[pi] 1 1 1 1 ---- = 4 ( - - ----- + ----- - ----- + ...) 4 5 3.5^3 5.5^5 7.5^7 1 1 1 - ( --- - ------- + ------- - ...). 239 3.239^3 5.239^5 [617] "To a privateer, a privateer and a half." [618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance Society. He wrote _A Treatise on the Valuation of Annuities and Assurances on Lives and Survivorships; on the Construction of tables of mortality; and on the Probabilities and Expectations of Life_, London, 1815. Upon the basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed the mortality tables then in use and which were based upon the Northampton table of Dr. Price. His work revolutionized the actuarial science of the time. In later years he devoted his attention to natural history. [619] See note 576, page 252. He also wrote the _Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the equiangular spiral_ (London, 1840), which went through four editions, and the _Theory of Parallels. The proof that the three angles of a triangle are equal to two right angles looked for in the inflation of the sphere_ (London, 1853), of which there were three editions. [620] For the latest summary, see W. B. Frankland, _Theories of Parallelism, an historical critique_, Cambridge, 1910. [621] Joseph Louis Lagrange (1736-1813), author of the _Mecanique analytique_ (1788), _Theorie des functions analytiques_ (1797), _Traite de la resolution des equations numeriques de tous degres_ (1798), _Lecons sur le calcul des fonctions_ (1806), and many memoirs. Although born in Turin and spending twenty of his best years in Germany, he is commonly looked upon as the great leader of French mathematicians. The last twenty-seven years of his life were spent in Paris, and his remarkable productivity continued to the time of his death. His genius in the theory of numbers was probably never excelled except by Fermat. He received very high honors at the hands of Napoleon and was on the first staff of the Ecole polytechnique (1797). [622] "I shall have to think it over again." [623] Henry Goulburn (1784-1856) held various government posts. He was under-secretary for war and the colonies (1813), commissioner to negotiate peace with America (1814), chief secretary to the Lord Lieutenant of Ireland (1821), and several times Chancellor of the Exchequer. On the occasion mentioned by De Morgan he was standing for parliament, and was successful. [624] On Drinkwater Bethune see note 165, page 99. [625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He was town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_ (1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death. Thompson Cooper was his son, and the two collaborated in the _Athenae Cantabrigiensis_ (1858).