[p.111] THE DEVELOPMENT OF MATHEMATICAL EDUCATION IN MALTA TO 1798
A case-study of cross-cultural influences
1 cultural Background
All indicators point towards a very low level of literacy in the Maltese Islands before the coming of the Order in 1530; by inference, the level of numeracy could not have been much higher. Very few could read and write even their own name. This can be ascertained from a variety of sources, particularly from hundreds of receipts for payments extant in the long series of so-called "Mandati" in the Mdina Cathedral Archives; in several of them the payee had to resort to third parties to have the receipts written and signed on his behalf, confessing unashamedly apoca scripta manu...perche non sachu scriviri. The names of the few literate people who helped out on such occasions keep recurring and include mostly priests, notaries and a handful of other laymen. Often, people in high offices were illiterate. Thus, judge Fridericus de Bordino, witnessing a deed in 1486, had to denote his confirmation by the mark of a cross, admitting that he could not sign his name . Admittedly, de Bordino was not a "judex literatus" but a "judex ydiota", the crass incompetence of which judges attracted the censure of none less than the Viceroy himself in 1515.
[p.112] Judging by autographed receipts in the "Mandati" series quoted, most priests and religious involved, but by no means all of them, could draw up their own receipts. Among literate laymen who wrote their own or others' receipts one finds the pharmacist, the physician, and the school-master.
1.1 The Mdina Grammar School
The school-master referred to here was the teacher at the grammar school, or school of humanities, whose existence at Mdina is documented from 1461 onwards. It is by and large correct to state that most of the masters in the pre-1530 period were foreigners of Sicilian origin who were replaced by locals as convenient. The foreign origin of masters between 1460 and 1470 is clearly indicated. In 1470, the master was Fra Johannes of the Friars Minor, and a year later the incumbent's very name, Notary Jacobo Cannarella, also betrays his foreign origin. The first local school-master, the cleric Don Gilius Di Lia, appears in 1473, but is soon replaced by the foreigner Johannes Cirurgico in the biennium 1475-77. A determining factor that appears to have decided the choice between local and foreigner at this time was the financial aspect. When enough money was found by the UniversitÓ, the preference was to employ foreigners. When the salary offered was not attractive enough, then only locals were found to come forward. Thus in 1461, 1467, 1470 and in 1476, the foreign master's salaries were 4 uncie, 7 uncie, 6 uncie and 6 uncie respectively, whereas Di Lia was offered a mere 3 uncie in 1473 which [p.113] was raised to 4 uncie when he was re-employed in 1477. Two years later he was threatening the town-council to stop teaching altogether unless he was given SOME salary. It is possible that the school was closed down in the 1480s as the recurrent problem of appointing school-masters and what salaries to give them does not figure at all in the very full records of minutes of the period. In 1496 then, Padre Martin de Certia is encountered signing a contract whereby he bound himself to run the school for a fee of four uncie to be paid equally by the cathedral and the UniversitÓ.
Other foreign masters appear on the scene in the early decades of the sixteenth century. Between 1514 and 1516 one encounters Thomas di Abraham, followed by Andrea Gaytano in 1516-17, by Don Antonio Callami who came from Syracuse in 1517, and by Don Francesco Gallo between 1518 and 1519. In July 1519 the ent Maltese Notary Jacobo Bondino took over for a relatively long stretch till October 1531, interrupted only in September 1525 at his request to be able to go to the Eternal City and attend the "Santo Jubileo". During his absence between 1525 and 1527, the post was filled by the Sicilian Don Santoro de Nativo. Bondin was paid 10 uncie annually, 7 paid by the University and 3 by the Cathedral, the same amount paid to Don Santoro, as per deed of 6th April 1526 in the acts of Notary [p.114] Pietro de Alaymo. The same Andrea Gaytano or Gaytanello who was employed in 1517, stepped in after Notary Bondino, and before yet another Maltese, this time the Carmelite Friar Joannes Bugeia, undertook the teaching in 1535 for four whole years; at one time in 1537, however, the town-council considered the possibility of replacing Bugeia by the foreign master Marcantonio Jacomino. With the establishment of the Order the school began to be run solely by local masters. Following Bugeia, the notorious Don Andrea Axac took over and soon involved himself in a clash with the Inquisition, among other things, on account of his Lutheran ideas which he did not refrain from propagating among his students.
1.2 Other Centres of Learning
Even in late medieval times, the Mdina Grammar School was not the only catalyst for the diffusion of knowledge. In 1495, a certain Clericus Jacobus was described as a "discipulus" of Donnus Lemo de Fauczono, who was then "Cappellanus" at Naxxar. There is also abundant evidence that several Maltese undertook further studies outside our shores. Thus, Antonio de Sarlo was suported financially by the University to go for further studies in Sicily in 1467, and similar assistance was considered for the Augustinian Frati Antoni Sabar in 1479. In 1558, the famous Joseph alias Mattew Callus, himself a foreign graduate "artium et medicine doctor", left in his will all his books and medical apparata to his adoptive son Mattew with the proviso that the young Callus should go to Sicily and take up his studies there. In 1576, the very wealthy Gozitan merchant Rayneli Machnuc, in constituting his son [p.115] Antonio his universal heir, endowed him with funds to enable him further his studies for a J.U.D. in Naples where he was at the time, having received his initial training at the Mdina school of humanities.
It transpires from Inquisitorial proceedings carried out in the 1570s, against a number of intellectuals suspected of Lutheran leanings that the Mdina school of humanities was by no means the only one of its kind in the 1540s. One of the trials is particularly revealing. During the interrogation of the seventy year-old parish priest of Birkirkara, Don Josephus Bellia, on the activities of Josephus Farruge, Bellia confesses that they first came in contact with each other at the school of Giulio Cassarino, where Bellia stayed for eight months after which he went to Messina for two years. On his return to Malta, whereas Farruge was still at the same (Cassarino's) school, Bellia started frequenting Bugeia's school at Mdina, where he stayed for another seven months. For a second time he returned to Messina and again on his return renewed his acquaintance with Farruge, who was this time either at Andrea Axac's school or in that run by Fra Francesco Gesualdo (who was later burnt at the stake for his unorthodoxy); thirty years after the event Bellia could not recall with certainty which school it was but he said that it was likelier to have been Gesualdo's because Farruge was then staying at the Borgo. Bellia stayed in Malta for three or four years after that and then went, this time, to Palermo for thirteen months to further his studies there. This little episode illustrates how a number of educational nuclei co-existed in sixteenth century Malta and how travel abroad for further studies was not as uncommon as one might have expected.
It can also be deduced from another trial that Axac moved his school quite freely from one locality to another. Don Petro Cassia in the witness stand in 1575, recalled how Don Andrea Axac, at the request of Dottor Vassallo and of Diego Galan, went to Birgu with his whole entourage of disciples and taught there for a whole year at a place not far from the "Infirmaria". On their return to the "Citta Vecchia", school was held in a warehouse belonging to Vincenzo Cagege and later at Cassia's own house. The informal atmosphere at the school is captured by statements like:
[p.116] Axac...andava a spasso in una chiesa hora in un altra overo in qualche giardino con noi altri scolari;
this took place at times in Rabat, in the "cortile" of Sant'Agatha, or at Santa Venera, or at the convent of San Francesco.
1.3 Maltese Intelligentsia
The pattern of initial foreign influences and subsequent flowering of local intellectuals exhibited in the case of the school of humanities has parallels in other contemporary cultural and educational spheres. In the fifteenth century local medicine, for instance, was exclusively in the hands of foreigners. Doctors were either Jews or Catalans, but by the first decades of the sixteenth century the numbers of local medics began to multiply steadily. Safaradi and the rest of the Jewish community were expelled in 1492, the Monbrons and Ferriolos of Catalan origin had become naturalized Maltese and completely assimilated in the local community by their third generation, whereas Beniveni, de Assaldo, de Munda and other Sicilians had ceded their place to Callus, the Bonellos, Schembri, Mamo and later ones. The same can be said of the "aromatarii" or pharmacists who, before 1500 were practically exclusively Sicilian - so were Passa, Mastru Paulo of Noto, Rufrigiato of Modica, Jarratana, and Speciano - but were practically all Maltese thereafter, starting with Callus, father and son, the two Zammits and later ones.
The medical profession particularly and expectedly received an energizing boost with the arrival of the hospitallers. Several medics employed with the Order, many of whom were of Rhodian origin, came in its wake and settled here to the island's benefit. Among them were the Rhodian surgeon Leonardo Myriti, who had two sons who studied at the University of Paris and at Montpellier, and who requested and was granted citizenship of the town and island of Malta in 1534. There was also the Rhodian physician Joannes [p.117] Ramundo Calamia who became town-doctor after Callus, Antonius Rochorio, a pharmacist, who was also granted citizenship in 1540, and Antonio Perurelio, a Sicilian surgeon who married and settled in Birkirkara in 1539.
This situation is likewise reflected in the musical and artistic spheres. The preponderance of foreign, especially Sicilian, musicians and artists, as at the Cathedral, is evident before 1530 but it gradually gave way to an increasing number of local artists and craftsmen.
Among other literate laymen in late medieval Malta one encounters the notaries, perhaps five or six of them working contemporaneously, the "judices literati" and members of the upper social classes. These people regularly appear as members of the town-council and as occupying responsible positions such as the office of Capitano della Verga, or that of Giurato, procuratorships of institutions like Santo Spirito Hospital, the Cathedral, nunneries and convents, offices like that of "thesaurerius" or administrator of various gabelles of the Universita, "supramarammerius" or overseer of public works, "accatapanus" or civil servant responsible for, among other things, the control of weights and measures, and consultantships as experts to determine the price of wheat, cumin and other commodities. On very rare but illuminating occasions one comes across evidence of a solitary luminous mind such as Pietru Caxaro.
2.1 The Late Middle Ages
The large number of documents of the period is in stark contrast with the paucity of information that can be gleaned as to the familiarity of people with numbers and with numerical operations. Thus, among the voluminous notarial registers, one only seldom comes across additions, say, of sums of money, [p.118] which would be a sure sign that the notary could at least add. Nor are explicit operations of division common, as would occur in, say, division of acreage of land among heirs. Yet certain other documents provide ample evidence of numerical notation and of arithmetical computations. Procurators normally had to give account of all revenues and expenses, so that their "Conti" or books of accounts containing detailed lists, prices, sub-totals and grand totals under both "Introytus" and "Exitus" provide a plethora of figures and lengthy additions. Extant examples from the late medieval period (Pl. 1) are the Santo Spirito books of accounts covering the period 1494-1562, various lists of sundry expenses (spisi minuti) by the "thesaureri" of the University scattered among the hundreds of folios in the Mandati Series (1506-), an interesting book of the expenses incurred by the "supramarammerius" of Castel Sant'Angelo in repairing the walls of that fort in c.1502, and a similar, somewhat later one relating to the Mdina walls, the "Libri di Procura" of the cathedral "yconomo" and "massaro", dating from around 1480, and so many other later ones. Records, going back to 1522, of revenues and of dues were also kept by the collectors of tithes, that is the cathedral Archdeacon, the Deacon and the Treasurer; tithes were computed in measures of wheat and barley but were often paid in cash. Grain, and a number of other substances, such as lime, were measured by the salma of 16 tumina and the tumino of 6 mondelli; the currency most commonly used was the uncia of 30 tareni and the tareno of 20 grani. One concludes that all who handled money and grain, and that included many otherwise illiterate farmers, could perform operations of division by 6, by 16, by 20 and by 30. Various early lists of quantities of grain are still extant, including one of around 1460 entitled "Li sommi di fora taxati [p.119] alu Jmpruntu dili frumenti", and another of around 1480, apparently drawn up in connexion with wheat subsidies to the Rabat population, entitled "Summanu li buky dilu Rabbatu millj trichentu lxxxj". Also of interest are several "Pandette" or meat price lists ("Meta Carnium") issued by the UniversitÓ early in September of each year to regulate prices of meat and other commodities for that year. These "pandette", like all "bandi" proclaimed by the town-crier in public places, must have been understood by the man-in-the-street and hence indicate at least some rudimentary knowledge of numbers by all and sundry. One should also note the presence in Mdina of the cathedral mechanical clock, which was also the town-clock, documented with clock-work regularity from 1461 onwards; no doubt, the figures on its dial must have meant something to a number of people in the city. More important still is the linguistic evidence of highly developed names of numerals in Maltese indicating use by the common people. Of particular interest, both linguistically and numerically, is the Maltese word-list including numerals published in 1611 by Megiser.
Perhaps a case can be made that numeracy was after all more diffused than literacy; indeed, one can work out necessary computations in one's head to check whether one has been cheated or not in a particular transaction, or perhaps even aid one's powers of concentration with the use of the ages-old mini-computer, the abacus, and still be quite incapable of writing one's own name.
Yet, it is hard to pin-point where, if anywhere, formal training in the art of numbers was imparted. The most likely place to look for this kind of instruction would be the Grammar School. Unfortunately, the only extant records that have anything to say on what went on there are the Inquisitor's records and the Inquisitor's beady eye, generally speaking, tended to be more interested in reading between the lines of Erasmus' Colloquys than in innocuous numerals. Andrea Axac's school of humanities is known to have comprised [p.120] three successive streams or classes, so called "essamini". While at Birgu, there were two students in the first, four in the second, and four others in the third. In the first two classes the master read Cicero, De Officiis and l'Epistole, and Horace, whereas in the third he read Terence and Ovid. To all of them that were ripe for it he read the works of Erasmus and a certain suspect Novo Testamento; elsewhere, mention is made of Plautus and of Vergil. Be that as it may, student numbers being as few as ten in all three streams taken together, teaching at the grammar school could not have accounted for popular familiarity with numbers so that one must postulate basic skills acquired over centuries of continued use, orally transmitted from generation to the next to explain this phenomenon.
2.2 Johannes Myriti
Perhaps the earliest truly mathematical Maltese mile-stone is Joannes Myriti, very probably, the son of the surgeon Leonardo mentioned earlier. Born in Malta around the year 1534, of Rhodian parents who had been granted citizenship of Mdina, he became a chaplain of the Order and later appointed to the Commandery of Ratisbon by 1561. While at Ratisbon he registered as a student in the University of Freiburg-im-Breisgau to study both mathematics under Erasmus Oswald Schreckenfuchs and Henricus Loritus Glareanus, and classics under Johannes Hartungus. The penchant of latter-day scholars for narrow specialization was quite alien to intellectuals of Myriti's time who often delved deep in both arts and sciences. Myriti's own Swiss mentor Loritus was not only a famous mathematician of his time but also lectured in humanities at the College de France in Paris.
3. The Collegium Melitense
One cannot say that Myriti contributed much to the fostering of mathematics in Malta. He remains best known for his "Opusculum Geographic..." published [p.121] in Ingolstadt in 1590, wherein he makes use of spherical trigonometry to identify geographical locations. Most of his academic years were, at any rate, spent abroad. The real breakthrough in local education generally, and in mathematical instruction, particularly, came soon after Myriti's eclipse, with the opening of the Jesuit "Collegium Melitense" in 1593. A variety of reasons converged to bring about this important event. The Jesuit Order was conceived as the church's bulwark against the powerful challenge of the Reformation. Lutheranism, as indicated, had gained a firm foot-hold among Maltese intelligentsia so that as early as 1553 Bishop Cubelles, who was also invested with inquisitorial powers, naturally sought the assistance of the purposely-founded order. His wishes could not be acceded to on the grounds that not enough men could be mustered to erect a college here. But in a few years the Jesuits' attention to Malta was drawn again from a totally different source: the sheikh of Tagiora in Barbary requested Jesuit missionaries to preach Christianity there in Arabic. Ignatius' eyes turned immediately to Malta seeing it as an invaluable potential catchment area whence Arabic-speaking solid Christians could be recruited for missionary activity among infidel Moslems in North Africa. In spite of early evidence of recruitment from Malta, Ignatius' dream, albeit transformed, had to wait for half a century before it could be realized. Protracted multi-partite negotiations between the Bishop, the Inquisitor, the General of the Jesuits and the Casati brothers, Cateliano and Padre Pietro, on the possibility of opening a College in Malta had been going on at least since 1578, but only in 1593, after the great plague of the previous year had abated, could a pioneering group of twelve Jesuits from the neighbouring Sicilian province start classes here. Initially, the curriculum was [p.122] the standard fare of "Grammatica et Litterae Humaniores" based on the well-beaten track of the medieval trivium. Student numbers were somewhat less than a hundred within a few decades and exceeded 400 by 1706.
It can perhaps be argued that mathematics in Malta benefited from the presence of the Jesuits and their international connexions. It is certainly thanks to their existence on the island that in 1637 Malta was visited by the famous German Jesuit mathematician P. Athanasius Kircher, but he appears to have been more interested in the troglodytic settlement at Għar il-Kbir, than to expound any mathematical results of his. Both Mifsud and Pecchiai, quoting no sources, associate Prior Salvatore Imbroll with Kircher and attribute Imbroll's Specula Melitensis to him. This is highly unlikely. In spite of the "instrumenta physico-mathematica" mentioned in the rather astic full title of the work, there is nothing relating it either to mathematics or to Kircher; the pamphlet is merely a hotchpotch of pseudo-scientific drivel.
3.1 The Class of Mathematics
The Jesuit fathers' zeal soon made their presence felt in these islands and not all felt terribly comfortable with them around. The profligacy of several of the knights of the Order was notorious and the arrogant licentiousness of many of them could not stomach the censure hurled at them by the intransigent preachers. Things came to a head in Carnival of 1639 when the Jesuits were summarily sent packing out of the island by a vociferous, influential minority in the Order. It has been suggested by Mifsud, that it was in atonement for this incident that Grandmaster Lascaris, on the fathers' repatriation, established a class of Mathematics at their college. This could only have been partly the reason, judging by the rather long stretch of time between Carnival [p.123] 1639 and May 1655 when the deed of foundation was signed. Further, it appears from correspondence extant at the Curia Generalizia of the Jesuits in Rome that, on the contrary, it was the Jesuits who were obviously pandering to the merest wish and whim of his ence, treating him with kid's gloves, and showing particular anxiousness to avoid repetitions of show-downs and entanglements with his Order. The compliance by Fr. General to the Grandmaster's wish to establish a class of Mathematics at the Maltese college must be seen in this light. The Grandmaster's interest in founding this class is intelligible in view of his narrowly functional vision of the discipline as "slave and servant" of the utilitarian sciences of navigation and of artillery. He made no bones about his attitude:
Havendo la nostra religione maggior bisogno di soldati e di marinai che non ha di dottori e d'altre genti otiose de quali e ripiena hoggi l'Isola.
