Before revision: Under gnomonic projection every great circle on the sphere that passes through the center is projected to a straight line in the plane (a great circle is a geodesic on the sphere, the shortest path between any two points, analogous to a straight line on the plane).
After revision: Under gnomonic projection every great circle on the sphere is projected to a straight line in the plane (a great circle is a geodesic on the sphere, the shortest path between any two points, analogous to a straight line on the plane).