 | Bewick Bridge - Algebra - 1818 - 254 pages
...c±.d. Til. 8. " If four quantities be proportional, then the sum " of (.he first and second is to their difference, as the sum of " the third and fourth is to their difference." For by THEOR. 6, £L+Ô=ÎI±^ and ^=£^; invert the two last udud .. . , bd , a + bbc + dd fractions,... | |
 | Bewick Bridge - Algebra - 1821 - 284 pages
...c+_d. Tн. 8. " If four quantities be proportional, then the sum " of the first and second is to their difference, as the sum of " the third and fourth is to their difference." For by _ ., a + bc + d , a— t c—d . , ,, , THEOR. 6, — : — =• , and — — = — — : invert... | |
 | John Playfair - Geometry - 1829 - 210 pages
...B^fA^::D^C:C (35). 40. If four quantities be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference. Let A : B : : C : D, then (by mixing) A+B:AB::CJ+D:C — D. ForA + B:B::C +D;D(37), .-. A + B : C •+... | |
 | George Peacock - Algebra - 1830 - 732 pages
...: c — d. 411. " If four magnitudes be proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference." Let a : b :: c : d, then also a + b : a — b :: c + d : c — d. T. .ac Forif 6-3' x, , a + bc + da... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...: с Тн. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, g ' c~*~ ; ; ' bd . a — bb — d ... bd and — — — ; invert the last two... | |
 | John D. Williams - Algebra - 1840 - 216 pages
...;• c TH. 8. If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. For, by theorem 6, ~|~ ~\ • od , a — bb — d , . . . . . bd and — ; — = — j- ; invert the... | |
 | James Wood - Algebra - 1841 - 492 pages
...с — d. 236. When four quantities are proportionals, the sum of the ßrst and second is to their difference, as the sum of the third and fourth is to their difference. By Art. 233, a + bc + d • , . a -b с- d and by Art. 234, — ~ — = - ; therefore ^±5 н~ ^ -... | |
 | Bewick Bridge - Algebra - 1841 - 260 pages
...c±d. TH. 8. " If four quantities be proportional, then the sum of the first and second is to their difference as the sum of the third and fourth is to their difference." For by TH. 6^ — =— = — =- , and od — T— = — — ; invert the last two fractions, then £=... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...and 84-4 = 2. 8. If four quantities are proportionals, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference; thus, if 6 : 3 :: 8: 4, then 6+3 : 6-3 :: 8+4 : 8-4, or 9 : 3 :: 12 : 4, for 94-3=3, and 124-4 = 3.... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...12—3:3:: 8—2 : 2. Hence, If four magnitudes, <Sfc. Cor. The sum of the fir?t and second is to their difference, as the sum of the third and fourth is to their difference. Since - - AB : B : : C— D : D; Then, (8. 3,) AB : CD : : B : D. And, (16. 3,) A+B : B : : C+D : D... | |
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If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
