# A Course of Mathematics: For the Use of Academies, as Well as Private Tuition ...

S. Campbell & son, E. Duyckinck, 1822 - Mathematics

### Contents

 GENERAL Principles 1 Roman Notation 7 Multiplication 13 Reduction 23 Compound Addition 32 Golden Rule or Rule of Three 44 Vulgar Fractions 51 Addition of Vulgar Fractions 61
 Piling of Balls 223 Simple Equations 230 Quadratic Equations 249 Resolution of Cubic and Higher Equations 257 Simple Interest 266 GEOMETRY 275 AxiomsTheorems 281 Of Ratios and Proportions 319

 Subtraction of Vulgar Fractions 62 Subtraction of Decimals 68 Rule of three in Decimals 76 Ratios Proportions and Progressions 110 Musical Proportion 119 Compound Interest 127 Single Position 135 Practical Questions 150 To compute Logarithms 159 Multiplication by Logarithms 167 Addition 175 Multiplication 181 Algebraic Fractions 188 Involution 199 Surds 206 Infinite Series 213
 Of Planes and SolidsDefinitions 336 Problems 353 Applications of Algebra to Geometry 369 Plane Trigonometry 377 Heights and Distances 393 Mensuration of Planes 402 Mensuration of Solids 419 Land Surveying 429 Artificers Work 458 Timber Measuring 486 466 Of the Ellipse 473 Of the Hyperbola 491 Of the Parabola 514 Of the Conic Sections as expressed by Algebraic equations called 532 Problems relative to the Divison of Surfaces 558 Construction of Geometrical Problems 571

### Popular passages

Page 312 - THE angle formed by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment.
Page 292 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 2 - The sum of the three angles of any triangle is equal to two right angles, this is a Theorem, the truth of which is demonstrated by Geometry.
Page 189 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 293 - EBF, there are two angles in the one equal to two angles in the other, each to each ; and the...
Page 18 - The number to divide by, is the Divisor.- — And the number of times the dividend contains the divisor, is called the Quotient.
Page 280 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.
Page 157 - Thus, the index or logarithm of 4, in the above series, is 2 ; and if this number be multiplied by 3, the product will be = 6 ; which is the logarithm of 64, or the third power of 4. And, if the logarithm of any number be divided by the index of its root, the quotient will be equal to the logarithm of that root.
Page 81 - Distinguish the given number into periods of two figures each, by putting a point over the place of units, another over the place of hundreds, and so on over every second figure, both to the left hand in integers, and to the right hand in decimals, which points will show the number of figures the root will consist of.
Page 278 - A Pentagon is a polygon of five sides ; a Hexagon, of six sides ; a Heptagon, seven; an Octagon, eight; a Nonagon, nine ; a Decagon, ten ; an Undecagon, eleven ; and 4 Dodecagon, twelve sides.