Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
                    <lb/>
                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
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                  Scholium.
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                    <emph.end type="center"/>
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                  <s>Si corpus aliquod perpendiculariter verſus planum datum tra­
                    <lb/>
                  hatur, & ex data lege attractionis quæratur motus corporis: Sol­
                    <lb/>
                  vetur Problema quærendo (per Prop. </s>
                  <s>XXXIX) motum corporis recta
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                  deſcendentis ad hoc planum, & (per Legum Corol. </s>
                  <s>2.) componen­
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                  do motum iſtum cum uniformi motu, ſecundum lineas eidem plano
                    <lb/>
                  parallelas facto. </s>
                  <s>Et contra, ſi quæratur Lex attractionis in planum
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                  ſecundum lineas perpendiculares factæ, ea conditione ut corpus at­
                    <lb/>
                  tractum in data quacunque curva linea moveatur, ſolvetur Proble­
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                  ma operando ad exemplum Problematis tertii. </s>
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                <p type="main">
                  <s>Operationes autem contrahi ſolent reſolvendo ordinatim appli­
                    <lb/>
                  catas in Series convergentes. </s>
                  <s>Ut ſi ad baſem A in angulo quovis
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                  dato ordinatim applicetur longitudo B, quæ ſit ut baſis dignitas
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                  quælibet A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m/n
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                    <emph.end type="sup"/>
                  ; & quæratur vis qua corpus, ſecundum poſitionem
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                  ordinatim applicatæ, vel in baſem attractum vel a baſi fugatum,
                    <lb/>
                  moveri poſſit in curva linea quam ordinatim applicata termi­
                    <lb/>
                  no ſuo ſuperiore ſemper attingit: Suppono baſem augeri parte
                    <lb/>
                  quam minima O, & ordinatim applicatam —(A+O)
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                  reſolvo in
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                  Seriem infinitam A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  +
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                  OA
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-n/n
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                  )
                    <emph.end type="sup"/>
                  +(
                    <emph type="italics"/>
                  mm-mn/2nn
                    <emph.end type="italics"/>
                  ) OOA
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-2n/n
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                  )
                    <emph.end type="sup"/>
                  &c. </s>
                  <s>at­
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                  que hujus termino in quo O duarum eſt dimenſionum, id eſt, ter­
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                  mino (
                    <emph type="italics"/>
                  mm-mn/2nn
                    <emph.end type="italics"/>
                  ) OOA
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-2n/n
                    <emph.end type="italics"/>
                  )
                    <emph.end type="sup"/>
                  vim proportionalem eſſe ſuppono. </s>
                  <s>Eſt
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                  igitur vis quæſita ut (
                    <emph type="italics"/>
                  mm-mn/nn
                    <emph.end type="italics"/>
                  )A
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-2n/n
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                  )
                    <emph.end type="sup"/>
                  , vel quod perinde eſt, ut
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                  (
                    <emph type="italics"/>
                  mm-mn/nn
                    <emph.end type="italics"/>
                  )B
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-2n/m
                    <emph.end type="italics"/>
                  )
                    <emph.end type="sup"/>
                  . </s>
                  <s>Ut ſi ordinatim applicata Parabolam attingat,
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                  exiſtente
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  =2, &
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  =1: fiet vis ut data 2B°, adeoQ.E.D.bi­
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                  tur. </s>
                  <s>Data igitur vi corpus movebitur in Parabola, quemad­
                    <lb/>
                  modum
                    <emph type="italics"/>
                  Galilæus
                    <emph.end type="italics"/>
                  demonſtravit. </s>
                  <s>Quod ſi ordinatim applicata
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                  Hyperbolam attingat, exiſtente
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  =o-1, &
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  =1; fiet vis ut
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                  2A
                    <emph type="sup"/>
                  -3
                    <emph.end type="sup"/>
                  ſeu 2B
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  : adeoque vi, quæ ſit ut cubus ordinatim applicatæ,
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                  corpus movebitur in Hyperbola. </s>
                  <s>Sed miſſis hujuſmodi Propoſiti­
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                  onibus, pergo ad alias quaſdam de Motu, quas nondum attigi. </s>
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