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 ## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...AD (VI. 16). I'JtorOSITJON D. THEOBEM. 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 any quadrilateral ABCD inscribed in a circle, and join AC and BD ; to prove that the rectangle... ## Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...vertex C to the base, AE, of the other : ie BA . AC : EC . CA = AD : perp. from C. PROP. D. — THEOR. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Cow. 23, 1. DEM. 21, Ш. 4, VI. 16, VI. 1, II. If there be two st. lines, one of which is divided into... ## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...touch the circle. VOLUNTARY PORTION. 1. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides. 2. If two straight lines are at right angles to the same plane they shall be parallel to each other. 3.... ## Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...equilateral triangle, and compare the area of the hexagon so inscribed with the area of the triangle. a quadrilateral figure inscribed in a circle is equal...both the rectangles contained by its opposite sides. If the diagonals of the quadrilateral intersect at right angles, show that the sum of the squares of... ## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...(vI. 1 6.) If therefore from. any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained bg the diagonals of a quadrilateral figure inscribed...circle, is equal to both the rectangles contained bg its opposite sides. Let ABCD be any quadrilateral figure inscribed in a circle, and join AC, BD.... ## The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...equal to the rectangle EA, AD. (vi. 16.) If, therefore, from any angle, &c. QED PROP. D.— THEOKEM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. (References— Prop. i. 23 ; n. 1; III. 21 ; VL 4, 16.) Let ABCD be any quadrilateral figure inscribed... ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...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 A BCD be any quadrilateral figure inscribed in a circle, and join AC, BD. The rectangle contained... ## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 358 pages
...to <be rectangle EA.AD. PROP. D. THEOR. The Ttttangl*. contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles, contained by ut opposite sides, I >et ABCD bo any quadrilateral inscribed in a circle, and let AC, BD be drawn ;... ## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...rectangle EA, AD. ' [VI. 16. Wherefore, if from the vertical angle &c. QED PROPOSITION 2). THEOREM. The rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. Let ABCD be any quadrilateral figure inscribed in a circle, and join AC, BD: the rectangle contained... 