Complex emotions as compositions of the primitives
Formal Statement
Every complex emotion is a combination of the three primitives — joy, sadness, and desire — shaped by whether the underlying ideas are adequate or inadequate. Love is joy with the idea of an external cause; hate is sadness with an external cause; hope is inconstant joy from the image of a future thing whose outcome is in doubt. The General Definition of the Emotions defines a passion as a confused idea whereby the mind affirms a greater or lesser force of existence in the body. Active emotions, by contrast, flow from adequate ideas.
In Plain Language
Spinoza spends the rest of Part III cataloguing dozens of emotions — love, hate, hope, fear, pity, envy, pride, humility, remorse, and many more. But his method is always the same: take one or more of the three primitives, attach them to a specific kind of idea (of an external cause, of a past event, of something uncertain), and check whether the idea is adequate or inadequate. The result is either a passion — something that happens to you because you only partially understand the situation — or an active affect, where you are the full cause. This is not a catalogue to memorize but a grammar to internalize. Once you see the pattern, you can parse any emotion you feel.
Why This Follows
From ce-04, activity tracks adequate ideas and passivity tracks inadequate ideas. From ce-14, all emotions reduce to joy, sadness, and desire. Combining these results: any specific emotion is one (or more) of the three primitives filtered through a particular cognitive state. The General Definition of the Emotions (end of Part III) formalizes this by defining passion as a confused idea affirming a change in the body's force of existing.
Every emotion can be parsed as a primitive affect (joy, sadness, desire) combined with a type of idea (adequate or inadequate, of self or other, of past, present, or future).
Connected Concepts
Spinoza says we do not feel emotions about things we understand adequately in the same way we feel them about things we grasp only confusedly. Can you think of an example where understanding something more deeply actually changed the emotion you felt about it?