“Professor Casey’s aim has been to collect within reasonable compass all those propositions of Modern Geometry to which reference is often made, but which are as yet embodied nowhere.…We can unreservedly give the highest praise to the matter of the book. In most cases the proofs are extraordinarily neat.…The notes to the Sixth Book are the most satisfactory. Feuerbach’s Theorem (the nine-points circle touches inscribed and escribed circles) is favoured with two or three proofs, all of which are elegant. Dr. Hart’s extension of it is extremely well proved.…We shall have given sufficient commendation to the book when we say, that the proofs of these (Malfatti’s Problem, and Miquel’s Theorem), and equally complex problems, which we used to shudder to attack, even by the powerful weapons of analysis, are easily and triumphantly accomplished by Pure Geometry.
“After showing what great results this book has accomplished in the minimum of space, it is almost superfluous to say more. Our author is almost alone in the field, and for the present need scarcely fear rivals.”
The \Academy.”
“Dr. Casey is an accomplished geometer, and this little book is worthy of his reputation. It is well adapted for use in the higher forms of our schools. It is a good introduction to the larger works of Chasles, Salmon, and Townsend. It contains both a text and numerous examples.”
The \Journal of Education.”
“Dr. Casey’s ‘Sequel to Euclid’ will be found a most valuable work to any student who has thoroughly mastered Euclid, and imbibed a real taste for geometrical reasoning.…The higher methods of pure geometrical demonstration, which form by far the larger and more important portion, are admirable; the propositions are for the most part extremely well given, and will amply repay a careful perusal to advanced students.”
PREFACE.
Frequent applications having been made to Dr. Casey requesting him to publish a ”Key” containing the Solutions of the Exercises in his ”Elements of Euclid,” but his professorial and other duties scarcely leaving him any time to devote to it, I undertook, under his direction, the task of preparing one. Every Solution was examined and approved of by him before writing it for publication, so that the work may be regarded as virtually his.
The Exercises are a joint selection made by him and the late lamented Professor Townsend, s.f.t.c.d., and form one of the finest collections ever published.
JOSEPH B. CASEY.