 | Euclides, James Thomson - 1845 - 382 páginas
...whatever 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... | |
 | Euclides - 1845 - 544 páginas
...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... | |
 | Euclid - 1845 - 218 páginas
...ratio to the second, than the fifth has to the sixth. PROPOSITION 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... | |
 | Dennis M'Curdy - 1846 - 168 páginas
...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 páginas
...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.... | |
 | Euclides - 1846 - 292 páginas
...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,... | |
 | John Playfair - 1846 - 332 páginas
...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 - 1848 - 52 páginas
...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 páginas
...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 páginas
...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... | |
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The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple... 
