Works of Philo of Alexandria

Philo — Works Vol. I, Yonge — Section 48

The rectangular tinangle, which is the beginning of all qualities, consists of the numbers three* and four, and five ; and the three and the four, which are the essence of the seven, contain the right angle ; for the obtuse angle and the acute angle show irregularity, and disorder, and inequality; for one may be more acute or more obtuse than another. But a right angle does not admit of comparison, nor is one right angle more a right angle than another : but one remains similar to another, never changing its peculiar nature. But if the right-angled triangle is the beginning of all figures and of all qualities, and if the essence of the number seven, that is to say, the numbers three and four together, supply the most necessary part of this, namely, the right angle, then seven may be rightly thought to be the fountain of every figure and of every quality. And besides what has been already advanced, this also may be as- serted that three is the number of a plane figure, since a point has been laid down to be, according to a unit, and a line ac- cording to the number two, and a plane superficies according to * This discussion about numbers is not very intelligible ; but here Philo is probably referring to the problem of Euclid on the subject of the square of the hypothenuse. Thus, if 3 and 4 represent the sides containing the angle, and 5 the side subtending it, we get 3x3= 9 5x5=25. 4x4=16 25. and ON THE CREATION OF THE WORLD. 29 to the number three. Also, four is the number of a cube, by the addition of one to the number of a plane superficies, deptli being added to the superficies. From which it is plain that the essence of the number seven is the foundation of geometry and trigonometry ; and in a word, of all incorporeal and corpo- real substances.