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THE following short Treatise on Geometry as a Science makes no pretence of entering into competition with Euclid's Elements-the most wonderful book perhaps, with one exception, in existence. But as it cannot be denied, that Euclid presents Geometry in a diffuse and somewhat repulsive form, whereby a large proportion of those, who ought to be acquainted with the subject, are deterred from venturing upon it at all, I have thought that good service might be rendered to the cause of popular education by framing a work, which shall neither terrify by its size, nor repel, as Euclid does, by a studied avoidance of all practical illustration. At the same time I have endeavoured, except in a single instance, to preserve the strictness of the ancient geometers, at least to the extent of laying down a solid and trustworthy foundation for that which is to follow. I cannot discover any good reason, why the mensuration taught in our Schools should be built, as it mostly is, upon no foundation but the memory only; I think it need not, and I am sure it ought not, to be so. But as it is, we reap the fruits of this bad system of mental culture in the very general ignorance of right principles of construction and design, which notoriously prevails among English artists and workmen. Public attention has been lately directed to the necessity of removing this stigma from our character as a people by the institution of

Schools of Design and Practical Art*.

Let me urge

upon the managers of such Schools the expediency of beginning their work at the right end. Let principles be taught before rules. Let Geometry as an Art be systematically preceded by Geometry as a Science. Then, but not till then, we may hope to see the desired result in the improved taste and skill of our designers, and to be saved the continuance of that sense of humiliation which every Englishman must experience on reading the statement here subjoined.


April 20, 1854.

T. L.

* On a late public occasion, at the inauguration of one of these Schools, the Duke of Argyll remarked that "a very large proportion of the works of art preparing for the Crystal Palace are being executed almost entirely by foreign artists, and that our manufacturers also have been obliged to send abroad for designs; and, as he was convinced that there was no natural disqualification in our population for such work, he trusted that the defect would be remedied by the adoption of a more complete system of education."

By the same Author,

1. WOOD'S ALGEBRA, much enlarged and improved, with numerous Examples and Easy Exercises. Fourteenth Edition, 12s. 6d. boards.

2. COMPANION to WOOD'S ALGEBRA, containing SOLUTIONS of all the difficult Questions and Problems in the former work. Second Edition, 6s. boards.

3. A SHORT AND EASY COURSE OF ALGEBRA, with Easy Exercises. Second Edition, 3s. 6d. boards.

4. KEY to the EXERCISES in the Short and Easy Course of Algebra, 5s.

5. The NECESSITY of a STUDIOUS and LEARNED CLERGY. A Visitation Sermon, preached at the primary visitation of John, Lord Bishop of Lichfield, ls.

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