date

22 Aug. 1814 Logic Ch. Division
22 Aug. 1814

Logic

Ch. Division

'. Synthesis and Analysis

correspond not

In Geometry /Algebra/ as well as in Geometry in Geometry as well as in Algebra, that which is unknown or supposed to be unknown, is inferred from its relation to that which is known, or supposed to be known: in Algebra, unknown quantities, as expressed by letters, are made known by means of the relation they bear to known ones, as expressed by figures; in Geometry, unknown quantities, as expressed by figure, and supposed to exist as between figure and figure, or parts of the same figure, are made known by means of the relations they bear to known quantities, as expressed by figure.

In Geometry, true it is, that objects are put together; quantities known and unknown are put together; whereupon, of such as are unknown, a description is given, and a conception conveyed by means of the relation they bear to certain known ones.

Of Geometry this is true; nor is it less so when applied to Algebra.

A quantity is mentioned to me, of which I wish to know the amount, it being as yet unknown to me. By the amount, in this case, is always meant the amount in numbers; for, in truth, the subject of Algebra is number - numbers and nothing else. Suppose the number in question six; - in answer to my question, What is the number ? the number six is not mentioned by that name; but I am told it is that number which is as great again as number three, or half as great exactly as number twelve. Simple as they are, either of these answers is already Algebra.

And it is thus that, by Algebra, the known and unknown quantities being put together, a description of such as are unknown is given, and a conception conveyed by means of the relation they bear to certain known ones.

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