390370GEOMETRIÆ
erunt, vt rectangulum, OEN, ad rectangulum ſub, OE, &
, NM,
vna cum rectang. ſub compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME.
vna cum rectang. ſub compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME.
Quia verò omnia quadrata trianguli, DMF, ſunt {1/3}.
omnium
1124. l. 2. quadratorum, SF, ideò ad omnia quadrata fruſti, HDFG, erunt
vt {1/3}. rectanguli, OEN, ad rectangulum ſub, OE, & , NM, vna cũ
rectangulo ſub compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME, vel vt
horum tripla . i. vt rectangulum, OEN, ad rectangulum ſub, OE,
& tripla, NM, vna cum rectangulo ſub compoſita ex ſexquialte-
ra, ON, . i. ex, NX, & ON, & {2/3}. NE, & ſub, ME, quę oſtendere opus
erat.
1124. l. 2. quadratorum, SF, ideò ad omnia quadrata fruſti, HDFG, erunt
vt {1/3}. rectanguli, OEN, ad rectangulum ſub, OE, & , NM, vna cũ
rectangulo ſub compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME, vel vt
horum tripla . i. vt rectangulum, OEN, ad rectangulum ſub, OE,
& tripla, NM, vna cum rectangulo ſub compoſita ex ſexquialte-
ra, ON, . i. ex, NX, & ON, & {2/3}. NE, & ſub, ME, quę oſtendere opus
erat.
THEOREMA IV. PROPOS. IV.
IN eadem antecedentis figura productis, CH, RG, ver-
ſus baſem, DF, cui incidant in, PQ, regula eadem re-
tenta, oſtendemus omnia quadrata, SF, ad omnia quadra-
ta fruſti, HDFG, demptis omnibus quadratis, HQ, eſſe vt
rectangulum, OEN, ad rectangulum ſub, EM, & ſub com-
poſita ex {1/3}. EM, integra, MN, & {1/2}. NO: Omnia verò quadra-
ta trianguli, DMF, ad eadem eſſe oſtendemus, vt rectang.
OEN, ad rect. ſub compoſita ex, EX, dupla, NM, & ſub, ME.
ſus baſem, DF, cui incidant in, PQ, regula eadem re-
tenta, oſtendemus omnia quadrata, SF, ad omnia quadra-
ta fruſti, HDFG, demptis omnibus quadratis, HQ, eſſe vt
rectangulum, OEN, ad rectangulum ſub, EM, & ſub com-
poſita ex {1/3}. EM, integra, MN, & {1/2}. NO: Omnia verò quadra-
ta trianguli, DMF, ad eadem eſſe oſtendemus, vt rectang.
OEN, ad rect. ſub compoſita ex, EX, dupla, NM, & ſub, ME.
Omnia .
n.
quadrata, SF, ad omnia qu adrata fruſti, HDFG
22In antec.
267[Figure 267]
oſtenſa ſunt eſſe, vt rectangulum, OEN, ad
rectangulum ſub, OE, & NM, vna cum,
rectangulo ſub compoſita ex {1/2}. ON, & {1/3}.
ME, & ſub, ME: Omnia verò quadrata-
SF, ad omnia quadrata, HQ, ſunt vt qua
dratum, DF, ad quadratum, PQ, vel ad
339. l. 2. quadratum, HG, . i. vt rectangulum, OEN,
ad rectangulum, OMN, ergo eadem ad re-
4439. & Sch.
40. l. 1. liquum omnium quadratorum fruſti, DH
GF, demptis omnibus quadratis, HQ, e-
runt vt rectangulum, OEN, ad reliquum,
dempto rectangulo, OMN, à rectangulis
ſub, OE, MN, & ſub compoſita ex {1/2}. ON,
& {1/3}. ME, & ſub, ME, eſt autem rectangu-
551. 2. Elem. lum ſub, OE, MN, æquale rectangulis ſub, OM, MN, & ſub, EM,
MN, ergo dempto rectangulo, OMN, à rectangulo ſub, OE, MN,
remanet rectangulum, EMN, ad quod vna cum rectangulo ſub
compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME, ipſum rectangulum
OEN, erit vt omnia quad. SF, ad omnia quad. fruſti, HDFG,
22In antec.
rectangulum ſub, OE, & NM, vna cum,
rectangulo ſub compoſita ex {1/2}. ON, & {1/3}.
ME, & ſub, ME: Omnia verò quadrata-
SF, ad omnia quadrata, HQ, ſunt vt qua
dratum, DF, ad quadratum, PQ, vel ad
339. l. 2. quadratum, HG, . i. vt rectangulum, OEN,
ad rectangulum, OMN, ergo eadem ad re-
4439. & Sch.
40. l. 1. liquum omnium quadratorum fruſti, DH
GF, demptis omnibus quadratis, HQ, e-
runt vt rectangulum, OEN, ad reliquum,
dempto rectangulo, OMN, à rectangulis
ſub, OE, MN, & ſub compoſita ex {1/2}. ON,
& {1/3}. ME, & ſub, ME, eſt autem rectangu-
551. 2. Elem. lum ſub, OE, MN, æquale rectangulis ſub, OM, MN, & ſub, EM,
MN, ergo dempto rectangulo, OMN, à rectangulo ſub, OE, MN,
remanet rectangulum, EMN, ad quod vna cum rectangulo ſub
compoſita ex {1/2}. ON, & {1/3}. ME, & ſub, ME, ipſum rectangulum
OEN, erit vt omnia quad. SF, ad omnia quad. fruſti, HDFG,
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib