TODHUNTER.-Works by I. Todhunter, M.A.-Continued. A TREATISE on the INTEGRAL CALCULUS. Third Edition, revised and enlarged. With Examples. Crown 8vo. cloth, 10s. 6d. A TREATISE on ANALYTICAL STATICS. With Examples. Third Edition, revised and enlarged. Crown 8vo. cloth, IOS. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the ALGEBRA. Edition. Fourth This work contains all the propositions which are usually included in elementary treatises on Algebra, and a large number of Examples for Exercise. The author has sought to render the work easily intelligible to students without impairing the accuracy of the demonstrations, or contracting the limits of the subject. The Examples have been selected with a view to illustrate every part of the subject, and as the number of them is about Sixteen hundred and fifty, it is hoped they will supply ample exercise for the student. Each set of Examples has been carefully arranged, commencing with very simple exercises, and proceeding gradually to those which are less obvious. For Schools and Colleges. Third Edition. Crown 8vo. cloth, 5s. The design of this work has been to render the subject intelligible to beginners, and at the same time to afford the student the opportunity of obtaining all the information which he will require on this branch of Mathematics. Each chapter is followed by a set of Examples; those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously reserved by the student for exercise after he has made some progress in the subject. In the Second Edition the hints for the solution of the Examples have been considerably increased. A TREATISE ON SPHERICAL TRIGONOMETRY. Crown 8vo. cloth, 4s. 6d. This work is constructed on the same plan as the Treatise on Plane Trigo EXAMPLES of ANALYTICAL GEOMETRY of THREE 7s. 6d. WILSON-ELEMENTARY GEOMETRY FOR SCHOOLS. PART I. The Angle, Triangle, Parallels, and Equivalent Forces, with the Application of Problems. By J. M. WILSON, M.A., Fellow of St. John's College, Cambridge, and Assistant Master in Rugby School. [In the Press. A TREATISE on DYNAMICS. By W. P. WILSON, M.A., WOLSTENHOLME.-A BOOK of MATHEMATICAL PROB- CONTENTS: Geometry (Euclid).-Algebra.-Plane Trigonometry.-Conic Sections, Geometrical.-Conic Sections, Analytical.-Theory of Equations. -Differential Calculus.-Integral Calculus.-Solid Geometry -Statics.Dynamics, Elementary.-Newton.-Dynamics of a Point.-Dynamics of a Rigid Body.-Hydrostatics.-Geometrical Optics.-Spherical Trigonometry and Plane Astronomy. In each subject the order of the Text-Books in general use in the University of Cambridge has been followed, and to some extent the questions have been arranged in order of difficulty. The collection will be found to be unusually copious in problems in the earlier subjects, by which it is designed to make the work useful to mathematical students, not only in the Universities, but in the higher classes of public schools. SCIENCE. GEIKIE.-ELEMENTARY LESSONS in PHYSICAL GEOLOGY. BY ARCHIBALD GEIKIE, F.R.S., Director of the Geological Survey of Scotland. [Preparing. HUXLEY.-LESSONS in ELEMENTARY PHYSIOLOGY. With numerous Illustrations. By T. H. HUXLEY, F.R.S., Professor of Natural History in the Royal School of Mines. Fifth Thousand. 18mo. cloth, 4s. 6d. "It is a very small book, but pure gold throughout. There is not a waste sentence, or a superfluous word, and yet it is all clear as daylight. It exacts close attention from the reader, but the attention will be repaid by a real acquisition of knowledge. And though the book is so small, it manages to touch on some of the very highest problems. . . . . The whole book shows how true it is that the most elementary instruction is best given by the highest masters in any science."-Guardian. "The very best descriptions and explanations of the principles of human physiology which have yet been written by an Englishman.”—Saturday Review. With centre A and distance AB describe a circle, in which place BD = AC. Join AD; ABD is the triangle required. Join DC. ABD, DBC are similar triangles IV. 4. And therefore DC=DB= AC, whence CAD CDA, and ABD DCB= twice CAD. = 9. To inscribe a regular pentagon in a given circle. The inscription of a regular figure in a circle depends upon our being able to divide the circumference into as many equal parts as the figure has sides. We have seen how to divide a circumference into 3 parts or 4 parts, and since every arc can be bisected, we can divide a circumference into 6, 12, 24, &c. or 8, 16, 32, &c. parts. The preceding construction gives us an angle CDB equal to one-fifth of two right angles. If therefore DC be produced to meet the circumference, it will intercept one-fifth part of it, Complete the construction. 10. To inscribe a regular decagon in a given circle. 11. To inscribe a regular quindecagon in a given circle. 12. On a given straight line to construct a polygon similar to a given polygon. 13. To inscribe a square in a triangle. 14. To inscribe a square in a given segment of a circle. 15. To describe a circle touching two straight lines and passing through a fixed point. 16. To describe a circle touching a straight line and passing through two fixed points. 17. To divide a triangle into two parts in the ratio of two given lines by a line drawn parallel to its base. 18. To produce a line AB to C so that AB, AC may be equal to a given square. 19. To construct a rectangle equal to a given square, and such that the difference of its sides may be equal to a given straight line. 20. To construct a figure similar to either of two given similar figures, and equal to their sum or their difference. 21. To construct a figure equal to one and similar to another given figure. 1. O is a point within the angle ACB. To draw through O a straight line AOB, so that it may be bisected in 0. 2. A and B are two points on the same side of the straight line CD. Find in CD a point P such that PA+ PB may be the least possible. 3. In the figure of III. 12 shew that AL, CF, BK pass through one point. 4. An equilateral triangle is inscribed in a circle, if the intercepted arcs be bisected and the points of bisection joined, the sides of the triangles are trisected, 5. Through four given points to draw lines forming a square. 6. Shew that the circumference of a circle is more than three times and less than four times as great as the diameter. 7. Draw from the vertex of a triangle a line to the base such that it may be a mean proportional between the segments of the base. 8. AB is the diameter of a circle, DE a chord, OP a perpendicular on AB from any point 0 of DE. Shew that AP.PB=DO. OE+ OP2. 9. The part of a variable tangent intercepted between two fixed tangents subtends a constant angle at the centre. 10. ABC is a triangle. AD, BE, CF are lines drawn through one point O to meet the opposite sides. Shew that AF.BD.CE=FB.DC. EA. 11. The common tangents to two circles meet in a point O; and through O a chord OKGMN is drawn meeting the circumferences in K, G, M and N. Shew that OK. ON OG. OM. = 12. Given the perpendiculars to construct the triangle. CAMBRIDGE: PRINTED AT THE UNIVERSITY PRESS. |