| Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...(a.) The centres of equal straight lines in a circle. 9. When is the first of four magnitudes said to have a greater ratio to the second than the third has to the fourth? When is a straight line said to be cut in extreme and mean ratio ? Define alternando, componendo, and... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...therefore A has a greater ratio to B than E has to F. EUCLID'S ELEMENTS. COROLLARY. And if the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth that tha fifth has to the sixth, it may be shewn, in the... | |
| Euclid - Mathematics, Greek - 1908 - 456 pages
...(from above) me^nf. Therefore a : b> e :/. Simson adds as a corollary the following : " If the first have a greater ratio to the second than the third has to the fourth, but the third the same ratio to the fourth which the fifth has to the sixth, it may be demonstrated... | |
| Sir Thomas Little Heath - Mathematics - 1921 - 474 pages
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth ' ; this (possibly for brevity's sake) states only one criterion, the other possible criterion being... | |
| Sir Thomas Little Heath - Mathematics - 1921 - 482 pages
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has. to the fourth ' ; this (possibly for brevity's sake) states only one criterion, the other possible criterion being... | |
| Morris Kline - Mathematics - 1990 - 434 pages
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth. The definition states that if for even one m and one n,ma>nb but mc is not greater than nd, then ajb >... | |
| Euclid - 452 pages
...but the multiple of the third does not exceed the multiple of the fourth, then the first is said to have a greater ratio to the second than the third has to the fourth. 8. A proportion in three terms is the least possible. 9. When three magnitudes are proportional, the... | |
| |