 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.  Elements of Geometry - Page 5by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 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
...less than a 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
...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...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 - 554 pages
...wholes will be unequal in the same order. (10.) The whole is greater than any of its parts. (n.) The whole is equal to the sum of all its parts. (12.)...PLANE GEOMETRY BOOK I FIGURES FORMED BY STRAIGHT LINES . Defs. — An angle is a figure formed by two straight lines diverging from the same point. This point... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...lesser to the lesser and the greater to the greater, the wholes will be unequal in the same order. v (10.) The whole is greater than any of its parts....than the third. 12. Def. — Plane Geometry treats of f1gures in the same plane. 13. Def. — Solid Geometry, or the geometry of space, treats of figures... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...geometric truth to another the following general axioms are also employed, viz.: (1.) Things equal to the same thing are equal to each other. (2.) If equals...third, then the first is greater than the third. 12. Def.—-Plane Geometry treats of f1gures in the same plane. PLANE GEOMETRY BOOK I FIGURES FORMED BY... | |
 | 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
...sense. 7. The whole is greater 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 than the third, then the first is greater than the third. 10. If the greater of two magnitudes... | |
 | 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 the second, and the second is greater than the third, then the first is greater than the third). QED 105. NOTE. The essential... | |
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