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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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Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 σελίδες
...the multiple of the first exceeds that of the second, but the multiple of the third does not exceed that of the fourth; then the first is said to have...a greater ratio than the third has to the fourth. Annotation. multiples, if the ratios be equal. If any one set of multiples fail to satisfy that test...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 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...

Pelicotetics, Or, The Science of Quantity: An Elementary Treatise on Algebra ...

Archibald Sandeman - 1868 - 464 σελίδες
...CONTINUEDLY PROPORTIONATE or IN A CONTINUED PROPORTIONALITY. 246. Def. The first of four magnitudes is said to have to the second a GREATER RATIO than the third has to the fourth when the first is greater than some fraction of the second but the third is not greater than the same...

Pelicotetics, Or, The Science of Quantity: An Elementary Treatise on Algebra ...

Archibald Sandeman - 1868 - 464 σελίδες
...as the like multiples severally of the third and fourth. 252. PROP. The first of four magnitudes has to the second a greater ratio than the third has to the fourth precisely when some multiples of the first and second are in descending order of greatness but the...

Practical geometry for the architect, engineer, surveyor and mechanic

Edward Wyndham Tarn - 1871 - 242 σελίδες
...multiple of the second, the multiple of the third is also greater, equal to, or less than the multiple of the fourth ; then the first is said to have to the second the same ratio or proportion as the third has to the fourth. Magnitudes which have the same ratio to...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 σελίδες
...magnitudes, tiiken as in Def. v., the multiple of the first is greater than [or is equal to] the multiple of the second, but the multiple of the third is not greater than [or is less than] the multiple of the fourth, then the first is said to have to the second a greater...

Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...When of the equi-multiples of the four magnitudes, taken as in the fifth definition, the multiple of the first is greater than that of the second, but...have to the second a greater ratio than the third to the fourth ; or, which is the same thing, the ratio of the third to the fourth is said to be less...

The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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...

Euclid, Book V Proved Algebraically So Far as it Relates to Commensurable ...

Charles Lutwidge Dodgson - 1874
...magnitudes, taken as in the fifth definition, the multiple of the first is greater than the multiple 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...

Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 62 σελίδες
...magnitudes, taken as in the fifth definition, the multiple of the first is greater than the multiple 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...




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