diff --git a/Cargo.lock b/Cargo.lock
index 77fc43393..0d29d3eb6 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -755,7 +755,6 @@ version = "0.6.0"
 dependencies = [
  "anyhow",
  "anymap",
- "approx 0.5.1",
  "fj-interop",
  "fj-math",
  "map-macro",
diff --git a/crates/fj-kernel/Cargo.toml b/crates/fj-kernel/Cargo.toml
index e6a9873f2..a52a838a3 100644
--- a/crates/fj-kernel/Cargo.toml
+++ b/crates/fj-kernel/Cargo.toml
@@ -15,7 +15,6 @@ categories = ["encoding", "mathematics", "rendering"]
 [dependencies]
 anyhow = "1.0.57"
 anymap = "1.0.0-beta.2"
-approx = "0.5.1"
 map-macro = "0.2.0"
 parking_lot = "0.12.0"
 robust = "0.2.3"
diff --git a/crates/fj-kernel/src/algorithms/intersection.rs b/crates/fj-kernel/src/algorithms/intersection.rs
index 01f3e54fd..4d1b64a31 100644
--- a/crates/fj-kernel/src/algorithms/intersection.rs
+++ b/crates/fj-kernel/src/algorithms/intersection.rs
@@ -1,8 +1,8 @@
 //! Intersection algorithms
 
-use fj_math::{Point, Scalar, Vector};
+use fj_math::{Line, Point, Scalar, Vector};
 
-use crate::geometry::{Curve, Line, Surface};
+use crate::geometry::{Curve, Surface};
 
 /// Test intersection between two surfaces
 pub fn surface(a: &Surface, b: &Surface) -> Option<Curve> {
diff --git a/crates/fj-kernel/src/geometry/curves/line.rs b/crates/fj-kernel/src/geometry/curves/line.rs
deleted file mode 100644
index 3a95fd173..000000000
--- a/crates/fj-kernel/src/geometry/curves/line.rs
+++ /dev/null
@@ -1,133 +0,0 @@
-use fj_math::{Point, Transform, Vector};
-
-/// A line, defined by a point and a vector
-#[derive(Clone, Copy, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
-pub struct Line {
-    /// The origin of the line's coordinate system
-    pub origin: Point<3>,
-
-    /// The direction of the line
-    ///
-    /// The length of this vector defines the unit of the line's curve
-    /// coordinate system. The coordinate `1.` is always were the direction
-    /// vector points, from `origin`.
-    pub direction: Vector<3>,
-}
-
-impl Line {
-    /// Create a line from two points
-    pub fn from_points([a, b]: [Point<3>; 2]) -> Self {
-        Self {
-            origin: a,
-            direction: b - a,
-        }
-    }
-
-    /// Access the origin of the curve's coordinate system
-    pub fn origin(&self) -> Point<3> {
-        self.origin
-    }
-
-    /// Create a new instance that is reversed
-    #[must_use]
-    pub fn reverse(mut self) -> Self {
-        self.direction = -self.direction;
-        self
-    }
-
-    /// Create a new instance that is transformed by `transform`
-    #[must_use]
-    pub fn transform(self, transform: &Transform) -> Self {
-        Self {
-            origin: transform.transform_point(&self.origin),
-            direction: transform.transform_vector(&self.direction),
-        }
-    }
-
-    /// Convert a point in model coordinates to curve coordinates
-    ///
-    /// Projects the point onto the line before computing curve coordinate. This
-    /// is done to make this method robust against floating point accuracy
-    /// issues.
-    ///
-    /// Callers are advised to be careful about the points they pass, as the
-    /// point not being on the line, intentional or not, will never result in an
-    /// error.
-    pub fn point_model_to_curve(&self, point: &Point<3>) -> Point<1> {
-        let t = (point - self.origin).scalar_projection_onto(&self.direction)
-            / self.direction.magnitude();
-        Point::from([t])
-    }
-
-    /// Convert a point on the curve into model coordinates
-    pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
-        self.origin + self.vector_curve_to_model(&point.coords)
-    }
-
-    /// Convert a vector on the curve into model coordinates
-    pub fn vector_curve_to_model(&self, vector: &Vector<1>) -> Vector<3> {
-        self.direction * vector.t
-    }
-}
-
-impl approx::AbsDiffEq for Line {
-    type Epsilon = <f64 as approx::AbsDiffEq>::Epsilon;
-
-    fn default_epsilon() -> Self::Epsilon {
-        f64::default_epsilon()
-    }
-
-    fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
-        self.origin.abs_diff_eq(&other.origin, epsilon)
-            && self.direction.abs_diff_eq(&other.direction, epsilon)
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use approx::assert_abs_diff_eq;
-    use fj_math::{Point, Scalar, Transform, Vector};
-
-    use super::Line;
-
-    #[test]
-    fn transform() {
-        let line = Line {
-            origin: Point::from([1., 0., 0.]),
-            direction: Vector::from([0., 1., 0.]),
-        };
-
-        let transform = Transform::translation([1., 2., 3.])
-            * Transform::rotation(Vector::unit_z() * (Scalar::PI / 2.));
-        let line = line.transform(&transform);
-
-        assert_abs_diff_eq!(
-            line,
-            Line {
-                origin: Point::from([1., 3., 3.]),
-                direction: Vector::from([-1., 0., 0.]),
-            },
-            epsilon = 1e-8,
-        );
-    }
-
-    #[test]
-    fn point_model_to_curve() {
-        let line = Line {
-            origin: Point::from([1., 0., 0.]),
-            direction: Vector::from([2., 0., 0.]),
-        };
-
-        verify(line, -1.);
-        verify(line, 0.);
-        verify(line, 1.);
-        verify(line, 2.);
-
-        fn verify(line: Line, t: f64) {
-            let point = line.point_curve_to_model(&Point::from([t]));
-            let t_result = line.point_model_to_curve(&point);
-
-            assert_eq!(Point::from([t]), t_result);
-        }
-    }
-}
diff --git a/crates/fj-kernel/src/geometry/curves/mod.rs b/crates/fj-kernel/src/geometry/curves/mod.rs
index 0bb26324c..1b70e5e02 100644
--- a/crates/fj-kernel/src/geometry/curves/mod.rs
+++ b/crates/fj-kernel/src/geometry/curves/mod.rs
@@ -1,9 +1,8 @@
 mod circle;
-mod line;
 
