'De motu corporum in mediis regulariter cedentibus'

'De motu corporum in mediis regulariter cedentibus' Isaac Newton c. 1,673 words The Newton Project Falmer 2010 Newton Project, University of Sussex

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Late 1684/5, in Latin, c. 1,686 words, 4 pp. 4 pp.

in Latin

MS Add. 3965.5, ff. 25r-26r, 23r-24r, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Portsmouth Collection MS Add. 3965.5, ff. 25r-26r, 23r-24r </msItem> </msContents> </msDesc> </sourceDesc> </fileDesc> <profileDesc> <creation> <origDate when="1684-12-02">Late 1684/5</origDate> <origPlace>England</origPlace> </creation> <langUsage> <language ident="lat">Latin</language> </langUsage> <handNotes> <handNote xml:id="unknown" scribe="unknown">Unknown Hand</handNote> <handNote sameAs="#in">Holograph</handNote> </handNotes> </profileDesc> <encodingDesc> <classDecl><taxonomy><category><catDesc n="Science">Science</catDesc><category><catDesc n="Physics">Physics</catDesc></category></category></taxonomy></classDecl> </encodingDesc> <revisionDesc> <change when="2001-01-01" type="metadata">Catalogue information compiled by Rob Iliffe, Peter Spargo & John Young</change> <change when="2010-10-01">Tagged transcription by <name xml:id="ys">Yvonne Santacreu</name></change> <change when="2010-10-29" status="released">Transcription reviewed by <name xml:id="jy">John Young</name></change> <change when="2011-03-05">Proofed by <name>Robert Iliffe</name></change> <change when="2011-09-29" type="metadata">Catalogue exported to teiHeader by <name xml:id="mjh">Michael Hawkins</name></change> </revisionDesc> </teiHeader> <facsimile xml:base="http://cudl.lib.cam.ac.uk/newton/images/"> <graphic xml:id="MS-ADD-03965-005-00001.jpg" url="MS-ADD-03965-005-00001.jpg" n="21r"/> <graphic xml:id="MS-ADD-03965-005-00002.jpg" url="MS-ADD-03965-005-00002.jpg" n="21v"/> <graphic xml:id="MS-ADD-03965-005-00003.jpg" url="MS-ADD-03965-005-00003.jpg" n="22r"/> <graphic xml:id="MS-ADD-03965-005-00004.jpg" url="MS-ADD-03965-005-00004.jpg" n="22v"/> <graphic xml:id="MS-ADD-03965-005-00005.jpg" url="MS-ADD-03965-005-00005.jpg" n="23r"/> <graphic xml:id="MS-ADD-03965-005-00006.jpg" url="MS-ADD-03965-005-00006.jpg" n="23v"/> <graphic xml:id="MS-ADD-03965-005-00007.jpg" url="MS-ADD-03965-005-00007.jpg" n="24r"/> <graphic xml:id="MS-ADD-03965-005-00008.jpg" url="MS-ADD-03965-005-00008.jpg" n="24v"/> <graphic xml:id="MS-ADD-03965-005-00009.jpg" url="MS-ADD-03965-005-00009.jpg" n="25r"/> <graphic xml:id="MS-ADD-03965-005-00010.jpg" url="MS-ADD-03965-005-00010.jpg" n="25v"/> <graphic xml:id="MS-ADD-03965-005-00011.jpg" url="MS-ADD-03965-005-00011.jpg" n="26r"/> <graphic xml:id="MS-ADD-03965-005-00012.jpg" url="MS-ADD-03965-005-00012.jpg" n="26v"/> </facsimile> <text> <body> <div> <pb xml:id="p25r" n="25r" facs="#MS-ADD-03965-005-00009.jpg"/><fw type="pag" place="topRight" hand="#unknown">25</fw><head rend="center" xml:id="hd1">De motu corporum in medijs <lb xml:id="l1"/>regulariter cedentibus. <lb type="intentional" xml:id="l2"/>Definitiones.</head> Def. 1. Tempus absolutum est quod sua natura abs<choice><orig></orig><reg>que</reg></choice> <lb xml:id="l3"/>relatione ad aliud quodvis æquabiliter fluit. Tale est, <lb xml:id="l4"/>cujus æquationem <add hand="#in" indicator="yes" place="supralinear">in</add>vestigant Astronomi, alio nomine dictum <lb xml:id="l5"/>Duratio. Def. 2. Tempus relative <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="3"/></del> <add hand="#in" indicator="yes" place="supralinear">spectatum</add> est quod <del type="strikethrough">&c rei alterius fluxione</del> <lb xml:id="l6"/><del type="strikethrough">seu transitu mensuratur</del> <add hand="#in" indicator="yes" place="interlinear"><del type="strikethrough">alicujus sensibilis transitu seu</del> respectu fluxionis seu transitus rei alicujus sensibilis consideratur ut æquabile.