 The sum of the diagonals of a quadrilateral is less than the sum and greater than half the sum of tht. sides. * 21. Each side of a triangle is less than half the perimeter.  Exercise Manuals - Page 5by George Albert Wentworth - 1889Full view - About this book
 | Euclides - 1846 - 292 pages
...and DF is greater than that of any other two lines drawn from E and D to meet in. the line AB. 13. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...Prop. 1 . The difference between any two sides of a triangle is less than the third side. Prop. 2- The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...THEOREMS. Prop. 1. The difference between any two sides of a triangle is less than the third side. Prop. 2. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...the opposite angle. 17. 0 is any point within the triangle ABC, shew that OA, OB, OC together, are less than the sum, and greater than half the sum, of the sides of the triangle. 1 8. ABC is a triangle, AB greater than BC . BD bisects the base AC, and BE the angle... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...Prop. 1 . The difference between any two sides of a triangle is less than the third side. Prop. 2. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
 | André Darré - 1872 - 226 pages
...being given, to construct it. 17. To construct a square and a regular hexagon on a given line. 18. The sum of the diagonals of a quadrilateral is less than the sum of four lines drawn to the vertices of the angles from any point within the figure different from the... | |
 | Euclides - 1874 - 120 pages
...the 17. The sum of the straight lines drawn from any points within a triangle to each of its angles is less than the sum and greater than half the sum of the sides of the triangle. 18. Show that the last exercise is true if a square be substituted for the triangle.... | |
 | Charles Mansford - 1879 - 112 pages
...base. 17. The sum of the straight lines drawn from any point within a triangle to each of its angles is less than the sum and greater than half the sum of the sides of the triangle. 18. Show that the last exercise is true if a square be substituted for the triangle.... | |
 | Euclides - 1879 - 146 pages
...any point from the angular points of a quadrilateral is greater than half the sum of the sides. 3. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...the angular points is the least possible when P is situated at the intersection of the diagonals. 8. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals)... | |
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