"On the comparison of transcendents, with certain applications to the theory of definite integrals." In: Philosophical Transactions of the Royal Society of London. For the year MDCCCLVII. Vol. 147, Part III, pp. 745-803.
London: Taylor & Francis, 1858. 4to. [iv], vi, [iv], 621-906, 19 pp. FIRST EDITION. With 6 plates (1 extra large folding). Original printed wrappers; uncut and unopened. Item #13926
First edition. Boole states his intention to demonstrate "a fundamental theorem for the summation of integrals whose limits are determined by the roots of an algebraic equation," as well as the "application of that theorem to the problem of the comparison of algebraic transcendents."
This is the complete Part III of the Philosophical Transactions, which also includes:
CAYLEY, "Memoir on the resultant of a system of two equations."
CAYLEY, "On the symmetric functions of the roots of certain systems of two equations."
CAYLEY, "A memoir on the conditions for the existence of given systems of equalities among the roots of an equation."
CAYLEY, "Tables of the sturmian functions for equations of the second, third, fourth, and fifth degrees."
AIRY, "Account of the construction of the new national standard of length, and of its principal copies."
WILLIAMS, C. Greville, "On some of the products of the destructive distillation of boghead coal."
HOPKINS, "Experimental researches on the conductive powers of various substances, with the application of the results to the problem of terrestrial temperature."
HODGKINSON, Eaton, "Experimental researches on the strength of pillars of cast iron...."