how do mystical writers interpret the 47th proposition of euclid in craft masonry

The 47th Proposition of Euclid, represented in the Master Mason degree by the right-angled triangle with sides in the ratio of 3, 4, and 5, is interpreted mystically through its connection to ancient Egyptian cosmology and the teachings of Pythagoras 1.

In this reading, the triangle symbolizes universal nature and the generative principles of creation 1. The perpendicular side, measuring three parts, represents Isis or the female principle; the base of four parts represents Osiris or the male principle; and the hypotenuse of five parts signifies Horus, the offspring or product resulting from the union of the two 1. Mathematically, this mirrors the esoteric concept that the product of the male and female principles generates the divine offspring, corresponding to the rule that the sum of the squares of the two shorter sides equals the square of the hypotenuse 1.

Beyond the triadic deity concept, the geometric components of the symbol—the triangle and the square—carry additional esoteric meaning 1. The triangle or delta represents Deity, active force, and the divine or higher nature of humanity, whereas the square signifies passive matter, the material world, and humanity itself 1. The elevation or dominance of the divine force over material matter signifies that the higher portion of human nature should increase in power and govern baser tendencies 1.

Masonically, the adoption of this emblem serves as a memento instructing Masons to be lovers of the arts and sciences, honoring the devotion to learning demonstrated by ancient initiates who preserved these mathematical and divine truths 1.