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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.
Plane Geometry - Page 21
by John Charles Stone, James Franklin Millis - 1916 - 278 pages

## A Short View of the First Principles of Differential Calculus

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...

## A system of practical mathematics; being no.xvi. of a new series of school-books

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...

## A Treatise on the Differential and Integral Calculus: And the Calculus of ...

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^);...

## A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

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...

## Elements of Geometry, Part 1

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...

## Elements of Geometry, Part 1

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...

## The Elements of Geometry

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...

## Plane Geometry by the Suggestive Method

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,...