m ON THE EARLY 



2. To find the area of an equilateral triangle. Multiply the square 

 of a quarter -of the square of one of the sides by three: the square root 

 of the product is the area required.* 



Chapter second, treats of the mensuration of curvilinear surfaces. 

 For the circle the rule delivered in many common books of mensuration 

 is given: viz. multiply the square of the diameter by n, and divide the 

 product by 14 .*[■ 



Chapter third, on the mensuration of solids, contains nothing of sin- 

 gularity sufficient to merit particular notice. This chapter concludes 

 with the following sentence. ^ The demonstrations of all these rules are 

 " contained in my greater work, entitled Bahr-itl-Hisab (the ocean of 

 " calculation,) may God grant me grace to finish it." 



Book seventh, treats of practical geometry. Chapter first on levelling, 



fe :-■-■■■ ... . - " 



a b + c x b — c 



Therefore a? = — - 



2 2a 



See the geometrical demonstration in the elements of plane trigonometry, annexed to Simsom'<s 

 Euclid, prop. 7. 



* Let a side of the triangle be a and the perpendicul 



ar x, 



a x 

 i'he area is — - 

 2 





a % 3a* 





But x 2 = a* • j- == — -— 



4 4 





sc = V 



4 





■f This is founded on the rough proportion of the diameter, to the circumference as 7 : 22. 

 Bha'scara, in the Lilavatf, assigns 1250:3927, which is 1:3.1416 and differs only 0.000007 

 from the most accurate computation hitherto made. 



