328308GEOMETRIÆ
Sit ſemiparabola, AOCB, in baſi, BC, &
axis, vel diameter
integræ, AB, compleaturq; parallelogrammum, DB, & circa, A
B, BC, tanquam ſemiaxes, vel ſemidiametros coniugatas, deicri-
batur quarta circuli, vel ellipſis, AICB, deinde ſumatur in baſi, B
C, vtcunque punctum, P, & per, P, ducaturipſi, AB, parallela,
PH, ſecans curuam parabolæ in, X, & circuli, vel ellipſis, AIC,
220[Figure 220]
in, I.
Dico ergo, IP, eſſe mediam
proportionalem inter, HP, PX, pro-
ducatur, CB, verſus, B, in, Z, ita
vt, BZ, ſit æqualis, BC, eſt ergo
quadratum, AB, vel quadratum, H
P, ad quadratum, PI, vt rectangu-
lum, ZBC, ad rectangulum, ZPC,
. i. vt, AB, vel, HP, ad, PX, ergo
vt, HP, ad, PI, ita erit, IP, ad, PX.
integræ, AB, compleaturq; parallelogrammum, DB, & circa, A
B, BC, tanquam ſemiaxes, vel ſemidiametros coniugatas, deicri-
batur quarta circuli, vel ellipſis, AICB, deinde ſumatur in baſi, B
C, vtcunque punctum, P, & per, P, ducaturipſi, AB, parallela,
PH, ſecans curuam parabolæ in, X, & circuli, vel ellipſis, AIC,
proportionalem inter, HP, PX, pro-
ducatur, CB, verſus, B, in, Z, ita
vt, BZ, ſit æqualis, BC, eſt ergo
quadratum, AB, vel quadratum, H
P, ad quadratum, PI, vt rectangu-
lum, ZBC, ad rectangulum, ZPC,
. i. vt, AB, vel, HP, ad, PX, ergo
vt, HP, ad, PI, ita erit, IP, ad, PX.
Iungantur puncta, A, C, &
ſum-
1140.cum
Sch.l.1.
3.huius. pto vtcunq. puncto, V, in, AB, per ipſum ducaturipſi, BC, pa-
rallela, VF, ſecans curuam parabolæ in, O, & rectam, AC, in, N.
Dico ergo, vt, FV, ad, VO, ita eſſe, VO, ad, VN; eſt enim
quadratum, BC, vel quadratum, FV, ad quadratum, VO, vt, B
A, ad, AV, . i. vt, BC, vel, FV, ad, VN, ergo erit, vt, FV, ad,
VO, ſic, VO, ad, VN, quæ oſtendere oportebat.
1140.cum
Sch.l.1.
3.huius. pto vtcunq. puncto, V, in, AB, per ipſum ducaturipſi, BC, pa-
rallela, VF, ſecans curuam parabolæ in, O, & rectam, AC, in, N.
Dico ergo, vt, FV, ad, VO, ita eſſe, VO, ad, VN; eſt enim
quadratum, BC, vel quadratum, FV, ad quadratum, VO, vt, B
A, ad, AV, . i. vt, BC, vel, FV, ad, VN, ergo erit, vt, FV, ad,
VO, ſic, VO, ad, VN, quæ oſtendere oportebat.
HInc patet, concluſiones, quę de parallelogrammis collectæ ſun@
in Propoſ 5. 6. 7. 8. Lib. 2. ſuppoſitis quibuſdam conditionibus in
lateribus, vel in altitudine, & baſi dictorum parallelogrammorum, poſ-
ſe colligi etiam pro parabolis eaſdem conditiones in axibus, vel diame-
tris, vel altitudinibus, & baſtbus habentes; quia enim tunc dictæ
in Propoſ 5. 6. 7. 8. Lib. 2. ſuppoſitis quibuſdam conditionibus in
lateribus, vel in altitudine, & baſi dictorum parallelogrammorum, poſ-
ſe colligi etiam pro parabolis eaſdem conditiones in axibus, vel diame-
tris, vel altitudinibus, & baſtbus habentes; quia enim tunc dictæ