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Title page of Sir Isaac Newton's *Mathematical Principles of Natural Philosophy* (1687)

A treatise is a formal and systematic written discourse on some subject concerned with investigating or exposing the principles of the subject and its conclusions.^[1] A monograph is a treatise on a specialized topic.^[2]

Etymology

The word "treatise" has its origins in the early 14th century, derived from the Anglo-French term tretiz, which itself comes from the Old French traitis, meaning "treatise" or "account." This Old French term is rooted in the verb traitier, which means "to deal with" or "to set forth in speech or writing".^[3]

The etymological lineage can be traced further back to the Latin word tractatus, which is a form of the verb tractare, meaning "to handle," "to manage," or "to deal with".^[4]^[5] The Latin roots suggest a connotation of engaging with or discussing a subject in depth, which aligns with the modern understanding of a treatise as a formal and systematic written discourse on a specific topic.^[6]

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
De architectura	Vitruvius	~30BCE	Architecture	Reference
Almagest	Claudius Ptolemaeus	200s	Astronomy	Reference
The Book of Pastoral Rule	Pope Gregory I	590	Responsibility	Reference
Vivekacūḍāmaṇi	Adi Shankara	700s	Philosophy	Reference
Treatise on Tea	Emperor Huizong of Song	1107	Appreciation
First Grammatical Treatise	Anonymous	1200s	Linguistics
De re aedificatoria	Leon Battista Alberti	1485	Architecture	Reference
The Prince	Niccolò Machiavelli	1532	Politics	Reference
Treatise on Relics	John Calvin	1543	Authenticity
De revolutionibus orbium coelestium	Nicolaus Copernicus	1543	Astronomy	Reference
Discourse on the Method	René Descartes	1637	Philosophy	Reference
Two Treatises of Government	John Locke	1660	Government	Reference
Treatise on Man	René Descartes	1662	Biology
Philosophiæ Naturalis Principia Mathematica	Isaac Newton	1687	Physics	^[7]^[8]^[9]
Treatise on Light	Christiaan Huygens	1690	Natural World
Opticks	Isaac Newton	1704	Physics	Reference
Principles of Human Knowledge	George Berkeley	1710	Philosophy
A Treatise of Human Nature	David Hume	1739	Philosophy
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	Reference
Das Kapital	Karl Marx	1867	Political Economy	Reference
A Treatise on Electricity and Magnetism	James Clerk Maxwell	1873	Physics	Reference
A Treatise on Probability	John Maynard Keynes	1921	Mathematics
A Treatise on Money	John Maynard Keynes	1930	Economy

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.^[10]

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.^[11] 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.^[12] 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.^[11]

Hertz's experimental work in electromagnetism stimulated interest in the possibility of 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.^[12] But it was Oliver Heaviside, an enthusiastic supporter of Maxwell's electromagnetic theory, who deserves most of the credit for shaping how people understood and applied Maxwell's work for decades to come; he was responsible for considerable progress in electrical telegraphy, telephony, and the study of the propagation of electromagnetic waves. Independent of Gibbs, Heaviside assembled a set of mathematical tools known as vector calculus to replace the quaternions, which were in vogue at the time but which Heaviside dismissed as "antiphysical and unnatural."^[13]

References

^ "Treatise." Merriam-Webster Online Dictionary. Accessed September 12, 2020.
^ "Monograph." Merriam-Webster Online Dictionary. Accessed September 12, 2020.
^ "treatise | Etymology of treatise by etymonline". www.etymonline.com. Retrieved 2024-08-11.
^ "treatise | Etymology of treatise by etymonline". www.etymonline.com. Retrieved 2024-08-11.
^ "Treatise Definition & Meaning | YourDictionary". www.yourdictionary.com. Retrieved 2024-08-11.
^ Publishers, HarperCollins. "The American Heritage Dictionary entry: treatise". ahdictionary.com. Retrieved 2024-08-11.
^ J. M. Steele, University of Toronto, (review online from Canadian Association of Physicists) Archived 1 April 2010 at the Wayback Machine 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.).
^ Katz, Victor (2009). "Chapter 3: Euclid". A History of Mathematics – An Introduction. Addison-Wesley. ISBN 978-0-321-38700-4.
^ ^a ^b Baigrie, Brian (2007). "Chapter 9: The Science of Electromagnetism". Electricity and Magnetism: A Historical Perspective. United States of America: Greenwood Press. ISBN 978-0-313-33358-3.
^ ^a ^b Baigrie, Brian (2007). "Chapter 10: Electromagnetic Waves". Electricity and Magnetism: A Historical Perspective. United States of America: Greenwood Press. ISBN 978-0-313-33358-3.
^ Hunt, Bruce (November 1, 2012). "Oliver Heaviside: A first-rate oddity". Physics Today. 65 (11): 48–54. Bibcode:2012PhT....65k..48H. doi:10.1063/PT.3.1788.