| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...... BA: AD :: EA: AC; Prop.65. ... BA. AC = AD. EA. If therefore any angle, &c. PROP. LXXX. THEOR. **The rectangle contained by the diagonals of a quadrilateral...inscribed in a circle, is equal to both the rectangles** together, con-tained by its opposite sides. Let ABCD be any quadrilateral fig. inscrib. in a 0 ; draw... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...BA : AD :: EA : AC ; Prop. ss. ... B A. AC = AD. EA. If therefore any angle, &c. PROP. LXXX. THEOR. **The rectangle contained by the diagonals of a quadrilateral...inscribed in a circle, is equal to both the rectangles** togetlier, contained by its opposite sides. Let ABCD be any quadrilateral fig. inscrib. in a 0 ; draw... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...the rectangle EA.AD. JD PROP. D. THEOR. 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 let AC, BD be drawn ; the rectangle AC.BD... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...; c)p. 4,6; . (d) p. lli, 6. QED D Th. The rectangle contained by the diagonals of a quadrilateral **inscribed in a circle, is equal to both the rectangles contained by its opposite sides.** Given ABCD any quadrilateral inscribed in a circle ; also AC, BD, diagonals joining its oppo6ite angles:... | |
| Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...will intersect the hyperbola in the four points required. ST JOHN'S COLLEGE. DEC. 1841. (No. XII.) **1. 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. Four circles are drawn, of which each... | |
| Euclides - 1848 - 52 pages
...by the perpendicular and the diameter of the circle described about the triangle. PROP. D. THEOREM. **The rectangle contained by the diagonals of a quadrilateral...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... | |
| Education - 1851 - 502 pages
...SECTION III. — 1. The sides 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... | |
| 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 contained by its opposite sides.** Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD : the rectangle contained by AC,... | |
| 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... | |
| Euclid, John Playfair - Geometry - 1853 - 317 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 by its opposite sides.** Let ABCD be any quadrilateral inscribed in a circle, and let AC, BD be drawn ; the rectangle AC.BD... | |
| |