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... The elements of algebra. [With] Answers - Page 166by Robert Fowler - 1861Full view - About this book
| John Playfair - Mathematics - 1806 - 320 pages
...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 - Trigonometry - 1806 - 546 pages
...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 - Geometry, Plane - 1809 - 522 pages
...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... | |
| Euclid - Geometry - 1810 - 554 pages
...therefore E is to G, so isc F to H. Therefore, if the first, &c. QED C0R. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any equimultiple!; 1 3. 5. b Hypoth. KEA GM L' FCDHN whatever of the first and third have the'... | |
| John Mason Good - 1813 - 714 pages
...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 pages
...: 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 - Mathematics - 1814 - 540 pages
...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 pages
...the less can be multiplied so as to exceed the other. y. 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 - Geometry - 1817 - 456 pages
...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 pages
...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... | |
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