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Euclid truck in use at Chuquicamata copper mine in 1984

The Euclid Company of Ohio was a company specialized in heavy equipment for earthmoving, namely dump trucks and wheel tractor-scrapers, that operated from the United States of America from the 1920s to the 1950s, then it was purchased and converted into a section of General Motors and later on by Hitachi, Ltd.

History[link]

Founding[link]

The Euclid Company of Ohio specialised in off-road heavy haulers, specifically designed as off-road haulers - as compared to other companies, that modified OTR^{[disambiguation needed ]} trucks for off-road earth-hauling.

The Euclid Crane and Hoist Co, owned by George A. Armington and his 5 sons, was a large, respected and profitable operation, when they introduced the Euclid Automatic Rotary Scraper in 1924 - soon followed by the Euclid Wheeler (wheeled) scraper. These earthmoving products were conceived by George's eldest son, Arthur, who envisioned a good future in designing earthmoving equipment, and steered the company into the earthmoving field. The two models of scrapers were successful, and a third model, the Euclid Contractors Special, designed to cope with hard ground, was even more successful.

Arthur and his father had built a successful prototype crawler, and tested it on the family farm, but the idea was dropped for reasons unknown. The success of the scrapers led to the formation of the Road Machinery Division, of Euclid Crane and Hoist, in 1926. Big public works construction programs of 1927 and 1928, requiring large excavations, saw further success of the Euclid Road Machinery division.

Euclid produced crawler wagons on tracks (similar to Athey Wagons) known as Euclid Tu-Way haulers. The crawler track speed restriction was seen as a problem, and the next version used steel wheels for improved speed. George Armington Jr was a keen hydraulics designer, and produced the first hydraulic Euclid dumpers around 1930.

Great Depression[link]

The Great Depression did not appear to affect Euclid greatly, and the expansion of the earthmoving portion of the Euclid business, led to the incorporation of the Euclid Road Machinery Co, on July 11, 1931. This company remained a subsidiary of Euclid Armington Corp, until January 1, 1933, when the companies were separated - and Euclid Road Machinery, became a producer of fast, off-road earthmoving haulers.

The Euclid company produced its first specifically designed, 7 yards (6.4 m) long, off-road dump truck, the Model 1Z, in January 1934. It was powered by a 100HP Waukesha gasoline engine. It used a specially designed, extremely heavy duty, Euclid rear axle, fitted with a new 17.5 x 24 tire, which had just been released by the tire industry. Although Mack had produced a 14 yards (13 m) long, heavy duty off-road hauler in 1931 specifically for the Boulder Dam project (the Model AP Super-Duty) - it was basically a beefed-up, road-going, chain-drive AC Bulldog Mack.

The next Euclid design, was an articulated, tractor/trailer style (in the style of the Caterpillar DW10), bottom dumper. This was known as the Model Z or ZW.

Company expansion[link]

Euclid went on to produce thousands of off-road haulers and scrapers, of improving and larger design and became a large corporation by the early 1950s. In 1953 the Euclid Corporation was purchased by General Motors, in what the leaders of both companies saw as an advantageous deal, with complementary product lines. This deal came about, due to GM's already awakened desire to enter into the earthmoving manufacturing field and the realisation by the Armington family, that a GM takeover would provide capital and design ability that they could only dream about. The GM takeover deal was announced on September 30, 1953, with the official takeover date being January 1, 1954.

Arthur Armington had died suddenly in 1937, leading to a stumble in Euclids fortunes - but George Armington died in 1954, at the age of 89, after overseeing the sale of Euclid to GM. Sons Stuart & Everett Armington retired in 1953, and George Jr retired in 1958 - with the youngest son Ray, being the last Armington to retire in 1960, after 7 years as General Manager of GM's Euclid Division.

The 1950s and 1960s were good years for Euclid Trucks. Euclid produced the industry's first 50 ton, 3 axle dump truck, with twin Cummins power, in 1951. Euclid produced two and three axle dump trucks with capacities up to 105 tons, in this period. Some of the largest three axle units, being used as tractors for even larger end dumps, and bottom dump haulers.

