Probus, Signed (1 results)

[Bede, the Venerable (672/73 - 735).] De computo, vel loquela per gestum digitorum [and] De ratione unciarum. In Hoc in volumine haec continentur M. Val. Probus de notis Roma. ex codice manuscript castigatior . . . , ed. Giovanni Tacuino (Venice: G. Tacuino, 1525), ff. LV - LVII. Whole volume, 4to. [4], LXXIX [i.e., LXXXI], [1]ff. Title in red and black. Full-page woodcut of a sibyl within an architectural setting, signed "b. M." in the block (probably Benedetto Montagna), a few woodcut initials. 211 x 153 mm. Modern vellum. Fine. Probably the Earliest Printings of Bede's accounts of finger-reckoning and duodecimal fractions. Bede's "De computo, vel loquela per gestum digitorum" (On calculating and speaking with the fingers) and "De ratione unciarum" (On calculating duodecimal fractions) form part of the introduction to his treatise De temporum ratione (On the reckoning of time), written around 725 A.D. The editio princeps of De temporum ratione was published by Sichardus in 1529, four years after the present work. Portions of De temporum ratione appeared in print as early as 1505, but these do not appear to have included the section on finger-reckoning. Smith, in his Rara arithmetica, states that the 1522 edition of Johannes Aventinus's Abacus atque vetustissima, veterum latinorum per digitos manusque numerandi contains a description of Bede's finger-reckoning; however, we think this may be an error, since we have not been able to find any record of this edition in OCLC or the Karlsruhe Virtual Catalogue. Smith himself described only the 1532 edition of Aventinus's work (see Rara arithmetica, pp. 136-138). Bede's two disquisitions are contained in a collection of works on Latin abbreviations, symbols, weights, measures and inscriptions edited by Giovanni Tacuino. The collection is devoted primarily to works on deciphering the abbreviations used in classical-era stone or bronze inscriptions, a subject of great interest to humanistic scholars eager to discover more about the ancient world. Included in the collection is the editio princeps of Petrus Diaconus' De notus literarum more Romano liber (which Tacuino had discovered), along with a new edition of M. Valerius Probus' De notus Romanorum and several transcriptions of Roman inscriptions in quasi-facsimile. The typographic design of the title is reminiscent of an ancient text in stone. Finger-reckoning, a method of computation in which numbers are represented by finger and hand gestures, had been practiced since ancient times and was commonly used during the Middle Ages; however, there are very few written accounts of the technique dating from these times, probably because it was used primarily by "common or illiterate people" (Menninger, p. 201) who passed its methods on orally. Bede's account of the practice, although not the first, was the best and most influential. His purpose was to provide a useful method for calculating the Christian calendar, most importantly the date of Easter and other movable feasts. Bede listed finger- and hand symbols for the numerals 1 through 9999; these "roughly work like a placement system. The middle, ring, and little fingers of the left hand denote the digits; the thumb and index fingers on the left hand express the tens; the thumb and index finger on the right hand the hundreds; and the middle, ring and little fingers the thousands . . . The informal manner in which Bede explains how to flex the fingers and form gestures seems to retain traces of oral instruction" (Kusukawa, pp. 28-29). Prior to Europe's adoption of Arabic numerals, finger-reckoning provided a rudimentary method of place-value calculation. "Neither Bede nor any of his contemporaries in Western Europe knew about place value or zero, but finger reckoning enabled them to proceed as if they did. Finger joints supplied place value-one joint 10s, another 100s and so on-and zero was indicated by the normal relaxed position of the fingers-by nothing, so to speak. The system was ev.