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

Harper & brothers, 1855 - 178 pàgines

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### Continguts

 THE NATURE AND PROPERTIES OF LOGARITHMS 7 Multiplication by Logarithms 14 PLANE TRIGONOMETRY 20 Explanation of the Trigonometrical Tables 32 Instruments used in Drawing 42 Values of the Sines Cosines c of certain Angles 48 Computation of a Table of Sines Cosines c 57 Area of a Regular Polygon 64
 Explanation of the Vernier 94 The Determination of Areas 103 To find the Area of a Field 109 Variation of the Needle 117 Topographical Maps 123 Surveying Harbors 130 Plane Sailing 138 Parallel Sailing 144

 Mensuration of Solids 71 Railway Excavations or Embankments 77 The three Round Bodies 84 Definitions 90
 Nautical Charts 153 Examples of Rightangled Triangles 163 Examples of Obliqueangled Triangles 175

### Passatges populars

Pàgina 22 - 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.
Pàgina 165 - 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 56 - 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 85 - Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop.
Pàgina 74 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Pàgina 125 - 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 19 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Pàgina 65 - 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.
Pàgina 49 - ... upon 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...
Pàgina 75 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.