M ATHEMATIC S. 
532 
and elevated from fenfible matter, it difrincfly views pure 
forms, conceives the beauty of ideas, and inveftigates the 
harmony of proportions; the manners themfelves are 
fenfibly corrected and improved, the affections compofed 
and rectified, the fancy calmed and fettled, and the un- 
cterftanding raifed and excited to more divine contem¬ 
plations.” 
Many of our readers will probably not be difpofed to 
admit, to the full extent, the jultnefs of Dr. Barrow’s pa¬ 
negyric ; they may think he has over-rated the value of 
mathematical acquifition, and that fome of his affertions 
are founded in felf-fufficiency and pride. But thofe who 
form the latter opinion mult be unacquainted w ith the 
true character of this celebrated author; and thofe who 
entertain the former are not probably initiated into the 
myfteries of thefe fciences, and therefore are not com¬ 
petent judges of their value. 
.We are aware that mathematics have had calumniators, 
as well as eulogilts; it has even been reprefented as a fci- 
ence which blunts all the tender feelings of our nature; 
that it renders its profelfors vain, arrogant, and prelump- 
tuous; as deftroying all relifh for works of tafte and ima¬ 
gination; hardening the heart againft every truth but 
thofe of the demonlfrative kind ; and, confequentiy, as 
having a tendency to lead us into infidelity and afheifm. 
The celebrated author of the Rambler indulged fome 
of thefe notions. It was, he oblerved, “ the great praife 
of Socrates, that he drew the wits of Greece, by his in- 
ftrucdion and example, from the vain purfuits of natural 
philofophy to moral enquiries; and turned their thoughts 
from ftars and tides, and matter and motion, to the va¬ 
rious modifications of virtue, and relations of life.” He 
purfues this thought Hill farther, and i 11 u ft rates it by a 
•flory which he tells of one Gelidus, a mathematician, who 
was fo abforbed in his fpeculations, that when his fer- 
vants came to acquaint him that a houfe was on fire, and 
the whole neighbourhood in danger of being burnt, he 
only replied, that it was very likely, for it was the nature 
of fire to act in a circle. He even diverts this pfeudo- 
phiiofopher of the common feelings of humanity, and 
makes him as infenfible to the wants of his family as to 
the diftreffes of his neighbours. But fuch illiberal no¬ 
tions are a difgrace to their author, and fliow a narrownefs 
of mind that one would not expect to have found affo- 
{Ctated with fo much talent. A great and comprehendve 
genius excludes none of the fciences : they all contribute, 
by various means, to adorn and einbellifh life; and for 
this reafon ought to be cultivated and improved. Happy 
as the mind that is not contracted by the ltudy of philo¬ 
fophy, nor enervated by the charms of the belles lettres ; 
that can be rtrengthened by Locke, initruCfed by Clarke 
and Newton; impartioned by Cicero and Demofthenes, 
and elevated by the powers of Homer and Virgil. 
That fome mathematicians may have been vain and 
prefumptuous, perhaps cannot be denied; but many, and 
thofe amonglt the molt eminent, have been equally dif- 
tinguifhed for their modefty and unaffuming manners, of 
which our Newton furnifhes an illuftrious example. Ad¬ 
mitting, therefore, that the charge is juft with refpeift to 
certain individuals, unlefs it can be ihown (and which 
we believe it cannot) that it applies to a greater propor¬ 
tion of the profelfors of this fcience than of any other, the 
injullice of the acculation, as applied to the fcience itfelf, 
is evident. What fcience or what lubjecl can be named, 
in which the lame charge will not apply to indivi¬ 
duals; even that which above all might be fuppofed to 
have the greatert influence in checking thole paffions, the 
great Founder of which was a pattern of humility, meek- 
nefs, and peace; even this facred caufe has been but too 
frequently difgraced by the bigotry and intolerance of its 
profelfors. 
