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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quos terminos æquales appellamus ſeriei terminatio-
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nem.</
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invenire.</
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quantitatem quæ eodem modo componitur ex termi-
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nis convergentibus
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,
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, quo ex terminis convergentibus
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{ca + bd - ad/c}, {bc - bc + ae/c}, hoc autem facile fit hoc modo: </
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<
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quantitas quæ multiplicata in
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& </
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multiplicata in
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quantitatem data m, eandem quantitatem facit ac ſi multi-
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plicaretur in {ca + bd - ad/c} & </
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<
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">adderetur {bc - be + ae/c} multiplicata etiam
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in eandem quantitatem data\m m. </
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<
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, & </
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inde za + bm æquatur {zca + zbd - zad + mbe - mbe + mae/c}, & </
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reducta invenitur {z = mac - mbe/ad - bd}; </
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<
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">quæ quantitas ſive multiplica-
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ta in
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& </
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, ſive multiplicata in {ca + bd - ad/c} & </
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{mbe - mbe + mae/c} efficit eandem in utroque caſu quantitatem nempe
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{maae - mbae + mbad - mbbd/cd - bd}: </
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<
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<
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">proinde prædicta quantitas eodem mo-
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do componitur ex terminis convergentibus
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,
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, quo compo-
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nitur ex terminis convergentibus {ca + bd - ad/c}, {bc - be + ae/c}. </
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& </
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quoniam ſunt quantitates indefinitæ poſſunt eſſe quili-
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bet totius ſeriei termini convergentes, modò termini con-
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vergentes immediatè ſequentes ſint {ca + bd - ad/c} & </
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proinde quantitas {maae - mbae + mbad - mbbd/cd - bd} eodem modo componi-
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tur ex quibuslibet totius ſeriei terminis convergentibus quo
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componitur ex terminis convergentibus
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,
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; </
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