Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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jor eſt quam E, & </
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& </
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">igitur AE + CC minor eſt quam 2 CC: </
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eſt ad 2 CC ut A + E ad 2 C, ſed A + E minor eſt quam
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2 C; </
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<
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A C + E C + A E + CC minor eſt quam 4 CC; </
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">igitur
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C - A minor eſt quadruplo ipſius E - C, quod demon-
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ſtrare oportuit.</
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">PROP. XVI. THEOREMA.</
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A # B
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C # D
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E # F
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nempe A extra hyperbolæ ſecto-
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rem & </
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vergens horum polygonorum complica-
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torum ſecundum noſtram methodum
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ſubduplam deſcriptorum, ita ut polygona extra hyperbolem
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ſint A, C, E, &</
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+ E majorem eſſe quam 2 C. </
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">ex prædictis manifeſtæ ſunt ſe-
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quentes duæ Analogiæ, prima quoniam A, C, B, ſunt con-
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tinue proportionales; </
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harmonicè proportionales; </
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A - C:C - B::A:C
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C - B:C - D::A + C:A
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proinde exceſſus A ſupra C,
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hoc eſt A - C, eſt ad ex ceſſum
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C ſupra D ſeu C - D; </
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compoſita ex proportione A ad C & </
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ad A hoc eſt in ratione A + C ad C, at A + C eſt ma-
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jor quam C & </
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<
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ſupra D, eſt autem E major quam D; </
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<
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ſupra C multo major eſt exceſſu C ſupra E; </
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igitur A + E majorem eſſe quam 2 C, quod demonſtrare
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oportuit.</
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