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Athanasius Kircher on Marin Getaldić’s Promotus Archimedes
Ivica Martinović
orcid.org/0000-0003-0424-1242
; Dubrovnik,Hrvatska
Sažetak
Athanasius Kircher, first as professor of mathematics at the Collegium Romanum, and later as scholar, expounded the foundations of hydrostatics in three of his works. In his synthesis on magnetism Magnes sive de arte magnetica opus tripartitum (1643), he mentions only Archimedes as his source, while in the first tome of his geological work Mundus subterraneus (1665), Archimedes is joined by Getaldić and Galileo. Only in his Mundi subterranei tomus secundus (1665), completed in the middle of 1663, does the Roman professor expound hydrostatics more thoroughly, and in so doing fully leans on Getaldić. Namely, within experimental metalostatics Kircher focuses on two practical problems solved by Getaldić at the end of his Promotus Archimedes, whereby a number of Getaldić’s examples he transforms into his ‘propositions.’ Although in the exposition he leans only on Getaldić’s examples, Kircher ultimately admits that Getaldić has proved the general theorem for determining the portion of one metal in the alloy. Finally, Kircher also adopted Getaldić’s tables, as he enclosed the so-called abacus, a table which he composed of Getaldić’s two tables of relative weights.
By using the comparative method, this research comes forth with a number of other valuable results, given here in chronological order.
While writing his Promotus Archimedes, Getaldić consulted Commandino’s 1565 edition of Archimedes’s De iis quae vehuntur in aquis, yet far better and with more scrutiny than Commandino and his predecessors chose the key terms for body and volume – corpus and magnitudo. From Commandino’s edition the Ragusan learnt how a physical problem can be expressed graphically, and be reduced to a geometric proportion. However, when referring to Archimedes’s work De sphaera et cylindro, Getaldić uses the 1544 edition of Archimedes’s Opera omnia published in Basel.
The quotation on Hiero’s problem from the third chapter of the ninth book of Vitruvius’s De Architectura the Ragusan borrowed from Philander’s edition, and not from that of Daniele Barbaro. By doing so, he not only opted for an edition providing more scientific information, but also for an edition that was closer to his methodology and scientific goals, without any reference to Aristotle’s concepts of light and heavy and without any link with the medieval tradition of the term ‘weight by species’ (gravitas in specie).
While Getaldić turned a tin sample in the form of an equilateral cylinder, Tartaglia until 1551 weighed a “cube of brick” (cubo di cotta), balls of iron and lead, and coins of gold, silver and copper, Villalpando used a cubic vessel with copper walls (paratus cubus), and Riccioli a lead cube. This helped establish a distinctive feature of Getaldić’s methodology.
In his approach to the problem of Hiero’s wreath, Kircher, in addition to Getaldić’s instruction for determining gold quality also referred to Mersenne, while the latter in his work Cogitata physico-mathematica (1644) referred to Petit. Thus traced is one channel of the French reception of Getaldić’s Promotus Archimedes. In his Quaestiones celeberrimae in Genesim (1623), Mersenne fully adopted Getaldić’s three tables of data: his note on the first table informs that it is preceded by an elaborate proof procedure composed of 9 theorems and 17 propositions; Getaldić’s fifth and sixth table he introduced with a remark containing Getaldić’s ratios of weights measured in air and water for gold, silver, and copper.
Pierre Petit, official in the French gunnery, published two tables at the end of his opuscle “Construction de la regle et compas de proportion,” within a broader edition entitled L’usage ou le moyen de pratiquer par une regle toutes les operations du Compas de Proportion (1634). The first of the two tables follows Getaldić’s fourth table, while the second, which provides relative weights to the value of 100 for gold, differs from Getaldić’s second table in the selection of materials, yet the obtained values do not differ significantly. In addition, Petit recommends the reader to consult “Avant-propos,” which contains detailed explanations of Petit’s sources, description of his methodology, and 15 references to Getaldić. Moreover, the preface reveals that the French measurer, with scientific scrutiny, applies Getaldić’s methodology in the French context, i.e. by using Parisian measures for length and weight.
In a later work Cogitata physico-mathematica (1644), Mersenne referred to Getaldić in two treatises: “De hydraulicis et pneumaticis phaenomenis,” and “Ars navigandi,” which opens with a short exposition on hydrostatics. In the first treatise he included a corollary “De Ghetaldi tabulis,” in which he adopts and interprets Getaldić’s two tables of relative weights. Regarding the relative weights of wine, he had only one objection to Getaldić’s research results, 14 years prior to Schott. Mersenne concludes his corollary on Getaldić with Petit’s table of the relative weights of metals, stones, and liquids. In the treatise “Ars navigandi,” the French polymath also refers to “Getaldić’s tables offering the weights for 12 bodies,” but not to Getaldić’s proposition that accompanies these tables theoretically. Mersenne describes the method of weighing a solid body in liquid, in which the equilibrium is attained with the use of horsehair on both pans of the balance, and in doing so makes no mention that he is following Getaldić’s methodology.
In his works, Schott pointed to several authors who in their expositions of hydrostatic problems came forward with their views on Getaldić’s Promotus Archimedes, or who used Getaldić’s tables of relative weights: Mersenne, Bettini, Odierna, Cabeo, and Harsdörffer.
