Magic, Natural and Supernatural

Magic, whether white or black, was the art and science of compassing natural ends by supernatural (though not divine) means. All witches made use of magic and the powers of more or less evil spirits; but some of them were also adherents of what in Italy was called la vecchia religione.

Now the problem is that magic existed from the ancient times, but the notion of the supernatural, as demonstrated by de Lubac and more (see Marshall Sahlins for the perspective from anthropology), didn't exists before the second axial age. How did the notion of magic and witchcraft transformed during this period, and what was it like before the transformation. Is the above quoted paragraph correct in its characterization of magic as the art and science of compassing natural ends by supernatural means?

To read:

Edward Bever, The Realities of Witchcraft and Popular Magic in Early Modern Europe
James Edward Myers, Pamela A. Moro, Arthur C. Lehmann, Magic, Witchcraft, and Religion: an anthropological study of the supernatural

Also, various meanings of the word “magic” and “magician”. In fantasy settings we have the distinction between mage and sorcery, the latter always more primitive and “evil”, while the former can at times be quite prestigious - high, learned practice. I've never seen an esotericism/philosophy that associated itself with sorcery, but there are some with magic. Though

Some scholars distinguish sorcery from witchcraft by noting that it is learned rather than intrinsic. (from Britannica)
In the early Christian era, the term was applied to any magician or wizard but by the Middle Ages only to those who allegedly practiced magic intended to harm others. In Western popular culture, and in Western children’s literature in particular, the sorcerer often assumes a more positive guise.

Also note the following passage:

"In order to clear the ground," writes Miss Margaret Murray in the introduction of her valuable study, The Witch-Cult in Western Europe, “I make a sharp distinction between Operative Witchcraft and Ritual Witchcraft. Under Operative Witchcraft I class al charms and spells, whether used by a professed witch or a professed Chris tian, whether intended for good or for evil, for killing or for curing. Such charms and spells are common to every nation and country, and are practised by the priests and people of every religion. They are part of the common heritage of the human race. • Ritual Witchcraft-or, as I propose to call it, the Dianic cult--embraces the reli gious beliefs and ritual of the people known in late me· dieval times as 'Witches.' The evidence proves that, under lying the Christian religion was a cult practised by many classes of the community, chiefly, however, by the more ignorant or those in the less thickly inhabited parts of the country. It can be traced back to pre-Christian times and appears to be the ancient religion of Western Europe.”

Maybe

Magic: A History: From Alchemy to Witchcraft, from the Ice Age to the Present