Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/233.jpg" pagenum="205"/>
                  ſingulis ſeparatim uniformis, at in diverſis diverſa; & per jam de­
                    <lb/>
                    <arrow.to.target n="note181"/>
                  monſtrata, ſinus incidentiæ in planum primum
                    <emph type="italics"/>
                  Aa
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                  erit ad ſinum
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                  emergentiæ ex plano ſecundo
                    <emph type="italics"/>
                  Bb,
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                  in data ratione; & hic ſinus,
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                  qui eſt ſinus incidentiæ in planum ſecundum
                    <emph type="italics"/>
                  Bb,
                    <emph.end type="italics"/>
                  erit ad ſinum
                    <lb/>
                  emergentiæ ex plano tertio
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                  Cc,
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                  in data ratione; & hic ſinus ad
                    <lb/>
                  ſinum emergentiæ ex plano quarto
                    <emph type="italics"/>
                  Dd,
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                  in data ratione; & ſic in
                    <lb/>
                  infinitum: & ex æquo, ſinus incidentiæ in planum primum ad ſi­
                    <lb/>
                  num emergentiæ ex plano ultimo in data ratione. </s>
                  <s>Minuantur jam
                    <lb/>
                  planorum intervalla & augeatur numerus in infinitum, eo ut attra­
                    <lb/>
                  ctionis vel impulſus actio, ſecundum legem quamcunque aſſignatam,
                    <lb/>
                  continua reddatur; & ratio ſinus incidentiæ in planum primum ad
                    <lb/>
                  ſinum emergentiæ ex plano ultimo, ſemper data exiſtens, etiam­
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                  num dabitur.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note181"/>
                  LIBER
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                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XCV. THEOREMA XLIX.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis; dico quod velocitas corporis ante incidentiam eſt
                    <lb/>
                  ad ejus velocitatem poſt emergentiam, ut ſinus emergentiæ ad
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                  ſinum incidentiæ.
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                  </s>
                </p>
                <p type="main">
                  <s>Capiantur
                    <emph type="italics"/>
                  AH, Id
                    <emph.end type="italics"/>
                  æquales, & erigantur perpendicula
                    <emph type="italics"/>
                  AG, dK
                    <emph.end type="italics"/>
                    <lb/>
                  occurrentia lineis incidentiæ & emergentiæ
                    <emph type="italics"/>
                  GH, IK,
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K.
                    <emph.end type="italics"/>
                    <lb/>
                  In
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  TH
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  IK,
                    <emph.end type="italics"/>
                  & ad planum
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  demittatur
                    <lb/>
                  normaliter
                    <emph type="italics"/>
                  Tv.
                    <emph.end type="italics"/>
                  Et (per Legum Corol. </s>
                  <s>2) diſtinguatur motus cor­
                    <lb/>
                  poris in duos, unum planis
                    <emph type="italics"/>
                  Aa, Bb, Cc,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>perpendicularem, al­
                    <lb/>
                  terum iiſdem parallelum. </s>
                  <s>Vis attractionis vel impulſus, agendo ſe­
                    <lb/>
                  cundum lineas perpendiculares, nil mutat motum ſecundum paralle­
                    <lb/>
                  las, & propterea corpus hoc motu conficiet æqualibus temporibus
                    <lb/>
                  æqualia illa ſecundum parallelas intervalla, quæ ſunt inter lineam
                    <lb/>
                    <emph type="italics"/>
                  AG
                    <emph.end type="italics"/>
                  & punctum
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  interque punctum
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  & lineam
                    <emph type="italics"/>
                  dK
                    <emph.end type="italics"/>
                  ; hoc eſt,
                    <lb/>
                  æqualibus temporibus deſcribet lineas
                    <emph type="italics"/>
                  GH, IK.
                    <emph.end type="italics"/>
                  Proinde velo­
                    <lb/>
                  citas ante incidentiam eſt ad velocitatem poſt emergentiam, ut
                    <lb/>
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  IK
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  TH,
                    <emph.end type="italics"/>
                  id eſt, ut
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Id
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  vH,
                    <emph.end type="italics"/>
                  hoc eſt
                    <lb/>
                  (reſpectu radii
                    <emph type="italics"/>
                  TH
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  IK
                    <emph.end type="italics"/>
                  ) ut ſinus emergentiæ ad ſinum inci­
                    <lb/>
                  dentiæ.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
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