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

Table of contents

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[191.] VI. Demonſtratio Æquilibrii bilancis.
Page: 397 (282)
[192.] VII. De potentiis fila funesve trahentibus.
Page: 405 (287)
[193.] VIII. Solitio problematis a G G. Leibnitio propoſiti in diario (cui titulus Nouvelles de la Republi-que des Lettres) menſis Sept. 1687. PROBLEMA.
Page: 408 (290)
[194.] Solutio.
Page: 408 (290)
[195.] IX. Chriſtiani Hugenii, Solutio Problematis de linea in quam flexile ſe pondere pro-prio curvat.
Page: 409 (291)
[196.] X. Hugenii Annotationes in librum Pariſiis 1689. editum, de Manuaria Nautica.
Page: 410 (292)
[197.] XI. Reſponſum Dni Renaldi ad Dominum Hugenium.
Page: 414 (296)
[198.] XII. Exceptio Dni Hugenii ad Reſponſum Dni Renaldi.
Page: 423 (305)
[199.] FINIS.
Page: 426 (308)
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          <head xml:id="echoid-head116" xml:space="preserve">PROPOSITIO II.</head>
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            <emph style="sc">De centro</emph>
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            <emph style="sc">OSCILLA-</emph>
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            <emph style="sc">TIONIS.</emph>
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          TAB. XVIII.
            <lb/>
          Fig. 1.</note>
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            <s xml:id="echoid-s2845" xml:space="preserve">POſitis quæ prius, ſi pondera omnia A, B, C,
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            ſint æqualia; </s>
            <s xml:id="echoid-s2846" xml:space="preserve">dico ſummam omnium perpendi-
              <lb/>
            cularium A D, B E, C F, æquari perpendicula-
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            ri, à centro gravitatis ductæ, G H, multiplici
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            ſecundum ponderum numerum.</s>
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            <s xml:id="echoid-s2848" xml:space="preserve">Quum enim ſumma productorum, à ponderibus ſingulis
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            in ſuas perpendiculares, æquetur producto ex G H in pon-
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            dera omnia; </s>
            <s xml:id="echoid-s2849" xml:space="preserve">ſitque hìc, propter ponderum æqualitatem,
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            ſumma illa productorum æqualis producto ex uno pondere
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            in ſummam omnium perpendicularium; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">itemque productum
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            ex G H in pondera omnia, idem quod productum ex pon-
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            dere uno in G H, multiplicem ſecundum ponderum nume-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s2851" xml:space="preserve">patet ſummam perpendicularium neceſſario jam æquari
              <lb/>
            ipſi G H, multiplici ſecundum ponderum numerum. </s>
            <s xml:id="echoid-s2852" xml:space="preserve">quod
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            erat demonſtrandum.</s>
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          <head xml:id="echoid-head117" xml:space="preserve">PROPOSITIO III.</head>
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            <s xml:id="echoid-s2854" xml:space="preserve">SI magnitudines quædam deſcendant omnes, vel
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            aſcendant, licet inæqualibus intervallis; </s>
            <s xml:id="echoid-s2855" xml:space="preserve">alti-
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            tudines deſcenſus vel aſcenſus cujusque, in ipſam
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            magnitudinem ductæ, efficient ſummam producto-
              <lb/>
            rum æqualem ei, quæ fit ex altitudine deſcenſus
              <lb/>
            vel aſcenſus centri gravitatis omnium magnitudi-
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            num, ducta in omnes magnitudines.</s>
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            <s xml:id="echoid-s2857" xml:space="preserve">Sunto magnitudines A, B, C, quæ ex A, B, C, deſcen-
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              <note position="right" xlink:label="note-0183-02" xlink:href="note-0183-02a" xml:space="preserve">TAB. XVIII.
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              Fig. 2.</note>
            dant in D, E, F; </s>
            <s xml:id="echoid-s2858" xml:space="preserve">vel ex D, E, F, aſcendant in A, B, C.
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            </s>
            <s xml:id="echoid-s2859" xml:space="preserve">Sitque earum centrum gravitatis omnium, dum ſunt in
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            A, B, C, eadem altitudine cum puncto G; </s>
            <s xml:id="echoid-s2860" xml:space="preserve">cum vero ſunt in
              <lb/>
            D, E, F, eadem altitudine cum puncto H. </s>
            <s xml:id="echoid-s2861" xml:space="preserve">Dico ſummam
              <lb/>
            productorum ex altitudine A D in A, B E in B, C F in C,
              <lb/>
            æquari producto ex G H in omnes A, B, C.</s>
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