Given three points $a_1$, $a_2$, $a_3$ in an affine space such that $\dim \langle a_1, a_2, a_3\rangle = 1$ (i.e. they are co-linear) and $a_1\ne a_2$, my professor defined the "simple ratio" (making a literal translation) as the unique scalar $$ (a_1a_2a_3) := \lambda \in\mathbb{K} \qquad\text{such that}\qquad \overrightarrow{a_1a_3}=\lambda\, \overrightarrow{a_1a_2}\,. $$
I haven't found any equivalent term in English sources. Is such a concept defined in other places, or does it happen to be "popular" where I live?
For example, this notation is used in "Álgebra Lineal i Geometria" by M. Castellet and I. Llerena.