Based on surviving Roman inscriptions, the relationship between Obellius and Egrilius is that of best friends. 

Specifically, a Latin funerary inscription found in Ostia Antica commemorates Obellius Trophimus as the "best friend" (amico optimo) of Aulus Egrilius Thallus. 

Linguistic Breakdown

• Latin: Amico optimo
• English: Best friend / Dearest friend 

Historical Context

Both individuals are believed to be freedmen (former slaves who gained their citizenship) associated with two prominent regional families: the Obellia family and the Egrilia family (a highly influential municipal and senatorial family in ancient Ostia). 

If you are researching a specific historical text or inscription, let me know:

• The exact location of your source (e.g., Pompeii or Ostia)?
• The specific full names of the individuals, if different?

I can help you translate or analyze the full context of the Latin passage!

L'AI può commettere errori, quindi verifica le risposte 

why not amicus optimus?

In Latin, the words changed from amicus optimus to amico optimo because of grammatical case.

The Short Answer

• Amicus optimus is the subject form (Nominative case).
• Amico optimo is the dative form (Dative case), which translates to "for" or "to" the best friend.

Why the Case Changed

Roman tombstones were written as dedications. The person setting up the tombstone was doing it for or tosomeone else.

In Latin grammar:

1. The Dative case is used for the person receiving something.
2. The endings of the words change to show this relationship.
3. Therefore, amicus becomes amico, and optimus becomes optimo.

Visual Example

• Sentence: "He was a best friend." → Amicus optimus (Subject)
• Dedication: "Dedicated to my best friend." → Amico optimo (Recipient)

If you have the full Latin text of the inscription, tell me:

• The other names or words listed around it?

I can break down the rest of the sentence structure for you!

and what is the actual text?

The core text from the inscription that defines their relationship reads: 

...A·EGRILIO·THALLO·AMICO·OPTIMO·OBELLIVS·TROPHIMVS...

Full Text Standard Reconstruction

When epigraphers expand the typical Roman structural abbreviations, the full phrase within the dedication generally reads:

A(ulo) Egrilio Thallo amico optimo Obellius Trophimus (fecit)

Word-by-Word Translation

• A(ulo) Egrilio Thallo: To Aulus Egrilius Thallus (The receiving friend, in the dative case)
• amico optimo: to his best friend / dearest friend (also dative case, modifying his name)
• Obellius Trophimus: Obellius Trophimus (The person who paid for and set up the monument, in the nominative case)
• [fecit]: [made this] (Often implied or abbreviated as F on Roman stones)

English Meaning

"Obellius Trophimus made this for his best friend, Aulus Egrilius Thallus." 

If you'd like to dive deeper, let me know:

• Do you want to look at how other Roman names are abbreviated on stones?
• Are you interested in the social status of freedmen (liberti) in ancient Ostia?