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I'm not a math wizard, but I recently started reading through a few math books to prepare myself for some upcoming classes and I'm starting to really get into it. Then I noticed a few antique math books at a used bookstore and bought them thinking that, if nothing else, they would look cool on my bookshelf. But as it turns out, I enjoy both reading and collecting them. I find myself constantly browsing used book stores, thrift stores, antique stores ect. looking for the next book to add to my library.

So do you know of an antique book that you found interesting, helpful, or historically relevant?

(Just some insight- some of the books I have that I like are: The Laws of Thought by George Boole; Mathematical Methods of Statistics by Harald Cramer; and Introduction to Mathematical Analysis by F.L. Griffin. I've also enjoyed reading online about probablity, logic, and math history. But any area of mathematics is fine as I'm still discovering which areas interest me.)

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If you find "Geometry and the Imagination" by Hilbert and Cohn-Vossen, snap it up! –  Asal Beag Dubh Apr 13 '13 at 22:32
    
I found a copy of Ramanujan's notebooks in our university library. They're worth reading, although one should bear in mind that a number of things he does aren't actually rigorous or valid –  Cocopuffs Apr 13 '13 at 22:42
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It would help if you told us the books you liked, to give us an idea of the level you are looking for. "Antique" is vague. –  Thomas Andrews Apr 13 '13 at 22:47
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Cauchy's Cours d'analyse would be interesting. –  user10444 Apr 13 '13 at 23:02
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I read some of Euclid's Elements found here once. Probably not the best resource to learn math from, but very historically important, very antique, and quite fun to read. –  Alfonso Fernandez Apr 14 '13 at 0:11

9 Answers 9

Of course the obvious choice will be "A Course of Modern Analysis" by Whittaker and Watson, Cambridge 1902. Some say it is this the BOOK (the only one) on real analysis.

You can find old copy of this book easily. I have an edition of the 40's and it looks great.

I have not seen the new edition but they say is done by photographing the old one and does not look good. The old one is amazing. It's difficult to know how they did all that in 1902 without latex. Some of the exercises of the book are ancient problems from Cambridge exams.

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I will try to find a copy. Thanks. –  Austin Apr 14 '13 at 0:59
    
You can find them even in amazon, if you check in the section 'other sellers'. Sometimes they specify the year of the book and be sure is in good condition. –  Ambesh Apr 14 '13 at 8:52

Many old books can be found in pdf form online for free. I got Hardy's A Course in Pure Mathematics from here:

http://www.gutenberg.org/wiki/Mathematics_%28Bookshelf%29

Just scrolling through the authors is good in itself

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+1: Or the excellent archive.org. –  Raymond Manzoni Apr 14 '13 at 7:59
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Awesome link. Thanks. –  Austin Apr 14 '13 at 12:25

Euclid's Elements, written about 2300 years ago, is certainly one of the most important textbooks of all time. It has been continuously in print since at least 1482.

It is very readable, and the subject matter is still current.

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I love my Oliver Byrne edition of Euclid. Originally from 1843, the author promoted a visual teaching method using colours instead of the conventional letters & symbols for angles, which made it very unique for its time. The reprinted edition can be had for around $40 on Amazon and comes nicely boxed & bound. Even for non-mathematicians the colourful pages & classic typography are just beautiful to look through. –  Andrew Vit Apr 14 '13 at 8:44
    
I will be looking for this. –  Austin Apr 14 '13 at 12:25
    
Got a copy as described, love it, thanks for the reference. –  Greg Hill Jun 1 '13 at 18:38

And then of course you could well find copies of G. H. Hardy's wonderful Pure Mathematics (first published in 1908), the first real maths book for generations of students, and still well worth looking at.

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Just found one on ebay, very expensive. But I will be keeping my eye out for this. Thanks. –  Austin Apr 14 '13 at 12:41
    
Try abebooks.com for second-hard books: abebooks.com/servlet/… –  Peter Smith Apr 14 '13 at 13:00

I think E.C. Titchmarsh's books (also Classical analysis) may not be much further behind.

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There is a Dover edition of A Source-Book of Mathematics with translations of classic works like the Treviso Arithmetick from the 15th century.

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What about Disquisitiones Arithmeticæ? There is at least one modern translation into English.

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For a book that is not going to teach you any new math, but will give you a window into how a mathematical personality might think or act, I would recommend I Want to be a Mathematician by Paul Halmos. Quite a fun read, full of all of the joys and nuisances of being a high class working mathematician.

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I Second Euclid's Elements (Green Lion Edition is nice; Byrne's edition mentioned above is beautiful.

There's also a Dover edition of The Works of Archimedes.

Green Lion also has a nice publication of Apollonius' Conics that is more accessible than Dover's edition of Archimedes.

Although I have far to go in both books, I also second Hardy's Course in Pure Mathematics, as well as Inequalities.

I love Geometry and the Imagination by Hilbert which is mentioned above. It's not too hard to find the German Anshauliche Geometrie as well as the English edition.

And, lastly, Casey's A Sequel to the Elements of Euclid (late 19th century). U. Michigan Libraries has a nice reprint.

Some books on my wishlist would be (as above) Cauchy's Cours d'Analyse, original works of Möbius, Omar Khayyam's early mathematical explorations, Pappus, Ptolemy ...

I have looked for some of the books on my wishlist, but have sofar located only prohibitively expensive copies.

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I guess if $D$ is supposed to be the center of the circle the claim $AB\cdot BC = AD^2 - BD^2$ is correct. A proof is $AB \cdot BC$ is the power of the point $B$, so is $(AD+BD)\cdot (AD-BD) = AD^2 - BD^2$. –  Peter Patzt Apr 22 at 16:42
    
@PeterPatzt It looks like I stand corrected --- I appreciate your pointing that out. I will take another look at the presentation in Byrne. –  Greg Hill Apr 26 at 23:03

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