Kitabı oku: «Notes and Queries, Number 27, May 4, 1850», sayfa 3
BP. COSIN'S MSS.—INDEX TO BAKER'S MSS
Your correspondent "J. SANSOM" (No. 19. p. 303.) may perhaps find some unpublished remains of Bp. Cosin in Baker's MSS.; from the excellent index to which (Cambridge, 1848, p. 57.) I transcribe the following notices, premising that of the volumes of the MSS. the first twenty-three are in the British Museum, and the remainder in the University Library, (not, as Mr. Carlyle says in a note in, I think, the 3d vol. of his Letters. &c. of Cromwell in the library of Trin. Coll.).
"Cosin, Bp.– Notes of, in his Common Prayer, edit. 1636, xx. 175. Benefactions to See of Durham, xxx. 377-380. Conference with Abp. of Trebisond, xx. 178. Diary in Paris, 1651, xxxvi. 329. Intended donation for a Senate-House, xxx. 454. Letters to Peter Gunning, principally concerning the authority of the Apocrypha, vi. 174-180. 230-238. Manual of Devotion, xxxvi. 338."
As the editors of the Index to Baker's MSS. invite corrections from those who use the MSS., you will perhaps be willing to print the following additions and corrections, which may be of use in case a new edition of the Index should be required:—
Preface, p. vii. add, in Thoresby Correspondence, one or two of Baker's Letters have been printed, others have appeared in Nichols's Literary Anecdotes.
Index, p. 2. Altars, suppression of, in Ely Diocese, 1550, xxx. 213. Printed in the British Magazine, Oct. 1849, p. 401.
P. 5. Babraham, Hullier, Vicar of, burnt for heresy. Brit. Mag. Nov. 1849, p. 543.
P. 13. Bucer incepts as Dr. of Divinty, 1549, xxiv. 114. See Dr. Lamb's Documents from MSS. C.C.C.C. p. 153.
Appointed to lecture by Edw. VI., 1549, xxx. 370. See Dr. Lamb, p. 152.
Letter of University to Edw., recommending his family to care, x. 396. Dr. Lamb, p. 154.
P. 14. Buckingham, Dr. Eglisham's account of his poisoning James I., xxxii. 149-153. See Hurl. Misc.
Buckmaster's Letter concerning the King's Divorce, x. 243. This is printed in Burnet, vol. iii. lib. 1. collect. No. 16., from a copy sent by Baker, but more fully in Dr. Lamb, p. 23., and in Cooper's Annals.
P. 25. Renunciation of the Pope, 1535. See Ant. Harmer, Specimen, p. 163.
P. 51. Cowel, Dr., charge against, and defence of his Antisanderus. Brit. Mag. Aug. 1849, p. 184.
Cranmer, extract from C.C.C. MS. concerning. Brit. Mag. Aug. 1849, p. 169, seq.
Cranmer, life of, xxxi. 1-3. Brit. Mag. Aug. 1849, p. 165.
P. 57. Convocation, subscribers to the judgment of, xxxi. 9. British Magazine, Sept. 1849, p. 317.
P. 68. Ely, Altars, suppression of, 1550, xxx. 213. Brit. Mag. Oct. 1849, p. 401.
P. 77. Several of the papers relating to Bishop Fisher will be found in Dr. Hymers' edition of The Funeral Sermon on Lady Margaret.
P. 80. Gloucester, Abbey of, &c., a Poem by Malvern, v. 285-7. Brit. Mag. xxi. 377.; Caius Coll. MSS. No. 391. art 13.
Goodman, Declaration concerning the articles in his book. Strype's Annals, I. i. 184.
P. 89. Henry VII., Letter to Lady Margaret, xix. 262. See Dr. Hymers, as above, p. 160.
P. 91. Henry VIII., Letter to, giving an account of the death of Wyngfield, &c. See Sir H. Ellis, Ser. III. No. 134.
P. 94. Humphrey, Bishop, Account, &c., xxxv. 1-19. Rend xxvi. 1-19.
Humphrey, Bishop, Images and Relics, &c., xxx. 133-4. Brit. Mag. Sept. 1849, p. 300.
P. 121-2. Lady Margaret. Several of the articles relating to Lady Margaret have been printed by Dr. Hymers (ut sup.).
P. 137. Pole Card. Oratio Johannis Stoyks, &c., v. 310-312. Dr. Lamb, p. 177.
P. 143. Redman, Dr., Particulars of, xxxii. 495.—Brit. Mag. Oct. 1849, p. 402.
P. 151. Spelman's Proposition concerning the Saxon Lecture, &c. Sir H. Ellis Letters of Eminent Literary Men, Camd. Soc. No. 59.
