such tables were used in conjunction with the abacus. Throughout the geometry and
arithmetic sections, he emphasizes ratio and proportion. As in Ptolemy’s Almagest,the
solution of triangles relies on the application of areas and the Pythagorean theorem.For reasons he does not make clear, Al-Biruni discusses conic sections in the
Tafhim,an example of the aide-mémoire character of this text. Clearly he must have
explained the relevance of conic sections to astrology to Rayhana, but he does not
make it clear to the reader. If it were not known that scientists in his day (and even in
Ptolemy’s day) knew that light expanded in cone shapes, and that the theory was fair-
ly widely held that astrological influence was transmitted from heaven to earth via the
light of the stars, there would be no hint as to why he included this discussion at all.
Al-Biruni also includes a discussion of the five regular Platonic polyhedra,
equating them, in good Neoplatonic fashion, with the five elements. Paragraph 107
treats the powers of numbers from the first power to the fourth. Paragraph 108 pre-
sents the eleventh-century Persian understanding of the decimal notation of the Hin-
dus, including the use of the cipher as a placeholder. Al-Biruni’s handling of arith-
metic includes an introduction to algebra, which, in his day, was truly “occult.” The
laws regulating it were not yet known, and his very short exposition shows this fact by
its incompleteness. Al-Biruni then introduces astronomy, beginning with the sphere.
Step by step he explains basic geocentric astronomy, discussing the celestial circles,
their subdivisions, the movements of the luminaries (the Sun and Moon) and the
planets, the constellations, and the planetary theories of his day. He, like John Dee,
brings his geocentric astronomy into his geocentric astrology (paragraph 387), inter-
preting the meaning of planets at perigee and apogee and on different places on their
epicycles. He discusses and voices skepticism about the trepidation theory, which held
that the precession of the equinoxes was not constant in a retrograde direction but
oscillated back and forth—an incorrect idea first put forth by Tha ̄bit ben Qurrah in
the tenth century. He discusses the World Days and Year according to the Persian
astrologer Abu ̄ Ma‘shar and the Hindu conceptions of yugas (the four ages of Hindu
world cycle), kalpas, and manvantaras as found in the Siddhantas.
Al-Biruni next discusses the size and distance of the planets and elements, the
distribution of the land and water masses, and terrestrial longitude and latitude. He
discusses the gnomon (a kind of sundial) and its shadow (so basic for chronology) in
between discussing details of the horizon system of celestial coordinates (azimuth and
altitude).
Having prepared the student with the basics, Al-Biruni then discusses geogra-
phy, including the seven climates, their extent, and their characteristics. His presenta-
tion of the various cities in the climates shows that, although he has a fairly accurate
mathematical sense of the terrestrial globe, his knowledge of exact latitude and longi-
tude on Earth is approximate. One of the surprises of this book is Al-Biruni’s mention
in paragraph 239 of the mythological mountain Meru (the World Axis), under which
angels dwell, and the island Lanka (modern Sri Lanka), where the demons dwell. This
lore is Indian, not Persian, and definitely not Islamic. Could it be that the Persian Al-
Biruni sought to keep ancient traditions common to both Iran and Aryan India alive?
Likewise, paragraph 240 contains another surprise—red as well as white men lived inAl-Biruni
[16] THEASTROLOGYBOOK