt abſurdum: ratio verò diſpa­<lb></lb>ritatis eſt, quia mobile, quod motu circulari voluitur circa centrum, <lb></lb>quod eſt in ipſo mobili duplicis mobilis vicem gerit, quorum vnum im­<lb></lb>pedit motum alterius, nec moueri poſſunt, niſi motibus oppoſitis. </s>
				</p>
				<p id="N21DD4" type="main">
					<s id="N21DD6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21DE2" type="main">
					<s id="N21DE4"><emph type="italics"></emph>Si applicetur pondus in<emph.end type="italics"></emph.end> K, <emph type="italics"></emph>minus erit illius<emph type="sup"></emph>a<emph.end type="sup"></emph.end> momentum, quàm in A, erit­<lb></lb>que ad momentum in A, vt LE ad AE<emph.end type="italics"></emph.end>; </s>
					<s id="N21DFB">quod ſæpiùs iam ſuprà dictum <lb></lb>eſt; </s>
					<s id="N21E01">præſertim lib.4. Inde tamen egregium deduco paradoxum, ſcilicet <lb></lb>minimam vim ſufficere ad deprimendum ſemicirculum BA DE ſiue ſit <lb></lb>applicata in A ſiue in K; faciliùs tamen id præſtare in C, quàm in K, <lb></lb>id eſt velociore motu. </s>
				</p>
				<p id="N21E0B" type="main">
					<s id="N21E0D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21E19" type="main">
					<s id="N21E1B"><emph type="italics"></emph>Potentia in C applicata etiam minima per lineam CN, mouebit ſemicir­<lb></lb>culum DE BE ſurſum<emph.end type="italics"></emph.end>; vt patet; </s>
					<s id="N21E26">nullum tamen producet impetum, ſi <lb></lb>minima ſit; </s>
					<s id="N21E2C">ratio eſt, quia eodem modo ſe habet, ac ſi detraheret partem <lb></lb>ponderis ſemicirculi DC BE, qua detracta non eſt ampliùs æquili­<lb></lb>brium; </s>
					<s id="N21E34">igitur oppoſitus ſemicirculus BA DE præualere debet; </s>
					<s id="N21E38">vnde <lb></lb>ideo aſcendit ille, quia deſcendit iſte; </s>
					<s id="N21E3E">qui ideo deſcendit, quia vel de­<lb></lb>trahitur aliquid de momento alterius, vel impeditur; </s>
					<s id="N21E44">atqui impedire <lb></lb>tantùm poteſt, vel per productionem impetus, vel per applicationem po­<lb></lb>tentiæ per CN, quæ actione communi cum toto impetu ſemicirculi <lb></lb>BA DE iuuat eius deſcenſum; </s>
					<s id="N21E4E">nam perinde ſe habet potentia, ſiue ſit, <lb></lb>applicata in A per lineam AO ſiue in C per CN: quod certè manife­<lb></lb>ſtum eſt. </s>
				</p>
				<p id="N21E56" type="main">
					<s id="N21E58"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21E64" type="main">
					<s id="N21E66"><emph type="italics"></emph>Hinc etiam habes duo paradoxa<emph.end type="italics"></emph.end>; </s>
					<s id="N21E6F">primum eſt, potentiam immediatè <lb></lb>concurrere ad motum ſemicirculi, cui non eſt applicata, &amp; mediatè tan­<lb></lb>tùm ad motum illius, cui applicata eſt; nam potentia applicata in C per <lb></lb>CN concurrit immediatè ad motum A deorſum, &amp; ſimul cum A ad mo­<lb></lb>tum Curſum. </s>
					<s id="N21E7B">Secundum eſt, ſolam negationem eſſe cauſam motus, ſci­<lb></lb>licet detractionem partis momenti, quod clarum eſt. </s>
				</p>
				<p id="N21E80" type="main">
					<s id="N21E82"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21E8E" type="main">
					<s id="N21E90"><emph type="italics"></emph>Hinc etiam alia deduco paradoxa.<emph.end type="italics"></emph.end></s>
					<s id="N21E97"> Primum eſt, faciliùs ſuſtineri maius <lb></lb>pondus, quàm minus. </s>
					<s id="N21E9C">Secundum plùs addi ponderis, quò plùs detrahi­<lb></lb>tur. </s>
					<s id="N21EA1">Tertium plùs detrahi, quò plùs additur, v.g. ſi detrahatur aliqua por­<lb></lb>tio ex ſemicirculo BC DE, ſemicirculus rotæ oppoſitus deſcendet, niſi <lb></lb>ſit potentia in CA, qua ſuſtineatur; </s>
					<s id="N21EAB">&amp; quò maior portio detrahetur po­<lb></lb>tentiæ, maius pondus incumbet; quò minor, minus. </s>
					<s id="N21EB1">Sed hæc clara <lb></lb>ſunt. </s>
				</p>
				<p id="N21EB6" type="main">
					<s id="N21EB8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21EC4" type="main">
					<s id="N21EC6"><emph type="italics"></emph>Impetus productus in rota conſeruatur aliquamdiu.<emph.end type="italics"></emph.end></s>
					<s id="N21ECD"> Duplex impetus con­<lb></lb>ſiderari poteſt in rota; </s>
					<s id="N21ED3">primus eſt productus ad intra accedente, ſcilicet <lb></lb>minima vi ponderis alteri ſemicirculo, putâ puncto A, qua poſita tolla-<pb pagenum="284" xlink:href="026/01/318.jpg"></pb>tur æquilibrium, quo ſublato ſua ſponte mouetur rota; </s>
					<s id="N21EDE">hic autem impe­<lb></lb>tus primò durat in toto deſcenſu quadrantis AD; </s>
					<s id="N21EE4">immò acceleratur tan­<lb></lb>tillùm motus, licèt longè minùs, quàm in funependulo propter reſiſten­<lb></lb>tiam ſemicirculi oppoſiti contranitentis; </s>
					<s id="N21EEC">vbi verò A peruenit in D, <lb></lb>non acceleratur ampliùs motus, ſed tantillùm aſcendit verſus C &amp;, dein­<lb></lb>de deſcendit, tandemque quieſcit in D paucis confectis vibrationibus; </s>
					<s id="N21EF4"><lb></lb>ſed de hoc curſu, &amp; recurſu agemus fusè lib.  ſequenti; </s>
					<s id="N21EF9">alter impetus eſt <lb></lb>productus ab extrinſeco, applicata ſcilicet valida potentiá, qui rotam <lb></lb>agit velociore motu, vt patet, cùm præter impetum ad intra ſit etiam im­<lb></lb>petus productus ab extrinſeca cauſa; </s>
					<s id="N21F03">igitur maior eſt impetus; igitur <lb></lb>maior motus: </s>
					<s id="N21F09">porrò hic impetus aliquandiu conſeruatur, vt patet expe­<lb></lb>rientiâ; nec eſt vlla cauſa ſufficiens applicata, à qua tam citò de­<lb></lb>ſtruatur. </s>
				</p>
				<p id="N21F11" type="main">
					<s id="N21F13"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21F1F" type="main">
					<s id="N21F21"><emph type="italics"></emph>Quando voluitur rota ab applicata valida potentia in A. v.g. per AO, <lb></lb>non modo producitur impetus in ſemicirculo BA DE, ſed etiam in oppoſito<emph.end type="italics"></emph.end>; <lb></lb>cùm vtrique mediatè vel immediatè ſit applicata ſufficienter, exemplo <lb></lb>vectis. </s>
				</p>
				<p id="N21F32" type="main">
					<s id="N21F34"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21F40" type="main">
					<s id="N21F42"><emph type="italics"></emph>Non destruitur per ſe impetus productus in rota ab extrinſeco.<emph.end type="italics"></emph.end></s>
					<s id="N21F49"> Probatur, <lb></lb>quia licèt ſingulis inſtantibus mutetur eius determinatio, vt conſtat ex <lb></lb>dictis; </s>
					<s id="N21F51">nam per ſe impetus in hoc motu eſt determinatus ad lineam re­<lb></lb>ctam; </s>
					<s id="N21F57">nullus tamen impetus eſt fruſtrà: </s>
					<s id="N21F5B">quippè illud ſpatium acquiritur <lb></lb>in linea curua, quod in recta percurreretur ſi nullum eſſet impedimen­<lb></lb>tum; </s>
					<s id="N21F63">quemadmodum enim in reflexione, quæ fit à plano immobili, nul­<lb></lb>lus deſtruitur impetus; </s>
					<s id="N21F69">ita nullus hîc deſtruitur; tàm enim centrum il­<lb></lb>lud immobile ad ſe quaſi mobile trahit, quàm planum immobile ad ſe re­<lb></lb>pellit. </s>
				</p>
				<p id="N21F71" type="main">
					<s id="N21F73">Quæreret fortè aliquis, vtrum in ſemicirculo aſcendente impetus de­<lb></lb>ſtruatur ab impetu naturali grauitationis. </s>
					<s id="N21F78">Reſpondeo negando, quia <lb></lb>nunquam aſcendit C, niſi deſcendat A; </s>
					<s id="N21F7E">nunquam verò deſcendit A, niſi <lb></lb>ſit maior vis in A quam in C, quod certum eſt; </s>
					<s id="N21F84">igitur grauitatio C impe­<lb></lb>dit quidem, ne ſit tantus motus in A, nunquam tamen impedit totum <lb></lb>motum, cum maius eſt momentum in A; </s>
					<s id="N21F8C">quod ſi æquale ſit vtrinque mo­<lb></lb>mentum; certè totus motus vtrinque impeditur, &amp; hæc eſt vera ratio <lb></lb>æquilibrij, de quo aliàs. </s>
				</p>
				<p id="N21F94" type="main">
					<s id="N21F96"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21FA2" type="main">
					<s id="N21FA4"><emph type="italics"></emph>Hinc ſi nullus ſit partium affrictus, eſſet motus ille perpetuus<emph.end type="italics"></emph.end>; quia nul­<lb></lb>lus deſtruitur impetus per Th. 34. igitur ille motus eſſet perpetuus. </s>
				</p>
				<p id="N21FAF" type="main">
					<s id="N21FB1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21FBD" type="main">
					<s id="N21FBF"><emph type="italics"></emph>In maiore rota eſt maior affrictus partium, &amp; impetus citiùs destruitur.<emph.end type="italics"></emph.end><lb></lb>Secunda pars ſequitur ex prima; hæc autem ex maiore ponderis grauita­<lb></lb>tione, vel in axem, vel in ſubjectum planum. </s>
				</p>
				<pb pagenum="285" xlink:href="026/01/319.jpg"></pb>
				<p id="N21FCF" type="main">
					<s id="N21FD1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N21FDD" type="main">
					<s id="N21FDF"><emph type="italics"></emph>Licèt impetus non destruatur in motu rotæ, &amp; impediatur determinatio <lb></lb>prima, vt patet; </s>
					<s id="N21FE7">attamen impedimentum non poteſt minus excogitari<emph.end type="italics"></emph.end>; </s>
					<s id="N21FEE">cùm <lb></lb>nulla poſſit duci linea recta declinans ab AO, per quam noua determi­<lb></lb>natio fieri poſſit; </s>
					<s id="N21FF6">fit enim ratione anguli contingentiæ; </s>
					<s id="N21FFA">igitur determi­<lb></lb>natio noua proximè accedit ad priorem; igitur eſt minimum impedi­<lb></lb>mentum. </s>
				</p>
				<p id="N22002" type="main">
					<s id="N22004"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22010" type="main">
					<s id="N22012"><emph type="italics"></emph>Hinc in maiori rota minus eſt impedimentum<emph.end type="italics"></emph.end>; </s>
					<s id="N2201B">quia ſcilicet minor eſt <lb></lb>angulus contingentiæ; </s>
					<s id="N22021">maius verò in minori rota: </s>
					<s id="N22025">porrò minor rota à <lb></lb>maiore ſeparata citiùs ſuos gyros abſoluit; </s>
					<s id="N2202B">quia ſunt minores, (ſuppono <lb></lb>æqualem impetum in extremo orbe rotæ vtriuſque productum,) idque <lb></lb>pro rata; ſi enim minor ſit ſubdupla maioris, maior vnum tantum gyrum <lb></lb>aget eo tempore, quo minor duos percurret. </s>
				</p>
				<p id="N22035" type="main">
					<s id="N22037">Obſerua primò, pondus applicatum in A non modò producere impe­<lb></lb>tum in toto radio AE; </s>
					<s id="N2203D">ſed etiam in toto radio oppoſito EC; </s>
					<s id="N22041">ratio eſt, <lb></lb>quia ſi impetus radij AE producit impetum in radio EC; </s>
					<s id="N22047">certè pondus <lb></lb>additum radio AE cenſetur pars eiuſdem radij; </s>
					<s id="N2204D">igitur impetus illius <lb></lb>ponderis immediatè producit impetum in radio EC; </s>
					<s id="N22053">quia impedit hic <lb></lb>radius oppoſitus motum alterius AE; </s>
					<s id="N22059">igitur, vt tollat impedimentum, <lb></lb>producit AE impetum in EC; </s>
					<s id="N2205F">ſi autem produceretur tantùm impetus in <lb></lb>EC ab impetu radij AE; </s>
					<s id="N22065">igitur, vel aliquid impetus eſſet fruſtrà, vel <lb></lb>nunquam radius minor poſſet attollere maiorem, quacunque accedente <lb></lb>potentia; </s>
					<s id="N2206D">ſit enim radius FE, in quo producatur quilibet impetus, ſit­<lb></lb>que radius oppoſitus maior duplo EC; </s>
					<s id="N22073">certè ſi impetus radij FE produ­<lb></lb>cit impetum in radio EC, vel producit æqualem, vel minorem, maiorem <lb></lb>enim producere non poteſt; ſi minorem, vel æqualem; </s>
					<s id="N2207B">igitur remiſſio­<lb></lb>rem, quia pluribus partibus ſubjecti diſtribuitur; </s>
					<s id="N22081">igitur vel motus eſſet <lb></lb>remiſſior radij EC quàm radij FE, quod dici non poteſt; </s>
					<s id="N22087">vel aliquid <lb></lb>impetus radij FE eſſet fruſtrà, quod etiam dici non poteſt; itaque poten­<lb></lb>tia applicata in F, mediante ſcilicet organo, quodcumque tandem illud <lb></lb>ſit.v.g. </s>
					<s id="N22091">pugno, producit impetum in ipſo organo, impetus verò organi, <lb></lb>ſeu pugni producit impetum primò in toto radio FE, tùm in toto radio <lb></lb>EC, id eſt totus impetus tùm pugni, tùm radij FC, ſcilicet innatus pro­<lb></lb>ducit impetum in alio radio EC; </s>
					<s id="N2209B">nec enim producitur tantùm ab impe­<lb></lb>tu radij propter rationem ſuprà allatam, cùm ſit maior impetus in radio <lb></lb>EC quàm in radio FE; </s>
					<s id="N220A3">nec tantùm ab impetu pugni, vel organi admo­<lb></lb>ti; </s>
					<s id="N220A9">quia etiamſi nullus accederet nouus impetus radio AE, ſed tantùm <lb></lb>minimum pondus; </s>
					<s id="N220AF">haud dubiè attolleret radium EC: </s>
					<s id="N220B3">Adde quod ra­<lb></lb>dius EC impedit motum radij FE; </s>
					<s id="N220B9">igitur ab impetu huius producitur <lb></lb>etiam in illo impetus; igitur tùm ab impetu pugni, vel organi, tùm ab <lb></lb>impetu radij FE producitur impetus in radio EC. </s>
				</p>
				<pb pagenum="286" xlink:href="026/01/320.jpg"></pb>
				<p id="N220C7" type="main">
					<s id="N220C9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N220D5" type="main">
					<s id="N220D7"><emph type="italics"></emph>Hæc inæqualis distributio impetus eſt veriſſima cauſa girationis illius, quam <lb></lb>videmus in cylindro projecto per vibrationem ſiue brachium ſurſum ſiue deor­<lb></lb>ſum vibretur<emph.end type="italics"></emph.end>; </s>
					<s id="N220E4">quod ab omnibus facilè obſeruari poteſt ſit enim cylin­<lb></lb>drus ED libratus per arcum AD, ſtatimque demittatur; </s>
					<s id="N220EA">vbi attigit <lb></lb>punctum D, eſt quidem determinatus ad Tangentem DP, &amp; punctum I <lb></lb>ad Tangentem IR; </s>
					<s id="N220F2">quia tamen eſt minor impetus in I, quàm in D, &amp; <lb></lb>minor adhuc in E; </s>
					<s id="N220F8">certè D debet moueri velociùs quàm I, &amp; I quam E; </s>
					<s id="N220FC"><lb></lb>igitur motu recto moueri non poteſt prædictus cylindrus ED; </s>
					<s id="N22101">moueri <lb></lb>motu recto, id eſt in ſitu parallelo ED; </s>
					<s id="N22107">igitur extremitas D gyros aget, <lb></lb>quia retinetur ab aliis punctis, quorum tardior eſt motus; </s>
					<s id="N2210D">ſed hîc erit <lb></lb>motus mixtus, de quo in lib.9.agemus, &amp; totam rem iſtam fusè explica­<lb></lb>bimus; </s>
					<s id="N22115">hîc tantùm ſufficiat dixiſſe cauſam legitimam illius circuitionis <lb></lb>eſſe tantùm inæqualem illam diſtributionem impetus in cylindro ED; <lb></lb>aſſignauimus autem ibidem lineam, quam ſuo motu deſcribit extremitas <lb></lb>D, &amp; centrum, circa quod ſuos gyros agit. </s>
				</p>
				<p id="N2211F" type="main">
					<s id="N22121"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2212D" type="main">
					<s id="N2212F"><emph type="italics"></emph>Diu durat motus impreſſus rotæ in circulo verticali, ſi vel modicus ſit par­<lb></lb>tium affrictus<emph.end type="italics"></emph.end>; </s>
					<s id="N2213A">Probatur, quia cùm non deſtruatur impetus aliunde, quàm <lb></lb>ab affrictu, dicendum eſt minimum etiam ſingulis inſtantibus deſtrui <lb></lb>impetum; </s>
					<s id="N22142">igitur diu durat impetus; </s>
					<s id="N22146">igitur diu durat motus: nec eſt alia <lb></lb>ratio vulgaris illius experimenti, quo videmus perforatam acum circa <lb></lb>cylindrum leuigatiſſimum diu rotari. </s>
				</p>
				<p id="N2214E" type="main">
					<s id="N22150"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2215C" type="main">
					<s id="N2215E"><emph type="italics"></emph>Cum rota voluitur in circulo horizontali, non poteſt moueri applicata mini­<lb></lb>ma potentia<emph.end type="italics"></emph.end>; </s>
					<s id="N22169">Probatur, quia nullo modo rotatur ad intra, id eſt non pro­<lb></lb>ducit in ſe impetum, vt patet; </s>
					<s id="N2216F">igitur debet produci impetus in illa à po­<lb></lb>tentia applicata; igitur tot partes impetus, quot ſunt ſaltem in tota rota, <lb></lb>cum ſingulæ partes moueantur. </s>
				</p>
				<p id="N22177" type="main">
					<s id="N22179"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22185" type="main">
					<s id="N22187"><emph type="italics"></emph>Hinc difficiliùs mouetur in circulo horizontali quàm in verticali<emph.end type="italics"></emph.end>; patet, <lb></lb>quia in hoc à minima potentia applicata poteſt moueri per Th.21. ſecus <lb></lb>verò in illo per Th.41. igitur in horizontali difficiliùs moueri poteſt, <lb></lb>quàm in verticali. </s>
					<s id="N22196">Obſeruabis autem tribus modis volui poſſe huiuſmodi <lb></lb>rotam. </s>
					<s id="N2219B">Primò ſi in plano horizontali leuigatiſſimo voluatur. </s>
					<s id="N2219E">Secundò, ſi <lb></lb>circa cylindrum immobilem, qui aperto foramini inſeritur. </s>
					<s id="N221A3">Tertiò, ſi <lb></lb>vno concauo vnius axis ducatur per centrum rotæ, inſeratur vnus ſoli­<lb></lb>dus, quo fulcitus orbis conſiſtat in æquilibrio, difficiliùs voluitur primo <lb></lb>modo rota propter affrictum plurimarum partium; ſecundo faciliùs, ſed <lb></lb>longè faciliùs tertio ſic autem voluitur acus magnetica. </s>
				</p>
				<p id="N221AF" type="main">
					<s id="N221B1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N221BD" type="main">
					<s id="N221BF"><emph type="italics"></emph>Potentia applicata talis eſſe debet, vt poſſit imprimere impetum toti rota<emph.end type="italics"></emph.end>; </s>
					<s id="N221C8"><pb pagenum="287" xlink:href="026/01/321.jpg"></pb>cum enim non poſſit moueri vna pars rotæ ſine alia; </s>
					<s id="N221D0">certè, vel impetus <lb></lb>imprimitur omnibus, vel nulli per Th.37. lib.1.præſertim cùm totus im­<lb></lb>petus, qui rotæ imprimitur, ſit ab extrinſeco; nec enim accidit huic rotæ, <lb></lb>quod alteri, quæ ſitum verticalem habet, cuius ſemicirculus, cui admoue­<lb></lb>tur potentia per lineam deorſum motu naturali ex parte deorſum fertur, <lb></lb>vt ſupra explicatum eſt. </s>
					<s id="N221DE">Hinc totus impetus in rota horizontali produ­<lb></lb>citur ab extrinſeco; hinc ab ea tantùm potentia volui poteſt, quæ tot <lb></lb>partes impetus poteſt producere, quot ſunt neceſſariæ, vt omnibus parti­<lb></lb>bus plani illius circularis diſtribuantur, iuxta propagationem, quæ motui <lb></lb>circulari competit. </s>
				</p>
				<p id="N221EA" type="main">
					<s id="N221EC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N221F8" type="main">
					<s id="N221FA"><emph type="italics"></emph>Hinc in vtroque ſemicirculo plani producitur impetus ab ipſa potentia ap­<lb></lb>plicata, non vero ab impetu producto in altero ſemicirculo producitur impetus <lb></lb>in alio,<emph.end type="italics"></emph.end> vt conſtat ex dictis; </s>
					<s id="N22207">ſit enim rota horizonti parallela ABCD, &amp; <lb></lb>applicetur potentia in A per AO, non poteſt produci impetus in radio <lb></lb>AE, niſi tollatur impedimentum; </s>
					<s id="N2220F">impedit autem radius EC eo primo <lb></lb>inſtanti; </s>
					<s id="N22215">igitur debet ſimul tolli impedimentum, &amp; produci impetus in <lb></lb>AE; </s>
					<s id="N2221B">ſed non poteſt tolli impedimentum, niſi per impetum; </s>
					<s id="N2221F">igitur non <lb></lb>modò producitur impetus in AE, ſed etiam in EC; </s>
					<s id="N22225">atqui impetus in <lb></lb>EC non producitur ab impetu producto in EA; </s>
					<s id="N2222B">applicetur enim poten­<lb></lb>tia in F; </s>
					<s id="N22231">certè minùs impetus producetur in FE, quàm in EC, vt con­<lb></lb>ſtat; </s>
					<s id="N22237">igitur impetus in EC producitur ab ipſa potentia applicata in A, <lb></lb>vel in F; ſi verò rota ſit verticalis, ab eadem potentia, &amp; impetu innato <lb></lb>radij AE. vel ſemicirculi DA BE. </s>
				</p>
				<p id="N22240" type="main">
					<s id="N22242"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2224E" type="main">
					<s id="N22250"><emph type="italics"></emph>Hinc faciliùs mouetur rota motu illo circulari, quàm recto<emph.end type="italics"></emph.end>; </s>
					<s id="N22259">quia ſit dia­<lb></lb>meter AC, vt moueatur  motu recto per ſe debet produci impetus eiuſ­<lb></lb>dem perfectionis in omnibus partibus AC, vt conſtat ex dictis lib.  1. ſi <lb></lb>enim motus omnium partium eſt æqualis; </s>
					<s id="N22263">igitur &amp; impetus, at verò, vt <lb></lb>moueatur motu circulari in plano horizontali facto ſcilicet circulo <lb></lb>ABCD, &amp; admota potentia in A; </s>
					<s id="N2226D">certè impetus qui producitur in A, <lb></lb>&amp; in C, eſt minor impetu producto in F, &amp; in H; </s>
					<s id="N22273">igitur ſi producatur <lb></lb>in A impetus eiuſdem perfectionis ad motum circularem cum eo, qui <lb></lb>produceretur admotum rectum; </s>
					<s id="N2227B">haud dubiè totus impetus productus in <lb></lb>AC ad motum rectum eſt perfectior toto impetu producto ad circula­<lb></lb>rem; igitur difficiliùs ille, hic faciliùs producitur. </s>
				</p>
				<p id="N22283" type="main">
					<s id="N22285"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22291" type="main">
					<s id="N22293"><emph type="italics"></emph>Si applicetur potentia in F, difficiliùs mouebit rotam, quàm ſi applicetur in <lb></lb>A<emph.end type="italics"></emph.end>; </s>
					<s id="N2229E">ratio clara eſt, quia producet in F impetum eiuſdem perfectionis, <lb></lb>quem produceret in A, vt certum eſt; </s>
					<s id="N222A4">igitur maior erit impetus in to­<lb></lb>ta AC; </s>
					<s id="N222AA">igitur difficiliùs mouebitur rota: adde quod longitudo vectis <lb></lb>iuuat motum EC. </s>
				</p>
				<pb pagenum="288" xlink:href="026/01/322.jpg"></pb>
				<p id="N222B5" type="main">
					<s id="N222B7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 47.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N222C3" type="main">
					<s id="N222C5"><emph type="italics"></emph>Facilè cognoſcitur, in qua proportione potentia applicata puncte A faciliùs <lb></lb>vertat rotam, quàm applicata puncto F in circulo ſcilicet horizontali<emph.end type="italics"></emph.end>; </s>
					<s id="N222D0">ſit enim <lb></lb>ſolus vectis FC, cuius centrum ſit E; </s>
					<s id="N222D6">certè ſi vertatur in circulo hori­<lb></lb>zontali, potentia applicata extremitati C faciliùs verſabit, quàm appli­<lb></lb>cata puncto F, iuxta proportionem CE ad EF, vel ad HE; igitur po­<lb></lb>tentia applicata puncto H, vectis CF eſt eiuſdem momenti, cuius eſt ea­<lb></lb>dem applicata puncto F, quia æqualem prorſus effectum, ſcilicet impe­<lb></lb>tum, debet producere in vecte CF, vt moueatur in circulo horizontali <lb></lb>circa centrum E. </s>
					<s id="N222E7">Probatur vlteriùs, quia motus, æquabiles ſcilicet, ſunt <lb></lb>vt ſpatia, impetus vt motus, vires vt impetus; </s>
					<s id="N222ED">igitur applicata potentiæ <lb></lb>in C producat impetum in vecte CF, vt vertatur in plano horizontali, &amp; <lb></lb>C eo motu acquirat CS ſegmentum CE ſectorem CES; </s>
					<s id="N222F5">ſegmentum <lb></lb>verò FE ſectorem FEV; </s>
					<s id="N222FB">applicetur autem eadem potentia in F, vt ver­<lb></lb>tatur, idem vectis FC, &amp; producatur in F impetus æqualis impetui an­<lb></lb>tè producto in C; </s>
					<s id="N22303">haud dubiè punctum F percurret arcum FG eo tem­<lb></lb>pore, quo C priore motu percurrebat CS, vt patet; </s>
					<s id="N22309">quia arcus CS eſt <lb></lb>æqualis quadranti FG; igitur ſegmentum FE quadrantem FEG, &amp; ſeg­<lb></lb>mentum EC quadrantem CED. </s>
				</p>
				<p id="N22311" type="main">
					<s id="N22313"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 48.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2231F" type="main">
					<s id="N22321"><emph type="italics"></emph>Ex his determinantur omnes aliæ proportiones<emph.end type="italics"></emph.end>; </s>
					<s id="N2232A">ſi enim fit vectis AC <lb></lb>(quem ſuppono æqualem in omnibus ſuis partibus &amp; volubilem circa <lb></lb>centrum E in plano horizontali) &amp; applicetur potentia in puncto A, in <lb></lb>quo producat minimum impetum, quem poteſt immediatè producere ex <lb></lb>hypotheſi toties repetita, ita vt dato tempore percurrat A arcum AK, ſi <lb></lb>ſit vectis AH, &amp; applicetur potentia in A, mouebit faciliùs, quàm AC <lb></lb>iuxta proportionem 8/5; </s>
					<s id="N2233A">nam in vecte AC ſpatium eſt compoſitum ex <lb></lb>gemino ſectore AEK, CES, &amp; in vecte AH ſpatium eſt compoſitum <lb></lb>ex ſectore AEK &amp; ZEH, qui ſubquadruplus eſt AEK; </s>
					<s id="N22342">igitur hoc ſpa­<lb></lb>tium totum confectum hoc vltimo motu eſt ad prius ſpatium vt 5. ad 8. <lb></lb>igitur &amp; motus; </s>
					<s id="N2234A">igitur &amp; impetus; </s>
					<s id="N2234E">ſed quò minor eſt impetus, eſt maior <lb></lb>facilitas; igitur facilitas vltimi motus eſt ad facilitatem primi, vt 8. ad 5. <lb></lb>idem dico, ſi applicetur potentia in H. </s>
				</p>
				<p id="N22357" type="main">
					<s id="N22359">Si verò retento ſemper eodem vecte AC applicetur potentia tùm in <lb></lb>A, tùm in F, facilitas motus potentiæ applicatæ in A eſt ad facilitatem <lb></lb>motus potentiæ applicatæ in F, vt AE ad FE, vel vt AB ad AK, vel <lb></lb>vt AEB ad AEK, quæ omnia conſtant ex dictis; igitur applicata in F <lb></lb>in vecte AC eſt ad applicatam in F in vecte FE vt 5. ad 8. ſed hæc ſunt <lb></lb>ſatis clara, nec vlteriore explicatione indigent. </s>
				</p>
				<p id="N22367" type="main">
					<s id="N22369"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 49.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22375" type="main">
					<s id="N22377"><emph type="italics"></emph>Hinc quò propiùs ad centrum applicatur potentia, eò maior eſt difficultas <lb></lb>motus<emph.end type="italics"></emph.end>; </s>
					<s id="N22382">igitur ſi applicetur ipſi centro mathematicè conſiderato eſt infi­<lb></lb>nita difficultas; </s>
					<s id="N22388">igitur nulla potentia ſuperare poſſet hanc difficultatem; </s>
					<s id="N2238C"><pb pagenum="289" xlink:href="026/01/323.jpg"></pb>hinc vt artifices ſuas verſent rotas faciliùs, vel maximè curuum manu­<lb></lb>brium adhibent, vel affixo verſus circumferentiam in plano rotæ clauo <lb></lb>rotam agunt in orbes; quæ omnia clarè ſequuntur ex dictis. </s>
				</p>
				<p id="N22398" type="main">
					<s id="N2239A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 50.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N223A6" type="main">
					<s id="N223A8"><emph type="italics"></emph>Minor rota faciliùs vertitur in circulo horizontali; </s>
					<s id="N223AE">quàm maior.<emph.end type="italics"></emph.end> v. g.ro­<lb></lb>ta FGHI, quàm AB CD; </s>
					<s id="N223B9">quia ſcilicet producitur minùs impetus in <lb></lb>minore, quàm in maiore, vt patet; </s>
					<s id="N223BF">ſunt enim pauciores partes in mino­<lb></lb>re, plures in maiore; </s>
					<s id="N223C5">mouetur autem faciliùs minor, quàm maior iuxta <lb></lb>rationem diametrorum, permutando; </s>
					<s id="N223CB">Probatur, quia producatur impe­<lb></lb>tus in A maioris rotæ, ita vt dato tempore conficiat AK; </s>
					<s id="N223D1">tùm æqualis <lb></lb>impetus in F minoris rotæ; </s>
					<s id="N223D7">certè eodem tempore conficiet punctum F <lb></lb>arcum FG æqualem AK; </s>
					<s id="N223DD">ſed quadrans FEG eſt ad ſectorem AEK, vt <lb></lb>FE ad AE, vt conſtat; </s>
					<s id="N223E3">igitur facilitas motus minoris rotæ eſt ad facili­<lb></lb>tatem motus maioris, vt FE ad AE; </s>
					<s id="N223E9">igitur &amp; impetus; ſed quò minor <lb></lb>eſt impetus, eſt maior facilitas, &amp;c. </s>
				</p>
				<p id="N223EF" type="main">
					<s id="N223F1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 51.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N223FD" type="main">
					<s id="N223FF"><emph type="italics"></emph>Hinc tantæ molis poſſet eſſe rota in ſitu horizontali, vt à potentia etiam ve­<lb></lb>geta minimè verti poſſes,<emph.end type="italics"></emph.end> vt clarum eſt; </s>
					<s id="N2240A">neque hîc vllo modo conſidero <lb></lb>reſiſtentiam, quæ petitur à compreſſione, &amp; affrictu partium, qui haud <lb></lb>dubiè maior eſt in maiore rota; </s>
					<s id="N22412">ſed tantùm conſidero reſiſtentiam ne­<lb></lb>gatiuam, hoc eſt eam, quæ tantùm petitur à maiore numero partium ro­<lb></lb>tæ; </s>
					<s id="N2241A">quò enim ſunt plures ſubjecti partes, plures etiam partes impetus de­<lb></lb>ſiderantur, vt ſæpè dictum eſt; igitur maior potentia. </s>
				</p>
				<p id="N22420" type="main">
					<s id="N22422"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 52.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2242E" type="main">
					<s id="N22430"><emph type="italics"></emph>Destruitur impetus productus in hac rotæ horizontali, ſed ſenſim ſine ſenſu <lb></lb>propter affrictum,<emph.end type="italics"></emph.end> vt ſuprà dictum eſt: </s>
					<s id="N2243B">hinc eſſet motus perpetuus, ſi nul­<lb></lb>lus eſſet affrictus; </s>
					<s id="N22441">minùs impetus deſtruitur in maiore rota, quàm in mi­<lb></lb>nore: hinc gyrus minoris citiùs peragitur, &amp; deſinit minor citiùs <lb></lb>moueri. </s>
				</p>
				<p id="N22449" type="main">
					<s id="N2244B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 53.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22457" type="main">
					<s id="N22459"><emph type="italics"></emph>Minor rota citiùs ſuum gyrum abſoluit, quàm maior,<emph.end type="italics"></emph.end> vt dictum eſt ſuprà, <lb></lb>ſiue ſit in ſitu verticali, ſiue in ſitu horizontali; </s>
					<s id="N22464">ſed non eſt determinata <lb></lb>proportio, quàm hîc deſideramus; dico enim tempora motuum eſſe, vt <lb></lb>radios. </s>
					<s id="N2246C">v.g.tempus, quo rota minor FGHI ſuum gyrum abſoluit, eſſe ad <lb></lb>tempus, quo maior ABCD ſuum perficit, vt eſt radius FE ad radium <lb></lb>AE, quod demonſtro; </s>
					<s id="N22474">quia ſit impetus æqualis impreſſus puncto A ma­<lb></lb>ioris rotæ puncto F minoris, ita vt A &amp; F moueantur æquali motu; </s>
					<s id="N2247A">mi­<lb></lb>nor rota conficit duos orbes eo tempore, quo maior vnum conficit, vt <lb></lb>conſtat ex dictis; quia ſuppono. </s>
					<s id="N22482">v. g. circulum minoris eſſe ſubduplum; <lb></lb></s>
					<s id="N22483">igitur tempus, quo peragitur maior eſt ad tempus, quo peragitur minor <lb></lb>in ratione dupla; </s>
					<s id="N22484">igitur vt radius AE ad radium FE, quod erat demon­<lb></lb>ſtrandum. </s>
				</p>
				<pb pagenum="290" xlink:href="026/01/324.jpg"></pb>
				<p id="N22494" type="main">
					<s id="N22496"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 54.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N224A2" type="main">
					<s id="N224A4"><emph type="italics"></emph>Hinc ſi tantùm habeatur ratio vectis, maior difficiliùs verſatur in plano <lb></lb>horizontali, quàm minor.<emph.end type="italics"></emph.end> v.g. AE circa centrum E quam FE, producto <lb></lb>ſcilicet æquali motu in extremitate vtriuſque A &amp; F; </s>
					<s id="N224B3">ſi enim A dato <lb></lb>tempore percurrit AK; </s>
					<s id="N224B9">certè F percurret FG; </s>
					<s id="N224BD">ſed quadrans FEG eſt <lb></lb>ſubduplus ſectoris AEK, vt conſtat; </s>
					<s id="N224C3">igitur faciliùs vertitur FE, quàm <lb></lb>AE in proportione AE, ad FE: </s>
					<s id="N224C9">ſi tamen non conſideretur pondus ſeu <lb></lb>reſiſtentia vectis, haud dubiè ſi pondus ſit in Q, faciliùs mouebitur ope­<lb></lb>ra maioris vectis AE, quàm minoris FE; </s>
					<s id="N224D1">quia opera maioris mouetur <lb></lb>motu vt QT; </s>
					<s id="N224D7">operâ verò minoris motu vt QY, igitur difficiliùs opera <lb></lb>minoris in proportione QY ad QT; </s>
					<s id="N224DD">denique ſi pondus ſit in F maioris <lb></lb>vectis, &amp; in <foreign lang="grc">δ</foreign> minoris, ſitque AE ad AF, vt FE ad F <foreign lang="grc">δ</foreign>, æquale erit <lb></lb>momentum vtriuſque vectis ad mouendum pondus; </s>
					<s id="N224ED">quia arcus FV erit <lb></lb>æqualis arcui <foreign lang="grc">δ</foreign> Y; </s>
					<s id="N224F7">hîc autem nullomodo conſideratur vectis reſiſten­<lb></lb>tia; </s>
					<s id="N224FD">ſi verò producatur <expan abbr="tantũdem">tantundem</expan> impetus in toto vecte AE quamtum <lb></lb>in FE; </s>
					<s id="N22507">certè pro rata ſingulæ partes FE duplum habent; </s>
					<s id="N2250B">igitur tempo­<lb></lb>ra gyrorum erunt in ratione duplicata radiorum; </s>
					<s id="N22511">quia cum F habeat du­<lb></lb>plum impetum A, certè deſcribit orbem integrum eo tempore, quo A <lb></lb>quadrantem; </s>
					<s id="N22519">ergo F 4. orbes, dum A vnicum: ſed hæc ſunt facilia. </s>
				</p>
				<p id="N2251D" type="main">
					<s id="N2251F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 55.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2252B" type="main">
					<s id="N2252D"><emph type="italics"></emph>Si vectis BH ita pellatur in B in plano horizontali, in quo liberè moueri <lb></lb>poſſit<emph.end type="italics"></emph.end> <emph type="italics"></emph>v.g. dum aquæ ſupernatat, nulli centro immobili affixus, ſit que aqualis <lb></lb>denſitatis in omnibus ſuis partibus; mouebitur circa aliquod centrum, etiamſi <lb></lb>nulli centro affigatur.<emph.end type="italics"></emph.end></s>
					<s id="N22543"> Probatur, quia punctum B velociùs mouebitur, quàm <lb></lb>A vel H, vt patet experientiâ: </s>
					<s id="N22549">ratio eſt, quia minùs impetus producitur <lb></lb>in toto cylindro BH, applicata potentia in B, quàm in A, quod eſt cen­<lb></lb>trum grauitatis cylindri BA, vt iam oſtendimus Th. 68. 69. BB; </s>
					<s id="N22551">porrò <lb></lb>ratio à priori eſt, quia cùm impetus producatur tantùm ad extra, vt tol­<lb></lb>latur impedimentum motus, vt fusè oſtendimus lib.  1. certè in tantùm <lb></lb>amouetur impedimentum, in quantum amouetur corpus impediens mo­<lb></lb>tum alterius; </s>
					<s id="N2255D">atqui amoueri tantùm poteſt per motum; </s>
					<s id="N22561">igitur eo motu <lb></lb>amouetur, quo faciliùs amoueri poteſt, &amp; minore ſumptu, vt ita dicam, <lb></lb>id eſt minore impetu: </s>
					<s id="N22569">porrò cum potentia ſit determinata ad producen­<lb></lb>dum tabem impetum, immediatè ſcilicet, id eſt, in ea parte, cui immedia­<lb></lb>tè admouetur; </s>
					<s id="N22571">alioqui ſi poſſet minorem, &amp; minorem in infinitum pro­<lb></lb>ducere poſſet etiam immediatè ſine operâ organi mechanici quodlibet <lb></lb>pondus mouere, quod eſt abſurdum, de quo iam ſuprà; </s>
					<s id="N22579">ſit igitur potentia <lb></lb>applicata in A, ſcilicet in centro grauitatis cylindri BH; </s>
					<s id="N2257F">certè producit <lb></lb>maximum impetum, quem poteſt producere in cylindro BH (ſuppono <lb></lb>enim eſſe cauſam neceſſariam, &amp; producere perfectiſſimum impetum, <lb></lb>quem producere poſſit) producit inquam maximum ratione numeri; </s>
					<s id="N22589"><lb></lb>cùm in toto cylindro BH producat impetum eiuſdem perfectionis; </s>
					<s id="N2258E">igi­<lb></lb>tur mouetur motu recto; </s>
					<s id="N22594">igitur æquali in omnibus partibus; </s>
					<s id="N22598">igitur æqua­<lb></lb>lis eſt impetus in omnibus partibus, id eſt, æquè intenſus; </s>
					<s id="N2259E">ſit autem po-<pb pagenum="291" xlink:href="026/01/325.jpg"></pb>tentia applicata in B, ita vt in puncto B producatur impetus eiuſdem <lb></lb>perfectionis, de quo ſuprà: </s>
					<s id="N225A9">ſi mouetur motu circulari circa aliquod cen­<lb></lb>trum v. g. circa centrum H, &amp; punctum B conficiat arcum BD æqua­<lb></lb>lem rectæ b I, vel BL quam æquali tempore B vel A antè percurrebant <lb></lb>motu recto; </s>
					<s id="N225B7">certè totus cylindrus BH acquiret tantùm ſpatium BHD <lb></lb>motu circulari circa centrum H; </s>
					<s id="N225BD">ſed motu recto acquiſiuit ſpatium re­<lb></lb>ctanguli BK, quod maius eſt, vt patet; </s>
					<s id="N225C3">igitur motus circularis circa H <lb></lb>cylindri BH eſt ad rectum, vt ſector BHD ad rectangulum BK; </s>
					<s id="N225C9">igitur <lb></lb>facilitas motus circularis eſt ad facilitatem motus recti præſentis, vt re­<lb></lb>ctangulum BK ad ſectorem BHD; </s>
					<s id="N225D1">quænam verò ſit hæc proportio pa­<lb></lb>tet ex Cyclometria, ſuppoſitâ ratione Archimedis periphæriæ ad diame­<lb></lb>trum; </s>
					<s id="N225D9">igitur cum cylindrus impulſus in B faciliùs moueri poſſit motu <lb></lb>circulari, quàm recto, vt conſtat ex dictis; </s>
					<s id="N225DF">&amp; cùm eo motu moueatur, <lb></lb>quo faciliùs moueri poteſt; </s>
					<s id="N225E5">modò poſſit ad illum determinari, non mirum <lb></lb>eſt ſi eo moueatur, &amp; minor impetus producatur in eodem cylindro <lb></lb>BH; debet autem eſſe aliquod centrum huius motus, quod determina­<lb></lb>bimus paulò pòſt, poſtquam breuiter exilem quamdam objectionem de <lb></lb>impetu refutauerimus. </s>
				</p>
				<p id="N225F1" type="main">
					<s id="N225F3">Itaque obiiciunt aliqui, impetum non produci ad extra ab impetu; </s>
					<s id="N225F7"><lb></lb>quia ſcilicet impetus habet iam effectum ſcilicet motum; </s>
					<s id="N225FC">igitur aliud <lb></lb>munus non eſt illi imponendum; </s>
					<s id="N22602">igitur non producit alium effectum; <lb></lb>igitur non eſt cauſa impetus. </s>
				</p>
				<p id="N22608" type="main">
					<s id="N2260A">Reſpondeo primò, calor eſt cauſa rarefactionis; </s>
					<s id="N2260E">igitur non producit <lb></lb>alium calorem, quia habet iam vnum effectum; ſi tuum argumentum <lb></lb>concludit, meum quoque concludet. </s>
					<s id="N22616">Reſpondeo ſecundò, anima produ­<lb></lb>cit viſionem, ergo auditionem producere non poteſt, cùm iam habeat <lb></lb>vnum effectum: </s>
					<s id="N2261E">Dices, eandem cauſam poſſe habere plures effectus; cur <lb></lb>igitur negas de impetu? </s>
				</p>
				<p id="N22624" type="main">
					<s id="N22626">Reſpondeo tertiò directè, motum eſſe effectum impetus ad intra, quem <lb></lb>præſtat in ſuo ſubjecto; </s>
					<s id="N2262C">igitur eſt effectus formalis ſecundarius; </s>
					<s id="N22630">nec <lb></lb>alius eſſe poteſt, vt lib.1. demonſtrauimus; </s>
					<s id="N22636">at verò impetus eſt effectus <lb></lb>alterius impetus ad extra; </s>
					<s id="N2263C">igitur impetus eſt cauſa efficiens impetus, id­<lb></lb>que ad extra &amp; cauſa formalis, vel exigitiua motus ad intra; </s>
					<s id="N22642">ſicut calor <lb></lb>eſt cauſa formalis, vel exigitiua rarefactionis ad intra, cauſa verò effi­<lb></lb>ciens alterius caloris ad extra; </s>
					<s id="N2264A">&amp; verò nullo argumento probabis calo­<lb></lb>rem à calore produci, quo ego non probem impetum ab impetu produ­<lb></lb>ci; </s>
					<s id="N22652">igitur impetus eſt cauſa alterius impetus; </s>
					<s id="N22656">quia phyſicè loquendo il­<lb></lb>lud vocamus cauſam, ex cuius applicatione ſequitur neceſſariò effectus; </s>
					<s id="N2265C"><lb></lb>atqui applicato corpore ſolo ſine impetu nullus impetus producitur ad <lb></lb>extra, vt patet; </s>
					<s id="N22663">applicato verò cum impetu, producitur ſtatim alius im­<lb></lb>petus; </s>
					<s id="N22669">igitur ipſe impetus eſt cauſa: </s>
					<s id="N2266D">nec dicas requiri, vt conditionem; </s>
					<s id="N22671"><lb></lb>quia primò, nullum eſſet munus huius conditionis; nec enim applica­<lb></lb>ret cauſam ſubjecto, nec remoueret vllum impedimentum. </s>
					<s id="N22678">Secundò di­<lb></lb>cam ſimiliter calorem eſſe conditionem. </s>
					<s id="N2267D">Tertiò, dicerem etiam eſſe con­<lb></lb>ditionem ad motum. </s>
					<s id="N22682">Quartò, quis dicat corpus graue producere impe-<pb pagenum="292" xlink:href="026/01/326.jpg"></pb>tum ſurſum immediatè per ſe; ſed hæc omittamus, quæ leuia ſunt, præ­<lb></lb>ſertim cùm demonſtrauerimus luculenter lib.1.impetum produci ab im­<lb></lb>petu, vt ſcilicet tollatur impedimentum. </s>
				</p>
				<p id="N2268F" type="main">
					<s id="N22691"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 56.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2269D" type="main">
					<s id="N2269F"><emph type="italics"></emph>Quando pellitur cylindrus innatans<emph.end type="italics"></emph.end> <emph type="italics"></emph>in puncto L non vertitur circa cen­<lb></lb>trum A.<emph.end type="italics"></emph.end></s>
					<s id="N226AF"> Probatur, quia vertatur circa centrum A. v.g. &amp; percurrat B <lb></lb>arcum BC, &amp; totus cylindrus duos ſectores BAC, GAH; </s>
					<s id="N226B7">ſit autem <lb></lb>BC ſubduplus quadrantis BE, &amp; duo ſectores prædicti æquales qua­<lb></lb>dranti BAE; </s>
					<s id="N226BF">hoc poſito, ſpatium totius cylindri erit, vt quadrans; </s>
					<s id="N226C3">igi­<lb></lb>tur motus; igitur impetus: </s>
					<s id="N226C9">iam verò vertatur circa centrum H, ita vt B <lb></lb>percurrat arcum BD æqualem BC (erit autem BD ſubquadruplus qua­<lb></lb>drantis BF;) igitur totus cylindrus circa centrum H percurret ſpatium <lb></lb>ſectoris BHD æqualis quadranti BAE; </s>
					<s id="N226D3">igitur motus circa centrum H <lb></lb>eſt æqualis motui circa centrum A; </s>
					<s id="N226D9">igitur eſt eadem difficultas motus; <lb></lb>igitur non vertitur potiùs circa centrum A, quàm circa centrum H. </s>
				</p>
				<p id="N226E0" type="main">
					<s id="N226E2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 57.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N226EE" type="main">
					<s id="N226F0"><emph type="italics"></emph>Poteſt determinari centrum, circa quod vertitur cylindrus BH innatans <lb></lb>humido, modo ſupponatur æqualis denſitatis, &amp; craſſitudinis<emph.end type="italics"></emph.end>; </s>
					<s id="N226FB">diuidatur enim <lb></lb>AH bifariam in M: </s>
					<s id="N22701">Dico vertiginem futuram circa centrum M, quod <lb></lb>demonſtro; </s>
					<s id="N22707">quia vertatur circa M, &amp; extremitas B moueatur æquali <lb></lb>motu, quo priùs moueri ſupponebatur circa A, vel circa H; </s>
					<s id="N2270D">certè cùm <lb></lb>arcus BR ſit ad arcum BE vt BM ad BA, id eſt vt 3. ad 2. erit BN <lb></lb>ſubtripla BR, cùm ſit æqualis BC ſubdupla BE; </s>
					<s id="N22715">totum autem ſpatium <lb></lb>confectum hoc motu erit conflatum ex ſectoribus BMN, &amp; HMO, vt <lb></lb>patet: </s>
					<s id="N2271D">porrò ſector BMN eſt ſubtriplus quadrantis BMR, qui quadrans <lb></lb>eſt ad priorem BAE, vt 9. ad 4. id eſt, vt quadratum 3. ad quadratum 2. <lb></lb>vt conſtat; </s>
					<s id="N22725">igitur conflatum ex ſectore BMN, &amp; ſectore HMO eſt ad <lb></lb>quadrantem BAE, vel conflatum ex geminis ſectoribus BAC, HAG <lb></lb>vt 3 1/3 ad 4. ſi autem accipiatur centrum, vel inter MA, vel MH, maius <lb></lb>erit ſpatium, vt conſtat ex Geometria; </s>
					<s id="N2272F">igitur circa centrum M eſt mini­<lb></lb>mum ſpatium; </s>
					<s id="N22735">igitur minimus motus; </s>
					<s id="N22739">igitur minimus impetus; igitur <lb></lb>maxima facilitas; igitur ſi pellatur in B, vertetur circa M, quod hactenus <lb></lb>non explicatum modò ab aliquo, quod ſciam, verùm etiam ne propoſitum <lb></lb>quidem fuit. </s>
				</p>
				<p id="N22743" type="main">
					<s id="N22745"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 58.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22751" type="main">
					<s id="N22753"><emph type="italics"></emph>Hinc facilè dictu eſt, cur naues ita impulſæ ab altera extremitate circa al­<lb></lb>teram extremitatem non vertantur,<emph.end type="italics"></emph.end> vt patet experientiâ; </s>
					<s id="N2275E">quia hæc tendit <lb></lb>in partem oppoſitam; </s>
					<s id="N22764">nec etiam circa centrum grauitatis nauis, quod <lb></lb>etiam manifeſtis experientiis confirmatur, cùm ſcilicet impulſa extremi­<lb></lb>tas maiorem arcum deſcribat, ſed circa medium centrum inter vtrum­<lb></lb>que, ex quo principio tota remigationis ratio pendet: </s>
					<s id="N2276E">immò &amp; guber­<lb></lb>naculi, quod puppi affigitur, vt conſideranti patebit, quod ſufficiat indi­<lb></lb>caſſe; </s>
					<s id="N22776">ſi verò pellatur idem cylindrus in T. v.g. mouebitur circa cen-<pb pagenum="293" xlink:href="026/01/327.jpg"></pb>trum, quod eſt inter MH, licèt propiùs accedat ad M, quàm ad H, vt <lb></lb>conſtat ex calculatione; </s>
					<s id="N22783">eſt autem aliquod punctum inter TA, ex quo ſi <lb></lb>pellatur, mouebitur circa punctum H; </s>
					<s id="N22789">ſi verò aſſumantur alia puncta <lb></lb>verſus A, ex quibus pellatur, centra motus, erunt extra BH, ac proinde <lb></lb>extremitas B pulſa ex B mouetur per arcum BN; </s>
					<s id="N22791">pulſa ex A per rectam <lb></lb>AL; pulſa denique ex punctis, quæ ſunt inter BA, per arcus maiorum <lb></lb>circulorum, eò ſanè maiorum, quò propiùs punctum, ex quo pellitur, ac­<lb></lb>cedit ad A. </s>
				</p>
				<p id="N2279C" type="main">
					<s id="N2279E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 59.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N227AA" type="main">
					<s id="N227AC"><emph type="italics"></emph>Si pellatur nauis, vel cylindrus BH in puncto T, difficiliùs mouebitur, etiam <lb></lb>ex ſuppoſitione, quòd circa centrum M moueatur<emph.end type="italics"></emph.end>; </s>
					<s id="N227B7">quod eodem modo de­<lb></lb>monſtratur, quo ſuprà; </s>
					<s id="N227BD">accipiatur TZ æqualis BC; </s>
					<s id="N227C1">ſit autem BT æqua­<lb></lb>lis TA; </s>
					<s id="N227C7">certè arcus TS erit æqualis arcui BE; </s>
					<s id="N227CB">igitur ſector VMB erit <lb></lb>ſubduplus quadrantis BMR: </s>
					<s id="N227D1">ſimiliter ſector HMX erit ſubduplus qua­<lb></lb>drantis HMP; </s>
					<s id="N227D7">igitur motus erit, vt aggregatum ex his duobus ſectori­<lb></lb>bus; </s>
					<s id="N227DD">ſed cum applicatur potentia in B, motus eſt vt aggregatum ex duo­<lb></lb>bus ſectoribus BMN, HNO; </s>
					<s id="N227E3">ſit autem quadrans BMR, vt 9. &amp; qua­<lb></lb>drans HMP vt 1. igitur cum applicatur potentia in B, motus eſt ad mo­<lb></lb>tum cum applicatur in T vt 3 1/3 ad 5. igitur &amp; impetus; igitur facilitas <lb></lb>primi motus eſt ad facilitatem ſecundi, vt 5. ad 3 1/3 igitur in T diffici­<lb></lb>liùs pellitur, quàm in B. </s>
				</p>
				<p id="N227EF" type="main">
					<s id="N227F1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 60.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N227FD" type="main">
					<s id="N227FF"><emph type="italics"></emph>Hinc maxima difficultas eſt ad minimam, vt rectangulum BK ad aggre­<lb></lb>tum ex duobus ſectoribus BMN &amp; HMO, id eſt vt<emph.end type="italics"></emph.end> 6. 2/7 ad 2. (13/21): </s>
					<s id="N2280A">hinc <lb></lb>nauis, quæ pellitur è lateris puncto, quod reſpondet centro A, difficiliùs <lb></lb>longè mouetur; ſuppono enim nauim eſſe eiuſdem latitudinis, &amp; denſi­<lb></lb>tatis, nec ſabulo adhærere. </s>
				</p>
				<p id="N22814" type="main">
					<s id="N22816"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 61.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22822" type="main">
					<s id="N22824"><emph type="italics"></emph>Si ſuperponatur corpus plano rotæ, quæ voluitur in circulo horizontali, pro­<lb></lb>iicietur per Tangentem extremam.<emph.end type="italics"></emph.end> v.g. ſit rota ABCD horizontali pa­<lb></lb>rallela quæ vertatur ab A verſus B celeri motu, ſitque planum eius le­<lb></lb>uigatiſſimum; </s>
					<s id="N22835">imponatur globus etiam leuigatiſſimus puncto A: </s>
					<s id="N22839">dico <lb></lb>quod proiicietur per Tangentem AF, quia impetus, qui in illo impri­<lb></lb>mitur in puncto F eſt determinatus ad Tangentem A <foreign lang="grc">θ</foreign>; </s>
					<s id="N22845">ſed non impe­<lb></lb>ditur, quominus habeat ſuum motum; </s>
					<s id="N2284B">nec enim globus prædictus ita <lb></lb>affigitur plano rotæ, quin liberè ſeorſim moueri poſſit: </s>
					<s id="N22851">dixi per Tangen­<lb></lb>tem extremam, quia ſi imponatur globus puncto F; </s>
					<s id="N22857">certè non impelle­<lb></lb>tur per Tangentem F <foreign lang="grc">υ</foreign>, vt patebit ex ſequenti propoſitione; quod à nul­<lb></lb>lo hactenus, quod ſciam, obſeruatum fuit. </s>
				</p>
				<p id="N22863" type="main">
					<s id="N22865"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 62.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22871" type="main">
					<s id="N22873"><emph type="italics"></emph>Si imponatur globus puncto F plani horizontalis rotæ ABCD, non proii­<lb></lb>cietur per Tangentem F<emph.end type="italics"></emph.end> <foreign lang="grc">υ</foreign> quod primò manifeſtis experimentis comproba­<lb></lb>tum eſt. </s>
					<s id="N22883">Secundò probatur, quia dum globus his punctis, in quibus re-<pb pagenum="294" xlink:href="026/01/328.jpg"></pb>cta F <foreign lang="grc">υ</foreign> ſecat alios maiores circulos concentricos, ab his punctis nouum <lb></lb>impetum accipit, ratione cuius debet mutare lineam, quod certum eſt; </s>
					<s id="N22892"><lb></lb>cum autem circuli maiores rotæ moueantur velociùs, quàm FGH, po­<lb></lb>tiori iure mutari debet determinatio currentis globi in prædicto plano; </s>
					<s id="N22899"><lb></lb>quænam verò ſit hæc linea motus, difficilè dictu eſt; dicemus tamen <lb></lb>Tomo ſequenti, cum de lineis motus. </s>
				</p>
				<p id="N228A0" type="main">
					<s id="N228A2"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N228AE" type="main">
					<s id="N228B0">Obſeruabis primò, ſi ſit rota ABCD verticali circulo parallela, proii­<lb></lb>ci corpus ab eius periphæria per lineam minùs diſtantem ab ipſa peri­<lb></lb>phæria, quò maior eſt circulus; </s>
					<s id="N228B8">quia ſcilicet tunc angulus contingentiæ <lb></lb>eſt maior; </s>
					<s id="N228BE">hinc ſi terra moueretur (licèt reuerâ, quieſcat) non eſſet pe­<lb></lb>riculum, ne proiicerentur lapides per Tangentem, quæ vix diſtaret per <lb></lb>longum ſpatij tractum ab ipſo arcu terræ, vt obſeruat Galileus, &amp; res <lb></lb>ipſa facilis eſt; vnde miror nonnullos Philoſophos, alioquin doctiſſi­<lb></lb>mos, id argumenti contra motum terræ áttuliſſe, cuius nulla penitus <lb></lb>vis eſt, vt nonnemo in elementis Geometricis etiam mediocriter tinctus <lb></lb>facilè demonſtrabit. </s>
				</p>
				<p id="N228CE" type="main">
					<s id="N228D0">Obſerua ſecundò, ex his peti rationes projectionis fundæ, quæ in quo­<lb></lb>cunque circulo ſuos gyros habet; eſt enim eadem ratio. </s>
				</p>
				<p id="N228D6" type="main">
					<s id="N228D8">Obſerua tertiò, cum aliquod corpus incubat plano, quod motu recto <lb></lb>mouetur, numquam ab eo ſeparari, quamdiu planum ipſum æquabili mo­<lb></lb>tu mouetur; </s>
					<s id="N228E0">quià non mutatur determinatio impetus împreſſi corpori <lb></lb>incubanti; &amp; cùm æqualis ſit impetus tùm in plano, tùm in globo. </s>
					<s id="N228E6">v.g. <lb></lb>ſuperimpoſito, vtrumque æquali motu neceſſario mouetur; </s>
					<s id="N228ED">igitur ſine <lb></lb>projectione; </s>
					<s id="N228F3">ſic dum nauis recto curſu mouetur ſecundo flumine, omnia <lb></lb>quæ naui inſunt, æqualiter cum ipſa naui mouentur; at verò ſi planum <lb></lb>mouetur motu circulari, mutatur determinatio ſingulis inſtantibus, vnde <lb></lb>ſequitur projectio, vt dictum eſt ſuprà. </s>
				</p>
				<p id="N228FD" type="main">
					<s id="N228FF">Obſerua quartò, globum impoſitum rotæ ABCD initio tardiùs, tùm <lb></lb>deinde velociùs moueri, quò ſcilicet plùs recedit à centro E, quia à pun­<lb></lb>ctis plani, in quibus rotatur, &amp; quæ maiore motu vertuntur, maiorem <lb></lb>quoque impetus vim accipit. </s>
				</p>
				<p id="N22908" type="main">
					<s id="N2290A">Obſerua quintò, globum in plano ABCD per lineam FVB rotatum <lb></lb>moueri velociùs ipſis punctis plani, in quibus rotatur, excepto primo <lb></lb>inſtanti motus; </s>
					<s id="N22912">quia accipit à ſingulis punctis æqualem impetum ipſi <lb></lb>impetui, qui ipſis ineſt; qui cum priori conjunctus diagonalem facit, vt <lb></lb>ſuprà dictum eſt, cum de motu mixto &amp; lib.  1. cum de determinatione <lb></lb>motus. </s>
				</p>
				<p id="N2291C" type="main">
					<s id="N2291E">Obſeruabis ſextò, moueri motu accelerato maiori &amp; maiori, quod <lb></lb>certè mirum eſt; </s>
					<s id="N22924">cum tamen rota in cuius plano horizontali rotatur, <lb></lb>motu æquali moueatur; </s>
					<s id="N2292A">maximè autem creſcit ille motus, quia priorem <lb></lb>ſemper impetum ſeruat, cui nouus ſemper accedit, exceptis paucis <lb></lb>gradibus, qui ob conflictum determinationum, &amp; impetuum excidunt; <pb pagenum="295" xlink:href="026/01/329.jpg"></pb>quia quotieſcunque nouus impetus ad nouam lineam determinatus ac­<lb></lb>cedit priori, non eſt dubium, quin deſtruatur aliquid impetus, quia ali­<lb></lb>quid fruſtrà eſt, vt lib.  1. demonſtratum eſt. </s>
				</p>
				<p id="N2293B" type="main">
					<s id="N2293D">Obſerua ſeptimò, aliud mirabilius, ſcilicet impetum poſſe produci in <lb></lb>eo mobili, cui iam ineſt maior impetus, quàm inſit alteri, à quo nouus <lb></lb>imprimitur; quod certè nunquam fieri poteſt, cum nouus impetus ad <lb></lb>eandem lineam eſt determinatus, ad quam prior impetus, qui mobili <lb></lb>ineſt, iam determinatus eſt. </s>
				</p>
				<p id="N22949" type="main">
					<s id="N2294B">Obſeruabis octauò; </s>
					<s id="N2294E">quotieſcunque planum, quod mouetur motu re­<lb></lb>cto, vel deſinit illicò moueri, vel tardiùs mouetur, tunc globus incubans <lb></lb>mouetur vlteriùs, &amp; quaſi proiicitur; </s>
					<s id="N22956">hoc ipſum vidimus in naui: </s>
					<s id="N2295A">ratio <lb></lb>clara eſt; quia prior impetus in globo productus, qui manet intactus, <lb></lb>ſuum effectum habet. </s>
				</p>
				<p id="N22962" type="main">
					<s id="N22964">Obſeruabis nonò, ſi terra moueretur ex hypotheſi Copernici, quæ <lb></lb>tamen falſiſſima eſt, idem Parallelus terreſtris globi inæquali motu mo­<lb></lb>ueretur. </s>
					<s id="N2296B">v. g. idem punctum Æquatoris, dum Soli directè reſpondet de <lb></lb>meridie tardiore motu; </s>
					<s id="N22975">oppoſitum verò de media nocte velociùs moue­<lb></lb>retur; </s>
					<s id="N2297B">ex qua tamen inæqualitate motus aliqui malè ſuſpicantur æſtum <lb></lb>maris oriri; </s>
					<s id="N22981">quippe licèt fortè aliquis æſtus maris ex illa hypotheſi ſe­<lb></lb>queretur, longè tamen diuerſus ab eo, qui nunc eſt; nam primò, iis omni­<lb></lb>bus qui eidem Meridiano ſubſunt eodem tempore accideret æſtus ſcili­<lb></lb>cet de meridie. </s>
					<s id="N2298B">Secundò his, qui propiùs accedunt ad polos longè minor <lb></lb>æſtus eſſet; vtrumque autem falſum eſſe conſtat. </s>
					<s id="N22991">Tertiò, eadem ſemper <lb></lb>hora in ſingulis punctis eiuſdem Paralleli ſeorſim ferueret æſtus; ſed de <lb></lb>his aliàs plura. </s>
				</p>
				<p id="N22999" type="main">
					<s id="N2299B">Obſeruabis decimò, quò diutius potentia motrix manet applicata, ac­<lb></lb>cedente continenter maiore niſu, maior quoque impetus producitur in <lb></lb>rota, quod clarum eſt; vnde diutiùs deinde rota verſatur. </s>
				</p>
				<p id="N229A3" type="main">
					<s id="N229A5">Obſeruabis vndecimò, trochum in gyros actum ita aliquando verſari, <lb></lb>vt ſtare prorſus immobilis videatur; quia ferreum fulcrum, cui ligneus <lb></lb>conus innititur vel excauato ſibi foramine excurrere vltrà non poteſt, <lb></lb>vel motu centri penitus quieſcente ſupereſt tantùm motus orbis. </s>
				</p>
				<p id="N229AF" type="main">
					<s id="N229B1">Obſeruabis duodecimò, antequam quieſcat trochus, inclinata verti­<lb></lb>gine per aliquod tempus verſari, moxque, vbi decidit, in plano ipſo ad <lb></lb>inſtar globi adhuc rotari; </s>
					<s id="N229B9">ſed quia hæc pertinent ad motum mixtum ex <lb></lb>circularibus in libro 9. remitto: &amp; verò multa ſunt in hoc trochi motu, <lb></lb>quæſi attentè conſiderentur, maximam admirationem mouere poſſint. </s>
				</p>
				<p id="N229C1" type="main">
					<s id="N229C3">Obſeruabis decimotertiò, ſi ferrum, quo trochus armatur, ita eſſet <lb></lb>infixum vt reuerâ centrum grauitatis cum puncto contactus plani con­<lb></lb>necteret; </s>
					<s id="N229CB">nulla eſſet inclinata vertigo, antequam impetus extinguere­<lb></lb>tur; cur enim potiùs in vnam partem, quàm in aliam. </s>
				</p>
				<p id="N229D1" type="main">
					<s id="N229D3">Obſeruabis decimoquarto aquam in vorticibus facilè circulari motu <lb></lb>conuolui, &amp; aëra, vel halitum in turbinibus; </s>
					<s id="N229D9">quia ſcilicet vel nullus, vel <lb></lb>modicus eſt obex: idem dico de nube, fumo, acu magnetica, trocho, vel <lb></lb>ſphæra læuigata in plano leuigato. </s>
				</p>
				<pb pagenum="296" xlink:href="026/01/330.jpg"></pb>
				<p id="N229E5" type="main">
					<s id="N229E7">Obſeruabis decimoquintò, ſi in eadem parte plani diu vertatur Tro­<lb></lb>chus, quaſi excauat ſibi foramen; </s>
					<s id="N229ED">arrodit enim plani partes ſuis denti­<lb></lb>culis; etiam pelitum ferrum: </s>
					<s id="N229F3">inde etiam impetum deſtrui certum eſt; <lb></lb>nec enim ſine reſiſtentia id fieri poteſt. </s>
				</p>
				<p id="N229F9" type="main">
					<s id="N229FB">Obſeruabis decimoſextò, impetum eundem habere poſſe motum cir­<lb></lb>cularem, &amp; rectum in ſublunaribus, &amp; per accidens determinari tantùm <lb></lb>ad motum circularem, ratione ſcilicet impedimenti, vt conſtat ex dictis. </s>
				</p>
				<p id="N22A02" type="main">
					<s id="N22A04">Obſeruabis decimoſeptimò, motum rectum accelerari, ſed diu non <lb></lb>durare; </s>
					<s id="N22A0A">retardari verò violentum, ac æquè diu durare; </s>
					<s id="N22A0E">circularem <lb></lb>verò non accelerari, ſed minùs retardari, atque adeo <lb></lb>longè diutiùs durare; quia tantùm per accidens <lb></lb>retardatur, ſed de his <lb></lb>ſatis. <lb></lb><figure id="id.026.01.330.1.jpg" xlink:href="026/01/330/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N22A20">
				<pb pagenum="297" xlink:href="026/01/331.jpg"></pb>
				<figure id="id.026.01.331.1.jpg" xlink:href="026/01/331/1.jpg"></figure>
				<p id="N22A2A" type="head">
					<s id="N22A2C"><emph type="center"></emph>LIBER OCTAVVS, <lb></lb><emph type="italics"></emph>DE MOTV FVNEPENDVLORVM.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N22A3A" type="main">
					<s id="N22A3C">NIHIL inuenio apud antiquos, quod ad <lb></lb>hoc genus motus pertineat; </s>
					<s id="N22A42">ſunt tamen <lb></lb>plerique recentiores qui fusè de illo di­<lb></lb>ſputarunt, quorum haud dubiè princi­<lb></lb>pem locum obtinet Galileus, qui ſanè <lb></lb>mirabiles aliquas huius motus affectiones explicat <lb></lb>tùm in gemino Syſthemate; tùm in Dialogis, cui ac­<lb></lb>cedunt Balianus Mercennus, &amp; nonnulli alij. </s>
				</p>
				<p id="N22A52" type="main">
					<s id="N22A54">Ego verò in hoc libro omnium vibrationum cau­<lb></lb>ſas inquiram, quæ ſunt duplicis generis: </s>
					<s id="N22A5A">Primum eſt <lb></lb>earum, quibus vibrata hinc inde funependula agun­<lb></lb>tur, quæ titulum huic libro fecerunt; ſunt autem tres <lb></lb>funependulorum ſpecies. </s>
					<s id="N22A64">Prima eſt eorum, quæ in al­<lb></lb>tera extremitate fune appenſa vibrantur in circulo <lb></lb>verticali. </s>
					<s id="N22A6B">Secunda eſt eorum, quæ ab altera etiam ex­<lb></lb>tremitate appenſa fune priùs obtorto in circulo ho­<lb></lb>rizontali ſuos agunt gyros. </s>
					<s id="N22A72">Tertia eſt chordarum, <lb></lb>quarum vtraque extremitas clauo immobili affigi­<lb></lb>tur. </s>
					<s id="N22A79">Secundum genus vibrationum eſt earum, quibus <lb></lb>aguntur grauia cum à ſuo centro grauitatis remouen­<lb></lb>tur, vt ſeſe reducant, quarum ſunt duæ ſpecies; prima <lb></lb>eſt earum, quibus vibratur in circulo verticali corpus <lb></lb>aliquod circa alteram extremitatem, vt campana. </s>
					<s id="N22A85"><lb></lb>Secunda eſt earum, quibus vibrantur grauia circa <pb pagenum="298" xlink:href="026/01/332.jpg"></pb>punctum proximum ſuo centro grauitatis, ſic v. g. <lb></lb>trabs trabi ſuperimpoſita libratur, &amp; vibratur. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N22A96" type="main">
					<s id="N22A98"><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 id="N22AA4" type="main">
					<s id="N22AA6"><emph type="italics"></emph>VIbratio funependuli primæ ſpeciei eſt motus circularis, quo aſcendit, &amp; <lb></lb>deſcendit funependulum<emph.end type="italics"></emph.end>; </s>
					<s id="N22AB1">ſunt autem aliæ æquales, aliæ inæquales: </s>
					<s id="N22AB5"><lb></lb>æquales ſunt, quæ ſunt eiuſdem radij, inæquales è contrario: </s>
					<s id="N22ABA">aliæ ſimi­<lb></lb>les, quæ ſimiles arcus complectuntur; diſſimiles è contrario: </s>
					<s id="N22AC0">aliæ æquè <lb></lb>diuturnæ, quæ temporibus æqualibus perficiuntur: </s>
					<s id="N22AC6">aliæ integræ, quarum <lb></lb>deſcenſus integrum quadrantem comprehendit; non integræ è contra­<lb></lb>rio; </s>
					<s id="N22ACE">portio vetò vibrationis eſt arcus; ſed hæc omnia in propoſito. </s>
					<s id="N22AD2">Sche­<lb></lb>mate explicamus; </s>
					<s id="N22AD8">ſit enim plumbeus globus E appenſus fune EA ex <lb></lb>puncto A immobili, AE eſt radius, vel longitudo funependuli E, NEC <lb></lb>eſt vibratio integra, LER non integra, LE portio vibrationis NEC, <lb></lb>NL &amp; MF portiones ſimiles, MDB, NEC vibrationes inæquales: ex <lb></lb>his reliqua facilè intelligi poterunt. </s>
				</p>
				<p id="N22AE4" type="main">
					<s id="N22AE6"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22AF3" type="main">
					<s id="N22AF5"><emph type="italics"></emph>Momentum eſt exceſſus virtutis mouentis ſupra reſistentiam alterius.<emph.end type="italics"></emph.end> v. g. <lb></lb>ſint brachia vectis inæqualia, momentum eſt in longiore ea vis, qua de­<lb></lb>ſcendens deorſum ſurſum attollit minus ſeu breuius. </s>
				</p>
				<p id="N22B04" type="main">
					<s id="N22B06"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22B13" type="main">
					<s id="N22B15"><emph type="italics"></emph>Tenſio eſt vis allata ab extrinſeco corpore, qua augetur eius extenſio<emph.end type="italics"></emph.end>; </s>
					<s id="N22B1E">res <lb></lb>eſt clara in tenſo fune, quomodocunque id fiat, quod hîc non diſcutio; <lb></lb>compreſſio verò eſt vis illata ab extrinſeco corpori, qua contrahitur eius <lb></lb>extenſio v.g. in intorto fune. </s>
				</p>
				<p id="N22B2A" type="main">
					<s id="N22B2C">Obſeruabis autem ad tenſionem, &amp; compreſſionem requiri, vt ſubla­<lb></lb>ta illa vi extrinſeca, vel impedimento admoto corpus tenſum, vel com­<lb></lb>preſſum ad priſtinam extenſionem ſeſe reducat; neque diſputo de mo­<lb></lb>do, quo id fieri poſſit, qui alterius loci eſt. </s>
				</p>
				<p id="N22B38" type="main">
					<s id="N22B3A"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22B47" type="main">
					<s id="N22B49"><emph type="italics"></emph>Corpus graue funependulum à ſuæ quiete, vel è ſuo centro grauitatis remo­<lb></lb>tum deſcendit ſuâ ſponte, iterumque aſcendit, id eſt vibratur<emph.end type="italics"></emph.end>; cer­<lb></lb>tum eſt. </s>
				</p>
				<p id="N22B56" type="main">
					<s id="N22B58"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22B65" type="main">
					<s id="N22B67"><emph type="italics"></emph>Funependula longiora maiore tempore ſuam vibrationam conficiunt, bre­<lb></lb>uiora minore<emph.end type="italics"></emph.end>; quod etiam certum eſt. </s>
				</p>
				<p id="N22B72" type="main">
					<s id="N22B74"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22B81" type="main">
					<s id="N22B83"><emph type="italics"></emph>Motus naturalis eſt acceleratus in tempore ſenſibili in proportione nume­<lb></lb>rorum<emph.end type="italics"></emph.end> 1.3.5.7. <emph type="italics"></emph>&amp;c.<emph.end type="italics"></emph.end> quod multis explicatum eſt lib.  2. ſi verò acceleratio <pb pagenum="299" xlink:href="026/01/333.jpg"></pb>aſſumatur in ſingulis inſtantibus finitis, eſt iuxta ſeriem ſimplicem nu­<lb></lb>merorum 1. 2. 3. 4. &amp;c. </s>
				</p>
				<p id="N22B9A" type="main">
					<s id="N22B9C"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22BA9" type="main">
					<s id="N22BAB"><emph type="italics"></emph>Motus in plano inclinato eſt ad motum in perpendiculari, vt perpendicula­<lb></lb>ris ad inclinatam<emph.end type="italics"></emph.end>; </s>
					<s id="N22BB6">quod etiam lib.5.fusè explicatum eſt; eſt autem ſem­<lb></lb>per in plano inclinato motus prioris grauis. </s>
				</p>
				<p id="N22BBC" type="main">
					<s id="N22BBE"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22BCB" type="main">
					<s id="N22BCD"><emph type="italics"></emph>In quadrante incubante perpendiculariter plano horizontali, tot ſunt di­<lb></lb>uerſa plana inclinata, quot ſunt puncta, ſeu Tangentes<emph.end type="italics"></emph.end>; hoc etiam certum <lb></lb>eſt, &amp; angulus contingentiæ maior eſt in minore circulo, minor in <lb></lb>maiore. </s>
				</p>
				<p id="N22BDC" type="main">
					<s id="N22BDE"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22BEB" type="main">
					<s id="N22BED"><emph type="italics"></emph>Nullus arcus circuli eſt vt linea recta, nec ſine errore accipi poteſt vt recta,<emph.end type="italics"></emph.end><lb></lb>contrariam hypotheſim aliqui ſupponunt, quam tamen falſam eſſe ſciunt; </s>
					<s id="N22BF7"><lb></lb>licèt enim quoad ſenſum error ſubeſſe non poſſit; </s>
					<s id="N22BFC">attamen repugnat <lb></lb>Geometriæ: </s>
					<s id="N22C02">hinc ſuppoſitio noſtra Geometricè vera eſt; ſed de hoc in­<lb></lb>frà fusè. </s>
				</p>
				<p id="N22C08" type="main">
					<s id="N22C0A"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C17" type="main">
					<s id="N22C19"><emph type="italics"></emph>Tamdiu durat motus, quandiu durat impetus; hic autem tandiu durat, <lb></lb>quamdiu non eſt frustrà.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N22C23" type="main">
					<s id="N22C25"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C32" type="main">
					<s id="N22C34"><emph type="italics"></emph>Noua determinatio impotus cum priore facit mixtum ſi determinatio mixta <lb></lb>facit nouam lineam.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N22C3D" type="main">
					<s id="N22C3F"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C4C" type="main">
					<s id="N22C4E"><emph type="italics"></emph>Quotieſcunque fit mixta determinatio per acceſſionem noni impetus, de­<lb></lb>ſtruitur aliquid impetus prioris, patet.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N22C57" type="main">
					<s id="N22C59"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C66" type="main">
					<s id="N22C68"><emph type="italics"></emph>Impetus innatus non concurrit ad motum ſurſum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N22C6F" type="main">
					<s id="N22C71"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C7E" type="main">
					<s id="N22C80"><emph type="italics"></emph>In inclinata minùs destruitur impetus dato tempore, quàm in perpendicu­<lb></lb>lari ſurſum, plùs verò destruitur, quò propiùs accedit ad verticalem<emph.end type="italics"></emph.end>; hæc <lb></lb>omnia quæ loco Axiomatum hîc propoſui, in ſuperioribus libris, præ­<lb></lb>ſertim in Quinto abundè demonſtraui. </s>
				</p>
				<p id="N22C8F" type="main">
					<s id="N22C91"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22C9E" type="main">
					<s id="N22CA0"><emph type="italics"></emph>Funependulum deſcendit motu accelerato<emph.end type="italics"></emph.end>; </s>
					<s id="N22CA9">experientia certa eſt, eius <lb></lb>ratio eſt eadem cum ea, quam attuli lib.2. de motu naturali, vt eius ac­<lb></lb>celerationem demonſtrarem; </s>
					<s id="N22CB1">ſcilicet impetus nouus ſingulis inſtantibus <lb></lb>producitur, cùm ſit ſemper eadem cauſa applicata; </s>
					<s id="N22CB7">corpus enim graue <lb></lb>ſua ſponte deſcendit; </s>
					<s id="N22CBD">quod autem impetui priori accedat, patet; </s>
					<s id="N22CC1">nec <lb></lb>enim deſtruitur ſaltem totus alioqui fruſtrà produceretur, contra Axio­<lb></lb>ma primum, adde quòd in plano inclinato deorſum graue deſcendit motu <pb pagenum="300" xlink:href="026/01/334.jpg"></pb>naturaliter accelerato; </s>
					<s id="N22CCE">igitur in arcu NLE. v. g. qui habet rationem <lb></lb>plani inclinati in omnibus ſuis punctis per hypotheſim 5. Præterea ictus <lb></lb>eſt maior, quò maior eſt arcus vibrationîs; </s>
					<s id="N22CDA">igitur impetus maior; </s>
					<s id="N22CDE">igitur <lb></lb>creſcit impetus; </s>
					<s id="N22CE4">igitur motus eſt acceleratus; </s>
					<s id="N22CE8">deinde maior vibratio, &amp; <lb></lb>minor eiuſdem penduli fiunt ferè temporibus æqualibus; </s>
					<s id="N22CEE">igitur neceſſa­<lb></lb>riò acceleratur motus: </s>
					<s id="N22CF4">Denique probatur euidenter non deſtrui totum <lb></lb>priorem impetum; </s>
					<s id="N22CFA">quia ſcilicet idem eſt impedimentum, ſi quod eſt ad <lb></lb>productionem noui, quod eſt ad conſeruationem prioris; </s>
					<s id="N22D00">ſed illud im­<lb></lb>pedimentum, id eſt inclinatio plani, non impedit productionem noui, <lb></lb>licèt minoris, vt videbimus paulò pòſt; </s>
					<s id="N22D08">quia ſcilicet in omni plano in­<lb></lb>clinato corpus graue mouetur per hypoth.4. igitur non impedit conſer­<lb></lb>uationem prioris, ſaltem totam, licèt fortè aliquid deſtrueretur, de quo <lb></lb>paulò pòſt; </s>
					<s id="N22D12">igitur acceleratur neceſſariò ille motus: </s>
					<s id="N22D16">Et hæc eſt ratio à <lb></lb>priori huius effectus, quòd ſcilicet plùs addatur impetus, quàm tollatur; </s>
					<s id="N22D1C"><lb></lb>igitur remanet maior; </s>
					<s id="N22D21">igitur velocior motus; in qua verò ratione minùs <lb></lb>deſtruatur quàm producatur, vel nouus ſit minor priore, dicemus <lb></lb>infrà. </s>
				</p>
				<p id="N22D29" type="main">
					<s id="N22D2B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22D38" type="main">
					<s id="N22D3A"><emph type="italics"></emph>In motu funependuli decreſcunt ſemper incrementa motus.<emph.end type="italics"></emph.end></s>
					<s id="N22D41"> Probatur faci­<lb></lb>lè; </s>
					<s id="N22D46">quia cùm in ſingulis punctis deſcenſus arcus NE mutetur ratio plani <lb></lb>inclinati diuerſa ab ea, quæ eſt in puncto <expan abbr="q;">que</expan> ſunt enim vt Tangentes; </s>
					<s id="N22D50"><lb></lb>certè Tangentes punctorum, quæ propiùs accedunt ad N, accedunt <lb></lb>etiam propiùs ad perpendicularem deorſum, à qua longiùs recedunt <lb></lb>Tangentes, quæ accedunt propiùs ad E, vt conſtat; </s>
					<s id="N22D59">at qui motus in planis, <lb></lb>quæ accedunt propiùs ad horizontalem, minor eſt; </s>
					<s id="N22D5F">igitur incrementa <lb></lb>motus quæ in deſcenſu NE accedunt, minora ſunt verſus E, maiora ver­<lb></lb>ſus N; igitur decreſcunt, quod erat demonſtrandum. </s>
				</p>
				<p id="N22D67" type="main">
					<s id="N22D69">Obſeruabis iam demonſtratum lib.5. Th.62.63. hæc incrementa eſſe, <lb></lb>vt ſinus arcus reſidui, quæ tu conſule, ne hic repetere cogar. </s>
				</p>
				<p id="N22D6E" type="main">
					<s id="N22D70"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22D7D" type="main">
					<s id="N22D7F"><emph type="italics"></emph>Hinc ſemper creſcit motus funependuli in deſcenſu arcus NE, ſed minori­<lb></lb>bus ſenſim incrementis<emph.end type="italics"></emph.end>; </s>
					<s id="N22D8A">quod etiam aliàs obſeruatum eſt; </s>
					<s id="N22D8E">vnde neceſſariò <lb></lb>concludo minùs accelerari in quadrante NE, quàm in perpendiculari <lb></lb>NS, quod demonſtratum eſt, &amp; minus ſpatium percurri in arcu NE <lb></lb>æquali ſcilicet tempore, quàm in perpendiculari NS, quod neceſſarium <lb></lb>eſt: </s>
					<s id="N22D9A">Nec eſt quod aliquis ſua experimenta opponat, ſcilicet quadrantem <lb></lb>NE percurri tempore vnius ſecundi, ſi radius AE ſit tripedalis, cùm <lb></lb>alioqui perpendiculum AE graue corpus percurrat eodem tempore, <lb></lb>quorum alterum, vel potiùs vtrumque falſum eſſe neceſſe eſt; </s>
					<s id="N22DA4">nam primò <lb></lb>quadrans NE eſt maior radio AE; </s>
					<s id="N22DAA">igitur percurrit citiùs AE quàm <lb></lb>NE: ſecundò, minora ſunt motus incrementa in quadrante, quia ſin­<lb></lb>gula puncta illius habent rationem plani inclinati, quis autem tam ac­<lb></lb>curatè in tripedali <expan abbr="pẽdulo">pendulo</expan> iuſtum tempus obſeruare poſſit? </s>
					<s id="N22DB8">nec accuratæ <pb pagenum="301" xlink:href="026/01/335.jpg"></pb>illæ obſeruationes eſſe poſſunt, quæ ſenſibiles non ſunt, ſiue aures con­<lb></lb>ſulas, quæ ſonum excipiunt, ſiue oculos, qui motum ipſum obſeruant. </s>
					<s id="N22DC2"><lb></lb>Tertiò, ſi oculos conſulis; num ipſi potiùs vident motum vibrati pendu­<lb></lb>li eſſe tardiorem, quàm demiſſi per lineam perpendicularem? </s>
					<s id="N22DC9">nec alius <lb></lb>nodus hic ſoluendus eſt, nec aër ſenſibiliter pilæ plumbeæ reſiſtit, nec <lb></lb>minùs reſiſtit motui circulari quàm recto. </s>
					<s id="N22DD0">Denique compertum eſt à me <lb></lb>in longiore pendulo motum in arcu eſſe tardiorem, quàm in perpendi­<lb></lb>culo: </s>
					<s id="N22DD8">nodus obſeruationis facilis eſt, nam adhibui AE planum durum <lb></lb>reſpondens accuratè perpendiculari, cui aliud planum E <foreign lang="grc">β</foreign> ad angulos <lb></lb>rectos affixum erat <expan abbr="reſpõdens">reſpondens</expan> Tangenti; </s>
					<s id="N22DE8">tùm demiſſo ex A globulo plum­<lb></lb>beo ſimulque alio æquali pendulo ſcilicet circa A ex N per NE; </s>
					<s id="N22DEE">ex quo <lb></lb>accidit citiùs auditum eſſe ictum globi cadentis perpendiculariter, quàm <lb></lb>vibrati per arcum NE: quis autem hoc non videat, ſiue ſenſum ipſum, <lb></lb>ſiue rationem conſulat? </s>
					<s id="N22DF8">fuit meum pendulum 12. pedes longum. </s>
				</p>
				<p id="N22DFB" type="main">
					<s id="N22DFD">Quæreret aliquis primò quanta fuerit differentia temporum Secundò, <lb></lb>quanto tempore globus pendulus ex N in E peruenerit. </s>
					<s id="N22E02">Reſpondeo inu­<lb></lb>tilem eſſe quæſtionem; </s>
					<s id="N22E08">nec enim minimas illas temporum differentias <lb></lb>ſenſu metiri poſſumus; </s>
					<s id="N22E0E">ſi enim affirmarem cum nonnullis corpus graue <lb></lb>per medium liberum 12. ſpatij pedes conficere vno temporis ſecundo; </s>
					<s id="N22E14"><lb></lb>certè ſi quis contenderet vel deeſſe, vel ſupereſſe 1000. inſtantia; quonam <lb></lb>argumento, vel experimento contrarium euincere poſſem? </s>
					<s id="N22E1B">quod certè <lb></lb>dictum eſſe velim, vt vel inde oſtendatur in caſſum laborare eos, qui <lb></lb>hanc ſcientiam his tantùm experimentis confirmant, quæ circa inſenſi­<lb></lb>bilia verſantur. </s>
					<s id="N22E24">Equidem magnifacio in rebus phyſicis experimentum, <lb></lb>ſine quo nulla hypotheſis eſſe poteſt; </s>
					<s id="N22E2A">at modo ſenſibile ſit, alioqui cer­<lb></lb>tum eſſe non poteſt; </s>
					<s id="N22E30">ſi autem ſenſibile eſt, omnibus commune eſſe debet, <lb></lb>sum ſenſus applicent; </s>
					<s id="N22E36">igitur nunquam vir prudens ſeſe accinget ad in­<lb></lb>dagandam rationem alicuius experimenti, quod certum eſſe non poteſt: </s>
					<s id="N22E3C"><lb></lb>vnde ſi quis omnes obſeruationes, tùm à Plinio, tùm à Cardano, tùm à <lb></lb>Fracaſtorio, tùm à Porta, tùm ab aliis propoſitas ad principia phyſica re­<lb></lb>ducere velit, per me ſtat, non contradico; numquam tamen illa mihi <lb></lb>mens erit, cui ſatis eſt rationes, &amp; cauſas phyſicas illorum tantùm expe­<lb></lb>rimentorum explicare, quæ mihi certa ſunt, ſuntque omnibus commu­<lb></lb>nia, vel eſſe poſſunt. </s>
				</p>
				<p id="N22E4B" type="main">
					<s id="N22E4D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22E5A" type="main">
					<s id="N22E5C"><emph type="italics"></emph>In motu funependuli ſingulis instantibus eſt noua determinatio motus.<emph.end type="italics"></emph.end></s>
					<s id="N22E63"> Pro­<lb></lb>batur, quia ſingulis inſtantibus eſt quaſi nouum planum; </s>
					<s id="N22E69">tot ſunt enim <lb></lb>plana in quadrante NE, quot Tangentes, &amp; tot Tangentes quot pun­<lb></lb>cta, tot denique puncta, quot inſtantia; </s>
					<s id="N22E71">atqui in ſingulis nouis planis <lb></lb>mutatur determinatio; </s>
					<s id="N22E77">igitur in ſingulis punctis; igitur in ſingulis in­<lb></lb>ſtantibus. </s>
				</p>
				<p id="N22E7D" type="main">
					<s id="N22E7F"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N22E8B" type="main">
					<s id="N22E8D">Obſeruabis eſſe aliqua Lemmata præmittenda antequam proportio­<lb></lb>nes motus per arcum NE demonſtrentur. </s>
				</p>
				<pb pagenum="302" xlink:href="026/01/336.jpg"></pb>
				<p id="N22E96" type="main">
					<s id="N22E98"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22EA5" type="main">
					<s id="N22EA7"><emph type="italics"></emph>Poteſt determinari tempus, quo percurruntur duo ſpatia æqualia motu na­<lb></lb>turaliter accelerato inæquali.<emph.end type="italics"></emph.end> ſit v.g. tempus AF; </s>
					<s id="N22EB4">ſit velocitas EF ac­<lb></lb>quiſita tempore AF motu ſcilicet naturaliter accelerato minore; </s>
					<s id="N22EBA">ſit <lb></lb>etiam velocitas FD acquiſita alio motu maiore eodem tempore AF; </s>
					<s id="N22EC0"><lb></lb>haud dubiè ſpatium acquiſitum primo motu erit ad acquiſitum ſecundo, <lb></lb>æquali ſcilicet tempore, vt triangulum EAF ad triangulum DAF, vt <lb></lb>conſtat ex dictis lib.2. in controuerſia; </s>
					<s id="N22EC9">ſpatium verò acquiſitum tempo­<lb></lb>re AF primo motu, ſcilicet minore, idque v.g. in ratione ſubdupla erit <lb></lb>ad ſpatium acquiſitum ſecundo motu maiore tempore ſubduplo AI, vt <lb></lb>triangulum EAF ad triangulum BAI, ſed BAI, eſt ſubduplum EAF, <lb></lb>id eſt, vt FA ad IA, vt patet: </s>
					<s id="N22ED7">vt autem inueniantur tempora, quæ re­<lb></lb>ſpondent ſpatiis inæqualibus; </s>
					<s id="N22EDD">ſit AH media proportionalis inter AI &amp; <lb></lb>AF; </s>
					<s id="N22EE3">haud dubiè triangulum CHA eſt ſubduplum DAF; </s>
					<s id="N22EE7">igitur æquale <lb></lb>EAF; </s>
					<s id="N22EED">igitur velocitas acquiſita tempore AF ſit FE, motu ſcilicet mi­<lb></lb>nore; </s>
					<s id="N22EF3">acquiſita verò tempore AH motu maiore ſit HC; </s>
					<s id="N22EF7">certè ſpatia <lb></lb>erunt vt CHA &amp; DAF: </s>
					<s id="N22EFD">ſed hæc ſunt æqualia; igitur motu maiore con­<lb></lb>ficitur æquale ſpatium tempore AH &amp; motu minore tempore AF. </s>
				</p>
				<p id="N22F04" type="main">
					<s id="N22F06"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22F13" type="main">
					<s id="N22F15"><emph type="italics"></emph>Si accipiantur tempora æqualia cum motibus inæqualibus, ſpatia ſunt vt <lb></lb>baſes triangulorum<emph.end type="italics"></emph.end>; </s>
					<s id="N22F20">ſit enim tempus AI, quo motu maiore acquiratur ve­<lb></lb>locitas IB, &amp; minore IK; </s>
					<s id="N22F26">certè ſpatia ſunt vt triangula BAI, KAI; </s>
					<s id="N22F2A"><lb></lb>ſed hæc ſunt vt baſes BI, KI, immò ſunt vt rectangula BA KA; nec <lb></lb>in his eſt quidquam difficultatis. </s>
				</p>
				<p id="N22F31" type="main">
					<s id="N22F33"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22F40" type="main">
					<s id="N22F42">Poſſunt determinari vel ſpatia inæqualia temporibus æqualibus, vel <lb></lb>tempora inæqualia ſpatiis æqualibus in chordis eiuſdem quadrantis, &amp; <lb></lb>in perpendiculari, ſit tempus DI; </s>
					<s id="N22F4A">ſit motus per ipſam perpendicula­<lb></lb>rem AP, vel DI; </s>
					<s id="N22F50">ſit motus etiam per chordam inclinatam DP; </s>
					<s id="N22F54">velo­<lb></lb>citas primi eſt ad velocitatem ſecundi in tempore DI, vt DP ad DI, <lb></lb>vel vt AK ad ſinum VK, vel vt IP ad NP, vel vt quadratum IA ad <lb></lb>rectangulum NA; </s>
					<s id="N22F5E">ſed ſpatia ſunt vt velocitates ſuppoſitis temporibus <lb></lb>æqualibus; </s>
					<s id="N22F64">igitur ſpatium, quod percurritur in ipſa perpendiculari eſt <lb></lb>ad ſpatium, quod percurritur in inclinata DP temporibus æqualibus, vt <lb></lb>quadratum IA ad rectangulum NA, vel vt DP ad DI, vel vt DT ad <lb></lb>DP, quæ omnia conſtant; </s>
					<s id="N22F6E">ſit autem motus in inclinata FP; certè ſpa­<lb></lb>tium acquiſitum in perpendiculari eſt ad ſpatium acquiſitum in FP, vt <lb></lb>QZP ad ZI, vel FP ad FY, vel AP ad PR, vel AL ad LX, vel  PI <lb></lb>ad PM, vel vt quadratum IA, ad rectangulum MA, vel vt F <foreign lang="grc">δ</foreign> ad PF, <lb></lb>ſed F <foreign lang="grc">δ</foreign> eſt æqualis DT, quia cum DP &amp; FP percurrantur temporibus <lb></lb>æqualibus, <expan abbr="ſiq́ue">ſique</expan> eo tempore quo percurritur DP, percurritur DT, &amp; <lb></lb>eo quo percurritur FP, percurritur. </s>
					<s id="N22F8A">F <foreign lang="grc">δ</foreign>; certè DT &amp; F <foreign lang="grc">δ</foreign> ſunt <lb></lb>quales. </s>
				</p>
				<pb pagenum="303" xlink:href="026/01/337.jpg"></pb>
				<p id="N22F9B" type="main">
					<s id="N22F9D">Idem dico de omnibus aliis chordis, quarum motus, &amp; velocitates, <lb></lb>ſpatia temporibus æqualibus acquiſita ſunt ad motus, velocitates, ſpatia <lb></lb>acquiſita in perpendiculari, vt ipſarum longitudines ad DT, vel duplam <lb></lb>DI, vel vt earum ſubduplæ ſeu ſinus recti ſubdupli ſui arcus ad ſinum to­<lb></lb>tum DI, vel vt rectangula ſub illis ſinubus comprehenſa, &amp; ſinu toto <lb></lb>ad quadratum ſinus totius. </s>
				</p>
				<p id="N22FAA" type="main">
					<s id="N22FAC"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N22FB9" type="main">
					<s id="N22FBB"><emph type="italics"></emph>Si ſint duæ quantitates in data ratione, &amp; aliæ duæ in data, ſed minore; </s>
					<s id="N22FC1">ſi ſit <lb></lb>media proportionalis inter duas primas &amp; media inter duas posteriores, ſitque <lb></lb>data noua quantitas ad aliam, vt prima priorum quantitatum ad primam <lb></lb>mediam proportionalem, ſit denique eadem quantitas noua ad aliam vt prima <lb></lb>poſteriorum quantitatum ad ſecundam mediam proportionalem, certè erit mi­<lb></lb>nor ratio noua quantitatis ad ſecundam queſitam, quàm ad primam<emph.end type="italics"></emph.end> v. g. ſit <lb></lb>DE prima quantitas, &amp; LK ſecunda; </s>
					<s id="N22FD8">ſit KR tertia, VZ quarta; </s>
					<s id="N22FDC">ſitque <lb></lb>prima ad ſecundam, vt 4. ad 9. &amp; tertia ad quartam, vt 3. ad 12. certè eſt <lb></lb>minor ratio tertiæ ad quartam, quàm primæ ad ſecundam; </s>
					<s id="N22FE4">inter primam <lb></lb>&amp; ſecundam ſit media proportionalis AC æqualis FH, id eſt <foreign lang="grc">σ</foreign>, &amp; ſit <lb></lb>quinta quantitas; </s>
					<s id="N22FF0">ſit etiam alia inter tertiam &amp; quartam; </s>
					<s id="N22FF4">ſit TS æqualis <lb></lb>VY, ſcilicet <foreign lang="grc">σ</foreign>; ſitque ſexta quantitas, &amp; vt prima ad ſecundam, ita <lb></lb>ſeptima quantitas v. g. DE ad octauam AC, ſitque vt tertia quantitas <lb></lb>VX vel QR ad ſextam VY, vel TS, ita eadem ſeptima DE ad nonam <lb></lb>AC. </s>
					<s id="N23009">Dico eſſe minorem ratione ſeptimæ DE ad nonam AT, quàm <lb></lb>eiuſdem ſeptimæ DE ad octauam AC, quia AB vel DE eſt ad AC vt <lb></lb>2. ad 3. &amp; ad X, vt a. </s>
					<s id="N23010">ad 4. quæ omnia conſtant ex Geometria. </s>
				</p>
				<p id="N23014" type="main">
					<s id="N23016"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23023" type="main">
					<s id="N23025"><emph type="italics"></emph>Si ſint<emph.end type="italics"></emph.end> <emph type="italics"></emph>duæ chordæ in quadrante EIB, &amp; producatur BI vſque ad G; </s>
					<s id="N23031">ſit­<lb></lb>que EM perpendicularis, in quam cadat IH, quæ cum EI faciat angulum <lb></lb>rectum; </s>
					<s id="N23039">ex eodem puncto H ducatur HQ perpendicularis in EB: </s>
					<s id="N2303D">dico mino­<lb></lb>rem eſſe proportionem EQ ad EB, quàm GI ad GB<emph.end type="italics"></emph.end>; </s>
					<s id="N23046">ſit enim IP paral­<lb></lb>lela EG, vt EP eſt ad EB, ſic GI ad GB; </s>
					<s id="N2304C">igitur EQ habet minorem <lb></lb>proportionem ad EB, quam GI ad GB; </s>
					<s id="N23052">ſimiliter ſint chordæ EIL, <lb></lb>EL; </s>
					<s id="N23058">ducatur HK perpendicularis in EL: </s>
					<s id="N2305C">dico EK habere minorem <lb></lb>rationem ad EL, quàm FI ad FL; </s>
					<s id="N23062">nam vt EO eſt ad EL, ita FI ad FL; </s>
					<s id="N23066"><lb></lb>igitur minor eſt ratio EK ad EL, quàm FI ad FL; </s>
					<s id="N2306B">Idem dico de om­<lb></lb>nibus aliis chordis: </s>
				</p>
				<p id="N23071" type="main">
					<s id="N23073"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23080" type="main">
					<s id="N23082"><emph type="italics"></emph>Cognite tempore, quo percurritur ſegmentum, lineæ cognoſci poteſt tempus, que <lb></lb>aliud ſegmentum percurretur motu ſcilicet propagate<emph.end type="italics"></emph.end>; </s>
					<s id="N2308D">ſit v. g. perpendicu­<lb></lb>laris deorſum DI; </s>
					<s id="N23097">ſit primum ſegmentum DG decurſum tempore AB; </s>
					<s id="N2309B"><lb></lb>ſit vt DC ad DH, ita DH ad DI; </s>
					<s id="N230A0"><expan abbr="ſitq́ue">ſitque</expan> vt DG ad DH, ita tempus <lb></lb>AB ad AC; dico quod ſecundum ſegmentum percurretur tempore BC <lb></lb>poſt primum decurſum, patet ex dictis lib.2. &amp; 5. </s>
				</p>
				<pb pagenum="304" xlink:href="026/01/338.jpg"></pb>
				<p id="N230B0" type="main">
					<s id="N230B2"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N230BE" type="main">
					<s id="N230C0"><emph type="italics"></emph>Cognito tempore, quo percurritur chorda cuiuſlibet arcus, cognoſci poteſt <lb></lb>quantum ſpaty eodem tempore percurratur in <expan abbr="perpẽdiculari">perpendiculari</expan> &amp; in alia chorda<emph.end type="italics"></emph.end>; </s>
					<s id="N230CF"><lb></lb> ſit chorda EL; </s>
					<s id="N230D4">fiat angulus rectus ELM, itemque MDE: </s>
					<s id="N230D8">dico quod <lb></lb>eodem tempore percurretur EL EM ED; </s>
					<s id="N230DE">ſimiliter fiat angulus re­<lb></lb>ctus EIH, itemque HKE, HQE: dico quod eodem tempore percur­<lb></lb>rentur EI, EH, EK,EQ. idem dico de omnibus aliis chordis, quæ <lb></lb>omnia conſtant ex his quæ diximus lib.2. &amp; 5. </s>
				</p>
				<p id="N230ED" type="main">
					<s id="N230EF"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N230FB" type="main">
					<s id="N230FD"><emph type="italics"></emph>Due chorda ELB citiùs percurruntur quàm ſola EB; </s>
					<s id="N23103">itemque due EIB, <lb></lb>quàm EB<emph.end type="italics"></emph.end>; </s>
					<s id="N2310C">quia eodem tempore percurruntur EI, <expan abbr="Eq;">Eque</expan> &amp; IB eodem <lb></lb>tempore percurritur ſiue à G incipiat motus ſiue ab E; </s>
					<s id="N23116">nam ab æquali <lb></lb>altitudine æqualis acquiritur impetus, ſed minor eſt proportio EQ ad <lb></lb>EB, quam GI ad GB per Lemma quintum; </s>
					<s id="N2311E">igitur ſi ſit media propor­<lb></lb>tionalis inter GI, GB, &amp; ſecunda inter EQEB, ſitque vt GI ad pri­<lb></lb>mam proportionalem; </s>
					<s id="N23126">ita tempus, quo percurritur EI ad aliud X, &amp; vt <lb></lb>EQ ad ſecundam proportionalem, ita idem tempus, quo percurritur EI, <lb></lb>vel EQ ad aliud Z; </s>
					<s id="N2312E">certè tempus Z eſt maius tempore X per Lemma <lb></lb>4. ſed EQB percurritur tempore Z, &amp; EIB tempore X; </s>
					<s id="N23134">EQ verò, &amp; <lb></lb>EI tempore æquali per Lemma 7. igitur duæ EIB citiùs percurruntur, <lb></lb>quàm EB; </s>
					<s id="N2313C">idem dico de aliis: hoc ipſum etiam demonſtrauit Galil. in <lb></lb>dialogis. </s>
				</p>
				<p id="N23144" type="main">
					<s id="N23146"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23152" type="main">
					<s id="N23154"><emph type="italics"></emph>Tres chordæ faciliùs percurruntur, quàm duæ<emph.end type="italics"></emph.end>; </s>
					<s id="N2315D">ſint enim tres EILB; </s>
					<s id="N23161"><lb></lb>ſint duæ ELB. Primò, duæ EIL citiùs percurruntur quàm EL, quia <lb></lb>IL eodem tempore percurritur, ſiue initium motus ducatur ab F, ſiue ab <lb></lb>E; </s>
					<s id="N2316A">&amp; minor eſt ratio EK ad EL, quàm FI ad FL per Lem.5.EI, &amp; EK <lb></lb>æquè citò percurruntur per Lem. 7. igitur ſit vt FI ad mediam propor­<lb></lb>tionalem inter FI &amp; FL; </s>
					<s id="N23174">ita tempus Z ad tempus X, &amp; vt EK ad me­<lb></lb>diam proportionalem inter EK EL, ita tempus Z ad tempus Y; </s>
					<s id="N2317A">certè <lb></lb>tempus Y erit maius tempore X per Lem. 8. igitur citiùs percurrentur <lb></lb>duæ EIL, quàm EL; </s>
					<s id="N23184">ſed ſi eodem tempore percurrerentur duæ EIL <lb></lb>cum EL; </s>
					<s id="N2318A">certè LB æquali tempore percurreretur, quia eſt idem impetus <lb></lb>in L, ſiue ab E per EL, ſiue ab F per FL incipiat motus, vt conſtat, &amp; eſt <lb></lb>idem in I, ſiue ab E, ſiue ab F incipiat; </s>
					<s id="N23192">igitur idem in L ſiue ab E per <lb></lb>EIL, ſiue ab F per FL, ſiue ab E per EL; </s>
					<s id="N23198">igitur LB æquali tempore <lb></lb>percurretur, ſiue motus ſit ab E per ELB, ſiue ab E per EI, LB, poſito <lb></lb>quòd EIL &amp; EL æquali tempore percurrantur; </s>
					<s id="N231A0">ſed EIL percurrun­<lb></lb>tur citiùs quàm EL; </s>
					<s id="N231A6">igitur citiùs EILB, quàm ELB; </s>
					<s id="N231AA">igitur cùm ELB <lb></lb>percurrantur citiùs, quàm EB, &amp; EILB, quàm ELB; </s>
					<s id="N231B0">certè EILB per­<lb></lb>curruntur citiùs, quàm EB: Eodem modo demonſtrabitur 4. chordas ci­<lb></lb>tiùs percurri, quàm 3. 5. quàm 4. atque ita deinceps. </s>
				</p>
				<pb pagenum="305" xlink:href="026/01/339.jpg"></pb>
				<p id="N231BC" type="main">
					<s id="N231BE"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N231CA" type="main">
					<s id="N231CC"><emph type="italics"></emph>Velocitas acquiſita in duabus chordis EIB eſt æqualis acquiſitæ in EB<emph.end type="italics"></emph.end>; </s>
					<s id="N231D5"><lb></lb>quia acquiſita in EI eſt æqualis acquiſitæ in GI; </s>
					<s id="N231DA">ſunt enim eiuſdem al­<lb></lb>titudinis; </s>
					<s id="N231E0">igitur acquiſita in EIB æqualis acquiſitæ in GB: </s>
					<s id="N231E4">ſed acqui­<lb></lb>ſita in GB eſt æqualis acquiſitæ in EIB; </s>
					<s id="N231EA">igitur acquiſita in EB eſt æqua­<lb></lb>lis acquiſitæ in EIB, itemque acquiſita in ELB acquiſitæ in EB: </s>
					<s id="N231F0">immò <lb></lb>acquiſita in tribus EILB eſt æqualis acquiſitæ in EB; </s>
					<s id="N231F6">quia acquiſita in <lb></lb>EIL eſt æqualis acquiſitæ in EL; </s>
					<s id="N231FC">igitur acquiſita in EILB æqualis <lb></lb>acquiſitæ in ELB: </s>
					<s id="N23202">ſed acquiſita in ELB eſt æqualis acquiſitæ in EB; igi­<lb></lb>tur acquiſita in EB æqualis acquiſitæ in EILB idem dico de 5. chordis, <lb></lb>6.7. atque ita deinceps. </s>
				</p>
				<p id="N2320B" type="main">
					<s id="N2320D">Quod certè mirabile eſt, &amp; quaſi paradoxon; </s>
					<s id="N23211">præſertim cùm duplici <lb></lb>motu acquiratur æqualis velocitas in ſpatiis inæqualibus, quorum mauis <lb></lb>citiùs percurritur; </s>
					<s id="N23219">Equidem in AB, EB acquiritur æqualis velocitas, <lb></lb>vel impetus, ſed breuius ſpatium, ſcilicet AB citius percurritur; </s>
					<s id="N2321F">at verò <lb></lb>in EB, &amp; ELB acquiritur æqualis velocitas; </s>
					<s id="N23225">licèt ſpatium longius ELB <lb></lb>percurratur citiùs, quàm EB; ſimiliter EILB velociùs, quam ELB &amp; EB. </s>
				</p>
				<p id="N2322C" type="main">
					<s id="N2322E">Hinc ſuprà velocitas acquiſita in perpendiculari ſeu radio quadrantis <lb></lb>non eſt ad velocitatem acquiſitam in toto arcu quadrantis vt quadratum <lb></lb>ſub radio ad ipſum quadrantem, quia ſcilicet velocitas acquiſita per ar­<lb></lb>cum ELB eſt æqualis acquiſitæ per omnes chordas facto initio motus <lb></lb>ab E; ſed velocitas acquiſita in 6. chordis. </s>
					<s id="N2323A">v. g. eſt æqualis acquiſitæ in <lb></lb>5. 4. 3. 2. 1. igitur velocitas acquiſita in EB eſt æqualis acquiſitæ in ar­<lb></lb>cu ELB, &amp; in ipſa perpendiculari ER. </s>
				</p>
				<p id="N23245" type="main">
					<s id="N23247"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23253" type="main">
					<s id="N23255"><emph type="italics"></emph>Hinc Lemma vniuerſaliſſimum ſtatuitur, ſcilicet ab eodem puncto altitudi­<lb></lb>nîs ad <expan abbr="eãdem">eandem</expan> horizontalem, vel ab eadem horizontali ad idem punctum <lb></lb>deorſum, vel ab eadem horizontali ad aliam horizontalem aquales acquiri <lb></lb>velocitates, ſiue plures ſint lineæ, ſine vnica, ſiue ſimplices, ſiue compoſitæ, ſiue <lb></lb>recta, ſiue curua<emph.end type="italics"></emph.end>; quæ omnia ex Lemmate decimo manifeſta redduntur. </s>
				</p>
				<p id="N2326A" type="main">
					<s id="N2326C"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23278" type="main">
					<s id="N2327A"><emph type="italics"></emph>Velocitas acquiſita in toto arcu quadrantis ELB non debet aſſumi in area <lb></lb>tota quadrantis AEB, ſed in linea recta æquali toti arcui ELB, ductis ſci­<lb></lb>licet lineis rectis tranſuerſis, qua ſint ipſis ſinubus rectis æquales, cuius conſtru­<lb></lb>ctionis<emph.end type="italics"></emph.end>; </s>
					<s id="N23289">ſit enim linea AN æqualis arcui quadrantis, &amp; NT radio; </s>
					<s id="N2328D">igi­<lb></lb>tur totum triangulum mixtum ex rectis AN, NT, &amp; curua TQH, eſt <lb></lb>velocitas acquiſita in toto arcu quadrantis; ſit autem A <foreign lang="grc">σ</foreign> æqualis lateri <lb></lb>quadrati inſcripti qua eſt ad AN proximè vt 10. ad 11. eſt enim AB ra­<lb></lb>dix quad. </s>
					<s id="N2329D">98. ſitque AE ſinus rectus quad. </s>
					<s id="N232A0">45. certè rectangulum NE <lb></lb>eſt velocitas acquiſita in chorda A <foreign lang="grc">σ</foreign>, ſed hæc eſt æqualis acquiſitæ in <lb></lb>toto arcu quadrantis AN; </s>
					<s id="N232AC">igitur rectangulum NE eſt æquale triangulo <lb></lb>mixto NTOA, denique velocitas acquiſita in radio A 4. æquali AF, <lb></lb>eſt vt quadratum 4 F, ſed quadratum 4. F eſt æquale rectangulo BE, vt <lb></lb>conſtat, nam A <foreign lang="grc">σ</foreign> eſt dupla AE; </s>
					<s id="N232BA">igitur rectangulum eſt ſubduplum qua-<pb pagenum="306" xlink:href="026/01/340.jpg"></pb>drati ſub A <foreign lang="grc">σ</foreign>, ſed quadratum ſub A <foreign lang="grc">σ</foreign> eſt duplum quadrati 4 F; </s>
