Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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ad radium, ita ſint {2/3} C B ad B E. </
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trum gravitatis ſemicirculi baſeos, ideoque in A E centra
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gravitatis omnium ſegmentorum ſemiconi A B D, baſi pa-
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rallelorum.</
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<
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<
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<
s
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xml:space
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">Et figura quidem porro proportionalis à latere ponenda,
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O V V, eadem eſt quæ in cono toto ſupra deſcripta fuit:
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</
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<
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xml:space
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">per quam nempe invenietur ſumma quadratorum, à diſtan-
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tiis particularum ſemiconi à plano horizontali N D, per
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centrum gravitatis ducto. </
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<
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">Verum quadrata diſtantiarum, à
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plano verticali M D O, ut colligantur, altera quoque figu-
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ra proportionalis S Y Z, ſicut ſupra prop. </
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<
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eſt, cujus nempe ſectiones verticales, exhibeant lineas pro-
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portionales ſectionibus ſibi reſpondentibus in ſemicono A B C. </
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& </
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<
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">hujus figuræ cognoſcenda eſt diſtantia centri gr. </
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<
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">F ab S Y,
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quam æqualem eſſe conſtat diſtantiæ D N, centri gr. </
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<
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à plano trianguli A B. </
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<
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">poſitâque H G ſubcentricâ cunei ab-
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ſciſſi ſuper figura S Z Y, ducto plano per S Y, noſcendum
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eſt rectangulum G F H, cujus nempe multiplex, ſecundum
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numerum particularum ſemiconi A B C, æquabitur quadra-
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tis diſtantiarum ſemiconi in planum M D O. </
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<
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">Licebit vero
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cognoſcere rectangulum illud G F H, etiamſi ſubcentricæ
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H G longitudo ignoretur, hoc modo.</
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<
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">Diximus ſupra, cum de cono ageremus, quadrata diſtan-
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tiarum à plano per axem ejus, æquari {3/80} quadrati à diametro
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baſis, ſive {3/20} quadrati à ſemidiametro, multiplicis per nu-
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merum particularum coni totius. </
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<
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<
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">hic, in ſemicono
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A B C, quadrata diſtantiarum à plano A B æqualia erunt
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{3/20} quadrati B C, multiplicis per numerum particularum i-
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pſius ſemiconi. </
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<
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<
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">rectangulum H G F, multiplex per nu-
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merum particularum ſemiconi A B C, æquatur quadratis
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diſtantiarum à plano A B, ut patet ex propoſitione 9. </
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<
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rectangulum H G F æquale {3/20} quadrati B C. </
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<
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A B = a; </
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<
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">& </
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<
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xml:space
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">quadrantem circumferentiæ, radio
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B C deſcriptæ, = q; </
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<
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<
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">Cujus cum N D
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tribus quartis æquetur, fiet proinde N D, ſive G F = {1 b b/2 q @}.</
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