t in the theory of probabilities to which De Morgan
also gave much thought. His introduction of imaginary quantities into
trigonometry was an event of importance in the history of mathematics, and
the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]
+ i sin n[phi], is one of the most important ones in all analysis.

[767] John Dolland (1706-1761), the silk weaver who became the greatest
maker of optical instruments in his time.

[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from
his loom at Spitalfields to teach mathematics. His _New Treatise on
Fluxions_ (1737) was written only two years after he began working in
London, and six years later he was appointed professor of mathematics at
Woolwich. He wrote many works on mathematics and Simpson's Formulas for
computing trigonometric tables are still given in the text-books.

[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his
eyesight through smallpox when only a year old. At the age of 25 he began
lecturing at Cambridge on the principles of the Newtonian philosophy. His
_Algebra_, in two large volumes, was long the standard treatise on the
subject.

[770] He was not in the class with the others mentioned.

[771] Not known in the literature of mathematics.

[772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in
1842, with a third edition in 1855.

[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university
education. He studied mathematics privately and became president of the
Mathematical Society. De Morgan knew him professionally through the fact
that he was prominent in actuarial work.

[774] Referring to the contributions of Archimedes (287-212 B.C.) to the
mensuration of the sphere.

[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the
_Almagest_, a treatise founded on the works of Hipparchus.

[776] Dr. Whewell, when I communicated this song to him, started the
opinion, which I had before him, that this was a very good idea, of which
too little was made.--A. De M.

[777] See note 117, page 76.

[778] The common epithet of rank: _nobilis Tycho_, as he was a nobleman.
The writer had been at history.--A. De M.

See note 117, page 76.

[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary,
T. B. Laurus, insinuates that they fought to settle which was the best
mathematician! This seems odd, but it must be remembered