| 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 - 496 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 - 274 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 - 237 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 - 154 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 - 434 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 - 544 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 - 380 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... | |
| |