By Jens Høyrup
This publication bargains with one of many earliest surviving "abbacus" treatises, one who is via way more orderly than any of the extant predecessors and is usually the 1st to comprise a presentation of algebra. The ebook includes an variation and an English translation of a manuscript from c. 1450. moreover, it positive factors an in depth dialogue of the contents of the treatise and its place inside of early abbacus tradition.
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Additional resources for Jacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus Culture (Science Networks. Historical Studies)
Sample text
To this comes the homogeneity of V. On all levels – orthography, vocabulary, discourse, pedagogical style – the treatise is a seamless whole, also on points where it differs from M+F or other abbacus writings. Instances of such idiosyncrasies that were already referred to are the preferential use of the spelling fact and the consistent spellings dicto/dicta and dericto/diricto, the use of pigliare when fractions (or square roots) are taken, the io/tu shift and the way diagrams are referred to. Another example is the copious use of the phrase et poi, “and then”, in sequences of numerical operations in all chapters of V where the occasion presents itself (including Chapters 16, 18, 19 and 22); it is completely absent from M+F (whereas this version employs it occasionally in the stepwise description of general procedures).
20 Jacopo, His Treatise, and Abbacus Culture (for once after the statement, not after the solution): “simigliantemente il mostriamo materialmente per figure come si fae lo deto alegamento”. 7 (fol. 49v), we read “Et simile〈mente〉 porremo la figura. Nel modo si fa como abbiamo facto de sopra nell’altra ragione”. 21 (fol. )”. Many other features of the manuscripts also point to the conclusion that V is close to an original of which M+F is an adaptation. Most striking is the shift from “io” to “tu” when reasons for a step are given.
14/17 2 de denaio”, and also one “dìne 6/97 13 de dìne” (“days 6/97 13 of day”). Ch. 14, “de regole de saldare ragione” (fols 44r–51r). Loan contracts containing invocation of God, names and dates, thus real or pretendedly real, leading to the problem of settling the accounts for several loans made within a single year, that is, bringing all to the same term of repayment; only simple interest is involved. Everything is independent of the Liber abbaci. There are copious instances of expressions of the type “d.