Brief biography of Euclid. Further development of science

EUCLID (Eukleides)

III century BC e.

Euclid (otherwise Euclid) is an ancient Greek mathematician, the author of the first theoretical treatise on mathematics that has reached us. Biographical information about Euclid is extremely scarce. It is only known that Euclid’s teachers in Athens were students of Plato, and during the reign of Ptolemy I (306-283 BC) he taught at the Alexandria Academy. Euclid is the first mathematician of the Alexandrian school.

The main work of Archimedes is “Principles” (lat. Elementa) – contains a presentation of planimetry, stereometry and a number of issues in number theory (for example, Euclidean algorithm); consists of 13 books, to which are added two books on the five regular polyhedra, sometimes attributed to Hypsicles of Alexandria. In the "Elements" he summed up the previous development of Greek mathematics and created the foundation for the further development of mathematics. For more than two thousand years, Euclidean's Elements remained the main work of elementary mathematics.

Among other mathematical works of Euclid, it should be noted “On the division of figures”, preserved in Arabic translation, four books “Conic Sections”, the material of which was included in the work of the same name by Apollonius of Perga, as well as “Porisms”, an idea of which can be obtained from the “Mathematical Collection” Pope of Alexandria.

The works of Euclid give a systematic presentation of the so-called. Euclidean geometry, the system of axioms of which is based on the following basic concepts: point, line, plane, motion and the following relations: “a point lies on a line on a plane”, “a point lies between two others”. In modern presentation, the system of axioms of Euclidean geometry is divided into the following five groups.

I. Axioms of combination. 1) Through every two points you can draw a straight line and, moreover, only one. 2) Each line contains at least two points. There are at least three points that do not lie on the same line. 3) Through every three points that do not lie on the same line, you can draw a plane, and only one. 4) On every plane there are at least three points and there are at least four points that do not lie in the same plane. 5) If two points of a given line lie on a given plane, then the line itself lies on this plane. 6) If two planes have a common point, then they have another common point (and, therefore, a common line).

II. Axioms of order. 1) If point B lies between A and C, then all three lie on the same straight line. 2) For each points A, B, there is a point C such that B lies between A and C. 3) Of the three points on a straight line, only one lies between the other two. 4) If a straight line intersects one side of a triangle, then it intersects its other side or passes through a vertex (segment AB is defined as the set of points lying between A and B; the sides of the triangle are determined accordingly).

III. Axioms of motion. 1) The movement associates points with points, straight lines, and planes of a plane, preserving the belonging of points to straight lines and planes. 2) Two successive movements give again movement, and for every movement there is an inverse. 3) If points are given A, A" and half-planes a, a", bounded by extended half-lines a, a", which come from points A, A", then there is a movement, and, moreover, the only one that translates A, A, a V A", a", a"(half-line and half-plane are easily defined based on the concepts of combination and order).

IV. Axioms of continuity. 1) Archimedes' axiom: any segment can be covered by any segment by postponing it on the first one a sufficient number of times (postponing a segment is carried out by movement). 2) Cantor's axiom: if given a sequence of segments embedded one within the other, then they all have at least one common point.

V. Euclid's parallelism axiom. Through the point A out of line A in a plane passing through A And A, you can only draw one straight line that does not intersect A.

The emergence of Euclidean geometry is closely related to visual ideas about the world around us (straight lines - stretched threads, rays of light, etc.). The long process of deepening our understanding has led to a more abstract understanding of geometry. N.I. Lobachevsky's discovery of geometry other than Euclidean showed that our ideas about space are not a priori. In other words, Euclidean geometry cannot claim to be the only geometry that describes the properties of the space around us. The development of natural science (mainly physics and astronomy) has shown that Euclidean geometry describes the structure of the space around us only with a certain degree of accuracy and is not suitable for describing the properties of space associated with the movement of bodies at speeds close to light. Thus, Euclidean geometry can be considered as a first approximation for describing the structure of real physical space.

Euclid or Euclid(ancient Greek Εὐκλείδης , from “good fame”, flourishing time - about 300 BC. BC) - ancient Greek mathematician, author of the first theoretical treatise on mathematics that has come down to us. Biographical information about Euclid is extremely scarce. The only thing that can be considered reliable is that his scientific activity took place in Alexandria in the 3rd century. BC e.

