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

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              <pb o="147" file="0211" n="231" rhead="HOROLOG. OSCILLATOR."/>
            larum ſolidi A B C D à plano E C, ad ſummam quadrato-
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              <note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" 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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            rum, à diſtantiis omnium particularum cylindri vel prisma-
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            tis B D S S ab eodem plano, rationem eam quæ componi-
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            tur ex ratione numeri particularum ſolidi A B C D, ad nu-
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            merum particularum cylindri vel prismatis B D S S, & </s>
            <s xml:id="echoid-s3332" xml:space="preserve">ex
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            ratione ſpatii Z ad rectangulum B C K: </s>
            <s xml:id="echoid-s3333" xml:space="preserve">hoc eſt, rationem
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            quam habet rectangulum Z, multiplex per numerum parti-
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            cularum ſolidi A B C D, ad rectangulum B C K, multi-
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            plex per numerum particularum cylindri vel prismatis B D S S.
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            </s>
            <s xml:id="echoid-s3334" xml:space="preserve">Atqui quarta harum magnitudinum æqualis eſt ſecundæ
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            nempe rectangulum B C K, multiplex per numerum parti-
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            cularum cylindri vel prismatis B D S S, æquale ſummæ
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            quadratorum, à diſtantiis particularum ejusdem prismatis
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            vel cylindri B D S S à plano E C; </s>
            <s xml:id="echoid-s3335" xml:space="preserve">ſiquidem rectangulum
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            idem B C K, multiplex per numerum particularum ſegmen-
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            ti B N N D, æquatur quadratis diſtantiarum particularum
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            ejusdem ſegmenti à plano E C . </s>
            <s xml:id="echoid-s3336" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s3337" xml:space="preserve">tertia primæ
              <note symbol="*" position="right" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">Prop. 10.
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              huj.</note>
            quabitur; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">nempe planum Z, multiplex per numerum parti-
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            cularum ſolidi A B C D, ſummæ quadratorum, à diſtantiis
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            particularum ſolidi ejusdem A B C D à plano E C . </s>
            <s xml:id="echoid-s3339" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0211-03" xlink:href="note-0211-03a" xml:space="preserve">Prop. 14.
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              lib. 5. Eucl.</note>
            erat demonſtrandum.</s>
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            <s xml:id="echoid-s3341" xml:space="preserve">Notandum vero, quando ſolidum A B D rotundum eſt
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            circa axem A C, fieri ſemper rectangulum B C K æquale
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            quartæ parti quadrati B C; </s>
            <s xml:id="echoid-s3342" xml:space="preserve">quoniam ſubcentrica cunei, ab-
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            ſciſſi ſuper circulo B D, plano per tangentem in B, nempe
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            recta B K, æquatur {5/4} radii B C. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">Unde, ſi P V æqualis
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            poſita ſit B C, ſequitur, faciendo ut Ρ Δ ad Ρ Φ ita rectan-
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            gulum B C K, hoc eſt, {1/4} quadrati B C, hoc eſt, qu. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">Ρ Δ
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            ad planum aliud Z, fore hoc rectangulo Δ Ρ Φ æquale. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">Ac
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            proinde tunc ipſum rectangulum Δ Ρ Φ, multiplex ſecun-
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            dum numerum particularum ſolidi A B D, æquari ſummæ
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            quæſitæ quadratorum à perpendicularibus omnibus, quæ à
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            particulis iisdem cadunt in planum E C.</s>
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