Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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.</
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<
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<
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ſub, AB, & </
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<
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<
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xml:space
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<
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xml:space
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B, CD, cui ſi iunxeris parallelepipedum ſub, BC, & </
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<
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BD, DC, componeour parallelepipedum ſub, BC, & </
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<
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0214-01
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ADC, quod additum parallele-
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pipedo ſub, AB, & </
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<
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ctangulo, ADC, componet pa-
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">35. huius.</
note
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rallelepipedum ſub, AC, & </
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<
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ctangulo, ADC, quod quidem
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æquale erit alteri ſummæ prædi-
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ctæ, nempè parallelepipedo ſub,
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BC, & </
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<
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C, vna cum, {1/3}, cubi, BC, ergo & </
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<
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">eorum tripla æqualia erunt ſci-
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licet parallelepipedum ter ſub, AC, & </
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<
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">rectangulo, ADC, ſeu ter
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xlink:label
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">Schol. 35.
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huius.</
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ſub, AD, & </
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<
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">rectangulo, ACD, æquabitur parallelepipedo ter ſub,
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BC, & </
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<
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cum cubo, BC, additis verò communibus cubis, AC, CD, fiet pa-
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xlink:label
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">38. huius.</
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rallelepipedum ter ſub, AD, & </
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C, CD, ideſt totus cubus, AD, æqualis parallelepipedo ter ſub, B
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<
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xlink:label
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D, & </
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<
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">rectangulo, BCD, cum cubis, BC, CD, (quæ integrant
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cubum, BD,) & </
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<
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">cum cubo, AC, eſt igitur cubus, AD, æqualis
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duobus cubis, AC, BD. </
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<
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tum fuit.</
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tarecta linea, vt, AB, minor, AC, poſſibile eſſe inuenire duos
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eubos, vt, AD, DB, ita vt eorum differentia ſit æqualis cubo dato,
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AC, & </
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rentia ſit data, eſt. </
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<
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<
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">cubus, AC, æqualis dictæ cuborum, AD, DB,
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differentiæ, vt eſtenſum eſt. </
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<
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tripla ratione linearum, ſeu later um bomologorum eorumdem, ideò
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erunt, vt cubi ipſarum linearum, ſeu laterum bomologoroum, & </
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<
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eandem rationem, quam babet cubus, AD, ad cubum, DB, babebit
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ex. </
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latere, BD, prædicto bomologo, & </
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ita erit Icoſaedrum, AD, ad Icoſaedrum, AC, nec non colligendo, vt
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cubus, AD, ad cubos, AC, BD, ita erit Icoſaedrum, AD, ad Ico-
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ſaedra, AC, BD, ergo Icoſaedrum, AD, æquabitur Icoſaedris, AC,
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BD, & </
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<
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