Mathematical Recreations: Containing Solutions of Many Very Difficult and Important Equations, and of Several Useful Problems in Geometry, Surveying and Astronomy, Together with a Method of Finding the Roots and Equations by Projection

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E.H. Pease & Company, 1851 - Mathematics - 86 pages
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Page 62 - ... angle and half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference.
Page 18 - The difference of the angles at the base of any triangle, is double the angle contained by a line drawn from the vertex perpendicular to the base, and another bisecting the angle at the vertex.
Page 24 - A straight line drawn from the vertex of an equilateral triangle inscribed in a circle, to any point in the opposite circumference, is equal to the sum of the two lines which are drawn from the extremities of the base to the same point.
Page 61 - II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference.
Page 28 - Given one angle, a side opposite to it, and the difference of the other two sides ; to construct the triangle.
Page 54 - To determine a Right-angled Triangle ; having given the Hypothenuse, and the Difference of two Lines drawn from the two acute angles to the Centre of the Inscribed Circle. PROBLEM XIX.
Page 57 - From this half sum subtract each side separately. Then, multiply the half sum and the three remainders together, and extract the square root of the product : the result will be the area (Geom.
Page 25 - In any triangle if a line be drawn from the vertex at right angles to the base, the difference of the squares of the sides is equal to the difference of tlie squares of the segments of the base.
Page 8 - Find two numbers whose" product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.

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