# Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

## 416.THEOREMA VIII. PROPOS. VIII.

SI ad baſim datæ parabolæ ordinatim applicetur recta li-
nea, ſub qua, & ſub portione baſis abſciſſa, ac earum ex-
trema iungente, fiattriangulum, portio parabolæ abſciſſa ad
triangulum ſibi inſcriptum erit, vt ad reliquam baſis, dempta
abſciſſa, eadem reliqua cum, {1/3}, ipſius abſciſſæ.

Sit parabola, HGA, in baſi, HA, ad quam ordinatim applicetur
vtcunque recta linea, ST, fiat autem triangulum ſub, ST, & vtrauis
duarum, HT, TA, vt ſub, HT, & ſub, SH,
quod ſit, HST. Dico portionem, HST, ad
triangulum, HST, eſſe vt compoſitam ex, A
T, & , {1/3}, TH; ad, AT, compleatur paralle-
logrammum, CT, eſt ergo parallelogrammum,
poſitam ex, {1/2}, AT, & , {1/6}, TH, & anteceden-
tium dimidia ſcilicet triangulum, HST, ad
portionem, HST, erit vt dimidia, AT, ad
compoſitam ex, {1/2}, AT, & , {1/6}, TH, ideſt vt,
AT, ad, AT, cum, {1/3}, HT, & conuertendo,
portio, HST, ad triangulum, HST, erit vt
compoſita ex, {1/3}, HT, & tota, TA, ad, TA,
quod oſtendendum nobis erat.

5. Huius.

## 417.SCHOLIV M.

_P_Oteſt autem, & dicta ratio ſic conſtitui, triplicatis terminis, ſcili-
cet, quod portio, HST, ad triangulum, HST, ſit bt bna, HA,
cum duabus, AT, ad tres, AT, bel ſic, quod ſit, bt dimidia, HA, cum,

## 418.PROBLEMA I. PROPOS. IX.

A Data parabola portionem abſcindere per lineam ab
eiuſdem baſim ordinatim ductam, quę ad triangulum
ſub eadem ordinatim ducta, & abſciſſa per eandem à baſi pa-