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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., by J.A. Galbraith and S. Haughton

Euclides - 1859
...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. DEFINITION XIV. "Opoç ii'. — -Aváira\iv \oyoç larl XijJ/tC TOV iiropivov ¿íç 177011JJií.VOV...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...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's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 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...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...— 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 Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - 1862 - 79 σελίδες
...to that of the fourth ? If not, why? 18. If, particular equimultiples being taken, the multiple of the first is greater than that of the second, but the multiple of the third not greater than that of the fourth ; has the first necessarily a greater ratio to the second than...

The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...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 school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...vn. 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 college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...VIL 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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 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...

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

Euclid, Isaac Todhunter - 1867 - 400 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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