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

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            <s xml:id="echoid-s1838" xml:space="preserve">
              <pb o="83" file="0125" n="134" rhead="HOROLOG. OSCILLATOR."/>
            inſuper eſt tangente V S, omnibusque partibus ſuis magis
              <lb/>
              <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            erectus quam ulla pars tangentis V S. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">Adeo ut omnino ma-
              <lb/>
            jus ſit futurum tempus per tangentem V S cum celeritate ex
              <lb/>
            B S, tempore per arcum B S poſt N B. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">Similiter tempus
              <lb/>
            per tangentem M T, cum celeritate ex B T, majus erit
              <lb/>
            tempore per arcum S T poſt N S, & </s>
            <s xml:id="echoid-s1841" xml:space="preserve">tempus per tangen-
              <lb/>
            tem Π Y cum celeritate ex B Y, majus tempore per arcum
              <lb/>
            T Y poſt N T. </s>
            <s xml:id="echoid-s1842" xml:space="preserve">Atque ita tempora motuum æquabilium
              <lb/>
            per tangentes omnes usque ad infimam quæ tangit cycloi-
              <lb/>
            dem in E, cum celeritatibus per ſingulas quantæ acquirun-
              <lb/>
            tur cadendo ex B adusque punctum ipſarum contactus, ma-
              <lb/>
            jora ſimul erunt tempore per arcum B E poſt N B. </s>
            <s xml:id="echoid-s1843" xml:space="preserve">Eadem
              <lb/>
            vero & </s>
            <s xml:id="echoid-s1844" xml:space="preserve">minora eſſent, ut nunc oſtendemus.</s>
            <s xml:id="echoid-s1845" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1846" xml:space="preserve">Conſiderentur enim denuo tempora eadem motuum æqua-
              <lb/>
            bilium per tangentes cycloidis. </s>
            <s xml:id="echoid-s1847" xml:space="preserve">Et eſt quidem tempus per
              <lb/>
            tangentem V S cum celeritate ex B S, ad tempus per re-
              <lb/>
            ctam Β Λ cum celeritate dimidia ex F A, ut tangens cir-
              <lb/>
            cumferentiæ Δ Χ ad partem axis F P . </s>
            <s xml:id="echoid-s1848" xml:space="preserve">Similiterque
              <note symbol="*" position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">Prop.
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              præced.</note>
            pus per tangentem M T, cum celeritate ex B T, ad tem-
              <lb/>
            pus per rectam Λ Ξ cum eadem dimidia celeritate ex F A,
              <lb/>
            ut tangens Γ Σ ad rectam P Q. </s>
            <s xml:id="echoid-s1849" xml:space="preserve">Atque ita deinceps ſingula
              <lb/>
            tempora per tangentes cycloidis, quæ ſunt eadem ſupradi-
              <lb/>
            ctis, erunt ad tempora motus æquabilis per partes ſibi re-
              <lb/>
            ſpondentes rectæ B I cum celeritate dimidia ex B Θ, ſicut
              <lb/>
            tangentes circumferentiæ F H, iisdem parallelis compre-
              <lb/>
            henſæ, ad partes rectæ F G ipſis reſpondentes.</s>
            <s xml:id="echoid-s1850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1851" xml:space="preserve">Sunt igitur quantitates quædam rectæ F P, P Q, &</s>
            <s xml:id="echoid-s1852" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">& </s>
            <s xml:id="echoid-s1854" xml:space="preserve">
              <lb/>
            totidem aliæ, tempora ſcilicet quibus percurruntur rectæ
              <lb/>
            Β Λ, Λ Ξ &</s>
            <s xml:id="echoid-s1855" xml:space="preserve">c, motu æquabili cum celeritate dimidia ex
              <lb/>
            Β Θ; </s>
            <s xml:id="echoid-s1856" xml:space="preserve">Et unaquæque quantitas in prioribus ad ſequentem ea-
              <lb/>
            dem proportione refertur, qua unaquæque poſteriorum ad
              <lb/>
            ſuam ſequentem; </s>
            <s xml:id="echoid-s1857" xml:space="preserve">ſunt enim utrobique inter ſe æquales. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">Qui-
              <lb/>
            bus autem proportionibus priores quantitates ad alias quas-
              <lb/>
            dam, nempe ad tangentes circuli Δ Χ, Γ Σ, &</s>
            <s xml:id="echoid-s1859" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">referun-
              <lb/>
            tur, iisdem proportionibus & </s>
            <s xml:id="echoid-s1861" xml:space="preserve">eodem ordine poſteriores quo-
              <lb/>
            que referuntur ad alias quasdam, nempe ad tempora </s>
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