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WORKING ON THE SUBJECT OF FUNDAMENTALS OF GRAPHIC ILLUSTRATION
Bakhromova Muhayyo Bahrom kizi
“Fine Arts and Engineering Graphics”
Bachelor's student
Annotation:
This article presents the development of assignments in the subject of
Fundamentals of Graphical Representation. It highlights the importance of structured tasks
aimed at improving students' understanding of basic concepts in technical drawing, including
orthographic projection, axonometry, and section views. The study focuses on task-based
learning as a method to enhance visualization, precision, and independent problem-solving skills.
Special attention is given to the integration of didactic principles and modern teaching
technologies to make the learning process more effective and engaging.
Keywords:
graphical representation, technical drawing, task development, orthographic
projection, engineering graphics, visualization, didactic principles, axonometric drawing
In ancient Egypt, geometry was used mainly for practical purposes, in land surveying and
architectural construction. They were based on simple but accurate measurement methods and
used laws similar to the Pythagorean theorem. In the art of depiction, a method known as the
"Egyptian rule" was formed, in which people and objects were depicted in frontal and side views.
Ancient Greek scientists, including Thales, Pythagoras, Euclid, and Archimedes, developed
geometry on a theoretical basis and formulated its rules. Euclid developed an axiomatic system
of geometry in his work "Elements". The Greeks introduced realism into art by focusing on
relative size, proportion, and perspective in their methods of depiction.
In general, while the Egyptians used geometry for practical purposes, the Greeks studied it in
depth theoretically and created its scientific foundations. In terms of depiction methods, while
Egypt relied on a frontal and schematic approach, Greek art was based more on naturalism and
proportion. These studies also had a great influence on the development of science and art in the
later period.
Geometry and depiction methods in ancient Egypt
In ancient Egypt, geometry was associated with vital needs and played an important role mainly
in land surveying, the construction of pyramids and temples, and in the agricultural system.
Since the boundaries of land areas disappeared as a result of the floods of the Nile River, the
Egyptians developed special measurement systems. They used simple arithmetic and geometric
formulas to determine the surface of the earth, correctly place buildings, and perform
engineering calculations.
In ancient Egyptian art, depiction methods had a unique schematic approach, in which the human
div was depicted according to certain rules. For example, a person's head and legs are depicted
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from the side, while the chest and eyes are depicted directly. This "Egyptian rule" has long
dominated art, used to express holiness and order.
Research by ancient Greek scientists in geometric and representational methods
In ancient Greece, geometry was not only a practical field, but also the focus of philosophical
and scientific research. Thales was the first to explain geometry on a theoretical basis, while
Pythagoras studied the relationship between numbers and shapes. Euclid's "Elements" set out the
basic rules of geometry and had a great influence on subsequent centuries. Archimedes, on the
other hand, discovered new principles for calculating the area of a circle, measurements,
and volume.
In the field of fine arts, the Greeks tried to depict the human div in a way that was proportional
and natural. They understood perspective and tried to reflect depth in landscape paintings.
Through this, ancient Greek art had a realistic and dynamic appearance, unlike the traditional
frontal images in Egypt.
Comparison of geometry and methods of depiction in ancient Egypt and Greece
There are a number of differences between the geometry and methods of depiction of ancient
Egyptian and Greek scientists:
• While the Egyptians used geometry for practical purposes (land surveying, construction and
engineering), the Greeks developed it theoretically and used it to create mathematical
foundations. Figure 1
• Egyptian fine art was schematic and formalized, while Greek art was based on naturalness and
proportion.
• The Egyptians used measurements and shapes in practice, while Greek scientists studied the
general laws of geometry and developed it with abstract concepts.
These scientific and artistic researches later developed further in the Roman, European and
Islamic worlds, laying the foundation for the formation of modern geometry and fine arts.
Some of the methods of representation described in the works of "Geometry" and "Astronomy"
by the great Central Asian scholars and encyclopedists Muhammad al-Khwarizmi, Abu Nasr al-
Farabi, Ahmad Farghani, Abu Rayhan al-Biruni, Abu Ali ibn Sina, Omar Khayyam and others,
who lived in the 9th-11th centuries and mastered one or more fields of science and conducted
major research in various areas, are presented. We present some information about the lives and
research of these scholars.
Muhammad al-Khwarizmi (783-850). Al-Khwarizmi's full name is Muhammad ibn Musa al-
Khwarizmi. He is a famous mathematician and astronomer from Central Asia. Al-Khwarizmi
was born in 783 in Khorezm (Khiva) and died in 850 in Baghdad (Iraq). Al-Khwarizmi arrived
in Baghdad at the end of the 8th century. Scholars and people of various professions began to
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settle in Baghdad. The development of science dates back to the period of the caliphate of Harun
al-Rashid (786-809) and his son al-Ma'mun (813-833).
