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Mathematical Treasure: Francis Maseres's Doctrine of Permutations

Frank J. Swetz and Victor J. Katz

Maseres title page


This is the title page of The Doctrine of Permutations and Combinations, being an essential and fundamental part of the Doctrine of Chance, compiled and published by Francis Maseres, in London in 1795. Maseres (1731 -- 1824) was a London solicitor and minor mathematician. In this book, he collects some of the writings of leading mathematicians of his time dealing with permutations and chance. Its contents include: an English language translation of the first three chapters of the second part of Jacob Bernoulli's Ars Conjectandi; Isaac Newton’s discussions of the binomial theorem and comments by John Wallis, Thomas Simpson, Charles Hutton, Nicholas Saunderson, Gottfried Leibniz and others.


Maseres p. 282


Page 282 of the Doctrine of Permutations introduces the section by Wallis on counting techniques.


Maseres p. 283


Page 283 of the Doctrine of Permutations and Combinations contains John Wallis’ discussion of techniques of counting.

See images of Maseres’ Doctrine of Permutations from the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasure: Francis Maseres's Doctrine of Permutations," Convergence (January 2011)


Mathematical Treasures from the Smith and Plimpton Collections at Columbia University