The doctrine of ratios and proportion is introduced by Euclid as a part of his system of geometry ; and the student seldom fails to remark, that in the treatises on algebra, the same subject is presented under a considerably different form; though he is usually quite unable to determine wherein the essential difference consists; and would probably find but few teachers who could precisely point out the distinction to him.
Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.omar khayyám
Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.isaac newton
Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."john backus
In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster.ivor grattan-guinness
An ounce of algebra is worth a ton of verbal argument.j. b. s. haldane
I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen’s, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell’s equations.kenneth e. iverson
My algebra was relatively poor. I found it very difficult to use equations that substituted numbers — to which I had a synesthetic and emotional response — for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.daniel tammet
The elements of justice are identical with those of algebra.Pierre-Joseph Proudhon
Addition and multiplication In our study of oscillating systems we shall have occasion to use one of the most remarkable, almost astounding, formulas in all of mathematics. From the physicist's point of view we could bring forth this formula in two minutes or so, and be done with it. But science is as much for intellectual enjoyment as for practical utility, so instead of just spending a few minutes, we shall surround the jewel by its proper setting in the grand design of that branch of mathematics called elementary algebra.Richard Feynman, Robert B. Leighton, ?Matthew Sands (1963), The Feynman Lectures on Physics, Vol. I, p. 22 : on Euler's formula, of which Euler's identity is a special case, in
The truth is that Mozart , Pascal , Boolean algebra, Shakespeare , parliamentary government, baroque churches, Newton , the emancipation of women, Kant , Marx , and Balanchine ballets don't redeem what this particular civilization has wrought upon the world. The white race is the cancer of human history.Susan Sontag
Linear Programming is a generalization of Linear algebra. It is capable of handling a variety of problems, ranging from ?nding schedules for airlines or movies in a theater to distributing oil from re?neries to markets. The reason for this great versatility is the ease at which constraints can be incorporated into the model.Steven J. Miller (2007) An Introduction to Linear Programming
The absolute scholar is in fact a rather uncanny being. He is instinct with Nietzsche's finding that to be interested in something, to be totally interested in it, is a libidinal thrust more powerful than love or hatred, more tenacious than faith or friendship — not infrequently, indeed, more compelling than personal life itself. Archimedes does not flee from his killers, he does not even turn his head to acknowledge their rush into his garden when he is immersed in the algebra of conic sections.George Steiner
In mathematics he was greater Than Tycho Brahe, or Erra Pater: For he, by geometric scale, Could take the size of pots of ale; Resolve, by sines and tangents straight, If bread and butter wanted weight; And wisely tell what hour o' th' day The clock doth strike, by algebra.Hudibras, Part I, Canto I, line 119 (1663–1664).
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