 | Benjamin Peirce - Algebra - 1851 - 294 pages
...— CB — D mA-\-nC:mB-\-nD = mA — nC:mB — n D ; or, transposing the means as in art. 87, A -f- C : A — C = B + D : B — D mA-\-nC:mA — nC —...consequents, or as either antecedent is to its consequent. Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their... | |
 | William Smyth - Algebra - 1851 - 272 pages
...of the consequents, as any one anetcedent is to its consequent. In like manner it may be shown, that the difference of the antecedents is to the difference of the consequents, as any one antecedent is to its consequent. Let there be next a series of quantities, a, 6, c, d, e,... | |
 | Euclides - 1860 - 288 pages
...D:D. PROPOSITION XIX. THEOREM. (EUCLID XIX.) If four magnitudes of the same kind be proportionals, the difference of the antecedents is to the difference of the consequents as either antecedent to its consequent. Given four magnitudes of the same kind, such that A : B : r... | |
 | Richard Wormell - 1876 - 268 pages
...antecedents of a proportion is to the sum of its consequents as either antecedent is to its consequent ; and the difference of the antecedents is to the difference of the consequents in the same ratio. The sum of the antecedents of a proportion is to their difference as the sum of... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...sum of the consequents as either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents is to the difference of the consequents as either antecedent is to its consequent. (Explain.) Thus: a + x:b + y = a : b = x : y. 296. THEOREM.... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...sum of the consequents as either antecedent is to its consequent. (Explain.) Also, in any proportion the difference of the antecedents is to the difference of the consequents as either antecedent is to its consequent. (Explain.) Thus: a + x : b+ y = a : b - x : y. 296. THEOREM.... | |
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Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. Ratio of Sum of two first Terms to that of two last. Moreover, in finding... 
