Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

ET 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 v 960 ,
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.

76. 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 immediatè

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