SIMSON. 



fay that he amufed himfelf in his favourite purfuit, vsrhile 

 he was aftually preparing his exercilcs for the divinity hall. 

 When fatigued with fpeculations, in which he could not 

 meet with certainty to reward his labours, he relieved his 

 mind, ardent in the purfuit of truth, by turning to mathe- 

 matics, with which he never failed to meet with what would 

 fatisfy and refrefli him. For a long time he rellritted him- 

 felf to a very moderate ufe of the cordial, fearing that he 

 Ihould foon exhauft the ftock which fo limited and abftraft 

 a fcience was capable of yielding ; at length, however, his 

 fears were difTipated on this head, for he found that the 

 more he learned, and the farther he advanced, the more 

 there was to learn, and a dill wider field opened to his view. 

 He accordingly determined to make the mathematics the 

 profeffion of his life, and gave himfelf up to the ftudy with- 

 out referve. It is faid, that his original incitement to this 

 fcience as a treat, as fomething to pleafe and refrefli the 

 mind in the midft of feverer tallis, gave a particular turn to 

 his mathematical purfuits, from which he could never deviate. 

 He devoted himfelf chiefly to the ancient method of pure 

 geometry, and felt a decided diflike to the Cartefian method 

 of fubilituting fymbols for the operations of the mind, and 

 ftill lefs was he wilHng to admit fymbols for the objefts of 

 difcuflion, for lines, furfaces, folids, and their afteftions. 

 He was rather difpofed in the folution of an algebraical 

 problem, where quantity alone is to be confidered, to fub- 

 ilitute figure and its afFeftions for the algebraical fymbols, 

 and to convert the algebraic formula into an analogous geo- 

 metrical theorem. In fo little refpcft did he come at laft 

 to confider algebraic analyfis, as to denominate it a mere 

 mechanical knack, in which he would fay we proceed with- 

 out ideas of any kind, and retain a refult without meaning, 

 and therefore without any convidlion of its truth. 



About the age of twenty-five Dr. Simfon was chofen 

 profeflor of mathematics in the univerfity of Glafgow. He 

 immediately went to London, and there formed an ac- 

 quaintance with the moil eminent men who at that time 

 flourifhed in the metropolis. Among thefe was the cele- 

 brated Halley, of whom he always fpoke with the moil 

 marked refpeft, faying that he had more acute penetration, 

 and the moll juft talte in that fcience, of any man he had 

 ever known. Dr. Simfon alfo admired the malterly fteps 

 which fir liaac Newton was accuftnmed to take in his in- 

 veftigations, and his manner of fubftitnting geometrical 

 figures for the quantities which are obferved in the pheno- 

 mena of nature. He was accullomed to fay, that the 39th 

 propofition of the firit book of the Principia, was the moil 

 important propofilion that had ever been exhibited to the 

 phyfico-mathematical philofopher, and he ufed to illuilrate 

 to the higher clafles of his pupils, the fuperiority of the 

 geometrical over the algebraic analyfis, by comparing the 

 folution given by Newton, of the inverfe problem of cen- 

 tripetal forces, in the 42d propofition of that book, with 

 the one given by John Bernouilli, in the Memoirs of the 

 Academy of Sciences at Paris, for the year 1713. 



Returning to his mathematical chair, Dr. Simfon dif- 

 charged the duties of a profeiibr, for more than half a cen- 

 tury, with great honour to the nmiverfity and to himfelf. 

 It is fcarcely neceffary to add, that in his ledlures he always 

 made ufe of the geometry of Euclid, in preference to thofe 

 works which he thought leaned too much to analyfis. His 

 method of teaching was fimple and perfpicuous, his elocu^ 

 tion clear, and his manner eafy and impreffive. He uni- 

 formly engaged the refpecl and affeftion of his pupils. 



