Although just beyond your 50-year scope, this may be of interest. Among the series $\mathsf A_n, \mathsf B_n, \mathsf C_n, \mathsf D_n$ in the Cartan-Killing classification of simple Lie groups, everyone (I believe) always agreed to call $\mathsf A_n$ the special linear group, $\mathbf{SL}(n)$, and $\mathsf B_n$ and $\mathsf D_n$ the special orthogonal groups, $\mathbf{SO}(2n+1)$ and $\mathbf{SO}(2n)$.

But $\mathsf C_n$? Jordan in his *Traité des substitutions* (1870) called it (or rather its product with dilations) the *abelian group*, because of its role in Hermite's "important investigations on the transformation of abelian functions"; p.172:

It is clear that if two [linear] substitutions $S, S'$ multiply $\varphi\ [=x_1\eta_1-\xi_1y_1+\dots+x_n\eta_n-\xi_ny_n]$ respectively by constant integers $m, m'$, $SS'$ will multiply $\varphi$ by the constant integer $mm'$. Hence the sought substitutions form a group. We will call it the *abelian group*, and its substitutions *abelian*.

This was well entrenched by the time Dickson wrote his *Linear groups* (1901); p.89:

A linear homogeneous substitution on $2m$ indices (...) is called *Abelian* if (...) it leaves formally invariant up to a factor (belonging to the field) the bilinear function
$$
\varphi\equiv\sum_{i=1}^m
\begin{vmatrix}
\xi_{i1}&\eta_{i1}\\
\xi_{i2}&\eta_{i2}
\end{vmatrix}.
$$
The totality of such substitutions constitutes a group called the *general Abelian linear group* ${}^2)$ $GA(2m,p^n)$. These of its substitutions which leave $\varphi$ absolutely invariant form the *special Abelian linear group* $SA(2m,p^n)$.

${}^2)$ To distinguish these groups from the ordinary Abelian , i.e. commutative, groups, we prefix the adjective *linear*. The Abelian linear group is not commutative in general.

On the other hand, Sophus Lie and his school called $\mathsf C_n$ the *linear complex group* because it consists of symmetries of Plücker's *linear line complex* (a degree 1 hypersurface in the 4-dimensional space of affine lines in $\mathbf R^3$; Plücker (1866), p.341: "The latin word *complexus*, which means an *intertwining*, an *inter-crossing*, has seemed to us very appropriate to express the new idea we are presenting here. For lack of a better term, we ask for permission to introduce it in the mathematical language.") Thus for instance one finds in Lie and Engel's *Transformationsgruppen*, vol. II (1890), p.522:

One can say that the Pfaffian equation (73) represents a *linear complex* of the space $x'_1\cdots x'_n$, $y'_1\cdots y'_n$, $z'$. The group (72) should therefore be called the projective *linear complex group*.

Needless to say, both proposed names came into conflict with other spreading usages of these words. Hence Weyl's famous footnote in *The classical groups* (1938), p.165:

$$\text{CHAPTER VI}$$
$$\textbf{THE SYMPLECTIC GROUP}$$
$$\text{1. Vector Invariants of the Symplectic Group}^*$$
* The name "complex group" formerly advocated by me in allusion to line complexes,
as these are defined by the vanishing of antisymmetric bilinear forms, has become more and
more embarrassing through collision with the word "complex" in the connotation of
complex number. I therefore propose to replace it by the corresponding Greek adjective
"symplectic." Dickson calls the group the "Abelian linear group" in homage to Abel
who first studied it.

Weyl's change was (obviously) highly successful. Ironically, Plücker's *linear line complex* term had won over Chasles' proposed *focal system* (1837). If it hadn't, today's symplectic geometers would probably all be doing "focal geometry"!

but when you say that dy/dx refers to the standard part, you're dragging in Robinson's non-standard analysisCheck out the link in my earlier comment, p. 10. Fermat and Leibniz had a notation, ${}_{\ulcorner\!\urcorner}$, and a term, "adequality," that expressed essentially the same notion as Robinson's standard part (subject to the limitations of the development of mathematics at that time). The idea is much more generic than NSA. – Ben Crowell Jul 12 at 14:45