What Is Ilm-e-Awfaq? Spiritual Number Squares, Uses, Benefits and Calculations

What happens when numbers are placed inside a square in such a way that every row, column and main diagonal produces exactly the same total?

At first glance, it may seem like an interesting numerical puzzle. But within several historical Islamic intellectual and spiritual traditions, such arrangements became the subject of an entire field of study.

Scholars examined how these squares could be constructed, why particular numbers were arranged in specific places, and how numerical balance related to wider ideas about letters, names, harmony and spiritual properties.

This tradition is known as Ilm-e-Awfaq (علم الأوفاق).

Ilm-e-Awfaq is especially interesting because its history includes both carefully developed numerical procedures and spiritual interpretations of the arrangements produced by those procedures.

It is closely connected with subjects such as Ilm-e-Abjad, Ilm-ul-Huroof and certain branches of traditional spiritual scholarship.

But what exactly is a Wafq? Why were these arrangements created? What did practitioners seek through them? How can a beginner calculate one correctly?

This article explains the subject in detail, beginning with its historical background and progressing to practical numerical and letter-based examples.

What Is Ilm-e-Awfaq?

The Arabic word Wafq (وفق) is associated with agreement, correspondence or harmony. Its plural is Awfaq (أوفاق).

In the context of traditional numerical arrangements, a Wafq commonly refers to a square containing numbers arranged according to a particular rule.

The most familiar form is a magic square: an arrangement in which the total of every horizontal row, every vertical column and both principal diagonals is identical.

For example, consider this three-by-three square:

Add the first row:

8 + 1 + 6 = 15

Add the second row:

3 + 5 + 7 = 15

Add the third row:

4 + 9 + 2 = 15

Every column and both main diagonals also total 15.

This equality is the defining numerical feature of the square.

Historically, some writers studied this arrangement as a mathematical structure, while others incorporated such squares into wider traditions concerning spiritual properties, names, letters and symbolic correspondences.

The English expression magic square is a historical mathematical term. It does not mean that the numerical arrangement automatically constitutes a religious act or establishes a particular spiritual outcome.

Why Was Ilm-e-Awfaq Studied?

The purposes of Ilm-e-Awfaq differed according to the author and tradition.

Some scholars were interested in solving the problem of arranging distinct numbers into perfectly balanced patterns.

They developed procedures for squares of different sizes, including arrangements that became increasingly complicated as the number of cells increased.

Other scholars regarded the equality and arrangement of the numbers as meaningful within a broader spiritual understanding of harmony and correspondence.

In these traditions, the arrangement was more than a numerical puzzle.

Numbers and letters were sometimes associated with names, spiritual qualities, selected times and symbolic relationships.

Practitioners investigated how these elements could be brought together within a structured square.

Questions That Traditionally Motivated This Study

A student of Awfaq might ask:

• How can different numbers be arranged to produce equal totals?
• Why is the central cell important in some squares?
• What is the relationship between the numbers and the letters of Abjad?
• How were divine names or other expressions represented numerically in certain manuscripts?
• Why did practitioners give particular importance to numerical harmony?
• How did historical writers connect Awfaq with spiritual properties?
• Why were some arrangements associated with particular purposes?
• How were different sizes of squares constructed and checked?

These questions show why the subject developed in several directions.

A serious understanding of Ilm-e-Awfaq requires knowledge of both the numerical procedure and the particular tradition through which its meaning was explained.

Historical Background of Ilm-e-Awfaq

Numerical squares have a long history across different cultures.

One of the oldest widely known examples is the Chinese three-by-three arrangement often called the Luoshu square.

However, the history of numerical squares in Arabic scholarship developed through its own extensive written tradition.

By the tenth century, Arabic mathematical authors were describing methods of constructing magic squares.

Important names associated with early Arabic discussions include Ali ibn Ahmad al-Antaki and Abu al-Wafa al-Buzjani.

Historical research by Jacques Sesiano examines these early Arabic treatises and the methods they preserved.

The development of numerical squares was not limited to a single author or historical period.

The Early Three-by-Three Square

The United States National Library of Medicine records that an early three-by-three Wafq appears in alchemical writings attributed to Jabir ibn Hayyan.

This square contained the numbers one to nine, with five at the center and fifteen as the sum of every row, column and principal diagonal.

In those early writings, it appeared in connection with a traditional childbirth-related charm.

