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193 Exam. 13, for 1. read +. 2}. 2} 201 Exam. 23, for 17; read 17;. Exam. 24, for 4+, read 43. 206 Exam. 16, for 4l. 11s. 6d. # read 911. 11s. 4d}. Exam. 19, for 8l. 19s. 6d. *, *, read 91. 11s. 6d. Toor. Exam. 20, for ll. 2s. 5d. read ll. 13s. 7d.4. 235 Exam. 13, for 5.47 read 5.47, for 3.2 read 3.2, and for .123 read .i.23. 236 Art. 253, the demonstration of this rule is by mistake omitted. 240 Exam. 7, for 1.14435839, &c. read 6,683127, &c. 253 Exam. 20, for .295803989, &c. read .935414, &c. 257 Exam. 1, in the subtrahend, for 576, read 5768. 274 Exam. 23, for 1162358667 read 1162261467. 315 Add at the bottom, as a note on the word Algebra. “Algebra, according to Lucas de Burge, derives its name from the Arabic name of the science, viz. Alghebra e Almucabala, or the art of Restitution and Comparison. 337 Line 19, for Leipsigc read Leipsic. 434 Exam. 12, for 2 y read 30.

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IN order to ensure success in the cultivation of any branch of learning, it is a matter of prime importance to take care that the first principles and elements be thoroughly understood, and firmly fixed in the memory, by a sufficient number of suitable exercises and examples. This salutary maxim we have the advantage of hearing so frequently repeated, that an inattentive observer might reasonably be led to suppose its truth had obtained universal suffrage; but in this he would be mistaken, for though all seem agreed on the subject, the assent is for the most part merely verbal, and, like our assent to truths of higher importance, has too little influence on the practice. It would be beneficial to learning, and consequently to society, if no instance could be adduced to justify this conclusion; but whoever will take the trouble to examine the plan on which the business of some of our schools is conducted, will find abundant reason to acknowledge its truth—he will find that too little attention is paid to the introductory parts of learning, and that pupils are too frequently hurried on from one subject to another, with a rapidity which does not admit of their fully understanding any thing they pass through. This conduct is both cruel and impolitic; it deprives both the learner and society at large, of the benefits which might be expected from talents properly -cultivated. But if part of the blame rest with the preceptor, a much larger share attaches itself to his employers, whose impatience for their children's hasty improvement is too generally productive of this abuse. The VOL. I. b

preceptor, indisputably the fittest judge of his own business, and consequently of what methods ought to be pursued for the real benefit and improvement of his scholars, cannot always presume to follow the dictates of his own unbiassed understanding; if he did, he might soon “vaunt and vapour in an empty school.” . - But one of the greatest impediments to successful teaching, is the undue deference which it is the fashion to pay to juvenile opinion; for although the extravagant doctrines of liberty, asserted by some modern philosophers, as far as they relate to politics, are justly exploded as absurd and impracticable, they still possess a considerable degree of influence on our system of education. No sooner has a young gentleman assumed the neckcloth, than he feels himself invested with a degree of consequence, which, a century or two ago, would have been thought dangerous in such hands, and is allowed a right to offer his opinion with unlimited freedom on every subject. It frequently happens that a father entertains such an extraordinary respect for his son's judgment and penetration, that almost every thing, relating to his future studies, is submitted to his own decision: of course, he determines on that which he expects will be attended with the least difficulty to himself; but as he prefers amusements of his own choosing, mone that are proposed will-suit him exactly. He objects to grammar because its rules are dry; and if he is obliged to learn them, he is sure that his memory will not retain them—he has not a genius for numbers, his father never had—he would consent to learn Algebra, but he has been informed that the symbols employed mean nothing; how then can the science have any meaning or use? but admitting it to be useful, the operations appear so difficult and complicated, that the advantage of acquiring it cannot be worth the trouble. Geometry, according to his determination (for he is always positive), is of no use to any but

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