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AC+CB altitude angle ACB Arcturus BA+AC base bisecting the angle centre circle cuts circumference complete the square compute cones Conic Sections Cubic equations cubic inches cuts the parabola cylinder describe a circle describe the 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 isosceles latitude Let ABC let fall line CD line drawn line given logarithm longer side Math minus Multiply numbers parallel perceive plane problem quadratic real roots Recreations represented right ascension Scholium segments sinCq Spica square chains square root stone straight line subtract Take VD tana tangent theorem theory of equations tion trapezoid trigonometry vertex whence
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 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 88 - OR, THE CONNECTION BETWEEN SCIENCE AND THE ART OF PRACTICAL Farming. Prize Essay of the New York State Agricultural Society. By JOHN P. NORTON, MA, Professor of Scientific Agriculture in Yale College. Adapted to tb
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.