| Euclides - 1845 - 546 pages
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED COB. 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 second... | |
| Dennis M'Curdy - 1846 - 168 pages
...having some common property ^ can have a ratio to one another. 5. The first of four magnitudes has **the same ratio to the second which the third has to the fourth, when** equimultiples of the first and third, also of the second and fourth, being taken ; if the multiple... | |
| Dennis M'Curdy - 1846 - 166 pages
...multiple, &c. QED Recite (a) definitions 1, 2, A of b 5 -B D-0 H4 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.... | |
| Euclid, John Playfair - 1846 - 334 pages
...two numbers. Let A=mB, and B=nC ; then A=mnC. PROP. IV. THEOR. If the first of four magnitudes has **the same ratio to the second which the third has to the fourth,** and if any equimultiples whatever be taken of the first and third, and any whatever of the second and... | |
| 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 - 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 - 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 - 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 - 230 pages
...b = 6, which is the first case in Euclid. PROPOSITION A. THEOREM.—If the first of four magnitudes **have the same ratio to the second which the third has to the fourth,** then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,... | |
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