(The reverberations of this ominous statement were still bling in 1977.) Nor were the Jesuits themselves better motivated in this regard. The class does not appear to have been started out of any great conviction of its importance but merely to please His ence who had requested it. So much so that no sooner had Lascaris departed this life than the class was forthwith stopped indefinitely.
[p.124] In order that the Mathematics class should have a sound financial footing, Lascaris had decreed that the proceeds, up to the value of 100 scudi per annum, accruing from the of "il maglio", played at what is still called il-Mall in present-day Floriana (See Pl. 2) should be channelled to this cause. The College Rector, P. Giuseppe Mantia, had asked for P. Fabri to be the first incumbent of the lectureship but his request could not be acceded to. Instead, the Sicilian P. Jacobus Mas˛ was assigned to the post which he filled for four years. It appears that Mas˛ was not at all happy teaching in Malta, and accordingly he made repeated requests to Fr. General to be re-assigned to the Veneto which had then only recently opened its gates to foreign missionaries. The opportunity soon came and was well taken when Lascaris died.
In contrast with the much longer stay of a number of Mas˛'s successors, about whose teaching we know next to nothing, his brief sojourn here yielded a precious document that recorded the kind of mathematics he used to impart. The Castiglian knight Fra Emmanuele Arias y Porres, a student in Mas˛'s class, dutifully recorded and published in Malta his "Problemi Geometrici Cavati...dal Trattato della Geometria Militare dettato in Malta dal P. Giacomo Mas˛ della Compagnia di Giesu Professore della Matematica" (Pl. 3). In 1661, soon after his departure from Malta, Mas˛ himself published in Palermo, where he was teaching, a four-part work entitled "Corso Matematico del P. Giacomo Mas˛ Siracusano della Compagnia di Giesu Lettore gia delle Matematiche ne' Collegi di Roma, e Malta, e nel presente di Palermo"; a copy of [p.125] the fourth volume, subtitled "Sferologia nella quale...si spiega...la sfera Armillare, o...Cerchi del Cielo", is kept at the National Library.
The Mathematics class was forgotten till 1681, when kindred-spirited Grandmaster Gregorio Caraffa made a second request to Fr. General Oliva to have the classes restarted. The same functional motivations on the part of the Order, and the same attempts on the part of Fr. General to please the Grandmaster are again very much in evidence. This time, Messina-born fully-fledged, four-vowed P. Vincentius Alias was sent in 1682 and taught here for full 18 years till the end of the century.
Alias retired from teaching when he was 76 and, while staying on at the Melitense, a younger mathematician, the French father George (de) Mothu, took over his duties; Mothu was then 36 and six years after his solemn profession of four vows. Correspondence about him between the General [p.126] and the Rector shows that he was a misfit in the Maltese community, being very particular about eating and recreational habits. It is hardly surprising that by 1708 he had left only to be replaced, full seven years later, by yet another unsuccessful Frenchman, Father Jean Baptiste Thiolis from Lyons. Nearly 70 years old Pere Thiolis had problems both with the language and with the climate. He stuck it out for a year and in 1717 one encounters yet a third bird of passage called Padre Melchior Spitaleri from Palermo, who was here for just two years; he may have left the Society or died before his solemn profession. Stability only returned in 1719, when 43-year old Padre Angelo Aguillera, perhaps related to the famous Sicilian Jesuit historian Padre Emmanuele Aguillera, came and stayed till his at the college on 27th June 1744. He taught, year in year out, throughout his stay except during the last two years of his life when he is recorded to have been infirm; he was also rector of the college between June 1736 and April 1739.
3.2 The Curriculum
It is thanks to these four years of Aguillera's rectorship, during which he retained his mathematics lectureship and was also prefect of studies, that some light can be thrown on the sort of mathematical curriculum followed at the Jesuit college. Apart from Mas˛'s lecture notes already referred to, just one other mathematical manuscript has survived and encountered to date that can [p.127] definitely be ascribed to the set of mathematical texts utilized at the college. It consists of a set of notes dictated by Aguillera between 19th October 1735 and 28th December 1738, coinciding roughly with his term of office as rector; it is entitled "Trattato dell'Aritmetica Prattica". It is divided into two parts: Arithmetic and what may be untechnically termed Algebra. The method of presentation is the classical, rigorous format of axioms, definitions, scholia, lemmata, theorems and riders. The first part deals with counting, the four rules, arithmetic, harmonic and geometric sequences, quadratic and cubic roots extraction, and applications to problems of proportion, mainly taken from commercial life. Aguillera appears to have been unacquainted both with decimal notation as well as with logarithms. The "Algebra" section deals with symbolic notation, the translation of every-day problems into equational form, the manipulation of these equations and the solutions of linear and quadratic polynomial equations. Some applications to Euclidean Geometry are also discussed.
3.3 The Decline of the College
During Aguillera's lectureship, the mathematics class was at its peak, enjoying a long period of stability during which it consolidated its achievements. At this time too, the "Melitense" was raised to the status of a University empowered to bestow on its graduands the degrees of Master and Doctor of Philosophy and of Theology; the Magistral Bull of Fra Antonio de Vilhena granting University status was issued on 7th June 1727. Within a couple of decades of Aguillera's demise, the wave of intollerance for and persecution of the Society that was then sweeping Europe, engulfed also the Maltese Islands. In 1743, the ailing Padre Aguillera was replaced by his co-national P. Filippo Arena from Piazza. For the next decade, the Professor of Mathematics [p.128] was yet another Sicilian, P. Ignatius Spatafora, who hailed from Palermo. Over the next five years, two other Sicilians had come and gone; these were P. Francesco Speciale from Nicosia, who was here certainly till 1759, and P. Placido Cuzzaniti from Messina, who had replaced Speciale by the end of 1761 and taught till 1763. No mathematics was taught in the followin year, but the French father Francois de la Madalene from Lyons, appeared in 1764 only to be thrown out again by Pinto on the fateful night of 28th April 1768. By the time these events came about, even financially the chair of mathematics was no longer a going concern.
4 Mathematics Outside the Jesuit College
Although the Jesuit College in Valletta was certainly the leading teaching institution in seventeenth and eighteenth century Malta, it was by no means the only one. In spite of the Order's plans to have its men trained at the "melitense", it appears that other institutions, with specific aims, were set up independently. These included a school for the Grandmaster's pages and a school of navigation. Further to these colleges, enterprising individuals set up their own schools in both urban and rural areas.
4.1 Primary schools in towns and villages
The early existence of Grammar schools or schools of Humanities which may or may not have imparted numerical skills has been discussed above. It has [p.129] also been indicated that already in the sixteenth century these were certainly not confined to Mdina but were to be found also at Birgu and possibly also in some of the villages As time went by the numbers of these schools, mostly run by priests and notaries, increased and spread throughout Malta and Gozo so that by 1588 there were already five of them operating in Vittoriosa and Senglea alone and by 1650 others were to be found also in Mqabba, Naxxar, Żebbuġ, Żurrieq and in Gozo. Towards the end of the seventeenth and increasingly so in the eighteenth century one encounters explicit mention of topics like abacus, arithmetic, mercantile arithmetic and navigation in these schools' curricula. The following table, derived from the data collected by Borg, shows dates when the schools were granted licence to operate, locality, name of school-master and mathematical subject taught:
Antonio di Barro
Fra Baldassare del Fiore
Giovanni Battista Calleja
Don Salvatore Callus
Don Luca Fiteni
4.2 The Pages' College
Lascaris' intention I founding the chair of mathematics at the Jesuit College was clearly to give, first and foremost, adequate training to members of his order. There is evidence, however, that the Grandmaster's own pages received their education elsewhere, at least in later years.
[p.130] An interesting document dated February 1750 is entitled:
Trattenimento Accademico in Algebra Finita, Geometria Elementare, Trigonometria, Geometria Sublime e Geografia, da dimostrarsi da Paggi di S. A. entissima Fra D. Emmanuele Pinto.
It consists of a list of "theses" (theorems/propositions) that were to be defended in the Grandmaster's presence, by the eleven pages whose names are given, as if for public entertainment. The event was, in all probability, an end of course viva voce in the Italian style. Be that as it may, the list affords a fairly clear insight into the sort of mathematics indulged in at the pages' school and can fruitfully be compared with the curriculum at the Jesuit college. The "algebra" included simple simultaneous linear and quadratic equations as well as problems involving geometric progressions including convergent infinite series; these are not encountered in Aguillera's treatise. The propositions of Elementary Geometry are taken from Euclid, whereas what is termed Geometria Sublime comprises a treatment of conic sections referred to their foci, axes, asymptotes and so on, in the classical fashion, ignoring completely the Cartesian analytic approach that had been introduced a century earlier.
In less than two decades after this "trattenimento", the same Pinto was to take over the Jesuit University and supplant it with his own Pubblica UniversitÓ di Studi. Attached to Pinto's University, was a Collegio di Educazione, a sort of Junior College, which initially catered for the needs of the clerics and conventual deacons and which, for a short while, absorbed also the pages' college. In the 1770s the master of arithmetic and of calligraphy is known to have been the Cappellano d'Obbedienza Fra Matteo Gili.
