Late 19th century: from paedo- 'of children' + Greek iatros 'physician' + -ics.

• page from late 16th century:

  The page of a book goes back to Latin pagina ‘page’, from pangere ‘to fasten’. The connection between fastening and the page of a book is probably because pagina was originally used of a scroll, made up of strips of papyrus glued together, and then transferred to the page of a book when books replaced scrolls. Before the 16th century older forms, such as pagne, were in use. The other page (Middle English) is first found in the sense ‘youth, male of uncouth manners’ and comes via Old French from Greek paidíon ‘boy, lad’. Page boys at a wedding date from the late 19th century. Paidíon is also the source of the word-element paed- or ped found in words such as paediatrics ‘the medical care of children’ [M19], paedophile ‘child-lover’ [M20], and pedagogue (Late Middle English) formed from the Greek words for ‘child’ and ‘leader’, which was the word in ancient Greece for the slave who took a child to school, but became a term for a teacher in Latin. The Italian pedante ‘teacher’, which entered the language in the late 16th century as pedant may be from pedagogue. See also encyclopedia, pageant