Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Et hinc, ſi corpora plura minora revolvantur circa maxi­
                    <lb/>
                    <arrow.to.target n="note147"/>
                  mum, colligere licet quod Orbitæ deſcriptæ propius accedent ad
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                  Ellipticas, & arearum deſcriptiones fient magis æquabiles, ſi cor­
                    <lb/>
                  pora omnia viribus acceleratricibus, quæ ſunt ut eorum vires ab­
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                  ſolutæ directe & quadrata diſtantiarum inverſe, ſe mutuo trahant
                    <lb/>
                  agitentque, & Orbitæ cujuſque umbilicus collocetur in communi
                    <lb/>
                  centro gravitatis corporum omnium interiorum (nimirum umbi­
                    <lb/>
                  licus Orbitæ primæ & intimæ in centro gravitatis corporis maxi­
                    <lb/>
                  mi & intimi; ille Orbitæ ſecundæ, in communi centro gravi­
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                  tatis corporum duorum intimorum; iſte tertiæ, in communi cen­
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                  tro gravitatis trium interiorum; & ſic deinceps) quam ſi corpus
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                  intimum quieſcat & ſtatuatur communis umbilicus Orbitarum
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                  omnium. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note147"/>
                  LIBER
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                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXIX. THEOREMA XXIX.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  In Syſtemate corporum plurium
                    <emph.end type="italics"/>
                  A, B, C, D,
                    <emph type="italics"/>
                  &c. </s>
                  <s>ſi corpus aliquod
                    <emph.end type="italics"/>
                    <lb/>
                  A
                    <emph type="italics"/>
                  trahit cætera omnia
                    <emph.end type="italics"/>
                  B, C, D,
                    <emph type="italics"/>
                  &c. </s>
                  <s>viribus acceler atricibus
                    <lb/>
                  quæ ſunt reciproce ut quadrata diſtantiarum a trahente; &
                    <lb/>
                  corpus aliud
                    <emph.end type="italics"/>
                  B
                    <emph type="italics"/>
                  trahit etiam cætera
                    <emph.end type="italics"/>
                  A, C, D,
                    <emph type="italics"/>
                  &c. </s>
                  <s>viribus quæ
                    <lb/>
                  ſunt reciproce ut quadrata diſtantiarum a trahente: erunt Ab­
                    <lb/>
                  ſolutæ corporum trahentium
                    <emph.end type="italics"/>
                  A, B
                    <emph type="italics"/>
                  vires ad invicem, ut ſunt
                    <lb/>
                  ipſa corpora
                    <emph.end type="italics"/>
                  A, B,
                    <emph type="italics"/>
                  quorum ſunt vires.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam attractiones acceleratrices corporum omnium
                    <emph type="italics"/>
                  B, C, D
                    <emph.end type="italics"/>
                  ver­
                    <lb/>
                  ſus
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  paribus diſtantiis, ſibi invicem æquantur ex Hypotheſi; &
                    <lb/>
                  ſimiliter attractiones acceleratrices corporum omnium verſus
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                    <lb/>
                  paribus diſtantiis, ſibi invicem æquantur. </s>
                  <s>Eſt autem abſoluta vis
                    <lb/>
                  attractiva corporis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad vim abſolutam attractivam corporis
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                  attractio acceleratrix corporum omnium verſus
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad attractionem
                    <lb/>
                  acceleratricem corporum omnium verſus
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  paribus diſtantiis; &
                    <lb/>
                  ita eſt attractio acceleratrix corporis
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ad attractionem
                    <lb/>
                  acceleratricem corporis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  B.
                    <emph.end type="italics"/>
                  Sed attractio acceleratrix cor­
                    <lb/>
                  poris
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  eſt ad attractionem acceleratricem corporis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  verſus
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  ut maſſa corporis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad maſſam corporis
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ; propterea
                    <lb/>
                  quod vires motrices, quæ (per Definitionem ſecundam, ſepti­
                    <lb/>
                  mam & octavam) ex viribus acceleratricibus in corpora attracta
                    <lb/>
                  ductis oriuntur, ſunt (per motus Legem tertiam) ſibi invicem æqua-</s>
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