This book offers a detailed and insightful examination of two important topics in geometry: the general properties of cones of the second degree, and the spherical conics. Written by the renowned French mathematician Michel Chasles, it is a must-read for anyone interested in the history of mathematics and the development of geometric theory. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Excerpt from Two Geometrical Memoirs on the General Properties of Cones of the Second Degree, and on the Spherical Conics The two Memoirs by M. Chasles, On the Properties of Cones of the second Degree, and On the Spherical Conics, of which a translation is now presented to Eng lish geometers, were printed in the sixth volume of the Transactions of the Royal Academy of Brussels. Whe ther they are considered merely as exercises of pure geometry, exhibiting its elegance and power in a re markable degree, or as a rich and early contribution to the theory of spherical curves, they possess strong claims on the attention of mathematicians. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)

From New York Times bestselling author Sam Kean comes incredible stories of science, history, finance, mythology, the arts, medicine, and more, as told by the Periodic Table. Why did Gandhi hate iodine (I, 53)? How did radium (Ra, 88) nearly ruin Marie Curie's reputation? And why is gallium (Ga, 31) the go-to element for laboratory pranksters? The Periodic Table is a crowning scientific achievement, but it's also a treasure trove of adventure, betrayal, and obsession. These fascinating tales follow every element on the table as they play out their parts in human history, and in the lives of the (frequently) mad scientists who discovered them. The Disappearing Spoon masterfully fuses science with the classic lore of invention, investigation, and discovery -- from the Big Bang through the end of time. Though solid at room temperature, gallium is a moldable metal that melts at 84 degrees Fahrenheit. A classic science prank is to mold gallium spoons, serve them with tea, and watch guests recoil as their utensils disappear.

As a result of his visits to classrooms across the nation, Brown has compiled an engaging, thought-provoking collection of classroom vignettes which show the ways in which national, state, and local school politics translate into changed classroom practices. "Captures the breadth, depth, and urgency of education reform".--Bill Clinton.

Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.