 | George Washington Hull - Geometry - 1897 - 408 pages
...THEOREM. QED 133. In a series of equal ratios, the sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Let a: b— c : d= e:f. Let r •» the common ratio, Then £ = r, and a = br. (1) b Let And Then And Multiplying, Whence... | |
 | George Albert Wentworth - Algebra - 1898 - 428 pages
...kind as a and b. In applying alternation, however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. _, .. a с eg For'lf -b = d = f = -h' r may be put for each of these ratios. г_, a с eg Then, -b... | |
 | George Albert Wentworth - Algebra - 1898 - 434 pages
...however, all four quantities must be of the same kind. 340. In a Series of Equal Ratios, the sum of th e antecedents is to the sum of the consequents as any antecedent is to its consequent. _< .„ aeet) For, if - = - = - = £, bdfh r may be put for each of these ratios. . aeeg Then, - -... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...two terms is to their difference. Let a : b = c : d. , § 333 Q, ED. PROPOSITION IX. THEOREM. 335. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Let a:b = c:d = e:f = g:h. To prove that a + c + e + yb + d -\-f + h = a : b. _ acea Let r=y = - = - =... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...A'B' = DC : B'C' = CD : C'D', etc. § 351 .'. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the hases of a trapezoid... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...A'B' = BC : B'C' = CD: C'D', etc. § 351 .-. AB + BC + etc. : A'B' + B'C' + etc. = AB : A'B', § 335 (in a series of equal ratios the sum of the antecedents...consequents as any antecedent is to its consequent). That is, P:P' = AB:A'B'. QED Ex. 252. If the line joining the middle points of the bases of a trapezoid... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...two terms is to the second term as the difference of the last two terms is to the fourth term. 335. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. 338. Like powers of the terms of a proportion are in proportion. 342. If a line is drawn through two... | |
 | William James Milne - Geometry - 1899 - 404 pages
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a: b = c:d = e:f=g:li. To prove a + c + e + g:b + d +/+ A = a... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...of any antecedent to its consequent? 2. Transform similarly and investigate other series. Theorem. In a series of equal ratios, the sum of the antecedents...consequents as any antecedent is to its consequent. Data : Any series of equal ratios, as a:b = c:d = e :/= g : h. To prove a + c + e + g:b + d +/+ ft... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...AB: A'B' = BC: B'C' = CD: C'D', etc. § 351 .'. AB + BC + etc.: A'B' + B'C' + etc. = AB: A'B', § 335 (in a series of equal ratios the sum of the antecedents...the sum of the consequents as any antecedent is to Us consequent). That is, P:P' = AB: A'B'. Q . ED Ex. 252. If the line joining the middle points of... | |
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In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent. 
