"...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Augustus De Morgan, The Differential and Integral Calculus (1836)
https://en.wikiquote.org/wiki/History_of_calculus
Revision History
No revisions have been submitted for this quote.
Categories
History of calculus
146 quotes on TrueQuotesView all quotes by History of calculus →
Related Quotes
"In Sorbière's day, European thinkers and intellectuals of widely divergent religious and political affiliations campa…"
"On the one side were ranged the forces of hierarchy and order—Jesuits, Hobbesians, French Royal Courtiers, and High C…"
"[Joseph-Louis Lagrange's] lectures on differential calculus form the basis of his Theorie des fonctions analytiques w…"
"Nothing is easier... than to fit a deceptively smooth curve to the discontinuities of mathematical invention. Everyth…"
"Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method …"
"Descartes' method of finding tangents and normals... was not a happy inspiration. It was quickly superseded by that o…"
"Archimedes was the earliest thinker to develop the apparatus of an infinite series with a finite limit ...starting on…"
"The fundamental definitions of the calculus, those of the derivative and integral, are now so clearly stated in textb…"
"The precision of statement and the facility of application which the rules of the calculus early afforded were in a m…"
"Nothing in Descartes' work led directly to Leibniz's calculus, but Descartes' discoveries in mathematics were certain…"