Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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pro axiſumptum eſt) & </
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tur, erunt proximè, vt baſis eiuſdem parallelogrammi ad ſui
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reliquum, demptis ab ea, {11/14}, rectæ lineæ, quæ ſit æqualis
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dimidiæ ſecundæ diametri Prædicti circuli, vel ellipſis, ſi-
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mul cum exceſſu, quo dicti, {11/14}, excedunt, {2/3}, tertiæ propor-
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tionalis duarum, quarum prima eſt dicta baſis, ſecunda au-
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tem dicta ſecundæ diametri dimidia.</
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quam circa diametrum (intellige autem ſemper diametrum hic, & </
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in ſequentibus, vt eſt nomen commune diametro, & </
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<
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">axi) integri ſic
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deſcriptus ſemicirculus, vel ſemiellipſis, FQB, cuius curua, FQB,
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neque tangat, neque ſecet latus, ZD, oppoſitum lateri, FB, bifa-
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riam autem diuiſa, FB, in, A, & </
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<
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">per, A, ipſi, BD, baſi ducta pa-
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rallela, AP, ſeceturà curua, FQB, vtcunq; </
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<
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<
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Q, dimidia ſecundæ axis circuli, vel ellipſis, cuius centrum, A; </
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<
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catur inſuperper, Q, ipſi, FB, parallela, HC, quæ tanget circu-
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lum dictum, vel ellipſim, & </
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de, vt, DB, ad, BC, ita, BC, ad, BI, & </
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{2/3}, BI, &</
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<
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">, BE, quæ fit, {11/14}, ipſius, CB, &</
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0240-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0240-01
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ipſi, ER, regula verò ſit, BD. </
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<
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go omnia quadrata parallelogrammi, FD,
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ad omnia quadrata figuræ, quæ compre-
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henditur tribus lateribus, FZ, ZD, DB,
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& </
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<
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proximè. </
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grammi, FD, ad rectangula ſub paralle-
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logrammo, FD, & </
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26.lib.2.</
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ellipſis, FQB, ſunt vt parallelogram-
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mum, FD, ad eundem ſemicirculum, vel
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ſemiellipſim, FQB; </
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<
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grammum, FD, ad parallelogrammum, FC, eſt vt, DB, ad, BC,
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& </
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<
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">item parallelogrammum, FC, ad ſemicirculum, vel ſemiellipſim,
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Arch. de
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Dim.Cir.</
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FQB, eſt proximè vt 14. </
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æquali parallelogrammum, FD, ad ſemicirculum, vel ſemiellipſim,
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FQB, erit vt, DB, ad, BE, & </
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mi, FD, ad rectangula ſub parallelogrammo, FD, & </
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vel ſemiellipſi, FQB, erunt vt, DB, ad, BE,.</
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muni altitudine erunt, vt quadratum, DB, ad rectangulum ſub, D
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B, BE, quodſerua.</
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<
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