Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/208.jpg" pagenum="180"/>
                    <arrow.to.target n="note156"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note156"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Eadem valent ubi attractio oritur a Sphæræ utriuſque
                    <lb/>
                  virtute attractiva, mutuo exercita in Sphæram alteram. </s>
                  <s>Nam viri­
                    <lb/>
                  bus ambabus geminatur attractio, proportione ſervata. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Si hujuſmodi Sphæræ aliquæ circa alias quieſcentes re­
                    <lb/>
                  volvantur, ſingulæ circa ſingulas, ſintQ.E.D.ſtantiæ inter centra re­
                    <lb/>
                  volventium & quieſcentium proportionales quieſcentium diame­
                    <lb/>
                  tris; æqualia erunt Tempora periodica. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. Et viciſſim, ſi Tempora periodica ſunt æqualia; diſtan­
                    <lb/>
                  tiæ erunt proportionales diametris. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  8. Eadem omnia, quæ ſuperius de motu corporum circa
                    <lb/>
                  umbilicos Conicarum Sectionum demonſtrata ſunt, obtinent ubi
                    <lb/>
                  Sphæra attrahens, formæ & conditionis cujuſvis jam deſcriptæ, lo­
                    <lb/>
                  catur in umbilico. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  9. Ut & ubi gyrantia ſunt etiam Sphæræ attrahentes, con­
                    <lb/>
                  ditionis cujuſvis jam deſcriptæ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXVII. THEOREMA XXXVII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ad ſingula Sphærarum puncta tendant vires centripetæ, proper­
                    <lb/>
                  tionales diſtantiis punctorum a corporibus attractis: dico quod
                    <lb/>
                  vis compoſita, qua Sphæræ duæ ſe mutuo trahent, est ut di­
                    <lb/>
                  ſtantia inter centra Sphærarum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Sit
                    <emph type="italics"/>
                  AEBF
                    <emph.end type="italics"/>
                  Sphæra,
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.208.1.jpg" xlink:href="039/01/208/1.jpg" number="118"/>
                    <lb/>
                  centrum ejus,
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corpuſculum at­
                    <lb/>
                  tractum,
                    <emph type="italics"/>
                  PASB
                    <emph.end type="italics"/>
                  axis Sphæræ per
                    <lb/>
                  centrum corpuſculi tranſiens,
                    <emph type="italics"/>
                  EF,
                    <lb/>
                  ef
                    <emph.end type="italics"/>
                  plana duo quibus Sphæra ſe­
                    <lb/>
                  catur, huic axi perpendicularia &
                    <lb/>
                  hinc inde æqualiter diſtantia a
                    <lb/>
                  centro Sphæræ;
                    <emph type="italics"/>
                  G, g
                    <emph.end type="italics"/>
                  interſectio­
                    <lb/>
                  nes planorum & axis, &
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  pun­
                    <lb/>
                  ctum quodvis in plano
                    <emph type="italics"/>
                  EF.
                    <emph.end type="italics"/>
                  Pun­
                    <lb/>
                  cti
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  vis centripeta in corpuſculum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ſecundum lineam
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  exer­
                    <lb/>
                  cita, eſt ut diſtantia
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ; & (per Legum Corol. </s>
                  <s>2.) ſecundum li­
                    <lb/>
                  neam
                    <emph type="italics"/>
                  PG,
                    <emph.end type="italics"/>
                  ſeu verſus centrum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  ut longitudo
                    <emph type="italics"/>
                  PG.
                    <emph.end type="italics"/>
                  Igitur pun­
                    <lb/>
                  ctorum omnium in plano
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  hoc eſt plani totius vis, qua corpuſ­
                    <lb/>
                  culum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  trahitur verſus centrum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  eſt ut numerus punctorum
                    <lb/>
                  ductus in diſtantiam
                    <emph type="italics"/>
                  PG:
                    <emph.end type="italics"/>
                  id eſt, ut contentum ſub plano ipſo
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                    <lb/>
                  & diſtantia illa
                    <emph type="italics"/>
                  PG.
                    <emph.end type="italics"/>
                  Et ſimiliter vis plani
                    <emph type="italics"/>
                  ef,
                    <emph.end type="italics"/>
                  qua corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  </s>
                </p>
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