denly the work that the Greeks had done from pure love of theory became the key to warfare
and astronomy.
The Romans were too practical-minded to appreciate Euclid; the first of them to mention him is
Cicero, in whose time there was probably no Latin translation; indeed there is no record of any
Latin translation before Boethius (ca. A.D. 480). The Arabs were more appreciative: a copy was
given to the caliph by the Byzantine emperor about A.D. 760, and a translation into Arabic was
made under Harun al Rashid, about A.D. 800. The first still extant Latin translation was made
from the Arabic by Athelhard of Bath in A.D. 1120. From that time on, the study of geometry
gradually revived in the West; but it was not until the late Renaissance that important advances
were made.
I come now to astronomy, where Greek achievements were as remarkable as in geometry.
Before their time, among the Babylonians and Egyptians, many centuries of observation had
laid a foundation. The apparent motions of the planets had been recorded, but it was not known
that the morning and evening star were the same. A cycle of eclipses had been discovered,
certainly in Babylonia and probably in Egypt, which made the prediction of lunar eclipses fairly
reliable, but not of solar eclipses, since those were not always visible at a given spot. We owe to
the Babylonians the division of the right angle into ninety degrees, and of the degree into sixty
minutes; they had a liking for the number sixty, and even a system of numeration based upon it.
The Greeks were fond of attributing the wisdom of their pioneers to travels in Egypt, but what
had really been achieved before the Greeks was very little. The prediction of an eclipse by
Thales was, however, an example of foreign influence; there is no reason to suppose that he
added anything to what he learnt from Egyptian or Babylonian sources, and it was a stroke of
luck that his prediction was verified.
Let us begin with some of the earliest discoveries and correct hypotheses. Anaximander thought
that the earth floats freely, and is not supported on anything. Aristotle, * who often rejected the
best hypotheses of his time, objected to the theory of Anaximander, that the earth, being at the
centre, remained immovable because there was
* De Caelo, 295b.