Le Mecaniche ("The Mechanics"; sometimes spelled Le Meccaniche in modern Italian) is a short treatise by Galileo Galilei, composed while he was teaching mathematics in Padua. The precise date of its most refined form is difficult, if not impossible, to determine, but it is generally dated around 1600 or earlier, and was unlikely revised after 1608. It was preceded by a brief version written around 1593, Galileo's first full year in Padua. The work was never printed during his lifetime but circulated in manuscript form among his students and colleagues.
The treatise examines the theory of simple machines, such as the lever, pulley, winch (i.e., windlass and capstan), screw, and inclined plane, drawing on classical sources such as Aristotle, Archimedes, Pappus, Philoponus, and Jordanus de Nemore, but reformulated through Galileo's mathematical perspective.
In the text, Galileo discusses principles of equilibrium, mechanical advantage, virtual velocities (speeds), and the impossibility of "cheating" nature, emphasizing that machines do not create force but only transform and transmit it.
Although Galileo's Mechanics is referenced in the Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638)), including a literal citation to the Mecaniche in amendments added by Vincenzo Viviani at the behest of Galileo, only selected portions appear there; most of the treatise is omitted, as the focus of the Two New Sciences was on the "new" aspects of his research.
The principle of virtual speeds, in its elementary form originating from Aristotle (whom Galileo credits), had remained undeveloped until Galileo. Certain ideas of conservation laws also emerge, particularly a local form of the conservation of energy. Galileo was the first to perceive that simple machines cannot create force or work but merely transform its application. His restricted principle of inertia, first stated in De Motu, also finds implicit application in the Mecaniche. Lastly, Galileo's early development of his Mechanics around 1595-97 would mark his first use and adoption of the term "moment" (momento) within a technical sense.
Early drafts and publication history According to Vincenzo Viviani's testimony, the first draft of the Mecaniche was written in 1593.
A few early drafts have been accounted for. One was discovered in Regensburg by Antonio Favaro in 1898 (found after the version in the Edizione Nazionale had been published) which differed from all the other copies of the manuscript. Favaro believed the Regensburg to be the first draft, used by Galileo as a guide for both public and private lessons held during his Padua period. The Regensburg copy includes an inscription that indicates that it was read by Galileo in the year 1594, which appears to confirm Viviani's claim. However, another draft was discovered by Stillman Drake in 1955, found in the Bauer Collection of the Institute of Technology in Pasadena, containing the coat of arms of Count Rocco on the cover. The Pasadena draft lacks a date inscription; however, it presents similarities with the Regensburg version and lacks the first six chapters. Drake argues that this Pasadena draft is the earliest and that it served as an outline for Galileo's lectures. Thus, the Pasadena version is presumed to have been written in 1593, as Viviani's testimony suggests. The definitive draft included in the Edizione Nazionale is believed to be dated 1598-1600. Neither the Pasadena nor Regensburg versions provide the initial "definitions" of which the final edition includes. Moreover, in both the Pasadena and Regensburg versions, "momento" appears in only one paragraph, used in the sense of a weight so small that it can be disregarded.
Galileo's manuscript on mechanics in Italian was widely circulated among his students and colleagues, often without listing his authorship, as he believed the work did not offer any novel ideas of his own.
Marin Mersenne translated the manuscript into French in 1634.
The first printed edition of the Mecaniche was produced in 1649 under the care of Cavalier Luca Danesi.
It was translated into English twice during the seventeenth century: first by Robert Payen in 1636 (unpublished), then by Thomas Salusbury in 1662 in volume 2 of his Mathematical Collections and Translations; however, most copies were destroyed in the great London fire—only eight copies have been found.
Carlo Manolessi would publish Mecaniche in volume 1 of his 1655 edition of the Opere di Galileo Galilei. Eugenio Albèri's edition of the Opere di Galileo Galilei, published in 1854, includes it in volume 11. Years later, in 1891, Antonio Favaro published Le Mecaniche in volume 2 of the Opere di Galileo Galilei.
In 1960 an English translation of the Le Mecaniche was published together with the De Motu under the title On Motion and On Mechanics, translated by I. E. Drabkin and Stillman Drake; it is based upon the Favaro edition.
Critical reception Clavelin argues that the Le Mecaniche combined three distinct trends in statics into an orderly and rational theory of simple machines: the Peripatetic tradition, whose origins are traced back to the Mechanical Problems; the Archimedean tradition; and a 13th century tradition originated by Jordanus Nemorarius, who produced the first proof in statics based expressly on the idea of virtual displacements, and a correct explanation of motion on an inclined plane.
The Mechanical Problems of the Peripatetic school provided the earliest known analysis of why small forces can move great weights by means of the lever, treating the problem implicitly as one in statics, using an approach that contained the beginnings of the principle of virtual velocities, but it should be emphasized that the Mechanical Problems never treated virtual displacements but only virtual velocities. It also described the behavior of the wedge, the pulley, the tackle, the forceps, and the nutcracker, reducing each to that of the lever; however, it failed to adduce a systematic theory of simple machines.
