in Geometry, a solid standing on a triangular, square, or polygonal base, and terminating in a point at the top; or, according to Euclid, it is a solid figure, consisting of several triangles, whose bases are all in the same plane, and have one common vertex.

Pyramids are sometimes used to preserve the memory of singular events, and sometimes to transmit to posterity the glory and magnificence of princes. But as they are esteemed a symbol of immortality, they are most commonly used as funeral monuments and temples to the gods. Such is that of Cestius at Rome; the pyramids of Dahur drawn by Pococke; and those other celebrated ones of Egypt, as famous for the enormity of their size as their antiquity. Of these the largest are the pyramids of Giza, so called from a village of that name on the banks of the Nile, distant from them about 11 miles. The three which most attract the attention of travellers stand near one another on the west side of the river, almost opposite to Grand Cairo, and not far from the place where the ancient Memphis stood. They were visited by M. Savary, of whose description of them we shall here give an abstract.

He took his journey in the night time, in order to get up to the top of the great one by sunrise. Having got within sight of the two great ones, while the full moon shone upon them, he informs us, that they appeared, at the distance of three leagues, like two points of rock crowned by the clouds.

It is in the rich territory which surrounds them that fable has placed the Elysian fields. The canals which intersect them are the Styx and Lethe.

"The aspects of the pyramids, varied according to the circuits he made in the plain, and the position of the clouds, displayed themselves more and more to view.

At half past three in the morning we arrived (says he) at the foot of the greatest. We left our clothes at the gate of the passage which leads to the inside, and descended, carrying each of us a flambeau in his hand. Towards the bottom you must creep like serpents to get into the interior passage, which corresponds with the former. We mounted it on our knees, supporting ourselves with our hands against the sides. Without this precaution one runs the risk of slipping on the inclined plane, where the flight notches are insufficient to stop the foot, and one might fall to the bottom. Towards the middle we fired a pistol, the frightful noise of which, repeated in the cavities of this immense edifice, continued a long time, and awakened thousands of bats, which flying round us, struck against our hands and faces, and extinguished several of our wax candles. They are much larger than the European bats. Arrived above, we entered a great hall, the gate of which is very low. It is an oblong square, wholly composed of granite. Seven enormous stones extend from one wall to the other, and form the roof. A sarcophagus made of a single block of marble lies at one end of it. It is empty; and the lid of it has been wrenched off. Some pieces of earthen vases lie around it. Under this beautiful hall is a chamber not so large, where you find the entrance to a conduit filled with rubbish. After examining these caves, where daylight never penetrated, we descended the same way, taking care not to fall into a well, which is on the left, and goes to the very foundations of the pyramid. Pliny makes mention of this well, and says it is 26 cubits deep. The internal air of this edifice never being renewed, is so hot and mephitic that one is almost suffocated. When we came out of it, we were dropping with sweat, and pale as death. After refreshing ourselves with the external air, we lost no time in ascending the pyramid. It is composed of more than 200 layers of stone. They overlap each other in proportion to their elevation, which is from two to four feet. It is necessary to climb up all these enormous steps to reach the top. We undertook it at the north-east angle, which is the least damaged. It took us, however, half an hour with great pains and many efforts to effect it.

"The sun was rising, and we enjoyed a pure air, with a most delicious coolness. After admiring the prospect around us, and engraving our names on the summit of the pyramid, we descended cautiously, for we had the abyss before us. A piece of stone detaching itself under our feet or hands might have sent us to the bottom.

"Arrived at the foot of the pyramid, we made the tour of it, contemplating it with a sort of horror. When viewed close, it seems to be made of masses of rocks; but at a hundred paces distance, the largeness of the stones is lost in the immensity of the whole, and they appear very small.

"To determine its dimensions is still a problem. From the time of Herodotus to our days it has been measured by a great number of travellers and learned men, and their different calculations, far from clearing up doubts, have only increased the uncertainty. The following table will serve at least to prove how difficult it is to come at the truth." | Height of the great Pyramid | Width of one of its sides | |---------------------------|--------------------------| | Ancients | French Feet | | Herodotus | 800 | | Strabo | 625 | | Diodorus Siculus | 600 and a fraction | | Pliny | 708 | | Moderns | | | Le Bruyn | 616 | | Prosper Alpinus | 625 | | Thevenot | 520 | | Niebuhr | 440 | | Greaves | 444 |

Number of layers of Stone which form it.

| Greaves | Maillet | Albert Liewenstein | Pococke | Belon | Thevenot | |---------|---------|--------------------|---------|-------|----------| | | | | | | | | 207 | 208 | 260 | 212 | 250 | 208 |

