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

Page concordance

< >
Scan Original
111 69
112 70
113 71
114 72
115
116
117
118 73
119 74
120 75
121 76
122
123
124
125 77
126 78
127 79
128 80
129 81
130 82
131
132
133
134 83
135 84
136 85
137 86
138
139
140
< >
page |< < (86) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div127" type="section" level="1" n="48">
          <p>
            <s xml:id="echoid-s1914" xml:space="preserve">
              <pb o="86" file="0128" n="137" rhead="CHRISTIANI HUGENII"/>
            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
              <lb/>
            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>
            <s xml:id="echoid-s1937" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum