# A Treatise of Practical Mathematics, Part 2

W. & R. Chambers, 1842

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### Contents

 Page 76 Cask Gauging 95 Table of Contents of Standard Casks 103 WEIGHTS AND DIMENSIONS OF BALLS AND SHELLS 112 PROJECTILES 119 Geometrical Construction of Problems 129 Practical Gunnery 137 Table of Actual and Potential Ranges in Terms of F 144 FORTIFICATION 151 Cormontaignes and the Modern System 165 Field Fortifications 172 PROJECTIONS 178 STEREOGRAPHIC PROJECTION OF THE CASES OF SPHERICAL 187 Definitions 192 Qnadrantal Triangles 206 Projection of Cases in ObliqueAngled Trigonometry 189 207
 Problems 58 275 Methods of finding Latitude 283 Lunar Distances 291 NAVIGATION 299 Plane Sailing 309 Globular Sailing 316 Nautical Astronomy 329 Globular Projection 335 Page 338 GEODETIC SURVEYING 344 Reduction of a Base to the Level of the Sea 352 Example of Triangulation 363 Figure of the Earthits Elements 370 Problems regarding the Length Radius of Curvature and Number 376 The Relative and Absolute Heights of Stations 382 Table of Mean Refraction 389

### Popular passages

Page 196 - Fig. 9. Case 1. Let AB, AC be each less than a quadrant. Let AE, AG be quadrants ; G will be the pole of AB, and E the pole of AC, and EC a quadrant; but, by prop. 12. CE is greater than CB, since CB is farther off from CGD than CE. In the same manner, it is shown...
Page 95 - To the square of the bung diameter add the square of the head diameter ; multiply the sum by the length, and the product again by .0014 for ale gallons, or by .0017 for wine gallons.
Page 96 - RULE. — To the square of the bung diameter add the square of the head diameter ; multiply the sum by the length, and the product by .0014 for ale gallons, or by .0017 for wine gallons.
Page 42 - A magnitude which has length, breadth, and thickness. Solution. The process by which the answer to a question is obtained. Specific gravity of a substance. The ratio of the weight of a given volume of it to that of an equal volume of water.
Page 192 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre. The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Page 227 - ZODIAC.— The Zodiac is an imaginary belt, or broad circle, extending quite around the heavens. The ecliptic divides the zodiac into two equal parts, the zodiac extending 8 degrees on each side of the ecliptic, and therefore is 16 degrees wide.
Page 196 - BC will be greater than a quadrant : for let AE be a quadrant, then E is the pole of AC, and EC will be a quadrant. But CB is greater than CE by Prop. 12.
Page 195 - Oj the same affection with the angles opposite to them, that is, if the sides be greater or less than quadrants, the opposite angles will be greater or less than right angles, and conversely.
Page 195 - IN a right angled spherical triangle, the sides are of the same affection with the opposite angles ; that is, if the sides be greater or less than quadrants, the opposite angles will be greater or less than right angles. Let ABC be a spherical triangle right angled at A, any side AB, will be of the same affection with the opposite angle ACB. Case 1.
Page 195 - ... will be greater than a quadrant. Let ABC be a right angled spherical triangle ; according as the two sides AB, AC are of the same or of different affection, the hypotenuse BC will be less, or greater than a quadrant. The...