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

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            <s xml:id="echoid-s3853" xml:space="preserve">
              <pb o="170" file="0244" n="269" rhead="CHRISTIANI HUGENII"/>
            ad radium, ita ſint {2/3} C B ad B E. </s>
            <s xml:id="echoid-s3854" xml:space="preserve">Tunc enim E eſt cen-
              <lb/>
              <note position="left" xlink:label="note-0244-01" xlink:href="note-0244-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            trum gravitatis ſemicirculi baſeos, ideoque in A E centra
              <lb/>
            gravitatis omnium ſegmentorum ſemiconi A B D, baſi pa-
              <lb/>
            rallelorum.</s>
            <s xml:id="echoid-s3855" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3856" xml:space="preserve">Et figura quidem porro proportionalis à latere ponenda,
              <lb/>
            O V V, eadem eſt quæ in cono toto ſupra deſcripta fuit:
              <lb/>
            </s>
            <s xml:id="echoid-s3857" xml:space="preserve">per quam nempe invenietur ſumma quadratorum, à diſtan-
              <lb/>
            tiis particularum ſemiconi à plano horizontali N D, per
              <lb/>
            centrum gravitatis ducto. </s>
            <s xml:id="echoid-s3858" xml:space="preserve">Verum quadrata diſtantiarum, à
              <lb/>
            plano verticali M D O, ut colligantur, altera quoque figu-
              <lb/>
            ra proportionalis S Y Z, ſicut ſupra prop. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3860" xml:space="preserve">adhibenda
              <lb/>
            eſt, cujus nempe ſectiones verticales, exhibeant lineas pro-
              <lb/>
            portionales ſectionibus ſibi reſpondentibus in ſemicono A B C. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3862" xml:space="preserve">hujus figuræ cognoſcenda eſt diſtantia centri gr. </s>
            <s xml:id="echoid-s3863" xml:space="preserve">F ab S Y,
              <lb/>
            quam æqualem eſſe conſtat diſtantiæ D N, centri gr. </s>
            <s xml:id="echoid-s3864" xml:space="preserve">ſemiconi
              <lb/>
            à plano trianguli A B. </s>
            <s xml:id="echoid-s3865" xml:space="preserve">poſitâque H G ſubcentricâ cunei ab-
              <lb/>
            ſciſſi ſuper figura S Z Y, ducto plano per S Y, noſcendum
              <lb/>
            eſt rectangulum G F H, cujus nempe multiplex, ſecundum
              <lb/>
            numerum particularum ſemiconi A B C, æquabitur quadra-
              <lb/>
            tis diſtantiarum ſemiconi in planum M D O. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">Licebit vero
              <lb/>
            cognoſcere rectangulum illud G F H, etiamſi ſubcentricæ
              <lb/>
            H G longitudo ignoretur, hoc modo.</s>
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            <s xml:id="echoid-s3868" xml:space="preserve">Diximus ſupra, cum de cono ageremus, quadrata diſtan-
              <lb/>
            tiarum à plano per axem ejus, æquari {3/80} quadrati à diametro
              <lb/>
            baſis, ſive {3/20} quadrati à ſemidiametro, multiplicis per nu-
              <lb/>
            merum particularum coni totius. </s>
            <s xml:id="echoid-s3869" xml:space="preserve">Unde & </s>
            <s xml:id="echoid-s3870" xml:space="preserve">hic, in ſemicono
              <lb/>
            A B C, quadrata diſtantiarum à plano A B æqualia erunt
              <lb/>
            {3/20} quadrati B C, multiplicis per numerum particularum i-
              <lb/>
            pſius ſemiconi. </s>
            <s xml:id="echoid-s3871" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3872" xml:space="preserve">rectangulum H G F, multiplex per nu-
              <lb/>
            merum particularum ſemiconi A B C, æquatur quadratis
              <lb/>
            diſtantiarum à plano A B, ut patet ex propoſitione 9. </s>
            <s xml:id="echoid-s3873" xml:space="preserve">Ergo
              <lb/>
            rectangulum H G F æquale {3/20} quadrati B C. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">Ponendo autem
              <lb/>
            A B = a; </s>
            <s xml:id="echoid-s3875" xml:space="preserve">B C = b; </s>
            <s xml:id="echoid-s3876" xml:space="preserve">& </s>
            <s xml:id="echoid-s3877" xml:space="preserve">quadrantem circumferentiæ, radio
              <lb/>
            B C deſcriptæ, = q; </s>
            <s xml:id="echoid-s3878" xml:space="preserve">fit E B = {2 b b/3 q}. </s>
            <s xml:id="echoid-s3879" xml:space="preserve">Cujus cum N D
              <lb/>
            tribus quartis æquetur, fiet proinde N D, ſive G F = {1 b b/2 q @}.</s>
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