Man, I know that Jacobs text of which you speak. I LOVE that book. I learned geometry from the 1974 imprint. Love-love-love.
{sigh}
What mystifies me is that a few decades' worth of research
should have made for a landscape filled with examples like it-- and it hasn't for the reasons that Val illustrates so amply (both in her original post and in the one above).
Spiraling is a complete disaster in the hands of a publishing industry that doesn't actually pay Subject-Expert AUTHORS to write textbooks. I'm convinced that the people assembling such a dog's breakfast genuinely fail to appreciate that they
haven't taught the students some of the things they're presenting out of order. Nutty as Christmas fruitcake, but there it is.