Archimedes, the renowned mathematician, was said to have used a burning glass ( or more likely a large number of angled hexagonal mirrors ) as a weapon in 212 BC, when Syracuse was besieged by Marcus Claudius Marcellus.

* Three small apple trees, said to have been grown from cuttings taken from the apple trees in Sir Isaac Newton's garden, are planted by the archway containing a statue of Archimedes in his bath by Thompson Dagnall.

One of Wren's friends, another great scientist and architect and a fellow Westminster Schoolboy, Robert Hooke said of him " Since the time of Archimedes there scarce ever met in one man in so great perfection such a mechanical hand and so philosophical mind.

Archimedes, on discovering the principle of displacement needed to measure the density of the crown is said to have shouted " eureka, eureka!

Galileo said of Cavalieri, " few, if any, since Archimedes, have delved as far and as deep into the science of geometry.

E. T. Bell in his 1937 book Men of Mathematics ( page 237 ) claims that Gauss said " There have been but three epoch-making mathematicians, Archimedes, Newton, and Eisenstein ", and this has been widely quoted in writings about Eisenstein.

" Condon said he replied: " I believe in Archimedes ' Principle, formulated in the third century B. C.

This is the law of the lever, which was proven by Archimedes using geometric reasoning.

Archimedes ' cattle problem ; its solution ( absent from the manuscript ) requires solving an indeterminate quadratic equation ( which reduces to what would later be misnamed Pell's equation ).

Brahmagupta ( 628 CE ) started the systematic study of indefinite quadratic equations — in particular, the misnamed Pell equation, in which Archimedes may have first been interested, and which did not start to be solved in the West until the time of Fermat and Euler.

For instance, Archimedes ' cattle problem may be solved using a Pell equation, the fundamental solution of which has 206545 digits if written out explicitly.

Germain decided that if geometry, which at that time referred to all of pure mathematics, could hold such fascination for Archimedes, it was a subject worthy of study.

He rigorously developed Antiphon's method of exhaustion, a precursor to the integral calculus which was also used in a masterly way by Archimedes in the following century.

However, unlike Archimedes ' method, which was based on Euclidean geometry, Newton's and Leibniz's integral calculus did not have a rigorous foundation.

The principle is also found in pescalators, which are Archimedes screws designed to lift fish safely from ponds and transport them to another location.

A variant of the Archimedes ' screw can also be found in some injection molding machines, die casting machines and extrusion of plastics, which employ a screw of decreasing pitch to compress and melt the material.

Although the machine would not work, the idea was that water from the top tank turns a water wheel ( bottom-left ), which drives a complicated series of gears and shafts that ultimately rotate the Archimedes ' screw ( bottom-center to top-right ) to pump water to refill the tank.

* 236 BC – The date ascribed by Vitruvius for the first documented elevator, which he reports as having been built by Archimedes.

* Although Marcellus wishes to spare the lives of the Syracusans, he is unable to prevent the sack of the city by his soldiers, which includes the killing of Archimedes.

The RiscPC ( codenamed Medusa ) was Acorn Computers's next generation RISC OS / Acorn RISC Machine computer, launched on 15 April 1994, which superseded the Acorn Archimedes.

Apple Macintosh computers or IBM compatible PCs eclipsed the Archimedes in their multimedia capabilities, which led to an erosion of the Archimedes market share.

The Tesco Computers for Schools scheme later changed partnership from Acorn to RM plc and many other computer-related suppliers, which also led to the decrease of the Archimedes ' educational market share.

Though the original text has been lost, a reference in Archimedes ' book The Sand Reckoner ( Archimedis Syracusani Arenarius & Dimensio Circuli ) describes another work by Aristarchus in which he advanced the heliocentric model as an alternative hypothesis.

It has historically been read as stating that the angle subtended by the Sun's diameter is 2 degrees, but Archimedes states in The Sand Reckoner that Aristarchus had a value of ½ degree, which is much closer to the actual average value of 32 ' or 0. 53 degrees.

He discusses the use of the touchstone for assaying gold and gold alloys, an important property which would require the genius of Archimedes to resolve in quantitative detail when he was asked to investigate the suspected debasement of a crown a few years later.

In 2002 Natalie Tchernetska of Trinity College, Cambridge discovered fragments of two speeches of Hypereides, which had been considered lost, in the Archimedes Palimpsest.

In 2006, the Archimedes Palimpsest project together with imagers at Stanford University used powerful X-ray fluorescence imaging to read the final pages of the Palimpsest, which contained the material by Hypereides.

Furthermore, he is noted for having conquered the fortified city of Syracuse in a protracted siege during which Archimedes, the famous inventor, was killed.

The Town successfully advocated Prince George's County Government for a new state-of-the-art $ 6 million facility, which received recognition for its utilization of three massive Archimedes Screws, a flood pumping technology developed by the ancient Greek mathematician rarely utilized on such a scale in the United States.

According to Archimedes in the Sandreckoner ( 2. 1 ), Aristarchus of Samos estimated the distance to the Sun to be 10, 000 times the Earth's radius ( the true value is about 23, 000 ).

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time.

However, an episode of Richard Hammond's Engineering Connections relating to the Keck Observatory ( whose reflector glass is based on the Archimedes ' Mirror ) did successfully use a much smaller curved mirror to burn a wooden model, though not made of the same quality of materials as in the MythBusters effort.

Bryozoa are abundant in some regions ; the fenestellids including Fenestella, Polypora, and Archimedes, so named because it is in the shape of an Archimedean screw.

Archimedes used to demand just one firm and immovable point in order to shift the entire earth ; so I too can hope for great things if I manage to find just one thing, however slight, that is certain and unshakable.

This is effectively Archimedes ' principle as generated by centrifugal force as opposed to being generated by gravity.

The trammel of Archimedes or ellipsograph is a mechanical device that implements this principle.

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.

" 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.

Archimedes ( 287-212 BC ), of Syracuse, Sicily, when it was a Greek city-state, is often considered to be the greatest of the Greek mathematicians, and occasionally even named as one of the three greatest of all time ( along with Isaac Newton and Carl Friedrich Gauss ).

It is not known whether Archimedes himself had a method of solution.

An ordered field K is the real number field if it satisfies the axiom of Archimedes and every Cauchy sequence of K converges within K.

An exception is the Archimedes palimpsest ( see below ).

* PBS NOVA: " The Archimedes Palimpsest " Click on " What is a Palimpsest?

This formula was first derived by Archimedes, who showed that the volume of a sphere is 2 / 3 that of a circumscribed cylinder.

This formula was first derived by Archimedes, based upon the fact that the projection to the lateral surface of a circumscribed cylinder ( i. e. the Lambert cylindrical equal-area projection ) is area-preserving.

The city is notable for its rich Greek history, culture, amphitheatres, architecture, and as the birthplace of the preeminent mathematician and engineer Archimedes.

It is believed to have fallen due to a peace party opening a small door in the wall to negotiate a peace, but the Romans charged through the door and took the city, killing Archimedes in the process.

Archimedes was possibly the first scientist that is known to have described nature with axioms ( or principles ) and then deduce new results from them.

The gravitational force acting on the hydrometer is simply its weight, mg. From the Archimedes buoyancy principle, the buoyancy force acting on the hydrometer is equal to the weight of liquid displaced.

However ancient sources contain several accounts of techniques that foreshadow the concepts of forensic science that is developed centuries later, such as the " Eureka " legend told of Archimedes ( 287 – 212 BC ).