PREFACE.
This little work, so far as I know, is new in its object and plan.
Its design is, to place a body of interesting, practical, and useful mathematical knowledge within reach of that large class in middle and elementary schools, who have not time for Euclid or any such course. The pupil can work at it mostly by himself, with occasional superintendence by the teacher; or it may be used as a lesson book in classes. He will learn from it the nature of geometrical figures; how to do the leading problems in practical geometry; how to construct the leading kinds of place figures; to read and understand algebraic expressions, including the simpler equations; and to solve the principal questions in mensuration, in which numerous practical exercises are given. He will thus become initiated in mathematical language and ideas; be subjected to a valuable mental exercise; acquire a body of useful knowledge, thorough so far as it goes; and lay such a foundation as will make it easy for him to take up the subject afterwards, should taste or professional requirements lead him to recur to it. In
