 | Webster Wells - 1899 - 450 σελίδες
...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...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), ad = bc. (§ 232) .-.... | |
 | George Albert Wentworth - 1899 - 500 σελίδες
...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 Albert Wentworth - 1899 - 248 σελίδες
...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 - 1899 - 272 σελίδες
...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 Edward Atwood - 1900 - 276 σελίδες
...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... | |
 | James Harrington Boyd - 1901 - 818 σελίδες
...: c. [H86] 488. THEOREM V. — In any proportion, the terms are in proportion by alternation; tliat is, the first term is to the third as the second term, is to the fourth. Let the proportion be a : b = c : d . Then ad = be, [8482] a : c = b : d. [2486] 489. Unless the numbers are of the same kind,... | |
 | George Albert Wentworth - 1902 - 248 σελίδες
...A central angle is measured by its intercepted arc. 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... | |
 | Middlesex Alfred Bailey - 1902 - 336 σελίδες
...as an equality of two fractions. See p. 214. PROPOSITION LXXIX. THEOREM In any proportion, the terms 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 : с : : b : d ad = bc (The product of the extremes... | |
 | American School (Chicago, Ill.) - 1903 - 390 σελίδες
...that : a : c = b : d b:d — a:c c : d = a : b, etc. THEOREH III. 131. In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second is to the fourth. Let a : 6 = c : d By (128) ad = be By (130) a:c = b:d THEOREn IV. 132. In any proportion... | |
 | Fletcher Durell - 1904 - 382 σελίδες
...different ways as possible. PROPOSITION IV. THEOKEM 307. 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. t Given the proportion a : b = c : d. To prove a . c = b : d. Proof. a : b = c :... | |
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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. 
