diff --git a/crates/fj-kernel/src/algorithms/approx/curve.rs b/crates/fj-kernel/src/algorithms/approx/curve.rs
index 9ec6a211d..783729e23 100644
--- a/crates/fj-kernel/src/algorithms/approx/curve.rs
+++ b/crates/fj-kernel/src/algorithms/approx/curve.rs
@@ -38,7 +38,7 @@ impl Approx for GlobalCurve {
     ) -> Self::Approximation {
         match self.kind() {
             CurveKind::Circle(curve) => approx_circle(curve, range, tolerance),
-            CurveKind::Line(_) => Vec::new(),
+            CurveKind::Line(_) => vec![range.start()],
         }
     }
 }
diff --git a/crates/fj-kernel/src/algorithms/approx/edge.rs b/crates/fj-kernel/src/algorithms/approx/edge.rs
index 1ac553167..cf76001e0 100644
--- a/crates/fj-kernel/src/algorithms/approx/edge.rs
+++ b/crates/fj-kernel/src/algorithms/approx/edge.rs
@@ -34,26 +34,6 @@ impl Approx for Edge {
             }
         };
 
-        let mut points = self.curve().approx(tolerance, range);
-
-        // Insert the exact vertices of this edge into the approximation. This
-        // means we don't rely on the curve approximation to deliver accurate
-        // representations of these vertices, which they might not be able to
-        // do.
-        //
-        // If we used inaccurate representations of those vertices here, then
-        // that would lead to bugs in the approximation, as points that should
-        // refer to the same vertex would be understood to refer to very close,
-        // but distinct vertices.
-        let vertices = self
-            .vertices()
-            .convert(|vertex| (vertex.position(), vertex.global().position()));
-        if let Some([(point_curve, point_global), _]) = vertices {
-            let point_surface =
-                self.curve().kind().point_from_curve_coords(point_curve);
-            points.insert(0, (point_surface, point_global));
-        }
-
-        points
+        self.curve().approx(tolerance, range)
     }
 }