Newton, Isaac, Philosophia naturalis principia mathematica, 1713
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                  ſitione XXV conſtructa & demonſtrata ſunt, erit vis qua corpus
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                  olcnlans urgetur in loco quovis
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                  D,
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                  ad vim reſiſtentiæ ut arcus
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                    <emph type="italics"/>
                  CD
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                  ad arcum
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                  CO,
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                  qui ſemiſſis eſt differentiæ illius
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                  Aa.
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                  Ideoque
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                  vis qua corpus oſcillans urgetur in Cycloidis principio ſeu puncto
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                  altiſſimo, id eſt, vis gravitatis, erit ad reſiſtentiam ut arcus Cy­
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                  cloidis inter punctum illud ſupremum & punctum infimum
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                  C
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                  ad
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                  arcum
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                  CO
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                  ; id eſt (ſi arcus duplicentur) ut Cycloidis totius arcus,
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                  ſeu dupla penduli longitudo, ad arcum
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                  Aa. </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. D.
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                  LIBER
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                  SECUNDUS.</s>
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                  PROPOSITIO XXIX. PROBLEMA VI.
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                  Poſito quod Corpori in Cycloide oſcillanti reſiſtitur in duplicata ra­
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                  tione velocitatis: invenire reſiſtentiam in locis ſingulis.
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                  <s>Sit
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                  Ba
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                  (Fig. </s>
                  <s>Prop. </s>
                  <s>XXV) arcus oſcillatione integra deſcriptus,
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                  ſitque
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                  C
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                  infimum Cycloidis punctum, &
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                  CZ
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                  ſemiſſis arcus Cycloi­
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                  dis totius, longitudini Penduli æqualis; & quæratur reſiſtentia cor­
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                  poris in loco quovis
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                  D.
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                  Secetur recta infinita
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                  OQ
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                  in punctis
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                  O,
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                  C, P, Q,
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                  ea lege, ut (ſi erigantur perpendicula
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                  OK, CT, PI, QE,
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                  centroque
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                  O
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                  & Aſymptotis
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                  OK, OQ
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                  deſcribatur Hyperbola
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                  TIGE
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                  ſecans perpendicula
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                  CT, PI, QE
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                  in
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                  T, I
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                  &
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                  E,
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                  & per punctum
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                  I
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                  agatur
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                  KF
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                  parallela Aſymptoto
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                  OQ
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                  occurrens Aſymptoto
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                  OK
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                  in
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                    <emph type="italics"/>
                  K,
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                  & perpendiculis
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                  CT
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                  &
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                  QE
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                  in
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                  L
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                  &
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                  F
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                  ) fuerit area Hyperboliea
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                    <emph type="italics"/>
                  PIEQ
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                  ad aream Hyperbolicam
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                  PITC
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                  ut arcus
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                  BC
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                  deſcenſu cor­
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                  poris deſcriptus ad arcum
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                  Ca
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                  aſcenſu deſcriptum, & area
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                  IEF
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                  ad </s>
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