Skip to main content

G

  • Chapter
  • 540 Accesses

Abstract

Gaitian is the Chinese name for a scheme of cosmography, i.e. a description of the overall layout of heaven and earth. The term may be interpreted as “umbrella [-like] heaven”.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Cullen, Christopher. Astronomy and Mathematics in Ancient China, the Zhou Bi Suan Jung. Cambridge: Cambridge University Press, 1996.

    Google Scholar 

  • David W. Hughes. “Was Galileo 2,000 Years Too Late?” Nature 296: 199, 1982.

    Google Scholar 

  • Qutan Xida. Kaiyuan Zhanjing (The Kaiyuan Treatise on Astrology). Taipei: Taiwan Commercial Press, 1985 reprint.

    Google Scholar 

  • Xi Zezong. “The Discovery of Jupiter’s Satellite Made by Gan De 2,000 Years Before Galileo.” Chinese Physics 2 (3): 664–667, 1982.

    Google Scholar 

  • Yang Zhengzong, Jiang Shiyang, and Hao Xiangliang. “Experimental Test for Jupiter’s Satellites to the Naked Eye.” Kexue Tongbao 28 (7): 927–929, 1983.

    Google Scholar 

  • Imbert, [Laurent-Joseph-Marius]. “[Letters of Sept. 1826 and later from Wutongqiao, Jiadingfu, and Ziliujing in Sichuan].” Annales de l’association de la propagation de la foi 3: 369–381, 1828, and 4: 414–418, 1830.

    Google Scholar 

  • Li Jung. “An Account of the Salt Industry at Tzu-liu-ching. Tzu-liuching-chi.” Trans. Lien-Che Tu-Fang. Isis 39: 228–234, 1948. Needham, Joseph. Science and Civilisation in China. Cambridge: Cambridge University Press, 1954.

    Google Scholar 

  • Sun, E-Tu Zen, and Shiou-Chuan Sun, trans. Tien-kung k’ai-wo: Chinese Technology in the Seventeenth Century, by Sung YingHsing. University Park and London: Pennsylvania State University Press, 1966.

    Google Scholar 

  • Vogel, Hans Ulrich. “Feuerbrunnen in China und ihre Bedeutung für die Technikgeschichte.” Heidelberger Jahrbücher 35: 199218, 1991.

    Google Scholar 

  • Vogel, Hans Ulrich. Naturwissenschaften und Technik im vormodernen China: Historie, Historiographie und Ideologie, Kurseinheit 3: Geschichte der Tiefbohrtechnik im vormodernen China: Invention, Innovation, Diffusion, Transmission. Hagen: Fern Universität Gesamthochschule - in Hagen, 1993.

    Google Scholar 

  • Vogel, Hans Ulrich. “The Great Well of China.” Scientific American 268 (6): 116–121, 1993.

    Google Scholar 

  • Vogel, Hans Ulrich. “Chinese and Western Scientific Explanations of Sichuan Brine and Natural Gas Deposits prior to 1900.” To be published in T’oung Pao.

    Google Scholar 

  • Vogel, Hans Ulrich, Joseph Needham et al. “The Salt Industry”. Section 37 of Science and Civilisation in China. Ed. Joseph Needham. Cambridge: Cambridge University Press, forthcoming.

    Google Scholar 

  • Needham, Joseph, with Ho, Peng Yoke, Lu Gwei-Djen and Nathan Sivin. Science and Civilisation in China, vol 5 part 3. Cambridge: Cambridge University Press, 1976.

    Google Scholar 

  • Ware, James R. Alchemy, Medicine and Religion in the China of AD320: the Nei P’ien of Ko Hung, (Pao p’u tzu). Cambridge, Massachusetts: MIT Press, 1966.

    Google Scholar 

  • Goodrich, L.C. “Cotton in China.” Isis 34: 408–410, 1942–43.

    Google Scholar 

  • Mumford, Lewis. The Myth of the Machine: Technics and Human Development. New York: Harcourt, Brace, Jovanovich, 1966.

    Google Scholar 

  • Needham, Joseph, Wang Ling, and Lu Gwei-Djen. Science and Civilisation in China, Vol. 4, part 3, Civil Engineering and Nautics. Cambridge: Cambridge University Press, 1971, p. 249.

    Google Scholar 

  • Roberts, J.M. The Pelican History of the World. Harmondsworth: Penguin, 1983, p. 73 (reprinted from History of the World. New York: Knopf, 1976 ).