"It appears that Messrs Greaves and Niebuhr have prodigiously deceived themselves in measuring the perpendicular height of the great pyramid. All the travellers allow that it has at least 200 layers of stone. These layers are from two to four feet high. According to Pococke, they are from four feet and a half to four feet high, being not so high at the top as at the base. Prosper Alpinus informs us, that the elevation of the first layer is five feet, but it diminishes infinitely in proportion as one mounts. Thevenot mentions 208 steps of large stones, the thickness of which makes the height of them about two feet and a half one with another; He measured some of them more than three feet high. I have measured several of them which were more than three feet high, and I found none less than two; the least height of them we can take as a medium therefore is two feet and a half, which, even according to Mr Greaves's calculation, who reckons 207 layers, would make 517 feet 6 inches perpendicular height. Messrs Greaves, Maillet, Thevenot, and Pococke, who only differ in the number of the layers from 207 to 212, all mounted by the north-east angle, as the least injured. I followed the same route, and counted only 208 steps. But if we reflect that the pyramid has been open on the side next the desert, that the stones on that side have been thrown down, that the sand which covers them has formed a considerable hill, we shall not be astonished that Albert Liewenstein, Belon, and Prosper Alpinus, who must have mounted by the south-east or south-west angle, which are less exposed to the sands of Libya, should have found a greater number of steps: so that the calculation of these travellers, agreeing with that of Diodorus Siculus and Strabo, appears to be nearest the true height of the pyramid taken at its natural base; whence we may conclude with reason that it is at least 600 feet high. Indeed this is authenticated by a passage of Strabo. These are his words: 'Towards the middle of the height of one of the sides is a stone that may be raised up. It shuts an oblique passage which leads to a coffin placed in the centre of the pyramid.' This passage, open in our days, and which in the time of Strabo was towards the middle of one face of the pyramid, is at present only 100 feet from the base. So that the ruins of the covering of the pyramid, and of the stones brought from within, buried by the sand, have formed a hill in this place 200 feet high. Pliny confirms this opinion. The great sphinx was in his time upwards of 62 feet above the surface of the ground. Its whole body is at present buried under the sand. Nothing more appears of it than the neck and head, which are 27 feet high. If even the sphinx, though defended by the pyramids against the northerly winds, which bring torrents of sand from Libya, be covered as high as 38 feet, what an immense quantity must have been heaped up to the northward of an edifice whose base is upwards of 700 feet long? It is to this we must attribute the prodigious difference between the accounts of the historians who have measured the great pyramid at distant periods, and at opposite angles. Herodotus, who saw it in the age nearest to its foundation, when its true base was still uncovered, makes it 800 feet square. This opinion appears very probable. Pliny also says that it covered the space of eight acres.

"Messrs Shaw, Thevenot, and the other travellers who pretend that this pyramid was never finished, because it is open and without coating, are in an error. It is only necessary to observe the remains of the mortar, with the splinters of white marble which are to be found in many parts of the steps, to see that it has been coated. After reading attentively the description given of it by the ancients, every doubt vanishes, and the truth is as clear as day-light. Herodotus tells us, 'The great pyramid was covered with polished stones, perfectly well jointed, the smallest of which was 30 feet long. It was built in the form of steps, on each of which were placed wooden machines to raise the stones from one to another.' According to Diodorus, 'The great pyramid is built of stones, very difficult of workmanship, but of an eternal duration. It is preferred to our days (towards the middle of the Augustan age) without being in the least injured. The marble was brought from the quarries of Arabia.' This historian thought that the whole building was composed of stones, similar to those of the coating, which were of very hard marble. Had there been some pieces torn off, he would have perceived under that covering a calcareous stone rather soft. Pliny says that it 'is formed of stones brought from the quarries of Arabia. It is not far from the village of Bufiris (which still exists under the name of Boufr), where those persons reside who are so skilful as to climb up to the top.'

"This passage shows that Pliny, deceived by the appearance, was in the same error with Diodorus Siculus. It demonstrates also that it was covered: for what difficulty would there have been for the inhabitants of Bufiris to scale a building raised by steps? but it was really a prodigy for them to get up it when it formed a mountain, the four inclined planes of which presented a surface covered with polished marble. It is indeed an incontrovertible fact, that the great pyramid was coated. It is as certain too that it has been flat, as Strabo gives us to understand; and that by removing a stone placed in the middle of one of the sides, one found a passage which led to the tomb of the king. But I shall leave Mr Maillet, who visited it 40 times with all imaginable..." imaginable attention, the honour of relating the means employed to open it. I have examined the inside of it in two different journeys: twice I have mounted it; and I cannot help admiring the sagacity with which that author has developed the mechanism of that astonishing edifice."

