Euclid's Elements Of Geometry - Books I. Ii. Iii. Iv., Vi And Portions Of Books V. And Xi. - By A. E. Layng - PREFACE - In this edition of those parts of Euclids Elements most commonly read in schools and required for examinations, no fundamental changes have been made, the axioms and enunciations remaining the same as in Simsons edition. Minor changes have, however, been frequently introduced, when it appeared that, either by the insertion of an additional step or reference, the path of the beginner could be made smoother, or conciseness and clearness gained by the removal of redundant and antiquated phrases. In some cases, moreover, Euclids proofs have been displaced in favour of shorter ones based on his................