Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/108.jpg" pagenum="80"/>
                    <arrow.to.target n="note56"/>
                  Concipe igitur punctum
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                  G
                    <emph.end type="italics"/>
                  motu continuo percurrere puncta om­
                    <lb/>
                  nia figuræ primæ, & punctum
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                  g
                    <emph.end type="italics"/>
                  motu itidem continuo percurret
                    <lb/>
                  puncta omnia figuræ novæ & eandem deſcribet. </s>
                  <s>Diſtinctionis gra­
                    <lb/>
                  tia nominemus
                    <emph type="italics"/>
                  DG
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                  ordinatam primam,
                    <emph type="italics"/>
                  dg
                    <emph.end type="italics"/>
                  ordinatam novam;
                    <lb/>
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  abſciſſam primam,
                    <emph type="italics"/>
                  ad
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                  abſciſſam novam;
                    <emph type="italics"/>
                  O
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                  polum,
                    <emph type="italics"/>
                  OD
                    <emph.end type="italics"/>
                  ra­
                    <lb/>
                  dium abſcidentem,
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  radium ordinatum primum, &
                    <emph type="italics"/>
                  Oa
                    <emph.end type="italics"/>
                  (qno
                    <lb/>
                  parallelogrammum
                    <emph type="italics"/>
                  OABa
                    <emph.end type="italics"/>
                  completur) radium ordinatum novum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note56"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Dico jam quod, ſi punctum
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  tangit rectam Lineam poſitione da­
                    <lb/>
                  tam, punctum
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  tanget etiam Lineam rectam poſitione datam. </s>
                  <s>Si
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  tangit Conicam ſectionem, punctum
                    <emph type="italics"/>
                  g
                    <emph.end type="italics"/>
                  tanget etiam
                    <lb/>
                  Conicam ſectionem. </s>
                  <s>Conicis ſectionibus hic Circulum annumero. </s>
                  <s>
                    <lb/>
                  Porro ſi punctum
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  tan­
                    <lb/>
                    <figure id="id.039.01.108.1.jpg" xlink:href="039/01/108/1.jpg" number="55"/>
                    <lb/>
                  git Lineam tertii ordinis
                    <lb/>
                  Analytici, punctum
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                  g
                    <emph.end type="italics"/>
                    <lb/>
                  tanget Lineam tertii iti­
                    <lb/>
                  dem ordinis; & ſic de
                    <lb/>
                  curvis lineis ſuperiorum
                    <lb/>
                  ordinum. </s>
                  <s>Lineæ duæ e­
                    <lb/>
                  runt ejuſdem ſemper or­
                    <lb/>
                  dinis Analytici quas pun­
                    <lb/>
                  cta
                    <emph type="italics"/>
                  G, g
                    <emph.end type="italics"/>
                  tangunt. </s>
                  <s>Et­
                    <lb/>
                  enim ut eſt
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                    <lb/>
                  ita ſunt
                    <emph type="italics"/>
                  Od
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OD, dg
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DG,
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                  &
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  ; adeoque
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis eſt (
                    <emph type="italics"/>
                  OAXAB/ad
                    <emph.end type="italics"/>
                  ), &
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  æqualis eſt (
                    <emph type="italics"/>
                  OAXdg/ad
                    <emph.end type="italics"/>
                  ). Jam ſi punc­
                    <lb/>
                  tum
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  tangit rectam Lineam, atque adeo in æquatione quavis,
                    <lb/>
                  qua relatio inter abſciſſam
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  & ordinatam
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  habetur, in­
                    <lb/>
                  determinatæ illæ
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  ad unicam tantum dimenſionem
                    <lb/>
                  aſcendunt, ſcribendo in hac æquatione (
                    <emph type="italics"/>
                  OAXAB/ad
                    <emph.end type="italics"/>
                  ) pro
                    <emph type="italics"/>
                  AD,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  (
                    <emph type="italics"/>
                  OAXdg/ad
                    <emph.end type="italics"/>
                  ) pro
                    <emph type="italics"/>
                  DG,
                    <emph.end type="italics"/>
                  producetur æquatio nova, in qua abſciſſa no­
                    <lb/>
                  va
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  & ordinata nova
                    <emph type="italics"/>
                  dg
                    <emph.end type="italics"/>
                  ad unicam tantum dimenſionem aſcen­
                    <lb/>
                  dent, atque adeo quæ deſignat Lineam rectam. </s>
                  <s>Sin
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                    <lb/>
                  (vel earum alterutra) aſcendebant ad duas dimenſiones in æquati­
                    <lb/>
                  one prima, aſcendent itidem
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  dg
                    <emph.end type="italics"/>
                  ad duas in æquatione ſecun­
                    <lb/>
                  da. </s>
                  <s>Et ſic de tribus vel pluribus dimenſionibus. </s>
                  <s>Indeterminatæ
                    <lb/>
                    <emph type="italics"/>
                  ad, dg
                    <emph.end type="italics"/>
                  in æquatione ſecunda &
                    <emph type="italics"/>
                  AD, DG
                    <emph.end type="italics"/>
                  in prima aſcendent ſem­
                    <lb/>
                  per ad eundem dimenſionum numerum, & propterea Lineæ, quas
                    <lb/>
                  puncta
                    <emph type="italics"/>
                  G, g
                    <emph.end type="italics"/>
                  tangunt, ſunt ejuſdem ordinis Analytici. </s>
                </p>
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