An Elementary Geometry and Trigonometry
Thompson, Bigelow, and Brown, 1872 - Geometry - 238 pages
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adjacent altitude base become bisect Book called centre chord circle circumference coincide comp cone construct Converse convex surface Corollary corresponding Cosine Cotang decr DEFINITIONS demonstration describe diagonals diameter difference direction distance divided draw drawn equal equiangular equivalent feet figures four given angle given line given point greater half height hypothenuse included angle infinite inscribed isosceles joining known less Logarithm mean measured meet Method multiplied opposite side parallel parallelogram perimeter perpendicular plane polygon prism PROBLEM proportion proved pyramid quantities radius ratio rectangle respectively right angle RULE secant segment sides similar Sine sphere square straight line supplement Tang tangent THEOREM third triangle triangle ABC vertex vertices volume
Page 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 49 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 12 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.
Page 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Page 23 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.