Sir James George Frazer, The Golden Bough: a study of magic and religion, 1890:

If we analyse the principles of thought on which magic is based, they will probably be found to resolve themselves into two: first, that like produces like, or that an effect resembles its cause; and, second, that things which have once been in contact with each other continue to act on each other at a distance after the physical contact has been severed. The former principle may be called the Law of Similarity, the latter the Law of Contact or Contagion. From the first of these principles, namely the Law of Similarity, the magician infers that he can produce any effect he desires merely by imitating it: from the second he infers that whatever he does to a material object will affect equally the person with whom the object was once in contact, whether it formed part of his body or not. Charms based on the Law of Similarity may be called Homoeopathic or Imitative Magic. Charms based on the Law of Contact or Contagion may be called Contagious Magic. [...]

The other great branch of sympathetic magic, which I have called Contagious Magic, proceeds upon the notion that things which have once been conjoined must remain ever afterwards, even when quite dissevered from each other, in such a sympathetic relation that whatever is done to the one must similarly affect the other. Thus the logical basis of Contagious Magic, like that of Homoeopathic Magic, is a mistaken association of ideas; its physical basis, if we may speak of such a thing, like the physical basis of Homoeopathic Magic, is a material medium of some sort which, like the ether of modern physics, is assumed to unite distant objects and to convey impressions from one to the other. The most familiar example of Contagious Magic is the magical sympathy which is supposed to exist between a man and any severed portion of his person, as his hair or nails; so that whoever gets possession of human hair or nails may work his will, at any distance, upon the person from whom they were cut. This superstition is world-wide[...]"

Georg Luck, Arcana Mundi, 1985:

In the present context, I would define magic as a technique grounded in a belief in powers located in the human soul and in the universe outside ourselves, a technique that aims at imposing the human will on nature or on human beings by using supersensual powers. Ultimately, it may be a belief in the unlimited powers of the soul.

[...] Incidentally, the borrowing of names, concepts, and rituals from foreign religions is one of the characteristics of ancient witchcraft, as the magical papyri attest. Even though cities like Alexandria and Rome were already full of sanctuaries of exotic deities, apparently there was still room for more speculation and more experiment. No doubt the religions of ancient Egypt were similarly misinterpreted or at least simplified by the Greeks of the Hellensitic period who lived in Egypt, and these religious practices survived, through a series of transformations, in the mainstream of magical doctrine.

Henry Cornelius Agrippa, Three Books of Occult Philosophy, 1651

Magick is a faculty of wonderfull vertue, full of most high mysteries, containing the most profound Contemplation of most secret things, together with the nature, power, quality, substance, and vertues thereof, as also the knowledge of whole nature, and it doth instruct us concerning the differing, and agreement of things amongst themselves, whence it produceth its wonderfull effects, by uniting the vertues of things through the application of them one to the other, and to their inferior sutable subjects, joyning and knitting them together thoroughly by the powers, and vertues of the superior Bodies. This is the most perfect and chief Science, that sacred and sublimer kind of Phylosophy, and lastly the most absolute perfection of all most excellent Philosophy.

Washington Irving, The Alhambra, 1894:

A word more to the curious reader. There are many persons in these skeptical times who affect to deride everything connected to the occult sciences, or black art; who have no faith in the efficacy of conjurations, incantations, or divinations; and who stoutly contend that such things never had existence. To such determined unbelievers the testimony of past ages is as nothing; they require the evidence of their own senses, and deny that such arts and practices have prevailed in days of yore, simply because they meet with no instance of them in the present day. They cannot perceive that, as the world became versed in the natural sciences, the supernatural became superfluous and fell into disuse, and that the hardy inventions of art superseded the mysteries of magic. Still, say the enlightened few, those mystic powers exist though in a latent state, and untasked by the ingenuity of man. A talisman is still a talisman, possessing all its indwelling and awful properties; though it may have lain dormant for ages at the bottom of the sea, or in the dusty cabinet of the antiquary.