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,
CT, ad portionem, HST, vt, AT, ad com-
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.

416.1.

0316-01
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,
AT, ad ipſam, AT.

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-
rabolæ ad eandem partem, ad quam abſcinditur portio, ha-
beat datam rationem, dummodò hæc ſit maior ſexquialtera.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer