Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/215.jpg" pagenum="187"/>
                    <arrow.to.target n="note163"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note163"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  1. Si vis centripeta ad ſingulas Sphæræ particulas ten­
                    <lb/>
                  dens ſit reciproce ut diſtantia; pro V ſcribe diſtantiam
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  ; dein
                    <lb/>
                  2
                    <emph type="italics"/>
                  PSXLD
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  PEq,
                    <emph.end type="italics"/>
                  & fiet
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SL-1/2LD-(ALB/2LD).
                    <emph.end type="italics"/>
                    <lb/>
                  Pone
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  æqualem duplo ejus 2
                    <emph type="italics"/>
                  SL-LD-(ALB/LD)
                    <emph.end type="italics"/>
                  : & ordinatæ
                    <lb/>
                  pars data 2
                    <emph type="italics"/>
                  SL
                    <emph.end type="italics"/>
                  ducta in longitudinem
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  deſcribet aream rectan­
                    <lb/>
                  gulam 2
                    <emph type="italics"/>
                  SLXAB
                    <emph.end type="italics"/>
                  ; & pars indefinita
                    <emph type="italics"/>
                  LD
                    <emph.end type="italics"/>
                  ducta normaliter in
                    <lb/>
                  eandem longitudinem per motum continuum, ea lege ut inter mo­
                    <lb/>
                  vendum creſcendo vel decreſcendo æquetur ſemper longitudini
                    <lb/>
                    <emph type="italics"/>
                  LD,
                    <emph.end type="italics"/>
                  deſcribet aream (
                    <emph type="italics"/>
                  LBq-LAq
                    <emph.end type="italics"/>
                  /2), id eſt, aream
                    <emph type="italics"/>
                  SLXAB
                    <emph.end type="italics"/>
                  ; quæ
                    <lb/>
                  ſubducta de area priore 2
                    <emph type="italics"/>
                  SLXAB
                    <emph.end type="italics"/>
                  relinquit aream
                    <emph type="italics"/>
                  SLXAB.
                    <emph.end type="italics"/>
                    <lb/>
                  Pars autem tertia (
                    <emph type="italics"/>
                  ALB/LD
                    <emph.end type="italics"/>
                  ) ducta itidem per motum localem norma­
                    <lb/>
                  liter in eandem longitudinem, deſcribet
                    <lb/>
                    <figure id="id.039.01.215.1.jpg" xlink:href="039/01/215/1.jpg" number="122"/>
                    <lb/>
                  aream Hyperbolicam; quæ ſubducta de
                    <lb/>
                  area
                    <emph type="italics"/>
                  SLXAB
                    <emph.end type="italics"/>
                  relinquet aream quæſitam
                    <lb/>
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  Unde talis emergit Proble­
                    <lb/>
                  matis conſtructio. </s>
                  <s>Ad puncta
                    <emph type="italics"/>
                  L, A, B
                    <emph.end type="italics"/>
                    <lb/>
                  erige perpendicula
                    <emph type="italics"/>
                  Ll, Aa, Bb,
                    <emph.end type="italics"/>
                  quorum
                    <lb/>
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  LB,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Bb
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  LA
                    <emph.end type="italics"/>
                  æquetur. </s>
                  <s>
                    <lb/>
                  Aſymptotis
                    <emph type="italics"/>
                  Ll, LB,
                    <emph.end type="italics"/>
                  per puncta
                    <emph type="italics"/>
                  a, b
                    <emph.end type="italics"/>
                  de­
                    <lb/>
                  ſcribatur Hyperbola
                    <emph type="italics"/>
                  ab.
                    <emph.end type="italics"/>
                  Et acta chor­
                    <lb/>
                  da
                    <emph type="italics"/>
                  ba
                    <emph.end type="italics"/>
                  claudet aream
                    <emph type="italics"/>
                  aba
                    <emph.end type="italics"/>
                  areæ quæſitæ
                    <lb/>
                    <emph type="italics"/>
                  ABNA
                    <emph.end type="italics"/>
                  æqualem. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  2. Si vis centripeta ad ſingulas Sphæræ particulas ten­
                    <lb/>
                  dens ſit reciproce ut cubus diſtantiæ, vel (quod perinde eſt) ut cubus
                    <lb/>
                  ille applicatus ad planum quodvis datum; ſcribe (
                    <emph type="italics"/>
                  PEcub/2ASq
                    <emph.end type="italics"/>
                  ) pro V,
                    <lb/>
                  dein 2
                    <emph type="italics"/>
                  PSXLD
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  PEq
                    <emph.end type="italics"/>
                  ; & fiet
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  (SLXASq/PSXLD)-(ASq/2PS)
                    <lb/>
                  -(ALBXASq/2PSXLDq),
                    <emph.end type="italics"/>
                  id eſt (ob continue proportionales
                    <emph type="italics"/>
                  PS, AS, SI
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ut
                    <emph type="italics"/>
                  (LSI/LD)-1/2SI-(ALBXSI/2LDq).
                    <emph.end type="italics"/>
                  Si ducantur hujus partes tres
                    <lb/>
                  in longitudinem
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  prima (
                    <emph type="italics"/>
                  LSI/LD
                    <emph.end type="italics"/>
                  ) generabit aream Hyper-</s>
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