 | George Sturton Ward - 1862 - 104 pagina’s
...is different from that above, being as follows : — " The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth when, any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1863 - 122 pagina’s
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and auy equimultiples whatsoever... | |
 | Robert Potts - 1865 - 528 pagina’s
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclides - 1865 - 402 pagina’s
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | Euclid, Isaac Todhunter - 1867 - 424 pagina’s
...Wherefore, if the first &c. QED COROLLARY. Also if the first have the same ratio to the second that the third has to the fourth, then any equimultiples...of the first and third shall have the same ratio to the second and fourth; and the first and third shall have the same ratio to any equimultiples whatever... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pagina’s
...Wherefore, if the first &c. QEB COROLLARY. Also if the first have the same ratio to the second that the third has to the fourth, then any equimultiples...of the first and third shall have the same ratio to the second and fourth; and the first and third shall have the same ratio to any equimultiples whatever... | |
 | Euclid - 1868 - 138 pagina’s
...Kai то ífúrfpov roo rfráprov fieiÇov iarai' Kq.v íaov, laov Kfv i\aaaov, I\aaaov. If the first has the same ratio to the second which the third has to the fourth; and if the first be greater than the third, the second is greater than the fourth; if equal, equal;... | |
 | Robert Potts - 1868 - 434 pagina’s
...less can be multiplied so as to exceed the other. V. , The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever... | |
 | James Hamblin Smith - 1869 - 412 pagina’s
...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 the fourth, when any equimultiples whatsoever of the first and third being taken and any equimultiples whatsoever... | |
 | James Hamblin Smith - 1870 - 452 pagina’s
...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 the fourth, when any equimultiples whatsoever of the first and third being takeu and any equimultiples whatsoever... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple... 