Al-Ma'mun built the "Bayt al-Hikmat" ("House of Wisdom") in Baghdad. The "House of
Wisdom" had a well-equipped observatory and a rich library. It could be called the
Academy of Sciences of its time.
Upon arriving in Baghdad, Al-Khwarizmi engaged in scientific research. He diligently
studied the works of the ancient Greek mathematicians Euclid, Archimedes, and
Apollonius, as well as the works of ancient Indian astronomers and mathematicians. His
first research work in Baghdad was editing an Arabic translation of the Indian astronomical
work "Sindhanta".
Al-Khwarizmi soon gained fame throughout the Middle East in mathematics, astronomy,
geography, history, and medicine. He supervised the library, observatory, and all scientific
research work in the "Bayt al-Hikmat." If we call the "House of Wisdom" the Academy of
Sciences, then Al-Khwarizmi was the president of that Academy.
Khwarizmi's contribution to the development of mathematics is incomparable. His treatise
"Indian Calculus" is devoted to the decimal system of numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
which he supplemented by introducing the number "zero". Khwarizmi simplified these
numbers, discovered in India, and for the first time described them in Arabic. These
numbers passed from the Indians to the Arabs, and then to Europe, thanks to Khwarizmi's
treatise in the 11th century.
Khwarizmi is considered the founder of the science of algebra. The term "algebra" comes
from the Latin spelling of the word "Al jabr" in his work "Al jabr wal muqabala".
Abul Abbas ibn Muhammad ibn Kathir Farghani (797-865). He is a great astronomer,
mathematician and geographer. In European scientific literature, he was called Alfraganus.
Ahmad Farghani worked in Baghdad during the reign of al-Ma'mun, son of Harun al-
Rashid (813-833), together with Central Asian scholars Muhammad ibn Musa al-
Khwarizmi, Abbas ibn Sa'id al-Jawhari, and others. They initially translated the works of
Greek scholars into Arabic, and then created independent works in Arabic themselves.
Caliph al-Ma'mun built an observatory in 829 under the "Bayt al-Hikmat" (House of
Wisdom) in Baghdad, and in 832 in Damascus.
Farghani's first work was called "Introduction to Astronomy." With this work, Farghani
showed that he was an accomplished astronomer. Farghani had previously demonstrated his
deep knowledge of astronomy by predicting a solar eclipse in 812.
Interest in Ferghani's works continued in Europe after the 13th century. His Elements of
Astronomy was translated into Latin by Jacob Gallius in 1969 and published in Amsterdam
with an Arabic text.
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Ferghani wrote a work entitled "Thirty Chapters on the Introduction to the Almagest" dedicated
to the commentary on Ptolemy's "Almagest". He continued to write books on astronomical
instruments and also created a complete book on the "Asturlobe" and works such as "On the
Making of the Asturlobe".
In his work "On the Making of the Asturlobe", Ferghani gave the following concepts about
stereographic projection. He described the method of projecting a sphere from a point S onto a
plane
drawn from a point S1 diametrically opposite to this point and its properties:
1. Circles lying on the sphere are projected onto the
plane through the center S as circles. If
the circles pass through the center of the sphere, they are projected as straight lines.
2. In stereographic projection, the angles between the curves lying on the sphere when projected
onto the
plane are equal to the angles between the curves that are their projections.
3. When the sphere rotates around the diameters S and S1, the tangent plane
also rotates
around that point by the same angle.
These properties are also found in the works of some scientists who lived before Ferghani (for
example, Ptolemy). However, they did not prove these properties. Ferghani gives a complete
proof of the first property in the above-mentioned work. In this, he bases his proof on the
following lemma: suppose that when a circle is projected onto a straight line, the points M and N
of the circle pass through the points M′ and N′ of the straight line. Then SMN = SN′M′, SNM =
SM′N′ (Fig. 1.2.1, Appendix 2).
Abu Nasr al-Farabi (873-950). Al-Farabi is a great Central Asian encyclopedist. His full name is
Abu Nasr Muhammad ibn Muhammad ibn Uzlug Tarkhan Al-Farabi. He was born near the city
of Aris, Shymkent region, present-day Kazakhstan. His father was from the Turkic tribes and
was a military officer. He received his initial education in his native land, in the cities of
Tashkent (Shosh), Bukhara and Samarkand. Later, his passion for science led him to Baghdad,
the scientific center of that time. In Baghdad, Al-Farabi, like other scientists, first studied
medieval science and various languages, and then began to write independent works.
Al-Farabi defines mathematics as a science that studies the quantitative and spatial relationships
of objects and divides it into seven parts.
The first part is arithmetic - the science of numbers, which consists of theoretical and practical
parts.
The second part - geometry - arose from the fact that different parts of existing things have
different shapes and the need for a science that studies their measurement. "Thus, geometry is a
measuring science, through which we know the measurement, compare lines, surfaces and
volumes with each other," writes Farabi.
The third part - optics - the science of observation - also belongs to geometry, it studies the
shapes of figures, distances between objects using light and light.
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The fourth part is devoted to the science of stars and is the science of astronomy.
The fifth part is the science of music. The reason for the inclusion of the science of music in
mathematics is that Al-Farabi studied the mathematical principles of the harmony of melodies.
In his work "The Great Book of Music", he also presents various tables and geometric drawings
of the harmony of melodies. This work does not only consist of music theory, but also gives
musical instruments known in the East such as the rubab, tanbur, drum, flute, and the rules for
playing melodies on them.
Al-Farabi also wrote many works on mathematics. These include "A Word on Volume and
Quantity", "A Short Book on Introduction to the Geometry of Space", "The Book of
Applications" and "The Book of Subtle Secrets of Geometric Figures and the Book of
Intelligent Methods of Thinking".
Abu Rayhan Al-Biruni (973-1048). Beruni's full name is Abu Rayhan Beruni Muhammad ibn
Ahmad) - a great medieval encyclopedist. He was born in the city of Qiyat in Khorezm. Qiyat
was located on the site of the present-day city of Beruni.
Beruni was interested in science and knowledge from a very young age. His favorite subjects
were astronomy, mathematics, geodesy, geography and mineralogy. He writes in his work
"Geodesy" that he determined the geographical latitude of the city of Qiyat.
In 1022-1024, Mahmud of Ghaznavi took Beruni with him on his campaign to India. During the
trip, Beruni also studied science. He measured the length of one degree of the meridian of the
globe near the Nandna fortress in Punjab and determined that it was 110,895 km. This
information is compared with the result of modern measurements of 111.1 km, and the accuracy
of Biruni's measurements is much closer. He collected material for his future work "History of
India" in India and completed it in 1030. That year, Mahmud died and was succeeded by his son
Mas'ud. Mas'ud showed many favors to Biruni. For this reason, Biruni dedicated his
masterpiece to Mas'ud and called it "The Canon of Mas'udi".
Biruni's contribution to mathematics and other fields of science can also be seen in the more
than 100 works he wrote down. The largest of them are "India", "Monuments", "The Canon of
Mas'udi", "Geodesy", "Minerology" and "Astronomy".
Abu Ali ibn Sino (980-1037). Abu Ali Al Hasayin ibn 'Abdullah Ibn Ali (980.8, Hussein). When
Hussein, Ibn Sino joined the capital-Bukhara and to study it They will give them the age of 10
years old. He also reads the fields of Ibn Sina, who reads the Arabic language and literature. He
reads the Arabic language and literature perfectly. Ibn Sina was known as a skillful physician of
the Greek Authors as well as Ibn Sina, in this book, and in this book. Ibn 'Mamun (997-1009) and
Mamun ibn' Mamun (1009-1017) were very interestive in science and created a comfortable
environment for scientists for scientific creatures. These include large mathematical and
astronomy Abu Sahl Christmi. , honor, "Hujat Al Khaqq" (Evidence "(" Indeed, "Ibn Sina in the
history of the world. The various sources have written more than 450 works, but it is the name of
its medical legacy, especially in the West. at -category: Interpretation - Interpretation: Al Burhan -
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Proof; al-Signica - Rialectics; Al Knismica - Regretic; Ash-poem-poetry -Poetics (the art of
poem); 2) Nature (here minerals, plants, animals and humans are discussed in separate sections;
3) Mathematics - divided into 4 disciplines: arithmetic, geometry, astronomy and music;
4) Metaphysics or theology. Parts of this work have been published in Latin, Syriac, Hebrew,
German, English, French, Russian, Persian and Uzbek.
Ibn Sina's worldview is shaped by the teachings of Aristotle and the works of Al-Farabi. The
simplest indivisible form of matter consists of 4 elements: air, fire, water, and earth. As a result
of their various combinations, complex material objects are formed. Complex objects can change
in form, but the 4 elements that are their material basis do not disappear, they are preserved
forever. According to Ibn Sina, first mountains and rocks appeared, then plants, animals, and as a
result of development, man appeared, who differs from other creatures in his mind, ability to
think, and language.
“Logic,” writes Ibn Sina, “gives man such a rule that, with the help of this rule, a person is
protected from errors in drawing conclusions.” He deeply studied logical methods, the issues of
description, judgment, conclusion, and proof, and developed the science of logic after Al-Farabi
as the correct method of knowledge.
In his opinion, volcanoes are actually associated with mountain formation and earthquakes.
Mountain formation itself occurs in 2 ways:
1) the uplift of the earth's crust during strong earthquakes;
2) the gradual action of water and air, which causes deep ravines to form, and as a result, a
height is formed near them. There are also several reasons for the occurrence of earthquakes.
