1811.] 
he said, would bave known how to make 
' performance. 
a republic without church or king, if such 
was the idea of a perfect commonwealth 
formed by their wisest man; but the 
people could never know how to realize 
even that which they intended to obtain. 
Fransham was willingly busied in nu- 
merical and mathematical computation. 
He had calculated that the average pay 
of his pupils was three-pence an hour; 
and the average income of his life eight 
shillings a week ; yet with these narrow 
means, So severe was his frugality, that he 
progressively bettered his condition. He 
practised and exacted a punctilious 
pecuniary probity, and could not bear 
that the loan of a penny should go un- 
paid, 
** As a mathematician * he was emi- 
nent rather for the solidity than the ex- 
tent of his knowledge. His love of ac- 
€uracy rendered him an enthusiastic ad- 
mirer of the ancient mathematicians, or, 
perhaps more properly, his early atten- 
tion to these writers rendered him accu- 
rate. He had a higher veneration for 
Euclid than for Newton, and preferred 
the Elements of Geometry of the former, 
to the Principia of the latter. Indeed 
he never could understand thecelebrated 
doctine of Fluxions, and bas been heard 
to pronounce the Analist of bishop Berke- 
ley, a work written in confutation of 
that doctrine, to be one of the finest 
specimens of reasoning among the pro- 
ductions of the moderns, 
“ The authors whom he most esteem- 
ed on mathematics were, Euclid, Apol- 
lonius, and Archimedes; of the former 
of these he preferred the editions of 
Clavius, and Dr. Simson; and of the 
latter, that of Dr. Barrow, probably be- 
cause he had never seen the Oxford edi- 
tion, 
“ Among the modern writers on these 
subjects, one only escaped his censure, 
this was Dr. Hamilton, dean of Armagh, 
whose treatise on Conic Sections he 
considered as a truly classical and elegant 
To this work he has been 
heard to say, that he devoted two whole 
* Had the excellent letter, addressed on 
Fransham’s death to My. Rigby, of Nor- 
‘wich, by Mr, William Saint, (late one of 
the mathematical masters at Woolwich Aca- 
demy) been made public, the foregoing me- 
moir would in a great degree have been need- 
Jess. For the permivsion thence to copy his 
fearned anid satisfactory appretiation of Fran- 
" ghaxy’s mathematical aconirements, my grati- 
Gude will be partakon by your renders, 
‘ a , 
© 
« 
Memoir of the late John Fransham. 
s47 
years, and that he derived the most ex- 
quisite pleasure from its. distinguished 
aceuracy and simplicity. It is, however, 
to be regretted that he had never seer 
the quarto work of Dr. Robertson, of 
Oxford, on the same subject, as he would 
there have met with a history of the 
Conic Sections written in elegant latin, 
which to a man of his peculiar attain- 
-™ments would have afforded exquisite de- 
light. 
“There is one amid his manuseript 
volumes, which he seems to have consj-= 
dered as a complete Manual for the 
young mathematician. It contains the 
first principles of algebra, some of the 
leading properties of numbers, some cu- 
rious questions relative to the applicas 
tion of algebra to geometry, a smal} 
table of square and cube roots, with a 
great variety of miscellaneous problems. 
“ Ofalgebra, however, or the analyti¢ 
art, he entertained a very low opinion, 
Iie was well satisfied with the grounds 
and methods of operation employed by 
algebraists fur the solution of simple and 
quadratic equations, but the resolution 
of cubics by Cardan’s rule; by Sir Isaage 
Newton’s method of divisors, or by the 
different methods of approximation, he 
considered only as so many mechanical 
tricks, or arts of legerdemain, em- 
ployed by their authors for the purpose 
of displaying skill in quirks and quibbles 
to the great detriment of the mathemati- 
cal sciences.” 
‘« It must however be confessed that 
he carried his veneration for the ancients 
to an unreasonable pitch; since he could 
seldom be induced to look at any modern 
book on mathematics, This prejudice of 
his is much to be regretted, as he would 
have found that some of the later writers 
on these subjects, particularly Huygens, 
Halley, Keill, and Bonnycastle, not only 
possess all the elegance of the ancients, 
but have improved upen their accuracy; 
the last more especially, who, in the notes 
affixed to his geometry, has pointed out 
several inaccuracies inthe reasoning of 
Euclid in his Elements, : 
6° To this admiration, however, of the 
ancient geometry must be attributed that 
closeness of reasoning and logical preci- 
sion, for which Fransham was s0 emj-~ 
nently distinguished; yet it must be al. 
lowed that he was thoroughly sceptica', 
for scarcely a sentence could be uttered 
in his hearing, or any information com- 
‘ ONS 4 ‘ 
municated ih his presence, without his 
rejoining, Are you sure that is true? 
Wiicveon, du you ground your bel f? A 
mathe: tician 
