We need not quarrel with this valuation, but we would point out that there is an omission in it. The scientific man is an instrument, but he is an indispensable instrument. The human race has endured all the different “new directions” given to it by the “true” philosophers of the past without any marked increase in its spiritual stature. The philosopher, however commanding, who would really lead us in any but a circular direction must have _knowledge_. This knowledge, to be valuable, must be clear and trustworthy; it must be scientific. And if the inspirations and impulses of our leaders should prove to be incompatible with deductions from scientific knowledge, then we may be sure that the Promised Land does not lie their way. The scientific man is merely an instrument. But it is this instrument alone that can show to mankind which, of all the goals it desires, are possible goals, and which, of all the leaders it trusts, are trustworthy leaders. The scientific man is an instrument, but it is by this instrument that those who would use it are first tested. Scientific knowledge is, if you like, as dispassionate and inhuman as is the universe with which it concerns itself--and it can as little be ignored. PARALLEL STRAIGHT LINES Geometry, it has been satisfactorily shown, had a purely empirical origin. It appears that the earliest geometrical formulæ which have been discovered belong to ancient Egypt, and that all these formulæ served a useful purpose. The oldest of them are concerned with the measurements of areas, a class of problem which the yearly sinking of the Nile rendered of great importance. The formulæ obtained by the ancient Egyptians were usually wrong, although they were approximately correct; they evidently rested on no theoretical basis, but were compendious statements of the results of somewhat rough measurements, a point of view which is borne out by the fact that no proof, nor even an attempt at a proof, is anywhere hinted at. So far as the evidence goes, it seems to be established that geometry, as consisting of logical deductions from stated premises, began with the Greeks. A number of theorems of a fair degree of complexity had been developed before they were reduced to a system; before, that is, the assumptions on which they were based were made explicit. The task of discovering the necessary and sufficient assumptions on which a system of geometry rests is one of the greatest difficulty; the necessary combination of subtlety and rigour is rare. The great systematisation of Greek geometry was effected, of course, by Euclid, and although his reduction of the system to its essential assumptions was not final, his performance was such as to awaken the admiration of great mathematicians in every succeeding century. But there is one point in which this great reduction is notably imperfect--the so-called parallel axiom. It says, essentially, that through a given point only one line