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

Table of contents

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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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98380CHRISTIANI HUGENII M L rectangulo contento lineis B L, S P: rectangulum au-
tem B L P majus eo quod ſub B L, S P continetur: erit
quadratum N L majus quadrato M L, & N L linea major
quam M L. Idem autem continget ubicunque inter B & S
aliqua ordinatim applicabitur. Igitur partem circumferentiæ
B F totam extra parabolam ferri neceſſe eſt, eâdemque ra-
tione partem B G. Rurſus quia rectangulum B D P æquale
eſt quadrato D A; rectangulum verò ſub B D, S P conten-
tum quadrato D H; erit H D major quam A D potentiâ,
ideoque & longitudine. Idemque eveniet ubicunque inter
S, D, ordinatim aliqua applicabitur. Quare partes circum-
ferentiæ F A, itemque G C intra parabolam cadent. Fiunt
igitur ſpatia quædam F N B M, & B Q G, itemque alia
H F A, G C K. Quorum hæc cum tota ſint infra lineam
F G, etiam centrum commune gravitatis eorum infra eandem
erit. At parabolicæ portionis H B K centrum grav eſt in
ipſa F G, nimirum S punctum . Ergo partis 118. lib. 2.
Archim. de
Æquipond. A F M B Q G C centrum grav. erit ſupra rectam F G.
Sed ſupra hanc ſitum quoque apparet centrum grav. ſpatio-
rum F M B N, B Q G, quum tota ſint ſupra ipſam
F G. Ergo & ſpatii ex hiſce duobus & A F M B Q G C
compoſiti, hoc eſt, portionis circuli A B C centrum grav.
ſupra lineam F G reperietur: quumque ſit in B D diametro,
minus aberit à vertice B quam punctum S. Quod erat oſten-
dendum.
Theor. XV. Propos. XVIII.
CIrculi portio ſemicirculo minor ad inſcriptum
triangulum maximum majorem rationem habet
quam ſeſquitertiam, minorem vero quam diameter
portionis reliquæ tripla ſeſquitertia ad circuli diame-
trum cum tripla ea, quæ à centro circuli pertingit
ad portionis baſin.

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