The Babylonian Talmud, Rosh ha-Shana 20b makes a problematic statement about the first possibility sighting of the lunar crescent at the beginning of the lunar month:
נולד קודם חצות בידוע שנראה סמוך לשקיעת החמה לא נולד קודם חצות בידוע שלא נראה סמוך לשקיעת החמה
This is usually taken to mean that if the new moon is “born”, i.e., moves out of conjunction with the sun, before mid-day, then it can be seen around sunset; but if it is born after mid-day, then it will not be seen around sunset. One can interpret this in many ways, but on the face of it, it states that six hours suffices for the moon to be distant enough from the sun so as to be visible at sunset—something which is patently not true. I believe that Hallevi was aware of this fact, and he brilliantly appropriated it for his own purposes, which is to have the Sabbath centered on Jerusalem, in line with his Land-of-Israel-centric ideology. He cites the Talmudic passage correctly, but adds, “it is as if it said (ka-‘annahu qāla)”; and he then reproduces the statement in Hebrew, but with some significant additions:
נולד קודם חצות יום שבת בירושלים בידוע שנראה ביום שבת סמוך לשקיעת החמה
Some astute commentators saw that Hallevi is in fact “correcting” the Talmud so as to allow 24 hours for the moon to distance itself from the sun, which is a reasonable value; they are cited by Michael Schwarz, p. 84 note 182: “ Since, according to the Sages, the moon is not visible until about 24 hours have passed since its “birth”, then, if the moon is “born” around noon in Israel, which is a little before the beginning of the Sabbath in China, it will be seen there [in Israel] around the time that it [the Sabbath] ends there [in China]”. I found it necessary to identify the pronominal suffixes in the Hebrew passage. The idea is that we take the 24 hours to be measured from the beginning of the Sabbath in China, after which time—if the moon left conjunction at the beginning of the Sabbath in China, which is noon in Israel—it will be visible in Israel around sunset—that is, sunset on Sunday evening, meaning that we have given the moon 30 hours to move away from the sun, thus greatly increasing the chances of it being visible.
In short, Hallevi has totally appropriated the Talmudic discussion of visibility theory for his own doctrine of the centrality of Israel. He is not talking at all about visibility theory, though, as I understand him, he clearly sees the need to allow thirty hours to pass from conjunction. His concern is with the Sabbath; he says this over and over again. His highly original appropriation of the Talmudic passage led him to make one of the first and most important statements about the date line in Jewish literature.