Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/241.jpg" pagenum="213"/>
                  ris, decreſcet recta
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  in ratione Geometrica ad modum veloci­
                    <lb/>
                    <arrow.to.target n="note189"/>
                  tatis, & partes rectæ
                    <emph type="italics"/>
                  AC
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                  æqualibus temporibus deſcriptæ decre­
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                  ſcent in eadem ratione. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note189"/>
                  LIBER
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                  SECUNDUS.</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO III. PROBLEMA I.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corporis, cui dum in Medio ſimilari recta aſcendit vel deſcendit,
                    <lb/>
                  reſiſtitur in ratione velocitatis, quodque ab uniformi gravitate
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                  urgetur, definire motum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Corpore aſcendente, ex­
                    <lb/>
                    <figure id="id.039.01.241.1.jpg" xlink:href="039/01/241/1.jpg" number="142"/>
                    <lb/>
                  ponatur gravitas per datum
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                  quodvis rectangulum
                    <emph type="italics"/>
                  BC,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  reſiſtentia Medii initio aſ­
                    <lb/>
                  cenſus per rectangulum
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                    <lb/>
                  ſumptum ad contrarias par­
                    <lb/>
                  tes. </s>
                  <s>Aſymptotis rectangulis
                    <lb/>
                    <emph type="italics"/>
                  AC, CH,
                    <emph.end type="italics"/>
                  per punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  de­
                    <lb/>
                  ſcribatur Hyperbola ſecans per­
                    <lb/>
                  pendicula
                    <emph type="italics"/>
                  DE, de
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  G, g;
                    <emph.end type="italics"/>
                  &
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                  corpus aſcendendo, tempore
                    <emph type="italics"/>
                  DGgd,
                    <emph.end type="italics"/>
                  deſcribet ſpatium
                    <emph type="italics"/>
                  EGge,
                    <emph.end type="italics"/>
                  tem­
                    <lb/>
                  pore
                    <emph type="italics"/>
                  DGBA
                    <emph.end type="italics"/>
                  ſpatium aſcenſus totius
                    <emph type="italics"/>
                  EGB
                    <emph.end type="italics"/>
                  ; tempore
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                    <lb/>
                  ſpatium deſcenſus
                    <emph type="italics"/>
                  BF
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  atque tempore 2
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ſpatium
                    <lb/>
                  deſcenſus 2
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  : & velocitates corporis (reſiſtentiæ Medii
                    <lb/>
                  proportionales) in horum temporum periodis erunt
                    <emph type="italics"/>
                  ABED,
                    <lb/>
                  ABed,
                    <emph.end type="italics"/>
                  nulla,
                    <emph type="italics"/>
                  ABF
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  D, AB
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                  2
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  reſpective; atque maxima
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                  velocitas, quam corpus deſcendendo poteſt acquirere, erit
                    <emph type="italics"/>
                  BC.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Reſolvatur enim rectan­
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                    <figure id="id.039.01.241.2.jpg" xlink:href="039/01/241/2.jpg" number="143"/>
                    <lb/>
                  gulum
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  in rectangula
                    <lb/>
                  innumera
                    <emph type="italics"/>
                  Ak, Kl, Lm, Mn,
                    <emph.end type="italics"/>
                    <lb/>
                  &c. </s>
                  <s>quæ ſint ut incrementa
                    <lb/>
                  velocitatum æqualibus tot­
                    <lb/>
                  idem temporibus facta; & e­
                    <lb/>
                  runt nihil,
                    <emph type="italics"/>
                  Ak, Al, Am, An,
                    <emph.end type="italics"/>
                    <lb/>
                  &c. </s>
                  <s>ut velocitates totæ, at­
                    <lb/>
                  que adeo (per Hypotheſin)
                    <lb/>
                  ut reſiſtentiæ Medii princi­
                    <lb/>
                  pio ſingulorum temporum
                    <lb/>
                  æqualium. </s>
                  <s>Fiat
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  ABHC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ABkK,
                    <emph.end type="italics"/>
                  ut vis gra­
                    <lb/>
                  vitatis ad reſiſtentiam in principio temporis ſecundi, deque vi gravi-</s>
                </p>
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          </chap>
        </body>
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