Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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hoc eſt, ſicut quadratum B D ad quadratum N N. </
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rectangulum B C K, multiplex per numerum particularum
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ſectionis B D, ad rectangulum N X F, multiplex per nu-
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merum particularum ſectionis N N, duplicatam habebit ra-
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tionem quadrati B D ad quadratum N N; </
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<
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xml:space
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">hoc eſt, eam
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quam quadratum V V ad quadratum R R, in figura pro-
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portionali. </
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<
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">Erit igitur & </
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">dicta prior ſumma quadratorum, à
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diſtantiis particularum ſegmenti B N N D à plano E C, ad
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ſummam alteram quadratorum, à diſtantiis particularum ſe-
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gmenti N M M N, ut qu. </
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<
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<
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">Eademque
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ratione oſtendetur, ſummas quadratorum à diſtantiis parti-
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larum in reliquis ſegmentis ſolidi A B C D, eſſe inter ſe in
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ratione quadratorum quæ fiunt à rectis in figura O V V,
<
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quæ baſi cujusque ſegmenti reſpondent. </
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<
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echoid-s3321
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xml:space
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">Quare ſumma qua-
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dratorum, à diſtantiis particularum omnium ſegmentorum
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ſolidi A B C D à plano E C, erit ad ſummam quadrato-
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rum, à diſtantiis particularum ſegmentorum totidem, maxi-
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mo ſegmento æqualium, hoc eſt, cylindri vel prismatis
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B D S S, eandem cum ſolido A B C D baſin altitudinem-
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que habentis, ſicut quadrata omnia rectarum V V, R R, Q Q,
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&</
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<
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<
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xml:space
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">ad quadrata totidem maximo V V æqualia, hoc eſt,
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ſicut ſolidum rotundum O V V circa axem O P, ad cylin-
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drum V V Ω Ω, qui baſin & </
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<
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">altitudinem habeat eandem.
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</
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<
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">Hanc vero rationem ſolidi O V V ad cylindrum V V Ω Ω,
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componi conſtat ex ratione planorum quorum converſione
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generantur, hoc eſt, ex ratione plani O P V, ad rectangu-
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lum P Ω, & </
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<
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">ex ratione diſtantiarum quibus horum plano-
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rum centra gravitatis abſunt ab axe O P; </
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<
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">hoc eſt, & </
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<
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xml:space
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">ex ra-
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tione P Φ ad P Δ. </
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<
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xml:space
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">Et prior quidem harum rationum, nem-
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pe plani O P V ad rectangulum P Ω, eadem eſt quæ ſolidi
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A B C D ad cylindrum vel prisma B D S S, hoc eſt, ea-
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dem quæ numeri particularum ſolidi A B C D, ad nume-
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rum particularum cylindri vel prismatis B D S S. </
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<
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">Altera
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vero ratio, nempe P Φ ad P Δ, eſt eadem, ex conſtru-
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ctione, quæ ſpatii Z ad rectangulum B C K. </
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<
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que dicta ſumma quadratorum, à diſtantiis omnium </
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