| Herbert Edwin Hawkes, Frank Charles Touton - 1920 - 305 sider
...more usual statement is : A straight line is the shortest line between two points. Theorem 40 147. **The sum of any two sides of a triangle is greater than the** sum of two lines drawn from a paint within it to the extremities of the third side. 1C AB Given the... | |
| David Eugene Smith - 1923 - 296 sider
...know that ZA> Z5. Accordingly, we conclude that the theorem is true. 88 Exercises. Inequalities 1. **The sum of any two sides of a triangle is greater than the third side,** and the difference between any two sides is less than the third side. Use Post. 3 for the first statement... | |
| John Telford, Benjamin Aquila Barber - 1866
...that there is a Continent of America, but know that we arc alive, that two and two make four, and that **the sum of any two sides of a triangle is greater than the third side.** This is a distinction of practical value : but in Sir W. Hamilton's use of the term, it is the intuitive... | |
| 1878
...that there is a Continent of America, but know that we are alive, that two and two make four, and that **the sum of any two sides of a triangle is greater than the third side.** This is a distinction of practical value ; but in Sir William Hamilton's use of the term it is the... | |
| Morris Kline - 1990 - 390 sider
...because in it AE is extended its own length to F, and it must be possible to do this. Proposition 20. **The sum of any two sides of a triangle is greater than the third side.** This theorem is as close as one comes in Euclidean geometry to the fact that the straight line is the... | |
| Gregory Vlastos - 1995 - 796 sider
...(322. 4ff.)19 which Crönert thinks was Zeno's is the one directed against Euclid's proof of 1.20: that **the sum of any two sides of a triangle is greater than the third.** If the author of this criticism was Zeno, why should Proclus refer to him only as "Epicureans"? 17... | |
| Richard Courant, Herbert Robbins, Ian Stewart - 1996 - 566 sider
...hence, PR + RQ = P'R + RQ = P'Q and PR' + R'Q = P'R' + R'Q. But P'R' + R'Q is greater than P'Q (since **the sum of any two sides of a triangle is greater than the third side),** hence PR' + R'Q is greater than PR + RQ, which was to be proved. In what follows we assume that neither... | |
| Howard Whitley Eves - 1997 - 344 sider
...is opposite the greater angle. 19. In a triangle the greater angle is opposite the greater side. 20. **The sum of any two sides of a triangle is greater than the third side.** 21. If two straight line segments are drawn from the ends of a side of a triangle to a point within... | |
| V. P. Bhatnagar - 1997 - 794 sider
...less than | A*| + | B*| ? Explain. [Ans. | A*| + 1 §*! £ | A*+ §\ This follows from the fact that **the sum of any two sides of a triangle is greater than the third side.** Alternatively [|A>| + |B>|]2-[A>+BT = 4|A>||B>|sin2| which is always positive or zero.] B 18. If area... | |
| Gary R. Jensen - 2003 - 383 sider
...these two sets of square feet. which will have 124 + 235 ft2. ( 18) (Triangle Inequality) Explain why **the sum of any two sides of a triangle is greater than the third side.** In your argument. you may assume known that the straight line is the shortest path joining two points.... | |
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