384 Mr, T. S. Davies on Geometry and Geometers. 



reasons can now, of course, only be conjectured from the alter- 

 ations which he made : but it only requires careful collation 

 to assign what those changes were. I am fortunately enabled 

 to give these from a MS. of the late Mr. S. P. Rigaud, Savi- 

 lian Professor of Geometry in the University of Oxford, drawn 

 up in 1815, 1816, and undertaken at the request of the late 

 Professor Leybourn of the Royal Military College, Sandhurst. 

 I believe that all who had the privilege of Professor Rigaud's 

 friendship will admit that he was, from his habitual care and 

 accuracy, eminently likely to observe even the most minute 

 variation : — they would trust his eye quite as much as their 

 own, and feel even more confidence in his transcripts than if 

 made by themselves. This collation, too, was made three 

 times over; and by a scholar resident on the spot, who could 

 examine the MSS. at his leisure, and who moreover thoroughly 

 understood the subject to which they relate. 



It was for the use of Mr. Mark Noble, one of the then 

 Sandhurst staff of Professors, that Mr. Leybourn procured 

 this collation. Mr. Noble had some years previously pub- 

 lished two short papers on Porisms, into the analysis of which 

 he conceived he had introduced material improvements. [See 

 Leybourn's Mathematical Repository, vol. i. p. 35, N.S., 

 and Gentleman's Mathematical Companion, vol. ii. p. 42.] 

 That venerable mathematician placed the papers in my hands 

 a short time ago, with the hope that they might be of use to 

 Mr. Potts and myself in preparing our notes to the translation 

 of Simson's Porisms ; and, knowing the casualties to which 

 loose papers are liable when they are vested in private families, 

 I have thought it better to secure for the public a correct copy 

 in print, whilst the MS. remains in my possession. It will 

 save, too, a good deal of trouble, and remove in some degree 

 the vagueness with which we all estimate the value of infor- 

 mation which is not generally accessible. If, too, other MSS. 

 (the Paris and Burney, for instance) were collated with the 

 same care, and printed in the same manner, all the informa- 

 tion that literature can supply on this subject would be open 

 to all; instead of being, as now, confined to a few, and ob- 

 tained even by them with much trouble and expense. 



Any notes made by Simson in his copy of Commandine 

 would also tend to utility. The Adversaria^ too, might contri- 

 bute something, were those valuable papers carefully examined. 

 Glasgow, however, has her own resident geometers ; and it is 

 not too much to hope, that regard for her own honour, and 

 veneration for her great men of past days, will operate as 

 sufficient incentives to this illustration of a book so intimately 

 connected with Simson's and with Scotland's fame. 



A short summary of the contents of the mathematical col- 



