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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...
Euclidian Geometry - Page 157
by Francis Cuthbertson - 1874 - 349 pages

## A Treatise on Elementary Algebra

James Hamblin Smith - 1869 - 412 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : " The first of four magnitudes is said to have the same...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...

## Elementary Algebra

James Hamblin Smith - Algebra - 1870 - 468 pages
...representing the ratios must be equal. Euclid's test is given in Book Y. Def. 5, where it stands thus: " The first of four magnitudes is said to have the same...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...

## Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...only one 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,...

## Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...third is also 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...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 '...

## Euclid, book v. proved algebraically, so far as it relates to commensurable ...

Charles Lutwidge Dodgson - 1874 - 96 pages
...third is also 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...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 '...

## The Elements of Euclid, containing the first six books, with a selection of ...

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...

## The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 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, third has to the fourth, when any equimultiples whatsoever of the first and third being taken, the second is contained as often in...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 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...