transgression (n.)

early 15c., transgressour, "sinner, evil-doer, breaker of God's law," from Anglo-French transgressour, Old French transgressor (14c.), and directly from Latin transgressor, agent noun from transgredi (see transgression).

Proto-Indo-European root meaning "to walk, go." 

It forms all or part of: aggress; aggression; aggressive; centigrade; congress; degrade; degree; degression; digress; digression; egress; gradation; grade; gradual; graduate; grallatorial; gravigrade; ingredient; ingress; plantigrade; progress; progression; regress; regression; retrograde; retrogress; tardigrade; transgress; transgression.

It is the hypothetical source of/evidence for its existence is provided by: Latin gradus "a step, a pace, gait," figuratively "a step toward something, a degree of something rising by stages;" gradi "to walk, step, go;" Lithuanian gridiju, gridyti "to go, wander;" Old Church Slavonic gredo "to come;" Old Irish in-greinn "he pursues."  

word-forming element meaning "across, beyond, through, on the other side of; go beyond," from Latin trans (prep.) "across, over, beyond," perhaps originally present participle of a verb *trare-, meaning "to cross," from PIE *tra-, variant of root *tere- (2) "cross over, pass through, overcome" [Watkins].

Besides its use in numerous English words taken from Latin words with this prefix, it is used to some extent as an English formative .... It is commonly used in its literal sense, but also as implying complete change, as in transfigure, transform, etc. [Century Dictionary]

In chemical use indicating "a compound in which two characteristic groups are situated on opposite sides of an axis of a molecule" [Flood].

Many trans- words in Middle English via Old French arrived originally as tres-, due to sound changes in French, but most English spellings were restored later; trespass and trestle being exceptions.