A quotes list created by Lee Sonogan
This man is not without Euler whose quotes/methods are quite similar. (Euler–Lagrange equation L = T − V, where T is the kinetic energy and V the potential energy of the system in question) Lagrangian mechanics defines systems of a configuration space based on the variations of 18th-century calculus. Today our number/group theory and analysis itself is from both this classical and celestial optimizing functionality represented. This is more philosophical than maths as a metaphysical multiplier finding local maxima and minima of subject function to equality constraints.
- We have already various treatises on Mechanics, but the plan of this one is entirely new. I intend to reduce the theory of this Science, and the art of solving problems relating to it, to general formulae, the simple development of which provides all the equations necessary for the solution of each problem. I hope that the manner in which I have tried to attain this object will leave nothing to be desired. No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain.
- As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection.
- An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.
- The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
- Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty [of the parallel axiom]. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed : he muttered II faut que fy songe encore, and put the paper in his pocket.
- The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive and even elegant. All this is necessary to resemble Lagrange.
- Lagrange, struck with the circumstance that the calculus had never given any inequalities but such as were periodical, applied himself to the investigation of a general question, from which he found by a method peculiar to himself and independent of any approximation, that the inequalities produced by the mutual action of the planets must in effect be all periodical; that the periodical changes are confined within narrow limits; that none of the planets ever has been or ever can be a comet moving in a very eccentric orbit; but that the planetary system oscillates as it were round a medium state from which it never deviates far: that amid all the changes which arise from the mutual actions of the planets, two things remain perpetually the same, viz. the length of the greater axis of the ellipse which the planet describes, and its periodical time round the sun; or, which is the same thing, the mean distance of each planet from the sun and its mean motion remain constant. The plane of the orbit varies, the species of the ellipse and its eccentricity change, but never, by any means whatever, the greater axis of the ellipse, or the time of the entire revolution of the planet. The discovery of this great principle, which we may consider as the bulwark that secures the stability of our system, and excludes all access to confusion and disorder, must render the name of Lagrange for ever memorable in science, and ever revered by those who delight in the contemplation of whatever is excellent and sublime. After Newton’s discovery of the elliptic orbits of the planets from gravitation, Langrange’s discovery of their periodical inequalities is, without doubt, the noblest truth in physical astronomy, and in respect of the doctrine of final causes, it may truly be regarded as the greatest of all.
- The questions here dealt with have occupied me since my earliest youth, when my interest for them was powerfully stimulated by the beautiful introductions of Lagrange to the chapters of his Analytic Mechanics…
- The treatment of the kinetics of a material system by the method of generalised coordinates was first introduced by Lagrange, and has since his time been greatly developed by the investigations of different mathematicians.
- Independently of the highly interesting, although purely abstract science of theoretical dynamics which has resulted from these investigations, they have proved of great and continually increasing value in the application of mechanics to thermal, electrical and chemical theories, and the whole range of molecular physics.
- The value of his work [Mécanique Analytique] consists in the exposition of a general method by which every mechanical question may be stated in a single algebraic equation. The entire history of any mechanical system, as for example, the solar system, may thus be condensed into a single sentence; and its detailed interpretation becomes simply a question of algebra. No one who has not tried to cope with the difficulties presented by almost any mechanical problem can form a just appreciation of the great utility of such a labor-saving and thought-saving device. It has been well called ‘a stupendous contribution to the economy of thought.’
- Lagrange… was the first to draw sharply the line of demarcation between physics and metaphysics. The mechanical ideas of Descartes, Leibnitz, Maupertius, and even of Euler, had proved to be more or less hazy and unfruitful from a failure to separate those two distinct regions of thought. Lagrange put an end to this confusion, for no serious attempt has since been made to derive the laws of mechanics from a metaphysical basis.
The distinctions between the process of Lagrange can be explained by slimy.com’s “find the highest elevation along the given path” or “minimize the cost of materials for a box enclosing a given volume”. In observing space, the orbit types calculate the third point from two separate gravitational forces. Altering the three-dimensional points themselves.