| John Playfair - Euclid's Elements - 1806 - 311 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... | |
| Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...exactly resemble the changes usually effected in the reduction of equations. According to Euclid, " **The first of four magnitudes is said to have the same...being taken, and any equimultiples whatsoever of the** aecmxd and fourth ; if the multiple of the first be less than that of the second, the multiple of the... | |
| Euclid - Geometry - 1810 - 518 pages
...as 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... | |
| John Mason Good - 1813
...of the second, and the other of the fourth. Prop. IV. Thecir. If the first of four magnitue!p| lias **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... | |
| Charles Butler - Mathematics - 1814
...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 - 1814
...the first, &c. QED A 33 CV C J> Boo' V. PROP. IV. THEOR. SeeN. 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... | |
| John Playfair - Euclid's Elements - 1819 - 333 pages
...A = mB, therefore A~mn C. Therefore, &c. Q, ED PROP. IV. THEOR. If thefirst 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 thefirst and third, and any whatever of the second and... | |
| John Mason Good - 1819
...to the fourth, and if any equimultiples whatever he taken of the first and third, and any whatever **of the second and fourth ; if the multiple of the first be** equal to the multiple of the second, the multiple of the third will be equal to the multiple of the.... | |
| Euclid - 1822 - 179 pages
...be defined, is still a subject of controversy among geometers. Euclid defines them thus: The Jirst **of four magnitudes is said to have the same ratio...fourth, when any equi-multiples whatsoever of the** Jirst and third being taken, and any equi-multiples whatsoever of the second and fourth being taken,... | |
| George Crabb - Industrial arts - 1823
...the ratio of 6 to 2 is the same as that of 15 to 5, which is expressed thus : as 6 : 2 : : 15 : 5. **The first of four magnitudes is said to have the same...the multiple of the first be less than that of the** third, the multiple of the second is also less than that of the fourth ;• if equal, equal ; and if... | |
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