Ibn Sina was interested in astronomy from his youth and maintained this interest until the end of
his life. He devoted separate chapters to astronomy in 8 independent treatises and in the
mathematical parts of the "Book of Healing" and "Donnishnama". He revised Ptolemy's
"Almagest" and created a manual on practical astronomy on its basis.
References:
1.
Uralovich, T. F. (2021). Conducting classes on fine arts based on information and
communication technologies.
International Engineering Journal For Research &
Development
,
6
, 3-3.
2.
Turapova, R. N. (2023). Mechanisms for Improving Children's Dialogical Speech.
Vital
Annex: International Journal of Novel Research in Advanced Sciences
,
2
(9), 49-53.Холмуродов,
Ш. О. (2022). СИСТЕМА ИНФОРМАЦИОННЫХ ТЕХНОЛОГИЙ В ОБРАЗОВАНИИ
СТУДЕНТОВ-ИНФОРМАТИКОВ.
Digital
,
3
(1), 1.
3.
Uralovich, T. F. (2023). The Role Of Applied Art In The Development Of Aesthetic
Volume 15 Issue 04, April 2025
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343
Skills Of Students.
International Journal of Advance Scientific Research
,
3
(05), 111-118.
4.
Urolovich, T. F. (2023, May). METHODOLOGICAL ASPECTS OF DEVELOPING
AESTHETIC SKILLS IN FUTURE DRAWING TEACHERS. In
International Scientific and
Current Research Conferences
(pp. 108-114).
5.
Uralovich, T. F. (2023). PEDAGOGICAL CHARACTERISTICS OF DEVELOPING
AESTHETIC SKILLS IN FUTURE DRAWING TEACHERS.
International Journal of
Pedagogics
,
3
(05), 139-144.
6.
Холмуродов, Ш. О. (2021). СИСТЕМА ИНФОРМАЦИОННЫХ ТЕХНОЛОГИЙ В
ОБРАЗОВАНИИ СТУДЕНТОВ ИНФОРМАТИКОВ.
Digital
,
3
(1).
7.
Xolmurodov, S. O. (2024). O ‘QUVCHI TAFAKKURINI RIVOJLANTIRISHDA
INTERFAOL METODLAR (O ‘YINLAR) DAN FOYDALANISH (1-MODUL).
Inter
education & global study
, (4 (1)), 188-196.
8.
Turapova, R. B. (2025). VARIATIV YONDASHUV ASOSIDA O ‘QUVCHILARNING
DIALOGIK NUTQINI RIVOJLANTIRISH DOLZARB MASALALARI.
Inter education &
global study
, (3), 279-288.
9.
Uralovich, T. F. (2024). THE MECHANISM OF FORMING AESTHETIC SKILLS OF
STUDENTS THROUGH TEACHING THE SCIENCE OF DRAWING.
Ethiopian International
Journal of Multidisciplinary Research
,
11
(08), 36-38.
10.
Uralovich, T. F. Conducting classes on fine arts based on information and communication
technologies International Engineering Journal For Research & Development.-2021.
11.
Toshpulatov, F. U. (2022). Murodaliyevna TF DEVELOPMENT OF THE SKILLS OF
STUDENTS TO AVOID TYPICAL ERRORS WHEN PERFORMING CUTTING AND
CUTTING.
Spectrum Journal of Innovation, Reforms and Development
,
5
, 70-74.
12.
Turapova, R. N. (2023). Mechanisms for Improving Children's Dialogical Speech.
Vital
Annex: International Journal of Novel Research in Advanced Sciences
,
2
(9), 49-53.
13.
BAJARISHDA, T. F. Q. V. K. (2022). OQUVCHILARDA TIPIK XATOLARGA YOL
QOYMASLIK KO ‘NIKMALARINI RIVOJLANTIRISH.
Физико-технологического
образование.–2022
,
4
.
14.
Toshpulatov, F. U. (2022). Issues of Developing the Culture of Measurement in Drawing
Lessons (In the Case of General Secondary Schools).
Vital Annex: International Journal of
Novel Research in Advanced Sciences
,
1
(5), 111-119.
15.
Toshpulatov, F. U., Mominov, B. K., & Mamatkulov, I. C. (2020). Determination of
Sections of General Surfaces of the Second Order on Predetermined Circles.
The American
Journal of Interdisciplinary Innovations and Research
,
2
(11), 21-26.
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16.
Urolovich, T. F. (2023, May). METHODOLOGICAL ASPECTS OF DEVELOPING
AESTHETIC SKILLS IN FUTURE DRAWING TEACHERS. In
International Scientific and
Current Research Conferences
(pp. 108-114).
17.
Uralovich, T. F. (2023). The Role Of Applied Art In The Development Of Aesthetic
Skills Of Students.
International Journal of Advance Scientific Research
,
3
(05), 111-118
