Magic Squares and Planetary Powers

If there is one field supposed to be completely impervious to the inexplicable, it is certainly mathematics. And yet, since the Renaissance, Agrippa’s magic squares have intrigued, fascinated, and inspired those interested in magic, esotericism, and the forces structuring the universe. Behind these mathematical arrangements lies knowledge, where each number, each sum, each shape follows a... sacred logic. For Agrippa, a great 16th-century Hermetic thinker, these squares represented much more than an intellectual game: they were a language in their own right, a way to connect with planetary forces and make them act in the world. Exploration.

The origins of magic squares

The earliest known magic squares date back to ancient Asia. A Chinese legend from around 650 BC tells of the mysterious appearance of a small three-by-three square on the back of a sacred turtle that emerged from the Luo River. This square, called Lo Shu ("writing of the Luo River"), contained the numbers 1 to 9 arranged so that their sum was always 15, symbolizing the balance between the forces of yin and yang. A true treasure of Chinese thought, the Lo Shu was seen as a symbol harmonizing Heaven and Earth. Other Asian civilizations also explored these figures: in India, for example, references to magic squares appear in ancient texts. One of them, the Garga Samhita, advised using a 3×3 square to soothe the influences of the nine planets (navagraha) of Hindu astrology. Thus, in Asia, the magic square was both a mathematical curiosity and a sacred sign, endowed with spiritual or astrological meaning.

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Subsequently, knowledge of magic squares spread westward. Scholars of the Islamic Golden Age played a decisive role in this transmission. As early as the 8th century, Arab scholars studied and compiled magic squares they had discovered in Indian and Chinese traditions. The 9th-century Arab mathematician Thabit ibn Qurra discussed these squares, and the encyclopedia of the Brethren of Purity (circa 990) described examples of orders 3 to 9. In the Arab-Muslim world, these squares were called wafq (harmonious arrangement of numbers) and were sometimes used as talismans by inscribing letters instead of numbers. The great Sufi mage Ahmed al-Būnī, in the 13th century, taught the construction of magic squares and their association with celestial spheres in his grimoire Shams al-Ma’arif. Through these exchanges, the concept of magic squares reached medieval Europe: by the 14th century, Latin manuscripts presented squares of orders 3 to 9, already linked to the seven traditional planets (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon) in an astrological and talismanic context.

Mathematical sciences and occult philosophy

During the Renaissance, magic squares sparked enthusiasm among both mathematicians and esoteric practitioners. It was a time of rediscovering ancient knowledge: European humanists acquired Arabic and Eastern compilations and marveled at these strange mathematical objects. In 1514, the German artist Albrecht Dürer immortalized a 4×4 magic square (constant 34) in his famous engraving Melencolia I. This square, discreetly integrated on the wall of the scene, is not there by chance: it evokes talismanic squares while demonstrating the intellectual mastery and melancholy of the genius man (melancholy being associated with Saturn at the time). Dürer thus gave the magic square an unexpected visibility in Western art, halfway between a mathematical game and a symbolic allusion.

Engraving Melencolia I, Albrecht Dürer. Source: Research Gate

At the same time, scholars like Girolamo Cardano (in 1539) and Claude de Boissière (known as Bachet de Méziriac) took an interest in methods for constructing these "magic" squares. Cardano published the so-called "diamond" method for building odd-order squares, helping to spread the concept among the learned circles. However, beyond the mathematical pleasure, it is in Renaissance occultism that magic squares took on a new dimension. They became central tools of the "occult philosophy" that sought to unify science, mysticism, and astrology.

It is in this context that Heinrich Cornelius Agrippa von Nettesheim comes into play. In 1531, this German philosopher, physician, and mage published his treatise De Occulta Philosophia (Occult Philosophy), a monumental work in three books aiming to synthesize the magical knowledge of his time. Agrippa devotes chapter 22 of Book II to the seven planetary magic squares, inherited from medieval tradition but presented in a structured and reformed way for an educated audience. He calls them the “sacred tables of the planets,” asserting that they possess great celestial virtues, reflecting the divine harmony of celestial numbers. Agrippa reprises the classical correspondence between each planet and a square of a determined order (from 3 to 9 squares per side), and he associates a whole symbolic apparatus with them: divine names, angels (Intelligences) and demons (Spirits) governing each planet, seals, and mystical characters. By systematizing the esoteric use of magic squares in this way, Agrippa offers the Renaissance a bridge between mathematics and magic, where numbers become keys to invoke astral influences.

