What is the first modern maths text?

Question

I am aware that this question might appear subjective to some, but inasmuch as there is a definite difference between the algorithmic/algebraic type of mathematics practised by Euler (just like there is a definite difference between that mathematics and the Euclidean geometrical tradition), it appears reasonable to suppose that this shift was caused by some major work(s) which spread through to the rest of mathematics.

My questions are:

1. What was this particular work (or works) which started the modern abstract style of mathematics?

2. Is the difference in style to be attributed to the new branches of mathematics themselves, or is it more a difference of method (modus operandi)? In other words, is it possible to treat say Euclidean geometry qua Euclidean geometry but using the modern style, or is the ancient geometrical method somehow embedded/inseparable from Euclidean geometry?

Answer 1

I don't know about first, but I'd venture to say Moderne Algebra by van der Waerden, because of its impact.

Wikipedia says this about it:

The book was one of the first textbooks to use an abstract axiomatic approach to groups, rings, and fields, and was by far the most successful, becoming the standard reference for graduate algebra for several decades. It "had a tremendous impact, and is widely considered to be the major text on algebra in the twentieth century"

Also, A Course of Pure Mathematics by Hardy.