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

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[41.] Theor. XII. Prop. XV.
[42.] Theor. XIII. Prop. XVI.
[43.] Theorema XIV. Propos. XVII.
[44.] Theor. XV. Propos. XVIII.
[45.] Theor. XVI. Propos. XIX.
[46.] Problema IV. Propos. XX.
[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.
[48.] LEMMA.
[49.] Probl. II. Cubum invenire dati cubi duplum.
[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.
[51.] ALITER.
[52.] ALITER.
[53.] Probl. IV.
[54.] Probl. V.
[55.] Probl. VI.
[56.] Probl. VII.
[57.] Utrumque præcedentium Aliter.
[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.
[59.] FINIS.
[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.
[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.
[62.] DEFINITIONES.
[63.] PETITIONES.
[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.
[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.
[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.
[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.
[69.] PROP. V. THEOREMA.
[70.] SCHOLIUM.
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139PRÆFATIO AD LECTOREM. lum hinc fructum colliges.
DEFINITIONES.
1 Si in circulo, ellipſe vel hyperbola ducantur è centro
in ejus perimetrum duæ rectæ, appellamus planum
ab illis rectis &
perimetri ſegmento comprehenſum,
ſectorem.
2 Si perimetri ſegmentum inter illas rectas comprehenſum à
rectis quotcumque ſubtendatur, ita ut triangula rectili-
nea (quorum communis vertex eſt ſectionis centrum &

baſes rectæ ſubtendentes) ſint æqualia;
vocamus rectili-
neum illud ab iſtis triangulis conflatum, polygonum re-
gulare inſcriptum, ſi ſectio conica fuerit circulus vel el-
lipſis;
quod ſi fuerit hyperbola, vocamus illud rectili-
neum polygonum regulare circumſcriptum.
3 Si perimetri ſegmentum inter illas rectas comprehenſum à
rectis quotcunque tangatur &
à tactibus ad ſectionis cen-
trum ducantur rectæ;
ſi inquam omnia trapezia, a tan-
gentibus proximis &
rectis ad centrum comprehenſa, fue-
rint æqualia;
appello rectilineum ab illis conflatum, poly-
gonum regulare circumſcriptum, ſi ſectio conica ſit elli-
pſis vel circulus, &
polygonum regulare inſcriptum ſi
fuerit hyperbola.
4 Si omnes anguli (excepto illo ad ſectionis centrum) po-
lygoni regularis à ſubtendentibus comprehenſi

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