= Gear line of action
The <gear line of action> is the common normal along which ideal tooth contact transmits force. For meshing <involute> profiles in a transverse plane, it is a straight common tangent to the two <gear base circles>. The angle it makes with the common tangent to the <operating pitch circles> is the <operating pressure angle>.<Elements of Metric Gear Technology by SDP-SI>[§3.1, line of action as common tangent to base circles]{ref}
Its intersection with the line of gear centers is the <gear pitch point>. The actual contact point moves along only a finite portion, the <gear path of contact>, bounded by usable tooth profiles. Thus a diagram's infinite straight line is a geometric construction, not a claim that teeth can contact everywhere on it.
The geometry explains constant ratio. Let the tooth-normal force magnitude be $F_n$ and the base radii $r_{b1},r_{b2}$. The perpendicular distance from each gear center to the <gear line of action> is its base radius, so the ideal transmitted moments have magnitudes
$$
|\tau_1|=F_n r_{b1},\qquad |\tau_2|=F_n r_{b2}.
$$
These moment arms do not change as the contact point advances along that line. The no-penetration contact condition correspondingly gives $r_{b1}\omega_1+r_{b2}\omega_2=0$ for an external pair. Compatible profiles have $r_{b2}/r_{b1}=N_2/N_1$, recovering the tooth-count <gear ratio>.
For example, reference radii $20$ and $40\,\mathrm{mm}$ at reference <gear pressure angle> $20\,{}^{\circ}$ give base radii approximately $18.794$ and $37.588\,\mathrm{mm}$. A $100\,\mathrm N$ normal force produces moment magnitudes $1.8794$ and $3.7588\,\mathrm{N\,m}$. Their ratio stays two as the point of contact moves.
Ideal normal transmission does not eliminate <gear tooth sliding>. Relative surface slip generally changes along the <gear path of contact> and vanishes at the <gear pitch point> for the ideal external pair. Actual <friction> associated with that slip adds a tangential contact force; its resultant need not lie exactly on the geometric <gear line of action>.
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