305285GEOMETRIÆ
CAVALER II
LIBER QVARTVS.
In quo de Parabola, & ſolidis ab eadem
genitis enucleatur doctrina.
genitis enucleatur doctrina.
THEOREMAI. PROPOS. I.
SI PARALLELOGRAMMVM, &
trian-
gulum fuerint in eadem baſi, & circa
eundem axim, vel diametrum cum pa-
rabola; parallelogrammum erit para-
bolæ ſexquialterum, triangulum au-
tem erit eiuſdem parabolæ ſubſexqui-
tertium.
gulum fuerint in eadem baſi, & circa
eundem axim, vel diametrum cum pa-
rabola; parallelogrammum erit para-
bolæ ſexquialterum, triangulum au-
tem erit eiuſdem parabolæ ſubſexqui-
tertium.
Sit ergo parabola, FCH, in baſi, FH, circa axim, vel diame-
trum, CG, ſit autem in eadem baſi, FH, & circa eundem axim, vel
diametrum parallelogrammum quoq; AH, & triangulum, CFH.
199[Figure 199]
Dico ergo parallelogrammum, AH,
eſſe ſexquialterum parabolæ, FCH;
triangulum autem, CFH, eſſe eiuſdem
parabolæ, FCH, ſubſexquitertium.
Sumatur ergoin, CE, quæ tangit pa-
rabolam in puncto, C, vtcunque pun-
ctum, N, & per, N, ducatur ipſi, CG,
parallela, NO, producta vſque ad ba-
ſim, FH, cui occurrantin, O; quæ pa-
riter ſecet curuam parabolæin, M, &
per, M, ducatur ipſi baſi, FH, parallela, IL. Eſtergo
trum, CG, ſit autem in eadem baſi, FH, & circa eundem axim, vel
diametrum parallelogrammum quoq; AH, & triangulum, CFH.
eſſe ſexquialterum parabolæ, FCH;
triangulum autem, CFH, eſſe eiuſdem
parabolæ, FCH, ſubſexquitertium.
Sumatur ergoin, CE, quæ tangit pa-
rabolam in puncto, C, vtcunque pun-
ctum, N, & per, N, ducatur ipſi, CG,
parallela, NO, producta vſque ad ba-
ſim, FH, cui occurrantin, O; quæ pa-
riter ſecet curuam parabolæin, M, &
per, M, ducatur ipſi baſi, FH, parallela, IL. Eſtergo