Institutio Oratoria

If Nicias had known this when he commanded in Sicily, he would not have shared the terror of his men nor lost the finest army that Athens ever placed in the field. Dion for instance when he came to Syracuse to overthrow the tyranny of Dionysius, was not frightened away by the occurrence of a similar phenomenon. However we are not concerned with the uses of geometry in war and need not dwell upon the fact that Archimedes singlehanded succeeded in appreciably prolonging the resistance of Syracuse when it was besieged.

It will suffice for our purpose that there are a number of problems which it is difficult to solve in any other way, which are as a rule solved by these linear demonstrations, such as the method of division, section to infinity, [*]( Quintilian is perhaps referring to the measurement of the area of an irregular figure by dividing it into a number of small equal and regular figures the size of which was calculable. ) and the ratio of increase in velocity. From this we may conclude that, if as we shall show in the next book an orator has to speak on every kind of subject, he can under no circumstances dispense with a knowledge of geometry.