6. Do not attempt to demonstrate anything that is so evident in itself that there is nothing more simple by which to prove it.
7. Prove whatever is in the least obscure, using in the demonstration only axioms that are perfectly evident in themselves, or propositions already demonstrated or allowed.
8. In case of any uncertainty arising from a term employed, always substitute mentally the definition for the term itself.
Bibliography. Heath, Euclid, as cited; Frankland, The First Book of Euclid, as cited; Smith, Teaching of Elementary Mathematics, p. 257, New York, 1900; Young, Teaching of Mathematics, p. 189, New York, 1907; Veblen, On Definitions, in the Monist, 1903, p. 303.
CHAPTER XIII
HOW TO ATTACK THE EXERCISES
The old geometry, say of a century ago, usually consisted, as has been stated, of a series of theorems fully proved and of problems fully solved. During the nineteenth century exercises were gradually introduced, thus developing geometry from a science in which one learned by seeing things done, into one in which he gained power by actually doing things. Of the nature of these exercises ("originals," "riders"), and of their gradual change in the past few years, mention has been made in Chapter VII. It now remains to consider the methods of attacking these exercises.
It is evident that there is no single method, and this is a fortunate fact, since if it were not so, the attack would be too mechanical to be interesting. There is no one rule for solving every problem nor even for seeing how to begin. On the other hand, a pupil is saved some time by having his attention called to a few rather definite lines of attack, and he will undoubtedly fare the better by not wasting his energies over attempts that are in advance doomed to failure.