common mechanics, and as he is not intended for one, it ean be of no service to him. A pupil of this hopeful description, however he may object to the difficulties of learning, has generally sense enough to see the necessity of pursuing (at least in appearance) some one or more of these studies, in order to secure that respectability to which, in spite of indolence, his pride prompts him to aspire. In doing this, if he employs any effort of mind, it is only in contriving how to evade difficulties of every kind, get through the uninteresting rudiments as hastily as possible, and arrive at those parts which seem to promise more pleasure, or less expense of mental exertion. But in this, ere long, he finds his mistake; for, having obtained his wish, he does not fail to prove an incessant torment to his tutor, whose painful duty it now becomes to teach him the application of those fundamentals which he would never take the pains either to understand or remember, and which nothing can induce him InOw to resume *. ... • o * The consequences resulting from both the above cases, are in general the same. *The pupil, weary of a pursuit which he is at length convinced will yield neither pleasure hor advantage, the moment he is completely at his own disposal, quits it with disgust—the money spent on that part of his education is totally thrown away, or would have been better employed in acts of charity; and, what is far worse, those precious hours, days, months, perhaps years, which * - If what M. Rollin says be true, viz. “That it is the end of masters to Jiabituate their scholars to serious application; to make them love and value the sciences, and cultivate such a taste as shall make them thirst after the sciences when they are gone from school;” what grief, vexation, and disappointment must that master experience who is unfortunate enough to have in his school half a dozen such pupils as we have described. The best preceptor confined to the tuition of such would be in great danger of soon becoming good for nothing; and indeed, opposition of any kind, from whatever quarter it may arise, if it be sufficiently efficacious to disappoint or subvert the tutor's plans, will have a strong tendency to relax his ardour; it will by degrees bring on an increasing indifference to his duty, and at length reduce him to the state of a constituted the only proper season for his improvement, are irrecoverably lost. When arrived at the state of manhood, he cannot but feel his deficiency, and is sometimes almost half inclined to regret his former obstinate misconduct. Nevertheless, he palliates it with the mild name of juvenile indiscretion; attributes the whole to the ignorance or negligence of his tutors, whose peculiarities (and perhaps their virtues) are the occasional subjects of his merriment; and if he has children, he educates them as nearly as possible after the same plan on which he himself was educated. These are some of the bad effects which follow from parental authority being misapplied, ineffectually exerted, or not exerted at all; and might easily be avoided, if parents, with due attention to their children's talents, would themselves resolve on the studies to be pursued, and leave the plan and execution entirely to the wisdom and known fidelity of the master; and it is a happy circumstance for learning and mankind, that to the prevailing custom there are many exceptions of this kind. We readily admit, that our ancestors erred, by introducing too much strictness and rigid formality into their mode of instruction; but it is no less certain that the present generation deviate in theirs full as widely towards the opposite extreme, and, from a due comparison of both, it appears that the last error is by far, the worst": but as the removal of the cause is not likely to be effected, various contrivances have been resorted to, in order to counteract as much as possible its bad effects: every possible means has been employed to allure the dull, the mere machine. b 2 - idle, and the frivolous of every description, to the pursuit of - * * Dr. Knox delivers his opinion very freely on this subject; let the attentive observer determine how far it is correct. “It is certain” (says the Doctor), “ that schools often degenerate with the community, and continue greatly to increase the general depravity, by diffusing it at the most susceptible periods of iife. The old scholastic descipline relaxes, habits of idleness and intemperance are contracted, and the scholar often comes from them with the acquisition of effrontery alone, to compensate for his ignorance.” Honor on Education, p. 31. knowledge, as well as to assist and promote the progress of real genius and industry, by removing obstacles, and making the way plain and easy. Hence arises the multiplicity of easy introductions, easy grammars, games, &c. which we have in every branch of learning, works which are all useful as far as they go; but it must be remarked, that if they remove difficulties out of the scholar's way, instead of teaching him how to encounter and surmount them, these performances, however they may be patronized and praised, are of but little value. Scientific games, it is allowed, are pleasing and instructive amusements for the nursery; but whatever they may seem to promise, it is making sad game of the sciences, to suppose that these can be acquired by play. I am persuaded that none ever did, or ever will attain to