Plane trigonometry and logarithms

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C.F. Hodgson, 1865 - Logarithms - 182 pages

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Page 77 - Suppose a* =n, then x is called the logarithm of n to the böge a ; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The- logarithm of n to the base a is written Iog0 n ; thus log„ii = a; expresses the same relation, as a* = n.
Page 109 - A, and at a distance of a from it, the elevation is 18°. Show that the height of the tower is — ; the tangent of 18° being 25.
Page 112 - On the bank of a river there is a column 200 feet high supporting a statue 30 feet high ; the statue to an observer on the opposite bank subtends an equal angle with a man 6 feet high standing at the base of the column; required the breadth of th
Page 23 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Page 81 - Hence the characteristic is n — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and is positive.
Page 121 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.
Page 122 - ... 66. Construct an equilateral triangle, having given the length of the perpendicular drawn from one of the angles on the opposite side. 67. Having given the straight lines which bisect the angles at the base of an equilateral triangle, determine a side of the triangle. 68. Having given two sides and an angle of a triangle, construct the triangle, distinguishing the different cases.
Page 22 - Find the distance of the lighthouse from each position of the ship.
Page 121 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 109 - The elevation of a tower standing on a horizontal plane is observed ; a feet nearer, it is found to be 45°...

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