22 Aug. 1814

Logic

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Ch. Division

'. Synthesis and Analysis

correspond not

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'. 5. Misapplication of the Terms Synthesis and Analysis to Geometry and Algebra.

Marking /Expressing/ the difference between Geometry and Algebra is another of the purposes to which the opposite terms Synthesis and Analysis, with the methods respectively denominated from them, viz. the Synthetic method, and the Analytic method, have been employed.

But, between these two branches of science, no such difference or distinction will be found as that of which intimation is given, by that pair of correspondent and opposite appellatives.

In Geometry, quantity is never considered but with relation to figure; in Algebra it never is considered with relation to figure: of the difference between these two branches of Mathematics, this account is at once true, short, and clear, and no other account that is in equal, if in any degree at all endowed with these qualities, will, it is believed, be found.

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