A Collection of Curious Travels and Voyages, Volume 2 · Observations 2 · Section 1
A Deſcription of the firſt and faireſt Pyramid.
THE firſt and faireſt of the three greater Pyramids is ſituated on the top of a rocky Hill, in the Sandy Deſart of Lybia, about a quarter of a mile diſtant to the Weſt, from the Plains of Aegypt, above which the Rock riſeth an hundred feet or better, with a gentle and eaſie aſcent. Upon this advantageous Riſe, and upon this ſolid Foundation the Pyramid is erected; the heighth of the ſituation adding to the beauty of the Work, and the ſolidity of the Rock giving the Superſtructure a permanent and ſtable ſupport. Each ſide of the Pyramid, computing it according to Herodotus, contains in length 800 Graecian feet: And in Diodorus Siculus account 700 Strabo reckons it leſs than a furlong, that is leſs than 600 Graecian feet, or Six hundred twenty five Roman. And Pliny equals it to 883. That of Diodorus Siculus, in my judgment, comes neareſt to the Truth, and may ſerve in ſome kind to confirm thoſe proportions, which in another Diſcourſe I have aſſigned to the Graecian meaſures: For meaſuring the North ſide of it, near the Baſis, by an exquiſite radius of ten feet in length, taking two ſeveral ſtations, as Mathematicians uſe to do, when any Obſtacle hinders their approach, I found it to be Six hundred ninety three feet, according to the Engliſh Standard; which quantity is ſomewhat leſs than that of Diodorus. The reſt of the ſides were examined by a line, for want of an even level and a convenient diſtance to place my Inſtruments, both which the Area on the former ſide afforded.
The Altitude of this Pyramid was long ſince meaſured by Thales Mileſius, who according to Tatianus Aſſyrius lived about the fiftieth Olympiad, but his Obſervations is no where by the Ancients expreſſed: Only Pliny tells us of a courſe propoſed by him, how it might be found, and that is by obſerving ſuch an hour, when the ſhadow of the body is equal to its height. A way at the beſt, by reaſon of the faintneſs and ſcattering of the extremity of the ſhadow, in ſo great an Altitude, uncertain, and ſubject unto Error. And yet Diogenes Laertius, in the life of Thales, hath the ſame Story, from the Authority of Hieronymus. Hieronymus reports, That he meaſured the Pyramids by their ſhadow, marking when they are of an equal quantity. Wherefore I ſhall paſs by his, and give my own Obſervations. The Altitude is ſomething defective of the Latitude; though in Strabo's computation it exceeds; but Diodorus rightly acknowledges it to be leſs, which if we meaſure by its perpendicular, is Four hundred eighty one feet; but if we take it as the Pyramid aſcends inclining (as all ſuch Figures do) then it is equal, in reſpect of the lines ſubtending the ſeveral angles, to the Latitude of the Baſis, that is to ſix hundred ninety three feet.
What exceſſive heighths ſome fancy to themſelves, or borrow from the relations of others, I ſhall not now examine. This I am certain of, that the Shaft or Spire of Pauls in London, before it was caſually burnt, being as much, or ſomewhat more than the altitude of the Tower now ſtanding (1647) did exceed the height of this Pyramid. For Cambden deſcribes it to have been in a perpendicular, five hundred and twenty feet from the Ground.
If we imagine upon the ſides of the Baſis, which is perfectly ſquare, four equilateral triangles mutually propending, and enclining, till they all meet on high as it were in a point (for ſo the top ſeems to them which ſtand below) then ſhall we have a true notion of the juſt dimenſion and figure of this Pyramid: The Perimeter of each triangle comprehending two thouſand ſeventy nine feet (beſides the Latitude of a little Plain, or Flat on the top) and the perimeter of the Baſis Two thouſand ſeven hundred ſeventy two feet: Whereby the whole area of the Baſis (to proportion it to our meaſures) contains four hundred eighty thouſand, two hundred forty nine ſquare feet, or eleven Engliſh Acres of Ground, and 1089 of 43560 parts of an Acre. A proportion ſo monſtrous, that if the Ancients did not atteſt as much, and ſome of them deſcribe it to be more, this Age would hardly be induced to give credit to it. But Herodotus deſcribing each ſide to contain eight hundred feet, the area muſt of neceſſity be greater than that by me aſſigned, the ſum amounting to ſix hundred and forty thouſand; or computing it as Diodorus Siculus doth, the area will comprehend four hundred and ninety thouſand feet: And in the calculation of Pliny, if we ſhall ſquare eight hundred eighty three (which is the number allotted by him to the meaſure of each ſide) the Product ſeven hundred ſeventy nine thouſand ſix hundred eighty nine, will much exceed both that of Herodotus and this of Diodorus. Though certainly Pliny is much miſtaken, in aſſigning the meaſure of the ſide to be eight hundred eighty three feet, and the Baſis of the Pyramid to be but eight iugera, or Roman Acres: For if we take the Roman iugerum to contain in length two hundred and forty feet, and in breadth one hundred and twenty, as may be evidently proved out of Varro, and is expreſly affirmed by Quintilian, then will the ſuperficies, or whole extention, of the iugerum be equal to twenty eight thouſand eight hundred Roman feet; with which if we divide ſeven hundred ſeventy nine thouſand ſix hundred eighty nine, the reſult will be twenty ſeven Roman iugera, and 2089 of 28800 parts of an Acre. Wherefore if we take thoſe numbers eight hundred eighty three of Pliny to be true, then I ſuppoſe he writ twenty eight iugera, inſtead of eight, or elſe in his proportion of the ſide, to the area of the Baſis he hath erred.