This tells us something important about its historical application: some practitioners considered the arrangement meaningful in contexts involving protection or relief.

The historical account documents what the practitioners sought; it should not be read as a medical recommendation.

The same basic square later became extremely well known in the wider tradition.

Ahmad al-Buni and the Science of Letters

Ahmad al-Buni, associated with the thirteenth century, is an important figure in the history of spiritual letter-based traditions and Awfaq.

Texts connected with his name include discussions of divine names, letters, numbers and numerical arrangements.

Recent scholarship has clarified an important historical issue.

Not every work circulated under al-Buni's name was necessarily written by him.

The large compilation commonly known as Shams al-Ma'arif al-Kubra contains later material and cannot simply be treated as an entirely authentic thirteenth-century text.

Jean-Charles Coulon's 2026 study examines the construction of magic squares within the Buni-related textual tradition and carefully distinguishes older materials from later attributions.

This distinction allows readers to appreciate the historical importance of the tradition without attributing every procedure to one person.

The Ottoman Scholarly Perspective

The sixteenth-century Ottoman scholar Tashkopruzade discussed the science of Awfaq in his classification of knowledge.

He described square tables containing numbers or letters arranged so that the sides and diagonals have equal numerical totals.

His description is particularly relevant because it discusses two aspects of the subject.

One concerns the arrangement and calculation of numbers.

The other concerns the special spiritual properties attributed to harmonious numerical or letter arrangements by practitioners.

This historical perspective helps explain why Ilm-e-Awfaq was studied in different intellectual settings rather than belonging exclusively to a single kind of literature.

A Surviving Arabic Manuscript

Princeton University Library preserves an Arabic manuscript titled:

Kitab al-Nur al-Sati wa-al-Sirr al-Qati fi Ilm al-Awfaq

Its catalogue dates the manuscript to approximately 1820–1860 and identifies Muhammad al-Khalwati as the author.

The work addresses squares with three through ten cells on each side, while its final chapter concerns the properties of letters.

This surviving manuscript offers direct evidence of the connection between the construction of numerical squares and the study of letters.

What Are the Main Types of Awfaq?

The subject includes various kinds of arrangements.

Numerical Awfaq

These contain numerical values placed within cells.

Their structure can be checked through addition and other prescribed rules.

Letter-Based Awfaq

In certain traditions, letters are placed in cells according to a numerical correspondence.

A common foundation for such work is the Abjad system, which assigns numerical values to Arabic letters.

Squares of Different Sizes

A square is described by the number of cells on each side.

Examples include:

• 3×3 — nine cells
• 4×4 — sixteen cells
• 5×5 — twenty-five cells
• 6×6 — thirty-six cells
• 7×7 — forty-nine cells

Traditional authors also investigated larger squares and more elaborate arrangements.

Other Historical Arrangements

Some Awfaq manuscripts contain bordered squares, special patterns or arrangements incorporating additional properties.

Other historical materials extend beyond ordinary square-shaped grids.

Not every figure appearing in an Awfaq manuscript satisfies the same conditions as a standard mathematical magic square.

Therefore, the exact structure must be identified before interpreting or verifying it.

What Makes a Numerical Wafq Correct?

For an ordinary numerical magic square using consecutive numbers from 1 through n², three important conditions apply.

First: Every integer in the required sequence must appear exactly once.

Second: The sums of every horizontal row and vertical column must be equal.

Third: Both principal diagonals must produce the same total.

The shared result is called the magic constant.

For a normal square of order n, the constant is:

M = n(n² + 1) ÷ 2

Here, n represents the number of cells on one side.

For example, a 3×3 square has n = 3.

Therefore:

M = 3(3² + 1) ÷ 2

M = 3(9 + 1) ÷ 2

M = 30 ÷ 2

M = 15

For a 4×4 square:

M = 4(16 + 1) ÷ 2

M = 68 ÷ 2

M = 34

This formula provides a direct way to verify the required total before constructing the square.

It applies to ordinary normal squares containing the consecutive integers from 1 to n². Special historical constructions may use different starting numbers or other rules.

Practical Example 1: Constructing a 3×3 Wafq

The first complete example uses the numbers 1 through 9.

Our goal is to place all nine numbers in a three-by-three square so that each row, column and main diagonal totals 15.

One valid result is:

Step 1: Prepare Nine Cells

Draw a square and divide it into three rows and three columns.

This produces nine equal positions.

Step 2: Place Number 1

Using a standard construction method for odd-sized squares, place 1 in the middle cell of the top row.

