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Demonstrative geometry is taught for the purpose of giving the student an insight into deductive reasoning, of allowing him to know what it means to prove a statement, of giving him the privilege of "standing upon the vantage ground of truth,” of cultivating his habits of independent investigation, of enabling him to develop his own rules in applied mathematics, and of stimulating his appreciation of the beauties of the science.
In some schools the course of study permits of doing this work thoroughly, while in other schools the pressure upon the curriculum is such as to allow less time than might profitably be used. On this account it is necessary to adjust a textbook so that it may permit of such flexibility in its use as will adapt it to curricula of various kinds. To accomplish this purpose the propositions and corollaries have been limited to those that are actually necessary for the proof of subsequent statements or that are needed for a considerable number of important exercises. The lists of propositions prepared under the authority of the National Committee on Mathematical Requirements and of the College Entrance Examination Board have been followed as closely as the best principles of sequence and selection seem to warrant. The exercises have been carefully selected and have been made so numerous that any school may find abundant material for a long and thorough course, while another school may easily limit the course without destroying the sequence.