 | Euclides, James Thomson - Geometry - 1845 - 382 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 - 444 pages
...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 - 168 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 - 292 pages
...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 - 52 pages
...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 - 334 pages
...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 - 400 pages
...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 - 176 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 - 270 pages
...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 - 230 pages
...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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If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... 
