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 observation, and, by suggesting new relations, furnish a valuable means of formulating new laws. Their importance in solving many problems in applied mathematics is also very generally recognized. In interpreting analytical expressions and illustrating analytical processes in pure mathematics such methods arc 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 applications 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 thinking.

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