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numeral calculation of the perimeters of the certain progressions of numbers, whose inscribed and circumscribed polygous: from terms are similar to the inscribed figures ; which calculation it appears that the peri- this was still done without considering such meter of the circumscribed regular polygon series as continued ad infinitum, and then of 192 sides is to the diameter in a less collecting or summing up the terms of such ratio than that of 34 or 348 to 1 ; and that infinite series. the perimeter of the inscribed polygon of There have been various editions of the 96 sides is to the diameter in a greater existing writings of Archimedes. But the fatio than that of 348 to 1; and consequent most complete of any is the magnificent ly that the ratio of the circumference to the edition, in folio, Jately printed at the Cladiameter lies between these two ratios. rendon press, Oxford, 1792. This edition Now the first ratio, of 3 to 1, reduced to was prepared ready for the press by the whole numbers, gives that of 22 to 7, for learned Joseph Torelli, of Verona, and in 34:1::22 : 7; which therefore is nearly that state presented, to the university of the ratio of the circunference to the diame- Oxford. The Latin translation is a new ter. From this ratio between the circum one. Torelli also wrote a preface, a comference and the diameter, Archimedes com- mentary on some of the pieces, and notes on puted the approximate area of the circle, the whole. An account of the life and and he found that it is to the square of the writings of Torelli is prefixed, by Clemens diameter, as 11 is to 14. He determined Sibiliati. And at the end a large appendix also the relation between the circle and is added, in two parts ; the first being a ellipse, with that of their similar parts. And Commentary on Archimedes's paper upon it is probable that he likewise attempted Bodies that float on Fluids, by the Rev. the hyperbola; but it is not to be expected Adam Robertson of Christ Church Colthat he met with any success, since ap- lege; and the latter is a large collection of proximatious to its area are all that can be various readings in the manuscript works of given by the various methods that have Archimedes, found in the library of the late since been invented.

King of France, and of another at Florence, Beside these figures, be determined the as collated with the Basil edition abovemeasures of the spiral, described by a point mentioned. moving uniformly along a right line, the line ARCHITECTURE is the art of forming at the same time revolving with a uniform dwellings, or erecting buildings of any kind. angular motion; determining the propor Animals of acute feelings, exposed to distion of its area to that of the circumscribed agreeable extremes of seasons, uncertainties circle, as also the proportion of their sec of weather, and to the depredations and tors.

attacks of each other, must have a strong Throughout the whole works of this great desire to shelter and secure themselves. man, we every where perceive the deepest Consequently, those favoured by nature design, and the finest invention. He seenis either for digging in the earth or building to have been, with Euclid, exceedingly care- would, under these pressing circumstances, ful of admitting into his demonstrations soon form places of retirement for themnothing but principles perfectly geometri- selves; and other animals, without such cal and unexceptionable: and although his powers, would endeavour to seek such most general method of demonstrating the places of shelter as are either furnished by relations of curved figures to straight ones, be nature itself, or formed by others. Thus þy inscribing polygons in them : yet to de. birds and insects build themselves nests; termine those relations, he does not in- many kinds of quadrupeds form subterranecrease the number, and diminish the magni ous retreats; and in time of storms cattle tude, of the sides of the polygon ad infinitum; flee, and endeavour to shelter themselves but from this plain fundamental principle, among rocks, trees, &c. There can be little allowed in Euclid's Elements, (riz. that any doubt but building began first among the quantity may be so often multiplied, or brutes; but their modes of working have added to itself, as that the result shall ex been uniformly the same from time to time, ceed any proposed finite quantity of the without improvementMan, with feelings same kind), he proves that to deny his much more acute than any other animal, and figures to have the proposed relations would also superior, both from his reasoning powers, involve an absurdity. And when he de- and the construction of his frame, in being monstrated many geometrical properties, adapted to lift, remove, shape, and place particularly in the parabola, by means of inanimated matter wherever his mind di