Agrippa’s seven planetary squares

According to the traditional cosmology adopted by Agrippa, each planet of classical astrology (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon¹) has an associated magic square, whose size and numbers reflect the attributes of the celestial body. These seven squares, of orders 3 to 9, form a coherent set: the smallest square (3×3) corresponds to Saturn, the slowest and most distant planet, while the largest known square (9×9) is attributed to the Moon, the mobile star of the first heaven. Each of these squares has a unique magic constant, as well as a series of sacred names whose numerical value corresponds to the digits of the square. Agrippa also indicates how to draw for each planet a mystical sign or character derived from the numerical pattern, by connecting certain numbers of the square. This sign, as well as the seals of the Intelligence (guardian angel) and the Genius (planetary spirit), serve as graphic symbols summarizing the power of the square.

Note that there are several possible arrangements for the same magic square. The tables presented here correspond to the form transmitted in the old editions of Heinrich Cornelius Agrippa’s work, but other versions may appear in some more modern books: these simply result from a rotation or inversion of the square, which does not change its mathematical properties.

The Saturn square (3×3)

The Saturn square is the most famous and probably the oldest. It is a 3 by 3 square containing the numbers from 1 to 9. Its magic constant is 15, since 1+5+9 = 15 in each column, and the same applies to each row and diagonal. The sum of all the numbers in the square is 45 (which also corresponds to 15×3). Agrippa presents Saturn as the "first table" and notes that whichever row or column is chosen, the sum of the three numbers is invariably fifteen. This small perfect square (represented by the Chinese Lo Shu pattern) is associated with Saturn’s traditional qualities: time, austere wisdom, restriction but also protection against evil. In Renaissance magic, Saturn is an ambivalent planet, considered malefic if poorly aspected, but potentially beneficial when mastered.

From the Saturn square come the seal of Saturn (an abstract geometric symbol representing the spirit of Saturn) and the character of Saturn, which can be engraved on a talisman. Agrippa indicates that from this square divine and angelic names are derived, including an angel (the Intelligence Agiel) for good and a demon (the Genius Zazel) for evil, each associated with the total sum 45.

The Saturn square was traditionally engraved on a lead plate (Saturnian metal) during a favorable hour of Saturn. When used correctly, it served as a talisman of protection and stability; it could ward off harmful influences, repel enemies or evil spirits, and grant the contemplative wisdom associated with Saturn. However, if activated under an unfavorable astrological conjunction, it was said to produce the opposite effect (discord, obstacles, and curses).

The Jupiter square (4×4)

The square of Jupiter is a 4th order square, therefore containing 4 rows and 4 columns of numbers. It includes numbers from 1 to 16 and has a magic constant of 34. In other words, each vertical or horizontal row added gives 34, and the sum of all the numbers in the square is 136. Agrippa describes it as «a square containing sixteen numbers [...] whose addition in each row is thirty-four, and the total sum one hundred thirty-six». In astrological symbolism, Jupiter is the planet of expansion, benevolence, and prosperity. Its magic square reflects these attributes by an order higher than Saturn’s square, a sign of a more expansive power.

The Jupiter square also generates a character specific to the planet and seals associated with its Intelligence and Genius. The Hebrew names of the angel Yophiel and the spirit Hismael of Jupiter each have a numerical value of 136, equal to the total sum of the square. The seal of Jupiter can be drawn by connecting the boxes of the square according to a given sequence, this seal then being engraved on Jupiter talismans.

Traditionally, the Jupiter talisman is made by engraving its square on tin (metal attributed to Jupiter), preferably on a Thursday at Jupiter’s hour, when the planet is astrologically "fortunate." This talisman is reputed to attract luck, wealth, and divine favor. Renaissance magicians saw Jupiter as a beneficial star: its square was meant to bring success, honors, health, and inner peace to the wearer by channeling the "great fortune" that Jupiter governs.

The Mars square (5×5)

The square of Mars is a 5th order square, containing 25 boxes filled with numbers from 1 to 25. Its magic constant is 65: each row, each column, and each main diagonal sums to 65, and the total of all numbers added is 325. Agrippa states about it: «It is a square of twenty-five digits […] their total per column or row is sixty-five, their total sum three hundred twenty-five». Mars being the planet of war, vigor, and iron, its magic square is associated with strength, courage, and protection in conflicts.

