204 Mr. T. T. Wilkinson's Additions to the late 



tliem under the name of " Original Theorems on the Circle," 

 and appears to have taken more than ordinary pains to complete 

 the demonstrations, and apply the properties deduced to pro- 

 blems corresponding to the theorems and others related to them. 

 The latter portion of this MS. is fully prepared for the press : — 

 five theorems are distinctly enunciated, demonstrated, and applied 

 to the solution of ten collateral problems under the extended 

 title of " Original Theorems on the Circle, with their use in the 

 detcrmuiation of some Geometrical Problems." Mr. Davies's 

 attention had evidently been drawn to this remarkable portion 

 of the MSS., for his pencilled autograph occurs at the head 

 of the page, indicating that what follows is a repetition of 

 the preceding theorems and problems. An earlier manuscript 

 appears to have been destroyed in order to form this ; and as 

 such is the case with several of the remaining ones, we may 

 reasonably account for the absence of those of earlier dates : — no 

 doubt the contents of those destroyed had already found their 

 way into periodical works and his own Geometrical Amusements, 

 and hence could readily be dispensed with after transferring what 

 was considered worthy of preservation to the manuscripts still 

 remaining. Volume IV., which is endorsed " Geometiy and 

 Algebra,'' commences with a few problems on Loci, which he 

 notes as having been "sent to Mr. Shepherd, 12th Nov. 1830." 

 The general problem of Inclinations occupies pages 2, 89, 91, 93, 

 of which a " General Analysis and Construction " are given ; 

 other portions of the volume are devoted to the consideration of 

 isolated geometrical problems from various sources, some of which 

 are noticed as sent to him by ]\Iessrs. Whitley and Shepherd ; 

 pages 101 to 132 contain a connected series of foity-two geome- 

 trical exercises originally compiled as " Lessons " for his son ; 

 and amongst these are interspersed solutions of some difficult 

 Diophantine problems, one of which is Question 310 of the Ma- 

 thematical Repository, where the " Prize Medal " is awarded to 

 "A Lady" {Mrs. Somerville) for her solution. An obituary 

 notice of Mr. William Hilton, editor of the Liverpool Student, 

 justly designated by Professor Davies as "a work of rare merit," 

 occurs in page 102, where he is stated to have died "of Apoplexy, 

 at Liverpool, on the 8th of May 1826." 



The fifth manuscript volume is entitled " Mathematical 

 Scraps," and commences with a variety of methods for drawing 

 tangents to a given circle, so as to be divided by a line given in 

 position and the point of contact into parts having a given ratio. 

 Pages 20 and 21 contain no fewer than eight methods of drawing 

 " through a given point P, a line that shall tend to the point of 

 concourse of two other lines AB and CD given in position ;" a 

 problem, for whose ready solution, by draughtsmen, the " Centre- 