    Google Scholar 

  • Mercier, Raymond P. “Geodesy.” ln Cartography in the Traditional Islamic and South Asian Societies. In The History of Cartography,Vol. 2, Book 1. Ed.

    Google Scholar 

  • J.B. Harley and David Woodward. Chicago: University of Chicago Press, 1992, pp. 175–188.

    Google Scholar 

  • Burger, Julian. The Gaia Atlas of First Peoples. London: Gaia Books, 1990.

    Google Scholar 

  • Buttimer, Anne. Geography and the Human Spirit. Baltimore and London: John Hopkins University Press, 1993.

    Google Scholar 

  • Lawlor, Robert. Voices of the First Day (Awakenings in Aboriginal Dreamtime). Vermont: Inner Traditions International, 1991.

    Google Scholar 

  • Marsden, Maori. “God, Man and Universe: A Maori View.” In Te Ao Hurihuri (Aspects of Maoritanga). Ed. Michael King. Auckland: Reed Books, 1992, pp. 118–139.

    Google Scholar 

  • Matsubayashi, Kazuo. “Spirit of Place: The Modern Relevance of an Ancient Concept.” In The Power of Place (Sacred Ground in Natural and Human Environments). Ed. James Swan. Madras: Quest Books, 1991, pp. 334–346.

    Google Scholar 

  • Mowaljarlai, David and Jutta Malnic. Yorro Yorro: Everything Standing up Alive, Spirit of the Kimberley. Broome, Western Australia: Magabala Books Aboriginal Corporation, 1993.

    Google Scholar 

  • Myers, Fred. Pintupi Country, Pintupi Self. Washington, D.C.: Smithsonian Institution Press, 1986.

    Google Scholar 

  • Said, Edward. Culture and Imperialism. London: Chatto and Win-dus; New York: Knopf, 1993.

    Google Scholar 

  • Tellenbach, Hubertus and Bin Kimura. “The Japanese Concept of Nature.” In Nature in Asian Traditions of Thought (Essays in Environmental Philosophy). Ed. Baird Callicott and Roger Ames. New York: State University of New York Press, 1989, pp. 153–163.

    Google Scholar 

  • Yoon, Hong-Key. Maori Mind, Maori Land (Essays on the Cultural Geography of the Maori People from an Outsider ‘s Perspective). Berne: Peter Lang, 1986.

    Google Scholar 

  • Cao, Wanru. “Some Questions concerning the History of Chinese Geography.” Zi Ran Ke Xue Shi Yan Jiu 1 (30): 242–250, 1982.

    Google Scholar 

  • Fung, Yee-wang. “The Development of Geographical Education in Hong Kong and China (1949–1988): A Comparative Study.” In International Perspectives on Geographic Education. Ed. A. David Hill. Skokie, Illinois: Rand McNally, 1992, pp. 51–61.

    Google Scholar 

  • Hou, Renzhi. Selected Readings ofFamous Geographical Writings in Ancient China (in Chinese). Beijing: Kexue Chubanshe, 1959.

    Google Scholar 

  • Hsu, Mei-Ling. “The Han Maps and Early Chinese Cartography.” Annals of the Association of American Geographers 68: 45–60, 1978.

    Google Scholar 

  • Hsu, Mei-Ling. “The Qin Maps: A Clue to Later Chinese Cartographic Development.” Imago Mundi 45: 90–100, 1993.

    Google Scholar 

  • Lu, Jonathan J. “China’s Geographic Education.” In International Perspectives on Geographic Education. Ed. A. David Hill. Skokie, Illinois: Rand McNally, 1992, pp. 63–76.

    Google Scholar 

  • Needham, Joseph and Ling Wang. Science and Civilisation in China. Volume 3, Chapter 23. Cambridge: Cambridge University Press, 1959.

    Google Scholar 

  • Ali, S. M. The Geography of The Purczuas. New Delhi: People’s Publishing House, 1966.

    Google Scholar 

  • Cunningham, Alexander. The Ancient Geography of India. Varanasi: Indological Book House, 1979.

    Google Scholar 

  • De Bary, W. M. Theodore, ed. Introduction to Oriental Civilizations: Sources of Indian Tradition. New York and London: Columbia University Press, 1967.

    Google Scholar 

  • Goyal, S.R. Kautilva and Megasthenes. Meerut: Kusumanjali Prakashan, 1985.

    Google Scholar 

  • Majumdar, R. C. and A.D. Pusalker, eds. The History and Culture of the Indian People: The Vedic Age. London: George Allen and Unwin Ltd, 1951.

