Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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non ſunt regula, eſſe vt parallelogrammum, HF, ad circulum, vel
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ellipſim, MBEG. </
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<
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xml:space
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">quadrata parallelogrammi, HF, ſunt
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huit S.</
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ſexquialtera omnium quadratorum circuli, vel ellipſis, MBEG, & </
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ideò ſunt ad illa, vt parallelogrammum, HF, ad ſui ipſius duas ter-
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tias, quod ſerua.</
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<
s
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xml:space
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gula ſub eodem, & </
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26.l.2.</
note
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mum, AF, ad ſemiportionem, AEG, eadem verò ad omnia qua-
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drata ſemiportionis, AEG, ſunt ſexquialtera .</
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<
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<
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grammum, AF, ad ſui ipſius, {2/3}, igitur eadem ad reliqua. </
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<
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gula ſub ſemiportione, AEG, & </
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">trilineo, GEF, erunt vt parallelo-
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grammum, AF, ad exceſium, quo ſemiportio, AEG, excedit, {2/3}, pa-
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rallelogrammi, AF, omnia autem quadrata, BF, ſunt quadrupla om-
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nium quadratorum, AF, ergo omnia quadrata, BF, ad rectangula
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note
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ſub ſemiportione, AEG, & </
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<
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lelogra nmum, AF, ad dictum exceſſum.</
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<
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0243-01
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F, ad dictum exceſſum, & </
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quadruplicatis, omnia quadrata paralle
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logrammi, BF, adrectangula quater ſub
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ſemiportione, AEG, & </
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<
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<
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</
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<
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<
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trilineo, GEF, erunt vt, HF, ad dictum ex
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ceſſum quater ſumptum, quia enim, AE,
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eſt diameter bifariam diuidit in portione,
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BEG, omnes ipſi, DF, æquidiſtantes, & </
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ideò rectangula quater ſub ſemiportione,
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AEG, & </
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<
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bis ſub portione, BEG, & </
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<
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lelogrammi, BF, ad rectangula bis ſub portione, BEG, & </
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<
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xml:space
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EF, vel eorum dupla. </
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<
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<
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note
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ctangula bis ſub circulo, vel ellipſi, MBEG, & </
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F, erunt vt parallelogrammum, HF, ad quatuor exceſſus ſemiportio-
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nis, AEG, ſuper duas tertias parallelogrammi, AF, .</
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<
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culi, vel ellipſis, MBEG, ſuper, {2/3}, parallelogrammi, HF, erant autem
<
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omnia quadrata parallelogrammi, HF, ad omnia quadrata circuli,
<
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vel ellipſis, MBEG, vtidem parallelogrammum, HF, ad, {2/3}, ſui ipſius,
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ergo omnia quadrata parallelogrammi, HF, ad omnia quadrata cir-
<
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culi, vel ellipſis, MBEG, ſimul cum rectangulis bis ſub eodem circulo,
<
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vel ellipſi, MBEG, & </
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<
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grammum, HF, ad ſui ipſius, {2/3}, vna cum exceſſu circuli, vel ellipſis, M
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BEG, ſuper eaſdem duas tertias .</
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<
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F, ad circulum, vel ellipſim, MBEG, quod erat oſtendendum.</
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