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Mathematics
Browse Mathematics as a public-domain reading list on Rivro, with free classics, authors, subjects, and related books.
Amusements in Mathematics
Henry Ernest Dudeney
Amusements in Mathematics
"Amusements in Mathematics" by Henry Ernest Dudeney is a collection of mathematical puzzles and problems written in the early 20th century. This engaging work aims to entertain readers while stimulating their mathematical reasoning and logic skills through a variety of intriguing puzzles, ranging from arithmetic and algebra to geometry and logic. The opening of the book provides context on the puzzles’ approach and serves as a prelude to the content that follows. Dudeney emphasizes the universal nature of puzzles, suggesting that everyone engages in problem-solving throughout their daily lives, often unconsciously applying logical thinking. He intends to keep the tone light and enjoyable, allowing readers of all levels to participate in the fun while presenting an array of puzzles, including those involving money, age, kinship, and more. Each puzzle invites the reader to think critically and creatively, often with the promise of discovering surprising insights along the way.
The First Six Books of the Elements of Euclid
Euclid
The First Six Books of the Elements of Euclid
No description available.
Encyclopaedia Britannica, 11th Edition, "Groups, Theory of" to "Gwyniad" Volume 12, Slice 6
Various
Encyclopaedia Britannica, 11th Edition, "Groups, Theory of" to "Gwyniad" Volume 12, Slice 6
"Encyclopaedia Britannica, 11th Edition, 'Groups, Theory of' to 'Gwyniad'" by Various is a scientific publication written during the early 20th century. This segment of the encyclopaedia delves into the mathematical concept of groups, presenting a detailed examination of group theory, including definitions, operations, and particular characteristics of both continuous and discontinuous groups. At the start of this volume, the focus is on establishing the foundational concepts of group theory. It begins by defining a group as a set of operations that can be performed on a set of objects, highlighting the relationship between operations and their inverses, and introduces key terms such as subgroups and conjugate operations. The definitions are accompanied by algebraic notation and examples, transitioning seamlessly into discourse on various types of groups, including finite and infinite groups, ultimately setting the stage for more intricate discussions of specific groups and their mathematical implications.
Flatland: A Romance of Many Dimensions
Edwin Abbott Abbott
Flatland: A Romance of Many Dimensions
"Flatland: A Romance of Many Dimensions" by Edwin Abbott Abbott is a satirical novella published in 1884. Set in a two-dimensional world inhabited by geometric shapes, the story follows a Square who encounters beings from other dimensions. Through his journey from Flatland to higher and lower dimensional worlds, the novella explores both the mathematical concept of dimensions and critiques Victorian society's rigid class and gender hierarchies. Unable to convince others of what he's witnessed, the Square faces imprisonment for preaching forbidden truths about reality beyond two dimensions.
Philosophiae Naturalis Principia Mathematica
Isaac Newton
Philosophiae Naturalis Principia Mathematica
"Philosophiae Naturalis Principia Mathematica" by Isaac Newton is a three-volume work first published in 1687. Written in Latin, it presents Newton's revolutionary laws of motion and universal gravitation, transforming scattered observations into a unified mathematical framework for understanding the physical universe. The work explains planetary motion, tides, comets, and Earth's shape through geometric propositions and empirical investigation. Hailed as perhaps the greatest scientific treatise ever written, it launched modern physics and astronomy, fundamentally altering humanity's comprehension of nature.
Encyclopaedia Britannica, 11th Edition, "Logarithm" to "Lord Advocate" Volume 16, Slice 8
Various
Encyclopaedia Britannica, 11th Edition, "Logarithm" to "Lord Advocate" Volume 16, Slice 8
"Encyclopaedia Britannica, 11th Edition, 'Logarithm' to 'Lord Advocate'" by Various is a scientific reference work written in the early 20th century. This volume is part of a comprehensive collection covering various topics in arts, sciences, and literature. It includes detailed entries on subjects ranging from mathematical concepts like logarithms to geographical locations and historical figures such as the Lord Advocate. The content serves as an authoritative guide for readers seeking knowledge across a wide array of disciplines. At the start of this volume, we find a detailed discussion on logarithms, beginning with their definition and core properties as a mathematical function. The text explains the historical context of logarithms, attributing their invention to John Napier and discussing their significance in simplifying arithmetic calculations. It introduces logarithmic calculations and includes various examples, highlighting the applications of logarithms in mathematical analysis and other fields. This opening segment establishes the foundational importance of logarithms in mathematics and their practical implications in computation and scientific inquiry.
1001 задача для умственного счета
Sergei Aleksandrovich Rachinskii
1001 задача для умственного счета
"1001 задача для умственного счета" by Sergei Aleksandrovich Rachinskii is a mathematical workbook written in the late 19th century. This collection contains a vast array of arithmetic problems designed for educational purposes, particularly for use in classrooms. The problems are presented in a straightforward language, often contextualized in practical scenarios, enabling learners to enhance their mental calculation skills. The opening of this workbook introduces the format and structure of the challenges included. It details that the tasks are tailored for students and can be applied in arithmetic lessons. The first few examples presented illustrate various calculations involving reading, purchasing land, and budgeting, emphasizing real-world situations that require mental arithmetic. Each problem is followed by a solution, which helps learners verify their understanding and mastery of the concepts presented.
Our Calendar The Julian calendar and its errors. How corrected by the Gregorian. Rules for finding the dominical letter, and the day of the week of any event from the days of Julius Caesar 46 B.C. to the year of our Lord four thousand; a new and easy method of fixing the date of Easter. Hebrew calendar; showing the correspondence in the date of events recorded in the Bible with our present Gregorian calendar. Illustrated by valuable tables and charts.
