Greek Texts & Translations

Most people calculate the area merely from the ^note length of the circumference [of towns or camps]. Accordingly, when one says that the city of Megalopolis has a circuit of fifty stades, and that of Sparta forty-eight, but that Sparta is twice the size of Megalopolis, they look upon the assertion as incredible. And if one, by way of increasing the difficulty, were to say that a city or camp may have a circuit of forty stades and yet be double the size of one having a perimeter of a hundred, the statement would utterly puzzle them. The reason of this is that we do not remember the lessons in geometry taught us at school. I was led to make these remarks because it is not only common people, but actually

some statesmen and military commanders, who have puzzled themselves sometimes by wondering whether it were possible that Sparta should be bigger, and that too by a great deal, than Megalopolis, while having a shorter circuit; and at other times by trying to conjecture the number of men by considering the mere length of a camp's circuit. A similar mistake is also made in pronouncing as to the number of the inhabitants of cities. For most people imagine that cities in which the ground is broken and hilly contain more houses than a flat site. But the fact is not so; because houses are built at right angles not to sloping foundations but to the plains below, upon which the hills themselves are excrescences. And this admits of a proof within the intelligence of a child. For if one would imagine houses on slopes to be raised until they were of the same height; it is evident that the plane of the roofs of the houses thus united will be equal and parallel to the plane underlying the hills and foundations.

So much for those who aspire to be leaders and statesmen and are yet ignorant and puzzled about such facts as these. . . .

Those who do not enter upon undertakings with good will and zeal cannot be expected to give real help when the time comes to act. . . .