					<s id="N232CB">igitur <lb></lb>quadratum 4 F eſt æquale rectangulo <foreign lang="grc">σ</foreign> E; igitur &amp; triangulo mixto <lb></lb>NTQA. </s>
				</p>
				<p id="N232D7" type="main">
					<s id="N232D9"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N232E5" type="main">
					<s id="N232E7">Inde Corollarium cyclometricum deduci poteſt, ſcilicet proportio, <lb></lb>quam habet triangulum mixtum NTQA ad quadrantem, cuius arcus <lb></lb>æqualis eſt rectæ AN, &amp; radius rectæ AF. v.g. ad quadrantem AFL, <lb></lb>vel INT, vel LAC; </s>
					<s id="N232F3">porrò triangulum prædictum eſt maius quadrante <lb></lb>ſectione ex curua TQA, &amp; rectâ AT; </s>
					<s id="N232F9">aut certè qui inuenerit triangu­<lb></lb>lum mixtum KLQ æquale mixto FQ <foreign lang="grc">δ</foreign>, habebit rectangulum KF æqua­<lb></lb>le quadranti AFL; </s>
					<s id="N23305">&amp; vt res iſta promoueatur à Geometris: </s>
					<s id="N23309">dico qua­<lb></lb>dratum ſub radio eſſe ad ſemicirculum, vt triangulum mixtum NTQA <lb></lb>ad rectangulum NF; </s>
					<s id="N23311">porrò mixtum FTQA conſtat ex omnibus ſinu­<lb></lb>bus verſis collectis; </s>
					<s id="N23317">illud verò ex omnibus ſinubus rectis; vt autem in­<lb></lb>ueniatur illud collectum, accipi debet motus qui creſcat ſecundum pro­<lb></lb>portionem ſinuum verſorum v.g. in linea FT, velocitas puncti F eſt vt <lb></lb>FA, in <foreign lang="grc">θ</foreign>, vt <foreign lang="grc">θ</foreign> O in <foreign lang="grc">β</foreign>, vt <foreign lang="grc">β</foreign> P, &amp;c. </s>
				</p>
				<p id="N23333" type="main">
					<s id="N23335"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N23341" type="main">
					<s id="N23343">Obſeruabis autem primò lineas tranſuerſas FA, <foreign lang="grc">θ</foreign> O, <foreign lang="grc">β</foreign> P, <foreign lang="grc">δ</foreign> Q, CR, <lb></lb>&amp;c. </s>
					<s id="N23354">eſſe æquales lineis CB <foreign lang="grc">μ υ</foreign> ZT <foreign lang="grc">ω</foreign> S, <foreign lang="grc">υ</foreign> R, &amp;c. </s>
					<s id="N23363">quia BC figura <lb></lb> quam vocemus <expan abbr="figurã">figuram</expan> primam, eſt æqualis AF, fig. </s>
					<s id="N2336C">quam vocemus <lb></lb>ſecundam. </s>
					<s id="N23371">O <foreign lang="grc">θ</foreign> ſecundæ eſt æqualis H <foreign lang="grc">θ</foreign>, minùs HO; </s>
					<s id="N2337D">ſed HO ſecundæ <lb></lb>eſt æqualis QM primæ, vel BD; </s>
					<s id="N23383">igitur O <foreign lang="grc">θ</foreign> ſecundæ eſt æqualis DC <lb></lb>primæ; </s>
					<s id="N2338D">ſed DC eſt æqualis VA, quia VD eſt quadratum, ſed V <foreign lang="grc">μ</foreign> eſt <lb></lb>æqualis VA; </s>
					<s id="N23397">igitur DC; </s>
					<s id="N2339B">igitur O <foreign lang="grc">θ</foreign> ſecundæ: </s>
					<s id="N233A3">præterea IP ſecundæ eſt <lb></lb>æqualis AD, quæ eſt ſubdupla AF; </s>
					<s id="N233A9">igitur æqualis P <foreign lang="grc">β</foreign>; </s>
					<s id="N233B1">ſed IP eſt æqua­<lb></lb>lis BT primæ; </s>
					<s id="N233B7">igitur BT, cui etiam eſt æqualis TZ; </s>
					<s id="N233BB">igitur TZ æqualis <lb></lb>P <foreign lang="grc">β</foreign> ſecundæ: </s>
					<s id="N233C5">idem dico de aliis tranſuerſis: immò demonſtrabimus tom. <lb></lb></s>
					<s id="N233CA"><expan abbr="ſeq.">ſeque</expan> quadratricem quadrantis, cuius radius ſit NA terminari ad punctum <lb></lb>T, ita vt NT ſit baſis quadratricis, &amp; NA latus; non tamen propterea <lb></lb>hæc linea ſinuum eſt quadratrix, vt demonſtrabimus. </s>
				</p>
				<p id="N233D5" type="main">
					<s id="N233D7"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N233E3" type="main">
					<s id="N233E5"><emph type="italics"></emph>Diuerſæ chordæ acquirunt diuerſam velocitatem pro diuerſa ratione ſinuum <lb></lb>verſorum ſuorum arcuum.<emph.end type="italics"></emph.end> v. g. velocitas acquiſita in chorda AM eſt <lb></lb>æqualis acquiſitæ in ſinu verſo AQ, &amp; acquiſita in chorda AL æqualis <lb></lb>acquiſitæ in ſinu verſo AR, atque ita deinceps; donec acquiſita in AC <lb></lb>ſit æqualis acquiſitæ in ſinu toto AB. </s>
				</p>
				<p id="N233FB" type="main">
					<s id="N233FD">Itaque in chorda quæ ducitur ab A, velocitas creſcit vt in ſinu verſo <lb></lb>eiuſdem.v.g. </s>
					<s id="N23402">in AM, AL, AK; in chorda verò, quæ ducitur ab aliquo <lb></lb>puncto arcus AC vſque ad C, creſcit vt in ſinu recto. </s>
					<s id="N23407">v.g. velocitas ac­<lb></lb>quiſita in chorda LC eſt æqualis acquiſitæ in perpendiculari LE, quæ <lb></lb>eſt ſinus rectus arcus LC; item acquiritur æqualis velocitas in duabus <lb></lb>at que in vna, dum ſcilicet communes terminos habeant. </s>
					<s id="N23413">v.g. in duabus <pb pagenum="307" xlink:href="026/01/341.jpg"></pb>AKC acquiritur æqualis acquiſitæ in AC; </s>
					<s id="N2341E">nam in AK, A <foreign lang="grc">ω</foreign> acquiritur <lb></lb>æqualis; </s>
					<s id="N23426">tùm etiam in KC, <foreign lang="grc">ω</foreign> C; Item in tribus acquiritur æqualis ac­<lb></lb>quiſitæ in duabus, atque ita deinceps. </s>
				</p>
				<p id="N23430" type="main">
					<s id="N23432">Præterea velocitas acquiſita in chordis mediis.v.g. </s>
					<s id="N23435">in chorda LI eſt <lb></lb>æqualis acquiſitæ in LZ, vel RT, vel in ſinu toto AB, minùs ſinu verſo <lb></lb>arcus LA, &amp; ſinu recto arcus IC; ſed hæc ſunt ſatis facilia. </s>
				</p>
				<p id="N2343D" type="main">
					<s id="N2343F">Idem dico de chordis arcus quadrantis funependuli AEB figura Lem­<lb></lb>ma.4. v. g. de chorda IB, in qua velocitas acquiſita eſt æqualis acqui­<lb></lb>ſitæ in RB, vel in duabus ILB, vel in tribus 4. 5. atque ita deinceps: <lb></lb>hinc etiam vides in quadrante EB acquiri æqualem velocitatem, ſiue <lb></lb>EA ſit perpendicularis deorſum, ſiue AB. </s>
				</p>
				<p id="N23450" type="main">
					<s id="N23452"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2345E" type="main">
					<s id="N23460"><emph type="italics"></emph>Citiùs deſcendet corpus per duas EIB, quàm per IB<emph.end type="italics"></emph.end>; </s>
					<s id="N23469">quia deſcenſus eſt <lb></lb>æquè diuturnus per EB, &amp; IB; ſed citiùs deſcendit per EIB, quàm per <lb></lb>EB, vt iam ſuprà dictum eſt in Lem. 8. igitur citiùs per EIB, quàm <lb></lb>per IB. </s>
				</p>
				<p id="N23475" type="main">
					<s id="N23477"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23483" type="main">
					<s id="N23485"><emph type="italics"></emph>Citiùs deſcendet per<emph.end type="italics"></emph.end> <emph type="italics"></emph>duas chordas BHF, quàm per duas BGF, à quiete<emph.end type="italics"></emph.end><lb></lb>B; </s>
					<s id="N23495">ſint enim duæ BHF, ſitque BH. v.g. chorda arcus 30.grad.ſc.5 1764. <lb></lb>earum partium, quarum ſinus totus eſt 100000. ſit Tangens BE; </s>
					<s id="N2349D">ſit HD <lb></lb>perpendicularis in BH, &amp; HT in BD; </s>
					<s id="N234A3">certè HT eſt media proportio­<lb></lb>nalis inter DT, &amp; TB; </s>
					<s id="N234A9">eſtque differentia ſinus totius, &amp; ſinus OH 60. <lb></lb>grad. eſt autem OH 86603. igitur HT 13397. quadretur HT, produ­<lb></lb>ctum diuidatur per BT 50000. quotiens dabit TD 3589. quæ ſi adda­<lb></lb>tur BT, habebitur tota BD 53589. quadretur BD; </s>
					<s id="N234B5">aſſumatur ſubduplum <lb></lb>quadrati, ex quo extrahatur radix; </s>
					<s id="N234BB">habebitur KD, vel BK 37893. ſit <lb></lb>autem LF 200000. ad 141422. æqualem BF, ita BF ad LH 100000. <lb></lb>certè tempus per LH eſt ad tempus per BH, vt LH ad BH; </s>
					<s id="N234C3">ſed tempus <lb></lb>per LH eſt ad tempus per LF, vt LH ad 141422.igitur tempus per BH <lb></lb>eſt ad tempus per HF facto initio motus ex L, vt BH 51764. ad 41422. <lb></lb>igitur ad tempus per BHF, vt 51764.ad 93186. porrò BH &amp; BK æqua­<lb></lb>li tempore percurruntur; </s>
					<s id="N234CF">igitur tempus per BK eſt BH, id eſt 51764. <lb></lb>cùm autem ſpatia in eadem linea ſint in ratione duplicata temporum; <lb></lb>certè ſpatium BK acquiſitum tempore 51764.eſt ad ſpatium acquiſitum <lb></lb>in BF tempore 93186. vt quadratum 51764. ad quadratum 93186.id eſt, <lb></lb>vt 2679511696.ad 8676630576.vnde factâ regulâ trium habeo ſpatium <lb></lb>decurſum in BF 122702. tempore 93186. ſed tota BF eſt 141422. igitur <lb></lb>citiùs percurruntur duæ BHF, quàm BF. </s>
				</p>
				<p id="N234DF" type="main">
					<s id="N234E1">Præterea ſint duæ BGF, BG eſt 100000.ſit perpendicularis G 4 cùm <lb></lb>angulus GB 4.ſit grad.30. erit vt 5 G ad GB, ita BG ad B 4. igitur B 4. <lb></lb>erit 115469. ſit 4.3.perpendicularis in BF, quadratum B 4. eſt duplum <lb></lb>quadrati B 3.igitur B 3. erit 81655. iam verò FN eſt ſecans grad.75. ſci­<lb></lb>licet 386370.igitur GN eſt 334606. detracta ſcilicet FG æquali BH; </s>
					<s id="N234ED">ſit <lb></lb>autem NG ad 359557. vt hæc ad NF; </s>
					<s id="N234F3">certè tempus per BG eſt ad tem-<pb pagenum="308" xlink:href="026/01/342.jpg"></pb>pus per NG, vt BG ad NG, &amp; ad tempus per GF, vt BG ad 24951. &amp; <lb></lb>ad tempus per BGF, vt BG id eſt, 100000. ad 124951. porrò tempus <lb></lb>per B 3. eſt BG; </s>
					<s id="N23500">ergo vt quadratum temporis per BG ad quadratum <lb></lb>temporis per BGF, ſcilicet vt 10000000000. ad 1561475241. ita B 3. <lb></lb>ſcilicet 81655. ad aliam, hæc erit 123496. igitur in BF, quæ eſt partium <lb></lb>141422. percurruntur partes 123496. eo tempore, quo percurruntur <lb></lb>BGF; </s>
					<s id="N2350C">at verò eo tempore, quo percurruntur BHF; </s>
					<s id="N23510">percurruntur in <lb></lb>BF 122702. igitur pauciores; </s>
					<s id="N23516">igitur minore tempore; igitur duæ BHF <lb></lb>percurruntur minore tempore, quàm duæ BGF, quod erat demon­<lb></lb>ſtrandum. </s>
				</p>
				<p id="N2351E" type="main">
					<s id="N23520">Similiter deſcendet citiùs per duas BHF, quàm per duas BZF: </s>
					<s id="N23524">immò <lb></lb>quod mirabile eſt, patetque ex analytica, citiùs per duas BGF, quàm per <lb></lb>duas BZF; </s>
					<s id="N2352C">(ſuppono enim BZ eſſe arcum grad. 45.) ſit enim Z <foreign lang="grc">υ</foreign> per­<lb></lb>pendicularis, itemque Z <foreign lang="grc">δ, δ</foreign> B eſt æqualis BR. igitur 70711. Z <foreign lang="grc">δ</foreign> eſt <lb></lb>29289. igitur <foreign lang="grc">δ υ</foreign> 1223. igitur B <foreign lang="grc">υ</foreign> 71924. igitur B <foreign lang="grc">β</foreign> 51858. iam tempus <lb></lb>per BZ eſt ad tempus per YZ vt BZ ad YZ. id eſt, vt 76536. ad 184777. <lb></lb>ſit autem vt AYF 261313. ad aliam 219737.ita hæc ad YZ; </s>
					<s id="N23552">certè tem­<lb></lb>pus per BZ eſt ad tempus per BZF, vt BZ ad 111496. igitur B <foreign lang="grc">β</foreign> fit <lb></lb>tempore BZ; ergo vt quadratum BZ ad quadratum 111496. id eſt, vt <lb></lb>4857759296. ad 12431358016. ita ſit B <foreign lang="grc">β</foreign>, id eſt 51858.ad 132708.igitur <lb></lb>eo tempore, quo percurruntur BZF, percurruntur in BF 132708.earum <lb></lb>partium, quarum BF eſt 141422. ſed pauciores percurruntur eo tempo­<lb></lb>re, quo fit deſcenſus per BHF, vel BGF. </s>
				</p>
				<p id="N2356A" type="main">
					<s id="N2356C"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23578" type="main">
					<s id="N2357A"><emph type="italics"></emph>Citiùs percurruntur duæ inferiores.v.g. </s>
					<s id="N2357F">HGF, quàm duæ BHF<emph.end type="italics"></emph.end>; </s>
					<s id="N23586">eſt enim <lb></lb>PF ſubdupla ſecantis NF; </s>
					<s id="N2358C">igitur 193185. FG eſt 51764. GP 141421. <lb></lb>ſit autem PG ad 165285.vt hæc ad PF; </s>
					<s id="N23592">certè tempus per HG eſt ad <lb></lb>tempus per PG, vt HG ad PG; </s>
					<s id="N23598">igitur tempus per HG eſt ad tempus <lb></lb>per HGF, vt 51764. ad 75628. ſed BX eſt æqualis, eiuſdemque incli­<lb></lb>nationis cum HG; </s>
					<s id="N235A0">igitur tempus, quo percurritur BX eſt BX. vel HG; </s>
					<s id="N235A4"><lb></lb>ſit autem vt BX ad 75628. ita hæc ad aliam 111092. igitur eo tempore, <lb></lb>quo percurruntur HGF, percurruntur in BF 111092. minor BF; igitur <lb></lb>citiùs percurruntur HGF quàm BHF, vel BZF, &amp;c. </s>
					<s id="N235AD">igitur duæ infe­<lb></lb>riores citiùs, quàm duæ ſuperiores. </s>
				</p>
				<p id="N235B2" type="main">
					<s id="N235B4">Ex his manifeſtum eſt, quænam ſint quaſi termini progreſſionis in aſ­<lb></lb>ſumptis duabus chordis; ſi enim diuidatur arcus BF in 6.arcus æquales, <lb></lb>BF tardiſſimè, BHF velociſſimè, &amp;c. </s>
					<s id="N235BC">poſt BHF, BGF, tùm ſingulæ ab <lb></lb>H verſus Z &amp; verſus V reſpondent ſingulæ immediatè AG verſus Z, &amp; <lb></lb>verſus <foreign lang="grc">θ. </foreign></s>
				</p>
				<p id="N235C6" type="main">
					<s id="N235C8"><emph type="center"></emph><emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N235D4" type="main">
					<s id="N235D6"><emph type="italics"></emph>Si ſint duo pendula inæqualia, tempora deſcenſuum per chordas ſimiles, <lb></lb>ſunt in ratione ſubduplicat a earumdem; </s>
					<s id="N235DE">hæ verò ſunt vt radij<emph.end type="italics"></emph.end>; </s>
					<s id="N235E5">ſit enim qua­<lb></lb>drans A <foreign lang="grc">α ρ</foreign>, cuius radius A <foreign lang="grc">α</foreign> ſit ſubquadruplus radij AB; </s>
					<s id="N235F3">ſint chordæ <lb></lb>ſimiles <foreign lang="grc">α ρ</foreign>, BF; </s>
					<s id="N235FD">hæc eſt quadrupla illius; </s>
					<s id="N23601">igitur cum ſit eadem vtriuſ-<pb pagenum="309" xlink:href="026/01/343.jpg"></pb>que inclinatio; </s>
					<s id="N2360A">eo tempore, quo percurretur tota <foreign lang="grc">α ρ</foreign> percurretur tan­<lb></lb>tùm quarta pars BF; </s>
					<s id="N23614">igitur ſuperſunt 1/4 BF; </s>
					<s id="N23618">ſed ſecundo tempore ſen­<lb></lb>ſibili æquali primo percurritur ſpatium triplum ſpatij primi temporis; </s>
					<s id="N2361E"><lb></lb>igitur tota BF percurritur tempore duplo, &amp; <foreign lang="grc">α ρ</foreign> ſubduplo; </s>
					<s id="N23627">igitur tem­<lb></lb>pora ſunt vt radices 1. &amp; 4. igitur in ratione ſubduplicata; </s>
					<s id="N2362D">præterea ſint <lb></lb>chordæ <foreign lang="grc">α</foreign> X <foreign lang="grc">ρ</foreign>, &amp; aliæ duæ BZF ſimiles prioribus; certè ſi prima mino­<lb></lb>ris quadrantis <foreign lang="grc">α</foreign> X percurratur vno tempore. </s>
					<s id="N23641">Prima maioris BF, percur­<lb></lb>ritur duobus temporibus; </s>
					<s id="N23647">ſed in eadem proportione percurrentur duæ <lb></lb>X <foreign lang="grc">β</foreign> ZF, vt patet; </s>
					<s id="N23651">quia vt eſt <foreign lang="grc">ω</foreign> X ad X <foreign lang="grc">ρ</foreign>, ita XZ ad ZF: idem prorſus di­<lb></lb>co, ſi accipiantur tres chordæ, 4.5.6. &amp;c. </s>
					<s id="N2365F">in vtroque arcu. </s>
				</p>
				<p id="N23662" type="main">
					<s id="N23664"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23671" type="main">
					<s id="N23673"><emph type="italics"></emph>Vibratio minor eiuſdem, vel æqualis funependuli breuiore tempore percurri­<lb></lb>tur.<emph.end type="italics"></emph.end></s>
					<s id="N2367C"> Probatur quia percurruntur citiùs duæ chordæ inferiores HGF, <lb></lb>quàm duæ ſuperiores quæcunque per Lem. 16. immò &amp; tres inferiores, <lb></lb>quàm tres ſuperiores, atque ita deinceps; igitur totus arcus inferior <lb></lb>HGF, qui conſtat ex his chordis minoribus ſemper, &amp; minoribus per­<lb></lb>curretur citiùs, quàm ſuperior, &amp; maior.v.g. </s>
					<s id="N2368A">BHF. </s>
				</p>
				<p id="N2368D" type="main">
					<s id="N2368F">Adde quod, multis conſtat experimentis minorem vibrationem citiùs <lb></lb>peragi, quod pluſquam centies à me probatum eſt; </s>
					<s id="N23695">ſi enim ſimul demit­<lb></lb>tantur duo funependula æqualia; </s>
					<s id="N2369B">alterum quidem è ſummo quadrantis <lb></lb>puncto, alterum ex decimo, vel decimoquinto altitudinis gradu, appoſito <lb></lb>in puncto quietis aliquo ſonoro corpore; </s>
					<s id="N236A3">haud dubiè ictum, qui ſequitur <lb></lb>ex minori vibratione, priùs audies; </s>
					<s id="N236A9">tùm ſtatim alium; </s>
					<s id="N236AD">immò ſi numeren­<lb></lb>tur vibrationes vtriuſque eodem tempore plures minoris, maioris verò <lb></lb>pauciores numerabuntur; </s>
					<s id="N236B5">ſæpiùs numeraui 11.minores eo tantùm tem­<lb></lb>pore, quo alter, qui mecum erat 10. maiores numerabat, &amp; 40. circiter <lb></lb>minores dum alter 37.maiores recenſeret; </s>
					<s id="N236BD">&amp; certè ſi vibratio vtraque <lb></lb>maior ſcilicet, &amp; minor per <expan abbr="eũdem">eundem</expan> arcum recurreret, centum minores <lb></lb>eo ferè tempore agerentur, quo 90.maiores; licèt enim vtraque decreſ­<lb></lb>cat, maior tamen decreſcit in maiore proportione, quàm minor, cuius <lb></lb>rei rationem afferemus infrà. </s>
				</p>
				<p id="N236CD" type="main">
					<s id="N236CF">Nec eſt quod aliquis cum Galileo, Baliano, &amp; aliis opponat, omnes <lb></lb>vibrationes, ſiue maiores ſint, ſiue minores eſſe æquè diuturnas, idque <lb></lb>manifeſtis conſtare experimentis, quibus ego alia certiſſima experimen­<lb></lb>ta oppono, quibus etiam vltrò aſſentitur P. Merſennus, Galileo alioqui <lb></lb>addictiſſimus, in verſione eiuſdem Galilei lib.  1. art. </s>
					<s id="N236DA">18. &amp; verò docti <lb></lb>omnes Galileo ſunt addictiſsimi; </s>
					<s id="N236E0">in qua verò proportione minor vibra­<lb></lb>tio breuiore tempore peragatur, quàm major, difficilè dictu eſt, &amp; vix <lb></lb>determinari poteſt, niſi fortè dicatur in ea proportione arcum HF citiùs <lb></lb>percurri, quàm arcum BHF, in qua duæ chordæ HGF citiùs percur­<lb></lb>runtur, quàm duæ BZF; ſed de his fusè aliàs. </s>
				</p>
				<p id="N236EC" type="main">
					<s id="N236EE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N236FB" type="main">
					<s id="N236FD"><emph type="italics"></emph>Velocitates acquiſita in vibrationibus inæqualibus ſunt vt altitudines<emph.end type="italics"></emph.end>; </s>
					<s id="N23706">ſint <lb></lb>enim vibrationes duæ BF, HF; </s>
					<s id="N2370C">dico velocitatem acquiſitam in deſcen-<pb pagenum="310" xlink:href="026/01/344.jpg"></pb>ſu BF eſſe ad acquiſitam in deſcenſu HP, vt vecta AF ad rectam OF, <lb></lb>quod facilè probatur; </s>
					<s id="N23717">quia ex B in F æqualis acquiritur velocitas ſiue <lb></lb>per rectam BF <expan abbr="deſcẽdat">deſcendat</expan> mobile, ſiue per duas BHF, ſiue per tres BHGF, <lb></lb>ſiue per totum quadrantem BHF; </s>
					<s id="N23723">ſed æqualis eſt acquiſita per BF ac­<lb></lb>quiſitæ per AF, vel BE; </s>
					<s id="N23729">quæ omnia conſtant per Lemm.10.&amp; 11.ſimili­<lb></lb>ter acquiſita in recta HF eſt æqualis acquiſitæ in recta OF in duabus <lb></lb>HGF; </s>
					<s id="N23731">immò &amp; in arcu HZF; </s>
					<s id="N23735">igitur acquiſita in arcu BHF eſt ad <lb></lb>acquiſitam in arcu HZF, vt acquiſita in AF ad acquiſitam in OF; </s>
					<s id="N2373B">ſed <lb></lb>illa eſt ad hanc vt AF ad OF, vt conſtat; igitur ſunt vt altitudines, quod <lb></lb>erat probandum. </s>
				</p>
				<p id="N23743" type="main">
					<s id="N23745">Hinc non ſunt vt chordæ, neque vt arcus; </s>
					<s id="N23749">hinc acquiſita in arcu <lb></lb>BHF eſt dupla acquiſitæ in arcu HZF; </s>
					<s id="N2374F">cùm tamen arcus BF non ſit <lb></lb>duplus; ſed ſeſquialter arcus HZF. </s>
				</p>
				<p id="N23755" type="main">
					<s id="N23757"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23763" type="main">
					<s id="N23765"><emph type="italics"></emph>Hinc ſunt diuerſi ictus inæqualium vibrationum in eadem altitudinum ra­<lb></lb>tione<emph.end type="italics"></emph.end>; </s>
					<s id="N23770">quia eadem eſt ratio ictuum, quæ velocitatum acquiſitarum in <lb></lb>puncto percuſsionis; </s>
					<s id="N23776">ſed ratio velocitatum eſt eadem quæ altitudinum, <lb></lb>ſeu perpendicularium per Th.7. igitur eadem ratio ictuum, quæ altitu­<lb></lb>dinum; </s>
					<s id="N2377E">ſed inæqualium vibrationum eiuſdem funependuli diuerſæ ſunt <lb></lb>altitudines; igitur diuerſi ictus, quod erat demonſtrandum. </s>
				</p>
				<p id="N23784" type="main">
					<s id="N23786"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23792" type="main">
					<s id="N23794"><emph type="italics"></emph>In diuerſis funependulis ſimilium vibrationum velocitates ſunt vt chordæ<emph.end type="italics"></emph.end>; </s>
					<s id="N2379D"><lb></lb>ſint enim duo funependula inæqualis A <foreign lang="grc">ρ</foreign>, AF; </s>
					<s id="N237A6">certè ſit vibratio maio­<lb></lb>ris BF, &amp; minoris vibratio ſimilis <foreign lang="grc">α ρ</foreign>, velocitas vibrationis BF eſt vt al­<lb></lb>titudo AF &amp; minoris <foreign lang="grc">α ρ</foreign>, vt altitudo A <foreign lang="grc">ρ</foreign>; </s>
					<s id="N237BA">ſed vt AF eſt ad A <foreign lang="grc">ρ</foreign>, ita BF <lb></lb>ad <foreign lang="grc">α ρ</foreign>; </s>
					<s id="N237C8">ſunt enim triangula proportionalia; </s>
					<s id="N237CC">idem dico de aliis.v.g ZF <lb></lb>&amp; X <foreign lang="grc">ρ</foreign>, iu quo non eſt difficultas: hinc percuſsiones vtriuſque erunt etiam <lb></lb>vt chordæ, quia ſunt vt altitudines. </s>
				</p>
				<p id="N237D8" type="main">
					<s id="N237DA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N237E6" type="main">
					<s id="N237E8"><emph type="italics"></emph>Tempora, quibus peraguntur vibrationes ſimiles funependulorum inæqua­<lb></lb>lium ſunt ferè in ratione ſubduplicata longitudinum, ſeu radiorum<emph.end type="italics"></emph.end>: </s>
					<s id="N237F3">Probatur, <lb></lb>quia tempora deſcenſuum per chordas ſimiles ſunt in ratione ſubdupli­<lb></lb>cata earumdem chordarum, ſiue ſint 2.ſiue ſint tres, &amp; per Lemma 17. <lb></lb>ſed ſi accipiantur plures chordæ, tandem habebitur arcus; </s>
					<s id="N237FD">igitur vibra­<lb></lb>tio per arcum eſt veluti deſcenſus per infinitas ferè chordas æquales; </s>
					<s id="N23803">ſed <lb></lb>tempora horum deſcenſuum ſunt in ratione ſubduplicata chordarum; </s>
					<s id="N23809">&amp; <lb></lb>hæc eſt eadem ratio cum ſubduplicata radiorum; igitur tempora vibra­<lb></lb>tionum ſimilium ſunt ferè in ratione ſubduplicata radiorum. </s>
				</p>
				<p id="N23811" type="main">
					<s id="N23813">Obſeruabis rem <expan abbr="iſtã">iſtam</expan> accuratè, &amp; analyticè diſcuti poſſe, ſit enim qua­<lb></lb>drans ADH maioris vibrationis, &amp; quadrans CED minoris; </s>
					<s id="N2381D">ſitque <lb></lb>CD ſubquadrupla AD, &amp; arcus DE ſubquadruplus DKH; </s>
					<s id="N23823">aſſumatur <lb></lb>DN ſubquadruplus DH; </s>
					<s id="N23829">ſitque DN æqualis DE; </s>
					<s id="N2382D">certè eo tempore, <pb pagenum="311" xlink:href="026/01/345.jpg"></pb>quo percurretur DE, percurretur pluſquam DN; </s>
					<s id="N23836">quippe DN eſt minùs <lb></lb>inclinatus, quàm DE: </s>
					<s id="N2383C">porrò recta NH eodem deinde tempore percur­<lb></lb>retur, ſiue ducatur initium motus AD per arcum DN, ſiue AD per re­<lb></lb>ctam DN, ſiue ab O per rectam ON; quia in N eſt æqualis velocitas <lb></lb>per Lemm. </s>
					<s id="N23846">11. igitur tempus, quo percurritur recta NH, facto initio <lb></lb>motus ex D per rectam, vel arcum DN, eſt ad tempus, quo percurritur <lb></lb>DN, vt 42466.ad DN, id eſt ad 390181. ſit enim vt ON ad 111347. <lb></lb>ita hæc ad OH 179995. detrahatur ON ex 111347.ſupereſt 42466.igi­<lb></lb>tur eo tempore, quo percurritur DE, percurritur pluſquam DN; </s>
					<s id="N23852">per­<lb></lb>curritur tamen minùs, quàm DL; </s>
					<s id="N23858">quia tempus, quo percurritur DL eſt <lb></lb>ad tempus quo percurritur LH facto initio motus in D, vt DL 51764. <lb></lb>ad 41422. igitur eo tempore, quo percurritur DE; percurritur minùs <lb></lb>quàm DL. </s>
				</p>
				<p id="N23862" type="main">
					<s id="N23864">Adde quod rectæ DE, DM, æquali tempore percurruntur; </s>
					<s id="N23868">ſed DM <lb></lb>breuiore tempore percurritur, quàm arcus DL, immò arcus DE citiùs <lb></lb>peragitur, quàm recta DE; </s>
					<s id="N23870">igitur citiùs quàm arcus DL; </s>
					<s id="N23874">ſi verò acci­<lb></lb>piatur arcus DR; </s>
					<s id="N2387A">certè tempus per arcum DE eſt paulò minus tempo­<lb></lb>re per arcum DR; quia tempus, quo percurritur DR eſt ad tempus, quo <lb></lb>percurretur RH, facto initio motus in D, vt 45444.ad 41705.ſed vtrum­<lb></lb>que tempus debet eſſe æquale, vt ſcilicet arcus in DH æquali tempore <lb></lb>cum arcu DE percurratur. </s>
				</p>
				<p id="N23886" type="main">
					<s id="N23888">Obſeruabis præterea, vt inueniatur arcus quadrantis DH, cuius tem­<lb></lb>pus ſit ſubduplum ipſius quadrantis, vel æquale tempori per arcum DE, <lb></lb>aſſumendum eſſe punctum in arcu DH, puta N; </s>
					<s id="N23890">per quod ſi ducatur <lb></lb>HNO, ſitque vt ON ad OV, ita OV ad OH, ipſa NV erit æqualis <lb></lb>ipſi ND; </s>
					<s id="N23898">quippè tempus per DN eſt ad tempus per ON, vt ipſa DN ad <lb></lb>ON; </s>
					<s id="N2389E">ſed tempus per ON eſt ad tempus per NH, vt ON ad NV; </s>
					<s id="N238A2">igi­<lb></lb>tur tempus per DN eſt ad tempus per NH, vt DN ad NV; </s>
					<s id="N238A8">igitur DN, <lb></lb>&amp; NH facto initio motus à D fiunt tempore æquali; </s>
					<s id="N238AE">ſed vt tempus per <lb></lb>rectam DN ad tempus per rectam NH; </s>
					<s id="N238B4">ita tempus per duas DXN ad <lb></lb>tempus per duas NZH; </s>
					<s id="N238BA">ita tempus per 4. æquales inſcriptas arcui DN <lb></lb>ad tempus per 4.æquales inſcriptas arcui NZH, atque ita deinceps; igi­<lb></lb>tur ita tempus per arcum DN ad tempus per arcum NZH. </s>
				</p>
				<p id="N238C2" type="main">
					<s id="N238C4">Quomodo verò poſſit inueniri punctum N, viderint Geometræ; </s>
					<s id="N238C8">nec <lb></lb>enim phyſici eſt inſtituti; habetur autem ex analytica, ſi excipiatur ar­<lb></lb>cus DN. 24. gra. </s>
					<s id="N238D0">20′. </s>
					<s id="N238D3">circiter; ſitque HO ſecans anguli AHO grad.57. <lb></lb>10′. </s>
					<s id="N238D8">ſitque ON, ad OV vt OV ad OH, ipſa NV erit proximè æqualis <lb></lb>ipſi ND: igitur DN. &amp; NH æqualibus temporibus percurrentur. </s>
					<s id="N238DE">Simili­<lb></lb>ter opera eiuſdem analyticæ habebitur arcus, qui peragitur in DZH eo <lb></lb>tempore, quo arcus DNF percurritur, poſſuntque hæc omnia in cano­<lb></lb>nes redigi. </s>
				</p>
				<p id="N238E7" type="main">
					<s id="N238E9"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N238F5" type="main">
					<s id="N238F7"><emph type="italics"></emph>In diuerſis punctis arcus diuerſus impetus producitur.<emph.end type="italics"></emph.end></s>
					<s id="N238FE"> Prob. </s>
					<s id="N23901">ſit enim <lb></lb>pendulum fune ex centro immobili A; </s>
					<s id="N23907">ſitque AO horizontalis, AD <pb pagenum="312" xlink:href="026/01/346.jpg"></pb>perpendicularis; </s>
					<s id="N23910">haud dubiè producit maiorem impetum in O, quàm in <lb></lb>LH quippè in D nullo modo grauitat in ſuppoſitam manum, in H mi­<lb></lb>nùs grauitat, in O maximè; ſed qua proportione plùs, vel minùs graui­<lb></lb>tat, producit maiorem vel minorem impetum, vt patet. </s>
				</p>
				<p id="N2391A" type="main">
					<s id="N2391C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23928" type="main">
					<s id="N2392A"><emph type="italics"></emph>Impetus, quem producit in H, eſt ad impetum, quem producit in O, vt HC <lb></lb>ad DA vel OA.<emph.end type="italics"></emph.end></s>
					<s id="N23933"> Probatur, quia grauitatio in H eſt ad grauitationem in <lb></lb>O, vt CH ad DA, vt demonſtratum eſt ſuprà lib.  de motu in planis in­<lb></lb>clinatis; </s>
					<s id="N2393B">ratio eſt, quia in ea proportione maior eſt, vel minor grauita­<lb></lb>tio, in qua plùs vel minùs impeditur; </s>
					<s id="N23941">atqui in O non impeditur; </s>
					<s id="N23945">quia li­<lb></lb>nea determinationis ad motum eſt eadem cum linea grauitationis; </s>
					<s id="N2394B">quip­<lb></lb>pè globus O grauitat per <expan abbr="Oq;">Oque</expan> ſed OQ eſt Tangens puncti O; </s>
					<s id="N23955">igitur eſt <lb></lb>linea determinationis in puncto O; </s>
					<s id="N2395B">igitur linea determinationis in pun­<lb></lb>cto O eſt eadem cum linea grauitationis; at verò in H linea grauitatio­<lb></lb>nis eſt HG, &amp; determinationis HF diuerſa à priore, ſed de his iam plu­<lb></lb>ra aliàs. </s>
				</p>
				<p id="N23965" type="main">
					<s id="N23967"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N23973" type="main">
					<s id="N23975">Obſeruabis globum prædictum in H diuerſimode poſſe ſuſtineri. </s>
					<s id="N23978">Pri­<lb></lb>mò, per Tangentem HI. </s>
					<s id="N2397E">Secundò applicata potentia in F per FH. Tertiò, <lb></lb>per horizontalem HV tracto ſcilicet fune. </s>
					<s id="N23983">Quartò, per HK. Quintò, per <lb></lb>GH. </s>
					<s id="N23988">Sextò denique in aliis punctis intermediis applicari poteſt poten­<lb></lb>tia; </s>
					<s id="N2398E">ſi primo modo, &amp; ſecundo potentia ſuſtinens pondus in H eſt ad <lb></lb>ſuſtinentem in D ex A vel in O ex Q vt HC ad DA vel HA; </s>
					<s id="N23994">ad ſuſti­<lb></lb>nentem verò ex A in H, vt CH ad CA, ſi tertio per HV potentia ap­<lb></lb>plicata in V eſt ad applicatam in A, dum vtraque ſimul agat vt HC ad <lb></lb>HA; </s>
					<s id="N2399E">ſi quarto modo applicata in K æqualis eſt applicatæ in A, itemque <lb></lb>applicata in Y per YH, vel in O per OH, poſita HZ æquali HA; </s>
					<s id="N239A4">ſi <lb></lb>quinto modo applicata in G per GHS ſuſtinet totum pondus, itemque <lb></lb>applicata in S per SH; ſi denique ſexto modo, pro rata. </s>
				</p>
				<p id="N239AC" type="main">
					<s id="N239AE">Obſeruabis ſecundò rem omninò ſcitu digniſſimam, eſſe duas tantùm <lb></lb>lineas, quibus applicata potentia totum pondus ſuſtinet, ſcilicet GH, HS, <lb></lb>eſſe quoque duas quibus applicata potentia pondus pendulum ſuſtinens <lb></lb>in dato puncto puta H, habet minimam rationem, quæ haberi poſſit ad <lb></lb>potentiam applicatam in A per AH; ſunt autem illæ CH, HV, quæ eſt <lb></lb>ipſa horizontalis. </s>
				</p>
				<p id="N239BC" type="main">
					<s id="N239BE">Obſeruabis tertiò, applicatam in puncto C per CH eſſe minimam <lb></lb>earum omnium, quæ cum alia applicata in A per HA pendulum pondus <lb></lb>ſuſtinere poſſit; </s>
					<s id="N239C6">aliàs verò hinc inde applicatas eſſe maiores, v.g. applica­<lb></lb>tam in E per EH eſſe ad applicatam in A per HA, vt EH ad HA; </s>
					<s id="N239CE">appli­<lb></lb>catam verò in Z eſſe ad <expan abbr="eãdem">eandem</expan> vt ZH ad HA; applicatam in T vt <lb></lb>TH ad HA, &amp;c. </s>
					<s id="N239DA">ſunt autem 4.æquales exceptis maxima, quæ totum pon­<lb></lb>dus ſuſtinet per lineas HS GH, &amp; minimâ, quæ cum applicata in A mi­<lb></lb>nimis viribus ſuſtinet, per lineas CH HV; </s>
					<s id="N239E2">ſi verò aſſumantur quæcum­<lb></lb>que aliæ lineæ, ſunt 4. æquales v.g. accipiatur EH, ſit HB ipſi æqualis <pb pagenum="313" xlink:href="026/01/347.jpg"></pb>producta per H ad X; </s>
					<s id="N239EF">erunt haud dubiè 4.lineæ, quibus eadem applica­<lb></lb>ta potentia cum altera in A ſuſtinebit pondus, ſcilicet HE &amp; oppoſita <lb></lb>HI, HB cum oppoſita HX, ſuppono enim HB eſſe æqualem HE, &amp; BH <lb></lb>pellere verſus H: quæ omnia certè obſeruaſſe non piget, præſertim cùm <lb></lb>tota res iſta iucunda iuxta, atque vtilis eſſe videatur. </s>
				</p>
				<p id="N239FB" type="main">
					<s id="N239FD"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23A0A" type="main">
					<s id="N23A0C">Colligo primò ex his determinationem impetus producti in puncto <lb></lb>O eſſe omninò ſimplicem à propria ſcilicet ponderis penduli grauitatio­<lb></lb>ne, nec quidquam facere potentiam applicatam in A; </s>
					<s id="N23A14">quippe impetus <lb></lb>determinatur ad Tangentem OQ, quæ eſt eadem cum linea grauitatio­<lb></lb>nis; vnde reuerâ ſuſtinetur totum pondus in O. </s>
				</p>
				<p id="N23A1D" type="main">
					<s id="N23A1F"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23A2C" type="main">
					<s id="N23A2E">Secundò, ſi pondus ſit in D, eſt determinatio mixta vtraque æqualis, <lb></lb>nam neque potentia retinens in A eſt maior potentia grauitationis in­<lb></lb>clinantis deorſum; </s>
					<s id="N23A36">alioquin ſi maior eſſet, præualeret; </s>
					<s id="N23A3A">igitur mobile fer­<lb></lb>retur verſus A; </s>
					<s id="N23A40">cùm tamen quieſcat in D, nec etiam maior eſt potentia <lb></lb>grauitationis; </s>
					<s id="N23A46">alioqui pondus ferretur deorſum, nec dicas nullam eſſe <lb></lb>potentiam applicatam in A; </s>
					<s id="N23A4C">nam reuerâ, ſi quis ex puncto A ſuſtinet <lb></lb>pendulum pondus, maximè defatigatur, &amp; maximè agit eius potentia mo­<lb></lb>trix; quomodo verò ſuſtineantur pondera, dicemus lib.  10. </s>
				</p>
				<p id="N23A54" type="main">
					<s id="N23A56"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23A63" type="main">
					<s id="N23A65">Tertiò, ſi pondus ſit in H vel in L eſt determinatio mixta ex duabus <lb></lb>inæqualibus, ita vt determinatio potentiæ, quæ eſt applicata in A ſit mi­<lb></lb>nor determinatione, quæ eſt à grauitatione ponderis; </s>
					<s id="N23A6D">ſit enim pondus in <lb></lb>H, ſitque determinatio altera per lineam HA, altera per lineam HG; </s>
					<s id="N23A73">ſi <lb></lb>vtraque æqualis eſt, linea determinationis mixtæ non eſſet Tangens HF; </s>
					<s id="N23A79"><lb></lb>nec enim angulus AHG diuidit æqualiter bifariam ipſam HF; atqui <lb></lb>cum vtraque determinatio eſt æqualis, poſita quod vtraque linea faciat <lb></lb>angulum, linea nouæ determinationis facit angulum vtrimque æqualem, <lb></lb>vt demonſtrauimus ſuprà. </s>
				</p>
				<p id="N23A85" type="main">
					<s id="N23A87"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23A94" type="main">
					<s id="N23A96">Quartò hinc colligo, determinationem, quæ eſt à potentia applicata <lb></lb>in A creſcere continuè ab O ad D, ita vt in O ſit nulla, in D ſit maxima, <lb></lb>id eſt æqualis alteri determinationi propriæ grauitationis; </s>
					<s id="N23A9E">in reliquis ve­<lb></lb>rò punctis prima eſt ad ſecundam, vt ſinus rectus ſuperioris arcus ad ſi­<lb></lb>num totum, v.g.ſi pondus ſit in L, determinatio grauitationis eſt ad aliam <lb></lb>vt LA ad LR, ſi ſit in H vt HA ad HS, ſi ſit in O vt OA ad nihil; </s>
					<s id="N23AA8">ſi <lb></lb>ſit in D vt DA ad DA; idem dico de omnibus aliis punctis inter­<lb></lb>mediis. </s>
				</p>
				<p id="N23AB0" type="main">
					<s id="N23AB2"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23ABF" type="main">
					<s id="N23AC1">Quintò colligo, impetum grauitationis productum in ſingulis pun­<lb></lb>ctis eſſe ad impetum productum in O, id eſt ad maximum, qui poſſit <pb pagenum="314" xlink:href="026/01/348.jpg"></pb>produci </s>
					<s id="N23ACB">vno inſtanti ab ipſo corpore grani, vt ſinum rectum arcus infe­<lb></lb>rioris ad ſinum totum; </s>
					<s id="N23AD1">ſit enim pondus in L, impetus productus in L <lb></lb>eſt ad productum in O, vt ſinus BL ad LA; </s>
					<s id="N23AD7">ſit in H, vt ſinus HC ad <lb></lb>HA; </s>
					<s id="N23ADD">ſit in O vt OA ad OA, ſit in D vt nihil ad DA: </s>
					<s id="N23AE1">hinc vides con­<lb></lb>trarias vices impetus producti in ſingulis punctis, &amp; determinationis, <lb></lb>quæ eſt à potentia applicata in A; </s>
					<s id="N23AE9">quippè ille continuò imminuitur ab <lb></lb>O ad D; </s>
					<s id="N23AEF">hæc verò continuo creſcit; </s>
					<s id="N23AF3">ille totus eſt in O nullus in D; </s>
					<s id="N23AF7">hæc <lb></lb>tota in D, nulla in O; </s>
					<s id="N23AFD">ille eſt ad totum, vt ſinus arcus inferioris ad ſi­<lb></lb>num totum; hæc verò eſt ad totam, ſeu maximam, vt ſinus arcus ſuperio­<lb></lb>ris ad ſinum totum. </s>
				</p>
				<p id="N23B05" type="main">
					<s id="N23B07"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23B14" type="main">
					<s id="N23B16">Sextò, hinc colligo rationem à priori huius imminutionis impetus; </s>
					<s id="N23B1A"><lb></lb>cum enim impetus deſtruatur ne ſit fruſtrà; </s>
					<s id="N23B1F">certè propter <expan abbr="eãdem">eandem</expan> ratio­<lb></lb>nem non producitur, ne ſcilicet ſit fruſtrà; </s>
					<s id="N23B29">cùm enim impetus ſit vt mo­<lb></lb>tus, ſit mobile in L cum duplici determinatione alteram per lineam LA <lb></lb>alteram L <foreign lang="grc">δ</foreign>; </s>
					<s id="N23B35">ſit autem hæc ad illam vt LA ad LR, vel vt L <foreign lang="grc">δ</foreign> æqualis <lb></lb>LA ad L <foreign lang="grc">β</foreign> æqualem LR, ſitque arcus LO grad. 30. LR eſt ſubdupla <lb></lb>LA; </s>
					<s id="N23B47">ſit <foreign lang="grc">β υ</foreign> æqualis L <foreign lang="grc">δ</foreign>, ipſique parallela, &amp; <foreign lang="grc">υ δ</foreign> æqualis L <foreign lang="grc">β</foreign> &amp; paralle­<lb></lb>la; </s>
					<s id="N23B5D">certè hoc poſito, motus erit per L <foreign lang="grc">υ</foreign>, ſcilicet per diagonalem, vt ſæ­<lb></lb>piùs ſuprà demonſtrauimus; </s>
					<s id="N23B67">igitur ſi tantùm eſſet determinatio L <foreign lang="grc">δ</foreign> mo­<lb></lb>tus eſſet L <foreign lang="grc">δ</foreign>; </s>
					<s id="N23B75">ſi verò conjungatur determinatio L <foreign lang="grc">β</foreign>, motus erit L <foreign lang="grc">υ</foreign>; </s>
					<s id="N23B81">ſed <lb></lb>impetus eſt vt motus; </s>
					<s id="N23B87">igitur impetus L <foreign lang="grc">δ</foreign>, cum vtraque determinatione <lb></lb>conjunctus non haberet totum ſuum effectum, id eſt motum L <foreign lang="grc">δ</foreign>; </s>
					<s id="N23B95">igitur <lb></lb>aliquid illius eſt fruſtrà; </s>
					<s id="N23B9B">igitur producitur tantùm impetus vt L <foreign lang="grc">υ</foreign>; </s>
					<s id="N23BA3">ſed <lb></lb>vt L <foreign lang="grc">υ</foreign> ad L <foreign lang="grc">δ</foreign>, ita LB ad LA; nam triangula L <foreign lang="grc">υ δ</foreign>, &amp; BLA ſunt æqua­<lb></lb>lia, &amp; æquiangula, vt patet. </s>
				</p>
				<p id="N23BB7" type="main">
					<s id="N23BB9"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23BC5" type="main">
					<s id="N23BC7">Septimò colligo, ſingulis inſtantibus mutari determinationem quæ eſt <lb></lb>ab A, &amp; conſequenter determinationem mixtam, ipſamque acceſſionem <lb></lb>impetus noui: </s>
					<s id="N23BCF">hinc etiam rectè explicatur, in quo poſitum ſit illud impe­<lb></lb>dimentum ratione cuius corpus rectà deorſum non tendit; quippè in <lb></lb>eo tantùm poſitum eſt, quod ſit noua determinatio, idem dico de reſi­<lb></lb>ſtentia. </s>
				</p>
				<p id="N23BD9" type="main">
					<s id="N23BDB">Obſeruabis autem idem præſtare funem affixum in A ratione conti­<lb></lb>nuitatis, &amp; vnionis ſuarum partium, quod præſtaret potentia in A fune <lb></lb>ipſo trahens, vt conſtat, ſeu pondus contranitens ex rotula appenſum. </s>
				</p>
				<p id="N23BE2" type="main">
					<s id="N23BE4"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23BF0" type="main">
					<s id="N23BF2">Octauò colligo, creſcere impedimentum ab O in D in ratione ſi­<lb></lb>nuum verſorum arcus ſuperioris; </s>
					<s id="N23BF8">cùm enim in L v. g. motus ſit ad mo­<lb></lb>tum liberum in O vt L <foreign lang="grc">υ</foreign> ad L <foreign lang="grc">δ</foreign> vel vt LB ad LA, impeditur motus vt <lb></lb>RO; </s>
					<s id="N23C0C">nam motus, vel impetus in L eſt minor impetu in O, differentia <lb></lb>vtriuſque RO, ſed RO eſt ſinus verſus arcus OL; idem dico de <lb></lb>reliquis. </s>
				</p>
				<pb pagenum="315" xlink:href="026/01/349.jpg"></pb>
				<p id="N23C18" type="main">
					<s id="N23C1A"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23C26" type="main">
					<s id="N23C28">Nonò colligo hoc impedimentum facere quidem, ne tantus impetus <lb></lb>nouus accidat, non tamen facere vt productus antè pereat; </s>
					<s id="N23C2E">quippe ni­<lb></lb>hil impetus antè producti deſtruitur per ſe; </s>
					<s id="N23C34">licèt determinatio noua per <lb></lb>Tangentem nouam accedat in ſingulis punctis; </s>
					<s id="N23C3A">nihil tamen impetus eſt <lb></lb>fruſtrà; </s>
					<s id="N23C40">vt in reflexione dictum eſt, adde quod determinatio prior, nihil <lb></lb>prorſus confert; </s>
					<s id="N23C46">quia tota impeditun à potentia retinente in A immo­<lb></lb>biliter; dixi per ſe, quia per accidens propter aliquam tenſionem chor­<lb></lb>dæ poteſt aliquid deſtrui, quæ tenſio eſt prorſus per accidens. </s>
				</p>
				<p id="N23C4E" type="main">
					<s id="N23C50"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23C5C" type="main">
					<s id="N23C5E">Decimò colligo inde reddi rationem à priori, cur ille motus vibra­<lb></lb>tionis funependuli ſit acceleratus; </s>
					<s id="N23C64">quia impetus additur ſingulis inſtan­<lb></lb>tibus, &amp; nihil deſtruitur; </s>
					<s id="N23C6A">immò ſi deſtrueretur iuxta rationem prædicti <lb></lb>impedimenti, &amp; pondus eſſet in H, cùm ratio impedimenti ſit SO, &amp; <lb></lb>ratio noui impetus CH æqualis SO; </s>
					<s id="N23C72">haud dubiè in H <expan abbr="tantũdem">tantundem</expan> pro­<lb></lb>duceretur impetus, quantum deſtrueretur; igitur nullum ſentiretur pon­<lb></lb>dus in H, quod abſurdum eſt. </s>
				</p>
				<p id="N23C7E" type="main">
					<s id="N23C80"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23C8C" type="main">
					<s id="N23C8E"><emph type="italics"></emph>Velocitates acquiſitæ in funependulis inæqualibus ſunt vt altitudines<emph.end type="italics"></emph.end>; ſit <lb></lb>enim in figura. </s>
					<s id="N23C99">Th. 10. Funependulum maius AH, minus GH; </s>
					<s id="N23C9D">ſit vi­<lb></lb>bratio minoris FYH; </s>
					<s id="N23CA3">ſit vibratio maioris DKH: </s>
					<s id="N23CA7">dico velocitatem <lb></lb>acquiſitam in prima vibratione eſſe ad acquiſitam in ſecunda, vt AH ad <lb></lb>GH; </s>
					<s id="N23CAF">ſi verò vibratio maioris ſit tantùm LKH; </s>
					<s id="N23CB3">dico eſſe æqualem ve­<lb></lb>locitatem vtriuſque, quæ omnia patent ex dictis: hinc ſeruari poſſunt <lb></lb>quæ cumque proportiones ictuum inflictorum à malleis, vel ſimul, vel <lb></lb>ſucceſſiue, &amp;c. </s>
				</p>
				<p id="N23CBD" type="main">
					<s id="N23CBF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23CCB" type="main">
					<s id="N23CCD"><emph type="italics"></emph>Ex dictis poſſunt multa determinari, ſeu cognoſci primo cognito numero vi­<lb></lb>brationum funependulorum inæqualium, quæ eodem tempore peraguntur, co­<lb></lb>gnoſci poſſunt altitudines, ſeu longitudines funium<emph.end type="italics"></emph.end>; </s>
					<s id="N23CDA">ſunt enim longitudines, <lb></lb>vt quadrati numerorum permutando; </s>
					<s id="N23CE0">ſint enim duo funependula A, &amp; <lb></lb>B, &amp; numerentur vibrationes 5. penduli A &amp; 7. penduli B æquali tem­<lb></lb>pore; aſſumantur quadrati vtriuſque 25. &amp; 49. certè longitudo penduli <lb></lb>A, erit ad longitudinem penduli B vt 49. ad 25. Secundò, ex cognita <lb></lb>minima longitudine cognoſcitur maxima v.g.ſit funependulum tripeda­<lb></lb>le, cuius integra vibratio tempore vnius ſecundi minuti peragitur, vt <lb></lb>aliqui volunt (quod tantùm exempli gratia aſſumptum ſit) numerentur. </s>
					<s id="N23CF0"><lb></lb>v.g. 10. vibrationes huius tripedalis funependuli eo tempore, quo duæ <lb></lb>æntùm vibrationes alterius maioris numerantur; ſint quadrati 100. &amp; <lb></lb>4. certè longitudo maioris eſt ad longitudinem maioris vt 4. ad 100.igi­<lb></lb>tur ſi 4. dant 100. quid dabunt 3. habeo 75. igitur longitudo maioris <lb></lb>funependuli eſt 75. pedum. </s>
					<s id="N23CFF">Tertiò, poteſt cognoſci altitudo putei quan­<lb></lb>tumuis altiſſimi, vel alterius loci editi, ex quo demittitur corpus graue; </s>
					<s id="N23D05"><pb pagenum="316" xlink:href="026/01/350.jpg"></pb>ſi enim toto eo tempore, quo corpus graue cadit, numerentur 6. vibratio­<lb></lb>nes tripedalis funependuli; </s>
					<s id="N23D0F">haud dubiè motus ille durauit ſex minutis <lb></lb>ſecundis; igitur ſi præcognoſcatur quantum ſpatij percurratur deorſum, <lb></lb>dum fluit vnum ſecundum minutum, quod ſit.v.g. </s>
					<s id="N23D17">ſpatium pedum 18 6/7 <lb></lb>hoc poſito, quadrentur tempora ſcilicet, &amp; 6. habeo 1. &amp; 36. iam facio <lb></lb>regulam trium, ſi 1.dat. </s>
					<s id="N23D1E">18 6/7 quid dabunt 36. &amp; habeo 619. pedes mi­<lb></lb>nus 1/2. </s>
				</p>
				<p id="N23D25" type="main">
					<s id="N23D27">Obſeruabis autem dictum fuiſſe à me ſuprà funependulum tripedale <lb></lb>peragere ſuam integram vibrationem tempore vnius ſecundi minuti; </s>
					<s id="N23D2D"><lb></lb>quod certè, vt ait eruditus Merſennus, ſæpiùs obſeruatum eſt; </s>
					<s id="N23D32">hæc autem <lb></lb>eſt obſeruatio Merſenni, quam habet in Baliſt. prop.15.eamque ſæpiùs, <lb></lb>vt ipſe ait, iteratam: </s>
					<s id="N23D3C">Itaque dicit tripedalis ſili ſpatio quadrantis horæ, <lb></lb>nongentas vibrationes fuiſſe numeratas, ſed in quadrante horæ ſunt 15. <lb></lb>minuta prima; </s>
					<s id="N23D44">igitur nongenta ſecunda; igitur cum ſingulæ vibrationes <lb></lb>æquali tempore peragantur ſingulis ſecundis minutis reſpondent. </s>
				</p>
				<p id="N23D4A" type="main">
					<s id="N23D4C">Inde inſignem difficultatem educit idem auctor; </s>
					<s id="N23D50">cum enim in per­<lb></lb>pendiculari deorſum percurrantur 12. pedes tempore vnius ſecundi mi­<lb></lb>nuti, &amp; 48. tempore duorum ſecundorum, quod multis obſeruationibus <lb></lb>comprobatum eſt; </s>
					<s id="N23D5A">certè tempore ſemiſecundi minuti 3. tantùm pedes <lb></lb>confici neceſſe eſt; </s>
					<s id="N23D60">igitur eo tempore, quo radius tripedalis percurritur, <lb></lb>totus etiam percurritur quadrantis arcus, qui eſt 4 3/7; </s>
					<s id="N23D66">igitur maior eſt <lb></lb>motus in arcu, quàm in perpendiculari, quod dici non poteſt; cùm ne <lb></lb>æqualis quidem ſit. </s>
				</p>
				<p id="N23D6E" type="main">
					<s id="N23D70">Ad ſoluendum hunc nodum ſupponendum eſt vibrationes minores <lb></lb>citiùs peragi, quàm maiores; </s>
					<s id="N23D76">quod etiam ibidem obſeruat idem auctor; </s>
					<s id="N23D7A"><lb></lb>igitur non eſt dubium, quin longè plures vibrationes fiant, quàm fierent <lb></lb>ſi omnes eſſent æquales arcui quadrantis; </s>
					<s id="N23D81">ſi enim numeres minores dum <lb></lb>alius numerat maiores; </s>
					<s id="N23D87">cum numerabis 10. ille vix 9. habebit, &amp; ſi <lb></lb>omnes maiores eſſent æquales primæ integræ, dum habes 9. vix haberet <lb></lb>8. itaque non reſpondent ſingulæ vibrationes æquales primæ integræ <lb></lb>ſingulis ſecundis minutis; ſed ferè ſingulis plùs 16. vel 17. minutis <lb></lb>tertiis. </s>
				</p>
				<p id="N23D93" type="main">
					<s id="N23D95">Quare eo tempore, quo percurritur arcus quadrantis funependuli tri­<lb></lb>pedalis non percurruntur in perpendiculo 6. pedes; </s>
					<s id="N23D9B">quia in perpendi­<lb></lb>culo percurruntur 6. pedes eo tempore, quo diagonalis quadrati, ſeu latus <lb></lb>quadrati inſcripti percurritur; </s>
					<s id="N23DA3">v.g. in figura Lem.3.percurruntur DT <lb></lb>dupla radij ID, eo tempore, quo percurritur DP; </s>
					<s id="N23DAB">ſed DP percurritur <lb></lb>tardiùs, quàm arcus DKP; </s>
					<s id="N23DB1">igitur DKP citiùs quàm DT; </s>
					<s id="N23DB5">igitur non <lb></lb>percurritur ſpatium 6. pedum in perpendiculo eo tempore, quo percur­<lb></lb>ritur arcus quadrantis DKP, cuius radius ID ſit tripedalis; </s>
					<s id="N23DBD">præterea <lb></lb>non percurruntur tantùm in perpendiculo eodem tempore pedes ſpatij <lb></lb>4 5/7, vel vndecim, ſi radius conſtat 7. pedibus, vt voluit idem auctor l. 2. <lb></lb>de cauſis ſonorum Prop. 27. Cor. 3. quia ſi radius habet 3. arcus <lb></lb>quadrantis habet 4 5/7. ſi radius habet 7. arcus quadrantis habet 11. <lb></lb>ſed eodem tempore conficitur maius ſpatium in perpendiculo, quàm in <pb pagenum="317" xlink:href="026/01/351.jpg"></pb>arcu, cuius ratio conſtat clariſſimè ex dictis, quia dum mobile mouea­<lb></lb>tur in perpendiculo ſingulis inſtantibus nouum impetum æqualem pri­<lb></lb>mo producit, in arcu verò minorem; </s>
					<s id="N23DD8">igitur minor eſt motus; </s>
					<s id="N23DDC">igitur mi­<lb></lb>nus ſpatium eodem tempore percurritur in arcu, &amp; maius in perpendi­<lb></lb>culo; </s>
					<s id="N23DE4">igitur non percurruntur 11. tantùm in perpendiculo eo tempore <lb></lb>quo 11. percurruntur in arcu; quantum verò ſpatium in perpendiculo <lb></lb>percurratur eo tempore, quo arcus quadrantis dati conficitur, determi­<lb></lb>nabimus infrà. </s>
				</p>
				<p id="N23DEE" type="main">
					<s id="N23DF0">Denique obſeruabis, ex hoc etiam poſſe concludi omnes vibrationes <lb></lb>eiuſdem funependuli non eſſe æquè diuturnas; </s>
					<s id="N23DF6">nam reuerà ſi æquè diu­<lb></lb>turnæ eſſent, &amp; nongentæ numeratæ eſſent ſpatio 15. minutorum; </s>
					<s id="N23DFC">haud <lb></lb>dubiè ſingulæ ſingulis ſecundis minutis reſponderent; igitur eo tempore, <lb></lb>quo tres ſpatij pedes decurrerentur in perpendiculo, in quadrantis arcu <lb></lb>4. 3/7 conficerentur, quod fieri non poteſt. </s>
				</p>
				<p id="N23E06" type="main">
					<s id="N23E08"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23E14" type="main">
					<s id="N23E16"><emph type="italics"></emph>In aſcenſu vibrationis funependuli deſtruitur impetus<emph.end type="italics"></emph.end>; patet, quia deſinit <lb></lb>motus; </s>
					<s id="N23E21">igitur &amp; impetus, ne ſit fruſtrà; </s>
					<s id="N23E25">præterea applicatum eſt princi­<lb></lb>pium deſtructionis impetus; </s>
					<s id="N23E2B">igitur deſtruitur; antecedens ex dicendis <lb></lb>infra clariſſimum euadet. </s>
				</p>
				<p id="N23E31" type="main">
					<s id="N23E33">Deſtruitur autem impetus propter impetum innatum, qui ſingulis in­<lb></lb>ſtantibus contranititur; </s>
					<s id="N23E39">quemadmodum enim in motu violento ſurſum <lb></lb>ideo deſtruitur impetus ab innato, quia hic eſt determinatus ad lineam <lb></lb>deorſum; </s>
					<s id="N23E41">ille verò ſurſum, ex quo determinatio mixta oritur; </s>
					<s id="N23E45">vnde ali­<lb></lb>quid impetus deſtruitur, ne ſit fruſtrà; idem prorſus dicendum eſt in aſ­<lb></lb>cenſu per arcum. </s>
				</p>
				<p id="N23E4D" type="main">
					<s id="N23E4F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23E5B" type="main">
					<s id="N23E5D"><emph type="italics"></emph>Singulis inſtantibus inæqualiter deſtruitur impetus in aſcenſu illo vibratio­<lb></lb>nis<emph.end type="italics"></emph.end>; prob. </s>
					<s id="N23E6A">quia ſingulis inſtantibus mutatur determinatio, id eſt ratio <lb></lb>plani inclinati; </s>
					<s id="N23E70">nam quodlibet punctum arcus, vt ſæpè dictum eſt, facit <lb></lb>planum inclinatum diuerſum; </s>
					<s id="N23E76">igitur lineæ vtriuſque determinationis <lb></lb>faciunt diuerſum angulum; </s>
					<s id="N23E7C">igitur determinatio noua mixta diuerſa eſt; <lb></lb>igitur plùs vel minùs impetus deſtruitur, quia plùs vel minùs eſt fruſtrà, <lb></lb>quod ex dicendis patebit. </s>
				</p>
				<p id="N23E84" type="main">
					<s id="N23E86"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23E92" type="main">
					<s id="N23E94"><emph type="italics"></emph>Deſtruitur impetus in ſingulis punctis iuxta rationem ſinuum rectorum ar­<lb></lb>cuum inferiorum<emph.end type="italics"></emph.end> v.g. ſit arcus aſcenſus DIO, ſitque mobile pendulum in <lb></lb>H; </s>
					<s id="N23EA3">impetus qui deſtruitur in H, eſt ad impetum qui deſtruitur in per­<lb></lb>pendiculari ſurſum (ſuppoſito ſcilicet <expan abbr="tẽpore">tempore</expan>) vt ſinus HC ad ſinum HA; </s>
					<s id="N23EAD"><lb></lb>nam deſtruitur in ea ratione, iuxta quam deſtrueretur in plano inclinato <lb></lb>EH; </s>
					<s id="N23EB4">ſed in planis inclinatis iuxta prædictam rationem impetum deſtrui <lb></lb>demonſtratum eſt ſuo loco; </s>
					<s id="N23EBA">adde quod impetus innatus determinat mo­<lb></lb>bile ad lineam deorſum HG, alius verò ad lineam HM; </s>
					<s id="N23EC0">atqui ſi eſſent <lb></lb>duo gradus impetus, quorum alter eſſet determinatus per HM, alter per <pb pagenum="318" xlink:href="026/01/352.jpg"></pb>HGV, motus fieret per HX, ſed HX eſt æqualis HM; </s>
					<s id="N23ECC">igitur deſtruitur <lb></lb>ſubduplus impetus, quia eſt fruſtrà; </s>
					<s id="N23ED2">ſed HC eſt ſubdupla HA: </s>
					<s id="N23ED6">præterea <lb></lb>impetus innatus retrahit mobile per HE minùs, quàm AD iuxta eam <lb></lb>proportionem, in qua motus per HE eſt minor quàm motus per AD; </s>
					<s id="N23EDE">ſed <lb></lb>motus per HE eſt ad motum per AD vt HE ad AE, vel vt HC ad HA; </s>
					<s id="N23EE4"><lb></lb>igitur illa vis, quæ retrahit mobile per HE eſt ad eam, qua retrahitur <lb></lb>per AD vt HC ad HA; </s>
					<s id="N23EEB">ſed in eadem proportione deſtruitur impetus, <lb></lb>quo mobile fertur ſurſum, in qua retrahitur deorſum; </s>
					<s id="N23EF1">igitur impetus de­<lb></lb>ſtructus in H eſt ad deſtructum in perpendiculo vt HC ad HA; ergo <lb></lb>vt ſinus rectus arcus inferioris eſt ad ſinum totum. </s>
				</p>
				<p id="N23EF9" type="main">
					<s id="N23EFB">Dictum eſt eodem tempore; </s>
					<s id="N23EFF">nam minori tempore minùs impetus de­<lb></lb>ſtruitur, plùs verò maiori; </s>
					<s id="N23F05">vnde quando comparatur impetus deſtructus <lb></lb>in plano inclinato ſurſum cum deſtructo in verticali, ſemper intelligi­<lb></lb>tur vtrumque deſtrui eodem tempore; </s>
					<s id="N23F0D">alioquin vitioſa eſſet proportio, <lb></lb>&amp; comparatio; idem dico de impetu producto, quod de deſtructo. </s>
				</p>
				<p id="N23F13" type="main">
					<s id="N23F15"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N23F21" type="main">
					<s id="N23F23">Inde colliges in eadem proportione minùs impetus deſtrui in aſcenſu <lb></lb>per planum inclinatum, quâ minùs producitur in deſcenſu. </s>
				</p>
				<p id="N23F28" type="main">
					<s id="N23F2A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23F36" type="main">
					<s id="N23F38"><emph type="italics"></emph>Totus impetus qui concurrit ad deſcenſum funependuli, non concurrit ad <lb></lb>aſcenſum,<emph.end type="italics"></emph.end> prob. </s>
					<s id="N23F42">quia impetus innatus non concurrit ad aſcenſum, vt <lb></lb>conſtat ex dictis alibi; ſed hic concurrit ad deſcenſum. </s>
				</p>
				<p id="N23F48" type="main">
					<s id="N23F4A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23F56" type="main">
					<s id="N23F58"><emph type="italics"></emph>Aliquis etiam gradus impetus concurrit ad aſcenſum, qui non concurrit <lb></lb>ad deſcenſum,<emph.end type="italics"></emph.end> probatur, quia vltimo inſtanti deſcenſus aliquid impetus <lb></lb>noui producitur quantumuis minimi, quia ſingulis inſtantibus motus <lb></lb>deorſum aliquid impetus accedit; </s>
					<s id="N23F67">ſed ille impetus non concurrit ad mo­<lb></lb>tum deorſum; </s>
					<s id="N23F6D">quia cum primo illo inſtanti, quo eſt, non concurrat ad <lb></lb>motum, cumque illud inſtans ſit vltimum motus deorſum; </s>
					<s id="N23F73">certè ad mo­<lb></lb>tum deorſum non concurrit, ſed ad motum ſurſum concurrit, nam pri­<lb></lb>mo inſtanti, quo eſt, exigit motum pro ſequenti; eſt autem ſequens <lb></lb>inſtans primum aſcenſus. </s>
				</p>
				<p id="N23F7D" type="main">
					<s id="N23F7F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23F8B" type="main">
					<s id="N23F8D"><emph type="italics"></emph>Aſcenſus funependuli non eſt æqualis deſcenſui:<emph.end type="italics"></emph.end> patet experientiâ; ratio <lb></lb>eſt manifeſta; </s>
					<s id="N23F98">quia impetus innatus non concurrit ad aſcenſum, licèt ad <lb></lb>deſcenſum concurrat; </s>
					<s id="N23F9E">nec dicas impetus gradum vltimum non concur­<lb></lb>rere etiam ad deſcenſum, licèt concurrat ad aſcenſum; </s>
					<s id="N23FA4">nec enim eſt pa­<lb></lb>ritas; </s>
					<s id="N23FAA">quia impetus innatus, ſeu primus gradus eſt perfectiſſimus omnium <lb></lb>productorum; </s>
					<s id="N23FB0">vltimus verò imperfectiſſimus, tùm quia producitur mi­<lb></lb>nori tempore, tùm quia producitur in plano inclinatiſſimo; igitur ſi <lb></lb>comparetur cum primo, pro nullo ferè haberi deber impetus. </s>
				</p>
				<pb pagenum="319" xlink:href="026/01/353.jpg"></pb>
				<p id="N23FBC" type="main">
					<s id="N23FBE"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N23FCA" type="main">
					<s id="N23FCC">Hinc manifeſta ratio, cur funependulum poſt vibrationem deſcenſus <lb></lb>non perueniat in aſcenſu ad tantam altitudinem; </s>
					<s id="N23FD2">nec eſt quod aliqui di­<lb></lb>cant aëra interceptum efficere, ne ad æqualem altitudinem aſcendat, <lb></lb>cùm aër non minùs reſiſtat deſcenſui, quàm aſcenſui; quod quomodo <lb></lb>fiat, iam alibi explicuimus. </s>
				</p>
				<p id="N23FDC" type="main">
					<s id="N23FDE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N23FEA" type="main">
					<s id="N23FEC"><emph type="italics"></emph>Maioris vibrationis aſcenſus imminuitur in maiori proportione, quàm mi­<lb></lb>noris<emph.end type="italics"></emph.end>; </s>
					<s id="N23FF7">certa experientia, cuius ratio eſt, quia in arcu ſuperiore plùs im­<lb></lb>petus deſtruitur, in inferiore minùs; </s>
					<s id="N23FFD">igitur plùs ſpatij detrahitur maiori <lb></lb>vibrationi, quàm minori, ſcilicet in aſcenſu; </s>
					<s id="N24003">hæc ratio demonſtratiua eſt, <lb></lb>quia quò minùs impetus deſtruitur ſingulis inſtantibus, plùs ſpatij ac­<lb></lb>quiritur, vt conſtat ex planis inclinatis; </s>
					<s id="N2400B">ſit enim in eadem figura pla­<lb></lb>num inclinatum DO, &amp; verticale DA; </s>
					<s id="N24011">imprimatur impetus mobili ex D, <lb></lb>certè cum eodem impetu aſcendet per DA &amp; per DO, vt demonſtraui­<lb></lb>mus cum de planis inclinatis; </s>
					<s id="N24019">igitur ſingulis inſtantibus minùs impetus <lb></lb>in DO deſtruitur, quàm in DA; </s>
					<s id="N2401F">vnde maius ſpatium conficitur; </s>
					<s id="N24023">eſt enim <lb></lb>DO maior DA: </s>
					<s id="N24029">ita prorſus accidit in arcu aſcenſus funependuli; </s>
					<s id="N2402D">ſit enim <lb></lb>arcus aſcenſus DH æqualis arcui deſcenſus oppoſiti; </s>
					<s id="N24033">certè tantillùm im­<lb></lb>petus deſtruetur; </s>
					<s id="N24039">igitur arcus aſcenſus ferè accedet ad A; </s>
					<s id="N2403D">ſi vetò arcus <lb></lb>deſcenſus ſit æqualis DL, plùs impetus deſtruetur in aſcenſu; igitur ar­<lb></lb>cus aſcenſus habebit minorem proportionem ad DL, quàm prior ad DH, <lb></lb>&amp; hæc eſt veriſſima ratio luculentiſſimi experimenti, quod ferè omnibus <lb></lb>notum eſt. </s>
				</p>
				<p id="N24049" type="main">
					<s id="N2404B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24057" type="main">
					<s id="N24059"><emph type="italics"></emph>Si proijciatur mobile per ipſum perpendiculum DA cum eo impetu, quo <lb></lb>ex D feratur in A motu naturaliter retardato; </s>
					<s id="N24061">certè cum eodem impetu fere­<lb></lb>tur in O per DO, &amp; per arcum DLO:<emph.end type="italics"></emph.end> probatur quia ex A in D, vel ex O <lb></lb>in D ſiue per chordam OD, ſiue per arcum OHD æqualis impetus ac­<lb></lb>quiritur per Lemma 11. ſed cum eodem impetu, quo ex A fertur in D. <lb></lb>vel ex O in D motu naturaliter accelerato, ex D ferri poteſt in A vel in <lb></lb>O: </s>
					<s id="N24072">dixi cum eodem impetu, ita vt tot gradus impetus concurrant ad aſ­<lb></lb>cenſum, quot ad deſcenſum; </s>
					<s id="N24078">ſi enim aliquis gradus concurrens ad deſ­<lb></lb>cenſum, non concurreret ad aſcenſum; </s>
					<s id="N2407E">haud dubiè non perueniret mo­<lb></lb>bile ad <expan abbr="eãdem">eandem</expan> altitudinem; quod autem æquale ſpatium reſpondeat <lb></lb>aſcenſui, &amp; deſcenſui ſuppoſito æquali impetu, iam demonſtratum eſt ſu­<lb></lb>prà l. 3. &amp; 5. ſed iam examinandæ ſunt proportiones huius deſtructio­<lb></lb>nis impetus in maioribus, &amp; minoribus vibrationibus. </s>
				</p>
				<p id="N24090" type="main">
					<s id="N24092"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2409E" type="main">
					<s id="N240A0"><emph type="italics"></emph>Poteſt determinari in qua parte arcus deſinat motus ſurſum in aſcenſu <lb></lb>vibrationis, ſi cognoſcatur ad quam altitudinem ferretur mobile per ipſum <lb></lb>perpendiculum<emph.end type="italics"></emph.end>; </s>
					<s id="N240AD">fit cum punctum infimum D, ſitque in pendule ille impe­<lb></lb>tus, haud dubiè per arcum ferretur in <foreign lang="grc">α</foreign>, ducatur <foreign lang="grc">α</foreign>Q parallela AO; </s>
					<s id="N240B7">haud <pb pagenum="320" xlink:href="026/01/354.jpg"></pb>dubiè per arcum feretur in Q &amp; per chordam DO perueniet in <foreign lang="grc">θ</foreign>; </s>
					<s id="N240C4">ſi ve­<lb></lb>rò illo impetu ferri tantùm poſſit in B per per DA, fertur in 4.per DO, <lb></lb>&amp; in L per arcum; </s>
					<s id="N240CC">denique ſi ferri tantùm poſſit illo impetu per DA in <lb></lb>G, feretur in 3 per DO, &amp; in H per arcum; </s>
					<s id="N240D2">quæ omnia conſtant ex Th. <lb></lb>20. quia cum eodem impetu aſcendit mobile ad <expan abbr="eãdem">eandem</expan> altitudinem <lb></lb>ſiue per ipſum perpendiculum, ſiue per chordas, ſiue per arcus; ex hoc <lb></lb>confirmatur maximè Th.10. quia ſi diuidatur perpendiculum in partes <lb></lb>æquales ductis parallelis AO, arcus ita diuidetur, vt ſuperior arcus ſit <lb></lb>minor. </s>
					<s id="N240E5">v.g. diuidatur DA in B æqualiter bifariam; </s>
					<s id="N240EB">ducatur BL parallela <lb></lb>AO, non diuidit arcum OD bifariam, cùm arcus OL ſit ſubtriplus arcus <lb></lb>OD; </s>
					<s id="N240F3">igitur cùm eo tantùm impetu, quo in perpendiculo acquireretur in <lb></lb>aſcenſu DB ſubduplum DA, in arcu acquiretur DL, quæ eſt 2/3 totius D­<lb></lb>O; igitur minores vibrationes minùs imminuuntur in aſcenſu, quàm <lb></lb>maiores. </s>
				</p>
				<p id="N240FD" type="main">
					<s id="N240FF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2410B" type="main">
					<s id="N2410D"><emph type="italics"></emph>Hinc tam facilè vibratur funependulum per minimum arcum, v. g. cum <lb></lb>primo impetu, quo aſcenderet ex D in C vel in<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>aſcendit in H<emph.end type="italics"></emph.end>; quia ſcilicet <lb></lb>cum eo impetu, quo minimum ferè ſpatium acquirit in perpendiculo, <lb></lb>notabile ſatis ſpatium decurrit in arcu. </s>
				</p>
				<p id="N24126" type="main">
					<s id="N24128"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24134" type="main">
					<s id="N24136"><emph type="italics"></emph>Hinc tamdiu durant minimæ illa vibrationes; </s>
					<s id="N2413C">quia ſingulæ minima por­<lb></lb>tione imminuuntur, &amp; maiores è contrariò tam citò decurtantur<emph.end type="italics"></emph.end>; </s>
					<s id="N24145">cuius reſ <lb></lb>non eſt alia ratio præter eam, quam ſuprà adduximus, quæ rem ipſam <lb></lb>euincit; eſt tamen inſignis difficultas, quam paulò poſt diſcutiemus in <lb></lb>ſequenti Schol. <emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2415A" type="main">
					<s id="N2415C"><emph type="italics"></emph>Hinc ratio, cur minimo ſerè curſu funependulum etiam grauiſſimum modi­<lb></lb>ca libratione vibretur<emph.end type="italics"></emph.end>; </s>
					<s id="N24168">immò, quod fortè alicui mirum videretur, ipſo an­<lb></lb>helitu grauiſſima pondera moueri poſſunt, quod quiuis facilè probare <lb></lb>poterit; </s>
					<s id="N24170">pro quo diligenter obſeruandum eſt, vt eo dumtaxat ordine an­<lb></lb>helitus repetatur, quo vibrationes fiunt, ita vt iam euntem molem à <lb></lb>tergo impellat; vnde accidet, vt repetito tandem anhelitu maiore motu <lb></lb>funependulum vibretur. </s>
				</p>
				<p id="N2417A" type="main">
					<s id="N2417C"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24188" type="main">
					<s id="N2418A">Obſeruabis primò maximam occurrere difficultatem contra ea, quæ <lb></lb>hactenus demonſtrauimus; ſit enim quadrans AIE, ſitque EA diuiſa <lb></lb>in 4. partes æquales. </s>
					<s id="N24192">v.g. ex A cadat corpus graue in E, &amp; ex E aſcen­<lb></lb>dat denuò per EA eâ lege, vt omnes gradus impetus acquiſiti in deſcen­<lb></lb>ſu concurrant ad aſcenſum, excepto primo gradu impetus innati; </s>
					<s id="N2419C">certè <lb></lb>non aſcendet in A, vt conſtat ex dictis; </s>
					<s id="N241A2">igitur aſcendat in B, &amp; ex B ite­<lb></lb>rum deſcendat in E, redeatque verſus A; </s>
					<s id="N241A8">haud dubiè perueniet tantùm <lb></lb>in C; </s>
					<s id="N241AE">ita vt tantum detrahatur ſpatij in hoc ſecundo aſcenſu, quantum <lb></lb>detractum eſt in primo: idem dico de tertio, quarto, &amp;c. </s>
					<s id="N241B4">ducantur BH, <pb pagenum="321" xlink:href="026/01/355.jpg"></pb>CG, D F parallelæ AI; </s>
					<s id="N241BD">cum ſpatium eo modo decidatur ex area EI, quo <lb></lb>ex perpendiculo EA maiori vibrationi detrahitur IH, ſecundæ minori <lb></lb>HG, tertiæ GF, quartæ FE; igitur plùs detrahitur minoribus, quàm <lb></lb>maioribus. </s>
				</p>
				<p id="N241C7" type="main">
					<s id="N241C9">Reſpondeo, maius ſpatium percurri ſurſum maiore tempore, quàm <lb></lb>minus; </s>
					<s id="N241CF">ſit enim EA conſtans 36. ſpatia iuxta nouam progreſſionem <lb></lb>arithmeticam, ſintque 8. gradus impetus acquiſiti in deſcenſu AE con­<lb></lb>iuncti cum innato: </s>
					<s id="N241D7">primo inſtanti, ſeu tempore percurrentur tantùm 7. <lb></lb>ſpatia, <expan abbr="deſtrueturq́ue">deſtrueturque</expan> vnus gradus impetus, ſecundo 6. <expan abbr="deſtrueturq́ue">deſtrueturque</expan> al­<lb></lb>ter gradus impetus; denique tertio 5. quatto 4. &amp;c. </s>
					<s id="N241E7">igitur 28. ſpatia 7. <lb></lb>inſtantibus; igitur non perueniet in A mobile, ſed conficiet ſpatium, <lb></lb>quod erit ad EA, vt 28. ad 36. porrò ſi cadat ex 28. acquiret 7. gradus <lb></lb>impetus præter innatum, quorum ope ſecundo aſcendet ad 21. tertio ad <lb></lb>15. quartò ad 10. quinto ad 6. ſextò ad 3. ſeptimo ad 1. igitur ſpatium <lb></lb>quod amittit in aſcenſu continet 8. in ſecundo 7. in tertio 6. in quarto <lb></lb>5. in quinto 4. in ſexto 3. in ſeptimo 2. igitur eſt maxima inæqualitas, <lb></lb>quæ pari modo explicari poteſt in progreſſione Galilei. </s>
				</p>
				<p id="N241FA" type="main">
					<s id="N241FC">Secundò, obijci poteſt: </s>
					<s id="N241FF">amitti tantùm ſpatij ſingulis temporibus, <lb></lb>quantum acquiritur primo tempore, vel inſtanti, cum impetu innato: ſed <lb></lb>cum primo ille velocitatis gradu vix intra multos annos conficeretur <lb></lb>modicum ſpatium. </s>
					<s id="N2420A">Reſpondeo, ſi conſideretur tantùm illud ſpatium, <lb></lb>quod acquiritur primo tempore cum impetu non impedito; </s>
					<s id="N24210">haud dubiè <lb></lb>inſenſibile eſt, &amp; licèt infinitus ferè repetatur illud idem ſpatium; </s>
					<s id="N24216">haud <lb></lb>dubiè inſenſibile manet: vnde ſi aſcenſus fiat in 10000. inſtantibus, to­<lb></lb>ties accipi debet illud ipſum ſpatium, ex quo modicum tantùm reſultat, <lb></lb>quod minuitur in ſecundo aſcenſu, itemque in tertio, quarto, &amp;c. </s>
				</p>
				<p id="N24220" type="main">
					<s id="N24222">Vnde tenſio funis, ex quo pendet corpus graue conſideranda eſt, qui <lb></lb>cum propter impetum deſcenſus mox dilatetur, &amp; tendatur, mox contra­<lb></lb>hatur, tùm in aſcenſu, tùm in deſcenſu; </s>
					<s id="N2422A">certè multùm impetus deſtruitur, <lb></lb>quod autem tendatur maximè in deſcenſu prædictus funis, conſtat <lb></lb>multis experimentis ſi minor eſt; nam reuerâ; ſi maior, eſſet multum re­<lb></lb>tardaret motum tùm aëris reſiſtentia, quæ etiam aliquid facit, licèt totus <lb></lb>hic effectus ab illa pendere non poſſit, vt aliqui volunt, tùm etiam partes <lb></lb>funis propiùs ad centrum accedentes, quæ citiùs deſcendunt, &amp;c. </s>
				</p>
				<p id="N24238" type="main">
					<s id="N2423A">Tertiò, ſunt tres determinationes in aſcenſu; </s>
					<s id="N2423E">prima eſt impetus pro­<lb></lb>ducti in deſcenſu determinati ad Tangentem; ſecunda funis per ſuam li­<lb></lb>neam quaſi retrahentis pendulum. </s>
					<s id="N24246">tertia ipſius impetus innati quaſi tra­<lb></lb>hentis deorſum idem pondus; atqui ex pugna trium determinationum in <lb></lb>eodem mobili deſtruitur multùm impetus, vt patet ex dictis alibi. </s>
				</p>
				<p id="N2424E" type="main">
					<s id="N24250">Quartò, cum eo impetu, cuius ope non poſſet corpus aſcendere per <lb></lb>ipſum perpendiculum EA, aſcendit adhuc per arcum EI; </s>
					<s id="N24256">licèt enim cum <lb></lb>co impetu, quo fertur in F poſſit fieri in D, ſed tardiori motu; </s>
					<s id="N2425C">attamen <lb></lb>quia impetus qui pendulo ineſt, eſt determinatus ad talem gradum ve­<lb></lb>locitatis, quo certè per ipſam ED ferri non poteſt; </s>
					<s id="N24264">quod etiam euincitur <lb></lb>ex organis mechanicis, &amp; planis inclinatis; </s>
					<s id="N2426A">nam reuerà moueret aliquis <pb pagenum="322" xlink:href="026/01/356.jpg"></pb>per planum tantillùm inclinatum maximam corporis molem, quam per <lb></lb>aliud planum inclinatius, &amp; accedens propiùs ad verticale minimè mo­<lb></lb>uere poſſet; </s>
					<s id="N24277">cuius effectus alia ratio non eſt, niſi quod impetus, qui im­<lb></lb>primitur mobili ad talem gradum velocitatis ſit determinatus; atqui in <lb></lb>perpendiculo eo motu moueri non poteſt, vt conſtat, ſed in plano lon­<lb></lb>giore. </s>
				</p>
				<p id="N24281" type="main">
					<s id="N24283">Quintò, hinc vera ratio, cur in ſuperiore arcu deſtruatur citò impe­<lb></lb>tus; </s>
					<s id="N24289">tardiùs verò in in inferiore; </s>
					<s id="N2428D">quia, cùm Tangens cuiuſlibet puncti ar­<lb></lb>cus ſit eius planum, &amp; hæc in arcu ſuperiore accedat propiùs ad perpen­<lb></lb>diculum; non mirum eſt, ſi cum eo impetu per arcum ſuperiorem mo­<lb></lb>ueri non poſſit mobile cò non aſcendat, cuius tantùm ope per inferio­<lb></lb>rem arcum aſcendit. </s>
				</p>
				<p id="N24299" type="main">
					<s id="N2429B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N242A7" type="main">
					<s id="N242A9"><emph type="italics"></emph>Omnes vibrationes numerari non poſſunt<emph.end type="italics"></emph.end>; </s>
					<s id="N242B2">certum eſt, cùm ſint infinitæ <lb></lb>ferè inſenſibiles, nec poteſt ſenſu diſcerni, quantus ſit arcus minimæ vi­<lb></lb>brationis; </s>
					<s id="N242BC">ſi tamen deſtrueretur tantùm impetus in aſcenſu ab impetu <lb></lb>innato, nec tenſio funis, triplex determinatio, reſiſtentia aëris, &amp; diuerſæ <lb></lb>partes funis, quarum minores vibrationes impediuntur quidquam fa­<lb></lb>cerent, cognita differentia prima vibrationis &amp; ſecunda, fortè cognoſci <lb></lb>poſſet numerus vibrationum cognito principio progreſſionis; </s>
					<s id="N242C8">quantus <lb></lb>verò ſit numerus vibrationum, quæ incipiunt à maiore, &amp; quantus illa­<lb></lb>rum quæ incipiunt à minore etiam incertum eſt, v.g. ſi funependulum <lb></lb>AD demittatur ex O, &amp; deinde ex L; </s>
					<s id="N242D4">certum eſt quidem eſſe plures vi­<lb></lb>brationes cum demittitur ex O toto eo vibrationum numero, quæ re­<lb></lb>cenſentur, donec perueniatur ad illam vibrationem, cuius aſcenſus con­<lb></lb>ſtat arcu DL; </s>
					<s id="N242DE">nam deinceps æqualis erit numerus earum, quæ conſe­<lb></lb>quentur, &amp; earum, quarum prima demittitur ex L, vt patet; </s>
					<s id="N242E4">quot verò <lb></lb>præcedant vibrationes antequam perueniatur ad illam, cuius aſcenſus <lb></lb>eſt arcus DL; equidem aliqua obſeruatione affixo ſcilicet maiore qua­<lb></lb>drante parieti iu ſuos gradus diſtributo cognoſci poteſt, ſed nunquam <lb></lb>ſatis acurata. </s>
				</p>
				<p id="N242F0" type="main">
					<s id="N242F2">Itaque certum eſt primò accelerari motum in deſcenſu, &amp;c retardari <lb></lb>in aſcenſu. </s>
				</p>
				<p id="N242F7" type="main">
					<s id="N242F9">Secundò, certum eſt impetum nouum accedere in deſcenſu in ſingu­<lb></lb>lis punctis arcus iuxta rationem ſinus recti arcus inferioris; in aſcenſu <lb></lb>verò imminui acquiſitum impetum in eadem ratione, omiſſa ea parte <lb></lb>impetus, quæ deſtruitur tùm in aſcenſu tùm in deſcenſu propter tenſio­<lb></lb>nem funis, &amp; reſiſtentiam aëris. </s>
				</p>
				<p id="N24305" type="main">
					<s id="N24307">Tertiò, certum eſt, primum gradum impetus ſcilicet innatum concur­<lb></lb>rere ad deſcenſum; </s>
					<s id="N2430D">ſecus verò ad aſcenſum, &amp; contra vltimum gradum <lb></lb>concurrere ad aſcenſum, ſecus ad deſcenſum; ſed hic vltimus gradus mi­<lb></lb>nimus eſt, &amp; pro nihilo reputandus. </s>
				</p>
				<p id="N24315" type="main">
					<s id="N24317">Quartò, certum eſt aſcenſum minorem eſſe deſcenſu, nec funependu­<lb></lb>lum ad <expan abbr="cãdem">eandem</expan>, vnde dimiſſum eſt priùs, aſcendere altitudinem. </s>
				</p>
				<pb pagenum="323" xlink:href="026/01/357.jpg"></pb>
				<p id="N24324" type="main">
					<s id="N24326">Quintò, certum eſt arcum deſcenſus maioris vibrationis habere ma­<lb></lb>iorem proportionem ad arcum aſcenſus, qui ſequitur, quàm habeat ar­<lb></lb>cus deſcenſus minoris vibrationis ad ſuum aſcenſum. </s>
				</p>
				<p id="N2432D" type="main">
					<s id="N2432F">Sextò, certum eſt non tantùm imminui arcum aſcenſus ab aëre obſi­<lb></lb>ſtente ſed maximè ab impetu innato retrahente deorſum funependulum; </s>
					<s id="N24335"><lb></lb>tùm etiam maximè ab ipſa tenſione funis, tùm ab ipſo fune adducente <lb></lb>pondus; tùm denique à diuerſis partibus funis, quæ dum ab aliis retinen­<lb></lb>tur, quaſi cum illis pugnant, ex qua pugna ſequitur aliqua clades in <lb></lb>motu. </s>
				</p>
				<p id="N24340" type="main">
					<s id="N24342">Septimò, certum eſt acquiri æqualem impetum ex eadem altitudine <lb></lb>in motu deorſum, ſiue per arcum, ſiue per chordam, ſiue per ipſum per­<lb></lb>pendiculum inæquali tamen tempore; ſimiliter deſtrui æqualem im­<lb></lb>petum in aſcenſu, qui ad <expan abbr="eãdem">eandem</expan> altitudinem pertingit. </s>
				</p>
				<p id="N24350" type="main">
					<s id="N24352">Octauò, certum eſt eo tempore, quo deſcendit mobile per arcum in <lb></lb>ipſo perpendiculo acquirere ſpatium maius ipſo arcu, minus tamen du­<lb></lb>plo radij. </s>
				</p>
				<p id="N24359" type="main">
					<s id="N2435B">Nonò, certum eſt, non accelerari motum per arcum in deſcenſu iuxta <lb></lb>proportionem numerorum 1.3.5.7. vt volunt aliqui; </s>
					<s id="N24361">quia hæc accele­<lb></lb>ratio ex ipſo Galileo ſupponit principium illud, æqualibus temporibus <lb></lb>acquiruntur æqualis velocitatis momenta, ſed inæqualia acquiruntur in <lb></lb>arcu; vt patet ex dictis; </s>
					<s id="N2436B">multò minùs intenditur iuxta proportionem <lb></lb>arcuum qui ſecantur à lineis ductis parallelis horizontali ab iis punctis <lb></lb>perpendiculi, in quibus ſecatur iuxta hos numeros 1. 3. 5. 7. certum eſt <lb></lb>etiam non retardari iuxta <expan abbr="eãdem">eandem</expan> proportionem in aſcenſu: quippe in <lb></lb>hoc in eadem proportione retardatur, qua in illo acceleratur. </s>
				</p>
				<p id="N2437B" type="main">
					<s id="N2437D">Decimò, certum eſt omnes vibrationes non poſſe numerari cuiuſcum­<lb></lb>que longitudinis ſit ipſum funependulum: immò hoc valdè eſſet inutile, <lb></lb>vt inutile eſt noſſe numerum granorum arenæ maris. </s>
				</p>
				<p id="N24385" type="main">
					<s id="N24387">Vndecimò, <expan abbr="certũ">certum</expan> eſt vibrationes minores citiùs abſolui, quàm maiores. </s>
				</p>
				<p id="N2438E" type="main">
					<s id="N24390">Duodecimò, certum eſt tempora vibrationum funependulorum inæ­<lb></lb>qualium eſſe ferè, vt radices longitudinum, &amp; longitudines, vt quadrata <lb></lb>temporum dixi: ferè, nec enim omninò res ita ſe habet. </s>
				</p>
				<p id="N24398" type="main">
					<s id="N2439A">Conſtat ex iis quæ ſuprà diximus, ea omnia, quæ hactenus enumerata <lb></lb>ſunt, certa eſſe cum aliis plurimis ſuprà recenſitis; ſunt etiam aliqua in­<lb></lb>nota. </s>
					<s id="N243A2">Primò incertum fuit hactenus, in qua proportione temporum per­<lb></lb>curratur arcus: </s>
					<s id="N243A8">Equidem certum eſt in qua proportione velocitas creſcit, <lb></lb>vt ſuprà demonſtratum eſt; incertum, quænam ſit progreſſio ſpatiorum <lb></lb>ſeu proportio motus in ſpatio arcus, dato ſcilicet tempore ſenſibili. </s>
				</p>
				<p id="N243B0" type="main">
					<s id="N243B2">Obſeruo tamen, ſi conſideretur hic motus in inſtantibus, demitta­<lb></lb>túrque funependulum è ſummo arcu, ſpatium quod acquiritur primo in­<lb></lb>ſtanti eſt ad ſpatium, quod acquiritur ſecundo, vt ſinus totus ad colle­<lb></lb>ctum ex ſinu toto &amp; ſinu recto immediato arcus inferioris, qui proximè <lb></lb>accedit ad totum; eſt autem ad ſpatium, quod acquiritur tertio inſtan­<lb></lb>ti, vt ſinus totus ad collectum ex ſinu toto &amp; duobus ſinubus rectis im­<lb></lb>mediatis, atque ita deinceps. </s>
				</p>
				<pb pagenum="324" xlink:href="026/01/358.jpg"></pb>
				<p id="N243C6" type="main">
					<s id="N243C8">Obſeruo ſecundò iuxta progreſſionem Galilei, ſi aſſumatur pars tem­<lb></lb>poris ſenſibilis, in qua percurratur ſpatium ſuperius in arcu, non poſſe <lb></lb>cognoſci quanto tempore percurratur reliquus arcus; </s>
					<s id="N243D0">ſit enim trian­<lb></lb>gulum mixtum ABE, quale iam expreſſimus, ſitque primus arcus dato <lb></lb>tempore decurſus ad reliquum vt AD ad DE; </s>
					<s id="N243D8">ducatur DC, ſitque v.g. <lb></lb>trapezus DCBA ad triangulum ABE vt 2. ad.7.dico velocitatem, quæ <lb></lb>acquiritur in arcu AD, eſſe ad illam, quæ acquiritur in AE vt 2.ad 7. &amp; <lb></lb>ad illam, quæ acquiritur in DE, vt 2.ad 5.ſed in hoc motu tempora non <lb></lb>ſunt vt velocitates; </s>
					<s id="N243E5">quia temporibus æqualibus non acquiruntur æqua­<lb></lb>les velocitatis gradus; </s>
					<s id="N243EB">igitur nec ſpatia vt temporum, ſeu velocitatum <lb></lb>quadrata; igitur incertum eſt hactenus, in qua proportione temporum <lb></lb>percurrantur duo arcus dati in quadrante, &amp; quæ proportio ſpatiorum <lb></lb>reſpondeat temporibus datis. </s>
				</p>
				<p id="N243F5" type="main">
					<s id="N243F7">Secundò, incertum etiam hactenus in qua proportione percurratur <lb></lb>velociùs arcus, quàm chorda, &amp; tardiùs, quàm radius in perpendiculo, <lb></lb>&amp; quantum ſpatium in eodem perpendiculo percurratur eo tempore, <lb></lb>quo totus arcus quadrantis peragitur. </s>
				</p>
				<p id="N24400" type="main">
					<s id="N24402">Tertiò incertum eſt, in qua proportione minor vibratio citiùs peraga­<lb></lb>tur, quàm maior; </s>
					<s id="N24408">licèt cognoſci poſſit in qua proportione peragantur ci­<lb></lb>tiùs duæ chordæ inſcriptæ arcui minori, quàm duæ inſcriptæ arcui maio­<lb></lb>ri; &amp; licèt certum ſit omnes chordas ſeorſim ſumptas æqualibus tem­<lb></lb>poribus decurri, &amp; citiùs decurri duas eidem arcui inſcriptas, quàm ſo­<lb></lb>lam inferiorem. </s>
				</p>
				<p id="N24414" type="main">
					<s id="N24416">Quartò incertum eſt, in qua proportione imminuatur impetus tùm in <lb></lb>deſcenſu, tùm in aſcenſu, tùm propter reſiſtentiam aëris, tùm propter ten­<lb></lb>ſionem chordæ, tùm ratione triplicis determinationis in ſingulis pun­<lb></lb>ctis arcus; </s>
					<s id="N24420">licèt certum ſit quantum ſingulis inſtantibus detrahatur im­<lb></lb>petus in aſcenſu ab impetu innato retrahente pendulum deorſum; incer­<lb></lb>tum eſt tamen, quantus ſit ille impetus innatus. </s>
				</p>
				<p id="N24428" type="main">
					<s id="N2442A">Quintò, incertum eſt in qua proportione aſcenſus primæ vibrationis <lb></lb>ſit minor deſcenſu eiuſdem; </s>
					<s id="N24430">incertum etiam, in qua proportione aſcen­<lb></lb>ſus ſecundæ ſit minor aſcenſu prime; </s>
					<s id="N24436">incertum denique, in qua proportio­<lb></lb>ne plùs imminuatur aſcenſus maiorum vibrationum, quàm minorum; li­<lb></lb>cèt certum ſit plùs imminui. </s>
				</p>
				<p id="N2443E" type="main">
					<s id="N24440">Sextò, incertum eſt, quot peragantur vibrationes dati funependulis <lb></lb>item quantus ſit arcus vltimæ vibrationis; </s>
					<s id="N24446">item in qua proportione ma­<lb></lb>ior ſit numerus vibrationum, quarum prima maior eſt numero vibratio­<lb></lb>num, quarum prima minor eſt; denique quot intercipiantur vibratio­<lb></lb>nes in differentia data duorum arcuum. </s>
				</p>
				<p id="N24450" type="main">
					<s id="N24452">Hæc, quæ hactenus propoſuimus in 6. vltimis capitibus, ſunt omninò <lb></lb>incerta, ita vt neque ſenſu percipi poſſint, neque fuerit hactenus vllum <lb></lb>principium, per quod poſsint demonſtrari; niſi fortè primum caput ex­<lb></lb>cipias, de quo infrà. </s>
				</p>
				<p id="N2445C" type="main">
					<s id="N2445E">Primò dubium eſt an numerus vibrationum funependuli maioris ſit <lb></lb>maior numero vibrationum funependuli minoris, poſito quòd primam <pb pagenum="325" xlink:href="026/01/359.jpg"></pb>vtriuſque vibratio ſit ſimilis. </s>
				</p>
				<p id="N24468" type="main">
					<s id="N2446A">Secundò dubium eſt, an numerus vibrationum funependuli longio­<lb></lb>ris ſit æqualis numero vibrationum alterius minoris, poſito quòd prima <lb></lb>vtriuſque ab eadem altitudine demittatur; vel poſito quòd arcus primæ <lb></lb>maioris funependuli ſit æqualis arcui primæ minoris. </s>
				</p>
				<p id="N24474" type="main">
					<s id="N24476">Tertiò dubium eſt, in qua proportione pendula materiæ grauiores <lb></lb>ſuas vibrationes citiùs peragant, quàm pendula materiæ leuioris; </s>
					<s id="N2447C">item­<lb></lb>que dubium, quanto tempore citiùs extinguantur vibrationes penduli <lb></lb>materiæ leuioris, quàm grauioris: </s>
					<s id="N24484">licèt certum ſit citiùs abſolui vibra­<lb></lb>tiones funependuli materiæ leuioris, quàm grauioris; hæc ſunt dubia, <lb></lb>quæ breuiter diſcutiemus in ſequentibus Theorematis. </s>
				</p>
				<p id="N2448D" type="main">
					<s id="N2448F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2449B" type="main">
					<s id="N2449D"><emph type="italics"></emph>Funependula longiora diutiùs vibrantur, quàm breuiora, ſi prima vtriuſ­<lb></lb>que vibratio ſit ſimilis<emph.end type="italics"></emph.end>; </s>
					<s id="N244A8">experientia manifeſta eſt; </s>
					<s id="N244AC">ratio etiam euidens, <lb></lb>quia vt ſe habent ſingulæ vibrationes minoris ad ſingulas maioris; </s>
					<s id="N244B2">ita <lb></lb>omnes minoris ſe habent ad omnes maioris, vt patet; </s>
					<s id="N244B8">ſed ſingulæ maio­<lb></lb>ris diutiùs durant, quàm ſingulæ minoris; </s>
					<s id="N244BE">igitur omnes maioris diutiùs <lb></lb>durant, quàm omnes minoris; igitur funependula longiora diutiùs vi­<lb></lb>brantur, &amp;c. </s>
				</p>
				<p id="N244C6" type="main">
					<s id="N244C8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N244D4" type="main">
					<s id="N244D6"><emph type="italics"></emph>Tot ſunt vibrationes maioris funependuli per ſe, quot ſunt minoris, poſito <lb></lb>quod vtriuſque vibratio prima ſit ſimilis<emph.end type="italics"></emph.end>; </s>
					<s id="N244E1">demonſtratur, ſit enim fune­<lb></lb>pendulum maius AG, &amp; minus AO ſubquadruplum ſcilicet AG, demit­<lb></lb>tatur AG ex AD, &amp; AO ex AB, impetus acquiſitus in G per DG eſt <lb></lb>æqualis acquiſito in perpendiculo AG; </s>
					<s id="N244EB">&amp; impetus acquiſitus in O per <lb></lb>BO eſt æqualis acquiſito in perpendiculo per AO; </s>
					<s id="N244F1">ſed acquiſitus in per­<lb></lb>pendiculo AG eſt duplus acquiſiti in perpendiculo AO, vt conſtat; </s>
					<s id="N244F7">ſunt <lb></lb>enim velocitates, vel impetus acquiſiti in ratione ſubduplicata ſpatio­<lb></lb>rum; </s>
					<s id="N244FF">præterea impetus, qui deſtruitur in aſcenſu GK, eſt æqualis acquiſi­<lb></lb>to in deſcenſu DG, excepto primo gradu; </s>
					<s id="N24505">itemque deſtructus in aſcenſu <lb></lb>OM æqualis acquiſito in deſcenſu BO; </s>
					<s id="N2450B">igitur deſtructus in aſcenſu GK <lb></lb>eſt duplus deſtructi in aſcenſu OM; </s>
					<s id="N24511">itaque poſt deſcenſum BO aſcendat <lb></lb>funependulum in N, ita vt aſcenſus ON ſit minor deſcenſu arcu NM: </s>
					<s id="N24517"><lb></lb>quia ſcilicet ad aſcenſum non concurrit impetus innatus: </s>
					<s id="N2451C">dico quòd poſt <lb></lb>deſcenſum DG aſcendet tantùm in H; </s>
					<s id="N24522">ita vt aſcenſus GH ſit minor deſ­<lb></lb>cenſu toto arcu HK quadruplo MN: </s>
					<s id="N24528">porrò tempus aſcenſus per GK <lb></lb>eſt duplum aſcenſus per OM; </s>
					<s id="N2452E">&amp; ſi concurreret impetus innatus, aſcen­<lb></lb>ſus eſſet æqualis deſcenſui per ſe; </s>
					<s id="N24534">igitur perueniret in K; </s>
					<s id="N24538">igitur ſi non <lb></lb>concurrat vno tempore deeſt ſpatium NM, vel IK, id eſt toto eo tem­<lb></lb>pore, quo aſcendit pendulum AO; </s>
					<s id="N24540">impetus innatus cum aliis concur­<lb></lb>rens ad aſcenſum promoueret mobile toto ſpatio NM, quod deeſt tan­<lb></lb>tùm defectu illius concurſus; </s>
					<s id="N24548">igitur, ſi æquali tempore non concurrat ad <lb></lb>aſcenſum GK; </s>
					<s id="N2454E">certè ex aſcenſu detrahetur tantùm IK æqualis v.g. MN; </s>
					<s id="N24554"><lb></lb>ſi verò duobus temporibus æqualibus non concurrat; </s>
					<s id="N24559">certè ex aſcenſu <pb pagenum="326" xlink:href="026/01/360.jpg"></pb>detrahetur HK quadruplum MN; </s>
					<s id="N24562">nam ſicut idem impetus concurrens <lb></lb>duobus temporibus addit quadruplum ſpatium propter motum accele­<lb></lb>ratum; </s>
					<s id="N2456A">ita ſi non concurrat duobus temporibus, deerit ſpatium qua­<lb></lb>druplum illius quod deeſſet, ſi tantùm vno tempore non concurreret; </s>
					<s id="N24570"><lb></lb>igitur aſcenſus maioris funependuli erit OH; </s>
					<s id="N24575">igitur OH, ON erunt vi­<lb></lb>brationes ſimiles; </s>
					<s id="N2457B">igitur ſi deſcendat AG ex H, &amp; AO ex N, vibrationes <lb></lb>aſcenſus ſecundi erunt adhuc ſimiles propter <expan abbr="cãdem">eandem</expan> rationem; </s>
					<s id="N24585">igitur <lb></lb>&amp; vibrationes tertij aſcenſus, quarti, quinti, atque ita deinceps; </s>
					<s id="N2458B">igitur tot <lb></lb>erunt vibrationes maioris, quot minoris per ſe, ſi prima vtriuſque vi­<lb></lb>bratio ſit ſimilis: dixi per ſe; nam per accidens ratione funis ferè ſemper <lb></lb>accidit mutari iſtum ordinem vibrationum. </s>
				</p>
				<p id="N24595" type="main">
					<s id="N24597">Præterea, cùm impetus, quo pendulum maius aſcendit per GK, <lb></lb>ſit duplus illius, quo minus aſcendit per OM, cùm in ſingulis punctis <lb></lb>aſcenſus OM, &amp; ſingulis aſcenſus GK deſtruatur impetus; </s>
					<s id="N2459F">cum GK ſit <lb></lb>quadruplum OM; </s>
					<s id="N245A5">certè in ſingulis punctis GK impetus deſtruitur ſub­<lb></lb>duplus illius, qui in ſingulis punctis OM deſtruitur; ſi enim æqualis; </s>
					<s id="N245AB">igi­<lb></lb>tur impetus per GK eſſet quadruplus impetus per OM; </s>
					<s id="N245B1">ſi minor ſubdu­<lb></lb>plo v. g. ſubquadruplus; </s>
					<s id="N245BB">igitur impetus per GK eſſet æqualis impetui <lb></lb>per OM; </s>
					<s id="N245C1">ſed eſt tantum duplus; </s>
					<s id="N245C5">igitur ſubduplus deſtruitur in ſingulis <lb></lb>punctis, igitur in æquali punctorum GK numero, ſubduplus tantùm im­<lb></lb>petus deſtrueretur; </s>
					<s id="N245CD">in duplo punctorum numero, æqualis, in quadruplo <lb></lb>punctorum numero, duplus; </s>
					<s id="N245D3">deſtruitur autem in ſingulis punctis GK <lb></lb>ſubduplus; quia ſubduplum tantùm tempus reſpondet ſingulis punctis G <lb></lb>K illius temporis, quod reſpondet ſingulis punctis OM. </s>
				</p>
				<p id="N245DB" type="main">
					<s id="N245DD"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N245EA" type="main">
					<s id="N245EC">Primò colligo, ſolutionem primi dubij propoſiti ſuprà, ita vt non iam <lb></lb>dubium, at certum omninò ſuperſit. </s>
				</p>
				<p id="N245F1" type="main">
					<s id="N245F3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24600" type="main">
					<s id="N24602">Secundò colligo, ſolutionem ſecundi dubij, ſi enim funependulum P <lb></lb>G demittatur ex PR &amp; AG ex AT; </s>
					<s id="N24608">haud dubiè plures erunt vibrationes <lb></lb>penduli PG, quàm AG; </s>
					<s id="N2460E">quia tot eſſent AG, quot PG, ſi AG demittere­<lb></lb>tur ex AD; </s>
					<s id="N24614">ſed plures ſunt vibrationes funependuli AG demiſſi ex AD, <lb></lb>quàm eiuſdem ex AT; </s>
					<s id="N2461A">ergo plures funependuli PG demiſſi ex PR, <lb></lb>quàm AG demiſſi ex AT; vnde ſoluitur prima pars dubij ſecundi, </s>
				</p>
				<p id="N24620" type="main">
					<s id="N24622"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2462F" type="main">
					<s id="N24631">Tertiò colligo, ſolutionem ſecundæ partis eiuſdem dubij; </s>
					<s id="N24635">ſi enim A <lb></lb>O demittatur ex AB, &amp; AG ex AS; </s>
					<s id="N2463B">ita arcus GS ſit æqualis arcui OB; </s>
					<s id="N2463F"><lb></lb>certè erunt plures vibrationes AO, quàm AG, vt patet ex dictis; quod <lb></lb>ſpectat ad tertium dubium, illud ipſum ſoluemus paulò pòſt. </s>
				</p>
				<p id="N24646" type="main">
					<s id="N24648"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24655" type="main">
					<s id="N24657">Quartò ſi demittatur funependulum AG ex AV, vt deſcendat in A <lb></lb>G, ſitque clauus horizonti parallelus in P, non aſcendet ſegmentum PG <lb></lb>in PR, vt vult Galileus; </s>
					<s id="N2465F">quia AV non aſcenderet in AT, quod ipſe ſup-<pb pagenum="327" xlink:href="026/01/361.jpg"></pb>ponit; </s>
					<s id="N24668">atqui ſuprà demonſtrauimus aſcenſum minorem eſſe deſcenſu, non <lb></lb>tantùm propter reſiſtentiam aëris, vt vult ipſe Galileus; ſed propter prin­<lb></lb>cipium intrinſecum deſtructiuum impetus acquiſiti in deſcenſu, de quo <lb></lb>ſuprà. </s>
				</p>
				<p id="N24672" type="main">
					<s id="N24674"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24681" type="main">
					<s id="N24683">Quintò equidem, ſi AG demittatur ex AR, affixo clauo in P, non <lb></lb>modò ſegmentum PG aſcendet in PR, verùm etiam altiùs aſcendet ver­<lb></lb>ſus A; immò gyri plures erunt, ſi clauus affigatur propiùs ad punctum <lb></lb>G, qui certè gyri quò minores erunt, eò citiùs conficientur. </s>
				</p>
				<p id="N2468D" type="main">
					<s id="N2468F"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2469C" type="main">
					<s id="N2469E">Poteſt determinari numerus iſtorum gyrorum; </s>
					<s id="N246A2">ſit enim primò clauus <lb></lb>in P, ſint que APG æquales; </s>
					<s id="N246A8">ſi AG poſt deſcenſum KG aſcenderet in <lb></lb>AD; </s>
					<s id="N246AE">certè ſegmentum PG aſcenderet per ſemicircumferentiam GR <lb></lb>A, in PA, ratio eſt, quia pendulum G deſcendent ex K; </s>
					<s id="N246B4">ſed ex hypotheſi <lb></lb>Galilei ſi deſcenderet ex Y aſcenderet in R; </s>
					<s id="N246BA">igitur cùm aſcendet cum illo <lb></lb>impetu acquiſito in deſcenſu KG, aſcenderet in D ex hypotheſi Galilei; <lb></lb>ſed arcus GD eſt æqualis GRA. </s>
				</p>
				<p id="N246C2" type="main">
					<s id="N246C4">Obſeruabis primò iuxta noſtram hypotheſim, qua diximus pendulum <lb></lb>AG poſt deſcenſum per KG non aſcendere in D, vix poſſe cognoſci <lb></lb>affixo clauo, ad quod punctum circuli GRA ex G pendulum peruentu­<lb></lb>rum ſit; </s>
					<s id="N246CE">ſi enim per GD aſcendat in F, &amp; aſſumatur AZ æqualis DF, non <lb></lb>deeſſent fortè, qui exiſtimarent arcum aſcenſus per GRA eſſe GRZ <lb></lb>æqualem GF; </s>
					<s id="N246D6">ſed plùs impetus deſtruitur in arcu GRZ, quàm in arcu <lb></lb>GF, vt patet ex dictis; </s>
					<s id="N246DC">nam nullum eſt punctum in arcu GF, in quo plùs <lb></lb>impetus deſtruatur, quàm in alio dato arcus GRZ; </s>
					<s id="N246E2">cùm tamen ſint ali­<lb></lb>qua puncta in arcu GRZ, in quibus plùs impetus deſtruitur, quàm in <lb></lb>arcu GF, v.g. in puncto R; </s>
					<s id="N246EC">itaque ducatur FD parallela AD: </s>
					<s id="N246F0">dico quòd <lb></lb>perueniet pendulum in <foreign lang="grc">δ</foreign>; </s>
					<s id="N246FA">quippe cum eodem impetu ad <expan abbr="eãdem">eandem</expan> altitu­<lb></lb>dinem aſcenditur; quæ omnia certa ſunt. </s>
				</p>
				<p id="N24704" type="main">
					<s id="N24706">Obſeruabis ſecundò, ſi affigatur clauus in <foreign lang="grc">θ</foreign>, ſintque P<foreign lang="grc">θ</foreign>G æquales, ex <lb></lb>hypotheſi Galilei; </s>
					<s id="N24714">pendulum G primò ex G perueniet in P, cum eo ſcili­<lb></lb>cet impetu, quo perueniet in T; </s>
					<s id="N2471A">tùm deinde ex P per <foreign lang="grc">β</foreign> redit in G aucto <lb></lb>ſcilicet impetu in deſcenſu P <foreign lang="grc">β</foreign> G, &amp; ex G iterum aſcendit in P; atque ita <lb></lb>deinceps; quippe gyri perennes eſſent, niſi tandem totum filum circa <lb></lb>clauum conuolueretur. </s>
				</p>
				<p id="N2472C" type="main">
					<s id="N2472E">Obſeruabis præterea, aliquid ſimile contingere, cum pondus filo pen­<lb></lb>dulum in gyros, agimus circa mobilem digitum, v.g. quippe vltimi gyri <lb></lb>citiùs abſoluuntur; </s>
					<s id="N24738">quia ſcilicet breuiores ſunt, ſed hæc ſunt facilia; </s>
					<s id="N2473C">ob­<lb></lb>ſeruabis tamen cum voluitur filum illud circa digitum pendulum, non <lb></lb>moueri motu circulari, ſed ſpirali; vnde cùm motus mixtus ſit, in librum <lb></lb>ſequentem reiicimus. </s>
				</p>
				<p id="N24746" type="main">
					<s id="N24748">Obſeruabis deinde, cum pendulum AG deſcendit ex V in G, &amp; prop­<lb></lb>ter clauum, à quo retinetur, filum aſcendit in R, aſcenſum GR ferri bre­<lb></lb>uiore tempore, quàm aſcenſum GT; </s>
					<s id="N24750">quia aſcenſus GT &amp; GD æquali ſe-<pb pagenum="328" xlink:href="026/01/362.jpg"></pb>rè tempore peraguntur; </s>
