I.When the capital of the empire was besieged by the Goths, the circuit of the walls was accurately measured, by Ammonius, the mathematician, who found it equal to twenty-one miles.

[67] It should not be forgotten that the form of the city was almost that of a circle; the geometrical figure which is known to contain the largest space within any given circumference.

II.
The architect Vitruvius, who flourished in the Augustan age, and whose evidence, on this occasion, has peculiar weight and authority, observes, that the innumerable habitations of the Roman people would have spread themselves far beyond the narrow limits of the city; and that the want of ground, which was probably contracted on every side by gardens and villas, suggested the common, though inconvenient, practice of raising the houses to a considerable height in the air.

[68] But the loftiness of these buildings, which often consisted of hasty work and insufficient materials, was the cause of frequent and fatal accidents; and it was repeatedly enacted by Augustus, as well as by Nero, that the height of private edifices within the walls of Rome, should not exceed the measure of seventy feet from the ground.

[69] III.