Whenever any number of natural persons, not less than three, shall file with the governing body of any county of this state an application in writing for authority to incorporate in such county a public corporation under the provisions of this article, and if it shall be made to appear to such governing body that each of said persons is a duly qualified elector of and owner of property in said county and if the governing body of said county shall adopt a resolution which shall be duly entered upon the minutes of such governing body wherein it shall be found and determined that it is wise, expedient, necessary or advisable that such a corporation be formed and that the persons filing said application shall be authorized to proceed to form such corporation, then said persons shall proceed to organize such corporation by executing, acknowledging and filing a certificate of incorporation as provided in this article. No corporation shall be formed under this article unless the application provided for in this section shall be made and unless the resolution provided for in this section shall be adopted. The granting of authority for the incorporation of one public corporation under this article shall not preclude the granting of authority by the governing body of the same county for the incorporation of other public corporations under this article; provided, that such other public corporations shall be required to adopt a name or designation sufficient to distinguish them from any public corporation theretofore incorporated by such county under this article.