Our author next proceeds to give a particular description of the methods by which it is most probable that the pyramids were closed, and the immense labour requisite to open them. We must remark, that the final outlet to the workmen he supposes to have been the well at the entrance formerly mentioned. This well descends towards the bottom of the pyramid by a line not quite perpendicular to the horizon, but slanting a little, in such a manner as to resemble the figure of the Hebrew letter Lamed. About 60 feet from the aperture there is a square window in this passage, from whence we enter a small grotto hewn out of the mountain; which in this place is not a solid stone, but a kind of gravel concreted together. The grotto extends about 15 feet from east to west, where there is another groove hollowed likewise, but almost perpendicular. It is two feet four inches wide by two and a half in height. It descends through a space of 123 feet, after which we meet with nothing but sand and stones. M. Savary is convinced that the only use of this passage was to serve as a retreat for the labourers who constructed the pyramid; and of this he looks upon the slope of the conduit, its winding road, its smallness, and its depth, to be certain proofs. The way out of it he supposes to have been formed by a passage over which hung a row of stones, which they had discovered the secret of suspending, and which falling down into the passage by the means of some spring they set in motion, shut up the entrance forever, as soon as the workmen were withdrawn from the pyramid.

It seems to be an unquestionable fact, that this pyramid was a mausoleum of one of the kings of Egypt, and it is very probable that all the rest answered similar purposes. We do not, however, think that this was their primary use or the original design of their builders. Mr. Bryant is of opinion that they were temples erected in honour of the Deity; and a very ingenious writer in the Gentleman's Magazine for June 1794 has done much to prove that they were altars dedicated to the sun, the first and greatest god in every pagan kalendar.

"Our English word pyramid (says he) is directly derived from the Latin pyramis, and mediately from the Greek πυραμίς; all denoting the same mathematical figure. The original of the whole seems to be the Egyptian word pyramoua, which we are told by Oriental scholars, signifies light, or a ray of light. From this Coptic vocable the word πυρ in Greek, signifying fire, is probably descended; as the flames of fire assume that conical or pyramidal form which the solar rays commonly display; and as it is natural for the mind to distinguish its objects rather by their external qualities, and those obvious and interesting appearances which they exhibit to the senses, than by their constituent and inseparable properties.

"The ancient Egyptians seem to have penetrated very far into the mysteries of nature; and although their superstition appears at first sight to be extremely gross and absurd, yet it is very probable that their deities were only emblematical personages, representing by sensible images the grand effects or presiding principles which they supposed to exist in the universe. Thus the moon was called Ifis, and the sun Qiris; and to the honour of this last deity, from whose visible influence and creative energy all things seem to spring into existence, it is not improbable that the Egyptians erected those stupendous monuments, and dedicated them to him as temples or altars. It was natural to build them in that shape which the rays of the sun display when discovered to the eye, and which they observed to be the same in terrestrial flame, because this circumstance was combined in their imaginations with the attribute which they adored. If they were temples dedicated to the sun, it seems a natural consequence that they should likewise be places of sepulture for kings and illustrious men, as the space which they covered would be considered as consecrated ground. This hypothesis is common, and is not contradicted by the present reasoning. But, considering them as altars, and as most travellers agree that they were never finished, but terminate in a square horizontal surface, it would not be refining too much to venture an assertion that, in great and solemn acts of adoration, the Egyptians constructed fires, the flames of which should terminate in the vertex of the pyramid, and so complete that emanation of their deity which they admired and adored. As far, therefore, as we are justified in forming any conclusion on so dark a subject, we may venture to say, that the Egyptian pyramids were temples or altars dedicated to the sun, as the material representative of that invisible power which creates, governs, and pervades, the whole system of nature."

This reasoning has some force; and it certainly receives additional strength from the undoubted fact, that the first statues for idolatrous worship were erected on the tops of mountains, and of a pyramidal or conical form. (See Polytheism, No. 13 and 21.) It is likewise corroborated by other circumstances discovered by the members of the Asiatic Society. In the second volume of their transactions we have an account of several large statues of the gods Seva and Mchedeo, all of a conical or pyramidal figure; but it has been shown in the article already referred to, that the idolatry of Hindoostan was probably of Egyptian origin.