From the Mars square, a character of the Hammer or Shield (symbolizing Martian energy) is extracted, as well as the seal of the intelligence Graphiel and that of the genius Barzabel, spiritual entities linked to Mars. These symbols are engraved alongside the square on martial amulets.

Historical talisman engraved with the Mars magic square (5×5) on the back. Source: Museum of Witchcraft and Magic

The Mars talisman is engraved on iron or steel (martian metal) on a Tuesday (Mars' day) at an auspicious time. Its purpose is to symbolically arm its wearer: it was believed to grant courage in battle, victory over enemies, and protection against attacks. A striking example has come down to us: a 17th-century talisman found in England shows on one side the Mars square carefully inscribed, and on the other side the Mars seal surrounded by various spiritual names. This small metal object, likely carried by a soldier or traveler, concretely illustrates the faith placed in the Mars square as a protective amulet.

The Sun's square (6×6)

The Sun's square is a 6th order square, containing the numbers from 1 to 36. It is remarkable for its magic constant of 111: indeed, six numbers per line form a total of 111, and the sum of all the elements of the square is 666. Agrippa describes this solar square by noting that "these numbers added vertically or horizontally give one hundred eleven and their total sum is six hundred sixty-six". The number 6 (the size of the square) is linked to the Sun because it represents balance and harmony at the center of the seven stars (the Sun being in the middle of the traditional planets). Moreover, the number 666 evokes in Christian symbolism the perfection of Creation in 6 days, before it was later associated with other connotations.

The Sun's square provides the Sun's seal (sometimes called Sorath's seal after the solar spirit) and the solar character, represented by a circle containing a radiant cross. The names attributed to the Sun include the Intelligence Nachiel (value 111) and the Genius Sorath (value 666), among others.

Engraved on pure gold (metal of the Sun) on a Sunday at sunrise, the solar square is a talisman of glory, vitality, and success. It strengthens physical and spiritual vitality, brings success in endeavors, and protects against depression or inner darkness.

The Venus square (7×7)

The Venus square is an order 7 square, containing 49 cells with numbers from 1 to 49. Its magic constant is 175: each series of 7 aligned numbers gives 175, and the sum of all numbers in the square is 1225 (that is 175×7). Agrippa presents it as « the fifth table, that of Venus: 49 numbers […] their addition by column or row gives one hundred seventy-five, the total sum is one thousand two hundred twenty-five». Venus, planet of love, beauty, and harmony, is attributed a more complex magic square, but always perfectly balanced.

From it is derived the Venus seal (which takes the form of a graceful interlace) and the character of Venus, as well as sacred names like the angel Hagiel and the genius Kedemel, whose numerical values correspond to 49 and 175 respectively. 

The Venus square, engraved on copper (Venusian metal) on a Friday at the hour of Venus, serves as a talisman for love, harmony, and creativity. Magic practitioners attribute to it the power to attract affection and goodwill from others, to stimulate beauty and artistic inspiration, or to soothe quarrels. Wearing this square (or its seal) enhances personal charm and promotes harmony in the home.

The Mercury square (8×8)

The Mercury square is an order 8 square, comprising 64 cells occupied by the numbers from 1 to 64. Its magic constant is 260, as each row of 8 numbers totals 260, the sum of all numbers being 2080 (that is 260×8). Agrippa notes about it: « the sixth table is that of Mercury dedicated to the number eight: it is a square […] the numbers it contains, added by column or by row, give two hundred sixty, their total is two thousand eighty». Mercury, planet of intelligence, communication, and movement, is associated with the largest square after the Moon, reflecting the mental agility and complexity of this messenger of the gods.

From the square of Mercury come a specific symbol (the seal of Mercury, sometimes depicted by a shape reminiscent of the caduceus or quick writing) and the character of Mercury. Agrippa indicates that the names of its Intelligence Tiriel (value 260) and its Genius Taphthartharath (value 2080) correspond exactly to the sums characterizing the square.

A mercurial talisman was engraved on quicksilver metal (Mercury) or on a consecrated alloy/paper, on Wednesday (Mercury’s day). It was attributed the power to enhance memory, eloquence, cunning, and speed. A student, a merchant, or a traveler could, for example, wear the square of Mercury to promote success in exams, commercial success, or protection during travels, Mercury being the patron of travelers. This square was also used to facilitate divination and prophetic dreams, due to Mercury’s psychopomp aspect capable of moving between worlds.

