This list is by no means complete, for Pólya had many other quotes which he treasured. It is, perhaps, worth mentioning, that he was especially fond of the final two quote by Condorcet.
Pólya's favourite quotes
Proclus: In the discovery of lemmas the best aid is a mental aptitude for it.
Newton: Examples are better than precepts for learning the arts.
Leibniz: Thus I stick to the idea that a plain man having the advantage of these helpful precepts and of some practice could surpass the very best, just as a child can draw better lines with a ruler than the greatest master without such artificial aid.
Leibniz: The helps offered to improve the mind consist in certain ways of thinking which facilitate thinking.
Bolzano: At each step that we take it should be comprehensible to the reader why we take that step.
Maxwell: It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state.
Descartes: Good logic can be the worst enemy of good teaching.
Plato: The ideas should be born in the student's mind and the teacher should only act as midwife.
Condorcet: Euler preferred the instruction of his pupils to the little satisfaction of amazing them. He would have thought not to do enough for science if he should have failed to add to the discoveries with which he enriched science the candid exposition of the ideas which led him to those discoveries.
Condorcet: Mathematics is the science that yields the best opportunity to observe the working of the mind. Its study is the best training of our abilities as it develops both the power and the precision of our thinking. Mathematics is valuable on account of the number and variety of its applications. And it is equally valuable in another respect: By cultivating it, we may acquire the habit of a method of reasoning which can be applied afterwards to this study of any subject and can guide us in life's great and little problems.