Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  LIBER
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                  PRIMUS.</s>
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                  SECTIO VII.
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                  De Corporum Aſcenſu & Deſcenſu Rectilineo.
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                  PROPOSITIO XXXII. PROBLEMA XXIV.
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                  Poſito quod Vis centripeta ſit reciproce proportionalis quadrato di­
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                  ſtantiæ loeorum a centro, Spatia definire quæ corpus recta cadendo
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                  datis temporibus deſcribit.
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                  Cas.
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                  1. Si Corpus non cadit perpendicu­
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                  lariter deſcribet id, per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XIII,
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                  Sectionem aliquam Conicam cujus umbili­
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                  cus congruit cum centro virium. </s>
                  <s>Sit Sec­
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                  tio illa Conica
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                  ARPB
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                  & umbilicus ejus
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                  S.
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                  Et primo ſi Figura Ellipſis eſt, ſuper hu­
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                  jus axe majore
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                  AB
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                  deſcribatur Semicirculus
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                    <emph type="italics"/>
                  ADB,
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                  & per corpus decidens tranſeat rec­
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                  ta
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                  DPC
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                  perpendicularis ad axem; actiſque
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                    <emph type="italics"/>
                  DS, PS
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                  erit area
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                  ASD
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                  areæ
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                  ASP
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                  at­
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                  que adeo etiam tempori proportionalis. </s>
                  <s>Ma­
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                  nente axe
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                  AB
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                  minuatur perpetuo latitudo
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                  Ellipſeos, & ſemper manebit area
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                  ASD
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                  tempori proportionalis. </s>
                  <s>Minuatur latitudo
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                  illa in infinitum: &, Orbe
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                  APB
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                  jam coin­
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                  cidente cum axe
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                  AB
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                  & umbilico
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                  S
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                  cum
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                  axis termino
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                  B,
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                  deſcendet corpus in recta
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                    <emph type="italics"/>
                  AC,
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                  & area
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                  ABD
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                  evadet tempori pro­
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                  portionalis. </s>
                  <s>Dabitur itaque Spatium
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                  AC,
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                  quod corpus de loco
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                  A
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                  perpendiculariter
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                  cadendo tempore dato deſcribit, ſi modo tempori proportiona­
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                  lis capiatur area
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                  ABD,
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                  & a puncto
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                  D
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                  ad rectam
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                  AB
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                  demit­
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                  tatur perpendicularis
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                  DC.
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                  E. I.
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