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ABCD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle DAE angle DEF angle equal angle HBK angular points base bisectors chord HK circle ABC circle whose centre circles touch circumscribed circle coincide Constr diagonal diameter distance duplicate ratio equal to AC equiangular exterior angle externally given angle given circle given point given ratio given straight line greater Hence hypotenuse identically equal inscribed circle isosceles triangle less Let ABC magnitudes meet the circumference middle point minor arc multiple nine-points circle opposite angle opposite sides orthocentre parallelogram perpendicular point of contact polygon Prob produced proportional Prove Q.E.D. Theor quadrilateral radii radius ratio compounded rectangle AC rectangle contained rectilineal figure rhombus right angles Shew side BC square on AC straight line drawn tangent Theor Theorem triangle ABC triangle DEF twice the rectangle vertical angle
41 ページ - 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.
182 ページ - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
67 ページ - 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.
167 ページ - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
32 ページ - Any two sides of a triangle are together greater than the third side.
34 ページ - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
23 ページ - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
63 ページ - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
39 ページ - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.