Summa minutiae

“A facility for quotation covers the absence of original thought.” —Lord Peter Wimsey

The fundamental laws of ordinary algebra

Continuing with George Chrystal's Algebra: An Elementary Text-Book [archive, google], the 1904 Adam & Charles Black edition.

Chrystal's Algebra, chapter 1, section 2.

The operations of algebra are just the consequences of a very small number of fundamental principles found in arithmetic.

Ordinary algebra is simply the general theory of those operations with quantity of which the operations of ordinary abstract arithmetic are a particular case.

The fundamental laws of this algebra are therefore to be sought for in ordinary arithmetic.

However various and complex the operations of arithmetic may seem, it appears on consideration that they are merely the result of the application of a very small number of fundamental principles. To make this plain we return for a little to the very elements of arithmetic

Fear not, O student - there's nothing scary coming up…