P. 169. Noy's Will, xxxvi. 375., read 379.
Many of the articles relating to Cambridge in the MSS. have been printed by Mr. Cooper in his Annals of Cambridge: some relating to Cromwell are to be found in Mr. Carlyle's work; and several, besides those which I have named, are contained in Dr. Lamb's Documents.
J.E.B. MAYOR.
Marlborough Coll., March 30.
ARABIC NUMERALS AND CIPHER
Will you suffer me to add some further remarks on the subject of the Arabic numerals and cipher; as neither the querists nor respondents seem to have duly appreciated the immense importance of the step taken by introducing the use of a cipher. I would commence with observing, that we know of no people tolerably advanced in civilisation, whose system of notation had made such little progress, beyond that of the mere savage, as the Romans. The rudest savages could make upright scratches on the face of a rock, and set them in a row, to signify units; and as the circumstance of having ten fingers has led the people of every nation to give a distinct name to the number ten and its multiples, the savage would have taken but a little step when he invented such a mode of expressing tens as crossing his scratches, thus X. His ideas, however, enlarge, and he makes three scratches, thus [C with square sides], to express 100. Generations of such vagabonds as founded Rome pass away, and at length some one discovers that, by using but half the figure for X, the number 5 may be conjectured to be meant. Another calculator follows up this discovery, and by employing [C with square sides], half the figure used for 100, he expresses 50. At length the rude man procured a better knife, with which he was enabled to give a more graceful form to his [C with square sides], by rounding it into C; then two such, turned different ways, with a distinguishing cut between them, made CD, to express a thousand; and as, by that time, the alphabet was introduced, they recognised the similarity of the form at which they had thus arrived to the first letter of Mille, and called it M, or 1000. The half of this DC was adopted by a ready analogy for 500. With that discovery the invention of the Romans stopped, though they had recourse to various awkward expedients for making these forms express somewhat higher numbers. On the other hand, the Hebrews seem to have been provided with an alphabet as soon as they were to constitute a nation; and they were taught to use the successive letters of that alphabet to express the first ten numerals. In this way b and c might denote 2 and 3 just as well as those figures; and numbers might thus be expressed by single letters to the end of the alphabet, but no further. They were taught, however, and the Greeks learnt from them, to use the letters which follow the ninth as indications of so many tens; and those which follow the eighteenth as indicative of hundreds. This process was exceedingly superior to the Roman; but at the end of the alphabet it required supplementary signs. In this way bdecba might have expressed 245321 as concisely as our figures; but if 320 were to be taken from this sum, the removal of the equivalent letters cb would leave bdea, or apparently no more than 2451. The invention of a cipher at once beautifully simplified the notation, and facilitated its indefinite extension. It was then no longer necessary to have one character for units and another for as many tens. The substitution of 00 for cb, so as to write bdeooa, kept the d in its place, and therefore still indicating 40,000. It was thus that 27, 207, and 270 were made distinguishable at once, without needing separate letters for tens and hundreds; and new signs to express millions and their multiples became unnecessary.
I have been induced to trespass on your columns with this extended notice of the difficulty which was never solved by either the Hebrews or Greeks, from understanding your correspondent "T.S.D." p. 367, to say that "the mode of obviating it would suggest itself at once." As to the original query,—whence came the invention of the cipher, which was felt to be so valuable as to be entitled to give its name to all the process of arithmetic?—"T.S.D." has given the querist his best clue in sending him to Mr. Strachey's Bija Ganita, and to Sir E. Colebrooke's Algebra of the Hindus, from the Sanscrit of Brahmegupta. Perhaps a few sentences may sufficiently point out where the difficulty lies. In the beginning of the sixth century, the celebrated Boethius described the present system as an invention of the Pythagoreans, meaning, probably, to express some indistinct notion of its coming from the east. The figures in MS. copies of Boethius are the same as our own for 1, 8, and 9; the same, but inverted, for 2 and 5; and are not without vestiges of resemblance in the remaining figures. In the ninth century we come to the Arabian Al Sephadi, and derive some information from him; but his figures have attracted most notice, because though nearly all of them are different from those found in Boethius, they are the same as occur in Planudes, a Greek monk of the fourteenth century, who says of his own units, "These nine characters are Indian," and adds, "they have a tenth character called [Greek: tziphra], which they express by an 0, and which denotes the absence of any number." The date of Boethius is obviously too early for the supposition of an Arabic origin; but it is doubted whether the figures are of his time, as the copyists of a work in MS. were wont to use the characters of their own age in letters, and might do so in the case of figures also.
H.W.
