 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...that line. 92. If one of two parallel lines is perpendicular to a third line, the other is also. 107. The sum of any two sides of a triangle is greater than the third side. 109. The sum of the angles of a triangle is equal to two right angles. 114. In an equiangular triangle... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...the legs are the sides adjacent to the right angle. 78. Property of a triangle immediately inferred. The sum of any two sides of a triangle is greater than the third aide. For a straight line is the shortest line joining two points. (§ 9.) Ex. 1. Point out the hypothesis... | |
 | David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...know that ZA> Z5. Accordingly, we conclude that the theorem is true. 88 Exercises. Inequalities 1. The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side. Use Post. 3 for the first statement... | |
 | Cambridge Philosophical Society - Mathematics - 1927 - 1078 pages
...triangle is 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... | |
 | William Lonsdale Watkinson, William Theophilus Davison - Theology - 1866 - 556 pages
...that there 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
...that there 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
...because in 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
...(322. 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
...hence, PR + 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... | |
| |
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. 
