The first constructor in the header should not end with a semicolon. #include <string> is missing in the header. string is not qualified with std:: in the .cpp file. Those are all simple syntax errors. More importantly: you are not using references, when you should. Also the way you use the ifstream is broken. I suggest learning C++ before trying to use it.
Let's fix this up:
//polygone.h
# if !defined(__POLYGONE_H__)
# define __POLYGONE_H__
#include <iostream>
#include <string>
class Polygone {
public:
// declarations have to end with a semicolon, definitions do not
Polygone(){} // why would we needs this?
Polygone(const std::string& fichier);
};
# endif
and
//polygone.cc
// no need to include things twice
#include "polygone.h"
#include <fstream>
Polygone::Polygone(const std::string& nom)
{
std::ifstream fichier (nom, ios::in);
if (fichier.is_open())
{
// keep the scope as tiny as possible
std::string line;
// getline returns the stream and streams convert to booleans
while ( std::getline(fichier, line) )
{
std::cout << line << std::endl;
}
}
else
{
std::cerr << "Erreur a l'ouverture du fichier" << std::endl;
}
}