 | 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. 3,) A+B : B : : C+D : D... | |
 | James Wood - Algebra - 1845 - 442 pages
...— d : c; and inversely, a : a — b :: с : с — d. 247. When four quantities are proportionals, the sum of the first and second is to their difference,...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 + d By Art. 244, bd a —b... | |
 | 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...sum of the third and fourth is to their difference. •dn di. "+' c+^ j T» KIT. •"-* c — ^ For Prop. 5th — =-— , and Prop. 6th— 7-=— y-. a+bb... | |
 | Admiralty - 1845 - 152 pages
...-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 to their difference,...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 . \a— bc — d a~bc +... | |
 | 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,...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 : c — d From the same... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 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... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...b : : c : c — a. or a : b — a : : c : d — c. (Theorem 4.) Jf four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth i* to their difference. Admitting that a : b : : c : d , we are to prove that a+6 : a — b : : c+rf... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...— PROPOSITION IX. — If four quantities are in proportion, the sum of the first and second will be to their difference, as the sum of the third and fourth is to their difference. Let a:6::c:d, (1.) Then will a+6 : a— 6 : : c+d : c—d. From the 1st, by composition, Art. 250,... | |
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Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When... 
