 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...  The First Six Books with Notes - Page 168by Euclid - 1822 - 179 pagesFull view - About this book
 | André Darré - 1872 - 226 pages
...hitherto devised that applies equally to commensurable and incommensurable quantities ; " the first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken,... | |
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio...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
...with one which differs from the latter by less than any assignable quantity. DEFINITION. The first of four magnitudes is said to have the same ratio...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... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio...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 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... | |
 | Euclid - 1876 - 240 pages
...Or, to bring it still nearer to the language of Euclid's definition: — The first of four magnitades is said to have the same ratio to the second, which...the fourth, when any equimultiples whatsoever of the first and third being taken, the second is contained as often in the equimultiple of the first, as... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...± ?-b : : a : b. Ч Ч QED 272. DBF. Euclid's test of a proportion is as follows : — "The first of four magnitudes is said to have the same ratio...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... | |
 | Samuel H. Winter - 1877 - 452 pages
...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 pages
...magnitudes of the same kind to one 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... | |
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