iii) Accepting that 'Henry the Haberdasher' was by no means an 'authority' on either math or on the Greek language (with respect to Greek math), the question I'd like to ask is how come (i.e., HOW? and WHY?) all the 'experts' of that time 400 years ago - as well as all the 'experts' that succeeded them since - never thought it necessary to check things out a bit??? AMAZING!!!
============= The ratio of Euclid to mathematics in 16th century England is to the ratio of Tendulkar to cricket in 21st century India.
In other words whatever Euclid said was the culmination of Greek logical proof.
So believe it or not, the words of eminent mathematicians, written in Latin, were changed upon translation into English to match the binary operational logic of Henry Billingsley.
Editors and translators thought they were clarifying the explanations of modern mathematicians to be consistent with Euclid, while all along they were trashing elementary mathematical logic.
It seems nobody has undertaken an analysis of the original German, Latin Russian and other languages, that explained multiplication before Euclid's definition of multiplication was incorrectly translated.
In the early 1800s in England, there was some public debate about what is now, the incorrect 'ab = a added to itself b times' definition of multiplication. Yet the definitions quoted to support this incorrect definition had both been changed to match Euclid's words in English, which were really the buggy logic of Henry Billingsley.
Also mathematicians never question definitions. Definitions are the foundation up which propositions are proven. Definitions are almost common notions and are thus, considered untouchable.
Had England studied Sanskrit as well as Latin and Greek in grammar schools, perhaps this situation would not have arisen.
Euclid never said multiplication is repeated addition. Yet who reads ancient Greek? A haberdasher said Euclid defined multiplication as, anachronistically, ab = a added to itself b times, and we all read English.
The British Empire then exported the haberdasher's logic to the many countries it colonized.