 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...AC) = rectangle (AH, AR). THEOREM (h). The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by the opposite sides. Let FGHK be a quadrilateral figure inscribed in the a FGHK, and FH, GK its diagonals.... | |
 | alexander thom - 1875 - 758 pages
...reciprocally proportional ? Prove the propositions referred to. 4. Prove that the rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. Hence calculate the side of a regular quindecagon... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...(VI. 16.) If therefore from any angle, &c. QED PROPOSITION D. THEOREM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...the rectangles contained by its opposite sides. Let ^ .BCD be any quadrilateral figure inscribed in a circle, and join^C, BD. The rectangle contained by... | |
 | Richard Wormell - 1876 - 268 pages
...the triangle. . . . . . . . . . . 240 D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides. . , 240 E. If a segment of a circle be bisected, and from the extremities of the base of the segment,... | |
 | D. Tierney - 1877 - 126 pages
...readily proved that AB is divided as required in the points b, b', &c. 7. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. Euclid, Book VI., Prop. D. 8. Define the tangent of an angle, find the value of tan60°, and prove... | |
 | Euclides - 1878 - 398 pages
...rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles, contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a ®. Join AC, BD. Then reet. AC, BD=rect. AB, CD together with rect. AD, BC. Make L ABE... | |
 | Great Britain. Civil Service Commission - 1879 - 620 pages
...and Q respectively. Show that it' PD=QD, then BP : CQ: :BA : CA. 9. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. PLANE TRIGONOMETRY. Time allowed, 3 hours. 1. Explain what is meant by the circular measure of an angle.... | |
 | Sandhurst roy. military coll - 1880 - 68 pages
...given straight line may be divided into any number of equal parts. 7. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a...both the rectangles contained by its opposite sides. 8. Define the tangent of an angle, find the value of tan 60°, and prove that tan (180 — A) = —... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...length of the arc PQ, LP always meets OA produced in a fixed point. 11. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by the opposite sides. ALGEBEA. 1 . Show that the result is the... | |
 | Oxford univ, local exams - 1880 - 396 pages
...a given triangle by a straight line drawn parallel to the base. 11. 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. 12. If a straight line stand at right angles... | |
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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. 
