Article ID: CBB001510295

Spherical Interpretation of Plane Geometry in Menelaus of Alexandria's Sphaerica (2013)


Amini, Hasan (Author)

Tarikh-e Elm (The Iranian Journal for the History of Science)
Volume: 11, no. 1
Issue: 1
Pages: 31-46

Publication Date: 2013
Edition Details: [Translated title.] In Persian.
Language: Persian

Menelaus' Sphaerica can be considered as the most important classical text in the tradition of spherics books, written with the aim of the solution of problems arising in spherical astonomy. Euclid's Elements is the the most important book on plane geometry. This article aims at a comparative study of Menelaus's Sphaerica and Euclid's Elements, to show that Book I of Sphaerica is an attempt to reconstruct Book I of the Elements for the case of spherical figures. We mention Menelaus' achievements as well as the limits of his project. The topic of the congruent triangles is treated with special reference to the differences which exist between the plane and the spherical cases. We also show that the spherical counterpart of Euclid's important theorm on the sum of the interior angles of a triangle (Euclid, I/32) has been put forward, for the first part, by Nasir al-Din al-Tusi in his Recension of Menelaus's Sphaerica.

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Authors & Contributors
Sidoli, Nathan Camillo
De Young, Gregg
Acerbi, Fabio
Ragep, F. Jamil
Morelon, Régis
Dallal, Ahmad S.
Tarikh-e Elm (The Iranian Journal for the History of Science)
Arabic Sciences and Philosophy
Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften
Historia Mathematica
Sciamvs: Sources and Commentaries in Exact Sciences
Archive for History of Exact Sciences
Pennsylvania State University
Arab/Islamic world, civilization and culture
Plane geometry
al-Ṭūsī, Abū Jaʿfar Muḥammad Naṣīr al-Dīn
Menelaos of Alexandria
Quṭb al-Dīn Shīrāzī
Theodosius of Bithynia
Sadr al-Shari'a
Time Periods
13th century
14th century
11th century
7th century
16th century
Alexandria (Egypt)
Rome (Italy)

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