"All who intend to study these pages would do well to read attentively the following directions and observations; for the subject upon which they are written is considered one really difficult. Why it should be considered so, will readily be conceived when such men as Legendre, Leslie, [Thomas] Keith, Bonnycastle, Austin, Brewster, Young, and in fact every one who has attempted to treat the doctrine of Geometrical Proportion on any plan differing from Euclid's, have committed errors, overlooked mistakes, retrenched the generality of Euclid's reasonings, fallen into logical absurdities, or confined the general application of a subject which pervades a whole course of mathematics; while there is not one mistake, oversight, or logical objection in the whole of Euclid's Fifth Book. "In fact, Euclid's Fifth Book is a master-piece of human reasoning.""