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By Brehm U., Kuhnel W.

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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.

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15-vertex triangulations of an 8-manifold by Brehm U., Kuhnel W.

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