Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/083.jpg" pagenum="55"/>
                    <emph type="italics"/>
                  SPXQT
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                  ut area dato tempore deſcripta, id eſt, per Prop. </s>
                  <s>XIV. </s>
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                <p type="main">
                  <s>
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                  in ſubduplicata ratione lateris recti.
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                  Q.E.D.
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                  </s>
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                  <s>
                    <margin.target id="note31"/>
                  LIBER
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                  PRIMUS.</s>
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                <figure id="id.039.01.083.1.jpg" xlink:href="039/01/083/1.jpg" number="25"/>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Latera recta principalia ſunt in ratione compoſita ex
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                  duplicata ratione perpendiculorum & duplicata ratione veloci­
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                  tatum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Velocitates corporum in maximis & minimis ab umbi­
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                  lico communi diſtantiis, ſunt in ratione compoſita ex ratione di­
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                  ſtantiarum inverſe & ſubduplicata ratione laterum rectorum princi­
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                  palium directe. </s>
                  <s>Nam perpendicula jam ſunt ipſæ diſtantiæ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  3. Ideoque velocitas in Conica ſectione, in maxima vel
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                  minima ab umbilico diſtantia, eſt ad velocitatem in Circulo in ea­
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                  dem à centro diſtantia, in ſubduplicata ratione lateris recti princi­
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                  palis ad duplam illam diſtantiam. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Corporum in Ellipſibus gyrantium velocitates in medi­
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                  ocribus diſtantiis ab umbilico communi ſunt eædem quæ corporum
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                  gyrantium in Circulis ad eaſdem diſtantias; hoc eſt (per Corol 6.
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                  Prop. </s>
                  <s>IV.) reciproce in ſubduplicata ratione diſtantiarum. </s>
                  <s>Nam
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                  perpendicula jam ſunt ſemi-axes minores; & hi ſunt ut mediæ
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                  proportionales inter diſtantias & latera recta. </s>
                  <s>Componatur hæc
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                  ratio inverſe cum ſubduplicata ratione laterum rectorum directe, &
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                  fiet ratio ſubduplicata diſtantiarum inverſe. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  5. In eadem figura, vel etiam in figuris diverſis, quarum </s>
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