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

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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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74362CHRISTIANI HUGENII
Eſto circulus cujus centrum A, & inſcribatur ipſi polygo-
11TAB. XXXVIII.
Fig. 6. num lateribus æqualibus, quorum unum ſit B C; & ali-
ud ſimile circumſcribatur F E G, cujus latera circulum con-
tingant ad occurſum angulorum polygoni prioris. Dico cir-
culum minorem eſſe duabus tertiis polygoni F E G ſimul
cum triente polygoni B C. Ducantur namque ex centro re-
ctæ A B, A C. Igitur quoniam ſuper baſi portionis B D C
conſiſtit triangulum B E C, cujus latera portionem contin-
gunt, erit ipſa minor duabus tertiis trianguli B E C . 22per. 4. huj. taque ſi triangulo A B C addantur duæ tertiæ trianguli B E C,
hoc eſt, duæ tertiæ exceſſus quadrilateri A B E C ſupra tri-
angulum A B C, ex utriſque compoſitum ſpatium majus
erit ſectore circuli A B C. Idem eſt autem, ſive triangulo
A B C addantur duæ tertiæ exceſſus dicti, ſive addantur duæ
tertiæ quadrilateri A B E C, contraque auferantur duæ ter-
tiæ trianguli A B C: hinc autem fiunt duæ tertiæ quadri-
lateri A B E C cum triente trianguli A B C. Ergo apparet
ſectorem A B C minorem eſſe duabus tertiis quadrilateri
A B E C & triente trianguli A B C. Quare ſumptis omni-
bus quoties ſector A B C circulo continetur, totus quoque
circulus minor erit duabus tertiis polygoni circumſcripti
F E G & triente inſcripti B C. Quod erat oſtendendum.
Theor. VII. Prop. VII.
OMnis circuli circumferentia major eſt perime-
tro polygoni æqualium laterum ſibi inſcripti,
& triente exceſſus quo perimeter eadem ſuperat pe-
rimetrum alterius polygoni inſcripti ſubduplo late-
terum numero.
Eſto circulus A B, centro O, cui inſcribatur polygonum
33TAB. XXXVIII.
Fig. 7. æquilaterum A C D, atque alterum duplo laterum nume-
ro A E C B D F. Sitque recta G I æqualis perimetro po-
lygoni A E C B D F, G H vero æqualis perimetro

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