merit in speaking of the red triangle instead of the triangle ABC, but
not enough to give the method any standing. His _Dual Arithmetic_
(1863-1867) was also a curious work.

[706] Brenan also wrote on English composition (1829), a work that went
through fourteen editions by 1865; a work entitled _The Foreigner's English
Conjugator_ (1831), and a work on the national debt.

[707] See note 211, page 112.

[708] See note 592, page 261.

[709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions
(1852), was an infant prodigy, competing with Zerah Colburn as a child. He
was a linguist of remarkable powers, being able, at thirteen years of age,
to boast that he knew as many languages as he had lived years. When only
sixteen he found an error in Laplace's _Mecanique celeste_. When only
twenty-two he was appointed Andrews professor of astronomy, and he soon
after became Astronomer Royal of Ireland. He was knighted in 1835. His
earlier work was on optics, his _Theory of Systems of Rays_ appearing in
1823. In 1827 he published a paper on the principle of _Varying Action_. He
also wrote on dynamics.

[710] "Let him not leave the kingdom,"--a legal phrase.

[711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807),
who edited Lambert's _Logische und philosophische Abhandlungen_, Berlin,
1782. He was astronomer of the Academy of Sciences at Berlin.

[712] Jacob Bernoulli (1654-1705) was one of the two brothers who founded
the famous Bernoulli family of mathematicians, the other being Johann I.
His _Ars conjectandi_ (1713), published posthumously, was the first
distinct treatise on probabilities.

[713] Johann Heinrich Lambert (1728-1777) was one of the most learned men
of his time. Although interested chiefly in mathematics, he wrote also on
science, logic, and philosophy.

[714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, and
founder of the _Annales de mathematiques_ (1810).

[715] Gottfried Ploucquet (1716-1790) was at first a clergyman, but
afterwards became professor of logic at Tuebingen.

[716] "In the premises let the middle term be omitted; what remains
indicates the conclusion."

[717] Probably Sir William Edmond Logan (1789-1875), who became so
interested in geology as to be placed at the head of the geological survey
of Canada (1842). The University of Montreal conferred the title LL.D. upon
him, and Napoleon III gave him the cross of the Legion of Honor.

[