Euclide"s elements
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Euclide"s elements

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Published by printed by R. Daniel, for William Nealand... in London .
Written in English

Subjects:

  • Mathematics, Greek.,
  • Geometry -- Early works to 1800.

Book details:

Edition Notes

Statementthe whole fifteen books compendiously demonstrated by Mr. Isaac Barrow..., and translated out of the Latin.
ContributionsBarrow, Isaac, 1630-1677.
The Physical Object
Pagination349 p. :
Number of Pages349
ID Numbers
Open LibraryOL18342622M

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The Elements begins with a list of definitions. Some of these indicate little more than certain concepts will be discussed, such as Def.I.1, Def.I.2, and Def.I.5, which introduce the terms point, line, and surface. Within his foundational textbook "Elements," Euclid presents the results of earlier mathematicians and includes many of his own theories in a systematic, concise book that utilized meticulous proofs and a brief set of axioms to solidify his deductions/5(13). Euclid's Elements is the most famous mathematical work of classical antiquity, and has had a profound influence on the development of modern Mathematics and Physics. This volume contains the definitive Ancient Greek text of J.L. Heiberg (), together with an English translation.5/5(3). Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Little .

Also Book X on irrational lines and the books on solid geometry, XI through XIII, discuss ratios and depend on Book V. The books on number theory, VII through IX, do not directly depend on Book V since there is a different definition for ratios of numbers. Definitions I. Definition 1. Those magnitudes are said to be commensurable which are measured by the same measure, and those incommensurable which cannot have any common measure.. Definition 2. Straight lines are commensurable in square when the squares on them are measured by the same area, and incommensurable in square when the squares on them cannot possibly have any area as a . Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion. Finally, Book 13 investigates the five so-called Platonic solids. This edition of Euclid’s Elements presents the definitive Greek text—i.e., that edited by J.L. Heiberg (–. Logical structure of Book II The proofs of the propositions in Book II heavily rely on the propositions in Book I involving right angles and parallel lines, but few others. For instance, the important congruence theorems for triangles, namely I.4, I.8, and I, are not invoked even once.

Euclid has books on Goodreads with ratings. Euclid’s most popular book is Euclid's Elements. Euclid's Elements is the foundation of geometry and number theory. There is no long-winded explanation; instead, from a set of 23 definitions, 5 postulates, and 5 common notions, Euclid lays out 13 books of geometrical proofs/5. The Elements-- Book III Euclid begins with the basics: III To find the center of a given circle. III If on the circumference of a circle two points be take at random, the straight line joining the points will fall within the circle. The Elements-- Book III III If two circles cut (touch) one another, they will . Euclid’s Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics.