... 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 ... explaining why this is so requires a new, and moreabstract, concept of algebra (see Chapter 19).J. Stillwell, Mathematics and Its History, Undergraduate Texts in Mathematics, 87DOI 10.1007/978-1-4419-6053-56,c ... late for them to be influential. Arabic mathematics developed at the right time and place to absorb both the geometry of theWest and the algebra of the East and to recognize algebra as a separate...