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. THE SUBJECT MATTER.