A treatise is a formal and systematic written

discourse
Discourse is a generalization of the notion of a conversation to any form of communication. Discourse is a major topic in social theory, with work spanning fields such as sociology, anthropology, continental philosophy, and discourse analysis. F ...

on some subject, generally longer and treating it in greater depth than an essay
An essay is, generally, a piece of writing that gives the author's own argument, but the definition is vague, overlapping with those of a Letter (message), letter, a term paper, paper, an article (publishing), article, a pamphlet, and a short ...

, and more concerned with investigating or exposing the principles of the subject and its conclusions."Treatise
A treatise is a Formality, formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusi ...

." Merriam-Webster Online Dictionary. Accessed September 12, 2020. A monograph
A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject.
In Library catalog, library catalo ...

is a treatise on a specialized topic.
Etymology

The word 'treatise' first appeared in the fourteenth century as the Medieval English word ''tretis'', which evolved from the Medieval Latin ''tractatus'' and the Latin ''tractare'', meaning to treat or to handle.Historically significant treatises

Table

The works presented here have been identified as influential by scholars on the development of human civilization.Discussion of select examples

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 asTheon of Alexandria
Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greeks, Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's ''Euclid's Elements, Elements'' and wr ...

, 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
Archimedes of Syracuse (;; ) was a Greeks, Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenistic Sicily, Sicil ...

and Apollonius of Perga
Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος, Apollṓnios ho Pergaîos; la, Apollonius Pergaeus; ) was an Ancient Greece, Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from t ...

, 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 ofMichael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, ...

, 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
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
Th ...

. 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
Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...

. 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
Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch people, Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived ...

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
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...

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
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

thus found a new foundation in electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

.
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
Guglielmo Giovanni Maria Marconi, 1st Marquis of Marconi (; 25 April 187420 July 1937) was an Italians, Italian inventor and electrical engineering, electrical engineer, known for his creation of a practical radio wave-based Wireless telegrap ...

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
Radio broadcasting is transmission of audio signal, audio (sound), sometimes with related metadata, by radio waves to radio receivers belonging to a public audience. In terrestrial radio broadcasting the radio waves are broadcast by a land-b ...

became extremely popular in the twentieth century and remains in common use in the early twenty-first. But it was Oliver Heaviside
Oliver Heaviside Fellow of the Royal Society, FRS (; 18 May 1850 – 3 February 1925) was an English Autodidacticism, self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the La ...

, 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 the Josiah Willard Gibbs, Heaviside assembled a set of mathematical tools known as vector calculus
Vector calculus, or vector analysis, is concerned with derivative, differentiation and integral, integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for ...

to replace the quaternion
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...

s, which were in vogue at the time but which Heaviside dismissed as "antiphysical and unnatural."
See also

* Compilation thesis *Edited volume An edited volume or edited collection is a collection of scholarly or scientific chapters written by different authors. The chapters in an edited volume are original works (not republished works).
Alternative terms for edited volume are ''contribut ...

*Legal treatise
A legal treatise is a scholarly legal publication containing all the law relating to a particular area, such as criminal law or trusts and estates. There is no fixed usage on what books qualify as a "legal treatise", with the term being used broadl ...

* Tractate
* Tractatus
References

External links

* {{Authority control Philosophical literature Science books Architectural history