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Overview of Punctorum Relatio ad Planum Spectatoris (1684 – 1687)

This manuscript probably belongs to a period between Leibniz’s beginnings on perspective and his last attempts, as it shows a similar approach to the later writings, yet less refined. Here we find one of Leibniz’s most important theorems about perspective: the ratio between the two coordinates used to identify a point in the apparent and in the objective plane (“inclinatio” and “declinatio”) is equal to the ratio between the distance of the spectator both from the tabula and the objective plane. The difference with the later writings is that here an unnecessary third plane is introduced, that is the plane parallel to the tabula, in which belongs the eye of the spectator. Since this introduction leads to a slightly different formulation of the theorem and considering Leibniz’s aim for simplicity in perspective’s writings, there are reasons to believe that Punctorum Relatio ad Planum Spectatoris precedes Scientia perspectiva.

See manuscript’s transcription