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Alexandroff's beautiful and elegant introduction to topology was originally published in 1932 as an extension of certain aspects of Hilbert's Anschauliche Geometrie. The text has long been recognized as one of the finest presentations of the fundamental concepts, vital for mathematicians who haven't time for extensive study and for beginning investigators.The book is not a substitute for a systematic text, but an unusually useful intuitive approach to the basic concepts. Its aim is to present these concepts in a clear, elementary fashion without sacrificing their profundity or exactness and to give some indication of how they are useful in increasingly more areas of mathematics. The author proceeds from the basics of set-theoretic topology, through those topological theorems and questions which are based upon the concept of the algebraic complex, to the concept of Betti groups which binds together central topological theories in a whole and upon which applications of topology largely rest.Wholly consistent with current investigations, in which a larger and larger part of topology is governed by the concept of homology, the book deals primarily with the concepts of complex, cycle, and homology. It points the way toward a systematic and entirely geometrically oriented theory of the most general structures of space.First English translation, prepared for Dover by Alan E. Farley. Preface by David Hilbert. Author's Foreword. Index. 25 figures.

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"One of the greatest problems of education," Kant observes, "is how to unite submission to the necessary restraint with the child's capability of exercising his free will." He explores potential solutions to this dilemma, stressing the necessity of treating children as children and not as miniature adults. His positive outlook on the effects of education include a conviction that human nature could be continually improved; to achieve this end, he advocated that pedagogy, the science of education, be raised to academic status and studied at a university level  an innovative notion for the 18th century.

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The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brought to the foreground, placing their logical structure in sharp relief.Because the concept of a vector has been greatly generalized in geometry and mathematical physics, this text concludes with a brief introduction to abstract vector spaces, together with the ideas of linear dependence, basis, and dimension. The exposition of these abstract concepts is kept simple and clear. Numerous figures appear throughout the text.

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While out on a hunting trip, a king encounters a lovely maiden, and the course of their secret romance sweeps the audience from a forest hermitage to a dazzling palace to ethereal celestial realms. The tale of King Dusyanta and Sakuntala, who meet by chance and are separated by a curse, was derived from an episode in the Mahabharata, India's grand religious epic. The Recognition of Sakuntala, written in the 5th century by the greatest of the ancient Indian playwrights, offers a classic introduction to Indian theater and aesthetics.In addition to its enchanting love story, this play presents a religious drama. It promotes the doctrine of karma, in which all experiences are influenced by actions from earlier in life, and it represents an allegory of the relationship between the worshiper and the sacred. Students of drama, religious studies, and world literature will appreciate this affordable and accessible edition of a timeless play.

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Ernst Rettelbusch's great Stilhandbuch [Handbook of Styles] was the lifework of a connoisseur and practicing professional in the fields of architecture, interior design, and furniture design. Intended as an introduction for students and amateurs, it contains over 1,200 examples of ornamental and decorative design produced by many cultures over five millennia.This volume is an unabridged republication, with new English translations of the Preface and descriptions of the plates of this great classic. Ranging from the time of ancient Egypt to nineteenth- century Germany, it documents a wealth of designs from Assyrian, Greek, Roman, Byzantine, and other ancient cultures, along with material from the European Renaissance, Baroque and Rococo periods. Also included are English furniture designs by Chippendale, Sheraton, and Hepplewhite, French Empire designs, Nordic motifs, Chinese and Japanese material, and much more.Beautifully rendered in meticulous detail, these plates will serve as a comprehensive historical review for students of decorative design, an invaluable treasury of art and design for royalty-free use, and a rich source of inspiration for anyone working in the fine or applied arts.

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Heraldic Designs for Artists and Craftspeople

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Graphic artists, illustrators, and crafters looking for imaginative designs featuring medieval flair and aristocratic ambience will find this collection invaluable. Over 1,400 heraldic motifs, in a rich variety of styles and sizes, include shields, coats-of-arms, seals, logos, flags, insignia, scrolls, mottoes, bookplates, and a wealth of other designs and illustrations.Incorporating finely detailed images of flora and fauna, American flags and eagles, sailing vessels and steam-powered ships, mythical creatures, castle turrets, weaponry and armor, human figures, and much more, these authentic designs represent an indispensable archive of immediately usable, royalty-free art.

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By forbidding the representation of the human figure, the Mohammedan religion helped push Islamic art along a path much different from that of traditional European art. European abounds with perspective renderings of figures and landscapes, while Islamic translates artistic impulse into elaborate geometric patterns and linear designs. Through centuries of practicing this purely abstract art, Muslim artists have perfected it to an incomparable elegance.This book contains 190 examples exhibiting the wide range of Islamic geometrical art: hexagon designs, octagon designs, dodecagon designs, combinations of stars and rosettes (of many variations), combinations of squares and octagons, heptagon designs, and pentagon designs. These fundamental shapes give rise to hundreds of different designs, and merely altering an angle or curving a straight line can create an entirely new pattern. When transferred to metal, wood, stucco, mosaic, and paint, these patterns make up the elaborate ornamentation for which Arabic architecture is noted, and twenty-eight examples of actual applications from Cairo and Damascus are included: sanctuary doors, openwork windows, inlaid marble pavements, and ceilings. The reader may wish to try his own hand at drawing patterns, to which purpose dotted construction lines are given for sections of the plates. Artists and designers will appreciate this book as a valuable source for Islamic art and design, which they may use directly or vary at will, and with the added use of color they will find that striking and beautiful results can often be achieved.

