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

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altitude angle base bearing called chord circle circumference column complement computed correction corresponding cosine cotangent course cubic feet decimal departure determine diameter difference direction distance divided draw drawn earth east edge entire surface equal equator example faces feet field figure four Geometry given greater ground half height Hence horizontal hypothenuse inches latitude length less logarithm longitude manner means measured meridian method middle miles minutes Multiply natural object obtain opposite parallel perpendicular places plane pole portion positive preceding PROBLEM Prop proportional pyramid quadrant radius regular remaining represent Required rods RULE sailing scale secant sector segment ship side similar sine solidity spherical triangle square station subtract surface tang tangent Theorem third triangle ABC vertical yards

### 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 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...

Page 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.

Page 83 - Also, similar pyramids are to each other as the cubes of their homologous edges (Geom., Prop.

Page 72 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 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?

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 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.

Page 47 - ... 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...

Page 73 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.