THE 47TH PROPOSITION OF EUCLID Among the enduring emblems by which Freemasonry has expressed its reverence for geometry and disciplined reason, the Forty-Seventh Proposition of Euclid occupies a distinguished place. The proposition concerns the right-angled triangle, and declares that the square constructed upon its longest side is equal in area to the two squares constructed upon the remaining sides. In familiar mathematical form, a^2 + b^2 = c^2. Number and geometrical form here reveal the same proportion under different expressions, and the human intellect is capable of discerning the law which governs them. Its Hermetic significance arises from this intelligibility of nature. The heavens, the proportions of bodies, the motions of celestial spheres, and the structures discovered by geometry all testify to a cosmos governed by relation, measure, and law. Number gives these relations abstract expression; geometry gives them visible form. Together they furnish the mind with instruments by which the order of creation may be contemplated. From this conception of natural law proceeds the moral lesson. Man belongs to the same ordered universe which he studies. His conduct therefore possesses measure, consequence, and proper relation. Justice establishes due proportion between persons; temperance governs appetite by measure; fortitude preserves order within the soul; prudence discerns the proper relation between means and ends. The Forty-Seventh Proposition thus becomes a fitting Masonic emblem of cosmic and moral order: a geometrical truth through which the mind perceives law in nature, and from that law derives a pattern for the disciplined government of life.