Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ quadrata, HN, ad omnia quadrata ſemiportionis, HMNC, vt
patet in eiuſdem Lib. Propoſ. I.

Quod ſi velimus comparare parallelogramma, quæ ſunt in baſi-
bus æqualibus axi, vel diametro, inueniemus infraſcriptas rationes
ſcilicet parallelogrammum, BT, ad portionem, HST, eſſe vt re-
ctangulum ſub, HO, & tripla, OA, ad rectangulum ſub, HT, & ſub compoſita ex, TA, & , AO, ſicuti ſunt omnia quadrata, HZ,
ad omnia quadrata ſemiportionis, HTV. Eadem ratione, BC, ad
portionem, HGE
C, erit vt rectangu-
lum ſub, HO, & tripla, OA, ad re-
ctangulum ſub, H
C, & ſub compoſi-
ta ex, CA, & , AO,
ſic enim ſunt om-
nia quadrata, HI,
ad omnia quadrata
ſemiportionis, HM
NC, vt patet in eo-
dem Lib. 3. Prop. 2.

411.1.

0312-01

Sitandem ſuma-
musparallelogram-
mum, PC, cui in-
ſcripta eſt parabolę
portio, TSGEC,
incluſa duabus, ST,
EC, ad baſim, HA, vtcunq; ordinatim applicatis, ſiue intercipiant
axem, vel diametrum, GO, ſiue non, ſiue axis, vel diameter, GO,
ſit altera harum duarum ad baſim, HA, ordinatim applicatarum,
ſiue non; reperiemus parallelogrammum, PC, ad portionem, TS
GEC, eſſe vt rectangulum, HOA, ad rectangulum ſub, AC, & ſub compoſita ex, {1/2}, CT, & tota, TH, vna cum rectangulo ſub, T
C, & ſub compoſita ex, {1/6}, TC, & , {1/2}, TH, ſic enim eſſe inuenie-
mus omnia quadrata, TI, ad omnia quadrata quadrilinei, TVM
NC, vt patet eodem Lib. Propoſ. 4.

412. COROLLARIV M.

_H_Inc habetur ſi fiant triangulæ, ductis, SH, PH, GH, QT, hæc
ad portiones, quibus inſcribuntur habere eaſdem rationes, quas
habent dimidia antecedentium ad eadem conſequentia ſuperius expoſita,
ſunt enim & ipſa triangula dictorum parallelogrammorum dimedia.

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