Augustus De Morgan - Algebra Quotes

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... nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.

Augustus De Morgan
I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical.

Augustus De Morgan
The absolute requisites for the study of this work... are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.

Augustus De Morgan
I think the time may come when double algebra will be the beginner's tool; and quaternions will be where double algebra is no. The Lord only knows what will come above the quaternions.

Augustus De Morgan