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AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle equal base BC bisect centre circle ABC circumference constr CONSTRUCTION Take DEMONSTRATION diameter divided double draw equal angles equal straight lines equal to F equilateral and equiangular equimultiples exterior angle four magnitudes fourth given circle given point given rectilineal angle given straight line gnomon greater ratio inscribed less Let ABC meet multiple opposite angles parallel to BC parallelogram pentagon perpendicular plane polygon produced proposition Q. E. D. PROP rectangle contained References—Prop remaining angle right angles segment solid angle square of AC straight line AC straight line drawn Theorem third three straight lines touches the circle triangle ABC twice the rectangle wherefore
Página 144 - 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...
Página iv - 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.
Página 37 - 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.
Página x - 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.
Página 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Página iv - 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.
Página xli - 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'.
Página 73 - 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.