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which erpresies tee care of 3 into the square root of 3 2 ; but die true result is 3 to the cube root of 3 a, or 3 V 32. See P. 401, Tchi.

Aacher instance of the error into which this method of expression resizably leačs, when the radical is preceded by another gaanoty, is the fol swing, taken from p. 405, vol. i.

« Divide 12V 43 by 672 Thus 12 48

=2/24=2V8X3=4 vs the quo6V 2 tient.

The true solution to this example, as it now stands, is the following: 1248

=2/24=2V4X6=2*V6, 6'12 or 16V6, and not 4/3 or 6473, as given above. Mr. Butler's meaning, however, we apprehend to be : divide 12 48 by 6/2, and then we have 12V 48 =23/24

62 =28X3–413, the true answer. Examples of this kind are very numerous, but these are sufficient to show the errors to which this im proper position of the figure may lead; to put the student upon his guard; and to show the author the necessity of attending more particularly to the setting of every figure ; and especially where the radical expression is a factor of a quantity; for av x is uniformly printed a'V x'; but the slightest degree of algebraic knowledge is sufficient to shew that they are expressions of very different values.

Geometry is the next subject in the work. It commences with an historical account, and some observations on the usefulness of geometry, which are followed by a description of mathematical instruments, observations on some parts of the first six books of Euclid's Elements, with an appendix, containing some useful propositions which are not in the elements ; practical geometry, methods of constructing scales, with the mensuration of a variety of plane and solid figures. The extent of our previous remarks must preclude enlargements here ; we shall therefore only observe that we think the definition of geometry, as the science of magnitude, or local extension,” to be obscure, and that it might very advantageously be superseded by the following: “ Geometry is that science which treats of the proper

ties and relations of space, or continuous quantity; and which is exhibited under the various dimensions of length, breadth, and thickness.” This definition contributes more to accuracy of conception, than the other; and perspicuity is of the utmost importance at the commencement of every branch of science. Definition 18, in the note on page 267, wants the phrase part of the, before the word “ circumference,” to make it correct. Article 109, page 275, relative to converse propositions, is not sense as it now stands. Mr. Butler, however, does not mean his observations on geometry to supersede the use of Euclid's Elements, but to assist the student in comprehending them.

Trigonometry is next treated of, and, besides the historical introduction, definitions, and introductory propositions, includes the investigation of formulæ, the constructions of tables of sines, tangents, &c. the fundamental theorems and the solution of the various cases of plane triangles. These principles are then applied to the mensuration of heights and distances, and accompanied by descriptions of the requisite instruments, and problems for exercise.

A short treatise on Conic Sections concludes the whole. The author commences with the Parabola, and has followed the methods adopted by Boscovich, Dr. Simson, Dr. Robertson, &c. and derived the properties from curves described in plano; demonstrating those only, which are necessary to enable the student to read Newton's Principia, or any other work on Mathematical Philosophy or Astronomy. The curve lines in these figures are in general badly drawn, and the ellipses appear to be only two segments of a circle.

We have thus endeavoured to present our readers with a view of the work, and pointed out a few instances in which the learner might either be perplexed or misled, and which appear to merit the author's notice in a future edition.

We refrain from following the example of some of our brother critics, who endeavour to display their knowledge at the expense of their author, by enumerating subjects which might have been included in the work, without any inquiry whether his object required or his plan admitted of them." Though we think Mr. Butler is not quite correct when he denominates his work “ a complete system of elementary instruction,” yet his object of enabling the student to make a considerable progress in mathematical knowledge, without the assistance of a master, was an arduous undertaking, in which he has labored with laudable zeal, exemplary industry, and great success. To many

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readers he will appear prolix, and in some places is more so than necessary : but they should remember that the nature of his plan required him to be popular and copious in his explanations; and those who have had the greatest experience in teaching mathematics, are the most convinced that by these alone can many learners be made to comprehend even the very elements of the science. We are persuaded that Mr. Butler is too well acquainted with the fallibility of human nature, and has shown too much candor in the composition of his work, to attribute our remarks to any other motive than that by which his pen was guided--a desire to exhibit truth in its true colors.

