 | Horatio Nelson Robinson - 1863 - 362 sider
...EG. Because EF is equal to EG we have EF'—EF=EF'—EG. But EF' — EG, is less than F'G, because the difference of any two sides of a triangle is less than the third side. That is, EF' — EF is less than A' A; consequently the point E is without the curve (Prop. 2), and... | |
 | Euclides - 1863 - 74 sider
...than CE : And BA -f- AC > BE + CE, which are equal to BC. Therefore any two sides, &c. QED CoR. — The difference of any two sides of a triangle is less than the rem. side. D. 1 by P. 20. The sides AC and BC are > AB ; 2 Sub. take AC both from (AC + BC,) and also... | |
 | Euclides - 1864 - 448 sider
...however near the 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 ;... | |
 | Queensland. Department of Public Instruction - 1866 - 336 sider
...any two sides of a 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... | |
 | Euclides - 1865 - 402 sider
...be drawn from the given point to the given straight line, one on each side of the perpendicular. 19. The difference of any two sides of a triangle is less than the third. 20. The three sides of a triangle taken together are greater than the double of any one side, but less... | |
 | Gerardus Beekman Docharty - 1867 - 474 sider
...Corol. If from both 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,... | |
 | Robert Potts - 1868 - 434 sider
...however near the 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 ;... | |
 | Euclides - 1870 - 270 sider
...and AC > BE and CE, which arc' equal to BC. Recap. Therefore, any two sides, &c. QED COR. — Tlie difference of any two sides of a triangle is less than the remaining side. DEM. 1 by P. 20. Sub. Ax. 5. The sides AC and BC are >AB ; take away AC both from (AC... | |
 | Elias Loomis - 1871 - 302 sider
...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 - 1872 - 472 sider
...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 —... | |
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AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. 
