will do well to obferve, and which he will find of great use to him in the profecution of his ftudies: but having faid thus much, he must excufe us if we add, that fome of his remarks do not appear to us to be true: we have juft now in view, as one of the moft material, the paffage on p. 126 of the first volume, where he contends, if we understand him right, that straight lines, triangles, parallelograms between the fame parallel lines, angles, circumferences and fectors of equal circles, are all the magnitudes which we can multiply agreeably to Euclid's two firft definitions of his fifth book. Now it appears to us, from what is done in the eleventh and twelfth books, that Euclid was of a very different opinion; for he has there taken multiples of folids of very different forms, as cylinders and parallelopipedons; and we fee no reason why he might not, with equal ease, have done the fame of prifms of any kind, as well as of pyramids, whofe bafes are either triangles or parallelograms; and, perhaps, of many others.

Mr. Williamfon concludes his first volume, which contains the first fix books, with fome remarks that we recommend to the perufal and attention of every learner.

In the feventh differtation, which begins the fecond volume, Mr. W. endeavours to fhew the infufficiency of modern algebra for fupplying the place of what Euclid has delivered in his feventh, eighth, ninth, and tenth books, on the properties of numbers, and commenfurable and incommenfurable magnitudes but notwithstanding all that he has faid on this head, we remain convinced that every thing which can be done in Euclid's manner of treating the fubject, and much more, may be effected by the modern analytics; but, we will allow, not always with the fame elegance and perfpicuity. This differtation is comprized in four chapters, on the following subjects : principles of, and method of reasoning in, algebra-the two different methods of measuring the ratios of proportional quantities, and their confiftence with each other-the arrangement of the books of Euclid's Elements-the difference between the measures of magnitudes and the measures of ratios. Then follow the feventh, eighth, ninth, and tenth books.

The eighth and laft differtation relates entirely to the ele-venth book, and is contained in three chapters; on the difficulties arifing from the reprefentation of lines in the fame plane when they are in different planes-of planes and their inclinations remarks on fome of the first nineteen propofitions of the eleventh book. In this differtation Mr. W. has twice: attacked Dr. Simfon; and once, at leaft, in our opinion, with fome fuccefs. After mentioning the Doctor's objections to,

and notes on the ninth, tenth, and eleventh definitions of Euclid's eleventh book, and allowing in fome meafure the juftice of them, he adds, However, in vindication of Euclid, it may be faid, that his definitions will apply to all the figures about which he reafons; and it is not very clear that he meant them to extend to any other. For the fubject, according to my apprehenfion of it, becomes unmanageable, if we admit as foId angles thofe which would be formed at the top of pyramids erected upon a base with outward angles; for then a folid angle might certainly be made, the plane angles of which would make more than four right angles.'

As a defence of Euclid, we do not think the preceding extract very strong in argument: but, as an attack on Dr. Simfon's emendation of him, it is forcible enough. To conclude that Euclid's definition of fimilar folids is good, because he has confidered none but thofe to which it will apply, is just as found reasoning as it would be to affert, that the fquare on the greater fide of every triangle is equal to the fquares on the other two fides, fuppofing that Euclid had confidered the properties of no triangle but right-angled triangles. On the other hand, we frankly confefs, that, in this paffage, Mr. Williamfon has fhewn us, for the first time, that Simion's definitions of fimilar folids is, to fay the best of it, no better than that of Euclid: for, taking folids in the very general fenfe of them, for which Simfon's definition is intended to provide, they involve a fort of angles very different from folid angles, at leaft in Euclid's fenfe of folid angles; becaufe, as Mr. Williamson juftly obferves, if we admit those to be folid angles, which are formed at the tops of pyramids erected on bafes that have outward angles, a folid angle may be fo made, that the plane angles forming it may, together, be greater than four right angles; which is contrary to the twenty-firft propofition of the

eleventh book.

That there are innumerable folid figures which are contained by fimilar planes, equal in multitude,' which are not fimilar, muft be obvious to every one; confequently, Euclid's definition must be defective; and Simfon has rendered his equally faulty, by bringing into it the confideration of folid angles, when the angles that are chiefly concerned are not folid angles, in Euclid's fenfe of them. It appears to us, that all which was wanting on this head in Euclid, was to have added the words, "and fimilarly fituated with refpect to each other," to the ninth definition; to have cancelled the tenth; and to have demonftrated the equality of folid figures, inftead of defining it, as Simfon has done in the three new propofitions which follow the twenty-third in his edition. REV. NOV. 1790. T

Mr.

Mr. Williamfon's other criticism relates to Simfon's note on the feventh propofition of the fame book: but notwithftanding that our author undoubtedly fees the propofition in its right point of view, and that Simfon did not, his attack on the latter is, in our opinion, utterly indefenfible. The propofition stands in Mr. Williamfon's tranflation thus: If there be two parallel ftraight lines, but let there be taken any points which may accidentally happen in each of them, the straight line joining the points is in the fame plane with the parallels.' It is much more clearly, as well as more concisely, expreffed by Sinfon, thus: "If two ftraight lines be parallel, the ftraight line drawn from any point in one to any point in the other is in the fame plane with the parallels." We may fafely appeal to any geometrician, whether, in the plain literal meaning of the words here put down, the propofition does not follow from the feventh and thirty-third definitions of the first book; and whether it is not affumed, as Simfon afferts, all the way through the first fix books, as well as in the third and fixth propofitions of the eleventh book; which is the fubftance of Simfon's objection to it, and the ground of his reason for rejecting it. However, that Euclid and Simfon were thinking of quite different things' in this place, as Mr. W. expreffes it, we readily allow, as there can be no doubt that the propofition fhould be to this effect: If two ftraight lines be parallel, and a point be taken in each of them, there can be no ftraight line drawn from one of these points to the other; but that which is in the fame plane with the parallels. In this fenfe, the propofition could evidently have no place in the firft fix books, where all the lines are exprefsly drawn in the fame plane; neither does the propofition, taken in this fenfe, follow from the feventh and thirty-third definitions of the firft book; and, laftly, it is in this sense that it is applied, whereever it is cited, throughout the eleventh book. These reasons clearly evince that this is the true fenfe in which the propofition ought to be taken; and that, in this inftance, Simfon's ufual penetration failed him, in as much as that he did not difcover the true method of reftoring the propofition, though he faw plainly that it could not be admitted as it stood in his author: but furely an editor who has done fo much toward reftoring the genuine reading of Euclid, did not deserve quite fuch harsh treatment, as to be told that nothing can be more abfurd than his objections' are, merely because he propofed an improper amendment of a paffage which is really corrupt.

