 | Euclides - 1860 - 288 pages
...than a 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 pages
...greater than 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 - Mathematics - 1888 - 518 pages
...the two lines are equal M r H /f once and only once, viz., when both are 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...(continuously and indefinitely) while the greater decreases ; they must become equal 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...(continuously and indefinitely) while the greater decreases ; they must become equal 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... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...the first 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...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... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...either opposite int. Z ). Much more, then, is /.BAC (which is greater than Zs) greater than ZC, Ax. 12. (if, of three quantities, the first is greater than...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:... | |
 | 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...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... | |
 | 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,...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:... | |
 | 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...and the second is greater than the third, then the Jirst is greater than the third). QED 105. NOTE. The essential steps of the above proof may be arranged... | |
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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. 
