 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
 | George Clinton Shutts - Geometry - 1912 - 392 pages
...the reverse order. (8) 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. (9) In considerations involving size only, the whole is greater than any of its parts and is always... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...a — 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 have already been established : The... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 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 > 6, and if b > c, then a > c. 53. Postulates. The following are among the most important... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...halves of equals are equal.) 9. If one of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. 10. The whole is equal to the sum of all its parts. 11. The whole is greater than any of its parts.... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
....-./.BAO/-B. Ax. 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.) QE D, PROPOSITION XXII. THEOREM 114. If two angles of a triangle are unequal, the sides opposite these... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...halves of equals are equal.) 9. If one of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. 10. The whole is equal to the sum of all its parts. 11. The whole is greater than any of its parts.... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 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 6 > c, then a > c. 53. Postulates. The following are among the most important... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 pages
...increasing. Zy>Zx. Axiom. // 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. 180. Straight Line. The expression straight line is derived from words meaning a stretched linen cord,... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Ax. 11. Like powers of equals, or like roots, are equal. Ax. 12. // three magnitudes are such that the first is greater than the second and the second...the third, then the first is greater than the third. Ax. 13. The whole is greater than any of its parts. Ax. 14. The whole is equal to the sum of all its... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Ax. 11. Like powers of equals, or like roots, are equal. Ax. 12. // three magnitudes are such that the first is greater than the second and the second...the third, then the first is greater than the third. Ax. 13. The whole is greater than any of its parts. PLANE GEOMETRY [I, § n 11. Examining various geometric... | |
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