The square of the Moon (9×9)

The square of the Moon is the last in the series: a 9th order square, made up of 81 cells containing the numbers from 1 to 81. Its magic constant is 369, meaning that each row or column sums to 369, and the total of all the numbers in the square reaches 3321 (369×9). Agrippa describes it as follows: « the seventh table is that of the Moon: it is a square based on the ennead (9) divided into eighty-one cells […] the numbers, added by column or row, give three hundred sixty-nine; their sum is three thousand three hundred twenty-one ». The Moon, star of change, imagination, and emotions, is associated with the largest square, reflecting its nature encompassing all flows (like the 81 possible aspects of personality, one could symbolically say).

From the lunar square, we derive the seal of the Moon (a symbol in the form of a complex geometric figure or a soft sigil) and the lunar character. The sacred names aligned with the Moon include, for example, the Intelligence Malka betharsith and the Genius Chasmodai (or Hasmoday), whose numerical value corresponds to the key numbers of the lunar square (we find 9, 81, 369 in certain combinations of the Hebrew letters).

The Moon talisman is engraved on pure silver (lunar metal) on a Monday, ideally during a full moon night. It is used for protection during night travels, spiritual growth, dreams, and psychic receptivity. It is said to help develop intuition, promote fertility (the Moon being linked to female cycles and plant germination), and protect against dangerous lunar influences such as madness or enchantments. By wearing or placing the Moon square, the practitioner seeks to capture the changing benefits of the nocturnal star while shielding themselves from its instability.

Talismans and practices with magic squares

Planetary magic squares, as systematized by Agrippa, were widely used in Renaissance and later talismanic practices. Magicians conceived these squares as condensers of astral influences: by inscribing them on suitable material supports and ritually consecrating them, they hoped to capture the “virtue” of the corresponding planet and direct it toward a specific goal. Concretely, making a planetary talisman followed a whole protocol: choosing the right astrological moment (for example, when the planet was dominant in the sky, not afflicted by negative aspects), using the associated metal or material (lead for Saturn, tin for Jupiter, iron for Mars, gold for the Sun, copper for Venus, mercury² for Mercury, silver for the Moon), and sometimes also writing sacred names or drawing seals derived from the square. Once the square was engraved or written, the talisman was consecrated with prayers, incense, and appropriate formulas to “fix” the planetary influence in the object.

Ritual uses could vary: some talismans were worn as a personal amulet, others placed in the home or on the altar during astrological ceremonies. One could wear the Jupiter square around the neck to attract prosperity, or bury the Saturn square at the entrance of their property to seal its protection. Many grimoires and practical magic manuscripts from the 16th–17th centuries reproduce instructions for making such objects. The Petit Albert or the Heptameron attributed to Pierre d’Abano (inspired by earlier traditions) notably mention planetary talismans as means to obtain favors from celestial intelligences.

Historically, some material evidence of these practices has been found. Besides the Mars talisman mentioned above, magic squares have been found engraved on jewelry or pendants. In late medieval Europe, it was also customary to inscribe a magic square on parchment with religious symbols and hang it in the home as domestic protection – a practice also found elsewhere, in pre-Islamic Arabia where magic squares were hung at home to ward off evil spirits. Far from being confined to books, Agrippa’s squares thus had an active life in popular esoteric culture. They circulated among alchemists, astrologers, and even some educated clerics (who saw in them a form of number science given by God). Of course, their use was generally clandestine or discreet, as the line between pious amulet and blameworthy superstition was thin. Nevertheless, these magic squares endured in practice: they appear even in some rituals of the Golden Dawn in the 19th century or among occultists of the 20th century, a sign that their reputation for power has endured through the ages.

Beyond Agrippa

Agrippa has left a lasting mark on the Western tradition of planetary magic squares, to the point that these squares are sometimes called “kameas” in esotericism (from the Hebrew term for “seal”). However, the idea of associating numeric squares with higher influences exists in many cultures, independently of the system of the seven classical planets.

In China, the small Lo Shu square mentioned above gave rise to a rich numerological symbolism. It inspired the He Tu diagram and was linked to the eight trigrams of the Yi Jing (Book of Changes). In Taoism and feng shui, this magic square is considered a model of universal harmony: it appears in amulets, architectural layouts (the plans of certain imperial tombs or temples are designed according to a 3×3 magic square), and even in the ideal organization of the home to channel qi (vital energy). It is not so much a precise ritual tool as an omnipresent cosmological symbol, representing the perfect balance of yin and yang through numbers. Even today, in China and East Asia, the 3×3 square pattern with the sum of 15 is recognized as a bearer of good fortune and celestial order.

