ANCIENT ANALYSIS. POEISMS. 69 



then persuaded to let the book appear, and it was published 

 in 1746. His former scruples and alarms recurred ; he 

 stopped the publication ; he bought up the copies that had 

 been sold ; he kept them three years longer by him ; and it 

 was only in 1749 that the work really appeared. Thus had a 

 geometrician complied with the rule prescribed by Horace for 

 those who have no standard by which to estimate with exact- 

 ness the merit of their writings. 



In the meantime he had extended his researches into other 

 parts of the subject. Among the rest he had restored and 

 greatly extended the work on Determinate Section, or the 

 various propositions respecting the properties of the squares 

 and rectangles of segments of lines passing through given 

 points. There is no doubt that the prolixity, however 

 elegant, with which the ancients treated this subject, is 

 somewhat out of proportion to its importance ; and as it is 

 peculiarly adapted to the algebraical method, presenting, 

 indeed, little difficulty, to the analyst, the loss of the Per- 

 gsean treatise is the less to be deplored, and its restoration 

 was the less to be desired. Apollonius had even thought it 

 expedient to give a double set of solutions ; one by straight 

 lines, the other by semicircles. Dr. Simson's restoration is 

 most full, certainly, and contains many and large additions of 

 his own. It fills above three hundred quarto pages. His 

 predecessors had been Snellius, whose attempt, published in 

 1608, was universally allowed to be a failure ; and Anderson, 

 a professor of Aberdeen, whose work, in 1612, was much 

 better, but confined to a small part only of the subject. 



About the time that Dr. Simson finally published the Loci 

 Plani, he began his great labour of giving a correct and full 

 edition of the Elements. The manner in which this has been 

 accomplished by him is well known. The utmost care was 

 bestowed on the revision of the text ; no pains were spared in 

 collating editions ; all commentaries were consulted ; and the 

 elegance and perfect method of the original has been so 

 admirably preserved, that no rival has ever yet risen up to 

 dispute with Simson's Euclid the possession of the schools. 



