By Lumer G.
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The Greek text is more elliptic than my translation. Here the lines mentioned do share a point, but they are not at right angles to each other. , the rectangle contained by ΚΒ, ΑΝ – lines which do not share a point. This class is not exhausted by examples such as the above (so-called ‘geometrical algebra’). g. in Aristarchus’ On Sizes and Distances, owes nothing to the diagram. It should be noted that even ‘geometrical algebra’ is still ‘geometrical’: the text does not speak about multiplications, but about rectangles.
E; and, of course, Rep. c. g. APr. b; Meteor. b; Cat. b; Metaph. a, a; SE a. Mem. . Knorr () –. g. –. . ), is especially curious: it appears that Hero set out to prove various results with as few lines as possible, preferably with none at all, but with a single line if the complete avoidance of lines was impossible (one is reminded of children’s puzzles – ‘by moving one match only, the train changes into a balloon’). Hero’s practice is comparable to the way a modern mathematician would be interested in proving the result X on the basis of fewer axioms than his predecessors.
E. continuous configurations of lines. g. ), the problem of transmission becomes acute. Given our current level of knowledge on the transmission of diagrams, nothing can be said on such diagrams. g.
Aigebres de fonctions et espaces de Hardy by Lumer G.