How was euclid achievement important for the study of geometry

Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry. The standard geometry most of us learned in school is called Euclidian Geometry. Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called 'The Elements' (c300 BCE). This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time.

Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory. The books are organized by subjects, covering every area of mathematics developed by the Greeks:

Books I - IV, and Book VI: Plane Geometry Books XI - XIII: Solid Geometry Books V and X: Magnitudes and Ratios Books VII - IX: Whole Numbers

The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed 465 propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.' He looked at mathematics as a whole, but was concentrated on geometry and that particular discipline formed the basis of his work.

Aunitary state is a form of state where power is concentrated and there is a single center of power that extends its actions throughout the territory of the respective state. this, through its agents and local authorities, delegates of that same central power, and in its majority; it can count on a single legislating apparatus; except for certain exceptions, which legislate for the entire country; a judicial power, which applies the current law to the entire territory of the state and within which a supreme court of justice is established, which has jurisdiction at the national level; a single executive power, that is conformed by all the governors (president, governors, mayors, etc.); and a single political constitution, which governs all the territory and to which all the authorities and inhabitants of the state are subject.a confederation (from the latin: confœderatĭo) consists of the union of states that retain their sovereignty and are governed by certain common laws. initially there was talk of "confederation" in the case of alliances, for this reason the word "confederation" is still used in non-governmental civil society institutions. for this reason, the term confederation is also used to describe any type of organization that combines the authority derived from other semi-autonomous entities. in this case, sports confederations can be cited as some examples. however, the word confederation takes much more relevance when it comes to some permanent alliance of states or some association or association of states.characteristics of a federal government system

  a) written constitution. also known as magna carta and a necessity of the democracies that form federations to regulate the principles by which the government will be governed, because if they had to act without a body of specific laws would produce confrontations.

b) territorial division. federalism is constituted by the division of powers on the geographical basis of each territory.

c) decentralization. in a federal system there is both a central government and units of government lower than the central one, each making decisions regarding the provision of certain public services in their respective geographical jurisdictions.

d) supreme court of justice. to counteract the rigidity of the written constitution, judicial action is required to interpret said constitution and necessary changes can be made.

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