ART. XVII. De Prisca Ægyptiorum Litteratura Commentatio Prima, THERE can be little doubt, that, next to the formation of a phonetic alphabet, by which every articulate combination of language may be expressed, and the invention of printing, by which copies of books may be multiplied without limit, the discovery which has contributed most largely to the advancement of knowledge, and the improvement of mankind, is that of the signs commonly called the Arabic Numerals. The latter, indeed, are to the different modes of notation which obtained prior to the period of their introduction, what the phonetic alphabet was to the rude and untractable forms of pictorial or symbolical writing, which, in the natural progress of events, it succeeded and finally superseded; namely, a series of signs denoting the simplest elements of numerical expression, yet susceptible of indefinite combination, precisely as the alphabet in question, though representing only the elementary sounds of the human voice, is, nevertheless, the basis of written language, Both discoveries, in fact, were the result of an analysis so refined, a simplification so perfect, as not only to fill us with unbounded admiration of the wonderful subtlety of genius by which they were achieved, but, which is of far greater importance, to afford, when accommodated with appropriate signs, the inestimable advantage of universal expressions. The nine digits, or Arabic Numerals, therefore, are to the science of numbers what the phonetic alphabet, in its simplest form of the Kadmean, or double octave, is to spoken or written language; that is, rà πρштα oroixɛĩa, prima elementa, or first principles, by the synthesis or composition of which, results, astonishing in themselves, and otherwise wholly unattainable, have been produced. And it is worthy of observation, as a remarkable fact in the history of the human mind, that the only two discoveries which no one has ever claimed as his own, are precisely those which succeeding ages have found it impossible to extend or improve, and which, at the period of their first introduction, were, in all respects, as complete and as universal in their application as they are at the present moment. But, without pushing the parallel further, or going into any nice metaphysical distinctions, it may be observed, that all the methods of notation, which obtained prior to the introduction of the Arabic, were singularly clumsy and imperfect. That adopted and employed both by the Greeks and Romans, was the literal method; but this, when carried to any extent, and applied to the resolution of questions involving either fractional exponents or the higher powers of numbers, necessarily became excessively complicated and operose, to say nothing of the extreme diffi culty of expressing, in this form, by means of literal signs, certain properties of numbers which enter into all but the very simplest arithmetical computations. The Greeks, it is true, felt these difficulties and obstructions; and accordingly, at a very early period of their history, their characteristic ingenuity was successfully exerted in devising sundry forms of abbreviation and other contrivances, some of them equally felicitous and original, in order to overcome the obstacles which this method of notation opposed to the prosecution of scientific investigations. But such was the untractable nature of the instrument they employed, and so essentially ill-adapted was it to all the higher pursuits of science, that the utmost efforts of their ingenuity failed to render it available for this purpose, or to accommodate it to those refined researches to which they were so much devoted, and for which no people upon earth ever manifested greater intellectual aptitude. Among the warlike and unscientific Romans, on the other hand, the imperfections inherent in this method seem scarcely to have been perceived; notwithstanding their practice of reckoning by defect must have tended mightily to complicate any computations in which they may have had occasion to engage. Unconscious of the difficulty, and most probably incapable of estimating the inconvenience arising from such a method, they appear to have been content to take their science, like their literature, at second hand, and to borrow, as they had occasion, from the Greeks what they could neither discover nor invent for themselves. But be this as it may, it is certainly very remarkable that the latter people, who were indebted to the Egyptians for the elements of that science which they afterwards so greatly improved, should have failed to discern the advantages of the method of notation employed by their masters, or neglected to transplant it into their own country, and, having pruned and dressed it with due care, to substitute it in the room of the literal system, to the inconveniencies of which they were far from being insensible. Nor will our surprise be lessened when we call to mind that, down to a comparatively recent period of Grecian history, no Greek seems to have been accounted truly learned who had not sojourned for a time in the land of the Pharaohs, conversed with the priests of Thebes or Memphis on the mysteries of their science, studied the laws, government, and institutions of the most remarkable nation that ever existed, examined and explored its everlasting monuments, and, in a word, become initiated in all" or at least in part of "the learning of the Egyptians." It is to a small but by no means insignificant portion of that "learning" that we purpose at present directing the attention of our readers; namely, the basis of the numeral system, or the method of notation, which obtained in ancient Egypt. This method, like that employed by the Greeks and Romans, and still in use among ourselves, was the decimal; which, indeed, is the most natural as well as the best adapted for combination, and has accordingly prevailed among all nations, whether ancient or modern, who have made any progress in civilization. But although the Egyptians shared this method in common with other nations who had emerged out of barbarism, or rather perhaps were the first to employ a method which afterwards recommended itself to universal adoption, nothing can be conceived more unique and peculiar, or, in other words, more characteristic of this remarkable people, than