Halakhah for Bava Kamma 163:7

There is an ancient enactment, from the time of Moshe, that the Torah is read in public on Shabbat day, Monday, and Thursdays from a scroll written with ink on parchment, so that three days never pass without the study of Torah. The Sages teach that this enactment was instituted based on the verse, “They traveled for three days in the desert without finding any water” (Shemot 15:22). Moshe and his disciples, the elders and the prophets, understood that the thirst for water was a result of three consecutive days in which Israel did not engage publicly in Torah (BK 82a). Torah is likened to water, for just as water sustains all animal and plant life, so too Torah sustains the soul. When the people disconnected themselves from the Torah even slightly, water sources also ceased to flow. Although the Torah scholars of that generation presumably studied Torah during those three days, the meaning here is that for three days the people of Israel did not engage in Torah publicly. Therefore, it was established that the Torah would be read every Monday, Thursday, and Shabbat, so that never again will more than three days pass without Israel publicly reading from the Torah.

Ezra the Scribe further instituted that the Torah be read at Minḥa on Shabbat because of  “yoshvei keranot” (BK 82a). Some say that yoshvei keranot are merchants and craftsmen who are unable to hear the reading on Mondays and Thursdays, and so the Shabbat Minḥa reading was added as a make-up opportunity for them. Others maintain that yoshvei keranot are frivolous individuals. There was concern that after they finish Shaḥarit on Shabbat they would turn to drink and idleness, and so Torah reading was instituted at Minḥa (see Peninei Halakha: Shabbat 5:8). The Sages further enacted that relevant Torah portions are read on all festivals and Rosh Ḥodesh.

1. The Laws Pertaining to Marital Intimacy on Shabbat, 2 Seifim: Marital intimacy is one of the expressions of Shabbos pleasure. Accordingly, [our Sages] determined that healthy Torah scholars, who are obligated to fulfill their conjugal duties once a week, should do so each Friday night.