Moses ordained that the Torah be read every Sabbath (Talmud
Yerushalmi, Megillah 3:1), but he didn't specify how much
should be read each week. The custom in Babylonia was to
read the Torah completely each year; thus they had a system
of parshiyos similar to ours. In Eretz Yisroel, however,
smaller parshiyos (called sedarim) were read, so it took
three years to read the entire Torah (see Megillah 29b).
The three year cycle was followed in some places, especially
in Egypt, until the Rambam's time (after the 1100's). There
was some variation in the parshiyos used in both systems,
but most or all of them had become fixed by Talmudic times
and had acquired their present names (see Megillah 30a).
Each parsha had to be divided into (at least) seven parts,
but the division into aliyahs was not definitely fixed, and
still occasionally varies among different communities
(such as Ashkenazim vs. Sephardim).
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