Biography

The most reliable information about the life of Euclid is considered to be the little that is given in Proclus’s comments to the first book Started Euclid (although it should be taken into account that Proclus lived almost 800 years after Euclid). Noting that “those who wrote on the history of mathematics” did not bring the development of this science to the time of Euclid, Proclus points out that Euclid was younger than Plato’s circle, but older than Archimedes and Eratosthenes, “lived in the time of Ptolemy I Soter,” “because Archimedes, who lived under Ptolemy the First, mentions Euclid and, in particular, says that Ptolemy asked him if there was a shorter way to study geometry than Beginnings; and he replied that there is no royal path to geometry.”

Additional touches to Euclid's portrait can be gleaned from Pappus and Stobaeus. Pappus reports that Euclid was gentle and kind to everyone who could contribute even in the slightest degree to the development of mathematical sciences, and Stobaeus relates another anecdote about Euclid. Having begun to study geometry and having analyzed the first theorem, one young man asked Euclid: “What benefit will I get from this science?” Euclid called the slave and said: “Give him three obols, since he wants to make a profit from his studies.” The historicity of the story is questionable, since a similar one is told about Plato.

Some modern authors interpret Proclus's statement - Euclid lived in the time of Ptolemy I Soter - to mean that Euclid lived at the court of Ptolemy and was the founder of the Alexandrian Museion. It should be noted, however, that this idea was established in Europe in the 17th century, while medieval authors identified Euclid with the student of Socrates, the philosopher Euclid of Megara.

Arab authors believed that Euclid lived in Damascus and published there " Beginnings» Apollonia. An anonymous 12th-century Arabic manuscript reports:

Euclid, son of Naucrates, known as "Geometra", a scientist of old times, Greek by origin, Syrian by residence, originally from Tyre...

The name of Euclid is also associated with the formation of Alexandrian mathematics (geometric algebra) as a science. In general, the amount of data about Euclid is so scarce that there is a version (though not widespread) that we are talking about the collective pseudonym of a group of Alexandrian scientists.

« Beginnings» Euclid

Euclid's main work is called Started. Books with the same title, which consistently presented all the basic facts of geometry and theoretical arithmetic, were previously compiled by Hippocrates of Chios, Leontes and Theudius. However Beginnings Euclid pushed all these works out of use and remained the basic textbook of geometry for more than two millennia. When creating his textbook, Euclid included in it much of what was created by his predecessors, processing this material and bringing it together.

Beginnings consist of thirteen books. The first and some other books are preceded by a list of definitions. The first book is also preceded by a list of postulates and axioms. As a rule, postulates define basic constructions (for example, “it is required that a straight line can be drawn through any two points”), and axioms - general rules of inference when operating with quantities (for example, “if two quantities are equal to a third, they are equal between yourself").

Euclid opens the gates of the Garden of Mathematics. Illustration from Niccolò Tartaglia’s treatise “The New Science”

In Book I the properties of triangles and parallelograms are studied; This book is crowned with the famous Pythagorean theorem for right triangles. Book II, going back to the Pythagoreans, is devoted to the so-called “geometric algebra”. Books III and IV describe the geometry of circles, as well as inscribed and circumscribed polygons; when working on these books, Euclid could have used the writings of Hippocrates of Chios. In Book V, the general theory of proportions, built by Eudoxus of Cnidus, is introduced, and in Book VI it is applied to the theory of similar figures. Books VII-IX are devoted to number theory and go back to the Pythagoreans; the author of Book VIII may have been Archytas of Tarentum. These books discuss theorems on proportions and geometric progressions, introduce a method for finding the greatest common divisor of two numbers (now known as the Euclid algorithm), construct even perfect numbers, and prove the infinity of the set of prime numbers. In the X book, which is the most voluminous and complex part Started, a classification of irrationalities is constructed; it is possible that its author is Theaetetus of Athens. Book XI contains the basics of stereometry. In the XII book, using the method of exhaustion, theorems on the ratios of the areas of circles, as well as the volumes of pyramids and cones are proved; The author of this book is generally acknowledged to be Eudoxus of Cnidus. Finally, Book XIII is devoted to the construction of five regular polyhedra; it is believed that some of the constructions were developed by Theaetetus of Athens.

