 | Bewick Bridge - Algebra - 1841 - 260 pages
...: c±d : c, .-. inversely a : a±6 : : c : 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... | |
 | James Wood - Algebra - 1841 - 492 pages
...inversely, a : a - b :: с : 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, — ~ — = - ;... | |
 | George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...8:4, then 6 : 6-3 :: 8 : 8-4, or 6 : 3 :: 8 : 4; for 6—3=2. and 84-4 = 2. 8. If four quantities are proportionals, the sum of the first and second is...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... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...then, by division, 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.... | |
 | James Wood - Algebra - 1845 - 442 pages
...— b : a :: с — d : c; and inversely, a : a — b :: с : с — d. 247. When four quantities are proportionals, the sum of the first and second is...their difference, as the sum of the third and fourth is to their difference. If a : b :: с : d; then a + b : a — b :: с + d : с — d. a + Ъ с +... | |
 | Admiralty - 1845 - 152 pages
...ac For = .'. -jl=-jl (Art. 17.) a—bc — d ''• ~b~'~~d~ Or, ab:b::cd:d 89. If 4 quantities are proportionals, the sum of the first and second, is...their difference, as the sum of the third and fourth, is to their difference. That is, if a : b : : c : d then will a-\-b : a — b :: c-\-d : c— d For... | |
 | Scottish school-book assoc - 1845 - 444 pages
...108. Prop. 7- When four quantities are proportional, they are also proportional by mixing; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. •dn di. "+' c+^ j T» KIT. •"-* c — ^ For Prop. 5th — =-— , and Prop.... | |
 | Euclides - 1845 - 546 pages
...similar triangles it may be proved that of any three of the consecutive circles, the sum of the radii of the first and second, is to their difference, as the sum of the radii of the second and third, is to their difference. HINTS, &c. TO THE THEOREMS. BOOK VI. 3. THIS... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...:: C + D : C — D: that is, if four numbers be proportional, the sum of the first and second terms is to their difference, as the sum of the third and fourth terms is to their difference. It is evident, that if B be greater than A, the analogy would become... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...— b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes 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. Admitting that a : b :: c : d, we are to prove that a-\-b : a — b :: c-\-d... | |
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If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference. 