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Turn-of-the-Century Tile Designs in Full Color

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Carefully selected from a rare 1905 French tile catalog, this splendid full-color collection of tile designs features scores of eye-catching motifs. A valuable resource for today's artists and designers, this volume of authentic images can also serve as inspiration for craftspeople working in a variety of areas. The 250 illustrations include panels and borders of all sizes, decorated with lotus blossoms, lilies-of-the-valley, irises, and other delicate florals; multicolored designs promoting meat markets, dairies, and other commercial establishments; decorative wall tiles for bathrooms; stenciled friezes with ornate floral and foliate motifs; vibrantly colored enameled squares; geometrics; and much more. Rich in Art Nouveau flavor and elegance, these versatile copyright-free designs not only constitute an invaluable archive of usable art and design inspiration but also a magnificent browsing book for lovers of the decorative arts.

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This superb collection is a reproduction of 60 plates from the lavishly illustrated three-volume set Chants et Chansons Populaires de la France, first published in Paris during the early 1840s. Generally regarded as one of the finest illustrated books of the Romantic period, it is often compared with the masterpieces of 18th-century book illustration. In this rare French edition, pages of commentary and musical arrangements accompany the exquisite engravings. The original French texts of the songs, bordered by these lovely 19th-century illustrations, have been omitted here. What is left are unique vignette borders that may be used in a wide variety of graphic projects.The selection of these 60 plates has been made with an eye toward retaining the finest works from the original collection and providing those designs that will best serve the needs of today's artists and designers.

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Borders, Frames and Decorative Motifs from the 1862 Derriey Typographic Catalog

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In the mid-19th century, typefounders plied their trade with an extraordinary exuberance, creating a new and dazzling range of typefaces and ornamentation that in sheer versatility, ornate beauty, and sumptuousness remain unsurpassed. Today, as never before, their work is sought by artists, designers, and craftspeople for its elegance, expressiveness, and ability to command attention.This unique volume contains the work of one of the most celebrated typefounders of that glorious era in type design: Charles Derriey, who, from his Parisian foundry, fed the Victorians' insatiable appetite for decoration and embellishment with a truly fabulous assortment of display types and printers' ornaments. The 113 plates reprinted here from his 1862 typographic catalog include over 2,500 royalty-free type forms and ornamental designs.Here is an incredibly rich source of intricately ornamented typefaces along with an eye-catching array of vignettes (dingbats, headpieces, tailpieces, etc.), rules, flourishes, corner elements, and much more, including a wide selection of Victorian frames and border material. Leaf through it and you will find it to be not only a fascinating presentation of type design, but also an extensive sampler of Victorian ornamentation  a valuable reference book and source of royalty-free graphics, sturdily yet inexpensively produced, that will offer you years of inspiration, enjoyment, and practical use.

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Swiss etcher and engraver Matthaeus Merian the Elder (to distinguish him from his son, Matthaeus Merian the Younger, a portrait and historical painter), was born in Basel in 1593. He studied in Zurich, Paris, Stuttgart, and the Netherlands, eventually settling in Frankfurt where he worked for the publisher Johann Theodor de Bry, whose daughter he later married. On the death of his father-in-law in 1623, Merian took over the publishing house, while continuing his own artistic efforts. Perhaps best known for his many detailed topographic prints of European cities, he also produced numerous engravings of battles and hunts, as well as such prints as Dance of Death, illustrations for Gottfrieds Chronik, and the series Theatrum Europaeum.Among Merian's most notable accomplishments was the creation and publication of the Icones Biblicae (16251630), a monumental collection of engravings of scenes from the Bible, accompanied by descriptive texts in German, Latin and French. The present volume reproduces all 230 of these superb images, minus the accompanying texts, but with new titles for the plates, and citations of book, chapter and verse. Reminiscent of seventeenth-century European landscapes, and full of wonderful details of plants and animals, clothing, weapons, buildings, cities, and more, Merian's images retain a mood of piety, awe and reverence, while avoiding the saccharine and sentimental. Instead, the artist has given us honest, straightforward renderings of a host of memorable scenes and characters from both the Old and New Testaments, and the Apocrypha, that capture the high drama, heartrending tragedy, and transcendent religious experience of this most influential of books.Remarkably detailed illustrations depict Adam and Eve Driven Out of the Garden of Eden, The Flood, David Slaying Goliath, Christ in the Manger, The Raising of Lazarus, The Crucifixion, and many other scenes. A wonderful pictorial dimension to age-old stories. All 230 plates from the classic 1625 edition.

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When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and electromagnetic theory. The text stresses geometrical and physical aspects, but it also casts the material in such a way that the logical structure of the subject is made plain. Serious students of mathematics can rigorize the treatment to their own satisfaction. Although intended primarily as a college text, this volume may be used as a reference in vector techniques or as a guide to self-education.

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Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics.Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.

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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.