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

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[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)
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154427ET HYPERBOLÆ QUADRATURA. exponentem rationis Y ad A; denique ſemper demonſtrabi-
tur terminos convergentes ſeriei exponentium eſſe exponen-
tes rationum, terminorum convergentium ſeriei propoſitæ
ad primam ſeriei quantitatem A, modò utriuſque ſeriei ter-
mini convergentes ſint in eodem ab initio ordine: & proin-
de terminatio ſeriei exponentium per hujus 7 inventa, quæ
Ex: Gr: ſit L, erit exponens rationis, terminationis ſeriei
propoſitæ ad primum terminum A: inveniatur igitur ratio
Z ad A quæ ſit multiplicata rationis datæ B ad A in ratio-
ne data L ad H; eritque Z terminatio quæſita, quam in-
venire oportuit.
Ad hoc problema in numeris illuſtrandum ſit M 4, N 2,
O I, A 6, B 10; erunt ſecundi termini convergentes v960,
V992160, tertii termini convergentes V9997776000, V9999100776960000000.
& ſeriei terminatio Vc360.
Aliud exemplum, ſit M 6, N 2, O 3, A 5, B 10;
erunt ſecundi termini convergentes Vc250, Vq50, tertii termini
convergentes Vqcc488281250000000, Vqqc7812500000, & ſeriei terminatio
Vſ12500. hactenus terminavimus omnes ſeries convergentes quæ
fieri poſſunt vel à ſola proportione arithmetica vel a ſola pro-
portione geometrica, nunc vero methodum aggredimur, cu-
jus ope omnium ſerierum convergentium terminationes (ſi
modò ſint in rerum natura) inveniri poſſunt.
PROP. X. PROBLEMA.
Ex data quantitate, eodem modo compoſita à duo-
bus terminis convergentibus cujuſcunque ſeriei
convergentis, quo componitur ex terminis con-
vergentibus ejuſdem ſeriei immediatè ſe-
quentibus; ſeriei propoſitæ terminationem
invenire.
Sit ſeries convergens, cujus duo termini convergentes
quicunque ſint a, b, & termini convergentes

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