Mathematical and Astronomical Tables: For the Use of Students of Mathematics, Practical Astronomers, Surveyors, Engineers, and Navigators; with an Introduction, Containing the Explanation and Use of the Tables, Illustrated by Numerous Problems and Examples

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Oliver & Boyd, 1827 - Astronomy - 322 pages
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Page x - The whole 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 147 - ... once what is the weight of a quantity of water, equal in bulk to the solid matter in the sand ; and by comparing this with the weight of the sand, we have its true specific gravity.
Page 52 - A sphere is a solid figure described by the revolution of a semicircle about its diameter, which remains fixed.
Page 167 - 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 162 - 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 12 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 42 - ... part of the fathoms above found, and add them if the mean temperature be above 31, but subtract them if the mean temperature be below 31; and the sum or difference will be the true altitude in fathoms : or, being multiplied by 6, it will be the Altitude in feet. 392. Example 1. Let the state of the barometers and thermometers be as follows; to find the
Page 136 - ... the spheroid will be oblate or prolate, according as the revolution is performed about the minor or major axis of the ellipse.
Page 52 - ... 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 26 - ... 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.

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