					<s id="N24759">ſunt enim vibrationes eiuſdem funependuli; </s>
					<s id="N2475D"><lb></lb>quippe licèt minor vibratio minore tempore fiat; </s>
					<s id="N24762">illud tamen ſenſu diſ­<lb></lb>cerni non poteſt, niſi in ſerie multarum vibrationum; </s>
					<s id="N24768">atqui GR perfici­<lb></lb>tur æquali tempore, ſiue pendulum deſcendat ex V; ſiue ex Y; </s>
					<s id="N2476E">acquiritur <lb></lb>enim æqualis impetus vtroque modo; </s>
					<s id="N24774">ſed aſcenſus GR fieret æquali <lb></lb>tempore cum deſcenſu YG; </s>
					<s id="N2477A">hic verò breuiore, quàm VG, vt patet; ſunt <lb></lb>enim numeri vibrationum, vt radices longitudinum. </s>
				</p>
				<p id="N24780" type="main">
					<s id="N24782">Obſeruabis denique poſſe funependulum, PG ſolidum demitti ex A, <lb></lb>ſi tantillùm inclinctur; fed de hoc funependulorum genere agemus <lb></lb>infrà. </s>
				</p>
				<p id="N2478A" type="main">
					<s id="N2478C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24798" type="main">
					<s id="N2479A"><emph type="italics"></emph>Funependulum in fine aſcenſus non quieſcit vno inſtanti<emph.end type="italics"></emph.end>; </s>
					<s id="N247A3">quia numquam <lb></lb>ad perfectam æqualitatem peruenitur; quod eodem modo probatur, <lb></lb>quo ſuprà l. 3. eſt enim par ratio. </s>
				</p>
				<p id="N247AD" type="main">
					<s id="N247AF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N247BB" type="main">
					<s id="N247BD"><emph type="italics"></emph>Figura penduli multum facit ad motum vibrationis<emph.end type="italics"></emph.end>: </s>
					<s id="N247C6">ſphærica omnium <lb></lb>ferè aptiſſima eſt præter Conchoidem, &amp; eam, quæ conſtaret ex duobus <lb></lb>conis in communi baſi coniunctis, vel in gemina pyramide; ratio conſtat <lb></lb>ex cis, quæ diximus de motu naturali. </s>
				</p>
				<p id="N247D0" type="main">
					<s id="N247D2"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N247DE" type="main">
					<s id="N247E0"><emph type="italics"></emph>Funis multùm etiam facit<emph.end type="italics"></emph.end>; </s>
					<s id="N247E9">omnium optimus eſt tenuiſſimus, qui ſci­<lb></lb>licet faciliùs aëra ſecat; </s>
					<s id="N247EF">nec enim dubium eſt, quin huic diuiſioni reſiſtat <lb></lb>aër, cuius reſiſtentiæ analogiam videmus in aqua, quam funis oblongus <lb></lb>non niſi cum ſenſibili reſiſtentia diuidit, vt videre eſt in iis funibus, qui­<lb></lb>bus ab equis naues trahuntur; </s>
					<s id="N247F9">aliqui adhibent ductum auri filum; </s>
					<s id="N247FD">ſed <lb></lb>vnum præſertim obſeruandum eſt, ſcilicet ne præ nimia tenuitate maio­<lb></lb>ris fortè vi ponderis vlterius ducatur, vel dilatetur; </s>
					<s id="N24805">vtrumque enim mo­<lb></lb>tum vibrationis retardat: </s>
					<s id="N2480B">immò pendulum ipſum non deſcriberet ſemi­<lb></lb>circulum; an verò ſemiellypſim vt volunt aliqui, definiemus ſuo loco, <lb></lb>cum de lineis motus. </s>
				</p>
				<p id="N24813" type="main">
					<s id="N24815"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24821" type="main">
					<s id="N24823"><emph type="italics"></emph>Pondus funependuli multùm facit ad vibrationis motum<emph.end type="italics"></emph.end>; </s>
					<s id="N2482C">ſi enim granu­<lb></lb>lum plumbeum appendatur, vix ſuperabit reſiſtentiam funis, qui vt vi­<lb></lb>bretur, optimè tenſus eſſe debet; atqui notabili pondere tendi tantùm <lb></lb>poteſt. </s>
				</p>
				<p id="N24836" type="main">
					<s id="N24838"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24844" type="main">
					<s id="N24846"><emph type="italics"></emph>Materia funependuli multùm etiam facit ad vibrationis motum ſuppoſita <lb></lb>ſcilicet eadem figura<emph.end type="italics"></emph.end>; </s>
					<s id="N24851">quippe tam leuis eſſe poſſet materia, vt nec aëris <lb></lb>vim nec funis reſiſtentiam ſuperaret: </s>
					<s id="N24857">hinc globus ſubereus vel è ſambu­<lb></lb>cea medulla conſtans, tardiùs deſcendit, quàm plumbeus; </s>
					<s id="N2485D">habes apud <lb></lb>Merſennum has proportiones; </s>
					<s id="N24863">globus plumbeus pendulus fune pedum <lb></lb>3. 1/2 è ſummo quadrantis arcu demiſſus aſcendit per arcum oppoſitum <pb pagenum="329" xlink:href="026/01/363.jpg"></pb>æqualem minus vno digito; </s>
					<s id="N2486E">ſubereus verò minus 4/9 arcus quadrantis; </s>
					<s id="N24872"><expan abbr="ſã-buceus">ſam­<lb></lb>buceus</expan> minus 6/7 cereus minus tribus digitis; </s>
					<s id="N2487B">addit præterea <expan abbr="plumbeũ">plumbeum</expan> in <lb></lb>perpendiculo conficere 48. pedes tempore duorum ſecundorum, cereum <lb></lb>paulò maiore tempore; </s>
					<s id="N24887">quod tamen percipi non poteſt; </s>
					<s id="N2488B">ſubereum in eo­<lb></lb>dem ſpatio percurrendo ponere tria ſecunda medullarum 5. veſicam piſ­<lb></lb>cis inflatam 8. ſed hæc accuratè obſeruari non poſſunt; </s>
					<s id="N24893">ſi enim dicam <lb></lb>ſupereſſe, vel deeſſe aliquid, vel ſpatij, vel temporis, quod tamen ſenſu <lb></lb>minimè percipiatur; quis eſt qui contrarium probare poſſit. </s>
				</p>
				<p id="N2489B" type="main">
					<s id="N2489D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N248A9" type="main">
					<s id="N248AB">Obſeruabis primò non eſſe omittendum, quod habet Galileus in dia­<lb></lb>logis, &amp; facilè ex dictis colligi poteſt, ſcilicet pendula diuerſæ longitu­<lb></lb>dini sita poſſe componi, vt vnum vnicam vibrationem efficiat, dum aliud <lb></lb>percurrit 2. vel 3. &amp;c. </s>
					<s id="N248B4">atque ita haberi poſſe quemdam oculorum quaſi <lb></lb>concentum non ſonorum ſed motuum, v.g. ſi ſit alter funis longus 4. pe­<lb></lb>des; </s>
					<s id="N248BE">alter verò vnum, pendulum ex illo duas percurret; </s>
					<s id="N248C2">quia numeri <lb></lb>vibrationum ſunt, vt tempora; </s>
					<s id="N248C8">hæc verò ſubduplicata longitudinum; </s>
					<s id="N248CC">hîc <lb></lb>autem vides quadam ſpeciem diapaſon, cuius proportio in his numeris <lb></lb>poſita eſt 1/2; </s>
					<s id="N248D4">ſi vero aliud funependulum ſit longum 9. pedes, conficiet <lb></lb>&amp; alterum vnum hoc eodem tempore tres vibrationes; </s>
					<s id="N248DA">ſi ſit aliud, 16. <lb></lb>pedes longum, &amp; alterum vnum; </s>
					<s id="N248E0">hec eodem tempore conficiet 4. vibra­<lb></lb>tiones, atque ita deinceps poteris habere quamlibet proportionem in <lb></lb>numeris vibrationum ex ipſa combinationum regula; ſed profectò non <lb></lb>magnam voluptatem ex hac quaſi oculorum muſicâ percipies, ſaltem <lb></lb>ego modicam percipere potui. </s>
				</p>
				<p id="N248EC" type="main">
					<s id="N248EE">Obſeruabis ſecundò, hactenus actum eſſe à nobis de primo funepen­<lb></lb>dulorum genere ſatis longa tractatione; iam ergo ſupereſt, vt de aliis <lb></lb>agamus. </s>
				</p>
				<p id="N248F6" type="main">
					<s id="N248F8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24904" type="main">
					<s id="N24906"><emph type="italics"></emph>Pondus pendulum contorto fune gyros agit reciprocos in plano horizontali<emph.end type="italics"></emph.end>; </s>
					<s id="N2490F"><lb></lb>ratio petitur tantùm ex compreſſione intorti funis, qui dum ſe ſe redu­<lb></lb>cit ad priſtinum ſtatum, pendulum pondus in gyros agit; </s>
					<s id="N24916">cum verò acce­<lb></lb>leretur motus, &amp; nouus ſemper accedat impetus, pendulum ipſum funi <lb></lb>etiam priſtino ſtatui reſtituto quaſi primam gratiam refert, cùm impe­<lb></lb>tum in eum refundat; </s>
					<s id="N24920">ſi enim funis ſolus adeſſet nullo pendulo pondere <lb></lb>tenſus; </s>
					<s id="N24926">haud dubiè ſtatim quieſceret, vbi ſublata eſſet compreſſio; </s>
					<s id="N2492A">at verò <lb></lb>quia impetus ponderi pendulo impreſſus adhuc durat funem ipſum in <lb></lb>contrariam partem intorquet; donec tandem poſt multos gyros repeti­<lb></lb>tos pendulum pondus quieſcat. </s>
				</p>
				<p id="N24934" type="main">
					<s id="N24936"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24942" type="main">
					<s id="N24944">Obſeruabis plures eſſe huius funependuli motus affectiones, quæ certè <lb></lb>demonſtrari poſſunt; quia tamen cauſa huius, qui ſequitur ex compreſ­<lb></lb>ſione eſt noua potentia motrix, quàm mediam vocamus, cuius mirifica <lb></lb>vis vix cognoſci poteſt, niſi probè cognoſcatur ratio denſi, rari, &amp;c. </s>
					<s id="N2494E">tra-<pb pagenum="330" xlink:href="026/01/364.jpg"></pb>ctationem hanc in alium Tomum reiicimus, in quo fusè agemus de om­<lb></lb>nibus affectionibus huius potentiæ. </s>
				</p>
				<p id="N24958" type="main">
					<s id="N2495A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24966" type="main">
					<s id="N24968"><emph type="italics"></emph>Corpus oblongum flexibile in altera extremitate immobiliter affixum, ſi in­<lb></lb>curuetur non modò reducit ſeſe ad priſtinum ſtatum, verùm etiam multas <lb></lb>tremulas vibrationes hinc inde facit<emph.end type="italics"></emph.end>; </s>
					<s id="N24975">quarum cauſa eſt motus acceleratus <lb></lb>eiuſdem potentiæ motricis mediæ; has quoque vibrationes remitti­<lb></lb>mus. </s>
				</p>
				<p id="N2497D" type="main">
					<s id="N2497F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 36.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2498B" type="main">
					<s id="N2498D"><emph type="italics"></emph>Funis tenſus in vtraque extremitate affixus, ſi pulſetur infinitas ferè tremu­<lb></lb>laſque vibrationes hinc inde peragit<emph.end type="italics"></emph.end>; ſunt etiam mirabiles harum vibra­<lb></lb>tionum affectiones, quas multis Theorematis in eodem volumine pro­<lb></lb>ſequemur. </s>
				</p>
				<p id="N2499C" type="main">
					<s id="N2499E">Diceret aliquis; </s>
					<s id="N249A1">igitur in hoc tractatu omnia, quæ ſpectant ad motum <lb></lb>non habentur; Reſpondeo, tractatum hunc eſſe potiſſimum inſtitutum <lb></lb>ad demonſtrandas omnes affectiones tùm motus grauium, tùm motus <lb></lb>impreſſi à principio extrinſeco, intactis prorſus iis motibus, qui ſunt vel <lb></lb>à potentia motrice animantium, in ipſis dumtaxat animantibus, de qui­<lb></lb>bus agemus ſuo loco, quales ſunt progredi, currere, volare, notare, repe­<lb></lb>re, &amp;c. </s>
					<s id="N249B1">vel à leuitate corporum, ſi fortè aliquis motus eſt à leuitate, <lb></lb>quod hîc non diſcutio, ſed remitto in librum de graui &amp; leui; </s>
					<s id="N249B7">vel de­<lb></lb>nique ab illa potentiâ mediâ, cui omnes motus tenſorum; compreſſorum, <lb></lb>arcuum; reique tormentariæ tùm hydraulicæ, pneumaticæ, &amp;c. </s>
					<s id="N249BF">tribue­<lb></lb>mus: </s>
					<s id="N249C4">de his certè motibus in hoc tractatu non agemus; </s>
					<s id="N249C8">quia cùm non <lb></lb>poſſint demonſtrari illorum affectiones, niſi cognoſcantur illorum cau­<lb></lb>ſæ; </s>
					<s id="N249D0">neque hæ cognoſci poſſint, niſi multa alia cognoſcantur, vt certiſſi­<lb></lb>mum eſt; minùs prudenter factum eſſet, ſi de iis hoc loco diſputatio <lb></lb>inſtitueretur. </s>
				</p>
				<p id="N249D8" type="main">
					<s id="N249DA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 37.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N249E6" type="main">
					<s id="N249E8"><emph type="italics"></emph>Eſt aliud corporis libratilis genus<emph.end type="italics"></emph.end> ſi ſit v. g. corpus oblongum, grane, <lb></lb>&amp; ſolidum AF in ſitu horizontali innixum plano verticali EBCD; </s>
					<s id="N249F7">ſi <lb></lb>enim extremitas F attollatur per arcum FG circa centrum B; </s>
					<s id="N249FD">haud du­<lb></lb>biè altera A deprimetur per arcum AI circa idem centrum B; </s>
					<s id="N24A03">at ſtatim <lb></lb>G deſcendet motu naturaliter accelerato in F, &amp; propter acquiſitum in <lb></lb>deſcenſu, deſcendet infra horizontalem GF per arcum FH, circa cen­<lb></lb>trum C, &amp; I aſcendet in A, tùm in K, ſed K ſtatim deſcendet, atque ita <lb></lb>deinceps; </s>
					<s id="N24A0F">donec tandem poſt multas vibrationes quieſcat AF in ſitu <lb></lb>horizontali; </s>
					<s id="N24A15">porrò G deſcendit, quia GI non eſt in æquilibrio, cùm <lb></lb>centrum grauitatis ſit in M; igitur BG, quæ eſt longior BI, deſcen­<lb></lb>det. </s>
				</p>
				<p id="N24A1D" type="main">
					<s id="N24A1F"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24A2C" type="main">
					<s id="N24A2E">Primò colligo, motum accelerari in deſcenſu GF, quia impetus acqui­<lb></lb>ſitus in G remanet adhuc in Q, &amp; nouus acquiritur, vt ſæpe dictum eſt. </s>
				</p>
				<pb pagenum="331" xlink:href="026/01/365.jpg"></pb>
				<p id="N24A37" type="main">
					<s id="N24A39"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24A46" type="main">
					<s id="N24A48">Secundò, impetum acquiſitum in G eſſe minorem acquiſito in <expan abbr="q;">que</expan> &amp; <lb></lb>acquiſitum in Q minorem acquiſito in F; quia momentum in G eſt ad <lb></lb>momentum in E, vt OB ad FB, vt ſuprà dictum eſt multis locis. </s>
				</p>
				<p id="N24A54" type="main">
					<s id="N24A56"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24A63" type="main">
					<s id="N24A65">Tertiò colligo, eſſe inuerſas rationes accelerationis in funependulo, &amp; <lb></lb>in priori, quod vibratur in plano verticali: quippe in iſto impetus ac­<lb></lb>quiſitus in ſuperiore arcu eſt maior acquiſito in inferiore, ſecus in illo. </s>
				</p>
				<p id="N24A6D" type="main">
					<s id="N24A6F"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24A7C" type="main">
					<s id="N24A7E">Quartò colligo, iſtas vibrationes non eſſe perpetuas, quia ſecunda eſt <lb></lb>minor prima, &amp; tertia minor ſecunda, atque ita deinceps propter ratio­<lb></lb>nem, quam attulimus ſuprà. </s>
				</p>
				<p id="N24A85" type="main">
					<s id="N24A87"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24A94" type="main">
					<s id="N24A96">Quintò colligo, vibrationes minores fieri citiùs, quàm maiores, v. g. <lb></lb>QF quàm GF, quod multis conſtat experimentis, &amp; ratio eſt manifeſta; </s>
					<s id="N24A9F"><lb></lb>quia QF ſit æqualis QG; certè QF accedit propiùs ad perpendicularem <lb></lb>quàm GQ; </s>
					<s id="N24A9G"> igitur cùm ſit æqualis, breuiore tempore percurretur, quod <lb></lb>clariſſimum eſt. </s>
				</p>
				<p id="N24AAC" type="main">
					<s id="N24AAE"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24ABB" type="main">
					<s id="N24ABD">Sextò colligo, eaſdem vel ſimiles ſequi ſi AF ſuſpendatur ex LN; eſt <lb></lb>enim prorſus eadem ratio. </s>
				</p>
				<p id="N24AC3" type="main">
					<s id="N24AC5"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24AD1" type="main">
					<s id="N24AD3">Septimò colligo, alia corpora etiam cubica, vel alterius figuræ plano <lb></lb>horizontali v. g. ipſi ſolo incubantia, ſi tantillùm è ſuo ſitu remouean­<lb></lb>tur per ſimiles vibrationes ſeſe in illum reſtituere; immò ex minima <lb></lb>percuſſione multis huiuſmodi vibrationibus percuſſum corpus contre­<lb></lb>miſcit. </s>
				</p>
				<p id="N24AE3" type="main">
					<s id="N24AE5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 38.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24AF1" type="main">
					<s id="N24AF3"><emph type="italics"></emph>Si corpus ſolidum pendulum circa punctum immobile ita voluatur, vt ex <lb></lb>verticali ſitu amoueatur; </s>
					<s id="N24AFB">haud dubiè deſcendet, aſcendetque per vibrationes <lb></lb>repetitas<emph.end type="italics"></emph.end>; </s>
					<s id="N24B04">&amp; hoc eſt vltimum vibrationum genus, quarum eadem eſt <lb></lb>prorſus ratio, &amp; cauſa, quam ſuperioribus tribuimus, iis ſcilicet, quæ in <lb></lb>plano verticali à pendulo pondere deſcribuntur; </s>
					<s id="N24B0C">nam in vtroque genere <lb></lb>vibrationum primò acceleratur motus; </s>
					<s id="N24B12">ſecundò plùs initio, minùs ad fi­<lb></lb>nem vibrationis, tertiò non ſunt perpetuæ vibrationes; </s>
					<s id="N24B18">quartò ad aſcen­<lb></lb>ſum non concurrit impetus innatus; quintò, impetus deſtruitur cum ma­<lb></lb>iore proportione in maiore vibratione, quàm in minore, &amp;c. </s>
					<s id="N24B20">quæ vtri­<lb></lb>que generi ſunt communia. </s>
				</p>
				<p id="N24B25" type="main">
					<s id="N24B27"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 39.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24B33" type="main">
					<s id="N24B35"><emph type="italics"></emph>Funependulum, &amp; corpus oblongum eiuſdem longitudinis non deſcendunt <lb></lb>equè velociter, ſi ex eadem altitudine demiſſa circa <expan abbr="centrũ">centrum</expan> immobile vibrentur<emph.end type="italics"></emph.end>; </s>
					<s id="N24B44"><pb pagenum="332" xlink:href="026/01/366.jpg"></pb> ſit enim corpus oblongum AB vibratum circa centrum immobile A <lb></lb>per arcum BC, ſitque pendulum pondus C fune CA, demiſſum, &amp; vi­<lb></lb>bratum per arcum BC; </s>
					<s id="N24B50">certè tardiùs funependulum hoc arcum BC per­<lb></lb>curret, quàm corpus oblongum, quod multis experimentis comprobatum <lb></lb>eſt; </s>
					<s id="N24B58">ratio eſt, quia in pondere funependulo ſolum pondus E cenſeri de­<lb></lb>bet cauſa motus; </s>
					<s id="N24B5E">quippe, licèt funis aliquid conferat; </s>
					<s id="N24B62">quia tamen tam <lb></lb>exilis eſſe poteſt, vt vix quidquam addat póderis, pro nihilo computatur; </s>
					<s id="N24B68"><lb></lb>igitur totus motus eſt ab ipſo pondere pendulo; at verò in corpore ob­<lb></lb>longo AB, quod ſit v. g. parallelipedum, vel cylindricum, non tantùm eſt <lb></lb>motus à puncto B, verùm etiam à punctis FE, &amp;c. </s>
					<s id="N24B75">cum enim punctum <lb></lb>F, v. g. ſi ſeorſim ſumatur, percurrat arcum FG citiùs quàm punctum B <lb></lb>ſeorſim arcum BC, certè punctum F, quaſi deorſum rapit punctum B igi­<lb></lb>tur totum corpus AB citiùs abſoluit ſuam vibrationem, quàm funepen­<lb></lb>dulum, quod erat probandum. </s>
				</p>
				<p id="N24B84" type="main">
					<s id="N24B86"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 40.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24B92" type="main">
					<s id="N24B94"><emph type="italics"></emph>Vt ſuſtineatur corpus oblongum AB, faciliùs ſuſtinetur in B, quàm in P, <lb></lb>&amp; in F, quàm in E, &amp; in E quàm in H,<emph.end type="italics"></emph.end> atque ita deinceps (ſuppono autem, <lb></lb>quòd poſſit volui circa centrum A) ratio clara eſt ex vecte, de quo ſuo <lb></lb>loco; immò licèt AB penderet tantùm vnam vnciam, poſſet aliquod <lb></lb>aſſignari punctum iuxta A, in quo ab homine robuſtiſſimo ſuſtineri non <lb></lb>poſſet in ſitu horizontali AB. </s>
				</p>
				<p id="N24BA8" type="main">
					<s id="N24BAA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 41.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24BB6" type="main">
					<s id="N24BB8"><emph type="italics"></emph>Si deſcendat cylindrus AB in AC circa centrum A, &amp; occurrat in AC <lb></lb>alteri corpori, ictum maximum infliget ex puncte F, ſi AF eſt media pro­<lb></lb>portionalis inter AE, AB, &amp; habeatur tantum ratio impetus abſolutè ſumpti <emph.end type="italics"></emph.end>; </s>
					<s id="N24BC5"><lb></lb>hoc fuit iucundiſſimum Theorema, quod in lib.  1. demonſtrauimus; </s>
					<s id="N24BCA">ne­<lb></lb>que hîc repeto; </s>
					<s id="N24BD0">vnum tantùm addo valdè paradoxon in punctum G eſſe <lb></lb>maximum ictum, non tamen maximam vim, ſcilicet ad mouendum; </s>
					<s id="N24BD6"><lb></lb>nam in D maior erit vis, quàm in G, &amp; in I, quàm in D; erit tamen mi­<lb></lb>nor motus, ſeu minor impreſſio. </s>
				</p>
				<p id="N24BDD" type="main">
					<s id="N24BDF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 42.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24BEB" type="main">
					<s id="N24BED"><emph type="italics"></emph>In maiori proportione deſtruitur impetus in aſcenſu vibrationis eiuſdem <lb></lb>corporis oblongi, quam in aſcenſit vibrationis funependuli<emph.end type="italics"></emph.end>; </s>
					<s id="N24BFA">conſtat certè cla­<lb></lb>riſſimis experimentis; </s>
					<s id="N24C00">ratio eſt, quia plures partes impetus innati reſi­<lb></lb>ſtunt; quippè impetus innatus funis tam paruus eſt, vt pro nullo ha­<lb></lb>beatur. </s>
				</p>
				<p id="N24C08" type="main">
					<s id="N24C0A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 43.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24C16" type="main">
					<s id="N24C18"><emph type="italics"></emph>Hinc ſunt pauciores vibrationes corporis oblongi, quàm funependuli,<emph.end type="italics"></emph.end> cum <lb></lb>ſinguli aſcenſus plùs impetus deſtruant in vibrationibus corporis ob­<lb></lb>longi, quàm funependuli: </s>
					<s id="N24C2B">Hinc citiùs quieſcit corpus oblongum vibra­<lb></lb>tum, quàm funependulum; </s>
					<s id="N24C31">licèt vtrumque ex eadem altitudine demitta­<lb></lb>tur; quod etiam multis experimentis comprobatur, &amp; ratio patet ex <lb></lb>dictis. </s>
				</p>
				<pb pagenum="333" xlink:href="026/01/367.jpg"></pb>
				<p id="N24C3D" type="main">
					<s id="N24C3F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 44.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24C4B" type="main">
					<s id="N24C4D"><emph type="italics"></emph>Vibrationes minores corporis oblongi citiùs peraguntur, quàm minores<emph.end type="italics"></emph.end>; ex­<lb></lb>perientia certa eſt, ratio verò eadem cum ea, quam explicuimus ſuprà <lb></lb>in funependulis. </s>
				</p>
				<p id="N24C5A" type="main">
					<s id="N24C5C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 45.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24C68" type="main">
					<s id="N24C6A"><emph type="italics"></emph>Minùs producitur impetus in E, v.g. corporis oblongi, ſcilicet in deſcenſu, <lb></lb>quàm ſi AE ſeparata eſſet ab AB<emph.end type="italics"></emph.end>; </s>
					<s id="N24C77">patet, plùs tamen producitur, quàm ſi <lb></lb>E deferretur à B, vt accidit in funependulis; </s>
					<s id="N24C7D">prima pars eſt certa; </s>
					<s id="N24C81">quia <lb></lb>corpus oblongum AE perficit citiùs ſuam vibrationem, quàm AB; ſecun­<lb></lb>da etiam probatur, quia alioqui vibratio corporis oblongi, &amp; vibratio <lb></lb>funependuli eiuſdem longitudinis æquali tempore percurreretur. </s>
				</p>
				<p id="N24C8B" type="main">
					<s id="N24C8D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 46.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24C99" type="main">
					<s id="N24C9B"><emph type="italics"></emph>Si punctum H eſſet nodus longè grauior reliquo AB, extremitas B percur­<lb></lb>reret citius arcum BC, quàm ipſum perpendiculum<emph.end type="italics"></emph.end>; </s>
					<s id="N24CA8">quia ſcilicet impetus <lb></lb>nodi A ſeg mentum HB ſecum abriperet; </s>
					<s id="N24CAE">ſed eo tempore, quo percurri­<lb></lb>tur arcus HI, non percurritur, perpendiculum æquale arcui BC, vt pa­<lb></lb>tet; </s>
					<s id="N24CB6">immò poſſet ita componi corpus oblongum, vt punctum B tùm in <lb></lb>perpendiculo, tùm in arcu BC, æquè citò moueretur; multa haud <lb></lb>dubiè dicenda ſuperſunt de hoc pendulorum genere, quæ <lb></lb>remittimus in appendicem, quam huic Tomo <lb></lb>ſubnectimus. <lb></lb><figure id="id.026.01.367.1.jpg" xlink:href="026/01/367/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N24CC8">
				<pb pagenum="334" xlink:href="026/01/368.jpg"></pb>
				<figure id="id.026.01.368.1.jpg" xlink:href="026/01/368/1.jpg"></figure>
				<p id="N24CD2" type="head">
					<s id="N24CD4"><emph type="center"></emph>LIBER SECVNDVS, <lb></lb><emph type="italics"></emph>DE MOTV NATVRALI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24CE1" type="head">
					<s id="N24CE3"><emph type="center"></emph>LIBER NONVS, <lb></lb><emph type="italics"></emph>DE MOTV MIXTO EX RECTO, ET <lb></lb>Circulari, vel ex pluribus Circularibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24CF2" type="main">
					<s id="N24CF4">MOTVS mixtus eſſe poteſt vel ex recto, <lb></lb>&amp; circulari, vel ex duobus rectis, &amp; <lb></lb>circulari, vel ex duobus circularibus, &amp; <lb></lb>recto, vel ex pluribus circularibus, at­<lb></lb>que ita deinceps: de iis acturus ſum in <lb></lb>hoc libro, reiectis tamen lineis iſtorum motuum in <lb></lb>Tomum ſequentem. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N24D07" type="main">
					<s id="N24D09"><emph type="center"></emph><emph type="italics"></emph>DEFINITIO<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24D16" type="main">
					<s id="N24D18"><emph type="italics"></emph>MOtus mixtus ex circulari &amp; recto ille eſt, ad quem concurrit duplex <lb></lb>impetus, quorum vnus ſit determinatus ad motum rectum, &amp; alius <lb></lb>ad circularem, vel vnus tantum impetus, ad cremam, &amp; rectam lineam ſim <lb></lb>modo determinatus.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N24D25" type="main">
					<s id="N24D27">Hunc modum explicabimus infrà in Theorematis; </s>
					<s id="N24D2B">interea definitio, <lb></lb>ſatis clara eſt mihi videtur: exemplum habes in rota, quæ in recto plano <lb></lb>voluitur. </s>
				</p>
				<p id="N24D33" type="main">
					<s id="N24D35"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24D42" type="main">
					<s id="N24D44"><emph type="italics"></emph>Motus mixtus ex duobus circularibus eſt, ad quem concurvit impetus, vel <lb></lb>vnicus, vel duplex ad duas lineas circulares determinatus<emph.end type="italics"></emph.end>; </s>
					<s id="N24D4F">ſimiliter de­<lb></lb>finiri poteſt mixtus in duobus, &amp; circulari; duobus circularibus &amp; recto, <lb></lb>pluribus circularibus. </s>
				</p>
				<p id="N24D57" type="main">
					<s id="N24D59">Sed quæſo, cum audis motum mixtum ex duobus, caue credas, duos <lb></lb>motus ineſſe eidem mobili; quod certè fieri non poteſt, ſed tantùm plu­<lb></lb>res impetus, vel vnicum ad diuerſas lineas determinatum. </s>
				</p>
				<pb pagenum="335" xlink:href="026/01/369.jpg"></pb>
				<p id="N24D65" type="main">
					<s id="N24D67"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24D74" type="main">
					<s id="N24D76"><emph type="italics"></emph>Illa partes mouentur velociùs, quæ tempore aquali maius ſpatium acquirunt <lb></lb>tardiùs verò, que minus ſpatium, clariſſimum eſt, nec maiori indiget expli­<lb></lb>catione.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N24D82" type="main">
					<s id="N24D84"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24D91" type="main">
					<s id="N24D93"><emph type="italics"></emph>Cum vtraque determinatio motus ad <expan abbr="eãdem">eandem</expan> partem ſpectat, acquiritur <lb></lb>maius ſpatium; </s>
					<s id="N24D9F">tum verò ad diuerſas partes minus, at que ita prorata<emph.end type="italics"></emph.end>; hoc <lb></lb>etiam Axioma certum eſt. </s>
				</p>
				<p id="N24DA8" type="main">
					<s id="N24DAA"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24DB6" type="main">
					<s id="N24DB8"><emph type="italics"></emph>Rotæ circa idem centrum mobilis ſemicirculi oppoſiti in partes contrarias <lb></lb>feruntur, motu ſcilicet orbis per arcus ſcilicet æquales<emph.end type="italics"></emph.end>; </s>
					<s id="N24DC7">nam anguli oppoſiti <lb></lb>æquales ſunt; ſed arcus ſunt vt anguli. </s>
				</p>
				<p id="N24DCD" type="main">
					<s id="N24DCF"><emph type="center"></emph><emph type="italics"></emph>Poſtulatum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N24DDB" type="main">
					<s id="N24DDD"><emph type="italics"></emph>Liceat rotare orbem in plana ſuperficie, in conuexa, in concaua, in æquali. </s>
					<s id="N24DE4"><lb></lb>inæquali, ita vt motus orbis conueniat cum motu centri, vel ab eo diuerſus ſit.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N24DEA" type="main">
					<s id="N24DEC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24DF9" type="main">
					<s id="N24DFB"><emph type="italics"></emph>Rota, quæ mouetur in ſuperficie plana, mouetur motu mixto ex recto centri <lb></lb>&amp; circulari orbis<emph.end type="italics"></emph.end>; </s>
					<s id="N24E0A">ſit enim AQLZ incubans plano AD in quo rotatur, <lb></lb>ſitque AD recta æqualis arcui <expan abbr="Aq;">Aque</expan> certè poſito quod motus orbis ſit æ­<lb></lb>qualis motui centri, id eſt poſito quod æqualibus temporibus ſegmentum <lb></lb>plani percurratur motu centri v.g. QE vel AD æquale arcui, qui circa <lb></lb>centrum O conuoluitur motu orbis, v.g. arcui AQ, quodlibet punctum <lb></lb>peripheriæ rotæ mouebitur motu mixto ex recto, &amp; circulari v. g. pun­<lb></lb>ctum L motu centri fertur verſus V &amp; motu orbis verſus Q; ſi enim <lb></lb>eſſet tantum motus centri verſus E, omnes partes mouerentur motu recto <lb></lb>v.g. L per rectam LV, A per rectam AD; </s>
					<s id="N24E30">ſi verò eſſet tantùm motus <lb></lb>orbis, omnes partes mouerentur tantùm motu circulari v. g. L, per ar­<lb></lb>cum LZ; A per arcum AZ; </s>
					<s id="N24E3C">at cum ſimul ſit vterque motus, id eſt vtraque <lb></lb>determinatio, certè vtraque confert de ſuo; igitur eſt motus mixtus. </s>
				</p>
				<p id="N24E42" type="main">
					<s id="N24E44"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24E51" type="main">
					<s id="N24E53"><emph type="italics"></emph>Vnicum tantùm punctum rotæ mouetur metu recto, ſcilicet centrum, cætera <lb></lb>per lineam curuam<emph.end type="italics"></emph.end>; </s>
					<s id="N24E60">de centro conſtat, quia cùm ſemper æqualiter diſter <lb></lb>à planis AD &amp; LV, ſcilicet eodem radio OL, ON; </s>
					<s id="N24E66">certè percurrit OE <lb></lb>parallelam vtrique; ſed parallela vtrique eſt recta, punctum verò L mo­<lb></lb>uetur per lineam curuam, vt conſtabit ex illius deſcriptione, quàm tra­<lb></lb>demus infrà. </s>
				</p>
				<p id="N24E72" type="main">
					<s id="N24E74"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24E81" type="main">
					<s id="N24E83"><emph type="italics"></emph>Si diuidatur arcus LQ in tres arcus aquales &amp; planum AD in tres par­<lb></lb>tes æquales, poteſt aſſignari punctum, in quo ſit L decurſo prime arcu LK<emph.end type="italics"></emph.end>; </s>
					<s id="N24E92">ſi <lb></lb>enim eſſet tantùm <expan abbr="coętri">centri</expan>, eſſet in <foreign lang="grc">μ</foreign>, ſi motus orbis eſſet in K; </s>
					<s id="N24E9C">igitur <lb></lb>ſit recta MI parallela LV, ſitque KI æqualis AB, vel L <foreign lang="grc">μ</foreign>; </s>
					<s id="N24EA6">haud dubiè erit <pb pagenum="336" xlink:href="026/01/370.jpg"></pb>in I; </s>
					<s id="N24EAF">nec enim deſcendet infra MI, vt conſtat: </s>
					<s id="N24EB3">ſic motus orbis dat LK, <lb></lb>vel MK motus centri L <foreign lang="grc">μ</foreign> vel KI; </s>
					<s id="N24EBD">igitur vterque ſimul LI vel KI: </s>
					<s id="N24EC1">ſi­<lb></lb>militer decurſo arcu KH, punctum rotæ L erit in G; </s>
					<s id="N24EC7">nam motus orbis <lb></lb>dat LH, vel NH, vel motus centri AC vel LV; igitur ſi aſſumatur HG <lb></lb>æqualis LV, vterque motus dabit LIG. </s>
				</p>
				<p id="N24ECF" type="main">
					<s id="N24ED1"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24EDE" type="main">
					<s id="N24EE0">Hinc colligo, deſcriptionem lineæ, quam ſuo motu ſeu flux^u deſcri­<lb></lb>bit punctum L, cuius infinita puncta aſſignari poſſunt, ſi enim diuidatur <lb></lb>planum æquale arcui LQ in tot partes, in quot diuiditur arcus LQ, &amp; <lb></lb>cuilibet ſinui recto arcus aſſumpti addatur ſegmentum plani conſtans <lb></lb>tot partibus, quot partibus arcus aliis arcubus v.g.ſinui MK, KI æqua­<lb></lb>lis L <foreign lang="grc">μ</foreign>, ſinui NH, LV, denique ſinui toti OQ tota LY, habebuntur ſin­<lb></lb>gula puncta huius lineæ L, I, G, F quam rotatilem appellamus; quæ certè <lb></lb>eò acuratiùs deſcribetur, quò plura eius puncta ſignabuntur, id eſt quò <lb></lb>diuidetur arcus LQ in plures arcus, &amp; planum LV in plures partes. </s>
				</p>
				<p id="N24EFA" type="main">
					<s id="N24EFC"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24F09" type="main">
					<s id="N24F0B">Linea quoque rotatilis puncti A deſcribi poteſt diuiſo arcu AZ in <lb></lb>tres arcus, &amp; plano AD in 3. pattes; </s>
					<s id="N24F11">ſint enim ſinus TX, Y <foreign lang="grc">π</foreign> ſitque TS <lb></lb>æqualis AB, YR æqualis AG, &amp; ZP æqualis AD; </s>
					<s id="N24F1B">certè deſcribetur hæc <lb></lb>linea per puncta ASRP à quo plura puncta ſignabuntur, eò accuratiùs <lb></lb>deſcribetur, quæ omnia conſtant ex dictis; </s>
					<s id="N24F23">nam motus orbis dat AT vel <lb></lb>XT motus centri AB; igitur TS. </s>
				</p>
				<p id="N24F29" type="main">
					<s id="N24F2B"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24F38" type="main">
					<s id="N24F3A">Hinc vides punctum L oppoſitum puncto contactus ita moueri, vt <lb></lb>motus orbis addatur motui centri; punctum verò A ita mouetur, vt mo­<lb></lb>tus orbis detrahatur motui centri. </s>
				</p>
				<p id="N24F42" type="main">
					<s id="N24F44"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24F51" type="main">
					<s id="N24F53">Hinc etiam deſcribi poteſt linea, quam deſcribit quodlibet punctum <lb></lb>interioris circuli v.g. punctum E; </s>
					<s id="N24F5B">deſcribatur enim arcus quadrátis &amp; 2. <lb></lb>diuidatur in 3. arcus æquales, ducanturque per puncta ſignata 3.4. rectæ <lb></lb>parallelæ OE, aſſumatur 3. 5. æqualis L <foreign lang="grc">μ</foreign> &amp; 4, 6, æqualis LV; denique <lb></lb>2.7. æqualis LV, <expan abbr="connectanturq́ue">connectanturque</expan> puncta ſignata per lineam nouam, E <lb></lb>5.6.7. hæc eſt linea quam deſcribit ſuo motu mixto punctum C, quæ <lb></lb>conſtat ex dictis. </s>
				</p>
				<p id="N24F71" type="main">
					<s id="N24F73"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24F80" type="main">
					<s id="N24F82">Aliter deſcribi poteſt hæc linea rotatilis; </s>
					<s id="N24F86">ſit enim AD diuiſa v.g. in <lb></lb>tres partes æquales, <expan abbr="itemq́ue">itemque</expan> OE ex punctis <foreign lang="grc">ρ</foreign> Q, deſcribantur circuli <lb></lb>æquales rotæ, <expan abbr="aſſumanturq́ue">aſſumanturque</expan> arcus BS æqualis LK &amp; arcus CR æqua­<lb></lb>lis LK, &amp; habebis puncta SR: </s>
					<s id="N24F9E">ſimiliter aſſumatur arcus <foreign lang="grc">μ</foreign> I æqualis LK <lb></lb>&amp; alter V.G. æqualis LH, &amp; habebis puncta IG, idem fiet pro aliis pun­<lb></lb>ctis; hinc vides rotatiles deſcribi poſſe per ſinus, &amp; per arcus. </s>
				</p>
				<pb pagenum="337" xlink:href="026/01/371.jpg"></pb>
				<p id="N24FAE" type="main">
					<s id="N24FB0"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24FBD" type="main">
					<s id="N24FBF">Collige punctum L in arcu deſcenſus LQ ita moueri, vt motus orbis <lb></lb>addat ſinus rectos motui centri v.g. motus orbis LK addit ſinum rectum <lb></lb>MK; punctum vero oppoſitum A ita mouetur in arcu AZ, vt motus or­<lb></lb>bis detrahat ſinus rectos motui centri v. g. motus orbis AT detrahit <lb></lb>ſinum XT, punctum Z ita vt aſcendit per arcum ZL, vt motus orbis <lb></lb>addat motui centri ſinus verſos v. g. motus orbis arcus ZQ addit ſinum <lb></lb>verſum Z 11. denique punctum oppoſitum Q ita deſcendit per arcum <lb></lb>QA vt motus orbis detrahat motui ſinus verſos v. g. motus orbis arcus <lb></lb>QT detrahit ſinum verſum Q 13. hinc vides quàm benè conueniant, <lb></lb>ſingulæ quadrantes rotæ cuius rei ratio clariſſima eſt. </s>
				</p>
				<p id="N24FE3" type="main">
					<s id="N24FE5"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N24FF1" type="main">
					<s id="N24FF3">Hinc punctum Z in aſcenſu Z, 10.grad. </s>
					<s id="N24FF6">60. tantùm addit motui cen­<lb></lb>tri, quantum L in deſcenſu L, 10.grad.30. aſcenſus verò 10. L grad. 30. <lb></lb>tantum addet quantum aſcenſus 10, Q grad. denique ſi accipiatur primus <lb></lb>arcus aſcenſus addit ſinum verſum, ſi vltimus, rectum; at verò primus <lb></lb>deſcenſus in ſemicirculo dumtaxat ſuperiore addit ſinum rectum, vlti­<lb></lb>mus verſum, quæ omnia certiſſimè conſtant. </s>
				</p>
				<p id="N25008" type="main">
					<s id="N2500A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N25016" type="main">
					<s id="N25018">Obſeruabis hanc eſſe liueam rotatilem, quàm à multis annis cum in­<lb></lb>finitis ferè rotatilium ſpeciebus &amp; proprietatibus noſter Philoſophus in­<lb></lb>uenit, de quibus ſequenti Tomo. </s>
				</p>
				<p id="N25020" type="main">
					<s id="N25022"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2502F" type="main">
					<s id="N25031"><emph type="italics"></emph>Omnia puncta rotæ AQLZ, quæ rotatur in plano, mouentur inæquali mo­<lb></lb>tu<emph.end type="italics"></emph.end>; </s>
					<s id="N2503C">de duobus oppoſitis LA conſtat manifeſtè, quia æquali tempore <lb></lb>L acquirit maius ſpatium, quàm A, v. g. ſpatium LI eo tempo­<lb></lb>re quo A acquirit ſpatium AS: </s>
					<s id="N25048">de duobus QZ etiam conſtat; </s>
					<s id="N2504C">nam <lb></lb>Z ita mouetur verſus L, vt motus orbis addat ſinum verſum motui centri <lb></lb>Q verò ita mouetur, vt detrahat <expan abbr="eũdem">eundem</expan> ſinum; </s>
					<s id="N25058">igitur Z mouetur velo­<lb></lb>ciùs, quàm <expan abbr="q;">que</expan> de duobus K &amp; 10. certum eſt, nam 10. plùs addit aſcen­<lb></lb>dendo quàm K deſcendendo æquali tempore; </s>
					<s id="N25064">nam 10. in arcu 10. L ad­<lb></lb>dit motui centri 10. M, &amp; K in deſcenſu KH addit addit tantùm 14. H; </s>
					<s id="N2506A"><lb></lb>ſed hæc eſt minor.10. M, vt conſtat toto ſinu verſo arcus HQ; &amp; licèt <lb></lb>punctum 10. in aſcenſu eodem tempore addat 10. M quo punctum L <lb></lb>in deſcenſu addit MK æqualem; </s>
					<s id="N25077">non tamen propterea mouentur æquè <lb></lb>velociter; </s>
					<s id="N2507D">quia punctum L initio mouetur velociùs, &amp; ſub finem tardiùs; </s>
					<s id="N25081"><lb></lb>at verò punctum 10. initio mouetur tardiùs; vnde quocunque arcu aſ­<lb></lb>ſumpto inter 10. L, &amp; alio æquali inter LK, punctum L mouebitur <lb></lb>velociùs initio. </s>
				</p>
				<p id="N2508A" type="main">
					<s id="N2508C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25099" type="main">
					<s id="N2509B">Hinc colligo, punctum L omnium velociſſimè moueri initio &amp; pun­<lb></lb>ctum A omnium tardiſſimè; ratio eſt quia puncto L motus orbis addit <pb pagenum="338" xlink:href="026/01/372.jpg"></pb>totum id quod poteſt addere, poſito quod ſit æqualis motui centri, &amp; pun­<lb></lb>cto A detrahit totum id, quod poteſt detrahere. </s>
				</p>
				<p id="N250A8" type="main">
					<s id="N250AA"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N250B7" type="main">
					<s id="N250B9">Colligo ſecundò, duo puncta eodem tempore ſpatia æqualia poſſe ac­<lb></lb>quire, licèt vtrumque mobile inæquali motu moueatur. </s>
				</p>
				<p id="N250BE" type="main">
					<s id="N250C0"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N250CD" type="main">
					<s id="N250CF">Tertiò, ſi aſſumatur punctum <foreign lang="grc">β</foreign> grad.45, illud ipſum eſſe, quod maxi­<lb></lb>mum omnium ſpatium conficit eo tempore, quo reuoluitur quadrans, <lb></lb>id eſt eo tempore, quo percurrit lineam L, I, G, F; nam percurrit ſegmen­<lb></lb>tum rotatilis, cuius chorda eſt <foreign lang="grc">δ β</foreign>, ſeu percurrit duplam ſegmenti L 15. <lb></lb>atqui dupla L 15. eſt maior LF, vt conſtat. </s>
				</p>
				<p id="N250E3" type="main">
					<s id="N250E5"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N250F2" type="main">
					<s id="N250F4">Centrum O mouetur velociùs, quàm punctum contactus A, vt certum <lb></lb>eſt; nam eo tempore quo centrum conficit OP æqualem AB, punctum A <lb></lb>conficit tantùm AS. </s>
				</p>
				<p id="N250FC" type="main">
					<s id="N250FE"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2510B" type="main">
					<s id="N2510D"><emph type="italics"></emph>Punctum A non regreditur, ſed tantillùm accedit dextrorſum<emph.end type="italics"></emph.end>; </s>
					<s id="N25116">ratio eſt, <lb></lb>quia dextrorſum acquirit AB, v. g. ſiniſtrorſum verò acquirit XT æ­<lb></lb>qualem arcui AV; </s>
					<s id="N25122">ſed arcus eſt mâior ſuo ſinu; </s>
					<s id="N25126">igitur plùs acquirit dex­<lb></lb>trorſum, quàm ſiniſtrorſum; igitur non regreditur, nec etiam remanet in <lb></lb>linea AO. </s>
				</p>
				<p id="N2512E" type="main">
					<s id="N25130"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2513D" type="main">
					<s id="N2513F"><emph type="italics"></emph>Omnia puncta inter OQ mouentur tardiùs, quàm centrum O<emph.end type="italics"></emph.end>; </s>
					<s id="N25148">ſit enim <lb></lb>punctum P v.g. certè perueniet in 7. ita vt OPR 7. ſint æquales; </s>
					<s id="N25150">ſed P <lb></lb>7. eſt minor OE, licèt P 7. tantillùm incuruetur; </s>
					<s id="N25156">è contrario verò nullum <lb></lb>eſt punctum inter GZ, quod non moueatur velociùs, quàm O, vt patet; </s>
					<s id="N2515C"><lb></lb>hinc Z mouetur velociſſimè omnium punctorum diametri ZQ, Q verò <lb></lb>tardiſſimè; </s>
					<s id="N25163">O denique medio quaſi motu inter vtrumque; </s>
					<s id="N25167">tardiùs qui­<lb></lb>dem cæteris inter ZO, velociùs tamen aliis, quæ ſunt inter OQ; immò <lb></lb>omnia puncta radiorum OA, OQ, quæ diſtant æqualiter ab O eo tem­<lb></lb>pore, quo centrum O percurrit totam OE, acquirunt æqualia ſpatia, <lb></lb>itemque æqualia, quæ ſunt in radiis OL, OZ, licèt prioribus maiora: <lb></lb>ſimiliter motus aliarum partium, quæ ſunt intra circulum, <expan abbr="earumq́ue">earumque</expan> <lb></lb>ſpatia, dato tempore cognoſci poſſunt, &amp; ex dictis facilè intelliguntur. </s>
				</p>
				<p id="N2517F" type="main">
					<s id="N25181"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2518E" type="main">
					<s id="N25190">Hînc collige vulgi ſenſum; nam plerique omnes exiſtimant tùm om­<lb></lb>nes partes peripheriæ rotæ moueri æquè velociter, tùm nullam eſſe par­<lb></lb>tem intra circulum vel arcum, quæ non moueatur tardiùs, tùm partibus <lb></lb>peripheriæ, tum ipſo centro. </s>
				</p>
				<p id="N2519A" type="main">
					<s id="N2519C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N251A9" type="main">
					<s id="N251AB">Colligo ſecundò, fi fiat quadrans A, 18. 16. vt eſt arcus 18.16.ad rectá <pb pagenum="339" xlink:href="026/01/373.jpg"></pb>18.A.ita rectam 18. A eſſe ad LA; </s>
					<s id="N251B5">quia A 16. eſt æqualis ſemicirculo L <lb></lb>QA, &amp; hic arcui quadrantis L. 19. ſed vt 16.18.ad 18.A vel L 19. æqua­<lb></lb>lem, ita L 19. ad LA; igitur A eſt media proportionalis inter LA, &amp; ar­<lb></lb>cum 18. 16. ſed de hoc aliàs. </s>
				</p>
				<p id="N251BF" type="main">
					<s id="N251C1"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N251CD" type="main">
					<s id="N251CF"><emph type="italics"></emph>Punctum L mouetur velociùs, &amp; velociùs in infinitum puncto A<emph.end type="italics"></emph.end>; </s>
					<s id="N251D8">aſſumatur <lb></lb>enim motus puncti L per vnicum gradum quadrantis LQ addatur ſinus <lb></lb>rectus vnius grad. 1745. ipſi gradui, ſcilicet 1746. eritque ſpatium con­<lb></lb>ſectum 3491. paulò plùs; </s>
					<s id="N251E8">detrahatur autem gradus ex ſinu ſupereſt I, ſit­<lb></lb>que ſinus verſus vnius gradus 15. certè erit ſpatium decurſum ab A da­<lb></lb>to illo tempore paulò plùs; </s>
					<s id="N251F0">ſed velocitates motuum æquàli tempore ſunt <lb></lb>vt ſpatia; </s>
					<s id="N251F6">igitur velocitas motus puncti L eſt ad velocitatem motus pun­<lb></lb>cti A, vt 3491.ad 15.id eſt vt 232.ad I; atqui ſi accipiatur in orbe ſpatium <lb></lb>minus vno gradu, erit adhuc maior proportio motus puncti L ad motum <lb></lb>puncti A. </s>
				</p>
				<p id="N25201" type="main">
					<s id="N25203">Immò, ſi ponas ſinum totum partium 1000000. &amp; aſſumat motum L, <lb></lb>&amp; A per vnum minutum arcus erit 2910, &amp; eius ſinus rectus 2908.ver­<lb></lb>ſus verò; igitur motus A erit vt 2. motus L 5818. igitur motus L ad mo­<lb></lb>tum A per vnum minutum quadrantis, vt 2909. ad I, <expan abbr="atq;">atque</expan> ita in infinitú. </s>
				</p>
				<p id="N25211" type="main">
					<s id="N25213"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2521F" type="main">
					<s id="N25221"><emph type="italics"></emph>Minor rota incluſa maiori ita mouetur, vt ſit maior in illa motus centri, <lb></lb>quàm motus orbis<emph.end type="italics"></emph.end>; </s>
					<s id="N2522C">ſit enim minor rota P <foreign lang="grc">π</foreign>; </s>
					<s id="N25234">haud dubiè centrum O acqui­<lb></lb>ret ſpatium OE duplò maius arcu P <foreign lang="grc">ω</foreign> eo tempore, quo motus orbis per­<lb></lb>curret <expan abbr="eũdem">eundem</expan> arcum P <foreign lang="grc">ω</foreign>; an verò ſingula puncta quadrantis P <foreign lang="grc">ω</foreign> reſ­<lb></lb>pondeant ſingulis punctis plani <foreign lang="grc">ω θ</foreign>, vel ſingula duobus, vulgaris diffi­<lb></lb>cultas eſt, quæ ab Ariſtotelica rota ſibi nomen fecit, quam hîc breuiter <lb></lb>diſcutimus. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N2525A" type="main">
					<s id="N2525C"><emph type="center"></emph>DIGRESSIO<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25263" type="main">
					<s id="N25265"><emph type="center"></emph><emph type="italics"></emph>De Rota Ariſtotelica.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N25271" type="main">
					<s id="N25273">ARiſtoteles hanc difficultatem habet, quæſt. </s>
					<s id="N25276">24. Mechanicorum, <expan abbr="quã">quam</expan> <lb></lb>etiam explicat Blancanus, <expan abbr="proponitq́">proponitque</expan>; </s>
					<s id="N25284">Merſennus in præfatione ſuæ <lb></lb>verſionis <expan abbr="mechanicarũ">mechanicarum</expan> Galilei; nos illam hoc loco breuiter diſcutiemus. </s>
				</p>
				<p id="N2528E" type="main">
					<s id="N25290">1. Tribus modis poteſt moueri rota in plano 1°. </s>
					<s id="N25293">ita vt motus centri <lb></lb>motui orbis ſit æqualis, id eſt vt centrum percurrat lineam rectam æqua­<lb></lb>lem arcui orbis, qui <expan abbr="eodẽ">eodem</expan> <expan abbr="tẽpore">tempore</expan> conuertitur. </s>
					<s id="N252A2">2°. </s>
					<s id="N252A5">ita vt motus orbis ſit mi­<lb></lb>nor motu centri, id eſt vt centrum percurrat lineam rectam <expan abbr="maiorẽ">maiorem</expan> arcu, <lb></lb>qui <expan abbr="eodẽ">eodem</expan> <expan abbr="tẽpore">tempore</expan> conuoluitur. </s>
					<s id="N252B8">3°. </s>
					<s id="N252BB">ita vt motus centri ſit minor motu orbis. </s>
				</p>
				<p id="N252BE" type="main">
					<s id="N252C0">2. Primum motus modum diſcuſſimus in ſuperioribus Theorematis, <lb></lb>2. verò, &amp; 3. diſcutiemus hoc loco. </s>
					<s id="N252C5">ſit ergo in præſenti fig. </s>
					<s id="N252C8">rota incubans <lb></lb>plano CN in puncto C centro A, radio AC, quæ <expan abbr="aliã">aliam</expan> includat <expan abbr="concẽtricã">concentricam</expan> <pb pagenum="340" xlink:href="026/01/374.jpg"></pb>radio AB; </s>
					<s id="N252DB">ſitque v.g. AB ſubdupla AC; </s>
					<s id="N252E1">ſit planum CE æquale arcui C <lb></lb>H; </s>
					<s id="N252E7">ita vt in decurſu ſingula puncta CH reſpondeant ſingulis CE; </s>
					<s id="N252EB">cùm <lb></lb>autem rapiatur rota ABD à maiore; </s>
					<s id="N252F1">haud dubiè punctum D peruenit <lb></lb>in F, cum punctum A peruenit in G; id eſt radius AD conuenit <lb></lb>cum GF. </s>
				</p>
				<p id="N252F9" type="main">
					<s id="N252FB">3. Porrò caput difficultatis potiſſimum in eo poſitum eſt, quod BF ſit <lb></lb>dupla arcus BD; </s>
					<s id="N25301">igitur vel ſingula puncta arcus BD reſpondent in de­<lb></lb>curſu ſingulis BF, vel ſingula BD reſpondent duobus BF, vel alterna <lb></lb>puncta BF ſaltuatim remanent penitus intacta; </s>
					<s id="N25309">ſed nihil horum dici <lb></lb>poſſe videtur: </s>
					<s id="N2530F">non primum.quia alioquin tot eſſent puncta in arcu DB, <lb></lb>quot in plano BF æquali arcui CH, igitur ſubduplus arcus eſſet æqualis <lb></lb>duplo, quòd dici non poteſt; </s>
					<s id="N25317">licèt aliqui vltrò concedant, quod ego mi­<lb></lb>nimè concedere, nedum concipere poſſum; </s>
					<s id="N2531D">non poteſt etiam dici quod <lb></lb>ſingula puncta arcus DB reſpondeant duobus punctis plani BF; </s>
					<s id="N25323">cùm <lb></lb>enim puncta D, &amp; C ſint in eodem radio AC; </s>
					<s id="N25329">certè ſi punctum tangit in <lb></lb>motu punctum plani proximè ſequens dextrorſum; </s>
					<s id="N2532F">igitur AB cadit per­<lb></lb>pendiculariter in BF; </s>
					<s id="N25335">igitur &amp; AC in CE; </s>
					<s id="N25339">igitur punctum C tangit <lb></lb>etiam in motu punctum proximè ſequens plani CE; </s>
					<s id="N2533F">igitur planum CE <lb></lb>eſſet duplum arcus CH, ſed eſt æquale per conſtructionem; </s>
					<s id="N25345">nec eſt quod <lb></lb>aliqui prouocent ad experimentum, quod nullum eſt; quippe quod certæ <lb></lb>&amp; geometricæ demonſtrationi repugnaret. </s>
				</p>
				<p id="N2534D" type="main">
					<s id="N2534F">4. Non poteſt etiam dici, quòd alterna puncta plani BF quaſi ſaltua­<lb></lb>tim remaneant intacta; </s>
					<s id="N25355">nam eo tempore, quo aliquod punctum plani C <lb></lb>E reſpondens puncto intacto plani BF tangitur; </s>
					<s id="N2535B">haud dubiè aliquod pun­<lb></lb>ctum arcus BD tangit planum BF; </s>
					<s id="N25361">alioquin centrum A deſcenderet ſu­<lb></lb>pra lineam AG; </s>
					<s id="N25367">igitur maior rota non incubaret plano CE contra hy­<lb></lb>potheſim; </s>
					<s id="N2536D">igitur quolibet inſtanti aliquod punctum arcus BD tangit <lb></lb>planum BF; </s>
					<s id="N25373">igitur nullum punctum plani BF intactum eſt; </s>
					<s id="N25377">quippe om­<lb></lb>ne punctum contactus plani CE, &amp; maioris circuli reſpondet puncto <lb></lb>contactus oppoſito plani BF, &amp; minoris circuli; igitur non remanent al­<lb></lb>terna puncta plani BF quaſi ſaltuatim intacta. </s>
				</p>
				<p id="N25381" type="main">
					<s id="N25383">5. Hinc reiicies infinita illa vacuola Galilei; </s>
					<s id="N25387">ſi enim in linea BM re­<lb></lb>manent infinita puncta intacta, non verò in CN; </s>
					<s id="N2538D">certè vbi punctum, <lb></lb>quod immediatè ſequitur C tangitur, &amp; fit punctum contactus, vel nul­<lb></lb>lum punctum in BF tangitur vel aliquod; ſi <expan abbr="primũ">primum</expan>; </s>
					<s id="N25399">igitur radius minoris <lb></lb>rotæ imminuitur, quod eſt abſurdum: ſi ſecundum; </s>
					<s id="N2539F">igitur nullum vacuo­<lb></lb>lum intercipitur, quod eſt contra Galileum; </s>
					<s id="N253A5">quod verò ſpectat ad poli­<lb></lb>gona concentrica determinabimus paulò pòſt; </s>
					<s id="N253AB">ſint enim duo poligona <lb></lb>concentrica centro D, quorum maius ita voluatur, vt AI reſpondeat AF, <lb></lb>id eſt circa centrum A; </s>
					<s id="N253B3">certè M mouebitur per arcum MI, D per arcum <lb></lb>DE, B per arcum BM; </s>
					<s id="N253B9">igitur ſingula puncta mouebuntur motu ſimplicis <lb></lb>circulari <expan abbr="coq́ue">coque</expan> velociùs, quò recedent longiùs ab A: hinc punctum B <lb></lb>mouebitur omnium velociſſimè, quia longiſſimè diſtat à puncto A. </s>
				</p>
				<p id="N253C6" type="main">
					<s id="N253C8">6. Si verò minus poligonum dirigat motum, qui primò fiat ciat cen­<lb></lb>trum D; </s>
					<s id="N253CE">haud dubiè punctum A mouebitur per arcum AV, per <expan abbr="quẽ">quem</expan> retro-<pb pagenum="341" xlink:href="026/01/375.jpg"></pb>agetur; </s>
					<s id="N253DB">igitur ſi maius poligonum dirigat motum, relinquentur plura <lb></lb>ſegmenta in plano CH intacta æqualia DE; ſi verò minus dirigat latera <lb></lb>maioris poligoni, aliquid ſemper de priori ſpatio in plano BF quaſi re­<lb></lb>petent per regreſſum. </s>
				</p>
				<p id="N253E5" type="main">
					<s id="N253E7">7. Hinc tamen malè concludit Galileus ſimile quid accidere in mo­<lb></lb>tu circulorum concentricorum; </s>
					<s id="N253ED">eſt enim maxima diſparitas: Primò, quia <lb></lb>centrum A circuli in priori figurâ nunquam recedit à linea AL, alio­<lb></lb>qui radij circuli eiuſdem eſſent inæquales, cùm tamen M poligoni aſcen­<lb></lb>dat ſupra MI. Secundò, quia nullum punctum peripheriæ circuli quieſ­<lb></lb>cit. </s>
					<s id="N253F9">Tertiò, quia omnia puncta circuli mouentur motu mixto ex recto, <lb></lb>&amp; circulari, excepto centro, cùm tamen omnia puncta poligoni motu <lb></lb>circulari moueantur, excepto puncto contactus, quod quieſcit. </s>
				</p>
				<p id="N25402" type="main">
					<s id="N25404">8. Et ne omittam aliud, quod miraculi loco eſt apud <expan abbr="eũdem">eundem</expan> <expan abbr="Galileã">Galileam</expan>, <lb></lb>quo ſcilicet primum illud ſuum effectum confirmare concendit, ſcilicet <lb></lb>punctum dici poſſe æquale lineæ ſit enim ſemicirculus ABMC, rectan­<lb></lb>gulum BN, triangulum ALN, recta KD parallela BC, denique AI circa <lb></lb>axem AM; </s>
					<s id="N2541A">voluantur hæc tria; </s>
					<s id="N2541E">certè rectangulum relinquit cylindrum, <lb></lb>triangulum, conum, &amp; ſemicirculus hemiſphærium; </s>
					<s id="N25424">ſit autem idem pla­<lb></lb>num KD parallelum BC ſecans hæc tria; </s>
					<s id="N2542A">haud dubiè ſectio coni HF <lb></lb>erit circulus, iſque æqualis plano contento duobus circulis parallelis, <lb></lb>quorum maior habeat diametrum KD, &amp; minor IE, quod breuiter de­<lb></lb>monſtratur; </s>
					<s id="N25434">quia quando IA eſt æquale quadratis IGA, led BA eſt æ­<lb></lb>qualis AI, &amp; BC æqualis KD dupla AI; </s>
					<s id="N2543A">igitur quadratum KD eſt qua­<lb></lb>druplum quadrati KG, vel IA; </s>
					<s id="N25440">igitur continet quatuor quadrata AI, &amp; <lb></lb>AI quatuor AG, vel HG; </s>
					<s id="N25446">igitur continet quadratum IE, &amp; HF; </s>
					<s id="N2544A">ſed cir­<lb></lb>culi ſunt vt quadrata diametrorum; </s>
					<s id="N25450">igitur circulus diametri KD conti­<lb></lb>net circulos diametri IE, &amp; HF; </s>
					<s id="N25456">igitur, ſi ex circulo diametri CD de­<lb></lb>trahatur circulus diametri IE, ſupereſt corona illa, cuius latitudo eſt IK, <lb></lb>&amp; ED, de qua ſuprà; igitur æqualis eſt circulo diametri AF. </s>
				</p>
				<p id="N2545F" type="main">
					<s id="N25461">9. Hinc concludit Galileus punctum apicis coni A eſſe æquale cir­<lb></lb>culo diametri BC; </s>
					<s id="N25467">quod certè non mihi videtur ſequi; </s>
					<s id="N2546B">cùm ſemper aga­<lb></lb>tur de baſi coni, quæ non eſt punctum, &amp; licèt conus HF A ſit æqualis <lb></lb>ſolido KIB in orbem ſcilicet ducto, detracto dumtaxat hemiſphærio ex <lb></lb>cylindro, quod tamen non demonſtrat Galileus, ſed demonſtrarum ſup­<lb></lb>ponit à Luca Valerio; </s>
					<s id="N25477">nunquam paoſectò perueniet ad punctum mathe­<lb></lb>maticum; </s>
					<s id="N2547D">quippe ſemper habebit conum æqualem alteri ſolido; ſi verò <lb></lb>quis admittat puncta phyſica, concedi poſſet vltrò punctum phyſicum <lb></lb>conicum æquale eſſe alteri ſolido maximè dilatato propter angulum <lb></lb>contingentiæ KBI in quo non videtur eſſe difficultas. </s>
				</p>
				<p id="N25488" type="main">
					<s id="N2548A">10. Quod autem conus HAF ſit æqualis prædicto ſolido, quod Ga­<lb></lb>lileus vocat ſcalprum orbiculare, breuiter demonſtro; </s>
					<s id="N25490">quia cum baſis HF <lb></lb>ſit æqualis KI, ED, id eſt coronæ, itemque ſingulæ baſes ſupra HF vſque <lb></lb>adverticem A; </s>
					<s id="N25498">certè totum HFA conflatum ex omnibus baſibus eſt æ­<lb></lb>quale toti ſolido ſeu ſcalpro conflato ex omnibus coronis; hæc obiter <lb></lb>attigiſſe volui, ne fortè diſſimulatum à nobis eſſe quiſquam exiſtimaret, <pb pagenum="342" xlink:href="026/01/376.jpg"></pb>ſed iam hoc potiſſimum ſupereſt, vt difficultatem propoſitam de rota <lb></lb>Ariſtotelica breuiter ſoluamus, </s>
				</p>
				<p id="N254A9" type="main">
					<s id="N254AB">11. Certum eſt primò in hypotheſi, quæ componit continuum ex <lb></lb>punctis mathematicis vix poſſe explicari, ſiue dicantur eſſe infinita, vt <lb></lb>vult Galileus, ſiue finita vt alij volunt; </s>
					<s id="N254B3">quia nec idem punctum minoris <lb></lb>rotæ pluribus ſui plani reſpondet, nec ſingula ſingulis reſpondent, nec <lb></lb>etiam fiunt illi ſaltus intactis finitis, vel infinitis vacuolis; immò talis eſt <lb></lb>motus circularis natura, vt minimè concipi, nedum explicari poſſit iuxta <lb></lb>hypotheſim punctorum mathematicorum. </s>
				</p>
				<p id="N254BF" type="main">
					<s id="N254C1">12. Certum eſt ſecundò, vix etiam explicari poſſe iuxta hypotheſim <lb></lb>partium proportionalium infinitarum actu; </s>
					<s id="N254C7">quia contactus ipſe globi, &amp; <lb></lb>plani tam obſcurè in hac hypotheſi explicatur, vt etiam authores ipſi, <lb></lb>qui huic ſententiæ patrocinantur, vltrò aſſerant inſeparabilem eſſe diffi­<lb></lb>cultatem; </s>
					<s id="N254D1">quod enim dicunt contactum fieri in parte indeterminata, <lb></lb>neſcio an aliquis ſi non blandiens capere poſſit: nunquid enim contactus <lb></lb>eſt determinatus qui realis eſt, &amp; ſingularis, id eſt hic &amp; non alius? </s>
					<s id="N254DB">nun­<lb></lb>quid eſt aliquid, quod tangit ab omni, eo quod tangit, diſtinctum? </s>
					<s id="N254E0">quip­<lb></lb>pe tangere, &amp; non tangere ſunt prædicata contradictoria; ſed de his fusè <lb></lb>in Metaphyſica. </s>
				</p>
				<p id="N254E8" type="main">
					<s id="N254EA">13. Adde quod, licèt contactus globi in plano explicari poſſet, ſupe­<lb></lb>reſſet tamen eadem difficultas; nam cùm nulla ſit pars, ſiue indetermina­<lb></lb>ta, ſiue determinata in plano BF, quæ ſit intacta, &amp; cum eadem pars <lb></lb>arcus BD non reſpondeat pluribus partibus plani BF, &amp; cùm ſingu­<lb></lb>læ partes arcus ſingulis partibus non reſpondeant (quæ omnia <lb></lb>conſtant ex dictis) profectò eadem eſt difficultas iuxta hypotheſim par­<lb></lb>tium proportionalium infinitarum actu, quæ eſt iuxta hypotheſim pun­<lb></lb>ctorum mathematicorum finitorum, vel infinitorum. </s>
				</p>
				<p id="N254FE" type="main">
					<s id="N25500">14. His poſitis, ſupereſt tantùm vt ſoluatur hæc difficultas iuxta hy­<lb></lb>potheſim punctorum phyſicorum, vel partium diuiſibilium in infini­<lb></lb>tum potentiâ, cuius principia &amp; difficultates in Metaphyſica diſcu­<lb></lb>tiemus. </s>
				</p>
				<p id="N25509" type="main">
					<s id="N2550B">Dico ergo ſatis facilè iuxta hanc hypotheſim explicari, &amp; ſolui poſſe <lb></lb>nodum rotæ Ariſtotelicæ: </s>
					<s id="N25511">quippe punctum phyſicum curuum tangit <lb></lb>punctum phyſicum planum, ſed non adæquatè; </s>
					<s id="N25517">quippè nullum curuum <lb></lb>adæquari poteſt plano, ſeu cum plano conuenire, quod nemo Geometra <lb></lb>negare poterit: </s>
					<s id="N2551F">quippe duæ quantitates poſſunt duobus modis conſide­<lb></lb>rari: Primò in ordine ad æqualitatem, vel inæqualitatem. </s>
					<s id="N25525">Secundò, in <lb></lb>ordine ad commenſurationem, vel conuenientiam, vel <expan abbr="incommenſura-bilitatẽ">incommenſura­<lb></lb>bilitatem</expan>; </s>
					<s id="N25531">ſi primo modo, vna quantitas, vel dicitur alteri æqualis, vel inæ­<lb></lb>qualis; </s>
					<s id="N25537">ſi inæqualis, vel maior, vel minor; </s>
					<s id="N2553B">ſi maior vel minor, dicitur <lb></lb>rationalis, vel irrationalis ſeu aloga; ſed hæc ſunt vulgaria, paulò obſcu­<lb></lb>riora, quæ ſequuntur. </s>
				</p>
				<p id="N25543" type="main">
					<s id="N25545">15. Si enim ſecundo modo conſiderentur, vel poſſunt commenſurari, <lb></lb>vel non poſſunt; </s>
					<s id="N2554B">ſi primum, ſunt neceſſariò æquales; </s>
					<s id="N2554F">ſi inæquales illæ ſunt <lb></lb>vel alogæ eædem quæ ſuprà, ſic diagonalis <expan abbr="cõparata">comparata</expan> cum latere quadrati <pb pagenum="343" xlink:href="026/01/377.jpg"></pb>eſt aloga, hoc eſt ita inæqualis, vt nulla ſit vtrique pars aliquota commu­<lb></lb>munis; </s>
					<s id="N25560">alogæ quidem in ordine ad commenſurationem, non tamen in <lb></lb>ordines ad partes aliquotas; </s>
					<s id="N25566">ſic maior arcus comparatus cum linea recta <lb></lb>ſubdupla non eſt alogus primo modo ſed <expan abbr="ſecũdo">ſecundo</expan>, id eſt illa linea, quæ eſt <lb></lb>ſubdupla arcus, non poteſt conuenire cum arcu toto, nec cum aliqua <lb></lb>eius parte; </s>
					<s id="N25574">ſi verò ſint æquales, poſſunt etiam dici alogæ in ordine ad <lb></lb>commenſurationem, ſi nullo modo conuenire poſſunt quamtumuis diui­<lb></lb>dantur; </s>
					<s id="N2557C">ſic angulus, quem faciunt duæ circumferentiæ, poteſt quidem eſſe <lb></lb>ęqualis angulo dato rectilineo; </s>
					<s id="N25582">nunquam tamen cum eo conuenire po­<lb></lb>teſt; </s>
					<s id="N25588">ſic arcus æqualis rectæ, ſic denique punctum curuum æquale puncto <lb></lb>plano; </s>
					<s id="N2558E">licèt enim totum punctum tangatur ab alîo puncto, non tamen <lb></lb>adæquatè, quia extenſio vnius eſt aloga cum extenſione alterius; </s>
					<s id="N25594">analo­<lb></lb>giam habes in duobus Angelis; </s>
					<s id="N2559A">quorum vnus figuram ſphæricam <expan abbr="pedalẽ">pedalem</expan> <lb></lb>induat, alter cubicam, &amp; alter alterum tangat; </s>
					<s id="N255A4">nam reuerâ totus Angelus <lb></lb>tangitur, quia caret partibus, non tamen adæquatè, vt certum eſt; </s>
					<s id="N255AA">immò <lb></lb>poſſet Angelus cuius eſt figura ſphærica, ita duobus aliis, quorum eſſet <lb></lb>figura cubica adhærere, vt <expan abbr="vtriq;">vtrique</expan> inadæquatè adhæreret v.g. Angelus A <lb></lb>punctis BC ita vt ipſum punctum contactus eſſet in ipſa quaſi commiſ­<lb></lb>ſura: </s>
					<s id="N255BC">immò poteſt Angelus, cuius eſt figura ſphærica habere diuerſos con­<lb></lb>tactus inadæquatos in tota facie Angeli, cuius eſt figura cubica v.g. An­<lb></lb>gelus A vel in D vel in E, vel in F; </s>
					<s id="N255C6">immò ſunt infiniti potentia huiuſmodi <lb></lb>inadæquatè diuerſi; </s>
					<s id="N255CC">denique Angelus A poteſt longo tempore in ſuper­<lb></lb>ficie v.g. Angeli C ſucceſſiuè moueri, acquirendo ſcilicet nouos conta­<lb></lb>ctus inadæquatos; </s>
					<s id="N255D6">vocetur autem contactus E centralis, ſeu medius; con­<lb></lb>tactus verò B extremus. </s>
				</p>
				<p id="N255DC" type="main">
					<s id="N255DE">16. Nec A eſt; </s>
					<s id="N255E1">quòd aliqui neſcio quas partes viruales in angelo ex­<lb></lb>tenſo agnoſcant, quæ certè à me concipi non poſſunt; </s>
					<s id="N255E7">niſi fortè aliquid <lb></lb>extrinſecum ſonent, ſcilicet Angelum extenſum multis ſimul partibus <lb></lb>alicuius corporis coextendi poſſe; </s>
					<s id="N255EF">vnde fit ſingulis inadæquatè coexten­<lb></lb>di; quod nemo negabit; </s>
					<s id="N255F5">ſed ne dici moremur in hac materia, quam hîc <lb></lb>ex profeſſo non tractamus; </s>
					<s id="N255FB">cettum eſt iuxta hanc hypotheſim punctorum <lb></lb>phyſicorum facilè explicari motum rotæ Ariſtotelicæ: </s>
					<s id="N25601">quippe dum pun­<lb></lb>ctum quod proximè accedit ad C in arcu CH incubat puncto plani C <lb></lb>E, quòd immediatè ſequitur C, idque centrali contactu punctum, quod <lb></lb>proximè ſequitur B in arcu BD, quem ſubduplum CH ſuppono, tangit <lb></lb>punctum, quod ſequitur immediatè B in plano BF contactu extremo, id <lb></lb>eſt commiſſura puncti B &amp; alterius contactu medio, tangit <expan abbr="punctũ">punctum</expan> plani <lb></lb>quod probatur; </s>
					<s id="N25615">quia punctum, quod immediatè ſequitur B in arcu BDC <lb></lb>quod vocabimus deinceps ſecundum, tangit contactu tertium punctum <lb></lb>plani BF eo inſtanti, quo tertium punctum arcus CH tangit contactu <lb></lb>medio tertium plani CE; igitur eo inſtanti, quo ſecundum CH tangit <lb></lb>contactu medio ſecundum CE, ſecundum BD tangit contactu extremo <lb></lb>primum BF, extremo inquam ratione puncti arcus, non ratione puncti <lb></lb>plani. </s>
				</p>
				<p id="N25625" type="main">
					<s id="N25627">17. Si verò eſſet maior rota, eîuſque contactus eſſet inter BC, eſſent <pb pagenum="344" xlink:href="026/01/378.jpg"></pb>alij contactus inadæquati, vt facilè intelligi poteſt ex dictis, poteſt au­<lb></lb>tem fieri, vt dixi, vt ſint plures contactus inadæquati etiam arcus CH, <lb></lb>niſi velociſſimè moueatur ratione loci, id eſt niſi punctum phyſicum <lb></lb>mobile acquirat ſingulis inſtantibus punctum loci immediatum non <lb></lb>participans de priori; </s>
					<s id="N25638">quod certè poteſt acquirere duplici motu, ſcilicet <lb></lb>vel recto vel mixto ex recto, &amp; circulari; nec eſt enim dubium, quin An­<lb></lb>gelus v. g. inducta figura ſphærica non poſſit volui circa ſe ipſum velo­<lb></lb>ciùs, &amp; velociùs in infinitum. </s>
				</p>
				<p id="N25646" type="main">
					<s id="N25648">18. V. g.. angelus A poteſt circa centrum mathematicum, id eſt <lb></lb>imaginatum B immobile agi in orbem tardiùs, &amp; tardiùs quidem, ſi <expan abbr="vnũ">vnum</expan> <lb></lb>orbem faciat pluribus, &amp; pluribus inſtantibus; velociùs verò, ſi pauciori­<lb></lb>bus; </s>
					<s id="N25656">quot verò inſtantibus vnum integrum orbem peragat, ſi tempus <lb></lb>conſtet finitis inſtantibus; </s>
					<s id="N2565C">exiſtimo primò, poſſe pluribus, &amp; pluribus pe­<lb></lb>ragere quia tardiùs, &amp; tardiùs in infinitum moueri poteſt; </s>
					<s id="N25662">ſecundò pau­<lb></lb>cioribus, &amp; paucioribus, donec tandem vno inſtanti conficiat integrum <lb></lb>orbem; </s>
					<s id="N2566A">vt autem moueatur adhuc velociùs in infinitum; aget quidem ſin­<lb></lb>gulos orbes ſingulis inſtantibus, ſed minoribus, ſeu breuioribus. </s>
				</p>
				<p id="N25670" type="main">
					<s id="N25672">19. Obſeruabis Angelum A poſſe tribus modis moueri; </s>
					<s id="N25676">primò circa <lb></lb>centrum B immobile, vt iam dictum eſt, idque velociùs, &amp; tardiùs in in­<lb></lb>finitum, &amp; hic motus eſt perfectè circularis: </s>
					<s id="N2567E">Secundò motu recto ſimpli­<lb></lb>ci per lineas BE, IH, idque etiam tardiùs, &amp; velociùs; </s>
					<s id="N25684">tardiùs quidem, ſi <lb></lb>plura ponat inſtantia, vt centrum B reſpondeat E, vel totus circulus A <lb></lb>toti F; </s>
					<s id="N2568C">velociùs uerò ſi pauciora donec tandem vno inſtanti circulus A <lb></lb>reſpondeat F adæquatè, id eſt acquirat locum immediatum non partici­<lb></lb>pantem, quod adhuc fiet velociùs, &amp; velociùs in infinitum; quia poteſt id <lb></lb>fieri per inſtantia breuiora, &amp; breuiora. </s>
				</p>
				<p id="N25696" type="main">
					<s id="N25698">20. Tertiò poteſt moueri motu mixto ex duobus præcedentibus, ita <lb></lb>vt quaſi rotetur in plano IH, quod tribus modis fieri poteſt: </s>
					<s id="N25699">primo ſi D <lb></lb>punctum ſcilicet <expan abbr="reſpõderet">reſponderet</expan> H; </s>
					<s id="N256A4">ſecundo, ſi aliud punctum inter DI tertio; </s>
					<s id="N256A8"><lb></lb>ſi aliquod inter DCI, primo poteſt fieri, vel ſucceſſiuè per contactus <lb></lb>inadæquatos, vel in inſtanti, idem dico de ſecundo, &amp; tertio, donec <lb></lb>tandem eo motu tranſeat in F, ita vt punctum F reſpondeat H &amp; circa B <lb></lb>totum orbem confecerit; ſed de his plura cum de Angelis. </s>
				</p>
				<p id="N256B4" type="main">
					<s id="N256B6">21. Porrò punctum B eo inſtanti, quo ſecundum CH tangit conta­<lb></lb>ctu medio, ſecundum CE tangit extremo ſecundum BF; </s>
					<s id="N256BC">igitur ſimul <lb></lb>cum alio id eſt cum ſecundo BD; </s>
					<s id="N256C2">ſi verò accipiatur quodlibet aliud pun­<lb></lb>ctum inter RC; </s>
					<s id="N256C8">illud certè non tangit vllo modo ad primum BF eo in­<lb></lb>ſtanti, quo ſecundum CH tangit contactu medio ſecundum CE; </s>
					<s id="N256CE">ſi ta­<lb></lb>men accipiatur aliquod punctum inter BA v.g. R; certè punctum R tan­<lb></lb>git ſolum ſecundum RV, ſed contactu, qui nec eſt extremus, nec medius, <lb></lb>ſed inter vtrumque, eo ſcilicet inſtanti, quo ſecundum CH tangit con­<lb></lb>tactu medio primum CE. </s>
				</p>
				<p id="N256DC" type="main">
					<s id="N256DE">22. Ex his facilè intellegi poteſt hic motus; quic ſcilicet idem punctum <lb></lb>rotæ minoris poteſt reſpondere diuerſis punctis ſui plani, ſed diuerſo <lb></lb>contactu, quod facilè explicatur, tùm per analogiam motus angelici, tùm <pb pagenum="345" xlink:href="026/01/379.jpg"></pb>per analogiam partium curuarum rotæ extenſarum. </s>
					<s id="N256ED">Vnde ex ſuperiori­<lb></lb>bus reſponſionibus, duæ ſi rectè explicentur ſoluunt hunc nodum. </s>
					<s id="N256F2">Tertia <lb></lb>verò omninò falſa eſt; </s>
					<s id="N256F8">nam primùm dici poteſt fieri aliquos ſaltus con­<lb></lb>tactuum inadæquatorum; </s>
					<s id="N256FE">quia ſcilicet punctum ſecundum BD tangit ſe­<lb></lb>cundum BF contactu quidem extremo in puncto arcus, ſed medio in <lb></lb>puncto plani; </s>
					<s id="N25706">igitur plures contactus inadæquati inter extremum &amp; me­<lb></lb>dium quaſi omittuntur per ſaltus; nullum eſt tamen inſtans, quod ali­<lb></lb>quo punctum plani non tangatur aliquo contactu, ab aliquo puncto ar­<lb></lb>cus, vel etiam à duobus in ipſa commiſſura, quæ commiſſura ad inſtar <lb></lb>puncti mathematici imaginarij concipi poteſt. </s>
				</p>
				<p id="N25712" type="main">
					<s id="N25714">23. Secundò dici poteſt, quod idem punctum arcus BD tangat duo <lb></lb>puncta plani BF ſed diuerſo contactu; nec enim duo puncta plani tan­<lb></lb>guntur ab eodem puncto arcus contactu medio in ipſo puncto arcus. </s>
					<s id="N2571C"><lb></lb>Tertiò denique dici non poteſt ſingula puncta BD ſingulis punctis B <lb></lb>F reſpondere, vt conſtat ex dictis, atque ita ex iis, quæ hactenus diximus <lb></lb>ſufficienter explicatus eſt ſecundus modus motus rotæ in plano. </s>
				</p>
				<p id="N25724" type="main">
					<s id="N25726">Quod verò ſpectat ad tertium; </s>
					<s id="N2572A">ſi minor globus centro G in eadem <lb></lb>figura moueatur, vt motus orbis ſit æqualis motui centri v.g. ex G mo­<lb></lb>ueatur in I, ex K perueniat in M, ſitque FM vel GI æqualis arcus FK, <lb></lb>&amp; rota minor GF ſecum rapiat maiorem GE; </s>
					<s id="N25736">haud dubiè motus orbis <lb></lb>maioris rotæ eſt maior motu centri, vt patet; quippe eo tempore, quo re­<lb></lb>uoluitur arcus quadrantis, &amp; centrum acquirit tantùm GI ſubduplum <lb></lb>eiuſdem arcus. </s>
				</p>
				<p id="N25740" type="main">
					<s id="N25742">24. Eſt autem in hoc motu eadem difficultas; </s>
					<s id="N25746">nam vel ſingula pun­<lb></lb>cta EI reſpondent ſingulis EN, vel duæ EI reſpondent eidem EN vel <lb></lb>alterna EI non tangunt per ſaltus; </s>
					<s id="N2574E">atqui nihil horum dici poſſe videtur: </s>
					<s id="N25752"><lb></lb>non primum, quia ſunt plura puncta EI quam EN: </s>
					<s id="N25757">non ſecundum, <lb></lb>quia ſi duo puncta EI tangerent idem EN; </s>
					<s id="N2575D">igitur duo FK tangerent <lb></lb>idem FM quod falſum eſt, non denique tertium; </s>
					<s id="N25765">quia ſi punctum ſecun­<lb></lb>dum FK tangat contactu tantum extremo primum FK, ita vt ſit conta­<lb></lb>ctus extremus in vtroque id eſt in ſecundo plani, &amp; in ſecundo arcus; <lb></lb>haud dubiè ſecundus EI tangit ſecundum EN contactu medio in pun­<lb></lb>cto arcus &amp; extremo in puncto plani </s>
				</p>
				<p id="N25771" type="main">
					<s id="N25773">25. Itaque hic motus explicari debet per diuerſos contactas inadæ­<lb></lb>quatos; non poteſt tamen fieri, quin minor rota ſuum motum componat <lb></lb>cum motu maioris, vt explicauimus abundè, cum de motu circulari, v.g. <lb></lb>non poteſt minor rota ita moueri, vt acquirat quodlibet eius punctum <lb></lb>locum immediatè non participantem vno inſtanti, ſi ex eo ſequatur aliud <lb></lb>punctum, vel eiuſdem rotæ, vel alterius coniunctæ moueri velociùs, vt <lb></lb>conſtat ex dictis. </s>
				</p>
				<p id="N25784" type="main">
					<s id="N25786">26. Vides autem primò, motum maioris rotæ accedere propiùs ad cir­<lb></lb>cularem, cum mouetur hoc ſecundo motus genere; </s>
					<s id="N2578C">quia ſcilicet motus <lb></lb><expan abbr="cẽtri">centri</expan> ſi <expan abbr="cõparetur">comparetur</expan> cum motu orbis maioris rotæ, minor eſt; </s>
					<s id="N25799">ſi enim nullus <lb></lb>eſſet motus centri, ſed tantùm motus orbis, eſſet motus perfectè circula­<lb></lb>ris; </s>
					<s id="N257A1">igitur quo minor eſt motus centri, &amp; maior motus orbis, accedit ille <pb pagenum="346" xlink:href="026/01/380.jpg"></pb>motus propiùs ad circularem, &amp; è contrario quò maior eſt motus centri, <lb></lb>vt accidit in ſecundo genere motus, accedit propiùs ad motum rectum; <lb></lb>cum verò alter alteri æqualis eſt motus mixtus, quem medium appellare <lb></lb>poſſumus. </s>
				</p>
				<p id="N257B0" type="main">
					<s id="N257B2">27. Aliqua puncta maioris rotæ; </s>
					<s id="N257B6">cuius motus à minori dirigitur re­<lb></lb>troëunt, ſcilicet, quæ accedunt propiùs ad punctum contactus E, v. g. <lb></lb>ipſum E vbi centrum rotæ eſt in KI regreditur in O: </s>
					<s id="N257C1">immò regredi vi­<lb></lb>detur vſque ad X, id eſt, donec ſecus lineam BM; </s>
					<s id="N257C7">igitur cum arcus ZE <lb></lb>M, ſit ſubduplus arcus ZIM, vt conſtat, &amp; cùm motus centri ſit ſubduplus <lb></lb>motus orbis, etiam arcus, qui regreditur, eſt ſubduplus illius, qui non re­<lb></lb>greditur; ſed <expan abbr="motũ">motum</expan> centri ſequitur. </s>
					<s id="N257D5">Tertiò, ſi ducas multas parallelas AL, <lb></lb>quæ diuidant YE in arcus æquales, habebis puncta lineæ motus v.g. ſit E <lb></lb>V ſubduplus EY ſit, VO ſubdupla EN, ſit EZ 2/3 XY; </s>
					<s id="N257DF">ſit IX 2/3 EN; deni­<lb></lb>que ipſa YP æqualis EN. </s>
				</p>
				<p id="N257E5" type="main">
					<s id="N257E7">28. Quartò, aliquod punctum nec progreditur, nec regreditur vno <lb></lb>inſtanti, eo ſcilicet; </s>
					<s id="N257ED">quo tantum detrahit motus orbis, quantum addit <lb></lb>motus centri, <expan abbr="poteſtq́ue">poteſtque</expan> determinari punctum illud; </s>
					<s id="N257F7">imò &amp; proportiones <lb></lb>motus cuiuſlibet puncti; ſed hæc ex poſitis principiis facilè colligitur <lb></lb>operâ analytices. </s>
				</p>
				<p id="N257FF" type="main">
					<s id="N25801">Quintò punctum E mouetur velociùs, cum dirigitur motus â minori <lb></lb>rota, quàm punctum C, cum dirigitur motus à maiori; </s>
					<s id="N25807">quia motus orbis <lb></lb>multùm illud retroagit: </s>
					<s id="N2580D">immò non mouetur tardiſſimè omnium; </s>
					<s id="N25811">ſed pun­<lb></lb>ctum illud, quod nec progreditur, nec regreditur, ſed modicùm vel aſcen­<lb></lb>dit vel deſcendit; ſunt autem duo huiuſmodi puncta, alterum in arcu I <lb></lb>E, alterum in YE. </s>
				</p>
				<p id="N2581C" type="main">
					<s id="N2581E">29. Sextò denique ex his principis benè èxplicatur quomodo maior <lb></lb>vel minor rota, cuius motus ab alia minore dirigitur, moueri poteſt; </s>
					<s id="N25824">nec <lb></lb>eſt quod in his diutiùs immoremur, vt tandem interruptam noſtro­<lb></lb>rum Theorematum ſeriem repetamus, ſunt enim plures alij motus mixti <lb></lb>non tantùm ex recto, &amp; circulari, ſed ex duobus &amp; pluribus circularibus; <lb></lb>quorum omnium rationes niſi me veritas ipſa fallit (quæ tamen falle­<lb></lb>re non poteſt) ad ſua principiæ phyſica reducemus. </s>
				</p>
				<p id="N25833" type="main">
					<s id="N25835"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25841" type="main">
					<s id="N25843"><emph type="italics"></emph>Globus, qui deſcendit deorſum in plano inclinato, mouetur motu mix­<lb></lb>to ex recto centri, &amp; circulari orbis<emph.end type="italics"></emph.end>; </s>
					<s id="N25850">patet ex dictis, cum more rotæ <lb></lb>moueatur, ſic etiam mouetur globus deorſum demiſſus cum aliqua in­<lb></lb>clinatione; </s>
					<s id="N25858">cuius certè nulla pars aſcendit, ſen regreditur; </s>
					<s id="N2585C">eſt enim <lb></lb>eadem illius ratio; </s>
					<s id="N25862">cur autem moueatur ille motu mixto, &amp; non <lb></lb>recto ſimplici: </s>
					<s id="N25868">ratio eſt, quia propter primam illam inclinationem <lb></lb>tollitur eius æquilibrium; </s>
					<s id="N2586E">cùm enim globus perfectus in aëre vibratus, <lb></lb>ſi nulla adſit inclinatio, ſit in perfecto æquilibrio, certè, ſi vel modica in­<lb></lb>clinatio accedat vel in C vel in D tolletur æquilibrium, quia illa incli­<lb></lb>natio <expan abbr="idẽ">idem</expan> præſtat quod pondus nouum <expan abbr="additũ">additum</expan>; porrò huius inclinationis: <pb pagenum="347" xlink:href="026/01/381.jpg"></pb>ratio ex eo petitur primò, quòd prius globus demittatur per planum <lb></lb>inclinatum, ſiue cadat ex ipſa manu, ſiue ex alio plano v.g. ex recto vel <lb></lb>alio plano decliui. </s>
					<s id="N2588B">Secundò ex eo, quòd priùs moueatur altera extremi­<lb></lb>tas putà C, quàm D; </s>
					<s id="N25891">igitur acquirit C plùs impetus motu naturaliter ac­<lb></lb>celerato; </s>
					<s id="N25897">igitur retinetur à puncto; </s>
					<s id="N2589B">quòd licèt deinde moueatur, tardiùs <lb></lb>tamen mouetur; </s>
					<s id="N258A1">igitur C vbi ad imum deſcendit iterum videtur aſcen­<lb></lb>dere tùm propter determinationem nouam; </s>
					<s id="N258A7">tùm quia ab oppoſito pun­<lb></lb>cto deſcendente quaſi attollitur: </s>
					<s id="N258AD">non dixi aſcendere, ſed tantùm videri <lb></lb>aſcendere, quia reuerâ non aſcendit; </s>
					<s id="N258B3">alioquin aliquod punctum regrede­<lb></lb>retur, quod falſum eſt; nec enim poteſt aſcendere, niſi regrediatur, vt <lb></lb>conſtat. </s>
				</p>
				<p id="N258BB" type="main">
					<s id="N258BD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N258C9" type="main">
					<s id="N258CB"><emph type="italics"></emph>Hinc non deſtruitur ille impetus ab impetu innato, vt fit in funependulis<emph.end type="italics"></emph.end>; </s>
					<s id="N258D4"><lb></lb>quia ſcilicet deſtruitur tantùm ab innato in aſcenſu; </s>
					<s id="N258D9">ſed nullum pun­<lb></lb>ctum globi aſcendit, vt dictum eſt, quod vt meliùs intelligatur, ſit in fi­<lb></lb>gura Th. 1. globus centro O; </s>
					<s id="N258E1">ſitque OF perpendicularis deorſum, quæ <lb></lb>percurritur ab eodem centro O motu centri; </s>
					<s id="N258E7">ſitque motus orbis ab L <lb></lb>in <expan abbr="q;">que</expan> intelligatur autem planium AI 6; </s>
					<s id="N258F1">certè punctum A, quod perinde <lb></lb>ſe habet, atque ſi eſſet punctum contactus, deſcribit lineam ARP ergo <lb></lb>non aſcendit; igitur non deſtruitur impetus productus ab impetu in­<lb></lb>nato. </s>
				</p>
				<p id="N258FB" type="main">
					<s id="N258FD"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N25909" type="main">
					<s id="N2590B">Obſeruabis 1°. </s>
					<s id="N2590E">mirificam eſſe impetus propagationem in hoc motu; <lb></lb>quippe omnes partes mouentur inæquali motu, licèt moueantur à prin­<lb></lb>cipio intrinſeco. </s>
				</p>
				<p id="N25916" type="main">
					<s id="N25918">1. Non tantum accelerari motum centri, ſed etiam motum orbis, vt <lb></lb>patet experientiâ in globo deſcendente per decliue planum. </s>
				</p>
				<p id="N2591F" type="main">
					<s id="N25921">3. Si globus non deſcendat in plano declini ſed in libero aëre poſt <lb></lb>primam librationem motus orbis non creſcit; </s>
					<s id="N25929">quia omnes partes ten­<lb></lb>dere poſſunt deorſum, nec ab vllo obice impediuntur; non eſt autem <lb></lb>par ratio pro motu in plano decliui, vt patet. </s>
				</p>
				<p id="N25931" type="main">
					<s id="N25933">4. Hinc motus orbis ſenſim deceſcit, ſed omninò inſenſibiliter; </s>
					<s id="N25937"><lb></lb>quia non deſtruitur ab impetu innato, vt iam dictum eſt; </s>
					<s id="N2593C">nec enim ſic <lb></lb>motus circularis eſt contrarius motui recto; </s>
					<s id="N25942">quippe modò centrum <lb></lb>grauitatis globi feratur motu recto, hoc ſatis eſſe videtur, ſiue partes mo­<lb></lb>tu circulari ferantur: circa idem centrum, ſiue omnes motu recto per <lb></lb>lineas parallelas ferantur:</s> 
					<s id="N25943">ratio à priori eſt, quia in tantum vnus impe­<lb></lb>tus deſtruit alium in eadem parte mobilis, in quantum impeditur ab eo <lb></lb>eius motus deorſum totius globi nullo modo impeditur ab illo motu <lb></lb>circulari, quia globus æquè citò deſcendit vno, atque alio motu, vt con­<lb></lb>ſtat mille experientiæ. </s>
				</p>
				<p id="N25957" type="main">
					<s id="N25959"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25965" type="main">
					<s id="N25967"><emph type="italics"></emph>Si corporis grauis altera extremitas ſit grauior demittaturque in eo ſitu,<emph.end type="italics"></emph.end><pb pagenum="348" xlink:href="026/01/382.jpg"></pb><emph type="italics"></emph>in quo ſit parallelum horizonti; </s>
					<s id="N25976">haud dubiè extremitas grauior præit motu <lb></lb>mixto<emph.end type="italics"></emph.end>; </s>
					<s id="N2597F">quia ſcilicet quaſi ab aliâ leuiore retinetur, exemplum habes in <lb></lb>ſagittâ ferro armatâ, &amp; in fune ex quo plumbum pendet; ratio euiden­<lb></lb>tiſſima eſt; </s>
					<s id="N25987">quia illa extremitas faciliùs medij reſiſtentiam ſuperat, igitur <lb></lb>præire debet; </s>
					<s id="N2598D">igitur motu mixto; </s>
					<s id="N25991">illa tamen tardiùs deſcendit, quàm <lb></lb>deſcenderet, ſi à leuiore eſſet ſeparata; </s>
					<s id="N25997">leuior verò velociùs, quàm ſi eſ­<lb></lb>ſet ſolitaria; quod autem non ſit alia ratio, patet potiſſimum ex eo, quòd <lb></lb>plumbum ita demiſſum, vt funis præeat, tandem funem aſſequitur, &amp; tan­<lb></lb>dem à tergo relinquit. </s>
				</p>
				<p id="N259A1" type="main">
					<s id="N259A3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N259B0" type="main">
					<s id="N259B2">Hinc petenda eſt vera ratio illius phœnomeni, quod iam ſuprà l. 3. <lb></lb>indicauimus, ſcilicet ſagittam plùs temporis ponere in deſcenſu, quàm <lb></lb>in aſcenſu minoremque infligere ictum, quàm leuius lignum, &amp; multò <lb></lb>leuior penna cuſpidis ferreæ motum retardat. </s>
				</p>
				<p id="N259BD" type="main">
					<s id="N259BF"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N259CC" type="main">
					<s id="N259CE">Si altera extremitas ſagittæ plumis inſtruatur, licèt proijciatur motu <lb></lb>violento ſurſum extremitas ferro armata præit plumis à tergo relictis; </s>
					<s id="N259D4"><lb></lb>ratio eſt, quia aër fortiùs reſiſtit pluuis, quàm ferro, vel ligno; igitur ca­<lb></lb>rum motum retardat. </s>
				</p>
				<p id="N259DB" type="main">
					<s id="N259DD"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N259EA" type="main">
					<s id="N259EC">Hinc ſagitta pennis attonſis fertur in incertum, &amp; ſcopum fallit, cui <lb></lb>fuerat deſtinata; </s>
					<s id="N259F2">quia licèt lignum minore vi polleat, quàm ferrum; </s>
					<s id="N259F6">vix <lb></lb>tamen ſenſibilis eſt differentia; </s>
					<s id="N259FC">adde quod minima deflexio, vel decli­<lb></lb>natio ad retrò agendum ferrum ſufficit; corpus enim facilè mouetur mo­<lb></lb>tu mixto ex recto, &amp; circulari. </s>
				</p>
				<p id="N25A04" type="main">
					<s id="N25A06"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25A13" type="main">
					<s id="N25A15">Hinc ratio illius iaculi breui cuſpide armati, cuius altera extremitas <lb></lb>decuſſatim fiſſa craſſiore charta paululùm expanſa munitur, quę deflexio­<lb></lb>nem impedit; </s>
					<s id="N25A1D">cuius rei analogiam habes in nauis gubernaculo; </s>
					<s id="N25A21">eſt enim <lb></lb>ad inſtar quadruplicis claui motum dirigentis; </s>
					<s id="N25A27">quîppe inclinari non <lb></lb>poteſt, niſi multum aëris pellant alæ illæ chartaceæ: In ſagitta aliquid <lb></lb>ſimile habes. </s>
				</p>
				<p id="N25A2F" type="main">
					<s id="N25A31"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25A3E" type="main">
					<s id="N25A40">Hinc ſi euibretur iaculum illud per horizontalem v.g. circa pro­<lb></lb>prium axem conuoluitur; </s>
					<s id="N25A48">quia aër tenues illas tranſuerberat alas, ex <lb></lb>qua aëris vel colliſione, vel appulſu, vel quaſi reflexione facilè ſequitur <lb></lb>circularis motus, qui nullatenus impedit rectum, vt iam dixi ſuprà; </s>
					<s id="N25A50">ſed <lb></lb>cum eo motum mixtum componit, de quo paulò pòſt; nunc tantùm ſuf­<lb></lb>ficiat attigiſſe veriſſimam rationem illorum gyrorum. </s>
				</p>
				<p id="N25A58" type="main">
					<s id="N25A5A"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25A67" type="main">
					<s id="N25A69">Simile phœnomenum habes in illis volatilibus calamis, qui multis <lb></lb>copiam ludi faciunt; </s>
					<s id="N25A6F">nam primò tignea illa, vel oſſea theca, cui com-<pb pagenum="349" xlink:href="026/01/383.jpg"></pb>mittuntur plumæ, plumas ipſas præit propter rationem prædictam; </s>
					<s id="N25A78">nam <lb></lb>aëra faciliùs diuidit; </s>
					<s id="N25A7E">ſecundò vertiginem illam habet, de qua ſuprà; </s>
					<s id="N25A82">quia <lb></lb>aër quaſi reuerberat, <expan abbr="torquetq;">torquetque</expan> plumas; de hoc motu paulò pòſt agemus. </s>
				</p>
				<p id="N25A8D" type="main">
					<s id="N25A8F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25A9B" type="main">
					<s id="N25A9D"><emph type="italics"></emph>Cum Cylindrus ita dimittitur, vt altera extremitas motu circulari praeat, <lb></lb>remanente initio aliquo centro immobili, deſcendit motu mixto ex recto &amp; <lb></lb>circulari<emph.end type="italics"></emph.end>; </s>
					<s id="N25AAA">vt conſtat ex iis, quæ diximus de globo deorſum cadente hoc <lb></lb>genere motus; ſunt tamen hîc multa obſeruanda. </s>
					<s id="N25AB0">Primò omnes partes <lb></lb>globi initio moueri, ſed inæqualiter, cùm tamen aliqua pars cylindri non <lb></lb>moueatur. </s>
					<s id="N25AB7">Sit enim cylindrus AC ita innixus B, vt liberè moueri poſſit; </s>
					<s id="N25ABB"><lb></lb>haud dubiè, cùm non ſit æquilibrium, ſegmentum BC præualebit; </s>
					<s id="N25AC0">igitur <lb></lb>circa centrum B extremitas C deſcendet per arcum CD, &amp; A per arcum <lb></lb>AE; donec tandem punctum B moueatur per rectam BF, ſeu per aliam <lb></lb>proximè accedentem, ſi. </s>
					<s id="N25ACA">tantillùm à plano BF repellatur; </s>
					<s id="N25ACE">punctum verò <lb></lb>C motu mixto ex recto deorſum, &amp; circulari circa B; </s>
					<s id="N25AD4">ea tamen lege, vt <lb></lb>motus orbis nullo modo acceleretur, ſed tantùm motus centri; igitur <lb></lb>hic motus conſtat ex motu centri accelerato, &amp; motu orbis quaſi æqua­<lb></lb>bili, cuius linea deſcribi poteſt, vt videbimus l. 12. dixi, ferè æquabilem, <lb></lb>quia aliquid deſtruitur ſingulis inſtantibus ratione nouæ determinatio­<lb></lb>nis, vt diximus ſuprà cum de motu circulari, ſed parùm pro nihilo repu­<lb></lb>tatur. </s>
				</p>
				<p id="N25AE6" type="main">
					<s id="N25AE8"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N25AF4" type="main">
					<s id="N25AF6">Obſerua 1°. </s>
					<s id="N25AF9">eſſe plures huius motus mixti ſpecies. </s>
					<s id="N25AFC">Primò eſt mixtus <lb></lb>ex motu centri &amp; motu orbis æquali. </s>
					<s id="N25B01">Secundo ex 1°. </s>
					<s id="N25B04">maiore &amp; 2°. </s>
					<s id="N25B07">mi­<lb></lb>nore. </s>
					<s id="N25B0C">Tertiò ex 1°. </s>
					<s id="N25B0F">minore &amp; 2°. </s>
					<s id="N25B12">maiore. </s>
					<s id="N25B15">Quartò ex 1°. </s>
					<s id="N25B18">accelerato 2°. <lb></lb></s>
					<s id="N25B1C">æquabili Quintò ex 1°. </s>
					<s id="N25B1F">accelerato 2°. </s>
					<s id="N25B22">retardato. </s>
					<s id="N25B25">Sextò ex vtroque retar­<lb></lb>dato. </s>
					<s id="N25B2A">Septimò ex vtroque accelerato. </s>
					<s id="N25B2D">Octauò ex 1°. </s>
					<s id="N25B30">æquabili 2°. </s>
					<s id="N25B33">accele­<lb></lb>rato.Nono ex 1°. </s>
					<s id="N25B38">retardato 2°. </s>
					<s id="N25B3B">accelerato. </s>
					<s id="N25B3E">Decimò ex 1°. </s>
					<s id="N25B41">æquabili 2°. </s>
					<s id="N25B44">ac­<lb></lb>celerato.Vndecimò ex 1°. </s>
					<s id="N25B49">æquabili 2°. </s>
					<s id="N25B4C">retardato &amp;c. </s>
					<s id="N25B4F">nec enim hîc deeſt <lb></lb>maxima motuum ſylua, quorum tamen, quia eſt eadem ratio, nimis acu­<lb></lb>ratam diſtributionem omittimus, non facilè haberi poteſt; </s>
					<s id="N25B57">cùm enim <lb></lb>ſint tres termini, ſcilicet æquabilis, retardatus, acceleratus, erunt 9. <lb></lb>combinationes; </s>
					<s id="N25B5F">&amp; cùm ſingulæ tres differentias habeant; nam vel mo­<lb></lb>tus orbis eſt æqualis motui centri, vel maior, vel minor, ducantur 9.in 3. <lb></lb>&amp; erunt 27. </s>
				</p>
				<p id="N25B67" type="main">
					<s id="N25B69">Obſerua ſecundò centrum motus poſſe vel propiùs accedere ad A <lb></lb>v.g.ſi eſſet in G, vel ad C v.g. ſi eſſet Z. ſi primum, maior eſt motus orbis, <lb></lb>id eſt velocior, licèt pauciores circuitus fiant; </s>
					<s id="N25B73">quia extremitas C ma­<lb></lb>iorem arcum deſcribens plùs temporis in deſcenſu ponit; </s>
					<s id="N25B79">igitur maio­<lb></lb>rem velocitatem acquirit; ſi verò ſecundum, è contrario. </s>
				</p>
				<p id="N25B7F" type="main">
					<s id="N25B81"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25B8D" type="main">
					<s id="N25B8F"><emph type="italics"></emph>Cum cylindrus proijcitur ſurſum it a vt aliquod punctum rectà feratur, cir­<lb></lb>ca quod voluitur cylindrus, </s>
					<s id="N25B98">est motus mixtus ex recto centri, &amp; circulari orbis,<emph.end type="italics"></emph.end><pb pagenum="350" xlink:href="026/01/384.jpg"></pb>pro quo non eſt noua difficultas; nam eſt prorſus eadem ratio, niſi <lb></lb>quod primò debet priùs imprimi motus rectus omnibus partibus erecto <lb></lb>cylindro tùm vbi ſeparatur à manu circulariis. </s>
					<s id="N25BA8">Secundò centrum poteſt <lb></lb>accedere propiùs ad ſummam extremitatem vel ad imam. </s>
					<s id="N25BAD">Tertiò, aſcendit <lb></lb>eò altiùs cylindrus, quò centrum motus orbis accedit propiùs ad ſum­<lb></lb>mam extremitatem. </s>
					<s id="N25BB4">Quartò, poteſt extremitas ima impelli duobus mo­<lb></lb>dis: </s>
					<s id="N25BBA">primò ſi retrò agitur, ſecundò ſi antè; </s>
					<s id="N25BBE">ſed quia hæc omnia perti­<lb></lb>nent ad diuerſos oblongæ haſtæ motus iucundaque militaris illius exer­<lb></lb>citationis phœnomena, quorum omnium rationem in ſingulari Theo­<lb></lb>remate afferemus; eò totam rem iſtam remittimus. </s>
				</p>
				<p id="N25BC8" type="main">
					<s id="N25BCA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25BD6" type="main">
					<s id="N25BD8"><emph type="italics"></emph>Quando globus, ſeu rota voluitur in ſuperficie curua immobili, omnes eius <lb></lb>partes mouentur motu mixto ex duobus circularibus, ſcilicet ex motu circula­<lb></lb>ri centri, &amp; circulari orbis,<emph.end type="italics"></emph.end> eſt enim motus centri circularis ſi voluatur <lb></lb>globus in orbe, hoc eſt in ſuperficie curua; </s>
					<s id="N25BE7">porrò hæc ſuperficies vel eſt <lb></lb>conuexa, vel concaua, vel eſt circuli maioris, vel minoris; </s>
					<s id="N25BED">itemque ſi con­<lb></lb>caua vel eſt circuli æqualis, vel maioris, vel minoris; igitur ſunt 6. nouæ <lb></lb>combinationes, quæ ſi ducantur in 27. habebis 162. ſed quia, ſi eſt con­<lb></lb>caua minoris, vel æqualis, non poteſt globus in ea rotari. </s>
					<s id="N25BF7">Hinc ſunt tan­<lb></lb>tùm 4. legitimæ combinationes nouæ, quæ ſi ducantur in 27, habebis <lb></lb>108; ſed iam ſeorſim rem iſtam conſideremus. </s>
				</p>
				<p id="N25BFF" type="main">
					<s id="N25C01"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25C0D" type="main">
					<s id="N25C0F"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena rotæ, quæ circa æqualem rotam immo­<lb></lb>bilem it a rotatur, vt arcus mobilis, &amp; immobilis decurſi ſint æquales.<emph.end type="italics"></emph.end></s>
					<s id="N25C18"> Sit rota <lb></lb>immobilis centro L, radio AB; ſit alia centro C æqualis priori, quæ ita <lb></lb>moueatur, vt ſinguli arcus BE reſpondeant ſingulis arcubus BT, &amp; pun­<lb></lb>ctum E tangat in T, D in X, F in D. </s>
					<s id="N25C23">Primò centrum mouetur motu cir­<lb></lb>culari, deſcribitque circulum radio AC, ſcilicet duplum circuli immobi­<lb></lb>lis ABX. </s>
					<s id="N25C2A">Secundò motus centri eſt duplò maior motu orbis, id eſt eo <lb></lb>tempore, quo in ſuperficie conuexa decurſus eſt arcus BT, centrum C <lb></lb>confecit arcum CV duplum; cuius phœnomeni ratio clara eſt, quia ſci­<lb></lb>licet centrum C diſtat ſemper ab A toto radio AC duplo AB. </s>
				</p>
				<p id="N25C35" type="main">
					<s id="N25C37">Tertiò poteſt deſcribi linea, quam punctum B ſuo fluxu deſcribit; <lb></lb>ducatur ſemicirculus CVT; diuidatur in 12. partes æquales ductis radiis <lb></lb>AC, AL, AV &amp;c.qui ſecant circulum ABX in punctis YZ <foreign lang="grc">δγ</foreign> &amp;c. </s>
					<s id="N25C43">tùm <lb></lb>ex punctis, quæ terminant ductos radios in ſemicirculo CVT deſcri­<lb></lb>bantur circuli radio CB; haud dubiè tangent hi circuli circulum ABX <lb></lb>in punctis YZ <foreign lang="grc">δγ</foreign> &amp;c. </s>
					<s id="N25C51">denique accipiatur arcus YG æqualis YB, tùm <lb></lb>ZH æqualis ZB, tùm <foreign lang="grc">δ</foreign> I æqualis <foreign lang="grc">δ</foreign> B, atque ita deinceps, &amp; per puncta <lb></lb>BGHIK. &amp;c. </s>
					<s id="N25C60">ducantur curua BGLMOQS, atque idem fiat ſini­<lb></lb>ſtrorſum, &amp; habebitur linea, quam ſuo fluxu deſcribit punctum B; </s>
					<s id="N25C66">quod <lb></lb>breuiter demonſtratur, quia quando centrum C eſt in L, decurrit arcum <lb></lb>CL ſubduplum CV; </s>
					<s id="N25C6E">igitur tangit in <foreign lang="grc">δ</foreign>; </s>
					<s id="N25C76">igitur decurrit B <foreign lang="grc">δ</foreign> ſubduplum <lb></lb>BT; </s>
					<s id="N25C80">igitur circa centrum C motu orbis conuerſus eſt arcus ſubduplus <pb pagenum="351" xlink:href="026/01/385.jpg"></pb>BE eſt æqualis <foreign lang="grc">δ</foreign> B; </s>
