Domenico Guglielmini

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Biography

Domenico Guglielmini was born in Bologna on September 27 1655. He studied medicine with Marcello Malpighi and mathematics with Geminiano Montanari at the University of Bologna and graduated in medicine in 1678 (August 29). In the years of his training he attended the meetings of the “Accademia della Traccia” organized by Montanari and the abbot Carlo A. Sampieri. Guglielmini's first writings dealt with astronomic problems. The first was the Volantis flammae… epitropeia in defense of Montanari, involved in controversy with Pietro Maria Cavina (1637 -?1690) about a meteor seen in Romagna in 1666. A second work, De cometarum natura et ortu epistolica dissertatio, in which Guglielmini proposes a hypothesis on the genesis of comets by the encountering of oppositely directed vortices raised in the external part of different planets, was originated by the 1680’s “great comet”.

In 1681, Guglielmini is appointed “theorical mathematician” by the Assunteria di Confini ed Acque in Bologna to analyze a proposal advanced by Ferrara to restore navigability between the two towns; from 1686 to 1704 he was Superintendent of Bologna’s region waters. This position implied the involvement in the “question of the Reno”, the sharp debate on the path to be given to the river. The fame progressively acquired by Guglielmini and his vast work of analysis of the various projects played a relevant role in the decision taken in 1693 by the Pontifical State to favor Bologna’s project, the inlet of the Reno in the Po Grande. The work did not start because of Ferrara’s opposition; the ephemeral success of Guglielmini had however the consequence of convincing Bologna’s Senate to establish for him the first chair of hydrometry in Europe in 1694 (formally recognized as an independent chair only in 1699).

In 1690, he obtained the chair of mathematic at Bologna’s University and published the first part of his first major work in hydraulic, De aquarum fluentis mensuram, followed by the second part in 1691, that originated a controversy with Denis Papin. The frame of the text is the application of Galilei’s law of free fall to the movement of water, in the path settled by Torricelli, whose law of efflux Guglielmini applies to the flow of rivers by considering a channel as a single opening or as composed by infinite openings. In doing so, Guglielmini abandon Castelli’s law and states the proportionality of average speed to the square root of height. The text gave Guglielmini a wide fame through Europe, favoring, together with Cassini's friendship, whom he helped in the restoration of San Petronio’s sundial in 1695, his admission as associated member to the Académie royale des sciences in 1696, followed by the affiliation to the Royal society in 1697. In this same year, Guglielmini published his second hydraulic masterpiece, Sulla natura de’ fiumi. Often interpreted, partially by Gugliemini himself, as the first example of a new branch of hydraulic, it is characterized by a new, medical inspired, approach that aimed at “anatomizing” riverbeds, abandoning the abstract idealization of the method of mixed mathematics. In the case of rivers, the relevant causal factors are too many to rely on a method that, for Guglielmini, is suitable only for simple objects such as light or sound that can safely be considered as moving in uniform matter or in void. As a result, uniform motion of water is treated as a combination of activity (gravity) and passivity (resistance of the riverbed). The equilibrium among forces and resistances is also the key concept for interpreting the morphology and the direction of beds. The new approach implied also a different analysis of the structure of fluid matter: while in De aquarum fluentium mensura, Guglielmini dealt with water as a continuous fluid, here it is considered as made of small smooth solid globes, called minimal spheres or physical points.

Apparently because of contrast with other professors, in 1698 Guglielmini moved to Padua, where the Republic of Venice had offered him the chair of mathematics and astronomy and in 1702 he switched to the chair of medicine. Alongside with hydraulic projects in various region of the Republic of Venice, this last part of Guglielmini’s life is characterized by many medical treatises, sometimes published under pseudonym in which he defends rational medicine and the iatromechanic approach against the “empirical school”. After some month of illness, Guglielmini died in Padua on July the 12th 1710.

