Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRI Æ
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<
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<
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<
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">habetur cylindricum in ea dem baſi, & </
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<
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">altitudine cum
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fruſto conici conſtitutum, ad idem, eſſe (ſumptis duabus homologis
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in oppoſitis fruſti conici baſibus) vt quadratum maioris dictarum homo-
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logarum ad rectangulum ſub dictis homologis vna cum, {1/3}, quadrati dif-
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ferentiæ earumdem homologarum. </
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<
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">Sit eylindricus, AC, in baſi figura
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quacumque plana, BC, in eadem autem baſi, & </
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<
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">altitudine ſit fruſtum
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conici, EBCI, ſic tamen ſe habens, vt ducto plano per latera cylindri-
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0206-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0206-01
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ci, AC, idemtranſeat per latera fruſti conici
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BEIC, ſit autem ductum tale planum, quod
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faciat in cylindrico, AC, parallelogram-
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mum, AC, & </
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<
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">in fruſto, BEIC, trapezium,
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BEIC, erunt igitur rectæ, BC, EI, lineæ
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oppoſitarum baſium fructi inter ſe bomologæ,
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_lib. 1._</
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& </
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">quia cylindricus, AC, eſt ſolidum ſimi-
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lare genitum ex, AC, iuxta regulam, BC,
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<
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">_Coroll. 3._
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_34. huius._
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_33. huius._
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_27. huius._</
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& </
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<
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">fruſtum, EBCI, eſt ſolidum prædicto ſimilare genitum ex trapezio,
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EBCI, ſunt autem h æc ſolida ſimilaria, vt omnia eorumdem quadrata,
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& </
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<
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">omnia quadrata, AC, regula, BC, ad omnia quadrata trapezij, E
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BCI, regula eadem ſunt, vt quadratum, BC, ad rectangulum ſub, BC,
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EI, vna cum, _{1/3},_ quadrati differentiæ earumdem, ergo cylindricus, A
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C, ad fruſtum conicum, EBCI, & </
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titudine cum hoc conſtitutum (quo niam exiſtet huic æquale) erit vt qua-
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_Coroll._
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_Gener._</
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dratum, BC, ad rectangulum ſub, BC, EI, vna cum, _{1/3}_, quadrati dif-
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ferentiæ earu mdem, BC, EI, quæ ſunt duarum oppoſitarum baſium, E
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I, BC, bomologæ vtcumque ſumptæ, nam planum eadem ſolida ſecans
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">_Corol. 21._
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_lib. I._</
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ductum eſt vtcumque, dummodo per eorumdem latera tranſeat.</
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">_H_Inc pátet ſi in eadem baſi, BC, figura, fuerit conicus, & </
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<
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altitudine cum fruſto, ideſt cum cylindrico, AC, qui ſit conicus,
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<
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_Corollar._
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_Gener._</
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BOC, quod hic erit, _{1/3}_, cylindrici, AC, & </
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<
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">ideò ad fruſtum, EBCI, erit
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vt, _{1/3}_, quadrati, BC, ad rect angulum ſub, BC, EI, vna cum, _{1/3}_, qua-
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drati differentiæ, BC, EI, ideſt vtt otum quadr atum, BC, ad rectangu-
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lum ſub, BC, & </
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<
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">tripla, EI, vna cumtoto quadrato differentiæ earum-
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dem, BC, EI. </
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<
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">Vide igitur quam ſit amplior hæc demonſtratio ea, qua
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alij oſtenderunt cylindrum eſſe triplum coni, & </
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<
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dem baſi, & </
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titudine cum ipſo conſtitute, nam ad tot varia ſolida </
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