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to speak their sentiments on the most common occurrences; fufpicious of cherishing government fpies in their household fervants; diftruftful of their own relations and most intimate companions, and at all times expofed to the oppreffion of men in power, and to the infolence of their favourites ?-No confufion, in my mind, can be more terrible than the stern difciplined regularity and vaunted police of arbitrary governments, where every heart is depreffed by fear, where mankind dare not affume their natural characters, where the free fpirit muft crouch to the flave in office, where genius muft reprefs her effufions, or, like the Egyptian worshippers, offer them in facrifice to the calves of power; and where the human mind, always in fhackles, fhrinks from every generous effort.'

We hear that these letters are the production of Dr. Moore, a medical gentleman who accompanied the Duke of Hamilton on his travels. If the Doctor understands the fick part of mankind, as well as thofe in health, he is, doubtless, a very valuable member of the faculty.

ART. XI. A Reftitution of the Geometrical Treatise of Apollonius Pergaus an Inclinations. Alfo the Theory of Gunnery; or, the Doctrine of Projectiles in a non-refifting Medium. By Reuben Burrow. 4to. 2 S. Nourfe. 1779.

HE celebrated problem of Apollonius to apply a RIGHT Tline, of given length, between two lines, given in position, fo that when produced out it may pass through a given point, has employed the thoughts of feveral able geometricians, fome of whom have given us the solution of one cafe, fome that of another; but none, that we know of, have published any attempts towards a general reftitution of the problem before our Author, except Alexander Anderfon, Ghetaldus, and the Rev. Dr. Horsley.

It was never, fo far as we know, efteemed difficult to give a folution, of fome kind or other, to this problem: the great point was, to discover the original one, given by Apollonius himfelf, to diftinguifh the feveral problems and cafes into which he divided it, to exhibit them in the fame order; and, above all, to derive the determinations by means of those lemmata -given us by Pappus for that purpose, of which, doubtless, Apollonius made ufe. In every one of those circumstances Anderson appears to have been very defective. The principle on which Ghetaldus founded his method of folution does not seem to be very materially different from that which Apollonius must have made ufe of, if we may judge from the account which Pappus has given concerning it; but his subdivision of the pro


blem is confufed, and his determinations are tedious, unartificial, and, without doubt, very different from those which were given by the original author. Of Dr. Horfley's an opinion has already been given in our Review for January 1771. He has, perhaps, come nearest to Apollonius in the general divifion of the problem; but yet we apprehend the Doctor must agree with us, that his analyfis of the problem is effentially different from that given by Apollonius; neither are we clear that his method of deriving the limitations is genuine.

Mr. Burrow, we conceive, has come nearer to the Apollonian method of folution than any who preceded him, as will be evident to every one that takes the trouble of comparing his folution with the lemmas which Pappus has left us for the analyfis of the problem. He has alfo fhewn great address in his determinations, which are elegant and concife; perhaps not inferior to those which were given by Apollonius himfelf; but that they are not the fame, will be evident from the first-mentioned lemmas. On the whole, we are confident this little tract will be read with pleasure by every one who has a true tafte for pure geometry; and we cannot help congratulating the Author of it on his attainment to a better taste in these matters: for he has here given, not only the analytical, but also the synthetical effections of each problem, notwithstanding we recollect to have feen him formerly maintaining, "That to give a demonftration in form, after a clear analytical investigation, would be moft ridiculous pedantry;" the contrary of which, we make no doubt, he is now thoroughly convinced of. And, although there are fome little defects and blemishes in the prefent performance, which a longer and more attentive perufal of the best writers on geometry will teach him to avoid in future; yet it exhibits fuch marks of real genius as are not often to be met with in young geometricians.

Sincerely could we have wifhed to congratulate him also on his attainment to a better temper and difpofition of mind; but we are forry to obferve that no evidence of this appears in his preface. The violence of his temper feems, indeed, to have hurried him into inconfiftencies which he could not otherwise have fallen into, as the following extract will fufficiently testify:

The Author having fince [completing his work] had a fight of Pappus's Collections, finds reason to conjecture that he has come nearer to the spirit of the great original than the production of the reverend Compiler.' What reverend Compiler? No compiler, reverend, or otherwife, is mentioned by Mr. B. before; but we apprehend Dr. Horfley is to be understood, and then the obvious meaning of the fentence will be, that his performance


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formance comes nearer to the spirit of the great original than it does to Dr. Horfley's compilation, as he is pleased to term it. He adds, For as to the work of Dr. Horfley, it is split into fuch an infinity of different cafes, frittered into fo many divifions and fubdivifions, and treated befides in a manner fo clofely bordering upon algebra, that it does not appear to have the leaft fimilarity to any of the genuine productions of Apollonius; and what is still more defective, he has not only left his conftructions undemonftrated, but has entirely omitted thofe very material propofitions which make the third and fourth of the following book; not to mention the inelegance of his method, his virulent remarks, and his arrogant and contemptuous expreffions against former writers. The Author therefore hopes, that if the following fhould meet with the approbation of mathematicians, any apology for treating the fame subject after the Doctor will be entirely needless.'