ROMAN NUMERALS
There are several points connected with the subject of numerals that are important in the history of practical arithmetic, to which neither scientific men nor antiquaries have paid much attention. Yet if the principal questions were brought in a definite form before the contributors to the "NOTES AND QUERIES," I feel quite sure that a not inconsiderable number of them will be able to contribute each his portion to the solution of what may till now be considered as almost a mystery. With your permission, I will propose a few queries relating to the subject,
1. When did the abacus, or the "tabel" referred to in my former letters, cease to be used as calculating instruments?
The last printed work in which the abacal practice was given for the purposes of tuition that I have been able to discover, is a 12mo. edition, by Andrew Mellis, of Dee's Robert Recorde, 1682.
2. When did the method of recording results in Roman numerals cease to be used in mercantile account-books? Do any ledgers or other account-books, of ancient dates, exist in the archives of the City Companies, or in the office of the City Chamberlain? If there do, these would go far towards settling the question.
3. When in the public offices of the Government? It is probable that criteria will be found in many of them, which are inaccessible to the public generally.
4. When in the household-books of royalty and nobility? This is a class of MSS. to which I have paid next to no attention; and, possibly, had the query been in my mind through life, many fragments tending towards the solution that have passed me unnoticed would have saved me from the necessity of troubling your correspondents. The latest that I remember to have particularly noticed is that of Charles I. in the Fitzwilliam Museum at Cambridge; but I shall not be surprised to find that the system was continued down to George I., or later still. Conservatism is displayed in its perfection in the tenacious adherence of official underlings to established forms and venerable routine.
T.S.D.
Shooter's Hill, April 8.
[Our correspondent will find some curious notices of early dates of Arabic numerals, from the Rev. Edmund Venables, Rev. W. Gunner, and Mr. Ouvry, in the March number of the Archæological Journal, p. 75-76.; and the same number also contains, at p. 85., some very interesting remarks by the Rev. Joseph Hunter, illustrative of the subject, and instancing a warrant from Hugh le Despenseer to Bonefez de Peruche and his partners, merchants of a company, to pay forty pounds, dated Feb. 4, 19 Edward II., i.e. 1325, in which the date of the year is expressed in Roman numerals; and on the dorso, written by one of the Italian merchants to whom the warrant was addressed, the date of the payment, Feb. 1325. in Arabic numerals, of which Mr. Hunter exhibited a fac-simile at a meeting of the Institute.]
Arabic Numerals.—In the lists of works which treat of Arabic Numerals, the following have not been noticed, although they contain a review of what has been written on their introduction into this part of Europe:—Archæologia, vols. x. xiii.; Bibliotheca Literaria, Nos. 8. and 10., including Huetiana on this subject; and Morant's Colchester, b. iii. p. 28.
T.J.
ERROR IN HALLAM'S HISTORY OF LITERATURE
If Mr. Hallam's accuracy in parvis could be fairly judged by the following instance, and that given by your correspondent "CANTAB." (No. 4, p. 51.), I fear much could not be said for it. The following passage is from Mr. Hallam's account of Campanella and his disciple Adami. My reference is to the first edition of Mr. Hallam's work; but the passage stands unaltered in the second. I believe these to be rare instances of inaccuracy.
"Tobias Adami, … who dedicated to the philosophers of Germany his own Prodromus Philosophiæ Instauratio, prefixed to his edition of Campanella's Compendium de Rerum Naturæ, published at Frankfort in 1617. Most of the other writings of the master seem to have preceded this edition, for Adami enumerates them in his Prodromus."—Hist. of Literature, iii. 149.
The title is not Prodromus Philosophiæ Instauratio, which is not sense; but Prodromus Philosophiæ Instaurandæ (Forerunner of a philosophy to be constructed). This Prodromus is a treatise of Campanella's, not, as Mr. Hallam says, of Adami. Adami published the Prodromus for Campanella, who was in prison; and he wrote a preface, in which he gives a list of other writings of Campanella, which he proposes to publish afterwards. What Mr. Hallam calls an "edition," was the first publication.
Mere accident enabled me to detect these errors. I am not a bibliographer and do not know a ten-thousandth part of what Mr. Hallam knows. I extract this note from my common-place book, and send it to you, hoping to elicit the opinions of some of your learned correspondents on the general accuracy in biography and bibliography of Mr. Hallam's History of Literature. Has Mr. Bolton Corney, if I may venture to name him, examined the work? His notes and opinion would be particularly valuable.
As a few inaccuracies such as this may occur in any work of large scope proceeding from the most learned of men, and be accidentally detected by an ignoramus, so a more extensive impeachment of Mr. Hallam's accuracy would make a very trifling deduction from his great claims to respect and well-established fame. I believe I rightly understand the spirit in which you desire your periodical to be the medium for emending valuable works, when I thus guard myself against the appearance of disrespect to a great ornament of literature.
C.
