At the root of Socratic teaching was the idea that wisdom is the attribute of the Godhead, and Plato, for twenty years the companion and most favoured pupil of Socrates, was imbued with that doctrine, and, having arrived at the conclusion that the impulse to find out TRUTH was the necessity of intellectual man, he saw in Geometry the keystone of all Knowledge, because, among all other channels of thought, it alone was the exponent of absolute and undeniable truth. He tells us that "Geometry rightly treated is the Knowledge of the Eternal"; and Plutarch gives us yet another instance of Plato's teaching concerning this subject, in which he looks upon God as the Great Architect, when he says, "Plato says that God is always geometrising." Holding, therefore, as Plato did, that God was a great Geometer, and that the aim of philosophy was the acquisition of a knowledge of the Eternal, it is natural that he should make a knowledge of Geometry imperative on those wishing to study philosophy. This was continued also by those philosophers who succeeded Plato in the management of the Academy, as we are told that Zenocrates turned away an applicant for admission, who knew no geometry, with the words: [Greek: poreuou, labas gar ouk echeis tes philosophias.] "Depart, for thou hast not the _grip_ of philosophy." In connection with the idea that God was a Geometer, must be taken the contention held by the Egyptians, and after them the Greeks and Arabs, that the Right-Angled Triangle symbolised the nature of the Universe; it was called the law of the three squares, because in every Right-Angled Triangle, as expounded by the Pythagorean Theorem, the squares, formed on the two sides containing the Right Angle, must together be exactly equal to the square on the third side, whatever the shape of the triangle may be. The Right Angle at an early date gave its name to the odd numbers, which were called, by the Greeks, gnomonic numbers, as personifying the male sex, and the Right-Angled Triangle was also called the Nuptial Figure, or Marriage, the Pythagorean Theorem receiving the name, [Greek: to theorema tes nymphes] (the Theorem of the Bride). Plutarch, in his _Osiris and Isis_, tells us in explanation of this, "The Egyptians imagined the nature of the Universe like this most beautiful triangle, as Plato also seems to have done in his work on the _State_, when he sketches the picture of Matrimony under the form of a Right-Angled Triangle. That triangle contains one of the perpendiculars of three, the base of four, and the hypotenuse of five parts, the square of which is equal to the squares of those sides containing the right angle. The perpendicular (three) is the Male, Osiris, the originating principle ([Greek: arche]); the base (four) is the Female, Isis, the receptive principle ([Greek: hypodoche]); and the Hypotenuse (five) is the offspring of both, Horus, the product ([Greek: apotelesma])." The