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8/3/2019 Minerals and Their Uses
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Minerals and Their Uses
Every segment of society uses minerals and mineral resources everyday. The
roads we ride or drive on and the buildings we live learn and work in all contain minerals.
Below is a selected list of commonly used metallic and nonmetallic minerals, ore
minerals, mineral byproducts, aggregates, and rock types that are used to make products
we use in our daily life.
Aggregates
Natural aggregates include sand, gravel, and crushed stone. Aggregates are
composed of rock fragments that may be used in their natural state or after mechanical
processing, such as crushing, washing, or sizing. Recycled aggregates consist mainly of
crushed concrete and crushed asphalt pavement.
Aluminum
Aluminum is the most abundant metallic element in the Earth's crust. Bauxite ore
is the main source of aluminum. Aluminum is used in automobiles and airplanes (36%),
bottling and canning industries (25%), building and electrical (14%) and in other
applications (25%).
Antimony
Antimony is a silvery-gray, brittle semi-metal. It rarely occurs in nature as a
native element, but is found in a number of different minerals. Antimony is used
principally for flame retardants as well as in ammunition and automotive batteries and as
a decolorizing agent in glassmaking.
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Asbestos
Asbestos is a class of minerals that can be readily separated into thin, strong fibers that
are flexible, heat resistant, and chemically inert. Asbestos minerals are used in fireproof
fabrics, yarn, cloth, and paper and paint filler. Asbestos is used to make friction products,
asbestos cement pipes and sheets, coatings and compounds, packing and gaskets, roofing
and flooring products, paints and caulking, and chemical filters. Fibers are dangerous
when breathed, so users must protect against fibers becoming airborne.
Basalt
Basalt is an extrusive igneous rock. Crushed basalt is used for railroad ballast,
aggregate in highway construction, and is a major component of asphalt.
Barium
Barium is an element, derived primarily from the mineral barite, and used as a
heavy additive in oil-well-drilling mud, paints, rubber, plastic and paper; production of
barium chemicals; and glass manufacturing.
Beryllium
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Beryllium, an element commonly associated with igneous rocks, has industrial
and nuclear defense applications and is used in light, very strong alloys for the aircraft
industry. Beryllium salts are used in x-ray tubes and as a deoxidizer in bronze metallurgy.
The gemstones of beryl, a beryllium mineral, are emerald and aquamarine.
Bismuth
Bismuth is used in a number of very different applications. The majority is
consumed in bismuth alloys, and in pharmaceuticals and chemicals. The remainder is
used in ceramics, paints, catalysts, and a variety of minor applications. Bismuth metal is
relatively inert and non-toxic. It has replaced toxic lead in many applications such as
plumbing, bullets, birdshot, metal alloys, and soldering. Bismuth compounds are used in
stomach-upset medicines (hence the trademarked name Pepto-Bismol), treatment of
stomach ulcers, soothing creams, and cosmetics.
Boron
Boron compounds are used for many different purposes in industry and the home.
Boron is used to make glass, ceramics, enamels, fiberglass, make water softeners, soaps
and detergents. Other uses are in agricultural chemicals, pest controls, fire retardants,
fireworks, medicine, and various minor applications. Boron nitride is one of the hardest
known substances and is used for abrasives and cutting tools.
Bromine
Bromine, recovered commercially through the treatment of seawater brines, is
used in leaded gasoline, fire extinguishers and retardants, well-completion fluids, and
sanitary preparations. Bromine is the only liquid nonmetallic element.
Cadmium
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Cadmium is used in plating and alloying, pigments, plastics, and batteries.