In the manuscripts that have reached us, two more books were added to these thirteen books. Book XIV belongs to the Alexandrian Hypsicles (c. 200 BC), and Book XV was created during the life of Isidore of Miletus, builder of the temple of St. Sophia in Constantinople (beginning of the 6th century AD).

Beginnings provide a general basis for subsequent geometric treatises by Archimedes, Apollonius and other ancient authors; the propositions proven in them are considered generally known. Comments to Let's start in antiquity were Heron, Porphyry, Pappus, Proclus, Simplicius. A commentary by Proclus on Book I has been preserved, as well as a commentary by Pappus on Book X (in Arabic translation). From ancient authors, the commentary tradition passes to the Arabs, and then to Medieval Europe.

In the creation and development of modern science Beginnings also played an important ideological role. They remained a model of a mathematical treatise, strictly and systematically presenting the main provisions of a particular mathematical science.

Other works of Euclid

Of the other works of Euclid, the following have survived:

Data (δεδομένα ) - about what is necessary to define a figure;
About division (περὶ διαιρέσεων ) - partially preserved and only in Arabic translation; gives the division of geometric figures into parts that are equal or consist of each other in a given ratio;
Phenomena (φαινόμενα ) - applications of spherical geometry to astronomy;
Optics (ὀπτικά ) - about the rectilinear propagation of light.

From brief descriptions we know:

Porisms (πορίσματα ) - about the conditions that determine the curves;
Conic sections (κωνικά );
Superficial places (τόποι πρὸς ἐπιφανείᾳ ) - about the properties of conic sections;
Pseudaria (ψευδαρία ) - about errors in geometric proofs;

Euclid is also credited with:

Euclid and ancient philosophy

Texts and translations

Old Russian translations

Euclidean elements from twelve neftonic books were selected and reduced into eight books through the professor of mathematics A. Farkhvarson. / Per. from lat. I. Satarova. St. Petersburg, 1739. 284 pp.
Elements of geometry, that is, the first foundations of the science of measuring distance, consisting of axis Euclidean books. / Per. from French N. Kurganova. St. Petersburg, 1769. 288 pp.
Euclidean elements eight books, namely: 1st, 2nd, 3rd, 4th, 5th, 6th, 11th and 12th. / Per. from Greek St. Petersburg,

Euclid or Euclid (ancient Greek Εὐκλείδης, from “good fame”, time of prosperity). Lived around 300 BC. e. Ancient Greek mathematician, author of the first theoretical treatise on mathematics that has come down to us. Biographical information about Euclid is extremely scarce. The only thing that can be considered reliable is that his scientific activity took place in Alexandria in the 3rd century. BC e.

Euclid is the first mathematician of the Alexandrian school. His main job "Beginnings"(Στοιχεῖα, in Latinized form - “Elements”) contains a presentation of planimetry, stereometry and a number of issues in number theory; in it he summed up the previous development of Ancient Greek mathematics and created the foundation for the further development of mathematics.

Among other works on mathematics it should be noted "On the division of figures", preserved in Arabic translation, 4 books “Conic Sections”, the material of which was included in the work of the same name by Apollonius of Perga, as well as “Porisms”, an idea of which can be obtained from the “Mathematical Collection” of Pappus of Alexandria. Euclid - author of works on astronomy, optics, music, etc.

The most reliable information about the life of Euclid is usually considered to be the little that is given in the Commentaries of Proclus to the first book of Euclid’s Elements. Noting that “those who wrote on the history of mathematics” did not bring the development of this science to the time of Euclid, Proclus points out that Euclid was older than Plato’s circle, but younger than Archimedes and Eratosthenes and “lived in the time of Ptolemy I Soter,” “because Archimedes, who lived under Ptolemy the First, mentions Euclid and, in particular, says that Ptolemy asked him if there was a shorter way to study geometry than the Elements; and he replied that there is no royal path to geometry.”

Additional touches to the portrait of Euclid can be gleaned from Pappus and Stobaeus. Pappus reports that Euclid was gentle and kind to everyone who could contribute even in the slightest degree to the development of mathematical sciences, and Stobaeus relates another anecdote about Euclid.