useful or honourable proficiency in any branch of learning, without proportionate labour and application". * If what has been said be correct, it will not only account for the great number of easy elementary treatises that has appeared, but will shew that an almost endless variety is absolutely necessary to accommodate the various tastes of learners; it will be a sufficient apology for adding one to the number, as well as for the plan on which it is written. In the following work, it is proposed to combine more advantages than are to be met with in any single book on the subject, viz. historical, theoretical, and practical knowledge, and to accompany the whole with explanations so exceedingly simple and easy, that it is presumed to be im • “ Nothing can be more absurd” (says the author of Hermes) “ than the common notion of instruction; as if science were to be poured into the mind like water into a cistern, that passively waits to receive all that comes. The growth of knowledge resembles the growth of fruit; however external causes may in some degree co-operate, it is the internal vigour and virtue of the tree that must ripen the juices to their just maturity.” Harris. “To lead a child to suppose, that he is to do nothing which is not conducive to pleasure, is to give him a degree of levity, and a turn for dissipation, which will certainly prevent his improvement, and may perhaps occasion, his ruin.” JKnor on Education, p. 19. possible that any person of moderate talents will fail to understand them. It supposes the learner to be, in the proper sense of the word, a beginner, consequently unacquainted with even the rudiments of science; and from common principles known and acknowledged by all, it proceeds by easy and almost imperceptible gradations, to lead him on (with the aid of Simson's Euclid and a Table of . Logarithms, both which it explains) to the attainment of a considerable degree of mathematical knowledge, with scarcely any assistance from a master. The work is divided into ten parts, in which the subjects treated of are—Arithmetic, Algebra, Logarithms, Common Geometry, Trigonometry, and the Conic Sections; each preceded by a popular history of its rise and progressive improvements: to which are added, by way of notes, brief memoirs of the principal authors mentioned in the text; some account of their writings, discoveries, improvements, &c. with a variety of useful information of a miscellaneous nature, respecting the Mathematical Sciences. Part I. begins with an Historical Account of Arithmetic", explaining, to a considerable extent, the nature and construction of numbers, and proceeds by laying down in a plain and simple manner, what are usually called the four fundamental rules: next follow in order, Reduction, the Compound Rules, Proportion Direct, Inverse, and Compound; the Rules of Practice, the theory and practice of Fractional Arithmetic, Vulgar, Decimal, and Duodecimal; Involution, Evolution, and Progression, both Arithmetical and Geometrical; the whole demonstrated, exemplified, and explained: and as simplicity and clearness were always the objects aimed * * Plato calls Arithmetic and Geometry “The wings of the mathematician;” “Arithmetic” (says M, Ozanam) “may be considered as the mathematician's right wing, because without this Geometry would be very imperfect; this justifies the common practice of beginning the Mathematics with the study of Arithmetic.” at, it is hoped no obstacle will be found in the learner's way which may not easily be surmounted. Under these heads, which comprise the whole of Elementary Arithmetic, is given a great number of particular rules and observations, not to be found in any other work, but which are necessary, in order fully to explain the theory, and facilitate the practice of numbers. Besides the examples fully wrought out and explained, several others are introduced under each rule, with their answers only, and a few are given without answers. Part II. contains an Historical Account of Logarithms, the theory and practice of Logarithmical Arithmetic, with numerous examples, problems, and explanations. Part III. contains the History of Algebra, and its fundamental rules; Rules for solving Simple and Quadratic Equations, in which one, two, three, or more unknown quantities are included; and, lastly, a collection of Problems, teaching the application of Simple and Quadratic Equations, in a great variety of ways; the whole accompanied with notes and easy explanations as above. This completes the first volume. The second volume (Part IV.) begins with Literal Algebra, in which the . Problems: are analytically investigated, and likewise demonstrated by the method of Synthesis. General conclusions are applied to particular examples, and the methods of converting numeral Problems into general ones; deducing Theorems, Rules, and Corollaries; registering the steps of operations, &c. are laid down and applied in a variety of cases. The doctrine of Ratios, Proportion, Progression, Variable and Dependant Quantities, Interest, Discount, Permutations, Combinations, the Properties of Numbers, &c. are Algebraically investigated, with numerous examples. Part V. explains the nature and theory of Equations in general, their Composition, Depression, Transformation, and Resolution, according to the methods of Newton, Cardan, Euler, Simson, Des Cartes, and others. Various. methods of Approximation as laid down by Simson, Raphson, |