George Nichols Packer
Our Calendar The Julian calendar and its errors. How corrected by the Gregorian. Rules for finding the dominical letter, and the day of the week of any event from the days of Julius Caesar 46 B.C. to the year of our Lord four thousand; a new and easy method of fixing the date of Easter. Hebrew calendar; showing the correspondence in the date of events recorded in the Bible with our present Gregorian calendar. Illustrated by valuable tables and charts.
"Our Calendar" by George Nichols Packer is a scholarly treatise on the history and mathematical principles of calendar systems, written in the late 19th century. The work delves into the transition from the Julian calendar to the Gregorian calendar, discussing the relevant historical reforms made by significant figures such as Julius Caesar and Pope Gregory XIII. Through detailed calculations and rules, Packer aims to simplify the complex processes involved in determining dates and understanding the calendar's structure, targeting those who seek a practical understanding of timekeeping. At the start of the book, the author introduces the topic by detailing the origin and evolution of the calendar. He emphasizes his personal journey through the subject, which began as a teaching endeavor and later grew into an extensive exploration prompted by his own circumstances. The opening chapters lay out definitions, the historical context of the Roman calendar, and the adjustments made under Julius Caesar and Pope Gregory XIII to correct discrepancies in timekeeping. Packer also hints at the mathematical rules that will follow, establishing a foundation for readers interested in not just the theoretical aspects but also the practical applications of calendar calculations in everyday life.
Über die Geometrie der alten Aegypter. Vortrag, gehalten in der feierlichen Sitzung der Kaiserlichen Akademie der Wissenschaften am 29. Mai 1884.
Emil Weyr
Über die Geometrie der alten Aegypter. Vortrag, gehalten in der feierlichen Sitzung der Kaiserlichen Akademie der Wissenschaften am 29. Mai 1884.
"Über die Geometrie der alten Aegypter" by Emil Weyr is a scholarly publication that was presented in the late 19th century. This work explores the geometrical knowledge and methodologies of ancient Egyptian civilization, highlighting their contributions to the development of geometry as a science. The book is aimed at readers interested in the history of mathematics and the intellectual achievements of ancient cultures. In this publication, Emil Weyr delves into the origins and progress of geometrical understanding in ancient Egypt, arguing that it was not solely the birthplace of mathematics, but rather that various cultures developed geometrical concepts out of practical necessities. The author examines historical accounts from Greek philosophers, such as Herodotus and Plato, detailing how the Greeks acquired their geometrical knowledge from Egyptian priests. Furthermore, Weyr analyzes ancient texts and artifacts, including the Rhind Papyrus, to substantiate claims of advanced understanding in land measurement, geometry construction, and practical applications. The work concludes with an assertion about the sophistication of Egyptian geometry, revealing a cultural legacy that significantly influenced subsequent mathematical thought.
On Growth and Form
D'Arcy Wentworth Thompson
On Growth and Form
"On Growth and Form" by D'Arcy Wentworth Thompson is a scientific work published in 1917. This mathematical exploration of biology challenges evolution as the sole explanation for living organisms' shapes and structures. Thompson demonstrates how physical laws and mechanics govern biological forms, drawing striking parallels between jellyfish and falling liquid drops, bird bones and engineering trusses, and plant spirals and mathematical sequences. His famous transformation method reveals how animal skulls can be mathematically related through coordinate grids, pioneering an entirely new approach to understanding life's architecture.
The Canterbury Puzzles, and Other Curious Problems
Henry Ernest Dudeney
The Canterbury Puzzles, and Other Curious Problems
"The Canterbury Puzzles and Other Curious Problems" by Henry Ernest Dudeney is a collection of mathematical puzzles and riddles written in the early 20th century. The work reflects Dudeney's expertise in puzzle creation and draws inspiration from Geoffrey Chaucer’s "Canterbury Tales," intertwining the themes of travel and inquiry with the allure of problem-solving. It features a variety of engaging puzzles, each designed to challenge the reader's wit and logic. The opening of this intriguing collection presents a preface where Dudeney discusses the art of puzzling, the enjoyment it brings, and the mental exercise it provides. He harmonizes his work with historical references to puzzles, emphasizing their universal appeal throughout history. With examples of various puzzles that are both entertaining and thought-provoking, readers are quickly immersed in a world where wit meets ingenuity. Dudeney encourages participation by inviting readers to solve these cleverly crafted challenges, rich with a narrative that evokes the charm of medieval storytelling.
Encyclopaedia Britannica, 11th Edition, "Equation" to "Ethics" Volume 9, Slice 7
Various
Encyclopaedia Britannica, 11th Edition, "Equation" to "Ethics" Volume 9, Slice 7
"Encyclopaedia Britannica, 11th Edition, 'Equation' to 'Ethics'" by Various is a comprehensive scientific publication written in the early 20th century. This volume serves as a section of the larger 11th Edition of the Encyclopaedia Britannica, providing in-depth articles on a range of topics, from mathematical equations to ethical theories. The text leans towards mathematical and scientific discourse, offering insights into the nature of equations and their solutions. The opening of this volume begins with a detailed discussion about equations, explaining their significance and classification within mathematics. It defines an equation as a statement of equality between two quantities and elaborates on the different types of equations, including linear, quadratic, cubic, and biquadratic forms, as well as discussing historical developments in the theories behind these equations. The text introduces various mathematical concepts, methods for solving equations, and provides examples to clarify the definitions, making it a valuable reference for those looking to deepen their understanding of mathematical principles.
