vol. ii. (subject "History of Algebra")

15. Huet, Demonstratio Evangelica.

16. Dr. John Taylor's Translation of the Lilawati. (Bombay, 1816.)

17. Strachey's Translation of the Bija Ganita².

18. Colebrooke's Algebra of the Hindus.

Would it not be worth while to give a facsimile of the "Tabel for all manere of merchauntes," in the "Notes and Queries"? It is not only a curiosity, but an important element (and unique as far as is known) in the philosophic history of our arithmetic. It was, no doubt, an actual instrument in constant use in the merchant's office, as much so as an almanac, interest-tables, a "cambist" and a copying-press, are now.

As regards the cipher, the difficulty only commenced with writing numbers in the new symbology. With persons accustomed to the use of this instrument, there is no doubt that the mode of obviating the difficulty of "keeping the place," would suggest itself at once. In this instrument an empty hole (without its peg) signified "none of this denomination." What then more simple than to make the outline of the empty hole which occupied the "local position" of any denomination, when none of that precise denomination occurred in the number itself? Under this view the process at least becomes simple and natural; and as the early merchants contributed so largely to the improvement of our arithmetical processes, such a conclusion is wholly divested of improbability on any other ground. The circle would then naturally become, as it certainly has practically become, the most appropriate symbol of nothingness.

As regards the term cipher or zero (which are so obviously the same as to need no remark), it is admitted on all hands to be derived from one or other of the Semitic languages, the Hebrew or the Arabic. It is customery with the mathematical historians to refer it to the Arabic, they being in general more conversant with it than with the Hebrew. The Arabic being a smaller hand than the Hebrew, a dot was used instead of the circle for marking the "place" at which the hiatus of any "denomination" occurred. If we obtained our cipher from this, it would be made hollow (a mere ceinture, girdle, or ring) to save the trouble of making a dot sufficiently large to correspond in magnitude with our other numerals as we write them. Either is alike possible—probability must be sought, for either over the other, from a slightly different source.

The root-words in Hebrew and in Arabic are precisely the same (ts-ph-r), though in the two languages, and at different ages of the same language, they might have been vowelised differently. In some shape or other, this name is used in all countries that have derived their arithmetic from mediæval Italy, or from the Saracens. It is with some cipher, with others chiffre, and with all zero. The word is certainly no more Italian than it is French or English. Be it remembered, too, that ezor (quoted at p. 268.), as a girdle, is radically the same word, somewhat mutilated. The cardinal meaning of the word (denuded of the conventional accretions of signification, which peculiar applications of it adds to the cardinal meaning) appears to be emptiness, hollowness, nothingness. It may be further remarked, that in the fine Chartres MS. of Boetius, described by Chasles, the 0 is called sipos:—the same name, he remarks, that Graves found in use in the East. The modern Turks call the 0, tsifra.

It is curious enough that in all languages, the term ciphering is popularly used to denote all arithmetical operations whatever. Our schoolboys do their "ciphering," and write carefully in their "ciphering-books." This all seems to point to the art of dispensing with the use of the abacus or counting table.

T.S.D.

Shooter's Hill, March 5.

Arabic Numerals.—I had replied to "E.V." (No. 15. p. 230.), when I saw by your "Notice to Correspondents," that the question was answered. I therefore waited the publication of the replies, which I find do not embrace any one of the points to which I would call the attention of "E.V."—Diophantus of Alexandria, who flourished about 150 years after Christ, and who wrote thirteen books of algebra or arithmetic in the Greek language, is generally supposed to be the oldest writer on the subject that has come down to our time; but it was not from him that we received the knowledge of algebra in Europe. It appears certain that the first knowledge of this science in England was from Italy or Spain, after the Moors settled in the latter country; and the Arabians and Persians appear to have derived their arithmetical method of computing by ten characters from the Indians: who, in their turn, have most probably borrowed from the Chinese, and improved on their method by the adoption of a zero, which was one of the most important improvements effected by the Hindoos. In China, the words ancient and modern are almost synonymous; their usages and customs being so unchangeable, as appears by their instrument of computation, the swanpan, which is still used in all their calculations. The Oriental scholar will find much curious and interesting information connected with this subject in the Sanscrit Vija Ganita and Lilivati of Bhaskara Acharya: the former was translated into Persian at Agra, or Delhi, in 1634, and the latter by Fyzee in 1587; but there are also English translations, all of which are in the library of the Royal Asiatic Society. The Khalasah-ul-Hisah is another work of repute in India. Mr. Strachey wrote and printed in India, for the Asiatic Researches, a valuable paper, which contains most conclusive evidence of the Indian (if not Chinese) origin of our numerals. See also Astronomie Indienne, of M. Bailly; 2d vol. Asiatic Researches, "On the Astronomical Computations of the Hindoos," by Saml. Davis; "Two Dissertations on Indian Astronomy and Trigonometry," by Professor Playfair, in the 2d and 4th vols. of the Edinburgh Philosophical Transactions. And many others might be referred to; but all tending to prove that our numbers came originally from China and India, through Persia, Arabia, Africa, Spain, and Italy, by gradual and successive changes in form, several of them still retaining a close resemblance to the ancient and modern Sanscrit, Chinese, Arabic, Persian, and Hindoo numerals.

Henry Wilkinson.

REPLIES TO MINOR QUERIES.

I send you a few Notes on Queries scattered through some of the later numbers of your very valuable publication:

Anonymous Ravennas.—In the library of the Royal Geographical Society, I believe there is a copy of an 8vo. edition of that cosmography.

Selago.—This plant, I should think it probable, is the Lycopodium clavatum of modern botanists; the seeds of which, when ripe, and when the plant is struck, rise like smoke ("fumum" of Pliny), and may have been supposed, from their remarkable inflammability when dashed into a flame, igniting with a sudden flash, to have possessed wonderful virtues. The species known as Lycopodium selago is rare in comparison to the other.

Portugal.—In the library of the Geographical Society are some of the more recent works published in Lisbon on the topography of that country, but they are generally very meagre and unsatisfactory. In a periodical published in Lisbon in numbers, on the plan of the Penny Magazine, there is a good deal of information, with engravings, regarding many places of interest in Portugal. I think it is called The Album, but I am sorry I have not at present the power of sending you more correct