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ABCD adjacent angle BAC applied base bisects called centre chords circumference coincide construction containing Corollary corresponding DEFINITION denominator described diameter difference dihedral angle distance divided double draw drawn equal EXAMPLES exterior angle extremities figure follows four given circle given plane given point given ratio given straight line greater half homologous inscribed inter intersection join length less Let ABC line joining locus magnitudes meet middle point multiple opposite sides pair parallel parallelogram passing perpendicular plane polygon position possible PROBLEM produced Prop proportional PROPOSITION Prove radius ratio rectangle regular remaining respectively respectively equal right angles segments sides similar Similarly situated square Take taken tangent third touching triangle ABC triangle DEF
Side 15 - If two triangles have two sides of the one equal to two sides of the...
Side 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Side 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 204 - 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'.
Side 14 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 12 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Side 161 - Ir there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words