An essay on the foundations of geometry
Bertrand Russell
An essay on the foundations of geometry
"An Essay on the Foundations of Geometry" by Bertrand Russell is a scholarly work exploring the philosophical and logical underpinnings of geometry, written in the late 19th century. The book delves into historical perspectives on geometric principles, particularly focusing on non-Euclidean geometries and the implications of various axioms. It addresses the epistemological questions surrounding the nature of geometric knowledge and the necessary conditions for spatial reasoning. The opening of the essay outlines the structure and intent of Russell's investigation into geometry. It sets up a distinction between a priori knowledge and subjective experience, and highlights the influence of key philosophers such as Kant on the discourse surrounding geometric foundations. Russell establishes a framework for exploring the historical evolution of geometry, particularly the development of metageometry and non-Euclidean systems, while preparing for a detailed examination of the essential axioms that govern geometric thought and the relationship between geometry and logic. This introduction primes the reader for a critical analysis of prior philosophical theories and sets the stage for Russell's own contributions to the field.
The Teaching of Geometry
David Eugene Smith
The Teaching of Geometry
"The Teaching of Geometry" by David Eugene Smith is an educational publication written in the early 20th century. This work explores the methodology and philosophy behind teaching geometry, emphasizing the importance of the subject in the education curriculum and advocating for its evolution rather than drastic reforms. It focuses on the needs and concerns of teachers and proposes ways to improve the teaching of geometry to better engage students. At the start of the text, the author discusses the current state of geometry education in America, laying out various debates among educators regarding its content and methods of instruction. He reflects on the balance between traditional approaches and modern necessities, recognizing the diverse opinions within the teaching community. Smith is particularly focused on providing a framework that appeals to both progressive teachers eager for improvement and those who prefer established methods, with an overarching goal of making geometry interesting and relevant to students.
Autobiography of Sir George Biddell Airy
George Biddell Airy
Autobiography of Sir George Biddell Airy
"Autobiography of Sir George Biddell Airy" by George Biddell Airy is a historical account written during the late 19th century. The book recounts the life and accomplishments of Sir George Biddell Airy, who served as the Astronomer Royal for 46 years, detailing his scientific work at the Greenwich Observatory along with his interactions with notable figures in both science and government. The opening of the autobiography provides a context for understanding Airy’s character and work ethic. It describes Airy as a dedicated and methodical individual, emphasizing his strict adherence to order and detail in both his personal life and professional duties. The introduction highlights how Airy’s autobiography blends personal anecdotes with his scientific endeavors, setting the stage for a detailed exploration of his contributions to astronomy, mathematics, and various scientific issues during his lifetime. The text suggests that readers will glean insights not only into Airy’s scientific achievements but also into the broader scientific landscape of his era.
Encyclopaedia Britannica, 11th Edition, "Geodesy" to "Geometry" Volume 11, Slice 6
Various
Encyclopaedia Britannica, 11th Edition, "Geodesy" to "Geometry" Volume 11, Slice 6
"Encyclopaedia Britannica, 11th Edition, 'Geodesy' to 'Geometry'" by Various is a scientific publication written in the early 20th century. This volume serves as a comprehensive reference on various topics related to geodesy and geometry, detailing fundamental concepts, historical contexts, and significant figures in the field of surveying and earth sciences. The text aims to provide readers with an understanding of the principles and applications of these scientific disciplines. At the start of this volume, the section on "Geodesy" introduces the science of surveying large areas of land, particularly focusing on the accurate measurement and mapping of the Earth's surface. It discusses techniques like triangulation, the importance of measuring base lines, and the technologies utilized in these processes. The opening also highlights the historical significance of various geodesists and their contributions, providing context for the development of geodetic methods and tools that are crucial for accurate navigation and cartography.
The Logic of Chance, 3rd edition An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
John Venn
The Logic of Chance, 3rd edition An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
"The Logic of Chance, 3rd edition" by John Venn is a scientific publication written in the late 19th century. This work focuses on the foundations and theoretical aspects of probability, exploring its implications and applications in moral and social sciences, as well as statistics. The author aims to bridge the gap between mathematical probability and philosophical inquiry, arguing against the common perception that probability is merely a mathematical discipline devoid of substantive philosophical value. At the start of the text, Venn establishes the foundations of probability, emphasizing the importance of understanding the nature of series and how they relate to probability theory. He discusses the distinction between various types of assertions in natural phenomena, noting that while individual instances may appear chaotic, larger aggregates often reveal underlying patterns of regularity. Venn critiques the prevailing views of probability as purely mathematical, asserting that its principles are integral to broader philosophical discussions. He sets the stage for a rigorous exploration of probabilistic concepts, addressing misconceptions and laying the groundwork for the subsequent analysis of probabilistic laws and applications.
The Hindu-Arabic Numerals
David Eugene Smith
The Hindu-Arabic Numerals
"The Hindu-Arabic Numerals" by David Eugene Smith and Louis Charles Karpinski is a historical account written in the early 20th century. This work delves into the origins and evolution of the numeral system commonly used today, which is often misnamed "Arabic" despite its true roots in Hindu mathematics. The authors aim to compile and clarify the fragmented history of these numerals, exploring their development, usage, and eventual widespread acceptance in commerce and science. The opening of the book establishes the premise that the Hindu-Arabic numeral system is relatively recent in its widespread adoption, only becoming prominent in Europe and the Americas over the past few centuries. It discusses misconceptions about the origins of these numerals, tracing their evolution from earlier notational systems used by ancient civilizations. The authors highlight the contributions of various scholars, particularly in assessing the claims of both Hindu and Arabic origins for these numerals and setting the stage for a deeper exploration into their journey from India to Europe, emphasizing the complexity involved in this mathematical history.
