Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note13"/>
                  evaneſcent, & rationem ultimam habebunt æqualitatis.
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                  Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note13"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Unde ſi per
                    <emph type="italics"/>
                  B
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                  ducatur tangenti parallela
                    <emph type="italics"/>
                  BF,
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                  rectam
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                  quamvis
                    <emph type="italics"/>
                  AF
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                  per
                    <emph type="italics"/>
                  A
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                  tranſe­
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                    <figure id="id.039.01.056.1.jpg" xlink:href="039/01/056/1.jpg" number="9"/>
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                  untem perpetuo ſecans in
                    <emph type="italics"/>
                  F,
                    <emph.end type="italics"/>
                    <lb/>
                  hæc
                    <emph type="italics"/>
                  BF
                    <emph.end type="italics"/>
                  ultimo ad arcum e­
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                  vaneſcentem
                    <emph type="italics"/>
                  AB
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                  rationem
                    <lb/>
                  habebit æqualitatis, eo quod
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                  completo parallelogrammo
                    <emph type="italics"/>
                  AFBD
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                  rationem ſemper habet æqua­
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                  litatis ad
                    <emph type="italics"/>
                  AD.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et ſi per
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A
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                  ducantur plures rectæ
                    <emph type="italics"/>
                  BE, BD, AF,
                    <lb/>
                  AG,
                    <emph.end type="italics"/>
                  ſecantes tangentem
                    <emph type="italics"/>
                  AD
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                  & ipſius parallelam
                    <emph type="italics"/>
                  BF
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                  ; ratio ulti­
                    <lb/>
                  ma abſciſſarum omnium
                    <emph type="italics"/>
                  AD, AE, BF, BG,
                    <emph.end type="italics"/>
                  chordæque & ar­
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                  cus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad invicem erit ratio æqualitatis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Et propterea hæ omnes lineæ, in omni de rationibus ul­
                    <lb/>
                  timis argumentatione, pro ſe invicem uſurpari poſſunt. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA VIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si rectæ datæ
                    <emph.end type="italics"/>
                  AR, BR
                    <emph type="italics"/>
                  cum arcu
                    <emph.end type="italics"/>
                  AB,
                    <emph type="italics"/>
                  chorda
                    <emph.end type="italics"/>
                  AB
                    <emph type="italics"/>
                  & tangente
                    <emph.end type="italics"/>
                    <lb/>
                  AD,
                    <emph type="italics"/>
                  triangula tria
                    <emph.end type="italics"/>
                  ARB, ARB, ARD
                    <emph type="italics"/>
                  conſtituunt, dein
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                  puncta
                    <emph.end type="italics"/>
                  A, B
                    <emph type="italics"/>
                  accedunt ad invicem: dico quod ultima forma
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                  triangulorum evaneſcentium est ſimilitudinis, & ultima ratio
                    <lb/>
                  æqualitatis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam dum punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ad punctum
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.056.2.jpg" xlink:href="039/01/056/2.jpg" number="10"/>
                    <lb/>
                  accedit,
                    <expan abbr="intelligãtur">intelligantur</expan>
                  ſemper
                    <emph type="italics"/>
                  AB, AD, AR
                    <emph.end type="italics"/>
                    <lb/>
                  ad puncta longinqua
                    <emph type="italics"/>
                  b, d
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  r
                    <emph.end type="italics"/>
                  produci,
                    <lb/>
                  ipſique
                    <emph type="italics"/>
                  RD
                    <emph.end type="italics"/>
                  parallela agi
                    <emph type="italics"/>
                  rbd,
                    <emph.end type="italics"/>
                  & arcui
                    <lb/>
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſimilis ſemper ſit arcus
                    <emph type="italics"/>
                  Ab.
                    <emph.end type="italics"/>
                  Et coe­
                    <lb/>
                  untibus punctis
                    <emph type="italics"/>
                  A, B,
                    <emph.end type="italics"/>
                  angulus
                    <emph type="italics"/>
                  bAd
                    <emph.end type="italics"/>
                  eva­
                    <lb/>
                  neſcet, & propterea triangula tria ſemper
                    <lb/>
                  finita
                    <emph type="italics"/>
                  rAb, rAb, rAd
                    <emph.end type="italics"/>
                  coincident, ſunt­
                    <lb/>
                  que eo nomine ſimilia & æqualia. </s>
                  <s>Unde
                    <lb/>
                  & hiſce ſemper ſimilia & proportionalia
                    <lb/>
                    <emph type="italics"/>
                  RAB, RAB, RAD
                    <emph.end type="italics"/>
                  ſient ultimo ſibi
                    <lb/>
                  invicem ſimilia & æqualia.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Et hinc triangula illa, in omni de rationibus ultimis argu­
                    <lb/>
                  mentatione, pro ſe invicem uſurpari poſſunt. </s>
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