...is equal to the rectangle E AA D (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let AB С D be any quadrilateral figure inscribed in a circle, and A С and BD its diagonals. The rectangle...

...which makes BAE an isosceles triangle: shew that BC or DE is a mean proportional to BE and CD. 11. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. 13. If in the same circle there be inscribed two triangles of equal area, then the rectangle contained...

...PROPOSITION D. (a) VI. 5. (6) III. 21 (c) III. 31. (<Z) VI. 4. (e) VI. 16. THEOREM.—The rectangle under the diagonals of a quadrilateral figure inscribed...both the rectangles contained by its opposite sides. DEMONSTRATION. Let ABCD be any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle...

...ас Т«* hence Oa.bc=0b.ac+0c. ab. Or, the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides; as we know by Euclid, book vi., prop. D. Again, it is known that if О be any point in the circumference...

...rectangle EA.AD. PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed ma circle, is equal to both the rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD...

...a polygon of irregular shape, how would it have to be dealt with in the course of construction ? 6. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. EUCLID. BOOKS I. II. III.—(B.) For all Candidates for a SA Degree. 2. If a straight line fall upon...

...duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. SECT. II, — 1. Describe a rhombus, of which one diagonal shall be double the other. 2. In a given...

...Approximate to the value of the real root of the equation xs — 6*= 100. 4. Prove that the rectangle under the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles under the opposite sides ; and hence calculate the side of a regular quindecagon...

...equal to the rectangle EA, AD. (Vi. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let AB CD be any quadrilateral figure inscribed in a circle, and join AC, BD. The rectangle contained...

...a) VI. 5. 6) III. 21 ) III. 31. ) VI. 4. e) VI. 16. PROPOSITION D. THEOREM. — The rectangle under the diagonals of a quadrilateral figure inscribed...both the rectangles contained by its opposite sides. DEMONSTRATION. Let ABCD he any quadrilateral figure inscribed in a circle, and join AC, BD : the rectangle...