Historically Speaking—: A History of Extraneous Solutions
The assertion that before the rise of abstract algebra in the mid-nineteenth century, algebra was concerned more with the use of algorithms and rules than with investigations of logical foundations for the subject could well be tested by a de tailed study of the treatment of extraneous solutions throughout that period. A treat ment of extraneous solutions at a particu lar time in history would, because of the subtle mathematical principles involved in that treatment, reflect on the state of algebra at least as much as, and perhaps more than, any one topic in mathematics. However, the main purpose of this paper is to reveal the history of extraneous solutions, though reflections on the state of algebra seen from this historical account will be mentioned whenever appropriate.