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" Any side of a triangle is less than the sum of the other two sides. "
Elements of Plane and Solid Geometry - Σελίδα 38
των George Albert Wentworth - 1877 - 398 σελίδες
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Junior High School Mathematics Book 1-3 [and] 1 Book Course, Βιβλίο 1

Theodore Lindquist - 1920
...triangle. The side opposite the right angle is named hypotenuse. The symbols are A ABC and IX MNK. Any side of a triangle is less than the sum of the other two sides, because it is shorter to go from A to B along the straight line AB than from A to C to B. In symbols...

The New International Encyclopædia, Τόμος 7

1922
...other in solid geometry, as •when the terms triangle and trihedral angle are interchanged; eg, one side of a triangle is less than the sum of the other two sides; one face angle of a trihedral angle is less than the sum of the other two face angles. The term duality...

A First Course in Mathematical Analysis

J. C. Burkill - 1978 - 186 σελίδες
...differ by a multiple ofl.ri). Observe that the geometrical counterpart of the sumtheorem is that one side of a triangle is less than the sum of the other two. We must of course give an analytical proof. Proof. (1) To prove the statement about the product zw,...
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - 1997 - 512 σελίδες
...than the sum of the other two. Proof From the Triangle Inequality we already know that the length of any side of a triangle is less than the sum of the lengths of the other two sides. We now prove the converse. Without loss of generality we may suppose...
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A First Course in Real Analysis

Murray H. Protter, Charles B. Jr. Morrey - 1997 - 536 σελίδες
...At; in this case yt — AiXf = 0 for every i. D We recall that in the Euclidean plane the length of any side of a triangle is less than the sum of the lengths of the other two sides. A generalization of this fact is known as the Triangle inequality....
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ST(P) Mathematics 5A Second Edition, Τόμος 5

...square is A sq. units and the perimeter of the same square is P units then A < P. * 1 5. The length of any side of a triangle is less than the sum of the lengths of the *16. All positive whole numbers can be expressed as the sum of a selection from the...
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Minds-on Physics: Interactions

William J. Leonard, Kendall/Hunt Publishing Company - 1999 - 372 σελίδες
...of the magnitudes is not the magnitude of the sum) • Some geometry might help here: The length of any side of a triangle is less than the sum of the other two lengths, unless one of the angles is 180°. There are different types of pairs of vectors that will...
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Introduction to Calculus and Analysis Volume II/2: Chapters 5 - 8

Richard Courant, Fritz John - 1999 - 412 σελίδες
...triangle inequality for complex numbers. Thus, the triangle inequality expresses the fact that any one side of a triangle is less than the sum of the other two. The essentially new concept that we now consider is that of the limit of a sequence of complex numbers....
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The Countingbury Tales: Fun with Mathematics

Miguel de Guzm n - 2000 - 121 σελίδες
...that t has a common point M with the ellipse. Could it have more? No, because 5F[ + SN > NF\ = 2a (one side of a triangle is less than the sum of the other two). So t is the tangent to the ellipse at M. Now, when a ball bounces off a curve, it bounces as if the...
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USA and International Mathematical Olympiads, 2003

Titu Andreescu, Zuming Feng - 2004 - 85 σελίδες
...with sides lengths a |, \ß\, and a + ß\. The triangle inequality restates the fact the the length of any side of a triangle is less than the sum of the lengths of the other two sides. Trigonometric Identities sin2x + cos2 z = 1, sinx 1 tan x = , cot x...
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