Double-Mirror Method for Rangefinding: A Scientific Development by al-Khāzinī

Document Type : Research/Original/Reqular Article

Author

PhD Candidate, Institute for the History of Science, University of Tehran

10.22059/jihs.2025.406070.371861

Abstract

The use of mirrors for measuring distance and height has its origins in ancient Greek science. In his Optics, Euclid demonstrated how the reflection of light could be geometrically employed to determine an object’s altitude or range with remarkable precision. During the Islamic Golden Age, scholars adopted and further developed his methods. For example, ʿAbd al-Raḥmān al-Khāzinī (active ca. 1115–1130 CE), in his treatise On Marvelous Instruments, not only explained Euclid’s single-mirror method but also introduced an innovative Double-Mirror Method. This innovation enabled the simultaneous determination of both height and distance of an object through one observation. Al-Khāzinī’s contribution represents a significant step in linking theoretical geometry with practical applications in surveying and engineering within the scientific tradition of the medieval Islamic world. This article examines his methods in detail.

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References

Abattouy, Muhammed. (1997). “Al-Khāzinī.” Encyclopedia of the History of Science, Technology, and Medicine in Non-Western Cultures, Springer.
Al-Khāzinī, ʿAbd al-Raḥmān. (n.d.). Risāla fī al-Ālāt al-ʿAjība (On Marvelous Instruments). Manuscript, Sepahsālār Mosque Library (Tehran).
Kheirandish, Elahe. (1998). The Arabic Version of Euclid’s Optics. (First edition.) Vol. 1 New York City: Springer-Verlag.
Kiani Movahed, R. (2019). “ʿAbd al-Raḥmān al-Khāzinī’s treatise Fī Ālāt al-ʿAjiba: A short Review. ”Journal for the History of Science, 187-214.
Sezgin, Fuat. (2001). Manuscript of Arabic Mathematical and Astronomical Treatises. Vol. 66. Frankfurt: Institute for the History of Arabic-Islamic Science.

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