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" Any side of a triangle is less than the sum of the other two sides... "
Elements of Geometry - Page 8
by Adrien Marie Legendre - 1841 - 235 pages
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Junior High School Mathematics, Volume 1

Theodore Lindquist - Mathematics - 1920 - 256 pages
...triangle. The side opposite the right angle is named hypotenuse. The symbols are A ABC and 1\ 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...
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Junior High School Mathematics, Volume 1

Theodore Lindquist - Mathematics - 1920 - 260 pages
...triangle. The side opposite the right angle is named hypotenuse. The symbols are A ABC and 1\, 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...
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Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...triangle ABK, show that the angle KB A is greater than the angle AM B. 146. Postulate VI. Any »ide of a triangle is less than the sum of the other two sides. A still broader and more usual statement is : A straight line is the shortest line between two...
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Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...7. In the same figure, prove BD greater than DC. 8. In the same figure, prove BK greater than KC. 9. One side of a triangle is less than the sum of the other two and greater than their difference. CHAPTER X LOCI The basic principle is the definition: The locus...
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Solid Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...unequals are subtracted from equals, the results are unequal in the reverse order. 146. Postulate VI. Any side of a triangle is less than the sum of the other two sides. DEFINITIONS 15. Angle. A plane angle (symbol Z) is the figure formed by two rays which meet....
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Junior High School Mathematics Book 1-3 [and] 1 Book Course, Book 1

Theodore Lindquist - Mathematics - 1920 - 252 pages
...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...
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Advanced Calculus

William Fogg Osgood - Calculus - 1925 - 560 pages
...1/z. 3. Inequalities. If Sf and S3 be any two complex numbers, then (1) |a + »|£|a| + |»|. For, any side of a triangle is less than the sum of the other two sides ; cf. Fig. 117, § 2. Hence, for a true triangle, only the sign of inequality can hold. But if...
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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...perpendicular, cutting off equal distances from" the foot of the perpendicular, are equal. 127. Prop. LII. Any side of a triangle is less than the sum of the other twc sides. Euclid seems to have employed two very advanced truths to establish an axiom. 128. Locus...
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Advanced Calculus

William Fogg Osgood - Calculus - 1925 - 554 pages
...3. Inequalities. If 21 and ?) be any two complex numbers, then (1) |& + «|£ |H| + |«|. For, any side of a triangle is less than the sum of the other two sides ; cf. Fig. 117, § 2. Hence, for a true triangle, only the sign of inequality can hold. But if...
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A First Course in Mathematical Analysis

J. C. Burkill - Mathematics - 1978 - 200 pages
...(or 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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