 | Robert Simson - 1762 - Liczba stron: 488
...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 - Liczba stron: 534
...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 - Liczba stron: 552
...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 - Liczba stron: 196
...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 - Liczba stron: 530
...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 - Liczba stron: 546
...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 - Liczba stron: 320
...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 - Liczba stron: 522
...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 - Liczba stron: 554
...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 - Liczba stron: 714
...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... | |
| |
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... 