Now, to pafs over the injuftice of blaming a man for not doing what he never intended, or perhaps thought of (for it may eafily be fhewn that Mr. B.'s third and fourth problems made no part of the work of Apollonius, which Dr. Horsley alone attended to), it is very extraordinary in Mr. B. at least, to cenfure the Doctor for avoiding a conduct which he himself has declared to be most ridiculous pedantry: and it is yet more fo to affert, that diftinguishing the feveral cafes of the problem has rendered the Doctor's work totally unlike that of Apollonius, when it is well known to every perfon, intimately acquainted with the method of the ancient geometricians, that it was on this particular specification of the cafes that they much valued themselves; and when there yet remain the lemmas which Apollonius made ufe of to facilitate the analysis of the feveral particular cafes of this very problem. Moreover, if the Doctor's expreffions, which Mr. Burrows fays are virulent, arrogant, and contemptuous, with respect to former writers, have rendered him unworthy of attention, a fimilar conduct must render Mr. B. fo likewife.

The tract on Gunnery contains demonftrations of the principal propofitions in the doctrine of projectiles, confidered as being made in a non-refifting medium. They are elegant, and purely geometrical; and Mr. Burrow has extended them to fome points, more general than thofe which had been treated on by former writers. But it is, like the former tract, preceded by a very ill-natured preface, in which the Author has defcended to downright ribaldry.


ART. XII. A Paraphrafe or Poetical Expofition of the Thirteenth Chapter of the First Book of St. Paul's Epiftles to the Corinthians. By Christopher Anfty, Efq. Folio. I s. DodЛley.


F paraphrafes in any form, or for any purpose, any purpose, we acknowledge ourselves no great admirers. When they are made ufe of as comments on an author, they perhaps as frequently obfcure or pervert, as elucidate his meaning. When they are employed to unfold the beauties of fentiment or language, they often deviate from the true character, and lose the distinguishing excellencies of the original. The compound produced by the ill-beftowed labours of the paraphraft, is, like wine diluted with water, vapid and tastelefs.

We find ourselves under the neceffity of confidering the verses before us, though the work of an able mafter, as a confirmation of the truth of these remarks. The beautiful fimplicity and ftrength of the original appears to us almost entirely loft in the imitation. Had the poem been lefs diffuse, it would probably have been a lefs imperfect copy. This may be in part inferred from comparing the two following imitations of the fame paffage, the firft from our Author, the fecond from Prior:

"Tis thine the raging paffions to controul,

To calm, to ftrengthen, and confirm the foul;
Teach flighted worth with patience to fuftain
The powerful man's neglect, the fool's disdain,
The ungrateful friend's revolt; or keener pang
(Keen as the bearded fteel, or ferpent's fang)
That waits too oft, alas! the perjur'd vow,
And loft affection's cold and fcornful brow:
The filent eloquence of kindness meck.
Beams from thine eyes, and mantles in thy cheek;
From Envy free, and Pride's c'erbearing fway,
Thou tak'it thy mild and inoffenfive way:

Grace in thy geftures and thy looks is feen,
Gentle thy words, and courteous is thy mien ;
Thòu fcorn'it to caft the proud indignant frown
On other's merits, or to boat thine own,
O'er anger, hatred, or revenge to brood,
Record the evil, and forget the good:

Or aught that can thy neighbour's peace destroy
Make the baie fubject of thy barbarous joy;
If just the cenfure that affects his fame,
'Tis thine to pity, not increase his shame;
If falle the charge, thy foul can know no reft,
Till Truth appear, and heal his wounded breast.
Forbearing all, and trufting ftill to find
Some virtues 'mid the failings of mankind,
Thou o'er their faults canft draw the friendly veil,
The better part believe, the worse conceal,

Still hope that time their frailties may remove,
And wait the hour with patience and with love,



Charity, decent, mcdeft, eafy, kind, Softens the high, and rears the abject mind; Knows with just reins and gentle hand to guide, Betwixt vile fhame, and arbitrary pride. Not foon provok`d, fhe eafily forgives, And much the fuffers, as the much believes. Soft peace the brings wherever the arrives; She builds our quiet as the forms our lives; Lays the rough paths of peevish nature ev'n, And opens in each heart a little heav'n. Notwithstanding the respective merits of these paffages, uncorrupted tafte will, we doubt not, pronounce sentence in favour of the following artlefs, yet touching, language of the Apoftle-"Charity fuffereth long, and is kind; Charity envieth not; Charity vaunteth not itself; is not puffed up; doth not behave itself unfeemly; feeketh not her own; is not eafily provoked; thinketh no evil; rejoiceth not in iniquity, but rejoiceth in the truth; beareth all things; believeth all things; hopeth all things; endureth all things."

To thefe general obfervations we muft fubjoin a particular remark or two on the execution of the poem. And first, the Author does not appear to us to have clearly afcertained, or at leaft expreffed, his idea of his subject. As if Charity and Love were diftin& things, and not different words to express that benevolent principle which the Apoftie calls ayan, addreffing **rect Charity," he fays,

If thy sweet virtues from my foul depart,

The Chriftian Love be foreign from my heart.

There appears, moreover, a great inequality in the execution of this piece: fometimes the poet rifes into the obscure of rublimar, and fometimes creeps in humble profe. The following lines on the ftate of knowledge in the life to come are of Me tower klad:

His vain attainments hall like fades depart,
Arà action Intima of truths divine,

That the bevond bis weak conception Aine
Denon the Fuat glimmerangs of his mental rays
èr one als perverfu, and smimovral blaze.

Of the keer fort are there ines:

When th` Almigan's presence we fall fhine,
Soe, and adore his attributes ¿lvine,

His power, his widom, and his mercy own,

Ara Em hay know, as we drielves are known.

Ca the whole, we cannot think that Mr. Anfly would have lot arx share of poetical reputation, if he had confined himself za dis suzie walk of satirical humour, which he has fo frequently Wojden with Trecek.


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