 | William John M'Clelland - 1885 - 182 pages
...equation for a plane triangle. 0. A spherical quadrilateral is circumscribed to a small circle: show that the sum of one pair of opposite sides is equal to the sum of the other pair. 7. In a spherical triangle, prove that — (1) If three sides are acute, two angles are acute ; (2)... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...to the inner from points on the outer are equal. 3. If a quadrilateral be circumscribed to a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. 4. If a parallelogram be circumscribed to a circle it must be a lozenge, and its diagonals intersect... | |
 | Euclides - 1885 - 340 pages
...to the inner from points on the outer are equal. 3. If a quadrilateral be circumscribed to a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. 4. If a parallelogram be circumscribed to a circle it must be a lozenge, and its diagonals intersect... | |
 | Samuel H. Winter - 1887 - 260 pages
...required. FIG. 78. PROBLEM LXXXVI. To inscribe a circle in (i.) a given rhombus; (ii.) a trapezium when the sum of one pair of opposite sides is equal to the sum of the others; (iii.) a given sector. G. 79. (i.) Draw the diagonals. The point of their intersection is the... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...between the diagonals. Proposition 2O. Theorem. 252. In any quadrilateral circumscribing a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. Hyp. Let ABCD be a quadrilateral circumscribing a OTo prove AB + CD = AD + BC. Proof. From the centre... | |
 | Euclid - Geometry - 1892 - 460 pages
...which subtends a right angle at the centre. . 11. In any quadrilateral circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair. 12. Any parallelogram which can be circumscribed about a circle, must be equilateral. 13. If a quadrilateral... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...2. The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair. 3. If 0 be the point of intersection of the perpendiculars drawn from the... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...If the diagonals of a quadrilateral intersect at right angles, prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair. SOLID GEOMETRY. CHAPTER VI. LINES AND PLANES. Definitions. 394. Geometry... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...2. The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair. 3. If O be the point of intersection of the perpendiculars drawn from the... | |
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The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair. 
