(b. Forli, Italy, 8 November 1846; d. Pisa, Italy, 24 February 1933)
In 1863 Bertini registered at the University of Bologna, intending to study engineering, but after taking the course taught by Luigi Cremona, he turned to pure mathematics. In 1866 he fought with Garibaldi in the third war for Italian independence. On the advice of Cremona, he resumed his studies and transferred to the University of Pisa, from which he received his degree in mathematics in 1867. During the academic year 1868–1869 he attended the course in Milan taught by L. Cremona, F. Brioschi, and F. Casorati. This course, dealing with Abel’s integrals, exerted considerable influence on Bertini’s own research.
In 1870 Bertini began his teaching career in the secondary schools of Milan, and in 1872 taught in Rome. There, on the recommendation of Cremona, he was appointed a special lecturer to teach descriptive and projective geometry. In 1875 he accepted the professorship of advanced geometry at the University of Pisa. From 1880 to 1892 he taught at the University of Pavia, and then returned to his former professor ship at Pisa, a post he held until his retirement at the age of seventy-five. For the next ten years he taught an elective course in geometrical complements, which he had started as an introductory course to higher geometry.
Bertini’s research deals particularly with algebraic geometry and constitutes definite progress in relation to the studies pursued by the school of Cremona. In this connection it is necessary to note that Cremona, having formulated the theory on plane and space transformations that bears his name, availed himself of the same transformations to change higher geometric figures into simpler figures and then apply to the higher figures the properties of the simpler ones. Bertini studied the geometric properties that remain constant during such transformations. He conceived the idea of exploring this field after studying the problem of the classification of plane involutions. In 1877 he succeeded in determining the various types, irreducible from each other, in which the planar in volutions may be reduced through Cremona’s transformations. His treatises are noteworthy for their order and clarity.
I. Original Works. Bertini’s works include “La geometria delle serie lineari sopra una curva piana, secondo il metodo algebrico,” in Annali di matematica pura ed applicata, 2nd ser., 22 (1894), 1–40; Introduzione alla gemetria proiettiva degli iperpazi (Pisa, 1906; Messina, 1923); and Complementi di geometria proiettiva (Bologna, 1927).
II. Secondary Literature. More information on Bertini may be found in G. Castelnuovo, “Commemorzione del socio Eugenio Bertini,” in Atti della Reale Accademia nazionale dei Lincei. Rendiconti, Classe di scienze fisiche, matematiche e naturali, 6th ser., 17 (1933), 745–748; and F. Enriques, Le matematiche nella storia e nella cultura (Bologna, 1938), pp. 284, 286, 287, 292.
"Bertini, Eugenio." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (April 23, 2019). https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/bertini-eugenio
"Bertini, Eugenio." Complete Dictionary of Scientific Biography. . Retrieved April 23, 2019 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/bertini-eugenio
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.