In the Archimedean tradition, Archimedes set out to transform statics into a demonstrative science, refusing, in his theory of the lever, to treat equilibrium in terms of virtual motions of the motive force and the resistance.
In the medieval statics tradition, Jordanus based the determination of equilibrium on the virtual motions of the ends of the balance beam. However, his arguments lacked rigor but led to an important transformation: equilibrium was based on the relative displacements of two weights, whereas, instead of considering speeds as the Mechanical Problems did, Jordanus considered the distances, which took the first step toward enunciating the general principle of virtual work.
By linking the 13th-century tradition with the other two traditions, their synthesis in the Mecaniche became a direct prelude to the modern reconstruction of statics on the principle of virtual work. Not only did Galileo take a view opposite to that of his chief predecessors and contemporaries (among them Guido Ubaldo del Monte and Benedetti), but by assimilating and then dominating the traditions, he was able to turn his Mecaniche into the first truly modern treatise on statics.
Regarding the analysis of the balanced lever, Clavelin agrees with Mach in his criticism that, just as Archimedes did, Galileo relied on the implicit assumption that the moment of a heavy body depends exclusively on its weight and on the distance of its center of gravity from its point of suspension. However, unlike Archimedes, Galileo’s approach was more general and efficient since it treated incommensurable and commensurable weights on the same footing.
The beginnings of Galilean momento Galileo's Mecaniche presents his early adoption and transformation of momento into a technical term. Prior to drafting his Mecaniche, Galileo had made several attempts to correct the deficiencies and contradictions of his De motu, particularly with the system and definitions relating to gravitas, levitas, and his concept of force, virtus impressa; however, he ultimately abandoned the work.
Galluzzi indicates that, during the period spanning 1593 through 1600, Galileo consciously dedicated himself to reforming his lexicon, including his use of momento. As Galluzzi notes, the Pasadena and Regensburg versions of the Mecaniche first used momento without definition and only within a few sentences, wherein the term indicated a negligible amount of weight, which reflected the biblical expression momentum staterae. The years 1595-1597 then marked a period of intense research, definition, and introduction of the term that we now find in the definitive version of the text, making Galileo's momento a Paduan achievement. During the academic year of 1597-98, Galileo taught a course dedicated to the pseudo-Aristotelian Questions of Mechanics at the University of Padua. Galluzzi argues that, while preparing for this task, and stimulated by extensive readings of mechanical texts (he would have certainly have revisited, among others, Archimedes, Commandino, and Guidobaldo's Mechanicorum liber, he perhaps understood precisely then all the advantages that could derive from adopting momento.
In the analysis of the Mecaniche, Galluzzi argues that momento, as used in the text, "indicated both, in its etymology and in its most common use (the text and main commentaries and expositions of Aristotle's Physics), the tendency, the endeavor of bodies toward their 'proper' place, and, consequently, the speed with which they would have moved toward that goal. Such tendency derived directly from weight. Momento, therefore, indicated the 'instinct', the natural 'desire' of the heavy body to fulfill itself: ultimately, a rather intangible cause of motion, an 'occult' quality."
Clavelin argues that Galileo’s definition of momento is remarkable in that it enabled Galileo to accept the concept of moment in three distinct ways:
In the first, moment was used to refer to the force exerted by a heavy body as determined by its distance from the axis of the system, making it equivalent to the concept of static moment. Jordanus had only implicitly used the concept of static moment in his study of the bent lever, whereas Galileo’s Mecaniche was the first to make explicit use, which presided over his treatment of all simple machines. Galileo also added a definition of the center of gravity (i.e., center of heaviness), which used momento in the static sense. This definition of center of gravity was inspired by those of Pappus and Guido Ubaldo del Monte. Pappus, in his Collections, had defined the center of gravity as a point in a body such that if the body were suspended from it, it would remain at rest. In practice, the center of gravity is the point marking the intersection of all the vertical planes that can be drawn through all the points from which bodies are suspended successively. Guido Ubaldo del Monte, in his Paraphrasis, remarked that the two parts determined by each vertical plane (whatever the point of suspension) were merely “equiponderant,” that is, they had the same effect, but when separated from each other, they would not have the same weight. Galileo converted Guido Ubaldo’s remark into a definition and removed any remaining uncertainties with his concept of moment.
In the second, moment is used to express a product of weight and the velocity of its virtual motion; in this second sense, the concept reflected the dynamic approach of the Mechanical Problems and the works of Jordanus, and thus bears witness to Galileo’s interest in all the traditions that combined in the development of the science of equilibrium. Galileo uses this dynamic version of moment in his analysis of the lever and his theory of the inclined plane through virtual motions.