ELEMENTS of geometry are by no means numerous in this country, a circumstance to be attributed to the almost universal preference given to Euclid; not, indeed, because the elements of Euclid is a faultless performance, but because its blemishes are so inconsiderable when compared with its extraordinary merits, that to reach higher perfection in this department of science has been generally supposed to be scarcely within the bounds of possibility, an opinion which the fruitless efforts of succeeding geometers to establish a better system have in a great measure confirmed. The superiority of Euclid's performance consists chiefly in the rigorous and satisfactory manner in which he establishes all his assertions, preferring in every case the most elaborate reasoning rather than weaken the evidence of his conclusions by the introduction of the smallest assumption. On the continent, however, this high opinion of Euclid does not appear to prevail, and the rigour and elegance of his demonstrations seem to be less appre |