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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              <pb o="307" file="0393" n="425" rhead="MECHANICAM."/>
            ut quadratum B G ad quadratum B K, non vero ut B G
              <lb/>
            ad B K, quod ego contendo, & </s>
            <s xml:id="echoid-s6825" xml:space="preserve">inde tota res pendet.</s>
            <s xml:id="echoid-s6826" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6827" xml:space="preserve">Ut determinemus cujus ſententia veraſit, concipiamus pla-
              <lb/>
            num, in quo noſtra figura exiſtit, ita ad Horizontem erectum,
              <lb/>
            ut linea B G ad eundem ſit perpendicularis, & </s>
            <s xml:id="echoid-s6828" xml:space="preserve">ſit R B X funis
              <lb/>
            affixus in R, ad quem in B alligatum & </s>
            <s xml:id="echoid-s6829" xml:space="preserve">ſuſpenſum ſit pon-
              <lb/>
            dus Q: </s>
            <s xml:id="echoid-s6830" xml:space="preserve">Ponamus ulterius portionem B X perpendicularem
              <lb/>
            ad R B a manu retineri in X; </s>
            <s xml:id="echoid-s6831" xml:space="preserve">clarum eſt, id exacte re-
              <lb/>
            præſentare caſum navis, de quo eſt quæſtio; </s>
            <s xml:id="echoid-s6832" xml:space="preserve">nam loco ven-
              <lb/>
            ti, qui impingendo in velum C D propellat navim ſecun-
              <lb/>
            dum B G, hic habemus pondus Q quod trahit punctum B
              <lb/>
            juxta B G; </s>
            <s xml:id="echoid-s6833" xml:space="preserve">& </s>
            <s xml:id="echoid-s6834" xml:space="preserve">funis B R, qui cenſetur infinitæ longitudinis,
              <lb/>
            & </s>
            <s xml:id="echoid-s6835" xml:space="preserve">impedit, quo minus navis aliam plagam versùs, quam
              <lb/>
            B K poſſit progredi, hic eundem edit effectum reſpectu no-
              <lb/>
            di B.</s>
            <s xml:id="echoid-s6836" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6837" xml:space="preserve">Utergo vis, qua ventus propellit navem ſecundum B G, eſt
              <lb/>
            ad vim, qua hanc propellit ſecundum B K, ita eſt pondus Q
              <lb/>
            ad gravitatem, quæ agit in manum quæ in X cohibet, quò
              <lb/>
            minus nodus B moveatur verſus B K; </s>
            <s xml:id="echoid-s6838" xml:space="preserve">illa enim gravitas æ-
              <lb/>
            quipollet vi, qua nodus ſecundum B K trahitur. </s>
            <s xml:id="echoid-s6839" xml:space="preserve">Cum au-
              <lb/>
            tem G K parallela ſit ipſi B R, certum eſt ex notiſſimis Me-
              <lb/>
            chanicæ regulis, quod pondus Q ſit ad id quod retinet chor-
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            dam B X, vel ad gravitatem quæ in X agit in manum ut
              <lb/>
            B G ad B K. </s>
            <s xml:id="echoid-s6840" xml:space="preserve">Vis ergo, qua navim propellit ventus ſecun-
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            dum B G, eſt ad vim, qua propulſa eſt verſus B K, ut
              <lb/>
            B G ad B K non vero, ut illarum linearum quadrata, ut
              <lb/>
            D
              <emph style="super">nus</emph>
            Renaldus contendit.</s>
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          </p>
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            <s xml:id="echoid-s6842" xml:space="preserve">Ponamus porro, navem H M, quæ undas eadem undi-
              <lb/>
            que facilitate ſecat, propelli per ventum Z B vel A B
              <lb/>
            (perinde enim eſt) quo naviget certo tempore per B G,
              <lb/>
            velo exiſtente in C D, & </s>
            <s xml:id="echoid-s6843" xml:space="preserve">determinandum eſſe, quan-
              <lb/>
            tum progreſſura ſit ſecundum B K æquali tempore eodem
              <lb/>
            vento, eodemque veli ſitu. </s>
            <s xml:id="echoid-s6844" xml:space="preserve">Cum celeritates navis in dua-
              <lb/>
            bus illis viis tales debeant eſſe, ut reſiſtentiæ, quas in-
              <lb/>
            ferit ipſi aqua, ſint ut vires, quibus propellitur (nam in eo
              <lb/>
            caſu ſolo motu æquabili progreditur), & </s>
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