Numbers, Magnitudes, Ratios, and Proportions in Euclid'sElements:How Did He Handle Them?: Volume 23, Number 4 (1996), pages 355–375

✍ Scribed by Ivor Grattan-Guinness

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 64 KB
• Volume: 24
• Category: Article
• ISSN: 0315-0860
• DOI: 10.1006/hmat.1997.2155

✦ Synopsis

In the passage beginning on page 372, line 26, and ending on page 373, line 3, quotation marks were inadvertently omitted. The passage-and paragraph following-should read as follows:

Second, in his reply to Unguru, van der Waerden clearly explains that he uses the word ''algebra'' ''for expressions like (a ϩ b) 2 , and how to solve linear and quadratic equations'' [40, 200]. van der Waerden then takes (2.prop.1), in Heath's translation (see Fig. 3): ''If there be two straight lines, and one of them be cut into any number of segments, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments,'' and comments: ''Geometrically, this theorem just means that every rectangle can be cut into rectangles by lines parallel to one of the sides. This is evident: everyone sees it by just looking at the diagram. Within the framework of geometry there is no need for such a theorem: Euclid never makes use of it in his first four books.'' But Euclid's text and van der Waerden's version say different things: Euclid builds up the full rectangle R from its components to form rectangles and state a property of them [30,[54][55][56][57][58][59][60]; van der Waerden breaks it up into those components from R. Of course the theorem is very simple; hence its location at the head of Book 2. But the construction embodied here (recall from Section 2.4 that he often conflated them with the theorems themselves) underlies or at least relates to many theorems from Book 2 onwards, starting with (2.prop.2), long before Book 5 is reached.

Historia Mathematica regrets the error. This erratum is Article No. HM972155.