C8 9 3 
III. On the necessary Tmth of certain Conclusions obtained by 
Means of imaginary Quantities. By Robert Woodhouse, 
A. M. Fellow ' of Caius College. Communicated by the Rev. 
S. Vince, A. M. Plumian Professor of Astronomy in the Uni- 
versity of Cambridge . 
Read January 8, 1801. 
Amongst the various objections urged against mathematical 
science, few oppose its evidence and logical accuracy; and, 
since its demonstrations have been acknowledged to proceed by 
a series of the strictest inferences, from the most evident prin- 
ciples, the study of abstract science has generally been deemed 
peculiarly proper to habituate the mind to just reasoning. But 
of late, the dissentions of mathematicians have subjected to 
doubt, 'even this “ collateral and intervenient use;" for, not 
only has the mode of applying analysis to physical objects 
been controverted, but certain parts of the pure mathematics 
have become the subject of dispute. Much has been heard of 
the science of quantity being vitiated with jargon, absurdity, 
and mystery, and perplexed with paradox and contradiction ; so 
that, from the very complaints of the patrons of mathematics, 
its opponents may derive their most potent arguments, and 
abundant matter for triumphant invective. 
The introduction of impossible quantities, is assigned as a 
great and primary cause of the evils under which mathematical 
science labours. During the operation of these quantities, 
N 
MDCCCI,. 
