 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and, on the contrary, the third is said to hare to the fourth a less... | |
 | Euclides - 1826 - 226 pages
...compared with the equimultiples of the second second, than the third is when compared to the fourth, the first is said to have to the second a greater ratio than the third has to the fourth." " 4. If the first of four magnitudes be less, «hen compared to the second, than the third is when... | |
 | Euclid - 1826 - 234 pages
...compared with the equimultiples of the second second, than the third is when compared to the fourth, the first is said to have to the second a greater ratio than the third has to the fourth." " 4. If the first of four magnitudes be less, when compared to the second, than the third is when compared... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...that of the second, but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth : and, on the contrary, the third is said to have to the fourth a less... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and, on the contrary, the third is said to have to the fourth a less... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...demonstrated more it large in Prop. [9]. Def. [8]. If there be two magnitudes of fhe same kind, and other two, the first is said to have to the second a greater ratio than the third has to the fourth, when the first contains some measure of the second a greater number of times Iban the third contains... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...of the second, but the multiple of the third is not greater than the multiple of the fourth : then the first is said to have to the second a greater ratio than the third has to the fourth ; and on the contrary the third is said to have to the fourth a less ratio than the first has to the... | |
 | Perry Fairfax Nursey - Industrial arts - 1833 - 502 pages
...latitude to the meaning of the seventh definition, we are entitled to conclude, that the first has to the second a greater ratio than the third has to the fourth. Dr. Simson, it is true, has demonstrated that the multiple of the first is greater than the multiple... | |
 | Mathematics - 1835 - 684 pages
...number of times, with or without a remainder, than the third contains the like part of the fourth, the first is said to have to the second a greater ratio than the third has to the fourth : also, in this case, the third is said to have to the fourth a less ratio than the first has to the... | |
 | James Ryan, Robert Adrain - Algebra - 1835 - 388 pages
...the second, but the multiple of the third is not greater than that of the fourth ; then the firs'! is said to have to the second a greater ratio than the third has to the fourth ; and, on the contrary, the third is said to have to the fourth a less ratio than the first has to... | |
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When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have... 
