Warwick L Nixon Wrote:
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> I am not discussing multiplication in general...
>
> But the AE's method of doing so

Warwick:
That's my point...!
The definition of multiplication is to add a number a specified number of times.
That's exactly what we do and so did the AE.
How you go about performing this feat is up to you...you can use fingers, toes, paper and pen as long as the proceedure is correct.
To divide is to "subtract" a number from a given number a specified number of times.
As for Hermione's post...I'm disregarding it because I think she misinterpreted my comment to you...I was serious and like to constantly remind others that multiplication and division is no more than adding and subtracting...period.

> the idea is to forget what you know not
> superimpose it onto what you see

That could be if you are "not" looking for something, but I "am" looking for something.

The AE could add and subtract, they also knew ratios because multiplication and division of numbers "are" ratios...!

So...we use what is given and try find ratios that make sense, but for heavens sake...don't bother looking for a 2:1 or 3:1 ratio...it's too simple and has no added intellectual meaning. Any ratio discovered must contain knowledge "and" at least a second example provided to confirm the intent...if not then the ratio 'ain't worth a hoot.

Best.
Clive