Briefly Discuss about Abul Wafa Al Buzjani.

1. ASSIGNMENT
SUBMITTED TO.
RESPECTED SIR ZAFAR.
SUBMITTED BY.
TAYYABA HUSSAIN.
BS HISTORY 8TH SEMESTER.
UNIVERSITY OF SARGODHA

2. Topic.
Abul Wafa MuhammadAl-Buzjani
(940- 997-8 C.E.)

3. Introduction.
 Buzjani was one of the leading astronomers and mathematicians of
the middle Ages, with significant contributions in observational
astronomy.
 His achievements in trigonometry paved the way for more precise
astronomical calculations.
 He made important innovations in spherical trigonometry, and his
work on arithmetics for businessmen, contains the first instance of
using negative numbers in a medieval Islamic text.

4. His Life.
 Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani was
born in (June 10,940-july 15,998) in Buzjan in Nishapur in the Khurasan
region of Iran. Khurasan is an area that gave birth to and raised many famous
Muslim scholars.
 He was a child, Abu al Wafa intelligence was already apparent and this
was supported by his great interest in the natural sciences. He studied
mathematics from his uncle, Abu Umar al Maghazli, and Abu Abdullah
Muhammad Ibn Ataba. While the knowledge of geometry is known from
Abu Yahya al Marudi and Abu al-Ala Ibn Karnib. He flourished as a great
mathematician and astronomer at Baghdad.

5.  Abul Wafa obtained his basic education in Mathematics in his hometown,
or nearby Nishapur, before leaving for Baghdad. After successfully
completing his primary and secondary education in 959 CE, Al Buzjani
who was then aged 19 moved to Baghdad. He continued his education
there and stayed for forty years. At that time, Baghdad was well known as
a center of knowledge.
 Buzjani became actively involved in the construction of a new observatory
in Baghdad.
 He covers numerous topics in the fields of plane and spherical
trigonometry, planetary theory, and solutions to determine the direction
of Qibla.

6. His Title.
 The Persian mathematician and astronomer Abul Wafa al-
Buzjani (AD 940-997) was awarded by the title of
“mohandes” geometer a title for the most skillful and
knowledgeable. He was professional geometer of his day.
 He is widely considered one of the most Outstanding
Islamic mathematician-scientists of the tenth century.
 He introduce the concepts of tangent, secant and cosecant
for the first time.

7. His Contribution.
 Abul Wafa's main contribution lies in several branches of mathematics,
especially geometry and trigonometry.
 Abul Wafa's contribution to the development of trigonometry was
extensive.
 He was the first to show the generality of the sine theorem relative to
spherical triangles.
 2sin2(a/2)=1-cosa,and
sin a = 2 sin (a/2) cos (a/2)
 In addition, he made a special study of the tangent and calculated a
table of tangents.
 He was also one of the last Arabic translators and commentators of Greek
works.

8. Astronomy
 Abu Al-Wafa' was the first to build a wall quadrant to observe the sky. It
has been suggested that he was influenced by the works of Al Battani as
the latter describes a quadrant instrument in his Kitab az Zij. His use of
tangent helped to solve problems involving right-angled spherical
triangles, and developed a new technique to calculate sine tables, allowing
him to construct more accurate tables than his predecessors.
 He studied and discussed different movements of the Moon and discovered
variations.

9. Almagest.
 His Almagest was widely read by medieval Arabic
astronomers in the centuries after his death. He is known to
have written several other books that have not survived.
Among Al Buzjani works on astronomy, only the first seven
treatises of his Almagest (Kitab al-Majisti) are now extant.
 In Al Majisti Buzjani introduced for the first time the tangent
function and hence facilitated the solutions to problems of the
spherical right‐angled triangle in his astronomical calculations.

10. Mathematics.
 He introduced the secant and cosecant for the first time, knew the
relations between the trigonometric lines, which are now used to
define them, and undertook extensive studies on conics.
 He established several trigonometric identities such as sin (a ± b)
in their modern form.
 He also discovered the law of sines for spherical triangles.
 His impressive resume includes the introduction of the concepts of
tangent, secant and cosecant for the first time, the compilation of in-
depth mathematical manuals for use by businessmen and artisans.

11. His Books.
 He wrote a large number of books on mathematics and other subjects, most of
which have been lost or exist in modified forms. His contribution includes.
 Kitab al-Hisab (a practical book of arithmetic) In the introduction to this book, he
wrote that his book comprised all that an experienced or novice, subordinate or an
expert in arithmetic needs to know, the art of civil servants, the employment of
land taxes and all kinds of business needed in administrations, rations and
proportions, multiplication, division, measurements, land taxes, distribution,
exchange and all other practices used by various categories of men for doing
business and which are useful to them in their daily life.
 Al Kitab al Kamil (the complete book).
 Kitab al Handsa (Applied Geometry).

12.  Al Buzjani also wrote a complete textbook on astronomy from a mathematical
point of view with Explicit solution
 He was the Author of the “Book on What is necessary from the science of
Arithmetic for Scribes & businessman” & “a Book on those geometric
construction which are necessary for craftsmen
 He also wrote translations and commentaries on the algebraic works
of Diophantus, al-Khwarizmi, and Euclid's Elements.
 Buzjani seems to have been a prolific scholar. He is said to have written 22
books and treatises.
 In the sixth chapter of al Majisti the book, Al-Buzjani defines the terms
tangent, cotangent, sine, sine of the complement (cosine), secant and cosecant,
establishing all the elementary relations between them.

13. Abul Wafa's achievements
 Abul Wafa achievements in the development of trigonometry,
specifically in the improvement of tables and in the means of solving
problems of spherical trigonometry, are undoubted.
 For the tabulation of new sine tables he computed sin 30 more
precisely, applying his own method of interpretation.
 This method, based on one theorem of Theon of Alexandria, gives an
approximation that can be stated in modern terms by the inequalities

14. GreatAstronomer.
 Historical evidence, as well as the judgments of Buzjani colleagues
and generations of scholars who came after him, all attest to the fact
that he was one of the greatest astronomers of his age.
 He was also said to have been a man with great moral virtues who
dedicated his life to astronomy and mathematics.
 A crater on the Moon has been named for Buzjani.
 On June 2015 Google has changed its logo in memory of Abu al-Wafa
Buzjani.

16. Death.
 Abu al Wafa died in Baghdad on July 15, 998 AD
He was respected by almost all people in the
entire Caliphate, especially those who loved
mathematics & science.