According to the dictionary of the **Royal Spanish Academy** (**RAE** ), the term **disquisition** derives from the Latin word *disquisite* And it has two meanings. The first refers to a **Exhaustive analysis** something is done, studying its various components or parts in detail.

For example: *“In his new test , the Spanish author carried out a profound disquisition about the human condition ”*,

*"The acquisition of profitability is key in any productive project"*,

*"The coach embarked on the disquisition of statistics last year to try to discover what are the aspects that the team should improve more urgently"*.

** "Arithmetic Disquisitions"** (or

**), meanwhile, is the title of a**

*“Arithmeticae Disquisitions”***book**published by the German mathematician, physicist and astronomer

**Carl Friedrich Gauss**(1777-1855). In this work, the author investigates different number theories proposed by other specialists and incorporates various own discoveries.

With respect to **Gauss** It is important to note that it was a scientist whose knowledge covered mathematics, astronomy and physics, among other fields, and his contributions were really considerable for the study of statistics, algebra, differential geometry, optics, mathematical analysis and number theory. In fact, within mathematics it is one of the figures that greatest **influence** He has had in history.

The book about the disquisitions was published in 1801, although later more versions were published. Some of the mathematicians specialized in the field of **theory** of numbers whose results Gauss compiled in this work are **Euler, Fermat, Legendre** and **Lagrange** , four characters of great recognition for the connoisseurs of the subject.

In addition to his discoveries about elementary number theory, Gauss included in the book some concepts that are currently framed in the **algebraic number theory** . In its pages, however, there is no explicit recognition of *group* as a concept, although today it is a fundamental part of **algebra** . In the preface he described the approach of the work, where he established that it would deal with integers and, to a lesser extent, fractions, but not irrational numbers.

The seven sections in which the book is divided *"Arithmetic Disquisitions"* are the following, according to **themes** that address: congruent numbers in general; 1st grade congruences; power residues; 2nd grade congruences; indeterminate equations and 2nd grade forms; fields of application of all the above; sections of circles and equations to define them. Gauss wrote one more section, but it was only published after his death.

The **idea** of disquisition, on the other hand, may refer to a **digression** or a **talk** , according to the second meaning mentioned by the **RAE** . In these cases, the disquisitions consist of speeches that move away from the main issue or subject to which reference was being made, or that develop without a specific purpose: *"Let's not waste more time on disquisitions and get to the point"*, *"If you allow me the disquisition, I would like to tell you how I met Dr. Frollometti more than twenty years ago"*, *"After a brief methodological disquisition, the scientist began to develop his theory before an audience that listened to it with great attention"*.

Although this word is not for everyday use, it has several synonyms that do appear in popular language. Through them we can delve a little deeper into the meaning of *disquisition*: *reasoning, reflection, investigation* and

*commentary*. As with other terms of a similar nature,

*disquisition*It does not have a direct antonym, since in any case we could talk about the "lack of disquisition" or "investigation", for example.