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ON THE NOTION AND BOUNDARIES OF ALGEBRA. 
[347 
and therefore 2S = (n + 1) + (n + 1) + ... (n terms) = n(n + 1) or 3 = (n + 1); or by 
indnction by showing that the theorem, if true for n, is true for (n +1), (this depends 
on the equation \n(n + 1) + {n + 1) =(n + 1) 1) = ^ (n + 2) ; the proof is equally a 
tactical one; it is always tactic which determines what logistical operations are to be 
performed. 
Although it may not be possible absolutely to separate the tactical and logistical 
operations; for in (at all events) a series of logistical operations, there is always some 
thing that is tactical, and in many tactical operations (e.g. in the Partition of Numbers) 
there is something which is logistical, yet the two great divisions of Algebra are Tactic 
and Logistic. Or if, as might be done, we separate Tactic off altogether from Algebra, 
making it a distinct branch of Mathematical Science, then (assuming in Algebra a 
knowledge of all the Tactic which is required) Algebra will be nothing else than Logistic.