 | Charles Lutwidge Dodgson - 1874 - 96 pagine
...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... | |
 | Euclides - 1874 - 342 pagine
...the less can be multiplied so as to exceed the other. 5. 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, Lewis Carroll - 1874 - 80 pagine
...by this Definition, to exclude infinite magnitudes. 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 - 1876 - 240 pagine
...= n . m . a and » . B = n . m . b that is, n . A, n . B are equimultiples of a and b. PROPOSITION IV. THEOREM. — If the first of four magnitudes has...ratio to any equimultiples of the second and fourth, i. «. " the equimultiple of the first shall have the same ratio to that of the second which the equimultiple... | |
 | Robert Potts - 1876 - 446 pagine
...greater ratio to the second, than the fifth has to the sixth. PROPOSITION XIv. THEOREM; Jf the first has the same ratio to the second which the third has to the fourth i then, if thefrst be greater than the third, the second shall be greater than the fourth ; and if... | |
 | George Albert Wentworth - 1877 - 426 pagine
...DEF. Euclid's test of a proportion is 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... | |
 | Samuel H. Winter - 1877 - 452 pagine
...into three, and also into five equal parts. 6. When is the first of four magnitudes said to have the the same ratio to the second which the third has to the fourth ? Prove that triangles which have the same altitude are to one another as their bases. Show also that... | |
 | Āryabhaṭa - 1878 - 100 pagine
...another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being taken, ai;d any equimultiples... | |
 | Robert Potts - 1879 - 668 pagine
...c, d are proportionals by Eue. V., def. 5, namely : — 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... | |
 | University of Oxford - 1879 - 414 pagine
...figures. 2. About a given circle describe a triangle equiangular to a given triangle. 3. If the first have the same ratio to the second which the third has to the fourth, but the third to the fourth a greater ratio than the fifth to the sixth, the first shall have to the... | |
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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... 
