Elements of Plane and Spherical Trigonometry: With Their Applications to Mensuration, Surveying, and Navigation

Harper & brothers, 1868 - 194 pàgines
The following treatise constitutes the third volume of a course of Mathematics designed for colleges and high schools ... [I]t contains those principles which are most important on account of their applications, or their connection with other parts of a course of mathematical study... The most important instruments used in Surveying are fully described, and are illustrated by drawings.

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Continguts

 Description of the Theodolite 90 The Determination of Areas 103 To find the Area of a Field 117 Topographical Maps 123 Surveying Harbors 130 Definitions c 138 pºsimº 149
 BOOK 155 Examples of Rightangled Triangles 165 Examples of Obliqueangled Triangles 175 LOGARITHMIC SINES AND TANGENTS 21 iii NATURAL SECANTs 134 xi 160 2 171 4

Passatges populars

Pàgina 163 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Pàgina 83 - Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop.
Pàgina 72 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Pàgina 123 - 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?
Pàgina 20 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Pàgina 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.
Pàgina 54 - 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.
Pàgina 17 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Pàgina vi - To find the Logarithm of any Number between 1 and 100. Look on the first page of the table, along the column of numbers under N, for the given number, and against it, in the next column, will be found the logarithm, with its characteristic. Thus, opposite 13 is 1.113943, which is the logarithm of 13 ; " 65 is 1.812913, " " 65. To find tht Logarithm of any Number consisting of three Figures.
Pàgina 63 - 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.