diff --git a/src/contains.js b/src/contains.js
index 952a62d..0a2f710 100644
--- a/src/contains.js
+++ b/src/contains.js
@@ -1,6 +1,6 @@
 import {default as polygonContains} from "./polygonContains";
 import {default as distance} from "./distance";
-import {epsilon, radians} from "./math";
+import {epsilon2, radians} from "./math";
 
 var containsObjectType = {
   Feature: function(object, point) {
@@ -59,10 +59,23 @@ function containsPoint(coordinates, point) {
 }
 
 function containsLine(coordinates, point) {
-  var ab = distance(coordinates[0], coordinates[1]),
-      ao = distance(coordinates[0], point),
-      ob = distance(point, coordinates[1]);
-  return ao + ob <= ab + epsilon;
+  var ao, bo, ab;
+  for (var i = 0, n = coordinates.length; i < n; i++) {
+    bo = distance(coordinates[i], point);
+    if (bo === 0) return true;
+    if (i > 0) {
+      ab = distance(coordinates[i], coordinates[i - 1]);
+      if (
+        ab > 0 &&
+        ao <= ab &&
+        bo <= ab &&
+        (ao + bo - ab) * (1 - ((ao - bo) / ab) ** 2) < epsilon2 * ab
+      )
+        return true;
+    }
+    ao = bo;
+  }
+  return false;
 }
 
 function containsPolygon(coordinates, point) {
diff --git a/test/contains-test.js b/test/contains-test.js
index 94f7c53..7864963 100644
--- a/test/contains-test.js
+++ b/test/contains-test.js
@@ -31,6 +31,35 @@ tape("a LineString contains any point on the Great Circle path", function(test)
   test.end();
 });
 
+tape("a LineString with 2+ points contains those points", function(test) {
+  var points = [[0, 0], [1,2], [3, 4], [5, 6]];
+  var feature = {type: "LineString", coordinates: points};
+  points.forEach(point => {
+    test.equal(d3.geoContains(feature, point), true);
+  });
+  test.end();
+});
+
+tape("a LineString contains epsilon-distant points", function(test) {
+  var epsilon = 1e-6;
+  var line = [[0, 0], [0, 10], [10, 10], [10, 0]];
+  var points = [[0, 5], [epsilon * 1, 5], [0, epsilon], [epsilon * 1, epsilon]];
+  points.forEach(point => {
+    test.true(d3.geoContains({type:"LineString", coordinates: line}, point));
+  });
+  test.end();
+});
+
+tape("a LineString does not contain 10*epsilon-distant points", function(test) {
+  var epsilon = 1e-6;
+  var line = [[0, 0], [0, 10], [10, 10], [10, 0]];
+  var points = [[epsilon * 10, 5], [epsilon * 10, epsilon]];
+  points.forEach(point => {
+    test.false(d3.geoContains({type:"LineString", coordinates: line}, point));
+  });
+  test.end();
+});
+
 tape("a MultiLineString contains any point on one of its components", function(test) {
   test.equal(d3.geoContains({type: "MultiLineString", coordinates: [[[0, 0], [1,2]], [[2, 3], [4,5]]]}, [2, 3]), true);
   test.equal(d3.geoContains({type: "MultiLineString", coordinates: [[[0, 0], [1,2]], [[2, 3], [4,5]]]}, [5, 6]), false);
@@ -113,3 +142,4 @@ tape("null contains nothing", function(test) {
   test.equal(d3.geoContains(null, [0, 0]), false);
   test.end();
 });
+