Textual Apparatus

I. Substantive Contextual & Accounting Cruxes

These places represent passages where two distinct readings both fit the syntax, or where the 1494 print presents an obvious historical or mathematical knot:

• p458 L12–15 — dilimistri (cantara di lane):
  An entry in the Recordanze (memoranda) at the end of the treatise, not in the merchandise ledger. The meaning is unresolved. Anthony Mellor takes it to be a description of the type of wool wanted from England; its exact sense is not settled. Hernández Esteve (1994, pp. 22–27) surveys competing readings of limistri and leaves it open.
• p435 L21, p442 L45 — rubi coculegni:
  Description of unset gemstones. Anthony Mellor reads coculegni as “uncut” (his judgement). Other readings: raw rubies in the husk or shell (coccola), cone-shaped stones (Jäger), or a specific regional trade origin (Gitti). Hernández Esteve (1994, pp. 22–27) treats the term as contested.
• p435 L22 — diamanti greççi a tavola e põtidi:
  Describes diamond inventory. Greççi may be rough (grezzi) or Greek (greci); the sense of põtidi is not settled. Neither reading is attributed to a source here.
• p451 L32, L34, L38 — An arithmetic slip in Chapter 28 ("g 5"):
  In the carry-forward example (the account of Martino), the print gives the remainder as ℔8 ß6 g 5 p7. Subtracting ℔72 ß9 g3 p17 from ℔80 ß15 g15 p24 gives g 12 (15 − 3), so “5” is a slip, whether the printer’s or Pacioli’s. The reading is kept as printed.
• p450 L56 / p451 L00 — A sentence that stops at the foot of the page:
  The foot of folio 206v (Zenodo p450) ends mid-sentence: “E se el tuo commesso fosse i le bande…” (“And if your commesso [agent] were in the regions…”). The next page (folio 207r, Zenodo p451) opens with the heading of Chapter 27. The sentence is left as printed.
• p435 L34, L36 — Spices: çeçari michini / bellidi:
  Our Italian renders these as zenzeri (ginger), michini and bellidi being kinds of it. Heyd reads michini as ginger from Mecca and bellidi as native ginger. Anthony Mellor agrees with Heyd but cannot see the word zenzeri in the printed çeçari. Open.
• p446 L1 and elsewhere — ditta (as in assegnatione de ditta):
  Anthony Mellor reads it as credit, “on credit” (his judgement). Edler (1934) takes it as an entry or deposit certificate in a banker’s book, and lists a termine as a separate method of purchase. Hernández Esteve (1994, pp. 31–32, 45–48) takes it as a verbal payment order against a customer’s bank account. Open.
• p446 L8 — creditore el banco:
  In the merchant’s own books a bank account that receives money is debited, as p449 L36–42 says, so creditore looks backwards here. Anthony Mellor reads it as probably a slip; Hernández Esteve (1994, pp. 47–48) suspects the print should read debitore el banco. The print is kept as printed.
• p434 L10–11 — V. D. S. Magnanimo D.:
  Not known. Sangster and Santini (2022) think the Doge of Venice much more likely, and say it cannot be known; Antinori reads “Vostro Dominio Soggetti, Magnanimo Duca”. Open.
• p434 L46 — i cãpo:
  The print reads cãpo to us, and the 1523 reprint prints “in campo”. Sangster and Santini read “in capo”, in chapter. Open; two machines disagreed about whether a tilde stands over the i.

II. Historical Draft 2 Low-Confidence List (26 Entries)

One entry in this table, p440 L56, was subsequently read as Se trarai in Draft 3. Three other later decisions mentioned in the reading history — p438 L20 ꝓ in produrli, p450 L46 ꝓ in pro e danno, and p434 L51 aꝑtamẽte — are outside this 26-entry table. Their inclusion here would confuse later decisions with the original list. A decision on one printed reading does not settle every translation or interpretation question at that place.

These 26 places were flagged in Draft 2 because of difficult type or print surfaces in the Library of Congress exemplar. The table preserves the earlier review record; it is not a present-day open-doubt count:

III. Historical Draft 2 Mark-Level List (44 Entries)

In these 44 recorded instances, the first-pass reading was preserved while both second-opinion models (GPT-6-Sol and Gemini 3.1 Pro) favored an alternate reading of suspension marks, tildes, or r-rotunda glyphs. This table preserves that Draft 2 comparison. No row-by-row current status has been established for all 44:

IV. Recheck on corrected line crops (12 October 2026)

The lists above were drawn up in the early stages, and nine of the 26 rested on line crops that were cut off or showed a neighbouring line. All 69 rows were therefore read again, blind, from correctly cut crops of the page by two machines (GPT-6-Sol and Gemini 3.1 Pro), with the options shuffled and no edition shown. Nine lines were cut again to the full page width where the money signs stand in the right margin. The two machines often disagree with each other, which shows how hard these marks are at this resolution. The table gives our reading (Draft 7 text), what each machine read, and what that means. Of the 69: 20 confirmed; 4 changed in Draft 7; 1 decided earlier; 44 remain open. Each change rests on both machines seeing the sign and on the sense of the passage (daꝑte, ſꝑgiurano, ꝑche, ꝑo che); the strokes are faint, so they are medium confidence and are not proofread by a person.

The 20 audit words (words all five first machines agreed on but the two second-opinion models did not match): both models agree with the first-pass word at 12; one agrees at 7; at 1 both prefer another reading (faꝛai against farai, a round r against a plain one). Several of the earlier mismatches came from the old crops.

Words Gitti found difficult: both machines read coculegni (twice), põtidi, michini, bellidi, došši, bellegiare and dilimištri (dilimi at the line end, štri at the start of the next) as we do, so the spelling is not in doubt, only the meaning. At guato one machine saw a t and the other an r; the sense (the seller gives the buyer the woad, guado) favours guato. At p435 L9 one machine read potrai and the other poꝛrai; on the image it is a round r followed by a plain r, so poꝛrai (porrai, you will put), as we read it.

Earlier decisions that cited Gitti (40): both machines agree with the decision at 14; for the rest the options offered to the machines were incomplete or the machines differ, so they remain as decided, unchanged by this check.

Source: Luca Pacioli, Summa de arithmetica, geometria, proportioni et proportionalita (Venice: Paganino de' Paganini, 1494). Distinctio IX, Tractatus XI: Particularis de computis et scripturis.