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

Table of Notes

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            quarum unaquæque minor ſit arcus cycloidis B N altitudine,
              <lb/>
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                <emph style="sc">De motu</emph>
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                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
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            itemque minor altitudine arcus circumferentiæ F L; </s>
            <s xml:id="echoid-s1888" xml:space="preserve">& </s>
            <s xml:id="echoid-s1889" xml:space="preserve">ad-
              <lb/>
            ditâ ad F G unâ earum partium G ζ, ducantur à punctis di-
              <lb/>
            viſionum rectæ baſi D C parallelæ, & </s>
            <s xml:id="echoid-s1890" xml:space="preserve">ad tangentem B Θ
              <lb/>
            terminatæ, P O, Q K, &</s>
            <s xml:id="echoid-s1891" xml:space="preserve">c; </s>
            <s xml:id="echoid-s1892" xml:space="preserve">itemque à puncto ζ recta ζ Ω
              <lb/>
            quæ ſecet cycloidem in V, circumferentiam in η; </s>
            <s xml:id="echoid-s1893" xml:space="preserve">quibus-
              <lb/>
            que in punctis ductæ parallelæ ſecant circumferentiam F H,
              <lb/>
            ab iis tangentes deorſum ducantur usque ad proximam quæ-
              <lb/>
            que parallelam, velut θ Δ, Γ Σ: </s>
            <s xml:id="echoid-s1894" xml:space="preserve">Quarum infima à puncto
              <lb/>
            Η ducta occurrat rectæ ζ Ω in X. </s>
            <s xml:id="echoid-s1895" xml:space="preserve">Similiter vero & </s>
            <s xml:id="echoid-s1896" xml:space="preserve">à pun-
              <lb/>
            ctis, in quibus dictæ parallelæ occurrunt cycloidi, ducan-
              <lb/>
            tur totidem tangentes deorſum, velut S Λ, T Ξ, &</s>
            <s xml:id="echoid-s1897" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1898" xml:space="preserve">qua-
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            rum infima, tangens nempe à puncto E ducta, occurrat re-
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            ctæ ζ Ω in R.</s>
            <s xml:id="echoid-s1899" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1900" xml:space="preserve">Quia igitur P ζ æqualis eſt F G altitudini arcus B E,
              <lb/>
            cui æqualis eſt ex conſtructione altitudo arcus N M, erit & </s>
            <s xml:id="echoid-s1901" xml:space="preserve">
              <lb/>
            P ζ æqualis altitudini arcus N M. </s>
            <s xml:id="echoid-s1902" xml:space="preserve">Eſt autem recta P O ex
              <lb/>
            conſtructione ſuperior termino N. </s>
            <s xml:id="echoid-s1903" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1904" xml:space="preserve">ζ Ω, & </s>
            <s xml:id="echoid-s1905" xml:space="preserve">in ea
              <lb/>
            punctum V, ſuperius termino M. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">Quare, cum arcus S V
              <lb/>
            æqualis ſit altitudinis cum arcu N M, ſed termino S ſubli-
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            miore quam N, erit tempus per S V brevius tempore per N M.</s>
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          <note symbol="*" position="right" xml:space="preserve">Prop. 22.
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          huj.</note>
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            <s xml:id="echoid-s1908" xml:space="preserve">Atqui tempus per tangentem S Λ, cum celeritate æqua-
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            bili ex B S, brevius eſt tempore deſcenſus accelerati per ar-
              <lb/>
            cum S T, incipientis in S. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">Nam celeritas ex B S, qua to-
              <lb/>
            ta S Λ transmiſſa ponitur, æqualis eſt celeritati ex S T
              <note symbol="*" position="right" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">Prop. 8.
                <lb/>
              huj.</note>
            quæ motui per arcum S T in fine demum acquiritur; </s>
            <s xml:id="echoid-s1910" xml:space="preserve">ipſa-
              <lb/>
            que S Λ minor eſt quam S T. </s>
            <s xml:id="echoid-s1911" xml:space="preserve">Similiter tempus per tangen-
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            tem T Ξ, cum celeritate æquabili ex B T, brevius eſt tem-
              <lb/>
            pore deſcenſus accelerati per arcum T Y poſt S T; </s>
            <s xml:id="echoid-s1912" xml:space="preserve">quum
              <lb/>
            celeritas ex B T, qua tota T Ξ transmiſſa ponitur, ſit æqua-
              <lb/>
            lis celeritati ex S Y, quæ in fine demum acquiritur motui
              <lb/>
            dicto per arcum T Y poſt S T; </s>
            <s xml:id="echoid-s1913" xml:space="preserve">ipſaque T Ξ minor ſit arcu
              <lb/>
            T Y. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">Atque ita tempora omnia motuum æquabilium per
              <lb/>
            tangentes cycloidis, cum celeritatibus per ſingulas quantæ
              <lb/>
            acquiruntur deſcendendo ex B usque ad punctum ipſarum
              <lb/>
            contactus, breviora ſimul erunt tempore deſcenſus </s>
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