> Just a thought.
>
> Could Veronese been a link? I recall that in Note IV of the appendix to
> his 1891 Fondamenti di geometria a piu dimensioni e a piu specie di unita
> rettilinee, espositi in forma elementare, Veronese comments on the work of
> Bettazzi. The Fondamenti was translated into German in 1894.
>
Bettazzi is also mentioned by Veronese in the introduction to his
*Fondamenti* (p xxvi; also same page number in Schepp's translation into
German). The note concerns the status of "actual" infinitely large and
infinitely small numbers. Veronese points to something Bettazzi wrote but
didn't follow up which showed, Veronese indicates, that Bettazzi had an
idea along the lines of own on this matter.
It probably isn't relevant to the original question, but as I noted in the
first paragraph of my article *Veronese's Non-archimedean linear
continuum*, published in the book *Real Numbers, Generalizations of the
Reals, and Theories of Continua* edited by P. Ehrlich (1994), Hans Hahn in
an article on non-archimedean systems of quantities notes that Bettazzi
handled some questions of this kind in his *Teoria delle grandezza* (1890),
and Hahn also cites Vernonese's *Fondamenti ... ". Hahn expresses an
opinion that the study of such systems goes back to Paul du Bois-Reymond
(work published between 1870 and 1882), and Otto Stolz (appeared from 1879
to 1896). To which I added the comment that there was some study of such
systems much earlier, e.g. involving so-called horn angles in ancient
Greece. And since the Archimedean property was known to and stated
explicitly by various classical Greek mathematicians, presumably they saw
a need for it, which may be taken to imply that they had some concern for
quantities which didn't behave according to that property.
Gordon Fisher gfisher@shentel.net