ID, by Euc. III. 35; therefore the rectangle contained by OD and DG is equal to that contained by FD and ID; that is, to the rectangle contained by OD and ND, by conftruction: confequently GD is equal to ND; GA is, therefore, equal to KA, and the rectangle AHFD is the greatest that can be inforibed in the triangle FGK, by Prop. VIII. p. 199, of Simp. Geom. but the rectangle thus infcribed in the triangle FGK, is always equal to the triangle ABC infcribed in the circle ABEC, by Euc. I. 42; the triangle ABC is, therefore, the greatest that can be infcribed in the given circle BACE, when the difference of the fegments of the bafe is equal to the given line CE.

An elegant conftruction was also given to this question by Mr. W. Richards.

48. QUESTION (III. March)

anfwered by ELTONIENSIS.

Take Maclaurin's example, page 185: viz. x3—px2+qx—r, and let the greater root (or value of x) be a, the mean b, and the leaft c. Then (by articles 13 and 19) a+b+c=p; ab+ac + bc=9; and abc=r; •• q2—2 pr=a2 b2+a2c2 +b2 c2; but a is greater than corb; 3a4 is greater than a2 b2+a2c2+b2 c2; (q2-2pr) therefore, by putting e+ = q2—2pr, =a2 b2+a2c2+ b2 c2,

£4

is lefs than

In the fecond theorem, x-px-1+qx”—2—rx^3+5x-4, &c. by fe&t. 13, and the doctrine of combinations, the terms in q (or number of products that can be 1-1; and in r (of

NI

made by multiplying any two of the roots) are equal to n x- -2

by multiplying any four of the roots, is equal to z x

2

22-2

X- X
3

4

whence it is manifeft that the number of terms a2 b2 + a2c2, &c. in q2, is equal to

2

; and the number of terms in 2pr (a2bc+a2bc+b2ac+b2ac, &c.) is

&c. is equal to 222 X

rule fails when the roots are nearly equal, and n greater than 3. For example, in the biquadratic x-px3+qx2-rx+s=0;q=ab+ac+ad, &c.

ton X *=1 (6) terms, and q2 = a2 b2 + a2 c2 + a2 d2, &c. to n2 ×

2

terms; and those of 2pr=a2bc+a2cd, &c. to 2n2 × 7

1-2
X - X
3

(2) terms:

4

terms in q2—zpr+25, when the roots are all equal to a; is manifeftly equal to 6;

6a4 and the 46x= is greater than a,which is

In the furfolid equation x5-px4+qx3—rx2+$x→t—o :

= 4√ 10 a. And the fame might be fhewn for all the

49. QUESTION

49. QUESTION (IV. March) anfwered by A COBBLER.

Let L represent the place where the fhips met, B and C the ports they failed from, LD the difference of latitude, LB, LC the distances run by the two fhips, and which, confequently, are to each other as 5 to 3, or as 1 to 3, which put=m: make p260 (not 250, as was printed in the question) the fum of the three fides, LB, LC, and BC; a=LD,=64, and xLB. Then, because 1: m :: x: mx, LC; and, by the queftion, x+mx+ √ x2—a2 + √ m2x2-a2 = p. Hence, x2--a2

C D

L

B

+√ m2x2—a2 = p-a-mx; and, by fquaring both fides of the equation, and making proper reduction, x-a2 × m2x2 - a2 = { p2 + a2—px-pmx+mx2. Put b= p2+a2, and npm, and again, fquaring both fides, we obtain 2mnx3-x2 × a2 —a2 m2 — n2a2+a2 m2 + n2+2bm abnx b2-a4 2bm+2bnx=b2-a4; or x3—

=

which in numbers is x3-448,92179487x2+63160x=2843208,33, &c. Now, in order to refolve this equation, it may be confidered that as LD is = 64, LC cannot be less than 64; and, as LC is to LB as 3 to 5, LB (x) cannot be lefs than 1063. Again, as LB cannot be less than 1063, and LD is 64, DB cannot be less than 10632 2-6412, 85,4 confequently, LB (x) cannot be fo great as 110,6. Having thus got LB within fuch narrrow limits, we readily find x 106,83, by the common methods of approximation: LC, the distance run by the other fhip, is, therefore, 64,1; and the distance of the ports 89,07 miles. The courfe of one of them is S. 53° 12′ W. and of the other S. 3° 12' E.

1=

MATHEMATICAL QUESTIONS.

64. QUESTION I. by NUMERICUS.

Q. E. I.

What three numbers are thofe, the fum of which is a cube number; and if this cube be increased by half the product of the two leaft, the fum will then be a fquare number: moreover, the fum of the fquares of the two leaft is equal to the fquare of the greatest.

65. QUESTION II. by R. M*.

Given the bafe of a plane triangle, and the fum of the fides and perpendicular, to determine the triangle when the vertical angle is a maximum.