					<s id="N25C8D">ſed <foreign lang="grc">δ</foreign> I eſt æqualis <foreign lang="grc">δ</foreign> B; igïtur punctum circuli mo­<lb></lb>bilis eſt in I, idem prorſus demonſtrabitur de aliis punctis. </s>
				</p>
				<p id="N25C9B" type="main">
					<s id="N25C9D">Quartò, hinc triangula curuilinea BYG, BZH, B <foreign lang="grc">δ</foreign> I ſunt Iſoſcelia; </s>
					<s id="N25CA5"><lb></lb>ipſum vero BVK eſt æquilaterum quia AK eſt Tangens, vt conſtat; </s>
					<s id="N25CAA"><lb></lb>immò ſinguli circuli debent tangere ſuum radium, vt patet; porrò miri­<lb></lb>fica eſt huius lineæ figura, quæ ſectionem cordis exhibet, quam ideo <lb></lb>deinceps lineam cordis appellabimus, cuius ſunt inſignes omninò pro­<lb></lb>prietates, quas ſuo loco demonſtrabimus. </s>
				</p>
				<p id="N25CB5" type="main">
					<s id="N25CB7">Quintò, punctum B initio tardiſſimè mouetur cum eo tempore, quo <lb></lb>decurrit BG punctum oppoſitum D decurrat D6; </s>
					<s id="N25CBD">ratio eſt, quia motus <lb></lb>centri defert D in I, cui motus orbis cum motu centri conſentiens ad­<lb></lb>dit P6, cùm tamen motus orbis puncti B ſit contrarius motui centri; </s>
					<s id="N25CC5"><lb></lb>adde quod motus centri circa centrum A tribuit maiorem motum <lb></lb>puncto D, quàm B iuxta proportionem radiorum; igitur cùm DA <lb></lb>ſit tripla BA, motus centri D eſt triplus motus centri B, igitur duplici <lb></lb>nomine motus puncti B eſt tardior. </s>
					<s id="N25CD0">Primò, quia motus orbis <lb></lb>tantùm addit D, quantum detrahit B. Secundò, quia motus centri addit <lb></lb>D motum triplum illius, quem addit B. </s>
				</p>
				<p id="N25CD7" type="main">
					<s id="N25CD9">Sextò poſſunt haberi per <expan abbr="analyticã">analyticam</expan> proportiones arcuum lineæ motus, <lb></lb>quos B ęqualibus <expan abbr="tẽporibus">temporibus</expan> percurrit v.g.BG, GH, HI, IK, KL, LM, <expan abbr="deniq;">denique</expan> <lb></lb>vltimus RS æqualis D6; </s>
					<s id="N25CED">indico breuiter huius proportionem, cum BGDP <lb></lb>eſt tripla BY, &amp; P6; </s>
					<s id="N25CF3">eſt quadrupla; </s>
					<s id="N25CF7">igitur ferè æqualis BV, ſi ducantur <lb></lb>duæ rectæ YB, YG angulus rectilineus GYB eſt æqualis YAB, id eſt <lb></lb>15 grad.igitur ita ſe habet arcus BG ad BY vt recta BY ad BA, id eſt ferè, <lb></lb>vt 1.ad 4.paulò minùs; </s>
					<s id="N25D01">ſed D6 eſt quadruplus BY; </s>
					<s id="N25D05">igitur BG eſt ad D6 <lb></lb>vt 1. ad 16.paulò minus; </s>
					<s id="N25D0B">ſed eo maior erit proportio motus D, quo aſ­<lb></lb>ſumetur minor arcus; </s>
					<s id="N25D11">vt autem habeatur proportio aſſumpto arcu in­<lb></lb>tegro quadrantis eſt vt M S ad MB; porrò eſt ferè eadem proportio <lb></lb>motuum punctorum appoſitorum rotæ mobilis, ſiue rotetur in plano re­<lb></lb>ctilineæ, ſiue in ſuperficie curua. </s>
				</p>
				<p id="N25D1B" type="main">
					<s id="N25D1D">Septimò, puncta B &amp; E de tempore, quo percurritur arcus quadran­<lb></lb>tis percurrunt ſpatia æqualia: </s>
					<s id="N25D23">hinc ET, BM ſunt æquales; </s>
					<s id="N25D27">immò <lb></lb>ſi ducantur rectæ BEMTB, erit ET perfectum quadratum vt conſtat, <lb></lb>cuius diagonalis erit BM; </s>
					<s id="N25D2F">igitur æqualis BX, quæ omnia conſtant ex <lb></lb>ipſis elementis; porrò punctum B velociſſimè omnium mouetur, vt pa­<lb></lb>tet ex dictis. </s>
				</p>
				<p id="N25D37" type="main">
					<s id="N25D39">Octauò, quodlibet punctum circuli mobilis BEDF ſuo motu de­<lb></lb>ſcribit arcum lineæ cordis, vt certum eſt, qui in mille punctis decuſ­<lb></lb>ſantur cum linea puncti, quam deſcribit punctum B v.g. linea puncti D <lb></lb>decuſſatur cum linea puncti B in <expan abbr="q.">que</expan> quippe D q, S q ſunt æquales, linea <lb></lb>puncti E cum linea puncti B in L; denique deſcribi poteſt hæc linea <lb></lb>BKMN &amp;c. </s>
					<s id="N25D4D">ductis radiis ex centro ad libitum ſine vllo diuiſionis <lb></lb>ordine v.g. ducatur A <foreign lang="grc">δ</foreign>; </s>
					<s id="N25D59">L nulla habita diuiſionis ratione; </s>
					<s id="N25D5D">ex L deſcri­<lb></lb>batur arcus radio L <foreign lang="grc">δ</foreign>; </s>
					<s id="N25D67">aſſumantur <foreign lang="grc">δ</foreign> I, <foreign lang="grc">δ</foreign> B æquales, per I; </s>
					<s id="N25D73">haud dubiè <lb></lb>ducetur linea; idem dico de aliis punctis. </s>
				</p>
				<pb pagenum="352" xlink:href="026/01/386.jpg"></pb>
				<p id="N25D7D" type="main">
					<s id="N25D7F">Nonò, ſi aſſumatur quodlibet punctum intra rotam v.g. punctum <lb></lb>X perueniet in A eo tempore, quo B erit in M, vt patet; </s>
					<s id="N25D87">hinc moue­<lb></lb>bitur per lineam motus mixti, qui accedit propiùs ad circularem; <lb></lb>quemadmodum enim cum rota mouetur in plano rectilineo, punctum <lb></lb>illius, quod accedit propiùs ad centrum mouetur eo motu, qui accedit <lb></lb>propiùs ad motum centri, id eſt ad motum rectum. </s>
					<s id="N25D93">Similiter punctum, <lb></lb>quod accedit propiùs ad Q in hac rota mouetur eo motu, qui accedit <lb></lb>propiùs ad motum centri C, id eſt ad motum circularem; igitur hic mo­<lb></lb>tus puncti X plùs participat de motu centri, quàm de motu orbis, qui <lb></lb>ſcilicet in eo minimus eſt. </s>
				</p>
				<p id="N25D9F" type="main">
					<s id="N25DA1">Decimò, hinc ſi motus minoris rotæ radio CX dirigatur à motu ma­<lb></lb>ioris radio CB; </s>
					<s id="N25DA7">hæc quidem ita mouetur vt ſingula puncta BE re­<lb></lb>ſpondeant ſingulis BT, non tamen ſingula XY ſingulis XB; </s>
					<s id="N25DAD">ſed hic <lb></lb>etiam accerſendi ſunt contactus illi inadæquati extremi plùs, minuſue, <lb></lb>de quibus ſuprà; eſt enim prorſus eadem difficultas, quam ſuprà diſcuſ­<lb></lb>ſimus ſuo titulo rotæ Ariſtotelicæ, quam hîc tantùm indicaſſe ſufficiat, <lb></lb>cùm ex prædictis principiis omninò ſoluatur. </s>
				</p>
				<p id="N25DB9" type="main">
					<s id="N25DBB">Vndecimò ſimiliter, ſi minor rota motum maioris dirigat; </s>
					<s id="N25DBF">haud du­<lb></lb>biè maioris idem punctum pluribus punctis ſuperficiei curuæ, cui in­<lb></lb>cumbit inadæquato dumtaxat contactu reſpondebit, eritque diuerſa li­<lb></lb>nea huius motus, &amp; aliqua puncta retroagentur; </s>
					<s id="N25DC9">quod quomodo fiat, <lb></lb>iam ſuprà explicuimus; quod verò ſpectat ad proprietates iſtarum linea­<lb></lb>rum, in ſingularem tractatum cas remittimus. </s>
				</p>
				<p id="N25DD1" type="main">
					<s id="N25DD3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25DDF" type="main">
					<s id="N25DE1"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena, quæ in ſuperficie curua circuli <lb></lb>maioris rotatur<emph.end type="italics"></emph.end>; </s>
					<s id="N25DEC">ſit enim ſuperficies curua BF radius AB, ſitque rota <lb></lb>radio NB, cuius peripheria eſt æqualis BF; </s>
					<s id="N25DF2">igitur M tanget C, O tan­<lb></lb>get D, &amp; B tandem tanget F; igitur mouetur hæc rota motu mixto ex <lb></lb>duobus circularibus. </s>
				</p>
				<p id="N25DFA" type="main">
					<s id="N25DFC">Primò, ſignari poſſunt omnia puncta huius lineæ v. g. MIHF <lb></lb>per quæ ducenda eſt linea curua, cuius etiam affectiones aliàs demon­<lb></lb>ſtrabimus. </s>
				</p>
				<p id="N25E07" type="main">
					<s id="N25E09">Secundò, punctum B mouetur initio tardiſſimè, O velociſſimè; </s>
					<s id="N25E0D">ratio­<lb></lb>nem iam bis attulimus; </s>
					<s id="N25E13">quia ſcilicet maior eſt motus, cum motus centri <lb></lb>conuenit cum motu orbis; minor verò è contrario. </s>
				</p>
				<p id="N25E19" type="main">
					<s id="N25E1B">Tertiò, motus huius rotæ accedit propiùs ad motum rotæ in plano <lb></lb>rectilineo, quàm motus rotæ ſuperioris; quia BF, quæ eſt ſuperficies ma­<lb></lb>ioris circuli, accedit propiùs ad lineam rectam. </s>
				</p>
				<p id="N25E23" type="main">
					<s id="N25E25">Quartò, ſi ſit minor rota radio NR cuius motus dirigatur à motu <lb></lb>maioris radio NB, deſcribit lineam, quæ accedit propiùs ad lineam <lb></lb>rectam RSTVX, ſeu potiùs ad motum centri, quod mouetur motu <lb></lb>circulari per arcum NG, à quo non recedit, vt patet: </s>
					<s id="N25E2F">porrò minor <lb></lb>rota percurrit maiorem ſuperficiem ſua peripheria, quod etiam expli-<pb pagenum="353" xlink:href="026/01/387.jpg"></pb>candum eſt per contactus inadæquatos; tunc enim motus centri longè <lb></lb>ſuperat motum orbis. </s>
				</p>
				<p id="N25E3C" type="main">
					<s id="N25E3E">Quintò, ſi vera eſſet hypotheſis Copernici, terra moueretur hoc vlti­<lb></lb>mo motu mixto ex motu centri, &amp; motu orbis; </s>
					<s id="N25E44">vnde omnia puncta <lb></lb>eiuſdem circuli paralleli mouerentur inæquali motui tardiſſimo qui­<lb></lb>dem punctum contactus hoc eſt meridiano reſpondens, velociſſimo ve­<lb></lb>rò ipſi oppoſitum, ſcilicet de media nocte: porrò in hoc motu motus <lb></lb>centri eſſet ferè maior motu orbis iuxta communem de diametro ma­<lb></lb>gni orbis ſententiam. </s>
				</p>
				<p id="N25E52" type="main">
					<s id="N25E54">Sextò, ſi motus maioris rotæ dirigatur à minore res eodem modo <lb></lb>explicanda eſt, quo explicuimus illam per <expan abbr="cõtactus">contactus</expan> diuerſos inadæquatos <lb></lb>tùm Th. 15. num. </s>
					<s id="N25E5F">11. tùm in digreſſione multis locis: </s>
					<s id="N25E63">porrò poſſunt eſſe <lb></lb>diuerſæ proportiones circuli mobilis, &amp; immobilis; qui ſi maximus eſt, <lb></lb>minimus illius arcus accipi poteſt pro linea recta. </s>
				</p>
				<p id="N25E6B" type="main">
					<s id="N25E6D">Septimò, poteſt ita rota moueri, vt pars ſuperior retrò agatur, id eſt, <lb></lb>vt motus orbis ſit oppoſitus motui <expan abbr="cétri">centri</expan> v.g.ſi punctum N moueatur qui­<lb></lb>dem dextrorſum motu centri, O verò ſiniſtrorſum motu orbis; </s>
					<s id="N25E75">ſed tunc <lb></lb>punctum B mouebitur dextrorſum motu orbis, ſed eſt noua difficultas: </s>
					<s id="N25E7B"><lb></lb>quippe ex hac hypotheſi punctum O deſcriberet ſuo motu lineam ſimi­<lb></lb>lem, &amp; æqualem lineæ rotatili BMIHF; punctum verò B moueretur <lb></lb>iuxta hanc hypotheſin eo modo, quo mouetur punctum O iuxta prio­<lb></lb>rem. </s>
					<s id="N25E86">Sic autem moueri dicuntur quidam Epicycli ab Aſtronomis, quo­<lb></lb>rum centrum mouetur in conſequentia, hoc eſt ſecundum ſeriem <lb></lb>ſignorum; </s>
					<s id="N25E8E">ſummum verò punctum, ſeu ſtella apogæa retrò agitur, ſeu <lb></lb>in partem aduerſam contendit, vel vt vocant, in præcedentia: </s>
					<s id="N25E94">tales <lb></lb>vulgò ponuntur Solis Epicycli &amp; Lunæ; vnde obiter colligo, quàm ſit <lb></lb>neceſſaria Aſtronomis hæc de motu mixto ſententia, vt ſua phœnome­<lb></lb>na ad ſuas cauſas phyſicas reducant. </s>
				</p>
				<p id="N25E9E" type="main">
					<s id="N25EA0">Octauò denique, poſſunt eſſe diuerſæ lineæ huius motus pro diuerſa <lb></lb>circulorum proportione, quarum figuras, deſcriptiones, affectiones ſuo <lb></lb>loco demonſtrabimus, &amp; nouos latices tum Geometris, tùm Phyſicis <lb></lb>aperiemus, ex quibus vbertim fluit infinitarum ferè demonſtrationum <lb></lb>materia. </s>
				</p>
				<p id="N25EAD" type="main">
					<s id="N25EAF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25EBB" type="main">
					<s id="N25EBD"><emph type="italics"></emph>Explicari poſſunt cuncta phœnomena rotæ maioris mobilis circa minorem̨ <lb></lb>immobilem<emph.end type="italics"></emph.end>; ſit enim rota minor centro A, cui incubet maior rota cen­<lb></lb>tro K, radio KB duplo BA, roteturque circa ſuperficiem BDFTH <lb></lb>punctum 5 reſpondebit F &amp; Q poſt decurſam ſuperficiem puncto B, <lb></lb>eritque motus mixtus. </s>
				</p>
				<p id="N25ECE" type="main">
					<s id="N25ED0">Primò, centrum K mouebitur motu circulari, quia ſemper æqualiter <lb></lb>diſtat à puncto A; igitur deſcribit circulum, cuius radius eſt KA. </s>
				</p>
				<p id="N25ED6" type="main">
					<s id="N25ED8">Secundò, poteſt facilè deſcribi linea motus puncti B v.g. diuidatur <lb></lb>enim BDFH in 8 arcus æquales, &amp; B5 in 4; tùm per puncta <pb pagenum="354" xlink:href="026/01/388.jpg"></pb>CDE &amp;c. </s>
					<s id="N25EE5">deſcribantur circuli radio KB; </s>
					<s id="N25EE9">&amp; aſſumatur CR æqualis <lb></lb>B 2; tùm DL æqualis B 3, tùm EM æqualis B 4, tùm FN æqualis B 5, <lb></lb>atque ita deinceps, vt per puncta ſignata deſcribatur linea curua <lb></lb>BRLMNOPRQ, hæc eſt linea huius motus. </s>
				</p>
				<p id="N25EF3" type="main">
					<s id="N25EF5">Tertiò, omnia puncta mouentur inæqualiter, B quidem tardiſſimè, <lb></lb>Q velociſſimè; </s>
					<s id="N25EFB">nam eo tempore, quò B conficit BR, modicum illud <lb></lb>ſpatium IQ decuerit QS, cuius proportio ex analyſi cognoſci poteſt; </s>
					<s id="N25F01"><lb></lb>idem dico de motu aliorum punctorum; eſt etiam eadem ratio huius <lb></lb>inæqualitatis, de qua ſuprâ, cuius omnes proportiones aſſignari poſ­<lb></lb>ſunt. </s>
				</p>
				<p id="N25F0A" type="main">
					<s id="N25F0C">Quartò obſerua, figuram huius lineæ, quæ accedere videtur ad ſpi­<lb></lb>ralem: præterea linea puncti B, ſcilicet BRLMNOPRQ, ſecat li­<lb></lb>neam puncti Q in 8 mirabili implicatione, cuius interior portio exhibet <lb></lb>ſectionem cordis ſcilicet BRLMN 8 XY <foreign lang="grc">δ</foreign> B. </s>
				</p>
				<p id="N25F1A" type="main">
					<s id="N25F1C">Quintò, deinde pro diuerſa proportione rotarum maioris, ſcilicet &amp; <lb></lb>minoris rotæ, ſunt diuerſæ lineæ, &amp; motus mixti diuerſi; immò poſſet <lb></lb>rota immobilis, circa quam alia rotatur, tam parua eſſe, vt linea tantùm <lb></lb>poſt multas gyrationes perfici poſſet. </s>
				</p>
				<p id="N25F26" type="main">
					<s id="N25F28">Sextò, poſſunt etiam determinari lineæ aliorum punctorum intra <lb></lb>rotam mobilem v, g.puncti T; </s>
					<s id="N25F2E">quod vt fiat, ſemper eſt aſſumendus ra­<lb></lb>dius KB, qui ſcilicet, dum K eſt in <foreign lang="grc">μ</foreign>, incubat <foreign lang="grc">μ</foreign> R, dum eſt in M incubat <lb></lb>ML, dum eſt in <foreign lang="grc">θ</foreign> reſpondet <foreign lang="grc">θ</foreign> M; </s>
					<s id="N25F46">denique dum eſt in 9 reſpondet <lb></lb>9 N; itaque aſſumantur <foreign lang="grc">μ</foreign> 3, M <foreign lang="grc">ω, θ</foreign> 7, 9 <foreign lang="grc">β</foreign> æquales K, &amp; ducatur per <lb></lb>ſignata puncta linea curua T3 <foreign lang="grc">π</foreign> 7 <foreign lang="grc">β</foreign>, hæc eſt linea motus mixti pun­<lb></lb>cti T. </s>
				</p>
				<p id="N25F64" type="main">
					<s id="N25F66">Septimò, quando motus minoris rotæ radio KT dirigitur à motu <lb></lb>maioris radio KB, rotatur illa in ſuperficie circuli radio AT, ſed ita <lb></lb>quadratus TV quaſi repat per contactus inadæquatos in ſemicirculo <lb></lb>T 11 10; </s>
					<s id="N25F70">porrò in hoc caſu maxima eſſet difficultas rotæ Ariſtotelicæ; <lb></lb>denique, quando maior dirigitur à minori, quadrans B5 quaſi contra­<lb></lb>hitur in arcu minore BC, quæ contractio explicatur per contractus in­<lb></lb>adæquatos, vt iam ſæpè diximus in aliis motibus. </s>
				</p>
				<p id="N25F7A" type="main">
					<s id="N25F7C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N25F88" type="main">
					<s id="N25F8A"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena rotæ mobilis in ſuperficie concaua <lb></lb>maioris circuli<emph.end type="italics"></emph.end>; dixi maioris circuli; </s>
					<s id="N25F95">quia in ſuperficie concaua mi­<lb></lb>noris, vel æqualis moueri non poteſt, vt conſtat; </s>
					<s id="N25F9B">ſit ergo fig.4. rota <lb></lb>mobilis radio PC; </s>
					<s id="N25FA1">ſit ſuperficies concaua circuli dupli prioris in <lb></lb>peripheria CGK; </s>
					<s id="N25FA7">diuidatur CGK in 8 arcus æquales; haud <lb></lb>dubiè tota ſuperficies rotæ mobilis ſucceſſiuè percurret totam <lb></lb>ſuperficiem concauam CGK, cùm illa ſit huic æqualis, hoc po­<lb></lb>ſito. </s>
				</p>
				<p id="N25FB1" type="main">
					<s id="N25FB3">Primò, punctum C percurret rectam CAK, nec vnquam ab <lb></lb>ea diſcedet, &amp; centrum P percurret ſemicirculum PQN; </s>
					<s id="N25FB9">quippe <pb pagenum="355" xlink:href="026/01/389.jpg"></pb>ſemper æqualem ſeruabit diſtantiam à ſuperficie concaua CGK; </s>
					<s id="N25FC2">ſed illa <lb></lb>eſt PC; </s>
					<s id="N25FC8">igitur ſemper diſtabit æqualiter à centro A; igitur deſcribit ſe­<lb></lb>micirculum PQN. </s>
				</p>
				<p id="N25FCE" type="main">
					<s id="N25FD0">Secundò, quod ſpectat ad primum; </s>
					<s id="N25FD4">certè punctum A rotæ mobilis <lb></lb>tanget ipſum G; </s>
					<s id="N25FDA">eſt enim quadrans CG æqualis ſemicirculo CA, ſed <lb></lb>cum A tanget G, C erit in A; </s>
					<s id="N25FE0">denique C tanget K; </s>
					<s id="N25FE4">igitur C percurret <lb></lb>rectam CAK; </s>
					<s id="N25FEA">porrò facilè oſtendetur punctum C moueri per alia pun­<lb></lb>cta v.g.per punctum T; </s>
					<s id="N25FF0">nam punctum 9.tanget E; </s>
					<s id="N25FF4">igitur TY eſt tangens <lb></lb>igitur AY &amp; YE; </s>
					<s id="N25FFA">igitur ET, TA ſunt æquales, vt conſtat; igitur C duce­<lb></lb>tur per. </s>
					<s id="N26000">T; </s>
					<s id="N26003">præterea C 4. DV ſunt arcus æquales, quia angulus CAD eſt <lb></lb>ſubduplus CP 4. vel YTD, vt conſtat; </s>
					<s id="N26009">igitur arcus DV eſt æqualis C 4. <lb></lb>igitur C ducitur per V: idem oſtendetur pro aliis punctis. </s>
				</p>
				<p id="N2600F" type="main">
					<s id="N26011">Tertiò, hinc poteſt determinari longitudo diſtantiarum CV, VT, &amp;c. </s>
					<s id="N26014"><lb></lb>nam AE eſt chorda arcus 135. id eſt, eſt dupla ſinus grad. 67. 1/2 AT eſt <lb></lb>chorda arcus 90. id eſt latus quadrati inſcripti: denique RA eſt chorda <lb></lb>arcus 45. id eſt dupla ſinus 22. 1/2 hinc vides quàm acuratè recta AC ſe­<lb></lb>cet omnes arcus DV, ET, &amp;c.ita vt ſint æquales aliis arcubus maioris cir­<lb></lb>culi, ſcilicet DC, DV, EC, ET, PR, PC, &amp;c. </s>
				</p>
				<p id="N26023" type="main">
					<s id="N26025">Quartò, hinc vides punctum C initio tardiſſimè moueri, &amp; continuè <lb></lb>ſuum motum accelerare, donec perueniat in A, quem ab A in K retar­<lb></lb>dat in eadem proportione, in qua AC in A accelerat, CV eſt ferè ſubtri­<lb></lb>pla VT, ſcilicet 15224. ad 43354.TR eſt ad CT vt 64886.ad 58578. vt <lb></lb>conſtat ex tabulis ſinuum. </s>
				</p>
				<p id="N26030" type="main">
					<s id="N26032">Quintò, non modò punctum C rotæ mobilis mouetur motu recto, <lb></lb>verùm etiam alia puncta circumferentiæ eiuſdem rotæ; </s>
					<s id="N26038">eſt enim par om­<lb></lb>nium ratio v.g. punctum 2. mouetur per rectam 3.A punctum 4.per re­<lb></lb>ctam DA. punctum 9.per rectam EA; quod certè mirabile videtur, &amp; <lb></lb>primo intuitu vix credi poſſet. </s>
				</p>
				<p id="N26044" type="main">
					<s id="N26046">Sextò, ſi aſſumatur aliud punctum intra rotam deſcribi poterit facilè <lb></lb>linea illius motus; </s>
					<s id="N2604C">ſit v.g. punctum 6. ducantur rectæ TYYTZR; nam <lb></lb>radius PR migrat in TV, YTZRQA, ſumantur TV, YT, Z<foreign lang="grc">δ</foreign>, QX æ­<lb></lb>quales P6.&amp; per ſignata puncta deſcribatur curua 6. T<foreign lang="grc">δ</foreign>X, hæc eſt linea <lb></lb>motus puncti 6. cuius motus initio eſt tardior, ſub finem velocior. </s>
				</p>
				<p id="N26060" type="main">
					<s id="N26062">Septimò, hinc poteſt dirigi motus minoris à motu maioris, &amp; viciſſim, <lb></lb>quod explicandum eſt eodem prorſus modo, quo iam ſæpè explicatum <lb></lb>eſt per diuerſos ſcilicet contactus inadæquatos, pro quo tantùm obſerua, <lb></lb>ſi minor dirigatur à maiore, puncta minoris dextrorſum mouentur <lb></lb>tùm ſiniſtrorum; contra verò ſi maior dirigatur à minore, puncta maio­<lb></lb>ris mouentur ſiniſtrorſum, tùm dextrorſum, quæ omnia ex dictis facilè <lb></lb>intelligi poſſunt, &amp; explicari. </s>
				</p>
				<p id="N26072" type="main">
					<s id="N26074">Octauò, præterea puncta radij RC aſſumpta, quæ propiùs ad extre­<lb></lb>mitatem C accedunt, deſcribunt lineam, quæ propiùs accedit ad rectam; </s>
					<s id="N2607A"><lb></lb>quæ verò accedunt propiùs ad centrum P, deſcribunt lineam magis cur­<lb></lb>uam; </s>
					<s id="N26081">idem de punctis in radio PA; </s>
					<s id="N26085">nam eſt eadem ratio, quæ omnia ex <lb></lb>dictis conſtant; </s>
					<s id="N2608B">an fortè cùm punctum C deſcribat rectam, punctum P <pb pagenum="356" xlink:href="026/01/390.jpg"></pb>circulum, &amp; quæ propiùs accedunt ad C minùs curuam, quæ propiùs <lb></lb>ad P magis curuam; ſed tractatu ſequenti omnes iſtas lineas explica­<lb></lb>bimus. </s>
				</p>
				<p id="N26098" type="main">
					<s id="N2609A">Nonò, ſi ſuperficies ſit minoris circuli quàm dupli; </s>
					<s id="N2609E">certè punctum C, <lb></lb>v.g. non deſcribet rectum CK, ſed aliam curuam ſiniſtrorſum; ſi verò <lb></lb>ſit maioris circuli quàm dupli, deſcribet aliam curuam dextrorſum, quæ <lb></lb>omnia conſtant ex dictis. </s>
				</p>
				<p id="N260AA" type="main">
					<s id="N260AC"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N260B8" type="main">
					<s id="N260BA">Non videntur omittenda aliqua Corollaria Cyclomètrica, quæ ex di­<lb></lb>ctis ſua ſponte naſci videntur; </s>
					<s id="N260C0">nam primò ſemicirculus AQG eſt æqua­<lb></lb>lis triangulo mixto ex arcubus GC, &amp; GA, &amp; recta AC; quia quadrans <lb></lb>AGC eſt æqualis circulo A9.CB, vt patet. </s>
				</p>
				<p id="N260C8" type="main">
					<s id="N260CA">Secundò, omnes radij eodem modo ſecantur à circulo v.g. AC, AD. <lb></lb>AE: ſunt enim CVE <foreign lang="grc">ω</foreign>, D4.æquales, item C 3. T, VE9. &amp;c. </s>
				</p>
				<p id="N260D6" type="main">
					<s id="N260D8">Tertiò, omnes arcus intercepti inter radios ſunt æquales v.g. DY, C 4. <lb></lb>T4. E4. GF, F9.9 <foreign lang="grc">δ. </foreign></s>
					<s id="N260E3">&amp;c. </s>
				</p>
				<p id="N260E6" type="main">
					<s id="N260E8">Quartò, præterea arcus à puncto contactus maioris, &amp; dupli circuli <lb></lb>vſque ad quemlibet radium ſunt æquales, v.g. G9, A &amp; GC, G9. <foreign lang="grc">δ</foreign> GD, <lb></lb>G9. &amp; GE, GF, &amp; GC, tùm FR, &amp; FC, F <foreign lang="grc">β</foreign>, &amp; FD, F <foreign lang="grc">ω</foreign> &amp; FE, tùm ET, <lb></lb>&amp; EC, E 4. &amp; ED; denique DV, DC. </s>
				</p>
				<p id="N26101" type="main">
					<s id="N26103">Quintò, triangula illa mixta ex duplici arcu æquali maioris, &amp; minoris <lb></lb>circuli, &amp; altero latere recto, ſunt æqualia ſectionibus minoribus circuli, <lb></lb>quarum arcus æquales ſunt prioribus minoris circuli, ſic triangulum <lb></lb>mixtum ex arcubus GC, G9. A, &amp; recta AE eſt æquale ſemicirculo G9. <lb></lb>A; </s>
					<s id="N2610F">mixtun verò ex arcubus FC, FR, &amp; recta RC, eſt æquale ſectioni VA <lb></lb>vel E9. A, mixtum ex arcubus ET, EC &amp; recta, æquale eſt ſectioni TA <lb></lb>vel 9. <foreign lang="grc">δ</foreign> A; denique mixtum ex arcu DC, DV, &amp; recta CV eſt æquale <lb></lb>ſectioni RA. </s>
				</p>
				<p id="N2611D" type="main">
					<s id="N2611F">Sextò ſubtracto ex prædictis triangulis alio triangulo mixto per da­<lb></lb>tum radium quemcumque, ſubtrahitur portio æqualis ex ſemicirculo <lb></lb>minore, &amp; reſiduum æquale eſt reſiduo v.g.ex triangulo mixto G9. AC <lb></lb>G ducto radio AF, detrahitur triangulum mixtum GF <foreign lang="grc">ρ</foreign>, ex ſemicir­<lb></lb>culo A9. C, detrahitur portio æqualis 7. A; </s>
					<s id="N2612F">igitur reſiduum ſemicirculi <lb></lb>eſt æquale reſiduo trianguli mixti; </s>
					<s id="N26135">deinde ducto radio AC detrahitur <lb></lb>triangulo mixto prædicto aliud mixtum minus GE9. ex ſemicirculo A <lb></lb>9. C detrahitur portio A9. æqualis detracto; igitur Trapezus reſiduus, E <lb></lb>9. A 7. E, eſt æqualis triangulo mixto CA9. C. idem dico de aliis. </s>
				</p>
				<p id="N2613F" type="main">
					<s id="N26141">Septimò, cùm ſector AFG ſit æqualis quadranti AP9. ſectio ACZ, <lb></lb>eſt maior quadrante prædicto triangulo mixto GCF vel ſectiore 7. A; </s>
					<s id="N26147"><lb></lb>atqui ſectio ACZ habet arcum 135. &amp; A 7. arcum 90. igitur ſectio ar­<lb></lb>cus 135. eſt æqualis quadranti plus ſectione arcus; </s>
					<s id="N2614E">igitur triangulum A <lb></lb>7.4.A eſt æquale quadranti; triangulum verò mixtum GCA eſt æquale <lb></lb>quadranti, minùs prædicta ſectione arcus 90. </s>
				</p>
				<p id="N26156" type="main">
					<s id="N26158">Octauò, hinc triangulum mixtum ex arcubus A 7.9. GG &amp; recta AG <pb pagenum="357" xlink:href="026/01/391.jpg"></pb>eſt æquale quadrato radij AQ; idem dico de mixto ex arcubus AT9. 9. <lb></lb>C, &amp; recta AC; </s>
					<s id="N26167">hinc vtrumque ſimul ſumptum detracta ſcilicet duplici <lb></lb>portione A 7.9. TA eſt æquale quadrato inſcripto, &amp; duplex illa ſectio <lb></lb>figura ouali eſt æqualis triangulo mixto ex tribus arcubus G9. 9. C, C <lb></lb>G; quod facilè geometricè demonſtratur; </s>
					<s id="N26171">ſit enim circulus centro B; </s>
					<s id="N26175"><lb></lb>ſint duæ diametri, GE, AC, quibus in 4. quadrantes diuidatur circulus; </s>
					<s id="N2617A"><lb></lb>tùm aſſumatur arcus GF, æqualis FC, &amp; CD; </s>
					<s id="N2617F"><expan abbr="ducãtur">ducantur</expan> rectæ AD, AF, GF, <lb></lb>IF: </s>
					<s id="N26188">dico triangulum mixtum ex rectis AF, FG, &amp; arcu GA, eſſe æquale <lb></lb>quadranti, quod demonſtro; </s>
					<s id="N2618E">triangula KAL, KFG ſunt æquiangula, quia <lb></lb>anguli K vtrinque ſunt æquales: </s>
					<s id="N26194">ſed DAF, &amp; AFG, ſuſtinent æquales ar­<lb></lb>cus; </s>
					<s id="N2619A">igitur ſunt æquales; </s>
					<s id="N2619E">igitur ſunt proportionalia; igitur vt quadr. </s>
					<s id="N261A2">BA ad <lb></lb>quadr. </s>
					<s id="N261A7">IF: ſed quadr. </s>
					<s id="N261AA">BF eſt duplum quadr. </s>
					<s id="N261AD">IF; </s>
					<s id="N261B0">igitur &amp; BA eſt duplum; </s>
					<s id="N261B4"><lb></lb>igitur KAL duplum KFG; </s>
					<s id="N261B9">igitur BAK æquale; </s>
					<s id="N261BD">igitur tantum additur, <lb></lb>quantum tollitur; igitur prædictum triangulum eſt æquale quadranti. </s>
				</p>
				<p id="N261C3" type="main">
					<s id="N261C5">Nonò præterea, Trapezus FC9. AEF eſt æqualis triangulo mixto ex <lb></lb>arcubus ABC, TAR, &amp; recta RC; </s>
					<s id="N261CB">Trapezus verò E9. TA, CE æqualis <lb></lb>mixto triangulo ex arcubus ABCAT, &amp; recta TC; </s>
					<s id="N261D1">Trapezus verò D<foreign lang="grc">μ</foreign>A <lb></lb>CD eſt æqualis mixto ex arcubus ABC, AV, &amp; recta VC; </s>
					<s id="N261DB">hinc lulu­<lb></lb>la DCBAVD eſt æqualis ſectori ACD; </s>
					<s id="N261E1">igitur quadranti P9. C: </s>
					<s id="N261E5">hinc <lb></lb>altera lulula AT 4. ECBA eſt dupla prioris; </s>
					<s id="N261EB">igitur æqualis ſemicircu­<lb></lb>lo AC, vel ſectori AEC: hinc tota figura ex AC, CE, &amp; recto CA, eſt <lb></lb>æqualis circulo A9. CB. </s>
				</p>
				<p id="N261F4" type="main">
					<s id="N261F6">Decimò, Trapezus E <foreign lang="grc">ω β</foreign> RCE eſt æqualis quadranti P9. C: </s>
					<s id="N261FE">hinc ſi <lb></lb>detrahatur ex prædicto Trapezo triangulum mixtum E 4. TCE, illa <lb></lb>figura E <foreign lang="grc">ω β</foreign> RT 4. E eſt æqualis triangulo rectilineo AP9. ſimiliter <lb></lb>aliæ figuræ T 4. DVT, R <foreign lang="grc">β</foreign> 4. TRA <foreign lang="grc">μ β</foreign> RA, A <foreign lang="grc">μ</foreign> 9. <foreign lang="grc">ρ</foreign> F <foreign lang="grc">ω</foreign> RA; item 9. <lb></lb><foreign lang="grc">ρ</foreign> F <foreign lang="grc">π ρ</foreign>, &amp;c. </s>
				</p>
				<p id="N26229" type="main">
					<s id="N2622B">Vndecimò, ſector ACE diuiditur in duas partes æquales ab arcu R <lb></lb><foreign lang="grc">ω</foreign>; </s>
					<s id="N26234">item ſector ADF ab arcu <foreign lang="grc">μ ρ</foreign>; </s>
					<s id="N2623C">item totus quadrans AGC ab arcu A <lb></lb>9. G; </s>
					<s id="N26242">denique illa figura E <foreign lang="grc">ω</foreign> RTE eſt æqualis Trapezo D <foreign lang="grc">β</foreign> RVD; </s>
					<s id="N2624E">igi­<lb></lb>tur Trapezus æqualis rectilineo A9.P, itemque Trapezus T9.ECT <lb></lb>æqualis quadranti P9. C; </s>
					<s id="N26256">igitur Trapezo E <foreign lang="grc">π</foreign> RCE; </s>
					<s id="N2625E">igitur triangulum <lb></lb>mixtum <foreign lang="grc">β</foreign> 9. <foreign lang="grc">ω β</foreign> æquale mixto T <foreign lang="grc">β</foreign> R; </s>
					<s id="N26270">ſed de his ſatis, quæ tantùm indi­<lb></lb>caſſe ſufficiat; omitto enim infinita alia, de quibus in Cyclometria. </s>
				</p>
				<p id="N26276" type="main">
					<s id="N26278"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26284" type="main">
					<s id="N26286"><emph type="italics"></emph>Si ita moueatur cylindrus per quamcunque lineam, vt eius axis moueatur <lb></lb>motu recto, totuſque cylindrus circa axem motu circulari moueatur, motus <lb></lb>mixtus eſt, cuius diuerſa ſunt phœnomena.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N26291" type="main">
					<s id="N26293">Primò, axis mouetur tantùm motu recto; </s>
					<s id="N26297">aliæ verò partes motu mixto <lb></lb> ſit enim cylindrus CH, cuius axis ſit AB, circa quem moueatur cylin­<lb></lb>drus motu circulari, &amp; qui per <expan abbr="eãdem">eandem</expan> lineam AB indefinitè produ­<lb></lb>ctam mouetur; certè punctum C, v.g. mouetur motu mixto ex motu cen­<lb></lb>tri A, vel axis AB, &amp; motus orbis. </s>
				</p>
				<p id="N262A9" type="main">
					<s id="N262AB">Secundò, punctum C mouetur motu ſpiræ; nam ſi tantùm motu orbis <pb pagenum="358" xlink:href="026/01/392.jpg"></pb>moueretur, decurſo ſemicirculo peruenire in L, F, N, &amp;c. </s>
					<s id="N262B4">igitur ſi eo <lb></lb>tempore, quo C decurrit motu centri, ſemicirculum CD; </s>
					<s id="N262BA">punctum axis <lb></lb>A decurrit AK; </s>
					<s id="N262C0">haud dubiè punctum C erit in E, tùm in F, tùm in G, tùm <lb></lb>in T; ſed hic motus ſpiralis eſt, vt conſtat. </s>
				</p>
				<p id="N262C6" type="main">
					<s id="N262C8">Tertiò, omnia puncta peripheriæ CD mouentur æquali motu; quia <lb></lb>ſcilicet æqualem motum centri, &amp; orbis participant. </s>
				</p>
				<p id="N262CE" type="main">
					<s id="N262D0">Quartò, ſi motus centri vel axis ſit minor, frequentiores ſunt Helices <lb></lb>v.g. ſi eo tempore, quo C decurrit ſemicirculum CD, A decurreret tan­<lb></lb>tùm AR, C perueniret tantùm in Q, mox in I, atque ita deinceps moue­<lb></lb>retur per frequentiores ſpiras; ſi verò motus axis ſit maior, ſpiræ erunt <lb></lb>rariores, vt patet, v.g. ſi eo tempore, quo C motu centri decurrit ſemi­<lb></lb>circulum CD, punctum A decurrit AL, punctum C decurret ſpiram C <lb></lb>M, mox MT, &amp;c. </s>
				</p>
				<p id="N262E4" type="main">
					<s id="N262E6">Quintò, areæ circuli CAD mouebuntur motu ſpirali, excepto centro <lb></lb>A, minores tamen ſpiras conficeret, ſcilicet circa cylindrum cuius minor <lb></lb>eſt baſis, vt patet; </s>
					<s id="N262EE">vnde minore motu mouentur, quàm C vel D; </s>
					<s id="N262F2">igitur <lb></lb>axis AB tardiſſimo motu mouentur; </s>
					<s id="N262F8">partes verò ſuperficiei cylindri <lb></lb>velociſſimè; aliarum verò partium, quæ accedunt propiùs ad periphæ­<lb></lb>riam, velociùs. </s>
					<s id="N26300">quæ propiùs ad centrum, tardiùs: </s>
					<s id="N26304">hoc motu mouentur alæ <lb></lb>auium; </s>
					<s id="N2630A">quæ directo volatu tendunt per lineam rectam, vt grues; nam <lb></lb>quælibet pars alæ motum axis habet, &amp; orbis. </s>
				</p>
				<p id="N26310" type="main">
					<s id="N26312"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2631E" type="main">
					<s id="N26320"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena calami volatilis<emph.end type="italics"></emph.end> ſit enim calamus <lb></lb>ſeu cylindrus DA, in altera extremitate D ita excauatus, vt duæ pennæ <lb></lb>BD, CE inſeri poſſint eo ferè modo, quo vides. </s>
				</p>
				<p id="N2632C" type="main">
					<s id="N2632E">Primò, mouetur axis FA motu recto; reliquæ verò partes motu mix­<lb></lb>to ex recto axis, &amp; circulari orbis eo modo, quo diximus de cylindro <lb></lb>in ſuperiore Theoremate. </s>
				</p>
				<p id="N26337" type="main">
					<s id="N26339">Secundò, ſemper calamus DA præit, ſcilicet ipſa baſis A, &amp; ſequun­<lb></lb>tur pennæ; </s>
					<s id="N2633F">ratio eſt, quia pennîs reſiſtit fortiùs aër, vt pater; </s>
					<s id="N26343">igitur earum <lb></lb>vim faciliùs ſuperat; </s>
					<s id="N26349">hinc ſemper retinentur à tergo, nec alia ratio eſſe <lb></lb>poteſt; </s>
					<s id="N2634F">præſertim cùm pennæ ita ſint compoſitæ propter diuaricationem, <lb></lb>vt multum aëra verberent; </s>
					<s id="N26355">quod autem pennis maximè reſiſtat aër, patet <lb></lb>ex auium volatu; </s>
					<s id="N2635B">imò ex ipſo plumarum deſcenſu; </s>
					<s id="N2635F">hinc pennæ illæ, qui­<lb></lb>bus ornantur equitum pilei, ſemper à tergo ſequuntur currentem equi­<lb></lb>tem; </s>
					<s id="N26367">idem dico de faſciis illis tranſuerſariis, quibus iunguntur equites; <lb></lb>idem de militaribus ſignis, ſeu vexillis. </s>
				</p>
				<p id="N2636F" type="main">
					<s id="N26371">Tertiò, hinc ratio motus recti calami, quia, cùm ſemper præeat, <lb></lb><expan abbr="eũdem">eundem</expan> ſitum ſeruat, pennaſque ipſas quaſi reluctantes trahit, ſuntque <lb></lb>ipſæ ad inſtar claui, qui puppim regit. </s>
				</p>
				<p id="N2637B" type="main">
					<s id="N2637D">Quartò, cum plumæ ita deuaricatæ quaſi à reflante aëra pellantur ſe­<lb></lb>quitur neceſſario motus orbis circa axem calami DA; </s>
					<s id="N26383">quippe hîc motus <lb></lb>facilis eſt; </s>
					<s id="N26389">ſic enim voluitur vectis ſeu cylindrus, quotieſcumque ab altera <pb pagenum="359" xlink:href="026/01/393.jpg"></pb>tremitate pellitur; </s>
					<s id="N26392">igitur cum pellantur D &amp; C; quid mirum ſi totus ca­<lb></lb>lamus cum ipſis pennis conuertatur. </s>
				</p>
				<p id="N26398" type="main">
					<s id="N2639A">Quintò, hinc motus calami eſt mixtus ex recto axis, &amp; circulari or­<lb></lb>bis; </s>
					<s id="N263A0">igitur ſpiralis eſt; </s>
					<s id="N263A4">ſpiræ autem maiores ſunt, vel minores pro diuerſa <lb></lb>diſtantia partium ab axe AF, qui debet cenſeri productus vſque ad G; </s>
					<s id="N263AA"><lb></lb>nam partes, quæ longiùs diſtant ab axe, maiores ſpiras decurrunt; aliæ <lb></lb>verò minores; porrò ſpiræ ipſæ eò frequentiores ſunt, quò motus orbis <lb></lb>velocior eſt, &amp; contrà rariores, quò tardior. </s>
				</p>
				<p id="N263B3" type="main">
					<s id="N263B5">Sextò, ſi ſit tantùm vnica penna, calamus non mouetur hoc motu; </s>
					<s id="N263B9"><lb></lb>quia vix aër verberatur; </s>
					<s id="N263BE">adde quod in eam partem, quæ caret penna im­<lb></lb>pulſus neceſſariò inclinatur; idem accidit cum altera penna fracta eſt, <lb></lb>vel minus aptè diuaricata. </s>
				</p>
				<p id="N263C6" type="main">
					<s id="N263C8">Septimò, in cam partem conuertitur, ſeu ſpiras agit, in quam pennæ <lb></lb>ipſæ detorquentur; </s>
					<s id="N263CE">alioquin non eſſet, cur potiùs in vnam, quàm in aliam <lb></lb>ſuos agerent orbes; </s>
					<s id="N263D4">igitur ita diuaricantur pennæ, vt earum plana ſibi in­<lb></lb>uicem ſint obliqua; </s>
					<s id="N263DA">cuius rei ratio prædicta clariſſima cùm ſit; non eſt <lb></lb>quod amplius de hac re laboremus. </s>
				</p>
				<p id="N263E0" type="main">
					<s id="N263E2">Octauò, ſi pennæ diſtractiones ſunt, &amp; maximè diuaricatæ; </s>
					<s id="N263E6">motus <lb></lb>axis eſt tardior; ratio eſt, quia in eo ſtatu multum aëra pellunt, ſeu venti­<lb></lb>lant, à quo retinentur. </s>
				</p>
				<p id="N263EE" type="main">
					<s id="N263F0">Nonò, ſi diſtractiores ſunt, motus orbis eſt etiam tardior, ſuntque <lb></lb>rariores ſpiræ; </s>
					<s id="N263F6">ratio eſt eadem, quia cùm motus orbis eſt maior, etiam <lb></lb>plùs aëris vertigo illa ſecum abripit; </s>
					<s id="N263FC">hinc maior eſt reſiſtentia; vnde <lb></lb>obſeruabis, vt motus orbis minùs impediatur, ita pennas eſſe componen­<lb></lb>das, vt aëra ſua quaſi acie cæſim diuidant, ne ſi pellant tota ſua ſuperficie, <lb></lb>maior ſit reſiſtentia. </s>
				</p>
				<p id="N26406" type="main">
					<s id="N26408">Decimò, ſi demum plùs æquo ſint diuaricatæ, ita vt angulum obtuſiſ­<lb></lb>ſimum faciant, ceſſat omninò motus orbis propter maiorem reſiſtentiam, <lb></lb>quæ vertiginem illam impedit. </s>
				</p>
				<p id="N2640F" type="main">
					<s id="N26411">Vndecimò, ita pennæ aptari debent, vt ſenſim inflexæ à radice DE <lb></lb>verſus apices BC afflatum aëris diuerſum excipiant, &amp; diſſimilem: vnde <lb></lb>accidit, vt partes ipſæ, quæ retardantur, &amp; maiore vi pollent in vertigi­<lb></lb>nem agantur, in eam ſcilicet partem, in quam aliqua inclinatio conducit <lb></lb>ſic globus retentus à corpore oppoſito in orbem agitur propter rationem <lb></lb>prædictam, ne ille impetus ſit fruſtrà, qui adhuc ſupereſt. </s>
					<s id="N2641F">Hinc vides <lb></lb>motum orbis non imprimi calamo à pennis, ſed pennis à calamo; </s>
					<s id="N26425">qui <lb></lb>cùm ab illis retardetur, ne aliquid impetus ſit fruſtrà, ſupplet motu cir­<lb></lb>culari, quod recto difficiliori propter reſiſtentiam orbis conſequi non <lb></lb>poteſt; </s>
					<s id="N2642F">determinatur quidem motus circularis in talem partem ab ipſa <lb></lb>pennarum deflexione; </s>
					<s id="N26435">non tamen imprimitur: </s>
					<s id="N26439">hinc ſi fortè in via pen­<lb></lb>næ ex ſua theca decidant, calamus ipſe ſine nouo impulſu longiùs ſpa­<lb></lb>tium conficito; tribuit enim motui recto non impedito, quod circulari, <lb></lb>vel ſpirali, ſi pennæ adeſſent tribueret. </s>
				</p>
				<p id="N26443" type="main">
					<s id="N26445">Duodecimò, ſi pennæ contractiores ſunt, &amp; angulum acutiorem fa­<lb></lb>ciant, calamus velociùs mouetur motu axis; </s>
					<s id="N2644B">ratio eſt, quia reſiſtentia mi-<pb pagenum="360" xlink:href="026/01/394.jpg"></pb>nùs retardat; </s>
					<s id="N26454">ſunt enim pauciores partes, quæ valde obliquè cadunt: </s>
					<s id="N26458"><lb></lb>hinc minor eſt appulſus, quod clarum eſt; hinc, vt calamus velociùs per­<lb></lb>gat, conſtringuntur pennæ. </s>
				</p>
				<p id="N2645F" type="main">
					<s id="N26461">Decimotertiò, ſi contractiores ſunt, &amp; rectè compoſitæ, cum illa ſcili­<lb></lb>cet inflexione, <expan abbr="eoq;">eoque</expan> ſitu, de quo n.11.non modò velocior erit motus axis, <lb></lb>ſed etiam motus orbis; </s>
					<s id="N2646D">ratio eſt, quia minor orbis citiùs perficitur: </s>
					<s id="N26471">adde <lb></lb>quod minus aëris huic motui reſiſtit; </s>
					<s id="N26477">vnde vides ita eſſe aptandas pen­<lb></lb>nas, vt reſiſtentia aëris inæqualis cauſet illam vertiginem, quæ tamen <lb></lb>tanta eſſe non debet; alioquin ipſum motum orbis omninò impediret, <lb></lb>vt diximus n. </s>
					<s id="N26481">10. </s>
				</p>
				<p id="N26484" type="main">
					<s id="N26486">Decimoquartò, denique ſi plùs æquo contractæ ſunt, eſſet motus or­<lb></lb>bis; quippe modica eſt aëris reſiſtentia, quæ ad motum illum non ſufficit, <lb></lb>licèt ſemper ſint aliqui gyri, ſed rariores. </s>
				</p>
				<p id="N2648E" type="main">
					<s id="N26490">Decimoquintò, tres aliquando, aliquando duæ inſeruntur pennæ; </s>
					<s id="N26494">eſt <lb></lb>enim eadem vertiginis cauſa, imò quatuor inſeri poſſent; ſunt enim quaſi <lb></lb>totidem claui, qui dirigunt illum motum. </s>
				</p>
				<p id="N2649C" type="main">
					<s id="N2649E">Decimoſextò, ſi pennæ delicatioribus pilis tenera lanugine veſtian­<lb></lb>tur, tardiùs mouetur calamus vtroque motu; quia vix aëra penetrare poſ­<lb></lb>ſunt delicatiores mollioreſque pili. </s>
				</p>
				<p id="N264A6" type="main">
					<s id="N264A8">Decimoſeptimò, ſi proiicitur ſurſum, deſcendatque deorſum rectà, eſt <lb></lb>motus mixtus ex recto &amp; circulari; </s>
					<s id="N264AE">ſi verò proiiciatur per horizontalem, <lb></lb>vel inclinatam, eſt motus mixtus ex duobus rectis &amp; circulari, vt con­<lb></lb>ſtat; </s>
					<s id="N264B6">ex quo motu fit linea mixta ex Parabola &amp; Helice; </s>
					<s id="N264BA">ſit enim cylin­<lb></lb>drus CH, cuius motus ſpiralis ſit CEFGT mixtus ex recto CT, &amp; cir­<lb></lb>culari orbis CD; ſit etiam mixtus LTQ ex accelerato LM, &amp; æquabili <lb></lb>MQ certè ſi addatur LQ circulus ſeu ſpira CEF, &amp;c. </s>
					<s id="N264C7">ſitque RC æqua­<lb></lb>lis IE, &amp; VT æqualis NG, habebitur ſpira mixta LCSVQ </s>
				</p>
				<p id="N264D0" type="main">
					<s id="N264D2">Decimooctauò, ſi pennæ latiores ſunt, ſeu maiorem habent ſuperfi­<lb></lb>ciem, minùs aptæ ſunt ad vtrumque motum, ſcilicet axis, &amp; centri; quia <lb></lb>aër plùs æquo reſiſtit, nam plures illius pelluntur partes. </s>
				</p>
				<p id="N264DA" type="main">
					<s id="N264DC">Decimononò, ſi verò contractiores ſunt, etiam minùs aptæ videntur: <lb></lb>quippe aëra facilè diuidunt. </s>
				</p>
				<p id="N264E2" type="main">
					<s id="N264E4">Vigeſimò, ſi breuiores, certiſſimus eſt motus orbis; quia minor circu­<lb></lb>lus citiùs perficitur. </s>
				</p>
				<p id="N264EA" type="main">
					<s id="N264EC">Vigeſimoprimò, ſi longiores, è contrario: adde quod ab axis leuioris <lb></lb>motu, dirigi vix poſſunt. </s>
				</p>
				<p id="N264F2" type="main">
					<s id="N264F4">Vigeſimoſecundò, ſi altera pennarum ſit fracta, eſſet motus orbis; quia <lb></lb>ſegmentum fractum aliarum partium motum non ſequitur, vt patet. </s>
				</p>
				<p id="N264FA" type="main">
					<s id="N264FC">Vigeſimotertiò, ſi calamus ſit leuior, ineptus eſt; </s>
					<s id="N26500">quia reſiſtentiam <lb></lb>pennarum non ſuperat; quippe contra reflantis aëris vim, calami præua­<lb></lb>lens impetus leuiores pennas ſecum abripere debet. </s>
				</p>
				<p id="N26508" type="main">
					<s id="N2650A">Vigeſimoquartò, ſi longior ſit calamus, minùs aptus eſt; quia ſcilicet <lb></lb>plures partes impetus quæ inſunt grauiori calamo nullo negotio reſi­<lb></lb>ſtentiam aëris, &amp; retardationem pennarum ſuperant. </s>
				</p>
				<p id="N26512" type="main">
					<s id="N26514">Vigeſimoquintò, ſi longior ſit calamus, minùs aptus eſt; </s>
					<s id="N26518">tùm quia gra-<pb pagenum="361" xlink:href="026/01/395.jpg"></pb>uior eſt, tùm quia difficiliùs conuertitur, vt ſemper præeat; eſt enim ma­<lb></lb>ior reſiſtentia ad conuertendum longius corpus, vt patet. </s>
				</p>
				<p id="N26523" type="main">
					<s id="N26525">Vigeſimoſextò, ſi breuior &amp; leuior, ineptus eſt propter rationem alla­<lb></lb>tam; </s>
					<s id="N2652B">nam ſi breuiſſimus ſit, eius tamen grauitatis, quæ ſufficiat ad ſupe­<lb></lb>randam aëris vim, aptiſſimus cenſeri debet: hinc aliquando globulus per­<lb></lb>foratus calami vicem gerit. </s>
				</p>
				<p id="N26533" type="main">
					<s id="N26535">Vigeſimoſeptimò, extremitas calami, quæ præit, debet eſſe paulò maior, <lb></lb>&amp; quaſi nodo armata, vt ſcilicet faciliùs præire poſſit, ne alia extremitas <lb></lb>quaſi reluctetur; igitur ad inſtar clauæ calamus componi debet. </s>
				</p>
				<p id="N2653D" type="main">
					<s id="N2653F">Vigeſimooctauò, in vacuo nulla prorſus eſſet vertigo huius volatilis <lb></lb>calami; </s>
					<s id="N26545">quia nulla eſſet aëris reſiſtentia; ſed de his ſatis. </s>
				</p>
				<p id="N26549" type="main">
					<s id="N2654B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26557" type="main">
					<s id="N26559"><emph type="italics"></emph>Cuncta phœnomena teli ſeu iaculi volatilis explicari poſſunt<emph.end type="italics"></emph.end>: </s>
					<s id="N26562">huius teli <lb></lb>figuram habes rudiore manu adumbratam; hîc habes. </s>
					<s id="N26568">cuſpis eſt C, du­<lb></lb>plex clauus ſeu quadruplex BGDABE, ex aliqua leuiore materia <lb></lb>conſtans v.g. ex charta duplicata, vel pennis, hoc poſito. </s>
				</p>
				<p id="N26571" type="main">
					<s id="N26573">Primò, cuſpis C poſt eiaculationem ſemper præit; </s>
					<s id="N26577">ratio eſt, quia <lb></lb>alæ illæ leuiores à tergo ſequuntur; minùs enim aëris vim frangere <lb></lb>queunt. </s>
				</p>
				<p id="N2657F" type="main">
					<s id="N26581">Secundò, in eo ſtatu ſemper remanet iaculum; </s>
					<s id="N26585">quia non poteſt ſurſum <lb></lb>attolli extremitas B, nec deorſum deprimi; </s>
					<s id="N2658B">quia ala ABE impedit; </s>
					<s id="N2658F">nec <lb></lb>etiam dextrorſum, vel ſiniſtrorſum inclinari; </s>
					<s id="N26595">quia ala BGD prohibet; </s>
					<s id="N26599"><lb></lb>igitur ſi nec ſurſum, neque deorſum, nec ſiniſtrorſum, nec extrorſum <lb></lb>inclinari poteſt; haud dubiè in eodem ſitu remanebit. </s>
				</p>
				<p id="N265A0" type="main">
					<s id="N265A2">Tertiò, citiſſimo motu fertur hoc iaculi genus; </s>
					<s id="N265A6">quia nihil prohibet; </s>
					<s id="N265AA"><lb></lb>quippe aër facilè diuiditur ab ipſo iaculo CB; </s>
					<s id="N265AF">tùm deinde ab ipſis alis <lb></lb>cæſim quaſi ſecatur acie dumtaxat, nunquam ſuperficie oppoſita; adde <lb></lb>quod, aër facilè fluit per 4. illas cauitates BGFE, DGFA, &amp;c. </s>
					<s id="N265B7">ſemper <lb></lb>enim aëri opponitur acies anguli; ſed hæc ſunt facilia. </s>
				</p>
				<p id="N265BD" type="main">
					<s id="N265BF">Quartò, non agitur in vertiginem hoc iaculum; </s>
					<s id="N265C3">quia ſcilicet non eſt <lb></lb>tanta aëris reſiſtentia, quantam eſſe oportet; </s>
					<s id="N265C9">adde quod nulla eſt alarum <lb></lb>inflexio, quæ faciat inæqualem reſiſtentiam, vt in calamo volatili; </s>
					<s id="N265CF">igitur <lb></lb>eſt tantùm motus axis; vbi tamen vibratur per horizontalem, vel incli­<lb></lb>natam, mouetur motu mixto ex duobus rectis, de quo iam aliàs. </s>
				</p>
				<p id="N265D7" type="main">
					<s id="N265D9">Quintò, huc reuoca ſagittas, quæ tribus inſtructæ pennis <expan abbr="eũdem">eundem</expan> <lb></lb>ſemper retinent ſitum in motu, vt ferrum ſeu mucro præeat; vnde vides <lb></lb>eumdem ſemper ſequi effectum, ſiue tres ſint alæ, ſiue quatuor. </s>
				</p>
				<p id="N265E5" type="main">
					<s id="N265E7">Sextò, huc reuoca minima illa ſpicula ſpicâ inſtructa, quæ per tubum <lb></lb>pneumaticum pueri flatu eiaculantur; </s>
					<s id="N265ED">nam cuſpis ſemper præit, quia <lb></lb>motus alterius extremitatis leuiore ſpica retardatur; ſed hæc ſunt fa­<lb></lb>cilia. </s>
				</p>
				<p id="N265F5" type="main">
					<s id="N265F7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26603" type="main">
					<s id="N26605"><emph type="italics"></emph>Explicatur etiam motus illius, quaſi velaris moletrinæ, qua pueri curren­<lb></lb>tes ſæpiſſimè ludum<emph.end type="italics"></emph.end>; cuius figuram hîc habes; nam eo tempore, <pb pagenum="362" xlink:href="026/01/396.jpg"></pb>quo DA fertur per ipſum D, BC cum ſuis velus vertitur circa DA. </s>
				</p>
				<p id="N26616" type="main">
					<s id="N26618">Primò, hinc eſt motus mixtus, &amp; recto axis DA &amp; circulari CB. </s>
				</p>
				<p id="N2661C" type="main">
					<s id="N2661E">Secundò, hinc eſt motus perfectè ſpiralis, nec enim differt à motu cy­<lb></lb>lindri; de quo ſuprà. </s>
				</p>
				<p id="N26624" type="main">
					<s id="N26626">Tertiò, ſpiræ ſunt frequentiores, quò motus eſt velocior motu centri <lb></lb>A, maiores è contrario. </s>
				</p>
				<p id="N2662B" type="main">
					<s id="N2662D">Quartò, debet conſtare debet CB ex leuiſſima materia; alioquin non <lb></lb>mouebitur motu orbis. </s>
				</p>
				<p id="N26633" type="main">
					<s id="N26635">Quintò, debet facilè poſſe moueri circa A; alioquin vis illa reflantis <lb></lb>aëris, quæ CB motum circularem imprimit, non ſufficeret. </s>
				</p>
				<p id="N2663B" type="main">
					<s id="N2663D">Sextò, ideo BC mouetur circa A; </s>
					<s id="N26641">quia cum vela C &amp; B polleant mul­<lb></lb>tum aëra, maior eſt reſiſtentia; </s>
					<s id="N26647">hinc propter modicam inclinationem <lb></lb>axis DA aër in ſuperficies C &amp; B obliquè incidens illas impellit; ſed <lb></lb>quia axis BA reſiſtit neceſſariò circa A, motu circulari cientur. </s>
				</p>
				<p id="N2664F" type="main">
					<s id="N26651"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2665D" type="main">
					<s id="N2665F"><emph type="italics"></emph>Explicari poſſunt omnes motus ponderis, ſeu plumei à tergo valuarum fu­<lb></lb>nependuli, cuius vi valuæ ipſa claudantur,<emph.end type="italics"></emph.end> v.g.ſit fores AE quarum va­<lb></lb>rum eſt AF; ſit funis CDG, cuius extremitas immobiliter affixa ſit C, <lb></lb>pondus appenſum ſit G, cuius vi ſeu motu fores ipſæ clauduntur. </s>
				</p>
				<p id="N2666E" type="main">
					<s id="N26670">Primò, certum eſt pondus G non moueri motu recto; quia cum ip­<lb></lb>ſo rectangulo AE mouetur circa axem immobilem AB. </s>
				</p>
				<p id="N26677" type="main">
					<s id="N26679">Secundò, certum eſt non moueri motu purè circulari, qui mouetur <lb></lb>per lineam GD. </s>
				</p>
				<p id="N2667E" type="main">
					<s id="N26680">Tertiò, certum eſt rectangulum A moueri motu purè circulari, vt pa­<lb></lb>tet; ita vt DE ſuo motu deſcribat cylindrum, cuius radius ſeu ſemidia­<lb></lb>meter baſis eſt BE. </s>
				</p>
				<p id="N26689" type="main">
					<s id="N2668B">Quartò, certum eſt, quodlibet punctum huius rectanguli deſ­<lb></lb>cribere circulum, maiorem ſcilicet vel minorem pro diuerſa diſtan­<lb></lb>tia ab axe AB, v. g. punctum D deſcribit circulum, cuius radius <lb></lb>eſt DA, punctum verò I deſcribit circulum, cuius radius eſt HI. </s>
				</p>
				<p id="N26699" type="main">
					<s id="N2669B">Quintò, certum eſt pondus G moueri motu mixto ex circulari forium. <lb></lb></s>
					<s id="N2669F">&amp; recto deorſum. </s>
				</p>
				<p id="N266A2" type="main">
					<s id="N266A4">Sextò, habes ſchema huius motus in cylindro A quem deſcribunt <lb></lb>fores ſuo motu, ſi enim A moueatur per ſemicirculum AB, &amp; rectam A <lb></lb>C; </s>
					<s id="N266AC">haud dubiè mouebitur per AD; igitur hic motus eſt ſpiralis, nec eſt <lb></lb>alia difficultas. </s>
				</p>
				<p id="N266B2" type="main">
					<s id="N266B4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N266C0" type="main">
					<s id="N266C2"><emph type="italics"></emph>Quando voluitur funis circa cylindrum, vel axem, mouetur motu <lb></lb>ſpirali, ſed diuerſo à prioribus<emph.end type="italics"></emph.end>; </s>
					<s id="N266CF">ſunt enim veræ ſpiræ ad inſtar ſapien­<lb></lb>tia in diuerſa volumina contorti; </s>
					<s id="N266D5">ſic funis circa digitum ſæpè <lb></lb>rotatur.; </s>
					<s id="N266DB">eſt enim motus mixtus ex diuerſis circularibus: </s>
					<s id="N266E1">quippè <pb pagenum="363" xlink:href="026/01/397.jpg"></pb>in ſingulis punctis eſt diuerſa determinatio ad nouum circulum, quia <lb></lb>eſt nouus radius, quia continuò radius huius vertiginis imminuitur; <lb></lb>porrò duobus modis poteſt funis circa axem vel cylindrum conuolui. </s>
					<s id="N266EE"><lb></lb>Primò, ſi ſemper circa <expan abbr="eũdem">eundem</expan> cylindri circulum voluatur; </s>
					<s id="N266F7">tunc autem <lb></lb>facit veras ſpiras, vt vides in A. Secundò, ſi circa diuerſos eiuſdem axis <lb></lb>circulos, vel potius diuerſa eiuſdem axis puncta voluatur, &amp; hic eſt mo­<lb></lb>tus ſpiralis conicus, vt vides in cono FDE; </s>
					<s id="N26701">idem eſſet motus ſi conus <lb></lb>circa axem volueretur ſimulque aliquod punctum peripheriæ baſis coni <lb></lb>rectà ab ipſa peripheria ad verticem coni tenderet; </s>
					<s id="N26709">ſi enim totus conus <lb></lb>moueatur motu axis recto, quodlibet punctum ſuperficiei coni mouetur <lb></lb>motu ſpirali cylindrico, excepto dumtaxat ipſo vertice; hoc denique <lb></lb>motu mouerentur ſingula puncta baculi ED, qui in conum rotaretur à <lb></lb>vertice E eo tempore, quo rotans ipſe per rectam EG moueretur. </s>
				</p>
				<p id="N26715" type="main">
					<s id="N26717"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26723" type="main">
					<s id="N26725"><emph type="italics"></emph>Similiter poſſunt explicari motus ſpirales ſphærici, quos habes in<emph.end type="italics"></emph.end>; </s>
					<s id="N2672E">hic au­<lb></lb>tem motus duplex eſt; </s>
					<s id="N26734">primus mixtus ex recto per axem KL, quo totus <lb></lb>globus mouetur, &amp; ex circulari circa axem KL, qui reuerâ eſt ſpiralis <lb></lb>cylindricus; </s>
					<s id="N2673C">ſecundus mixtus ex duobus circularibus, ſcilicet ex circulari <lb></lb>circa axem KL, &amp; circulari per arcum IL, v.g. ſi punctum eo tempore <lb></lb>voluatur circa axem KL per arcum IO, quo fertur per arcum IL vnde <lb></lb>habes in hac figura tres motus ſpirales, quorum ſinguli conſtant ex circu­<lb></lb>lari circa axem KL; </s>
					<s id="N2674A">ſed deinde conſtant ſinguli ex ſingulis motibus di­<lb></lb>uerſis, ſcilicet ſpiralis cylindricus ex motu puncti I v.g. per rectam IN <lb></lb>parallelam KL; </s>
					<s id="N26754">ſpiralis conicus per rectam IL, &amp; ſpiralis ſphæricus <lb></lb>per arcum IPL; </s>
					<s id="N2675A">hinc duo primi conſtant ex circulari, &amp; recto; certius <lb></lb>verò ex duobus circularibus. </s>
				</p>
				<p id="N26760" type="main">
					<s id="N26762">Denique poteſt eſſe ſpiralis concoidicus qualem vides in iſque du­<lb></lb>plex; </s>
					<s id="N26768">primò ſi vertatur conois circa axem SV; </s>
					<s id="N2676C">ſecundò, ſi vertatur circa <lb></lb>axem XZ: </s>
					<s id="N26772">quippe hoc modo ſpiræ erunt maiores; </s>
					<s id="N26776">ſunt quoque ſinguli <lb></lb>triplicis generis; </s>
					<s id="N2677C">eſt enim vel parabolicus, vel ellipticus, vel hyperboli­<lb></lb>cus; porrò, qui dicunt motus cœleſtes eſſe ſpirales, viderint an ſint cy­<lb></lb>lindrici vel ſphærici, vel conici, vel elliptici &amp;c. </s>
					<s id="N26784">omitto ſpiralem in pla­<lb></lb>no, mixtum ſcilicet ex circulari &amp; recto, cuius ſchema habes Th.24. tùm <lb></lb>L 5. Th.79. de quo etiam aliàs, cum de lineis motus. </s>
				</p>
				<p id="N2678B" type="main">
					<s id="N2678D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26799" type="main">
					<s id="N2679B"><emph type="italics"></emph>Cum taleola ſupra planum rectilineum ita repit, vt etiam circa proprium̨ <lb></lb>centrum voluatur, est motus mixtus ex recto &amp; circulari<emph.end type="italics"></emph.end>; </s>
					<s id="N267A6">neque hic motus <lb></lb>diuerſus eſt à motu rotæ in plano, ſit enim taleola centro A, circa quod <lb></lb>vertitur dum centrum A repit motu recto per rectam AD, perinde ſe <lb></lb>habet, atque ſi rota in plano BE vel CF rotaretur; </s>
					<s id="N267B0">immò poteſt tabella <lb></lb>GK ita moueri, vt eius centrum A moueatur per AD, dum reliquæ par­<lb></lb>tes circa centrum A voluuntur; </s>
					<s id="N267B8">tunc enim punctum H eodem motu <lb></lb>moueretur, quo alia puncta peripheriæ huius rotæ; </s>
					<s id="N267BE">punctum verò I eo <lb></lb>modo quo I in radio BA, dum rota mouetur, quod ſuprà fusè explicui-<pb pagenum="364" xlink:href="026/01/398.jpg"></pb>mus; denique ita moueri poteſt taleola, vt primò B moueatur motu or­<lb></lb>bis verſus. </s>
					<s id="N267CB">Secundò, verſus K; Tertiò, vt motus centri ſit maior vel minor <lb></lb>motu orbis. </s>
					<s id="N267D0">Quartò, vt ſit æqualis. </s>
				</p>
				<p id="N267D3" type="main">
					<s id="N267D5">Denique, ne omittam motum illum, quo clauis ſeu planum ſolidum <lb></lb>in læuigata menſa mouetur, dico mixtum eſſe ex recto alicuius centri &amp; <lb></lb>circularis orbis; </s>
					<s id="N267DD">ſit enim v.g.baculus AD, qui ita repat in plano læui­<lb></lb>gato vt altera eius extremitas fortiùs impellatur, mouebitur motu mixto <lb></lb>ex circulari circa centrum C per Th.55.l.7. &amp; recto orbis circa C; </s>
					<s id="N267E5">de­<lb></lb>ſcribent autem duæ extremitates A &amp; D lineas rotatiles diuerſas; hic au­<lb></lb>tem motus diuerſus erit pro diuerſa coniugatione motus orbis, &amp; mo­<lb></lb>tus centri, cùm hic poſſit eſſe vel maior, vel minor motu orbis, vel <lb></lb>æqualis, </s>
				</p>
				<p id="N267F1" type="main">
					<s id="N267F3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N267FF" type="main">
					<s id="N26801"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena motus globi.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N26808" type="main">
					<s id="N2680A">Primò, ita globus rotatur aliquando in plano, vt motus orbis deſcri­<lb></lb>bat circulos perpendiculariter incubantes plano; </s>
					<s id="N26810">ſic vulgò proijcitur <lb></lb>globus, nec differt hic motus à motu rotæ in plano; eſt enim mixtus ex <lb></lb>recto centri &amp; circulari orbis. </s>
				</p>
				<p id="N26818" type="main">
					<s id="N2681A">Secundò, ita rotatur aliquandò, vt ſit ſemper idem punctum contactus, <lb></lb>&amp; motus orbis deſcribat circulos parallelos plano in quo rotatur; non <lb></lb>differt etiam hic motus à motu rotæ, quæ in plano verticali rotaretur. </s>
				</p>
				<p id="N26822" type="main">
					<s id="N26824">Tertiò, ita rotatur, vt motus orbis deſcribat circulos inclinatos plùs, <lb></lb>vel minùs; </s>
					<s id="N2682A">non differt autem hic motus à motu rotæ, quæ in plano in­<lb></lb>clinato rotaretur; mutatur autem continue punctum contactus in 1°. <lb></lb></s>
					<s id="N26831">&amp; 3°. </s>
					<s id="N26834">motu. </s>
				</p>
				<p id="N26837" type="main">
					<s id="N26839">Porrò, ſæpiùs obſeruabis iſtos motus globi in aqua, in qua ſcilicet fa­<lb></lb>cilè circa centrum voluitur per quodcunque planum. </s>
				</p>
				<p id="N2683E" type="main">
					<s id="N26840">Quartò, ita mouetur vt conſtet hic motus ex duobus quaſi circulari­<lb></lb>bus, &amp; ex recto; </s>
					<s id="N26846">quando ſcilicet inflectitur ita motus centri, vt mouea­<lb></lb>tur centrum per lineam curuam; </s>
					<s id="N2684C">dixi curuam; non verò circularem; </s>
					<s id="N26850"><lb></lb>quia non habet centrum motus purè circularem, ſed mixtum ex <lb></lb>recto &amp; circulari; </s>
					<s id="N26857">exemplum habes clariſſimum in illo deflexu <lb></lb>globi, qui valdè familiaris eſt iis, qui trunculorum ludum exercent; <lb></lb>quippe tantillùm detorquetur circa horizontalem, ex qua declinatione <lb></lb>ſequitur motus mixtus ex tribus, ſcilicet ex motu orbis in circulo hori­<lb></lb>zontali, ex motu orbis in verticali, &amp; motu centri recto. </s>
				</p>
				<p id="N26863" type="main">
					<s id="N26865">Quintò, ita proijcitur globus aliquandò, vt motus centri ſit contrarius <lb></lb>motui orbis; tunc autem vel ſiſtit globus, vel etiam redit, cum motus or­<lb></lb>bis intenſior eſt, de quo iam ſuprà. </s>
				</p>
				<p id="N2686D" type="main">
					<s id="N2686F">Sextò, cum proijcitur ſurſum per lineam perpendicularem, ita vt non <lb></lb>modò motus centri, verùm etiam motus orbis imprimatur, mouetur mo­<lb></lb>tu mixto ex recto centri &amp; circulari orbis, nec differt hic motus à motu <lb></lb>rotæ in plano recto, idem dico de deſcenſu &amp; de iactu circuli ferrei vel <lb></lb>lignei. </s>
				</p>
				<pb pagenum="365" xlink:href="026/01/399.jpg"></pb>
				<p id="N2687E" type="main">
					<s id="N26880">Septimò, cum proijcitur globus per inclinatam, mouetur motu mixto <lb></lb>ex tribus ſcilicet ex recto violento centri, ex naturali deorſum &amp; ex cir­<lb></lb>culari orbis, eſtque idem motus, qui eſſet, ſi globus rotaretur in plano <lb></lb>curuo ferè parabolico; </s>
					<s id="N2688A">quippe centrum deſcribit hanc lineam; ſed linea <lb></lb>centri eſt ſemper parallela plano, in quo rotatur globus. </s>
				</p>
				<p id="N26890" type="main">
					<s id="N26892">Octauò, cum rotatur globus in plano decliui per lineam inclinatam <lb></lb>mouetur motu mixto ex tribus, ſcilicet ex duobus rectis centri, &amp; circu­<lb></lb>lari orbis; </s>
					<s id="N2689A">hic motus ſimilis eſt priori; </s>
					<s id="N2689E">quippe centrum deſcribit ferè Pa­<lb></lb>rabolam; hinc facilis methodus deſcribendæ Parabolæ ex iactu globuli <lb></lb>atramento tincti, quam etiam tradit Galileus. </s>
				</p>
				<p id="N268A7" type="main">
					<s id="N268A9">Nonò, ſi globi alterum hemiſphærium ſit grauius, cum rotatur in recto <lb></lb>plano, deflectit in cam partem quam ſpectat hemiſphærium grauius; </s>
					<s id="N268AF"><lb></lb>imò deinde detorquetur in oppoſitam, eſtque motus mixtus ex duobus <lb></lb>circularibus, altero ſcilicet librationis, altero gyri rotatilis, &amp; recto cen­<lb></lb>tri; </s>
					<s id="N268B8">porrò mouetur centrum motu curuo qui aliquando accedit propiùs <lb></lb>ad circularem; </s>
					<s id="N268BE">huc etiam reuoca motum paropſidis rotulæ, quæ in mul­<lb></lb>tos agitur gyros &amp; ſpiras; quia præualet portio grauior, eóque detorquet <lb></lb>centrum motus. </s>
				</p>
				<p id="N268C6" type="main">
					<s id="N268C8">Decimò, hinc quod iucundum eſſet, ſi huiuſmodi globum in datum <lb></lb>ſcopum proijceres; </s>
					<s id="N268CE">haud dubiè alium feriret; </s>
					<s id="N268D2">igitur vt ſcopum ſignatum <lb></lb>tangas, aliò collimare debes; </s>
					<s id="N268D8">porrò linea huius motus eadem eſt, quæ <lb></lb>eſſet, ſi globus rotaretur in linea parallela lineæ, quam deſcribit cen­<lb></lb>trum; </s>
					<s id="N268E1">quæ vel eſt ſpira, vel circulus, vel alia curua, iuxta diuerſam con­<lb></lb>iugationem motum; illa autem facilè haberi poteſt ex dictis ſuprà. </s>
				</p>
				<p id="N268E7" type="main">
					<s id="N268E9">Vndecimo, ſi in plano recto ita rotetur cylindrus, vt ſinguli circuli <lb></lb>paralleli baſi rotentur æqualiter, ſinguli circuli mouentur motu mixto <lb></lb>ex recto centri, &amp; circulari orbis, eſtque hic motus ſimilis motui rotæ <lb></lb>in plano recto, de quo ſuprà. </s>
				</p>
				<p id="N268F2" type="main">
					<s id="N268F4">Duodecimò, ſi verò ita rotetur, vt altera eius extremitas velociore <lb></lb>motu feratur, eſt alius motus mixtus ex curuo axis &amp; circulari orbis, <lb></lb>dixi curuum axis; quia non eſt neceſſariò circularis. </s>
				</p>
				<p id="N268FC" type="main">
					<s id="N268FE">Decimotertiò, cum rotatur conus, mouetur motu mixto ex curuo axis <lb></lb>&amp; circulari orbis, hic motus ſatis communis eſt; eius porrò ratio eſt; </s>
					<s id="N26904"><lb></lb>quia cùm ſinguli circuli ſuperficiei coni ita rotentur, vt motus orbis ſu <lb></lb>æqualis motui centri; certè cùm ſint omnes inæquales, ſpatium decur­<lb></lb>runt. </s>
					<s id="N2690D">Hinc vertex retrò relinquitur à baſi; </s>
					<s id="N26911">hinc baſis neceſſariò retor­<lb></lb>quetur; </s>
					<s id="N26917">dixi autem curuum axis; </s>
					<s id="N2691B">quippe centrum baſis non mouetur <lb></lb>motu purè circulari; nam tantillùm verticem promouet, quia motus <lb></lb>eius centri maximè iuuatur à motu eius orbis, qui longè maior eſt. </s>
				</p>
				<p id="N26923" type="main">
					<s id="N26925">Decimoquartò, huc demum reuoca gyros illarum pyxidum, quarum <lb></lb>margines oppoſiti ſunt circuli inæquales; quippe ſunt veluti fruſta co­<lb></lb>ni, cuius angulus verticis eſt valde acutus. </s>
				</p>
				<p id="N2692D" type="main">
					<s id="N2692F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2693B" type="main">
					<s id="N2693D"><emph type="italics"></emph>Morus diſci facilè explicari potest;<emph.end type="italics"></emph.end>; </s>
					<s id="N26946">eſt enim planum circulare, cuius <pb pagenum="366" xlink:href="026/01/400.jpg"></pb>centrum deſcribit ferè Parabolam; </s>
					<s id="N2694F">vnde eius motus eſt mixtus ex para­<lb></lb>bolico centri, &amp; circulari orbis in circulo horizontali; </s>
					<s id="N26955">igitur motus cen­<lb></lb>tri conſtat ex duobus rectis, ſcilicet ex violento, &amp; naturali deorſum; <lb></lb>porrò eſt idem motus qui eſſet, ſi circulus verticali parallelus rotaretur <lb></lb>in linea parabolica deſcripta in plano horizontali. </s>
				</p>
				<p id="N2695F" type="main">
					<s id="N26961">Obſeruo autem primò motum orbis diſci eſſe poſſe maiorem motu <lb></lb>centri, vel minorem, vel ipſi æqualem; quod quomodo fieri poſſit, fusè <lb></lb>ſuprà explicuimus. </s>
				</p>
				<p id="N26969" type="main">
					<s id="N2696B">Secundò, ſi altera eius portio ſit grauior motus orbis, non eſt idem <lb></lb>cum centro diſci, vt patet; præualet enim portio grauior, ſed propiùs <lb></lb>accedit ad portionem grauiorem. </s>
				</p>
				<p id="N26973" type="main">
					<s id="N26975">Tertiò, hinc cùm diſcus cadit in terram, reſitit altera eius portio, ſci­<lb></lb>licet leuior; </s>
					<s id="N2697B">quia cùm deſcribat maiorem circulum orbis, maiorem im­<lb></lb>petum habet; hinc conuertitur diſcus. </s>
				</p>
				<p id="N26981" type="main">
					<s id="N26983">Quartò, imprimitur motus orbis in ipſo iactu; </s>
					<s id="N26987">quia ſcilicet vna pars <lb></lb>mouetur, antequam alia diſcedat è manu proijcientis; vnde ſequitur <lb></lb>neceſſariò motus orbis. </s>
				</p>
				<p id="N2698F" type="main">
					<s id="N26991"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2699D" type="main">
					<s id="N2699F"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena longioris<emph.end type="italics"></emph.end> <emph type="italics"></emph>haſtæ vel ſariſſæ.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N269AC" type="main">
					<s id="N269AE">Primò, ſit haſta in plano horizontali BG; ſi motu ſimplici attollatur <lb></lb>extremitas B, mouebitur per arcum BA circa centrum G. </s>
				</p>
				<p id="N269B5" type="main">
					<s id="N269B7">Secundò, ſi non modò attollatur, ſed euibretur cum aliquo viſu, ele­<lb></lb>uata ſcilicet tantillùm extremitate G, mouebitur vtraque extremitas; <lb></lb>non certè circa F, ſed circa E, vel D, ita vt GE ſit 1/4 AG per Th.55.l.7. </s>
				</p>
				<p id="N269BF" type="main">
					<s id="N269C1">Tertiò, ſi extremitas G non adducatur ſed B per aliquam Tangentem <lb></lb>arcus BA euibretur pro diuerſa Tangente diuerſus erit motus, ſi v.g.per <lb></lb>Tangentem BH punctum D aſſurget per DE, igitur G redibit in C, B <lb></lb>verò ſpatium compoſitum ex tota v. g. &amp; eius ſubdupla BC; </s>
					<s id="N269CF">eſt autem <lb></lb>hic motus mixtus ex recto centri D &amp; circulari orbis; </s>
					<s id="N269D5">ſi verò extremi­<lb></lb>tas B euibretur per Tangentem HL &amp; D, vel E per EK; haud dubiè ex­<lb></lb>tremitas G minùs retroagetur, &amp; acquiret dextrorſum maius ſpatium. </s>
				</p>
				<p id="N269DD" type="main">
					<s id="N269DF">Quartò, ſi nullo modo adducatur centrum D, vel extremitas G; </s>
					<s id="N269E3">nun­<lb></lb>quam G ad manum ludentis perueniet, id eſt nunquam perueniet in B; <lb></lb>vnde manifeſtè patet hunc motum circularem non fieri circa C. </s>
				</p>
				<p id="N269EC" type="main">
					<s id="N269EE">Quintò, ſi ita euibretur haſta, vt tantillùm adducatur centrum motus <lb></lb>circularis, ſcilicet D; </s>
					<s id="N269F4">haud dubiè altera extremitas G cadere poterit in <lb></lb>B, id eſt peruenire ad manum ludentis; </s>
					<s id="N269FA">ſi verò plùs æquo adducatur, <lb></lb>manum ludentis fallet, ſeu præteribit; </s>
					<s id="N26A00">ſi denique minùs adducatur, por­<lb></lb>rigi manum oportet, vt extremitates G excipiat: porrò hic motus eſt <lb></lb>mixtus ex tribus, ſcilicet ex duobus rectis centri, &amp; circulari orbis. </s>
				</p>
				<p id="N26A08" type="main">
					<s id="N26A0A">Sextò, ita poterit adduci centrum D, &amp; ſimul euibrari B, vt haſtæ me­<lb></lb>dium C facto ſemicircuitu in dextram erectam cadat, quadretque ad in­<lb></lb>ſtar iaculi miſſilis, cuius mucro deorſum vergens prædæ plagam inten­<lb></lb>tat; hoc ludi genus oſtentationem Hiſpanicam vulgò vocant. </s>
				</p>
				<pb pagenum="367" xlink:href="026/01/401.jpg"></pb>
				<p id="N26A18" type="main">
					<s id="N26A1A">Septimò, erigitur haſta, ſi extremitas G tantillùm eleuata cum altera <lb></lb>oppoſita B, tùm ſtatim B deprimatur; </s>
					<s id="N26A20">vnde accidit ipſam G noua acceſ­<lb></lb>ſione impetus ſurſum promoueri; </s>
					<s id="N26A26">quippe ſi deprimatur B circa aliquod <lb></lb>centrum, attollitur G; </s>
					<s id="N26A2C">adde aliquam refluxionem ipſius G, quæ valdè <lb></lb>initio remouetur à manu, vt cum deinde adducitur, maiorem faciat ar­<lb></lb>cum; </s>
					<s id="N26A34">igitur maiore tempore; </s>
					<s id="N26A38">igitur ſenſim ab ipſa manu maior in illam <lb></lb>deriuatur impetus; denique vt deinde maiore quoque arcu extremitas B <lb></lb>deprimatur, remoueaturque, &amp; conſequenter oppoſita G magis attolla­<lb></lb>tur, &amp; accedat. </s>
				</p>
				<p id="N26A42" type="main">
					<s id="N26A44">Octauò, duobus aliis modis erigitur haſta è ſitu horizontali. </s>
				</p>
				<p id="N26A47" type="main">
					<s id="N26A49">Primò, conuerſo introrſum brachio; </s>
					<s id="N26A4D">eleuatur enim extremitas G. <lb></lb>&amp; deprimitur illicò B; </s>
					<s id="N26A53">vnde minore conatu deinde attollitur; </s>
					<s id="N26A57">minus eſt <lb></lb>enim momentum vectis; </s>
					<s id="N26A5D">ſit enim vectis in ſitu horizontali LN, ſitque <lb></lb>eius momentum vt LN; </s>
					<s id="N26A63">certè ſi attollatur in LO, eius momentum erit <lb></lb>tantùm vt LM; </s>
					<s id="N26A69">hinc facilè eleuatur pertica poſt aliquam inclinationem <lb></lb>ſurſum; ſecundus modus, cum torquetur extrinſecus brachium, pro quo <lb></lb>eſt eadem prorſus ratio. </s>
				</p>
				<p id="N26A71" type="main">
					<s id="N26A73">Nonò, erigitur adhuc duobus modis haſta. </s>
				</p>
				<p id="N26A76" type="main">
					<s id="N26A78">Primò, intorto extrinſecus brachio, detortoque. </s>
					<s id="N26A7B">Secundò, contorte <lb></lb>introrſum reductóque traiecto ſub haſtam capite; eſt autem eadem ra­<lb></lb>tio, quæ ſuprà. </s>
				</p>
				<p id="N26A83" type="main">
					<s id="N26A85">Decimò, cum erecta haſta ſurſum ita proijcitur, vt poſt circuitum pot <lb></lb>medium truncum excipiatur, mouetur motu mixto ex recto centri, &amp; <lb></lb>circulari orbis; quod duobus modis fieri poteſt. </s>
					<s id="N26A8D">Primò, ſi extremitas quæ <lb></lb>tenetur manu, retrò agatur, vbi priùs ſurſum tota haſta impulſa eſt; quip­<lb></lb>pe ex eo duplici motu centri, &amp; orbis ſequetur conuerſio haſtæ, &amp; is <lb></lb>deſcenſus in quo commodè per medium truncum excipi poſſit. </s>
					<s id="N26A97">Secundò. </s>
					<s id="N26A9A"><lb></lb>hoc eodem motu mouebitur, eritque ſimile phœnomenum, ſi extremitas, <lb></lb>quæ tenetur manu impulſa primò ſurſum cum tota haſta, tùm deinde <lb></lb>antè pellatur, ita vt extremitas oppoſita retrò agatur. </s>
				</p>
				<p id="N26AA2" type="main">
					<s id="N26AA4">Vndecimò, motus orbis poteſt aliquando eſſe maior, aliquando minor, <lb></lb>pro diuerſo ſcilicet impulſu: </s>
					<s id="N26AAA">idem dico de motu centri; </s>
					<s id="N26AAE">imò poſſet <lb></lb>eſſe tantus motus centri, vt conuerſio haſtæ perfici non poſſet; </s>
					<s id="N26AB4">eſt au­<lb></lb>tem motus centri velocior initio in aſcenſu, &amp; tardior in fine; &amp; contrà <lb></lb>tardior initio deſcenſus, &amp; in fine velocior, vt conſtat ex dictis l.2. &amp; 3. </s>
				</p>
				<p id="N26ABD" type="main">
					<s id="N26ABF">Duodecimò, cum motus centri modicus eſt, parùm aſſurgit haſta, &amp; <lb></lb>licèt morus orbis ſit maximus vix integram conuerſionem perficere <lb></lb>poteſt; cum verò motus centri maximus eſt, &amp; motus orbis modicus, <lb></lb>etiam ſuam conuerſionem non perficit, ſed altiùs aſſurgit mucro. </s>
				</p>
				<p id="N26AC9" type="main">
					<s id="N26ACB">Decimotertiò, centrum motus orbis non videtur eſſe aliud ab ipſis <lb></lb>3/4 verſus mucronem, vt iam ſæpe indicauimus: porrò niſi hoc centrum <lb></lb>motus orbis retroagatur tantillùm, id eſt 1/4 longitudinis haſtæ, non po­<lb></lb>terit excipi per medium truncum, niſi maius producatur. </s>
				</p>
				<p id="N26AD5" type="main">
					<s id="N26AD7">Decimoquartò, poteſt centrum orbis, vel plùs æquo retrò agi, vel ante <lb></lb>pelli, vt conſtat; </s>
					<s id="N26ADD">vnde tota ferè induſtria poſita eſt in temperando illius <pb pagenum="368" xlink:href="026/01/402.jpg"></pb>motu recto; </s>
					<s id="N26AE6">denique non eſt omittendum etiam haſtam eratam ſolo <lb></lb>nixam ſurſum intorto pugno ita proijci poſſe, vt poſt circuitum excipia­<lb></lb>tur, nec eſt noua difficultas; communicatur enim primò motus centri <lb></lb>rectus, tùm motus orbis, immò, ſi ſit breuior, etiam geminos circuitus <lb></lb>facit, antequam iuſta manu excipiatur. </s>
				</p>
				<p id="N26AF2" type="main">
					<s id="N26AF4">Decimoquintò, extremitas, quæ manu tenetur velociùs deinde moue­<lb></lb>tur. </s>
					<s id="N26AF9">Primò, patet experientia. </s>
					<s id="N26AFC">Secundò, maius ſpatium conficit; </s>
					<s id="N26AFF">ratio eſt, <lb></lb>quia mouetur circa centrum maiore ſemidiametro, quas conſtat 1/4 totius <lb></lb>haſtæ, quod vt faciliùs videatur, ſit haſta AE, quæ pellatur ſurſum mo­<lb></lb>tu recto CE, ſitque motus orbis circa centrum C; </s>
					<s id="N26B09">vbi verò C peruenit <lb></lb>in D, A peruenit in L, &amp; D in I; </s>
					<s id="N26B0F">vbi verò C peruenit in E, A peruenit in <lb></lb>G &amp; D rediit in D; </s>
					<s id="N26B15">vides quanta ſit differentia motus; </s>
					<s id="N26B19">nam eo tempore, <lb></lb>quo A decurrit ſpatium AKL, D decurrit tantùm DHI; </s>
					<s id="N26B1F">quænam por­<lb></lb>rò ſit hæc figura; </s>
					<s id="N26B25">certè ſi non eſt Ellipſis, propiùs ad illam accedit: <lb></lb>idem dico de deſcenſu haſtæ, quod dictum eſt de aſcenſu. </s>
				</p>
				<p id="N26B2B" type="main">
					<s id="N26B2D">Decimoſextò, duobus aliis modis poteſt haſta in aëre <expan abbr="cõuerti">conuerti</expan>; </s>
					<s id="N26B35">primò, ſi <lb></lb>mucro agatur retrò, vtraque manu admota alteri extremitati: </s>
					<s id="N26B3B">hic autem <lb></lb>modus differt à prioribus, quod in illis motus centri rectus præcedat <lb></lb>motum orbis; in hoc verò vterque ſimul incipiat. </s>
					<s id="N26B43">Secundò, ſi primò in <lb></lb>humeris liberetur haſta, tùm ſurſum euibretur; ſed hæc ſunt facilia. </s>
				</p>
				<p id="N26B49" type="main">
					<s id="N26B4B">Decimoſeptimò, ad haſtam reuocabis baculum rotatum ab altera ex­<lb></lb>tremitate; ſit enim baculus AE rotatus circa extremitatem A, tùm ſta­<lb></lb>tim demiſſus. </s>
					<s id="N26B53">Primò, E poſt ſemicirculum peruenit in A. Secundò, E im­<lb></lb>primitur maior impetus, vt patet: hinc tertiò mouetur velocius. </s>
					<s id="N26B59">Quartò, <lb></lb>A non deſcendit infra AE, poſt quam demiſſus eſt baculus, vt pater ex­<lb></lb>perientiâ; ratio eſt, quia E per tangentem EL determinata impedit, ne <lb></lb>A deorſum tendat. </s>
					<s id="N26B63">Quintò, E per arcum EG non mouetur; </s>
					<s id="N26B67">alioquin A <lb></lb>eſſet immobilis: </s>
					<s id="N26B6D">præterea F. non mouetur motu circulari, niſi retineatur <lb></lb>in A; </s>
					<s id="N26B73">ſed non retinetur; igitur non mouetur per EG. Sextò, non moue­<lb></lb>tur quoque per rectam EF, quia retinetur E ab A, &amp; reliquis partibus, <lb></lb>quæ minùs habent impetus. </s>
					<s id="N26B7B">Septimò, mouetur E per lineam curuam, quæ <lb></lb>accedit ad ellipſim, ſcilicet per EHA; </s>
					<s id="N26B81">A verò aſſurgit ſupra AE; </s>
					<s id="N26B85">ratio <lb></lb>huius motus petitur ex eo quod, neque per EF, neque per arcum EG <lb></lb>mouetur extremitas E; igitur per curuam de vtraque participan­<lb></lb>tem. </s>
				</p>
				<p id="N26B8F" type="main">
					<s id="N26B91">Decimooctauò, cum ita proijcitur baculus, vt altera extremitas citíùs <lb></lb>moueatur quàm alia, ſequitur motus mixtus ex recto centri, &amp; circulari <lb></lb>orbis; </s>
					<s id="N26B99">quia ſcilicet illa pars, quæ maiorem impetum habet, quaſi retrò <lb></lb>agitur ab alia, quæ minorem habet, non quidem motu purè circulari; <lb></lb>alioqui omninò retineretur ab alia extremitate, ſed alio mixto, quia non <lb></lb>omninò retinetur. </s>
				</p>
				<p id="N26BA3" type="main">
					<s id="N26BA5">Decimononò, hinc poteſt ita temperari motus ille orbis, vt tantùm <lb></lb>ſemicircuitum in toto curſu impleat, cum ſcilicet partes omnes æquali <lb></lb>ferè cum impetu mouentur; </s>
					<s id="N26BAD">ſi enim æqualitas eſt in motu omnium <lb></lb>partium, mouentur omnes motu recto; </s>
					<s id="N26BB3">ſi verò motus ſingularum ſunt <pb pagenum="369" xlink:href="026/01/403.jpg"></pb>vt radij, motus eſt purè circularis; ſi verò eſt alia inæqualitas, erit <lb></lb>mixtus, qui magis accedet ad circularem, quò maior erit inæqualitas, &amp; <lb></lb>magis ad rectum, quò minor erit. </s>
				</p>
				<p id="N26BC0" type="main">
					<s id="N26BC2">Vigeſimò, hinc qui ludunt trunculis illis luſoriis inuerſo tamen mo­<lb></lb>re, quod ſæpè hic fit, quo ſcilicet non globus in trunculos, ſed trunculi <lb></lb>in globum proijciantur, arripiunt trunculum ipſum per medium trun­<lb></lb>cum, vt ſcilicet æqualem impetum ſingulis partibus imprimant; vnde <lb></lb>ſequitur motus rectus, &amp; ex motu recto vniformis trunculi caſus, ne ſi <lb></lb>altera extremitas ante aliam ſolum tangat, ſtatim reſiliat alia per ali­<lb></lb>quot gyros, &amp; à ſcopo diſcedat. </s>
				</p>
				<p id="N26BD2" type="main">
					<s id="N26BD4">Vigeſimoprimò, mouetur baculus proiectus eo modo, de quo num. </s>
					<s id="N26BD7">18. <lb></lb>circa aliquod centrum, quod tribus quartis tribuimus verſus eam ex­<lb></lb>tremitatem, quæ vltimò à manu dimittitur; quippe faciliùs circa hoc <lb></lb>centrum mouetur, de quo alibi, vnde eſt motus mixtus ex recto centri, <lb></lb>ex recto naturali, &amp; ex circulari orbis, quæ omnia ex dictis ſatis intelli­<lb></lb>guntur. </s>
				</p>
				<p id="N26BE5" type="main">
					<s id="N26BE7">Vigeſimoſecundò, non ſunt omittenda aliquot phœnomena, quæ in <lb></lb>trunculorum ludo ferè ſemper occurrunt. </s>
					<s id="N26BEC">1°. </s>
					<s id="N26BEF">ſi iuxta verticem tangan­<lb></lb>tur faciliùs decutiuntur, quia maior eſt vectis, 2°. </s>
					<s id="N26BF4">minùs deflectit glo­<lb></lb>bus à ſuo tramite, ſi per ſummos vertices decutiat, quia minùs reſiſtunt. </s>
					<s id="N26BF9"><lb></lb>3°. </s>
					<s id="N26BFD">hinc, ſi etiam per imum pedem directo ictu verberentur, plùs reſi­<lb></lb>ſtunt, quia minor eſt vectis, 4°. </s>
					<s id="N26C02">hinc ſtatim à recta via globus deflectit, <lb></lb>5°. </s>
					<s id="N26C07">ſi obliquè globus feriat trunculum, quaſi lambendo, parùm declinat <lb></lb>à ſuo curſu, quia minima eſt reſiſtentia, quía obliquus ictus minimus <lb></lb>eſt, vt conſtat ex dictis ſæpiùs in ſuperioribus libris. </s>
					<s id="N26C10">6. cum ſic obliquè <lb></lb>decutitur trunculus, hic decuſſus deinde alios decutit; </s>
					<s id="N26C16">quia ex obliquo <lb></lb>ictu craſſioris pedis agitur in vertiginem circa verticem ad inſtar coni, <lb></lb>de quo ſuprà; &amp; cum maiorem gyrum deſcribit, vix vnquam accidit, vt <lb></lb>in ſatis frequenti ſylua in alium trunculum non incidat, quem etiam <lb></lb>decutit. </s>
					<s id="N26C22">7°. </s>
					<s id="N26C25">aliqui tradunt artem, qua nouem trunculi decuti poſſunt, <lb></lb>quod multis modis præſtari poteſt, ſed ad rem præſentem non ſpe­<lb></lb>ctat. </s>
				</p>
				<p id="N26C2C" type="main">
					<s id="N26C2E">Vigeſimotertiò, eſt etiam aliud ludi genus, quo pueri ruſticani ludunt; </s>
					<s id="N26C32"><lb></lb>eſt autem minimum parallelipedum gemino mucrone hinc inde inſtru­<lb></lb>ctum, vel cuius vtraque extremitas eſt emarginata, vel ad inſtar fuſi in <lb></lb>apicem coni, hinc inde deſinens; ſi enim baculo roſtrum illud ferias, <lb></lb>ſtatim aſſurgit. </s>
					<s id="N26C3D">Sit enim primò parallelipedum emarginatum AD in­<lb></lb>cubans ſolo EC; </s>
					<s id="N26C43">ſi roſtrum A baculo percutiatur, deprimitur A circa <lb></lb>centrum E, &amp; attollitur D maiore quidem arcu; igitur maiore impe­<lb></lb>tu, qui quia non retinetur omninò non mouetur circulari motu D, <lb></lb>ſed curuo mixto circa centrum E, quod ab extremitate D tantillùm <lb></lb>eleuatur. </s>
					<s id="N26C4F">Secundò, ex hoc phœnomeno manifeſtè confirmatur, quod <lb></lb>diximus ſuprà de baculo num. </s>
					<s id="N26C54">17. quod ſcilicet aſſurgat extremitas illa, <lb></lb>quæ manu tenetur ſupra horizontalem. </s>
					<s id="N26C59">Tertiò, idem prorſus accidet <pb pagenum="370" xlink:href="026/01/404.jpg"></pb> ſi ſupra planum horizontale BA v. g. ſit cylindrus CB extans aliqua <lb></lb>ſui parte putà FC; </s>
					<s id="N26C68">ſi percutiatur baculo ED in C, aſſurget propter <lb></lb><expan abbr="eãdem">eandem</expan> rationem motu mixto; </s>
					<s id="N26C71">nam primò circa centrum F deprimi­<lb></lb>tur C, &amp; attollitur B; </s>
					<s id="N26C77">B quidem velociore motu, vt patet; igitur ſecum <lb></lb>attollit extremitatem oppoſitam C motu mixto propter rationem iam <lb></lb>ſuprà allatam. </s>
				</p>
				<p id="N26C7F" type="main">
					<s id="N26C81">Vigeſimoquartò, AB ſi baculus in aëre libratus perpendiculariter. </s>
					<s id="N26C84"><lb></lb>v. g. percutiatur altero baculo ED. Primò, in centro grauitatis C <lb></lb>baculi AB, mouebitur AB motu recto; </s>
					<s id="N26C8F">ratio eſt, quia omnes partes mo­<lb></lb>uentur æqualiter; igitur motu recto. </s>
					<s id="N26C95">Secundò, tunc erit maximus <lb></lb>iactus, ſi ED percutiat C, ita vt EC media proportionalis inter ED, <lb></lb>&amp; eius ſubduplam EG; </s>
					<s id="N26C9D">quia ED producit maximum impetum &amp; to­<lb></lb>tum; eſt enim C centrum grauitatis impetus totius ED, &amp; centrum gra­<lb></lb>uitatis corporis impedientis AB. Tertiò, hinc ſi ED feriat in puncto G, <lb></lb>non erit tantus iactus licèt AB proijciatur motu recto. </s>
					<s id="N26CA7">Quartò, ſi <lb></lb>percutiatur in F, non mouebitur motu recto, vt conſtat experientiâ; </s>
					<s id="N26CAD"><lb></lb>quippe maior impetus producetur in extremitate B, quàm in A; </s>
					<s id="N26CB2">igitur <lb></lb>non mouebitur motu recto, ſed mixto circa centrum mobile H. Quintò, <lb></lb>non producetur totus impetus, qui poteſt produci ab ipſo ED; </s>
					<s id="N26CBA">quia <lb></lb>non impedietur totus, vt patet: quippe extremitas B faciliùs cedit. </s>
					<s id="N26CC0"><lb></lb>Sextò, quo punctum ictus accedet propiùs ad extremitatem B, minor <lb></lb>erit motus centri, <expan abbr="maiorq́ue">maiorque</expan> motus circularis, &amp; conſequenter minor <lb></lb>iactus, &amp; contrà, quò punctum ictus accedet propiùs ad centrum C. <lb></lb>Septimò, ſunt 6. ictuum combinationes in hoc caſu; </s>
					<s id="N26CCF">nam vel ictus <lb></lb>cadet in centrum grauitatis C baculi AB vel extra; ſi primum, tribus <lb></lb>modis id fieri poteſt. </s>
					<s id="N26CD7">Primò, ſi centrum grauitatis impetus baculi ED <lb></lb>feriat ſcilicet ipſum C. Secundò, ſi aliud punctum inter CD putà K. <lb></lb>Tertiò, ſi aliquod inter CE putà G; </s>
					<s id="N26CDF">ſi verò ſecundum iiſdem tribus mo­<lb></lb>dis fieri poteſt, ſed de his ſatis; ſupereſt tantùm, ni fallor, vt ea phœno­<lb></lb>mena, quæ in tudiaria gladiatura obſeruari poſſunt, eorumque cauſas <lb></lb>explicemus, ſed illud præſtabimus in lib.  ſequenti. </s>
				</p>
				<p id="N26CE9" type="main">
					<s id="N26CEB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26CF7" type="main">
					<s id="N26CF9"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena turbinis ſen trochi circumacti<emph.end type="italics"></emph.end>: </s>
					<s id="N26D02">Tur­<lb></lb>binum puerilium duo ſunt genera: primum eſt eorum, qui ferro mu­<lb></lb>niuntur, qui certè diuerſæ ſunt figuræ, ſphæricæ, conicæ &amp;c. </s>
					<s id="N26D0A">communi­<lb></lb>ter tamen fiunt iuxta figuram cordis, vt vides in A. </s>
					<s id="N26D10">Secundum eſt eo­<lb></lb>rum, qui ferro carent, quorum ſunt etiam diuerſæ figuræ, communior eſt <lb></lb>conois, vt vides in</s>
				</p>
				<p id="N26D17" type="main">
					<s id="N26D19">Primò, circumagitur vel ſcutica vt B, vel funiculo intorto vt A: <lb></lb>vtriuſque ratio eadem eſt; cùm enim circumuolutus funiculus reduci­<lb></lb>tur, haud dubiè trochum ipſum in orbem agit. </s>
				</p>
				<p id="N26D21" type="main">
					<s id="N26D23">Secundò, cum mouetur trochus circa axem CD immobilem, eſt mo­<lb></lb>tus purè circularis. </s>
				</p>
				<pb pagenum="371" xlink:href="026/01/405.jpg"></pb>
				<p id="N26D2C" type="main">
					<s id="N26D2E">Tertiò, cùm mouetur circa axem mobilem motu recto, eſt motus mix­<lb></lb>tus ex recto &amp; circulari ſimilis motui rotæ; cum verò mouetur  axis in <lb></lb>orbem, mouetur motu mixto ex duobus circularibus, &amp; hic eſt motus <lb></lb>veriſſimus turbinationis. </s>
				</p>
				<p id="N26D38" type="main">
					<s id="N26D3A">Quartò, cauſa motus orbis eſt prima reductio ſcuticæ, ſeu funiculi, <lb></lb>quæ circumagit turbinem; </s>
					<s id="N26D40">cauſa verò motus axis eſt extremitas funicu­<lb></lb>li, vel ſcuticæ, quæ trochum aliquo modo, vel adducit, vel quaſi explodit, <lb></lb>vel expellit; </s>
					<s id="N26D48">adducit quidem funiculus, cuius altera extremitas etiam <lb></lb>adducitur; </s>
					<s id="N26D4E">expellitur verò trochus, cum verbere adigitur: ſed de his <lb></lb>paulò pòſt. </s>
				</p>
				<p id="N26D54" type="main">
					<s id="N26D56">Quintò, ideò trochus mouetur motu orbis, ſeu motu circulari, quia <lb></lb>impetus contrarii ſimul imprimuntur, v.g.in fig.B imprimitur impetus E <lb></lb>per artum EHF, &amp; F per arcum FGE: </s>
					<s id="N26D5E">vndè ſequitur neceſſariò motus <lb></lb>circularis; hinc digitis in contrarias partes exploſis turbo in orbem <lb></lb>agitur. </s>
				</p>
				<p id="N26D66" type="main">
					<s id="N26D68">Sextò, diu durat iſte motus circularis turbinis, quia non deſtruitur <lb></lb>ab impetu contrario grauitationis, vt iam diximus alibi, ſed tantùm ab <lb></lb>affrictu ad planum illud, in quo vertitur, &amp; à noua determinatione, quæ <lb></lb>ſingulis inſtantibus ponitur, quæ pro nihilo ferè haberi debet; hinc quò <lb></lb>vertex turbinis, politior eſt, &amp; planum in quo ſuos gyros agit, læuiga­<lb></lb>tius, diutiùs durat eius motus. </s>
				</p>
				<p id="N26D76" type="main">
					<s id="N26D78">Septimò, aliquando dormire dicitur turbo cum celerrimè mouetur, <lb></lb>defixo ſcilicet axe in eodem loco, &amp; ſitu, ratio petitur ex eo quòd ver­<lb></lb>tex certè componitur cum ipſo plano factâ ſibi veluti inſenſibili apo­<lb></lb>theca ſeu foſſula, cuius tenuis margo impedit motum centri; igitur mo­<lb></lb>tus orbis vnicus eſt, igitur maior. </s>
				</p>
				<p id="N26D84" type="main">
					<s id="N26D86">Octauò, verbere adigitur trochus, <expan abbr="ipſiq́ue">ipſique</expan> imprimitur primò motus <lb></lb>orbis, quia lora illa ſcuticæ trocho aduoluta, vbi deinde explicantur, tro­<lb></lb>chum ipſum circumagunt: </s>
					<s id="N26D92">ſecundò motus centri, quia eadem lora ad in­<lb></lb>ſtar fundæ quaſi trochum explodunt; </s>
					<s id="N26D98">ſic plerumque accidit adhiberi lora, <lb></lb>vt longiùs ligneus orbis proijciatur; </s>
					<s id="N26D9E">quippe dum explicantur lora, du­<lb></lb>plex ille motus neceſſariò imprimitur; </s>
					<s id="N26DA4">primus quidem, quia explicari <lb></lb>non poſſunt, niſi trochus circumagatur; </s>
					<s id="N26DAA">ſecundus verò, quia explicari <lb></lb>lora non poſſunt niſi in aliquam partem ferantur, &amp; trochum ipſum tra­<lb></lb>hant, vel ſaltem impellant; </s>
					<s id="N26DB2">adde quod diutiùs manet potentia applicata; <lb></lb>hinc maior effectus, analogiam habes in funda. </s>
				</p>
				<p id="N26DB8" type="main">
					<s id="N26DBA">Nonò, quando turbo ferro inſtructus, cui funiculus aduolutus eſt, re­<lb></lb>tentâ alterà funiculi extremitate, &amp; explicato eodem funiculo circum­<lb></lb>agitur; </s>
					<s id="N26DC2">haud dubiè maiore vi pollet hic motus, <expan abbr="duratq́ue">duratque</expan> diù, tùm quie <lb></lb>funiculus eſt, longior, tùm quia maiore niſu quaſi euibratur, tùm quia <lb></lb>diù manet potentia applicata; </s>
					<s id="N26DCE">porrò duobus modis explicatur funiculus; </s>
					<s id="N26DD2"><lb></lb>primò enim adducitur, ſeu retrahitur, ex quo accidit, vt motus centri <lb></lb>determinetur in <expan abbr="eãdem">eandem</expan> partem; </s>
					<s id="N26DDD">ſecundò non adducitur, ſed tantùm <lb></lb>altera extremitas retinetur; vnde fit, vt motus centri nullus ferè ſit. </s>
				</p>
				<p id="N26DE3" type="main">
					<s id="N26DE5">Decimò, motus centri circularis in cam ſemper eſt partem, in quam <pb pagenum="372" xlink:href="026/01/406.jpg"></pb>exterior turbinis portio motu orbis conuoluitur; </s>
					<s id="N26DEE">v.g. turbo B mouetur <lb></lb>motu orbis per arcum EHF; </s>
					<s id="N26DF6">igitur motu circulari centri vel axis moue­<lb></lb>bitur per DK, ſi ſupponatur erectus perpendiculariter in plano LDK; </s>
					<s id="N26DFC"><lb></lb>ratio eſt, quia circularis axis determinatur à circulari orbis; igitur vter­<lb></lb>que fit in <expan abbr="eãdem">eandem</expan> partem. </s>
				</p>
				<p id="N26E07" type="main">
					<s id="N26E09">Vndecimò, diuerſa ſcabrities plani in quo circumagitur turbo mul­<lb></lb>tùm immutat turbinationis modum; tunc enim vel diuerſa plani incli­<lb></lb>natî ratio, vel diuerſæ quaſi foſſulæ, vel inſenſibiles ſcopuli turbinem eò <lb></lb>ſæpe adigunt, quo impreſſi motus indoles minimè ferret. </s>
					<s id="N26E13"><lb></lb>Duodecimò, licèt imprimatur motus rectus axi per adductionem, vel <lb></lb>emiſſionem funiculi, non tamen mouetur axis motu recto; quia hic mo­<lb></lb>tus rectus ab ipſo motu orbis immutatur, ita vt ex vtroque motus fiat <lb></lb>mixtus, ipſeque adeò axis motu quaſi ſpirali, reliquæ verò partes inæ­<lb></lb>quali motu circumagantur. </s>
				</p>
				<p id="N26E20" type="main">
					<s id="N26E22">Decimotertiò, quando axis mouetur motu circulari, poteſt eſſe circu­<lb></lb>lus, quem deſcribit maior vel minor; </s>
					<s id="N26E28">ſi maior eſt, iſque duplus circuli <lb></lb>baſis trochi ſingula puncta baſis deſcribunt lineam cordis, dum motus <lb></lb>orbis, &amp; axis æquali numero circulorum conſtent; </s>
					<s id="N26E30">ſi verò axis deſcribit <lb></lb>circulum æqualem baſi, <expan abbr="ſitq́ue">ſitque</expan> numerus circulorum <expan abbr="vtriuſq́ue">vtriuſque</expan> motus æ­<lb></lb>qualis, deſcribit quodlibet punctum periphæriæ baſis lineam nouam, <lb></lb>cuius ſchema hic habes, ſit enim circulus, quem deſcribit punctum <lb></lb>axis, quod eſt centrum baſis ſupremæ trochi, <expan abbr="AHKq;">AHKque</expan> ſitque baſis ipſa <lb></lb>circulus EDBC; </s>
					<s id="N26E4A">hoc poſito moueatur centrum A per circulum AHK <lb></lb>Q, cum erit in G, erit in F, cum in H erit in D, cum in D, erit in L; &amp;c. </s>
					<s id="N26E50"><lb></lb>igitur punctum periphæriæ baſis E deſcribit ſuo motu lineam curuam <lb></lb>EFADLMPCAE, quæ ſuas habet proprietates, de quibus ſuo loco. </s>
				</p>
				<p id="N26E56" type="main">
					<s id="N26E58">Decimoquartò, obſeruas, niſi fallor, mirabilem huius motus analo­<lb></lb>giam; </s>
					<s id="N26E5E">ſit enim centrum circuli, qui circa alium immobilem conuertitur, <lb></lb>decurrat circulum duplò maiorem, deſcribit lineam cordis, de qua ſuprà, <lb></lb>ſi maiorem duplo (eâ tamen lege vt centrum, &amp; orbis æquali tempore <lb></lb>ſuum circulum decurrant) deſcribitur linea, quæ accedit propiùs ad cir­<lb></lb>culum; </s>
					<s id="N26E6A">ſi verò circulus centri ſit æqualis circulo orbis, habes lineam in <lb></lb>ſuperiore ſchemate, quæ geminum <expan abbr="circulũ">circulum</expan> imperfectum præfert, qui eò <lb></lb>propiùs ad ſe inuicem <expan abbr="accedũt">accedunt</expan>, quo circulus centri minor eſt; </s>
					<s id="N26E7A">cùm enim <lb></lb>nullus eſt omninò <expan abbr="cẽtri">centri</expan> circulus, tunc ambo circuli imperfecti in vnum <lb></lb><expan abbr="perfectũ">perfectum</expan> coëunt; ſi verò circulus centri ſit minor duplò, ſed maior æquali, <lb></lb>minor erit ſuperior illa figura EFA, &amp;c. </s>
					<s id="N26E8B">donec tandem vbi circulus cen­<lb></lb>tri eſt duplus circuli orbis vnica tantùm figura deſcribatur, ſcilicet linea <lb></lb>cordis. </s>
					<s id="N26E92">Sed de his omnibus fusè ſuo loco; ſunt enim mirificæ harum <lb></lb>linearum proprietates. </s>
				</p>
				<p id="N26E98" type="main">
					<s id="N26E9A">Decimoquintò, ſaltitat initio proiectus turbo; </s>
					<s id="N26E9E">ratio eſt, quia motus <lb></lb>centri maior eſt; </s>
					<s id="N26EA4">igitur ob maiorem affrictum ſæpiùs reſilit; quod pro­<lb></lb>fectò non accideret, ſi planum læuigatiſſimum eſſet, &amp; ferreus mucro <lb></lb>politiſſimus hinc ſtatim primus ille ardor deferueſcit, &amp; miliùs turbi­<lb></lb>natur. </s>
				</p>
				<pb pagenum="373" xlink:href="026/01/407.jpg"></pb>
				<p id="N26EB2" type="main">
					<s id="N26EB4">Decimoſextò, antequam quieſcat turbo, inclinatur, ſuoſque orbes agit <lb></lb>inclinato quaſi corpore, &amp; obliquo axe; </s>
					<s id="N26EBA">ratio eſt, quia vel axis ſeu ferreus <lb></lb>mucro tantillùm abeſt à grauitatis centro, vel aliquis plani ſcopulus, vel <lb></lb>decliuis plaga turbinem ipſum inclinat; agit tamen adhuc aliquot obli­<lb></lb>quos gyros propter vim prioris impetus, quæ ſenſim à grauitatione tur­<lb></lb>binis frangitur, &amp; tandem omninò ſuperatur. </s>
				</p>
				<p id="N26EC6" type="main">
					<s id="N26EC8">Decimoſeptimò, hinc, vbi terrarum tangit depreſſus turbo, ad inſtar <lb></lb>rotæ deindæ rotatur; ratio eſt, quia multus adhuc remanet impetus ad <lb></lb>motum orbis determinatus, qui vbi tangitur, ſolum trochum ipſum cum <lb></lb>centro ad inſtar rotæ præcipitem agit. </s>
