HISTORY OF ALGEBRA. 



171 



©k the other rules, nothing is delivered differing so much from those 

 contained in our common books of arithmetic, as to require specific men- 

 tion. 



Book second, contains the arithmetic of fractions ; and book third, the 

 rule of three, or to find an unknown number by four proportionals. 

 Book fourth, delivers the rule of position, or to find an unknown number 

 by assuming, one once or twice, and comparing the errors. Book fifth, 

 gives the method of finding an unknown number, by reversing all the 

 steps of the process described in the question^ 



The sixth book, treats of mensuration. The introduction contains 

 geometrical definitions; Chapter I. treats of the mensuration of rec- 

 tilinear surfaces. Under this head the two following articles are deserv- 

 ing of notice. I. To find the point in the base of a triangle where it will 

 be cut by a perpendicular, let fall from the opposite angle., Call the 

 greatest side the base ; multiply the sum of the two lesser sides by their 

 difference ; divide the product by the base, and subtract the quotient from 

 the base ; one half the remainder will shew the place on the base, where 

 the perpendicular falls towards the least side.* 



* Let a be the base, or longest side, h the middle, c the 

 smallest, and x the distance of the perpendicular from the 

 least side. Then x 



b * rs a * -Pc 2 — 2 ax (Eucl. 13. 2.) ' 

 lax—a* + c z — b z 



x = 



b 2 — c 



But J'-c^Ha b 



