A Characteristic to Unify all Characteristics and Link Them in Harmony. Unification of equations in De la méthode de l’universalité

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Living in Paris is known to have a significant influence on the development of Leibnizian thought. During this period, Leibniz met many scientists, discovered mathematics and became a prolific writer. This is also the time when he began to develop the central concepts of his philosophy and the texts De la méthode de l’universalité I and II provide excellent examples of this. They provide the reader with vivid insight into a project which at the time was surprising, ingenious and very ambitious. The texts show Leibniz proposing a new system of mathematical notation of sufficient generality to handle concepts such as Harmony or Characteristic that were constantly present throughout his life. Text (II) is an introduction to this new method, his concepts and his philosophy. In text (I), Leibniz details his ambiguous system and extends the mathematical considerations far enough to be able to exhibit a general equation capable of generating all possible conical sections. The aim of this article is to present a review of both mathematical and philosophical concepts used by Leibniz to achieve these goals.