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

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            <s xml:id="echoid-s3250" xml:space="preserve">
              <pb o="143" file="0207" n="227" rhead="HOROLOG. OSCILLATOR."/>
            mam quadratorum à perpendicularibus, quæ ab univerſis
              <lb/>
              <note position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            iiſdem particulis cadunt in rectam datam per E punctum.</s>
            <s xml:id="echoid-s3251" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3252" xml:space="preserve">Illa vero prior quadratorum ſumma colligetur hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s3253" xml:space="preserve">Ponatur primò figuram planam dari O Q P, ad latus figu-
              <lb/>
            ræ ſolidæ A B C D, ejuſdem cum ipſa altitudinis, quæque
              <lb/>
            ſit ejuſmodi, ut ſecta lineis rectis Q Q, R R, quæ reſpon-
              <lb/>
            deant planis figuram ſolidam A B C D ſecantibus M M,
              <lb/>
            N N, & </s>
            <s xml:id="echoid-s3254" xml:space="preserve">his parallelis; </s>
            <s xml:id="echoid-s3255" xml:space="preserve">eadem ſit dictarum linearum inter
              <lb/>
            ſe, quæ & </s>
            <s xml:id="echoid-s3256" xml:space="preserve">planorum horum ratio, ſi nempe ſumantur utrin-
              <lb/>
            que quæ in ordine ſibi reſpondent. </s>
            <s xml:id="echoid-s3257" xml:space="preserve">Ut ſi linea R R ſit ad
              <lb/>
            Q Q quemadmodum planum N N ad M M. </s>
            <s xml:id="echoid-s3258" xml:space="preserve">Quod ſi igitur
              <lb/>
            figura plana O Q P, in totidem particulas minimas æquales
              <lb/>
            diviſa intelligatur, quot intelliguntur in ſolido A B C D,
              <lb/>
            erunt etiam in unoquoque ſegmento figuræ planæ, velut
              <lb/>
            Q Q R R, tot numero particulæ, quot ſunt in figuræ ſoli-
              <lb/>
            dæ ſegmento M M N N, iſti ſegmento reſpondente; </s>
            <s xml:id="echoid-s3259" xml:space="preserve">ac
              <lb/>
            proinde & </s>
            <s xml:id="echoid-s3260" xml:space="preserve">ſumma quadratorum, à perpendicularibus o-
              <lb/>
            mnium particularum figuræ O Q P in planum E G, æqua-
              <lb/>
            bitur ſummæ quadratorum, à perpendicularibus omnium par-
              <lb/>
            ticularum figuræ ſolidæ, in idem planum E G productis. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Il-
              <lb/>
            la autem quadratorum ſumma data erit, ſi dentur in figura
              <lb/>
            O Q P, cuneoque illius, quæ propoſ. </s>
            <s xml:id="echoid-s3262" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3263" xml:space="preserve">huj. </s>
            <s xml:id="echoid-s3264" xml:space="preserve">requiri dixi-
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            mus. </s>
            <s xml:id="echoid-s3265" xml:space="preserve">Ergo his datis, dabitur quoque ſumma quadratorum,
              <lb/>
            à perpendicularibus quæ, à particulis omnibus ſolidi A B C D,
              <lb/>
            ducuntur in planum E G.</s>
            <s xml:id="echoid-s3266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3267" xml:space="preserve">Ponatur nunc alia item figura plana S Y T Z, cjuſdem cum
              <lb/>
            ſolido A B C D latitudinis, hoc eſt, quam includant plana B Y,
              <lb/>
            D Z ſolidum contingentia, ac parallela plano E A C, quæque
              <lb/>
            ſit ejuſmodi, ut, ſecta lineis rectis V V, X X &</s>
            <s xml:id="echoid-s3268" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3269" xml:space="preserve">quæ reſpon-
              <lb/>
            deant planis figuram A B C D ſecantibus, K K, L L, & </s>
            <s xml:id="echoid-s3270" xml:space="preserve">his
              <lb/>
            parallelis, faciat eandem inter ſe rationem linearum harum
              <lb/>
            atque illorum planorum, ſi ſumantur quæ ſibi mutuo reſpon-
              <lb/>
            dent. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">Itaque rurſus quadrata ſimul omnia perpendicularium,
              <lb/>
            à particulis figuræ S Y T Z in rectam S T cadentium,
              <lb/>
            æqualia erunt quadratis omnibus perpendicularium quæ, à
              <lb/>
            particulis ſolidi A B C D, ducuntur in planum A C. </s>
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