It is not known in Europe when the pyramids were built; but we have reason to expect a history of them soon from Shamsfur records examined by Mr Wilford lieutenant of engineers. It is as little known at what time, or from what motive, the great pyramid was opened. Some think it was done by one of the Khalifs about the beginning of the eighth century, in expectation of finding a great treasure; but all he met with was the king's body, with some golden idols which had been buried along with it.—By others it is supposed to have been done by the celebrated Harun Al Raschid khalif of Bagdad; but all are agreed that this pyramid was opened in the time of the Arabs. The second pyramid has likewise been opened; and an attempt was made not long ago upon the third by one of the Beys of Cairo: but after removing a number of stones at a considerable expense, he thought proper to desist from the enterprise.—Mr Bryant is of opinion that the pyramids, at least the three great ones, are not artificial structures of stone and mortar, but solid rocks cut into a pyramidal shape, and afterwards cased with stone; and to this Pyramid, this we find that Mr Bruce likewise affirms. The reason given for this opinion is, that the passages within it seem rather to answer to the natural cavities and rents in rocks than to the artificial ones in buildings. The opinion, however, we think sufficiently confuted by Savary and Maillet; and, as an acute critic observes, it is in itself as improbable, as that the caverns inhabited by the Troglodytes were dug by the hands of man.

See Troglodytes.

On the east side of the second pyramid is the Sphinx, an enormous mass of one solid stone, but so buried in the sand that only the top of the back is visible, which is 100 feet long. Its head rises, as we have seen, 27 feet above the sand; and its face has been disfigured by the Arabs, who hold all representations of men and living animals in detestation. Other travellers say that this Sphinx is a huge mishapen rock, by no means worthy of the attention which has been bestowed upon it.

In the desert of Saccara there is a great number of pyramids, which, in Mr Bruce's opinion, are composed of clay. They terminate in what the inhabitants call a daguerre or false pyramid, about two miles from the Nile, between Suf and Woodan. This is no other than a hill cut into the shape of a pyramid, or naturally so formed, for a considerable height; on the top of which is a pyramidal building of brick terminating in a point, and having its basis so exactly adapted to the top of the hill, that at a distance the difference cannot be perceived; especially as the face of the stones resembles very nearly the clay of which the pyramids of the Saccara are composed.

But a very different opinion concerning the purpose to which the great pyramid was originally destined, and the period in which that extraordinary edifice was erected, is held by Mr Gabb, who has not long since published an elaborate treatise on this subject. According to this author not only the great pyramid, but also the smaller pyramids are of antediluvian origin; the immense accumulation of sand around those stupendous structures took place at the time of the deluge; the height of this sand, when the waters subsided, probably reached the summit of the pyramid, and the apex of the great pyramid was torn off by the violent agitation of the waters. The author contends that the sand round the pyramids could not have been collected by the force of the winds; and that it is equally improbable that it could have been deposited from the waters of the Nile during the inundations of that river; for the Nile was never known to rise to such a height, and the organized remains, such as shells and petrified oysters, found in the sands about the pyramids, are quite different from any shell-fish that inhabit the Nile. From all this the author concludes, that the great pyramid was erected by the Antediluvians, that the remarkable deposition of sand on the surface of the extensive rock on which that immense fabric stands can only be satisfactorily accounted for from the effects of the universal deluge or flood of Noah; and that the accumulation of sand is diminishing rather than increasing by the force of the wind. The author supposes that the other pyramids were also built before the flood, but at a later period than that of the great pyramid, which latter he thinks was the work of the immediate descendants of Seth. In proof of this, Josephus is quoted, who notices a memorial of an ancient tradition preserved among the Jews, that the direct descendants of Seth were much employed in astronomical observations. The perfect geometrical figure of the pyramid, the commensurability of its parts to the whole, the scientific approach of the tide of its base to a meridional degree of the circumference of the earth, and the useful solutions of problems deducible from it, lead to the same inference.

But the most curious part of this author's disquisition concerning the pyramid relates to the purpose for which that stupendous fabric was raised; and here he is decidedly of opinion, that it was originally intended as a standard of measure, and not as has been more generally supposed as a sepulchral monument; and farther that the excavation of the celebrated granite chest in the interior of the pyramid was intended not for the repository of a couple, but for a standard measure of capacity, as its length was for linear measure. This is also the opinion of the French savans who accompanied the army of Bonaparte to Egypt, and very successfully ascertained the dimensions of that remarkable building.

The plan of the pyramid is a geometrical square, the side of which is equal to 400 cubits of Cairo, or the great Egyptian stadium. The length of the granite chest in the upper chamber of the pyramid is exactly four cubits, which is precisely one hundredth part of the base of the side of the pyramid. The commensurability of the component parts of the pyramid now mentioned, as well as of others discussed by the author, is undoubtedly a curious circumstance. But we must refer our readers to the work itself, and for farther information concerning the pyramids, to Denon's Travels, &c.