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 ProjectionE.H. Pease & Company, 1851 - 86 ページ |
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AC+CB altitude angle ACB AO+OB Arcturus axis BA+AC base centre circle cuts circumference complete the square compute cones cos² Cubic equations cubic inches cuts the parabola cylinder describe a circle diameter distance divide draw expression exterior angle extract the square figure find the values fourth degree frustums geometrical given angle given in position greater half difference half sum hence hypothenuse inscribed circle latitude Let ABC let fall line CD line drawn line given logarithm longer side Math minus Multiply numbers parallel perceive perpendicular plane problem quadratic radius real roots represented right ascension Scholium segments sinCq sine Spica square chains square root stone straight line subtract Take VD tan sum tangent theorem theory of equations trapezoid trigonometrically vertex whence
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62 ページ - ... 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.
18 ページ - 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.
24 ページ - 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.
61 ページ - 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.
28 ページ - Given one angle, a side opposite to it, and the difference of the other two sides ; to construct the triangle.
54 ページ - 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.
57 ページ - 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.
25 ページ - 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.
8 ページ - 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.