1. We do not begin or end an Aliyah only two verses into the Parshah, or with only two verses left in the Parshah.
2. Each Aliyah must have a minimum of three verses.
3. The Gemara inquires into how many Aliyos are read on a fast day.
4. The Gemara explains that, generally, the extra Aliyos are due to an additional special event on that day.
5. The Gemara cites many possible reasons for why Rav did not fall on his face during Tachanun in Bavel.
A BIT MORE
1. A "Parshah" refers to a separate section of verses, not to what is commonly referred to as the Parshah.
2. There is a dispute in the Gemara about what to do when there are five verses remaining to be read, and there is a need for two Aliyos. This commonly occurs in the Torah reading on a Rosh Chodesh that falls on a weekday.
3. The primary opinion in the Gemara, and our custom today, is that only three Aliyos are read during the Torah reading on a fast day that occurs the week (except for Yom Kippur).
4. For example, the Gemara explains, there is an extra Aliyah on Rosh Chodesh and Chol ha'Mo'ed because there is a Korban Musaf on those days.
5. Some say that this is because an important person (when praying for the public; Tosfos) should not fall on his face unless he is sure he will be answered.