    Google Scholar 

  • Majumdar, R.C. and A.D. Pusalker, eds. The History and Culture of the Indian People: The Age of Imperial Unity. Bombay: Bharatiya Vidya Bhavan, 1953.

    Google Scholar 

  • Majumdar R.C. and A.D. Pusalker, eds. The History and Culture of the Indian People: The Classical Age. Bombay: Bharatiya Vidya Bhavan, 1954.

    Google Scholar 

  • Sircar, D. C. Studies in the Geography of Ancient and Medieval India. Delhi: Motilal Banarsidass, 1971.

    Google Scholar 

  • Thapar, Romila. A History of India 1. Middlesex, England: Penguin Books, 1966.

    Google Scholar 

  • Tripathi, Maya Prasad. Development of Geographic Knowledge in Ancient India. Varanasi: Bharatiya Vidya Prakashan, 1969.

    Google Scholar 

  • Alavi, S.M.Z. Geography in the Middle Ages. Delhi: Sterling Publishers Ltd, 1966.

    Google Scholar 

  • Arnold, T.W. “Arab Travellers and Merchants, AD 1000–5000.” In Newton, A.P. Travel and Travellers of the Middle Ages. London: Kegan Paul, 1926.

    Google Scholar 

  • Institut für Geschichte der Arabisch-Islamischen Wissenschaften. Islamic Geography. Frankfurt: Strauss Offsetdruck, 1992 (in Arabic).

    Google Scholar 

  • Kennedy, M.H. and E.S. Kennedy. Geographical Coordinates of Localities from Islamic Sources. Frankfurt: Institut für Geschichte der Arabisch—Islamischen Wissenschaften, 1987.

    Google Scholar 

  • Nafis, Ahmad. Muslim Contribution to Geography. Lahore: Muhammad Ashraf, 1972.

    Google Scholar 

  • Tibetts, G.R. A Study of the Arabic Texts Containing Material on South-east Asia. London: Royal Asiatic Society, 1979.

    Google Scholar 

  • Tozer, H.F. A History of Ancient Geography, 2nd ed. New York: Biblio and Tannen, 1964.

    Google Scholar 

  • Aveni, Anthony F., Horst Hartung, and J. Charles Kelley. “Alta Vista (Chalchihuites): Astronomical Implications of a Mesoamerican Ceremonial Outpost at the Tropic of Cancer.” American Antiquity 47: 316–335, 1982.

    Google Scholar 

  • Malmström, Vincent H. “Origin of the Mesoamerican 260-day Calendar.” Science 181: 759–60, 1973.

    Google Scholar 

  • Malmström, Vincent H. “A Reconstruction of the Chronology of Mesoamerican Calendrical Systems.” Journalfor the History of Astronomy 9: 105–116, 1978.

    Google Scholar 

  • Malmström, Vincent H. “Architecture, Astronomy, and Calendrics in PreColumbian Mesoamerica.” In Archaeoastronomy in the Americas Ed. Ray A. Williamson. Los Altos, California: Ballena Press/Center for Archaeoastronomy, 1981.

    Google Scholar 

  • Merrill, R. H. “Maya Sun Calendar Dictum Disproved.” American Antiquity 10: 307–11, 1945.

    Google Scholar 

  • Nuttall, Zelia. “Nouvelles lumières sur les civilisations américaines et le système du calendrier.” Proceedings of. the Twenty-second International Congress ofAmericanists. Rome, 1928, pp. 11948.

    Google Scholar 

  • Albers, Patricia and Jeanne Kay. “Sharing the Lands: A Study in American Indian Territoriality.” In A Cultural Geography of North American Indians. Ed. Thomas E. Ross and Tyrel G. Moore. Boulder, Colorado: Westview Press, 1987.

    Google Scholar 

  • Basehart, Harry. “The Resources Holding Corporation Among the Mescalero Apache.” Southwestern Journal of Anthropology 23: 277–291, 1967.

    Google Scholar 

  • Churchill, Ward. “The Earth is Our Mother: Struggles for American Indian Land and Liberation in the Contemporary United States.” In The State of Native America. Ed. Annette M. James. Boston: South End Press, 1992.

    Google Scholar 

  • Jackson, J.B. “The Order of a Landscape: Reason and Religion in Newtonian America.” In The Interpretation of Ordinary Landscapes: Geographical Essays. Ed. D.W. Meining. New York: Oxford University Press, 1976.

    Google Scholar 

  • Johnston, Basil. Ojibway Heritage. New York: Columbia University Press, 1976.