The aſcent to the top of the Pyramid is contrived in this manner. From all the ſides without we aſcend by degrees; the lowermoſt degree is near four foot in height, and three in breadth. This runs about the Pyramid in a level; and at the firſt, when the Stones were entire, which are now ſomewhat decay'd, made on every ſide of it a long but narrow Walk. The ſecond degree is like the firſt, each Stone amounting to almoſt four feet in height, and three in breadth; it retires inward from the firſt near three feet, and this runs about the Pyramid in a level, as the former. In the ſame manner is the third row placed upon the ſecond, and ſo in order the reſt, like ſo many Stairs riſe one above another to the top. Which ends not in a point, as Mathematical Pyramids do, but in a little flat or ſquare. Of this Herodotus hath no where left us the dimenſions, but Henricus Stephanus, an able and deſerving man, in his Comment hath ſupplied it for him; for he makes it to be eight orgyiae; where if we take the orgyia, as both Heſychius and Suidas do, for the diſtance between the Hands extended at length, that is for the fathom, or ſix feet, then ſhould it be forty eight feet in breadth at the top. But the truth is, Stephanus, in this particular, whilſt he corrects the Errors of Valla's Interpretation, is to be corrected himſelf; for that Latitude which Herodotus aſſigns to the admirable Bridge below (of which there is nothing now remaining) he hath carried up, by a miſtake, to the top of the Pyramid. Diodorus Siculus comes nearer to the truth, who deſcribes it to be but nine feet. Pliny makes the breadth at the top to be twenty five feet, Altitudo (I would rather read it latitudo) à cacumine pedes 25. By my meaſure it is 13 feet, and 280 of 1000 parts of the Engliſh foot. Upon this flat, if we aſſent to the Opinion of Proclus, it may be ſuppoſed that the Aegyptian Prieſts made their Obſervations in Aſtronomy; and that from hence, or near this place, they firſt diſcovered, by the riſing of Sirius, their annus foreign, or Canicularis, as alſo their periodus Sothiaca, or annus magnus foreign, or annus Heliacus, or annus Dei, as it is termed by Cenſorinus, conſiſting of 1400 ſidereal years, in which ſpace their Thoth Vagum, and fixum, came to have the ſame beginning. That the Prieſts might near theſe Pyramids make their obſervations, I no way queſtion, this riſing of the Hill being, in my Judgment, as fit a place as any in Aegypt for ſuch a deſign, and ſo much the fitter by the vicinity of Memphis. But that theſe Pyramids were deſigned for Obſervatories, (whereas by the teſtimonies of the Ancients I have proved before, that they were intended for Sepulchres) is no way to be credited upon the ſingle authority of Proclus. Neither can I apprehend to what purpoſe the Prieſts with ſo much difficulty ſhould aſcend ſo high, when below with more eaſe, and as much certainty, they might from their own Lodgings hewn in the Rocks upon which the Pyramids are erected, make the ſame obſervations: For ſeeing all Aegypt is but as it were one continued plain, they might from theſe Cliffs have, over the Plains of Aegypt, as free and open a proſpect of the Heavens, as from the tops of the Pyramids themſelves. And therefore Tully writes more truly, Aegyptii, aut Babylonii, in camporum patentium aequoribus habitantes, cum ex terra ad nihil emineret, quod contemplationi coeli officere poſſet, omnem curam in ſiderum cognitione poſuerunt. The top of this Pyramid is covered not with (d)Les voyages de Seign. Villamont.one or (e)Sands Travels.three maſſy Stones, as ſome have imagined, but with nine, beſides two which are wanting at the Angles. The degrees by which we aſcend up (as I obſerved in meaſuring many of them) are not all of an equal depth, for ſome are near four feet, others want of three, and theſe, the higher we aſcend, do ſo much the more diminiſh: neither is the breadth of them alike, the difference in this kind being, as far as I could conjecture, proportionable to their depth. And therefore a right line extended from any part of the Baſis without, to the top, will equally touch the outward angle of every degree. Of theſe