Anti-trust lawsuit[link]

In 1959 the Department of Justice under Attorney General William P. Rogers initiated an anti-trust suit, under the Clayton Act, against General Motors Corporation. It charged that GM was too dominant, and its business methods stifled competition in the off-road hauler and earthmoving market. GM fought the suit for 8 years, finally surrendering in 1968, agreeing to sell the Euclid Division.

After the sale of Euclid to White Motor Corporation, GM formed the Terex brand. Under the sale agreement with White, GM was not allowed to produce trucks in competition with White for 4 years – from July 1, 1968 to July 1, 1972. GM could produce off-road haul trucks in this period, but could not sell them in the US. GM equipment dealers in the US were offered a franchise deal from White to sell the White/Euclid line of trucks for a period of 4 years. The international Euclid dealerships were still owned by GM, thus forcing White to form all-new international dealerships. GM produced haul trucks in the 1968-1972 period that it had developed during its ownership of Euclid from plants in Canada and Scotland, that it had been allowed to keep. These were sold as Terex, but were essentially the same as the Euclid line.

The Euclid Company lost its prominence after the sale to White, and never achieved the standing that it enjoyed before the GM acquisition.

Current state[link]

After the company was purchased by Hitachi Construction Machinery Co. Ltd. it is now producing a range of models of truck under the Hitachi name (although it is commonly branded as a Euclid, and several components bear the Euclid name). There are two classes of the machines that are currently in production - both are "rigid dumper" models (dump trucks with a rigid frame, non-articulated). The smaller construction and quarry trucks (30 ton - 90 ton) are dwarfed by the larger mining trucks in the 140ton - 450ton range.

Production was moved from Euclid, Ohio to Guelph in Ontario, Canada. The trucks are modern and are equipped with mufflers and computer controllers to meet environmental requirements for sound and exhaust emissions.

There are some trucks currently in use in mines in the US, they can be seen in Canada at Fort McMurray, and throughout China, Australia, Africa, Indonesia and South America as well. Although the heady days of American needs for infrastructure have abated, there is still much need for infrastructure and mining.

Smaller construction trucks, of 32 tons and 36tons capacity, are being built in India by Telcon, a joint venture between Tata and Hitachi Construction Machinery Co. Ltd. from Japan. These smaller trucks are of older technology - they were previously manufactured in Poland under license from VME (Volvo Michigan Euclid). The intended market for these older technology construction trucks is India.

White sold Euclid, Inc. to Daimler Benz AG of Stuttgart, Germany in August, 1977, and in January 1984, Daimler-Benz sold Euclid to one of Euclid’s former competitors, Clark Equipment Company and it became part of the Clark Michigan Company, as Clark’s construction machinery division was then called. The following April, Clark formed a 50/50 joint venture with Sweden’s Volvo AB, now known as Volvo Construction Equipment to manufacture Volvo, Michigan and Euclid construction equipment under the name of VME Group NV. VME underwent several rather confusing divisions amongst its American and European operations, culminating in 1991 in the creation of a VME North Americas unit to handle only the Euclid lines.

In December 1993, VME North America entered into a joint venture of its own with Japan’s Hitachi Construction Machinery Co. Ltd., called Euclid-Hitachi Heavy Equipment. Hitachi Construction Machinery Co. Ltd., a manufacturer of hydraulic construction machinery like excavators and cranes, gradually increased its share of the joint venture until it owned 100% of the venture in 2000. Hitachi obtained Euclid to fill the gap which in their ability to offer a complete mining package, as mining excavators and dump trucks usually are needed in combination. Euclid-Hitachi became Hitachi Construction Truck Manufacturing on January 1, 2004, and the famous Euclid green was replaced with Hitachi orange. The Euclid name was phased out by the end of the year, ending 80 years of the Euclid name on construction machinery.

