# A Course of Mathematics: Composed for the Use of the Royal Military Academy

William Tegg, 1860 - Mathematics - 895 pages
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### Contents

 General Principles 1 5 MechanicsDynamical Part 5 Subtraction 12 Tables of Weights and Measures 21 Compound Subtraction 27 Golden Rule or Rule of Three 33 Vulgar Fractions 39 Addition of Vulgar Fractions 45
 Piling of Balls and Shells 326 Investigation of Binomial Theorem 332 Exponential Equations 340 Interest and Annuities 346 29 358 Definitions 650 Problems 659 Solid Geometry 666

 Division of Decimals 52 Evolution 58 Integration of Differentials of Punc 62 To Extract the Cube Root 62 Definitions and Yotation 84 Subtraction 92 Division by Detached Coefficients 108 Least Common Multiple 115 Extraction of Roots 127 Binomial Theorem 172 Ratios and Proportion 185 EquationsPreliminary Remarks 196 Page 227 Nature of Equations 274 Transformation of Equations 280 Budans Criterion 292 Horners Method of Resolving 301 Progressions 311 Permutations and Combinations 318 27 325
 Spherical Geometry 675 Problems in Maxima and Minima 492 682 Definitions 689 Practical Questions in Mensuration 557 706 Introduction and Definitions 712 Construction of Trigonometrical Maxima and Minima 720 Use of Subsidiary Angles 728 Problems in Trigonometrical Survey 749 SPHERICAL TRIGONOMETRY 758 Integration by Parts 762 Integration of Irrational Functions 771 on Exponential Functions 786 Integration by Series 795 MECHANICSSTATICAL PART 803 Exercises on Forces 809 The Pulley 815 Examples on the Mechanical Powers 821 The Centre of Gravity 833 Resistance of Fluids 893

### Popular passages

Page 338 - EC, have also the same altitude ; and because triangles of the same altitude are to each other as their bases, therefore the triangle ADE : BDE : : AD : DB, and triangle ADE : CDE : : AE : EC.
Page 354 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Page 332 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Page 21 - OF TIME. 60 Seconds = 1 Minute. 60 Minutes = 1 Hour. 24 Hours = 1 Day. 7 Days = 1 Week. 28 Days = 1 Lunar Month.
Page 344 - CD. conseconsequently the whole polygon, or all the triangles added together which compose it, is equal to the- rectangle of the common altitude CD, and the halves of all the sides, or the half perimeter of the polygon. Now, conceive the number of sides of the polygon to be indefinitely increased ; then will its perimeter coincide with the circumference of the circle, and consequently the altitude CD will become equal to the radius, and the whole polygon equal to the circle. Consequently the space...
Page 303 - The Height or Altitude of a figure is a perpendicular let fall from an angle, or its vertex, to the opposite side, called the base.
Page 30 - Multiply the number in the lowest denomination by the multiplier, and find how many units of the next higher denomination are contained in the product, setting down ,what remains.
Page 62 - From these theorems may readily be found any one of these five parts ; the two extremes, the number of terms, the common difference, and the sum of all the terms, when any three of them are given, as in the following Problems : PROBLEM I.
Page 332 - Proportional, when the ratio of the first to the second, is equal to the ratio of the second to the third.
Page 62 - SUBTRACT the less extreme from the greater, and divide the difference by 1 more than the number of means required to be found...