Treatise

A treatise is a formal and systematic written discourse on some subjects concerned with investigating or exposing the main principles of the subject and its conclusions."Treatise." Merriam-Webster Online Dictionary. Accessed September 12, 2020. A monograph is a treatise on a specialized topic."Monograph." Merriam-Webster Online Dictionary. Accessed September 12, 2020.

Etymology The word "treatise" originated in the early 14th century. It is derived from the Anglo-French term tretiz, which itself comes from the Old French traitis, meaning "treatise" or "account." This in turn was derived from the verb traitier, which means "to deal with" or "to set forth in speech or writing".

The etymological lineage can be traced further back to the Latin word tractatus, which is a form of the verb tractare, meaning "to drag about" or "to deal with".

Historically significant treatises

Table The works presented here have been identified as influential by scholars on the development of human civilization. Title Author Year of first edition Subject Influence reference The Art of War Sun Tzu ~500BCE War Reference The Elements Euclid ~300BCE Mathematics Reference Arthashastra Kautilya ~200BCE Statecraft Reference Vitruvius ~30BCE Architecture Reference Almagest Claudius Ptolemaeus 200s Astronomy Reference The Book of Pastoral Rule Pope Gregory I 590 Ethics Reference Vivekacūḍāmaṇi Adi Shankara 700s Philosophy Reference First Grammatical Treatise Anonymous 1200s Linguistics Leon Battista Alberti 1485 Architecture Reference The Prince Niccolò Machiavelli 1532 Politics Reference De revolutionibus orbium coelestium Nicolaus Copernicus 1543 Astronomy Reference Discourse on the Method René Descartes 1637 Philosophy ReferenceLa GéométrieRené Descartes1637MathematicsReference Two Treatises of Government John Locke 1660 Government ReferencePhilosophiæ Naturalis Principia MathematicaIsaac Newton1687PhysicsJ. M. Steele, University of Toronto, (review online from Canadian Association of Physicists) of N. Guicciardini's "Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science".(in French) Alexis Clairaut, "Du systeme du monde, dans les principes de la gravitation universelle", in "Histoires (& Memoires) de l'Academie Royale des Sciences" for 1745 (published 1749), at p. 329 (according to a note on p. 329, Clairaut's paper was read at a session of November 1747).G. E. Smith, "Newton's Philosophiae Naturalis Principia Mathematica", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), E. N. Zalta (ed.). Treatise on Light Christiaan Huygens 1690 Physics Opticks Isaac Newton 1704 Physics Reference Principles of Human Knowledge George Berkeley 1710 Philosophy A Treatise of Human Nature David Hume 1739 PhilosophyIntroductio in analysin infinitorumLeonhard Euler1748Mathematics The Wealth of Nations Adam Smith 1776 Political Economy Reference Treatise on Instrumentation Hector Berlioz 1844 Music On the Origin of Species Charles Darwin 1859 Biology ReferenceDas Kapital Karl Marx 1867 Political Economy ReferenceA Treatise on Electricity and MagnetismJames Clerk Maxwell1873PhysicsReferenceThe Principles of Quantum MechanicsPaul Dirac1930PhysicsReferenceThe General Theory of Employment, Interest and MoneyJohn Maynard Keynes1936EconomicsReferenceTheory of Games and Economic BehaviorJohn von Neumann, Oskar Morgenstern1944Economics

Discussion

Euclid's Elements Euclid's Elements has appeared in more editions than any other books except the Bible and is one of the most important mathematical treatises ever. It has been translated to numerous languages and remains continuously in print since the beginning of printing. Before the invention of the printing press, it was manually copied and widely circulated. When scholars recognized its excellence, they removed inferior works from circulation in its favor. Many subsequent authors, such as Theon of Alexandria, made their own editions, with alterations, comments, and new theorems or lemmas. Many mathematicians were influenced and inspired by Euclid's masterpiece. For example, Archimedes of Syracuse and Apollonius of Perga, the greatest mathematicians of their time, received their training from Euclid's students and his Elements and were able to solve many open problems at the time of Euclid. It is a prime example of how to write a text in pure mathematics, featuring simple and logical axioms, precise definitions, clearly stated theorems, and logical deductive proofs. The Elements consists of thirteen books dealing with geometry (including the geometry of three-dimensional objects such as polyhedra), number theory, and the theory of proportions. It was essentially a compilation of all mathematics known to the Greeks up until Euclid's time.

