Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/168.jpg" pagenum="140"/>
                    <arrow.to.target n="note116"/>
                  dæ & accelerationes ſubſequentes, his partibus proportionales, ſunt
                    <lb/>
                  etiam ut totæ; & ſic deinceps. </s>
                  <s>Sunt igitur accelerationes atque
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                  adeo velocitates genitæ & partes his velocitatibus deſcriptæ par­
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                  teſQ.E.D.ſcribendæ, ſemper ut totæ; & propterea partes deſcriben­
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                  dæ datam ſervantes rationem ad invicem ſimul evaneſcent, id eſt,
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                  corpora duo oſcillantia ſimul pervenient ad perpendiculum
                    <emph type="italics"/>
                  AR.
                    <emph.end type="italics"/>
                    <lb/>
                  Cumque viciſſim aſcenſus perpendiculorum de loco inſimo
                    <emph type="italics"/>
                  R,
                    <emph.end type="italics"/>
                  per
                    <lb/>
                  eoſdem arcus Cycloidales motu retrogrado facti, retardentur in
                    <lb/>
                  locis ſingulis a viribus iiſdem a quibus deſcenſus accelerabantur,
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                  patet velocitates aſcenſuum ac deſcenſuum per eoſdem arcus fa­
                    <lb/>
                  ctorum æquales eſſe, atque adeo temporibus æqualibus fieri; &
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                  propterea, cum Cycloidis partes duæ
                    <emph type="italics"/>
                  RS
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  RQ
                    <emph.end type="italics"/>
                  ad utrumque per­
                    <lb/>
                  pendiculi latus jacentes ſint ſimiles & æquales, pendula duo oſcil­
                    <lb/>
                  lationes ſuas tam totas quam dimidias iiſdem temporibus ſemper
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                  peragent.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note116"/>
                  DE MOTU
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                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Vis qua corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  in loco quovis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  acceleratur vel retar­
                    <lb/>
                  tur in Cycloide, eſt ad totum corporis ejuſdem Pondus in loco
                    <lb/>
                  altiſſimo
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                  ut Cycloidis arcus
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  ad ejuſdem arcum
                    <emph type="italics"/>
                  SR
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  QR.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LII. PROBLEMA XXXIV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Definire & Velocitates Pendulorum in locis ſingulis, & Tempora
                    <lb/>
                  quibus tum oſcillationes totæ, tum ſingulæ oſcillationum partes
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                  peraguntur.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Centro quovis
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  Cycloidis arcum
                    <emph type="italics"/>
                  RS
                    <emph.end type="italics"/>
                  æquante,
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                  deſcribe ſemicirculum
                    <emph type="italics"/>
                  HKMG
                    <emph.end type="italics"/>
                  ſemidiametro
                    <emph type="italics"/>
                  GK
                    <emph.end type="italics"/>
                  biſectum. </s>
                  <s>Et
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                  ſi vis centripeta, diſtantiis loeorum a centro proportionalis, tendat
                    <lb/>
                  ad centrum
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  ſitque ea in perimetro
                    <emph type="italics"/>
                  HIK
                    <emph.end type="italics"/>
                  æqualis vi centripetæ
                    <lb/>
                  in perimetro Globi
                    <emph type="italics"/>
                  QOS (Vide Fig. </s>
                  <s>Prop.
                    <emph.end type="italics"/>
                  L.) ad ipſius cen­
                    <lb/>
                  trum tendenti; & eodem tempore quo pendulum
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  dimittitur e
                    <lb/>
                  loco ſupremo
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  cadat corpus aliquod
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  ab
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  G:
                    <emph.end type="italics"/>
                  quoniam
                    <lb/>
                  vires quibus corpora urgentur ſunt æquales ſub initio & ſpatiis
                    <lb/>
                  deſcribendis
                    <emph type="italics"/>
                  TR, LG
                    <emph.end type="italics"/>
                  ſemper proportionales, atque adeo, ſi æ­
                    <lb/>
                  quantur
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  LG,
                    <emph.end type="italics"/>
                  æquales in locis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  ; patet corpora illa
                    <lb/>
                  deſcribere ſpatia
                    <emph type="italics"/>
                  ST, HL
                    <emph.end type="italics"/>
                  æqualia ſub initio, adeoque ſubinde per­
                    <lb/>
                  gere æqualiter urgeri, & æqualia ſpatia deſcribere. </s>
                  <s>Quare, per Prop. </s>
                  <s>
                    <lb/>
                  XXXVIII, tempus quo corpus deſcribit arcum
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  eſt ad tempus </s>
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