extension n.

early 14c., "to value, assess," from Anglo-French estendre (late 13c.), Old French estendre "stretch out, extend, increase," transitive and intransitive (Modern French étendre), from Latin extendere "stretch out, spread out; increase, enlarge, prolong, continue," from ex "out" (see ex-) + tendere "to stretch," from PIE root *ten- "to stretch."

Original sense in English is obsolete. From late 14c. as "lengthen or extend in time," also "straighten" (an arm, wing. etc.). Meaning "make longer and/or broader in space" is from early 15c., as is intransitive sense of "cover an area, have a certain extent in space;" sense of "expand, grow distended" is from 1753. Related: Extended; extending.