# Surveying and Navigation, with a Preliminary Treatise on Trigonometry and Mensuration

Van Antwerp, Braggs & Company, 1864 - Measurement - 490 pages
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### 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 92
 Oblique Triangles 124 Mensuration 150 Mensuration of Volumes 174 SURVEYING 185 Survey of Public Lands 216 Variation of the Needle 265 Preliminary Calculations 284 Area of Land 296

### Popular passages

Page 110 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
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 258 - 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 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 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 144 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Page 124 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 65 - 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 145 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 162 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...