Any person or corporation who has filed objections and had a hearing as herein provided for, feeling aggrieved by the decision and judgment of the board of supervisors, may appeal to the district court within and for the county in which the drainage district was originally established, upon giving a bond conditioned the same as in appeals to the district court as from civil actions in county court in this state and payable to the drainage district, and in addition thereto conditioned that he will pay all damages which may accrue to the drainage district by reason of such appeal. The bond shall be approved by the secretary of the board of supervisors, and filed with the secretary within ten days after the rendition of the decision appealed from. Within ten days after the filing of the bond the secretary shall make and file a transcript of the proceedings appealed from, together with all the papers relating thereto, with the clerk of the district court in which said matter has been appealed. Upon the filing of the transcript and bond the district court shall have jurisdiction of the cause, and the same shall be docketed and filed as in appeals in other civil actions to such court. The court shall hear and determine all such objections in a summary manner as in a case in equity, and shall increase or reduce the amount of benefit on any tract where the same may be required in order to make the apportionment equitable. All objections that may be filed shall be heard and determined by the court as one proceeding, and only one transcript of the final order of the board of supervisors, fixing the apportionments or benefits, shall be required. The clerk of the district court shall forthwith certify the decision of the court to the board of supervisors, which shall take such action as may be rendered necessary by such decisions.