[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and teacher of mathematics. For a while he taught under Pestalozzi. Disappointed in his ambition to be professor of mathematics at Tubingen, he became a confirmed misanthrope and is said never to have left his house during the last ten years of his life. He wrote several works: _Ein Wort ueber Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814); _Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _Ueber Tradition und Schrift, Logos und Kabbala_ (1829), besides the one mentioned above. The word _coss_ in the above titles was a German name for algebra, from the Italian _cosa_ (thing), the name for the unknown quantity. It appears in English in the early name for algebra, "the cossic art." [602] See note 174, page 101. [603] See note 589, page 257. [604] He seems to have written nothing else. [605] See note 596 on page 270. The name is here spelled correctly. [606] Joseph Jacotot (1770-1840), the father of this Fortune Jacotot, was an infant prodigy. At nineteen he was made professor of the humanities at Dijon. He served in the army, and then became professor of mathematics at Dijon. He continued in his chair until the restoration of the Bourbons, and then fled to Louvain. It was here that he developed the method with which his name is usually connected. He wrote a _Mathematiques_ in 1827, which went through four editions. The _Epitome_ is by his son, Fortune. [607] He wrote on educational topics and a _Sacred History_ that went through several editions. [608] "All is in all." [609] "Know one thing and refer everything else to it," as it is often translated. [610] A writer of no reputation. [611] Sir John Lubbock (1803-1865), banker, scientist, publicist, astronomer, one of the versatile men of his time. [612] See note 165, page 99. [613] "Those about to die salute you." [614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist. He also experimented with burning mirrors, his results appearing in his _Invention des miroirs ardens pour bruler a une grande distance_ (1747). The reference here may be to his _Resolution des problemes qui regardent le jeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_ (36 volumes, 1749-1788) has overshadowed the credit due to him for his translation of Newton's work on Fluxions. [615] See page 285. This article was a supplement to No. 14 in the _Athenaeum_ Budget.--A. De M. [616] There are many similar series and products. Among the more interesting are the following: [pi] 2.2.4.4.6.6.8... ---- = ----------------, 2 1.3.3.5.5.7.7... [pi]-3 = 1 1 1 ------ = ----- - ----- + ----- - ..., 4 2.3.4 4.5.6 6.7.8 [pi] 1 1 1 1 1 ---- = sqrt - . (1 - --- + ----- - ----- + ----- - ...), 6 3 3.3 3^2.5 3^3.7 3^4.9