Abarim Publications' online Biblical Greek Dictionary
αρι
The common and inseparable prefix αρι (ari) — also occurring as ερι (eri) — is used to strengthen the meaning of a word. It often can be translated by 'very much' or constructions to that extent: αριδακρυς (aridakrus) means very tearful; αριφρων (ariphron) means very wise; αριηκοος (ariekoos) means much heard of.
Our prefix αρι (ari) shares its root with noun αρετη (arete), which denotes excellence:
αρετη
In older texts, the feminine noun αρετη (arete) appears to have denoted excellence of any kind but mostly of manly qualities (comparable to the Latin word virtus). Plato used it to convey moral excellence and virtue, and later authors ascribed the plural of αρετη (arete) to gods, in the meaning of glorious deeds, wonders, miracles.
The Septuagint uses αρετη (arete) to translate some instances of הוד (hod), meaning splendor or majesty, and תהלה (tehilla), meaning praise.
In the New Testament it occurs 5 times; 5 see full concordance. In 1 Peter 2:9 it occurs in plural and is commonly translated with excellencies or praises. In 2 Peter 1:3-5 it's commonly translated with moral excellence or virtue. On this occasion it appears juxtaposed with δοξα (doxa), meaning "glory" or excellent reputation.
Paul uses this word in Philippians 4:8, where he writes, "Finally, brethren, whatever is true, whatever is honorable, whatever is right, whatever is pure, whatever is lovely, whatever is of good repute, if there is any excellence and if anything worthy of praise, let your mind dwell on these things."
αριστευω
Doubtlessly connected to the above are the verb αριστευω (aristeuo) and noun αριστος (aristos), meaning (to be) the best or bravest. These words are not actually used in the Bible (apart from their contribution to a few names) but in the classics they may refer to people being the best at a certain activity (such as fighting) or of items such as fruits or lands as being of a superior quality. In English these words survives in the word aristocracy and of course the name Aristotle. There may also be a link with a word that originally denoted virtue in war. This quality was later deified as Ares, the destroying and slaughtering son of Zeus and Hera, which eventually evolved into the more reasonable Roman god Mars.
αριστερος
The adjective αριστερος (aristeros) is one of a few words to mean left, on the left or leftward (Matthew 6:3, Luke 23:33 and 2 Corinthians 6:7 only). Craftspeople would keep their most common tools readily available at their right hand and special tools at their left, which is how society's aristocratic elite became associated with the left — or rather how special tools that were kept separate to the left, away from the common tools on the right came to be known as elite tools, rather than simply tools for rare occasions. The same euphemistic distinction exists in our modern terms "blue collar" and "white color."
Another common Greek word for left was the adjective ευωνυμος (euonumos), literally meaning good-named or of good name. What these good-named aristocrats on society's left were up to was a mystery to the common man on society's right, and their dealings became subsequently known by the Latin word for left: sinister. Read our article on the adjective δεξιος (dexios), meaning right, for more on this.
The formation of the verb αρισταο (aristao), meaning to have a meal at whatever time, may have been helped along by its obvious similarity with the previous word. It takes a good measure of luxury to be able to enjoy a meal whenever one wants and most people were bound by meal times prescribed by employers. But even though our verb may look closely related, technically it's formed from the particle of negation α (a), meaning not or without, plus the noun ορος (horos), meaning boundary or limit.