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

Table of Notes

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            <s xml:id="echoid-s1914" xml:space="preserve">
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            per arcum S V. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">Eadem vero & </s>
            <s xml:id="echoid-s1916" xml:space="preserve">longiora eſſent, ut nunc
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            oſtendemus.</s>
            <s xml:id="echoid-s1917" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1918" xml:space="preserve">Eſt enim tempus dictum per tangentem S Λ, cum cele-
              <lb/>
            ritate æquabili ex B S, ad tempus per rectam O K cum ce-
              <lb/>
            leritate æquabili dimidia ex B Θ, ſicut tangens ſemicirculi
              <lb/>
            θ Δ ad rectam P Q . </s>
            <s xml:id="echoid-s1919" xml:space="preserve">ſimiliterque tempus per
              <note symbol="*" position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            Τ Ξ, cum celeritate æquabili ex B T, eſt ad tempus per
              <lb/>
            rectam Κ Ψ cum celeritate æquabili dimidia ex B Θ, ut tan-
              <lb/>
            gens Γ Σ ad rectam Q Π. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">Atque ita deinceps ſingula tem-
              <lb/>
            pora per tangentes cycloidis, quæ ſunt eadem ſupra dictis,
              <lb/>
            erunt ad tempora motus æquabilis per partes ſibi reſponden-
              <lb/>
            tes rectæ O Ω, cum celeritate dimidia ex B Θ, ut tangen-
              <lb/>
            tes circumferentiæ θ η, iisdem parallelis incluſæ, ad partes
              <lb/>
            rectæ P ζ ipſis reſpondentes. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">Unde, ut in priori parte de-
              <lb/>
            monſtrationis, concludetur omnes ſimul rectas P Q, Q Π
              <lb/>
            &</s>
            <s xml:id="echoid-s1922" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1923" xml:space="preserve">hoc eſt, totam P ζ eſſe ad omnes ſimul tangentes θ Δ,
              <lb/>
            Γ Σ, &</s>
            <s xml:id="echoid-s1924" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">ſicut tempus quo percurritur tota O Ω, cum ce-
              <lb/>
            leritate dimidia ex B Θ, ad tempora omnia motuum quales
              <lb/>
            diximus per tangentes cycloidis S Λ, T Ξ, &</s>
            <s xml:id="echoid-s1926" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s1928" xml:space="preserve">
              <lb/>
            convertendo, tempora omnia per tangentes cycloidis, eam
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            rationem habebunt ad tempus dictum motus æquabilis per
              <lb/>
            rectam Ο Ω, ſive per B I, quam dictæ tangentes omnes ar-
              <lb/>
            cus θ η ad rectam P ζ vel F G, ac proinde majorem quam
              <lb/>
            arcus L H ad rectam F G; </s>
            <s xml:id="echoid-s1929" xml:space="preserve">eſt enim arcus θ H, adeoque
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0128-03" xlink:href="note-0128-03a" xml:space="preserve">Prop. 20.
                <lb/>
              huj.</note>
            etiam omnino arcus L H, minor dictis tangentibus arcus θ η .</s>
            <s xml:id="echoid-s1930" xml:space="preserve"> Sed tempus per N M poſuimus ab initio ad idem tempus per
              <lb/>
            B I ſe habere ut arcus L H ad rectam F G. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">Ergo tempus per
              <lb/>
            N M, multoque magis tempus per S V, minuserit tempore
              <lb/>
            per tangentes cycloidis. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">Quod eſt abſurdum, cum hoc tempus,
              <lb/>
            illo per arcum S V, antea minus oſtenſum fuerit. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">Patet igi-
              <lb/>
            tur tempus per arcum cycloidis B E ad tempus per tangen-
              <lb/>
            tem B I cum celeritare æquabili dimidia ex B Θ, non mi-
              <lb/>
            norem rationem habere quam arcus F H ad rectam F G.
              <lb/>
            </s>
            <s xml:id="echoid-s1934" xml:space="preserve">Sed nec majorem habere oſtenſum fuit. </s>
            <s xml:id="echoid-s1935" xml:space="preserve">Ergo eandem habeat
              <lb/>
            neceſſe eſt. </s>
            <s xml:id="echoid-s1936" xml:space="preserve">quod erat demonſtrandum.</s>
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