Verwandte Artikel zu The Fundamental Principles Of Algebra (1899)
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Inhaltsangabe
The Fundamental Principles of Algebra is a comprehensive textbook written by Alexander MacFarlane and first published in 1899. The book is intended for students studying algebra and covers the fundamental principles of the subject in a clear and concise manner. The book is divided into two parts. The first part covers the basic principles of algebra, including the theory of equations, the properties of algebraic expressions, and the solution of equations. The second part of the book covers more advanced topics such as the theory of groups, the theory of determinants, and the theory of matrices.The text is written in a clear and accessible style, with numerous examples and exercises to help the reader understand the concepts being presented. The book also includes a number of appendices, which provide additional information on topics such as the history of algebra and the use of algebra in geometry.Overall, The Fundamental Principles of Algebra is an essential textbook for anyone studying algebra, whether at the high school or college level. Its clear and concise presentation of the subject makes it an invaluable resource for students and teachers alike.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
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Reseña del editor
This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
Reseña del editor
This, it may be remarked, does not arise from any analogy existing in the nature of the operations which may be totally dissimilar, but merely from the fact that they are all subject to the same laws of combination. It is true that these laws have been in many cases suggested (as Mr. Peacock has aptly termed it) by the laws of the known operations of number; but the step which is taken from arithmetical to symbolical algebra is, that leaving out of view the nature of the operations which the symbols we use represent, we suppose the existence of classes of unknown operations subject to the same laws. We are thus able to prove certain relations between the different classes of operations, which, when expressed between the symbols, are called algebraical theorems. And if we can show that any operations in any science are subject to the same laws of combination as these classes, the theorems are true of these as included in the general case; provided always that the resulting combinations are all possible in the particular operation under consideration. It will be observed that he places algebra on a formal basis ;for its symbols are defined, not to represent real operations, but by laws of combination arbitrarily chosen. In a subsequent paper, however, entitled On aD ifficulty in the Theory of A lgebra, he practically gave up the formal view, and appears inclined to adopt the realist view instead. He says :I nprevious papers on the theory of algebra I have maintained the doctrine that a symbol is defined algebraically when its laws of combination are given; and that a symbol represents a given operation when the laws of combination of the latter are the same as those of the former. This, or a similar theory of the nature of algebra seems to be generally entertained by those who have turned their attention to the subject; but without in any degree leaning on it,
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