\ 
» 
~ 
1800: ]. fall 
cafe x°-++-1—-0; and when he has found a 
few thoufand roots of + 1 and —1 the 
publication of them may afford to. pofterity 
a ftrong proof of the ingenuity of ‘their 
predeceflors, and the “application of the 
powers of their mind to ufeful and import- 
ant truths. _ In this exercife may be'con- 
fulted the method giyen by the profeflor, 
of finding a quantity, which, multiplied 
into a given irrational quantity, will pro- 
duce a rational produét, or confequently 
exterminate irrational quantities out of a 
given equation; but if an_irratio al 
quantity cannot come into an equation, the 
utility of tlis invention will not be ad- 
mitted without hefitation. 
The Proprietates Aleebraicarum Cur- 
varum, publifhed in 4772, neceffarily la- 
bour under the fame defects with the Mif- 
celianea Analytica, the Meditationes Al- 
gebraice, publifhed-in 1770, and the 
Meditationes Analyticee, which were in 
the preis during the years 1773,.17745 
1775, and 1776. Thefe were the chief 
andthe moft laborious works edited by the 
profeiior ; and in the Philofophical Tranf- 
actions is to be found a variety of pa- 
pers, which alone would be fufficient to 
place him in the firft rank in the mathe- 
matical world. ‘The nature of them may 
_be {een from the following catalogue. 
Vol. LILI. page 294, Mathematical 
Problems.—LIV. 193, New Properties 
in Conics.—LV. 143, Two Theorems in 
Mathematics. —LXiX. Problems con- 
cerning Interpolations—36, A general 
Refolution of Aleebraical Equations.— 
LXXVI. $81,- On Infinite Series. — 
‘LXXVII. 71, On finding the Values of 
Algebraical Quantities by converging’ {e- 
riefes, and demonftrating and extending 
propofitions given by Pappus and others. — 
LXXVIII. 67, On Centripetal Forces. 
ib. 588, On fome Properties of the Sum 
of the Divifion of Numbers. —LXXIX. 
366, Onthe Method of correfpondent Va- 
lues, &c. ib. 185, On the Refolution of 
attractive Powers. —LXXXI. 146, On 
infinite Seriefes.—LX XXIV. 385—ars, 
On the Summation of thofe Seriefes whole 
general term is a determinate funtion 
of x, the diftance of the term of the 
Series. ee ‘ | 
For thefe papers, the profeffor was, in 
1724,delervedly honoured by the Royal 
Society with Sir GodfreyCopley’s medal; 
and moft of them afford very {trong proofs 
of the powers of his mind, both in abftract 
{cience, and the application of it to philo- 
fophy;. though they labour in» common 
with his other works under the difadvan- 
tage of being clothed in a very unattractive 
form. The mathematician who has refo- 
MONTHLY MAG, NO, 55; . 
Memoirs of Dr. Waring. 
49 
lution to go through them, will not only 
add much tg his own knowledge, but be 
ufefully employed in dilating on thofe ar- 
ticles for the benefit of the more general 
reader, We might add in this place a 
work written on morals and metaphyfics 
in the Englifh language: but.as a few co- 
pies only were, prefented to his friends, 
and it was the profeffor’swifh that they 
fhould not have a’more extenfive circula- « 
tion, we fhall not here enlarge upon its 
contents. 
In the mathematical world the life of 
aring may be confidered as a diftin- 
guifhed-zra. The {triétnefs of demonftra- 
tion required by the ancients had gras 
dualiy fallen into difufe, and a more com- 
modious though almoft mechanical mode 
by Algebra and Fluxions took its place, 
and was carried to the utmoft limit by the 
profeflor. Hence. many new demonitra- 
tions may be attributed to him, but four 
hundred difcoveries can tcarcely fall tothe 
lot of a human being. If we examine 
thoroughly thofe which our | profeflor 
would diftinguifh by fuch names, we fhall 
find many to be mere deductions, others, 
as in the folution of biquadratics, antie 
cipated by former writers. But if we can- 
not allow to him the merit of fo inventive 
a genius, we muft- applaud his affiduity ; 
and, diftinguifhed as he was in the {cien- 
tific world, the purity of his life, the fim- 
plicity of his manners, and the zeal which 
he always manifefted for the truths of the 
Gofpel, will intitle him to the refpect of 
all who do not efteem the good qualities 
of the heart inferior to thofe of the head. 
Loudon, Nov. 1799. F. 
ORIGINAL LETTER OF H. BAKER, AUs= 
THOR GF THE ‘* MICROSCOPE MADE 
EASY,’ TO DR. DODDRIDGE. 
DEAR SIR, , 
Your laft favour came to London 
whilft I was at Ditton with his Grace 
the Duke of Montague, where and 
with whom I conftantly {pend a week or 
ten days every Chriftmas and Eafter; and 
I have no other holidays during the whole 
year. At thefe times feveral noblemen 
and gentlemen meet there to enjoy a perfect 
freedom, and throw off that ceremony and 
reftraint which their rank fubjeéts them to 
at London. Our company this Chriftmas 
was his Grace,’ the Earls of Pembroke 
and Cardigan, the Lords Tyrawley, Edg- 
cumbe, and Herbert, the Marquis Nico- 
lini, our worthy prefident of the Royal 
Society, and feven or eight gentlemen of 
difiinétion. The rules of the duke’s houfe 
are, for every body to go to bed and rife 
at his own time, and amute himfell in 
G what 

