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The legendary Renaissance math duel that ushered in the modern age of algebraThe Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolò Tartaglia was a talented and ambitious teacher who possessed a secret formula—the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret.Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel.A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.

For this new anthology, Anthony Bonner has chosen central texts from his acclaimed two-volume compilation Selected Works of Ramon Llull (Princeton, 1985). Available for the first time in an affordable format, these works serve as an introduction to the life and writings of the Catalan (properly, Majorcan) philosopher, mystic, and theologian who lived from 1232 to 1316. Founder of a school of Arabic and other languages, Llull was also a poet and novelist and one of the creators of literary Catalan. This volume contains three prefaces on Llull's life, thought, and reputation. Of Llull's works, it offers Book of the Gentile and the Three Wise Men, his seminal Christian apology; the Ars brevis, a summary of his philosophical system; The Book of the Lover and the Beloved, a celebration of mystical love in the courtly tradition; and his wittily scathing Book of the Beasts.

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals.Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals.Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

The legendary Renaissance math duel that ushered in the modern age of algebraThe Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolò Tartaglia was a talented and ambitious teacher who possessed a secret formula—the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret.Set against the backdrop of sixteenth-century Italy, The Secret Formula provides new and compelling insights into the peculiarities of Renaissance mathematics while bringing a turbulent and culturally vibrant age to life. It was an era when mathematicians challenged each other in intellectual duels held outdoors before enthusiastic crowds. Success not only enhanced the winner's reputation, but could result in prize money and professional acclaim. After hearing of Tartaglia's spectacular victory in one such contest in Venice, Cardano invited him to Milan, determined to obtain his secret by whatever means necessary. Cardano's intrigues paid off. In 1545, he was the first to publish a general solution of the cubic equation. Tartaglia, eager to take his revenge by establishing his superiority as the most brilliant mathematician of the age, challenged Cardano to the ultimate mathematical duel.A lively account of genius, betrayal, and all-too-human failings, The Secret Formula reveals the epic rivalry behind one of the fundamental ideas of modern algebra.

Cardano, next to Vesalius the greatest physician of his day, was also a devoted and skilled gambler who played for personal pleasure and profit. His mathematical genius enabled him to devise simple rules of probability for his own benefit and for his gambling contemporaries. These he collected in his Book on Games of Chance and embellished them with essays on the tricks of cheats and kibitzers, as well as on psychological rules of play. In this biography of a stormy Renaissance personality, Cardano's gambling studies are deciphered for the first time, and a translation of the Book on Games of Chance is appended. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Cardano, next to Vesalius the greatest physician of his day, was also a devoted and skilled gambler who played for personal pleasure and profit. His mathematical genius enabled him to devise simple rules of probability for his own benefit and for his gambling contemporaries. These he collected in his Book on Games of Chance and embellished them with essays on the tricks of cheats and kibitzers, as well as on psychological rules of play. In this biography of a stormy Renaissance personality, Cardano's gambling studies are deciphered for the first time, and a translation of the Book on Games of Chance is appended. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Jesuit Science and the End of Nature’s Secrets explores how several prominent Jesuit naturalists - including Niccolò Cabeo, Athanasius Kircher, and Gaspar Schott - tackled the problem of occult or insensible causation in the seventeenth century. The search for hidden causes lay at the heart of the early modern study of nature, and included phenomena such as the activity of the magnet, the marvelous powers ascribed to certain animals and plants, and the hidden, destructive forces churning in the depths of the Earth. While this was a project embraced by most early modern naturalists, however, the book demonstrates that the Jesuits were uniquely suited to the study of nature’s hidden secrets because of the complex methods of contemplation and meditation enshrined at the core of their spirituality. Divided into six chapters, the work documents how particular Jesuits sought to reveal and expose nature’s myriad secrets through an innovative blending of technology, imagery, and experiment. Moving beyond the conventional Aristotelianism mandated by the Society of Jesus, they set forth a vision of the world that made manifest the works of God as Creator, no matter how deeply hidden those works were. The book thus not only presents a narrative that challenges present-day assumptions about the role played by Catholic religious communities in the formation of modern science, but also captures the exuberance and inventiveness of the early modern study of nature.

The Society of Jesus was founded by Ignatius Loyola on a principal of strict obedience to papal and superiors’ authorities, yet the nature of the Jesuits's work and the turbulent political circumstances in which they operated, inevitably brought them into conflict with the Catholic hierarchy. In order to better understand and contextualise the debates concerning obedience, this book examines the Jesuits of south-western Europe during the generalate of Claudio Acquaviva. Acquaviva’s thirty year generalate (1581-1615) marked a challenging time for the Jesuits, during which their very system of government was called into doubt. The need for obedience and the limits of that obedience posed a question of fundamental importance both to debates taking place within the Society, and to the definition of a collective Jesuit identity. At the same time, struggles for jurisdiction between political states and the papacy, as well as the difficulties raised by the Protestant Reformation, all called for matters to be rethought. Divided into four chapters, the book begins with an analysis of the texts and contexts in which Jesuits reflected on obedience at the turn of the seventeenth century. The three following chapters then explore the various Ignatian sources that discussed obedience, placing them within their specific contexts. In so doing the book provides fascinating insights into how the Jesuits under Acquaviva approached the concept of obedience from theological and practical standpoints.

Jesuit Science and the End of Nature’s Secrets explores how several prominent Jesuit naturalists - including Niccolò Cabeo, Athanasius Kircher, and Gaspar Schott - tackled the problem of occult or insensible causation in the seventeenth century. The search for hidden causes lay at the heart of the early modern study of nature, and included phenomena such as the activity of the magnet, the marvelous powers ascribed to certain animals and plants, and the hidden, destructive forces churning in the depths of the Earth. While this was a project embraced by most early modern naturalists, however, the book demonstrates that the Jesuits were uniquely suited to the study of nature’s hidden secrets because of the complex methods of contemplation and meditation enshrined at the core of their spirituality. Divided into six chapters, the work documents how particular Jesuits sought to reveal and expose nature’s myriad secrets through an innovative blending of technology, imagery, and experiment. Moving beyond the conventional Aristotelianism mandated by the Society of Jesus, they set forth a vision of the world that made manifest the works of God as Creator, no matter how deeply hidden those works were. The book thus not only presents a narrative that challenges present-day assumptions about the role played by Catholic religious communities in the formation of modern science, but also captures the exuberance and inventiveness of the early modern study of nature.