322292GEOMETR. PRACT.
III.
IIII.
V.
THEOR. 1. PROPOS. 1.
AREA cuiuslibet trianguli æqualis eſt rectangulo comprehenſo ſub
11Triangulum
quodcunque
cuirectangulo
aquale ſit. perpendiculari â vertice ad baſim protracta, & dimidia parte baſis.
Item rectangulo comprehenſo ſub ſemiſſe perpendicularis, & tota
baſe. Vel denique ſemiſsi rectanguli ſub tota perpendiculari, & tota
baſe comprehenſi.
11Triangulum
quodcunque
cuirectangulo
aquale ſit. perpendiculari â vertice ad baſim protracta, & dimidia parte baſis.
Item rectangulo comprehenſo ſub ſemiſſe perpendicularis, & tota
baſe. Vel denique ſemiſsi rectanguli ſub tota perpendiculari, & tota
baſe comprehenſi.
Sit triangulum A B C, ex cuius vertice A, ad baſim BC, ducatur perpendi-
cularis A D, diuidatque primò baſim BC, bifa-
213[Figure 213]
riam, vt in prima figura.
Per A, ducatur E A F,
in vtramque partem æquidiſtans rectæ B C,
compleatur que rectangulum B E F C, 2241. primi. erit duplum trianguli A B C; Item 3336. primi. rectanguli ADBE. Quare rectangulum ADBE,
quod nimirum continetur ſub perpendiculari
AD, & dimidio baſis BD, æquale eſt triangulo ABC, diuidat ſecundo perpendi-
cularis AD, baſim BC, non bifariam, vel etiã cadat in baſim CB, protra ctam, vt in
2. & 3. figura; Et per A, ducatur rurſus AF, in vtramq; partẽ æquidiſtãs rectę BC,
compleaturq; rectangulũ ADCF. Diuiſa deinde baſe BC, bifariã in G,
cularis A D, diuidatque primò baſim BC, bifa-
in vtramque partem æquidiſtans rectæ B C,
compleatur que rectangulum B E F C, 2241. primi. erit duplum trianguli A B C; Item 3336. primi. rectanguli ADBE. Quare rectangulum ADBE,
quod nimirum continetur ſub perpendiculari
AD, & dimidio baſis BD, æquale eſt triangulo ABC, diuidat ſecundo perpendi-
cularis AD, baſim BC, non bifariam, vel etiã cadat in baſim CB, protra ctam, vt in
2. & 3. figura; Et per A, ducatur rurſus AF, in vtramq; partẽ æquidiſtãs rectę BC,
compleaturq; rectangulũ ADCF. Diuiſa deinde baſe BC, bifariã in G,