it was impoſſible for me to take an exact meaſure, ſince in ſuch a revolution of time, if the inner parts of the Pyramid have not loſt any thing of their firſt perfection, as being not expoſed to the Injury of the *The Air of Aegypt is confeſſed by the Ancients to be often full of Vapors; which appears both by the great dews that happen'd after the Deluge of Nilus for ſeveral months; as alſo in that I have diſcovered at Alexandria, in the Winter time, ſeveral obſcure Stars in the conſtellation of Ʋrſa major, not viſible in England; the which could not be diſcerned there, were there not a greater refraction at that time, than with us, and conſequently a greater condenſation of the medium, or Air, as the Opticks demonſtrate.Air, yet the outward parts, that is theſe degrees or rows of Stone, have been much waſted and impaired by both. And therefore they cannot conveniently now be aſcended, but either at the South ſide, or at the Eaſt angle on the North. They are well ſtiled by Herodotus foreign, that is, little Altars, for in the form of Altars they riſe one above another to the top: And theſe are all made of maſſy and poliſh'd Stones, hewn according to Herodotus and Diodorus, out of the Arabian Mountains, which bound the upper part of Aegypt, or that above the Delta, on the Eaſt, as the Lybian Mountains terminate it on the Weſt, being ſo vaſt, that the breadth and depth of every ſtep is one ſingle and entire Stone. The relation of Herodotus and Pomponius Mela, is more admirable, who make the leaſt Stone in this Pyramid to be thirty feet. And this I can grant in ſome, yet ſurely it cannot be admitted in all, unleſs we interpret their words, that the leaſt Stone is thirty ſquare, or to ſpeak more properly, thirty cubical feet; which dimenſion, or a greater, in the exteriour ones, I can without any difficulty admit. The number of theſe Steps is not mentioned by the Ancients, and that cauſed me, and two that were with me, to be the more diligent in computing them, becauſe by modern Writers, and ſome of thoſe too of repute, they are deſcribed with much diverſity and contrariety. The degrees, ſaith Bellonius, are two hundred and fifty, each of them ſingle contains in height forty five digits, at the top it is two paces broad; for this I take to be the meaning of what Cluſius renders thus: Abaſi autem ad cacumen ipſius ſupputationem facientes, comperimus circiter, 250 gradus, ſinguli altitudinem habent 5 ſolearum calcei 9 pollicum longitudinis, in faſtigio duos paſſus habet. Where I conceive his paſſus is in the ſame ſence to be underſtood here above, as not long before he explains himſelf in deſcribing the Baſis below, which in his account is 324 paſſus paululum extenſis cruribus. Albertus Lewenſtainius reckons the Steps to be two hundred and ſixty, each of them a foot and a half in depth. Johannes Helfricus counts them to be two hundred and thirty. Sebaſtianus Serlius, upon a relation of Grimano the Patriarch of Aquileia, and afterwards Cardinal, (who in his Travels in Aegypt meaſured theſe degrees) computes them to be two hundred and ten, and the height of every ſtep to be equally three palms and a half. It would be but loſt labour to mention the different and repugnant relations of ſeveral others; that which by experience and by a diligent calculation I and two others found, is this, that the number of degrees from the bottom to the top, is two hundred and ſeven, though one of them in deſcending reckoned two hundred and eight.
Such as pleaſe, may give credit to thoſe fabulous Traditions of ſome, That a Turkiſh Archer ſtanding at the top, cannot ſhoot beyond the bottom, but that the Arrow will neceſſarily fall upon theſe ſteps. If the Turkiſh bow (which by thoſe figures which I have ſeen in ancient Monuments, is the ſame with that of the Parthians, ſo dreadful to the Romans) be but as ſwift and ſtrong as the Engliſh; as ſurely it is much more, if we conſider with what incredible force ſome of them will pierce a Plank of ſix inches in thickneſs, (I ſpeak what I have ſeen) it will not ſeem ſtrange, that they ſhould carry twelve ſcore in length, which diſtance is beyond the Baſis of this Pyramid.