A Budget of Paradoxes, Volume II
Augustus De Morgan
A Budget of Paradoxes, Volume II
"A Budget of Paradoxes, Volume II" by Augustus De Morgan is a philosophical and mathematical treatise written in the mid-19th century. This volume continues to explore and critique various paradoxes and fallacies found in mathematical reasoning and philosophical arguments, particularly focusing on the works and thoughts of notable figures such as Laplace and Euler. De Morgan presents a unique combination of humor and rigorous analysis, discussing topics ranging from atheism in philosophy to the intricacies of astronomical theories. The opening of the volume discusses philosophical atheism, utilizing anecdotes about prominent historical figures like Laplace and Euler to illustrate the tensions between belief and reason. De Morgan provides insightful commentary on the nature of gods as hypotheses in philosophical discourse and critiques the approaches of modern paradoxers who challenge established scientific understanding. Through humorous storytelling, he presents critiques of absurd mathematical arguments, engaging readers with questions that challenge both their logical reasoning and understanding of science and belief.
The Fibonacci Number Series
Michael Husted
The Fibonacci Number Series
"The Fibonacci Number Series" by Michael Husted is a scientific publication, likely written in the late 20th century or early 21st century. This work presents a detailed enumeration of the Fibonacci numbers up to the first thousand terms, showcasing their fascinating properties and sequences. At the start of the publication, the author provides a structured list of the Fibonacci numbers, spanning from the very first number, 1, to the 1,073,210,323,786,401st, highlighting the increasing number of digits in each successive term. The layout is straightforward, featuring simple entries that incrementally present each Fibonacci number alongside its corresponding number in the sequence, which is useful for readers interested in number theory or mathematical properties related to Fibonacci sequences. The meticulous presentation suggests that the book is designed both for educational purposes and for enthusiasts seeking an extensive resource on Fibonacci numbers.
Memorabilia Mathematica; or, the Philomath's Quotation-Book
Unknown
Memorabilia Mathematica; or, the Philomath's Quotation-Book
"Memorabilia Mathematica; or, the Philomath's Quotation-Book" by Robert Edouard Moritz is a collection of mathematical quotations written in the early 20th century. This work brings together over a thousand quotations from various thinkers, discussing diverse perspectives on mathematics and its significance in understanding the world. The book aims to serve as a valuable resource for teachers, writers, and enthusiasts of mathematics, providing inspiration and insight into the discipline's philosophical and practical implications. The beginning of the book includes a preface in which Moritz outlines the purpose and scope of the collection. He notes the importance of precise references for each quote and discusses the challenges of compiling such a comprehensive anthology. The opening introduces the reader to a series of notable thoughts on the nature of mathematics, indicating that it encompasses a wide range of views from poets, philosophers, and mathematicians, all conveying a deep appreciation for the subject. Moritz expresses hope that the work will encourage both mathematicians and laypersons to engage more fully with the beauty and depth of mathematical thought.
The Quarterly Journal of Science, Literature and the Arts, July-December, 1827
Various
The Quarterly Journal of Science, Literature and the Arts, July-December, 1827
"The Quarterly Journal of Science, Literature and the Arts, July-December, 1827" is a scientific publication produced in the early 19th century. The journal includes a collection of scholarly articles covering a wide range of topics in science, art, and literature, presenting research findings, reviews, and experimental observations. Readers can expect insights into various scientific advancements, artistic inquiries, and intellectual discourses reflective of the period's pursuit of knowledge. The opening of this volume begins by establishing the broad scope of the journal and its content. It features articles that explore mathematical relationships in aesthetics, such as the beauty inherent in ovals and elliptic curves, as well as examinations of novel applications in microscopy using diamond lenses. The discourse introduces geometrical concepts in aesthetic appreciation and highlights the significance of scientific inquiry into the properties of natural phenomena, setting a tone that promises a blend of art and science throughout the publication. This opening section emphasizes a commitment to rigorous scientific analysis and aesthetic philosophy, appealing to readers interested in the intersections of these fields.
The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
Henri Poincaré
The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method
"The Foundations of Science: Science and Hypothesis, The Value of Science" by Henri Poincaré is a philosophical work published in 1904. This French mathematician and physicist explores fundamental questions about how science works, examining the interplay between intuition and logic in mathematics, and the deep connections between mathematical theory and physical reality. Poincaré investigates how scientists choose theories, why mathematical language proves essential for physics, and confronts emerging crises challenging established principles like energy conservation and Newton's laws at the dawn of the twentieth century.
Archimedes
Thomas Little Heath
Archimedes
"Archimedes" by Sir Thomas Little Heath is a historical account written in the early 20th century. The book explores the life and contributions of Archimedes, one of the greatest mathematicians of antiquity, detailing his discoveries in mathematics and mechanics as well as his innovative mechanical inventions. It highlights Archimedes's profound influence on science and mathematics, showcasing both his theoretical advancements and practical applications. The opening of the text introduces Archimedes as a figure often remembered for popular anecdotes—like his famed "Eureka" moment—but suggests that few understand the depth of his mathematical genius. The narrative provides a brief overview of his life, including significant events such as his role during the siege of Syracuse and his tragic death. It mentions his friendships with other intellectuals of his time and states his dedication to mathematics over practical mechanics, indicating that his greatest achievements lie in theoretical research rather than in invention for everyday utility.
