"A masterly though neglected work", Boscovich's treatise on conic sections

In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found inspiration in Boscovich’s work to write their treatises on conic sections.In questo lavoro delineamo la genesi del Sectionum Conicarum Elementa di Boscovich, e discutiamo le motivazioni che indussero Boscovich a scrivere quest’opera. Inoltre, analizzando in dettaglio la struttura di questo trattato, mostriamo come egli sviluppò l’idea completamente nuova di “cerchio eccentrico”, e costruì partendo da questa nozione l’intera teoria delle sezioni coniche. Commentiamo anche sulla ricezione del suo trattato, sia in Italia che all’estero, specialmente in Inghilterra, dove—a partire dalla fine del diciottesimo secolo—vari autori si ispirarono all’opera di Boscovich per scrivere i loro trattati sulle sezioni coniche

Borelli’s edition of books V–VII of Apollonius’s Conics,and Lemma 12 in Newton’s Principia

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli’s edition of books V-VII of Apollonius’s Conics before the printing of the Principia

Il processo Galileo e la Repubblica Romana del 1849

In 1849, Giacomo Manzoni, at that time Minister of Finances of the Roman Republic, and Silvestro Gherardi, substitute of the Minister of the Public Education and later on Minister ad interim, had easy access to the Archives of the Holy Office in Rome. From those Archives Manzoni took away a huge number of manuscripts and books, aiming to shed some light on the history of Religious Reform in Italy. In his turn Gherardi was interested only in Galileo’s trial. In this paper we reconstruct, also on the base of unpublished documents, the circumstances of Manzoni’s removals and the events that followed. In particular we trace the story of the manuscript that Gherardi used, in 1870, for the publication of thirty-one “decreta” of Galileo’s trial. From our research it turns out also that Manzoni brought away documents concerning other inquisitorial trials, that never returned to the Holy Office in Rome

On projective varieties admitting a bielliptic or trigonal curve-section

We study smooth projective varieties X ⊆ PN of dimension n ≥ 3, such that for some linear (N-n+1)-dimensional space Π ⊆ PN, C=X∩Π is either a bielliptic or a trigonal curve. We give a description of X when deg ≥ 18 and when deg X ≤ 8