Cadmium is obtained from the ore minerals Sphalerite (Zn,Cd)S and Greenockite (CdS)
Calcium
The primary use of calcium is not in its silvery-white metal form, but as calcium
carbonate. It used in adhesives and sealants, cosmetics, foods, paint, paper,
pharmaceuticals, plastics, rubber, for the production of lime, and as crhused stone in
construction. Immense quantities of calcium are found in sedimentary rock deposits of
gypsum, limestone, and shale. Some common calcium-bearing minerals include apatite(calcium phosphate), calcite (calcium carbonate), dolomite (calcium magnesium
carbonate), fluorite (calcium fluoride), and gypsum (calcium sulfate). Calcium metal is
produced in Canada, China, France, Russia, and the United States. Total world output is
thought to be less than 6,000 metric tons per year. United States consumption of calcium
metal is small. On a worldwide basis, more than 100 million metric tons per year of
apatite and gypsum are mined, and calcite and dolomite are produced in billions of metric
tons per year.
Cement
Cement is used for building materials, stucco, and mortar. Cement is :a mixture of
powdered lime, clay, and other minerals that crystallize to form a hard solid when water
is added (hydraulic cement) or as a binding material in concrete" (Kesler, 1994). An
excellent overview of cement, its chemistry, and properties can be found in MacLaren
and White (2003).
Chromium
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Chromium is used in the production of stainless and heat-resistant steel, full-alloy
steel, super alloys and other alloys. Chromium is obtained from the ore mineral Chromite
(Mg,Fe)(Cr,Al,Fe)2O4
Clays
There are many different clay minerals that are used for industrial applications.
Clays are used in the manufacturing of paper, refractories, rubber, ball clay, dinnerware
and pottery, floor and wall tile, sanitary wear, fire clay, firebricks, foundry sands, drilling
mud, iron-ore pelletizing, absorbent and filtering materials, construction materials, and
cosmetics.
Cobalt
Half of the consumption of cobalt is used in corrosion- and abrasion-resistant
alloys with steel, nickel, and other metals for the production of industrial engines. Other
uses of cobalt metal include magnets and cutting tools. Cobalt salts are used to produce a
blue color in paint pigments, porcelain, glass, and pottery. Cobalt is obtained from the ore
minerals Linneaite (Co3S4), Cobaltite CoAsS, and (Fe,Ni,Co)1-xSx.
Copper
Copper is used in electric cables and wires, switches, plumbing; heating, electrical, and
roofing materials; electronic components; industrial machinery and equipment;
transportation; consumer and general products; coins; and jewelry.
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Diamond
Industrial diamonds are those that can not be used as gems. Large diamonds are
used in tools and drilling bits to cut rock and small stone. Small diamonds, also known as
dust or grit, are used for cutting and polishing stone and ceramic products.
Diatomite
Diatomite is a rock composed of the skeletons of diatoms, single-celled organisms
with skeletons made of silica, which are found in fresh and salt water. Diatomite is
primarily used for filtration of drinks, such as juices and wines, but it is also being used
as filler in paints and pharmaceuticals and environmental cleanup technologies.
Dolomite
Dolomite is the near twin-sister rock to limestone. Like limestone, it typically
forms in a marine environment but also as has a primary magnesium component.
Dolomite is used in agriculture, chemical and industrial applications, cement
construction, refractories, and environmental industries.
Feldspar
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Feldspar is a rock-forming mineral. It is used in glass and ceramic industries;
pottery, porcelain and enamelware; soaps; bond for abrasive wheels; cement; glues;
fertilizer; and tarred roofing materials and as a sizing, or filler, in textiles and paper
applications.
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Fluorite
Fluorite is used in production of hydrofluoric acid, which is used in the pottery,
ceramics, optical, electroplating, and plastics industries. It is also used in the
metallurgical treatment of bauxite, as a flux in open-hearth steel furnaces, and in metal
smelting, as well as in carbon electrodes, emery wheels, electric arc welders, and
toothpaste as a source of fluorine.
Garnet
Garnet is used in water filtration, electronic components, ceramics, glass, jewelry,
and abrasives used in wood furniture and transport manufacturing. "Garnet is a common
metamorphic mineral that becomes abundant enough to mine in a few rocks" (Kesler,
1994).
Germanium
"Most germanium is recovered as a byproduct of zinc smelting. It is also found in
some copper ores" (Kesler, 1994). Applications include use in fiber-optic components,
which are replacing copper in long-distance telecommunication lines, as well as in
camera lenses and other glasses and infrared lenses.
