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The most influential mathematics textbook of ancient times is easily named, for the Elements of Euclid has set the pattern in elementary geometry ever since. The most effective textbook of the medieval age is less easily designated; but a good case can be made out for the Al-jabr of Al-Khwarizmi, from which algebra arose and took its name. Is it possible to indicate a modern textbook of comparable influence and prestige? Some would mention the Géométrie of Descartes or the Principia of Newton or the Disquisitiones of Gauss; but in pedagogical significance these classics fell short of a work by Euler titled Introductio in analysin infinitorum.
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Carl B. Boyer on Euler's Introduction to the Analysis of the Infinite in "The Foremost Textbook of Modern Times" (1950)

 

Leonhard Euler

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MacUser: Which person do you most admire?
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Jef Raskin

 

Our textbook is the Bible. Besides a title, many books also have a sub-title. We could write as a subtitle on the front of the Bible: "A Textbook for Becoming Completely Happy".

 

Elias Aslaksen

 

I tried to persuade him that he was too logical, a concept which he could neither accept nor understand...I do not recall meeting anyone else with a mind that had such a power of acquiring knowledge. At one stage when Enoch was detailed to become an expert on town and country planning, he acquired the standard textbook and read it from page to page, as an ordinary mortal would read a novel. Within a matter of weeks he had fully grasped both the principles of the problem and the details of the legal situation. Within a matter of a few months he was writing to the author of the textbook, pointing out the errors that he had made.

 

Enoch Powell

 

Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i.e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.

 

Hans Reichenbach

 

There is a traditional story about Newton: as a young student, he began the study of geometry, as was usual in his time, with the reading of the Elements of Euclid. He read the theorems, saw that they were true, and omitted the proofs. He wondered why anybody should take pains to prove things so evident. Many years later, however, he changed his opinion and praised Euclid. The story may be authentic or not ...

 

Isaac Newton