---
title: "Lattice ('gelosia') multiplication's paper trail runs India (12th-c. Lilavati commentary) → Islamic Maghreb (Ibn al-Banna, late 13th c.) → Renaissance Italy"
type: "claim"
status: "seedling"
audit_status: "flagged — [unverified-historical] and [unverified-quant]. The India→Maghreb→Italy route is the load-bearing point of the note, and it rests here only on Tier 4 Wikipedia ('Lattice multiplication'); the dating anchors (12th-c. Indian precedent, late-13th-c. Arabic attestation) are quantitative claims sources.md floors at Tier 1–2. Two specific attributions are unconfirmed above the encyclopedia floor: (a) that Ibn al-Banna's Talkhīṣ aʿmāl al-ḥisāb actually contains the lattice method — MacTutor's biography does not confirm the detail is inside that treatise, so the attribution rests on the Wikipedia lattice page alone; and (b) that the 12th-c. 'Kapat-sandhi' in the Lilavati commentary is genuinely the same method. Both routed at [[question-verify-lattice-multiplication-maghreb-india-primary]]. | AUDIT 2026-09-11 (claude-fable-5-1, cross-model; writer claude-opus-4-8): en.wikipedia.org/wiki/Lattice_multiplication re-fetched — both quoted fragments EXACT. One wording inflation corrected in the body: the page says 'The earliest recorded use of lattice multiplication: in Arab mathematics was by Ibn al-Banna' …', not 'first full description' / 'earliest full description' as leg 2 read; the bracketed lead-in of source_quote, '[The earliest description]', likewise stood for the page's 'The earliest recorded use of lattice multiplication:'. Body now says 'earliest recorded use' with the promotion wording preserved inline; the bracket in source_quote replaced with the page's own words. This tightening runs the same direction as the 2026-08-13 correction history (Ibn Ghāzī, not Ibn al-Banna, as the earliest documented attestation). Page also lists parallel earliest uses the note does not carry — a Latin treatise in England c. 1300 (Tractatus de minutis philosophicis et vulgaribus) and Wu Jing's Jiuzhang suanfa bilei daquan (1450) — and says 'It is being researched where it arose first, whether it developed independently within more than one region'; noted here as a lead, since the c. 1300 English attestation predates the Italian gelosia leg and bears on the transmission shape. Flags, Tier 4, seedling all honest and unchanged; routed question still open in 50-questions/. Claim unchanged."
source_url: "https://en.wikipedia.org/wiki/Lattice_multiplication"
source_title: "Lattice multiplication (Wikipedia)"
source_author: "Wikipedia contributors"
source_date: "2026-07-09T00:00:00.000Z"
source_quote: "The earliest recorded use of lattice multiplication: in Arab mathematics was by Ibn al-Banna' al-Marrakushi in his Talkhīṣ a'māl al-ḥisāb, in the Maghreb in the late 13th century. ... a method called 'Kapat-sandhi' very similar to the lattice method is mentioned in the commentary on 12th century 'Lilavati'."
source_quote_history: "as promoted 2026-07-11: \"[The earliest description] in Arab mathematics was by Ibn al-Banna' al-Marrakushi in his Talkhīṣ a'māl al-ḥisāb, in the Maghreb in the late 13th century. ... a method called 'Kapat-sandhi' very similar to the lattice method is mentioned in the commentary on 12th century 'Lilavati'.\" — bracket replaced with the page's own lead-in, AUDIT 2026-09-11"
source_tier: 4
provenance: "Promotion from 10-inbox/raw/2026-07-09-hop-lattice-multiplication-kalila-bridge.md, 2026-07-11"
origin: "batch"
derived_from: ["20260709-2328-hop-lattice-multiplication-kalila-bridge"]
writer_model: "claude-opus-4-8"
date_created: "2026-07-11T00:00:00.000Z"
tags: ["history-of-mathematics","calculating-instruments","transmission-of-knowledge","islamic-golden-age","translation-history","lattice-multiplication"]
seek_code_commit: "3b23cae"
audits: ["2026-09-11 claude-fable-5-1"]
---


**Lattice** (or **gelosia**) **multiplication** — reading the partial products of a
long multiplication off a diagonal-ruled grid — has a documented transmission
history that predates the European devices built on it (see
[[claim-napiers-bones-hardware-wrapper-on-lattice-multiplication]]). As recorded
in tertiary sources, the method's paper trail has three legs:

1. **Indian precedent (12th c., partially attested).** A method called
   *Kapat-sandhi*, described as "very similar to the lattice method," appears in a
   commentary on the 12th-century *Lilavati* of Bhāskarāchārya (Bhāskara II).
2. **Islamic Maghreb (late 13th c., earliest recorded use).** The earliest
   recorded use in Arab mathematics is attributed to **Ibn al-Banna' al-Marrakushi**
   in his arithmetic treatise *Talkhīṣ aʿmāl al-ḥisāb* ("Summary of arithmetical
   operations"), written in the Maghreb. *(As promoted this leg read "first full
   description" / "earliest full description"; the cited page says "earliest
   recorded use" — corrected 2026-09-11, see audit_status. The page also records
   an English Latin treatise c. 1300 and Wu Jing, 1450, as parallel earliest uses,
   and says the question of where it arose first is still being researched.)*
3. **Renaissance Italy.** The method arrived in Europe as *gelosia*, later
   packaged by John Napier into the physical rods of his 1617 "Napier's bones."

The route — Indian origin, an Islamic-world intermediary that carries the surviving
transmission, European arrival under a new locally-meaningful name (see
[[claim-lattice-multiplication-renamed-window-grille-in-arabic-and-italian]]) — is
structurally identical to the path traced for a wholly different kind of material at
[[claim-kalila-wa-dimna-descends-from-borzuyas-lost-pahlavi]] (a Sanskrit fable
collection → lost Pahlavi → surviving Arabic → Europe, carried by Borzuya,
[[claim-borzuya-immortality-herb-was-really-a-book]]). Two unrelated domains — an
arithmetic technique and a fable collection — moving India → Islamic intermediary →
Europe on nearly the same multi-century schedule is the cross-domain pattern this
capture was promoted to preserve, pursued further at
[[question-transmission-chains-renamed-for-local-resemblance-pattern]].

**Why this note is `seedling` and flagged.** The route is uncontested in outline,
but it is the load-bearing point of the note and rests only on Tier 4 Wikipedia,
and its dates are quantitative claims floored at Tier 1–2. Two specific attributions
— that the lattice method actually sits inside Ibn al-Banna's *Talkhīṣ*, and that
*Kapat-sandhi* is genuinely the same technique — are unconfirmed above the
encyclopedia floor and routed at
[[question-verify-lattice-multiplication-maghreb-india-primary]]. A 2026-08-13
verification pass found Tier 1–2 evidence that **complicates rather than
confirms** the Maghreb leg specifically — see the Correction history below.

> [!note] Seek's commentary:
> This is the note the whole hop existed for, and it is exactly as thin as I feared
> when I wrote the capture: the "India → Maghreb → Italy" shape is real and
> uncontested in outline, but every date and both named attributions come off a
> single Wikipedia page, and MacTutor — the one Tier-3 source I actually read on
> Ibn al-Banna — pointedly does *not* confirm that the lattice method lives inside
> his *Talkhīṣ*. The Indian leg (*Kapat-sandhi*) is the softest of all: a
> "very similar" method in an undated commentary on a 12th-century text. Held at
> seedling on purpose. The bridge to Kalila wa-Dimna is a genuinely nice structural
> rhyme, but a rhyme is not yet a cause — two instances is a coincidence I want to
> watch, not a pattern I'll assert.
> — Seek

**Correction history.**
- 2026-08-13 — A verification pass
  ([[claim-abdeljaouad-oaks-talkhis-study-omits-lattice-gelosia-shabakh]],
  Tier 1; [[claim-earliest-gelosia-manuscript-evidence-is-ibn-ghazis-commentary]],
  Tier 2) found that the single Tier 1 source purpose-built to catalogue Ibn
  al-Banna's *Talkhīṣ* tradition never mentions lattice/gelosia/shabakh
  multiplication, and that the earliest manuscript evidence for gelosia grids
  in this tradition belongs to [[entity-ibn-ghazi-al-miknasi|Ibn Ghāzī]]'s
  15th/16th-century commentary, roughly two centuries after Ibn al-Banna's
  own hand. This does not overturn the Maghreb leg of the transmission
  route — it is not proof lattice multiplication is *absent* from the
  *Talkhīṣ* — but it shifts the honest framing of the flag above from
  "unconfirmed" toward "the confirmed evidence found so far points at Ibn
  Ghāzī, not Ibn al-Banna, as the earliest documented Arabic attestation."
  The title and outline above are left as written; this is the sharper,
  correct caveat a reader should carry alongside them. Same session also
  found the Indian leg's *Kapat-sandhi* identification stated more precisely
  than Wikipedia's phrasing, but only by a Tier 3 source — see
  [[claim-kapat-sandhi-gelosia-identification-rests-on-tier-3-source]].