Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  1. Jam ſi Figura
                    <emph type="italics"/>
                  DES
                    <emph.end type="italics"/>
                  Circulus eſt vel Hyperbola, biſece­
                    <lb/>
                    <arrow.to.target n="note85"/>
                  tur ejus tranſverſa diameter
                    <emph type="italics"/>
                  AS
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  & erit
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                    <figure id="id.039.01.137.1.jpg" xlink:href="039/01/137/1.jpg" number="84"/>
                    <lb/>
                    <emph type="italics"/>
                  SO
                    <emph.end type="italics"/>
                  dimidium lateris recti. </s>
                  <s>Et quoniam eſt
                    <lb/>
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  Cc
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Dd,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  TD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TS
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SY,
                    <emph.end type="italics"/>
                  erit ex æquo
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TS
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  CDXCc
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SYXDd.
                    <emph.end type="italics"/>
                  Sed per Corol. </s>
                  <s>1. Prop. </s>
                  <s>
                    <lb/>
                  XXXIII, eſt
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TS
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AO,
                    <emph.end type="italics"/>
                  puta ſi
                    <lb/>
                  in coitu punctorum
                    <emph type="italics"/>
                  D, d
                    <emph.end type="italics"/>
                  capiantur linearum
                    <lb/>
                  rationes ultimæ. </s>
                  <s>Ergo
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  eſt ad (
                    <emph type="italics"/>
                  AO
                    <emph.end type="italics"/>
                  ſeu)
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  CDXCc
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SYXDd.
                    <emph.end type="italics"/>
                  Porro corporis
                    <lb/>
                  deſcendentis velocitas in
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  eſt ad velocitatem
                    <lb/>
                  corporis Circulum intervallo
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  circa cen­
                    <lb/>
                  trum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  deſcribentis in ſubduplicata ratione
                    <lb/>
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad (
                    <emph type="italics"/>
                  AO
                    <emph.end type="italics"/>
                  vel)
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  (per Prop. </s>
                  <s>XXXIII.) Et
                    <lb/>
                  hæc velocitas ad velocitatem corporis deſcri­
                    <lb/>
                  bentis Circulum
                    <emph type="italics"/>
                  OKk
                    <emph.end type="italics"/>
                  in ſubduplicata ratione
                    <lb/>
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  per Cor. </s>
                  <s>6. Prop. </s>
                  <s>IV, & ex æquo velo­
                    <lb/>
                  citas prima ad ultimam, hoc eſt lineola
                    <emph type="italics"/>
                  Cc
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  arcum
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  in ſubduplicata ratione
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SC,
                    <emph.end type="italics"/>
                    <lb/>
                  id eſt in ratione
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CD.
                    <emph.end type="italics"/>
                  Quare eſt
                    <emph type="italics"/>
                  CDXCc
                    <emph.end type="italics"/>
                    <lb/>
                  æquale
                    <emph type="italics"/>
                  ACXKk,
                    <emph.end type="italics"/>
                  & propterea
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  ACXKk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SYXDd,
                    <emph.end type="italics"/>
                    <expan abbr="indeq;">indeque</expan>
                    <emph type="italics"/>
                  SKXKk
                    <emph.end type="italics"/>
                  æqua­
                    <lb/>
                  le
                    <emph type="italics"/>
                  SYXDd,
                    <emph.end type="italics"/>
                  & 1/2
                    <emph type="italics"/>
                  SKXKk
                    <emph.end type="italics"/>
                  æquale 1/2
                    <emph type="italics"/>
                  SYXDd,
                    <emph.end type="italics"/>
                    <lb/>
                  id eſt area
                    <emph type="italics"/>
                  KSk
                    <emph.end type="italics"/>
                  æqualis areæ
                    <emph type="italics"/>
                  SDd.
                    <emph.end type="italics"/>
                  Singulis
                    <lb/>
                  igitur temporis particulis generantur arearum
                    <lb/>
                  duarum particulæ
                    <emph type="italics"/>
                  KSk,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SDd,
                    <emph.end type="italics"/>
                  quæ, ſi mag­
                    <lb/>
                  nitudo earum minuatur & numerus augeatur in infinitum, ratio­
                    <lb/>
                  nem obtinent æqualitatis, & propterea (per Corollarium Lem­
                    <lb/>
                  matis IV) areæ totæ ſimul genitæ ſunt ſemper æquales,
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note85"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  2. Quod ſi Figura
                    <emph type="italics"/>
                  DES
                    <emph.end type="italics"/>
                  Parabola ſit, invenietur eſſe ut ſu­
                    <lb/>
                  pra
                    <emph type="italics"/>
                  CDXCc
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SYXDd
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TS,
                    <emph.end type="italics"/>
                  hoc eſt ut 2 ad 1, ad­
                    <lb/>
                  eoque 1/4
                    <emph type="italics"/>
                  CDXCc
                    <emph.end type="italics"/>
                  æquale eſſe 1/2
                    <emph type="italics"/>
                  SYXDd.
                    <emph.end type="italics"/>
                  Sed corporis caden­
                    <lb/>
                  tis velocitas in
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  æqualis eſt velocitati qua Circulus intervallo 1/2
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                    <lb/>
                  uniformiter deſcribi poſſit (per Prop. </s>
                  <s>XXXIV) Et hæc velocitas ad ve­
                    <lb/>
                  locitatem qua Circulus radio
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  deſcribi poſſit, hoc eſt, lineola
                    <lb/>
                    <emph type="italics"/>
                  Cc
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  (per Corol. </s>
                  <s>6. Prop. </s>
                  <s>IV) eſt in ſubduplicata ratione
                    <lb/>
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  SC,
                    <emph.end type="italics"/>
                  id eſt, in ratione
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  CD.
                    <emph.end type="italics"/>
                  Quare eſt 1/2
                    <emph type="italics"/>
                  SKXKk
                    <emph.end type="italics"/>
                    <lb/>
                  æquale 1/4
                    <emph type="italics"/>
                  CDXCc,
                    <emph.end type="italics"/>
                  adeoque æquale 1/2
                    <emph type="italics"/>
                  SYXDd,
                    <emph.end type="italics"/>
                  hoc eſt, area
                    <emph type="italics"/>
                  KSk
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis areæ
                    <emph type="italics"/>
                  SDd,
                    <emph.end type="italics"/>
                  ut ſupra.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
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