Draw oneself quite out

Maroseika

Moderator
Russian
From Fuller's "The holy state" (1642):

[Paula] built one mo∣nasterie for men, and three for women. It will be worth our pains to take notice of some principall of the orders she made in those feminine Academies; because Paula's practice herein was a leading case, though those that came after her went beyond her. For in the rules of monasticall life, Paula stood at the head game, and the Papists in after ages, desirous to better her hand, drew themselves quite out.

What does mean "drew themsleves quite out"? Just failed? Or failed due to not "standing at the head game", i.e. not governing monasteries personally? Or there is not "fail" sense at all and he says just that papists did not govern them personally?
 
  • Maroseika

    Moderator
    Russian
    So "went beyond her" means they went farther? And in this case does "stood on the head game" mean that she headed the monasteries?
     
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