316296GEOMETRIÆ
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.
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
210[Figure 210]
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,
115. Huius. 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.
vtcunque recta linea, ST, fiat autem triangulum ſub, ST, & vtrauis
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,
115. Huius. 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.
SCHOLIV M.