Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/222.jpg" pagenum="194"/>
                    <arrow.to.target n="note170"/>
                  cujuſvis diſtantiarum: attractiones acceleratrices in corpora tota
                    <lb/>
                  erunt ut corpora directe & diſtantiarum dignitates illæ inverſe. </s>
                  <s>Ut
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                  ſi vires particularum decreſcant in ratione duplicata diſtantiarum
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                  a corpuſculis attractis, corpora autem ſint ut
                    <emph type="italics"/>
                  A cub.
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                  &
                    <emph type="italics"/>
                  B cub.
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                  ad­
                    <lb/>
                  eoque tum corporum latera cubica, tum corpuſculorum attracto­
                    <lb/>
                  rum diſtantiæ a corporibus, ut
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B:
                    <emph.end type="italics"/>
                  attractiones acceleratri­
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                  ces in corpora erunt ut (
                    <emph type="italics"/>
                  Acub./Aquad.
                    <emph.end type="italics"/>
                  ) & (
                    <emph type="italics"/>
                  Bcub./Bquad.
                    <emph.end type="italics"/>
                  ) id eſt, ut corporum la­
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                  tera illa cubica
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B.
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                  Si vires particularum decreſcant in ra­
                    <lb/>
                  tione triplicata diſtantiarum a corpuſculis attractis; attractiones
                    <lb/>
                  acceleratrices in corpora tota erunt ut (
                    <emph type="italics"/>
                  Acub./Acub.
                    <emph.end type="italics"/>
                  ) & (
                    <emph type="italics"/>
                  Bcub./Bcub.
                    <emph.end type="italics"/>
                  ), id eſt, æqua­
                    <lb/>
                  les. </s>
                  <s>Si vires decreſcant in ratione quadruplicata; attractiones in
                    <lb/>
                  corpora erunt ut (
                    <emph type="italics"/>
                  Acub./Aqq.
                    <emph.end type="italics"/>
                  ) & (
                    <emph type="italics"/>
                  Bcub./Bqq.
                    <emph.end type="italics"/>
                  ) id eſt, reciproce ut latera cubi­
                    <lb/>
                  ca
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B.
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                  Et ſic in cæteris. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note170"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Unde viciſſim, ex viribus quibus corpora ſimilia tra­
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                  hunt corpuſcula ad ſe ſimiliter poſita, colligi poteſt ratio decre­
                    <lb/>
                  menti virium particularum attractivarum in receſſu corpuſculi at­
                    <lb/>
                  tracti; ſi modo decrementum illud ſit directe vel inverſe in ratione
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                  aliqua diſtantiarum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXXVIII. THEOREMA XLV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si particularum æqualium Corporis cujuſcunque vires attractivæ
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                  ſint ut diſtantiæ loeorum a particulis: vis corporis totius ten­
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                  det ad ipſius centrum gravitatis; & eadem erit cum vi Globi
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                  ex materia conſimili & æquali conſtantis & centrum habentis
                    <lb/>
                  in ejus centro gravitatis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Corporis
                    <emph type="italics"/>
                  RSTV
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                  particulæ
                    <emph type="italics"/>
                  A,
                    <lb/>
                  B
                    <emph.end type="italics"/>
                  trahant corpuſculum aliquod
                    <lb/>
                    <figure id="id.039.01.222.1.jpg" xlink:href="039/01/222/1.jpg" number="126"/>
                    <lb/>
                    <emph type="italics"/>
                  Z
                    <emph.end type="italics"/>
                  viribus quæ, ſi particulæ æ­
                    <lb/>
                  quantur inter ſe, ſint ut diſtan­
                    <lb/>
                  tiæ
                    <emph type="italics"/>
                  AZ, BZ
                    <emph.end type="italics"/>
                  ; ſin particulæ ſta­
                    <lb/>
                  tuantur inæquales, ſint ut hæ par­
                    <lb/>
                  ticulæ in diſtantias ſuas
                    <emph type="italics"/>
                  AZ, BZ
                    <emph.end type="italics"/>
                    <lb/>
                  reſpective ductæ. </s>
                  <s>Et exponan­
                    <lb/>
                  tur hæ vires per contenta illa
                    <lb/>
                    <emph type="italics"/>
                  AXAZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  BXBZ.
                    <emph.end type="italics"/>
                  Jungatur
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                    <lb/>
                  & ſecetur ea in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  AG
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BG
                    <emph.end type="italics"/>
                  ut particula
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ad particulam
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ; </s>
                </p>
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