Translating a reflexive pronoun in a sentence with accusative

Question

Translating a sentence from Vieta's In artem analyticen isagoge (available here) I'm having trouble:

Et hic se praebet Geometram Analysta, opus verum efficiundo post alius, similis vero, resolutionem : illic Logistam, potestates quascumque numero exhibitas, sive puras, sive adfectas, solvendo.

My trouble is with the first clause, Et hic se praebet Geometram Analysta, which I thought was a simple clause, but there's a catch.

The word analysta (analysta, -ae) is not found in any of the usual references, and I've narrowed its etymology down to two possibilities:

1. Derives from Latin analysis with the Latin suffix -tus -ta -tum used for adjectives meaning 'provided with'

2. Derives from Latin analysis with the French suffix -iste for nouns meaning 'someone who performs an action'

I think both are feasible considering Vieta was French, and further the term analyste first appears in French derived in this way about 50 years later. If it's a Latin adjective, it is used exclusively in the feminine (which isn't uncommon in my experience when deriving new words); otherwise it's a feminine noun.

The word geometres, geometrae is a 1st declension Greek noun, but seemingly used with the standard Latin accusative -am.

The translation of the sentence (clause) seems to be:

And this [Analyst] shows itself [a/the Geometer]

or

And this shows itself [with the/an analyst] [the/a Geometer].

I can't quite figure this out, maybe there are misspellings or maybe this isn't a complete clause at all? How do I translate this?

-- Edit --

As pointed out in the comments, another (much more likely) possibility for etymology is the ancient Greek -ιστης suffix, which became the Latin -iste used for nouns of agency, which fits the noun form.

-- Edit 2 --

Another helpful hint from @TKR, 'hic' is paired with 'illic', so it's used as the adverbial 'here' (hīc) rather than the demonstrative. With this in mind, more translation attempts:

If 'analysta' (nom.):

And here the Analyst shows itself the Geometer, ...

If 'analystā' (abl.):

And here it shows itself the Geometer with the Analyst

(I might be using the wrong ablative, but it might be close?)

Answer 1

If a verb has both a reflexive pronoun and an accusative object, it has effectively two accusative objects. That is not so uncommon in Latin – quite a few verbs take a “double accusative.”

Some are a little surpising, for example with celare:

Catilina consilium senatum celavit.
Catiline concealed his plan from the senate.

But there is another class of verbs in which someone is made, considered, called something, e.g.:

Populus Romanus Ciceronem consulem fecit.
The Roman people made Cicero a consul.

Quem prudentem putabat.
They considered him a wise man.

… and so on, and this is precisely the case with reflexive praebere, as you can read in the dictionary (“and with se, to show, approve, behave one's self in a certain manner”). So I very much agree with your reading:

And here the Analyst shows itself the Geometer

… or you could say “proves to be a geometer.”

Answer 2

To add to Sebastian's answer, there are two ways in which classical Latin can borrow Greek words. The stem of the word is normally always written in Latin letters representing the sound of the Greek word semi-phonetically, e.g. αι becomes ae and ησ becomes es. But the ending can be written in two ways:

1. Write the word like the stem, in Latin letters semi-phonetically, representing the Greek sound. The (feminine nominative) ending -ης becomes -es, the 3rd-declension accusative -α becomes -a.

2. Use the endings from the most similar Latin declension. This is usually about similarity in gender and theme vowel (or lack thereof). Accusative ending -α becomes -em, nominative ending -ης becomes -a. This is very common, as seen in words like poeta, nauta, etc. It is what happened with analysta.

In prae-classical times, they also used other ways.