Gold
Gold is used in dentistry and medicine, jewelry and arts, medallions and coins,
and in ingots. It is also used for scientific and electronic instruments, computer circuitry,
as an electrolyte in the electroplating industry, and in many applications for the aerospace
industry.
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GraniteGranite can be cut into large blocks and used as a building stone. When polished,
it is used for monuments, headstones, countertops, statues, and facing on buildings. It is
also suitable for railroad ballast and for road aggregate in highway construction.
GraphiteGraphite is the crystal form of carbon. Graphite is used as a dry lubricant and steel
hardener and for brake linings and the production of "lead" in pencils. Most graphite
production comes from Korea, India, and Mexico.
GypsumProcessed gypsum is used in industrial or building plaster, prefabricated
wallboard, cement manufacture, and for agriculture.
Halite
Halite (salt) is used in the human and animal diet, primarily as food seasoning and
as a food preservation. It is also used to prepare sodium hydroxide, soda ash, caustic
soda, hydrochloric acid, chlorine, and metallic sodium, and it is used in ceramic glazes,
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metallurgy, curing of hides, mineral waters, soap manufacture, home water softeners,
highway deicing, photography, and scientific equipment for optical parts.
Iodine
Iodine is used as an antibacterial agent in soaps and cleaning products in
restrooms, in iodized salt to prevent goiter, and in first aid boxes as an antiseptic.
Iron Ore
Iron ore is used to manufacture steels of various types and other metallurgical products, such as magnets, auto parts, and catalysts. Most U.S. production is from
Minnesota and Michigan. The Earth's crust contains about 5% iron, the fourth most
abundant element in the crust.
Lead
Lead is used in batteries, construction, ammunition, television tubes, nuclear
shielding, ceramics, weights, and tubes or containers. The United States is largest
producer (mainly from Missouri), consumer, and recycler of lead metal.
Limestone
"A sedimentary rock consisting largely of the minerals calcite and aragonite,
which have the same composition CaCO3". Limestone, along with dolomite, is one of the
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basic building blocks of the construction industry. Limestone is used as aggregate,
building stone, cement, and lime and in fluxes, glass, refractories, fillers, abrasives, soil
conditioners, and a host of chemical processes.
Lithium
Batteries made from lithium metal or lithium carbonate are used in smoke alarms,
pacemakers, defibrillator machines, many other types of portable medical equipment, and
in emergency communications equipment, including computers and cell phones.
Magnesium
Magnesium (see dolomite) is used in cement, rubber, paper, insulation, chemicals
and fertilizers, animal feed, and pharmaceuticals. Magnesium is obtained from the ore
minerals Olivine (Fe,Mg)2SiO4, Magnesite MgCO3, and Dolomite CaMg(CO3)2.
Manganese
Manganese is essential to iron and steel production. Manganese is obtained from
the ore minerals Braunite (Mn,Si)2O3, Pyrolusite MnO2, and Psilomelane
BaMn9O18*2H2O.
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Mercury
Mercury is extracted from the mineral cinnabar and is used in electrical products,
electrolytic production of chlorine and caustic soda, paint, and industrial and control
instruments (thermometers and thermostats).
Mica
Mica minerals commonly occur as flakes, scales, or shreds. Sheet muscovite
(white) mica is used in electronic insulators, paints, as joint cement, as a dusting agent, in
welldrilling mud and lubricants, and in plastics, roofing, rubber, and welding rods.
Molybdenum
Molybdenum is used in stainless steels (21%), tool steels (9%), cast irons (7%),
and chemical lubricants (8%), and in other applications (55%). It is commonly used to
make automotive parts, construction equipment, gas transmission pipes, and as a puremetal molybdenum is used as filament supports in light bulbs, metalworking dies, and
furnace parts because of its high melting temperature (2,623C).
Nickel
Nickel is vital as an alloy to stainless steel, and it plays a key roll in the chemicaland aerospace industries. Leading producers are Canada, Norway, and Russia.
