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

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              <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-
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            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"/>
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          <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-
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            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-
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            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>
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            <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-
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            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-
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            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>
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