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

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[41.] Theor. XII. Prop. XV.
Page: 91 (376)
[42.] Theor. XIII. Prop. XVI.
Page: 95 (377)
[43.] Theorema XIV. Propos. XVII.
Page: 96 (378)
[44.] Theor. XV. Propos. XVIII.
Page: 98 (380)
[45.] Theor. XVI. Propos. XIX.
Page: 100 (382)
[46.] Problema IV. Propos. XX.
Page: 102 (384)
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
Page: 109
[48.] LEMMA.
Page: 111 (390)
[49.] Probl. II. Cubum invenire dati cubi duplum.
Page: 112 (391)
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
Page: 114 (393)
[51.] ALITER.
Page: 115 (394)
[52.] ALITER.
Page: 116 (395)
[53.] Probl. IV.
Page: 117 (396)
[54.] Probl. V.
Page: 118 (397)
[55.] Probl. VI.
Page: 118 (397)
[56.] Probl. VII.
Page: 123 (399)
[57.] Utrumque præcedentium Aliter.
Page: 125 (401)
[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.
Page: 127 (403)
[59.] FINIS.
Page: 128 (404)
[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.
Page: 132
[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.
Page: 134
[62.] DEFINITIONES.
Page: 139
[63.] PETITIONES.
Page: 141 (414)
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 142 (415)
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
Page: 142 (415)
[66.] PROP. II. THEOREMA. Dico trapezia A B F P, A B I P ſimul, eſſe ad du- plum trapezii A B I P, ſicut trapezium A B F P ad polygonum A B D L P.
Page: 143 (416)
[67.] PROP. III. THEOREMA. Dico triangulum B A P, & trapezium A B I P ſimul, eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.
Page: 144 (417)
[68.] PROP. IV. THEOREMA. Dico polygonum A B E I O P eſſe medium pro- portionale inter polygonum A B D L P & trapezium A B I P.
Page: 144 (417)
[69.] PROP. V. THEOREMA.
Page: 145 (418)
[70.] SCHOLIUM.
Page: 146 (419)
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73361DE CIRCULI MAGNIT. INVENTA. rectis A D, D C & arcu A B C comprehenſum majus erit
portionis A B C dimidio. Ac proinde triangulum A D C
majus quam portionis A B C ſeſquialterum. Quod erat de-
monſtrandum.
Theor. V. Prop. V.
OMnis circulus major eſt pylogono æqualium
laterum ſibi inſcripto & triente exceſſus quo
id polygonum ſuperat aliud inſcriptum ſubduplo la-
terum numero.
Eſto circulus centro C; ſitque ipſi inſcriptum polygonum
11TAB. XXXVIII.
Fig. 5. æqualium laterum, quorum unum ſit A B. Atque alterum
item polygonum ſit inſcriptum, cujus bina latera A D, D B,
ſubtendat A B. Hoc igitur priore polygono majus eſt. Sit
autem exceſſus trienti æquale H ſpatium. Dico circulum ma-
jorem eſſe polygono A D B una cum ſpatio H. Ducantur
enim ex centro rectæ C A, C B. Quoniam igitur portio
circuli A D B major eſt quam ſeſquitertia trianguli A D B ſibi
inſcripti ; erunt portiones A D, D B, ſimul majores 22per. 3. huj. ente trianguli A D B. Quamobrem & ſector C A B major
erit utriſque ſimul quadrilatero C A D B & triente trian-
guli A D B. Sicut autem ſector C A B ad circulum totum,
ita eſt quadrilaterum C D B A ad polygonum A D B, &
ita quoque triens trianguli A D B ad trientem exceſſus po-
lygoni A D B ſupra polygonum A B. Ergo manifeſtum eſt
circulum quoque totum majorem fore polygono A D B una
cum triente exceſſus quo polygonum A D B ſuperat poly-
gonum A B, hoc eſt, unà cum ſpatio H. Quod erat demon-
ſtrandum.
Theor. VI. Prop. VI.
Omnis circulus minor eſt duabus tertiis polygo-
ni æqualium laterum ſibi circumſcripti & tri-
ente polygoni ſimilis inſcripti.

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