Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/141.jpg" pagenum="113"/>
                  corpus cadendo deſcribit lineolam
                    <emph type="italics"/>
                  DE,
                    <emph.end type="italics"/>
                  ut lineola illa directe &
                    <lb/>
                    <arrow.to.target n="note89"/>
                  velocitas V inverſe, eſtque vis ut velocitatis incrementum I directe
                    <lb/>
                  & tempus inverſe, adeoque ſi primæ naſcentium rationes ſuman­
                    <lb/>
                  tur, ut (IXV/
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ), hoc eſt, ut longitudo
                    <emph type="italics"/>
                  DF.
                    <emph.end type="italics"/>
                  Ergo Vis ipſi
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  EG
                    <emph.end type="italics"/>
                    <lb/>
                  proportionalis facit ut corpus ea cum Velocitate deſcendat quæ ſit
                    <lb/>
                  ut areæ
                    <emph type="italics"/>
                  ABGE
                    <emph.end type="italics"/>
                  latus quadratum.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note89"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>Porro cum tempus, quo quælibet longitudinis datæ lineola
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                    <lb/>
                  deſcribatur, ſit ut velocitas inverſe adeoque ut areæ
                    <emph type="italics"/>
                  ABFD
                    <emph.end type="italics"/>
                  latus
                    <lb/>
                  quadratum inverſe; ſitque
                    <emph type="italics"/>
                  DL,
                    <emph.end type="italics"/>
                  atque adeo area naſcens
                    <emph type="italics"/>
                  DLME,
                    <emph.end type="italics"/>
                    <lb/>
                  ut idem latus quadratum inverſe: erit tempus ut area
                    <emph type="italics"/>
                  DLME,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  ſumma omnium temporum ut ſumma omnium arearum, hoc eſt
                    <lb/>
                  (per Corol. </s>
                  <s>Lem. </s>
                  <s>IV) Tempus totum quo linea
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  deſcribitur ut
                    <lb/>
                  area tota
                    <emph type="italics"/>
                  AME.
                    <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"/>
                  1. Si
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ſit locus de quo corpus cadere debet, ut, urgen­
                    <lb/>
                  te aliqua uniformi vi centripeta nota (qualis vulgo ſupponitur
                    <lb/>
                  Gravitas) velocitatem acquirat in loco
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  æqualem velocitati
                    <lb/>
                  quam corpus aliud vi quacunque cadens acquiſivit eodem loco
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                    <lb/>
                  & in perpendiculari
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  DR,
                    <emph.end type="italics"/>
                  quæ ſit ad
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ut vis illa
                    <lb/>
                  uniformis ad vim alteram in loco
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  & compleatur rectangulum
                    <lb/>
                    <emph type="italics"/>
                  PDRQ,
                    <emph.end type="italics"/>
                  eique æqualis abſcindatur area
                    <emph type="italics"/>
                  ABFD;
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  locus
                    <lb/>
                  de quo corpus alterum cecidit. </s>
                  <s>Namque completo rectangulo
                    <lb/>
                    <emph type="italics"/>
                  DRSE,
                    <emph.end type="italics"/>
                  cum ſit area
                    <emph type="italics"/>
                  ABFD
                    <emph.end type="italics"/>
                  ad aream
                    <emph type="italics"/>
                  DFGE
                    <emph.end type="italics"/>
                  ut VV ad
                    <lb/>
                  2VI, adeoque ut 1/2 V ad I, id eſt, ut ſemiſſis velocitatis totius
                    <lb/>
                  ad incrementum velocitatis corporis vi inæquabili cadentis; & ſi­
                    <lb/>
                  militer area
                    <emph type="italics"/>
                  PQRD
                    <emph.end type="italics"/>
                  ad aream
                    <emph type="italics"/>
                  DRSE
                    <emph.end type="italics"/>
                  ut ſemiſſis velocitatis to­
                    <lb/>
                  tius ad incrementum velocitatis corporis uniformi vi cadentis;
                    <lb/>
                  ſintQ.E.I.crementa illa (ob æqualitatem temporum naſcentium)
                    <lb/>
                  ut vires generatrices, id eſt, ut ordinatim applicatæ
                    <emph type="italics"/>
                  DF, DR,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque ut areæ naſcentes
                    <emph type="italics"/>
                  DFGE, DRSE
                    <emph.end type="italics"/>
                  ; erunt (ex æquo)
                    <lb/>
                  areæ totæ
                    <emph type="italics"/>
                  ABFD, PQRD
                    <emph.end type="italics"/>
                  ad invicem ut ſemiſſes totarum ve­
                    <lb/>
                  locitatum, & propterea (ob æqualitatem velocitatum) æquantur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Unde ſi corpus quodlibet de loco quocunque
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  data
                    <lb/>
                  cum velocitate vel ſurſum vel deorſum projiciatur, & detur lex vis
                    <lb/>
                  centripetæ, invenietur velocitas ejus in alio quovis loco
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  erigen­
                    <lb/>
                  do ordinatam
                    <emph type="italics"/>
                  eg,
                    <emph.end type="italics"/>
                  & capiendo velocitatem illam ad velocitatem in
                    <lb/>
                  loco
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ut eſt latus quadratum rectanguli
                    <emph type="italics"/>
                  PQRD
                    <emph.end type="italics"/>
                  area curvili­
                    <lb/>
                  nea
                    <emph type="italics"/>
                  DFge
                    <emph.end type="italics"/>
                  vel aucti, ſi locus
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                  eſt loco
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  inferior, vel diminuti,
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                  ſi is ſuperior eſt, ad latus quadratum rectanguli ſolius
                    <emph type="italics"/>
                  PQRD,
                    <emph.end type="italics"/>
                  id
                    <lb/>
                  eſt, ut √
                    <emph type="italics"/>
                  PQRD
                    <emph.end type="italics"/>
                  +vel-
                    <emph type="italics"/>
                  DFge
                    <emph.end type="italics"/>
                  ad √
                    <emph type="italics"/>
                  PQRD.
                    <emph.end type="italics"/>
                  </s>
                </p>
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