"They who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination. Every system of interpretation which does not affect the truth of the relations supposed, is equally admissible, and it is thus that the same process may, under one scheme of interpretation, represent the solution of a question on the properties of numbers, under another, that of a geometrical problem, and under a third, that of a problem of dynamics or optics. This principle is indeed of fundamental importance; and it may with safety be affirmed, that the recent advances of pure analysis have been much assisted by the influence which it has exerted in directing the current of investigation."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Introduction, p. ii.
https://en.wikiquote.org/wiki/History_of_algebra
Revision History
No revisions have been submitted for this quote.
Categories
History of algebra
112 quotes on TrueQuotesView all quotes by History of algebra →
Related Quotes
"All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the…"
"The precision of statement and the facility of application which the rules of the calculus early afforded were in a m…"
"The most influential mathematics textbook of ancient times is easily named, for the Elements of Euclid has set the pa…"
"We think only through the medium of words.—Languages are true analytical methods.—Algebra, which is adapted to its pu…"
"As regards algebra, the early Arabs failed to adopt either the Diophantine or the Hindu notations. An examination of …"
"Admitting the Hindu and Alexandrian authors [such as Diophantus], to be nearly equally ancient, it must be conceded i…"
"al-Khwārizmī “not having taken algebra from the Greeks,. . . must have either invented it himself, or taken it from t…"
"My specific... object has been to contain, within the prescribed limits, the whole of the student's course, from the …"
"The following Treatise... has been endeavoured to make the theory of limits, or ultimate ratios... the sole foundatio…"
"I have decided first to consider the majority of the authors who up to now have written about [algebra], so that I ca…"