Non Euclidean Geometry a Critical And Historical Study of Its Development
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 i
...n 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.
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