The angle scale is absolute, and Euclid uses the right angle as his basic unit, so that, e. g., a 45-degree angle would be referred to as half of a right angle.

Euclid uses right angles in definitions 11 and 12 to define acute angles ( those smaller than a right angle ) and obtuse angles ( those greater than a right angle ).

One may argue that, even if postulate 4 can be proven from the preceding ones, in the order that Euclid presents his material it is necessary to include it since without it postulate 5, which uses the right angle as a unit of measure, makes no sense.

In addition, Euclid uses ideas that were in such common usage that he did not include definitions for them.

The proof of Euclid uses the so-called parallel postulate ( numbered 5 ).

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

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 ).

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

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

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

The term “ Euclidean ” distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.

It is named after the Greek mathematician Euclid, who described it in Books VII and X of his Elements.

Euclid, Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.

Long before the first photographs were made, Chinese philosopher Mo Di and Greek mathematicians Aristotle and Euclid described a pinhole camera in the 5th and 4th centuries BC.

* Proclus ' Commentary on Euclid, Book I. PDF scans of Friedlein's Greek edition, now in the public domain ( Classical Greek )

" The phrase was used by many early Greek mathematicians, including Euclid and Archimedes.

Catholics charge that modalistic monarchianism has its origin by means of influence in Greek pagan philosophy, including pagan philosophers like Euclid and Aristotle, who based their logic on Monism and Aristotle's arguments around his concept energeia ( i. e. energy ) called metaphysics.

Concerns about the soundness of arguments involving infinitesimals date back to ancient Greek mathematics, with Euclid replacing such proofs with ones using other techniques such as the method of exhaustion.

* 300 Euclid, Greek mathematician, publishes Elements, treating both geometry and number theory ( see also Euclidean algorithm ).

While Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, non-Euclidean geometries were not widely accepted as legitimate until the 19th century.

The discoveries of several Greek mathematicians, including Pythagoras, Euclid, and Archimedes, are still used in mathematical teaching today.

* Euclid, Greek mathematician who will come to live in Alexandria ( d. c. 275 BC )

He edited works of Euclid, Apollonius, Archimedes, and other Greek mathematicians.

Mathematical proofs were revolutionized by Euclid ( 300 BCE ), who introduced the axiomatic method still in use today, starting with undefined terms and axioms ( propositions regarding the undefined terms assumed to be self-evidently true from the Greek " axios " meaning " something worthy "), and used these to prove theorems using deductive logic.

Euclidean ( or, less commonly, Euclidian ) relates to Euclid ( an ancient Greek mathematician ), a town or others.

In 1797, Moses Cleaveland named the area east of the Cuyahoga River Euclid, after the Greek mathematician and patron saint of surveyors.

Mentor is named after the Greek figure Mentor, in keeping with the Connecticut Western Reserve settlers ' tradition, as well as that of most other Americans at the time, of celebrating aspects of Greek classicism ( nearby Solon, Macedonia, Euclid, and Akron also were named using that principle ).

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

Euclid ( ; Eukleidēs ), fl.

* Heath, Thomas L. ( 1908 ), " Euclid and the Traditions About Him ", in Euclid, Elements ( Thomas L. Heath, ed.

212 BCE ), a colorful figure about whom many historical anecdotes are recorded, is remembered along with Euclid as one of the greatest of ancient mathematicians.

Euclid ( c. 325-265 BC ), of Alexandria, probably a student of one of Plato ’ s students, wrote a treatise in 13 books ( chapters ), titled The Elements of Geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as Euclidean geometry.

Proclus ( 410-485 ), author of Commentary on the First Book of Euclid, was one of the last important players in Hellenistic geometry.

Under the instruction of Cosmas, who also taught John's orphan friend ( the future St. Cosmas of Maiuma ), John is said to have made great advances in music, astronomy and theology, soon rivalling Pythagoras in arithmetic and Euclid in geometry.

Euclid ( c. 300 BC ), Archimedes ( c. 287 – 212 BC ) and Apollonius of Perga ( c. 262 – 190 BC ).

In a work titled Euclides ab Omni Naevo Vindicatus ( Euclid Freed from All Flaws ), published in 1733, Saccheri quickly discarded elliptic geometry as a possibility ( some others of Euclid's axioms must be modified for elliptic geometry to work ) and set to work proving a great number of results in hyperbolic geometry.

By comparing his own measurements with those of Timocharis of Alexandria ( a contemporary of Euclid who worked with Aristillus early in the 3rd century BC ), he found that Spica's longitude had decreased by about 2 ° in about 150 years.

Unlike many commentators on Euclid before and after him ( including of course Saccheri ), Khayyám was not trying to prove the parallel postulate as such but to derive it from an equivalent postulate he formulated from " the principles of the Philosopher " ( Aristotle ):

They also created the main thoroughfare of Euclid Avenue ( California Highway 83 ), with its distinctive wide lanes and grassy median.

Many illustrations: author portraits ( many of ancient Greeks – Socrates, Plato, Euclid, Pythagoras ), birds, tables and diagrams of geomantic significance.

Zoning laws are, of course, the classic example, see Hadacheck v. Sebastian, 239 U. S. 394 ( 1915 ) ( prohibition of brickyard operations within certain neighborhoods ); Village of Euclid, Ohio v. Ambler Realty Co., 272 U. S. 365 ( 1926 ) ( prohibition of industrial use ); Gorieb v. Fox, 274 U. S. 603, 608 ( 1927 ) ( requirement that portions of parcels be left unbuilt ); Welch v. Swasey, 214 U. S. 91 ( 1909 ) ( height restriction ), which have been viewed as permissible governmental action even when prohibiting the most beneficial use of the property.

* Henry Billingsley ( died 1606 ), Lord Mayor of London and the first translator of Euclid into English

The Cooke Manuscript traces masonry to Jabal son of Lamech ( Genesis 4, 20-22 ), and tells how this knowledge came to Euclid, from him to the Children of Israel ( while they were in Egypt ), and so on through an elaborate path to Athelstan.

As was common in ancient mathematical texts, when a proposition needed proof in several different cases, Euclid often proved only one of them ( often the most difficult ), leaving the others to the reader.

The rope stretchers of ancient Egypt stretched corded ropes between two points to measure the path which minimized the distance of separation, and Claudius Ptolemy, in his Geographia ( Bk 1, Ch 2 ), emphasized that one must correct for " deviations from a straight course "; in ancient Greece Euclid states in his Catoptrica that, for the path of light reflecting from a mirror, the angle of incidence equals the angle of reflection ; and Hero of Alexandria later showed that this path was the shortest length and least time.

* Hitachi Construction Machinery ( Europe ), subsidiary of Hitachi, Ltd., now parent of Euclid Trucks