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ABCD adjacent altitude axis base bisector bisects called centre chord circle circumference circumscribed coincide common cone construct cylinder denote describe diagonals diameter diedral divided draw drawn equal respectively equally distant equilateral equivalent EXERCISES extremities faces fall figure Find formed four frustum given given point greater Hence homologous hypotenuse included inscribed intersection isosceles triangle joining lateral area length less line drawn manner mean measured meet middle point multiplied parallel parallelogram parallelopiped passing perimeter perpendicular plane polygon prism PROBLEM produced Prop proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular respectively right angles right triangle secant segment sides similar sphere spherical triangle square straight line surface tangent tetraedron THEOREM third trapezoid triangle ABC unit vertex vertices volume Whence
Page 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 65 - 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 172 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 122 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 355 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 52 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 140 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 123 - In any proportion the terms are in proportion by composition and division ; that is, the sum of the first two terms is to their difference as the sum of the last two terms to their difference.