RECTOB OF 8WANSC0MBE, KENT. 151 



" The two books of Apollonius Pergaeus, concerning Deter- 

 minate Section, as they have been restored by Willebrordus 

 Snellius," appeared in 1772; to which were added & second 

 restoration of " the same two books by William Wales," sub- 

 sequently mathematical master of Christ's Hospital, London. 

 Mr. Lawson was induced to publish this translation from the 

 circumstance that " these pieces of Snellius" were " exceed- 

 ingly scarce in England. His Resuscitata Geometria de 

 Sectione Rationis et Spatii, 1607," he had " never once had 

 an opportunity of seeing" and "lest the other tract, De 

 Sectione Determinata, should undergo the same fate as the 

 original Apollonius, [he] was determined to rescue it there- 

 from, or respite it at least for a time, by putting it into an 

 English dress." Both this, however, and Mr. Wales's more 

 successful effort are now entirely superseded by the elaborate 

 restoration left us by Dr. Robert Simson in his Opera 

 Reliqua, which not only includes the propositions noticed by 

 Snellius and Wales, under the purest forms of the ancient 

 geometry, but adds a third and fourth book on the same 

 subject to those enumerated by Pappus. The publication by 

 which Mr. Lawson is best known is the '* Dissertation on the 

 Geometrical Analysis of the Antients; with a Collection of 

 Theorems and Problems, without Solutions, for the Exercise 

 of Young Students." It was published anonymously at 

 Canterbury in 1774, but its contents and the nature of the 

 subject left no doubt in the minds of geometers as to who 

 was the real author. At this period there was but one per- 

 son known to the mathematical world who was likely to 

 undertake such a discussion, and his propria persona was all 

 but revealed in an advertisement attached to the work. In 

 this dissertation the true principles of the ancient geometrical 

 analysis are very clearly laid down and illustrated by a variety 

 of examples, both original and selected ; various methods of 

 conducting the solution of the same geometrical proposition 

 are instanced for the encouragement of young students, and 



