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, 2. To draw a line through a given point and through the inter- To find the geometric mean between two given lines . To divide a given line so that the rectangle contained by its segments is equal to the square on a given line. To divide a line medially, or in extreme and mean proportion 8. To find graphically a series of terms in geometrical progression Given two ratios, to determine graphically their product To determine graphically the square root of any number To find the harmonic mean between two given lines. To find the third term of an harmonic progression, the first two To find a fourth proportional to three given lines To divide a line of given length similarly to a given divided 14. Through a given point to draw a line meeting two given lines 15. To draw a triangle with its sides passing through three given points and its vertices on three concurrent lines 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 16. 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 26. To describe a circle to pass through three given points 21. To describe a circle to pass through two given points and to To describe a circle to pass through a given point and to touch To describe a circle to touch three given lines To describe a circle to touch a given circle and a given straight ib. 23 ib. 36. To describe a parabola with given focus and directrix To describe a circle to touch three given circles. To draw a circular arc through three given points without using To describe a parabola with given focus and to pass through To describe a parabola with given focus, to pass through a given point and to touch a given line 42. To describe a parabola with given focus and to touch two given |