Plane trigonometry. [With] Solutions of examples


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Page 84 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 11 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 4 - When the three sides are given, it may be known whether one of the angles is obtuse. For any angle of a triangle is obtuse or acute, according as the square of the side subtending the angle is greater, or less, than the sum of the squares of the sides containing the angle.
Page 125 - Ratios, than the numbers themselves. As the sines and cosines of all angles, and the tangents of angles less than 45°, are less than unity, their logarithms are negative ; and in order to avoid the introduction and use of negative quantities, the logarithms of the Trigonometrical Ratios are all increased by the addition of the number 10, and are so registered in the tables of log-sines, log-cosines, &c. In the adaptation...
Page 7 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &,c. marked with the characters °,','','", &c. Thus, 32° 24...
Page 117 - Although the mantissae are only given in the Tables for sequences of five figures, yet they may be readily found for sequences of six or seven figures by the following considerations.
Page 108 - At the top of a tower, 108 feet high, the angles of depression of the top and bottom of...
Page 110 - If, therefore, a number is an exact power of 10, its logarithm is a whole number. If a number is not an exact power of 10, its logarithm will not be a whole number, but will be made up of an entire part plus a fractional part, which is generally expressed decimally. The entire part of the logarithm is called the characteristic ; the decimal part is called the mantissa.
Page 63 - The shadows of two vertical walls, which are at right angles to each other, and are a and a...
Page 135 - Elements of. (The parts read in the University of Cambridge) from the Text of Dr. Simson, with a large collection of Geometrical Problems, selected and arranged under the different Books. Designed for the use of Schools. By the Rev. JW COLENSO,, AM, late Fellow of St.

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