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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diarum arithmeticè continuè proportionalium inter duas
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inæquales quantitates majorem eſſe quam major duarum me-
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diarum Geometricè continuè proportionalium inter eaſdem,
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& </
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<
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">igitur hujus propoſitionis approximationem præcedentis
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eſſe exactiorem, quod etſi fiat; </
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tem potius utimur.</
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A B # A
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C D # C
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E F # G
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K L # H
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Z # X
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A, B, nempè A extra hyperbolæ
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ſectorem, B intra. </
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ries convergens horum polygono-
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rum complicatorum ſecundum me-
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thodum noſtram ſubduplam de-
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ſcriptorum, ita ut polygona extra
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hyperbolam ſint A, C, E, K, &</
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D, F, L, &</
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perbolæ ſector Z. </
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ente exceſſus A ſupra C. </
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exceſſus A ſupra C, & </
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ceſſus C ſupra G, continueturque hæc ſeries in infinitum ut
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ejus terminatio ſit X. </
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plo exceſſus C ſupra E, & </
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eſt exceſſus C ſupra G, eſt ergo E major quam G. </
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exceſſus C ſupra E major eſt quadruplo exceſſus E ſupra K,
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& </
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">ideo exceſſus C ſupra G multò major eſt quadruplo ex-
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ceſſu E ſupra K, & </
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">igitur exceſſus G ſupra H major eſt
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exceſſu E ſupra K; </
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nifeſtum eſt K etiam majorem eſſe quam H: </
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ſus modo demonſtratur in omni ſerierum A, C, E, K; </
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C, G, H, continuatione, terminum quemcumque ſeriei A,
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C, E, majorem eſſe quam idem numero terminus ſeriei </
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