 | 1878 - 1022 sider
...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 - 434 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 - 380 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 - 1996 - 596 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 - 370 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 - 672 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 - 402 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.... | |
 | 1888 - 204 sider
...What is the length ol a chord one inch nearer the centre ? 4. When is a triangle possible? Prove that the sum of any two sides of a triangle is greater than the third side. 5. A rectangle and a square have same area. How do their perimeters compare? Prove. 6. One acute angle... | |
 | H.K. Dass & Rama Verma - 1032 sider
...respectively, the vertex R of the parallelogram OPRQ represents the sum z; + zr Also, we know that the sum of any two sides of a triangle is greater than the third side. Hence, in A OPR, OR < OP + PR => | z, + z2 | < | z, | + 1 z2 | Note : For any л complex numbers z,,... | |
 | Cambridge Philosophical Society - 1927 - 1058 sider
...triangle is opposite to the greater angle), and from i. 18 its converse i. 19, from which he deduces I. 20 (the sum of any two sides of a triangle is greater than the third side). Now propositions i. 18, 19 and 20 are true for triangles of all magnitudes in the Elliptic Plane, although... | |
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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. 
