Plane and Solid Geometry (Classic Reprint) - Tapa blanda

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Excerpt from Plane and Solid Geometry

Many of the exercises at the foot of the page require the student to infer the truth involved in the relations given. The interrogative form is employed for the purpose of compelling the student to obtain the ideas for himself, and the answers he must give to the questions furnish an admirable training in accuracy of expression.

A great abundance of undemonstrated theorems and of unsolved prob lems is supplied, and teachers will find them quite numerous enough for the needs of any class. The demonstration of original theorems and the solution of original problems are of so great consequence in developing the power to reason that every teacher should insist upon such work.

Much aid in originating demonstrations may be obtained from the Summaries which follow each of the first six books. These summaries are not collections of propositions that have been demonstrated, but are rather groups of the truths established in the book to which they are appended. If the student makes himself thoroughly acquainted with them, much of the difficulty experienced in demonstrating original theorems, in solving problems, and in determining loci will be removed.

A very small proportion of those who study elementary geometry expect to become mathematicians in any broad sense of the term, and so geometry must serve to give them almost the only training they will get in formal and logical argument in secondary schools and in colleges. For this reason mathematical elegance in demonstrations and in solu tions has often been sacrificed in the interest of clear and simple steps, even though such a plan has required some expansion of the text. Ele gant demonstrations are appreciated by mathematicians, but training in formal deductive reasoning is of more consequence to most students.

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