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

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

 ARITHMETIC 1 Reduction 14 Tables of Weights and Measures 21 Compound Subtraction 27 Golden Rule or Rule of Three 33 Vulgar Fractions 39 Addition of Vulgar Fractions 45 Division of Decimals 52
 Parabola 449 Ellipse 457 Hyperbola 472 Application of Algebra to Geometry 487 PLANE TRIGONOMETRY 493 Application to Heights Distances 504 Mensuration of Planes 510 Mensuration of Solids 520

 Evolution 58 Ratios Proportions Progressions 65 ALGEBRA 84 Multiplication 95 Division by Detached Coefficients 108 39 120 48 126 88888 154 95 163 109 175 115 182 172 201 185 243 197 256 merical Equations of all Orders 301 Inequations 308 Piling of Balls and Shells 326 Logarithms 335 Interest and Annuities 346 Definitions 357 Problems 403 Exercises in Plane Geometry 417 Solid Angles 427 Spherical Geometry 442
 Artificers Works and Timber Mea 548 Practical Questions in Mensuration 557 General Formul� 574 Formul� for the Solution of Triangles 588 Use of Subsidiary Angles 608 Of Three Dimensions 673 Definitions 689 Inverse Functions 706 Examples in differentiation 712 Maxima and Minima 720 Method of Least Squares 726 Method of Limits 749 Integration by Parts 762 Integration of Rational Functions 771 Integration by Series 795 Definitions Fundamental Notions 803 The Pulley 815 Examples on the Mechanical Powers 821 Equilibrium of Pier and Arch 831 Centres of Percussion Oscillation 861 MISCELLANEOUS SUBJECTS 868 The Pump 887 Measurement of Altitudes by 892

### Popular passages

Page 336 - 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 352 - 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 330 - 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 17 - OF TIME. 60 Seconds = 1 Minute. 60 Minutes = 1 Hour. 24 Hours = 1 Day. 7 Days = 1 Week. 28 Days = 1 Lunar Month.
Page 342 - 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 301 - 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 26 - 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 330 - 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...