 If the first of three things is greater than the second, and the second greater than the third, then the first is greater than the third.  Solid Geometry - Page 443by John Charles Stone, James Franklin Millis - 1916 - 174 pagesFull view - About this book
 | Arthur Browne (M.A.) - Differential calculus - 1824 - 232 pages
...+ #c. (3). involving the positive integer powers of the same unknown quantity ; and if the first be greater than the second, and the second greater than the third, then A' is either equal to one of the quantities A and A", or else it lies between them. Since first series... | |
 | Scottish school-book assoc - 1845 - 444 pages
...third, the other is also less than the third. 14. If there are three magnitudes, such that the first is greater than the second, and the second greater than the third, much more is the first greater than the third. 15. If there are three magnitudes, such that the first... | |
 | Thomas Grainger Hall - Calculus - 1846 - 480 pages
...B^cc, and A + Вгт be three algebraical expressions taken in order of magnitude, viz., the first greater than the second, and the second greater than the third, then shall A^ = A, whatever be the value of ее. For (A + Bos) - (A + B2œ) is > (A + Bv) - (At + B^);... | |
 | Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...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...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 - Geometry - 1896 - 276 pages
...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...the third, then the first is greater than the third. 12. Def.—-Plane Geometry treats of figures in the same plane. PLANE GEOMETRY BOOK I FIGURES FORMED... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...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...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 - Geometry - 1897 - 254 pages
...than the second. (8) Of three quantities, if the first is greater than the second and the second is greater than 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 - Geometry, Modern - 1903 - 136 pages
...sum of its parts. 9. If, 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. 10. If the greater of two magnitudes is continuously decreasing, and the smaller continuously increasing,... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...than ZC, Ax. 12. (if, 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). 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
...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 two given points only one straight line can be passed. 2. A geometric... | |
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