| Robert Simson - 1762 - 466 pagine
...IV. THEO R. '"fee N.' JF the firft of four magnitudes has the fame ratio to the '•• ''. fecond **which the third has to the fourth; then any equimultiples whatever of the** firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth, viz. ' the... | |
| Robert Simson - 1775 - 520 pagine
...Book V. SccN. I PRO P. IV. THEO R. F the firft of four magnitudes has the fame ratio to _ the fecond **which the third has to the fourth ; then any equimultiples whatever of the** firft and third fhall » have the fame ratio to any equimultiples of the fecond and fourth, viz. «... | |
| Euclid - 1781 - 520 pagine
...Hypoth. c 3. def. PRO P. IV. THEO R. IF the firft of four magnitudes has the fame ratio td the fecond **which the third has to the fourth ; then any equimultiples whatever of the** firft and third mail have the fame ratio to any equimultiples of the fecond and fourth, viz. * the... | |
| Nicolas Vilant - 1798 - 170 pagine
...m В==я пг X Bi PROPOSITION IV.— THEOREM; if the firft of four magnitudes have the fame ratio **which the third has to the fourth ; then any equimultiples whatever of the** firft and third mall have the fame ratio to any equimultiples of the fécond and fourth* viz. the equimultiple... | |
| Robert Simson - 1804
...C^ED Kr EABGC I D PROP. IV. THE OR. IF the firft of four magnitudes has the fame ratio to the fecond **which the third has to the fourth; then any equimultiples whatever of the** firft and third fhall have the fame ratio to any equimultiples of the fecond and fourth, viz. * the... | |
| Robert Simson - 1806 - 518 pagine
...sixth, is of the fourth D. If, therefore, the first, &c. QED K H EABGCD BookV. PROP. IV. THEOR. See N. **IF the first of four magnitudes has the same ratio to the second which the third** hath to the fourth, then any equimultiples whatever of the first and third shall have the same ratio... | |
| John Playfair - 1806 - 311 pagine
...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 - 1809 - 493 pagine
...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 - 1810 - 518 pagine
...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
...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... | |
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