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Who is Euclid?

Euclid of Alexandria (ancient Greek Εὐκλείδης Eukleídēs, Latin Euclid) was a Greek mathematician who probably lived in the 3rd century BC. He is often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323-283 BC). His Elements is one of the most influential works in the history of mathematics, and from the time of its publication to the main thread for teaching mathematics (particularly geometry) from the time of its publication to the late 19th or early 20th century, in Elements, Euclid deduced from a small set of axioms the theorems of what is now called Euclidean geometry. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigor.

The Life of Euclid

Almost nothing is known about Euclid's life. From a note he gave to Pappus of Alexandria, it was concluded that he was working in the city of Alexandria, Egypt. Their life date is unknown, except that it is assumed to be around 300 BC. This assumption is based on a list of mathematicians in Proclus, but other evidence suggests that Euclid was slightly younger than Archimedes. It was concluded from a study in Proklos that he lived around 360 BC. Born in Athens, he received his education at Plato's Academy and later studied in Alexandria under Ptolemäus I. Not to be confused with „Euclid of Megara“, as was often the case until the early modern period. So much so that the name of Euclid from Megara was also included in the titles of the editions of the elements. Because the lack of biographical information was unusual for the period (extensive biographies exist for the most important Greek mathematicians several centuries before and after Euclid), some scholars have suggested that Euclid was not a historical figure and that his works were written by a team: Euclid's Adini Euclid of Megara. from mathematicians. However, this hypothesis is not well accepted by scientists and there is little evidence in favor of it.

Works

The surviving works cover all areas of ancient Greek mathematics: these are the theoretical disciplines of arithmetic and geometry (elements, data) or applied studies (optics, astronomical phenomena). In his most famous work The Elements (ancient Greek Στοιχεῖα Stoicheia, „The Elements“), he brought together the knowledge of Greek mathematics of his time. Russell argued that The Elements is the greatest book ever written. In this book, he showed the construction of geometric bodies, natural numbers and certain dimensions, and examined their properties. For this he used definitions, postulates (acceptable or rejectable, according to Aristotelian principles) and axioms (according to Aristotle's general and undoubted principles). Many theorems of the elements apparently do not come from Euclid himself. Its main achievement consisted mostly of the collection and uniform representation of mathematical knowledge, as well as the rigid argumentation that became the model for later mathematics.

Postulate:

  • It is possible to draw a straight line from any point to any other point.
  • It is possible to extend one line segment continuously in both directions.
  • It is possible to define a circle with any center and any radius.
  • It is true that all right angles are equal.
  • EGER If a line is drawn that intersects two lines, if the sum of the two angles on the side of the two lines facing each other and on one side of the line intersecting them is less than two perpendicular Acids, these two lines continue to be extended on the side where the sum of the angles is less than two perpendicular Acids. It is true that they will intersect. (This postulate is known as parallel lines do not intersect.)

Axioms:

  • Things that are equal to one thing are also equal to each other.
  • If equal quantities are added to equal quantities, the resulting quantities are also equal to each other.
  • If equal quantities are subtracted from equal quantities, the remainders are also equal.
  • Things that overlap (in terms of properties) are equal to each other.
  • The whole is greater than the part.
Elements were the basis of geometry lessons in many places, especially in the Anglo-Saxon region, until the 20th century. The surviving Writings of Euclid, in addition to the elements, the data, and the division of the canon, are: Optika, On the division of numbers (preserved in quotations in an Arabic translation), Phaenomena (a treatise on spherical astronomy survives in Greek; Autolykos von Pitane' developed around 310). Quite similar to 's On the Moving Sphere.). Only the names of other works are known: Pseudaria (false), Katoptrika.





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