 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...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... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...— d : c. PROPOSITION VII. — 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 is to their difference. If a : b = с : d, we are to prove that a-{-b : a — b = c-\-d : с — d.... | |
 | Benjamin Greenleaf - 1863 - 338 pages
...— d : d. THEOREM VIII. 322. 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 is to their difference. Let a : b : : с : d; Then, а-\-b : a — 6: : с -\- d : с — d By Theo.... | |
 | Isaac Todhunter - Algebra - 1863 - 302 pages
...therefore a : ab :: c : cd. 367. When four numbers 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 ; that is, if a : b :: c : d, then a+b : ab :: c + d : c—d. T> t ! ,,.A jo/.*... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...— b : b : : c — d : d. 317. If four quantities be in proportion, the sum of the Jirst and second is to their difference as the sum of the third and fourth is to their difference. If a : b : : c : d, then a -j- b : a — b : : c -\- d : c — d. By Art. 315,... | |
 | Isaac Todhunter - Algebra - 1866 - 618 pages
...is called converlendo. 396. W/ten 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 t/ieir difference. If a : b : : с : d, then a + b : a—I : : c + d : c — d. By Art. 393,... | |
 | James Pryde - Navigation - 1867 - 506 pages
...a—bc—db — ad—c 41. THEOREM.. — 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. This change is called proportion by Mixing. /- • ii. *. ac i_ .. й + ^ c... | |
 | Elias Loomis - Algebra - 1868 - 386 pages
...: 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
...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... | |
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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. 