				</p>
				<p id="N26ED4" type="main">
					<s id="N26ED6">Decimooctauò, hinc vides naturam maximè gaudere motu recto qui <lb></lb>paulò ante turbini erecto minimè concedebatur; cur enim in vnam po­<lb></lb>tiùs partem, quàm in aliam? </s>
					<s id="N26EDE">at verò lapſo iacentique facilè permittitur; <lb></lb>nam in plano motus orbis rotæ facilè determinat motum rectum <lb></lb>centri. </s>
				</p>
				<p id="N26EE6" type="main">
					<s id="N26EE8">Decimononò, ad turbinem reuoco cubum illum, ſuis numeris vel <lb></lb>characteribus inſtructum, &amp; duobus hinc inde in ſuprema, &amp; ima facie, <lb></lb>quaſi paxillis, vel communi axe munitum, cuius figuram hîc habes; vol­<lb></lb>uitur enim hic cubus circa ſuum axem, neque eſt noua difficultas. </s>
				</p>
				<p id="N26EF2" type="main">
					<s id="N26EF4">Vigeſimò, huc etiam reuoca fuſum, qui dum turbinatim verſatur, di­<lb></lb>uerſis etiam motibus moueri poteſt ſurſum, deorſum, dextrorſum, ſini­<lb></lb>ſtrorſum, ïta vt in eo mira motuum varietas obſeruari poſſit. </s>
				</p>
				<p id="N26EFB" type="main">
					<s id="N26EFD">Vigeſimoprimò, reuocabis quoque motum paropſidis, dum digito <lb></lb>quaſi flagellatur; eſt enim quoddam turbinationis genus, cuius ratio <lb></lb>facilis eſt, &amp; conſtat ex dictis. </s>
				</p>
				<p id="N26F05" type="main">
					<s id="N26F07"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26F13" type="main">
					<s id="N26F15"><emph type="italics"></emph>Explicari poſſunt phœnomena<emph.end type="italics"></emph.end> <emph type="italics"></emph>motus Excentricorum<emph.end type="italics"></emph.end>; </s>
					<s id="N26F24">ſit circulus ALK <lb></lb>M centro E; </s>
					<s id="N26F2A">ſit alius excentricus ACOD centro B, circa quod mouea­<lb></lb>tur punctum A v.g. motu orbis; </s>
					<s id="N26F32">Primò, nulla erit inæqualitàs motus, ſed <lb></lb>tantùm videbitur eſſe; </s>
					<s id="N26F38">nam <expan abbr="punctũ">punctum</expan> A, in quo ſit aſtrum poſt decurſum <lb></lb>quadrantem; </s>
					<s id="N26F42">videbitur in N; </s>
					<s id="N26F46">igitur videbitur tantùm confeciſſe arcum A <lb></lb>N minorem quadrante; </s>
					<s id="N26F4C">hinc motus ab A ad C indicabitur tardior; </s>
					<s id="N26F50">at ve­<lb></lb>AC ad O videbitur velocior; </s>
					<s id="N26F56">quia credetur confeciſſe arcum maiorem <lb></lb>NK, æquali ſcilicet tempore, quo AN; </s>
					<s id="N26F5C">hinc ab A ad C, id eſt ab apogæo <lb></lb>dicitur eſſe tardior; vel ocior verò AC ad I, id eſt ad perigæum, ſed hæc <lb></lb>ſunt facilia, &amp; communia, per quæ explicantur anomaliæ, &amp; inæquali­<lb></lb>tates ſimpliciores motuum cæleſtium. </s>
				</p>
				<p id="N26F66" type="main">
					<s id="N26F68">Secundò, ſi voluatur circulus radio AE circa centrum E, nec ſit vllus <lb></lb>motus circa centrum B; haud dubiè omnes partes excentrici ADOC <lb></lb>mouebuntur motu circulari ſed inæquali, vt patet. </s>
				</p>
				<p id="N26F70" type="main">
					<s id="N26F72">Tertiò, ſi ſit motus circularis circa vtrumque centrum; certè centrum <lb></lb>B circumagetur per circellum BGHF, punctum verò A excentrici <lb></lb>deſcribet hanc lineam APIQBSIRA, vt conſtat ex dictis Th. 30. <lb></lb>num. </s>
					<s id="N26F7C">30. </s>
				</p>
				<pb pagenum="374" xlink:href="026/01/408.jpg"></pb>
				<p id="N26F83" type="main">
					<s id="N26F85">Quartò, hine in ſingulis circuitionibus videretur facere duas, &amp; pe­<lb></lb>rigæum videretur verſus eam partem, verſus quam videretur apogæum. </s>
				</p>
				<p id="N26F8A" type="main">
					<s id="N26F8C">Quintò, centrum B poſſet moueri per circellum minorem BGHF, <lb></lb>vel per alium, cuius centrum eſſet inter BE; per hos autem circellos <lb></lb>explicant Aſtronomi diuerſas excentricitatis mutationes. </s>
				</p>
				<p id="N26F94" type="main">
					<s id="N26F96">Sextò, moueretur punctum A inæqualiter, v.g. eo tempore, quo per­<lb></lb>currit AP, percurrit tantùm SI, vt conſtat ex dictis ſuprà. </s>
				</p>
				<p id="N26F9D" type="main">
					<s id="N26F9F">Septimò, poſſunt etiam determinari illi arcus, qui tardiùs licèt de­<lb></lb>curſi, velociùs tamen decurri viderentur; </s>
					<s id="N26FA5">nam in A videretur moueri <lb></lb>tardiſſimè; at verò velociſſimè in B. </s>
				</p>
				<p id="N26FAB" type="main">
					<s id="N26FAD">Octauò, poſſunt plures excentrici ſimul componi cum pluribus etiam <lb></lb>concentricis; </s>
					<s id="N26FB3">ſed de iis fusè in Aſtronomia; hîc tantum ſufficiat indi­<lb></lb>caſſe, &amp; quaſi reduxiſſe ad principia motuum mixtorum. </s>
				</p>
				<p id="N26FB9" type="main">
					<s id="N26FBB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N26FC7" type="main">
					<s id="N26FC9"><emph type="italics"></emph>Poſſunt explicari omnia phœnomena<emph.end type="italics"></emph.end> <emph type="italics"></emph>Epiciclorum.<emph.end type="italics"></emph.end></s>
					<s id="N26FD6"> Primò ſit circulus H <lb></lb>BCK centro A, ſit epicyclus LIQG, centro G; </s>
					<s id="N26FDC">aſſumatur quodlibet <lb></lb>eius punctum, putà G, quod moueatur  motu mixto id eſt, motu centri, <lb></lb>&amp; motu orbis: poſſunt aſſignari omnia puncta lineæ huius motus, om­<lb></lb>nes velocitatis proportiones, &amp;c. </s>
				</p>
				<p id="N26FE6" type="main">
					<s id="N26FE8">Secundò, ſi H moueatur verſus K, &amp; G verſus Q deſcribet ſpeciem <lb></lb>lineæ cordis GZMNE. </s>
				</p>
				<p id="N26FED" type="main">
					<s id="N26FEF">Tertiò, G mouebitur velociùs, in G quam in N, E, &amp;c. </s>
					<s id="N26FF2">tardiſſimè in <lb></lb>perigæo E, velociſſimè in Apogæo G. </s>
				</p>
				<p id="N26FF8" type="main">
					<s id="N26FFA">Quartò, temporibus æqualibus diuerſos arcus deſcribit, ſcilicet ar­<lb></lb>cum compræhenſum angulo HAN, NAC. </s>
				</p>
				<p id="N26FFF" type="main">
					<s id="N27001">Quintò, ſi G moueatur verſus L &amp; H verſus K, tardiſſimus motus <lb></lb>erît in apogæo G, velociſſimus in perigæo E; nam eo tempore, quo à pe­<lb></lb>rigæo conficit arcum compræhenſum angulo CAM, conficit ab apo­<lb></lb>gæo arcum compræhenſum angulo MAH. </s>
				</p>
				<p id="N2700B" type="main">
					<s id="N2700D">Sextò, ſi motus epicycli ſit inæqualis motui centri, diuerſa erit linea <lb></lb>huîus motus mixti, diuerſæ motuum, &amp; velocitatum proportiones. </s>
				</p>
				<p id="N27012" type="main">
					<s id="N27014">Septimò, ſi ſint duo Epicycli, erit etiam diuerſa linea, &amp; diuerſa mo­<lb></lb>tuum proportio; poteſt autem accidere, vt vel vterque in <expan abbr="eãdem">eandem</expan> par­<lb></lb>tem, vel in diuerſas tendant. </s>
				</p>
				<p id="N27020" type="main">
					<s id="N27022">Octauò, poteſt etiam Epicyclus rotari in excentrico, in quo caſu di­<lb></lb>uerſus erit motus, diuerſa linea; quæ omnia facilè ex dictis conſtant, de <lb></lb>quibus fusè agemus ſuo loco. </s>
				</p>
				<p id="N2702A" type="main">
					<s id="N2702C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27038" type="main">
					<s id="N2703A"><emph type="italics"></emph>Si rota moueatur in circulo parallelo illi plane, cui incubat perpendicula­<lb></lb>riter eodem ferè motu moneri videtur, quo turbo, de quo ſuprà<emph.end type="italics"></emph.end>; </s>
					<s id="N27045">aſſumatur <lb></lb>enim figura prima Th. 15. in qua ſit circulus immobilis in plano hori­<lb></lb>zontali BTXD, &amp; erigatur rota BEDF, ita vt ſit parallela circulo <lb></lb>verticali, tangatque priorem circulum in B, cuius deinde periphæriam <lb></lb>ſenſim percurrat; </s>
					<s id="N27051">haud dubiè punctum B deſcribet ſuo motu lineam, quæ <pb pagenum="375" xlink:href="026/01/409.jpg"></pb>poteſt declinari; </s>
					<s id="N2705A">ſit enim circulus immobilis BDFC, mobilis FEG, <lb></lb>punctum F poſt decurſum quadrantem FD extat ſupra planum hori­<lb></lb>zontis tota ID erecta; </s>
					<s id="N27062">poſt decurſum verò ſemicirculum tota BK <lb></lb>erecta æquali BF, vt conſtat; </s>
					<s id="N27068">igitur vertatur FBK, circa FB, donec incu­<lb></lb>bet perpendiculariter plano horizontali in BF; </s>
					<s id="N2706E">tùm circa FK, ita ere­<lb></lb>ctam vertatur planum, donec incubet DI, erecta in I, fiet planum, in quo <lb></lb>deſcribetur linea huius motus; </s>
					<s id="N27076">aſſumatur autem DH æqualis AI; </s>
					<s id="N2707A">dico <lb></lb>quod ducetur per FHK: </s>
					<s id="N27080">ſimiliter inuenientur alia puncta, quod ſuffi­<lb></lb>ciat indicaſſe; </s>
					<s id="N27086">eſt autem hic motus maximè inæqualis propter ratio­<lb></lb>nem, de qua ſuprà: </s>
					<s id="N2708C">ſed de his ſatis; </s>
					<s id="N27090">immò certum eſt punctum F ſuo <lb></lb>motu prædicto deſcribere perfectum circulum duplum circuli rota­<lb></lb>ti, cuius centrum eſt D erectum in A, nam DH, DF, DK ſunt æqua­<lb></lb>les; </s>
					<s id="N2709A">ſi enim circulus tangat in M, punctum F erectum toto arcu FM, <lb></lb>reſpondebit perpendiculariter puncto O, ita vt OM ſit æqualis PB, vel <lb></lb>HS, vel AN; erigatur autem OR, donec incubet perpendiculariter, <lb></lb>extat ſuper AD erecta in A tota QR, ita OQ ſit æqualis AD. </s>
					<s id="N270A5">Sed <lb></lb>quad. </s>
					<s id="N270AA">AO eſt æquale quadratis AM, MO; igitur ſit quad. </s>
					<s id="N270AE">AM qua­<lb></lb>dratum MO erit 8. igitur quadratum A 24. ſed extat ſuper MO, QR, <lb></lb>æqualis OM; </s>
					<s id="N270B6">igitur ſi à D erecto ducantur duæ rectæ, altera ad Q, altera <lb></lb>ad R, lineæ OR erectæ; </s>
					<s id="N270BC">certè DQ erit æqualis AO; </s>
					<s id="N270C0">eſt enim ipſi pa­<lb></lb>rallela; </s>
					<s id="N270C6">tùm fiet triangulum ortogon ex tribus DQ, QR, DR; igitur <lb></lb>quadr. </s>
					<s id="N270CC">DR eſt æquale duobus DQ, QR, ſed DQ eſt æqualis A <lb></lb>O; igitur quadr. </s>
					<s id="N270D2">DQ eſt 24. QR eſt æqualis OM; igitur quadr. </s>
					<s id="N270D6">QR <lb></lb>eſt 8. igitur quadratum DR eſt 32. ſed quadr. </s>
					<s id="N270DB">DF eſt 32. poſito <lb></lb>quadrato AF 16.igitur DR erit æqualis DF; igitur circu­<lb></lb>lus duplus, &amp;c. </s>
					<s id="N270E3">quod erat demon­<lb></lb>ſtrandum. <lb></lb><figure id="id.026.01.409.1.jpg" xlink:href="026/01/409/1.jpg"></figure></s>
				</p>
			</chap>
			<chap id="N270EE">
				<pb pagenum="376" xlink:href="026/01/410.jpg"></pb>
				<figure id="id.026.01.410.1.jpg" xlink:href="026/01/410/1.jpg"></figure>
				<p id="N270F8" type="head">
					<s id="N270FA"><emph type="center"></emph>LIBER DECIMVS, <lb></lb><emph type="italics"></emph>DE DIVERSIS MOTIONVM, VEL <lb></lb>imprimendi motus rationibus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N27109" type="main">
					<s id="N2710B">HACTENVS explicauimus naturam cau­<lb></lb>ſæ formalis motus, ideſt impetus in <lb></lb>libro primo: proprietates motus natu­<lb></lb>ralis ſecundo: tertio violenti affectio­<lb></lb>nes; </s>
					<s id="N27117">quarto mixti ex pluribus rectis: </s>
					<s id="N2711B"><lb></lb>quinto motum in diuerſis planis conſiderauimus; <lb></lb>ſexto reflexum; ſeptimo circularem; octauo fune­<lb></lb>pendulorum vibrationes; nono mixtum ex circulari, <lb></lb>quæ omnia ſpectant, vel ad cauſam formalem, vel <lb></lb>ad principium intrinſecum, vel ad modum etiam <lb></lb>intrinſecum, vel ad ſpatium, &amp;c. </s>
					<s id="N2712A">iam verò conſi­<lb></lb>deramus diuerſos modos, quibus impetus imprimi <lb></lb>poteſt; poteſt enim mobile proijci, pelli, trahi, percuti, <lb></lb>premi, ſuſtineri, tornari, &amp;c. </s>
					<s id="N27134">de quibus omnibus iam <lb></lb>nobis, hoc decimo libro agendum videtur, vt dein­<lb></lb>de vndecimo de organis motus, &amp; duodecimo de li­<lb></lb>neis tandem agamus. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N27140" type="main">
					<s id="N27142"><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 id="N2714E" type="main">
					<s id="N27150"><emph type="italics"></emph>IMpreſſio eſt productio impetus in exteriore mobili, vel niſus ad illam.<emph.end type="italics"></emph.end><lb></lb>Explicatione multa non indiget hæc definitio; </s>
					<s id="N2715A">dicitur productio <lb></lb>impetus, quia reuerâ quando proijcitur lapis, in eum deriuatur aliquid <pb pagenum="377" xlink:href="026/01/411.jpg"></pb>ab ipſo proijciente mediatè, vel immediatè, cuius vi deinde mouetur; </s>
					<s id="N27165">at­<lb></lb>qui vnus impetus illud ipſum præſtare poteſt, vr conſtat ex dictis, toto, <lb></lb>lib.  1. additum eſt, vel niſus ad illam, vt producitur impetus in omni <lb></lb>pulſione, nec in omni percuſſione; </s>
					<s id="N2716F">cum enim quis pellit ingentem rupem <lb></lb>ſeu percutit pugno; nullum certè producit impetum, niſi aliqua pars <lb></lb>auolet, quæ omnia conſtant ex dictis l.1. </s>
				</p>
				<p id="N27177" type="main">
					<s id="N27179"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27186" type="main">
					<s id="N27188"><emph type="italics"></emph>Reſiſtentia mobilis eſt illa ratio, que mobili ineſt, cuius vi vel motum omnem <lb></lb>ipſum mobile ab applicata potentia renuit vel tardiorem tantum permittit.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27191" type="main">
					<s id="N27193">Quid verò ſit illa ratio, &amp; in quo poſita ſit explicabimus infrà; </s>
					<s id="N27197">nihil <lb></lb>enim aliud nomine reſiſtentiæ intelligi poteſt, quàm id, quo mobile re­<lb></lb>ſiſtit motui; </s>
					<s id="N2719F">reſiſtere autem motui, eſt vel totum impedire motum vel <lb></lb>eius partem, per quid autem reſiſtat, &amp; propter quid dicemus infrà: ſatis <lb></lb>eſt dixiſſe, quid ſit reſiſtere &amp; reſiſtentia. </s>
				</p>
				<p id="N271A7" type="main">
					<s id="N271A9"><emph type="center"></emph><emph type="italics"></emph>Hypotheſis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N271B5" type="main">
					<s id="N271B7">Lapis 20. librarum difficiliùs proijcitur, vel ſuſtinetur ab eadem po­<lb></lb>tentiâ, quàm lapis vnius libræ; hypotheſis certa eſt. </s>
				</p>
				<p id="N271BD" type="main">
					<s id="N271BF">Axiomata nulla præmittemus cum Theoremata lib.  1. demonſtrata <lb></lb>ſufficiant. </s>
				</p>
				<p id="N271C4" type="main">
					<s id="N271C6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N271D3" type="main">
					<s id="N271D5"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena ſuſtentationis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N271DC" type="main">
					<s id="N271DE">Primò, vt manus ſuſtineat pondus in ſitu horizontali producit in ſe <lb></lb>impetum; </s>
					<s id="N271E4">quia, cùm brachium libero motu librari poſſit, ſuo pondere <lb></lb>deſcenderet, niſi aliquod reſiſteret; </s>
					<s id="N271EA">ſed ipſum brachium non reſiſtit; </s>
					<s id="N271EE">igi­<lb></lb>tur aliquid quod brachio ineſt; igitur impetus. </s>
				</p>
				<p id="N271F4" type="main">
					<s id="N271F6">Secundò, impetus, quem ipſa potentia motrix in brachio producit, <lb></lb>non eſt maior impetu grauitationis ipſius brachij; </s>
					<s id="N271FC">quia alioquin præua­<lb></lb>leret; igitur brachium aſcenderet, contra hypotheſim. </s>
				</p>
				<p id="N27202" type="main">
					<s id="N27204">Tertiò, ille impetus non eſt etiam minor; </s>
					<s id="N27208">quia alioqui impetus gra­<lb></lb>uitationis præualeret; igitur brachium deſcenderet, contra hypo­<lb></lb>theſim. </s>
				</p>
				<p id="N27210" type="main">
					<s id="N27212">Quartò, hinc ſequitur eſſe æqualem, cùm ſit per n.1.nec ſit maior per <lb></lb>2.nec minor per 3. ſequitur neceſſariò eſſe æqualem. </s>
				</p>
				<p id="N27217" type="main">
					<s id="N27219">Quintò, ſingulis inſtantibus impetus productus priore inſtanti de­<lb></lb>ſtruitur; probatur, quia quotieſcumque ad lineas oppoſitas ex diame­<lb></lb>tro determinantur duo impetus æquales, deſtruuntur, ſi deſtrui poſſunt <lb></lb>per Theorema 123.lib.1. at verò impetus innatus deſtrui non poteſt, per <lb></lb>Theorema 77. libro 2. igitur deſtruitur productus à potentia mo­<lb></lb>trice. </s>
				</p>
				<p id="N27227" type="main">
					<s id="N27229">Sextò, propter molliores partes organi, v. g. muſculorum, neruo­<lb></lb>rum, impetus naturalis aliquem ſemper effectum ſortitur, com­<lb></lb>preſſionis, diuiſionis, tenſionis: </s>
					<s id="N27235">ratio eſt, quia anima non produ-<pb pagenum="378" xlink:href="026/01/412.jpg"></pb>cit impetum in omnibus immediatè; vt patet; </s>
					<s id="N2723E">alioquin etiam reſectis <lb></lb>neruis brachij poſſet brachium moueri; </s>
					<s id="N27244">igitur illæ partes, quæ tan­<lb></lb>tùm habent impetum grauitationis deorſum, quaſi pugnant cum <lb></lb>aliis, quæ impetum grauitationis habent impetum ab ima; </s>
					<s id="N2724C">quemad­<lb></lb>modum enim, cum aliquod pondus humeris incubat, vel manui; ſen­<lb></lb>tio ponderis vim, cuius effectus rationem afferemus paulò pòſt, ita <lb></lb>prorſus partes, quæ immediatè ab anima impetum non accipiunt, alias <lb></lb>deprimunt. </s>
				</p>
				<p id="N27258" type="main">
					<s id="N2725A">Septimò, ſingulis inſtantibus anima producit impetum in organo; <lb></lb>quia ſingulis deſtruitur per num. </s>
					<s id="N27260">5. igitur cùm reſiſtat continuò graui­<lb></lb>tationi, tùm ipſius organi, tùm partium coniunctarum cum organo, <lb></lb>ſiue ſint animatæ, ſiue inanimes, debet adeſſe cauſa huius reſiſtentiæ; <lb></lb>igitur nouus impetus, cùm prior deſtruatur. </s>
				</p>
				<p id="N2726A" type="main">
					<s id="N2726C">Octauò, impetus productus in organo, quod mouetur, produ­<lb></lb>cit impetum in aliis partibus cum ipſo organo coniunctis; pro­<lb></lb>batur; </s>
					<s id="N27274">cum enim ſingulæ partes mouentur, ſingulæ habent impe­<lb></lb>tum, ſed ſingulæ impetum ab anima non habent immediatè, vt <lb></lb>conſtat; </s>
					<s id="N2727C">igitur aliquæ partes habent impetum ab impetu ipſius <lb></lb>organi: </s>
					<s id="N27282">ſecundò eodem prorſus modo moueo vnguem, quo lapil­<lb></lb>lum; </s>
					<s id="N27288">ſed lapillus, quem moueo manu, non accipiet impetum imme­<lb></lb>diatè ab anima, ſed ab organo, vel potiùs ab impetu organi; igitur nec <lb></lb>vnguis, nec aliæ partes, quæ non ſunt organum motus, licèt cum eo <lb></lb>coniunctæ ſint. </s>
				</p>
				<p id="N27292" type="main">
					<s id="N27294">Nonò, cum verò organum non mouetur.v.g.manus quantumuis ex­<lb></lb>tenſa, vel erecta, non producit impetum in aliis partibus coniun­<lb></lb>ctis, licèt animatis; probatur primò, fruſtrà produceretur, cùm <lb></lb>impediri poſſit earum motus deorſum ſine impetu, alioquin menſa, <lb></lb>quæ ſuſtinet pondus, produceret in eo impetum, quod eſt ridicu­<lb></lb>lum. </s>
					<s id="N272A2">Secundò, quia ſi impetus organi producit impetum in partibus <lb></lb>vnitis, quo eas quaſi reducit ſurſum; </s>
					<s id="N272A8">igitur impetus grauitationis <lb></lb>partium vnitarum producit etiam impetum deorſum in organo; <lb></lb>immò daretur proceſſus in infinitum, de quo paulò pòſt. </s>
				</p>
				<p id="N272B0" type="main">
					<s id="N272B2">Decimò, cum manus ſuſtinet aliquod pondus immobiliter, non <lb></lb>producit in eo impetum; </s>
					<s id="N272B8">Primò, quia, ſi non producitur impe­<lb></lb>tus in alijs partibus vnitis, licèt animatis, multò minùs in alijs; </s>
					<s id="N272BE"><lb></lb>Secundò, quia eodem modo ſuſtinetur pondus à manu, quo ab alio <lb></lb>corpore inanimo, v. g. à menſa; </s>
					<s id="N272C9">ſed hæc non producit impetum in <lb></lb>pondere, quod ſuſtinet, vt dicam paulò pòſt; </s>
					<s id="N272CF">Tertiò, quia fruſtrà pro­<lb></lb>duceretur; </s>
					<s id="N272D5">quia modò manus ſuſtinens ſtet immobilis; haud dubiè etiam <lb></lb>ſublato omni extrinſeco impetu à pondere adhuc ſuſtinebitur. </s>
				</p>
				<p id="N272DB" type="main">
					<s id="N272DD">Dices; </s>
					<s id="N272E0">igitur fruſtrà produceretur impetus in manu; </s>
					<s id="N272E4">Reſp. negando <lb></lb>quia niſi potentia motrix produceret impetum in manu, ab ipſo pon­<lb></lb>dere deprimeretur; igitur non eſt fruſtrà omninò ille impetus. </s>
				</p>
				<p id="N272EC" type="main">
					<s id="N272EE">Dices, non habet motum; </s>
					<s id="N272F2">igitur eſt fruſtrà; </s>
					<s id="N272F6">Reſp. omnem impetum <lb></lb>non eſſe fruſtrà, licèt careat motu, vt patet in ipſo impetu innato, <pb pagenum="379" xlink:href="026/01/413.jpg"></pb>cuius duplex eſt effectum; </s>
					<s id="N27301">ſcilicet grauitatio, &amp; motus, vt aliàs iam in­<lb></lb>dicauimus; </s>
					<s id="N27307">ſimiliter impetus productus à potentia motrice, in ſuo or­<lb></lb>gano habere poteſt duplicem effectum; </s>
					<s id="N2730D">primus eſt motus; </s>
					<s id="N27311">ſecundus eſt <lb></lb>niſus ſeu conatus oppoſitus extrinſeco motui; </s>
					<s id="N27317">quemadmodum enim in­<lb></lb>natus ſemper habet motum, niſi impediatur ab alio corpore, ita &amp; im­<lb></lb>petus organi potentiæ motricis, nec eſt magna difficultas; immò cla­<lb></lb>riſſima vtriuſque potentiæ analogia. </s>
				</p>
				<p id="N27321" type="main">
					<s id="N27323">Vndecimò, hinc benè explicatur, quomodo defatigetur tenſum bra­<lb></lb>ſiue coniunctum ſiue coniunctum; </s>
					<s id="N27329">ſit cum extrinſeco <expan abbr="põdere">pondere</expan>, ſiue <expan abbr="cũ">cum</expan> pro­<lb></lb>pria tantùm grauitate; </s>
					<s id="N27337">quia partes aliquæ tendunt deorſum, aliæ verò ſur­<lb></lb>ſum; </s>
					<s id="N2733D">hinc ſemper fit aliqua tenſio; igitur aliqua diuiſio; </s>
					<s id="N27341">igitur dolor, ſic <lb></lb>enim tenditur funis à <expan abbr="põdere">pondere</expan> pendulo, pondus verò <expan abbr="incubãs">incubans</expan> tùm aliquas <lb></lb>partes premit, tùm alias maximè diſtrahit, in quo non eſt difficultas; </s>
					<s id="N27351">ſi <lb></lb>autem manus incubet menſæ, v. g. &amp; pondus manui fit tantùm com­<lb></lb>preſſio partium, quæ pro mollitie facilè cedunt &amp; ſeparantur; </s>
					<s id="N2735D">igitur <lb></lb>pondus producit impetum in manu &amp; neruis; alioquin nulla eſſet ten­<lb></lb>ſio, neque compreſſio. </s>
				</p>
				<p id="N27365" type="main">
					<s id="N27367">Duodecimò, hinc benè colligo non produci impetum à potentia mo­<lb></lb>trice in toto organo; </s>
					<s id="N2736D">quia ſi hoc eſſet, omnes partes ſtarent immobili­<lb></lb>ter; </s>
					<s id="N27373">eſſet enim hic impetus æqualis impetui grauitationis, tùm organi, <lb></lb>tùm ponderis; </s>
					<s id="N27379">tùm aliarum partium, cum organo coniunctarum; </s>
					<s id="N2737D">igitur <lb></lb>nulla eſſet defatigatio; quia tam facilè anima produceret impetum, <lb></lb>2°.inſtanti, 3°, 4°. </s>
					<s id="N27385">&amp;c. </s>
					<s id="N27388">quàm 1°; </s>
					<s id="N2738B">ſed nulla eſt defatigatio pro 1°; </s>
					<s id="N2738F">igitur <lb></lb>nulla eſſet in reliquis, quod tamen eſt contra hypotheſim; </s>
					<s id="N27395">immò poſſe­<lb></lb>mus liberè moueri per medium aëra; cum enim 1°. </s>
					<s id="N2739B">inſtanti poſſemus <lb></lb>producere impetum maiorem impetu grauitationis, vt patet; </s>
					<s id="N273A1">certè non <lb></lb>deſtrueretur totus, 2° inſtanti; igitur cum 2°. </s>
					<s id="N273A7">inſtanti poſſet æqualis <lb></lb>1°. </s>
					<s id="N273AC">impetus produci; </s>
					<s id="N273B0">ſemper intenderetur; </s>
					<s id="N273B4">igitur facilè moueremur, <lb></lb>quod abſurdum eſt; </s>
					<s id="N273BA">igitur poſſumus quidem ſaltu ſurſum totum cor­<lb></lb>pus attollere; </s>
					<s id="N273C0">at cùm in omnibus partibus potentia motrix non pro­<lb></lb>ducat impetum immediatè; </s>
					<s id="N273C6">certè deorſum tendunt, motu naturaliter <lb></lb>accelerato, vnde tandem organum ipſum deorſum ſecum trahunt; ſed <lb></lb>de his aliàs plura, cum de potentia progreſſiua. </s>
				</p>
				<p id="N273CE" type="main">
					<s id="N273D0">Decimotertiò, quando pondus ſuſtinetur à plano immobili, v. g. à <lb></lb>menſa, non producitur in eo impetus ſurſum à menſa; quia impetus <lb></lb>producitur tantùm ad extra ab alio impetu, per Th.42. l.1. ſed nullus eſt <lb></lb>impetus ſurſum in menſa, vt patet. </s>
				</p>
				<p id="N273DE" type="main">
					<s id="N273E0">Decimoquartò, pondus non producit impetum in ipſa menſa, niſi vel <lb></lb>tota menſa, vel aliquæ eius partes moueantur, vel comprimantur, vel <lb></lb>dilatentur; </s>
					<s id="N273E8">quod reuera ferè ſemper accidit; </s>
					<s id="N273EC">quia cum ſit perpetuum <lb></lb>corporum effluuium, multæ partes ſeparantur vi ponderis, quæ ab iis <lb></lb>corpuſculis, quæ auolarunt, continebantur; </s>
					<s id="N273F4">ſic tandem poſt multos an­<lb></lb>nos trabs lignea incubanti ponderi cedit; </s>
					<s id="N273FA">ſic lapis ſenſim terram de­<lb></lb>primit, ſic globus plumbeus diutiùs molæ incubans, ſibi quaſi foſſulam <lb></lb>fingit, depreſſis duntaxat mollioribus partibus; </s>
					<s id="N27402">quod certè fit vel in-<pb pagenum="380" xlink:href="026/01/414.jpg"></pb>ſenſibili motu vel per ſeparationem aliquarum partium; </s>
					<s id="N2740B">cum enim da­<lb></lb>to quocumque motu, dari poſſit tardior; certè poteſt eſſe continuus <lb></lb>motus, quo per centum annos, vix latus vnguis acquiratur, quod nemo <lb></lb>Philoſophus mirabitur, qui naturam motus circularis probè intelle­<lb></lb>xerit. </s>
				</p>
				<p id="N27417" type="main">
					<s id="N27419">Decimoquintò, brachium omninò explicatum difficiliùs ſuſtinet <lb></lb>pondus, quam contractum; </s>
					<s id="N2741F">quia maius eſt explicati momentum, vt pa­<lb></lb>tet; eſt enim quaſi longior vectis circa extremum humerum rotatus. </s>
				</p>
				<p id="N27425" type="main">
					<s id="N27427">Obijceret aliquis, contra ea quæ diximus num. </s>
					<s id="N2742A">14. ſit globulus libram <lb></lb>pendens incubans menſæ 99. librarum; </s>
					<s id="N27430">haud dubiè qui menſam pon­<lb></lb>derat, centum librarum pondus ſuſtinet; igitur globulus producit in <lb></lb>menſa impetum. </s>
					<s id="N27438">Reſp. neg. <expan abbr="conſeq.">conſeque</expan> nam ideò ſentitur pondus 100. li­<lb></lb>brarum; quia vtrumque pondus grauitatione communi in ſuppoſitam <lb></lb>grauitat manum. </s>
				</p>
				<p id="N27445" type="main">
					<s id="N27447"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27454" type="main">
					<s id="N27456"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena detentionis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2745D" type="main">
					<s id="N2745F">Primò, aliquis detinetur, ſimul, &amp; ſuſtinetur; </s>
					<s id="N27463">ſit globum pendulum <lb></lb>fune, cuius altera extremitas manu tenetur immobili; </s>
					<s id="N27469">nullus autem <lb></lb>producitur impetus in ipſo globo, quo ſurſum, quaſi attollatur; </s>
					<s id="N2746F">quod <lb></lb>probatur, iiſdem omninò rationibus, quibus probauimus in ſuperiori <lb></lb>Theo. de ſuſtentatione; </s>
					<s id="N27479">ipſa tamen chorda, ſi vel brachio, vel digito cir­<lb></lb>cumuoluatur, ſua vbique inurit veſtigia; </s>
					<s id="N2747F">premit enim molliorem car­<lb></lb>nem, &amp; neruos; huic aliqua diuiſio; hinc dolor: nec in hoc ſingularis <lb></lb>eſt difficultas. </s>
				</p>
				<p id="N27487" type="main">
					<s id="N27489">Secundò, retinetur aliquod mobile, per quamlibet lineam, vel fune, <lb></lb>vel vnco, vel manu, v.g. auolans auis filo, indomitus equus fræno, diſce­<lb></lb>dens homo pallio vel manu; </s>
					<s id="N27493">hoc poſito, non producitur impetus à reti­<lb></lb>nente in mobili retento per ſe; </s>
					<s id="N27499">quia perinde ſe habet, atque ſi rupes im­<lb></lb>mobilis retineret annulo ferreo, vel vnco; </s>
					<s id="N2749F">ſed rupes non producit im­<lb></lb>petum in eo corpore, quod retinet, dixi per ſe; </s>
					<s id="N274A5">nam ſi partes aliquæ <lb></lb>ſeparari poſſint vel dilatari; haud dubiè producitur in iis impetus. </s>
				</p>
				<p id="N274AB" type="main">
					<s id="N274AD">Tertiò, hinc ſi duo retineant ſe ſe inuicem vel fune, vel annulo, vel <lb></lb>cylindro, multus impetus producitur ab vtroque in altero; </s>
					<s id="N274B3">quippe ten­<lb></lb>duntur nerui &amp; muſculi, ex qua tenſione multæ partes ſeparantur; </s>
					<s id="N274B9">hinc <lb></lb>dolor &amp; defatigatio; </s>
					<s id="N274BF">igitur producitur impetus, quod certè clariſſimè <lb></lb>ſequitur ex noſtris principiis; </s>
					<s id="N274C5">cum enim potentia motrix alicui mobili <lb></lb>applicatur, quod ſimul totum mouere non poteſt propter reſiſtentiam <lb></lb>vel ipſius molis, vel impetus contrarij; </s>
					<s id="N274CD">ſi fortè aliqua pars amoueri po­<lb></lb>teſt, &amp; ſeparari ab aliis in eam potentia applicata ſuas vires exerit; quo­<lb></lb>modo verò rumpatur funis, vtrimque tractus, dicemus paulò pòſt, cum <lb></lb>de tractione. </s>
				</p>
				<p id="N274D7" type="main">
					<s id="N274D9">Quartò, retinetur aliquod mobile immobiliter in plano decliui, id­<lb></lb>que duobus modus; primò, quaſi trahendo: </s>
					<s id="N274DF">ſecundò, quaſi pellendo, nul­<lb></lb>lus impetus producitur per ſe in mobili retento à retinente; </s>
					<s id="N274E5">quod pro-<pb pagenum="381" xlink:href="026/01/415.jpg"></pb>batur eodem modo, quo ſuprà; </s>
					<s id="N274EE">per accidens autem producitur propter <lb></lb><expan abbr="eãdem">eandem</expan> rationem vnde ſuprà; </s>
					<s id="N274F7">ſuppono autem nullo modo vel trahi <lb></lb>ſurſum, vel pelli vtrimque: porrò retinetur ab æquali potentia, quod <lb></lb>iam alibi demonſtrauimus lib.5. in quo etiam fusè explicuimus diuer­<lb></lb>ſas lineas, quibus potentia applicari poteſt. </s>
				</p>
				<p id="N27501" type="main">
					<s id="N27503"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27510" type="main">
					<s id="N27512"><emph type="italics"></emph>Hinc facilè explicantur omnia phœnomena lationis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27519" type="main">
					<s id="N2751B">Primò, lationem appello illam impreſſionem, qua potentia motrix <lb></lb>aliquid ſuo organo, mediatè vel immediatè coniunctum ſecum vna de­<lb></lb>fert; </s>
					<s id="N27523">ſic dum quis ambulat, pileum etiam, quo caput tegitur, mouet; ſic <lb></lb>equus rapit, nauis vehit nautam, currus aurigam defert. </s>
				</p>
				<p id="N27529" type="main">
					<s id="N2752B">Secundò, imprimitur impetus in vtroque; probatur facilè; quia <lb></lb>vtrumque mouetur cum eo tamen diſcrimine, quod lator in ſe producit <lb></lb>impetum, qui in mobili delato alium producit. </s>
				</p>
				<p id="N27533" type="main">
					<s id="N27535">Tertiò, impetus latoris æqualis eſt impetui delato, quia vtrique ineſt <lb></lb>æqualis motus; igitur æqualis impetus. </s>
				</p>
				<p id="N2753B" type="main">
					<s id="N2753D">Quartò, hinc cùm nauis imprimat impetum iis omnibus, quæ vehit <lb></lb>æqualem ſuo, non eſt mirum ſi motus qui obſeruantur è naui mobili <lb></lb>tùm in proiectis, tùm in demiſſis, tùm in diſperſis, ſimiles omninò iis <lb></lb>appareant, qui obſeruantur è naui immobili, licèt omninò ſint diſſimi­<lb></lb>les; quæ omnia fusè explicui l.4. </s>
				</p>
				<p id="N27549" type="main">
					<s id="N2754B">Quintò, hinc quæ vehuntur naui non ſeparantur ab ipſa naui, quia <lb></lb>æquali motu feruntur, niſi nauis illicò ſiſtat; </s>
					<s id="N27551">quia impetus prior, non ſta­<lb></lb>tim deſtruitur, quod iam explicuimus alibi; </s>
					<s id="N27557">immò ſeſe aliquando ſub­<lb></lb>trahit equiti; </s>
					<s id="N2755D">quia, ſcilicet, demiſſo vel inflexo tantillùm dorſo, perni­<lb></lb>citer ſeſe eripit; </s>
					<s id="N27563">idem accidit globo, quem in plano horizontali læui­<lb></lb>gato ſuſtines; </s>
					<s id="N27569">ſi enim illicò demittas orbem velociter ductum, vel ſta­<lb></lb>tim ducas reducaſque; haud dubiè globus in eo plano mouebitur. </s>
				</p>
				<p id="N2756F" type="main">
					<s id="N27571">Sextò, quædam humeris &amp; collo, quædam capite, alia manu feruntur, <lb></lb>etiam liquida vaſe contenta; </s>
					<s id="N27577">vas autem ipſum effunditur, ſi motus ali­<lb></lb>qua notabili morula interrumpatur; </s>
					<s id="N2757D">cùm enim ſuperficies aquæ v. g. <lb></lb>in eam partem adhuc moueatur, in quam priùs erat denominata; certe <lb></lb>ſi maior eſt motus, effunditur aqua. </s>
				</p>
				<p id="N27588" type="main">
					<s id="N2758A">Septimò, hinc eſt aliquod artificium, quo ita poſſint in plano hori­<lb></lb>zontali verticali manubrio inſtructo deferri orbes pleni liquore, vt ni­<lb></lb>hil penitus effundatur; </s>
					<s id="N27592">ſi enim ita temperetur brachij motus, vt ſit con­<lb></lb>tinuus &amp; æquabilis, non modò nihil effundetur; </s>
					<s id="N27598">verùm etiam, ne ipſa <lb></lb>quidem ſuperficies liquoris mutabitur; </s>
					<s id="N2759E">vt autem ſit continuus ille bra­<lb></lb>chij motus, &amp; æquabilis; </s>
					<s id="N275A4">debet ita porrigi brachium, ſeu componi cum <lb></lb>inæquali reliqui corporis motu, vt eo aliquando tardior, aliquando ve­<lb></lb>locior ſit; porrò hæc inæqualitas motus progreſſiui procedit ex duplici <lb></lb>illo quaſi gemini crucis arcu, geminoque vtriuſque centro, ſed de hoc <lb></lb>alibi. </s>
				</p>
				<p id="N275B0" type="main">
					<s id="N275B2">Octauò, hinc quò velociùs corpus progredietur minoribuſque, licèt, <pb pagenum="382" xlink:href="026/01/416.jpg"></pb>frequentioribus paſſibus, brachij motus accedit propiùs ad æquabilem; </s>
					<s id="N275BB"><lb></lb>igitur minùs mutatur ſuperficies liquoris vaſe contenti; </s>
					<s id="N275C0">hinc in naui, <lb></lb>quæ velociſſimo motu fertur, ne tremit quidem ſuperficies aquæ, quam <lb></lb>repoſitam quis habet in vaſe; denique quò ſuperficies concaua orbis <lb></lb>ſeu vaſis eſt maioris circuli faciliùs effunditur liquor, quia planum eſt <lb></lb>minus decliue, &amp; minus recedit ab horizontali, &amp; contrà ſi eſt minoris <lb></lb>ſphæræ ſeu circuli, hinc fortè tantus eſt maris æſtus in Oceano, &amp; mo­<lb></lb>dicus valdè in Mediterraneo, ſed de his alibi. </s>
				</p>
				<p id="N275D0" type="main">
					<s id="N275D2">Nonò, his adde amphoras illas aqua, vel lacte ad ſummum vſque <lb></lb>marginem repletas, quas ruſticanæ fœminæ è ſummo capite ita portant, <lb></lb>vt nihil penitus effundatur, quia ſcilicet tenſo collo ambulant, vt capi­<lb></lb>tis motus ad æquabilem propius accedat. </s>
				</p>
				<p id="N275DB" type="main">
					<s id="N275DD">Decimò, non eſt omittendum ille orbis gyrus cum ſcypho pleno; <lb></lb>quod vt melius intelligatur. </s>
					<s id="N275E3">Sit orbis AFEG pendulus filo FA; </s>
					<s id="N275E7">ſit <lb></lb>ſcyphus EDC plenus aqua vel alio liquore, puncto circuli E inſidens, <lb></lb>tùm rotetur orbis circa centrum F; </s>
					<s id="N275EF">haud dubiè, ne gutta quidem aquæ <lb></lb>effundetur; </s>
					<s id="N275F5">ratio eſt, cùm E ſit ſemper punctum oppoſitum centro, mo­<lb></lb>tus F &amp; ſcyphus motu illo circulari maximè pellatur, prematurque ver­<lb></lb>ſus E, aqua ipſa etiam verſus E recipit impetum verſus fundum ſcyphi; </s>
					<s id="N275FD"><lb></lb>qui cùm ſit intenſior natiuo propriæ grauitationis aquæ, non eſt mirum <lb></lb>ſi præualeat, &amp; nihil penitus effundatur in gyro, præſertim cùm partes <lb></lb>omnes aquæ moueantur eo motu, quo in primo ſitu omninò relinquun­<lb></lb>tur; </s>
					<s id="N27608">adde quod licèt impetus innatus tantillùm obeſſet, impeditur ta­<lb></lb>men ab illa vligine, quæ cum aqua commixta eſt, de qua iam ſuprà; </s>
					<s id="N2760E"><lb></lb>quod autem ſcyphus impellatur verſus E, patet clariſſimè in funda, in <lb></lb>qua lapis circumagitur, ſed de funda infrà, cum de proiectione; tunc <lb></lb>enim rem iſtam demonſtrabimus. </s>
				</p>
				<p id="N27617" type="main">
					<s id="N27619">Vndecimò, vt feratur cylindrus humeris commodiùs in ſitu eſſe de­<lb></lb><arrow.to.target n="note3"></arrow.to.target><lb></lb>bet, vt ſuprà horizontalem eleuetur ad angulum 45. grad. ſit enim 60. <lb></lb>grad ſitque cylindrus AF, cuius centrum grauitatis C incubans puncto <lb></lb>humeri C, tunc humerus ſuſtinet totum pondus abſolutum cylindri, <lb></lb>&amp; manus nihil: </s>
					<s id="N2762B">ſi verò manu erectum ſuſtineatur in DG; haud du­<lb></lb>biè manus totum ſuſtinet pondus abſolutum, humerus nihil, ſi ſuſti­<lb></lb>neatur KCI in C, vel NCL in C, maius pondus ſuſtinebitur propter <lb></lb>rationem vectis de quo in lib.  ſequenti. </s>
					<s id="N27635">Denique, ſi ſuſtineatur in HCE <lb></lb>ad angulum HCA, 60. grad. humerus ſuſtinet vt BH, manus vt EI; </s>
					<s id="N2763D"><lb></lb>ergo non diſtribuitur pondus æqualiter humero &amp; manui; igitur com­<lb></lb>modiùs fieri poteſt, ſi æqualiter diſtribuitur, quod vt fiat debet eſſe ad <lb></lb>eleuationem anguli 45. ſed hæc pertinent ad libram, &amp; vectem de quibus <lb></lb>agemus infrà, etiam ſupra lib.5. ſæpiùs indicauimus. </s>
				</p>
				<p id="N27648" type="margin">
					<s id="N2764A"><margin.target id="note3"></margin.target>b <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end>28 <lb></lb><emph type="italics"></emph>Tab.<emph.end type="italics"></emph.end>4.</s>
				</p>
				<p id="N2765C" type="main">
					<s id="N2765E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2766B" type="main">
					<s id="N2766D"><emph type="italics"></emph>Aliquod mobile graue dimittitur deorſum multis modis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27674" type="main">
					<s id="N27676">Primò, per lineam perpendicularem, &amp; tunc eſt motus purè natura­<lb></lb>lis, ſimulque omnes partes mobilis dimittuntur. </s>
				</p>
				<pb pagenum="383" xlink:href="026/01/417.jpg"></pb>
				<p id="N2767F" type="main">
					<s id="N27681">Secundò, per planum inclinatum tuncque ſi globus eſt, rotatur, quia <lb></lb>tollitur æquilibrium. </s>
				</p>
				<p id="N27686" type="main">
					<s id="N27688">Tertiò, ita dimittitur globus, vt primò per manum quaſi decliuem ca­<lb></lb>dat, tuncque ſimiliter rotatur propter <expan abbr="eãdem">eandem</expan> rationem. </s>
				</p>
				<p id="N27691" type="main">
					<s id="N27693">Quartò, dimittitur funependulum, &amp; tunc deſcendit per arcum. </s>
				</p>
				<p id="N27696" type="main">
					<s id="N27698">Quintò, dimittitur cylindrus, cuius altera extremitas nititur ſolo, &amp; <lb></lb>tunc deſcendit etiam per arcum. </s>
				</p>
				<p id="N2769D" type="main">
					<s id="N2769F">Sextò, dimittitur baculus; </s>
					<s id="N276A2">ſed inæqualiter, ita vt altera eius extremitas <lb></lb>cadat, antequam alia dimittatur, &amp; tunc etiam circumagitur baculus; ſed <lb></lb>hæc ſunt facilis. </s>
				</p>
				<p id="N276AA" type="main">
					<s id="N276AC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N276B9" type="main">
					<s id="N276BB"><emph type="italics"></emph>Aliquotâ mobile proiectum excipitur manu multis modis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N276C2" type="main">
					<s id="N276C4">Primò, firma &amp; fixa manu, in quam cadit eodem modo, quo caderet <lb></lb>in parietem, vt patet. </s>
				</p>
				<p id="N276C9" type="main">
					<s id="N276CB">Secundò, manu repellente, tunque eſt maior ictus. </s>
				</p>
				<p id="N276CE" type="main">
					<s id="N276D0">Tertiò, manu ſenſim ſubſidente, vt fallat ictum; </s>
					<s id="N276D4">ſic lapidem ſurſum <lb></lb>proiectum cadentem ita excipimus manu, immò &amp; maiorem globum, <lb></lb>vt vix vllum ictum ſentiamus; </s>
					<s id="N276DC">quod vt fiat, manus retroagi debet, non <lb></lb>quidem pari velocitate cum globo, ſed paulò tardiore motu, vt ſcilicet <lb></lb>modicum impetum imprimat globus; </s>
					<s id="N276E4">ſi enim manus pari velocitate <lb></lb>moueretur, nullum prorſus impetum imprimeret globus; </s>
					<s id="N276EA">ſi verò non <lb></lb>moueretur, ſed omninò manus quieſceret, maximum ictum exceptus <lb></lb>globus infligeret; </s>
					<s id="N276F2">ſi verò moueatur ſed paulò tardius aliquid impetus <lb></lb>imprimetur ſingulis inſtantibus, donec tandem totus ictus extingua­<lb></lb>tur; </s>
					<s id="N276FA">adde quod mollities manus ad extinguendum ictum potiſſimum <lb></lb>confert; analogiam habes in lana, quæ tormentorum vim penitus <lb></lb>eneruat. </s>
				</p>
				<p id="N27702" type="main">
					<s id="N27704">Quartò, vt longiùs repellatur pila, ſecundus modus adhiberi debet <lb></lb>eritque motus mixtus ex directo &amp; reflexo. </s>
				</p>
				<p id="N27709" type="main">
					<s id="N2770B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27718" type="main">
					<s id="N2771A"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena tractionis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27721" type="main">
					<s id="N27723">Primò, trahitur mobile per productionem impetus; </s>
					<s id="N27727">nec enim po­<lb></lb>tentia motrix, quæ reuerâ cauſa eſt tractionis, quidquam aliud produce­<lb></lb>re poteſt; </s>
					<s id="N2772F">præterea quod trahitur, verè mouetur; igitur per impetum, <lb></lb>ſic differt tractio à mera detentione, de qua ſuprà. </s>
				</p>
				<p id="N27735" type="main">
					<s id="N27737">Secundò, hinc tractio eſt actio potentiæ motricis, qua mobile ipſum <lb></lb>propiùs accedit ad motorem; </s>
					<s id="N2773D">nam motor ad ſe trahit mobile; </s>
					<s id="N27741">igitur <lb></lb>mobile accedit ad motorem: </s>
					<s id="N27747">quod tantùm dictum ſit de tractione di­<lb></lb>recta; nam per reflexam, ipſe motor ad mobile accedit, de qua <lb></lb>infrà. </s>
				</p>
				<p id="N2774F" type="main">
					<s id="N27751">Tertiò, quando trahitur aliquod mobile, impetus producitur in om­<lb></lb>nibus illius partibus; </s>
					<s id="N27757">probatur, quia omnes mouentur; igitur omnes <lb></lb>recipiunt impetum. </s>
					<s id="N2775D">Secundò, quia ſi tantùm in vna produci impetum <pb pagenum="384" xlink:href="026/01/418.jpg"></pb>oporteret, vt reliquæ etiam mouerentur à quacumque potentia quodli­<lb></lb>bet mobile trahi poſſet, quod eſt abſurdum. </s>
				</p>
				<p id="N27767" type="main">
					<s id="N27769">Dices, alias partes reſiſtere. </s>
					<s id="N2776C">Reſp. igitur vt moueantur, ſuperari debet <lb></lb>illarum reſiſtentia; </s>
					<s id="N27772">igitur per aliquid de nouo proctum; </s>
					<s id="N27776">igitur per <lb></lb>impetum: </s>
					<s id="N2777C">immò non producitur in vna, niſi producatur in aliis; </s>
					<s id="N27780"><lb></lb>alioquin fruſtrà eſſet ille impetus, cui nullus effectus reſpon­<lb></lb>deret; </s>
					<s id="N27787">igitur ſi deſtruitur, quando fruſtrà eſſet, ſi conſeruaretur; </s>
					<s id="N2778B">ita <lb></lb>etiam non producitur quando fruſtrà eſſet, ſi produceretur; eſt enim <lb></lb>par vtrimque ratio. </s>
				</p>
				<p id="N27793" type="main">
					<s id="N27795">Quartò, hinc licèt trahatur ingens rupes, non propterea mouetur, <lb></lb>quia non poteſt impetus produci in omnibus illius partibus ab applica­<lb></lb>ta potentia; igitr in nulla per Th.33.l.1. </s>
				</p>
				<p id="N2779D" type="main">
					<s id="N2779F">Dices, eſt cauſa neceſſaria applicata. </s>
					<s id="N277A2">Reſp. eſſe quidem applicatam, ſed <lb></lb>eſſe impeditam propter maximam rupis reſiſtentiam, quam debiliores <lb></lb>potentiæ vires ſuperare non poſſunt. </s>
				</p>
				<p id="N277A9" type="main">
					<s id="N277AB">Quintò, hinc vna pars tracta non ſequitur aliam vltrò; </s>
					<s id="N277AF">ſi enim vltrò <lb></lb>ſequeretur minima potentia, ſufficeret ad trahendum maximum pondus; <lb></lb>præterea ſingulæ partes mouentur per impetum. </s>
				</p>
				<p id="N277B7" type="main">
					<s id="N277B9">Diceret aliquis, impetus productus in vna parte producit impetum <lb></lb>in alia. </s>
					<s id="N277BE">Reſp. negando; alioquin minima potentia quodlibet pondus <lb></lb>moueret contra experientiam. </s>
				</p>
				<p id="N277C3" type="main">
					<s id="N277C5">Dices, impetus vnius corporis producit impetum in alio, à quo eius <lb></lb>motus impeditur; igitur impetus vnius partis producit impetum in <lb></lb>alia, à qua eius motus impeditur. </s>
					<s id="N277CD">Reſp. impetum, qui reuerâ alicui <lb></lb>corpori ineſt, hoc ipſum præſtare; </s>
					<s id="N277D3">at impetus non producitur in vna <lb></lb>parte mobilis, niſi ſimul in aliis producatur; </s>
					<s id="N277D9">vel enim producitur in <lb></lb>omnibus, vel in nulla; </s>
					<s id="N277DF">hinc colliges quantum abſurdum ſequeretur, <lb></lb>niſi hoc eſſet; </s>
					<s id="N277E5">quia perpetua eſſet impetus productio, &amp; minimus im­<lb></lb>petus totam ipſam terram moueret; </s>
					<s id="N277EB">vide quæ diximus ſuper ea re toto <lb></lb>lib.1. nec enim totus impetus motoris producit totum ſuum effectum <lb></lb>in vnico puncto mobilis, quod ridiculum dictu eſt; </s>
					<s id="N277F3">alioquin produ­<lb></lb>ceretur impetus intenſiſſimus; </s>
					<s id="N277F9">igitur in pluribus; igitur in omnibus, <lb></lb>quæ ſimul moueri debent, vel in multa. </s>
				</p>
				<p id="N277FF" type="main">
					<s id="N27801">Diceret aliquis; </s>
					<s id="N27804">quando mouetur corpus equi, mouetur etiam ani­<lb></lb>ma; </s>
					<s id="N2780A">igitur ſine impetu; </s>
					<s id="N2780E">igitur per impetum corporis; </s>
					<s id="N27812">igitur nomine <lb></lb>tantùm vnionis; </s>
					<s id="N27818">igitur pars corporis alteri vnita etiam ſine impetu, <lb></lb>ſcilicet per impetum alterius moueri poteſt: hanc difficultatem iam <lb></lb>ſoluimus ſuprà l.1.Th.38.Cor.12. </s>
				</p>
				<p id="N27820" type="main">
					<s id="N27822">Sextò, producitur impetus æqualis in omnibus partibus, quod trahi­<lb></lb>tur motu recto; </s>
					<s id="N27828">quia ſcilicet motus eſt æqualis; igitur &amp; impetus. </s>
				</p>
				<p id="N2782C" type="main">
					<s id="N2782E">Septimò, funis trahi poteſt diuerſimodè. </s>
					<s id="N27831">Primò, ſi altera eius extre­<lb></lb>mitas annulo, ſeu clauo immobili affixa ſit; </s>
					<s id="N27837">alteri verò applicetur po­<lb></lb>tentia, vel pondus; ſiue ſit in ſitu horizontali, ſiue in verticali. </s>
					<s id="N2783D">Secundò, <lb></lb>ſi vtrique extremitati applicetur pondus vel alia potentia motrix. </s>
					<s id="N27842"><lb></lb>Tertiò, ſi vtraque extremitas clauo immobiliter affigatur in ſitu hori-<pb pagenum="385" xlink:href="026/01/419.jpg"></pb>zontali, admoueaturque pondus, ſeu potentia alicui chordæ puncto <lb></lb>deorſum trahens: </s>
					<s id="N2784E">denique ſi ponticulo maximè attollatur, &amp; tendatur <lb></lb>chorda poſita in priori ſitu; </s>
					<s id="N27854">ſi primò, rumpetur chorda per ſe in ea ex­<lb></lb>tremitate, quæ immobiliter clauo affigitur; </s>
					<s id="N2785A">ſi tertio &amp; quarto in ea <lb></lb>parte, in qua vel deprimitur, vel attollitur: dixi per ſe, quia per acci­<lb></lb>dens ſecus accidit, vt reuerâ ſæpè fit, vel propter inflexionem nodi, vel <lb></lb>aliquas partes debiliores, vel preſſionem maiorem cum tenſione con­<lb></lb>iunctam &amp;c. </s>
					<s id="N27866">ſed quia hæc phœnomena pertinent partim ad tenſionem, <lb></lb>&amp; compreſſionem, partim ad reſiſtentiam corporum, de quibus agemus <lb></lb>Tomo ſequenti; </s>
					<s id="N2786E">certè hoc loco demonſtrari non poſſunt; </s>
					<s id="N27872">igitur ſatis <lb></lb>eſt modò indicaſſe huius demonſtrationis locum, qui talis eſt: inter il­<lb></lb>las duas partes fieri debet diuiſio chordæ, quarum vna reuerâ trahitur, <lb></lb>alia verò non mouetur, vel quarum vtraque mouetur ſed in partes op­<lb></lb>poſitas, quod nemo negabit. </s>
					<s id="N2787E">Et hoc principio hæc omnia, demonſtrari <lb></lb>poſſunt; </s>
					<s id="N27884">ſed de his omnibus ſuo loco fusè agemus; hæc enim vberri­<lb></lb>mam demonſtrationum ſegetem dabunt, præſertim ſi comparentur inter <lb></lb>ſe omnes chordarum affectiones, v.g. materia, figura, pondus, longitudo, <lb></lb>craſſities, ſitus, diuerſa potentiæ applicatio. </s>
				</p>
				<p id="N27890" type="main">
					<s id="N27892">Octauò, quando corpus trahitur fune, quò funis eſt longior per ſe, <lb></lb>difficiliùs trahitur; </s>
					<s id="N27898">ratio eſt, quia funis tantæ longitudinis eſſe poteſt, <lb></lb>vt ne ipſe quidem ſine pondere trahi poſſit; </s>
					<s id="N2789E">igitur quâ proportione <lb></lb>erit breuior dum applicari poſſit potentia, faciliùs trahet, dixi per ſe; </s>
					<s id="N278A4"><lb></lb>quia funis longior, cuius plures partes ſunt, maiorem patitur tenſio­<lb></lb>nem; </s>
					<s id="N278AB">hinc vt partes ſeſe reducant corpus ipſum adducunt; </s>
					<s id="N278AF">adde quod, <lb></lb>quò aliquod corpus magis tenditur, maioris impetus eſt capax, quia <lb></lb>priori remanenti qui non eſt fruſtrà, quia ſuum effectum habet, ſecun­<lb></lb>dus accedit à ſecundo niſu, igitur, quando dico corpus trahi faciliùs <lb></lb>breuiori fine, nullam habeo rationem tenſionis; quæ certè facere po­<lb></lb>teſt, dum funis non ſit tantæ longitudinis, vt corpus faciliùs trahatur <lb></lb>propter illa duo capita, quæ indicauimus. </s>
				</p>
				<p id="N278BF" type="main">
					<s id="N278C1">Nonò, hinc vno fune faciliùs trahitur corpus, quàm duobus. </s>
					<s id="N278C4">Primò, <lb></lb>quia pluribus partibus funis diſtribuitur impetus; </s>
					<s id="N278CA">igitur eò minus ſin­<lb></lb>gulæ habent, quò plures ſunt; ſecundò, quia cum vnus eſt funis, eſt <lb></lb>maior tenſio, quæ iuuat corporis tracti motum. </s>
					<s id="N278D2">Tertiò, quia ſi ſunt duo <lb></lb>funis vel diuerſis partibus corporis tracti affliguntur, vel vni, ſi pri­<lb></lb>mum; </s>
					<s id="N278DA">igitur ſunt duæ lineæ directionis, ex quibus fit altera mixta; </s>
					<s id="N278DE"><lb></lb>ſed nunquam miſcentur duæ determinationes ſine aliqua iactura, quan­<lb></lb>do eſt duplex impetus, vt fusè ſatis demonſtratum eſt ſuprà, ſi ſecun­<lb></lb>dum etiam ſunt duæ, vt patet; </s>
					<s id="N278E7">igitur eadem valet ratio; </s>
					<s id="N278EB">cum verò ſunt <lb></lb>plures funes, minùs impetus ſingulis diſtribuitur; hinc plura fila te­<lb></lb>nuiſſima ſuſtinere poſſunt ingens pondus. </s>
				</p>
				<p id="N278F3" type="main">
					<s id="N278F5">Decimò, hinc facilè colligi poteſt, quid dicendum ſit de pluribus equis <lb></lb>trahentibus currum; </s>
					<s id="N278FB">qui certè ad currum iungi non poſſunt, niſi ſint <lb></lb>plures funes, qui tamen in communem ſeu funem ſeu temonem deſi­<lb></lb>nunt; ſit autem pondus A, linea directionis GE. </s>
					<s id="N27904">Si ſit tantùm vnus <pb pagenum="386" xlink:href="026/01/420.jpg"></pb>equus, vel trahet duobus funibus BECE, vel vnico GE, addito axe <lb></lb>DF, &amp; duobus funibus DHFH. </s>
					<s id="N2790E">Hoc ſecundo modo faciliùs trahet; <lb></lb>quia impetus meliùs deriuatur in pondus A per lineam EG, quæ per <lb></lb>centrum grauitatis ducitur. </s>
				</p>
				<p id="N27916" type="main">
					<s id="N27918">Obſeruabis autem, ſi cylindrus quo trahitur quodlibet pondus per <lb></lb>lineam AB; </s>
					<s id="N2791E">trahatur per duas CFDF, tùm æqualibus viribus per duas <lb></lb>CHGD, haud dubiè hoc ſecundo modo faciliùs trahetur, vt conſtat, <lb></lb>&amp; faciliùs per duas CFDF, quàm per duas CEDE; </s>
					<s id="N27926">ſuppono autem <lb></lb>ita trahi CF, vt æqualiter trahatur per DF; </s>
					<s id="N2792C">alioqui axis volueretur <lb></lb>circa B, in quo non eſt difficultas: </s>
					<s id="N27932">hoc poſito, dico poſſe aſſignari dif­<lb></lb>ferentiam iſtorum motuum; </s>
					<s id="N27938">aſſumatur enim punctum D, quod trahi­<lb></lb>tur per DF &amp; per DI parallelam CF æqualiter vtrimque; </s>
					<s id="N2793E">certè mo­<lb></lb>uebitur per DGL; ſi autem trahatur CD per duas CHDG æqualibus <lb></lb>viribus ab eadem potentia faciliùs trahetur iuxta rationem DF ad DG, <lb></lb>vel DFL ad DE, vt conſtat ex dictis l. 4. de motu mixto tùm etiam l.1. </s>
				</p>
				<p id="N2794A" type="main">
					<s id="N2794C">Vndecimò, ſi autem iungantur duo equi ad trahendum pondus A <lb></lb>axe DF, &amp; fune EG; </s>
					<s id="N27952">ſi æqualiter trahant, quod tamen vix accidere po­<lb></lb>teſt, licèt differentia ſit prorſus inſenſibilis; </s>
					<s id="N27958">ſi autem inæqualiter tra­<lb></lb>hant, perit aliquid impetus vtriuſque, vt patet; </s>
					<s id="N2795E">nam eo tempore, quo <lb></lb>D, cui maior vis ineſt v.g. progreditur, F regreditur; </s>
					<s id="N27966">igitur meo iudi­<lb></lb>cio, ne pereat quidquam impetus, ita debent collocari equi, vt pondus <lb></lb>ſit A, funis communis BC, primus axis DE, primus equus F trahens <lb></lb>funibus FDFE, tùm ſecundus axis GH coniunctus cum primo funibus <lb></lb>GDHE, ſecundus equus I trahens funibus IG, IH, atque ita deinceps: </s>
					<s id="N27972"><lb></lb>hoc poſito totus impetus productus à primo equo F <expan abbr="cõmunicatur">communicatur</expan> primo <lb></lb>axi DE; </s>
					<s id="N2797D">præterea totus impetus productus à ſecundo equo I communi­<lb></lb>catur ſecundo axi GH, &amp; ex hoc primo DE; </s>
					<s id="N27983">igitur DE recipit totum im­<lb></lb>petum ab vtroque equo productum; </s>
					<s id="N27989">qui certè intenſiſſimus eſſet, niſi axis <lb></lb>DE coniunctus eſſet cum pondere A; </s>
					<s id="N2798F">igitur totus impetus ab vtroque <lb></lb>equo productus toti ponderi diſtribuitur, niſi fortè maius ſit <expan abbr="põdus">pondus</expan>; </s>
					<s id="N27999">tunc <lb></lb>enim tertius equus M accedere deberet; igitur nihil prorſus perit impetus. </s>
				</p>
				<p id="N2799F" type="main">
					<s id="N279A1">Duodecimò, vterque equus producit impetum in pondere A actione <lb></lb>communi; probatur, quia, ſi quiſque ſingularem impetum produceret, <lb></lb>qui toti ponderi diſtribui non poſſet, cur potiùs his partibus quam aliis? </s>
					<s id="N279A9"><lb></lb>igitur cùm omnibus diſtribuatur; </s>
					<s id="N279AD">certè ab vtroque ſimul producitur; </s>
					<s id="N279B1"><lb></lb>nec enim alter equus trahit tantùm alteram partem ponderis; </s>
					<s id="N279B6">quæ enim <lb></lb>aſſignari poteſt, ſed ſinguli totum pondus, ſed coniunctim, id eſt quæli­<lb></lb>bet pars ponderis ab vtroque trahitur, ſed non ſola, totum pondus ab <lb></lb>altero trahitur, ſed non ſolo; </s>
					<s id="N279C0">equidem equus F non producit impetum in <lb></lb>funibus DGI, nec in axe GH, nec equus I in funibus DFE, quia nullo <lb></lb>modo impediunt motum, vnde equus I, vt æqualiter cum æquo F trahat <lb></lb>pondus A, debet paulò maiore niſu trahere; qui certè determinari poteſt; </s>
					<s id="N279CA"><lb></lb>ſuppono enim primò vtrumque F, I totis viribus eniti: </s>
					<s id="N279CF">ſecundò equum I <lb></lb>non minùs conferre ad motum ponderis A, quàm equum F 3. funes DG, <lb></lb>EH &amp; axem GH eſſe (1/1000) ponderis A; certè hoc poſito equus I eſt fortior <lb></lb>equo F (1/1000). </s>
				</p>
				<pb pagenum="387" xlink:href="026/01/421.jpg"></pb>
				<p id="N279DD" type="main">
					<s id="N279DF">Decimotertiò, currus initio difficiliùs trahitur; </s>
					<s id="N279E3">ratio eſt, quia nullus <lb></lb>impetus ineſt initio, qui vbi ſemel productus primo inſtanti; </s>
					<s id="N279E9">nec totus <lb></lb>deſtruatur ſecundo; </s>
					<s id="N279EF">nec enim totus fruſtrà eſt; </s>
					<s id="N279F3">habet enim aliquem effe­<lb></lb>ctum, id eſt motum; </s>
					<s id="N279F9">augetur per acceſſionem noui impetus ſecundo in­<lb></lb>ſtanti producti; idem dico de tertio, quarto, quinto, &amp;c. </s>
					<s id="N279FF">donec tandem <lb></lb>poſt aliquod tempus motu <expan abbr="æq́uabili">æquabili</expan> procedat currus; </s>
					<s id="N27A09">quia ſcilicet quan­<lb></lb>tum deſtruitur ſingulis inſtantibus, <expan abbr="tantũdem">tantundem</expan> ferè producitur, ſed mi­<lb></lb>nùs profectò, quàm initio; igitur faciliùs; </s>
					<s id="N27A15">igitur initio difficiliùs; </s>
					<s id="N27A19">hinc <lb></lb>equi totis neruis enituntur initio, præſertim in plano arduo; </s>
					<s id="N27A1F">at vbi cur­<lb></lb>rus primum impetum accepit, longè faciliùs deinde propagatur; </s>
					<s id="N27A25">hinc ſi <lb></lb>rumpatur funis, quo trahitur currus præcipiti equorum curſu, currus <lb></lb>ipſe deinde per aliquod tempus adhuc rotatur; </s>
					<s id="N27A2D">igitur prior impetus du­<lb></lb>rat adhuc; nec enim nouus producitur. </s>
				</p>
				<p id="N27A33" type="main">
					<s id="N27A35">Decimoquartò, ſi dum quis trahit toto niſu magnum aliquod pondus, <lb></lb>funis rumpatur, pronus corruit; </s>
					<s id="N27A3B">ratio eſt, quia totum <expan abbr="impetũ">impetum</expan> in ſe produ­<lb></lb>cit, quem in ſe ſimul &amp; pondere integro fune ſeruato produxiſſet; </s>
					<s id="N27A45">hinc <lb></lb>dum duo in partes aduerſas cylindrum, vel funem trahunt, ſi dimittat <lb></lb>vnus ſupinus, alter proruit; </s>
					<s id="N27A4D">quæ omnia ex noſtris principijs luce clariora <lb></lb>redduntur; </s>
					<s id="N27A53">non eſt tamen, quod aliquis exiſtimet huius phœnomeni ra­<lb></lb>tionem tantùm à priori impetu conſeruato eſſe; </s>
					<s id="N27A59">qui certè minor erat in <lb></lb>trahente, quàm vt hunc effectum præſtare poſſit, cùm toti ponderi di­<lb></lb>ſtribuatur; igitur potiſſima ratio duci debet ab impetu nouo producto, <lb></lb>quî cùm in auulſum pondus tranſire non poſſit, totus in ipſo trahente <lb></lb>quaſi ſubſiſtit. </s>
				</p>
				<p id="N27A65" type="main">
					<s id="N27A67">Decimoquintò, vt quis fortius trahat firmo pede, &amp; crure intento, ſo­<lb></lb>lum ipſum aduerſo niſu premit; </s>
					<s id="N27A6D">ratio in promptu eſt, quia dum manu <lb></lb>trahit corporis truncum lumborum vi, &amp; oſſium contractorum explica­<lb></lb>tione ſurſum attollit; </s>
					<s id="N27A75">igitur nouus impetus ponderi tracto accedit; </s>
					<s id="N27A79">hinc <lb></lb>pede, vel genu in partem aduerſam contranititur, qui trahit; </s>
					<s id="N27A7F">nam que­<lb></lb>madmodum gemino brachio fortiùs trahimus, quàm vno; ita prorſus, <lb></lb>cum brachiorum vis iuuatur à lumbis, cruribus, &amp;c. </s>
					<s id="N27A87">haud dubiè vali­<lb></lb>dior eſt. </s>
				</p>
				<p id="N27A8C" type="main">
					<s id="N27A8E">Decimoſextò, cum faciliùs amoueri poteſt, quod pellimus pede, vel <lb></lb>genu, quàm quod trahimus manu, vel vnco, illud ipſum mouetur; </s>
					<s id="N27A94">hinc <lb></lb>vnco, ſi quis annulum apprehenſum trahat quantumuis immobilem, &amp; <lb></lb>pede firmo nauim pellat in aduerſam partem; </s>
					<s id="N27A9C">haud dubiè, quia faciliùs <lb></lb>moueri poteſt nauis quàm annulus, verſus annulum ibit; </s>
					<s id="N27AA2">ſed ne diuer­<lb></lb>ſas impreſſionum rationes, quæ in motu nauis vulgò apparent diſtraha­<lb></lb>mus; hoc loco breuiter omnes congerendas eſſe putaui. </s>
					<s id="N27AAA">Primò ad lit­<lb></lb>tus tendit cum trahitur vnco annullus immobilis, vt iam dictum eſt. </s>
					<s id="N27AAF">Se­<lb></lb>cundò, ſi pellitur, vel fundum aquæ, vel aliud corpus immobile longio­<lb></lb>ri ligno, &amp; pede pellatur ipſa nauis in aduerſam partem, in cam ibit <lb></lb>propter <expan abbr="eãdem">eandem</expan> rationem; Tertiò ſi pellatur aqua remis fixo etiam pe­<lb></lb>de vel crure contranitente in aduerſam partem, idem ſequetur effectus. </s>
					<s id="N27ABF"><lb></lb>Quartò, hinc quò remus latior eſt, &amp; longior erit, maior erit effectus, <pb pagenum="388" xlink:href="026/01/422.jpg"></pb>modò ſuppetant vires. </s>
					<s id="N27AC8">Quintò, hinc latioris claui inflexione vertitur <lb></lb>nauis; </s>
					<s id="N27ACE">Sextò, inflata ventis ſecundis vela nauem agunt; </s>
					<s id="N27AD2">ratio clariſſima <lb></lb>eſt, quia non poſſunt vela impelli, niſi alia nauis, cui ſunt coniuncta mo­<lb></lb>ueatur; ſed de re nautica agemus fusè ſuo loco, atque adeo de tota re <lb></lb>hydraulica. </s>
				</p>
				<p id="N27ADC" type="main">
					<s id="N27ADE">Decimoſeptimò, denique ex dictis multa corollaria conſequi poſſunt. </s>
					<s id="N27AE1"><lb></lb>Certum eſt. </s>
					<s id="N27AE7">1°. </s>
					<s id="N27AEA">pars tracta non ſequitur trahentem ſua ſponte 2.°. </s>
					<s id="N27AED">reſiſtit <lb></lb>alteri trahenti, 3°. </s>
					<s id="N27AF2">non producit impetum pars trahens in tracta. </s>
					<s id="N27AF5">4°. </s>
					<s id="N27AF8">non <lb></lb>trahitur immediatè, &amp; aliæ mediatè, ſed omnes ſimul immediatè. </s>
					<s id="N27AFD">5°. </s>
					<s id="N27B00">nul­<lb></lb>lus impetus productus in corpore tracto impeditur. </s>
					<s id="N27B05">6°. </s>
					<s id="N27B08">impetus primæ <lb></lb>partis non producit impetum in aliis. </s>
					<s id="N27B0D">7°. </s>
					<s id="N27B10">quando dico tauri trahunt iu­<lb></lb>gum producunt impetum actione communi. </s>
					<s id="N27B15">8°. </s>
					<s id="N27B18">rota faciliùs trahitur, <lb></lb>quàm cubus; quia pauciores partes plani reſiſtunt. </s>
					<s id="N27B1E">9°. </s>
					<s id="N27B21">quando fracto <lb></lb>fune trahens pronus corruit, non tantùm hic caſus procedit à priore <lb></lb>impetu, ſed maximè à nouo. </s>
					<s id="N27B28">1°. </s>
					<s id="N27B2B">extremitas funis fracti reſilit propter <lb></lb>præcedentem tenſionem. </s>
					<s id="N27B30">11°. </s>
					<s id="N27B33">hinc cum diſcerpitur charta vel tela edi­<lb></lb>tur ſonus ſtridulus, qui prouenit à motu extremorum filorum quæ reſi­<lb></lb>liunt. </s>
					<s id="N27B3A">12°. </s>
					<s id="N27B3D">immò cum baculus frangitur, aliqua ſegmenta maxima vi eui­<lb></lb>brantur, ſentiturque in manu quaſi formicans dolor, propter illas tre­<lb></lb>mulas ſuccuſſiones. </s>
					<s id="N27B44">13°. </s>
					<s id="N27B47">cum trahitur cylindrus vtrimque in aduerſas <lb></lb>partes à duobus contranitentibus æqualium virium, ſi minimè inflecti <lb></lb>poſſit, ille præualebit, cuius vtraque manus propiùs ad medium cylin­<lb></lb>drum accedit; </s>
					<s id="N27B51">ſecùs verò, ſi inflectatur; eſt enim ad inſtar gemini vectis. </s>
					<s id="N27B55"><lb></lb>14°. </s>
					<s id="N27B59">cum trahitur cylindrus æqualiter vtrimque, qui neque flecti, ne­<lb></lb>que tendi poſſit; </s>
					<s id="N27B5F">haud dubiè nullum impetum habet, quia eſſet fruſtrà, <lb></lb>15. deſtruitur impetus in tractione, ne ſit fruſtrà: ex his reliqua facilè <lb></lb>intelligentur. </s>
				</p>
				<p id="N27B67" type="main">
					<s id="N27B69"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27B75" type="main">
					<s id="N27B77"><emph type="italics"></emph>Explicari poſſunt omnia, quæ pertinent ad impulſum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27B7E" type="main">
					<s id="N27B80">Primò, impulſus duplicis eſt generis: </s>
					<s id="N27B84">primus eſt coniunctus cum per­<lb></lb>cuſſione, ſic tudicula impulſus globus emittitur: ſecundus ſine percuſſio­<lb></lb>ne; </s>
					<s id="N27B8C">&amp; hic duplex eſt: </s>
					<s id="N27B90">Primus, quo mobile impulſum ſeparatur ab impel­<lb></lb>lente: </s>
					<s id="N27B96">Secundus, quo non ſeparatur, ſed ipſi continuò adhæret; </s>
					<s id="N27B9A">quia <lb></lb>continuo impulſu mouetur; de hoc tantùm vltimo impulſu agitur in <lb></lb>hoc Th. Secundò, ex dictis de tractatione colligi poſſunt ea, quæ dici debent <lb></lb>de impulſu, quatenus nulli percuſſioni nec emiſſioni coniunctus eſt. </s>
				</p>
				<p id="N27BA6" type="main">
					<s id="N27BA8"><lb></lb>1°. </s>
					<s id="N27BAC">impellens producit impetum in ſe ipſe; 2°. </s>
					<s id="N27BB0">impetus impellentis pro­<lb></lb>ducit impetum in corpore. </s>
					<s id="N27BB5">3°. </s>
					<s id="N27BB8">ſingulis inſtantibus deſtruitur aliquid <lb></lb>impetus impellentis, &amp; impulſi. </s>
					<s id="N27BBD">4°. </s>
					<s id="N27BC0">initio difficiliùs mobile mouetur <lb></lb>impulſu. </s>
					<s id="N27BC5">5°. </s>
					<s id="N27BC8">poſt primum motum tùm deinde faciliùs mouetur corpus <lb></lb>impulſum, nec tanto niſu potentiæ opus eſt. </s>
					<s id="N27BCD">6°. </s>
					<s id="N27BD0">cum æquali motu mo­<lb></lb>uetur impulſum tantùm impetus producitur, quantùm deſtruitur. </s>
					<s id="N27BD5">7°. </s>
					<s id="N27BD8"><lb></lb>cum pellitur rupes immobilis, nullus in ea producitur impetus, niſi <pb pagenum="389" xlink:href="026/01/423.jpg"></pb>fortè aliqua pars ſeparetur, vel comprimatur. </s>
					<s id="N27BE1">8°. </s>
					<s id="N27BE4">producitur tamen <lb></lb>împetus in organo; probatur ex niſu; immò &amp; compreſſione molliorum <lb></lb>partium. </s>
					<s id="N27BEC">9°. </s>
					<s id="N27BEF">quando duo ſeſe mutuò, &amp; æquali niſu pellunt, vterque in ſe <lb></lb>ipſo, &amp; in alio producit impetum; </s>
					<s id="N27BF5">in ſe quidem, quia maximè euitetur, <lb></lb>&amp; defatigatur potentia motrix; in alio verò, in quo fit aliqua partium <lb></lb>compreſſio, quæ ſine impetu <expan abbr="nũquam">nunquam</expan> fit. </s>
					<s id="N27C01">10°. </s>
					<s id="N27C04">ſi os pelleret os, ſeu corpus <lb></lb>durum aliud durum, natiua vi diſtincta à grauitatione, in neutro pro­<lb></lb>duceretur impetus; </s>
					<s id="N27C0C">quia eſſet fruſtrà: vide quæ diximus ſuprà de tra­<lb></lb>ctione. </s>
					<s id="N27C12">11°. </s>
					<s id="N27C15">pellens etiam firmo pede ſolum, in aduerſam partem pellit, <lb></lb>ſeu premit; rationem iam attulimus ſuprà. </s>
					<s id="N27C1B">12°. </s>
					<s id="N27C1E">ſi dum reluctantem alium <lb></lb>&amp; contranitentem pellis, ſeſe illicò cedens eripiat, pronus in terram <lb></lb>corrues. </s>
					<s id="N27C25">13°.ſí plures idem pondus pellant, actione communi impetum <lb></lb>producunt; hæc, &amp; alia multa ex dictis de tractione facilè per eadem <lb></lb>principia demonſtrantur. </s>
				</p>
				<p id="N27C2D" type="main">
					<s id="N27C2F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27C3B" type="main">
					<s id="N27C3D"><emph type="italics"></emph>Attolli aliquid poteſt &amp; eleuari,<emph.end type="italics"></emph.end> 1°. </s>
					<s id="N27C45">ſi producatur impetus maior impe­<lb></lb>tu grauitationis; ratio clara eſt, quia fortior præualet. </s>
					<s id="N27C4B">2°. </s>
					<s id="N27C4E">deſtruitur ſe­<lb></lb>cundo inſtanti aliquid impetus producti; quia eſt fruſtrà propter <lb></lb>impetum natiuum. </s>
					<s id="N27C56">3°. </s>
					<s id="N27C59">ſi tantùm producatur impetus ſingulis in­<lb></lb>ſtantibus, quantum deſtruitur, motus erit æquabilis, ſi plùs, acceleratus, <lb></lb>ſi minùs, retardatus, patet ex dictis.4°.pondus attollitur initio difficiliùs <lb></lb>propter rationem prædictam; minùs enim produci debet impetus ſecun­<lb></lb>do inſtanti, quàm primò. </s>
					<s id="N27C65">5°. </s>
					<s id="N27C68">ſub funem tamen valdè laborat potentia <lb></lb>propter <expan abbr="compreſſionẽ">compreſſionem</expan>, &amp; tenſionem partium, de qua ſuprà.6°. </s>
					<s id="N27C71">difficiliùs <lb></lb>attollitur ingens pondus, quàm modicum; ratio clara eſt, quia plures <lb></lb>partes impetus imprimi debent maiori, cui plures inſunt, quàm minori. </s>
					<s id="N27C79"><lb></lb>7°. </s>
					<s id="N27C7D">facilius attollitur per planum inclinatum, quàm per lineam vertica­<lb></lb>lem deorſum, rationem iam attulimus l. 5. 8°. </s>
					<s id="N27C84">hinc etiam organo me­<lb></lb>chanico faciliùs attollitur pondus, de quo lib.  11. 9°. </s>
					<s id="N27C89">licèt grauitas non <lb></lb>reſiſteret, corpus maius difficilius attolleretur, quàm minus; quia plures <lb></lb>partes impetus illius motus deſideraret, quàm huius, ſed maior impetus <lb></lb>difficiliùs imprimitur, quàm minor. </s>
				</p>
				<p id="N27C93" type="main">
					<s id="N27C95"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27CA1" type="main">
					<s id="N27CA3"><emph type="italics"></emph>Corpus<emph.end type="italics"></emph.end> 1°. <emph type="italics"></emph>deprimitur per impetum infra medium grauius, v. g. lignum̨ <lb></lb>infra aquam<emph.end type="italics"></emph.end>; ratio clara eſt. </s>
					<s id="N27CB8">2°. </s>
					<s id="N27CBB">deprimitur, vel trahendo, vel impellen­<lb></lb>do, vel calcando. </s>
					<s id="N27CC0">3°. </s>
					<s id="N27CC3">trahimus ſæpè deorſum, vt corpus attollatur ſur­<lb></lb>ſum, vt in trochleis. </s>
					<s id="N27CC8">4°. </s>
					<s id="N27CCB">quò corpus maius eſt, &amp; leuius difficiliùs depri­<lb></lb>mitur infra medium grauius, quia non poteſt deprimi niſi plures medij <lb></lb>grauiores partes attollantur, vt clarum eſt; exemplum habes in nauibus, <lb></lb>5°. </s>
					<s id="N27CD5">deprimimus aliquando corpora per tenſionem, vt ramos arborum, <lb></lb>ſeu per librationem, vt campanarum funes, ſeu extremos vectes. </s>
					<s id="N27CDA">6°. </s>
					<s id="N27CDD"><lb></lb>clauus deprimitur, vel palus tribus modis. </s>
					<s id="N27CE1">1°. </s>
					<s id="N27CE4">percuſſione; 2°. </s>
					<s id="N27CE7">ia­<lb></lb>ctu ſeu eiaculatione. </s>
					<s id="N27CEC">3°. </s>
					<s id="N27CEF">impulſione; de hac iam ſuprà actum eſt, de dua­<lb></lb>bus primis paulò pòſt agetur, ſed hæc ſunt facilia, &amp; faciles cauſæ. </s>
				</p>
				<pb pagenum="390" xlink:href="026/01/424.jpg"></pb>
				<p id="N27CF8" type="main">
					<s id="N27CFA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27D06" type="main">
					<s id="N27D08"><emph type="italics"></emph>Omnes gyrationum modi explicari, &amp; demonſtrari poſſunt.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27D0F" type="main">
					<s id="N27D11">Primò, vertitur baculus manu primo circa proprium axem, vt <expan abbr="veru">verum</expan>, <lb></lb>quia inflectitur eodem modo manus &amp; inferior brachij portio: </s>
					<s id="N27D17">ſecundo <lb></lb>circa alteram extremitatem quæ manu tenetur: tertio circa quodlibet <lb></lb>aliud punctum, ratio petitur tùm à tali brachij motu, tùm ab eo modo, <lb></lb>quo baculus tenetur, </s>
				</p>
				<p id="N27D21" type="main">
					<s id="N27D23">Secundò, circumagitur funis vel funda; </s>
					<s id="N27D27">quia producitur maior im­<lb></lb>petus in extremitate remota circa centrum immobile; hinc circulus; </s>
					<s id="N27D2D"><lb></lb>hinc quia extremitatis illius motus determinatur ſemper ad Tangentem, <lb></lb>tenditur funis; ſed de funda infrà, cum de proiectione. </s>
				</p>
				<p id="N27D34" type="main">
					<s id="N27D36">Tertiò, multos alios gyros facimus, manu, brachio, collo, pede, toto <lb></lb>denique corporis trunco; </s>
					<s id="N27D3C">quot enim habemus articulos, tot motus cir­<lb></lb>cularis habemus centra; </s>
					<s id="N27D42">hinc ſuæ apothecæ caput oſſis tam aptè inſe­<lb></lb>ritur, vt circa illam facilè moueatur; </s>
					<s id="N27D48">exemplum habes in oculo, dum <lb></lb>infra ſuam thecam voluitur; </s>
					<s id="N27D4E">ſed de tota corporis fabrica, quatenus con­<lb></lb>ducit ad motum, ſuo loco agemus; nec enim hi motus ad hunc tracta­<lb></lb>tum pertinent. </s>
				</p>
				<p id="N27D56" type="main">
					<s id="N27D58">Quartò, hinc reuoca deflexionem illam iacti globi, de qua ſuprà, quæ <lb></lb>familiaris eſt trunculorum ludo, item gyros globi, quem, vel inter duas <lb></lb>volas circumagis, vel inter volam, &amp; aliud planum, qui partim ad impul­<lb></lb>ſum, partim ad tractum pertinent; ſed neque hæc ſunt difficilia. </s>
				</p>
				<p id="N27D62" type="main">
					<s id="N27D64"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N27D70" type="main">
					<s id="N27D72">Obſeruabis vix poſſe vno Theoremate compræhendi omnia phœno­<lb></lb>mena percuſſionis, cuius ſunt tria veluti prima genera, ſcilicet ictus, ca­<lb></lb>ſus, iactus: ictum appello illam percuſſionem, quæ infligitur pugno, ma­<lb></lb>nu, calce, cornu, vel quolibet organo, cum potentia motrice coniuncto, <lb></lb>v.g. fuſte, ſaxo, flagello, &amp;c. </s>
					<s id="N27D80">caſus eſt percuſſio à corpore graui deorſum <lb></lb>cadente inflicta; iactus denique eſt percuſſio, quæ aliquam emiſſionem, <lb></lb>ſeu vibrationem ſupponit, lapidis, pilæ, &amp;c. </s>
					<s id="N27D88">itaque vt omnia percuſſio­<lb></lb>nis phœnomena diſtinctiùs explicemus, ſingulis Theorematis ſingulos <lb></lb>percuſſionis modos explicabimus. </s>
				</p>
				<p id="N27D8F" type="main">
					<s id="N27D91"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27D9D" type="main">
					<s id="N27D9F"><emph type="italics"></emph>Explicantur omnia phœnomena percuſſionis, quæ infligitur manu, pugno, <lb></lb>brachio, calce, cornu.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N27DA8" type="main">
					<s id="N27DAA">Primò, pugnus infligit ictum diuerſo motu; primò, motu recto; </s>
					<s id="N27DAE">ſit <lb></lb>enim humerus AB, caput cubiti B, os cubiti BF, fiat arcus AC, &amp; KI, <lb></lb>ita vt ABK ſit æqualis ABF; </s>
					<s id="N27DB6">certè ACI erit totum brachium tenſum, <lb></lb>caput B nunquam recedit ab arcu BC, nec extremitas F à recta FI; </s>
					<s id="N27DBC">vbi <lb></lb>autem F peruenit in G; </s>
					<s id="N27DC2">aſſumatur GE æqualis FB: </s>
					<s id="N27DC6">vbi verò F peruenit <lb></lb>in H; </s>
					<s id="N27DCC">aſſumatur HD æqualis FB, &amp; habebitur proportio motus extre­<lb></lb>mitatis F &amp; capitis B; vides motum rectum FI mixtum ex duobus cir­<lb></lb>cularibus circa centrum immobile A, &amp; mobile B. </s>
				</p>
				<p id="N27DD4" type="main">
					<s id="N27DD6">Secundò, poſſet moueri per omnem lineam, v. g. FN, FM, <pb pagenum="391" xlink:href="026/01/425.jpg"></pb>immò, &amp; per lineam perpendicularem ſurſum, vel deorſum, &amp; quò <lb></lb>plùs contrahetur brachium, motus rectus per horizontalem erit maior; </s>
					<s id="N27DE5"><lb></lb>ſit enim angulus cubiti ABO, ita vt BF ſit in BO; </s>
					<s id="N27DEA">certè extremitas <lb></lb>O percurret motu recto totam OP; </s>
					<s id="N27DF0">&amp; ſi omninò contrahatur brachium, <lb></lb>ita vt F ſit in A, percurret extremitas A totam rectam AP; </s>
					<s id="N27DF6">tunc au­<lb></lb>tem ictus eſt fortior, cum linea motus recti eſt maior; quippe ſingulis in­<lb></lb>ſtantibus nouus impetus accedit. </s>
				</p>
				<p id="N27DFE" type="main">
					<s id="N27E00">Tertiò, poteſt inueniri maximum ſpatium quod poteſt confici ab ex­<lb></lb>tremitate brachij motu recto; </s>
					<s id="N27E06">ſit enim centrum humeri immobile A, <lb></lb>ſit AC os humeri, CD cubiti, ſit AD perpendicularis deorſum; </s>
					<s id="N27E0C">ſit <lb></lb>angulus BAC maximæ deflexionis, qua os humeri poſſit retrò agi; </s>
					<s id="N27E12">ſit <lb></lb>CGK, item DFO, ſit BG recta, BH æqualis CD; </s>
					<s id="N27E18">ducatur EHL <lb></lb>perpendicularis ſurſum, ſitque CEOS cubiti: dico EL eſſe maximum <lb></lb>ſpatium, &amp;c. </s>
					<s id="N27E20">cùm enim caput cubiti C poſſit tantùm retroagi in B; </s>
					<s id="N27E24">certè <lb></lb>non poteſt extremitas D, in quocumque loco ſit, circuli DFO ſecare <lb></lb>BG, in puncto quod propiùs accedat ad centrum A quàm H; </s>
					<s id="N27E2C">ſed om­<lb></lb>nium linearum, quæ poſſunt duci per H ſurſum perpendiculariter, ma­<lb></lb>xima eſt EL; </s>
					<s id="N27E34">immò EL eſt omnium maxima, quæ duci poſſunt poſita <lb></lb>extremitate inter DE; </s>
					<s id="N27E3A">vt autem habeatur omnium maxima; </s>
					<s id="N27E3E">ſit punctum <lb></lb>K ſurſum, ad quod tantùm nodus, ſeu caput cubiti C peruenire poteſt; </s>
					<s id="N27E44"><lb></lb>aſſumatur KO æqualis CD, ex centro B fiat arcus AH, tùm ex O ad <lb></lb>arcum AH; </s>
					<s id="N27E4B">ducatur Tangens OQF; </s>
					<s id="N27E4F">certum eſt eſſe maximam lineam; <lb></lb>quia accedit propiùs ad centrum A, vt conſtat. </s>
				</p>
				<p id="N27E55" type="main">
					<s id="N27E57">Quartò, poteſt pugnus ferire motu perfectè circulari, idque duobus <lb></lb>modis. </s>
					<s id="N27E5C">Primò, ſi brachium extenſum AD circa centrum moueatur per <lb></lb>arcum DFO figura prima. </s>
					<s id="N27E61">Secundò, ſi moueatur  caput cubiti; </s>
					<s id="N27E65">ſit enim <lb></lb> os humeri AB, &amp; cubiti BC caput cubiti B; </s>
					<s id="N27E6B">ex A fiat arcus BEL; </s>
					<s id="N27E6F"><lb></lb>tùm ex aliquo puncto ſuprà A, putà ex N radio NC fiat arcus CI; </s>
					<s id="N27E74">tùm <lb></lb>aſſumpta AK æquali AB fiat arcus KH ſecans priorem in I; </s>
					<s id="N27E7A">certè extre­<lb></lb>mitas C moueri poterit per arcum CI, donec brachium extentum ſit <lb></lb>in AI, quod non eſt difficile; hîc porrò vides motum circularem ex <lb></lb>duobus alijs circularibus mixtum. </s>
				</p>
				<p id="N27E84" type="main">
					<s id="N27E86">Quintò, moueri per quamcumque aliam lineam curuam, ellipticam, <lb></lb>parabolicam &amp;c. </s>
					<s id="N27E8B">immò per infinitas alias nouas; </s>
					<s id="N27E8F">vides nouam FDC, <lb></lb>quæ vt fiat cubitus IF eſt ſemper ſibi ipſi parallelus; </s>
					<s id="N27E95">quod vt fiat, caput <lb></lb>I &amp; extremitas F debent moueri æquali motu; </s>
					<s id="N27E9B">ſunt enim CBLDEK <lb></lb>FI æquales &amp; parallelæ: </s>
					<s id="N27EA1">ex quo fit hanc curuam eſſe ſpeciem nouæ <lb></lb>Conchoidis, de qua aliàs; mouetur autem initio tardiùs, &amp; ſub <lb></lb>finem velociùs, non quidem proprio motu circa centrum I, ſed motu <lb></lb>mixto. </s>
				</p>
				<p id="N27EAB" type="main">
					<s id="N27EAD">Sextò, eſt maximus ictus inflictus à pugno, qui mouetur motu re­<lb></lb>cto per longiorem lineam, quæ accedit propiùs ad lineam brachij dein­<lb></lb>de extenti; </s>
					<s id="N27EB5">quò enim eſt longior linea producitur ſenſun maior impe­<lb></lb>tus; </s>
					<s id="N27EBB">eſt enim motus naturaliter acceleratus, cùm ſit applicata con­<lb></lb>tinuô potentia motrix: </s>
					<s id="N27EC1">præterea ictus eſt magis directus, ſi linea <pb pagenum="392" xlink:href="026/01/426.jpg"></pb>motus propiùs accedit ad lineam brachij extenti: hinc quò plus cotra­<lb></lb>hitur brachium ad infligendum ictum eſt validior ictus, quia eſt lon­<lb></lb>gior linea &amp; magis directa, quod natura ipſa docuit pueros pugnis con­<lb></lb>tendentes. </s>
				</p>
				<p id="N27ED0" type="main">
					<s id="N27ED2">Septimò, auerſa manu impingitur validior colaphus, quàm aduerſa; </s>
					<s id="N27ED6"><lb></lb>quia mouetur manus per arcum paulò maiorem ſemicirculo; </s>
					<s id="N27EDB">in quo <lb></lb>motus continuò creſcit; at verò ſi aduerſâ; </s>
					<s id="N27EE1">non validus eſt ictus; </s>
					<s id="N27EE5">pri­<lb></lb>mò quia quando auerſa infligitur, &amp; eſt motus circa duplex centrum, <lb></lb>vterque circularis in <expan abbr="eãdem">eandem</expan> partem tendit; </s>
					<s id="N27EF1">igitur maior eſt; </s>
					<s id="N27EF5">ſecus <lb></lb>accidit cum aduerſà: </s>
					<s id="N27EFB">Secundò, non tam extendi poteſt brachium impa­<lb></lb>ctum introrſum, quàm in aduerſam partem; igitur minor eſt arcus, <lb></lb>vel os humeri ſiſtitur, atque ita ex parte extinguitur ictus. </s>
					<s id="N27F03">Tertiò <lb></lb>manus auerſa durior eſt, quàm aduerſa; </s>
					<s id="N27F09">eſt enim vola mollior; </s>
					<s id="N27F0D">hæc <lb></lb>verò mollities extinguit vim ictus, vt ſæpè demonſtrauimus: de rota­<lb></lb>tione brachij, quæ maximè vim auget, dicemus infrà, cum de Tudicu­<lb></lb>la, clauâ, baculo, de lineis verò dicemus lib.12. </s>
				</p>
				<p id="N27F17" type="main">
					<s id="N27F19">Octauò, qui longioribus brachijs inſtructi ſunt, maiores ictus <lb></lb>infligunt; </s>
					<s id="N27F1F">patet, quia maiorem deſcribunt arcum; </s>
					<s id="N27F23">igitur velociore <lb></lb>motu rotatur pugnus; </s>
					<s id="N27F29">cum tamen motu circulari mouetur brachium; <lb></lb>certum eſt maiorem ictum minimè infligi ab extremitate, vt conſtat <lb></lb>ex dictis de baculo lib.1. Th.73. niſi fortè ratione contracti pugni, quod <lb></lb>iam ibidem indicauimus. </s>
				</p>
				<p id="N27F33" type="main">
					<s id="N27F35">Nonò, cum deorſum impingitur pugnus, creſcit ictus propter acceſ­<lb></lb>ſionem motus naturalis accelerati; </s>
					<s id="N27F3B">eſt enim corpus graue; </s>
					<s id="N27F3F">cum ſurſum, <lb></lb>è contrario imminuitur motus: in qua verò proportione, dicemus in­<lb></lb>frà cum de malleo. </s>
				</p>
				<p id="N27F47" type="main">
					<s id="N27F49">Decimò, aliquando rotatur brachium, antequam infligatur ictus, <lb></lb>vel introrſum, vel in partem oppoſitam, præſertim vt longiùs ia­<lb></lb>ciatur lapis, vt pila reticulo, vel auerſo, vel aduerſo procul <lb></lb>emittatur, &amp;c. </s>
					<s id="N27F52">ratio eſt, quia continuò augetur motus, vt iam di­<lb></lb>ctum eſt. </s>
				</p>
				<p id="N27F57" type="main">
					<s id="N27F59">Vndecimò, breuiter indico ictum inflictum ab ipſo cubiti capi­<lb></lb>te retrò acto, ſatis grauem eſſe; </s>
					<s id="N27F5F">tùm quia durior eſt ille nodus; tùm <lb></lb>quia ad eius motum non modò ſuperius brachij ſegmentum, verùm <lb></lb>etiam inferius concurrit. </s>
				</p>
				<p id="N27F67" type="main">
					<s id="N27F69">Duodecimò, infligitur etiam grauis ictus calce, cuius eſt eadem <lb></lb>ratio, quæ ſuprà; eſt enim duplex centrum, duplex motus, &amp;c. </s>
					<s id="N27F6F">Ob­<lb></lb>ſeruabis tamen. </s>
					<s id="N27F74">Primò ictum maiorem infligi, ſi crura longiora ſunt. </s>
					<s id="N27F77"><lb></lb>Secundò aduerſo calce quam auerſo; eſt enim oppoſita brachiorum <lb></lb>ratio, cùm genu aduerſum ſit, &amp; auersum cubiti caput. </s>
					<s id="N27F7E">Tertiò, equi <lb></lb>è contrario calcem fortiùs retroagunt, quia tibiæ poſterioris ge­<lb></lb>nu auerſum eſt; </s>
					<s id="N27F86">adde quoque ictum ab ipſo genu inflictum; </s>
					<s id="N27F8A">de <lb></lb>quo idem dicendum eſt, quod de ictu à nodo cubiti inflicto iam <lb></lb>diximus; quippe in eo tantùm differunt, quòd habeant contrarios <lb></lb>ſitus. </s>
				</p>
				<pb pagenum="393" xlink:href="026/01/427.jpg"></pb>
				<p id="N27F98" type="main">
					<s id="N27F9A">Decimotertiò, exploſione intenſi digiti talitrum imprimitur, cuius <lb></lb>ſunt tres modi; primus eſt, cum vngue medij, vel alterius digiti pulſo <lb></lb>tantiſper molliore ſummi pollicis apice, intenſus deinde digitus eo­<lb></lb>dem vngue talitrum impingit. </s>
					<s id="N27FA4">Secundum eſt, cum retento ſummo di­<lb></lb>gito ab aliquo molliori corpore ſtatim dimittitur. </s>
					<s id="N27FA9">Tertium eſt, cum <lb></lb>mollior medij digiti, &amp; pollicis apex poſt aliquam preſſionem, non <lb></lb>ſine aliquo ſtrepitu exploditur; </s>
					<s id="N27FB1">ratio primi eſt, quia dum vnguis mol­<lb></lb>liorem ſubſtantiam premit, auget impetum potentia motrix in illa <lb></lb>mora, neruuſque maximè intenditur; </s>
					<s id="N27FB9">igitur maior eſt ictus; </s>
					<s id="N27FBD">eadem <lb></lb>ratio valet pro ſecundo, &amp; tertio modo; </s>
					<s id="N27FC3">ſtrepitus ille oritur à colli­<lb></lb>ſione, vel compreſſione: </s>
					<s id="N27FC9">immò ſi nulla fieret compreſſio aut certè <lb></lb>ſi nulla cederet mollior materia, non eſſet maior ictus; adde quod <lb></lb>non tantùm augetur impetus à potentia motrice diutiùs agente, ſed <lb></lb>etiam ratione compreſſionis noua ſit impetus acceſſio, vt patet in <lb></lb>arcu. </s>
				</p>
				<p id="N27FD5" type="main">
					<s id="N27FD7">Decimoquartò, denique quod ſpectat ad cornu facilè explicari poteſt <lb></lb>quomodo ab irato tauro intendatur, vno ſcilicet durioris capitis motu, <lb></lb>atque adeò totius corporis. </s>
				</p>
				<p id="N27FDE" type="main">
					<s id="N27FE0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N27FEC" type="main">
					<s id="N27FEE"><emph type="italics"></emph>Explicari poſſunt omnes ictus, qui infliguntur impacto ſcilicet ſaxo, fuſte, <lb></lb>flagello, &amp; alio quouis organo, cui ſemper potentia motrix coniuncta eſt, nec <lb></lb>ab ea ſeparatur,<emph.end type="italics"></emph.end> excepto dumtaxat omni malleorum genere, gladiorum, <lb></lb>&amp;c. </s>
					<s id="N27FFC">primò manus inſtructa ſaxo grauiorem ictum infligit; </s>
					<s id="N28000">tùm quia <lb></lb>multus impetus imprimitur graui ſaxo; </s>
					<s id="N28006">tùm quia durior eſt materia; </s>
					<s id="N2800A"><lb></lb>igitur nihil cedit: </s>
					<s id="N2800F">porrò maior eſt ictus, ſi deorſum intendatur, cùm <lb></lb>accedat impetus grauitatis ipſius ſaxi: adde ferream manicam, quæ prop­<lb></lb>ter <expan abbr="eãdem">eandem</expan> rationem petentem colaphum infringit. </s>
				</p>
				<p id="N2801B" type="main">
					<s id="N2801D">Secundò, fuſtis impingi poteſt duobus modis; </s>
					<s id="N28021">primò motu recto, <lb></lb>cùm ſcilicet porrecto brachio extremitas fuſtis ſcopum attingit; </s>
					<s id="N28027">ſecundò <lb></lb>motu circulari rotato ſcilicet brachio: </s>
					<s id="N2802D">primo modo infligitur ictus pun­<lb></lb>ctim, vt vulgò dicunt: ſecundo quaſi cæſim, vterque ſua phœnomena <lb></lb>habet. </s>
				</p>
				<p id="N28035" type="main">
					<s id="N28037">Tertiò, cum punctim impingitur fuſtis, quò hic maior eſt, maiorem <lb></lb>incutit ictum; </s>
					<s id="N2803D">præſertim, ſi gemina manu intenditur; </s>
					<s id="N28041">quia ſcilicet ma­<lb></lb>jor impetus imprimitur; </s>
					<s id="N28047">huc reuoca ſariſſæ grauiſſimum ictum, quo <lb></lb>ferrea lorica perfodi poteſt; </s>
					<s id="N2804D">quia ſcilicet maior impetus imprimitur in­<lb></lb>tentis priùs, &amp; vibratis brachijs; </s>
					<s id="N28053">multùm enim confert, tum illa bra­<lb></lb>chiorum, atque adeò totius ſariſſæ vibratio; </s>
					<s id="N28059">tùm etiam neruorum ten­<lb></lb>ſio, vt videmus in arcu; </s>
					<s id="N2805F">ſed hoc iam ſuprà explicuimus; huc etiam <lb></lb>reuoca craſſiorem illum vectem, quo fores ipſi pulſati perrum­<lb></lb>puntur. </s>
				</p>
				<p id="N28067" type="main">
					<s id="N28069">Quartò, longitudo ſariſſæ compenſari poteſt craſſitie; </s>
					<s id="N2806D">ſit enim <lb></lb>ſariſſa 12. pedes alta pendens 12. libras; </s>
					<s id="N28073">ſit alia 6. pedes alta pendens <pb pagenum="394" xlink:href="026/01/428.jpg"></pb>12. libras vtraque æquali niſu, &amp; modo ab eadem potentia impacta æ­<lb></lb>qualem ictum infligit; </s>
					<s id="N2807E">probatur quia tantumdem impetus imprimitur <lb></lb>vni, quantum alteri; </s>
					<s id="N28084">nam aëris reſiſtentia vix quidquam facit; </s>
					<s id="N28088">licèt pau­<lb></lb>lò plùs reſiſtat aër breuiori, cuius baſis latior eſt in ratione dupla, quàm <lb></lb>longiori; hinc craſſiori fuſte licèt breuiore maximus ictus infringitur, <lb></lb>vt patet experientiâ. </s>
				</p>
				<p id="N28092" type="main">
					<s id="N28094">Diceret aliquis hæc repugnare omnibus experimentis, quibus ſcili­<lb></lb>cet clariſſimè conſtat minorem eſſe breuiorum ſariſſarum vim. </s>
				</p>
				<p id="N28099" type="main">
					<s id="N2809B">Reſp. hoc ipſum accidere; quia breuiores ſariſſæ, quas habemus, vel <lb></lb>exiliores ſunt longioribus, vel ſaltem non craſſiores, cùm tamen craſſio­<lb></lb>res eſſe oporteat in eadem ratione, in qua illæ longiores ſunt vt æqualis <lb></lb>ſit ictus. </s>
				</p>
				<p id="N280A4" type="main">
					<s id="N280A6">Quintò, cur verò maior fuſtis maiorem impetum à brachiorum vi <lb></lb>recipiat; </s>
					<s id="N280AC">ratio eſt, primò quia maiori vtrumque brachium admouetur: </s>
					<s id="N280B0"><lb></lb>ſecundò, quia vibratur antequam intendatur; </s>
					<s id="N280B5">atqui ex ea vibratione <lb></lb>multus impetus accedit, vt patet ex vibrato ariete: </s>
					<s id="N280BB">tertiò, quia maior <lb></lb>fuſtis tardiùs mouetur, vt conſtat; </s>
					<s id="N280C1">igitur plùs impetus in eo producit <lb></lb>potentia motrix, quæ ſingulis inſtantibus toto niſu fuſtem impellit; </s>
					<s id="N280C7">&amp; <lb></lb>hæc eſt vera ratio à priori: </s>
					<s id="N280CD">quartò, adde quod pondus maioris fuſtis <lb></lb>quaſi neruos extendit; </s>
					<s id="N280D3">atqui tenſi nerui fortiores ſunt; </s>
					<s id="N280D7">in qua verò <lb></lb>proportione ſit maior ictus, dicemus numero ſequenti; eſt enim res <lb></lb>ſcitu digniſſima. </s>
				</p>
				<p id="N280DF" type="main">
					<s id="N280E1">Sextò, determinari poteſt proportio ictuum maioris, &amp; minoris <lb></lb>fuſtis, cum vterque punctim impingitur ab eadem potentiâ per eam­<lb></lb>dem lineam æquali niſu; </s>
					<s id="N280E9">ſit fuſtis minor H duarum librarum; </s>
					<s id="N280ED">ſit <lb></lb>maior I 8. librarum; </s>
					<s id="N280F3">ſit datum tempus L, quo I ſuam lineam K <lb></lb>motu accelerato ſpatium conficit: </s>
					<s id="N280F9">dico H eodem tempore L con­<lb></lb>ficere tantùm ſpatium prioris ſubquadruplum; </s>
					<s id="N280FF">igitur duplo tem­<lb></lb>pore conficit ſpatium K: </s>
					<s id="N28105">ſed æqualibus temporibus acquiruntur <lb></lb>æqualia velocitatis momenta motu accelerato; </s>
					<s id="N2810B">igitur vbi H confi­<lb></lb>cit ſpatium K, habet ſubduplam velocitatem illius, quam habet I <lb></lb>confecto eodem ſpatio K; </s>
					<s id="N28113">ſed moles H eſt quadrupla molis I; </s>
					<s id="N28117">igi­<lb></lb>tur impetus H eſt duplus impetu I; </s>
					<s id="N2811D">igitur duplò maior ictus: </s>
					<s id="N28121">quod <lb></lb>vt clariùs videatur, in ſchemate hoc ipſum demonſtro, producitur <lb></lb>æqualis impetus eodem tempore in H &amp; in I; </s>
					<s id="N28129">eſt enim eadem poten­<lb></lb>tia, idem niſus, ſed diſtribuitur in H numero partium quadru­<lb></lb>plo numeri partium I; </s>
					<s id="N28131">igitur velocitas, vel intenſio impetus H eſt <lb></lb>ſubquadrupla; </s>
					<s id="N28137">igitur ſi I tempore L percurrit AG; </s>
					<s id="N2813B">certè H eodem <lb></lb>tempore percurrit AB ſubquadruplam AG; </s>
					<s id="N28141">igitur duplo tempore <lb></lb>AC æqualem AG; </s>
					<s id="N28147">ſed H decurſa AC, habet ſubuplam veloci­<lb></lb>tatem I, decurſa AG; </s>
					<s id="N2814D">quia decurſa AF habet æqualem: </s>
					<s id="N28151">ſed AF eſt <lb></lb>quadrupla AC; igitur decurſa AC habet ſubduplam, &amp;c. </s>
					<s id="N28157">ſed ra­<lb></lb>tione molis habet H quadruplum impetus; igitur ratione vtriuſque <lb></lb>duplum. </s>
				</p>
				<pb pagenum="395" xlink:href="026/01/429.jpg"></pb>
				<p id="N28163" type="main">
					<s id="N28165">Obſeruabis autem primò ratione ponderis H, quod ſuſtińetur, aliquid <lb></lb>impetus detrahendum eſſe. </s>
					<s id="N2816A">Secundò, vt accuratè procedatur vtrumque <lb></lb>fuſtem funependulum eſſe poſſe. </s>
					<s id="N2816F">Tertiò, ictus eſſe vt impetus; impetus <lb></lb>verò in ratione ſubduplicata ponderum, hoc eſt, vt radices quadratas. </s>
					<s id="N28175"><lb></lb>v.g. fuſtis maior pendit 36. libras, minor 4; </s>
					<s id="N2817C">ictus maioris eſt ad ictum <lb></lb>minoris vt 6. ad 2. Quartò, denique plures partes percuti à maiore <lb></lb>fuſte, cuius baſis latior eſt, nec tam facilè comprimi, nec ipſum fuſtem <lb></lb>incuruari; ac proinde minùs ictui detrahi, ſed de his ſatis. </s>
				</p>
				<p id="N28186" type="main">
					<s id="N28188">Septimò, ſi fuſtis cæſim impingatur, maiorem ictum infligit. </s>
					<s id="N2818B">Primò, <lb></lb>non circa extremitatem ſed circa 2/3, vt demonſtrabimus infrà. </s>
					<s id="N28190">Secundò, <lb></lb>quò maior eſt arcus fuſtis eſt maior ictus; </s>
					<s id="N28196">ratio patet ex dictis; cùm ſit <lb></lb>motus acceleratus. </s>
					<s id="N2819C">Tertiò, poteſt hic motus totum implere orbem, ſiue <lb></lb>fieri auerſa, ſiue aduerſa manu. </s>
					<s id="N281A1">Quartò, auerſa manu impactus fuſtis ma­<lb></lb>iorem ictum infligit, quia brachium hoc modo intentum maiore vi <lb></lb>pollet, vt dictum eſt ſuprà. </s>
					<s id="N281A8">Quintò, hinc ſæpè ita inflecti ſeu tornari po­<lb></lb>teſt brachium, vt deſcribat arcum minoris circuli, ſed maiorem, ſeu po­<lb></lb>tius lineam ſpiralem, in qua deſcribenda diutiùs moratur; </s>
					<s id="N281B0">hinc motus fit <lb></lb>maior, quia eſt acceleratus; igitur maior ictus. </s>
					<s id="N281B6">Sextò, ſi fuſtis deorſum <lb></lb>feratur motu circulari, impetus naturalis accedit impreſſo. </s>
					<s id="N281BB">Septimò, ſi <lb></lb>vtraque manu intendatur fuſtis, maior erit ictus, vt conſtat ex dictis. </s>
					<s id="N281C0"><lb></lb>Octauò denique, quod dictum eſt de fuſte impacto cæſim, dici debet <lb></lb>enſe. </s>
				</p>
				<p id="N281C6" type="main">
					<s id="N281C8">Octauò, aliquando fuſtis inflectitur; </s>
					<s id="N281CB">quia flexibilis eſt; </s>
					<s id="N281CF">cum ſcilicet <lb></lb>motu circulari, ſeu cæſim diuerberat, ſeu flagellat; </s>
					<s id="N281D5">ſit enim fuſtis CA, <lb></lb>qui rotetur circa centrum C; </s>
					<s id="N281DB">certè vbi B peruenerit in E, A perueniet <lb></lb>in H; </s>
					<s id="N281E1">igitur inflexus eſt fuſtis HEC, vel GFC; ratio eſt, quia cùm po­<lb></lb>tentia applicata in C agat toto niſu. </s>
					<s id="N281E7">v. g. ſi ſegmentum CB ſeiunctum <lb></lb>eſſet à ſegmento BA; </s>
					<s id="N281F1">haud dubiè punctum B perueniet citiùs in F, quàm <lb></lb>ſi vtrumque ſegmentum coniunctum eſſet, vt notum eſt; </s>
					<s id="N281F7">quia maior im­<lb></lb>petus imprimitur B ſeiuncta; </s>
					<s id="N281FD">atqui licèt CB ſit coniunctum BA, ab eo <lb></lb>tamen facilè, non quidem omninò ſeiungi, ſed deflecti, dimoueri poteſt <lb></lb>propter flexibilitatem materiæ; </s>
					<s id="N28205">igitur B relinquet à tergo BA; </s>
					<s id="N2820B">igitur <lb></lb>fuſtis inflectetur, &amp; hæc eſt vera ratio huius phœnomeni: hinc virgulæ <lb></lb>ſucco &amp; humore plenæ, nerui bubuli latiores, canones, funiculi, lora, <lb></lb>enſes, manubria Tudiculæ maioris, &amp; alia huiuſmodi propter rationem <lb></lb>prædictam inflectuntur. </s>
				</p>
				<p id="N28217" type="main">
					<s id="N28219">Nonò, extremitas fuſtis inflexi, cum deinde redit, maiorem ictum in­<lb></lb>fligit: </s>
					<s id="N2821F">ratio eſt, v.g. A vbi attingit D poſt inflexionem; </s>
					<s id="N28225">quia maiorem <lb></lb>impetum habet; </s>