Phosphate rock
Primarily a sedimentary rock used to produce phosphoric acid and ammoniated
phosphate fertilizers, feed additives for livestock, elemental phosphorus, and a variety of
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phosphate chemicals for industrial and home consumers. The majority of U.S. production
comes from Florida, North Carolina, Idaho, and Utah.
Platinum Group Metals (PGMs)
PGM's include platinum, palladium, rhodium, iridium, osmium, and ruthenium.
These elements commonly occur together in nature and are among the scarcest of the
metallic elements. Platinum is used principally in catalytic converters for the control of
automobile and industrial plant emissions; in jewelry; in catalysts to produce acids,
organic chemicals, and pharmaceuticals; and in dental alloys used for making crowns and
bridges.
Potash
Potash is an industry term that refers to a group of water-soluble salts containing
the element potassium, as well as to ores containing these salts (Kesler, 1994). Potash is
used in fertilizer, medicine, the chemical industry, and to produce decorative color effects
on brass, bronze, and nickel.
Pyrite
Pyrite (fools gold) is used in the manufacture of sulfur, sulfuric acid, and sulfur
dioxide; pellets of pressed pyrite dust are used to recover iron, gold, copper, cobalt, and
nickel.
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Quartz
Quartz crystals are popular as a semiprecious gemstone; crystalline varieties
include amethyst, citrine, rose quartz, and smoky quartz. Because of its piezoelectric
properties (the ability to generate electricity under mechanical stress), quartz is used for
pressure gauges, oscillators, resonators, and wave stabilizers. Quartz is also used in the
manufacture of glass, paints, abrasives, refractories, and precision instruments.
Sandstone
Sandstone is used as a building stone, road bases and coverings, construction fill,
concrete, railroad ballast, and snow and ice control.
Silica / Silicon
Silica is used in the manufacture of computer chips, glass and refractory
materials, ceramics, abrasives, and water filtration; and is a component of hydraulic
cements, a filler in cosmetics, pharmaceuticals, paper, and insecticides; as an anti-caking
agent in foods; a flatting agent in paint, and as a thermal insulator.
Silver
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Silver is used in photography, chemistry, electrical and electronic products
(because of its very high conductivity), fine silverware, electroplated wire, jewelry, coins,
and brazing alloys and solders.
Strontium
Photoluminescent exit signs use a class of newly developed phosphorescent
pigments that are based on strontium oxide aluminate chemistry.
Sulfur
Sulfur is of importance to every sector of the world's manufacturing processes,
drugs, and fertilizer complexes. Sulfur is used as an industrial raw material through its
major derivative, sulfuric acid. Sulfuric acid production is the major end use for sulfur.
Most sulfur goes into fertilizer; oil refining is another major use as well as a source of
sulfur.
Talc
The primary use for talc is in the production of paper. Ground talc is used as filler
in ceramics, paint, paper, roofing, plastics, cosmetics, and in agriculture. Talc is found in
many common household products, such as baby (talcum) powder, deodorant, and
makeup. Very pure talc is used in fine arts and is called soapstone. It is often used to
carve figurines.
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Tin
Tin is used in the manufacture of cans and containers, electrical equipment, and
chemicals.
Titanium
Titanium is a metal used mostly in jet engines, airframes, and space and missile
applications. In powdered form, titanium is used as a white pigment for paints, paper,
plastics, rubber, and other materials.
Trona
Trona is used in glass container manufacture, fiberglass, specialty glass, flat glass,
liquid detergents, medicine, food additives, photography, cleaning and boiler compounds,
and control of water pH. Trona is mined mainly in Wyoming.
Tungsten
Tungsten is used in steel production, metalworking, cutting applications,
construction electrical machinery and equipment, transportation equipment, light bulbs,
carbide drilling equipment, heat and radiation shielding, textile dyes, enamels, paints, and
for coloring glass.
Uranium
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Uranium is a radioactive material used in nuclear defense systems and for nuclear
generation of electricity. It also used in nuclear-medicine x-ray machines, atomic dating,
and electronic instruments.
