# A Course of Mathematics ...: Designed for the Use of the Officers and Cadets of the Royal Military College, Volume 2

C. Glendinning, 1806 - Mathematics

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### Contents

 Page A LGE BRA 1 Addition 7 Division 16 Reduction of Fructions 22 Addition of Fractions 29 Resolution of Simple Equations 39 Of Ratios and Proportions 50 Of Involution 59
 Sections 254 Tofind the content of an ellipsoid 272 Paralola 285 Tºfind the content of a Paraboloid 294 Mechanics 300 ndicular descent and ascent of bodies 309 9Prºjectile Motion according to the Parabolic Theory 323 dekenton inclined Planes 339

 Rule for crtracting the roots of Numbers 66 Questions producing Simple Equations 82 Question respecting the march of Troops 91 Questions producing Quadratic Plation 101 Of Indeterminate Problems 118 Of Figurate Numbers 127 Of Geometrical Progressions 133 Of Permutations Combinations c 146 Continued Fractions 152 Of the Differential Method 161 OfCubic Equations 173 Summation of particular Series 185 Appirional ExAMples in Algebra 203 Application of Algebra to Geometry 229 Thºrem for finding an angle when the three sides of a triangle are given 242
 lever 356 Pulley 364 Heavy Lever 380 Thickness of the Piers for a semicircular Arch 387 Of the Centres of Percussion Oscillation and Gyration 395 Descent of a Cylinder when it rolls 406 Hyd Rost AT ICs 418 Spécific Gravities 420ſ 424 Hydrostatic Paradox 434 Method of determining the mean velocity of water in a River or Canal 442 Pelocity with which Air would rush into a vacuum 448 Oſ measuring Heights by the Barometer 455 Qſ the RESIsr ANCE and Force of FLUIDs 462 Resistance of the 4ir to a Projectile e 4 67 469

### Popular passages

Page 238 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 55 - If any number of magnitudes are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents.
Page 67 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 66 - Subtract the power from the given quantity, and divide the first term of the remainder by the...
Page 302 - Every body continues in its state of rest, or uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Page 116 - How much gold of 15, of 17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine ? Ans.
Page 134 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 23 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Page 39 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.