
From, T. L. Heath, Mathematics and Astronomy,
in R.W. Livingstone (ed.), The Legacy of Greece, Oxford University Press, 1921.
Page 2
To quote from a brilliant review of a wellknown work: 'To be a Greek was to seek to know, to know the primordial substance of matter, to know the meaning of number, to know the world as a rational whole. In no spirit of paradox one may say that Euclid is the most typical Greek: he would know to the bottom, and know as a rational system, the laws of the measurement of the earth. Plato, too, loved geometry and the wonders of numbers; he was essentially Greek because he was essentially mathematical.... And if one thus finds the Greek genius in Euclid and the Posterior Analytics, one will understand the motto written over the Academy, μηδεις αγεωμετρητος εισιτω {mêdeis ageômetrêtos eisitô}. To know what the Greek genius meant you must (if one may speak εν αινιγματι {en ainigmati}) begin with geometry.'
Mathematics, indeed, plays an important part in Greek philosophy: there are, for example, many passages in Plato and Aristotle for the interpretation of which some knowledge of the technique of Greek mathematics is the first essential. Hence it should be part of the equipment of every classical student that he should have read substantial portions of the works of the Greek mathematicians in the original, say, some of the early books of Euclid in full and the definitions (at least) of the other books, as well as selections from other writers. Von WilamowitzMoellendorff has included in his Griechisches Lesebuch extracts from Euclid, Archimedes and Heron of Alexandria; and the example should be followed in this country.
Acquaintance with the original works of the Greek mathematicians is no less necessary for any mathematician worthy of the name. Mathematics is a Greek science. So far as pure geometry is concerned, the mathematician's technical equipment is almost wholly Greek. The Greeks laid down the principles, fixed the terminology and invented the methods ab initio; moreover, they did this with such certainty that in the centuries which have since elapsed there has been no need to reconstruct, still less to reject as unsound, any essential part of their doctrine.
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