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The edge of the scalpel is a wedge. When you press straight down you have
the mechanical advantage of the full wedge angle. In effect you look
at the angle made by the surface in a plane perpendicular to the edge.
When drawn sideways the effective angle is the angle made by the surface
in a plane at a much reduced angle to the edge. This smaller angle gives
a much greater mechanical advantage. (The mechanical advantage is
proportional to the inverse of the tangent.)