    Google Scholar 

  • Matthiessen, Peter. Indian Country. New York: Penguin Books, 1979.

    Google Scholar 

  • Rundstrom, Robert A. “A Cultural Interpretation of Inuit Map Accuracy.” Geographical Review 80 (2): 155–168, 1990.

    Google Scholar 

  • Sack, Robert David. Conceptions of Space in Social Throught: A Geographical Perspective. Minneapolis: University of Minnesota Press, 1980.

    Google Scholar 

  • Tuan, Yi Fu. Topophilia: A Study of Environmental Perception, Attitudes and Values. Minneapolis: University of Minnesota Press, 1976.

    Google Scholar 

  • De Groot, J.J.M. The Religious System of China. Vol. 3. Leiden: Librairie et Imprimeries, 1897.

    Google Scholar 

  • Feuchtwang, Stephan D.R. An Anthropological Analysis of Chinese Geomancy. Vientianne: Editions Vithagna, 1974.

    Google Scholar 

  • Hsu Shan-chi and Hsu Shan-shu (Ming Dynasty). Jen-tsu Hsu-chih. Taipei: Chulin Shu-chu, Hsin-chu, 1969.

    Google Scholar 

  • Kuo Pu. “Tsang-shu.” In Till Chen-tsung (commentary by Chiang Kuo) Shin-chu: Chu-lin Shu-chu, 1967.

    Google Scholar 

  • March, Andrew. “An Appreciation of Chinese Geomancy.”Journal of Asian Studies. 27 (2): 252–267, 1968.

    Google Scholar 

  • Rossbach, Sarah. Feng shui: The Chinese Art of Placement. New York: E.P. Dutton, 1983.

    Google Scholar 

  • Yoon, Hong-key. Geomantic Relationships Between Culture and Nature in Korea. Taipei: Oriental Culture Service, 1976.

    Google Scholar 

  • Yoon, Hong-key. “The Image of Nature in Geomancy.” GeoJournal. 4 (4): 341–348, 1980.

    Google Scholar 

  • Yoon, Hong-key. “An Early Chinese Idea of a Dynamic Environmental Cycle.” GeoJournal 10 (2): 211 212, 1980.

    Google Scholar 

  • Yoon, Hong-key. “Environmental Determinism and Geomancy: Two Cultures, Two Concepts.” GeoJournal. 6 (1): 77–80, 1982.

    Google Scholar 

  • Bascom, William. IA Divination: Communication Between Gods and Men in West Africa. Bloomington, Indiana: Indiana University Press, 1969.

    Google Scholar 

  • Charmasson, Thérèse. Recherches sur une technique divinatoire: la géomancie dans I ‘occident médiéval. (Centre de Recherches d’Histoire et de Philologie, V, Hautes Etudes Médiévales et Modernes, 44.) Geneva: Librairie Droz and Paris: Librairie H. Champion, 1980.

    Google Scholar 

  • Fand, Toufic. La divination arabe: études religieuses, sociologiques et folkloriques sur le milieu natif de l ‘Islam. Leiden: Brill, 1966.

    Google Scholar 

  • Jaulin, Robert. La Géomancie: analyse formelle. (École Pratique des Hautes Etudes, Sorbonne, Cahiers de l’Homme, n.s., t. 4.) Paris: Mouton and Co., 1966.

    Google Scholar 

  • Pedrazzi, Maino. “Le Figure della Geomanzie: Un Gruppo Finito Abeliano.” Physis 14 (2): 146–161, 1972.

    Google Scholar 

  • Peek, Philip M., ed. African Divination Systems — Ways of Know- ing. Bloomington, Indiana: Indiana University Press, 1991.

    Google Scholar 

  • Savage-Smith, Emilie and Marion B. Smith. Islamic Geomancy and a Thirteenth-Century Divinatory Device. (UCLA Von Grunebaum Center, Studies in Near Eastern Culture and Society, 2.) Malibu: Undena Publications, 1980.

    Google Scholar 

  • Savage-Smith, Emilie. “Geomancy.” In The Oxford Encyclopedia of the Modern Islamic World. Ed. John L. Esposito. New York: Oxford University Press, 1995, pp. 53–55.

    Google Scholar 

  • Skinner, Stephen. Terrestrial Astrology: Divination by Geomancy. London: Routledge and Kegan Paul, 1980.

    Google Scholar 

  • Smith, Marion B. “The Nature of Islamic Geomancy with a Critique of a Structuralist’s Approach.” Studia Islamica 49: 5–38, 1979.

