We are told that Pythagoras on one occasion, when some young men were led astray by their passions to commit an outrage on a respectable family, calmed them by ordering the piper to change her strain to a spondaic measure, while Chrysippus selects a special tune to be used by nurses to entice their little charges to sleep.

Further I may point out that among the fictitious themes employed in declamation is one, doing no little credit to its author's learning, in which it is supposed that a piper is accused of manslaughter because he had played a tune in the Phrygian mode as an accompaniment to a sacrifice, with the result that the person officiating went mad and flung himself over a precipice. If an orator is expected to declaim on such a theme as this, which cannot possibly be handled without some knowledge of music, how can my critics for all their prejudice fail to agree that music is a necessary element in the education of an orator?

As regards geometry, Geometry here includes all mathematics. it is granted that portions of this science are of value for the instruction of children: for admittedly it exercises their minds, sharpens their wits and generates quickness of perception. But it is considered that the value of geometry resides in the process of learning, and not as with other sciences in the knowledge thus acquired. Such is the general opinion.

But it is not without good reason that some of the greatest men have devoted special attention to this science. Geometry has two divisions; one is concerned with numbers, the other with figures. Now knowledge of the former is a necessity not merely to the orator, but to any one who has had even an elementary education. Such knowledge is frequently required in actual cases, in which a speaker is regarded as deficient in education, I will not say if he hesitates in making a calculation, but even if he contradicts the calculation which he states in words by making an uncertain or inappropriate gesture with his fingers. There was a separate symbol for each number, depending on the hand used and the position of the fingers. See Class. Review, 1911, p. 72 Again linear geometry is frequently required in cases, as in lawsuits about boundaries and measurements.

But geometry and oratory are related in a yet more important way than this.

In the first place logical development is one of the necessities of geometry. And is it not equally a necessity for oratory? Geometry arrives at its conclusions from definite premises, and by arguing from what is certain proves what was previously uncertain. Is not this just what we do in speaking? Again are not the problems of geometry almost entirely solved by the syllogistic method, a fact which makes the majority assert that geometry bears a closer resemblance to logic than to rhetoric? But even the orator will sometimes, though rarely, prove his point by formal logic.

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. But this is false, for everything depends on the shape of the figure formed by these lines,

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.