66. QUESTION III. by Mr. THOMAS MOSS.

If upon any indefinite right line, DQ, two circles be defcribed whofe diameters DB, DC, are in any given ratio to each other, and two other circles be defcribed upon another indefinite D right line, dq, whofe diameters, db and dc are likewife in the fame given ratio of DB to DC; and if from the points B and b,

as centers, two other circles be

F

R

B

Q

*This gentleman is requested to fend anfwers to fuch questions as yet remain with the editor, as the motives for propofing thofe questions do not appear to him without them.

1784.

fo defcribed as to cut the peripheries of the two larger circles in G and g, equidiftant from the points D and d: then if any two lines be drawn from the two points D, d, cutting the peripheries of the circles in R, S, E, and F, and in r, s, e, and ƒ; and fo as to make DS = ds: I fay that the correfponding chords DR, dr, and SF, sf; as alfo the diftances RS,

rs, and RF, rf, intercepted by the two peripheries will be refpectively equal to

each other.

The answers to thefe queftions may be directed (poft-paid) to Mr. Baldwin, in Paternofter-row, London, before the 1ft of October.

BIOGRAPHY.

an

THE LIFE OF CHARLES HARLES CHURCHILL*, CHAR eminent fatiric poet, was born in Vine-street, in the parish of St. John's, Westminster, in the year 1731. His father, who was a very refpectable clergyman, was curate and lecturer of the parish, and was poffeffed, befides, of a living in the country. Young Charles, as might be expected, from the vicinity of his fituation, received his grammatical education at Weltminfter fchcol; in which he foon diftinguished himfelf fo far, as to make his tutors fentible that he was a lad of confiderable abilities. His application, however, as is too frequently the cafe with youths of lively parts, by no means kept pace with his natural talents; fo that the chief character he, obtained was, that he was a boy who One day, could do well if he would. having been enjoined to make an exercife, he failed in bringing it at the time appointed; for which reafon his mafter not only chaftifed him with fome feverity, but even charged him with, ftupidity. The laft reproach made a Charles ftrong impreffion Churchill's mind, and the fear of fhame wrought an effect which the fear of ftripes could not produce. On LOND. MAG. July, 1784.

upon

CHURCHILL.

the next day, he brought his exercife, finished in fuch a manner, that he This inftance received the public thanks of the matters of the school. of his fenfibility, and of the applaufe, that refulted from it, was not followed by a complete reformation of con lust.. The vivacity of his imagination, and the diffipation of his temper, ftill prevented his walking regularly forward in the trammels of a fcholallic educa tion. When, therefore, he was fent by, his father to the University of Oxford, he was refufed an admittance into that illuftrious feat of literature, upon account of his want of a proper skill in the learned languages. This, no doubt, was a great mortification to himself, as well as a fevere difappointment to a worthy parent. Churchill, in the fubfequent parts of his life, often mentioned his repulfe at Oxford; and the was given to it by following turn himfelf and his friends. He and they frequently afferted, that he could have anfwered the college examination had he thought proper; but that he fo much deipifed the trifling questions which were propofed to him, that, inftead of returning fuitable replies, he flections only launched out into fatical re

D

* This life is abstracted from that inforted in the new volume of the Biographia Britannisa,

flections on the abilities of the gentleman whofe office it was to make the trial of his literary improvements. If this was really the truth of the cafe, Mr. Churchill's conduct, to fay the leaft of it, was highly imprudent. Whoever wishes to receive the benefit of an univerfity education muft comply with the customary forms of admiffion; and it would be perfectly ridiculous for a young man to have it in his own power to prefcribe in what mode he fhould be examined, previoufly to his matriculation. Churchill's rejection from Oxford will fupply one very probable reafon for the feverity with which, in the courfe of his writings, he hath fometimes treated that famous feminary.

After this event, Mr. Churchill continued to profecute his ftudies at Westminster school; and there can be no caufe to doubt, but that he would foon have been efteemed properly qualified for an entrance into one of our learned univerfities, if his views of this kind had not been prevented by an act of imprudence, which had a confiderable effect upon the colour of his future life. When he was little more than feventeen years of age, he contracted an intimacy with a young lady in the neighbourhood, which fprang up into a warm affection, and was followed by a hafty marriage. This, like many others, was a match which began in paffion and ended in difguft. Their regard, however, for each other, which in its origin was mutual and fincere, was preferved in its purity and ardour for a number of years. In the fequeftered life which Mr. Churchill was now obliged to lead, he made fuch a progrefs in literature, and fuftained fo good a character, that, notwithstanding is want of an univerfity education, he was thought worthy of being admitted into holy orders, at the ufual age of obtaining them, and accordingly was ordained by Dr. Sherlock, at that zime Bishop of London. The first preferment he received in the church was a very trifling one, being only a fmall curacy of thirty pounds a-year, in Wales. To this remote part of the kingdom he carried his wife, and,

