Plane and Spherical Trigonometry

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Ginn, 1876 - Trigonometry - 208 pages
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Page 13 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 71 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 71 - 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 91 - From a station B at the base of a mountain its summit A is seen at an elevation of 60°; after walking one mile towards the summit up a plane making an angle of 30° with the horizon to another station C, the angle BCA is observed to be 135°.
Page 50 - Taylor's Calculus was found to be in use in about sixty colleges. The Nation, New York: In the first place, it is evidently a most carefully written book.... We are acquainted with no text-book of the Calculus which compresses so much matter into so few pages, and at the same time leaves the impression that all that is necessary has been said. In the second place, the number of carefully selected examples, both of those worked out in full in illustration of the text, and of those left for the student...
Page 5 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 75 - Formulas for the area of a triangle, in terms of two sides and the included angle ; in terms of one side and the adjacent angles; and in terms of s and the three sides.
Page 20 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 49 - SJ, St. Louis Univ. : I have given the book a thorough examination, and I am satisfied that it is the best work on the subject I have seen. I mean the best work for what it was intended, — a textbook. I would like very much to introduce it in the University. (Jan.

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