Page 123 - Textos de Matemática Vol. 34

MATHEMATICS IN COIMBRA IN THE 19TH CENTURY 113
Lu´ıs da Costa e Almeida (1841-1919) worked mainly on differential equations, calculus of variations and determinants. Eight of his publications were reviewed in the “Jahrbuch u¨ber die Fortschritte der Mathematik” between 1890 and 1899; seven were reviewed in “Le r´epertoire bibliographique des sciences math´ematiques” between 1872 and 1878.
Francisco Gomes Teixeira (1851-1933) was the most important Portuguese mathematician of the 19th century (and first quarter of the 20th century). He was a brilliant student in Coimbra and published two papers while still a student, in analysis, his main area of work during most of his life. He was a professor in Coimbra form 1876 to 1883 and then moved to the Polytechnic Academy of Oporto of which he became the director; while still in Coimbra he founded the “Jornal de sciencias matem´aticas e astron´omicas” that became known as “Teixeira’s Journal”. His monumental work “Trait´e des courbes sp´eciales remarquables planes et gauches” (tome I, 1908, tome II, 1909 et tome III, 1915), is still a unique work on the history and properties of curves and has been reprinted recently by editor Jacques Gabay.
A. d’Arzilla Fonseca (1853-1912) Well known because he published the books “Elementary principles of the calculus of quaternions” in 1884 and “Applications of quaternions to mechanics” in 1885. Four of his publications were reviewed in the “Jahrbuch u¨ber die Fortschritte der Mathematik” between 1890 and 1895.
Henrique de Figueiredo (1861-1922) In 1885 he published the book “Algebraic plane curves” and in 1887 the book “Riemann Surfaces” where, shortly after the work done by Riemann, Henrique de Figueiredo showed to understand this difficult area, much more quickly than usual, as noted by Jeremy Gray and Eduardo L. Ortiz [7].
Jos´e Bruno de Cabedo (1860-1922) was noted for his work on analysis. He was the first to teach the “Higher Analysis” discipline created in 1898. Seven of his publications were reviewed in the “Jahrbuch u¨ber die Fortschritte der Mathematik” between 1889 and 1894; two were reviewed in “Le r´epertoire bibliographique des sciences math´ematiques” in 1886 and 1889; he published most of his works in the so called “Teixeira’s Journal”. We will mention briefly some of his papers to give an idea of his work.
In the paper “Two analysis formulas” (Teixeira J. IX. 129-131, 1889), Bruno de Cabedo gives a generalisation of a formula presented by F. Gomes Teixeira in the paper “Sur une formule d’analyse” (Nouv. Ann. (3) V. 36-39, 1886): if the functions F(z), F1(z), f′(z) and f1′(z) are finite in the interval (x,x + h) and if furthermore in the same interval F1(z) + hf1′ (z) ≷ 0, then we have, for some θ between zero and one:
F(x)+f(x+h)−f(x) = F(x)+hf′(x+θh) . F1(x) + f1(x + h) − f1(x) F1(x) + hf1′(x + θh)
.