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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

## Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...straight line. Hence show how a given straight line may be divided into any number of equal parts. 7. The rectangle contained by the diagonals of a quadrilateral...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) = —...

## Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...Show that, whatever be the 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...

## Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 394 pages
...their homologous sides. Bisect 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...

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

Euclides - Euclid's Elements - 1881 - 236 pages
...is equal to the rectangle E A. AD (VI. 16). Therefore, if from any angle, &c. QED PROP. D. THEOR,EM. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle, is equa I to both the rectangles contained by its opposite sides. Let ABCD he any quadrilateral figure...

## A Short History of Greek Mathematics

James Gow - Mathematics - 1884 - 350 pages
...now appended to Euclid vi. (D), that " the rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both the rectangles contained by its opposite sides1", and then proceeds to shew how from the chords of two arcs that of their sum and difference...

## Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. 1 1 . The rectangle contained by the diagonals of a...quadrilateral figure inscribed in a circle is equal to the two rectangles contained by the opposite sides. II. ARITHMETIC. (Including the use of Common Logarithms.)...

## Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...similar triangles are to one another in the duplicate ratio of their homologous sides. 6. Prove that the rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides. What does this theorem become when the quadrilateral is a rectangular parallelogram ? ' 7. Prove that...

## Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890 - 530 pages
...is divided by the point of contact of the inscribed circle is equal to the area of the triangle. 7. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by pairs of opposite sides. If the quadrilateral cannot be inscribed...

## A history of elementary mathematics

Florian Cajori - Mathematics - 1896 - 338 pages
...which seems original with him. After proving the proposition, now appended to Euclid, VI. (D), that "the rectangle contained by the diagonals of a quadrilateral...both the rectangles contained by its opposite sides," he shows how to find from the chords of two arcs the chords of 1 JL HEIRERG in Bibliotheca Mathematica,...

## School Science and Mathematics, Volume 17

Education - 1917 - 908 pages
...PTOLEMY'S THEOREM. By ALBERT BABBITT, University of Nebraska, Lincoln. Ptolemy's theorem states that "the rectangle contained by the diagonals of a quadrilateral...equal to both the rectangles contained by its opposite sides."1 By means of this theorem and the Law of Sines, the addition and subtraction formulas of trigonometry...