Developments[link]

A Euclid R60 Dump truck

The Euclid company of Euclid, OH, was synonymous with off-road haul trucks, and earthmoving equipment such as bottom dumpers, and to a lesser extent, scrapers, in the 1950s. As described in Herbert L. Nicholas' "Moving the Earth",^[1] now in its 5th edition, Euclid was everywhere.

GM's work on heavy duty automatic transmissions during the Second World War had produced the Allison heavy duty automatic in 1945 — Euclid was the first to use this transmission in heavy duty off-road dump trucks in the late 1940s — because it met the need for an industrial transmission with huge power capacity, as engine sizes were increasing to the point where transmissions could not cope with the power.

Euclid had pioneered the use of twin engines (Twin-Power) in a bottom dumper (model 50FDT-102W), in November 1948. Their first Twin-Power scraper prototype (model 51FDT-13SH) appeared in February 1949, and production model Twin-Power scrapers were released in 1950 (GM powered model 68FDT-17SH - and the Cummins powered model, 66FDT-16SH). Prior to GM's purchase of Euclid, the engine preferred by Euclid was Cummins diesels, with GM's 2-stroke Detroit Diesel offered as an option. When GM purchased Euclid, it led to dismay at Cummins, because of loss of an important customer. The takeover led to GM engines being the engine of choice, but the Cummins option was still available, although Cummins-engined trucks sold in lower numbers after the GM takeover.

Ranging from 10 to 62 ton capacity, these giants roamed strip mines, heavy construction sites and quarries worldwide. Euclid's end dumps reached 210 tons in capacity in the 1980s.

Euclid trucks were usually loaded by cable-operated crawler shovels and draglines of other manufacturers, but Euclid also developed mobile belt loaders to load its bottom dump trucks.

Euclid also pioneered the high speed tractor belly dumper. This combined an off road tractor (with a fifth wheel) and a very large, up to 100-ton capacity, belly dump trailer. This machine, descended from bottom dump wagons drawn by crawler tractors, discharged its load through longitudinal gates in the bottom of the trailer. The first such trucks carried 13 cubic yards, but by the early 1960s capacities reached 110 tons.

Euclid also manufactured wheeled tractor scrapers, such as were invented by R. G. LeTourneau (later to become LeTourneau-Westinghouse, after the purchase of R. G LeTourneau, Inc. by Westinghouse Air Brake Company)^[2]and now almost singularly manufactured by Caterpillar. Euclid's tractor scrapers were powered by the same tractors as their belly dumps. Euclid was the first major manufacturer to commercialize the now ubiquitous articulated rubber tired loader; the mainstay of many heavy equipment manufacturers nowadays, particularly Caterpillar.

Euclid R24 Dump Truck

References[link]

• Euclid Earth-Moving Equipment 1924-1968 (Orlemann, Eric C., MBI, 2004);
• Euclid and Terex Earth-Moving Machines (Orlemann, Eric C., MBI, 1997)
• The Earthmover Encyclopedia (Haddock, Keith, MBI, 2006).

External links[link]

• Euclid dumpers (at Volvo Construction Equipment) – includes sub-pages on 22 Euclid models, with photos and technical specs.
• History of Hitachi Construction Equipment Europe - mentioning acquisition of Euclid

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Euclid
Euclid in Raphael's School of Athens
Born	Unknown
Died	Unknown
Residence	Alexandria, Egypt
Fields	Mathematics
Known for	Euclidean geometry Euclid's Elements

Euclid ( /ˈjuːklɪd/ EWK-lid; Ancient Greek: Εὐκλείδης Eukleidēs), fl. 300 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 Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.^[1][2][3] 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".^[4]

Life[link]

Little is known about Euclid's life, as there are only a handful of references to him. The date and place of Euclid's birth and the date and circumstances of his death are unknown, and only roughly estimated in proximity to contemporary figures mentioned in references. No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art is the product of the artist's imagination.

