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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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...compared with the equimultiples of the second second, than the third is when compared to the fourth, the first is said to have to the second a greater ratio than the third has to the fourth." " 4. If the first of four magnitudes be less, «hen compared to the second, than the third is when...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...compared with the equimultiples of the second second, than the third is when compared to the fourth, the first is said to have to the second a greater ratio than the third has to the fourth." " 4. If the first of four magnitudes be less, when compared to the second, than the third is when compared...

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

Euclid, John Playfair - 1826 - 320 σελίδες
...is greater than that of the seeond, hut the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the seeond a greater ratio than the third magnitude has to the fourth; and, on the eontrary, the third...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 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 third...

The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 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...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
...demonstrated more it large in Prop. [9]. Def. [8]. If there be two magnitudes of fhe same kind, and other two, the first is said to have to the second a greater ratio than the third has to the fourth, when the first contains some measure of the second a greater number of times Iban the third contains...

A Treatise on Algebra

George Peacock - 1830 - 685 σελίδες
...some equimultiples of the first and fifth, and also of the second and sixth, where the multiple of the first is greater than that of the second, but the multiple of the fifth not greater than that of the sixth : a conclusion by no means self evident, but requiring the...

The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 σελίδες
...substituted for the following : When of the equi-multiples of four magnitudes the multiple of thejirst 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...

Iron: An Illustrated Weekly Journal for Iron and Steel ..., Τόμος 18

Perry Fairfax Nursey - 1833
...latitude to the meaning of the seventh definition, we are entitled to conclude, that the first has to the second a greater ratio than the third has to the fourth. Dr. Simson, it is true, has demonstrated that the multiple of the first is greater than the multiple...

The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...any assigned. And this being so, those four magnitudes A, B, C, and D are proportional. contained in the fourth, then the first is said to have to the second a less ratio than the third has to the fourth ; and on the other hand, the third is said to have to the...