Thomas Simpson

b. 20 August 1710 Market Bosworth, Leicestershire
d. 14 May 1761

Thomas Simpson, although self-educated in mathematics, was quite able. He wrote a number of instructional works as well as did original research. However, Simpson was also sometimes accused of plagiarism. This latter was indeed the case with Moivre related to his work on annuities. As for his life, consult the one written by Hutton which is included in the edition of the Select Exercises noted below.

Among the several books he wrote, the following are of interest.

The Nature and Laws of Chance (1740)
The Doctrine of Annuities and Reversions (1742)
Select Exercises for young proficients in the mathematicks (1752) The link is to the reprint edited by Charles Hutton and published in 1792.
Miscellaneous Tracts on Some Curious Subjects in Mechanics, Physical Astronomy and Speculative Mathematics (1757).

The interest we have in Simpson lies in his study of the arithmetic mean. He contributed a paper to the Philosophical Transactions 49 in 1755. "A Letter to the Right Honourable George Earl of Macclesfield, President of the Royal Society, on the Advantage of taking the Mean of a Number of Observations, in practical Astronomy." This was followed in 1757 by a similar paper in the Miscellaneous Tracts. For which see the Advantages of the Mean at the York University site.