 | Euclides - 1860 - 288 σελίδες
...third, the other is also greater than the third. 15. If there be three magnitudes, of which the first is greater than the second, and the second is greater than the third, still more is the first greater than the third. ' DEFINITIONS OF TERMS. 1. A proposition is a portion... | |
 | Euclides - 1884 - 214 σελίδες
...one of two equal magnitudes it is also greater than the other. (v) If of three magnitudes the first is greater than the second and the second is greater than the third, much more then is the first greater than the third. (w) If one magnitude is greater than a second and... | |
 | Benjamin Franklin Finkel - 1888 - 518 σελίδες
...equal to the line IK. 16. 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. Thus, if A is greater than B and B greater than C, then A is greater than C. 17. Two straight lines... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 σελίδες
...once and but once. (13.) 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. 12. Def. — Plane Geometry treats of figures in the same plane. 13. Def. — Solid Geometry, or the... | |
 | Andrew Wheeler Phillips, Irving Fisher - 1896 - 554 σελίδες
...once and but once. (13.) 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. 12. Def. — Plane Geometry treats of figures in the same plane. 13. Def. — Solid Geometry, or the... | |
 | Henry W. Keigwin - 1897 - 254 σελίδες
...is equal to the second, or the first is less than the second. (8) Of three quantities, if the first is greater than the second and the second is greater...the third, then the first is greater than the third. 43. A theorem consists of two parts, the hypothesis and the conclusion. The hypothesis contains the... | |
 | John Alton Avery - 1903 - 136 σελίδες
...than any of its parts. 8. The whole equals the sum of its parts. 9. If, of three quantities, the first is greater than the second, and the second is greater...third, then the first is greater than the third. 10. If the greater of two magnitudes is continuously decreasing, and the smaller continuously increasing,... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...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...the third, then the first is greater than the third) . QED 105. NOTE. The essential steps of the above proof may be arranged in a single statement, thus:... | |
 | John Henry Tanner - 1904 - 398 σελίδες
...reversed, then the symbol of inequality must also be reversed. (vii) If the first of three numbers is greater than the second, and the second is greater...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... | |
 | Fletcher Durell - 1904 - 232 σελίδες
...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...the third, then the first is greater than the third. ' . GEOMETRIC AXIOMS. 1. Through two given points only one straight line can be passed. 2. A geometric... | |
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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. 
