Piers,
Your translation is excellent.
The translation was difficult for me. I still cannot 100 % understand the Japanese text, as it is grammatically incorrect. (But I might be wrong and it is just old-fashioned Japanese?)
[nonliteral translation]
A Kissaki of a Katana is basically compared to a fan shape which is naturally cut out from (coaxial) circles. And the original shape is completed as the kissaki of a Katana. From the right, O-kissaki, Chu-kissaki, Ko-kissaki.