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This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.

Are humans by nature hierarchical or egalitarian? Hierarchy in the Forest addresses this question by examining the evolutionary origins of social and political behavior. Christopher Boehm, an anthropologist whose fieldwork has focused on the political arrangements of human and nonhuman primate groups, postulates that egalitarianism is in effect a hierarchy in which the weak combine forces to dominate the strong.The political flexibility of our species is formidable: we can be quite egalitarian, we can be quite despotic. Hierarchy in the Forest traces the roots of these contradictory traits in chimpanzee, bonobo, gorilla, and early human societies. Boehm looks at the loose group structures of hunter-gatherers, then at tribal segmentation, and finally at present-day governments to see how these conflicting tendencies are reflected.Hierarchy in the Forest claims new territory for biological anthropology and evolutionary biology by extending the domain of these sciences into a crucial aspect of human political and social behavior. This book will be a key document in the study of the evolutionary basis of genuine altruism.

In this booklet, John G. Reisinger explores four aspects of the Lordship of Christ over the church. The nature, the extent, and the exercise of his Lordship and modern examples that deny Christ's Lordship. He postulates that one of the most serious theological implications for those who hold to reformed theology is their failure to recognize Christ as the New Lawgiver. This booklet goes a long way in explaining and contrasting the differences between (Old) Covenant Theology and New Covenant Theology.

TECTONlCS AND PHYSICS Geology, although rooted in the laws of physics, rarely has been taught in a manner designed to stress the relations between the laws and theorems of physics and the postulates of geology. The same is true of geophysics, whose specialties (seismology, gravimetIy, magnetics, magnetotellurics) deal only with the laws that govern them, and not with those that govern geology's postulates. The branch of geology and geophysics called tectonophysics is not a formalized discipline or subdiscipline, and, therefore, has no formal laws or theorems of its own. Although many recent books claim to be textbooks in tectonophysics, they are not; they are books designed to explain one hypothesis, just as the present book is designed to explain one hypothesis. The textbook that comes closest to being a textbook of tectonophysics is Peter 1. Wyllie's (1971) book, The Dynamic Earth. Teachers, students, and practitioners of geology since the very beginning of earth­ science teaching have avoided the development of a rigorous (but not rigid) scientific approach to tectonics, largely because we earth scientists have not fully understood the origin of the features with which we are dealing. This fact is not at all surprising when one considers that the database for hypotheses and theories of tectonics, particularly before 1960, has been limited to a small part of the exposed land area on the Earth's surface.

Grateful Prey uncovers the interaction between magico-religious ideology and hunting strategies among the Asinskâwôiniwak, or Rock Crees, of Northern Manitoba. Brightman maintains that subsistence strategies need to be analyzed in terms of the foragers' own ethnoecological categories and postulates, both sacred and secular, a position which poses a challenge to prevailing ecological and Marxist approaches to foraging societies and strategies. A major contribution to the study of foraging societies.

The Christian View of God and the World, one of the first major attempts at developing a unified Christian worldview, is still a classic today. The book resulted from a lecture series by James Orr, who covered topics such as general Christian worldview, the alternatives to Christianity, postulates about God's existence and sin, and the incarnation of Christ. The spoken nature of these lectures gives the text an understandable, conversational tone to even the heaviest theology. Orr is one of the best-known English-speaking theologians, and his brilliant mind produced a number of great works. These spoken lectures have a different feel than his prose, and fans of Orr will appreciate the new tone.

This book contains the basic definitions and postulates of Professor Andrew J. Galambos' (1924-1997) Volitional Science. The professor's work involves using the rigors of the scientific method and the principles of physics to understand human volition.

God’s first and primal work is the Creation of the universe. Creation constitutes the fundamental and essential postulate of all being and operation in the natural order as well as of all supernatural institutions, such as the Incarnation, Grace, the Sacraments, etc. Hence, the dogmatic treatise De Deo Creante et Elevante, which forms the subject matter of this volume, views God as the Author of Nature and the Supernatural. A true idea of Creation is indispensable to deepen and perfect the conception of God gained from the treatises De Deo Uno and De Deo Trino. Further, the consideration of the creation of men and angels and of their natures -- anthropology and angelology -- is the most important counterpart to the consideration of God as Creator.

Volume 7 of the Learn Math Fast System covers all the major topics of High School Geometry including Proofs, Theorems, Postulates, Sine, Cosine, Tangent, plus the interior and exterior angles of polygons and circles. All lessons, worksheets and test are included. The Answer Key is in the back of the book. Purchase the Smart Cards separately for more help.

1. Introduction . 1 2. Areas and Angles . . 6 3. Tessellations and Symmetry 14 4. The Postulate of Closest Approach 28 5. The Coexistence of Rotocenters 36 6. A Diophantine Equation and its Solutions 46 7. Enantiomorphy. . . . . . . . 57 8. Symmetry Elements in the Plane 77 9. Pentagonal Tessellations . 89 10. Hexagonal Tessellations 101 11. Dirichlet Domain 106 12. Points and Regions 116 13. A Look at Infinity . 122 14. An Irrational Number 128 15. The Notation of Calculus 137 16. Integrals and Logarithms 142 17. Growth Functions . . . 149 18. Sigmoids and the Seventh-year Trifurcation, a Metaphor 159 19. Dynamic Symmetry and Fibonacci Numbers 167 20. The Golden Triangle 179 21. Quasi Symmetry 193 Appendix I: Exercise in Glide Symmetry . 205 Appendix II: Construction of Logarithmic Spiral . 207 Bibliography . 210 Index . . . . . . . . . . . . . . . . . . . . 225 Concepts and Images is the result of twenty years of teaching at Harvard's Department of Visual and Environmental Studies in the Carpenter Center for the Visual Arts, a department devoted to turning out students articulate in images much as a language department teaches reading and expressing one­ self in words. It is a response to our students' requests for a "handout" and to l our colleagues' inquiries about the courses : Visual and Environmental Studies 175 (Introduction to Design Science), YES 176 (Synergetics, the Structure of Ordered Space), Studio Arts 125a (Design Science Workshop, Two-Dimension­ al), Studio Arts 125b (Design Science Workshop, Three-Dimensional),2 as well as my freshman seminars on Structure in Science and Art.

