Books Books The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides. Cambridge Problems: Being a Collection of the Printed Questions Proposed to ... - Page 112
1821 - 425 pages ## The Elements of Geometry, Symbolically Arranged

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... ## The Elements of Geometry, Symbolically Arranged

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

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... ## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

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:... ## The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

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

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... ## The English Journal of Education, Volume 5

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... ## 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 contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle, and join AC, BD : the rectangle contained by AC,... ## 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... 