Gittin, Chapter 9, Mishnah 6. This mishnah deals with two gittin written on a single sheet of paper, side by side in two columns: one get in the right-hand column and a second get in the left-hand column, with the witnesses signed beneath them in such a way that the signature runs from one get over to the other.
The rule for determining which get is valid:
If a witness signs "Reuven ben Yaakov" in Hebrew script, and his first name, "Reuven," falls beneath the right-hand get while "ben Yaakov" falls beneath the left-hand get, only the right-hand get is valid. What determines the matter is the placement of the first name, which is the primary name, and therefore the get above which the first name is written is the valid one.
Signing in Greek script:
Greek script is not written from right to left but from left to right, like English. Accordingly, when a Greek Jew signs the get in Greek script, his first name will be written beneath the left-hand get and his father's name beneath the right-hand get.
The mishnah discusses a case of four signatures: "Shnei gittin shekesavan zeh b'tzad zeh" - two gittin written in columns directly alongside one another, and beneath them:
"Ushnei eidim Ivrim ba'im mitachas zeh l'sachas zeh" - first two witnesses sign in Hebrew script, and their signature runs from the right-hand get over to the left-hand one: the name "Reuven" beneath the right-hand get, and "ben Yaakov" beneath the left-hand get.
"Ushnei eidim Yevanim ba'im mitachas zeh l'sachas zeh" - and after them two witnesses sign in Greek script, and their signature likewise runs from one get to the other, except that their first name falls beneath the left-hand get.
Regarding this the mishnah rules: "Es shehaeidim harishonim nikra'in imo - kasher" - the get beneath which the first witnesses are signed is the valid one. If the two Hebrew signatures came first, the right-hand get is valid; and if the two Greek signatures came first, the left-hand get is valid, and it alone.
The reason for the ruling:
Seemingly, if we knew with certainty that the two Greek signers had signed in the Greek manner, both gittin would be valid; even though the Hebrew signatures separate between them, the left-hand get could still be valid. The concern, however, is that the Greek signing after the Hebrew signer will be drawn after the practice of the one who preceded him and will write his first name on the right, even though his own way is to write from the left. If so, it is possible that all four first names are on the right side, and only the first two signatures, which were properly signed from the right, count.
And so too in the reverse case: if the Greeks signed first, the left-hand get is the valid one, since we are concerned that the Hebrew signatures that follow them were drawn after that same practice.
The second case - alternating signatures:
The mishnah continues: "Ed echad Ivri v'ed echad Yevani, v'ed echad Ivri v'ed echad Yevani, ba'im mitachas zeh l'sachas zeh - shneihem pesulin" - when the signatures alternate one with the other, and they too run from one get to the other, both gittin are invalid.
The reason: we are concerned that three of the four signatures are on one side and only one signature on the other. For the Hebrew signs first, and his first name is beneath the right-hand get; the Greek after him may be drawn after the Hebrew method and sign from the right as well; the third, a Hebrew, signs from the right as is his way; and only the last one, the Greek, might sign from the left. It emerges that the left-hand get has only a single witness. And so too in the reverse case.
In summary: In this mishnah we learned that when two gittin are written side by side, the placement of the witness's first name determines which get he is signed beneath. When two Hebrew witnesses signed and after them two Greek witnesses (or the reverse), only the get with which the first witnesses are read is valid, out of concern that the later ones were drawn after the practice of those who preceded them. And when the signatures alternate, a Hebrew and a Greek in turn, both gittin are invalid, out of concern that three signatures will turn out to be on one side and only one on the other.