 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.  The student's algebra - Page 13by John Darby (teacher of mathematics.) - 1829Full view - About this book
 | Elias Loomis - Algebra - 1868 - 386 pages
...b :: m:'n 9 m: U) c: d. n n c d : c : d. (i-) (2.) f f " 306." If four quantities 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. Let a : b : : c : d. By composition, Art. 304, d+b : b :: c+d: d. By alternation,... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...II., A:B::A+C + E:B + D + F. PROPOSITION XII. — THEOREM. 148. 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. Let A : B : : C : D ; then will A + B:A — B : : C + D : C — D. For, from the... | |
 | Ontario Chief Superintendent of Education - Education - 1869 - 450 pages
...the ordinary rule for Equation of Payments. 3. Prove that if any four quantities are in proportion the sum of the first and second is to their difference as the sum of the third and fourtli is to their difference. 4. Define what is meant by " Compound Proportion." 5. Give and prove... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...between the third and fourth. THEOREM IX. If four magnitudes are proportional, the sum ojthe^first and second is to their difference as the sum of the third and fourth is to their difference. Let A, B, C, and D be the four magnitudes which give the proportion A : B :: Q :... | |
 | Isaac Todhunter - Algebra - 1870 - 626 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tlie first and second is to their difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b : ab :: c + d : c — d. By Art. 393, "v-^, and by... | |
 | Isaac Todhunter - 1870 - 818 pages
...This operation is called convertendo. 396. When four quantities are proportionals, the sum of tJte first and second is to their difference as the sum of the third and fourth is to their difference. If a : b :: с : d, then a + b : ab :: c + d : cd. a + bc + d By Art. 393, -y- =... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...— c-\-d : d, a — 6 : b = с — d : d. PROPOSITION VU. — If four quantities be in proportion, the sum of the first and second is to their difference, as the sum of the third and fourth ù to their difference. If a : Ъ = с : d, we are to prove that a-\-b : a — b = c-\-d : с — d.... | |
 | Isaac Todhunter - Algebra - 1872 - 350 pages
...b а а с а с or а-Ъ : a :: cd : c; therefore a : а-Ъ :: с : cd. 367. JVhenfbur numbers are proportionals, the sum of the first and second is to their difference as the »um of the third and fourth is to their difference; that is, if a : Ъ :: с : d, then a+b : а-Ъ... | |
 | Elias Loomis - Algebra - 1873 - 396 pages
...and we have a , c , ,, . a—b c—d that is, -£- = -^-, 306. If four quantities are proportional, the sum of the first and second is to their difference, as the sum of the third and fourth it to their difference. Let a : b : : c : d. By composition, Art. 304, a+b: b::c+d: d. By alternation,... | |
 | Thomas Kimber - 1874 - 352 pages
...when a = 2 b : a , ab «* a*62 "r _ в _ 6* a* + 6* a* — b*' 7. Show that when> four numbers are proportionals, the sum of the first and second is...difference as the sum of the third and fourth is to their difference. If a : b : : с : d, show that (a* + c*) (b" + d") = (ab + с d)2. 8. Find the sum... | |
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