[18.] Again the Spartan Cleomenes, when proposing to take Megalopolis by a stratagem, arranged with the Cleomenes. See 2, [55]. guards of that part of the wall near what is called the Cavern to come out with all their men in the third watch, the hour at which his partisans were on duty on the wall; but not having taken into consideration the fact that at the time of the rising of the Pleiads the nights are very short, May 12.he started his army from Sparta about sunset. The result was that he was not able to get there in time, but being overtaken by daybreak, made a rash and ill-considered attempt to carry the town, and was repulsed with considerable loss and the danger of a complete overthrow. Now if he had, in accordance with his arrangement, hit the proper time, and led in his men while his partisans were in command of the entrance, he would not have failed in his attempt.
Similarly, once more, King Philip, as I have already stated, when carrying on an intrigue in the city of Meliteia, Philip’s attack on Meliteia. See 5, [97]. made a mistake in two ways. The ladders which he brought were too short for their purpose, and he mistook the time. For having arranged to arrive about midnight, when every one was fast asleep, he started from Larissa and arrived in the territory of Meliteia too early, and was neither able to halt, for fear of his arrival being announced in the city, nor to get back again without being discovered. Being compelled therefore to continue his advance, he arrived at the city while the inhabitants were still awake. Consequently he could neither carry the wall by an escalade, because of the insufficient length of the ladders; nor enter by the gate, because it was too early for his partisans inside to help him. Finally, he did nothing but irritate the people of the town, and, after losing a considerable number of his own men, retired unsuccessful and covered with disgrace; having only given a warning to the rest of the world to distrust him and be on their guard against him.
[19.] Again Nicias, the general of the Athenians, had it in his power to have saved the army besieging Syracuse, Nicias, B.C. 413. Thucyd. 7, 50.and had selected the proper time of the night for escaping the observation of the enemy, and retiring to a place of safety. And then because the moon was eclipsed, regarding it superstitiously as of evil portent, he stopped the army from starting. Thanks to this it came about that, when he started the next day, the enemy had obtained information of his intention, and army and generals alike fell into the hands of the Syracusans. Yet if he had asked about this from men acquainted with such phenomena, he might not only have avoided missing his opportunity for such an absurd reason, but have also used the occurrence for his own benefit owing to the ignorance of the enemy. For the ignorance of their neighbours contributes more than anything else to the success of the instructed.
Such then are examples of the necessity of studying celestial phenomena. But as for securing the proper length of scaling ladders, The method of judging of the length necessary for scaling ladders. the following is the method of making the calculation. Suppose the height of the wall to be given by one of the conspirators within, the measurement required for the ladders is evident; for example, if the height of the wall is ten feet or any other unit, the ladders must be full twelve; and the interval between the wall and the foot of the ladder must be half the length of the ladder, that the ladders may not break under the weight of those mounting if they are set farther away, nor be too steep to be safe if set nearer the perpendicular. But supposing it not to be possible to measure or get near the wall: the height of any object which rises perpendicularly on its base can be taken by those who choose to study mathematics.
[20.] Once more, therefore, those who wish to succeed in military projects and operations must have studied geometry, not with professional completeness, but far enough to have a comprehension of proportion and equations. For it is not only in such cases that these are necessary, but also for raising the scale of the divisions of a camp. For sometimes the problem is to change the entire form of the camp, and yet to keep the same proportion between all the parts included: at other times to keep the same shape in the parts, and to increase or diminish the whole area on which the camp stands, adding or subtracting from all proportionally. On which point I have already spoken in more elaborate detail in my Notes on Military Tactics. For I do not think that any one will reasonably object to me that I add a great burden to strategy, in urging on those who endeavour to acquire it the study of astronomy and geometry: for, while rather rejecting all that is superfluous in these studies, and brought in for show and talk, as well as all idea of enjoining their prosecution beyond the point of practical utility, I am most earnest and eager for so much as is barely necessary. For it would be strange if those who aim at the sciences of dancing and flute-playing should study the preparatory sciences of rhythms and music, (and the like might be said of the pursuits of the palaestra), from the belief that the final attainment of each of these sciences requires the assistance of the latter; while the students of strategy are to feel aggrieved if they find that they require subsidiary sciences up to a certain point. That would mean that men practising common and inferior arts are more diligent and energetic than those who resolve to excel in the best and most dignified subject, which no man of sense would admit....
THE COMPUTATION OF THE SIZE OF CITIES
[21.] Most people calculate the area merely from the length of the circumference [of towns or camps]. Sparta and Megalopolis. 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....