 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...herefore Az: ¡ PRO P. IV. THEO R. JF the firft of four magnitudes has the fame ratio to the fécond which the third has to the fourth, and if any equimultiples whatever be taken of the firlt and third, and any whatever of the fécond and. fourth ; the'multiple of the firft fhall have... | |
 | John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...Therefore, &c. . D. PROP. IV. THEOR. IF the firft of four magnitudes has the fame ratio to the fecond which th,e third has to the fourth, and if any equimultiples whatever be taken of the firft and third, and any whatever of the fecond and fourth ; the multiple of the firft fhall have the... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...sixth, is of the fourth D. If, therefore, the first, &c. ^- ED H EABGCD 126 BookV. SeeN. THE ELEMENTS PROP. IV. THEOR. 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... | |
 | 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... | |
 | Sir John Leslie - Geometry, Analytic - 1809 - 542 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
...G, so is c F to H. Therefore, if the first, &c. QED EABGM L' FCDHN COR. Likewise, if the first have the same ratio to the second, which the third has to the fourth, then also any equimultiples * IL" whatever of the first and third have the* same ratio to the second... | |
 | Sir John Leslie - Geometry - 1811 - 524 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 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
...sixth, is of the fourth D. If, therefore, 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... | |
 | Charles Butler - 1814 - 540 pages
...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... | |
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Therefore, &c. QED 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 whatever be taken of the first and third, and any whatever of the second and fourth; the multiple 
