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

Table of figures

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[Figure 1]
[Figure 2]
[Figure 3]
[4] Pag. 324.TAB. XXXIV.Fig. 1.O B E P L S Q M R N A K H G D F C
[5] Fig. 3.B Q P S O N R M E H K G A F D L C
[6] Fig. 2.B E A G M C D H R F K L
[7] Fig. 4.B M L K E A D F H C
[8] Fig. 5.B B A D C A D C E E
[9] Fig. 8.K G H M E F B L A D C
[10] Fig. 6.S E B P D
[11] Fig. 7.E S D P B
[12] Pag. 326.TAB. XXXV.Fig. 1.N H T Z Ψ G K X S Σ Α E Ξ Y F O L B Δ R P V C Q Ω D M
[13] Fig. 5.B L A C D F M G K E H
[14] Fig. 4.B L A C D F M G K H E
[15] Fig. 2.B Δ P R V C Q Ω D A L F O Y Ξ Α Σ X S G K Ψ Z T H E N M
[16] Fig. 3.B Δ P R V A D Ω Q C L F O Y Ξ Α Σ X S G K E Ψ Z T H E N M
[17] Pag. 328.Fig. 2.B L F A D C H E
[18] Fig. 1.B L F A D C H E
[19] Fig. 3.B E A D C
[20] Fig. 4.Q B H A F C E G R D K
[21] Fig. 5.B E D A C G F
[Figure 22]
[23] Pag. 340.TAB. XXXVII.Fig. 1.C G H F E DH A X Q Y T N V B G
[24] Fig. 3.γ A F D X B P N V E Q C
[25] Fig. 2.K C Δ R Θ Z O Γ D I
[26] Fig. 4.A B D C Π Φ N E S P F
[27] Fig. 2.M E Ψ Λ Φ S Ξ Π Ρ Σ Ω F L
[28] Fig. 5.K B Δ E Z A C R O D Θ Γ I
[Figure 29]
[Figure 30]
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              <pb o="336" file="0042" n="45" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            oſtenderat facili negotio deducatur, ut jam ſtatim appa-
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            rebit.</s>
            <s xml:id="echoid-s721" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">TAB. XXXVII.
            <lb/>
          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
              <lb/>
            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-
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            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
              <lb/>
            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
              <lb/>
            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
              <lb/>
            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
              <lb/>
            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-
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            bus octavis ſive uni quartæ ejuſdem parabolici cylindri; </s>
            <s xml:id="echoid-s750" xml:space="preserve">(eſt
              <lb/>
            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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