Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note61"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note61"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XXV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si parallelogrammi latera quatuor infinite producta tangant Sectio­
                    <lb/>
                  nem quamcunque Conicam, & abſcindantur ad tangentem quamvis
                    <lb/>
                  quintam; ſumantur autem laterum quorumvis duorum contermi­
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                  norum abſciſſæ terminatæ ad angulos oppoſitos parallelogrammi:
                    <lb/>
                  dico quod abſciſſa alterutra ſit ad latus illud a quo est abſciſſa, ut
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                  pars lateris alterius contermini inter punctum contactus & latus
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                  tertium, est ad abſciſſarum alteram.
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                  </s>
                </p>
                <p type="main">
                  <s>Tangant parallelogrammi
                    <emph type="italics"/>
                  MLIK
                    <emph.end type="italics"/>
                  latera quatuor
                    <emph type="italics"/>
                  ML, IK, KL,
                    <lb/>
                  MI
                    <emph.end type="italics"/>
                  ſectionem Conicam in
                    <emph type="italics"/>
                  A, B, C, D,
                    <emph.end type="italics"/>
                  & ſecet tangens quinta
                    <emph type="italics"/>
                  FQ
                    <emph.end type="italics"/>
                    <lb/>
                  hæc latera in
                    <emph type="italics"/>
                  F, Q, H
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.113.1.jpg" xlink:href="039/01/113/1.jpg" number="59"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  ; ſumantur autem
                    <lb/>
                  laterum
                    <emph type="italics"/>
                  MI, KI
                    <emph.end type="italics"/>
                  ab­
                    <lb/>
                  ſciſſæ
                    <emph type="italics"/>
                  ME, KQ,
                    <emph.end type="italics"/>
                  vel
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                  laterum
                    <emph type="italics"/>
                  KL, ML
                    <emph.end type="italics"/>
                  ab­
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                  ſciſſæ
                    <emph type="italics"/>
                  KH, MF:
                    <emph.end type="italics"/>
                  di­
                    <lb/>
                  co quod ſit
                    <emph type="italics"/>
                  ME
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  MI
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  BK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  KQ
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  &
                    <emph type="italics"/>
                  KH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MF.
                    <emph.end type="italics"/>
                  Nam
                    <lb/>
                  per Corollarium ſe­
                    <lb/>
                  cundum Lemmatis ſuperioris, eſt
                    <emph type="italics"/>
                  ME
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EI
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  ſeu)
                    <emph type="italics"/>
                  BK
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  BQ,
                    <emph.end type="italics"/>
                  & componendo
                    <emph type="italics"/>
                  ME
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MI
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  BK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="Kq.">Kque</expan>
                  Q.E.D.
                    <emph.end type="italics"/>
                    <lb/>
                  Item
                    <emph type="italics"/>
                  KH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  HL
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  BK
                    <emph.end type="italics"/>
                  ſeu)
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AF,
                    <emph.end type="italics"/>
                  & dividendo
                    <emph type="italics"/>
                  KH
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AM
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  MF. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi datur parallelogramum
                    <emph type="italics"/>
                  IKLM,
                    <emph.end type="italics"/>
                  circa datam Sec­
                    <lb/>
                  tionem Conicam deſeriptum, dabitur rectangulum
                    <emph type="italics"/>
                  KQXME,
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  & huic æquale rectangulum
                    <emph type="italics"/>
                  KHXMF.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et ſi ſexta ducatur tangens
                    <emph type="italics"/>
                  eq
                    <emph.end type="italics"/>
                  tangentibus
                    <emph type="italics"/>
                  KI, MI
                    <emph.end type="italics"/>
                    <lb/>
                  occurrens in
                    <emph type="italics"/>
                  q
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                  ; rectangulum
                    <emph type="italics"/>
                  KQXME
                    <emph.end type="italics"/>
                  æquabitur rectan­
                    <lb/>
                  gulo
                    <emph type="italics"/>
                  KqXMe
                    <emph.end type="italics"/>
                  ; eritque
                    <emph type="italics"/>
                  KQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Me
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  Kq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ME,
                    <emph.end type="italics"/>
                  & diviſim ut
                    <lb/>
                    <emph type="italics"/>
                  Qq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Ee.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Unde etiam ſi
                    <emph type="italics"/>
                  Eq, eQ
                    <emph.end type="italics"/>
                  jungantur & biſecentur, & recta
                    <lb/>
                  per puncta biſectionum agatur, tranſibit hæc per centrum Sectio­
                    <lb/>
                  nis Conicæ. </s>
                  <s>Nam cum ſit
                    <emph type="italics"/>
                  Qq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Ee
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  KQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Me,
                    <emph.end type="italics"/>
                  tranſibit ea-</s>
                </p>
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