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Art. 20. Obfervations on the prefent State of the Wafle Lands of
Great Britain. Published on Occasion of the Establishment of a
new Colony on the Obio. By the Author of the Tours through
England. Evo.
Nicoll. 4773,

2 S.

Ecce iterum Crifpinus!

What! Master Kaftril, the angry boy, come again!--March en, Mafter Kapril! March along, Sir!-We will have nothing more to fay to you.

EAST-INDIES.

Art. 21. The prefent State of the East India Company's Affairs : Containing the Eltimates and Accounts delivered by the Directors of the Company to the Lords of the Treafury, and laid before the Secret Committee appointed by the Houfe of Commons to enquire into the East India Affairs. 4to. I s. 6d. Bladon.

Thefe accounts are undoubtedly authentic. We have alfo in this publication the different plans propofed by feveral of the Directors, and other gentlemen*, for the re-establishment of the credit and circumstances of the company; together with remarks on each plan.

DRAMATIC.

Art. 22. The Wedding Ring. A Comic Opera. In two Acts. As it is performed at Drury Lane. Svo, I s. Becket. 1773

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Mr. Dibdin, the Author of this opera, in a modest adress to the public, acknowledges his obligations to Il Filofofo di Campagna, to Moliere, and to other writers, for feveral circumftances and paffages of his work. He fays, the dialogue is given for nothing more than fuch as would immediately arife from the fituations. This feems to have been the object of Shakespeare in the happiest parts of his plays. We muft, however, do Mr. Dibdin the justice to fay, that the dialogue has merit, on the very account on which he would have it but flightly regarded.-We are now of the fame opinion which we conceived at the reprefentation,-that Mr. Dibdin had fucceeded better in the dialogue, than in any part of the enter tainment. He fays, If the fongs are found to be irregular, I would beg leave to remark, that they were written fo on purpofe.' Mr. Dibdin is not fo happy when he writes on purpose, as when he does not; his fongs being almost all of them deftitute of merit. The mufic is like all Mr. Dibdin's compofitions, lively, pretty, and pleafing. The performers in general deferve his acknowledgments; none more than Mrs. Wrighten, who fupports her character with a Spirit and truth which we have feldom feen exceeded. We are glad to find Mr. Vernon is no longer to play the Dupe. It did not at all become him.

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Art. 23. The Golden Pippen: An English Burletta, in three Acts; as it is performed at Covent Garden. By the Author of Midas. 8vo. I s. 6d. Becket. 1773.

This gentleman feems refolved to continue the war against the poor heathen gods; we therefore conclude he is a good chriftian. He

* Viz. Thofe of Mr. Dempfer, Mr. Sullivan, Mr. Herries, and Mr. Bofanquet.

mistook,

miftook, however, the humour of an Englifh audience, when he attempted to make his burletta fill up the place of a play. We wish to laugh at thefe extravagancies only as a relief after an attention to fome objects of importance.

This piece is written on the well-known ftory of the judgment of Paris; and the feveral characters of the gods and goddeffes are very well burlefqued. The mufic, though not all new, is happily collected we fuppofe by Dr. Arne; the very pleafing overture having all the marks of his compofitions.-The fcenes are fhewy, and the merit of the performers will not be questioned when the Reader looks at the Dramatis Perfonæ.

Art. 24. The Golden Pippin: An English Burletta, in two Aas, as it is performed at Covent Garden. By the Author of Midas. 8vo. 1s. Becket. 1773.

This is the former burletta in its state of humiliation; and, like many a man, the better for its misfortune. It now holds its proper place of a farce; and we doubt not but that it will continue, in its turu, to give our good people, both above and below-stairs, a hearty laugh.

NOVELS.

Art. 25. The Hiftory of Tom Rigby. 12mo. 3 Vols. 75. 6 d fewed. Vernor, 1773.

A plentiful but homely entertainment, ill-fuited to the delicate tatte of those who are accustomed to the literary dainties provided by your Cervantefes, your Marivauxs, your Fieldings, and other celebrated mental cooks. It may, however, go down well enough with those who only gape and fwallow and to whom, like the oftrich. it is immaterial whether you are treating them with bifcuits or hobnails.

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Art. 26. The Mercenary Marriage, or the Hiftory of Miss Shenflone. 12mo. 2 Vols. 6 s. Noble. 1773.

