Translation:The man and the woman are signing the book.
"Subscribe" is εγγράφομαι in Greek. "Subscribe to" with the meaning of prepay for issues is γίνομαι συνδρομητής, with the meaning of sing up is εγγράφομαι or γίνομαι συνδρομητής and with the figurative meaning of agree with is προσυπογράφω.
The preposition is coming from the Ancient Greek: επί=on, υπό=under, down. So επιγραφή=something that it has been written on.
υπογραφή=something that is written under.
Also there are more words with these Ancient prepositions: εν+γραφή=εγγραφή=written in=registration, inscription, συν+γραφή=συγγραφή=authoring and συγγραφέας=author, προγραφή=proscription, αναγραφή= inscription, καταγραφή=register, διαγραφή=deletion, μεταγραφή=transcription, παραγραφή=lapse, αντιγραφή=copy, περιγραφή=description, απογραφή=census. There are also the corresponding verbs with the verb γράφω=write.
This is an example of how to use the Ancient prepositions to make new words in Greek. Not very different than in Latin and from there to English. Some of these word came to Modern Greek in a bit changed form, as i.e. ντύνω from the Ancient ενδύω=εν+δύω.
The Ancient prepositions that are used are (monotonic system): εν, εις, εκ, συν, προς, προ, ανά, κατά, διά, μετά, παρά, αμφί, περί, από, υπό, υπέρ.
More compound words can be made too i.e. with the noun στάση=stop -αντι+κατά+σταση or better, αντι+κατάσταση=αντικατάσταση=replacement.
Notice that before a vowel the last vowel of the preposition disappears. Also the last τ in the preposition before some words starting from a vowel, that were considered rough breathing words (you have to know them in Ancient Greek, they were represented by an h in English Greek words i.e. hypocrite ) becomes θ, i.e. ανθυπολοχαγός=αντί+υπό+λοχαγός= second lieutenant in the army, as υπολογαχός=lieutenant is a rough breathing word, every word that starts with υ.
*If you are not familiar with ranks in the army: λοχαγός=captain, υπολοχαγός=lieutenant, ανθυπολογαγός=second lieutenant. :-)
So, some, not all, make new words, it is like a game to find out which are the words than one can make with them.
Example as a game: Use the word θέση= position and the verb θέτω=put, to make new compound words. Then try to find out if this word exists in a dictionary as this one: http://www.wordreference.com/engr/ Any questions? :-)
Only in the sense that they both have the root graph-.
But "epigraph" is from επιγραφή, and υπογραφή would be "hypograph" if it existed in English.
And the words aren't cognates -- they didn't both evolve from a shared ancestor. Instead, the English word is a conscious borrowing from Greek.
The corresponding root in English words in some cases, not all, come from Latin, either directly or through French. The Latin verb is "scribere", present tense 1st person: scribo.
The root is I.E. in both verbs, Greek or Latin. In Greek: https://el.wiktionary.org/wiki/%CE%B3%CF%81%CE%AC%CF%86%CF%89#.CE.91.CF.81.CF.87.CE.B1.CE.AF.CE.B1_.CE.B5.CE.BB.CE.BB.CE.B7.CE.BD.CE.B9.CE.BA.CE.AC_.28grc.29.
In Latin: https://el.wiktionary.org/wiki/scribo The root is a bit different, but not too much. The Latin root was used in the Ancient Greek word σκάριφος, from which comes the Modern Greek σκαρίφημα=draft sketch. The English "scription" comes from Latin noun scriptio, see also: script, and more the compounds: inscription, prescription etc. These words are not very different in their roots as you can see by their sound. Also the word "write" coming from the Ancient German has the same root, not very different either.
Yes, you are right about epigraph, it is borrowed as a whole from Greek, but not "hypograph". The reason? I don't know. The only I could speculate about is that "epigraph" is a scientific term used in Archeology mostly, while "signature" is a more common, political, commercial etc word and of course the borrowing of επιγραφή took held some centuries after the Latin/French ones.
I forgot to explain the meaning of the Ancient Greek prepositions that help to make compound words in Ancient and in Modern Greek without remembering everything by heart. I googled a little and a found this image, very representative and amusing :) *It is in polytonic system of Ancient Greek, but you can use monotonic, according the rules of monotonic system, which is much more simplified.
A lingot for the picture and thanks a lot for all your interesting explanations. I discovered some more English words connected with γραφω: graph, diagram, paragraph. I do not know if they are directly from Greek or via French
I think "autograph" should be accepted here, unless someone can offer another way that Modern Greek would express the sentence: The man and the woman autograph the book.