Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students
Van Antwerp, Bragg & Company, 1868 - Geometry - 420 pages
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Treatise on Geometry and Trigonometry; for Colleges, Schools and Private ...
Eli T. (Eli Todd) Tappan
No preview available - 2012
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acute adjacent altitude applied arranged base called chord circle circumference coincide common cone construct Corollary corresponding Cosine Cotang curved demonstrated described diagonals diameter diedral difference direction distance divided draw edges equal equally distant equivalent example EXERCISES extend faces fall figure follows formed formula four functions Geometry given given point greater half Hence homologous hypotenuse included inscribed intersection Join length less limit logarithm means measured meet method opposite parallel parallel lines parallelogram pass perimeter perpendicular places plane position principle prism problem proportional pyramid radius ratio regular polygon respectively equal right angles secant sides similar similarly sine sphere square straight line student subtracting Suppose surface Tang tangent tetraedrons theorem Theorem.-The third triangle triedral true vertex vertices volume whole
Page 98 - If two triangles have two sides of the one equal to two sides of the...
Page 182 - ... the plane at equal distances from the foot of the perpendicular, are equal...
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.
Page 126 - Theorem. — Two parallelograms are equal when two adjacent sides and the included angle in the one, are respectively equal to those parts in the other.