Institutio Oratoria

For, if necessary, he will use the syllogism, and he will certainly make use of the enthymeme which is a rhetorical form of syllogism. [*]( See v. xiv. I for an example from the Pro Ligario. The cause was then doubtful, as there were arguments on both sides. Now, however, we must regard that cause as the better, to which the gods have given their approval. ) Further the most absolute form of proof is that which is generally known as linear demonstration. And what is the aim of oratory if not proof?

Again oratory sometimes detects falsehoods closely resembling the truth by the use of geometrical methods. An example of this may be found in connexion with numbers in the so-called pseudographs, a favourite amusement in our boyhood. [*](It is not known to what Quintilian refers.) But there are more important points to be considered. Who is there who would not accept the following proposition?

When the lines bounding two figures are equal in length, the areas contained within those lines are equal.

and historians have been taken to task by geometricians for believing the time taken to circumnavigate an island to be a sufficient indication of its size. For the space enclosed is in proportion to the perfection of the figure.

Consequently if the bounding line to which we have referred form a circle, the most perfect of all plane figures, it will contain a greater space than if the same length of line took the form of a square, while a square contains a greater space than a triangle having the same total perimeter, and an equilateral triangle than a scalene triangle.

But there are other points which perhaps present greater

But a square of 180 feet gives the same perimeter, yet contains a much larger area within its four sides. If the calculation prove irksome to any of my readers, he can learn the same truth by employing smaller numbers. Take a ten foot square: its perimeter is forty feet and it contains 100 square feet. But if the dimensions be fifteen feet by five, while the perimeter is the same, the area enclosed is less by a quarter.

On the other hand if we draw a parallelogram measuring nineteen feet by one, the number of square feet enclosed will be no greater than the number of linear feet making the actual length of the parallelogram, though the perimeter will be exactly as that of the figure which encloses an area of 100 square feet. Consequently the area enclosed by four lines will decrease in proportion as we depart from the form of a square.

It further follows that it is perfectly possible for the space enclosed to be less, though the perimeter be greater. This applies to plane figures only: for even one who is no mathematician can see that, when we have to consider hills or valleys, the extent of ground enclosed is greater than the sky over it.