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

Table of contents

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[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)
[71.] PROP. VI. THEOREMATA.
Page: 147 (420)
[72.] SCHOLIUM.
Page: 148 (421)
[73.] PROP. VII. PROBLEMA. Oportet prædictæ ſeriei terminationem invenire.
Page: 150 (423)
[74.] PROP. VIII. PROBLEMA.
Page: 152 (425)
[75.] PROP. IX. PROBLEMA.
Page: 153 (426)
[76.] PROP. X. PROBLEMA.
Page: 154 (427)
[77.] CONSECTARIUM.
Page: 155 (428)
[78.] PROP. XI. THEOREMA.
Page: 156 (429)
[79.] SCHOLIUM.
Page: 159 (432)
[80.] PROP. XII. THEOREMA.
Page: 161 (434)
[81.] PROP. XIII. THEOREMA.
Page: 161 (434)
[82.] PROP. XIV. THEOREMA.
Page: 162 (435)
[83.] PROP. XV. THEOREMA.
Page: 162 (435)
[84.] PROP. XVI. THEOREMA.
Page: 163 (436)
[85.] PROP. XVII. THEOREMA.
Page: 164 (437)
[86.] PROP. XVIII. THEOREMA.
Page: 164 (437)
[87.] PROP. XIX. THEOREMA.
Page: 165 (438)
[88.] CONSECTARIUM.
Page: 165 (438)
[89.] PROP. XX. THEOREMA.
Page: 165 (438)
[90.] PROP. XXI. THEOREMA.
Page: 166 (439)
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70358CHRISTIANI HUGENII anguli E B F. Huic autem triangulo æquantur ſingula A E B,
B F C. Ergo utriuſque ſimul triangulum A B C minus erit
quam quadruplum. Quod erat oſtendendum.
Theor. II. Prop. II.
Si fuerit circuli portio, ſemicirculo minor, & ſu-
per eadem baſi triangulum, cujus latera portio-
nem contingant; ducatur autem quæ contingat por-
tionem in vertice: Hæc à triangulo dicto triangu-
lum abſcindet majus dimidio maximi trianguli in-
tra portionem deſcripti.
Eſto circuli portio ſemicirculo minor A B C, cujus vertex
11TAB. XXXVIII.
Fig. 2. B. Et contingant portionem ad terminos baſis rectæ A E,
C E, quæ conveniant in E: convenient enim quia portio ſe-
micirculo minor eſt. Porro ducatur F G, quæ contingati-
pſam in vertice B; & jungantur A B, B C. Oſtendendum eſt
itaque, triangulum F E G majus eſſe dimidio trianguli
A B C. Conſtat triangula A E C, F E G, item A F B,
B G C æquicruria eſſe, dividique F G ad B bifariam. Utra-
que autem ſimul F E, E G, major eſt quam F G; ergo
E F major quam F B, vel quam F A. Tota igitur A E minor
quam dupla F E. Quare triangulum F E G majus erit quarta
parte trianguli A E C. Sicut autem F A ad A E, ita eſt al-
titudo trianguli A B C ad altitudinem trianguli A E C, &
baſis utrique eadem A C. Ergo, quum F A ſit minor quam
ſubdupla totius A E, erit triangulum A B C minus dimi-
dio triangulo A E C. Hujus vero quarta parte majus erat
triangulum F E G. Ergo triangulum F E G majus dimidio
trianguli A B C. Quod oſtendendum fuit.
Theor. III. Prop. III.
OMnis circuli portio, ſemicirculo minor, ad ma-
ximum triangulum inſcriptum majorem ratio-
nem habet quam ſeſquitertiam.

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