the hypothenuse of a right-angled triangle and the lengths of the sides? We are now so familiar with the solution, we have so mechanicalized the process by which the answer is arrived at, that the significance of both escapes us. But let us place ourselves, in imagination, back at the time when the question was as yet nsolved and was being eagerly investigated. In studying the earlier problems of Euclid, questions about lengths of lines are settled by striking circles with compasses (which is virtually a process of measuring); and questions of area, etc., by superposition. Everything is referred to certain axioms which act as a hurdle set up for the purpose of giving children the exercise of climbing over it. The formal Logic in the beginning of Euclid exercises a certain mental agility; but everything which is really found out, is found out by trusting to the evidence of our senses aided by some mechanical process.
But when we attempt to find a relation between the hypothenuse and sides of a right-angled triangle, all modes of measurement fail to show any fixed relation, and appear even to show that none exists. Those who were satisfied that nothing was valid except the evidence of the recognized instruments probably asserted that the existence of any fixed relation was disproved.
But there were true Free-Masons in those days, or rather there were Free Geometers, the founders of Free-Masonry; bold, untamable spirits, who dared invoke the All-Seeing Eye of the Great Unity to enlighten their blindness; and who well knew that rules limiting the play of the human intellect were made, chiefly, to be defied. They claimed the right to seek Truth outside the limits marked by orthodox compasses; they