</add>. Tale est tempus dierum mensium et <lb xml:id="l7"/>aliarum periodorum cœlestium, <del type="strikethrough">quod propterea cum hoc mundo</del> <lb xml:id="l8"/><del type="strikethrough"><unclear reason="del" cert="medium">cœpisse</unclear> creditur</del> <add hand="#in" indicator="no" place="interlinear"><del type="strikethrough">ex hypothesi quod hæ <add hand="#in" indicator="yes" place="supralinear"><del type="cancelled"><gap reason="illgblDel" unit="words" extent="1"/></del></add> periodi sunt æquabiles quas vulgus considerantur ut æquabiles considerat ex mente vulgi</del></add> apud vulgus. Def. 3. Spatium absolut<add hand="#in" indicator="no" place="inline">um</add> <del type="strikethrough">dictum</del> est quod sua natura abs<choice><orig></orig><reg>que</reg></choice> <lb xml:id="l9"/>relatione ad aliud quodvis semper manet immobile. Ut partium <lb xml:id="l10"/>temporis ordo immutabilis est sic etiam partium spatij. Moveantur <lb xml:id="l11"/>hæ de locis suis et movebunt<add hand="#in" indicator="no" place="inline">ur</add> de seipsis. Nam tempora et spatia <lb xml:id="l12"/>sunt suiipsorum et rerum omnium loca. In tempore quoad ordin<choice><orig>ē</orig><reg>em</reg></choice> <lb xml:id="l13"/>successionis, in spatio quoad ordinem situs locantur universa. De <lb xml:id="l14"/>illorum essentia est ut sint loca et loca<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> <add hand="#in" indicator="yes" place="supralinear">primaria</add> moveri <del type="cancelled">nequeunt</del> <add hand="#in" indicator="yes" place="supralinear">absurdum est<choice><sic>.</sic><corr type="noText"/></choice></add>. Porrò <lb xml:id="l15"/>vi illata moveatur una pars spatii et vi <del type="strikethrough">eadem</del> <add hand="#in" indicator="yes" place="supralinear">tanta</add> ad omnes <add hand="#in" indicator="yes" place="supralinear">in infinitum</add> partes ap<lb type="hyphenated" xml:id="l16"/>plicata movebitur totum, quod rursus absurdum est. Def. 4. Spatium relativum est quod respectu rei <del type="strikethrough">alterius</del> <add hand="#in" indicator="yes" place="supralinear">alicujus sensibilis</add> conside<lb type="hyphenated" xml:id="l17"/>ratur ut immobile: uti spatium aeris nostri respectu terræ. Distinguun<lb type="hyphenated" xml:id="l18"/>tur autem hæc spatia ab invicem ipso facto per descensum gravium <lb xml:id="l19"/>quæ in spatio absoluto rectà<del type="cancelled">m</del> petunt centrum in relativo absolute <lb xml:id="l20"/>gyrante deflectunt ad lat<del type="over"><gap reason="illgblDel" unit="chars" extent="3"/></del><add hand="#in" indicator="no" place="over">us</add>. Def. 5. Corpora <del type="cancelled">d<gap reason="illgblDel" unit="chars" extent="5"/> <unclear reason="del" cert="medium">res</unclear> extensa et</del> <add hand="#in" indicator="yes" place="supralinear"><del type="cancelled">quæ</del> in sensus <add hand="#in" indicator="yes" place="supralinear">omnium</add> incurrunt <del type="cancelled"><gap reason="illgblDel" unit="words" extent="2"/></del> ut res <del type="cancelled"><gap reason="illgblDel" unit="words" extent="1"/> et</del></add> mobiles quæ se mutuo <lb xml:id="l21"/>penetrare nequeunt. <add hand="#in" indicator="no" place="interlinear marginRight"><del type="strikethrough">Def. 6 Centrum corporis cujus<choice><orig></orig><reg>que</reg></choice> est quod vulgo dicitur centrum gravitatis et axis corporis</del> <add indicator="yes" place="supralinear">est</add> linea quævis recta per centrum transiens.