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TAYLOR, BROOK. 



TAYLOR, BROOK. 



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largest and moat important pictures is 'The Highland Larder 

 Weigbiug the Stag,' which has been excellently engraved in mezzotint 

 by Mr. C. Lewis. The ' Festival of the Popinjay,' ' Morning of the 

 12th of August Unkennelling the Hounds,' ' The Vicar of Wakefield's 

 Family going to Church," &c., are among the best known of his larger 

 compositions. Mr. Tayler has also drawn a good many illustrations 

 for books, 



TAYLOR, BROOK. Referring to the ARTS AND SCIENCES Division 

 of our work for an account of TAYLOR'S THEOREM, and of the methods 

 of algebraical development which are the consequences of it, we here 

 confine our attention to such points in the history of Taylor himself 

 and that of his theorem, as can be recovered from the neglect into 

 which they have fallen, at least in this country. 



Nothing is said of Brook Taylor in the ' Biographia Britannica,' or 

 Martin's 'Biographia Philosophica;' and Hutton, &c., give nothing but 

 the date of his birth and death, entrance into college and the Royal 

 Society. The ' Biographic Universelle ' was the first work which gave 

 any detail of his life, and this is due to the following circumstance : 

 In 1790, some members of the French Academy, struck with the 

 scantiness of the existing information relative to so celebrated a man, re- 

 quested Mr. W. Sevrard to make some inquiry on the subject in England. 

 This gentleman applied to Sir William Young, Brook Taylor's grandson, 

 who accordingly drew up an account of his ancestor from family 

 materials, and printed and circulated it privately. This account, 

 which was not published, was entitled ' Contemplatio Philosophica, a 

 posthumous work of the late Brook Taylor, LL.D., F.R.S., some time 

 secretary of the Royal Society. To which is prefixed a Life of the 

 author, by his grandson, Sir William Young, Bart., F.R.S., A.S.S., with 

 an appendix, containing sundry original papers, &c., London, printed 

 by W. Bulmer and Co., Shakspeare Printing-office, 1793.' The account 

 given by Prony in the 'Biographic Universelle' (1826) is, we are 

 almost sure, one drawn up at the time from Sir W. Young's manu- 

 script account as forwarded to Paris; with parenthetical sentences 

 inserted just before publication. It is from this work that the following 

 account is taken, as to the facts of his private life : 



Brook Taylor was born at Edmonton, August 18, 1635, and was the 

 son of John Taylor, of Bifrons House in Kent, by Olivia, daughter of 

 Sir Nicholas Tempest, of Durham, Baronet. John Taylor was the 

 eon of Nathaniel, who, to use a phrase of his own diary, "tugged and 

 wrestled with the Lord in prayer," and was member (elected by 

 Cromwell's summons) for the county of Bedford in the (Barebones) 

 parliament of 1653. Brook Taylor's father was the most despotic of 

 parents : his son was educated at home, where, besides enough of the 

 usual learning to enable him to begin residence at St. John's Cam- 

 bridge in 1701, he became excellent both in music and painting. 

 " His numerous family were generally proficient in music, but the 

 domestic hero of the art was the subject of this memoir. In a large 

 family picture he is represented, at the age of thirteen, sitting in the 

 centre of his brothers and sisters, the two elder of whom crown him 

 with laurel bearing the insignia of harmony," The paintings of the 

 future writer on perspective are represented as not needing the 

 allowance always made for amateurs, but as capable of bearing the 

 closest scrutiny of artists. At Cambridge he applied himself to 

 mathematics, and acquired early the notice of Keil, Machin, and 

 others. His first writing was on the centre of oscillation, in 1708, as 

 appears by a letter to Keil, (afterwards given in ' Phil. Trans.,' 1713, 

 No. 337). In 1709 he took the degree of LL.B., in 1714 that of 

 LL.D. : in 1712 he was elected to the Royal Society. As yet he had 

 published nothing : his letters to Machin (preserved in his family), 

 from 1709 to 1712, treat of various subjects; and, in particular, 

 contain a solution of Kepler's problem. We may here conveniently 

 put together a complete list of his works. 



In the ' Philosophical Transactions,' 1712 (No. 336), On the ascent 

 of water between two glass planes; 1713 (No. 337), On the centre of 

 oscillation ; also on the motion of a vibrating string : in the same 

 year, a paper on Music, not printed. 1713 (No. 344), Account of 

 experiment made with Hawksbeo on the law of attraction of the 

 magnet. 1717 (No. 352), Method of Approximation to the roots of 

 equations ; (No. 353), Appendix to Montmort on infinite series ; 

 (No. 354), Solution of a problem proposed by Leibnitz. 1719 

 (No. 360), lieply to the accusations of John Bernoulli. 1721 (No. 

 367), Propositions on the parabolic motion of projectiles; (No. 

 368), Experiments on magnetism. 1723 (No. 376), On the expan- 

 sion of the thermometer. Besides these, the separate publications 

 are : 



1715. Methodus incrementorum directa et inversa. Londiui 1715. 

 Linear perspective, or a new method of representing justly all manner 

 of objects as they appear to the eye in all situations. London. 1719. 

 New principles of Linear perspective, or the art of designing on a 

 plane the representations of all sorts of objects in a more general 

 and simple method than has been done before. London. A different 

 work from the former : its second edition (called the third, by an 

 obvious mistake) bears 'revised and corrected by John Colson, 

 London, 1749.' Joshua Kirby's well-known work, though called 

 Brook Taylor's perspective, is not an edition of Taylor, but a new 

 work founded on hid methods. 



