BISHOP TERROT ON THE SQUARE ROOTS OF NEGATIVE QUANTITIES, 350 
If n—1 be odd, then the several pairs give as before the product unity; but 
there remains the factor — AB, which has for its coefficient —1. 
@herefore, in either case, (AP,)x(AP,) .... (AP, 1)=2 R"-1. 
XIII. The symbolism employed in the foregoing propositions appears to be 
applicable to Plane Trigonometry in all its parts. To the elementary proposi- 
tions of Geometry it is either inapplicable, or applicable by processes and con- 
siderations unsuitable to the demonstration of elementary truths. Thus, if by 
this method we undertake to prove that the angles at the base of an isosceles tri- 
angle are equal to one another, we have (AC)=(BC). (Fig. 5.) 
A 
But AC=(AC) . 127=(AO). [a+/7—5] 
B 
CB=AD=(AC).1 27=(AC). [a +V/V—0) 
But AC+CB=AB. 
oe (AC). [at +/— 64+/—0]=AB a positive quantity ; consequently the im- 
_ possible or sinal parts of the coefficient of direction must destroy one another, or 
/—b=—/—b or b=-U- Therefore the angles A and B have their sines equal 
in length, but of different affections. The angles themselves, therefore, being to- 
gether less than 7, are geometrically equal to one another. 
Cor. Much in the same way we might prove that in every triangle the greater 
angle has the greater side opposite to it; and, conversely, that the greater side 
has the greater angle opposite to it. 

