Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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&</
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<
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xml:space
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">, ZX, ad portionem, ACXN, eſſe, vt omnia quádratà, ℟ X, ad
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omnia quadrata quadrilinei, NOEX, &</
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<
s
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xml:space
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">, AN, CX, ordinatim ad ba-
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ſim, FG, applicatæ ſumptæ ſunt vtcunq; </
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<
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xml:space
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">vnde patet.</
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</
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<
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xml:space
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">THEOREMA V. PROPOS. V.</
head
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<
s
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xml:space
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">DVctis vtcunque ad baſim parabolæ ordinatim applica-
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tis, parallelogramma ſub ipſis, & </
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<
s
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xml:space
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">portionibus baſis ab
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ijſdem abſciſſis ad ſibi inſcriptas portiones parabolæ infra-
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ſcriptam rationem habebunt.</
s
>
<
s
xml:id
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xml:space
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</
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<
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<
s
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xml:space
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">Sit ergo parabola, HGA, in baſi, HA, circa axim, vel diame-
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trum, GO, & </
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<
s
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xml:space
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">ſint ductæ ipſi, GO, parallelæ vtcunque, ST, EC,
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compleantur autem parallelogramma, LT, BO, DC, deinde pro-
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ducatur, GO, vtcunque in, M, & </
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<
s
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xml:space
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">circa ſemiaxes, vel ſemidiame-
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tros, HO, OM, intelligatur, HMA, ſemicirculus, vel ſemiellipſis,
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fig-0311-01
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number
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<
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0311-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0311-01
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cuius curuam, ST,
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EC, productæ ſe-
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cent in, VN, com-
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pleàtur pariter pa-
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rallelogramma, H
<
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V, HM, HN, pro-
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ducantur inſuper, Y
<
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M, BG, vſque in,
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& </
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<
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<
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">, SV, EN,
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vſq; </
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<
s
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xml:space
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">ad puncta, P,
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Z, Q, I, quæ ſunt
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in lateribus, B ℟, Y
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&</
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<
s
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xml:space
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">. Igitur paralle-
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logrammum, LT,
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ad portionem, HS
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T, erit vt omnia
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quadrata, HV, ad
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omnia quadrata ſe-
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miportionis, HT
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V, (regula, GM, pro hac Propoſ. </
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<
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">ſumpta). </
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xml:space
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">i. </
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ſitam ex {1/2}, TA, &</
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<
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xml:space
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">, {1/6}, HT, vt patet in Libro de Circulo, & </
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<
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">Ellipſi
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Propoſitione I.</
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<
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<
s
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xml:space
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">Similiter oſtendemus, BO, ſemiparabolæ, HGO, eſſe ſexqui-
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alterum, eſt enim vt omnia quadrata, HM, ad omnia quadrata, H
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VMO, ideſt in ratione ſexquialtera, vt patet in eadem Propoſit. </
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<
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xml:space
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">I.</
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<
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<
s
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xml:space
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">Pariter demonſtrabimus, DC, ad portionem, HGEC, eſſe vt,
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AC, ad compoſitam ex, {1/2}, AC, &</
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<
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xml:space
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">, {1/6}, CH, ſicenim ſunt </
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