1818 Necrology in memoriam of Vincenzo Brunacci by Gabrio Piola

Honori Amicitiaeque

VINCENTIJ BRUNACCI

Domo Florentia

Eq Leg. Honorator et Coron Ferr.

Matematicorum Huius Aetatis

Per Europam Facile Principis

Qui In Academia Ticinensi

Sublimioras Mathesis Disciplinas Tradidit

Cuius Consultissimum Elogium

Horis Mixus XL

GABRIUS PIOLA

Pem Fasciculum Nuperrimi Iunii Mensis

Ephemeridis Bibliothecae Italicae Trigesimum Evulgavit

CAESAR ROVIDIUS

Moderator Ephebei Caesariani Med.

Idemque Matesis Professor

In Lyceo Quoad Stetit Prope Aedes Eiusdem Ephebei

Typis Aere Suo Seorsum Mandari Coeravit

Iam Ad Nobilissimos Doctores Athenarum Ticinensium

Donum Destinat

It is extremely painful for us to announce in this document the death of a truly great man, who, as during his life was a glory for Italy, now moves, because of his loss, everybody inconsolably to tears. One of the most eminent mathematicians of our time, the illustrious professor Vincenzo Brunacci of Pavia, suffering for many years because of a painful disease, on the day 16th of the current month of June was attacked by those very strong convulsions which were consequence of it, ceased to live surrounded by friendship and religion. To recall the merits of the deceased person during the time while still everybody cries on his tomb it is really a way for increasing painful laments, even if it will be simply a meagre tribute of praise which will be written by our pen. Our intention is not that of presenting a formal elogium; this kind of encomium soon will be heard in the most erudite academies and in all palaces of sciences.

Vincenzo Brunacci was born in the fatherland of Galileo the day 3rd of March 1768, his father first name being Ignazio Maria and his mother being named Elisabetta Danielli.

This consideration is presenting itself even more spontaneous when we will remark that Brunacci was the first admirer in Italy of the luminous Lagrangian doctrines the scientist who diffused and supported them, the scientist who in his studies was always a very creative innovator in their applications.

His first Maestri were two famous Italians, Father Canovai and the great geometer Pietro Paoli. Although in his first youth he was diverted by other studies, which were opposed to his natural inclinations and from which, because of due respect he could not subtract himself, he still was able to cultivate at the same time those studies for which he had been born. Very soon he was pupil only of the classic textbooks and of himself. Very soon, as he did not allow to any man to see his genius while being born or in his first childhood, in the “opuscolo analitico”, printed in Livorno in the year 1792, he showed his fully developed creative ingenuity in that part of “sublime calculus” in which he was bound to find the subject for great discoveries.

Called as Professor of Nautical Sciences in the College of standard-bearers in Livorno in the year 1796 he published the Navigation Treatise of which were printed three more editions more and more improved and detailed. This work was and still is the only Italian textbook which is really suitable to educate the practical pilot.

In the year 1798 was printed in Florence the work entitled “Calculus of linear equations”. In this oeuvre our author showed that he could successfully compete with the most eminent geometers of Europe. Postponing to a later discussion, as it will be suitable to do so while talking about another book, the exposition of the many merits of this book we will limit ourselves here to say that while Laplace was calling falsely not-integrable certain linear equations in which second order partial differentials appear, while Paoli and Lacroix were investigating the same subject and started to doubt about the statements of the mentioned French geometer, Brunacci gave a method for integrating similar equations, being able to generalize it to all differential orders. Paoli himself, by exposing this method for a particular case in the third of the parts which form the supplement to his Elements of Algebra, calls illustrious geometer that scientist [i.e. Brunacci himself] who had been his student. A voice finally was uttered from that place which had given birth to such eminent scientists as Cavalieri, Frisi, Agnesi, and Oriani and Brunacci was called to occupy the empty chair [of mathematics] in Pavia. He arrived there in the year 1800 and although he arrived in a place where the Mathematical Sciences were not ignored he met the greatest expectations and advanced the fame [of that chair] to a yet unrivalled dignity.

Indeed it is not sufficient to be erudite in science to become its professor, it is necessary to have the gift of the word, the capacity of finding the right way to explain it. These gifts were given to him in the highest, unrivalled level. Whoever heard him will admit that my expressions although admired however are not enough to reveal the truth. The mathematical teaching when coming from his lips was losing every difficulty and bitterness, and developed with a peculiar charm and incantation was at the same time education for the mind and pleasure for the ears. It was then that the mathematical schools on the banks of Ticino river reached the prestige which also nowadays is honoring them. It was then that Vincenzo, having dedicated himself completely to his science, started with all his forces to promote it.

