In your schooldays most of you who read this book made acquaintance

with the noble building of Euclid's geometry, and you remember --

perhaps with more respect than love -- the magnificent structure, on

the lofty staircase of which you were chased about for uncounted hours

by conscientious teachers. By reason of our past experience, you would

certainly regard everyone with disdain who should pronounce even the

most out-of-the-way proposition of this science to be untrue. But

perhaps this feeling of proud certainty would leave you immediately if

some one were to ask you: "What, then, do you mean by the assertion

that these propositions are true?" Let us proceed to give this

question a little consideration.