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

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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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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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