Manual of Mongolian Astrology and Divination.The text deals with divination of various kinds, such as auspicious times for different undertakings. Ancient cultures used a common name for a certain collection of sciences (some now considered pseudoscience), including not only astrology and divination, but also calendrics, astronomy, and mathematics. Baumann uses mathematics for this conglomerate, a usage that is somewhat confusing to the modern reader; the Mongolian text does not contain any computational material (nor does Baumann's study). This aside, the book is a valuable contribution to the study of divination. Baumann's comprehensive study discusses time, metaphysics, divination, and other subjects, contextualizing the Mongolian text and explaining its dependence on other traditions. Especially valuable for a comparative study of omen material are some of Baumann's appendices, such as a list of omen protases from the Mongolian text. Overall, the book is a good starting point for a study of Mongolian divination and also a useful resource for those studying omens in the ancient world.
The Archaic and the Exotic: Studies in the History of Indian Astronomical Instruments by Sreeramula Rajeswara Sarma is a collection of 15 papers published by the author in the period between 1986 and 2004, most of them during the 1990s. The 15 papers have not been changed since their original publication, except that each of them is accompanied by a note explaining where and when the article was originally published. In addition, a brief preface and a very useful index have been included. What unifies the papers is that they all deal with the history of astronomical instruments in India.
The chapter studies the mathematics of ancient India, from the Vedic (Indo-European) period, ca1500–500 bce, and later. They used a decimal system to express numbers, often of great size. The texts called Śulba-sūtras (Rules of the Cord, ca 800–200 bce) prescribe detailed rituals involving geometrical arrangements of bricks forming altars, using pegs and ropes. These texts present a system of mathematics involving the full application of the Pythagorean theorem, a rather precise approximation to the square root of 2, and approximate methods for squaring the circle and circling the square. Around 500 bce, the place-value decimal system was created, including the zero. Moreover, the bhūta-saṃkhyā system allowed place-value numbers to be represented using a sequence of fixed words, e.g., “eyes” always meant “two.” The analysis of possible metrical forms led to the development of simple combinatorics, including a form of what we would call Pascal’s triangle. Jain mathematics speculated about types of infinity. Mathematical astronomy, from ca 400 ce, included computation of mean and true planetary positions, and computation of lunar and solar eclipses. The chapter concludes with brief surveys of notable Indian mathematicians.
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