A Treatise on Plane and Spherical Trigonometry |
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A Treatise on Plane and Spherical Trigonometry (Classic Reprint) Ephraim Miller No preview available - 2017 |
Common terms and phrases
A+B+C AC² acute angle altitude angle corresponding angle opposite angles or arcs angular arc-tan celestial sphere circumscribed colog column cos b cos cos b sin cos² cosb cosc cosec cosine cotangent decimal determine ecliptic equal equations equinoctial escribed circles EXAMPLES feet find the angle Find the area find the logarithmic Find the value formulæ four figures horizon hypothenuse inscribed isosceles triangle less than 90 Let ABC Fig log cot logarithmic functions logarithmic sine mantissa Napier's Analogies number corresponding oblique triangle obtain perpendicular pole quadrant radii right angle right ascension secant Show sin B sin sin c cos sin(s sin² sin³ sinb sines and cosines sins sin(sc solution Solve the triangle spherical right triangle spherical triangle star subtract sun's table of logarithmic tabular difference tanc triangle ABC trigonometric functions vertical zenith ΙΟ бо
Popular passages
Page 34 - 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 100 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 58 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page iv - The foregoing method is based on the assumption that the differences of logarithms are proportional to the differences of their corresponding numbers, which, though not strictly accurate, is sufficiently exact for practical purposes.
Page 51 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 100 - I. The logarithm of a product equals the sum of the logarithms of the factors.
Page 62 - Rules are . (1) The sine of the middle part equals the product of the tangents of the adjacent parts.
Page vii - In searching for the next less (or greater) logarithm, attention must be paid to the fact that the functions are found in different columns according as the angle is below or above 45°. If, for example, the next less logarithmic sine is found in the column with
Page 32 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.