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THE EARLY CHRISTIANS; THEIR MANNERS AND CUSTOMS, TRIALS AND SUFFERINGS. LIVES OF EMINENT CHRISTIANS. By R. B. HONE, M.A., Vicar of Hales Owen. Foolscap Octavo, Three Volumes, at 4s. 6d. each. LIVES OF ENGLISH SACRED POETS. With an INTRODUCTORY SKETCH of EARLY SACRED POETRY and POETS. DESCRIPTIVE GEOMETRY. 1. THE object of Descriptive Geometry is the invention of methods by which we may represent upon a plane, having only two dimensions, length and breadth, the form and position of a body which possesses three dimensions, length, breadth, and height. This definition of the chief object of descriptive geometry includes its application to points and lines situated above or below the plane, to which they are to be referred; and thus gives us means of drawing such lines and points with an accuracy unnecessary and unknown to common geometry. For the results obtained in plane geometry do not depend upon the faithfulness with which the figures are drawn, but upon the accuracy with which the reasoning is conducted. But even in these problems we often make assumptions with regard to the mechanical drawing of lines, which we should find it extremely difficult to execute. Thus in Proposition XI. of the Introduction we say, draw AD BC; but the practical difficulty of drawing AD is as great as that of drawing aн, the object of the problem. The means by which descriptive geometry attains ita object is the method of Projections, which we now prosset to explain. 2. The projection of a point upon a plane is the ins of the perpendicular let fall from the pond wor TR. plane. |