170 Science As no symbolic notation was developed, there are no general formulae, with one possible exception : *To make f of a fraction Stated in modern terminology, the following are examples of the types of problem successfully solved : 1. Subtract H A & A from f • (^' 4 + iV) 2. To a number §, | and } of it are added. The result is 37. What is the number ? (Ans. 16+ ^ + 579 + 775 •) 3. Divide 10 measures of barley among 10 men, in such a way that each gets \ more than his neighbour. This amounts to finding an arithmetical progression of ten numbers, whose sum is 10 and common difference g. 4. Divide 700 loaves among 4 men in the proportion of f , |, f , and J. (Ans. 266f, 200, 133 J, and 100.) 5. The area of a rectangular enclosure is 12 acres. The breadth is f of the length. Find the length and breadth. This example involves the solution of a simple equation with one unknown quantity. 6. A triangle of given area has the perpendicular height ^\ times the base. Find the base and the height. It seems certain that the properties of the isosceles, if not of any, triangle, now expressed by the formulae which follow, were known ; but it is not easy to prove this conclusion from the material available. bb ,11 AM , b where A = area, b = base and b = height. 7. Find the area of a circular field 9 cubits in diameter. The working implies the use of the following rule: 'Subtract | from the diameter and square the result.' This is equivalent to a value of TT (ratio of circumference to diameter) of 3 '1605. The fact that the area is expressed as a square points to the method of count- ing squares on a surface ruled in squares, in order to arrive at the