Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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">SI circulum, vel ellipſim duæ rectæ lineæ in terminis
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coniugatarum diametrorum tetigetint inter ſe conue-
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nientes, eiſdem diametris ductis. </
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">Omnia quadrata conſti-
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tuti parallelogrammiad omnia quadrata trilinei à dictis tan-
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gentibus, & </
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">ab incluſa curua comprehenſi, regula altera
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diametrorum, erunt vt dictum parallelogrammum ad ſui
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reliquum, dempto quadrante circuli, vel ellipſis iam dictæ,
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quod inſcribitur prædicto parallelogrammo, ſimul cum ex-
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ceſſu dicti quadrantis ſuper duas tertias iam dicti parallelo-
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grammi, quæ ratio erit proximè, vt 21. </
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">ad 2.</
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<
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">Sit circulus, vel ellipſis, ABCD, cuius diametri coniugatæ, A
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C, BD, in quorum terminis, C, D, duæ rectæ lineę ipſum tangen-
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tesinter ſe conueniant in, V. </
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diametrorum, vt, BD,) quod omnia quadrata parallelogrammi, O
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V, ad omnia quadrata trilinei, DCV, duabus tangentibus, DV,
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VC, & </
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<
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">ab ijs incluſa curua, DC, comprehenſi ſunt, vt idem paral-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0237-01
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lelogrammum, OV, ad ſui reliquum
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dempto quadrante, OCD, circuli,
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vel ellipſis, ABCD, ſimul cum eo
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ſpatio, quo idem quadrans excedit
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duas tertias parallelogrammi, OV.
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ctum, E, & </
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<
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D, parallela, EF, ſecans curuam, D
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C, in, I. </
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<
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rallelogrammi, OV, ad rectangula
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ſub parallelogrammo, OV, & </
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portione, OCD, ſunt vt parallelo
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26.lib.2.</
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grammum, OV, ad eandem ſemiportionem, OCD; </
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huius.</
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omnia quadrata ſemiportionis, OCD, ſunt ſexquialtera, ergo ad
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reſiduum erunt vt parallelogrammum, OV, ad reſiduum ſemipor-
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tionis, OCD, demptis ab ea, {2/3}, parallelogrammi, OV, quarum
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idem parallelogrammum, OV, eſt ſexquialterum; </
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<
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rectangulorum ſub parallelogrammo, OV, & </
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D, demptis omnibus quadratis ſemiportionis, OCD, ſunt rectan-
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dicta.</
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gula ſub ſemiportione, OCD, & </
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