</add> Def. <del type="cancelled">6</del> <add hand="#in" indicator="no" place="inline">7</add> Locus corporis est pars spatij in quo corpus existit, est<choice><orig></orig><reg>que</reg></choice> <lb xml:id="l22"/>pro genere spatij vel absolutus vel relativus Def. <del type="over">7</del><add hand="#in" indicator="no" place="over">8</add>. Quies corporis est perseverantia ejus in eodem loco, est<choice><orig></orig><reg>que</reg></choice> <pb xml:id="p26r" n="26r" facs="#MS-ADD-03965-005-00011.jpg"/><fw type="pag" place="topRight" hand="#unknown">26</fw> vel absoluta vel relativa pro genere loci. Def. <del type="over">8</del><add hand="#in" indicator="no" place="over">9</add>. Motus corporis est translatio ejus de loco in locum, est<choice><orig></orig><reg>que</reg></choice> <lb xml:id="l23"/>itidem vel absolutus vel relativus pro genere loci. Distinguitur autem <lb xml:id="l24"/>ipso facto motus absolutus a relativo in gyrantibus, per conatum rece<lb type="hyphenated" xml:id="l25"/>dendi a centro, quippe qui <del type="over">in</del><add hand="#in" indicator="no" place="over">ex</add> gyratione nudè relativa nullus est, in <lb xml:id="l26"/><add hand="#in" indicator="no" place="interlinear marginRight">relative quiescent<add hand="#in" indicator="no" place="infralinear">ibus</add> permagnus esse potest, ut in corporibus cœlestibus qu<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add hand="#in" indicator="no" place="over">a</add><del type="cancelled"><gap reason="illgblDel" unit="chars" extent="3"/></del> <add indicator="yes" place="supralinear">ex mente</add> Cartesian<add indicator="no" place="inline infralinear">orum</add> quies<add indicator="no" place="inline">cunt,</add> <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="3"/>buntur</del> <add indicator="no" place="infralinear">conantur</add> tamen a sole recedere. Conatus ille <del type="cancelled">qui</del> certus semper et determinatus arguit certam aliquam et determinatam esse motus realis quantitatem in singulis corporibus, a relationibus quæ innumeræ sunt totidem<choice><orig></orig><reg>que</reg></choice> motus relativos constituunt minime pendentem.</add> Porro motum et quietem absolute dict<del type="over">u</del><add hand="#in" indicator="no" place="over">o</add>s non pendere a situ et relatione <lb xml:id="l27"/>corporum ad invicem manifestum est ex eo quod hæ nunquam mutan<lb type="hyphenated" xml:id="l28"/>tur nisi vi in ipsum corpus motum vel quiescens impressa, tali aut<choice><orig>ē</orig><reg>em</reg></choice> <lb xml:id="l29"/>vi semper mutantur; at relativæ mutari possunt vi solummodo <lb xml:id="l30"/>impressa in altera corpora ad quæ fit relatio et non mutari vi <lb xml:id="l31"/>impressa in utra<choice><orig></orig><reg>que</reg></choice>, sic ut situs relativus conservetur. Def. <add hand="#in" indicator="no" place="inline">1</add><del type="over">9</del><add hand="#in" indicator="no" place="over">0</add>. <del type="strikethrough">Celeritas motus</del> <add hand="#in" indicator="no" place="supralinear">Velocitas</add> est quantitas <del type="strikethrough">momentanea</del> translatio<lb type="hyphenated" xml:id="l32"/>nis quoad longitudinem itineris <add hand="#in" indicator="yes" place="supralinear">certo tempore confecti</add>. <add hand="#in" indicator="no" place="inline interlinear">Iter verò est quod corporis puncto me<lb type="hyphenated" xml:id="l33"/>dio describitur a Geometris dicto centro gravitatis. Loquor de motu progressivo.