Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <arrow.to.target n="note48"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note48"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi agatur
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                  ſecans
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  r,
                    <emph.end type="italics"/>
                  & in
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  capiatur
                    <lb/>
                    <emph type="italics"/>
                  Pt
                    <emph.end type="italics"/>
                  in ratione ad
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  quam habet
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PR:
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  Bt
                    <emph.end type="italics"/>
                  tangens
                    <lb/>
                  Conicæ ſectionis ad punctum
                    <emph type="italics"/>
                  B.
                    <emph.end type="italics"/>
                  Nam concipe punctum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  coire
                    <lb/>
                  cum puncto
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ita ut, chorda
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  evaneſcente,
                    <emph type="italics"/>
                  BT
                    <emph.end type="italics"/>
                  tangens eva­
                    <lb/>
                  dat; &
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ac
                    <emph type="italics"/>
                  BT
                    <emph.end type="italics"/>
                  coincident cum
                    <emph type="italics"/>
                  CB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Bt.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et vice verſa ſi
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                    <lb/>
                    <emph type="italics"/>
                  Bt
                    <emph.end type="italics"/>
                  fit tangens, & ad quod­
                    <lb/>
                  vis Conicæ ſectionis punc­
                    <lb/>
                  tum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  conveniant
                    <emph type="italics"/>
                  BD,
                    <lb/>
                  CD
                    <emph.end type="italics"/>
                  ; erit
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  ut
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Pt.
                    <emph.end type="italics"/>
                  Et contra,
                    <lb/>
                  ſi ſit
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  Pt:
                    <emph.end type="italics"/>
                  convenient
                    <emph type="italics"/>
                  BD, CD
                    <emph.end type="italics"/>
                    <lb/>
                  ad Conicæ Sectionis punc­
                    <lb/>
                  um aliquod
                    <emph type="italics"/>
                  D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Conica ſectio
                    <lb/>
                  non ſecat Conicam ſectio­
                    <lb/>
                  nem in punctis pluribus quam quatuor. </s>
                  <s>Nam, ſi fieri poteſt, tranſ­
                    <lb/>
                  eant duæ Conicæ ſectiones per quinque puncta
                    <emph type="italics"/>
                  A, B, C, P, O
                    <emph.end type="italics"/>
                  ; eaſ­
                    <lb/>
                  que ſecet recta
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  in punctis
                    <emph type="italics"/>
                  D, d,
                    <emph.end type="italics"/>
                  & ipſam
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ſecet recta
                    <emph type="italics"/>
                  Cd
                    <emph.end type="italics"/>
                    <lb/>
                  in r. </s>
                  <s>Ergo
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  r ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ; unde
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  r ſibi
                    <lb/>
                  invicem æquantur, contra Hypotheſin. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XXI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si rectæ duæ mobiles & infinitæ
                    <emph.end type="italics"/>
                  BM, CM
                    <emph type="italics"/>
                  per data puncta
                    <emph.end type="italics"/>
                  B, C,
                    <emph type="italics"/>
                  ceu
                    <lb/>
                  polos ductæ, concurſu ſuo
                    <emph.end type="italics"/>
                  M
                    <emph type="italics"/>
                  deſcribant tertiam poſitione da­
                    <lb/>
                  tam rectam
                    <emph.end type="italics"/>
                  MN;
                    <emph type="italics"/>
                  & aliæ duæ infinitæ rectæ
                    <emph.end type="italics"/>
                  BD, CD
                    <emph type="italics"/>
                  cum
                    <lb/>
                  prioribus duabus ad puncta illa data
                    <emph.end type="italics"/>
                  B, C
                    <emph type="italics"/>
                  datos angulos
                    <emph.end type="italics"/>
                    <lb/>
                  MBD, MCD
                    <emph type="italics"/>
                  efficientes ducantur; dico quod hæ duæ
                    <emph.end type="italics"/>
                  BD,
                    <lb/>
                  CD
                    <emph type="italics"/>
                  concurſu ſuo
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  deſcribent ſectionem Conicam per puncta
                    <emph.end type="italics"/>
                    <lb/>
                  B, C
                    <emph type="italics"/>
                  tranſeuntem. </s>
                  <s>Et vice verſa, ſi rectæ
                    <emph.end type="italics"/>
                  BD, CD
                    <emph type="italics"/>
                  concurſu
                    <lb/>
                  ſuo
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  deſcribant Sectionem Conicam per data puncta
                    <emph.end type="italics"/>
                  B, C, A
                    <lb/>
                    <emph type="italics"/>
                  tranſeuntem, & ſit angulus
                    <emph.end type="italics"/>
                  DBM
                    <emph type="italics"/>
                  ſemper æqualis angulo dato
                    <emph.end type="italics"/>
                    <lb/>
                  ABC,
                    <emph type="italics"/>
                  anguluſque
                    <emph.end type="italics"/>
                  DCM
                    <emph type="italics"/>
                  ſemper æqualis angulo dato
                    <emph.end type="italics"/>
                  ACB:
                    <lb/>
                    <emph type="italics"/>
                  punctum
                    <emph.end type="italics"/>
                  M
                    <emph type="italics"/>
                  continget rectam poſitione datam.
                    <emph.end type="italics"/>
                  </s>
                </p>
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