Universal International Scientific Journal
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Ruzmatov Ilhomjon Gulomjon ugli
University of Science and Technology
Department of Social Sciences, Religious Studies Teacher
Uzbekistan
https://orcid.org/0009-0005-3878-93711
Abstract:
Algebra and geometry, two vital branches of mathematics, have deep historical roots,
evolving through centuries of intellectual efforts by different civilizations. This article provides a brief and
structured overview of their origins, key contributors, and practical applications. The origins of algebra and
geometry date back to ancient civilizations. Algebra, meaning "reunion of broken parts" in Arabic, was
systematically developed by the Persian mathematician Al-Khwarizmi in the 9th century. His work
introduced foundational concepts in solving equations and symbolic representation.
Geometry, rooted in ancient Egypt and Mesopotamia, initially emerged to address practical problems
like land division and construction. The Greeks, especially Euclid, advanced geometry significantly in the
3rd century BCE through his work Elements, which became a cornerstone for mathematical reasoning and
proofs. These two fields have since become indispensable in mathematics and have profoundly influenced
science, engineering, and technology, showcasing humanity's efforts to understand the natural and abstract
worlds.
Universal Xalqaro Ilmiy Jurnal
Jurnalning bosh sahifasi:
THE ORIGINS OF ALGEBRA AND GEOMETRY
Universal International Scientific
Year: 2025 Issue: 2 Volume: 1
Published: 14.01.2025
International indexes
Universal International Scientific Journal
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1
Keywords:
algebra, geometry, Al-Khwarizmi, euclid, elements, ancient civilizations, mathematical
foundations.
Annotatsiya:
Matematikaning ikki muhim tarmog'i bo'lgan algebra va geometriya chuqur tarixiy
ildizlarga ega bo'lib, turli sivilizatsiyalarning ko'p asrlik intellektual sa'y-harakatlari natijasida rivojlanadi.
Ushbu maqolada ularning kelib chiqishi, asosiy hissa qo'shuvchilari va amaliy qo'llanilishi haqida qisqacha
va tuzilgan. Algebra va geometriyaning kelib chiqishi qadimgi sivilizatsiyalarga borib taqaladi. Arabcha
“buzilgan qismlarning birlashishi” ma’nosini bildiruvchi algebra IX asrda fors matematigi Al-Xorazmiy
tomonidan tizimli ravishda ishlab chiqilgan. Uning ishi tenglamalar va ramziy tasvirni echishda asosiy
tushunchalarni kiritdi.
Qadimgi Misr va Mesopotamiyadan kelib chiqqan geometriya dastlab erlarni taqsimlash va qurish
kabi amaliy muammolarni hal qilish uchun paydo bo'lgan. Yunonlar, ayniqsa Evklid miloddan avvalgi 3-
asrda oʻzining “Elementlar” asari orqali geometriyani sezilarli darajada rivojlantirdi, bu matematik fikrlash
va isbotlash uchun asos boʻldi. Oʻshandan beri bu ikki soha matematikada ajralmas boʻlib qoldi va fan,
muhandislik va texnologiyaga chuqur taʼsir koʻrsatdi. insoniyatning tabiiy va mavhum dunyoni tushunishga
bo'lgan harakatlari.
Kalit so‘zlar:
algebra, geometriya, Al-Xorazmiy, evklid, elementlar, qadimgi sivilizatsiyalar,
matematik asoslar.
Аннотация:
Алгебра и геометрия, две жизненно важные отрасли математики, имеют глубокие
исторические корни, развиваясь на протяжении столетий интеллектуальных усилий разных
цивилизаций. В этой статье представлен краткий и структурированный обзор их происхождения,
основных участников и практических приложений. Истоки алгебры и геометрии восходят к
древним цивилизациям. Алгебра, что означает «воссоединение сломанных частей» на арабском
языке, была систематически разработана персидским математиком Аль-Хорезми в IX веке. Его
работа ввела основополагающие концепции решения уравнений и символического представления.
Геометрия, корни которой уходят в Древний Египет и Месопотамию, изначально возникла для
решения практических задач, таких как разделение земли и строительство. Греки, особенно Евклид,
значительно продвинули геометрию в III веке до н. э. благодаря своей работе «Начала», которая
стала краеугольным камнем математических рассуждений и доказательств. С тех пор эти две
области стали незаменимыми в математике и оказали глубокое влияние на науку, инженерию и
технологии, демонстрируя усилия человечества по пониманию естественного и абстрактного
миров.
