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Page:Carroll - Notes by an Oxford Chiel.djvu/47

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of rooms, which is always at Sixes and Sevens. Find the probable amount of reading done by A and B while the Eights are on.

We proceed to illustrate this hasty sketch of the Dynamics of a Parti-cle, by demonstrating the great Proposition on which the whole theory of Representation depends, namely:—"To remove a given Tangent from a given Circle, and to bring another given Line into contact with It."

To work the following problem algebraically, it is best to let the circle be represented as referred to its two tangents, i.e. first to WEG, WH, and afterwards to WH, GH. When this is effected, it will be found most convenient to project WEG to infinity. The process is not given here in full, since it requires the introduction of many complicated determinants.