"The true "principle of number," for Wallis as for Stevin, is the "nought". It is the sole numerical analogue of the geometric point (just as the instant is the temporary analogue)... Wallis expressly rejects the accusation that he is relinquishing the unanimous opinion of the ancients and the moderns, who all saw the unit as the element of number. ...the traditional opinion can be brought into accord with his own if the following distinction is taken account of: Something can be a "principle" of something (1) which is the "first which is such" (primum quod sic) as to be of the same nature as the thing itself and (2) which is the last which is not" (ultimum quod non) such as to be of the same nature of the thing itself. In the first sense the unit may indeed be called the "principle of number," while the nought is a "principle" in the second sense. ...The ancients... overlooked the fact that the analogy which exists is not between the "point" and the "unit," but between the point and the "nought." For this reason they were able to develop their algebra only for "geometric magnitudes"..."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
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…"