 | Arthur Schultze - 1901 - 260 pages
...THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Hyp. a: 6 = c : d. To prove a + b: a — b = c + d: c — d. Proof. 5L+J? = £±£ (270) a — b_c... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...THEOREM 272. If four quantities are in proportion, they are in proportion by composition and division, ie the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Hyp. a : b = c : d. To prove a + b: a — b = c + d: c — d. Proof. a±& = £±«!. (270) bd a~bc~dbd... | |
 | George Egbert Fisher - 1901 - 320 pages
...two proportions are said to be derived from the given proportion by Division. 15. In any proportion, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Let a : b = с : d. By Art. 13, a + b:b = c + d:d; and by Art. 14, a - b : b = с - d : d. Then by... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 646 pages
...two proportions are said to be derived from the given proportion by Division. 10. In any proportion, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Let a : b — с : d. By Art. 8, a + b:b = c + d:d; and by Art. 9, a — b:b = c — did, Then by Art.... | |
 | Arthur Schultze - 1901 - 260 pages
...four quantities are in proportion, they are in proportion by composition and division, ie the suni of the first two terms is to their difference as the...sum of the last two terms is to their difference. Hyp. a : 6 = c : d. To prove a + b: a — b = c + d:c — d. Proof. -. (27Q) bd a — b _ c — d __...,... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1902 - 504 pages
...two proportions are said to be derived from the given proportion by Division. 10. In any proportion, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Let a : b = с : d. By Art. 8, a + b:b = c + d:d; and by Art. 9, ct — Ь : 6 = с — d:d. Then by... | |
 | Middlesex Alfred Bailey - Algebra - 1902 - 336 pages
...LXXXIII. THEOREM In any proportion, the terms are in proportion by cornposition and division; that is, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. a—6 с — d (We divide the equations member by member.) Let To prove a : b : : that a + b : a —... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...If four quantities are in proportion, ihey are in proportion by composition and division ; that is, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. Let a : b = c : d. Then i±* = «±*. ac And ^Z* = £H*. § 333 ac r,. ., a + bc + d Divide, - r =... | |
 | Webster Wells - Algebra - 1904 - 642 pages
...terms are in proportion by Composition and Division ; that is, the sum of the first tico terms is <ri their difference as the sum of the last two terms is to their Difference. Let the proportion be a : b = с : d Then by § 497, £±* = « + *. (1) а с And by § 498, 5^' =... | |
 | John Charles Stone, James Franklin Millis - Algebra - 1905 - 776 pages
...process is division. 202. The terms of a proportion are in proportion by tion and subtraction ; ie, the sum of the first two terms is to their difference...sum of the last two terms is to their difference. §200. §201. Axiom 4. This and the preceding sections will enable us to obtain an equivalent proportion... | |
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In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference. 
