 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...HI. When four magnitudes A, B, C, D, are AC so related that =- is greater than .=- it is evident that the ratio of A to B is greater than the ratio of C to D ; or that the ratio of C to D is less than the ratio of A to B. The Fifth Definition according to Euclid.... | |
 | James Ryan - Algebra - 1824 - 550 pages
...When four magnitudes A, B, C, D, are AC so related that •=- is greater than ~r- it is evident that the ratio of A to B is greater than the ratio of C to D ; or that the ratio of C to D is less than the ratio of A to B. The Fifth Definition according to Euclid.... | |
 | Euclides - 1840 - 192 pages
...following pages, are thus read : A ~7 B, A is greater than B ; B "^ A, B is less than A ; A : B ~^C '. D, the ratio of A to B is greater than the ratio of C to D ; C : D ^TA : B, the ratio of C to D is less than the ratio of A to B. PROP. I. THEOR. If any number... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...divided by C prove equal; therefore the quotient of B by A is greater than that of F by E (d)—that it, the ratio of A to B is greater than the ratio of E to F. Wherefore, if the first has to the second, &c. QED Recite (a) def. 4, 5 ; (4) def. B, 5; (c)... | |
 | Euclid - Geometry - 1890 - 442 pages
...to B is equal to (or, is the same as) the ratio o/C to D.' Similarly A : B > C : D is to be read — 'the ratio of A to B is greater than the ratio of C to D.' And A : B < C : D is to be read — ' the ratio of A to B is less than the ratio o/c to D: Def. When... | |
 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...unequal ratios from the smaller thus : — Taking as a fundamental idea that if A be greater than E, then the ratio of A to B is greater than the ratio of E to B. Then changing in Prop. 12, B into E and C into B it follows that integers r, n exist such that... | |
 | Agriculture - 1916 - 682 pages
...designated "B" throughout, since the leaves of series B were not treated with Bordeaux mixture. If then the ratio of A to B is greater than the ratio of .A' to B, it follows that the rates of transpiration of the sprayed leaves have suffered a decrease... | |
 | Edinburgh Mathematical Society - Electronic journals - 1900 - 410 pages
...= С : D then В : A = D : С for the ratios A : В and С : D are each equal to the fraction — , n and their reciprocals are each equal to the fraction...truth of the other three. 10. When the ratio of A to В is greater than the ratio of С to D, the relation between the magnitudes may be expressed by the... | |
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AC so related that =- is greater than .=- it is evident that the ratio of A to B is greater than the ratio of C to D ; or that the ratio of C to D is less than the ratio of A to B. 