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

S. Cambell, 1818 - Mathematics
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### Contents

 GENERAL Principles 1 Roman Notation 7 Reduction 23 Compound Addition 32 Multiplication 38 Golden Rule or Rule of Three 44 Vulgar Fractions 51 Addition of Vulgar Fractions 61
 41 219 Piling of Balls 223 Simple Equations 230 Quadratic Equations 249 44 252 Resolution of Cubic and Higher Equations 257 Simple Interest 266 GEOMETRY 275

 Multiplication of Decimals 68 Rule of Three in Decimals 76 CONTENTS 77 To extract the Cube Root 85 Table of Squares Cubes SquareRoots and CubeRoots 110 Geometrical Progressi�n 119 Compound Interest 127 Single Position 135 Practical Questions 150 To compute Logarithms 159 11 161 Multiplication by Logarithms 167 25 174 Addition 175 Multiplication 181 32 188 Involution 199 Surds ? 206 38 210 Infinite Series 213
 51 278 Axioms Theorems 281 Of Ratios and Proportions 319 Of Planes and SolidsDefinitions 336 Problems 353 Applications of Algebra to Geometry 369 Plane Trigonometry 377 Multiplication 379 Heights and Distances 393 Mensuration of Planes 402 Mensuration of Solids 419 Land Surveying 429 Artificers Works 457 Conic Sections 469 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 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 410 - 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 251 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 25 - Weight is used by apothecaries and physicians in compounding dry medicines. TABLE. 20 Grains (gr.} = 1 Scruple, . . sc., or 3. 3 Scruples = 1 Dram, . . dr., or 3 . 8 Drams = 1 Ounce, . . oz., or � . 12 Ounces = 1 Pound, . . Ib., or ft,.
Page 220 - It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.
Page 306 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 55 - 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 257 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
Page 347 - The measure of any 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 221 - RULE. Transpose all the terms that involve the unknown quantity to one side of the equation, and the known terms to the other...