Polybius, Histories

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Need of Some Knowledge of Mathematics

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. . . .