The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria.^[5] 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."^[6] Although the purported citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before those of Archimedes.^[7][8][9] In addition, the "royal road" anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great.^[10] In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century that Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought."^[11] It is further believed that Euclid may have studied at Plato's Academy in Athens.

[edit] Elements

One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5.^[12]

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.^[13]

There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the edition of Theon" or the "lectures of Theon",^[14] while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.

Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.

Other works[link]

Euclid's construction of a regular dodecahedron 

Construction of a dodecahedron basing on a cube

In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.

• Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name Theon of Alexandria as a more likely author.^[15]
• Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.

Statue of Euclid in the Oxford University Museum of Natural History 

• Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal." In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

Other works are credibly attributed to Euclid, but have been lost.

• Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius's work come directly from Euclid. According to Pappus, "Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics." The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
• Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
• Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
• Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

See also[link]

• Axiomatic method
• Euclidean geometry
• Euclid's orchard
• Euclidean relation
• Euclidean algorithm
• Extended Euclidean algorithm
• List of topics named after Euclid
• Papyrus Oxyrhynchus 29

Notes[link]

References[link]

• "Euclid (Greek mathematician)". Encyclopædia Britannica, Inc. 2008. http://www.britannica.com/EBchecked/topic/194880/Euclid. Retrieved 2008-04-18. 
• Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.
• Ball, W.W. Rouse (1960) [1908]. A Short Account of the History of Mathematics (4th ed.). Dover Publications. pp. 50–62. ISBN 0-486-20630-0. 
• Boyer, Carl B. (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc.. ISBN 0-471-54397-7. 
• Heath, Thomas (ed.) (1956) [1908]. The Thirteen Books of Euclid's Elements. 1. Dover Publications. ISBN 0-486-60088-2. 
• Heath, Thomas L. (1908), "Euclid and the Traditions About Him", in Euclid, Elements (Thomas L. Heath, ed. 1908), 1:1–6, at Perseus Digital Library.
• Heath, Thomas L. (1981). A History of Greek Mathematics, 2 Vols. New York: Dover Publications. ISBN 0-486-24073-8 / ISBN 0-486-24074-6.
• Kline, Morris (1980). Mathematics: The Loss of Certainty. Oxford: Oxford University Press. ISBN 0-19-502754-X.
• O'Connor, John J.; Robertson, Edmund F., "Euclid of Alexandria", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Euclid.html .
• Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992. ISBN 978-0-691-02090-7.
• Struik, Dirk J. (1967). A Concise History of Mathematics. Dover Publications. ISBN 486-60255-9. 

Further reading[link]

• DeLacy, Estelle Allen (1963). Euclid and Geometry. New York: Franklin Watts. 
• Knorr, Wilbur Richard (1975). The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry. Dordrecht, Holland: D. Reidel. ISBN 90-277-0509-7. 
• Mueller, Ian (1981). Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge, MA: MIT Press. ISBN 0-262-13163-3. 
• Reid, Constance (1963). A Long Way from Euclid. New York: Crowell. 
• Szabó, Árpád (1978). The Beginnings of Greek Mathematics. A.M. Ungar, trans. Dordrecht, Holland: D. Reidel. ISBN 90-277-0819-3. 

External links[link]

Wikiquote has a collection of quotations related to: Euclid

Wikisource has original works written by or about: Euclid

Wikimedia Commons has media related to: Euclid

• Euclid's Elements, All thirteen books, with interactive diagrams using Java. Clark University
• Euclid's Elements, with the original Greek and an English translation on facing pages (includes PDF version for printing). University of Texas.
• Euclid's Elements, books I-VI, in English pdf, in a Project Gutenberg Victorian textbook edition with diagrams.
• Euclid's Elements, All thirteen books, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.
• Elementa Geometriae 1482, Venice. From Rare Book Room.
• Elementa 888 AD, Byzantine. From Rare Book Room.
• Euclid biography by Charlene Douglass With extensive bibliography.
• Texts on Ancient Mathematics and Mathematical Astronomy PDF scans (Note: many are very large files). Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources.

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