Phelipe Medrano

Philip was introduced in his Quadrados mágicos with poetic tributes by members of Madrid's literary elite, many of whom were high-ranking nobles, poets, and officials. These texts collectively elevate Phelipe Medrano as a paragon of mathematical virtue, enlightenment learning, and noble service. Collectively, the poetic tributes frame Quadrados mágicos as more than a mathematical treatise. Through imagery drawn from classical philosophy, biblical allegory, and the history of science, Medrano is depicted as a figure who unites erudition, noble lineage, and loyal service to the Crown. The verses consistently contrast ancient superstition with Christian rationality, recasting the magic square from an emblem of idolatry into a symbol of order, governance, and enlightened rule. In this literary context, Medrano’s work is celebrated not only for its technical precision but also as an expression of the Medrano family's enduring Doctrine of Medrar, understood as the advancement of knowledge and the state through disciplined structure and loyal service.^[14]

Among the poetic tributes prefacing the work is a laudatory sonnet by Joseph Cañizares,^[16] Theniente de Caballos Corazas, composed in honor of the author and his mathematical achievement:

Socrates immortal, Plato divine; If they ploughed numeric seas, They had a course, for the North they found, Following the Pythagorean path. If the Tarentine of the soul's affections, (and others with him) dealt in numbers, By Nicomachus they found the method, In learned and wandering Arithmos.

Only you (Phelipe), without north or guide, By influences of Sovereign Numen, Brilliant mists, showing the day; The cheerful, vain Egyptian may say, My weak Arithmetical harmony, If it began to medrar, it is because of Medrano.^[14]

The connection between medrar and Medrano is etymological, conceptual and programmatic. Classical sources from Antonio de Nebrija to Joan Corominas confirm that the surname Medrano derives from the verb medrar, meaning "to improve," "to advance," or "to prosper."^{[17][18][19][20][21]} The 18th-century poet José de Cañizares made this semantic unity explicit in his tribute to Phelipe Medrano, writing: "If my weak Arithmetic shows any medrar, it is because of Medrano."^[14]

His magic squares, structured, ascending, and centered, are symmetrical manifestations of social and cosmic order. As Àngel Campos-Perales has shown, the Spanish monarchy under the Habsburgs and Bourbons relied on Medrar to curate visual grammars, including chapels, funerary architecture, heraldry, and ceremonial emblems, to create a symbolic language that legitimized delegated power and kingship within the visual field of court society.^[22] Quadrados mágicos fulfills this same function in mathematical form. Through calibrated order and recursive harmony, Medrano’s squares become a visual geometry of Medrar: noble advancement through ordered legitimacy made intelligible through number. They inscribe, in mathematical structure, what the name Medrano etymologically and doctrinally signifies: improvement, legitimacy, and structured ascent. In this way, each magic square becomes not only a solution but a visible step in the Medrano Doctrine of Medrar.^[23]

The Elogio by Ignacio de Loyola y Oyanguren, 2nd Marqués de la Olmeda and dedicated to Phelipe Medrano in the Quadrados mágicos (1744) declares:

The Egyptians invented magic squares, And placed their deities in them, As though divinity resided In whatever had quantity, For the Supreme Deity Knows no bounds, nor permits summation, Their delirium ever shifting, A new literary labyrinth. But today your noble name Amazes the entire world, Lifting from such blind confusion The undeniable being of truths. I have gladly examined The work you’ve shared with me; In its progressions, You’ve refined the combinations So the world may see, If one studies with care, How distance conquered Turns ignorance into radiance. Your tested problems Leave my concerns so fully satisfied, That any studious mind To which they are applied, wise and attentive, Will find you have reached such depth of understanding, That, once acquired, your knowledge becomes inherited.

Since your father, in brief, Granted you the improvement of third and fifth, Your father, whose glory Was a living Archive of History, And in affairs of State, A Caliodorus of the world, celebrated far and wide, What wonder, then, if my rough wit Should stand in awe of a branch sprung from such a trunk? Our friendship, in short, is not of recent days, For it holds its proper place before the lady.

I’ve always known Your playful genius in study, And in your early green seasons, Like a rational bee you gathered blossoms So that those flowers would yield fruit. Mathematics is what you descend from, A sea of faculties, which, when grasped, Even in narrow chambers, Reduce to number and to measure. There is nothing in this life That cannot be reduced to number, Even human fate Finds its final unity in death. That beautiful planet, Which follows its luminous course, In the zenith of its rays, Turns its light into a foam-topped grave. The rose, which in various views Is seen as the living water of attentions, When its bud is threatened, Finds that from one unit alone it grows, And breaking the bud’s scarlet shell, Expands into countless forms. The poor little spring, Brief in its course, yet marvelous, When it becomes a deep arroyo, Offers a crystal torrent, And in time, as it animates its being, Its liquid flow multiplies.

