Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/140.jpg" pagenum="112"/>
                    <arrow.to.target n="note88"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note88"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXIX. PROBLEMA XXVII.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Poſita cujuſcunque generis Vi centripeta, & conceſſis figurarum
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                  curvilinearum quadraturis, requiritu, corporis recta aſcenden­
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                  tis vel deſcendentis tum Velocitas in locis ſingulis, tum Tempus
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                  quo corpus ad locum quemvis perveniet: Et contra.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>De loco quovis
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                  A
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                  in recta
                    <emph type="italics"/>
                  ADEC
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                  cadat corpus
                    <emph type="italics"/>
                  E,
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                  deque loco
                    <lb/>
                  ejus
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  erigatur ſemper perpendicularis
                    <emph type="italics"/>
                  EG,
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                  vi centripetæ in loco
                    <lb/>
                  illo ad centrum
                    <emph type="italics"/>
                  C
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                  tendenti proportio­
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                    <figure id="id.039.01.140.1.jpg" xlink:href="039/01/140/1.jpg" number="88"/>
                    <lb/>
                  nalis: Sitque
                    <emph type="italics"/>
                  BFG
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                  linea curva quam
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                  punctum
                    <emph type="italics"/>
                  G
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                  perpetuo tangit. </s>
                  <s>Coinci­
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                  dat autem
                    <emph type="italics"/>
                  EG
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                  ipſo motus initio cum
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                  perpendiculari
                    <emph type="italics"/>
                  AB,
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                  & erit corporis Ve­
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                  locitas in loco quovis
                    <emph type="italics"/>
                  E
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                  ut areæ cur­
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                  vilineæ
                    <emph type="italics"/>
                  ABGE
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                  latus quadratum.
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                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. I.
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                  </s>
                </p>
                <p type="main">
                  <s>In
                    <emph type="italics"/>
                  EG
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                  capiatur
                    <emph type="italics"/>
                  EM
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                  lateri quadra­
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                  to areæ
                    <emph type="italics"/>
                  ABGE
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                  reciproce proportio­
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                  nalis, & ſit
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                  ALM
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                  linea curva quam
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                  punctum
                    <emph type="italics"/>
                  M
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                  perpetuotangit, & erit Tem­
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                  pus quo corpus cadendo deſcribit li­
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                  neam
                    <emph type="italics"/>
                  AE
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                  ut area curvilinea
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                  ALME.
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                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Etenim in recta
                    <emph type="italics"/>
                  AE
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                  capiatur linea
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                  quam minima
                    <emph type="italics"/>
                  DE
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                  datæ longitudinis,
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                  ſitque
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                  DLF
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                  locus lineæ
                    <emph type="italics"/>
                  EMG
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                  ubi
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                  corpus verſabatur in
                    <emph type="italics"/>
                  D
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                  ; & ſi ea ſit vis centripeta, ut areæ
                    <emph type="italics"/>
                  ABGE
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                    <lb/>
                  latus quadratum ſit ut deſcendentis velocitas, erit area ipſa in du­
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                  plicata ratione velocitatis, id eſt, ſi pro velocitatibus in
                    <emph type="italics"/>
                  D
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                  &
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                  E
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                    <lb/>
                  ſcribantur V & V+I, erit area
                    <emph type="italics"/>
                  ABFD
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                  ut VV, & area
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                  ABGE
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                  ut
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                  VV+2 VI+II, & diviſim area
                    <emph type="italics"/>
                  DFGE
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                  ut 2 VI+II, adeoque
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                  (
                    <emph type="italics"/>
                  DFGE/DE
                    <emph.end type="italics"/>
                  ) ut (2VI+II/
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ), id eſt, ſi primæ quantitatum naſcentium
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                  rationes ſumantur, longitudo
                    <emph type="italics"/>
                  DF
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                  ut quantitas (2VI/
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ), adeoque e­
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                  tiam ut quantitatis hujus dimidium (IXV/
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ). Eſt autem tempus quo </s>
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