Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ad rectangulum ſub, BM, &</
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">, MOA, quod verum eſſe oſtendetur,
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vt in antecedente, etiam ſi parallelogrammum, DN, non ſit circa
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axim, vel diametrum, BM, vnde patet, &</
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">SI intra circulum, velellipſim, duæ ad axim, vel diame-
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trum ordinatim applicentur rectæ lineę, ſit autem paral-
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lelogrammum, & </
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<
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">triangulum in eadem altitudine cum por-
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tione inter applicatas concluſa, ſed in baſi altera applicata-
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rum: </
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<
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">Omnia quadrata dicti parallelogrammia ad omnia qua-
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drata concluſę portionis (regula baſi) erunt, vt rectangulum
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ſub partibus axis, vel diametri per baſim conſtitutis ad re-
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ctangulum ſub abſciſſa per baſim ab extremitate axis, vel
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diametri, & </
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<
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xml:space
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">ſub compoſita ex medietate portionis axis, vel
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diametri eiſdem applicatis intermedię, & </
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<
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">abſciſſa per aliam
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applicatam ab eiuſdem extremitate, vna cum rectangulo ſub
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eadem intermedia, & </
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<
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<
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">, {1/2}, ab-
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ſciſſæ per eandem applicatam ab eiuſdem extremitate: </
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nia verò quadrata incluſę portionis ad omnia quadrata dicti
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trianguli erunt, vt rectangulum ſub compoſita ex abſciſſis ab
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axi, vel diametro per ordinatim applicatas verſus terminum,
<
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cui baſis propinquior eſt, & </
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<
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xml:space
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">ſub ſexquialtera abſciſſæ ab alio
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extremo per applicatam, quę non eſt baſis, vna cum rectan-
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gulo ſub huius reliqua, & </
s
>
<
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xml:space
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">ſub dupla abſciſſę per baſim ab ex-
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tremo, cui ipſa baſis propinquior eſt, ad rectangulum ſub
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partibus axis, vel diametri per baſim conſtitutis.</
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">Sit ergo circulus, velellipſis, ACDF,
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0221-01
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centrum, O, axis, vel diameter, AD, duæ
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ad ipſam ordinatim applicatæ ſint, IS, C
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F, intercipientes portionem, ICFS, ſit
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autem parallelogrammum, BF, in baſi
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vtrauis applicatarum, vt in, CF, & </
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<
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">eadem
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altitudine cum fruſto, CISF, ſit etiam
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nunc circa axim, vel diametrum, MR, re-
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gula verò, CF; </
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<
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xml:space
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">Dico ergo omnia quadra-
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ta parallelogrammi, BF, ad omnia qua-
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drata portionis, ICFS, eſſe vt rectangulum, DRA, ad </
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