An Introduction to Plane and Spherical Trigonometry

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Harrison, 1865 - Plane trigonometry - 150 pages

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Page 28 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 67 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Page 143 - To prove that the altitude of the pole is equal to the latitude of the place.
Page 67 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 45 - 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 67 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...
Page 27 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 81 - A ladder 40 feet long may be so placed that it shall reach a window 33 feet from the ground on one side of the street, and by turning it over, without moving the foot out of its place, it will do the same by a window 21 feet high on the other side. Required the breadth of the street.
Page 59 - ... units from the totality for each complement employed. Involution. — " Multiply the log. of the number by the index of the power required. The antilog. of the result will be that power.
Page 36 - The RADIUS of a sphere is a straight line drawn from the centre to any point in surface, as the line C B.

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