Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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">SI intra parallelogrammum, quod circulo, vel ellipſi ſit
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circumſcriptum, ducatur lateribus eiuſdem parallela
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quædam rectalinea, per circuli, vel ellipſis centrum non
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tranſiens, altero reliquorum laterum regula exiſtente. </
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nia quadrata parallelogrammi, quod maiori portioni circu-
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li, vel ellipſis iam dicti, remanent circumſcriptum, ad om-
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nia quadrata figuræ compoſitæ ex maiori portione, & </
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bus trilineis, quiad baſim eiuſdem hinc inde extra conſtitu-
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untur, demptis eorundem trilineorum omnibus quadratis,
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erunt in circulo, vt parallelepipedum ſub baſi parallelo-
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grammo dictæ portioni maiori circumſcripto, altitudine
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eiuſdem portionis diametro ad cylindricum ſub baſi eadem
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maiori portione, altitudine differentia diametrorum maio-
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ris, acminoris factarum portionum, vna cum ſexta parte cu-
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bi baſis eiuſdem portionis In ellipſi verò erunt, vt paralle-
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lepipedum ſub baſi parallelogrammo maiori portioni ſimili-
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ter circumſcripto, altitudine eiuſdem portionis diametro,
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ad cylindricum ſub baſi eadem maiori portione, altitudine
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differentia diametrorum maioris, ac minoris factarum por-
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tionum, vna cum ea porte cubi baſis eiuſdem portionis, ad
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quam ſexta pars eiuſdem cubi ſit, vt quadratum primæ dia-
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metriad quadratum ſecundæ, vel, ſi diametrinon ſint axes,
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vna cum ea parte parallelepipedi ſub altitudine baſi eiu-
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ſdem portionis, ac ſub baſi rhombo ab eadem deſcripto, ad
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quam eiuſdem parallelepipedi pars ſexta ſit, vt quadratum
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primę diametri ad quadratum ſecundæ.</
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<
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">Sit ergo circulus, vel ellipſis, CFEH, cui ſit circumſcriptum pa-
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rallelogrammum, AQ, & </
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">centrum ſit, N, diametriautem tranſeun-
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tesper puncta contactuum laterum circumſcripti parallelogrammi,
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& </
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<
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ſiſtens, & </
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<
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">lateribus, AP, DQ, parallela intra ipſum ducta ſit, LG.
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<
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">Dico ergo omnia quadrata parallelogrammi, AG, ad omnia qua-
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drata figuræ, LCFEG, demptis omnibus quadratis trilineorum,
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CLI, YGE, eſſe, in circulo, vt parallelepipedum ſub </
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