1802. } 
little triangle, whofe fides are the dif- 
ference of two ordinates, infinitely near 
to each other, their perpendicular dif- 
tance, and the, element of the curve, as 
fimilar to the triangle formed by the or- 
dinate, the fub-tangent, and the tangent. 
He then fought, by means of the equation 
of the curve, the relation of the two fides 
of the little triangle, of which one ex 
prefles the difference and the other the 
diftance of the two ordinates, by forming 
this proportion. As the difference of the 
two ordinates is to their diftance, fo is 
the ordinate to- the fubtangent. ‘This 
rule, which is that of Fermat implified, 
differs from the method of the differential 
calculus in nothing but the notation. 
$3. Barrow had the bonour of num- 
bering Newton * among his pupils, and 
* Ifaac Newton was born on the 25th of 
December, 1642, at, Wolitrop, in the county 
of Lincoln. In his firft attempts he feemed 
rather to invent than to ftudy. Having but 
glanced over the Elements of Euclid, he 
paffed on to the Geometry of Defcartes, in 
which he found ideas proportioned to the force 
of his mind. Newton advanced in h'‘s fcien- 
tific career with the moft firm and rapid 
pace. In him we trace neither errors nor 
failures, and to him was properly applied the 
idea of Lucan on the river which waters 
Egypt, the fource of which was unknown to 
the ancients :—A%en have not been permitted to 
trace the Nile to its weak commencement. 
Barrow, on refigning his academical. chair 
at Cambridge, procured. it for Newton, who. 
was then but twenty-two years of age; but 
in his twenty-fourth year he was in poffef- 
fion of two of his fineft difcoveries, namely, 
the theory of light, and the method of 
fluxions. In 1687, he gave to the Jearned 
world his Mathematical Principles of Natu- 
ral Philofophy, an immortal work, in which 
the moit profound geometry is laid down as 
the bafis of ‘true phyfics, and which will 
always be confidered asone of the moft fub- 
lime productions of the human mind, 
Newton having been appointed Mater of 
the Mint in 1696, filled that ftation with 
equal genius and difintereftednefs.. Till his 
eighticth year, he poffefied that uninter- 
rupted health which he owed to his tem- 
perance, - But he then began to decline, and 
in the beginning of the year 1727, he was 
attacked with the fone, In this fatal con- 
juncture he thewed as much firmnefs as he 
vad difplayed fagacity during his life. The 
excruciating pangs which terminated his life, 
extorted from him neither complaints nor 
murmurs, At lait, in his 8§th year, he 
fiept in that tranquillity which he had al- 
ways puriued.. His body was conveyed to 
Weltminfer Abbey, and laid on a bed of 
fate, whence it was carried in great pomp 
Sketch of the Hiftory of Pure Mathematics. at 
of appreciating the merit of a man who 
difplayed the higheft powers of the hum wna 
intellect, 
$4. Scarcely had Newton commenced 
his mathematical ftudies, than he per- 
fected the ancient methods, and invented 
to. the place of interment. The family 
of Newton have fince erected a monument 
to his memory, on which is infcribed a mot 
honourable epitaph, which ends thus :—Sidi 
gratulentur mertales tale tantumque extitiffe bu- 
wiani generis decus. 
Nore by the Tranflator.——Here the avthor 
has added a French poetical paraphrafe of 
Pope’s well-known couplet :— 
Nature and Nature’s laws lay hid in night, 
God faid, Let Nezvton be—mand ali was lighe. 
But as that paraphrafe does not rife above 
mediocrity, I have taken the liberty to omit 
them, and to fubftitute the following lires, 
which I flatter myfelf will be the more cc- 
ceptable to the reader, as they do not appear 
to have ever been printed, except tn 1741, in 
Caribbeana, a colle&tion of papers which were 
interefting to few, and therefore known to 
few but the Welt Indians of taat period. 
Their author was the celebrated Dr. Pircairn,. 
who having been a good mathematician 
(Cheyne addrefied his Fluxiens to him in 
the epiitolary form) was the better able to 
Judge of the vaft extent and value of Sir 
Ifaac’s difcoveries and improvements. 
y DE NEWTONO, 
Pythagera ja&at Samius fe fundus alumnn, 
Newitono geflit terra Britanna fus. 
Par utriusgue, quidem vitiurague ghrta gleba 
Dum vaga Pieebeis terra vebctur eguis ; 
At Samius magno tantum fuperatur ab Anglo, 
Eft quanto major terra Britanna Samo. 
ON SIR ISAAC NEWTON. 
Samos much boafts Pythagoras’s birth, 
Nor Britain lefs th? illuftrious Newton’s 
worth. 
Both ifles, from each, like glory will derive, 
Whilft Sol attraéts the earth, their names 
fhall live ; 
But varying ftill in this, that Britain’s fon 
Much farther hath the Samian fage out-done, 
Than does th’ extent of fam’d Sritannia’s ifle 
The narrow confines of the Samian foil. 
In fome accounts of Newton’s life, the 
binomial theorem is {aid to be infcribed on 
his monument in Weftminfter Abbey. The 
fame thing is affirmed in the Mathema- 
tician, p. 273, and in Stone’s Mathematical 
Dictionary, article, ‘Binomial Root. But I 
have more than once infpeéted chat monv- 
ment very attentively, without being able 
to difcover the leaf trace of that. admirable 
formula,which affuredly would have been the 
mof lafting part of the monument. When 
Newton invented it, he might have jutly 
exclaimed—-Excgi monumeutum ere perennius ! 
hew 
