 | Queensland. Department of Public Instruction - Education - 1866 - 336 pages
...triangle are together greater than the third side. Show from this proposition that the difference of any two sides of a triangle is less than the third side. 4. Prove that in any right-angled triangle, the square which is described upon the side subtending... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...; hence BC can be neither equal to, nor greater, than AC; it is therefore less than AC. THEOREM XX. The difference between any two sides of a triangle is less than thj third side. Let ABCbe a A, in which ACis greater than AB; then we are to prove that AC — AB is... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...plane perpendicular to a plane;" "a dihedral angle;" "similar solid figures." 2. The difference of any two sides of a triangle is less than the third side. 3. The straight line drawn at right angles to the diameter of a circle from the extremity of it, falls... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...members of the inequality we subtract the side BC, we shall have AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. THEOREM XI. If from a point within a triangle two lines be drawn to the extremities of either side,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...these two unequals the side CB, we shall have the difference between AB and CB less than AC ; that is, the difference between any two sides of a triangle is less than the other side. . PROPOSITION X. — THEOREM. 64. The greater side of any triangle is opposite the greater... | |
 | Robert Potts - 1868 - 434 pages
...point A may be to the line BC. It may be easily shewn from this proposition, that the difference of any two sides of a triangle is less than the third side. Prop. xxn. When the sum of two of the lines is equal to, and when it is less than, the third line ;... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...hypothesis; hence BC can be neither equal to, nor greater, than AC; it is therefore less than AC. THEOREM XX. The difference between any two sides of a triangle is less than thi third side. Let ABCbe a A, in which ACis greater than AB; then we are to prove that AC —AB is... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...following problems, until Book V. has been studied GEOMETRICAL EXERCISES ON BOOK I. 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... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...same as the axiom that the shortest distance between two points is a straight liue. 275. COR. 2. — The difference between any two sides of a triangle is less than the third side. DEM.— Let a, b, and e be the sides. By Corollary 1st, a + b.> e. Therefore, transposing, a > с —... | |
 | Edward Olney - 1872 - 270 pages
...same as the axiom that the shortest distance between two points is a straight Hue. 273. COR. 2.—The difference between any two sides of a triangle is less than the third side. DEM.—Let «, b, and c he the sides. By Corollary 1st, a, + b > e. Therefore, transposing, a > c —... | |
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The difference between any two sides of a triangle is less than the third side. 
