[34] For example, if θ = 90° we should have 3 cos 30° = 1 + √(4 - sin2 90°), or 3.½ √3 = 1 + √3, or ½ √3 = 1.
[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at Serampore when the East India Company took over the control in 1807. He entered the British medical service and was invalided to England in 1828. His Plantae Asiaticae Rariores (3 vols., London, 1830-1832) was recognized as a standard. He became vice-president of the Linnean Society, F. R. S., and fellow of the Royal Asiatic Society.
[36] But if θ = 90° this asserts that
| cos 30° = | (sin 270° . cos 225° + sin2 90° . sin 225°) √(sin2 270° . cos2 225° + sin4 90° + sin 270° . sin 450° . sin2 90°) | , |
or that
| ½ √3 = | -1 . (-1 /√2) + 1 . (-1/√2) √(1 . ½ + 1 - 1 . 1 . 1) | = 0 / √½, |
so that De Morgan must have made some error in copying.
[37] John Bonnycastle (died in 1821) was professor of mathematics at Woolwich. His edition of Bossut's History of Mathematics (1803), and his works on elementary mathematics were well known.
[38] The bibliographies give Husaín Rifki as the translator, a practical geometry as the work, and 1802 as the date.
[39] See Vol. I, page 309, note 2 {670}.