Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/130.jpg" pagenum="102"/>
                    <arrow.to.target n="note78"/>
                  tionalis, id eſt, qui ſit ad quatuor rectos, ut eſt tempus quo corpus
                    <lb/>
                  deſcripſit arcum
                    <emph type="italics"/>
                  Ap,
                    <emph.end type="italics"/>
                  ad tempus revolutionis unius in Ellipſi. </s>
                  <s>Sit
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                  angulus iſte N. </s>
                  <s>Tum capiatur & angulus D ad angulum B, ut
                    <lb/>
                  eſt ſinus iſte anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  ad radium, & angulus E ad angulum
                    <lb/>
                  N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +D, ut eſt longitudo L ad longitudinem eandem L
                    <lb/>
                  coſinu anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  diminutam, ubi angulus iſte recto minor eſt,
                    <lb/>
                  auctam ubi major. </s>
                  <s>Poſtea capiatur tum angulus F ad angulum B,
                    <lb/>
                  ut eſt ſinus anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E ad radium, tum angulus G ad angu­
                    <lb/>
                  lum N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  -E+F ut eſt longitudo L ad longitudinem ean­
                    <lb/>
                  dem coſinu anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E diminutam ubi angulus iſte recto mi­
                    <lb/>
                  nor eſt, auctam ubi major. </s>
                  <s>Tertia vice capiatur angulus H ad an­
                    <lb/>
                  gulum B, ut eſt ſinus anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E+G ad radium; & angu­
                    <lb/>
                  lus I ad angulum N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  -E-G+H, ut eſt longitudo L ad
                    <lb/>
                  eandem longitudinem coſinu anguli
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E+G diminutam,
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                  ubi angulus iſte re­
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                    <figure id="id.039.01.130.1.jpg" xlink:href="039/01/130/1.jpg" number="76"/>
                    <lb/>
                  cto minor eſt, auc­
                    <lb/>
                  tam ubi major. </s>
                  <s>Et
                    <lb/>
                  ſic pergere licet in
                    <lb/>
                  infinitum. </s>
                  <s>DeNI­
                    <lb/>
                  que capiatur angu­
                    <lb/>
                  lus
                    <emph type="italics"/>
                  AOq
                    <emph.end type="italics"/>
                  æqualis
                    <lb/>
                  angulo
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E
                    <lb/>
                  +G+I+&c. </s>
                  <s>e t
                    <lb/>
                  ex coſinu ejus
                    <emph type="italics"/>
                  Or
                    <emph.end type="italics"/>
                    <lb/>
                  & ordinata
                    <emph type="italics"/>
                  pr,
                    <emph.end type="italics"/>
                  quæ
                    <lb/>
                  eſt ad ſinum ejus
                    <lb/>
                    <emph type="italics"/>
                  qr
                    <emph.end type="italics"/>
                  ut Ellipſeos axis minor ad axem majorem, habebitur corporis
                    <lb/>
                  locus correctus
                    <emph type="italics"/>
                  p.
                    <emph.end type="italics"/>
                  Si quando angulus N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +D negativus
                    <lb/>
                  eſt, debet ſignum+ipſius E ubique mutari in-, & ſignum-in+.
                    <lb/>
                  Idem intelligendum eſt de ſignis ipſorum G & I, ubi anguli
                    <lb/>
                  N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  -E+F, & N-
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  -E-G+H negativi prodeunt. </s>
                  <s>
                    <lb/>
                  Convergit autem ſeries infinita
                    <emph type="italics"/>
                  AOQ
                    <emph.end type="italics"/>
                  +E+G+I+&c. </s>
                  <s>quam
                    <lb/>
                  celerrime, adeo ut vix unquam opus fuerit ultra progredi quam
                    <lb/>
                  ad terminum ſecundum E. </s>
                  <s>Et fundatur calculus in hoc Theore­
                    <lb/>
                  mate, quod area
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                  ſit ut differentia inter arcum
                    <emph type="italics"/>
                  AQ
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  rectam ab umbilico
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  in Radium
                    <emph type="italics"/>
                  OQ
                    <emph.end type="italics"/>
                  perpendiculariter de­
                    <lb/>
                  miſſam. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note78"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Non diſſimili calculo conficitur Problema in Hyperbola. </s>
                  <s>Sit
                    <lb/>
                  ejus Centrum
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  Vertex
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  Umbilicus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  & Aſymptotos
                    <emph type="italics"/>
                  OK.
                    <emph.end type="italics"/>
                  Cog-</s>
                </p>
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