486 Abilities and Correfpondence of James I. &c. James had raised to the highest preferments in the ftate, beftowed the fame tribute of abfurd flattery to his memory, as they had fed him with during life. "I dare prefume to fay, you never read in your life more fully parallel amongst themselves, and diftinguished from all other kings, than King James and King Solomon. King Solomon is faid to be unigenitus coram matre fua, the only fon of his mother, fo was King James; Solomon was of a complexion white and ruddy, fo was King James; Solomon was learned above all the princes in the univerfal world; Solomon was a writer in profe and verse, fo in a very pure and exquifite manner was our fweet fovereign King James; Solomon was the greateft patron we ever read of to church and church-men, and yet no greater (let the house of Aaron now confefs) than King James-and for his words and eloquence, you know it well enough-it was rare and excellent in the highest degree-ProAuenti et quæ principem deceret eloquen. tia; as Tacitus faid to Auguftus, in a flowing and princely kind of elocution. Thofe fpeeches of his in the Parliament, ftar-chamber, council table, and other public audiences of the ftate (of which, as of Tully's orations; ea jemper optima quæ maxima: the longest still was held the beit) do prove him to be the most powerful fpeaker who ever wayed the fceptre of this kingdom." Rufbworth, vol. i. p. 160. As a fpecimen of the pure and exquifite manner of this feet fovereign's writing and fpeaking, I beg leave to lay before the reader a few quotations from his fpeeches and letters. Sept. ted him a lefs fum than was demanded, he thought proper to decline accepting it, for the following judicious reafons: "Nine fcore thoufand pounds, he could not accept, because nine was the number of the poets, who were always beggars; eleven was the number of the apostles when Judas was away, and therefore might beft be affected by his Majesty ; but there was a mean number, which might accord to both, and that was ten, a facred number, for fo many were God's commandments which tend to virtue and edification." Winwood's Memorials, vol. iii. p. 193. To illuftrate his princely elegance in his literary correspondence, take the following example from a letter to the Duke of Buckingham-" if thou be with me by four in the afternoon, it will be good time; and prepare thee to be a guard to me from keeping my heart unbroken with business, before my going to the progrefs. And thus God fend me a happy and joyful meeting with my fweet Stenny, this evening. Sweet-heart, when thou rifest keep thee from importunities of people who trouble thy mind, that at meeting I may fee thy white teeth fhine upon me." MSS. in the British Museum, n. 6987. But the ftile of the queen was fomewhat more extraordinary, and in an age and place where flattery was the moft current coin, undoubtedly infected the whole court. Queen ANN to King JAMES. "I am glad that our brother's horfe does please you, and that my dog Stenniet does well; for I did command him that he fhould make your ears hang like a fows lug, and when he comes home I will treat him better than any other dog." Queen ANN to Viscount VILLARS. You do well in tugging the fow's ear, and I thank you for it, and would have you do fo ftill, upon con dition you continue a watchful dog to him, and be always true to him." In a fpeech to the Parliament, anno 1610, he informs his fubjects, that "the King's heart is in the hand of the Lord, who can create and destroy, make and unmake; fo kings can give life and death, judge all and be judg§ ed by none. They can exalt low things, and abafe high things, making the fubjects like men at chefs, a pawn to take a bishop or a knight. And, as it is blafphemy to difpute what God may do, fo it is fedition in fubjects to difpute what kings may do in the height of their power." "Macaulay's Hift. of Eng. v. i. p. 61. When the fame Parliament had vo MSS. British Museum, fol. 6986. A fine courtly ftile truly! The following paffages from the Bifhop of Downe's fermon, and a letter from General Digby to the Marquis of Ormond, fhew the impious nonfense as well as flattery that was preach King of Denmark. + Duke of Buckingham. § King James. 