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

Table of figures

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[41] Fig. 2.D B G H C E F
Page: 93
[42] Fig. 4.E C G A F B D
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[43] Fig. 3.E C D F G H I
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[44] Fig. 5.B F R C P L M O
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[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
Page: 93
[46] Fig. 7.G F D M L E A K C B H
Page: 93
[47] Pag. 386.TAB. XL.Fig. 2.K B H F G E A I D L C
Page: 106
[48] Fig. 1.L K E D H C A G B
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[49] Fig. 3.B Q N L M F G S H K A D C P
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[50] Fig. 4.B G R A C D E H F
Page: 106
[51] Fig. 6.A C D M B
Page: 106
[52] Fig. 5.A E N F B L D M C G H I K O
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[Figure 53]
Page: 108
[Figure 54]
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[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
Page: 121
[56] Fig. 2.D E F B G H C A
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[57] Fig. 3.F D E G A B C
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[58] Fig. 4.G N B H D K A E C F
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[59] Fig. 8K A F c C E B h H G D d
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[60] Fig. 6.C E D A F B R Q
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[61] Fig. 5.G L B H D O A E C K
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[62] Fig. 7.K F A C D B E H G
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[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
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[64] Fig. 3.G R D B H F E N A X C M P Q K
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[65] Fig. 2.K A F c S C L E B T G D R d
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[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
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[67] Fig. 5.B C R E G A F M Q D O
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[68] Fig. 6.B C H G E A M Q P K D
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[69] Fig. 7.B C E G A M P Q K H D
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[Figure 70]
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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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