# Elements of Plane and Spherical Trigonometry

Harper, 1865 - Logarithms - 150 pages
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### Contents

 BOOK I 7 Description of the Table of Logarithms 14 BOOK II 20 Sines Tangents Secants c defined 32 Instruments used in Drawing 42 Geometrical Construction of Triangles 48 Trigonometrical Formulę 52 BOOK III 59
 Variation of the Needle 117 Topographical Maps 123 52 128 Surveying Harbors 130 Plane Sailing 138 57 142 Parallel Sailing 144 Nautical Charts 153

### Popular passages

Page 20 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Page 69 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.
Page 17 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 71 - ADD THE LENGTH OF THE EDGE TO TWICE THE LENGTH OF THE BASE, AND MULTIPLY THE SUM BY £ OF THE PRODUCT OF THE HEIGHT OF THE WEDGE AND THE BREADTH OF THE BASE.
Page 119 - A=gThat is, the difference between the true and the apparent level, is nearly equal to the square of the distance divided by the diameter of the earth. Ex. 1. What is the difference between the true and the apparent level, for a distance of one English mile, supposing the earth to be 7940 miles in diameter?
Page 59 - To find the area of an irregular polygon. RULE. Draw diagonals dividing the polygon into triangles, and find the sum of the areas of these triangles.
Page 45 - ... a scale of 100 rods to an inch, in which case the side AB will be represented by 4.32 inches ; or we may construct it upon a scale of 200 rods to an inch ; that is, 100 rods to a half inch, which is very conveniently done from a scale on which a half inch is divided like that described in Art.
Page 51 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 37 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 51 - A. sin (A + B) - sin A cos B + cos A sin B. sin (A - B) - sin A cos B - cos A sin B. cos (A + B) - cos A cos B - sin A sin B.