Theosophy Basics: Gupta Vidya, Atma Vidya, Brahma Vidya

Blavatsky gives a number of terms to designate Theosophy, including some oriental equivalents. One she gives is Gupta Vidya as per the following eloquent, poetic description:

The great science, called by the vulgar “magic,” and by its Eastern proficients Gupta-Vidya, embracing as it does each and every science, since it is the acme of knowledge, and constitutes the perfection of philosophy, is universal; hence—as very truly remarked cannot be confined to one particular nation or geographical locality.

But, as Truth is one, the method for the attainment of its highest proficiency must necessarily be also one. It cannot be subdivided, for, once reduced to parts, each of them, left to itself, will, like rays of light, diverge from, instead of converging to, its centre, the ultimate goal of knowledge; and these parts can re-become the Whole only by collecting them together again, or each fraction will remain but a fraction.

He is at one and the same time a Chaldaean Sage, a Persian Magi, a Greek Theurgist, an Egyptian Hermetist, a Buddhist Rahat, and an Indian Yogi. He has collected into one bundle all the separate fractions of Truth widely scattered over the nations, and holds in his hands the One Truth, a torch of light which no adverse wind can bend, blow out or even cause to waver. Not he the Prometheus who robs but a portion of the Sacred Fire, and therefore finds himself chained to Mount Caucasus for his intestines to be devoured by vultures, for he has secured God within himself, and depends no more on the whim and caprice of either or evil deities.”

(HPB CW 3, 266-68 - MADAME BLAVATSKY ON “THE HIMALAYAN BROTHERS” [The Spiritualist, London, August, 12, 1881])

Gupta means secret, Vidya means knowledge.  A similar term is guhya-vidya [ guhyavidyA ] meaning knowledge of Mantras or mystical incantations. (see Vishnu Purana. i, 9, 117; see also the Theosophical Glossary). Chapter 9 of the Gita  is titled Raja-Vidhya Yoga or the Raja-Guhya Vidhya. Etymologically, the term Vidya gives the Greek verb, to know, and in English, wisdom (Monier Williams, Sanskrit Lexicon):

• Greek εἶδον for ἐϝιδον, οἶδα for ϝοιδα(oida) = veda;
• Latin videre;
• Slavic věděti;
• Gothic witan, wait;
• Germanic wizzan, wissen;
• English wisdom, wit.

Elsewhere she outlines four types of Gupta-Vidya: “There are four (out of the many other) names of the various kinds of Esoteric Knowledge or Sciences given, even in the esoteric Purânas. There is
(1) Yajna-Vidya,1 knowledge of the occult powers awakened in Nature by the performance of certain religious ceremonies
(2) Maha-vidya, the "great knowledge," the magic of the Kabalists and of the Tantrika worship, often Sorcery of the worst description.
(3) Guhya-Vidya, knowledge of the mystic powers residing in Sound (Ether), hence in the Mantras (chanted prayers or incantations) and depending on the rhythm and melody used; in other words a magical performance based on Knowledge of the Forces of Nature and their correlation; and
(4) ATMA-VIDYA, a term which is translated simply "knowledge of the Soul," true Wisdom by the Orientalists, but which means far more.
This last is the only kind of Occultism that any theosophist who admires Light on the Path, and who would be wise and unselfish, ought to strive after.”(Occultism versus the Occult Arts, Lucifer, May, 1888)
Another term she uses is Brahma Vidya ((Mahabharata V. 30: “This weapon of Brahma is the science of Brahma or of the Veda. This choice of a boon  seeks the removal of all obstacles  to the attainment of divine knowledge.” See also the Brahmavidyā Upanishad): “Theosophy is the equivalent of Brahm-Vidya, divine knowledge” (Key, sect. 1 fn 1). A more expanded explanation is given elsewhere:

“Theosophy is synonymous with the Jnana-Vidya, and with the Brahma-Vidya (1) of the Hindus, and again with the Dzyan of the trans-Himalayan adepts, the science of the true Raj-Yogis, who are much more accessible than one thinks. This science has many schools in the East. But its offshoots are still more numerous, each one having ended by separating itself from the parent stem — the true Archaic Wisdom — and changing its form. (THE BEACON OF THE UNKNOWN La Revue Théosophique, Paris, Vol. I, Nos. 3,4,5,6; May 21 , 1889, pp. 1-9; June 21, 1889; pp. 1-7; July 21, 1889, pp. 1-6; August 21, 1889, pp. 1-9] CW 11, p.256

Blavatsky tends to relate Theosophy as a western term to Neoplatonism, and there is an early Neoplatonic text that relates the term Theosophy to Indian sources, Porphyry’s lengthy treatise On the Abstinence from Animal Foods
“In the land of Hindus, divided in many ethnicities exists the ilk of theosophos, and the Greeks are accustomed referring to them as gymnosophists ["naked philosophers”]. There are two sects of gymnosophists, one is headed by the Brahmans the others by the Shramana[5] (śramana). While Brahmans maintain the hereditary succession of Theosophia [Theosophy] - exactly as happens with priesthood - the Shramana comprises a social category composed by those who want to practice Theosophia [Theosophy].” [6] («Περí Αποχής Εμψύχων» 17, π 237, β. 4)

picture thanks to http://my.yoga-vidya.org/