2012/10/25 by Dimitris Sardelis, Sardelis, Dimitris, Theodoros M Valahas +2
Engineering · Mathematics · #00A05 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mechanics and Biomechanics Studies #math.GM #msc:00A05
paper · pdf · doi:10.48550/arxiv.1210.6842
8 pages, 9 figures. Figures 3 and 6 replaced. Equation (9) replaced
openalex publication_date 2012/10/25 · arxiv created 2012/10/28 · arxiv updated 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The method of application of areas as presented in Euclid's Elements, is employed to generate the three conics as the loci of points with Cartesian coordinates satisfying quadratic equations with coefficients defined by the initial settings of the geometric constructions produced by the applications method. This conceptual reconstruction supports the view that the conics were most probably discovered as plane curves by fusing the method of the application of areas with the concept of locus, long before Apollonius studied them as conic sections.