Questioni 26, 27 James Sylvester v. II (1864), p.29. The Questioni were related to the published Janni s papers

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2 Questioni 26, 27 James Sylvester v. II (1864), p.29 The Questioni were related to the published Janni s papers

3 Giuseppe Janni v. I (1863), pp ; ; ; ; v. II (1864), pp ; ;

4 The Questioni 26 and 27 were very difficult and four solutions were published by: -Enrico d'ovidio, -Salvatore Dino -Cremona -Battaglini [v.ii (1864), pp ]

5 Questioni 8-12 by Trudi: v.i (1863), p. 91 (it were related to the Trudi s paper on trilinear coordinates ) Solutions by F. Gambardella: v. I (1863), pp

6 In the Giornale were published also translations of foreign articles on subjects that kindled interesting debates in Italy and abroad. Battaglini gave particular importance to these debates, which obviously the young scholars were particularly interested in.the Giornale wanted to be an interpreter of different points of view expressed by the mathematicians who took part into the debate. For example in the Giornale di matematiche it is debated the controversial issue about the Elementi di Euclide as a text-book for the high schools. In England, like in other countries, was discussed the opportunity of mantain the Elementi as a text-book at school.

7 Wilson s speech translated by Raffaele Rubini v. VI (1868), pp In the Giornale, Battaglini published the translation made by Raffaele Rubini of the speech given by J.M. Wilson at the London Mathematical Society, and published in the Educational times of the first of September 1868, entitled Euclid as a textbook of elementary geometry

8 Hirst s report v. VI (1868),pp In the Giornale, it is also published the translation of the first session report of the Association of Geometrical Teaching, association that was born to promote a renewal in the teaching of geometry.

Letter to Battaglini wrote by Brioschi and Cremona v. VII (1869), pp. 51-54 Battaglini didn't take advantage of his position as director of the Giornale to impose his ideas.

9 Letter to Battaglini wrote by Brioschi and Cremona v. VII (1869), pp Battaglini didn't take advantage of his position as director of the Giornale to impose his ideas. He, in fact, allowed Brioschi and Cremona to publish a letter on the Giornale, in which the two mathematicians were defending their ideas in favour of the Elementi di Euclide.

10 The greatest credit of the Giornale was to represent the first and most important medium to the diffusion of the non-euclidean geometry in Italy: it was the official organ for the non-euclidean geometry.

11 Letter to Battaglini wrote by Hoüel v. VII (1869), p. 50 Hoüel is in favour of an Euclid revised instead of an Euclid disfigured.

12 Battaglini decided to translate these works (Hoüel s translation in French) in Italian and publish them in the Giornale: Études Géométriques sur la Théorie des Parallèles par Lobačevskij N. Lobačevskij, Pangéométrie, ou Précis de Géométrie fondée sur une théorie générale et rigoureuse des J. Bolyai, Appendix scientiam spatii absolute vera exhibens, a veritate aut falsitate axiomatis XI Euclidei (a priori haud unquam decidenda ) indipendentem: adjecta ad casum falsitatis quadratura circuli geometrica

13 v. V(1867), pp

14 v. VI (1868), pp

15 Battaglini s paper about non-euclidean geometry v. V (1867),pp

16 Eugenio Beltrami V. VI (1868),pp Beltrami published in the Giornale his important work Saggio di interpretazione della geometria non-euclidea where he demonstrated for the first time how all noneuclidean geometry theorems by Lobacevskji, admitted an interpretation on the negative constant curvature surfaces put in the Euclidean space. Afterwards this essay was translated in French by Houel.

17 All these examples show clearly how inside the Giornale there was an exchange among the students, between the professors and the students, and among the mathematicians coming from several nations, about the important academic issues discussed in the international journals and academies. The topics dealt and sources used in the articles give an idea of the great desire to bring young Italian scholars in Europe. The Giornale was a fascinating window on 'Europe and at the same time a gym where young scholars could train themselves and their value

18 Of course the Giornale, that acted also as a national information organ, published competition announcements and programmes, news about the university life, letters to the editor and bibliographic reviews.

19 Bibliography E. D Ovidio, Commemorazione del socio G.Battaglini, Mem. della R. Acc. dei Lincei, classe di scienze fisiche, s. 5, I, 1894, pp A. Zazo, Le scuole private universitarie a Napoli dal 1799 al 1860, Napoli ITEA, 1926 M. Castellana, F. Palladino, Giuseppe Battaglini, Raccolta di lettere ( ) di un matematico al tempo del Risorgimento d Italia, Bari, Levante, P. Calleri, L. Giacardi, Lettere di G. Battaglini a J. Hoüel ( ), Rivista di Storia della Scienza. 3 (1), 1995, pp R. Gatto, Storia di una Anomalia Lw facoltà di Scienze di Napoli tra l Unitò d Italia e la riforma Gentile , Fridericiana Editrice Universitaria, Napoli, 2000.

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