Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note60"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note60"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XXIV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si rectæ tres tangant quamcunque Coniſectionem, quarum duæ pa­
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                  rallelæ ſint ac dentur poſitione; dico quod Sectionis ſemidia­
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                  meter hiſce duabus parallela, ſit media proportionalis inter ha­
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                  rum ſegmenta, punctis contactuum & tangenti tertiæ inter­
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                  jecta.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sunto
                    <emph type="italics"/>
                  AF, GB
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                  pa­
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                    <figure id="id.039.01.112.1.jpg" xlink:href="039/01/112/1.jpg" number="58"/>
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                  rallelæ duæ Coniſec­
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                  tionem
                    <emph type="italics"/>
                  ADB
                    <emph.end type="italics"/>
                  tan­
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                  gentes in
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B; EF
                    <emph.end type="italics"/>
                    <lb/>
                  recta tertia Coniſec­
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                  tionem tangens in
                    <emph type="italics"/>
                  I,
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                    <lb/>
                  & occurrens prioribus
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                  tangentibus in
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  ſitque
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ſemidiame­
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                  ter Figuræ tangenti­
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                  bus parallela: Dico
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                  quod
                    <emph type="italics"/>
                  AF, CD, BG
                    <emph.end type="italics"/>
                    <lb/>
                  ſunt continue proportionales. </s>
                </p>
                <p type="main">
                  <s>Nam ſi diametri conjugatæ
                    <emph type="italics"/>
                  AB, DM
                    <emph.end type="italics"/>
                  tangenti
                    <emph type="italics"/>
                  FG
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                  occurrant
                    <lb/>
                  in
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  ſeque mutuo ſecent in
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  & compleatur parallelogram­
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                  mum
                    <emph type="italics"/>
                  IKCL
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                  ; erit, ex natura Sectionum Conicarum, ut
                    <emph type="italics"/>
                  EC
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  ita
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CL,
                    <emph.end type="italics"/>
                  & ita diviſim
                    <emph type="italics"/>
                  EC-CA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CA-CL,
                    <emph.end type="italics"/>
                  ſeu
                    <lb/>
                    <emph type="italics"/>
                  EA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AL,
                    <emph.end type="italics"/>
                  & compoſite
                    <emph type="italics"/>
                  EA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EA+AL
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  EL
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  EC
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  EC+CA
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  EB
                    <emph.end type="italics"/>
                  ; adeoque (ob ſimilitudinem triangulorum
                    <emph type="italics"/>
                  EAF,
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                  ELI, ECH, EBG) AF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  LI
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BG.
                    <emph.end type="italics"/>
                  Eſt itidem,
                    <lb/>
                  ex natura Sectionum Conicarum,
                    <emph type="italics"/>
                  LI
                    <emph.end type="italics"/>
                  (ſeu
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  ) ad
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  ; atque, adeo ex æquo perturbate,
                    <emph type="italics"/>
                  AF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BG.
                    <lb/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi tangentes duæ
                    <emph type="italics"/>
                  FG, PQ
                    <emph.end type="italics"/>
                  tangentibus parallelis
                    <lb/>
                    <emph type="italics"/>
                  AF, BG
                    <emph.end type="italics"/>
                  occurrant in
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  G, P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q,
                    <emph.end type="italics"/>
                  ſeque mutuo ſecent in
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  ;
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                  erit (ex æquo perturbate)
                    <emph type="italics"/>
                  AF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BG,
                    <emph.end type="italics"/>
                  & diviſim
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                  ut
                    <emph type="italics"/>
                  FP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  GQ,
                    <emph.end type="italics"/>
                  atque adeo ut
                    <emph type="italics"/>
                  FO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OG.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Unde etiam rectæ duæ
                    <emph type="italics"/>
                  PG, FQ
                    <emph.end type="italics"/>
                  per puncta
                    <emph type="italics"/>
                  P
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                  &
                    <emph type="italics"/>
                  G,
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                  F
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
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                  ductæ, concurrent ad rectam
                    <emph type="italics"/>
                  ACB
                    <emph.end type="italics"/>
                  per centrum Figuræ &
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                  puncta contactuum
                    <emph type="italics"/>
                  A, B
                    <emph.end type="italics"/>
                  tranſeuntem. </s>
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