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ABCD acute adjacent altitude approaches base bisector bisects called centre chord circle circumference circumscribed coincide common constant construct describe diagonals diameter difference distance divide Draw drawn equal equidistant equilateral triangle equivalent exterior external extremities fall feet figure Find formed given circle given line given point greater half Hence homologous hypotenuse inches included inscribed intercepted intersecting isosceles triangle joining legs length less limit locus mean measured meet middle point number of sides parallel parallelogram passes perimeter perpendicular plane PROBLEM Proof proportional PROPOSITION prove quantities radii radius ratio rectangle regular polygon respectively right angle right triangle segments sides similar square straight line supplementary Suppose tangent THEOREM third touch trapezoid triangle triangle ABC true unequal variable vertex vertices
Page 35 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 152 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Page 68 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 193 - 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 171 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 34 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 73 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Page 158 - 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 77 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 164 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.