# A Course of Mathematics: For the Use of Academies as Well as Private Tuition, Volume 1

Samuel Campbell, 1812 - Mathematics
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### Contents

 GENERAL Principles 1 Notation and Numeration 7 Subtraction 13 Division 23 Reduction 32 Multiplication 38 Golden Rule or Rule of Three 49 Reduction of Vulgar Fractions 61
 199 219 Arithmetical Proportion 238 Geometrical Proportion 248 Quadratic Equations 269 Resolution of Cubic and Higher Equations 277 Simple Interest 286 GEOMETRY 292 Of Planes and Solids Definitions 336

 Decimal Fractions 67 Reduction of Decimals 75 CONTENTS 77 Rule of Three in Decimals 76 96 To extract the Cube Root 85 105 Arithmetical Progression 111 Fellowship or Partnership 119 Compound Interest 127 127 Single Position 135 Double Position 159 LOGARITHMS 175 Description and use of the Table of Logarithms 165 183 Involution by Logarithms 169 189 ALGEBRA 191 180 200 Algebraic Fractions 208
 Problems 352 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 Problemas 571

### Popular passages

Page 277 - 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 n�meros 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 302 - 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 287 - 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 172 - 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 294 - 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 349 - 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 430 - 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 301 - 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.