In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.
The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.
From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.
Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions).
One night in 1661, Nicholas Fouquet, a superintendent under Louis XIV, was arrested. His crime was peculiar: He had dared to construct a grand geometrical garden. In doing so, he violated an irrefutable hierarchy: that geometry, in its perfection, was a testament to divine right. The elegant, symmetrical designs were more than just ornament; they were proofs of incontestable certainty, and thus the authority to rule. But how did the French royalty fall in love with this peculiar landscape design? Wherefore Versailles?
In Proof!, the award-winning historian Amir Alexander argues that Euclidean geometry has been uniquely responsible for how our societies are structured. It has shaped how our cities are built and been used as a rationale to explain political structures. The proofs in Euclid’s Elements were not only just true but were certain by reason alone. Alexander tracks the rediscovery of Euclidean geometry in fifteenth-century Italy and recounts the French royalty’s centuries-long love affair with geometrical gardening, which acted as a visual symbol of the king’s consolidation of power during a time of violence and upheaval, and which culminated with the gardens at Versailles. Proof! tells the monumental story of the geometries that were carved into our world, the beliefs they supported, and the ways they shape our lives to this day.
One of today's foremost feline experts, Haddon provides practical solutions to a myriad of perplexing situations that only cats can dream up in this valuable manual. Why does a cat suddenly stop using the litter box? Can an aloof kitty turn into an affectionate, cuddly cat? Is expensive cat food really worth it? The author unravels the mysteries of cat behavior and dispenses easy, affordable, and animal-friendly solutions to help both cats and their owners live happier lives. From kittens to senior cats, Haddon explains feline behavior that has puzzled cat owners for decades, including true-life and humorous cat tales that help illustrate her advice.
This charming and informative handbook is essential reading for anyone who has ever asked, "Why in the world does my cat do that?"