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

Table of figures

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[Figure 1]
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[Figure 2]
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[Figure 3]
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[4] Pag. 324.TAB. XXXIV.Fig. 1.O B E P L S Q M R N A K H G D F C
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[5] Fig. 3.B Q P S O N R M E H K G A F D L C
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[6] Fig. 2.B E A G M C D H R F K L
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[7] Fig. 4.B M L K E A D F H C
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[8] Fig. 5.B B A D C A D C E E
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[9] Fig. 8.K G H M E F B L A D C
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[10] Fig. 6.S E B P D
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[11] Fig. 7.E S D P B
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[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
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[13] Fig. 5.B L A C D F M G K E H
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[14] Fig. 4.B L A C D F M G K H E
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[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
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[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
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[17] Pag. 328.Fig. 2.B L F A D C H E
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[18] Fig. 1.B L F A D C H E
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[19] Fig. 3.B E A D C
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[20] Fig. 4.Q B H A F C E G R D K
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[21] Fig. 5.B E D A C G F
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[Figure 22]
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[23] Pag. 340.TAB. XXXVII.Fig. 1.C G H F E DH A X Q Y T N V B G
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[24] Fig. 3.γ A F D X B P N V E Q C
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[25] Fig. 2.K C Δ R Θ Z O Γ D I
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[26] Fig. 4.A B D C Π Φ N E S P F
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[27] Fig. 2.M E Ψ Λ Φ S Ξ Π Ρ Σ Ω F L
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[28] Fig. 5.K B Δ E Z A C R O D Θ Γ I
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[Figure 29]
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[Figure 30]
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45336ΕΞΕΤΑΣΙΣ CYCLOM. oſtenderat facili negotio deducatur, ut jam ſtatim appa-
rebit.
11TAB. XXXVII.
Fig. 3.
Repetitâ enim quatenus hîc neceſſe erit figurâ ipſius, quæ
eſt in propoſitione 99. lib. 9. Eſto Cylindrus Parabolicus,
baſes oppoſitas habens parabolas A B D, V C E; à quo ſit
abſciſſa Ungula A B C D, eâdem baſi & altitudine. Dico
Cylindrum ad hanc Ungulam habere rationem duplam ſeſ-
quialteram, ſive quam 5 ad 2.
Tranſcriptis enim reliquis ex figura eadem, eſt F B dia-
meter parabolæ A B D: & lineæ rectæ A B, B D. Ductâ
porrò B C rectâ in ſuperficie cylindri, ſumptâque ejus quar-
tâ parte C Q, abſcinditur plano P Q N ungula P Q C N
& junguntur C A, C D. Denique toti cylindro adjuncta eſt
pyramis A D γ C æqualis parti B X D E C, quæ à cylin-
dro abſciſſa eſt plano B D E C. Et hactenus quidem ſuffi-
ciet nobis conſtructionem Cl. V. repetiiſſe. Demonſtravit
autem hæc duo quæ ſequuntur, ſicut videre eſt in dicta prop.
99. lib. 9. Nimirum quod ungula A B C D eſt ad ungulam
P Q C N, ſicut 32 ad 1. Item quod hæc ungula P Q C N
eſt ad pyramidem totam A γ D B C, (quæ compoſita eſt
ex duabus pyramidibus A D B C & A D γ C) ut 1 ad
30.
Erit igitur ex æquo ungula A B C D ad pyramidem
A γ D B C ut 32 ad 30, hoc eſt, ut 16 ad 15. Porrò cùm
parabolæ A B D octava pars ſit ſegmentum B D X, erit
quoque ſegmentum ſolidum B X D E C vel huic æqualis
pyramis A D γ C, octava pars cylindri totius parabolici
A V C E D B: ſed pyramis altera A D B C æquatur dua-
bus octavis ſive uni quartæ ejuſdem parabolici cylindri; (eſt
enim ipſa tertia pars ſui priſmatis, quod æquale eſt tribus
quartis cylindri iſtius, ut ex quadratura parabolæ conſtat)
ergo tota pyramis A γ D B C tribus octavis æquatur cylin-
dri parab. A V C E D B. Cylindrus igitur parabolicus
A V C E D B erit ad pyramidem A γ D B C, ut 8 ad 3,
hoc eſt, ut 40 ad 15; ſed oſtenſum eſt eandem pyramidem
A γ D B C eſſe ad ungulam A B C D ut 15 ad 16.

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