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

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              <pb o="152" file="0216" n="236" rhead="CHRISTIANI HUGENII"/>
            quadrata (ſi O ſit punctum ſupremum figuræ O Q P, & </s>
            <s xml:id="echoid-s3424" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            O H ſubcentrica cunei ſuper ipſa abſciſſi, plano per rectam
              <lb/>
            O V, parallelam S F) æqualia ſunt rectangulo O T H & </s>
            <s xml:id="echoid-s3425" xml:space="preserve">
              <lb/>
            quadrato S T, multiplicibus ſecundum numerum particula-
              <lb/>
            rum dictæ figuræ, ſive magnitudinis A B C D. </s>
            <s xml:id="echoid-s3426" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">Prop. 9.
                <lb/>
              huj.</note>
            vero diſtantiarum magnitudinis A B C D à plano F E,
              <lb/>
            quantumcunque axis oſcillationis F diſtet à centro gravita-
              <lb/>
            tis E, ſemper eadem ſunt: </s>
            <s xml:id="echoid-s3427" xml:space="preserve">quæ proinde putemus æquari
              <lb/>
            ſpatio Z, multiplici ſecundum numerum particularum ma-
              <lb/>
            gnitudinis A B C D.</s>
            <s xml:id="echoid-s3428" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3429" xml:space="preserve">Itaque quoniam quadrata diſtantiarum magnitudinis
              <lb/>
            A B C D, ab axe oſcillationis F, æquantur iſtis, quadrato
              <lb/>
            nimirum S T, rectangulo O T H, & </s>
            <s xml:id="echoid-s3430" xml:space="preserve">plano Z, multipli-
              <lb/>
            cibus per numerum particularum ejusdem magnitudinis; </s>
            <s xml:id="echoid-s3431" xml:space="preserve">ſi
              <lb/>
            applicentur hæc omnia ad diſtantiam F E ſive S T, orietur
              <lb/>
            longitudo F G penduli iſochroni magnitudini A B C D .</s>
            <s xml:id="echoid-s3432" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            Sed ex applicatione quadrati S T ad latus ſuum S T, orie-
              <lb/>
            tur ipſa S T, ſive F E. </s>
            <s xml:id="echoid-s3433" xml:space="preserve">Ergo reliqua E G eſt ea quæ ori-
              <lb/>
            tur ex applicatione rectanguli O T H, & </s>
            <s xml:id="echoid-s3434" xml:space="preserve">plani Z, ad ean-
              <lb/>
            dem S T vel F E.</s>
            <s xml:id="echoid-s3435" xml:space="preserve"/>
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            <s xml:id="echoid-s3436" xml:space="preserve">Quare ſupereſt ut demonſtremus rectangulum O T H,
              <lb/>
            cum plano Z, æquari plano I. </s>
            <s xml:id="echoid-s3437" xml:space="preserve">Tunc enim conſtabit, etiam
              <lb/>
            planum I, applicatum ad diſtantiam F E, efficere longitu-
              <lb/>
            dinem ipſi E G æqualem. </s>
            <s xml:id="echoid-s3438" xml:space="preserve">Illud autem ſic oſtendetur. </s>
            <s xml:id="echoid-s3439" xml:space="preserve">Re-
              <lb/>
            ctangulum O T H, multiplex ſecundum numerum particu-
              <lb/>
            larum figuræ O Q P, ſive magnitudinis A B C D, æ-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">Prop. 10.
                <lb/>
              huj.</note>
            quatur quadratis diſtantiarum figuræ ab recta X T , quæ per centrum gravitatis T ducitur ipſi S F parallela; </s>
            <s xml:id="echoid-s3440" xml:space="preserve">ac pro-
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            inde etiam quadratis diſtantiarum magnitudinis A B C D,
              <lb/>
            à plano horizontali K K, ducto per centrum gravitatis E;
              <lb/>
            </s>
            <s xml:id="echoid-s3441" xml:space="preserve">cum diſtantiæ utrobique ſint eædem. </s>
            <s xml:id="echoid-s3442" xml:space="preserve">At vero planum Z, ſi-
              <lb/>
            militer multiplex, æquale poſitum fuit quadratis diſtantia-
              <lb/>
            rum magnitudinis A B C D à plano verticali F E. </s>
            <s xml:id="echoid-s3443" xml:space="preserve">Ac pa-
              <lb/>
            tet quidem quadrata hæc diſtantiarum à plano F E, una cum
              <lb/>
            dictis quadratis diſtantiarum à plano horizontali per E, æ-
              <lb/>
            qualia eſſe quadratis diſtantiarum ab axe gravitatis per </s>
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