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Description: This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 edition. Excerpt: ...to geometry; on the usefulness of which it is unnecessary to expatiate in an age when mathematical studies have so much engaged the attention of all classes of men. This treatise is one of those which have been borrowed, being a translation from the work of Mr. Le Clerc; and is not intended as more than the first initiation. In delivering the fundamental principles of geometry, it is necessary to proceed by slow steps, that each proposition may be fully understood before another is attempted. For which purpose it is not sufiicient, that when a question is asked in the words of the book, the scholar, likewise, can in the words of the book return the proper answer; for this may be only an act of memory, not of understanding: it is always proper to vary the words of the question, to place the proposition in different points of view, and to require of the learner an explanation in his own terms, informing him, however, when they are improper. By this method the scholar will become cautious and attentive, and the master will know with certainty the degree of his proficiency. Yet, though this rule is generally right, I cannot but recommend a precept of Pardie s, that when the student cannot. be made to comprehend some particular part, it should be, for that time, laid aside, till new light shall arise from subsequent observation. When this compendium is completely understood, the scholar may proceed to the perusal of Tacquet, afterwards of Euclid himself, and then of the modern improvers of geometry, such as Barrow, Keil, and Sir Isaac Newton. 3. The necessity of some acquaintance with geography and astronomy will not be disputed. If the pupil is born to the ease of a large fortune, no part of learning is more necessary to him than..