Description of the Project Pier Daniele Napolitani

m-à-j 14 août 2000

• 1  The Works of Francesco Maurolico
• 2  Problems with a Critical Edition of Maurolico's Scientific Opus
• 3  An "Electronic" Edition as Edition in Progress
• 4  Ordering of the Edition
• 5  Working Tools

1  The Works of Francesco Maurolico

Francesco Maurolico (1494-1575) was one of the most important mathematicians of the XVI century in Europe. He spent most of his life in Messina and in Sicily, a marginal location with respect to the main cultural centers of the time: Roma, Venezia, Firenze, Urbino. This fact did not prevent him from undertaking a complete program of restoration and recovering of classical mathematics. In 1575, at the end of his life, he had accomplished several publications consisting of editions, compendia and commentaries of the treatises of Euclid, Archimedes, Apollonius, Serenus, Theodosius, Menelaus, Ptolemaeus, Autolycus. In addition to the works on these authors, presented as ex traditione Maurolyci and hence philologically very approximative, he wrote a series of original treatises in several domains of mathematics (optics, arithmetic, statics, gnomonics, astronomy). The results and methods of proof that are presented by Maurolico in his works were going beyond the most advanced results and refined proof-methods of classical mathematics.

Several circumstances did not allow Maurolico to publish all of his works during his life. Only a few texts were in fact printed (the Cosmographia in 1543, his Theodosius in 1558, the Arithmeticorum libri duo and the Opuscula mathematica in 1575), but most of his production still remains in form of manuscript. As a consequence of the past time, the original corpus of manuscripts got scattered and partially lost. This fact was counterbalanced to a limited extent by the existence of some printed editions of Maurolico's works, dated in the XVII century, that regard the Optical treatises (1611), Mautolico's Apollonius (1654), and Maurolico's Archimedes (1685). Unfortunately the whole Maurolico's Euclidean work, as well as a remarkable series of treatises and minor writings, still remain unpublished until now.

Francesco Maurolico as a mathematician was therefore very interested to recover the body of knowledge of ancient mathematics in a new encyclopaedia. To this end he embarked on a life-lasting enterprise of scientific reconstruction. This did not profit by the subtelties of a philological approach, so that he was led to continually modify his works, producing new editions and new results following the availability of new texts from the growing community of XVI century mathematicians. Such a character of unending work-in-progress was one of the causes preventing him to publish most of his works, thus contributing to the process of dispersion of his writings.

2  Problems with a Critical Edition of Maurolico's Scientific Opus

Maurolico's works appear thus to be strongly interrelated, and recent studies have confirmed it. This constitutes a main problem to be faced in a critical edition of Maurolico's works. Maurolico's production amounts to over 5000 pages, about half of which still unpublished. The published ones can be dated back from the XVI to the XVII centuries even if some exceptions exist. Most texts have come to us through a single witness, whether in manuscripts (in which case most of them are autographs) or in printed form. For instance, this has happened with his Archimedes (the De mensura circuli excepted): our sole witness is the 1685 printed edition. Maurolico's Apollonius is preserved in the 1654 printed edition, an autograph copy containing the first four books, and in a XVII century apograph copy containing the Maurolician restitutio of the fifth and of the sixth book. The case of the optical works is the most complex one: we have two almost simultaneous editions (Napoli 1611 and Lyon 1613) of the Photismi de lumine et umbra and of the Diaphana, an autograph of the Diaphana only, and an apograph, with marginal corrections in Maurolico's hand, of both the Diaphana and the Photismi.

As suggested above, all this is a consequence of Maurolico's eagerness to revise his works, while concealing the traces of the preceding drafts. Then usually the final version was eventually copied in a sort of fair copy, and dated with great precision. The arithmetical writings appear to be the only exception, since a series of fragments and partial elaborations are extant whose composition precedes the dates we find in the Arithmeticorum libri duo.

Prima facie, the work of making an edition should simply consist in editing Maurolico's text in accordance with the last version dated by the author himself, a text often attested in one witness only.

However, a series of seminars held in Pisa at the ``Dipartimento di Matematica'' between 1993 and 1996 (All'alba della matematica moderna. Francesco Maurolico e il ritorno dei classici) and specifically devoted to the problems of the edition of Maurolico's mathematical opus led to a reconsideration of the whole issue, whose peculiar problems are now more clearly perceived. First of all, it has become apparent that the dates Maurolico put on his works are to be taken as purely indicative, in the sense that important interventions by their author have demonstrably occurred later. On the other hand, lost texts and textual strata actually preceding the received date have been shown to exist. The interrelationships among the various works further entangle the matter. In his Euclid a series of references is provided to the arithmetical treatises; several portions of his Archimedes are strictly related to his works on Apollonius and on conic sections, the latter referring in turn to researches in gnomonics.

