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THE rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.* Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD ; the.
The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ... - Page 79
by Āryabhaṭa - 1878

## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...diameter of the circle described about the triangle. PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. BOOK XL DEFINITIONS. I. A SOLID is that which hath length, breadth, and thickness. II. That which bounds...

## The English Journal of Education, Volume 5

Education - 1851 - 502 pages
...about the equal angles of equiangular triangles are proportionals. 3. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. 2. If one diagonal of a quadrilateral bisects...

## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...any angle, etc. QED PROPOSITION D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles...its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD : the rectangle contained by AC, BD is equal to the two rectangles...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 pages
...rectangle EA.AD. PROP. D. THEOR. The rectangle contained by the diagonals of a quadrilateral inscribed tn a circle, is equal to both the rectangles, contained...its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD is equal to the two rectangles...

## The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...angle, &c. QED PROPOSITION D. — THEOREM. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposiie sides. LET abcd be any quadrilateral inscribed in a circle, and join ac, bd ', the rectangle...

## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...D (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...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...

## Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...triangle: shew that BC or DE is a mean proportional to BE and CD. 11. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...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...

## The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...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 in a...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...