Mathematical and Astronomical Tables: For the Use of Students in Mathematics, Practical Astronomers, Surveyors, Engineers, and Navigators; Preceded by an Introduction, Containing the Construction of Logarithmic and Trigonometrical Tables, Plane and Spherical Trigonometry, Their Application to Navigation, Astronomy, Surveying, and Geodetical Operations, with an Explanation of the Tables, Illustrated by Numerous Problems and Examples
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Page xviii - The mhole numbers or integers in the logarithmic series are hence easily obtained, being always a unit less than the number of figures in the integral part of the corresponding natural number.
Page 223 - DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Page 214 - Multiply the number in the table of multiplicands, by the breadth and square of the depth, both in inches, and divide that product by the length, also, in inches; the quotient will be the weight in Jbs.t Example 1.
Page 15 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 70 - ... pyramids or cones are as the cubes of their like linear sides, or diameters, or altitudes, &c. And the same for all similar solids whatever, viz. that they are in proportion to each other, as the cubes of their like linear dimensions, since they are composed of pyramids every way similar. THEOREM CXVI.
Page 22 - Given the base, the vertical angle, and the difference of the sides, to construct the triangle. 127. Describe a triangle, having given the vertical angle, and the segments of the base made by a line bisecting the vertical angle. 128. Given the perpendicular height, the vertical angle and the sum of the sides, to construct the triangle. 129. Construct a triangle in which the vertical angle and the difference of the two angles at the base shall be respectively equal to two given angles, and whose base...
Page 73 - CD is an arp, meet ABC again in A, and let AC be the common section of the planes of these great circles, which will pass through E, the centre of the sphere...
Page 34 - ... hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 42 - ... logarithmic computation. The rule may, in that case, be thus expressed. Double the log. cotangents of the angles of elevation of the extreme stations, find the natural numbers answering thereto, and take half their sum ; from which subtract the natural number answering to twice the log. cotangent of the middle angle of elevation : then half the log. of this remainder subtracted from the log. of the measure distanced between the first and second, or the second and third stations, will be the log.