 | John Playfair - 1806 - 320 σελίδες
...hypothesis A=mB, therefore A=mnC. Therefore, &c. QED PROP. IV. THEOR. IF the first of four magnitudes have 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... | |
 | Robert Simson - 1806 - 546 σελίδες
...the less can be multiplied so as to exceed the other. V. 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... | |
 | Sir John Leslie - 1809 - 522 σελίδες
...in the reduction of equations. According to Euclid, " 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... | |
 | John Mason Good - 1813 - 714 σελίδες
...less can be multiplied so as to exceed the other; 5. The first of four magnitudes is enid to hav<? 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... | |
 | Euclides - 1814 - 560 σελίδες
...: As therefore E is to G, so is c F to H. Therefore, if the first, &c. QED See N. C0R. 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 have the same ra- Boox V. tio to the second... | |
 | Charles Butler - 1814 - 540 σελίδες
...you k The comparison of one number to another is called their ratio ; and when of four giren numbers the first has the same ratio to the second which the third has to the fourth, these four numbers are said to be proportionals. Hence it appears, that ratio is the comparison of... | |
 | Euclides - 1816 - 588 σελίδες
...: As therefore E is to G, so isc F to H. Therefore, if the first, &c. QED See N. COR. Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equiABGM LFCDHN multiples whatever of the first and third have the same ra- Boo* V. tio... | |
 | Sir John Leslie - 1817 - 456 σελίδες
...in the reduction of equations. According to Euclid, " 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... | |
 | John Playfair - 1819 - 354 σελίδες
...A = mB, therefore A— m«C. Therefore, &c. Q,. ED 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 whaterer be taken of the first and third, and any whatever of the second and... | |
 | Euclid - 1822 - 222 σελίδες
...controversy among geometers. Euclid defines them thus: The Jirst of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equi-multiples whatsoever of the Jirst and third being taken, and any equi-multiples whatsoever... | |
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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 and fourth... 
