 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...Similarly it may be shown that AC and CB are together greater than AB, and CB and BA than AC. QED COR. The difference of any two sides of a triangle is less than the third side. *Ex. 1 8. The straight line drawn from the vertex of a triangle to the middle point of the base is... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...sides AB, BC, as BC, for example, there remains (A. 5), AC - BC < AB ; that is, the difference between any two sides of a triangle is less than the third side. resent the sides of a triangle, the sum of any two must be greater than the third, and the difference... | |
 | Richard Anthony Proctor - Geometry - 1887 - 202 pages
...than P Q. Let QD cut AB in E, and join EP : with this construction the proof is obvious. PROP. 20. 54. The difference of any two sides of a triangle is less than the third side. 55. A point P is taken within the triangle ABC; show that the sum of the distances PA, PB, and PC is... | |
 | Euclid - Geometry - 1892 - 460 pages
...respectively: shew that, if AB is greater than AC, then OB is greater than OC. ON PROPOSITION 20. 7. The difference of any two sides of a triangle is less than the third side. 8. In a quadrilateral, if two opposite sides which are not parallel are produced to meet one another;... | |
 | Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 pages
...of the sides of a quadrilateral is greater tftan the sum of the diagonals. 5. The difference between any two sides of a triangle is less than the third side. 6. Given two points C, D and a straight line AB, find P in AB such that the difference between PC and... | |
 | 1894 - 1136 pages
...every respect. Prove Part i. only that is two angles and the adjacent side being given. (Prop. a6 V 7. The difference of any two sides of a triangle is less than> the third side. (From Prop-. 20) 8. .Construct a triangle, having given the base, one of the angles at the base, and... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...and AD and BC intersect at O. Prove tkat AOB is an isosceles triangle. Ex. 60. The difference between any two sides of a triangle is less than the third side. PROPOSITION XXXIII. THEOREM. 108. Converse of Prop.XXXII,!. The shortest lin* from, a point- to a line... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...VZACD = ZDCB. Stepl 4. .'.b>AD. Th. 7. State it 5. Similarly a> DB. 6. .'.a+b>c. Add 4 and 5 COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b, then a > c — b, by ax. 5. EXERCISES. 55. State the converse of each... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...ZDCB. Stepl 4. .'. b>AD. Th. 7. State it 5. Similarly a> DB. 6. .'. a + b>c. Add 4 and 5 COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b, then a > c — b, by ax. 5. EXERCISES. 55. State the converse of each... | |
 | Frederick Coate Wade - Catholic Church Education Manitoba - 1895 - 168 pages
...CLASS. EUCLID. 1. Any two sides of a triangle are greater than the third side. The difference between any two sides of a triangle is less than the third side. 2. The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects... | |
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AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. 