					<s id="N2822B">nam præter impreſſum à potentia applicata in C, acce­<lb></lb>dit alius ab ipſa inflexione, cuius rationem afferemus tractatu ſequenti, <lb></lb>cum de compreſſione, &amp; tenſione corporum; </s>
					<s id="N28233">eſt enim quædam potentia <lb></lb>media inter potentiam grauitationis, &amp; potentiam animatorum, quam <lb></lb>proinde mediam appellabimus; </s>
					<s id="N2823B">quâ ſcilicet corpora ſeſe reſtituunt pri­<lb></lb>ſtinæ extenſioni, cuius mirificos effectus habemus in arcu chordis pul-<pb pagenum="396" xlink:href="026/01/430.jpg"></pb>ſatis, vaſis pneumaticis, &amp; hydraulicis, denique in tota re tormentaria; <lb></lb>hinc primò Tudiculæ maioris manubrium inflexum multùm auget ipſam <lb></lb>vim ictus, de quo infrà. </s>
					<s id="N2824A">Secundò, neruus bubulus, primò inflexus, tùm <lb></lb>ſtatim rediens ſcapulas malè afficit. </s>
					<s id="N2824F">Tertiò, flexibiles virgæ tranſuerſas <lb></lb>plagas cum tanto dolore infligunt inuſtis vibicibus. </s>
					<s id="N28254">Quartò, idem dico <lb></lb>de regula illa latiore, qua remigiorum præſides, remiges tardos caſti­<lb></lb>gant &amp;c. </s>
				</p>
				<p id="N2825B" type="main">
					<s id="N2825D">Decimò, non videtur omittendum flagelli phœnomenum; </s>
					<s id="N28261">eſt autem <lb></lb>duplex flagellorum genus; </s>
					<s id="N28267">primum illorum eſt, quibus aurigæ ſuos <lb></lb>equos agunt; </s>
					<s id="N2826D">ſecundum eorum, quibus ſeges in area teritur; </s>
					<s id="N28271">quod ſpe­<lb></lb>ctat ad primum, vel loris vel funiculis conſtat; </s>
					<s id="N28277">acris verò eſt ictus, quem <lb></lb>inurit eius præſertim extremitas; </s>
					<s id="N2827D">ratio eſt, quia cùm partes funis, quæ <lb></lb>propius ad manubrium accedunt, citiùs moueantur, &amp; alias ponè relin <lb></lb>quant, iſtæ deinde in ſuo motu plùs temporis ponunt; </s>
					<s id="N28285">igitur, cùm ſit <lb></lb>motus acceleratus, maiorem induunt impetum, maioremque imprimunt: </s>
					<s id="N2828B"><lb></lb>adde quòd, continuò arcum minoris circuli extremitas ipſa deſcribit, <lb></lb>quæ vltimò tantum applicatur: </s>
					<s id="N28292">hinc nouus accelerationis modus, vt <lb></lb>clariſſimè videtur in funiculo circa digitum, cui aduoluitur in gyros <lb></lb>acto: </s>
					<s id="N2829A">Quod ſpectat ad flagellum frumentarium, mouetur motu mixto <lb></lb>ex duobus circularibus; </s>
					<s id="N282A0">conſtat enim de gemino fuſte, quorum alter <lb></lb>circa alterius extremitatem rotatur; </s>
					<s id="N282A6">hic verò circa centrum humeri: </s>
					<s id="N282AA"><lb></lb>porrò extremus fuſtis facit integrum circulum, vnde maximum ictum <lb></lb>infligit, quem ſcilicet præceſſit longior motus; </s>
					<s id="N282B1">adde quod quaſi à tergo <lb></lb>relinquitur extremus fuſtis ab altero; </s>
					<s id="N282B7">igitur diutiùs potentia maner ap­<lb></lb>plicata; </s>
					<s id="N282BD">igitur maiorem impetum producit, ex quo ſequitur maior ictus; </s>
					<s id="N282C1"><lb></lb>porrò vt vltima extremitas extremi fuſtis quaſi retroagitur; </s>
					<s id="N282C6">quod ſcilicet <lb></lb>eius centrum antè producatur, ſeu porrigatur; </s>
					<s id="N282CC">cùm enim attollitur fla­<lb></lb>gellum illud plicatile; haud dubiè extremitas deorſum tendit proprio <lb></lb>pondere, &amp; producto in aduerſam partem eius centro, vel altera extre­<lb></lb>mitate, quid mirum ſi perficit circulum? </s>
					<s id="N282D6">eius lineam deſcribemus l.12. </s>
				</p>
				<p id="N282D9" type="main">
					<s id="N282DB">Vndecimò, ſed aliquam huius phœnomeni adumbrationem iuuerit <lb></lb>exhibere; </s>
					<s id="N282E1">ſit flagellum plicatile DAB, ſitque AB ſolum areæ horizon­<lb></lb>ti parallelum; </s>
					<s id="N282E7">porrò ſit AB extremus fuſtis, qui voluitur circa cen­<lb></lb>trum A; </s>
					<s id="N282ED">DA verò ſit primus fuſtis ad inſtar manubrij volubilis circa <lb></lb>centrum D; </s>
					<s id="N282F3">ſit autem circellus DO, EF, &amp; brachium LMD, cuius <lb></lb>contractione dum erigitur flagellum, extremitas B deſcribit ſecirculum <lb></lb>DOE, &amp; A curuam AXG in aſcenſu, in deſcenſu GTA; </s>
					<s id="N282FB">B verò in <lb></lb>aſcenſu curuam BECK, in deſcenſu denique curuam KRB: </s>
					<s id="N28301">itaque <lb></lb>motus extremitas D mouetur motu circulari; </s>
					<s id="N28307">A verò motu mixto ex <lb></lb>circulari duplici, ſcilicet punctorum A &amp; D; </s>
					<s id="N2830D">D quidem per circellum <lb></lb>DFEO; </s>
					<s id="N28313">A verò per arcum AC, denique B motu mixto ex tribus cir­<lb></lb>cularibus D ſcilicet in circello DFEO, A in arcu AC, B denique in <lb></lb>circulo ABS; </s>
					<s id="N2831B">igitur B mouetur integro circulo circa A, A circa D per <lb></lb>arcum AC, &amp; D circa Y integro etiam circulo; </s>
					<s id="N28321">vbi verò A eſt in G, &amp; <lb></lb>D in E, B eſt in H; </s>
					<s id="N28327">mouetur autem B velociùs quàm A, tùm in aſcenſu, <pb pagenum="397" xlink:href="026/01/431.jpg"></pb>tùm deſcenſu; </s>
					<s id="N28330">quia tota GH eodem inſtanti cadit in AB; quippe H <lb></lb>participat motum A per GA, &amp; motum D per ED, quod clariſſimum <lb></lb>eſt. </s>
				</p>
				<p id="N28338" type="main">
					<s id="N2833A">Duodecimò, maior eſt ictus, ſi initio deſcenſus fuſtis AB tantillùm <lb></lb>retrò inclinet, vt GH; </s>
					<s id="N28340">quia B ab H in B plùs temporis ponit, quàm à <lb></lb>Q, vt patet; </s>
					<s id="N28346">igitur diutiùs potentia manet applicata; </s>
					<s id="N2834A">igitur maiorem <lb></lb>impetum producit; </s>
					<s id="N28350">igitur maior eſt ictus; </s>
					<s id="N28354">debet autem in eo ſitu eſſe, <lb></lb>in quo motus A in G ita temperetur cum motu B in H, vt eodem mo­<lb></lb>mento vtrumque feriat planum AB; </s>
					<s id="N2835C">ſi enim vel A attingat antè B, vel <lb></lb>B antè A, minor eſt ictus, vt conſtat; </s>
					<s id="N28362">quia totus motus ſimul non im­<lb></lb>peditur; </s>
					<s id="N28368">poteſt autem cognoſci ille ſitus vel illa inclinatio cognita pro­<lb></lb>portione motus circularis circa D, &amp; circa A; </s>
					<s id="N2836E">immò niſi retineatur <lb></lb>DA; </s>
					<s id="N28374">haud dubiè A tanget ſolum AB ex G, antequam B deſcendat in B <lb></lb>ex H; </s>
					<s id="N2837A">igitur attemperandus eſt motus fuſtis DA; </s>
					<s id="N2837E">præterea pondus in <lb></lb>deſcenſu auget ictum, deinde B deſcendit deorſum motu orbis &amp; motu <lb></lb>centri: </s>
					<s id="N28386">præterea B poteſt in aſcenſu maiorem arcum ſui orbis decurre­<lb></lb>re, quàm in deſcenſu, vel æqualem: denique maior eſt ictus quando po­<lb></lb>tentia toto niſu euidente fuſtis AB plùs temporis ante ictum in ſuo mo­<lb></lb>tu inſumit. </s>
				</p>
				<p id="N28390" type="main">
					<s id="N28392">Decimotertiò, eſt etiam aliud flagelli genus pluribus catenulis ferreis <lb></lb>inſtructi, ex quibus ſingulis ſinguli ferrei globi aliquando ſpiculis, &amp; <lb></lb>clauis armati pendent, quorum grauiſſimus eſt ictus propter rationes <lb></lb>prædictas; </s>
					<s id="N2839C">præſertim cùm catenula, ſeu funiculus, faciliùs adduci, &amp; in­<lb></lb>flecti poſſit, quàm extremus ille fuſtis, de quo ſuprà; </s>
					<s id="N283A2">neque deeſt ar­<lb></lb>tificium; quo quis hoc armorum genere vtens etiam contra plures ſeſe <lb></lb>tueri poſſit. </s>
				</p>
				<p id="N283AA" type="main">
					<s id="N283AC">Decimoquartò, denique vulgare eſt phœnomenum illud funiculi, ſen <lb></lb>flagelli, quo ſcilicet initio remouetur manubrij extremitas, mox ſtatim <lb></lb>adducitur, ex qua productione, &amp; adductione per vndantem funem <lb></lb>propagatur impetus vſque ad eiuſdem extremitatem nodo vt plurimùm <lb></lb>adſtrictam. </s>
					<s id="N283B7">Hinc primò ſtrepitus ille aurigis familiariſſimus; </s>
					<s id="N283BB">quippe <lb></lb>maxima fit aëris colliſio in extremo fune; immo, &amp; partium tenſio, ſeu <lb></lb>diſtractio propter motus illos contrarios productionis. </s>
					<s id="N283C3">Secundò, hinc <lb></lb>diſtrahitur funis, &amp; quaſi laceratur, diſtractis ſcilicet tenuiſſimis illis <lb></lb>filamentis, ex quibus conſtat. </s>
					<s id="N283CA">Tertiò, hinc ſtringitur illa extremitas no­<lb></lb>do, tùm vt acrior ſit ictus, tùm vt filamenta illa nodo illo contineantur. </s>
					<s id="N283CF"><lb></lb>Quartò, duplex eſt motus illius funis propter flexibilitatem; </s>
					<s id="N283D4">hinc illæ <lb></lb>vndæ ſeu ſpiræ; </s>
					<s id="N283DA">nam remouetur caput funis, quod deinde ſequuntur <lb></lb>aliæ partes per ſinuoſos flexus; ſed mox vbi adducitur idem caput, maios <lb></lb>impetus producitur in aliis partibus. </s>
					<s id="N283E2">Quintò, currentes vndæ ſeu flexus <lb></lb>adductionis, quæ fit maiore impetu, quàm productio, tandem in <lb></lb>primos flexus ſinuatos ab ipſa productione incurrunt: hinc augetur <lb></lb>impetus, &amp; motus extremitatis. </s>
					<s id="N283EC">Sextò, adde quod licèt ſit tantùm, vel <lb></lb>productio, vel adductio flagelli, ſunt iidem ſerè effectus, ſed minimè <lb></lb>æquales, quia augetur continuò motus flexuum; </s>
					<s id="N283F4">tùm quia funis verſus <pb pagenum="398" xlink:href="026/01/432.jpg"></pb>extremitatem ſenſim imminuitur; </s>
					<s id="N283FD">tùm quia minor eſt radius illius mo­<lb></lb>tus, quia circulari incipit: hinc extremitas funis velociſſimè tandem <lb></lb>mouetur, &amp; impacta acutiſſimum ictum incutit. </s>
					<s id="N28405">Septimò, obſerua pro­<lb></lb>pter illam inflexionem motum diutiùs perſeuerare; </s>
					<s id="N2840B">igitur potentia <lb></lb>manet diutiùs applicata; </s>
					<s id="N28411">igitur maiorem effectum producit, vnde re­<lb></lb>uocare poteſt: hunc effectum ad illud phænomenum baculi flexibilis, <lb></lb>de quo ſuprà. </s>
					<s id="N28419">Octauò, hinc pueri ſtrophiolis prædicto modo inflexis <lb></lb>inter ſe contendunt, pro quo eſt eadem ratio. </s>
					<s id="N2841E">Nonò, hinc vt excutiatur <lb></lb>puluis ex pannis, eodem modo ſuccutiuntur; </s>
					<s id="N28424">tùm propter tenſionem <lb></lb>filorum, quæ pulueri liberiores meatus aperit; </s>
					<s id="N2842A">tùm propter vibrationes <lb></lb>quæ puluerem abigunt: </s>
					<s id="N28430">immò flexibus aduerſis tapetes ita ſuccutiun­<lb></lb>tur, vt flexus hinc inde currentes quaſi tumentes fluctus, ſibi inuicem <lb></lb>occurrant in medio tapete, &amp; allidantur; </s>
					<s id="N28438">hinc ſequitur tenſio; </s>
					<s id="N2843C">hinc <lb></lb>vibratio, pulueris excuſſio, hinc etiam ſtrepitus; denique clariſſimè vi­<lb></lb>dentur flexus illi volubiles in extenſa mappa, quorum ratio patet ex <lb></lb>dictis. </s>
				</p>
				<p id="N28446" type="main">
					<s id="N28448"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N28454" type="main">
					<s id="N28456"><emph type="italics"></emph>Explicari poſſunt omnia percuſſionum phœnomena, quæ fiunt opera mallei,<emph.end type="italics"></emph.end><lb></lb>hîc conſideratur malleus quaſi incuſſus circulari motu, qui nullo mo­<lb></lb>do coniunctus ſit cum motu naturali deorſum, quod tamen infrà ex­<lb></lb>plicabimus; hoc poſito. </s>
				</p>
				<p id="N28464" type="main">
					<s id="N28466">Primò, quò maior eſt malleus eodem arcu impactus &amp; manubrio, <lb></lb>maior eſt ictus, quia tardiùs mouetur; </s>
					<s id="N2846C">igitur potentia manet diutiùs <lb></lb>applicata; igitur maior eſt ictus, vt conſtat ex dictis. </s>
				</p>
				<p id="N28472" type="main">
					<s id="N28474">Secundò, hinc ex hac hypotheſi ictus ſunt in ratione ſubduplicata <lb></lb>ponderum malleorum; conſtat etiam, poſita ſcilicet eadem longitudine <lb></lb>manubrij. </s>
				</p>
				<p id="N2847C" type="main">
					<s id="N2847E">Tertiò, maior incutitur ictus non quidem circa extremitatem <lb></lb>baſis mallei, nec circa medium, ſed circa mediam proportionalem <lb></lb>inter diametrum baſis, &amp; ſubduplum, patet per Th. 73. l. 1. Co­<lb></lb>rol. 4. </s>
				</p>
				<p id="N2848C" type="main">
					<s id="N2848E">Quartò, ſi ſit longius manubrium mallei, maiorem ictum infliget; </s>
					<s id="N28492"><lb></lb>quia tardius maiorem arcum decurrit, quàm minorem; </s>
					<s id="N28497">igitur potentia <lb></lb>manet diutiùs applicata; </s>
					<s id="N2849D">igitur maiorem effectum producit; </s>
					<s id="N284A1">quod au­<lb></lb>tem tardiùs ſuum arcum perficiat maior radius, patet experientia ma­<lb></lb>ioris perticæ &amp; breuioris fuſtis; cuius ratio eſt, quia idem impetus ma­<lb></lb>iori moli impreſſus remiſſior eſt, quia ſcilicet pluribus partibus diſtri­<lb></lb>buitur. </s>
				</p>
				<p id="N284AD" type="main">
					<s id="N284AF">Quintò, velocitates extremitatum, poſita diuerſa longitudine manu­<lb></lb>brij, ſunt vt ipſæ longitudines permutando: </s>
					<s id="N284B5">probatur, quia cùm ſit mo­<lb></lb>tus acceleratus, ſpatia ſunt vt quadrata temporum; ſed velocitates <lb></lb>ſunt vt tempora, &amp; tempora ſunt in ratione ſubduplicata ſpatiorum. </s>
					<s id="N284BD"><lb></lb>id eſt, vt diametri quadratorum, id eſt, vt longitudines, ſit enim lon­<lb></lb>gitudo AB, quæ dato tempore H decurrat ſpatium ABF, potentia <pb pagenum="399" xlink:href="026/01/433.jpg"></pb>ſcilicet toto niſu applicata, ſit etiam longitudo AC dupla AB: </s>
					<s id="N284C9">dico <lb></lb>quod eodem tempore H acquiret æquale ſpatium ſcilicet CAD; </s>
					<s id="N284CF">igitur <lb></lb>CAD eſt 1/4 CAG, quia eſt æquale BAF; </s>
					<s id="N284D5">igitur CD eſt 1/4 CG, ſed <lb></lb>CG eſt duplus BF; </s>
					<s id="N284DB">igitur CD eſt ſubduplus BF; </s>
					<s id="N284DF">igitur velocitas ex­<lb></lb>tremitatis C in CA eſt ſubdupla velocitatis B in BA: </s>
					<s id="N284E5">adde quod AC cùm <lb></lb>numerus partium AC ſit duplus numeri partium AB, &amp; cùm in eadem <lb></lb>proportione diſtribuatur impetus AC, &amp; AB; certè partes maioris ſi <lb></lb>comparentur cum partibus proportionalibus minoris, ſubduplam tan­<lb></lb>tùm habebunt portionem. </s>
				</p>
				<p id="N284F1" type="main">
					<s id="N284F3">Sextò, ictus inflicti à malleis, quorum manubria diuerſam longitu­<lb></lb>dinem habent, ſuppoſito eodem angulo, ſunt vt longitudines; </s>
					<s id="N284F9">ſi enim <lb></lb>eo tempore, quo AB facit ſpatium BAF, AC facit CAD; </s>
					<s id="N284FF">certè æquali <lb></lb>tempore AC faciet DAG, vt conſtat ex natura motus accelerati; </s>
					<s id="N28505"><lb></lb>igitur acquirit <expan abbr="tantũdem">tantundem</expan> impetus; </s>
					<s id="N2850E">ſed eo tempore, quo AC decurrit <lb></lb>CAD, acquirit æqualem impetum AB dum percurrit BAF, vt patet ex <lb></lb>dictis; </s>
					<s id="N28516">igitur AC decurſo CAG habet duplum impetum AB decurſo <lb></lb>BAF; </s>
					<s id="N2851C">igitur dupla eſt vis ictus; </s>
					<s id="N28520">igitur ictus ſunt in ratione ſubdupli­<lb></lb>cata CAG, BAF; igitur vt ACAB. </s>
				</p>
				<p id="N28526" type="main">
					<s id="N28528">Septimò, diceret aliquis velocitatem C decurſo CD, eſſe ſubduplam <lb></lb>velocitatis B decurſo BF; </s>
					<s id="N2852E">ſed velocitas C, decurſo CG, eſt dupla velo­<lb></lb>citatis eiuſdem C decurſo CD; </s>
					<s id="N28534">igitur velocitas C, decurſo CG, eſt <lb></lb>æqualis velocitati B, decurſo BF; igitur æqualis ictus. </s>
					<s id="N2853A">Reſp. conceſſa <lb></lb>primâ conſequentiâ, vltimâ verò negatâ; </s>
					<s id="N28540">quia non tantùm impetus <lb></lb>puncti C incutit ictum ſed totius CA, qui cenſetur eſſe collectus in <lb></lb>malleo in quo eſt quaſi centrum huius impetus, vt iam explicuimus <lb></lb>aliàs; ſed velocitas totius CA confecto CAD eſt æqualis velocitati <lb></lb>totius BA confecto BAF, cuius velocitas CA confecto CAG eſt dupla, <lb></lb>vt iam probatum eſt. </s>
				</p>
				<p id="N2854E" type="main">
					<s id="N28550">Octauò, hinc ictus CA confecto CAD eſt æqualis ictui AB con­<lb></lb>fecto BAF, &amp; ictus CA confecto CI duplo CD eſt ad ictum CA con­<lb></lb>fecto CD, vt radix CA ad radicem CI: </s>
					<s id="N28558">hinc vides hunc motum con­<lb></lb>uenire in eo cum recto, quòd ſcilicet ictus inflictus motu recto à mi­<lb></lb>nori mole, ſit ad ictum maioris, ſuppoſita linea motus æquali in ratio­<lb></lb>ne ſubduplicata ponderum; quòd dicitur etiam de motu circulari duo­<lb></lb>rum fuſtium inæqualium, quorum ictus ſunt in ratione ſubduplicata <lb></lb>longitudinum, aſſumptis duntaxat arcubus æqualibus ab extremitate <lb></lb>vtriuſque decurſis. </s>
				</p>
				<p id="N28568" type="main">
					<s id="N2856A">Nonò, cum mallei ſunt diuerſi ponderis, &amp; longitudinis, facilè co­<lb></lb>gnoſci poterit proportio ictuum; </s>
					<s id="N28570">eſt enim compoſita ex ratione lon­<lb></lb>gitudinum &amp; ſubduplicata ponderum v.g. ſit malleus A, cuius longitu­<lb></lb>do ſit 2. pondus 4. ſit malleus B cuius longitudo ſit pondus; </s>
					<s id="N2857A">rectè ra­<lb></lb>tio longitudinum eſt 2/3, &amp; ſubduplicata ponderum eſt 2/3; </s>
					<s id="N28580">ducatur vna <lb></lb>in aliam, vt euadat compoſita ſcilicet 4/1 vel longitudo A ſit I, &amp; B 2; </s>
					<s id="N28586"><lb></lb>habebitur ratio ſubduplicata ponderum 2/1, &amp; ratio longitudinum 3/2; </s>
					<s id="N2858D"><lb></lb>ducatur vna in aliam, habebitur ratio compoſita 2/2; </s>
					<s id="N28594">igitur ſunt æqua-<pb pagenum="400" xlink:href="026/01/434.jpg"></pb>les, quæ omnia facilè intelliguntur ex dictis; </s>
					<s id="N2859D">itaque habes 4. combina­<lb></lb>tiones duorum malleorum; </s>
					<s id="N285A3">vel enim eſt idem pondus vtrique, &amp; ea­<lb></lb>dem longitudo, vel idem pondus, ſed diuerſa longitudo, vel eadem lon­<lb></lb>gitudo &amp; diuerſum pondus, vel diuerſum pondus &amp; diuerſa longitudo; <lb></lb>ſi verò eſt diuerſa longitudo ſimul, &amp; diuerſum pondus, vel eidem ineſt <lb></lb>maius pondus, &amp; maior longitudo, vel maior longitudo, &amp; minus pon­<lb></lb>dus, &amp; contrà alteri minor longitudo, &amp; minus pondus, vel maius pon­<lb></lb>dus, &amp; minor longitudo, quorum omnium proportiones ſunt determi­<lb></lb>natæ. </s>
				</p>
				<p id="N285B5" type="main">
					<s id="N285B7">Decimò, quod ſpectat ad craſſitudinem manubrij, illa haud dubiè <lb></lb>auget aliquando vim ictus, aliquando imminuit; </s>
					<s id="N285BD">auget quidem, cum <lb></lb>malleus centrum impetus occupat eo modo, quo explicuimus l. 1.Th.73. <lb></lb>Corol.4. imminuit verò cum ab eo centro recedit, vt manifeſtum eſt ex <lb></lb>dictis ibidem, cum infligitur ictus eo mallei puncto, in quo non eſt <lb></lb>prædictum centrum, formicat manus infligentis, vt patet experientiâ; </s>
					<s id="N285CB"><lb></lb>quippe extremitas illa manubrij, quæ manu tenetur, vel attollitur, vel <lb></lb>deprimitur; </s>
					<s id="N285D2">attollitur quidem, ſi punctum contactus, vel ictus eſt inter <lb></lb>prædictum centrum &amp; manum; </s>
					<s id="N285D8">&amp; è contrario deprimitur, ſi centrum <lb></lb>ipſum ſit inter punctum contactus &amp; manum; </s>
					<s id="N285DE">&amp; quia manus im­<lb></lb>pedit, ne vel attollatur, vel deprimatur, impetus in illam qua­<lb></lb>ſi refunditur; </s>
					<s id="N285E6">hinc illa formicatio non ſine maximo ſæpiùs do­<lb></lb>loris ſenſu; </s>
					<s id="N285EC">denique obſerua nouem eſſe combinationes, ſi con­<lb></lb>ſiderentur in malleo longitudo, &amp; latitudo manubrij cum ipſo <lb></lb>pondere; quippe ſi 3. ducantur in 3. erunt 9. ſed hæc ſunt fa­<lb></lb>cilia. </s>
				</p>
				<p id="N285F6" type="main">
					<s id="N285F8">Vndecimò, ſi malleus impingatur deorſum creſcit ictus propter mo­<lb></lb>tum naturaliter acceleratum, additum ſcilicet extrinſecùs impreſſo; </s>
					<s id="N285FE"><lb></lb>ſi enim mallei cadunt ex eadem altitudine, ſuntque eiuſdem ponderis, <lb></lb>ictus æquales eſſe neceſſe eſt; </s>
					<s id="N28605">ſi verò ſunt eiuſdem ponderis, &amp; cadunt <lb></lb>ex diuerſa altitudine impetus acquiſiti motu naturali, ſunt in ratione <lb></lb>ſubduplicata altitudinum; </s>
					<s id="N2860D">ſi verò ſunt diuerſi ponderis, &amp; cadunt ex <lb></lb>diuerſa altitudine, ſunt in ratione compoſita aliquomodo ex vtraque; </s>
					<s id="N28613"><lb></lb>dico aliquo modo, quia non eſt omninò propria compoſitio rationum; </s>
					<s id="N28618"><lb></lb>poteſt tamen facilè proportio ictuum inueniri, v. g. ſit malleus A, &amp; <lb></lb>malleus B, ictus A ratione impetus impreſſi extrinſecus ſit vt 8, ratione <lb></lb>caſus ſit vt 2; </s>
					<s id="N28625">at verò ictus B ratione impetus impreſſi ſit vt 6, ratione <lb></lb>caſus vt 3: </s>
					<s id="N2862B">addantur 8, &amp; 2 erunt 10; </s>
					<s id="N2862F">adduntur 6, &amp; 3 erunt 9; </s>
					<s id="N28633">igitur <lb></lb>ictus ſunt in ratione (10/9), vt conſtat: </s>
					<s id="N28639">porrò quemadmodum nouus im­<lb></lb>petus accedit ratione motus naturalis, cum malleus impingitur deor­<lb></lb>ſum, ita aliquid impetus deſtruitur cum malleus impingitur ſurſum, vt <lb></lb>patet; </s>
					<s id="N28643">denique, quia ſunt 5 termini, quos reſpicit ictus, ſcilicet pondus <lb></lb>mallei, longitudo manubrij, craſſitudo arcus extremitatis, &amp; linea ſur­<lb></lb>ſum vel deorſum, ita ſunt 25. combinationes ictuum; ſed hoc fa­<lb></lb>cile eſt. </s>
				</p>
				<pb pagenum="401" xlink:href="026/01/435.jpg"></pb>
				<p id="N28651" type="main">
					<s id="N28653">Duodecimò, ictus eiuſdem mallei per diuerſos arcus ſunt in ra­<lb></lb>tione ſubduplicata arcuum. </s>
					<s id="N28658">v. g. ſit malleus AC arcus CD, tùm <lb></lb>arcus CG: </s>
					<s id="N28662">dico ictus per vtrumque arcum eſſe in ratione ſubdu­<lb></lb>plicata arcuum CD, EG, id eſt in ratione 2/3, vt conſtat ex dictis; <lb></lb>poteſt etiam facilè inueniri proportio, ſi ſit diuerſa longitudo, vel <lb></lb>diuerſum pondus &amp;c. </s>
					<s id="N2866C">hinc ratio manifeſta, cur per minimum ictum <lb></lb>nullus ferè ſit ictus: ſed hæc ex dicendis infrà de caſu clariſſimè intel­<lb></lb>ligentur. </s>
				</p>
				<p id="N28674" type="main">
					<s id="N28676">Decimotertiò, claua reduci debet ad malleum. </s>
					<s id="N28679">Primò, deter­<lb></lb>minari poteſt, ex quo puncto maiorem ictum infligit, quando mo­<lb></lb>uetur motu recto; </s>
					<s id="N28681">ſit enim centrum grauitatis clauæ I, in quo ſi <lb></lb>ſuſtineatur, ſtabit in æquilibrio; </s>
					<s id="N28687">ducatur FIE, maiorem ictum <lb></lb>infliget ex puncto E, quia <expan abbr="tantũdem">tantundem</expan> eſt impetus in ſegmento <lb></lb>FEK quantum in ſegmento FEA; </s>
					<s id="N28693">igitur totus impeditur impe­<lb></lb>tus; igitur maximus erit ictus ſi infligat ictum motu circulari circa <lb></lb>aliud eſt centrum percuſſionis, de quo infrà. </s>
					<s id="N2869B">Tertiò, hoc percuſſio­<lb></lb>nis organum validum ictum infligit propter illam extremam craſ­<lb></lb>ſitudinem, eſt enim quoddam mallei genus, &amp; valdè periculoſum; </s>
					<s id="N286A3"><lb></lb>præſertim ſi ferreis clauis armetur; </s>
					<s id="N286A8">hinc vulgò tribuitur Herculi tan­<lb></lb>quam inſigne fortitudinis ſymbolum; porrò tàm altè clauum infigit <lb></lb>ſibi coniunctum, quam infigeret, ſi claua ipſa erectum, &amp; quaſi expe­<lb></lb>ctantem ictum feriret. </s>
				</p>
				<p id="N286B2" type="main">
					<s id="N286B4">Decimoquartò, Tudicula maior reuocatur ad malleum. </s>
					<s id="N286B7">Primò <lb></lb>faciunt ad ictum longitudo manubrij, flexibilitas, inæqualitas, mal­<lb></lb>lei pondus, durities materiæ, arcus motus, vegetæ potentiæ vires; </s>
					<s id="N286BF"><lb></lb>omitto ea, quæ cum malleo habet communia, quorum ratio ex <lb></lb>dictis conſtare poteſt; igitur non videntur eſſe repetenda. </s>
					<s id="N286C6">Secundò, <lb></lb>flexibilitas manubrij auget vim ictus, tùm quia potentia diutiùs <lb></lb>manet applicata, cùm aliquo tempore in ipſa vibratione malleus à <lb></lb>tergo relinquatur, tùm quia potentia illa media, de qua ſupra, ſuum <lb></lb>impetum, impetui alterius adiungit. </s>
					<s id="N286D1">Tertiò, ita manubrium fa­<lb></lb>bricatur, vt continua imminutione verſus malleum decreſcat, quod <lb></lb>multum facit ad ictum, quia hæc inæqualitas inflexioni reſiſtit ver­<lb></lb>ſus caput manubrij; </s>
					<s id="N286DB">igitur initio inflectitur manubrium, non pro­<lb></lb>cul à malleo, tùm deinde aucto impetu in partibus remotioribus, <lb></lb>quæ difficiliùs inflectuntur; </s>
					<s id="N286E3">igitur inæqualiter partes illæ redeunt, <lb></lb>atque ſeſe priſtino ſtatui reſtituunt; </s>
					<s id="N286E9">atqui ex illa inæqualitate diu­<lb></lb>tiùs durat motus; </s>
					<s id="N286EF">igitur inde maior euadit: </s>
					<s id="N286F3">ſimile quid videmus in <lb></lb>arcu, cuius medium craſſius eſt: adde quod ſi æqualis ſit craſſitudo, <lb></lb>incipit inflexio verſus illam extremitatem, quæ propiùs accedit ad <lb></lb>manum, longiùs recedit à malleo, vt patet experientiâ, in fune, <lb></lb>virgâ &amp;c. </s>
					<s id="N286FF">ſed de arcu, tenſione, compreſſione fusè agemus <lb></lb>tractatu ſingulari: </s>
					<s id="N28705">hæc tantum obiter indicaſſe ſufficiat. <pb pagenum="402" xlink:href="026/01/436.jpg"></pb>Quartò, maximus eſt ictus, cum malleus eo inſtanti attingit pilam, quo <lb></lb>manubrium eſt rectum; </s>
					<s id="N28710">tunc enim eſt modum vibrationis ſeu reditus; <lb></lb>igitur maximus impetus. </s>
					<s id="N28716">Quintò, ſi altera extremitas mallei, quæ glo­<lb></lb>bum attingit, ſit obliqua, globum ipſum attollit propter punctum con­<lb></lb>tactus; quod certè clarum eſt. </s>
					<s id="N2871E">Sextò, durities mallei multùm facit ad <lb></lb>ictum; </s>
					<s id="N28724">ſi enim cedat lignum, imminuitur impetus, vt patet; hinc ar­<lb></lb>millâ, vel annulo ferreo armatur vtraque baſis mallei, vt firmior eua­<lb></lb>dat. </s>
					<s id="N2872C">Septimò, globi ratio multa habenda eſt, cui infligitur ictus; </s>
					<s id="N28730">quippe <lb></lb>ſi leuior eſt ab aëre ambiente impeditur, &amp; retinetur; </s>
					<s id="N28736">ſi verò mollior <lb></lb>minor ictus infligitur, quia cedit materies; </s>
					<s id="N2873C">hinc pilæ è duriore buxo <lb></lb>tornantur; </s>
					<s id="N28742">hinc etiam tunduntur pilæ malleo, vt materies denſior <lb></lb>euadat, impleanturque infinita ferè vacuola aëre plena, quæ pilam le­<lb></lb>uiorem reddunt; ſed hæc ad emiſſionem, &amp; proiectionem pertinent, <lb></lb>de quibus infrà. </s>
					<s id="N2874C">Octauò, vt recta via procedat pila debet in id punctum <lb></lb>malleus infligi, ex quo ducta per centrum pilæ linea, &amp; deinde produ­<lb></lb>cta concurrat cum ipſa linea directionis; nec enim aliter determinari <lb></lb>poteſt linea motus globi per Th... l.1. hinc manubrium debet ſemper <lb></lb>facere angulos rectos cum linea directionis. </s>
					<s id="N28758">Nonò, ad ictum inflictum <lb></lb>à maiori Tudicula tres potentiæ motrices concurrunt, ſcilicet ipſa po­<lb></lb>tentia impellentis, potentia motus deorſum, &amp; ipſa media; </s>
					<s id="N28760">igitur hæc <lb></lb>ars in eo præſertim poſita eſt, quod hæ potentiæ ita temperentur, ſeu <lb></lb>componantur, vt vna non obſit alteri, &amp; ſingulæ pro viribus agat: ex <lb></lb>his alia facilè intelligentur. </s>
				</p>
				<p id="N2876A" type="main">
					<s id="N2876C">Decimoquintò, ſupereſt familiaris ille ſoni effectus, quem mal­<lb></lb>leus cadens in incudem edit, quem tamen hîc non diſcutiemus; quia <lb></lb>naturam &amp; affectiones ſonorum alio Tomo de qualitatibus ſenſibilibus <lb></lb>libro ſingulari fusè explicabimus. </s>
				</p>
				<p id="N28776" type="main">
					<s id="N28778"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N28784" type="main">
					<s id="N28786"><emph type="italics"></emph>Ex dictis explicaris poſſum omnia phœnomena, quæ obſeruantur in ludo <lb></lb>rudis gladiatoriæ<emph.end type="italics"></emph.end>; </s>
					<s id="N28792">Primo, tria ſunt in hac arte, ad quæ reliqua facilè re­<lb></lb>ducuntur; </s>
					<s id="N28798">primum eſt declinatio; ſecundum petitio; tertium confla­<lb></lb>tum ex vtroque. </s>
					<s id="N2879E">Secundò, poteſt declinati, vel auerti ictus, ſeu petitio <lb></lb>duobus modis. </s>
				</p>
				<p id="N287A3" type="main">
					<s id="N287A5">Primò, ſi declinatio cum aliqua impactione coniungatur. </s>
				</p>
				<p id="N287A8" type="main">
					<s id="N287AA">Secundò, ſi tantùm cum mera reſiſtentia, vel ſimplici impul­<lb></lb>ſione. <lb></lb><arrow.to.target n="note4"></arrow.to.target></s>
				</p>
				<p id="N287B3" type="margin">
					<s id="N287B5"><margin.target id="note4"></margin.target>a <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 17 <lb></lb><emph type="italics"></emph>Tab.<emph.end type="italics"></emph.end> 5.</s>
				</p>
				<p id="N287C8" type="main">
					<s id="N287CA">Tertiò, vtriuſque modi ſunt 4. combinationes; </s>
					<s id="N287CE">ſiue enim duo gladij <lb></lb>AC, DF, capulares pilæ AD; </s>
					<s id="N287D4">ſit autem gladius AC declinans petitio­<lb></lb>nem alterius DF; id certè quatuor modis præſtare poteſt. </s>
					<s id="N287DA">Primò, ſi <lb></lb>punctum contactus ad mucronem vtriuſque propiùs accedat. </s>
					<s id="N287DF">v.g. ſi <lb></lb>vterque ſit in ſitu ACDF. Secundò, ſi propiùs accedat ad capulum <lb></lb>vtriuſque, talis eſt ſitus DFCH. Tertiò, ſi accedat propiùs ad mu­<lb></lb>cronem gladij petentis DF, &amp; propiùs ad capulum declinantis. <pb pagenum="403" xlink:href="026/01/437.jpg"></pb>Quartò, è contrario ſi accedat propiùs ad capulum petentis DF, &amp; pro­<lb></lb>piùs ad mucronem declinantis; addi poteſt quinta combinatio, cum <lb></lb>ſcilicet contactus eſt in medio vtriuſque. </s>
				</p>
				<p id="N287F6" type="main">
					<s id="N287F8">Quartò, ſi ſit mera impulſio ſine percuſſione, vel impactione, maxi­<lb></lb>ma vis eſt declinationis, cum punctum contactus accedit propiùs ad ca­<lb></lb>pulum declinantis, &amp; ad mucronem petentis iuxta tertiam combinatio­<lb></lb>nem, &amp; ſitum DFPE, &amp; punctum contactus in B; </s>
					<s id="N28802">ratio eſt, cum verta­<lb></lb>tur PE circa P applicatæ potentiæ in P, maius eſt momentum in B <lb></lb>quàm in alio puncto verſus E, vt patet; </s>
					<s id="N2880A">quippe B mouetur minore motu; </s>
					<s id="N2880E"><lb></lb>igitur faciliùs; </s>
					<s id="N28813">præterea FD mouetur circa D; igitur in B faciliùs pelli­<lb></lb>tur, quàm in vllo puncto verſus D ratione vectis. </s>
				</p>
				<p id="N28819" type="main">
					<s id="N2881B">Quintò, cum punctum contactus accedit propiùs ad capulum peten­<lb></lb>tis, &amp; ad mucronem impellentis, minima vis eſt declinationis, ſcilicet <lb></lb>iuxta quartam combinationem, &amp; ſitum DFRG: ratio eſt, quia minor <lb></lb>eſt vis potentiæ applicatæ in R, &amp; maior reſiſtentia applicatæ in D, vt <lb></lb>patet ex dictis. </s>
				</p>
				<p id="N28827" type="main">
					<s id="N28829">Sextò, cum punctum contactus accedit propiùs ad capulum vtrïuſque <lb></lb>iuxta ſecundam combinationem, &amp; ſitum DFSH, tunc eſt maxima vis <lb></lb>declinantis, &amp; maxima reſiſtentia petentis; </s>
					<s id="N28831">vnde vna compenſatur ab <lb></lb>alia; </s>
					<s id="N28837">cum verò punctum contactus accedit propiùs ad mucronem vtriuſ­<lb></lb>que, minima eſt vis impellentis, &amp; minima reſiſtentia impulſi iuxta pri­<lb></lb>mam combinationem, &amp; ſitum DFAC; ratio patet ex dictis. </s>
				</p>
				<p id="N2883F" type="main">
					<s id="N28841">Septimò, hinc tam facilè declinatur ictus gladij DF, ſiue fiat iuxta <lb></lb>primam combinationem, ſiue iuxta ſecundam, quia licèt ſit minima vis <lb></lb>in prima; </s>
					<s id="N28849">eſt etiam minima reſiſtentia; </s>
					<s id="N2884D">&amp; licèt ſit maxima reſiſtentia <lb></lb>in ſecunda, eſt etiam maxima vis; </s>
					<s id="N28853">igitur vna compenſat aliam, vt patet; </s>
					<s id="N28857"><lb></lb>immò iuxta ſitum DFQK, poſito puncto contactus in L, &amp; iuxta om­<lb></lb>nem alium ſitum, in quo punctum contactus æqualiter diſtat à mucro­<lb></lb>ne vtriuſque, vis declinantis æqualis eſt; eſt enim æqualis ratio virium, <lb></lb>&amp; reſiſtentiæ, vt conſtat, poſita vtriuſque longitudine. </s>
				</p>
				<p id="N28862" type="main">
					<s id="N28864">Octauò, ſi verò impulſio, vel declinatio fiat cum impactione, tribus <lb></lb>modis id fieri poteſt; </s>
					<s id="N2886A">primo, motu circulari circa pilam capularem A: </s>
					<s id="N2886E"><lb></lb>ſecundo, motu circulari circa centrum diſtans 3/4 à capulò, tertio, motu <lb></lb>recto ducto ſcilicet gladio dextrorſum, vel ſiniſtrorſum horizonti pa­<lb></lb>rallelo; primus modus peſſimus eſt, quia totum corpus, defectum manet. </s>
					<s id="N28877"><lb></lb>Tertius proximè ad priorem accedit propter <expan abbr="eãdem">eandem</expan> rationem. </s>
					<s id="N2887F">Secun­<lb></lb>dus optimus omnium, &amp; communis eſt, quia ſemper gladius tegit <lb></lb>corpus. </s>
				</p>
				<p id="N28886" type="main">
					<s id="N28888">Nonò, ſi primo modo declinatur ictus repulſo petentis gladio maxi­<lb></lb>ma vis erit; ſi punctum contactus fiat circa 2/3 de quo infrà, quod verò <lb></lb>ſpectat ad gladium, qui repellitur, eò faciliùs repellitur, quò punctum <lb></lb>contactus propiùs ad eius mucronem accedet. </s>
					<s id="N28892">Si tertio modo, &amp; gla­<lb></lb>dius ſolus ita libraretur maxima vis eſſet circa centrum eius grauitatis; </s>
					<s id="N28898"><lb></lb>in hoc enim puncto maximum ictum infligunt, quæ motu recto mo­<lb></lb>uentur; quia verò totum ſegmentum brachij, quod inter manum, &amp; <pb pagenum="404" xlink:href="026/01/438.jpg"></pb>caput cubiti intercipitur, mouetur ſimul cum gladio motu recto, circa <lb></lb>capulum erit maxima vis, cùm propiùs accedat ad centrum grauitatis <lb></lb>totius conflati ex illo ſegmento brachij, &amp; gladio. </s>
				</p>
				<p id="N288A8" type="main">
					<s id="N288AA">Decimò, denique ſi ſecundo modo declinetur ictus, idem dicendum <lb></lb>eſt quod de motu circulari dictum, mutato dumtaxat centro, v.g. ſit gla­<lb></lb>dius declinantis RG, ſitque IG 1/4 totius RG circa I ſit motus circula­<lb></lb>tis, centrum percuſſionis erit circa 2/3 IG, vel IR. </s>
				</p>
				<p id="N288B5" type="main">
					<s id="N288B7">Vndecimò, vix tamen ita acuratè hoc ſecundo modo declinatur ictus, <lb></lb>quin tertius etiam cum ſecundo coniunctus ſit, vt patet experientiâ; </s>
					<s id="N288BD"><lb></lb>rotatur autem manus declinantis vt illo quaſi gyro maiorem impetum <lb></lb>acquirat, de quo iam ſuprà: immò niſi tertius modus cum ſecundo eſſet <lb></lb>coniunctus, non poſſet delinari ictus, ſi contactus gladiorum fieret in <lb></lb>centro illius motus, vt patet. </s>
				</p>
				<p id="N288C8" type="main">
					<s id="N288CA">Duodecimò, quò longior eſt gladius declinantis, cum iuxta mucro­<lb></lb>nem fit contactus ſine impactione eſt vis debilior, quàm eſſet in breuio­<lb></lb>re, patet ex vecte; ſi verò ſit impactio iuxta ſecundum. </s>
					<s id="N288D2">n.10. vis maior <lb></lb>eſt cum gladius longior eſt; </s>
					<s id="N288D8">eſt enim maior motus; </s>
					<s id="N288DC">igitur maior ictus li­<lb></lb>cèt tardior; </s>
					<s id="N288E2">hinc longiore gladio equidem fortiùs auertitur ictus quàm <lb></lb>breuiore, ſed tardiùs; breuiore verò citiùs quàm longiore, ſed debiliùs, <lb></lb>vt patet ex dictis. </s>
				</p>
				<p id="N288EA" type="main">
					<s id="N288EC">Decimotertiò, longior gladius ſuſtinetur facilè opera capularis pilæ, <lb></lb>quæ momentum longitudinis gladij ſupplet, vt conſtat ex ſtatera, cuius <lb></lb>proportiones videbimus lib.ſeq. </s>
					<s id="N288F3">quippe ſi pila faciat æquipendium, cum <lb></lb>lamella manus ſuſtinet tantùm pondus abſolutum ſine momento, &amp;c. </s>
				</p>
				<p id="N288F8" type="main">
					<s id="N288FA">Decimoquartò, hinc gladius, qui in mucronem ita deſinit, vt ea por­<lb></lb>tio, quæ ad capulum propiùs accedit, ſit craſſior, faciliùs ſuſtineri poteſt, <lb></lb>licèt ſit eiuſdem ponderis cum alio; quia ſcilicet non eſt tantum mo­<lb></lb>mentum. </s>
				</p>
				<p id="N28904" type="main">
					<s id="N28906">Decimoquintò, mucro intentatus per lineam rectam horizonti pa­<lb></lb>rallelus difficiliùs excipitur, &amp; auertitur; </s>
					<s id="N2890C">certa eſt experientia, cuius <lb></lb>ratio in promptu eſt, quia vel gladius declinantis eſt horizonti paralle­<lb></lb>lus, vel non parallelus: ſi primum; </s>
					<s id="N28914">igitur vix excipere poteſt, quia cum <lb></lb>alia non decuſſatur; ſi verò ſecundum; </s>
					<s id="N2891A">plùs æquo demitti capulum opor­<lb></lb>tet; </s>
					<s id="N28920">hinc non modò manus debilior eſt; </s>
					<s id="N28924">verùm etiam corpus detegitur: <lb></lb>adde quod ictus validior eſt per lineam perpendicularem. </s>
				</p>
				<p id="N2892A" type="main">
					<s id="N2892C">Decimoſextò, hinc ita debet extremitas manus per horizontalem <lb></lb>porrigi &amp; brachium contractum explicari, vt maiorem lineam rectam <lb></lb>deſcribat; </s>
					<s id="N28934">acquiritur enim maior impetus in maiori ſpatio, quod per­<lb></lb>curritur motu accelerato, vt conſtat ex dictis, ſed quò brachium con­<lb></lb>tractius eſt, cò maiorem lineam eius extremitas motu recto decurrit: <lb></lb>adde quod impreſſio totius corporis, quod in <expan abbr="eãdem">eandem</expan> partem agitur, <lb></lb>multùm auget vim brachij mucronem in aduerſum pectus inten­<lb></lb>tantis. </s>
				</p>
				<p id="N28946" type="main">
					<s id="N28948">Decimoſeptimò, ſi longior eſt gladius impetus, hæc videntur eſſe <lb></lb>commoda. </s>
					<s id="N2894D">Primò, eius mucro longiùs producitur, &amp; procul attingit. <pb pagenum="405" xlink:href="026/01/439.jpg"></pb>Secundò maiorem ictum infligit, vt iam ſupra dictum eſt de ſariſſa, mo­<lb></lb>dò in eadem ratione aucta ſit craſſitudo; non deſunt tamen incommo­<lb></lb>da. </s>
					<s id="N2895A">Primò ratione vectis maius eſt illius pondus. </s>
					<s id="N2895D">Secundò faciliùs de­<lb></lb>clinatur ictus propter <expan abbr="eãdem">eandem</expan> rationem. </s>
					<s id="N28966">Tertiò, ſi tantillùm deflecte­<lb></lb>tur, corpus omninò detegit propter maiorem cum, ſunt enim arcus <lb></lb>vt radij, vel longitudines. </s>
					<s id="N2896D">Quartò, hinc pugiles faciliùs decuſſatis gla­<lb></lb>dijs ſeſe mutuò præhendunt, &amp; luctâ decernunt. </s>
				</p>
				<p id="N28972" type="main">
					<s id="N28974">Decimooctauò, niſi per lineam horizontali parallelam mucro inſen­<lb></lb>tetur, minor eſt vis ictus, quia obliquè cadit; </s>
					<s id="N2897A">igitur debilior eſt: </s>
					<s id="N2897E">ſi porrò <lb></lb>extante brachio mucro intenditur; haud dubiè ictus obliquus erit, cùm <lb></lb>circa extremum humerum brachium libretur. </s>
				</p>
				<p id="N28986" type="main">
					<s id="N28988">Decimononò, cum auertitur, ſeu repellitur impetus gladius, ferro <lb></lb>directo id fieri debet, ſcilicet iuxta ſecundum modum n. </s>
					<s id="N2898D">10. alioquin <lb></lb>ferrum læuigatum in alio læuigato facilè decurrit, ſi obliquè in ipſum <lb></lb>cadat; </s>
					<s id="N28995">porrò ex hac repercuſſione mucro impetens mouetur motu mixto, <lb></lb>dextrorſum ſcilicet vel ſiniſtrorſum declinante: hinc qui impetit id po­<lb></lb>tiſſimum curare debet, vt eius ferrum ferro alterius obliquè accidat. </s>
				</p>
				<p id="N2899D" type="main">
					<s id="N2899F">Vigeſimò, eodem niſu poteſt quis ictum aduerſarij declinare, ipſique <lb></lb>adeo ictum infligere, quod gladiatoribus valde familiare eſt; </s>
					<s id="N289A5">hinc autem <lb></lb>ſingulari motu mouetur manus, mixto ſcilicet ex recto, &amp; circulari; cir­<lb></lb>culari quidem iuxta ſecundum modum traditum n. </s>
					<s id="N289AD">10. recto verò iuxta <lb></lb>modum traditum n.15. quod certè ſi expeditè, &amp; accuratè fiat, imparatus <lb></lb>hoſtis intercipitur, vt vix ictum excipere poſſit. </s>
				</p>
				<p id="N289B4" type="main">
					<s id="N289B6">Vigeſimoprimò, ita hoſtis gladio impeti debet, vt corpus impetentis <lb></lb>tectum remaneat: omitto alia, quæ ad hanc artem pertinent v.g corporis <lb></lb>ſitum, gladiorum temperaturam, cochleam gladij, &amp;c. </s>
					<s id="N289BE">quæ cùm ad mo­<lb></lb>tum minimè ſpectent, huius loci eſſe non poſſunt: </s>
					<s id="N289C4">omitto etiam illos <lb></lb>ictus, qui cæſim infliguntur, quia ex dictis de baculo ſuprà facilè intelli­<lb></lb>gi poſſunt; denique omitto varios illos gladij breuioris latioriſque gyros, <lb></lb>quibus ſeſe quaſi, vt vulgò aiunt, induit qui contra plures ſeſe tuetur. </s>
				</p>
				<p id="N289CE" type="main">
					<s id="N289D0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N289DC" type="main">
					<s id="N289DE"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena percuſſionis, quæ infligitur à <lb></lb>corpore graui deorſum ſua ſponte cadente motu naturaliter accele­<lb></lb>rato.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N289E9" type="main">
					<s id="N289EB">Primò, corpus graue cadens ex maiore altitudine fortiùs ferit: ratio <lb></lb>eſt; </s>
					<s id="N289F1">quia deſcendit motu naturaliter accelerato; </s>
					<s id="N289F5">igitur maiorem acqui­<lb></lb>rit impetum; </s>
					<s id="N289FB">igitur maiorem impetum ad extra producit; igitur maio­<lb></lb>rem ictum infligit. </s>
				</p>
				<p id="N28A01" type="main">
					<s id="N28A03">Secundò, ſunt 4. combinationes grauium; </s>
					<s id="N28A07">vel enim eſt idem pondus <lb></lb>eſt altitudo; </s>
					<s id="N28A0D">vel idem pondus, diuerſa altitudo; </s>
					<s id="N28A11">vel eadem altitudo di­<lb></lb>uerſum pondus; </s>
					<s id="N28A17">vel diuerſum pondus &amp; diuerſa altitudo; addi poteſt <lb></lb>diuerſus incidentiæ angulus, immò diuerſa figura corporis cadentis, quæ <lb></lb>omnia infrà demonſtrabimus. </s>
				</p>
				<p id="N28A1F" type="main">
					<s id="N28A21">Tertiò, ſi ſit æquale pondus, &amp; æqualis altitudo ſuppoſito caſu <pb pagenum="406" xlink:href="026/01/440.jpg"></pb>perpendiculari æquales ſunt ictus, patet; quia eadem cauſa <expan abbr="eũdem">eundem</expan> ha<lb></lb>bet effectum. </s>
				</p>
				<p id="N28A31" type="main">
					<s id="N28A33">Quartò, ſi ſit æquale pondus, &amp; inæqualis altitudo, ictus ſunt in ra­<lb></lb>tione ſubduplicata altitudinum v.g. ſit altitudo 4. cubitorum, &amp; altera <lb></lb>tantum cubitalis; </s>
					<s id="N28A3D">certè cùm acquirantur æqualibus temporibus æqua­<lb></lb>lia velocitatis momenta, velocitates acquiſitæ ſunt vt tempora, impetus <lb></lb>vt velocitates, ictus vt impetus; </s>
					<s id="N28A45">ſed tempora ſunt in ratione ſubdupli­<lb></lb>cata ſpatiorum vel altitudinem; </s>
					<s id="N28A4B">igitur &amp; ictus; igitur ictus inflictus à <lb></lb>corpore cadente ex altitudine 4. cubitorum eſt duplus ictus eiuſdem <lb></lb>corporis cadentis ex altitudine cubitali. </s>
				</p>
				<p id="N28A53" type="main">
					<s id="N28A55">Quintò, ſi ſit æqualis altitudo, &amp; diuerſum pondus, ictus per ſe ſunt <lb></lb>vt pondera: </s>
					<s id="N28A5B">probatur facilè, quia eſt duplus impetus in corpora duplo, <lb></lb>non quidem ratione intenſionis, ſed ratione extenſionis, vt patet: dixi <lb></lb>per ſe, quia diuerſa ratio reſiſtentiæ medij hanc proportionem mutare <lb></lb>poteſt. </s>
				</p>
				<p id="N28A65" type="main">
					<s id="N28A67">Sextò, ſi ſint infinita inſtantia, eſt infinita proportio inter actum in­<lb></lb>flictum à corpore cadente, &amp; vim grauitationis eiuſdem; </s>
					<s id="N28A6D">quia dato quo­<lb></lb>cunque tempore poſſet dari minus, &amp; minus; igitur dato quocunque <lb></lb>ictu poſſet dari minor, &amp; minor in infinitum, quod ex illa hypotheſi <lb></lb>neceſſariò conſequitur. </s>
				</p>
				<p id="N28A77" type="main">
					<s id="N28A79">Septimò, immò ſi ſint infinita inſtantia, ſique infinita proportio in­<lb></lb>ter ictum inflictum à corpore cadente, &amp; vim grauitationis eiuſdem, eſt <lb></lb>etiam infinita proportio inter <expan abbr="eumdẽ">eumdem</expan> ictum, &amp; vim grauitationis cuiuſ­<lb></lb>libet alterius corporis quantumuis immenſi, inter duas grauitationes <lb></lb>duorum corporum datur proportio, vt conſtat; </s>
					<s id="N28A89">ſunt enim vt pondera; <lb></lb>igitur ſi nullam habet proportionem cum ictu corporis grauis cadentis, <lb></lb>nullam etiam habebit altera, vt patet ex elementis. </s>
				</p>
				<p id="N28A91" type="main">
					<s id="N28A93">Octauò, hinc negamus eſſe infinita illa inſtantia; </s>
					<s id="N28A97">quia ex illa hypothe­<lb></lb>ſi hoc abſurdum neceſſariò ſequitur, quod experimento repugnat; quis <lb></lb>enim neget maiorem eſſe vim 100000. librarum ferri in modicum cy­<lb></lb>lindrum plumbi incubantis, quàm modici granuli in <expan abbr="eũdem">eundem</expan> cylin­<lb></lb>drum ex altitudine lineæ cadentis. </s>
				</p>
				<p id="N28AA7" type="main">
					<s id="N28AA9">Nonò, ſi altitudo ſit diuerſa, &amp; pondus diuerſum, ictus ſunt in ratione <lb></lb>compoſita ex ratione ponderum, &amp; ſubduplicata altitudinum, patet ex <lb></lb>dictis. </s>
				</p>
				<p id="N28AB0" type="main">
					<s id="N28AB2">Decimò, ſi ſint infinita inſtantia dato ictu cuiuſlibet corporis caden­<lb></lb>tis ex quacunque altitudine, non poteſt dari vlla corporis moles, qua <lb></lb>ſuo pondere id præſtat, quod illud præſtitit ſuo caſu. </s>
					<s id="N28ABB">Probatur ex n. </s>
					<s id="N28ABE">7. <lb></lb>hinc fruſtrà proponitur hæc quæſtio ab ijs, qui agnoſcunt infinitos tar­<lb></lb>ditatis gradus, per quos propagatur motus; nam reuerâ ex hac hypotheſi <lb></lb>eſt infinita proportio inter ictum, &amp; vim grauitationis. </s>
				</p>
				<p id="N28AC8" type="main">
					<s id="N28ACA">Vndecimò, ſi tamen ponantur finita inſtantia; </s>
					<s id="N28ACE">haud dubiè hæc pro­<lb></lb>poſitio non eſt infinita; </s>
					<s id="N28AD4">ſit enim quodlibet corpus cadens ex quacun­<lb></lb>que data altitudine per 100. inſtantia, ſeu partes temporis æquales pri­<lb></lb>mo inſtanti quo mouetur; </s>
					<s id="N28ADC">haud dubiè ictus ab eo inflictus cadendo eſt <pb pagenum="407" xlink:href="026/01/441.jpg"></pb>ad vim grauitationis eiuſdem vt 1001. ad 1. cùm enim ſingulis inſtan­<lb></lb>tibus æqualibus acquirantur æqualia velocitatis momenta, ſeu æqualis <lb></lb>impetus; </s>
					<s id="N28AE9">certè 1000. inſtantibus, quibus mouetur acquiſiuit 1000. gra­<lb></lb>dus impetus æquales primo, quem habebat in prima grauitatione; </s>
					<s id="N28AEF">&amp; <lb></lb>qui fuit cauſa motus primi inſtantis; </s>
					<s id="N28AF5">igitur ſi hic addatur 1000. erunt <lb></lb>1001. hinc ſi corpus moueatur tantùm vno inſtanti, ictus erit duplus <lb></lb>tantùm grauitationis: ſuppono autem nullam eſſe medij reſiſtentiam, <lb></lb>ictumque infligi per lineam directam. </s>
				</p>
				<p id="N28AFF" type="main">
					<s id="N28B01">Duodecimò, hinc, ſi aſſumatur corpus, cuius pondus ſit ad pondus <lb></lb>corporis prædicti vt 1001. ad 1. idem erit effectus eius grauitationis, &amp; <lb></lb>illius ictus vno inſtanti. </s>
					<s id="N28B08">Probatur manifeſtè, quia, quæ habent <expan abbr="eũdem">eundem</expan> <lb></lb>rationem ad aliud tertium; </s>
					<s id="N28B12">ſunt æqualia; dixi vno inſtanti; nam reuerâ <lb></lb>corpus graue, quod primo inſtanti imprimit aliquid impetus primo in­<lb></lb>ſtanti, illum auget, ſecundo, tertio, &amp;c. </s>
					<s id="N28B1A">quod maximè obſeruandum eſt; <lb></lb>alioqui maxima erit hallucinatio. </s>
				</p>
				<p id="N28B1F" type="main">
					<s id="N28B21">Decimotertiò, hinc non poteſt determinari proportio corporis ca­<lb></lb>dentis, &amp; grauitantis, niſi ex hypotheſi; </s>
					<s id="N28B27">quia nemo ſcit quot fluxerint <lb></lb>inſtantia in dato motu; </s>
					<s id="N28B2D">quoad reuerâ ſciri poſſet ſi poſſet aliqua arte in­<lb></lb>ueniri corpus, cuius grauitatio haberet <expan abbr="effectũ">effectum</expan>, quem habet alterius ictus, <lb></lb>quod nec ſciri poteſt per depreſſum cylindrum cereum vel <expan abbr="plumbeũ">plumbeum</expan>, vel <lb></lb>alterius mollioris materiæ, quia æqualis depreſſio accuratè cognoſci non <lb></lb>poteſt; ſi quis enim diceret deeſſe, vel ſupereſſe 1000. ſuperficies, quà <lb></lb>ratione conuinci poſſet? </s>
					<s id="N28B43">non poteſt etiam ſciri operâ libræ, in cuius al­<lb></lb>terum brachium cadat mobile, quia ſunt ferè infiniti motus inſenſibiles, <lb></lb>vt conſideranti patebit; igitur proportio hæc tantùm, determinari poteſt <lb></lb>ex hypotheſi data, vt clariſſimè conſtat ex dictis. </s>
				</p>
				<p id="N28B4D" type="main">
					<s id="N28B4F">Decimoquartò, hinc maxima eſt proportio inter ictum, &amp; grauita­<lb></lb>tionem; </s>
					<s id="N28B55">cùm modicus malleoli caſus eum effectum præſtet, quem in­<lb></lb>gens corporis moles ſua grauitatione præſtare non poſſet; </s>
					<s id="N28B5B">non eſt tamen <lb></lb>infinita proportio, quia poteſt tanta eſſe moles grauitatis, &amp; tam par­<lb></lb>uum corporis cadentis pondus, vt illa præualeat, vt conſtat experientiâ, <lb></lb>quæ nobis euidentiſſimam ſuggerit rationem; </s>
					<s id="N28B65">quia reiicimus infinitos <lb></lb>illos tarditatis gradus, quos aſſumpſit Galilæus ad probandam ſuam <lb></lb>hypotheſim de motu accelerato, &amp; infinita eiuſdem &amp; aliorum multo­<lb></lb>rum inſtantia, de quibus alibi in Metaphyſicâ; </s>
					<s id="N28B6F">eſt tamen maxima illa <lb></lb>proportio, vt dixi; </s>
					<s id="N28B75">quia perexigua temporis pars infinitis ferè inſtanti­<lb></lb>bus conſtat; </s>
					<s id="N28B7B">quorum certè numerum recenſere poſſemus, ſi quis mo­<lb></lb>dum inueniat, quo poſſit abſolutè adæquare grauitationis dati corporis <lb></lb>effectum cum effectu ictus alterius cadentis: quod meo iudicio non <lb></lb>modo geometricè, verùm etiam mechanicè, ſaltem accuratè fieri non <lb></lb>poteſt. </s>
				</p>
				<p id="N28B87" type="main">
					<s id="N28B89">Decimoquintò, nec illud, quod habet Dominus Hobs apud Merſen­<lb></lb>num, in phœnom. </s>
					<s id="N28B8E">Mech. </s>
					<s id="N28B91">pr. 25. videtur ſatisfacere. </s>
					<s id="N28B96">Primè, quia ſup­<lb></lb>ponit primum illum conatum cylindri AB, &amp; puncti phyſici A&#039;C, <lb></lb>ſed non tradit modum, quo poſſit cognoſci. </s>
					<s id="N28B9D">Secundò, quia dicit cona-<pb pagenum="408" xlink:href="026/01/442.jpg"></pb>tum primum puncti AC, &amp; totius axis AB, quamdiu deſcendit vterque, <lb></lb>eſſe æqualem; </s>
					<s id="N28BA8">quod tamen dici non poteſt, quia conatus ſingulorum <lb></lb>punctorum ſeorſim ſunt æquales; </s>
					<s id="N28BAE">ſed conatus omnium coniunctim eſt <lb></lb>maior conatu ſingulorum; </s>
					<s id="N28BB4">nam ſingula habent ſuum impetum; verum <lb></lb>eſt quidem moueri motu æquali, quia ſingula æquali impetu mouentur. </s>
					<s id="N28BBA"><lb></lb>Tertiò, quia vult poſito cylindro ſupra baſim 4. illam immediatè premi <lb></lb>à puncto EB, hoc verò punctum à puncto DE, &amp; hoc ab CD, &amp; hoc ab <lb></lb>AC; </s>
					<s id="N28BC3">quod tamen dici non poteſt; quis enim dicat granulum ſuperpoſi­<lb></lb>tum rupi in illam grauitare? </s>
					<s id="N28BC9">Equidem cum illa grauitat grauitatione <lb></lb>communi, vt dictum eſt ſuprà, non tamen in illam. </s>
					<s id="N28BCE">Quartò, quia dicit <lb></lb>pumum B cum conatu totius cylinèri incubantis eo tempore, quo pun­<lb></lb>ctum AC conficeret AC, conficere AB, quod repugnat progreſſioni <lb></lb>Galilei, quam ſequitur ipſe; </s>
					<s id="N28BD8">quia conatus ſunt, vt velocitates; </s>
					<s id="N28BDC">hæ verò <lb></lb>vt tempora; ſed ſpatia in ratione duplicata temporum. </s>
				</p>
				<p id="N28BE2" type="main">
					<s id="N28BE4">Denique non video, quomodo ex his etiam datis demonſtret pro­<lb></lb>portionem quæſitam percuſſionis, &amp; grauitationis; </s>
					<s id="N28BEA">igitur non eſt conſu­<lb></lb>lendum ſpatium, ſed tempus eo modo, quo diximus; </s>
					<s id="N28BF0">ſi enim punctum <lb></lb>moueatur per 1000. inſtantia, acquiret mille puncta impetus; </s>
					<s id="N28BF6">igitur ha­<lb></lb>bebit 1001. igitur ſi aſſumatur corpus, quod conſtet 1001. punctis habe­<lb></lb>bit 1001. puncta impetus, id eſt ſingula in ſingulis; quæ cum omnia gra­<lb></lb>uitent grauitatione communi, æqualis eſt priori effectus. </s>
				</p>
				<p id="N28C00" type="main">
					<s id="N28C02">Decimoſextò, hinc vides, quàm ſit difficilis, vel potiùs impoſſibilis <lb></lb>huius proportionis inuentio, ex cuius cognitione tempus reſoluitur in <lb></lb>ſua inſtantia, immò &amp; quantitas in ſua puncta: primum quidem; </s>
					<s id="N28C0A">ſit enim <lb></lb>data moles, cuius grauitatio æqualis eſt ictui alterius cadentis dato <lb></lb>tempore; haud dubiè tot ſunt inſtantia in toto illo tempore, quoties <lb></lb>pondus cadens continetur in grauitante, vt patet ex dictis. </s>
				</p>
				<p id="N28C14" type="main">
					<s id="N28C16">Decimoſeptimò, poteſt aſſumi perexigua pars temporis pro inſtanti <lb></lb>phyſico, nec tam ſenſibilis erit error, &amp; modicum ſpatium pro puncto <lb></lb>phyſico, vt deinde mechanicè procedatur ad indagandam hanc propor­<lb></lb>tionem percuſſionis, &amp; grauitationis. </s>
				</p>
				<p id="N28C1F" type="main">
					<s id="N28C21">Decimooctauò, poteſt explicari quomodo defigatur palus ab ictu <lb></lb>corporis deorſum cadentis. </s>
					<s id="N28C26">Primò enim, ideò defigitur, quia materia <lb></lb>mollior cedit non ſine aliqua compreſſione. </s>
					<s id="N28C2B">Secundò, hinc in mucro­<lb></lb>nem deſinere debet, vt faciliùs penetret, quod ad cuneum reducemus <lb></lb>alibi: idem dico de ſecuri, gladio, enſe, &amp;c. </s>
					<s id="N28C33">Tertiò, initio faciliùs <lb></lb>defigitur, conſtat experientiâ; ratio eſt, quia plures partes deinde com­<lb></lb>primuntur propter longitudinem, &amp; craſſitudinem pali ſeu claui. </s>
					<s id="N28C3B">Quar­<lb></lb>tò, hinc minùs defigitur ſecundo ictu, quàm primo; </s>
					<s id="N28C41">igitur maiore niſu <lb></lb>opus eſt: </s>
					<s id="N28C47">in qua verò proportione difficilè dictu eſt; inueniri tamen po­<lb></lb>teſt de qua numero ſequenti. </s>
					<s id="N28C4D">Quintò, poteſt etiam dici vel poſito ſe­<lb></lb>cundô ictu æquali primo quantum defigat ſupra primum, vel poſita de­<lb></lb>fixione illa, qua defigitur ſecundo ictu æquali primæ, quam proportio­<lb></lb>nem habeant ictus. </s>
					<s id="N28C56">Tertiò, poſito vtroque inæquali, quæ ſit etiam vtriuſ­<lb></lb>que proportio. </s>
				</p>
				<pb pagenum="409" xlink:href="026/01/443.jpg"></pb>
				<p id="N28C5F" type="main">
					<s id="N28C61">Decimononò, ſi æqualis ſit ſecundus ictus. </s>
					<s id="N28C64">Primò, poteſt determina­<lb></lb>ri proportio iuxta quam defigitur palus, quod vt melius explicetur, ſit <lb></lb>cuneus BE, cuius ſolidum facilè demonſtratur; </s>
					<s id="N28C6C">eſt enim ſubduplum pa­<lb></lb>rallelipedi, cuius baſis ſit quadratum AC, &amp; altitudo RE; </s>
					<s id="N28C72">ſi enim trian­<lb></lb>gulum ADE ducatur in latus AB vel EF habebitur ſolidum cunci, vt <lb></lb>conſtat, vnde cunei eiuſdem latitudinis ſunt, vt triangula, v.g. cuneus A <lb></lb>F ad eumdem YF; </s>
					<s id="N28C7E">vt triangulum ADE ad triangulum YHE: </s>
					<s id="N28C82">hoc po­<lb></lb>ſito ſit triangulum MKN æqualis ADF, &amp; primo ictu tota EI vel N <lb></lb>Z ſecundo ictu defigitur, non quidem æquali altitudine, ſed æquali ſoli­<lb></lb>do; </s>
					<s id="N28C8C">cùm autem triangulum XZN ſit ſubquadruplum trianguli QON <lb></lb>ſit media proportionalis N inter NZNO, triangulum N <foreign lang="grc">β</foreign> Y eſt du­<lb></lb>plum NZX; </s>
					<s id="N28C98">igitur ſecundo ictu defigetur N <foreign lang="grc">β</foreign>: </s>
					<s id="N28CA0">ſimiliter ſi vt NZ ad N <lb></lb><foreign lang="grc">β</foreign>, ita N <foreign lang="grc">β</foreign> ad N. Tertio, ita defigetur NT, &amp; quarto NO dupla NI: ra­<lb></lb>tio eſt, quia æquales ictus æquales habent effectus. </s>
				</p>
				<p id="N28CAF" type="main">
					<s id="N28CB1">Vigeſimò, ſi æquales accipiantur altitudines ſingulis ictibus, ictus <lb></lb>ſunt in ratione duplicata altitudinum, ſuppoſitâ prædicta hypotheſi cunei <lb></lb>v.g.ſi dato ictu defigatur NZ, &amp; altero NO, ſecundus eſt ictus quadruplus <lb></lb>primi; </s>
					<s id="N28CBB">ſi verò tertio ictu defigatur N<foreign lang="grc">θ</foreign> tripla NZ, ictus eſt ad primum <lb></lb>in ratione 9/1. ſi denique dato ictu defigatur NM, ictus eſt ad primum <lb></lb>in ratione 36/3, vt patet ex dictis; ſi verò primo ictu defigatur NZ, ſecundo <lb></lb>ZO, tertio O <foreign lang="grc">θ</foreign>, quarto <foreign lang="grc">θ</foreign> M, ictus ſunt, vt numeri impares 1. <lb></lb>3. 7. 9. </s>
				</p>
				<p id="N28CD5" type="main">
					<s id="N28CD7">Vigeſimoprimò, hinc ſi dentur duo ictus, &amp; eorum proportio deter­<lb></lb>minari, vt poteſt proportio altitudinum, quæ defiguntur, quæ ſunt in <lb></lb>ratione ſubduplicata ictuum, ſuppoſito cuneo: </s>
					<s id="N28CDF">ſimiliter, ſi dentur alti­<lb></lb>tudines, carumque proportio, determinari poteſt proportio ictum; </s>
					<s id="N28CE5">ſunt <lb></lb>enim in ratione duplicata, vt patet ex dictis; porrò vtrumque poteſt <lb></lb>conſiderari duobus modis. </s>
					<s id="N28CED">Primò, coniunctim, ſi ſecundus ictus ſucce­<lb></lb>dat primo, &amp; eius altitudinem augeat. </s>
					<s id="N28CF4">Secundò, ſi ſeorſim vterque <lb></lb>conſideretur, &amp;c. </s>
				</p>
				<p id="N28CF9" type="main">
					<s id="N28CFB">Vigeſimoſecundò, in clauis, vel conis altitudines ſunt in ratione <lb></lb>ſubtriplicata <expan abbr="ictuũ">ictuum</expan>, &amp; ictus in ratione triplicata altitudinum defixarum, <lb></lb>quòd manifeſtum eſt ex Geometria; </s>
					<s id="N28D07">ſit enim conus BAF, qui defigatur <lb></lb>vno ictu; </s>
					<s id="N28D0D">ſitque alter ictus, quo defigatur tantùm FD ſubdupla FA: </s>
					<s id="N28D11"><lb></lb>cùm ictus ſint vt defixa ſolida; </s>
					<s id="N28D16">certè conus FD eſt ad conum FA in <lb></lb>ratione triplicata, id eſt vt cubus FD ad cubum FA, id eſt vt 1. ad 8. <lb></lb>quæ omnia conſtant: </s>
					<s id="N28D1E">idem dico de pyramide, quod de cono: hinc vi­<lb></lb>detur differentia ictuum, quibus defigitur cuneus, &amp; conus, </s>
				</p>
				<p id="N28D24" type="main">
					<s id="N28D26">Vigeſimotertiò, poteſt explicari quomodo deprimatur cylindrus con­<lb></lb>ſtans ex molliori materia; </s>
					<s id="N28D2C">nam primò deprimitur prima ſuperficies <lb></lb>cylindri, &amp; extenditur; quia cùm materia. </s>
					<s id="N28D32">ſit mollior, prematurque a <lb></lb>duobus corporibus duris vtrinque, ſcilicet ab vtraque baſi, cedit &amp; di­<lb></lb>latatur propter humorem in cauitatibus contentum. </s>
					<s id="N28D39">Secundò, aliquan­<lb></lb>do totus cylindrus deprimitur ſeruatà ſemper cylindri licet craſſio­<lb></lb>ris figurâ, quod vt fiat, molliſſimam materiam eſſe neceſſe eſt. </s>
					<s id="N28D40">Ter-<pb pagenum="410" xlink:href="026/01/444.jpg"></pb>tiò, aliquando primæ tantùm ſuperficies extenduntur, vt videmus in <lb></lb>capite, ſeu baſi cuneorum; quia materies durior multùm reſiſtit. </s>
					<s id="N28D4B">Quartò, <lb></lb>limbus baſis dilatatæ contrahitur deinde, ſeu retorquetur deorſum; </s>
					<s id="N28D51">quia <lb></lb>cùm interiores circuli dilatentur, deberet facere limbus ille maiorem <lb></lb>circulum; quod cùm fieri non poſſit, contrahitur ſeu incuruatur deor­<lb></lb>ſum, quod facilè ſine figura intelligi poteſt. </s>
					<s id="N28D5B">Quintò, poteſt deter­<lb></lb>minari proportio ictuum, quibus deprimuntur cylindri; </s>
					<s id="N28D61">ſi enim ſup­<lb></lb>ponatur eadem altitudo, ſeu linea depreſſionis, &amp; diuerſa craſſi­<lb></lb>tudo cylindrorum ictus, erunt vt baſes; </s>
					<s id="N28D69">nam quò plures partes de­<lb></lb>primendæ ſunt, maiore ictu opus eſt, ſi opponatur eadem craſſitudo <lb></lb>vtriuſque cylindri ſed diuerſa depreſſionis linea vel altitudo, ictus <lb></lb>erunt vt altitudines; </s>
					<s id="N28D73">ſi vtraque ſupponitur diuerſa, ictus erunt in ra­<lb></lb>tione compoſita ex ratione baſium, &amp; altitudinum; quæ omnia conſtant <lb></lb>ex dictis. </s>
				</p>
				<p id="N28D7B" type="main">
					<s id="N28D7D">Obſeruabis tamen creſcere reſiſtentiam ex duplici capite. </s>
					<s id="N28D80">Primò, <lb></lb>ex eo quod aliquæ vacuitates occupentur à partibus depreſſis, ac proin­<lb></lb>de cylindrus induretur; ſic intus durior euadit ſub malleo, &amp; &amp; pila <lb></lb>lignea ſub ictibus. </s>
					<s id="N28D8A">Secundò, latiorem illam ſuperficiem impedire di­<lb></lb>latationem aliarum partium: </s>
					<s id="N28D90">hinc variè diſcerpitur eius limbus, vt <lb></lb>videre eſt in cuneo ferreo: </s>
					<s id="N28D96">atqui in explicandis ſuprà ictuum propor­<lb></lb>tionibus, hoc geminum reſiſtentiæ caput nullo modo conſiderauimus: </s>
					<s id="N28D9C"><lb></lb>ſextò, quærunt aliqui dato ictu, quo deprimitur cylindrus data alti­<lb></lb>tudine, quantum pondus eſſe debeat, quod ſua grauitatione eum­<lb></lb>dem præſtet effectum; ſed profectò id nemo vnquam determinauit, <lb></lb>niſi primò inueniat pondus, cuius caſu prædictus cylindrus eodem <lb></lb>modo deprimatur. </s>
					<s id="N28DA9">Secundò, niſi ſciat quot inſtantibus deſcendat, vt <lb></lb>patet ex his quæ diximus ſuprà; vt autem comparetur ictus inflictus <lb></lb>à brachio cum ictu inflicto à pondere cadente, debet conſuli diuerſa <lb></lb>depreſſio, vel defixio. </s>
				</p>
				<p id="N28DB3" type="main">
					<s id="N28DB5">Vigeſimoqnartò, corpus cadens in planum horizontale per lineam <lb></lb>perpendicularem, maximum ictum infligit: </s>
					<s id="N28DBB">maiorem, cum cadit in pla­<lb></lb>num decliue, quod manifeſtum eſt; </s>
					<s id="N28DC1">poteſt autem determinari propor­<lb></lb>tio ictuum ratione planorum; </s>
					<s id="N28DC7">ſit enim perpendicularis KN cadens in <lb></lb>planum horizontale AD, erit maximus ictus; </s>
					<s id="N28DCD">ſit vt AD; </s>
					<s id="N28DD1">fiat quadrans <lb></lb>ADG: </s>
					<s id="N28DD7">ſit planum decliue AE, in quod cadit KM; </s>
					<s id="N28DDB">ducatur EC vel <lb></lb>EI; </s>
					<s id="N28DE1">primus ictus eſt ad ſecundum, vt AD ad AC vel IE; </s>
					<s id="N28DE5">ſit aliud <lb></lb>planum decliue AF, in quod cadit KN; </s>
					<s id="N28DEB">ducantur FBFH, primus eſt <lb></lb>ad tertium, vt AD ad AB; patet ex dictis ſuprà, cum de planis in­<lb></lb>clinatis. </s>
				</p>
				<p id="N28DF3" type="main">
					<s id="N28DF5">Vigeſimoquintò, ſi verò cadat corpus graue in globum, aſſumenda eſt <lb></lb>Tangens puncti contactus v. g. ſit globus centro A ſit corpus cadens <lb></lb>per FD; </s>
					<s id="N28E01">ſit punctum contactus D; </s>
					<s id="N28E05">ſit Tangens CE; </s>
					<s id="N28E09">idem eſt ictus, <lb></lb>qui eſſet, ſi corpus graue caderet in planum inclinatum CE; </s>
					<s id="N28E0F">ſi verò <lb></lb>globus cadat in aliud corpus v. g. globus A in corpus HG <lb></lb>per lineam RG; </s>
					<s id="N28E1B">ducatur AG, tùm GS, ictus in G eſt ad ictum <pb pagenum="411" xlink:href="026/01/445.jpg"></pb>in L vt SA ad AL: denique ſi globus cadat in globum, id poteſt fieri <lb></lb>duobus modis. </s>
					<s id="N28E26">Primò, ſi L cadat in X, id eſt linea directionis ducatur <lb></lb>per centrum vtriuſque, &amp; tunc maximus ictus. </s>
					<s id="N28E2B">Secundò, ſi ſecus v.g. ſi <lb></lb>globus A cadat in globum O, ſitque punctum contactus in M; ſic autem <lb></lb>ictus eſt ad priorem in compoſita ex OYZA ad compoſitam ex MO <lb></lb>MA vel vt chorda MY, ſeu MP ad diametrum LB, quæ omnia patent <lb></lb>ex dictis. </s>
				</p>
				<p id="N28E39" type="main">
					<s id="N28E3B"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N28E47" type="main">
					<s id="N28E49">Obſerua ſupereſſe tertium modum percuſſionis, qui fit emiſſione; cum <lb></lb>autem emiſſio tribus modis fieri poſſit.1°. </s>
					<s id="N28E4F">ſimplici impulſione ſine ictu, <lb></lb>&amp; proiectione. </s>
					<s id="N28E54">2°. Percuſſione. </s>
					<s id="N28E57">3°. Proiectione, cui adde eiaculationem, <lb></lb>vel euibrationem; de his tribus ſequentibus Theorematis agendum eſt. </s>
				</p>
				<p id="N28E5D" type="main">
					<s id="N28E5F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N28E6B" type="main">
					<s id="N28E6D"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena emiſſionis, quæ fit primo modo, ſcilicet <lb></lb>per meram impulſionem.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N28E76" type="main">
					<s id="N28E78">Primò, emittitur vt plurimùm globus, ſeu pila Tudiculâ dumtaxat <lb></lb>minori; vix enim eſſe poteſt alius emiſſionis modus, qui ad hunc facilè <lb></lb>non reuocetur. </s>
				</p>
				<p id="N28E80" type="main">
					<s id="N28E82">Secundò, imprimitur impetus Tudiculæ ſimul, &amp; globo, quia <expan abbr="vtrumq;">vtrumque</expan> <lb></lb>motum brachij impedit; hoc etiam demonſtrauimus lib.1. </s>
				</p>
				<p id="N28E8D" type="main">
					<s id="N28E8F">Tertiò, quò maior eſt Tudicula, tardiùs mouetur, vt patet: </s>
					<s id="N28E93">hinc po­<lb></lb>tentia manet diutiùs applicata; </s>
					<s id="N28E99">non tamen propterea globus velociùs <lb></lb>mouetur, vt patet, quia ſingulis inſtantibus minùs in eo producitur; </s>
					<s id="N28E9F">eſt <lb></lb>enim quaſi pars Tudiculæ; ſecus tamen accidit, ſi Tudicula verberet <lb></lb>pilam, de quo infrà. </s>
				</p>
				<p id="N28EA7" type="main">
					<s id="N28EA9">Quartò, ſi Tudicula ſit longior, longiùs emittitur pila; </s>
					<s id="N28EAD">ratio eſt, quia <lb></lb>diutiùs manet potentia applicata pilæ; </s>
					<s id="N28EB3">quippe magis contrahitur bra­<lb></lb>chium: hinc longiùs porrigitur, vt clarum eſt. </s>
				</p>
				<p id="N28EB9" type="main">
					<s id="N28EBB">Quintò, ſi maior ſit Tudicula, &amp; pila emittatur verberatione, longiùs <lb></lb>emittitur; </s>
					<s id="N28EC1">ratio eſt, quia maior impetus imprimitur Tudiculæ à potentia <lb></lb>diutiùs applicata; diutiùs autem applicatur maiori, quia tardiùs moue­<lb></lb>tur, vt ſuprà diximus. </s>
				</p>
				<p id="N28EC9" type="main">
					<s id="N28ECB">Sextò, pila emiſſa velociſſimè mouetur eo inſtanti, quo vltimo tan­<lb></lb>gitur à Tudicula; quia deinceps nihil prorſus impetus accedit, ac proin­<lb></lb>de continuò ſenſim deſtruitur ab eo inſtanti. </s>
				</p>
				<p id="N28ED3" type="main">
					<s id="N28ED5">Septimò, nunquam mouetur pila emiſſa velociùs ipſa Tudiculâ, cum <lb></lb>ſcilicet emiſſio fit per meram impulſionem; </s>
					<s id="N28EDB">quia ſcilicet vltimo inſtanti, <lb></lb>contactus velociſſimè mouetur pila; </s>
					<s id="N28EE1">ſed eo inſtanti æquè velociter mo­<lb></lb>uetur Tudicula, vt conſtat: porrò ideo emittitur pila, quia retinetur Tu­<lb></lb>dicula, ne longiùs recedat. </s>
				</p>
				<p id="N28EE9" type="main">
					<s id="N28EEB">Octauò, cum verò emittitur pila per verberationem; </s>
					<s id="N28EEF">haud dubiè, ſi <lb></lb>pila leuior eſt Tudicula, mouetur deinde velociùs; </s>
					<s id="N28EF5">ſecus verò, ſi grauior <lb></lb>eſt &amp; æquè velocior, ſi æqualis eſt grauitatis; </s>
					<s id="N28EFB">patet ex dictis de impetu; <pb pagenum="412" xlink:href="026/01/446.jpg"></pb>hinc vides emiſſionem cæteris paribus maiorem eſſe per verberationem, <lb></lb>quàm per meram impulſionem. </s>
				</p>
				<p id="N28F06" type="main">
					<s id="N28F08">Nonò, pila grauior emiſſa eodem niſu potentiæ grauiorem ictum in­<lb></lb>fligit occurrenti globo, quia ſcilicet plùs habet impetus; </s>
					<s id="N28F0E">nam diutiùs <lb></lb>potentia fuit applicata: adde quod, ſi tardiore motu mouetur propter <lb></lb>maiorem molem, diutiùs pila intacta manet applicata, de quo infrà. </s>
				</p>
				<p id="N28F16" type="main">
					<s id="N28F18"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N28F24" type="main">
					<s id="N28F26">Obſeruabis eſſe plura alia phœnomena in ludo minoris Tudiculæ <lb></lb>v.g. 1°.quod ſpectat ad proportionem ictuum ratione puncti contactus, <lb></lb>de qua idem dicendum eſt, quod ſuprà dictum eſt Th. 15. num. </s>
					<s id="N28F2F">25. <lb></lb>2°.quod ſpectat ad lineam motus, per quam pila impacta impellit aliam, <lb></lb>de qua lib.1. Th.50. 51. 52.&amp; alibi paſſim. </s>
					<s id="N28F36">3°. </s>
					<s id="N28F39">quod ſpectat ad reflexio­<lb></lb>nem, de qua fusè lib.6. à Th.62. ad 75. </s>
				</p>
				<p id="N28F3E" type="main">
					<s id="N28F40"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N28F4C" type="main">
					<s id="N28F4E"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena emiſſionum, quæ fiunt cum percuſſione.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N28F55" type="main">
					<s id="N28F57">Primò, ſit percuſſio minoris Tudiculæ v.g. eo maior eſt, quò Tudi­<lb></lb>cula maior eſt; rationem iam attulimus ſuprà num.5.Th.16. </s>
				</p>
				<p id="N28F5F" type="main">
					<s id="N28F61">Secundò, quo Tudicula longior eſt, maior ictus, &amp; emiſſio; quia <lb></lb>ſcilicet diutiùs potentia manet applicata, quia brachium longiùs extens <lb></lb>poteſt, vt diximus numero 4. Th.16. </s>
				</p>
				<p id="N28F6A" type="main">
					<s id="N28F6C">Tertiò, quod ſpectat ad ſecundum ictum, idem prorſus dicendum eſt <lb></lb>quod dictum eſt Theoremate ſuperiore num.9. </s>
				</p>
				<p id="N28F71" type="main">
					<s id="N28F73">Quartò, quod ſpectat ad Tudiculam maiorem, iam ſuprà explicuimus <lb></lb>cuncta illius phœnomena, cum de malleo: certum eſt enim primò ma­<lb></lb>iorem à maiore ictum infligi, cæteris partibus, quàm à minore propter <lb></lb>prædictum rationem. </s>
					<s id="N28F7D">Secundò, certum eſt longitudinem manubrij fle­<lb></lb>xibilitatem, inæqualitatem, materiem, duritiem mallei, æqualitatem baſis <lb></lb>&amp;c. </s>
					<s id="N28F84">multùm conferre ad maiorem cùm ictus. </s>
					<s id="N28F87">Tertiò certum eſt mino­<lb></lb>rem globum, in quem impingitur Tudicula, citiùs moueri, inaiorem tar­<lb></lb>diùs, cæteris paribus. </s>
					<s id="N28F8E">Quartò, globus maior in alium impactus Tudiculâ <lb></lb>maiorem ictum infligit, vt conſtat experientiâ; ratî; </s>
					<s id="N28F94">eſt, quia tardiùs <lb></lb>mouetur; </s>
					<s id="N28F9A">igitur diutiùs applicatur: Equidem globus proiectus in alium <lb></lb>fortiorem ictum infligit ex duplici capite, vt dicam infrà. </s>
					<s id="N28FA0">1°. </s>
					<s id="N28FA3">Quia ma­<lb></lb>iorem impetum à potentia diutiùs applicata.2°.Quia diutiùs applicatur <lb></lb>globo in quem impingitur; at verò quando impingitur Tudiculâ maiore, <lb></lb>ex duplici quoque capite creſcit ictus.1°.quia globus globo diutiùs ma­<lb></lb>net applicatus, cùm tardior motus dicat plùs temporis. </s>
					<s id="N28FAF">2°. </s>
					<s id="N28FB2">quia malleus <lb></lb>tardiorem motum imprimis globo; </s>
					<s id="N28FB8">igitur diutiùs manet applicatus: eſt <lb></lb>enim hæc abta lex agentium, vt longiore tempore maior effectus produ­<lb></lb>catur, minor verò minore, reliqua ex dictis facilè intelligentur. </s>
				</p>
				<p id="N28FC2" type="main">
					<s id="N28FC4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N28FD0" type="main">
					<s id="N28FD2"><emph type="italics"></emph>Explicari poſſunt omnia phœnomena emiſſionum, quæ fiunt per iactum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N28FD9" type="main">
					<s id="N28FDB">Primò, Iactus duobus modis fieri poteſt: primò brachio: </s>
					<s id="N28FDF">ſecundò, <lb></lb>aliquo organo; </s>
					<s id="N28FE5">eſt autem multiplex organi genus, de quo infrà; omitto <pb pagenum="413" xlink:href="026/01/447.jpg"></pb>enim iactum illum, qui fit pede miniſtro, cuius eadem eſt ratio, quæ <lb></lb>brachij. </s>
				</p>
				<p id="N28FF0" type="main">
					<s id="N28FF2">Secundò, iactu lapidis maioris, maior ictus infligitur; </s>
					<s id="N28FF6">ratio eſt, quia <lb></lb>diutiùs manet lapis applicatus potentiæ, ipſique adeo corpori, in quod <lb></lb>impingitur; </s>
					<s id="N28FFE">vtrumque certè, quia tardiùs mouetur, ergo tardiùs ſepara­<lb></lb>tur à manu; ergo etiam inſtans contactus maius eſt. </s>
				</p>
				<p id="N29004" type="main">
					<s id="N29006">Tertiò, hinc proportio ictuum ſatis facilè ex dictis ſuprà determinari <lb></lb>poteſt; </s>
					<s id="N2900C">ſi enim habeatur tantùm ratio impetus maioris, qui imprimitur <lb></lb>ſaxo ab ipſa potentia, ictus ſunt in ratione ſubduplicata ponderum, id <lb></lb>eſt, vt tempora, quibus ſaxum adhæret manui; </s>
					<s id="N29014">ſi verò habeatur ratio <lb></lb>contactus, ictus ſunt vt motus permutando, ſuppoſito æquali impetu; </s>
					<s id="N2901A"><lb></lb>igitur, ſi habeatur ratio vtriuſque, ictus ſunt in ratione compoſita ex ra­<lb></lb>tione ſubduplicata ponderum, &amp; ratione permutata motuum v. g. ſint <lb></lb>ſaxa AB ſit A 4.librarum, B vnius; </s>
					<s id="N29027">ratio ſubduplicata eſt 2/1 motus A eſt <lb></lb>vt velocitas; </s>
					<s id="N2902D">igitur eſt ad motum B, vt 1/2. permutetur, erit 2/1 componatur <lb></lb>vtraque ratio, eritque ratio 4/1; </s>
					<s id="N29033">igitur ictus lapidis ſunt vt pondera; quæ <lb></lb>omnia conſtant ex dictis ſuprà. </s>
				</p>
				<p id="N29039" type="main">
					<s id="N2903B">Quartò, leuiſſimi lapides vix iaciuntur ad modicam diſtantiam v. g. <lb></lb>granula ſabuli; ratio eſt, 1°. </s>
					<s id="N29044">quia accipiunt minùs impetus, quia citiùs <lb></lb>ſeparantur à iaciente manu, vt patet. </s>
					<s id="N29049">2°. </s>
					<s id="N2904C">quia mouetur initio velociùs in <lb></lb>aëre; </s>
					<s id="N29053">igitur ſingulis inſtantibus plùs impetus deſtruitur, vt conſtat; nam <lb></lb>in maiori ſpatio aëris eſt maior reſiſtentia. </s>
					<s id="N29059">3°.quia cùm aër perpetuo <lb></lb>motu agitetur, vt certum eſt, in leuiori corpore impetum imprimit; igi­<lb></lb>tur aliam ſiſtit vel deflectit. </s>
					<s id="N29061">4°.quia manu non poteſt rectè prehendi ia­<lb></lb>ciendus lapillus &amp;c. </s>
				</p>
				<p id="N29066" type="main">
					<s id="N29068">Quintò, grauior lapis ad modicam tantùm diſtantiam iacitur; ratio <lb></lb>eſt 1°.quia producitur remiſſior impetus, cùm ſcilicet pluribus partibus <lb></lb>ſubiecti diſtribuatur. </s>
					<s id="N29070">2°.quia impetus grauitationis citiùs deſtruit impe­<lb></lb>tum extrinſecus aduenientem. </s>
				</p>
				<p id="N29075" type="main">
					<s id="N29077">Sextò, figura corporis iacti multùm confert ad iactum, quia ratione <lb></lb>figuræ poteſt aër plùs, vel minùs reſiſtere: </s>
					<s id="N2907D">hinc figura circularis depreſ­<lb></lb>ſior aptiſſima eſt ad iactum; </s>
					<s id="N29083">quia minor eſt aëris reſiſtentia, qualis eſt <lb></lb>figura lenticularis: </s>
					<s id="N29089">hinc ſcabri corporis, qualis eſt tophus, iactus eſt <lb></lb>difficilior; </s>
					<s id="N2908F">quia ſcilicet aër ſalebris illis, vel aſperitatibus interceptus <lb></lb>magis reſiſtit: hinc ſibilus propter colliſionem aëris &amp;c. </s>
				</p>
				<p id="N29095" type="main">
					<s id="N29097">Septimò, iacitur lapis multis modis 1°. </s>
					<s id="N2909A">rotato infrà brachio extento: </s>
					<s id="N2909D"><lb></lb>ſic vulgò iaciuntur grauiora ſaxa; </s>
					<s id="N290A2">ad iactum autem conferunt vires po­<lb></lb>tentiæ, brachium longiùs, longior arcus, Tangens, per quam emittitur di­<lb></lb>miſſum ſaxum, quæ debet facere cum horizontali angulum grad.45. ma­<lb></lb>nus ſimul explicata; </s>
					<s id="N290AC">ſi enim vna pars ante aliam dimittatur, retinetur <lb></lb>iactus, vt vulgò dicitur, figura, &amp; moles lapidis; </s>
					<s id="N290B2">ſi enim maior eſt, non <lb></lb>procul emittitur præuia brachij gyratio, quia impetus augetur: denique <lb></lb>impreſſus toti corpori impetus, quæ omnia mirificè maiorem iactum ef­<lb></lb>ficiunt, vt conſtat ex dictis ſuprà. </s>
					<s id="N290BD">2°.iacitur lapis rotato quidem deorſum <lb></lb>brachio, ſed non ſiue aliqua eiuſdem brachij contractione, &amp; aliquot <pb pagenum="414" xlink:href="026/01/448.jpg"></pb>gyris: ſic vulgò iaciuntur ſaxa minora, tuncque præſertim contentis ner­<lb></lb>uis toti corpori impetus accedit, qui deinde ad augendam iactum in <lb></lb>ipſum brachium quaſi refunditur.3°. </s>
					<s id="N290CC">iacitur lapis negligenti quaſi niſu, <lb></lb>ſeu reiectione circumacta manu horizonti parallela, &amp; contracto tan­<lb></lb>tillùm brachio. </s>
					<s id="N290D3">4°. </s>
					<s id="N290D6">additur aliquando deflexio vel declinatio iactui <lb></lb>præſertim in ludo trunculorum, præſertim cùm trunculorum lineæ ad­<lb></lb>uerſæ omninò &amp; directæ iacienti reſpondens. </s>
					<s id="N290DD">5°.denique, iacitur ſaxum <lb></lb>rotato ſupra brachio implicatis gyris, qui reuerâ iactus augetur ex iiſ­<lb></lb>dem omninò capitibus; de quibus iam ſuprà, quorum omnium cauſæ &amp; <lb></lb>rationes parent manifeſtæ ex dictis. </s>
				</p>
				<p id="N290E7" type="main">
					<s id="N290E9">Octauò, corporis iacti impetus deſtruitur ſenſim, tùm ab impetu nati­<lb></lb>uo ab occurſu aliorum corporum; </s>
					<s id="N290EF">hinc in plano aſperiore citiùs rota­<lb></lb>tus globus ſiſtit; quæ certè omnia ſunt facilia. </s>
				</p>
				<p id="N290F5" type="main">
					<s id="N290F7">Nonò, eiaculatio eſt iactus ſeu vibratio alicuius miſſilis oblongi, qua­<lb></lb>le eſt iaculum vel telum, pro qua non eſt difficultas; </s>
					<s id="N290FD">fit enim porrecto <lb></lb>antè per ſuperiorem arcum brachio; infligetur autem maior ictus, cum <lb></lb>1°. </s>
					<s id="N29105">iaculum eſt maius, propter eandem rationem quam ſuprà attulimus <lb></lb>pro ſariſſa.2°.cum directus eſt ictus; </s>
					<s id="N2910B">poteſt autem eſſe obliquus, vel quia <lb></lb>in planum cadit obliquè, licèt non declinet telum à ſua linea, vel quia à <lb></lb>ſua linea declinat, quæ cadit alioquin perpendiculariter in planum, vel <lb></lb>denique ex vtroque capite: omitto alia capita, quæ maiorem vim ictui <lb></lb>conciliant, de quibus ſuprà num.7. 3°. </s>
					<s id="N29117">multùm facit ad maiorem ictum <lb></lb>concitatus in eam partem equus, in quam vibratur telum; hinc equites <lb></lb>antiquioris militiæ telis &amp; iaculis pugnabant. </s>
				</p>
				<p id="N2911F" type="main">
					<s id="N29121">Decimò, iactus fieri poteſt multiplici organo ejaculatorio, 1°. </s>
					<s id="N29124">ſypho­<lb></lb>ne, 2°.fiſtula tormentaris, 3°.arcu, 4°.funda, 5°. </s>
					<s id="N29129">reticulo pilari vel cla­<lb></lb>uula denique infinita eſt ferè organorum huiuſmodi ſuppellex; </s>
					<s id="N2912F">omitto <lb></lb>motus omnes rei tormentariæ, balliſticæ, hydraulicæ, &amp; pneumaticæ, de <lb></lb>quibus fusè Tomo ſequenti; </s>
					<s id="N29137">quod ſpectat ad ſyphonem, quo aquam vel <lb></lb>globulos ejaculari ſolemus, non eſt dubium quin illa ejaculatio ſit effe­<lb></lb>ctus compreſſionis, de qua etiam, Tomo ſequenti; igitur ſuperſunt tan­<lb></lb>tùm duo prædictorum organorum genera, ſcilicet funda &amp; pilaris cla­<lb></lb>uula. </s>
				</p>
				<p id="N29143" type="main">
					<s id="N29145">Vndecimò, funda vulgare eſt organum iactus, cuius phœnomena fa­<lb></lb>cilè explicari poſſunt.1°. </s>
					<s id="N2914A">rotatur vt maiorem impetum acquirat ad mo­<lb></lb>tus reticulo lapis, 2°.quò longior eſt funda, longiùs lapis abigitur, quia <lb></lb>diutiùs manet applicatus, cùm maiorem arcum decurrat, 3°.lapis in reti­<lb></lb>culo fundæ retinetur; quia cùm per Tangentem lineam ſingulis inſtanti­<lb></lb>bus determinetur, vt conſtat ex dictis ſuprà, impeditur &amp; retinetur à re­<lb></lb>ticulo, per quod Tangens illa duci tantùm poteſt, eſt eadem ratio, quæ <lb></lb>orbis rotati, de quo Th.3.num.10. 4°. </s>
					<s id="N2915A">hinc demiſſo altero fundæ funi­<lb></lb>culo lapis iacitur, quia nihil eſt à quo retineri ampliùs queat. </s>
					<s id="N2915F">5°. </s>
					<s id="N29162">quò <lb></lb>maior eſt lapis cæteris paribus, tardiùs rotatur funda, at maior impetus <lb></lb>lapidi imprimitur; quia diutiùs manet applicatus. </s>
					<s id="N2916A">6°. </s>
					<s id="N2916D">tenditur conti­<lb></lb>nuò rota, quantumuis rotetur; quia ſcilicet non quidem à pondere <pb pagenum="415" xlink:href="026/01/449.jpg"></pb>lapidis, ſed ab eius impetu ad Tangentem determinato eò trahitur. </s>
					<s id="N29178"><lb></lb>Septimò, quod autem ad Tangentem continuò determinetur linea mo­<lb></lb>tus, patet ex dictis, cum de motu circulari. </s>
					<s id="N29180">Octauò, longiſſimus erit ia­<lb></lb>ctus, ſi Tangens, ad quam motus lapidis determinatur, eo inſtanti, quo <lb></lb>demittitur faciat angulum 45. grad. cum horizontali. </s>
					<s id="N29189">Nonò, vt rectè <lb></lb>collimetur, ſeu dirigatur lapis ad propoſitum ſcopum, egregium artifi­<lb></lb>cium eſſe poteſt; quod totum in eo poſitum eſt, vt inueniatur illa Tan­<lb></lb>gens, quæ ducitur ad ſcopum. </s>
					<s id="N29193">Decimò, ad fundam reuocari poteſt, li­<lb></lb>nea illa fiſſi baculi furca, cui ſi lapis inſeratur, facilè deinde emittitur; </s>
					<s id="N29199"><lb></lb>ſit enim linea furca AB; </s>
					<s id="N2919E">ſit lapis inſertus B, ſi rotetur maximo niſu furca <lb></lb>AB circa centrum A, vel circa centrum humeri; </s>
					<s id="N291A4">haud dubiè lapis B <lb></lb>cum aliquo impetu diſcedet: ratio eſt, quia cùm ſtatim retineatur furca <lb></lb>impreſſa priùs maxima impetus vi, tùm lapidi tùm furcæ, ſuperat vis <lb></lb>illa impetus, quæ lapidi ineſt, modicam illam ſtrictionem fiſſæ rimæ, <lb></lb>nec eſt alia difficultas. </s>
				</p>
				<p id="N291B0" type="main">
					<s id="N291B2">Vndecimò, ad fundam reuocabis vibrationes arietis, Tudiculæ, æris <lb></lb>campani, &amp; omnium funependulorum, quas ſuis vibrationibus aliquod <lb></lb>corpus eiaculantur, vel ictum infligunt. </s>
				</p>
				<p id="N291B9" type="main">
					<s id="N291BB">Duodecimò, claua pilaris, ſeu reticulum notum eſt omnibus or­<lb></lb>ganum, cuius phœnomena clariſſima ſunt. </s>
					<s id="N291C0">Primò, reticulo longiùs <lb></lb>emittitur pila, quàm clauiculâ, propter tenſionem &amp; reditum chordarum. </s>
					<s id="N291C5"><lb></lb>Secundò, quò longiùs eſt clauulæ manubrium, longiùs abigitur pila. </s>
					<s id="N291C9"><lb></lb>Tertiò, vt ſuſtineatur ictus breui manubrio, reticulo opus eſt. </s>
					<s id="N291CD">Quartò, <lb></lb>auerſa manu impacto reticulo, pila longiùs emittitur. </s>
					<s id="N291D2">Quintò, quò ſunt <lb></lb>tenſiores chordæ reticuli, maior eſt ictus. </s>
					<s id="N291D7">Sextò, hinc recens reticulum <lb></lb>veteri, &amp; iam attrito præferri debet; hinc ille chordarum ſonus. </s>
					<s id="N291DD">Septimò <lb></lb>poteſt aſſignari clauulæ locus, in quo ſi fiat percuſſio, fit maximus ictus, <lb></lb>ſit enim clauula AE, cuius centrum grauitatis ſit C; </s>
					<s id="N291E5">haud dubiè, ſi mo­<lb></lb>ueatur motu recto, maximum ictum infliget in C; </s>
					<s id="N291EB">ſi verò motu circu­<lb></lb>lari circa E eſt aliud centrum percuſſionis, de quo infrà; </s>
					<s id="N291F1">ſi tamen reticu­<lb></lb>lum propter tenſionem chordarum, quæ maximum addit momentum in <lb></lb>centro reticuli, erit ferè maximus ictus in linea AD, ſiue ſit reticulum, <lb></lb>ſiue ſit clauula, debet fieri contactus; alioqui ſi in F, v.g. fieret declina­<lb></lb>ret planum clauulæ, vt patet. </s>
					<s id="N291FF">Nonò, craſſitudo clauulæ multùm facit ad <lb></lb>augendam vim ictus; eſt enim eadem prorſus ratio, quæ mallei. </s>
					<s id="N29205">Decimò, <lb></lb>firmitas, &amp; quaſi tenſio carpi multùm facit ad ictum; </s>
					<s id="N2920B">præſertim cùm pila <lb></lb>retorquetur; quia ſcilicet ratione vectis ferè circa extremitatem manu­<lb></lb>brij pellitur clauula ab immiſſa pilâ. </s>
					<s id="N29213">Vndecimò, vt ſit maior ictus, ali­<lb></lb>quo tempore reticulum comitatur pilam, adhæretque à tergo: </s>
					<s id="N29219">ratio eſt, <lb></lb>quia potentia manet diutiùs applicata: vide alia, quæ pertinent ad de­<lb></lb>flexionem pilæ, &amp; reflexionem lib.6. de motu reflexo à Th.75. ad 81. </s>
				</p>
				<p id="N29221" type="main">
					<s id="N29223"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2922F" type="main">
					<s id="N29231"><emph type="italics"></emph>Aliæ ſunt plurimæ motionum ſpecies, quas in hoc Theoremate exponi­<lb></lb>mus.<emph.end type="italics"></emph.end></s>
				</p>
				<pb pagenum="416" xlink:href="026/01/450.jpg"></pb>
				<p id="N2923E" type="main">
					<s id="N29240">Primò, occurrit preſſio, &amp; dilatatio: </s>
					<s id="N29244">premitur corpus ab impetu <lb></lb>impreſſo à circumferentia ad centrum; </s>
					<s id="N2924A">ſic premitur aër, &amp; aqua intra <lb></lb>vas; </s>
					<s id="N29250">dilatatur verò per impetum à centro ad circumferentiam; ſed mira­<lb></lb>biles ſunt preſſionis &amp; dilatationis effectus, qui propterea librum ſingu­<lb></lb>larem deſiderant. </s>
				</p>
				<p id="N29258" type="main">
					<s id="N2925A">Secundò, intruſio, &amp; extruſio: </s>
					<s id="N2925D">illa eſt impulſio introrſum; </s>
					<s id="N29261">hæc verò <lb></lb>extrorſum: </s>
					<s id="N29267">vtraque fit vt plurimùm cum preſſione; </s>
					<s id="N2926B">ſic defigîtur clauus; <lb></lb>vi mallei; </s>
					<s id="N29271">ſic excluditur alius: </s>
					<s id="N29275">ad intruſionem &amp; extruſionem reuocari <lb></lb>poteſt ductus auri, vel argenti, vel alterius ductilis materiæ; ſed hunc <lb></lb>rei ductilis ſtatum Tomo quinto explicabimus cum alijs corporeum ſta­<lb></lb>tibus. </s>
				</p>
				<p id="N2927F" type="main">
					<s id="N29281">Tertiò, diſpoſitio fit per eiaculationem, vel minimarum partium, quæ <lb></lb>ſimul omnes vno iactu demittuntur manu; </s>
					<s id="N29287">ſit plura grana tritici vel <lb></lb>arenæ iaciuntur, vel alicuius corporis, cuius partes ſeparantur in ipſo <lb></lb>iactu; cur verò vna per hanc lineam, alia per aliam feratur, determi­<lb></lb>natur vel à concurſu cum alia parte, vel à ſitu, quem ſingulæ in iacien­<lb></lb>tis manu habebant priùs, vel ab ordine, quo ſingulæ proceſſerunt. </s>
				</p>
				<p id="N29293" type="main">
					<s id="N29295">Quartò, adductio ad tractionem reuocari poteſt; </s>
					<s id="N29299">ſunt tamen plures <lb></lb>illius modi; </s>
					<s id="N2929F">vel enim per meram tractionem; </s>
					<s id="N292A3">ſic adducitur clauus, vel <lb></lb>truncus, vel per circuitionem ſimplicem, ſic adducitur rotati baculi ex­<lb></lb>tremitas; vel per circuitionem mixtam: </s>
					<s id="N292AB">ſic adducitur extremitas funis <lb></lb>flagelli; vel cum aliquo iactu; </s>
					<s id="N292B1">ſic adducitur pulmentum vt in vaſe <lb></lb>optimè commiſceatur v.g. ſic coqui adducunt frixum &amp; inuertunt, por­<lb></lb>recto tantillùm, tùm deinde rotato ſartaginis manubrio: </s>
					<s id="N292BB">ſi enim eſſet <lb></lb>vera rotatio, frixum per Tangentem erit; at verò propter motum rectum <lb></lb>poſt inuerſionem ab ipſa ſartagine minimè recedit. </s>
				</p>
				<p id="N292C3" type="main">
					<s id="N292C5">Quintò, ventilatio eſt motio, quâ frumentum excernitur vanno; </s>
					<s id="N292C9">van­<lb></lb>nus circuli eſt vulgare ſatis frumentarium organum duabus anſis inſtru­<lb></lb>ctum, quibus vibratur tùm in aduerſam partem, vt ipſo ſuccuſſu paleæ, <lb></lb>ariſtæ, &amp; aliæ feſtucæ auolent; </s>
					<s id="N292D3">tùm dextrorſum ſiniſtrorſumque libratur <lb></lb>vt leuior materia extet; </s>
					<s id="N292D9">triticum enim grauius eſt; </s>
					<s id="N292DD">igitur deorſum ten­<lb></lb>dit; palea verò ſurſum; </s>
					<s id="N292E3">ideo verò attollitur, ſubſultatque triticum in van­<lb></lb>no, quia poſt impreſſum impetum per vibrationem ſurſum, manus ipſa <lb></lb>deorſum cum aliquo impetu truditur, in quo non eſt difficultas, alio <lb></lb>verò motu quaſi recto repit frumentum in vanni aluo, quia per addu­<lb></lb>ctionem vanni impulſæ priùs ſiniſtrorſum frumentum in eam partem <lb></lb>adhuc propter priorem impetum fertur; ſic cum nauis illicò ſiſtit in <lb></lb>potu, qui ſunt in ea &amp; portum aſpiciunt, proni cadunt, de quo iam <lb></lb>ſuprà. </s>
				</p>
				<p id="N292F5" type="main">
					<s id="N292F7">Sextò, remigatio fit pellendo, trahendoque, de qua iam ſuprà Th. 6. <lb></lb>16.longior &amp; latior remus maiorem vim aquæ impellit; </s>
					<s id="N292FD">difficiliùs taman <lb></lb>mouetur, quò maior eſt illius portio à centro motus verſus manum re­<lb></lb>migantis, faciliùs mouetur propter rationem vectis; </s>
					<s id="N29305">faciliùs mouetur, ſi <lb></lb>aduerſo flumine feratur nauis: </s>
					<s id="N2930B">ratio eſt, quia aqua pulſa verſus eam <lb></lb>partem, in quam fluit minùs reſiſtit, quando eundem remum tractant, <pb pagenum="417" xlink:href="026/01/451.jpg"></pb>ille plus confert, qui ad extremitatem propiùs accedit; ratio clara eſt: </s>
					<s id="N29316"><lb></lb>ſed de re nautica aliàs; vide interim locum citatum. </s>
				</p>
				<p id="N2931B" type="main">
					<s id="N2931D">Septimò, tritus fit, cum ab impacto aliquo duriore corpore malleo, <lb></lb>v.g. vel pilo aliud teritur, quod ſcilicet impetus partibus illis impreſſis <lb></lb>ſuperet vim implicationis, vel vnionis partium; </s>
					<s id="N29327">eſt etiam eadem ratio <lb></lb>fracturæ eadem tenſionis, vel inflexionis; per quid verò corpus ipſum <lb></lb>ſit vel friabile, vel fragile, vel flexibile, fusè explicamus Tomo <lb></lb>quinto. </s>
				</p>
				<p id="N29331" type="main">
					<s id="N29333">Octauò, ſuccuſſus eſt impetus impreſſus repetito frequenti niſu; </s>
					<s id="N29337">ſic <lb></lb>vulgò ſuccutiuntur arbores, vt fructus maturi cadant; </s>
					<s id="N2933D">excuti verò ali­<lb></lb>quid dicitur, cum impetus vi ab alio ſeparatur; </s>
					<s id="N29343">ſic excuti dicuntur den­<lb></lb>tes; ſic excutitur malleo marmoris fragmentum, &amp;c. </s>
					<s id="N29349">in quo non eſt <lb></lb>difficultas; </s>
					<s id="N2934F">nam quoties maior eſt vis impetus, quàm implicationis par­<lb></lb>tium, vel vnionis, tunc aliqua pars auolat ab ictu: </s>
					<s id="N29355">denique caſus alicuius <lb></lb>corporis facilè intelligi poteſt; </s>
					<s id="N2935B">periculoſior eſt altioris hominis, quàm <lb></lb>puſilli: </s>
					<s id="N29361">hinc animalcula cadentia vix quidquam detrimenti à <lb></lb>caſu accipiunt: </s>
					<s id="N29367">præterea ictus grauior eſt, ſi quis cadat in eam partem, <lb></lb>verſus quam ſummo niſu fertur; </s>
					<s id="N2936D">quia impetus grauitatis augetur ab alio <lb></lb>impreſſo: </s>
					<s id="N29373">deinde pars illa corporis, quæ caſu altitudine multùm auget <lb></lb>vel imminuit grauitatem ictus, vt certum eſt; </s>
					<s id="N29379">immò corpus illud, cui <lb></lb>alliditur: </s>
					<s id="N2937F">hinc caput in marmor impactum grauiſſimum ictum refert: </s>
					<s id="N29383"><lb></lb>hinc tybiæ, vel brachij os ita impingitur caſu, vt frangatur, vel propter <lb></lb>rationem vectis, vel propter inæqualitatem corporis, in quod impingi­<lb></lb>tur; </s>
					<s id="N2938C">hinc franguntur oſſa facilè modico ictu, ſi vtrimque ſuſtineantur; </s>
					<s id="N29390"><lb></lb>in medio vero abſit fulcrum: ſed hæc pertinent ad reſiſtentiam corporum, <lb></lb>de qua Tomo ſequenti, </s>
				</p>
				<p id="N29397" type="main">
					<s id="N29399">Nonò, exploſio fit, cum aliquid emittitur, vel cum aliquo ſtrepitu, <lb></lb>vt glans è fiſtula, vel per continuam preſſionem digitorum; </s>
					<s id="N2939F">ſic nucleus <lb></lb>ceraſi vulgo exploditur à pueris: </s>
					<s id="N293A5">Ratio eſt, quia propter vliginem nu­<lb></lb>clei recenter extracti digiti in eius ſuperficie conuexa facilè repunt; </s>
					<s id="N293AD">hinc <lb></lb>aucto ſemper impetu, &amp; nouo etiam addito ex porrecto brachio pro­<lb></lb>cul exploditur: ſic omnia lubrica è manibus facilè elabuntur, vt ſæpè <lb></lb>piſces, &amp;c. </s>
				</p>
				<p id="N293B7" type="main">
					<s id="N293B9">Decimò, reſiſtentia corporum procedit tum ex impenetrabilitate <lb></lb>tùm ex duritie, tùm ex denſitate; </s>
					<s id="N293BF">nos verò hos ſtatus alio Tomo expli­<lb></lb>cabimus; </s>
					<s id="N293C5">eſt autem duplex reſiſtentia; </s>
					<s id="N293C9">prima eſt formalis, quæ in eo <lb></lb>poſita eſt, quod non corpus impediat motum alterius, non per aliquid <lb></lb>contrarium, quod in eo producat, ſed vel per ſuam impenetrabilitatem, <lb></lb>vel per ſuam duritiem, vel per ſuam molem; </s>
					<s id="N293D3">nam inde oritur noua de­<lb></lb>terminatio, vt alibi explicuimus, vel denique per ſuam grauitationem, <lb></lb>&amp;c, ſecunda eſt actiua, vt cum imum corpus imprimit alteri impetum; <lb></lb>ſed hæc facilè ex dictis intelligi poſſunt. </s>
				</p>
				<p id="N293DD" type="main">
					<s id="N293DF">Vndecimò, omitto varias motiones corporis humani. </s>
					<s id="N293E2">Primò, motum <lb></lb>progreſſiuum ſiue fiat curſu, ſiue lentiore gradu: quippè tùm coxæ <lb></lb>mouentur motu mixto ex duobus circularibus. </s>
					<s id="N293EA">&amp; crura ex tribus. </s>
					<s id="N293ED">Se-<pb pagenum="418" xlink:href="026/01/452.jpg"></pb>cundò, ſaltum. </s>
					<s id="N293F5">Tertiò, luctum. </s>
					<s id="N293F8">Quartò, chorum, ſeu numeroſam ſalta­<lb></lb>tionem. </s>
					<s id="N293FD">Quintò denique aliorum animalium motus, qui reuerâ huius <lb></lb>loci eſſe non poſſunt; nam perfectam muſculorum, atque adeo totius <lb></lb>fabricæ corporis humani cognitionem ſupponunt, quam trademus ſuo <lb></lb>loco, cum de homine, addemuſque alios motus v.g. reſpirationis, ſter­<lb></lb>nutationis, tuſſis, ſingultus, oſcitationis, riſus, fletus, fiſtoles, &amp; diaſto­<lb></lb>les, &amp;c. </s>
					<s id="N2940D">quorum omnium veriſſimas cauſas afferemus; </s>
