wife with loud adulation and Bacchanalian rejoicings to the insulted Church of Notre Dame, thus publicly disowning the God of the Universe and discarding the sweetest of all hopes, the hope of immortality and eternal youth after the weariness of age, would be found to be very small.  This was indeed a new version of the old story of Godiva, wherein implacable, inhuman hate sadly enough took the place of the sweet Christian charity of that dear lady.  Let us recognize its deep significance, and acknowledge that many things of very great importance lie beyond the utmost limits of human reason.

But let us not forget, meanwhile, that within its own sphere this same Human Reason is an apt conjuror, marshalling and deftly controlling the powers of the earth and air to a degree wonderful and full of interest.  And nowhere have all its possibilities so fully found expression in vast attainment as in those studies preeminently called the mathematics, as embracing all [Greek:  mathaesis], all sound learning.  Casting about for some sure anchorage, drifting hither and thither over changeful seas of phenomena, a large body of men, deep, clear thinkers withal, some twenty-four centuries since, fancied that they had found all truth in the fixed, eternal relations of number and quantity.  Hence that wide-spread Pythagorean philosophy, with its spheral harmonics and esoteric mysteries, uniting in one brotherhood for many years men of thought and action,—­dare we say, our inferiors?  Why allude to the old fable of the dwarf upon the giant’s shoulders?  Let us have a tender care for the sensitive nature of this ultimate Nineteenth Century, and refrain.  They were not so far wrong either, those old philosophers; they saw clearly a part of the boundless expanse of Truth,—­and somewhat prematurely, as we believe, pronounced it the true Land’s End, stoutly asserting that beyond lay only barren seas of uncertain conjecture.

But mark what followed!  Presently, under their hands, fair and clear of outline as a Grecian temple, grew up the science of Geometry.  Perfect for all time, and as incapable of change or improvement as the Parthenon, appear the Elements of Euclid, whose voice comes floating down through the ages, in that one significant rejoinder,—­“Non est regia ad mathematicam via.”  It is the reply of the mathematician, quiet-eyed and thoughtful, to the first Ptolemy, inquiring if there were not some less difficult path to the mysteries.  But the Greek Geometry was in no wise confined to the elements.  Before Euclid, Plato is said to have written over the entrance to his garden,—­“Let no one enter, who is unacquainted with geometry,”—­and had himself unveiled the geometrical analysis, exhibiting the whole strength and weakness of the instrument, and applying it successfully in the discussion of the properties of the Conic Sections.  Various were the discoveries, and various the discoverers also, all now at rest, like Archimedes, the greatest of them all, in his Sicilian tomb, overgrown with brambles and forgotten, found only by careful research of that liberal-minded Cicero, and recognized only by the sphere and circumscribed cylinder thereon engraved by the dead mathematician’s direction.