 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...the difference of the consequents, as one antecedent is to its consequent ; Whence it follows that the sum of the antecedents is to their difference...the sum of the consequents is to their difference, If we have a series of equal ratios A:B::C:D::E:F, by considering only the two first, which form the... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...the difference of the consequents, as one antecedent is to its consequent ; Whence it follows, that the sum of the antecedents is to their difference,...the sum of the consequents is to their difference. If we have a series of equal ratios A : B ; ;: C : D : : E : F, by considering only the two first,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...difference of the consequents, as one antecedent is to its consequent ; Whence it follows, ihat'the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. If we have a series of equal ratios A:B::C:D::E:F, by considering only the two first, which form the... | |
 | William Smyth - Algebra - 1830 - 278 pages
...is to the sum or difference of the consequents, as one antecedent is to its consequent, and the turn of the antecedents is to their difference, as the sum of the consequents is to their difference. 181. Let there be the series of equal ratios a : b::c : d::e :f::g : h . . . . or -=± -==-=aceg Making... | |
 | Charles Hutton - Mathematics - 1831 - 632 pages
...antecedents, is to that of the consequents, as any one of the antecedents is to its consequent. THEOREM v. The sum of the antecedents is to their difference,...the sum of the consequents is to their difference. In like manner, if there be a series of equal ratios, f = V = V = f* ; *e ha™ 6+10+14+30 14 80 THEOREM... | |
 | William Smyth - Algebra - 1833 - 288 pages
...antecedents is to the »um or difference of the consequents, as one antecedent is to its consequent, and the sum of the antecedents is to their difference,...the sum of the consequents is to their difference. 167. Let there be the series of equal ratios a : b : : c : d : : e : f : : g : h . . . . Making - =... | |
 | Olinthus Gregory - Mathematics - 1834 - 472 pages
...the antecedents is to that of the consequents, as either antecedent is to its consequent And, that the sum of the antecedents is to their difference,...the sum of the consequents is to their difference. 5+15 ,6+15 5>-i5 Thus gtF = * - V, and 3^=— If there be a series of equal ratios represented by |... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...gives A + C:B+ D = A:B = C:D whence A + C : B + D = A — C : B— D, or A + C-.A — C = B + DB— D; that is, the sum of the antecedents of a proportion...the sum of the consequents is to their difference. If the proportion A : B = C : D is written A : C = B : D, and the preceding rules applied, we have... | |
 | Thomas Sherwin - Algebra - 1841 - 314 pages
...the consequents, as the difference of the antecedents is to the difference of the consequents ; also, the sum of the antecedents is to their difference,...the sum of the consequents is to their difference. 14. If in any proportion, the antecedents are alike or equal, the consequents must be equal; also,... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...the difference of the consequents, as one antecedent is to its consequent; Whence it follows, that the sum of the antecedents is to their difference...the sum of the consequents is to their difference. If we have a series of equal ratios A:B::C:D::E:F, by considering only the two first, which form the... | |
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Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference. 
