Mathematics

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1980.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.

Contents: (1) Historical Overview; & Descartes’s Perspectivist Sources; (2) Analysis of Refraction: Cartesian Light-Theory; & A Critical Evaluation; (3) The Foundations of Perspectivist Optics: Perspectivist Light-Theory; Quantization of Light; & Comparison with Descartes’s Theory of Light; (4) The Perspectivist Analysis of Refraction: Physical Model; Physical “Explanation” & The Final Cause; (5) Perspectivist Grounds of the Cartesian Proof: Mathematical Implications; From Cosines to Sines; & Descartes Revisited; (6) Cartesian Light-Theory as a Culmination; Toward a Kinetic Theory of Light; & Epistemological Consequences. App.: The Sine-Law Before Descartes; The Fermat-Descartes Controversy; & Kepler, Descartes & the Anaclastic. Illustrations.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1965.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.

Contents: (I) The Place of Practical Geometry in the Middle Ages: The Nature of Practical Geometry; Practical Geometry in Education; Theory and Practice in Geometry; and Practical Geometry and Practical Concerns; (II) The Contents of “Artis cuiuslibet consummatio” and the “Pratike de geometrie”; (III) Procedures in the Editions, Translations, and Commentary: Editing “Artis cuiuslibet consummatio”; Editing the “Pratike de geometrie”; Translating the Texts; and About the commentary; and (IV) English translation of “Arts cuiuslibet consummatio” and of the “Pratike de geometrie.” Selected Bibliography, Index of Latin Technical Terms, Index of Old French Technical Terms, and Index of Astronomical Parameters. Illus.

This is a print on demand edition of an important, hard-to-find publication. Illustration.

This is a print on demand edition of an important, hard-to-find publication.

Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege’s primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege’s meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell.

Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege’s exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the system’s semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege’s precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege’s ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance to modern philosophical inquiries into meaning and language.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1979.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1981.