Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/252.jpg" pagenum="224"/>
                    <arrow.to.target n="note200"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note200"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Et ſi Globi moveantur in Mediis diverſis; ſpatium in
                    <lb/>
                  Medio, quod cæteris paribus magis reſiſtit, diminuendum erit in
                    <lb/>
                  ratione majoris reſiſtentiæ. </s>
                  <s>Tempus enim (per hanc Propoſitio­
                    <lb/>
                  nem) diminuetur in ratione reſiſtentiæ auctæ, & ſpatium in ra­
                    <lb/>
                  tione temporis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA II.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Momentum Genitæ æquatur Momentis laterum ſingulorum gene­
                    <lb/>
                  rantium in eorundem laterum indices dignitatum & coefficien­
                    <lb/>
                  tia continue ductis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Genitam voco quantitatem omnem quæ ex lateribus vel termi­
                    <lb/>
                  nis quibuſcunque, in Arithmetica per multiplicationem, diviſionem,
                    <lb/>
                  & extractionem radicum; in Geometria per inventionem vel con­
                    <lb/>
                  tentorum & laterum, vel extremarum & mediarum proportionalium,
                    <lb/>
                  abſque additione & ſubductione generatur. </s>
                  <s>Ejuſmodi quantita­
                    <lb/>
                  tes ſunt Facti, Quoti, Radices, Rectangula, Quadrata, Cubi, Latera
                    <lb/>
                  quadrata, Latera cubica, & ſimiles. </s>
                  <s>Has quantitates ut indeterminatas
                    <lb/>
                  & inſtabiles, & quaſi motu fluxuve perpetuo creſcentes vel decre­
                    <lb/>
                  ſcentes, hic conſidero; & earum incrementa vel decrementa momen­
                    <lb/>
                  tanea ſub nomine Momentorum intelligo: ita ut incrementa pro
                    <lb/>
                  momentis addititiis ſeu affirmativis, ac decrementa pro ſubductitiis
                    <lb/>
                  ſeu negativis habeantur. </s>
                  <s>Cave tamen intellexeris particulas fiNI­
                    <lb/>
                  tas. </s>
                  <s>Particulæ finitæ non ſunt momenta, ſed quantitates ipſæ ex
                    <lb/>
                  momentis genitæ. </s>
                  <s>Intelligenda ſunt principia jamjam naſcentia fi­
                    <lb/>
                  nitarum magnitudinum. </s>
                  <s>Neque enim ſpectatur in hoc Lemmate
                    <lb/>
                  magnitudo momentorum, ſed prima naſcentium proportio. </s>
                  <s>Eo­
                    <lb/>
                  dem recidit ſi loco momentorum uſurpentur vel velocitates incre­
                    <lb/>
                  mentorum ac decrementorum, (quas etiam motus, mutationes
                    <lb/>
                  & fluxiones quantitatum nominare licet) vel finitæ quævis quanti­
                    <lb/>
                  tates velocitatibus hiſce proportionales. </s>
                  <s>Lateris autem cujuſque
                    <lb/>
                  generantis Coefficiens eſt quantitas, quæ oritur applicando GeNI­
                    <lb/>
                  tam ad hoc latus. </s>
                </p>
                <p type="main">
                  <s>Igitur ſenſus Lemmatis eſt, ut, ſi quantitatum quarumcunque
                    <lb/>
                  perpetuo motu creſcentium vel decreſcentium A, B, C, &c. </s>
                  <s>mo­
                    <lb/>
                  menta, vel mutationum velocitates dicantur
                    <emph type="italics"/>
                  a, b, c,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>momentum
                    <lb/>
                  vel mutatio geniti rectanguli AB fuerit
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  B+
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  A, & geniti con­
                    <lb/>
                  tenti ABC momentum fuerit
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  BC+
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  AC+
                    <emph type="italics"/>
                  c
                    <emph.end type="italics"/>
                  AB: & genitarum </s>
                </p>
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