# A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well as Private Tuition, Volume 1

Samuel Campbell, Evert Duyckinck, T. & J. Swords, 1816 - Mathematics

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### Contents

 GENERAL Principles 3 Roman Notation 9 Division 18 Compound Proportion 49 Addition of Vulgar Fractions 61 Multipacation of Decimals 66 Addition of Dec mals 07 68 Reduction of Decimals 73
 Definitions and Notation 171 GEOMETRY 275 AxiomsTheorems 281 Of Ratios and Proportions 319 Of Planes and Solids Definitions 336 Problems 353 Applications of Algebra to Geometry 369 Piune Trigonometry 398

 CONTENTS 77 Evolution 79 To extract the Cube Root 85 110 92 To extract any Root whatever 110 Musical Proportion 119 Compound Interest 127 Single Position 135 Practical Questions 150 Multiplication 167
 Mensuration of Solids 419 Land Surveying 429 Artificers Works 457 Timer 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 Probleins relative to the Division of Surfaces 558 Construction of Geometrical Problems 571

### Popular passages

Page 6 - 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 285 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
Page 438 - 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 187 - 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 202 - Subtract its power from that term, and bring down the second term for a dividend. 3. Involve the root, last found, to the next lowest -power, and multiply it by the index of the given power for a divisor.
Page 290 - A perpendicular is the shortest line that can be drawn from a given point to a given line.
Page 86 - Then say, by the rule of three, as the sum of the given number and double the assumed cube is to the sum of the assumed cube and double the given number, so is the root of the assumed cube to the root required, nearly ; Or as the first sum is to the difference of the given and assumed...
Page 398 - Two ships of war, intending to cannonade a fort, are, by the shallowness of the water, kept so far from it, that they suspect their guns cannot reach it with effect. In order, therefore, to measure the distance, they separate from each other a quarter of a mile, or 440 yards ; then each ship observes and measures the angle which the other ship and the fort subtend, which angles are 83° 45
Page 355 - B draw chords BA, BC, to the two other points, and bisect these chords perpendicularly by lines meeting in O, which will be the centre. Then from the centre O, at the distance of any one of the points, as ( ) A, describe a circle, and it will pass through the two other points B, C, as required.
Page 56 - To reduce an improper fraction to a whole, or mixed number. Divide the numerator by the denominator, and the quotient will be the whole, or mixed number required.