The next objection to thefe purfuits is, that they de- 
ftroy all relilh for works of tafte; and that genius is un- 
vteceffary, and only great labour required, in order to attain 
the firft rank in the fciences. To this we will let Boffut 
reply: “Is it,” fays {he philafopher, “ at all aftomfhing, 
that the ignorant and fuperficial many fhould confound 
the fruits of that knowledge, which is acquired by ftudy, 
with thofe new' and original truths to which genius alone 
can give birth ? To be juft, we mult weigh the great ma¬ 
thematicians of well-eftablilhed reputation againft the 
great poets and great orators* Thus, on the one fide, let 
us place Homer, Virgil, Racine, Pope, Demofthenes, Ci¬ 
cero, and Boffuet; and on the other, Archimedes, Hip¬ 
parchus, Galileo, Defcartes, Huygens, Leibnitz, and New¬ 
ton ; and it will not then be fo eafily determined to which 
fide the balance, in ppint of genius, ought to incline.” 
We might purfue this fubjeft to a much greater length, 
and enter into a formal defence ef the other charges 
brought againft mathematics and mathematicians; but 
they may be all anfwered in a word : Their greateft ca¬ 
lumniators, amongft whom w ; e place Jofepli Scaliger, the 
abbe Desfontaines, and our countryman Hobbes, were 
men who coveted fame, and thought themfelves competent 
to acquire it in every branch of human knowledge ; they, 
therefore, attempted the molt difficult problems, and their 
little knowledge of the fubjeff led them into errors which 
made them the ridicule of all fcientific men : thus exaf- 
perated and difappointed, they became the enemies of 
that fcience in which they had before fo vainly defired 
to thine ; and reproached it merely to gratify their pride 
and revenge. 
We are hence clearly of opinion that mathematical fci¬ 
ence muff ever form a high itep in the gradation of men¬ 
tal culture. The loweft branch of it is arithmetic. Learnt 
merely as an art, _it is not without its utility in the cul¬ 
ture of the mind. The commencement of habits of clear 
perception, of abftracfion, of regularity and correcfnefs in 
practice, of acutenefs, of ufing definite means in order to 
obtain definite ends, and of afting upon general rules, 
may reafonably be expended from the proper mode of learn¬ 
ing this fcience. It then becomes an introduffion to fci¬ 
entific inveftigation ; and in this view it is peculiarly va¬ 
luable, from the exact arrangement of our notation, and 
the certainty of the refults of our operations. Algebra 
pofTefles nearly the fame advantages, and, in addition to 
them, others more important to a higher degree of mental 
culture. It generates the power of invention and com¬ 
bination, and it acculloms the mind to general reafoning, 
at the fame time leaving it the power to check and cor¬ 
rect that reafoning at every ftep. Geometry forms a habit 
of clear and cautious reafoning. It ferves as a correftive 
to the wild flights of imagination, and gives proportional 
vigour to the judgment. The higher branches of mathe¬ 
matical fcience refemb-lp, in their elfefts upon the mind, 
the one of thefe elementary branches which they mod re- 
fetnble in their mode of iuvertigation. If there were no¬ 
thing valuable in the mathematical fciences for the ufes of 
human life, yet they are well worth our ftudy ; for by per¬ 
petual examples they teach us to conceive with clearnefs, 
to connefi our ideas in a train of dependence, to reafon 
with ftrength and deinonftration, and to diftinguifli be¬ 
tween truth and falfehood. Something of thefe fciences 
fhould be fiudied by every one ; and that, as Mr. Locke 
exprefiVs it, not fo much to make us mathematicians as to 
make us reafonable creatures. 
Another fource of the utility of the mathematics is 
their fubferviency to natural philofophy. To deferibe 
the phenomena of the univerfe, to inveftigafe their caufes 
and the connection of thefe caufes, are the principal objects 
of this fcience. To mention thefe .objects, is nearly all 
that is neceftary to indicate its valuable effefls on the 
mind. The habits of accurate and perfevering obferva- 
tion, of inveftigation, of abftraftion, and of correff rea¬ 
foning, are more or lefs produced and cultivated by the 
ftudy of the philofophy of nature. It furnifhes abundant 
fcope for the molt fublime fpeculations, and calls forth 
the nobieft exercifes of tlie imagination, yet reftrains the 
mind within the limits of reality. It carries us beyond 
the boundaries of fenfe, and lelfens ourintereft in felf by 
i increaling 