Common sense suggests that reality can be discovered. In contrast, constructivism postulates that what we call reality is a personal interpretation, a particular way of looking at the world acquired through communication. Reality is, therefore, not discovered, but literally invented.This book examines how individual, social, scientific, and ideological "realities" are constructed, after which we naively assume they are the "real" realities. Contributors include Ernst von Glaserfeld (known for his cognitive studies with chimpanzees); cybeneticist Heinz von Foerster; David L. Rosenhan (author of On Being Sane in Insane Places); microbiologist Francisco J. Varela; and Gabriel Stolzenberg, professor of mathematics at Northeastern University. Paul Watzlawick has contributed commentary, an introduction and an epilogue, and two of the ten essays.For educated readers, this is the first multidisciplinary presentation of a subject of vital importance to the way we think and live.

Reviews from the First Edition: "An excellent text ? The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist) "No matter how gently one introduces students to the concept of Dirac?s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin) Reviews of the Second Edition: "This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. ? It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews) R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book?s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

Are humans by nature hierarchical or egalitarian? Hierarchy in the Forest addresses this question by examining the evolutionary origins of social and political behavior. Christopher Boehm, an anthropologist whose fieldwork has focused on the political arrangements of human and nonhuman primate groups, postulates that egalitarianism is in effect a hierarchy in which the weak combine forces to dominate the strong.The political flexibility of our species is formidable: we can be quite egalitarian, we can be quite despotic. Hierarchy in the Forest traces the roots of these contradictory traits in chimpanzee, bonobo, gorilla, and early human societies. Boehm looks at the loose group structures of hunter-gatherers, then at tribal segmentation, and finally at present-day governments to see how these conflicting tendencies are reflected.Hierarchy in the Forest claims new territory for biological anthropology and evolutionary biology by extending the domain of these sciences into a crucial aspect of human political and social behavior. This book will be a key document in the study of the evolutionary basis of genuine altruism.

All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica­ tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.

What fundamental account of the world is implicit in physical theory? Physics straightforwardly postulates quarks and electrons, but what of the more intangible elements, such as laws of nature, universals, causation and the direction of time? Do they have a place in the physical structure of the world? Tim Maudlin argues that the ontology derived from physics takes a form quite different from those most commonly defended by philosophers. Physics postulates irreducible fundamental laws, eschews universals, does not require a fundamental notion of causation, and makes room for the passage of time. In a series of linked essays The Metaphysics Within Physics outlines an approach to metaphysics opposed to the Humean reductionism that motivates much analytical metaphysics.

Delta Green brings the Cthulhu Mythos, and the men and women who encounter it, squarely into the modern day. Delta Green postulates a secret group dedicated to investigating alien and supernatural horrors. Packed full of secret organizations, shadowy conspiracies and alien invaders, Delta Green has all the material you need to play using Call of Cthulhu d20. Hardcover RPG Core Book, 336 pp.

Public choice, an important subdiscipline in the field of political theory, seeks to understand how people and societies make decisions affecting their collective lives. Relying heavily on theoretical models of decision making, public choice postulates that people act in their individual interests in making collective decisions. As it happens, however, reality does not mirror theory, and people often act contrary to what the principal public choice models suggest. In this book, Russell Hardin looks beyond the models to find out why people choose to act together in situations that the models find quite hopeless. He uses three constructs of modern political economy--public goods, the Prisoner's Dilemma, and game theory--to test public choice theories against real world examples of collective action. These include movements important in American society in the past few decades--civil rights, the Vietnam War, women's rights, and environmental concerns. This classic work on public choice will be of interest to theoreticians and graduate students in the fields of public choice, political economy, or political theory--and to those in other disciplines who are concerned with the problem of collective action in social contexts.

This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. Lebesgue integration theory and complex variables are sometimes involved, but most of the book can be understood without them. Exercises at the end of each chapter provide helpful reinforcement.

This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference. The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the modern student's knowledge of the atomic nature of matter. Another unique aspect of the book is the treatment of the mathematics involved. The essential mathematical concepts are briefly reviewed before using them, and the similarity of the mathematics to that employed in other fields of physics is emphasized. The text gives in depth treatments of low density gases, harmonic solids, magnetic and dielectric materials, phase transitions, and the concept of entropy. The microcanonical, canonical, and grand canonical ensembles of statistical mechanics are derived and used as the starting point for the analysis of fluctuations, blackbody radiation, the Maxwell distribution, Fermi-Dirac statistics, Bose-Einstein condensation, and the statistical basis of computer simulations.Supplementary material including PowerPoint slides and detailed worked solutions can be downloaded online at http://booksupport.wiley.com