Retrofpedt of Domeftic Literature.—Mathematics and Aftronomy. 655 
vead with more inftruction as a gazetteer, 
than with pleafure as a pcem 
MATHEMATICS AND ASTRONOMY. 
*< An Account of the Afironomical Lifco- 
wveries of Kepler; including an bijforical 
Review of the Syftems which had fuccef- 
Svely prevailed before his Time. By Ro- 
BERT SMALL, D.D.” 
This volume will be highly prized by 
the mathematician, as bringing forward 
the laborious and moft minute invefiga- 
tion of a man whofe merits are infuffi- 
ciently appreciated. Kepler is known to 
have been the difcoverer of the great laws 
of the planetary motions ; but in order to 
be fenfible of the extent of obligation 
which we are under to this great man in. 
the {cience of aftronomy, it is neceffary to 
be acquainted with the more ancient atiro- 
nomical theories, and the principal phe- 
nomena they were fuppofed to explain. 
Dr, Small has accordingly devoted his 
firft four chapters to the fyftems of Pto- 
lemy, Copernicus, and Tycho Brahe. 
The next chapter is entitled, ‘‘ OF the 
the Preparations to Kepler's Difcoveries, 
and of his Original intentions.” In this 
chapter we have an interefting accvunt of 
Kepler’s life, and of the circumitances 
which led 
‘¢ his foul to ftray 
Far as the folar walk and milky way.” 
The work is altogether that of a pre- 
ficient in the [cience : Dr. Smail has, with 
great fagacity and clearneis, pointed out 
the inefiicacy of the ancient theories, and 
the valuable difcoveries elaborated by 
Kepler. 
A fecond edition is publifhed of Mon- 
Tucua’s “ Hffory of tte Mathematics.” 
Baron Masexes has publithed a vo- 
Jume of ‘§ Tracts on the Refolution of Cu- 
bic and Biquadratic Equations.” 
It conilts of fix tracts, befides a long 
preface, explanatory of their ccntents. 
‘The frit and fourth traéts are fupplements 
to Mr. Frend’s Principles of Algebra, 
containing further remarks on cubic equa- 
tion and Cardan’srule. The second isa 
very valuable comparifon made between 
the methods of Ferrari and Defcartes for 
re(ulving certain biquadratic equations ; 
the preference is given to the former, and 
the tract is appropriately called Ferrarius 
Redivivis. The third tract obviates 
fome difficulties in the application of Fer- 
rari’s method to the rriolution of four 
forms of biquadratic equations. The 
fifth contains remarks on the doétrine of 
the generation of algebraic equations ; 
end the laft, a comparifon between the re- 
9 ee or. 
folution of the biquadratic rx—gx?+-p23 
— «ts, by the method of Dr. Waring 
and that of Ferrari. Al) thefe traéts are 
written with the accuracy, diligence, and 
fkill for which the author has long been 
ditinguifthed. The Baron maintains with 
great firmnefs his opinion cn the injury 
done to {cience by the introduction of ne- 
galive quantities. 
Mr. Morcan has publifhed a new edi- 
tion (ihe fixth) of Dr. Price’s ** 06- 
ervations on Reverfionary Payments, 
&e.” 
The work is newly arranged and en- 
larged by the addition of algebraic and 
other notes, by folutions of feveral new 
problems in the doctrine of annuities, and 
by a general introduction. 
To tran‘cribe the tit'e of the following 
work is fufficient: ‘+ Evening Amufe- 
ments, or, the Beauty of the Heavens 
difployed ; in which feveral firtking Ap- 
pearances to be objerved on various 
Evenings in the Heavens during the Year 
1804 are defcribed; and feveral Means 
within Daors are pointed out by which 
the Time of young Perfons may be inno- 
cently, agreeably, and ufefially, employed, 
By WitiiaM Frenp, fg. M.A, Ge.” 
Under fo excellent a tutor as Mr. Frend, 
the principles of aftronomy mult be com- 
prehentibly explained. This is the only 
work of the kind extant, and we are hap- 
py to fee that Mr. Frend intends to conti- 
nue it annually. 
Mr. BONNYCASTHE has tranflated from 
the French of Boffuet a ‘* General Hiftory 
of Maiheniatics Jrom the earlief? Times to 
the Middle of the Eighteenth Century.” 
This work will be read with interet 
and advantage .by thole who fhrink from 
engaging an the more elaborate and com- 
prehenfive work of Lr. Montucla: the 
tranflation is execedingly well executed. 
The work is divided into four periods, 
preceded by an introduétien, containing 
a general view of the mathematica] {ci- 
ences, with an account of the nations by 
wnom they have been cultivated. The 
firfk period contains the fate of mathema. 
tics, from their origin to the de!truétion 
of the Alexandrine tchool ; including the 
origin and progrefs of arithmetic, geome- 
try, mechanics, hydrodynamics, aftrono-, 
my, optics, and acouitics, The fecond 
period comprchends the ftate of mathema- 
tics from their revival among the Arabs 
to the end of the fifteenth century ; and 
this includes the arithmetic, algebra, geo- 
metry, and aftronomy, of the Arabs; 
the ftate of f{cience among the Perfians, 
and particularly that of altronomy ae 
ate 
