Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Si corpus in ſuperficiem quamvis
                    <emph type="italics"/>
                  CD,
                    <emph.end type="italics"/>
                  ſecundum lineam
                    <lb/>
                    <arrow.to.target n="note185"/>
                  rectam
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  lege quavis ductam incidens, emergat ſecundum aliam
                    <lb/>
                  quamvis rectam
                    <emph type="italics"/>
                  DK,
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.237.1.jpg" xlink:href="039/01/237/1.jpg" number="139"/>
                    <lb/>
                  & a puncto
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  duci in­
                    <lb/>
                  telligantur Lineæ curvæ
                    <lb/>
                    <emph type="italics"/>
                  CP, CQ
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  AD, DK
                    <emph.end type="italics"/>
                    <lb/>
                  ſemper perpendiculares:
                    <lb/>
                  erunt incrementa linea­
                    <lb/>
                  rum
                    <emph type="italics"/>
                  PD, QD,
                    <emph.end type="italics"/>
                    <expan abbr="atq;">atque</expan>
                  ad­
                    <lb/>
                  eo lineæ ipſæ
                    <emph type="italics"/>
                  PD, QD,
                    <emph.end type="italics"/>
                    <lb/>
                  incrementis iſtis genitæ,
                    <lb/>
                  ut ſinus incidentiæ & e­
                    <lb/>
                  mergentiæ ad invicem:
                    <lb/>
                  & contra. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note185"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XCVIII. PROBLEMA XLVIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis, & circa axem
                    <emph.end type="italics"/>
                  AB
                    <emph type="italics"/>
                  deſcripta ſuperficie quacunque
                    <lb/>
                  attractiva
                    <emph.end type="italics"/>
                  CD,
                    <emph type="italics"/>
                  regulari vel irregulari, per quam corpora de
                    <lb/>
                  loco dato
                    <emph.end type="italics"/>
                  A
                    <emph type="italics"/>
                  exeuntia tranſire debent: invenire ſuperficiem ſe­
                    <lb/>
                  cundam attractivam
                    <emph.end type="italics"/>
                  EF,
                    <emph type="italics"/>
                  quæ corpora illa ad locum datum
                    <emph.end type="italics"/>
                  B
                    <lb/>
                    <emph type="italics"/>
                  convergere faciat.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Juncta
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſecet ſuperficiem primam in
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  & ſecundam in
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                    <lb/>
                  puncto
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  utcunque aſſumpto. </s>
                  <s>Et poſito ſinu incidentiæ in ſuper­
                    <lb/>
                  ficiem primam ad ſinum emergentiæ ex eadem, & ſinu emergentiæ
                    <lb/>
                  e ſuperficie ſecunda ad ſinum incidentiæ in eandem, ut quantitas
                    <lb/>
                  aliqua data M ad aliam datam N; produc tum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  BG
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  ut M-N ad N, tum
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  AG,
                    <emph.end type="italics"/>
                  tum
                    <lb/>
                  etiam
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DH
                    <emph.end type="italics"/>
                  ut N ad M. </s>
                  <s>Junge
                    <emph type="italics"/>
                  KB,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  centro
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  DH
                    <emph.end type="italics"/>
                  deſcribe circulum occurrentem
                    <emph type="italics"/>
                  KB
                    <emph.end type="italics"/>
                  pro­
                    <lb/>
                  ductæ in
                    <emph type="italics"/>
                  L,
                    <emph.end type="italics"/>
                  ipſique
                    <emph type="italics"/>
                  DL
                    <emph.end type="italics"/>
                  parallelam age
                    <emph type="italics"/>
                  BF:
                    <emph.end type="italics"/>
                  & punctum
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  tan­
                    <lb/>
                  get Lineam
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  quæ circa axem
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  revoluta deſcribet ſuperfi­
                    <lb/>
                  ciem quæſitam.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam concipe Lineas
                    <emph type="italics"/>
                  CP, CQ
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  AD, DF
                    <emph.end type="italics"/>
                  reſpective, & Li­
                    <lb/>
                  neas
                    <emph type="italics"/>
                  ER, ES
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  FB, FD
                    <emph.end type="italics"/>
                  ubique perpendiculares eſſe, adeoque
                    <lb/>
                    <emph type="italics"/>
                  QS
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  ſemper æqualem; & erit (per Corol. </s>
                  <s>2. Prop. </s>
                  <s>XCVII)
                    <lb/>
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  QD
                    <emph.end type="italics"/>
                  ut M ad N, adeoque ut
                    <emph type="italics"/>
                  DL
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  FB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                  ; </s>
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