In this episode, we return to our mechanics series to explore a key new idea: aligned trios of mechanical quantities. After showing in earlier episodes how pairs of mass-carrying quantities describe space, time, and motion—and how non-aligned trios give rise to objective events and turning points—we now examine what happens when all three quantities are parallel.  Focusing on the special case of horizontal alignment, we see how mechanical quantities combine to produce lengths, opening the door to a fully mechanical approach to geometry. This leads us to revisit the ancient connection between geometry and mechanics, and to question why most existing models mix mechanical and geometric concepts rather than relying purely on mechanical ones.  Although this lack of fully mechanical geometric models poses challenges for teaching, it also reveals a rich and largely unexplored research landscape.