Mia and sia: whose is it?

Possessives: add -a

-a is the adjective ending, so mia is literally me-ish: belonging to me. That has one consequence. A possessive agrees with its noun like any adjective, taking -j for several and -n for the object:

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1. 1mia avino
2. 2mia avo
3. 3mia patrino
4. 4mia patro
5. 5mia onklo
6. 6mi
7. 7mia frato

The girl at the bottom is speaking: everyone else in the tree is mia, my.

• Mia libro estas tie. - My book is there.
• Ĉu vi vidas miajn librojn? - Do you see my books?

The possessive agrees with the thing owned, not the owner. Miaj libroj has -j because there are several books; there is still only one of me. No la is needed either:

• Nia tago estis bona. - Our day was good.

Si and sia: his own, her own

English he sees his book cannot tell you whose book it is. Esperanto can. In the third person, sia points back at the subject; lia, ŝia and ilia point at someone else.

Sia agrees like any possessive, and si has the object form sin:

• Ili vidas siajn librojn. - They see their own books.
• Li lavas sin. - He washes himself.

Two limits. It is third person only, because mi and vi are never ambiguous:

• Mi vidas mian libron. - I see my book.

And it never goes inside the subject:

• Lia libro estas bona. - His book is good. (never sia libro here)

The full treatment is in the reflexive.