Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                  PROPOSITIO XCVII. PROBLEMA XLVII.
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                  Poſito quod ſinus incidentiæ in ſuperficiem aliquam ſit ad ſinum e­
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                  mergentiæ in data ratione, quodQ.E.I.curvatio viæ corporum
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                  juxta ſuperficiem illam fiat in ſpatio breviſſimo, quod ut pun­
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                  ctum conſiderari poſſit; determinare ſuperficiem quæ corpuſcula
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                  omnia de loco dato ſucceſſive manantia convergere faciat ad
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                  alium locum datum.
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                  </s>
                </p>
                <p type="main">
                  <s>Sit
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                  A
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                  locus a quo corpuſcula divergunt;
                    <emph type="italics"/>
                  B
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                  locus in quem con­
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                  vergere debent;
                    <emph type="italics"/>
                  CDE
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                  curva linea quæ circa axem
                    <emph type="italics"/>
                  AB
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                  revoluta
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                  deſcribat ſuperficiem quæſitam;
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                  D, E
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                  curvæ illius puncta duo quæ­
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                  vis; &
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                  EF, EG
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                  perpendicula in corporis vias
                    <emph type="italics"/>
                  AD, DB
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                  demiſſa. </s>
                  <s>
                    <lb/>
                  Accedat punctum
                    <emph type="italics"/>
                  D
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                  ad punctum
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                  E
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                  ; & lineæ
                    <emph type="italics"/>
                  DF
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                  qua
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                  AD
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                  au­
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                  getur, ad lineam
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                  DG
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                  qua
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                  DB
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                  diminuitur, ratio ultima erit ea­
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                  dem quæ ſinus incidentiæ ad ſinum emergentiæ. </s>
                  <s>Datur ergo ratio
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                  incrementi lineæ
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                  AD
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                  ad decrementum lineæ
                    <emph type="italics"/>
                  DB
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                  ; & propterea
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                  ſi in axe
                    <emph type="italics"/>
                  AB
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                  ſumatur ubivis punctum
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                  C,
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                  per quod curva
                    <emph type="italics"/>
                  CDE
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                    <lb/>
                  tranſire debet, & capiatur ipſius
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                  AC
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                  incrementum
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                  CM,
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                  ad ipſius
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                    <emph type="italics"/>
                  BC
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                  decrementum
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                  CN
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                  in data illa ratione; centriſque
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                  A, B,
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                  & in­
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                  tervallis
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                  AM, BN
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                  deſcribantur circuli duo ſe mutuo ſecantes in
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                    <emph type="italics"/>
                  D:
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                  punctum illud
                    <emph type="italics"/>
                  D
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                  tanget curvam quæſitam
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                  CDE,
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                  eandemque
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                  ubivis tangendo determinabit.
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                    <expan abbr="q.">que</expan>
                  E. I.
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                <p type="main">
                  <s>
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                  Corol.
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                  1. Faciendo autem ut punctum
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                  A
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                  vel
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                  B
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                  nunc abeat in in­
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                  finitum, nunc migret ad alteras partes puncti
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                  C,
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                  habebuntur Fi­
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                  guræ illæ omnes quas
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                  Carteſius
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                  in Optica & Geometria ad Refra­
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                  ctiones expoſuit. </s>
                  <s>Quarum inventionem cum
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                  Carteſius
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                  maximi
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                  fecerit & ſtudioſe celaverit, viſum fuit hac propoſitione expo­
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                  nere. </s>
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