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

Page concordance

< >
Scan Original
141 87
142 88
143
144 90
145 91
146 92
147
148
149
150 93
151 94
152 95
153 96
154
155
156
157 97
158 98
159 99
160 100
161 101
162 102
163 103
164 104
165
166
167
168 105
169 106
170
< >
page |< < (151) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div297" type="section" level="1" n="108">
          <p>
            <s xml:id="echoid-s3404" xml:space="preserve">
              <pb o="151" file="0215" n="235" rhead="HOROLOG. OSCILLATOR."/>
            quæque ſuſpenſa ab axe, qui per punctum F ad planum hu-
              <lb/>
              <note position="right" xlink:label="note-0215-01" xlink:href="note-0215-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            jus paginæ erectus intelligitur, habeat centrum oſcillationis
              <lb/>
            G. </s>
            <s xml:id="echoid-s3405" xml:space="preserve">Porrò axi per F intelligatur axis alius, per centrum gra-
              <lb/>
            vitatis E transiens, parallelus. </s>
            <s xml:id="echoid-s3406" xml:space="preserve">Diviſaque magnitudine cogita-
              <lb/>
            tu in particulas minimas æquales, ſit quadratis diſtantiarum,
              <lb/>
            ab axe dicto per E, æquale planum I, multiplex nempe ſe-
              <lb/>
            cundum numerum dictarum particularum; </s>
            <s xml:id="echoid-s3407" xml:space="preserve">applicatoque pla-
              <lb/>
            no I ad diſtantiam F E, fiat recta quædam. </s>
            <s xml:id="echoid-s3408" xml:space="preserve">Dico eam æ-
              <lb/>
            qualem eſſe intervallo E G, quo centrum oſcillationis infe-
              <lb/>
            rius eſt centro gravitatis magnitudinis A B C D.</s>
            <s xml:id="echoid-s3409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3410" xml:space="preserve">Ut enim univerſali demonſtratione quod propoſitum eſt
              <lb/>
            comprehendamus: </s>
            <s xml:id="echoid-s3411" xml:space="preserve">intelligatur plana figura, magnitudini
              <lb/>
            A B C D analoga, ad latus adpoſita, O Q P; </s>
            <s xml:id="echoid-s3412" xml:space="preserve">quæ nempe,
              <lb/>
            ſecta planis horizontalibus iisdem cum magnitudine A B C D,
              <lb/>
            habeat ſegmenta intercepta inter bina quæque plana, in ea-
              <lb/>
            dem inter ſe ratione cum ſegmentis dictæ magnitudinis, quæ
              <lb/>
            ipſis reſpondent; </s>
            <s xml:id="echoid-s3413" xml:space="preserve">ſintque ſegmenta ſingula figuræ O Q P,
              <lb/>
            diviſa in tot particulas æquales, quot continentur ſegmentis
              <lb/>
            ipſis reſpondentibus in figura A B C D. </s>
            <s xml:id="echoid-s3414" xml:space="preserve">Hæc autem intel-
              <lb/>
            ligi poſſunt fieri, qualiscunque fuerit magnitudo A B C D,
              <lb/>
            ſive linea, ſive ſuperficies, ſive ſolidum. </s>
            <s xml:id="echoid-s3415" xml:space="preserve">Semper vero cen-
              <lb/>
            trum gravitatis figuræ O Q P, quod ſit T, eadem altitu-
              <lb/>
            dine eſſe manifeſtum eſt cum centro gravitatis magnitudinis
              <lb/>
            A B C D; </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ideoque, ſi planum horizontale, per F ductum,
              <lb/>
            ſecet lineam centri figuræ O Q P, velut hic in S, æquales
              <lb/>
            eſſe diſtantias S T, F E.</s>
            <s xml:id="echoid-s3417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3418" xml:space="preserve">Porrò autem conſtat quadrata diſtantiarum, ab axe oſcil-
              <lb/>
            lationis F, applicata ad diſtantiam F E, multiplicem ſecun-
              <lb/>
            dum numerum particularum, efficere longitudinem penduli
              <lb/>
            iſochroni ; </s>
            <s xml:id="echoid-s3419" xml:space="preserve">quæ longitudo poſita fuit F G. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">Illorum
              <note symbol="*" position="right" xlink:label="note-0215-02" xlink:href="note-0215-02a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            quadratorum ſummam, æqualem eſſe perſpicuum eſt, qua-
              <lb/>
            dratis diſtantiarum à plano horizontali per F, unà cum qua-
              <lb/>
            dratis diſtantiarum à plano verticali F E, per axem F & </s>
            <s xml:id="echoid-s3421" xml:space="preserve">cen-
              <lb/>
            trum gravitatis E ducto . </s>
            <s xml:id="echoid-s3422" xml:space="preserve">Atqui quadrata diſtantiarum
              <note symbol="*" position="right" xlink:label="note-0215-03" xlink:href="note-0215-03a" xml:space="preserve">Prop. 47.
                <lb/>
              lib. 1. Eucl.</note>
            gnitudinis A B C D à plano horizontali per F, æquantur
              <lb/>
            quadratis diſtantiarum figuræ O Q P ab recta S F. </s>
            <s xml:id="echoid-s3423" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum