Plane trigonometry. [With] Solutions of examples


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Side 9 - 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.
Side 85 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Side 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...
Side 5 - 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...
Side 96 - Express the radius of the inscribed circle of a triangle in terms of the radii of its three escribed circles.
Side 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.
Side 109 - The length of a road in which the ascent is 1 foot in 5, from the foot of the hill to the top is a mile and twothirds. What will be the length of a zigzag road in which the ascent is 1 foot in 12?
Side 113 - Logm" = wlogm, or the logarithm of any power of a number is obtained by multiplying the logarithm of the number by the index of the power. For m" = (a*)" = a"*, and .-. log(»z") = nx = nlogm.
Side 93 - To find the radius of the inscribed and escribed circles of a triangle, in terms of its sides and angles.
Side 74 - ... grain of dust that may be seen sticking to an orange. The Sun. To us who are accustomed to think of such bodies as stones and trees, hills and mountains, the size of the earth appears immense. But the earth, large as it appears, is a small body compared with the sun, which gives us light and heat. The sun is more than a million times as large as the earth. Day and Night.

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