Page:The Rhind Mathematical Papyrus, Volume I.pdf/56

40 In the geometrical problems he has several rules that he uses without comment, rules for getting areas and volumes and for changing from one unit of measure to another. Perhaps the most striking single operation that is often used is that by which in the third step of a multiplication of the second kind he determines the multiplier that will produce as product the reciprocal of a given number (see page 6).

A striking, though natural, characteristic of the Egyptian’s work is his tendency noted above to take particular cases or particular numbers and generalize from them. This is seen especially in his method of adding fractions by taking them as parts of some number and adding their values when applied to this number (see pages 7-10). See also a remark on page 36.

It is quite possible that the writer of the papyrus, and the Egyptian mathematicians who preceded him, kept the results of their multiplications and other calculations in the form of tables, and often, when they had a multiplication or division to perform, took the result from these tables instead of working it out in full. This would explain the fact that details are often omitted that are more difficult than other details that are put in. Some one must have worked out these details in some way, but the result of a multiplication once worked out could be used in two or three ways (see page 83). We have called the first part of the papyrus a table and next after this there is a table given in full just before Problem 1. There are also tables for fractions of a hekat in Problems 47, 80, and 81.

Much has been written about the mistakes that we ﬁnd in the Rhind papyrus. There are occasional mistakes, mostly numerical, that are merely accidental. Some of them are found in the group of Problems 7-20 (see page 64); five times in the first table 60 is written for 80; in two problems (43 and 59) the two given numbers are interchanged in the statement as compared with the solution; in Problem 49 the dimensions given in the statement are 10 and 2, but in the solution 10 and 1; in Problem 64 the mean share is given as $1/undefined$ hekat when it is 1 hekat; in Problem 43 a second method of solution is preceded by one step of the first; in the last part of Problem 82 there is a numerical mistake in the division of a quantity of grain by 2. These are examples. At the beginning it is stated that this work is a copy of writings of an earlier period, and some of the mistakes seem to be mistakes of copying. Peet has