T A Y 



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T A Y 



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 

 x Biographic Universelle' was the first work which gave 

 any detail of his life, and this is due to the following cir- 

 cumstance : In 1790, some members of the French Aca- 

 demy, struck with the scantiness of the existing informa- 

 tion relative to so celebrated a man, requested Mr. William 

 Seward 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 cir- 

 culated it privately. It is from this work that the follow- 

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



lirook Taylor was born at Edmonton, August 18, 1685, 

 and was the son of John Taylor, of Bifrons House in Kent, 

 liy Olivia, daughter of Sir Nicholas Tempest, of Durham, 

 Baronet. John Taylor was the son of Nathaniel, who, to 

 use a phrase of his ownt diary, 'tugged and wrestled with 

 the Lord in prayer,' and was member (elected by Crom- 

 well's summons; for the county of Bedford in the (Bare- 

 bones) 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, Cambridge, 

 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 nge 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 

 1 709 he took the degree of I.L.B., in 1714 that of LL.D. : in 

 I712hewaselected to the Royal Society. As yet he had pub- 

 lished nothing: his letters to Machin (preserved in his fa- 

 mily , 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. 33C), On 

 the ascent of water between two glass planes ; 1713 

 (No. 337), On the centre of oscillation ; also on the mo- 

 tion of a vibrating string : in the same year, a paper on 

 Music, not printed. 1713 (No. 344), Account of experi- 

 ment made with Hawksbee on the law of attraction of the 

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

 the roots of equations; (No. 353) Appendix to Mont- 

 mort on infinite series; (No. 354) Solution of a problem 

 proposed by Leibnitz. 1719 (No. 360), Reply to the accu- 

 .-ittions of John Bernoulli. 1721 (No. 367"), Propositions 

 on the parabolic motion of projectiles ; (No. 368) Expe- 

 riments on magnetism. 1723 (No. 376), On the expansion 

 of the thermometer. Besides these, the separate publi- 

 cations are : 



1715. Methodus incrementorum directa et inversa. Lon- 

 dini. 



1715. Linear perspective, or a new method of represent- 

 ing 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 

 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 

 culled Brook Taylor's perspective, is not an edition of 

 Taylor, but a new work founded on his methods. 



Not publinhrtl. Contemplatio Philo-'oiihica; a jK^lhiimons work of tho 

 Ule Brook T:i' lor. I.L.I).. F.ll S., Rome linn- secretary of the Uo>al Society. 

 Tow hi- h i- pn'li \.-.l a Lite of tin: author, by liii ;.'VIM<|-[.H. Sir William YUMI',.. 

 Hurt. F.K.S., A.SS., \ilh ;in anjjemlix, containing Mindly original ii.qjcjs, 

 .rul .ti, | rinf-'l liy W. Hiilmcr nnil t'o., shakspcrue I'rint'iiiL' -illi'-c, 17'.i;{ ' 

 Th.' n. r.unt !fh'-n h> I'l-.ii', in thr ' l;in;:r.i]>lii>' I "nn (TM'lle ' (l^Jt'O is, we are 

 aimo-it Min-, out- drawn tip .-it tlie tim" from Sir W. Young's manirri i : ,i ..n-^nttt 

 m for ! sentences inserted just before i ul) 



t Hi* ^rnnlv>t)'t l*|'tisrnal name waa probably in memory of the noted 

 puritan, Lord Brouk. 



In January, 1714, he was chosen secretary of the Ko.yal 

 Society. In 1716 he visited Kits friends Montmort anil 

 Cpnti 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 ' Contcmplatio Philosophical seems to contain 

 his latest thoughts on the opinions of Malebranche and 

 Leibnitz. In France he formed the acquaintance of Bi- 

 shop Bossuet and Lord and Lady Bolingbroke, with all of 

 whom Sir W. Young has printed some of the correspon- 

 dence. 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 mathematics 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 Or- 

 leans, 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 had 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 reconcilia- 

 tion between her husband and his father. On this she fixed 

 her mind with such earnestness, that on finding herself 

 in due 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 

 1729 he succeeded to the family estate by the death of his 

 father, and in the following year his wife died in giving 

 birth to a daughter, afterwards the mother of the writer of 

 the memoir from which we cite. This blow was fatal ; 

 Lord Bolingbroke, now settled again in England, endea- 

 voured to divert the thoughts of his friend by inducing 

 him to pass some 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 in 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 older 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 

 tn 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 mathematital, 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 byGuidoUbaldi, 

 though he thinks Taylor could not have seen that method. 

 The work referred to is ' Guidi Ubaldi Perspectives Libri 

 Sex,'_Pisauri, 1600, at which we have looked in conse- 

 quence. 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 nave seen that 

 whereas the formert 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 appli- 

 cation. We cannot think that he had never seen LIbaldi'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 generalized, the method given by 

 Ubaldi. If indeed any one between the two is asserted to 

 have a claim, that claim, when proposed, must be dis- 

 cussed : but a general charge of plagiarism from John 

 Bernoulli is literally no more than a record of the fact that 



* Fontenpllc, in his Kloge of Malebranche, says that the * Kecherche cle la 

 Vi'riliV was translate*! into I'.iiylish liy a relative of Taylor of the same name. 



+ 'Hie very title pfi^e of tTbaUH's work announces by a diagram that its 

 distinctive feature is the use of vanuliing points all at the height of the eve. 



