Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/178.jpg" pagenum="150"/>
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                  bent circum ſe mutuo Figuras eaſdem ac prius, & propterea Figuræ
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                    <emph type="italics"/>
                  pqv
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                  ſimiles & æquales.
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                  Q.E.D.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note126"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc corpora duo Viribus diſtantiæ ſuæ proportionali­
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                  bus ſe mutuo trahentia, deſcribunt (per Prop. </s>
                  <s>X,) & circum com­
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                  mune gravitatis centrum, & circum ſe mutuo, Ellipſes concentri­
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                  cas: & vice verſa, ſi tales Figuræ deſcribuntur, ſunt Vires diſtan­
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                  tiæ proportionales. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Et corpora duo Viribus quadrato diſtantiæ ſuæ recipro­
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                  ce proportionalibus deſcribunt (per Prop. </s>
                  <s>XI, XII, XIII) & circum
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                  commune gravitatis centrum, & circum ſe mutuo, Sectiones conicas
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                  umbilicum habentes in centro circum quod Figuræ deſcribuntur. </s>
                  <s>Et
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                  vice verſa, ſi tales Figuræ deſcribuntur, Vires centripetæ ſunt qua­
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                  drato diſtantiæ reciproce proportionales. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  3. Corpora duo quævis cirum gravitatis centrum com­
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                  mune gyrantia, radiis & ad centrum illud & ad ſe mutuo ductis,
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                  deſcribunt areas temporibus proportionales. </s>
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                    <emph type="center"/>
                  PROPOSITIO LIX. THEOREMA XXII.
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                  <s>
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                  Corporum duorum
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                  S
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                  &
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                  P
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                  circa commune gravitatis centrum
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                  C
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                    <emph type="italics"/>
                  revolventium Tempus periodicum eſſe ad Tempus periodicum cor­
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                  poris alterutrius
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                  P,
                    <emph type="italics"/>
                  circa alterum immotum
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                  S
                    <emph type="italics"/>
                  gyrantis & Figu­
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                  ris quæ corpora circum ſe mutuo deſcribunt Figuram ſimilem &
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                  æqualem deſcribentis, in ſubduplicata ratione corporis alterins
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                  S,
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                    <emph type="italics"/>
                  ad ſummam corporum
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                  S+P. </s>
                </p>
                <p type="main">
                  <s>Namque, ex demonſtratione ſuperioris Propoſitionis, tempora
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                  quibus arcus quivis ſimiles
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                  deſcribuntur, ſunt in ſub­
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                  duplicata ratione diſtantiarum
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  sp,
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                  hoc eſt, in ſub­
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                  duplicata ratione corporis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad ſummam corporum
                    <emph type="italics"/>
                  S+P.
                    <emph.end type="italics"/>
                  Et com­
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                  ponendo, ſummæ temporum quibus arcus omnes ſimiles
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                    <lb/>
                  deſcribuntur, hoc eſt, tempora tota quibus Figuræ totæ ſimiles de­
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                  ſcribuntur, ſunt in eadem ſubduplicata ratione.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
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