4.3 Pagnini and The School of Navigation
The usefulness of mathematics as a tool for the practical sciences of navigation and of artillery had been recognized by both Lascaris, who established a class [p.131] of mathematics with this express purpose, and Caraffa who ensured its revitalization to the same end. Yet it was to Perellos' credit that a school, dedicated to navigation, pilotage and related subjects was established early in the eighteenth century. It was thanks to this institution that Malta attracted to her shores a leading European engineer of the time who came to lecture at this college under the title of "Hydrographer of the Order". This was Giovanni Pagnini who was born in Lucca but spent most of his life in Malta and became a naturalized Maltese citizen. He was a prolific author on various subjects relating mostly to Mathematics and its applications. His "publications list" includes the following works:
(i) Compendio di Trigonornetria Piazza (1724)
(ii) Trionfo in Mare ossia Scuola di Commandare Annate e Vascelli da Guerra cosý per la manovra come per Caccia e Combattere il Nemico, (?,1728).
(iii) Dell'Estrazione delle radici quadrati e cube, undated manuscript.
(iv) Trattato della Sfera ed Introduzione alla Navigazione per uso dei Piloti, (Venezia, 1750).
(v) Costruzione del Compasso di Proporzione e suo uso, (Napoli, 1753).
Most of the mathematics Pagnini wrote about had one eye on applications. His root extractions using classical methods had a treatment very similar [p.132] to Aguillera's, his contemporary; both ignore logarithms altogether and, in some instances, examples discussed were even identical. Perhaps Pagnini's most "applicable" mathematical text was his Compasso di Proporzioni, which may be sub-titled "mathematics for the layman". In it he discusses various so-called "compassi" consisting of compasses-like instruments which were two-armed, pivoted at one end, and which had markings down both arms. Pagnini explains how the markings are arrived at and how the instruments can be of use, particularly to architects and engineers with an unsound mathematical background, to achieve various measurements mechanically and avoiding all computations.
The simplest of these instruments is "La Linea Aritmetica" among whose many applications Pagnini includes the division of a line segment into n equal parts, and the reproduction, reduction and magnification of site-plans and similar designs. Pagnini's constructions are not original. This instrument is also described in an undated, probably eighteenth-century, manuscript in French entitled "Traite des MathÚmatique et Elemens de GÚomÚtrie". Pagnini's next instrument, "La Linea dei Piani [o] Linea Geometrica" appears to have been invented by Galileo for use by military engineers; it appeared for the first time in his pamphlet of 1606 Le Operazioni del Compasso Geometrico et Militare. Among its uses Pagnini lists square root extractions and the construction of 2-dimensional figures proportional to other given figures. A similar instrument, used for cube-root extraction and the construction of proportional 3-dimensional figures is called "La Linea Cubica [o] Linea de Solidi". Other instruments include "La Linea delle Corde", for finding the angle subtended at the centre of a given circle by a given arc, "La Linea de Poligoni", for inscribing any polygon in a given circle, and "La Linea Metallica" used for comparing diameters of spheres of different metals; metals considered are gold, mercury, lead, silver, copper, iron and tin (Pl. 4).
Pagnini's "Linea Geometrica" is also treated in yet another manuscript, which is both undated and anonymous, where listed among its uses is the measurement of the capacity of barrels, given their depth and circumference, and of the capacity of ships' holds. It is very likely that these problems were considered in the school of navigation, where Pagnini lectured, and that this [p.133] and other anonymous texts treating similar topics, were actually in use there.
Another topic Pagnini wrote about with a view to deriving several applications was trigonometry, both plane and spherical. In his treatise "Compendio di Trigonometria Piana" he defines the standard circular ratios of sine, tangent, secant etc., and proceeds to apply them to the solutions of triangles. Practical applications follow, included among which is the measuring of distances between inaccessible objects; these problems are illustrated profusely with life-like diagrams. The treatise is concluded with a detailed table of sines, tangents and secants. It is only here that Pagnini reveals that he was, after all, acquainted with logarithms, whose use he recommends in the solution of trigonometrical problems. Spherical trigonometry is dealt with in his "Trattato della Sfera...".
4.4 The School at St. Elmo
The school of navigation was established well before Pinto's UniversitÓ degli Studi was erected. As yet, it is not at all clear how long this institution survived. It is known, however, that towards the end of the Order's stay in Malta, the need was felt to establish what may be termed as a technical college in Fort St. Elmo. Perhaps this college replaced the school of navigation which may have been discontinued during the strictures of Ximenes' rule. Fortunately, an incomplete list of "theses", dated 1796 and defended by three of the mathematics students in an end of the year viva, not unlike the pages' "Trattenimento" discussed above, has survived to record for us the sort of mathematics taught there. The "Algebra" part of the syllabus included manipulation of polynomials, problems involving arithmetic and geometric progressions among which were also discussed problems of convergence including Zeno's paradox. It is also apparent that the students were familiar with Newton's method of approximating to roots of polynomials. Further to the usual treatment of Euclidean Geometry, a short but interesting part of the syllabus called stereometry included a section on Platonic solids in which problems of their existence and regularity properties were discussed. A final section tied up together the [p.134] foregoing headings discussing algebraic methods of solution to 2- and 3-dimensional geometric problems.
4.5 The Diocesan Seminary
Plans to establish a Diocesan Seminary for the training of priests had been laid soon after the council of Trent. Following long drawn out squabbles as to who should be paying and how much should be paid for it, it was decided by Bishop Gargallo to divert funds earmarked for the Seminary to the establishment of the Jesuit College. When the Seminary's financial difficulties were finally sorted out and the institution was on its feet a century later, the principal courses taught there were, naturally, those of Philosophy and Theology. With-in the context of the former, however, and under the general title of cosmology, a certain amount of mathematics was also covered. This is evident from yet another "defence of theses" dated 1791. The defendants were the seminarians Subdeacon Joseph Farrugia and the seven clerics Paulus Busuttil, Philippus Pulicino, Petrus Mallia, Joseph Grima, Joseph Principato, Paulus Borg, and Franciscus Agius. This defence took place inside the Mdina Cathedral and in the presence of their Professor of Philosophy and Mathematics who was none other than Don Xaverius Caruana. The theses, couched in typical Scholastic Latin, are of great interest. They deal mostly with classical Newtonian statics and dynamics, including problems of finding least times of descent along various specified arcs, circular motion, machines, and direct and oblique impact. A smaller section deals with hydrostatics, hydro-dynamics, and with optics.
5 The University
Following the unceremonious dismissal of the Jesuits in 1768, Pinto took immediate steps to transform their college into the university of his dreams. To this end he invited from abroad some of the best men in Europe of the time. Everything augured very well for mathematics, in particular, as the person [p.135] Pinto chose to lead the new institution as Rector Magnificus was himself a mathematician of some renown. This was the Florentine Servite Padre Roberto Raineri Maria Costaguti.
Costaguti arrived in Malta to take up the rectorship of the University on 1.ii.1771 and, sidestepping much petty antagonism and opposition, got down to the serious business of writing the constitutions for the Pubblica UniversitÓ, to which as already stated, was attached a "Collegio d'Educazione". According to these statutes, the full university course, lasting eight years, was divided into two. The first three years led to the degree of Master of Arts in subjects common to all faculties, whereas the last five were dedicated to studies in the traditionally professional courses of Theology, Jurisprudence and Medicine; this pattern survived till very recently. Mathematics formed part of the curriculum of the initial three years, on which Costaguti predictably had to say: "alle matematiche si deve dare particolare importanza".
The first incumbent of the chair of mathematics was Giovanni Alberico Archinto who was also Secretary of the University and of the College of Education. For some unknown reason he resigned his position soon after his appointment and was soon replaced by the famous astronomer Padre Giuseppe Piazzi who was a Theatine. Piazzi's stay was also of short duration. Soon after his appointment, a P. Atanasio Cavalli is encountered as "Professore delle Matematiche"; he is known to have read an oration in honour of Pinto's successor Ximenes. Labouring under severe financial constraints, Ximenes soon frittered away most of these educational achievements. On 14.ix.1773, the Grandmaster dismissed all foreign university staff, giving them one month's notice and replaced them with locals. New statutes were drawn up, reducing the number of chairs to eight; luckily, mathematics was one of those spared, the Maltese incumbent of the chair being Dr. Fisico Don Carlo Azzupardo.
[p.136] 5.1 Mathematics at the University
Fortunately for everyone Ximenes' rule lasted less than three years and under de Rohan, his successor, the University and the College of Education were restored to their former status. The importance of mathematics teaching was reconfirmed in no uncertain terms. In 1778, the Mathematician Domenico Malabri was appointed new Rector; besides his administrative duties, Malabri also saw to the teaching of mathematics and of philosophy.
