public school

noun3

1. •
   (US, Australia) A publicly funded and administered school; (UK, Ireland) such schools in the context of other countries.

   • The Court voted for the erecting a Publick Schooll or Colledge in Cambridge. — 1636
2. •
   (UK, Ireland) Certain private schools, particularly (initially) any grammar school operated apart from the personal lands of its students or (from the 19th century) the feepaying secondary schools which developed from or were modelled upon them; a British boarding school.

   • All such School-masters as have charge of Children and do instruct them either in Publick Schools, or Private Houses. — 1580
3. •
   (no longer used) A college or university.

   • Thither [to Douai] he went, where after a yeres great diligence and many excercises done booth in house and publike scholes, he proceded bachilier of diuinitie [bachelor of divinity]. — 1582