BALDI, BERNARDINO

(b. Urbino, Italy, 5 June 1553; d. Urbino, Italy, 10 October 1617)

mechanics, mathematics. For the original article on Baldi see DSB, vol. 1.

Baldi is one of the most illustrious representatives of the circle of scientists that formed in Urbino in the second half of the sixteenth century. Polyglot, polygraph, and poet, as well as scientist, expert on architecture, and skilled draftsman, Baldi is the author of numerous works that were still in manuscript form at the time of his death; many of them remained unpublished as of 2007. In the corpus of his manuscripts of particular interest is the Vite de’ matematici (Lives of the mathematicians; almost two thousand manuscript pages), which in part constitutes the base for the brief summary collected in the Cronica de’ matematici (posthumous, 1707; Chronicle of mathematicians). His major contribution to the field of mechanics is his commentary on the pseudo-Aristotelian Mechanical Problems, published posthumously in the work In mechanica Aristotelis problemata exercitationes (1621; Exercises in the mechanical problems of Aristotle). Among the literary works that reflect the scientific formation of the author are the Cento apologi (1590; One hundred apologues) and two poems, the Invenzione del bossolo da navigare (manuscript dated 1579; The invention of the navigational compass) and La nautica (1590; Navigation).

Among his contemporaries Baldi was famous for his extraordinary mastery of languages (his biographers report that he knew at least a dozen). In this respect the decisive factors were his early studies at Urbino under the guidance of Giovanni Antonio Turoneo and his later acquaintance in Rome with Giovanni Battista Raimondi, the inspiration and promoter of the Tipografia Medicea Orientale. From him he learned Arabic, which permitted him to pursue in depth his meticulous work in scientific and literary sources.

History of Mathematics. The Vite de’ matematici constitutes a kind of history of the mathematical sciences, the first example of its genre in the modern era. With it Baldi intended to fill a historiographic gap and to accord to mathematicians the same dignity that up to that time had been reserved for artists, philosophers, and orators. The work was begun after the death of the mathematician Federico Commandino (1575), and most of it was completed around 1590. The idea of presenting mathematics in its historical context was not new to the Renaissance, but the encyclopedic scope that Baldi gave to his work made it exemplary. He took a similar all-encompassing approach in the De verborum Vitruvianorum significatione(1612; On the meaning of Vitruvius’s terms), a meticulous analysis of the obscure passages in Vitruvius’s De architectura(On architecture; first century BCE).

Mechanical Problems. Baldi’s In Mechanica Aristotelis Problemata Exercitationes offers the same compositional originality, which in this case directly involves the scientific content. The Mechanical Problems of the Pseudo-Aristotle (Baldi agrees with the attribution of the work to Aristotle, although doubts about its authorship had already been raised)was the object of numerous editions and commentaries during the sixteenth and seventeenth centuries, but the Exercitationes show a singular independence from previous publications. The thirty-five problems become the pretext for long digressions on the topic, in which the influence of Archimedes’s work is evident and openly acknowledged: “Considerantes enim Aristotelem aliis principijs usum, ac probatissimi post eum fecerint Mechanici, demonstrasse, morem huiusce facultatis studiosis gesturos nos fore arbitrati sumus, si easdem illas quaestiones Mechanicis, hoc est, Archimedeis probation-ibus confirmaremus” (Praefatio [Preface], n.p. [Considering that Aristotle in his demonstrations relied on principles that were different from those adopted by the best mechanicians coming after him, we have judged that it would have been possible to explain the method of this investigation treating these same questions in accordance with the criteria of mechanics, that is in agreement with those adopted by Archimedes]). Baldi’s commentaries offer original considerations that impart a distinctly innovative character to the treatment. This is what occurs, for example, in the commentary to Quaestio XVI (problem sixteen). Taking as his point of departure the problem enunciated by the Pseudo-Aristotle (“Dubitatur, quare, quo longiora sunt ligna, tanto imbecilliora fiant, & si tolluntur, inflectuntur magis: tametsi quod breve est ceu bicubitum fuerit, tenue, quod vero cubitorum centum crassum”; Mechanica Aristotelis…, p. 95 [We ask why the pieces of wood become weaker the longer they become; and, if they are raised, they bend more, even though the short piece of wood, which may measure two cubits for example, is thin, and that one hundred cubits long is very thick]), Baldi undertakes a careful analysis of certain themes of mechanics as applied to architecture, and he anticipates the interpretation of the mechanism of the fracture of a beam that will later be described by Galileo in the Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638; Dialogues … concerning two new sciences). This treatment has no parallel in any previously published text. The resistentia solidorum (resistance of solids) is placed at the center of a study that compares the static-constructive experience with the principles of mechanics. Baldi’s interest in this field of research, situated on the boundary between mechanics and architecture, is further confirmed by his studies on Vitruvius and by his consulting work as an expert in architecture in Urbino, Guastalla, and Rome (in Cardinal Cinzio Aldobrandini’s circle). Moreover, Baldi numbers Vitruvius and Leon Battista Alberti among the mathematicians.

The originality of the Exercitationes poses the problem of identifying possible links with earlier unpublished sources. Pierre Duhem takes for granted that certain ideas found in Leonardo da Vinci’s manuscripts exerted an influence on Baldi. Knowledge of some of those manuscripts cannot be excluded a priori, for the greatest dispersion of Leonardo’s papers occurred at the end of the sixteenth century in Milan, a city that Baldi knew well from his having frequented the circle of Carlo Borromeo. Nevertheless, there is no proof confirming the hypothesis advanced by Duhem, who on other points of Baldian bibliography as well gives evidence of conducting an overly hasty analysis of the sources. In the case of the Quaestio XVI, moreover, one can note how the approach chosen by Baldi to the problem of structural mechanics differs in both substance and method from the one that Leonardo adopts on several occasions in his manuscripts (for example, as regards the mechanism of the fracture of arches).

