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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...
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 458
by Sir John Leslie - 1809 - 493 pages

## Elementary Algebra

James Hamblin Smith - 1870 - 452 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...equimultiples whatsoever of the first and third being takeu and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be...

## Elementary algebra

James Hamblin Smith - 1872 - 454 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...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...

## 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 - 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 '...

## Euclidian Geometry

Francis Cuthbertson - 1874 - 400 pages
...be compared 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...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...

## 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 elementary geometry of the right line and circle

William Alexander Willock - 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...being taken, and any equimultiples whatsoever of the second and fourth being taken, if the equimultiples of the first and third together exceed, or are...