    Google Scholar 

  • Amma, T.A. Sarasvati. Geometry in Ancient and Medieval India. Delhi: Motilal Banarsidass, 1979.

    Google Scholar 

  • Berggren, J.L. Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986.

    Google Scholar 

  • Closs, Michael P., ed. Native American Mathematics. Austin: University of Texas Press, 1986.

    Google Scholar 

  • Gillings, Richard J. Mathematics in the Time of the Pharaohs. Cambridge, Massachusetts: MIT Press, 1972.

    Google Scholar 

  • Joseph, George Gheverghese. The Crest of the Peacock.- NonEuropean Roots of Mathematics. London: I.B. Tauris, 1991.

    Google Scholar 

  • Kaye, G.R. Indian Mathematics. Calcutta: Thacker, Spink and Co., 1915.

    Google Scholar 

  • Kulkarni, R. P. Geometry According to Sulba Sutra. Pune: Vaidika Samsodhana, 1983.

    Google Scholar 

  • Li Yan and Du Shiran. Chinese Mathematics: A Concise History. Trans. John N. Crossley and Anthony W. C. Lun. Oxford: Clarendon Press, 1987.

    Google Scholar 

  • Seidenberg, Abraham. “The Ritual Origin of Geometry.” Archive for History of Exact Sciences 1: 488–527, 1962.

    Google Scholar 

  • Swetz, Frank J. The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China. University Park, Pennsylvania.: The Pennsylvania State University Press, 1992.

    Google Scholar 

  • Youschkevitch, A.P. Les Mathématiques Arabes (VIIe XVe Siècles). Paris: J. Vrin, 1976.

    Google Scholar 

  • Ascher, Marcia. “Graphs in Cultures (II): a Study in Ethnomathematics.” Archive for History of Exact Sciences 39 (1): 75–95, 1988.

    Google Scholar 

  • Fontinha, Mario. Desenhos na areia dos Quiocos do Nordeste de Angola. Lisbon: Instituto de Investigaçäo Cientifica Tropical, 1983.

    Google Scholar 

  • Gerdes, Paulus. “On Mathematical Elements in the Tchokwe `Sona’ Tradition”. For the Learning of Mathematics I0(1): 3134, 1990.

    Google Scholar 

  • Gerdes, Paulus. Lusona: Geometrical Recreations of Africa. Maputo: Mozambique’s Higher Pedagogical Institute, 1991.

    Google Scholar 

  • Gerdes, Paulus. Geometria sona: Reflexóes sobre uma tradiçäo de desenho ern povos da Africa ao sul do Equador. Maputo: Mozambique’s Higher Pedagogical Institute, 1993 (3 vols).

    Google Scholar 

  • Ang Tian Se. “Chinese Interest in Right-angled Triangles.” Historia Mathematica 5 (3): 253–266, 1978.

    Google Scholar 

  • Ang Tian-Se, and F.J. Swetz. “A Chinese Mathematical Classic of the Third Century: the Sea Island Manual of Liu Hui.” Historia Mathematica 13: 99–117, 1986.

    Google Scholar 

  • Dijksterhuis, E.J. Archimedes. Trans. C. Dikshoorn. Princeton, New Jersey: Princeton University Press, 1987.

    Google Scholar 

  • Elia, Pasquale d’. “Prezentazione della Prima Traduzione Cinese di Euclide.” Monumenta Serica 15: 161–202, 1956.

    Google Scholar 

  • Graham, A. C. Later Mohist Logic Ethics and Science. London and Hong Kong: The Chinese University Press and the School of Oriental and African Studies, 1978.

    Google Scholar 

  • Ho Peng-Yoke. “Liu Hui.” In Dictionary of Scientific Biography, vol. 8. Ed. Charles C. Gillipsie. New York: Scribners, 1973, pp. 418–425.

    Google Scholar 

  • Kokomoor, F.W. “The Distinctive Features of Seventeenth Century Geometry.” Isis 10 (34): 367–415, 1928.

    Google Scholar 

  • Lam Lay Yong and Shen Kangshen. “Right-angled Triangles in Ancient China.” Archive for the History of Exact Sciences 30 (2): 87–112, 1984.

    Google Scholar 

  • Lam Lay Yong and Ang Tian Se. “Circle Measurements in Ancient China.” Historia Mathematica 13: 325–340, 1986.

    Google Scholar 

  • Li Di. Zhongguo shuxue shijianbian (A Concise History of Chinese Mathematics). Shenyang: Liaoning Renmin Chubanshe, 1984.

