Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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AD ANIM. HUGENII.
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<
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xml:space
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<
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xml:space
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ſimile circumſcriptum; </
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<
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xml:space
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gonorum &</
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X eodem modo compoſita à terminis C, D, quo Z à ter-
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minis A, B; </
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<
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<
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indefinitè æquales, ſit inter illas indefinita differentia a, & </
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continuetur ſeries convergens in terminos convergentes I, K,
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ita ut eorum differentia ſit minor quam a; </
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A # B
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C # D
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E # F
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G # H a
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I # K
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L # M
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# Z
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# X
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enim abſque dubio concipi poteſt, etiamſi hic
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omnes quantitates ſint indefinitæ, quoniam
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definitis quantitatibus A, B, definitur etiam a,
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ſed adhuc reſtat K-1 quantitas indeterminata
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in infinitum decreſcens. </
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ctorem Z eſſe indefinitè minorem quam K, & </
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majorem quam I: </
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">item quoniam Zeodem mo-
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do componitur ex quantitatibus A, B, quo X. </
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<
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tibus C, D, & </
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quam I, patet ex Proprietatibus ſerierum convergentium,
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X etiam eſſe indefinitè majorem quàm I, & </
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K (eſt enim revera indefinitè major quàm L & </
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M) & </
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maxima & </
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& </
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">ideo differentia extremarum K-I major eſt quàm a diffe-
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rentia mediarum, quod eſt abſurdum, ponitur enim minor:
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</
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ideo ſunt indefinitè æquales, quod demonſtrandum erat. </
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Manifeſtum eſt hanc demonſtrationem eodem modo appli-
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cabilem eſſe omni ſeriei convergenti.</
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<
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nes argumentatur Hugenius: </
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mo in Scholio propoſit. </
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nam propoſitionem eſſe Particularem, unamquamque ſuo ca-
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ſui; </
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<
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tuo) evidenter ſuppono, & </
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<
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eo modo compoſitam ex primis, quo ex ſecundis terminis
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convergentibus; </
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