The mayor and city council may, at any regular meeting, or at any special meeting called for that purpose, by a vote of three- fourths (3/4) of the members of the city council or by a vote of a majority of the council upon a petition of three-fourths (3/4) of the property owners of not less than one side of a block, by an order entered upon the minutes of such meeting, direct the construction of sidewalks on any street, block or part of a block, within the city, assessing the cost thereof to the property in front of which the same shall be paid, and may direct the owner thereof to lay the same at his own expense. (Prior code §24-17)