Having begun to study geometry and having analyzed the first theorem, one young man asked Euclid: “What benefit will I get from this science?” Euclid called the slave and said: “Give him three obols, since he wants to make a profit from his studies.” The historicity of the story is questionable, since a similar one is told about Plato.

Some modern authors interpret Proclus's statement - Euclid lived during the time of Ptolemy I Soter - in the sense that Euclid lived at the court of Ptolemy and was the founder of the Alexandrian Museion. It should be noted, however, that this idea was established in Europe in the 17th century, while medieval authors identified Euclid with Socrates’ student, the philosopher Euclid of Megara.

In general, the amount of data about Euclid is so scarce that there is a version (though not widespread) that we are talking about the collective pseudonym of a group of Alexandrian scientists.

Euclid's "Elements":

Euclid's main work is called the Elements. Books with the same title, which consistently presented all the basic facts of geometry and theoretical arithmetic, were previously compiled by Hippocrates of Chios, Leontes and Theudius. However, Euclid's Elements displaced all these works from use and remained the basic textbook of geometry for more than two millennia. When creating his textbook, Euclid included in it much of what was created by his predecessors, processing this material and bringing it together.

The Beginnings consist of thirteen books. The first and some other books are preceded by a list of definitions. The first book is also preceded by a list of postulates and axioms. As a rule, postulates define basic constructions (for example, “it is required that a straight line can be drawn through any two points”), and axioms - general rules of inference when operating with quantities (for example, “if two quantities are equal to a third, they are equal between yourself").

In Book I the properties of triangles and parallelograms are studied; This book is crowned with the famous theorem for right triangles.

Book II, going back to the Pythagoreans, is devoted to the so-called “geometric algebra”.

Books III and IV describe the geometry of circles, as well as inscribed and circumscribed polygons; when working on these books, Euclid could have used the writings of Hippocrates of Chios.

In Book V, the general theory of proportions, built by Eudoxus of Cnidus, is introduced, and in Book VI it is applied to the theory of similar figures.

Books VII-IX are devoted to number theory and go back to the Pythagoreans; the author of Book VIII may have been Archytas of Tarentum. These books discuss theorems on proportions and geometric progressions, introduce a method for finding the greatest common divisor of two numbers (now known as the Euclid algorithm), construct even perfect numbers, and prove the infinity of the set of prime numbers.

In Book X, which represents the most voluminous and complex part of the Elements, a classification of irrationalities is constructed; it is possible that its author is Theaetetus of Athens.

Book XI contains the basics of stereometry.

In the XII book, using the method of exhaustion, theorems on the ratios of the areas of circles, as well as the volumes of pyramids and cones are proved; The author of this book is generally acknowledged to be Eudoxus of Cnidus.

Finally, Book XIII is devoted to the construction of five regular polyhedra; It is believed that some of the constructions were developed by Theaetetus of Athens.

The Elements provide a general basis for subsequent geometric treatises by Archimedes, Apollonius and other ancient authors; the propositions proven in them are considered generally known. Commentaries on the Elements in antiquity were composed by Heron, Porphyry, Pappus, Proclus, and Simplicius. A commentary by Proclus on Book I has been preserved, as well as a commentary by Pappus on Book X (in Arabic translation). From ancient authors, the commentary tradition passes to the Arabs, and then to Medieval Europe.

In the creation and development of modern science, the Principles also played an important ideological role. They remained a model of a mathematical treatise, strictly and systematically presenting the main provisions of a particular mathematical science.

Euclid is the first mathematician of the Alexandrian school. His main work “Principia” (????????, in Latinized form - “Elements”) contains a presentation of planimetry, stereometry and a number of questions in number theory; in it he summed up the previous development of Greek mathematics and created the foundation for the further development of mathematics. Among other works on mathematics, it should be noted “On the division of figures”, preserved in Arabic translation, 4 books “Conic Sections”, the material of which was included in the work of the same title by Apollonius of Perga, as well as “Porisms”, an idea of which can be obtained from the “Mathematical collection" by Pope of Alexandria. Euclid - author of works on astronomy, optics, music, etc.