rects, and from his imitative disposition, pertraps by combining both these methods would be compelled by pressing necessity together, so as to make his hut still more to form some kind of habitation where he durable: in this manner the first walls might breathe the temperate air, amid the might have been made, or by collecting the summer's heat, or winter's cold, secure him- most portable and shapely stones, and rearself from the attacks of ferocious animals, ing a rough wall to a sufficient height: the and when nature calls he might rest and roof would be constructed of the conic or sleep in ease and security. It is probable pyramidal figure, as formerly, and the whole that the original habitations of men were plastered over with mud, or any other tenanatural caverns in the earth, and hollows in cious material. the trunks of trees. Also, from the example As mankind began to associate, they of brutes, he might excavate the ground; would improve each other hy degrees; and but being disgusted with darkness and baving found the use of tools, trunks of trees, damps, taking example from the birds, he divested of their bark and branches, would would begin to baild hats of such materials be used as pillars, and beams or lintels, inas the situations would afford: the natural stead of ramified bougls. In this improved taverns might suggest the idea of using carth state of joining and cutting the timbers, the or stones. That the first attempts at build- beams would no doubt suggest a rectilineal ing must have been extremely rude there plan instead of the circular one, as beams of can be little doubt; men, without cutting the circular form could not be so readily instruments or tools, could not shape, smooth, procured as those of the straighit form, the break, and join timbers or stones, as they triangle being the only figure that includes do in the present day; timbers could only a space by the fewest sides, it may first have be supported by balancing each other, or been employed for the plan; but finding driving them fast into the ground, or piling this form of building inconvenient, on acstones or other materials around their lower count of the acuteness of its angles, the ends, or interlacing them with slender twigs rectangle would be adopted in its stead, the or boughs.

hut erected thereon would have the form of • It is reasonable to conjecture, that wher a rectangular prism, which figure has been ever wood is found, the primitive hut would generally retained to the present day, with be constructed of a conic figure, not only little variation, by almost the whole inhabifrom its form being the most simple of all tants of the globe, and exactly by those who solids, but also from the ease with which live in the mildest climates; but in countries this covering is made. The builder collect- liable to rain, pyramidal and wedge-formed ing a few boughs, and perhaps breaking roofs have been coustantly in use. From them to determinate lengths, would support this state of the hut has civil architecture them by leaning them against each other at advanced progressively to the present state the top, and spreading them out at the bot. of improvement. Vetruvius, the most antom, so as to make the interior of sufficient cient writer of architecture, informs us nearly capacity, leaving an aperture on one side as above, in the following words: for entrance: the interstices he would in “ Mankind began to make themselves terweave with smaller branches, and to ren coverings with the boughs of trees; some. der it impervious to disagreeable changes, dug caves in the mountains; and others, in or excesses of the surrounding element, he imitation of the nests of swallows, with would plaster the interstices with mud, sprigs and loam made shelters which they slime, or clay; such are the wigwams of the might lye under; and by observing each North American Indians, and the kraals of others work and turning their thoughts to the Hottentots and Caffrees, in the present discover something new, they by degrees day. It would not be long before the inha- improved and made better kinds of habitabitant saw the inconvenience of the simple tions ; but men being of an imitative and ccnic form, on account of its inclined sides, docile nature, glorying in their daily invenin preventing him from standing erect at tions, and shewing one another the houses the extremities of the floor, His former they had made, they by these endeavours dwelling would readily suggest the plan on and exertions of their faculties became in which he was to build. He might perhaps be time more skilful. gin to dispose the timbers upright, and fasten “ At first for the walls they erected forktheir bottom ends as above, or by setting them ed stakes, and disposing twigs between upon the ground only, and interweaving in them, covered them with loam ; others piled jerstices in the manner of basket work; or up dry clods of olay, binding them togethee

