The number of English arithmetics before the sixteenth century is very small. This is hardly to be wondered at, as no one requiring to use even the simplest operations of the art up to the middle of the fifteenth century was likely to be ignorant of Latin, in which language there were several treatises in a considerable number of manuscripts, as shown by the quantity of them still in existence. Until modern commerce was fairly well established, few persons required more arithmetic than addition and subtraction, and even in the thirteenth century, scientific treatises addressed to advanced students contemplated the likelihood of their not being able to do simple division. On the other hand, the study of astronomy necessitated, from its earliest days as a science, considerable skill and accuracy in computation, not only in the calculation of astronomical tables but in their use, a knowledge of which latter was fairly common from the thirteenth to the sixteenth centuries. The arithmetics in English known to me are:-- (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.]