 | L. I. M. Chevigné - Mathematics - 1807 - 294 pages
...componendo, that we shall have dcirahendo, a—c\b—d '.'.a'.b ; that is to say, that in every proportion, the difference of the antecedents, is to the difference of the consequents, as an antecedent is to its consequent. ARITHMETIC PROGRESSIONS. An arithmetic progression is a series... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...following enunciation ; The sum of the antecedents of a proportion is to the sum of the consequents, and the difference of the antecedents is to the difference of the consequents, as one antecedent is to its consequent ; Whence it follows that the sum of the antecedents is to their... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...following enunciation ; The sum of the antecedents of a proportion is to the sum of the consequents, and the difference of the antecedents is to the difference of the consequents, as one antecedent is to its consequent ; Whence it follows, that the sum of the antecedents is to their... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...following enunciation ; The sum of the antecedents of a proportion is to the sum of the consequents, and the difference of the antecedents is to the difference of the consequents, as one antecedent is to its consequent ; Whence it follows, ihat'the sum of the antecedents is to their... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...transposing the means, as in art. 63, A + C; A — C= B + D :B — D mA-{-nC:mA — nC=mB -\-nD :mB — nD; that is, the sum of the antecedents of a proportion...provided its consequent is multiplied by the same number. 72. Corollary. These rules may also be applied to the proportion A : C = B : D obtained from A : B... | |
 | 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...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... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...transposing the means, as in art. 63, A-\-C:A — C=B + D .B — D mA-\-nC:mA — nC =mB -\-nD :mB — that is, the sum of the antecedents of a proportion...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... | |
 | Benjamin Peirce - Geometry - 1841 - 186 pages
...antecedents of a proportion is to the sum of its consequents as either antecedent is to Us consequent ; and the difference of the antecedents is to the difference of the consequents in the same ratio. Theorem V. The sum of the antecedents of a proportion is to their difference, as... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...following enunciation ; The sum of the antecedents of a proportion is to the sum of the consequents, and the difference of the antecedents is to the difference of the consequents, as one antecedent is to its consequent; Whence it follows, that the sum of the antecedents is to their... | |
 | Thomas Hill - Arithmetic - 1845 - 110 pages
...test will apply. That is, 7, 21, 2, 6, are known to be in proportion by the fact, that 2x21 = 7x6. 41. The difference of the antecedents is to the difference of the consequents as either antecedent is to its consequent. That is, if equal ratios be subtracted from each other,... | |
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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... 
