1802.] 
that equations of three dimenfions afforded 
a folution of thofe famous problems— 
the duplication of the cube, and the cri- 
fection of an angle. In fine, to tim we 
owe tne elements of the do&trine of angu- 
far fefiions, the cbjest of which is fo find 
general expreflions of the chords or the 
fines for a feries of arcs which are nmul- 
tiples of each other, and reciprocally the 
expreffions of the arcs, when the chords or 
the fines are known. 
60. But, of all the centuries in which 
the mathematics have beeen fuccellively 
advanced, the feventeenth exhibits the 
moft brilliant foectacle. Italy, France, 
the Netherlands, Germany, Switzerland, 
and Great Britam, produced, at that pe- 
riod, celebrated mathematicians, whofe 
labours have raifed the accurate fciences 
to an elevation which commands refpect. 
Some by puriuing geometry in the manner 
of the ancients, and others by cultivating 
the algebraic analyfis, prepared the way 
for-thofe methods of calculation which 
may be faid to have enlarged the limits of 
the human mind. 
62. In the beginning of the feventeenth 
century, Lucas Valerius, Proteflor of the 
Mathematics at Rome, extended geometry 
beyond the ftate in which the ancients 
had Jeft it. Swellzus* improved, in fome 
refpeéts, one of the difcoveries of Archi- 
medes, namely, that of fnding the pro- 
portion between the diameter and the cir- 
cumference of the circle. Kepler,t in his 
Stereometria  doliorum (Catk- gauging) 
Opened new profp<éts, which feem to have 
had great influence on the revolution 
which geometry has experienced. Gu/- 
dimus { invented the centrobaric method, 
which is founded os» a fine theorem, of 
which Pappus had an idea, and which is 
* Willebrod Snell, the fon of Ralph Snell, 
Profeflor of the iia hematies at Leyden, was 
born in that town in 1591, and aed in-it in 
3626. He fucceeded his father in the ma- 
thematica] chair there; and to him we owe 
an exaét method of afcertaining the magni- 
tude of the earth. 
+ John Kepler was born in the Dutchy of 
Wirtemberg in 1571, and died at Ratifbon in 
1631. Thename of this celebrated man will 
endure as long as aftronomy fhail be culti- 
vated. i 
- jf Father Guldinus was born at St. Gall in 
1577,entered into the Society of the Jefuits in 
1597, after abjuring the Proteftant religion, 
and died in 1643. Having been fent to Rome 
to improve his talencs,he became Profeflor of 
philofophy and the mathematics in that city. 
fie allo publicly taught the fame fciences at 
Gratz and at Vienna. 
& 
Obfervations on the Salt-Duties. 
parts of the goaft, 
329 
this :—* Every plain or folid figure ge- 
nevated by the motion of a line or a fur. 
face, is equal to the produét of the gene- 
rating quantity and the line, or way, de- 
feribed by its centre of gravity. 
(To be continued ) 
a EEL 
OBSERVATIONS oz ihe SALT- -DUTIES. 
[ Continued from page 123, of Vol. XII il,] 
(al HE ule of falt in the fitheries, and 
JL, the advantage which would be de- 
rived to thele from the repeal of the daty 
on falt, form a fecond very important 
object of confideration. 
The fitheries constitute another of thofe 
abundant fources of wealth which nature 
has favoured this ifland with; whether re- 
garded as an excellent nurfery for our fea- 
men; or as the means of furnifhing a large 
fupply of a ufeful article of food, either 
for home confumption, or for exportation. 
The principal caufes which have tended 
to check the extenfion of the fifheries have 
been, the heavy duty on falt; and the re- 
gulations to prevent the fmugegling of it, 
which this has occaficned. The falt, it 
is true, is allowed to be ufed, “free of 
duty, for ‘the purpofe of curing and pre- 
ferving fith;°?? but it is Biaeed that 
“any perfon intending fo to ufe it fhall, 
before being per mitted to receive any fuch 
falt, make ent try at the next office of ex- 
cife of the number and fituation of his 
ftorehoules for ftoring and keeping fait ; 
which ftorehoufes are to be firlt deemed 
fecure by the Supervifor of Excife of the 
diffi.” 
It might appear to be no great hard- 
fhip or inconvenience to be “obliged to 
make entry of a warehoufe; and to have 
that good and fecure: but let us only 
confider the operation of fuch a reftri€tion. 
Tr firft has the eife& of limiting exceed- 
ingly the number of thofe who engage’ in 
this employment. “The bold and hardy, 
if needy,adventurer is debarred this oppor- 
tunity. None but a petfon poffefling a 
pretty confiderable capital can become a 
curer of fifth, no other being able to pro- 
vide himfelf with fuch “ good and fecure 
ftorchoufe,”” as the A& requires. The 
framers of the A€t were in ome meafure 
fenfible of this, and there is a claufe in it 
intended to diminifh the evil; but it muft 
be evident how partially itis calculated ro 
do this. In this claule it is ftated, that 
“whereas many inhabitants of ‘certain 
thicly inhabited, are 
employed in the taking and faltinig of 
herrings, and being unable to provide 
themlelves with proper cellars or ware- 
houies 
