Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. ad rectangulum ſub, BM, & , MOA, quod verum eſſe oſtendetur,
vt in antecedente, etiam ſi parallelogrammum, DN, non ſit circa
axim, vel diametrum, BM, vnde patet, & c.

302.1.

0220-01
Exant.
5. Lib.2.
PerB.Co.
rollar.22.
lib.2.
Ex 40. l.1.
& eiuſdẽ
Scholio.
24. Lib. 2.
8. Lib.2.

303. THEOREMA III. PROPOS. III.

SI intra circulum, velellipſim, duæ ad axim, vel diame-
trum ordinatim applicentur rectæ lineę, ſit autem paral-
lelogrammum, & triangulum in eadem altitudine cum por-
tione inter applicatas concluſa, ſed in baſi altera applicata-
rum: Omnia quadrata dicti parallelogrammia ad omnia qua-
drata concluſę portionis (regula baſi) erunt, vt rectangulum
ſub partibus axis, vel diametri per baſim conſtitutis ad re-
ctangulum ſub abſciſſa per baſim ab extremitate axis, vel
diametri, & ſub compoſita ex medietate portionis axis, vel
diametri eiſdem applicatis intermedię, & abſciſſa per aliam
applicatam ab eiuſdem extremitate, vna cum rectangulo ſub
eadem intermedia, & ſub compoſita ex, @, eiuſdem, & , {1/2}, ab-
ſciſſæ per eandem applicatam ab eiuſdem extremitate: Om-
nia verò quadrata incluſę portionis ad omnia quadrata dicti
trianguli erunt, vt rectangulum ſub compoſita ex abſciſſis ab
axi, vel diametro per ordinatim applicatas verſus terminum,
cui baſis propinquior eſt, & ſub ſexquialtera abſciſſæ ab alio
extremo per applicatam, quę non eſt baſis, vna cum rectan-
gulo ſub huius reliqua, & ſub dupla abſciſſę per baſim ab ex-
tremo, cui ipſa baſis propinquior eſt, ad rectangulum ſub
partibus axis, vel diametri per baſim conſtitutis.

Sit ergo circulus, velellipſis, ACDF,
centrum, O, axis, vel diameter, AD, duæ
ad ipſam ordinatim applicatæ ſint, IS, C
F, intercipientes portionem, ICFS, ſit
autem parallelogrammum, BF, in baſi
vtrauis applicatarum, vt in, CF, & eadem
altitudine cum fruſto, CISF, ſit etiam
nunc circa axim, vel diametrum, MR, re-
gula verò, CF; Dico ergo omnia quadra-
ta parallelogrammi, BF, ad omnia qua-
drata portionis, ICFS, eſſe vt rectangulum, DRA, ad rectangu-

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