A Philosophical Essay on Probabilities
Pierre Simon Laplace
A Philosophical Essay on Probabilities
"A Philosophical Essay on Probabilities" by Pierre Simon, Marquis de Laplace is a scientific publication written in the early 19th century. This work delves deeply into the concepts of probability, analyzing its foundational principles and applying them to various aspects of life, mathematics, and the natural sciences. It aims to establish a framework for understanding probability and its relation to human knowledge, decision-making, and hope. At the start of the essay, Laplace introduces the topic of probability by discussing its relevance and application to everyday life, emphasizing that much of human knowledge is inherently probabilistic. He reflects on how historical interpretations of chance have evolved from mystical understandings to a more analytical perspective. He articulates the relationship between causes and effects, setting the stage for a detailed exploration of probability theory, its definitions, principles, and its implications across different fields. The discussion is framed in a formal and philosophical context, inviting readers to consider the significant role that probability plays in our understanding of the universe.
Flatland: A Romance of Many Dimensions
Edwin Abbott Abbott
Flatland: A Romance of Many Dimensions
"Flatland: A Romance of Many Dimensions" by Edwin Abbott Abbott is a satirical novella published in 1884. The story takes place in a two-dimensional world inhabited by geometric shapes, where social status is determined by the number of one's sides. When a Square encounters beings from other dimensions—including a one-dimensional Lineland and a three-dimensional Spaceland—his understanding of reality is profoundly challenged. Through this imaginative premise, Abbott satirizes Victorian class and gender hierarchies while exploring the concept of dimensions beyond human perception.
Logic: Deductive and Inductive
Carveth Read
Logic: Deductive and Inductive
"Logic: Deductive and Inductive" by Carveth Read is a scientific publication written in the late 19th century. The book explores the principles of logic, focusing on how propositions can be proved, classified, and employed in various fields of knowledge. It delves into both deductive and inductive reasoning, aiming to provide a comprehensive examination of logical principles and methods. The opening of the book introduces logic as a science that determines what conditions must be fulfilled for propositions to be proved, distinguishing between quantitative and qualitative propositions. Read discusses different types of proof, including immediate and mediate inference, and emphasizes that while logic outlines the structure of arguments, it does not seek to establish the truth of its foundational principles. The initial chapters are geared towards defining fundamental concepts in logic, such as propositions and terms, paving the way for deeper explorations of logical reasoning throughout the text.
The puzzle king : $b Amusing arithmetic, book-keeping blunders, commercial comicalities, curious "catches", peculiar problems, perplexing paradoxes, quaint questions, queer quibbles, school stories, interesting items, tricks with figures, cards, draughts, dice, dominoes, etc., etc., etc.
John Scott
The puzzle king : $b Amusing arithmetic, book-keeping blunders, commercial comicalities, curious "catches", peculiar problems, perplexing paradoxes, quaint questions, queer quibbles, school stories, interesting items, tricks with figures, cards, draughts, dice, dominoes, etc., etc., etc.
"The Puzzle King" by John Scott is a collection of amusing mathematical puzzles and problems written in the late 19th century. This engaging compilation features various entertaining math challenges, intriguing anecdotes, and whimsical stories aimed at both educating and amusing the reader. The author’s intention is to present these mathematical concepts in a light-hearted manner, making them accessible and enjoyable to a broad audience. The opening of "The Puzzle King" introduces the reader to the author's perspective on puzzles, emphasizing the importance of patience in solving them. Scott provides a whimsical preface where he references the legendary Gordius and his knot, hinting at the complexities that lie ahead. The excerpt features a series of intriguing mathematical concepts and entertaining anecdotes, such as a humorous take on the difficulties of misreading bills and amusing examples of puzzles that play with words and logic. This sets the tone for a book that promises not only to challenge the minds of readers but also to elicit a few laughs along the way.
Of the Just Shaping of Letters
Albrecht Dürer
Of the Just Shaping of Letters
"Of the Just Shaping of Letters" by Albrecht Dürer is a scientific publication written in the early 16th century. The book serves as a practical guide on the geometric principles behind the construction and design of letters, focusing particularly on the Latin alphabet and its applications in various artistic fields. Dürer, a renowned artist and theorist of the Northern Renaissance, emphasizes the importance of mathematics in artistic creation, advocating for a disciplined approach to the craft of writing and lettering. In this work, Dürer outlines detailed instructions for drawing each letter of the alphabet through a combination of geometric shapes and measurements. Each letter is encapsulated within a square, with specific ratios and proportions provided for achieving aesthetically pleasing results. Dürer's methodical approach includes visual illustrations demonstrating the step-by-step process for creating each letter, from "A" to "Z." The book not only instructs artists and artisans but also promotes a broader understanding of the relationship between geometry and the visual arts, thereby enriching the practice of letter-making in the context of the fine arts and craftsmanship of his time.