This work is written in the general manner of modern novels. It is well intended; for it aims at combating the vanity and avarice of young people in the most important event of life. We wish it had merit enough to make its way to the notice of thofe high and mighty offenders, who might profit by the leflons which it affords. Art. 27. The Hiftory of Pamela Howard. By the Author of Indiana Danby. 12mo. 2 Vols. 6s. Lowndes. 1773 Comedy and Tragedy have here joined to furnish an entertainment with which the Ladies in general will be pleased; and even the Gentlemen, (the fentimental Gentleman, we mean) may make tolerable shift to ubile away a vacant hour on the perufal of a story, the beginning of which will divert them: but the conclufion is pregnant with that kind of horrible diftrefs which humanity will think too much.-It is not a finished piece; but there are touches in it which prove the Writer poffeffed of abilities for this kind of writing. It feems to be the product of a female pen. This branch of the literary trade appears, now, to be almost entirely engroffed by he Ladies.

• See Review, vols. xxxii, and xxxvii. ·

Art.

Art. 28. The Way to please him: Or the Hiftory of Lady Sedley. 12mo. 2 Vols. 5 s. Noble. 1773.

*

See the next enfuing article.

Art. 29. The Way to lofe him: Or the Hiftory of Mifs Wyndham. By the Author of The Way to please him!' 12mo. 2 Vols. 5s. Noble. 1773.

The leffons inculcated in the two above-mentioned novels, are of very ufeful tendency. They will inftruct indiscreet females, not only how to merit the love of a worthy man, but how to fecure the permanency of his affection. The language is eafy, and, in general, not inelegant; but the story of the latter of thefe productions is fo barren of incidents as to render the narrative part of the work somewhat tedious. The merit of the first piece, with refpect to compofition, though both are written by the fame Author, is confiderably fuperior to that of its fifter-performance.

Art. 30. Love at first Sight: Or the History of Mifs Caroline
Stanhope. 12mo. 3 Vols. 7 s. 6d. fewed. Jones. 1773.
A tolerable story, delivered in the ufual familiar epiftolary flile;
but bearing all the marks of hafte and inattention.

Paper-makers and printers certainly owe fome public monument of gratitude to the memories of Fielding, Richardfon, and Sterne, for the amazing consumption of paper and print which the numerous imitations of their patterns have occafioned within the last twenty years. Whether the boookfellers will be forward to join in any fuch fubfcription, must be left for bookfellers to determine, if the occafion fhould offer.

MATHEMATIC s. Art. 31. Elements of Trigonometry, plain and spherical; with the Principles of Perspective and Projection of the Sphere. By John Wright. 8vo. 5s. Boards. Edinburgh. Kincaid, &c. 1772. Sold by Nourfe in London.

The theory of trigonometry has been very little altered or improved fince the time of Purbachius and Regiomontanus, the firft of whom died in 1461, and the last in 1476. The chief improvement in modern times is the invention and application of logarithms. We can therefore expect little more in treatifes on this fubject than fome alteration in the order and form of the propofitions, or in the method of demonftrating and applying them. Though the Author of these Elements propoles no new difcovery, he has made a judicious collection of feveral things that relate more immediately, or more remotely, to his main fubject; and, in fome particulars, he has improved on former writers. He informs us, that it is not his intention to fuperfede the use of any standard book that is taught as a part of a regular courfe of geometry;' but he rather fuppotes that the learner is acquainted with feveral of them before he can benefit any thing by this. He has given, in his preface, a compendium of the hitory of this branch of mathematical fcience; from which we fhall make the following extracts:

The trigonometry of the ancients, as appears from Ptolemy, was in form very different from ours. The trigonometrical canon of this author is conftructed by supposing the diameter of the circle to be divided into 120 equal parts, and by finding, in parts of the diame

ter,

ter, the chord of each degree and 6oth part of a degree of the whole femicircle, or 180 degrees, each of the 120 parts of the diameter is supposed to be divided into 60 equal parts, and each of thefe again into 60 parts more, &c.

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At what time the ancient trigonometry came to be reduced to the regular form in which we find it in Ptolemy, I have not hitherto been able to difcover; but it feems to have been pofterior to Ariltarchus the Samnite, who flourished about 280 years before the Chriftian era. It would appear alfo, that this invention was pofterior to the time of Archimedes; for in his treatise called the Arenarius, the way in which he expreffes the angle fubtended by the diameter of the fun is, that it is less than the 104th, but greater than the zocdth part of a right angle. Probably the invention was by Hipparchus, who began to flourish about 50 years after the death of Archimedes; that is, about 160 years before the Chrif tian æra for we are told, that Hipparchus wrote a treatise upon the use of chords. The Arabians afterwards, though it is uncertain at what time, altered the form of the ancient trigonometry. The alteration appears to have been made before the time of Albatenius, who flourished about the latter end of the ninth century. They made ufe of the radius of the circle instead of the diameter; but continued to divide it into 60th parts as before they made ufe of half the chord, which is now called the fine, instead of the chord itfelf, and found it in parts of the radius: and they recuced the cafes of triangles to fimple propofitions of four proportionals. The reafon of the name finus is faid to be, that the halves of the chodș, femifjes inferiptarum, might often be contracted thus, S. Inf. and that the ignorant (copiators) made one word (finus) of both.'

