Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/129.jpg" pagenum="101"/>
                  Quo facto, cape
                    <emph type="italics"/>
                  GK
                    <emph.end type="italics"/>
                  in ratione ad Rotæ perimetrum
                    <emph type="italics"/>
                  GEFG,
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <arrow.to.target n="note77"/>
                  eſt tempus quo corpus progrediendo ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  deſcripſit arcum
                    <emph type="italics"/>
                  AP,
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  tempus revolutionis unius in Ellipſi. </s>
                  <s>Erigatur perpendiculum
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                    <lb/>
                  occurrens Trochoidi in
                    <emph type="italics"/>
                  L,
                    <emph.end type="italics"/>
                  & acta
                    <emph type="italics"/>
                  LP
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  KG
                    <emph.end type="italics"/>
                  parallela occurret
                    <lb/>
                  Ellipſi in corporis loco quæſito
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note77"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>Nam centro
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  deſcribatur ſemicirculus
                    <emph type="italics"/>
                  AQB,
                    <emph.end type="italics"/>
                    <lb/>
                  & arcui
                    <emph type="italics"/>
                  AQ
                    <emph.end type="italics"/>
                  occurrat
                    <emph type="italics"/>
                  LP
                    <emph.end type="italics"/>
                  producta in
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                  junganturque
                    <emph type="italics"/>
                  SQ,
                    <expan abbr="Oq.">Oque</expan>
                    <emph.end type="italics"/>
                    <lb/>
                  Arcui
                    <emph type="italics"/>
                  EFG
                    <emph.end type="italics"/>
                  occurrat
                    <emph type="italics"/>
                  OQ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  F,
                    <emph.end type="italics"/>
                  & in eandem
                    <emph type="italics"/>
                  OQ
                    <emph.end type="italics"/>
                  demittatur per­
                    <lb/>
                  pendiculum
                    <emph type="italics"/>
                  SR.
                    <emph.end type="italics"/>
                  Area
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                  eſt ut area
                    <emph type="italics"/>
                  AQS,
                    <emph.end type="italics"/>
                  id eſt, ut diffe­
                    <lb/>
                  rentia inter ſectorem
                    <emph type="italics"/>
                  OQA
                    <emph.end type="italics"/>
                  & triangulum
                    <emph type="italics"/>
                  OQS,
                    <emph.end type="italics"/>
                  ſive ut differen­
                    <lb/>
                  tia rectangulorum 1/2
                    <emph type="italics"/>
                  OQXAQ
                    <emph.end type="italics"/>
                  & 1/2
                    <emph type="italics"/>
                  OQXSR,
                    <emph.end type="italics"/>
                  hoc eſt, ob datam
                    <lb/>
                  1/2
                    <emph type="italics"/>
                  OQ,
                    <emph.end type="italics"/>
                  ut differentia inter arcum
                    <emph type="italics"/>
                  AQ
                    <emph.end type="italics"/>
                  & rectam
                    <emph type="italics"/>
                  SR,
                    <emph.end type="italics"/>
                  adeoque (ob
                    <lb/>
                  æqualitatem datarum rationum
                    <emph type="italics"/>
                  SR
                    <emph.end type="italics"/>
                  ad ſinum arcus
                    <emph type="italics"/>
                  AQ, OS
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OA,
                    <lb/>
                  OA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OG, AQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GF,
                    <emph.end type="italics"/>
                  & diviſim
                    <emph type="italics"/>
                  AQ-SR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                  -ſin. </s>
                  <s>arc.
                    <emph type="italics"/>
                  AQ
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ut
                    <emph type="italics"/>
                  GK
                    <emph.end type="italics"/>
                  differentia inter arcum
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                  & ſinum arcus
                    <emph type="italics"/>
                    <expan abbr="Aq.">Aque</expan>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Cæterum, cum difficilis ſit hujus Curvæ deſcriptio, præſtat ſolu­
                    <lb/>
                  tionem vero proximam adhibere. </s>
                  <s>Inveniatur tum angulus quidam
                    <lb/>
                  B, qui ſit ad angulum graduum 57,29578, quem arcus radio æqualis
                    <lb/>
                  ſubtendit, ut eſt umbilieorum diſtantia
                    <emph type="italics"/>
                  SH
                    <emph.end type="italics"/>
                  ad Ellipſeos diame­
                    <lb/>
                  trum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ; tum etiam longitudo quædam L, quæ ſit ad radium in
                    <lb/>
                  eadem ratione inverſe. </s>
                  <s>Quibus ſemel inventis, Problema deinceps
                    <lb/>
                  confit per ſequentem Analyſin. </s>
                  <s>Per conſtructionem quamvis (vel. </s>
                  <s>
                    <lb/>
                  utcunque conjec­
                    <lb/>
                    <figure id="id.039.01.129.1.jpg" xlink:href="039/01/129/1.jpg" number="75"/>
                    <lb/>
                  turam faciendo)
                    <lb/>
                  cognoſcatur cor­
                    <lb/>
                  poris locus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  pro­
                    <lb/>
                  ximus vero ejus lo­
                    <lb/>
                  co
                    <emph type="italics"/>
                  p.
                    <emph.end type="italics"/>
                  Demiſſaque ad
                    <lb/>
                  axem Ellipſeos or­
                    <lb/>
                  dinatim applicata
                    <lb/>
                    <emph type="italics"/>
                  PR,
                    <emph.end type="italics"/>
                  ex propor­
                    <lb/>
                  tione diametrorum
                    <lb/>
                  Ellipſeos, dabitur
                    <lb/>
                  Circuli circumſcri­
                    <lb/>
                  pti
                    <emph type="italics"/>
                  AQB
                    <emph.end type="italics"/>
                  ordinatim applicata
                    <emph type="italics"/>
                  RQ,
                    <emph.end type="italics"/>
                  quæ ſinus eſt anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  exi­
                    <lb/>
                  ſtente
                    <emph type="italics"/>
                  AO
                    <emph.end type="italics"/>
                  radio. </s>
                  <s>Sufficit angulum illum rudi calculo in numeris
                    <lb/>
                  proximis invenire. </s>
                  <s>Cognoſcatur etiam angulus tempori propor-</s>
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