The mystery of space : $b a study of the hyperspace movement in the light of the evolution of new psychic faculties and an inquiry into the genesis and essential nature of space
Robert T. Browne
The mystery of space : $b a study of the hyperspace movement in the light of the evolution of new psychic faculties and an inquiry into the genesis and essential nature of space
"The Mystery of Space" by Robert T. Browne is a scientific publication written in the early 20th century. The book delves into the concept of hyperspace, exploring its implications on both mathematical thought and the evolution of human consciousness. It examines how the understanding of space has developed historically and philosophically, considering its relationship with mathematics, psychology, and spirituality. The opening of the book sets the stage for a deep intellectual inquiry into the nature of space and the emergence of new psychic faculties. Browne discusses the limitations of conventional thought and the necessity for intellectual evolution in order to grasp higher dimensions beyond the three-dimensional reality humans typically perceive. He argues that the journey to understanding hyperspace reflects humanity's broader evolutionary potential, suggesting that the development of thought itself is a dynamic process that progresses through distinct stages. Through this framework, he invites readers to reconsider their understanding of space and encourages the exploration of intuitive insights that lie beyond mere mathematical reasoning.
Jerome Cardan: A Biographical Study
W. G. (William George) Waters
Jerome Cardan: A Biographical Study
"Jerome Cardan: A Biographical Study" by W. G. Waters is a historical account written in the late 19th century. This work centers on the life and contributions of Girolamo Cardano, a notable figure of the Renaissance known for his work in mathematics and medicine, as well as his tumultuous personal life marked by adversity and the stigma of illegitimacy. The narrative explores his childhood, education, and the challenges he faced as he grew into a polymath whose contributions would resonate through history. The opening of the biography introduces Cardano's background, highlighting the circumstances surrounding his illegitimate birth and the significant health challenges he faced from infancy. It portrays a complex family dynamic, particularly with his father, Fazio Cardano, who imparted both knowledge and a certain harshness. As the story unfolds, it reveals Cardano's early physical ailments, the difficult relationships with his parents, and the personal toll that his upbringing took on him. These themes set the stage for a life characterized by both brilliance and struggle, emphasizing how his early experiences shaped his later achievements and misfortunes.
A Tangled Tale
Lewis Carroll
A Tangled Tale
"A Tangled Tale" by Lewis Carroll is a collection of 10 humorous stories published serially between 1880 and 1885. Each "Knot" presents mathematical puzzles cleverly disguised within witty narratives featuring recurring characters—knights debating distances, an overbearing aunt and her sharp niece, befuddled professors, and hapless travelers. Carroll later published solutions, playfully critiquing readers' answers by name. These tales combine arithmetic, algebra, and geometry with Carroll's signature charm, creating an ingenious blend of storytelling and mathematical challenge that delighted some readers while perplexing others.
A List of Factorial Math Constants
Unknown
A List of Factorial Math Constants
"A List of Factorial Math Constants" by Unknown is a scientific publication likely composed in the late 20th century. This work serves as a compilation of factorial values for integers ranging from 1 to 10,000, categorized in groups to facilitate access for researchers or students needing precise mathematical constants. The opening of this compilation provides a structured list of factorials for numbers 1! through 99!, displayed alongside their decimal representations, and indicates the factorials from 100! to 10,000! will follow in larger increments. It specifies the method used for calculation, a simple Scheme program whose source code has unfortunately been lost. Each entry denotes the factorial and concludes with a note indicating the number of digits in the result, illustrating an organized and systematic approach to presenting mathematical information.
The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements
Proclus
The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements
"The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements" is a scholarly work likely written in the late 18th century. This publication delves into the intricate relationship between mathematics and philosophy, emphasizing how geometry serves as a pathway to understanding higher theological concepts. Proclus, revered for his interpretations of Platonic and Pythagorean thought, brings to light the profound significance of mathematics beyond practical applications, positioning it within the realms of metaphysics and divine understanding. The opening of this work introduces the author’s design to explore the nature and purpose of mathematics, particularly geometry, through a philosophical lens. Proclus posits that true understanding of geometry leads one towards divine knowledge, contrasting this intellectual pursuit with the mere mechanical application of mathematics in mundane activities. Additionally, the Preface highlights the challenges of translating ancient philosophical texts due to their profound and complex nature, suggesting that mastery of these ideas requires not only intellectual rigor but a deep engagement with the philosophical tradition to truly grasp the universal truths that geometry embodies.
The Game of Logic
Lewis Carroll
The Game of Logic
"The Game of Logic" by Lewis Carroll is a book published in 1886. Using a playful board game with colored coins, Carroll transforms abstract logical propositions into tangible puzzles. Players place red and gray coins across quadrants representing variations of statements like "Some fresh cakes are sweet." The system progresses from simple two-part diagrams to complex three-dimensional problems, teaching syllogisms and logical reasoning through interactive play. This mathematical work reveals Carroll's lesser-known identity as an academic logician.
The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara
John Dee
The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara
"The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara" by John Dee is a scholarly work associated with mathematical literature written in the late 16th century. This treatise serves as an introduction to the translations of Euclid's geometric works, providing significant insights into the importance of mathematics and geometry for personal and societal development. The book emphasizes the foundational nature of Euclidian principles in understanding more complex mathematical concepts and applications. The opening of the text sets a contemplative tone, highlighting the value of mathematical sciences and their influence on the soul and mind of humankind. Dee stresses that true knowledge is gained through diligent study of geometry, specifically through Euclid’s methodical approach. He outlines the different mathematical disciplines, includes a historical context for their significance, and addresses the challenges faced by scholars in bringing this knowledge to a wider English-speaking audience. John Dee’s preface ultimately serves as an encouragement for readers to engage deeply with the studies of mathematics in pursuit of wisdom and a better understanding of the natural world.