Confirmation of the progress achieved in the subject is yet another "defence of theses" that has survived. Four "studenti di matematica nella pubblica university di Malta", Salvadore Psaila, Giovanni Zammit, Vincenzo Marchesi, and Giuseppe Guido, in 1780 defended various theses under the general title of Arithmetic which included the following subheadings: "Calcolo di numeri Interi, Calcolo delle Frazioni, Delle Frazioni Decimali, dell'Algebra, delle Potenze e della loro Analisi, Calcolo degli Esponenti, Calcolo de Radicali, delle Radici Immaginarie, dell'Equazioni, delle Ragioni Aritmetica e Geometrica, delle Progressioni Aritmetica e Geometrica, de Logaritmi". Much of the material is included in similar syllabi already discussed in connexion with the Pages' College and the School at St. Elmo. A few topics, however, stand out as being of a more theoretical nature. Worthy of note, in view of the relative novelty of the ideas at the time, is the presence of a section on complex numbers. Coupled with the fact that reference is made to the work of Euler, who was then still living, one can say that the university syllabus was well abreast with what was happening in Europe at the time. Newton's work is represented by his Binomial Theorem; no reference is made, however, to his infinitesimal calculus, although a treatise entitled "Arithmetica" is hardly the place to look for it. It is still unknown whether the calculus was considered at all at the university in this period. It is known, however, that at least one member of the Order was familiar with the concept, having studied the subject abroad. This is evident from an "Essai de MathÚmatiques dÚdiÚ Ó Son Altesse entissme Monseigneur le Prince Emmanuel de Rohan" by Jean Baptiste Latreille de Lavarde, published in Toulouse in 1784, wherein he states that he was a deacon [p.137] of the Order who had studied at the College of Christian Doctrine [sic]; the 18-page booklet is on exhibit at the National Library.
5.2 Maltese Mathematicians
At the time the University was giving such sterling service in the promotion of mathematics, a number of Maltese nationals were making a name for themselves in this field elsewhere. Reference is made here to three medical doctors of the eighteenth century who showed keen interest in the subject. Dr. Giuseppe De Marco (1712-1789 of Cospicua, about whose medical achievements a lot has been written, received his early education at the Jesuit College; he must have had his initial mathematical training under Aguillera. Further to his several medical publications he wrote two mathematical treatises entitled "Trattato della Trigonometria Piana" and "Vulgaris Arithmeticae Elementaris Theoria et Praxis", which appear at the end of his "Breve Compendio dell'Idrostatica". Another medic and mathematician who was an exact contemporary ntemporary of Demarco's was Filippo Zammit (1719-1796) of Zurrieq.
Pride of place, however, goes to Giuseppe Zahra who was born in 1730 and received his early education at the Jesuit College; it is very probable that, like Demarco, he too was trained by Aguillera. He proceeded to Naples for his medical studies but soon returned to Malta in Pinto's employ both as a precentor for his pages and to work on the Order's scientific projects connected with "idrauliche", fortifications, navigation, and the silk industry. Through his maritime connexions he made his way to St. Petersburgh and the Royal Court, where it is highly likely that he came in contact with Euler himself. He left Russia in 1779 and, by way of Paris and Messina, ended up in Catania to teach mathematics at the Benedictine monastery and later also at the [p.138] university. Having made a name for himself in that city, on 23.vi.1786 he became Professor of Geometry at the University of Catania, being considered then "il pi¨ valido matematico che fosse in Sicilia". According to a portrait that graces the office of the present incumbent of the Chair of Geometry at the University of Catania (P1.5), Zahra died in 1821.
This sketchy overview of how mathematical education in Malta developed from lowly beginnings in late medieval times to a burgeoning structure by 1800 is yet another illustration of fruitful cross-cultural, international exchanges. Malta, at the cross-roads of various cultures, played hostess once again to several learned men from outside her shores who came from diverse European centres of excellence and left behind them a rich legacy of a sound mathematical tradition. In producing a number of practitioners and masters of her own, Malta reciprocated, making her own modest, but none the less valid, contribution for her own benefit and that of her neighbours.
The assistance of the following persons that include, librarians, curators of archives and of their staffs is gratefully acknowledged:
Rev. Can. John Azzopardi, Curator Cathedral Museum, Mdina.
Mons. Prof. Vincent Borg.
Rev. Fr. Francis Edwards S.J., Curator, Archives of the Society of Jesus, Rome. Mr. Salv. Mallia.
Dr. Franco Pellegrini, Notary to Government.
Rev. Fr. Anthony Sapienza S.J., Librarian, Pope John XXIII Library, Valletta. Rev. Fr. Robert Soler S.J., Provincial, Maltese Province of the Society of Jesus. Mr. John Sultana, Librarian, National Library of Malta.
Dr. Paul Xuereb, Librarian, University of Malta.
[p.139] DOCUMENT I
NAV Not. Pietro Vella R476/38 (21.iii.1655) 81v-85.
A declaration by Grandmaster Fra. Joannes Paulus Lascaris whereby, inter alia, the class of mathematics is founded in the Collegiunn Melitense.
f.81v. Declaratio per entissimum Dominum Magnum Magistrum D. Fra Jo: Paulum Lascaris.
Adi 21 del mese di Marzo de11655 dalla NativitÓ di Nostro Signor Gies¨ Xpo. correndo l'Indizione ottava.a
Constituto personalmente in anti me notario et testimoni infrascritti l'Eminentissimo e Reverendissimo Signor Fra Gio: Paolo Lascaris Castellar Gran Maestro della Sacra Religione Gierosolimitana nel suo palazzo magistrale et in virt¨ della facultÓ ch'have a se riservato di dichiarare modificare restringere aggiungere ˛ rivocare le conditioni e li modi dall'Eminenza sua lasciati e prescritti nella fundatione che institui et eresse in servitio di detta sua Sacra Religione per giuste cause moventi l'animo suo have declarato, Ŕ determinato che...
f.83v. ...Jnoltre l'Eminenza Sua ha lasciato e lascia in titulo di legato a quel lettore purche sia Padre religioso della Compagnia di Giesu che sarÓ mandato e verrÓ qui in Malta per leger la matematica alli Signori Cavalieri et altri Religiosi dell'Ordine e di San Gio: Gerosolimitano scudi cento l'anno da pagarsi per li suoi alimenti /al/ Ven. Colleggio di detta Compagnia sito in questa CitÓ Valletta e non altrimentre della detta fundatione e suoi essequitori per quel tempo che attualmente legera et ammaestrara alli predetti la suddetta metamatica e non altrimentre.
f.85. ...E con suo giuramento toccando la sua Croce Magistrale have giurato et affirmato quanto sa. si contiene Unde etc.
[p.140] fatto in Malta Ŕ nel magistral Palazzo in presentia del religioso di detta Sacra Religione il signor frÓ Michaele Barruel et di Giovanne la Costa testimoni chiamati etc.
AOM 119 (9.vi.1656), f.156v.
Decree whereby revenues accruing from the of "il maglio" are channelled to the maintenance of the chair of mathematics.
Decreto sopra la casetta da fabricarsi nel gioco del maglio.
Die eadem. Havendo l'Eminentissimo e Reverendissimo Signor Gran Maestro proposto che voleva mandar fabricare una casetta appresso il gioco del Maglio per maggior commoditÓ de giocatori, e trattenimento publico dichiarandosi d'applicare, come in effetto ha applicato l'emolumenti che si caveranno dell'affitto di detto gioco, e casetta per la sua fondatione, e per il mantenimento della Cathedra della Mathematica. L'Illustrissimo Signor luogotenente, e il Venerabile Consiglo Compto. col scrutigno delle palle approbarono, e gradirono detta propositione dando il loro consenso, che detta casetta si faccia in luogo che li Venerandi Commissarij delle fortificationi stimeranno, che non sia d'inconveniente all'istesso.
Typical entries in a book of accounts, showing sub-totals
at the foot of each column. The peculiar fifteenth-century notation for 'one
half' is of interest.
Facsimile of CMM CA Misc. 438 No. 1 (1494-96), if 15v-16.
Courtesy of the Curator, Cathedral Museum, Mdina.
Map of Valletta showing "Il Gioco del Maglio".
Oliver Dapper. Valetta civitas nova Malthae olim Millitae. Amsterdam, 1668. 283 x 365 mm.
Reproduced by kind permission of Chev Dr Albert Ganado.
Frontispiece of Giacomo Mas˛'s undated Problemi Geometrici...Dettato
Reproduced by courtesy of the Librarian, The National Library, Malta.
Il Compasso dei Poligoni.
French workmanship. Photo credit: Museums
Reproduced by courtesy of the Curator, The Maritime Museum, Vittoriosa.
Portrait of Giuseppe Zahra (1732-1821),
Professore di Geometria, UniversitÓ di Catania.
Photo credit: Prof Filippo Milazzo.
Courtesy Dipartimento di Matematica, UniversitÓ di Catania.
 CMM CA M1 - M4.
 NAV Not. G. Zabbara R494/1(1) (11.v. Ind.IIII [ = 1486]), f. 26: "+ Ego Fridericus de Bordino quod supra Judex meliveti nesciens scribere feci manu propria signum vencrabilis sancte crucis".
 NLM Univ. 12 (10.ix.1515), f. 123: "In notariatu officio...dila curti di quista chitati chi hanno concurso alcuni ydioti et ignoranti medianti Ii quali ignorancia loru lu populo fu et e mali servito ne e Justa cosa li ydioti concurriri ad dicto officio...et...de cetero nixuno pocza concurrirj si non persunj Iiteratj doctj et actj et non ydiotj".
 Ibid. (28.v.1506), f. 15 et passim.
 Ibid. (28.v.1506), f. 15 et passim.
 Ibid. (25.v.1506), f. 11v et passim.
 Ibid. (23.xi.1515), f. 22 et passim.
 NLM Univ.11 (18.xi.1461), ff. 135-137.
 Ibid; also. Univ.13 (5.v.1467), f. 22, (15.xi.1467), f. 9; Univ.11(10.ii.1470), f. 586v(bis).
