Mr. T. S. Davies's Notes on Geometry and Geometers. 205 



linead" was expressly invented. The eighth method being re- 

 markably simple is hei'e transcribed : — 



"Draw PH, PK, parallel to AB and CD; and the required 

 line PQ will pass through L the poiiat of bisection of HK.-''' 



"Some problems (19) on the Maxima'^ and their application 

 occupy pages 32-45, one of which is noted as " sent to Whitley," 

 and another difficult theorem "to puzzle Shepherd;" — a "new 

 Theorem from ]\Ir. Whitley " and a " Locus from Mr. Shepherd " 

 are merely enunciated whilst the rest are constructed only. The 

 latter portion of the MS. contains solutions to some of the most 

 difficult equations in Bland's algebraical problems, several of 

 which exhibit a ready command of algebraical artifice, and the 

 remainder is filled up with extracts from works having no relation 

 to mathematical subjects. 



The title of volume VI. almost sufficiently explains its con- 

 tents : — it is " Memorandums, Scraps, Mathematical, Poetical, 

 Biographical, Satirical, &c. &c. &c. ;" and a slight inspection 

 proves that its designation is not unaptly chosen. A letter to a 

 friend occurs at page 42, in which he complains that " scientific 

 matters are with [him] at such a very low ebb that [he] cannot 



treat him with any novelties In the mean time " he hopes 



his friend, " yet in the spring of life, is not unmindful of those 

 ennobling subjects in which [he] had evinced so much ardour 

 and ability. In the midst of analytical inquiries," he adds, " be 

 pleased to recollect that Euclid existed 300 years before Christ, 

 and that you are yet nearly a stranger to those Elements which 

 have confen-ed imperishable renown on their Author and Com- 

 piler." j\Ir. Swale was ever anxious that the ancient geometry 

 should be in the ascendant ; nor did he ever omit an opportunity 

 of impressing the beauties of his " Divine Geometry " upon the 

 minds of his younger correspondents. The statical problems 

 alluded to by Professor Davies occur in this volume, but present 

 no difficulties worthy of notice, since they relate principally to 

 the equilibrium of cones, cylinders, and spheres on an inclined 

 plane, most of which admit of easy geometrical constructions. 

 In a letter to Mr. John Whitley, pages 74-77, dated "9th Feb. 

 1809," he inquires why the "Inscription Problem," as Mr. Davies 

 terms it, has b; en repi-oposed in the Companion, since all "must 

 allow that Mr. Lowry's general method in the Repositozy is suf- 

 ficiently elegant;" but almost immediately adds, "I have disco- 

 vered a general method of inscribing polygons in a given circle, 

 each side passing through a given ])oint, which is also applicable 

 to the ellipse." The method itself was subsequently published 

 in the Apollonius, No. II. pj). 41-52, and has already attracted 

 the attention of several of our ablest geometers, amongst whom 

 may be mentioned Messrs. Potts, Gaskin and Davies ; it is inter- 