Zeolites
Some of the uses of zeolite minerals include aquaculture (for removing ammonia
from the water in fish hatcheries), water softener, catalysts, cat litter, odor control, and
removing radioactive ions from nuclear-plant effluent.
Zinc
Zinc is used as protective coating on steel, as die casting, as an alloying metal
with copper to make brass, and as chemical compounds in rubber and paint. Additional
uses include galvanizing iron, electroplating, metal spraying, automotive parts, electrical
fuses, anodes, dry-cell batteries, nutrition, chemicals, roof gutters, cable wrapping, and pennies. Zinc oxide is used in medicine, paints, vulcanizing rubber, and sun-block
lotions.
Zirconium
Zirconium is a metal recovered from zircon. "Zircon is used in mineral form in
refractory products, where it is valued for its high melting temperature of 2,550C. Some
zircon is processed by chemical leaching to yield elemental zirconium. The best known
use for zirconium metal is in nuclear reactors, where zirconium contains the fuel"
(Kesler, 1994).
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Ren Descartes
en DescartesFrench pronunciation: [ne dekat]; (31 March 1596 11 February
1650) (Latinized form: Renatus Cartesius; adjectival form: "Cartesian")[3] was a French
philosopher and writer who spent most of his adult life in the Dutch Republic. He has
been dubbed the 'Father of Modern Philosophy', and much subsequent Western
philosophy is a response to his writings, which are studied closely to this day. In
particular, his Meditations on First Philosophy continues to be a standard text at most
university philosophy departments. Descartes' influence in mathematics is equally
apparent; the Cartesian coordinate system allowing algebraic equations to be
expressed as geometric shapes, in a 2D coordinate system was named after him. He is
credited as the father ofanalytical geometry, the bridge between algebra and geometry,
crucial to the discovery ofinfinitesimal calculus and analysis. Descartes was also one of
the key figures in the Scientific Revolution.
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Descartes frequently sets his views apart from those of his predecessors. In the
opening section of the Passions of the Soul, a treatise on the Early Modern version of
what are now commonly called emotions, Descartes goes so far as to assert that he will
write on this topic "as if no one had written on these matters before". Many elements of
his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th
century, or in earlier philosophers like St. Augustine. In his natural philosophy, he differs
from the schools on two major points: First, he rejects the analysis ofcorporeal substance
into matter and form; second, he rejects any appeal to endsdivine or naturalin
explaining natural phenomena.[4] In his theology, he insists on the absolute freedom of
Gods act of creation.
Descartes was a major figure in 17th-century continental rationalism, lateradvocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist
school of thought consisting of Hobbes, Locke, Berkeley, Jean-Jacques Rousseau, and
Hume. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as
philosophy, and Descartes and Leibniz contributed greatly to science as well.
He is perhaps best known for the philosophical statement "Cogito ergo sum"
(French: Je pense, donc je suis; English: I think, therefore I am; or I am thinking,
therefore I existorI do think, therefore I do exist), found in part IV ofDiscourse on the
Method(1637 written in French but with inclusion of "Cogito ergo sum") and 7 of part
I ofPrinciples of Philosophy (1644 written in Latin).
Descartes was born in La Haye en Touraine (now Descartes), Indre-et-Loire,
France. When he was one year old, his mother Jeanne Brochard died. His father Joachim
was a member in the provincial parliament. At the age of eight, he entered the Jesuit
Collge Royal Henry-Le-Grand at La Flche.[5] After graduation, he studied at the
University of Poitiers, earning aBaccalauratandLicence in law in 1616, in accordance
with his father's wishes that he should become a lawyer.[6]
"I entirely abandoned the study of letters. Resolving to seek no knowledge other
than that of which could be found in myself or else in the great book of the world, I spent
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the rest of my youth traveling, visiting courts and armies, mixing with people of diverse
temperaments and ranks, gathering various experiences, testing myself in the situations
which fortune offered me, and at all times reflecting upon whatever came my way so as
to derive some profit from it." (Descartes,Discourse on the Method).
