In order to see the difference which exists between... studies,—for in — Augustus De Morgan

"My specific... object has been to contain, within the prescribed limits, the whole of the students course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him."

"Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could."

"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."

"...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."

"The following Treatise... has been endeavoured to make the theory of limits, or ultimate ratios... the sole foundation of the science, without any aid whatsoever from the theory of series, or algebraical expansions. I am not aware that any work exists in which this has been avowedly attempted, and I have been the more encouraged to make the trial from observing that the objections to the theory of limits have usually been founded either upon the difficulty of the notion itself, or its unalgebraical character, and seldom or never upon anything not to be defined or not to be received in the conception of a limit..."

"If much difficulty should be experienced in the elementary chapters, I know of no work which I can so confidently recommend to be used with the present one, as that of M. Duhamel."

"The wound is the place where the Light enters you."

"Be the change that you wish to see in the world."

"In philosophy equally as in poetry it is the highest and most useful prerogative of genius to produce the strongest impressions of novelty, while it rescues admitted truths from the neglect caused by the very circumstance of their universal admission."

"An [hypertext] encyclopaedia will be an overall attempt by the knowledgeable, the learned societies or anyone else, to represent the state-of-the-art in their field. An encyclopaedia will be a living document, as up to date as it can be, instantly accessible at any time. It will contain carefully authored explanations and summaries of the subject, as well as computer-generated indexes of literature. A reference to a paper from the encyclopaedia conveys authority and acceptance by academic society. A measure of a paper’s standing may be conveyed by the number of links it is away from an encyclopaedia."

"The British intellectual tradition is empirical and liberal, the French is rationalist and aristocratic, and the German is idealist and conservative. ...In the great ontological debate between mind and matter, German philosophy comes down solidly on the side of mind. Its emphasis is intuition as opposed to reason, ideas as opposed to facts."

"To know the mighty works of God, to comprehend His wisdom and majesty and power; to appreciate, in degree, the wonderful workings of His laws, surely all this must be a pleasing and acceptable mode of worship to the Most High, to whom ignorance cannot be more grateful than knowledge."