Old English þis, neuter demonstrative pronoun and adjective (masc. þes, fem. þeos), probably from a North Sea Germanic pronoun *tha-si-, formed by combining the base *þa- (see that) with -s, which is probably identical with Old English se "the" (representing here "a specific thing"), or with Old English seo, imperative of see (v.) "to behold." Compare Old Saxon these, Old Frisian this, Old Norse þessi, Middle Dutch dese, Dutch deze, Old High German deser, German dieser.
Once fully inflected, with 10 distinct forms (see table below); the oblique cases and other genders gradually fell away by 15c. The Old English plural was þæs (nominative and accusative), which in Northern Middle English became thas, and in Midlands and Southern England became thos. The Southern form began to be used late 13c. as the plural of that (replacing Middle English tho, from Old English þa) and acquired an -e (apparently from the influence of Middle English adjective plurals in -e; compare alle from all, summe from sum "some"), emerging early 14c. as modern those.
About 1175 thes (probably a variant of Old English þæs) began to be used as the plural of this, and by 1200 it had taken the form these, the final -e acquired via the same mechanism that gave one to those.