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This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of sufficiently small domains, spherical and analytical geometry, the Klein model, and other topics. Appendixes include a table of values of hyperbolic functions.

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Before the widespread development of modern interior decoration, builders and homeowners often relied on commercially available stencils to decorate ceilings and walls of houses and other structures. This volume reproduces two rare catalogs of such stencils, manufactured ca. 1918 and ca. 1920 by H. Roessing of Chicago. Over 2,200 stencil designs include an enormous variety of attractive and boldly printed images: ornamental borders, corners and frames with intricate floral and foliate patterns, architectural ornaments and design elements, religious symbols and figures, numerous animals (horses, lions, birds, etc.), mosaics, landscapes, and much more.Meticulously reprinted from original catalogs in the collection of The Athenaeum of Philadelphia, these masterfully executed designs are an important source of copyright-free material invaluable for artists, illustrators, and craftspeople working with textiles, wallpaper, and other decorative products. Moreover, these ornamental motifs provide an invaluable record of American decorative tastes in the early years of the twentieth century.

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One of the eighteenth century's greatest mathematicians, Lagrange made significant contributions to all fields of analysis and number theory. He survived the French Revolution to deliver these lectures in 1795 at the Ecole Normale, a training school for teachers. An exemplar among elementary expositions, Lagrange's talks feature both originality of thought and elegance of expression.The five lectures begin with discussions of arithmetic that focus on fractions and logarithms as well as theory and applications. Subsequent talks consider algebra, with emphasis on the resolution of equations of the third and fourth degree, the resolution of numerical equations, and the employment of curves in the solution of problems. Students, teachers, and others with an interest in mathematics will find this volume a unique reading book in mathematics, with fascinating historical and philosophical remarks by a distinguished mathematician.

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Lectures on Partial Differential Equations

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The field of partial differential equations is an extremely important component of modern mathematics. It has great intrinsic beauty and virtually unlimited applications. This book, written for graduate-level students, grew out of a series of lectures the late Professor Petrovsky gave at Moscow State University. The first chapter uses physical problems to introduce the subjects and explains its division into hyperbolic, elliptic, and parabolic partial differential equations. Each of these three classes of equations is dealt with in one of the remaining three chapters of the book in a manner that is at once rigorous, transparent, and highly readable.Petrovsky was a leading figure in Russian mathematics responsible for many advances in the field of partial differential equations. In these masterly lectures, his commentary and discussion of various aspects of the problems under consideration will prove valuable in deepening students understanding and appreciation of these problems.

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Patterns and Designs from the Twenties in Full Color

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Reprinted in full color from a rare portfolio of abstract design published in Paris in the 1920s, these images splendidly capture the emergence of the Art Deco aesthetic in the years following World War I. The work of two notable French illustrators, this rich kaleidoscope of arcs and angles represents a transitional period between the luxuriant curvilinear designs of Art Nouveau and the streamlined modernism of Art Deco.Deeply influenced by Cubism, Neo-Impressionism, and other modernist movements, the Verneuils created a dazzling series of designs that reflect the spirit of these dynamic movements and the developing sensibilities of Art Deco design. Wallpaper and textile designers, graphic designers, and others in the arts and crafts will find pleasure and inspiration on every page of this handsome book. The collection includes 87 designs in a variety of useful shapes and sizes, each faithfully reproduced and copyright-free.

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Pictorial Encyclopedia of Historic Ornament

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One of the great anthologies of historic ornament and design, on a par with Owen Jones' Grammar of Ornament and Racinet's Historic Ornament, Dolmetsch's dazzling collection of over 1,500 illustrations  most in full color  is a veritable treasure chest of royalty-free images. Artists, designers, and hobbyists will also find design inspiration on every page, with images of artistic ornaments from antiquity through the 19th century, when this volume was originally assembled. Arranged chronologically, coverage begins in the ancient world, with designs from Roman architecture and sculpture, mosaic floors of Pompeii, and Byzantine embroidery. From the Middle Ages come illuminated manuscripts and stained glass decorations. Items dating from the Renaissance and later include Italian glass painting, pottery, and lace; French tapestry and block printing; and German metal work and weaving.

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Heck's Pictorial Archive of Art and Architecture

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2,200 illustrations from 19th-century archive include tombs, bridges, temples, mythological and religious figures, Egyptian painting, Greek sculpture, much more.

