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When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have...
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 329
των James Ryan - 1826 - 383 σελίδες
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...number of times, with or without a remainder, than the third contains the like part of the fourth, the first is said to have to the second a greater ratio than the third has to the fourth : also, in this case, the third is said to have to the fourth a less ratio than the first has to the...

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

Euclid - 1835 - 513 σελίδες
...VII. When of the equimultiples of four magnitudes (taken as in the fifth definition,) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then, the first is said to have to the second a greater ratio than the...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...7. When of the equimultiples of four magnitudes, taken as in the fifth definition, the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth; then the first is said to have to the second a greater ratio than the third...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...14. When of the equimultiples of four magnitudes, taken as in the tenth definition, the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the...

A Treatise on the Elements of Algebra

James Bryce - 1837 - 80 σελίδες
...When the second of four quantities is contained in the first oftener than the fourth in the third, the first is said to have to the second a greater ratio than the third to the fourth. Thus, 4 : 2 is a greater ratio than 4 : 3, and 8 : 5 a less ratio than 7:4; because...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...7. When, of the equimultiples of four magnitudes, taken as in the fifth definition, the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first magnitude is said to have to the second a greater ratio...

The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 σελίδες
...is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth : and, on the contrary, the third is said to have to the fourth a less...

The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 σελίδες
...VII When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...equimultiples of the second and fourth we have 154, 154,24S6, 24S5; then the multiple of the first is equal to that of the second, but the multiple of the third is not equal to that of the fourth; consequently the proposed numbers cannot constitute a proportion, because...

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

John Playfair - 1842 - 317 σελίδες
...7. When of the equimultiples of four magnitudes, taken as in the fifth definition, the multiple of the first is greater than that of the second, but the multiple of the jhird is not greater than the multiple of the fourth : then the first is said to have to the second...