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I.—Elimination in the case of Equality of Fractions whose Numerators and Denominators are Linear Functions of the Variables.

Published online by Cambridge University Press:  06 July 2012

Thomas Muir
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Extract

(1) It is well known that if equations of the type referred to in the title be dealt with like ordinary quadrics, the eliminant obtained is marred by association with an irrelevant factor. Thus, to take the simplest case, viz.

the left-hand member of which contains the irrelevant factor |α2β2|, being readily shown to be equal to

The object of the present short paper is to draw attention to other modes of procedure, and to formulate the results for n variables.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 45 , Issue 1 , 1906 , pp. 1 - 7
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

page 5 note * This and a cognate identity are formally proved in the Messenger of Math., xxxv. pp. 118–122.Google Scholar

† Note the identity,