>
> I hope it isn't necessary to point out in this newsgroup that Euclidean
> geometry was a widely taught part of mathematics in the 19th century;
> the modern fashion among many people of denigrating anything except what's
> done algebraically hadn't come in in Faraday's time.
>
> John Harper, School of Mathematical and Computing Sciences,
> Victoria University, Wellington, New Zealand
> e-mail john.harper@vuw.ac.nz phone (+64)(4)463 5341 fax (+64)(4)463 5045
> (I'm currently in UK but please continue to use the above e-mail address)
How much of geometry was in fact taught in (say) the mid 19th century
through classical, synthetic methods?
Over the past week I have started to work my way through Salmon's
'Conic Sections'. I get the impression that this well-known textbook
would have been pitched at students in the earlier years of a
university mathematics course. Reading it, I conclude that Salmon
takes it for granted that students are familiar with Euclid's elements.
He opens the treatise with a discussion of the method of coordinates,
developed ab initio, and using oblique axes in diagrams etc., unless
the result under consideration requires rectangular axes. He discusses
in detail such basic topics as the equation for a straight line. Through
out the treatise he makes occasional reference to 'O'Brien's Coordinate
Geometry' for elementary results, but very little prior knowledge seems
to be assumed. (Incidentally, who was O'Brien?)
The emphasis in Salmon's 'Conic Sections' is very much on algebraic
methods from the beginning. And this leads me to ask whether 19th
century students of mathematics were taught much geometry from a
classical synthetic approach, once they had worked their way through
Euclid. Or did they progress fairly directly from Euclid to
'analytic geometry' or 'coordinate geometry', effectively abandoning
the classical approach?
(In passing I note, in relation to that infamous question 'Why do we
use m for slope?', that Salmon gives the equation of the line in
Cartesian coordinates as 'y = mx + b'. Would Salmon be continuing
a tradition already established in the textbooks of his day? Would
it be plausible to suppose that Salmon's textbook would have influenced
those American textbooks identified by Fred Rickey in earlier postings
on another list?)
David Wilkins
dwilkins@maths.tcd.ie