Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/091.jpg" pagenum="63"/>
                  ad
                    <emph type="italics"/>
                  sq,
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                  quæque conſtituat angulum
                    <emph type="italics"/>
                  vsp
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                  angulo
                    <emph type="italics"/>
                  hsq
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                  & angulum
                    <lb/>
                    <arrow.to.target n="note39"/>
                    <emph type="italics"/>
                  vsh
                    <emph.end type="italics"/>
                  angulo
                    <emph type="italics"/>
                  psq
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                  æquales, triangula
                    <emph type="italics"/>
                  svh, spq
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                  erunt ſimilia, & prop­
                    <lb/>
                  terea
                    <emph type="italics"/>
                  vh
                    <emph.end type="italics"/>
                  erit ad
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  sh
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  sq,
                    <emph.end type="italics"/>
                  id eſt (ob ſimilia triangula
                    <lb/>
                    <figure id="id.039.01.091.1.jpg" xlink:href="039/01/091/1.jpg" number="34"/>
                    <lb/>
                    <emph type="italics"/>
                  VSP, hsq
                    <emph.end type="italics"/>
                  ) ut eſt
                    <emph type="italics"/>
                  VS
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  ab
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="pq.">pque</expan>
                    <emph.end type="italics"/>
                  Æquantur ergo
                    <lb/>
                    <emph type="italics"/>
                  vh
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ab.
                    <emph.end type="italics"/>
                  Porro ob ſimilia triangula
                    <emph type="italics"/>
                  VSH. vsh,
                    <emph.end type="italics"/>
                  eſt
                    <emph type="italics"/>
                  VH
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  SH
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  vh
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  sh,
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                  id eſt, axis Conicæ ſectionis jam deſcriptæ ad
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                  illius umbilieorum intervallum, ut axis
                    <emph type="italics"/>
                  ab
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                  ad umbilieorum inter­
                    <lb/>
                  vallum
                    <emph type="italics"/>
                  sh
                    <emph.end type="italics"/>
                  ; & propterea Figura jam deſeripta ſimilis eſt Figuræ
                    <lb/>
                    <emph type="italics"/>
                  apb.
                    <emph.end type="italics"/>
                  Tranſit autem hæc Figura per punctum
                    <emph type="italics"/>
                  P,
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                  eo quod trian­
                    <lb/>
                  gulum
                    <emph type="italics"/>
                  PSH
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                  ſimile ſit triangulo
                    <emph type="italics"/>
                  psh
                    <emph.end type="italics"/>
                  ; & quia
                    <emph type="italics"/>
                  VH
                    <emph.end type="italics"/>
                  æquatur ipſius
                    <lb/>
                  axi &
                    <emph type="italics"/>
                  VS
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                  biſecatur perpendiculariter a recta
                    <emph type="italics"/>
                  TR,
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                  tangit eadem
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                  rectam
                    <emph type="italics"/>
                  TR. q.E.F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note39"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XVI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  A datis tribus punctis ad quartum non datum inflectere tres rectas
                    <lb/>
                  quarum differentiæ vel dantur vel nullæ ſunt.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Sunto puncta illa data
                    <emph type="italics"/>
                  A, B, C
                    <emph.end type="italics"/>
                  & punctum quartum
                    <emph type="italics"/>
                  Z,
                    <emph.end type="italics"/>
                    <lb/>
                  quod invenire oportet; Ob datam differentiam linearum
                    <emph type="italics"/>
                  AZ, BZ,
                    <emph.end type="italics"/>
                    <lb/>
                  locabitur punctum
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  in Hyperbola cujus umbilici ſunt
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  principalis axis differentia illa data. </s>
                  <s>Sit axis ille
                    <emph type="italics"/>
                  MN.
                    <emph.end type="italics"/>
                  Cape
                    <emph type="italics"/>
                  PM.
                    <emph.end type="italics"/>
                  </s>
                </p>
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