---
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]]."
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 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'."
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"]
---


**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., first full description).** The earliest full
   description 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.
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]].

> [!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