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

Table of Notes

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            <s xml:id="echoid-s6131" xml:space="preserve">Quidam Geometræ parumper mutando hanc demonſtra-
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            tionem tentarunt defectum minus ſenſibilem reddere, ſed
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            in totum fuiſſe ſublatum mihi non videtur. </s>
            <s xml:id="echoid-s6132" xml:space="preserve">Igitur conatus
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            ſum alio modo eandem propoſitionem demonſtrare uti ſequi-
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            tur.</s>
            <s xml:id="echoid-s6133" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6134" xml:space="preserve">1°. </s>
            <s xml:id="echoid-s6135" xml:space="preserve">Poſtulatur cum Archimede, duo pondera æqualia
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            appenſa extremitatibus brachiorum æqualium libræ fore in
              <lb/>
            æquilibrio.</s>
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            <s xml:id="echoid-s6137" xml:space="preserve">2°. </s>
            <s xml:id="echoid-s6138" xml:space="preserve">Poſitis ponderibus æqualibus, & </s>
            <s xml:id="echoid-s6139" xml:space="preserve">brachiis libræ, cui
              <lb/>
            appenſa ſunt, inæqualibus, illam inclinari ad latus brachii
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            longioris.</s>
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            <s xml:id="echoid-s6141" xml:space="preserve">3°. </s>
            <s xml:id="echoid-s6142" xml:space="preserve">Poſtulatur poſſe concipi, lineas & </s>
            <s xml:id="echoid-s6143" xml:space="preserve">plana, de quibus
              <lb/>
            loquimur in hac demonſtratione, inflexilia & </s>
            <s xml:id="echoid-s6144" xml:space="preserve">ſine gravitate
              <lb/>
            eſſe.</s>
            <s xml:id="echoid-s6145" xml:space="preserve"/>
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            <s xml:id="echoid-s6146" xml:space="preserve">PROP. </s>
            <s xml:id="echoid-s6147" xml:space="preserve">I. </s>
            <s xml:id="echoid-s6148" xml:space="preserve">Si ſuper planum Horizontale quod imponitur
              <lb/>
            lineæ rectæ, quæ id dividit in duaspartes, applicetur pondus,
              <lb/>
            vis, quam illud pondus habebit ad deflectendum planum par-
              <lb/>
            tem verſus ad quam applicatur erit major, quam ſi poſitum
              <lb/>
            ſit prope dictam lineam.</s>
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            <s xml:id="echoid-s6150" xml:space="preserve">Sit planum Horizontale A B impoſitum lineæ rectæ
              <lb/>
              <note position="right" xlink:label="note-0367-01" xlink:href="note-0367-01a" xml:space="preserve">TAB. XXXII.
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              Fig. 5.</note>
            C D, & </s>
            <s xml:id="echoid-s6151" xml:space="preserve">cui applicetur pondus E, cujus diſtantia a C D li-
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            neâ perpendiculari E H menſuratur; </s>
            <s xml:id="echoid-s6152" xml:space="preserve">& </s>
            <s xml:id="echoid-s6153" xml:space="preserve">cui porro applice-
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            tur idem pondus in F, ita ut diſtantia F H minor ſit quam
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            E H, dico, quod habebit plus virium ad planum deflecten-
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            dum, ſi ſit applicatum in E quam in F.</s>
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            <s xml:id="echoid-s6155" xml:space="preserve">Nam producta recta E F H in G & </s>
            <s xml:id="echoid-s6156" xml:space="preserve">poſitis H G & </s>
            <s xml:id="echoid-s6157" xml:space="preserve">H F
              <lb/>
            æqualibus, certum eſt, pondus æquale illi, de quo locuti
              <lb/>
            ſumus, applicatum in G in æquilibrio futurum cum altero
              <lb/>
            in F, propter æqualia brachia F H, H G.</s>
            <s xml:id="echoid-s6158" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6159" xml:space="preserve">Sed pondus tranſlatum ex F in E deflectet planum, quo-
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            niam plano exiſtente ſine gravitate effectus idem eſt ac in
              <lb/>
            bilance brachiorum inæqualium quæ æqualibus ponderibus
              <lb/>
            gravantur, idem ergo pondus poſitum in E plus virium ha-
              <lb/>
            bet ad planum deflectendum quam ſi eſt in F; </s>
            <s xml:id="echoid-s6160" xml:space="preserve">Q.</s>
            <s xml:id="echoid-s6161" xml:space="preserve">E.</s>
            <s xml:id="echoid-s6162" xml:space="preserve">D.</s>
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            <s xml:id="echoid-s6164" xml:space="preserve">PROP. </s>
            <s xml:id="echoid-s6165" xml:space="preserve">II. </s>
            <s xml:id="echoid-s6166" xml:space="preserve">Si planum Horizont@le; </s>
            <s xml:id="echoid-s6167" xml:space="preserve">oneratum plurimis pon-
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            deribus, maneat in æqualibrio, impoſitum lineæ rectæ, </s>
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Impressum