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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...
A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845

## Elementary Algebra: With Brief Notices of Its History

Robert Potts - Algebra - 1879
...VII., def. 20. Hence it follows that a, b, 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,...

## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...of E. Wherefore, if two magnitudes &c. QED PROPOSITION A. THEOREM. If the first of four magnitudes have the same ratio to the second that the third has to the fourth, then, if thejftrtt be greater than the second, the third thatt also be greater than the fourth, and...

## Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1881 - 250 pages
...a ± ? a : b ± ?-b : : a : b. Ч 1 QED 272. DEP. 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,...

## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...they cannot be said to be of the same kind, and so cannot have any ratio to each other. T. The Brst 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,...

## Elementary algebra. To which is now added an appendix

James Hamblin Smith - 1883
...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 ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken...

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...of E. Wherefore, if two magnitudes &c. QKD PROPOSITION A. THEOREM. If the first of four magnitudes have the same ratio to the second that the third has to the fourth, then, if the first be greater than the second, the third shall also be greater than the fourth, and...

## The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...of the fourth, equal to it, or less. 6. Magnitudes are said to be proportionals when the first has the same ratio to the second that the third has to the fourth; and the third to the fourth the same ratio which the fifth has to the sixth ; and so on, whatever be...

## Notes on algebra

Howard Candler - Algebra - 1885 - 94 pages
...fourth, that is, д, l>, c, d are said to be proportionals if — = b а The geometrical definition is 2. 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 whatever being taken of the ist and 3rd,...