In India and in Hindu and Buddhist traditions, magic squares are also found in the form of yantras. A well-known example is the Kubera Kolam, a 3×3 square drawn at the entrance of houses in South India, with a particular arrangement of nine numbers whose sum is 72 in every direction – this square being dedicated to the god of wealth, Kubera, to attract prosperity. More broadly, the Navagraha Yantras (talismans of the nine planets) sometimes incorporate magic squares: each planet of Vedic astrology (including Rahu and Ketu, the lunar nodes) can be represented by a geometric pattern that includes a square of conjuring numbers. Thus, the practice of using number squares as astrological remedies (to pacify a malefic planet or strengthen a beneficial influence) is documented in medieval Sanskrit texts and continues in popular astrology in India.

The Islamic and Arab-Persian world, for its part, developed an esoteric tradition of magic squares that partially diverged from the European lineage. Called wafq or afaq, these squares can contain either numbers or letters of the Arabic alphabet (used with numerical value according to the abjad). For example, a very common 4×4 square inscribed the Arabic word B U D U H (corresponding to the numbers 2-6-4-5 in abjad) in such a way as to have the constant 18, and was considered a powerful protective talisman in Islamic magic. Sufi masters, such as al-Būnī mentioned earlier, as well as authors of Ottoman grimoires, used these squares for various purposes: protection against the ʿayn (evil eye), healing diseases, success in Quran recitation exams,... Sometimes these squares were inserted into talismanic calligraphies, mixed with verses from the Quran, to multiply their spiritual effectiveness. This parallel tradition shows that the magic square, as a concept, transcends religious boundaries: it can fit equally well within a monotheistic framework (as a support for the divine word encoded in numbers) as well as pagan or esoteric contexts.

Passion Façade of the Sagrada Família. Source: Vacatis

Finally, in modern Western culture, magic squares continue to appear occasionally as esoteric symbols or nods. The famous architect Antoni Gaudí included a 4×4 magic square on the Passion façade of the Sagrada Família in Barcelona (constant 33, symbolizing the age of Christ). Although this particular square is not directly linked to Agrippa's planets, its integration into a basilica shows how the idea of the magic square has permeated the collective imagination as a sign of order and mystery. Today, magic squares are found in literary works, mathematical games, or "new age" content, and contemporary occultists remain interested in Agrippa's planetary kameas, whether in ceremonial magic, Kabbalistic astrology, or eclectic witchcraft. The persistence of these squares across time and space testifies to their universal significance: born from a simple number game, they have transformed into a powerful symbol of humanity's quest for harmony between the heavens, numbers, and earthly life.

Agrippa's magic squares thus represent a fascinating crossroads between the science of numbers and Renaissance spirituality. Educational through their arithmetic simplicity, poetic through their symmetry, and mystical through the beliefs they inspired, they have sparked the curiosity of beginners while challenging scholars' analysis. Whether approached as a mathematical pastime or as an esoteric legacy, these squares remain a testament to the ancient conviction that number is the secret language of the Universe.

Notes:

¹ In Agrippa's time, only seven "planetary" bodies influencing Earth were known: five planets in the astronomical sense (Saturn, Jupiter, Mars, Venus, Mercury) plus the Sun and the Moon, often called "planets" in ancient astrology.

² Mercury (quicksilver) being liquid, some Mercury talismans were engraved on a metal alloy containing mercury or on yellow/orange parchment meant to represent this elusive metal.

Sources:

• De Occulta Philosophia Libri Tres, Heinrich Cornelius Agrippa, 1531 (Latin edition)

• Three Books of Occult Philosophy, translated by J.F., edited by Donald Tyson, Llewellyn Publications

• A History of Magic, Witchcraft and the Occult, DK Publishing, 2020

• The Magic Squares of the Planets in Occult Philosophy, Stephen Skinner, Golden Hoard Press

• Occult Sciences in the Renaissance, Frances A. Yates, Éditions Gallimard

• Kabbalah and Occult Sciences, Gershom Scholem, Payot

• Magical Squares: Their History and Use in Western Occultism, Journal of Esoteric Studies, Vol. 22, 2017