An Elementary Treatise on Determinants - With Their Application to Simultaneous Linear Equations and Algebraical Geometry #271654

Of the seventy Propositions contained in the following treatise ten are substantially taken from Baltzer's treatise on Determinants; also the Geometrical Tests, given in Chapter VIII, are to he found in most works on Algebraical Geometry: the rest of the matter is, so far as I know, original, and consists of a series of Propositions which the object I had in view obliged me to introduce. That object was to present the subject as a continuous claim of argument, separated from all accessories of explanation or illustration, a form which I venture to think better suited for a treatise on exact science than the semi-colloquial semi-logical form often adopted by Mathematical writers. I say 'semi-logical' advisedly, for nothing is more easy than to forget, in an argument thus interwoven with illustrative matter, what has, and what has not, been proved.<br><br>With this object in view I have introduced all such explanation and illustration as seemed necessary for a beginner, either in the form of footnotes, or, where that would have occupied too much room, of Appendices.<br><br>New words and symbols are always a most unwelcome addition to a Science, especially to one already burdened with an enormous vocabulary, yet I think the Definitions given of them will be found to justify their introduction, as the only way of avoiding tedious periphrasis.