COURSE MATH E MATIC S. IN TWO VOLUMES. COMPOSĖD FOR THE USE OF THE ROYAL MILITARY ACADEMY. BY CHARLES HUTTON, LL.D. F.R.S. LATE PROFESSOR OF MATHEMATICS IN THAT INSTITUTION. VOL. II. THE ELEVENTH EDITION, WITH MANY CORRECTIONS AND IMPROVEMENTS. BY OLINTHUS GREGORY, LL.D. F.R.A.S. Society of New York, of the New York Historical Society, of the Literary and Philosophical, and the LONDON: PRINTED FOR LONGMAN, Rees, & co.; T. CADELL; J. RICHARDSON ; J. M. RICHARDSON; BALDWIN & CRADOCK; J. G. & F. RIVINGTON ; BOOKER & DOLMAN; HARDING & co. ; CONTENTS ELEMENTS of Isoperimetry............... Analytical Plane Trigonometry ......... 17 Plane Trigonometrical Surveying ...... Spherical Trigonometry, in seven sec- tions .................................... Principles of Polygonometry ............ The Conic Sections ......................, The Ellipse, in two sections ............ Geodesic Operations, in three sections 156 The Geometry of Co-ordinates ........ 185 The Doctrine of Fluxions ............... 203 Mechanics .............................. Statics Parallelogram of Forces Mechanical Powers ........................ The Centre of Gravity ..................... Equilibrium of Structures; as Beams Pressure of Earth against Walls ... 288 Collision of Spherical Bodies ............ 312 The Laws of Gravity .......... Projectiles in a Non-resisting Medium Descents on Inclined Planes .......... Centres of Oscillation, Percussion, and Gyration .......... ................ 344 Ballistic Pendulum ....................... Hydrostatics ............................. Specific Gravity ............................ Buoyancy of Pontoons .................... Practical Exercises in Hydrostatics, &c. 383 Weight and Dimensions of Balls and .................................... 385 Distances by the Velocity of Sound ... 387 Exercises in Mechanics, &c. ............ 388 Practical Exercises concerning Forces 391 Motion of Bodies in Fluids ............... 412 APPENDIX-Elements of the Differen- tial Calculus .......................... 423 Functions and Differentials............... Differential Coefficients, &c. ............ Differentiation of Transcendental Func- Differentiation of Circular Functions ... 445 Vanishing Fractions ........................ 450 Maxima and Minima ..................... 454 2n 74 334 339 48, in the answer to Question 1, inclose a + B, and ß +y in vincula. 61, note, for c read C throughout. 78, Ex. 5, for wall read ball. 80, line 30, for some read same. 191, Ex. 10, for cos. read cos. Os and in i °; and in Ex. 12, for straight is, read straight line is. 193, for Chapter II. read Chapter III. 195, for Chapter III. read Chapter IV. 197, for Chapter IV. read Chapter V. 213, line 12, for function read fluxion. 315, in the diagram, for A, B, C, read B, 6, C. 331, line 8 from bottom, for g :- 400, line 5 from bottom, for (2 rx — x2 X, read (2 r x — 2) x. 405, line 9 from bottom, for 240 oz. 15 lb., read 240 oz. or 15 lb. 426, bottom line, for d z, read A %. 431, line 9, for fractions, read functions. PREFACE TO THE SECOND VOLUME. In this New Edition of the Woolwich Course, the substance of the second and third volumes of the former Edition is, by a new arrangement, incorporated into one. The matter, also, of several portions of the volume is entirely remodified ; and my colleague, Mr. Davies, has been at the pains considerably to enlarge the part which relates to the Conic Sections; as well as to prepare a sketch of the Geometry of Co-ordinates. The doctrine of Fluxions is now introduced before the subject of Mechanics, a change which has enabled me to improve that department by introducing various propositions which could only be treated adequately by the fluxionary or an analogous calculus. I had intended to attempt a concise sketch of the Elements of the Differential Calculus, according to my own view of the principle of limits, first defining the sense in which the term limit may be unobjectionably employed, and then, as occasion required, resorting to the familiar axiom, that “what is true up to the limit, is true at the limit;" but a very serious and continued indisposition, which commenced just at the time this should have been undertaken, compelled me to adopt another course. I got one of my own family to translate the Lehrbuch des Höhern Kalkuls, für Lehrer und Selbstlernende, of S. F. LUBBE of the University of Berlin : not because it was in all respects so satisfactory as I could have wished, for it sometimes falls into the paralogisms of various other authors in this department of science; but because several of its processes of investigation are both elegant and complete; and because it was |