					<s id="N29411">omitto etiam <lb></lb>cauſas phyſicas motuum cœleſtium, quas certè, niſi me veritas fallit, <lb></lb>Tomo ſequenti demonſtrabimus per ſimpliciſſima principia, cum aliquo <lb></lb>ſaltem rei aſtronomicæ incremento: denique omitto alios motus, qui <lb></lb>certæ materiæ affiguntur v.g.æſtus maris, libræ motus, fluuiorum fluxus, <lb></lb>ventorum vis, fluminis ira, magnetis virtus, &amp; electri, &amp;c. </s>
					<s id="N2941F">de quibus <lb></lb>ſuo loco: quippe hoc loco conſideramus tantùm motiones, quatenus <lb></lb>certæ materiæ copulantur. </s>
				</p>
				<p id="N29426" type="main">
					<s id="N29428"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29434" type="main">
					<s id="N29436"><emph type="italics"></emph>Explicari poſſunt ſingulares aquarum motus,<emph.end type="italics"></emph.end> quod tantum hîc breuiter <lb></lb>præſtabimus: </s>
					<s id="N29441">itaque primò, aqua fluit cum plano decliui, quod liquo­<lb></lb>ris proprium eſt; </s>
					<s id="N29447">ideo verò fluit, quia cum vna pars alteri extare non <lb></lb>poſſit; nec enim leuior eſt, deorſum fluit, de quo aliàs fusè. </s>
				</p>
				<p id="N2944D" type="main">
					<s id="N2944F">Secundò, ſtillatim cadit, quia ſcilicet colligitur in ſphærulas, quæ <lb></lb>tandem proprio pondere deorſum eunt; cur verò in ſphærulas torne­<lb></lb>tur, veriſſimam rationem dabimus ſuo loco. </s>
				</p>
				<p id="N29457" type="main">
					<s id="N29459">Tertiò, ſtillicidium facilè reſiſtit, quia ſcilicet aquæ partes, quæ tan­<lb></lb>tùm modico glutine continentur, diuelluntur facilè, &amp; repercuſſu illo, <lb></lb>præſertim ſi à corpore duriore fiat, in omnem partem eunt. </s>
				</p>
				<p id="N29460" type="main">
					<s id="N29462">Quartò, aſperſio aquæ valdè familiaris eſt, quod ſcilicet vi iàctus mi­<lb></lb>nutim emittatur aqua, in quo non eſt vlla difficultas; nam aqua facilè <lb></lb>diuiditur. </s>
				</p>
				<p id="N2946A" type="main">
					<s id="N2946C">Quintò, aqua diluit facilè tùm alios liquores; quia facilè miſcetur <lb></lb>tùm corpora ſpongioſa, quorum poros, &amp; cauitates facilè ſubit. </s>
				</p>
				<p id="N29472" type="main">
					<s id="N29474">Sextò, abluit corpora, quibus ſcilicet facilè adhæret, &amp; denique cum <lb></lb>ſordibus exprimitur. </s>
				</p>
				<p id="N29479" type="main">
					<s id="N2947B">Septimò, aqua fluit, quæ ſcilicet in minutiſſimas particulas diſtincta <lb></lb>ſenſim liqueſcente vapore in terram cadit. </s>
				</p>
				<p id="N29480" type="main">
					<s id="N29482">Octauò, infunditur ex vno ſcilicet vaſe in aliud; </s>
					<s id="N29486">affunditur, ſubiectis <lb></lb>ſcilicet manibus; effunditur, ſcilicet ex ſuo vaſe. </s>
				</p>
				<p id="N2948C" type="main">
					<s id="N2948E">Nonò, exundat ſæpiùs v. g. fluuius alueo; </s>
					<s id="N29496">ſic palus etiam &amp; mare <lb></lb>reſtagnant propter nimiam aquarum copiam: hinc ſæpè terram in­<lb></lb>undat. </s>
				</p>
				<p id="N2949E" type="main">
					<s id="N294A0">Decimò, libratur ſæpiùs in ſuo vaſe v.g. in latiore cratere; </s>
					<s id="N294A6">nam facilè <lb></lb>aſcendit per planum modicè inclinatum, reditque per diuerſas vices; fa­<lb></lb>ciliùs tamen in latiori, quàm in anguſtiore calice. </s>
				</p>
				<p id="N294AE" type="main">
					<s id="N294B0">Vndecimò, fluctuat, cum ſcilicet eius ſuperficies agitatur ventorum <lb></lb>vi; eſt enim aqua corpus facilè mobile. </s>
				</p>
				<pb pagenum="419" xlink:href="026/01/453.jpg"></pb>
				<p id="N294BA" type="main">
					<s id="N294BC">Duodecimò, criſpatur, cum ſcilicet vel leuior eſt afflatus, vel tremu­<lb></lb>lo ſuccutitur motu vas illud, in quo continetur. </s>
				</p>
				<p id="N294C1" type="main">
					<s id="N294C3">Decimotertiò, in circulos agitur, cum aliquod corpus immergitur <lb></lb>quia <expan abbr="tantũdem">tantundem</expan> aquæ attollitur ſenſim; </s>
					<s id="N294CD">quod quia extare non poteſt, in <lb></lb>orbem ſuperficiei reliquæ coextenditur: hinc continuò illius circuli, <lb></lb>tantillùm extantis decreſcit tumor. </s>
				</p>
				<p id="N294D5" type="main">
					<s id="N294D7">Decimoquartò, facilè miſcetur cum aqua; quia facilè partes aquæ mi­<lb></lb>nimo ſcilicet impetu diuiduntur. </s>
				</p>
				<p id="N294DD" type="main">
					<s id="N294DF">Decimoquintò, feruet aqua calore; quia ſcilicet partes calidiores <lb></lb>in vaporem conuerſæ retentæ in bullis ſurſum eas attollunt in ſpu­<lb></lb>mam. </s>
				</p>
				<p id="N294E7" type="main">
					<s id="N294E9">Decimoſextò, ſaltitat aqua, cum ſcilicet aluei fundum eſt paulò aſpe­<lb></lb>rius: ratio clariſſima eſt, quia à ſaxis occurrentibus repercutitur. </s>
				</p>
				<p id="N294EF" type="main">
					<s id="N294F1">Decimoſeptimò, agit verticem ſæpius, cum ſcilicet tractu reſpondet <lb></lb>profundiori, vel cum repellitur à littore, remo, &amp;c. </s>
				</p>
				<p id="N294F6" type="main">
					<s id="N294F8">Decimooctauò, agitatur facilè ſeu baculo, ſeu libratione vaſis: </s>
					<s id="N294FC">ſed <lb></lb>hæc tantùm breuiter indicaſſe ſufficiat, quæ alibi ſuis locis fusè omninò <lb></lb>explicabimus: atque hæc de diuerſis motionibus ſint ſatis. <lb></lb><figure id="id.026.01.453.1.jpg" xlink:href="026/01/453/1.jpg"></figure></s>
				</p>
				<pb pagenum="420" xlink:href="026/01/454.jpg"></pb>
				<figure id="id.026.01.454.1.jpg" xlink:href="026/01/454/1.jpg"></figure>
				<p id="N29513" type="main">
					<s id="N29515"><emph type="center"></emph>APPENDIX PRIMA <lb></lb>PHYSICOMATHEMATICA,<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2951E" type="main">
					<s id="N29520"><emph type="center"></emph><emph type="italics"></emph>De centro percuſsionis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2952B" type="main">
					<s id="N2952D">DE duplici centro hactenus actum eſt, <lb></lb>magnitudinis, ſcilicet, &amp; grauitatis; <lb></lb>præſertim de hoc vltimo: </s>
					<s id="N29535">in quo certè <lb></lb>opere non ſine maxima laude præ­<lb></lb>ſtantiſſimi Mathematici deſudarunt, <lb></lb>ſcilicet Archimedes, Commandinus, Lucas Vale­<lb></lb>rius, Steuinus, Guldinus, Galileus paucis: </s>
					<s id="N29541">ſed du­<lb></lb>plex aliud centrum conſiderari poteſt; </s>
					<s id="N29547">primum di­<lb></lb>citur centrum impreſſionis: vtrumque prorſus inta­<lb></lb>ctum aliis doctâ paucarum licèt propoſitionum co­<lb></lb>ronâ, vel peripheria in hac appendice corona­<lb></lb>mus. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N29556" type="main">
					<s id="N29558"><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 id="N29564" type="main">
					<s id="N29566"><emph type="italics"></emph>CEntrum grauitatis eſt punctum, quod omnia grauitatis momenta æqua­<lb></lb>liter dirimit.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2956F" type="main">
					<s id="N29571">Clara eſt definitio; centrum enim grauitatis eſt illud punctum, ex <lb></lb>quo pendulum corpus per quamlibet lineam ſeruat æquilibrium. </s>
				</p>
				<p id="N29577" type="main">
					<s id="N29579"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29586" type="main">
					<s id="N29588"><emph type="italics"></emph>Centrum impreſſionis eſt illud, per quod, ſi ducatur planum vtrimque, di­<lb></lb>rimit æqualem impetum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29591" type="main">
					<s id="N29593">Hæc etiam clara eſt; </s>
					<s id="N29597">conſideratur autem impetus non modò ratione <pb pagenum="421" xlink:href="026/01/455.jpg"></pb>intenſionis verùm etiam extenſionis; debet etiam accipi punctum illud <lb></lb>in linea motus. </s>
				</p>
				<p id="N295A2" type="main">
					<s id="N295A4"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N295B1" type="main">
					<s id="N295B3"><emph type="italics"></emph>Centrum percuſſionis eſt punctum illud corporis impacti in quo ſi contactus <lb></lb>fiat, maximus ictus infligitur.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N295BC" type="main">
					<s id="N295BE"><emph type="center"></emph><emph type="italics"></emph>Definitio<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N295CB" type="main">
					<s id="N295CD"><emph type="italics"></emph>Linea directionis eſt linea motus centri grauitatis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N295D4" type="main">
					<s id="N295D6"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N295E3" type="main">
					<s id="N295E5"><emph type="italics"></emph>Centrum grauitatis dirigit linea motus aliorum punctorum.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N295EC" type="main">
					<s id="N295EE"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N295FB" type="main">
					<s id="N295FD"><emph type="italics"></emph>Si percuſſio ita fiat, vt totus impetus corporis impacti impediatur maxi­<lb></lb>ma eſt.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29606" type="main">
					<s id="N29608"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29615" type="main">
					<s id="N29617"><emph type="italics"></emph>Momenta ſunt, vt diſtantiæ.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2961E" type="main">
					<s id="N29620"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2962D" type="main">
					<s id="N2962F"><emph type="italics"></emph>Omnes partes corporis, quod mouetur motu recto, mouentur æqua­<lb></lb>liter.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29638" type="main">
					<s id="N2963A"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29647" type="main">
					<s id="N29649"><emph type="italics"></emph>Corpus graue ſuſtinetur in æquilibrio, cum ſuſtinetur in linea dire­<lb></lb>ctionis.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29652" type="main">
					<s id="N29654"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29661" type="main">
					<s id="N29663"><emph type="italics"></emph>Centrum percuſſionis eſt in illa linea, quæ dirimit vtrimque momenta, tùm <lb></lb>ratione impetus, tùm ratione diſtantiæ.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2966C" type="main">
					<s id="N2966E"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2967A" type="main">
					<s id="N2967C"><emph type="italics"></emph>Si pondera inæqualia ſunt in æquilibrio, diſtantiæ ſunt, vt pondera per­<lb></lb>mutando; vel collectio diſtantiarum eſt ad maiorem, vt collectio ponderum ad <lb></lb>alterum pondus, quod maius est, &amp;c.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29688" type="main">
					<s id="N2968A"><emph type="center"></emph><emph type="italics"></emph>Poſitiones<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29696" type="main">
					<s id="N29698"><emph type="italics"></emph>Maximus ictus infligitur in linea directionis, per ſe,<emph.end type="italics"></emph.end> vt conſtat ex <lb></lb>poſ.5.6.2. </s>
				</p>
				<p id="N296A2" type="main">
					<s id="N296A4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N296B1" type="main">
					<s id="N296B3"><emph type="italics"></emph>Centrum percuſſionis lineæ mobilis motu recto eſt idem cum centro graui­<lb></lb>tatis eiuſdem.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N296BC" type="main">
					<s id="N296BE">Sit enim linea AC, horizonti parallela, v.g. quæ cadat perpendi­<lb></lb>culariter; </s>
					<s id="N296C6">ſit eius centrum grauitatis B, quod ſcilicet vtrimque æqua­<lb></lb>liter diſtat ab AC; </s>
					<s id="N296CC">centrum percuſſionis eſt in B. Probatur; </s>
					<s id="N296D0">quia cùm <lb></lb>in B impediatur totus impetus; </s>
					<s id="N296D6">quippe neutrum ſegmentum præualere <lb></lb>poteſt; eſt enim vtrimque æqualis impetus, per poſit. </s>
					<s id="N296DC">3. 4. certè maxi­<lb></lb>ma percuſſio eſt in B, per poſit.2. igitur eſt centrum percuſſionis per <pb pagenum="422" xlink:href="026/01/456.jpg"></pb>def.5. igitur centrum percuſſionis eſt idem cum centro grauitatis, quod <lb></lb>erat dem. </s>
				</p>
				<p id="N296E8" type="main">
					<s id="N296EA"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N296F7" type="main">
					<s id="N296F9">Hinc quatuor centra concurrunt in idem punctum, ſcilicet magni­<lb></lb>tudinis, grauitatis, impreſſionis, &amp; percuſſionis. </s>
				</p>
				<p id="N296FE" type="main">
					<s id="N29700"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2970D" type="main">
					<s id="N2970F">Idem prorſus dicendum eſt de Rectangulo, Parallelogrammate, Cir­<lb></lb>culo, Ellipſi, Cylindro, Priſmate, Parallelipedo, Sphæra, &amp;c. </s>
					<s id="N29714">in quibus <lb></lb>poſito motu recto, hæc quatuor centra in eodem plano, immò &amp; linea <lb></lb>reperiuntur. </s>
				</p>
				<p id="N2971B" type="main">
					<s id="N2971D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2972A" type="main">
					<s id="N2972C"><emph type="italics"></emph>Si planum triangulare cadat motu recto deorſum, v.g. horizonti paralle­<lb></lb>lum, centrum percuſſionis eſt idem cum centro grauitatis eiuſdem.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N29737" type="main">
					<s id="N29739">Sit enim triangulare planum FBH, cuius centrum grauitatis ſit I: </s>
					<s id="N2973D"><lb></lb>dico eſſe centrum percuſſionis; </s>
					<s id="N29742">quia, cùm ſit æqualis motus, &amp; impetus <lb></lb>omnium partium plani, ſi ſuſtineatur in I, ſtat in æquilibrio, per def.1. <lb></lb>igitur totus impetus impeditur; igitur eſt maxima percuſſio, per <lb></lb>Poſ. 2. </s>
				</p>
				<p id="N2974F" type="main">
					<s id="N29751"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2975D" type="main">
					<s id="N2975F">Obſeruabis punctum I poſſe haberi duobus modis; </s>
					<s id="N29763">Primò, ſi ducatur <lb></lb>FC diuidens æqualiter HB; </s>
					<s id="N29769">diuidit etiam æqualiter GA, &amp; omnes alias <lb></lb>parallelas HB; </s>
					<s id="N2976F">igitur in FC eſt centrum grauitatis: </s>
					<s id="N29773">ſimiliter ducatur <lb></lb>HD diuidens æqualiter FB, centrum grauitatis erit etiam in HD; </s>
					<s id="N29779">igi­<lb></lb>tur in communi puncto I. Secundò, ita diuidatur FH in G, vt FG ſit <lb></lb>dupla GH, ducaturque GA: </s>
					<s id="N29781">ſimiliter ducatur KE diuidens HB eodem <lb></lb>modo, punctum communis ſectionis I eſt centrum grauitatis; </s>
					<s id="N29787">quippe <lb></lb>duo triangula DIC, FIH ſunt proportionalia; </s>
					<s id="N2978D">igitur vt DC ad FH, <lb></lb>ita DI ad IH, ſed DC eſt ſubdupla FH; </s>
					<s id="N29793">igitur DI ſubdupla IH: </s>
					<s id="N29797">ſimi­<lb></lb>liter IC ſubdupla IF; </s>
					<s id="N2979D">igitur GH ſubdupla GF; igitur inuentum eſt <lb></lb>centrum grauitatis, quod erat faciendum. </s>
				</p>
				<p id="N297A3" type="main">
					<s id="N297A5"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N297B2" type="main">
					<s id="N297B4"><emph type="italics"></emph>Si planum triangulare cadat parallelum lineæ verticali,<emph.end type="italics"></emph.end> v. g. in ſitu FH <lb></lb>B, ita vt FH ſit parallela horizonti, centrum percuſſionis eſt in G; </s>
					<s id="N297C3">cùm <lb></lb>enim GA ducatur per centrum grauitatis I, ſitque parallela HB, eſt <lb></lb>linea directionis, per def.4. igitur ſi ſuſtineatur in G, ſtabit in æquili­<lb></lb>brio, per p.5. igitur totus impetus impeditur, vt patet; igitur eſt maxi­<lb></lb>ma percuſſio per p. </s>
					<s id="N297CF">2. igitur centrum percuſſionis eſt G, quod erat de­<lb></lb>monſt. </s>
				</p>
				<p id="N297D4" type="main">
					<s id="N297D6"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N297E3" type="main">
					<s id="N297E5">Hinc corpus ſolidum ex multis huiuſmodi triangulis æqualibus quaſi <lb></lb>conflatum, idem prorſus percuſſionis centrum habet; ſiue cadat lineæ <lb></lb>verticali parallelum, ſiue ipſi verticali. </s>
				</p>
				<pb pagenum="423" xlink:href="026/01/457.jpg"></pb>
				<p id="N297F1" type="main">
					<s id="N297F3"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29800" type="main">
					<s id="N29802">Hinc etiam ad Mechanicam reduci poteſt inuentio praxis prædictæ; </s>
					<s id="N29806"><lb></lb>ſit enim triangulum AGD; </s>
					<s id="N2980B">diuidatur AD in tres partes in BC; </s>
					<s id="N2980F">du­<lb></lb>cantur BI, CH, parallelæ DG, itemque IE, HF parallelæ AD; </s>
					<s id="N29815">ſuſti­<lb></lb>neaturque prædictum planum erectum in C, ſtabit in æquilibrio; </s>
					<s id="N2981B">cùm <lb></lb>enim momenta ponderum æqualium ſint vt diſtantiæ, rectangulo CE <lb></lb>reſpondet æquale, &amp; æquediſtans CI, itemque trianguli EHK, æquale <lb></lb>&amp; æquediſtans IKD, triangulo demum GHE, triangulum ſubduplum <lb></lb>AIB, cuius momentum adæquat momentum alterius dupli GHB; quia <lb></lb>diſtantia eſt dupla. </s>
				</p>
				<p id="N29829" type="main">
					<s id="N2982B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29838" type="main">
					<s id="N2983A"><emph type="italics"></emph>Si Pyramis, cuius axis ſit parallela horizonti, cadat deorſum; </s>
					<s id="N29840">centrum <lb></lb>percuſſionis eſt in linea derectionis, quæ ſcilicet ducetur deorſum à centro gra­<lb></lb>tatis,<emph.end type="italics"></emph.end> quod eodem modo demonſtratur, quo ſuprà; </s>
					<s id="N2984B">eſt autem centrum <lb></lb>grauitatis illud punctum, quod ita axem diuidit, vt ſegmentum verſus <lb></lb>baſim ſit ſubtriplum alterius verſus verticem, quod multi hactenus de­<lb></lb>monſtrarunt, ſcilicet Commandinus, Valerius, Steuinus, Galileus; ſit <lb></lb>enim conus ENI, ſit axis AI diuiſus in 4. partes æquales BCD, pa­<lb></lb>rallelus horizonti, ſuſtineatur in M, ſtabit in æquilibrio. </s>
				</p>
				<p id="N29859" type="main">
					<s id="N2985B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29868" type="main">
					<s id="N2986A"><emph type="italics"></emph>Si quodlibet aliud planum, vel corpus, deorſum cadat, motu recto, cen­<lb></lb>trum percuſſionis eſt in linea directionis<emph.end type="italics"></emph.end>; </s>
					<s id="N29875">quod eodem modo probatur, quo <lb></lb>ſuprà: </s>
					<s id="N2987B">quodnam verò ſit centrum grauitatis omnium corporum, plano­<lb></lb>rum, figurarum, hîc non diſputamus; conſulantur authores citati, quibus <lb></lb>addatur La Faille, qui egregiè centrum grauitatis partium circuli, &amp; <lb></lb>Eclipſis demonſtrauit. </s>
				</p>
				<p id="N29885" type="main">
					<s id="N29887"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29894" type="main">
					<s id="N29896"><emph type="italics"></emph>Si linea circa centrum immobile mobilis, voluatur, centrum percuſſionis <lb></lb>non eſt centrum grauitatis<emph.end type="italics"></emph.end>; </s>
					<s id="N298A1">ſit enim linea AD, quæ voluatur circa cen­<lb></lb>trum A; </s>
					<s id="N298A7">diuidatur bifariam in G, punctum G eſt centrum grauitatis: vt <lb></lb>conſtat; </s>
					<s id="N298AD">non tamen eſt centrum percuſſionis, quia in ſegmento GD eſt <lb></lb>quidem æquale momentum ratione diſtantiæ, ſed maius ratione impe­<lb></lb>tus; quippe GD mouetur velociùs, quàm GA vt certum eſt. </s>
				</p>
				<p id="N298B5" type="main">
					<s id="N298B7"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N298C3" type="main">
					<s id="N298C5"><emph type="italics"></emph>In hac eadem hypotheſi centrum percuſſionis non eſt idem cum centro im­<lb></lb>preſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N298D0">diuidatur enim AD in M, ita vt AM, ſit media propor­<lb></lb>tionalis inter AG, &amp; AD; </s>
					<s id="N298D6">certè M eſt centrum impreſſionis, vt de­<lb></lb>monſtratum eſt lib.  1.non tamen eſt centrum percuſſionis; </s>
					<s id="N298DC">quia ſeg­<lb></lb>mentum MA habet quidem æqualem impetum cum ſegmento MD; </s>
					<s id="N298E2">ha­<lb></lb>bet tamen maius momentum, quia maiorem habet diſtantiam; igitur <lb></lb>non erit æquilibrium in M. </s>
				</p>
				<pb pagenum="424" xlink:href="026/01/458.jpg"></pb>
				<p id="N298EE" type="main">
					<s id="N298F0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N298FC" type="main">
					<s id="N298FE"><emph type="italics"></emph>Si diuidatur AD in tres partes æquales, ſit que ID<emph.end type="italics"></emph.end> 1/3 <emph type="italics"></emph>centrum percuſſio­<lb></lb>nis erit in I<emph.end type="italics"></emph.end>; </s>
					<s id="N2990F">demonſtratur, quia impetus puncti G eſt ad impetum pun­<lb></lb>cti D; </s>
					<s id="N29915">vt arcus EG, ad arcum BD; </s>
					<s id="N29919">ſit autem DC æqualis DB; </s>
					<s id="N2991D">ducatur <lb></lb>AC, triangulum ACD erit æquale ſectori ADB, vt conſtat; impetus in <lb></lb>D erit, vt recta DC, &amp; in I, vt recta IH, &amp; in G, vt recta GF, &amp;c. </s>
					<s id="N29925">igi­<lb></lb>tur perinde ſe habet impetus, qui ineſt puncto D, atque ſi incubaret ipſi <lb></lb>D.DC, &amp; I, IH, &amp; G, GF, &amp;c. </s>
					<s id="N2992C">atqui ſi hoc eſſet, centrum grauitatis <lb></lb>eſſet in I, vt patet ex dictis; ibique eſſet percuſſionis, per Th. 3. igitur <lb></lb>I eſt centrum percuſſionis. </s>
				</p>
				<p id="N29934" type="main">
					<s id="N29936"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N29942" type="main">
					<s id="N29944">Colligo primò, ex dictis in hac hypotheſi tria centra ſeparari. </s>
				</p>
				<p id="N29947" type="main">
					<s id="N29949">Secundò ſi nullum eſſet momentum ratione diſtantiæ, centrum per­<lb></lb>cuſſionis idem eſſet cum centro impreſſionis. </s>
				</p>
				<p id="N2994E" type="main">
					<s id="N29950">Tertiò, centrum percuſſionis lineæ circa alteram extremitatem mo­<lb></lb>bilis; </s>
					<s id="N29956">idem eſſe cum centro percuſſionis trianguli, ſeu plani triangula­<lb></lb>ris; de quo ſuprà. </s>
				</p>
				<p id="N2995C" type="main">
					<s id="N2995E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2996A" type="main">
					<s id="N2996C"><emph type="italics"></emph>Si rotetur planum rectangulum circa alterum laterum centrum percuſſionis <lb></lb>eſt in linea, quæ diuidit rectangulum æqualiter, &amp; cadit perpendiculariter <lb></lb>in axem, circa quem rotatur<emph.end type="italics"></emph.end>; </s>
					<s id="N29979">v.g. ſit rectangulum CF, rotatum circa C <lb></lb>A; </s>
					<s id="N29981">ſit BG, dirimens æqualiter CA &amp; HF, centrum grauitatis eſt in <lb></lb>BG; quia eſt æquale momentum in BF &amp; BH, tùm ratione impetus, <lb></lb>tùm ratione diſtantiæ, vt pater per p.6. </s>
				</p>
				<p id="N29989" type="main">
					<s id="N2998B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 10.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29997" type="main">
					<s id="N29999"><emph type="italics"></emph>Si BG diuidatur in tres partes æquales B, D, I, G, rotetur que circa CA, <lb></lb>vt dictum eſt ſuprà, centrum percuſſionis eſt in I<emph.end type="italics"></emph.end>; </s>
					<s id="N299A4">quia ſi volueretur ſola <lb></lb>AF, eſſet in E, ſi ſola CH, eſſet in K, ſi ſola BG, eſſet in I, per Th. 8. <lb></lb>igitur centra percuſſionis omnium ſunt in linea EK; ſed lineæ EK, cuius <lb></lb>ſingula puncta mouentur æquali motu, centrum percuſſionis eſt in I, per <lb></lb>Th.1. igitur centrum percuſſionis totius CF acti circum CA, eſt in I, <lb></lb>quod erat demonſtr. </s>
				</p>
				<p id="N299B2" type="main">
					<s id="N299B4"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N299C0" type="main">
					<s id="N299C2">Primò, ſi rotetur circa CH, eodem modo inuenietur centrum per­<lb></lb>cuſſionis, ſcilicet N ita vt NO ſit 1/3 MO. </s>
				</p>
				<p id="N299C7" type="main">
					<s id="N299C9">Secundò, ſi rotetur circa OM rectangulum CF; </s>
					<s id="N299CD">diuidatur in tres <lb></lb>partes æquales, ſitque PG 1/3 NG, centrum percuſſionis eſt P; </s>
					<s id="N299D3">eſt enim <lb></lb>eadem ratio, quæ ſuprà; </s>
					<s id="N299D9">nec eſt minor ictus, quàm in I; </s>
					<s id="N299DD">rotato ſcilicet <lb></lb>rectangulo circa CA; quia eſt æqualis impetus. </s>
				</p>
				<p id="N299E3" type="main">
					<s id="N299E5">Tertiò, ſi rotetur circa BR, in quam AH cadit perpendiculariter, eſt <lb></lb>alia ratio, de qua infrà. </s>
				</p>
				<pb pagenum="425" xlink:href="026/01/459.jpg"></pb>
				<p id="N299EE" type="main">
					<s id="N299F0"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 11.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N299FC" type="main">
					<s id="N299FE"><emph type="italics"></emph>Si<emph.end type="italics"></emph.end> <emph type="italics"></emph>triangulum BIG voluatur circa CA, in quam BH cadit perpendi­<lb></lb>culariter, ſitque BH axis per centrum grauitatis ductus, diuiſuſque in<emph.end type="italics"></emph.end> 4. <lb></lb><emph type="italics"></emph>partes æquales B.F.E.D.H. centrum percuſſionis eſt in D<emph.end type="italics"></emph.end>; quod facilè de­<lb></lb>monſtratur; </s>
					<s id="N29A18">nam IG in iſto motu deſcribit ſuperficiem cylindri, &amp; <lb></lb>triangulum GBI deſcribit, vt ſic loquar, ſectorem cylindri; </s>
					<s id="N29A1E">igitur im­<lb></lb>petus in IG eſt ad impetum in NM, vt ſuperficies curua terminata in I <lb></lb>G, ad ſuperficiem terminatam in NM, ſub eodem ſcilicet angulo; </s>
					<s id="N29A26">vel vt <lb></lb>baſis pyramidis IG, ad baſim NM; igitur perinde ſe habet IG, ac ſi <lb></lb>incumberet prædicta baſis, itemque NM, &amp;c. </s>
					<s id="N29A2E">igitur ac ſi eſſet ſolida <lb></lb>pyramis quadrilatera; ſed pyramidis centrum grauitatis eſt D, per <lb></lb>Theorema 4. </s>
				</p>
				<p id="N29A37" type="main">
					<s id="N29A39"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 12.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29A45" type="main">
					<s id="N29A47"><emph type="italics"></emph>Si idem triangulum GIB voluatur circa IG, centrum percuſſionis eſt in <lb></lb>E, quod diuidit HB bifariam æqualiter<emph.end type="italics"></emph.end>; </s>
					<s id="N29A52">quod vt demonſtretur, perinde <lb></lb>ſe habet triangulum BGI circumactum, atque ſi ſingulis partibus in­<lb></lb>cumberent perpendiculares, quæ eſſent vt earumdem partium motus; </s>
					<s id="N29A5A"><lb></lb>ſit autem triangulum BAC æquale priori; </s>
					<s id="N29A5F">baſis cunei ABHKDC; </s>
					<s id="N29A63"><lb></lb>ducatur planum DBA, quod dirimat cuneum in duo ſolida, ſcilicet in <lb></lb>pyramidem ABHKD, &amp; ſolidum ABDC; </s>
					<s id="N29A6A">pyramis continet 2/3 totius <lb></lb>cunei, vt conſtat; </s>
					<s id="N29A70">eſt enim prædictus cuneus ſubduplus priſmatis, cuius <lb></lb>baſis ſit HA, &amp; altitudo ID; </s>
					<s id="N29A76">cuius pyramis prædicta continet 1/3; </s>
					<s id="N29A7A">igitur <lb></lb>ſi priſma ſit vt 6. pyramis erit vt 2. &amp; cuneus vt 3. igitur pyramis conti­<lb></lb>net 2/3 cunci; </s>
					<s id="N29A82">igitur alterum ſolidum ABDC eſt 1/3 cunei; </s>
					<s id="N29A86">cunei cen­<lb></lb>trum grauitatis idem eſt, quod trianguli HKD, per Corol. 1. Th.3.igi­<lb></lb>tur eſt in linea directionis MF.ita vt IM ſit 1/3 totius ID, per Th 3. py­<lb></lb>ramidis verò centrum grauitatis eſt in linea NG, ita vt IN ſit 1/4 totius <lb></lb>ID, per Th.4. igitur ſi eſt NM ad ML, vt ſolidum ABDC ad pyra­<lb></lb>midem AHD, id eſt vt 1.ad 2. certè NI, &amp; NL erunt æquales; </s>
					<s id="N29A96">ſed IN <lb></lb>eſt 1/4 totius ID; igitur IL 1/2 ergo L dirimit æqualiter ID, quod erat <lb></lb>demonſtr. </s>
					<s id="N29A9E">ſit ID 12.IN 3.IM 4. IL 6. </s>
				</p>
				<p id="N29AA2" type="main">
					<s id="N29AA4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 13.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29AB0" type="main">
					<s id="N29AB2"><emph type="italics"></emph>Si voluatur ſector circa axem parallelum ſubtenſæ, determinari poteſt cen­<lb></lb>trum percuſſionis, dato centro grauitatis ſectoris, quod tantum hactenus in­<lb></lb>uentum eſt ex ſuppoſita circuli quadratura<emph.end type="italics"></emph.end>: </s>
					<s id="N29ABF">ſit enim ſector AKHM, ſub­<lb></lb>tenſa KM; </s>
					<s id="N29AC5">diuidatur AI in tres partes æquales ADFI, item AH, in <lb></lb>tres æquales AEGH, centrum grauitatis ſectoris non eſt in F, quod eſt <lb></lb>centrum grauitatis trianguli AMK, ſed propiùs accedit ad H; </s>
					<s id="N29ACD">nec <lb></lb>etiam eſt in G, quod eſt centrum grauitatis trianguli ALN, ſed propiùs <lb></lb>accedit ad A; </s>
					<s id="N29AD5">ergo eſt inter FG, v.g. in R, ita vt AH ſit ad AR vt arcus <lb></lb>MHK ad 2/3 ſubtenſæ MK; </s>
					<s id="N29ADD">id eſt ad MP; </s>
					<s id="N29AE1">vt demonſtrat La Faille Prop. <lb></lb>34. poteſt etiam haberi centrum grauitatis ſegmenti circuli; </s>
					<s id="N29AE8">ſit enim <lb></lb>ſegmentum FCHI cuius centrum ſit B; </s>
					<s id="N29AF0">ſint BC. BI. BH. diuidens æ-<pb pagenum="426" xlink:href="026/01/460.jpg"></pb>qualiter CI; </s>
					<s id="N29AF9">ſitque D centrum grauitatis trianguli BCI; </s>
					<s id="N29AFD">ſit E centrum <lb></lb>grauitatis ſectoris BCHI, ſitque vt ſectio FCHI, ad triangulum BEI, <lb></lb>ita DE ad EG, vel vt ſectio ad ſectorem, ita DE ad DG; G eſt centrum <lb></lb>grauitatis ſectionis, per p.7. </s>
				</p>
				<p id="N29B07" type="main">
					<s id="N29B09">His poſitis voluatur ſector AKHM, circa axem CB, perinde ſe ha­<lb></lb>bet circumactus, atque ſi ſingulis partibus incumberent rectæ, quæ eſſent <lb></lb>vt motus earumdem pretium, vt conſtat ex dictis; </s>
					<s id="N29B11">igitur ſit ſector AEF <lb></lb>D, æqualis priori, perinde ſe habet, atque ſolidum AEFDCB, quod <lb></lb>ſcilicet conſtat ex pyramide AEDCB, &amp; ſegmento cylindri EFDCB; </s>
					<s id="N29B19"><lb></lb>pyramidis centrum grauitatis ſit I, ita vt IG ſit 1/4 GA, ſit M centrum <lb></lb>grauitatis ſegmenti ſolidi, ſeu potiùs ſit terminus perpendicularis deor­<lb></lb>ſum, quæ ducatur per centrum grauitatis eiuſdem ſolidi; </s>
					<s id="N29B22">diuidatur IM <lb></lb>in N, ita vt IN ſit ad NM, vt ſegmentum cylindri GEFDCB, ad <lb></lb>pyramidem AEDCB; certè N eſt centrum grauitatis ſolidi AEFDCHB, <lb></lb>per p.7. igitur N eſt centrum percuſſionis ſectoris circumacti. </s>
				</p>
				<p id="N29B2C" type="main">
					<s id="N29B2E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 14.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29B3A" type="main">
					<s id="N29B3C"><emph type="italics"></emph>Si<emph.end type="italics"></emph.end> <emph type="italics"></emph>ſector AKHM voluatur circa Tangentem NHL, determinari <lb></lb>poteſt centrum percuſſionis eodem modo<emph.end type="italics"></emph.end>; </s>
					<s id="N29B4D">nam aſſumi poteſt cuneus, vt ſuprà, <lb></lb>cuius baſis ſit ſegmentum cylindri; </s>
					<s id="N29B53">tùm pyramis cum eadem baſi; </s>
					<s id="N29B57">tùm in­<lb></lb>ueniri centrum grauitatis vtriuſque; </s>
					<s id="N29B5D">tùm detracta pyramide ex cuneo, <lb></lb>haberi reſiduum ſolidum, cuius centrum grauitatis inuenietur, iuxta prę­<lb></lb>dictam praxim; quippe hoc erit centrum percuſſionis quæſitum. </s>
				</p>
				<p id="N29B65" type="main">
					<s id="N29B67"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 15.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29B73" type="main">
					<s id="N29B75"><emph type="italics"></emph>Si voluatur<emph.end type="italics"></emph.end> <emph type="italics"></emph>triangulum FBH circa FM, in quam cadit HF perpen­<lb></lb>diculariter: </s>
					<s id="N29B83">ſi aſſumatur NH<emph.end type="italics"></emph.end> 1/4 <emph type="italics"></emph>FI, ducaturque NP parallela HB, ſe­<lb></lb>cans FC in O, dico punctum O eſſe centrum percuſſionis<emph.end type="italics"></emph.end>; quod eodem modo <lb></lb>probatur quo ſuprà Th.11. </s>
				</p>
				<p id="N29B95" type="main">
					<s id="N29B97"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 16.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29BA3" type="main">
					<s id="N29BA5"><emph type="italics"></emph>Si voluatur quodlibet triangulum circa angulum rectum, determinari pe­<lb></lb>test centrum percuſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N29BB0">ſit enim triangulum ABC; </s>
					<s id="N29BB4">ducatur quælibet <lb></lb>linea Tangens angulum, v.g. DBE, circa quam voluatur triangulum, du­<lb></lb>cantur AE, CD perpendiculares AD; </s>
					<s id="N29BBE">aliæ duæ ipſis æquales AFCG, <lb></lb>perpendicularis in AC; </s>
					<s id="N29BC4">tùm FG connectantur; </s>
					<s id="N29BC8">eleueturque Trapezus <lb></lb>AG, donec AF, CG incubent perpendiculariter plano ABC; </s>
					<s id="N29BCE">denique <lb></lb>à B ducantur rectæ ad omnia puncta Trapezi erecti, habebitur pyramis, <lb></lb>cuius centrum grauitatis, dabit centrum percuſſionis quæſitum, per Th. <lb></lb>11. quod vt fiat, inueniatur centrum grauitatis Trapezi AG, modo di­<lb></lb>cto, ducta ſcilicet FC, aſſumptoque I centro grauitatis trianguli FGC <lb></lb>&amp; L centro grauitatis trianguli FAC; </s>
					<s id="N29BDD">ſi enim ducatur LI, ſitque LI <lb></lb>ad LP, vt Trapezium AG, ad triangulum FGC; </s>
					<s id="N29BE3">certè P eſt centrum <lb></lb>grauitatis Trapezij per p.7. tùm ex P erecto ducatur recta ad B, hæc erit <lb></lb>axis pyramidis; </s>
					<s id="N29BEB">porrò ſi ducatur perpendicularis PO; </s>
					<s id="N29BEF">tùm BO habebi-<pb pagenum="427" xlink:href="026/01/461.jpg"></pb>tur orthogonium POB; denique aſſumatur OR 1/4 totius OB, R erit <lb></lb>centrum percuſſionis trianguli ACB per Th. 11. </s>
				</p>
				<p id="N29BFA" type="main">
					<s id="N29BFC"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N29C08" type="main">
					<s id="N29C0A">Hinc colligo quid dicendum ſit de rectangulo ita rotato, vt diagona­<lb></lb>lis cadat perpendiculariter in axem, circa quem rotatur; </s>
					<s id="N29C10">ſit enim re­<lb></lb>ctangulum CF, cuius diagonalis AIA, axis circa quem voluitur BR, in­<lb></lb>ueniantur centra percuſſionis vtriuſque trianguli ſeorſim AFH, ACH, <lb></lb>rotati circa axem BR per Th. 16. connectantur rectâ, in hac erit cen­<lb></lb>trum percuſſionis totius rectanguli; </s>
					<s id="N29C1C">cù diſtantiæ à centro communi <lb></lb>ſint vt pyramides permutando per p.7. vt conſtat ex dictis; ex quibus <lb></lb>etiam ſatis intelligetur quid de alijs planis, tùm regularibus, tùm irre­<lb></lb>gularibus dicendum ſit, cù ſcilicet poſſint in triangula diuidi. </s>
				</p>
				<p id="N29C26" type="main">
					<s id="N29C28"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 17.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29C34" type="main">
					<s id="N29C36"><emph type="italics"></emph>Si voluatur triangulare planum parallelum circulo, in quo voluitur, deter­<lb></lb>minari poteſt eius centrum percuſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N29C41">ſit enim triangulum AFH, quod <lb></lb>ita voluatur, vt extremitas H deſcribat arcum HS, &amp; F arcum FR; </s>
					<s id="N29C47">certè <lb></lb>F mouetur velociùs quàm H iuxta rationem AF ad AH; </s>
					<s id="N29C4D">ſit ergo FM æ­<lb></lb>qualis FA, &amp; HN æqualis HA; </s>
					<s id="N29C53">ducatur MN, erigatur Trapezus FN, <lb></lb>donec incubet plano AFH, &amp; cenſeantur ductæ ab A rectæ ad puncta <lb></lb>MN erecta; </s>
					<s id="N29C5B">habebitur pyramis; </s>
					<s id="N29C5F">ſit autem centrum grauitatis L, Trapezij <lb></lb>FN, ſitque LG perpendicularis in FH, ducatur AG, aſſumaturque DG <lb></lb>1/4 AG; </s>
					<s id="N29C67">haud dubiè D eſt centrum grauitatis huius; </s>
					<s id="N29C6B">ſit linea directionis <lb></lb>DC; </s>
					<s id="N29C71">quippe punctum D mouetur per Tangentem: </s>
					<s id="N29C75">quod etiam de alijs <lb></lb>punctis dictum eſto; </s>
					<s id="N29C7B">eſt enim hæc ratio motus circularis; igitur maximus <lb></lb>ictus erit in C per p. </s>
					<s id="N29C81">8. igitur C eſt centrum percuſſionis. </s>
				</p>
				<p id="N29C84" type="main">
					<s id="N29C86"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29C93" type="main">
					<s id="N29C95">Collige perinde ſe habere motum puncti F, atque ſi ipſi incumberet <lb></lb>linea FM, &amp; puncto H, HN. </s>
				</p>
				<p id="N29C9A" type="main">
					<s id="N29C9C"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29CA9" type="main">
					<s id="N29CAB">Præterea centrum percuſſionis aliquando eſſe extra rectam AH, cum <lb></lb>ſcilicet angulus circa, quem voluitur eſt minùs acutus, ſit enim trian­<lb></lb>gulum AGL quod voluatur circa A, ſitque centrum grauitatis Trapezij <lb></lb>E, de quo ſuprà; </s>
					<s id="N29CB5">ducantur EC, AC, ſit CB 1/4 AC, ducatur linea dire­<lb></lb>ctionis BI; vides I eſſe extra AL. </s>
				</p>
				<p id="N29CBC" type="main">
					<s id="N29CBE"><emph type="center"></emph><emph type="italics"></emph>Corollarium<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29CCB" type="main">
					<s id="N29CCD">Præterea oſtendi poſſe longè faciliùs totam rem iſtam; </s>
					<s id="N29CD1">ſit enim tri­<lb></lb>angulum ABD; </s>
					<s id="N29CD7">ducatur HBG æqualis BA, perpendicularis in BD; </s>
					<s id="N29CDB"><lb></lb>diuidatur AD bifariam æqualiter in L; </s>
					<s id="N29CE0">aſſumatur DE æqualis DL, <lb></lb>rùm ducantur HL, GE; </s>
					<s id="N29CE6">inueniatur centrum grauitatis C, Trapezij H <lb></lb>LEG; </s>
					<s id="N29CEC">ducatur AC, cuius KC ſit 1/4 ducatur KD perpendicularis in <lb></lb>AC, punctum D eſt centrum percuſſionis; </s>
					<s id="N29CF2">quippe ſi vertatur Trapezus <lb></lb>HE, circa axem BD, donec AD cadat in illum perpendiculariter, ſit-<pb pagenum="428" xlink:href="026/01/462.jpg"></pb>que ſectio communis BD; certè habebitur baſis pyramidis, cuius axis <lb></lb>erit AC, quæ omnia conſtant. </s>
				</p>
				<p id="N29CFF" type="main">
					<s id="N29D01"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 18.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29D0D" type="main">
					<s id="N29D0F"><emph type="italics"></emph>Determinari poteſt centrum percuſſionis in latere orthogonij ſubtenſo angulo <lb></lb>recto<emph.end type="italics"></emph.end>; </s>
					<s id="N29D1A">ſit enim AGB, latuſque ſubtenſum angulo recto AB, ſit Trape­<lb></lb>zus KD, eo modo quo diximus, cuius centrum grauitatis ſit H, ducatur <lb></lb>AH, aſſumatur IH 1/4: </s>
					<s id="N29D22">AH, ducatur IM perpendicularis in AH: dico <lb></lb>punctum M eſſe centrum percuſſionis, quod demonſtratur per Theo­<lb></lb>rema 17. </s>
				</p>
				<p id="N29D2A" type="main">
					<s id="N29D2C"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 19.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29D38" type="main">
					<s id="N29D3A"><emph type="italics"></emph>Si voluatur triangulum prædictum, circa angulum rectum, determinari <lb></lb>poteſt<emph.end type="italics"></emph.end> <emph type="italics"></emph>centrum percuſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N29D4B">ſit enim triangulum ABH, quod voluatur <lb></lb>circa centrum B; </s>
					<s id="N29D51">motus puncti A eſt ad motum H, vt BA, ad BH; </s>
					<s id="N29D55">ſit ergo <lb></lb>Trapezus MG, cuius latus ML ſit æquale AB, &amp; GI æquale BH; </s>
					<s id="N29D5B">erit <lb></lb>pyramis, eo modo, quo diximus ſuprà; </s>
					<s id="N29D61">ſit autem D centrum grauitatis <lb></lb>baſis, ſeu Trapezij, &amp; AD axis; </s>
					<s id="N29D67">ſit KD 1/4 BD; </s>
					<s id="N29D6B">ſit denique KE perpen­<lb></lb>dicularis in DB: dico punctum E eſſe centrum percuſſionis, quod co­<lb></lb>dem modo demonſtratur, quo ſuprà. </s>
				</p>
				<p id="N29D73" type="main">
					<s id="N29D75"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N29D81" type="main">
					<s id="N29D83">Hinc colligo primò, de omni triangulo idem prorſus dicendum eſſe, <lb></lb>eſt enim eadem ratio, vt conſideranti patebit. </s>
				</p>
				<p id="N29D88" type="main">
					<s id="N29D8A">Secundò, ſi voluatur circa punctum aliquod lateris, poſſe determinari <lb></lb>centrum percuſſionis; </s>
					<s id="N29D90">ſit enim triangulum ABC; </s>
					<s id="N29D94">aſſumatur punctum <lb></lb>M, circa quod voluatur mode prædicto, motus puncti C, eſt ad motum <lb></lb>puncti A, vt MC, vel DX, ad MA, vel PO; </s>
					<s id="N29D9C">hinc Trapezus DPOX, id eſt <lb></lb>baſis pyramidis, cuius axis eſt MG, &amp; centrum grauitatis K: </s>
					<s id="N29DA4">ſimiliter <lb></lb>habetur Trapezus DRNX; </s>
					<s id="N29DAA">id eſt baſis alterius pyramidis, cuius axis eſt <lb></lb>MV, &amp; centrum grauitatis H; </s>
					<s id="N29DB0">fiat autem vt vtraque pyramis ad eam, cuius <lb></lb>axis eſt MG, ita tota HK, ad HI; </s>
					<s id="N29DB6">dico I eſſe centrum commune graui­<lb></lb>tatis; </s>
					<s id="N29DBC">ducatur IL perpendicularis in IM; dico L eſſe centrum percuſ­<lb></lb>ſionis quæſitum. </s>
				</p>
				<p id="N29DC2" type="main">
					<s id="N29DC4">Tertiò, ſi voluatur circa aliud punctum, res eodem modo ſuc­<lb></lb>cedet. </s>
				</p>
				<p id="N29DC9" type="main">
					<s id="N29DCB">Quartò, ſi ſit ſolidum ad inſtar cunei, conſtans ſcilicet ex multis pla­<lb></lb>nis triangularibus, quæ probè inter ſe conueniant; idem etiam accidet, <lb></lb>quæ omnia ex ſuprà dictis clariſſima efficiuntur. </s>
				</p>
				<p id="N29DD3" type="main">
					<s id="N29DD5">Quintò, ſi ſit triangulum EAD, fig. </s>
					<s id="N29DD8">quod ita voluatur circa centrum <lb></lb>A, vt latus AE, modò accedat ad CB, modò recedat; </s>
					<s id="N29DDE">ſitque ita diuiſa AS <lb></lb>in R, vt RS ſit 1/4 AS, ſi ducatur RN, centrum percuſſionis erit in N, <lb></lb>quia R eſt centrum grauitatis geminæ pyramidis; </s>
					<s id="N29DE6">igitur RN linea di­<lb></lb>rectionis inſtanti percuſſionis; ſi verò producatur AS in G, ſintque I &amp; <lb></lb>M centra grauitatis pyramidum ducanturque IF, MF perpendiculares <lb></lb>in AI. AM, centrum percuſſionis erit F, vt conſtat ex dictis. </s>
				</p>
				<pb pagenum="429" xlink:href="026/01/463.jpg"></pb>
				<p id="N29DF4" type="main">
					<s id="N29DF6"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 20.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29E02" type="main">
					<s id="N29E04"><emph type="italics"></emph>Sectoris minoris quadrante determinari poteſt centrum percuſſionis, cum <lb></lb>ſcilicet voluitur in plano, cui eiuſdem planum eſt parallelum<emph.end type="italics"></emph.end>; </s>
					<s id="N29E0F">ſit enim <lb></lb>quadrans BAI; </s>
					<s id="N29E15">ducatur BI, ſit pyramis cuius baſis ſit ſectio cylindri, <lb></lb>erectis, ſcilicet perpendicularibus tranſuerſis ſupra arcum BTI, eo <lb></lb>modo, quo ſuprà iam ſæpè diximus; </s>
					<s id="N29E1D">v.g. ducta ſit Tangens ZT, diuiſa bi­<lb></lb>fariam in C, puncto ſcilicet contactus, quæ tandiu voluatur circa CA, <lb></lb>dum ſecet arcum ad angulos rectos: </s>
					<s id="N29E27">idem fiat in alijs punctis arcus; </s>
					<s id="N29E2B">de­<lb></lb>nique ad extremitates Tangentium ducantur vtrimque à centro A rectæ, <lb></lb>&amp; habebitur prædicta pyramis mixta, cuius centrum grauitatis inuen­<lb></lb>tum dabit centrum percuſſionis; </s>
					<s id="N29E35">quod vt meliùs oculo ſubijciatur, ſit <lb></lb>triangulum ZTA, voluatur circa CA, donec eius planum ſecet ad an­<lb></lb>gulos iectos planum quadrantis BAI; </s>
					<s id="N29E3D">tùm in eo ſitu voluatur axis AC <lb></lb>per totum arcum BI, &amp; habebitur ſolidum quæſitum, cuius centrum gra­<lb></lb>uitatis ita poteſt inueniri; </s>
					<s id="N29E45">ducatur BI, tùm AC diuidens BI bifariam <lb></lb>in E, centrum grauitatis eſt in AC; </s>
					<s id="N29E4D">aſſumatur GE 1/4 totius AE; </s>
					<s id="N29E51">certè G <lb></lb>eſt centrum grauitatis pyramidis ABEI; </s>
					<s id="N29E57">ſit autem D centrum grauitatis <lb></lb>reliqui ſolidi BEIC, ſitque vt hoc ſolidum ad pyramidem ABEI, ita <lb></lb>GF ad FD: dico F eſſe centrum grauitatis per p. </s>
					<s id="N29E5F">7. ducatur FK perpen­<lb></lb>dicularis in AC, K eſt centrum percuſſionis per Th.17. </s>
				</p>
				<p id="N29E65" type="main">
					<s id="N29E67"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N29E73" type="main">
					<s id="N29E75">Colligo primò; </s>
					<s id="N29E78">prædictam pyramidem mixtam eſſ 2/3 ſectoris cylindrj; </s>
					<s id="N29E7C"><lb></lb>ſit enim triangulum ACZ erectum, atque îta voluatur per totam pe­<lb></lb>ripheram IBPVI. fiet ſolidum cauum, cuius cauitas erit conus, cuius <lb></lb>altitudo erit CZ, &amp; baſis orbis BPVI; </s>
					<s id="N29E85">ſed hic conus eſt 1/3 cylindri, ſub <lb></lb>eadem baſi, &amp; altitudine; </s>
					<s id="N29E8B">igitur ſolidum, quod ſupereſt, continet 2/3 cy­<lb></lb>lindri ſub altitudine CZ, &amp; baſi BPVI; </s>
					<s id="N29E91">ſed cauum BAI de quo ſuprà <lb></lb>eſt 1/3 totius; igitur reliquum continet 2/3 ſectoris cylindri BA, ſub alti­<lb></lb>tudine CT. </s>
				</p>
				<p id="N29E99" type="main">
					<s id="N29E9B">Secundò colligo, ſi aſſumatur ſemicirculus PBI momentum quadran­<lb></lb>tis PBA, æquale eſſe momento quadrantis IA <foreign lang="grc">β</foreign>, vt conſtat; nam I, per <lb></lb>IM, idem præſtat quod P, per PQ, &amp; S per SR, idem quod L, <lb></lb>per LV, &amp;c. </s>
				</p>
				<p id="N29EA9" type="main">
					<s id="N29EAB">Tertiò, ſi voluatur tantùm triangulum ABI, ducaturque GX per­<lb></lb>pendicularis in AC punctum X erit centrum percuſſionis; quid mirum <lb></lb>igitur, ſi addito ſegmento BCIE, ſit in K? </s>
				</p>
				<p id="N29EB3" type="main">
					<s id="N29EB5">Quartò, ſi quadrans AI <foreign lang="grc">β</foreign> trahat deorſum adducto filo ex K, certè in <lb></lb>K erit centrum percuſſionis, vt conſtat. </s>
				</p>
				<p id="N29EBE" type="main">
					<s id="N29EC0">Quintò, ſi vterque quadrans BI <foreign lang="grc">β</foreign> A ſimul cadat, centrum percuſſio­<lb></lb>nis erit in K, ſed duplò maior ictus. </s>
				</p>
				<p id="N29EC9" type="main">
					<s id="N29ECB">Sexto, ſi ſemicirculus APBI cadar, centrum etiam percuſſionis erit <lb></lb>in K, quia quadrans PBA æquiualet quadranti A <foreign lang="grc">β</foreign> I. </s>
				</p>
				<p id="N29ED5" type="main">
					<s id="N29ED7">Septimò, ſi aſſumatur ſector maior quadrante, ſed minor ſemicirculo, <lb></lb>v.g. ASBI, ſit BAC æqualis BAS; </s>
					<s id="N29EDF">inueniatur centrum grauitatis BA <pb pagenum="430" xlink:href="026/01/464.jpg"></pb>C eodem modo, quo inuentum eſt centrum F quadrantís rotati: </s>
					<s id="N29EEC">ſimili­<lb></lb>ter inueniatur centrum grauitatis TAI rotati; </s>
					<s id="N29EF2">connectantur rectâ hæc <lb></lb>duo centra inuenta, ſitque vt duplum BAC ad CAI, ita ſegmentum <lb></lb>connectentïs centra, quod terminatur in centro CAI ad aliud ſegmen­<lb></lb>tum; punctum diuidens ſegmenta erit centrum grauitatis quæſitum, à <lb></lb>quo ſi ducatur perpendicularis, eo modo, quo diximus, hæc dabit cen­<lb></lb>trum percuſſionis. </s>
				</p>
				<p id="N29F00" type="main">
					<s id="N29F02">Octauò, ſi aſſumatur ſector maior ſemicirculo, v.g. AVBL, eodem <lb></lb>modo procedendum eſt; quippe PAV æquiualet CAB, &amp; IAL æquiua­<lb></lb>let CAI, &amp; BAP æquiualet BAI, nec eſt noua difficultas. </s>
				</p>
				<p id="N29F0C" type="main">
					<s id="N29F0E">Nonò, hinc ſi circulus integer circa centrum voluatur, centrum per­<lb></lb>cuſſionis erit in K, ſed ictu quadruplo ictus inflicti à quadrante. </s>
				</p>
				<p id="N29F13" type="main">
					<s id="N29F15"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 21.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29F21" type="main">
					<s id="N29F23"><emph type="italics"></emph>Si rotetur circulus circa punctum circumferentia vel circa Tangentem, <lb></lb>determinari poteſt centrum percuſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N29F2E">ſit enim centro B, ANCP, rota­<lb></lb>tus circa TA, in quam diameter AC cadit perpendiculariter; </s>
					<s id="N29F34">aſſumatur <lb></lb>RC 1/3 AC: </s>
					<s id="N29F3A">dico R eſſe centrum percuſſionis; quia motus C eſt ad mo­<lb></lb>tum R, vt CF ad RH, &amp; ad motum B, vt CF ad BL, &amp;c. </s>
					<s id="N29F40">igitur perinde <lb></lb>ſe habet planum ANCP, atque ſi ſemicylindrus ACF ipſi incubaret, <lb></lb>vt patet, ſed centrum grauitatis huius ſolidi eſt X in quo CL &amp; FB de­<lb></lb>cuſſantur; </s>
					<s id="N29F4A">ſed vt demonſtratum eſt ſuprà, ſi ducatur HXR, RC eſt 2/3 <lb></lb>totius AC; igitur R eſt centrum percuſſionis. </s>
				</p>
				<p id="N29F50" type="main">
					<s id="N29F52"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N29F5E" type="main">
					<s id="N29F60">Primò colligo, ſi ſegmentum circuli voluatur: </s>
					<s id="N29F64">ſimiliter haberi poteſt <lb></lb>centrum percuſſionis, inuento ſcilicet centro grauitatis baſis vtriuſque <lb></lb>v.g. ſi ſegmentum OAQ voluatur circa TA, inueniri debet centrum <lb></lb>grauitatis eiuſdem &amp; ad illud à puncto H recta ducenda; </s>
					<s id="N29F70">itemque in­<lb></lb>ueniendum eſt centrum grauitatis ſegmenti Ellipſeos HAI, &amp; ad illud <lb></lb>à puncto R ducenda recta; nam vtriuſque decuſſationis punctum dabit <lb></lb>centrum grauitatis huius ſolidi, ex qua ſi ducatur perpendicularis in AR, <lb></lb>extremitas dabit centrum percuſſionis. </s>
				</p>
				<p id="N29F7D" type="main">
					<s id="N29F7F">Secundò, ſi voluatur circulus CNAH circa PN, habebitur centrum <lb></lb>percuſſionis eodem modo, inuentis ſcilicet centris grauitatis ſemicir­<lb></lb>culi PNC, &amp; ſemiellipſeos, cuius altera ſemidiameter ſit BF, altera BP, <lb></lb>vt conſtat ex dictis, </s>
				</p>
				<p id="N29F88" type="main">
					<s id="N29F8A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 22.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N29F96" type="main">
					<s id="N29F98"><emph type="italics"></emph>Si voluatur circulus circa punctum circumferentia in circulo parallelo ſuo <lb></lb>plano, determinari poteſt centrum percuſſionis, quod diſtat <emph.end type="italics"></emph.end>2/3 <emph type="italics"></emph>diametri à cen­<lb></lb>tro motus<emph.end type="italics"></emph.end>; </s>
					<s id="N29FB1">ſit enim circulus ACFG, centro B, qui voluatur circa cen­<lb></lb>trum A; </s>
					<s id="N29FB7">motus puncti F eſt ad motum puncti B, vt recta AF ad rectam <lb></lb>AD, &amp; ad motum puncti C, vt AF ad AC; </s>
					<s id="N29FBD">idem dico de alis punctis; </s>
					<s id="N29FC1"><lb></lb>ſit EH æqualis AF, diuiſa bifariam in F, quæ tandiu voluatur, donec <pb pagenum="431" xlink:href="026/01/465.jpg"></pb>ſecet arcum CFG ad angulos rectos; idem prorſus fiat in aliis punctis <lb></lb>peripheriæ, aſſumptis ſcilicet lineis æqualibus ſubtenſis arcuum, v.g. in <lb></lb>puncto D, aſſumpta linea æquali AD, in puncto C, aſſumpta æquali AC, <lb></lb>&amp;c. </s>
					<s id="N29FD3">hoc poſito habetur ſolidum, quod facilè vocauerim Elliptico cylin­<lb></lb>dricum, cuius conſtructio talis eſt, ſit cylindrus RI, cuius diameter <lb></lb>baſis ſit KI, æqualis diametro AF circuli prioris; </s>
					<s id="N29FDB">ſit etiam altitudo KR, <lb></lb>æqualis prædictæ diametro KI, ſit KR diuiſa bifariam in L, ſitque pla­<lb></lb>num IL ſecans cylindrum, itemque alterum LP, vtraque ſectio Ellipſis <lb></lb>eſt, vt patet; </s>
					<s id="N29FE5">ac proinde habetur ſolidum quæſitum LIP conſtans gemi­<lb></lb>na baſi LI. &amp; LP Elliptica, &amp; reliqua circumferentià cylindricâ, cuius <lb></lb>centrum grauitatis eſt in N, id eſt in puncto decuſſationis rectarum PM, <lb></lb>IS, quæ diuidunt ILPL bifariam æqualiter, eſt autem NO 1/3 totius <lb></lb>LO, per Sch. Th.2. hoc poſito ſit XF 1/3 totius AF: dico eſſe centrum <lb></lb>percuſſionis quæſitum circuli ACFG rotati circa A, quia perinde ſe <lb></lb>habet, atque ſi puncto X incubaret prædictum ſolidum ellipticocylindri­<lb></lb>cum, cuius X eſſet centrum grauitatis. </s>
				</p>
				<p id="N29FF9" type="main">
					<s id="N29FFB"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A007" type="main">
					<s id="N2A009">Obſeruabis primò, in plano ACFG, vt punctum X ſit centrum per­<lb></lb>cuſſionis, incidendam eſſe ſtriam quamdam, ſeu rimam, quæ termi­<lb></lb>netur in X. </s>
				</p>
				<p id="N2A011" type="main">
					<s id="N2A013">Secundò, idem eſſe centrum percuſſionis rectæ AF, quæ voluitur <lb></lb>circa A, ſiue ſit ſimplex linea, ſiue diameter circuli. </s>
				</p>
				<p id="N2A018" type="main">
					<s id="N2A01A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 23.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A026" type="main">
					<s id="N2A028"><emph type="italics"></emph>Si voluatur rectangulum parallelum orbi in quo voluitur determinari<emph.end type="italics"></emph.end> <emph type="italics"></emph>po­<lb></lb>test centrum percuſſionis<emph.end type="italics"></emph.end>; </s>
					<s id="N2A039">ſit enim rectangulum AD, quod voluatur circa <lb></lb>centrum A, eo modo, quo dictum eſt ſit ducta AD, inueniatur centrum <lb></lb>I, trianguli ABD; </s>
					<s id="N2A041">itemque centrum H, trianguli ADF, per Th. 17. <lb></lb>tùm ducta IH, diuidatur bifariam in K; </s>
					<s id="N2A047">ducatur AK, tùm GK perpen­<lb></lb>dicularis in AK: dico G eſſe centrum percuſſionis, per poſ.7.&amp; Theo­<lb></lb>rema 17. </s>
				</p>
				<p id="N2A04F" type="main">
					<s id="N2A051"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A05D" type="main">
					<s id="N2A05F">Colligo ex his facilè poſſe determinari centrum percuſſionis in alijs <lb></lb>figuris planis; quia diuidi poſſunt in plura triangula. </s>
				</p>
				<p id="N2A065" type="main">
					<s id="N2A067"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 24.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A073" type="main">
					<s id="N2A075"><emph type="italics"></emph>Poteſt determinari centrum percuſſionis ſolidi<emph.end type="italics"></emph.end> <emph type="italics"></emph>trium facierum ABDE<emph.end type="italics"></emph.end>; </s>
					<s id="N2A084"><lb></lb>vt demonſtretur centrum percuſſionis pyramidis, &amp; priſmatis, præmitti <lb></lb>debuit hoc ſolidum; </s>
					<s id="N2A08B">ſit enim ſolidum priori ſimile, A.M. G.C. motus <lb></lb>puncti M, eſt ad motum puncti G, vt recta BM ad rectam BG; </s>
					<s id="N2A091">igitur ſit <lb></lb>NK ad OH, vt BM ad BG; </s>
					<s id="N2A097">certè perinde ſe habet punctum M, atque <lb></lb>ſi NMK incubaret, non quidem per MG, ſed per lineam perpendicu­<lb></lb>larem ductam in BM, vt patet ex dictis: </s>
					<s id="N2A09F">idem dico de puncto G, quod <lb></lb>perinde ſe habet, atque ſi incubaret OGH; </s>
					<s id="N2A0A5">itaque inuenire oportet <lb></lb>centrum grauitatis ſolidi ACHKNOA, quod vt fiat, aſſumatur IP <pb pagenum="432" xlink:href="026/01/466.jpg"></pb>æqualis AC; </s>
					<s id="N2A0B0">ducantur AP, CI centrum grauitatis ſolidi ACIKNP <lb></lb>reſpondet per lineam directionis puncto E, ita vt EG ſit 1/3 GB per Co­<lb></lb>roll.1. Th.3.ſi autem aſſumatur FG 1/4 totius BG, ſitque linea QFX, <lb></lb>&amp; ex puncto F ſuſtineatur vtraque pyramis AOPN, &amp; CIHK, erit <lb></lb>perfectum æquilibrium per Th. 4. igitur ſit FE ad ED, vt ſolidum <lb></lb>ACHKNO ad vtramque pyramidem AOPN, CIHK, certè pun­<lb></lb>ctum D erit centrum grauitatis ſolidi ACHKNO, per p.7. aſſumatur <lb></lb>GL æqualis GD; </s>
					<s id="N2A0C2">ducatur BL, hæc eſt axis vt patet, modò GM ſit æqua­<lb></lb>lis GB; </s>
					<s id="N2A0C8">ſi enim inæqualis eſt, ſit GL ad GM, vt GD ad GB: </s>
					<s id="N2A0CC">præterea <lb></lb>ducatur DR parallela GM; </s>
					<s id="N2A0D2">denique ducatur perpendicularis FR in B <lb></lb>L; </s>
					<s id="N2A0D8">dico F eſſe centrum percuſſionis, vt patet ex dictis ſuprà, præſertim in <lb></lb>Th. 17. &amp; alibi paſſim, ne toties eadem repetere cogar ad nauſeam; <lb></lb>quamquam enim hæc ſatis noua ſunt, illa tamen indicanda potiùs, quàm <lb></lb>fusè tractanda eſſe putaui. </s>
				</p>
				<p id="N2A0E2" type="main">
					<s id="N2A0E4"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 25.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A0F0" type="main">
					<s id="N2A0F2"><emph type="italics"></emph>Poteſt determinari centrum percuſſionis pyramidis, cum voluitur circa <lb></lb>verticem<emph.end type="italics"></emph.end>; </s>
					<s id="N2A0FD">ſit enim ſolidum, de quo ſuprà ABCGM, fitque aliud ſoli­<lb></lb>dum ABCHKMNOG, cuius axis ſit BL &amp; centrum grauitatis R, <lb></lb>hoc ipſum eſt centrum percuſſionis ſolidi ABCGM, ducta ſcilicet RF, <lb></lb>per Th.24. iam verò ſi ex ſolido ACIKNP, detrahatur prædictum <lb></lb>ſolidum ABCGM, ſupereſt vtrimque integra pyramis, ſcilicet CMK <lb></lb>IG, &amp; AMNPG, cuius axis communis erit eadem BL, vt patet; </s>
					<s id="N2A10B">itaque <lb></lb>aſſumatur LY 1/4 LB, Y reſpondebit centrum percuſſionis ſolidi ACIK <lb></lb>NP per Corol.4. Th.19. igitur ſit vt vtraque pyramis ANPG, &amp; AK <lb></lb>IG, ad reliquum ſolidum ABCGM, ita RY, ad YZ; </s>
					<s id="N2A115">dico Z eſſe cen­<lb></lb>trum percuſſionis vtriuſque pyramidis, ductâ ſcilicet perpendiculari <lb></lb>Z <foreign lang="grc">δ</foreign>, vt conſtat ex dictis; quare in axe pyramidis aſſumatur æqualis BZ, <lb></lb>&amp; habebitur intentum. </s>
				</p>
				<p id="N2A123" type="main">
					<s id="N2A125"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A131" type="main">
					<s id="N2A133">Obſeruabis primò, ſolidum integrum AKNPI eſſe ſubduplum priſ­<lb></lb>matis eiuſdem altitudinis &amp; baſis NI; pyramidem verò CMI eſſe 1/6 <lb></lb>eiuſdem priſmatis, ergo vtramque æqualem 1/3 igitur ſolidum ABCGM <lb></lb>1/6. igitur æquale alteri pyramidum, igitur RY duplam eſſe YZ. </s>
				</p>
				<p id="N2A13E" type="main">
					<s id="N2A140">Secundò, obſeruabis punctum Z dici poſſe centrum percuſſionis in­<lb></lb>terius, à quo deinde ſi ducatur recta Z <foreign lang="grc">δ</foreign> perpendicularis in BL, termi­<lb></lb>nabitur in <foreign lang="grc">δ</foreign>, quod dici poteſt centrum percuſſionis exterius. </s>
				</p>
				<p id="N2A14F" type="main">
					<s id="N2A151">Tertiò, obſeruabis, centrum percuſſionis exterius aliquando eſſe in <lb></lb>ipſa facie, ſeu linea BG, cum ſcilicet angulus MPG eſt valdè acutus, <lb></lb>aliquando eſſe extra ſuperficiem corporis, v. g. in <foreign lang="grc">δ</foreign>, cum ſcilicet an­<lb></lb>gulus MBG eſt obtuſior, quod iam ſuprà obſeruatum eſt, cum de trian­<lb></lb>gulo Cor.2. Th.17. </s>
				</p>
				<pb pagenum="433" xlink:href="026/01/467.jpg"></pb>
				<p id="N2A169" type="main">
					<s id="N2A16B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 26.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A177" type="main">
					<s id="N2A179"><emph type="italics"></emph>Poteſt determinari centrum percuſſionis parallelipedi<emph.end type="italics"></emph.end>; </s>
					<s id="N2A182">ſit enim paralle­<lb></lb>lipedum MF quod voluatur circa MK; </s>
					<s id="N2A188">ſit rectangulum LE ſecans bifa­<lb></lb>riam æqualiter parallelipedum; </s>
					<s id="N2A18E">centrum percuſſionis erit in plano re­<lb></lb>ctanguli LE; </s>
					<s id="N2A194">ducatur LE, diagonalis; </s>
					<s id="N2A198">inueniatur centrum percuſſionis <lb></lb>rectanguli LE, per Th.23. ſitque N, v.g. ducatur NO, dico O eſſe cen­<lb></lb>trum percuſſionis quæſitum, ſcilicet exterius, vt patet ex dictis; </s>
					<s id="N2A1A2">poteſt <lb></lb>etiam determinari, ſi voluatur circa AC, vel circa PR, nam perinde <lb></lb>ſe habet prædictum parallelipedum, atque ipſum rectangulum; hoc verò <lb></lb>atque ipſum triangulum, in quo nulla prorſus eſt difficultas. </s>
				</p>
				<p id="N2A1AC" type="main">
					<s id="N2A1AE">Poteſt etiam determinari centrum percuſſionis cunei, id eſt ſemipa­<lb></lb>rallelipedi, ſiue circa MK, ſine circa IG voluatur; quæ omnia pa­<lb></lb>tent ex dictis. </s>
				</p>
				<p id="N2A1B6" type="main">
					<s id="N2A1B8"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 27.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A1C4" type="main">
					<s id="N2A1C6"><emph type="italics"></emph>Determinari<emph.end type="italics"></emph.end> <emph type="italics"></emph>poteſt centrum percuſſionis ſolidi ABDE, ſi voluatur circa <lb></lb>axem IDH<emph.end type="italics"></emph.end>; </s>
					<s id="N2A1D7">nam motus puncti C eſt ad motum puncti E, vt DC ad <lb></lb>DE, vel vt BN æqualis DC ad LK æqualem ED; </s>
					<s id="N2A1DD">mouentur enim AC <lb></lb>B æquali motu; </s>
					<s id="N2A1E3">itaque perinde ſe habet prædictum ſolidum in ordine <lb></lb>ad percuſſionem, atque ſi eſſet ſolidum BMKLD; </s>
					<s id="N2A1E9">id eſt duplex pyra­<lb></lb>mis, ſcilicet DNMKL, &amp; DMNBA, quarum centra grauitatis ſint <lb></lb>PQ, &amp; commune vtriuſque ſit R iuxtam modum ſuprà poſitum; </s>
					<s id="N2A1F1">duca­<lb></lb>tur SR perpendicularis in RD: dico S eſſe centrum percuſſionis exte­<lb></lb>rius quæſitum, quod eodem modo probatur, quo ſuprà. </s>
				</p>
				<p id="N2A1F9" type="main">
					<s id="N2A1FB"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A207" type="main">
					<s id="N2A209">Primò colligo inde, vbi ſit centrum percuſſionis cylindri, ſiue volua­<lb></lb>tur circa Tangentem baſis, ſiue circa diametrum eiuſdem; nam idem de <lb></lb>cylindro dicendum eſt, quod de parallelipedo dictum eſt Th.26. </s>
				</p>
				<p id="N2A211" type="main">
					<s id="N2A213">Secundò colligo, centrum percuſſionis coni; quippe vt ſe habet pyra­<lb></lb>mis ad priſma, ita ſe habet conus ad cylindrum. </s>
				</p>
				<p id="N2A219" type="main">
					<s id="N2A21B">Tertiò, colligo centrum percuſſionis Pyramidis quando voluitur cir­<lb></lb>ca latus baſis per Th.27. </s>
				</p>
				<p id="N2A220" type="main">
					<s id="N2A222">Quartò, colligo centrum percuſſionis cylindri; cum voluitur circa <lb></lb>Tangentem parallelum axi per Th.22. </s>
				</p>
				<p id="N2A229" type="main">
					<s id="N2A22B">Quintò, colligo centrum grauitatis priſmatis, ſiue voluatur circa la­<lb></lb>tus baſis; </s>
					<s id="N2A231">tunc enim idem prorſus dicendum eſt, quod de parallelipedo; </s>
					<s id="N2A235"><lb></lb>ſiue circa lineam parallelam axi; tunc enim centrum percuſſionis co­<lb></lb>gnoſcitur ex centro percuſſionis baſis cognito, ſi voluatur in circulo ſuo <lb></lb>plano parallelo per Cor. Th.22. </s>
				</p>
				<p id="N2A241" type="main">
					<s id="N2A243">Sextò denique, colligo centrum percuſſionis cuiuſlibet alterius <lb></lb>ſolidi, planis rectilineis contenti, quod ſcilicet in pyramides diui­<lb></lb>di poteſt. </s>
				</p>
				<pb pagenum="434" xlink:href="026/01/468.jpg"></pb>
				<p id="N2A24E" type="main">
					<s id="N2A250"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A25C" type="main">
					<s id="N2A25E">Obſeruabis non deeſſe fortè aliquos, quibus centrum grauitatis Py­<lb></lb>ramidos difficile inuentu videatur; </s>
					<s id="N2A264">quare in eorum gratiam facilem de­<lb></lb>monſtrationem ſubijcio; </s>
					<s id="N2A26A">ſit enim pyramis EFBA, cuius baſis ſit trian­<lb></lb>gularis EFB; </s>
					<s id="N2A270">ducatur EC diuidens bifariam FB, ſitque DC 1/3 totius <lb></lb>EC, centrum grauitatis baſis EFB eſt D, per Sch.Th.2. ducatur AD, id <lb></lb>eſt axis pyramidos, per communem definitionem; </s>
					<s id="N2A278">quippe axis eſt recta <lb></lb>ducta à vertice ad centrum grauitatis baſis oppoſitæ; </s>
					<s id="N2A27E">ducatur AC, diui­<lb></lb>dens BF bifariam æqualiter; </s>
					<s id="N2A284">aſſumatur GC, 1/3 AC, ducatur EG, hæc <lb></lb>eſt axis, vt patet ex dictis; </s>
					<s id="N2A28A">aſſumatur autem triangulum AEC, ſitque HO <lb></lb>K maioris claritatis gratia, ſintque gemini axes HL, OI, centrum py­<lb></lb>ramis eſt in OI &amp; in HL; igitur in M; </s>
					<s id="N2A292">ſed ML eſt 1/4 totius LH, quod <lb></lb>ſic demonſtro; </s>
					<s id="N2A298">triangula PIM, OLM ſunt æquiangula; </s>
					<s id="N2A29C">igitur propor­<lb></lb>tionalia; </s>
					<s id="N2A2A2">itemque duo HIN, &amp; HKO; </s>
					<s id="N2A2A6">igitur vt HK ad KO, ita HI ad <lb></lb>IN; </s>
					<s id="N2A2AC">ſed HI continet 2/4 HK, per hypotheſim; </s>
					<s id="N2A2B0">igitur IN continet 2/3 KO; </s>
					<s id="N2A2B4"><lb></lb>igitur IN eſt æqualis LO; </s>
					<s id="N2A2B9">igitur vt IP eſt ad LO, ita PM ad ML; ſed <lb></lb>PI eſt ad LO vt 2. 2/3 ad 8. id eſt vt 3. ad 9. nam ſit OK 12. IN æqualis <lb></lb>LO eſt 8.igitur PM eſt ad ML, vt 3. ad 9. vel vt 1. ad 3. igitur ſit HL <lb></lb>12. PL erit 4. igitur PM 1. ML 3. igitur ML eſt 1/4 LH, quod erat <lb></lb>demonſtrandum. </s>
				</p>
				<p id="N2A2C5" type="main">
					<s id="N2A2C7">Si verò pyramidos baſis ſit quadrilatera, vel polygona, diuidi poteſt in <lb></lb>plures, quarum baſis ſit trilatera; quare in omni pyramide facilè de­<lb></lb>monſtratur centrum grauitatis ita dirimere axem, vt ſegmentum verſus <lb></lb>baſim ſit 1/4 totius. </s>
				</p>
				<p id="N2A2D1" type="main">
					<s id="N2A2D3"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 28.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A2DF" type="main">
					<s id="N2A2E1"><emph type="italics"></emph>Determinari poteſt centrum percuſſionis coni mixti, cuius baſis ſit portio <lb></lb>ſuperficiei ſphæræ, cuius centrum ſit in apice coni<emph.end type="italics"></emph.end>; </s>
					<s id="N2A2EC">quia vt ſe habet triangu­<lb></lb>lum Iſoſceles ad conum, ita ſe habet ſector ſub eodem angulo ad prædi­<lb></lb>ctum conum mixtum, vt patet; </s>
					<s id="N2A2F4">quia vt conus ille rectus formatur a trian­<lb></lb>gulo circa ſuum axem circumacto, ita &amp; mixtus formatur à ſectore circa <lb></lb>ſuum axem circumuoluto; </s>
					<s id="N2A2FC">igitur vt ſe habet diſtantia inter centrum vel <lb></lb>apicem trianguli, circa quem voluitur, &amp; centrum percuſſionis eiuſdem <lb></lb>ad diſtantiam inter eoſdem terminos in cono recto, ita ſe habet diſtan­<lb></lb>tia inter eoſdem terminos in ſectore, ad diſtantiam inter eoſdem termi­<lb></lb>nos in prædicto cono mixto; </s>
					<s id="N2A308">ſed cognoſcuntur ex dictis ſuprà tres pri­<lb></lb>mi termini huius proportionis; igitur cognoſci poteſt quartus, igitur <lb></lb>determinari centrum percuſſionis, quod erat demonſtrandum. </s>
				</p>
				<p id="N2A310" type="main">
					<s id="N2A312"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A31E" type="main">
					<s id="N2A320">Colligo primò, ex his facilè cognoſci poſſe centrum percuſſionis ſe­<lb></lb>ctoris ſphæræ, nam vt ſe habet conus rectus ad pyramidem, ita ſe habes <lb></lb>prædictus conus mixtus ad ſectorem, ſub eodem ſcilicet angulo. </s>
				</p>
				<p id="N2A327" type="main">
					<s id="N2A329">Colligo ſecundò, etiam poſſe cognoſci centrum percuſſionis eiuſdem <lb></lb>ſectoris circumacti, non tantùm circa centrum ſphæræ, ſed circa radium; </s>
					<s id="N2A32F"><pb pagenum="435" xlink:href="026/01/469.jpg"></pb>immò gemini ſectoris coniuncti, ſeu quartæ partis ſphæræ, ex quo etiam <lb></lb>ſequitur determinatio centri grauitatis Hemiſphærij, atque adeo totius <lb></lb>ſphæræ; quæ omnia pendent ex dictis ſuprà. </s>
				</p>
				<p id="N2A33B" type="main">
					<s id="N2A33D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A349" type="main">
					<s id="N2A34B">Obſeruabis ſupereſſe innumeras ferè corporum rationes, v.g.ſphæram <lb></lb>ex dato puncto ſuperficiei libratam, tùm elliptica ſolida, parabolica, hy­<lb></lb>perbolica, &amp;c. </s>
					<s id="N2A352">quorum centra percuſſionis determinari poſſunt; ſed ab­<lb></lb>ſtineo, tùm quia cum multam matheſim deſiderent, vix habent aliquem <lb></lb>in phyſica locum, tùm quia plura excerpere non potui, ex innumeris pe­<lb></lb>nè, quæ apud ſe noſter Philoſophus habet. </s>
				</p>
				<p id="N2A35C" type="main">
					<s id="N2A35E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 29.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A36A" type="main">
					<s id="N2A36C"><emph type="italics"></emph>Determinari poteſt centrum impreſſionis, tùm in linea, tùm in plano, tùm̨ <lb></lb>in ſolido quæ circumaguntur<emph.end type="italics"></emph.end>; quia poteſt diuidi bifariam, tùm planum illud <lb></lb>ſi ſit linea, tùm ſolidum, ſi planum vel ſolidum, vt patet per def.2. </s>
				</p>
				<p id="N2A379" type="main">
					<s id="N2A37B"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 30.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A387" type="main">
					<s id="N2A389"><emph type="italics"></emph>Si linea rigida libretur circa alteram extremitatem immobilem aſſuma­<lb></lb>turque funependulum, cuius longitudo contineat<emph.end type="italics"></emph.end> 2/3 <emph type="italics"></emph>prædictæ lineæ, vibrationes <lb></lb>vtriuſque erunt æquediuturnæ<emph.end type="italics"></emph.end>; quod demonſtratur; </s>
					<s id="N2A39C">quia centrum percuſ­<lb></lb>ſionis prædictæ lineæ diſtat 2/3 ab altera extremitate immobili per Th.8. <lb></lb>atqui centrum percuſſionis in hoc motu circulari dirigit motum aliorum <lb></lb>punctorum; </s>
					<s id="N2A3A6">quia defungitur munere centri grauitatis, vt patet ex dictis; </s>
					<s id="N2A3AA"><lb></lb>nec enim alterum ſegmentorum præualet; </s>
					<s id="N2A3AF">ſed totus motus impeditur, <lb></lb>per poſ.2. igitur perinde ſe habet atque ſi totum pondus, vel totam vim <lb></lb>collectam haberet; </s>
					<s id="N2A3B7">ſed in hoc caſu eſſet ad inſtar funependuli, in quo <lb></lb>non habetur vlla ratio fili, ſed ponderis appenſi; igitur eius vibratio eſt <lb></lb>æquediuturna cum vibratione prædicti funependuli quod erat demon­<lb></lb>ſtrandum. </s>
				</p>
				<p id="N2A3C1" type="main">
					<s id="N2A3C3"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A3CF" type="main">
					<s id="N2A3D1">Obſeruabis, ex hoc vno certiſſimo principio egregium experimentum <lb></lb>mirificè comprobari; nempè ſæpiùs compertum eſt innumeris ferè expe­<lb></lb>rimentis, tùm ab erudito Merſenno, tùm à noſtro Philoſopho longitu­<lb></lb>dinem funependuli iſochroni cum cylindro continere 2/3 cylindri. </s>
				</p>
				<p id="N2A3DB" type="main">
					<s id="N2A3DD"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 31.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A3E9" type="main">
					<s id="N2A3EB"><emph type="italics"></emph>Si voluatur planum rectangulum circa alterum laterum, funependulum <lb></lb>iſochronum continet duas tertias<emph.end type="italics"></emph.end>; probatur eodem modo; nam perinde ſe <lb></lb>habet illud planum, atque ſi multæ lineæ parallelæ ſimul volueren­<lb></lb>tur. </s>
				</p>
				<p id="N2A3FA" type="main">
					<s id="N2A3FC"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 32.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A408" type="main">
					<s id="N2A40A"><emph type="italics"></emph>Si voluatur planum triangulare circa angulum, eo modo quo diximus in <lb></lb>Th.<emph.end type="italics"></emph.end>11. <emph type="italics"></emph>funependulum iſochronum continet<emph.end type="italics"></emph.end> 3/4 <emph type="italics"></emph>axis prædicti trianguli<emph.end type="italics"></emph.end>; quia in <lb></lb>1/4 eſt centrum percuſſionis per Th. 11. </s>
				</p>
				<pb pagenum="436" xlink:href="026/01/470.jpg"></pb>
				<p id="N2A428" type="main">
					<s id="N2A42A"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 33.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A436" type="main">
					<s id="N2A438"><emph type="italics"></emph>Si voluatur prædictum planum circa baſim eo modo, quo dictum eſt Th.<emph.end type="italics"></emph.end>12. <lb></lb><emph type="italics"></emph>funependulum iſochronum continet<emph.end type="italics"></emph.end> 1/2 <emph type="italics"></emph>eiuſdem axis<emph.end type="italics"></emph.end>; quod eodem modo de­<lb></lb>monſtratur per Th.12. </s>
				</p>
				<p id="N2A450" type="main">
					<s id="N2A452"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A45E" type="main">
					<s id="N2A460">Colligo primò, cuilibet ſectori funependulum iſochronum poſſe aſſi­<lb></lb>gnari, quia cuiuſlibet ſectoris, qui voluitur circa angulum, eo modo <lb></lb>quo diximus Th.13. centrum percuſſionis determinatum eſt. </s>
				</p>
				<p id="N2A467" type="main">
					<s id="N2A469">Colligo ſecundò, ſi rotetur planum circulare, eo modo quo diximus <lb></lb>Th.21. funependuli iſochroni longitudinem continere 2/3 diametri eiuſ­<lb></lb>dem circuli, quia ibi eſt centrum percuſſionis eiuſdem circuli, per <lb></lb>Th. 21. </s>
				</p>
				<p id="N2A472" type="main">
					<s id="N2A474">Colligo tertiò, ſi rotetur planum circulare circa diametrum, etiam <lb></lb>poſſe determinari ex centro percuſſionis inuento, longitudinem fune­<lb></lb>penduli iſochroni, vt patet ex dictis. </s>
				</p>
				<p id="N2A47B" type="main">
					<s id="N2A47D"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 34.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A489" type="main">
					<s id="N2A48B"><emph type="italics"></emph>Quando voluitur planum triangulare parallelum plano in quo voluitur, <lb></lb>determinari poteſt longitudo funependuli iſochroni<emph.end type="italics"></emph.end>; ſit enim AFH, cuius <lb></lb>centrum extrinſecum percuſſionis fit C, longitudo funependuli iſochro­<lb></lb>ni erit AC, quod eodem modo demonſtratur. </s>
				</p>
				<p id="N2A49A" type="main">
					<s id="N2A49C"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A4A8" type="main">
					<s id="N2A4AA">Colligo primò, etiam determinari poſſe, quando ita voluitur vt latus <lb></lb>in quo fit percuſſio ſuſtineat angulum rectum, v.g. triangulum AGB <lb></lb>circumactum circa A, habet centrum percuſſionis in M; igitur AM eſt <lb></lb>longitudo funependuli iſochroni. </s>
				</p>
				<p id="N2A4B6" type="main">
					<s id="N2A4B8">Secundò, ſi voluatur circa angulum rectum; </s>
					<s id="N2A4BC">v.g. triangulum ABH <lb></lb>circa B, centrum percuſſionis eſt in E; igitur BE eſt longitudo funepen­<lb></lb>duli iſochroni. </s>
				</p>
				<p id="N2A4C6" type="main">
					<s id="N2A4C8">Tertiò, aliquando longitudo prædicta eſt minor latere, in quo fit <lb></lb>percuſſio, vt patet in exemplis adductis; </s>
					<s id="N2A4CE">aliquando eſt æqualis, vt in <lb></lb>triangulo ABD volutum circa A, nam centrum percuſſionis eſt D; </s>
					<s id="N2A4D4">igi­<lb></lb>tur longitudo funependuli iſochroni eſt AD; </s>
					<s id="N2A4DA">aliquando eſt maior, vt <lb></lb>videre eſt in triangulo ALG, quod voluitur circa A; nam longitudo fu­<lb></lb>nependuli iſochroni eſt AI, quæ eſt maior AL. </s>
				</p>
				<p id="N2A4E3" type="main">
					<s id="N2A4E5">Quartò, ſi coniungantur duo triangula v.g. EAS. ADS. voluan­<lb></lb>turque ſimul circa A, eo modo quo diximus ſcilicet parallela plano, in <lb></lb>quo voluuntur, longitudo iſochroni funependuli erit AF, poſito quòd <lb></lb>F ſit centrum percuſſionis, vt dictum eſt ſuprà Corol. 5. Th.19. </s>
				</p>
				<p id="N2A4F2" type="main">
					<s id="N2A4F4">Quintò, hinc vides rationem egregij experimenti, quod ſæpè Doctus <lb></lb>Merſennus propoſuit, ſcilicet longitudinem funependuli iſochroni eſſe <lb></lb>ferè quadruplam perpendicularis ductæ in baſim trianguli Iſoſcelis, li­<lb></lb>brati circa angulum verticis 150.grad. </s>
					<s id="N2A4FD">quod certè ad veritatem tam pro­<lb></lb>pè accedit ex geometrica calculatione, vt nullum prorſus diſcrimen <pb pagenum="437" xlink:href="026/01/473.jpg"></pb>eſſe videatur, methodus huius calculationis facilis eſt, &amp; à mediocri <lb></lb>Logiſta haberi poteſt. </s>
				</p>
				<p id="N2A509" type="main">
					<s id="N2A50B">Sextò, hinc etiam habetur longitudo funependuli iſochroni, ſi vol­<lb></lb>uatur planum circulare parallelum plano, in quo voluitur, continet <lb></lb>enim 2/3 diametri circuli, qui voluitur; vt patet ex Th. 22. idem dico de <lb></lb>quolibet ſectore, qui eodem modo voluatur. </s>
				</p>
				<p id="N2A515" type="main">
					<s id="N2A517"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 35.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A523" type="main">
					<s id="N2A525"><emph type="italics"></emph>Si voluatur pyramis circa verticem, determinari poteſt longitudo funepen­<lb></lb>duli iſochroni, idem dico de parallelipedo, priſmate, cono, cylindro, &amp;c.<emph.end type="italics"></emph.end> per <lb></lb>Th.25. 26. &amp; Corollaria; </s>
					<s id="N2A532">quia inuento centro percuſſionis extrinſeco, <lb></lb>habetur prædicta longitudo; idem dico de cono mixto, ſectore ſolido, <lb></lb>&amp;c. </s>
					<s id="N2A53A">per Th.28. &amp; Coroll. </s>
				</p>
				<p id="N2A53E" type="main">
					<s id="N2A540"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A54C" type="main">
					<s id="N2A54E">Hinc colligo primò ex dato centro percuſſionis extrinſeco, dari ſtatim <lb></lb>longitudinem funependuli iſochroni, &amp; viciſſim. </s>
				</p>
				<p id="N2A553" type="main">
					<s id="N2A555">Secundò, data quacunque longitudine funependuli iſochroni, v. g. <lb></lb>tripla perpendicularis, cadentis in baſim trianguli iſoſcelis, dari poſſe <lb></lb>triangulum, cuius libratio ſit æquediuturna, ſed hæc breuiter indicaſſe <lb></lb>ſufficiat. <lb></lb><figure id="id.026.01.473.1.jpg" xlink:href="026/01/473/1.jpg"></figure></s>
				</p>
				<pb pagenum="438" xlink:href="026/01/474.jpg"></pb>
				<figure id="id.026.01.474.1.jpg" xlink:href="026/01/474/1.jpg"></figure>
				<p id="N2A570" type="main">
					<s id="N2A572"><emph type="center"></emph>APPENDIX SECVNDA.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A579" type="main">
					<s id="N2A57B"><emph type="center"></emph><emph type="italics"></emph>DE PRINCIPIO PHYSICOSTATICO, <lb></lb>ad mouenda ingentia pondera.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A588" type="main">
					<s id="N2A58A">DVo ſunt in Statica, quæ demonſtrationem deſidera­<lb></lb>re poſſunt; Primum eſt, quod ſpectat ad proportio­<lb></lb>nes potentiarum, ponderum, reſiſtentiæ, motuum, <lb></lb>temporum, diſtantiarum, &amp;c. </s>
					<s id="N2A594">Secundum pertinet <lb></lb>ad cauſas Phyſicas huiuſmodi effectuum, qui cùm ſint <lb></lb>naturales, &amp; ſenſibiles, ſua cauſa carere non poſſunt. </s>
					<s id="N2A59B"><lb></lb>Primum ſanè quod ad Matheſim attinet egregiè præ­<lb></lb>ſtiterunt hactenus doctiſſimi viri Vbaldus, Steuinus, Galileus, &amp;c. </s>
					<s id="N2A5A1"><lb></lb>ita vt nihil amplius deſiderari poſſit; </s>
					<s id="N2A5A6">Secundum tamen quod iuris phy­<lb></lb>ſici eſt, vix, ac ne vix quidem delibatum inuenio; quare ad huius libri <lb></lb>calcem principium Phyſicoſtaticum breuiter explicandum ſuſcipio, per <lb></lb>quod duntaxat illi omnes mirifici effectus ad ſuas cauſas reducantur, <lb></lb>quod niſi fallor huic tractatui deeſſe videtur. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N2A5B5" type="main">
					<s id="N2A5B7"><emph type="center"></emph><emph type="italics"></emph>AXIOMA<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A5C4" type="main">
					<s id="N2A5C6"><emph type="italics"></emph>AB eadem potentiâ faciliùs producitur in eodem mobili minor motus, <lb></lb>quam maior.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2A5CF" type="main">
					<s id="N2A5D1">Hoc Axioma manifeſtum redditur ex ijs, quæ paſſim habentur in lib. <lb></lb>1. de impetu; </s>
					<s id="N2A5D8">quippe motus ex duplici tantùm capite minor eſſe poteſt; </s>
					<s id="N2A5DC"><lb></lb>primò, ex eo quòd ſingulis partibus mobilis pauciores partes impetus <lb></lb>inſint; </s>
					<s id="N2A5E3">ſecundò ex eo quòd imperfectior impetus mobili imprimatur; </s>
					<s id="N2A5E7"><lb></lb>atqui ex vtroque capite faciliùs producit ut minor motus; quia faciliùs <lb></lb>imprimitur minor, vel imperfectior impetus, nempe minore niſu agit <lb></lb>potentia. </s>
				</p>
				<p id="N2A5F0" type="main">
					<s id="N2A5F2"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A5FF" type="main">
					<s id="N2A601"><emph type="italics"></emph>Quò maiore tempore datum ſpatium percurritur, eò minor eſt motus, id eſt <lb></lb>tardior, vt patet ex dictis l.<emph.end type="italics"></emph.end>1. </s>
				</p>
				<pb pagenum="439" xlink:href="026/01/475.jpg"></pb>
				<p id="N2A60F" type="main">
					<s id="N2A611"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A61E" type="main">
					<s id="N2A620"><emph type="italics"></emph>Quò minus ſpatium decurritur dato tempore minor, &amp; tardior eſt motus<emph.end type="italics"></emph.end>; <lb></lb>hoc etiam conſtat ex eadem dem. </s>
				</p>
				<p id="N2A62B" type="main">
					<s id="N2A62D"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A63A" type="main">
					<s id="N2A63C"><emph type="italics"></emph>Maiore tempore potentia applicata ſi ſemper agit, plus agit.<emph.end type="italics"></emph.end></s>
					<s id="N2A643"> Quid clarius? </s>
				</p>
				<p id="N2A646" type="main">
					<s id="N2A648"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A655" type="main">
					<s id="N2A657"><emph type="italics"></emph>Pondus alteri æquale illud mouere tantum non poteſt motu æquali<emph.end type="italics"></emph.end>; </s>
					<s id="N2A660">cur <lb></lb>enim pondus A mouebit B potiùs quàm B. A: quod certum eſt. </s>
				</p>
				<p id="N2A666" type="main">
					<s id="N2A668"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A675" type="main">
					<s id="N2A677"><emph type="italics"></emph>Pondus alteri æquale mouere poteſt illud motu minore<emph.end type="italics"></emph.end>; </s>
					<s id="N2A680">quia cùm æquali <lb></lb>mouere tantùm non poſſit, &amp; cùm poſſit faciliùs minore, quàm maiore; <lb></lb>certè minore mouere poteſt. </s>
				</p>
				<p id="N2A68A" type="main">
					<s id="N2A68C"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A698" type="main">
					<s id="N2A69A"><emph type="italics"></emph>Pondus minus poteſt mouere maius motu minore, ſi maior ſit proportio mo­<lb></lb>tuum, quàm ponderum,<emph.end type="italics"></emph.end> v.g. pondus duarum librarum quod mouetur <lb></lb>motu vt 3.poteſt mouere pondus 4.librarum motu vt 1.vt patet ex dictis. </s>
				</p>
				<p id="N2A6A8" type="main">
					<s id="N2A6AA"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A6B6" type="main">
					<s id="N2A6B8"><emph type="italics"></emph>Eò faciliùs mouetur pondus per inclinatam, quàm per ipſum perpendicu­<lb></lb>lum, quò inclinata maior eſt perpendiculo<emph.end type="italics"></emph.end>; vt patet ex ijs, quæ dicta ſunt l.5. <lb></lb>de planis inclinatis. </s>
				</p>
				<p id="N2A6C5" type="main">
					<s id="N2A6C7"><emph type="center"></emph><emph type="italics"></emph>Axioma<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A6D3" type="main">
					<s id="N2A6D5"><emph type="italics"></emph>Pondus maius mouet tantùm minus motu maiore, cum eſt maior proportio <lb></lb>ponderum quàm motuum,<emph.end type="italics"></emph.end> vt patet. </s>
				</p>
				<p id="N2A6DF" type="main">
					<s id="N2A6E1"><emph type="center"></emph><emph type="italics"></emph>Problema vniuerſaliſſimum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A6EC" type="main">
					<s id="N2A6EE"><emph type="italics"></emph>Mouere quodcumque pondus à qualibet applicata potentia moueatur motu <lb></lb>minore, ita vt ſit maior proportio motuum, quàm ponderum,<emph.end type="italics"></emph.end> per Ax. 7. </s>
				</p>
				<p id="N2A6F8" type="main">
					<s id="N2A6FA"><emph type="center"></emph><emph type="italics"></emph>Coroll. vniuerſaliſſimum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A707" type="main">
					<s id="N2A709">Hinc colligo, in eo tantùm poſitam eſſe induſtriam, qua poſſint <lb></lb>pondera moueri, vt minore, &amp; minore motu moueantur; igitur, qua <lb></lb>proportione imminues motum, eâdem maius pondus mouebis. </s>
				</p>
				<p id="N2A711" type="main">
					<s id="N2A713"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 1.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A720" type="main">
					<s id="N2A722"><emph type="italics"></emph>Æqualia pondera æquali vtrimque brachio libræ appenſa ſunt in æquilibrio<emph.end type="italics"></emph.end><lb></lb>per Ax.5. </s>
				</p>
				<p id="N2A72C" type="main">
					<s id="N2A72E"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 2.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A73B" type="main">
					<s id="N2A73D"><emph type="italics"></emph>In æqualia pondera inæquali brachio librata faciunt æquilibrium ſi ſit ea­<lb></lb>dem proportio brachiorum quæ ponderum permutando<emph.end type="italics"></emph.end>; </s>
					<s id="N2A748">quia eſt eadem pro­<lb></lb>portio motuum, quæ brachiorum, vt patet; igitur ſunt in æquilibrio nec <lb></lb>enim minus pondus attolli poteſt à maiori per Ax.9.nec maius à mino­<lb></lb>re per Ax.7. igitur ſunt in æquilibrio. </s>
				</p>
				<pb pagenum="440" xlink:href="026/01/476.jpg"></pb>
				<p id="N2A756" type="main">
					<s id="N2A758"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A764" type="main">
					<s id="N2A766">Hinc collige omnes rationes, quæ ſpectant ad libram; </s>
					<s id="N2A76A">hinc vulgare <lb></lb>illud dictum mechanicum: Si pondera ſint vt diſtantiæ, ſunt in æqui­<lb></lb>librio. </s>
				</p>
				<p id="N2A772" type="main">
					<s id="N2A774">Hinc coniugari poſſunt infinitis modis pondera, &amp; diſtantiæ, quorum <lb></lb>omnium rationes compoſitæ obſeruari debent. </s>
				</p>
				<p id="N2A779" type="main">
					<s id="N2A77B">Hinc etiam obliqua libra, &amp; inclinata, ſi ſupponantur brachia adin­<lb></lb>ſtar lineæ indiuiſibilis facit æquilibrium. </s>
				</p>
				<p id="N2A780" type="main">
					<s id="N2A782"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 3.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A78F" type="main">
					<s id="N2A791"><emph type="italics"></emph>Ideo facilè ingens pondus attollitur vecte, quia mouetur motu minore iux­<lb></lb>ta <expan abbr="eãdem">eandem</expan> rationem, de quo ſuprà<emph.end type="italics"></emph.end>; </s>
					<s id="N2A7A0">cùm enim ſupponatur in vecte pun­<lb></lb>ctum immobile, quod certo nititur fulcro; </s>
					<s id="N2A7A6">neceſſe eſt vtrimque moueri <lb></lb>ſegmenta vectis motu circulari, <expan abbr="eoq́ue">eoque</expan> inæquali; </s>
					<s id="N2A7B0">quia ſunt inæqualia; </s>
					<s id="N2A7B4">igi­<lb></lb>tur altero minore; &amp; hæc eſt prima ratio imminuendi motus. </s>
				</p>
				<p id="N2A7BA" type="main">
					<s id="N2A7BC"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A7C8" type="main">
					<s id="N2A7CA">Hinc datum quodcunque pondus attollitur vecte; hinc quò ſegmen­<lb></lb>tum, quod à fulcro porrigitur verſus pondus quod attollitur eſt breuius, <lb></lb>eò maius pondus attolli poteſt. </s>
				</p>
				<p id="N2A7D2" type="main">
					<s id="N2A7D4">Hinc vectis per Tangentem ſemper attolli debet, vt maiorem præſtet <lb></lb>effectum, vt conſtat ex ijs, quæ diximus l.4. </s>
				</p>
				<p id="N2A7D9" type="main">
					<s id="N2A7DB"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 4.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A7E8" type="main">
					<s id="N2A7EA"><emph type="italics"></emph>Ideo facilè attollitur ingens pondus trochlea, quia mouetur motu minorę, <lb></lb>vt manifeſtum eſt<emph.end type="italics"></emph.end>; </s>
					<s id="N2A7F5">eſt autem minor motus in ea proportione, in qua lon­<lb></lb>gitudo funis adducti ſuperat altitudinem ſpatij decurſi à pondere, quod <lb></lb>attollitur; mirabile ſanè inuentum, ſi quod aliud. </s>
				</p>
				<p id="N2A7FD" type="main">
					<s id="N2A7FF"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A80B" type="main">
					<s id="N2A80D">Hinc, ſi funis adducatur deorſum, vnica rotula non iuuat potentiam; </s>
					<s id="N2A811"><lb></lb>quia longitudo funis adducti eſt æqualis altitudini ſpatij decurſi à pon­<lb></lb>dere; </s>
					<s id="N2A818">ſi verò adducatur ſurſum vnica rotula duplicat potentiam; </s>
					<s id="N2A81C">quia lon­<lb></lb>gitudo prædicta funis adducti eſt dupla prædictæ altitudinis; </s>
					<s id="N2A822">igitur mo­<lb></lb>tus ponderis aſcendentis eſt ſubduplus; </s>
					<s id="N2A828">igitur duplum pondus eadem po­<lb></lb>tentia attollet, vel idem pondus ſubdupla per Ax. 1. ſi verò ſint duæ ro­<lb></lb>tulæ adducaturque deorſum, duplum etiam pondus attollet eadem po­<lb></lb>tentia; </s>
					<s id="N2A832">quia longitudo funis adducti eſt dupla altitudinis; ex his reliqua <lb></lb>de trochlea facilè intelligentur, </s>
				</p>
				<p id="N2A838" type="main">
					<s id="N2A83A"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A846" type="main">
					<s id="N2A848">Equidem demonſtrari poteſt aliter à debili potentia ſuſtineri poſſe <lb></lb>ingens pondus operâ trochleæ; </s>
					<s id="N2A84E">quia ſcilicet pluribus diſtribuitur ſuſti­<lb></lb>nendi munus, vt clarum eſt; </s>
					<s id="N2A854">quod verò ſpectat ad motum, vnum tantùm <lb></lb>eſt illius principium, ſcilicet potentia, quæ trahit; licèt enim clauus, cui <lb></lb>affigitur altera extremitas funis poſſit ſuſtinere, non tamen mouere. </s>
				</p>
				<p id="N2A85C" type="main">
					<s id="N2A85E">Hinc demum ratio, cur ſi multiplicentur funes, &amp; orbiculi ingens-<pb pagenum="441" xlink:href="026/01/477.jpg"></pb>etiam pondus perexiguis fuſciculis ſuſtineri poſſit; </s>
					<s id="N2A867">quia pluribus diſtri­<lb></lb>buitur: hinc, ſi plura eſſent araneæ fila, maximum ſaxum ſuſtinere poſſent. </s>
				</p>
				<p id="N2A86D" type="main">
					<s id="N2A86F"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 5.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A87C" type="main">
					<s id="N2A87E"><emph type="italics"></emph>Ideo mouetur ingens pondus operâ axis, vel ſuculæ; quia ſcilicet imminuitur <lb></lb>matus,<emph.end type="italics"></emph.end> vt clarum eſt. </s>
				</p>
				<p id="N2A889" type="main">
					<s id="N2A88B"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A897" type="main">
					<s id="N2A899">Hinc, quò minor eſt diameter axis, maius pondus attollitur ſeu mo­<lb></lb>uetur; </s>
					<s id="N2A89F">quia cùm circulorum peripheriæ ſint vt ſemidiametri, quò minor <lb></lb>eſt diameter axis cui aduoluitur funis ductarius, eſt minor motus; </s>
					<s id="N2A8A7">igi­<lb></lb>tur maius pondus attollitur; </s>
					<s id="N2A8AD">igitur ſi longitudo vectis ſit dupla ſemidia­<lb></lb>metri ſuculæ, duplum pondus attollitur; ſi tripla, triplum, &amp;c. </s>
				</p>
				<p id="N2A8B3" type="main">
					<s id="N2A8B5">Huc reuoca terebraś, &amp; manubria, &amp;c. </s>
				</p>
				<p id="N2A8B8" type="main">
					<s id="N2A8BA"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 6.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A8C7" type="main">
					<s id="N2A8C9"><emph type="italics"></emph>Ideo cochlea mouet ingens pondus<emph.end type="italics"></emph.end>; quia imminuit motum, vt videre eſt <lb></lb>in torcularibus, in quibus Helicis opera ingens priſma attollitur. </s>
				</p>
				<p id="N2A8D4" type="main">
					<s id="N2A8D6"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A8E2" type="main">
					<s id="N2A8E4">Hinc quò ſunt plures Helices, &amp; decliuiores motus rectus eſt minor; <lb></lb>hinc faciliùs attollitur pondus; ſi enim longitudo ſpiræ eſt decupla axis, <lb></lb>potentia decuplum pondus attollet. </s>
				</p>
				<p id="N2A8ED" type="main">
					<s id="N2A8EF"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 7.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A8FB" type="main">
					<s id="N2A8FD"><emph type="italics"></emph>Ideò tantæ ſunt cunei vires, quia motum imminuit.<emph.end type="italics"></emph.end></s>
				</p>
				<p id="N2A904" type="main">
					<s id="N2A906"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A912" type="main">
					<s id="N2A914">Hinc quò angulus cunei eſt acutior, maius pondus attollitur eius ope­<lb></lb>râ; hinc proportiones omnes demonſtrari poſſunt, hinc cuneus ad angu­<lb></lb>lum 45. &amp; ſuprà non iuuat potentiam, ſecus infrà, ad cuneum reuoca <lb></lb>clauos &amp; gladios. </s>
				</p>
				<p id="N2A920" type="main">
					<s id="N2A922"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A92E" type="main">
					<s id="N2A930"><emph type="italics"></emph>Ideo rotis denticulatis mouetur ingens pondus<emph.end type="italics"></emph.end>; quia imminuitur motus, <lb></lb>vt clarum eſt. </s>
				</p>
				<p id="N2A93B" type="main">
					<s id="N2A93D"><emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A949" type="main">
					<s id="N2A94B">Obſeruabis huius organi operâ imminui poſſe motum in infinitum, <lb></lb>atque ad eo maius ſemper pondus, &amp; maius in infinitum attolli poſſe. </s>
				</p>
				<p id="N2A950" type="main">
					<s id="N2A952"><emph type="center"></emph><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A95E" type="main">
					<s id="N2A960">Ex his facilè colliges ad mouenda pondera in eo tantùm poſitam eſſe <lb></lb>induſtriam, vt motus imminuatur, &amp; vnicum illud eſſe principium phy­<lb></lb>ſicomechanicum. </s>
				</p>
				<p id="N2A967" type="main">
					<s id="N2A969"><emph type="center"></emph><emph type="italics"></emph>Theorema<emph.end type="italics"></emph.end> 9.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A975" type="main">
					<s id="N2A977"><emph type="italics"></emph>Vt pondus attollatur adhiberi poteſt alia induſtria ſcilicet plani inclinati, in <lb></lb>quo faciliùs pondus attollitur, quàm in verticali,<emph.end type="italics"></emph.end> de quo iam ſuprà in lib. 5.<emph type="center"></emph><emph type="italics"></emph>Scholium.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A98D" type="main">
					<s id="N2A98F">Obſeruabis autem, organum mechanicum adhiberi poſſe ad mouen-<pb pagenum="442" xlink:href="026/01/478.jpg"></pb>dum pondus per omne planum, in plano horizontali facillimè ingens <lb></lb>pondus moueri poteſt; præſertim ſi plani ſcabrities non impediat motum. </s>
				</p>
				<p id="N2A99A" type="main">
					<s id="N2A99C">Hinc modico organo ingentem nauim facilè mouebat Archimedes, <lb></lb>quam ſine organo tota ciuitas non mouere poterat. </s>
				</p>
				<p id="N2A9A1" type="main">
					<s id="N2A9A3">Quæres, quot ſint potentiæ mechanicæ? </s>
					<s id="N2A9A6">Reſp. quinque hactenus <lb></lb>numeratas eſſe, quæ ſunt, vectis, trochlea, axis, cuneus, cochlea; addi <lb></lb>poſſunt rotæ denticulatæ. </s>
				</p>
