CHAPTER XXIV Early Greek Mathematics and AstronomyI AM concerned in this chapter with mathematics, not on its own account, but as it was related to
Greek philosophy--a relation which, especially in Plato, was very close. The preeminence of the
Greeks appears more clearly in mathematics and astronomy than in anything else. What they did
in art, in literature, and in philosophy, may be judged better or worse according to taste, but what
they accomplished in geometry is wholly beyond question. They derived something from Egypt,
and rather less from Babylonia; but what they obtained from these sources was, in mathematics,
mainly rules of thumb, and in astronomy records of observations extended over very long periods.
The art of mathematical demonstration was, almost wholly, Greek in origin.
There are many pleasant stories, probably unhistorical, showing what practical problems
stimulated mathematical investigations. The earliest and simplest relates to Thales, who, when in
Egypt, was asked by the king to find out the height of a pyramid. He waited for the time of day
when his shadow was as long as he was tall; he then measured the shadow of the pyramid, which
was of course equal to its height. It is said that the laws of perspective were first studied by the
geometer Agatharcus, in order to paint scenery for the plays of Aeschylus. The problem of finding
the distance of a ship at sea, which was said to have been studied by Thales, was correctly solved
at an early stage. One of the great problems that occupied Greek geometers, that of the duplication
of the cube, originated, we are told, with the priests of a certain temple, who were informed by the
oracle that the god wanted a statue twice as large as the one they had. At first