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

Table of contents

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[11.] Theorema III.
Page: 17 (317)
[12.] Theorema IV.
Page: 18 (318)
[13.] Lemma.
Page: 19 (319)
[14.] Theorema V.
Page: 20 (320)
[15.] Theorema VI.
Page: 23 (323)
[16.] Theorema VII.
Page: 24 (324)
[17.] Theorema VIII.
Page: 29 (326)
[18.] ἘΞἘΤΑΣΙΣ CYCLOMETRIÆ CLARISSIMI VIRI, GREGORII à S. VINCENTIO, S. J. Editæ Anno D. cIↄ Iↄc XLVII.
Page: 34 (328)
[19.] FINIS.
Page: 49 (340)
[20.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S.I. EPISTOLA, Qua diluuntur ea quibus Ε’ξε{τα}{σι}ς Cyclometriæ Gregorii à Sto. Vincentio impugnata fuit.
Page: 53
[21.] CHRISTIANI HUGENII, Const. F. AD C. V. FRAN. XAVERIUM AINSCOM. S. I. EPISTOLA. Cl. Viro D°. XAVERIO AINSCOM CHRISTIANUS HUGENIUS S. D.
Page: 55
[22.] CHRISTIANI HUGENII, Const. F. DE CIRCULI MAGNITUDINE INVENTA. ACCEDUNT EJUSDEM Problematum quorundam illuſtrium Conſtructiones.
Page: 63
[23.] PRÆFATIO.
Page: 65
[24.] CHRISTIANI HUGENII, Const. f. DE CIRCULI MAGNITUDINE INVENTA. Theorema I. Propositio I.
Page: 69
[25.] Theor. II. Prop. II.
Page: 70 (358)
[26.] Theor. III. Prop. III.
Page: 70 (358)
[27.] Theor. IV. Prop. IV.
Page: 72 (360)
[28.] Theor. V. Prop. V.
Page: 73 (361)
[29.] Theor. VI. Prop. VI.
Page: 73 (361)
[30.] Theor. VII. Prop. VII.
Page: 74 (362)
[31.] Theor. VIII. Prop. VIII.
Page: 76 (364)
[32.] Theor. IX. Prop. IX.
Page: 77 (365)
[33.] Problema I. Prop. X. Peripheriæ ad diametrum rationem invenire quamlibet veræ propinquam.
Page: 78 (366)
[34.] Problema II. Prop. XI.
Page: 83 (368)
[35.] Aliter.
Page: 84 (369)
[36.] Aliter.
Page: 84 (369)
[37.] Problbma III. Prop. XII. Dato arcui cuicunque rectam æqualem ſumere.
Page: 85 (370)
[38.] Theor. X. Prop. XIII.
Page: 86 (371)
[39.] Lemma.
Page: 87 (372)
[40.] Theor. XI. Prop. XIV.
Page: 87 (372)
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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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