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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            K C. </s>
            <s xml:id="echoid-s6331" xml:space="preserve">Similiter verò duobus his, filo G K tracto à potentia
              <lb/>
            quæ ſit ut tripla G K, & </s>
            <s xml:id="echoid-s6332" xml:space="preserve">filo D K tracto à potentia quæ ſit
              <lb/>
            ut ſimplex longitudo D K, æquipollet filum H K tractum
              <lb/>
            à potentia quæ ſit ut quadrupla H K. </s>
            <s xml:id="echoid-s6333" xml:space="preserve">Ergo hoc æquipollet
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            filis onmibus K A, K B, K C, K D, punctum K uti di-
              <lb/>
            ctum eſt trahentibus. </s>
            <s xml:id="echoid-s6334" xml:space="preserve">Atqui filo K H in directum opponitur
              <lb/>
            filum K E tractum à potentia quæ eſt ut longitudo K E, id
              <lb/>
            eſt ut quadrupla K H. </s>
            <s xml:id="echoid-s6335" xml:space="preserve">Ergo cum filis K E, K H, in partes
              <lb/>
            directè oppoſitas trahentibus cum potentiis æqualibus, pun-
              <lb/>
            ctum K neceſſario in locum ſuum ſervatum ſit, ſequitur & </s>
            <s xml:id="echoid-s6336" xml:space="preserve">filis
              <lb/>
            K A, K B, K C, K D, uti dictum eſt trahentibus & </s>
            <s xml:id="echoid-s6337" xml:space="preserve">ex
              <lb/>
            alia parte filo K E nodum reſtare immotum. </s>
            <s xml:id="echoid-s6338" xml:space="preserve">Quod erat de-
              <lb/>
            monſtrandum.</s>
            <s xml:id="echoid-s6339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6340" xml:space="preserve">Poſſunt autem & </s>
            <s xml:id="echoid-s6341" xml:space="preserve">binorum quorumque punctorum centra
              <lb/>
            gravitatis primò deſignari, & </s>
            <s xml:id="echoid-s6342" xml:space="preserve">per hæc deinceps centra gra-
              <lb/>
            vitatis quaternorum, & </s>
            <s xml:id="echoid-s6343" xml:space="preserve">per hæc octonorum & </s>
            <s xml:id="echoid-s6344" xml:space="preserve">ſic porro;
              <lb/>
            </s>
            <s xml:id="echoid-s6345" xml:space="preserve">qua ratione ſimplicior plerumque efficitur demonſtratio, ac
              <lb/>
            præſertim ſi datorum punctorum numerus fuerit pariter
              <lb/>
            par.</s>
            <s xml:id="echoid-s6346" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6347" xml:space="preserve">Ut ſi quatuor data fuerint A, B, C, D; </s>
            <s xml:id="echoid-s6348" xml:space="preserve">ſive in eodem
              <lb/>
              <note position="right" xlink:label="note-0375-01" xlink:href="note-0375-01a" xml:space="preserve">TAB. XXXIII.
                <lb/>
              Fig. 3.</note>
            plano, ſive non: </s>
            <s xml:id="echoid-s6349" xml:space="preserve">junctis A B, C D, diviſisque bifariam in
              <lb/>
            E & </s>
            <s xml:id="echoid-s6350" xml:space="preserve">F; </s>
            <s xml:id="echoid-s6351" xml:space="preserve">ductâque inde F E, quæ rurſus bifariam ſecetur in
              <lb/>
            G; </s>
            <s xml:id="echoid-s6352" xml:space="preserve">conſtat G eſſe centrum gravitatis punctorum A, B, C,
              <lb/>
            D. </s>
            <s xml:id="echoid-s6353" xml:space="preserve">Quod ſi jam nodus G trahatur filis G A, G B, G C,
              <lb/>
            G D, à potentiis quæ ſint inter ſe ut hæ ipſæ filorum longi-
              <lb/>
            tudines; </s>
            <s xml:id="echoid-s6354" xml:space="preserve">dico fieri æquilibrium.</s>
            <s xml:id="echoid-s6355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6356" xml:space="preserve">Conſtat enim filis G A, G B, æquipollere filum G E
              <lb/>
            tractum à potentia quæ ſit ut dupla G E; </s>
            <s xml:id="echoid-s6357" xml:space="preserve">filis verò G C,
              <lb/>
            G D, æquipollere filum G F tractum à potentia quæ ſit ut
              <lb/>
            dupla G F. </s>
            <s xml:id="echoid-s6358" xml:space="preserve">Cum ergo G E, G F æquales ſint, unamque
              <lb/>
            lineam rectam efficiant, eodem modo nodus G trahitur, ac
              <lb/>
            ſi traheretur à potentiis æqualibus per fila G E, G F. </s>
            <s xml:id="echoid-s6359" xml:space="preserve">Un-
              <lb/>
            de immotum manere neceſſe eſt.</s>
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            <s xml:id="echoid-s6361" xml:space="preserve">Conſtat verò ſi puncta A, B, C, D non ſint in eodem
              <lb/>
            plano, fore G centrum gravitatis pyramidis cujus anguli hæc
              <lb/>
            ipſa quatuor puncta; </s>
            <s xml:id="echoid-s6362" xml:space="preserve">cum in omni pyramide idem ſit </s>
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