 | James Hamblin Smith - Algebra - 1872 - 454 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...whatsoever of the first and third being taken and auy equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than... | |
 | André Darré - 1872 - 226 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." THEOREM. 77. If lines which intersect tiro sides of a triangle and... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...be proportionals, and any equimultiples be taken of the first and third, and also any equimultiples of the second and fourth, if the multiple of the first be greater than that of the second, the multiple of the third must be greater than that of the fourth... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second which the third is of the fourth '... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...latter by less than any assignable quantity. DEFINITION. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth when, if the first be divided into any number whatever of equal parts and the third be divided into the same... | |
 | Euclides - 1874 - 342 pages
...ratio to the second, than the fifth has to the sixth. PROPOSITION 14.— Theorem. 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 ; ana if... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...OAv OB, be proportional, and the following statement hold good:— If there be four magnitudes, and any equimultiples whatsoever of the first and third...equimultiples whatsoever of the second and fourth being taken, if the equimultiples of the first and third together exceed, or are equal to, or are less... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...any integers, m,*l. mA. or m/ll : na, : : m/f, : na,. That i«, 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 game ratio to any equimultiples... | |
 | James Hamblin Smith - Algebra - 1877 - 418 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...of the third is also less than that of the fourth : " If the multiple of the first be equal to that of the second, the multiple of the third is also... | |
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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... 
