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In the second method all lines have direction as well as magnitude, and the proofs are given in such a form that they are general and hold for every possible figure. This would seem to be the logical method of developing the subject; for Trigonometry is the connecting link between elementary Geometry and those subjects in which Algebra and Geometry are combined in such a way that the directed line must be used constantly. This second method has been employed in this work, which is in tended as a text-book for a fifty hour course in high schools and the ordinary first year classes in college, and is, therefore, made as elementary as possible. All matter not required for such a course has been excluded.
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