It was owing to the advice of Dr. Halley that our author 

 fo early direfted his efforts to the reiloration of the ancient 

 geoijieters. He had recommended this to him as the moil 



certain means of acquiring a high reputation, as well as to 

 improve his talte, and he prefented him with a copy of 

 Pappus's Mathematical Colleftions, enriched with his own 

 notes. The perfpicuity of the ancient geometrical analyfis, 

 and the elegance of the folutions which it affords, induced 

 him to engage in an arduous attempt, which was nothing lefs 

 than the entire recovery of this method. His firft tadt was 

 the reftoration of Euclid's Porifms, from the fcanty and 

 mutilated account of that work in a fingle pafiage of Pappus. 

 He, however, fucceeded, and fo early as 1 7 1 8, feems to 

 have been in poffeffion of this method of inveitigation, which 

 was confidered by the eminent geometers of antiquity as their 

 fureft guide through the intricate labyrinths of the higher 

 geometry. In 1723 Dr. Simfon gave a fpecimen of this 

 difcovery in the Philofophical Tranfaftions ; and after that 

 period he continued with unremitting afliduity to reitore 

 thofe choice porifms which Euclid had colledled, as of the 

 moil general ufe in the folution of difficult problems. 

 Having obtained the objeft of which he was in purfuit, he 

 turned his thoughts to other works of the ancient geo- 

 meters, and tlie Porifms of Euchd had now only an occa- 

 fional fhare of his attention. The Loci Plani of ApoUonius 

 were the next taflc in which he engaged, and which he com- 

 pleted in the year 1738 ; but after it was printed he was far 

 from being fatisfied that he had given the identical propo- 

 fitions of that ancient geometer ; he withheld the impreffion 

 feveral years, and it was with extreme reluftance that he 

 yielded to the entreaties of his mathematical friends in pub - 

 lifhing the work in 1 746, with fome emendations, in thofe 

 cafes in which he thought he had deviated the moil from 

 the author. Anxious for his own reputation, and fearing that 

 he had not done juilice to ApoUonius, he foon recalled all 

 the copies that were in the hands of the bookfellers, and 

 the impreffion lay by him feveral years. He afterwards 

 revifed and correifted the work, and even then did not, with- 

 out fome degree of hefitation, allow it to come into the 

 world as the reiloration of ApoUonius. The work was, 

 however, received by the public with great approbation ; the 

 author's name became better known ; and he was now con- 

 fidered as among the very firft and mod elegant geometers 

 of the age. He had, previoufly to this, publifhed his Conic 

 Sedlions, a treatife of uncommon merit, whether confidered 

 as a complete reftitution of the celebrated work of Apol- 

 lonius Perga:us, or as an excellent fyilem of this ufeful branch 

 of mathematics. This work was intended as an introduction, 

 or preparatory piece, to the ftudy of ApoUonius, and he has 

 accordingly accommodated it to this purpofe. The inti- 

 mate acquaintance which Dr. Simfon had now acquired 

 with aU the original works of the ancient geometers, as well 

 as with their com.mentators and critics, encouraged him to 

 hope that he ihould be able to rellore to its original itate 

 that molt ufeful of them all, the Elements of Euclid, and 

 under the impreffion of this idea, he began ferioufly to make 

 preparation for a new and more perfetl edition. The errors 

 which had crept into this celebrated work appeared to re- 

 qi;ire the mofl careful efforts for their extirpation ; and the 

 data alfo, which were in like manner the introduftion to tiie 

 whole art of geometrical inveitigation, feemed to call for the 

 nobleft exertions of a real mailer in the fcience. The data 

 of Euclid have fortunately been preferved, but the work 

 was neglected, and the few ancient copies, which amount only 

 to three or four, are faid to be wretchedly mutilated and er- 

 roneous. It had, however, been rellored, with fome degree 

 of fuccefs, by previous authors ; but Dr. Simfon's view of 

 the whole analytical fyilem pointed out to him many parts 

 which ftill required amendment. He therefore made its 

 reftitution a joint talk with that of the Elements, and all 



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