In England two noteworthy attempts have been made within a century, looking to a more satisfactory sequence and selection of propositions than is found in Euclid. Each began with a list of propositions arranged in proper sequence, and each was thereafter elaborated into a textbook. Neither accomplished fully the purpose intended, but each was instrumental in provoking healthy discussion and in improving the texts from which geometry is studied. The first of these attempts was made by Professor Augustus de Morgan, under the auspices of the Society for the Diffusion of Useful Knowledge, and it resulted in a textbook, including "plane, solid, and spherical" geometry, in six books. According to De Morgan's plan, plane geometry consisted of three books, the number of propositions being as follows: Book I. Rectilinear figures 60 Book II. Ratio, proportion, applications 69 Book III. The circle 65 ---- Total for plane geometry 194 Of the 194 propositions De Morgan selected 114 with their corollaries as necessary for a beginner who is teaching himself. In solid geometry the plan was as follows: Book IV. Lines in different planes, solids contained by planes 52 Book V. Cylinder, cone, sphere 25 Book VI. Figures on a sphere 42 ---- Total for solid geometry 119 Of these 119 propositions De Morgan selected 76 with their corollaries as necessary for a beginner, thus making 190 necessary propositions out of 305 desirable ones, besides the corollaries in plane and solid geometry. In other words, of the desirable propositions he considered that about two thirds are absolutely necessary. It is interesting to note, however, that he summed up the results of his labors by saying: It will be found that the course just laid down, excepting the sixth book of it only, is not of much greater extent, nor very different in point of matter from that of Euclid, whose "Elements" have at all times been justly esteemed a model not only of easy and progressive instruction in geometry, but of accuracy and perspicuity in reasoning.