The original Greek word is μαγαρίτης (magarites) or plural μωαγαρίται (moagaritai) and it looks like this word is more Byzantine than Koine which makes sense considering it is referring to Muslims. Koine usually refers to Greek up until about 300 AD and Muhammad wasn't born until 610.
The best reference I could find was in "Greek lexicon of the Roman and Byzantine periods (from B.C. 146 to A.D. 1100)" by E.A. Sophocles which you can find at archive.org
Here are the relevant entries. I only included the most relevant parts as I couldn't just copy and paste them due to the format. I've included the relevant page numbers if you want to take a look yourself.
The page numbers are the page numbers you should navigate to if you click "Read Online" not the page numbers at the top of the page.
Page 750 last entry in the third column.
μαγαρίτης, οῦ, ὁ, (μαγαρίζω 2) renegade, one who renounces the Christian religion and adopts Islamism.
The "μαγαρίζω 2" (magarizo) is a reference to a verb on the same page three entries higher.
μαγαρίζω A travesty of ἀγαρίζω (agarizo)
This entry also notes "The word is of Semitic origin." and then gives some Hebrew words but I don't know Hebrew so I don't really know how relevant they are.
Page 88 about three quarters of the way down in the fourth column.
ἀγαρίζω To be or become a Mohammedan
Which references the entry (four entries up):
Ἄγαρ (Agar), Hagar, the mother of Ishmael the progenitor of the Arabs.
Which refers back to μαγαρίζω.
I should also point out that agarizo is just Agar with the verbal suffix -izo so it could easily be read as 'to Hagar'.
You may also want to check out page 51 which has a section on "The Foreign Elements of the Greek Language"
That’s the workbook, this is the textbook
You’ll want both. The textbook is valuable on its own but using the workbook helps you utilize and put into practice the concepts from each chapter.
thanks for the advice, I searched it up on Amazon and I found a paperback version for much cheaper but I don't know if it's the same things with all the same content, because It seems a bit "too good to be true".
is this the one? could you let me know please, thanks
It would help, yes. From what I know Modern/Demotic Greek despite being 2000 years removed from Koine retains a lot of the same vocabulary and grammar. I assume that's largely thanks to regular reading and study of the Bible and other important Greek works.
But learning Modern Greek is a huge undertaking. It would be a ton of effort, more than learning Koine. I would only recommend it if you can move to Greece for total immersion. Otherwise those efforts are better spent studying Koine.
I'd recommend buying an Intermediate Grammar. Online resources are of various quality and use. This one is amazing. Extremely thorough.
I recommend the following book which covers the history of Greek from classical to modern.
Chrys C. Caragounis, The Development of Greek and the New Testament: Morphology, Syntax, Phonology, and Textual Transmission