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adjacent angles altitude angles equal angles formed apothem base bisect chord circle circumference circumscribed coincide cone Corollary—The Cosine Cotang demonstrated diagonals diameter dicular diedral angle distance divided draw equal angles equally distant equivalent EXERC1SES extent faces figure formula four right angles frustum Geometry given angle given line given point given straight line given triangle gles greater Hence homologous lines hypotenuse included angle inscribed intersection isosceles triangle Join less let fall line parallel logarithm mantissa measured by half number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron prism problem proportional pyramid quadrilateral radii radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged sine slant hight sphere spherical triangle square student subtracted symmetrical tangent tetraedrons Theorem Theorem—If Theorem—The triangle ABC triangles are equal triedral vertex vertices
Page 98 - If two triangles have two sides of the one equal to two sides of the...
Page 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Page 84 - If a circle have any number of equal chords, what is the locus of their points of bisection? 21. If any point, not the center, be taken in a diameter of a circle, of all the chords which can pass through that point, that one is the least which is at right angles to the diameter. 22. If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them....
Page 117 - ABC, so that DE shall be equal to the difference of BD and CE. 22. In a given circle, to inscribe a triangle similar to a given triangle. 23. In a given circle, find the locus of the middle points of those chords which pass through a given point. 25. If a line bisects an exterior angle of a triangle, it divides the base produced into segments ^A which are proportional to the adjacent sides.
Page 307 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 237 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 233 - The volume of a rectangular parallelepiped is equal to the product of its three dimensions.