6.3: Footnotes

1

The Greek word for the abacus, \(\alpha \beta \alpha \xi\), is borrowed from a Phoenician root from which come words for “dust” and “flying away.”

2

Only first-degree transformations like those of TMS XVI #1 and TMS IX #3 may be seen as constituting a partial exception; TMS XVI #1 is indeed an explanation of how operations directly on the words of the equation are to be understood in terms of the geometric representation. Once that had been understood, TMS IX #3 could probably operate directly on the level of words. But TMS XVI #1 is no problem solution, and in TMS IX #3 the first-degree transformation is subordinate to geometric operations.

3

See TMS XVI #2 line 16 and TMS VII #1 line 4 (below, pages 117 and 118); the two terms seem to be synonymous. This “separation ” or “dispersion,” which is no subtraction, is the inverse operation of “heaping.”

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