Step 3: Move Up and Right

For each subsequent number, attempt to move one cell upward and one cell to the right.

If a move crosses an edge, continue from the opposite edge.

This is known as wrapping around the square.

Step 4: Handle an Occupied Cell

If the destination cell is already occupied, move one cell downward from the position of the previously placed number instead.

Step 5: Continue Until Number 9

Repeat the process until all nine numbers are placed.

The result is the square shown above.

This construction method is often called the Siamese method in mathematical literature.

It is presented here as an accessible way to produce the correct pattern, not as a claim that every historical Awfaq manuscript used this particular procedure.

Practical Example 2: Verify Every Row, Column and Diagonal

We now check the complete square.

Horizontal Rows

8 + 1 + 6 = 15

3 + 5 + 7 = 15

4 + 9 + 2 = 15

Vertical Columns

8 + 3 + 4 = 15

1 + 5 + 9 = 15

6 + 7 + 2 = 15

Main Diagonals

8 + 5 + 2 = 15

6 + 5 + 4 = 15

Every required direction gives the same total.

The square is therefore correctly constructed.

Rotating or reflecting this square gives other valid arrangements.

A printed Arabic square may have a different visual orientation, including right-to-left conventions, without changing its fundamental numerical balance.

Why Is the Middle Number Five?

In the standard three-by-three square containing the numbers 1 through 9, the central number is five.

This is not merely a decorative convention.

The total of all nine numbers is:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

The common row total is:

45 ÷ 3 = 15

In any three-by-three magic square, the center is one-third of the common row sum.

Therefore:

15 ÷ 3 = 5

The remaining numbers are arranged around the center.

Opposite cells across the center add to ten.

For example:

8 + 2 = 10

1 + 9 = 10

6 + 4 = 10

3 + 7 = 10

These relationships provide another way to understand the balance of the square.

What Is the Buduh Square?

The traditional three-by-three arrangement is particularly well known in Islamic sources under the name Buduh, also transliterated as Buduh or Baduh.

The name is associated with four Arabic letters:

ب — د — و — ح

In the Eastern Abjad system, they correspond to:

These four even numbers occupy the four corners of the familiar three-by-three arrangement, although their visible order can vary with rotation or reflection.

The National Library of Medicine specifically identifies Buduh as a traditional name for this numerical square.

Historical writers associated Buduh with different symbolic and protective purposes.

Its importance in the Awfaq tradition comes from both its recognizable construction and its place in historical spiritual literature.

It should not be confused with a standalone religious formula or treated as a universal guarantee of protection.

Practical Example 3: Converting a Numerical Square into Letters

Now we can examine the relationship between Awfaq and Ilm-e-Abjad.

In the Eastern Abjad system, the first nine values correspond to these Arabic letters:

Take our numerical square:

Now replace each number with its corresponding letter.

The upper row corresponds numerically to:

8 + 1 + 6 = 15

The middle row corresponds to:

3 + 5 + 7 = 15

The lower row corresponds to:

4 + 9 + 2 = 15

This demonstrates how a numerical arrangement can be represented through letters.

However, the resulting rows are not automatically meaningful Arabic words.

Nor does a valid numerical transformation establish a particular ritual purpose.

A historical letter-based Wafq may require additional conventions defined in the text from which it comes.

Practical Example 4: A Complete 4×4 Numerical Square

The three-by-three square is only the beginning.

A four-by-four square contains sixteen cells.

When constructed from the numbers 1 through 16, its required total is 34.

Consider this arrangement:

This is a valid four-by-four magic square.

Check the Rows

16 + 3 + 2 + 13 = 34

5 + 10 + 11 + 8 = 34

9 + 6 + 7 + 12 = 34

4 + 15 + 14 + 1 = 34

Check the Columns

16 + 5 + 9 + 4 = 34

3 + 10 + 6 + 15 = 34

2 + 11 + 7 + 14 = 34

13 + 8 + 12 + 1 = 34

Check the Diagonals

16 + 10 + 7 + 1 = 34

13 + 11 + 6 + 4 = 34

The square satisfies all the required conditions.

This well-known configuration also appears in the history of European art and mathematics. Its use here demonstrates a valid numerical arrangement, not a specific historical talismanic prescription.

Why Do Larger Awfaq Require Different Methods?

A 3×3 square has nine cells, while a 4×4 square has sixteen.

