Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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majorem rationem quam quadratum A B ad quadratum
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C D, nempe eam quam quadratum A B ad quadratum C
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G, ſumta C G minore quam C D, & </
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<
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pars D H, minor quam D G exceſſus C D ſupra C G,
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atque ita ut reliqua H C commenſurabilis ſit ipſi A B;
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</
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<
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<
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C G. </
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<
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">Atqui ut quadratum temporis A B ad quadratum tem-
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poris C H, ita ſpatium E, quod tempore A B peractum
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eſt, ad ſpatium peractum tempore C H, per ſuperiùs oſten-
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ſa. </
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<
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curritur, nempe ſpatium F. </
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nor eſt ratio quam quadrati A B ad quadratum C H. </
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<
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autem ſpatium E ad F, ita ponebatur eſſe quadratum A B
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ad quadratum C G; </
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<
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xml:space
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">ergo minor quoque erit ratio quadrati
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A B ad quadratum C G, quam quadrati A B ad quadra-
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tum C H, ac proinde quadratum C G majus quadrato C
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H; </
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<
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">quod eſt abſurdum, quum C H major dicta ſit quam
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C G. </
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<
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quam quadratum A B ad quadratum C D.</
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<
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">ſitque ratio ſpatii E ad
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F eadem quæ quadrati A B ad quadratum C L, ſumptâ C L
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majore quam C D, & </
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<
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">à C L auferatur L K minor ex-
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ceſſu L D, quo C D ſuperatur à C L, atque ita
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ut reliqua K C ſit commenſurabilis A B. </
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<
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">Quia ergo ut qua-
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dratum temporis A B ad quadratum temporis C K, ita eſt
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ſpatium E, peractum tempore A B, ad ſpatium peractum
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tempore C K. </
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<
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tempore C D, nempe ſpatium F. </
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<
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F major ratio quam quadrati A B ad quadratum C K. </
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<
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ut autem ſpatium E ad F, ita ponebatur eſſe quadratum
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A B ad quadratum C L. </
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<
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">Ergo major erit ratio quadrati A B
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ad quadratum C L quam ejuſdem quadrati A B ad quadra-
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tum C K, ideoque quadratum C L minus erit quam qu. </
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<
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Ergo neque minorem rationem habet ſpatium E ad F </
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