We fhall conclude by repeating, that Mr. Williamson's differtations contain feveral pertinent and ufeful remarks, though there are very many which are puerile and trifling. W. ART.

ART. IV. An Inquiry into the Principles of Taxation; chiefly applicable to Articles of immediate Confumption.

Motto. I will make thine exactors righteoufnefs.-Violence fball no longer be heard in thy land; wafting nor deftruction within thy borders. Ifaiah, lx. 17, and 18. 4to. pp. 296. 12s. Boards. Debrett. 1790.

WE

E had, lately, occafion to remark * that political economy, efpecially that part of it which refpects taxation, though, as yet, but little understood, begins to be studied as a science; -and the volume before us proves the juftness of that obfervation. We have not, indeed, in the courfe of our literary peregrinations, met with fuch a fyftematic performance on the fubject of taxation, as the prefent; and as many ideas are here developed, which tend to overturn a pernicious fyftem that too long prevailed in this refpect, we fhall be more particular in our account of it, than we ufually are in regard to performances of a fimilar kind, which only confift of trite obfervations dressed up in a new fashion.

The author of this work confines his view entirely to the taxation of articles of immediate confumption; and he thus explains the plan which he is to purfue in this investigation: His object he says, is,

In the first place, to take a view of the manner in which our financiers have extracted a revenue from articles of immediate consumption. In doing this, it will be neceffary to give a short his torical account of fome of the duties, with the attempts which have been made to fecure them; and to point out the most important errors into which the Legislature have fallen, and which have proved injurious to the revenue, by effectually obstructing its improvement. This forms the subject of the first book, which contains a pretty full account of what I have taken the liberty to call the over-tax fyftem.

But befide thefe practical opinions which prevent the increase of the revenue, there are fpeculative principles which often unite with them to check any plan of general reformation. Thefe it is neceffary to ftate and examine. In doing this, I shall have occafion, firft, to inquire into the manner in which a ftate or commonwealth fhould encrease its revenue with the growing wealth of the people. Secondly, to afcertain the circumstances which occafion the great expence of collecting duties on articles of immediate confumption; and, thirdly, to confider the queftion, on whom taxes on fuch articles ultimately fall. Thefe particulars form the fubjects of the fecond book.

• Nobody fuppofes that revenue laws, and fifcal regulations, have an unlimited power to fecure duties. It feems to be a matter of the highest importance, therefore, to afcertain the extent and

* See the first article of our Review for September.

limitation of that power. This fubject, fo far as I am acquainted, has never been treated of; nor do I know of any attempts that have been made, to afcertain principles by which the power of fiscal regulations may be estimated; this is the fubject of the third book. In it, I endeavour to mark the circumstances which fit or unfit commodities to be fubjects of taxation; to point out the general circumstances on which the power of fifcal reftraints depend; and to exhibit a fpecimen of the manner of fuiting the rate of a duty on any given article to the power of fifcal regulations, fo that fmug. gling fhall be prevented, and the numerous evils of the fyftein hitherto pursued may be avoided.'

Such is the general plan of this publication; and it will be admitted that, if the objects propofed fhall be fully accomplished, it must be confidered as a work of great importance. It fhall be our study, by ftating a few of the moft remarkable facts and characteristic obfervations, to enable our readers, in fome measure, to judge of this matter.

The author begins by explaining what he means by the overtax fyftem of taxation. Whenever a tax is fo high that no fiical regulations can infure the payment of it, he very properly calls it over-taxed; and he finds no difficulty in proving that this mode of taxation has been long adopted in this country.

The firft article that he felected as a fubject of illustration, is beer. The duties on beer in England, from the year 1660 to 1694, he obferves, were 2s. 6d. per barrel on ftrong beer, and 6d. on fmall,-on an average of ten years, from 1684 to 1693, the amount of ale charged was,

Offtrong, 4,567,293 barrels, Of fmall, 2,376,278 ditto. In 1694, the duties were railed to 4s. 9d. the ftrong, and 2s. 6d. the fmall, per barrel,-and for the next ten years, the Of ftrong, 3,374,604 barrels, Of fmall, 2,180,764 ditto. and down to the year 1750, they continue nearly a million of barrels of ftrong ale below what they were before 1690.'

amounts were,

The fame appearances took place in Scotland.At the union, the duty on a particular kind of beer there called twopenny, was 2s. id. q. per barrel, which continued till the year 1760, when the duty was raifed to 3s. 4 d. q. This blow (he obferves) the Scotch brewery never recovered. Instead of 3, 4, or 500,000, the officers' books now feldom exceed 100,000 barrels.

He next examines low wines, refpecting which the fame phenomena occur. Before the year 1750, the duties on the .corn diftillery in England, he fays, amounted to 11 d. 39. on the gallon of proof spirits, equal to about 1d. q on the gal

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