Purbachius made ufe of decimals in the division of the radius inftead of fexagefimals. And Regiomontanus improved on his preceptor, by fuppofing the radius unit with 7 cyphers, inflead of becoccoc, and dividing it into decimal parts. He alfo added the ufe of Tangents, calculated tables in parts of the radius for every degree and minute of the quadrant, and difcovered the method of folving the two laft cafes of oblique-angled fpherical triangles. Rheticus foon after made use of fecants. Vieta, towards the latter end of the fixteenth century, made fome farther improvements in this as well as in the other parts of mathematics. Baron Napier, by his invention of logarithms, and his two compendious theorems for folving the numerous cafes of spherical triangles, greatly contributed to the perfection of this art. To all which might be added, that the modern difcoveries in algebra and fluxions have very much facilitated the conftruction of trigonometrical tables.

The intelligent Reader will find great fatisfaction in the perufal of this treatife.

Art. 32. An Introduction to Marine Fortification and Gunnery; in Two Parts; illuftrated with feveral Copper-plates. By J. P. Ardefoif, Lieutenant of the Royal Navy. 8vo. 4 s. 6 d. Boards. Printed at Gofport, and fold by Johnfon in London. 1772. This Introduction is principally intended for the ufe of young gentlemen in the navy; the rules and directions it contains feem well

calculated

calculated to answer the purpose which our ingenious Author had in view; and we hope that thofe, with whom the honour and welfare of the British nation are fo immediately intrufted, will be hereby induced to make these important branches of naval fcience the objects of their particular attention and study.

Art. 33. The two Books of Apollonius Pergaus, concerning Tangen cies, c. By John Lawfon, B. D. Rector of Swanscombe in Kent, Second Edition. Together with two Supplements, &c. 4to.

6 s. Boards. White, &c.

We shall refer our Readers to Art. 5 in our Review for Jan. 1771, (vol. xliv.) for a general account of the attempts that have been made towards reftoring thofe valuable works of the great geometer Apollonius, which are perifhed in the ruins of time.

With respect to the volume before us, it will be fufficient to obferve, that it includes a tranflation of the two books concerning tangencies, as restored by Vieta and Ghetaldus, together with two fupplements, one by the Tranflator, and another containing Monf. Fermat's treatise concerning fpherical tangencies; and the two books of the fame celebrated geometer concerning determinate fection, as reftored by Willebrordus Snellius, together with a new attempt for the recovery of the fame books by William Wales. The first of thefe was published in the year 1764; the merit of the original is known and allowed by all geometricians, and the tranflation is faithful and accurate. The other tract De Sectione determinatâ, by Snellius, was in danger of being loft, and this confideration induced Mr. L. the Tranflator, to give it to the public in an English dress, that it might not share the fate of the original of Apollonius. The whole of this work, by Snellius, contains but four problems; whereas we are informed by Pappus, in his preface to the feventh volume of Mathematical Collections, that the original tract of Apollonius was divided into two books, the firft of which contained fix problems, and the fecond three this defect Mr. Wales propofes to fupply, and the intelligent Reader will be pleafed both with the attempt and the manner of its execution. In the conftructions (lays he) my chief aim was novelty and uniformity; I could have given more fimple conAtructions to one or two of them; in particular the fixth of Book I. but it was not my intention to give any thing that I knew had been done before. I know of many imperfections, but no falfe reasonings, and hope none will be found; but if there should, I hope the candid geometer will be more inclined to excufe than exult, when I affure him the greatest part of the work has been executed at different times, amidst the hurry and perplexities which it may easily be conceived attend the fitting out for a three year's voyage to the South Seas.'

POETICAL.

Art. 34. An Epiftolary Poem, humbly infcribed to the Right Honourable Frederick Lord North, First Lord of the Treasury, &c. &c. on the prefent Mode of imprifonment for Debr. 4to. 1 s. Wilkie, &c. 1773.

The Author fays, in the advertisement, that this Poem is addreffed to Lord North, ioliciting his protection and fupport of a bill in

tended

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