...inscribed angle subtended by the difference of the opposite intercepted arcs. PROPOSITION XVII. THEOREM. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two right angles. The opposite angles A, C, or ABC, ADC, of the inscribed quadrilateral ABCD, are together equal to two...

...other given angle, to which it is external or internal, contrary to prop. 16, b. 1. PROP. 22. THEOR. The opposite angles of a quadrilateral inscribed in a circle, are together equal to two rig/it angles. For of either triangle, into which one of the diagonals resolves the quadrilateral,...

...which joins their centres, shall pass through the point of contact. 10. The opposite angles of any quadrilateral inscribed in a circle, are together equal to two right angles. 11. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting...

...Therefore zAOC + zBOD =* 2zEBC + 2/ECB, = 2ZAEC. 1851. (A). The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles, (in. 22.) (jB). If a polygon of an even number of sides be inscribed in a circle, the sum of the alternate...

...the difference of the angles BDE, ADE, will be invariable. SECTION III. 1. The opposite angles of Buy quadrilateral inscribed in a circle, are together equal to two right angles. No parallelogram can be inscribed in a circle, unless it be rectangular. 2. In equal circles the angles...

...the square on the other part. Deduce the same from the preceding propositions of the Second Book. 6. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two .right angles. Shew that no parallelogram, except a rectangle, can be inscribed in a circle. 7. If a straight line...

...a; into — x, we have [-*]"" = (~1)a ; also, [-*]» - 1. * 1531 (Proposed by Dr. BOOTH, FRS)— " The opposite angles of a quadrilateral inscribed in...a circle are together equal to two right angles." What is the more general theorem in the conic sections, of which this is a particular case P Solution...

...square of half the line is equal to the square of the line made up of the half and the produced part. 3. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. o. If the opposite angles of a quadrilateral are together equal to two right angles, the quadrilateral...

...into — x, we have [-*]-* = (~1)» ; also, [-*]" = 1. O-rp 1 53 1 (Proposed by Dr. BOOTH, PES)— " The opposite angles of a quadrilateral inscribed in...a circle are together equal to two right angles." What is the more general theorem in the conic sections, of which this is a particular case ? Solution...

...more than four aides, shew that at least one of its angles must be greater than a right angle. III. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. IV. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the...