In 1618, Descartes was engaged in the army ofMaurice of Nassau in the Dutch
Republic, but as a truce had been established between Holland and Spain, Descartes used
his spare time to study mathematics. Because of this he was acquainted to Isaac
Beeckman, principal of Dordrecht school. Beeckman had proposed a difficult
mathematical problem, and to his astonishment, it was the young Descartes that found the
solution. Both men shared the idea that it was necessary to create a method that
thoroughly linked mathematics and physics.
[7]
While in the service of the DukeMaximilian of Bavaria, Descartes was present at the Battle of the White Mountain
outside Prague, in November 1620.[8]
On the night of 1011 November 1619, while stationed inNeuburg an der Donau,
Germany, Descartes experienced a series of three powerful dreams orvisions that he later
claimed profoundly influenced his life. Descartes concluded from these visions that the
pursuit of science would prove to be, for him, the pursuit of true wisdom and a central
part of his life's work.[9]. Descartes also saw very clearly that all truths were linked ones
to others, so that finding a fundamental truth, and proceeding with logic, would open the
way to all science. This basic truth, Descartes found quite soon: his famous "I think". [7]
In 1622 he returned to France, and during the next few years spent time in Paris
and other parts of Europe. It was during a stay in Paris that he composed his first essay on
method: Regulae at Directionem Ingenii (Rules for the Direction of the Mind).[7] He
arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided
a comfortable income for the rest of his life. Descartes was present at the siege of La
Rochelle by Cardinal Richelieu in 1627.
He returned to the Dutch Republic in 1628, where he lived until September 1649.
In April 1629 he joined the University of Franeker, living at the Sjaerdemaslot, and the
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next year, under the name "Poitevin", he enrolled at the Leiden University to study
mathematics with Jacob Golius and astronomy with Martin Hortensius.[10] In October
1630 he had a falling out with Beeckman, who he accused of plagiarizing some of his
ideas. In Amsterdam, he had a relationship with a servant girl, Helena Jans van der
Strom, with whom he had a daughter, Francine, who was born in 1635 in Deventer, at
which time Descartes taught at the Utrecht University. Francine Descartes died in 1640 in
Amersfoort, from Scarlet Fever.
While in the Netherlands he changed his address frequently, living among other
places in Dordrecht (1628), Franeker (1629), Amsterdam (162930), Leiden (1630),
Amsterdam (163032), Deventer(163234), Amsterdam (163435), Utrecht (163536),
Leiden (1636), Egmond (163638), Santpoort (16381640), Leiden (164041),Endegeest (a castle near Oegstgeest) (164143), and finally for an extended time in
Egmond-Binnen (164349).
Despite these frequent moves he wrote all his major work during his 20 plus years
in the Netherlands, where he managed to revolutionize mathematics and philosophy. In
1633, Galileo was condemned by the Roman Catholic Church, and Descartes abandoned
plans to publish Treatise on the World, his work of the previous four years. Nevertheless,
in 1637 he published part of this work in three essays: Les Mtores (The Meteors), La
Dioptrique (Dioptrics) and La Gomtrie (Geometry), preceded by an introduction, his
famous Discours de la Mtode (Discourse on the Method). In it Descartes lays out four
rules of thought, meant to ensure that our knowledge rests upon a firm foundation.
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Ren Descartes with Queen Christina of Sweden
Descartes continued to publish works concerning both mathematics and
philosophy for the rest of his life. In 1641 he published a metaphysics work,
Meditationes de Prima Philosophia (Meditations on First Philosophy), written in Latin
and therefore addressed to the learned. It was followed, in 1644, by Principia
Philosophi (Principles of Philosophy), a kind of synthesis of the Meditations and the
Discourse. In 1643, Cartesian philosophy was condemned at the University of Utrecht,
and Descartes began his long correspondence with Princess Elisabeth of Bohemia, mainly
devoted to moral and psychological subjects. Connected with this correspondence, in
1649 he publishedLes Passions de l'me (Passions of the Soul), that he dedicated to thePrincess. In 1647, he was awarded a pension by the King of France. Descartes was
interviewed by Frans Burman at Egmond-Binnen in 1648.