Possible Influence on Galileo. Another important historiographic problem regards Galileo Galilei’s knowledge of the Exercitationes. Numerous testimonies demonstrate that Baldi’s work was immediately discussed by several scientists of the age (for example, Isaak Beeckman and Marin Mersenne). In the work of Daniel Mögling Mechanischer Kunst-Kammer Erster Theil … (1629), one can even find a translation of the Exercitationes, with the addition of an iconographic apparatus that corrects many of the printing errors of the original edition. The same Quaestio XVI, moreover, becomes the base of explicit inspiration for the five theorems on vaults described by Henry Wotton in his Elements of Architecture (1624). Similar attention to Baldi’s commentaries can be found in Giovanni de Guevara’s In Aristotelis Mechanicas Commentarij (1627, Commentaries on problems of mechanics). See Giovanni de Guevara, Ioannis de Guevara Cler. Reg. Min. in Aristotelis Mechanicas Commentarij: una cum additionibus quibusdam ad eandem materiam pertinentibus, Iacobum Mascardum, Roma 1627, cited by Galileo in his Discorsi. It is known that Guevara corresponded with Galileo and asked him on several occasions for his opinion on the commentaries to the Mechanical Problems. Despite this wide knowledge of Baldi’s work throughout Europe, Galileo never cites him in his Discorsi, and his name does not appear in the extensive correspondence of the Pisan scientist. It seems nevertheless very unlikely that he was not familiar with the content of Baldi’s work, at least indirectly and through mutual interlocutors.

There has been much discussion about the dating of the manuscript of the Exercitationes, and historians have usually settled on a date around 1590. To formulate credible hypotheses one must keep in mind that the principal biographers (Giovan Mario Crescimbeni and Ireneo Affò) refer to at least two manuscripts devoted to the Mechanical Problems. Certainly Baldi’s interest in the subject goes back to his formative years in Urbino under the tutelage of Commandino and during his friendship with Guidobaldo del Monte, and to the time of his studies at the University of Padua. Nevertheless, the first manuscripts dedicated to the subject were to be reworked many times in subsequent years, and what was eventually given to the press was certainly revised during the author’s final years. On the basis of these considerations we can affirm that the Exercitationes, like many other Baldian works, were reexamined, refined, and reorganized in the 1609–1617 period, when Baldi returned to live permanently in Urbino after the long stay in Guastalla.

SUPPLEMENTARY BIBLIOGRAPHY

WORKS BY BALDI

Bernardino Baldi, Le vite de’ matematici: Edizione annotata e commentata della parte medievale e rinascimentale [Bernardino Baldi, The lives of mathematicians: annotated edition of the medieval and Renaissance parts, with commentary]. Edited by Elio Nenci. Milan: FrancoAngeli, 1998.

“In mechanica Aristotelis problemata exercitationes.” Mainz: Viduae Ioannis Albini, 1621. As part of the Archimedes project, available from http://archimedes2.mpiwg-berlin.mpg.de/archimedes/archimedes_templates.

OTHER SOURCES

Battiferri, Marc’Antonio Vergilii. Oratione funebre in lode di monsignor Bernardino Baldi d’Urbino Abbate di Guastalla[Funerary oration in praise of Monsignor Bernardino Baldi of Urbino, Abbot of Guastalla]. Urbino: A. Corvini, 1617. The first biographical profile of Baldi. Reprinted in Seminario di studi su Bernardino Baldi Urbinate (1553–1617) [Seminar of studies on Bernardino Baldi of Urbino], edited by Giorgio Cerboni Baiardi. Urbino: Accademia Raffaello, 2006.

Becchi, Antonio. Q. XVI.Leonardo, Galileo, e il caso Baldi: Magonza, 26 marzo 1621. Traduzione dei testi latini, note e glossario a cura di Sergio Aprosio [Q. XVI: Leonardo, Galileo, and the Baldi Case: Magonza, 26 March 1621. Translation of Latin texts, notes, and glossary prepared by Sergio Aprosio]. Venice: Marsilio, 2004.

Crescimbeni, Giovan Mario. La vita di Bernardino Baldi, abate di Guastalla [The life of Bernardino Baldi, abbot of Guastalla]. Edited by Ilaria Filograsso. Urbino: Quattro Venti, 2001. Transcription of the manuscript La vita di Bernardino Baldi (1703–1704).

Gamba, Enrico. “Saggio bibliografico sull’ambiente scientifico del ducato di Urbino” [Bibliographic essay on the scientific environment of the duchy of Urbino]. Studia Oliveriana, nos. 8–9 (1988–1989): 35–67.

Gamba, Enrico, and Vico Montebelli. Le scienze a Urbino nel tardo Rinascimento [The sciences in Urbino in the high Renaissance]. Urbino: QuattroVenti, 1988.

Nenci, Elio, ed. Bernardino Baldi (1553–1617) studioso rinascimentale: Poesia, storia, linguistica, meccanica, architettura; Atti del convegno di studi di Milano, 19–21 Novembre 2003. [Bernardino Baldi, 1553–1617, Renaissance scholar: poetry, history, linguistics, mechanics, architecture]. Milan: FrancoAngeli, 2005.

Rose, Paul Lawrence. The Italian Renaissance of Mathematics: Studies on Humanists and Mathematicians from Petrarch to Galileo. Geneva: Droz, 1975.

Serrai, Alfredo. Bernardino Baldi. La vita, le opere, la biblioteca[Bernardino Baldi: his life, his works, his library]. Milan: Bonnard, 2002.

Antonio Becchi