Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  LIBER
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                  PRIMUS.</s>
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                    <emph type="center"/>
                  PROPOSITIO LXXXII. THEOREMA XLI.
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                  <s>
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                  In Sphæra centro
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                  S
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                  intervallo
                    <emph.end type="italics"/>
                  SA
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                  deſcripta, ſi capiantur
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                  SI, SA,
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                  SP
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                  continue proportionales: dico quod corpuſculi intra Sphæ­
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                  ram in loco quovis
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                  I
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                  attractio est ad attractionem ipſius extra
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                  Sphæram in loco
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                  P,
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                  in ratione compoſita ex ſubduplicata ratione
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                  diſtantiarum a centro
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                  IS, PS
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                  & ſubduplicata ratione virium
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                  centripetarum, in locis illis
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  &
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                  I,
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                  ad centrum tendentium.
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                  <s>Ut ſi vires centripetæ particularum Sphæræ ſint reciproce ut di­
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                  ſtantiæ corpuſculi a ſe attracti; vis, qua corpuſculum ſitum in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <lb/>
                  trahitur a Sphæra tota, erit ad vim qua trahitur in
                    <emph type="italics"/>
                  P,
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                  in ratione
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                  compoſita ex ſubduplicata ratione diſtantiæ
                    <emph type="italics"/>
                  SI
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                  ad diſtantiam
                    <emph type="italics"/>
                  SP
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                    <lb/>
                  & ratione ſubduplicata vis centripetæ in loco
                    <emph type="italics"/>
                  I,
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                  a particula aliqua
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                  in centro oriundæ, ad vim centripetam in loco
                    <emph type="italics"/>
                  P
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                  ab eadem in cen­
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                  tro particula oriundam, id eſt, ratione ſubduplicata diſtantiarum
                    <lb/>
                    <emph type="italics"/>
                  SI, SP
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                  ad invicem reciproce. </s>
                  <s>Hæ duæ rationes ſubduplicatæ
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                  componunt rationem æqualitatis, & propterea attractiones in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
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                  P
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                    <lb/>
                  a Sphæra tota factæ æquantur. </s>
                  <s>Simili computo, ſi vires particu­
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                  larum Sphæræ ſunt reciproce in duplicata ratione diſtantiarum, col­
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                  ligetur quod attractio in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  ſit ad attractionem in
                    <emph type="italics"/>
                  P,
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                  ut diſtantia
                    <emph type="italics"/>
                  SP
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                    <lb/>
                  ad Sphæræ ſemidiametrum
                    <emph type="italics"/>
                  SA:
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                  Si vires illæ ſunt reciproce in tr­
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                  plicata ratione diſtantiarum, attractiones in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erunt ad invi-</s>
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