Who is the author of Principles of Geometry and who is the original author of Geometry ?

Principia Geometry, also known as the Geometric Primitives, was written by the Greek mathematician Euclid around 300 BC and is the earliest example of using axiomatic methods to establish a system of deductive mathematics. It is the most widely circulated and influential mathematical masterpiece in the world so far.

The Geometry Originals consists of 13 volumes. Each volume, or several volumes together, begins with a definition. Volume I first gives 23 definitions, such as "a point has no parts", "a line has only a length but no width", and there are also definitions of plane, right angle, acute angle, obtuse angle, parallel line, etc.

After that, there are 5 public establishments. Euclid first assumed that the following diagram was possible:

1) Draw a straight line from one point to another;

2) a finite straight line is continuously extended;

3) Make a circle with an arbitrary center and radius. That is, he postulated the existence of points, lines, and circles as the basic elements of his geometry, so that he could prove the existence of other figures.

The fourth postulator assumes that all right angles are equal.

The fifth common assumption is the so-called parallel public assumption: If a straight line intersects two straight lines so that the inner angles of the same side are less than two right angles, then the two straight lines, if extended, must intersect on one side of the two inner angles less than two right angles. 」

Since then, many scholars have believed that this public hypothesis can be proven, and have tried to prove it, but without success. It was not until the 19th century that Gauss, Lobachevsky and Poljo independently developed non-Euclidean geometry from this. The axioms are followed by 5 axioms, which together form the basis of the entire work.

At that time, axioms were considered applicable to all disciplines. As in the first axiom that things that are equal to the same thing are equal to each otherProceeding from these basic definitions, assumptions, and axioms, Euclid uses the tools of rigorous logic to introduce a total of 48 propositions in Book I, which is characteristic of the entire work.

The first 6 volumes of Geometry Originals are plane geometry content. Volume I deals with points, lines, triangles, squares, and parallelograms. Book I proposition 47 is the famous Pythagorean theorem:

The square on the hypotenuse of a right triangle is equal to the sum of the two squares on the straight edge. 」

Greek mathematician Euclid.

Geometry OriginalsOriginallyAncient GreeceMathematicianEuclidWritten by Xu Guangqi, a famous Chinese scientist in the Ming Dynasty, and Matteo Ricci, an Italian missionary. Euclid's Geometry consists of fifteen volumes, and Xu Guangqi and others translated the first six volumes.

In the process of translation, Xu Guangqi created a set of mathematical terms in order to better express the meaning of the original book, such as geometry, point, line, surface, plane, curve, right angle, obtuse angle, acute angle, diameter, quadrilateral, polygon, and diagonal.

and so on, which are still used by the mathematics community in the country.

Xu Guangqi translated this book, trying to use it to solve some problems in ancient Chinese mathematics, and adhered to the principle of "no test, no use", pointing out that mathematics should be tested by practice. The translation and publication of this book has played a great role in the development of Chinese mathematics.

Content overview

The Geometry Prima consists of thirteen chapters: the first to the fourth deal with the basic properties of straight sides and circles (including parallel lines, the Pythagorean theorem).

Geometric Diagrams, Equivalences, etc.), the first of which gives a definition of the concepts used in the first part. The fifth is the theory of proportionality (the relationship between two ratios), that is, the theory of proportionality about measurable quantities (quantities whose ratios can be expressed as integer ratios), and at the same time generalizes it to non-common measurables.

The sixth article focuses on similar shapes. Clause.

Chapters 7, 8, and 9 are number theory, that is, they describe the nature of the ratio of integers to integers, and they are the only places in the book that pleases hunger and cherry blossoms on arithmetic. The tenth article is the classification of non-measurable quantities, which classifies irrational quantities. Chapters 11 to 13 are solid geometry.

and exhaustion method.

Geometry OriginalsThe author isEuclid

Geometry is an ancient Greek original.

An immortal work by mathematician Euclid, a collection of the entire mathematical achievements and spirit of ancient Greece in one book. It is not only a mathematical masterpiece, but also a philosophical masterpiece, and for the first time, the human understanding of space has been completed. Since its publication, the book has been translated and revised many times over a period of more than 2,000 years, and since the first printing in 1482, there have been more than 1,000 different editions.

Introduction

In each volume, Euclid adopts a completely different narrative than his predecessors, i.e., first presenting axioms, guessing postulates, and definitions, and then proving them from simple to complex, whereas the earliest Chinese translation is by an Italian missionary.

Matteo Ricci and Ming Dynasty scientist Xu Guangqi.

It was done collaboratively in 1607, but they translated only the first six volumes.

It was this fragment that laid the foundation for the basic terminology of modern Chinese mathematics, such as triangles.

Angles, right angles, and so on. The last nine volumes were translated in 1857 by the Chinese Qing Dynasty mathematician Li Shanlan and the Englishman Wei Li. Japan, India and other Oriental countries have used the Chinese translation, which is still used today.

Euclid's Geometry consists of thirteen volumes.

Directory. Volume 1 Fundamentals of Geometry.

Volume II: Geometry and Algebra.

Volume III: Circles and Corners.

Volume IV Circles and Regular Polygons.

Volume V Proportions.

Volume VI Similar.

Volume VII Number Theory (I).

Volume VIII Number Theory (II).

Volume 9 Number Theory (3).

Volume 10 Unreasonableness.

Volume 11 Solid Geometry.

Volume 12 Three-dimensional measurements.

Volume 13 Orthodox.

Introduction to each volume. Volume 1 Fundamentals of Geometry. The main topics are the conditions for the congruence of triangles, the relationship between the magnitude of the sides and corners of triangles, the theory of parallel lines, the conditions for the equal area (equal area) of triangles and polygons, and the last two propositions in the first volume are the positive and inverse theorems of the Pythagorean theorem;

Volume II: Geometry and Algebra. Talk about how to turn a triangle into an equal-area square; where the proposition is equivalent to the cosine theorem.

Volume III: Circles and Corners are discussed.

Volume IV: Discussion of the practice and properties of circumscribed and inscribed polygons in circles;

Volume V: Discussion of the Theory of Proportions, most of which are inherited from Eudox's Theory of Proportions.

Volume 6: Similar Polygon Theory;

Clause. V.

VII. VIII.

IX. and TEN: Theories of Proportions and Arithmetic; Book 10 is the largest and deals with irrational quantities (quantities that are not commensurate with a given quantity), the first of which is the rudiments of limit thinking.

Vol. XI, x.

2. Ten Circles and Three Volumes: Finally, the content of three-dimensional geometry is introduced.

From these contents, it can be seen that the main content of elementary geometry, which is currently part of the secondary school curriculum, has been completely included in the Geometry Originals. For this reason, it has long been considered the standard textbook for the dissemination of geometric knowledge for more than 2,000 years. Geometry, which belongs to the content of the Geometry Primitives, is called Euclidean geometry, or simply Euclidean geometry.

Principia Geometry is a work by the famous Greek mathematician Euclid (323-235 BC).

Geometry is an immortal work that combines the ideas of its predecessors and Euclid's personal creativity. The book covers more than 400 years of mathematical development in geometry, from the 7th century BC to ancient Greece and the 4th century BC, the time of Euclid's life.

We know very little about Euclid's origins, but his Geometry is probably a textbook at the University of Alexandria. The University of Alexandria was the last place where Greek culture was concentrated, because Alexander himself had visited Alexandria, so he built the city of North Africa at that time, leaning on the Mediterranean.

It not only preserves many of the early geometric theories of ancient Greece, but also carries forward these ancient mathematical ideas through Euclid's groundbreaking systematic organization and complete elaboration. It pioneered the study of classical number theory, and on the basis of a series of axioms, definitions, and postulators, it created the Euclidean geometry system, which became the earliest example of the mathematical deduction system established by axiomatic methods.

Euclid character evaluation:

Euclid was one of the most famous and influential mathematicians in ancient Greece. Euclid's Geometry had a great influence on the future development of geometry, mathematics and science, and on the whole way of thinking of Westerners.

The Geometry Prima was the pinnacle of the development of mathematics in ancient Greece. Euclidean sorted out the rich achievements of Greek geometry accumulated since the 7th century B.C. in a rigorous logical system of calculations, making geometry an independent and deductive science.

Ancient Greek mathematician: Euclid, whose book "Geometry Primitives" is the earliest geometry.

Euclid is known as the "Father of Geometry". Active in Ptolemy I, born in 323 BC and died in Alexandria in 283 BC, his most famous work, Geometry Primitives, is the foundation of European mathematics, proposing the five major postulates and developing Euclidean geometry, which is widely regarded as the most successful textbook in history. Euclid also wrote works on perspective, conic curves, spherical geometry, and number theory, and was the founder of limb geometry.