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. Plane Geometry - Page 21by John Charles Stone, James Franklin Millis - 1916 - 278 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. 13. Def. — Solid Geometry, or the... | |
| 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... | |
| 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,... | |
| 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... | |
| 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:... | |
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