Polybius, Histories

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Example: Why Nicias Failed at Syracuse

Again Nicias, the general of the Athenians, had it in his power to have saved the army besieging Syracuse, and had selected the proper time of the night for escaping the observation of the enemy, and retiring to a place of safety.

Nicias, B.C. 413. Thucyd. 7, 50.

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

The method of judging of the length necessary for scaling ladders.

phenomena. But as for securing the proper length of 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.