A 5×5 square has twenty-five.

The number of possible arrangements increases rapidly as the square becomes larger.

Historical mathematicians therefore developed specialized procedures for constructing squares of different sizes.

Some methods apply to odd-sized squares, others to sizes divisible by four, and still others to even sizes not divisible by four.

The terminology and algorithms may also differ between manuscripts.

Common Magic Constants

For ordinary squares containing consecutive integers:

These totals are useful when examining traditional numerical squares.

However, when a historical Wafq is constructed using a different number sequence, these particular constants may not apply.

The correct verification must follow the actual numerical system being used.

How Were Abjad Values Connected with Awfaq?

Some historical practitioners began with Arabic words, names or expressions.

They calculated their numerical values through Abjad and then used particular rules to construct squares containing related numbers.

This created a connection between the science of letters and the science of numerical arrangements.

Consider a simple example.

The Arabic word:

ملك — Malik, meaning king

Using Eastern Abjad:

م = 40

ل = 30

ك = 20

Total:

40 + 30 + 20 = 90

Jean-Charles Coulon's study of historical Awfaq literature discusses a manuscript procedure involving the value 90 for Malik.

However, a numerical total does not, by itself, tell us which square should be constructed.

Different historical methods might treat that total as the desired row sum, a central value or another parameter.

These choices produce different squares.

This distinction is important when trying to understand original manuscripts accurately.

Practical Example 5: Making a Square with a Row Sum of 90

We can construct a simple educational example starting with the three-by-three square whose row total is 15.

Suppose our desired row sum is 90.

We want to increase each row total from 15 to 90.

The difference is:

90 − 15 = 75

There are three cells in every row.

Therefore:

75 ÷ 3 = 25

Add 25 to every cell.

The result is:

Now check:

33 + 26 + 31 = 90

28 + 30 + 32 = 90

29 + 34 + 27 = 90

The columns and diagonals also total 90.

For example:

33 + 30 + 27 = 90

31 + 30 + 29 = 90

This example is a valid numerical construction.

It demonstrates how a chosen total can be incorporated into a balanced square when the required arithmetic conditions are satisfied.

It is not presented as a reproduction of a particular medieval manuscript or a prescribed spiritual operation.

Can Any Abjad Total Be Placed into a 3×3 Square?

The answer depends on what we mean by placed into.

If we want a three-by-three square of integers whose row sum equals a given Abjad total, that total must be divisible by three.

For example, the Abjad value of نور is:

ن = 50

و = 6

ر = 200

Total = 256

But 256 is not divisible by three.

Therefore, a three-by-three magic square consisting entirely of integers cannot have 256 as its common row sum.

That does not mean the number 256 cannot appear inside a square.

It can be placed in the center of a valid three-by-three square through another construction.

For example:

Here:

259 + 252 + 257 = 768

254 + 256 + 258 = 768

255 + 260 + 253 = 768

The columns and diagonals also total 768.

The center is 256.

This is a second mathematically valid arrangement using the number 256.

It highlights an essential principle: the numerical role of a name's Abjad value must be specified before its square can be constructed or interpreted.

A central-value construction and a row-sum construction are not the same method.

Why Did Traditional Practitioners Associate Awfaq with Spiritual Properties?

This question goes beyond numerical addition and reaches the historical purpose of the subject.

In certain spiritual traditions, numerical harmony was regarded as meaningful.

The equality of the square's rows, columns and diagonals was understood within broader conceptions of order, correspondence and balance.

Some practitioners associated numerical and letter arrangements with divine names, selected times, spiritual properties or particular intentions.

Historical manuscripts contain examples involving protection, well-being, reconciliation, assistance, and other desired outcomes.

Their purposes differed widely.

Some authors focused on spiritual contemplation and the symbolic significance of the arrangement.

Others incorporated Awfaq into talismanic or ceremonial procedures.

These traditions should be understood according to their own terminology, texts and intended applications.

A balanced square does not have only one universal spiritual interpretation. Its meaning within a tradition may depend on the words used, the numerical procedure, the time selected and the wider interpretive framework.

What Benefits Did Practitioners Seek Through Ilm-e-Awfaq?

Historically, practitioners associated Awfaq with a variety of purposes.

Protection and Well-Being

Some traditional sources used numerical squares in protective contexts.

An early example appears in writings attributed to Jabir ibn Hayyan, where a three-by-three square is associated with childbirth.

