( 7t ) 
Thefe Theorems follow eafily from the third Corol- 
lary of the Propofition. The firft eafily appears 
thus, d = — % D' = (by that Corollary) 
mYa* — 'IM DF+ 'Lm CG — "Lm m AI—z^K. 
— xDF -|- 8^ CG — 1 8 32. A I — 5'o K. 
= m E" — I X 2 D F 4-T4 x 2 C G — 
m + 9 xxBH + m i6xz Al^ m + X zK^ 
The other Theorems are deduced from the fame Co- 
rollary compared with Cor, i. Prop, viii, 
PROP. XII. 
!tl?e fame T’hhgs being fuppofed as in the feconct 
Corollary of the viih^ Propoffition, 
i.» 2 E* — + i X2 DF + /^’+4 X a CG — z» + ^ 
— '»^4 "MXaK - - - j 
a. w' E* — z m' D F + — . la x a C G — m — 7a x^ 
a B H+ m — 240 x a A I — m ' — 600 x a K - - - J 
3. m' E* — a D F + 2 m" CG — m" 4- 3^0 x ^ 
a BH+Ji^'M- x8x 2AI 35X2KJ “* ^ ' 
4.w'"xE* — aDF + a CG-aBH-F^" — 75° ^ 
A I — m"" — 7200 X 28 X a K 
Thefe Theorems follow from the third Corollary of 
the,vF*^ Propofition compared with the fecond Corollary 
of the eighth Propofition, The firfi: is the fame with 
the firfi: of the lafi Propofition. The fecond is de- 
monfirated by fubfiituting in^^i^'E^E^ — 24 C'G^ = 
The Values of E'E' and C G' given in the third 
j Cor,. 