Biography

Additional touches to the portrait of Euclid can be gleaned from Pappus and Stobaeus. Pappus reports that Euclid was gentle and kind to everyone who could, even in the slightest degree, contribute to the development of mathematical sciences, and Stobaeus relates another anecdote about Euclid. Having begun to study geometry and having analyzed the first theorem, one young man asked Euclid: “What benefit will I get from this science?” Euclid called the slave and said: “Give him three obols, since he wants to make a profit from his studies.”

According to his philosophical views, Euclid was most likely a Platonist.

Euclid's Elements

In Book I the properties of triangles and parallelograms are studied; This book is crowned with the famous Pythagorean theorem for right triangles. Book II, going back to the Pythagoreans, is devoted to the so-called “geometric algebra”. Books III and IV describe the geometry of circles, as well as inscribed and circumscribed polygons; when working on these books, Euclid could have used the writings of Hippocrates of Chios. In Book V, the general theory of proportions, built by Eudoxus of Cnidus, is introduced, and in Book VI it is applied to the theory of similar figures. Books VII-IX are devoted to number theory and go back to the Pythagoreans; the author of Book VIII may have been Archytas of Tarentum. These books discuss theorems on proportions and geometric progressions, introduce a method for finding the greatest common divisor of two numbers (now known as the Euclid algorithm), construct even perfect numbers, and prove the infinity of the set of prime numbers. In Book X, which represents the most voluminous and complex part of the Elements, a classification of irrationalities is constructed; it is possible that its author is Theaetetus of Athens. Book XI contains the basics of stereometry. In the XII book, using the method of exhaustion, theorems on the ratios of the areas of circles, as well as the volumes of pyramids and cones are proved; The author of this book is generally acknowledged to be Eudoxus of Cnidus. Finally, Book XIII is devoted to the construction of five regular polyhedra; It is believed that some of the constructions were developed by Theaetetus of Athens.

Other works of Euclid

Of the other works of Euclid, the following have survived:

Data (?????????) - about what is needed to define a figure;
About division (???? ????????????) - partially preserved and only in Arabic translation; gives the division of geometric figures into parts that are equal or consist of each other in a given ratio;
Phenomena (?????????) - applications of spherical geometry to astronomy;
Optics (??????) - about the rectilinear propagation of light.

From brief descriptions we know:

Porisms (?????????) - about the conditions that determine curves;
Conic sections (??????);
Superficial places (????? ???? ?????????) - about the properties of conic sections;
Pseudarius (??????????) - about errors in geometric proofs;

Euclid is also credited with:

Catoptrics (????????????) - theory of mirrors; the treatment of Theon of Alexandria has survived;
Division of the Canon (???????? ?????????) - a treatise on elementary music theory.

Euclid and ancient philosophy

Already from the time of the Pythagoreans and Plato, arithmetic, music, geometry and astronomy (the so-called “mathematical” sciences; later called quadrivius by Boethius) were considered as a model of systematic thinking and a preliminary stage for the study of philosophy. It is no coincidence that a legend arose according to which the inscription “Let no one who does not know geometry enter here” was placed above the entrance to Plato’s Academy.

Geometrical drawings, in which by drawing auxiliary lines the implicit truth becomes obvious, serve as an illustration for the doctrine of recollection developed by Plato in the Meno and other dialogues. Propositions of geometry are called theorems because to comprehend their truth it is necessary to perceive the drawing not with simple sensory vision, but with the “eyes of the mind.” Every drawing for a theorem represents an idea: we see this figure in front of us, and we reason and draw conclusions for all figures of the same type at once.

Some “Platonism” of Euclid is also connected with the fact that in Plato’s Timaeus the doctrine of the four elements is considered, which correspond to four regular polyhedra (tetrahedron - fire, octahedron - air, icosahedron - water, cube - earth), the fifth polyhedron, dodecahedron, “ belonged to the figure of the universe." In this regard, the Principia can be considered as a doctrine developed with all the necessary premises and connections about the construction of five regular polyhedra - the so-called “Platonic solids”, ending with a proof of the fact that there are no other regular solids besides these five.

For Aristotle's doctrine of evidence, developed in the Second Analytics, the Elements also provide rich material. Geometry in the Elements is constructed as an inferential system of knowledge in which all propositions are sequentially deduced one after another along a chain based on a small set of initial statements accepted without proof. According to Aristotle, such initial statements must exist, since the chain of inference must begin somewhere in order not to be endless. Further, Euclid tries to prove statements of a general nature, which also corresponds to Aristotle’s favorite example: “if it is inherent in every isosceles triangle to have angles that add up to two right angles, then this is inherent in it not because it is isosceles, but because it is a triangle” (An. Post.85b12).

