Loria, Gino

(b. Mantua, Italy, 19 May 1862; d. Genoa, Italy, 30 January 1954)

mathematics, history of mathematics.

After graduating in 1883 from Turin University, where higher geometry was taught by Enrico D’Ovidio, Loria attended a postgraduate course at Pavia University taught by Beltrami, Bertini, and F. Casorati. Loria became D’Ovidio’s assistant in November 1884; on 1 November 1886 he was appointed extraordinary professor of higher geometry at Genoa University, becoming full professor in 1891. He held the chair of higher geometry at Genoa for forty-nine years, until he retired in 1935; he also taught the history of mathematics, descriptive geometry, and mathematics education. He wrote a number of treatises on descriptive geometry that were appreciated for their simplicity, elegant constructions, and generality. In them he introduced elements of photogrammetry. He was a member of the Accademia Nazionale dei Lincei and of various other academies.

Loria’s geometrical research, at first carried out in cooperation with Corrado Segre, was especially concerned with new applications of algebraic concepts to the geometry of straight lines and spheres, with hyperspatial projective geometry, with algebraic correspondence between fundamental forms, and with Cremona transformations in space. But the field in which Loria’s scientific activity was most extensive was the history of mathematics from antiquity down to his own time.

Special mention should be made of Le scienze esatte neltantica Grecta (1914), a reworking of the articles which appeared in the Memorie delta Regia Accademia di scienze, lettere e arti In Modern in 1893-1902. It constitutes a rich source of information on Greek mathematics. Storia della geometria descrit-fiva (1921) shows Loria’s liking for the subject. Guida alio studio della storia delle matematiche (last ed.t 1946) is methodological in character and places at scholars’ disposal the rich source materials and collections on the subject with which he had worked for years. Full bibliographical information is in Ilpassato eil presente delle principali teorle geometriche, updated in the editions of 1897, 1907, and 1931.

Loria devoted two works to special algebraic and transcendental curves which have attracted the attention of mathematicians. The first of these works was published in German in 1902, and only much later (1930-1931) in Italian, with the title Curve piane speciali algebriche e trascendenti;the other is Le curve sghembe speciali algebriche e transcendenti (1925). As F. Enriques has pointed out, the curves studied by Loria are of special interest because the study of particular cases often leads to general results.

Many of Loria’s writings are biographical, notably those on Archimedes, Newton, Cremona, Beltrami, and Tannery. With G. Vassura he edited the largely unpublished writings of Torricelli (E. Torricelli,Opere, 4 vols. [Faenza, 1919-1944]). Jn 1897 Loria recognized, in one of Torricelli’s manuscripts, the first known rectification of a curve: the logarithmic spiral.

Some of Loria’s works have been collected in the Volume Scritti, conferenze e discorsi sulla storia delle matematiche(1937); and an overall view of the evolution of mathematical thought, from ancient times to the end of the nineteenth century, is provided in his Storia delle matematiche(2nd ed.,1950).

Loria’s library, containing history of mathematics, was left to the University of Genoa.

BIBLIOGRAPHY

I. Original Works. A list of Loria’s works is in the commemorative address delivered by A. Terracini at the Accademia dei Lincei (see below) and includes 386 writings.

Some of his more important articles are: “Sur les diffùrentes especes de complexes du second degre des droites qui coupent harmoniquement deux surfaces du second lorry ordre,” inMathematische Annalen, 23 (1883), 213-235, written with C. Segre; “Sulle corrispondenze proiettive fra due piani e fra due spazi,” in Giomale di matematiche,22 (1883), 1-16; “Ricerche mtorno alia geometria della sfera e loro applicazione alio studio ed alia classificazione delle superficie di quarto ordine aventi per linea doppia il cerchio immaginario all’lnfinito,“inMemorie della Reale Accademia delle scienze di Torino, 2nd ser., 36 (1884), 199-297; “Sulla classificazione delle trasformazioni razionali dello spazio, in particolare sulle trasformazioni di genere uno,” in Rendiconti delTlstituto lombardo di scienze e lettere, 2nd ser., 23 (1890), 824-834; “Della varia fortuna d’Euclide in relazione con i problemi deH’insegnamento della geometria elementare,” inPeriodico di matematica per l insegnamento secondario,8 (1893), 81-113; “Evange-lista Torricelli e la prima rettificazione di una curva,” inAttl deW’Accademia nazionak del Lineei, Rendiconti, 5th ser., 6 , no. 2 (1897), 318-323; “Eugenio Beltrami e le sue opere maiematiche,” inBibliotheca mathematica, 3rd ser., 2 (1901), 392-440; “Commemorazione di L. Cremona,” inAtti della Società ligustica di scienze natural! e geografiche,15 (1904), 19; “Necrologio. Paolo Tannery,” in Bollettino di biblbgrafia e storia delle scienze matematiche pubbticato per cura di Gino Loria, 8 (1905), 27-30; and “La storia della matematica vista da un veterano,” in Bollettino delfUnione matematica italiana,3rd ser., 5 (1950), 165-170.

His books includeSpezielle algebraische mid transscendente ebene Curmn (Leipzig, 1902), trans, by author as Curve plane speciali algebriche e trascendenti, 2 vols. (Milan, 1930 1931); Le scienze esatte nelVantica Grecia (Milan, 1914);Newton (Rome, 1920);Storia della geometria descrittiva dalle origini sino at nostri giorni (Milan, 1921); Le curve sghembe speciali algebriche e trascendenti,2 vols. (Bologna, 1925); Archimede (Milan, 1928); Storia delle matematiche, 2 vols. (Torino, 1929-1931; 2nd ed., Milan, 1950); 11 passato e il presente delle principal!’ teorie geome-triche (Padua, 1931), an updating of arts. In Memorie della Reale Accademia delle scienze di Torino, sers. 2,38 (1887);Scritti, confer enze e discorsi sulla storia delle matematiche (Padua, 1937); and Guida alio studio della storia delle matematiche (Milan, 1946).

II. Secondary Literature. See A. Terracim, “Gino Loria. Cenni commemorativi,” inAtti dell’’Accademia delle scienze di Torino,88 (1953-1954), 6-11; and “Commemorazione del socio Gino Loria,” inAtti della Accademia Nazhnale dei Lincei, Rendiconti, 8th ser., Classe di scienze fisiche, matematiche enaturali, 17 (1954), 402-421, with bibliography,

Ettore Carruccio