# Analytic geometry and principles of algebra by Alexander Ziwet, Louis Allen Hopkins

By Alexander Ziwet, Louis Allen Hopkins

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Extra info for Analytic geometry and principles of algebra

Example text

In this context, the activities of the imagination represent a form of reflective judgment in the production of concepts of nature as art. It is an expression of the embodied subject’s powers of production, so that geometry becomes expressed, not as an objective or cognitive knowledge but as a technical activity brought about through the powers of the imagination. The imagination therefore modifies the relationship between cognitive limit and sensation into an embodied series of enactments that belong to the ‘freely acting individual’.

Between these two encounters we find that the absolute geometric method becomes embodied into the aesthetic powers of the reflective subject, and the geometric method is therefore presented both in the body of the 32 Space, Geometry and Aesthetics reflective subject and in the geometric diagram or figure so that an ‘aesthetic origin’ of geometry is instantiated. Kant’s Critical philosophy suggests a shift from an external to an internal aesthetic geometry in the first and third Critiques. First, Kant’s synthetic a priori judgment, although radical in positing the particular and a priori difference of individual states, remains a problematic notion of difference because it is determined by the ‘external’ limit.

Scholia) of an ‘absolute’ geometry, thereby further highlighting how the imagination generates legitimate content in reflective thinking. But it is in the supplementary note to this passage in which the aesthetic power of the Drawing Figures 25 productive and ‘geometric’ imagination is promoted most strongly, when he writes: This pure and, precisely because of that purity, sublime, science of geometry seems to comprise some of its dignity if it confesses that on its elementary level it needs instruments to construct its concepts, even if only two: compass and ruler.