book recommendation for Euclidean geometry without coordinates or any modern math (math that has been discovered after the 16th century.)

Question

I want to learn Euclidean geometry But I always find books about it that use coordinates and even some linear algebra and other stuff that was discovered thousands of years after geometry but I want to learn how many ideas of geometry has been discovered and evolved for thousands of years without any modern techniques like analytical geometry or linear algebra or integration ...etc.

I also want 3 types of books

1-and the more important books that cover many of theorems of Euclid geometry before Desecrates without coordinates or any modern math like How Archimedes found out the volume of solids like sphere and area of parabolas without integration etc.. .

2-books that are more focus on problem solving and hard and practise questions like IMO training books

3- books that cover more advanced topics in Euclidean geometry after Desecrates that use modern methods.

Answer 1

I'm fond of Lachlan, Modern Pure Geometry, (1893).

Lots more where that came from - geometry textbooks from the period 1825-1925 - most of them on archive.org. Some are mentioned in Lachlan's introduction, so you can search for them in archive.org.

For something completely different, take a look at the opinionated and idiosyncratic Coolidge, A History of the Conic Sections and Quadric Surfaces (1945). Since you ask about Archimedes, the book mentions J.I. Heath, The Works Of Archimedes (1817) which contains translations of Archimedes' works On The Sphere and Cylinder and Quadrature of the Parabola. See also T.L. Heath's 1896 translation of Apollonius, Conic Sections, pgs lviii-lxvii

Answer 2

The book series you are looking for is Kiselev's Geometry. These are small yet beautifully bound hardcover books that cover planimetry and stereometry.

Kiselev's page can be found on Amazonwhich contains both books. I do not recommend buying them there because their price is way off the mark. I have both copies and I don't believe I paid more than $\$30$ for each book. In fact, I may have paid less.

Answer 3

Perhaps you can have a look to the book of Akopyan. It is free on his webpage, but you can also buy it via Amazon.. This book contains no coordinates, but no text neither. You have plenty of theorems explained by a picture, and you have to prove it by yourself..

https://users.mccme.ru/akopyan/papers/EnGeoFigures.pdf

Answer 4

If you want to study Euclidean geometry, why not get hold of Euclid’s Elements? Old and still good, inexpensive and easy to find. He doesn’t tell you how to find things out, but rather gives you an orderly, step-by-step, and dramatic demonstration of results.

Answer 5

I guess I'll recommend the book reviewed in this video https://youtu.be/1B2BtvWsz-M