    Google Scholar 

  • Libbrecht, Ulrich. Chinese Mathematics in the Thirteenth Century: the Shu-shu chiu-chang of Ch ‘in Chiu-shao (i.e. Qin Jiushao). Cambridge, Massachusetts: MIT Press, 1973.

    Google Scholar 

  • Martzloff, Jean-Claude. Histoire des mathématiques chinoises. Paris: Masson, 1987. English translation by Stephen S. Wilson: History of Chinese Mathematics. New York: Springer-Verlag, 1995.

    Google Scholar 

  • Martzloff, Jean-Claude. “Eléments de réflexion sur les réactions chinoises à la géométrie euclidienne à la fin du XVIIe siècle—le Jihe lunyue de Du Zhigeng vu principalement à partir de la préface de l’auteur et de deux notices bibliographiques rédigées par des lettres illustrées.” Historia Mathematica 20(2): 160–179 and 20 (3): 460–463, 1993.

    Google Scholar 

  • Waerden, B. L. van der. Geometry and Algebra in Ancient Civilizations. Berlin: Springer-Verlag, 1983.

    Google Scholar 

  • Wagner, D.B. “Liu Hui and Tsu Keng-chih on the Volume of a Sphere.” Chinese Science 3: 59–79, 1978.

    Google Scholar 

  • Wagner, D.B. “An Early Derivation of the Volume of a Pyramid: Liu Hui, Third Century AD” Historia Mathematica 6: 164–188, 1979.

    Google Scholar 

  • Wu Wenjun, ed. Jiuzhang suanshu yu Liu Hui (Liu Hui and the Jiuzhang suanshu). Beijing: Beijing Shifan Daxue Chubanshe, 1982.

    Google Scholar 

  • Ziggelaar, August. Le physicien Ignace-Gaston Pardies S.J. Odense: Odense University Press, 1971.

    Google Scholar 

  • Colebrook, H.T. Algebra with Arithmetic and Mensuration from the Sanscrit ofBrahmegupta and Bhascara. London: John Murray, 1817.

    Google Scholar 

  • Datta, B. The Science of the Sulbas: A Study in Early Hindu Geometry. Calcutta: Calcutta University Press, 1932.

    Google Scholar 

  • Gupta, R.C. “Paramesvara’s Rule for the Circumradius of a Cyclic Quadrilateral.” Historia Mathematica 4: 67–74, 1977.

    Google Scholar 

  • Joseph, G.G. The Crest of the Peacock: Non-European Roots of Mathematics. London: Penguin, 1992.

    Google Scholar 

  • Joseph, G.G. “What is a Square Root ? A Study of Geometrical Representation in Different Mathematical Traditions.” In Proceedings of 1993 Annual Meeting of the Canadian Mathematics Education Study Group. Ed. M.Quigley, University of Calgary, 1994, pp. 1–14.

    Google Scholar 

  • Kulkarni, R.P. Geometry according to Sulba Stiitra. Pune: Vadika Sarnsodhana Mandala, 1983.

    Google Scholar 

  • Varma, T. Rama and A. Aiyer, eds. Yuktibhâsaz. (in Malayalam). Trichur: Mangalodayam, 1948.

    Google Scholar 

  • Sarasvati Amma, T.A. Geometry in Ancient and Medieval India. Delhi: Motilal Banarisidass, 1979.

    Google Scholar 

  • Sarma, K.V., ed. Lilavati of Bhaskaracara with the Commentary Kriyakramkari. Hoshiarpur: Vishveshvaranand Institute, 1975.

    Google Scholar 

  • Staal, F. Agni: The Vedic Ritual of the Fire Altar. Berkeley: Asian Humanities Press, 1983.

    Google Scholar 

  • Rosenfeld, Boris. A History of Non-Euclidean Geometry. New York: Springer-Verlag, 1988.

    Google Scholar 

  • Youschkevitch, Adolphe. Les mathématiques arabes (VIII—XV siècles). Paris: Vrin, 1976.

    Google Scholar 

  • Zarfatti, Gad B. Munhe ha-mathematikah ba-sifrut ha-mada’it ha’ivrit shel yeme habenayim (Mathematical Terminology in the Hebrew Scientific Literature of the Middle Ages). Jerusalem: Hebrew University, 1968.

    Google Scholar 

  • Hayashi, Tsuruichi. Wasan Kenkyu Shuroku (Collected Papers on Old Japanese Mathematics), vols 1 and 2. Tokyo: Kaiseikan, 1913.

