without referring to any special treatise on Projection. The ordinary pseudo-perspective diagrams usually given in books on Conics are I think unsatisfactory, and the method of referring the solid to two rectangular planes seems to me in every way preferable. When the mental conception of a plan and elevation is once thoroughly realised the student is well repaid by the exactness with which he is able to lay down on paper any point or line on the surface of the cone. The later chapters cannot be read without some knowledge of trigonometry, but the practice of translating a trigonometrical expression into something which can be represented to the eye is a valuable one, and the hints given in the chapter on the Graphic Solution of Equations will I trust be found useful. My warmest thanks are due to my friend and colleague Professor Minchin for much valuable advice and assistance most freely and readily given: without his help the book would have been much less complete than it is, whatever its imperfections may be found to be. It would be too much to hope that a work of this character should have been compiled and gone through the press without some errors creeping in. I hope they are not more numerous than from the nature of the case may be considered unavoidable, and I shall be thankful for any such being brought to my notice. COOPERS HILL, Oct. 1885. TABLE OF CONTENTS. To divide a line of given length similarly to a given divided 8. 9. To divide a line medially, or in extreme and mean proportion To find graphically a series of terms in geometrical progression Given two ratios, to determine graphically their product 14. Through a given point to draw a line meeting two given lines 19 16. To draw a triangle with its vertices on three given lines and its 17. To determine the locus of the vertex of a triangle on a given To construct a rectangle equal in area to the sum or difference 19. From a given point P in a given straight line PM, to draw lines making equal angles with PM and cutting a second given line CM at equal distances from C ib. 23 26. To describe a circle to touch a given circle and a given straight ib. |