Etymology
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Words related to intensify

intense (adj.)
early 15c., of situations or qualities, "great, extreme," from Old French intense (13c.), from Latin intensus "stretched, strained, high-strung, tight," originally past participle of intendere in its literal sense of "stretch out, strain" (see intend). From 1630s of persons, "high-strung." Related: Intensely; intenseness.
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-ify 
variant of verbal suffix -fy with connective -i-. Related: -ific; -ification.
intend (v.)
c. 1300, entenden, "direct one's attention to, pay attention, give heed," from Old French entendre, intendre "to direct one's attention" (in Modern French principally "to hear"), from Latin intendere "turn one's attention, strain (in quest of something), be zealous," literally "stretch out, extend," from in- "toward" (from PIE root *en "in") + tendere "to stretch," from PIE root *ten- "to stretch."

Sense of "have as a plan, have in mind or purpose" (late 14c.) was present in Latin. A Germanic word for this was ettle, from Old Norse ætla "to think, conjecture, propose," from Proto-Germanic *ahta "consideration, attention" (source also of Old English eaht, German acht). Related: Intended; intending.
intensification (n.)
1835, noun of action from intensify.