This is a historical example of its intended use, not a substitute for medical care.

Harmony and Reconciliation

Certain traditions associated letter and number arrangements with the hope of harmony or reconciliation in relationships.

The exact arrangements and interpretations differed among authors.

Livelihood and Prosperity

Historical talismanic literature sometimes connected numerical arrangements with the pursuit of livelihood, prosperity or assistance.

These were traditional purposes attributed to particular procedures, not fixed results of every Awfaq square.

Spiritual Reflection

For some readers, the arrangement of numbers and letters provided a focus for contemplating order, symbolism and relationships within their spiritual worldview.

Learning Letters and Numbers

Awfaq also provided a practical way to study how numbers, Arabic letters and mathematical arrangements could interact.

These different uses help explain why the subject attracted the attention of mathematicians, compilers, manuscript authors and spiritual practitioners.

What Can a Person Learn from Ilm-e-Awfaq?

A student can obtain several types of knowledge.

Numerical structure: How numbers can be organized into balanced arrangements.

Construction methods: How squares of different sizes can be created.

Verification: How to calculate and check common totals.

Abjad relationships: How letters and numerical values can be connected.

Historical symbolism: Which spiritual meanings particular authors assigned to specific arrangements.

Manuscript interpretation: How to recognize and understand Awfaq tables appearing in historical works.

Differences between methods: Why two arrangements connected with the same name may have different constructions.

Traditional applications: Why practitioners examined Awfaq for matters involving spiritual reflection, protection or other intentions.

However, a numerical square alone does not provide a universal formula for discovering another person's intentions, determining an individual's entire future or guaranteeing a particular outcome.

Such interpretations depend on additional traditions and assumptions that must be identified separately.

What Is the Connection Between Ilm-e-Awfaq and Ilm-e-Saat?

Some historical systems associated numerical or letter arrangements with particular times.

In those systems, the timing of a procedure could be considered important alongside the chosen square.

This explains a connection with Ilm-e-Saat, the study of traditional planetary hours.

For example, a manuscript might prescribe that a particular arrangement be prepared or considered at a time selected under its own traditional rules.

But not every Awfaq manuscript follows the same timing procedure.

Likewise, simply knowing the planetary ruler of an hour does not automatically tell someone how to construct a valid Wafq.

The two subjects are related in some traditions, but their core calculations are different.

For more background, read What Is Ilm-e-Saat?.

Ilm-e-Awfaq Compared with Other Traditional Sciences

Some historical authors used elements from more than one field.

However, an Abjad calculation is not automatically an Awfaq square, and an Awfaq square is not itself a Ramal chart.

For more information, explore What Is Ilm-ul-Huroof? and What Is Ilm-e-Abjad?.

Common Mistakes When Learning Ilm-e-Awfaq

Mistake 1: Checking Only Horizontal Rows

A standard magic square must also satisfy the required columns and both principal diagonals.

Mistake 2: Repeating Numbers in a Normal Square

A normal square using numbers from 1 to n² requires each number exactly once.

Mistake 3: Assuming Every Square Has the Same Magic Constant

The required total depends on the size and numerical construction.

Mistake 4: Confusing a Central Number with a Row Total

A name's Abjad value may play different roles in different historical procedures.

Mistake 5: Treating Letters as Numbers Without a Defined Convention

Letter-based squares require a specified correspondence, such as Eastern Abjad.

Mistake 6: Assigning Every Historical Method to Ahmad al-Buni

The Buni-related textual tradition contains works from different periods, including later attributed writings.

Mistake 7: Assuming Every Diagram Is a Standard Magic Square

Some historical Awfaq diagrams follow different arrangement rules.

Mistake 8: Treating Every Balanced Square as a Guaranteed Spiritual Result

A square's numerical construction and the spiritual properties attributed to it are two distinct aspects of the tradition.

Frequently Asked Questions

What does Ilm-e-Awfaq mean?

It is the traditional study of harmonious number and letter arrangements, especially numerical squares constructed according to particular balancing rules.

What is a Wafq?

A Wafq commonly refers to a numerical or letter arrangement. In its familiar magic-square form, all rows, columns and main diagonals have equal numerical totals.

Why did spiritual practitioners use Awfaq?

Various historical practitioners associated the arrangements with symbolic harmony, divine names, protection, well-being and other purposes according to their particular traditions.

Is Ilm-e-Awfaq the same as Ilm-e-Abjad?

