20\> Mr. T. S. Davies on Geometry and Geometers. 



with the Societie. Whether has the Scribbleriad any connexion 

 with this affair, and against whom is it intended ? for I have seen 

 only the first part of it. adieu." 



These three letters fully prove the period of the publication 

 of the Loci Plani ; whilst the quaint stile and the indications 

 of Simson's methodical habits, give independent interest to 

 them. I find amongst these letters no further reference to 

 the work in question till near the close of the correspondence, 

 namely in a letter dated June 29, 1767, a few months before 

 his death, and when he had nearly completed his eightieth 

 year. He says : — 



" I am sorry the Loci plani do not Sell, but indeed the taste for 

 the Antient Geometry or indeed any Geometry seems to be quite 

 worn out, and for want of acquaintance with it not a few blunders 

 appear in the modern books ; I know not if you have observed one 

 in Kirkby's book of the doctrine of ultimators, which even a tolerable 

 knowledge in the Algebraick doctrine of Loci might have prevented ; 

 in page 1 15 at the bottom you see there and in next page he makes 

 the curve which he calls Pyriformis to be of a different kind from the 

 Ellipsis, but in page 125 where he gives you the ^Equation of it, viz: 

 2cv—vv i —v=s it appears to be formed by two arches of two equal 

 and Similar Ellipses meeting one another. I could not prevail with 

 myself to read his doctrine of Ultimators tho Mr. Will. Trail lent me 

 the book to consider Something about that Doctrine ; Pray let me 

 know what you or any of your friends that deal in these things think 

 of his performance, and if he sufficiently makes out what he designed. 



" Could I think I were able, both in respect of memory and eye 

 Sight, to print Apollonius two books de Sectione Determinate, 

 which Mr. Trail who is here, and is to stay till October, has from 

 me for some weeks past to read over and observe any errors, I would 

 when I published them put the Loci plani after them ; perhaps the 

 Novelty of the first might help off the other. Mr. Trail is very 

 urgent with me to make the wooden cuts, which I believe I shall do 

 even tho' they should never be used by me ; If I come the length 

 of resolving to print, I shall write to you for paper. 



" I wish your health and business, both which I heartily pray may 

 encrease, could allow you to write to me oftener, it would refresh 

 me much. Pray let me know how much I am in your debt, and let 

 our Accounts be Settled and cleared. I believe I wrote to you for- 

 merly that, if I can do no better, I design to send you the copies of 

 the Loci plani and the Latin 4 t0 Euclide of which I have a good 

 number, for any price you think fit, or for no price at all rather than 

 let them lie useless beside me." 



The last letter of this series is dated Sept. 11, 1767 (pro- 

 bably his last letter to Nourse), a few months before his death. 

 As I have intentionally left the correspondence respecting the 

 publication of his eight books of Euclid and the data to form 



