Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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exponentem rationis Y ad A; </
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">denique ſemper demonſtrabi-
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tur terminos convergentes ſeriei exponentium eſſe exponen-
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tes rationum, terminorum convergentium ſeriei propoſitæ
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ad primam ſeriei quantitatem A, modò utriuſque ſeriei ter-
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mini convergentes ſint in eodem ab initio ordine: </
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">& </
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<
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de terminatio ſeriei exponentium per hujus 7 inventa, quæ
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Ex: </
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">Gr: </
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<
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">ſit L, erit exponens rationis, terminationis ſeriei
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propoſitæ ad primum terminum A: </
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">inveniatur igitur ratio
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Z ad A quæ ſit multiplicata rationis datæ B ad A in ratio-
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ne data L ad H; </
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">eritque Z terminatio quæſita, quam in-
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venire oportuit.</
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</
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<
s
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">Ad hoc problema in numeris illuſtrandum ſit M 4, N 2,
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O I, A
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, B
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; </
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<
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">erunt ſecundi termini convergentes v
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">960</
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,
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<
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">V992160,</
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tertii termini convergentes
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">V9997776000, V9999100776960000000.</
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& </
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<
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">Aliud exemplum, ſit M 6, N 2, O 3, A 5, B 10;
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</
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">erunt ſecundi termini convergentes
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">Vc250, Vq50,</
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tertii termini
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convergentes
<
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style
="
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">Vqcc488281250000000, Vqqc7812500000,</
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& </
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">ſeriei terminatio
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<
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hactenus terminavimus omnes ſeries convergentes quæ
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fieri poſſunt vel à ſola proportione arithmetica vel a ſola pro-
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portione geometrica, nunc vero methodum aggredimur, cu-
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jus ope omnium ſerierum convergentium terminationes (ſi
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modò ſint in rerum natura) inveniri poſſunt.</
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">Ex data quantitate, eodem modo compoſita à duo-
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bus terminis convergentibus cujuſcunque ſeriei
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convergentis, quo componitur ex terminis con-
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vergentibus ejuſdem ſeriei immediatè ſe-
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quentibus; </
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invenire.</
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<
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">Sit ſeries convergens, cujus duo termini convergentes
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quicunque ſint
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& </
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