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

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          <pb o="291" file="0377" n="409" rhead="MECHANICAM."/>
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          <head xml:id="echoid-head251" xml:space="preserve">IX.</head>
          <head xml:id="echoid-head252" style="it" xml:space="preserve">Chriſtiani Hugenii, Solutio Problematis de
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          linea in quam flexile ſe pondere pro-
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          prio curvat.</head>
          <p>
            <s xml:id="echoid-s6379" xml:space="preserve">Si Catena C V A ſuſpenſa ſit ex filis F C, E A utrin-
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              <note position="right" xlink:label="note-0377-01" xlink:href="note-0377-01a" xml:space="preserve">TAB.XXXIII.
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              Fig. 5.</note>
            que annexis, ac gravitate carentibus, itaut capita C & </s>
            <s xml:id="echoid-s6380" xml:space="preserve">A
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            ſint pari altitudine, deturque Angulus inclinationis filorum
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            productorum C G A, & </s>
            <s xml:id="echoid-s6381" xml:space="preserve">catenæ totius poſitus, cujus vertex
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            ſit V, axis V B.</s>
            <s xml:id="echoid-s6382" xml:space="preserve"/>
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            <s xml:id="echoid-s6383" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6384" xml:space="preserve">Licebit hinc invenire tangentem in dato quovis catenæ
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            puncto. </s>
            <s xml:id="echoid-s6385" xml:space="preserve">Velut ſi punctum datum ſit L, unde ducta appli-
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            cata L H dividat æqualiter axem B V. </s>
            <s xml:id="echoid-s6386" xml:space="preserve">Jam ſi angulus C G A
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            ſit 60°, erit inclinanda a puncto A ad axem recta A W, æ-
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            qualis {1/2} A B, cui ducta parallela L R, tanget curvam in pun-
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            cto L. </s>
            <s xml:id="echoid-s6387" xml:space="preserve">Item ſi latera G B, B A, A G ſint partium 3, 4, 5,
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            erit A W ponenda partium 4 {1/2}.</s>
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          </p>
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            <s xml:id="echoid-s6389" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6390" xml:space="preserve">Invenitur porrò & </s>
            <s xml:id="echoid-s6391" xml:space="preserve">recta linea catenæ æqualis, vel da-
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            tæ cuilibet ejus portioni. </s>
            <s xml:id="echoid-s6392" xml:space="preserve">Semper enim dato angulo C G A,
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            data erit ratio axis B V ad curvam V A. </s>
            <s xml:id="echoid-s6393" xml:space="preserve">Velut ſi latera
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            G B, B A, A G ſint ut 3, 4, 5, erit curva V A tripla
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            axis V B.</s>
            <s xml:id="echoid-s6394" xml:space="preserve"/>
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            <s xml:id="echoid-s6395" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6396" xml:space="preserve">Item definitur radius curvitatis in vertice V, hoc eſt,
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            ſemidiameter circuli maximi, qui per verticem hunc deſcri-
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            ptus totus intra curvam cadat. </s>
            <s xml:id="echoid-s6397" xml:space="preserve">Nam ſi angulus C G A ſit 60°,
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            erit radius curvitatis ipſi axi B V æqualis. </s>
            <s xml:id="echoid-s6398" xml:space="preserve">Sin vero angulus
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            C G A ſit rectus, erit radius curvitatis æqualis curvæ V A.</s>
            <s xml:id="echoid-s6399" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s6400" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6401" xml:space="preserve">Poterit & </s>
            <s xml:id="echoid-s6402" xml:space="preserve">circulus æqualis inveniri ſuperficiei conoidis,
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            ex revolutione catenæ circa axem ſuum. </s>
            <s xml:id="echoid-s6403" xml:space="preserve">Ita ſi angulus C G A
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            ſit 60°, erit ſuperficies conoidis ex catena C V A genita æ-
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            qualis circulo, cujus radius poſſit duplum rectangulum
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            B V G.</s>
            <s xml:id="echoid-s6404" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s6405" xml:space="preserve">5. </s>
            <s xml:id="echoid-s6406" xml:space="preserve">Inveniuntur etiam puncta quotlibet curvæ K N, cujus
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            evolutione, una cum recta K V, radio curvitatis in </s>
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