Excerpt from On the Application of a New Analytic Method to the Theory of Curves and Curved Surfaces

I fear that brevity and compression have been but too much studied in the following essay, but the necessity of comprising the whole matter in a small compass, and the pressure of other avocations, will plead, I hope, a sufficient apology.

From the same cause I have been obliged to omit altogether subjects which might have been with propriety introduced, for example, the general theory of shadows and have only touched upon others which would require perhaps further development.

Among other applications of the method, I trust that to the theory of reciprocal polars will be found simple and satisfactory.

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