Thus it is seen in light, in crimson, and in foam, The multiplication, the line, and the smoke. Books of the clearest minds Often carry more contradiction, But your book, in superior fortune, Suffers neither flaw nor failing, For to criticize it, One must first comprehend it. So much consequence You place in demonstration, That what you prove Silences the Babel of dispute, For in mathematics, Only "ergo" makes the proof. You are today a new Ganymede, Grasping Archimedes' spheres, Drawing from their motions New problems from Euclid’s torrent. And as Isidore once said With truth on his lips and a golden pen, That to join the whole with its parts Is the science of sciences and art of the arts, Let my crude tongue cease its applause, For here, silence itself is eloquence.^[14]

The tribute to Phelipe Medrano, composed by Ignacio de Loyola y Oyanguren, 2nd Marqués de la Olmeda is a doctrinal witness, a compressed theology of number, authority, and lineage that situates Medrano's work within both the Christian tradition and the universal Doctrine of Medrar. Loyola begins by recalling that the Egyptians "invented magic squares" and placed their deities within them, as though divinity could be reduced to quantity. Against this, he asserts that the "Supreme Deity knows no bounds, nor permits summation." The elogio echoes the Medrano doctrine: number is not itself divine, but a sign of divine order. Medrano is praised as the one who purifies mathematics from superstition and re-anchors it in theology and law.^[2]

The tribute contrasts the "delirium" and "labyrinth" of pagan systems with the clarity that comes "today" through the Medrano name. To say "your noble name amazes the entire world" is not presented as flattery alone. It positions Medrano identity, rooted in medrar meaning to rise and to advance, as a public emblem that transforms confusion into truth. The name itself is presented as a doctrinal sign of order.^[2]

In describing Medrano's "progressions" and "combinations," Loyola moves from technical vocabulary to moral theology. Mathematical method disciplines not only the intellect but also desire, converting ignorance into radiance. The problems Medrano sets are "tested," and the "inheritance" of his knowledge is emphasized. His mathematics is portrayed as transmissible, forming future generations. Nobility is presented here as pedagogical as much as genealogical. The image of the "rational bee" gathering blossoms underscores this point, presenting Medrano's learning as ordered play that yields lasting fruit.^[2]

Specifically, In the Elogio, the 2nd Marquess of La Olmeda described Phelipe Medrano as a "rational bee," gathering from varied flowers to form a disciplined and ordered sweetness. The metaphor of the bee had already appeared in the Medrano tradition: in his República Mista, Tomás Fernández de Medrano compared political unity to the natural order of bees, "in whom one queen rules; as in the flock one shepherd; in the world one God; and in the kingdom one prince."^[3]

Read together, these images illustrate how Spanish society employed the bee as a recurring symbol, at once of intellectual formation in the Elogio and of political and theological order in Tomás's treatise.^[3] By drawing on the same image, Ignacio de Loyola's tribute connected Phelipe Medrano's mathematical treatise and his surname to the legitimacy and continuity of the established doctrines for Spain that the Medrano family had been cultivating for centuries.^[2]

Loyola further insists that Phelipe Medrano's book suffers "neither flaw nor failing" and that his demonstrations silence the "Babel of dispute." Proof rather than patronage confers legitimacy. In the same way that governance depends on demonstrable justice, mathematics depends on the necessity of demonstration. Medrano is described as a "new Ganymede" grasping Archimedes' spheres, a metaphor for noble ascent joined to service of sovereign authority. Loyola concludes by invoking Isidore of Seville's maxim that wisdom joins the whole with its parts, suggesting that Medrano's magic squares achieve this union by binding throne and subject, unit and sum, universal and particular.^[2]

The elogio presents Phelipe Medrano as reformer of number and demonstrator of the Doctrine of Medrar. It frames his name as a sign of order revealed to the world, lifting mathematics from superstition into truth. The reaction and amazement of the world that Loyola describes is recognition of Medrano and a precept inscribed in creation: that true nobility lies in transmitting order from the One to the many, and from the many back to the One.^[2]

His friend Joaquín de Aguirre wrote the following "on the occasion of publishing the Treatise" of the Magic Squares:

Darkness teaches, which exhales vice In clumsy fumes that nourish error, All that is obscure is driven away by Light, And sacrilege transforms into Sacrifice. An irrational reef, where the Egyptian Treads misguided steps in bloodied ways, Now becomes a heroic blazon, no longer a shame, If frenzy slumbers, let judgment rise. That which was once impossible is now conquered, That which was mute now speaks and is explained: That error, converted into truth. Sacrilege is now a consecrated emblem, It spreads nobility to the public, The prodigious name of a Crusader.^[15]

Aguirre wrote a second sonnet dedicated to Medrano:

