(1) Bodl. 790 G. VII. (2653) f. 146-154 (15th c.) _inc._ “Of angrym
ther be IX figures in numbray . . .” A mere unfinished fragment,
only getting as far as Duplation.
(2) Camb. Univ. LI. IV. 14 (III.) f. 121-142 (15th c.) _inc._
“Al maner of thyngis that prosedeth ffro the frist begynnyng . . .”
(3) Fragmentary passages or diagrams in Sloane 213 f. 120-3
(a fourteenth-century counting board), Egerton 2852 f. 5-13,
Harl. 218 f. 147 and
(4) The two MSS. here printed; Eg. 2622 f. 136 and Ashmole 396
f. 48. All of these, as the language shows, are of the fifteenth
century.
The CRAFTE OF NOMBRYNGE is one of a large number of scientific
treatises, mostly in Latin, bound up together as Egerton MS. 2622 in
the British Museum Library. It measures 7” × 5”, 29-30 lines to the
page, in a rough hand. The English is N.E. Midland in dialect. It is a
translation and amplification of one of the numerous glosses on the _de
algorismo_ of Alexander de Villa Dei (c. 1220), such as that of Thomas
of Newmarket contained in the British Museum MS. Reg. 12, E. 1.
A fragment of another translation of the same gloss was printed by
Halliwell in his _Rara Mathematica_ (1835) p. 29.[1*] It corresponds, as
far as p. 71, l. 2, roughly to p. 3 of our version, and from thence to
the end p. 2, ll. 16-40.
[Footnote 1*: Halliwell printed the two sides of his leaf in the
wrong order. This and some obvious errors of transcription--
‘ferye’ for ‘ferthe,’ ‘lest’ for ‘left,’ etc., have not been
corrected in the reprint on pp. 70-71.]
The ART OF NOMBRYNG is one of the treatises bound up in the Bodleian MS.
Ashmole 396. It measures 11½” × 17¾”, and is written with thirty-three
lines to the page in a fifteenth century hand. It is a translation,
rather literal, with amplifications of the _de arte numerandi_
attributed to John of Holywood (Sacrobosco) and the translator had
obviously a poor MS. before him. The _de arte numerandi_ was printed in
1488, 1490 (_s.n._), 1501, 1503, 1510, 1517, 1521, 1522, 1523, 1582, and
by Halliwell separately and in his two editions of _Rara Mathematica_,
1839 and 1841, and reprinted by Curze in 1897.
Both these tracts are here printed for the first time, but the first
having been circulated in proof a number of years ago, in an endeavour
to discover other manuscripts or parts of manuscripts of it, Dr. David
Eugene Smith, misunderstanding the position, printed some pages in a
curious transcript with four facsimiles in the _Archiv für die
Geschichte der Naturwissenschaften und der Technik_, 1909, and invited
the scientific world to take up the “not unpleasant task” of editing it.
ACCOMPTYNGE BY COUNTERS is reprinted from the 1543 edition of Robert
Record’s Arithmetic, printed by R. Wolfe. It has been reprinted within
the last few years by Mr. F. P. Barnard, in his work on Casting
Counters. It is the earliest English treatise we have on this variety of
the Abacus (there are Latin ones of the end of the fifteenth century),
but there is little doubt in my mind that this method of performing the
simple operations of arithmetic is much older than any of the pen
methods. At the end of the treatise there follows a note on merchants’
and auditors’ ways of setting down sums, and lastly, a system of digital
numeration which seems of great antiquity and almost world-wide
extension.
After the fragment already referred to, I print as an appendix the
‘Carmen de Algorismo’ of Alexander de Villa Dei in an enlarged and
corrected form. It was printed for the first time by Halliwell in
_Rara Mathemathica_, but I have added a number of stanzas from various
manuscripts, selecting various readings on the principle that the verses
were made to scan, aided by the advice of my friend Mr. Vernon Rendall,
who is not responsible for the few doubtful lines I have conserved. This
poem is at the base of all other treatises on the subject in medieval
times, but I am unable to indicate its sources.