with wood, and to avoid rain and heat, they peatedly exercising their faculties and ta-made a covering with reeds and boughs; but lents arrived at the full knowledge of the finding that this roof could not resist the art, those who were most experienced prowinter rains, they made it sloping and point- fessing themselves artificers. When there. ing at the top, plastering it over with clay, fore these things were thus far advanced, and by that means discharged the rain water, as nature had not only given to mankind That the origin of things was as above writ- sense in common with other animals, but ten may be concluded from observing, had also furnished their minds with judgthat to this day some foreign nations con ment and foresight, and had subjected otber struct their dwellings of the same kind of animals to their power, they from the art of materials, as in Gaul, Spain, Lusitania, and building gradually proceeded to other arts Aquitain, they use oak shingles or straw. and sciences, and from a savage and rustic The Colchians, in the kingdom of Pontus, way of life became humane and civilized. where they abound in forests, fix trees in Then when their minds were thus enlightenthe earth, close together in ranks to the ed, and they became more judicious by ex, right and left, leaving as mucha space be- perience, and the advancement of the varitween them as the length of the trees will ous arts and sciences, they no longer built perinit; upon the ends others are laid trans- huts, but founded houses with walls conversely, which cirenmclude the place of ha- structed with bricks, stones, or other matebitation in the middle; then at the top the rials, covering the roofs with tiles." four angles are braced together with alternate beams; and thus the walls, by fixing

HISTORY OF ARCHITECTURE. other trees perpendicularly on these below, The origin of architecture is, like that of may be raised to the height of towers. The most other arts, involved in great obscurity. interstices which, on account of the coarse We are informed by Moses that Cain built a ness of the materials, remain, are stopped city, and called it after the name of his son with chips and loam. The roof is also Enoch; but concerning the mode of conraised by beams laid across from the ex- structing the houses, or the quality of the treme angles, gradually converging, and materials, he is quite silent. The same rising from the four sides to the middle point anthor also inforins us that Jabal was the at the top, and then covered with boughs father of such as dwell in tents. In the and loam. In this manner the barbarians days of Noah architecture must have armake the testudinal roofs of their towers. rived at great perfection: to construct the The Phrygians, who inhabit a champaign ark of sufficient stiength to withstand the country, being destitute of timbers by rea tempests raging over the surface of the son of the want of forests, select little patu- watery element would require considerable ral hills, excavate them in the middle, dig skill in the art of carpentry. Ashur built an entrance, and widen the space within as the cities of Nineveh, Rehoboth Calah, and much as the nature of the place will permit: Resen. The city and tower of Babel were ahove they fix stakes in a pyramidal form, built of well-burnt brick, and slime for bind them together and cover them with mortar. Brick-making must have been well reeds or straw, heaping thereon great piles understood then, and perhaps at a period of earth. This kind of covering renders much anterior. Moses does not say, what them very warm in winter and cool in sum- either the dimensions or tigure of the tower mer; some also cover the roofs of their huts was, but that it was the intention of the people with the weeds of lakes; and thus in all na- to make its top reach unto heaven: this vain tions and countries the dwellings are formed design being frustrated by the intervention of upon similar principles. At Marseilles we the Almighty, the building was left unfinished. may observe the roofs without tiles, and whether this city and tower be the same covered with earth and straw. At Athens Babylon and tower as described by Hero. the Areopagus is an example of the ancient dotus and Strabo is uncertain; the former roofs of loam: at the Capitol also the house says it was a square building, each side of of Romulus in the sacred citadel may re which at the base was a furlong, consequently mind us of the ancient manner of covering half a mile in circumference; from a windour roof with straw. By these examples ing stair, or rather an inclined plane, which therefore we may be assured, that the first went around the exterior, making eight réinventions of building happened in the man- volutions, the building appeared as if eight ner we have related; but at length man- stories had been placed one upon the other; kind by daily practice improved, and by re- each such story was 75 feet high, and con

sequently the whole height 600 feet: the plinth. The shafts of the columns are gene. inclined plane was so broad as to allow car rally divided into two or more compartriages to pass each other.

