... v2v, 2u,u2+ v2v and u2− w2w, 2u,u2+ w2wfor some rational v and w. Putting the two together (Figure 5.2) gives an ar-bitrary rational triangle, and its sides and altitude are of ... passed, and the wedding had to be called off. The hapless L¯ıl¯avat¯ı never married, and now she is remembered only through the book that bears her name.Preface to the Second Edition This edition ... are three new chapters, on Chinese and Indian number theory,on hypercomplex numbers, and on algebraic number theory. Thesefill some gaps in the first edition and give more insight into laterdevelopments.•...