The method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.
Bernhard RiemannRelated topics
beginning best calculus century concept considering grounding increase infinitesimal number place position speaking sure transition value viz newton pointsRelated quotes
Recently in our country, there has been a steadily increasing number of people who dislike work and pursue leisure and extravagance. Almost everywhere individuals and organizations are fighting with resultant loss of energy that is needed for positive action. In order to save them from this situation, a principle of judo, based on the maximum efficiency concept should be applied as one aspect of modern society and as a natural result of the application of the principle of maximum efficiency, a mutual welfare and prosperity is believed to be the only effective way to ease and neutralize the forces among these individuals and organizations.
Jigoro Kano
When a body is let fall from a higher position to lower one, it has, at the instant when it is let go, energy of motion; but it gains, in falling, as much energy of motion as it loses energy of position. It is found that the sum of energy of motion and energy of position is always constant. ...Energy is a quantity which can be greater or less but has no direction. ...This constancy is expressed by including them in common name of Energy, and saying that energy is conserved, or is indestructible. This form of speech might be applied to other cases of alternate immortality, where one of two things comes into existence on disappearance of the other.
William Kingdon Clifford
Around 1950-51... I was finally getting away from the pictographs and looking for something... So it was necessary to find other forms, a different changed concept. So finally after a certain period of transition I hit on dividing the canvas into two parts, which then became like an imaginary landscape... What I was really trying to do when I got away from the pictographs was to make this notion of the kind of polarity clearer and more extreme. So the most extreme thing that I could think of doing at the time was dividing the canvas in half, make two big divisions and put something in the upper division and something in the lower section. So I painted that way... I would say roughly from 1952 to 56/57. About five years.
Adolph Gottlieb
When... we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.
Augustus De Morgan
In all cases, wherein the mind feels itself in danger of being confounded by variety, it is sure to rest upon a few strong points, or perhaps upon a single instance. Amongst a multitude of proofs, it is one that does the business. If we observe in any argument, that hardly two minds fix upon the same instance, the diversity of choice shows the strength of the argument, because it shows the number and competition of the examples. There is no subject in which the tendency to dwell upon select or single topics is so usual, because there is no subject, of which, in its full extent, the latitude is so great, as that of natural history applied to the proof of an intelligent Creator.
William Paley