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ABC fig AC AC adjacent angles altitude angle BAC arc BC base and altitude bisect centre chord circumference coincide convex surface Corollary cylinder DEF fig Definitions denote diameter divided equal arcs equal distances equiangular with respect equilateral equilateral polygon equivalent frustum given angle given circle given line given point given polygon given sides given square gles greater half the product Hence homologous sides hypothenuse infinite number infinitely small Inscribed Angle inscribed circle isosceles Join AC line AB fig line BC mean proportional measure half number of sides oblique lines parallel lines parallel to BC parallelogram parallelopipeds perimeter perpendicular polyedron polygon ABCD &c preceding prism Problem Proof radii rectangles regular polygon respectively equal right triangles Scholium secant segment side BC similar polygons similar triangles solid angle Solution sphere spherical triangle tangent Theorem trapezoid triangles ABC vertex vertices
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 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 24 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page xv - The first term of a ratio is called the antecedent, and the second term the consequent.
Page 16 - Theorem. In an isosceles triangle the angles opposite the equal sides are equal.
Page 136 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.
Page 76 - AB (fig. 132) equal to the side of ono of the given squares. Draw BC, perpendicular to AB, and equal to the side of the second given square.
Page 20 - The sum of the three angles of any triangle is equal to two right angles.