MHB Looking for a good analytic geometry book

[Ragnarok7]

I am always entranced when I read in calculus books about various curves like lemniscates, cardioids, the spiral of Archimedes, the witch of Agnesi, and similar things. But in calculus books they are generally just little asides or relegated to the exercises. Presumably there is more to analytic geometry than just these things, but I have trouble finding anything above the level of basic middle/high school coordinate geometry but below the level of an advanced undergraduate text requiring modern algebra and analysis and whatnot.

Does anyone know of a good book covering such topics and other such interesting things? It seems like in previous centuries these things were studied a lot more, and now no one is very interested at the elementary level. I would like to study plane and solid Euclidean geometry analytically (i.e. not through constructions) on its own, and not wrapped up with some more important subject, and not as only a special case of some very general and complicated theory. I.e., I would like what is taught in high schools/college as analytic geometry, but in much more detail. Does such a thing exist?

Thank you for any suggestions/corrections of my misconceptions!

 

[symbolipoint]

Maybe, for the Analytic Geometry and some (slightly unusual ) curves graphs. My own copy is now physically ruined and so checking the instructive text inside is nearly impossible, but there was a book from about 1977, College Algebra And Trigonometry, second edition, by Bryant, Karush, Nower, & Saltz, ISBN 0-87620-171-0. I would ordinarily recommend other, and probably better-known Pre-Calculus books but which may not exactly have the content you asked about. (Some authors to watch for are Larson & Hostetler; and Aufman, Barker, & Nation).

I wish I knew better what to tell you about Solid Geometry. Some GOOD Geometry books (like for community colleges and high schools) will give some instruction just as way to make their instruction more thorough; but maybe not a fully as you are asking. The Prentiss-Hall book by Bass et. al. called Geometry (from about year 2003) was an excellent book.

(Yours was an old, unanswered question from year 2014. Maybe others are interested in the same question today.)