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

Campbell, 1812 - Mathematics

### Contents

 GENERAL Principles 1 Roman Notation 7 Multiplication 13 Reduction 23 Compound Addition 32 Compound Proportion 49 Addition of Vulgar Fractions 61 55 Addition of Decimals 67 55
 Infinite Series 215 235 Piling of Balls 223 243 Simple Equations 230 250 Quadratic Equations 249 269 Resolution of Cubic and Higher Equations 257 277 Simple Interest 266 286 GEOMETRY 292 Definitions 275 319

 Reduction of Decimals 73 CONTENTS 77 Evolution 80 To extract the Square Root 81 101 To extract any Root whatever 88 108 Geometrical Progression 116 Double Fellowship 122 Alligation Medial 129 Single Position 135 Practical Questions 150 Definitions and Notation 171 To compute Logarithms 159 179 Multiplication by Logarithms 167 187 Subtraction 180 200 Algebraic Fractions 188 208 Involution 199 219 Surds 206 226
 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 Works 457 Timber Measuring 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 Division of Surfaces 558 Construction of Geometrical Problems 571

### Popular passages

Page 275 - 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 4 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...
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 300 - 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 285 - In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular.
Page 170 - When the index of the logarithm to be divided is negative, and does not exactly contain the divisor without some remainder, increase the index by such a number as will make it exactly divisible by the index, carrying the units borrowed, as so many tens, to the left-hand place of the decimal, and, then divide as in whole numbers. EXAMPLES. 1.
Page 292 - 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 347 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on. Hence a semicircle contains 180 degrees, and a quadrant 90 degrees. 58. The Measure of an angle is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.
Page 428 - BRICKLAYERS- WORK. — Brickwork is estimated at the rate of a brick and a half thick. So that, if a wall be more or less than this standard thickness, it must be reduced to it, as follows : — Multiply the superficial content of the wall by the number of half bricks in the thickness, and divide the product by 3. The...
Page 299 - Three quantities are said to be proportional when the ratio of the first to the second is equal to the ratio of the second to the third.