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

Page concordance

< >
Scan Original
71 44
72 45
73 46
74
75
76
77 47
78 48
79
80
81
82 49
83 50
84 51
85 52
86
87
88
89 53
90 54
91 55
92 56
93 57
94 58
95 59
96 60
97 61
98 62
99 63
100 64
< >
page |< < (130) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div244" type="section" level="1" n="93">
          <p>
            <s xml:id="echoid-s2955" xml:space="preserve">
              <pb o="130" file="0190" n="208" rhead="CHRISTIANI HUGENII"/>
            titudinibus iſtis in ſua pondera, erit ſumma productorum
              <lb/>
              <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS.</emph>
              </note>
            major quam {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2956" xml:space="preserve">quæ proinde major quoque
              <lb/>
            probatur quam {a d y + b d y + c d y/x}. </s>
            <s xml:id="echoid-s2957" xml:space="preserve">Nam quia poſita eſt longitudo
              <lb/>
            x æqualis {a e e + b f f + g g/a d + b d + c d}; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">erit a d x + b d x + c d x æquale
              <lb/>
            a e e + b f f + c g g. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">Et ductis omnibus in y, & </s>
            <s xml:id="echoid-s2960" xml:space="preserve">dividen-
              <lb/>
            do per x x, erit {a d y + b d y + c d y/x} æquale {a e e y + b f f y + c g g y/x x}. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Unde
              <lb/>
            quod dictum eſt conſequitur. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">Eſt autem ſumma iſta produ-
              <lb/>
            ctorum æqualis ei, quod fit ducendo altitudinem, ad quam
              <lb/>
            aſcendit centrum gravitatis commune ponderum A, B, C, in
              <lb/>
            ſummam ipſorum ponderum, a + b + c; </s>
            <s xml:id="echoid-s2963" xml:space="preserve">ſi nempe ſingu-
              <lb/>
            la, uti dictum, ſeorſim quousque poſſunt moveantur. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">Quan-
              <lb/>
            titas vero {a d y + b d y + c d y/x} producitur ex deſcenſu centri gravi-
              <lb/>
            tatis eorundem ponderum, (qui deſcenſus eſt R Q, ſive {d y/x},
              <lb/>
            ut ſupra inventum fuit,) in eandem quoque ponderum ſum-
              <lb/>
            mam a + b + c. </s>
            <s xml:id="echoid-s2965" xml:space="preserve">Ergo quum prius productum altero hoc
              <lb/>
            majus oſtenſum fuerit, ſequitur aſcenſum centri gravitatis
              <lb/>
            ponderum A, B, C, ſi, relicto pendulo ubi pervenere in
              <lb/>
            T, V, X, ſingula celeritates acquiſitas ſurſum convertant,
              <lb/>
            majorem fore ejusdem centri gravitatis deſcenſu, dum ex
              <lb/>
            A, B, C, moventur in T, V, X. </s>
            <s xml:id="echoid-s2966" xml:space="preserve">quod eſt abſurdum, cum
              <lb/>
            dictus aſcenſus deſcenſui æqualis eſſe debeat, per anteceden-
              <lb/>
            tem.</s>
            <s xml:id="echoid-s2967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">Eodem modo, ſi dicatur celeritatem puncti L, ubi per-
              <lb/>
            venerit in P, minorem eſſe celeritate ponderis G quum in O
              <lb/>
            pervenerit; </s>
            <s xml:id="echoid-s2969" xml:space="preserve">oſtendemus aſcenſum poſſibilem centri gravitatis
              <lb/>
            ponderum A, B, C, minorem eſſe quam deſcenſum, quod
              <lb/>
            eidem propoſitioni antecedenti repugnat. </s>
            <s xml:id="echoid-s2970" xml:space="preserve">Quare relinquitur
              <lb/>
            ut eadem ſit celeritas puncti L, ad P tranſlati, quæ ponde-
              <lb/>
            ris G in O. </s>
            <s xml:id="echoid-s2971" xml:space="preserve">Unde, ut ſuperius dictum, ſequitur pendulum
              <lb/>
            ſimplex F G compoſito ex A, B, C, iſochronum eſſe.</s>
            <s xml:id="echoid-s2972" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div250" type="section" level="1" n="94">
          <head xml:id="echoid-head120" xml:space="preserve">PROPOSITIO VI.</head>
          <p style="it">
            <s xml:id="echoid-s2973" xml:space="preserve">DAto pendulo ex quotcunque ponderibus æqua-
              <lb/>
            libus compoſito; </s>
            <s xml:id="echoid-s2974" xml:space="preserve">ſi ſumma quadratorum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum