Abu Ja'far Muhammad ibn al-Husayn al- Khazin al-Kurasani

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the whole are more accurate than those of Ptolemy.
Abūa Ja’far developed a solar model, in which the sun moves in a circle with
the earth as its center, in such a way that its motion is uniform with respect
to a point which does not coincide with the center of the earth. Finally, he
dealt with the effect of gravity 9 and thus precedes Newton.
Professional Career:
According to the Islamic Encyclopedia, Khazin served as a treasurer during
the reign of the Samanid Prince Mansur ibn Nūh I (961-976) and then as
a Vizier in Nishapur 10 . He became close to the Buwayhid Prince 11 Rukn
ad-Dawlah and his erudite Vizier al-’Amid, and spent part of his life in
Rayy. During peace negotiations between the Buwayhids and the Samanids,
al-Khazin acted as the envoy of the Buwayhids. Al-Khazin later developed
close friendship with the Vizier, al-’Amid, and spent the rest of his life in
research and authoring books under his protection.
Abū Ja’far al-Khazin realized that a cubic equation could be solved geometrically
by means of conic sections. Al-Māhān (ca. AC 850) had shown that
an unsolved problem in Archimedes’ On the Sphere and Cylinder 12 could be
reduced to the cubic equation:
x 3 + C = ax 2 .
Abū Ja’far based on a commentary to Archimedes’ work by Eutocius of
Ascalon (fifth century AC) realized that the equation x 3 + C = ax 2 could
also be solved by means of conic sections.
Abū Ja’far also studied the equation x 3 + y 3 = z 3 and stated (without proof)
that it has no solution in positive integers. He also worked on the isoperimetric
problem (see Lorch, 1986), and he wrote a commentary to Book X of
Euclid’s Elements 13 .
9 See the Islamic Encyclopedia, http://islamicencyclopedia.org/public/index/
topicDetail/page/11/id/543.
10 Nishapur or Nishabur is a city in the Khorasan Province in northeastern Iran.
11 The Buyid dynasty controlled most of modern-day Iran and Iraq in the 10th and 11th
centuries.
12 On the Sphere and Cylinder (about 225 BC) was written by Archimedes in two volumes.
Proposition 4 of Book II deals with the problem how to find the surface area of a
sphere and the volume of the contained ball and the analogous values for a cylinder.
13 Euclid’s Elements consist of 13 books written by the Greek mathematician Euclid in
Alexandria about 300 BC. Book X attempts to classify incommensurable magnitudes by
using the method of exhaustion, a precursor to integration.