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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quadruplo exceſſus C ſupra E. </
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<
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">ex prædictis manifeſtæ
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ſunt ſequentes tres analogiæ; </
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<
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continuè proportionales; </
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<
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">ſecunda, quoniam C, D, B, ſunt
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harmonicè proportionales; </
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<
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<
s
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xml:space
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">tertia, quoniam C, E, D, ſunt
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continuè proportionales; </
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<
s
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">ideo exceſſus A ſupra C, hoc eſt
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A - C, eſt ad exceſſum C ſupra E, hoc eſt C - E in ratio-
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ne compoſita ex proportionibus
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A - C:C: - B::A:C
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C - B:C - D::A + :CA
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C - D:C - E::E + C:C
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A ad C, A + C ad A & </
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<
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ut A C + E C + A E + CC ad
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CC; </
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<
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">at B minor eſt quam E,
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& </
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<
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">igitur AE +
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CC major eſt quam 2 CC. </
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<
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A + E ad 2 C; </
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A C + E C major eſt quam 2 CC; </
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+ C C major eſt quam 4 CC; </
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<
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">igitur A - C major eſt qua-
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druplo ipſius C - E, quod demonſtrare oportuit.</
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<
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# E
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A # C # B
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# D
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minor, B major, C media geome-
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trica, D media arithmetica. </
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majorem eſſe quam C, quoniam B, C,
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A, ſunt continuè proportionales; </
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dendo, permutando, & </
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ad exceſſum C ſupra A, ita A + C ad A, atque A + C major eſt
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duplo ipſius A; </
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exceſſus C ſupra; </
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D ſupra A, & </
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