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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<
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A # B
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C # D
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E # F
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pe A intra circuli vel ellipſeos ſectorem & </
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B extra: </
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<
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">continuetur ſeries convergens horum
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polygonorum complicatorum ſecundum no-
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ſtram methodum ſubduplam deſcriptorum, ita
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ut polygona intra circulum ſint A, C, E, &</
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<
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<
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culum B, D, F, &</
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<
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</
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">ex prædictis manifeſtæ ſunt ſequentes analogiæ; </
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niam A, C, B, ſunt continue pro-
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C - A:B - C::A:C
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B - C:D - C::A + C:A
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portionales; </
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C, D, B, ſunt harmonice pro-
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portionales: </
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<
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<
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C ſupra A, hoc eſt C — A, eſt ad exceſſum D ſupra C ſeu
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D - C in ratione compoſita ex proportione A ad C & </
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proportione A + C ad A, hoc eſt in ratione A + C ad C;
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major quam exceſſus D ſupra C, eſt autem D major quam
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E, & </
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exceſſus E ſupra C; </
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quod demonſtrare oportuit.</
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druplo exceſſus E ſupra C. </
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ſequentes tres analogiæ, prima quoniam A, C, B, ſunt con-
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tinuè proportionales; </
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monicè proportionales; </
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<
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tinuè proportionales; </
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C - A:B - C::A:C
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B - C:D - C::A + C:A
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D - C:E - C::E + C:C
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exceſſus C ſupra A (hoc eſt)
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C - A eſt ad exceſſum E ſu-
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pra C ſeu E - C, ut A C + E C
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+ AE + CC ad CC; </
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