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

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          <pb o="82" file="0122" n="130" rhead="CHRISTIANI HUGENII"/>
          <p>
            <s xml:id="echoid-s1812" xml:space="preserve">Itaque tempus aliquod brevius tempore per B E (ſit hoc
              <lb/>
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                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
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            tempus Z) erit ad dictum tempus per B I ut arcus F H ad
              <lb/>
            rectam F G. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">Quod ſi jam in Cycloide ſupra punctum B ſu-
              <lb/>
            matur punctum aliud N, erit tempus per B E poſt N B,
              <lb/>
            brevius tempore per B E. </s>
            <s xml:id="echoid-s1814" xml:space="preserve">Manifeſtum eſt autem punctum N
              <lb/>
            tam propinquum ſumi poſſe ipſi B, ut differentia eorum
              <lb/>
            temporum ſit quamlibet exigua, ac proinde ut minor ſit
              <lb/>
            ea qua tempus Z ſuperatur à tempore per B E. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">Sit ita-
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            que punctum N ita ſumptum. </s>
            <s xml:id="echoid-s1816" xml:space="preserve">unde quidem tempus per
              <lb/>
            B E poſt N B majus erit tempore Z, majoremque pro-
              <lb/>
            inde rationem habebit ad tempus dictum per B I cum di-
              <lb/>
            midia celeritate ex B Θ, quam arcus F H ad rectam
              <lb/>
            F G. </s>
            <s xml:id="echoid-s1817" xml:space="preserve">Habeat itaque eam quam arcus F H O ad rectam
              <lb/>
            F G.</s>
            <s xml:id="echoid-s1818" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1819" xml:space="preserve">Dividatur F G in partes æquales F P, P Q, &</s>
            <s xml:id="echoid-s1820" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1821" xml:space="preserve">qua-
              <lb/>
            rum unaquæque minor ſit altitudine lineæ N B, atque item
              <lb/>
            altitudine arcus H O; </s>
            <s xml:id="echoid-s1822" xml:space="preserve">hoc enim fieri poſſe manifeſtum eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s1823" xml:space="preserve">& </s>
            <s xml:id="echoid-s1824" xml:space="preserve">à punctis diviſionum agantur rectæ, baſi D C parallelæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1825" xml:space="preserve">ad tangentem B Θ terminatæ P Λ, Q Ξ, &</s>
            <s xml:id="echoid-s1826" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1827" xml:space="preserve">Quibus-
              <lb/>
            que in punctis hæ ſecant circumferentiam F H, ab iis,
              <lb/>
            itemque à puncto H, tangentes ſurſum ducantur usque
              <lb/>
            ad proximam quæque parallelam, velut Δ Χ, Γ Σ &</s>
            <s xml:id="echoid-s1828" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">Si-
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            militer vero & </s>
            <s xml:id="echoid-s1830" xml:space="preserve">à punctis, in quibus dictæ parallelæ Cy-
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            cloidi occurrunt, tangentes ſurſum ducantur velut S V,
              <lb/>
            T M &</s>
            <s xml:id="echoid-s1831" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1832" xml:space="preserve">additâ vero ad rectam F G parte una G R æ-
              <lb/>
            quali iis quæ ex diviſione, ductaque R Φ parallelâ ſimi-
              <lb/>
            liter ipſi D C, patet eam occurrere circumferentiæ F H A
              <lb/>
            inter H & </s>
            <s xml:id="echoid-s1833" xml:space="preserve">O, quia G R minor eſt altitudine puncti H ſupra
              <lb/>
            O. </s>
            <s xml:id="echoid-s1834" xml:space="preserve">Jam vero ſic porro argumentabimur.</s>
            <s xml:id="echoid-s1835" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1836" xml:space="preserve">Tempus per tangentem V S cum celeritate æquabili quæ
              <lb/>
            acquireretur ex B S, majus eſt tempore motus continue ac-
              <lb/>
            celerati per arcum B S poſt N B. </s>
            <s xml:id="echoid-s1837" xml:space="preserve">Nam celeritas ex B S mi-
              <lb/>
            nor eſt celeritate ex N B, propterea quod minor altitudo
              <lb/>
            B S quam N B. </s>
            <s xml:id="echoid-s1838" xml:space="preserve">At celeritas ex B S æquabiliter continuari
              <lb/>
            ponitur per tangentem V S, cum celeritas acquiſita ex N B
              <lb/>
            continue porro acceleretur per arcum B S, qui arcus </s>
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