The books cover plane and solid euclidean geometry. On a given finite straight line to construct an equilateral triangle. Book 1 outlines the fundamental propositions of plane geometry, includ ing the three cases in which triangles are. Euclids elements, book i department of mathematics and. Euclids elements is one of the most beautiful books in western thought. Proposition 1, constructing equilateral triangles duration. The elements of euclid, book 1 by euclid goodreads. This work has been selected by scholars as being culturally. Definitions, postulates, axioms and propositions of euclids elements, book i. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.
The classic treatise in geometry written by euclid and used as a textbook for more than. Heiberg 1883 1885accompanied by a modern english translation, as well as a greekenglish lexicon. Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion. The paperback of the the thirteen books of the elements, vol.
It focuses on how to construct an equilateral triangle. This is the first proposition in euclids first book of the elements. This book may have occasional imperfections such as missing or blurred pages. Euclid s elements is one of the most beautiful books in western thought. To construct an equilateral triangle on a given finite straight line.
Click anywhere in the line to jump to another position. It is a collection of definitions, postulates, propositions theorems and constructions, and mathematical proofs of the propositions. For one thing, the elements ends with constructions of the five regular solids in book xiii, so it is a nice aesthetic touch to begin with the construction of a regular triangle. Some of these indicate little more than certain concepts will be discussed, such as def. To place at a given point as an extremity a straight line equal to a given straight line. Since euclid uses this postulate as if it includes the uniqueness as part of it, he really ought to have stated the uniqueness explicitly. Each proposition falls out of the last in perfect logical progression. Stoicheia is a mathematical treatise consisting of books attributed to the ancient greek mathematician euclid in alexandria, ptolemaic egypt c. To produce a finite straight line continuously in a straight line. Everyday low prices and free delivery on eligible orders. The last three books of the elements cover solid geometry, and for those, the two points mentioned in the postulate may be any two points in space.
Book 1 contains 5 postulates including the famous parallel postulate and 5 common notions, and covers important topics of plane geometry such as the. Note that for euclid, the concept of line includes curved lines. Euclids elements of geometry university of texas at austin. This is a reproduction of a book published before 1923. In any triangle, if one of the sides is produced, then the exterior angle is greater. Buy euclids elements by euclid, densmore, dana, heath, thomas l.