| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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