<head>VI. Sicilian Affairs</head>Most people judge of the size of cities simply from their circumference.
So that when one says that <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a> is fifty stades in circumference and <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> forty-eight, but that <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> is twice as large as <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a>, the statement seems incredible to me.
And when in order to puzzle them still most, one tells them that a city or camp with a circumference of forty stades may be twice as large as one the circumference of which is one hundred stades, this statement seems to them absolutely astounding.
The reason of this is that we have forgotten the lessons in geometry we learnt as children.
I was led to make these remarks by the fact that not only ordinary men but even some statesmen and commanders of armies are thus astounded, and wonder how it is possible for <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> to be larger and even much larger than <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a>, although its circumference is smaller;
or at other times attempt to estimate the number of men in a camp by taking into consideration its circumference alone.
Another very similar error is due to the appearance of cities. Most people suppose that cities set upon broken and hilly ground can contain more houses than those set upon flat ground.
This is not so, as the walls of the houses are not built at right angles to the slope, but to the flat ground at the foot on which the hill itself rests.
The truth of this can be made manifest to the intelligence of a child.
For if one supposes the houses on a slope to be raised to such a height that their roofs are all level with each other, it is evident that the flat space thus formed by the roofs will be equal in area and parallel to the flat space in which the hill and the foundations of the houses rest.
So much for those who aspire to political power and the command of armies but are ignorant of such things and surprised by them.
Walbank Commentary