Three Verses, Seventy-Two Names
The full method by which Exodus 14:19–21 yields the 72-fold Name — attributed to Rashi and recorded independently in Sefer HaBahir.
Three verses, each 72 letters
Exodus 14:19–21 describes the pillar of cloud moving behind the Israelites at the Red Sea. In the Masoretic text, each of these three consecutive verses — v.19, v.20, and v.21 — happens to contain exactly 72 Hebrew letters. This numerical coincidence is the entire foundation of the system.
Explained by Rashi (on b. Sukkah 45a) and, independently, in Sefer HaBahir (c. 1150–1200).
Read boustrophedonically
The three verses are stacked and read boustrophedon — "as the ox plows," alternating direction line by line, the way a farmer turns at the end of each furrow rather than walking back to the start.
This produces 72 vertical columns — one letter contributed by each verse per column.
Each column is a name
Reading down each of the 72 columns gives a three-letter root. These 72 triliteral roots are the raw material of the Names — not yet pronounceable on their own, but already fixed in order and sequence.
Adding the suffix — mercy and severity
A bare three-letter root isn't pronounceable as a name. Following Reuchlin's explanation (De Arte Cabalistica, 1517), each root is completed with one of two divine suffixes, applied in strict alternation across the sequence:
+ אֵל (-El)
Associated with divine mercy (Chesed). E.g. root + El → a pronounceable angelic name.
+ יָהּ (-Yah)
Associated with divine severity (Gevurah). Alternates with -El down the full list of 72.
The result is 72 complete names — later systematized by Agrippa, Kircher, and eventually the Golden Dawn into the correspondences shown on the names table.
From letters to angels
The step from "72 divine names" to "72 angels" happened later, and outside strict Kabbalistic tradition. Johann Reuchlin was the first to describe the 72 as angelic individuations of God's will; later Christian Hermeticists (Agrippa, then Athanasius Kircher) formalized angel-by-angel correspondences — zodiac degree, sigil, and function — that most modern sources, including the names table on this site, ultimately draw from.
Where these later systems disagree with each other or with the earlier Judaic sources, that's addressed directly on the History page rather than smoothed over here.