 If four quantities are in proportion, they are in proportion by Inversion; that is, the second term is to the first as the fourth term is to the third.  Grammar School Algebra - Page 236by George Edward Atwood - 1900 - 253 pagesFull view - About this book
 | Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...in dealing with proportions: If four quantities are in proportion, they are in proportion by 281. I. Alternation; that is, the first term is to the third as the second is to the fourth. For if a : b = с : d, a _ с b~d' Multiplying by -i - = — i с cd . ' . а: с =b:d. 282. II. Inversion... | |
 | Webster Wells - Algebra - 1897 - 434 pages
...manner, we may prove that a : с — b : d, с : d = a : b, etc. 310. In any proportion, the terms are in proportion by Alternation; that is, the first term is to the third as the second term is to the fourth. Let the proportion be a : b = с : d. Then, ad = be. (§ 306) Whence, a : с... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...an interpretation in geometry. 222. THEOREMS IN PRO PORTION. I. If four magnitudes of the fame kind are in proportion, they are in proportion by Alternation; that is, the first is to the third as the second is to the fourth. Let A, B, C, D be four magnitudes of the same kind... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...- • bd bd bd That is, a:b = c: d. QED PROPOSITION III. THEOREM. 202. In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth. Let a : b = c : d. Then (by 199) ad = be. PROPOSITION IV. 203. If four quantities... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...like manner^ a : c = b : d, b : a = d : c, etc. PROP. III. THEOREM. 235. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first term is to the third as the second term is to the fourth. Given the proportion a : b = c : d. (1) To Prove a : c = b : d. Proof. From... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...Divide both members of the given equation by bd. iiPROPOSITION IV. THEOREM. 330. If four quantities are in proportion, they are in proportion by alternation...term is to the third as the second is to the fourth. Let a : b = c : d. To prove that a:c = b:d. No-w ad = be. § 327 Divide each member of the equation... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...proportion the product of the extremes is equal to the product of the means. 330. If four quantities are in proportion, they are in proportion by alternation...term is to the third as the second is to the fourth. 333. If four quantities are in proportion, they are in proportion by division ; that is, the difference... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...members of the given equation by bd. Then f = Jbd PROPOSITION IV. THEOREM. 330. If four quantities are in proportion, they are in proportion by alternation;...term is to the third as the second is to the fourth. Let a : b = c : d. To prove that a:c = b:d. Now ad = be. § 327 Divide each member of the equation... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...228, a : b = c : d. In like manner, a:c = b:d, PROP. III. THEOREM. 235. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first term is to the third as the second term is to the fourth. Given the proportion a:b = c:d. (1) To Prove a : c = 6 : d. Proof. From (1),... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...a : b = c : d. In like manner, a : c = b : d, PROP. III. THEOREM. 235. In any proportion, the terms are in proportion by ALTERNATION ; that is, the first term is to the third as the second term is to the fourth. Given the proportion a:b = c:d. (1) To Prove a : c = b : d. Proof. From (1),... | |
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