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Note-book on Practical Solid or Descriptive Geometry, containing Problems with help for Solutions

Nature volume 5, page 80 | Download Citation



WHEN our Civil and Military Engineering Examinations are daily making larger demands for geometrical proficiency a new and exceedingly lucid Note-book on Descriptive Geometry comes well-timed. Though much has been done to expand this collateral offshoot of geometrical science since M. Monge, of the Ecole Polytechnique, first started it, the co-ordinative characteristic of a science has hitherto been wanting; it has contained, doubtlessly, all the abstract principles of orthographic projection, but principles, to be available, must be interdependent and derivative. Messrs, Edgar and Pritchard have felt this deficiency, and have done much to remove it. Their book, unlike the majority of cheap hand-books, is neither “patchy nor scrappy,” but a continuous and coherent whole. “Elementary Explanations, Definitions, and Theorems” come first, followed by twenty-eight problems on “The Straight Line and Plane,” to these succeed Solids, first singly, and then in “Groups and Combinations.” In like logical order we next have “Solids with the inclinations of the plane of one face, and of one edge or line in that face given,” and then “Solids with the inclinations of two adjacent edges given,” and, lastly, in this category, “Solids with the inclinations of two adjacent faces given.” So far we have the principles of projection in a much more perfectly co-ordinated arrangement than we have hitherto found them in, and we must say that the mere act of mentally assimilating this interdependence of principles would be wholesome discipline, even if it did not, as it unquestionably does, facilitate each successive step in progress, and, most of all, conduce to an integral entertainment of the subject. Again, as naturally derivable from the consideration of the inclined faces of solids, we arrive at “Sections by oblique planes,” and “Developments,” or the spreading out in one plane of the adjacent faces of such solids; and, finally, the development of curved surfaces. “Miscellaneous Problems” now have place, and amongst them we notice one from the “Science Examinations” of last year. The sequence of the four next chapters is judicious. “Tangent Planes,” “Intersections of solids with plane surfaces,” “Intersections of solids with curved surfaces,” “Spherical Triangles.” A short chapter on Isometric Projection (quite as long as it deserves) ends the work, the authors of which we rejoice to find (in these days of “result-seeking”) much more desirous of results actual than results visible, and accordingly, foregoing a somewhat too popular profusion of diagrams, which, while it undoubtedly facilitates the bare apprehension of subject-matter, by no means enforces that comprehension of the subject which attends upon the act of accomplishing a mental diagram for ourselves. In this expression of their conviction the authors, we observe, are at one with Mr. Binns, who, with the same sincerity, and for like reason, resisted the systematic use of models in the teaching of “mechanical drawing.”

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