Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  2. Sin corpus aſcendit, & gravitas ſit ut
                    <emph type="italics"/>
                  ABq-BDq
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note227"/>
                  linea
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  (Fig. </s>
                  <s>Caſ. </s>
                  <s>2. Prop. </s>
                  <s>XIII) erit (
                    <emph type="italics"/>
                  ABq-BDq
                    <emph.end type="italics"/>
                  /Z), &
                    <emph type="italics"/>
                  DTq
                    <emph.end type="italics"/>
                    <lb/>
                  erit ad
                    <emph type="italics"/>
                  DPq
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DFq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  DBq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BPq-BDq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  APq+
                    <lb/>
                  2BAP+ABq-BDq,
                    <emph.end type="italics"/>
                  id eſt, ad
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  XZ+
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  XZ ſeu
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ. </s>
                  <s>
                    <lb/>
                  Ideoque area
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  erit ad aream
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DBq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note227"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  3. Et eodem argumento, ſi corpus deſcendit, & propterea
                    <lb/>
                  gravitas ſit ut
                    <emph type="italics"/>
                  BDq-ABq,
                    <emph.end type="italics"/>
                  & linea
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  (Fig. </s>
                  <s>Caſ.3. Prop. </s>
                  <s>præced.)
                    <lb/>
                  æquetur (
                    <emph type="italics"/>
                  BDq-ABq
                    <emph.end type="italics"/>
                  /Z) erit area
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  ad aream
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DBq
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ: ut ſupra. </s>
                </p>
                <p type="main">
                  <s>Cum igitur areæ illæ ſemper ſint in hac ratione; ſi pro area
                    <lb/>
                    <emph type="italics"/>
                  DTV,
                    <emph.end type="italics"/>
                  qua momentum temporis ſibimet ipſi ſemper æquale ex­
                    <lb/>
                  ponitur, ſcribatur determinatum quodvis rectangulum, puta
                    <lb/>
                    <emph type="italics"/>
                  BDXm,
                    <emph.end type="italics"/>
                  erit area
                    <emph type="italics"/>
                  DPQ,
                    <emph.end type="italics"/>
                  id eſt, 1/2
                    <emph type="italics"/>
                  BDXPQ
                    <emph.end type="italics"/>
                  ; ad
                    <emph type="italics"/>
                  BDXm
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  XZ ad
                    <emph type="italics"/>
                    <expan abbr="BDq.">BDque</expan>
                    <emph.end type="italics"/>
                  AtQ.E.I.de fit
                    <emph type="italics"/>
                  PQXBD cub.
                    <emph.end type="italics"/>
                  æquale
                    <lb/>
                  2
                    <emph type="italics"/>
                  BDXmXCK
                    <emph.end type="italics"/>
                  XZ, & areæ
                    <emph type="italics"/>
                  AbNK
                    <emph.end type="italics"/>
                  momentum
                    <emph type="italics"/>
                  KLON
                    <emph.end type="italics"/>
                  ſu­
                    <lb/>
                  perius inventum, fit (
                    <emph type="italics"/>
                  BPXBDXm/AB
                    <emph.end type="italics"/>
                  ). Auferatur areæ
                    <emph type="italics"/>
                  DET
                    <emph.end type="italics"/>
                  mo­
                    <lb/>
                  mentum
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  BDXm,
                    <emph.end type="italics"/>
                  & reſtabit (
                    <emph type="italics"/>
                  APXBDXm/AB
                    <emph.end type="italics"/>
                  ). Eſt igi­
                    <lb/>
                  tur differentia momentorum, id eſt, momentum differentiæ area­
                    <lb/>
                  rum, æqualis (
                    <emph type="italics"/>
                  APXBDXm/AB
                    <emph.end type="italics"/>
                  ); & propterea (ob datum (
                    <emph type="italics"/>
                  BDXm/AB
                    <emph.end type="italics"/>
                  ))
                    <lb/>
                  ut velocitas
                    <emph type="italics"/>
                  AP,
                    <emph.end type="italics"/>
                  id eſt, ut momentum ſpatii quod corpus aſcen­
                    <lb/>
                  dendo vel deſcendendo deſcribit. </s>
                  <s>IdeoQ.E.D.fferentia arearum
                    <lb/>
                  & ſpatium illud, proportionalibus momentis creſcentia vel decre­
                    <lb/>
                  ſcentia & ſimul incipientia vel ſimul evaneſcentia, ſunt proportio­
                    <lb/>
                  nalia.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Igitur ſi longitudo aliqua V ſumatur in ea ratione ad du­
                    <lb/>
                  plum longitudinis M, quæ oritur applicando aream
                    <emph type="italics"/>
                  DET
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BD,
                    <emph.end type="italics"/>
                    <lb/>
                  quam habet linea
                    <emph type="italics"/>
                  DA
                    <emph.end type="italics"/>
                  ad lineam
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ; ſpatium quod corpus aſcen­
                    <lb/>
                  ſu vel deſcenſu toto in Medio reſiſtente deſcribit, erit ad ſpatium
                    <lb/>
                  quod in Medio non reſiſtente eodem tempore deſcribere poſſet,
                    <lb/>
                  ut arearum illarum differentia ad (
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  XV
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  /4
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ), ideoque ex dato tem­
                    <lb/>
                  pore datur. </s>
                  <s>Nam ſpatium in Medio non reſiſtente eſt in dupli­
                    <lb/>
                  cata ratione temporis, ſive ut V
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  , & ob datas
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  ut </s>
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