If faith could secure the noble effort Of that other Philosopher who once claimed That one soul passed through many bodies, Then yours, Medrano, stands above his. Madness it seemed, or error, or a foolish dream, Yet the world itself praises you, Though some denied it with lesser assent, Their judgment diminished by their own pride. Indeed, Pythagoras said the soul Could not remain in a single form, But the soul that animated you wins the crown. So let them discuss, invent, write, teach, dispute, The greatest minds now stand aside, Asking: was that soul his, or is yours the better?^[14]

Among the poetic tributes prefacing the work is a sonnet by Don Miguel de Villa-Fuerte, lawyer of the Royal Councils, composed in praise of the author and his learned achievement:

By what rule, instruction, or teaching Humbly I ask, have you uncovered That uncultivated path, long smothered, Which thought alone deemed unapproaching? If in nine Problems you staked your aim To discern and resolve where lofty heights dwell, The subtle art you studied well, Revealing clear your Arguments’ flame. Ah, do not answer how to understand you; Jealousy more than ignorance would know you, Let the Egyptians themselves bow down in awe. Nearly impossible to imitate you, None may presume to grasp what you do, In the difficult, you are the law.^[14]

Don Francisco de Quadros, Knight of the Order of Santiago, offers a poetic tribute titled "Heroic Romance" applauding the tireless study of Phelipe Medrano and his accomplishment in composing the Magic Squares once devised by the Egyptians:

If the Egyptians, with errant trace, Worshipped fabled deities' delight, And in the unfathomable gulf of guile, Sought to fix their foot in glory’s place, Tearing bronze in solemn rite, Their fraud hid under hardness bright, Numbers they privileged with divine right, Though no Numen they adored with grace. Superstitious simulacra made Votive smoke serve as torchlight’s aid, Letting their madness burn once more. And in their study, void of guide, They left no trace or text behind, So none might follow, none explore. But what applause now may be born, Lesser (O great MEDRANO) than your scorn, If daring measured the impossible's form? Your golden pen has sealed their mouths forlorn. Magic, they called your noble aims, Yet only fools would make such claims, For in their error, none believed A man such glory could achieve. Arithmetic, in you its purest height, Crowns you with its diadem bright, And from the secret path of numbers’ might, You pass still further when it takes flight. The strange Problems your labor posed Shamed curiosity’s boastful prose, For insight prefigured all you chose, Before the page your logic froze.^[14]

The Medrano name and doctrine had been formally articulated in the República Mista by Tomás Fernández de Medrano, and the Mirror of Princes by Diego Fernández de Medrano y Zenizeros, and later codified into sacred numbers by Phelipe Medrano.^[3][24] The poetic tributes accompanying Quadrados mágicos present Phelipe Medrano not only as a mathematician but as a successor to this family tradition of loyalty expressed through structured and symbolic order. Taken together, the tributes situate Quadrados mágicos within this lineage, portraying the work as both a technical achievement in mathematics and a continuation of the Medrano family's role in uniting scholarship, governance, and noble duty.^[25]

• Medrano, Phelipe de (1744). Quadrados mágicos (in Spanish). Madrid: Imprenta de Antonio Marín. Retrieved 2025-05-08.

• Medrano, Phelipe de (1744). Quadrados mágicos (Biblioteca Nacional de España) (in Spanish). Madrid: Biblioteca Nacional de España.

• Oller Marcén, Antonio M. "Felipe Medrano y sus cuadrados mágicos". FUNES. Repositorio de Documentos (in Spanish). Universidad de los Andes. Retrieved 2025-05-09.

• Díez Borque, José María (2017). "Anotaciones sobre la Academia Poética Matritense del siglo XVIII" (PDF). Dramaturgo y espectáculo en el teatro español del siglo XVIII (in Spanish): 205–225.
• Mendoza Caamaño Sotomayor, Antonio Domingo de (1672-03-05). "Billete de Antonio de Mendoza a Pedro Medrano, secretario del Consejo de Estado, sobre su nombramiento de residente en Génova con el título de enviado". Archivo General de Simancas (in Spanish). Madrid. Retrieved 2025-05-10.
• Relación de Sucesos: Manuscrito XVII-8907-58 (PDF) (in Spanish). BIDISO, Universidad de Alicante. Retrieved 2025-05-10.
• Ludeña, Carlos (2023). José de Cañizares (1676–1750): vida y obra de un libretista entre el Barroco y la Ilustración. Anejos de Cuadernos de Estudios del Siglo XVIII, ACESXVIII 12 (in Spanish). Oviedo: IFESXVIII / Ediciones Trea. pp. 1–173. doi:10.17811/acesxviii.12.2023.1-173. Retrieved 2025-05-18.

• Full Google Books edition of Quadrados mágicos
• Biblioteca Nacional de España edition
• FUNES repository version