Domenico Guglielmini and Leibniz

Leibniz met Guglielmini on December 26-27 1689 in Bologna, during his travel in Italy, thanks to a letter of recommendation from Antonio Magliabechi. Their friendly meeting originated an irregular correspondence that lasted up to 1705. Twelve letters are preserved; the first two from Leibniz, mentioned by Guglielmini, appear to be lost; a parallel indirect correspondence is granted by their common acquaintance, Magliabecchi. The first part of their correspondence, lasted up to 1692, immediately followed Leibniz’s journey.

Magliabechi’s sending to Guglielmini of two Leibnizian papers in 1696, the Lettre sur la connexion des Maison de Brunsvic et d’Este and the Relatio… de novo Antydissenterico gave Guglielmini the occasion to restore the correspondence. After a new interruption (1696-1703), in 1703 he informed Leibniz of Magliabechi’s project to have Guglielmini’s second replies to Papin printed, and that he would move to the chair of medicine. Leibniz’s reply and Guglielmini’s letter of November 20th 1705 appear to have ended the correspondence.

The main theme of the correspondence is Guglielmini’s controversy with Papin, in which Leibniz played an active role. Leibniz reviewed the first part of De aquarum fluentium mensura in the “Acta Eruditorum” (February 1691), and the survey was the basis for Papin remarks published in the April issue, in which he claims that fluid do not always fall Galilean law of free fall, relying on his Examen siphoni Wurtemburgici in vertice effluentis (“Acta eruditorum”, May 1690). Informed by Leibniz, Guglielmini replied with two letters, one to Leibniz, the other to Magliabechi, then printed as Epistolae duae hydrostaticae in 1692 in which argues both for the irrelevance and the fault of Papin’s example of syphon. A short review by Leibniz (“Acta eruditorum”, 1692) solicited a further reply from Papin. Papin will address it to Huygens and the text will appear only in 1695; Guglielmini will subsequently reply, once again with two letters, one to Magliabechi, the other to Leibniz, who will include it in 1710 Miscellanea Berolinensia. While on various occasions Leibniz shows appreciation for Guglielmini’s hydraulic writings, he never explicitly took side in the controversy: as a result, this part of the correspondence is quite asymmetric.

Another relevant issue is medicine. Guglielmini traces back his tentative to apply mathematical theorem to physiology to a suggestion by Leibniz, who had drawn a parallelism between Guglielmini's analysis of rivers and the circulation of fluid within the body. Nonetheless, while praising Guglielmini’s defense of rational medicine, he warns him about a too quick application of “the most remote principles of Democritean philosophy” to “special physic” and about the introduction of improbable conjecture as plausible hypothesis: conjecture can in some cases have a positive role only if recognized as such. Leibniz suggests also not to dismiss all the result of the empiricist and to admit an experimental determination of functions. In his last letter, Leibniz will anyhow show his appreciation of Guglielmini’s De natura Sanguinis et constitutione.

Besides the appraisal of Guglielmini’s hydraulic and medical writings, Leibniz will also favorably comment both in the correspondence and with Magliabechi (A I 5, p. 497) Guglielmini’s Riflessioni filosofiche dedotte dalla natura dei Sali, later expanded in the 1705 De salibus dissertation, where Guglielmini, by a corpuscolar conception of matter argues that crystals have the same shape of their minima, stating the constancy both of the angles and of the inclination of the planes.

The correspondence with Leibniz testifies also to Guglielmini’s role as an advocate of the new calculus. Albeit not mastering it (A III 7, p. 450), he supported its introduction in Italy. In this light, his switch to the chair of medicine became of the greater importance, since he actively supported (Cavazza 1987, p. 76) Leibniz and J. Bernoulli’s candidate, Jacob Hermann, who obtained the chair in 1707 as his successor to the chair of Mathematic in Padua. Moreover, it is from Guglielmini that Leibniz came to know an objection of Johann Jacob Sturm’s against his calculus (A I 9, p, 458; A I 10, p. 358).

Finally, in his last letter, Leibniz mentions his correspondence with Michelangelo Fardella, and thus tries to introduce metaphysical issues: monads as non-spatial immaterial unity and pre-established harmony. Guglielmini did not respond to Leibniz’s metaphysical hints.

Bibliography

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