Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/213.jpg" pagenum="185"/>
                <p type="main">
                  <s>Etenim ſtantibus quæ in Lemmate & Theoremate noviſſimo
                    <lb/>
                    <arrow.to.target n="note161"/>
                  conſtructa ſunt, concipe axem Sphæræ
                    <emph type="italics"/>
                  AB
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                  dividi in particulas
                    <lb/>
                  innumeras æquales
                    <emph type="italics"/>
                  Dd,
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                  & Sphæram totam dividi in totidem
                    <lb/>
                  laminas Sphæricas concavo-convexas
                    <emph type="italics"/>
                  EFfe
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                  ; & erigatur perpen­
                    <lb/>
                  diculum
                    <emph type="italics"/>
                  dn.
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                  Per Theorema ſuperius, vis qua lamina
                    <emph type="italics"/>
                  EFfe
                    <emph.end type="italics"/>
                    <lb/>
                  trahit corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  eſt ut
                    <emph type="italics"/>
                  DEqXFf
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                  & vis particulæ unius ad
                    <lb/>
                  diſtantiam
                    <emph type="italics"/>
                  PE
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                  vel
                    <emph type="italics"/>
                  PF
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                  exercita conjunctim. </s>
                  <s>Eſt autem per Lem­
                    <lb/>
                  ma noviſſimum,
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS,
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                  & inde
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  æqualis
                    <lb/>
                  (
                    <emph type="italics"/>
                  PSXDd/PE
                    <emph.end type="italics"/>
                  ); &
                    <emph type="italics"/>
                  DEqXFf
                    <emph.end type="italics"/>
                  æquale
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  in (
                    <emph type="italics"/>
                  DEqXPS/PE
                    <emph.end type="italics"/>
                  ), & propter­
                    <lb/>
                  ea vis laminæ
                    <emph type="italics"/>
                  EFfe
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                  eſt ut
                    <emph type="italics"/>
                  Dd
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                  in (
                    <emph type="italics"/>
                  DEqXPS/PE
                    <emph.end type="italics"/>
                  ) & vis particulæ ad
                    <lb/>
                  diſtantiam
                    <emph type="italics"/>
                  PF
                    <emph.end type="italics"/>
                  exercita conjunctim, hoc eſt (ex Hypotheſi) ut
                    <lb/>
                    <emph type="italics"/>
                  DNXDd,
                    <emph.end type="italics"/>
                  ſeu area evaneſcens
                    <emph type="italics"/>
                  DNnd.
                    <emph.end type="italics"/>
                  Sunt igitur laminarum
                    <lb/>
                  omnium vires in corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  exercitæ, ut areæ omnes
                    <emph type="italics"/>
                  DNnd,
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                  hoc
                    <lb/>
                  eſt, Sphæræ vis tota ut area tota
                    <emph type="italics"/>
                  ABNA. Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note161"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc ſi vis centripeta, ad particulas ſingulas tendens,
                    <lb/>
                  eadem ſemper maneat in omnibus diſtantiis, & fiat
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  (
                    <emph type="italics"/>
                  DEqXPS/PE
                    <emph.end type="italics"/>
                  ): erit vis tota qua corpuſculum a Sphæra attrahitur,
                    <lb/>
                  ut area
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si particularum vis centripeta ſit reciproce ut diſtantia
                    <lb/>
                  corpuſculi a ſe attracti, & fiat
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  DEqXPS/PEq
                    <emph.end type="italics"/>
                  ): erit vis qua
                    <lb/>
                  corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  a Sphæra tota attrahitur ut area
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Si particularum vis centripeta ſit reciproce ut cubus di­
                    <lb/>
                  ſtantiæ corpuſculi a ſe attracti, & fiat
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  DEqXPS/PEqq
                    <emph.end type="italics"/>
                  ): erit
                    <lb/>
                  vis qua corpuſculum a tota Sphæra attrahitur ut area
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Et univerſaliter ſi vis centripeta ad ſingulas Sphæræ
                    <lb/>
                  particulas tendens ponatur eſſe reciproce ut quantitas V, fiat au­
                    <lb/>
                  tem
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut (
                    <emph type="italics"/>
                  DEqXPS/PEXV
                    <emph.end type="italics"/>
                  ); erit vis qua corpuſculum a Sphæra tota
                    <lb/>
                  attrahitur ut area
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  </s>
                </p>
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          </chap>
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