Sources 14

Al-Hawārī’s Essential Commentary

Arabic Arithmetic in the Fourteenth Century
We give an edition and English translation of al-Hawārī’s book, together with a passage-by-passage mathematical, conceptual, and historical commentary and an introduction to Arabic arithmetic to put it in context.

We give an edition and English translation of al-Hawārī’s book, together with a passage-by-passage mathematical, conceptual, and historical commentary and an introduction to Arabic arithmetic to put it in context.

This publication is licensed under a Creative Commons Attribution-Share Alike 4.0 International (CC BY-SA 4.0) Licence.

Al-Hawārī completed his Essential Commentary in Marrakesh in 1305. This modest book was written with the goal of supplying numerical examples to the rules of calculation explained in the famous Condensed Book on the Operations of Arithmetic of his teacher Ibn al-Bannāʾ. It is partly because of its modesty that al-Hawārī’s book is a good vehicle for presenting the various facets of practical Arabic arithmetic, which in al-Hawārī’s time included not just computational techniques but also algebra and other problem-solving methods. In this book we give an edition, English translation, and running commentary of al-Hawārī’s commentary, together with a general introduction to Arabic arithmetic to situate it in context. We cover not just the rules for operating on known and unknown numbers, but also their conceptual and historical background. Numbers in Arabic arithmetic were conceived as amounts or measures of something, and thus could be any positive quantity, including fractions and irrational roots. Thus they were neither founded in the Greek notion of multitudes of an indivisible unit, nor were they defined axiomatically as they are today. This way of understanding numbers informed both their ways of expressing numbers and algebraic expressions and how they performed their calculations. On the historical front, we witness the ways that different local arithmetical traditions interacted, and how Greek arithmetic, even if fundamentally incompatible with its Arabic counterparts, was partially absorbed into practical books like al-Hawārī’s.
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A

Abū Kāmil

Abū Yaʿqūb

Abū l-Wafāʾ

ʿAlī al-Sulamī

Apollonius

Archimedes

Aristotle

B

al-Baghdādī

al-Bīrūnī

Brahmagupta

D

Descartes, René

Diophantus

E

Eratosthenes

Euclid

F

al-Fārābī

al-Fārisī

Fibonacci

H

Ḥabīb ibn Bihrīz

al-Ḥajjāj

al-Ḥanbalī

Hārūn al-Rashīd

al-Ḥaṣṣār

Hero

Hilbert, David

Hipparchus

I

Ibn al-Hāʾim

Ibn al-Haytham

Ibn al-Khawwām

Ibn al-Maghribī

Ibn al-Nadīm

Ibn al-Samḥ

Ibn al-Yāsamīn

Ibn Badr

Ibn Fallūs

Ibn Ghāzī

Ibn Haydūr

Ibn Munʿim

Ibn Qunfudh

Ibn Sīnā

Ibn Turk

Ikhwān al-Ṣafāʾ

Isḥāq ibn Ḥunayn

J

Jean de Murs

K

al-Karajī

al-Kāshī

al-Khayyām

al-Khwārazmī

al-Khwārazmī (lexicographer)

Kūshyār ibn Labbān

M

Madyan

al-Māhānī

al-Maʾmūn

al-Mawāḥidī

N

Naṣīr al-Dīn al-Ṭūsī

Nesselmann, G.H.F.

Nicomachus

Nine Chapters

P

Pacioli, Luca

Ptolemy

Q

al-Qalaṣādī

al-Qurashī

Qusṭā ibn Lūqā

R

Rhind Papyrus

S

Saidan, A.S.

al-Samawʾal

Sebokht, Severus

Şeker Zāde

Sibṭ al-Māridīnī

Stifel, Michael

T

Thābit ibn Qurra

U

Ulugh Beg

al-ʿUqbānī

al-Uqlīdisī

V

Viète, François

Information

ISBN

978-3-945561-63-8

DOI

10.34663/9783945561638-00

Pages

531

Publication Date

Nov. 24, 2021

Suggested Citation

Abdeljaouad, Mahdi and Oaks, Jeffrey (2021). Al-Hawārī’s Essential Commentary: Arabic Arithmetic in the Fourteenth Century. Berlin: Max-Planck-Gesellschaft zur Förderung der Wissenschaften.