So Far as it Relates to Commensurable Magnitudes, with Notes
Preface
The theory of Incommensurable Magnitudes, without which the whole subject of Geometrical Proportion is so incomplete as to be, from a logical point of view, utterly valueless, is nevertheless omitted, as far as possible, from the following treatise.
My reasons for this omission are two: first, that I believe it to be much too abstruse a subject for the ordinary Pass Examination; secondly, that it is not required in it. The exemption is a most necessary one, though the effect of it is to reduce the Vth and VIth Books, in the form in which they are now learned and accepted in the Schools, to a logical absurdity.
Whether it would not be preferable to substitute for these Books an equivalent quantity of Algebra, perhaps as far as Permutations and Combinations, is a question I do not here enter on. To supply, in its shortest form, that knowledge of the subject which is at present required and accepted in the Schools, is my object in putting forth this treatise. I hope that it may not be long wanted.