. Holdred versus Nicholson. 37'? 



SiNCF. the publication of my Tract, entitled " A new Method 

 bf solving Equations," &c. Mr. Nicholson has added a Postscript 

 to his Essay on Involution and Evolution, for the purpose of re- 

 probating me, as if I had injured him, instead of his having in- 

 jured me. 



In my original manuscript [ had written the letter a for the 

 unknown root, and the letter g for the first assumed root. Mr^ 

 Nicholson would insist I should not be understood, unless I wrote 

 X for the unknown root ; the g also displeased him by its hav- 

 ing so long a tail. I had also the initials of two alphabets of 

 capital letters. Mr. Nicholson recommended to use but one, 

 and to make the distinction by a small figure underneath. 



After Mr. Nicholson had discovered another demonstration, 

 he requested me to annex it to my Tract, by way of Supplement j 

 lest any other person should discover the same way of demon- 

 strating the rule after it should be published, as quic-k as he 

 had done before ; by which he should lose the honour of being 

 first. This being agreed to, he requested me to adopt his no- 

 tation, in the general demonstration, to pave the way to his 

 Supplement ; for which I have been blamed by a very good 

 mathematician. Many more v\ords appeared to be necessary 

 to explain the matter, than bv the old notation. 



Mr. Nicholson did recommend arithmetical equivalents ; but 

 I saw no reason why he should be complimented as the inven- 

 tor, since he took it from ]Mr. Henry Briggs, the calculator of 

 logarithms. It is very convenient for practice, but has nothing 

 to do with the theory. 



I was master of the figiirate method in theorv in the year 

 17S0, but poverty kept me from publishing or jiractising it: 

 and liad it not been for Mr. Robert Gibson, I doubt if it would 

 have been publisiied yet. 



In October 131S Mr. Nicholson put an article into the Phi- 

 losophical Magazine, shov/ing how to cube a number in a man- 

 ner which was the reverse of my method of extracting the cube 

 root. It would be a great satisfaction to me, if I could certainly 

 know wliether Mr. Horner had any idea of solving ecpiations, bv 

 means of the figiirate numbers, before that circumstance ; or 

 whether it were in consequer.ee thereof. It is certaiidy remark- 

 able, that no one seemed to have any idea of the kind, until I 

 communicated it to Mr. Nicholson. 



After the manuscript was re-written, upon looking over sonic 

 examples in the old manuscript, I was .surprised at Mr. Nichol- 

 son's saying, " Why tliis would have been easy enough under- 

 stood." I Jim indeed of Mr. Nichol'oon's opinion; for if it could 

 not be understood, none of the ar.cient authors could have been 

 understood; all the exainple'i being in the 'amc form with all 

 the ancient autlu-r':. /.:; 



