Key to Robinson's New Geometry and Trigonometry, and Conic Sections and Analytical Geometry: With Some Additional Astronomical Problems. Designed for Teachers and Students

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Ivison, Blakeman, Taylor & Company, 1875

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Page 97 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 84 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 40 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Page 46 - 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 29 - 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.
Page 45 - If from any point within an equilateral triangle perpendiculars be drawn to the three sides, their sum is equal to a perpendicular drawn from one of the angles on the opposite side. Required proof. From the point within the triangle draw...
Page 52 - 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 eame point.
Page 59 - Given one angle, a side opposite to it, and the difference of the other two sides ; to construct the triangle.

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