"Origin" would be a more "ordinary" way of putting it, but I would tend to go for "lineage", which captures the tone more accurately, I think.

The meaning of "solar" here is:

"1. m. Casa, descendencia, linaje noble. Su padre venía del solar de Vegas."

Or as the first RAE dictionary puts it in 1739:

"Significa también el suelo de la casa antigua, de donde descienden los hombres nobles".

So by using this word Sor Juana is really suggesting that her mind is as "noble" as the bishop's. It's quite a challenging way of putting it. They are both human spirits, and as such, they are equal.

You might almost say "of the same pedigree".

This has been translated "as both come from the same house". That would be OK, though as I say I think it would be nice to preserve the echo of noble descent.


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Note added at 18 mins (2015-10-05 22:17:32 GMT)
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Sorry; in the last paragraph I meant to say "from the same source". I think this is the same reference that Ana has quoted:
https://books.google.es/books?id=NcCnAgAAQBAJ&pg=PA344&lpg=P...

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Note added at 10 hrs (2015-10-06 08:13:54 GMT)
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I think the alternative interpretation, cited by Bea, is mistaken. It apparently interprets "es un de solar" as meaning approximately "it is innate" (and God-given).

According to Dufort, Sor Juana's argument is that "no había elegido esta desgraciada habilidad sino que por el contrario, como ella misma lo presenta, había nacido con dicha carga". I find hard to see how she has derived this idea from the text. By "habilidad" Dufort means "don", a special ability that Sor Juana possesses, and that did not choose but it obliged to use. I see nothing in the text to support this. Sor Juana is not claiming any special ability (actually I think she did consider herself cleverer than her Jesuit adversaries, but she's not saying that here). She is merely claiming to possess the same mental freedom as anyone else, and specifically the same mental freedom as Vieyra.

Linguistically, "es de un solar" would be a very strange way of saying "it is innate"; in fact, I don't think it can mean that. "Un solar" would mean one particular "solar", one particular origin. If she had written "es de solar", she might have meant "it is part of my heritage". But she didn't. "Solar" is origin in relation to lineage and descent. It's not a word that would normally be used to refer to innate qualities or faculties.

"De un solar" could very well imply "de un mismo solar" or "de un solo solar", in much the same way as we say "Cristo es de una sustancia con Dios", for example, meaning "de una misma sustancia" or "de una sola sustancia". Similarly, we say in English "of one substance". "De un solar", in this interpretation, means "of one lineage". So she is saying that her mind (entendimiento) is "of one lineage" with Vieyra's, taking "con el suyo" as understood. Linguistically this is perfectly normal seventeenth-century usage.

And this is surely what she's talking about here. Of course Sor Juana, like any Christian, would have accepted that her mental faculties were God-given, attributes of her soul, which is of divine origin. But here she is emphasising freedom. By this she does not mean licence; she means freedom to interpret religious matters within the teaching of the Church. And the crux is that she is claiming the same freedom to do so as Vieyra.

The whole passage is built on a comparison between what she is accused of and what Vieyra himself has done, and it is highly aggressive towards Vieyra. She accuses him of monumental presumption, of equating his opinions with the principles of the Faith, requiring blind obedience. If the Church allows me to express my view, who is he to forbid me? If I am blamed for disagreeing with him, why is he not blamed for disagreeing with the Fathers of the Church? My "entendimiento" is as free as his. The statement "[mi entendimiento] es un de solar" is offered to support the proposition that "es tan libre como el suyo": it refers to her equality with him, equality of freedom to interpret within the Faith, freedom to disagree with him.

In the light of all this, it seems to me that the linguistic and contextual arguments all firmly support the reading of "un" as "un mismo" or "un solo", and militate against Dufort's reading (as far as I can understand it).