 | Webster Wells - Algebra - 1897 - 422 pages
...b : d, c:d — a:b, etc. 310. In any proportion, the terms are in proport1on by Alternation; tluü 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 = bс. (§ 306) Whence, a : с = b : d, (§ 309) 311.... | |
 | 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... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...ad be ac — = —, or — = - • bd bd bd That is, a:b = c: d. QED PROPOSITION III. THEOREM. 202. In any proportion the terms are in proportion by Alternation...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 are in proportion,... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...Given ad = bc. (1) To Prove a : 6 = c : d. Proof. Dividing both members of (1) by bd, ad_bc_ bd~bd Then by § 228, a : b = c : d. In like manner, a :...second term is to the fourth. Given the proportion a:b = c:d. (1) To Prove a : c = b : d. Proof. From (1), ad = bc. (§ 232) .-. a : c = b : d. (§ 234)... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...(1) by bd, ad _ be bd~bd' Or aC. °r' b~d Then by § 228, a : b = c : d. In like manner, a:c = b:d, PROP. III. THEOREM. 235. In any proportion, the terms...second term is to the fourth. Given the proportion a:b = c:d. (1) To Prove a : c = 6 : d. Proof. From (1), ad = be. (§ 232) .-. a:c = b:d. (§234) PROP.... | |
 | Webster Wells - Algebra - 1899 - 444 pages
...prove that d : с = b : d, с : d = a : b, etc. 310. In any proportion, the terms are in proportion b;/ 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 = Ьс. (§ 300) Whence, a : с = b : d. (§ 309) 311.... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...the extremes is equal to the product of the means. 330. If four quantities are in proportion, they are in proportion by alternation ; that is, the first 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... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...equation by bd. Then f = Jbd PROPOSITION IV. THEOREM. 330. If four quantities are in proportion, they are in proportion by alternation; that is, the first 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... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...equation by bd. Then 4.-jac bd PROPOSITION IV. THEOREM. 330. If four quantities are in proportion, they are in proportion by alternation; that is, the first term is to the third as the second is to the fourth. Let a: b = c : d. To prove that a:c = b:d. , T ac Now — = — • bd Multiply each... | |
 | George Edward Atwood - 1900 - 276 pages
...third. If a : b = c : d ad = bc be— ad .: b:a = d:c 430. If four numbers are in proportion, they are in proportion by alternation; that is, the first term is to the third as the second is to the fourth. If a: b = c: d ad = bc .: a:c = b:d 431. If four numbers are in proportion, they... | |
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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. 
