Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
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">IN eadem figura, ducta per, I, IL, æquidiſtante ipſi, A
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Q, adhuc oſtendemus omnia quadrata trilinei, DGP,
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ad omnia quadrata trilinei, DTI, habere rationem compo-
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ſitam ex ea, quam habet rectangulum, ZPG, cum. </
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<
s
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xml:space
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drati, PG, ad rectangulum, STI, cum quadrati, TI, & </
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<
s
xml:id
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xml:space
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">ex ea,
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quam habet quadratum, PG, ad quadratum TI.</
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<
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xml:space
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<
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<
s
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xml:space
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">Nam omnia quadrata, DGP, ad omnia quadrata, DIT, ha-
<
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bent rationem compoſitam ex ea, quam habent omnia quadrata,
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DGP, ad omnia quadrata, DG, .</
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<
s
xml:id
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xml:space
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">i. </
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<
s
xml:id
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xml:space
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">ex ea, quam habet {1/3}. </
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<
s
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xml:space
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{1/6}. </
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<
s
xml:id
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<
s
xml:id
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xml:space
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">i. </
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>
<
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">ſumpta, PG, communi altitudine, ex ea, quam
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habet rectangulum ſub {1/3}. </
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<
s
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xml:space
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">ZP, & </
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>
<
s
xml:id
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xml:space
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">{1/6}. </
s
>
<
s
xml:id
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xml:space
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">PG, & </
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>
<
s
xml:id
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xml:space
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">ſub, PG, ad rectangu-
<
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/>
lum, ZPG, item ex ratione omnium quadratorum, DG, ad om-
<
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nia quadrata, DI, ſcilicet compoſita ex ea, quam habet, PD, ad, D
<
lb
/>
T, & </
s
>
<
s
xml:id
="
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xml:space
="
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">quadratum, PG, ad quadratum, TI, eſt autem, vt, PD, ad,
<
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DT, ita rectangulum, ZPG, ad rectangulum, STI; </
s
>
<
s
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xml:space
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">Tandem
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verò componitur ex ea, quam habent omnia quadrata, DI,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0364-01
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ad omnia quadrata, DIT,
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ideſt ex ratione, ST, ad {1/3}.
<
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</
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<
s
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<
s
xml:id
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xml:space
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">TI, ideſt ſum-
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pta, TI, communi altitudi-
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ne, ex ea, quam habet rectan-
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gulum, STI, ad rectangulum
<
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fub, TI, & </
s
>
<
s
xml:id
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xml:space
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">compoſita ex {1/3}. </
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>
<
s
xml:id
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T, & </
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<
s
xml:id
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xml:space
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">{1/6}. </
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<
s
xml:id
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xml:space
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">TI, iſtæ autem ratio-
<
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<
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xlink:label
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xml:space
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nes .</
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<
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xml:id
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">ſ. </
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<
s
xml:id
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xml:space
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">quam habet rectangu-
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lum ſub {1/3}. </
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<
s
xml:id
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xml:space
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<
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xml:space
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">{1/6}, PG, & </
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<
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<
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ſub, PG, ad rectangulum, ZPG, & </
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<
s
xml:id
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xml:space
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">huius ad rectangulum, STI,
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& </
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<
s
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xml:space
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">taudem rectanguli, STI, ad rectangulum ſub, TI, & </
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<
s
xml:id
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xml:space
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">{1/3}. </
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>
<
s
xml:id
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xml:space
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">ST,
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cum {1/6}. </
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<
s
xml:id
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xml:space
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">TI, componunt rationem rectanguli fub {1/3}. </
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<
s
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<
s
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<
s
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xml:space
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">PG,
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& </
s
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<
s
xml:id
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xml:space
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">ſub, PG, ad rectangulum ſub {1/3}. </
s
>
<
s
xml:id
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">ST, & </
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>
<
s
xml:id
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">{1/6}. </
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<
s
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">TI, & </
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<
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.</
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<
s
xml:id
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">i, tri-
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plicatis terminis, componunt rationem rectanguli ſub, ZP, PG,
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cum rectangulo, ſub {3/6}. </
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<
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xml:id
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<
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<
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<
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xml:id
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">cum {1/2}. </
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<
s
xml:id
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">quadrati, PG,
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ad rectangulum ſub, ST, TI, cum rectanguio ſub {3/6}. </
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<
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<
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I, .</
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<
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<
s
xml:id
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<
s
xml:id
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xml:space
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">quadrati, TI, & </
s
>
<
s
xml:id
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">remanſit ſola ratio quadrati, PG, ad
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quadratum, TI, ergo omnia quadrata trilinei, DGP, ad om-
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nia quadrata trilinei, DIT, habebunt rationem compoſitam </
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