| | | | | 4 | 6 | +Quotient.+ +----+----+-----+-----+----+----+ [Footnote 4*: These figures are removed at the next step.] DIVISION. 8000 ÷ 606. +-------------+-----------+ | Thousands | | +---+---+-----+---+---+---+ | H.| T.| U. | H.| T.| U.| +---+---+-----+---+---+---+ | | | | | 9 | | Difference (making 700 trial divisor). | | | | | | 4 | Difference. | | | | 6 | | 6 | Divisors. +---+---+-----+---+---+---+ | | |[4*]8| | | | +Dividend.+ | | | 1 | | | | Remainder of dividend. | | | | 9 | 4 | | Product of difference 1 and 2 with | | | | | | | 1st Quotient (1). +---+---+-----+---+---+---+ | | |[4*]1| 9 | 4 | | New dividends. | | | | 3 | | | Remainder of greatest dividend. | | | | | 9 | 4 | Product of difference 1 and 2 with 2nd | | | | | | | Quotient (1). +---+---+-----+---+---+---+ | | |[4*]1| 3 | 3 | 4 | New dividends. | | | | 3 | | | Remainder of greatest dividend. | | | | | 9 | 4 | Product of difference 1 and 2 with 3rd | | | | | | | Quotient (1). +---+---+-----+---+---+---+ | | | | 7 | 2 | 8 | New dividends. | | | | 6 | | 6 | Product of divisors by 4th Quotient (1). +---+---+-----+---+---+---+ | | | | 1 | 2 | 2 | +Remainder.+ | | | | | | 1 | 4th Quotient. | | | | | | 1 | 3rd Quotient. | | | | | | 1 | 2nd Quotient. | | | | | 1 | | 1st Quotient. +---+---+-----+---+---+---+ | | | | | 1 | 3 | +Quotient.+ +---+---+-----+---+---+---+ [Footnote 4*: These figures are removed at the next step.] The chief Abacists are Gerbert (tenth century), Abbo, and Hermannus Contractus (1054), who are credited with the revival of the art, Bernelinus, Gerland, and Radulphus of Laon (twelfth century). We know as English Abacists, Robert, bishop of Hereford, 1095, “abacum et lunarem compotum et celestium cursum astrorum rimatus,” Turchillus Compotista (Thurkil), and through him of Guilielmus R. . . . “the best of living computers,” Gislebert, and Simonus de Rotellis (Simon of the Rolls). They flourished most probably in the first quarter of the twelfth century, as Thurkil’s treatise deals also with fractions. Walcher of Durham, Thomas of York, and Samson of Worcester are also known as Abacists. Finally, the term Abacists came to be applied to computers by manual arithmetic. A MS. Algorithm of the thirteenth century (Sl. 3281, f. 6, b), contains the following passage: “Est et alius modus secundum operatores sive practicos, quorum unus appellatur Abacus; et modus ejus est in computando per digitos et junctura manuum, et iste utitur ultra Alpes.”