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A Grammar of Japanese Ornament and Design

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With the opening of Japan to the West in the mid-19th century, much of Japanese life that had been sealed off from the rest of the world for centuries was now revealed to the public at large  including the artistic styles and subjects depicted in this excellent collection. Rendered by a trained British architect, the images comprise one of the most comprehensive surveys of Japanese art and ornamentation. Included are graceful details from landscapes, floral motifs, abstracts, sea life, and other designs  ideal for use in modern textiles, graphics, and a host of other art and craft projects. A delight for anyone interested in Japanese art and culture, this volume will be an invaluable source of permission-free graphics for designers and decorators in search of new subjects with authentic Japanese flavor. Over 300 figures on 65 plates.

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The decorative arts of the Middle Ages  richly ornate, filled with religious and mythic symbolism  were especially remarkable for the complexities of their design and their inspired craftsmanship. This fascinating volume presents nearly 1,000 illustrations of medieval ornament, consisting mostly of architectural elements from German Romanesque and Gothic churches and other buildings.Originally compiled by the German architect, painter, and engraver Karl Alexander von Heldeloff (17881865) as a source of study and inspiration for practicing artists and architects, this grand pictorial archive has been exactingly reproduced from a rare original edition, complete with new English translations of the German captions.The book is filled with precisely detailed engravings of doors, windows, decorative stonework, columns, pedestals, and more. It remains a richly varied resource of authentic images of medieval ornament, ideal for students of architecture and the decorative arts and essential for graphic artists and designers in search of royalty-free illustrations.

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Swirling with gargoyles, devils, dragons, griffins, and other images that haunt both dreams and nightmares, this otherworldly assortment features more than 100 decorations from a rare nineteenth-century volume. Decorations include:Cartouches in the style of Louis XIII; stone balustrades; arabesques; roof cornices; Renaissance-era drawing-room cabinets; Elizabethan chimney pieces; plus friezes for textiles and wallpaper, decorative scutcheons, mirror frames, and much more. These versatile royalty-free illustrations are equally suitable for immediate use, adaptation, and inspiration.

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Translated from Cours de Philosophie Positive by W. M. Gillespie

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Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value. The two-part treatment begins with a general view of mathematical analysis and advances to algebra, continuing with an exploration of geometry's ancient and modern methods.

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Formulated to assist scientists and engineers engaged in army ordnance research and development programs, this well-known and highly regarded handbook is a ready reference for advanced undergraduate and graduate students as well as for professionals seeking engineering information and quantitative data for designing, developing, constructing, and testing equipment. Topics include characterizing and comparing the measured performance of a material, product, or process; general considerations in planning experiments; statistical techniques for analyzing extreme-value data; use of transformations; and many other practical methods. 1966 edition. Index. 52 figures. 76 tables.

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This singular collection displays pairs of letters, transforming ornamental initials into Art Nouveau masterpieces. Undulating lines, sensuous curves, writhing vines, and tendrils of leafy flora decorate every two-character combination, from A to Z. Featuring 990 imaginative illustrations, this treasury is perfect for tracing and copying. The marvelous monograms will also be enjoyed for their fine aesthetic beauty, and are sure to provide a wealth of inspiration for art projects of any kind.

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This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structure. A combination of matrix and vector methods reinforces both techniques. "Applied" students learn that general theory is a natural and useful culmination of their computations, and "pure" students learn that concrete problems from the physical world have traditionally keynoted abstract intellectual pursuits.Geared toward upper-level undergraduates, the text features approximately 50 provocative problems at each chapter's end that test students' choice of techniques. Each chapter is also followed by about 25 mental exercises that stimulate imaginative reflection. Answers are given to selected questions.

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The numbers that we call Arabic are so familiar throughout Europe and the Americas that it can be difficult to realize that their general acceptance in commercial transactions is a matter of only the last four centuries and they still remain unknown in parts of the world.In this volume, one of the earliest texts to trace the origin and development of our number system, two distinguished mathematicians collaborated to bring together many fragmentary narrations to produce a concise history of Hindu-Arabic numerals. Clearly and succinctly, they recount the labors of scholars who have studied the subject in different parts of the world; they then assess the historical testimony and draw conclusions from its evidence. Topics include early ideas of the origin of numerals; Hindu forms with and without a place value; the symbol zero; the introduction of numbers into Europe by Boethius; the development of numerals among Arabic cultures; and the definitive introduction of numerals into Europe and their subsequent spread. Helpful supplements to the text include a guide to the pronunciation of Oriental names and an index.

