 | 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...intersection of the diagonals) to the four angles. 14. Construct a triangle, having given one side, an adjacent angle, and the sum or difference of the... | |
 | 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...intersection of the diagonals) to the four angles. Prop. 3. If a straight line which bisects the vertical angle of a triangle also bisects the base, the... | |
 | 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...intersection of the diagonals) to the four angles. Prop. 3. If a straight line which bisects the vertical angle of a triangle also bisects the base, the... | |
 | Euclides - 1860 - 288 pages
...quadrilateral figure whose diagonals bisect each other is a parallelogram. 30. The sum of the diagonals of any quadrilateral is less than the sum of any four lines that can be drawn to the four corners from any point which is not the intersection of the diagonals. 31. Half the base... | |
 | 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...intersection of the diagonals) to the four angles. Prop. 3. If a straight line which bisects the vertical angle of a triangle also bisects the base, the... | |
 | 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...less than the third side. See Prop. 8. Prop. 2. The sum of the diagonals of a quadrilateral is lesa than the sum of any four lines that can be drawn from...intersection of the diagonals) to the four angles. See Prop. 8. Prop. 3. If a straight line which bisects the vertical angle of a triangle also bisects... | |
 | 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...intersection of the diagonals) to the four angles. 4. In rider 2 to prop. 15, show that the sum of the two straight lines is less than the sum of any... | |
 | 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...intersection of the diagonals) to the four angles. &. Prove that the sum of the distances of any point from the angular points of a quadrilateral is greater... | |
 | Euclides - 1884 - 434 pages
...perimeter of a quadrilateral is greater than the sum and less than twice the sum of the two diagonals. 12. The sum of the diagonals of a quadrilateral is less than the sum of the four straight lines which can be drawn to the four angles from any other point except the intersection... | |
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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) to the four angles. 
