i28 
2. The form (A), according to Wallis, was first introduced 
by Harriot, a distinguished English mathematician at 
Oxford in the middle of the 16th century. He was the 
friend and tutor of Sir Walter Kaleigh. 
In consequence of the* very general application of this 
method of forming algebraical equations of all dimensions, 
Wallis speaks of it in terms of high commendation. The 
following opinions are gathered from his Algebra, pub- 
lished in 1685 : — 
“ Wherein lyes the main mystery of Algebra.” (Wallis* 
Algebra, page 128.) 
“ In this method of producing higher equations Harriot 
is followed by Des Cartes.” (Wallis’ Algebra, page 140.) 
“ Which is the great key that opens the most abstruce 
mysteries in Algebra.” (Wallis’ Algebra, page 199.) 
I can hardly expect any new improvement of pure 
Algebra, other than what is built on the foundation laid by 
Harriot, and assumed by Des Cartes.” (Wallis’ Algebra, 
page 213.) 
This is certainly high praise in favour of Harriot and his 
discoveries in Algebra by the foremost thinker in specula- 
tive mathematics before the Newtonian era. 
It may be, however, fair to mention that both the French 
and Italian Algebraists disagree with the above view of the 
subject, and accuse Wallis of possessing an unfair partiality 
for the inventions of his countryman Harriot. 
The truth seems to me to be this. The revival of learning 
in Europe in the 15th century no doubt had considerable 
power in stimulating independent thinkers in the fields of 
pure and mixed science. It is, therefore, only natural to 
suppose that publication should disclose some remarkable 
coincidences in the results of such independent investiga- 
tions. 
This conclusion is in strict accordance with the experience 
of our own times* Here, then, is the solution of the con* 
