# A Course of Mathematics: In Two Volumes. For the Use of Academies as Well as Private Tuition, Volume 2

J. Johnson; W.J. and J. Richardson, 1807 - Mathematics

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### Contents

 PLANE Trigonometry Q e s 1 Heights and Distances 17 Mensuration of Planes or Areas 26 Mensuration of Solids e e s 43 Land Surveying 53 Artificers Works 81 Timber Measuring 90 Of the Ellipse 97
 of Hydrostatics 210 of Hydraulics 221 Of the Syphon 236 Of the Barometer 241 Practical Exercises in Mensuration 248 Weights and Dimensions of Balls and Shells 258 Of Distances by the Velocity of Sound 264 The Doctrine of Fluxions 275

 of the Hyperbola e e 106 Of the Parabola J 15 115 Laws of Motion Forces c 129 Composition and Resolution of Forces 137 Laws of Gravity Projectiles c 148 Practical Gunnery e e 160 Mechanical Powers 174 Centres of Percussion Oscillation and Gyration 201
 The Inverse Method of Fluxions 290 Of Maxima and Minima 303 Rectification of Curves 310 To make Logarithms 316 Involutes and Evolutes 323 Practical Exercises on Forces 330 The Motion of Bodies in Fluids 354

### Popular passages

Page 56 - 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 165 - MECHANICAL POWERS are certain simple instruments employed in raising greater weights, or overcoming greater resistance than could be effected by the direct application of natural strength. They are usually accounted six in number; viz. the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Wedge, and the Screw.
Page 38 - How many cubic feet in a block of marble, of which the length is 3 feet 2 inches, breadth 2 feet 8 inches, and height or thickness 2 feet 6 inches ? Ans.
Page 80 - WORK. — Glaziers take their dimensions either in feet, inches, and parts ; or feet, tenths, and hundredths. And they compute their work in square feet. In taking the length and breadth of a window, the cross bars between the squares are included. Also, windows of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass.
Page 203 - BPC) ; or, the pressure of a fluid on any surface is equal to the weight of a column of the fluid...
Page 239 - In turning a one-horse chaise within a ring of a certain diameter, it was observed that the outer wheel made two turns, while the inner made but one : the wheels were both 4 feet high •, and supposing them fixed at the distance of 5 feet asunder on the axletree, what was the circumference of the track described by the outer wheel ? Ans. 62-33 feet. QUEST. 12. What is the side of that equilateral triangle, whose area cost as much paving at 8d.
Page 247 - Then say, As the weight lost in water, Is to the whole weight, So is the specific gravity of water, To the specific gravity of the body.
Page 322 - ... and the relation between these three quantities being universally expressed by this equation m = qf, it follows that, by means of it, any one of the three may be expelled out of the calculation, or else brought into it. Also, the momentum, or quantity of motion in a moving body, is qv, the product of the velocity and matter. It is also to be observed, that the theorems equally hold good for the destruction of motion and velocity, by means of retarding forces, as for the generation of the same,...
Page 165 - A LEVER is any inflexible rod, bar, or beam, which, serves to raise weights, while it is supported at a point by a fulcrum or prop, which is the centre of motion. The lever is supposed to be void of gravity or weight, to render the demonstrations easier and simpler.