-pub use self::{circle::Circle, line::Line};
+pub use self::circle::Circle;
 
-use fj_math::{Point, Transform, Vector};
+use fj_math::{Line, Point, Transform, Vector};
 
 /// A one-dimensional shape
 ///
@@ -20,7 +19,7 @@ pub enum Curve {
     Circle(Circle),
 
     /// A line
-    Line(Line),
+    Line(Line<3>),
 }
 
 impl Curve {
@@ -52,7 +51,7 @@ impl Curve {
     pub fn origin(&self) -> Point<3> {
         match self {
             Self::Circle(curve) => curve.origin(),
-            Self::Line(curve) => curve.origin(),
+            Self::Line(curve) => curve.origin,
         }
     }
 
@@ -70,7 +69,7 @@ impl Curve {
     pub fn transform(self, transform: &Transform) -> Self {
         match self {
             Self::Circle(curve) => Self::Circle(curve.transform(transform)),
-            Self::Line(curve) => Self::Line(curve.transform(transform)),
+            Self::Line(curve) => Self::Line(transform.transform_line(&curve)),
         }
     }
 
@@ -86,7 +85,7 @@ impl Curve {
     pub fn point_model_to_curve(&self, point: &Point<3>) -> Point<1> {
         match self {
             Self::Circle(curve) => curve.point_model_to_curve(point),
-            Self::Line(curve) => curve.point_model_to_curve(point),
+            Self::Line(curve) => curve.convert_point_to_line_coords(point),
         }
     }
 
@@ -94,7 +93,7 @@ impl Curve {
     pub fn point_curve_to_model(&self, point: &Point<1>) -> Point<3> {
         match self {
             Self::Circle(curve) => curve.point_curve_to_model(point),
-            Self::Line(curve) => curve.point_curve_to_model(point),
+            Self::Line(curve) => curve.convert_point_from_line_coords(point),
         }
     }
 
@@ -102,7 +101,7 @@ impl Curve {
     pub fn vector_curve_to_model(&self, point: &Vector<1>) -> Vector<3> {
         match self {
             Self::Circle(curve) => curve.vector_curve_to_model(point),
-            Self::Line(curve) => curve.vector_curve_to_model(point),
+            Self::Line(curve) => curve.convert_vector_from_line_coords(point),
         }
     }
 }
diff --git a/crates/fj-kernel/src/geometry/mod.rs b/crates/fj-kernel/src/geometry/mod.rs
index 4781fe43d..1455f48bd 100644
--- a/crates/fj-kernel/src/geometry/mod.rs
+++ b/crates/fj-kernel/src/geometry/mod.rs
@@ -10,7 +10,7 @@ mod points;
 mod surfaces;
 
 pub use self::{
-    curves::{Circle, Curve, Line},
+    curves::{Circle, Curve},
     points::Point,
     surfaces::{Surface, SweptCurve},
 };
diff --git a/crates/fj-kernel/src/geometry/surfaces/swept.rs b/crates/fj-kernel/src/geometry/surfaces/swept.rs
index ae04a3886..c8d2b3513 100644
--- a/crates/fj-kernel/src/geometry/surfaces/swept.rs
+++ b/crates/fj-kernel/src/geometry/surfaces/swept.rs
@@ -16,7 +16,7 @@ impl SweptCurve {
     /// Construct a plane from 3 points
     #[cfg(test)]
     pub fn plane_from_points([a, b, c]: [Point<3>; 3]) -> Self {
-        use crate::geometry::Line;
+        use fj_math::Line;
 
         let curve = Curve::Line(Line::from_points([a, b]));
         let path = c - a;
@@ -63,9 +63,9 @@ impl SweptCurve {
 #[cfg(test)]
 mod tests {
 
-    use fj_math::{Point, Vector};
+    use fj_math::{Line, Point, Vector};
 
-    use crate::geometry::{Curve, Line};
+    use crate::geometry::Curve;
 
     use super::SweptCurve;
 
diff --git a/crates/fj-kernel/src/topology/builder.rs b/crates/fj-kernel/src/topology/builder.rs
index 6f17eef6d..66c72fb12 100644
--- a/crates/fj-kernel/src/topology/builder.rs
+++ b/crates/fj-kernel/src/topology/builder.rs
@@ -1,7 +1,7 @@
-use fj_math::{Point, Scalar, Vector};
+use fj_math::{Line, Point, Scalar, Vector};
 
 use crate::{
-    geometry::{Circle, Curve, Line, Surface},
+    geometry::{Circle, Curve, Surface},
     shape::{Handle, Shape, ValidationResult},
 };