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Please expound and simplify the semantic progression behind "reduce"?

I don't understand the "semantic progression" that I emboldened below. The steps in the "semantic progression" feel too farfetched and unconnected.  Can someone please fill in, and expound, the steps in Simple English? 

>### reduce [14]

>‘Lessen, diminish’ is a
comparatively recent semantic development for
*reduce*. Its Latin ancestor was certainly not used
in that sense. This was *redūcere*, a compound
verb formed from the prefix *re-* ‘back, again’ and
*dūcere* ‘lead, bring’ (source of English *duct,
duke, educate*, etc). It meant literally ‘bring
back’, hence ‘restore’ and also ‘withdraw’. The
original ‘bring back’ made the journey to
English, and even survived into the early 17th
century (‘reducing often to my memory the
conceit of that Roman stoic’, Sir Henry Wotton,
*Elements of Architecture* 1624). **The sense
‘lessen, diminish’ seems to be the result of a
semantic progression from [1.] ‘bring back to a
particular condition’ via [2.] ‘bring back to order’
and [3.] ‘bring to subjection’.**

*Word Origins* (2005 2e) by John Ayto. p 417 Right column.