| 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
...A : Cor : : B : D, B — A:D—C::Ai C or : : B : D, answer to the 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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...A : C or : : B : D, B — A:D—C::A: C or : : B i D, answer to the 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... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...C : : A : C or : : B : D, B — A\D—C: :A:CoT::B:D, answer to the 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... | |
| 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... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...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 is to the' sum...antecedents is to the difference of the consequents, or as either antecedent is to its consequent. Likewise, the sum of the antecedents is to their difference... | |
| Benjamin Peirce - Algebra - 1837 - 300 pages
...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 is to the sum of...antecedents is to the difference of the consequents, or as either antecedent is to its consequent. Ratio of Sum of two first Terms to that of two last.... | |
| Thomas Sherwin - Algebra - 1841 - 314 pages
...difference of the consequents, as either antecedent is to its consequent ; the sum of the antecedents is to the sum of the consequents, as the difference...antecedents is to the difference of the consequents ; also, the sum of the antecedents is to their difference, as the sum of the consequents is to their... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...: D + C ::A: C,oi ::B:D, B — A:D—C::A:C,or::B:D, answer to the 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... | |
| 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... | |
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