“We have noticed (‘Nature,’ vol. xxiv., p. 52; vol. xxvi., p. 219) two previous editions of this book, and are glad to find that our favourable opinion of it has been so convincingly indorsed by teachers and students in general. The novelty of this edition is a Supplement of Additional Propositions and Exercises. This contains an elegant mode of obtaining the circle tangential to three given circles by the methods of false positions, constructions for a quadrilateral, and a full account—for the first time in a text-book—of the Brocard, triplicate ratio, and (what the author proposes to call) the cosine circles. Dr. Casey has collected together very many properties of these circles, and, as usual with him, has added several beautiful results of his own. He has done excellent service in introducing the circles to the notice of English students.…We only need say we hope that this edition may meet with as much acceptance as its predecessors, it deserves greater acceptance.” The \Mathematical Magazine,” Erie, Pennsylvania. “Dr. Casey, an eminent Professor of the Higher Mathematics and Mathematical Physics in the Catholic University of Ireland, has just brought out a second edition of his unique ‘Sequel to the First Six Books of Euclid,’ in which he has contrived to arrange and to pack more geometrical gems than have appeared in any single text-book since the days of the self-taught Thomas Simpson. ‘The principles of Modern Geometry contained in the work are, in the present state of Science, indispensable in Pure and Applied Mathematics, and in Mathematical Physics; and it is important that the student should become early acquainted with them.’ “Eleven of the sixteen sections into which the work is divided exhibit most excellent specimens of geometrical reasoning and research. These will be found to furnish very neat models for systematic methods of study. The other five sections contain 261 choice problems for solution. Here the earnest student will find all that he needs to bring himself abreast with the amazing developments that are being made almost daily in the vast regions of Pure and Applied Geometry. On pp. 152 and 153 there is an elegant solution of the celebrated Malfatti’s Problem. “As our space is limited, we earnestly advise every lover of the ‘Bright Seraphic Truth’ and every friend of the ‘Mathematical Magazine’ to procure this invaluable book without delay.” The \Schoolmaster.”