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ABCD angle ABC angle BAC assumed base bisect Book centre circle circle ABC circumference common compounded constr CONSTRUCTION conversely definition DEMONSTRATION describe diameter Dictionary divided double draw drawn Edition Elements English equal angles equiangular equilateral equimultiples Exercises exterior angle extremity fall four fourth French given rectilineal given straight line Grammar greater greater ratio half History inscribed interior join Latin less magnitudes manner meet multiple parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals proposition proved Q. E. D. PROP ratio reason rectangle contained rectilineal figure References References-Prop Relating remaining angle right angles Schools segment shown sides similar square taken THEOREM third triangle ABC wherefore whole
Page 140 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 310 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 4 - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Page 310 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page xxxvii - 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 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.