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I want to learn about conics, but I don't really like the chapter on our textbook or the calculus & analytic geometry book that I'm following.

Conics are so interesting, ellipse and hyperbola specially, needless to say. I've learned about Dandelin's theorem, which explains why slicing a cone with a slanted horizontal plane always cross sects the cone into an ellipse, of all shapes.

Which is really beautiful right? But our textbook ain't. I'd like to learn about conics from a book that covers super cool stuff like Dandelin's theorem and generalized Dandelin's theorem (I don't really know much about conics other than that cool theorem haha) so I'm hoping you guys know such a book.

(Also, on a quick side note, I want to learn about hyperbolic functions and their inverses from a book that just doesn't discuss their derivatives and integrals; and approaches the concept like the unit circle definition for circular functions does. Any suggestion is appreciated.)

HERO
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    Hyperbolic functions by V.G Shervatov is a good book about hyperbolic functions, it discuses the geometrical definition etc and it's short, it only has 61 pages. – Donlans Donlans May 25 '20 at 06:24
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    See the books I cited here, along with Elements of Analytical Geometry by George Alexander Gibson and Peter Pinkerton (1911) and Plane and Solid Analytic Geometry by William Fogg Osgood and William Casper Graustein (1921). The last two books are especially complete. Also, this google search (also, replace "analytical" with "analytic"). – Dave L. Renfro May 25 '20 at 11:11
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    For hyperbolic functions, try this search. – Dave L. Renfro May 25 '20 at 11:20
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    @DaveL.Renfro I see you're suggesting books on analytic geometry. My intuition too, says, conics are an integral part of this particular branch of mathematics. But analytic geometry books that take on a calculus approach just suck at demonstrating the beauty of conics to the readers (I personally find it so). I guess I'm looking for books that are euclidean in nature (if you know about Dandelin's theorem, you know what I mean), but I'd like to read ones that follow the old style without old literature, old literature is just... so hard to read Do you think your books fit my description? – HERO May 25 '20 at 12:25
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    Try geometrical conics and this google books search. For something relatively recent, the best thing I can think of is Conics by Keith Kendig (2005; review; more info.) --- looking at this book now (I got a copy a few years ago), this seems pretty close to what you're looking for. – Dave L. Renfro May 25 '20 at 12:38
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    You can consider reading a very good books on conics by Akopyan and Zaslavsky, available here: http://geometry.ru/books/conic_e.pdf – Intelligenti pauca May 25 '20 at 15:28
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    @Intelligentipauca What a beautiful recommendation. By the way, I recently saw your brilliant geometric solution in a problem that involves tangents of parabolas (Arztz parabolas). What books do you recommend that involves that kind of problems and solutions? – rowcol Sep 12 '20 at 05:56
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    @AbrahamHernández Most ruler-and-compass construction involving conics (and much more) are given in Eagles' book "Constructive geometry of plane curves" – Intelligenti pauca Sep 12 '20 at 10:26
  • I am curious what book did you end using and did you find what you wanted? I have the same problem btw – pie May 26 '23 at 16:52
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    @Ahmed I took a liking to Conics by Keith Kendig, but all the suggestions are great honestly you should check them out – HERO Jun 04 '23 at 16:46
  • @HERO do you have pdf file of it ? – pie Jun 05 '23 at 01:28
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    @Ahmed Unfortunately I could only manage a .djvu file – HERO Jun 22 '23 at 13:40

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