				<figure id="id.026.01.478.1.jpg" xlink:href="026/01/478/1.jpg"></figure>
				<p id="N2A9B3" type="main">
					<s id="N2A9B5"><emph type="center"></emph>APPENDIX TERTIA.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A9BD" type="main">
					<s id="N2A9BF"><emph type="center"></emph><emph type="italics"></emph>DE PRINCIPIO PHYSICO­<lb></lb>mechanico impreſsionis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A9CC" type="main">
					<s id="N2A9CE">NON ago hîc de impreſſione, quæ fit operâ pulueris tormen­<lb></lb>tarij, vel nerui tenſi, vel aëris compreſſi; nec enim eſt huius­<lb></lb>loci, ſed de illâ, quæ fit operâ alterius potentiæ motricis. </s>
				</p>
				<p id="N2A9D6" type="main">
					<s id="N2A9D8">Iniactu duo tantùm conſiderari debent: </s>
					<s id="N2A9DC">Primum eſt po­<lb></lb>tentia, ſecundum linea directionis, quod ſpectat ad primum, <lb></lb>commune eſt iactui &amp; percuſſioni; de ſecundo iam ſuprà dictum eſt lib.4. <lb></lb>vbi diximus maximum iactum fieri ad angulum ſemirectum. </s>
				</p>
				<p id="N2A9E6" type="main">
					<s id="N2A9E8"><emph type="center"></emph><emph type="italics"></emph>Principium vniuerſaliſſimum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2A9F3" type="main">
					<s id="N2A9F5"><emph type="italics"></emph>Quò diutius potentia manet applicata maior eſt impreſſio<emph.end type="italics"></emph.end>; veritas huius <lb></lb>axiomatis certiſſima eſt, &amp; conſtat ex Ax.13. l.1.n.4. ad hoc autem reuo­<lb></lb>cari poſſunt omnia organa, quæ potentia motrix adhibet ad motum im­<lb></lb>primendum. </s>
				</p>
				<p id="N2AA04" type="main">
					<s id="N2AA06"><emph type="center"></emph><emph type="italics"></emph>Corollaria.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2AA11" type="main">
					<s id="N2AA13">1. Hinc diu rotatum brachium maiorem ictum infligit; </s>
					<s id="N2AA17">hinc rotatum <lb></lb>pendulum fune plumbum fortiſſimè ferit; </s>
					<s id="N2AA1D">hinc fundæ iactus potentior; <lb></lb>hinc longior funda longiorem iactum præſtat, &amp;c. </s>
				</p>
				<p id="N2AA23" type="main">
					<s id="N2AA25">2. Hinc pertica longior, quæ diu vibratur propter maiorem arcum <lb></lb>validum ictum incutit; adde fuſtem, flagellum, <expan abbr="lõgum">longum</expan> mallei manubrium. </s>
				</p>
				<p id="N2AA2F" type="main">
					<s id="N2AA31">3. Hinc corpus diu cadens deorſum grauius ferit; hinc aries ille, <lb></lb>cuius caſus pali figuntur. </s>
				</p>
				<p id="N2AA37" type="main">
					<s id="N2AA39">4. Hinc maius ſaxum, vel grauior ſudes maiorem ictum infligit. </s>
				</p>
				<p id="N2AA3C" type="main">
					<s id="N2AA3E">5. Hinc trochus ductario funiculo vibratus celerrimè agitur; </s>
					<s id="N2AA42">hinc <lb></lb>etiam plani orbes explicata, &amp; exporrecta zona procul abiguntur; quia <lb></lb>ſcilicet potentia diu manet applicata. </s>
				</p>
				<p id="N2AA4A" type="main">
					<s id="N2AA4C">6. Hinc antiquus aries diu vibratus, ita verberabat muros, vt ſtatim <lb></lb>diſijceret propter eandem rationem. </s>
				</p>
				<p id="N2AA51" type="main">
					<s id="N2AA53">7. Hinc demum antiquæ illæ machinæ, quarum opera ingentia ſaxa <lb></lb>iaciebantur; hæc &amp; innumera propemodum alia ex eodem principio <lb></lb>conſequuntur. </s>
				</p>
				<pb pagenum="443" xlink:href="026/01/479.jpg"></pb>
				<figure id="id.026.01.479.1.jpg" xlink:href="026/01/479/1.jpg"></figure>
				<p id="N2AA64" type="main">
					<s id="N2AA66"><emph type="center"></emph>APPENDIX QVARTA.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2AA6D" type="main">
					<s id="N2AA6F"><emph type="center"></emph><emph type="italics"></emph>DE PRINCIPIO PHYSICO <lb></lb>Rationis duplicatæ Phyſicæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2AA7C" type="main">
					<s id="N2AA7E">VIx credi poteſt quam multis effectibus naturalibus hæc <lb></lb>duplicata ratio affigatur, aliquos curſim indicabo vt ve­<lb></lb>rum germanumque illius principium ſtatuatur. </s>
				</p>
				<p id="N2AA85" type="main">
					<s id="N2AA87">1. In motu recto naturaliter accelerato, decurſa ſpatia <lb></lb>ſunt in ratione duplicata temporum, id eſt vt temporum <lb></lb>quadrata; dixi in motu recto, tùm eo, qui fit deorſum in perpendiculo, <lb></lb>tùm eo, qui fit in plano inclinato. </s>
				</p>
				<p id="N2AA91" type="main">
					<s id="N2AA93">2. Si iaciantur lapides inæqualis ponderis à potentia toto niſu agente <lb></lb>&amp; eodem arcu, lapides ſunt in ratione duplicata inflictorum ictuum. </s>
				</p>
				<p id="N2AA98" type="main">
					<s id="N2AA9A">3. Si impingantur ſudes inæquales eodem brachiorum arcu, pondera <lb></lb>ſunt in ratione duplicata ictuum. </s>
				</p>
				<p id="N2AA9F" type="main">
					<s id="N2AAA1">4. Si malleus impingatur diuerſo arcu ab eadem potentia, arcus ſunt <lb></lb>in ratione duplicata ictuum. </s>
				</p>
				<p id="N2AAA6" type="main">
					<s id="N2AAA8">5. Si ex tubis erectis eiuſdem cauitatis æqualique foramine fluat aqua, <lb></lb>longitudines tuborum ſunt in ratione duplicata quantitatum aquæ, quæ <lb></lb>ex tubis æquali tempore fluunt. </s>
				</p>
				<p id="N2AAAF" type="main">
					<s id="N2AAB1">6. Similiter ſi ex ſiphonibus fluat aqua æquali foramine, longitudines <lb></lb>ſiphonum ſunt in ratione duplicata quantitatum aquæ, &amp;c. </s>
					<s id="N2AAB6">vt ſuprà. </s>
				</p>
				<p id="N2AAB9" type="main">
					<s id="N2AABB">7. Si chordæ tenſæ eiuſdem longitudinis appendantur inæqualia pon­<lb></lb>dera, hæc ſunt in ratione duplicata ſonorum in ratione acuti &amp; grauis. </s>
				</p>
				<p id="N2AAC0" type="main">
					<s id="N2AAC2">8. Si chordæ tenſæ ſint eiuſdem longitudinis &amp; diuerſæ craſſitiei, ba­<lb></lb>ſes ſunt in ratione duplicata ſonorum permutando. </s>
				</p>
				<p id="N2AAC7" type="main">
					<s id="N2AAC9">9. Lumen ita propagatur vt lumina propagata ſub eodem angulo, &amp; <lb></lb>cono ſint in ratione duplicata diſtantiarum permutando. </s>
				</p>
				<p id="N2AACE" type="main">
					<s id="N2AAD0">10. Idem dico prorſus de propagatione ſonorum, immò auſim dicere <lb></lb>toti rei ſonorum familiariſſimam eſſe hanc rationem duplicatam. </s>
				</p>
				<p id="N2AAD5" type="main">
					<s id="N2AAD7">11. In funependulis res eſt clariſſima; nam longitudines ſunt in ratio­<lb></lb>ne duplicata temporum quibus vibrationes perficiuntur. </s>
				</p>
				<p id="N2AADD" type="main">
					<s id="N2AADF">12. Non eſt omittendum quod in humana voce obſeruatur pro ratio­<lb></lb>ne grauis &amp; acuti, ſcilicet niſus eſſe in ratione duplicata <expan abbr="ſonorũ">ſonorum</expan>. </s>
					<s id="N2AAE8">Omitto <lb></lb>infinita ferè alia quæ huic rationi duplicatæ ſubſunt, ſed iam principia <lb></lb>phyſica his effectibus quibus ineſt hæc ratio duplicata, tribuamus. </s>
				</p>
				<p id="N2AAEF" type="main">
					<s id="N2AAF1">Primum caput &amp; vndecimum hoc principio nituntur, eadem cauſa <lb></lb>æquali tempore æqualem effectum producit vnde illud; corpus graue <lb></lb>æqualibus temporibus æqualia acquirit velocitatis momenta, de quo lib. <lb></lb>2. Ex hoc principio demonſtrauimus in partibus temporis ſenſibilibus <lb></lb>ſpatia eſſe temporum quadrata. </s>
				</p>
				<pb pagenum="444" xlink:href="026/01/480.jpg"></pb>
				<p id="N2AB02" type="main">
					<s id="N2AB04">Secundum &amp; tertium hoc principio nituntur, motus impreſſi diuerſis <lb></lb>corporibus ab eadem potentia æquali tempore ſunt vt corpora permu­<lb></lb>tando v.g.motus impreſſus corpori vnius libræ eſt ad motum impreſſum <lb></lb>corpori quatuor librarum vt 4.ad 1.æquali ſcilicet tempore quod clarum <lb></lb>eſt, igitur graue 4.librarum decurrit tantùm quartam partem arcus, igitur <lb></lb>ſecundo tempore æquali decurrit tres alias partes, vide quę diximus l.10. </s>
				</p>
				<p id="N2AB11" type="main">
					<s id="N2AB13">Quartum nititur hoc principio ſpatia ſunt quadrata temporum, ve­<lb></lb>locitates ſunt vt tempora, ictus vt velocitates. </s>
				</p>
				<p id="N2AB18" type="main">
					<s id="N2AB1A">Quintum, ſextum, ſeptimum habent hoc commune principium: </s>
					<s id="N2AB1E">eadem <lb></lb>eſt proportio effectuum quæ cauſarum; </s>
					<s id="N2AB24">quippe cauſa quæ aquam excu­<lb></lb>dit eſt pondus ſuperimpoſitum, igitur cum imprimat motum pluribus <lb></lb>partibus, velociorem imprimit ſingulis, igitur ex duplici capite creſcit <lb></lb>effectus, ſcilicet ex maiore <expan abbr="quãtitate">quantitate</expan> aquæ &amp; ex velociore motu; ſit enim <lb></lb>v.g.maior tubus quadruplus alterius cauſa eſt quadrupla, igitur duplam <lb></lb>quantitatem aquæ extrudet æquali tempore, quia duplo velociore motu. </s>
					<s id="N2AB36"><lb></lb>nam extrudere æqualem quantitatem duplo velociore motu eſt effectus <lb></lb>duplus; igitur duplam quantitatem extrudere duplo velociore motu eſt <lb></lb>effectus quadruplus, igitur eſt eadem proportio cauſę quæ effectus. </s>
					<s id="N2AB3F">De ſi­<lb></lb>phone idem dictum eſto, præſtat enim <expan abbr="eũdem">eundem</expan> effectum trahendo, quem <lb></lb>tubus aquæ pellendo, denique vnica vibratio chordæ tenſæ duplo velo­<lb></lb>cior eſt effectus duplus, igitur duæ duplo velociores effectus quadruplus. </s>
				</p>
				<p id="N2AB4C" type="main">
					<s id="N2AB4E">Octauum habet idem principium, nam chordæ eiuſdem longitudinis <lb></lb>ſunt vt baſes, ſit vna quadrupla alterius v. g. appendatur vtrique æquale <lb></lb>pondus, tenſio maioris eſt ſubquadrupla; </s>
					<s id="N2AB5A">igitur ſi huic appendatur pon­<lb></lb>dus quadruplum ſonum edet duplo acutiorem; igitur baſes ſunt vt qua­<lb></lb>drata ſonorum. </s>
				</p>
				<p id="N2AB62" type="main">
					<s id="N2AB64">Nonum, &amp; decimum nituntur hoc principio, lumen minus eſt in ea <lb></lb>proportione in qua plus diſtrahitur; igitur lumina ſunt vt baſes permu­<lb></lb>tando, ſed baſes ſunt in ratione duplicata diſtantiarum, idem dico de ſono. </s>
				</p>
				<p id="N2AB6C" type="main">
					<s id="N2AB6E">Duodecimum denique idem principium habet cum ſeptimo: </s>
					<s id="N2AB72">vis enim <lb></lb>illa ſeu niſus quo adducitur arteria æquiualet ponderi; ſed de his ſatis. </s>
				</p>
				<p id="N2AB78" type="main">
					<s id="N2AB7A"><emph type="center"></emph><emph type="italics"></emph>Schol. quod pertinet ad reflexionem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2AB87" type="main">
					<s id="N2AB89">Obſeruaſti in Th.8.l.6.quoſdam noluiſſe impetum in reflexione pro­<lb></lb>duci propter compreſſionem, vel corporis reflexi, vel reflectentis, vel <lb></lb>vtriuſque, quod certè fieri non poteſt, alioquin ſit globus reflexus; </s>
					<s id="N2AB91">certè <lb></lb>comprimitur neceſſariò à puncto contactus verſus centrum quod certum <lb></lb>eſt; </s>
					<s id="N2AB99">igitur redit neceſſariò per lineam ductam à puncto contactus per <lb></lb>idem centrum quod falſum eſt vt patet; igitur eſt alia cauſa huius motus <lb></lb>ſcilicet præuius impetus. </s>
				</p>
				<p id="N2ABA1" type="main">
					<s id="N2ABA3">Quidam etiam volunt hunc impetum produci ab ipſo corpore re­<lb></lb>flectente quod tamen abſurdum eſt, alioquin per <expan abbr="eãdem">eandem</expan> lineam ductam <lb></lb>à puncto contactus per centrum globi fieret reflexio, ſic enim globus <lb></lb>tantùm impelli poteſt, vt demonſtratum eſt lib.1. ſed de his fatis. </s>
				</p>
				<pb pagenum="445" xlink:href="026/01/481.jpg"></pb>
				<p id="N2ABB4" type="main">
					<s id="N2ABB6"><emph type="center"></emph><emph type="italics"></emph>Schol. pag.<emph.end type="italics"></emph.end> 217. <emph type="italics"></emph>num.<emph.end type="italics"></emph.end>8.<emph.end type="center"></emph.end></s>
				</p>
				<p id="N2ABCA" type="main">
					<s id="N2ABCC">Obſeruabis primò, fœdatam eſſe pulcherrimam demonſtrationem quæ <lb></lb>habetur loco citato innumeris propemodum mendis, qua ſcilicet pro­<lb></lb>batur omnium inclinatarum, quæ ab eodem horizontalis puncto ad <lb></lb>idem perpendiculum ducuntur, cam quæ eſt ad angulum 45. grad. bre­<lb></lb>uiſſimo tempore decurri; </s>
					<s id="N2ABDA">ſit enim Fig.49. Tab.2. in qua ſit EC diuiſa <lb></lb>bifariam in A, ex quo ducatur circulus radio AC, ſit AB perpendicula­<lb></lb>ris in AC; </s>
					<s id="N2ABE4">ducantur BC.BR.BM. dico BC breuiore tempore quàm B <lb></lb>R, BM, percurri, quod breuiter demonſtro: </s>
					<s id="N2ABEA">ducatur AH perpendicula­<lb></lb>ris in BC, ſitque vt BH ad BI, ita BI ad BC; </s>
					<s id="N2ABF0">certè BH &amp; AC æquali <lb></lb>tempore percurruntur; ſit autem tempus quo percurritur BH, vel AC <lb></lb>vt. </s>
					<s id="N2ABF8">BH; </s>
					<s id="N2ABFB">haud dubiè tempus quo percurretur BC erit vt BI, eſt autem B <lb></lb>I æqualis AC,, quæ eſt media proportionalis inter BC &amp; BH, vt con­<lb></lb>ſtat; </s>
					<s id="N2AC03">ſit autem BR dupla AR, &amp; angulus ABR 30. grad. ducatur BY <lb></lb>perpendicularis in BR, certè RY eſt dupla BR, ſunt enim triangula RB <lb></lb>A, RBY proportionalia; </s>
					<s id="N2AC0D">igitur BR &amp; YR perpendicularis eodem tem­<lb></lb>pore percurruntur; </s>
					<s id="N2AC13">ſed YR eſt maior EC, nam EC eſt dupla AB, &amp; R <lb></lb>Y dupla RB, quæ eſt maior AB, ergo YR maiore tempore percurritur <lb></lb>quam CE, igitur BR quam BC, ſimiliter ducatur BM ad angulum ABM <lb></lb>60. grad. ſit QB perpendicularis in BM; </s>
					<s id="N2AC1F">igitur QM eſt dupla QB, <lb></lb>igitur maior EC; </s>
					<s id="N2AC25">igitur maiore tempore percurritur; </s>
					<s id="N2AC29">ſed BM &amp; QM <lb></lb>æquali tempore decurruntur; igitur BM maiore tempore, quam BC <lb></lb>quod erat demonſtrandum. </s>
				</p>
				<p id="N2AC31" type="main">
					<s id="N2AC33">Obſeruabis ſecundò BM &amp; BR æquali tempore decurri, vnde quod <lb></lb>ſanè mirificum eſt, ſi pariter vtrimque creſcat, &amp; decreſcat angulus in <lb></lb>puncto B, ſupra &amp; infra BC, æquali tempore percurrentur duo plana in­<lb></lb>clinata; v.g.angulus RBA detrahit angulo ABC angulum CBR 15.grad. <lb></lb></s>
					<s id="N2AC3E">&amp; angulus ABM addit angulum CBM 15.grad. </s>
					<s id="N2AC41">motus per BR &amp; B <lb></lb>M fient æqualibus temporibus, vt conſtat ex dictis. </s>
				</p>
				<p id="N2AC46" type="main">
					<s id="N2AC48">Obſeruabis tertiò rationem à priori inde eſſe ducendam; </s>
					<s id="N2AC4C">quod cum <lb></lb>perpendiculum ſeu diagonalis quæ ſuſtinet angulum rectum ſit regula <lb></lb>temporis quo decurritur omnis inclinata, diagonalis quadrati ſit om­<lb></lb>nium aliarum minima in rectangulis quorum minus latus ſit maius ſe­<lb></lb>midiagonali quadrati, in eodem ſcilicet perpendiculo; </s>
					<s id="N2AC58">v.g. ſit diagona­<lb></lb>lis EC, ſint latera quadrati EBC, ducatur infra BA quælibet recta, v.g. <lb></lb>BR, &amp; in BR ducatur perpendicularis BY, certè YR eſt maior EC, <lb></lb>quia vt eſt RA ad AB, ita AB ad AY, igitur AB eſt media proportionalis <lb></lb>communis; </s>
					<s id="N2AC67">ſed collectum ex extremis inæqualibus, eſt ſemper maius <lb></lb>collecto ex æqualibus, poſita ſcilicet eadem media proportionali; </s>
					<s id="N2AC6D">ſi enim <lb></lb>ſunt æqualia, media proportionalis eſt ſemidiameter circuli cuius dia­<lb></lb>meter eſt æqualis collecto; </s>
					<s id="N2AC75">ſi verò ſunt inæqualia, media proportiona­<lb></lb>lis eſt ſunicorda circuli, cuius diameter eſt æqualis collecto; igitur col­<lb></lb>lectum iſtud eſt maius priore, ſed hæc ſunt ſatis clara. </s>
				</p>
				<p id="N2AC7D" type="main">
					<s id="N2AC7F">Quod ſpectat ad demonſtrationem num. </s>
					<s id="N2AC82">9. ibidem poſitam, &amp; peni-<pb pagenum="446" xlink:href="026/01/482.jpg"></pb>tus mendis fædatam, duces ſpongiam vſque ad lineam 22. pag.214. vbi <lb></lb>legis hæc verba, adde quod præſertim, cùm illam alibi, ſcilicet lib.  8. de­<lb></lb>monſtremus. </s>
				</p>
				<p id="N2AC8E" type="main">
					<s id="N2AC90">Cæterum vnum obſeruabis in Fig. 1.Tab.4. ſi diuidatur BE bifariam <lb></lb>æqualiter in T ducaturque FTG, fore vt mobile citiùs decurrat BTF <lb></lb>facto initio motus in B, quam chordam BF: </s>
					<s id="N2AC9A">cum enim FG ſit dupla FT, <lb></lb>ſit media proportionalis inter GT, GF; haud dubiè quadratum illius erit <lb></lb>duplum quadr. </s>
					<s id="N2ACA2">TF, &amp; ſubduplum quadr.BF, igitur ſit EG 4.ET 2FT erit <lb></lb>Rad. </s>
					<s id="N2ACA7"><expan abbr="q.">que</expan> 20. igitur FG rad. </s>
					<s id="N2ACAD"><expan abbr="q.">que</expan> 80. igitur media proportionalis (quæ ſit, <lb></lb>v.g. G <foreign lang="grc">μ</foreign>) rad. </s>
					<s id="N2ACBB"><expan abbr="q.">que</expan> 40. igitur ſi ſubtrahatur GT, id eſt rad. </s>
					<s id="N2ACC1">q.20. id eſt 4. <lb></lb>1/2 paulò minùs, ſed plùs quàm 4. 1/3 ex G <foreign lang="grc">μ</foreign>; id eſt ex rad. </s>
					<s id="N2ACCB">q.40. id eſt 6. <lb></lb>1/3 paulò minùs ſupereſt <foreign lang="grc">τμ</foreign>, quæ minor eſt 2. ſed ſi tempore BT, per­<lb></lb>curritur BT, æquali tempore percurretur tripla BT; </s>
					<s id="N2ACD7">igitur tempus quo <lb></lb>percurritur dupla BE, eſt vt BE; </s>
					<s id="N2ACDD">ſed tempus quo percurritur BTF eſt vt <lb></lb>BT <foreign lang="grc">μ</foreign>; </s>
					<s id="N2ACE7">atqui T <foreign lang="grc">μ</foreign> eſt minor TE; </s>
					<s id="N2ACEF">id eſt 2. igitur breuiore tempore percur­<lb></lb>ritur BTF, quam dupla DE; </s>
					<s id="N2ACF5">ſed quo tempore percurritur dupla BE, <lb></lb>etiam percurritur BF; </s>
					<s id="N2ACFB">igitur BTF breuiore tempore percurritur quam <lb></lb>BF; </s>
					<s id="N2AD01">vt autem ſcias quantum percurritur in perpendiculari, quo tempore <lb></lb>percurritur BTF, ſit FE 100000. erit FT 111800. igitur G <foreign lang="grc">μ</foreign> 151657. <lb></lb>igitur ſi vt BT 50000. ad BT <foreign lang="grc">μ</foreign>, id eſt ad 89857. ita BT <foreign lang="grc">μ</foreign> ad aliam, hæc <lb></lb>erit 161485. hoc ſpatium decurretur in perpendiculari, vides quam ſit <lb></lb>minor dupla BE, id eſt 200000. Si autem accipis Fig.1. Tab.3. BZE ſit <lb></lb>GP 100000.GZ 42265.ſit etiam vt EZ ad EY ita EY ad CB; GZ erit <lb></lb>87757. igitur acquiretur in perpendiculari 182253.eo tempore quo per­<lb></lb>curretur GZB, facto initio motus à G, ſed hæc eſt minor dupla GP, id <lb></lb>eſt 200000. accedit tamen propiùs quam ſuperior, igitur longiore tem­<lb></lb>pore decurit duas GZB huius figuræ quam duas BTF ſuperioris fig. </s>
				</p>
				<p id="N2AD23" type="main">
					<s id="N2AD25">Denique in Fig. 32. Tab. 3.ſit BY ita vt angulus BYA ſit grad.15.ſitque <lb></lb>v.g. vt YZ, ad YL, ita YL ad YB; </s>
					<s id="N2AD31">iuxta canonem ſinuum BY erit 386370. <lb></lb>YL 330171. ZL 47739. EZ 73205. ELZ 120944. igitur acquiretur in <lb></lb>perpendiculari 199814. quo tempore decurretur EZB; vides quàm pro­<lb></lb>ximè accedat ad duplam EM id eſt ad 200000. </s>
				</p>
				<p id="N2AD3D" type="main">
					<s id="N2AD3F">Denique ſi percurrat EMB, ſcilicet EM motu accelerato, tum MB <lb></lb>æquabili; </s>
					<s id="N2AD45">certè MB percurret ſubduplo tempore illius, quo percurrit E <lb></lb>M, vt conſtat; igitur ſit EM tempus quo percurrit EM v. g. 2.percurret <lb></lb>EMB tempore EMS ſcilicet 3. ſed ſi percurrat EM tempore EM, du­<lb></lb>plam decurrit tempore EB, ſed EB eſt minor EMS, eſt enim rad. </s>
					<s id="N2AD53">quadr. </s>
					<s id="N2AD56"><lb></lb>8. igitur EB decurritur citiùs quàm EMB, ſed de his ſatis. <lb></lb><gap desc="hr tag"></gap></s>
				</p>
				<p id="N2AD5D" type="main">
					<s id="N2AD5F"><emph type="center"></emph><emph type="italics"></emph>ERRATA.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
				</p>
				<p id="N2AD6A" type="main">
					<s id="N2AD6C"><emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 10. <emph type="italics"></emph>lin. 4<emph.end type="italics"></emph.end> magnete. <emph type="italics"></emph>p.13 l.vlt.<emph.end type="italics"></emph.end>non decreſcit <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>17.<emph type="italics"></emph>Th.<emph.end type="italics"></emph.end> 10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 2. non exigeret.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>20. <lb></lb><emph type="italics"></emph>l .ult.<emph.end type="italics"></emph.end> in ſe ipſo. <emph type="italics"></emph>p.21.t.26.l.2.<emph.end type="italics"></emph.end> non poteſt. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>24.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>32.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. duabus. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>25.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 33. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 15.tertiò <lb></lb>probatur. <emph type="italics"></emph>Caſtiga ibidem multas interpunctiones p.<emph.end type="italics"></emph.end>28.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 1. maioris. <emph type="italics"></emph>p .<emph.end type="italics"></emph.end>31 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. Ax. 12. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8 primo <emph type="italics"></emph>l.9. ſecundo l.35.<emph.end type="italics"></emph.end> cum tu. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>33.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 1. motus.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 35. min 5s. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 51.&amp; 52. fig.2. <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 55.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. immobilis A. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>36. fig.2. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>49.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>86.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.lib.2.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>54.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. Th. 81.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>25.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>17. in EL.</s> 
				</p>	
			</chap>
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				<back>
			<section>
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				<pb xlink:href="026/01/487.jpg"></pb>
				<figure id="id.026.01.487.1.jpg" xlink:href="026/01/487/1.jpg"></figure>
				<p id="N2C9BF" type="head">
					<s id="N2C9C1"> TABVLA I </s>
				</p>
				<pb/>
				<pb/>
				<pb xlink:href="026/01/488.jpg"></pb>
				<figure id="id.026.01.488.1.jpg" xlink:href="026/01/488/1.jpg"></figure>
				<p id="N2C9CC" type="head">
					<s id="N2C9CE"> TABVLA 2  </s>
				</p>
				<pb/>
				<pb/>
				<pb xlink:href="026/01/489.jpg"></pb>
				<figure id="id.026.01.489.1.jpg" xlink:href="026/01/489/1.jpg"></figure>
				<p id="N2C9D9" type="head">
					<s id="N2C9DB"> TABVLA TERTIA </s>
				</p>
				<pb/>
				<pb/>
				<pb xlink:href="026/01/490.jpg"></pb>
				<figure id="id.026.01.490.1.jpg" xlink:href="026/01/490/1.jpg"></figure>
				<p id="N2C9E6" type="head">
					<s id="N2C9E8"> TABVLA QVARTA </s>
				</p>
				<pb/>
				<pb/>
				<pb xlink:href="026/01/491.jpg"></pb>
				<figure id="id.026.01.491.1.jpg" xlink:href="026/01/491/1.jpg"></figure>
				<p id="N2C9F3" type="head">
					<s id="N2C9F5"> TABVLA QVINTA </s>
				</p>
				<pb/>
				<pb/>
				<pb pagenum="Tabula sexta" xlink:href="026/01/471.jpg"></pb>
				<p><s>TABVLA SEXTA</s></p>
				<pb/>
				<pb xlink:href="026/01/483.jpg"></pb>
					<p>
					<s><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>38.AB ad GB, id eſt vt 1.ad 5.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>66.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>137.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. AD &amp; AB.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>738.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. tota AC. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>140<lb></lb>fig. </s>
					<s id="N2AE60">15.tab.1. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>80.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3. idem eſſet, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>83.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>20. non eſt.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>88.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. ſecundo erunt, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>89. <emph type="italics"></emph>in <lb></lb>Sch.l.<emph.end type="italics"></emph.end>5. 1.ſpatium, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 7, <emph type="italics"></emph>caſtiga interpunctionem, p.<emph.end type="italics"></emph.end>90, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>41.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. terminus ſit 1.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>43. <emph type="italics"></emph>lege <lb></lb>ter<emph.end type="italics"></emph.end> rad.q. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>91 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. <emph type="italics"></emph>dele hac verba<emph.end type="italics"></emph.end> quàm ſpatij quod, &amp;c. </s>
					<s id="N2AECD">vſque ad quàm, <emph type="italics"></emph>p.92.l.<emph.end type="italics"></emph.end> 15. <lb></lb>&amp; 17. <emph type="italics"></emph>caſtiga interpunctiones p.<emph.end type="italics"></emph.end> 101. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 10. perticam, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>26. proportionis primæ. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>39. <lb></lb>æquales AC.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>42. 1/4 ſed, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>102. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>17. minimæ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>104.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.acceditur. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.diſcerni.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>105. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 6, BI, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>32 igitur tertio. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>33. FM, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>106.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. toties, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. &amp; 10. AFM, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>108.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>27.in­<lb></lb>ſtantia illud 1. 1/2 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. ſi 9. continet 1. 4/5 ſi 10. 1. (9/12) <emph type="italics"></emph>Coroll.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. <emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end>2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.q.4. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 109.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. <lb></lb>q.4. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. q.2. <emph type="italics"></emph>Cor.<emph.end type="italics"></emph.end>6. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>20. &amp; 22. vbicationem, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>30. phyſica minora. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>32. ſecundo in­<lb></lb>ſtanti, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 113.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>64.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. ſectam, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>65.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.primum inſtans. </s>
					<s id="N2AFC3">1.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.tertium. (5/11) <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>66.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1.aliqua <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. minore CD.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>115. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>70.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.primo eſt rad.q.2. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. tria rad.q.3.<emph type="italics"></emph>Th.<emph.end type="italics"></emph.end>71-<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.nullum <lb></lb>eſſet. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>116.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>76. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.vel communis qua grauitat, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. de quo aliàs, vel ſingularis, <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 117. <lb></lb><emph type="italics"></emph>in Sch.l.<emph.end type="italics"></emph.end>12. materiæ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>118.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>81. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. extrudi, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>123. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 103.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. vel diuerſæ grauitatis, <lb></lb>&amp; mollitiei, <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 124. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. grauioris, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>104. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5. ſecunda eiuſdem materiæ, &amp; figuræ ter­<lb></lb>tia.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. vel eadem vel diuerſa <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>125.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>109.<emph type="italics"></emph>L.B.K.L. t.<emph.end type="italics"></emph.end>110.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. diuiſione, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>127.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>25. <lb></lb>cubo minori, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>128.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.mouent, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. aëre repellitur. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 14. permeat, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>112. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. actiui­<lb></lb>tatis vnius.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. motum retardat; cum.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>16. modicus ventus.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>129. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>114.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.acuto. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>6. mobile, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.maior eſt.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. ſemiperipheriæ, <emph type="italics"></emph>l.vlt.<emph.end type="italics"></emph.end> illam cauam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>130.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.alter grauior <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>123.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. intruſus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>133.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. in hoc agemus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>13.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. adſtantibus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>137. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. produ­<lb></lb>ctum. <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 143.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. accidit <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. producto.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>145. <emph type="italics"></emph>habes.<emph.end type="italics"></emph.end> v.g. pro R, Q, &amp; radices 4. pro <lb></lb><expan abbr="q.">que</expan> <emph type="italics"></emph>&amp; alibi paſſim<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>pro Q, t.<emph.end type="italics"></emph.end>47. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. ſubduplicata. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>151. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. ſi loquamur. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>14. di­<lb></lb>ſtinctiones, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>21. deſcenderet. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>154.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. determinatum, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. inclinatam ſurſum.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>256. <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>13, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.IM.ſeq.fig.pro fig.37. lege 13. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>157.<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 3.partis.<emph type="italics"></emph>l<emph.end type="italics"></emph.end>28. ita vt, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 37. non dati.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>158.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 19.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 6. parallela.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>161.l.12. æquabilitas. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. primo æquabibi <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 162.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>39. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. <lb></lb>vtcumque, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. EO æquali.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>165.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>42.<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 3. violento.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>167.fig.47.<emph type="italics"></emph>Th.<emph.end type="italics"></emph.end>57. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. decreſcit. <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>173.<emph type="italics"></emph>c.<emph.end type="italics"></emph.end> 1.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. linea motus accedit, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>172. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. QR (2/16) in X.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 19.EB.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>31.EYEZ. <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>137.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. infra.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10 maximam <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 66 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. BG. l. 12. æqualem RK. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 174. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. diffe­<lb></lb>rentiam, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 9. tendere, centrum, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>16.erit AE, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>18.totus ille, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>62 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. inclinatiorem, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. <lb></lb>detrahi, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>175.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>35. reſiſtentiam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>176.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>70.fig. </s>
					<s id="N2B2C1">54.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9.in E ſed.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>177.<emph type="italics"></emph>l<emph.end type="italics"></emph.end>7.debet. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>72. <lb></lb>tab.2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 5. æqualis CR.<emph type="italics"></emph>l.vlt.<emph.end type="italics"></emph.end> demittatur, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>178.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>77.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3.eadem ratio.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>78.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1.excepta. <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>80.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.motus mixtus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 179.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. motus terræ, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24. AK. tab.2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>27.AD.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>28. DE <emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>180.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. 20 .<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 33. imum malum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>18 1.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11.rapietur.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>32.ſi verò.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>182.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.FA, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>183.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. <lb></lb>mixtus EB denique, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6. ad quam.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>27. cum impetu, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>29. ex verticali.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>184.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.parte. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. æqualem IK, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. recidit.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>26. mobile, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>29. rhedis. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>185.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. motu non aſſimi­<lb></lb>lem.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>186. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. oppoſitam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>187.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. arcu <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>188. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. ad GM, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>28. puncto Z, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>189. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>24. ſubduplam, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>31.ſagittam AR.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>190.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>14. erit KI inclinata KC, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>37.quam ſup­<lb></lb>pono.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>38. caſt.interpunct.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>191.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>107.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.eſt AH.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>92.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>109.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. ſit AE.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.ſit HN, <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. AO &amp; FG.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. &amp; EM.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>16. AM, caſt.interp.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>110.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>193.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. è naui. <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8. <lb></lb><emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 3. ex ABAF, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>197.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>38. tantum I, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>28. BAI.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>198.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. CA. nam.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.fune DB.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. <lb></lb>EA.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 12.AC verſus E.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 13.ad BA.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 34. EO, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>40. vt RF, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>41. vel in B vt PR.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>199. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. LM.vt SR.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 35.ſinui.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>200.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>70.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.non deſcendit.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. BAE, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>10. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. lib.2. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>201.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. innato, <emph type="italics"></emph>l. vlt.<emph.end type="italics"></emph.end> eodem. <emph type="italics"></emph>in Sch.<emph.end type="italics"></emph.end>fig.26.tab. 1. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>202.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.AD.fig.27, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 30. vt AD. <lb></lb>Th. 16.Fig. </s>
					<s id="N2B52F">31. Tab.2.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>203.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. in A.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>21. GD.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>205 <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>18.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15.ducatur LE.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.DG. <emph type="italics"></emph>l. <lb></lb>vlt.<emph.end type="italics"></emph.end> FP.DN, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>206. <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.AIFD, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. in AG.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>207.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>19.<emph type="italics"></emph>habes<emph.end type="italics"></emph.end> L pro G.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>209.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>25. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. ducatur, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>26.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. AF.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>210.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.deſcendet fig.42.tab.2. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>28.loco B.lege X.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 30.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. <lb></lb>ad KA.<emph type="italics"></emph>t,<emph.end type="italics"></emph.end> 30. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.petcurritur A.D.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>211.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. longitudinum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>212.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. ad BC ducatur <lb></lb>BG. </s>
					<s id="N2B5F6">Si non eſſet maior 5. CF, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 14. CF ferè 2. 1/2 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 30, BKAK, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>213.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>41.ſit rad. </s>
					<s id="N2B611"><lb></lb>q.8.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>20.GED.num. 8, &amp; 9.ſcatent mendis tu caſtigabis iuxta Sch. vltimæ appendicis. <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>215. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>37.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. vel AFC. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>216. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>38.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. conficeret per AF. <emph type="italics"></emph>l. vlt.<emph.end type="italics"></emph.end> aſcenſum. </s>
					<s id="N2B64C">Th.40. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. MA <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>41.fig.3.tab, 3.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>217. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.21.22. E.pro C.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>218.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>47.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. ſubduplus impetus <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>49. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. vt ſubdupla BC <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> a, quia vſque vt verò, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>219. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. vt ſubdupla GF <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. vt ſubdupla BC.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. quadruplum AB.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>220.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 8.perpendicularis GH.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11.paral­<lb></lb>lela EG.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 56. habes Y lege &amp; <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>58. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. verſus E, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>221.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>60, Y pro &amp; <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>62. V pro <foreign lang="grc">γ</foreign>, <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.puta <foreign lang="grc">β.</foreign><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>64. T pro <foreign lang="grc">τ</foreign> <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>222.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. æqualis.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>65. X pro &amp; <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10.in plano.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>66 P &amp; <emph type="italics"></emph>t<emph.end type="italics"></emph.end>68. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.vt planum fig.7, tab. </s>
					<s id="N2B727">3. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>223. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11.per KA vt DC ad CA, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. EPPEEA, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>37. <lb></lb>enotum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>225.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. non eſt <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>228.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>86.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. LC.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. maior <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>87.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. inſerte.<emph type="italics"></emph>t,<emph.end type="italics"></emph.end> 89 <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>8.an-<pb xlink:href="026/01/484.jpg"></pb>tecedentia.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>219.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>93. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 17. accedit.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>230.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>97.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 90. tum QP. &amp; EI.æqualia QYA <lb></lb>D.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>231.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>98.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6, MK.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. ſupra C.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. arcus MGP.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>14.ſi verò in V.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>99.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11.in 4. <lb></lb>vt AZ.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. 3 E.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. TBE <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>232.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>100.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. inſerto.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>33. &amp; ratione. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. EQE.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>27. <lb></lb>ad AT ad A <foreign lang="grc"><expan abbr="q.">θυε</expan></foreign><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>36. motum per AC.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>37. per AC.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>233.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.eſſet. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.debet eſſe <emph type="italics"></emph>co.<emph.end type="italics"></emph.end>4. <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5 deſcendant.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>235.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>20. ADG.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>39. vbi eſt motus.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>238.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. totum agit. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>240.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end><lb></lb>17.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. atque, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>241.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>20.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. lib.  1.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>23.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. horizontalis.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. GD ad AB. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>243.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. D <lb></lb>G. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>17. ad DA.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>19. dele GO, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>244.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>33.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. volunt.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>246.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>19.&amp; 23. G <foreign lang="grc">δ.</foreign><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>24. Th. <lb></lb>40.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>42. idque duobus.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>248.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>38. motum.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>249:<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>41.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 11. PD æqualis, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>250.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>44.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. <lb></lb>&amp; hic GDK.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>251.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. G <foreign lang="grc">δ.</foreign><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>252.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. quieſcit vt vult; ſed rem demonſtraui.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>253. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. quod dum.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>17.&amp; 36.atterantur.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>39.cedit.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 254.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 13.atterantur, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>253. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>59.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 1. <lb></lb>deſtruitur.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>254.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>62.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. oppoſitam.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>255.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>34. DBM. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>266.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. verò 60.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>64. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>19. ſubdupla habent ſæpius V.pro <foreign lang="grc">γ.</foreign><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>21.detrahatur <foreign lang="grc">δ</foreign> H.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>28. 1 1/2 <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>257..<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12.FAN <lb></lb>C. fig.23. tab. </s>
					<s id="N2B9BC">3. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>258.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>68.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3 autem ſic <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. Th. 135. lib.  1.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 67. <emph type="italics"></emph>habes ſæpius<emph.end type="italics"></emph.end> <foreign lang="grc">ν</foreign><lb></lb>pro <foreign lang="grc">γ.</foreign><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>259.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>14. globus B. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>31. globi B. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>29. aſſumatur M <foreign lang="grc">θ</foreign>, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 262. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. reſilit. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>264. Th.90.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. lineæ.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. ſed mox.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 265. <foreign lang="grc">υ</foreign> pro <foreign lang="grc">γ</foreign> <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>266. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>93. inſtanti. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>97.<emph type="italics"></emph>in Sch. <lb></lb>l.<emph.end type="italics"></emph.end>1. cauſas multiplices.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>267.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. an fortè.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>26. lumine.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>39: fori.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>268, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>40. rectam. <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>269.<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 7. eſt minor 3 1/2 &amp; eius quadr.minus 31.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. eſt 8.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 9. igitur hæc. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>14. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end><lb></lb>non <emph type="italics"></emph>in hac pa.&amp; ſup. </s>
					<s id="N2BA9B">legs <foreign lang="grc">γ</foreign> pro n. </s>
					<s id="N2BAA2">p.<emph.end type="italics"></emph.end>270. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.aliæ. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>273.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. lineam LM. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>274.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>17.vnus <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>275.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13.<emph type="italics"></emph>dele.<emph.end type="italics"></emph.end>A, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>21.<emph type="italics"></emph>dele<emph.end type="italics"></emph.end> non, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>25. vix in.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>276.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1.LM.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>278.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>15.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. QR. <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>279.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.locis.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9, <expan abbr="q.">que</expan><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>280.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 19. <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> L pro T.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>281.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11.ſi motus.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 14.intenſum.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>21. <lb></lb>A.<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 283. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>29.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. DC.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>30.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. C ſurſum.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>284.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>34.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. à ſe. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 286. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 42.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. cono <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. cuius axis, conus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>287.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>45.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.maior, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>288.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>48.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>18.FC.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>289.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>50.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 10.ad AE <lb></lb>permutando, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>292.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>57, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. ſubduplæ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>293.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>61.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. A <foreign lang="grc">θ</foreign>, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6, puncto A, <emph type="italics"></emph>ibidem lege<emph.end type="italics"></emph.end><lb></lb>Y <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> V.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>298.<emph type="italics"></emph>def,<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. corpori, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. à moto, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>299. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. corporis, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>22. mixtam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>300. <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>2.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. L, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>131.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. motus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>302. <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end>1, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. æqualibus, <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end>3. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 13. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> Q, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>18. <lb></lb>æquales, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 303. <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. ſit QR, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. ad quintam, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 15. Ax.rationem, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>17. Ax.<emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end><lb></lb>6.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. <emph type="italics"></emph>in DG, p.<emph.end type="italics"></emph.end>303. <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end> 10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. maius, <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end>12.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> cuius conſtructionis <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. <lb></lb>TQA, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. quæ AB, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. quad.45.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. BE, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>306 <emph type="italics"></emph>in Sch l,<emph.end type="italics"></emph.end> 2. <foreign lang="grc">μ α</foreign>, YR, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>307.<emph type="italics"></emph>Lem<emph.end type="italics"></emph.end> 15. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>23.ad BG, B 4, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>308. <foreign lang="grc">υ</foreign> <emph type="italics"></emph>pro <foreign lang="grc">γ</foreign> paſſim, l.<emph.end type="italics"></emph.end> 17. vt YZF, <emph type="italics"></emph>Lem.<emph.end type="italics"></emph.end> 16. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. quinam, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 307. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. <foreign lang="grc">α</foreign> ad BZ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>310.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1, recta, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>8, <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 2. inæqualia, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. in quo, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>311.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>36. 34.grad.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 313. <lb></lb><emph type="italics"></emph>Cor.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.angulum ipſa.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>316. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 36. percurritur, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>317.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>16. fig.3. Tab.4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4, tempore <lb></lb>æquali, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>319.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 20.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. ad H <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>22.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3.enim, <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 4. impetus quo aſcendat in <foreign lang="grc">ω</foreign> dele hæc <lb></lb>verba haud dubiè per arcum ferretur in <foreign lang="grc">ω</foreign> <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>320.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 1. perueniet in <foreign lang="grc">θ</foreign> <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. C fertur, <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> 23. <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1, niſit, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 321 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6, ſpatiis, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15.primo aſcenſu, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34. ferri, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 322.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>26.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.primæ, ſecun­<lb></lb>dæ, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 323.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 34. ignota, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 324.<emph type="italics"></emph>l vlt.<emph.end type="italics"></emph.end> prima, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>326. <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. ita vt, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>327.<emph type="italics"></emph>cor.<emph.end type="italics"></emph.end> 5 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. de­<lb></lb>ſcenderet, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33.ferri, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>329 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. medullaceum, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 17.quamdam, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> conficiet, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 19. <lb></lb>conficiet tres, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>41. huius motus <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 331. <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>2.l.3. in F. <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>3. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1 in hoc &amp; <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end> 5.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. <lb></lb>quia enim, <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. ſuſpendatur, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>332.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. pondus, C. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>41. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 5. puncto, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 333. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 2. <lb></lb>quam maiores, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>334. <emph type="italics"></emph>def.<emph.end type="italics"></emph.end> 1 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. curuam, <emph type="italics"></emph>def<emph.end type="italics"></emph.end> 2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3. ex duobus rectis &amp; <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 335 <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 1.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12. <lb></lb>LQA. <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 336 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. vel MI, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 4. &amp; motus <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>1 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6, L <foreign lang="grc">γ</foreign>, <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. AC, &amp; <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4.&amp; quo <lb></lb><emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2 <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 2 <emph type="italics"></emph>cor<emph.end type="italics"></emph.end> 5.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4. LH, &amp; <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>337. <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5.<emph type="italics"></emph>dele,<emph.end type="italics"></emph.end> vt <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6.Z, 9, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 10. ſinguli. <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>7 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>3.9.grad <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>338. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 5 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 2. AB, æqualem arcui AV. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3. æqualem XV, id eſt arcum <lb></lb>ſious AV, ſed, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2 OPDL 4. OZP, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>339.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. A. 18. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>7.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.ſinus ex gradu, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 11. <lb></lb>aſſumas, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13. vero 1.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>8. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1. rota, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>340.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. puncta B, punctum B, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>25. aſcenderet. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>39 centro M, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>41. ſimplici, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>42. punctum P, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>44 circa centrum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>341.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2.illum <lb></lb>fig.10 tab.4, lib.10 quadrat IA, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. KD, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>16. HF, <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. profecto, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>342. <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>12 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. <lb></lb>inſuperabilem <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6.ſibi non, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. non tangit, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>343 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>21 huiuſmodi contactus, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>25.DN, <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. ne diu, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. arcu BD, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14. contactu medio, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>344. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> non n 18.fig 12. tab.4. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. <lb></lb>imaginarium, <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 20. DC primum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>345 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. quod n.24 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. duo, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>346.n.27. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3.in K, <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4. ſecet, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. <emph type="italics"></emph>lege <foreign lang="grc">γ</foreign> pro<emph.end type="italics"></emph.end> V, ſit ZX n.28.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4 colliguntur, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 347.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5. puncto D. <emph type="italics"></emph>in Sch.l. </s>
					<s id="N2C0F1"><lb></lb>vlt<emph.end type="italics"></emph.end> experientia, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 348.<emph type="italics"></emph>l, vlt<emph.end type="italics"></emph.end> lignea, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>349 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. nam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>350. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>15. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 3. centro A, lege <foreign lang="grc">τ</foreign><lb></lb><emph type="italics"></emph>pro<emph.end type="italics"></emph.end> T, ter, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>351. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. qui eſt, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 5.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3 in P, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. BGDP, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.p.6. igitur BD eſt qua­<lb></lb>drupla BV, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. oppoſitorum, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12. rectilineo, <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> <foreign lang="grc">τ</foreign> pro T bis, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>352 <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 9 &amp; 10 <emph type="italics"></emph>paſ­<lb></lb>ſim lege<emph.end type="italics"></emph.end> <foreign lang="grc">ρ</foreign> pro X <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. ad C, <foreign lang="grc">μ</foreign> 10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. BT non ſingula <foreign lang="grc">ρ α</foreign> ſingulis <foreign lang="grc">ρ</foreign> B <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>16.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. rotæ, <lb></lb>quæ <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>353. <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 5.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. motu, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6. triplo maior, <emph type="italics"></emph>t<emph.end type="italics"></emph.end> 17.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3.<emph type="italics"></emph>dele<emph.end type="italics"></emph.end> T, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>354 <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 3 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. configit BG,. <lb></lb>I 3 <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> I, <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> 6.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5.KT, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>7.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. vt quadrans <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6. contactus, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>13. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> 4 <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 355 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>2 <emph type="italics"></emph>l,<emph.end type="italics"></emph.end><pb xlink:href="026/01/485.jpg"></pb>8. VTD, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> nam AV, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>4. AC, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 6 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. TVY, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. radius PCTV ſumantur <foreign lang="grc">τ γ</foreign> Y <lb></lb>YT: <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.6 T <foreign lang="grc">δ</foreign>, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1.PC, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.igitur cum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>356.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.rectam in Coroll.ita peccatum eſt <lb></lb>vt errata caſtigati vix poſſint <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>358.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 5 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. partes areæ, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. conficient, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. mouetur, <lb></lb><emph type="italics"></emph>t.<emph.end type="italics"></emph.end>20.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>3. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8, cinguntur, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>359.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. B &amp; C, <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> 11.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. aëris, <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 360 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 14.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1.ceſſat motus, <lb></lb><emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 17. tab. </s>
					<s id="N2C2F3">5.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>20. citiſſimus, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>22.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1 ceſſat motus, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>24.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. ſi grauior, <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 361.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>21.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>2. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. nec dextrorſum, <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> 362.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. ipſam DA, velis, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. ex recto, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5. motus orbis, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 11. <lb></lb>pollant, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>23.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1. plumbi, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. ſint, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. quia, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 9. <foreign lang="grc">α</foreign>, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 6.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. adde, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>25. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. ſerpentis, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>363.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>25 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>13. conoidicus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>364.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. verſus G, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>27.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. motum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>365.<emph type="italics"></emph>n<emph.end type="italics"></emph.end> 9.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6.rota­<lb></lb>tæ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 366.<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 12. reſilit., <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>29 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. niſu, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10.faciet vero, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 14.AI, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>23.extremitatem.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>367. <lb></lb><emph type="italics"></emph>n.<emph.end type="italics"></emph.end>13. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4.manus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 368.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. erectam, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. quæ, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>1.<emph type="italics"></emph>l<emph.end type="italics"></emph.end>6 5. libretur, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 17.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 6. EL, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end><lb></lb>369.<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> 1. qua, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>370 <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 24.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>24. rudiaria <emph type="italics"></emph>lege paſſim<emph.end type="italics"></emph.end> G <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>t<emph.end type="italics"></emph.end> 30.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 7. vt C, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>371.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. <lb></lb>qui, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>372 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>13.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. GE cum in I, erit in L, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>15.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. mitius, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>373.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.terram <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>374.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end><lb></lb>33.fig.13 tab.4.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>375. <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> Q <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> K <emph type="italics"></emph>paſſim<emph.end type="italics"></emph.end> LB erectæ, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1.delineari fig.8.tab.5.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>16 ita <lb></lb>vt, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17.quadratum AM 16.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17. quadratum AO, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 377.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. nec producitur, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>1 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4.ali­<lb></lb>quid, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 378.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4 anima, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 379.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. effectus, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.brachium, <emph type="italics"></emph>l penult.<emph.end type="italics"></emph.end> volæ, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>380.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>2 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2.ali­<lb></lb>quid ſic globus pendulus, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>381.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>3 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. æquitem capiti, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18. imo equus, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>26 determi­<lb></lb>nata, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 36. cruris, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 392.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>10.fig 28.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 21. omittendus, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>11.fig.27.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9 vt BC <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 383.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. <lb></lb>facilia, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>384.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. productum, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 385 n.8.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 10, fune; </s>
					<s id="N2C5A7"><emph type="italics"></emph>n.<emph.end type="italics"></emph.end>9.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5. funes, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>386 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>15. ad DL, <lb></lb><emph type="italics"></emph>n.<emph.end type="italics"></emph.end>11, fig.31.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 7.fig.30 <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>388.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.etiam nauis, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. duo tauri, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>7.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>10. ſe ipſo, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 11. corpore <lb></lb>impulſo, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>389.<emph type="italics"></emph>t<emph.end type="italics"></emph.end> 8 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. finem, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>390.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>11.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, arcus BC, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>392.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.ABC, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>194.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>6. <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 8. conficit, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>18. ſubduplam, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>395.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. ſe iuncto, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 396.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>21.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. de <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>399. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 9. <lb></lb>proportionem, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>3 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. vt radix CD, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. ſit 1 pondus 2. certè, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 401.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. arcum, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>15. circa K, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>402.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2. medium, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 22. agant, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>14.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9. ſint, in hoc Th. affige literas af­<lb></lb>firas mucroni gladij ipfi capulari pilæ, &amp; viciſſim, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>403.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>7.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.æquali vtriuſque, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 8. <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. detectum, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 404 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>13.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. æquipondium, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 15.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. alio, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>405 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>18.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. intentetur, <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.extento, <emph type="italics"></emph>n<emph.end type="italics"></emph.end> 19.<emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1. impetens gladius, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>23 <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. &amp; eadem altitudo, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>406. <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>5.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. <lb></lb>corpore <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 6 <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. ictum, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. quæ, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>11.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. proportio, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3: 1000.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>407.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.gradus, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end><lb></lb>12.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. <expan abbr="eãdem">eandem</expan>, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>409.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>19.fig.20.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>11. P <foreign lang="grc">ν</foreign> N <foreign lang="grc">β γ.</foreign><emph type="italics"></emph>n.<emph.end type="italics"></emph.end>22. fig. </s>
					<s id="N2C7AF">16.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>410. <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>24.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. mino­<lb></lb>rem, <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> N, <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>411.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. vt <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. vt chorda MV, <emph type="italics"></emph>l.vlt.<emph.end type="italics"></emph.end>velociter, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>402. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>17.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5.ex­<lb></lb>tendi, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. prædictam, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>24. imprimit, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>25. certa.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>413.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>4.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3. mouentur, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7. alium, <lb></lb><emph type="italics"></emph>p.<emph.end type="italics"></emph.end>414.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. augendum, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. tormentaria, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>11. reticulo in fig. </s>
					<s id="N2C84D">24. tab. </s>
					<s id="N2C850">5. adhibe <lb></lb>H ſub G tum L ſub Z, in fig.22. adhibe omnes literas in quadrante AGD, in fig. </s>
					<s id="N2C855">25. <lb></lb>tab. </s>
					<s id="N2C85A">lege C inter BA, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>415.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>12. fig.37. tab. </s>
					<s id="N2C869">3.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>11.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. quæ, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end> 12.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 12. tamen ſit <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14. <lb></lb>octauo, in <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>416.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>2.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. corporum, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>1. diſperſio, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. ſic <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>3.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. vannus autem; <emph type="italics"></emph>l.<emph.end type="italics"></emph.end><lb></lb>12.portu, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>6.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. quando duo, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>417.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4.impreſſus, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>8.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 11. cadit, <emph type="italics"></emph>n.<emph.end type="italics"></emph.end>9.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6.ſapo.<emph type="italics"></emph>n.<emph.end type="italics"></emph.end>10.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. <lb></lb>vnum corpus, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. vnum corpus <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>418.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>9.luctam, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 12. fulminis, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> 20. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>2. in plano, <lb></lb><emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8.reſilit, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 18. pluit, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 419. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 14. vorticem, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> 421. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 9. lineas, <emph type="italics"></emph>lege paſſim<emph.end type="italics"></emph.end> poſitio <lb></lb>propoſitiones, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>423.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>7.triangulo, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>8. IKD, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end>426.<emph type="italics"></emph>t.<emph.end type="italics"></emph.end>15.rig.12. <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>16. <emph type="italics"></emph>l.<emph.end type="italics"></emph.end>5. perpendi­<lb></lb>culares,. 427.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>6. AH, <emph type="italics"></emph>cor.<emph.end type="italics"></emph.end>2.fig.14.<emph type="italics"></emph>p.<emph.end type="italics"></emph.end>430<emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 32. CNAP, <emph type="italics"></emph>t.<emph.end type="italics"></emph.end>22.<emph type="italics"></emph>l.<emph.end type="italics"></emph.end>4. D vt. </s>
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					<s id="N2C9A7"><emph type="center"></emph><emph type="italics"></emph>FINIS,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
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