From chapter XI page 80.
Quintus os aperit atque medico linguam ostendit.
which I translate as:
“Quintus opens his mouth and sticks out his tongue for the doctor.”
medico, being in the ablative case indicating that the action
was done on his behalf. correct?
and then there is…
page 82
Aemilia non putat medicum puerum aegrum sanare posse.
“Aemilia doesn’t think the doctor can cure the sick boy”
here you have medicum puerum aegrum. An accusative acting
upon another accusative. And posse is used instead of potest because sanare is infinitive?
My two cents:
For 1., I would translate medico as dative: “…shows his tongue to the doctor.” I’m not sure when the ablative can indicate that an action can be done on the behalf of another person or thing; someone else will have to clear that up.
For 2., it looks like you’re dealing with an indirect statement. Certain verbs such as putare can introduce indirect discourse: if they do, the subject of the subordinate clause becomes accusative, and the verb becomes infinitive. So puto/credo medicum but puto medicum puerum iuvare or medicus putat se puerum aegrum sanare posse. Translate posse in the present active, thus: “Aemilia does not think that the doctor can/is able to cure the sick boy.”
Quickly,
thanks for your two cents 
“For 1., I would translate medico as dative: “…shows his tongue to the doctor.” I’m not sure when the ablative can indicate that an action can be done on the behalf of another person or thing; someone else will have to clear that up.”
…I would have to agree with you that medico is in the dative form.
" Translate posse in the present active, thus: “Aemilia does not think that the doctor can/is able to cure the sick boy.”
but wouldn’t potest also work here?
Hey everyone,
Yes, medico is dative. (Your understanding of it was right all along, it seems like you just confused the names “ablative” and “dative.”) And to explain it in a slightly different way, since the verb ostendo means ‘to show’ or ‘to hold/stick out’, by its very nature it will usually be accompanied by a verb in the dative, expressing ‘to whom’ the thing is shown or held out to.
As Quickly was saying, you can’t have potest because it is indirect discourse. What Aemelia thinks (expressed directly) is, “Medicus puerum aegrum sanare non potest.” When you turn it into indirect discourse, introduced by puto, it requires both the subject and object to be accusative, and the verb to be an infinitive (the so-called “accusative-infinitive construction,” which is very common).
Hope that helps!
Hey everyone,
Yes, medico is dative. (Your understanding of it was right all along, it seems like you just confused the names “ablative” and “dative.”) And to explain it in a slightly different way, since the verb ostendo means ‘to show’ or ‘to hold/stick out’, by its very nature it will usually be accompanied by a verb in the dative, expressing ‘to whom’ the thing is shown or held out to.
As Quickly was saying, you can’t have potest because it is indirect discourse. What Aemelia thinks (expressed directly) is, “Medicus puerum aegrum sanare non potest.” When you turn it into indirect discourse, introduced by puto, it requires both the subject and object to be accusative, and the verb to be an infinitive (the so-called “accusative-infinitive construction,” which is very common).
Hope that helps!
Damoetas,
Yes, thanks for your reply. It’s great to have this resource of knowledgeable latinists who can answer my newbie questions!
Since both the dative and ablative cases have many of the same endings I do sometimes confuse them. I tend to “read deliberately” that
is identify noun cases as I read.
g.ph