Bonola's Non-Euclidean Geometry is an elementary historical and critical study of the development of that subject. Based upon his article inENRiQUEs' collection of Monographs on Questions of Elementary Geometry^, in its final form it still retains its elementary character, and only in the last chapter is a knowledge of more advanced mathematics required. Recent changes in the teaching of Elementary Geometry in England and America have made it more then ever necessary that those who are engaged in the training of the teachers should be able to tell them something of the growth of that science; of the hypothesis on which it is built; more especially of that hypotheses on which rests Euclid's theory of parallels; of the long discussion to which that theory was subjected; and of the final discovery of the logical possibility of the different Non-Euclidean Geometries. – From translator’s preface.
A work on non-Euclidean geometry, the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system, characterized by a non-vanishing Riemann curvature tensor.