</add> Def. 1<del type="over">0</del><add hand="#in" indicator="no" place="over">1</add>. Quantitas motus est quæ oritur <add hand="#in" indicator="yes" place="supralinear"><del type="cancelled"><gap reason="illgblDel" unit="words" extent="1"/></del></add> ex velocitate et <lb xml:id="l34"/>quantitate corporis translati conjunctim. Æstimatur autem quantitas <lb xml:id="l35"/>corporis ex copia materiæ corporeæ quæ gravitati suæ <del type="cancelled"><unclear reason="del" cert="medium">fer</unclear></del> pro<lb type="hyphenated" xml:id="l36"/>portionalis esse solet. Pendulis æqualibus numerentur oscillati<lb type="hyphenated" xml:id="l37"/>ones corporum duorum ejusdem ponderis, et copia materiæ in <lb xml:id="l38"/>utro<choice><orig></orig><reg>que</reg></choice> erit reciprocè ut numerus oscillation<del type="over">is</del><add hand="#in" indicator="no" place="over">u</add>m eodem tempore <lb xml:id="l39"/>factorum. Def. 1<del type="over">1</del><add hand="#in" indicator="no" place="over">2</add>. <del type="strikethrough">Vis corporis seu</del> <del type="over">c</del><add hand="#in" indicator="no" place="over">C</add>orporis <del type="cancelled">insita et innata</del> <add hand="#in" indicator="yes" place="supralinear">vis insita, innata et essentialis</add> est potentia qua <lb xml:id="l40"/>id <del type="strikethrough">conatur</del> perseverat<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> in statu suo quiescendi vel movendi unifor<lb type="hyphenated" xml:id="l41"/>miter in linea recta, est<choice><orig></orig><reg>que</reg></choice> corporis quantitati proportionalis, <add hand="#in" indicator="no" place="inline interlinear">exercetur verò proportionaliter mutationi <del type="cancelled"><unclear reason="del" cert="low">allatae</unclear></del> <add indicator="no" place="infralinear">status</add>. <del type="strikethrough">Hujus <unclear reason="del" cert="low">generis</unclear></del> <add indicator="yes" place="supralinear">et quatenus exercetur dici potest corporis vis exercita <unclear reason="hand" cert="low">conatus</unclear> et <unclear reason="hand" cert="low">relucto</unclear> <add place="infralinear" indicator="no">Hujus una species</add></add> est vis centrifuga gyrantium.</add> <del type="blockStrikethrough">Def. 1<del type="over">2</del><add hand="#in" indicator="no" place="over">3</add>. Vis motus seu corpori ex motu <add hand="#in" indicator="yes" place="supralinear"><del type="strikethrough">sua</del></add> adventitia est qua <lb xml:id="l42"/>corpus quantitatem <add hand="#in" indicator="yes" place="supralinear">totam</add> sui motus conservare conatur<add hand="#in" indicator="no" place="inline">.</add> <del type="over">et</del><add hand="#in" indicator="no" place="over">Ea</add> vulgo dicitur <lb xml:id="l43"/>imp<del type="over">i</del><add hand="#in" indicator="no" place="over">e</add>tus est<choice><orig></orig><reg>que</reg></choice> motui proportionalis, et pro genere motus vel absoluta <lb xml:id="l44"/>est vel relativa. <add hand="#in" place="inline" indicator="no"><del type="strikethrough">Ad absolutam referenda est vis centrifuga gyrantium</del></add></del> <addSpan spanTo="#addend25v-01" place="p025v" startDescription="f 25v" endDescription="f 26r" hand="#in" resp="#mjh"/> 6 Densitas corporis est quantitas <add indicator="yes" place="supralinear">seu copia</add> materiæ collata cum quantitate <lb xml:id="l45"/><del type="strikethrough">spatij quod</del> occupati spatij. 7. Per pondus intelligo quantitatem <del type="strikethrough">materiæ abstracta consideratione</del> <add indicator="yes" place="supralinear">seu copiam materiæ movendæ abstracta</add> <lb xml:id="l46"/>gravitationis consideratione quoties de gravitantibus non agitur. <lb xml:id="l47"/>Quippe <del type="strikethrough">copiæ materia</del> pondus gravitantium proportionale est quantitati <lb xml:id="l48"/>materiæ, <add indicator="yes" place="supralinear">analoga per se invicem exponare et designare licet. Analogia<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> verò sic collig<del type="cancelled">at</del>itur</add> Pendulis æqualibus numerentur oscillationes