| John Hind - Arithmetic - 1840 - 224 pages
...Elements, that " Proportion is the Similitude of Ratios; and theJirst of four magnitudes is said to have **the same ratio to the second, which the third has to the fourth, when any equimultiples** whatever of the^rst and third being taken, and any equimultiples whatever of the second anA fourth... | |
| Euclides - 1840
...multiples or submultiples which are equal, those pairs of numbers are proportional, or the first has **the same ratio to the second which the third has to the fourth.** But it must be remembered that there are incommensurable magnitudes, the relative values of which,... | |
| Oliver Byrne - Euclid's Elements - 1841 - 98 pages
...this definition before proceeding further. с 2 PROP. IV. THEO. If the first of four magnitudes have **the same ratio to the second, which the third has to the fourth,** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - Geometry - 1841 - 351 pages
...the fourth. If, therefore, the first, &c. QED PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1842
...Definition of proportion according to Euclid, (Def. V., Book " The first of four magnitudes is said to have **the same ratio " to the second, which the third has...second and " fourth ; if the multiple of the first be** equal to, greater " than, or less than the multiple of the second, the multiple " of the third is also... | |
| Wales Christopher Hotson - 1842
...Geometrical Definition of Proportion. (Euclid, book v. def. 5). The first of four magnitudes is said to have **the same ratio to the second which the third has to...first and third being taken, and any equimultiples** whatsover of the second and fourth ; if the multiple of the first, be less than that of the second,... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...mB=mnC, and by hypothesis A=mB, therefore A=wmC PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
| George Peacock - Algebra - 1842
...of the second, the multiple of the thii will be equal to that of the fourth : and if the multiple of **first be less than that of the second, the multiple of the** will be less than that of the fourth. It is this proposition which is deduced as a necessary consequence... | |
| Euclid - Geometry - 1845 - 199 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION XIV. THEOR. — If the first has **the same ratio to the second which the third has to the fourth;** then, if the first be greater than the third, the second shall be greater than the fourth ; and if... | |
| Euclides - 1845
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. Likewise, if the first has **the same ratio to the second, which the third has to the fourth,** then also any equimultiples whatever of the first and third shall have the*same ratio to the second... | |
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