Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/227.jpg" pagenum="199"/>
                  qua Sphærois trahit corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erit ad vim qua Sphæra, diametro
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note175"/>
                  deſcripta, trahit idem corpus, ut (
                    <emph type="italics"/>
                  ASXCSq-PSXKMRK/PSq+CSq-ASq
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ad (
                    <emph type="italics"/>
                  AS cub/3PS quad
                    <emph.end type="italics"/>
                  ). Et eodem computandi fundamento invenire licet
                    <lb/>
                  vires ſegmentorum Sphæroidis. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note175"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Quod ſi corpuſculum intra Sphæroidem, in data qua­
                    <lb/>
                  vis ejuſdem diametro, collocetur; attractio erit ut ipſius diſtantia a
                    <lb/>
                  centro. </s>
                  <s>Id quod facilius colligetur hoc argumento. </s>
                  <s>Sit
                    <emph type="italics"/>
                  AGOF
                    <emph.end type="italics"/>
                    <lb/>
                  Sphærois attrahens,
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  centrum ejus &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corpus attractum. </s>
                  <s>Per
                    <lb/>
                  corpus illud
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  agantur tum ſemidiameter
                    <emph type="italics"/>
                  SPA,
                    <emph.end type="italics"/>
                  tum rectæ duæ
                    <lb/>
                  quævis
                    <emph type="italics"/>
                  DE, FG
                    <emph.end type="italics"/>
                  Sphæroidi hinc inde occurrentes in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  E, F
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  G:
                    <emph.end type="italics"/>
                  Sintque
                    <emph type="italics"/>
                  PCM, HLN
                    <emph.end type="italics"/>
                  ſuperficies Sphæroidum duarum in­
                    <lb/>
                  teriorum, exteriori ſimilium & concentricarum, quarum prior tranſ­
                    <lb/>
                  eat per corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  & ſecet rectas
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  FG
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  poſterior
                    <lb/>
                  ſecet eaſdem rectas in
                    <emph type="italics"/>
                  H, I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K, L.
                    <emph.end type="italics"/>
                  Habeant autem Sphæroides
                    <lb/>
                  omnes axem communem, & erunt rect­
                    <lb/>
                    <figure id="id.039.01.227.1.jpg" xlink:href="039/01/227/1.jpg" number="131"/>
                    <lb/>
                  arum partes hinc inde interceptæ
                    <emph type="italics"/>
                  DP
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  BE, FP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CG, DH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  IE, FK
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  LG
                    <emph.end type="italics"/>
                  ſibi mutuo æquales; propterea
                    <lb/>
                  quod rectæ
                    <emph type="italics"/>
                  DE, PB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  biſecan­
                    <lb/>
                  tur in eodem puncto, ut & rectæ
                    <emph type="italics"/>
                  FG,
                    <lb/>
                  PC
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  KL.
                    <emph.end type="italics"/>
                  Concipe jam
                    <emph type="italics"/>
                  DPF,
                    <lb/>
                  EPG
                    <emph.end type="italics"/>
                  deſignare Conos oppoſitos, an­
                    <lb/>
                  gulis verticalibus
                    <emph type="italics"/>
                  DPF, EPG
                    <emph.end type="italics"/>
                  infi­
                    <lb/>
                  nite parvis deſcriptos, & lineas etiam
                    <lb/>
                    <emph type="italics"/>
                  DH, EI
                    <emph.end type="italics"/>
                  infinite parvas eſſe; & Conorum particulæ Sphæroidum
                    <lb/>
                  ſuperficiebus abſciſſæ
                    <emph type="italics"/>
                  DHKF, GLIE,
                    <emph.end type="italics"/>
                  ob æqualitatem linearum
                    <lb/>
                    <emph type="italics"/>
                  DH, EI,
                    <emph.end type="italics"/>
                  erunt ad invicem ut quadrata diſtantiarum ſuarum a
                    <lb/>
                  corpuſculo
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  & propterea corpuſculum illud æqualiter trahent. </s>
                  <s>
                    <lb/>
                  Et pari ratione, ſi ſuperficiebus Sphæroidum innumerarum ſimilium
                    <lb/>
                  concentricarum & axem communem habentium dividantur ſpatia
                    <lb/>
                    <emph type="italics"/>
                  DPF, EGCB
                    <emph.end type="italics"/>
                  in particulas, hæ omnes utrinque æqualiter tra­
                    <lb/>
                  hent corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in partes contrarias. </s>
                  <s>Æquales igitur ſunt vires
                    <lb/>
                  Coni
                    <emph type="italics"/>
                  DPF
                    <emph.end type="italics"/>
                  & ſegmenti Conici
                    <emph type="italics"/>
                  EGCB,
                    <emph.end type="italics"/>
                  & per contrarietatem ſe
                    <lb/>
                  mutuo deſtruunt. </s>
                  <s>Et par eſt ratio virium materiæ omnis extra Sphæ­
                    <lb/>
                  roidem intimam
                    <emph type="italics"/>
                  PCBM.
                    <emph.end type="italics"/>
                  Trahitur igitur corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  a ſola Sphæ­
                    <lb/>
                  roide intima
                    <emph type="italics"/>
                  PCBM,
                    <emph.end type="italics"/>
                  & propterea (per Corol. </s>
                  <s>3. Prop. </s>
                  <s>LXXII) at­
                    <lb/>
                  tractio ejus eſt ad vim, qua corpus
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  trahitur a Sphæroide tota
                    <lb/>
                    <emph type="italics"/>
                  AGOD,
                    <emph.end type="italics"/>
                  ut diſtantia
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad diſtantiam
                    <emph type="italics"/>
                  AS.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
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