Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/244.jpg" pagenum="216"/>
                    <arrow.to.target n="note192"/>
                  inde eſt, cape
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                  Rr
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                  æqualem (
                    <emph type="italics"/>
                  GTIE
                    <emph.end type="italics"/>
                  /N); & Projectile tempore
                    <emph type="italics"/>
                  DRTG
                    <emph.end type="italics"/>
                    <lb/>
                  perveniet ad punctum
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                  r,
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                  deſcribens curvam lineam
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                  DraF,
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                  quam
                    <lb/>
                  punctum
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                  r
                    <emph.end type="italics"/>
                  ſemper tangit, perveniens autem ad maximam altitudi­
                    <lb/>
                  nem
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                  a
                    <emph.end type="italics"/>
                  in perpendiculo
                    <emph type="italics"/>
                  AB,
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                  & poſtea ſemper appropinquans ad A­
                    <lb/>
                  ſymptoton
                    <emph type="italics"/>
                  PLC.
                    <emph.end type="italics"/>
                  Eſtque velocitas ejus in puncto quovis
                    <emph type="italics"/>
                  r
                    <emph.end type="italics"/>
                  ut Cur­
                    <lb/>
                  væ Tangens
                    <emph type="italics"/>
                  rL.
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note192"/>
                  DE MOTU
                    <lb/>
                  CORPORUN</s>
                </p>
                <p type="main">
                  <s>Eſt enim N ad
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  DR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  RV,
                    <emph.end type="italics"/>
                  adeoque
                    <emph type="italics"/>
                  RV
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis (
                    <emph type="italics"/>
                  DRXQB
                    <emph.end type="italics"/>
                  /N), &
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                  (id eſt
                    <emph type="italics"/>
                  RV-Vr
                    <emph.end type="italics"/>
                  ſeu (
                    <emph type="italics"/>
                  DRXQB-tGT
                    <emph.end type="italics"/>
                  /N))
                    <lb/>
                  æqualis (
                    <emph type="italics"/>
                  DRXAB-RDGT
                    <emph.end type="italics"/>
                  /N). Exponatur jam tempus per are­
                    <lb/>
                  am
                    <emph type="italics"/>
                  RDGT,
                    <emph.end type="italics"/>
                  & (per Legum
                    <lb/>
                    <figure id="id.039.01.244.1.jpg" xlink:href="039/01/244/1.jpg" number="146"/>
                    <lb/>
                  Corol. </s>
                  <s>2.) diſtinguatur motus
                    <lb/>
                  corporis in duos, unum aſcen­
                    <lb/>
                  ſus, alterum ad latus. </s>
                  <s>Et cum
                    <lb/>
                  reſiſtentia ſit ut motus, diſtin­
                    <lb/>
                  guetur etiam hæc in partes duas
                    <lb/>
                  partibus motus proportionales
                    <lb/>
                  & contrarias: ideoque longitu­
                    <lb/>
                  do, a motu ad latus deſcripta, e­
                    <lb/>
                  rit (per Prop. </s>
                  <s>11. hujus) ut linea
                    <lb/>
                    <emph type="italics"/>
                  DR,
                    <emph.end type="italics"/>
                  altitudo vero (per Prop. </s>
                  <s>
                    <lb/>
                  111. hujus) ut area
                    <emph type="italics"/>
                  DRXAB
                    <lb/>
                  -RDGT,
                    <emph.end type="italics"/>
                  hoc eſt, ut linea
                    <emph type="italics"/>
                  Rr.
                    <emph.end type="italics"/>
                    <lb/>
                  Ipſo autem motus initio area
                    <lb/>
                    <emph type="italics"/>
                  RDGT
                    <emph.end type="italics"/>
                  æqualis eſt rectangulo
                    <lb/>
                    <emph type="italics"/>
                  DRXAQ,
                    <emph.end type="italics"/>
                  ideoque linea illa
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                    <lb/>
                  (ſeu (
                    <emph type="italics"/>
                  DRXAB-DRXAQ
                    <emph.end type="italics"/>
                  /N))
                    <lb/>
                  tunc eſt ad
                    <emph type="italics"/>
                  DR
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AB-AQ
                    <emph.end type="italics"/>
                    <lb/>
                  ſeu
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ad N, id eſt, ut
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  ; atque adeo ut motus
                    <lb/>
                  in altitudinem ad motum in
                    <lb/>
                  longitudinem ſub initio. </s>
                  <s>Cum
                    <lb/>
                  igitur
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                  ſemper ſit ut altitu­
                    <lb/>
                  do, ac
                    <emph type="italics"/>
                  DR
                    <emph.end type="italics"/>
                  ſemper ut longi­
                    <lb/>
                  tudo, atque
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DR
                    <emph.end type="italics"/>
                  ſub
                    <lb/>
                  initio ut altitudo ad longitudinem: neceſſe eſt ut
                    <emph type="italics"/>
                  Rr
                    <emph.end type="italics"/>
                  ſemper ſit ad
                    <lb/>
                    <emph type="italics"/>
                  DR
                    <emph.end type="italics"/>
                  ut altitudo ad longitudinem, & propterea ut corpus movea­
                    <lb/>
                  tur in linea
                    <emph type="italics"/>
                  DraF,
                    <emph.end type="italics"/>
                  quam punctum
                    <emph type="italics"/>
                  r
                    <emph.end type="italics"/>
                  perpetuo tangit.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
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