Unpublished paper, 'Second memoir upon the determination of unknown functions that are involved under definite integrals' by Joaquim Gomes de Souza

Description

De Souza proposes to himself the problem of determining the function ϕ which ( f, F being given functions, and the limits α, β of the integration being also given) satisfies the equation ∫βαf(x, θ) ϕ (x + θ) dθ = Fx. He observes, that, unlike the methods employed in his former memoir, and the solutions there employed, which are quite rigorous, the methods of the present memoir depend upon developments into series, the strictness of which has been contested by some mathematicians ; but that passing over these difficulties, he has solved the famous problem, the solution of which has been vainly sought after for the last two hundred years, because on the above-mentioned equation depends the integration of the generally linear equation of any order whatever of two variables, and consequently the whole integral calculus.

Subject: Mathematics / Calculus

Received 25 April 1836. Communicated by Dr [William] Sharpey.

Written by de Souza at 29 Brompton Square, London.

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 8 of the Proceedings of the Royal Society as 'On the determination of unknown functions that are involved under definite integrals'.

Reference number

AP/38/26

Earliest possible date

25 April 1856

Physical description

Ink on paper

Page extent

125 pages

Format

Manuscript