Mr. T. S. Davies on Geometry and Geometers. 537 



A small number of copies only must have been printed, as I have 

 never seen a single copy for sale or catalogued in any shape. 

 The work, in fact, to use a common expression, " fell still-born 

 from the press j" and it is not only generally imknovvn to mere 

 amateur geometers, but almost without exception to the working 

 geometers of the present day. I do not remember to have seen 

 it quoted even once in the ])eriodicals more especially devoted to 

 geometry, so that it stands in almost the same position as it 

 would have done amongst the author's J\ISS. It is no wonder, 

 then, that the promised parts 2 and 3 never made their ap- 

 pearance. 



Nevertheless this volume contains some of the most elaborate 

 and elegant geometry (in the true spirit of the ancients, but per- 

 fectly unshackled as to any anterior works) that exist in our 

 language, or probably in any language whatever. The part 

 actually published is composed wholly of problems : first, the 

 constructions and demonstrations alone being succinctly given ; 

 and then a more difficidt sei'ies (including amongst them, and 

 indeed forming the simplest of them, the i\.pollonian series) ^ith 

 the analyses prefixed to the constructions. The entire series is 

 founded on a single lemmatical problem : — 

 i " Having two points and three right lines given in position : 

 to draw from the given points, two right lines intersecting each 

 other at a point in one of the lines given in position, and making 

 equal angles with the two remaining lines given in position." 



He gives the construction and demonstration of all the cases 

 that are essentially different : but any further analysis of the 

 work would require more space than it would be proper to occupy 

 in the Philosophical Magazine with reference to a printed work, 

 however valuable, scarce and inaccessible. He states that "parts ii. 

 and Hi. are ready for press :" but I am ignorant as to what 

 became of the MS. 



Though to call a work of such difficulty " amusements " might 

 seem to savour of affectation, yet by Mr. Swale I am convinced 

 that the term might be used with perfect propriety : but of this, 

 anon. 



Mr. Swale, finding that, like Simson's Loci Plani, his amuse- 

 ments " did not sell," seems to have abandoned his purpose. At 



numerous references to tlie writinj^s of the late Professor, and his memoir 

 was reprinted with some alterations in No. 42 of the Educational Times. 

 The Westminster Review for the i)rescnt month (April) also contains an 

 article on ' English Mathematical Literature,' which will be read with in- 

 terest h\ the cultivators of that science of which Professor Davies was so 

 great a master. — James Cockle. 



" 2 Pump Court, Temple, 

 April 23, 1851."] 



Phil. May. S. 4. No. 7. Supjd. Vol. 1. 2 