corporum duo<lb xml:id="l49"/>rum <del type="cancelled">ejusdem ponderis</del> <add indicator="no" place="supralinear">ejusdem ponderis</add> et copia materiæ <del type="strikethrough">materiæ</del> in utro<choice><orig></orig><reg>que</reg></choice> erit reci<lb xml:id="l50"/>procè ut numerus oscillationum eodem tempore factarum. Experi<lb xml:id="l51"/>mentis autem in auro, argento, plumbo, <del type="cancelled">sale commu</del> vitro, <add indicator="yes" place="supralinear">arena</add> sale commu<lb xml:id="l52"/>ni, aqua, ligno, tri<del type="over">c</del><add indicator="no" place="over">t</add>ico <del type="cancelled">&</del> diligenter <del type="strikethrough">institutis reperi</del> <add indicator="yes" place="supralinear">fàctis incidi</add> semper <add indicator="yes" place="supralinear">in</add> eundem <lb xml:id="l53"/>oscillationum numerum. [Ob hanc analogiam <add indicator="yes" place="supralinear">& defectu vocis commodioris</add> expono et designo quan<lb xml:id="l54"/>titatem materiæ per pondus, etiam in <del type="strikethrough">non gravitantibus</del> corporibus <lb xml:id="l55"/>quorum gravitatio non consideratur.] 8 Locus 9 Quies 10 Motus 11 Velocitas 12 Quantitas motus est quæ oritur ex velocitate et pondere corporis translati <lb xml:id="l56"/>Motus additione corporis alterius tanto cum motu fit duplus et dupli<lb xml:id="l57"/>catata velocitate quadru<del type="over">l</del><add indicator="no" place="over">p</add>lus <anchor xml:id="addend25v-01"/> Def. 1<del type="over">3</del><add hand="#in" indicator="no" place="over">5</add>. Vis <del type="cancelled"><unclear reason="del" cert="low">impaleus</unclear></del> <add hand="#in" indicator="yes" place="supralinear"><del type="cancelled">impressa <gap reason="illgblDel" unit="chars" extent="2"/></del> corpori illata et impressa</add> est qua corpus urgetur mutare statum <lb xml:id="l58"/>suum movendi vel quiescendi est<choice><orig></orig><reg>que</reg></choice> diversarum specierum, <add hand="#in" indicator="yes" place="supralinear"><unclear reason="hand" cert="low">sivit</unclear></add> pulsus seu pressio <lb xml:id="l59"/><add hand="#in" indicator="no" place="infralinear"> percutientis, pressio continua, vis centripeta, resistentia <del type="cancelled"><unclear reason="del" cert="medium">eo</unclear></del> medij <del type="strikethrough"><unclear reason="del" cert="low">eant</unclear> corporis cujusvis alterius</del>. <add hand="#in" indicator="no" place="supralinear">&</add></add> <addSpan spanTo="#addend025v-02" place="p025v" startDescription="f 25v" endDescription="f 26r" hand="#in" resp="#mjh"/> <del type="blockStrikethrough">Def 14 Corporis vis exercita est qua id cona<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del>tur <add indicator="no" place="supralinear"><del type="strikethrough">singulis momentis</del></add> conservare <lb xml:id="l60"/>status sui movendi vel quiescendi partem <del type="strikethrough"><unclear reason="del" cert="medium">amissam</unclear></del> <add indicator="yes" place="supralinear">illam quam singulis momentis amittit</add>, est<choice><orig></orig><reg>que</reg></choice> status illius <lb xml:id="l61"/>mutationi seu parti <add indicator="yes" place="supralinear">singulis momentis</add> amissæ proportionalis, nec improprie <add indicator="yes" place="supralinear">reluctatio vel</add> resistentia <del type="cancelled">dici<lb type="hyphenated" xml:id="l62"/>tur</del> <add indicator="yes" place="supralinear"><del type="strikethrough">vel reluctatio</del></add> corporis dicitur. Hujus <del type="strikethrough"><unclear reason="del" cert="medium">reperienda</unclear></del> <add indicator="no" place="supralinear">una species</add> est vis centrifuga gyrantium.