Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                    <pb xlink:href="039/01/246.jpg" pagenum="218"/>
                    <arrow.to.target n="note194"/>
                  datur latus rectum Parabolæ, ut
                    <lb/>
                  notum eſt. </s>
                  <s>Et ſumendo 2
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                    <lb/>
                  ad latus illud rectum, ut eſt vis
                    <lb/>
                  gravitatis ad vim reſiſtentiæ,
                    <lb/>
                  datur
                    <emph type="italics"/>
                  DP.
                    <emph.end type="italics"/>
                  Dein ſecando
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                    <lb/>
                  in
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  CPXAC
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                  ad
                    <lb/>
                    <emph type="italics"/>
                  DPXDA
                    <emph.end type="italics"/>
                  in eadem illa rati­
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                  one gravitatis ad reſiſtentiam,
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                  dabitur punctum
                    <emph type="italics"/>
                  A.
                    <emph.end type="italics"/>
                  Et inde
                    <lb/>
                  datur Curva
                    <emph type="italics"/>
                  DraF.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note194"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  5. Et contra, ſi datur
                    <lb/>
                    <figure id="id.039.01.246.1.jpg" xlink:href="039/01/246/1.jpg" number="147"/>
                    <lb/>
                  Curva
                    <emph type="italics"/>
                  DraF,
                    <emph.end type="italics"/>
                  dabitur & ve­
                    <lb/>
                  locitas corporis & reſiſtentia
                    <lb/>
                  Medii in locis ſingulis
                    <emph type="italics"/>
                  r.
                    <emph.end type="italics"/>
                  Nam
                    <lb/>
                  ex data ratione
                    <emph type="italics"/>
                  CPXAC
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  DPXDA,
                    <emph.end type="italics"/>
                  datur tum reſiſten­
                    <lb/>
                  tia Medii ſub initio motus, tum
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                  latus rectum Parabolæ: & inde
                    <lb/>
                  datur etiam velocitas ſub initio
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                  motus. </s>
                  <s>Deinde ex longitudine
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                  tangentis
                    <emph type="italics"/>
                  rL,
                    <emph.end type="italics"/>
                  datur & huic
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                  proportionalis velocitas, & ve­
                    <lb/>
                  locitati proportionalis reſiſten­
                    <lb/>
                  tia in loco quovis
                    <emph type="italics"/>
                  r.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Cum autem longitu­
                    <lb/>
                  do 2
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  ſit ad latus rectum
                    <lb/>
                  Parabolæ ut gravitas ad reſiſtentiam in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ; & ex aucta velocitate
                    <lb/>
                  augeatur reſiſtentia in eadem ratione, at latus rectum Parabolæ au­
                    <lb/>
                  geatur in ratione illa duplicata: patet longitudinem 2
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                  augeri
                    <lb/>
                  in ratione illa ſimplici, adeoque velocitati ſemper proportionalem
                    <lb/>
                  eſſe, neque ex angulo
                    <emph type="italics"/>
                  CDP
                    <emph.end type="italics"/>
                  mutato augeri vel minui, niſi mu­
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                  tetur quoque velocitas. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. Unde liquet methodus determinandi Curvam
                    <emph type="italics"/>
                  DraF
                    <emph.end type="italics"/>
                    <lb/>
                  ex Phænomenis quamproxime, & inde colligendi reſiſtentiam &
                    <lb/>
                  velocitatem quacum corpus projicitur. </s>
                  <s>Projiciantur corpora duo
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                  ſimilia & æqualia eadem cum velocitate, de loco
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  ſecundum
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                  angulos diverſos
                    <emph type="italics"/>
                  GDP, cDp
                    <emph.end type="italics"/>
                  (minuſcularum literarum locis ſub­
                    <lb/>
                  intellectis) & cognoſcantur loca
                    <emph type="italics"/>
                  F, f,
                    <emph.end type="italics"/>
                  abi incidunt in horizontale
                    <lb/>
                  planum
                    <emph type="italics"/>
                  DC.
                    <emph.end type="italics"/>
                  Tum, aſſumpta quacunque longitudine pro
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  Dp,
                    <emph.end type="italics"/>
                  fingatur quod reſiſtentia in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ſit ad gravitatem in ra-</s>
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