SIMSON. 491 



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 whose writings 

 have no standard by which to estimate their merits 

 with exactness. 



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 Determi- 

 nate Section, or the various propositions respecting 

 the properties of the squares and rectangles of seg- 

 ments 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 pecu- 

 liarly adapted to the algebraical method, presenting, 

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

 Pergeean treatise is the less to be deplored, and its re- 

 storation was the less to be desired. Apollonius had 

 even thought it expedient to give a double set of solu- 

 tions ; 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 