The “Analisi Derivata” (Analysis of Derivatives) was printed in Pavia in the year 1802. It is in this book that one can find one of the most sublime concepts which was ever conceived by the human mind, that is the Principle of Derivation. Because of it all the different parts of Mathematical Sciences are tied and interconnected and it is opened an endless view which allows us to consider as possible their infinite development. Soon he conceived the challenging thought which lead him to re-write the whole body of the doctrine of his science in many volumes, enriched by every novel concept which had been formulated in the modern works.

This endeavour may have frightened everybody except him: he was also pushed by the advice of that Sovereign who was an investigator of the stars who, being in Milan, wrote to persuade him to start this oeuvre in the year 1800, believing that he was the only one among the Italians who was capable to complete it successfully. The oeuvre of the Course of Sublime Mathematics was printed in Florence in four volumes in the years 1804, 1806, 1807, 1808.

One would need a very long time to expound as it should be done the merits of this book, but I will want to shortly describe here its contents. The first volume contains the Calculus of Finite Differences. This Calculus, which was originated among the obscure calculations presented by Taylor, which was developed in many Memoirs disseminated here and there in the Proceedings of many Academies, for the first time was given scientific order and method by the Florentine Geometer. He wrote it finding in his ingenuous mind all that which was lacking in order to form a perfect theoretical frame, and he infused in it all novels results which he had obtained in his already mentioned works. It was his original contribution the integration of linear equations of second order with variable coefficients, it was his contribution a new formula for the integration of linear equation of all orders with constant coefficients; it was his own the method to complete the integrals to be replaced to the one proposed by D’Alembert, [method] which he successfully introduced also in the differential calculus; but the idea of the variable probability and the solution of the related problems, with which he metaphorically could seize the wheel of the fortune and advanced in the field where the genius of Lagragia had stopped, when in the Proceedings of the Academy of Berlin (1775) he had given the solution of those problems only in the case of constant probability.

While citing the name of Lagrangia I will not neglect to say that Brunacci was the first in Italy to see that admirable light which the Theory of Analytical Functions can spread among the mysterious smog which was obscuring the Infinitesimal Analysis. He immediately conceived the idea of introducing it also among us: but oh! how difficult was that endeavour! The Lagrangian notation, completely new, produced a kind of revulsion: not all minds were firm enough to be able to maintain -in the middle of a Revolution- their contact with the spirit of the Calculus: He himself told me many times about the great obstacles which he needed courageously to confront in pursuing his effort. He finally managed to reach his aim, by reconciling the Lagrangian ideas with the Leibnitz notation, together with the brackets introduced by Fontaine.

In this way are written the other three volumes of the said Course, where, however, the author did not neglect to introduce with great skill whenever possible the notation of the Geometer of Turin in order to make it familiar to us.
We will only add that in the remaining part of his great oeuvre one can find the rich results of Mathematical Analysis gathered from the most recent Memoirs of the most celebrated Geometers and especially from the immense body of works of the great Euler which he called his delight and from which he admitted to have learnt that lucid order which makes his own works so brilliant.
I will only mention that one on some particular solutions for the finite difference equations, which our author treats in a way which is similar to the one used by Lagrangia for differential equations, and where he discovered some very elegant theorems valid for finite difference equations which are not true for differential equations and the other one on shock waves in fluids which embellishes the last Volume printed by said Società, Memoir where the analytical spirit really is triumphant. Also the Istituto Nazionale Italiano was immediately honored in its first Volume with a Memoir by Brunacci on the Theory of Maxima and High Minima; subject which was remarkably advanced later in another Memoir. The Società Italiana and the Istituto oh! how greatly will grieve the loss of a man who honored them with many and valuable works!

Oh! How many times I heard him talking about Euler with a great enthusiasm and to urge me, and many of his other students, to study the work of the only author who is suitable to educate a geometer! The great men, even when are quoting the results of other authors are able to give to the subject their own mark. This statement is true for that book where Brunacci infused many of his ideas, not only those which we mentioned but also many others which equally would merit to be mentioned, and in particular in those various problems of every kind of applied mathematics and in the calculus of variations which is reduced to the differential calculus and is there exposed with a great detail, and finally in the mixed calculus, of which he was the first to give the true principles and to expound in orderly way the doctrine.

However a triumph which Brunacci obtained in front of all his rivals. The Theory of the hydraulic water hammer, which seemed to be rebellious to the lordship of Mathematical Analysis, and which was demanded with a golden prize -without success- by the Academy of Berlin to the greatest geometers of Europe in the year 1810 and then again in the year 1812 doubling the prize, since 1810 was discovered by Brunacci who should have had received the promised reward if an accident -which I do not want to recall here- had not defrauded him of the deserved glory; this Theory was published in the Treatise of the hydraulic water hammer of which were printed two editions; in this Treatise said Theory, reduced to formulas and problems, is expounded in the most efficacious way.

