Books Books
If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
An Elementary Geometry - Page 30
by William Frothingham Bradbury - 1872 - 110 pages

## Regents Examination Papers

University of the State of New York. Examination dept - Examinations - 1895 - 436 pages
...imaginary. 6-7 Complete and prove the following theorem : if any number of quantities are in proportion the sum of all the antecedents is to the sum of all the consequents as ... 8-9 Write three terms of the expansion of [a -\- b~\ n and prove that it is true when n is any...

## A Complete Algebra: For High Schools, Academies and Normal Schools

George Washington Hull - Algebra - 1895 - 358 pages
...nq Multiplying, \$P--JJ26n dq Whence, am :bn = cp: dq. THEOREM XVI. In a series of equal ratios, (he sum of all the antecedents is to the sum of all the consequents as any antecedent is to its consequent. Let a : 6 = с : d, And m:n=p:q. Then а с t Ь d' And ™=£....

## New Practical Algebra: Adapted to the Improved Methods of Instruction in ...

James Bates Thomson - 1896 - 336 pages
...number of quantities are proportional, any antecedent is to Us consequent, as ¿he sum of all ¿he antecedents is to the sum of all the consequents. Let a : b :: e : d :: e : f, etc. Then a : b :: a+e+e : Ь + d+f, etc. For (Th. i), ad = be And, " af=be Also,...

## Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1897 - 522 pages
...Dividing (I) by (2), —b = ~dWhence, a + b: a — o = c + d:c — d. 315. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a: b = c:d = e:f. Then by § 306, ad = be, and af= be. Also, ab = ba. Adding, a (b + d +f) = b(a + c + e)....

## Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1897 - 422 pages
...-J--- a — о с — a Whence, a + b : a — b = с + d : с — d. 315. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a : b = с : d = e : f. Then by § 306, ad = bс, and af= be. Also, ab = ba. Adding, a(b + d+f) = b(a + c...

## Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1897 - 386 pages
...Dividing (1) by (2), f±£ = Whence, a + b: a — b = c + d: c — d. 315. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a:b = c:d = e:f. Then by § 306, ad = be, and a/= be. Also, ab = ba. Adding, a(b + d+f) = b(a + c +...

## Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1904 - 384 pages
...Dividing (1) by (2), ±= Whence, a + b: a — b = c + d: с — d. 315. In a series of equal ratios, any antecedent is to its consequent as the sum of...antecedents is to the sum of all the consequents. Let a:b = c: d = e:f. Then by § 306, ad = be, and a/= be. Also, ab = ba. Adding, a (6 + d +/) = b (a +...

## Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...are proportional. §111 §111 Ax. 2 PROPOSITION XV. 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...