There are special rules for spell acquisition that are unlike most other skills in the game. What you actually do is learn the ability to cast a spell of a particular level, and not the specific individual spell. This is known as a “Spell Slot.” You can then fill that Spell Slot with any spell you can memorize of that level or lower.
For example: Belthivis purchases a 1st level Spell Slot. He has a spell book with three 1st level spells in it. He picks one spell at that level and memorizes it for that day. The Logistics staff checks his spell book to make sure he has the spell in front of him to memorize and then gives adds that spell to his battle board. Belthivis later learns another 1st level Spell Slot. He can now memorize two different 1st level spells from his spell book or can memorize a single spell twice.
Spell Slots are purchased in a proportional pyramid as described in the examples below. If you wish to buy a particular Spell Slot, you must first have two more Spell Slots on the level below in order to support it. Imagine the pyramid as needing the proper support to keep it from collapsing from being top heavy.
Similarly, you can’t have more than one “gap” of two spells between two levels—for example, you couldn’t have four 1st level spells, two 2nd level spells, and zero 3rd level spells.
This means that a character has very little choice in the manner in which spells may be purchased when starting their career; if you have three 1st level Spell Slots and two 2nd level Spell Slots, the next Spell Slot you will have to buy is 3rd level.
Once you have purchased four Spell Slots of any particular level, you need not buy any more Spell Slots of that level to support the level above. Imagine now the pyramid being an obelisk like the Washington Monument.
You may buy more than four Spell Slots per level but there must always be at least as many Spell Slots below that level in order to support the new amount. Further, the pyramid must be constantly building, which means that the level above must have only one less than the amount you are buying.
This means that in order to buy a fifth 2nd level Spell Slot, you must have a fifth 1st level Spell Slot and a fourth 3rd level Spell Slot.
For example: Belthivis has a 3rd level Spell Slot, two 2nd Spell Slots, and three 1st level Spell Slots. His pyramid is fine (see figure one). He wants to learn a 4th level Spell Slot eventually. He must build the foundation of the pyramid so it can support a 4th level Spell Slot. First he buys another 1st level Spell Slot and another 2nd level Spell Slot. He must next purchase another 3rd level Spell Slot (see figure two). Now his pyramid is ready for the new Spell Slot. The foundation of support for the 4th level Spell Slot has been made by making sure there are two 3rd level Spell Slots below. He can now buy his first 4th level Spell Slot (see figure three). If Belthivis wants to buy a 5th level Spell Slot, he can do so without buying any more 1st level Spell Slots because four is the maximum required. He must support the 5th level Spell Slot by buying a 2nd, 3rd and 4th in that order to make the pyramid (see figure four). Belthivis now has a perfect pyramid and is the envy of all his friends. If he wants, he can stop buying 2nd level Spell Slots, as four is the minimum required. His pyramid will then progress with the purchase of a 3rd level Spell Slot, then a 4th, 5th and finally his first 6th level Spell Slot, in that order. If Belthivis has all of the Spell Slots listed in figure four and then decides that he wants a fifth 2nd level Spell Slot, he must first buy another 1st level Spell Slot to support the 2nd level Spell Slot. After that, he must buy the 3rd level Spell Slot (see figure five).
Note that the pattern is very set as to which Spell Slots have to be purchased unless you wish to buy more than four Spell Slots of any one level.
There is potentially no limit as to the number of Spell Slots per level that can be purchased as long as this pattern is maintained.
You can have a spell pyramid with nine 1st level Spell Slots, eight 2nd level Spell Slots, seven 3rd level Spell Slots, and so on up to one 9th level Spell Slot.