 | William Lonsdale Watkinson, William Theophilus Davison - Theology - 1866 - 556 pages
...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... | |
 | England - 1878 - 1022 pages
...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 - Mathematics - 1990 - 434 pages
...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 - Philosophy, Ancient - 1995 - 380 pages
...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 - Juvenile Nonfiction - 1996 - 596 pages
...+ 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... | |
 | V. P. Bhatnagar - Science - 1997 - 672 pages
...| 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... | |
 | Howard Whitley Eves - Mathematics - 1997 - 370 pages
...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... | |
 | Gary R. Jensen - Education - 2003 - 402 pages
...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.... | |
 | H.K. Dass & Rama Verma - Mathematics - 1032 pages
...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 - Mathematics - 1927 - 1058 pages
...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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The sum of any two sides of a triangle, is greater than the third side. 
