Excerpt from Graphic Algebra: Or Geometrical Interpretation of the Theory of Equations of One Unknown Quantity
OF late years Graphical Methods have been used with great profit in many departments of science. Such methods give a clear and comprehensive View of the facts of observa tion, and, by suggesting new relations, furnish a valuable means of formulating new laws. Their importance in solv ing many problems in applied mathematics is also very generally recognized. In interpreting analytical expressions and illustrating analytical processes in pure mathematics such methods are equally valuable. They accustom the student to take into account not merely one detail at a time of a complex operation, but show at a glance all the results in their proper relations.
Such methods are well adapted to the presentation of the principles and processes of the Theory of Equations. The Theory of Equations is a subject so essential in all the appli cations of Mathematical Analysis that the student should be made familiar with it early in his course. But at this stage he is not prepared to appreciate the very general analytical demonstrations found in treatises on this subject. He is not accustomed to such methods of reasoning, and, although he may not be able to find any ﬂaws in the logic, he is not familiar with the conceptions employed, and cannot give any tangible form to his ideas. Therefore they are vague and unsatisfactory. Knowledge so sought is soon lost, and the only permanent result of such study is a loose way of think ing. On the other hand, the Graphical Method presentsthese abstract principles in a concrete form. Each principle therefore becomes firmly impressed on the mind, and the student escapes the tendency to substitute a form of words for clear conceptions of ideas.
This work is based on some years' experience in teaching the Theory of Equations to the Freshman Class in Yale Col lege, and is adapted to students who have mastered quadratic equations and the principle of similar triangles.
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