1. An Introductory Account of Certain Modern Ideas and Methods in Plane Analytic Geometry (1894), by Charlotte Angas Scott.
Bull. Amer. Math. Soc. 2 (1896), 265-271.
A minor excellence of this book, for which many readers will feel truly grateful, is the fact that it is written in the English of English speaking and writing people. ... The book modestly designated by the author as an "introduction" and certainly well adapted to the needs of the learner, is in fact a compact scholarly work on the more accessible principles and methods of modern analytical geometry. It exhibits to a marked degree that genial breadth of treatment and conciseness which are associated only with mature scholarship and extensive and accurate information. Everything fits naturally in place, nothing is cramped or forced out of its natural relations. In the limited space of less than three hundred pages the great ideas of geometry, including the doctrine of coordinates, projection and dualism, correspondence, and the absolute, are clearly and skillfully developed, and illustrated by application to an ample list of well-chosen examples, a sufficient number of the latter being reserved as an exercise for the reader. We notice with pleasure that the book is entirely free from the criticism, so often and so properly urged against many English mathematical works, that their authors exhibit no adequate conception of the distinction between a general principle and a particular example. Miss Scott is not only keenly alive to this distinction; she is also perfectly aware of the importance of choosing methods adapted to the subject, which is here primarily geometry, not algebra. ... At the beginning the justification of the line as an element, co-important with the point, of the plane is well stated. The infinite and imaginary elements - line at infinity, circular points, isotropic lines, etc., are skillfully managed. The chapter on the Absolute is an admirably lucid and elementary exposition. The author aims throughout at generality and elasticity of treatment. Her success in this respect is very pronounced, and is in fact one of the most acceptable features of the book. ... [We] trust that Miss Scott's very successful present venture into this field will not be her last. ... The book will be found to gain continually in interest on repeated reading, and this is due especially to its eminently suggestive character. The author succeeds admirably in conveying to the reader, if he be fit, an accurate knowledge and command of general principles. We know of no introductory work which is better adapted in this particular for the use of those who desire not merely to learn but also to master geometry.
Bull. Amer. Math. Soc. 32 (1926), 295.
Perhaps the most noteworthy fact about this second edition of Miss Scott's book is that no change has been made in the text. It differs from the first edition (1894) only in the insertion of a short "Author's Note" and five pages of "Notes and Corrections," - in which "a few misprints and misleading statements have been corrected; a few proofs and discussions have been simplified: one new section has been added."
2.2. Review by: Virgil Snyder.
Amer. Math. Monthly 32 (10) (1925), 513.
The first edition of this book was published in 1894 and immediately met with hearty approval, as it furnished about the only account in English of many of the "modern ideas and methods in plane analytical geometry." But the book has long been out of print, and of the recent works which have appeared in the meantime, none in English occupies itself with just this field. In this interval some of the fundamental concepts have undergone extensive changes, and now some of the aspects are rather old-fashioned, but the student of geometry will still find all of it profitable reading, and some of the chapters are as useful today as they ever were. ... We welcome the reappearance of this instructive and interesting volume.
The Mathematical Gazette 4 (67) (1907), 163-164.
This introduction to Analytical Geometry appears at a most opportune moment, when there is a general desire to see the dead bones of Mathematics come to life again in our schools and higher places of education. It differs as much from the ordinary elementary textbook as light from darkness; and we sincerely hope that it will become generally adopted. For the success of such a book there are two requisites: first, that it should become generally known to teachers, and second, that examining boards should make it a rule to accept only questions on what is important, and reject questions on what is unimportant. For years we have suffered from the evils of over-elaboration, although we now recognize that it is an evil, and are making a determined and successful effort to introduce a better system. The reader of this book will not waste his time over details and unimportant things, but will find every page, with the exception of the last chapter, a direct help to future progress. Its distinctive feature is the systematic use of line (tangential) co-ordinates concurrently with point coordinates. This, in our opinion, simply presents the subject in its proper light, and gives it completeness; it neither makes it easier nor more difficult than it was before. Conics are specially adapted for treatment by line co-ordinates; and they suffice to bring out the fact that to every property concerning points and lines there is a corresponding property concerning lines and points. "Not to be too radical, however," the author has "left the balance of power with point co-ordinates." ... the average student can easily master [the] contents (excepting the last chapter), and that after doing so he will have a vivid idea of the elementary properties of conics, including those of diameters, tangents, asymptotes, poles and polars, and the circular points; and will have learnt to change the axes with ease, and to trace the conic from its equation. The last chapter deals with miscellaneous examples; these should certainly not be taken in the lump. Geometrical methods are used instead of analytical whenever they have the advantage in clearness and simplicity.