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adjacent altitude applied base bisect called centre chord circle circumference coincide common cone consequently construct contained Corollary cylinder Definitions denote described diameter difference direction divided Draw equal equal distances equiangular equilateral equivalent erect extremities fall figure formed give given given circle given polygon given square greater half the product Hence homologous sides hypothenuse included infinitely small inscribed intersection isosceles Join less maximum measure meet middle number of sides opposite parallel parallel lines parallelogram parallelopipeds passes perimeter perpendicular plane preceding prism Problem Proof proportional prove pyramid quantities radii radius ratio rectangles regular polygon remainder respectively right angles right triangle Scholium sector segment side BC similar similar polygons solidity Solution sphere spherical square straight line Suppose Take tangent Theorem third triangles ABC vertex vertices whence
Page 141 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 20 - The sum of the three angles of any triangle is equal to two right angles.
Page 16 - Theorem. In an isosceles triangle the angles opposite the equal sides are equal.
Page 87 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Page 31 - Theorem. In the same circle, or in equal circles, equal arcs are subtended by equal chords.
Page 17 - Jl will be equal to C. 56. Corollary. An equilateral triangle is also equiangular. 57. Theorem. The line BD (fig. 32), which...
Page 68 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 71 - Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245.
Page 135 - ... equal as to the magnitude of those parts. Hence, those two triangles, having all their sides respectively equal in both, must either be absolutely equal, or at least symmetrically so; in both of which cases their corresponding angles must be equal, and lie opposite to equal sides.