Section 280-Y. Extension of the district

A county district may be extended
  so as to include territory not previously included within its boundaries
  in  the  same  manner  as  hereinbefore  prescribed  for  the   original
  establishment  of  the  district.  If  the  cost of establishment af the
  original district and of providing the improvement therein was assessed,
  levied and collected pursuant to the provisions of section  two  hundred
  eighty-u, then the cost of the extension and of the improvements therein
  shall  be  assessed,  levied and collected pursuant to the provisions of
  said section.  If the cost of establishment of the original district and
  of providing  of  the  improvement  therein  was  assessed,  levied  and
  collected  pursuant  to  the provisions of section two hundred eighty-v,
  then the cost of the extension and of the improvement therein  shall  be
  assessed,  levied  and  collected  pursuant  to  the  provisions of said
  section. The cost of the extension shall include such proportion of  the
  cost  of the system of the original district as the governing body shall
  determine.