Of course, the problem of the sources is made very tangled in the case of works composed during a lapse of time of several decades. Looking at the Archimedean treatises, for instance, it is clear that in his first elaborations Maurolico only employs a supply of pseudo-Archimedean text of medieval origin, whereas in the last ones he makes large use of the editio princeps printed in Basel and of Apollonius' Conics.

A further problem emerged in the course of the above-mentioned preliminary investigations is related to the XVII century editions, in particular those of the Problemata mechanica (Messina, 1613), of the Emendatio et restitutio conicorum Apollonii Pergaei (Messina, 1654), and of the Admirandi Archimedis Syracusani Monumenta (Palermo 1685). In the case of the latter two (amounting to about a quarter of Maurolico's production) the problem is to determine the extent to which the editions have been corrected by the editors. This is important in that it has recently been proved of the best Italian mathematicians of the period, namely Giovanni Alfonso Borelli, was involved in the edition. Borelli was in the best position to introduce weighty corrections and variants in the text.

Summing up, the main problems of an edition of Maurolico's writings lie in the extent of the opus and in the composite character of it. Moreover, four problems can hardly be solved editing each work separately: dating, interrelationships between the several treatises, sources, existence of very late witnesses.

3  An "Electronic" Edition as Edition in Progress

A serious edition of just one among Maurolico's works seems therefore to crucially depend on the preliminary existence of a complete edition of his mathematical opus. Put this way, the problem cannot have a solution, if the solution is to be arrived at in a limited time and with limited resources.

The editorial committee resolved to regarded as primary the exigency of having at least the complete transcription of all texts, possibly originating from a collation of all available witnesses, in a reasonable time: turning to an "electronic" edition was thus mandatory. As a by-product, the several scholars involved in the project would profit by the feedback effect primed by the progress of their co-editors' work.

Our main goal in choosing to employ the electronic tools at our disposal is thus to complete the edition in a reasonable time: we are not interested in a fashionable product, rich in images, animations, and colours.

Of course, our edition will actually make use of the potentialities the electronic medium makes available; nevertheless, our intention is to balance our resources between elaborating "electronic" pages on the one hand and studying and editing on the other (with special emphasis on the latter aspect). The text are located in the site in accordance with a certain procedure, whose main points are outlined in what follows.

4  Ordering of the Edition

The present editorial project is therefore, very much in line with the characteristics of its object, a work in progress. This fact, and the decision of postponing the printed edition, would permit delaying the choice of a final ordering for several years. None the less such a choice must be taken from the very outset, in order to provide the guiding lines of the edition.

As we have seen, a chronological ordering of Maurolico's works is unfeasible. Maurolico has been working to some works for several years, as is the case e.g. for the De momentis aequalibus, reworked on several occasions from the Twenties up to the Sixties of XVI century. It is clear that it is impossible to find a convenient place to such a treatise in a strict chronological ordering. If a chronological ordering may result more "objective" than an ordering by argument, in the case of the De momentis aequalibus an intolerable degree of arbitrariness in its dating would be introduced. To avoid such a drawback while keeping the chronological ordering, portions of the same work that can be differentiated by their date of composing should be placed far away the one from the other, but a confused and unfriendly ordering would result, even for someone deeply acquainted with Maurolician matters.

Granted the ordering by argument, but where to subdivide? It is to be recalled that Maurolico summarized his own production in several Indices lucubrationum. The main point of such Indices is the subdivision between aliena and propria production. Several reasons stood against using the Indices as guides for determining the structure of the edition. First, the subdivision between aliena et propria leads again to separating what is instead strictly related. Second, several texts that are present in the last redactions of the Index got lost, whereas we do have texts not included in such redactions. Moreover, the Index lucubrationum is more properly an index of Maurolico's production than an editorial plan. Hence, we have not followed this route, entailing in addition the separation of the texts from their own compendia.

The problem of subdividing Maurolico's works can find a satisfying solution by using an encyclopedic project by Maurolico himself (see Moscheo:1988, pp. 533-47 e Matton:1990, pp.~283-306). This way, the exigencies of following both one of the ideas of their author and criteria of opportunity and of convenience are met. We have thus partitioned Maurolico's scientific production into Mathematicae purae and Mathematicae mixtae. A third large partition contains the writings of method and the correspondence. Eleven volumes result:

Such a subdivision is a representation, in rough outline, of our project.

5  Working Tools

A few working tools are at any interested scholar's disposal. In the present site they are clearly differentiated from the texts; in the printed edition they will be published as separate volumes.

The Instrumenta Maurolyciana are: several catalogues useful to find one's bearings in Maurolico's manuscripts and printed works; a bibliography on Maurolico - complete to the largest possible extent -; a biographic section where the edition of the Vita dell'abate del Parto written by his nephew Francesco Maurolico jr. will be found, as well as a chronology of his writings and more generally all documents related to his life and works; lastly an iconographic section.

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