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numeral calculation of tlie perimeters of the 
inscribed and circumscribed polygons: from 
which calculation it appears that the peri- 
meter of the circumscribed regular polygon 
of 192 sides is to the diameter in a less 
ratio than that of 3) or 3$ to 1 ; and that 
the perimeter of the inscribed polygon of 
96 sides is to the diameter in a greater 
ratio than that of 312 to 1 ; and consequent- 
ly that the ratio of the circumference to the 
diameter lies between these two ratios. 
Now the first ratio, of 3} to 1, reduced to 
whole numbers, gives that of 22 to 7, for 
ty : 1 : : 22 : 7 ; which therefore is nearly 
the ratio of the circumference to the diame- 
ter. From this ratio between the circum- 
ference and the diameter, Archimedes com- 
puted the approximate area of the circle, 
and he found that it is to the square of the 
diameter, as 11 is to 14. He determined 
also the relation between the circle and 
ellipse, with that of their similar parts. And 
it is probable that he likewise attempted 
the hyperbola; but it is not to be expected 
that he met with any success, since ap- 
proximations to its area are all that can be 
given by the various methods that have 
since been invented. 
Beside these figures, he determined the 
measures of the spiral, described by a point 
moving uniformly along a right line, the line 
at the same time revolving with a uniform 
angular motion ; determining the propor- 
tion of its area to that of the circumscribed 
circle, as also the proportion of their sec- 
tors. 
Throughout the whole works of this great 
man, we every where perceive the deepest 
design, and the finest invention. He seems 
to have been, with Euclid, exceedingly care- 
ful of admitting into his demonstrations 
nothing but principles perfectly geometri- 
cal and unexceptionable : and although his 
most general method of demonstrating the 
relations of curved figures to straight ones, be 
by inscribing polygons in them : yet to de- 
termine those relations, he does not in- 
crease the number, and diminish the magni- 
tude, of the sides of the polygon adinfinitum ; 
]but from this plain fundamental pi inciple, 
allowed in Euclid's Elements, (viz. that any 
.quantity may be so often multiplied, or 
added to itself, as that the result shall ex- 
ceed any proposed finite quantity of the 
same kind), lie proves that to deny his 
figures to have the proposed relations would 
involve an absurdity. And when lie de- 
monstrated many geometrical properties, 
particularly in the parabola, by means of 
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certain progressions of numbers, who. to 
terms are similar to the inscribed figures $ 
this was Still done without considering such 
series as- continued ad infinitum, and then 
collecting or summing up the terms of such 
infinite series. 
There have been various editions of the 
existing writings of Archimedes. But the 
most complete of any is the magnificent 
edition, in folio, lately printed at the Cla- 
rendon press, Oxford, 1792. This edition 
was prepared ready for the press by the 
learned Joseph Torelli, of Verona, and in 
that state presented to the university of 
Oxford. The Latin translation is a new 
One. Torelli also wrote a preface, a com- 
mentary on some of the pieces, and notes on 
the whole. An account of the life and 
writings of Torelli is prefixed, by Clemens 
bibiliatn And at the end a large appendix 
is added, in two parts ; the first being a 
Commentary on Archimedes’s paper upon 
Bodies that float on Fluids, by the Rev*. 
Adam Robertson of Christ Church Col- 
lege ; and the latter is a large collection of 
various readings in the manuscript works of 
Archimedes, found in the library of the late 
King of France, and of another at Florence, 
as collated with the Basil edition above- 
mentioned. 
ARCHITECTURE is the art of forming 
dwellings, or erecting buildings of any kind. 
Animals of acute feelings, exposed to dis- 
agreeable extremes of seasons, uncertainties 
of weather, and to the depredations and 
attacks of each other, must have a strong 
desire to shelter and secure themselves. 
Consequently, those favoured by nature 
either for digging in the earth or building 
would, under these pressing circumstances, 
soon form places of retirement for them- 
selves; and other animals, without such 
powers, would endeavour to seek such 
places of shelter as are either furnished by 
nature itself, or formed by others. Thus 
birds and insects build themselves nests; 
many kinds of quadrupeds form subterrane- 
ous retreats ; and in time of storms cattle 
flee, and endeavour to shelter themselves 
among rocks, trees, &c. There can be little 
doubt but building began first among the 
brutes; but their modes of working have 
been uniformly the same from time to time, 
without improvement. Man, with feelings 
much more acute than any other animal, and 
also superior, both from his reasoning powers, 
and the construction of his frame, in being 
adapted to lift, remove, shape, and place 
inaniinated matter wherever his mind dj- 
