calculus - Why Cauchy's definition of infinitesimal is not widely used?

Cauchy defined infinitesimal as a variable or a function tending to zero, or as a null sequence.

While I found the definition is not so popular and nearly discarded in math according to the following statement.

(1). Infinitesimal entry in Wikipedia:

Some older textbooks use the term "infinitesimal" to refer to a variable or a function tending to zero

Why textbooks involved with the definition is said to be old ?

(2). Robert Goldblatt, Lectures on the Hyperreals: An Introduction to Nonstandard Analysis, P15 (His = Cauchy's) Why says 'Even'?

(3). Abraham Robinson, Non-standard analysis, P276 why Cauchy's definition of infinitesimal, along with his 'basic approach' was superseded?

Besides, I found most of the Real analysis or Calculus textbooks, such as Principles of mathematical analysis(Rudin) and Introduction to Calculus and Analysis(Richard Courant , Fritz John), don't introduce Cauchy's definition of infinitesimal, Why ? Why Cauchy's definition of infinitesimal was unpopular and not widely used, and nearly discarded?

P.S. I refered some papers still cannot find the answer.