Page:The Rhind Mathematical Papyrus, Volume I.pdf/55

 THE METHODS AND AIMS OF THE EGYPTIAN MATHEMATICIAN

The Rhind mathematical papyrus is our chief authority for the state of mathematical knowledge in Egypt about the year 1650 B.C., and while some scholars such as E. and V. Revillout (1881) see in it only the work of a school-boy, most writers have recognized the scientific character of its procedure. The Egyptians of this date did not have the mental development reached by the Greeks a thousand years later. They had a smaller store of mathematical facts and less skill in mathematical operations. Yet their skill was remarkable and there was a scientific quality in their mathematics. The author of this papyrus had an idea of general methods applicable to groups of problems, and within the groups simple problems are followed by more complicated ones that are of the same kind and are solved by the same methods.

The methods of the Egyptian were largely those of trial and what we might call approximation. That is, if he could not get the answer at once he would try to get nearly the answer first and then make up what was lacking. This appears especially in what we have called the second kind of multiplication, where he has the multiplicand and product given to find the multiplier (see page 5), while the method of false position is also a method of trial.

Yet he was quick to generalize and when he had found a solution for a simple problem he did not hesitate to solve in the same way more difficult problems of the same kind, and occasionally to state the solution as a rule. He expresses this idea at the end of Problem 66, where he says, “Do the same thing in any example like this.” Some processes are repeated again and again, showing that he had a method clearly in mind, even if he did not express it as a rule. One rule is put in words in Problem 61B, and is employed in several places (see pages 24-25) as if it were well understood. There are other operations and methods of solution that are taken for granted as being familiar at least to the author. His method of dividing a number in given proportions follows a definite rule which is employed without explanation, although not formulated (see page 28). Problem 79 illustrates, as I believe, a rule for ﬁnding the sum of a geometrical progression (see page 30).