</del> <anchor xml:id="addend025v-02"/> Def. 1<del type="over">4</del><add hand="#in" indicator="no" place="over">6</add>. Vim centripetam appello qua corpus impellitur vel <lb xml:id="l63"/>attrahitur versus punctum aliquod quod ut centrum spectatur. Hujus <lb xml:id="l64"/>generis est gravitas tendens ad centrum terræ, vis magnetica ten<lb type="hyphenated" xml:id="l65"/>dens ad centrum magnetis et vis cœlestis cohibens Planetas re <lb xml:id="l66"/>abeant in tangentibus <del type="strikethrough">orbi terram</del> orbitarum. <del type="strikethrough">Def. 1<del type="over">6</del><add hand="#in" indicator="no" place="over">7</add>. <add hand="#in" indicator="yes" place="inline supralinear">Per medij</add> Resistentia<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="supralinear" hand="#in" indicator="no">m</add> <del type="cancelled">est</del> <add hand="#in" indicator="yes" place="supralinear">in sequentibus intelligo</add> vi<del type="over">m</del><add hand="#in" indicator="no" place="over">s</add> medij regulariter impedientis. Aliam</del> <pb xml:id="p023r" n="23r" facs="#MS-ADD-03965-005-00005.jpg"/><fw type="pag" place="topRight" hand="#unknown">23</fw> <del type="blockStrikethrough"><del type="strikethrough">resistentiam <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="4"/>tibus</del> non considero</del>. <add hand="#in" indicator="no" place="inline infralinear">Sunt et aliæ vires ex corporum <add hand="#in" place="supralinear" indicator="no"><del type="strikethrough"><gap reason="illgblDel" unit="chars" extent="5"/></del></add> elasticitate, mollitie, tenacitate & pendentes quos hic non considero.</add></del> <del type="blockStrikethrough">Def. 16. Momenta quantitatum sunt ipsarum principia gene<lb type="hyphenated" xml:id="l67"/>rantia vel alterantia fluxu continuo: ut tempus præsens præte<lb type="hyphenated" xml:id="l68"/>riti et futuri, motus præsens, præteri et futuri, vis centripeta <lb xml:id="l69"/>aut alia quævis momentanea impetus, punctum lineæ, linea super<lb type="hyphenated" xml:id="l70"/>ficiei, superficies solidi et angulus contactus anguli rectilinei.</del> Def. 1<del type="over">7</del><add hand="#in" indicator="no" place="over">8</add>. Exponentes temporum spatiorum motuum celeritat<choice><orig>ū</orig><reg>um</reg></choice> <lb xml:id="l71"/>et virium sunt quantitates quævis proportionales exponendis Hæc omnia fusius explicare visum est ut Lector <del type="strikethrough">claris</del> <add hand="#in" indicator="yes" place="supralinear"><choice><sic>præjudcijs</sic><corr>præjudicijs</corr></choice> quibusdam vulgaribus liberatus</add> et distinctis <lb xml:id="l72"/>principiorum <del type="over">m</del><add hand="#in" indicator="no" place="over">M</add>ec<add hand="#in" indicator="yes" place="supralinear">h</add>anicorum conceptibus imbutus accederet ad sequentia. <lb xml:id="l73"/>Quantitates autem absolutas et relativas ab invicem <del type="cancelled">acriter</del> <add hand="#in" indicator="no" place="supralinear">sedulò</add> distingue<lb type="hyphenated" xml:id="l74"/>re <del type="cancelled">coactus f<gap reason="illgblDel" unit="chars" extent="2"/></del> <add hand="#in" indicator="no" place="supralinear">recesse f<del type="over"><gap reason="illgblDel" unit="chars" extent="2"/></del><add hand="#in" indicator="no" place="over">ui</add>t</add> eò, quod phænomena omnia prendeant ab absolutis, <lb xml:id="l75"/>vulgus autem qui cogitationes a sensibus abstrahere nesciunt <lb xml:id="l76"/>semper loquuntur de relativis, us<choice><orig></orig><reg>que</reg></choice> adeo ut absurdum foret vel <lb xml:id="l77"/>sapientibus <del type="cancelled">aut</del> <add hand="#in" indicator="yes" place="supralinear">vel etiam</add> <del type="over">p</del><add