171 is the eighteenth triangular number, the sum of the integers from 1 to 18. In the Qabalistic system of Liber 777, it serves as the Mystic Number of the 18th Path (Teth, Leo), which connects Chesed (4) to Geburah (5) on the Tree of Life.

Position on the Tree of Life

As the Mystic Number of Path 18, 171 corresponds to the 18th path of the Tree of Life, the path of Teth (Leo). This path runs horizontally between the fourth and fifth Sephiroth, representing the balance of mercy and severity through the solar fire of Leo.

Astrological and planetary correspondence

The number 171 reduces to 9 (1+7+1=9), the number of Yesod, the lunar foundation. This reduction ties the fiery, solar nature of Path 18 to the receptive, formative sphere of Yesod, suggesting a hidden lunar undercurrent within the Leo current.

Historical context

Triangular numbers have been recognized since Pythagorean times as symbols of completeness and accumulation. The formula T_n = n(n+1)/2 was known to the Greeks and later adopted by Jewish mystics for gematria and sephirotic enumeration. In the Qabalistic tradition, each Sephirah and path has a mystic number derived from its position in the sequence of the Tree. The number 171 specifically appears in the 777 table as the summation of the first 18 integers, reflecting the idea that the 18th path contains within it all the preceding steps of creation. Medieval Qabalists such as the author of the Sefer Yetzirah would have recognized the significance of triangular numbers in the structure of the 32 paths. The 18th path itself is described in the Sepher Yetzirah as the "Intelligence of the House of Influence," and its mystic number 171 encodes the total emanations from Kether down to this point.

In Liber 777, the cell for Path 18 under "Mystic Numbers of the Sephiroth" lists 171, representing the complete summation of the path's numerical essence.