# The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models

@article{Duke2005TheEI, title={The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models}, author={Dennis W. Duke}, journal={Archive for History of Exact Sciences}, year={2005}, volume={59}, pages={563-576} }

The planetary models of ancient Indian mathematical astronomy are described in several texts.1 These texts invariably give algorithms for computing mean and true longitudes of the planets, but are completely devoid of any material that would inform us of the origin of the models. One way to approach the problem is to compare the predictions of the Indian models with the predictions from other models that do have, at least in part, a known historical background. Since the Indian models compute… Expand

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#### References

SHOWING 1-10 OF 17 REFERENCES

The Transmission of Planetary Theories in Ancient and Medieval Astronomy

- Physics
- 1983

In Toledo in the year A.D. 1068 Abū’l-Qāsim Sā’id ibn Ahmad, also known as Qādi Sā’id, wrote a book entitled The Categories of Nations.1 In this work he discusses the people of the world from the… Expand

Giovanni Antonio Magini's “Keplerian” Tables of 1614 and Their Implications for the Reception of Keplerian Astronomy in the Seventeenth Century

- Philosophy
- 2001

The magnitude of Isaac Newton's achievement continues to colour and distort our understanding of science in the sixteenth and seventeenth centuries. Newton's status as the terminus ad quem of the… Expand

Ancient heliocentrists, Ptolemy, and the equant

- Physics
- 1987

Evidence is presented suggesting an ancient heliocentrist origin for geocentrist C. Ptolemy’s planetary orbit elements and the equant. Pliny’s data for Venus are shown to be inconsistent with… Expand

Archive for History of Exact Sciences

- Nature
- 1960

The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of mathematical and quantitative thought and the precise theory… Expand

Ausgleichspunkt, „Methode der Perser“ und indische Planetenrechnung

- 1960

ZusammenfassungBekanntlich läßt Ptolemaios in seiner Planetentheorie den Epizykelmittelpunkt so auf einem Exzenter laufen, daß die Bewegung, von einem Ausgleichspunkt G aus gesehen, gleichmäßig… Expand

Astronomical tables in the Twelfth century

- Adelard of Bath, an English Scientist and Arabist of the early Twelfth century,
- 1987

The yuga system and the computation of mean and true planetary longitudes ”

- Indian Journal of History of Science
- 1985