hand="#in" indicator="no" place="over">P</add>rophetis apud hos aliter loqui. Vnde et sacræ lite<lb type="hyphenated" xml:id="l78"/><del type="over">t</del><add hand="#in" indicator="no" place="over">r</add>æ et S<del type="over">s</del><add hand="#in" indicator="no" place="over">c</add>ripta Theologorum de relativis semper intelligenda sunt, <lb xml:id="l79"/>et crasso laboraret præjudicio qui inde de rerum naturalium <lb xml:id="l80"/>motibus absolutis <add hand="#in" indicator="no" place="supralinear">philosophicis</add> disputationes mover<del type="over">a</del><add hand="#in" indicator="no" place="over">e</add><del type="cancelled">n</del>t. <del type="strikethrough">Perinde est ac si quis <lb xml:id="l81"/>Lusam <add hand="#in" indicator="yes" place="supralinear"><del type="strikethrough">(in <unclear reason="copy" cert="medium">Gemut</unclear>)</del></add> magnitudine non apparente sed absoluta <unclear reason="del" cert="medium">numerari</unclear> inter duo <lb xml:id="l82"/>maxima lumina G<gap reason="illgblDel" unit="chars" extent="4"/> numerari contenderet. <unclear reason="del" cert="medium">Gemut</unclear></del> <ab type="head" rend="center" xml:id="hd2">Leges motus.</ab> Lex 1. Vi insi<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del>ta corpus <del type="cancelled">semper</del> <add hand="#in" indicator="no" place="supralinear">omne</add> perseverare in statu suo quies<lb type="hyphenated" xml:id="l83"/>cendi vel movendi uniformitèr <del type="strikethrough">in linea recta</del> <add hand="#in" indicator="no" place="supralinear">in linea recta</add> nisi quatenus viribus <lb xml:id="l84"/>impressis <del type="cancelled">et impedi<add hand="#in" indicator="yes" place="supralinear"><del type="cancelled">m</del></add>entisur</del> cogitur statum illum mutare. Motus autem <add hand="#in" indicator="no" place="inline marginRight">uniformis hic est duplex, progressivus secundum lineam rectam quam corpus centro suo æquabilitur lato describit & circularis circa axem suum quemvis qui vel quiescit vel motu uniformi latus semper manet <del type="strikethrough">sibi ipsi<gap reason="illgblDel" unit="chars" extent="3"/></del> positionibus suis <del type="cancelled"><gap reason="illgblDel" unit="words" extent="1"/></del> <add hand="#in" indicator="no" place="supralinear">prioribus</add> parallelus.</add> Lex 2. Mutationem motus proportionalem esse vi impressæ et fieri <lb xml:id="l85"/>secundum lineam rectam quâvis illa imprimitur. Hisce duabus Legibus <add hand="#in" indicator="no" place="interlinear marginRight">jam receptissimis Galilæus invenit projectilia gravitate uniformiter et secundum lineas parallelas agente in medio non resistente linea<del type="over">t</del><add hand="#in" indicator="no" place="over">s</add> Parabolica<del type="over">m</del><add hand="#in" indicator="no" place="over">s</add> describere. Et suffragatur experientia nisi quatenus motus projectilium <del type="strikethrough">ab</del> resistentia aeris <del type="strikethrough"><unclear reason="hand" cert="low">retans</unclear></del> aliquantulum retardatur. Ab.</add> Lex 3. Corpus omne tantum pati reactione quantum agit in <lb xml:id="l86"/>alterum. <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="2"/>go</del> <add hand="#in" indicator="yes" place="supralinear">Quicquid premit vel trahit alterum, ab eo tantum premitur vel trahitur.</add> Si vesica aere plena premit vel ferit alteram <lb xml:id="l87"/>sibi consimilem cedet utra<choice><orig></orig><reg>que</reg></choice> æqualiter introrsum. <del type="strikethrough">Si magnestra<lb xml:id="l88"/>hit ferrum ipse vicissim tantum trahitur.