1776. Notorious Inftances of Flattery expofed. ed and propagated after the death of King Charles I. "The perfon now murdered, fays the Bishop, was not the Lord of Glory, but a glorious Lord, Chrift's own vicar, his lieutenant and vicegerent here on earth." One would imagine he was speaking of his Holiness of Rome. "Albeit he was an inferior to Christ as man is to God, yet was his privilege of inviolability far more clear than was Chrift's ; for Chrift was not a temporal prince, his kingdom was not of this world, and therefore when he vouchfafed to come into this world, and to become the fon of man, he did fubject himself to the law; but our gracious fovereign was well known to be a temporal prince, a free monarch, to whom they did all owe and had fworn allegiance. The Parliament is the great council, and hath acted all and more against their lord and fovereign, than the other did against Christ. The proceedings against our fovereign were more illegal, and in many things more cruel." From the creation of the world," fays General Digby, "to the accurfed day of this damnable murder, nothing parallel to it was ever heard of. Even the crucifying our bleffed Saviour, if we confider him only in human nature, did nothing equal this." State Letters, vol. iii. p. 607. Timoleon, having expelled the tyrants, and restored Syracufe to its ancient liberty, his wildom, valour and glory, were very much extolled in his prefence; but fuch was his modefty, moderation, and uncommon averfion for all flattery, that he made no other answer, but that he thought himself 487 obliged to exprefs his thankfulness to the gods, who, having decreed to reftore peace and liberty to Sicily, had vouchfafed to make choice of him, in preference to all others, for fo honourable a miniftration; for he was fully perfuaded, that all human events are guided and difpofed by the fecret decrees of Divine Providence. What a treasure, what an happiness for the ftate, is fuch a minifter! Corn. Nep. in Timol. c. iv. As Canute the Great, King of England, was walking on the fea-fhore at Southampton, accompanied by his courtiers, who offered him the groffeft flattery, comparing him to the greatest heroes of antiquity, and afferting that his power was more than human, he ordered a chair to be placed on the beach, while the tide was coming in. Sitting down with a majestic air, he thus addreffed himself to the Sea: "Thou Sea, that art a part of my dominions, and the land whereon I fit is mine, no one ever broke my commands with impunity; I therefore charge thee to come no farther upon my land, and not to prefume to wet either my feet or my robe, who am thy fovereign." But the fea rolling on, as before, and without any respect, not only wet the fkirts of his robe, but likewife fplafhed his thighs. On which he rofe up fuddenly, and addreffing himself to his attendants, upbraided them with their ridiculous flattery; and very judiciously expatiated on the narrow and limited power of the greatest monarchs on earth. HUNTINGDON, lib. vi. MATHEMATICAL CORRESPONDENCE. LET * = the difference between the ages of the two extremes, in abitween We' 488 Mathematical Correspondence. Sept. We were favoured with elegant anfwers to this queftion by Mr. Thomas Atkinson, of Dunholm, near Lincoln, Mr. Merrit, Mr. Hampshire, Eltonienfis, Mr. Le Gos, Snapp, Cleonicus and others. [65] QUESTION II. Anfwered by the Propofer Mr. Moss. Conceive ABCD to represent a trapezium, fimilar to that which is to be infcribed in the given one RIMP, draw the diagonal IP. Upon either of the two oppofite fides AB and CD (or AD and BC) of the trapezium ABCD, defcribe (by Eu. 33. 3.) two fegments of circles capable of containing angles equal to either of the two oppofite angles of the given trapezium RIMP. Let (for inftance) that fegment defcribed upon AB contain an angle RIM, and that defcribed upon CD contain another angle RPM. Make thofe fegments complete circles; then from their centers E and F, draw the radii EB and FC, &c. and make the angle BEm = twice MIP (or AEm = twice RIP) alfo make CFn = twice MPI (or DFn = twice RPI) through the points m and n (being in the peripheries of the circles) draw the right-line bd, terminating in the faid peripheries in b and d; then, from the points b and d, through the angular points of the trapezium ABCD, draw four K right-lines till they meet in b B I E G P the points a and c, and a b c d will be fimilar to the given trapezium RIMP : divide the four fides of the given trapezium RIMP in the points D, E, F, G; fo that ID: DM::b B: Bc, and ME: EP : C: Cd, &c. draw DE, EF, FG, and GD; and the thing is done. Demonftr. The angles AbB and CdD (by confir.) are refpectively equal to the angles RIM and RPM; but (by Eu. 20. 3.) the angle dbc is = half BEm = MIP (by conftr.) moreover, by the very fame method of reafoning, the angle bac is half CF MPI; then, fince, (by confr.) the angles at b and d are refpectively equal to thofe at I and P, it is evident that the triangles bcd and dab are refpectively fimilar to the triangles IMP and PRI ; and confequently (by Eu. 18. 