    Google Scholar 

  • Meiji Zen Nippon Sugakushi (History of Japanese Mathematics before the Meiji Period, 5 vols) Tokyo: Noma Kagaku Igaku Kenkyu Shiryo, 1979.

    Google Scholar 

  • Michiwaki, Yoshimasa, Makoto Oyama, and Toshio Hamada. “An Invariant Relation in Chains of Tangent Circles.” Mathematics Magazine 48 (2): 80–87, 1975.

    Google Scholar 

  • Michiwaki, Yoshimasa, and Noriko Kimura. “ On the Relevancy of the Descartes Circle Theorem and Links of Six Spheres Theorem.” Journal of History of Science, Japan, Series 2, 22 (147), 1983 (in Japanese).

    Google Scholar 

  • Michiwaki, Yoshimasa. “An Investigation of Mathematics Education.” 2nd International Congress on the Cultural History of Mathematics,1993, Japan.

    Google Scholar 

  • Ogura, Kin-osuke. Nihon no Sugaku, pp. 120–142, Tokyo: Iwanami Shoten, 1964.

    Google Scholar 

  • Smith, David and Yoshio Mikami: A History of Japanese Mathematics. Chicago: Open Court, 1914.

    Google Scholar 

  • Chace, Arnold Buffum. Ludlow Bull, and Henry Parker Manning. The Rhind Mathematical Papyrus. Oberlin, Ohio: Mathematical Association of America, 1929.

    Google Scholar 

  • Struve, W.W. Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau. Berlin: Julius Springer, 1930.

    Google Scholar 

  • Friberg, Jöran. “Mathematik.” In Reallexikon der Assyriologie und Vorderasiatischen Archäologie VII. Berlin and New York: de Gruyter, 1990, pp. 531–585.

    Google Scholar 

  • Vogel, Kurt. Vorgriechische Mathematik. II. Die Mathematik der Babylonier. Hannover: Hermann Schroedel; Paderborn: Ferdinand Schöningh, 1959.

    Google Scholar 

  • Gillings, Richard J. Mathematics in the Time of the Pharaohs. Cambridge, Massachusetts: MIT Press, 1972.

    Google Scholar 

  • Iversen, Erik. Canon and Proportion in Egyptian Art. 2nd ed. Warminster, England: Aris and Phillips, 1975.

    Google Scholar 

  • Hoyrup, Jens. “The Formation of `Islamic Mathematics’. Sources and Conditions.” Science in Context 1: 281–329, 1987.

    Google Scholar 

  • Brieux, Alain, and Francis R. Maddison. Répertoire des facteurs d’astrolabes et de leurs oeuvres: Première partie, Islam. Paris: Centre National des Recherches Scientifiques. In press.

    Google Scholar 

  • Maddison, Francis R., and Emilie Savage-Smith. Science, Tools and Magic. (The Nasser D. Khalili Collection of Islamic Art, Vol. XII.) London: The Nour Foundation in association with Azimuth Editions and Oxford University Press, 1996.

    Google Scholar 

  • Savage-Smith, Emilie. Islamicate Celestial Globes: Their History, Construction, and Use. (Smithsonian Studies in History and Technology 46.) Washington, D.C.: Smithsonian Institution Press, 1985.

    Google Scholar 

  • Savage-Smith, Emilie. “The Classification of Islamic Celestial Globes in the Light of Recent Evidence.” Der Globusfreund 38/39: 23–35 and plates 2–6, 1990.

    Google Scholar 

  • Savage-Smith, Emilie. “Celestial Mapping.” In The History of Cartography. ‘Volume Two, Book One: Cartography in the Traditional Islamic and South Asian Societies. Ed. J. B. Harley and David Woodward. Chicago: University of Chicago Press, 1992, pp. 12–70.

    Google Scholar 

  • Savage-Smith, Emilie. “The Islamic Tradition of Celestial Mapping.” Asian Art 5 (4): 5–27, 1992.

    Google Scholar 

  • Burgess, E. Súrya-Siddhanta. Calcutta: University of Calcutta, 1935.

    Google Scholar 

  • Kennedy, E.S. The Exhaustive Treatise on Shadows by al-Biruni, 2 vols. Syria: University of Aleppo, 1976.

    Google Scholar 

  • Neugebauer, O., and D. Pingree. The Pancasiddantika of Varahamihira. Copenhagen: Munksgaard, 1970–72.

    Google Scholar 

  • Pingree, David. The Yayanajataka of Sphujidhvaja. Cambridge, Massachusetts: Harvard University Press, 1978.

