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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

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 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,...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...ratio that the third has to the fourth. VI. 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...

## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Analytic - 1809 - 493 pages
...exactly resemble the changes usually effected in the reduction of equations. According to Euclid, " 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: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. y. 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,...

## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 432 pages
...resemble exactly the changes usually effected in the reduction of equations. According to Euclid, " 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,...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...multiple of the third, when divided by the fourth, the four magnitudes are proportionals, or the first has the same ratio to the second that the third has to the fourth. We are now arrived very nearly at Euclid's definition ; for, let A, B, C, D be four proportionals,...

## The First Six Books with Notes

Euclid - 1822 - 179 pages
...be defined, is still a subject of controversy among geometers. Euclid defines them thus: The Jirst of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equi-multiples whatsoever of the Jirst and third being...

## Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823
...the ratio of 6 to 2 is the same as that of 15 to 5, which is expressed thus : as 6 : 2 : : 15 : 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,...