Sinjari and al-Sijazi; Persian: ابوسعید سجزی; Al-Sijzi is
short for "Al-Sijistani") was an Iranian Muslim
astronomer, mathematician, and astrologer. He is notable for
his correspondence with al-Biruni and for proposing that
the Earth rotates around its axis in the 10th century.
He dedicated work to 'Adud al-Daula, who was probably his patron, and
to the prince of Balkh. He also worked in Shiraz making
astronomical observations from 969 to 970.
Al-Sijzi's full name is Abu Said Ahmad ibn Muhammad ibn Abd al-Jalil al-Sijzi. Very
little is known about his life but we can give fairly accurate dates for his life
since we know that he corresponded with al-Biruni and quoted results
by him in his own work.
He dedicated works to a
prince of Balkh, then the capital of Khorasan. Another work he dedicated to
'Adud ad-Dawlah who ruler over all southern Iran and most of what is now Iraq
from 949 to 983. It is quite possible that 'Adud ad-Dawlah was al-Sijzi's
patron since he was a leader well known for patronising the arts and science.
We also know that
al-Sijzi worked in Shiraz making astronomical observations during 969-970. It
was certainly at Shiraz at this time that he wrote some of his mathematical
works. As well as writing original works he copied other mathematical works and
they were dated 969 at Shiraz. In particular he copied, and dated the copy
969, Thabit ibn Qurra's treatise on complete quadrilaterals.
We mentioned above that
al-Sijzi corresponded with al-Biruni. The paper contains a letter
that al-Biruni wrote to Abu Said, who is almost certainly al-Sijzi.
The letter contains proofs of both the plane and spherical versions of the sine
theorem, which al-Biruni says were due to his teacher Abu Nasr
Mansur ibn Ali ibn Iraq. An English translation of the letter appears in.
In Y
Dold-Samplonius writes:
Al-Sijzi's main
scientific activity was in astrology, and he had a vast knowledge of the older
literature. He usually compiled and tabulated, adding his own critical
commentary. ... Al-Sijzi's mathematical papers are less numerous but more
significant than his astrological ones, and he is therefore better known as a
geometer.
The book contains an English translation (as well as the Arabic text)
of al-Sijzi's treatise on geometrical problem solving. Among the problems
al-Sijzi discusses are the following. Given a circle, find a point outside the
circle where the tangent to the circle and diameter produced, have a
given ratio. Given a triangle and three given numbers, find a point inside the
triangle where the lines to the three vertices divide the triangle into three
triangles having areas proportional to the three given numbers.
A treatise on spheres
by al-Sijzi Book of the measurement of spheres by spheres is
of considerable interest. The treatise, dated by al-Sijzi 969, contains twelve
theorems investigating a large sphere containing between one and three smaller spheres.
The small spheres are mutually tangent and tangent to the big sphere. Al-Sijzi
finds the volume inside the large sphere which is outside the small ones inside
it. He expresses this volume as that of a sphere of a particular radius which
he computes in terms of the radii of the spheres in the given system. The
authors of claim that the main interest of the work lies in the last two
propositions in which al-Sijzi considered four-dimensional spheres. In [5]
the author again suggests that in these propositions al-Sijzi is dealing with
spheres in a space of four dimensions. However J P Hogendijk
reviewing writes:
One could also assume
that the crucial identity ... is due to an oversight made by Al-Sijzi, who does
not use four-dimensional spheres anywhere else in his treatise. We note that
the treatise was written around 969 AD, at a
time when al-Sijzi was a very young and perhaps inexperienced geometer.
Another short work by al-Sijzi is the Treatise on how to imagine
the two lines which approach but do not meet when they are produced
indefinitely, which the excellent Apollonius mentioned in the second
Book of the Conics. In this treatise al-Sijzi classifies geometrical
theorems into five types, one of which is:
... propositions which
are difficult to imagine even though the proof of them is correct.
In work on geometrical
algebra al-Sijzi proves geometrically that
(a + b)3 = a3 +
3ab(a + b) + b3.
He does this by decomposing a cube of side a + b into
the sum of two cubes of sides a and b and a
number of parallelepipeds of total volume 3ab(a + b).
This is considered by most historians to be a three-dimensional extension by
al-Sijzi of the geometrical algebra propositions in Book 2 of Euclid's
Elements.
Al-Sijzi studied intersections of conic sections and circles. He replaced
the old kinematical trisection of an angle by a purely geometric
solution (intersection of a circle and an equilateral hyperbola).
Earth's rotation
Al-Biruni tells us that Al-Sijzi invented an astrolabe, called
"al-zūraqī", whose design was based on the idea that the Earth
rotates:
I have seen the
astrolabe called Zuraqi invented by Abu Sa'id Sijzi. I liked it very much and
praised him a great deal, as it is based on the idea entertained by some to the
effect that the motion we see is due to the Earth's movement and not to that of
the sky. By my life, it is a problem difficult of solution and refutation.
[...] For it is the same whether you take it that the Earth is in motion or the
sky. For, in both cases, it does not affect the Astronomical Science. It is
just for the physicist to see if it is possible to refute it.
Al-Biruni also referred to Al-Sijzi as a prominent astronomer who defended
the theory that the earth rotates in al-Qānūn al-Masʿūdī.
The fact that some people did believe that the earth is moving on its own
axis is further confirmed by a reference from the 13th century which states:
"According to the
geometers [or engineers] (muhandisīn), the earth is in constant circular
motion, and what appears to be the motion of the heavens is actually due to the
motion of the earth and not the stars.
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