You can factor out your common logic to a private method, for example called Initialize that gets called from both constructors.
Due to the fact that you want to perform argument validation you cannot resort to constructor chaining.
Example:
public Point2D(double x, double y)
{
// Contracts
Initialize(x, y);
}
public Point2D(Point2D point)
{
if (point == null)
throw new ArgumentNullException("point");
// Contracts
Initialize(point.X, point.Y);
}
private void Initialize(double x, double y)
{
X = x;
Y = y;
}