 Ibid. Univ.11 (12xi.1470), ff. 219-219v, 194, text in E.R. Leopardi, "Appointment of a School-master in 1470", MH iii, 2 (1961), 55-58.
 NLM Univ.11 (20.x.1471), f. 214.
 Ibid. Univ.11 (30.xi.1473), f. 269v.
 Ibid. (10.ii.1476), f. 347v. CMM CA Misc. 36 (19.iii.1477), f. 22.
 Ibid. (18.xi.1461), ff. 135-7; Univ.13 (15.xi.1467); Univ.11 (12.xi.1470), ff. 219-219v,194; (10.ii.1476), f. 347v.
 Ibid.. Univ. 11 (30.xi.1473), f. 269v.
 CMM CA Misc.36 (16.iv.1477), f. 29.
 NLM Univ.11(27.1.1479), ff. 394-394v: "Consilium super facto quod Donnus Gilius Dilia non vult regere scolas nisi detur sibi aliquid salarii"; some council members suggested he should be given 2 uncie and others that he should be given nothing.
 NAV Not. G. Zabbara R494/1(IV) (2.viii.1496), f. 15.
 CMM CA Ml (21.xi.1514), f. 55; (25.xi.1515), f. 22. See also NLM Univ.13 (6.x.1531), f. 41.
 CMM CA Ml (17.vii.1517), f. 67.
 Ibid. (?.ix.1517), f. 63. NLM Univ.12 (14.xii.1516), f. 150v.
 CMM CA Ml (30.iii.1518), f. 41; (2.viii.1518), f. 39. NLM Univ.12 (26.ii.1518), f. 175v.
 CMM CA Ml (18.xii.1520), f. 144; (10.1.1521), f. 445; (23.iv.1521), f. 407; (5.xii.1521), f. 353; (2.i.1522), f. 346; (3.v.1522), f. 308; ibid. M2 (16.iv.1523), f. 30; (1.i.1524), f. 11; (28.v.1528), f. 405; Misc. 36 (30.v.1528), f. 558; (8.iv.1529), f. 598; (30.viii.1529), f. 640; (30.v.1530), f. 442; (21.viii.1531), f. 457.
 CMM CA M2 (2.v.1525), f. 4. While at Rome and in Naples he also conducted business on behalf of the University and the Maltese diocese in connexion with the granting of the Leonine Bulla Beneficiorum: NLM Univ.12 (19.iv.1526), f. 405. On this Bull see V. Borg, "Important Canonical Enactments on the Ecclesiastical Benefices of the Maltese Islands" (unpublished doctoral thesis, Royal University of Malta, 1960).
 NLM Univ.12 (6.iv.1526), f. 402.
 CMM CA M2 (16.v.1526), f. 373; (20.ix.1526), f. 369; (8.i.1527), f. 156; (8.v.1527), f. 212.
 Deed untraced.
 CMM CA M3 (10.xii.1532), f. 35; (19.iv.1533), f. 77; (27.vi.1533), f. 65.
 NLM Univ.13 (?.ii.1536), ff. 100-102; CMM CA M4 (13.iii.1536), f. 85, (2.ix.1536), f. 24; ibid. M3 (13.ii.1537), f. 479; (20.vi.1537), f. 436; (3.x.1537), f. 395; (16.ii.1538), f. 677; (8.vii.1538), f. 593; (5.x.1538), f. 517; ibid. M4 (25.ii.1539), f. 225.
 NLM Univ.13 (28.ix.1537), f. 151.
 The details of the later history of the Mdina Grammar School can be found in G. Gatt, "It-Tagħlim f'Malta jew l-Iskejjel tal- Gvern", Is-Sebħ (25.iii.1957-3.iii.1958) (44 articles).
 Sec e.g. G. Wettinger, "Concubinage among the Clergy of Malta and Gozo ca.1420-1550", Journal of the Faculty of Arts vi, 4 (1977), 182-3.
 NAV Not. G. Zabbara R494/1(III) (4.ix.1495), f. 11; R494/1(I) (19.xii.1486), f. 46v.
 NLM Univ.13 (15.xi.1467), f. 9v.
 NLM Univ.11 (2.viii.1479), f. 400v.
 NAV Not. Placido Abela MS. 514/1 (2.vi.1558), unpaginated.
 NAV Not. F. Ciappara R185/3 (1.ix.1576), ff. 1-5v: "...Antonio eius filio tam hic melite dum ipse antonius vacabat in schola humanitatis quam in...dicta civitate Neapolis at alibi...et sibi voluit et mandavit quod...pro coniscenda et adaptanda Arte Sacre Pagine seu verius pro coniscenda et adaptanda arte utriusque Juris et confectum fuit doctor Sacre Pagine constitutus Iuris dictus Antonius...".
 AIM Processi Vol. 4b No. 41 (20.xii.1575), f. 595v.
 AIM Processi Vol. 3a No. 65 (sive XIV), ff. 319v-320v.
 S. Fiorini, Santo Spirito Hospital at Rabat, Malta: the early years to 1575 (Malta,1989), Chapter 7.
 S. Fiorini, "A Prescriptions List of 1546", Maltese Medical Journal i, 1 (1988), 31 fn. 66.
 AOM 415 (20.iv.1533), f. 243.
 NLM Univ.13 (18.iv.1534), f. 67.
 44 NLM Univ. 84 (11.iii.1562), f. 346v and several other similar entries up to Univ. 85 (30.xi.1572), f. 107.
 NLM Univ.13 (19.xii.1540), f. 206v.
 S. Fiorini, "A Freelance Medical Practitioner at Birkirkara in the Early Sixteenth Century" (forthcoming).
 S. Fiorini, "Church Music and Musicians in Late Medieval Malta", MH x, 1 (1988), 1-11.
 NLM Lib. MS. 4 ff. 742-818
 G. Wettinger and M. Fsadni, L-Ghaija ta' Pietru Caxaru (Malta,1983).
 It would not be very surprising if it were to turn out that notaries in medieval times generally lacked numerical skills. It is clearly documented that this was the situation even in the eighteenth century; vide NLM Lib. MS. 429, Vol. 5 (1765-1772), ff. 146-146v. This reference was kindly provided by Rev. Fr. George Aquilina O.F.M.
 CMM CA Misc.438 No.1 (1494-96), Misc.438 No.2 (1518-20), Misc.438 No.4 (1554-55), Misc.440 Parts I-III (1540-48), Parts IV-VI (1560-62).
 CMM CA M1-M4.
 CMM CA Misc.439 Nos. 1-10 (1502-1525).
 CMM CA Misc.441 Part B: "Cunti de la dispisa dell'opera the si fa ala Cita di Malta 1559-1564" (ff. 1-36).
 CMM CA Procura PR1 (ca.1480-1595), Quaderni Diversi Nos 1-10 (ca.1480-1606) (uncatalogued).
 CMM CA Prebende 3 (Archidecanali, 1546), 6 (Decanali, 1522), 5 (Decanali, 1536), 7 (Decanali, 1601), 8 (Decanali, 1648), 11 (Tesoreriali, 1541), 12 (Tesoreriali, 1648), etc.
 NLM Univ.11 (ca.1460), ff. 77-79v.
 CMM CA Misc. 437 No.2.
 For example, NLM Univ.11 (1470), ff. 27v-28; (1461), f. 159; (1480), f. 448.
 NLM Univ.11 (11.ix.1461), f. 133; (?.viii.1463), f. 192; (19.xii.1470), f. 196. CMM CA Ml (3.ix.1518), f. 36; (22.i.1514), f. 49; (5.ii.1514), f. 57; (31.v.1515), f. 78, and several others.
 William Cowan, "Early Maltese Word List", Journal of the Faculty of Arts ii (1964), 222. Arnold Cassola, "Una edizione diversa della Iista di voci maltesi del seicento di Hieronimus Megiser", Incontri Siculo-Maltesi, ed. G. Brincat (1988), 72-86.
 AIM Processi Vol.3a No.65 (live XIV) (5.xii.1575), f. 320.
 Ibid (24.xi.1575), f. 320v, (15.xii.1575), f. 322.
 Ibid. No.11 (24.xi.1575), f. 223v.
 M. Agius-Vadala, "Giovanni Myriti (1536-1590?) - His Life and Work", Proceedings of History Week 1983, ed. M. Buhagiar, (Malta, 1984), 39-54. A copy of Myriti's Opusculum can be found at the National Library (DE.5.2).
 P. Johannes Alphonsus Polanco, Chronicon iii, 228: "Dominicus Cubelles Episcopus MelitensisRomae instanter agebat cum P. Ignatio ut aliquos de Societate daret ut collegium in illa insula, quae arabice utitur lingua, inchoare posset" = MHSJ v 490-91, Letter No. 3758(18.ix.1553) to P. Hieronimus Domenecchi.
 P. Johannes Alphonsus Polanco, Chronicon iv 217-8 =MHSJ vi 163-4, Letter No. 4055 (13.i.1554) to P. Jacobus Laynez.
 Aloysius (alias Ludovicus) Agata born in Malta c.1540 joined the Jesuits at Palermo inc. 1557 (ARSJ Sic. 59 ff. 152, 213v.) He died on l.iii.1585 at Monreale (P. Lukacz, Historia SocietatisJesu 42 f.73). See also P. J. Fejer S.J., Defuncti Primi Saeculi Socictatis Jesu: 1540-1640, i (Roma, 1982), 2.
 P. Pecchiai, "I1 Collegio dci Gesuiti in Malta", ASM ix (1938), 129-202, 273-325. See also copious correspondence in ARSJ Sic.2, 3 (1576-83-95) starting (31.i.1578) f. 12, letter to P. Pietro Casati.
 ARSJ Sic. 67, f. 16: Student population in the Humanities class in 1658 was 97. For numbers in 1706 see text in Pecchiai, 305.
 J. MacDonnell S.J.,"Jesuit Mathematicians before the Suppression", Archivutn Historicum Societatis Jesu 45 (1976), 139.48. K.A.F. Fischer, "Jesuiten-Mathematiker in der Deutschen Assistenz bis 1773", ibid. 47 (1978), 159-224.
 Kircher's book was first published at Amsterdam in 1665; a copy is held at the National Library (L.16.8/9). See A. T. Luttrell, "Malta Troglodytica: Għar-il-Kbir", Heritage ii (1979), 461-4.
 A. Mifsud, "L'Espulsione dei Gesuiti in Malta",Archivum Melitense ii, 17 (1914), 40 fn. 1.
 Pecchiai, 165.
 Published in Naples in 1638; copy held at National Library (BS-I-27).
 Mifsud, 1-56.
 ARSJ Sic 15(I) Epist. Gen. (19.iii.1648), f. 63 No.410 (to Fr. Rector), recommendation on behalf of Dionigi Passerini "paggio del Gran Maestro"; 16(I) (13.ii.1653), f. 105 No. 584 (to Fr. Provincial): "Si stringa il P. Manthia peril rettorato di Malta perchÚ ha dato maraviglia anche a Mons. Gran Maestro il veder questo Collegio senza rettore"; (5.vi.1563), f. 161 No. 185 (to the Vice Rector): "Siamo obligatissimi a Mons. entissimo Gran Maestro per haver scritto at suo Ambaxatore a favor dell'Collegio e la sua autorita potra giovar motto".
 Ibid Sic 16(I) Epist. Gen. (19.vi.1653), f. 165v No. 214 (to the Grand Master): "La Somma Pieta di Vostra enza e l'amor suo cordiale verso la Compagnia mi danno ardire di comparirie avanti con questa mia humillima supplicatione..."; (1.i.1654), f. 229 No. 520 (to Fr. Rector): "...noi saremo sempre pronti a servire Sua enza e con la matematica e con ogn'altra cosa che potra venire da noi"; ff. 230v-231 (to Fr. Provincial): "La matematica chiesta da Mons. Gran Maestro net Collegio di Malta si deve concedere con ogni prontezza".
 Ibid. Sic 15(I) Epist. Gen. (20.v.1649), f. 194 (to Fr. Rector): "Pi¨ volte e stato raccomandato che i nostri non s'intrighino in negotii de secolari e publici et in particolare di cotesta Sacra Religione".
 Text in Mifsud, 41 and fn. 2.
 Grand Master Lascaris died 14.viii.1657. In less than a month from his , Fr. General had written to the Provincial: "Le cose di Malta con l'occasione delta nuova elettione del Gran Maestro [De Redin] hanno mutato faccia. Del P. Mas˛ scrissi che si richiamasse..." (ARSJ Sic 17 Epist. Gen. (13.ix.1657), f. 83 No. 649). In November 1658 the master of Mathematics had already left the island and was not replaced: "Levandosi it P. Mast) di Malta e non havendo V.R. successore si scusi con Mons. Gran Maestro" (ibid. (21.xi.1658), f. 215 No. 398 (to Fr. Provincial).
 Documents I and II. The legal playing of the of "il maglio" was restricted to one locality for at least two reasons: it became possible to tax it (see Doc. II) and it helped clear the streets of a public nuisance (see AOM 97 (9.xi.1587), f. 114v; (18.i.1588), f. 118).
 ARSJ Sic 16(II) Epist. Gen. (9.vii.1654), f. 301 No. 252 (to Fr. Rector).
 Jacobus Mas˛ was born in Syracuse on 31.vii.1626 and joined the Society on 26.xii.1641: ARSJ Sic 67 Cat. Trien. (1655)(1) 75.
 ARSJ Sic 17 Epist. Gen. (31.v.1657), f. 60 No. 493 (to Mas˛) in reply to his request to go to Venice "che ha aperto una gran porta per dilatar la gloria divina"; (5.vii.1657), f. 68 No. 547 (to Mas˛) in reply to a second request to go to Venice, in which letter Mas˛ asserts that "1'opera [sua] non e cosi pi¨ necessaria" (perhaps in view of the Grandmaster's imminent ); (16.viii.1657), f. 78 No. 615 (to Fr. Provincial): "II P. Mas˛ riesce molesto alla disciplina in Malta epare svogliato - Lo richiami, e dovendo continuarsi la matematica, dia successore"; (16.iii.1658), f. 137 No. 32 (to Rector): "Mi rallegro del frutto...nelle scuole sebene quella della matematica camina scarsamente".
 The existence in the National Library of this volume (NLM Bc.b.38) has been kindly pointed out to me by Mr. William Zammit B.Ed.(Hons).
 NLM E.VI.15.
 ARSJ Sic 23(11) Epist. Gen. (24.ii.1681), f. 384v No. 30 (to Fr. Rector): "Godo poi che in cotesta provincia si sia trovato chi possa degnatamente servire il Gran Maestro nella lettura di matematica desiderata da Sua enza per ammaestramento de suoi Cavalieri"; (1.xii.1680), f. 361 (to Fr. Provincial): "L'Eminentissimo Gran Maestro desidera in Malta un de nostri il quale sia maestro di matematica a suoi cavalieri...Vegga se in cotesta vi sia persona almeno abile nella professione di matematica che possa sostenere quivi la cattedra con decoro e me ne dia avviso"; (7.iv.1681), f. 398v (to Fr. Rector): "Sto io con sollecitudine singolare aspettando...per vedere una volta adempiti i comandi del Gran Maestro. Ma molto pi¨ sollecito vivo ch'egli nella lettura della matematica pienamente incontri le sodisfationi di Sua enza e'l servitio de' cavalieri".
 ARSJ Sic 23(I1) Epist. Gen. (11.viii.1681), f. 452 (to Fr. Vincenzo Alias): "V.R. [deve] rendersi viva alle istanze di cotesti cavalieri che dopo haver udito spiegare da lei i fondamenti gettati da Euclide della scienza matematica desiderano hora di essere ammaestrati in quella parte che riguarda la militare. Cessan corti le difficoltÓ per le quali altrove i nostri lettori di matematica si debbono astenere dal trattato della fortificatione: mentre in cotesta reggia dell'Ordine Gerosolimitano tali insegnamenti sono indirizzati alla sola difesa del christianesimo".
 ARSJ Sic 23(I1) Epist. Gen. (9.xi.1681), f. 486 (to Fr. Provincial): "[per] le obbligationi somme che gli debbo".
 ARSJ Sic 80 Cat. Trien. (1685), f. 135: Vincentio Alias was born in Messina on 17.iii.1624 and joined the Society on 9.vi.1640. He made his profession of four vows on 1.xi.1658. Besides mathematics he also taught Hebrew for ten years. At the beginning of his long career in Malta, he received instructions from Fr. General himself as to what was expected of him; see fn. 92 (infra).
 ARSJ Sic 162 Cat. Brev. ff. 184, 228v, 274v, 322; Sic 163 ff. 31, 136, 183, 239, 292; Sic 164 ff. 19v, 102, 202, 283, 362v; Sic 163 (1699-1700), f. 439: "P. Vincentius Alias docet mathematicam hic per annos 18".
 Fr. George (de) Mothu was born in France on 4.ix.1664 and joined the Society on 9.ix.1681. His solemn profession of four vows took place on 2.ii.1694 and he started teaching mathematics in Malta in 1700: ARSJ Sic 95 Cat. Trien. (1705)(1) f. 45 No. 5.
 ARSJ Sic 41 Epist. Gen. (21.vi.1706), f. 105 (to Fr. Rector).
 P. Joannes Baptista Thiolis was born at Lyons on 24.ix.1646. joined the Society on 23.ix.1693 and made his solemn profession of four vows on 2.ii.1710: ARSJ Lugdunensis 24 Cat. Trien. (1711- 20), f. 55. On the difficulties P. Thiolis encountered in Malta, see ARSJ Sic 46 Epist. Gen. (25.iii.1715), f. 150 (to Fr. Rector), (25.iii.1715), f.150 (to P. Scipione Costanzo), (29.iii.1715), f. 151 (to P. Joannes Baptista Thiolis), (3.vi.1715), f. 160 (to Fr. Rector), (16.ix.1715), f. 179.
 P. Melchior Spedalieri (sive Spitalieri) was born at Palermo on 5.i.1685 and joined the Society on 13.xi.1701. By 1717, he had completed his fourth year of theological studies and had taught mathematics for five years; the date of his profession is not given: ARSJ Sic 101 Cat. Trien. (1717)(I), f. 33 No. 7.
 P. Angelus Aguillera was born at Licata on 11.viii.1676, joined the Society on 8.vi.1691 and made his solemn profession of four vows on 15.viii.1709; he had taught mathematics for four years before coming to Malta: ARSJ Sic 110 Cat. Trien. (1727)(I), f. 34 No. 2.