Ключевые слова:
алгебра, геометрия, Аль-Хорезми, Евклид, элементы, древние
цивилизации, математические основы.
Language:
English
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Citation:
Ruzmatov , I. (2025). THE ORIGINS OF ALGEBRA AND GEOMETRY. Universal
International
Scientific
Journal,
2(1),
90–93.
Retrieved
from
https://universaljurnal.uz/index.php/jurnal/article/view/1405
Doi:
https://doi.org/10.5281/zenodo.14677119
https://scholar.google.com/scholar?hl=ru&as_sdt=0%2C5&q=THE+ORIGINS+OF+ALGEBRA+AND+GEOMETRY&btnG=
Algebra: From Ancient Methods to
Modern Symbolism
The development of algebra began
with the ancient Babylonians around 2000
BCE. They used primitive methods to
solve quadratic equations by relying on
arithmetic procedures. Unlike today's
symbolic approach, their techniques were
more verbal and numeric.
Significant progress in algebra was
made in the Islamic Golden Age. Al-
Khwarizmi, a Persian scholar, wrote "Al-
Kitab al-Mukhtasar fi Hisab al-Jabr wal-
Muqabala",
introducing
systematic
solutions
for
linear
and
quadratic
equations. The term algebra itself is
derived from the Arabic word al-jabr,
meaning 'restoration.'
In the 12th century, Al-Khwarizmi's
work was translated into Latin, influencing
European
scholars.
Later,
in
the
Renaissance period, symbolic algebra
emerged, pioneered by François Viète and
René Descartes. Their methods laid the
groundwork for modern algebraic notation.
Key Historical Figures and Tools
-
Babylonians:
Early
quadratic
equation solvers.
- Al-Khwarizmi: The 'father of
algebra,' known for his comprehensive
treatise on algebraic methods.
- François Viète: Introduced symbolic
representation of variables.
-
René
Descartes:
Developed
Cartesian geometry, bridging algebra and
geometry.
Geometry: Practical Beginnings to
Theoretical Foundations
Geometry's origins can be traced back
to ancient Egypt and Mesopotamia, where
it was initially used for practical purposes
like measuring land and constructing
buildings. The ancient Egyptians applied
geometric rules in building pyramids,
while the Mesopotamians created early
geometric tables for measurement.
Greek scholars transformed geometry
into a formal science. Around 300 BCE,
Euclid
authored
'Elements',
a
comprehensive compilation of geometric
knowledge. His axiomatic approach, based
on postulates and logical deductions,
became the foundation of Euclidean
geometry.
In later centuries, during the Islamic
Golden Age, scholars such as Alhazen (Ibn
al-Haytham) contributed to the field by
applying geometric principles to optics. In
the 19th century, the study of non-
Euclidean geometry by mathematicians
like Gauss, Lobachevsky, and Bolyai
revolutionized the field and opened new
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horizons for modern physics.
Key Historical Figures and Tools
- Egyptians: Pioneers in applied
geometry.
- Euclid: Known as the 'father of
geometry,' author of 'Elements.'
-
Alhazen:
Made
significant
contributions to geometric optics.
- Gauss & Lobachevsky: Founders of
non-Euclidean geometry.
Conclusion
Algebra and geometry have evolved
from
practical
tools
to
theoretical
disciplines that are crucial for modern
science and technology. Their rich histories
highlight the intellectual progress of
humanity and their application in various
fields today, such as engineering, computer
science, and physics.
REFERENCES USED
1. Katz, Victor J. A History of Mathematics: An Introduction. Addison-Wesley, 1998.
2. Boyer, Carl B. A History of Mathematics. Wiley, 1991.
3. Burton, David M. The History of Mathematics: An Introduction. McGraw-Hill,
2007.
4. Smith, D.E. History of Mathematics, Vol. 1 & 2. Dover Publications, 1958.
5. Al-Khwarizmi. Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala, 9th century.
6. Bell, E.T. Men of Mathematics. Simon & Schuster, 1937.
7. Cajori, Florian. A History of Mathematics. Macmillan, 1894.
8. Stewart, Ian. The Story of Mathematics. Quercus, 2008.
9. Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of
Mathematics. Princeton University Press, 1991.
10. Kline, Morris. Mathematics: The Loss of Certainty. Oxford University Press, 1980.
