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acute adjacent altitude arc A B base bisect called centre chord circle circumference circumscribed coincide common Cons construct contained COROLLARY describe diagonals diameter difference direction divided Draw equal distances equal respectively equilateral equivalent erected extremities fall figure formed four Geometry given greater Hence homologous sides hypotenuse included inscribed intersect isosceles joining less Let A B limit line drawn mean measured meet middle point multiplied number of sides one-half opposite sides parallelogram perimeter perpendicular placed plane position PROBLEM proportional prove Q. E. D. PROPOSITION quadrilateral quantities radii radius equal ratio rect rectangles regular polygon right angles segment Show similar similar polygons square straight line Substitute subtend surface symmetrical Take taken tangent THEOREM triangle variable vertex vertices
Page 144 - 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 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 200 - In any proportion, the product of the means is equal to the product of the extremes.
Page 173 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 159 - In any triangle the product of two sides is equal to the product of the diameter...
Page 132 - 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.
Page 70 - I) is a parallelogram, E and F the middle points of AD and BC respectively ; show that BE and DF will trisect the diagonal A C.
Page 48 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...