Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/229.jpg" pagenum="201"/>
                  vis qua planum quodvis
                    <emph type="italics"/>
                  mHM
                    <emph.end type="italics"/>
                  trahit punctum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  eſt reciproce ut
                    <lb/>
                    <arrow.to.target n="note177"/>
                    <emph type="italics"/>
                  CH
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                  .
                    <emph.end type="italics"/>
                  In plano
                    <emph type="italics"/>
                  mHM
                    <emph.end type="italics"/>
                  capiatur longitudo
                    <emph type="italics"/>
                  HM
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  CH
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  re­
                    <lb/>
                  ciproce proportionalis, & erit vis illa ut
                    <emph type="italics"/>
                  HM.
                    <emph.end type="italics"/>
                  Similiter in planis ſin­
                    <lb/>
                  gulis
                    <emph type="italics"/>
                  lGL, nIN, oKO,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>capiantur longitudines
                    <emph type="italics"/>
                  GL, IN, KO,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  ipſis
                    <emph type="italics"/>
                  CG
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                  , CI
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                  , CK
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>reciproce proportionales; & vi­
                    <lb/>
                  res planorum eorundem erunt ut longitudines captæ, adeoque
                    <lb/>
                  ſumma virium ut ſumma longitudinum, hoc eſt, vis Solidi totius ut
                    <lb/>
                  area
                    <emph type="italics"/>
                  GLOK
                    <emph.end type="italics"/>
                  in infinitum verſus
                    <emph type="italics"/>
                  OK
                    <emph.end type="italics"/>
                  producta. </s>
                  <s>Sed area illa (per
                    <lb/>
                  notas quadraturarum methodos) eſt reciproce ut
                    <emph type="italics"/>
                  CG
                    <emph type="sup"/>
                  n-3
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  & prop­
                    <lb/>
                  terea vis Solidi totius eſt reciproce ut
                    <emph type="italics"/>
                  CG
                    <emph type="sup"/>
                  n-3
                    <emph.end type="sup"/>
                  . </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note177"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Collocetur jam corpuſculum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ex parte plani
                    <emph type="italics"/>
                  lGL
                    <emph.end type="italics"/>
                  in­
                    <lb/>
                  tra Solidum, & capiatur diſtantia
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  æqualis diſtantiæ
                    <emph type="italics"/>
                  CG.
                    <emph.end type="italics"/>
                  Et So­
                    <lb/>
                  lidi pars
                    <emph type="italics"/>
                  LGloKO,
                    <emph.end type="italics"/>
                  planis parallelis
                    <emph type="italics"/>
                  lGL, oKO
                    <emph.end type="italics"/>
                  terminata, cor­
                    <lb/>
                  puſculum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  in medio ſitum nullam in partem trahet, contrariis op­
                    <lb/>
                  poſitorum punctorum actionibus ſe mutuo per æqualitatem tollenti­
                    <lb/>
                  bus. </s>
                  <s>Proinde corpuſculum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ſola vi Solidi ultra planum
                    <emph type="italics"/>
                  OK
                    <emph.end type="italics"/>
                  ſiti tra­
                    <lb/>
                  hitur. </s>
                  <s>Hæc autem vis (per Caſum primum) eſt reciproce ut
                    <emph type="italics"/>
                  CK
                    <emph type="sup"/>
                  n-3
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                    <lb/>
                  hoc eſt (ob æquales
                    <emph type="italics"/>
                  CG, CK
                    <emph.end type="italics"/>
                  ) reciproce ut
                    <emph type="italics"/>
                  CG
                    <emph type="sup"/>
                  n-3
                    <emph.end type="sup"/>
                  . </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi Solidum
                    <emph type="italics"/>
                  LGIN
                    <emph.end type="italics"/>
                  planis duobus infinitis pa­
                    <lb/>
                  rallelis
                    <emph type="italics"/>
                  LG, IN
                    <emph.end type="italics"/>
                  utrinque terminetur; innoteſcit ejus vis attra­
                    <lb/>
                  ctiva, ſubducendo de vi attractiva Solidi totius infiniti
                    <emph type="italics"/>
                  LGKO
                    <emph.end type="italics"/>
                    <lb/>
                  vim attractivam partis ulterioris
                    <emph type="italics"/>
                  NICO,
                    <emph.end type="italics"/>
                  in infinitum verſus
                    <emph type="italics"/>
                  KO
                    <emph.end type="italics"/>
                    <lb/>
                  productæ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si Solidi hujus infiniti pars ulterior, quando attractio e­
                    <lb/>
                  jus collata cum attractione partis citerioris nullius pene eſt momen­
                    <lb/>
                  ti, rejiciatur: attractio partis illius citerioris augendo diſtantiam de­
                    <lb/>
                  creſcet quam proxime in ratione poteſtatis
                    <emph type="italics"/>
                  CG
                    <emph type="sup"/>
                  n-3
                    <emph.end type="sup"/>
                  .
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Et hinc ſi corpus quodvis finitum & ex una parte pla­
                    <lb/>
                  num trahat corpuſculum e regione medii illius plani, & diſtantia
                    <lb/>
                  inter corpuſculum & planum collata cum dimenſionibus corpo­
                    <lb/>
                  ris attrahentis perexigua ſit, conſtet autem corpus attrahens ex
                    <lb/>
                  particulis homogeneis, quarum vires attractivæ decreſcunt in
                    <lb/>
                  ratione poteſtatis cujuſvis pluſquam quadruplicatæ diſtantiarum;
                    <lb/>
                  vis attractiva corporis totius decreſcet quamproxime in ratione
                    <lb/>
                  poteſtatis, cujus latus ſit diſtantia illa perexigua, & Index terna­
                    <lb/>
                  rio minor quam Index poteſtatis prioris. </s>
                  <s>De corpore ex particulis
                    <lb/>
                  conſtante, quarum vires attractivæ decreſcunt in ratione poteſtatis
                    <lb/>
                  triplicatæ diſtantiarum, aſſertio non valet; propterea quod, in hoc
                    <lb/>
                  caſu, attractio partis illius ulterioris corporis infiniti in Corollario
                    <lb/>
                  ſecundo, ſemper eſt infinite major quam attractio partis citerioris. </s>
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