6.) the trapezium abcd, whofe fides (by confir.) pass through the angular points of a trapezium fimilar to that which is to be infcribed in RIMP, is likewife fimilar to the given one RIMP.-Furthermore (by conft.) bB Bc ID: DM, or (by compofition) bB + Be Be ID + DM : that is be: IM: Bc DM: moreover, by the very fame reasoning, we have be: IM (:: de: PM by confr.): Cc: EM; whence (by equality, &c.) Bes Cc:: DM: EM; and therefore the triangles Br C and DME are fimilar: and by proceeding in the very fame manner, it may be proved that the other correfponding triangles are fimilar; and confequently the trapeziums ABCD and : GDEF 2 1776. Mathematical Correfpondence. 489 GDEF are also fimilar. Q. E. D.-Cor. I. Hence it appears, by the former part of this contruction, that about any quadrilateral figure, another quadrilateral fimilar to a given one may be defcribed.Cor. II. Hence it alfo appears, that the trapezium, GDEF, to be infcribed in the given one RIMP, will manifeftly admit of various pofitions with refpect to the fituation of the angles at G, D, E, and F in the given fides RI, IM, MP, and PR: But the method of folution will not differ, in any affigned pofition, from that given above. [66.] We not having received a fatisfactory answer, as yet, to this question, hope fome of our ingenious correfpondents will confider it against the next. ERRATA in the fig, to queft. III. in our last, instead of rn, rn, read rM, rk. Quelt. I. for 16a4 read 16a2. NEW MATHEMATICAL QUESTIONS. [70.] QUESTION I. By Mifs Jenny Watson. A merchant doth go with money from London to Paris where he gained 20 per cent. and doth spend 10 per cent. of stock and profit, and then finds he, hath got sool. clear. Query, How much money he took from London? [71.] QUESTION II. By Theon. There is a given circular wood, the diameter of which is 1000 miles, it is required to find the rate per day which a traveller must walk round the fame, walking equally, to meet another traveller fetting off at the fame point of the circumference, and walking backward and forward in the diameter, the first day 1 mile, the fecond 2 miles, the third day 4 miles, and fo on in geometrical progreffion, fo that they may exactly meet again when the first arrives at the fame point in the circumference from whence they fet off. [72.] QUESTION III. By Mr. John Hampshire. In a plane triangle there is given the fum of the fquares of the fides, the line bifecting the vertical angle, and the difference of the fegments of the ba made by a perpendicular from the vertical angle on the bafe, to determine the triangle. We have been favoured with an elegant answer to the firft queftion from Mr. Fdler, teacher of the Mathematics at Mr. Lloyd's Academy near Vauxhall Gardens, and at Mrs. Ames's Boarding School; alfo folutions to the ft (by three methods of fubftitution) and 2d by Mr. Jonathan Mabbott of Oldham near Manchefter, but too late for infertion. -We efteem the correspondence of these ingenious gentlemen a favour, and hope to receive their future favours before the 10th of each month. An Impartial Review of New Publications. ARTICLE CXXXIII. "Canon I. When ufe is divided as to employed by the other part never admits a different fenfe, both perfpicuity and variety require, that the form of expreffion which is in every inftance ftri&ly univocal, be preferred. Canon II. The fecond canon is, in doubtful cafes regard ought to be had in our decifions to the analogy of the language. Canon III. The third canon is, when the terms or expreffions are in other re pects equal, that ought to be preferred which is mcft agreeable to the ear. Canon IV. The fourth canon is, in cafes wherein none of the foregoing rules gives either fide a ground of preference, a regard to fimplicity (in which I include etymology when manifeft) ought to determine our choice. Canon V. The fifth and only canon that occurs to me on the fubject of divided use is, 3 R in 490 Review of New Publications in the few cafes wherein neither perfpicuity nor analogy, neither found nor fimplicity, affifs us in fixing our choice, it is fafeft to prefer that manner which is most conformable to ancient usage. Canon VI. The firft canon on this fubject is, all words and phrafes which are remarkably harsh and unharmonious, and not abfolutely neceffary, may justly be judged worthy of this fate. Canon VII. The fecond canon on this fubject is, when etymology plainly points to fignification different from that which the word commonly bears, propriety and