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adjacent angles apothem AXIOM base and altitude bisect bisectrix chord circle whose center circumference circumscribed coincide Conclusion concurrent lines cone Construction Corollary cylinder Demonstration diagonals diameter dicular distance divided draw equal angles equal circles equal to half equally distant equiangular equilateral equivalent exterior extremities figure Find the locus frustum given line given point given straight line greater hypotenuse included angle interior angles intersection isosceles triangle lateral edges lateral surface less line joining middle point MISCELLANEOUS EXERCISES number of sides oblique lines opposite sides parallelogram parallelopiped perimeter perpen perpendicular plane angles prism PROP PROPOSITION proved equal pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right-angled triangle Scholium secant segments similar slant height sphere spherical angle spherical triangle square tangent Theorem third side trapezoid triangle is equal trihedral angle unequal vertex vertical angle
Page 176 - 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 will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 91 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 135 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 154 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the center; as the figure ADB E.
Page 76 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 293 - The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
Page 139 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Page 53 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.