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David Eugene Smith, Louis Charles Karpinski

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The extraordinary creations of expert engraver F. Knight defined the lavish style of ornamentation associated with Victorian design. With clean lines and artful shading, Knight captured the spirit of the age in fanciful illustrations that combined the sentimental, the intricate, and the fantastic. This extravagant collection of Knight's work, reproduced directly from a rare original 19th-century edition, contains a fabulous assortment of images: elaborate wall murals with trompe-l'oeil effects of chandeliers and fountains; scenes of hunters, flanked by mythological figures; idealized damsels in rustic settings, framed by majestic swirls and garlands of flowers and ivy; and numerous other florid designs. Teeming with motifs in a variety of sizes and styles, this volume boasts a luxuriant supply of designs both floral (leaves, running vines, and blossoms) and animal (realistic and grotesque). A nearly inexhaustible source of versatile, copyright-free designs for artists, illustrators, and craftspeople, this volume will also fascinate all lovers of Victoriana.

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History of the Theory of Numbers, Volume II

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The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.

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Stunning sourcebook of 60 full-page, royalty-free designs  30 in full color and 30 in black-and-white  depict a marvelous selection of allover, subtly colored patterns for textiles, wallpaper, rugs, and wall hangings. Imaginative, Art Nouveau-inspired renderings of ferns, flowers, berries, human figures, masks, exotic dancers and a host of other subjects.

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A Full-Color Restoration of the Ancient Mexican Manuscript

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Considered by many scholars the finest extant Mexican codex and one of the most important original sources for the study of pre-Columbian religion, the Codex Borgia is a work of profound beauty, filled with strange and evocative images related to calendrical, cosmological, ritual, and divinatory matters. Generally similar to such Mixtec manuscripts as the Codex Nuttall, the Codex Borgia is thought to have its origin (ca. A.D. 1400) in the southern central highlands of Mexico, perhaps in Puebla or Oaxaca. It is most probably a religious document that once belonged to a temple or sacred shrine.One use of the Codex many have been to divine the future, for it includes ritual 260 day calendars, material on aspects of the planet Venus, and a sort of numerological prognostic of the lives of wedded couples. Another section concerns various regions of the world and the supernatural characters and attributes of those regions. Also described are the characteristics of a number of deities, while still other passages relate to installation ceremonies of rulers in pre-Columbian kingdoms.Until the publication of this Dover edition, the Codex Borgia has been largely inaccessible to the general public. The priceless original is in the Vatican Library and previous photographic facsimiles are very rare or very expensive or both. Moreover, the original Codex has been damaged over the centuries, resulting in the obscuration and loss of many images. In order to recapture the beauty and grandeur of the original, Gisele Diaz and Alan Rodgers have painstakingly restored the Codex by hand a seven-year project  employing the most scrupulous research and restoration techniques. The result is 76 large full-color plates of vibrant, striking depictions of gods, kings, warriors, mythical creatures, and mysterious abstract designs  a vivid panorama that offers profound insights into pre-Columbian Mexican myth and ritual. Now students, anthropologists, lovers of fine art and rare books  anyone interested in the art and culture of ancient Mexico  can study the Codex Borgia in this inexpensive, accurate, well-made edition. An informative introduction by noted anthropologist Bruce E. Byland places the Codex in its historical context and helps elucidate its meaning and significance.

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Traditional Japanese Family Crests for Artists and Craftspeople

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The custom of using family crests as a matter of pride on the part of the family still remains in the nations of Europe although it is being upheld by a limited number of households. In Japan it became a highly important matter of etiquette among the aristocrats and Samurai of the eleventh century to wear one's family crest in formal attire. It is commonly acknowledged that from this originated the custom of family crests in Japan that has been handed down traditionally through the years. The various crests you will find in this volume are those that are considered "classics" of their kind: that is, they are considered a part of the family history. Over 1,700 compact, graceful designs are featured in this handsome, versatile collection. Depicting plant, leaf, animal, and fan designs in circular motifs; astronomical images, and more, the authentic, royalty-free crests are ideal for use as spot illustrations in a variety of graphic projects.