The November 1494 Venice print by Paganino de' Paganini was the only source for the first reading. Five machines, run separately, read its page images, including the 15th-century abbreviations, suspension marks and ligatures: Claude (Anthropic, Sonnet 5.5), GPT-6-Sol at two settings and GPT-6-Astra (OpenAI), and Gemini 3.1 Pro (Google). That is four models from three companies. A recorded hold applied: no modern or human edition was used in this step. Kraken, an ordinary text-recognition program (not a language model), supplied a reference text.
Where the machines disagreed (about 1,400 places), the readings were decided by looking at line and word crops of the page images, done by further Claude instances.
GPT-6-Sol and Gemini 3.1 Pro, which were already among the five machines, then gave a second, blind opinion on the doubtful places and on a 200-word audit sample. Their disagreements were decided against the page images under recorded rules, which produced the resolved reading (Draft 2). Later checks (Gitti-open words, the 1523 reprint, and Sangster and Santini’s paper) led to Draft 7, which is the version linked above and published on the 1494 page.
Gitti’s 1878 Italian edition was not the base of the reading. It was used in two ways: as a check when the first disagreements were decided (his matching words were shown beside most of those places, and he is cited in 29 of the 77 changes made in Draft 2, always together with the page image), and as a word-by-word comparison afterwards. The comparison changed nothing by itself; differences were recorded and then checked against the page images.
In the first draft, 2,601 of 3,034 aligned abbreviated words (85.7%) agreed with Gitti’s expanded forms. Most of the remainder are his modernising of spelling, mismatches in the alignment, or changes he made without saying so; a few are our own misreadings, which were corrected.
From the resolved reading, a modern Italian version and then an English version were drafted separately by GPT-6-Sol and Gemini 3.1 Pro and reconciled. These steps worked from our own reading, not from Gitti or any earlier translation. A cross-check against the 1523 Toscolano reprint (ETH Zürich scan) prompted further corrections; the reprint was set from a 1494 copy, so it helps read the type but is not an independent witness. The translation was then compared with Sangster and Santini’s 2022 translation of Chapter 1 (Accounting History 27(3)), which led to changes including “reckoner” for ragioniere.
The reading and translation work began on 9 October 2026, and this version is dated 13 October 2026. The Italian and English are machine output and have not been checked line by line by a person. The judgement calls recorded as Anthony Mellor’s are his own, from fifty years in accountancy and business. The Project Status page says what is done and what is open. Our English and Italian drafts, the account of how Gitti was used and the 1523 cross-check are published. The textual apparatus preserves earlier flagged readings and substantive cruxes for scholarly scrutiny; it has not been reconciled into a complete current list of unresolved readings:
→ View Textual Apparatus: Historical Draft 2 Flags & Editorial Cruxes →
The treatise has been translated or edited many times, and Sangster and Santini (2022) examine ten translations of Chapter 1. This is where we stand with each, as of 12 October 2026.
Compared with our readings:
Used as reference, not as a translation: Hernández Esteve (1994, his paper on obscure points), Edler’s glossary (1934, search excerpts only) and Du Cange’s Latin glossary.
Searched for but not obtained, so not compared:
We have no university library or subscription-database access, and our searches were made by automated tools, which many sites block, so some works could not be reached for that reason. We found library catalogue records for some of these, but no text we could read. Whether they can be obtained is not certain. There may be translations we do not know of. If any become available they will be considered, and any differences will be added here.
The machines that read and translated make mistakes, some of them confident ones, and an important part of the author’s role has been to find and correct them. Errors found along the way, in the readings, in the translations and in many earlier versions of these pages, have been corrected, and the changes are recorded in the project files. The results here are therefore a checked draft made by AI under human control, not a finished or reliable edition.
We call something an error only where it can be shown: a misreading (the page image shows something else), a mistranslation (the print’s word is clear and the English is wrong), or a slip (an arithmetic or logical inconsistency, which may be the printer’s or Pacioli’s own). Everything else is marked uncertain, open, or the author’s reading.
We are grateful to Professor Alan Sangster for his work on this matter.
Source: Luca Pacioli, Summa de arithmetica, geometria, proportioni et proportionalita (Venice: Paganino de' Paganini, 1494). Distinctio IX, Tractatus XI: Particularis de computis et scripturis.