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

Page concordance

< >
Scan Original
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
231 147
232 148
233 149
234 150
235 151
236 152
237 153
238 154
239
240
< >
page |< < (148) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div286" type="section" level="1" n="105">
          <pb o="148" file="0212" n="232" rhead="CHRISTIANI HUGENII"/>
        </div>
        <div xml:id="echoid-div291" type="section" level="1" n="106">
          <head xml:id="echoid-head132" xml:space="preserve">PROPOSITIO XVI.</head>
          <note position="left" xml:space="preserve">
            <emph style="sc">De centro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s3347" xml:space="preserve">FIgura quævis, ſive linea fuerit, ſive ſuperſi-
              <lb/>
            cies, ſive ſolidum; </s>
            <s xml:id="echoid-s3348" xml:space="preserve">ſi aliter at que aliter ſuſpen-
              <lb/>
            datur, agiteturque ſuper axibus inter ſe paralle-
              <lb/>
            lis, quique à centro gravitatis figuræ æqualiter di-
              <lb/>
            ſtent, ſibi ipſi iſochrona eſt.</s>
            <s xml:id="echoid-s3349" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3350" xml:space="preserve">Proponatur magnitudo quævis, cujus centrum gravitatis
              <lb/>
            E punctum, ſitque primo ſuſpenſa ab axe, qui per F intel-
              <lb/>
              <note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">TAB. XXI.
                <lb/>
              Fig. 3.</note>
            ligitur hujus paginæ plano ad angulos rectos. </s>
            <s xml:id="echoid-s3351" xml:space="preserve">Itaque idem
              <lb/>
            planum erit & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">planum oſcillationis. </s>
            <s xml:id="echoid-s3353" xml:space="preserve">In quo ſi centro E, ra-
              <lb/>
            dio E F, deſcribatur circumferentia F H G, ſumptoque in
              <lb/>
            illa puncto quovis, ut H, magnitudo ſecundò ſuſpendi intel-
              <lb/>
            ligatur ab axe in hoc puncto infixo, atque agitari, manente
              <lb/>
            eodem oſcillationis plano. </s>
            <s xml:id="echoid-s3354" xml:space="preserve">Dico iſochronam fore ſibi ipſi agi-
              <lb/>
            tatæ circa axem in F.</s>
            <s xml:id="echoid-s3355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3356" xml:space="preserve">Intelligatur enim dividi magnitudo propoſita in particu-
              <lb/>
            las minimas æquales. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Itaque, quia in utraque illa ſuſpenſio-
              <lb/>
            ne idem manet oſcillationis planum, reſpectu partium ma-
              <lb/>
            gnitudinis; </s>
            <s xml:id="echoid-s3358" xml:space="preserve">manifeſtum eſt, ſi ab omnibus particulis, in quas
              <lb/>
            diviſa eſt magnitudo, perpendiculares cadere concipiantur
              <lb/>
            in dictum oſcillationis planum, illas utraque ſuſpenſione oc-
              <lb/>
            currere ipſi in punctis iisdem. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Sint autem hæc puncta ea
              <lb/>
            quæ apparent in ſpatio A B C D.</s>
            <s xml:id="echoid-s3360" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3361" xml:space="preserve">Quum igitur E ſit centrum gravitatis magnitudinis pro-
              <lb/>
            poſitæ, ipſaque proinde circa axem, qui per E punctum
              <lb/>
            erectus eſt ad planum A B C D, quovis ſitu æquilibrium
              <lb/>
            ſervet; </s>
            <s xml:id="echoid-s3362" xml:space="preserve">facile perſpicitur, quod ſi punctis omnibus ante di-
              <lb/>
            ctis, quæ in ſpatio A B C D ſignantur, æqualis gravitas
              <lb/>
            tribuatur, eorum quoque omnium centrum gravitatis futu-
              <lb/>
            rum eſt punctum E. </s>
            <s xml:id="echoid-s3363" xml:space="preserve">Quod ſi vero, ut fieri poteſt, in pun-
              <lb/>
            cta aliqua plures perpendiculares coincidant, illa puncta
              <lb/>
            quaſi toties geminata intelligenda ſunt, gravitatesque toties
              <lb/>
            multiplices accipiendæ. </s>
            <s xml:id="echoid-s3364" xml:space="preserve">Atque ita conſideratorum, patet
              <lb/>
            rurſus centrum gravitatis eſſe E punctum.</s>
            <s xml:id="echoid-s3365" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum