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

Page concordance

< >
Scan Original
201 126
202 127
203 128
204
205
206
207 129
208 130
209 131
210 132
211 133
212 134
213 135
214 136
215
216
217
218 137
219 138
220 139
221 140
222 141
223 142
224
225
226
227 143
228 144
229 145
230 146
< >
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