@incollection {2116243, title = {The rule of quantity by {C}huquet and de la {R}oche and its influence on {G}erman {C}ossic algebra}, booktitle = {Pluralit{\'e} de l{\textquoteright}alg{\`e}bre {\`a} la Renaissance}, year = {2012}, pages = {127{\textendash}147}, publisher = {Honor{\'e} Champion}, abstract = {

The importance of Larismethique of de La Roche, published in 1520, has been seriously underestimated. One reason for the neglect is related to the inscrutable way he is referred to. Buteo and Wallis called him Stephanus {\`a} Rupe de Lyon. Other obscure references, such as Gosselin calling him Villafrancus Gallus have been overlooked by many commentators. His influence can be determined in several works that do not credit him but use problems or definitions from the Larismethique. However, most damaging for its historical assessment was Aristide Marre?s misrepresentation of the Larismethique as a grave case of plagiarism. Marre discovered that the printed work of 1520 by Estienne de la Roche contained large fragments that were literally copied from Chuquet?s manuscript of the Triparty. Especially on the Appendice, which contains the solution to a large number of problems, Marre writes repeatedly that it is a literal copy of Chuquet. However, he fails to mention that the structure of the text of de la Roche, his solution methods and symbolism differs significantly from Chuquet. De la Roche introduces several improvements, especially with regards to the use of the second unknown. We provide an in-depth comparison of some problems solved by the so-called regle de la quantite by Chuquet with those of de la Roche. We further report on the surprising finding that Christoff Rudolff{\textquoteright}s solution to linear problems by means of the second unknown in his Behend vnnd Hubsch Rechnung of 1525 depends on Chuquet and de la Roche. As it is generally considered that algebra was introduced in Germany through Italy this provides a new light on the transmission of algebraic knowledge from France to the rest of Europe.

}, isbn = {9782745323989}, author = {Heeffer, Albrecht}, editor = {Rommevaux, Sabine and Spiesser, Maryvonne and Massa Esteve, Maria Rosa} } @article {Heeffer2011, title = {The Rhetoric of Problems in Algebra Textbooks from Pacioli to Euler}, year = {2011}, abstract = {

The selection of problems by Euler in his Vollst{\"a}ndige Anleitung zur Algebra displays a great familiarity with the typical recreational and practical problems of Renaissance and sixteenth-century algebra books. A detailed study into the sources of Euler reveals that he copied most of his problems from Christoff Rudolff’s Coss which was first published in 1525 and reissued in 1553 by Michael Stifel. Why would Euler found his popular textbook on algebra on a book published 250 years before? We propose an explanation based on the evolving rhetorical function of problems in algebra textbooks since the Renaissance. We discern six stages in the evolution from abacus problem solving to algebraic theory. The first theory emerged through the extraction of general principles from the practice of problem solving. The algebra textbooks of the eighteenth century close a circle of continuous rhetorical development by using problems for practicing general principles and applying the algebraic language. Euler’s Algebra is a prime example of the new rhetoric of problems still prominent in today’s textbooks.

}, author = {Heeffer, Albrecht} } @incollection {1029910, title = {The Reception of Ancient Indian Mathematics by Western Historians}, booktitle = {Ancient Indian Leaps into Mathematics}, year = {2010}, pages = {135{\textendash}152}, publisher = {Birkh{\"a}user Verlag}, abstract = {

While there was an awareness of ancient Indian mathematics in the West since the sixteenth century, historians discuss the Indian mathematical tradition only after the publication of the first translations by Colebrooke in 1817. Its reception cannot be comprehended without accounting for the way that the new European mathematics was shaped by Renaissance humanist writings. We sketch this background and show with one case study on algebraic solutions to a linear problem how the understanding and appreciation of Indian mathematics was deeply influenced by the humanist prejudice that all higher intellectual culture, in particular all science, had risen from Greek soil.

}, isbn = {978-0-8176-4694-3}, author = {Heeffer, Albrecht}, editor = {Yadav, B.S. and Mohan, Man} } @article {1092888, title = {Regiomontanus and Chinese mathematics}, journal = {PHILOSOPHICA}, volume = {82}, number = {2}, year = {2008}, pages = {87{\textendash}114}, abstract = {

This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem (CRT) through the Sh{\`u} sh\={u} Ji\v{u} zh\={a}ng (SSJZ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ. CRT problems appear in earlier European arithmetic and can be solved by the method of the Sun Zi, as did Fibonacci. Secondly, we pro-vide evidence that remainder problems were treated within the European abbaco tradition independently of the CRT method. Finally, we discuss the role of recre-ational mathematics for the oral dissemination of sub-scientific knowledge.

}, issn = {0379-8402}, author = {Heeffer, Albrecht}, editor = {Weber, Erik} } @article {353368, title = {R{\'e}cr{\'e}ations math{\'e}matiques (1624): a study on its authorship, sources and influence}, journal = {Gibeci{\`e}re}, volume = {1}, number = {2}, year = {2006}, pages = {77{\textendash}167}, abstract = {

In 1624 a small octavo was published in the French university town Pont-{\`a}-Mousson. It was the first time a reference was made to ‘recreational mathematics’ in the title of a book. This work is pivotal in the history of science and mathematics. It brings together two sixteenth-century traditions, mercantile arithmetic and natural magic, and creates two new ones: recreational mathematics and popular science. The booklet did not abound in new ideas. Several of the recreational problems treated, can be traced back to Babylonian, Greek and Hindu sources and the infatuation with mechanical contrivances dates from Hero of Alexandria. But the fact that the book stands on the crossroad of traditions, its popularity with the natural philosophers of the seventeenth century and its complex history makes it a grateful subject for study. Some of the complexities about the numerous editions and confusing claims about its authorship will be clarified. The author’s direct sources will be exposed. The arithmetical and combinatorial problems were copied from Bachet, problems on practical geometry from Jean Errard. Salomon de Caus was the source of inspiration for problems on perspective, mechanical devices and fountains. Several problems were recipies by Alexis of Piemont from the classic book by Ruscelli. The book was influencial on early seventeenth-century natural philosophers such as Descartes, Mersenne and Leibniz.

}, issn = {1558-8149}, author = {Heeffer, Albrecht} }