Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note258"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note258"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Nam ſi uniformis ſit reſiſtentia
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                  DK,
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                  Figura
                    <emph type="italics"/>
                  aBKkT
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                  rectangu­
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                  lum erit ſub
                    <emph type="italics"/>
                  Ba
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                  &
                    <emph type="italics"/>
                  DK
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                  ; & inde rectangulum ſub 1/2
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                    <lb/>
                  erit æquale rectangulo ſub
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DK,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  æqualis erit 1/2
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                  Aa.
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                    <lb/>
                  Quare cum
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  ſit exponens reſiſtentiæ, & longitudo penduli ex­
                    <lb/>
                  ponens gravitatis, erit reſiſtentia ad gravitatem ut 1/2
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ad longi­
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                  tudinem Penduli; omnino ut in Prop. </s>
                  <s>XXVIII demonſtratum eſt. </s>
                </p>
                <p type="main">
                  <s>Si reſiſtentia ſit ut velocitas, Figura
                    <emph type="italics"/>
                  aBKkT
                    <emph.end type="italics"/>
                  Ellipſis erit quam
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                  proxime. </s>
                  <s>Nam ſi corpus, in Medio non reſiſtente, oſcillatione
                    <lb/>
                  integra deſcriberet longitudinem
                    <emph type="italics"/>
                  BA,
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                  velocitas in loco quovis
                    <emph type="italics"/>
                  D
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                    <lb/>
                  foret ut Circuli diametro
                    <emph type="italics"/>
                  AB
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                  deſcripti ordinatim applicata
                    <emph type="italics"/>
                  DE.
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                    <lb/>
                  Proinde cum
                    <emph type="italics"/>
                  Ba
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                  in Medio reſiſtente, &
                    <emph type="italics"/>
                  BA
                    <emph.end type="italics"/>
                  in Medio non reſi­
                    <lb/>
                  ſtente, æqualibus circiter temporibus deſcribantur; adeoque velo­
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                  citates in ſingulis ipſius
                    <lb/>
                    <figure id="id.039.01.310.1.jpg" xlink:href="039/01/310/1.jpg" number="180"/>
                    <lb/>
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  punctis, ſint quam
                    <lb/>
                  proxime ad velocitates
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                  in punctis correſpon­
                    <lb/>
                  dentibus longitudinis
                    <lb/>
                    <emph type="italics"/>
                  BA,
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BA
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  erit velocitas
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  Medio reſiſtente ut Cir­
                    <lb/>
                  culi vel Ellipſeos ſuper
                    <lb/>
                  diametro
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  deſcripti
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                  ordinatim applicata; adeoque Figura
                    <emph type="italics"/>
                  BKVTa
                    <emph.end type="italics"/>
                  Ellipſis, quam pro­
                    <lb/>
                  xime. </s>
                  <s>Cum reſiſtentia velocitati proportionalis ſupponatur, ſit
                    <emph type="italics"/>
                  OV
                    <emph.end type="italics"/>
                    <lb/>
                  exponens reſiſtentiæ in puncto Medio
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  ; & Ellipſis
                    <emph type="italics"/>
                  aBRVS,
                    <emph.end type="italics"/>
                    <lb/>
                  centro
                    <emph type="italics"/>
                  O,
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                  ſemiaxibus
                    <emph type="italics"/>
                  OB, OV
                    <emph.end type="italics"/>
                  deſcripta, Figuram
                    <emph type="italics"/>
                  aBKVT,
                    <emph.end type="italics"/>
                    <lb/>
                  eique æquale rectangulum
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                  AaXBO,
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                  æquabit quamproxime. </s>
                  <s>Eſt
                    <lb/>
                  igitur
                    <emph type="italics"/>
                  AaXBO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OVXBO
                    <emph.end type="italics"/>
                  ut area Ellipſeos hujus ad
                    <emph type="italics"/>
                  OVXBO
                    <emph.end type="italics"/>
                  :
                    <lb/>
                  id eſt,
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OV
                    <emph.end type="italics"/>
                  ut area ſemicirculi ad quadratum radii, ſive ut
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                  11 ad 7 circiter: Et propterea (1/11)
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ad longitudinem penduli ut
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                  corporis oſcillantis reſiſtentia in
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  ad ejuſdem gravitatem. </s>
                </p>
                <p type="main">
                  <s>Quod ſi reſiſtentia
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  ſit in duplicata ratione velocitatis, Fi­
                    <lb/>
                  gura
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                  BKVTa
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                  Parabola erit verticem habens
                    <emph type="italics"/>
                  V
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                  & axem
                    <emph type="italics"/>
                  OV,
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                  id­
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                  eoque æqualis erit rectangulo ſub 2/3
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  OV
                    <emph.end type="italics"/>
                  quam proxime. </s>
                  <s>Eſt
                    <lb/>
                  igitur rectangulum ſub 1/2
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  æquale rectangulo ſub 2/3
                    <emph type="italics"/>
                  Ba
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  OV,
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                  adeoque
                    <emph type="italics"/>
                  OV
                    <emph.end type="italics"/>
                  æqualis 1/4
                    <emph type="italics"/>
                  Aa:
                    <emph.end type="italics"/>
                  & propterea corporis oſcillan­
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                  tis reſiſtentia in
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  ad ipſius gravitatem ut 1/4
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ad longitudi­
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                  nem Penduli. </s>
                </p>
                <p type="main">
                  <s>Atque has concluſiones in rebus practicis abunde ſatis accuratas
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                  eſſe cenſeo. </s>
                  <s>Nam cum Ellipſis vel Parabola
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                  BRVSa
                    <emph.end type="italics"/>
                  congruat </s>
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