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Overview of Ars Representatoria (1691)

The Ars Representatoria is a general and programmatic paper interested in problems of characteristics. Leibniz reaffirms the starting point and purpose of his analysis situs, meant to avoid the use of extrinsic algebraic proceedings in geometry, without however having to give up the advantages of the characteristica speciosa and go back to the elegant, but complicated and unproductive, synthetic geometry. It is a matter of reforming algebraic formalism and finding another one that may be proper to geometry. Although it can be blindly manipulated, such formalism must have this advantage on ordinary algebra: that, when interpreted, it immediately offers the geometrical object to our imagination. It is therefore a cogitatio caeca that promises a vast view. The discussion in the Ars Representatoria in many respects anticipates Leibniz’s late essays on the theory of knowledge and interlocks with the theory of the imaginatio distincta that a little earlier Leibniz began to envision as the solution to several epistemological questions in mathematics.

See a translation for the manuscript [ENG] [FRN]