### Contents

 INTRODUCTION 9 Multiplication by Logarithms 18 Trigonometrical Functions 27 Table of Natural Functions 41 Right Triangles 47 Oblique Triangles 55 Application to Heights and Distances 69 Applications 108
 Oblique Triangles 124 Mensuration 150 SURVEYING 185 Survey of Public Lands 213 Field Operations 274 Preliminary Calculations 284 Area of Land 296 PAGE 405

### Popular passages

Page 34 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Page 94 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 232 - All the corners marked in the surveys, returned by the surveyor general, or by the surveyor of the lands south of the state of Tennessee, respectively, shall be established as the proper corners of sections, or subdivisions of sections, which they were intended to designate ; and the corners of half and quarter sections, not marked on said surveys, shall be placed as nearly as possible equidistant from those two corners which stand on the same line.
Page 19 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 22 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 108 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 10 - The integral part of a logarithm is called the characteristic and the decimal part is called the mantissa.
Page 183 - Then carefully turn the arm half way over, until it rests upon the adjuster by the opposite faces of the rectangular blocks, and again observe the position of the sun's image. If it remains between the lines as before, the...
Page 21 - Find the logarithm of the number, and multiply it by the exponent of the power; then find the number corresponding to the resulting logarithm, and it will be the power required.
Page 22 - Divide the logarithm of the given number by the index of the root ; and the quotient will be the logarithm of the required root (Art.