By Sir Thomas Heath
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Additional info for A History of Greek Mathematics, Vol. 1: From Thales to Euclid
In this book I have adopted a new arrangement, mainly according to subjects, the nature of which and the reasons for which will be made clear by an illustration. Take the case of a famous problem which plays a great part in the history of Greek geometry, the doubling of the cube, or its equivalent, the finding of two mean proportionals in continued proportion between two given straight lines. Under a chronological arrangement this problem comes up afresh on the occasion of each new solution. Now it is obvious that, if all the recorded solutions are collected together, it is much easier to see the relations, amounting in some cases to substantial identity, between them, and to get a comprehensive view of the history of the problem.
The history of Greek astronomy furnishes a good example of this, as well as of the fact that no visible phenomenon escaped their observation. We read in Cleomedes7 that there were stories of extraordinary lunar eclipses having been observed which ‘the more ancient of the mathematicians’ had vainly tried to explain; the supposed ‘paradoxical’ case was that in which, while the sun appears to be still above the western horizon, the eclipsed moon is seen to rise in the east. The phenomenon was seemingly inconsistent with the recognized explanation of lunar eclipses as caused by the entrance of the moon into the earth’s shadow; how could this be if both bodies were above the horizon at the same time?
2 We see this first of all in their love of adventure. 4 Coming nearer to historical times, we find philosophers and statesmen travelling in order to benefit by all the wisdom that other nations with a longer history had gathered during the centuries. Thales travelled in Egypt and spent his time with the priests. Solon, according to Herodotus,5 travelled ‘to see the world’ (θωρίης ἵνκν), going to Egypt to the court of Amasis, and visiting Croesus at Sardis. At Sardis it was not till ‘after he had seen and examined everything’ that he had the famous conversation with Croesus; and Croesus addressed him as the Athenian of whose wisdom and peregrinations he had heard great accounts, proving that he had covered much ground in seeing the world and pursuing philosophy.