Lexicographical Neighbors of Permanences
Literary usage of Permanences
Below you will find example usage of this term as found in modern and/or classical literature:
1. A Treatise on Algebra: For the Use of Schools and Colleges by Stephen Chase (1849)
"... the single signs immediately preceding and following are always unlike.
Hence the number of permanences may be diminished, but cannot be increased. ..."
2. Elements of Algebra by George Albert Wentworth (1895)
"No. of permanences, 2. Hence there are 2 positive and 2 negative roots. 4. ...
No. of permanences, 1. Hence there are 3 positive and 1 negative roots. ..."
3. An Elementary Treatise on Curves, Functions, and Forces by Benjamin Peirce (1846)
"In one case, therefore, the whole number of lost permanences is one greater than the
... When the loss of permanences does not arise from a real root of the ..."
4. An Elementary Treatise on Algebra: To which are Added Exponential Equations by Benjamin Peirce (1864)
"The whole number of successions of signs of an equation, that is, the sum of the
permanences and variations, is one less than the number of terms, ..."
5. An Elementary Treatise on Algebra: To which are Added Exponential Equations by Benjamin Peirce (1870)
"The whole number of successions of signs of an equation, that is, the sum of the
permanences and variations, is one less than the number of terms, ..."
6. The Collected Mathematical Papers of James Joseph Sylvester by James Joseph Sylvester (1908)
"... cannot exceed the difference between the number of double permanences in
the (/, G) couple, less the number of double permanences in this couple, ..."
7. Ray's Algebra, Part Second: An Analytical Treatise, Designed for High by Joseph Ray (1857)
"Again, if we change the signs of the alternate terms, the roots will be changed
from positive to negative, and conversely (Art. 400). Hence, the permanences ..."
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