An Elementary Course in Synthetic Projective Geometry
Derrick Norman Lehmer
An Elementary Course in Synthetic Projective Geometry
"An Elementary Course in Synthetic Projective Geometry" by Derrick Norman Lehmer is a scientific publication written in the early 21st century. This work focuses on the principles and fundamental concepts of synthetic projective geometry, aiming to present the topic in an accessible manner for both college students and potentially for secondary education. The text emphasizes the importance of understanding geometric relationships and structures without reliance on measurement, highlighting the significance of one-to-one correspondences and projective properties. The beginning of the course outlines the author's motivations and pedagogical approach, which departs from traditional methods to provide a clearer understanding of synthetic projective geometry. Lehmer explains the foundational concepts, such as one-to-one correspondence and the relationships among different geometric forms, like point-rows and pencils of rays. He stresses the necessity of a solid grounding in elementary geometry for students, suggesting that those with additional knowledge in analytical geometry and calculus will find the material easier to comprehend. This foundation prepares readers for a deeper exploration of projective relations, constructions, and theorems laid out in subsequent chapters.
Mathématiques et Mathématiciens: Pensées et Curiosités
Unknown
Mathématiques et Mathématiciens: Pensées et Curiosités
"Mathématiques et Mathématiciens: Pensées et Curiosités" by A. Rebière is a collection of philosophical reflections and curiosities related to mathematics, written in the late 19th century. This work explores various mathematical concepts, theories, and the significance of mathematics in different fields through insights from historical and contemporary thinkers. The opening of this work sets the stage by discussing the nature of mathematics and its various branches such as arithmetic, geometry, and astronomy. It poses essential questions about the definition and scope of mathematics, indicating that it deals primarily with notions of order and measurement. The text includes quotes from influential philosophers and mathematicians like Aristotle, Descartes, and Kant, offering a glimpse into the foundational ideas that shape mathematical inquiry. Rebière emphasizes the importance of mathematics as a science of measuring and understanding the relationships between quantities, hinting at the book's broader examination of both abstract concepts and their practical applications.
Introduction to Mathematical Philosophy
Bertrand Russell
Introduction to Mathematical Philosophy
Wikipedia page about this book: https://en.wikipedia.org/wiki/Introduction_to_Mathematical_Philosophy
Sir Christopher Wren : $b Scientist, scholar and architect
Lawrence Weaver
Sir Christopher Wren : $b Scientist, scholar and architect
"Sir Christopher Wren: Scientist, Scholar and Architect" by Lawrence Weaver is a historical account written in the early 20th century. The book explores the life and contributions of Sir Christopher Wren, renowned for his achievements in architecture, science, and mathematics. Weaver aims to present impressions of Wren's multifaceted life rather than a comprehensive biography, capturing the essence of a man who significantly shaped England's architectural landscape. The opening of the book introduces Wren's background, highlighting his birth into a well-regarded family and detailing his early education. It emphasizes his precociousness and diverse talents, particularly in mathematics and invention, noting that Wren developed significant ideas from a young age. Furthermore, the author discusses the importance of Wren's father as a guiding influence during his vulnerable childhood and sets the stage for Wren's eventual ascent as one of England's most important figures in both science and architecture.
Geschichte der Mathematik im Altertum in Verbindung mit antiker Kulturgeschichte
Max Simon
Geschichte der Mathematik im Altertum in Verbindung mit antiker Kulturgeschichte
"Geschichte der Mathematik im Altertum in Verbindung mit antiker Kulturgeschichte" by Dr. Max Simon is a historical account written in the early 20th century. This work explores the evolution of mathematics in ancient civilizations, particularly focusing on its connections with cultural developments in Egypt, Babylon, and beyond. Through detailed analysis, the book aims to provide insights into how mathematical concepts and practices influenced and were influenced by the respective societies of the time. The opening of this text serves as a preface and introduction to the author’s extensive examination of ancient mathematics. Dr. Simon outlines the lack of historical accounts prior to the 18th century and emphasizes the necessity of historical context in understanding mathematical development. He highlights significant figures and their contributions, such as Montucla and Cantor, and discusses early civilizations’ mathematical practices, including Egypt and Babylon. Simon also sets the stage for a discussion of various mathematical concepts that have evolved over centuries, suggesting that mathematics, far from being a rigid discipline, reflects the dynamic cultural and intellectual landscapes of the ancient world.
Elements of arithmetic
Augustus De Morgan
Elements of arithmetic
"Elements of Arithmetic" by Augustus De Morgan is a mathematical textbook written in the mid-19th century. The work serves as a foundational guide to arithmetic, focusing on principles and reasoning rather than rote calculations, making it suitable for both students and educators. The text aims to establish a solid understanding of arithmetic concepts, laying out the basic operations, such as addition, subtraction, multiplication, and division, while emphasizing the importance of reasoning in mathematics. The opening of the book includes a preface that outlines De Morgan's intent, stating that this edition contains significant appendixes aimed at aiding advanced students. It discusses the importance of teaching arithmetic through reasoning rather than mere routine and highlights the need for a rational approach to mathematics. Following the preface, the first section introduces numeration, illustrating how different counting methods were used throughout history with examples of simple counting techniques and their evolution into more complex systems, ultimately leading into structured numeral systems. This thoughtful approach sets a clear foundation for understanding arithmetic principles.