 P. Emmanuele Aguillera S.J. is the author of an oft-quoted history of the Sicilian province of the Society, published at Palermo in 1740 and entitled Provinciae Siculae S.J. Orals et Res Gestae; copies can be found both at the National Library (L/15/29,30) and in the Maltese Jesuits' provincial archives.
 ARSJ Sic 174 Cat. Brev. (1744), f. 353.
 A copy can be found at the National Library (Libr. Ms. 1246).
 V. Borg, "On Fixing the Foundation-Day Date of the Royal University of Malta", Seminariuni Melitense, x (1955) 1-14.
 Mifsud, "L'Espulsione".
 P. Philippus Arena was born in Piazza on 1.v.1708, joined the Society on 14.xi.1723 and made his four-vows profession on 15.viii.1741: ARSJ Sic 134 Cat. Trien. (1746), f. 37v No. 13. Ile was "professor mathematicae" till 1747: ARSJ Sic 174 Cat. Brev. (1743), f. 243v, (1744), f. 317v, 175 Cat. Brev. (1745), f. 35v, (1746), f. 99, (1747), f. 168v.
 ARSJ Sic 175 Cat. Brev. (1748), f. 242v, Sic 176 Cat. Brev. (1749), f. 38v, (1750), f. 112, (1751), f. 186, (1752), f. 261v, (1753), f. 339, Sic 177 Cat. Brev. (1754), f. 13v, (1755), f. 34, (1756), f. S1v, (1757), f. 73v.
 Ignatius Spatafora was born in Palermo on 1.x.1704, joined the Society on 2.xii.1719 and made his four-vows profession on 2.ii.1737: ARSJ Sic 140 Cat. Trien. (1759), f. 37 No. 8.
 Francesco Speciale was born in Nicosia on 19.x.1729 and joined the Society on 27.x.1743: ARSJ Sic 146 Cat. Trien. (1761)(I), f. 45 No. 7. His profession is not recorded by the time of the Society's suppression.
 ARSJ Sic 177 Cat. Brev. (1758), f. 101v.
 Placidus Cuzzaniti was born in Messina on 3.xi.1724, joined the Society on 20.xi.1738 and made his profession of four vows on 2.ii.1758: ARSJ Sic 146 Cat. Trien. (1761)(I), f. 35v, No. 10.
 ARSJ Sic 177 Cat. Brev. (Exeunte 1761), f. 137v, (Exeunte 1762), f. 173v.
 ARSJ Sic 177 Cat. Brev. (Exeunte 1763), f. 21.
 Franciscus de la Maddalena was born in Lyons on 31xii.1723, joined the Society on 8.ix.1738 and made his solemn profession of four vows on 2.ii.1757: ARSJ Sic 149 Cat. Trien. (1765)(I), f. 33, No. 3.
 Mifsud, "L'Espulsione", 13, 14.
 ARSJ Sic 153 Cat. Trien. (1765)(III), f. 12: "Ad mathematicam ex annua pensione centum scutorum melitensium ... vix scuta Romana 45 efficiunt".
 V. Borg, "Developments in Education outside the Jesuit 'Collegium Melitense'", MH vi, 2 (1974), 215-54.
 According to V. Denaro ("More Houses in Valletta", MH iii, 2 (1961), 3), the pagery was situated at No. 46 Old Theatre Street, corner with Strait Street and facing the Palace Square.
It was published in Catania at the Stamperia del Bisagni in 1750; a copy is held at the National Library (1:P313 Ext. 24). Details of contents can be found in T. Buhagiar, "Mathematics in the University of Malta up to 1900", unpublished B. Ed. (Dons) dissertation (University of Malta, 1986). Similar defence of theses published in Malta are referred to as "Conclusioni"; vide S. Fiorini and W. Zammit, Catalogue of the Records of the Order of St. John of Jerusalem in the Royal Malta Library, xiii [Archives 2038-20711 (Malta, 1991), 4, 5, 9 et passim.
 V. Laurenza, Il Primo Rettore e i Primi Statuti dell' UniversitÓ di Malta (Malta, 1934), 12-13. The pages' college was merged on 10.xi.1771 to avoid reduplication of effort (ibid., 19) but soon after Pinto's and Ximenes' election, it reverted to its original independent existence (ibid., 22).
 Ibid, 18.
 Mifsud, "L'Espulsione", 41 fn. 2 who gives a mistaken reference (AOM 6389); this was quite rightly pointed out by G. Gatt, "It-Tagħlim f'Malta", No. 12 Is-Sebħ (3.vi.1957), 6, but he, in turn and consistently with his usual very unscholarly practice, concealed altogether the source he was quoting.
 On the title page of several of his books he describes himself as "Maltese oriundo Lucchese" and " Idrografo dell'Ordine Gierosolimitano"; e.g. see Costruzione ed uso del Compasso di Proporzione. On Pagnini see G.A. Vassalli, "Biografia: Giovanni Pagnini", L'Arte iv (1866), 5-6 and R. Mifsud Bonnici, Dizzjunarju Bijobiblijografiku Nazzjonali (Malta, 1960), 396.
 The manuscript can be found at the National Library (Lib. 568).
 Copy held at the National Library where one can also view the manuscript version (NLM Lib. 172).
 NLM Lib. 57.
 Copy held at the National Library (AL.19.29). The existence of a second copy at the Maritime Museum, Vittoriosa, was kindly pointed out to me by Mr. Antonio Espinoza-Rodriguez, Curator of Fine Arts.
 Copy held at the National Library (AN.7.31), where one can also view an earlier unexpanded original manuscript version, dated 1736 (NLM Lib. 58).
 NLM Lib. 57.
 Compare NLM Lib. 57, p. 76 (Pagnini) with Lib. 1246 p. 71 (Aguillera).
 NLM Lib. 100 p. 89 where "La Linea Aritmetica" is called "Compas de Proportion".
 C.B. Boyer, A History of Mathematics (New York, 1968), 351.
 NLM Lib. 1134.
 For example NLM Lib. 100.
 Esercizio di Matematica e Problemi d'Algebra e di Geometria (Malta,1796); copy held at the National Library (Misc. 235:6). The three students defending the theses were the Diacono Conventuale Gio. Maria Vasse, Francesco Ruiz, and Vincenzo Barbara.
 R. Valentini, "Scuole, Seminario e Collegio dei Gesuiti in Malta: 1467-1591", ASM viii, 1 (1936-7), 18-32.
 V. Borg, "First Efforts to Build a Seminary in Malta", Seminarium Melitense v (1950), 28-36. M, "Nei Quinto Cinquantenario del Seminario", Seminarium Melitense ix (1954), 5-9.
 The copy of this publication in the National Library [P.1288] was kindly indicated to me by Mr. William Zammit B.Ed.(Hons).
 Laurenza, "II Primo Rettore". Professor Laurenza's paper is based on an "elogio" by Costaguti's close personal friend, Francesco Gherardi Dragomanni, delivered on 10.1.1836, a few years after Costaguti's . It is shown there that Costaguti had been appointed "Iettore di mathematiche" in 1757 at Mantua (p.4), that he had visited Malta in 1766 to preach lenten sermons to the knights at St. John's (p.7), and that he had been nominated member of the "Accademia Etrusca di Cortona e la Regia Accademia di Scienze e Belle Lettere di Mantova" in recognition of his prowess both as an orator and as a mathematician.
 Ibid., 10-15.
 Ibid., 22. Elsewhere he is described as "Professore di Fisica" [AOM 2053 (2.61.1772), f. 1].
 Ibid, 16-23. A.P. Vella, The University of Malta (Malta,1969), 49. AOM577, 211.
 AOM 309 (11.i.1776), ff. 44-45 = Document VII in Laurenza, 41.
 Vella, 54, fn. 1.
 Psaila Salvatore et alii, Saggio di Aritmetica Universale, dedicato a Sua Altezza Serenissima F. Emmanuele de Rohan, (Stamperia del Palazzo Malta, 1780); copy held at the National Library: NLM Misc. 635:23. The contents are described in Buhagiar.
 Rare Binding glass case No.10; its existence was kindly pointed out by Mr. Noel Caruana-Dingli.
 N. Zammit, "Biografie", L'Arte 44 (1864), 3, 5-6. P. Cassar, Medical History of Malta, (London, 1964),passim. J. Galea, "Dr. Giuseppe De Marco", The St. Luke's Hospital Gazette, vii, 1 (1972), 3-13. R. Ellul Micallef, "Tobba Maltin matul iż-Żminijiet", L-IdentitÓ Kulturali ta' Malta, ed. T. Cortis (Malta, 1989), 246-7. Mifsud Bonnici, Dizzjunarju, 171-2.
 NLM Lib. 1345. The "Trattato" bears the date 25.ix.1742. I should like to thank Prof. R. Ellul Micallef for bringing this reference to my attention.
 Ellul Micallef, 243.
 See NLM Lib. 2, 140, 142 (Cat. pp.12, 47, 49).
 R. Grillo, "Giuseppe Zahra, Maltese Professore nell'UniversitÓ di Catania", MH vii, 3 (1978), 234-236.
 C. Buda, Elogio biografico di Salvatore Zahra Buda e cenni del padre di lui adottivo, professore Giuseppe Zahra (Catania, 1848).
b Instructions on how his relatives can benefit from his foundation.
c Other instructions including the appointment of a consultant.