A history of Greek mathematics - Wilbourhall.org

MENELAUS'S SPHAERICA 273
But, by III. 1 applied to the triangle BC\A l
cut by the
transversal PC A..,
sinJ.jJ.3 sin C^C 3
sin PA
T
sin BA 3
sin BC 3
sin PC\
sin A, A- sin PA sinBA., sin PA sin PC
sin C 1
C 3
sin PC
Y
sin BC 3
sin PC 1
sin PC. 3
Br
7\? 1'3
from above,
Part 2 of the proposition proves that, if PC' 2^. 2
be drawn
such that sin 2 PC 2
= sin PA 2
. sin PC, or r 2
2 = Rr (where r2 is
the radius of the parallel circle through (7 2 ), BC 2
—BA 2
is a
maximum, while Parts 3, 4 discuss the limits to the value of
the ratio between the arcs A^A 3
Nothing is known of the life of
and Cfi^.
Claudius Ptolemy except
that he was of Alexandria, made observations between the
years a.d. 125 and 141 or perhaps 151, and therefore presumably
wrote his great work about the middle of the reign of
Antoninus Pius (a.d. 138-61). A tradition handed down by
the Byzantine scholar Theodorus Meliteniota (about 1361)
states that he was born, not at Alexandria, but at
Ptolemais
17 'Epfieiov. Arabian traditions, going back probably to
Hunain b. Ishaq, say that he lived to the age of 78, and give
a number of personal
not be attached.
details to which too much weight must
The MaOrj/iaTLKT) o-vvTagts (Arab. Almagest).
Ptolemy's great work, the definitive
astronomy, bore the title MaOrj/xaTiKrjs
achievement of Greek
Zwrdgem /3i/3\ia i-y,
the Mathematical Collection in thirteen Books. By the time
of the commentators who distinguished the lesser treatises on
astronomy forming an introduction to Ptolemy's work as
fXLKpb? dcrTpoyo/jiov/iepo? (7677-09), the 'Little Astronomy', the
book came to be called the ' Great Collection ',
fieydXrj