The document discusses the contributions of several important Islamic mathematicians from the 8th to 15th centuries including Al-Khwarizmi, Al-Kindi, Al-Battani, Omar Khayyam, and Al-Tusi. It summarizes that they invented the concept of algebra, introduced Arabic numerals and the decimal system, and made advances in trigonometry, including defining trigonometric functions and the sine law. Their work was foundational to the development of modern arithmetic.

2.  In Khwarizmi's words
"...what is easiest and most useful in arithmetic, such as
men constantly require in cases of inheritance,
legacies, partition, lawsuits, and trade, and in all their
dealings with one another, or where the measuring of
lands, the digging of canals, geometrical
computations, and other objects of various sorts and
kinds are concerned..."

3. • The Muslims invented the symbol for zero (The
word "cipher" comes from Arabic ‫)صفر‬
• And they organized the numbers into the
decimal system - base 10
• Additionally, they invented the symbol to
express an unknown quantity, i.e. variables like x

4. Al-Battani
Al-
Kindi
Al-Tusi Omer
Al-Khwarizimi
Khayyam

5. Muhammad ibn Musa al-
Khwarizmi (780 A.D-840),
Khwarzim
 Mathematician
 Astronomer
 Geographer

6. The word "algebra"
comes from "Al-Jabr”,
which is taken from the
title of Khwarizmi's
book
“Hisab Al-Jabr wal Muqabala”

7. In this book
Khwarizmi
explained that the
unknowns in one
side of the equation
is called al-Jabr
and collecting the
knowns in the
other side of the
equation is called
al- Mukabalah Manuscript copy of Hisab Al-Jabr wal
Muqabala

9. Al-Khwarizmi
also introduced
the Arabic
numerals

10.  Mathematician
 Islamic Philosopher
 Astrologer
 Astronomer
 Physicist
 Chemist

11. Al-Kindi wrote four
volumes on the
number system
“Ketab fi Isti’mal
al-’Adad al-Hindi”
and laid the
foundation of a
large part of
modern arithmetic

12.  Astronomer
 Mathematician
 Astrologer

13. Al-Batani
introduced
trig0nometric
ratios

14.  Mathematician
 Astronomer
 Philosopher
 Poet

15. This book is a
master- piece on
algebra and has
great importance
in the
development of
algebra

16.  He offered geometric
solutions of cubic
equations and partial
geometric solutions of the
other equations

17.  Astronomer
 Mathematician
 Philosopher
 Physicist
 Chemist

18.  In his book al-Tusi made
enormous advances in
plane and spherical
trigonometry

20.  The well-known sine law
is also stated in this
work: a/sin A = b/sin B =
c/sin C

21.  Thabit bin Qurra (836–901),
 Abu Kamil (about 850–930)
 Ibrahim ibn Sinan (908–946)
 Muhammad Abu'l Wafa (940–998), Khurasan

22.  Abu Bakr ibn Muhammad ibn al-Husayn al-Karaji
(953–1029)
 Abu Abd Allah Muhammad ibn Muadh Al-Jayyani
(989–1079), Andalusia
 Ghiyath al-Din al-Kashi (1393–1449)