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The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Pure Mathematics - Page 273
1874

## Mathematical problems and examples, arranged according to subjects, from the ...

Mathematics - 1836
...two, the plane which passes through them, is parallel to the plane passing through the others. 1831 9. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 10. Describe an equilateral and equiangular pentagon about a given circle. 11. Triangles and parallelograms...

## The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...equal angles are similar. PROP. XIV. THEOR. The opposite angles of any quadrilateral figure described in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,...

## A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Geometry - 1836 - 128 pages
...circle from any one point but the centre, ibid. ART. 69. The opposite angles of a four-sided rectilineal figure inscribed in a circle are together equal to two right angles, 53. ART. 70. The angles in the same segment of a circle are equal, 55. AIIT. 71. The angle in the segment...

## Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - Geometry - 1836 - 220 pages
...OF THE ANGLES AND SIDES OF INSCRIBED FIGURES. THEOREM I. 26. The opposite angles of a quadrilatéral inscribed in a circle, are together equal to two right angles. Let AB С D be a quadrilateral inscribed in the circle A С D ; the opposite angles AB С, AD С are together...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...BEC, 2. that, similarly, Z CAD, =: Z CED, 3. that .'. whole Z BAD — whole Z BED. PROPOSITION XXII. Theorem. The opposite angles of any quadrilateral...in a circle are together equal to two right angles. Steps of the Demonstration. 1. Prove that whole Z ADC = Zs BAG + ACB, 2. that Zs ADC + CBA = the 3...

## Lessons on form; or, Introduction to geometry as given in a Pestalozzian ...

Charles Reiner - 1837
...intersect each other at right angles, the four straight lines joining their extremities form a square. 15. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 16. A square,—a rectangle,—and a trapezium of which the opposite angles are together equal to two...

## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...whole angle BED. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure described in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...segment, &c. * PROP. XXII. THEOR. THE opposite angles of any quadrilateral figure described in a circle, t are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right angles. Join AC,...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...equal to the whole angle BED. Therefore the angles in the same segment, &c. QE n. PROP. XXII. THEOR. The opposite angles of any quadrilateral figure inscribed...two right angles. Let ABCD be a quadrilateral figure in the circle ABCD; any two of its opposite angles shall together be equal to two right angles. Join...

## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...XXI. THEOR. All angles in the same segment of a circle are equal to one another. PROP. XXII. THEOR. The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. PROP. XXIII. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two...