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2. The second place is assigned 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 sufficient, 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[2], 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 the knowledge of the situation of nations, on which their interests generally depend; if he is dedicated to any of the learned professions, it is scarcely possible that he will not be obliged to apply himself, in some part of his life, to these studies, as no other branch of literature can be fully comprehended without them; if he is designed for the arts of commerce or agriculture, some general acquaintance with these sciences will be found extremely useful to him; in a word, no studies afford more extensive, more wonderful, or more pleasing scenes; and, therefore, there can be no ideas impressed upon the soul, which can more conduce to its future entertainment.

In the pursuit of these sciences, it will be proper to proceed with the same gradation and caution as in geometry. And it is always of use to decorate the nakedness of science, by interspersing such observations and narratives as may amuse the mind, and excite curiosity. Thus, in explaining the state of the polar regions, it might be fit to read the narrative of the Englishmen that wintered in Greenland, which will make young minds sufficiently curious after the cause of such a length of night, and intenseness of cold; and many stratagems of the same kind might be practised to interest them in all parts of their studies, and call in their passions to animate their inquiries. When they have read this treatise, it will be proper to recommend to them Varenius’s Geography, and Ferguson’s Astronomy.

4. The study of chronology and history seems to be one of the most natural delights of the human mind. It is not easy to live, without inquiring by what means every thing was brought into the state in which we now behold it, or without finding in the mind some desire of being informed, concerning the generations of mankind that have been in possession of the world before us, whether they were better or worse than ourselves; or what good or evil has been derived to us from their schemes, practices, and institutions. These are inquiries which history alone can satisfy; and history can only be made intelligible by some knowledge of chronology, the science by which events are ranged in their order, and the periods of computation are settled; and which, therefore, assists the memory by method, and enlightens the judgment by showing the dependence of one transaction on another. Accordingly it should be diligently inculcated to the scholar, that, unless he fixes in his mind some idea of the time in which each man of eminence lived, and each action was performed, with some part of the contemporary history of the rest of the world, he will consume his life in useless reading, and darken his mind with a crowd of unconnected events; his memory will be perplexed with distant transactions resembling one another, and his reflections be like a dream in a fever, busy and turbulent, but confused and indistinct.