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

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            qualem diximus per tangentes cycloidis V S, M T &</s>
            <s xml:id="echoid-s1862" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1863" xml:space="preserve">Er-
              <lb/>
              <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            go, ſicut ſe habent omnes ſimul priores ad omnes eas ad
              <lb/>
            quas ipſæ referuntur, hoc eſt, ſicut tota F G ad tangentes
              <lb/>
            omnes Χ Δ, Γ Σ, &</s>
            <s xml:id="echoid-s1864" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1865" xml:space="preserve">ita tempus quo percurritur tota B I
              <lb/>
            cum celeritate dimidia ex Β Θ, ad tempora omnia motuum
              <lb/>
            quales diximus per tangentes cycloidis V S, M T, &</s>
            <s xml:id="echoid-s1866" xml:space="preserve">c .</s>
            <s xml:id="echoid-s1867" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">Prop. 2.
                <lb/>
              Archimedis
                <lb/>
              de Sphæ-
                <lb/>
              roid. &
                <lb/>
              Conoid.</note>
            Et invertendo itaque, tempora motuum dictorum per tan-
              <lb/>
            gentes cycloidis, ad tempus per rectam B I cum celeritate
              <lb/>
            dimidia ex B Θ, eandem rationem habebunt quam dictæ tan-
              <lb/>
            gentes omnes circumferentiæ F H ad rectam F G; </s>
            <s xml:id="echoid-s1868" xml:space="preserve">ac mi-
              <lb/>
            norem proinde quam arcus F O ad rectam eandem F G;
              <lb/>
            </s>
            <s xml:id="echoid-s1869" xml:space="preserve">quia arcus F Φ, ideoque omnino & </s>
            <s xml:id="echoid-s1870" xml:space="preserve">arcus F O major eſt
              <lb/>
            dictis omnibus arcus F H tangentibus . </s>
            <s xml:id="echoid-s1871" xml:space="preserve">Atqui tempus
              <note symbol="*" position="left" xlink:label="note-0126-03" xlink:href="note-0126-03a" xml:space="preserve">Prop. 20.
                <lb/>
              huj.</note>
            B E poſt N B, ad tempus per B I cum celeritate dimidia ex
              <lb/>
            B Θ, poſuimus eſſe ut arcus F O ad rectam F G. </s>
            <s xml:id="echoid-s1872" xml:space="preserve">Ergo
              <lb/>
            dicta tempora omnia per tangentes cycloidis minora ſimul
              <lb/>
            erunt tempore per B E poſt N B, cum antea majora eſſe os-
              <lb/>
            tenſum ſit; </s>
            <s xml:id="echoid-s1873" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s1874" xml:space="preserve">Itaque tempus per arcum
              <lb/>
            cycloidis B E, ad tempus per tangentem B I, cum celerita-
              <lb/>
            te dimidia ex Β Θ vel ex F A, non habet majorem rationem
              <lb/>
            quam arcus circumferentiæ F H ad rectam F G.</s>
            <s xml:id="echoid-s1875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1876" xml:space="preserve">Habeat jam, ſi poteſt, minorem. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">Ergo tempus aliquod
              <lb/>
            majus tempore per arcum B E, (ſit hoc tempus Z) erit ad
              <lb/>
            tempus dictum per B I, ut arcus F H ad rectam F G.</s>
            <s xml:id="echoid-s1878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1879" xml:space="preserve">Quod ſi jam ſumatur arcus N M æqualis altitudine cum
              <lb/>
              <note position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">TAB. X.
                <lb/>
              Fig. 2.</note>
            arcu B E, ſed cujus terminus ſuperior N ſit humilior puncto
              <lb/>
            B, erit tempus per arcum N M majus tempore per arcum
              <lb/>
            BE . </s>
            <s xml:id="echoid-s1880" xml:space="preserve">Manifeſtum autem quod punctum N tam
              <note symbol="*" position="left" xlink:label="note-0126-05" xlink:href="note-0126-05a" xml:space="preserve">Prop. 22.
                <lb/>
              huj.</note>
            ſumi poteſt puncto B, ut differentia dictorum temporum ſit
              <lb/>
            quamlibet exigua, ac proinde minor ea qua tempus Z ſupe-
              <lb/>
            rat tempus per arcum B E. </s>
            <s xml:id="echoid-s1881" xml:space="preserve">Sit itaque punctum N ita ſum-
              <lb/>
            ptum. </s>
            <s xml:id="echoid-s1882" xml:space="preserve">Unde quidem tempus per N M minus erit tempore Z,
              <lb/>
            habebitque proinde ad dictum tempus per B I, cum dimi-
              <lb/>
            dia celeritate ex Β Θ, minorem rationem quam arcus F H ad
              <lb/>
            rectam F G. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">Habeat ergo eam quam arcus L Had rectam F G.</s>
            <s xml:id="echoid-s1884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1885" xml:space="preserve">Dividatur jam F G in partes æquales F P, P Q, &</s>
            <s xml:id="echoid-s1886" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1887" xml:space="preserve"/>
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