their system of numerical signs, as exemplified in the monumental inscriptions and other forms of writing, which modern industry and ingenuity have succeeded in deciphering. That system is neither literal, like the Grecian or Roman, nor altogether figurate, like the Arabic, but something, if we may so express it, intermediate between both. It is constructed, in fact, upon principles altogether peculiar, and expressed by means of certain characters or signs which, although totally distinct from the characters or signs employed in the graphic system, are nevertheless framed upon a strict analogy with those symbols, and adapted with much apparent nicety to the particular form of writing in which they happen to be used. Accordingly, as there were three forms of writing among the ancient Egyptians, viz. the hieroglyphic, the hieratic, and the enchorial or demotic, so in like manner there were three forms of notation used by them, one adapted to each of those particular kinds of writing, and now known by the name of the variety to which it belongs, as the hieroglyphic, the hieratic, and the enchorial. But it is known to Egyptian scholars that the hieroglyphic, or monumental writing, is the basis of the two other forms, which, to incurious observers, appear to be altogether distinct and independent modes; in other words, the hieratic is merely a tachygraphy of the hieroglyphic, and the enchorial of the hieratic, the last, or the enchorial, being consequently the shortest form, and as such that generally used throughout the country. The same analogy holds in the system of numerical expression, in which we find that, with some exceptions, the hieratic is a modified form of the hieroglyphic, and the enchorial or demotic a correspondingly modified form of the hieratic: but in the two last forms, namely the hieratic and enchorial, there is this peculiarity, that separate modes of notation, or rather of numerical expression, are employed to designate the days of the month, and that in both these modes several of the numerals which we now denominate Arabic are clearly recognisable. This very remarkable fact, which we now for the first time bring under the notice of the learned in our own country, will be strikingly exemplified when we come to display the Egyptian system of tripartite notation in detail. In the mean while it may be observed, that it does not very clearly appear which of these forms, or whether any of them, was used in preference to the others in scientific or ordinary computations. Judging from analogy, however, it is probable that the enchorial notation, like the enchorial writing, was that employed in the common transactions of life; and with respect to scientific computations, all that can be gathered from such monuments as the zodiacks of Dendera and Esneh, and the inscriptions generally, is merely this, that the numerical expressions employed are uniformly accommodated to the particular kind of writing in which they appear. The principal writers who have treated of the hieroglyphic signs of numbers are Jomard, in his Notice sur les Signes Numériques des Egyptiens; Dr. Thomas Young, in his Hieroglyphical Vocabulary, and also in his elaborate article on Egypt in the fourth volume of the Supplement to the Encyclopædia Britannica; and Champollion, who published several hieratic signs of numbers, found in a fragment of a hieratic papyrus, in the second fasciculus of a work entitled Hieroglyphics, which made its appearance in London in the year 1823. By the labours of these and other individuals of scarcely inferior note, who have applied themselves to the study of Egyptian literature and antiquities, the hieroglyphic signs of numbers from 1 to 1000 have been ascertained and verified beyond the possibility of doubt or error; and as these signs constitute the simplest of the three forms of notation in use among the ancient Egyptians, being that employed in monumental inscriptions, we shall endeavour to represent them in such a manner as to render the principle of their arrangement as obvious as it is plain and inartificial, and thus to prepare the reader for details of a more complex and intricate description. The nine digits are not represented upon the Arabic principle of a separate sign for each, but simply by repeating the sign of unity as often as there are units in any digit from one to nine, the latter inclusive. Thus unity itself is represented by a short thick stroke or line, I, two by a couple of such strokes or lines II, three by III, and so on to ten; the higher digits, however, such as seven, eight, and nine, being represented frequently by strokes arranged in double columns of three and four, four and four, and five and four, apparently for the purpose of saving space. The mark or sign for ten is n, anciently П, and all the intermediate numbers between 10 and 20 are represented by units adscribed or affixed to the symbol for ten: thus is 10+1 or 11, N is 10+2 or 12, is 10+3 or 13, and so on. Twenty is represented by two tens on, and the interme diate numbers between 20 and 30 in the same way precisely as those between 10 and 20; thirty is represented by three tens nnn, forty by four tens noon, and so on to a hundred ; the tens in 60, 70, 80, and 90 being, like the higher digits, generally arranged in double columns of three and three, four and three, four and four, and five and four, and all the intermediate numbers being expressed in the way already explained. From 100, the mark or sign for which is 9, to 1000, the numbers ascend exactly upon the principle already explained in regard to the preceding part of the scale. Thus 200 is represented by the sign of 100 doubled 99, 300 by the sign of 100 tripled 999, 400 by the sign of 100 quadrupled 9999, and so on to 1000, the symbol of which is or Such is the hieroglyphical form of notation, as ascertained and determined by a vast number of readings and experimental verifications; and from what has been already stated, as well as from the nature of the signs themselves, and the principle upon which they are combined, it seems pretty evident, that they could never have been employed except in monumental inscriptions, for which alone they are adapted. To say nothing of other objections, it is by far too operose for ordinary purposes, and never could have been |