A history of Greek mathematics - Wilbourhall.org

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ANTHEMIUS 543
the focus to the intersection of two tangents bisects the angle
between the straight lines joining the focus to the two points
of contact respectively.
In the third portion of the fragment Anthemius proves that
parallel rays can be reflected
to one single point from a parabolic
mirror of which the point is the focus. The directrix is
used in the construction, which follows, mutatis mutandis, the
same course as the above construction in the case of the ellipse.
As to the supposition of Heiberg that Anthemius may also
be the author of the Fragmentum mathematicum Bobiense, see
above (p. 203).
. The Papyrus of Akhmvm.
Next in chronological order must apparently be placed
the Papyrus of Akhmlm, a manual of calculation written
in Greek, which was found in the metropolis of Akhmim,
the ancient Panopolis, and is now in the Musee du
Gizeh. It was edited by J. Baillet l in 1892. According
to the editor, it was written between the sixth and
ninth centuries by a Christian. It is interesting because
it preserves the Egyptian method of reckoning, with proper
fractions written as the sum of primary fractions or submultiples,
a method which survived alongside the Greek and
was employed, and even exclusively taught, in the East. The
advantage of this papyrus, as compared with Ahmes's, is that
we can gather the formulae used for the decomposition of
ordinary proper fractions into sums of submultiples. The
decomposing a proper fraction into the sum of
formulae for
two submultiples may be shown thus
1 1
0) t=-t-t. +
be b + c
7
b + c
c . b .
a
a
_ 2 11 3 1 1 18 11
Examples — =
» —
F
, , a 1 1
=
?
=
•
11 666 110 7077 323 34 38
am
be b + mc , b + mc 1
c. b.
a
1
Memoires publies par les membres de la Mission archeologique frangaise
au Caire, vol. ix, part 1, pp. 1-89.