It is custom of the brave to prepare himself to the new victories and not to be proud of the past ones. Therefore a new arena was chosen by our athlete where he managed to defeat strong rivals. If he competes for discovering the nature in hydraulic problems, Brunacci is awarded by the Società Italiana: if he needs to reach the highest abstraction in order to find the best metaphysics for the Calculus, Brunacci is awarded by the Accademia di Padova. The Proceedings of the Illustrious Società Italiana carry the name of Brunacci as author of many of the best Memoirs: too long would be to cite all of them.

Also the Academies of Berlin, Munich, Turin and Lucca, and the others to which he belonged, will perceive the great emptiness which is now left in them.

I simply quickly cite the textbook on the Elements of Algebra and Geometry written by our author for the high school in few days, of which one has to praise the order and the distribution of subjects and which was published in many editions.

I will mention as meriting great praise the Compendium of Sublime Calculus which was issued in two Volumes in the year 1811, where it is gathered everything which is sufficient to educate thoroughly a young geometer. In writing it the author greatly improved and carefully modified many parts of the complete course, and all added many new results and arguments.

It is not licit to neglect to indicate another subject in which -with honored efforts- our professor distinguished himself. The Journal of Physical Chemistry of Pavia was illustrated in many of his pages by his erudite pen; I will content myself to indicate here three Memoirs where he examines the doctrine of capillary attraction of Mister Laplace, comparing it with that of Pessutti and where with his usual frankness, which is originated by his being persuaded of how well-founded was his case, he proves with his firm reasonings, whatever it is said by the French geometers, some propositions which are of great praise for the mentioned Italian geometer.

One could think that a man who wrote so much in his short life actually should have been remained closed all the time alone in his office. On the contrary: he not only was a great theoretician but also he was excellent in all practical hydrometric and geodetic operations. He was Professor also in these disciplines and with great dedication he worked heavily along the banks of Ticino river in order to educate the best engineers.

He was a really skilled experimentalist and he often investigated natural phenomena, getting favorable answers. I know very well how much interest pushed him to these experimental activities, as is proven by the Hydrometry Laboratory of the University which he founded and improved (sometimes at his own expenses) with high quality instruments.

Also in these more practical activities his capabilities won him an universal esteem, so that he was called everywhere sometimes on the river banks in order to monitor their construction or for prevent their collapse or sometimes on the navigation canals, among which the famous one in Pavia was started under his direction which was confided to him by the past government. The same government nominated him inspector of waters and streets, inspector general of the public instruction and knight.

His character was strong in his resolutions, [it was] constant and resolute in his sentiments, vigorous in the spirit, ready to well reason and ponder, [it was] active and ready to engage in the [needed] efforts but above all he was friendly and urbane: [his character] made him the center of social life and the joy of friendship. Particularly with his students he was renouncing to all the superiority of the “maestro” and assumed the attitude of the father: I must avoid this memory, woe is me!, because it too strongly makes tears to come to my eyes. Those who need the evidence of my last statement has simply to see his how his students wanted to honor that great man and to manifest their sorrow: they carried on their shoulders his mortal remains, they decorated in an extraordinary way his funeral parlour and now are praising the departed’s merits with their tears and their silent grief which are more eloquent than all spoken lamentation.

Everybody who is now promising to contribute to exact sciences in Lombardy is a student of Brunacci, and indeed among his disciples there are those who, as their mentor himself often said, is now an eagle who can fly with his own wings. Such [an eagle] is the Professor in Bologna, author of the essay on Poligonometry, such is the other one who is the author of the Treatise on the Contours of the Shadows and whose noteworthy voice is entitled to succeed to that of his Maestro on the banks of Ticino, such is a third disciple who has already shown that Italy can hope to have soon a Geometer who will emulate the great genius who wrote the theory of celestial bodies.

What a great misfortune was to see the departure of a man in the age of his maturity who already had greatly contributed to science and who was bound to contribute even more copiously to it! I know very well, as I had many times the privilege of his confidences about the subject of his studies, how many precious works can be found in his manuscripts. Among them, some excellent documents which he wanted to gather to form a commentary to the Analytical Mechanics, many very beautiful discourses read on occasion of the defense of theses, some sequels of Memoirs containing the description and the calculation of many machines inspired by the Hydraulic Architecture authored by Belidor, gathering which he intended to complete an oeuvre which would have been of great utility.

May these last achievements of such an inventive and ingenious Geometer be delivered up to a capable and educated scholar, who could enlighten them as they deserve, for the advancement of SCIENCES, for the glory of the AUTHOR and for the prestige of ITALY.

Milan, 18 June 1818