Abu Ja'far Ahmad ibn Yusuf ibn Ibrahim ibn Tammam al-Siddiq Al-Baghdadi (Arabic: أبو جعفر أحمد بن يوسف بن ابراهيم بن تمام الصديق البغدادي; 835–912), known in the West by his Latinized name Hametus,
was a Muslim Arab mathematician, like his father Yusuf
ibn Ibrahim (Arabic: يوسف
بن ابراهيم الصدَيق البغدادي).
Life
Ahmad ibn Yusuf was
born in Baghdad and moved with his father to Damascus in
839. He later moved to Cairo, but the exact date is unknown: since he was
also known as al-Misri, which means the Egyptian, this
probably happened at an early age. Eventually, he also died in Cairo. He
probably grew up in a strongly intellectual environment: his father worked
on Mathematics, Astronomy and Medicine, produced
astronomical tables and was a member of a group of scholars. He achieved an
important role in Egypt, which was caused by Egypt's relative independence
from the Abbasid Caliph.
Work
In some of the works
attributed to Ahmad, it is not clear if the text came from him, his father, or
whether they wrote together. It is clear, however, that he worked on a book on
ratio and proportion. This was translated to Latin by Gherard of Cremona and
was a commentary of Euclid's Elements. This book influenced early European
mathematicians such as Fibonacci. Further, in On similar arcs, he commented on
Ptolemy's Karpos (or Centiloquium); many scholars believe that ibn Yusuf was in
fact the true author of that work. He also wrote a book on the astrolabe. He
invented methods to solve tax problems that were later presented in Fibonacci's
Liber Abaci. He was also quoted by mathematicians such as Thomas Bradwardine,
Jordanus de Nemore and Luca Pacioli.
After a little while he
moved again, taking his son Ahmed with him, and went to live in Cairo. Although
we are far from certain about the date of Ahmed's birth it is believed to have
been before the family moved to Damascus. Again it is unclear exactly when the
family moved again to Cairo but as Ahmed became known as "al-Misri "
meaning "the Egyptian" it is likely that he lived in Cairo from a
fairly young age.
It is worth saying a word or two about Yusuf ibn Ibrahim, Ahmed's father,
since scholars have had some difficulty in deciding which texts are due to the
father, which to the son, or perhaps to joint work of the two. Yusuf ibn
Ibrahim is known to have been a member of a group of scholars and this must
have provided a strong intellectual environment for Ahmed. As well as a text on
medicine, Yusuf is known to have written a work on astronomy and produced a
collection of astronomical tables.
Ahmed was to achieve an important role in Egypt and to understand this we
must examine how Egypt achieved relative independence from the Abbasid Caliph.
The Caliphs had strengthened their armies in the 9th century
with Turkish slaves and began to put their Turkish commanders into positions as
governors of certain territories in the Empire. In 868 the Turkish general
Babak was put in charge of Egypt and he chose to send his stepson Ahmad ibn
Tulun there to take control. Ahmad ibn Tulun soon built up an army under his
own control and managed to take control of the finances of the country.
Although he never declared complete independence from the Caliph he governed
Egypt, and after 878 also Syria which his armies conquered, as an autonomous
region.
Ahmad ibn Tulun had a large family who formed the administration of Egypt.
Ahmed ibn Yusuf was appointed as a private secretary to the family, in
particular he was employed by one of Ahmad ibn Tulun's sons. In 884 Ahmad ibn
Tulun died but his family continued to rule Egypt until the 905 when the Caliph
sent an army to retake Egypt for the Empire. The period had been a fruitful one
for Egypt during which agriculture, commerce and industry flourished. More
importantly for Ahmed ibn Yusuf, the learning and scholarship of Baghdad was
encouraged in Egypt, and he was able to pursue his mathematical researches
while working for the Tulunid dynasty.
We know of a work by Ahmed on ratio and proportion, a book On
similar arcs, a commentary on Ptolemy's Centiloquium and
a book about the astrolabe. All these works have survived and historians
are confident that they are indeed the work of Ahmed, but several other works
which some claim to be due to him are probably by other authors.
Ahmed's work on ratio and proportion was translated into Latin
by Gherard of Cremona. The book is largely a commentary on, and expansion
of, Book 5 of Euclid's Elements. It was a carefully
constructed work which influenced early European mathematicians such
as Fibonacci. However it was not without its defects and Campanus of
Novara pointed out a circular argument which occurs in Ahmed's reasoning.
The book On similar arcs was also translated into Latin
and influenced European mathematicians. In the treatise Ahmed proves that
similar arcs of circles can be equal and not equal. The proof, like that on
ratio and proportion, is based on Euclid. This time it is Propositions 20
and 21 of Book III of Euclid's Elements which are the
main tools used by Ahmed. The complete Arabic text of this treatise is given
in.
Ahmed ibn Yusuf also gave methods to solve tax problems which appear
in Fibonacci's Liber Abaci.
Sumber
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Mathematician
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