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" If three magnitudes of the same kind are so related that the first is greater than the second, and the second greater than the third, then the first is greater than the third. "
A Short View of the First Principles of Differential Calculus - Σελίδα 24
των Arthur Browne (M.A.) - 1824 - 198 σελίδες
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A Treatise on the Differential and Integral Calculus: And the Calculus of ...

Thomas Grainger Hall - 1846 - 480 σελίδες
...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^);...

Navigation

James Pryde - 1867 - 506 σελίδες
...than a third, the other is also < , > than the third. I less J (q .) If the first of three quantities be greater than the second, and the second greater than the third, still more is the first greater than the third. (r.) Any supposition which contains in it an absurdity,...

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

Benjamin Franklin Finkel - 1888 - 518 σελίδες
...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 B greater than C, then A is greater...

Elements of Geometry, Τόμος 1

Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 σελίδες
...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 of figures in the same plane....

Elements of Geometry, Μέρος 1

Andrew Wheeler Phillips, Irving Fisher - 1896 - 276 σελίδες
...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 of figures in the same plane....

Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 286 σελίδες
...its parts. 8. The whole is equal to the sum of all its parts. 9. 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. 31. GEOMETRIC AXIOMS. 1. Between two points only one straight...

Plane Geometry

Clara Avis Hart, Daniel D. Feldman - 1911 - 328 σελίδες
...unequal in the same order. 10. If three magnitudes of the same kind are so related that the first is greater than the second and the second greater than the third, then the first is greater than the third. 11. The whole is equal to the sum of all its parts. 12. The whole...

Solid Geometry

Clara Avis Hart, Daniel D. Feldman - 1912 - 220 σελίδες
...unequal in the same order. 10. If three magnitudes of the same kind are so related that the first is greater than the second, and the second greater than the third, then the first is greater than the third. 11. The whole is equal to the sum of all its parts. 12. The whole...

Plane Geometry

Edith Long, William Charles Brenke - 1916 - 292 σελίδες
...powers of equals, or like roots, are equal. Ax. 12. // three magnitudes are such that the first is greater than the second and the second greater than the third, then the first is greater than the third. Ax. 13. The whole is greater than any of its parts. Ax. 14. The...

Solid Geometry

John Charles Stone, James Franklin Millis - 1916 - 196 σελίδες
...of all of its parts, and is greater than any one of its parts. XI. 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. XII. A quantity may be substituted for its equal in any expression....




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