The History of algebra in Italy in the 14th and 15th centuries: some remarks on recent historiography (original) (raw)
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2008
Algebra as we encounter it in or Descartes (1637) looks wholly different from what we know from al-Khwārizmī and Fibonacci. Indeed, early Modern algebra did not build on these: its foundation was the algebra of the Italian Abbacus school. The paper follows the development of this tradition from 1307 onward, in particular the appearance of abbreviations, the naming of powers and roots, formal calculations, schemes, and the solution of higher-degree equations.
The Tortuous Ways toward a New Understanding of Algebra in the Italian Abbacus School 14th
Algebra as we encounter it in or Descartes (1637) looks wholly different from what we know from al-Khwārizmī and Fibonacci. Indeed, early Modern algebra did not build on these: its foundation was the algebra of the Italian Abbacus school. The paper follows the development of this tradition from 1307 onward, in particular the appearance of abbreviations, the naming of powers and roots, formal calculations, schemes, and the solution of higher-degree equations.
Polynomials and equations in medieval Italian algebra
A recent study (Oaks 2009) shows that the medieval Arabic concepts of polynomial and equation differ from those of modern algebra. We present here a continuation of this study for medieval Italian algebra, and show that Italian abbacus authors possessed essentially the same medieval concepts as their Arabic predecessors. In short, polynomials were regarded as aggregations of the different species (power) of the unknown, and medieval algebraists preferred to set up polynomial equations devoid of mathematical operations. These concepts are consistent with the various medieval Italian notations, and extended down to Bombelli's time
In 1942, Edgar Zilsel proposed that the sixteenth-seventeenth-century emergence of Modern science was produced neither by the university tradition, nor by the Humanist current of Renaissance culture, nor by craftsmen or other practitioners, but through an interaction between all three groups in which all were indispensable for the outcome. He only included mathematics via its relation to the "quantitative spirit". The present study tries to apply Zilsel's perspective to the emergence of the Modern algebra of Viète and Descartes (etc.), by tracing the reception of algebra within the Latin-Universitarian tradition, the Italian abbacus tradition, and Humanism, and the exchanges between them, from the twelfth through the late sixteenth and early seventeenth century.
Reinventing or Borrowing Hot Water? Early Latin and Tuscan Algebraic Operations with Two Unknowns
Ganita Bharati, 2020
In developed symbolic algebra, from Viète onward, the handling of several algebraic unknowns was routine. Before Luca Pacioli, on the other hand, the simultaneous manipulation of three algebraic unknowns was absent from European algebra and the use of two unknowns so rare that it has rarely been observed and never analyzed. The present paper analyzes the three occurrences of two algebraic unknowns in Fibonacci's writings; the gradual unfolding of the idea in Antonio de' Mazzinghi's Fioretti; the distorted use in an anonymous Florentine algebra from ca 1400; and finally the regular appearance in the treatises of Benedetto da Firenze. It asks which of these appearances of the technique can be counted as independent rediscoveries of an idea present since long in Sanskrit and Arabic mathematics, and raises the question why the technique once it had been discovered was not cultivated-pointing to the line diagrams used by Fibonacci as a technique that was as efficient as rhetorical algebra handling two unknowns and much less cumbersome, at least until symbolic algebra developed, and as long as the most demanding problems with which algebra was confronted remained the traditional recreational challenges. Contents
Jacopo da Firenze and the beginning of Italian vernacular algebra
Historia Mathematica, 2003
In 1307, a certain Jacopo da Firenze wrote in Montpellier a Tractatus algorismi that contains the earliest extant algebra in a European vernacular and probably, as is argued, the first algebra in vernacular Italian. Analysis of the text shows that it cannot descend from any of the algebras written in Latin, nor from any published Arabic treatise, for which reason it presents us with evidence for a so far unexplored level of Arabic algebra. Further, since it contains no Arabisms, it must build on an already existing Romance-speaking environment engaged in algebra. Comparison with other Italian algebras written during the next 40 years show that all are linked to Jacopo or to this environment (perhaps Catalan) and disconnected from Leonardo Fibonacci's Liber abbaci.Nel 1307, un certo Jacopo da Firenze scrisse a Montpellier un Tractatus algorismi che contiene la prima presentazione sopravvissuta dell'algebra in un volgare europeo – probabilmente la prima presentazione in volgare italiano in assoluto. L'analisi del testo dimostra che l'algebra di Jacopo non è basata su nessuno dagli scritti algebrici latini, e neanche su un trattato arabo pubblicato; è dunque una testimonianza di un livello finora inesplorato dell'algebra araba. D'altra parte, Jacopo non utilizza un solo arabismo, e deve dunque aver preso la sua ispirazione da un ambiente di lingua romanza. Un'ispezione attenta di altri scritti algebrici italiani risalenti alla prima metà del Trecento svela che tutti sono legati a Jacopo o a questo ambiente (possibilmente catalano) e che nessuno ha legami con il Liber abbaci di Leonardo Fibonacci.