in Mathematical Reasoning. 373 
A a et 
ABC = AB CD. 
The angle formed by the intersection of ares, will therefore stand 
thus, 
AB ‘CD. 
Surfaces are represented by the position of two lines above the 
letters, which indicate them, as 
“AB CD, 
and the angles which are formed by these, with other surfaces, or 
with lines, can be expressed on the principles already explained ; 
as for example, 
22K 
AB CDEF, 
is the angle formed by the line 4B, with the surface CDEF. When 
single letters are employed to denote lines, as a, b, c, the angles 
formed by them are represented thus a‘b, a’c, b'c. 
The effect of these few abbreviations, which, when once ex- 
plained, need no effort to fix them in the memory, is to render 
unnecessary the almost endless repetitions of the same words, and 
to convey the writer’s meaning in the fewest terms. In the calcu- 
lation of the values of annuities dependent on lives, if the question 
is in any degree complicated, the number of independent data is 
very considerable, and the letters which have been employed to 
denote them, have in many instances been selected, without the 
least regard to assisting the reader’s memory. The symbols made 
use of are far too numerous to be extracted, and the immense 
advantages which attend a judicious selection, can only be appre- 
ciated by those, who have had occasion to study the subject, im 
the writings of Price and Morgan, and have afterwards perused 
those of Mr. Baily or Mr. Milne; the former gentleman has had 
3B 2 
