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

Table of Notes

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            <emph style="sc">De de-</emph>
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            <emph style="sc">SOENSU</emph>
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            <emph style="sc">GRAVIUM</emph>
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          <head xml:id="echoid-head50" xml:space="preserve">PROPOSITIO V. </head>
          <p style="it">
            <s xml:id="echoid-s1279" xml:space="preserve">SPatium peractum certo tempore, à gravi è quie-
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            te caſum inchoante, dimidium eſſe ejus ſpatii
              <lb/>
            quod pari tempore transiret motu æquabili, cum
              <lb/>
            celeritate quam acquiſivit ultimo caſus momento.</s>
            <s xml:id="echoid-s1280" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1281" xml:space="preserve">Sit tempus deſcenſus totius A H, quo tempore mobile
              <lb/>
              <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">TAB. V.
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              Fig. 3.</note>
            peregerit ſpatium quoddam cujus quantitas deſignetur plano P.
              <lb/>
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            <s xml:id="echoid-s1282" xml:space="preserve">ductaque H L perpendiculari ad A H, longitudinis cujus-
              <lb/>
            libet, referat illa celeritatem in fine caſus acquiſitam. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Dein-
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            de completo rectangulo A H L M, intelligatur eo notari
              <lb/>
            quantitas ſpatii quod percurreretur tempore A H, cum ce-
              <lb/>
            leritate H L. </s>
            <s xml:id="echoid-s1284" xml:space="preserve">Oſtendendum eſt igitur planum P dimidium
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            eſſe rectanguli M H, hoc eſt, ducta diagonali A L, æqua-
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            le triangulo A H L.</s>
            <s xml:id="echoid-s1285" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1286" xml:space="preserve">Si planum P non eſt æquale triangulo A H L, ergo aut
              <lb/>
            minus eo erit, aut majus. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">Sit primo, ſi fieri poteſt, pla-
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            num P minus triangulo A H L. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">dividatur autem A H in tot
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            partes æquales A C, C E, E G &</s>
            <s xml:id="echoid-s1289" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1290" xml:space="preserve">ut, circumſcriptâ tri-
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            angulo A H L figurâ è rectangulis quorum altitudo ſingulis
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            diviſionum ipſius A H partibus æquetur, ut ſunt rectangula
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            B C, D E, F G, alterâque eidem triangulo inſcriptâ, ex
              <lb/>
            rectangulis ejusdem altitudinis, ut ſunt K E, O G &</s>
            <s xml:id="echoid-s1291" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1292" xml:space="preserve">ut,
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            inquam, exceſſus illius figuræ ſupra hanc, minor ſit exceſ-
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            ſu trianguli A H L ſupra planum P. </s>
            <s xml:id="echoid-s1293" xml:space="preserve">hoc enim fieri poſſe
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            perſpicuum eſt, cum totus exceſſus figuræ circumſcriptæ ſu-
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            per inſcriptam æquetur rectangulo infimo, baſin habenti H L.
              <lb/>
            </s>
            <s xml:id="echoid-s1294" xml:space="preserve">Erit itaque omnino exceſſus ipſius trianguli A H L ſupra
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            figuram inſcriptam minor quam ſupra planum P, ac proin-
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            de figura triangulo inſcripta major plano P. </s>
            <s xml:id="echoid-s1295" xml:space="preserve">Porro autem,
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            quum recta A H tempus totius deſcenſus referat, ejus par-
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            tes æquales A C, C E, E G, æquales temporis illius par-
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            tes referent. </s>
            <s xml:id="echoid-s1296" xml:space="preserve">Cumque celeritates mobilis cadentis creſcant
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0092-03" xlink:href="note-0092-03a" xml:space="preserve">Prop. I.
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              huj.</note>
            eadem proportione qua tempora deſcenſus ; </s>
            <s xml:id="echoid-s1297" xml:space="preserve">ſitque </s>
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