ments, and sometimes charged with hieroFrom very remote antiquity the Egyptians glyphics, as well as the walls and ceilings : have been celebrated for their cultivation the compartments are sometimes also ornaof architecture among other arts ; the ruins mented with vertical reeds, representing a of their ancient structures astonish the tra- bundle of rods, and separated from each veller of the present day, as may be seen in other by annular incisions, or beads, which their huge pyramids and proud tombs, which seem as bandages for tying the rods together. have long outlived the memory of the mighty The whole of the compartments are not alkings whose ashes they contain: granite ways reeded: sometimes there are only one temples as extensive as towns, which inclose or two, and the rest carved with hieroglyin their courts or support upon their roofs phics. The capitals sometimes swell out at villages of the modern inhabitants; long the bottom from the upper part of the shaft, avenues of sphinxes, colossal statues, and and diminish to the top, which is covered obelisks. Yet the art of building among with a square projecting abacus; sometimes them consisted of but few principles, for capitals have vases like the Corinthian order, they did not seem to understand the use of which rise with a small convexity from the the arch; all the apertures and intercolumns shaft, and change into a large concavity upof their walls were linteled with solid stone; wards, which as it approaches the top hias the roofs of the chambers of their temples more and more curvature until it terminates : were generally covered with massy slabs for above the termination it recedes with a conlintels; the ceiling or roof of the passage vexity to the abacus, which is also recessed within the great pyramid is formed of stones within the face of the linteling architrave. in horizontal courses, projecting equally over Sometimes the capitals are formed by the each other from the two opposite walls to head of Isis, with a temple in miniature the summit, like inverted Aights of steps: placed over it, and then crowned with the the roots of some of their tombs are indeed square abacus recessed; the lower parts of arch formed, but these are only excavations the intervals between the columns are shut cut out of the solid rock. Their walls were by a kind of parapet, reaching from three built of stones of an enormous size, without to three and a half diameters from the cement. The removal and placing of these ground. This parapet is sometimes flush huge materials would, even at this day, al- with the columns; but is not extended most bid defiance to the boldest and best so as to hide their convexity on the front, constructed of our mechanical inventions, which shews nearly a quarter of the cirthough conducted with all the science of cumference. modern times. The stones of their edifices Architecture has also been carried to a are squared and jointed with the utmost ac wonderful extent among the ancient inhacnracy; the hieroglyphic carvings with bitants of India, who have not only riwhich their walls and ceilings are charged valled the Egyptians, but have been sup. are all recessed, but projecting in relief from posed to be even anterior to them in the the bottoms or backs of the recesses. The knowledge of the art; their exertions were, forms of Egyptian temples and gates are however, directed almost exclusively to exgenerally truncated rectangular pyramids, cavation. crowned with a cove and fillet, or cavetto, The Assyrians have been much repnted as a cornice around the four angles of the for their knowledge in the art of building : sides, , and under the cornice project tori the walls of Nineveh and Babylon were of from each face. The entrance front of the wonderful magnitude. Those of the latter temples has generally a large rectangular were double, and surrounded with a ditch; opening, in which are placed columns for the outer wall was regularly fortified; it supporting the architrave and cornice: over was 15 miles square, or 60 in circumference, the middle of the door, and upon the lintel 200 royal cubits high, and 50 thick : in ing architrave, is carved a' winged globe: the circumference were placed 100 massy the height of the columns, according to gates of brass; and on the top, watchDenon's representation, is from five to six towers, corresponding to each other. The diameters. The colunins have in general materials used in the construction of these little or no diminution, and are frequently works, were square bricks, baked in a fur. placed upon a plinth, from which they nace, and heated bitumen, mixed with the sometimes rise in a convexity, forming what tops of reeds; this composition was placed is called by workmen a quirk above the between every thirteen courses of bricks :