In January 1714, he was chosen secretary of the Royal Society. In 

 1716, he visited his friends Montmort and Conti at Paris. He had 



just had a warm correspondence with the former on the Newtonian 

 doctrine, and on the tenets of Malebranche. His posthumous work, or 

 rather tract, the ' Coutemplatio Philosophica,' seems to contain his 

 latest thoughts on the opinions of Malebranche and Leibnitz. In 

 France he formed the acquaintance of Bishop Bossuet and Lord and 

 Lady Bolingbroke, with all of whom Sir W. Young has printed 

 some of the correspondence. He returned to England in February 

 1717; but his health was now impaired, and, throwing up the secre- 

 taryship in October 1718, he retired to Aix-la-Chapelle. On returning 

 to England early in 1719, he seems to have abandoned the mathe- 

 matics almost entirely ; among his papers of this period are essays on 

 Jewish Sacrifices, and on the lawfulness of eating blood. At the end 

 of 1720 he went to visit Lord Bolingbroke at La Source, near Orleans, 

 and returned to England in 1721. After the middle of this year he 

 wrote nothing for publication, nor could his grandson find anything of 

 a mathematical character among his papers, with the exception of 

 reference to a treatise on logarithms, which it seems he placed in the 

 hands of his friend Lord Paisley (afterwards Abercorn) to prepare for 

 the press, but which was never printed. 



At the end of 1721 he married a young lady of small fortune, a 

 circumstance which occasioned a rupture with his father. Some 

 months after his marriage, and when there appeared hope of issue, his 

 wife was informed that the birth of a son would probably accomplish 

 a reconciliation between her husband and his father. On this she 

 fixed her mind with such earnestness, that on finding herself in du 

 time actually delivered of a son, she " literally died of joy : " the infant 

 also perished. This melancholy event led to the reconciliation the 

 hope of which had caused it, but not till the autumn of 1723. Dr. 

 Taylor returned to his father's house, and in 1725, with his father's 

 consent, married the daughter of a neighbouring proprietor. In 17i"J 

 he succeeded to the family estate by the death of his father, and in the 

 following year his wife died iu giving birth to a daughter, afterwards 

 the mother of the writer of the memoir from which we cite. This 

 blow was fatal; Lord Boliugbroke, now settled again in England, 

 endeavoured to divert the thoughts of his friend by inducing him to 

 pass soine time in his house, but in about a year after the stroke, 

 Dr. Taylor died of decline (in London, we suppose), December 29, 

 1731, and was buried iu the churchyard of Saint Anne's, Soho. The 

 family estate of Bifrons is still in the possession of the descendants of 

 his brother Herbert. 



We shall dismiss other points with brief notice, and as well known, 

 in order to come to the history of the theorem : such are the celebrity 

 of Taylor's solution of the problem of vibrating chords, the questions 

 he proposed to the foreign mathematicians in the war of problems, 

 his answer to those of Leibnitz, the accusation of plagiarism made 

 against him by John Bernoulli, and his reply. With reference to the 

 celebrated works on perspective, the first was mathematical, the 

 second intended for artists who hardly knew anything of geometry. 

 Bernoulli charged Taylor with having taken his method from another, 

 and Prony states that it is in fact the one given by Guido Ubaldi, 

 though he thinks Taylor could not have seen that method. The work 

 referred to is ' Guidi Ubaldi Perspective Libri Sex,' Pisauri, 1600, 

 at which we have looked in consequence. Nothing is more easy than 

 assertion about old books : if Prony had really looked attentively at 

 the works of Ubaldi and of Taylor together, he would have seen that 

 whereas Ubaldi's work the very title page of which announces by a 

 diagram that its distinctive feature is the use of vanishing points all at 

 the height of the eye only introduced the use of vanishing points as 

 to lines which are horizontal (the picture being vertical), Taylor 

 introduced the method of vanishing points for all lines whatsoever, 

 and made them of universal application. We cannot think that he 

 had never seen Ubaldi's work : a man of learning, an artist from early 

 youth, was not likely to be ignorant of so celebrated a production. 

 He must have seen, and generalised, the method given, by Ubaldi. If 

 indeed any one between the two is asserted to have a claim, that 

 claim, when proposed, must be discussed : but a general charge of 

 plagiarism from John Bernoulli is literally no more than a record of 

 the fact that the party accused and John- Bernoulli had had a quarrel, 

 while what relates to Ubaldi is only so far true in that Ubaldi used 

 the particular and Taylor the general method. It is not credible 

 that Ubaldi was ignorant of the general proposition, or if he were so, 

 Stevinus (whose ' Sciagraphia ' was published in 1608) was not; 

 (' Sciagraphia,' prop, iii.) but Stevinus did not use any vanishing points, 

 except those of Hues parallel to the ground, nor Ubaldi neither : 

 while Taylor did use them, which is the distinctive feature of his 

 system. Again, it is a strong presumption in favour of Taylor's origi- 

 nality in this point, that works published abroad shortly after his 

 time do not contain it. For example, the ' Kurzgefasste Eiuleitung 

 zur Perspectiv, von J. C. Bischoff, 1741,' a quarter of a century after 

 the time of Taylor's publication, contains no use of vanishing poiuta 

 except at the height of the eye. 



The ' Methodus Incrementorum' is the first treatise in which what 

 is at this day called the calculus of finite differences is proposed for 

 consideration. Besides what are now the most common theorems in 

 this subject, there are various purely fluxional or infinitesimal theories, 

 such as the change of the independent variable integrations, J. Ber- 

 noulli's series, &c., and various applications to interpolation, the 

 vibrating chord, the catenary, dome, &c., centre of oscillation and per- 



