Article ID: CBB155287466

Harmonic Proportion: The Edition of Risāla Taʿlīfīyyah by Abu Isḥāq Kūbanānī (2018)

unapi

Harmonic mean, based on the concept of harmonic proportion, along with the arithmetic and geometric means are the three principal means discussed on ancient and medieval mathematics. This article intends to provide a survey of the concepts of harmonic mean and harmonic proportion in history of mathematics. In the first section the authors introduce the harmonic proportion and some relations obtained on its basis. In the second part a short history of this subjects is presented, while in the third part the monographs written in the Islamic period are introduced. In the two remaining sections, Abū Isḥāq Kūbanānī’s treatise on harmonic proportion, entitles Risālat Taʾlīfīyyah, has been introduced accompanied by a critical edition and mathematical commentary.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB155287466/

Similar Citations

Article Vahabzadeh, Bijan; (2002)
Al-Māhānī's Commentary on the Concept of Ratio (/isis/citation/CBB000200191/)

Article De Young, Gregg; (2009)
A Persian Translation of al-Jawharī's Additions to Elements, Book V (/isis/citation/CBB001510401/)

Article Vahabzadeh, Bijan; (2013)
Le commentaire d'Ibn Mu'Ā sur le concept de rapport (/isis/citation/CBB001321035/)

Article Abdounur, Oscar João; (2009)
A Preliminary Survey on the Emergence of an Arithmetical Theory of Ratios (/isis/citation/CBB000933568/)

Article Sutto, Jean-Pierre; (2000)
Le compendium du 5e livre des Éléments d'Euclide de Francesco Maurolico (/isis/citation/CBB000770893/)

Article Gandon, Sébastien; (2009)
La théorie des rapports chez Augustus de Morgan (/isis/citation/CBB000954528/)

Article Krol, Z.; (2007)
Introduction to Ancient Theories of Proportion (/isis/citation/CBB000931652/)

Book Borrelli, Arianna; (2008)
Aspects of the Astrolabe: “Architectonica Ratio” in Tenth- and Eleventh-Century Europe (/isis/citation/CBB000953090/)

Book Pelacani da Parma, Biagio; Biard, Joël; Rommevaux, Sabine; (2005)
Questiones circa tractatum proportionum magistri Thome Braduardini (/isis/citation/CBB001020074/)

Article Berggren, J. L.; Brummelen, Glen Van; (2000)
Abu Sahl al-Kuhi's “On the Ratio of the Segments of a Single Line that Falls on Three Lines” (/isis/citation/CBB000931681/)

Chapter Hogendijk, Jan; (2002)
Anthyphairetic Ratio Theory in Medieval Islamic Mathematics (/isis/citation/CBB000203455/)

Article Zahra Pournajaf; (2015-2016)
The First Proposition of 10th book of Euclid's Elements and Islamic Scholars' Alternatives (/isis/citation/CBB909710648/)

Chapter Hélène Bellosta; (2012)
La destinée arabe des Données d’Euclide (/isis/citation/CBB209738412/)

Article Mohamed Mahdi Abdeljaouad; (2013)
Kamāl al-Dīn al-Fārsī’s additions to Book XIII of al-Ṭūsī’s Taḥrīr (/isis/citation/CBB791536198/)

Authors & Contributors
Vahabzadeh, Bijan
Rommevaux, Sabine
De Young, Gregg
Zahra Pournajaf
Elif Baga
Abdeljaouad, Mahdi
Concepts
Mathematics
Ratio and proportion
Arab/Islamic world, civilization and culture
Geometry
Primary literature (historical sources)
Commentaries
Time Periods
Medieval
9th century
11th century
10th century
Qing dynasty (China, 1644-1912)
Ancient
Places
Mediterranean region
Greece
Europe
China
Ottoman Empire
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment