| Euclid, James Thomson - Geometry - 1845 - 352 pages
...of G, H: therefore (V. def. 5) as E : G : : F : H. Therefore, &c. Cor. Likewise, if the first have **the same ratio to the second, which the third has to the fourth,** then also any like multiples whatever of the first and third have the same ratio to the second and... | |
| Scottish school-book assoc - 1845
...multiple of the third is also equal to that of the fourth; or if the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth. NOTE. A multiple of a quantity is the result of repeating that quantity... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...5 Wherefore, if the first be the same multiple, &c. QED 4 Th. If the first of four magnitudes have **the same ratio to the second which the third has to the fourth;** then any equimultiples of the antecedents shall have the same ratio as any equimultiples of the consequents.... | |
| Euclides - 1846
...has a greater ratio to the second than the fifth has to the sixth. PROP. XIV. THEOR. If the first has **the same ratio to the second which the third has to the fourth,** then, if the first be greater than the third, the second shall be greater than the fourth, and if equal,... | |
| Euclides - 1848
...of the second, and the other of the fourth. PROP. IV. THEOREM. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth;** then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - Geometry - 1853
...is no necessity for all four to be of the same kind. OBS. 3. When the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** the third clearly has the same ratio to the fourth which the first has to the second. Such will appear... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...fourth D. If, therefore, the first, etc. QED PROPOSITION IV. THEOB. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** then any equimultiples •whatever of the first and third shall have the same ratio to any equimultiples... | |
| Euclides - Geometry - 1853 - 147 pages
...If, therefore, the first, &c. QED PROPOSITION IV. — THEOREM. If the first of four magnitudes has **the same ratio to the second which the third has to the** fowrth ; then any equimultiples whatever of tlie first and third shall have the same ratio to any equimultiples... | |
| Euclides - 1855
...respectively. If, therefore, the first, &c. QED PROP. IV. THEOREM. If the first of f oar magnitudes has **the same ratio to the second which the third has to the fourth** ; any equimultiples whatever of the first and third have the same ratio to any equimultiples of the... | |
| Euclides - 1855
...any whatever of G, H ; therefore as E is to G so is F to H (c). COROLLARY. Likewise, if the first has **the same ratio to the second, which the third has to the fourth,** then also any equimultiples whatever of the first and third shall have the same ratio to the KEA second... | |
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