    Google Scholar 

  • Sastri, T.S. Kuppanna. MahabhaskarÌya. Madras: Government Oriental Manuscripts Library, 1957.

    Google Scholar 

  • Sastri, Ganapati. TheArthsastra ofKautilya. Madras: Kuppuswami Sastri Research Institute, 1958.

    Google Scholar 

  • Sen, S.N., and A.K. Bag. The Sulbasútras. New Delhi: Indian National Science Academy, 1983.

    Google Scholar 

  • Sharma, R.S. Breihmasphuta Siddhanta. New Delhi: Indian Institute of Astronomical and Sanskrit Research, 1966.

    Google Scholar 

  • Shukla, K.S., and K.V. Sarma. Aryabhattya of,4ryabhata. New Delhi: Indian National Science Academy, 1976.

    Google Scholar 

  • Shukla, K.S. Mahabhaskariya. Lucknow University, 1960.

    Google Scholar 

  • Thibaut, G., and M.S. Dvivedi. The Pancasiddantikei. Benares: Medical Hall Press, 1889.

    Google Scholar 

  • Abraham, George. “The Gnomon in Early Indian Astronomy.” Indian Journal of History of Science 16 (2): 215–218, 1981.

    Google Scholar 

  • Pingree, David. “History of Mathematical Astronomy in India.” In Dictioncny of Scientific Biography, vol. 15. New York: Scribners, 1978, pp. 533–633.

    Google Scholar 

  • Smart, W.M. Text Book on Spherical Astronomy. Cambridge: Cambridge University Press, 1977.

    Google Scholar 

  • Somayaji, D.A. Ancient Hindu Astronomy. Dharwar: Karnataka University, 1971.

    Google Scholar 

  • Dauben, Joseph W. “The `Pythagorean Theorem’ and Chinese Mathematics. Liu Hui’s Commentary on the Gou-Gu Theorem in Chapter Nine of the Jiu Jang Suan Shu.” In Amphora. Festschrift in Honor of Hans Wussing. Leipzig: B.G. Teubner, 1992, pp. 133–155.

    Google Scholar 

  • Guo Shuchun. Jiu Zhang Suan Shu. Shenyang: Liaoning Educational Press, 1990, and Taipei: Taiwan Nine Chapters Press, 1990.

    Google Scholar 

  • Li Yan and Du Shi-Ran. Chinese Mathematics. A Concise History. Oxford: Clarendon Press, 1987.

    Google Scholar 

  • Martzloff, Jean-Claude. Histoire des mathématiques chinoises. Paris: Masson, 1988. English translation: History of Chinese Mathematics. New York: Springer-Verlag, 1995.

    Google Scholar 

  • Vogel, Kurt, trans. and ed., Chiu Chang Suan Shu. Neun Bücher arithmetischer Technik. Braunschweig: F. Vieweg and Sohn, 1968.

    Google Scholar 

  • Wagner, Donald B. “An Early Chinese Derivation of the Volume of a Pyramid: Liu Hui, Third Century AD.” Historia Mathematica 6: 164–188, 1979.

    Google Scholar 

  • Wu Wenchun. “The Out-In Complementary Principle.” In Ancient China’s Technology and Science. Beijing: Foreign Languages Press, 1983, pp. 66–89.

    Google Scholar 

  • Needham, Joseph. Gunpowder as the Fourth Power, East and West. Hong Kong: Hong Kong University Press, 1985.

    Google Scholar 

  • Needham, Joseph, et al. Science and Civilisation in China. Cambridge: Cambridge University Press, 1986.

    Google Scholar 

  • Biography of Guo Shoujing.“ In Ke Shaomin, Xin Yuanshi (New Official History of the Yuan Dynasty) Ch.171, Biographical chapter 68. First published 1922, reprinted Taipei: Yiwen Press (no date).

    Google Scholar 

  • Ho Peng Yoke and M. Wang. “Kuo Shou-ching.” In In the Service of the Khan. Eminent Personalities of the Early Mongolian Period (1200–1300). Ed.

    Google Scholar 

  • I. de Rachewiltz et al. Wiesbaden: Asiatische Forschungen,I993, pp. 282–299.

    Google Scholar 

  • Needham, Joseph. Science and Civilisation in China., vol. 3. Cambridge: Cambridge University Press, 1959.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Cullen, C. et al. (1997). G. In: Selin, H. (eds) Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1416-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1416-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-1418-1

  • Online ISBN: 978-94-017-1416-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics