 | Arthur Schultze, Frank Louis Sevenoak - 1925 - 504 pages
...equidistant from three given lines. UNEQUAL LINES AND UNEQUAL ANGLES PROPOSITION XXIX. THEOREM 128. The sum of two sides of a triangle is greater than the third side. A B Given AACB. To prove AB + AC > BC. HINT. See Axiom 14. Ex. 1. Is it possible to draw a triangle... | |
 | Winona Merle Perry - 1925 - 80 pages
...CH > AC'. 8. Or AC > AC'. 9. :. AC > A'C'. REASONS Common (or identical) . Right angles are equal. Sum of two sides of a triangle is greater than the third side. The difference of two sides of a triangle is less than the third side. Corresponding angles in... | |
 | William Weller Strader, Lawrence D. Rhoads - 1927 - 434 pages
...than the second. For example, if A and B are two quantities, A = B, or A > B, or A <B. 374. Corollary. The sum of two sides of a triangle is greater than the third side. In the annexed figure, AB + AC> BC Why ? Principle 23. The perpendicular from a point to a line... | |
 | Albert Edwin Avey - 1927 - 416 pages
...of proof by considering some examples of it. Take, to begin with, the theorem from plane geometry; The sum of two sides of a triangle is greater than the third side. In the proof it is customary to indicate first as clearly as possible what the data of the problem... | |
 | Pauline Sperry - 1928 - 88 pages
...c = 2 s. Then s - a = ±(b + c - a)', s — b = %(a + c — b), and 5 — c = %(a + b — c). Since the sum of two sides of a triangle is greater than the third side, these quantities are all positive. Then 1 — cos A _ sin (s — c) sin (s — 6). 2 sin b sin... | |
 | K. Ajdukiewicz - 1973 - 196 pages
...way in which moderate apriorism justifies its thesis, let us take the geometrical assertion affirming that the sum of two sides of a triangle is greater than the third side. According to the apriorist this is not an analytic assertion because it does not follow from... | |
 | John W. Dettman - 1988 - 450 pages
...of the parallelogram dctermined hy zl and za, the inequality l*l + zi! £ N + fol expresses the fact that the sum of two sides of a triangle is greater than the third side. This inequality can he extended hy induction to for n = 3, 4, 5 ..... 1t is easy to estahlish... | |
 | G. H. Hardy, J. E. Littlewood, George Pólya - 1952 - 344 pages
...variables, and express the facts that (1) the cosine of a real angle is numerically less than 1, and (2) the sum of two sides of a triangle is greater than the third side. The exceptional cases are those in which (1) the vectors (#! , yl , zj and (хг , уг , z2)... | |
 | Stefan Hildebrandt, Anthony Tromba - 1996 - 370 pages
...Note that the three angles a, a', and /3 at R are equal. Let R' be any other point on L. From the fact that the sum of two sides of a triangle is greater than the third it follows that PRQ is the shortest possible path joining Pand Q that touches /.. The shortest path... | |
 | M.N. Mukherjee - 2005 - 180 pages
...that of Q from P. Moreover, if P, Q, R are three points, then from our tacit acceptance of the fact that the sum of two sides of a triangle is greater than or equal to the third side (equality prevailing only if the points are collinear), it follows that... | |
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The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 
