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according acute angle adjacent angle application base calculated called circle corresponding cos a cos cos▓ cosc Cosine Cotang decimal definitions denote derived determined difference distance Dividing elements equal equation evident example expressed figure find the values formulŠ formulŠ of Art functions Geometry Given giving greater than 90 Hence increases less than 90 log cos log cosec log sin logarithm mantissa method middle negative Note observation obtained opposite angle perpendicular positive principle prove Putting quadrant radius relation remaining respectively right triangle rule sides Similarly sin A cos sin B sin sin▓ sinc Sine sins sinx siny solution spherical triangle Substituting subtract taken tanc Tang tangent theorem Trigonometry values Whence
Page 116 - 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.
Page 115 - 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 155 - 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░. (g'). If A'B'C' is the polar triangle of ABC...
Page 76 - This table is added simply for convenience, as the same mantissae are to be found in the other part of the table. To find the logarithm of any number consisting of four figures. Find, in the column headed N, the first three figures of the given number. Then the mantissa of the required logarithm will be found in the horizontal line corresponding, in the vertical column which has the fourth figure of the given number at the top. If only the last four figures of the mantissa are found, the first two...
Page 71 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 68 - If a number is not an exact power of 10, its common logarithm can only be expressed approximately ; the integral part of the logarithm is called the characteristic, and the decimal part the mantissa.
Page 69 - If the number is greater than 1, the characteristic is 1 less than the number of figures to the left of the decimal point.
Page 66 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a