Another two Jesuits, prior to Riccioli, both Biancani’s students, drew attention to Getaldić’s hydrostatic treatise: Mario Bettini in Apiaria universae philosophiae mathematicae (1642) and Niccolò Cabeo in In quatuor libros Meteorologicorum Aristotelis commentaria et quaestiones (1646). In his “apiary” of arithmetic Bettini emphasises the use of proportion in Getaldić’s solution for the problem of Hiero’s wreath. In his considerations on entire experimental philosophy, Cabeo formulates three hydrostatic questions in which he calls on Getaldić, both his methodology of weighing a body in water and his second table of relative weights.
In his commentary of Galileo’s hydrostatic treatise, published in Archimede redivivo (1644), Giovanni Battista Odierna from the Sicilian Ragusa published an excerpt from Getaldić’s second table of relative weights, supplemented with a new table in which Getaldić’s data for relative weights of metals and liquids he compared with the later data of Carlo Ventimiglia. He made a single comment on Getaldić’s data: that Getaldić’s relative weight for gold differs from that of Galileo.
The title page of the collection Delitiae mathematicae et physicae / Die mathematischen und philosophischen Erquickstunden (1651) by Georg Philipp Harsdörffer from Nürnberg already suggests that he included Marin Getaldić among ten major sources from which he drew his mathematical delicacies, while in the ninth part of his mathematical collection dedicated to the art of weighing, he included two exercises »from Getaldić« with direct references to Getaldić’s Promotus Archimedes. In the first problem, he adopts two examples by which Getaldić interprets his first table of relative weights, whereupon he encloses this table using German terms. In the second problem, on determining the composition of alloy, Harsdörffer follows Getaldić’s methodology for solving the problem of Hiero’s wreath: he describes Getaldić’s weighing with the hydrostatic balance with the help of horsehair, encloses Getaldić’s drawing and includes Getaldić’s example with equal numerical values.
Most certainly prior to Kircher, English mathematician William Oughtred examined the first and the second table of relative weights composed by Getaldić. In Oughtred’s adaptation “Ex Promoto Archimede Marini Ghetaldi,” published posthumously in his Opuscula mathematica hactenus inedita (1677), one table has been composed of the mentioned two by Getaldić, with 1/100 written on the diagonal. As the text of his adaptation mentions two tables, it appears likely that either the editor or printer merged the two tables into one.
In his university textbook Naturalis philosophiae, seu physicae tractatio prior (1756), Jesuit Michael Klaus from Bratislava, Viennese professor of philosophy, under the influence of Schott’s Magia universalis naturae et artis, emphasised that four authors objected to Archimedes’s method as described in Vitruvius: Getaldić, Galilei, Odierna, and Cabeo.
The works of Riccioli, Schott and Kircher, mature fruits of the Jesuit science in the mid-seventeenth century, in various ways emphasised and drew attention to the role of Getaldić’s treatise Promotus Archimedes (1603) in the history of hydrostatics. These works, together with the works of the previous generation of Jesuit scholars Mario Bettini and Niccolò Cabeo, promote Getaldić into the most influential hydrostatic expert within the Jesuit science of the seventeenth century. The works concerned include eight printed works, notably Riccioli’s Almagestum novum (1651), »Magia hydrostatica« in the third volume of Schott’s Magia universalis naturae et artis (1658), and »Ars metallostatica« in the second volume of Kircher’s Mundus subterraneus (1665). Jesuit production in natural philosophy and natural sciences has extended for seven decades the ‘scientific age’ of Getaldić’s methodology in all of its essential components: Archimedean use of proportion in the formulation of a physical problem, the use of horsehair in weighing with the help of a hydrostatic balance, a tin sample in the form of an equilateral cylinder, the relation between initial measuring and further calculations, tabular shaping of new data, applications to ballistics, foundry, and goldsmithery. Owing to a widespread network of scientific connections, besides the centres of Jesuit science in Rome, Parma, and Bologna, the influence of Getaldić’s Promotus Archimedes spread to France, Bavaria, England and Sicily, as evidenced by the names of Mersenne, Petit, Oughtred, Harsdörffer, and Odierna. This contributes to a profoundly different assessment of Getaldić’s role and influence in the birth of the early modern science at the dawn of the seventeenth century, i.e., positions Getaldić alongside Galileo.
Yet the works of the famous Jesuit scientists of the seventeenth century fail to note Getaldić’s two key insights in the philosophy of science:
(1) “the assertion which is more distant from the notion of principle should not be assumed, but should be proved;”
(2) “conjecture is not accepted as truth.”
Ključne riječi
Marin Getaldić; Archimedes; Vitruvius; Giovanni Battista Riccioli; Kaspar Schott; Athanasius Kircher; Federico Commandino; Niccolò Tartaglia; Juan Bautista Villalpando; Marin Mersenne; Pierre Petit; William Oughtred; 17th-century mathematics; 17th-century hydrostatics; 17th-century methodology; 17th-century philosophy of science; tables of relative weights; problem of Hiero’s golden votive wreath; determining of gold purity
Hrčak ID:
240971
URI
Datum izdavanja:
25.6.2020.
Posjeta: 1.023 *