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ART. XVI. The Traveller's New Guide through Ireland,

containing a new and accurate description of the roads, with particulars of all the different towns, villages, noblemen and gentlemen's seats, Churches, Monastic buildings, Antiquities, and Natural Curiosities: also the present state of Agriculture, Manufactures, and Commerce, with a complete list of all the Fairs throughout the Kingdom. Illustrated with a new and accurate map of Ireland ; plan of the Lakes of Killarney, views of the Giant's Causeway, delineations of the principal

post-roads, with other plates. pp. 574. Dublin. This ample title-page is also no bad table of contents, and the latter correspond well with the former. The work was compiled on the spot, and must consequently be among the most faithful pictures of Ireland that a stranger can obtain. The Compiler takes into consideration the Counties, Baronies and Parishes, in regular succession, commencing with the city and county of Dublin, and treating separately of the four great provinces into which the island is divided. His book must be a desirable Vademecum to the stranger who visits the sister-kingdom, and it will not only direct his course along the many cross-roads, but facilitate his researches into the state of the country: and even the stranger, who has not the opportunities of seeing Ireland, will derive a good deal of pleasure, and some profit, from a description of those wild and mountainous beauties with which she abounds.

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לָשׁוֹן הקדֶשׁ סֵפֶר הַבִּקְדוּק

.ART

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XVII
אֶל לָשׁוֹן
שַׁעַר הָרִאשׁוֹן

A Hebrew Grammar , in the English בְּלָשׁוֹן עַבְדֵי וּבְעֶנְגְלִישׁ:

Language, by Joseph Samuel C. F. Frey, Editor of Vanderhooght's Hebrew Bible. London: Gale and Curtis 1813.

8vo. pp. 104. +44.= 148. 10s. 6d. extra bds. Or late years Hebrew literature has occupied much of the public attention ; and, as might be expected, many Grammars have been published : notwithstanding this, however, much in this department is wanting. The Grammars in question are generally composed in the Latin language, and thus rendered entirely useless to the major and younger part of the community. The learned, indeed, have always been able to acquire the Hebrew Tongue, by means of the many learned Treatises on the subject : to them the circumstance above alluded to, presented no difficulties; it perhaps increased the facility of attaining the language ; but to the school-boy or the unlearned, it opposed a complete barrier. It is obvious, that, generally speaking, the rudiments of Hebrew should be learnt at school; and it were desirable that they should be studied, even before the pupil has acquired a perfect knowledge of the Latin language : in this case, the protracted use of a Latin Grammar presents a great impediment. Nor is this the only argument against the common custom of Hebrew Grammarians. Many persons, somewhat advanced in life, have desired to acquire a sufficient knowledge of Hebrew to read the Scriptures in the original ; but of Latin these persons are completely ignorant. Such is generally the case with Dissenting Teachers. They are sometimes taken from among the lower Orders of the People; and when they enter on what is generally termed their ministry' are completely ignorant of every species of Classical learning. To these men, however, the acquirement of Hebrew would be a great advantage; but in the present state of things how is it to be acquired?

It is but just, indeed, to state, that some grammars have been composed in English, but the number of these is small, and even these few are not free from considerable defects. The Grammar of Parkhurst is without points ; and without the true vowels all Hebrew becomes confusion : that by Newton labors under the same disadvantage : and Lyons's Hebrew Grammar,

although it teaches the system of the points, is too short to lead to a perfect knowledge of the language.

From all these defects, that before us is completely free: Mr. Frey has given all the necessary rules according to the best authorities : he has illustrated his rules with copious and apposite examples: he has given complete Tables of the Hebrew Particles; and at the end he has printed the whole book of Psalms from the excellent edition of the Hebrew Bible by Vander-Hooght.

Upon the whole, therefore, we cannot but recommend this Grammar to general notice. It will be found a complete Introduction to the study of Hebrew; and the Lexicon to be published by the same author, will, if executed with the same ability, materially assist in the cultivation of Hebrew Literature. With respect to the utility of these studies, it were needless to expatiate : besides its other advantages, Hebrew is the key to the other Oriental Languages : without some acquaintance with it, it were more difficult to learn the Arabic or Persian Tongues. In short, he who has attained a critical knowledge of Hebrew may regard himself as able to learn all other learned languages with facility. We hope, therefore, that Mr. F. will meet with encouragement in his endeavours to explain it. Of the price of his work no one will complain, when the difficulty and expense of printing Hebrew are considered: it is within the reach of all, and the addition of the Psalms will render it peculiarly useful in schools.

ART. XVIII. A Collection of Ancient and Modern Scottish

Ballads, Talis, and Songs, with Explanatory Notes and Observations. By John Gilchrist. In 2 Vols. Edinburgh:

Blackwood, 1815. Few objects can be more interesting than tracing the history of Poetry, and examining the causes of the changes it has undergone. This object has of late years been pursued with success, and the pursuit has had a visible and beneficial influence upon the poetical productions of the age. The works of W. Scott, and other living poets, are evidences of a taste and tone of composition formed, in many essential points, on the characteristic qualities of our early poetry. It is allowed that nothing can be a better criterion of the manners and spirit of an age, than the

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