fimpli. city both require its difmiffion. Canon VIII. The third canon is, when any words become obfolete, or at least are never ufed, except as conftituting part of particular phrafes, it is better to difpenfe with their fervice entirely, and give up the phrafes. Canon IX. The fourth and laft canon I propofe, is, all thofe phrafes, which, when a nalyfed grammatically, include a folecifm, and all thofe to which ufe, hath affixed a particular fenfe, but which, when explained by the general and established rules of the language, are fufceptible either of a different fenfe or of no fenfe, ought to be discarded altogether." Our author's language is in fome refpects faulty, and capable of amendment, but his reafoning and obfervations are perfpicuous and folid. Among the feveral fpecies of nonfenfe, he inftances the profound, which he fays is chiefly to be met with in political writings. No where elfe do we find the mereft nothings fet off with an air of folemnity, as the refult of very deep thought and fage reflection. Of this kind he produces a specimen from a juftly celebrated tract, of a justly celebrated pen: 'tis agreed, fays Swift, that in all governments there is an abfolute and unlimited power, which naturally and originally feems to be placed in the whole body, wherever the executive part of it lies, This holds in the body natural; for whereever we place the beginning of motion, whether from the head or the heart, or the animal fpirits in general, the body moves and acts by a confent of all its parts. "The first fentence of this paffage contains one of the moft hackneyed maxims of the writers on politics; a maxim, however, of which it will be more difficult than is commonly imagined, to difcover, I fay, not the justnefs, but the fenfe. The illuftration from the natural body, contained in the fecond fentence, is indeed more glaringly nonfenfical. What it is that conftitutes this confent of all the parts of the body, which muft be obtained previously to every motion, is, I will take upon me to affirm, utterly inconceivable. Yet the whole of the paragraph from which this quotation is taken, bath fuch a fpeciousness in it, that it is a Sept. hundred to one, even a judicious reader will not, on the firft perufal, be fenfible of the defect. CXXXIV. Original Works of William King, LL. D. Advocate of Doctors Commons: Judge of the High Court of Admiralty and Keeper of the Records in Ireland, and Vicar General to the Lord Primate. Now first collected into three Volumes: with Hifto rical Notes and Memoirs of the Author, 3 vels. 125. Conant. This is the Dr. King of whom 'tis faid, 'Twas from the bottle King derived his wit, Drank till he could not speak, and then he writ. and Mr. Pope defcribed him as writing verfes in a tavern three hours after he could not fpeak. He was a man of humour, and many of his writings are justly esteemed for their irony and fatire; particularly thofe against Sir Hans Sloane, the Royal Society➡ the naturalifts and antiquarians. Our author was a zealous tory, and had a great deal of Swift's difpofition and manner. The following extract from his "new method to teach learned men how to write unintelligibly," is both fenfible, and suitedfor the prefent day. "There are feveral that pretend to be mighty Grecians, to have Hehod, Mufæus, and Homer, at their fingers ends; but alas! they understand nothing of the modern Greek, nor the beauties of Du Frefne's "gloffary." Thefe perfons are left to be managed by coptic verses. This, being a baftard Greek, is mixed with multitude of other languages, and makes ufe of fome of the Greek characters, a little deformed, and intermixed with others. They, having been long enslaved to the Saracens, Mamalukes, and prefent Turks, have not had of latemuch time for learning only there is one Scornienfius a poet, that has lately rifen upamongst them, whofe works I have here upon the table: him you may imitate; faywhat you please in that language, and nobody will think it worth while to confute you. By reading over of Kircher's Prodromus Coptus, and an old door that Dr. Huntingdon fent from Grand Cario, I have made shift to put fome of the first lines into the Greek character: * Ω Φαραω, μαιγω? Φαραω κρεις, Σιςγέμι TEGATE. • Εργλεθε χιλδερκιν, αναβείες φληγίεθε φοσσετ. • Να συπυπ βρίσκλει, αν θεοπειθε καλούς • avoin, • Ση αναλύτες ; θες νων καν δρινκαν: λογίας By the help of a gentleman that had converfation with the king of the gypfies, I found out that it was plain English in Hexameter verfe, fuch as you may find in Sir Philip Sydney, and fuch as were fent Ben Jonfen, beginning, " Benjamin, |