Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of Notes

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            etiam V A ad A Φ longitudine, ut F A ad A H. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">Ratio
              <lb/>
              <note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
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                <emph style="sc">IN CY-</emph>
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                <emph style="sc">CLOIDE</emph>
              .</note>
            itaque M N ad O P, eadem erit quæ F A ad A H, hoc
              <lb/>
            eſt, propter triangula ſimilia F A H, F H Σ, eadem quæ
              <lb/>
            F H ad H Σ, ut dictum fuit. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">Itaque dicta ratio temporis
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            per M N ad tempus per O P, componitur ex rationibus
              <lb/>
            F X ad F H & </s>
            <s xml:id="echoid-s1793" xml:space="preserve">F H ad H Σ, ideoque eadem erit quæ
              <lb/>
            F X ſive X H ad H Σ. </s>
            <s xml:id="echoid-s1794" xml:space="preserve">Sicut autem radius X H ad H Σ,
              <lb/>
            ita eſt tangens S T ad rectam Q R; </s>
            <s xml:id="echoid-s1795" xml:space="preserve">hoc enim facile perſpi-
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            citur. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Igitur tempus motus qualem diximus per M N, ad
              <lb/>
            tempus per O P conſtat eſſe ſicut S T ad Q R. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">quod erat
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            demonſtrandum.</s>
            <s xml:id="echoid-s1798" xml:space="preserve"/>
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          <head xml:id="echoid-head70" xml:space="preserve">PROPOSITIO XXIV.</head>
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            <s xml:id="echoid-s1799" xml:space="preserve">SIt rurſus ut in præcedenti propoſitione Cyclois
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              <note position="right" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">TAB. X.
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              Fig. I.</note>
            A B C, cujus vertex A deorſum ſpectet, axis
              <lb/>
            A D ad borizontem erectus ſit; </s>
            <s xml:id="echoid-s1800" xml:space="preserve">& </s>
            <s xml:id="echoid-s1801" xml:space="preserve">ſumpto in ea
              <lb/>
            quovis puncto B, ducatur inde deorſum recta B Θ
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            quæ Cycloidem tangat, occurratque rectæ horizon-
              <lb/>
            tali A Θ in Θ: </s>
            <s xml:id="echoid-s1802" xml:space="preserve">recta vero B F ad axem perpendi-
              <lb/>
            cularis agatur, & </s>
            <s xml:id="echoid-s1803" xml:space="preserve">ſuper F A deſcribatur ſemicir-
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            culus F H A. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">Deinde alia recta G E, parallela
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            F B, ſecet Cycloidem in E, rectam B Θ in I, cir-
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            cumferentiam F H A in H, & </s>
            <s xml:id="echoid-s1805" xml:space="preserve">denique axem D A
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            in G.</s>
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            <s xml:id="echoid-s1807" xml:space="preserve">Dico tempus deſcenſus per arcum Cycloidis B E,
              <lb/>
            eſſe ad tempus per tangentem B I cum celeritate di-
              <lb/>
            midia ex B Θ, ſicut arcus F H ad rectam F G.</s>
            <s xml:id="echoid-s1808" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1809" xml:space="preserve">Si enim hoc verum non eſt, habebit tempus per arcum
              <lb/>
            B E ad dictum tempus per B I, vel majorem rationem quam
              <lb/>
            arcus F H ad rectam F G vel minorem. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">Habeat primo, ſi
              <lb/>
            fieri poteſt, majorem.</s>
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