 If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.  Elements of Geometry - Page 5by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pagesFull view - About this book
 | Fletcher Durell - Geometry - 1911 - 553 pages
...opposite int. Z. ). Much more, then, is /.BAG (which ix greater than /s) greater than Z 0, Ax. 12. (if, of three quantities, the first is greater than the second, and the second is greater than the third, then the Jirst is greater than the third). QED 105. NOTE. The essential... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...11. // unequals be subtracted fr<mi equals, the remainders are unequal in the reverse order, 12. //, of three quantities, the first is greater than the second, and the second is greater than the third, then the first is greater than the third. ' . GEOMETRIC AXIOMS. 1. Through... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...opposite int. Z ). Much more, then, is /.BAC (which is greater than Zs) greater than ZC, Ax. 12. ( */i °f three quantities, the first is greater than the second, and the second is greater than the third, then the first is greater than the third) . QED 105. NOTE. The essential... | |
 | John Henry Tanner - Algebra - 1904 - 398 pages
...also be reversed. (vii) If the first of three numbers is greater than the second, and the second is greater than the third, then the first is greater than the third; and conversely. Eg, 10 > 7 and 7 > 3, and 10 > 3 also. To prove this principle, let a > b and b > с... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...evidently с - a < с - b. 184. If the first of three numbers is greater than the second, and the second is greater than the third, then the first is greater than the third. 185. The sum or product of the corresponding members of two inequalities that subsist in the same sense... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...7. The whole is greater than any of its parts. 8. The whole is equal to the sum of all its parts. 9. If of three quantities, the first is greater than...the third, then the first is greater than the third. 31. GEOMETRIC AXIOMS. 1. Between two points only one straight line can be drawn. 2. Through a given... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...included in Axiom 9. 10. If the first of three quantities is greater than the second, and the second -is greater than the third, then the first is greater than the third. Thus if a > b, and if b > c, then a > c. 53. Postulates. The following are among the most important... | |
 | David Eugene Smith - Geometry - 1911 - 360 pages
...mathematical work. 10. If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. This axiom is needed several times in geometry. The case in which a > b and b = c, therefore a > c,... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...the sums are unequal in the same order. 10. If three magnitudes of the same kind are so related that the first is greater than the second, and the second...the third, then the first is greater than the third. 11. The whole is equal to the sum of all its parts. 12. The whole is greater than any of its parts.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...— c < 6 — d. 12. If of three magnitudes the first is greater than the second, and the second is greater than the third, then the first is greater than the third. That is, if a > b and b > c, then a > c. 223. Two inequalities ha^e already been established : The... | |
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