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Institutioni Analitiche ad uso della Gioventu Italiana.
Milan: nella Regia-Ducal Corte, 1748. First edition of this important work by “the first woman in the Western world who can accurately be called a mathematician” (DSB). “After the scientific revolution, in seventeenth- and eighteenth-century Italy in particular, learned women rose to intellectual prominence. Mathematically the most distinguished was Maria Agnesi, whose Institutioni Analitiche (1748) was the first general textbook of the new mathematics of the period.” (Grattan-Guinness, Encyclopedia, 1527). “In 1738, after the publication of the Propositiones philosophicae [her only other mathematical publication], Agnesi indicated that the constant public display of her talents at her father’s gatherings was becoming distasteful to her, and she expressed a strong desire to enter a convent. Persuaded by her father not to take that step, she nevertheless withdrew from all social life and devoted herself completely to the study of mathematics. In the advanced phases of the subject she was guided by Father Ramiro Rampinelli, a member of the Olivetan order of the Benedictines, who later became professor of mathematics at the University of Pavia. A decade of concentrated thought bore fruit in 1748 with the publication of her Istituzioni analitiche ad use della gioventu italiana, which she dedicated to Empress Maria Theresa of Austria. This book won immediate acclaim in academic circles all over Europe and brought recognition as a mathematician to Agnesi. The Islituzioni analitiche consisted of two huge quarto volumes containing more than a thousand pages. Its author’s objective was to give a complete, integrated, comprehensible treatment of algebra and analysis, with emphasis on concepts that were new (or relatively so) in the mid–eighteenth century. In this connection one must realize that Newton was still alive when Agnesi was born, so that the development of the differential and integral calculus was in progress during her lifetime. With the gioventu (youth) in mind, she wrote in Italian rather than in Latin and covered the range from elementary algebra to the classical theory of equations, to coordinate geometry, and then on to differential calculus, integral calculus, infinite series (to the extent that these were known in her day), and finally to the solution of elementary differential equations. She treated finite processes in the first volume and infinitesimal analysis in the second. In the introduction to the Istituzioni analitiche, Agnesi—modest as she was, with too great a tendency to give credit to others had to admit that some of the methods, material, and generalizations were entirely original with her. Since there were many genuinely new things in her masterpiece, it is strange that her name is most frequently associated with one small discovery which she shared with others: the formulation of the versiera, the cubic curve whose equation is x’v = a 2 (a–r) and which, by a process of literal translation from colloquial Italian, has come to be known as the ‘witch of Agnesi.’ She was apparently unaware (and so were historians until recently) that Fermat had given the equation of the curve in 1665 and that Guido Grandi had used the name versiera for it in 1703. The tributes to the excellence of Agnesi’s treatise were not numerous that it is impossible to list them all but those related to translations of the work will be noted. The French translation (of the second volume only) was authorized by the French Academy of Sciences. In 1749 an academy committee recorded its opinion: ‘This work is characterized by its careful organization, its clarity, and its precision. There is no other book, in any language, which would enable a reader to penetrate as deeply, or as rapidly, into the fundamental concepts of analysis. We consider this treatise the most complete and best written work of its kind.’ An English translation of the Istituzioni analitiche was made by John Colon, Lucasian professor of mathematics at Cambridge, and was published in 1801 at the expense of the baron de Maséres. In introducing the translation, John Hellins, its editor, wrote: ‘He [Colson] found her [Agnesi’s] work to be so excellent that he was at the pains of learning the Italian language at an advanced age for the sole purpose of translating her book into English, that the British Youth might have the benefit of it as well as the Youth of Italy.’ The recognition of greatest significance to Agnesi was provided in two letters from Pope Benedict XIV. The first, dated June 1749, a congratulatory note on the occasion of the publication of her book, was accompanied by a gold medal and a gold wreath adorned with precious stones. In his second letter, dated September 1750, the pope appointed her to the chair of mathematics and natural philosophy at Bologna. (DSB: I, 75-77). Honeyman 20; Riccardi I, 8; Parkinson, Breakthroughs, 165. 4to: 247 x 193 mm. 2 volumes. Pp. (20), 428, (2:errata) and 35 engraved folding plates; (2:title) 431-1020, (2:errata) and 24 plates. Title pages with one small rubber stamp, and traces of an older rubberstamp having been removed. Fine and clean throughout, in all a very good copy. Scarce.
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Last Found On: 2012-12-27           Check availability:      Direct From Bookseller    

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