Analytical geometry in {\it An elementary treatise on plane and spherical trigonometry, and on the application of algebra to geometry} by S. F. Lacroix. (English)

Bjarnadóttir, Kristín (ed.) et al., “Dig where you stand" 3. Proceedings of the third international conference on the history of mathematics education, Uppsala University, Sweden, September 25‒28, 2013. Uppsala: Uppsala University, Department of Education (ISBN 978-91-506-2444-1). 361-375 (2015).

Summary: Although most mathematics history books present Lacroix (1765‒1843) as a minor mathematician, he was to become recognized both in his own time and in our own for his work as a writer of mathematics textbooks. His importance lies in the way he presents the contents in his textbooks: in an orderly, clear and concise way, from the elementary to the most complex concepts, thus contributing to the dissemination of mathematical knowledge. His works were used during a large part of the nineteenth century, both in schools in France and in a good part of the rest of Europe, particularly in Spain. One example would be his {\it Tratado elemental de trigonometría aplicagion rectilínea y esférica, y de la aplicación del álgebra á la geometría} (An elementary treatise on plane and spherical trigonometry, and on the application of algebra to geometry), used as a textbook in Spanish secondary schools and universities for almost a century. In this work, which is part of a dissertation’ on the study of analytic geometry in Spain during the nineteenth century, we focus on the way Lacroix deals with this part of the mathematics in this book. It shows an analytic geometry typical of the nineteenth century in Spain that preserves some elements from the geometry of Descartes but it also includes elements from the algebraic geometry used nowadays.