IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together... A Treatise on the Elements of Algebra - Page 112by Bewick Bridge - 1821 - 227 pagesFull view - About this book
| Euclid - Geometry - 1765 - 492 pages
...ratio to B than E has to F. If therefore the firft of fix magnitudes has the fame ratio io the fecond, as the third to the fourth; and the third to the fourth has a greater ratio than the fifth to the fixth : then the firft to the fecond will have a greater... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...separately, be proportionals, see N. they shall also be proportionals when taken joindy, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth.... | |
| John Playfair - Mathematics - 1806 - 320 pages
...taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth.... | |
| John Mason Good - 1813 - 714 pages
...taken separately, he proportionals, they shall also be proportionals, when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall he to the second, as the third and fourth together to the fourth.... | |
| Charles Butler - Mathematics - 1814 - 528 pages
...both sides by bd, and (-—=—-, or) ~= 4-, that is,a:b::c:d. Euclid 17, 6. bd 61. If the first term be to the second, as the third to the fourth, and...as the fifth to the sixth, then will the first be to the second as the fifth to the sixth. Let a:b::c:d, and c : d : : e :f, then will a:b::e :f; for... | |
| Thomas Leybourn - Mathematics - 1814 - 420 pages
...found to be 3/. i8.r. g</, Required thejate per cent, per annum. a. If the first of six magnitudes be to the second as the third to the fourth, and the fifth to the second as the sixth to the fourth; Prove that the first and fifth together will be to... | |
| Charles Butler - Mathematics - 1814 - 540 pages
...or two more particulars will require an explanation. If four numbers are proportionals, that is, if the first be to the second as the third to the fourth, then will the first be to the third аз the second to the fourth; and this accounts for the usual... | |
| Bewick Bridge - Algebra - 1818 - 254 pages
...(dividing by cd) we have — = —,> or -=-1 5 .'. a : с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities,...the fifth to the sixth ; then will the first " be to the second as the fifth to the sixth." For let a : b :: с : d, ij г iл. ac , с eae . and с:... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...demonstrated, A : C : : B : D, and inversely (A. 5.) C : A : : D : B. Therefore, &c. q. ED PROP. C. THEOE. If the first be to the second as the third to the fourth ; and if the first be a multiple or a part of the second, ihe third is the same multiple or the same part... | |
| John Playfair - 1819 - 354 pages
...taken separately, be proportionals, they will also be proportionals -when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth.... | |
| |