Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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VERA CIRCULI
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metricum inter parallelogramma P D M L, F D M K, quod de-
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monſtrare oportuit.</
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fig. 4.</
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gentes in punctis F, L, ut compleatur trapezium A F E L,
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quod dico eſſe medium harmonicum inter parallelogramma
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P D M L, F D M K. </
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<
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xml:space
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& </
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<
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">medium harmonicum inter parallelogramma P D M L,
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F D M K, ſunt continuè proportionalia, quoniam triangu-
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lum A F L eſt medium arithmeticum & </
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<
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xml:space
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medium geometricum inter eadem parallelogramma, ut pa-
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tet ex hujus 13; </
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<
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xml:space
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">ſed triangulum A F L, trapezium A F G L,
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& </
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<
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">trapezium A F E L ſunt continuè proportionalia ex hujus
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1; </
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<
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inter parallelogramma P D M L, F D M K, quod demon-
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ftrare oportuit.</
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Dato circulo æquale invenire quadratum.</
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</
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<
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">erit ergo eidem inſcriptum 2000000000000000, inter quæ
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quadrata ſit medium geometricum 2828427124746190
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octagonum nempe intra circulum: </
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num intra circulum & </
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monicum, quod levi labore invenitur dividendoduplum
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quadrati octagoni intra circulum ſeu duplum rectanguli à
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quadratis intra & </
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octagoni intra; </
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gonum circumſcriptum, nempe 3313708498984760. </
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nuetur hæc ſeries convergens polygonorum complicatorum
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donec prima medietas notarum ſit eadem in utroque </
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