Bernardino Baldi

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(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is the author of numerous works that were still in manuscript form at the time of his death; many of them remained unpublished as of 2007.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.



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


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

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Baldi, Bernardino

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

After a classical education by private tutors at Urbino, Baldi studied mathematics with Guido Ubaldo del Monte, under Federico Commandino, beginning about 1570. At Commandino’s suggestion he translated the Automata of Hero of Alexandria into Italian, but left it unpublished until 1589. He also translated the Phenomena of Aratus of Soli and wrote didactic poems on the invention of artillery and the nautical compass, but did not publish them. In 1573 he enrolled at the University of Padua, and when it was closed shortly afterward because of plague, Baldi returned to Urbino. He was with Commandino during the latter’s final illness in 1575, and obtained from him an account of his life. Baldi’s studies at Padua centered on philology and literature, but he obtained no degree.

In 1580 Baldi went to Mantua in the service of Ferrante II Gonzaga, who in 1585 secured him the post of abbot of Guastalla. He then put in order his biographies of some 200 mathematicians, a work conceived during the writing of Commandino’s biography and completed in 1588–1589. About that time he also wrote his principal contribution to physics, a commentary on the pseudo–Aristotelian Questions of Mechanics posthumously published in 1621. In 1589 he published his translation of Hero’s Automata, prefaced by a history of mechanics.

Baldi visited Urbino in 1601 to compile materials for a life of Federico di Montefeltro, and in 1609 he resigned his abbacy to enter the service of the duke of Urbino as historian and biographer, remaining there until his death. A vast work on geography on which he worked in his later years remains unpublished, although many of his poetic and literary compositions were printed in his lifetime. His final scientific contribution was a translation of Hero’s Belopoeica into Latin, accompanied by the Greek text and by Baldi’s Latin Life of Hero (1616). Brief extracts from his lives of the mathematicians were published in 1707, and about forty of those biographies have since been published in full. Most of the work, however, remains in manuscript.

Except for that of Henri de Monantheuil, with which Baldi was certainly unacquainted, Baldi’s commentary on the Questions of Mechanics was the most important work of its kind to appear up to that time. He was probably influenced in his ideas on the continuance of motion by the earlier commentary of Alessandro Piccolomini. His account of dynamic equilibrium in spinning tops was superior to that of G. B. Benedetti, with whose principal work he appears to have been unfamiliar. The most significant aspect of Baldi’s approach to mechanics lay in the development and application of the concept of centers of gravity, particularly with regard to stable and unstable equilibrium. It was the opinion of Pierre Duhem that Baldi drew his chief ideas from manuscripts of Leonardo da Vinci. Duhem accepted the year 1582 for the original composition of Baldi’s commentary, as given by Baldi’s first biographer. That date is, however, inconsistent with passages in Baldi’s own preface and in the text of the work, which imply the year 1589. The latter year is also supported by textual indications that Baldi’s principal inspiration was drawn from Commandino’s translation of Pappus and from Guido Ubaldo’s commentary on the Plane Equilibrium of Archimedes, both of which were published in 1588. The influence of Baldi’s work was doubtless diminished by its delay in publication until after the Archimedean ideal had largely supplanted the Aristotelian among students of mechanics.


I. Original Works. An essentially complete bibliography of Baldi’s published works is given in Pierre Duhem, Études sur Léondard de Vinci, 1 (Paris, 1906; repr. 1955), 93–99; those of scientific interest are Di Herone Alessandrino de gli automati... (Venice, 1589; repr. 1601); Scamilli impares Vitruviani... (Augsburg, 1612); De Vitruvianorum verborum significatione... (Augsburg, 1612); Heronis Ctesibii Belopoeeca... et... Heronis vita... (Augsburg, 1616); In machanica Aristotelis problemata exercitationes... (Mainz, 1621); Cronica de’ matematici... (Urbino, 1707); “Vita di Federigo Commandino,” in Gironale di letterati de’Italia, 19 (1714), 140 ff.; “Vite inedite di matematici italiani,” in Bollettino di bibliograia e di storia delle scienze, 19 (1886), 335–640; 20 (1887), 197–308; and L’invenzione del bossolo da navigare, G. Canerazzi, ed. (Leghorn, 1901).

II. Secondary Literature. Principal biographical sources are Fabritio Scharloncini, De vita et scriptis Bernardini Baldi Urhinatis, prefaced to Baldi’s In mechanica Aristotelis...; Ireneo Affö, Vita di Bernardino Baldi (Parma, 1783); and R. Amaturo, “Bernardino Baldi,” in Dizionaio biografrco degli Italiani, V (Rome, 1963), 461–464. For Baldi’s scientific work and its influence, see Duhem, op. cit., pp. 89–156; for his relation to the central Italian mathematicians, see S. Drake and I. E. Drabkin, Mechanics in Sixteenth–Century Italy (Madison, Wis., 1968).

Stillman Drake