 | Euclides - 1864 - 448 pages
...being any integers, no, no, ' or mAl : na, : : mAt : no,. That is, 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 - 1865 - 402 pages
...greater ratio to the second, than the fifth has to the sixth. PROP. XIV.— THEOREM. If tlie 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... | |
 | Robert Potts - 1865 - 528 pages
...is to G, so is Fto H. (v. def. 5.) Therefore, if the first, &c. QED CoR. 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...whatever of the first and the third being taken, and any equimultiples whatever of the second and the fourth, if the multiple of the first be less than...of the third is also less than that of the fourth, and if the multiple of the first be equal to that of the second, the multiple of the third is also... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...multiple of the third is also equal to that of the fourth, and if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth. 6. Magnitudes which have the same ratio are called proportionals.... | |
 | Euclid - 1868 - 138 pages
...Sivripov Kai rfrápruv, кaQ' ùiroiovovv iro\\air\aaia.afièv, rbv àvrbv ejfi Xóyo»< If the first has the same ratio to the second which the third has to the fourth; any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of... | |
 | Robert Potts - 1868 - 434 pages
...fourth D. If, therefore, the first, &c. QED PROPOSITION IV. THEOREM. If the first of four magnitudes hat 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... | |
 | James Hamblin Smith - 1869 - 412 pages
...multiple of the third is also equal to that of the fourth : or, " If the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." We shall now shew, first, how to deduce Euclid's test of the equality... | |
 | James Hamblin Smith - Algebra - 1870 - 452 pages
...test is given in Book v. Def. 5, where it stands thus: " The first of four magnitudes is said to have the same ratio to the second which the third has to...equimultiples whatsoever of the first and third being takeu and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be... | |
 | James Hamblin Smith - Algebra - 1870 - 478 pages
...of the third is also equal to that of the fourth: or, • " If the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth." • . We shall now shew, first, how to deduce Euclid's test of the... | |
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If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... 
