Excerpt from Elements of Analytic Geometry

This discipline should consist first in training to think, and second in training to express thought.

This training to think will consist mainly in training to form clear, precise, and correct mathematical concep tions and to form trains of deductive reasoning constructed with perfect logical soundness and cogency. Hence the student should be frequently required to give clear, precise, and correct definitions of the terms he is using, to show every point, line and angle discussed in a neat clear and correct figure and to translate his final equation into ordinary lan guage until at last each letter and symbol in it shall at once, and clearly, express to him the magnitude or the operation for which it stands. He should also be required to state clearly and correctly each step in the argument, to state it in its log ical order and to fortify each step by quoting the proof for it; so that when he reaches his final equation he shall feel that it must necessarily be true. Hence an attempt has been made in this book to cast the demonstrations as far as possible in the form of those given in elementary geometry.

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