Pseudo-Euclid

Euclid is credited with two important treatises on ancient music theory: the Harmonic Introduction and the Division of the Canon. Nothing is known about the real author of these works. Heinrich Meibom (1555-1625) provided the Harmonic Introduction with extensive notes, and, together with the Division of the Canon, was the first to authoritatively attribute them to the works of Euclid. With the subsequent detailed analysis of these treatises, it was determined that the first has traces of the Pythagorean tradition (for example, in it all semitones are considered equal), and the second is distinguished by an Aristotelian character (for example, the possibility of dividing a tone in half is denied). The style of presentation of the “Harmonic Introduction” is distinguished by dogmatism and continuity; the style of the “Division of the Canon” is somewhat similar to Euclid’s “Elements”, since it also contains theorems and proofs.

Karl Jahn (1836-1899) was of the opinion that the treatise “Harmonic Introduction” was written by Kleonidas, since his name appears in some manuscripts. In addition to the names of Euclid and Cleonidas, the manuscripts mention Pappus and Anonymous as authors. In most scientific publications, they prefer to call the author Pseudo-Euclid.

The Greek treatise of Pseudo-Euclid with Russian translation and notes by G. A. Ivanov was published in Moscow in 1894

Biography

The most reliable information about the life of Euclid is considered to be the little that is given in the Commentaries of Proclus to the first book Started Euclid. Noting that “those who wrote on the history of mathematics” did not bring the development of this science to the time of Euclid, Proclus points out that Euclid was older than Plato’s circle, but younger than Archimedes and Eratosthenes and “lived in the time of Ptolemy I Soter,” “because Archimedes, who lived under Ptolemy the First, mentions Euclid and, in particular, says that Ptolemy asked him if there was a shorter way to study geometry than Beginnings; and he replied that there is no royal path to geometry"

Additional touches to Euclid's portrait can be gleaned from Pappus and Stobaeus. Pappus reports that Euclid was gentle and kind to everyone who could, even in the slightest degree, contribute to the development of mathematical sciences, and Stobaeus relates another anecdote about Euclid. Having begun to study geometry and having analyzed the first theorem, one young man asked Euclid: “What benefit will I get from this science?” Euclid called the slave and said: “Give him three obols, since he wants to make a profit from his studies.”

Euclid, son of Naucrates, known as "Geometra", a scientist of old times, Greek by origin, Syrian by residence, originally from Tyre...

According to his philosophical views, Euclid was most likely a Platonist.

Beginnings Euclid

Euclid's main work is called Beginnings. Books with the same title, which consistently presented all the basic facts of geometry and theoretical arithmetic, were previously compiled by Hippocrates of Chios, Leontes and Theudius. However Beginnings Euclid pushed all these works out of use and remained the basic textbook of geometry for more than two millennia. When creating his textbook, Euclid included in it much of what was created by his predecessors, processing this material and bringing it together.

Other works of Euclid

Statue of Euclid at the Oxford University Museum of Natural History

Of the other works of Euclid, the following have survived:

Data (δεδομένα ) - about what is necessary to define a figure;
About division (περὶ διαιρέσεων ) - partially preserved and only in Arabic translation; gives the division of geometric figures into parts that are equal or consist of each other in a given ratio;
Phenomena (φαινόμενα ) - applications of spherical geometry to astronomy;
Optics (ὀπτικά ) - about the rectilinear propagation of light.

From brief descriptions we know:

Porisms (πορίσματα ) - about the conditions that determine the curves;
Conic sections (κωνικά );
Superficial places (τόποι πρὸς ἐπιφανείᾳ ) - about the properties of conic sections;
Pseudaria (ψευδαρία ) - about errors in geometric proofs;

Euclid is also credited with:

Euclid and ancient philosophy

The Greek treatise of Pseudo-Euclid with Russian translation and notes by G. A. Ivanov was published in Moscow in 1894

Literature

Bibliography

Max Stack. Bibliographia Euclideana. Die Geisteslinien der Tradition in den Editionen der “Elemente” des Euklid (um 365-300). Handschriften, Inkunabeln, Frühdrucke (16.Jahrhundert). Textkritische Editionen des 17.-20. Jahrhunderts. Editionen der Opera minora (16.-20.Jahrhundert). Nachdruck, herausgeg. von Menso Folkerts. Hildesheim: Gerstenberg, 1981.

