central feature of this triangle, upon which its property is based, is the Right Angle. The Greeks gave to this Right Angle the name of _Gnomon_ (meaning Knowledge), and it has ever since been, under the form of a carpenter's "square," the emblem or symbol of an Architect, the Master Mason, as personifying the Great Architect of the Universe--namely, He who has the knowledge of Geometry; and, as the Right-Angled Triangle represented the Universe, it was upon the _perfection_ of this Gnomon, or knowledge, that the very existence of the Universe depended, because the law of the three squares only holds good when that angle is perfect. The Secret handed down in the Craft, from Architect to Architect, was how to form a perfect right angle, or, as it was called, the "Square," without possibility of Error, and this I have called "the Knowledge of the Square." Vitruvius, who, at the beginning of our Era, wrote his thesis on Tectonic art, which is still the text-book of Architecture for Ancient buildings, says Pythagoras taught his followers to form a gnomon, or square, as follows: "Take three rods, of three lengths, four lengths, and five lengths long; with these form a triangle, and, if each rod be squared, you have 9, 16, and 25, and the areas of the two former will be equal to the latter." Now let us come to the closing years of the tenth century. What a strange condition of the building craft was to be seen all over Europe; not a church was being built, nor had been built, for the last twenty years; the thousand years after Christ was drawing to its close, everybody was waiting for, and expecting, the world to come to an end; no new undertakings were begun. How much money went into the hands of the Monasteries and other Religious Houses, as peace offerings for the future welfare of the givers, nobody can say; it was probably enormous. When, however, the eleventh century was well started and the crisis was over, churches were built on a large scale, as shown by the numerous remains we have of Norman buildings of the last half eleventh century, and building was probably at its height about A.D. 1140 to 1150; but at this period an extraordinary thing happened. Hitherto the arches in the Norman style were round-headed and their columns enormously thick to carry them; but suddenly the style changed into the beautiful Gothic all over Europe. No single country can claim precedence, it was almost simultaneous; churches half finished in the round style were not only completed in the pointed, but had parts already built altered to the new style. What, then, determined this sudden change, resulting in a wonderful accession of beauty to Architectural design? We must go to the Monasteries and Religious Houses to find the explanation. These Houses had become the Patrons of Masonry, the providers of the funds for building Cathedrals, &c.; it naturally followed that, growing up alongside the Operative Science, there was a Religious symbolism being