e represented by writing down the symbol for 1, 10, 100, and so on as many times as the unit was in a given number. For example, the symbol for 1 was written five times to represent the number 5, the symbol for 10 was written six times to represent the number 60, and the symbol for 100 was written three times to represent the number 300. Together, these symbols represented the number 365. Addition was done by totaling separately the units-10s, 100s, and so forth-in the numbers to be added. Multiplication was based on successive doublings, and division was based on the inverse of this process. The Egyptians used sums of unit fractions (a), supplemented by the fraction B, to express all other fractions. For example, the fraction E was the sum of the fractions 3 and *. Using this system, the Egyptians were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra. In geometry, the Egyptians calculated the correct areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. To find the area of a circle, the Egyptians used the square on U of the diameter of the circle, a value of about 3.16-close to the value of the ratio known as pi, which is about 3.14. The Babylonian system of numeration was quite different from the Egyptian system. In the Babylonian system-which, when using clay tablets, consisted of various wedge-shaped marks-a single wedge indicated 1 and an arrowlike wedge stood for 10 (see table). Numbers up through 59 were formed from these symbols through an additive process, as in Egyptian mathematics. The number 60, however, was represented by the same symbol as 1, and from this point on a positional symbol was used. That is, the value of one of the first 59 numerals depended henceforth on its position in the total numeral. For example, a numeral consisting of a symbol for 2 followed by one for 27 and ending in one for 10 ...
