Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/048.jpg" pagenum="20"/>
              ſi in vacuo cecidiſſet de loco
                <emph type="italics"/>
              T.
                <emph.end type="italics"/>
              Exponatur igitur hæc velocitas
                <lb/>
                <arrow.to.target n="note9"/>
              per chordam arcus
                <emph type="italics"/>
              TA.
                <emph.end type="italics"/>
              Nam velocitatem Penduli in puncto in­
                <lb/>
              fimo eſſe ut chordam arcus quem cadendo deſcripſit, Propoſitio eſt
                <lb/>
              eſt Geometris notiſſima. </s>
              <s>Poſt reflexionem perveniat corpus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ad
                <lb/>
              locum
                <emph type="italics"/>
              s,
                <emph.end type="italics"/>
              & corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ad locum
                <emph type="italics"/>
              k.
                <emph.end type="italics"/>
              Tollatur corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              & invenia­
                <lb/>
              tur locus
                <emph type="italics"/>
              v
                <emph.end type="italics"/>
              ; a quo ſi corpus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              demittatur & poſt unam oſcillatio­
                <lb/>
              nem redeat ad locum
                <emph type="italics"/>
              r,
                <emph.end type="italics"/>
              ſit
                <emph type="italics"/>
              st
                <emph.end type="italics"/>
              pars quarta ipſius
                <emph type="italics"/>
              rv
                <emph.end type="italics"/>
              ſita in medio,
                <lb/>
              ita videlicet ut
                <emph type="italics"/>
              rs
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              tu
                <emph.end type="italics"/>
              æquentur; & per chordam arcus
                <emph type="italics"/>
              tA
                <emph.end type="italics"/>
              ex­
                <lb/>
              ponatur velocitas quam corpus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              proxime poſt reflexionem habuit
                <lb/>
              in loco
                <emph type="italics"/>
              A.
                <emph.end type="italics"/>
              Nam
                <emph type="italics"/>
              t
                <emph.end type="italics"/>
              erit locus ille verus & correctus, ad quem cor­
                <lb/>
              pus
                <emph type="italics"/>
              A,
                <emph.end type="italics"/>
              ſublata aeris reſiſtentia, aſcendere debuiſſet: Simili me­
                <lb/>
              thodo corrigendus erit locus
                <emph type="italics"/>
              k,
                <emph.end type="italics"/>
              ad quem corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              aſcendit, & in­
                <lb/>
              veniendus locus
                <emph type="italics"/>
              l,
                <emph.end type="italics"/>
              ad quem corpus illud aſcendere debuiſſet in va­
                <lb/>
              cuo. </s>
              <s>Hoc pacto experiri licet omnia perinde ac ſi in vacuo con­
                <lb/>
              ſtituti eſſemus. </s>
              <s>Tandem ducendum erit corpus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              in chordam ar­
                <lb/>
              cus
                <emph type="italics"/>
              TA
                <emph.end type="italics"/>
              (quæ velocitatem ejus exhibet) ut habeatur motus ejus in
                <lb/>
              loco
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              proxime ante reflexionem; deinde in chordam arcus
                <emph type="italics"/>
              tA,
                <emph.end type="italics"/>
              ut
                <lb/>
              habeatur motus ejus in loco
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              proxime poſt reflexionem. </s>
              <s>Et ſic
                <lb/>
              corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ducendum erit in chordam arcus
                <emph type="italics"/>
              Bb,
                <emph.end type="italics"/>
              ut habeatur motus
                <lb/>
              ejus proxime poſt reflexionem. </s>
              <s>Et ſimili methodo, ubi corpora duo
                <lb/>
              ſimul demittuntur de locis diverſis, inveniendi ſunt motus
                <expan abbr="utriuſq;">utriuſque</expan>
                <lb/>
              tam ante, quam poſt reflexionem; & tum demum conferendi ſunt
                <lb/>
              motus inter ſe & colligendi effectus reflexionis. </s>
              <s>Hoc modo in
                <lb/>
              Pendulis pedum decem rem tentando, idQ.E.I. corporibus tam
                <lb/>
              inæqualibus quam æqualibus, & faciendo ut corpora de intervallis
                <lb/>
              ampliſſimis, puta pedum octo vel duodecim vel ſexdecim, concurre­
                <lb/>
              rent; reperi ſemper ſine errore trium digitorum in menſuris, ubi
                <lb/>
              corpora ſibi mutuo directe occurrebant, quod æquales erant muta­
                <lb/>
              tiones motuum corporibus in partes contrarias illatæ, atque adeo
                <lb/>
              quod actio & reactio ſemper
                <lb/>
                <figure id="id.039.01.048.1.jpg" xlink:href="039/01/048/1.jpg" number="4"/>
                <lb/>
              erant æquales. </s>
              <s>Ut ſi corpus
                <lb/>
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              incidebat in corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              cum
                <lb/>
              novem partibus motus, & a­
                <lb/>
              miſſis ſeptem partibus perge­
                <lb/>
              bat poſt reflexionem cum du­
                <lb/>
              abus; corpus
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              reſiliebat cum
                <lb/>
              partibus iſtis ſeptem. </s>
              <s>Si cor­
                <lb/>
              pora obviam ibant
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              cum
                <lb/>
              duodecim partibus &
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              cum ſex, & redibat
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              cum duabus; redi­
                <lb/>
              bat
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              cum octo, facta detractione partium quatuordecim utrin­
                <lb/>
              que. </s>
              <s>De motu ipſius
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ſubducantur partes duodecim, & reſtabit </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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