Newton, Isaac, Philosophia naturalis principia mathematica, 1713
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                  Et tempora quibus corpus deſcribit arcus
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                  GH, HI,
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                  erunt in
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                    <arrow.to.target n="note209"/>
                  ſubduplicata ratione altitudinum
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                  LH, NI
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                  quas corpus tempo­
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                  ribus illis deſcribere poſſet, a tangentibus cadendo: & velocitates
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                  erunt ut longitudines deſcriptæ
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                  GH, HI
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                  directe & tempora in­
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                  verſe. </s>
                  <s>Exponantur tempora per T &
                    <emph type="italics"/>
                  t,
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                  & velocitates per
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                  (
                    <emph type="italics"/>
                  GH
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                  /T) & (
                    <emph type="italics"/>
                  HI/t
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                  ): & decrementum velocitatis tempore
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                  t
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                  factum ex­
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                  ponetur per (
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  /T)-(
                    <emph type="italics"/>
                  HI/t
                    <emph.end type="italics"/>
                  ). Hoc decrementum oritur a reſiſtentia
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                  corpus retardante & gravitate corpus accelerante. </s>
                  <s>Gravitas in
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                  corpore cadente & ſpatium
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                  NI
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                  cadendo deſcribente, generat ve­
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                  locitatem qua duplum illud ſpatium eodem tempore deſcribi po­
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                  tuiſſet (ut
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                  Galilæus
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                  demonſtravit) id eſt, velocitatem (2
                    <emph type="italics"/>
                  NI/t
                    <emph.end type="italics"/>
                  ): at
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                  in corpore arcum
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                  HI
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                  deſcribente, auget arcum illum ſola longi­
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                  tudine
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                  HI-HN
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                  ſeu (
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                  MIXNI/HI
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                  ), ideoque generat tantum velo­
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                  citatem (2
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                  MIXNI/tXHI
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                  ). Addatur hæc velocitas ad decrementum
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                  prædictum, & habebitur decrementum velocitatis ex reſiſtentia
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                  ſola oriundum, nempe (
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                  GH
                    <emph.end type="italics"/>
                  /T)-
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                  (HI/t)+(2MIXNI/tXHI).
                    <emph.end type="italics"/>
                  Proindeque
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                  cum gravitas eodem tempore in corpore cadente generet velocitatem
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                  (2
                    <emph type="italics"/>
                  NI/t
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                  ); Reſiſtentia erit ad Gravitatem ut (
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  /T)-
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                  (HI/t)+(2MIXNI/tXHI)
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                    <lb/>
                  ad (
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                  2NI/t
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                  ), ſive ut (
                    <emph type="italics"/>
                  tXGH
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                  /T)-
                    <emph type="italics"/>
                  HI+(2MIXNI/HI)
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                  ad 2
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                  NI.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note209"/>
                  LIBER
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                  SECUNDUS</s>
                </p>
                <p type="main">
                  <s>Jam pro abſciſſis
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                  CB, CD, CE
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                  ſcribantur -
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                  o, o,
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                  20. Pro
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                  Ordinata
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                  CH
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                  ſcribatur P, & pro
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                  MI
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                  ſcribatur ſeries quælibet
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                  Q
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  +R
                    <emph type="italics"/>
                  oo
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                  +S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
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                  +&c. </s>
                  <s>Et ſeriei termini omnes poſt primum,
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                  nempe R
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  +S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
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                  +&c. </s>
                  <s>erunt
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                  NI,
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                  & Ordinatæ
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                  DI, EK,
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                  &
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                  BG
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                    <lb/>
                  erunt P-Q
                    <emph type="italics"/>
                  o
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                  -R
                    <emph type="italics"/>
                  oo
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                  -S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  -&c, P-2Q
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  -4R
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  -8S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
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                  -&c,
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                  & P+Q
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  -R
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  +S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  -&c. </s>
                  <s>reſpective. </s>
                  <s>Et quadrando diffe­
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                  rentias Ordinatarum
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                  BG-CH
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                  &
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                  CH-DI,
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                  & ad quadrata pro­
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                  deuntia addendo quadrata ipſarum
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                  BC, CD,
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                  habebuntur arcuum
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                    <emph type="italics"/>
                  GH, HI
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                  quadrata
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                  oo
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                  +QQ
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                  oo
                    <emph.end type="italics"/>
                  +2QR
                    <emph type="italics"/>
                  o
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                    <emph type="sup"/>
                  3
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                  +&c, &
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  +QQ
                    <emph type="italics"/>
                  oo
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                    <lb/>
                  +2QR
                    <emph type="italics"/>
                  o
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                  +&c. </s>
                  <s>Quorum radices
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                  o
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                  √1+QQ-(QR
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                  oo
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                  /√1+QQ), & </s>
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