## 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 base bearing called circle circumference column complement computed correction corresponding cosine cotangent course cubic decimal departure determine diameter difference difference of latitude direction distance divided draw drawn earth east edge entire equal equator example fall feet field figure four Geometry given greater ground half height Hence horizontal hypothenuse inches included latitude length less logarithm longitude manner means measured meridian method middle miles minutes Multiply natural object observed obtain opposite parallel perpendicular plane portion positive preceding Prob PROBLEM Prop proportional quadrant radius remaining represent Required right-angled triangle RULE sailing scale secant ship side 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 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.