short, the adoption of the first proposition would be tantamount to the rejection of all that has been proved in Geometry. The propositions in Geometry would, in this respect, be divided into two classes: some would be absolutely rejected; e.g., those which relate to properties of the incommensurability and the commensurability of lines and planes, to rational and irrational lines, and all other propositions contained in the tenth book of Euclid, and in similar works. Other propositions would appear to be only partially correct; e.g., the solution of the problem to divide a line into two equal parts, if the line consists of an odd number of atoms; according to the theory of the Mutakallemim such a line cannot be bisected. Furthermore, in the well-known book of problems by the sons of Shakir are contained more than a hundred problems, all solved and practically demonstrated; but if there really were a vacuum, not one of these problems could be solved, and many of the waterworks [described in that book] could not have been constructed. The refutation of such propositions is a mere waste of time. I will now proceed to treat of the other propositions mentioned above. Fourth Proposition. “The accidents of things have real existence; they are elements superadded to the substance itself, and no material thing can be without them.” Had this proposition been left by the Mutakallemim in this form it would have been correct, simple, dear, and indisputable. They have, however, gone further, asserting that a substance which has not the attribute of life, must necessarily have that of death; for it must always have one of two contrasting properties. According to their opinion, colour, taste, motion or rest, combination or separation, etc., can be predicated of all substances, and, if a substance have the attribute of life, it must at the same time possess such other kinds of accidents, as wisdom or folly, freewill or the reverse, power or weakness, perception or any of its opposites, and, in short, the substance must have the one or the other of all correlative accidents appertaining to a living being. Fifth Proposition.