The student of the Differential Calculus may... be brought to think it possible that the terms and ideas which that science requires may exist in his… - Augustus De Morgan
" "The student of the Differential Calculus may... be brought to think it possible that the terms and ideas which that science requires may exist in his own mind in the same rude form as that of a straight line in the conceptions of a beginner in geometry. ...he must be prepared to stop his course until he can form exact notions, acquire precise ideas, both of resemblance between those things which have appeared most distinct, and of distinction between those which have appeared most alike. To do this... formal definitions would be useless; for he cannot be supposed to have one single notion in that precise form which would make it worth while to attach it to a word. One reason of the great difficulty which is found in treatises on this subject... the tacit assumption that nothing is necessary previously to actually embodying the terms and rules of the science, as if mere statement of definitions could give instantaneous power of using terms rightly. We shall here attempt... a wider degree of verbal explanation than is usual with the view of enabling the student to come to the definitions in some state of previous preparation.
English
Collect this quote
About Augustus De Morgan
Augustus De Morgan (June 27 1806 – March 18 1871) was an Indian-born British mathematician and logician; he was the first professor of mathematics at University College London. He formulated De Morgan's laws and was the first to introduce the term, and make rigorous the idea of mathematical induction. De Morgan crater on the Moon is named after him.
Related quotes. More quotes will automatically load as you scroll down, or you can use the load more buttons.
Additional quotes by Augustus De Morgan
The following is exactly what we mean by a <small>LIMIT</small>. ...let the several values of x... bea<sub>1</sub> a<sub>2</sub> a<sub>3</sub> a<sub>4</sub>. . . . &c.then if by passing from a<sub>1</sub> to a<sub>2</sub>, from a<sub>2</sub> to a<sub>3</sub>, &c., we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with a<sub>n</sub>, and continuing ad infinitum,a<sub>n</sub> a<sub>n+1</sub> a<sub>n+2</sub>. . . . &c.all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.
Limited Time Offer
Premium members can get their quote collection automatically imported into their Quotewise collections.
Aspiring to lead others, they have never given themselves the fair chance of being first led by other others into something better than they can start for themselves; and that they should first do this is what both those classes of others have a fair right to expect. New knowledge... must come by contemplation of old knowledge... mechanical contrivance sometimes, not very often, escapes this rule.
Loading...