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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 base bisectors chord HK circle ABC circle whose centre circles DEF circles touch circumscribed circle coincide Constr diagonal diameter distance equal circles 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 line joining 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 squares on BD straight line drawn tangent Theorem triangle ABC triangle DEF twice the rectangle vertical angle
Page 41 - 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.
Page 182 - 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.
Page 67 - 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.
Page 167 - 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.
Page 32 - Any two sides of a triangle are together greater than the third side.
Page 34 - 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.
Page 23 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Page 63 - 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.
Page 39 - 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.
Page 106 - Iff 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 of the other part, is equal to the square of the straight line which is made up of the whole and that part.