Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/33

Rh and contains rules for calculations both of an arithmetical and a geometrical character. The arithmetical problems mostly concern measures of corn and fruit, and deal particularly with such questions as the division of a number of measures among a given number of persons, the number of loaves or jars of beer that certain measures will yield, and the wages due to the workmen for a certain piece of work. It corresponds exactly, in fact, to the description of Egyptian arithmetic Plato gives us in the Laws, where he tells us that children learnt along with their letters to solve problems in the distribution of apples and wreaths to greater or smaller numbers of people, the pairing of boxers and wrestlers, and so forth. This is clearly the origin of the art which the Greeks called λογιστική, and they probably borrowed that from Egypt, where it was highly developed; but there is trace of what the Greeks called ἀριθμητική, the scientific study of numbers.

The geometry of the Rhind papyrus is of a similar character, and Herodotos, who tells us that Egyptian geometry arose from the necessity of measuring the land afresh after the inundations, is clearly far nearer the mark than Aristotle, who says it grew out of the leisure enjoyed by the priestly caste. The rules given for calculating areas are only exact when these are rectangular. As fields are usually more or less rectangular, this would be sufficient for practical purposes. It is even assumed that a right-angled triangle can be equilateral. The rule for finding what is called the seqt of a pyramid is, however, on a rather higher level, as we should expect. It comes to this. Given the "length across the sole of the foot," that as, the diagonal of the base, and that of the piremus or "ridge," to find a number which represents the ratio between them. This is