372 Mr. Bappace on the Influence of Signs 
trating his view of the application of Algebra to Geometry, pos- 
sesses in an eminent degree the qualifications we are now consider- 
ing; and although I cannot altogether agree with the conclusions, 
which it is the object of the author of that highly mgenious work, 
the ‘‘Geometry of Position,’ to establish, yet I am happy to 
acknowledge the instruction I have derived from the very original 
view which he has taken. 
To denote a line, M. Carnot places a bar over the letters which 
represent it, thus, 4B: an are of a circle or other curve, will 
naturally be represented by AB. To indicate the point where two 
lines meet, 4B CD is used, and similarly the points formed by 
the meeting of two ares, or an are and a circle, are denoted re- 
spectively, 
AB’ CD, and AB~ CD: 
according to these principles, the line drawn from the point F’, to 
the intersection of 4B and CD, will be represented thus, 
F 4B CD, 
and the two expressions, 
AB CD FG Hk, AB CD FG HK LM 
denote the first, the line which joins the points, where 4B, CD, 
and FG, HK respectively intersect each other: and the second, the 
point where that line cuts the arc LM, 
+ is used to signify coincidence with, as 
AB CD + FG HK, 
indicates, that the two points formed by the intersection of the lines 
AB, CD, and by the ares FG and HK, coincide. 
A 
The angle ABC, is indicated thus, ABC, and if it is formed 
by the two lines 4B and CD, it is thus expressed, 
