I had to look up your term, Faldage. Gurunet has:
pe·ti·ti·o prin·ci·pi·i (pə-tĭsh'ç-ô' prĭn-sĭp'ç-ç', -ç-î')
n. Logic.

The fallacy of assuming in the premise of an argument that which one wishes to prove in the conclusion; a begging of the question.

[Medieval Latin petîtiô prîncipiî : Latin petîtiô, request + Latin prîncipiî, genitive of prîncipium, beginning.]

For beg, Gurunet has:
v., begged, beg·ging, begs.

v.tr.
1. To ask for as charity: begged money while sitting in a doorway.
2. To ask earnestly for or of; entreat: begged me for help.
3.
a. To evade; dodge: a speech that begged the real issues.
b. To take for granted without proof: beg the point in a dispute.
v.intr.
1. To solicit alms.
2. To make a humble or urgent plea.
phrasal verb:
beg off

To ask to be released from something, such as an obligation: We were invited to stay for dinner, but we had to beg off.

[Middle English beggen, possibly from Anglo-Norman begger, from Old French begart, lay brother, one who prays. See beggar.]

You put: a defintion of beg that fits the usage in the name of the logical fallacy otherwise know as petitio principii and give me another instance of its being used with that meaning. Now--in dead seriousness, does 3.b. represent what you're asking for? Or is it yet another princip-thing?

I keep having to post this, then edit to add stuff: I need to see all the things together, to try and get my mind around the complete puzzle. If I think of any actual examples, I'll add them.