To Mathematical Students
Out of all the mathematical writings of Thomas Hariot, not without good reason has this work on Analysis been published first. For all his remaining works, remarkable for their manifold novelties of discovery, are written in precisely the same logical style, hitherto seldom seen, as is this treatise; whch is entirely composed of all manner of specimens of brilliant reasoning. And this was done with valid reason, so that a preliminary treatise, besides its own inestimable value, might well serve as a necessary preparation or introduction to Hariot's remaining works, the publication of which is now under serious consideration. Of this accessory use of the treatise we have thought it worth while to remind mathematical students in these brief remarks.[1]
The contents followed in Vieta's footsteps, with improvements in notation and some simplification in technique. But the chief thing in the book, and one of great importance, was the bringing over to one side all the terms of an equation and equating them to zero. It was a simple and yet a real step ahead. As Whitehead says, it started the study of algebraic forms. The resolution of an equation of the nth degree into n simple factors gave immediate rise to the fundamental theorem of algebra. And though there is the real temptation to read into the terse statements what may not have been thought out, the warning against Tennyson's expression
I thowt 'a said whot 'a owt to 'a said
may be borne in mind, and yet much claimed for Hariot.
How much more the painful lips might have said, or might have been recorded if the "serious consideration" above mentioned had matured, is of course difficult to know. It would take very careful work to read, digest, and judge the eight large volumes of Hariot's manuscripts lying untouched in the British Museum. There are more, apparently, at Petworth. They consist of fragmentary calculations, with occasional connected notes on a diversity of subjects—on astronomy, physics, fortifications, shipbuilding, and all the branches then known of mathematics. And yet even a cursory glance will show some gleams of gold. There is a well-formed analytical geometry, with rectangular coordinates and a recognition of the equivalence of equations and curves. There are notes on combinations and the tables of binomial coefficients worked out in both the forms we now call "Pascal's triangle" and "Fermats square." And there is one page, otherwise blank on which appears
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1 1
2 10
3 11
4 100
5 101
6 110
7 111
7 1000
- ↑ "Artis Analyticae Praxis" (London, 1631) p. 180.
