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

Table of contents

< >
[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)
[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)
< >
page |< < (399) of 568 > >|
123399ILLUST. QUORUND. PROB. CONSTRUCT. eſt in circulo, ſunt anguli C G B & B M C ſimul duobus
rectis æquales. Sed & anguli E D B, A D B. Quorum E D B
æqualis angulo C G B propter ſimilitudinem triangulorum
G B C, D B E. Ergo & angulus B M C æqualis erit an-
gulo A D B. Trianguli igitur A B M, A B D angulos M
& D inter ſe æquales habent. Verum & angulos ad A, &
latus A B commune. Itaque dicti trianguli ſimiles ſunt &
æquales. Quare A M æqualis A D, & M B æqualis B D,
& angulus M B A æqualis A B D. In triangulo igitur M B C
angulus B in duo æqualia dividitur à recta B A, ideoque
rectang. M B C minus quadrato B A æquatur rectangulo
M A C. Sed rectangulo C B M æquale eſt rectangulum
C B D; & rectangulo M A C æquale rectang. D A C. Igi-
tur rectang. C B D minus quadrato B A æquale rectangulo
C A D, uti dictum fuit. Eſt itaque G B ad B E ut quadr.
K ad rectangulum D A C. Sicut autem G B ad B E ita eſt
rectang. G B E, hoc eſt, rectang. C B D ad quadratum B E.
Ergo ut quadratum K ad rectang. D A C ita rectang. C B D
ad quadratum B E. Ratio autem rectanguli C B D ad quadr.
B E compoſita eſt ex ratione D B ad B E, hoc eſt, D C
ad C A, & ex ratione C B ad B E ſive B F, hoc eſt, C D
ad D A. Ergo & quadr. K ad rectang. D A C eam habet
rationem quæ componitur ex ratione D C ad C A & D C
ad D A. hoc eſt, eam quam quadratum D C ad rectang.
D A C. Quamobrem quadr. K. quadrato D C æquale eſt:
Et D C ipſi K longitudine. Quod erat demonſtrandum.
Probl. VII.
RHombo dato & duobus contiguis lateribus pro-
ductis, aptare ſub angulo interiorirectam ma-
gnitudine datam quæ per oppoſitum angulum tranſ-
eat. Oportet autem datam non minorem eſſe quam
duplam diametri quæ reliquos duos rhombi angulos
conjungit.

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index
Impressum