</del> Si corpus impingens in <lb xml:id="l89"/>alterum vi sua mutat motum alterius et ipsius motus (<del type="over">vi</del><add hand="#in" indicator="no" place="over">ob</add> æquali<lb type="hyphenated" xml:id="l90"/>tatem pressionis mutuæ) vi alterius tantum mutabitur. Si magnes <lb xml:id="l91"/>trahit ferrum ipse vicissim tantum trahitur, et sic in alijs. Constat <lb xml:id="l92"/><add hand="#in" indicator="no" place="interlinear marginRight">verò hæc Lex per Def. 1<del type="over"><unclear reason="del" cert="medium">3</unclear></del><add hand="#in" indicator="no" place="over">2</add> et 14 in quantum vis corporis ad status sui conservationem exercita sit eadem cum vi in corpus alterum ad illius statum mutandum impressa, et vi priori proportionalis sit mutatio status prioris posteriori ea posterioris.</add> Lex 4. Corporum dato spatio inclusorum eosdem esse motus <lb xml:id="l93"/>inter se sive spatium illud absolutè quiescat sive moveat id perpetuò <pb xml:id="p24r" n="24r" facs="#MS-ADD-03965-005-00007.jpg"/><fw type="pag" place="topRight" hand="#unknown">24</fw> et uniformiter in directum abs<choice><orig></orig><reg>que</reg></choice> motu circulari E. g. Motus rerum <lb xml:id="l94"/>in navi perinde se habent sive navis quiescat sive moveat ea uni<lb type="hyphenated" xml:id="l95"/>formiter in directum. Lex 5. Mutuis corporum actionibus commune centrum gra<lb type="hyphenated" xml:id="l96"/>vitatis non mutare statum suum motus vel quietis. Hæc lex <lb xml:id="l97"/>et duæ superiores se mutuò probant. <del type="blockStrikethrough">Lex 6. Resistentiam medij esse ut medij illius densitas et <lb xml:id="l98"/>sphærici corporis moti superficies et velocitas conjunctim. Hanc <lb xml:id="l99"/>legem exactam esse non affirmo. Sufficit quod sit vero proxima. <lb xml:id="l100"/>Corpora vero sphærica esse suppono in sequentibus, ne opus sit <lb xml:id="l101"/>circumstantias diversarum figurarum considerare</del> <ab type="head" rend="center" xml:id="hd3">Lemmata</ab> Lem. 1. Corpus viribus conjunctis diagonalem parallelo<lb type="hyphenated" xml:id="l102"/>grammi eodem tempore describere quo latera separatis. Si corpus dato tempore vi sola M ferretur <figure rend="floatRight"><graphic url="NATP00091-01.png"/><figDesc/></figure> <lb xml:id="l103"/>ab A ad B et vi sola N ab A ad C, com<lb type="hyphenated" xml:id="l104"/>pleatur parallelogrammum ABDC et vi <lb xml:id="l105"/>utra<choice><orig></orig><reg>que</reg></choice> feretur id eodem tempore ab A ad <lb xml:id="l106"/>D. Nam quoniam vis M agit secundum <lb xml:id="l107"/>lineam AC ipsi BD parallelam, hæc vis nihil mutabit celeri<lb type="hyphenated" xml:id="l108"/>tatem accedendi ad line<del type="over">i</del><add hand="#in" indicator="no" place="over">a</add>m illam BD vi altera impressam. Acce<lb type="hyphenated" xml:id="l109"/>det igitur corpus eodem tempore ad lineam BD sive vis AC im<lb type="hyphenated" xml:id="l110"/>prim<del type="over">i</del><add hand="#in" indicator="no" place="over">a</add>tur sive non, at<choice><orig></orig><reg>que</reg></choice> adeò in fine illius temporis reperietur <lb xml:id="l111"/>alicubi in linea illa BD. Eodem argumento in fine temporis <lb xml:id="l112"/>ejusdem reperietur alicubi in linea CD, et proinde in utrius<choice><orig></orig><reg>que</reg></choice> <lb xml:id="l113"/>lineæ concursu D reperiri necesse est. Lem. 2. Spatium quod corpus urgente quacun<choice><orig></orig><reg>que</reg></choice> vi centri<lb type="hyphenated" xml:id="l114"/>peta ipso motus initio describit, esse in duplicata ratione <lb xml:id="l115"/>temporis. Exponantur tempora per lineas AB, AD datis Ab Ad <lb xml:id="l116"/>proportional<del type="over">i</del><add hand="#in" indicator="no" place="over">e</add>s, et urgente vi centripeta æquabili exponentur <lb xml:id="l117"/>spatia descripta per areas rectilineas ABF ADH perpendiculis </div> </body> </text> </TEI>