Maxwell's Treatise

Drawing on the work of his predecessors, especially the experimental research of Michael Faraday, the analogy with heat flow by William Thomson (later Lord Kelvin) and the mathematical analysis of George Green, James Clerk Maxwell synthesized all that was known about electricity and magnetism into a single mathematical framework, Maxwell's equations. Originally, there were 20 equations in total. In his Treatise on Electricity and Magnetism (1873), Maxwell reduced them to eight. Maxwell used his equations to predict the existence of electromagnetic waves, which travel at the speed of light. In other words, light is but one kind of electromagnetic wave. Maxwell's theory predicted there ought to be other types, with different frequencies. After some ingenious experiments, Maxwell's prediction was confirmed by Heinrich Hertz. In the process, Hertz generated and detected what are now called radio waves and built crude radio antennas and the predecessors of satellite dishes. Hendrik Lorentz derived, using suitable boundary conditions, Fresnel's equations for the reflection and transmission of light in different media from Maxwell's equations. He also showed that Maxwell's theory succeeded in illuminating the phenomenon of light dispersion where other models failed. John William Strutt (Lord Rayleigh) and Josiah Willard Gibbs then proved that the optical equations derived from Maxwell's theory are the only self-consistent description of the reflection, refraction, and dispersion of light consistent with experimental results. Optics thus found a new foundation in electromagnetism.

The science of electromagnetism has made it possible to develop new technologies that have since become commonplace. One such example is Wireless communication, which did not require long and expensive cables and was faster than even the telegraph. Guglielmo Marconi adapted Hertz's equipment for this purpose in the 1890s. He achieved the first international wireless transmission between England and France in 1900 and by the following year, he succeeded in sending messages in Morse code across the Atlantic. Seeing its value, the shipping industry adopted this technology at once. Radio broadcasting became extremely popular in the twentieth century and remains in common use in the early twenty-first.

After contemplating Maxwell's Treatise, Gibbs and Oliver Heaviside independently sought to develop a new set of mathematical methods for physics and engineering known as vector calculus to replace the theory of quaternions, in vogue at the time but not ideal for describing electromagnetic phenomena. The modern notations for the vector cross and dot products were invented by Gibbs, whereas the idea of using bold letters to denote vectors came from Heaviside. But it was Maxwell himself who began the process of modernizing his own equations by identifying and naming some of the key vector operations, such as the "curl" and the "convergence" (or negative divergence) of a vector field, and the "slope" (or gradient) of a scalar field. Gibbs' lecture notes were later developed into a textbook, Vector Analysis (1901), by one of his students, Edwin Bidwell Wilson, and the subject itself has been applied to phenomena other than those of electricity and magnetism. On the other hand, Heaviside was largely responsible for shaping how people understood and applied Maxwell's work for decades to come. He wrote Maxwell's equations in the form familiar today, just four equations. He also made considerable progress in electrical telegraphy, telephony, and the study of the propagation of electromagnetic waves. Furthermore, the "operational calculus" employed by Heaviside in his work on electromagnetism and electrical engineering attracted much attention in the early twentieth century and was ultimately developed into the modern theory of the Laplace transform, now of ubiquitous usage and a standard part of the undergraduate curricula for the mathematical sciences and engineering.

One of Maxwell's guiding principles was that electromagnetic phenomena could be explained in terms of mechanical processes involving the stationary luminiferous ether, a hypothetical medium through which light travels, and this was how physicists initially interpreted the results of Hertz's experiments. However, the 1887 experiment of Albert Michelson and Edward Morley found no evidence for the Earth's motion through the ether. George Francis FitzGerald and Lorentz independently explained the Michelson–Morley experiment by proposing the contraction of objects as they move, a major step towards Albert Einstein's special theory of relativity. With special relativity, Einstein not only explained the FitzGerald–Lorentz contraction but also discarded the ether altogether.

But while Heaviside sought to banish potential functions from the theory, Maxwell's decision to keep them proved prescient. As Richard Feynman indicated in a 1964 lecture, "In the general theory of quantum electrodynamics, one takes the vector and scalar potentials as fundamental quantities."

Treatise

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