Comparing the first mathematics textbook with a modern one: How some famous geometry theorems have been illustrated over time Salvatore Enrico Indiogine & Gerald Kulm June 30, 2009 Contents 1 Introduction An important component of the instructional value of a textbook is its illustrations. A distinguishing feature of modern mathematics textbooks is the abundance of their illustrations. 1 However, illustrations in a textbook can be relevant or irrelevant. In geometry textbooks relevant illustrations are closely related to the explanation of a mathematical concept or the method of proof adopted by the author. Hence, illustrations in mathematics textbooks should not be an afterthought, but rather an integral part of the text. The production of proper mathematical illustrations is not a simple task. 2 Santos 3 found that even though the illustration in a mathematics test was just cosmetic, almost half of the students used it nonetheless. Bauman 4 noted figures in a science textbook that were inconsistent with the text of the book. Parzysz 5 described geometrical illustrations that lead to misconceptions because they contained many implicit conventions. 1 Santos-Bernard, 1996, 251 2 Lo Bello, 2003b, 236 3 Santos-Bernard, 1996, 256 4 Bauman, 1992 5 Parzysz, 1991 1