The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh and Twelfth

by Euclid

Excerpt from The Elements of Euclid

The Opinions of the Modems concerning the Author of the Elements of Geometry, which go under Euclid's name, are Very diferent and contrary to one another. Peter Ramos afcrihes the Propolitions. As well as their Demon?ra tions, to Theon; Others think the Propofitions to he Euclid's, but that the Demonfirations are Theon's; and others main tain that all the Propofitions and their Demonfirations are Enclid's own. John Buteo and Sir Hen b'avile are the Authors of greatefi Note who a?'ett this lg. And the greater part of Geometets have ever finoe been of this Opinion, as they thought it the mail probable. Sir Henry Savile, after the fevenl Arguments he brings to prove it, makes this Con clufion (page 13. Praelea) That, exceptin a very few Interpolations, Explications, and Additions, 'heon altered nothing in Euclid. But. By often confidenng and com paring together the Definitions and Demonlh'atiom as they are in the Greek Editions we now have, Hound that T heon, or whoever was the Editor of the prefent Greek. Text. By addin fome things, fuppte?ing others, and» mixing his own with iuclid's Demontttations, had changed ngre things to the vorfe than is commonly fn'ppofed, and thofe act of tmail moment, efpeeially in the Pi th and Eleventh Books, of the Elements, which this has greatly vitiated; for infiance, hy fnhfiituting a (boner, hut infuficient Demonfirstion of the tsth Prop. Of the sth Book, in place of the legitimate one which Euclid had wen; antlb taking out of this Book, hefides Other things, e good De nition which Eudoxus or Euclid had given of Compound Ratio, and giving an ahfurd one in place of it in the sth Definition of the oth Book, which neither Euclid, Archimedes, Appollonius, nor any Geometer befos's Theon'e time, ever made ufe of, and of which these is not to he found the leak appearance in any of their Writings; andt as this Definition did much embarafs Beginners, and is quite nfelefa, it is now thrown out of the Elements, and another, which, without doubt, Euclid had given, is put in its proper place among the Definitions of th.

524 pages, Paperback

First published January 1, 1957

About the author

Euclid (Ancient Greek: Εὐκλείδης Eukleidēs -- "Good Glory", ca. 365-275 BC) also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Stoicheia (Elements) is a 13-volume exploration all corners of mathematics, based on the works of, inter alia, Aristotle, Eudoxus of Cnidus, Plato, Pythagoras. It is one of the most influential works in the history of mathematics, presenting the mathematical theorems and problems with great clarity, and showing their solutions concisely and logically. Thus, it came to serve as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher.