 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 - 570 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 - Geometry, Modern - 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 - 898 pages
...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.... | |
| |
