Elements of Plane and Solid Geometry
Ginn and Heath, 1877 - 398 pages
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A B C ABCD altitude axis base bisect called centre chord circle circumference circumscribed coincide common cone Cons construct COROLLARY corresponding cylinder denote describe diagonals diameter difference dihedral angle direction distance divided draw edges element equal equal respectively equally distant equilateral equivalent extremities faces fall figure foot formed four frustum given greater Hence homologous sides included inscribed intersection joining less limit line drawn measured meet oblique opposite parallel parallelopiped pass perimeter perpendicular plane MN polyhedrons prism PROBLEM proportional PROPOSITION prove pyramid Q. E. D. PROPOSITION radii radius ratio rectangles regular polygon respectively right angles segment Show similar sphere spherical triangle square straight line surface symmetrical Take tangent tetrahedron THEOREM third triangle trihedral vertex vertices volume
Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 38 - Any side of a triangle is less than the sum of the other two sides.
Page 349 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 83 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.
Page 207 - To construct a parallelogram equivalent to a given square, and having the difference of its base and altitude equal to a given line.
Page 188 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 146 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. Let a: b = c: d — e :/= g: h.