Tin; 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. Science Examination Papers - Page 248by Great Britain. Education Department. Department of Science and Art - 1899Full view - About this book
| 1896 - 154 pages
...pair of opposite sides is equal to the rectangle contained by the perpendiculars on the diagonals. 3. **The rectangle contained by the diagonals of a quadrilateral...equal to the sum of the two rectangles contained by** the opposite sides. In a quadrilateral inscribed in a circle, the rectangle contained by the sides... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 pages
...equal to the sum of the other two sides (§ 1 76). 220. Exercise. — The sum of two opposite angles **of a quadrilateral inscribed in a circle is equal to the sum of the** other two angles, and is equal to two right angles. 230. Exercise. — Two circles are tangent externally... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...equal to the sum of the other two sides (§ 176). • 220. Exercise. — The sum of two opposite angles **of a quadrilateral inscribed in a circle is equal to the sum of the** other two angles, and is equal to two right angles. 230. Exercise. — Two circles are tangent externally... | |
| Arthur Cayley - Mathematics - 1896 - 663 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. D) relating to **the rectangle contained by the diagonals of a quadrilateral inscribed in a circle.** The Arabians made the improvement of using in place of the chord of an arc the sine, or half chord,... | |
| Arthur Cayley - Mathematics - 1896 - 676 pages
...the subject he gives there the theorem afterwards inserted in Euclid (Book VI. Prop. D) relating to **the rectangle contained by the diagonals of a quadrilateral inscribed in a circle.** The Arabians made the improvement of using in place of the chord of an arc the sine, or half chord,... | |
| Yale University - 1898 - 212 pages
...at the point of tangeiicy passes through the center of the circle. 3. The sum of two opposite angles **of a quadrilateral inscribed in a circle is equal to the sum of the** other two angles, and is equal to two right angles. 4. Construct with ruler and compass a circle passing... | |
| Mathematics - 1898 - 228 pages
...at the point of tangency passes through the center of the circle. 3. The sum of two opposite angles **of a quadrilateral inscribed in a circle is equal to the sum of the** other two angles, and is equal to two right angles. 4. Construct with ruler and compass a circle passing... | |
| Edward Brooks - 1901 - 278 pages
...+ AD\ And ^D^=ABxAC-BDx CD. Therefore, etc. PROPOSITION XXXVI. — THEOREM. The product of the two **diagonals of a quadrilateral inscribed in a circle is equal to the sum of the** products of its opposite sides. Given. — Let ABCD be any quadrilateral inscribed in a circle, AC... | |
| 1903
...circles pass through the centre of the third. Show that the radii are in harmonical progression. 4. Prove **that the rectangle contained by the diagonals of a...quadrilateral inscribed in a circle is equal to the sum of the** rectangles contained by the opposite sides. A circle is described round an equilatenil triangle ABC.... | |
| Euclid - Euclid's Elements - 1904 - 488 pages
...AD :: EA : AC; VI. 4. .-. the rect. BA, AC = the rect. EA, AD. VI. 16. QED PROPOSITION D. THEOREM. **The rectangle contained by the diagonals of a quadrilateral...the two rectangles contained by its opposite sides.** Let ABCD be a quadrilateral inscribed in a circle, and let AC, BD be its diagonals. Then the rect.... | |
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