Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Reg.
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                  8. Inventis longitudinibus
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                  AH, HX
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                  ; ſi jam deſideretur </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note219"/>
                  poſitio rectæ
                    <emph type="italics"/>
                  AH,
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                  ſecundum quam Projectile, data illa cum veloci­
                    <lb/>
                  tate emiſſum, incidit in punctum quodvis
                    <emph type="italics"/>
                  K:
                    <emph.end type="italics"/>
                  ad puncta
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                    <lb/>
                  erigantur rectæ
                    <emph type="italics"/>
                  AC, KF
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                  horizonti perpendiculares, quarum
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                    <lb/>
                  deorſum tendat, & æquetur ipſi
                    <emph type="italics"/>
                  AI
                    <emph.end type="italics"/>
                  ſeu 1/2
                    <emph type="italics"/>
                  HX.
                    <emph.end type="italics"/>
                  Aſymptotis
                    <emph type="italics"/>
                  AK,
                    <lb/>
                  KF
                    <emph.end type="italics"/>
                  deſcribatur Hyperbola, cujus conjugata tranſeat per punctum
                    <lb/>
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  centroque
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  & intervallo
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  deſcribatur Circulus ſecans Hy­
                    <lb/>
                  perbolam illam in puncto
                    <emph type="italics"/>
                  H;
                    <emph.end type="italics"/>
                  & Projectile ſecundum rectam
                    <emph type="italics"/>
                  AH
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                    <lb/>
                  emiſſum incidet in punctum
                    <emph type="italics"/>
                  K. Q.E.I.
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                  Nam punctum
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  ob
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                  datam longitudinem
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                  AH,
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                  locatur alicubi in Circulo deſcripto. </s>
                  <s>A­
                    <lb/>
                  gatur
                    <emph type="italics"/>
                  CH
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                  occurrens ipſis
                    <emph type="italics"/>
                  AK
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                  &
                    <emph type="italics"/>
                  KF,
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                  illi in
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                  E,
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                  huic in
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                  F;
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                  & ob
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                    <figure id="id.039.01.271.1.jpg" xlink:href="039/01/271/1.jpg" number="158"/>
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                  parallelas
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                  CH, MX
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                  & æquales
                    <emph type="italics"/>
                  AC, AI,
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                  erit
                    <emph type="italics"/>
                  AE
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                  æqualis
                    <emph type="italics"/>
                  AM,
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                    <lb/>
                  & propterea etiam æqualis
                    <emph type="italics"/>
                  KN.
                    <emph.end type="italics"/>
                  Sed
                    <emph type="italics"/>
                  CE
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                  eſt ad
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  FH
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  KN,
                    <emph.end type="italics"/>
                  & propterea
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  FH
                    <emph.end type="italics"/>
                  æquantur. </s>
                  <s>Incidit ergo punctum
                    <lb/>
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  in Hyperbolam Aſymptotis
                    <emph type="italics"/>
                  AK, KF
                    <emph.end type="italics"/>
                  deſcriptam, cujus conju­
                    <lb/>
                  gata tranſit per punctum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  atque adeo reperitur in communi in­
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                  terſectione Hyperbolæ hujus & Circuli deſcripti.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  No­
                    <lb/>
                  tandum eſt autem quod hæc operatio perinde ſe habet, ſive recta
                    <lb/>
                    <emph type="italics"/>
                  AKN
                    <emph.end type="italics"/>
                  horizonti parallela ſit, ſive ad horizontem in angulo quo­
                    <lb/>
                  vis inclinata: quodque ex duabus interſectionibus
                    <emph type="italics"/>
                  H, H
                    <emph.end type="italics"/>
                  duo pro­
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                  deunt anguli
                    <emph type="italics"/>
                  NAH, NAH
                    <emph.end type="italics"/>
                  ; & quod in Praxi mechanica ſufficit </s>
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