higher Look up higher at Dictionary.com
comparative of high (adj.), Old English hierra (West Saxon), hera (Anglian). Higher education is attested by 1839.
The French distinguish l'instruction secondaire, which includes what we term a liberal education, from l'instruction supérieure, which denotes professional education; but I do not think the corresponding English phrases are used with this distinction. [William Whewell, "Of a Liberal Education in General," 1850]
Higher-up (n.) "one in a superior post" is from 1905, American English.