Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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              <pb o="336" file="0042" n="45" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            oſtenderat facili negotio deducatur, ut jam ſtatim appa-
              <lb/>
            rebit.</s>
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          <note position="left" xml:space="preserve">TAB. XXXVII.
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          Fig. 3.</note>
          <p>
            <s xml:id="echoid-s722" xml:space="preserve">Repetitâ enim quatenus hîc neceſſe erit figurâ ipſius, quæ
              <lb/>
            eſt in propoſitione 99. </s>
            <s xml:id="echoid-s723" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s724" xml:space="preserve">9. </s>
            <s xml:id="echoid-s725" xml:space="preserve">Eſto Cylindrus Parabolicus,
              <lb/>
            baſes oppoſitas habens parabolas A B D, V C E; </s>
            <s xml:id="echoid-s726" xml:space="preserve">à quo ſit
              <lb/>
            abſciſſa Ungula A B C D, eâdem baſi & </s>
            <s xml:id="echoid-s727" xml:space="preserve">altitudine. </s>
            <s xml:id="echoid-s728" xml:space="preserve">Dico
              <lb/>
            Cylindrum ad hanc Ungulam habere rationem duplam ſeſ-
              <lb/>
            quialteram, ſive quam 5 ad 2.</s>
            <s xml:id="echoid-s729" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s730" xml:space="preserve">Tranſcriptis enim reliquis ex figura eadem, eſt F B dia-
              <lb/>
            meter parabolæ A B D: </s>
            <s xml:id="echoid-s731" xml:space="preserve">& </s>
            <s xml:id="echoid-s732" xml:space="preserve">lineæ rectæ A B, B D. </s>
            <s xml:id="echoid-s733" xml:space="preserve">Ductâ
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            porrò B C rectâ in ſuperficie cylindri, ſumptâque ejus quar-
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            tâ parte C Q, abſcinditur plano P Q N ungula P Q C N
              <lb/>
            & </s>
            <s xml:id="echoid-s734" xml:space="preserve">junguntur C A, C D. </s>
            <s xml:id="echoid-s735" xml:space="preserve">Denique toti cylindro adjuncta eſt
              <lb/>
            pyramis A D γ C æqualis parti B X D E C, quæ à cylin-
              <lb/>
            dro abſciſſa eſt plano B D E C. </s>
            <s xml:id="echoid-s736" xml:space="preserve">Et hactenus quidem ſuffi-
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            ciet nobis conſtructionem Cl. </s>
            <s xml:id="echoid-s737" xml:space="preserve">V. </s>
            <s xml:id="echoid-s738" xml:space="preserve">repetiiſſe. </s>
            <s xml:id="echoid-s739" xml:space="preserve">Demonſtravit
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            autem hæc duo quæ ſequuntur, ſicut videre eſt in dicta prop.
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            </s>
            <s xml:id="echoid-s740" xml:space="preserve">99. </s>
            <s xml:id="echoid-s741" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s742" xml:space="preserve">9. </s>
            <s xml:id="echoid-s743" xml:space="preserve">Nimirum quod ungula A B C D eſt ad ungulam
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            P Q C N, ſicut 32 ad 1. </s>
            <s xml:id="echoid-s744" xml:space="preserve">Item quod hæc ungula P Q C N
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            eſt ad pyramidem totam A γ D B C, (quæ compoſita eſt
              <lb/>
            ex duabus pyramidibus A D B C & </s>
            <s xml:id="echoid-s745" xml:space="preserve">A D γ C) ut 1 ad
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            30.</s>
            <s xml:id="echoid-s746" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s747" xml:space="preserve">Erit igitur ex æquo ungula A B C D ad pyramidem
              <lb/>
            A γ D B C ut 32 ad 30, hoc eſt, ut 16 ad 15. </s>
            <s xml:id="echoid-s748" xml:space="preserve">Porrò cùm
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            parabolæ A B D octava pars ſit ſegmentum B D X, erit
              <lb/>
            quoque ſegmentum ſolidum B X D E C vel huic æqualis
              <lb/>
            pyramis A D γ C, octava pars cylindri totius parabolici
              <lb/>
            A V C E D B: </s>
            <s xml:id="echoid-s749" xml:space="preserve">ſed pyramis altera A D B C æquatur dua-
              <lb/>
            bus octavis ſive uni quartæ ejuſdem parabolici cylindri; </s>
            <s xml:id="echoid-s750" xml:space="preserve">(eſt
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            enim ipſa tertia pars ſui priſmatis, quod æquale eſt tribus
              <lb/>
            quartis cylindri iſtius, ut ex quadratura parabolæ conſtat)
              <lb/>
            ergo tota pyramis A γ D B C tribus octavis æquatur cylin-
              <lb/>
            dri parab. </s>
            <s xml:id="echoid-s751" xml:space="preserve">A V C E D B. </s>
            <s xml:id="echoid-s752" xml:space="preserve">Cylindrus igitur parabolicus
              <lb/>
            A V C E D B erit ad pyramidem A γ D B C, ut 8 ad 3,
              <lb/>
            hoc eſt, ut 40 ad 15; </s>
            <s xml:id="echoid-s753" xml:space="preserve">ſed oſtenſum eſt eandem pyramidem
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            A γ D B C eſſe ad ungulam A B C D ut 15 ad 16. </s>
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