No. Abjad provides numerical values for letters. Awfaq involves arranging numerical values or letters according to additional structural rules.

What is the simplest Wafq for beginners?

The conventional three-by-three square containing the numbers one through nine is an excellent introduction.

What is the sum of a normal 3×3 square?

Fifteen in each row, column and main diagonal.

What is the sum of a normal 4×4 square?

Thirty-four in each row, column and main diagonal.

What is Buduh?

Buduh is a traditional name associated with the famous three-by-three square and four letters corresponding to the corner values 2, 4, 6 and 8.

Can an Awfaq square contain letters instead of numbers?

Yes. Historical writers describe letter-based arrangements, often related to numerical values.

Can a person's name be used in an Awfaq calculation?

Certain traditions employ the numerical values of names or other expressions. The exact method must be specified, since there is no single universal rule for every arrangement.

Is every text attributed to al-Buni authentic?

No. Recent manuscript studies distinguish historical works from later compilations circulated under his name.

Are numerical squares and talismans the same thing?

Not necessarily. A numerical square is an arrangement of values. Some traditions used squares within talismanic practices, but not every balanced grid is automatically a talisman.

Does a Wafq guarantee wealth, protection or another result?

A Wafq's numerical properties can be calculated precisely. Historical traditions attribute additional meanings or purposes to particular arrangements, but construction alone does not establish a guaranteed personal result.

Can beginners study this subject?

Yes. A beginner should start with normal squares, learn their common totals, understand Abjad values and then study historically documented interpretive traditions.

Conclusion

Ilm-e-Awfaq is a distinctive historical subject bringing together the arrangement of numbers, the study of letters and spiritual interpretations of numerical harmony.

Its mathematical procedures can be learned through practical examples such as the three-by-three and four-by-four squares.

Its historical importance becomes clearer when we examine why scholars developed these arrangements and how different practitioners interpreted them.

A serious student should understand both aspects: how a Wafq is constructed and what particular traditions believed it represented.

This requires accurate calculations, attention to historical sources and awareness that different schools may apply different methods to similar questions.

Through this approach, Ilm-e-Awfaq becomes more than a collection of unexplained numerical diagrams. It becomes an accessible subject of traditional knowledge with a rich historical and intellectual background.

References and Further Reading

1. Jean-Charles Coulon (2026) — “Magic Squares, Mathematical Tricks and Angels in Islamicate Occult Sciences: Perspectives from the Būnian Corpus.”

Published in Normative Texts and Occupational Practices, Springer, pages 219–270. An important recent open-access investigation of historical Awfaq construction methods and writings attributed to Ahmad al-Buni.

https://doi.org/10.1007/978-3-032-28419-8_9

2. United States National Library of Medicine — “Islamic Medical Manuscripts: Astrology, Divination and Magic.”

Historical overview of Arabic magic squares, the Buduh arrangement and their appearance in talismanic traditions.

https://www.nlm.nih.gov/hmd/arabic/astrology1.html

3. Jacques Sesiano (2017) — Magic Squares in the Tenth Century: Two Arabic Treatises by Antaki and Buzjani.

Springer. A detailed historical study of early Arabic mathematical texts concerning magic squares.

https://old.maa.org/node/862947

4. Princeton University Library — Kitab al-Nur al-Sati wa-al-Sirr al-Qati fi Ilm al-Awfaq.

Arabic manuscript, attributed to Muhammad al-Khalwati, catalogue date 1820–1860. Covers numerical squares of multiple sizes and the properties of letters.

https://digital-collections.princeton.edu/i/كتاب-النور-الساطع-والسر-القاطع/item/a10564a7-607f-465b-bca5-0fc5433cb2fa

5. Jean-Charles Coulon — “Amulets and Talismans in the Earliest Works of the Corpus Bunianum.”

A scholarly study of numerical and letter-based arrangements in early works associated with the Buni tradition.

https://doi.org/10.1163/9789004471481_011

6. Rosanna Budelli — “Come ricavare i nomi degli angeli e dei demoni nella divinazione con i quadrati magici.”

Kervan, a historical study of elaborate Awfaq practices in a later Arabic text.

https://doi.org/10.13135/1825-263X/1407

Editorial clarification: This article distinguishes reproducible numerical constructions from the spiritual and symbolic meanings attributed to them in historical traditions. The worked examples demonstrate correct arrangements; they are not presented as operative talismanic prescriptions or guarantees of specific outcomes.