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from this circumstance it is probable, that only to be found in the theatres and gyma
the method of reducing calcareons stones 'nasia; the apertures of walls and interco-
into lime for mortar was unknown at this lumns being linteled.
time. The walls of Babylon are described Greece, though a mild climate, is some-
to be one of the seven wonders of the times liable to rain ; the architects of this
world ; they were first built by queen Se- country, therefore, found it necessary to
miramis, in the time of her regency, dur- raise the roofs of their edifices, to a ridge
ing the minority of her son Ninias; and it in the middle, the section being that of a
would seem that they were afterwards im- rectilineal isosceles triangle: the base be.
proved by the great Nebuchadnezzar. Of ing the span or distance between the oppo-
these mighty works there

site walls. This form of roof, called a pemains, nor hardly any trace of the ancient diment roof, was frequently covered with city.

marble tiles. In the ruins of Persepolis, though the The Grecians surpassed all contempocolumns are of a character somewhat diffe- rary nations in the arts of design; the rerent from those of Egypt; yet the Egyp- mains of their ancient structures are motian style of buildivg may be retraced in dels of imitation, and confessed standards various parts of these ruins. Diodorus Siculus of excellence. They were the inventors says, that the famous palaces of Susa and of three orders of architecture, of which Persepolis were not built till after the con we have already hinted, and which we' quest of Egypt by Cambyses, and that they shall detail in a subsequent part of this arwere both conducted by Egyptian architects; ticle. The remains of their sculptures far it therefore seems probable that the Per- exceed that of any other people, and are, sians received the art of building in un even at this day, most perfect models. Mowrought stone from the Egyptians.

dern artists have no means so certain, in The Phænicians were also very cele- attaining a just knowledge of their profes-' brated for their arts of design, but few or sion, as in the study of those exquisite masnone of their works have reached the pre- ter-pieces. sent time.

The progress of Grecian architecture In the vast structures of Asia and Africa, appears to have occupied a period of about greatness of design, ponderosity of parts, three centuries, from the age of Solon to and stones of immense magnitude, seem to the death of Alexander; and in this period have been more regarded than elegance or it advanced rapidly, particularly from the utility: in all those great works there is no defeat of Xerxes, to the death of Pericles, trace of an arch, but what is excavated out at which time it attained its utmost degree of the solid rock, or may be made of a' of excellence, and continued to flourish single stone. The Greeks profess to have till the time it became a Roman province. derived the knowledge of architecture Prior to the Macedonian conquest, all from the Egyptians, but the art of building the temples of Greece, and its colonies in has been so much improved by trans- Sicily and Italy appear to have been of the plauting, that scarcely any trace of the ori Doric order; and' of one general form, ginal remains : their edifices were at first though slightly varied in particular parts, as constructed of wood and clay, but they occasional circumstances might require: soon began to imitate the wooden posts their plan was an oblong, having one coand beams of the original hut in stone and lumn more on the flank than double the marble: from this imitation arose the first number of those in front. order in architecture, which also gave birth The ancient Etrurians have left many to two others. This ingenious people, fa- excellent monuments of taste, and to them voured by nature with marble and other is generally ascribed the method of building building materials, and, like the Egyptians, with small stone and mortar, made of calbeing anxious to make their works durable, careous stone ; and this seems probable, as employed very weighty stones in the con the most ancient vestiges of cementitious struction, which, althorigh laid without ce buildings are to be found in the country ment, as was the practice of all ancient which the present Tuscans inhabit. nations, yet they were jointed with the ut They were employed by the Romans in most accuracy, which is the reason of the many public works; the walls of the city of perfect state of their edifices at this day. Rome were made of hewn stone, the capitol There is little doubt but that the Greeks and the cloaca maxima are of their conwere the inventors of the arch, though they struction; the last of these is esteemed a never considered it as an oruament; it is very extraordinary piece of architecture, as'

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