The Number Concept: Its Origin and Development
Levi L. (Levi Leonard) Conant
The Number Concept: Its Origin and Development
"The Number Concept: Its Origin and Development" by Levi L. Conant is a historical and scientific publication written in the late 19th century. This work delves into the origins and evolution of numerical systems across various cultures, exploring their significance in human development and communication. The likely topic of the book revolves around the concept of counting, the language of numbers, and how different societies have expressed numerical ideas. At the start of the book, Conant introduces the reader to the complex questions surrounding the origin of number systems and the ways primitive languages have approached counting. He discusses the limitations observed in various tribal languages, where concepts may only extend to basic numerals, often highlighting a disconnect in the ability to comprehend higher numbers. The opening chapters explore distinct numeral systems used by different cultures and assert that the idea of counting seems fundamental to humanity, tracing the evolution of numerical expression through both linguistic and practical methods.
Pascal
John Tulloch
Pascal
"Pascal" by John Tulloch is a biographical account written in the late 19th century. The book explores the life and works of Blaise Pascal, a prominent figure in literature, science, and religion, known for his precocious intellect and contributions to mathematics and philosophy. Through its chapters, the text delves into Pascal's family background, his early intellectual development, significant scientific discoveries, and his role within the religious and philosophical debates of his time. The opening of the work sets the stage for understanding the significance of Pascal's life and legacy. It begins with a preface that acknowledges various translations of Pascal's writings, notably his "Provincial Letters" and "Pensées." Tulloch then introduces Pascal's formative years, detailing his family's influence, his remarkable early achievements in mathematics, and the notable friendships he formed with contemporaries like Descartes and Mersenne. The narrative emphasizes Pascal's intellectual curiosity, extraordinary capabilities from a young age, and the challenges he faced, including health issues and an evolving spiritual life that led him to eventual religious fervor. The text offers a glimpse into the complex personality of Pascal, setting up an exploration of his lasting impact in multiple domains.
The philosophy of mathematics
Auguste Comte
The philosophy of mathematics
"The Philosophy of Mathematics" by Auguste Comte is a scientific publication written in the mid-19th century. The book delves into the fundamental aspects of mathematical science, analyzing its nature, scope, and methods. Through comprehensive examination, it aims to provide a deeper understanding of mathematics not merely as a collection of techniques but as a profound scientific discipline interconnected with various branches of knowledge. The opening of the book sets the stage for Comte's exploration of mathematical philosophy by discussing the historical context and necessity of clearly defining the scope and divisions of mathematics. Comte argues that while mathematics is the most ancient and perfected of sciences, its true nature is often misunderstood due to vague definitions. He emphasizes the importance of indirect measurement in mathematics and outlines the methodological evolution that has allowed mathematicians to derive quantities from one another using established relationships. He anticipates a systematic classification of mathematical inquiries, which further frames the discussion for the chapters that will follow. This introduction establishes a philosophical foundation that Comte will build upon as he navigates complex ideas related to both abstract and concrete mathematics.
The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion.
P. H. (Peter Hampson) Ditchfield
The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion.
"The Romance of Mathematics" by P. H. Ditchfield is a scientific publication written in the late 19th century. The work explores original mathematical theories and their social applications, particularly through the lens of a fictional Lady Professor from Girtham College. The book delves into topics such as the social properties of geometrical figures, the application of mathematics to politics, and the impact of mathematical principles on social dynamics. The opening of the text introduces the reader to the framework of the book, revealing that the Lady Professor's lectures and essays were discovered in a well-worn desk and promising an exploration of her groundbreaking thoughts. The introduction discusses her qualifications and the potential societal implications of her mathematical insights, suggesting that principles governing mathematics also apply to social structures. Ditchfield sets the stage for a thoughtful analysis of how various mathematical concepts relate to political science and social behaviors, particularly emphasizing the importance of women’s contributions to academia and progress.
The Atlantic Monthly, Volume 05, No. 28, February, 1860 A Magazine of Literature, Art, and Politics
Various
The Atlantic Monthly, Volume 05, No. 28, February, 1860 A Magazine of Literature, Art, and Politics
"The Atlantic Monthly, Volume 05, No. 28, February, 1860" by Various is a literary magazine written in the mid-19th century. This volume features a rich collection of essays, discussions, and reflective pieces on various topics, highlighting the themes of literature, art, and politics that were prominent during this era. In this installment, readers can expect an exploration of ideas ranging from counting and measuring in mathematics to deeper philosophical musings on human relationships and societal norms. At the start of this volume, the article on "Counting and Measuring" discusses the evolution of numerical systems and their implications for commerce and daily life. It emphasizes the historical significance of various counting methods from ancient civilizations, leading up to the nuanced understanding of binary and decimal systems. The beginning section is analytical, aiming to illustrate how these systems impact numerical operations and societal conventions. Additionally, it features a narrative segment, introducing a personal voice reflecting on themes of love and self-awareness, marking the transition into more personal and philosophical matters that are explored later in the volume.
The calculating engine
Charles Babbage
The calculating engine
"The Calculating Engine" by Charles Babbage is a scientific publication written in the early 19th century. This groundbreaking work discusses Babbage's innovative concept of a mechanical calculating machine intended to automate complex calculations and produce error-free numerical tables. It offers insight into the design, principles, and societal implications of his invention, positioning it as a transformative tool for both science and technology. The opening of the text establishes a context for Babbage's ambitious project, highlighting his intellectual stature and the significance of his work. It elaborates on the current state of mathematical tables, addressing the widespread inaccuracies in manually computed data and the urgent need for a reliable mechanism capable of producing precise calculations. Babbage argues for the immense utility of such machinery in various fields, particularly astronomy and navigation, and outlines the innovative mechanical principles behind his calculating engine. Through detailed descriptions, he aims to clarify the machine's design and capabilities, setting the stage for its eventual realization and the profound impact it could have on computation and information dissemination.