December 2013
Llull: Revista de la Sociedad Espanola de Historia de las Cienci;2013, Vol. 36 Issue 78, p283
Academic Journal
Before and after the invention of his differential calculus, Leibniz used widely the notions of analyticity and of equivalence of lines and figures. These two notions played an essential role in his mathematics and in his understanding of geometricity. My paper is divided into four sections. The first section studies the meaning of analysis and analyticity, as well as their relation to geometricity, which depends on the question of exactness. Exactness implies geometricity; analysis means calculus, whereas analyticity means calculability. The two parts of geometry correspond to two different types of analysis, one of them being Leibniz's new, certain, and general analysis. The second section deals with the notion of equivalence of curves, introduced by Leibniz in 1675. That enabled him to identify curves with polygons of infinitely many, infinitely small sides. The equivalence principle becomes the fundamental principle of his infinitesimal geometry and of his differential calculus, too. It is based on the notion of quadrature. The third section elaborates how Leibniz's classification of curves changes over time. On account of the perfection of analysis, non-geometrical curves are eventually judged as no longer existing. The final section summarizes Leibniz's theory of simple, analytical curves.


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