A French translation of Principia Philosofi, prepared by Abbot Claude Picot,
was published in 1647. For this edition Descartes made a dedication to Princess Elisabeth
of Bohemia, and a preface. Descartes used it to make a praise of true philosophy, as a
means to attain wisdom. He identifies four ordinary sources to reach wisdom, and finally
says that there is a fifth source, that is better and more secure, consisting in the search for
first causes.[11]
Ren Descartes died on 11 February 1650 in Stockholm, Sweden, where he had
been invited as a tutor for Queen Christina of Sweden. The cause of death was said to be
pneumonia accustomed to working in bed until noon, he may have suffered a
detrimental effect on his health due to Christina's demands for early morning study (the
lack of sleep could have severely compromised his immune system). Descartes stayed at
the French ambassadorPierre Chanut. In his recent book, Der rtselhafte Tod des Ren
Descartes (The Mysterious Death of Ren Descartes),[12] the German philosopher
Theodor Ebert[13] asserts that Descartes died not through natural causes, but from an
arsenic-laced communion wafer given to him by a Catholic priest. He believes that
Jacques Viogu, a missionary working in Stockholm, administered the poison because he
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feared Descartes's radical theological ideas would derail an expected conversion to
Roman Catholicism by the monarch of Protestant Lutheran Sweden.[14]
In 1663, the Pope placed his works on the Index of Prohibited Books.
As a Roman Catholic in a Protestant nation, he was interred in a graveyard mainly
used for unbaptized infants in Adolf Fredriks kyrka in Stockholm. Later, his remains
were taken to France and buried in the Abbey of Saint-Germain-des-Prs in Paris.
Although the National Convention in 1792 had planned to transfer his remains to the
Panthon, they are, two centuries later, still resting between two other gravesthose of
the scholarly monks Jean Mabillon and Bernard de Montfauconin a chapel of the
abbey. His memorial, erected in the 18th century, remains in the Swedish church.
Mathematical legacy
Descartes's theory provided the basis for the calculus ofNewton and Leibniz, by
applying infinitesimal calculus to the tangent line problem, thus permitting the evolution
of that branch of modern mathematics.[19] This appears even more astounding considering
that the work was just intended as an example to his Discours de la mthode pour bien
conduire sa raison, et chercher la verit dans les sciences (Discourse on the Method of
Rightly Conducting the Reason, and Searching for Truth in the Sciences , better known
under the shortened titleDiscours de la mthode; English,Discourse on the Method).
Descartes' rule of signs is also a commonly used method to determine the number
of positive and negative roots of a polynomial.
Descartes created analytic geometry, and discovered an early form of the law of
conservation ofmomentum (the term momentum refers to the momentum of a force). Heoutlined his views on the universe in his Principles of Philosophy.
Descartes also made contributions to the field of optics. He showed by using
geometric construction and the law of refraction (also known as Descartes's law or more
commonly Snell's law, who discovered it 16 years earlier) that the angular radius of a
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rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and
the ray passing from the sun through the rainbow's centre is 42).[20] He also
independently discovered the law of reflection, and his essay on optics was the first
published mention of this law.[21]
One of Descartes most enduring legacies was his development of Cartesian
geometry, which uses algebra to describe geometry. He "invented the convention of
representing unknowns in equations by x, y, andz, and knowns by a, b, and c". He also
"pioneered the standard notation" that uses superscripts to show the powers or exponents,
for example the 4 used in x4 to indicate squaring of squaring.[22
http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-19http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-19http://en.wikipedia.org/wiki/Law_of_reflectionhttp://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-20http://en.wikipedia.org/wiki/Cartesian_geometryhttp://en.wikipedia.org/wiki/Cartesian_geometryhttp://en.wikipedia.org/wiki/Superscripthttp://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-21http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-19http://en.wikipedia.org/wiki/Law_of_reflectionhttp://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-20http://en.wikipedia.org/wiki/Cartesian_geometryhttp://en.wikipedia.org/wiki/Cartesian_geometryhttp://en.wikipedia.org/wiki/Superscripthttp://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#cite_note-21