Euclid

Euclid does not go beyond a third measuring and gives no numerical examples.

Euclid ’ s algorithm appears as Proposition II in Book VII (" Elementary Number Theory ") of his Elements.

Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers ' common measure is in fact the greatest.

* Euclid of Megara ( 450-380 BC )

In his work Prodromo dell ' Arte Maestra ( 1670 ) he proposes a lighter-than-air vessel based on logical deductions from previous work ranging from Archimedes and Euclid to his contemporaries Robert Boyle and Otto von Guericke.

Here Dürer favours the methods of Ptolemy over Euclid.

Greek mathematician Euclid mentioned the special case of the binomial theorem for exponent 2 as did the 3rd century B. C.

After one pair of Bézout coefficients ( x, y ) has been computed ( using extended Euclid or some other algorithm ), all pairs may be found using the formula

: Foundations of Geometry ) published by Hilbert in 1899 proposes a formal set, the Hilbert's axioms, substituting the traditional axioms of Euclid.

They avoid weaknesses identified in those of Euclid, whose works at the time were still used textbook-fashion.

The axioms unify both the plane geometry and solid geometry of Euclid in a single system.

A clear exposition of the " errors " of Euclid and of the solutions presented in the Grundlagen der Geometrie, with reference to non-Euclidean geometry.

The city hosted such leading lights as the mathematician Euclid and anatomist Herophilus ; constructed the great Library of Alexandria ; and translated the Hebrew Bible into Greek ( called the Septuagint for it was the work of 70 translators ).

The Elements mentions neither symmetry nor reflexivity, and Euclid probably would have deemed the reflexivity of equality too obvious to warrant explicit mention.

# REDIRECT Euclid

Euclid ( ; Eukleidēs ), fl.

300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the " Father of Geometry ".

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.

" Euclid " is the anglicized version of the Greek name Εὐκλείδης, meaning " Good Glory ".

The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria.

Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, " Euclid replied there is no royal road to geometry.