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

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[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)
[91.] PROP. XXII. THEOREMA.
Page: 167 (440)
[92.] SCHOLIUM.
Page: 168 (441)
[93.] PROP. XXIII. THEOREMA.
Page: 168 (441)
[94.] PROP. XXIV. THEOREMA.
Page: 169 (442)
[95.] PROP. XXV. THEOREMA.
Page: 170 (443)
[96.] PROP. XXVI. THEOREMA.
Page: 171 (444)
[97.] PROP. XXVII. THEOREMA.
Page: 172 (445)
[98.] PROP. XXVIII. THEOREMA.
Page: 173 (446)
[99.] PROP. XXIX. PROBLEMA. Dato circulo æquale invenire quadratum.
Page: 173 (446)
[100.] PROP. XXX. PROBLEMA. Ex dato ſinu invenire arcum.
Page: 175 (448)
[101.] PROP. XXXI. PROBLEMA. Ex dato arcu invenire ſinum.
Page: 175 (448)
[102.] PROP. XXXII. PROBLEMA. Invenire quadratum æquale ſpatio hyperbolico con-tento à curva hyperbolica, uno aſymptoto & dua-bus rectis alteri aſymptoto parallelis; quod ſpatium æquale eſt ſectori hyperbolico cujus baſis eſt eadem curva.
Page: 176 (449)
[103.] PROP. XXXIII. PROBLEMA. Propoſiti cujuscunque numeri logorithmum invenire.
Page: 182 (452)
[104.] SCHOLIUM.
Page: 183 (453)
[105.] PROP. XXXIV. PROBLEMA. Ex dato logorithmo invenire ejus numerum.
Page: 189 (459)
[106.] Tom. II. Mmm
Page: 189 (459)
[107.] PROP. XXXV. PROBLEMA. Rectâ per datum punctum in diametro ductâ, ſemicirculum in ratione data dividere.
Page: 190 (460)
[108.] SCHOLIUM.
Page: 190 (460)
[109.] FINIS.
Page: 192 (462)
[110.] II. HUGENII OBSERVATIONES IN LIBRUM JACOBI GREGORII, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
Page: 193 (463)
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144417ET HYPERBOLÆ QUADRATURA.
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.
11TAB. XLIII.
Fig. 1. 2. 3.
In antecedente demonſtratum eſt trapezia A B F P, A B I P
ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
A B F P ad polygonum A B D L P: & permutando tra-
pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
ut duplum trapezii A B I P ad polygonum A B D L P. &
quoniam trapezium A B F P, trapezium A B I P & trian-
gulum A B P, ſunt continuè proportionalia; erit trape-
zium A B I P ad trapezium A B F P, ut triangulum A B P
ad trapezium A B I P; & componendo, ut trapezia A B I P,
A B F P ſimul, ad trapezium A B F P, ita triangulum
A B P & trapezium A B I P ſimul, ad trapezium A B I P:
erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
pezium A B F P, ita duplum trapezii A B I P ad polygo-
num A B D L P; & igitur ut triangulum A B P & trape-
zium A B I P ſimul, ad trapezium A B I P, ita duplum
trapezii A B I P ad polygonum A B D L P, quod demon-
ſtrare oportuit.
Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
ſecantes in punctis E & O, & rectas B I, I P, in H & M:
deinde jungantur rectæ B E, E I, I O, O P, ut complea-
tur polygonum A B E I O P.
PROP. IV. THEOREMA.
Dico polygonum A B E I O P eſſe medium pro-
portionale inter polygonum A B D L & trapezium A B I P.
22TAB. XLIII.
Fig. 1. 2. 3.
Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
pezium A I O P & triangulum A I P eſſe

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