Clavius, Christoph
,
Geometria practica
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LIBER SEXTVS.
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<
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vtrumque hunc modum hac ratione. </
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xml:space
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">Quando numerator
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in quadratum denominatoris ducitur, erit producti numeriradix cubica vnus
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duorum mediorum proportionalium inter numeratorem ac denominatorem
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collo candus iuxta denominatorem, vt conſtat ex iis, quæ propoſ. </
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<
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</
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<
s
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<
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"> Erit igitur proportio numeratoris ad denominatorem
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">10. defiu.
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quinti.</
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plicata proportionis radicis cubicæ inuentæ ad denominatorem: </
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<
s
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"> Eſt autem eadem proportio numeratoris ad denominatorem, tanquam cubi ad cubum,
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triplicata quoque proportionis radicis cubicæ numeratoris ad radicem cubi-
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cam denominatoris. </
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">Igitur erit radix cubica inuenta ad denominatorem, vt
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radix cubica numeratoris ad radicem cubicam denominatoris: </
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<
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xml:space
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rum ad finem
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lib. 9.</
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minutia, cuius numerator radix cubica inuenta, ac denominator ipſe denomi-
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nator, æqualis erit minutiæ, cuius numerator radix cubica numeratoris, ac
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denominator radix cubica denominatoris. </
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<
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">Quam ob rem ſicut hæc minu-
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tia eſt radix cubica fractionis propoſitæ, ita quoque illa eritradix cubica eiuſ-
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dem fractionis. </
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<
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">Diuiſa ergo radice illa cubica inuenta per denominatorem
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fractionis propoſitæ (quæ diuiſio fit, quia illa radix cubica inuenta eſt fractio,
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ac proinde, vt cognoſcatur val or minutiæ, cuius numerator radix illa inuen-
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ta, ac denominator ipſemet denominator fractionis propoſitæ, diuidendus eſt
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numerator huius minutiæ per eius denominatorem: </
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<
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">alio quin ſi illa radix cu-
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bica inuenta foret numerus integer, diuiſio facienda non eſſet) producetur ra-
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dix cubica fractionis propoſitæ: </
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<
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">quemadmodum ex diuiſione radicis cubicæ
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numeratoris per radicem cubicam denominatoris procreatur radix cubica fra-
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ctionis propoſitæ: </
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">quippe cum minutia nil aliud ſit, niſi numerator per deno-
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minatorem diuiſus.</
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verò denominator in quadratum numeratoris ducitur, erit
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numeri producti radix cubica vnus duorum mediorum proportionalium in-
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ter numeratorem, ac denominatorem, collocandus iuxta numeratorem, vt
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ex demonſtratis propoſ. </
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<
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<
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">manifeſtum eſt. </
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<
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">Ergo rurſus erit propor-
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tio numeratoris ad denominatorem triplicata proportionis numeratoris ad il-
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lam radicem cubicam inuentam, quemadmodum & </
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<
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">proportionis radicis cu-
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bicæ numeratoris ad radicem cubicam denominatoris, eadem illa proportio
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numeratoris ad denominatorem, tanquam cubi ad cubum, triplicata eſt: </
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<
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propterea, vt ſupra, minutia, cuius numerator ipſemet numerator fractio-
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nis propoſitæ, denominator verò radix illa cubica inuenta, æqualis erit mi-
<
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nutiæ, cuius numerator, radix cubica numeratoris fractionis propoſitæ, & </
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<
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nominator radix cubica denominatoris eiuſdem fractionis. </
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<
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numeratore per illam inuentam radicem cubicam, prodibit radix cubica fra-
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ctionis propoſitæ.</
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non cubicis per lineas Geometrice inuenire.</
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datus numerus 10. </
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