Elements of Plane and Spherical Trigonometry: With Their Applications to Mensuration, Surveying, and Navigation |
Other editions - View all
Common terms and phrases
altitude angle of elevation angle opposite angles to find chains circle circumference column complement computed cosecant cosine cotangent course and distance cubic feet decimal diameter diff difference of latitude difference of longitude divided draw earth east equal equator find the angles frustum Geom Given the angle Given two sides half height Hence horizontal inches included angle latitude and departure length logarithm logarithmic sine measured Mercator's middle latitude miles Multiply natural number nautical miles object opposite angle parallel parallel sailing perpendicular plane sailing pole pole star Prob Prop proportional quadrant radius Required the remaining right-angled spherical triangle right-angled triangle Sandy Hook scale secant ship sails side AC sine solidity spherical triangle ABC SPHERICAL TRIGONOMETRY square feet station subtract surface tang tangent telescope theodolite Trigonometry tude vernier vertical yards zoids
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 47 - 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 a half inch, which is very conveniently done from a scale on which a half inch is divided like that described in Art.
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 73 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.
Page 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.
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 55 - A. sin (A + B) - sin A cos B + cos A sin B. sin (A - B) - sin A cos B - cos A sin B. cos (A + B) - cos A cos B - sin A sin B.
Page 187 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.