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

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              <pb o="146" file="0210" n="230" rhead="CHRISTIANI HUGENII"/>
            hoc eſt, ſicut quadratum B D ad quadratum N N. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">Itaque
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              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS</emph>
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            rectangulum B C K, multiplex per numerum particularum
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            ſectionis B D, ad rectangulum N X F, multiplex per nu-
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            merum particularum ſectionis N N, duplicatam habebit ra-
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            tionem quadrati B D ad quadratum N N; </s>
            <s xml:id="echoid-s3315" xml:space="preserve">hoc eſt, eam
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            quam quadratum V V ad quadratum R R, in figura pro-
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            portionali. </s>
            <s xml:id="echoid-s3316" xml:space="preserve">Erit igitur & </s>
            <s xml:id="echoid-s3317" xml:space="preserve">dicta prior ſumma quadratorum, à
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            diſtantiis particularum ſegmenti B N N D à plano E C, ad
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            ſummam alteram quadratorum, à diſtantiis particularum ſe-
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            gmenti N M M N, ut qu. </s>
            <s xml:id="echoid-s3318" xml:space="preserve">V V ad qu. </s>
            <s xml:id="echoid-s3319" xml:space="preserve">R R. </s>
            <s xml:id="echoid-s3320" xml:space="preserve">Eademque
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            ratione oſtendetur, ſummas quadratorum à diſtantiis parti-
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            larum in reliquis ſegmentis ſolidi A B C D, eſſe inter ſe in
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            ratione quadratorum quæ fiunt à rectis in figura O V V,
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            quæ baſi cujusque ſegmenti reſpondent. </s>
            <s xml:id="echoid-s3321" xml:space="preserve">Quare ſumma qua-
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            dratorum, à diſtantiis particularum omnium ſegmentorum
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            ſolidi A B C D à plano E C, erit ad ſummam quadrato-
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            rum, à diſtantiis particularum ſegmentorum totidem, maxi-
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            mo ſegmento æqualium, hoc eſt, cylindri vel prismatis
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            B D S S, eandem cum ſolido A B C D baſin altitudinem-
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            que habentis, ſicut quadrata omnia rectarum V V, R R, Q Q,
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            &</s>
            <s xml:id="echoid-s3322" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3323" xml:space="preserve">ad quadrata totidem maximo V V æqualia, hoc eſt,
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            ſicut ſolidum rotundum O V V circa axem O P, ad cylin-
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            drum V V Ω Ω, qui baſin & </s>
            <s xml:id="echoid-s3324" xml:space="preserve">altitudinem habeat eandem.
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            </s>
            <s xml:id="echoid-s3325" xml:space="preserve">Hanc vero rationem ſolidi O V V ad cylindrum V V Ω Ω,
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            componi conſtat ex ratione planorum quorum converſione
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            generantur, hoc eſt, ex ratione plani O P V, ad rectangu-
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            lum P Ω, & </s>
            <s xml:id="echoid-s3326" xml:space="preserve">ex ratione diſtantiarum quibus horum plano-
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            rum centra gravitatis abſunt ab axe O P; </s>
            <s xml:id="echoid-s3327" xml:space="preserve">hoc eſt, & </s>
            <s xml:id="echoid-s3328" xml:space="preserve">ex ra-
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            tione P Φ ad P Δ. </s>
            <s xml:id="echoid-s3329" xml:space="preserve">Et prior quidem harum rationum, nem-
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            pe plani O P V ad rectangulum P Ω, eadem eſt quæ ſolidi
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            A B C D ad cylindrum vel prisma B D S S, hoc eſt, ea-
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            dem quæ numeri particularum ſolidi A B C D, ad nume-
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            rum particularum cylindri vel prismatis B D S S. </s>
            <s xml:id="echoid-s3330" xml:space="preserve">Altera
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            vero ratio, nempe P Φ ad P Δ, eſt eadem, ex conſtru-
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            ctione, quæ ſpatii Z ad rectangulum B C K. </s>
            <s xml:id="echoid-s3331" xml:space="preserve">Habebit ita-
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            que dicta ſumma quadratorum, à diſtantiis omnium </s>
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