Elements of Plane and Spherical Trigonometry: With Their Applications to Mensuration, Surveying, and NavigationHarper & Brothers, 1859 - 193 pages |
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Common terms and phrases
altitude angle of elevation angle opposite arithm base chains chord circle circumference complement computed cosecant cosine cotangent course and distance cubic feet decimal diameter diff difference of latitude difference of longitude divided draw equal equator figure find the angles find the area find the remaining found by Theorem frustum Geometry given side Given the angle Given the hypothenuse Given two sides height Hence horizontal inches included angle length logarithmic sine longitude measured meridian middle latitude miles Multiply natural numbers nautical miles parallel parallel sailing perpendicular plane sailing Prob Prop proportional quadrant radius right-angled spherical triangle right-angled triangle rods RULE Sandy Hook scale secant ship sails side AC slant height spherical triangle ABC SPHERICAL TRIGONOMETRY square feet station subtract tang tangent telescope theodolite three sides 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 153 - 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 44 - 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 63 - To find the volume of a pyramid, or of a cone. Multiply the area of the base by one third of the altitude.
Page 113 - 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 53 - 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 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 37 - ... 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 a half inch, which is very conveniently done from a scale on which a half inch is divided like that described in Art.
Page 72 - TO ONE OF THE SIDES. Or, MULTIPLY THE CUBE OF ONE OF THE EDGES, BY THE SOLIDITY OF A SIMILAR SOLID WHOSE EDGES ARE 1.
Page 33 - 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.