Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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      <text>
        <body>
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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/307.jpg" pagenum="279"/>
                  dicatur Y, atque areæ
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  decrementum
                    <emph type="italics"/>
                  RGgr
                    <emph.end type="italics"/>
                  detur, erit
                    <lb/>
                    <arrow.to.target n="note255"/>
                  incrementum areæ Y ut
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  -Y. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note255"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Quod ſi V deſignet vim a gravitate oriundam, arcui deſcribendo
                    <lb/>
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  proportionalem, qua corpus urgetur in
                    <emph type="italics"/>
                  D:
                    <emph.end type="italics"/>
                  & R pro reſiſten­
                    <lb/>
                  tia ponatur: erit V-R vis tota qua corpus urgetur in
                    <emph type="italics"/>
                  D.
                    <emph.end type="italics"/>
                  Eſt
                    <lb/>
                  itaQ.E.I.crementum velocitatis ut V-R & particula illa temporis
                    <lb/>
                  in qua factum eſt conjunctim: Sed & velocitas ipſa eſt ut incre­
                    <lb/>
                  mentum contemporaneum ſpatii deſcripti directe & particula ea­
                    <lb/>
                  dem temporis inverſe. </s>
                  <s>Unde, cum reſiſtentia (per Hypotheſin)
                    <lb/>
                  ſit ut quadratum velocitatis, incrementum reſiſtentiæ (per Lem. </s>
                  <s>II)
                    <lb/>
                  erit ut velocitas & incrementum velocitatis conjunctim, id eſt, ut
                    <lb/>
                  momentum ſpatii & V-R conjunctim; atque adeo, ſi momen­
                    <lb/>
                  tum ſpatii detur, ut V-R; id eſt, ſi pro vi V ſeribatur ejus ex­
                    <lb/>
                  ponens
                    <emph type="italics"/>
                  PIGR,
                    <emph.end type="italics"/>
                  & reſiſtentia R exponatur per aliam aliquam are­
                    <lb/>
                  am Z, ut
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  -Z. </s>
                </p>
                <p type="main">
                  <s>Igitur area
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  per datorum momentorum ſubductionem
                    <lb/>
                  uniformiter decreſcente, creſcunt area Y in ratione
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  -Y,
                    <lb/>
                  & area Z in ratione
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  -Z. </s>
                  <s>Et propterea ſi areæ Y & Z ſi­
                    <lb/>
                  mul incipiant & ſub initio æquales ſint, hæ per additionem æqua­
                    <lb/>
                  lium momentorum pergent eſſe æquales, & æqualibus itidem mo­
                    <lb/>
                  mentis ſubinde decreſcentes ſimul evaneſcent. </s>
                  <s>Et viciſſim, ſi ſimul
                    <lb/>
                  incipiunt & ſimul evaneſcunt, æqualia habebunt momenta & ſem­
                    <lb/>
                  per erunt æquales: id adeo quia ſi reſiſtentia Z augeatur, veloci­
                    <lb/>
                  tas una cum arcu illo
                    <emph type="italics"/>
                  Ca,
                    <emph.end type="italics"/>
                  qui in aſcenſu corporis deſcribitur, dimi­
                    <lb/>
                  nuetur; & puncto in quo motus omnis una cum reſiſtentia ceſſat
                    <lb/>
                  propius accedente ad punctum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  reſiſtentia citius evaneſcet quam
                    <lb/>
                  area Y. </s>
                  <s>Et contrarium eveniet ubi reſiſtentia diminuitur. </s>
                </p>
                <p type="main">
                  <s>Jam vero area Z incipit deſinitque ubi reſiſtentia nulla eſt, hoc
                    <lb/>
                  eſt, in principio & fine motus, ubi arcus
                    <emph type="italics"/>
                  CD, CD
                    <emph.end type="italics"/>
                  arcubus
                    <emph type="italics"/>
                  CB
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  Ca
                    <emph.end type="italics"/>
                  æquantur, adeoque ubi recta
                    <emph type="italics"/>
                  RG
                    <emph.end type="italics"/>
                  incidit in rectas
                    <emph type="italics"/>
                  QE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CT.
                    <emph.end type="italics"/>
                    <lb/>
                  Et area Y ſeu
                    <emph type="italics"/>
                  (OR/OQ)IEF-IGH
                    <emph.end type="italics"/>
                  incipit deſinitque ubi nulla eſt, ad­
                    <lb/>
                  eoque ubi
                    <emph type="italics"/>
                  (OR/OQ)IEF
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IGH
                    <emph.end type="italics"/>
                  æqualia ſunt: hoc eſt (per con­
                    <lb/>
                  ſtructionem) ubi recta
                    <emph type="italics"/>
                  RG
                    <emph.end type="italics"/>
                  incidit in rectas
                    <emph type="italics"/>
                  QE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CT.
                    <emph.end type="italics"/>
                  Proin­
                    <lb/>
                  deque areæ illæ ſimul incipiunt & ſimul evaneſcunt, & propterea
                    <lb/>
                  ſemper ſunt æquales. </s>
                  <s>Igitur area
                    <emph type="italics"/>
                  (OR/OQ)IEF-IGH
                    <emph.end type="italics"/>
                  æqualis eſt
                    <lb/>
                  areæ Z, per quam reſiſtentia exponitur, & propterea eſt ad aream
                    <lb/>
                    <emph type="italics"/>
                  PINM
                    <emph.end type="italics"/>
                  per quam gravitas exponitur, ut reſiſtentia ad gravita­
                    <lb/>
                  tem.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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