The geometry of Leonardo’s Vitruvian Man and the contents of the margin of uncertainty

"The problem of squaring of the circle /.../ attracted the attention of a class of persons who have, usually with a very inadequate equipment of knowledge of the true nature of the problem or of its history, devoted their attention to it, often with passionate enthusiasm. Such persons have frequently maintained, in the face of all efforts at refutation made by genuine Mathematicians, that they had obtained solution of the problem." ...but...