Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/262.jpg" pagenum="234"/>
                    <arrow.to.target n="note210"/>
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  √1+QQ+(QR
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  /√1+QQ) ſunt arcus
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  HI.
                    <emph.end type="italics"/>
                  Præterea ſi ab
                    <lb/>
                  Ordinata
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  ſubducatur ſemiſumma Ordinatarum
                    <emph type="italics"/>
                  BG
                    <emph.end type="italics"/>
                  ac
                    <emph type="italics"/>
                  DI,
                    <emph.end type="italics"/>
                    <lb/>
                  & ab Ordinata
                    <emph type="italics"/>
                  DI
                    <emph.end type="italics"/>
                  ſubducatur ſemiſumma Ordinatarum
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  EK,
                    <emph.end type="italics"/>
                  manebunt arcuum
                    <emph type="italics"/>
                  GI
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  HK
                    <emph.end type="italics"/>
                  ſagittæ R
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  & R
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  +3S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  . </s>
                  <s>
                    <lb/>
                  Et hæ ſunt lineolis
                    <emph type="italics"/>
                  LH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NI
                    <emph.end type="italics"/>
                  proportionales, adeoQ.E.I. du­
                    <lb/>
                  plicata ratione temporum infinite parvorum T &
                    <emph type="italics"/>
                  t,
                    <emph.end type="italics"/>
                  & inde ratio
                    <lb/>
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  /T eſt √(R+3S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  /R) ſeu (R+3/2S
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  /R): & (
                    <emph type="italics"/>
                  tXGH
                    <emph.end type="italics"/>
                  /T)-
                    <emph type="italics"/>
                  HI+(2MIXNI/HI),
                    <emph.end type="italics"/>
                    <lb/>
                  ſubſtituendo ipſorum
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  /T,
                    <emph type="italics"/>
                  GH, HI, MI
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NI
                    <emph.end type="italics"/>
                  valores jam in­
                    <lb/>
                  ventos, evadit (3S
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  /2R)√1+Qq. </s>
                  <s>Et cum 2
                    <emph type="italics"/>
                  NI
                    <emph.end type="italics"/>
                  ſit 2R
                    <emph type="italics"/>
                  oo,
                    <emph.end type="italics"/>
                  Re­
                    <lb/>
                  ſiſtentia jam erit ad Gravitatem ut (3S
                    <emph type="italics"/>
                  oo
                    <emph.end type="italics"/>
                  /2R)√1+QQ ad 2R
                    <emph type="italics"/>
                  oo,
                    <emph.end type="italics"/>
                    <lb/>
                  id eſt, ut 3S√1+QQ ad 4RR. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note210"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Velocitas autem ea eſt quacum corpus de loco quovis
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  ſe­
                    <lb/>
                  cundum tangentem
                    <emph type="italics"/>
                  HN
                    <emph.end type="italics"/>
                  egrediens, in Parabola diametrum
                    <emph type="italics"/>
                  HC
                    <emph.end type="italics"/>
                    <lb/>
                  & latus rectum (
                    <emph type="italics"/>
                  HNq/NI
                    <emph.end type="italics"/>
                  ) ſeu (1+QQ/R) habente, deinceps in vacuo
                    <lb/>
                  moveri poteſt. </s>
                </p>
                <p type="main">
                  <s>Et reſiſtentia eſt ut Medii denſitas & quadratum velocitatis
                    <lb/>
                  conjunctim, & propterea Medii denſitas eſt ut reſiſtentia directe
                    <lb/>
                  & quadratum velocitatis inverſe, id eſt, ut (3S√1+QQ/4RR) directe
                    <lb/>
                  & (1+QQ/R) inverſe, hoc eſt, ut (S/R√1+QQ).
                    <emph type="italics"/>
                  q.EI.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Si tangens
                    <emph type="italics"/>
                  HN
                    <emph.end type="italics"/>
                  producatur utrinQ.E.D.nec occurrat
                    <lb/>
                  Ordinatæ cuilibet
                    <emph type="italics"/>
                  AF
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  : erit (
                    <emph type="italics"/>
                  HT/AC
                    <emph.end type="italics"/>
                  ) æqualis √1+QQ, adeo­
                    <lb/>
                  Q.E.I. ſuperioribus pro √1+QQ ſcribi poteſt. </s>
                  <s>Qua ratione
                    <lb/>
                  Reſiſtentia erit ad Gravitatem ut 3SX
                    <emph type="italics"/>
                  HT
                    <emph.end type="italics"/>
                  ad 4RRX
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  Velo­
                    <lb/>
                  citas erit ut (
                    <emph type="italics"/>
                  HT/AC
                    <emph.end type="italics"/>
                  √R), & Medii denſitas erit ut (SX
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  /RX
                    <emph type="italics"/>
                  HT
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et hinc, ſi Curva linea
                    <emph type="italics"/>
                  PFHQ
                    <emph.end type="italics"/>
                  definiatur per rela­
                    <lb/>
                  tionem inter baſem ſeu abſciſſam
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  & ordinatim applicatam </s>
                </p>
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