The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
Appendix I
Indo-European Roots
ENTRY:
aug-
DEFINITION:
To increase. Oldest form *2eug-, colored to *2aug-. Variant *2weg- becoming *(a)weg-. Derivatives include nickname, auction, and auxiliary. 1.eke1, from Old English acan,can, to increase; b.nickname, from Old English aca, an addition. Both a and b from Germanic *aukan.2. Variant (metathesized) form *weg- (from *weg-), extended to *wegs- (o-grade *wogs-). a.wax2; woodwaxen, from Old English weaxan, to grow, from Germanic *wahsan;b.waist, from Old English *wæst, growth, hence perhaps waist, size, from Germanic *wahs-tu-.3. Form *aug--.auction, augend, augment, author, authorize, from Latin augre, to increase. 4.augur; inaugurate, from Latin augur, diviner (< “he who obtains favorable presage” < “divine favor, increase”). 5.august, from Latin augustus, majestic, august. 6. Suffixed form *aug-s-.a.auxiliary, from Latin auxilium, aid, support, assistance; b.auxin, auxesis, from Greek auxein,auxanein, to increase. (Pokorny aeg- 84.)
2eug-, colored to *
acan, 
eg- 84.) 
