Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/226.jpg" pagenum="198"/>
                    <arrow.to.target n="note174"/>
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                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note174"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Unde ſi Solidum
                    <lb/>
                    <figure id="id.039.01.226.1.jpg" xlink:href="039/01/226/1.jpg" number="129"/>
                    <lb/>
                  Cylindrus ſit, parallelogrammo
                    <lb/>
                    <emph type="italics"/>
                  ADEB
                    <emph.end type="italics"/>
                  circa axem
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  revo­
                    <lb/>
                  luto deſcriptus, & vires centri­
                    <lb/>
                  petæ in ſingula ejus puncta ten­
                    <lb/>
                  dentes ſint reciproce ut quadra­
                    <lb/>
                  ta diſtantiarum a punctis: erit
                    <lb/>
                  attractio corpuſculi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in hunc
                    <lb/>
                  Cylindrum ut
                    <emph type="italics"/>
                  AB-PE+PD.
                    <emph.end type="italics"/>
                    <lb/>
                  Nam ordinatim applicata
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                    <lb/>
                  (per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XC) erit ut 1-(
                    <emph type="italics"/>
                  PF/PR
                    <emph.end type="italics"/>
                  ). Hujus pars 1 ducta in lon­
                    <lb/>
                  gitudinem
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  deſcribit aream 1X
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ; & pars altera (
                    <emph type="italics"/>
                  PF/PR
                    <emph.end type="italics"/>
                  ) ducta
                    <lb/>
                  in longitudinem
                    <emph type="italics"/>
                  PB,
                    <emph.end type="italics"/>
                  deſcribit aream 1 in —(
                    <emph type="italics"/>
                  PE-AD
                    <emph.end type="italics"/>
                  ) (id quod
                    <lb/>
                  ex curvæ
                    <emph type="italics"/>
                  LIK
                    <emph.end type="italics"/>
                  quadratura facile oſtendi poteſt:) & ſimiliter pars
                    <lb/>
                  eadem ducta in longitudinem
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  deſcribit aream 1 in —(
                    <emph type="italics"/>
                  PD-AD
                    <emph.end type="italics"/>
                  ),
                    <lb/>
                  ductaQ.E.I. ipſarum
                    <emph type="italics"/>
                  PB, PA
                    <emph.end type="italics"/>
                  differentiam
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  deſcribit arearum
                    <lb/>
                  differentiam 1 in —(
                    <emph type="italics"/>
                  PE-PD
                    <emph.end type="italics"/>
                  ). De contento primo 1X
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  aufe­
                    <lb/>
                  ratur contentum poſtremum 1 in —(
                    <emph type="italics"/>
                  PE-PD
                    <emph.end type="italics"/>
                  ), & reſtabit area
                    <emph type="italics"/>
                  LABI
                    <emph.end type="italics"/>
                    <lb/>
                  æqualis 1 in —(
                    <emph type="italics"/>
                  AB-PE+PD
                    <emph.end type="italics"/>
                  ). Ergo vis, huic areæ proportiona­
                    <lb/>
                  lis, eſt ut
                    <emph type="italics"/>
                  AB-PE+PD.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Hinc etiam
                    <lb/>
                    <figure id="id.039.01.226.2.jpg" xlink:href="039/01/226/2.jpg" number="130"/>
                    <lb/>
                  vis innoteſcit qua Sphæ­
                    <lb/>
                  rois
                    <emph type="italics"/>
                  AGBCD
                    <emph.end type="italics"/>
                  attrahit
                    <lb/>
                  corpus quodvis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  exte­
                    <lb/>
                  rius in axe ſuo
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ſi­
                    <lb/>
                  tum. </s>
                  <s>Sit
                    <emph type="italics"/>
                  NKRM
                    <emph.end type="italics"/>
                  Se­
                    <lb/>
                  ctio Conica cujus ordi­
                    <lb/>
                  natim applicata
                    <emph type="italics"/>
                  ER,
                    <emph.end type="italics"/>
                  ipſi
                    <lb/>
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  perpendicularis, æ­
                    <lb/>
                  quetur ſemper longitu­
                    <lb/>
                  dini
                    <emph type="italics"/>
                  PD,
                    <emph.end type="italics"/>
                  quæ ducitur
                    <lb/>
                  ad punctum illud
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  quo applicata iſta Sphæroidem ſecat. </s>
                  <s>A Sphæroidis verticibus
                    <emph type="italics"/>
                  A, B
                    <emph.end type="italics"/>
                    <lb/>
                  ad ejus axem
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  erigantur perpendicula
                    <emph type="italics"/>
                  AK, BM
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  AP, BP
                    <emph.end type="italics"/>
                    <lb/>
                  æqualia reſpective, & propterea Sectioni Conicæ occurrentia in
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  ; & jungatur
                    <emph type="italics"/>
                  KM
                    <emph.end type="italics"/>
                  auferens ab eadem ſegmentum
                    <emph type="italics"/>
                  KMRK.
                    <emph.end type="italics"/>
                    <lb/>
                  Sit autem Sphæroidis centrum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  & ſemidiameter maxima
                    <emph type="italics"/>
                  SC:
                    <emph.end type="italics"/>
                  & vis </s>
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