Texts and translations

Old Russian translations

Euclidean elements from twelve non-phthonic books were selected and reduced into eight books through the professor of mathematics A. Farkhvarson. / Per. from lat. I. Satarova. St. Petersburg, 1739. 284 pp.
Elements of geometry, that is, the first foundations of the science of measuring distance, consisting of axis Euclidean books. / Per. from French N. Kurganova. St. Petersburg, 1769. 288 pp.
Euclidean elements eight books, namely: 1st, 2nd, 3rd, 4th, 5th, 6th, 11th and 12th. / Per. from Greek St. Petersburg, . 370 pp.
- 2nd ed. ...books 13 and 14 are attached to this. 1789. 424 pp.
Euclidean principles eight books, namely: the first six, 11th and 12th, containing the foundations of geometry. / Per. F. Petrushevsky. St. Petersburg, 1819. 480 pp.
Euclidean began three books, namely: the 7th, 8th and 9th, containing the general theory of numbers of ancient geometers. / Per. F. Petrushevsky. St. Petersburg, 1835. 160 pp.
Eight books of geometry Euclid. / Per. with him. pupils of a real school... Kremenchug, 1877. 172 pp.
Beginnings Euclid. / From input. and interpretations by M.E. Vashchenko-Zakharchenko. Kyiv, 1880. XVI, 749 pp.

Modern editions of Euclid's works

The beginnings of Euclid. Per. and comm. D. D. Mordukhai-Boltovsky, ed. with the participation of I. N. Veselovsky and M. Ya. Vygodsky. In 3 volumes (Series “Classics of Natural History”). M.: GTTI, 1948-50. 6000 copies

Books I-VI (1948. 456 pp.) on www.math.ru or on mccme.ru
Books VII-X (1949. 512 pp.) on www.math.ru or on mccme.ru
Books XI-XIV (1950. 332 pp.) on www.math.ru or on mccme.ru

Euclidus Opera Omnia. Ed. I. L. Heiberg & H. Menge. 9 vols. Leipzig: Teubner, 1883-1916.

Vol. I-IX at www.wilbourhall.org

Heath T. L. The thirteen books of Euclid's Elements. 3 vols. Cambridge UP, 1925. Editions and translations: Greek (ed. J. L. Heiberg), English (ed. Th. L. Heath)
Euclide. Les elements. 4 vols. Trad. et comm. B. Vitrac; intr. M. Caving. P.: Presses universitaires de France, 1990-2001.
Barbera A. The Euclidian Division of the Canon: Greek and Latin Sources // Greek and Latin Music Theory. Vol. 8. Lincoln: University of Nebraska Press, 1991.

Comments

Antique comments Started

Proclus Diadochos. Commentaries on the first book of Euclid's Elements. Introduction. Per. and comm. Yu. A. Shichalina. M.: GLK, 1994.
Proclus Diadochos. Commentaries on the first book of Euclid's Elements. Postulates and axioms. Per. A. I. Shchetnikova. ΣΧΟΛΗ , vol. 2, 2008, p. 265-276.
Proclus Diadochos. Commentary on the first book of Euclid's Elements. Definitions. Per. A. I. Shchetnikova. Arche: Proceedings of the cultural-logical seminar, vol. 5. M.: RSUH, 2009, p. 261-320.
Thompson W. Pappus’ commentary on Euclid’s Elements. Cambridge, 1930.

Research

ABOUT Beginnings Euclid

Alimov N. G. Magnitude and relation in Euclid. Historical and mathematical research, vol. 8, 1955, p. 573-619.
Bashmakova I. G. Arithmetic books of Euclid’s Elements. , vol. 1, 1948, p. 296-328.
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About other works of Euclid

Zverkina G. A. Review of Euclid’s treatise “Data”. Mathematics and practice, mathematics and culture. M., 2000, p. 174-192.
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