having taken a little houfe, he applied d himself to the duties of his station with affiduity and chearfulness. His behaviour gained him the love and efteem of his parishioners; and his fermons, of though fomewhat raised above the level of his audience, were commended and followed. What chiefly difturbed him was the fmallnefs of his income, which would, indeed, have been too narrow for the fupport of a family, even where a much greater degree of economy was exercifed than was fuitable to Mr. Churchill's natural difpo fition. To fupply, therefore, the deficiency of his feanty falary, he entered into a branch of trade, which he hoped might raife him to compe tence, and, perhaps, to riches; but which, in fact, involved him in debts that long involved him in perplexity and trouble. The bufinefs in which he engaged was that of keeping a cyder-warehoufe, with a view of vending that commodity in the different parts of the neighbouring country. A man of genius and a poet was but ill qualified for fuch an undertaking. Mr. Churchill could not defcend to the patience and frugality which are neceffary in the common courfe of merchandise, where fmall gains are to be quietly expected, and carefully accumulated. A kind of rural bankruptcy was, therefore, the confequence of the attempt.

The ill fuccefs of Mr. Churchill's

trading fcheme brought him back to London, and his father foon after dying, he fucceeded him as curate and lecturer in the parish of St. John's. The emoluments of his fituation not amounting to a full hundred pounds a year, in order to improve his finances, he undertook to teach young ladies to read and write English with propriety and correctnefs, and was engaged for this purpofe in the boarding-fchool of Mrs. Dennis, a governess, who had the honour of being one of the first introducers of a laudable cuftom, which hath fince been adopted in many of the reputable feminaries of female education. Mr. Churchill conducted himfelf in his new employment with all the decorum becoming his clerical profeffion. Still, however, his

method

1784

to his income; fo that he contracted a variety of debts, which he was totally incapable of paying; and a jail, the terror of indigent genius, feemed ready to clofe upon his miferies. From this wretched fituation he was relieved by the benevolent interpofition of Dr. Lloyd, the fecond mafter of Weftminfter-fchool, and father of Robert Lloyd, the poet. The Doctor undertook to treat with Churchill's creditors, and fucceeded in engaging them to confent to a compofition of five fhillings in the pound. In an inftance which fell under the knowledge of the writer of the prefent article, as an executor and a guardian, Mr. Churchill, when he had obtained money by his publications, voluntarily came, and paid the full amount of the original debt. It is highly probable, from this unfolicited and unexpected act of equitable retribution, that his conduct was the fame in fome other cafes.

method of living bore no proportion the orcheftra. From this place he thought that he could beft difcern the real workings of the paffions in the players, or the artifices which they fubftituted in the room of genuine nature and feeling. As Mr. Churchill was thus qualified, by judgement and experience, for delineating the excellencies and defects of the actors, fo the vigour of his fancy, and the ftrength of his conceptions, enabled him to do it in the moft lively colours. In the month of March 1761, the "Rofciad" appeared. The first edition stole as it were into the world, being very little advertifed, and published without a name. A fecond impreffion was foon called for, in the title page of which the author afferted his claim to his own performance. Scarcely ever was there an inftance of a poet's rifing fo fuddenly from the moft perfect obfcurity to the greateft celebrity. To this the players themfelves contributed more than any other fet of men. They ran about the town like fo many ftricken deer; and while they ftrove to extract the arrow from the wound, by communicating the knowledge of it to their friends, fpread abroad more and more the fame of the piece. It was pleasant enough to obferve how artfully fome of them, who were, in fact, the most hurt, pretended to be unaffected by the injury done to themfelves, but to feel extremely for the "Why obloquy thrown upon others. (exclaimed one of thefe difinterested perfons) fhould this man attack Mr. Havard? I am not concerned at all for myfelf; but what has poor Billy Havard done that he must be treated fo cruelly?"-" And pray (replied a gentleman who was prefent at this artificial declaration of benevolence) what has Mr. Havard done too, that he cannot bear his misfortunes as well as another?" Whilft the actors, in dif ferent ways, expreffed their refentment, the public enjoyed their diftrefs. The Rofciad was regarded, in general, as a pleafant and reasonable retaliation for the mirth which the ftage had conti nually excited, by the representation of the follies and frailties of mankind. The poem was not wholly employed in fatire. Mr. Garrick was commended

The time now approached for Mr. Churchill's appearing in the world as an author. Hitherto nothing had come from him in this character, though he was known among his acquaintance to be a man of a very vigorous imagination, and a ftrong understanding; and though he was in the habits of intimacy with Thornton, Colman, and Lloyd, who had already begun to make a confiderable figure in the republic of letters. With the laft of thefe gentlemen he was connected in the ties of the clofeft friendship. Mr. Lloyd had printed a poem, entitled the Actor, which met with a very favourable reception from the public, and juftly procured him a confiderable degree of reputation. By the fuccefs of his friend, Mr. Churchill is fuppofed to have been ftimulated (how truly we know not) to exert his poetical talents upon a fubject of a fimilar kind, though more appropriated and perfonal. The theme he pitched upon was admirably fuited to his genius and his tafte. He had long been a frequenter of the theatre, and had bestowed inceffant attention on ftage reprefentation.

The fcene of his obfervations was ufually the first row of the pit, next to

D 2

in